NDA MATHEMATICS QUIZ

Question 1:

Equation of the normal to the ellipse $9 x^{2}+16 y^{2}=180$ at the point $(2,3)$ is

$4 y=8 x-4$

$3 y-8 x-7=0$

$3 y-8 x+7=0$

$3 x+2 y+11=0$

Question 2:

Equation of the hyperbola having its accetricity 2 and the distance between the focii is will be

$\frac{x^{2}}{4}-\frac{y^{2}}{12}=1$

$\frac{x^{2}}{12}-\frac{y^{2}}{3}=1$

$\frac{x^{2}}{16}-\frac{y^{2}}{25}=1$

$\frac{x^{2}}{9}-\frac{y^{2}}{4}=1$

Question 3:

Square root of $(23-10 \sqrt{-2})$ is

$(5+\sqrt{2} i)$

$(5-\sqrt{2} i)$

$(3+\sqrt{2} i)$

$(3-\sqrt{2} i)$

Question 4:

The function $f: R_{0}^{t} \rightarrow R$ defined by $f(x)$ $=\log _{a} x(a>0)$ is

one-one only

one - one and into

abjection

Neither one - one nor onto

Question 5:

If $X=\left[\begin{array}{ll}3 & 2 \\ 2 & 5\end{array}\right]$ and $Y=\left[\begin{array}{cc}2 & 1 \\ -4 & 0\end{array}\right]$ then $(X Y)^{-1}=\ldots . .$

$\frac{1}{44}\left[\begin{array}{ll}2 & 3 \\ 16 & 2\end{array}\right]$

$\frac{1}{44}\left[\begin{array}{ll}2 & -3 \\ -16 & 2\end{array}\right]$

$\left[\begin{array}{ll}2 & -3 \\ 16 & -2\end{array}\right]$

$\frac{1}{-44}\left[\begin{array}{ll}-2 & 3 \\ -16 & 2\end{array}\right]$

Question 6:

Value of the determinant$\left|\begin{array}{ccc}a & b & c \\a+2 x & b+2 y & c+2 z \\x & y & z\end{array}\right|$ is

$x y z$

0

3

$a x+b y+c z$

Question 7:

Differential of $\log _{5}(\log x)$ w.r.t. $x$ will be

$\frac{1}{x \log x \log 5}$

$\frac{1}{5 x \log x}$

$\frac{5}{x \log x}$

$\frac{\log 5}{x \log x}$

Question 8:

If the tangent at $(2,3)$ on the curve $y^{2}=a x^{3}$ $+\mathrm{b}$ is $\mathrm{y}=4 x-5$ then value of $\mathrm{a}-\mathrm{b}$ equals

8.0

10.0

9.0

12.0

Question 9:

It the line $y=\mathrm{k} x$ is out side the circle $x^{2}+\mathrm{y}^{2}$ $-20 y+90=0$, then

$|k|>2$

$|k|=3$

$|k|<3$

$|k|>3$

Question 10:

Equation of common tangent to the parabola $y^{2}=4 a x$ and the circle $x^{2}+y^{2}=4 a x$ will be

$\mathrm{y}=x$

$\mathrm{y}=x+1$

$y=2 x+3$

None of these