IPMAT Indore (MCQ) PYQs

If $sin \theta + cos \theta = m$, then $sin^6 \theta + cos^6 \theta$ equals

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 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