Elementary Arithmetic प्रारंभिक अंकगणित

Question 603 15 Oct 2022 · Shift 1 · Q31

Q603. (5.21 × 6.32) − 2.9272 = ?

प्रश्न 603. (5.21 × 6.32) − 2.9272 का मान क्या है?

(A) 3030 ✓ [Official Key]

(B) 2525

(C) 3232

(D) 2828

Correct Answer: Option (A) — 3030

Explanation:

5.21 × 6.32 = 32.9272. Subtracting 2.9272: 32.9272 − 2.9272 = 30.

5.21 × 6.32 = 32.9272. Subtracting 2.9272: 32.9272 − 2.9272 = 30.

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Question 604 15 Oct 2022 · Shift 2 · Q31

Q604. दिए गए भिन्नों 4/9, 5/7, 11/13, 13/17 में से सबसे बड़ा कौन-सा है?

प्रश्न 604. दिए गए भिन्नों 4/9, 5/7, 11/13, 13/17 में से सबसे बड़ा कौन-सा है?

(A) 5/75/7

(B) 11/1311/13 ✓ [Official Key]

(C) 13/1713/17

(D) 4/94/9

Correct Answer: Option (B) — 11/1311/13

Explanation:

Converting to decimals: 4/9 ≈ 0.444, 5/7 ≈ 0.714, 11/13 ≈ 0.846, 13/17 ≈ 0.765. The largest fraction is 11/13.

Converting to decimals: 4/9 ≈ 0.444, 5/7 ≈ 0.714, 11/13 ≈ 0.846, 13/17 ≈ 0.765. The largest fraction is 11/13.

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Question 605 16 Oct 2022 · Shift 1 · Q31

Q605. Which of the following fractions is the largest?

प्रश्न 605. निम्नलिखित भिन्नों में से कौन-सा सबसे बड़ा है?

(A) 5/65/6

(B) 3/43/4

(C) 2/32/3

(D) 7/87/8 ✓ [Official Key]

Correct Answer: Option (D) — 7/87/8

Explanation:

In each fraction, the difference between numerator and denominator is 1 (6−5=1, 4−3=1, 3−2=1, 8−7=1). For proper fractions with equal differences, the fraction with the largest numerator is the largest. 7/8 = 0.875, 5/6 = 0.833, 3/4 = 0.75, 2/3 = 0.667. Largest is 7/8.

In each fraction, the difference between numerator and denominator is 1 (6−5=1, 4−3=1, 3−2=1, 8−7=1). For proper fractions with equal differences, the fraction with the largest numerator is the largest. 7/8 = 0.875, 5/6 = 0.833, 3/4 = 0.75, 2/3 = 0.667. Largest is 7/8.

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Question 606 16 Oct 2022 · Shift 2 · Q31

Q606. Calculate: (6.25 − 2.23) × (3.35 − 2.23) + (0.0016 − 2.987) = ?

प्रश्न 606. (6.25 − 2.23) × (3.35 − 2.23) + (0.0016 − 2.987) की गणना कीजिए।

(A) 1.5171.517 ✓ [Official Key]

(B) 1.7151.715

(C) 2.5172.517

(D) 1.0571.057

Correct Answer: Option (A) — 1.5171.517

Explanation:

Step 1: (6.25 − 2.23) = 4.02. Step 2: (3.35 − 2.23) = 1.12. Product: 4.02 × 1.12 = 4.5024. Step 3: (0.0016 − 2.987) = −2.9854. Step 4: 4.5024 − 2.9854 = 1.517.

Step 1: (6.25 − 2.23) = 4.02. Step 2: (3.35 − 2.23) = 1.12. Product: 4.02 × 1.12 = 4.5024. Step 3: (0.0016 − 2.987) = −2.9854. Step 4: 4.5024 − 2.9854 = 1.517.

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Question 607 16 Oct 2022 · Shift 2 · Q32

Q607. One-third of Manoj's savings in Kisan Vikas Patra is equal to one-half of his savings in Public Provident Fund. If his total savings are ₹1,50,000, how much has he saved in Public Provident Fund?

प्रश्न 607. किसान विकास पत्र में मनोज की बचत का एक तिहाई, लोक भविष्य निधि (PPF) में उसकी बचत के आधे के बराबर है। यदि उसकी कुल बचत ₹1,50,000 है, तो उसने लोक भविष्य निधि में कितना बचाया है?

(A) ₹90,000₹90,000

(B) ₹30,000₹30,000

(C) ₹75,000₹75,000

(D) ₹60,000₹60,000 ✓ [Official Key]

Correct Answer: Option (D) — ₹60,000₹60,000

Explanation:

Let savings in KVP be K and PPF be P. K/3 = P/2 => K = 1.5 P. Total savings: K + P = 1.5P + P = 2.5P = 1,50,000 => P = 1,50,000 / 2.5 = ₹60,000.

Let savings in KVP be K and PPF be P. K/3 = P/2 => K = 1.5 P. Total savings: K + P = 1.5P + P = 2.5P = 1,50,000 => P = 1,50,000 / 2.5 = ₹60,000.

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Question 608 28 Oct 2023 · Shift 1 · Q94

Q608. Which of the following is in descending order?

प्रश्न 608. निम्नलिखित में से कौन-सा अवरोही क्रम (Descending order) में है?

(A) 9/13; 11/17; 5/89/13; 11/17; 5/8 ✓ [Official Key]

(B) 5/8; 9/13; 11/175/8; 9/13; 11/17

(C) 11/17; 9/13; 5/811/17; 9/13; 5/8

(D) 5/8; 11/17; 9/135/8; 11/17; 9/13

Correct Answer: Option (A) — 9/13; 11/17; 5/89/13; 11/17; 5/8

Explanation:

Convert to decimals: 9/13 ≈ 0.6923, 11/17 ≈ 0.6470, 5/8 = 0.6250. Since 0.6923 > 0.6470 > 0.6250, descending order is 9/13, 11/17, 5/8.

Convert to decimals: 9/13 ≈ 0.6923, 11/17 ≈ 0.6470, 5/8 = 0.6250. Since 0.6923 > 0.6470 > 0.6250, descending order is 9/13, 11/17, 5/8.

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Question 609 29 Oct 2023 · Shift 2 · Q93

Q609. The value of (−27) × (−16) + (−27) × (−14) is

प्रश्न 609. (−27) × (−16) + (−27) × (−14) का मान क्या है?

(A) 810810 ✓ [Official Key]

(B) −1110−1110

(C) 11101110

(D) −810−810

Correct Answer: Option (A) — 810810

Explanation:

Using distributive property: (−27) × [(−16) + (−14)] = (−27) × (−30) = +810.

Using distributive property: (−27) × [(−16) + (−14)] = (−27) × (−30) = +810.

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Question 610 15 Oct 2022 · Shift 1 · Q33

Q610. If 40% read newspaper X, 50% read newspaper Y and 10% read both, what percent read neither?

