Consider a region R = {(x, y) $ \in $ R : x² $ \le $ y $ \le $ 2x}. if a line y = $\alpha $ divides the area of region R intotwo equal parts, then which of the following istrue?

1

If a curve y = f(x), passing through the point(1, 2), is the solution of the differential equation,2x2dy= (2xy + y2)dx,…

Topic: JEE Main 2 September 2020 (Evening)

2

The set of all possible values of $\theta $ in the interval (0, $\pi $) for which the points (1, 2) and (sin $\theta $,…

Topic: JEE Main 2 September 2020 (Evening)

3

Let f : (–1,$\infty $)$ \to $ R be defined by f(0) = 1 andLet A = {X = (x, y, z)T: PX = 0 andx2 + y2 + z2 = 1} where$P …

Topic: JEE Main 2 September 2020 (Evening)

4

Let f : (–1,$\infty $)$ \to $ R be defined by f(0) = 1 andf(x) = ${1 \over x}{\log _e}\left( {1 + x} \right)$, x $ \ne …

Topic: JEE Main 2 September 2020 (Evening)

5

The area (in sq. units) of an equilateral triangle inscribed in the parabola y2 = 8x, with one of its vertices on …

Topic: JEE Main 2 September 2020 (Evening)

6

Let f : R $ \to $ R be a function which satisfiesf(x + y) = f(x) + f(y) $\forall $ x, y $ \in $ R. If f(1) = 2 andg(n) …

Topic: JEE Main 2 September 2020 (Evening)

7

If the equation cos4 $\theta $ + sin4 $\theta $ +$\lambda $= 0 has real solutions for $\theta $, then$\lambda…

Topic: JEE Main 2 September 2020 (Evening)

8

Let a, b, c $ \in $ R be all non-zero and satisfy a3 + b3 + c3 = 2. If the matrix A = $\left( {\matrix{ a & b &am…

Topic: JEE Main 2 September 2020 (Evening)

1

For some $\theta \in \left( {0,{\pi \over 2}} \right)$, if the eccentricity of thehyperbola, x2–y2sec2$\theta $ = 10 …

Topic: JEE Main 2 September 2020 (Evening)

2

$\mathop {\lim }\limits_{x \to 0} {\left( {\tan \left( {{\pi \over 4} + x} \right)} \right)^{{1 \over x}}}$ is equal to

Topic: JEE Main 2 September 2020 (Evening)

3

The imaginary part of$${\left( {3 + 2\sqrt { - 54} } \right)^{{1 \over 2}}} - {\left( {3 - 2\sqrt { - 54} } \right)^{{1…

Topic: JEE Main 2 September 2020 (Evening)

4

If the sum of first $11$ terms of an A.P. $a_1, a_2, a_3, \ldots$ is $0 \; (a \neq 0)$, then the sum of the A.P. …

Topic: JEE Main 2 September 2020 (Evening)

5

Let EC denote the complement of an event E.Let E1, E2 and E3 be any pairwise independentevents with P(E1) > 0 and P(…

Topic: JEE Main 2 September 2020 (Evening)

6

Let n > 2 be an integer. Suppose that there are n Metro stations in a city located along a circular path. Each pair …

Topic: JEE Main 2 September 2020 (Evening)