JEE Maths PYQ Practice, chapter-wise

JEE Main 2021 (Online) 20th July Evening ShiftQuestion 5531

Let $A$, $B$ and $C$ be three events such that the probability that exactly one of $A$ and $B$ occurs is $(1-k)$, the probability that exactly one of $B$ and $C$ occurs is $(1-2k)$, the probability that exactly one of $C$ and $A$ occurs is $(1-k)$ and the probability of all $A$, $B$ and $C$ occur simultaneously is $k^2$, where $0<k<1$. Then the probability that at least one of $A$, $B$ and $C$ occur is :

Probability

greater than $\dfrac{1}{8}$ but less than $\dfrac{1}{4}$greater than $\dfrac{1}{2}$greater than $\dfrac{1}{4}$ but less than $\dfrac{1}{2}$exactly equal to $\dfrac{1}{2}$

JEE Main 2021 (Online) 20th July Evening ShiftQuestion 5532

The value of $\tan\left(2\tan^{-1}\left(\dfrac{3}{5}\right)+\sin^{-1}\left(\dfrac{5}{13}\right)\right)$ is equal to :

Inverse Trigonometric Functions

$\dfrac{-181}{69}$$\dfrac{220}{21}$$\dfrac{-291}{76}$$\dfrac{151}{63}$

JEE Main 2021 (Online) 20th July Evening ShiftQuestion 5533

If $f:\mathbf{R}\to\mathbf{R}$ is given by $f(x)=x+1$, then the value of $\displaystyle\lim_{n\to\infty}\dfrac{1}{n}\left[f(0)+f\left(\dfrac{5}{n}\right)+f\left(\dfrac{10}{n}\right)+\cdots+f\left(\dfrac{5(n-1)}{n}\right)\right]$ is :

Definite Integration

$\dfrac{3}{2}$$\dfrac{5}{2}$$\dfrac{1}{2}$$\dfrac{7}{2}$

JEE Main 2021 (Online) 20th July Evening ShiftQuestion 5534

Let $f:\mathbf{R}-\left\{\dfrac{\alpha}{6}\right\}\to\mathbf{R}$ be defined by $f(x)=\dfrac{5x+3}{6x-\alpha}$. Then the value of $\alpha$ for which $(f\circ f)(x)=x$, for all $x\in\mathbf{R}-\left\{\dfrac{\alpha}{6}\right\}$, is :

Functions

No such $\alpha$ exists$5$$8$$6$

JEE Main 2021 (Online) 20th July Evening ShiftQuestion 5535

For the natural numbers $m,\ n$, if $(1-y)^m(1+y)^n=1+a_1y+a_2y^2+\cdots+a_{m+n}y^{m+n}$ and $a_1=a_2=10$, then the value of $(m+n)$ is equal to :

Binomial Theorem · Coefficient of a Given Power / Term Independent of x

$88$$64$$100$$80$

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