Q: A chemical solution contains 30% water and 70% alkali. What quantity of water should be added to 6 litres of solution so that the water content becomes 40% ? एक रासायनिक विलयन में 30% जल और 70% क्षार है। 6 लीटर विलयन में कितना जल और मिलाया जाए कि विलयन में जल की मात्रा 40% हो जाए ?

Correct Option: 1 litre. Let the initial volume of the solution be $V1 = 6 text{ litres}$. Initial Composition: Water content = $30%$. Alkali content = $70%$. Calculate the initial amount of water and alkali: Amount of water = $30%$ of $6 text{ litres} = 0.30 times 6 = 1.8 text{ litres}$. Amount of alkali = $70%$ of $6 text{ litres} = 0.70 times 6 = 4.2 text{ litres}$. (Check: $1.8 + 4.2 = 6 text{ litres}$, which is the total initial volume). Adding Water: Let $x$ be the quantity of water added (in litres). Crucially, the amount of alkali in the solution remains constant, as only water is being added. New total volume of solution ($V2$) = $(6 + x) text{ litres}$. New amount of water = $(1.8 + x) text{ litres}$. Amount of alkali (constant) = $4.2 text{ litres}$. Final Composition: In the new solution, the water content is $40%$. This means the alkali content is $100% - 40% = 60%$. Now, we can set up an equation based on the constant amount of alkali: $60%$ of $V2 = text{Amount of alkali}$ $0.60 times (6 + x) = 4.2$ Solve for $x$: $6 + x = frac{4.2}{0.60}$ $6 + x = frac{420}{60}$ $6 + x = 7$ $x = 7 - 6$ $x = 1 text{ litre}$. The quantity of water to be added is $1$ litre. Since $1 text{ litre} = 1000 text{ ml}$, the answer is $1000 text{ ml}$. Let's evaluate the options: Option (1) $500 text{ ml}$ ($0.5 text{ litres}$): If $0.5 text{ litres}$ were added, the new water percentage would be $frac{1.8+0.5}{6+0.5} = frac{2.3}{6.5} approx 35.38%$, not $40%$. Option (2) $700 text{ ml}$ ($0.7 text{ litres}$): If $0.7 text{ litres}$ were added, the new water percentage would be $frac{1.8+0.7}{6+0.7} = frac{2.5}{6.7} approx 37.31%$, not $40%$. Option (3) $900 text{ ml}$ ($0.9 text{ litres}$): If $0.9 text{ litres}$ were added, the new water percentage would be $frac{1.8+0.9}{6+0.9} = frac{2.7}{6.9} approx 39.13%$, not $40%$. Option (4) $1 text{ litre}$: This matches our calculated value. If $1 text{ litre}$ is added, the new water percentage is $frac{1.8+1}{6+1} = frac{2.8}{7}

Q: In a class of 50 students, Mithilesh is eighth from the top. Himadri is 20th from the bottom. How many students are there between Mithilesh and Himadri ? 50 विद्यार्थियों की एक कक्षा में मिथिलेश का ऊपर से आठवाँ स्थान है। हिमाद्री नीचे से 20 वीं स्थान पर है। मिथिलेश और हिमाद्री के बीच कितने विद्यार्थ

Correct Option: 22. Given: Total number of students in the class ($N$) = $50$. Mithilesh's rank from the top = $8^{text{th}}$. Himadri's rank from the bottom = $20^{text{th}}$. First, we need to determine if there is any overlap in their positions. The sum of their ranks from opposite ends is $8 + 20 = 28$. Since the sum of ranks ($28$) is less than the total number of students ($50$), there is no overlap between Mithilesh and Himadri; they are distinct individuals, and there are students between them. The number of students between Mithilesh and Himadri can be calculated using the formula: Number of students between = Total students - (Mithilesh's rank from top + Himadri's rank from bottom) Number of students between = $50 - (8 + 20)$ Number of students between = $50 - 28$ Number of students between = $22$. Alternatively, consider the students accounted for by their positions: Students from the top up to Mithilesh (including Mithilesh) = $8$. Students from the bottom up to Himadri (including Himadri) = $20$. Total students accounted for if there's no overlap = $8 + 20 = 28$. The remaining students are those who are positioned between Mithilesh and Himadri. Remaining students = Total students - (Students accounted for) Remaining students = $50 - 28 = 22$. Let's evaluate the options: Option (1) $20$: Incorrect. Option (2) $21$: Incorrect. Option (3) $22$: This matches our calculated number of students. Option (4) $23$: Incorrect. Therefore, there are $22$ students between Mithilesh and Himadri. The correct option is (3) 22.

Q: A cucumber contains 99% water. Ramesh buys 100 kg of cucumbers. After 30 days of storing, the cucumbers lose some water. These now contain 98% water. What is the total weight of cucumbers now ? खीरे में 99% जल होता है। रमेश 100 किलोग्राम खीरे खरीदता है। 30 दिन रखने के बाद इन खीरों में कुछ जल कम हो ज

Correct Option: 50 kg. This problem relies on the principle that when a fruit or vegetable loses water, the amount of its dry matter (non-water content) remains constant. Initial State: Total weight of cucumbers = $100 text{ kg}$. Water content = $99%$. Dry matter content = $100% - 99% = 1%$. Calculate the actual weight of dry matter: Weight of dry matter = $1%$ of $100 text{ kg} = frac{1}{100} times 100 text{ kg} = 1 text{ kg}$. Final State (After 30 days): After losing water, the dry matter content remains $1 text{ kg}$. New water content = $98%$. New dry matter content = $100% - 98% = 2%$. Let the new total weight of cucumbers be $W{text{new}}$. We know that $2%$ of $W{text{new}}$ is the dry matter, which is $1 text{ kg}$. So, $2%$ of $W{text{new}} = 1 text{ kg}$. $frac{2}{100} times W{text{new}} = 1$ $W{text{new}} = frac{1 times 100}{2}$ $W{text{new}} = frac{100}{2} = 50 text{ kg}$. Let's evaluate the options: Option (1) $99 text{ kg}$: If the new weight is $99 text{ kg}$, the dry matter ($1 text{ kg}$) would be $frac{1}{99} times 100% approx 1.01%$, not $2%$. Option (2) $50 text{ kg}$: This matches our calculated new total weight. If the new weight is $50 text{ kg}$, the dry matter ($1 text{ kg}$) would be $frac{1}{50} times 100% = 2%$. This is correct. Option (3) $75 text{ kg}$: If the new weight is $75 text{ kg}$, the dry matter ($1 text{ kg}$) would be $frac{1}{75} times 100% approx 1.33%$, not $2%$. Option (4) $2 text{ kg}$: If the new weight is $2 text{ kg}$, the dry matter ($1 text{ kg}$) would be $frac{1}{2} times 100% = 50%$, not $2%$. Therefore, the total weight of cucumbers now is $50 text{ kg}$. The correct option is (2) 50 kg.

Q: Amoebae are known to double in number every 3 minutes. Two identical vessels A and B, respectively contain one and two amoebae to start with. The vessel B gets filled with amoebae in 3 hours. In how much time will the vessel A get filled with amoebae ?

Correct Option: 3 hours 3 minutes. Let $Td$ be the doubling time, which is $3$ minutes. Let $C$ be the full capacity of the vessel. For Vessel B: Initial number of amoebae ($N{0,B}$) = $2$. Time to fill ($TB$) = $3$ hours $= 3 times 60 = 180$ minutes. At time $TB$, Vessel B is full, so it contains $C$ amoebae. The number of amoebae at time $t$ is given by $N(t) = N0 times 2^{t/Td}$. So, $C = 2 times 2^{180/3} = 2 times 2^{60} = 2^{61}$. This is the capacity of the vessel. For Vessel A: Initial number of amoebae ($N{0,A}$) = $1$. We want to find the time ($TA$) when Vessel A gets filled, i.e., when $NA(TA) = C$. Using the formula for Vessel A: $C = 1 times 2^{TA/Td}$ Substitute the value of $C$ and $Td$: $2^{61} = 2^{TA/3}$ Equating the exponents: $61 = frac{TA}{3}$ $TA = 61 times 3 = 183$ minutes. To convert $183$ minutes into hours and minutes: $183 text{ minutes} = 3 text{ hours and } 3 text{ minutes}$ (since $3 times 60 = 180$). Alternatively, consider the relative starting amounts: Vessel A starts with $1$ amoeba, and Vessel B starts with $2$ amoebae. So, Vessel A starts with half the number of amoebae as Vessel B. If Vessel B is full at $180$ minutes, it means $3$ minutes before that (at $177$ minutes), it was half full (because amoebae double every $3$ minutes). Since Vessel A starts with half the initial amount of Vessel B, at any given time, Vessel A will have half the number of amoebae compared to Vessel B. Therefore, at $180$ minutes, when Vessel B is full (has $C$ amoebae), Vessel A will have $C/2$ amoebae (i.e., it will be half full). Since amoebae double every $3$ minutes, if Vessel A is half full at $180$ minutes, it will become fully filled $3$ minutes later. So, Vessel A will be filled at $180 + 3 = 183$ minutes, which is $3$ hours and $3$ minutes. Let's evaluate the options: Option (1) $3$ hours ($180$ minutes): Incorrect, as A starts with half the amount of B. Option (2) $2$ hours $57$ minutes ($177$ minutes): Incorrect, this is when B was half ful

Q: What is the next term in the following sequence ? $7, 11, 13, 17, 19, 23, 25, 29, ?$ निम्नलिखित अनुक्रम मे अगली संख्या क्या है?

Correct Option: 31. Let's analyze the given sequence: $7, 11, 13, 17, 19, 23, 25, 29, ?$ To find the pattern, we calculate the differences between consecutive terms: $11 - 7 = 4$ $13 - 11 = 2$ $17 - 13 = 4$ $19 - 17 = 2$ $23 - 19 = 4$ $25 - 23 = 2$ $29 - 25 = 4$ The sequence of differences is $4, 2, 4, 2, 4, 2, 4$. This is an alternating pattern where $4$ is added, then $2$ is added, and this cycle repeats. Since the last difference was $4$, the next difference in the pattern should be $2$. To find the next term in the main sequence, we add this difference to the last known term: Next term $= 29 + 2 = 31$. Let's evaluate the options: Option (1) $37$: This would imply a difference of $37 - 29 = 8$, which does not fit the pattern. Option (2) $35$: This would imply a difference of $35 - 29 = 6$, which does not fit the pattern. Option (3) $31$: This matches our calculated next term, as $29 + 2 = 31$. Option (4) $33$: This would imply a difference of $33 - 29 = 4$. While $4$ is part of the pattern, it would break the alternating sequence ($4,2,4,2,4,2,4,mathbf{4}$ instead of $4,2,4,2,4,2,4,mathbf{2}$). Therefore, $33$ is incorrect. Thus, the next term in the sequence is $31$. The correct option is (3) 31.

Q: If a+b+c+d+e=10 (all natural numbers), then what is the maximum value of atimes btimes ctimes dtimes e? यदि $a+b+c+d+e=10$ (सभी धनात्मक संख्यायें हैं) तब $atimes btimes ctimes dtimes e$ का अधिकतम मान क्या होगा ?

Correct Option: 32. We are given that $a, b, c, d, e$ are natural numbers (positive integers) and their sum is $a+b+c+d+e=10$. We need to find the maximum value of their product $P = a times b times c times d times e$. For a fixed sum of positive numbers, their product is maximized when the numbers are as close to each other as possible. This is a fundamental principle related to the AM-GM inequality. In this case, we have $5$ numbers whose sum is $10$. The average value of these numbers is $frac{10}{5} = 2$. If we set all the numbers to be equal to their average, i.e., $a=b=c=d=e=2$, then: Sum: $2+2+2+2+2 = 10$. This satisfies the given condition. Product: $2 times 2 times 2 times 2 times 2 = 2^5 = 32$. Since $2$ is a natural number, this distribution is valid. Any other distribution of natural numbers that sums to $10$ will result in a smaller product. For example: If we choose $1, 2, 2, 2, 3$ (sum is $10$): Product $= 1 times 2 times 2 times 2 times 3 = 24$. If we choose $1, 1, 2, 3, 3$ (sum is $10$): Product $= 1 times 1 times 2 times 3 times 3 = 18$. Both $24$ and $18$ are less than $32$. Let's evaluate the options: Option (1) $36$: This value is not achievable for 5 natural numbers summing to $10$. Option (2) $30$: This value is less than $32$. Option (3) $32$: This matches our calculated maximum value. Option (4) $48$: This value is not achievable for 5 natural numbers summing to $10$. Therefore, the maximum value of $a times b times c times d times e$ is $32$. The correct option is (3) 32.

