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Class 12 Maths Practice Test - Determinants
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Class 12 Maths Practice Test - Determinants
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25 Questions

1. Evaluate \(\begin{vmatrix}3&-1&3\\6&-5&4\\3&-2&3\end{vmatrix}\)
2. Find the value of x, if \(\begin{vmatrix}1&-1\\3&-5\end{vmatrix}\)=\(\begin{vmatrix}x&x^2\\3&5\end{vmatrix}\).
3. Find the value of x, if \(\begin{vmatrix}2&5\\3&x\end{vmatrix}\)=\(\begin{vmatrix}x&-1\\5&3\end{vmatrix}\).
4. If, x3 = 1, then, what will be the value of\(\begin{vmatrix}a & b & c \\b & c & a \\c & a & b \end {vmatrix}\)?
5. Evaluate \(\begin{vmatrix}1&1&-2\\3&4&5\\-1&2&1\end{vmatrix}\).
6. Evaluate \(\begin{vmatrix}\sqrt{3}&\sqrt{2}\\-1&2\sqrt{3}\end{vmatrix}\).
7. Evaluate \(\begin{vmatrix}sin⁡ \,y&0&sin⁡ \,y\\cos⁡ \,y&1&cos⁡ \,x\\sin⁡ \,y&1&sin ⁡\,y \end{vmatrix}\)
8. What will be the value of f(x) if \(\begin{vmatrix}1 & 1 & 1 \\x & y & z \\x^3 & y^3 & z^3 \end {vmatrix}\)?
9. Evaluate \(\begin{vmatrix}2&5\\-1&-1\end{vmatrix}\).
10. What will be the value of f(x) if \(\begin{vmatrix}1 & ab & (\frac{1}{a} + \frac{1}{b}) \\1 & bc & (\frac{1}{b} + \frac{1}{c}) \\1 & ca & (\frac{1}{c} + \frac{1}{a})\end {vmatrix}\)?
11. Find the determinant of the matrix A=\(\begin{bmatrix}9&8\\7&6\end{bmatrix}\)
12. Evaluate |A|2-5|A|+1, if A=\(\begin{bmatrix}7&4\\5&5\end{bmatrix}\)
13. 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 \(\begin{vmatrix}a & b & c \\b & c & a \\c & a & b \end {vmatrix}\)?
14. Which of the following matrices will not have a determinant?
15. What will be the value of f(x) if \(\begin{vmatrix}x & b & c\\a & y & c\\a & b & z \end {vmatrix}\)?
16. Find the value of x if \(\begin{vmatrix}3&x\\2&x^2 \end{vmatrix}\)=\(\begin{vmatrix}5&3\\3&2\end{vmatrix}\).
17. What will be the value of \(\begin{vmatrix}cos^2⁡ θ & cosθ \, sinθ & -sinθ \\cosθ\, sinθ & sin^2⁡θ & cosθ \\sinθ & -cosθ & 0 \end {vmatrix}\)?
18. Find the determinant of the matrix A=\(\begin{bmatrix}-cos⁡θ&-tan⁡θ\\cot⁡θ &cos⁡θ \end{bmatrix}\).
19. What is the value of \(\begin{vmatrix}1 & cosx-sinx & cosx + sinx \\1 & cosy-siny & cosy + siny \\1 & cosz-sinz & cosz + sinz \end {vmatrix}\)?
20. Evaluate \(\begin{vmatrix}5&4&3\\3&4&1\\5&6&1\end{vmatrix}\).
21. Evaluate \(\begin{vmatrix}i&-1\\-1&-i\end{vmatrix}\).
22. If A=\(\begin{bmatrix}2&5&9\\6&1&3\\4&8&2\end{bmatrix}\), find |A|.
23. Evaluate \(\begin{vmatrix}5&-4\\1&\sqrt{3}\end{vmatrix}\).
24. Evaluate \(\begin{vmatrix}-sinθ&-1\\1&sin⁡θ\end{vmatrix}\).
25. Evaluate \(\begin{vmatrix}5&0&5\\1&4&3\\0&8&6\end{vmatrix}\).

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