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If the function f(x) = ax³ + bx² +11x – 6 satisfies the conditions of Rolle’s theorem for the interval [1,3] and f’(2 + 1/√3) = 0, then the values of a and b are respectively

(1) 1, -6 (2) -2, 1 (3) -1, 2 (4) -1, 6 Solution: Given f(x) = ax3 + bx2 +11x... View Article

Let f(x + y) = f(x)f(y) for all x and y, suppose f(5) = 2, and f’(0) = 3, then f’(5) =

(1) 6 (2) 7 (3) 4 (4) 8 Solution: Given f(x + y) = f(x)f(y) f(5) = 2 f’(0) =... View Article

Let f(x) = ∫e^x (x-1)(x-2)dx. Then f decreases in the interval

(1) (-∞, -2) (2) (- 2, – 1) (3) (1, 2) (4) (2, ∞) Solution: Given f(x) = ∫ex (x-1)(x-2)dx... View Article

If for f(x) = 2x – x², Legranges’s theorem satisfies in [0, 1], then the value of c in [0,1] is

(1) c = 0 (2) c = ½ (3) c = ¼ (4) c = 1 Solution: According to Legranges’s... View Article

The function (e^2x – 1)/(e^2x + 1) is

(1) Increasing (2) Decreasing (3) Even (4) Strictly increasing Solution: Let f(x) = (e2x – 1)/(e2x + 1) = (e2x... View Article

If f(x) = x⁵ – 20x³ + 240x, then f(x) satisfies which of the following

(1) It is monotonically decreasing everywhere (2) It is monotonically decreasing only in (0, ∞) (3) It is monotonically increasing... View Article

The line 2x + √6y = 2 is a tangent to the curve x² – 2y² = 4. The point of contact is

(1) (4, -√6) (2) (7, -2√6) (3) (2, 3) (4) (√6, 1) Solution: Given equation of line 2x + √6y... View Article

The triangle formed by the tangent to the curve f(x) = x² + bx – b at the point (1, 1) and the co-ordinate axes, lies in the first quadrant. If its area is 2 then the value of b is

1) –1 2) 3 3) –3 4) 1 Solution: Given f(x) = x2 + bx – b Slope, m =... View Article

The length of sub-tangent to the curve x²y² = a⁴ at the point (-a, a) is

1) 3a 2) 2a 3) a 4) 4a Solution: Given x2y2 = a4 y2 = a4/x2 Differentiate w.r.t.x 2y dy/dx... View Article

The abscissa of the points of curve y = x(x – 2) (x – 4) : where tangents are parallel to x-axis is obtained as

(1) x = 2 ± 2/√3 (2) x = 1 ± 1/√3 (3) x = 2 ± 1/√3 (4) x... View Article

For the curve yⁿ = a^n-1x, the subnormal at any point is constant. The value of n must be

1) 2 2) 3 3) 0 4) 1 Solution: Given yn = an-1x Differentiate w.r.t.x nyn-1dy/dx = an-1 dy/dx =... View Article

On dropping a stone in stationary water circular ripples are observed. Rate of flow of ripples is 6 cm/sec. When radius of the circle is 10 cm, then fluid rate of increase in its area is

1) 120 sq. cm/sec 2) 12 sq. cm/sec 3) π sq. cm/sec 4) 120 π sq. cm/sec Solution: Given rate... View Article

The distance travelled by a particle moving in a straight line at time t is s = √(at² + 2bt + c). Acceleration of the particle is

(1) proportional to t (2) proportional to s (3) proportional to s-3 (4) none of these Solution: Given s =... View Article

A stone, thrown vertically upward from the surface of the moon at a velocity of 24 m/sec reaches a height of s = 24 t – 0.8t² metre after t second. The acceleration due to gravity in m/sec² at the surface of the moon is

1) 0.8 2) -1.6 3) 2.4 4) -4.9 Solution: Given s = 24 t – 0.8t2 Velocity is the derivative... View Article

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