NDA MATHEMATICS QUIZ-8

Question 1:

Area on closed by the $x$ axis, $x=2$ and the curve $y = log x$ is.

$\log 4$

$2 \log 2+1$

$2 \log 2-1$

$\log 2-1$

Question 2:

The direction cosine of the line $3 x+1=2 y-2=6 z-2$ will be

$\pm\frac{1}{\sqrt{14}}, \pm\frac{2}{\sqrt{14}}, \pm\frac{3}{\sqrt{14}}$

$\pm \frac{3}{\sqrt{14}}, \pm \frac{2}{\sqrt{14}} \pm \frac{1}{14}$

$\pm \frac{1}{\sqrt{14}}, \pm \frac{1}{2 \sqrt{14}} \pm \frac{1}{3 \sqrt{14}}$

$\pm \frac{2}{\sqrt{14}}, \pm \frac{3}{\sqrt{14}}, \pm \frac{1}{\sqrt{14}}$

Question 3:

The coordinates of the point $\mathrm{P}$ on the curve $\mathrm{y}^{2}=x^{3}$ the tangent at which is parallel to the line $3 x-4 y+2=0$ is given by

$\left(\frac{1}{2}, \frac{1}{2 \sqrt{2}}\right)$

$\left(\frac{1}{4}, \frac{1}{8}\right)$

$(1,1)$

$(0,0)$

Question 4:

What is the solution of the differential equation $x d y-y d x=x y^2 d x$ ?

$y+x^{-2}=C$

$y^2+2 x^{-1}=C$

$y+x^{-1}=C$

$x^2+2 xy^{-1}=C$

Question 5:

The number of solutions of the equation $\sin 2 \theta-12(\sin \theta-\cos \theta)+12=0$

$\theta\in[0,2 \pi]$ are possible?

3.0

2.0

4.0

1.0

Question 6:

If $\tan \alpha, \tan \beta$ are the roots of $x^{2}-5 x+6=0$ then $(\alpha+\beta)$ equal to:

$\frac{\pi}{4}$

$\frac{2 \pi}{3}$

$\frac{3 \pi}{4}$

$\frac{5 \pi}{4}$

Question 7:

$\operatorname{Lt}_{x \rightarrow 0}\left(\frac{1+3 x^{2}}{1+x^{2}}\right)^{\frac{1}{x^{2}}}=\ldots \ldots$

$e^{3}$

$\mathrm{e}$

$\mathrm{e}^{2}$

$\mathrm{e}^{4}$

Question 8:

If $F(\theta)=5\left(\sin ^{4} \theta+\cos ^{4} \theta\right)$ then maximum value of $F(\theta)$ will be:

5.0

9.0

7.0

4.0

Question 9:

A certain set $X$ contains 9 elements while another set Y contains 4 elements. The minimum number of elements in $X \cup Y$ will be:

5.0

4.0

9.0

13.0

Question 10:

The frequency distribution of a discrete variable $X$ with one missing frequency $f$ is given below.

If the arithmetic mean of $X$ is $\frac{23}{8}$, then what is the value of the missing frequency?

5

6

8

10