Related InterviewSolutions

• A particle moves on a line according to the law `s=at^(2)+bt+c`. If the displacement after 1 sec is 16 cm, the velocity after 2 sec is 24 cm/sec and acceleration is `8cm//sec^(2)`, thenA. a=4, b=8, c=4B. a=4, b=4, c=8C. a=8, b=4, c=4D. none of these
• A particle moves along the parabola `y^2=2ax` in such a way that its projection on y-axis has a constant velocity. Show that its projection on the x-axis moves with constant accelerationA. constant velocityB. constant accelerationC. variable velocityD. variable acceleration
• A spherical balloon is being inflated so that its volume increase uniformaly at the rate of `40 cm^(3)//"minute"`. The rate of increase in its surface area when the radius is 8 cm, isA. `10 cm^(2)` minuteB. `20 cm^(2)` minuteC. `40 cm^(2)` minuteD. none of these
• The edge of a cube is equal to the radius o the sphere. If the rate at which the volume of the cube is increasing is equal to `lambda`, then the rate of increase of volume of the sphere, isA. `(4pi lambda)/(3)`B. `4pi lambda`C. `(lambda)/(3)`D. none of these
• At an instant the diagonal of a square is increasing at the rate of 0.2 cm/sec and the area is increasing at the rate of `6 cm^(2)//sec`. At the moment its side, isA. `(30)/(sqrt(2))cm`B. `30sqrt(2)` cmC. 30 cmD. 15 cm
• The weight W of a certain stock of fish is given by W = nw, where n is the size of stock and w is the average weight of a fish. If n and w change with time t as n = `2t^(2)+3` and `w=t^(2)-t+2`, then the rate of change of W with respect to t at t = 1, isA. 1B. 13C. 5D. 8
• Side of an equilateral triangle expands at therate of 2 cm/sec. The rate of increase of its area when each side is 10 cm is(a)cm2/sec (b)cm2/sec(c) 10 cm2/sec (d) 5 cm2/secA. `10sqrt(2)cm^(2)//sec`B. `10sqrt(3)cm^(2)//sec`C. `10 cm^(2)//sec`D. `5cm^(2)//sec`
• The surface area of a cube is increasing at the rate of `2 cm^(2)//sec`. When its edge is 90 cm, the volume is increasing at the rate ofA. `1620 cm^(3)//sec`B. `810 cm^(3)//sec`C. `405 cm^(3)//sec`D. `45 cm^(3)//sec`
• A spherical iron ball 10cm in radius is coated with a layer of ice ofuniform thickness that melts at a rate of `50c m^3//m in`. When the thickness of ice is 5cm, then findthe rate at which the thickness of ice decreases.A. `(5)/(6pi)cm//min`B. `(1)/(54pi) cm//min`C. `(1)/(18pi) cm//min`D. `(1)/(36pi) cm//min`
• Find the surface area of a sphere when its volumeis changing at the same rate as its radius.A. 1B. `(1)/(2sqrt(pi))`C. `4pi`D. `(4pi)/(3)`