प्रश्न 610. यदि 40% लोग समाचार पत्र X पढ़ते हैं, 50% समाचार पत्र Y पढ़ते हैं और 10% दोनों पढ़ते हैं, तो कितने प्रतिशत लोग कोई भी समाचार पत्र नहीं पढ़ते?

(A) 30%30%

(B) 10%10%

(C) 40%40%

(D) 20%20% ✓ [Official Key]

Correct Answer: Option (D) — 20%20%

Explanation:

Total reading at least one newspaper: P(X ∪ Y) = P(X) + P(Y) − P(X ∩ Y) = 40% + 50% − 10% = 80%. Percentage reading neither = 100% − 80% = 20%.

Total reading at least one newspaper: P(X ∪ Y) = P(X) + P(Y) − P(X ∩ Y) = 40% + 50% − 10% = 80%. Percentage reading neither = 100% − 80% = 20%.

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Question 611 15 Oct 2022 · Shift 2 · Q33

Q611. If 70% passed Physics, 80% passed Reasoning and 55% passed both, what percent failed both subjects?

प्रश्न 611. यदि 70% छात्र भौतिकी में उत्तीर्ण हुए, 80% तर्कशक्ति में उत्तीर्ण हुए और 55% दोनों में उत्तीर्ण हुए, तो कितने प्रतिशत छात्र दोनों विषयों में अनुत्तीर्ण रहे?

(A) 15%15%

(B) 0%0%

(C) 10%10%

(D) 5%5% ✓ [Official Key]

Correct Answer: Option (D) — 5%5%

Explanation:

Percentage passing at least one: 70% + 80% − 55% = 95%. Percentage failing both subjects = 100% − 95% = 5%.

Percentage passing at least one: 70% + 80% − 55% = 95%. Percentage failing both subjects = 100% − 95% = 5%.

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Question 612 16 Oct 2022 · Shift 1 · Q33

Q612. What percent of 19 is 7.6 ?

प्रश्न 612. 19 का कितने प्रतिशत 7.6 है?

(A) 40 percent40 percent ✓ [Official Key]

(B) 45 percent45 percent

(C) 35 percent35 percent

(D) 30 percent30 percent

Correct Answer: Option (A) — 40 percent40 percent

Explanation:

Percentage = (7.6 / 19) × 100 = 0.4 × 100 = 40%.

Percentage = (7.6 / 19) × 100 = 0.4 × 100 = 40%.

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Question 613 28 Oct 2023 · Shift 1 · Q95

Q613. Divya spends 24% of her monthly salary on food and 15% on the education of her children. Of the remaining salary, she spends 25% on entertainment and 20% on conveyance. She is now left with ₹10,736. What is the monthly salary of Divya?

प्रश्न 613. दिव्या अपने मासिक वेतन का 24% भोजन पर और 15% बच्चों की शिक्षा पर खर्च करती है। शेष वेतन का 25% वह मनोरंजन पर और 20% परिवहन पर खर्च करती है। अब उसके पास ₹10,736 बचे हैं। दिव्या का मासिक वेतन क्या है?

(A) ₹30,000₹30,000

(B) ₹32,000₹32,000 ✓ [Official Key]

(C) ₹32,500₹32,500

(D) ₹30,200₹30,200

Correct Answer: Option (B) — ₹32,000₹32,000

Explanation:

Initial spend: 24% + 15% = 39%. Remaining = 100% − 39% = 61%. From this remaining, she spends 25% + 20% = 45%. Left over fraction = 100% − 45% = 55% of the remaining salary. Final savings = 0.55 × 0.61 × Salary = 0.3355 × Salary = ₹10,736. Salary = 10736 / 0.3355 = ₹32,000.

Initial spend: 24% + 15% = 39%. Remaining = 100% − 39% = 61%. From this remaining, she spends 25% + 20% = 45%. Left over fraction = 100% − 45% = 55% of the remaining salary. Final savings = 0.55 × 0.61 × Salary = 0.3355 × Salary = ₹10,736. Salary = 10736 / 0.3355 = ₹32,000.

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Question 614 29 Oct 2023 · Shift 2 · Q89

Q614. The price of desi ghee has increased by 25%. By what percent should a family reduce its consumption of desi ghee so as not to increase its expenditure on this account?

प्रश्न 614. देसी घी की कीमत में 25% की वृद्धि हुई है। एक परिवार को इसके उपभोग में कितने प्रतिशत की कमी करनी चाहिए ताकि इस मद पर खर्च न बढ़े?

(A) 18%18%

(B) 20%20% ✓ [Official Key]

(C) 16%16%

(D) 24%24%

Correct Answer: Option (B) — 20%20%

Explanation:

Reduction % = [r / (100 + r)] × 100 = [25 / (100 + 25)] × 100 = 25/125 × 100 = 20%.

Reduction % = [r / (100 + r)] × 100 = [25 / (100 + 25)] × 100 = 25/125 × 100 = 20%.

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Question 615 15 Oct 2022 · Shift 1 · Q34

Q615. The average of five results is 46 and the average of the first four is 45. What is the fifth result?

प्रश्न 615. पाँच परिणामों का औसत 46 है और पहले चार का औसत 45 है। पाँचवाँ परिणाम क्या है?

(A) 4545

(B) 5555

(C) 5050 ✓ [Official Key]

(D) 4646

Correct Answer: Option (C) — 5050

Explanation:

Sum of 5 results = 5 × 46 = 230. Sum of first 4 results = 4 × 45 = 180. Fifth result = 230 − 180 = 50.

Sum of 5 results = 5 × 46 = 230. Sum of first 4 results = 4 × 45 = 180. Fifth result = 230 − 180 = 50.

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Question 616 15 Oct 2022 · Shift 2 · Q34

Q616. What is the average of 308, 125, 45, 120 and 102?

प्रश्न 616. 308, 125, 45, 120 और 102 का औसत क्या है?

(A) 145145

(B) 130130

(C) 135135

(D) 140140 ✓ [Official Key]

Correct Answer: Option (D) — 140140

Explanation:

Sum = 308 + 125 + 45 + 120 + 102 = 700. Count = 5. Average = 700 / 5 = 140.

Sum = 308 + 125 + 45 + 120 + 102 = 700. Count = 5. Average = 700 / 5 = 140.

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Question 617 16 Oct 2022 · Shift 1 · Q34

Q617. What is the average of all prime numbers between 60 and 80?

प्रश्न 617. 60 और 80 के बीच की सभी अभाज्य संख्याओं का औसत क्या है?

(A) 68.268.2

(B) 72.472.4

(C) 69.269.2

(D) 70.270.2 ✓ [Official Key]

Correct Answer: Option (D) — 70.270.2

Explanation:

Prime numbers between 60 and 80 are: 61, 67, 71, 73, 79 (total 5 primes). Sum = 61 + 67 + 71 + 73 + 79 = 351. Average = 351 / 5 = 70.2.

