Number System - Study Mode

[#366] If a and b are two numbers such that ab = 0, then -
Correct Answer

(B) a = 0 or b = 0 or both

Explanation

Solution: ab = 0 ⇒ a = 0 or b = 0 or both are zero

[#367] The number of zeros at the end of 60! is :
Correct Answer

(B) 14

Explanation

Solution: Clearly, highest power of 2 is much higher as compared to that of 5 in 60!, So, Required number of zeros = Highest power of 5 = $$ left[ {frac{{60}}{5}}
ight] + left[ {frac{{60}}{{{5^2}}}}
ight]$$ = 12 + 2 = 14

[#368] In a division problem, the divisor is 7 times of quotient and 5 times of remainder. If the dividend is 6 times of remainder, then the quotient is equal to :
Correct Answer

(B) 1

Explanation

Solution: Divisor : = 7 × quotient = 5 × remainder and dividend = 6 × remainder Let remainder be x Then, divisor = 5x and dividend = 6x On dividing 6x by 5x, we get 1 as quotient and x as remainder. ∴ Quotient = 1

[#369] What should be the maximum value of q in the following equation? 5P9 - 7Q2 + 9R6 = 823
Correct Answer

(C) 7

Explanation

Solution: ⇒ 5P9 - 7Q2 + 9R6 = 823 ⇒ (500 + 10P + 9) - (700 + 10Q + 2) + (900 + 10R + 6) = 823 ⇒ (500 + 900 - 700) + 10 (P + R - Q) + (9 + 6 - 2) = 823 ⇒ 700 + 10 (P + R - Q) = 810 ⇒ 700 + 10 (P + R - Q) = 700 + 110 ⇒ 10 (P + R - Q) = 110 ⇒ P + R - Q = 11 ⇒ Q = (P + R - 11) To get maximum value of Q we take P = 9 and R = 9 This gives Q = (9 + 9 - 11) = 7 Hence, the maximum value of Q is 7

[#370] If 37 X 3 is a four-digit natural number divisible by 7, then the place marked as X must have the value :
Correct Answer

(A) 0

Explanation

Solution: 37 × 3 is divisible by 7 ⇒ (7 × 3 - 3) is either 0 or divisible by 7 ⇒ 7 × 0 is divisible by 7 ⇒ X = 0 or X = 7