Question Bank

Showing 7491-7495 of 7517 questions.

Page 1502 of 1507

JEE Main 2021 (Online) 20th July Evening ShiftQuestion 7491

If the mean and variance of six observations $7,\ 10,\ 11,\ 15,\ a,\ b$ are $10$ and $\dfrac{20}{3}$, respectively, then the value of $|a-b|$ is equal to :

Statistics

$9$$11$$7$$1$

JEE Main 2021 (Online) 20th July Evening ShiftQuestion 7492

Consider the following three statements : (A) If $3+3=7$ then $4+3=8$ (B) If $5+3=8$ then earth is flat. (C) If both (A) and (B) are true then $5+6=17$. Then, which of the following statements is correct?

Mathematical Reasoning

(A) is false, but (B) and (C) are true(A) and (C) are true while (B) is false(A) is true while (B) and (C) are false(A) and (B) are false while (C) is true

JEE Main 2021 (Online) 20th July Evening ShiftQuestion 7493

Let a curve $y=y(x)$ be given by the solution of the differential equation $\cos\left(\dfrac{1}{2}\cos^{-1}\left(e^{-x}\right)\right)dx=\sqrt{e^{2x}-1}\,dy$. If it intersects the $y$-axis at $y=-1$, and the intersection point of the curve with the $x$-axis is $(\alpha,0)$, then $e^{\alpha}$ is equal to $\_\_\_\_\_\_\_\_$ .

Differential Equation

Your answer

JEE Main 2021 (Online) 20th July Evening ShiftQuestion 7494

If the real part of the complex number $(1-\cos\theta+2i\sin\theta)^{-1}$ is $\dfrac{1}{5}$ for $\theta\in(0,\pi)$, then the value of the integral $\displaystyle\int_{0}^{\theta}\sin x\,dx$ is equal to:

Complex Numbers

$1$$2$$-1$$0$

JEE Main 2021 (Online) 20th July Evening ShiftQuestion 7495

If $\displaystyle\lim_{x\to0}\dfrac{\alpha xe^{x}-\beta\log_e(1+x)+\gamma x^2e^{-x}}{x\sin^2x}=10$, $\alpha,\beta,\gamma\in\mathbf{R}$, then the value of $\alpha+\beta+\gamma$ is $\_\_\_\_\_\_\_\_$ .

Limits & Continuity

Your answer