MCQ (Single Correct Answer)

1

If the mth term and the nth term of an A.P. are respectively $${1 \over n}$$ and $${1 \over m}$$, then the (mn)th term of the A.P. is

WB JEE 2008
2

The sum of the series $$(1 + 2) + (1 + 2 + {2^2}) + (1 + 2 + {2^2} + {2^3}) + ....$$ upto n terms is

WB JEE 2008
3

The 5th term of the series $${{10} \over 9},{1 \over 3}\sqrt {{{20} \over 3}} ,{2 \over 3}$$ is

WB JEE 2008
4

If a, b, c be in Arithmetic progression, then the value of $$(a + 2b - c)(2b + c - a)(a + 2b + c)$$ is

WB JEE 2008
5

If three real numbers a, b, c are in Harmonic Progression, then which of the following is true?

WB JEE 2008
6

The sum of the infinite series $${\left( {{1 \over 3}} \right)^2} + {1 \over 3}{\left( {{1 \over 3}} \right)^4} + {1 \over 5}{\left( {{1 \over 3}} \right)^6} + ...$$ is

WB JEE 2008
7

If a, b, c are G.P. (a > 1, b > 1, c > 1), then for any real number x (with x > 0, x $$\ne$$ 1) logax, logbx, logcx are in

WB JEE 2009
8

If three positive real numbers a, b, c are in A.P. and abc = 4 then the minimum possible value of b is

WB JEE 2009
9

For what value of m, $${{{a^{m + 1}} + {b^{m + 1}}} \over {{a^m} + {b^m}}}$$ is the arithmetic mean of a and b?

WB JEE 2009
10

The coefficient of xn, where n is any positive integer, in the expansion of (1 + 2x + 3x2 + ....... $$\infty$$)1/2 is

WB JEE 2009
11

The sum of the infinite series $$1 + {1 \over {2!}} + {{1\,.\,3} \over {4!}} + {{1\,.\,3\,.\,5} \over {6!}} + \,....$$ is

WB JEE 2009
12

If sum of an infinite geometric series is $${4 \over {3}}$$ and its 1st term is $${3 \over {4}}$$, then its common ratio is

WB JEE 2010
13

Sum of n terms of the following series 13 + 33 + 53 + 73 ......... is

WB JEE 2010
14

G.M. and H.M. of two numbers are 10 and 8 respectively. The numbers are

WB JEE 2010
15

The value of n for which $${{{x^{n + 1}} + {y^{n + 1}}} \over {{x^n} + {y^n}}}$$ is the geometric mean of x and y is

WB JEE 2010
16

If angles A, B and C are in A.P., then $${{a + c} \over b}$$ is equal to

WB JEE 2010
17

The value of $${2 \over {3!}} + {4 \over {5!}} + {6 \over {7!}} + $$ ............ is

WB JEE 2010
18
The value of $$\sum\limits_{r = 2}^\infty {{{1 + 2 + .... + (r - 1)} \over {r!}}} $$
WB JEE 2012
19

If the sum of ' $n$ ' terms of an A.P. is $3 n^2+5 n$ and its $m$ th term is 164 , then the value of $m$ is

WB JEE 2025
20

The sum of the first four terms of an arithmetic progression is 56 . The sum of the last four terms is 112. If its first term is 11, then the number of terms is

WB JEE 2025
21

If $a, b, c$ are in A.P. and if the equations $(b-c) x^2+(c-a) x+(a-b)=0$ and $2(c+a) x^2+(b+c) x=0$ have a common root, then

WB JEE 2025
22

Given an A.P. and a G.P. with positive terms, with the first and second terms of the progressions being equal. If $$a_n$$ and $$b_n$$ be the $$n^{\text {th }}$$ term of A.P. and G.P. respectively then

WB JEE 2024
23

If for the series $$a_1, a_2, a_3$$, ...... etc, $$\mathrm{a}_{\mathrm{r}}-\mathrm{a}_{\mathrm{r}+\mathrm{i}}$$ bears a constant ratio with $$\mathrm{a}_{\mathrm{r}} \cdot \mathrm{a}_{\mathrm{r}+1}$$; then $$\mathrm{a}_1, \mathrm{a}_2, \mathrm{a}_3 \ldots .$$. are in

