# NDA MATHEMATICS QUIZ-8

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## Question 1:

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

## Question 2:

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

## 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

## Question 4:

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

## 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?

## Question 6:

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

## Question 7:

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

## Question 8:

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

## 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:

## 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?