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WB JEE

Mathematical Induction and Binomial Theorem

Mathematics

Previous Years Questions

MCQ (Single Correct Answer)

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The number of zeros at the end of $$\left| \!{\underline {\, {100} \,}} \right. $$ is
WB JEE 2022
The coefficient of a3b4c5 in the expansion of (bc + ca + ab)6 is
WB JEE 2021
For x$$\in$$R, x $$\ne$$ $$-$$1, if $${(1 + x)^{2016}} + x{(1 + x)^{2015}} + {x^2}{(1 + x)^{2014}} + ..... + {x^{2016}} ...
WB JEE 2021
If c0, c1, c2, ......, c15 are the binomial coefficients in the expansion of (1 + x)15, then the value of $${{{c_1}} \ov...
WB JEE 2020
If n > 1 is an integer and x $$\ne$$ 0, then (1 + x)n $$-$$ nx $$-$$ 1 is divisible by
WB JEE 2011
If A and B are coefficients of xn in the expansions of (1 + x)2n and (1 + x)2n $$-$$ 1 respectively, then A/B is equal t...
WB JEE 2011
The number (101)100 $$-$$ 1 is divisible by
WB JEE 2011
The coefficient of xn om the expansion of $${{{e^{7x}} + {e^x}} \over {{e^{3x}}}}$$ is
WB JEE 2011
If $${(1 - x + {x^2})^n} = {a_0} + {a_1}x + {a_2}{x^2} + \,\,....\,\,{a_{2n}}{x^{2n}}$$, then the value of $${a_0} + {a_...
WB JEE 2010
Sum of the last 30 coefficients in the expansion of (1 + x)59, when expanded in ascending powers of x is...
WB JEE 2010
If in the expansion (a $$-$$ 2b)n, the sum of the 5th and 6th term is zero, then the value of $${a \over b}$$ is...
WB JEE 2010
$$({2^{3n}} - 1)$$ will be divisible by $$(\forall n \in N)$$
WB JEE 2010
using binomial theorem, the value of (0.999)3 correct to 3 decimal places is
WB JEE 2009
If the coefficients of x2 and x3 in the expansion of (3 + ax)9 be same, then the value of a is...
WB JEE 2009
If C0, C1, C2, ......, Cn denote the coefficients in the expansion of (1 + x)n then the value of C1 + 2C2 + 3C3 + ........
WB JEE 2009
For each n $$\in$$ N, 23n $$-$$ 1 is divisible by here N is a set of natural numbers.
WB JEE 2009
Product of any r consecutive natural numbers is always divisible by
WB JEE 2009
The coefficient of x$$-$$10 in $${\left( {{x^2} - {1 \over {{x^3}}}} \right)^{10}}$$ is
WB JEE 2008
If $${}^{16}{C_r} = {}^{16}{C_{r + 1}}$$, then the value of $${}^r{P_{r - 3}}$$ is
WB JEE 2008
If the magnitude of the coefficient of x7 in the expansion of $${\left( {a{x^2} + {1 \over {bx}}} \right)^8}$$, where a,...
WB JEE 2008

MCQ (More than One Correct Answer)

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The remainder when $${7^{{7^{{7^{{{..}^7}}}}}}}$$ (22 time 7) is divided by 48 is
WB JEE 2021

Subjective

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Prove by induction that for all n $$\in$$ N, n2 + n is an even integer (n $$\ge$$ 1).
WB JEE 2010
Show that, for a positive integer n, the coefficient of xk (0 $$\le$$ k $$\le$$ n) in the expansion of 1 + (1 + x) + (1 ...
WB JEE 2009
$$A = \left[ {\matrix{ 1 & 2 \cr 0 & 1 \cr } } \right]$$ then by the principle of mathematical induction, pr...
WB JEE 2008

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