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

• $70 \mathrm{\pi } {\mathrm{cm}}^2/\mathrm{s}$

• $70 {\mathrm{cm}}^2/\mathrm{s}$

• $80 \mathrm{\pi } {\mathrm{cm}}^2/\mathrm{s}$

• $80 {\mathrm{cm}}^2/\mathrm{s}$

The equation of normal at the point (0, 3) of the ellipse 9x² + 5y² = 45 is

• x-axis

• y-axis

• y + 3 = 0

• y - 3 = 0

The maximum value of x^1/x is :

• 1/e^e

• e

• e^1/e

• 1/e

The function f defined by f(x) = 4x⁴ - 2x + 1 is increasing for :

• x < 1

• x > 0

• x < 1/2

• x > 1/2

A particle moves in a straight line so that s = $\sqrt{\mathrm{t}}$, then its acceleration is proportional to :

• (velocity)³

• velocity

• (velocity)²

• (velocity)^3/2

If the line ax + by + c = 0 is a normal to the curve y =1, then :

• a > 0, b > 0

• a > 0, b < 0

• a < 0, b < 0

• Data is insufficient

The minimum value of $3\sin \left(\mathrm{\theta }\right) + 4\cos \left(\mathrm{\theta }\right)$ is :

• 5

• 1

• 3

• - 5

658.

Maximum value of sin(x) - cos(x) is equal to :

• $\sqrt{2}$

• 1

• 0

• none of these

If the distance 's' metres traversed by a particle int seconds is given by s = t³ - 3t², then the velocity of the particle when the acceleration is zero, in m/s is

• 3

• - 2

• - 3

• 2

If tangent to the curve x = at², y = 2at is perpendicular to X - axis, then its point of contact is

• (a, a)

• (0, a)

• (0, 0)

• (a, 0)