The maximum value of $f(x) = \left| {\matrix{ {{{\sin }^2}x} & {1 + {{\cos }^2}x} & {\cos 2x} \cr {1 + {{\sin }^2}x} & {{{\cos }^2}x} & {\cos 2x} \cr {{{\sin }^2}x} & {{{\cos }^2}x} & {\sin 2x} \cr } } \right|,x \in R$ is :

1

Let A denote the event that a 6-digit integer formed by 0, 1, 2, 3, 4, 5, 6 without repetitions, be divisible by 3. The…

Topic: JEE Main 2021 (16 March Evening Shift)

2

Let A($-$1, 1), B(3, 4) and C(2, 0) be given three points. A line y = mx, m > 0, intersects lines AC and BC at poin…

Topic: JEE Main 2021 (16 March Evening Shift)

3

Let the lengths of intercepts on x-axis and y-axis made by the circle x2 + y2 + ax + 2ay + c = 0, (a < 0) be 2${\sq…

Topic: JEE Main 2021 (16 March Evening Shift)

4

Given that the inverse trigonometric functions take principal values only. Then, the number of real values of x which s…

Topic: JEE Main 2021 (16 March Evening Shift)

5

Let $\alpha$ $\in$ R be such that the function $f(x) = \left\{ {\matrix{ {{{{{\cos }^{ - 1}}(1 - {{\{ x\} }^2}){{\sin…

Topic: JEE Main 2021 (16 March Evening Shift)

6

The least value of |z| where z is complex number which satisfies the inequality $\exp \left( {{{(|z| + 3)(|z| - 1)} \ov…

Topic: JEE Main 2021 (16 March Evening Shift)

7

Let A = {2, 3, 4, 5, ....., 30} and '$ \simeq $' be an equivalence relation on A $\times$ A, defined by (a, b) $ \simeq…

Topic: JEE Main 2021 (16 March Evening Shift)

8

Let P(x) = x2 + bx + c be a quadratic polynomial with real coefficients such that $\int_0^1 {P(x)dx} $ = 1 and P(x) lea…

Topic: JEE Main 2021 (16 March Evening Shift)

9

Let C1 be the curve obtained by the solution of differential equation $2xy{{dy} \over {dx}} = {y^2} - {x^2},x > 0$…

Topic: JEE Main 2021 (16 March Evening Shift)

10

Consider the integral $I = \int_0^{10} {{{[x]{e^{[x]}}} \over {{e^{x - 1}}}}dx} $, where [x] denotes the greatest int…

Topic: JEE Main 2021 (16 March Evening Shift)