31.

If y =  for , 2, then y'(3) is equal to

• $\frac{1}{3}$

• $\frac{2}{3}$

• $\frac{4}{3}$

• None of these

The minimum distance from the point (4, 2) to the parabola y² = 8x is

• $\sqrt{2}$

• $2\sqrt{2}$

• 2

• $3\sqrt{2}$

A particle moves so that the space described in time t is square root of a quadratic function of t. Then,

• $\mathrm{v} \propto \left(\frac{1}{\mathrm{s}}\right)$

• $\mathrm{acceleration} \propto \frac{1}{{\mathrm{s}}^3}$

• $\mathrm{acceleration} \propto {\mathrm{s}}^3$

• None of these

Cube root of 18 by using Newton-Raphson method will be

• 2.26

• 2.620

• 2.602

• None of these

The points at which the tangent to the curve y = x³ + 5 is perpendicular to the line x + 3y = 2 are

• (6, 1), (- 1, 4)

• (1, 6), (1, 4)

• (6, 1), (4, - 1)

• (1, 6), (- 1, 4)

Which one of the following is not defined?

• $\overrightarrow{\mathrm{a}} + \overrightarrow{\mathrm{b}}$

• $\overrightarrow{\mathrm{a}} \times 2\overrightarrow{\mathrm{b}}$

• $\left(3\overrightarrow{\mathrm{a}} \times 2\overrightarrow{\mathrm{b}}\right)4\overrightarrow{\mathrm{a}}$

• $\left(\overrightarrow{\mathrm{a}} . 2\overrightarrow{\mathrm{b}}\right)\overrightarrow{\mathrm{a}}$

The vectors $2\hat{\mathrm{i}} + 3\hat{\mathrm{j}} - 4\hat{\mathrm{k}}$ and $\mathrm{a}\hat{\mathrm{i}} + \mathrm{b}\hat{\mathrm{j}} + \mathrm{c}\hat{\mathrm{k}}$ are perpendicular, when

• a = 2, b = 3, c = - 4

• a = 4, b = 4, c = 5

• a = 4, b = 4, c = - 5

• None of the above

Value of a for which the vectors (2, - 1, 1) (1, 2, - 3) and (3, a, 5) become coplanar will be

• 4

• - 4

• no such exists

• None of these

A man runs due North at the rate of 20 km/h and the wind blows fromthe East at the rate of 15km/h. Then, the velocity of the wind relative to the man will be

• 2km/h

• 3 km/h

• 25 km/h

• None of these

If l , m, n are the DC's of a line, then

• l² + m² + n² = 0

• l² + m² + n² = 1

• l + m + n = 1

• l = m = n = 1