NDA MATHEMATICS QUIZ-9

Question 1:

If $\mathrm{ABC}$ be a triangle than

a secB $\sec C+b \sec A \sec C+c \sec A \sec B$ is equal to:

2 a tanB + tan c

2 ab tanB $\tan A$

2 c tan A + tan B

2 a tanB tanc secA

Question 2:

Segment of the tangent to the curve $x y=1$ contained between the coordinate axes is bisected at.

$(1,1)$

$(2,1)$

$(3,1)$

At The point of tangency

Question 3:

The function $f(x)=1+x^2+x^4$ is strictly increasing for

$x<0$

$x \geq 0$

$x>0$

None of these

Question 4:

If $n=10, \Sigma x=4, \Sigma y=3, \Sigma x^2=8, \Sigma y^2=9$ and $\Sigma x y=3$, then coefficient of correlation is

$\frac{1}{4}$

$\frac{1}{6}$

$\frac{3}{4}$

$\frac{7}{3}$

Question 5:

$\int \frac{d x}{\sqrt{6 x-x^{2}}}$ equals:

$\sin ^{-1}(x-3)$

$2 \sin ^{-1}\left(x \frac{-3}{2}\right)$

$\sin ^{-1} \frac{x-3}{3}$

$\sin ^{-1}\left(\frac{x-4}{3 x}\right)$

Question 6:

If $ A = $$\left\{6^{n}-{5} n-1: n \in N\right\}$ and $B=\{25(n-1) n \in N\}$

$A=B$

$\triangle \cap B=\phi$

B $\subseteq$ A and

$\triangle $$\subseteq$ B

Question 7:

What is the value of $\sin ^{-1} \frac{4}{5}+\sec ^{-1} \frac{5}{4}-\frac{\pi}{2}$ ?

$\frac{\pi}{4}$

$\frac{\pi}{2}$

$\pi$

0

Question 8:

The number of numbers between 200 and 4000 can be formed by using the digit 0,1 , $2,3,4$ and 5 , no digit being repeated in any number is.

160.0

260.0

180.0

240.0

Question 9:

If $\mathrm{i}^{2}=-1$ then value of $\sum \mathrm{i}^{2n+1} \mathrm{}$ is equal to:

1.0

$-1$

0.0

cannot be determined

Question 10:

It $2 a+3 b=18$ and $4 a^{2}+4 a b-3 b^{2}=36$ then

$b^{2}-2 a$ is

12.0

10.0

5.0

8.0