Practice Test


1) The velocity of a particle moving in a straight line is proportional to the square-root of its displacement. Then the particle is moving with


2) If the side of a cube is 8.004 cm, then its approximate volume is


3) For which of the following functions is Rolle's Theorem not applicable?


4) For which of the following functions is Rolle's Theorem not applicable?


5) A stone is dropped into a quite pond and waves spread in the form of concentric circles outward from the point where it strikes at a speed of 4 inch / sec. When the radius of the wave-ring is 3 ft, the enclosed area is increasing at the rate of


6) A kite is moving horizontally at a height of 151.5 m. If the speed of kite is 10 m/s, how fast is the string being let out, when the kite is 250 m away from the boy who is flying the kite? The height of boy is 1.5 m.


7) The sides of an equilateral triangle are increasing at the rate of 2 cm/s. The rate at which the area increases, when the side is 10 cm, is


8) If the volume of a sphere is increasing at a constant rate, then the rate at which its radius is increasing, is


9) If the radius of a sphere is measured as 7 m with an error of 0.02 m, then the approximate error in calculating its volume is


10) The product of the lengths of subtangent and subnormal at any point of a curve is


11) Which of the following is biggest?


12) In [0,1], Lagrange's mean value theorem is not applicable to


13) A stone is dropped into a quiet lake. If the waves moves in circles at the rate of 30cm/sec when the radius
is 50 m, the rate of increase of enclosed area is


14) An edge of a variable cube is increasing at the rate of 10cm/s. How fast the volume of the cube will
increase when the edge is 5 cm long?


15) A man of 2m height walks at a uniform speed of 6 km/h away from a lamp post of 6 m height. The rate at
which the length of his shadow increase is


16) If the distance s covered by a particle in time t is proportional to the cube root of its velocity, then the
acceleration is


17) If the error committed in measuring the radius of the circle is 0.05%, then the corresponding error in
calculating the area is


18) The smallest circle with centre on y-axis and passing through the point(7,3)has radius


19) If PQ and PR are the two sides of a triangle, then the angle between them which gives maximum area of the triangle, is


20) A spherical balloon is expanding. If the radius is increasing at the rate of 2 cm/min, the rate at which the
volume increase (in cubic centimeters per minute)when the radius is 5 cm, is


21) If the radius of a circle be increasing at a uniform rate of 2cm/s. The area of increasing of area of circle ,at
the instant when the radius is 20 cm, is


22) Let y be the number of people in a village at time t. Assume that the rate of change of the population is
proportional to the number of people in the village at any time and further assume that the population
never increase in time. Then, the population of the village at any fixed t is given by


23) The sum of two numbers is 20. If the product of the square of one number and cube of the other is
maximum, then the numbers are


24) A sphere of radius 100mm shrinks to radius 98mm, then the approximate decrease in its volume is


25) The edge of a cube is equal to the radius of a sphere. If the edge and the radius increase at the same rate,
then the ratio of the increases in surface areas of the cube and sphere is


26) In [0,1] Lagranges Mean value theorem is NOT applicable to


27) If the rate of change of area of a square plate is equal to that of the rate of change of its perimeter, then length of the side is


28) If there is an error of 2% in measuring the length of a simple pendulum, then percentage error in its period
is


29) If a particle moves such that the displacement is proportional to the square of the velocity acquired , then its acceleration is


30) Divide 12 into two parts such that the product of the square on one part and the fourth power of the second port is maximum, are


31) The denominator of a fraction is greatest then 16 of the square of numerator, then least value of fraction is


32) A cone of maximum volume is inscribed in given sphere, then ratio of the height of the cone to diameter of
the sphere is


33) If sum of two numbers is 6, the minimum value of the sum of their reciprocals is


34) The radius and height of a cylinder are equal. If the radius of the sphere is equal to the height of the
cylinder, then the ratio of the rates of increase of the volume of the sphere and the volume of the cylinder is


35) If there is 2% error in measuring the radius of sphere, then… will be the percentage error in the surface
area.


36) A circular sector of perimeter 60 m with maximum area is to be constructed .The radius the circular are in
metre must be


37) The radius of a cylinder is increasing at the rate of 3m/s and its altitude is decreasing at the rate of 4m/s.
The rate of change of volume when radius is 4m and altitude is 6m, is


38) The side of a square is equal to the diameter of a circle. If the side and radius change at the same rate, then
the ratio of the change of their area is


39) The perimeter of a sector is a constant. If its area is to be maximum, the sectorial angle is


40) If a particle is moving such that the velocity acquired is proportional to the square root of the distance
covered ,then its acceleration is


41) The circumference of a circle is measured as 56 cm with an error 0.02 cm. The percentage error in its area
is