$ \text{Suppose } a_1, a_2, \ldots, a_n, \ldots \text{ be an arithmetic progression of natural numbers. If } \dfrac{S_5}{S_9} = \dfrac{5}{17} \text{ and } 110 < a_{15} < 120, \text{ then the sum of the first ten terms of the progression is equal to:} $

1

The remainder when $(2021)^{2022} + (2022)^{2021}$ is divided by $7$ is

Topic: JEE Main 2022 (27 July Morning Shift)

2

Let $A = \begin{pmatrix} 1 & 2 \\ -2 & -5 \end{pmatrix}$. Let $\alpha, \beta \in \mathbb{R}$ be such that $\alpha A^2…

Topic: JEE Main 2022 (27 July Morning Shift)

3

$ \text{Let the minimum value } v_{0} \text{ of } v=\lvert z\rvert^{2}+\lvert z-3\rvert^{2}+\lvert z-6i\rvert^{2},\ z\i…

Topic: JEE Main 2022 (27 July Morning Shift)

4

$ \text{Let } f,g : \mathbb{N} - \{1\} \to \mathbb{N} \text{ be functions defined by } f(a) = \alpha, \text{ where } \a…

Topic: JEE Main 2022 (27 July Morning Shift)

5

$ \text{Let } R_1 \text{ and } R_2 \text{ be two relations defined on } \mathbb{R} \text{ by } a R_1 b \Leftrightarrow …

Topic: JEE Main 2022 (27 July Morning Shift)

1

$ \text{Let } f:\mathbb{R}\to\mathbb{R} \text{ be a function defined as } f(x)=a\sin\!\left(\frac{\pi\lfloor x\rfloor}…

Topic: JEE Main 2022 (27 July Morning Shift)

2

$ I = \int_{\pi/4}^{\pi/3} \left( \frac{8 \sin x - \sin 2x}{x} \right) dx. \ \text{ Then} $

Topic: JEE Main 2022 (27 July Morning Shift)

3

The area of the smaller region enclosed by the curves $y^2 = 8x + 4$ and $x^2 + y^2 + 4\sqrt{3}x - 4 = 0$ is equal to

Topic: JEE Main 2022 (27 July Morning Shift)

4

Let $y = y_{1}(x)$ and $y = y_{2}(x)$ be two distinct solutions of the differential equation $\dfrac{dy}{dx} = x + y$, …

Topic: JEE Main 2022 (27 July Morning Shift)

5

Let $\vec{a} = \alpha \hat{i} + \hat{j} + \beta \hat{k}$ and $\vec{b} = 3\hat{i} - 5\hat{j} + 4\hat{k}$ be two vectors,…

Topic: JEE Main 2022 (27 July Morning Shift)

6

Let $S$ be the sample space of all five digit numbers. It $p$ is the probability that a randomly selected number from $…

Topic: JEE Main 2022 (27 July Morning Shift)

7

If the circle $x^{2} + y^{2} - 2gx + 6y - 19c = 0,; g,c \in \mathbb{R}$ passes through the point $(6,1)$ and its centre…

Topic: JEE Main 2022 (27 July Morning Shift)

8

Let $A(1,1)$, $B(-4,3)$, $C(-2,-5)$ be vertices of a triangle $ABC$, $P$ be a point on side $BC$, and $\Delta_1$ and $\…

Topic: JEE Main 2022 (27 July Morning Shift)

9

Let a function $f: \mathbb{R} \rightarrow \mathbb{R}$ be defined as :$f(x)= \begin{cases}\int\limits_{0}^{x}(5-|t-3|) d…

Topic: JEE Main 2022 (27 July Morning Shift)