Let a, b, c $ \in $ R be all non-zero and satisfy a³ + b³ + c³ = 2. If the matrix A = $\left( {\matrix{ a & b & c \cr b & c & a \cr c & a & b \cr } } \right)$ satisfies A^TA = I, then a value of abc can be :

1

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

Topic: JEE Main 2 September 2020 (Evening)

2

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)

3

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)

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

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)

6

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)

7

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)

8

Consider a region R = {(x, y) $ \in $ R : x2 $ \le $ y $ \le $ 2x}. if a line y = $\alpha $ divides the area of regi…

Topic: JEE Main 2 September 2020 (Evening)

9

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)

10

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

Topic: JEE Main 2 September 2020 (Evening)