Solve the following questions  of EASY level on Calculus for GATE Mechanical Engineering.

Q1) The value of 'k' for which the equation  has two distinct roots in the interval [0,1].

  1. 1
  2. 3
  3. 5
  4. no such value exists

Q2) Point on the parabola,  where tha tangent is parallel to the chord joining (-2,0) and (0,4)  is

  1. (-1,1)
  2. (0,1)
  3. (1,2)
  4. none of these

Q3)  The interval in which the Lagrange's theorem is applicable for the function f(x) = 1/x is

  1. [-3,3]
  2. [-2,2]
  3. [2,3]
  4. [-1,1]

Q4) If f(x) = | x | , then for interval [-1, 1] ,f(x)

  1. satisied all the conditions of Rolle's Theorem
  2. satisfied all the conditions of Mean Value Theorem
  3. does not satisied the -conditions of Mean Value Theorem
  4. None of these

Q5) What is the derivative of f(x) =  | x | at x = 0 

  1. 1
  2. -1
  3. 0
  4. does not exist

Q6) If f (0) = 2 and f (x) = 2+[1 /  (5-x2)], then lower and upper bound of f(1) estimated by the mean value theorem are

  1. 1.9, 2.2
  2. 2.2, 2.25
  3. 2.25, 2.5
  4. none of these

Q7) Value of 'c' of the mean value theorem for the function f(x) = x(x - 2), when a = 0, b = 3/2, is

  1. 3/4
  2. 1/2
  3. 3/2
  4. 1/4

Q8) The value of the integral,  is 

  1. 0
  2. 1
  3. 0.25
  4. infinity

Q9) The minimum value of | x2-5x+21 | is

  1. -5
  2. 0
  3. -1
  4. -2

Q10) Sum of the perimeters of a circle and a square is 1. If sum of the area is least, then

  1. side of the square is double the radius of circle
  2. side of the square is 1/2 of the radius of the circle
  3. side of the square is equal to radius of the circle
  4. none of these

The next set of questions will be easy level questions on Vector Calculus.