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Class 12 Maths Practice Test - Application of Determinants
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Class 12 Maths Practice Test - Application of Determinants
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19 Questions

1. What is the value of k if \(\begin{vmatrix}y + z & x & x \\y & z + x & y \\z & z & x + y\end {vmatrix}\) ?
2. If, Si = ai + bi + ci then what is the value of \(\begin{vmatrix}S0 & S1 & S2 \\S1 & S2 & S3 \\S2 & S3 & S4 \end {vmatrix}\)?
3. What will be the value of the given determinant \(\begin{vmatrix}109 & 102 & 95 \\6 & 13 & 20 \\1 & -6 & 13 \end {vmatrix}\)?
4. 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)?
5. What will be the value of f(x) = \(\begin{vmatrix}p & 2 – i & i + 1 \\2 + i & q & 3 + i \\1 – i & 3 – i & r \end {vmatrix}\)?
6. What is the value of \(\begin{vmatrix}-bc & ca + ab & ca + ab \\ab + bc & -ca & ab + bc \\bc + ca & bc + ca & -ab \end {vmatrix}\) ?
7. What will be the value of x if \(\begin{vmatrix}2-x & 2 & 3 \\2 & 5-x & 6 \\3 & 4 & 10-x \end {vmatrix}\) = 0?
8. What is the relation between the two determinants f(x) = \(\begin{vmatrix}–a^2 & ab & ac \\ab & -b^2 & bc \\ac & bc & -c^2 \end {vmatrix}\) and g(x) = \(\begin{vmatrix}0 & c & b \\c & 0 & a \\b & a & 0 \end {vmatrix}\)?
9. Let, α and β be real. Find the set of all values of β for which the system of equation βx + sin α*y + cosα*z = 0, x + cosα * y + sinα * z = 0 , -x + sinα*y – cosα * z = 0 has a non-trivial solution. For β = 1 what are all values of α?
10. 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?
11. What will be the value of \(\begin{vmatrix}0 & i – 100 & i – 500 \\100 – i & 0 & 1000 – i \\500 – i & i – 1000 & 0 \end {vmatrix}\)?
12. Which one of the following is correct if a, b and c are the sides of a triangle ABC and \(\begin{vmatrix}a^2 & b^2 & c^2 \\(a + 1)^2 & (b + 1)^2 & (c + 1)^2 \\ (a – 1)^2 & (b – 1)^2 & (c – 1)^2 \end {vmatrix}\) ?
13. 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?
14. If f(x) = \(\begin{vmatrix}1 & a & bc \\1 & b & ca \\1 & c & ab \end {vmatrix}\) = \(\begin{vmatrix}1 & a & a^2 \\1 & b & b^2 \\1 & c & c^2 \end {vmatrix}\) then which one among the following is correct?
15. The co-ordinates of the vertices of a triangle are [m(m + 1), (m + 1)], [(m + 1)(m + 2), (m + 2)] and [(m + 2)(m + 3), (m + 3)]. Then which one among the following is correct?
16. 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?
17. Which one is correct, the following system of linear equations 2x – 3y + 4z = 7, 3x – 4y + 5z = 8, 4x – 5y + 6z = 9 has?
18. Which one among the following is correct if x, y, z are eliminated from, (\(\frac{bx}{y+z}\) = a, \(\frac{cy}{z+x}\) = b, \(\frac{az}{x+y}\) = c)?
19. What is the value of x if, \(\begin{vmatrix}x & 3 & 6 \\3 & 6 & x \\6 & x & 3 \end {vmatrix}\) = \(\begin{vmatrix}2 & x & 7 \\x & 7 & 2 \\7 & 2 & x \end {vmatrix}\) = \(\begin{vmatrix}4 & 5 & x \\5 & x & 4 \\x & 4 & 6 \end {vmatrix}\)?

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