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Determinants Maths - Determinants

Gujarat Board (GSEB) - STD 12 Science - Maths (GSEB - English Medium). 259 questions in this chapter.

Question types

Determinants question types

259 questions across 4 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

259
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4
Question groups
5
Question types
Sample Questions

Determinants questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 2M.C.Q (1 Marks)1 Mark
If $\text{D}_\text{k}=\begin{vmatrix}1&\text{n}&\text{n}\\2\text{k}&\text{n}^2+\text{n}+2&\text{n}^2+\text{n}\\2\text{k}-1&\text{n}^2&\text{n}^2+\text{n}+2\end{vmatrix} $ and $\sum\limits_{\text{k}=1}^\text{n}\text{D}_\text{k}=48,$ then n equals:
  1. 4
  2. 6
  3. 8
  4. None of these.
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Q 3M.C.Q (1 Marks)1 Mark
Let $\begin{vmatrix}\text{x}^2+3\text{x}&\text{x}-1&\text{x}+ 3\\\text{x}+1&-2\text{x}&\text{x}-4\\\text{x}-3&\text{x}+4&3\text{x}\end{vmatrix}=\text{ax}^4+\text{bx}^3+\text{cx}^2+\text{dx}+\text{e}$ be an identity in x, where a, b, c, d, e are independent of x. Then the value of e is:
  1. 4
  2. 0
  3. 1
  4. None of these.
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Q 4M.C.Q (1 Marks)1 Mark
If $\begin{vmatrix}\text{a}&\text{p}&\text{x}\\\text{b}&\text{q}&\text{y}\\\text{c}&\text{r}&\text{z}\end{vmatrix}=16,$ then the value of $\begin{vmatrix}\text{p}+\text{x}&\text{a}+\text{x}&\text{a}+\text{p}\\\text{q}+\text{y}&\text{b}+\text{y}&\text{b}+\text{q}\\\text{r}+\text{z}&\text{c}+\text{z}&\text{c}+\text{r}\end{vmatrix}$ is:
  1. 4
  2. 8
  3. 16
  4. 32
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Q 5M.C.Q (1 Marks)1 Mark
If $\text{f(x)}=\begin{vmatrix}0&\text{x}-\text{a}&\text{x}-\text{b}\\\text{x}+\text{a}&0&\text{x}-\text{c}\\\text{x}+\text{b}&\text{x}+\text{c}&0\end{vmatrix},$ then:
  1. f(a) = 0
  2. f(b) = 0
  3. f(0) = 0
  4. f(1) = 0
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Q 102 Marks2 Marks
If $\text{A}=\begin{bmatrix}1&2\\3&-1\end{bmatrix}$ and $\text{B}=\begin{bmatrix}1&0\\-1&0\end{bmatrix},$ find |AB|.
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Q 113 Marks3 Marks
Using determinants, find the value of k so that the points (k, 2 - 2k), (-k + 1, 2k) and (-4 - k, 6 - 2k) may be collinear.
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Q 123 Marks3 Marks
Find the value of x if the area of $\triangle$ is 35 square cms with vertices (x, 4), (2, -6) and (5, 4).
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Q 133 Marks3 Marks
For what value of x the matrix A is singular?
$\text{A}=\begin{vmatrix}\text{x}-1&1&1\\1&\text{x}-1&1\\1&1&\text{x}-1 \end{vmatrix}$
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Q 153 Marks3 Marks
Evaluate $\triangle=\begin{vmatrix}0&\sin\alpha&-\cos\alpha\\-\sin\alpha&0&\sin\beta\\\cos\alpha&-\sin\beta&0 \end{vmatrix}$
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Q 164 Marks4 Marks
Write the minors and cofactors of element of the first column of the following matrices and hence evaluate the determinant in case:
$\text{A}=\begin{vmatrix}0&2&6\\1&5&0\\3&7&1 \end{vmatrix}$
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Q 174 Marks4 Marks
Evaluate:
$\begin{vmatrix}\text{a}&\text{b}+\text{c}&\text{a}^2\\\text{b}&\text{c}+\text{a}&\text{b}^2\\\text{c}&\text{a}+\text{b}&\text{c}^2\end{vmatrix}$
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Q 184 Marks4 Marks
Solve the following system of homogeneous linear equations:
x + y - 2z = 0,
2x + y - 3z = 0,
5x + 4y - 9z = 0
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Q 194 Marks4 Marks
$\begin{vmatrix}\text{b}^2+\text{c}^2&\text{ab}&\text{ac}\\\text{ba}&\text{c}^2+\text{a}^2&\text{bc}\\\text{ca}&\text{cb}&\text{a}^2+\text{b}^2\end{vmatrix}=4\text{a}^2\text{b}^2\text{c}^2$
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Q 204 Marks4 Marks
Show that $\begin{vmatrix}\text{x}-3&\text{x}-4&\text{x}-\alpha\\\text{x}-2&\text{x}-3&\text{x}-\beta\\\text{x}-1&\text{x}-2&\text{x}-\gamma\end{vmatrix}=0,$ where $\alpha,\beta,\gamma$ are in A.P.
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