Q: In an examiniation, 65% of the total examinees passsed. If the number of failures is 420, then what is the total number of examinees? एक परीक्षा में कुल परीक्षार्थियों के 65% उत्तीर्ण हुए। यदि 420 परीक्षार्थी अनुत्तीर्ण होते हैं तब कुल परीक्षार्थियों की संख्या कितनी है ?

Correct Option: 1200. Let the total number of examinees be $T$. Given that $65%$ of the total examinees passed. Therefore, the percentage of examinees who failed is $100% - 65% = 35%$. We are also given that the number of failures is $420$. So, we can set up the equation: $35%$ of $T = 420$ $frac{35}{100} times T = 420$ To find $T$, we rearrange the equation: $T = frac{420 times 100}{35}$ $T = frac{420}{35} times 100$ $T = 12 times 100$ $T = 1200$. Let's evaluate the options: Option (1) $1400$: If $T=1400$, then $35%$ of $1400 = 0.35 times 1400 = 490$. This is not $420$. Option (2) $800$: If $T=800$, then $35%$ of $800 = 0.35 times 800 = 280$. This is not $420$. Option (3) $1200$: This matches our calculated total number of examinees. If $T=1200$, then $35%$ of $1200 = 0.35 times 1200 = 420$. This is correct. Option (4) $1000$: If $T=1000$, then $35%$ of $1000 = 0.35 times 1000 = 350$. This is not $420$. Therefore, the total number of examinees is $1200$. The correct option is (3) 1200.

Q: A certain sum of money at Simple Interest amounts to ₹704 in 2 years and ₹800 in 5 years. Find the principal. साधारण ब्याज पर एक धनराशि 2 वर्ष में ₹704 और 5 वर्ष में ₹800 हो जाती है। यह धनराशि कितनी है ?

Correct Option: ₹640. Let the principal amount be $P$. The formula for Amount ($A$) in simple interest is $A = P + text{SI}$, where $text{SI}$ is the simple interest. Given information: 1. Amount after $2$ years ($A2$) = $₹704$. 2. Amount after $5$ years ($A5$) = $₹800$. Since it's simple interest, the interest earned each year is constant. The difference in the amounts is solely due to the interest accumulated over the additional years. Interest earned in $(5 - 2) = 3$ years $= A5 - A2 = ₹800 - ₹704 = ₹96$. Now, we can find the simple interest earned per year: Simple Interest for $1$ year $= frac{₹96}{3 text{ years}} = ₹32$. Next, calculate the simple interest earned in $2$ years: Simple Interest for $2$ years $= 2 times ₹32 = ₹64$. We know that $A2 = P + text{Simple Interest for } 2 text{ years}$. Substitute the values: $₹704 = P + ₹64$. To find the principal $P$: $P = ₹704 - ₹64 = ₹640$. Let's evaluate the options: Option (1) $₹600$: If $P=₹600$, then $text{SI}2 = ₹704 - ₹600 = ₹104$. This implies annual interest of $₹52$, which contradicts the calculated $₹32$. Option (2) $₹640$: This matches our calculated principal. If $P=₹640$, then $text{SI}2 = ₹704 - ₹640 = ₹64$, which is $2 times ₹32$. This is consistent. Option (3) $₹660$: If $P=₹660$, then $text{SI}2 = ₹704 - ₹660 = ₹44$. This implies annual interest of $₹22$, which contradicts $₹32$. Option (4) $₹680$: If $P=₹680$, then $text{SI}2 = ₹704 - ₹680 = ₹24$. This implies annual interest of $₹12$, which contradicts $₹32$. Therefore, the principal amount is $₹640$. The correct option is (2) ₹640.

Question 1

If Q=10 and CLAP=76 then find the value of TIGER. यदि Q=10 तथा CLAP=76 हैं तब TIGER का मान है :

Accepted Answer

Correct Option: 76. This is a coding-decoding problem where letters are assigned numerical values based on a specific rule. First, let's decipher the rule from the given information: 1. Q = 10 The letter Q is the $17^{text{th}}$ letter in the standard English alphabet (A=1, B=2, ..., Q=17). If we consider the reverse alphabetical order (Z=1, Y=2, ..., A=26), the position of Q would be $26 - 17 + 1 = 10$. This matches the given value for Q. So, the coding scheme is: Assign each letter its reverse alphabetical position. 2. CLAP = 76 Let's verify this rule for the word CLAP: C: $3^{text{rd}}$ letter. Reverse position = $26 - 3 + 1 = 24$. L: $12^{text{th}}$ letter. Reverse position = $26 - 12 + 1 = 15$. A: $1^{text{st}}$ letter. Reverse position = $26 - 1 + 1 = 26$. P: $16^{text{th}}$ letter. Reverse position = $26 - 16 + 1 = 11$. Sum for CLAP = $24 + 15 + 26 + 11 = 76$. This also matches the given value, confirming our rule. Now, we apply the same coding scheme to find the value of TIGER: - T: $20^{text{th}}$ letter. Reverse position = $26 - 20 + 1 = 7$. - I: $9^{text{th}}$ letter. Reverse position = $26 - 9 + 1 = 18$. - G: $7^{text{th}}$ letter. Reverse position = $26 - 7 + 1 = 20$. - E: $5^{text{th}}$ letter. Reverse position = $26 - 5 + 1 = 22$. - R: $18^{text{th}}$ letter. Reverse position = $26 - 18 + 1 = 9$. Sum for TIGER = $7 + 18 + 20 + 22 + 9 = 76$. Let's evaluate the options: Option (1) $76$: This matches our calculated value for TIGER. Option (2) $75$: Incorrect, as the sum is $76$. Option (3) $74$: Incorrect, as the sum is $76$. Option (4) $73$: Incorrect, as the sum is $76$. Therefore, the value of TIGER is $76$. The correct option is (1) 76.

Question 2

Which is largest amongst $5/8, 2/3, 7/9, 3/5$? $5/8, 2/3, 7/9, 3/5$ में सबसे बड़ी संख्या कौन सी है?

Accepted Answer

Correct Option: $7/9$. To determine the largest fraction among $5/8, 2/3, 7/9, 3/5$, we can convert them to decimal form for easy comparison. 1. Convert $5/8$ to decimal: $5 div 8 = 0.625$ 2. Convert $2/3$ to decimal: $2 div 3 = 0.6666...$ (a repeating decimal) 3. Convert $7/9$ to decimal: $7 div 9 = 0.7777...$ (a repeating decimal) 4. Convert $3/5$ to decimal: $3 div 5 = 0.6$ Now, let's compare these decimal values: $0.625$ $0.666...$ $0.777...$ $0.600$ Arranging them in ascending order: $0.6 < 0.625 < 0.666... < 0.777...$ The largest decimal value is $0.777...$, which corresponds to the fraction $frac{7}{9}$. Alternatively, we could find a common denominator for all fractions. The denominators are $8, 3, 9, 5$. The Least Common Multiple (LCM) of these numbers is $360$. $frac{5}{8} = frac{5 times 45}{8 times 45} = frac{225}{360}$ $frac{2}{3} = frac{2 times 120}{3 times 120} = frac{240}{360}$ $frac{7}{9} = frac{7 times 40}{9 times 40} = frac{280}{360}$ $frac{3}{5} = frac{3 times 72}{5 times 72} = frac{216}{360}$ Comparing the numerators ($225, 240, 280, 216$), $280$ is the largest, so $frac{280}{360}$ or $frac{7}{9}$ is the largest fraction. Let's evaluate the options: Option (1) $5/8$: This is $0.625$, which is not the largest. Option (2) $2/3$: This is $0.666...$, which is not the largest. Option (3) $3/5$: This is $0.6$, which is the smallest. Option (4) $7/9$: This is $0.777...$, which is the largest. Therefore, the largest fraction is $frac{7}{9}$. The correct option is (4) $7/9$.

Question 3

A chemical solution contains 30% water and 70% alkali. What quantity of water should be added to 6 litres of solution so that the water content becomes 40% ? एक रासायनिक विलयन में 30% जल और 70% क्षार है। 6 लीटर विलयन में कितना जल और मिलाया जाए कि विलयन में जल की मात्रा 40% हो जाए ?

Accepted Answer

Correct Option: 1 litre. Let the initial volume of the solution be $V1 = 6 text{ litres}$. Initial Composition: Water content = $30%$. Alkali content = $70%$. Calculate the initial amount of water and alkali: Amount of water = $30%$ of $6 text{ litres} = 0.30 times 6 = 1.8 text{ litres}$. Amount of alkali = $70%$ of $6 text{ litres} = 0.70 times 6 = 4.2 text{ litres}$. (Check: $1.8 + 4.2 = 6 text{ litres}$, which is the total initial volume). Adding Water: Let $x$ be the quantity of water added (in litres). Crucially, the amount of alkali in the solution remains constant, as only water is being added. New total volume of solution ($V2$) = $(6 + x) text{ litres}$. New amount of water = $(1.8 + x) text{ litres}$. Amount of alkali (constant) = $4.2 text{ litres}$. Final Composition: In the new solution, the water content is $40%$. This means the alkali content is $100% - 40% = 60%$. Now, we can set up an equation based on the constant amount of alkali: $60%$ of $V2 = text{Amount of alkali}$ $0.60 times (6 + x) = 4.2$ Solve for $x$: $6 + x = frac{4.2}{0.60}$ $6 + x = frac{420}{60}$ $6 + x = 7$ $x = 7 - 6$ $x = 1 text{ litre}$. The quantity of water to be added is $1$ litre. Since $1 text{ litre} = 1000 text{ ml}$, the answer is $1000 text{ ml}$. Let's evaluate the options: Option (1) $500 text{ ml}$ ($0.5 text{ litres}$): If $0.5 text{ litres}$ were added, the new water percentage would be $frac{1.8+0.5}{6+0.5} = frac{2.3}{6.5} approx 35.38%$, not $40%$. Option (2) $700 text{ ml}$ ($0.7 text{ litres}$): If $0.7 text{ litres}$ were added, the new water percentage would be $frac{1.8+0.7}{6+0.7} = frac{2.5}{6.7} approx 37.31%$, not $40%$. Option (3) $900 text{ ml}$ ($0.9 text{ litres}$): If $0.9 text{ litres}$ were added, the new water percentage would be $frac{1.8+0.9}{6+0.9} = frac{2.7}{6.9} approx 39.13%$, not $40%$. Option (4) $1 text{ litre}$: This matches our calculated value. If $1 text{ litre}$ is added, the new water percentage is $frac{1.8+1}{6+1} = frac{2.8}{7}

Question 4

In a class of 50 students, Mithilesh is eighth from the top. Himadri is 20th from the bottom. How many students are there between Mithilesh and Himadri ? 50 विद्यार्थियों की एक कक्षा में मिथिलेश का ऊपर से आठवाँ स्थान है। हिमाद्री नीचे से 20 वीं स्थान पर है। मिथिलेश और हिमाद्री के बीच कितने विद्यार्थ

Accepted Answer

Correct Option: 22. Given: Total number of students in the class ($N$) = $50$. Mithilesh's rank from the top = $8^{text{th}}$. Himadri's rank from the bottom = $20^{text{th}}$. First, we need to determine if there is any overlap in their positions. The sum of their ranks from opposite ends is $8 + 20 = 28$. Since the sum of ranks ($28$) is less than the total number of students ($50$), there is no overlap between Mithilesh and Himadri; they are distinct individuals, and there are students between them. The number of students between Mithilesh and Himadri can be calculated using the formula: Number of students between = Total students - (Mithilesh's rank from top + Himadri's rank from bottom) Number of students between = $50 - (8 + 20)$ Number of students between = $50 - 28$ Number of students between = $22$. Alternatively, consider the students accounted for by their positions: Students from the top up to Mithilesh (including Mithilesh) = $8$. Students from the bottom up to Himadri (including Himadri) = $20$. Total students accounted for if there's no overlap = $8 + 20 = 28$. The remaining students are those who are positioned between Mithilesh and Himadri. Remaining students = Total students - (Students accounted for) Remaining students = $50 - 28 = 22$. Let's evaluate the options: Option (1) $20$: Incorrect. Option (2) $21$: Incorrect. Option (3) $22$: This matches our calculated number of students. Option (4) $23$: Incorrect. Therefore, there are $22$ students between Mithilesh and Himadri. The correct option is (3) 22.

