The differential equation of the family of circles passing through the origin and having centre on the line $y=x$ is:

1

Consider three vectors $\vec a,\vec b,\vec c$. Let $|\vec a|=2$, $|\vec b|=3$ and $\vec a=\vec b\times\vec c$. If $\alp…

Topic: JEE Main 2024 (5 April Evening Shift)

2

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)

3

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

Topic: JEE Main 2024 (5 April Evening Shift)

4

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)

5

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)

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

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)

8

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)

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

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)