JEE Main 2021 Question Paper (Jul 22, 2021) (Shift 2)

Question 1

If the domain of the function $f(x) = \frac{\cos^{-1}\sqrt{x^2-x+1}}{\sin^{-1}\left(\frac{2x-1}{2}\right)}$ is the interval $(\alpha, \beta]$, then $\alpha + \beta$ is equal to

Accepted Answer

$\frac{3}{2}$

Answer

1

Answer

2

Answer

$\frac{1}{2}$

Question 2

The number of solutions of $\sin^7x+\cos^7x=1$, $x\in [0, 4\pi]$ is equal to

Accepted Answer

5

Answer

7

Answer

9

Answer

11

Question 3

If the shortest distance between the straight lines $3(x-1)=6(y-2) = 2(z-1)$ and $4(x-2) = 2(y-\lambda) = (z-3)$, $\lambda\in R$ is $\frac{1}{\sqrt{38}}$, then the integral value of $\lambda$ is equal to :

Accepted Answer

3

Answer

-1

Answer

2

Answer

5

Question 4

Let $A = [a_{ij}]$ be a real matrix of order $3	imes3$, such that $a_{i1} + a_{i2} + a_{i3} = 1$, for $i=1, 2, 3$. Then, the sum of all the entries of the matrix $A^3$ is equal to

Accepted Answer

3

Answer

1

Answer

2

Answer

9

Question 5

Let $f  : R ightarrow R$ be defined as $ f(x) = \begin{cases} \frac{x^3}{(1 - \cos 2x)^2} \cdot \log_e\left(\frac{1 + 2xe^{-2x}}{(1 - xe^{-x})^2}ight), & x 
eq 0 \ \alpha, & x = 0 \end{cases} $  .If $f$ is continuous at $x = 0$, then $\alpha$ is equal to:

Accepted Answer

1

Answer

0

Answer

2

Answer

3