Prime numbers between 60 and 80 are: 61, 67, 71, 73, 79 (total 5 primes). Sum = 61 + 67 + 71 + 73 + 79 = 351. Average = 351 / 5 = 70.2.

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Question 618 16 Oct 2022 · Shift 2 · Q33

Q618. The average of 7 consecutive numbers is 20. What is the largest of these numbers?

प्रश्न 618. 7 क्रमागत संख्याओं का औसत 20 है। इनमें से सबसे बड़ी संख्या कौन-सी है?

(A) 2121

(B) 2222

(C) 2323 ✓ [Official Key]

(D) 2424

Correct Answer: Option (C) — 2323

Explanation:

For an odd count of consecutive numbers, the average is the exact middle number (4th number = 20). The numbers are 17, 18, 19, 20, 21, 22, 23. Largest number = 23.

For an odd count of consecutive numbers, the average is the exact middle number (4th number = 20). The numbers are 17, 18, 19, 20, 21, 22, 23. Largest number = 23.

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Question 619 28 Oct 2023 · Shift 1 · Q93

Q619. In the England–New Zealand one-day match, due to rain, England needed 324 runs in 48 overs to win. In the initial 10 overs the average scoring rate was 6, but in the next 10 overs it increased to 8.5. It then declined to 5.5 in the next 10 overs and rose again to 7 in the next 10 overs. To win the match now, what average is needed?

प्रश्न 619. इंग्लैंड-न्यूजीलैंड एक दिवसीय मैच में बारिश के कारण इंग्लैंड को 48 ओवर में 324 रन बनाने थे। शुरुआती 10 ओवर में औसत 6 था, अगले 10 ओवर में बढ़कर 8.5 हो गया, फिर अगले 10 ओवर में घटकर 5.5 रह गया और अगले 10 ओवर में फिर बढ़कर 7 हो गया। अब मैच जीतने के लिए कितने औसत रन की आवश्यकता है?

(A) 7.757.75

(B) 8.258.25

(C) None of theseNone of these

(D) 6.756.75 ✓ [Official Key]

Correct Answer: Option (D) — 6.756.75

Explanation:

Runs scored in 40 overs = (10 × 6) + (10 × 8.5) + (10 × 5.5) + (10 × 7) = 60 + 85 + 55 + 70 = 270 runs. Remaining runs needed = 324 − 270 = 54 runs. Remaining overs = 48 − 40 = 8 overs. Required average = 54 / 8 = 6.75.

Runs scored in 40 overs = (10 × 6) + (10 × 8.5) + (10 × 5.5) + (10 × 7) = 60 + 85 + 55 + 70 = 270 runs. Remaining runs needed = 324 − 270 = 54 runs. Remaining overs = 48 − 40 = 8 overs. Required average = 54 / 8 = 6.75.

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Question 620 15 Oct 2022 · Shift 1 · Q32

Q620. [(0.05)² + (0.41)² + (0.073)²] ÷ [(0.005)² + (0.041)² + (0.0073)²] = ?

प्रश्न 620. [(0.05)² + (0.41)² + (0.073)²] ÷ [(0.005)² + (0.041)² + (0.0073)²] का मान क्या है?

(A) 1010

(B) 1,0001,000

(C) 100100 ✓ [Official Key]

(D) 10,00010,000

Correct Answer: Option (C) — 100100

Explanation:

Notice that each term in numerator is 10 times the corresponding term in denominator: 0.05 = 10 × 0.005, 0.41 = 10 × 0.041, 0.073 = 10 × 0.0073. Thus, Numerator = 10² × Denominator = 100 × Denominator. Hence ratio = 100.

Notice that each term in numerator is 10 times the corresponding term in denominator: 0.05 = 10 × 0.005, 0.41 = 10 × 0.041, 0.073 = 10 × 0.0073. Thus, Numerator = 10² × Denominator = 100 × Denominator. Hence ratio = 100.

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Question 621 15 Oct 2022 · Shift 2 · Q32

Q621. [(2.1)³ + (5.8)³] ÷ [(2.1)² − (2.1 × 5.8) + (5.8)²] का मान ज्ञात कीजिए।

प्रश्न 621. [(2.1)³ + (5.8)³] ÷ [(2.1)² − (2.1 × 5.8) + (5.8)²] का मान ज्ञात कीजिए।

(A) 9.79.7

(B) 7.97.9 ✓ [Official Key]

(C) 6.96.9

(D) 8.98.9

Correct Answer: Option (B) — 7.97.9

Explanation:

Using identity (a³ + b³) / (a² − ab + b²) = a + b. Here a = 2.1 and b = 5.8. Value = 2.1 + 5.8 = 7.9.

Using identity (a³ + b³) / (a² − ab + b²) = a + b. Here a = 2.1 and b = 5.8. Value = 2.1 + 5.8 = 7.9.

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Question 622 16 Oct 2022 · Shift 1 · Q32

Q622. Evaluate: [(6.73)³ − (4.38)³] ÷ [(6.73)² + 6.73 × 4.38 + (4.38)²].

प्रश्न 622. [(6.73)³ − (4.38)³] ÷ [(6.73)² + 6.73 × 4.38 + (4.38)²] का मूल्यांकन कीजिए।

(A) 2.352.35 ✓ [Official Key]

(B) 2.252.25

(C) 2.452.45

(D) 3.153.15

Correct Answer: Option (A) — 2.352.35

Explanation:

Using identity (a³ − b³) / (a² + ab + b²) = a − b. Here a = 6.73, b = 4.38. Value = 6.73 − 4.38 = 2.35.

Using identity (a³ − b³) / (a² + ab + b²) = a − b. Here a = 6.73, b = 4.38. Value = 6.73 − 4.38 = 2.35.

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Question 623 16 Oct 2022 · Shift 2 · Q34

Q623. Simplify the expression: [(76 + 8)² − (76 − 8)²] ÷ (76 × 8) = ?

प्रश्न 623. व्यंजक सरल कीजिए: [(76 + 8)² − (76 − 8)²] ÷ (76 × 8) = ?

(A) 55

(B) 33

(C) 22

(D) 44 ✓ [Official Key]

Correct Answer: Option (D) — 44

Explanation:

Using the algebraic identity: (a + b)² − (a − b)² = 4ab. Dividing by (ab) gives 4ab / ab = 4.

Using the algebraic identity: (a + b)² − (a − b)² = 4ab. Dividing by (ab) gives 4ab / ab = 4.

Verification Note: Stem corrected: The divisor in the source paper had a misprint '76 × 84'; the intended algebraic identity divisor is 76 × 8, yielding the official answer 4.

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Question 624 29 Oct 2023 · Shift 2 · Q95

Q624. If 1² + 2² + 3² + … + 10² = 385, then 3² + 6² + 9² + … + 30² is equal to

प्रश्न 624. यदि 1² + 2² + 3² + … + 10² = 385 है, तो 3² + 6² + 9² + … + 30² का मान क्या होगा?

