Q15. Number of prime factors in (216)3/5 x (2500)2/5 x (300)1/5 is:
A. 8
B. 7
C. 6
D. None of these
Answer- Option 7
Explanation-
Given, (216)3/5 x (2500)2/5 x (300)1/5 = (33 x 23)3/5 x (54 x 22)2/5 x (52 x 22 x 3)1/5
= 3(3 x 3/5) x 2(3 x 3/5) x 5(4 x 2/5) x 2(2 x 2/5) x 5(2 x 1/5) x 2(2 x 1/5) x 31/5
= 39/5 x 29/5 x 58/5 x 24/5 x 52/5 x 22/5 x 31/5
= 3(9/5 + 1/5) x 2(9/5 + 4/5 + 2/5) x 5(8/5 + 2/5)
= 32 x 23 x 52. Hence, the number of prime factors = (2 + 3 + 2) = 7.
Q16. If abc = 1, then = ?
A. 1
B.
1 ab
C. ab
D. 0
Answer- Option A
Explanation-
Given expression = =
1 + a + b-1 1 + a + b-1
= 1.
Q17. If 2n - 1 - 2n + 1 = 320, then n is equal to:
= ?
= ?