Maximum value of f(x) = sin(x) + cos(x) is

• 1

• 2

• $\frac{1}{\sqrt{2}}$

• $\sqrt{2}$

The greatest value of f(x) = (x + 1)^1/3 - (x - 1)^1/3 on [0, 1] is

• 1

• 2

• 3

• 1/3

The equation of normal to the circle 2x² + 2y² - 2 - 5y + 3 = 0 at (1, 1) is

• 2x + y = 3

• x - 2y = 3

• x + 2y = 3

• None of these

The minimum value of the function f(x) = 2x³ - 21x² + 36x - 20 is

• - 128

• - 126

• - 120

• None of these

285.

If the function f(x) = 2x³ - 9ax² + 12a + 1, where a > 0, attains its maximum and minimum values at p and q respectively such that p² = q, then a equals

• 3

• 1

• 2

• $\frac{1}{2}$

For the function 3x⁴ - 8x³ + 12x² - 48x + 25 in the interval [1, 3]. The value of maxima and minima are

• 16, - 39

• - 16, 39

• 6, - 9

• None of these

f(x) = x³ - 27x + 5 is an increasing function when

• x < - 3

• $\left|\mathrm{x}\right| >\hspace{0.17em}3$

• $\mathrm{x} \le - 3$

• $\left|\mathrm{x}\right| <\hspace{0.17em}3$

In the interval $\left(0, \frac{\mathrm{\pi }}{2}\right)$ function log(sin(x)) is

• increasing

• decreasing

• neither increasing nor decreasing

• None of the above

A cone of maximum volume is being cut from sphere, then ratio between height of cone and diameter of sphere is

• $\frac{2}{3}$

• $\frac{1}{3}$

• $\frac{3}{4}$

• $\frac{1}{4}$

The function x⁵ - 5x⁴ + 5x³ - 10 has a maximum, when x is equal to

• 3

• 2

• 1

• 0