MCQOPTIONS
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MCQOPTIONS
This section includes 14 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. |
Find the value of \(\int \frac{1}{16x^2+16x+10}dx\). |
| A. | 1⁄8 sin-1(x + 1⁄2) |
| B. | 1⁄8 tan-1(x + 1⁄2) |
| C. | 1⁄8 sec-1(x + 1⁄2) |
| D. | 1⁄4 cos-1(x + 1⁄2) |
| Answer» C. 1⁄8 sec-1(x + 1⁄2) | |
| 2. |
Temperature of a rod is increased by moving x distance from origin and is given by equation T(x) = x2 + 2x, where x is the distance and T(x) is change of temperature w.r.t distance. If, at x = 0, temperature is 40 C, find temperature at x=10. |
| A. | 473 C |
| B. | 472 C |
| C. | 474 C |
| D. | 475 C |
| Answer» B. 472 C | |
| 3. |
Find the value of ∫(x4 – 5x2 – 6x)4 4x3 – 10x – 6 dx. |
| A. | \(\frac{(x^4-5x^2-6x)^4}{4}\) |
| B. | \(\frac{(x^4-5x^2-6x)^5}{5}\) |
| C. | \(\frac{(4x^3-10x-6)^5}{5}\) |
| D. | \(\frac{(4x^3-10x-6)^4}{4}\) |
| Answer» C. \(\frac{(4x^3-10x-6)^5}{5}\) | |
| 4. |
Find the area inside function \(\frac{(2x^3+5x^2-4)}{x^2}\) from x = 1 to a.a) a2⁄2 + 5a – 4ln(a)b) a2⁄2 + 5a – 4ln(a) – 11⁄2c) a2⁄2 + 4ln( |
| A. | a2⁄2 + 5a – 4ln(a) |
| B. | a2⁄2 + 5a – 4ln(a) – 11⁄2 |
| C. | a2⁄2 + 4ln(a) – 11⁄2 |
| D. | a2⁄2 + 5a – 11⁄2 |
| Answer» C. a2⁄2 + 4ln(a) – 11⁄2 | |
| 5. |
Find the area inside integral f(x)=\(\frac{sec^4(x)}{\sqrt{tan(x)}}\) from x = 0 to π. |
| A. | π |
| B. | 0 |
| C. | 1 |
| D. | 2 |
| Answer» C. 1 | |
| 6. |
Find the area inside a function f(t) = \( \frac{t}{(t+3)(t+2)} dt\) from t = -1 to 0. |
| A. | 4 ln(3) – 5ln(2) |
| B. | 3 ln(3) |
| C. | 3 ln(3) – 4ln(2) |
| D. | 3 ln(3) – 5 ln(2) |
| Answer» E. | |
| 7. |
Find the area ln(x)⁄x from x = x = aeb to a. |
| A. | b2⁄2 |
| B. | b⁄2 |
| C. | b |
| D. | 1 |
| Answer» B. b⁄2 | |
| 8. |
Find the area of a function f(x) = x2 + xCos(x) from x = 0 to a, where, a>0.a) a2⁄2 + aSin(a) + Cos(a) – 1b) a3⁄3 + aSin(a) + Cos(a)c) a3⁄3 + aSin(a) + Cos(a) – 1d) a3⁄3 + Cos(a) + Sin( |
| A. | a2⁄2 + aSin(a) + Cos(a) – 1 |
| B. | a3⁄3 + aSin(a) + Cos(a) |
| C. | a3⁄3 + aSin(a) + Cos(a) – 1 |
| D. | a3⁄3 + Cos(a) + Sin(a) – 1 |
| Answer» D. a3⁄3 + Cos(a) + Sin(a) – 1 | |
| 9. |
Find the value of ∫x3 ex e2x e3x….enx dx. |
| A. | \(\frac{2}{n(n+1)} e^{\frac{n(n+1)}{2}x} \left [x^3+3x^2 [\frac{2}{n(n+1)}]^1+6x[\frac{2}{n(n+1)}]^2 +6[\frac{2}{n(n+1)}]^3\right ]\) |
| B. | \(\frac{2}{n(n+1)} e^{\frac{n(n+1)}{2}x} \left [x^3+3x^2 [\frac{2}{n(n+1)}]^1+6x[\frac{2}{n(n+1)}]^2 +6[\frac{2}{n(n+1)}]^3\right ]\) |
| C. | \(\frac{2}{n(n+1)} e^{\frac{n(n+1)}{2}x} \left [x^3+3x^2 [\frac{2}{n(n+1)}]^1+6x[\frac{2}{n(n+1)}]^2 +6[\frac{2}{n(n+1)}]^3\right ]\) |
| D. | \(\frac{2}{n(n+1)} e^{\frac{n(n+1)}{2}x} \left [x^3+3x^2 [\frac{2}{n(n+1)}]^1+6x[\frac{2}{n(n+1)}]^2 +6[\frac{2}{n(n+1)}]^3\right ]\) |
| Answer» B. \(\frac{2}{n(n+1)} e^{\frac{n(n+1)}{2}x} \left [x^3+3x^2 [\frac{2}{n(n+1)}]^1+6x[\frac{2}{n(n+1)}]^2 +6[\frac{2}{n(n+1)}]^3\right ]\) | |
| 10. |
Find the value of ∫x7 Cos(x) dx. |
| A. | x7 Sin(x) + 7x6 Cos(x) + 42x5 Sin(x) + 210x4 Cos(x) + 840x3 Sin(x) + 2520x2 Cos(x) + 5040xSin(x) + 5040Cos(x) |
| B. | x7 Sin(x) – 7x6 Cos(x) + 42x5 Sin(x) – 210x4 Cos(x) + 840x3 Sin(x) – 2520x2 Cos(x) + 5040xSin(x) – 5040Cos(x) |
| C. | x7 Sin(x) + 7x6 Cos(x) + 42x5 Sin(x) + 210x4 Cos(x) + 840x3 Sin(x) + 2520x2 Cos(x) + 5040xSin(x) + 5040Cos(x) |
| D. | x7 Sin(x) + 7x6 Cos(x) + 42x5 Sin(x) + 210x4 Cos(x) + 840x3 Sin(x) + 2520x2 Cos(x) + 5040xSin(x) + 10080Cos(x) |
| Answer» B. x7 Sin(x) – 7x6 Cos(x) + 42x5 Sin(x) – 210x4 Cos(x) + 840x3 Sin(x) – 2520x2 Cos(x) + 5040xSin(x) – 5040Cos(x) | |
| 11. |
Value of ∫uv dx,where u and v are function of x. |
| A. | \(\sum_{i=1}^n(-1)^i u_i v^{i+1}\) |
| B. | \(\sum_{i=0}^nu_i v^{i+1}\) |
| C. | \(\sum_{i=0}^n(-1)^i u_i v^{i+1}\) |
| D. | \(\sum_{i=0}^n(-1)^i u_i v^{n-i}\) |
| Answer» D. \(\sum_{i=0}^n(-1)^i u_i v^{n-i}\) | |
| 12. |
Find the value of ∫x3 Sin(x)dx. |
| A. | x3 Cos(x) + 3x2 Sin(x) + 6xCos(x) – 6Sin(x) |
| B. | – x3 Cos(x) + 3x2 Sin(x) – 6Sin(x) |
| C. | – x3 Cos(x) – 3x2 Sin(x) + 6xCos(x) – 6Sin(x) |
| D. | – x3 Cos(x) + 3x2 Sin(x) + 6xCos(x) – 6Sin(x) |
| Answer» E. | |
| 13. |
Integration of (Sin(x) + Cos(x))ex is? |
| A. | ex Cos(x) |
| B. | ex Sin(x) |
| C. | ex Tan(x) |
| D. | ex (Sin(x) + Cos(x)) |
| Answer» C. ex Tan(x) | |
| 14. |
Find the value of ∫tan-1(x)dx. |
| A. | sec-1 (x) – 1⁄2 ln(1 + x2) |
| B. | xtan-1 (x) – 1⁄2 ln(1 + x2) |
| C. | xsec-1 (x) – 1⁄2 ln(1 + x2) |
| D. | tan-1 (x) – 1⁄2 ln(1 + x2) |
| Answer» C. xsec-1 (x) – 1⁄2 ln(1 + x2) | |