If $\{ {a_i}\} _{i = 1}^n$, where n is an even integer, is an arithmetic progression with common difference 1, and $\sum\limits_{i = 1}^n {{a_i} = 192} ,\,\sum\limits_{i = 1}^{n/2} {{a_{2i}} = 120} $, then n is equal to :

1

The sum of absolute maximum and absolute minimum values of the function $f(x) = |2{x^2} + 3x - 2| + \sin x\cos x$ in th…

Topic: JEE Main 2022 (24 June Morning Shift)

2

For the function $f(x) = 4{\log _e}(x - 1) - 2{x^2} + 4x + 5,\,x > 1$, which one of the following is NOT correct?

Topic: JEE Main 2022 (24 June Morning Shift)

3

The set of all values of k for which ${({\tan ^{ - 1}}x)^3} + {({\cot ^{ - 1}}x)^3} = k{\pi ^3},\,x \in R$, is the inte…

Topic: JEE Main 2022 (24 June Morning Shift)

4

If the sum of the squares of the reciprocals of the roots $\alpha$ and $\beta$ of the equation 3x2 + $\lambda$x $-$ 1 =…

Topic: JEE Main 2022 (24 June Morning Shift)

5

The number of values of $\alpha$ for which the system of equations :x + y + z = $\alpha$$\alpha$x + 2$\alpha$y + 3z = $…

Topic: JEE Main 2022 (24 June Morning Shift)

6

Bag A contains 2 white, 1 black and 3 red balls and bag B contains 3 black, 2 red and n white balls. One bag is chosen …

Topic: JEE Main 2022 (24 June Morning Shift)

7

The surface area of a balloon of spherical shape being inflated, increases at a constant rate. If initially, the radius…

Topic: JEE Main 2022 (24 June Morning Shift)

8

The remainder when 32022 is divided by 5 is :

Topic: JEE Main 2022 (24 June Morning Shift)

9

Let $A = \{ z \in C:1 \le |z - (1 + i)| \le 2\} $and $B = \{ z \in A:|z - (1 - i)| = 1\} $. Then, B :

Topic: JEE Main 2022 (24 June Morning Shift)

1

If x = x(y) is the solution of the differential equation $y{{dx} \over {dy}} = 2x + {y^3}(y + 1){e^y},\,x(1) = 0$; then…

Topic: JEE Main 2022 (24 June Morning Shift)

2

Let $\widehat a$, $\widehat b$ be unit vectors. If $\overrightarrow c $ be a vector such that the angle between $\wideh…

Topic: JEE Main 2022 (24 June Morning Shift)

3

The domain of the function $f(x) = {{{{\cos }^{ - 1}}\left( {{{{x^2} - 5x + 6} \over {{x^2} - 9}}} \right)} \over {{{\l…

Topic: JEE Main 2022 (24 June Morning Shift)