Binomial Theorem · Mathematics · WB JEE
MCQ (Single Correct Answer)
If the magnitude of the coefficient of x7 in the expansion of $${\left( {a{x^2} + {1 \over {bx}}} \right)^8}$$, where a, b are positive numbers, is equal to the magnitude of the coefficient of x7 in the expansion of $${\left( {ax + {1 \over {b{x^2}}}} \right)^8}$$, then a and b are connected by the relation
If $${}^{16}{C_r} = {}^{16}{C_{r + 1}}$$, then the value of $${}^r{P_{r - 3}}$$ is
The coefficient of x$$-$$10 in $${\left( {{x^2} - {1 \over {{x^3}}}} \right)^{10}}$$ is
If C0, C1, C2, ......, Cn denote the coefficients in the expansion of (1 + x)n then the value of C1 + 2C2 + 3C3 + ..... + nCn is
If the coefficients of x2 and x3 in the expansion of (3 + ax)9 be same, then the value of a is
using binomial theorem, the value of (0.999)3 correct to 3 decimal places is
$$({2^{3n}} - 1)$$ will be divisible by $$(\forall n \in N)$$
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
Sum of the last 30 coefficients in the expansion of (1 + x)59, when expanded in ascending powers of x is
If $${(1 - x + {x^2})^n} = {a_0} + {a_1}x + {a_2}{x^2} + \,\,....\,\,{a_{2n}}{x^{2n}}$$, then the value of $${a_0} + {a_2} + {a_4} + \,\,....\,\,{a_{2n}}$$ is
The coefficient of xn om the expansion of $${{{e^{7x}} + {e^x}} \over {{e^{3x}}}}$$ is
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 to
If n > 1 is an integer and x $$\ne$$ 0, then (1 + x)n $$-$$ nx $$-$$ 1 is divisible by
If $$\left(1+x+x^2+x^3\right)^5=\sum_\limits{k=0}^{15} a_k x^k$$ then $$\sum_\limits{k=0}^7(-1)^{\mathbf{k}} \cdot a_{2 k}$$ is equal to
The coefficient of $$a^{10} b^7 c^3$$ in the expansion of $$(b c+c a+a b)^{10}$$ is
The number of zeros at the end of $$\left| \!{\underline {\, {100} \,}} \right. $$ is
of (1 + x)15, then the value of $${{{c_1}} \over {{c_0}}} + 2{{{c_2}} \over {{c_1}}} + 3{{{c_3}} \over {{c_2}}} + ... + 15{{{c_{15}}} \over {{c_{14}}}}$$ is