JEE Maths PYQ Practice, chapter-wise

JEE Main 2021 (Online) 20th July Evening ShiftQuestion 5536

Consider the line $L$ given by the equation $\dfrac{x-3}{2}=\dfrac{y-1}{1}=\dfrac{z-2}{1}$. Let $Q$ be the mirror image of the point $(2,3,-1)$ with respect to $L$. Let a plane $P$ be such that it passes through $Q$, and the line $L$ is perpendicular to $P$. Then which of the following points is on the plane $P$?

3D Geometry

$(-1,1,2)$$(1,1,1)$$(1,1,2)$$(1,2,2)$

JEE Main 2021 (Online) 20th July Evening ShiftQuestion 5537

Let $g(t)=\displaystyle\int_{-\pi/2}^{\pi/2}\cos\left(\dfrac{\pi}{4}t+f(x)\right)dx$, where $f(x)=\log_e\left(x+\sqrt{x^2+1}\right)$, $x\in\mathbf{R}$. Then which one of the following is correct?

Definite Integration

$g(1)=g(0)$$\sqrt{2}\,g(1)=g(0)$$g(1)=\sqrt{2}\,g(0)$$g(1)+g(0)=0$

JEE Main 2021 (Online) 20th July Evening ShiftQuestion 5538

Let in a right angled triangle, the smallest angle be $\theta$. If a triangle formed by taking the reciprocal of its sides is also a right angled triangle, then $\sin\theta$ is equal to :

Trigonometric Ratio & Identities

$\dfrac{\sqrt{5}+1}{4}$$\dfrac{\sqrt{5}-1}{2}$$\dfrac{\sqrt{2}-1}{2}$$\dfrac{\sqrt{5}-1}{4}$

JEE Main 2021 (Online) 20th July Evening ShiftQuestion 5539

If $[x]$ denotes the greatest integer less than or equal to $x$, then the value of the integral $\displaystyle\int_{-\pi/2}^{\pi/2}\left[[x]-\sin x\right]dx$ is equal to :

Definite Integration

$-\pi$$\pi$$0$$1$

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