WB JEE 2024
24

If $$\alpha_1, \alpha_2, \ldots, \alpha_n$$ are in A.P. with common difference $$\theta$$, then the sum of the series $$ \sec \alpha_1 \sec \alpha_2+\sec \alpha_2 \sec \alpha_3+\ldots .+\sec \alpha_{n-1} \sec \alpha_n=k\left(\tan \alpha_n-\tan \alpha_1\right)$$ where $$\mathrm{k}=$$

WB JEE 2024
25

If the n terms $${a_1},{a_2},\,......,\,{a_n}$$ are in A.P. with increment r, then the difference between the mean of their squares & the square of their mean is

WB JEE 2023
26

If $$1,{\log _9}({3^{1 - x}} + 2),{\log _3}({4.3^x} - 1)$$ are in A.P., then x equals

WB JEE 2023
27

Consider a quadratic equation $$a{x^2} + 2bx + c = 0$$ where a, b, c are positive real numbers. If the equation has no real root, then which of the following is true?

WB JEE 2023
28

Let $${a_1},{a_2},{a_3},\,...,\,{a_n}$$ be positive real numbers. Then the minimum value of $${{{a_1}} \over {{a_2}}} + {{{a_2}} \over {{a_3}}}\, + \,...\, + \,{{{a_n}} \over {{a_1}}}$$ is

WB JEE 2023
29

If a, b, c are in G.P. and log a $$-$$ log 2b, log 2b $$-$$ log 3c, log 3c $$-$$ log a are in A.P., then a, b, c are the lengths of the sides of a triangle which is

WB JEE 2022
30

Let $${a_n} = {({1^2} + {2^2} + .....\,{n^2})^n}$$ and $${b_n} = {n^n}(n!)$$. Then

WB JEE 2022
31
Let a, b, c be real numbers, each greater than 1, such that $${2 \over 3}{\log _b}a + {3 \over 5}{\log _c}b + {5 \over 2}{\log _a}c = 3$$. If the value of b is 9, then the value of 'a' must be
WB JEE 2021
32
Consider the real valued function h : {0, 1, 2, ...... 100} $$\to$$ R such that h(0) = 5, h(100) = 20 and satisfying h(p) = $${1 \over 2}$$ {h(p + 1) + h(p $$-$$ 1)} for every p = 1, 2 ..... 99. Then the value of h(1) is
WB JEE 2021
33
The digit in the unit's place of the number 1! + 2! + 3! + .... + 99! is
WB JEE 2021
34
Three unequal positive numbers a, b, c are such that a, b, c are in G.P. while $$\log \left( {{{5c} \over {2a}}} \right),\log \left( {{{7b} \over {5c}}} \right),\log \left( {{{2a} \over {7b}}} \right)$$ are in A.P. Then a, b, c are the lengths of the sides of
WB JEE 2021
35
If a and b are arbitrary positive real numbers, then the least possible value of $${{6a} \over {5b}} + {{10b} \over {3a}}$$ is
WB JEE 2020
36
Let I(n) = nn, J(n) = 13.5 ......... (2n $$ - $$ 1) for all (n > 1), n $$ \in $$ N, then
WB JEE 2020
37
Given that n numbers of arithmetic means are inserted between two sets of numbers a, 2b and 2a, b where a, b $$ \in $$ R. Suppose further that the mth means between these sets of numbers are same, then the ratio a : b equals
WB JEE 2018
38
In a GP series consisting of positive terms, each term is equal to the sum of next two terms. Then, the common ratio of this GP series is
WB JEE 2017
39
If a, x are real numbers and | a | < 1, | x | < 1, then 1 + (1 + a) x + (1 + a + a2) x2 + ..... $$\infty $$ is equal to
WB JEE 2016
40
The sum of n terms of the following series $${1^3} + {3^3} + {5^3} + {7^3} + ...$$ is
WB JEE 2016

Subjective

MCQ (More than One Correct Answer)

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