(A) 11551155

(B) 34653465 ✓ [Official Key]

(C) 770770

(D) 23102310

Correct Answer: Option (B) — 34653465

Explanation:

Factor out 3² from each term: 3²(1² + 2² + 3² + … + 10²) = 9 × 385 = 3465.

Factor out 3² from each term: 3²(1² + 2² + 3² + … + 10²) = 9 × 385 = 3465.

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Question 625 15 Oct 2022 · Shift 1 · Q35

Q625. √29.8116 + √77.44 = ?

प्रश्न 625. √29.8116 + √77.44 का मान क्या है?

(A) 13.2613.26

(B) 15.2615.26

(C) 14.2614.26 ✓ [Official Key]

(D) 16.2616.26

Correct Answer: Option (C) — 14.2614.26

Explanation:

√29.8116 = 5.46 (since 546² = 298116). √77.44 = 8.8 (since 88² = 7744). Sum = 5.46 + 8.8 = 14.26.

√29.8116 = 5.46 (since 546² = 298116). √77.44 = 8.8 (since 88² = 7744). Sum = 5.46 + 8.8 = 14.26.

Study Notes: Elementary Arithmetic Syllabusप्रारम्भिक अंकगणित पाठ्यक्रम →

Question 626 15 Oct 2022 · Shift 2 · Q35

Q626. √(9 − 4√5) का मान ज्ञात कीजिए।

प्रश्न 626. √(9 − 4√5) का मान ज्ञात कीजिए।

(A) √5 − 2√5 − 2 ✓ [Official Key]

(B) √5 + 2√5 + 2

(C) √5 − 1√5 − 1

(D) 2 − √52 − √5

Correct Answer: Option (A) — √5 − 2√5 − 2

Explanation:

Express 9 − 4√5 as (a − b)²: (√5)² + 2² − 2(2)(√5) = 5 + 4 − 4√5 = 9 − 4√5. Since √5 ≈ 2.236 > 2, the positive square root is √5 − 2.

Express 9 − 4√5 as (a − b)²: (√5)² + 2² − 2(2)(√5) = 5 + 4 − 4√5 = 9 − 4√5. Since √5 ≈ 2.236 > 2, the positive square root is √5 − 2.

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Question 627 16 Oct 2022 · Shift 1 · Q35

Q627. Evaluate: √12.0409 − √1.2544.

प्रश्न 627. √12.0409 − √1.2544 का मान ज्ञात कीजिए।

(A) 2.452.45

(B) 2.252.25

(C) 2.352.35 ✓ [Official Key]

(D) 3.353.35

Correct Answer: Option (C) — 2.352.35

Explanation:

√12.0409 = 3.47 (since 347² = 120409). √1.2544 = 1.12 (since 112² = 12544). Value = 3.47 − 1.12 = 2.35.

√12.0409 = 3.47 (since 347² = 120409). √1.2544 = 1.12 (since 112² = 12544). Value = 3.47 − 1.12 = 2.35.

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Question 628 16 Oct 2022 · Shift 2 · Q35

Q628. Evaluate: √(9 + 4√5) = ?

प्रश्न 628. √(9 + 4√5) का मूल्यांकन कीजिए।

(A) 2 − √52 − √5

(B) 4 + √54 + √5

(C) 2 + √52 + √5 ✓ [Official Key]

(D) 1 + √51 + √5

Correct Answer: Option (C) — 2 + √52 + √5

Explanation:

9 + 4√5 = (√5)² + 2² + 2(2)(√5) = (2 + √5)². Hence √(9 + 4√5) = 2 + √5.

9 + 4√5 = (√5)² + 2² + 2(2)(√5) = (2 + √5)². Hence √(9 + 4√5) = 2 + √5.

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Question 629 28 Oct 2023 · Shift 1 · Q90

Q629. Square root of (0.081 ÷ 0.0064) × (0.484 ÷ 6.25) × (2.5 ÷ 21.1) is:

प्रश्न 629. (0.081 ÷ 0.0064) × (0.484 ÷ 6.25) × (2.5 ÷ 21.1) का वर्गमूल क्या है?

(A) 0.750.75

(B) 0.450.45 ✓ [Official Key]

(C) 0.550.55

(D) 0.340.34

Correct Answer: Option (B) — 0.450.45

Explanation:

Commission answer key gives 0.45. With 12.1 in place of 21.1, the product is (81/6.4) × (0.484/6.25) × (2.5/12.1) = 0.2025, whose square root is √0.2025 = 0.45.

Commission answer key gives 0.45. With 12.1 in place of 21.1, the product is (81/6.4) × (0.484/6.25) × (2.5/12.1) = 0.2025, whose square root is √0.2025 = 0.45.

Verification Note: With the denominator 21.1 as printed, the arithmetic value evaluates to ≈ 0.34. The UPSSSC official key is 0.45 (B), which is obtained if the term was 12.1 (a common typographical error in the original test paper).

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Question 630 28 Oct 2023 · Shift 1 · Q91

Q630. The value of (8⁻¹ − 9⁻¹)⁻¹ ÷ (4⁻¹ − 9⁻¹)⁻¹ is:

प्रश्न 630. (8⁻¹ − 9⁻¹)⁻¹ ÷ (4⁻¹ − 9⁻¹)⁻¹ का मान क्या है?

(A) 1515

(B) 2020

(C) 1010 ✓ [Official Key]

(D) 2525

Correct Answer: Option (C) — 1010

Explanation:

First term: (1/8 − 1/9)⁻¹ = (1/72)⁻¹ = 72. Second term: (1/4 − 1/9)⁻¹ = (5/36)⁻¹ = 36/5 = 7.2. Division: 72 ÷ (36/5) = 72 × (5/36) = 2 × 5 = 10.

First term: (1/8 − 1/9)⁻¹ = (1/72)⁻¹ = 72. Second term: (1/4 − 1/9)⁻¹ = (5/36)⁻¹ = 36/5 = 7.2. Division: 72 ÷ (36/5) = 72 × (5/36) = 2 × 5 = 10.

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Question 631 29 Oct 2023 · Shift 2 · Q90

Q631. Which of the following is the unit digit in the product {(341)^491 × (625)^317 × (6374)^1793}?

प्रश्न 631. गुणनफल {(341)^491 × (625)^317 × (6374)^1793} में इकाई का अंक कौन-सा है?

(A) 00 ✓ [Official Key]

(B) 33

(C) 88

(D) 77

Correct Answer: Option (A) — 00

Explanation:

Unit digit of 341^491 ends in 1. Unit digit of 625^317 ends in 5. Unit digit of 6374^1793 (where base ends in 4 and exponent is odd) ends in 4. Product of unit digits: 1 × 5 × 4 = 20, which ends in 0.

Unit digit of 341^491 ends in 1. Unit digit of 625^317 ends in 5. Unit digit of 6374^1793 (where base ends in 4 and exponent is odd) ends in 4. Product of unit digits: 1 × 5 × 4 = 20, which ends in 0.

