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12th CBSE Mathematics Unit 4 Determinants One Mark Question Paper with Answer Key

Published on: 26/08/2019

Determinants

Download CBSE Class 12th Standard CBSE Maths question papers, sample papers, important questions, and previous year solved papers in PDF format. Get free study materials, NCERT solutions, and exam preparation resources for Class 12th Standard CBSE Maths

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Std: 12th Standard CBSE - Maths

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Questions:

Generic 2

9 x 2 = 18

Find value of x, if \(\begin{vmatrix} 2 & 3 \\ x & 1 \end{vmatrix}=\begin{vmatrix} x & 3 \\ 2x & 5 \end{vmatrix}\)

If for matrix A,|A|=3 find |5A|, where matrix A is order 2x2.

Find the value of X, such that the points (0, 2), (1, x) and (3, 1) are collinear.

Given I₂. Find |I₂| . Also find |3 I₂|.

Find the value of p, such that the matrix \(\begin{bmatrix} -1 & 2 \\ 4 & p \end{bmatrix}\) is singular.

If A=\(\begin{bmatrix} 2 & 3 \\ 5 & -2 \end{bmatrix}\) write A^-1 in terms of A .

What positive value of x makes the following pair of determinants equal?
\(\begin{vmatrix} 2x & 3 \\ 5 & x \end{vmatrix},\begin{vmatrix} 16 & 3 \\ 5 & 2 \end{vmatrix}\)

Write the value of determinant \(\begin{vmatrix} 2 & 3 & 4 \\ 5 & 6 & 8 \\ 6x & 9x & 12x \end{vmatrix}\).

Evaluate \(\begin{vmatrix} a+ib & c+id \\ c-id & a-ib \end{vmatrix}\)

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Answers Key:

Generic 2

9 x 2 = 18

10 - 12 = 5x - 6x ⇒ x = 2

If points are collinear then area of triangle = 0.
\(\Rightarrow \frac{1}{2}\left|\begin{array}{ccc} 0 & 2 & 1 \\ 1 & x & 1 \\ 3 & 1 & 1 \end{array}\right|=0 \)
\(\Rightarrow \frac{1}{2}[0-2(1-3)+1(1-3 x)]=0 \)
\(\Rightarrow 4+1-3 x=0 \Rightarrow x=\frac{5}{3}\)

p=-8

\(A^{-1}=\frac{1}{|A|} \text { adj } A\)
\(|A|=\left[\begin{array}{lr} 2 & 3 \\ 5 & -2 \end{array}\right]=-4-15=-19 \)
\(\Rightarrow A^{-1}=-\frac{1}{19}\left[\begin{array}{rr} -2 & -3 \\ -5 & 2 \end{array}\right]=\frac{1}{19}\left[\begin{array}{cc} 2 & 3 \\ 5 & -2 \end{array}\right]=\frac{1}{19} A \)

\(2 x^{2}-15 =32-15 \Rightarrow x^{2}=16 \)
\(\Rightarrow x =\pm 4 \Rightarrow x=4( > 0)\)

(a + ib) (a - ib) + (c + id) (c - id) = a²+b²+c²+d²