1
JEE Main 2022 (Online) 29th July Evening Shift
Numerical
+4
-1
Change Language

Let $$\vec{a}$$ and $$\vec{b}$$ be two vectors such that $$|\vec{a}+\vec{b}|^{2}=|\vec{a}|^{2}+2|\vec{b}|^{2}, \vec{a} \cdot \vec{b}=3$$ and $$|\vec{a} \times \vec{b}|^{2}=75$$. Then $$|\vec{a}|^{2}$$ is equal to __________.

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2
JEE Main 2022 (Online) 29th July Evening Shift
Numerical
+4
-1
Change Language

$$\text { Let } S=\left\{(x, y) \in \mathbb{N} \times \mathbb{N}: 9(x-3)^{2}+16(y-4)^{2} \leq 144\right\}$$ and $$T=\left\{(x, y) \in \mathbb{R} \times \mathbb{R}:(x-7)^{2}+(y-4)^{2} \leq 36\right\}$$. Then $$n(S \cap T)$$ is equal to __________.

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3
JEE Main 2022 (Online) 29th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Two identical metallic spheres $$\mathrm{A}$$ and $$\mathrm{B}$$ when placed at certain distance in air repel each other with a force of $$\mathrm{F}$$. Another identical uncharged sphere $$\mathrm{C}$$ is first placed in contact with $$\mathrm{A}$$ and then in contact with $$\mathrm{B}$$ and finally placed at midpoint between spheres A and B. The force experienced by sphere C will be:

A
3F/2
B
3F/4
C
F
D
2F
4
JEE Main 2022 (Online) 29th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Match List I with List II.

List I List II
A. Torque I. Nms$$^{ - 1}$$
B. Stress II. J kg$$^{ - 1}$$
C. Latent Heat III. Nm
D. Power IV. Nm$$^{ - 2}$$

Choose the correct answer from the options given below :

A
A-III, B-II, C-I, D-IV
B
A-III, B-IV, C-II, D-I
C
A-IV, B-I, C-III, D-II
D
A-II, B-III, C-I, D-IV
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