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 these students is selected at random, then the probability that the student selected has opted neither for NCC nor for NSS is:

1

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)

2

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)

3

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)

4

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)

5

The set of all values of $\lambda$ for which the system of linear equations$x-2y-2z=\lambda x$$x+2y+z=\lambda y$$-x-y=\…

Topic: JEE Main 2019 (12 January Evening Shift)

6

The number of integral values of $m$ for which the quadratic expression $(1+2m)x^2-2(1+3m)x+4(1+m)$, $x\in\mathbb{R}$, …

Topic: JEE Main 2019 (12 January Evening Shift)

7

The total number of irrational terms in the binomial expansion of $(7^{1/5}-3^{1/10})^{60}$ is:

Topic: JEE Main 2019 (12 January Evening Shift)

8

If   nC4, nC5 and nC6 are in A.P., then n can be :

Topic: JEE Main 2019 (12 January Evening Shift)

9

If a circle of radius $R$ passes through the origin $O$ and intersects the coordinate axes at $A$ and $B$, then the loc…

Topic: JEE Main 2019 (12 January Evening Shift)

10

$\displaystyle \lim_{x\to1^-}\frac{\sqrt{x}-\sqrt{2\sin^{-1}x}}{\sqrt{1-x}}$ is equal to:

Topic: JEE Main 2019 (12 January Evening Shift)

1

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

Topic: JEE Main 2019 (12 January Evening Shift)

2

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)

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

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)

5

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)

6

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)-\…

Topic: JEE Main 2019 (12 January Evening Shift)