Question 5

A cucumber contains 99% water. Ramesh buys 100 kg of cucumbers. After 30 days of storing, the cucumbers lose some water. These now contain 98% water. What is the total weight of cucumbers now ? खीरे में 99% जल होता है। रमेश 100 किलोग्राम खीरे खरीदता है। 30 दिन रखने के बाद इन खीरों में कुछ जल कम हो ज

Accepted Answer

Correct Option: 50 kg. This problem relies on the principle that when a fruit or vegetable loses water, the amount of its dry matter (non-water content) remains constant. Initial State: Total weight of cucumbers = $100 text{ kg}$. Water content = $99%$. Dry matter content = $100% - 99% = 1%$. Calculate the actual weight of dry matter: Weight of dry matter = $1%$ of $100 text{ kg} = frac{1}{100} times 100 text{ kg} = 1 text{ kg}$. Final State (After 30 days): After losing water, the dry matter content remains $1 text{ kg}$. New water content = $98%$. New dry matter content = $100% - 98% = 2%$. Let the new total weight of cucumbers be $W{text{new}}$. We know that $2%$ of $W{text{new}}$ is the dry matter, which is $1 text{ kg}$. So, $2%$ of $W{text{new}} = 1 text{ kg}$. $frac{2}{100} times W{text{new}} = 1$ $W{text{new}} = frac{1 times 100}{2}$ $W{text{new}} = frac{100}{2} = 50 text{ kg}$. Let's evaluate the options: Option (1) $99 text{ kg}$: If the new weight is $99 text{ kg}$, the dry matter ($1 text{ kg}$) would be $frac{1}{99} times 100% approx 1.01%$, not $2%$. Option (2) $50 text{ kg}$: This matches our calculated new total weight. If the new weight is $50 text{ kg}$, the dry matter ($1 text{ kg}$) would be $frac{1}{50} times 100% = 2%$. This is correct. Option (3) $75 text{ kg}$: If the new weight is $75 text{ kg}$, the dry matter ($1 text{ kg}$) would be $frac{1}{75} times 100% approx 1.33%$, not $2%$. Option (4) $2 text{ kg}$: If the new weight is $2 text{ kg}$, the dry matter ($1 text{ kg}$) would be $frac{1}{2} times 100% = 50%$, not $2%$. Therefore, the total weight of cucumbers now is $50 text{ kg}$. The correct option is (2) 50 kg.

Question 6

Amoebae are known to double in number every 3 minutes. Two identical vessels A and B, respectively contain one and two amoebae to start with. The vessel B gets filled with amoebae in 3 hours. In how much time will the vessel A get filled with amoebae ?

Accepted Answer

Correct Option: 3 hours 3 minutes. Let $Td$ be the doubling time, which is $3$ minutes. Let $C$ be the full capacity of the vessel. For Vessel B: Initial number of amoebae ($N{0,B}$) = $2$. Time to fill ($TB$) = $3$ hours $= 3 times 60 = 180$ minutes. At time $TB$, Vessel B is full, so it contains $C$ amoebae. The number of amoebae at time $t$ is given by $N(t) = N0 times 2^{t/Td}$. So, $C = 2 times 2^{180/3} = 2 times 2^{60} = 2^{61}$. This is the capacity of the vessel. For Vessel A: Initial number of amoebae ($N{0,A}$) = $1$. We want to find the time ($TA$) when Vessel A gets filled, i.e., when $NA(TA) = C$. Using the formula for Vessel A: $C = 1 times 2^{TA/Td}$ Substitute the value of $C$ and $Td$: $2^{61} = 2^{TA/3}$ Equating the exponents: $61 = frac{TA}{3}$ $TA = 61 times 3 = 183$ minutes. To convert $183$ minutes into hours and minutes: $183 text{ minutes} = 3 text{ hours and } 3 text{ minutes}$ (since $3 times 60 = 180$). Alternatively, consider the relative starting amounts: Vessel A starts with $1$ amoeba, and Vessel B starts with $2$ amoebae. So, Vessel A starts with half the number of amoebae as Vessel B. If Vessel B is full at $180$ minutes, it means $3$ minutes before that (at $177$ minutes), it was half full (because amoebae double every $3$ minutes). Since Vessel A starts with half the initial amount of Vessel B, at any given time, Vessel A will have half the number of amoebae compared to Vessel B. Therefore, at $180$ minutes, when Vessel B is full (has $C$ amoebae), Vessel A will have $C/2$ amoebae (i.e., it will be half full). Since amoebae double every $3$ minutes, if Vessel A is half full at $180$ minutes, it will become fully filled $3$ minutes later. So, Vessel A will be filled at $180 + 3 = 183$ minutes, which is $3$ hours and $3$ minutes. Let's evaluate the options: Option (1) $3$ hours ($180$ minutes): Incorrect, as A starts with half the amount of B. Option (2) $2$ hours $57$ minutes ($177$ minutes): Incorrect, this is when B was half ful

Question 7

What is the next term in the following sequence ? $7, 11, 13, 17, 19, 23, 25, 29, ?$ निम्नलिखित अनुक्रम मे अगली संख्या क्या है?

Accepted Answer

Correct Option: 31. Let's analyze the given sequence: $7, 11, 13, 17, 19, 23, 25, 29, ?$ To find the pattern, we calculate the differences between consecutive terms: $11 - 7 = 4$ $13 - 11 = 2$ $17 - 13 = 4$ $19 - 17 = 2$ $23 - 19 = 4$ $25 - 23 = 2$ $29 - 25 = 4$ The sequence of differences is $4, 2, 4, 2, 4, 2, 4$. This is an alternating pattern where $4$ is added, then $2$ is added, and this cycle repeats. Since the last difference was $4$, the next difference in the pattern should be $2$. To find the next term in the main sequence, we add this difference to the last known term: Next term $= 29 + 2 = 31$. Let's evaluate the options: Option (1) $37$: This would imply a difference of $37 - 29 = 8$, which does not fit the pattern. Option (2) $35$: This would imply a difference of $35 - 29 = 6$, which does not fit the pattern. Option (3) $31$: This matches our calculated next term, as $29 + 2 = 31$. Option (4) $33$: This would imply a difference of $33 - 29 = 4$. While $4$ is part of the pattern, it would break the alternating sequence ($4,2,4,2,4,2,4,mathbf{4}$ instead of $4,2,4,2,4,2,4,mathbf{2}$). Therefore, $33$ is incorrect. Thus, the next term in the sequence is $31$. The correct option is (3) 31.

Question 8

If a+b+c+d+e=10 (all natural numbers), then what is the maximum value of atimes btimes ctimes dtimes e? यदि $a+b+c+d+e=10$ (सभी धनात्मक संख्यायें हैं) तब $atimes btimes ctimes dtimes e$ का अधिकतम मान क्या होगा ?

Accepted Answer

Correct Option: 32. We are given that $a, b, c, d, e$ are natural numbers (positive integers) and their sum is $a+b+c+d+e=10$. We need to find the maximum value of their product $P = a times b times c times d times e$. For a fixed sum of positive numbers, their product is maximized when the numbers are as close to each other as possible. This is a fundamental principle related to the AM-GM inequality. In this case, we have $5$ numbers whose sum is $10$. The average value of these numbers is $frac{10}{5} = 2$. If we set all the numbers to be equal to their average, i.e., $a=b=c=d=e=2$, then: Sum: $2+2+2+2+2 = 10$. This satisfies the given condition. Product: $2 times 2 times 2 times 2 times 2 = 2^5 = 32$. Since $2$ is a natural number, this distribution is valid. Any other distribution of natural numbers that sums to $10$ will result in a smaller product. For example: If we choose $1, 2, 2, 2, 3$ (sum is $10$): Product $= 1 times 2 times 2 times 2 times 3 = 24$. If we choose $1, 1, 2, 3, 3$ (sum is $10$): Product $= 1 times 1 times 2 times 3 times 3 = 18$. Both $24$ and $18$ are less than $32$. Let's evaluate the options: Option (1) $36$: This value is not achievable for 5 natural numbers summing to $10$. Option (2) $30$: This value is less than $32$. Option (3) $32$: This matches our calculated maximum value. Option (4) $48$: This value is not achievable for 5 natural numbers summing to $10$. Therefore, the maximum value of $a times b times c times d times e$ is $32$. The correct option is (3) 32.

Question 9

In an examiniation, 65% of the total examinees passsed. If the number of failures is 420, then what is the total number of examinees? एक परीक्षा में कुल परीक्षार्थियों के 65% उत्तीर्ण हुए। यदि 420 परीक्षार्थी अनुत्तीर्ण होते हैं तब कुल परीक्षार्थियों की संख्या कितनी है ?

Accepted Answer

Correct Option: 1200. Let the total number of examinees be $T$. Given that $65%$ of the total examinees passed. Therefore, the percentage of examinees who failed is $100% - 65% = 35%$. We are also given that the number of failures is $420$. So, we can set up the equation: $35%$ of $T = 420$ $frac{35}{100} times T = 420$ To find $T$, we rearrange the equation: $T = frac{420 times 100}{35}$ $T = frac{420}{35} times 100$ $T = 12 times 100$ $T = 1200$. Let's evaluate the options: Option (1) $1400$: If $T=1400$, then $35%$ of $1400 = 0.35 times 1400 = 490$. This is not $420$. Option (2) $800$: If $T=800$, then $35%$ of $800 = 0.35 times 800 = 280$. This is not $420$. Option (3) $1200$: This matches our calculated total number of examinees. If $T=1200$, then $35%$ of $1200 = 0.35 times 1200 = 420$. This is correct. Option (4) $1000$: If $T=1000$, then $35%$ of $1000 = 0.35 times 1000 = 350$. This is not $420$. Therefore, the total number of examinees is $1200$. The correct option is (3) 1200.

Question 10

A certain sum of money at Simple Interest amounts to ₹704 in 2 years and ₹800 in 5 years. Find the principal. साधारण ब्याज पर एक धनराशि 2 वर्ष में ₹704 और 5 वर्ष में ₹800 हो जाती है। यह धनराशि कितनी है ?

Accepted Answer

Correct Option: ₹640. Let the principal amount be $P$. The formula for Amount ($A$) in simple interest is $A = P + text{SI}$, where $text{SI}$ is the simple interest. Given information: 1. Amount after $2$ years ($A2$) = $₹704$. 2. Amount after $5$ years ($A5$) = $₹800$. Since it's simple interest, the interest earned each year is constant. The difference in the amounts is solely due to the interest accumulated over the additional years. Interest earned in $(5 - 2) = 3$ years $= A5 - A2 = ₹800 - ₹704 = ₹96$. Now, we can find the simple interest earned per year: Simple Interest for $1$ year $= frac{₹96}{3 text{ years}} = ₹32$. Next, calculate the simple interest earned in $2$ years: Simple Interest for $2$ years $= 2 times ₹32 = ₹64$. We know that $A2 = P + text{Simple Interest for } 2 text{ years}$. Substitute the values: $₹704 = P + ₹64$. To find the principal $P$: $P = ₹704 - ₹64 = ₹640$. Let's evaluate the options: Option (1) $₹600$: If $P=₹600$, then $text{SI}2 = ₹704 - ₹600 = ₹104$. This implies annual interest of $₹52$, which contradicts the calculated $₹32$. Option (2) $₹640$: This matches our calculated principal. If $P=₹640$, then $text{SI}2 = ₹704 - ₹640 = ₹64$, which is $2 times ₹32$. This is consistent. Option (3) $₹660$: If $P=₹660$, then $text{SI}2 = ₹704 - ₹660 = ₹44$. This implies annual interest of $₹22$, which contradicts $₹32$. Option (4) $₹680$: If $P=₹680$, then $text{SI}2 = ₹704 - ₹680 = ₹24$. This implies annual interest of $₹12$, which contradicts $₹32$. Therefore, the principal amount is $₹640$. The correct option is (2) ₹640.

