Let the solution curve of the differential equation $x,dy = \left(\sqrt{x^{2}+y^{2}}+y\right)dx,; x>0,$ intersect the line $x=1$ at $y=0$ and the line $x=2$ at $y=\alpha$. Then the value of $\alpha$ is:

1

Let $C$ be the centre of the circle $x^{2}+y^{2}-x+2y=\dfrac{11}{4}$ and $P$ be a point on the circle. A line passes th…

Topic: JEE Main 2022 (28 July Morning Shift)

1

Considering only the principal values of the inverse trigonometric functions, the domain of the function $f(x)=\cos^{-1…

Topic: JEE Main 2022 (28 July Morning Shift)

2

Let the vectors $\vec a=(1+t)\hat i+(1-t)\hat j+\hat k$, $\vec b=(1-t)\hat i+(1+t)\hat j+2\hat k$ and $\vec c=t\hat i-t…

Topic: JEE Main 2022 (28 July Morning Shift)

3

Considering the principal values of the inverse trigonometric functions, the sum of all the solutions of the equation $…

Topic: JEE Main 2022 (28 July Morning Shift)

4

Let a vector $\vec{a}$ has magnitude $9$. Let a vector $\vec{b}$ be such that for every $(x,y)\in\mathbb{R}\times\mathb…

Topic: JEE Main 2022 (28 July Morning Shift)

5

For $t\in(0,2\pi)$, if $\triangle ABC$ is an equilateral triangle with vertices $A(\sin t,-\cos t)$, $B(\cos t,\sin t)$…

Topic: JEE Main 2022 (28 July Morning Shift)

6

For $\alpha \in \mathbb{N}$, consider a relation $R$ on $\mathbb{N}$ given by $R={(x,y):3x+\alpha y \text{ is a multipl…

Topic: JEE Main 2022 (28 July Morning Shift)

7

Out of $60%$ female and $40%$ male candidates appearing in an exam, $60%$ candidates qualify it. The number of females …

Topic: JEE Main 2022 (28 July Morning Shift)

8

If $y=y(x),\; x\in(0,\pi/2)$ be the solution curve of the differential equation $$(\sin^{2}2x)\dfrac{dy}{dx}+(8\sin^…

Topic: JEE Main 2022 (28 July Morning Shift)

9

The remainder when $7^{2022}+3^{2022}$ is divided by $5$ is :

Topic: JEE Main 2022 (28 July Morning Shift)

10

Let $S_{1} = \{ z_{1} \in \mathbb{C} : |z_{1} - 3| = \tfrac{1}{2} \}$ and $S_{2} = \{ z_{2} \in \mathbb{C} : |z_{2} -…

Topic: JEE Main 2022 (28 July Morning Shift)