NDA MATHEMATICS QUIZ - 12

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Question 1:

$\int_{0}^{1} \frac{\tan ^{-1} x \cdot e^{\tan ^{-1} x}}{\left(1+x^{2}\right)} $ is equals.

Question 2:

The function defined by $f(x)=\frac{3 x}{\frac{2}{x}}+1+2 \mathrm{c}$, when $x \neq 0=0, x=0$ then $\mathrm{f}^{\prime}(0)$

Question 3:

If $X=\left[\begin{array}{ll}1 & 2 \\ 2 & 3\end{array}\right]$ and $X^{2}-k X-I_{2}=0$

then $k$ equals.

Question 4:

The function $y=x-\tan ^{-1} x$ decreases in the interval.

Question 5:

Value of the integral $\int \frac{\left(e^{x}\right) d x}{\left(e^{x}-2\right)\left(e^{2 x}-4 e^{x}+5\right)}$ is:

Question 6:

If the inverse of matrix $A=\left[\begin{array}{lll}1 & 2 & 3 \\ 4 & 5 & 6 \\ 3 & \lambda & 5\end{array}\right]$ exists then $\lambda$ must not be equal to.

Question 7:

Value of $\int_{0}^{1}$ tan $^{-1} \sqrt{x} \cdot d x$ will be

Question 8:

If $\sqrt{1-x^{2}}+\sqrt{1-y^{2}}=\alpha(x-y)$ then $\frac{d y}{d x}$ is:

Question 9:

The equation $a x^{2}+2 h x y+b y^{2}+2 g x+2 b y+c=0$ represents a pair of parallel straight lines if.

Question 10:

$\int_{\log \frac{3}{4}}^{\log _{2}} \sin \frac{a^{x}-1}{a^{x}+1} \cdot d x$ is.