If ${a_r} = \cos {{2r\pi } \over 9} + i\sin {{2r\pi } \over 9}$, r = 1, 2, 3, ....., i = $\sqrt { - 1} $, then the determinant $\left| {\matrix{ {{a_1}} & {{a_2}} & {{a_3}} \cr {{a_4}} & {{a_5}} & {{a_6}} \cr {{a_7}} & {{a_8}} & {{a_9}} \cr } } \right|$ is equal to :<

1

$\mathop {\lim }\limits_{x \to 0} {{{{\sin }^2}\left( {\pi {{\cos }^4}x} \right)} \over {{x^4}}}$ is equal to :

Topic: JEE Main 2021 (31 August Morning Shift)

2

If ${{dy} \over {dx}} = {{{2^{x + y}} - {2^x}} \over {{2^y}}}$, y(0) = 1, then y(1) is equal to :

Topic: JEE Main 2021 (31 August Morning Shift)

3

If the function $f(x) = \left\{ {\matrix{ {{1 \over x}{{\log }_e}\left( {{{1 + {x \over a}} \over {1 - {x \over b}}}…

Topic: JEE Main 2021 (31 August Morning Shift)

4

The length of the latus rectum of a parabola, whose vertex and focus are on the positive x-axis at a distance R and S (…

Topic: JEE Main 2021 (31 August Morning Shift)

5

If the following system of linear equations 2x + y + z = 5, x $-$ y + z = 3, x + y + az = b has no solution, then :

Topic: JEE Main 2021 (31 August Morning Shift)

6

cosec18$^\circ$ is a root of the equation :

Topic: JEE Main 2021 (31 August Morning Shift)

7

If p and q are the lengths of the perpendiculars from the origin on the lines,:- x cosec $\alpha$ $-$ y sec $\alpha$ = …

Topic: JEE Main 2021 (31 August Morning Shift)

8

The integral $\int {{1 \over {\root 4 \of {{{(x - 1)}^3}{{(x + 2)}^5}} }}} \,dx$ is equal to : (where C is a constant o…

Topic: JEE Main 2021 (31 August Morning Shift)

9

Which of the following is not correct for relation R on the set of real numbers ?

Topic: JEE Main 2021 (31 August Morning Shift)

10

Three numbers are in an increasing geometric progression with common ratio r. If the middle number is doubled, then the…

Topic: JEE Main 2021 (31 August Morning Shift)