If $\sin^{4}\alpha+4\cos^{4}\beta+2=4\sqrt{2},\sin\alpha\cos\beta;\ \alpha,\beta\in[0,\pi],$ then $\cos(\alpha+\beta)-\cos(\alpha-\beta)$ is equal to:

1

Let $S$ and $S'$ be the foci of an ellipse and $B$ be any one of the extremities of its minor axis. If $\triangle S'BS$…

Topic: JEE Main 2019 (12 January Evening Shift)

2

The integral $\displaystyle \int \frac{3x^{13}+2x^{11}}{(2x^{4}+3x^{2}+1)^{4}},dx$ is equal to: (where $C$ is a constan…

Topic: JEE Main 2019 (12 January Evening Shift)

3

If the function $f$ given by $f(x)=x^3-3(a-2)x^2+3ax+7$, for some $a\in\mathbb{R}$, is increasing in $(0,1]$ and decrea…

Topic: JEE Main 2019 (12 January Evening Shift)

4

Let $Z$ be the set of integers. If $A={x\in Z:2(x+2)(x^2-5x+6)=1}$ and $B={x\in Z:-3

Topic: JEE Main 2019 (12 January Evening Shift)

5

If   A = $\left[ {\matrix{ 1 & {\sin \theta } & 1 \cr { - \sin \theta } & 1 & {\sin \…

Topic: JEE Main 2019 (12 January Evening Shift)

6

In a class of $60$ students, $40$ opted for NCC, $30$ opted for NSS and $20$ opted for both NCC and NSS. If one of thes…

Topic: JEE Main 2019 (12 January Evening Shift)

7

Let $z_1$ and $z_2$ be two complex numbers satisfying $|z_1|=9$ and $|z_2-3-4i|=4$. Then the minimum value of $|z_1-z_2…

Topic: JEE Main 2019 (12 January Evening Shift)

8

Let $f$ be a differentiable function such that $f(1)=2$ and $f'(x)=f(x)$ for all $x\in\mathbb{R}$. If $h(x)=f(f(x))$, t…

Topic: JEE Main 2019 (12 January Evening Shift)

9

If a straight line passing through the point $P(-3,4)$ is such that its intercepted portion between the coordinate axes…

Topic: JEE Main 2019 (12 January Evening Shift)

10

The mean and the variance of five observations are $4$ and $5.20$, respectively. If three of the observations are $3, 4…

Topic: JEE Main 2019 (12 January Evening Shift)