1
JEE Main 2022 (Online) 29th July Morning Shift
+4
-1 A ball is thrown up vertically with a certain velocity so that, it reaches a maximum height h. Find the ratio of the times in which it is at height $$\frac{h}{3}$$ while going up and coming down respectively.

A
$$\frac{\sqrt{2}-1}{\sqrt{2}+1}$$
B
$$\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}$$
C
$$\frac{\sqrt{3}-1}{\sqrt{3}+1}$$
D
$$\frac{1}{3}$$
2
JEE Main 2022 (Online) 29th July Morning Shift
+4
-1 If $$\mathrm{t}=\sqrt{x}+4$$, then $$\left(\frac{\mathrm{d} x}{\mathrm{~d} t}\right)_{\mathrm{t}=4}$$ is :

A
4
B
zero
C
8
D
16
3
JEE Main 2022 (Online) 28th July Evening Shift
+4
-1 At time $$t=0$$ a particle starts travelling from a height $$7 \hat{z} \mathrm{~cm}$$ in a plane keeping z coordinate constant. At any instant of time it's position along the $$\hat{x}$$ and $$\hat{y}$$ directions are defined as $$3 \mathrm{t}$$ and $$5 \mathrm{t}^{3}$$ respectively. At t = 1s acceleration of the particle will be

A
$$-30 \hat{y}$$
B
$$30 \hat{y}$$
C
$$3 \hat{x}+15 \hat{y}$$
D
$$3 \hat{x}+15 \hat{y}+7 \hat{z}$$
4
JEE Main 2022 (Online) 28th July Morning Shift
+4
-1 A NCC parade is going at a uniform speed of $$9 \mathrm{~km} / \mathrm{h}$$ under a mango tree on which a monkey is sitting at a height of $$19.6 \mathrm{~m}$$. At any particular instant, the monkey drops a mango. A cadet will receive the mango whose distance from the tree at time of drop is: (Given $$g=9.8 \mathrm{~m} / \mathrm{s}^{2}$$ )

A
5 m
B
10 m
C
19.8 m
D
24.5 m
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