MCQ : Progression & Series

Q:1. If x , |x + 1|, |x – 1| are the three terms of an A.P its sum upto 20 terms is

(A) 90 or 175

(B) 180 or 350

(C) 360 or 700

(D) 720 or 1400

Q:2. If a, b and c are positive real numbers then $\frac{a}{b} + \frac{b}{c} + \frac{c}{a} $ is greater than or equal to

(A) 3

(B) 6

(C) 27

(D) none of these

Q:3. If a, b and c are positive real numbers, then least value of $(a + b + c)(\frac{1}{a} + \frac{1}{b} + \frac{1}{c}) $ is

(A) 9

(B) 3

(C) 10/3

(D) none of these

Q:4.The sum of the integers from 1 to 100 that are divisible by 2 or 5 is

(A) 3000

(B) 3050

(C) 3600

(D) none of these

Q:5. If the sides of a right-angled triangle form an A.P. then the sines of the acute angle is

(A) 3/5 , 4/5

(B) 3/4 , 3/5

(C) 2/5 , 3/5

(D) none of these

Q:6. If a, b , c, d and p are distinct real numbers such that
(a2 + b2 + c2)p2 – 2(ab + bc + cd ) p + (b2 + c2 + d2)  ≤ 0 , then a, b, c, d are in

(A) A.P.

(B) G.P.

(C) H. P.

(D) none of these

Q:7. If S be the sum, p the product and R the sum of the reciprocals of n terms of a G.P., then (S/R)n is equal to

(A) p2

(B) p3

(C) p

(D) none of these

Q:8. If $\large t_r = \frac{r+2}{r(r+1)}.\frac{1}{2^{r+1}}$ , then $\large \Sigma_{r=1}^{n} t_r $ is equal to

(A) $\large \frac{n 2^n – 1}{n + 1}$

(B) $\large \frac{n + 1}{2^{n + 1}(n+2)}$

(C) $\large \frac{n}{2^n} – 1$

(D) $\large \frac{(n+1) 2^n – 1}{2^{n + 1}(n+1)}$

Q:9. $\large \Sigma_{j=1}^{n} $\large \Sigma_{i=1}^{n} i $ is equal to

(A) $\large \frac{n(n+1)}{2}$

(B) $\large \frac{n(n+1)^2}{2}$

(C) $\large \frac{n^2 (n+1)}{2}$

(D) none of these

Q:10. If $\large \frac{1}{a} + \frac{1}{a-2b} + \frac{1}{c} + \frac{1}{c-2b} = 0 $ and a, b, c are not in A.P, then

(A) a, b, c are in G.P

(B) a , b/2 , c are in A.P

(C) a , b/2 , c are in H.P

(D) a, 2b, c are in H.P

Answer:  1. (A) 2. (C) 3. (B) 4. (B) 5. (A) 6. (B) 7. (A) 8. (D) 9. (C) 10. (D)