100+ TNPSC Number System Previous Year Questions - 1

Question: 1

(71 × 29 + 27 × 15 + 8 × 4) equals

(A) 2496

(B) 3450

(D) None of these

Ans: A

(71 × 29 + 27 × 15 + 8 × 4) = (80 - 9) × 29 + 405 + 32 = (80 × 29) - (9 × 29) + 437 = 2320 - 261 + 437 = 2757 – 261 = 2496.

Question: 2

If a and b be positive integers such that a² - b² = 19, then the value of a is

(A) 9

(B) 10

(D) 20

View Answer

Ans: B

(a² - b²) = 19 ⇒ (a + b) (a – b) = 19.

Clearly, a = 10 and b = 9.

Question: 3

A 6 digit number is formed by repeating a 3 digit number, for example, 256256 or 678678 etc. Any number of this form is always exactly divisible by

(A) 7 only

(B) 11 only

(D) 10001 only

View Answer

Ans: D

Numbers like 2525, 3636 etc. are divisible by 101.

Numbers like 256256, 678678 etc. are divisible by 1001.

Numbers like 32163216, 43754375 etc. are divisible by 10001 and so on.

Question: 4

If all the numbers from 501 to 700 are written, what is the total number of times the digit 6 appears?

(A) 138

(B) 139

(D) 141

View Answer

Ans: C

Numbers from 501 to 599 which have 6 as digits are 506, 516, 526, 536, 546, 556, 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 576, 586 and 596, i.e., occurs 20 times.

Number of times 6 occurs from 600 to 699 = 100 + 20 = 120.

∴ Total number of time 6 occurs = 20 + 120 = 140.

Question: 5

(4⁶¹ + 4⁶² + 4⁶³ + 4⁶⁴) is divisible by

(A) 3

(B) 11

(D) 17

View Answer

Ans: D

(4⁶¹ + 4⁶² + 4⁶³ + 4⁶⁴) = 4⁶¹(1 + 4 + 4 ² + 4³) = 4⁶¹ × 85, which is divisible by 17.

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100+ TNPSC Number System Previous Year Questions - 1

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