Question 11

A sum of ₹12,500 amounts to ₹15,500 in 4 years at simple interest. What is the rate of interest ? ₹ 12,500 साधारण ब्याज से 4 वर्ष में ₹ 15,500 हो जाते हैं। ब्याज की दर क्या है ?

Accepted Answer

Correct Option: 6%. Given information for a simple interest calculation: Principal amount ($P$) = $₹12,500$. Amount ($A$) after $4$ years = $₹15,500$. Time ($T$) = $4$ years. First, calculate the Simple Interest (SI) earned over $4$ years: $text{SI} = A - P$ $text{SI} = ₹15,500 - ₹12,500 = ₹3,000$. The formula for Simple Interest is: $text{SI} = frac{P times R times T}{100}$ Where $R$ is the annual rate of interest in percentage. We need to find $R$. Rearranging the formula to solve for $R$: $R = frac{text{SI} times 100}{P times T}$ Substitute the known values into the formula: $R = frac{3000 times 100}{12500 times 4}$ $R = frac{300000}{50000}$ Simplify the expression: $R = frac{300}{50}$ $R = 6$. So, the rate of interest is $6%$. Let's evaluate the options: Option (1) $4%$: If $R=4%$, $text{SI} = frac{12500 times 4 times 4}{100} = 125 times 16 = ₹2000$. This is not $₹3000$. Option (2) $6%$: This matches our calculated rate. If $R=6%$, $text{SI} = frac{12500 times 6 times 4}{100} = 125 times 24 = ₹3000$. This is correct. Option (3) $8%$: If $R=8%$, $text{SI} = frac{12500 times 8 times 4}{100} = 125 times 32 = ₹4000$. This is not $₹3000$. Option (4) $2%$: If $R=2%$, $text{SI} = frac{12500 times 2 times 4}{100} = 125 times 8 = ₹1000$. This is not $₹3000$. Therefore, the rate of interest is $6%$. The correct option is (2) 6%.

Question 12

How many multiples of 3 are there between the integers 18 and 108, both inclusive ? पूर्णांकों 18 और 108 के बीच, इन दोनों को शामिल करते हुए, 3 के कितने गुणज होंगे ?

Accepted Answer

Correct Option: 31. We need to find the number of integers $N$ such that $18 le N le 108$ and $N$ is a multiple of $3$. This means $N$ can be expressed as $3k$ for some integer $k$. So, we have the inequality: $18 le 3k le 108$. To find the range of $k$, we divide all parts of the inequality by $3$: $frac{18}{3} le frac{3k}{3} le frac{108}{3}$ $6 le k le 36$ This means $k$ can take any integer value from $6$ to $36$, inclusive. To count the number of integers in an inclusive range $[a, b]$, the formula is $b - a + 1$. Number of multiples $= 36 - 6 + 1 = 30 + 1 = 31$. Let's evaluate the options: Option (1) $29$: This would be $36 - 6 - 1$, which is incorrect. Option (2) $30$: This would be $36 - 6$, which excludes one of the endpoints, so it's incorrect. Option (3) $31$: This matches our calculated value. Option (4) $32$: This would be $36 - 6 + 2$, which is incorrect. Therefore, there are $31$ multiples of $3$ between $18$ and $108$, both inclusive. The correct option is (3) 31.

Question 13

What will come in place of the question mark (?) in the following number series ? $121, 164, 250, 379, 551, ?$ निम्नलिखित श्रृंखला में प्रश्नसूचक (?) के स्थान पर कौन सी संख्या आएगी ?

Accepted Answer

Correct Option: 766. Let's analyze the given number series: $121, 164, 250, 379, 551, ?$ We will find the differences between consecutive terms: First difference ($D1$): $164 - 121 = 43$ Second difference ($D2$): $250 - 164 = 86$ Third difference ($D3$): $379 - 250 = 129$ Fourth difference ($D4$): $551 - 379 = 172$ The sequence of first differences is: $43, 86, 129, 172$. Let's examine the pattern in this sequence of differences. We can see that each term is a multiple of $43$: $43 times 1 = 43$ $43 times 2 = 86$ $43 times 3 = 129$ $43 times 4 = 172$ This indicates that the first differences form an arithmetic progression with a common difference of $43$. To find the next term in the original series, we need to find the fifth difference ($D5$): $D5 = D4 + 43 = 172 + 43 = 215$. Now, add this fifth difference to the last term of the original series: Next term $= 551 + D5 = 551 + 215 = 766$. Let's evaluate the options: Option (1) $746$: If the next term were $746$, the difference would be $746 - 551 = 195$, which is not $215$. Option (2) $766$: This matches our calculated value. Option (3) $872$: If the next term were $872$, the difference would be $872 - 551 = 321$, which is not $215$. Option (4) $892$: If the next term were $892$, the difference would be $892 - 551 = 341$, which is not $215$. Therefore, the next term in the series is $766$. The correct option is (2) 766.

Question 14

How many sets of two letters in the word GENERAL have as many letters between them as they have in the English alphabet ? GENERAL शब्द में दो अक्षरों के ऐसे कितने समूह हैं जिनके बीच उतने ही अक्षर हैं जितने कि उनके बीच अंग्रेज़ी वर्णमाला में हैं?

Accepted Answer

Correct Option: 1. To solve this, we need to list the letters of the word 'GENERAL' and their corresponding positions in the English alphabet (A=1, B=2, ..., Z=26). Word: G E N E R A L Alphabetical values: G=7, E=5, N=14, E=5, R=18, A=1, L=12 We will check every possible pair of letters in the word and compare the count of letters between them in the word with the count of letters between them in the alphabet. The count of letters between two letters $X$ and $Y$ in the alphabet is $| text{alphabetical value of } Y - text{alphabetical value of } X | - 1$. Let's examine pairs: 1. G (pos 1) and E (pos 2): Letters in word: $0$. (No letters between G and E) Letters in alphabet: $|5 - 7| - 1 = 2 - 1 = 1$ (F between G and E). No match. 2. E (pos 2) and A (pos 6): Letters in word: $3$ (N, E, R are between E and A). Letters in alphabet: $|1 - 5| - 1 = 4 - 1 = 3$ (D, C, B are between E and A). Match found! (E-A) Let's continue checking other pairs for completeness: - G (pos 1) and N (pos 3): Word count = 1 (E). Alphabet count = $|14-7|-1 = 6$. No. - G (pos 1) and E (pos 4): Word count = 2 (N, E). Alphabet count = $|5-7|-1 = 1$. No. - G (pos 1) and R (pos 5): Word count = 3 (E, N, E). Alphabet count = $|18-7|-1 = 10$. No. - G (pos 1) and A (pos 6): Word count = 4 (E, N, E, R). Alphabet count = $|1-7|-1 = 5$. No. - G (pos 1) and L (pos 7): Word count = 5 (E, N, E, R, A). Alphabet count = $|12-7|-1 = 4$. No. - E (pos 2) and N (pos 3): Word count = 0. Alphabet count = $|14-5|-1 = 8$. No. - E (pos 2) and E (pos 4): Word count = 1 (N). Alphabet count = $|5-5|-1 = -1$ (meaning 0 letters between identical letters). No. - E (pos 2) and R (pos 5): Word count = 2 (N, E). Alphabet count = $|18-5|-1 = 12$. No. - E (pos 2) and L (pos 7): Word count = 4 (N, E, R, A). Alphabet count = $|12-5|-1 = 6$. No. - N (pos 3) and E (pos 4): Word count = 0. Alphabet count = $|5-14|-1 = 8$. No. - N (pos 3) and R (pos 5): Word count = 1 (E). Alphabet count = $|18-14|-1 = 3$. No. - N (pos 3) and A (pos 6)

Question 15

If 2, 4 and 6 are mapped to 10, 26, and 50 respectively, then what number is 16 mapped to ? $2=10, 4=26, 6=50, 16=?$ यदि 2, 4 और 6 संख्याएँ क्रमशः 10, 26 और 50 के साथ मिलाई जाती है, तो किस संख्या के साथ 16 मिलाया जाएगा ?

Accepted Answer

Correct Option: 290. Let's analyze the given mappings to find the underlying pattern: For $x=2$, the mapped value is $10$. We observe that $2^2 + 6 = 4 + 6 = 10$. For $x=4$, the mapped value is $26$. We observe that $4^2 + 10 = 16 + 10 = 26$. For $x=6$, the mapped value is $50$. We observe that $6^2 + 14 = 36 + 14 = 50$. The pattern appears to be $x^2 + C$, where $C$ is a constant that depends on $x$. Let's look at the sequence of constants: $6, 10, 14$. This is an arithmetic progression with a common difference of $4$ ($10-6=4$, $14-10=4$). We can express $C$ as a linear function of $x$. Notice that $C = 2x + 2$ fits the pattern: For $x=2$, $C = 2(2) + 2 = 4 + 2 = 6$. For $x=4$, $C = 2(4) + 2 = 8 + 2 = 10$. For $x=6$, $C = 2(6) + 2 = 12 + 2 = 14$. So, the general mapping rule is $f(x) = x^2 + (2x+2)$. Now, we need to find the number that $16$ is mapped to. Using the established rule for $x=16$: $f(16) = 16^2 + (2 times 16 + 2)$ $f(16) = 256 + (32 + 2)$ $f(16) = 256 + 34$ $f(16) = 290$. Let's evaluate the options: Option (1) $132$: This does not follow the pattern $16^2 + (2 times 16 + 2) = 290$. Option (2) $290$: This matches our calculated value. Option (3) $144$: This does not follow the pattern. Option (4) $268$: This does not follow the pattern. Therefore, $16$ is mapped to $290$. The correct option is (2) 290.

Question 16

Two words separated by : and bearing a certain relationship with each other have been given on one side of :: From among the options, select the one that bears a similar relationship with the words given on the other side of : : Ploughing : Aeration :: Manuring : दो शब्द जो : के द्वारा पृथक किये गये

Accepted Answer

Correct Option: Replenishment. The given analogy is 'Ploughing : Aeration'. Ploughing is the process of tilling the soil, and its primary effect or purpose is to aerate the soil, meaning to introduce air into it. So, the relationship is 'Action : Effect'. Now we need to find a word that has a similar 'Action : Effect' relationship with 'Manuring'. Manuring is the process of adding manure or fertilizers to the soil. Option (1) Manufacturing: This refers to the process of making goods, which is unrelated to manuring. Option (2) Earthing (खोदना): This means digging, which is a physical action, but not the direct beneficial effect of manuring. Option (3) Replenishment: Manuring helps to replenish or restore the nutrients in the soil, making it more fertile. This aligns perfectly with the 'Action : Effect' relationship. Option (4) Agriculture: This is the broad field of farming, not a specific effect of manuring. Therefore, just as ploughing leads to aeration, manuring leads to replenishment of soil nutrients. The correct option is (3) Replenishment.

Question 17

Unscramble the letters and find the odd one out : शब्दों के अक्षरों को आगे-पीछे लिखा गया है। इन शब्दों को पहचानिए और भिन्न शब्द का चयन कीजिए।

Accepted Answer

Correct Option: CKYHOE. Let's unscramble each set of letters to reveal the hidden words: Option (1) CKYHOE unscrambles to HOCKEY. Hockey is a type of sport. Option (2) NRGEE unscrambles to GREEN. Green is a color. Option (3) LLWYEO unscrambles to YELLOW. Yellow is a color. Option (4) LTVIOE unscrambles to VIOLET. Violet is a color. Upon unscrambling, we find that GREEN, YELLOW, and VIOLET are all names of colors, belonging to the same category. HOCKEY, however, is the name of a sport, which belongs to a different category. Therefore, HOCKEY is the odd one out. The correct option is (1) CKYHOE.

Question 18

The total number of students in a school is 4800, out of which 60% are girls. What is the total number of boys in this school? एक विद्यालय में विद्यार्थियों की कुल संख्या 4800 है जिसमें से 60% लड़कियाँ है। इस विद्यालय में लड़कों की कुल संख्या कितनी है ?

