The value of $\mathop {\lim }\limits_{x \to {0^ + }} {{{{\cos }^{ - 1}}(x - {{[x]}^2}).{{\sin }^{ - 1}}(x - {{[x]}^2})} \over {x - {x^3}}}$, where [ x ] denotes the greatest integer $ \le $ x is :

1

In a triangle PQR, the co-ordinates of the points P and Q are ($-$2, 4) and (4, $-$2) respectively. If the equation of …

Topic: JEE Main 2021 (17 March Morning Shift)

1

Which of the following statements is correct for the function g($\alpha$) for $\alpha$ $\in$ R such that $g(\alpha ) = …

Topic: JEE Main 2021 (17 March Morning Shift)

2

Which of the following is true for y(x) that satisfies the differential equation ${{dy} \over {dx}}$ = xy $-$ 1 + x $-…

Topic: JEE Main 2021 (17 March Morning Shift)

3

The sum of possible values of x for tan$-$1(x + 1) + cot$-$1$\left( {{1 \over {x - 1}}} \right)$ = tan$-$1$\left( {{8 \…

Topic: JEE Main 2021 (17 March Morning Shift)

4

The value of $4 + {1 \over {5 + {1 \over {4 + {1 \over {5 + {1 \over {4 + ......\infty }}}}}}}}$ is :

Topic: JEE Main 2021 (17 March Morning Shift)

5

The inverse of $y = {5^{\log x}}$ is :

Topic: JEE Main 2021 (17 March Morning Shift)

6

Two dies are rolled. If both dices have six faces numbered 1, 2, 3, 5, 7 and 11, then the probability that the sum of t…

Topic: JEE Main 2021 (17 March Morning Shift)

7

If the fourth term in the expansion of ${(x + {x^{{{\log }_2}x}})^7}$ is 4480, then the value of x where x$\in$N is equ…

Topic: JEE Main 2021 (17 March Morning Shift)

8

The system of equations kx + y + z = 1, x + ky + z = k and x + y + zk = k2 has no solution if k is equal to :

Topic: JEE Main 2021 (17 March Morning Shift)

9

In a school, there are three types of games to be played. Some of the students play two types of games, but none play a…

Topic: JEE Main 2021 (17 March Morning Shift)

10

If $\cot^{-1}(\alpha) = \cot^{-1}(2) + \cot^{-1}(8) + \cot^{-1}(18) + \cot^{-1}(32) + \ldots \text{ (upto 100 terms)},$…

Topic: JEE Main 2021 (17 March Morning Shift)