MCQOPTIONS
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MCQOPTIONS
This section includes 20 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 the car is having a displace from point 1 to point 2 in t sec which is given by equation y(x) = x2 + x + 1. Then? |
| A. | Car is moving with constant acceleration |
| B. | Car is moving with constant velocity |
| C. | Neither acceleration nor velocity is constant |
| D. | Both acceleration and velocity is constant |
| Answer» B. Car is moving with constant velocity | |
| 2. |
If z(x,y) = 2Sin(x)+Cos(y)Sin(x) find d2z(xy)⁄dxdy= ? |
| A. | –Cos(y)Cos(x) |
| B. | -Sin(y)Sin(x) |
| C. | –Sin(y)Cos(x) |
| D. | -Cos(y)Sin(x) |
| Answer» D. -Cos(y)Sin(x) | |
| 3. |
If the velocity of car at time t(sec) is directly proportional to the square of its velocity at time (t-1)(sec). Then find the ratio of acceleration at t=10sec to 9sec if proportionality constant is k=10 sec/mt and velocity at t=9sec is 10 mt/sec. |
| A. | 100 |
| B. | 200 |
| C. | is directly proportional to the square of its velocity at time (t-1)(sec). Then find the ratio of acceleration at t=10sec to 9sec if proportionality constant is k=10 sec/mt and velocity at t=9sec is 10 mt/sec.a) 100b) 200c) 150 |
| D. | 250 |
| Answer» C. is directly proportional to the square of its velocity at time (t-1)(sec). Then find the ratio of acceleration at t=10sec to 9sec if proportionality constant is k=10 sec/mt and velocity at t=9sec is 10 mt/sec.a) 100b) 200c) 150 | |
| 4. |
If y2 + xy + x2 – 2x = 0 then d2y⁄dx2 =? |
| A. | \((2y+x) \frac{d^2 y}{dx^2}+(\frac{dy}{dx})^2+2 \frac{dy}{dx}+2=0\) |
| B. | \((2y+x) \frac{d^2 y}{dx^2}+2(\frac{dy}{dx})^2+\frac{dy}{dx}+2=0\) |
| C. | \((2y+x) \frac{d^2 y}{dx^2}+2(\frac{dy}{dx})^2+2 \frac{dy}{dx}+2=0\) |
| D. | \(x \frac{d^2 y}{dx^2}+2(\frac{dy}{dx})^2+2 \frac{dy}{dx}+2=0\) |
| Answer» D. \(x \frac{d^2 y}{dx^2}+2(\frac{dy}{dx})^2+2 \frac{dy}{dx}+2=0\) | |
| 5. |
If Cos(y)=Cos(-1) (y) then? |
| A. | (1 – y2)(1 – Cos2 (y))=1 |
| B. | (1 – y2)(1 – Cos(y))=1 |
| C. | (1 – y2)(1 – Sin2 (y))=1 |
| D. | (1 – y2)(1 – Sin(y))=1 |
| Answer» B. (1 – y2)(1 – Cos(y))=1 | |
| 6. |
If Sin(y)=Sin(-1) (y) then? |
| A. | (1-y2)(1 – Cos2 y) = 1 |
| B. | (1-y2)(1 – Sin2 y) = 1 |
| C. | (1-y2)(1 – Siny)=1 |
| D. | (1-y2)(1 – Cosy)=1 |
| Answer» C. (1-y2)(1 – Siny)=1 | |
| 7. |
Evaluate y44 + 3xy3 + 6x2 y2 – 7y + 8 = 0. |
| A. | \(\frac{(7-12x^2 y-9xy^4-4y^3)}{(3y^3+12xy^2)}\) |
| B. | \(\frac{(7-12x^2 y-9xy^2-4y^3)}{(3y^3+12xy^2)}\) |
| C. | \(\frac{(7-12x^2 y-9xy^2-4y^3)}{(3y^4+12xy^2)}\) |
| D. | \(\frac{(7-12x^4 y-9xy^2-4y^3)}{(3y^3+12xy^2)}\) |
| Answer» C. \(\frac{(7-12x^2 y-9xy^2-4y^3)}{(3y^4+12xy^2)}\) | |
| 8. |
Implicit functions are those functions ____________ |
| A. | Which can be solved for a single variable |
| B. | Which can not be solved for a single variable |
| C. | Which can be eliminated to give zero |
| D. | Which are rational in nature. |
| Answer» C. Which can be eliminated to give zero | |
| 9. |
Find the derivative of Tan(x) = Tan(y). |
| A. | \(\frac{1+x^2}{1+y^2}\) |
| B. | \(\frac{1+y}{1+x^2}\) |
| C. | \(\frac{1+y^2}{1+x^2}\) |
| D. | \(\frac{1+y^2}{1+x}\) |
| Answer» D. \(\frac{1+y^2}{1+x}\) | |
| 10. |
Find differentiation of xSin(x) + ayCos(x) + Tan(y) = 0. |