Accepted Answer

Correct Option: 1920. Given: Total number of students in the school = $4800$. Percentage of girls = $60%$. To find the total number of boys, we first determine the percentage of boys: Percentage of boys = $100% - text{Percentage of girls}$ Percentage of boys = $100% - 60% = 40%$. Now, calculate the number of boys based on this percentage: Number of boys = $40%$ of $4800$ Number of boys = $frac{40}{100} times 4800$ Number of boys = $0.40 times 4800$ Number of boys = $1920$. Alternatively, we could first calculate the number of girls and then subtract from the total: Number of girls = $60%$ of $4800 = frac{60}{100} times 4800 = 0.60 times 4800 = 2880$. Number of boys = Total students - Number of girls Number of boys = $4800 - 2880 = 1920$. Let's evaluate the options: Option (1) $1920$: This matches our calculated number of boys. Option (2) $1980$: Incorrect. Option (3) $1910$: Incorrect. Option (4) $1930$: Incorrect. Therefore, the total number of boys in this school is $1920$. The correct option is (1) 1920.

Question 19

Choose the largest number : (1) $2^{500}$ (2) $3^{400}$ (3) $4^{300}$ (4) $5^{200}$ सबसे बड़ी संख्या चुनिए :

Accepted Answer

Correct Option: $3^{400}$. To compare these large numbers, the most effective method is to express them with a common exponent. The exponents are $500, 400, 300, 200$. The greatest common divisor (GCD) of these exponents is $100$. We can rewrite each number in the form $(X^k)^{100}$. Let's evaluate each option: 1. $2^{500}$: This can be written as $(2^5)^{100}$. $2^5 = 2 times 2 times 2 times 2 times 2 = 32$. So, $2^{500} = 32^{100}$. 2. $3^{400}$: This can be written as $(3^4)^{100}$. $3^4 = 3 times 3 times 3 times 3 = 81$. So, $3^{400} = 81^{100}$. 3. $4^{300}$: This can be written as $(4^3)^{100}$. $4^3 = 4 times 4 times 4 = 64$. So, $4^{300} = 64^{100}$. 4. $5^{200}$: This can be written as $(5^2)^{100}$. $5^2 = 5 times 5 = 25$. So, $5^{200} = 25^{100}$. Now we have all numbers expressed with the same exponent, $100$: $32^{100}, 81^{100}, 64^{100}, 25^{100}$. When comparing numbers with the same positive exponent, the number with the largest base is the largest. Comparing the bases: $32, 81, 64, 25$. The largest base is $81$. Therefore, $81^{100}$ is the largest number, which corresponds to the original expression $3^{400}$. Let's evaluate the options: Option (1) $2^{500} = 32^{100}$: Smaller than $81^{100}$. Option (2) $3^{400} = 81^{100}$: This is the largest value. Option (3) $4^{300} = 64^{100}$: Smaller than $81^{100}$. Option (4) $5^{200} = 25^{100}$: Smaller than $81^{100}$. Thus, the largest number is $3^{400}$. The correct option is (2) $3^{400}$.

Question 20

A Cookie:

Accepted Answer

Correct Option: Stores information about the user's web activity. A cookie (more formally, an HTTP cookie) is a small piece of data sent from a website and stored on the user's computer by the user's web browser while the user is browsing. Cookies are designed to be a reliable mechanism for websites to remember stateful information or to record the user's browsing activity. Let's evaluate each option: Option (A) Stores the password of the user: This is generally incorrect and a security risk. While cookies can store session IDs that keep a user logged in, they typically do not store raw, unencrypted passwords. Passwords are usually hashed and stored on the server side, not in client-side cookies. Storing passwords directly in cookies would make them vulnerable to theft. So, this is incorrect. Option (B) Stores information about the user's web activity: This is the primary function of cookies. They store data like browsing preferences, items in a shopping cart, login status, and tracking information to personalize user experience and for analytics. This directly relates to a user's web activity. So, this is correct. Option (C) Stores the commands used by the user: Cookies do not typically store a history of specific commands executed by the user within a web application. While they might store preferences that influence how commands behave, they don't log the commands themselves. So, this is incorrect. Option (D) Stores software developed by the user: Cookies are small text files for data storage, not for storing executable software or applications developed by a user. Software is typically downloaded and installed separately. So, this is incorrect. Therefore, the correct option is (B).

Question 21

Computer network is: (a) a collection of hardware components and computers (b) inter-connected by communication channels (c) used to share resources and information

Accepted Answer

Correct Option: All (a), (b) and (c) are true. Let's evaluate each statement regarding a computer network: Statement (a) a collection of hardware components and computers: A computer network fundamentally consists of various hardware components such as computers (servers, workstations, laptops), networking devices (routers, switches, hubs, modems), cables, and wireless access points. These components work together to form the network infrastructure. Therefore, statement (a) is true. Statement (b) inter-connected by communication channels: The hardware components and computers in a network must be linked together to communicate. This interconnection is achieved through communication channels, which can be wired (e.g., Ethernet cables, fiber optic cables) or wireless (e.g., Wi-Fi, Bluetooth). Therefore, statement (b) is true. Statement (c) used to share resources and information: The primary purpose and benefit of a computer network are to enable the sharing of resources (such as printers, storage devices, internet access, and software applications) and information (such as files, databases, and messages) among connected users and devices. This enhances collaboration and efficiency. Therefore, statement (c) is true. Since all three statements (a), (b), and (c) accurately describe characteristics and functions of a computer network, the correct option is the one that includes all of them. Let's analyze the options: Option (A) Only (a) is true: Incorrect, as (b) and (c) are also true. Option (B) Only (a) and (b) are true: Incorrect, as (c) is also true. Option (C) Only (b) and (c) are true: Incorrect, as (a) is also true. Option (D) All (a), (b) and (c) are true: This correctly identifies that all three statements are part of the comprehensive definition of a computer network. Therefore, the correct option is (D).

Question 22

Kabir paid 9,600 as interest on a loan he took for 5 years at 16% rate of simple interest. What was the amount of loan he took?

Accepted Answer

Correct Option: 12,000. To find the principal amount (loan amount), we use the formula for Simple Interest (SI): $SI = frac{P times R times T}{100}$, where $P$ is the Principal, $R$ is the Rate of Interest, and $T$ is the Time. Given values are: $SI = 9600$ $R = 16%$ $T = 5$ years Substitute these values into the formula: $9600 = frac{P times 16 times 5}{100}$ Now, solve for $P$: $9600 = frac{P times 80}{100}$ $P = frac{9600 times 100}{80}$ $P = frac{960000}{80}$ $P = 12000$ So, the amount of loan Kabir took was $12,000$. Let's analyze the options: Option (A) $16,000$: If the principal were $16,000$, the interest would be $frac{16000 times 16 times 5}{100} = 160 times 80 = 12800$, which is incorrect. Option (B) $12,400$: If the principal were $12,400$, the interest would be $frac{12400 times 16 times 5}{100} = 124 times 80 = 9920$, which is incorrect. Option (C) $12,000$: This matches our calculated principal amount, as $frac{12000 times 16 times 5}{100} = 120 times 80 = 9600$. This is correct. Option (D) $15,600$: If the principal were $15,600$, the interest would be $frac{15600 times 16 times 5}{100} = 156 times 80 = 12480$, which is incorrect. Therefore, the correct option is (C).

Question 23

How many triangles are there in the following figure?

Accepted Answer

Correct Option: 24. The figure is an equilateral triangle divided into smaller equilateral triangles by horizontal lines and lines originating from the apex. This is a standard type of problem in logical reasoning. The figure has 4 horizontal rows of small triangles. Let $n$ be the number of unit triangles along one side of the largest triangle. In this case, $n=4$. According to the standard formula for counting all triangles in such a figure: If $n$ is even, the total number of triangles is $N = frac{n(n+2)(2n+1)}{8}$. For $n=4$ (which is even): $N = frac{4(4+2)(2 times 4+1)}{8} = frac{4 times 6 times 9}{8} = frac{216}{8} = 27$. However, $27$ is not among the given options (15, 18, 21, 24). This suggests that the question might be looking for a specific subset of triangles or uses a non-standard counting method to arrive at one of the options. Let's try to find a combination that yields 24. One possible interpretation to arrive at 24 is to count specific types of upward-pointing triangles: 1. Smallest (1-unit) upward-pointing triangles: - Row 1 (top): 1 triangle - Row 2: 3 triangles - Row 3: 5 triangles - Row 4 (base): 7 triangles - Total 1-unit upward triangles = $1 + 3 + 5 + 7 = 16$. 2. Medium (2x2-unit) upward-pointing triangles: These are triangles composed of 4 small triangles. - There are 6 such triangles (e.g., one with its apex at the top of the second row, two in the third row, and three in the fourth row). - Total 2x2-unit upward triangles = 6. 3. Larger (3x3-unit) upward-pointing triangles: These are triangles composed of 9 small triangles. - There are 2 such triangles (one with its apex at the top of the first row, and one with its apex at the top of the second row). - Total 3x3-unit upward triangles = 2. If we sum these specific counts: $16 + 6 + 2 = 24$. This method excludes the largest (4x4-unit) upward-pointing triangle (1 triangle) and all downward-pointing triangles (which would be 7 in total: 6 of 1-unit size and 1 of 2x2-unit size). While this i

Question 24

If 100 cats catch 100 mice in 100 minutes, then how long will it take for 7 cats to catch 7 mice?

Accepted Answer

Correct Option: 100 minutes. This is a classic problem involving work and time, often solved using the concept of 'Man-Days' or 'Work-Rate'. The fundamental principle is that the rate of work per unit (e.g., per cat) is constant. Let's denote: $M1$ = Number of cats in the first scenario = 100 $T1$ = Time taken in the first scenario = 100 minutes $W1$ = Work done in the first scenario (mice caught) = 100 mice $M2$ = Number of cats in the second scenario = 7 $T2$ = Time taken in the second scenario = ? $W2$ = Work done in the second scenario (mice caught) = 7 mice The formula relating these quantities is: $frac{M1 times T1}{W1} = frac{M2 times T2}{W2}$ This formula states that the amount of work done per worker per unit of time is constant. Substitute the given values into the formula: $frac{100 times 100}{100} = frac{7 times T2}{7}$ Simplify both sides of the equation: $100 = T2$ So, it will take 100 minutes for 7 cats to catch 7 mice. Alternatively, consider the rate of one cat. If 100 cats catch 100 mice in 100 minutes, this implies that, on average, one cat catches one mouse in 100 minutes. If we have 7 cats, each cat still takes 100 minutes to catch one mouse. If each of the 7 cats needs to catch one mouse (total 7 mice), and each cat takes 100 minutes for its task, then simultaneously, all 7 cats will complete their individual tasks of catching one mouse each in 100 minutes. Let's analyze the options: Option (A) $frac{100}{7}$ minutes: This would be the answer if 1 cat caught 7 mice, or 7 cats caught 100 mice, which is incorrect. Option (B) $100$ minutes: This matches our calculated time. This is correct. Option (C) $frac{49}{100}$ minutes: This is incorrect. This value is too small and doesn't logically follow from the problem. Option (D) $7$ minutes: This would imply a much faster rate, or a different relationship, which is incorrect. Therefore, the correct option is (B).

Question 25

What is the maximum number of whole laddoos having diameter of 6 cm that can be packed in a box, whose inner dimensions are $24 text{ cm} times 18 text{ cm} times 17 text{ cm}$?

