1
JEE Main 2022 (Online) 27th June Morning Shift
+4
-1

A projectile is launched at an angle '$$\alpha$$' with the horizontal with a velocity 20 ms$$-$$1. After 10 s, its inclination with horizontal is '$$\beta$$'. The value of tan$$\beta$$ will be : (g = 10 ms$$-$$2).

A
tan$$\alpha$$ + 5sec$$\alpha$$
B
tan$$\alpha$$ $$-$$ 5sec$$\alpha$$
C
2tan$$\alpha$$ $$-$$ 5sec$$\alpha$$
D
2tan$$\alpha$$ $$+$$ 5sec$$\alpha$$
2
JEE Main 2022 (Online) 27th June Morning Shift
+4
-1

A girl standing on road holds her umbrella at 45$$^\circ$$ with the vertical to keep the rain away. If she starts running without umbrella with a speed of 15$$\sqrt2$$ kmh$$-$$1, the rain drops hit her head vertically. The speed of rain drops with respect to the moving girl is :

A
30 kmh$$-$$1
B
$${{25} \over {\sqrt 2 }}$$ kmh$$-$$1
C
$${{30} \over {\sqrt 2 }}$$ kmh$$-$$1
D
25 kmh$$-$$1
3
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.
4
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
$${{f - \alpha } \over {2(1 + \beta )}}$$
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