MCQOPTIONS
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MCQOPTIONS
This section includes 10 Mcqs, each offering curated multiple-choice questions to sharpen your Mathematics Questions and Answers knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
If f(x) = \(\begin{vmatrix}x^n & x^{n+2} & x^{2n} \\1 & x^p & p \\x^{n+5} & x^{p+6} & x^{2n+5} \end {vmatrix}\) = 0,then what will be the value of p? |
| A. | xn |
| B. | (n + 1) |
| C. | Either xn or (n + 1) |
| D. | Both xn and (n + 1) |
| Answer» E. | |
| 2. |
What will be the value of \(\begin{vmatrix}0 & i – 100 & i – 500 \\100 – i & 0 & 1000 – i \\500 – i & i – 1000 & 0 \end {vmatrix}\)? |
| A. | 100 |
| B. | 500 |
| C. | 1000 |
| D. | 0 |
| Answer» E. | |
| 3. |
If f(x) = \(\begin{vmatrix}sec x & cos x & sec^2 x + cot x\, cosec x \\cos^2 x & cos^2 x & cosec^2 x \\1 & cos^2 x & cos^2 x \end {vmatrix}\) then what is the value of 0∫π/2 f(x) dx = (π/4 + 8/15)? |
| A. | (π/4 + 8/15) |
| B. | (π/4 – 8/15) |
| C. | (π/4 + 8/15) |
| D. | (-π/4 + 8/15) |
| Answer» D. (-π/4 + 8/15) | |
| 4. |
What is the value of r = 1Σn f(x) if f(r) = \(\begin{vmatrix}2r & x & n(n + 1) \\(6r^2 – 1) & y & n^2 (2n + 3) \\(4r^3 – 2nr) & z & n^3(n + 1) \end {vmatrix}\) where n € N? |
| A. | 1 |
| B. | -1 |
| C. | 0 |
| D. | 2 |
| Answer» D. 2 | |
| 5. |
What will be the value of the given determinant \(\begin{vmatrix}109 & 102 & 95 \\6 & 13 & 20 \\1 & -6 & 13 \end {vmatrix}\)? |
| A. | constant other than 0 |
| B. | 0 |
| C. | 100 |
| D. | -1997 |
| Answer» C. 100 | |
| 6. |
What is the value of k if \(\begin{vmatrix}y + z & x & x \\y & z + x & y \\z & z & x + y\end {vmatrix}\) ? |
| A. | 4 |
| B. | -4 |
| C. | 1 |
| D. | 0 |
| Answer» B. -4 | |
| 7. |
Which one of the following is correct if a, b and c are the sides of a triangle ABC and \(\begin{vmatrix}a^2 & b^2 & c^2 \\(a + 1)^2 & (b + 1)^2 & (c + 1)^2 \\ (a – 1)^2 & (b – 1)^2 & (c – 1)^2 \end {vmatrix}\) ? |
| A. | ABC is an equilateral triangle |
| B. | ABC is an isosceles triangle |
| C. | ABC is a right angled triangle |
| D. | ABC is a scalene triangle |
| Answer» C. ABC is a right angled triangle | |
| 8. |
What is the value of x if, \(\begin{vmatrix}x & 3 & 6 \\3 & 6 & x \\6 & x & 3 \end {vmatrix}\) = \(\begin{vmatrix}2 & x & 7 \\x & 7 & 2 \\7 & 2 & x \end {vmatrix}\) = \(\begin{vmatrix}4 & 5 & x \\5 & x & 4 \\x & 4 & 6 \end {vmatrix}\)? |
| A. | 9 |
| B. | -9 |
| C. | 0 |
| D. | Can’t be predicted |
| Answer» C. 0 | |
| 9. |
If the system of equation 2x + 5y + 8z = 0, x + 4y + 7z = 0, 6x + 9y – αz = 0 has a non trivial solution then what is the value of α? |
| A. | -12 |
| B. | 0 |
| C. | 12 |
| D. | 2 |
| Answer» D. 2 | |
| 10. |
What is the value of \(\begin{vmatrix}-bc & ca + ab & ca + ab \\ab + bc & -ca & ab + bc \\bc + ca & bc + ca & -ab \end {vmatrix}\) ? |
| A. | Σab |
| B. | (Σab)2 |
| C. | (Σab)3 |
| D. | (Σab)4 |
| Answer» D. (Σab)4 | |