1
JEE Main 2022 (Online) 25th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let a, b $$\in$$ R be such that the equation $$a{x^2} - 2bx + 15 = 0$$ has a repeated root $$\alpha$$. If $$\alpha$$ and $$\beta$$ are the roots of the equation $${x^2} - 2bx + 21 = 0$$, then $${\alpha ^2} + {\beta ^2}$$ is equal to :

A
37
B
58
C
68
D
92
2
JEE Main 2022 (Online) 25th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let z1 and z2 be two complex numbers such that $${\overline z _1} = i{\overline z _2}$$ and $$\arg \left( {{{{z_1}} \over {{{\overline z }_2}}}} \right) = \pi $$. Then :

A
$$\arg {z_2} = {\pi \over 4}$$
B
$$\arg {z_2} = - {{3\pi } \over 4}$$
C
$$\arg {z_1} = {\pi \over 4}$$
D
$$\arg {z_1} = - {{3\pi } \over 4}$$
3
JEE Main 2022 (Online) 25th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The system of equations

$$ - kx + 3y - 14z = 25$$

$$ - 15x + 4y - kz = 3$$

$$ - 4x + y + 3z = 4$$

is consistent for all k in the set

A
R
B
R $$-$$ {$$-$$11, 13}
C
R $$-$$ {13}
D
R $$-$$ {$$-$$11, 11}
4
JEE Main 2022 (Online) 25th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

$$\mathop {\lim }\limits_{x \to {\pi \over 2}} \left( {{{\tan }^2}x\left( {{{(2{{\sin }^2}x + 3\sin x + 4)}^{{1 \over 2}}} - {{({{\sin }^2}x + 6\sin x + 2)}^{{1 \over 2}}}} \right)} \right)$$ is equal to

A
$${1 \over {12}}$$
B
$$-$$$${1 \over {18}}$$
C
$$-$$$${1 \over {12}}$$
D
$${1 \over {6}}$$
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