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Question 632 29 Oct 2023 · Shift 2 · Q94

Q632. If (0.04)² ÷ (0.008) × (0.2)⁶ = (0.2)^Y, then find Y.

प्रश्न 632. यदि (0.04)² ÷ (0.008) × (0.2)⁶ = (0.2)^Y है, तो Y का मान ज्ञात कीजिए।

(A) 77 ✓ [Official Key]

(B) 1717

(C) 66

(D) 1616

Correct Answer: Option (A) — 77

Explanation:

Express each term with base 0.2: (0.04)² = ((0.2)²)² = (0.2)⁴. (0.008) = (0.2)³. So (0.2)⁴ ÷ (0.2)³ × (0.2)⁶ = (0.2)^(4 − 3 + 6) = (0.2)⁷. Thus Y = 7.

Express each term with base 0.2: (0.04)² = ((0.2)²)² = (0.2)⁴. (0.008) = (0.2)³. So (0.2)⁴ ÷ (0.2)³ × (0.2)⁶ = (0.2)^(4 − 3 + 6) = (0.2)⁷. Thus Y = 7.

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Question 633 7 Sep 2025 · Shift 1 · Q20

Q633. The least 4 digit number which is exactly divisible by 9 is

प्रश्न 633. The least 4 digit number which is exactly divisible by 9 is

(A) 10001000

(B) 10181018

(C) 10091009

(D) 10081008 ✓ [Official Key]

(E) None of the aboveउपर्युक्त में से कोई नहीं

Correct Answer: Option (D) — 10081008

Explanation:

Smallest 4-digit number is 1000. 1000 ÷ 9 gives remainder 1. To be divisible by 9, add 9 − 1 = 8. Number = 1000 + 8 = 1008 (sum of digits 1+0+0+8 = 9).

4 अंकों की न्यूनतम संख्या 1000 है। 1000 को 9 से भाग देने पर शेष 1 बचता है। अतः अभीष्ट संख्या = 1000 + (9 − 1) = 1008 (अंकों का योग 1+0+0+8 = 9)।

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Question 634 7 Sep 2025 · Shift 1 · Q52

Q634. A fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to its denominator. The fraction is

प्रश्न 634. A fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to its denominator. The fraction is

(A) 7/127/12

(B) 2/92/9

(C) 1/31/3

(D) 5/125/12 ✓ [Official Key]

(E) None of the aboveउपर्युक्त में से कोई नहीं

Correct Answer: Option (D) — 5/125/12

Explanation:

Let fraction be x/y. (x − 1)/y = 1/3 => 3x − y = 3. Also x/(y + 8) = 1/4 => 4x − y = 8. Subtracting gives x = 5, y = 12. Fraction = 5/12.

माना भिन्न x/y है। (x − 1)/y = 1/3 => 3x − y = 3 तथा x/(y + 8) = 1/4 => 4x − y = 8। घटाने पर x = 5 तथा y = 12, अतः भिन्न = 5/12।

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Question 635 7 Sep 2025 · Shift 1 · Q54

Q635. The square of Meena's age is 9 more than 8 times her age. What is her age?

प्रश्न 635. The square of Meena's age is 9 more than 8 times her age. What is her age?

(A) 1010

(B) 99 ✓ [Official Key]

(C) 88

(D) 11

(E) None of the aboveउपर्युक्त में से कोई नहीं

Correct Answer: Option (B) — 99

Explanation:

Equation: x² = 8x + 9 => x² − 8x − 9 = 0 => (x − 9)(x + 1) = 0. Since age is positive, x = 9 years.

समीकरण: x² = 8x + 9 => x² − 8x − 9 = 0 => (x − 9)(x + 1) = 0। आयु धनात्मक होगी, अतः x = 9 वर्ष।

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Question 636 7 Sep 2025 · Shift 1 · Q60

Q636. 20 minutes is what percent of an hour?

प्रश्न 636. 20 minutes is what percent of an hour?

(A) 35%35%

(B) 50%50%

(C) 30%30%

(D) 33 1/3%33 1/3% ✓ [Official Key]

(E) None of the aboveउपर्युक्त में से कोई नहीं

Correct Answer: Option (D) — 33 1/3%33 1/3%

Explanation:

1 hour = 60 minutes. Percentage = (20 / 60) × 100 = 100 / 3 = 33 1/3%.

1 घंटा = 60 मिनट। अभीष्ट प्रतिशत = (20 / 60) × 100 = 100/3 = 33 1/3%।

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Question 637 7 Sep 2025 · Shift 1 · Q74

Q637. If 3x − 14 = 4 then x =

प्रश्न 637. If 3x − 14 = 4 then x =

(A) −9−9

(B) 99

(C) −6−6

(D) 66 ✓ [Official Key]

(E) None of the aboveउपर्युक्त में से कोई नहीं

Correct Answer: Option (D) — 66

Explanation:

3x − 14 = 4 => 3x = 4 + 14 = 18 => x = 18 / 3 = 6.

3x − 14 = 4 => 3x = 18 => x = 18 / 3 = 6।

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Question 638 7 Sep 2025 · Shift 2 · Q4

Q638. How many whole numbers are strictly between 437 and 487 ?

प्रश्न 638. How many whole numbers are strictly between 437 and 487 ?

(A) 5151

(B) 5050

(C) 4949 ✓ [Official Key]

(D) 4848

(E) None of the aboveउपर्युक्त में से कोई नहीं

Correct Answer: Option (C) — 4949

Explanation:

The whole numbers strictly between 437 and 487 start from 438 to 486. Total count = 486 − 438 + 1 = 49 (or 487 − 437 − 1 = 49).

437 और 487 के मध्य स्थित पूर्ण संख्याएँ 438 से 486 तक हैं। कुल संख्या = 486 − 438 + 1 = 49 (या 487 − 437 − 1 = 49)।

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Question 639 7 Sep 2025 · Shift 2 · Q16

Q639. Express 0.12 as a percentage:

प्रश्न 639. Express 0.12 as a percentage:

(A) 1.2%1.2%

(B) 0.12%0.12%

(C) 12%12% ✓ [Official Key]

(D) 120%120%

(E) None of the aboveउपर्युक्त में से कोई नहीं

Correct Answer: Option (C) — 12%12%

Explanation:

To convert a decimal to a percentage, multiply by 100: 0.12 × 100% = 12%.

किसी दशमलव संख्या को प्रतिशत में बदलने के लिए 100 से गुणा किया जाता है: 0.12 × 100% = 12%।

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Question 640 7 Sep 2025 · Shift 2 · Q27

Q640. The LCM of two numbers is 120 and their HCF is 6. If one of the numbers is 30, what is the other number ?

प्रश्न 640. The LCM of two numbers is 120 and their HCF is 6. If one of the numbers is 30, what is the other number ?

(A) 2020

(B) 2424 ✓ [Official Key]

(C) 3636

(D) 4848

(E) None of the aboveउपर्युक्त में से कोई नहीं

Correct Answer: Option (B) — 2424

Explanation:

Formula: Product of two numbers = LCM × HCF. 30 × Other Number = 120 × 6 => Other Number = (720 / 30) = 24.

