Revision Quiz on Rate, Errors and Tangents & Normal for JEE & BITSAT Exams

Question 1

Find the rate of change of breadth of a triangle (cm/sec). when the breadth is 15cm whose rate of change of altitude is 10cm/sec
and the area is constant at 150cm².

Question 2

A hemisphere of radius r is attached to the bottom of a cone of constant height h= 10 cm and radius r. Find the rate of increase of volume when r= 3cm and

=10 cm/sec.

Question 3

The solution of differential equation

is

Question 4

For what values of x are the rate of increase of function y = x³ - 5x² + 5x + 8 is twice the rate of increase of x?

Question 5

A rectangle is of side 20cm and 10cm as length and breadth. If the length starts to increase at 5cm/s, then what will be the rate of change of rectangular area at this moment?

Question 6

A pole is of height h has a lamp at its top. A man is moving away from the pole at v ft/s. The rate of change of his shadow when he is a distance ‘d’ from the base of the pole: (The height of the man is 6ft)

Question 7

A spherical balloons is filled with 4500 π cubic meters of helium gas. If a leak in the balloon caused the gas to escape at the rate of 72π cubic meters per minute, then the rate (in meters per minute) at which the radius of the balloon decreases 49 minutes 49 minutes after the leakage began is

Question 8

A boy falling from rest under gravity passes a certain point P. It was at a distance of 400 m from P, 4s prior to passing through P. If g = 10 m/s², then the height above the point P from where the body began to fall is

Question 9

If the curves ay +

= 7 and

= y cut orthogonally at (1,1) then a =

Question 10

X: The inclination of the curve y³ = 21x² at (1, 3√21) is 1
Y: As the value of y – increases the inclination increases keeping abscissa value as constant

Question 11

A family of curves is such that the length intercepted on the y-axis between the origin and the tangent at a point is three times the ordinate of the point of contact. The family of curves is

Question 12

A tangent to the curve,

meets x-axis at A and y-axis at B. If

and

, then the curve also passes through the point:

Question 13

The equation of normal to the curve y=(1+x)^y + sin^-1(sin²x) at x = 0 is

Question 14

P is the point of contact of the tangent from the origin to the curve y = log_ex. The length of the perpendicular drawn from the origin to the normal at P is

Question 15

Let C be a curve given by

. If P is a point on C, such that the tangent at P has slope

, then a point through which the normal at P passes, is: