MCQOPTIONS
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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 F(x) = f(x)g(x)h(x) and F (x) = 10F(x) and f (x) = 10f(x) , g (x) = 10g(x) and h (x) = 10kh(x), then find value of k. |
| A. | 0 |
| B. | 1 |
| C. | -1 |
| D. | 2 |
| Answer» D. 2 | |
| 2. |
If z = ex Sin(Cos(x))Cos(Sin(x)) Then find dz dx |
| A. | [e<sup>x</sup>Sin(Cos(x))Cos(Sin(x))-e<sup>x</sup>Cos(x)Cos(Cos(x))Cos(Sin(x))-e<sup>x</sup>Sin(x)Sin(Cos(x))Sin(Sin(x))] |
| B. | [e<sup>x</sup>Sin(Cos(x))Cos(Sin(x))-e<sup>x</sup>Sin(x)Cos(Cos(x))Cos(Sin(x))-e<sup>x</sup>Cos(x)Sin(Cos(x))Sin(Sin(x))] |
| C. | [e<sup>x</sup>Cos(Cos(x))Sin(Sin(x))-e<sup>x</sup>Sin(x)Cos(Cos(x))Cos(Sin(x))-e<sup>x</sup>Cos(x)Sin(Cos(x))Sin(Sin(x))] |
| D. | [e<sup>x</sup>Sin(Cos(x))Cos(Sin(x))-e<sup>x</sup>Cos(x)Cos(Cos(x))Cos(Sin(x))-e<sup>x</sup>Sin(x)Sin(Cos(x))Sin(Sin(x))] |
| Answer» C. [e<sup>x</sup>Cos(Cos(x))Sin(Sin(x))-e<sup>x</sup>Sin(x)Cos(Cos(x))Cos(Sin(x))-e<sup>x</sup>Cos(x)Sin(Cos(x))Sin(Sin(x))] | |
| 3. |
Evaluate differentiation of x2 Sin(x) w.r.t Tan(x)Cosec(x) |
| A. | ( frac{[2xSin(x)+x^2 Cos(x)]}{-Cosec(x)-Sec^2 (x)Cosec(x)} ) |
| B. | ( frac{[2xSin(x)+x^2 Cos(x)]}{-Cosec(x)+Cos(x)Sin(x)} ) |
| C. | ( frac{[2xSin(x)+x^2 Cos(x)]}{-Cosec(x)+Sec^2 (x)Cosec(x)} ) |
| D. | ( frac{[2xSin(x)+x^2 Cos(x)]}{+Cosec(x)+Sec^2 (x)Cosec(x)} ) |
| Answer» D. ( frac{[2xSin(x)+x^2 Cos(x)]}{+Cosec(x)+Sec^2 (x)Cosec(x)} ) | |
| 4. |
Evaluate d dx Cot(x)Cosec(x) |
| A. | -Cosec<sup>2</sup> (x) Cosec<sup>2</sup> (x)Cot(x) |
| B. | -Cosec<sup>3</sup> (x) Cosec<sup>2</sup> (x)Cot(x) |
| C. | -Cosec(x) Cosec<sup>2</sup> (x)Cot(x) |
| D. | -Cosec<sup>3</sup> (x) Cosec(x)Cot<sup>2</sup> (x) |
| Answer» C. -Cosec(x) Cosec<sup>2</sup> (x)Cot(x) | |
| 5. |
If y = Tan(x)Tan(x) then dy dx = ? |
| A. | Tan(x) [1 + lnTan(x)] Tan(x)<sup>Tan(x)</sup> |
| B. | Tan<sup>2</sup> (x) [1 + lnTan(x)] Tan(x)<sup>Tan(x)</sup> |
| C. | Sec<sup>2</sup> (x) [1 + lnTan(x)] Tan(x)<sup>Tan(x)</sup> |
| D. | Sec(x) [1 + lnTan(x)] Tan(x)<sup>Tan(x)</sup> |
| Answer» D. Sec(x) [1 + lnTan(x)] Tan(x)<sup>Tan(x)</sup> | |
| 6. |
Evaluate the differentiation of (tan^{-1} frac{cos(x)-sin(x)}{cos(x)+sin(x)} ) |
| A. | tan<sup>-1</sup> u2061x |
| B. | 1 |
| C. | 0 |
| D. | -1 |
