1
JEE Main 2022 (Online) 26th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let O be the origin and A be the point $${z_1} = 1 + 2i$$. If B is the point $${z_2}$$, $${\mathop{\rm Re}\nolimits} ({z_2}) < 0$$, such that OAB is a right angled isosceles triangle with OB as hypotenuse, then which of the following is NOT true?

A
$$\arg {z_2} = \pi - {\tan ^{ - 1}}3$$
B
$$\arg ({z_1} - 2{z_2}) = - {\tan ^{ - 1}}{4 \over 3}$$
C
$$|{z_2}| = \sqrt {10} $$
D
$$|2{z_1} - {z_2}| = 5$$
2
JEE Main 2022 (Online) 26th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If the system of linear equations.

$$8x + y + 4z = - 2$$

$$x + y + z = 0$$

$$\lambda x - 3y = \mu $$

has infinitely many solutions, then the distance of the point $$\left( {\lambda ,\mu , - {1 \over 2}} \right)$$ from the plane $$8x + y + 4z + 2 = 0$$ is :

A
$$3\sqrt 5 $$
B
4
C
$${{26} \over 9}$$
D
$${{10} \over 3}$$
3
JEE Main 2022 (Online) 26th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The odd natural number a, such that the area of the region bounded by y = 1, y = 3, x = 0, x = ya is $${{364} \over 3}$$, is equal to :

A
3
B
5
C
7
D
9
4
JEE Main 2022 (Online) 26th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Consider two G.Ps. 2, 22, 23, ..... and 4, 42, 43, .... of 60 and n terms respectively. If the geometric mean of all the 60 + n terms is $${(2)^{{{225} \over 8}}}$$, then $$\sum\limits_{k = 1}^n {k(n - k)} $$ is equal to :

A
560
B
1540
C
1330
D
2600
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