The volume of a sphere is increasing in volume at the rate of 3 πcm³ / sec. The rate of change of its radius when radius is \(\frac { 1 }{ 2 } \) cm

(a)

3 cm/s

(b)

2 cm/s

(c)

1 cm/s

(d)

\(\cfrac { 1 }{ 2 } cm/s\)

The slope of the line normal to the curve f(x) = 2cos 4x at \(x=\cfrac { \pi }{ 12 } \) is

(a)

\(-4\sqrt { 3 } \)

(b)

-4

(c)

\(\cfrac { \sqrt { 3 } }{ 12 } \)

(d)

\(4\sqrt { 3 } \)

The number given by the Rolle's theorem for the functlon x³ - 3x², x ∈ [0, 3] is

(a)

1

(b)

\(\sqrt { 2 } \)

(c)

\(\frac { 3 }{ 2 } \)

(d)

2

One of the closest points on the curve x² - y² = 4 to the point (6, 0) is

(a)

(2,0)

(b)

\(\left( \sqrt { 5 } ,1 \right) \)

(c)

\(\left( 3,\sqrt { 5 } \right) \)

(d)

\(\left( \sqrt { 13 } ,-\sqrt { 3 } \right) \)

If a particle moves in a straight line according to s = t³-6t²-15t, the time interval during which the velocity is negative and acceleration is positive is __________

(a)

2 < t < 5

(b)

2 ≤ t ≤ 5

(c)

t ≥ 2

(d)

t ≤ 2

The least value of a when f f(x) = x² + ax + 1 is increasing on (1, 2) is __________

(a)

-2

(b)

2

(c)

1

(d)

-1

The angle made by any tangent to the curve y = x⁵ + 8x + 1 with the X-axis is a __________

(a)

obtuse

(b)

right angle

(c)

acute angle

(d)

no angle

If the slope of the curve 2y² = ax²+b at (1,-1) is - 1, then the values of a, b is __________

(a)

2, 0

(b)

0, 2

(c)

0, 0

(d)

2, 2

The function -3x+12 is ________ function on R.

(a)

decreasing

(b)

strictly decreasing

(c)

increasing

(d)

strictly increasing

\(\underset { x\rightarrow 0 }{ lim } \frac { x }{ tanx } \) is _________

(a)

1

(b)

-1

(c)

0

(d)

∞