For all twice differentiable functions f : R $ \to $ R,with f(0) = f(1) = f'(0) = 0

1

The integral $\int\limits_1^2 {{e^x}.{x^x}\left( {2 + {{\log }_e}x} \right)} dx$ equals :

Topic: JEE Main 6 September 2020 (Evening)

2

Let z = x + iy be a non-zero complex numbersuch that ${z^2} = i{\left| z \right|^2}$, where i = $\sqrt { - 1} $ , then …

Topic: JEE Main 6 September 2020 (Evening)

3

The area (in sq. units) of the region enclosedby the curves y = x2 – 1 and y = 1 – x2 is equal to :

Topic: JEE Main 6 September 2020 (Evening)

4

Let L denote the line in the xy-plane with x and y intercepts as 3 and 1 respectively. Then the image of the point (–1,…

Topic: JEE Main 6 September 2020 (Evening)

5

For a suitably chosen real constant a, let afunction, $f:R - \left\{ { - a} \right\} \to R$ be defined by$f(x) = {{a -…

Topic: JEE Main 6 September 2020 (Evening)

1

Let f : R $ \to $ R be a function defined by f(x) = max {x, x2}. Let S denote the set of all points in R, where f is n…

Topic: JEE Main 6 September 2020 (Evening)

2

The set of all real values of $\lambda $ for which thefunction$f(x) = \left( {1 - {{\cos }^2}x} \right)\left( {\lambda …

Topic: JEE Main 6 September 2020 (Evening)

3

The common difference of the A.P. b1, b2, … , bm is 2 more than the common difference of A.P. a1, a2, …, an. If a40 =…

Topic: JEE Main 6 September 2020 (Evening)

4

If $\alpha $ and $\beta $ are the roots of the equation2x(2x + 1) = 1, then $\beta $ is equal to :

Topic: JEE Main 6 September 2020 (Evening)

5

The probabilities of three events A, B and C aregiven by P(A) = 0.6, P(B) = 0.4 and P(C) = 0.5.If P(A$ \cup $B) = 0.8, …

Topic: JEE Main 6 September 2020 (Evening)

6

Let $\theta = {\pi \over 5}$ and $A = \left[ {\matrix{ {\cos \theta } & {\sin \theta } \cr { - \sin \theta …

Topic: JEE Main 6 September 2020 (Evening)

7

If the constant term in the binomial expansionof ${\left( {\sqrt x - {k \over {{x^2}}}} \right)^{10}}$ is 405, then |…

Topic: JEE Main 6 September 2020 (Evening)