If the value of the integral $\int\limits_0^{{1 \over 2}} {{{{x^2}} \over {{{\left( {1 - {x^2}} \right)}^{{3 \over 2}}}}}} dx$ is ${k \over 6}$, then k is equal to :

1

Let R1 and R2 be two relation defined asfollows :R1 = {(a, b) $ \in $ R2 : a2 + b2 $ \in $ Q} andR2 = {(a, b) $ \in $ R…

Topic: JEE Main 3 September 2020 (Evening)

2

Let the latus ractum of the parabola y2 = 4x be the common chord to the circles C1 and C2 each of them having radi…

Topic: JEE Main 3 September 2020 (Evening)

3

Let a, b c $ \in $ R be such that a2 + b2 + c2 = 1. If $a\cos \theta = b\cos \left( {\theta + {{2\pi } \over 3}} \rig…

Topic: JEE Main 3 September 2020 (Evening)

4

Suppose f(x) is a polynomial of degree four,having critical points at –1, 0, 1. If T = {x $ \in $ R | f(x) = f(0)}, the…

Topic: JEE Main 3 September 2020 (Evening)

1

Let e1 and e2 be the eccentricities of theellipse, ${{{x^2}} \over {25}} + {{{y^2}} \over {{b^2}}} = 1$(b < 5) and t…

Topic: JEE Main 3 September 2020 (Evening)

2

The probability that a randomly chosen 5-digit number is made from exactly two digits is :

Topic: JEE Main 3 September 2020 (Evening)

3

If x3dy + xy dx = x2dy + 2y dx; y(2) = e and x > 1, then y(4) is equal to :

Topic: JEE Main 3 September 2020 (Evening)

4

$\mathop {\lim }\limits_{x \to a} {{{{\left( {a + 2x} \right)}^{{1 \over 3}}} - {{\left( {3x} \right)}^{{1 \over 3}}}} …

Topic: JEE Main 3 September 2020 (Evening)

5

If the surface area of a cube is increasing at a rate of 3.6 cm2/sec, retaining its shape; then the rate of change of i…

Topic: JEE Main 3 September 2020 (Evening)

6

If a $\Delta $ABC has vertices A(–1, 7), B(–7, 1) and C(5, –5), then its orthocentre has coordinates :

Topic: JEE Main 3 September 2020 (Evening)

7

Let xi (1 $ \le $ i $ \le $ 10) be ten observations of arandom variable X. If $\sum\limits_{i = 1}^{10} {\left( {{x_i} …

Topic: JEE Main 3 September 2020 (Evening)

8

If z1, z2 are complex numbers such that Re(z1) = |z1 – 1|, Re(z2) = |z2 – 1| , and arg(z1 - z2) = ${\pi \over 6}$, th…

Topic: JEE Main 3 September 2020 (Evening)

9

If $\int {{{\sin }^{ - 1}}\left( {\sqrt {{x \over {1 + x}}} } \right)} dx$ = A(x)${\tan ^{ - 1}}\left( {\sqrt x } \righ…

Topic: JEE Main 3 September 2020 (Evening)

10

If the term independent of x in the expansion of ${\left( {{3 \over 2}{x^2} - {1 \over {3x}}} \right)^9}$ is k, then 18…

Topic: JEE Main 3 September 2020 (Evening)