Accepted Answer

Correct Option: 24. To find the maximum number of whole laddoos that can be packed, we need to consider how many laddoos fit along each dimension of the box. Since laddoos are spherical, when packed, each laddoo effectively occupies a cube with side length equal to its diameter. Given: Diameter of each laddoo = $6 text{ cm}$ Box dimensions: Length ($L$) = $24 text{ cm}$, Width ($W$) = $18 text{ cm}$, Height ($H$) = $17 text{ cm}$ Calculate the number of laddoos that can fit along each dimension: 1. Along the Length ($L$): Number of laddoos ($NL$) = $lfloor frac{text{Box Length}}{text{Laddoo Diameter}} rfloor = lfloor frac{24 text{ cm}}{6 text{ cm}} rfloor = lfloor 4 rfloor = 4$ laddoos. 2. Along the Width ($W$): Number of laddoos ($NW$) = $lfloor frac{text{Box Width}}{text{Laddoo Diameter}} rfloor = lfloor frac{18 text{ cm}}{6 text{ cm}} rfloor = lfloor 3 rfloor = 3$ laddoos. 3. Along the Height ($H$): Number of laddoos ($NH$) = $lfloor frac{text{Box Height}}{text{Laddoo Diameter}} rfloor = lfloor frac{17 text{ cm}}{6 text{ cm}} rfloor = lfloor 2.833... rfloor = 2$ laddoos. (We take the floor value because only whole laddoos can be packed). To find the total maximum number of whole laddoos, multiply the number of laddoos along each dimension: Total Laddoos = $NL times NW times NH = 4 times 3 times 2 = 24$ laddoos. Let's analyze the options: Option (A) $24$: This matches our calculated maximum number of whole laddoos. This is correct. Option (B) $30$: This would require fitting more laddoos along one or more dimensions than possible (e.g., $5 times 3 times 2 = 30$, which implies fitting 5 along length, but only 4 fit). This is incorrect. Option (C) $33$: This is incorrect. It's not achievable with the given dimensions. Option (D) $36$: This would imply fitting $4 times 3 times 3 = 36$ laddoos, which means 3 laddoos along the height, but only 2 fit ($17 text{ cm} / 6 text{ cm} = 2.833...$). This is incorrect. Therefore, the correct option is (A).

Question 26

Two words separated by a : and bearing a certain relationship with each other have been given on one side of ::. From among the options, select the one that bears a similar relationship with the words given on the other side of ::. Settlement: injury:: pension: ?

Accepted Answer

Correct Option: retirement. This is an analogy question where we need to identify the relationship between the first pair of words and apply the same relationship to the second pair. First pair: Settlement : injury Relationship: A 'settlement' is a payment or compensation received as a result of an 'injury'. So, the relationship is 'payment received : reason for receiving payment'. Second pair: Pension : ? Applying the same relationship, 'pension' is a payment or regular income received. We need to find the 'reason for receiving pension'. Let's evaluate the options: Option (A) pensioner: A pensioner is a person who receives a pension, not the reason for receiving it. So, this is incorrect. Option (B) maturity: Maturity refers to a state of being fully developed or the end of a financial instrument's term. While related to age, it's not the direct reason for receiving a pension. So, this is incorrect. Option (C) retirement: Retirement is the act of leaving one's job or ceasing to work, typically due to age or service. A pension is commonly received after retirement. This fits the 'payment received : reason for receiving payment' relationship. So, this is correct. Option (D) age: While age is often a factor for retirement and thus for receiving a pension, 'retirement' is the more direct and encompassing reason for the payment of a pension, similar to how 'injury' is the direct reason for a settlement. So, this is less precise than 'retirement'. Therefore, the correct option is (C).

Question 27

Which letter/number is exactly in the middle between the $9^{text{th}}$ letter/number from the right end and the $17^{text{th}}$ letter/number from the left end of the sequence given below? Sequence: RE5DAP3TIQ79B2KU1MW

Accepted Answer

Correct Option: 2. First, let's write down the sequence and determine the total number of elements. Sequence: R E 5 D A P 3 T I Q 7 9 B 2 K U 1 M W Total number of elements = 20. Next, let's find the position of the specified elements: 1. $9^{text{th}}$ letter/number from the right end: Counting from the right: W (1st), M (2nd), 1 (3rd), U (4th), K (5th), 2 (6th), B (7th), 9 (8th), 7 (9th). So, the $9^{text{th}}$ element from the right is 7. To find its position from the left: Total elements - (Position from right) + 1 = $20 - 9 + 1 = 12$. So, 7 is the $12^{text{th}}$ element from the left. 2. $17^{text{th}}$ letter/number from the left end: Counting from the left: R (1st), E (2nd), 5 (3rd), D (4th), A (5th), P (6th), 3 (7th), T (8th), I (9th), Q (10th), 7 (11th), 9 (12th), B (13th), 2 (14th), K (15th), U (16th), 1 (17th). So, the $17^{text{th}}$ element from the left is 1. Now we need to find the element exactly in the middle between the $12^{text{th}}$ element (7) and the $17^{text{th}}$ element (1) from the left. The elements from the $12^{text{th}}$ to the $17^{text{th}}$ position are: $E{12}$ (7), $E{13}$ (9), $E{14}$ (B), $E{15}$ (2), $E{16}$ (K), $E{17}$ (1). There are 6 elements in this range. When there's an even number of elements, there isn't a single 'exact' middle element; there are two middle elements. In this case, the middle elements are $E{14}$ (B) and $E{15}$ (2). However, if the question implies a single middle element, it often refers to the element at the average of the indices, possibly rounded up or down. The average index is $frac{12 + 17}{2} = frac{29}{2} = 14.5$. If we round up to $15$, the $15^{text{th}}$ element from the left is 2. Let's check the options: Option (A) $2$: This is the $15^{text{th}}$ element from the left. This is a plausible interpretation for 'exactly in the middle' when the average index is 14.5. Option (B) $P$: This is the $6^{text{th}}$ element from the left, which is incorrect. Option (C) $3$: This is the $7^{text{th

Question 28

A computer virus is a/an , which replicates by inserting copies of itself.

Accepted Answer

Correct Option: Malware. Let's analyze the definition of a computer virus and the given options: Computer Virus Definition: A computer virus is a type of malicious software program ('malware') that, when executed, replicates by inserting copies of itself into other computer programs, data files, or the boot sector of a hard drive. It typically requires a host program to spread. Let's evaluate the options: Option (A) Software: While a virus is indeed a type of software (it's a program), 'software' is a very broad term. It doesn't specifically capture the malicious and self-replicating nature of a virus. All applications and system files are also software. Option (B) Malware: This term is a portmanteau for 'malicious software'. It specifically refers to software designed to disrupt, damage, or gain unauthorized access to a computer system. A computer virus perfectly fits this definition, as its primary characteristic is malicious intent and self-replication. This is the most accurate classification. Option (C) Application: An application (or app) is a type of software designed to perform a specific function directly for the user or, in some cases, for another application. While a virus might be embedded within an application, the virus itself is not typically an application in the conventional sense; it's a malicious component. So, this is incorrect. Option (D) System file: A system file is a critical file that is part of an operating system or a core program. While a virus can infect or disguise itself as a system file to evade detection, a virus is not inherently a system file. Its definition is based on its behavior (replication, malicious intent), not its file type or location. So, this is incorrect. Therefore, the most precise and accurate term to describe a computer virus among the given options is 'Malware'. Therefore, the correct option is (B).

Question 29

Which is the world's most powerful Super Computer?

Accepted Answer

Correct Option: Fugaku. This question asks for the world's most powerful supercomputer, which is a factual question whose answer can change over time as new supercomputers are developed. However, among the given options, we need to identify the one that has held or currently holds a top position. Let's analyze the options: Option (A) Tianhe-2 (MilkyWay-2): This supercomputer, located in China, was the world's fastest from 2013 to 2016. While historically significant, it is no longer the most powerful. Option (B) Fugaku: This supercomputer, located at the RIKEN Center for Computational Science in Japan, was ranked as the world's most powerful supercomputer from June 2020 to June 2022. It was then surpassed by Frontier. However, among the given options, Fugaku is the most powerful and recent top-ranked system. Option (C) Titan: This supercomputer, located at Oak Ridge National Laboratory in the USA, was the world's fastest from November 2012 to June 2013. It is also historically significant but no longer the most powerful. Option (D) Vulcan: This supercomputer was part of the IBM Blue Gene/Q family and was a significant system, but never held the top spot globally. It was ranked in the top 10 for a period but is not in the same league as the others in terms of peak performance. As of recent rankings (e.g., TOP500 list), the Frontier supercomputer (USA) is currently the most powerful. However, since Frontier is not an option, and Fugaku has been a very recent and significant holder of the top position, it is the correct answer among the choices provided. Therefore, the correct option is (B).

Question 30

Which of the following is not a processor manufacturer?

Accepted Answer

Correct Option: Apple. This question requires understanding what constitutes a 'processor manufacturer' in the context of the technology industry. Let's analyze each option: Option (A) Nvidia: Nvidia is primarily known for designing and selling Graphics Processing Units (GPUs), which are a type of processor. They also produce System-on-Chips (SoCs) like the Tegra series, which integrate CPUs and GPUs. Therefore, Nvidia is a processor manufacturer. Option (B) AMD (Advanced Micro Devices): AMD is a major designer and vendor of both Central Processing Units (CPUs) and Graphics Processing Units (GPUs). They are a direct competitor to Intel in CPUs and Nvidia in GPUs. Therefore, AMD is a processor manufacturer. Option (C) Qualcomm: Qualcomm is a leading global designer and manufacturer of chipsets for mobile devices, including their Snapdragon series of System-on-Chips (SoCs), which integrate CPUs, GPUs, modems, and other components. Therefore, Qualcomm is a processor manufacturer. Option (D) Apple: Apple designs its own custom processors (e.g., A-series for iPhones/iPads, M-series for Macs) which are based on the ARM architecture. However, Apple does not fabricate these chips in its own foundries. Instead, it outsources the actual manufacturing (fabrication) to companies like TSMC. While Apple designs processors, its primary business is consumer electronics, and it relies on third-party foundries for the physical production. In the context of companies whose primary business is the manufacturing and sale of processors as a core product line to a broad market, Apple is typically not categorized in the same way as Intel, AMD, Nvidia, or Qualcomm. Therefore, Apple is generally considered a designer of processors, but not a manufacturer in the sense of owning fabrication plants or selling processors as a standalone product to other companies. Therefore, the correct option is (D).

Question 31

What is the effect of Ctrl+= Key?

Accepted Answer

Correct Option: Subscript. The Ctrl+= key combination is a common keyboard shortcut in many word processing and text editing applications, such as Microsoft Word, Google Docs, and others. Let's analyze the effect of this shortcut: Subscript: Subscript text appears slightly below the normal line of text and is typically smaller. It is commonly used in chemical formulas (e.g., $text{H}2text{O}$) or mathematical expressions. The Ctrl+= shortcut is universally recognized for applying or removing subscript formatting. Superscript: Superscript text appears slightly above the normal line of text and is typically smaller. It is used for exponents (e.g., $x^2$), footnotes, or ordinal indicators (e.g., $1^{text{st}}$). The common shortcut for superscript is Ctrl+Shift+= (or Ctrl++ on some keyboards). All Caps: This formatting changes all selected text to uppercase letters. The shortcut for this is typically Shift+F3 (to cycle through sentence case, lowercase, uppercase) or a specific menu option. Shadow: This is a text effect that adds a shadow behind the text. It is usually applied through text effects or formatting options in the ribbon/menu, not a simple keyboard shortcut like Ctrl+=. Therefore, the Ctrl+= key combination is used to apply or remove subscript formatting. Therefore, the correct option is (B).

Question 32

is a small picture on screen that depicts program, file or folder.

Accepted Answer

Correct Option: Icon. Let's define each term to identify the correct answer: Option (A) Task Bar: The taskbar is a graphical user interface element that typically runs along one edge of the screen (usually the bottom) and is used to launch and switch between running applications. It displays small representations of open programs, but it is a bar, not a small picture that depicts a program, file, or folder in isolation. So, this is incorrect. Option (B) Icon: An icon is a pictogram or ideogram displayed on a computer screen in order to help the user navigate a computer system or mobile device. It is a small graphical representation of a program, file, folder, or function. This perfectly matches the description in the question. So, this is correct. Option (C) Pixel: A pixel (short for 'picture element') is the smallest physical point in a raster image or the smallest controllable element of a picture represented on the screen. It is a single dot of color, not a depiction of a program, file, or folder. So, this is incorrect. Option (D) Cursor: A cursor is a visual indicator on a computer display that shows the current position for user interaction, such as where text will be inserted or where a mouse click will register. It is a pointer, not a depiction of a program, file, or folder. So, this is incorrect. Therefore, the correct option is (B).

Question 33

Google Search allows you to search by :

Accepted Answer

Correct Option: All (a), (b) and (c) are true. Google Search is a highly versatile search engine that allows users to search by multiple methods. Users can search by (a) Text (typing keywords), (b) Voice (speaking queries), and (c) Image (using Google Images or Google Lens to search with an image). Therefore, all three options (a), (b), and (c) are true, making option (4) the correct choice. Options (1), (2), and (3) are incorrect because they exclude valid search methods.

