Evaluate the integral $ \displaystyle \int_{0}^{\infty}\frac{6}{e^{3x}+6e^{2x}+11e^{x}+6},dx $ is equal to:

1

The set of all $a\in\mathbb{R}$ for which the equation $x|x-1|+|x+2|+a=0$ has exactly one real root, is:

Topic: JEE Main 2023 (13 April Morning Shift)

2

A coin is biased so that the head is 3 times as likely to occur as tail. This coin is tossed until a head or three ta…

Topic: JEE Main 2023 (13 April Morning Shift)

3

Let $y=y_1(x)$ and $y=y_2(x)$ be the solution curves of the differential equation $\dfrac{dy}{dx}=y+7$ with initial con…

Topic: JEE Main 2023 (13 April Morning Shift)

4

For the system of linear equations$2 x+4 y+2 a z=b$$x+2 y+3 z=4$$2 x-5 y+2 z=8$which of the following is NOT correct?

Topic: JEE Main 2023 (13 April Morning Shift)

5

Let $\vec{a}=\hat{i}+4\hat{j}+2\hat{k}$, $\vec{b}=3\hat{i}-2\hat{j}+7\hat{k}$ and $\vec{c}=2\hat{i}-\hat{j}+4\hat{k}$. …

Topic: JEE Main 2023 (13 April Morning Shift)

6

Let $PQ$ be a focal chord of the parabola $y^{2}=36x$ of length $100$, making an acute angle with the positive $x$-axis…

Topic: JEE Main 2023 (13 April Morning Shift)

7

The area of the region enclosed by the curve $f(x)=\max\{\sin x,\cos x\},\ -\pi \le x \le \pi$ and the $x$-axis is:

Topic: JEE Main 2023 (13 April Morning Shift)

1

Let $s_1,s_2,s_3,\ldots,s_{10}$ respectively be the sum to $12$ terms of $10$ A.P.s whose first terms are $1,2,3,\ldots…

Topic: JEE Main 2023 (13 April Morning Shift)

2

Let $B=\left[\begin{array}{lll}1 & 3 & \alpha \\ 1 & 2 & 3 \\ \alpha & \alpha & 4\end{array}\right], \alpha > 2$ be the…

Topic: JEE Main 2023 (13 April Morning Shift)

3

The fractional part of the number $\dfrac{4^{2022}}{15}$ is equal to:

Topic: JEE Main 2023 (13 April Morning Shift)

4

$ \text{For } x\in\mathbb{R}, \text{ two real valued functions } f(x) \text{ and } g(x) \text{ are such that } g(x)=\sq…

Topic: JEE Main 2023 (13 April Morning Shift)

5

For the differentiable function $f:\mathbb{R}\setminus{0}\to\mathbb{R}$, let $3f(x)+2f!\left(\dfrac{1}{x}\right)=\dfrac…

Topic: JEE Main 2023 (13 April Morning Shift)

6

$\displaystyle \max_{0\le x\le \pi}\left\{x-2\sin x\cos x+\frac{1}{3}\sin(3x)\right\}=$

Topic: JEE Main 2023 (13 April Morning Shift)

7

$\text{The number of symmetric matrices of order }3\text{, with all entries from the set }{0,1,2,3,4,5,6,7,8,9}\text{ i…

Topic: JEE Main 2023 (13 April Morning Shift)