MCQOPTIONS
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MCQOPTIONS
This section includes 8 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. |
Let f(x)=\(\frac{x^{100}}{100}+\frac{x^{101}}{101}+…\infty\). Find a point c ∈ (- ∞, ∞) such that f'(c) = 0 |
| A. | 1 |
| B. | 2 |
| C. | = 0a) 1b) 2c) 0 |
| D. | -1view answer |
| Answer» D. -1view answer | |
| 2. |
Let f(x)=\(x-\frac{x^3}{3^2.2!}+\frac{x^5}{5^2.4!}-\frac{x^7}{7^2.6!}+…\infty\). Find a point nearest to c such that f'(c) = 1 |
| A. | 1 |
| B. | 0 |
| C. | = 1a) 1b) 0c) 2.3445 * 10-9 |
| D. | 458328.33 * 10-3view answer |
| Answer» E. | |
| 3. |
Let g(x) be periodic and non-constant, with period τ. Also we have g(nτ) = 0 : n ∈ N. The function f(x) is defined asf(x)=\(\begin{cases}2x+g(2x)& :x\in [0,\tau] \\ 2x+g(4x)& :x\in (\tau,2\tau] \\2x+g(6x)& :x\in (2\tau,3\tau]\\.\\.\\2x+g(2nx)& :x\in [(n-1)\tau,n\tau)\\.\\.\end{cases}\) How many points c ∈ [0, 18τ] exist such that f'(c) = tan-1(2) |
| A. | 325 |
| B. | 323 |
| C. | = tan-1(2)a) 325b) 323c) 324 |
| D. | 162view answer |
| Answer» D. 162view answer | |
| 4. |
For the infinitely defined discontinuous function\(\begin{cases}x+sin(2x)& :x\in [0,\pi] \\ x+sin(4x)& :x\in (\pi,2\pi] \\ x+sin(6x)& :x\in (2\pi,3\pi] \\.\\.\\x+sin(2nx)& :x\in [(n-1)\pi,n\pi)\\.\\.\end{cases}\) How many points c∈[0,16x] exist, such that f'(c) = 1 |
| A. | 256 |
| B. | 512 |
| C. | = 1a) 256b) 512c) 16 |
| D. | 0view answer |
| Answer» B. 512 | |
| 5. |
For a third degree monic polynomial, it is seen that the sum of roots are zero. What is the relation between the minimum angle to be rotated to have a Rolles point (α in Radians) and the cyclic sum of the roots taken two at a time c |
| A. | α = π⁄180 * tan-1(c) |
| B. | Can never have a Rolles pointc) α = 180⁄π tan-1(c)d) α = tan-1( |
| C. | Can never have a Rolles pointc) α = 180⁄π tan-1(c) |
| D. | α = tan-1(c)view answer |
| Answer» E. | |
| 6. |
What is the minimum angle by which the coordinate axes have to be rotated in anticlockwise sense (in Degrees), such that the function f(x) = 3x3 + 5x + 1016 has at least one Rolles point |
| A. | π⁄180 tan-1(5) |
| B. | tan-1(5) |
| C. | 180⁄π tan-1(5) |
| D. | -tan-1(5)view answer |
| Answer» D. -tan-1(5)view answer | |
| 7. |
For the function f(x) = x3 + x + 1. We do not have any Rolles point. The coordinate axes are transformed by rotating them by 60 degrees in anti-clockwise sense. The new Rolles point is? |
| A. | \(\frac{\sqrt{3}}{2}\) |
| B. | The function can never have a Rolles point |
| C. | \(3^{\frac{1}{2}}\) |
| D. | \(\sqrt{\frac{\sqrt{3}-1}{3}}\) view answer |
| Answer» E. | |
| 8. |
For the function f(x) = x2 – 2x + 1. We have Rolles point at x = 1. The coordinate axes are then rotated by 45 degrees in anticlockwise sense. What is the position of new Rolles point with respect to the transformed coordinate axes? |
| A. | 3⁄2 |
| B. | 1⁄2 |
| C. | 5⁄2 |
| D. | 1view answer |
| Answer» B. 1⁄2 | |