MCQs of Partial Derivatives (Mathematics - I - 3110014)

Showing 11 to 20 out of 43 Questions

11.

If $f (x, y) = c$ be an implicit function, then $q^{3} \frac{d^{2} y}{{dx}^{2}} =$ _____.

12.

The equation of tangent plane to the surface $z = xy - 2$ at point $P (1, 1, - 1)$ is _____.

13.

If $u = e^{xyz}$ , then $\frac{\partial u}{\partial z} =$ _____.

14.

The equation of normal line to the surface $x^{2} + y^{2} + z^{2} = 3$ at the point $(1, 1, 1)$ is _____.

15.

The another representation of $f_{xyxz}$ is _____.

(a)	$\frac{\partial^{4} f}{\partial x \partial y \partial x \partial z}$
(b)	$\frac{\partial^{4} f}{\partial x^{2} \partial y \partial z}$
(c)	$\frac{\partial^{4} f}{\partial z \partial x \partial y \partial x}$
(d)	$\frac{\partial^{4} f}{\partial z \partial x^{2} \partial y}$

16.

For the stationary point $(- 1, 2)$ , $f (x, y) = x^{3} + y^{3} - 3 x - 12 y + 20$ . Then

17.

Which of the following is not a stationary point of $f (x, y) = x + y + \frac{1}{x} + \frac{1}{y}$ ?

18.

If $x + y + z = 12$ , then $\max (xyz)$ is _____.

19.

Find $\frac{d u}{d t}$ , if $u = 4 x + y^{2}, x = \cos (2 t) & y = \sin (2 t) .$

20.

If $u = f (\frac{x}{y}, \frac{y}{z}, \frac{z}{x}),$ where $r = \frac{x}{y}, s = \frac{y}{z} & t = \frac{z}{x} .$ Which of the following is true?

(a)	$\frac{\partial u}{\partial r} = \frac{\partial u}{\partial x} \cdot \frac{\partial x}{\partial r} + \frac{\partial u}{\partial y} \cdot \frac{\partial y}{\partial r} + \frac{\partial u}{\partial z} \cdot \frac{\partial z}{\partial r}$
(b)	$\frac{\partial u}{\partial x} = \frac{\partial u}{\partial r} \cdot \frac{\partial r}{\partial x} + \frac{\partial u}{\partial s} \cdot \frac{\partial s}{\partial x} + \frac{\partial u}{\partial t} \cdot \frac{\partial t}{\partial x}$
(c)	$\frac{\partial u}{\partial s} = \frac{\partial u}{\partial x} \cdot \frac{\partial x}{\partial s} + \frac{\partial u}{\partial y} \cdot \frac{\partial y}{\partial s} + \frac{\partial u}{\partial z} \cdot \frac{\partial z}{\partial s}$
(d)	$\frac{\partial u}{\partial t} = \frac{\partial u}{\partial x} \cdot \frac{\partial x}{\partial t} + \frac{\partial u}{\partial y} \cdot \frac{\partial y}{\partial t} + \frac{\partial u}{\partial z} \cdot \frac{\partial z}{\partial t}$

Showing 11 to 20 out of 43 Questions