| A. | \(\frac{[ayCos(x)-Sin(x)+Cos(x)]}{[aCos(x)+Sec^2 (y)]}\) |
| B. | \(\frac{[ayCos(x)-Sin(x)+xCos(x)]}{[Cos(x)+Sec^2 (y)]}\) |
| C. | \(\frac{[ayCos(x)-Sin(x)+xCos(x)]}{[aCos(x)+Sec^2 (y)]}\) |
| D. | \(\frac{[ayCos(x)-Cos(x)+xCos(x)]}{[aCos(x)+Sec^2 (y)]}\) |
| Answer» D. \(\frac{[ayCos(x)-Cos(x)+xCos(x)]}{[aCos(x)+Sec^2 (y)]}\) | |
| 11. |
Find the differentiation of x4 + y4 = 0. |
| A. | – x3⁄y4 |
| B. | – x4⁄y3 |
| C. | – x3⁄y3 |
| D. | x3⁄y3 |
| Answer» D. x3⁄y3 | |
| 12. |
x3 Sin(y) + Cos(x) y3 = 0, its differentiation is? |
| A. | \(-\frac{[x^3 Sin(y)-3y^2 Sin(x)]}{[x^2 Cos(y)+y^3 Cos(x)]}\) |
| B. | \(-\frac{[3x^2 Sin(y)-y^3 Sin(x)]}{[x^3 Cos(y)+3y^2 Cos(x)]}\) |
| C. | \(-\frac{[3x^3 Sin(y)-y^3 Sin(x)]}{[x^3 Cos(y)+3y^3 Cos(x)]}\) |
| D. | 0 |
| Answer» C. \(-\frac{[3x^3 Sin(y)-y^3 Sin(x)]}{[x^3 Cos(y)+3y^3 Cos(x)]}\) | |
| 13. |
Find the differentiation of x3 + y3 – 3xy + y2 = 0? |
| A. | \(\frac{(x^2-y)}{x-y^2-2y}\) |
| B. | \(\frac{(3x^2-3y)}{3x-3y^2-2y}\) |
| C. | \(\frac{(3x^3-3y)}{3x-3y^2-2y}\) |
| D. | \(\frac{(3x^2-y)}{3x-3y^2-y}\) |
| Answer» C. \(\frac{(3x^3-3y)}{3x-3y^2-2y}\) | |
| 14. |
If z(x,y) = 2Sin(x)+Cos(y)Sin(x) find d2z(xy)‚ÅÑdxdy= ?$# |
| A. | –Cos(y)Cos(x) |
| B. | -Sin(y)Sin(x) |
| C. | –Sin(y)Cos(x) |
| D. | -Cos(y)Sin(x) |
| Answer» D. -Cos(y)Sin(x) | |
| 15. |
If the velocity of car at time t(sec) is directly proportional to the square of its velocity at time (t-1)(sec). Then find the ratio of acceleration at t=10sec to 9sec if proportionality constant is k=10 sec/mt and velocity at t=9sec is 10 mt/sec |
| A. | 100 |
| B. | 200 |
| C. | 150 |
| D. | 250 |
| Answer» C. 150 | |
| 16. |
If the car is having a displace from point 1 to point 2 in t sec which is given by equation y(x) = x2 + x + 1. Then, |
| A. | Car is moving with constant acceleration |
| B. | Car is moving with constant velocity. |
| C. | Neither acceleration nor velocity is constant. |
| D. | Both aceleration and velocity is contant. |
| Answer» B. Car is moving with constant velocity. | |
| 17. |
If Cos(y)=Cos(-1) (y) the? |
| A. | (1 – y<sup>2</sup> )(1 – Cos<sup>2</sup> (y))=1 |
| B. | (1 – y<sup>2</sup> )(1 – Cos(y))=1 |
| C. | (1 – y<sup>2</sup> )(1 – Sin<sup>2</sup> (y))=1 |
| D. | (1 – y<sup>2</sup> )(1 – Sin(y))=1 |
| Answer» B. (1 ‚Äö√Ñ√∂‚àö√ë‚àö¬® y<sup>2</sup> )(1 ‚Äö√Ñ√∂‚àö√ë‚àö¬® Cos(y))=1 | |
| 18. |
If Sin(y)=Sin(-1) (y) the? |
| A. | (1-y<sup>2</sup> )(1 – Cos<sup>2</sup> y) = 1 |
| B. | (1-y<sup>2</sup> )(1 – Sin<sup>2</sup> y) = 1 |
| C. | (1-y<sup>2</sup> )(1 – Siny)=1 |
| D. | (1-y<sup>2</sup> )(1 – Cosy)=1 |
| Answer» C. (1-y<sup>2</sup> )(1 ‚Äö√Ñ√∂‚àö√ë‚àö¬® Siny)=1 | |
| 19. |
Implicit functions are those functions |
| A. | Which can be solved for a single variable |
| B. | Which can not be solved for a single variable |
| C. | Which can be eliminated to give zero |
| D. | Which are rational in nature. |
| Answer» C. Which can be eliminated to give zero | |
| 20. |
Find the differentiation of x4 + y4 = 0 |
| A. | – <sup>x<sup>3</sup></sup>⁄<sub>y<sup>4</sup></sub> |
| B. | – <sup>x<sup>4</sup></sup>⁄<sub>y<sup>3</sup></sub> |
| C. | – <sup>x<sup>3</sup></sup>⁄<sub>y<sup>3</sup></sub> |
| D. | <sup>x<sup>3</sup></sup>‚ÅÑ<sub>y<sup>3</sup></sub> |
| Answer» D. <sup>x<sup>3</sup></sup>‚Äö√Ñ√∂‚àö√ñ‚àö√´<sub>y<sup>3</sup></sub> | |