If y = 4x-5 is a tangent to the curve y² = px³ + q at (2, 3), then

• p = 2, q = - 7

• p = - 2, q = 7

• p = - 2, q = - 7

• p = 2, q = 7

A missile is fired from the fround level rises x metre vertically upwards in t second, where x = 100t - $\frac{25}{2}$t². The maximum height recahed is

• 200 m

• 125 m

• 160 m

• 190 m

If the curves x² = 9A(9 - y) and x² = A(y + 1) intersect orthogonally, then the value of A is

• 3

• 4

• 5

• 7

If f (x) = 3x⁴ + 4x³ - 12x² + 12, then f(x) is

• increasing in (- $\infty$, - 2) and in (0, 1)

• increasing in (- 2, 0) and in (1, $\infty$)

• decreasing in (- 2, 0) and in (0, 1)

• decreasing in (- $\infty$, - 2) and in (1, $\infty$)

Gas is being pumped into a spherical balloon at the rate of 30 ft³/min. Then, the rate at which the radius increases when it reaches the value 15 ft is

• $\frac{1}{15\mathrm{\pi }} \mathrm{ft}/\min$

• $\frac{1}{30\mathrm{\pi }} \mathrm{ft}/\min$

• $\frac{1}{20} \mathrm{ft}/\min$

• $\frac{1}{25} \mathrm{ft}/\min$

A point on curve xy² = 1 which is at minimum distance from the origin is

• (1, 1)

• (1/4, 2)

• (2^1/6, 2^{- 1/3})

• (2^{- 1/3}, 2^1/6)

A spherical iron ball ofradius 10 cm, coated with a layer of ice of uniform thickness, melts at a rate of 100 $\mathrm{\pi }$ cm/min. The rate at which the thickness of decreases when the thickness of ice is 5 cm, is

• 1 cm/min

• 2 cm/min

• $\frac{1}{376} \mathrm{cm}/\min$

• 5 cm/min

If ax² + bx + 4 attains its minimum value - 1 at x = 1, then the values of a and bare respectively

• 5, - 10

• 5, - 5

• 5, 5

• 10, - 5

The function f(x) = (9 - x²)² increases in

• $\left(- 3, 0\right) \cup \left(3, \infty \right)$

• $\left(- \infty , - 3\right) \cup \left(3, \infty \right)$

• $\left(- \infty , - 3\right) \cup \left(0, 3\right)$

• (- 3, 3)

510.

Let $$\begin{gathered} \mathrm{g}\left(\mathrm{x}\right) = \left\{2\mathrm{e}, \mathrm{if} \mathrm{x} \le 1 \\ \log \left(\mathrm{x} - 1\right), \mathrm{if} \mathrm{x} > 1\right\} \end{gathered}$$. The equation  of the normal to y = g(x) at the point (3, log(2)), is

• y - 2x = 6 + log(2)

• y + 2x = 6 + log(2)

• y + 2x = 6 - log(2)

• y + 2x = - 6 + log(2)