If the system $11x+y+\lambda z=-5,\quad 2x+3y+5z=3,\quad 8x-19y-39z=\mu$ has infinitely many solutions, then $\lambda^{4}-\mu$ equals:

1

The coefficients $a,b,c$ in the quadratic $ax^{2}+bx+c=0$ are chosen from the set ${1,2,3,4,5,6,7,8}$. The probability …

Topic: JEE Main 2024 (5 April Morning Shift)

2

Let $f(x)=x^{5}+2x^{3}+3x+1,; x\in\mathbb{R}$, and let $g(x)$ be a function such that $g(f(x))=x$ for all $x\in\mathbb{…

Topic: JEE Main 2024 (5 April Morning Shift)

3

Let a circle $C$ of radius $1$ and closer to the origin be such that the lines passing through the point $(3,2)$ and pa…

Topic: JEE Main 2024 (5 April Morning Shift)

4

Let $A$ and $B$ be two square matrices of order $3$ such that $|A|=3$ and $|B|=2$. Then $\left|,A^{T}A,( \operatorname{…

Topic: JEE Main 2024 (5 April Morning Shift)

5

Consider the following two statements: Statement I: For any two non-zero complex numbers $z_1,z_2$, $(|z_1|+|z_2|)\lef…

Topic: JEE Main 2024 (5 April Morning Shift)

6

If the line $\dfrac{2-x}{3}=\dfrac{3y-2}{4\lambda+1}=4-z$ makes a right angle with the line $\dfrac{x+3}{3\mu}=\dfrac{1…

Topic: JEE Main 2024 (5 April Morning Shift)

7

Two straight lines through the origin $O$ intersect the line $3x+4y=12$ at points $P$ and $Q$ such that $\triangle OPQ$…

Topic: JEE Main 2024 (5 April Morning Shift)

8

Let $A={1,3,7,9,11}$ and $B={2,4,5,7,8,10,12}$. The total number of one–one maps $f:A\to B$ such that $f(1)+f(3)=14$ is:

Topic: JEE Main 2024 (5 April Morning Shift)

9

Let a rectangle $ABCD$ of sides $2$ and $4$ be inscribed in another rectangle $PQRS$ such that the vertices of $ABCD$ l…

Topic: JEE Main 2024 (5 April Morning Shift)

1

The integral $\displaystyle \int_{0}^{\pi/4}\frac{136\sin x}{3\sin x+5\cos x},dx$ is equal to:

Topic: JEE Main 2024 (5 April Morning Shift)

2

If $\dfrac{1}{\sqrt{1}+\sqrt{2}}+\dfrac{1}{\sqrt{2}+\sqrt{3}}+\cdots+\dfrac{1}{\sqrt{99}+\sqrt{100}}=m$ and $\dfrac{1}{…

Topic: JEE Main 2024 (5 April Morning Shift)

3

Let $d$ be the distance of the point of intersection of the lines $\dfrac{x+6}{3}=\dfrac{y}{2}=\dfrac{z+1}{1}$ and $\df…

Topic: JEE Main 2024 (5 April Morning Shift)

4

If the function $f(x)=\dfrac{\sin 3x+\alpha\sin x-\beta\cos 3x}{x^{3}},; x\in\mathbb{R},$ is continuous at $x=0$, then …

Topic: JEE Main 2024 (5 April Morning Shift)

5

Let the line $2x+3y-k=0,\ k>0$ intersect the $x$-axis and $y$-axis at points $A$ and $B$, respectively. If the circle h…

Topic: JEE Main 2024 (5 April Morning Shift)

6

The value of $\int_{-\pi}^{\pi}\dfrac{2y(1+\sin y)}{1+\cos^{2}y},dy$ is:

Topic: JEE Main 2024 (5 April Morning Shift)

7

Suppose $\theta\in[0,\tfrac{\pi}{4}]$ is a solution of $4\cos\theta-3\sin\theta=1$. Then $\cos\theta$ is:

Topic: JEE Main 2024 (5 April Morning Shift)

8

For $f(x)=\sin x+3x-\dfrac{2}{\pi}(x^{2}+x)$, where $x\in\left[0,\tfrac{\pi}{2}\right]$, consider: (I) $f$ is increasin…

Topic: JEE Main 2024 (5 April Morning Shift)

9

Suppose $\theta\in\left[0,\tfrac{\pi}{4}\right]$ is a solution of $4\cos\theta-3\sin\theta=1$. Then $\cos\theta$ is:

Topic: JEE Main 2024 (5 April Morning Shift)

10

If $y=y(x)$ solves the differential equation $\dfrac{dy}{dx}+2y=\sin(2x)$ with $y(0)=\dfrac{3}{4}$, then $y!\left(\dfra…

Topic: JEE Main 2024 (5 April Morning Shift)