1
JEE Main 2022 (Online) 25th June Evening Shift
+4
-1

Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R.

Assertion A : Two identical balls A and B thrown with same velocity 'u' at two different angles with horizontal attained the same range R. IF A and B reached the maximum height h1 and h2 respectively, then $$R = 4\sqrt {{h_1}{h_2}}$$

Reason R : Product of said heights.

$${h_1}{h_2} = \left( {{{{u^2}{{\sin }^2}\theta } \over {2g}}} \right)\,.\,\left( {{{{u^2}{{\cos }^2}\theta } \over {2g}}} \right)$$

A
Both A and R are true and R is the correct explanation of A.
B
Both A and R are true but R is NOT the correct explanation of A.
C
A is true but R is false.
D
A is false but R is true.
2
JEE Main 2022 (Online) 25th June Evening Shift
+4
-1

Two buses P and Q start from a point at the same time and move in a straight line and their positions are represented by $${X_P}(t) = \alpha t + \beta {t^2}$$ and $${X_Q}(t) = ft - {t^2}$$. At what time, both the buses have same velocity?

A
$${{\alpha - f} \over {1 + \beta }}$$
B
$${{\alpha + f} \over {2(\beta - 1)}}$$
C
$${{\alpha + f} \over {2(1 + \beta )}}$$
D
$${{f - \alpha } \over {2(1 + \beta )}}$$
3
JEE Main 2022 (Online) 24th June Morning Shift
+4
-1

A projectile is projected with velocity of 25 m/s at an angle $$\theta$$ with the horizontal. After t seconds its inclination with horizontal becomes zero. If R represents horizontal range of the projectile, the value of $$\theta$$ will be :

[use g = 10 m/s2]

A
$${1 \over 2}{\sin ^{ - 1}}\left( {{{5{t^2}} \over {4R}}} \right)$$
B
$${1 \over 2}{\sin ^{ - 1}}\left( {{{4R} \over {5{t^2}}}} \right)$$
C
$${\tan ^{ - 1}}\left( {{{4{t^2}} \over {5R}}} \right)$$
D
$${\cot ^{ - 1}}\left( {{R \over {20{t^2}}}} \right)$$
4
JEE Main 2021 (Online) 1st September Evening Shift
+4
-1
The ranges and heights for two projectiles projected with the same initial velocity at angles 42$$^\circ$$ and 48$$^\circ$$ with the horizontal are R1, R2 and H1, H2 respectively. Choose the correct option :
A
R1 > R2 and H1 = H2
B
R1 = R2 and H1 < H2
C
R1 < R2 and H1 < H2
D
R1 = R2 and H1 = H2
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