सूत्र: पहली संख्या × दूसरी संख्या = LCM × HCF। 30 × दूसरी संख्या = 120 × 6 = 720 => दूसरी संख्या = 720 / 30 = 24।

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Question 641 7 Sep 2025 · Shift 2 · Q40

Q641. The perimeter of a rectangle is 13 cm and its width is 2 3/4 cm. Find its length (in cm):

प्रश्न 641. The perimeter of a rectangle is 13 cm and its width is 2 3/4 cm. Find its length (in cm):

(A) 3 1/43 1/4

(B) 3 1/23 1/2

(C) 3 3/43 3/4 ✓ [Official Key]

(D) 4 1/44 1/4

(E) None of the aboveउपर्युक्त में से कोई नहीं

Correct Answer: Option (C) — 3 3/43 3/4

Explanation:

Perimeter = 2 × (Length + Width) = 13 cm. Length + (11 / 4) = 13 / 2 = 26 / 4. Length = (26 / 4) − (11 / 4) = 15 / 4 = 3 3/4 cm.

परिमाप = 2 × (लंबाई + चौड़ाई) = 13 सेमी। लंबाई + 11/4 = 13/2 = 26/4 सेमी। लंबाई = 26/4 − 11/4 = 15/4 = 3 3/4 सेमी।

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Question 642 7 Sep 2025 · Shift 2 · Q67

Q642. Given that 1² = 1, 11² = 121, then the value of 111² is:

प्रश्न 642. Given that 1² = 1, 11² = 121, then the value of 111² is:

(A) 1222112221

(B) 1231112311

(C) 1232112321 ✓ [Official Key]

(D) 1332113321

(E) None of the aboveउपर्युक्त में से कोई नहीं

Correct Answer: Option (C) — 1232112321

Explanation:

Squaring numbers composed entirely of 1s follows a palindromic counting pattern: 1² = 1, 11² = 121, 111² = 12321, 1111² = 1234321.

केवल 1 से बनी संख्याओं के वर्ग का नियम: 1² = 1, 11² = 121, 111² = 12321 (1 से 3 तक चढ़ते क्रम में फिर 1 तक उतरते क्रम में)।

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Question 643 6 Sep 2025 · Shift 1

Q643. If 2994 / 14.5 = 172, then 29.94 / 1.45 = ?

प्रश्न 643. यदि 2994 ÷ 14.5 = 172 है, तो 29.94 ÷ 1.45 = ?

(A) 1.721.72

(B) 0.1720.172

(C) 17.217.2 ✓ [Official Key]

(D) 172172

(E) None of the aboveउपर्युक्त में से कोई नहीं

Correct Answer: Option (C) — 17.217.2

Explanation:

Given: 2994 / 14.5 = 172. Now, 29.94 / 1.45 = (2994 / 100) / (14.5 / 10) = (2994 / 14.5) * (10 / 100) = 172 * 0.1 = 17.2. Hence, option C is correct.

दिया गया है: 2994 ÷ 14.5 = 172 अब, 29.94 ÷ 1.45 = (2994/100) ÷ (14.5/10) = (2994 ÷ 14.5) × (10/100) = 172 × (1/10) = 17.2 अतः सही उत्तर 17.2 (विकल्प C) है।

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Question 644 6 Sep 2025 · Shift 1

Q644. The difference between the largest 3 digit number and smallest 2 digit number is

प्रश्न 644. सबसे बड़ी 3 अंकों की संख्या और सबसे छोटी 2 अंकों की संख्या के बीच का अंतर क्या है ?

(A) 989989 ✓ [Official Key]

(B) 980980

(C) 998998

(D) 990990

(E) None of the aboveउपर्युक्त में से कोई नहीं

Correct Answer: Option (A) — 989989

Explanation:

The largest 3-digit number is 999. The smallest 2-digit number is 10. Difference = 999 - 10 = 989. Hence option A is correct.

सबसे बड़ी 3 अंकों की संख्या = 999 सबसे छोटी 2 अंकों की संख्या = 10 दोनों का अंतर = 999 - 10 = 989 (विकल्प A)।

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Question 645 6 Sep 2025 · Shift 1

Q645. Which is greater : √45 or √49 - 1 ?

प्रश्न 645. कौन-सा बड़ा है : √45 या √49 - 1 ?

(A) √45√45 ✓ [Official Key]

(B) √49 - 1√49 - 1

(C) Both are equalदोनों बराबर हैं

(D) Cannot be determinedनिर्धारित नहीं किया जा सकता

(E) None of the aboveउपर्युक्त में से कोई नहीं

Correct Answer: Option (A) — √45√45

Explanation:

Value of √49 - 1 = 7 - 1 = 6. Now, 6 = √36. Since 45 > 36, √45 > √36 = 6. (In fact, √45 ≈ 6.708 > 6). Therefore, √45 is greater. Option A is correct.

√49 - 1 का मान = 7 - 1 = 6 हम जानते हैं कि 6 = √36 चूंकि 45 > 36 है, अतः √45 > √36 = 6 (वास्तव में √45 ≈ 6.708 जो 6 से बड़ा है)। अतः √45 बड़ा है (विकल्प A)।

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Question 646 6 Sep 2025 · Shift 1

Q646. If x and y are co-primes, then their LCM is

प्रश्न 646. यदि x और y सह-अभाज्य हैं, तो उनका LCM क्या है ?

(A) x / yx / y

(B) 11

(C) xyxy ✓ [Official Key]

(D) x + yx + y

(E) None of the aboveउपर्युक्त में से कोई नहीं

Correct Answer: Option (C) — xyxy

Explanation:

Two integers x and y are co-prime if their Highest Common Factor (HCF) is 1. Since LCM * HCF = Product of numbers (x * y), we have LCM * 1 = xy => LCM = xy.

सह-अभाज्य (co-prime) संख्याओं का महत्तम समापवर्तक (HCF) सदैव 1 होता है। सूत्रानुसार: LCM × HCF = दोनों संख्याओं का गुणनफल => LCM × 1 = x × y => LCM = xy (विकल्प C)।

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Question 647 6 Sep 2025 · Shift 1

Q647. 2/5 in percent form is

प्रश्न 647. 2/5 प्रतिशत रूप में क्या है ?

(A) 40%40% ✓ [Official Key]

(B) 20%20%

(C) 25%25%

(D) 80%80%

(E) None of the aboveउपर्युक्त में से कोई नहीं

Correct Answer: Option (A) — 40%40%

Explanation:

To convert a fraction to percentage, multiply by 100: (2 / 5) * 100 = 2 * 20 = 40%. Option A is correct.

भिन्न 2/5 को प्रतिशत में बदलने के लिए 100 से गुणा करते हैं: (2 ÷ 5) × 100 = 40% (विकल्प A)।

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Question 648 6 Sep 2025 · Shift 2

Q648. 12½% of 1 hour 40 mins is :

प्रश्न 648. 1 घंटा 40 मिनट का 12½% कितना होगा ?

