MCQOPTIONS
Saved Bookmarks
MCQOPTIONS
This section includes 13 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 the rth term in the expansion of \(\left( \dfrac{x}{3} - \dfrac{2}{x^2} \right)^{10}\)contains x4, then r is equal to |
| A. | 3 |
| B. | 4 |
| C. | 2 |
| D. | None of these |
| Answer» B. 4 | |
| 2. |
Find the middle terms in the expansion of \(\rm \left(x - \frac 1 x \right)^{18}\) |
| A. | 18C9 |
| B. | - 18C9 |
| C. | - 18C10 |
| D. | None of the above |
| Answer» C. - 18C10 | |
| 3. |
In the expansion of \({\left( {3x - \frac{2}{{{x^2}}}} \right)^{15}}\) which term is free from x ? |
| A. | 4th |
| B. | 5th |
| C. | 6th |
| D. | 7th |
| Answer» D. 7th | |
| 4. |
If the coefficient of xr and xr+1 are equal in the expansion, then r is equal to |
| A. | n |
| B. | \(\frac{{2{\rm{n}} - 1}}{2}\) |
| C. | \(\frac{{2{\rm{n}} + 1}}{2}\) |
| D. | n + 1 |
| Answer» B. \(\frac{{2{\rm{n}} - 1}}{2}\) | |
| 5. |
In the expansion of \({\left( {\sqrt {\rm{x}} + \frac{1}{{3{{\rm{x}}^2}}}} \right)^{10}}\) the value of constant term (independent of x) is |
| A. | 5 |
| B. | 8 |
| C. | 45 |
| D. | 90 |
| Answer» B. 8 | |
| 6. |
If in the expansion of (x + a)n, the sum of odd terms is P and the sum of even terms is Q, then the value of (x + a)2n - (x - a)2n is: |
| A. | P + Q |
| B. | P - Q |
| C. | PQ |
| D. | 4PQ |
| Answer» E. | |
| 7. |
For every integer n > 2 the sum of the expansions \(1 - {}^n{C_1} + {}^n{C_2} + - - - {( - 1)^n}{}.^n{C_n}\) is______ |
| A. | n(n - 1)2n - 2 |
| B. | 0 |
| C. | n 2m - 1 |
| D. | \((2n_{c_n})^2\) |
| Answer» C. n 2m - 1 | |
| 8. |
If C0, C1, C2, _ _ _ _ _, Cn are the coefficients in the expansion of (1 + x)n, then what is the value of C1 + C2 + C3 + _ _ _ _ _ + Cn? |
| A. | 2n |
| B. | 2n - 1 |
| C. | 2n - 1 |
| D. | 2n - 2 |
| Answer» C. 2n - 1 | |
| 9. |
If (1 + x - 2x2)6 = 1 + a1x + a2x2 + ... + a12x12, then a2 + a4 + ... a12 is? |
| A. | 29 |
| B. | 30 |
| C. | 31 |
| D. | 32 |
| Answer» D. 32 | |
| 10. |
In the expansion of (1 + x)n, what is the sum of even binomial coefficients? |
| A. | 2n |
| B. | 2n - 1 |
| C. | 2n + 1 |
| D. | None of the above |
| Answer» C. 2n + 1 | |
| 11. |
If n is even, then the middle term in the expansion of \(\left(x^2 +\dfrac{1}{x}\right)^n\) is 924 x6. Find the value of n - |
| A. | 10 |
| B. | 12 |
| C. | 14 |
| D. | None of these |
| Answer» C. 14 | |
| 12. |
In binomial expansion of (a - b)n, n ≥ 5, the sum of the 5th and 6th terms is zero. Then \(\rm \dfrac{a}{b}\) is equal to - |
| A. | \(\rm \dfrac{n-5}{6}\) |
| B. | \(\rm \dfrac{n-4}{5}\) |
| C. | \(\rm \dfrac{5}{n-4}\) |
| D. | \(\rm \dfrac{6}{n-5}\) |
| Answer» C. \(\rm \dfrac{5}{n-4}\) | |
| 13. |
If x is so small that x2 and higher powers of x can be neglected, then \(\dfrac{(9+2x)^{1/2}(3+4x)}{(1-x)^{1/5}}\) is approximately equal to |
| A. | \(9 + \dfrac{74}{15}x\) |
| B. | \(9 + \dfrac{74}{5}x\) |
| C. | \(3 + \dfrac{74}{15}x\) |
| D. | \(3 + \dfrac{74}{5}x\) |
| Answer» C. \(3 + \dfrac{74}{15}x\) | |