Practice Test

Q1) 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 Show Answer

Q2) If the side of a cube is 8.004 cm, then its approximate volume is Show Answer

Q3) For which of the following functions is Rolle's Theorem not applicable? Show Answer

Q4) For which of the following functions is Rolle's Theorem not applicable? Show Answer

Q5) 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 Show Answer

Q6) 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. Show Answer

Q7) 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 Show Answer

Q8) If the volume of a sphere is increasing at a constant rate, then the rate at which its radius is increasing, is Show Answer

Q9) 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 Show Answer

Q10) The product of the lengths of subtangent and subnormal at any point of a curve is Show Answer

Q11) Which of the following is biggest? Show Answer

Q12) In [0,1], Lagrange's mean value theorem is not applicable to Show Answer

Q13) 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 Show Answer

Q14) 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? Show Answer

Q15) 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 Show Answer

Q16) If the distance s covered by a particle in time t is proportional to the cube root of its velocity, then the
acceleration is Show Answer

Q17) If the error committed in measuring the radius of the circle is 0.05%, then the corresponding error in
calculating the area is
Show Answer

Q18) The smallest circle with centre on y-axis and passing through the point(7,3)has radius Show Answer

Q19) If PQ and PR are the two sides of a triangle, then the angle between them which gives maximum area of the triangle, is Show Answer

Q20) 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 Show Answer

Q21) 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 Show Answer

Q22) 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 Show Answer

Q23) 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 Show Answer

Q24) A sphere of radius 100mm shrinks to radius 98mm, then the approximate decrease in its volume is Show Answer

Q25) 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 Show Answer

Q26) In [0,1] Lagranges Mean value theorem is NOT applicable to Show Answer

Q27) 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 Show Answer

Q28) If there is an error of 2% in measuring the length of a simple pendulum, then percentage error in its period
is
Show Answer

Q29) If a particle moves such that the displacement is proportional to the square of the velocity acquired , then its acceleration is Show Answer

Q30) 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 Show Answer

Q31) The denominator of a fraction is greatest then 16 of the square of numerator, then least value of fraction is Show Answer

Q32) A cone of maximum volume is inscribed in given sphere, then ratio of the height of the cone to diameter of
the sphere is Show Answer

Q33) If sum of two numbers is 6, the minimum value of the sum of their reciprocals is Show Answer

Q34) 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 Show Answer

Q35) If there is 2% error in measuring the radius of sphere, then… will be the percentage error in the surface
area. Show Answer

Q36) A circular sector of perimeter 60 m with maximum area is to be constructed .The radius the circular are in
metre must be Show Answer

Q37) 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 Show Answer

Q38) 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
Show Answer

Q39) The perimeter of a sector is a constant. If its area is to be maximum, the sectorial angle is Show Answer

Q40) If a particle is moving such that the velocity acquired is proportional to the square root of the distance
covered ,then its acceleration is Show Answer

Q41) The circumference of a circle is measured as 56 cm with an error 0.02 cm. The percentage error in its area
is Show Answer