JEE Maths PYQ Practice, chapter-wise

JEE Main 2021 (Online) 20th July Evening ShiftQuestion 5521

Let $P$ be a variable point on the parabola $y=4x^2+1$. Then, the locus of the mid-point of the point $P$ and the foot of the perpendicular drawn from the point $P$ to the line $y=x$ is :

Parabola

$(3x-y)^2+(x-3y)+2=0$$2(3x-y)^2+(x-3y)+2=0$$(3x-y)^2+2(x-3y)+2=0$$2(x-3y)^2+(3x-y)+2=0$

JEE Main 2021 (Online) 20th July Evening ShiftQuestion 5522

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 5523

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 5524

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 5525

The lines $x=ay-1=z-2$ and $x=3y-2=bz-2$, $(ab eq0)$ are coplanar, if :

3D Geometry

$b=1,\ a\in\mathbf{R}-\{0\}$$a=1,\ b\in\mathbf{R}-\{0\}$$a=2,\ b=2$$a=2,\ b=3$

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