If [x] is the greatest integer $\le$ x, then ${\pi ^2}\int\limits_0^2 {\left( {\sin {{\pi x} \over 2}} \right)(x - [x]} {)^{[x]}}dx$ is equal to :

1

Let f be any continuous function on [0, 2] and twice differentiable on (0, 2). If f(0) = 0, f(1) = 1 and f(2) = 2, then

Topic: JEE Main 2021 (31 August Evening Shift)

2

Let A be the set of all points ($\alpha$, $\beta$) such that the area of triangle formed by the points (5, 6), (3, 2) a…

Topic: JEE Main 2021 (31 August Evening Shift)

3

Let a1, a2, a3, ..... be an A.P. If ${{{a_1} + {a_2} + .... + {a_{10}}} \over {{a_1} + {a_2} + .... + {a_p}}} = {{100} …

Topic: JEE Main 2021 (31 August Evening Shift)

4

If z is a complex number such that ${{z - i} \over {z - 1}}$ is purely imaginary, then the minimum value of | z $-$ (3 …

Topic: JEE Main 2021 (31 August Evening Shift)

5

The sum of the roots of the equation:- $x + 1 - 2{\log _2}(3 + {2^x}) + 2{\log _4}(10 - {2^{ - x}}) = 0$, is :

Topic: JEE Main 2021 (31 August Evening Shift)

6

If $y{{dy} \over {dx}} = x\left[ {{{{y^2}} \over {{x^2}}} + {{\phi \left( {{{{y^2}} \over {{x^2}}}} \right)} \over {\ph…

Topic: JEE Main 2021 (31 August Evening Shift)

7

If ${{dy} \over {dx}} = {{{2^x}y + {2^y}{{.2}^x}} \over {{2^x} + {2^{x + y}}{{\log }_e}2}}$, y(0) = 0, then for y = 1, …

Topic: JEE Main 2021 (31 August Evening Shift)

8

The locus of mid-points of the line segments joining ($-$3, $-$5) and the points on the ellipse ${{{x^2}} \over 4} + {{…

Topic: JEE Main 2021 (31 August Evening Shift)

9

If $\alpha = \mathop {\lim }\limits_{x \to {\pi \over 4}} {{{{\tan }^3}x - \tan x} \over {\cos \left( {x + {\pi \ove…

Topic: JEE Main 2021 (31 August Evening Shift)

10

Let f : N $\to$ N be a function such that f(m + n) = f(m) + f(n) for every m, n$\in$N. If f(6) = 18, then f(2) . f(3) i…

Topic: JEE Main 2021 (31 August Evening Shift)

1

The mean and variance of 7 observations are 8 and 16 respectively. If two observations are 6 and 8, then the variance o…

Topic: JEE Main 2021 (31 August Evening Shift)