MCQOPTIONS
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MCQOPTIONS
This section includes 12 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 solution of differential equation, dy⁄dx = xy + x2, if y = 1 at x = 0. |
| A. | \(1-\frac{x^2}{2!}+\frac{3x^4}{4!}-\frac{15x^6}{6!}+…\) |
| B. | \(\frac{x}{1!}+\frac{3x^3}{4!}+\frac{15x^5}{6!}+…\) |
| C. | \(\frac{x}{1!}-\frac{3x^3}{4!}+\frac{15x^5}{6!}-…\) |
| D. | \(1+\frac{x^2}{2!}+\frac{3x^4}{4!}+\frac{15x^6}{6!}+..\) |
| Answer» E. | |
| 2. |
Expand (1 + x)1⁄x, gives ___________ |
| A. | e[1 + x⁄2 + 11x2⁄24 -…..] |
| B. | e[1 – x⁄2 + 11x2⁄24 -…..] |
| C. | e[x⁄2 – 11x2⁄24 -…..] |
| D. | e[x⁄2 + 11x2⁄24 -…..] |
| Answer» C. e[x⁄2 – 11x2⁄24 -…..] | |
| 3. |
Find the expansion of Sin(lSin-1 (x)). |
| A. | \(lx-\frac{l(1-l^2)}{3!}x^3+\frac{l(1-l^2)(9-l^2)}{5!} x^5-…\) |
| B. | \(lx+\frac{l(1-l^2)}{3!} x^3+\frac{l(1-l^2)(9-l^2)}{5!} x^5+…\) |
| C. | \(1-lx^2+\frac{l(1-l^2)}{3!} x^4-\frac{l(1-l^2)(9-l^2)}{5!} x^6+…\) |
| D. | \(1+lx^2+\frac{l(1-l^2)}{3!} x^4+\frac{l(1-l^2)(9-l^2)}{5!} x^6+…\) |
| Answer» C. \(1-lx^2+\frac{l(1-l^2)}{3!} x^4-\frac{l(1-l^2)(9-l^2)}{5!} x^6+…\) | |
| 4. |
Find the expansion of cos(xsin(t)). |
| A. | \(\sum_{n=1}^∞ (\frac{x^n [Cos(nt)]}{n!})\) |
| B. | \(\sum_{n=0}^∞ (\frac{x^n [Cos(nt)]}{n!})\) |
| C. | \(\sum_{n=1}^∞ (\frac{x^n [Sin(nt)]}{n!})\) |
| D. | \(\sum_{n=0}^∞ (\frac{x^n [Sin(nt)]}{n!})\) |
| Answer» C. \(\sum_{n=1}^∞ (\frac{x^n [Sin(nt)]}{n!})\) | |
| 5. |
Given f(x)= ln(cos(x)),calculate the value of ln(cos(π⁄2)). |
| A. | -1.741 |
| B. | 1.741 |
| C. | 1.563 |
| D. | -1.563 |
| Answer» B. 1.741 | |
| 6. |
Find the expansion of exSin(x)? |
| A. | \(e^{xSin(x)}=1+x^2-x^4/3+x^6/120-…\) |
| B. | \(e^{xSin(x)}=1+x^2+x^4/3+x^6/120+…\) |
| C. | \(e^{xSin(x)}=x+x^3/3+x^5/120+..\) |
| D. | \(e^{xSin(x)}=x+x^3/3-x^5/120+…\) |
| Answer» C. \(e^{xSin(x)}=x+x^3/3+x^5/120+..\) | |
| 7. |
Find the expansion of f(x) = ln(1+ex)? |
| A. | \(ln(2)+x/2+x^2/8-x^4/192+….\) |
| B. | \(ln(2)+x/2+x^2/8+x^4/192+….\) |
| C. | \(ln(2)+x/2+x^3/8-x^5/192+….\) |
| D. | \(ln(2)+x/2+x^3/8+x^5/192+….\) |
| Answer» B. \(ln(2)+x/2+x^2/8+x^4/192+….\) | |
| 8. |
Expansion of y = Sin-1(x) is? |
| A. | \(x+\frac{x^3}{6}+\frac{3}{40} x^5+\frac{5}{112} x^7+…..\) |
| B. | \(x-\frac{x^3}{6}+\frac{3}{40} x^5-\frac{5}{112} x^7+…..\) |
| C. | \(\frac{x^3}{6}-\frac{3}{40} x^5+\frac{5}{112} x^7…..\) |
| D. | \(x+\frac{x^2}{6}+\frac{3}{40} x^2+\frac{5}{112} x^2+…..\) |
| Answer» B. \(x-\frac{x^3}{6}+\frac{3}{40} x^5-\frac{5}{112} x^7+…..\) | |
| 9. |
The expansion of eSin(x) is? |
| A. | 1 + x + x2⁄2 + x4⁄8 +…. |
| B. | 1 + x + x2⁄2 – x4⁄8 +…. |
| C. | 1 + x – x2⁄2 + x4⁄8 +…. |
| D. | 1 + x + x3⁄6 – x5⁄10 +…. |
| Answer» C. 1 + x – x2⁄2 + x4⁄8 +…. | |
| 10. |
The expansion of f(a+h) is ______a) \(f(a)+\frac{h}{1!} f'(a)+\frac{h^2}{2!} f”(a)…….+\frac{h^n}{n!} f^n (a)\) b) \(f(a)+\frac{h}{1!} f'(a)+\frac{h^2}{2!} f”(a)…….\) c) \(hf(a)+\frac{h^2}{1!} f'(a)+\frac{h^3}{2!} f”(a)…….+\frac{h^n}{n!} f^n (a)\) d) \(hf(a)+\frac{h^2}{1!} f'(a)+\frac{h^3}{2!} f”( |
| A. | \(f(a)+\frac{h}{1!} f'(a)+\frac{h^2}{2!} f”(a)…….+\frac{h^n}{n!} f^n (a)\) |
| B. | \(f(a)+\frac{h}{1!} f'(a)+\frac{h^2}{2!} f”(a)…….\) |
| C. | \(hf(a)+\frac{h^2}{1!} f'(a)+\frac{h^3}{2!} f”(a)…….+\frac{h^n}{n!} f^n (a)\) |
| D. | \(hf(a)+\frac{h^2}{1!} f'(a)+\frac{h^3}{2!} f”(a)………\) |
| Answer» B. \(f(a)+\frac{h}{1!} f'(a)+\frac{h^2}{2!} f”(a)…….\) | |
| 11. |
The necessary condition for the maclaurin expansion to be true for function f(x) is __________ |
| A. | f(x) should be continuous |
| B. | f(x) should be differentiable |
| C. | f(x) should exists at every point |
| D. | f(x) should be continuous and differentiable |
| Answer» E. | |
| 12. |
Expansion of function f(x) is? |
| A. | f(0) + x⁄1! f‘ (0) + x2⁄2! f” (0)…….+xn⁄n! fn (0) |
| B. | 1 + x⁄1! f‘ (0) + x2⁄2! f” (0)…….+xn⁄n! fn (0) |
| C. | f(0) – x⁄1! f‘ (0) + x2⁄2! f” (0)…….+(-1)^n xn⁄n! fn (0) |
| D. | f(1) + x⁄1! f‘ (1) + x2⁄2! f” (1)…….+xn⁄n! fn (1) |
| Answer» B. 1 + x⁄1! f‘ (0) + x2⁄2! f” (0)…….+xn⁄n! fn (0) | |