MCQOPTIONS
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MCQOPTIONS
This section includes 5 Mcqs, each offering curated multiple-choice questions to sharpen your Differential Calculus knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
If r=b e cot a, where a, b are constants then s is represented by which one of the following equation? |
| A. | s=r sec(a)+c |
| B. | s=r cos(a)+c |
| C. | s=r+c |
| D. | s=r tan(a)+c |
| Answer» B. s=r cos(a)+c | |
| 2. |
For the curve in polar form ( sqrt{ frac{r}{a}} = sec ( frac{ }{2}) ,the , ,value , ,of , frac{ds}{d } ) is _____ |
| A. | r sec |
| B. | r sec (( frac{ }{2}) ) |
| C. | r sec (2 ) |
| D. | r cosec (( frac{ }{2}) ) |
| Answer» D. r cosec (( frac{ }{2}) ) | |
| 3. |
If the parametric equation of the curve is given by x=aet sin t & y=aet cos t the value of ( frac{ds}{dt} ) is given by _____ |
| A. | ae<sup>t</sup> |
| B. | 2ae<sup>t</sup> |
| C. | 3 ae<sup>t</sup> |
| D. | 2 ae<sup>t</sup> |
| Answer» E. | |
| 4. |
For the curve (y=a ,log ,sec( frac{x}{a}) ) what is the value of ( frac{ds}{dx} )? (where is the angle made by tangent to the curve with x-axis)? |
| A. | cos |
| B. | sec |
| C. | tan |
| D. | cot |
| Answer» C. tan | |
| 5. |
For the cartesian curve y=f(x) with s as arc length which of the following condition holds good? |
| A. | ( frac{ds}{dx} = sqrt{1+( frac{dy}{dx})^2} ) |
| B. | ( frac{d^2s}{dx^2} = sqrt{1-( frac{dy}{dx})^2} ) |
| C. | ( frac{dy}{dx} = sqrt{1+( frac{ds}{dx})^2} ) |
| D. | ( sqrt{( frac{ds}{dx})^2 + ( frac{dy}{dx})^2} = 1 ) |
| Answer» B. ( frac{d^2s}{dx^2} = sqrt{1-( frac{dy}{dx})^2} ) | |