NDA MATHEMATICS QUIZ - 10

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Question 1:

If number of terms in the expansion of $(2 x-3 y+5 z)^{n}$ is 45 then $n$ equals

Question 2:

Total number of terms in the expansion of $(a+1)^{200}+(1-a)^{200}$ is:

Question 3:

$\left(2^{3 n}-1\right)$ will be divisible by-

Question 4:

Value of $(\sqrt{2}+1)^{5}-(\sqrt{2}-1)^{5}$ is:

Question 5:

The approximate value of $(1.0004)^{2000}$ is:

Question 6:

The coefficient of $x^{54}$ in the expansion of $\sum_{k=0}^{200}{ }^{200} c_{k}(x-3)^{200-k} \cdot 2^{k}$ is:

Question 7:

In the polynomial $(\alpha -1)(\alpha-2)(\alpha-3) \ldots . .(\alpha-100)$. The coefficient of $\alpha^{99}$ is:

Question 8:

Consider $\left(1+\mathrm{p}+\mathrm{p}^{2}\right)^{2 \mathrm{n}}=\sum_{\mathrm{r}=0}^{4 \mathrm{n}} \mathrm{b}_{\mathrm{r}} \mathrm{p}^{\mathrm{r}}$ where $b_{0}, b_{1}, b_{2}, \ldots \ldots b_{4 n}$ are real numbers and $n$ is a positive integer then answer the following questions.

Value of $b_{2}$ is:

Question 9:

Consider $\left(1+\mathrm{p}+\mathrm{p}^{2}\right)^{2 \mathrm{n}}=\sum_{\mathrm{r}=0}^{4 \mathrm{n}} \mathrm{b}_{\mathrm{r}} \mathrm{p}^{\mathrm{r}}$ where $b_{0}, b_{1}, b_{2}, \ldots \ldots b_{4 n}$  are real numbers and $n$ is a positive integer then answer the following question.

The value of $b_{4 n-1}$ is:

Question 10:

Consider $\left(1+\mathrm{p}+\mathrm{p}^{2}\right)^{2 \mathrm{n}}=\sum_{\mathrm{r}=0}^{4 \mathrm{n}} \mathrm{b}_{\mathrm{r}} \mathrm{p}^{\mathrm{r}}$ where $b_{0}, b_{1}, b_{2}, \ldots \ldots b_{4 n}$  are real numbers and $n$ is a positive integer then answer the following question.

Which of the following statement is correct?

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