IPMAT Indore (MCQ) PYQs

The set of all real value of $p$ for which the equation $3 \sin^2x + 12 \cos x - 3 = p$ has at least one solution is

Ayesha is standing atop a vertical tower $200 m$ high and observes a car moving away from the tower on a straight, horizontal road from the foot of the tower. At 11:00 AM, she observes the angle of depression of the car to be $45^{\circ}$. At 11:02 AM, she observes the angle of depression of the car to be $30^{\circ}$. The speed at which the car is moving is approximately

The angle of elevation of the top of a pole from a point A on the ground is 30°. The angle of elevation changes to 45°, after moving 20 meters towards the base of the pole. Then the height of the pole, in meters, is