NDA MATHEMATICS QUIZ-6

Question 1:

In $\mathrm{a}$ triangle $\mathrm{ABC} \ \; \mathrm{b}=4$ and $\frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos C}{c}$ then area of triangle $\mathrm{ABC}$ is.

$\sqrt{3}$

$3 \sqrt{3}$

$4 \sqrt{3}$

$2 \sqrt{3}$

Question 2:

If $X=\left[\begin{array}{cc}3 & -5 \\ -4 & 2\end{array}\right]$ then the value of $X^{2}-5 X-14$ is equal to.

$3 \mathrm{I}$

0.0

$2 \mathrm{X}$

None of these

Question 3:

If number of terms in the expansion of $(2 x-3 y+5 z)^{n}$ is 45 then $n$ equals

9.0

10.0

7.0

8.0

Question 4:

If $x=\frac{3 a t}{1+t^{3}} ; y=\frac{3 a t^{2}}{1+t^{2}}$ then $\frac{d y}{d x}$ at $t=\frac{1}{2}$ equal is:

$\frac{1}{4}$

$\frac{3}{4}$

$\frac{7}{4}$

$\frac{5}{4}$

Question 5:

In a class of 180 students; the following data shows the number of students opting one or more than one subjects. Mathematics 120, physics 75 and chemistry 60, mathematics and physics 35, Maths and chemistry 32 physics and chemistry 25, Mathematics, physics and chemistry 18. How many students have offered Mathematics alone?

68

71

82

56

Question 6:

How many number of 4 digits can be formed with the digits $0,1,2,3,4,5$ if the repeatition of digits is not allowed?

300.0

360.0

240.0

120.0

Question 7:

$\operatorname{Lim}_{x \rightarrow 0} \frac{2\left(1-\cos ^{3} x\right)}{x \cdot \sin 2 x}$ is equals to:

7

3

2

5

Question 8:

$\sin \frac{\pi}{18} \cdot \sin \frac{5 \pi}{18} \cdot \sin \frac{7 \pi}{18}=\ldots \ldots$

$\frac{1}{2^{3}}$

$\frac{1}{2^{2}}$

$\frac{1}{2^{4}}$

$\frac{1}{2}$

Question 9:

For what value of $\theta$; tangent to the curve $x=a \sqrt{\cos 2 \theta} . \cos \theta$ ; $ y=a \sqrt{\cos 2 \theta} \cdot \sin \theta$ is parallel to axis of $x$ ?

$\frac{\pi}{4}$

$\frac{\pi}{6}$

$\frac{\pi}{3}$

$\frac{\pi}{2}$

Question 10:

Equation of the normal to the curve $x^{3}+y^{3}=6 x y$ at the point $(3,3)$ will be

$x-y=0$

$x+y=6$

$2 x+y=9$

$2 x-y=3$