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) Semivertical angle of a cone of maximum volume of given slant height is Show Answer

Q6) The denominator of a fraction exceeds the square of its numerator by 16. The least value of this fraction is Show Answer

Q7) If the radius of the circle changes at the rate of 0.04 cm/sec, then the rate of change of its area, when radius is 10 cm is Show Answer

Q8) If the circumference of a circle changes at the rate of 0.2 cm/sec, then, when the radius is 8 cm, its area is changing at the rate of Show Answer

Q9) If the diameter and area of a circle change at the same rate, then the radius of the circle is Show Answer

Q10) A stone dropped into a pond of still water sends out concentric circular waves of water, from the point of disturbance, at the rate of 4 cm/sec. When the radius of the wave-ring is 15 cm, the disturbed area is changing at the rate of Show Answer

Q11) 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

Q12) Perimeter of an isosceles triangle is 100 cm. It its base increase at the rate of 2 cm/min, then, when base is 30 cm, its altitude is changing at the rate of Show Answer

Q13) If the side of a cube increases at the rate of 0.04 cm/sec. then, when the side is 6 cm, surface area of the cube is increasing at the rate of Show Answer

Q14) If the side of a cube decreases at the rate of 0.02 cm/sec, then, when the side is 10 cm, volume of the cube decreases at the rate of Show Answer

Q15) If the radius of a sphere increases at the rate of 0.01 cm/sec, then, when the radius is 20 cm, volume of the sphere is increasing at the rate of Show Answer

Q16) If the surface area of a sphere increases at the rate of 2 sq. ft./sec. then, when the radius is 6 ft. its volume is increasing at the rate of Show Answer

Q17) If V is the volume of a sphere and S its surface area, then, when the radius of the sphere is 2 cm, the rate of change of V w.r.t. S is Show Answer

Q18) Oil is being filled in a cylindrical tank of diameter 18 cm. If the amount of oil in the tank is increasing at the rate 324 pi cc/min. then, the height of oil is increasing at the rate of Show Answer

Q19) Slant height of a cone is fixed at 7 cm. If its height increases at 0.6 cm/sec. then, when the height is 4 cm, its volume is increasing at the rate of Show Answer

Q20) A ladder of length 17 metres rests with one end against a vertical wall and the other on the level ground. If the lower end slips away at the rate of 1 m/sec, then, when it is 8 m away from the wall, its upper end is coming down at the rate of Show Answer

Q21) A ladder 5 m long rests against a vertical wall. If its top slides down at the rate of 10 cm/sec. then, when the foot of the ladder is 4 m away from the wall, the angle between the floor and the ladder is decreasing at the rate of Show Answer

Q22) A man of height 150 cm walks at the rate of 75 cm/sec. towards a lighted lamp-post which is 450 cm high. When he is 360 cm away from the lamp-post, his shadow is shortening at the rate of Show Answer

Q23) A kite is flying at a height of 40 meters. The boy who is flying it is carrying it at the rate of 3 m/sec. Height of the kite remains the same and the string is straight (taut). The rate at which the string is being paid out, when its length is 50 meters, is Show Answer

Q24) A man on the tower 15 metres above the water pulls in a rope, attached to a boat, at the rate of 0.8 m/sec. When the boat is 8 m from the tower, it is approaching the river bank at the rate of Show Answer

Q25) Pressure p and volume v of a certain mass of a gas, at constant temperature, are given by pv = 100. When the volume is 25 cc and increasing at the rate of 0.25 cc/sec., pressure is changing at the rate of Show Answer

Q26) If the rate of change of volume of a sphere is equal to the rate of change of its radius, then the radius is Show Answer

Q27) Two cars start from the same point at the same time. One travels westwards at 60 km./hr. and the other travels northwards at 45 km./hr. Two hours later, the distance between them is increasing at the rate of Show Answer

Q28) Side of a n equilateral triangle expands at the rate of 2 cm/sec. The rate of increase of its area when each side is 10 cm is Show Answer

Q29) Volume of a sphere is increasing at the rate of 4 pi cc/sec. The rate of increase of its radius when the volume is 288 pi cc is Show Answer

Q30) If the radius of a sphere increases at the rate of 0.4 cm/sec, then when the radius is 5 decimeters, its surface area is increasing at the rate of Show Answer

Q31) At a given instant, the legs (sides) of a right-angled triangle are 16 cm and 12 cm. If the first side decreases at 0.5 cm/sec and the second increases at 2 cm/sec. then, after 2 seconds, area of the triangle is increasing at the rate of Show Answer

Q32) At a given instant, the legs of a right angled triangle are 6 inch. And 8 inch. If the first leg increase at 2 inch/min and the second decreases at 1 inch/min, then, after 2 minutes, area of the triangle is changing at the rate of Show Answer

Q33) One leg of a right-angled triangle increases at 2 cm/sec. and the second decreases at 1 cm/sec. When the lengths of the two legs are 3 cm and 4 cm respectively, the hypotenuse changes at the rate of (in cm/sec.) Show Answer

Q34) At a certain instant, diameter and altitude of a cylinder are 20 cm and 40 cm respectively. If diameter is increasing at the rate of 2 cm/sec, then the rate of change in its altitude to keep the volume constant is Show Answer

Q35) Height of a right circular cylinder is increasing at the rate of 4 cm/sec., and its base radius decreasing at 3 cm/sec. When the base radius is 20 cm and height 10 cm, volume of the cylinder is changing at the rate of Show Answer

Q36) Radius of base of a cone is increasing at the rate of 6 cm/sec. and its altitude decreasing at 4 cm/sec. When the radius is 8 cm, and altitude 10 cm, its volume is changing at the rate of Show Answer

Q37) Radius of base of a cone is increasing at 3 cm/min, and its height decreasing at 4 cm/min. When the radius is 7 cm. and height 24 cm, its surface area is changing at the rate of Show Answer

Q38) A stone is dropped into a pond. Waves in the form of circles are generated and radius of outermost ripple increases at the rate of 5 cm/sec. Then area increased after 2 seconds is Show Answer

Q39) The edge of a cube is decreasing at the rate of 0.04 cm/sec. If the edge of the cube is 10 cms, then rate of decrease of surface area of the cube is Show Answer

Q40) A ladder is 10 m long rests against a vertical wall with the lower end on the horizontal ground. The lower end of the ladder is pulled along the ground away from the wall at the rate of 3 cm/s. The height of the upper end while it is descending at the rate of 4 cm/s is Show Answer

Q41) For a right circular cone of a slant height 3 cm, the volume is maximum if the height is Show Answer

Q42) The maximum volume of a right circular cylinder if the sum of its radius and height is 6 m is Show Answer

Q43) The maximum area of the rectangle that can be inscribed in a circle of radius r is Show Answer

Q44) If the velocity of a body moving in a straight line varies as the square roots of the distance travelled, then it moves with Show Answer

Q45) A triangular park is bounded on two sides by a fence, and on the third side by a straight river bank. If the two sides having the fence area of the same length x, then the maximum area of the park is Show Answer

Q46) A function is matched below against an interval where it is supposed to be increasing. Which of the following pairs is incorrectly matched? Show Answer

Q47) If the perimeter of a sector of a circle is p, then its area is maximum when its radius is Show Answer