Let the circle $C_1: x^2+y^2-2(x+y)+1=0$ and $C_2$ be a circle with centre $(-1,0)$ and radius $2$. If the line of the common chord of $C_1$ and $C_2$ meets the $y$-axis at the point $P$, then the square of the distance of $P$ from the centre of $C_1$ is:

1

Let $f, g: \mathbf{R} \rightarrow \mathbf{R}$ be defined as : $f(x)=|x-1| \text { and } g(x)= \begin{cases}\mathrm{e}^x…

Topic: JEE Main 2024 (5 April Evening Shift)

2

Let $ABCD$ and $AEFG$ be squares of side $4$ and $2$ units, respectively. The point $E$ is on the line segment $AB$ and…

Topic: JEE Main 2024 (5 April Evening Shift)

3

Let $(\alpha,\beta,\gamma)$ be the image of the point $(8,5,7)$ in the line $\dfrac{x-1}{2}=\dfrac{y+1}{3}=\dfrac{z-2}{…

Topic: JEE Main 2024 (5 April Evening Shift)

4

If the constant term in the expansion of $\left(\dfrac{\sqrt{3}}{x}+\dfrac{2x}{\sqrt{5}}\right)^{12}$, $x\ne 0$, is $\a…

Topic: JEE Main 2024 (5 April Evening Shift)

5

Let $\vec a=2\hat i+5\hat j-\hat k$, $\vec b=2\hat i-2\hat j+2\hat k$ and $\vec c$ be three vectors such that $(\vec c+…

Topic: JEE Main 2024 (5 April Evening Shift)

6

Let $A(-1,1)$ and $B(2,3)$ be two points and $P$ be a variable point above the line $AB$ such that the area of $\triang…

Topic: JEE Main 2024 (5 April Evening Shift)

7

Let $S_1=\{z \in \mathbf{C}:|z| \leq 5\}, S_2=\left\{z \in \mathbf{C}: \operatorname{Im}\left(\frac{z+1-\sqrt{3} i}{1-\…

Topic: JEE Main 2024 (5 April Evening Shift)

8

The values of $m, n$, for which the system of equations $\begin{aligned} & x+y+z=4, \\ & 2 x+5 y+5 z=17, \\ & x+2 y+\ma…

Topic: JEE Main 2024 (5 April Evening Shift)

9

. If $y(\theta)=\dfrac{2\cos\theta+\cos2\theta}{\cos3\theta+\cos2\theta+5\cos\theta+2}$, then at $\theta=\dfrac{\pi}{2}…

Topic: JEE Main 2024 (5 April Evening Shift)

10

Let $\beta(m,n)=\displaystyle\int_{0}^{1}x^{m-1}(1-x)^{,n-1},dx,; m,n>0$. If $\displaystyle\int_{0}^{1}(1-x^{10})^{20},…

Topic: JEE Main 2024 (5 April Evening Shift)