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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=\(\begin{bmatrix}1&3\\2&1\end{bmatrix}\), then ________
2. Evaluate \(\begin{vmatrix}cos⁡θ&-cos⁡θ&1\\sin^2⁡θ&cos^2⁡θ&1\\sin⁡θ&-sin⁡θ&1\end{vmatrix}\).
3. Evaluate \(\begin{vmatrix}1+m&n&q\\m&1+n&q\\n&m&1+q\end{vmatrix}\).
4. What will be the value of f(x) = \(\begin{vmatrix}p & 2 – i & i + 1 \\2 + i & q & 3 + i \\1 – i & 3 – i & r \end {vmatrix}\)?
5. Evaluate \(\begin{vmatrix}\sqrt{3}&\sqrt{2}\\-1&2\sqrt{3}\end{vmatrix}\).
6. 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)?
7. 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 \(\begin{vmatrix}a & b & c \\b & c & a \\c & a & b \end {vmatrix}\)?
8. If A=\(\begin{bmatrix}2&5&9\\6&1&3\\4&8&2\end{bmatrix}\), find |A|.
9. Find the value of x if \(\begin{vmatrix}3&x\\2&x^2 \end{vmatrix}\)=\(\begin{vmatrix}5&3\\3&2\end{vmatrix}\).
10. Find the cofactor of element -3 in the determinant Δ=\(\begin{vmatrix}1&4&4\\-3&5&9\\2&1&2\end{vmatrix}\).
11. Which of the following is the formula for cofactor of an element aij ?
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. What will be the value of f(x) if \(\begin{vmatrix}x & b & c\\a & y & c\\a & b & z \end {vmatrix}\)?
14. Find the determinant of A=\(\begin{bmatrix}c^2&cb&ca\\ab&a^2&-ac\\ab&bc&-b^2\end{bmatrix}\)
15. Find the minor and cofactor respectively for the element 3 in the determinant Δ=\(\begin{vmatrix}1&5\\3&6\end{vmatrix}\).
16. Evaluate |A|2-5|A|+1, if A=\(\begin{bmatrix}7&4\\5&5\end{bmatrix}\)
17. Evaluate \(\begin{vmatrix}i&-1\\-1&-i\end{vmatrix}\).
18. A given systems of equations is said to be inconsistent if _________________
19. For a given system of equations if |A|=0 and (adj A)B≠O(zero matrix), then which of the following is correct regarding the solutions of the given equations?
20. Find the determinant of the matrix A=\(\begin{bmatrix}-cos⁡θ&-tan⁡θ\\cot⁡θ &cos⁡θ \end{bmatrix}\).
21. Evaluate \(\begin{vmatrix}b-c&b&c\\a&c-a&c\\a&b&a-b\end{vmatrix}\).
22. Evaluate \(\begin{vmatrix}1&1&-2\\3&4&5\\-1&2&1\end{vmatrix}\).
23. Evaluate \(\begin{vmatrix}5&-4\\1&\sqrt{3}\end{vmatrix}\).
24. What is the value of \(\begin{vmatrix}-bc & ca + ab & ca + ab \\ab + bc & -ca & ab + bc \\bc + ca & bc + ca & -ab \end {vmatrix}\) ?
25. Evaluate \(\begin{vmatrix}8x+1&2x-2\\x^2-1&3x+5\end{vmatrix}\).

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