MCQOPTIONS
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MCQOPTIONS
This section includes 11 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. |
The expansion of f(x, y) = ex ln(1 + y), is |
| A. | f(x,y) = y + xy <sup>y<sup>2</sup></sup> <sub>2</sub> + . |
| B. | f(x,y) = y xy + <sup>y<sup>2</sup></sup> <sub>2</sub> - . |
| C. | f(x,y) = y + x <sup>y<sup>2</sup></sup> <sub>2</sub> + .. |
| D. | f(x,y) = x + y <sup>x<sup>2</sup></sup> <sub>2</sub> + .. |
| Answer» B. f(x,y) = y xy + <sup>y<sup>2</sup></sup> <sub>2</sub> - . | |
| 2. |
The expansion of f(x, y)=ex Sin(y), is |
| A. | x + xy + . |
| B. | y + y<sup>2</sup> x + . |
| C. | x + x<sup>2</sup> y + . |
| D. | y + xy + .. |
| Answer» E. | |
| 3. |
The expansion of f(x,y), is |
| A. | f(0,0)+ ([x frac{ f}{ x}+y frac{ f}{ y}]+ frac{1}{2!} [x^2 frac{ ^2 f}{ x^2}-2xy frac{ ^2 f}{ x y}+y^2 frac{ ^2 f}{ y^2}]+ . ) |
| B. | f(0,0)+ ([x frac{ f}{ x}+y frac{ f}{ y}]+ frac{1}{2!} [x^2 frac{ ^2 f}{ x^2}+2xy frac{ ^2 f}{ x y}+y^2 frac{ ^2 f}{ y^2}]+ ) |
| C. | f(0,0)+ ([x frac{ f}{ x}+y frac{ f}{ y}]+ frac{1}{2!} [x^2 frac{ ^2 f}{ x^2}-2xy frac{ ^2 f}{ x y}-y^2 frac{ ^2 f}{ y^2}]+ ) |
| D. | f(0,0)- ([x frac{ f}{ x}+y frac{ f}{ y}]+ frac{1}{2!} [x^2 frac{ ^2 f}{ x^2}+2xy frac{ ^2 f}{ x y}+y^2 frac{ ^2 f}{ y^2}]- ) |
| Answer» C. f(0,0)+ ([x frac{ f}{ x}+y frac{ f}{ y}]+ frac{1}{2!} [x^2 frac{ ^2 f}{ x^2}-2xy frac{ ^2 f}{ x y}-y^2 frac{ ^2 f}{ y^2}]+ ) | |
| 4. |
Find the value of ln(sin(31o)) if ln(2) = 0.69315 |
| A. | -0.653 |
| B. | -0.663 |
| C. | -0.764 |
| D. | -0.662 |
| Answer» C. -0.764 | |
| 5. |
Find the value of e 4 2 |
| A. | 1.74 |
| B. | 1.84 |
| C. | 1.94 |
| D. | 1.64 |
| Answer» B. 1.84 | |
| 6. |
Find the expansion of f(x) = ex 1+ex, given f(x)dx = ln (2), for x = 0 |
| A. | ( frac{1}{2}- frac{x}{4}- frac{x^3}{48}- ) |
| B. | ( frac{1}{2}+ frac{x}{4}- frac{x^3}{48}+ . ) |
| C. | ( frac{1}{2}+ frac{x}{4}+ frac{x^3}{48}+ . ) |
| D. | ( frac{1}{2}+ frac{x}{4}- frac{x^3}{48}+ . ) |
| Answer» C. ( frac{1}{2}+ frac{x}{4}+ frac{x^3}{48}+ . ) | |
| 7. |
Expand f(x) = 1 x about x = 1. |
| A. | 1 (x-1) + (x-1)<sup>2</sup> (x-1)<sup>3</sup> + . |
| B. | 1 + (x-1) + (x-1)<sup>2</sup> + (x-1)<sup>3</sup> + . |
| C. | 1 + (x-1) (x-1)<sup>2</sup> + (x-1)<sup>3</sup> + . |
| D. | 1 (x+1) + (x+1)<sup>2</sup> (x+1)<sup>3</sup> + . |
| Answer» B. 1 + (x-1) + (x-1)<sup>2</sup> + (x-1)<sup>3</sup> + . | |
| 8. |
Find the value of 10 |
| A. | 3.1633 |
| B. | 3.1623 |
| C. | 3.1632 |
| D. | 3.1645 |
| Answer» C. 3.1632 | |
| 9. |
Expand ln(x) in the power of (x-m). |
| A. | ln u2061(m)+ ( frac{h}{m}- frac{1}{2!} (h/m)^2+ frac{2}{3!} (h/m)^3- ) |
| B. | ln u2061(m)- ( frac{h}{m}- frac{1}{2!} (h/m)^2- frac{2}{3!} (h/m)^3- ) |
| C. | ln u2061(m)- ( frac{1}{2!} (h/m)^2+ frac{2}{3!} (h/m)^4- ) |
| D. | ln u2061(m)+ ( frac{h}{m}+ frac{2}{3!} (h/m)^3- ) |
| Answer» B. ln u2061(m)- ( frac{h}{m}- frac{1}{2!} (h/m)^2- frac{2}{3!} (h/m)^3- ) | |
| 10. |
Find the expansion of ex in terms of x + m, m > 0. |
| A. | (e^m [1+(x+m)+ frac{(x+m)^2}{2!}+ frac{(x+m)^3}{3!}+ .] ) |
| B. | (e^{-m} [1+(x-m)+ frac{(x-m)^2}{2!}+ frac{(x-m)^3}{3!}+ .] ) |
| C. | (e^m [1+(x-m)+ frac{(x-m)^2}{2!}+ frac{(x-m)^3}{3!}+ .] ) |
| D. | (e^{-m} [1+(x+m)+ frac{(x+m)^2}{2!}+ frac{(x+m)^3}{3!}+ .] ) |
| Answer» E. | |
| 11. |
The expansion of f(x), about x = a is |
| A. | (f(a)+ frac{h}{1!} f (a)+ frac{h^2}{2!} f (a) .+ frac{h^n}{n!} f^n (a) ) |
| B. | (f(a)+ frac{h}{1!} f (a)+ frac{h^2}{2!} f (a) . ) |
| C. | (hf(a)+ frac{h^2}{1!} f (a)+ frac{h^3}{2!} f (a) + frac{h^n}{n!} f^n (a) ) |
| D. | (hf(a)+ frac{h^2}{1!} f (a)+ frac{h^3}{2!} f (a) .. ) |
| Answer» B. (f(a)+ frac{h}{1!} f (a)+ frac{h^2}{2!} f (a) . ) | |