Define a relation R over a class of n $\times$ n real matrices A and B as "ARB iff there exists a non-singular matrix P such that PAP^$-$1 = B". Then which of the following is true?

1

In a triangle ABC, if $|\overrightarrow {BC} | = 8,|\overrightarrow {CA} | = 7,|\overrightarrow {AB} | = 10$, then the …

Topic: JEE Main 2021 (18 March Evening Shift)

2

Let in a series of 2n observations, half of them are equal to a and remaining half are equal to $-$a. Also by adding a …

Topic: JEE Main 2021 (18 March Evening Shift)

3

Let g(x) = $\int_0^x {f(t)dt} $, where f is continuous function in [ 0, 3 ] such that ${1 \over 3}$ $ \le $ f(t) $ \le …

Topic: JEE Main 2021 (18 March Evening Shift)

4

Let \; f:\mathbb{R}\to\mathbb{R} \text{ be defined as} \[ f(x) = \begin{cases} \dfrac{\sin\!\big((a+1)x\big)+\sin 2x}{2…

Topic: JEE Main 2021 (18 March Evening Shift)

5

Let a complex number be w = 1 $-$ ${\sqrt 3 }$i. Let another complex number z be such that |zw| = 1 and arg(z) $-$ arg(…

Topic: JEE Main 2021 (18 March Evening Shift)

6

Let $\overrightarrow a $ and $\overrightarrow b $ be two non-zero vectors perpendicular to each other and $|\overrighta…

Topic: JEE Main 2021 (18 March Evening Shift)

7

If 15sin4$\alpha$ + 10cos4$\alpha$ = 6, for some $\alpha$$\in$R, then the value of 27sec6$\alpha$ + 8cosec6$\alpha$ is…

Topic: JEE Main 2021 (18 March Evening Shift)

8

The area bounded by the curve 4y2 = x2(4 $-$ x)(x $-$ 2) is equal to :

Topic: JEE Main 2021 (18 March Evening Shift)

9

Let the system of linear equations4x + $\lambda$y + 2z = 0 ,2x $-$ y + z = 0 , $\mu$x + 2y + 3z = 0, $\lambda$, $\mu$$\…

Topic: JEE Main 2021 (18 March Evening Shift)

10

If 15sin4$\alpha$ + 10cos4$\alpha$ = 6, for some $\alpha$$\in$R, then the value of 27sec6$\alpha$ + 8cosec6$\alpha$ is …

Topic: JEE Main 2021 (18 March Evening Shift)

1

Let the centroid of an equilateral triangle ABC be at the origin. Let one of the sides of the equilateral triangle be a…

Topic: JEE Main 2021 (18 March Evening Shift)

2

Let f : R $-$ {3} $ \to $ R $-$ {1} be defined by f(x) = ${{x - 2} \over {x - 3}}$.Let g : R $ \to $ R be given as g(x)…

Topic: JEE Main 2021 (18 March Evening Shift)

3

Let S1 be the sum of first 2n terms of an arithmetic progression. Let S2 be the sum of first 4n terms of the same arith…

Topic: JEE Main 2021 (18 March Evening Shift)