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 $\triangle PAB$ is $10$. If the locus of $P$ is $ax+by=15$, then $5a+2b$ is:

1

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)

2

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)

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

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)

5

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)

6

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 …

Topic: JEE Main 2024 (5 April Evening Shift)

1

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)

2

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)

3

. 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)

4

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)

5

Let $f:[-1,2]\to\mathbb{R}$ be given by $f(x)=2x^{2}+x+\lfloor x^{2}\rfloor-\lfloor x\rfloor$, where $\lfloor t\rfloor$…

Topic: JEE Main 2024 (5 April Evening Shift)

6

Let the set $S={2,4,8,16,\ldots,512}$ be partitioned into three sets $A,B,C$ having equal number of elements such that …

Topic: JEE Main 2024 (5 April Evening Shift)

7

For $x\ge0$, the least value of $K$ for which $4^{,1+x}+4^{,1-x},\ \dfrac{K}{2},\ 16^{x}+16^{-x}$ are three consecutive…

Topic: JEE Main 2024 (5 April Evening Shift)

8

Let $\alpha \beta \neq 0$ and $A=\left[\begin{array}{rrr}\beta & \alpha & 3 \\ \alpha & \alpha & \beta \\ -\beta & \alp…

Topic: JEE Main 2024 (5 April Evening Shift)

9

The area enclosed between the curves $y=x|x|$ and $y=x-|x|$ is:

Topic: JEE Main 2024 (5 April Evening Shift)

10

60 words can be formed using all the letters of the word BHBJO (with or without meaning). If these words are arranged i…

Topic: JEE Main 2024 (5 April Evening Shift)