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Question Bank No: 1

1. The tangent to the curve y= $e^{2 x}$ at (0,1) meets the x-axis at

a)		(0,a)
b)		(2, 0)
c)		(-1/2, 0)
d)		None of these

2. A stone thrown vertically upwards satisfies the equation S = 80t - 16 $t^{2}$ . The time required to reach the maximum height is

a)		2
b)		4
c)		3
d)		2.5

3. If the volume of a sphere is increasing at a constant rate, then the rate at which its radius is increasing is

a)		a constant
b)		proportional to the radius
c)		inversely proportional to the radius
d)		inversely proportional to its surafce area

4. If the rate of change in the circumference of a circle is 0.3 cm / sec, then the rate of change in the area of the circle when the radius is 5 cm, is

a)		1.5 sq. cm / sec
b)		0.5 sq. cm / sec
c)		5 sq. cm / sec
d)		3 sq. cm / sec

5. The maximum value of $\frac{\log x}{x}$ is =

a)		2/e
b)		1/e
c)		e
d)		1

6. The maximum value of xy when x + 2y= 8 is

a)		20
b)		16
c)		24
d)		8

7. The value of x for which $| x |$ is continuous but not differentiable is

a)		-1
b)		1
c)		0
d)		differentiable every where

8. If $x^{y}$ = $e^{x - y}$ , then $\frac{dy}{dx}$ is equal to

a)		$\frac{\log x}{1 + \log x}$
b)		$\frac{\log x}{1 - \log x}$
c)		$\frac{\log x}{{(1 - \log x)}^{2}}$
d)		$\frac{\log x}{{(1 + \log x)}^{2}}$ ]

9. If y = $e^{\frac{1}{2} \log (1 + \tan^{2} x)}$ , then $\frac{dy}{dx}$ =

a)		1/2 sec2 X
b)		sec2X
c)		sec x tan x
d)		e $\frac{1}{2}$ log ( 1 + $\tan^{2} x)$

10. Derivative of $\sec^{- 1} (\frac{1}{1 - {2 x}^{2}}) w . r . t .$ $\sin^{- 1} (3 x - {4 x}^{3})$ is

a)		$\frac{1}{4}$
b)		$\frac{3}{2}$
c)		1
d)		$\frac{2}{3}$

11. x $\overset{Lt}{\to}$ 0 $(a^{x} - b^{x}) / x$ is

a)		0
b)		1
c)		log a - log b
d)		does not exist