Practice MCQ Questions and Answer on Number System

41.

Which one of the following is not a prime number?

(A) 31
(B) 61
(C) 71
(D) 91

42.

For what value of X, 211X will be a perfect square?

(A) 4
(B) 5
(C) 6
(D) 9

43.

The greatest perfect square number of digits is?

(A) 999001
(B) 998001
(C) 998009
(D) 998101

44.

A number when divided by three consecutive numbers 9, 11, 13 leaves the remainders 8, 9 and 8 respectively. If the order of divisors is reversed, the remainders will be :

(A) 10, 8, 9
(B) 10, 1, 6
(C) 8, 9, 8
(D) 9, 8, 8

45.

Three numbers which are co-prime to one another are such that the product of the first two is 551 and that of last two is 1073. The sum of the three numbers is:

(A) 75
(B) 81
(C) 85
(D) 89

Solution: HCF of 551 and 1073 is 29. So second number is 29 First number = $\frac{551}{29}$ = 19 Third number = $\frac{1073}{29}$ = 37 So, Required Sum = 19 + 29 + 37 = 85

46.

The square of a number greater than 1000 that is not divisible by three, when divided by three, leaves a remainder of

(A) 1 always
(B) 2 always
(C) Either 1 or 2
(D) 0

47.

A six digit number is formed by repeating a three digit number : For example, 256, 256 or 678, 678 etc. Any number of this form is always exactly divisible by -

(A) 7 only
(B) 11 only
(C) 13 only
(D) 1001 only

48.

Consider the following statements for the sequence of numbers given below :
11, 111, 1111, 11111, .....
1. Each number can be expressed in the form (4m + 3), where m is a natural number.
2. Some numbers are squares.
Which of the above statements is/are correct ?

(A) 1 only
(B) 2 only
(C) Both 1 and 2
(D) Neither 1 nor 2

49.

The unit digit in the sum of ${(124)}^{372}$ ÃÂÃÂ $+ {(124)}^{373}$ ÃÂÃÂ = ?

(A) 5
(B) 4
(C) 2
(D) 0

Solution: $\begin{aligned} {(124)}^{372} {(124)}^{373} \\ \overset{↓}{4^{372}} \overset{↓}{4^{373}} \end{aligned}$ When 4 has odd power then unit digit is 4, when 4 has even power then unit digit is 6 41 → 4 → 4 42 → 16 → 6 43 → 64 → 4 44 → 256 → 6 4372 4373 ↓ ↓ 6 + 4 = 10 = 0 Last (unit) digit = 0

50.

If 4x² - 12x + k is a perfect square. then the value of k is ?

(A) 2
(B) 9
(C) 12
(D) 10

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Practice MCQ Questions and Answer on Number System

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