Integer Answer Type Questions for JEE: Sequences & Series | Chapter-wise Tests for JEE Main & Advanced PDF Download

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Q.1. If the runs scored in the k^th match are k. 2^n+1-k and total runs scored in n matches is  then the number of matches played is

Ans. 7
Let S_n = total runs scored

Q.2. The interior angles of a polygon are in arithmetic progression. The smallest angle is 120° and the common difference is 5°. Find the number of sides of the polygon.

Ans. 9
Sum of the exterior angles of a polygon is 360°.
Also the greatest exterior angle is 60°.

Q.3. If a, b, c are in H.P., then the value of  is

Ans. 2
a, b, c are in H.P.


Again a, b, c are in H.P.

From (A) and (B),

Alternative solution:
We have

Q.4. Let a₁,a₂,....a₁₀ be in A.P. and h₁ ,h₂ ,...., h₁₀ be in H.P. If a₁₌ h₁ = 2 and a₁₀ = h₁₀ = 3, then a₄ h₇ is

Ans. 6

Q.5. Let S_n denote the sum of the first n terms of an A.P. if S_2n = 3S_n , then find the value of S_3n/S_n is ...

Ans. 6
Given S_2n = 3S_n

Now,

Q.6. If the sum of n terms of an A.P. is 2n² + n, then the common difference of the series is

Ans. 4


Compare the coeff of n²
d = 4 

Q.7. The value of  is

Ans. 4
We have,

Q.8. If the sum to infinity of the series  is 44/9, then the value of d is ....

Ans. 2

Q.9. An infinite G. P. has first term x and sum 5. Then, the number of integral value of x is

Ans. 9

For finite value of | r | <1

⇒ - 5 < x - 5 < 5 ⇒ 0 < x < 10 ⇒ x has 9 integrals values.

Q.10. The largest positive term of the H.P. whose first two terms are 2/5 and 12/23 is....

Ans. 6