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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. Evaluate \(\begin{vmatrix}2&5\\-1&-1\end{vmatrix}\).
2. Which of the following conditions holds true for a system of equations to be consistent?
3. If A=\(\begin{bmatrix}2&5&9\\6&1&3\\4&8&2\end{bmatrix}\), find |A|.
4. The cost of 8kg apple and 3kg is Rs 70. The cost of 10kg apple and 6kg orange is 90. Find the cost of each item if x is the cost of apples per kg and y is the cost of oranges per kg.
5. Find the value of x, if \(\begin{vmatrix}2&5\\3&x\end{vmatrix}\)=\(\begin{vmatrix}x&-1\\5&3\end{vmatrix}\).
6. Evaluate \(\begin{vmatrix}\sqrt{3}&\sqrt{2}\\-1&2\sqrt{3}\end{vmatrix}\).
7. 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?
8. If A=\(\begin{bmatrix}1&3\\2&1\end{bmatrix}\), then ________
9. The given system of equation is inconsistent.4x+2y=7 x+3y=9"
10. Find the value of x and y for the given system of equations.3x+2y=6 x+y=2"
11. What will be the value of \(\begin{vmatrix}a & b & c \\b & c & a \\c & a & b \end {vmatrix}\)?
12. If, Si = ai + bi + ci then what is the value of \(\begin{vmatrix}S0 & S1 & S2 \\S1 & S2 & S3 \\S2 & S3 & S4 \end {vmatrix}\)?
13. Find the value of x if \(\begin{vmatrix}3&x\\2&x^2 \end{vmatrix}\)=\(\begin{vmatrix}5&3\\3&2\end{vmatrix}\).
14. Find the cofactor of element -3 in the determinant Δ=\(\begin{vmatrix}1&4&4\\-3&5&9\\2&1&2\end{vmatrix}\).
15. Evaluate \(\begin{vmatrix}sin⁡ \,y&0&sin⁡ \,y\\cos⁡ \,y&1&cos⁡ \,x\\sin⁡ \,y&1&sin ⁡\,y \end{vmatrix}\)
16. Which of the following is the formula for cofactor of an element aij ?
17. What will be the value of f(x) if \(\begin{vmatrix}x & b & c\\a & y & c\\a & b & z \end {vmatrix}\)?
18. Evaluate \(\begin{vmatrix}b-c&b&c\\a&c-a&c\\a&b&a-b\end{vmatrix}\).
19. 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?
20. Find the values of x and y for the given system of equations.3x-2y=3 x+2y=4"
21. Evaluate \(\begin{vmatrix}1&1&-2\\3&4&5\\-1&2&1\end{vmatrix}\).
22. A given systems of equations is said to be inconsistent if _________________
23. Find the value of x, if \(\begin{vmatrix}1&-1\\3&-5\end{vmatrix}\)=\(\begin{vmatrix}x&x^2\\3&5\end{vmatrix}\).
24. Find the value of x and y for the given system of equations.3x+4y=6 x-4y=4"
25. What is the value of \(\begin{vmatrix}-bc & ca + ab & ca + ab \\ab + bc & -ca & ab + bc \\bc + ca & bc + ca & -ab \end {vmatrix}\) ?

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