| Answer» C. 0 | |
| 7. |
Evaluate ( frac{d[Tan^n (x)+Tanx^n+Tan^{-1} x+Tan(nx)}{dx}] ) is |
| A. | (nTan^{n-1} xSec^2 x+nx^{n-1} Sec^2 x^n+1/(1+x^2)+nTan(nx)Sec^2 (nx) ) |
| B. | (nTan^{n-1} xSec^2 x+nx^{n-1} Sec^2 x^n+1/(1+x^2)+nSec^2 (nx) ) |
| C. | (nTan^{n-1} xSec^2 x+nx^{n-1} Sec^2 x^n+1/(1-x^2)+nSec^2 (nx) ) |
| D. | (2nTan^{n-1} xSec^2 x+nx^{n-1} Sec^2 x^n+1/(1+x^2)+nSec^2 (nx) ) |
| Answer» C. (nTan^{n-1} xSec^2 x+nx^{n-1} Sec^2 x^n+1/(1-x^2)+nSec^2 (nx) ) | |
| 8. |
Find the derivative of Sin(x)Tan(x) w.r.t ex Tan(x) |
| A. | ( frac{Sin(x)(1+Sec^4 (x))}{e^x (1+Tan^2 (x)+Tan(x))} ) |
| B. | ( frac{Sin(x)(1+Sec^2 (x))}{e^x (1+Tan^4 (x)+Tan(x))} ) |
| C. | ( frac{Sin(x)(1+Sec^2 (x))}{e^x (1+Tan^2 (x)+Tan(x))} ) |
| D. | ( frac{Sin(x)(1+Sec^2 (x))}{e^x (2+Tan^2 (x)+Tan(x))} ) |
| Answer» D. ( frac{Sin(x)(1+Sec^2 (x))}{e^x (2+Tan^2 (x)+Tan(x))} ) | |
| 9. |
Value of d dx [(1 + xex}{1-Cos(x))]. |
| A. | ( frac{(1-Sin(x))(1+x) e^x + Cos(x)(1+xe^x)}{[1-Cos (x)]^2} ) |
| B. | ( frac{(1-Cos(x))(1+x) e^x + Sin(x)(1+xe^x)}{[1-Cos (x)]^4} ) |
| C. | ( frac{(1-Cos(x))(1+x) e^x + Sin(x)(1+xe^x)}{[1-Cos (x)]^2} ) |
| D. | ( frac{(1-Cos(x))(1+x) e^x Sin(x)(1+xe^x)}{[1-Cos (x)]^2} ) |
| Answer» D. ( frac{(1-Cos(x))(1+x) e^x Sin(x)(1+xe^x)}{[1-Cos (x)]^2} ) | |
| 10. |
If (y= frac{sin(x)e^x}{cos^2(x)} ), find dy dx . |
| A. | Sec<sup>2</sup> (x) e<sup>x</sup> [1 + Tan(x)] + e<sup>x</sup> Tan(x)Sec(x) |
| B. | Sec<sup>2</sup> (x) e<sup>x</sup> [Sec(x) + Tan(x)] + e<sup>x</sup> Tan(x)Sec(x) |
| C. | Sec<sup>2</sup> (x) e<sup>2x</sup> [Sec(x) + Tan(x)] + e<sup>x</sup> Tan(x)Sec(x) |
| D. | Sec(x) e<sup>x</sup> [Sec(x) + Tan(x)] + e<sup>x</sup> Tan(x)Sec(x) |
| Answer» D. Sec(x) e<sup>x</sup> [Sec(x) + Tan(x)] + e<sup>x</sup> Tan(x)Sec(x) | |
| 11. |
( frac{d( frac{u}{v})}{dx} ) is where u, v are the functions of x |
| A. | <sup>v u uv</sup> <sub>v<sup>2</sup></sub> |
| B. | <sup>vu uv </sup> <sub>v<sup>2</sup></sub> |
| C. | <sup>vu u v </sup> <sub>v<sup>2</sup></sub> |
| D. | 0 |
| Answer» C. <sup>vu u v </sup> <sub>v<sup>2</sup></sub> | |
| 12. |
( frac{d(uvw)}{dx} ) is where u ,v, w are the functions of x |
| A. | u vw + uv w + uvw |
| B. | uvw + uv w + u v w |
| C. | u v w + uv w + u vw |
| D. | uv w + u v w + uvw |
| Answer» B. uvw + uv w + u v w | |