Let $S=\{1,2,\ldots,20\}$. A subset $B$ of $S$ is said to be “nice”, if the sum of the elements of $B$ is $203$. Then the probability that a randomly chosen subset of $S$ is “nice” is :

1

If a hyperbola has length of its conjugate axis equal to $5$ and the distance between its foci is $13$, then the eccent…

Topic: JEE Main 2019 (11 January Evening Shift)

2

Let $x, y$ be positive real numbers and $m, n$ positive integers. The maximum value of the expression $\dfrac{x^m y^n…

Topic: JEE Main 2019 (11 January Evening Shift)

1

Let the length of the latus rectum of an ellipse with its major axis along the $x$-axis and centre at the origin be $8$…

Topic: JEE Main 2019 (11 January Evening Shift)

2

Let $f(x)=\dfrac{x}{\sqrt{a^{2}+x^{2}}}-\dfrac{d-x}{\sqrt{b^{2}+(d-x)^{2}}},\ x\in\mathbb{R}$, where $a,b,d$ are non-ze…

Topic: JEE Main 2019 (11 January Evening Shift)

3

The integral $\displaystyle \int_{\pi/6}^{\pi/4}\frac{dx}{\sin 2x\,(\tan^{5}x+\cot^{5}x)}$ equals :

Topic: JEE Main 2019 (11 January Evening Shift)

4

Let a function $f:(0,\infty)\to(0,\infty)$ be defined by $f(x)=\left|1-\dfrac{1}{x}\right|$. Then $f$ is :

Topic: JEE Main 2019 (11 January Evening Shift)

5

If $\displaystyle \int \frac{x+1}{\sqrt{2x-1}}\,dx = f(x)\,\sqrt{2x-1}+C$, where $C$ is a constant of integration, then…

Topic: JEE Main 2019 (11 January Evening Shift)

6

The area (in sq. units) in the first quadrant bounded by the parabola $y=x^{2}+1$, the tangent to it at the point $(2,5…

Topic: JEE Main 2019 (11 January Evening Shift)

7

$\displaystyle \lim_{x\to 0}\frac{x\cot(4x)}{\sin^{2}x\;\cot^{2}(2x)}$ is equal to :

Topic: JEE Main 2019 (11 January Evening Shift)

8

If \[ \begin{vmatrix} a-b-c & 2a & 2a\\ 2b & b-c-a & 2b\\ 2c & 2c & c-a-b \end{vmatrix} =(a+b+c)\,(x+a+b+c)^{2},\ x\ne…

Topic: JEE Main 2019 (11 January Evening Shift)

9

Let $\alpha$ and $\beta$ be the roots of the quadratic equation $x^{2}\sin\theta-x(\sin\theta\cos\theta+1)+\cos\theta=…

Topic: JEE Main 2019 (11 January Evening Shift)

10

Let $z$ be a complex number such that $|z|+z=3+i$ (where $i=\sqrt{-1}$). Then $|z|$ is equal to :

Topic: JEE Main 2019 (11 January Evening Shift)