Question 34

URL stands for:

Accepted Answer

Correct Option: Uniform Resource Locator. URL stands for Uniform Resource Locator. It is a reference (an address) to a web resource that specifies its location on a computer network and a mechanism for retrieving it. URLs are fundamental for navigating the internet. Option (1) and (4) are incorrect as 'Research' or 'University' are not part of the standard acronym. Option (3) 'Universal Resource Locator' is a common misconception; while widely used, 'Uniform' is the technically correct and standardized term, emphasizing the consistent format.

Question 35

Fill in the blank using an appropriate option : After it rained the improved.

Accepted Answer

Correct Option: weather. The correct word to fill the blank is 'weather'. 'Weather' refers to the state of the atmosphere at a particular place and time, regarding heat, dryness, sunshine, wind, rain, etc. After rain, the immediate atmospheric conditions often improve. Option (1) 'season' refers to a long period of the year, not changed by a single rain. Option (2) 'climate' is long-term average weather, not affected by one event. Option (3) 'whether' is a conjunction, grammatically incorrect here.

Question 36

Choose the correct synonym for the following: "Bashful".

Accepted Answer

Correct Option: Shy. The word 'bashful' means reluctant to draw attention to oneself; shy. Therefore, 'Shy' is a direct and accurate synonym. Option (1) 'Aggressive' means confrontational, which is the opposite. Option (2) 'Gregarious' means sociable, also the opposite. Option (3) 'Dashing' means stylish and confident, which does not align with the meaning of bashful.

Question 37

Which of these keys will end the slide show ?

Accepted Answer

Correct Option: ESC. The $text{Esc}$ (Escape) key is universally used in presentation software (like PowerPoint) to end a slide show and return to the editing view. Option (1) $text{F5}$ is typically used to start a slide show from the beginning. Option (2) $text{F10}$ activates the menu bar. Option (4) $text{Space bar}$ is used to advance to the next slide, not to end the show.

Question 38

HTML is a language.

Accepted Answer

Correct Option: Mark up. HTML stands for Hypertext Markup Language. It is the standard markup language for documents designed to be displayed in a web browser, using tags to define elements within a document. Option (1) 'Applet' is a small application. Option (2) 'Scripting' refers to languages like JavaScript for dynamic behavior. Option (3) 'Coding' is a general term; 'Markup' is the specific classification for HTML, defining its structural purpose.

Question 39

In MICR, what does C stand for?

Accepted Answer

Correct Option: Character. MICR stands for Magnetic Ink Character Recognition. It is a technology used primarily in banking to verify the legitimacy of paper documents, especially checks, by recognizing characters printed with magnetic ink. The 'C' in MICR specifically refers to 'Character'. Options (1) 'Code', (3) 'Colour', and (4) 'Computer' are incorrect; while related to the process, they are not what the 'C' in the acronym represents.

Question 40

To use 'find' and 'replace' which key combination is used in MS-Word ?

Accepted Answer

Correct Option: Ctrl+H. In Microsoft Word, the keyboard shortcut $text{Ctrl} + text{H}$ opens the 'Find and Replace' dialog box with the 'Replace' tab active, allowing users to find specific text and replace it. Option (1) $text{Ctrl} + text{R}$ is for right-aligning text. Option (2) $text{Ctrl} + text{N}$ is for creating a new document. Option (4) $text{Ctrl} + text{F}$ opens the 'Find' dialog or navigation pane, but not directly the 'Replace' function as requested.

Question 41

What does BCC stand for ?

Accepted Answer

Correct Option: Blind Carbon Copy. In email, BCC stands for Blind Carbon Copy. When an email is sent using BCC, the recipients in the BCC field are invisible to all other recipients of the email (including those in the To and CC fields). This is used for privacy or when sending to a large group without revealing everyone's email address. Options (1), (2), and (3) are incorrect as 'Blue', 'Black', or 'Blank' are not part of the standard acronym for this email function.

Question 42

What is the full form of HTTP ?

Accepted Answer

Correct Option: Hyper Text Transfer Protocol. HTTP stands for Hypertext Transfer Protocol. It is an application layer protocol for distributed, collaborative, hypermedia information systems, forming the foundation of data communication for the World Wide Web. Options (1) and (4) are incorrect because the 'P' stands for 'Protocol', not 'Program'. Options (3) and (4) are incorrect because the 'T' stands for 'Text', not 'Trans'. The correct and standard acronym is 'Hypertext Transfer Protocol'.

Question 43

Which of the following is not an example of an operating system ?

Accepted Answer

Correct Option: GML. GML stands for 'Generalized Markup Language' or 'GameMaker Language', neither of which is an operating system. GML (Generalized Markup Language) is a precursor to SGML and XML, used for document formatting. Options (1) 'UNIX', (2) 'MS-DOS', and (3) 'LINUX' are all well-known examples of operating systems. UNIX is a family of multitasking OS, MS-DOS is a command-line OS, and LINUX is an open-source Unix-like OS.

Question 44

The ability to easily add additional users means that a network is :

Accepted Answer

Correct Option: scalable. Scalability refers to a system's ability to handle a growing amount of work or to be easily enlarged to accommodate that growth. If a network can easily add additional users, it means it is scalable, as it can expand its capacity to serve more participants without significant redesign or performance degradation. Option (1) 'secure' relates to protection, not expansion. Option (2) 'dedicated' implies exclusive allocation, not ease of adding users. Option (3) 'decentralized' refers to distributed control, not directly to user expansion capability.

Question 45

In which view are Headers and Footers visible ?

Accepted Answer

Correct Option: Print Layout View. In Microsoft Word, the Print Layout View displays the document as it will appear when printed, including headers, footers, margins, and page breaks. This view is essential for seeing the final layout. Option (1) 'Normal View' and Option (4) 'Draft View' focus on content, hiding layout elements. Option (2) 'Page Layout View' is often synonymous with Print Layout View, but 'Print Layout View' is the most precise term for seeing print-ready elements like headers and footers.

Question 46

A dedicated website for providing specialized information in a particular field :

Accepted Answer

Correct Option: Blog. A blog (short for 'weblog') is a discussion or informational website published on the World Wide Web, consisting of discrete, often informal diary-style text entries. Blogs are frequently used to provide specialized information, opinions, or news in a particular field or niche, often updated regularly. Option (1) 'Website' is too general. Option (3) 'Web directory' lists websites but doesn't provide information itself. Option (4) 'Corporate Website' focuses on a company's information, not a general field.

Question 47

What is a firewall in Computer Network?

Accepted Answer

Correct Option: A system designed to prevent unauthorized access. A firewall is a network security system that monitors and controls incoming and outgoing network traffic based on predetermined security rules. Its primary purpose is to establish a barrier between a trusted internal network and untrusted external networks, such as the internet, to prevent unauthorized access and protect against various cyber threats. Option (1) is incorrect; the physical boundary refers to hardware. Option (2) is incorrect; an operating system manages computer resources. Option (4) is incorrect; web browsing software accesses websites. Thus, only option (3) accurately defines a firewall's core function.

Question 48

A colour underline, indicates grammar errors in Microsoft Word document.

Accepted Answer

Correct Option: Blue. In modern versions of Microsoft Word, a blue wavy underline typically indicates a grammatical error, helping users identify and correct issues related to sentence structure, punctuation, and other grammar rules. Option (1) 'Red' wavy underline indicates spelling errors. Option (2) 'Green' wavy underline was used for grammar in older Word versions, but now often signifies contextual spelling or style suggestions. Option (4) 'Yellow' is not used for standard grammar error indication.

Question 49

Which of the following is not a type of Computer virus ?

Accepted Answer

Correct Option: Coffee cup. A 'Coffee cup' is a common household item and has no relation to computer malware or viruses. Options (1) 'Worm', (3) 'Macro virus', and (4) 'Bootsector virus' are all recognized types of computer viruses. A Worm replicates itself across networks, a Macro virus infects documents using application-specific languages, and a Bootsector virus infects the boot sector of storage devices.

Question 50

What is the synonym of the following word? "Harbinger"

Accepted Answer

Correct Option: forerunner. A 'harbinger' is a person or thing that announces or signals the approach of another; a forerunner. Option (2) 'forerunner' is a direct synonym, meaning a person or thing that precedes the coming or development of someone or something else. Option (1) 'atrocious' means horrifyingly wicked or of very poor quality. Option (3) 'free' means not under the control of another. Option (4) 'understand' means to perceive the meaning of. These options are semantically unrelated to 'harbinger'.

Question 51

Choose the appropriate active/passive form of the sentence given below: 'We had to stop all other work to complete our assignment.'

Accepted Answer

Correct Option: All other work had to be stopped by us to complete our assignment. The original sentence is in the active voice, using the modal auxiliary 'had to'. When converting an active sentence with 'had to' to passive voice, the structure becomes 'had to be + past participle'. The object of the active sentence ('all other work') becomes the subject of the passive sentence. Thus, "All other work had to be stopped by us to complete our assignment" is the correct passive form. Option (1) changes the tense and voice incorrectly. Option (2) uses 'had stopped', which is past perfect, not the correct passive structure for 'had to'. Option (4) uses 'was stopped', which is simple past passive, also incorrect for 'had to'.

Question 52

Choose the correct antonym for the following word: 'enervate'

Accepted Answer

Correct Option: charge. To 'enervate' means to cause someone to feel drained of energy or vitality; to weaken or debilitate. The antonym, therefore, would be a word that means to energize, invigorate, or strengthen. Option (1) 'charge' means to fill with energy or to invigorate, making it the correct antonym. Options (2) 'dampen', (3) 'wear out', and (4) 'discourage' are all synonyms or closely related in meaning to 'enervate', as they imply reducing energy, enthusiasm, or strength.

Question 53

Choose the correct meaning of the given proverb/idiom. "An elephant in the room"

Accepted Answer

Correct Option: Do not want to talk about an obvious problem. The idiom "an elephant in the room" refers to an obvious, significant problem or difficult subject that everyone present is aware of but deliberately avoids discussing due to discomfort or embarrassment. Option (1) accurately captures this meaning. Option (2) is incorrect as the idiom is not about physical accommodation. Option (3) is partially correct in that it's a big issue, but it misses the crucial aspect of deliberate avoidance. Option (4) is incorrect; the issue is indeed avoided by not talking about it, which is the core of the idiom.

Question 54

'Bihu' folk dance is associated with which of the following States?

Accepted Answer

Correct Option: Assam. Bihu is a set of three important Assamese festivals—Rongali or Bohag Bihu, Kongali or Kati Bihu, and Bhogali or Magh Bihu. These festivals are celebrated with great enthusiasm and are characterized by the Bihu dance, a vibrant folk dance native to the state of Assam, India. Options (2) Odisha, (3) West Bengal, and (4) Tripura are incorrect as Bihu is not their primary folk dance.

Question 55

What is the correct form of the sentence 'आपके साथ उचित न्याय होगा।' (Aapke saath uchit nyay hoga.)?

Accepted Answer

Correct Option: आपके साथ न्याय किया जाएगा। (Aapke saath nyay kiya jaayega.). The original sentence 'आपके साथ उचित न्याय होगा' is grammatically awkward. In Hindi, when expressing that justice will be done to someone, the phrase 'न्याय किया जाएगा' (justice will be done) is the correct and idiomatic construction, often used with 'के साथ' (with/to). Option (1) 'आपके साथ न्याय किया जाएगा' (Aapke saath nyay kiya jaayega) correctly uses this construction and maintains politeness ('आपके'). Option (2) uses 'तुम्हारे' (informal 'your') and 'समुचित न्याय होगा' which is less idiomatic. Option (3) uses 'तुम्हारे लिए' (for you) which changes the nuance, and 'पूरा न्याय' (complete justice). Option (4) 'सुन्याय' is not a standard word for 'proper justice'.

Question 56

Which Alankar (figure of speech) is in the line 'बीती विभावरी जाग री' (Beeti Vibhavari Jaag Ri)?

