Practice MCQ Questions and Answer on Number System

601.

Find the unit digit in the product : ${(4387)}^{245}$ ÃÂÃÂ $\times {(621)}^{72}$

(A) 1
(B) 2
(C) 5
(D) 7

Solution: $\begin{matrix} unit place \\ [\begin{matrix} 7^{1} \to 7 \to 7 \\ 7^{2} \to 49 \to 9 \\ 7^{3} \to 343 \to 3 \\ 7^{4} \to 2401 \to 1 \end{matrix}] cycle \end{matrix}$ $\begin{aligned} {(4387)}^{245} \times {(621)}^{72} \\ \overset{↓}{{(7)}^{245}} \times {(1)}^{72} \\ \overset{↓}{{(7)}^{4 \times 61 + 1}} \times 1 \\ \overset{↓}{{(7)}^{4 \times 61} \times 7} \times 1 \\ \overset{↓}{{(1)}^{61} \times 7} \times 1 \end{aligned}$ unit digit = 7

602.

Which is not a prime number ?

(A) 13
(B) 19
(C) 21
(D) 17

603.

The quotient when 10¹⁰⁰ is divided by 5⁷⁵ is:

(A) 1025
(B) 275
(C) 275 × 1025
(D) 225 × 1075

Solution: $\begin{aligned} \frac{10^{100}}{5^{75}} \\ = \frac{2^{100} \times 5^{100}}{5^{75}} \\ = 2^{100} \times 5^{25} \\ = 2^{25} \times 2^{75} \times 5^{25} \\ = 2^{75} \times 10^{25} \end{aligned}$

604.

When 100²⁵ - 25 is written in decimal notation, the sum of its digits is :

(A) 444
(B) 445
(C) 446
(D) 448

Solution: 10025 - 25 = (102)25 - 25 = 1050 - 25 $= \underset{50 zeros}{\underset{⏟}{1000 . . . . .00}} - 25$ $= \underset{48 times}{\underset{⏟}{9999 . . . . . 9975}}$ ∴ Sum of digits = (48 × 9) + 7 + 5 = 432 + 7 + 5 = 444

605.

If the numbers $\sqrt[3]{9}, \sqrt[4]{2} 0, \sqrt[6]{25}$ ÃÂÃÂ are arranged in ascending order, then the right arrangement is -

(A) $\sqrt[6]{25}, \sqrt[4]{20}, \sqrt[3]{9}$
(B) $\sqrt[3]{9}, \sqrt[4]{20}, \sqrt[6]{25}$
(C) $\sqrt[6]{25}, \sqrt[3]{9}, \sqrt[4]{20}$
(D) $\sqrt[4]{20}, \sqrt[3]{9}, \sqrt[6]{25}$

Solution: $\sqrt[3]{9}, \sqrt[4]{20}, \sqrt[6]{25}$ Taking L.C.M of 3, 4 and 6 $\begin{aligned} = \sqrt[12]{9^{4}}, \sqrt[12]{20^{3}}, \sqrt[12]{25^{2}} \\ = \sqrt[12]{6561}, \sqrt[12]{8000}, \sqrt[12]{625} \end{aligned}$ So, ascending order $= \sqrt[6]{25}, \sqrt[3]{9}, \sqrt[4]{20}$

606.

The HCF and LCM of two numbers are 44 and 264 respectively. If the first number is divided by 2, the quotient is 44. The other number is:

(A) 147
(B) 528
(C) 132
(D) 264

607.

The divisor is 25 times the quotient and 5 times the remainder. If the quotient is 16, then the dividend is :

(A) 400
(B) 480
(C) 6400
(D) 6480

Solution: Quotient = 16, Divisor = (25 × 16) = 400 5 × Remainder = Divisor ⇒ Remainder = $\frac{400}{5}$ = 80 Divided = (400 × 16) + 80 = 6480

608.

On a road three consecutive traffic lights change after 36, 42 and 72 seconds respectively. If the lights are first switched on at 9:00 AM sharp, at what time will they change simultaneously?

(A) 9:08:04
(B) 9:08:24
(C) 9:08:44
(D) None of these

609.

Let x be the least number which when divided by 15,18, 20 and 27, the remainder in each case is 10 and x is a multiple of 31. What least number should be added to x to make it a perfect square?

(A) 39
(B) 37
(C) 43
(D) 36

610.

$\frac{1}{5}$ of a number exceeds $\frac{1}{7}$ of the same number by 10. The number is -

(A) 25
(B) 150
(C) 175
(D) 200

Solution: Let, the number be 'x' According to the question $\begin{aligned} \frac{1}{5} x - \frac{1}{7} x = 10 \\ \frac{7 x - 5 x}{35} = 10 \\ 2 x = 350 \\ x = \frac{350}{2} \\ x = 175 \end{aligned}$

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Practice MCQ Questions and Answer on Number System

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