MCQOPTIONS
Saved Bookmarks
MCQOPTIONS
This section includes 12 Mcqs, each offering curated multiple-choice questions to sharpen your Engineering Mathematics knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
If (u = e^{ frac{(x^2+y^2)}{x+y}} ) Then, (x^2 frac{ ^2 u}{ x^2}+y^2 frac{ ^2 u}{ y}+2xy frac{ ^2 u}{ x y} )=? |
| A. | u ln u2061(u) |
| B. | u ln u2061(u)<sup>2</sup> |
| C. | u [1+ln u2061(u)] |
| D. | 0 |
| Answer» C. u [1+ln u2061(u)] | |
| 2. |
If (u = Tan^{-1} ( frac{x^3+y^3}{x+y}) ) then, (x^2 frac{ ^2 u}{ x^2}+y^2 frac{ ^2 u}{ y}+2xy frac{ ^2 u}{ x y} ) is? |
| A. | Sin(4u) Cos(2u) |
| B. | Sin(4u) Sin(2u) |
| C. | Cos(4u) Sin(2u) |
| D. | Cos(4u) Cos(2u) |
| Answer» C. Cos(4u) Sin(2u) | |
| 3. |
If f(x,y)is a function satisfying euler s theorem then? |
| A. | (x^2 frac{ ^2 f}{ x^2}+2xy frac{ ^2 f}{ x y}+y^2 frac{ ^2 f}{ y^2}=n(n-1)f ) |
| B. | ( frac{1}{x}^2 frac{ ^2 f}{ x^2}+2/xy frac{ ^2 f}{ x y}+ frac{1}{y}^2 frac{ ^2 f}{ y^2}=n(n-1)f ) |
| C. | (x^2 frac{ ^2 f}{ x^2}+2xy frac{ ^2 f}{ x y}+y^2 frac{ ^2 f}{ y^2}=nf ) |
| D. | (y^2 frac{ ^2 f}{ x^2}+2xy frac{ ^2 f}{ x y}+x^2 frac{ ^2 f}{ y^2}=n(n-1)f ) |
| Answer» B. ( frac{1}{x}^2 frac{ ^2 f}{ x^2}+2/xy frac{ ^2 f}{ x y}+ frac{1}{y}^2 frac{ ^2 f}{ y^2}=n(n-1)f ) | |
| 4. |
If z = Sin-1 (x y) + Tan-1 (y x) then x z x + y z y is? |
| A. | 0 |
| B. | y |
| C. | 1 + <sup>x</sup> <sub>y</sub> Sin<sup>-1</sup> (<sup>x</sup> <sub>y</sub>) |
| D. | 1 + <sup>y</sup> <sub>x</sub> Tan<sup>-1</sup> (<sup>y</sup> <sub>x</sub>) |
| Answer» B. y | |
| 5. |
If (z=ln ( frac{x^2+y^2}{x+y})-e^{ frac{x^2+y^2}{x+y}} ) then find (x frac{ z}{ x}+y frac{ z}{ y} ). |
| A. | (x frac{ z}{ x}+y frac{ z}{ y}= frac{x^2+y^2}{x+y} e^{ frac{x^2+y^2}{x+y}} ) |
| B. | (x frac{ z}{ x}+y frac{ z}{ y}=1- frac{x^2+y^2}{x+y} e^{ frac{x^2+y^2}{x+y}} ) |
| C. | (x frac{ z}{ x}+y frac{ z}{ y}=1+ frac{x^2+y^2}{x+y} e^{ frac{x^2+y^2}{x+y}} ) |
| D. | (x frac{ z}{ x}+y frac{ z}{ y}=- frac{x^2+y^2}{x+y} e^{ frac{x^2+y^2}{x+y}} ) |
| Answer» C. (x frac{ z}{ x}+y frac{ z}{ y}=1+ frac{x^2+y^2}{x+y} e^{ frac{x^2+y^2}{x+y}} ) | |
| 6. |
If f1(x,y) and f2(x,y) are homogeneous and of order n then the function f3(x,y) = f1(x,y) + f2(x,y) satisfies euler s theorem. |
| A. | True |
| B. | False |
| Answer» B. False | |
| 7. |
Value of (x frac{ u}{ x}+y frac{ u}{ y} ) if (u= frac{Sin^{-1} ( frac{y}{x})( sqrt{x}+ sqrt{y})}{x^3+y^3} ) is? |
| A. | -2.5 u |
| B. | -1.5 u |
| C. | 0 |
| D. | -0.5 u |
| Answer» B. -1.5 u | |
| 8. |
If (z=sin^{-1} frac{x^3+y^3+z^3}{x+y+z} ) then, (x frac{ z}{ x}+y frac{ z}{ y} ). |
| A. | 2 tan(z) |
| B. | 2 cot(z) |
| C. | tan(z) |
| D. | cot(z) |
| Answer» B. 2 cot(z) | |
| 9. |
If (z=e^{ frac{x^2+y^2}{x+y}} ) then, (x frac{ z}{ x} + y frac{ z}{ y} ) is? |
| A. | 0 |
| B. | zln(z) |
| C. | z<sup>2</sup> ln u2061(z) |
| D. | z |
| Answer» C. z<sup>2</sup> ln u2061(z) | |
| 10. |
Necessary condition of euler s theorem is? |
| A. | z should be homogeneous and of order n |
| B. | z should not be homogeneous but of order n |
| C. | z should be implicit |
| D. | z should be the function of x and y only |
| Answer» B. z should not be homogeneous but of order n | |
| 11. |
If z = xn f(y x) then? |
| A. | y <sup> z</sup> <sub> x</sub> + x <sup> z</sup> <sub> y</sub> = nz |
| B. | 1/y <sup> z</sup> <sub> x</sub> + 1/x <sup> z</sup> <sub> y</sub> = nz |
| C. | x <sup> z</sup> <sub> x</sub> + y <sup> z</sup> <sub> y</sub> = nz |
| D. | 1/x <sup> z</sup> <sub> x</sub> + 1/y <sup> z</sup> <sub> y</sub> = nz |
| Answer» D. 1/x <sup> z</sup> <sub> x</sub> + 1/y <sup> z</sup> <sub> y</sub> = nz | |
| 12. |
In euler theorem x z x + y z y = nz, here n indicates? |
| A. | order of z |
| B. | degree of z |
| C. | neither order nor degree |
| D. | constant of z |
| Answer» B. degree of z | |