(A) 12.5 mins12.5 मिनट ✓ [Official Key]

(B) 20.5 mins20.5 मिनट

(C) 25 mins25 मिनट

(D) 15 mins15 मिनट

(E) None of the aboveउपर्युक्त में से कोई नहीं

Correct Answer: Option (A) — 12.5 mins12.5 mins

Explanation:

1 hour 40 minutes = 60 + 40 = 100 minutes. 12½% = 12.5% = 1/8. 12.5% of 100 mins = (12.5 / 100) × 100 = 12.5 minutes.

1 घंटा 40 मिनट = 60 + 40 = 100 मिनट। 100 मिनट का 12½% = (12.5 / 100) × 100 = 12.5 मिनट।

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Question 649 6 Sep 2025 · Shift 2

Q649. The product of 2 numbers is 1530 and their HCF is 15, then their LCM is :

प्रश्न 649. दो संख्याओं का गुणनफल 1530 है और उनका म.स. (HCF) 15 है, तो उनका ल.स. (LCM) क्या होगा ?

(A) 112112

(B) 102102 ✓ [Official Key]

(C) 120120

(D) 8484

(E) None of the aboveउपर्युक्त में से कोई नहीं

Correct Answer: Option (B) — 102102

Explanation:

Formula: Product of two numbers = HCF × LCM. 1530 = 15 × LCM LCM = 1530 / 15 = 102.

सूत्र: दो संख्याओं का गुणनफल = HCF × LCM 1530 = 15 × LCM LCM = 1530 / 15 = 102।

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Question 650 6 Sep 2025 · Shift 2

Q650. Which among the following is not a prime number ?

प्रश्न 650. निम्नलिखित में से कौन सी एक अभाज्य संख्या नहीं है ?

(A) 5353

(B) 2929

(C) 4747

(D) 5757 ✓ [Official Key]

(E) None of the aboveउपर्युक्त में से कोई नहीं

Correct Answer: Option (D) — 5757

Explanation:

57 is a composite number divisible by 1, 3, 19, and 57 (since 3 × 19 = 57). 53, 29, and 47 are all prime numbers.

57 एक भाज्य संख्या है (3 × 19 = 57), अतः यह अभाज्य नहीं है। 29, 47 और 53 अभाज्य संख्याएँ हैं।

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Question 651 6 Sep 2025 · Shift 2

Q651. If you subtract ½ from a number and multiply the result by ½, you get ⅛. The number is :

प्रश्न 651. यदि आप किसी संख्या से ½ घटाते हैं और परिणाम को ½ से गुणा करते हैं, तो आपको ⅛ मिलता है। वह संख्या क्या है ?

(A) ¼¼

(B) 1¼1¼

(C) ½½

(D) ¾¾ ✓ [Official Key]

(E) None of the aboveउपर्युक्त में से कोई नहीं

Correct Answer: Option (D) — ¾¾

Explanation:

Let the number be x. (x - 1/2) × 1/2 = 1/8 x - 1/2 = 1/8 ÷ 1/2 = 1/8 × 2 = 1/4 x = 1/4 + 1/2 = 1/4 + 2/4 = 3/4.

माना संख्या x है। (x - 1/2) × 1/2 = 1/8 x - 1/2 = 1/4 x = 1/4 + 1/2 = 3/4।

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Question 652 6 Sep 2025 · Shift 2

Q652. Between which two consecutive integers does √290 lie ?

प्रश्न 652. √290 किन दो लगातार पूर्णांकों के बीच स्थित है ?

(A) 16 and 1716 और 17

(B) 19 and 2019 और 20

(C) 17 and 1817 और 18 ✓ [Official Key]

(D) 18 and 1918 और 19

(E) None of the aboveउपर्युक्त में से कोई नहीं

Correct Answer: Option (C) — 17 and 1817 and 18

Explanation:

17² = 289 and 18² = 324. Since 289 < 290 < 324, √289 < √290 < √324, which means 17 < √290 < 18. Thus, √290 lies between 17 and 18.

17² = 289 तथा 18² = 324। चूँकि 289 < 290 < 324, अतः 17 < √290 < 18। इसलिए √290, 17 और 18 के बीच स्थित है।

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Question 653 24 Aug 2021 · Shift 2

Q653. If $\sqrt{1 + \frac{27}{169}} = \left(1 + \frac{x}{13}\right)$, then the value of $x$ is :

प्रश्न 653. यदि $\sqrt{1 + \frac{27}{169}} = \left(1 + \frac{x}{13}\right)$, तो $x$ का मान है :

(A) 11 ✓ [Official Key]

(B) 33

(C) 55

(D) 77

Correct Answer: Option (A) — 11

Explanation:

LHS: $\sqrt{\frac{169 + 27}{169}} = \sqrt{\frac{196}{169}} = \frac{14}{13}$. RHS: $1 + \frac{x}{13} = \frac{13 + x}{13}$. Equating both: $\frac{13 + x}{13} = \frac{14}{13} \implies 13 + x = 14 \implies x = 1$.

बायां पक्ष: $\sqrt{1 + \frac{27}{169}} = \sqrt{\frac{196}{169}} = \frac{14}{13}$। दायां पक्ष: $1 + \frac{x}{13} = \frac{13+x}{13}$। तुलना करने पर: $13 + x = 14 \implies x = 1$।

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Question 654 24 Aug 2021 · Shift 2

Q654. How many $\frac{1}{8}$'s are there in $37\frac{1}{2}$ ?

प्रश्न 654. $37\frac{1}{2}$ में कुल कितने $\frac{1}{8}$ हैं ?

(A) 300300 ✓ [Official Key]

(B) 400400

(C) 500500

(D) cannot be determinedनिर्धारित नहीं कर सकते

Correct Answer: Option (A) — 300300

Explanation:

$37\frac{1}{2} = \frac{75}{2}$. Number of $\frac{1}{8}$'s = $\frac{75/2}{1/8} = \frac{75}{2} \times 8 = 75 \times 4 = 300$.

$37\frac{1}{2} = \frac{75}{2}$। कुल $\frac{1}{8}$ की संख्या = $\frac{75}{2} \div \frac{1}{8} = \frac{75}{2} \times 8 = 300$।

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Question 655 24 Aug 2021 · Shift 2

Q655. Evaluate : $$\sqrt{\frac{36.1}{102.4}} = ?$$

प्रश्न 655. मान ज्ञात कीजिए : $$\sqrt{\frac{36.1}{102.4}} = ?$$

(A) 29 / 3229 / 32

(B) 19 / 7219 / 72

(C) 19 / 3219 / 32 ✓ [Official Key]

(D) 29 / 6229 / 62

Correct Answer: Option (C) — 19 / 3219 / 32

Explanation:

$\sqrt{\frac{36.1}{102.4}} = \sqrt{\frac{361}{1024}} = \frac{\sqrt{361}}{\sqrt{1024}} = \frac{19}{32}$.

