NDA MATHEMATICS QUIZ - 9

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Question 1:

The term independent of $t$ in the expansion of $(1+t)^{a} \cdot\left(1+\frac{1}{t}\right)^{b}$ is.

Question 2:

In the expansion of (1+x)m+n  where m, n are positive integers ; Consider the following statements.

(I) The coefficient of $x^{m}$ is $a_{m}$ and

(II) The coefficient of $x^{n}$ is $b_{n}$ then

Question 3:

In the expansion of $\left(1+2 x+x^{2}\right)^{\mathrm{n}}$ the coefficient of $x^{n}$ in the middle term will be.

Question 4:

If $(1+x)^{n}={ }^{n} C_{0}+{ }^{n} C_{1} x+{ }^{n} C_{2} x^{2}+\ldots \ldots \ldots+{ }^{n} C_{n} \cdot x^{n}$ then value of $\mathrm{C}_{0}^{2}+\mathrm{C}_{1}^{2}+\mathrm{C}_{2}^{2}+\mathrm{C}_{3}^{2}+\ldots \ldots . .+\mathrm{C}_{\mathrm{n}}^{2}$ equals

Question 5:

The remainder when $2^{2001}$ is divided by 17 is:

Question 6:

If in the expansion of $(1+x)^{46}$. The coefficient of $(2 r+1)^{\text {th }}$ term is equal to the coefficient of $(r+2)^{\text {th }}$ term then r equals

Question 7:

Which term will be independent of $x$ in the expansion of $\left(\frac{2}{3} x^{2}-\frac{7}{x}\right)^{9}$ ?

Question 8:

Value of ${ }^{8} \mathrm{c}_{1}+{ }^{8} \mathrm{c}_{2}+{ }^{8} \mathrm{c}_{3}+\cdots+{ }^{8} \mathrm{c}_{8}$ is.

Question 9:

In the expansion of $(1+x)^{n}$ the sum of coefficients is 4096 then the greatest coefficients in the expansion is.

Question 10:

If the coefficients of second, third and the fourth terms in the expansion of $(1+x)^{n}$ are in A.P. then $\mathrm{n}$ equals.....

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