Abhishek Ranjan

A 15 kg, 1m wide door which has frictionless hinges is closed but unlocked. A 400 g ball hits the exact middle of the door at a velocity of 35 m/s and bounces off elastically, thereby causing the door to slowly swing open. How long in seconds does it take...

A fair coin is flipped 3 times. The probability of getting exactly two heads, given that at least one flip results in a head, can be written as ab, where a and b are coprime positive integers. What is the value of a+b?

A monic polynomial f(x) of degree four satisfies f(1)=10, f(2)=20, and f(3)=30. Determine f(12)+f(−8)−19000.

Find the minimum possible value of 2cos4θ+8cos3θ+32cos2θ+56cosθ+100

a+b=419

2.82

426

10

41