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

• 5

• 1

• 3

• - 5

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)

The slope of the tangent to the curve x = 3t² + 1, y = t³ - 1 at x = 1 is

• $\frac{1}{2}$

• 0

• - 2

• $\infty$

The rate ofchange of the surface area ofthe sphere of radius r when the radius is increasing at the rate of 2 cm/sec is proportional to

• $\frac{1}{{\mathrm{r}}^2}$

• $\frac{1}{\mathrm{r}}$

• r²

• r

For the curve xy = c², the subnormal at any point varies as

• x³

• x²

• y³

• $\infty$

Let the function $\mathrm{f} : \mathrm{R} \to \mathrm{R}$ be defined by f(x) = 2x + cos(x), then f

• has maximum at x = 0

• has minimum at x = $\mathrm{\pi }$

• is an increasing function

• is a decreasing

The equation to the tangent to the curve y = be^{- x/a} at the point where it crosses the Y-axis is

• ax + by = 1

• $\frac{\mathrm{x}}{\mathrm{a}} - \frac{\mathrm{y}}{\mathrm{b}} = 1$

• $\frac{\mathrm{x}}{\mathrm{a}} + \frac{\mathrm{y}}{\mathrm{b}} = 1$

• ax - by = 1

230.

The height of the cylinder of maximum volume inscribed in a sphere of radius 'a' is

• $\frac{3\mathrm{a}}{2}$

• $\frac{\sqrt{2}\mathrm{a}}{3}$

• $\frac{\mathrm{a}}{\sqrt{3}}$

• $\frac{2\mathrm{a}}{\sqrt{3}}$