# MCQ | Progression & Series

Practice Test-I

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

Click to See Answer :
Ans: (A)

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

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Ans: (C)

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

Click to See Answer :
Ans: (B)

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

Click to See Answer :
Ans: (B)

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

Click to See Answer :
Ans: (A)

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

Click to See Answer :
Ans: (B)

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

Click to See Answer :
Ans: (A)

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

Click to See Answer :
Ans: (D)

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}$(D) none of these Click to See Answer : Ans: (C) Q:10. If$\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

Click to See Answer :
Ans: (D)

Click to See All Answers :
1. (A) 2. (C) 3. (B) 4. (B) 5. (A) 6. (B) 7. (A) 8. (D) 9. (C) 10. (D)