MCQOPTIONS
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MCQOPTIONS
This section includes 8 Mcqs, each offering curated multiple-choice questions to sharpen your Partial Differentiation knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
The determinant of the matrix whose eigen values are 6, 4, 3 is given by ___________ |
| A. | 3 |
| B. | 24 |
| C. | 72 |
| D. | 13 |
| Answer» C. 72 | |
| 2. |
Given ( _0^8x^{ frac{1}{3}}dx, ) find the error in approximating the integral using Simpson s 1/3 Rule with n=4. |
| A. | 1.8 |
| B. | 2.9 |
| C. | 0.3 |
| D. | 0.35 |
| Answer» E. | |
| 3. |
What is the value of ( frac{ ^2z}{ x y} ) for the z=3x2y+5y? |
| A. | 3xy |
| B. | 6x |
| C. | 3x+5 |
| D. | 6xy |
| Answer» C. 3x+5 | |
| 4. |
Which of the following relations hold true for division rule of differentiation? |
| A. | (( frac{f(x)}{g(x)}) = frac{f'(x)}{g'(x)} ) |
| B. | (( frac{f(x)}{g(x)}) = frac{g(x) f'(x)- g'(x)f(x)}{(f(x))^2} ) |
| C. | (( frac{f(x)}{g(x)}) = frac{g(x)f'(x)- g'(x)f(x)}{(g(x))^2} ) |
| D. | (( frac{f(x)}{g(x)}) = frac{f(x)g'(x)-f'(x)g(x)}{(g(x))^2} ) |
| Answer» D. (( frac{f(x)}{g(x)}) = frac{f(x)g'(x)-f'(x)g(x)}{(g(x))^2} ) | |
| 5. |
Volume of an object expressed in spherical coordinates is given by (V = int_0^{ frac{ }{2}} _0^{ frac{ }{3}} _0^1r cos dr d d . ) The value of the integral is _______ |
| A. | ( frac{ sqrt{3}}{2} ) |
| B. | ( frac{1}{ 2} ) |
| C. | ( frac{ sqrt{3}}{2} ) |
| D. | ( frac{ sqrt{3}}{8} ) |
| Answer» E. | |
| 6. |
Find the correct values for ( frac{ f}{ x} ,and , frac{ f}{ y} ) for the function (f= frac{2}{x^3}y^2+4y^3. ) |
| A. | ( frac{ f}{ x}= frac{-6}{x^2}, frac{ f}{ y}= frac{2}{x^3} y+8y^2 ) |
| B. | ( frac{ f}{ x}= frac{2}{x^4}, frac{ f}{ y}= frac{2}{x^3} y+12y^2 ) |
| C. | ( frac{ f}{ x}= frac{-6}{x^4}, frac{ f}{ y}= frac{4}{x^3} y+12y^2 ) |
| D. | ( frac{ f}{ x}= frac{-6}{x^4}, frac{ f}{ y}= frac{4}{x^3} y^2+12 ) |
| Answer» D. ( frac{ f}{ x}= frac{-6}{x^4}, frac{ f}{ y}= frac{4}{x^3} y^2+12 ) | |
| 7. |
The value of ( frac{ z}{ y} )=8x2+6xy2+4. What is the function z expressed as? |
| A. | z=8x<sup>3</sup>+2x<sup>2</sup> y<sup>2</sup>+4x |
| B. | z=8x<sup>2</sup> y+2xy<sup>3</sup>+4y |
| C. | z=8y+2xy<sup>2</sup>+4y |
| D. | z=16x+6y<sup>2</sup> |
| Answer» C. z=8y+2xy<sup>2</sup>+4y | |
| 8. |
If z=3xy+4x2, what is the value of ( frac{ z}{ x} )? |
| A. | 3y+8x |
| B. | 3x+4x<sup>2</sup> |
| C. | 3xy+8x |
| D. | 3y+3x+8x |
| Answer» B. 3x+4x<sup>2</sup> | |