1
JEE Main 2023 (Online) 8th April Morning Shift
+4
-1 Two projectiles A and B are thrown with initial velocities of $$40 \mathrm{~m} / \mathrm{s}$$ and $$60 \mathrm{~m} / \mathrm{s}$$ at angles $$30^{\circ}$$ and $$60^{\circ}$$ with the horizontal respectively. The ratio of their ranges respectively is $$\left(g=10 \mathrm{~m} / \mathrm{s}^{2}\right)$$

A
$$4: 9$$
B
$$2: \sqrt{3}$$
C
$$\sqrt{3}: 2$$
D
$$1: 1$$
2
JEE Main 2023 (Online) 6th April Evening Shift
+4
-1 A particle starts with an initial velocity of $$10.0 \mathrm{~ms}^{-1}$$ along $$x$$-direction and accelerates uniformly at the rate of $$2.0 \mathrm{~ms}^{-2}$$. The time taken by the particle to reach the velocity of $$60.0 \mathrm{~ms}^{-1}$$ is __________.

A
30s
B
6s
C
3s
D
25s
3
JEE Main 2023 (Online) 6th April Morning Shift
+4
-1 Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R

Assertion A : When a body is projected at an angle $$45^{\circ}$$, it's range is maximum.

Reason R : For maximum range, the value of $$\sin 2 \theta$$ should be equal to one.

In the light of the above statements, choose the correct answer from the options given below:

A
Both $$\mathbf{A}$$ and $$\mathbf{R}$$ are correct and $$\mathbf{R}$$ is the correct explanation of $$\mathbf{A}$$
B
$$\mathbf{A}$$ is true but $$\mathbf{R}$$ is false
C
$$\mathbf{A}$$ is false but $$\mathbf{R}$$ is true
D
Both $$\mathbf{A}$$ and $$\mathbf{R}$$ are correct but $$\mathbf{R}$$ is NOT the correct explanation of $$\mathbf{A}$$
4
JEE Main 2023 (Online) 1st February Morning Shift
+4
-1 An object moves with speed $$v_1,v_2$$ and $$v_3$$ along a line segment AB, BC and CD respectively as shown in figure. Where AB = BC and AD = 3AB, then average speed of the object will be: A
$${{{v_1}{v_2}{v_3}} \over {3({v_1}{v_2} + {v_2}{v_3} + {v_3}{v_1})}}$$
B
$${{({v_1} + {v_2} + {v_3})} \over 3}$$
C
$${{({v_1} + {v_2} + {v_3})} \over {3{v_1}{v_2}{v_3}}}$$
D
$${{3{v_1}{v_2}{v_3}} \over {({v_1}{v_2} + {v_2}{v_3} + {v_3}{v_1})}}$$
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