Exam_Focus_Math_Test

If a, b, c are in AP then

• (a) b = a + c

• (b) 2b = a + c

• (c) b² = a + c

• (d) 2b² = a + c

Three numbers form an increasing GP. If the middle term is doubled, then the new numbers are in Ap. The common ratio of GP is

• (a) 2 + √3

• (b) 2 – √3

• (c) 2 ± √3

• (d) None of these

The sum of n terms of the series (1/1.2) + (1/2.3) + (1/3.4) + …… is

• (a) n/(n+1)

• (b) 1/(n+1)

• (c) 1/n

• (d) None of these

If 1/(b + c), 1/(c + a), 1/(a + b) are in AP then

• (a) a, b, c are in AP

• (b) a², b², c² are in AP

• (c) 1/1, 1/b, 1/c are in AP

• (d) None of these

The sum of series 1/2! + 1/4! + 1/6! + ….. is

• (a) e² – 1 / 2

• (b) (e – 1)² /2 e

• (c) e² – 1 / 2 e

• (d) e² – 2 / e

The third term of a geometric progression is 4. The product of the first five terms is

• (a) 4³

• (b) 4⁵

• (c) 4⁴

• (d) none of these

Let Tr be the r th term of an A.P., for r = 1, 2, 3, … If for some positive integers m, n, we have Tm = 1/n and Tn = 1/m, then Tm n equals

• (a) 1/m n

• (b) 1/m + 1/n

• (c) 1

• (d) 0

The sum of two numbers is 13/6 An even number of arithmetic means are being inserted between them and their sum exceeds their number by 1. Then the number of means inserted is

• (a) 2

• (b) 4

• (c) 6

• (d) 8

If the sum of the roots of the quadratic equation ax² + bx + c = 0 is equal to the sum of the squares of their reciprocals, then a/c, b/a, c/b are in

• (a) A.P.

• (b) G.P.

• (c) H.P.

• (d) A.G.P.

If 1/(b + c), 1/(c + a), 1/(a + b) are in AP then

• (a) a, b, c are in AP

• (b) a², b², c² are in AP

• (c) 1/1, 1/b, 1/c are in AP

• (d) None of these