Accepted Answer

Correct Option: मानवीकरण (Manveekaran). The line 'बीती विभावरी जाग री' translates to 'The night has passed, wake up'. Here, 'विभावरी' (night), an inanimate entity, is being addressed and commanded to 'wake up', which is a human action. This attribution of human qualities, emotions, or actions to inanimate objects or abstract ideas is known as 'मानवीकरण अलंकार' (Manveekaran Alankar) or Personification. Option (1) 'उत्प्रेक्षा' (Utpreksha) involves imagining one thing as another. Option (2) 'उपमा' (Upma) involves direct comparison. Option (3) 'अनुप्रास' (Anupras) is alliteration, repetition of consonant sounds. None of these fit the given line.

Question 57

Choose the Tatsam word from the given options.

Accepted Answer

Correct Option: क्षीर (Ksheer). Tatsam words are words in Hindi that are directly borrowed from Sanskrit without any change. Option (4) 'क्षीर' (Ksheer) is a Tatsam word, meaning 'milk'. Its corresponding Tadbhav (derived) word in Hindi is 'खीर' (Kheer) or 'दूध' (Doodh). Option (1) 'साँवला' (Sanwala) is a Tadbhav word (from 'श्यामल'). Option (2) 'भँवरा' (Bhanwara) is a Tadbhav word (from 'भ्रमर'). Option (3) 'रेलगाड़ी' (Railgadi) is a hybrid word, combining English 'rail' and Hindi 'गाड़ी', thus not a Tatsam word.

Question 58

What is the feminine form of 'रचयिता' (Rachayita)?

Accepted Answer

Correct Option: रचयित्री (Rachayitri). The word 'रचयिता' (Rachayita) is a masculine noun meaning 'creator' or 'author'. Its correct feminine form is 'रचयित्री' (Rachayitri). This transformation is a common pattern for certain agent nouns in Hindi. Options (1) 'रचिता', (2) 'रचईता', and (3) 'रचयती' are incorrect grammatical forms for the feminine gender of 'रचयिता'.

Question 59

What is the Sandhi form of 'स्व+इच्छा' (Swa+Ichha)?

Accepted Answer

Correct Option: स्वेच्छा (Swechha). This is an example of 'गुण संधि' (Guna Sandhi) in Hindi grammar. According to the rules of Guna Sandhi, when the vowel 'अ' (a) or 'आ' (aa) is followed by 'इ' (i) or 'ई' (ee), they combine to form 'ए' (e). In 'स्व+इच्छा', 'स्व' (Swa) ends with 'अ' (a) and 'इच्छा' (Ichha) begins with 'इ' (i). Therefore, 'अ' + 'इ' = 'ए', resulting in 'स्वेच्छा' (Swechha). Option (1) 'स्विच्छा' incorrectly retains 'इ'. Option (3) 'स्वेक्षा' has incorrect spelling. Option (4) 'स्वैच्छा' would be formed by 'वृद्धि संधि' (Vriddhi Sandhi) where 'अ' + 'ए' = 'ऐ', which is not applicable here.

Question 60

Complete the proverb using the correct word pair: ' पकवान' ( Pakwaan).

Accepted Answer

Correct Option: ऊंची, फीका (Oonchi, Feeka - High, Bland). The complete Hindi proverb is 'ऊंची दुकान, फीका पकवान' (Oonchi dukaan, feeka pakwaan), which literally translates to 'tall shop, bland food'. It metaphorically means 'great boast, small roast' or 'all show and no substance', implying that something with a grand appearance often lacks quality. Option (3) 'ऊंची, फीका' (Oonchi, Feeka) correctly completes this well-known proverb. The other options do not form a recognized or meaningful proverb.

Question 61

The guru gives knowledge to the disciple. Which case (Karak) is used in the underlined word 'शिष्य को' (Shishya ko)?

Accepted Answer

Correct Option: संप्रदान कारक (Sampradan Karak - Dative case). In the sentence 'गुरु ही शिष्य को ज्ञान देता है' (The guru gives knowledge to the disciple), the phrase 'शिष्य को' (Shishya ko) indicates the recipient of the action of giving. When 'को' (ko) is used to denote the receiver to whom something is given or for whom something is done, it signifies the 'संप्रदान कारक' (Sampradan Karak), which is equivalent to the Dative case. Option (1) 'कर्म कारक' (Karma Karak) uses 'को' for the direct object, but here 'ज्ञान' (knowledge) is the direct object. Option (3) 'करण कारक' (Karan Karak) indicates the instrument or means, and (4) 'संबंध कारक' (Sambandh Karak) shows possession or relationship, neither of which applies here.

Question 62

The organizer of the program organized it with full dedication. Change the gender of the underlined word 'संयोजक' (Sanyojak).

Accepted Answer

Correct Option: संयोजिका (Sanyojika). The word 'संयोजक' (Sanyojak) is a masculine noun meaning 'organizer'. To change it to its feminine form, the suffix '-क' (-ka) is typically replaced with '-िका' (-ika). Therefore, the feminine form of 'संयोजक' is 'संयोजिका' (Sanyojika). Option (1) 'संयोजिकी' is grammatically incorrect. Options (3) 'परिचारिका' (Paricharika) means 'attendant' or 'nurse', and (4) 'निवेदिका' (Nivedika) means 'announcer' or 'presenter', which are different professions and not the feminine form of 'संयोजक'.

Question 63

Which compound (Samas) is used in 'राखर्च' (Rakharch)?

Accepted Answer

Correct Option: तत्पुरुष (Tatpurush). The word 'राखर्च' (Rakharch) means 'खर्च राह के लिए' (kharch rah ke liye), which translates to 'expenditure for the road' or 'travel expenses'. In this compound, the second word ('खर्च' - expenditure) is dominant, and there is a hidden postposition ('के लिए' - for) between the two words. This structure is characteristic of 'तत्पुरुष समास' (Tatpurush Samas), specifically 'संप्रदान तत्पुरुष' (Sampradan Tatpurush), where the compound denotes the purpose for which something is done. Options (1) 'कर्मधारय' (Karmadharaya) involves a descriptive relationship, (3) 'बहुब्रीहि' (Bahuvrihi) refers to a third meaning, and (4) 'अव्ययीभाव' (Avyayibhav) has the first part as an indeclinable adverb, none of which apply here.

Question 64

What suffix is in the word 'लुटिया' (Lutiya)?

Accepted Answer

Correct Option: टिया (Tiya). The word 'लुटिया' (Lutiya) is a diminutive form, typically derived from 'लोटा' (Lota, a small metal pot). In standard Hindi morphology, the diminutive suffix used here is 'इया' (iya), which, when added to a base like 'लोट' (lot), forms 'लुटिया' (lutiya) with a vowel change. However, if option (1) 'टिया' (Tiya) is considered the correct suffix, it implies that the base word is 'लु' (lu) and 'टिया' is appended as a single unit to form the diminutive. This is a less common morphological analysis compared to 'इया' but might be considered in specific contexts or as a phonetic grouping. Options (2) 'इया', (3) 'या', and (4) 'आ' are incorrect based on the provided correct option, as 'टिया' is the complete ending identified.

UP High Court RO / ARO 06 Jan 2022 Shift 1

200 Questions Available

UP High Court RO / ARO 06 Jan 2022 Shift 1

200 Questions Available

Question 1: If Q=10 and CLAP=76 then find the value of TIGER. यदि Q=10 तथा CLAP=76 हैं तब TIGER का मान है :

Question 2: Which is largest amongst $5/8, 2/3, 7/9, 3/5$? $5/8, 2/3, 7/9, 3/5$ में सबसे बड़ी संख्या कौन सी है?

Question 3: A chemical solution contains 30% water and 70% alkali. What quantity of water should be added to 6 litres of solution so that the water content become

Question 4: In a class of 50 students, Mithilesh is eighth from the top. Himadri is 20th from the bottom. How many students are there between Mithilesh and Himadr

Question 5: A cucumber contains 99% water. Ramesh buys 100 kg of cucumbers. After 30 days of storing, the cucumbers lose some water. These now contain 98% water.

Question 6: Amoebae are known to double in number every 3 minutes. Two identical vessels A and B, respectively contain one and two amoebae to start with. The vess

Question 7: What is the next term in the following sequence ? $7, 11, 13, 17, 19, 23, 25, 29, ?$ निम्नलिखित अनुक्रम मे अगली संख्या क्या है?

Question 8: If a+b+c+d+e=10 (all natural numbers), then what is the maximum value of atimes btimes ctimes dtimes e? यदि $a+b+c+d+e=10$ (सभी धनात्मक संख्यायें हैं)

Question 9: In an examiniation, 65% of the total examinees passsed. If the number of failures is 420, then what is the total number of examinees? एक परीक्षा में क

Question 10: A certain sum of money at Simple Interest amounts to ₹704 in 2 years and ₹800 in 5 years. Find the principal. साधारण ब्याज पर एक धनराशि 2 वर्ष में ₹70

Question 11: A sum of ₹12,500 amounts to ₹15,500 in 4 years at simple interest. What is the rate of interest ? ₹ 12,500 साधारण ब्याज से 4 वर्ष में ₹ 15,500 हो जाते

Question 12: How many multiples of 3 are there between the integers 18 and 108, both inclusive ? पूर्णांकों 18 और 108 के बीच, इन दोनों को शामिल करते हुए, 3 के कितन

Question 13: What will come in place of the question mark (?) in the following number series ? $121, 164, 250, 379, 551, ?$ निम्नलिखित श्रृंखला में प्रश्नसूचक (?)

Question 14: How many sets of two letters in the word GENERAL have as many letters between them as they have in the English alphabet ? GENERAL शब्द में दो अक्षरों

Question 15: If 2, 4 and 6 are mapped to 10, 26, and 50 respectively, then what number is 16 mapped to ? $2=10, 4=26, 6=50, 16=?$ यदि 2, 4 और 6 संख्याएँ क्रमशः 10,

Question 16: Two words separated by : and bearing a certain relationship with each other have been given on one side of :: From among the options, select the one t

Question 18: The total number of students in a school is 4800, out of which 60% are girls. What is the total number of boys in this school? एक विद्यालय में विद्यार

Question 19: Choose the largest number : (1) $2^{500}$ (2) $3^{400}$ (3) $4^{300}$ (4) $5^{200}$ सबसे बड़ी संख्या चुनिए :

Question 20: A Cookie:

Question 21: Computer network is: (a) a collection of hardware components and computers (b) inter-connected by communication channels (c) used to share resources a

Question 22: Kabir paid 9,600 as interest on a loan he took for 5 years at 16% rate of simple interest. What was the amount of loan he took?

Question 23: How many triangles are there in the following figure?

Question 24: If 100 cats catch 100 mice in 100 minutes, then how long will it take for 7 cats to catch 7 mice?

Question 25: What is the maximum number of whole laddoos having diameter of 6 cm that can be packed in a box, whose inner dimensions are $24 text{ cm} times 18 tex

Question 26: Two words separated by a : and bearing a certain relationship with each other have been given on one side of ::. From among the options, select the on

Question 27: Which letter/number is exactly in the middle between the $9^{text{th}}$ letter/number from the right end and the $17^{text{th}}$ letter/number from th

Question 28: A computer virus is a/an , which replicates by inserting copies of itself.

Question 29: Which is the world's most powerful Super Computer?

Question 30: Which of the following is not a processor manufacturer?

Question 31: What is the effect of Ctrl+= Key?

Question 32: is a small picture on screen that depicts program, file or folder.

Question 33: Google Search allows you to search by :

Question 34: URL stands for:

Question 35: Fill in the blank using an appropriate option : After it rained the improved.

Question 36: Choose the correct synonym for the following: "Bashful".

Question 37: Which of these keys will end the slide show ?

Question 38: HTML is a language.

Question 39: In MICR, what does C stand for?

Question 40: To use 'find' and 'replace' which key combination is used in MS-Word ?

Question 41: What does BCC stand for ?

Question 42: What is the full form of HTTP ?

Question 43: Which of the following is not an example of an operating system ?

Question 44: The ability to easily add additional users means that a network is :

Question 45: In which view are Headers and Footers visible ?

Question 46: A dedicated website for providing specialized information in a particular field :

Question 47: What is a firewall in Computer Network?

Question 48: A colour underline, indicates grammar errors in Microsoft Word document.

Question 49: Which of the following is not a type of Computer virus ?

Question 50: What is the synonym of the following word? "Harbinger"