CBSE Class 12 Maths Continuity and Differentiability Quiz 6

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CBSE / Class 12 / Maths / Continuity and Differentiability

1.

If y = (tan x), then $\frac{dy}{dx}$ is equal to
sec x + cos x
sec x+ log tan x
(tan x)
None of these

2.

If x= e then $\frac{dy}{dx}$ is
$\frac{1+x}{1+log x}$
$\frac{1-log x}{1+log y}$
not defined
$\frac{-y}{(1+log x)^2}$

3.

The derivative of y = (1 – x) (2 – x)…. (n – x) at x = 1 is equal to
0
(-1) (n – 1)!
n ! – 1
(-1)

4.

If f(x) = cos x, cos 2 x, cos 4 x, cos 8 x, cos 16 x, then the value of'( $\frac{π}{4}$ ) is
1
√2
$\frac{1}{√2}$
0

5.

x. y= 16, then the value of $\frac{dy}{dx}$ at (2, 2) is
-1
0
-1
None of these

6.

If y = e find $\frac{dy}{dx}$ =
$\frac{y^2}{1-y}$
$\frac{y^2}{y-1}$
$\frac{y}{y-1}$
$\frac{-y}{y-1}$

7.

If x = $\frac{1-t^2}{1+t^2}$ and y = $\frac{2t}{1+t^2}$ then $\frac{dy}{dx}$ is equal to dx
– $\frac{y}{x}$
$\frac{y}{x}$
– $\frac{x}{y}$
$\frac{x}{y}$

8.

If x = a cosθ, y = a sinθ. then $\frac{dy}{dx}$ at θ = $\frac{3π}{4}$ is
-1
1
-a²
a²

9.

If x = sin(3t – 4t³) and y = cos( $\sqrt{1-t^2}$ ) then $\frac{dy}{dx}$ is equal to
$\frac{1}{2}$
$\frac{2}{5}$
$\frac{3}{2}$
$\frac{1}{3}$

10.

If x = e sin t, y = e cos t, t is a parameter, then $\frac{dy}{dx}$ at (1, 1) is equal to
– $\frac{1}{2}$
– $\frac{1}{4}$
0
$\frac{1}{2}$

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