Let $S_{1} = \{ z_{1} \in \mathbb{C} : |z_{1} - 3| = \tfrac{1}{2} \}$ and $S_{2} = \{ z_{2} \in \mathbb{C} : |z_{2} - |z_{2} + 1|| = |z_{2} + |z_{2} - 1|| \}$. Then, for $z_{1} \in S_{1}$ and $z_{2} \in S_{2}$, the least value of $|z_{2} - z_{1}|$ is :

1

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

Topic: JEE Main 2022 (28 July Morning Shift)

2

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)

3

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)

4

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)

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

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)

7

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)

8

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)

9

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)

10

Let the solution curve of the differential equation $x,dy = \left(\sqrt{x^{2}+y^{2}}+y\right)dx,; x>0,$ intersect the l…

Topic: JEE Main 2022 (28 July Morning Shift)

1

If the minimum value of $f(x)=\dfrac{5x^{2}}{2}+\dfrac{\alpha}{x^{5}},; x>0,$ is $14$, then the value of $\alpha$ is eq…

Topic: JEE Main 2022 (28 July Morning Shift)

2

$ \text{Let } \alpha, \beta \text{ and } \gamma \text{ be three positive real numbers. Let } f(x) = \alpha x^{5} + \bet…

Topic: JEE Main 2022 (28 July Morning Shift)

3

The minimum value of the twice differentiable function $f(x)=\int_{0}^{x} e^{,x-t},f'(t),dt-(x^{2}-x+1)e^{x},; x\in\mat…

Topic: JEE Main 2022 (28 July Morning Shift)