1
JEE Main 2023 (Online) 13th April Evening Shift
+4
-1

The distance travelled by an object in time $$t$$ is given by $$s=(2.5) t^{2}$$. The instantaneous speed of the object at $$\mathrm{t}=5 \mathrm{~s}$$ will be:

A
$$5 \mathrm{~ms}^{-1}$$
B
$$12.5 \mathrm{~ms}^{-1}$$
C
$$62.5 \mathrm{~ms}^{-1}$$
D
$$25 \mathrm{~ms}^{-1}$$
2
JEE Main 2023 (Online) 13th April Evening Shift
+4
-1

A passenger sitting in a train A moving at $$90 \mathrm{~km} / \mathrm{h}$$ observes another train $$\mathrm{B}$$ moving in the opposite direction for $$8 \mathrm{~s}$$. If the velocity of the train B is $$54 \mathrm{~km} / \mathrm{h}$$, then length of train B is:

A
80 m
B
200 m
C
120 m
D
320 m
3
JEE Main 2023 (Online) 13th April Morning Shift
+4
-1

Two trains 'A' and 'B' of length '$$l$$' and '$$4 l$$' are travelling into a tunnel of length '$$\mathrm{L}$$' in parallel tracks from opposite directions with velocities $$108 \mathrm{~km} / \mathrm{h}$$ and $$72 \mathrm{~km} / \mathrm{h}$$, respectively. If train 'A' takes $$35 \mathrm{~s}$$ less time than train 'B' to cross the tunnel then. length '$$L$$' of tunnel is :

(Given $$\mathrm{L}=60 l$$ )

A
900 m
B
1200 m
C
1800 m
D
2700 m
4
JEE Main 2023 (Online) 12th April Morning Shift
+4
-1

A ball is thrown vertically upward with an initial velocity of $$150 \mathrm{~m} / \mathrm{s}$$. The ratio of velocity after $$3 \mathrm{~s}$$ and $$5 \mathrm{~s}$$ is $$\frac{x+1}{x}$$. The value of $$x$$ is ___________.

$$\left\{\right.$$ take, $$\left.g=10 \mathrm{~m} / \mathrm{s}^{2}\right\}$$

A
$$-5$$
B
10
C
5
D
6
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