Number System - Study Mode

[#276] What should come in place of * mark in the following equation ? 1 * 5 $ 4 ÷ 148 = 78
Correct Answer

(A) 1

Explanation

Solution: Let , xa0 $$frac{1x5y4}{148}$$ = 78 Then, 10000 + 1000x + 500 + 10y + 4 = 148 × 78 ⇒ 10000 + 1000x + 500 + 10y + 4 = 11544 ⇒ 10000 + 1000x + 500 + 10y + 4 = 10000 + 1000 + 500 + 40 + 4 ⇒ 1000x = 1000 ⇒ x = 1

[#277] 2 - 2 + 2 - 2 + ..... 101 terms = ?
Correct Answer

(C) 2

Explanation

Solution: The given series is such that the sum of first hundred terms is zero, and 101 st term is 2. So, the sum of 101 terms is 2.

[#278] The number formed from the last two digits (ones and tens) of the expression 2 12n - 6 4n , where n is any positive integer is :
Correct Answer

(B) 00

Explanation

Solution: We have : (2 12n - 6 4n ) = (2 12n - 2 4n × 3 4n ) = 2 4n (2 8n - 3 4n ) Putting n = 1, we get the number 2 4 (2 8 - 3 4 ) = 16 (256 - 81) = (16 × 175) = 2800 Hence, the number formed by last two digits is 00

[#279] If x, y, z and w be the digits of a number beginning from the left, the number is :
Correct Answer

(D) 10 3 x + 10 2 y + 10z + w

Explanation

Solution: Let the thousand's, hundred's, ten's, and one's digits be x, y, z, w respectively. Then, the number is 1000x + 100y + 10z + w = 10 3 x + 10 2 y + 10z + w

[#280] The digit in the unit place of the number represented by (7 95 - 3 58 ) is :
Correct Answer

(B) 4

Explanation

Solution: Unit digit of 7 4 is 1. So, the unit digit of (7 4 ) 23 is 1 ∴ Unit digit of 7 95 = Unit digit of (7 92 × 7 3 ) = (1 × 3) = 3 Unit digit of 3 4 is 1 So, the unit digit of (3 4 ) 14 is 1 ∴ Unit digit of 3 58 = unit digit of (3 56 × 3 2 ) = (1 × 9) = 9 Hence, the unit digit of (7 95 - 3) = (13 - 9) = 4