If ${I_n} = \int\limits_{{\pi \over 4}}^{{\pi \over 2}} {{{\cot }^n}x\,dx} $, then :
Previous 10 Questions — JEE Main 2021 (25 February Evening Shift)
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The minimum value of $f(x) = {a^{{a^x}}} + {a^{1 - {a^x}}}$, where a, $x \in R$ and a > 0, is equal to :
Topic: JEE Main 2021 (25 February Evening Shift)
If $\alpha$, $\beta$ $\in$ R are such that 1 $-$ 2i (here i2 = $-$1) is a root of z2 + $\alpha$z + $\beta$ = 0, then ($…
Topic: JEE Main 2021 (25 February Evening Shift)
Let A be a 3 $\times$ 3 matrix with det(A) = 4. Let Ri denote the ith row of A. If a matrix B is obtained by performing…
Topic: JEE Main 2021 (25 February Evening Shift)
cosec$\left[ {2{{\cot }^{ - 1}}(5) + {{\cos }^{ - 1}}\left( {{4 \over 5}} \right)} \right]$ is equal to :
Topic: JEE Main 2021 (25 February Evening Shift)
If 0 < x, y < $\pi$ and cosx + cosy $-$ cos(x + y) = ${3 \over 2}$, then sinx + cosy is equal to :
Topic: JEE Main 2021 (25 February Evening Shift)
Let $\alpha$ and $\beta$ be the roots of x2 $-$ 6x $-$ 2 = 0. If an = $\alpha$$n $-$ $\beta$n for n $ \ge $ 1, then the…
Topic: JEE Main 2021 (25 February Evening Shift)
The shortest distance between the line x $-$ y = 1 and the curve x2 = 2y is :
Topic: JEE Main 2021 (25 February Evening Shift)
Let A be a set of all 4-digit natural numbers whose exactly one digit is 7. Then the probability that a randomly chosen…
Topic: JEE Main 2021 (25 February Evening Shift)
The integral $\int {{{{e^{3{{\log }_e}2x}} + 5{e^{2{{\log }_e}2x}}} \over {{e^{4{{\log }_e}x}} + 5{e^{3{{\log }_e}x}} -…
Topic: JEE Main 2021 (25 February Evening Shift)
Let x denote the total number of one-one functions from a set A with 3 elements to a set B with 5 elements and y denote…
Topic: JEE Main 2021 (25 February Evening Shift)
Next 10 Questions — JEE Main 2021 (25 February Evening Shift)
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In a group of 400 people, 160 are smokers and non-vegetarian; 100 are smokers and vegetarian and the remaining 140 are …
Topic: JEE Main 2021 (25 February Evening Shift)
If for the matrix, $A = \left[ {\matrix{ 1 & { - \alpha } \cr \alpha & \beta \cr } } \right]$, $A{A^T…
Topic: JEE Main 2021 (25 February Evening Shift)
If the curve x2 + 2y2 = 2 intersects the line x + y = 1 at two points P and Q, then the angle subtended by the line seg…
Topic: JEE Main 2021 (25 February Evening Shift)
The following system of linear equations :- 2x + 3y + 2z = 9, 3x + 2y + 2z = 9, x $-$ y + 4z = 8
Topic: JEE Main 2021 (25 February Evening Shift)
A hyperbola passes through the foci of the ellipse ${{{x^2}} \over {25}} + {{{y^2}} \over {16}} = 1$ and its transverse…
Topic: JEE Main 2021 (25 February Evening Shift)