NDA MATHEMATICS QUIZ

Question 1:

The number of fractional roots of the equation $\left(t+\frac{1}{t}\right)^{2}=4+\frac{3}{2}\left(t-\frac{1}{t}\right)$

2

3

1

0

Question 2:

Three dice are rolled together

the number of possible outcomes in which at least one die shows 4 is

96

120

100

91

Question 3:

The number of non negative integral solutions of $p+q+r=5$ is

48

36

21

60

Question 4:

If in a triangle $\mathrm{ABC}$ the altitudes are in H.P. then $\sin A, \sin B$ and $\sin C$ are in

H.P.

G.P.

A.P.

None of these

Question 5:

In a triangle $\mathrm{ABC}$ if $\angle \mathrm{A}=90^{\circ}$ then $\frac{b^{2}+c^{2}}{b^{2}-c^{2}} \sin (\mathrm{B}-\mathrm{C})$

2

3

1

$-2$

Question 6:

$\operatorname{Lim}_{x \rightarrow 0}\left(\frac{1+7 x^{2}}{1+4 x^{2}}\right)^{\frac{1}{x^{2}}}=\ldots \ldots$

$e^{2}$

$e^{3}$

$e^{6}$

$e^{4}$

Question 7:

The circles $x^{2}+y^{2}+2 a x+2 b y+c=0$ and $x^{2}+y^{2}+2 b x+2 a y+c=0$ will touch if $\ldots . .$

$(a+b)^{2}=2 c$

$(a-b)^{2}=2 c$

$(a+b)^{2}=2 c^{2}$

$a^{2}-b^{2}=c^{2}$

Question 8:

Equation of the tangents to the parabola $\mathrm{y}^{2}=4 \mathrm{ax}$ which makes an angle $135^{\circ}$ with its axis is

$-x+y-a=0$

$x+y=a$

$x-y=a$

$x+y=-a$

Question 9:

Focus of the parabola $x^{2}-6 x-6 y+6=0$ will be

$(2,1)$

$(3,1)$

$(1,3)$

$(4,2)$

Question 10:

Locus of point of intersection of the lines $\frac{x}{a}+\frac{y}{b}=1$ and $\frac{x}{b}+\frac{y}{a}=1$ passes possibly through

$(2,1)$

$(0,0)$

$(1,2)$

$(2,3)$