MCQOPTIONS
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MCQOPTIONS
This section includes 11 Mcqs, each offering curated multiple-choice questions to sharpen your Mathematics knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
If, y = tan-1(x/a), then what is the value of y’? |
| A. | (2ax/(x2 – a2)2) |
| B. | -(2ax/(x2 – a2)2) |
| C. | (2ax/(x2 + a2)2) |
| D. | -(2ax/(x2 + a2)2) |
| Answer» E. | |
| 2. |
If, y = (sin-1x)2, then what is the value of (1 – x2)y” – xy’ + 4? |
| A. | 2 |
| B. | 4 |
| C. | 6 |
| D. | 8 |
| Answer» D. 8 | |
| 3. |
What is the value of (x + y)2y” if x = et sint and y = et cost? |
| A. | x/2(y’ + y) |
| B. | x/2(y’ – y) |
| C. | 2(xy’ + y) |
| D. | 2(xy’ – y) |
| Answer» E. | |
| 4. |
Given, y = tan-1 √(x2 – 1) then what is the value of (2x2 – 1)y’ + x(x2 – 1)y”? |
| A. | -1 |
| B. | 0 |
| C. | 1 |
| D. | 2 |
| Answer» C. 1 | |
| 5. |
What is the value of 4a cos3θ(d2y/dx2) if x = a sin2θ(1 + cos2θ) and y = a cos2θ(1 – cos2θ)? |
| A. | [1 + (d2y/dx2)2]3/2 |
| B. | [1 – (d2y/dx2)2]3/2 |
| C. | [1 + (d2y/dx2)2]1/2 |
| D. | [1 – (d2y/dx2)2]1/2 |
| Answer» B. [1 – (d2y/dx2)2]3/2 | |
| 6. |
What will be the form of the equation after eliminating a and b from the equation y = a sin-1x + b cos-1x? |
| A. | (1 – x2)y” + xy’ = 0 |
| B. | (1 – x2)y” – xy’ = 0 |
| C. | (1 + x2)y” – xy’ = 0 |
| D. | (1 + x2)y” + xy’ = 0 |
| Answer» C. (1 + x2)y” – xy’ = 0 | |
| 7. |
If, y = cos(2sin-1x), then what is the value of (1 – x2)y” – xy’ + 4y? |
| A. | –1 |
| B. | 0 |
| C. | 1 |
| D. | Depends on the value of x |
| Answer» C. 1 | |
| 8. |
What will be the domain of the function, if 3x + 3f(x) = minimum of Φ(t), where Φ(t) = minimum of (2t3 – 15t2 + 36t – 25, 2 + |sint|; 2 ≤ t ≤ 4} ? |
| A. | (-∞, 1) |
| B. | (-∞, loge3) |
| C. | (0, loge2) |
| D. | (-∞, loge2) |
| Answer» E. | |
| 9. |
Which of the following is correct for the nature of the roots x5 – a0x4 + 3ax3 + bx2 + cx + d = 0 if it is given that 2a02 < 15 and a0, a, b, c, d are real? |
| A. | Can’t be real |
| B. | Equal |
| C. | Real |
| D. | Depends on the value of x |
| Answer» B. Equal | |
| 10. |
The function y = f(x) is represented parametrically by x = t5 – 5t3 – 20t + 7 and y = 4t3 – 3t2 – 18t + 3 (-2 < t < 2). At which point does y = f(x) has a minimum value? |
| A. | t = -1 |
| B. | t = 0 |
| C. | t = 1/2 |
| D. | t = 3/2 |
| Answer» E. | |
| 11. |
Whichis greater (1/2)e or 1/e2 if there is a given function sinx(sinx), 0 < x < π? |
| A. | 1/e2 |
| B. | (1/2)e |
| C. | Data not sufficient |
| D. | Varies as the value of x changes |
| Answer» C. Data not sufficient | |