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Class 12 Mathematics: Determinants
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MCQs on determinant, determinants properties and applications, triangle area, minors and cofactors, adjoint and inverse of matrix, determinants and matrices applications.

Class 12 Mathematics: Determinants
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25 Questions

1. If A=\(\begin{bmatrix}2&5&9\\6&1&3\\4&8&2\end{bmatrix}\), find |A|.
2. Evaluate \(\begin{vmatrix}b-c&b&c\\a&c-a&c\\a&b&a-b\end{vmatrix}\).
3. Evaluate \(\begin{vmatrix}sin⁡ \,y&0&sin⁡ \,y\\cos⁡ \,y&1&cos⁡ \,x\\sin⁡ \,y&1&sin ⁡\,y \end{vmatrix}\)
4. Which one of the following is correct if a, b and c are the sides of a triangle ABC and \(\begin{vmatrix}a^2 & b^2 & c^2 \\(a + 1)^2 & (b + 1)^2 & (c + 1)^2 \\ (a – 1)^2 & (b – 1)^2 & (c – 1)^2 \end {vmatrix}\) ?
5. What will be the value of \(\begin{vmatrix}2bc – a^2 & c^2 & b^2 \\c^2 & 2ac – b^2 & a^2 \\b^2 & a^2 & 2ab – c^2 \end {vmatrix}\) if given another determinant \(\begin{vmatrix}a & b & c \\b & c & a \\c & a & b \end {vmatrix}\)?
6. 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?
7. Evaluate \(\begin{vmatrix}5&-4\\1&\sqrt{3}\end{vmatrix}\).
8. Evaluate \(\begin{vmatrix}1+m&n&q\\m&1+n&q\\n&m&1+q\end{vmatrix}\).
9. If, x3 = 1, then, what will be the value of\(\begin{vmatrix}a & b & c \\b & c & a \\c & a & b \end {vmatrix}\)?
10. Evaluate \(\begin{vmatrix}cos⁡θ&-cos⁡θ&1\\sin^2⁡θ&cos^2⁡θ&1\\sin⁡θ&-sin⁡θ&1\end{vmatrix}\).
11. Find the value of x, if \(\begin{vmatrix}1&-1\\3&-5\end{vmatrix}\)=\(\begin{vmatrix}x&x^2\\3&5\end{vmatrix}\).
12. Find the value of x, y, z for the given system of equations.2x+3y+2z=50 x+4y+3z=40 x+3y+5z=60"
13. Evaluate \(\begin{vmatrix}i&-1\\-1&-i\end{vmatrix}\).
14. Find the determinant of the matrix A=\(\begin{bmatrix}-cos⁡θ&-tan⁡θ\\cot⁡θ &cos⁡θ \end{bmatrix}\).
15. Find the values of x and y for the given system of equations.3x-2y=3 x+2y=4"
16. If, Si = ai + bi + ci then what is the value of \(\begin{vmatrix}S0 & S1 & S2 \\S1 & S2 & S3 \\S2 & S3 & S4 \end {vmatrix}\)?
17. What is the value of \(\begin{vmatrix}sin^2 ⁡a & sina\, cosa & cos^2 ⁡a \\sin^2 ⁡b & sinb\, cosb & cos^2 ⁡b \\sin^2⁡ c & sinc\, cosc & cos^2⁡ c \end {vmatrix}\)?
18. Which of the following conditions holds true for a system of equations to be consistent?
19. 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) = \(\begin{vmatrix}0 & c & b \\c & 0 & a \\b & a & 0 \end {vmatrix}\)?
20. 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?
21. Evaluate \(\begin{vmatrix}4&8&12\\6&12&18\\7&14&21\end{vmatrix}\).
22. What is the value of \(\begin{vmatrix}1 & cosx-sinx & cosx + sinx \\1 & cosy-siny & cosy + siny \\1 & cosz-sinz & cosz + sinz \end {vmatrix}\)?
23. What will be the value of \(\begin{vmatrix}0 & p-q & a – b\\q – p & 0 & x – y\\b – a & y – x & 0 \end {vmatrix}\)?
24. Find the value of x and y for the given system of equations.3x+2y=6 x+y=2"
25. Find the minor and cofactor respectively for the element 3 in the determinant Δ=\(\begin{vmatrix}1&5\\3&6\end{vmatrix}\).

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