If $\alpha$ and $\beta$ are the distinct roots of the equation ${x^2} + {(3)^{1/4}}x + {3^{1/2}} = 0$, then the value of ${\alpha ^{96}}({\alpha ^{12}} - 1) + {\beta ^{96}}({\beta ^{12}} - 1)$ is equal to :

1

The value of the integral $\int\limits_{ - 1}^1 {{{\log }_e}(\sqrt {1 - x} + \sqrt {1 + x} )dx} $ is equal to:

Topic: JEE Main 2021 (20 July Morning Shift)

2

The mean of 6 distinct observations is 6.5 and their variance is 10.25. If 4 out of 6 observations are 2, 4, 5 and 7, t…

Topic: JEE Main 2021 (20 July Morning Shift)

3

Let a be a positive real number such that $\int_0^a {{e^{x - [x]}}} dx = 10e - 9$ where [ x ] is the greatest integer l…

Topic: JEE Main 2021 (20 July Morning Shift)

1

Let $A = \left[ {\matrix{ 2 & 3 \cr a & 0 \cr } } \right]$, a$\in$R be written as P + Q where P is a sy…

Topic: JEE Main 2021 (20 July Morning Shift)

2

If z and $\omega$ are two complex numbers such that $\left| {z\omega } \right| = 1$ and $\arg (z) - \arg (\omega ) = {{…

Topic: JEE Main 2021 (20 July Morning Shift)

3

Let [ x ] denote the greatest integer $\le$ x, where x $\in$ R. If the domain of the real valued function $f(x) = \sqrt…

Topic: JEE Main 2021 (20 July Morning Shift)

4

Let y = y(x) be the solution of the differential equation $x\tan \left( {{y \over x}} \right)dy = \left( {y\tan \left( …

Topic: JEE Main 2021 (20 July Morning Shift)

5

Let $A = [{a_{ij}}]$ be a 3 $\times$ 3 matrix, where ${a_{ij}} = \left\{ {\matrix{ 1 & , & {if\,i = j} \cr …

Topic: JEE Main 2021 (20 July Morning Shift)

6

The number of real roots of the equation ${\tan ^{ - 1}}\sqrt {x(x + 1)} + {\sin ^{ - 1}}\sqrt {{x^2} + x + 1} = {\pi…

Topic: JEE Main 2021 (20 July Morning Shift)

7

Let y = y(x) be the solution of the differential equation ${e^x}\sqrt {1 - {y^2}} dx + \left( {{y \over x}} \right)dy =…

Topic: JEE Main 2021 (20 July Morning Shift)

8

Let 'a' be a real number such that the function f(x) = ax2 + 6x $-$ 15, x $\in$ R is increasing in $\left( { - \infty ,…

Topic: JEE Main 2021 (20 July Morning Shift)

9

Let a function f : R $\to$ R be defined as $f(x) = \left\{ {\matrix{ {\sin x - {e^x}} & {if} & {x \le 0} \cr…

Topic: JEE Main 2021 (20 July Morning Shift)

10

Words with or without meaning are to be formed using all the letters of the word EXAMINATION. The probability that the …

Topic: JEE Main 2021 (20 July Morning Shift)