The number of distinct real roots of $\left| {\matrix{ {\sin x} & {\cos x} & {\cos x} \cr {\cos x} & {\sin x} & {\cos x} \cr {\cos x} & {\cos x} & {\sin x} \cr } } \right| = 0$ in the interval $ - {\pi \over 4} \le x \le {\pi \over 4}$ is :

1

If [x] be the greatest integer less than or equal to x, then $\sum\limits_{n = 8}^{100} {\left[ {{{{{( - 1)}^n}n} \over…

Topic: JEE Main 2021 (25 July Evening Shift)

2

Let a, b and c be distinct positive numbers. If the vectors $a\widehat i + a\widehat j + c\widehat k,\widehat i+\wideha…

Topic: JEE Main 2021 (25 July Evening Shift)

3

The value of the integral $\int\limits_{ - 1}^1 {\log \left( {x + \sqrt {{x^2} + 1} } \right)dx} $ is :

Topic: JEE Main 2021 (25 July Evening Shift)

4

The lowest integer which is greater than ${\left( {1 + {1 \over {{{10}^{100}}}}} \right)^{{{10}^{100}}}}$ is _________…

Topic: JEE Main 2021 (25 July Evening Shift)

5

The value of $\cot \dfrac{\pi}{24}$ is :

Topic: JEE Main 2021 (25 July Evening Shift)

6

If the greatest value of the term independent of 'x' in the expansion of ${\left( {x\sin \alpha + a{{\cos \alpha } \o…

Topic: JEE Main 2021 (25 July Evening Shift)

7

If $f(x) = \begin{cases} \int_{0}^{x} \left( 5 + |1 - t| \right) dt, & x > 2 \\ 5x + 1, & x \leq 2 \end{cases}$, then

Topic: JEE Main 2021 (25 July Evening Shift)

8

The first of the two samples in a group has 100 items with mean 15 and standard deviation 3. If the whole group has 250…

Topic: JEE Main 2021 (25 July Evening Shift)

9

The sum of all those terms which are rational numbers in the expansion of (21/3 + 31/4)12 is :

Topic: JEE Main 2021 (25 July Evening Shift)

1

If $\left| {\overrightarrow a } \right| = 2,\left| {\overrightarrow b } \right| = 5$ and $\left| {\overrightarrow a \t…

Topic: JEE Main 2021 (25 July Evening Shift)

2

The number of real solutions of the equation, x2 $-$ |x| $-$ 12 = 0 is :

Topic: JEE Main 2021 (25 July Evening Shift)

3

Consider function f : A $\to$ B and g : B $\to$ C (A, B, C $ \subseteq $ R) such that (gof)$-$1 exists, then :

Topic: JEE Main 2021 (25 July Evening Shift)

4

If $P = \begin{bmatrix} 1 & 0 \\ \tfrac{1}{2} & 1 \end{bmatrix}$, then $P^{50}$ is :

Topic: JEE Main 2021 (25 July Evening Shift)

5

Let X be a random variable such that the probability function of a distribution is given by $P(X = 0) = {1 \over 2},P(X…

Topic: JEE Main 2021 (25 July Evening Shift)

6

If ${}^n{P_r} = {}^n{P_{r + 1}}$ and ${}^n{C_r} = {}^n{C_{r - 1}}$, then the value of r is equal to :

Topic: JEE Main 2021 (25 July Evening Shift)

7

Let y = y(x) be the solution of the differential equation xdy = (y + x3 cosx)dx with y($\pi$) = 0, then $y\left( {{\pi…

Topic: JEE Main 2021 (25 July Evening Shift)