The value of $\sin^{6}x+\cos^{6}x+3\sin^{2}x\cos^{2}x$ is …

1

If $\sin\theta+\csc\theta=2$, then $\sin^{n}\theta+\csc^{n}\theta$ equals …

Topic: JAMIA MCA 2017

2

Let $z$ be a complex number. Which of the following is a solution of $|z|-z=1+2i$?

Topic: JAMIA MCA 2017

3

If $\omega$ is a cube root of unity, the value of $(1-\omega-\omega^{2})(1+\omega^{3})$ is …

Topic: JAMIA MCA 2017

4

For which value of $x$, $\left(\dfrac{1+i}{1-i}\right)^{x}=1$ ?

Topic: JAMIA MCA 2017

5

The $\dfrac{(\sqrt3+i)^{17}}{(1-i)^{50}}$ is equal to …

Topic: JAMIA MCA 2017

6

Let $z=\sqrt{3}+i$ be a complex number and $\bar z$ its conjugate. The $|\arg z|+|\arg \bar z|$ is equal to

Topic: JAMIA MCA 2017

7

Let $A=\{1,2,3,4\}$ and $B=\{a,b\}$. The number of surjective mappings from A to B is

Topic: JAMIA MCA 2017

8

Let cardinality of A and B are 3 and 10 respectively. The number of one-to-one functions from A to B is

Topic: JAMIA MCA 2017

9

If $g:\mathbb{R}\to\mathbb{R}$ is defined by $g(x)=x^{2}-2$, then the value of $g^{-1}(23)$ is

Topic: JAMIA MCA 2017

10

Let $f:\mathbb{R}\to\mathbb{R}$ be defined by $f(x)=x^{2}+5$. Then the value of $f^{-1}(4)$ is

Topic: JAMIA MCA 2017

1

If $x=a\cos^{2}\theta\sin\theta$ and $y=a\sin^{2}\theta\cos\theta$, then $(x^{2}+y^{2})^{3}$ is …

Topic: JAMIA MCA 2017

2

The minimum value of $3\cos\theta+4\sin\theta+10$ is equal to …

Topic: JAMIA MCA 2017

3

$\sin6^\circ\,\sin42^\circ\,\sin66^\circ\,\sin78^\circ$ is equal to …

Topic: JAMIA MCA 2017

4

If $y=\tan^{-1}\!\left(\dfrac{1+x}{1-x}\right)$, then $\dfrac{dy}{dx}$ equals …

Topic: JAMIA MCA 2017

5

If $y=\log(\tan x)$, then $\dfrac{dy}{dx}$ equals …

Topic: JAMIA MCA 2017

6

If $y=\cos^{-1}x$ and $z=\sin^{-1}\!\sqrt{1-x^{2}}$, then $\dfrac{dy}{dz}$ equals …

Topic: JAMIA MCA 2017

7

If $y=e^{2x}$, then $\dfrac{d^{2}y}{dx^{2}}\cdot\dfrac{d^{2}x}{dy^{2}}$ equals …

Topic: JAMIA MCA 2017

8

If $\sqrt{x+y}+\sqrt{\,y-x\,}=\sqrt2$, then $\dfrac{d^{2}y}{dx^{2}}$ equals …

Topic: JAMIA MCA 2017

9

$\displaystyle \lim_{x\to0}\frac{1-\cos x}{x^{2}}$ is equal to …

Topic: JAMIA MCA 2017

10

$\displaystyle \lim_{x\to\infty}\Big(x-\sqrt{x^{2}+x}\,\Big)$ is equal to …

Topic: JAMIA MCA 2017