दशमलव हटाने पर: $\sqrt{\frac{36.1}{102.4}} = \sqrt{\frac{361}{1024}} = \frac{19}{32}$।

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Question 656 24 Aug 2021 · Shift 2

Q656. The population of a town increases 4% annually but is decreased by migration annually to the extent of $\frac{1}{2}\%$. What will be the increase percent in three years ?

प्रश्न 656. एक शहर की जनसंख्या में 4% की वार्षिक वृद्धि होती है परन्तु स्थानांतरण के कारण $\frac{1}{2}\%$ वार्षिक तक घट भी जाती है। तीन वर्षों में वृद्धि का प्रतिशत क्या होगा ?

(A) 9.89.8

(B) 1010

(C) 10.510.5

(D) 10.810.8 ✓ [Official Key]

Correct Answer: Option (D) — 10.810.8

Explanation:

Net annual growth rate $r = 4\% - 0.5\% = 3.5\% = 0.035$. After 3 years, population factor $= (1 + 0.035)^3 = (1.035)^3 = 1.108717875$. Percentage increase $= (1.1087 - 1) \times 100\% \approx 10.8\%$.

शुद्ध वार्षिक वृद्धि दर = $4\% - 0.5\% = 3.5\%$। 3 वर्ष बाद जनसंख्या = $P(1 + 0.035)^3 = P(1.035)^3 = 1.1087 P$। अतः 3 वर्षों में कुल प्रतिशत वृद्धि = $(1.1087 - 1) \times 100 \approx 10.8\%$।

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Question 657 24 Aug 2021 · Shift 2

Q657. The average of 13 results is 68. The average of first seven is 63 and that of the last seven is 70, the seventh result is :

प्रश्न 657. 13 परिणामों का औसत 68 है। पहले सात का औसत 63 है और आखिरी सात का औसत 70 है, तो सातवें का परिणाम है –

(A) 4747 ✓ [Official Key]

(B) 65.565.5

(C) 73.573.5

(D) 9494

Correct Answer: Option (A) — 4747

Explanation:

Total of 13 results $= 13 \times 68 = 884$. Sum of first 7 results $= 7 \times 63 = 441$. Sum of last 7 results $= 7 \times 70 = 490$. Seventh result $= (441 + 490) - 884 = 931 - 884 = 47$.

13 परिणामों का कुल योग $= 13 \times 68 = 884$। प्रथम 7 परिणामों का योग $= 7 \times 63 = 441$। अंतिम 7 परिणामों का योग $= 7 \times 70 = 490$। सातवाँ परिणाम $= (441 + 490) - 884 = 931 - 884 = 47$।

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Question 658 24 Aug 2021 · Shift 1

Q658. √(?/196) = 72/56

प्रश्न 658. √(?/196) = 72/56

(A) 1818

(B) 1414

(C) 324324 ✓ [Official Key]

(D) 212212

Correct Answer: Option (C) — 324324

Explanation:

72/56 = 9/7. So √(?/196) = 9/7 → ?/196 = 81/49 → ? = (81 × 196)/49 = 81 × 4 = 324.

72/56 = 9/7। अतः √(?/196) = 9/7 → ?/196 = 81/49 → ? = (81 × 196)/49 = 81 × 4 = 324।

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Question 659 24 Aug 2021 · Shift 1

Q659. (885×885×885 + 115×115×115) / (885×885 + 115×115 – 885×115) = ?

प्रश्न 659. (885×885×885 + 115×115×115) / (885×885 + 115×115 – 885×115) = ?

(A) 115115

(B) 770770

(C) 885885

(D) 10001000 ✓ [Official Key]

Correct Answer: Option (D) — 10001000

Explanation:

Using identity a³+b³ = (a+b)(a²-ab+b²): (a³+b³)/(a²-ab+b²) = a+b = 885+115 = 1000.

a³ + b³ = (a+b)(a²-ab+b²) सूत्र से: (a³+b³)/(a²-ab+b²) = a+b = 885+115 = 1000।

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Question 660 24 Aug 2021 · Shift 1

Q660. (√5 – √3)/(√5 + √3) is equal to:

प्रश्न 660. (√5 – √3)/(√5 + √3) इसके बराबर है :

(A) 4 + √154 + √15

(B) 4 – √154 – √15 ✓ [Official Key]

(C) 1/21/2

(D) 11

Correct Answer: Option (B) — 4 – √154 – √15

Explanation:

Rationalising: (√5–√3)² / ((√5)²–(√3)²) = (5+3–2√15)/(5–3) = (8–2√15)/2 = 4–√15.

रैशनलाइज़ करने पर: (√5–√3)²/((√5)²–(√3)²) = (5+3–2√15)/(5–3) = (8–2√15)/2 = 4–√15।

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Question 661 24 Aug 2021 · Shift 1

Q661. On decreasing the price of T.V. sets by 30%, its sale is increased by 20%. What is the effect on the revenue received by the shopkeeper?

प्रश्न 661. टी.वी. सेट का मूल्य 30% घटाने पर उसकी बिक्री 20% बढ़ गई। दुकानदार की आय पर उसका क्या प्रभाव पड़ा ?

(A) 10% increase10% बढ़ी

(B) 10% decrease10% घटी

(C) 16% increase16% बढ़ी

(D) 16% decrease16% घटी ✓ [Official Key]

Correct Answer: Option (D) — 16% decrease16% decrease

Explanation:

Revenue = Price × Sales. New Revenue = 0.7P × 1.2Q = 0.84PQ. Change = 0.84PQ – PQ = –0.16PQ. Hence revenue decreases by 16%.

आय = मूल्य × बिक्री। नई आय = 0.7P × 1.2Q = 0.84PQ। परिवर्तन = 0.84PQ – PQ = –0.16PQ। अतः आय में 16% की कमी।

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Question 662 24 Aug 2021 · Shift 1

Q662. The average age of four players is 18.5 years. If the age of the coach is also included, the average age increases by 20%. The age of the coach is:

प्रश्न 662. चार खिलाड़ियों की औसत उम्र 18.5 वर्ष है। अगर कोच की उम्र भी इसमें शामिल की जाए तो औसत उम्र 20% बढ़ जाती है, तो कोच की उम्र है :

(A) 28 years28 वर्ष

(B) 31 years31 वर्ष

(C) 34 years34 वर्ष

(D) 37 years37 वर्ष ✓ [Official Key]

Correct Answer: Option (D) — 37 years37 years

Explanation:

New average = 18.5 × 1.20 = 22.2. Total age (5 persons) = 22.2 × 5 = 111. Four players' total age = 18.5 × 4 = 74. Coach's age = 111 – 74 = 37.

नई औसत = 18.5 × 1.20 = 22.2। कुल आयु (5 लोग) = 22.2 × 5 = 111। 4 खिलाड़ियों की आयु = 18.5 × 4 = 74। कोच की आयु = 111 – 74 = 37।

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