The law of linear motion of a particle is given s = \(\frac{1}{3}\) t³-16t, the acceleration at the time when the velocity vanishes is __________

(a)

4

(b)

6

(c)

2

(d)

8

Equation of the normal to the curve y = 2x²+3 sin x at x = 0 is __________

(a)

x + y = 0

(b)

3y = 0

(c)

x + 3y = 7

(d)

x + 3y = 0

The value of \(\underset { x\rightarrow \infty }{ lim } { e }^{ -x }\) is __________

(a)

0

(b)

∞

(c)

e

(d)

\(\frac{1}{e}\)

The critical points of the function f(x) = \((x-2)^{ \frac { 2 }{ 3 } }(2x+1)\) are __________

(a)

-1, 2

(b)

1, \(\frac { 1 }{ 2 } \)

(c)

1, 2

(d)

none

In LMV theorem, we have f'(x₁) = \(\frac { f(b)-f(a) }{ b-a } \) then a < x₁ _________

(a)

<b

(b)

≤b

(c)

=b

(d)

≠b