# NDA MATHEMATICS QUIZ-7

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## Question 1:

It $\vec{a}, \bar{b}, \vec{c}$ be three vectors satisfing $\vec{a}+\bar{b}+\vec{c}$ $=0$ where $|\bar{a}|=|\bar{b}|=|\vec{c}|=1$ then the angle between $\bar{b}$ and $\vec{c}$ is

## Question 2:

Solution of the differential equation $x^{2}\frac{d y}{d x}+(1-2 x) y=x^{2}$ will be

## Question 3:

$\int \frac{x d x}{(x+2) \sqrt{x+1}}$ is equal to:

## Question 4:

The number of integral points at which the function $f(x)=\frac{1}{\log \left|\left(x^{2}-1\right)\right|}$ is discontinuous is:

## Question 5:

If $\alpha \neq \beta$ but $x^2=8 x-15$, then the equation with roots $\frac{\alpha}{\beta}, \frac{\beta}{\alpha}$ is:

## Question 6:

The Number of ways it which 6 beads of different colors to form a necklace is

## Question 7:

From which point the tangents to ellipse  $9 x^{2}+16 y^{2}=144$ are perpendicular?

## Question 8:

In a class of 20 students a foot ball team of 11 players is to be selected. number of selections when a particular student is  always left will be.

## Question 9:

If the line of shortest distance between two lines passing through respectively $\left(\alpha_{1}, \beta_{1},\gamma_{1}\right)$ and $\left(\alpha_{2}, \beta_{2},\gamma_{2}\right)$ is having $l, m, n$ as the direction cosines then the length of shortest distance between the lines will be

## Question 10:

If $\cos ^{-1} \frac{\alpha}{2}+\cos ^{-1} \frac{\beta}{3}=x$ then value of $9 \alpha^{2}-12 \alpha \beta \cos x+4 \beta^{2}$ is.