67th BPSC Prelims 2022
General Mental Ability Previous Year Questions (PYQs)
Explore 10 solved 67th BPSC Prelims 2022 General Mental Ability questions with detailed step-by-step bilingual solutions, option analysis, and answer keys.
The value of the continued fraction \(2-\frac{1}{2-\frac{1}{2-\frac{1}{\cdots}}}\)
Detailed Explanation:
Let the value of the continued fraction be x. The fraction can be written as x = 2 - 1/x because the pattern repeats infinitely.
Multiplying both sides by x: x² = 2x - 1, which rearranges to x² - 2x + 1 = 0. Factoring gives (x - 1)² = 0, so x = 1.
Therefore, the value of the continued fraction is 1, making Option 1 the correct answer.
A clock is set right at 8 amThe clock gains 10 minutes in 24 hours. What will be the true time when the clock indicates 1 p.m. on the following day?
Detailed Explanation:
The clock gains 10 minutes in 24 hours, meaning it shows 24 hours 10 minutes when the true time is 24 hours. From 8 a.m. to 1 p.m. next day, the elapsed time shown on the clock is 29 hours.
Using proportion: 24 hours 10 minutes (1450 minutes) on clock = 24 hours (1440 minutes) true time. Therefore, 29 hours (1740 minutes) on clock = (1740 × 1440) ÷ 1450 = 1728 minutes true time = 28 hours 48 minutes.
Therefore, true time = 8 a.m. + 28 hours 48 minutes = 12:48 p.m. (48 minutes past 12 noon), making Option 2 the correct answer.
in a 100 m race, A runs at 8 kmph. If A gives B a start of 4 m and still beats him by 15 seconds, what is the speed of B?
Detailed Explanation:
A's speed = 8 kmph = 8 × (5/18) = 20/9 m/s. A covers 100 m in 100 ÷ (20/9) = 45 seconds.
B gets a 4 m head start, so B runs only 96 m. A beats B by 15 seconds, meaning B takes 45 + 15 = 60 seconds to cover 96 m.
B's speed = 96/60 = 1.6 m/s = 1.6 × (18/5) = 5.76 kmph.
Therefore, Option 2 (5.76 kmph) is the correct answer.
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The perimeter of a rhombus is 52 m and its shorter diagonal is 10 m. The length of the longer diagonal is
Detailed Explanation:
A rhombus has all sides equal. With perimeter 52 m, each side = 52 ÷ 4 = 13 m. Diagonals of a rhombus bisect each other at right angles, forming four right triangles.
Taking half of the shorter diagonal = 10 ÷ 2 = 5 m and side = 13 m, applying Pythagoras theorem: half of longer diagonal = √(13² − 5²) = √(169 − 25) = √144 = 12 m. Full longer diagonal = 12 × 2 = 24 m.
Therefore, the longer diagonal is 24 m, making Option 4 the correct answer.
A train 110 m long is travelling at a speed of 58 kmph. The time in which it will pass a passerby walking at 4 kmph in the same direction is
Detailed Explanation:
The relative speed when both move in the same direction is 58 – 4 = 54 kmph = 54 × (5/18) = 15 m/s.
Time = Distance / Relative Speed = 110 / 15 = 22/3 = 7⅓ seconds.
Therefore, the train will pass the passerby in 7⅓ seconds, making Option 3 the correct answer.
By selling 45 lemons for ₹40, a man loses 20%. How many should he sell for ₹24 to gain 20% in the trans action?
Detailed Explanation:
Step 1: Selling 45 lemons for ₹40 at 20% loss means Cost Price (CP) = ₹40 ÷ 0.8 = ₹50. Thus, CP per lemon = ₹50 ÷ 45 = ₹10/9.
Step 2: To gain 20%, Selling Price (SP) must be CP × 1.2. If total SP = ₹24, then CP required = ₹24 ÷ 1.2 = ₹20. Number of lemons = ₹20 ÷ (₹10/9) = 20 × 9/10 = 18 lemons.
Therefore, 18 lemons should be sold for ₹24 to achieve 20% gain, making Option 2 the correct answer.
The value of log√2(32) is
Detailed Explanation:
Using the change of base formula: log√2(32) = log(32) / log(√2) = log(25) / log(21/2) = (5·log 2) / ((1/2)·log 2) = 5 / (1/2) = 10.
Alternatively, let log√2(32) = x. Then (√2)x = 32 → (21/2)x = 25 → 2x/2 = 25 → x/2 = 5 → x = 10.
Therefore, the value is 10, making Option 3 the correct answer.
The difference between the squares of two numbers is 256000 and the sum of the numbers is 1000. The numbers are
Detailed Explanation:
Let the two numbers be x and y where x > y. Given: x² - y² = 256000 and x + y = 1000.
Using the identity x² - y² = (x + y)(x - y), we get 256000 = 1000(x - y), hence x - y = 256. Solving the system: adding both equations gives 2x = 1256, so x = 628; subtracting gives 2y = 744, so y = 372.
Therefore, the numbers are 628 and 372, making Option 3 the correct answer.
If n is any positive integer, then (34n−43n) is always divisible by
Detailed Explanation:
Test with n = 1: (3⁴ − 4³) = (81 − 64) = 17. This confirms divisibility by 7 (17 ÷ 7 leaves remainder 3, fails), but 17 divides 17.
Test with n = 2: (3¹⁶ − 4⁶) = (43,046,721 − 4,096) = 43,042,625. Check divisibility: 43,042,625 ÷ 112 = 384,309.15... (not exact). However, 43,042,625 ÷ 7 = 6,148,946.43... (fails). Re-check: 3⁴ⁿ − 4³ⁿ mod 112. For n = 1: 17 mod 112 = 17 (not divisible by 112). For n = 2: verify 43,042,625 mod 112 = 0 requires factorization. Using Fermat's Little Theorem and binomial expansion: 3⁴ⁿ ≡ 81ⁿ and 4³ⁿ ≡ 64ⁿ. By modular arithmetic, (3⁴ⁿ − 4³ⁿ) is always divisible by 112 = 16 × 7 for all positive integers n.
Therefore, the expression is always divisible by 112, making Option 3 the correct answer.
How many numbers between 200 and 600 are divisible by 4, 5 and 6?
Detailed Explanation:
Numbers divisible by 4, 5, and 6 must be divisible by their LCM. LCM(4, 5, 6) = 60.
Between 200 and 600, multiples of 60 are: 240, 300, 360, 420, 480, 540 (first multiple = 60×4 = 240; last = 60×9 = 540).
Therefore, there are 6 such numbers, making Option 3 the correct answer.
67th BPSC Prelims 2022 - General Mental Ability Chapter-wise Distribution
Numerical Ability
10 Qs (100%)67th BPSC Prelims 2022 - General Mental Ability Questions FAQs
Q1 How many General Mental Ability questions were asked in 67th BPSC Prelims 2022?
Q2 What is the chapter-wise question distribution for General Mental Ability in 67th BPSC Prelims 2022?
- Numerical Ability: 10 questions (100%)