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Thursday, 28 January 2021

CBSE Class 12 Maths - MCQ and Online Tests - Unit 3 - Matrices

CBSE Class 12 Maths – MCQ and Online Tests – Unit 3 – Matrices

Every year CBSE conducts board exams for 12th standard. These exams are very competitive to all the students. So our website provides online tests for all the 12th subjects. These tests are also very effective and useful for those who preparing for competitive exams like NEET, JEE, CA etc. It can boost their preparation level and confidence level by attempting these chapter wise online tests.

These online tests are based on latest CBSE Class 12 syllabus. While attempting these our students can identify the weak lessons and continuously practice those lessons for attaining high marks. It also helps to revise the NCERT textbooks thoroughly.

CBSE Class 12 Maths – MCQ and Online Tests – Unit 3 – Matrices

Question 1.
Let A = $$\left[\begin{array}{cc} 1 & -1 \\ 2 & 3 \end{array}\right]$$ then
(a) A-1 = $$\left[\begin{array}{cc} \frac{3}{5} & \frac{1}{5} \\ \frac{-2}{5} & \frac{1}{5} \end{array}\right]$$
(b) |A| = 0
(c) |A| = 5
(d) A² = 1

Answer: (a) A-1 = $$\left[\begin{array}{cc} \frac{3}{5} & \frac{1}{5} \\ \frac{-2}{5} & \frac{1}{5} \end{array}\right]$$

Question 2.
A² – A + I = 0 then the inverse of A
(a) A
(b) A + I
(c) I – A
(d) A – I

Question 3.
If A = $$\left[\begin{array}{cc} 2 & 3 \\ 1 & -4 \end{array}\right]$$ and B = $$\left[\begin{array}{cc} 1 & -2 \\ -1 & 3 \end{array}\right]$$ then find (AB)-1
(a) $$\frac{1}{11}$$ $$\left[\begin{array}{cc} 14 & 5 \\ 5 & 1 \end{array}\right]$$
(b) $$\frac{1}{11}$$ $$\left[\begin{array}{cc} 14 & -5 \\ -5 & 1 \end{array}\right]$$
(c) $$\frac{1}{11}$$ $$\left[\begin{array}{cc} 1 & 5 \\ 5 & 14 \end{array}\right]$$
(d) $$\frac{1}{11}$$ $$\left[\begin{array}{cc} 1 & -5 \\ -5 & 14 \end{array}\right]$$

Answer: (a) $$\frac{1}{11}$$ $$\left[\begin{array}{cc} 14 & 5 \\ 5 & 1 \end{array}\right]$$

Question 4.
If A = $$\left[\begin{array}{cc} \cos x & -\sin x \\ \sin x & \cos x \end{array}\right]$$ then A + AT = I if the value of x is
(a) $$\frac{π}{6}$$
(b) $$\frac{π}{3}$$
(c) π
(d) 0

Answer: (b) $$\frac{π}{3}$$

Question 5.
If A = $$\left[\begin{array}{cc} a & b \\ c & d \end{array}\right]$$ then A² is equal to
(a) $$\left[\begin{array}{cc} a^{2} & b^{2} \\ c^{2} & d^{2} \end{array}\right]$$
(b) $$\left[\begin{array}{cc} b^{2}+bc & ab+bd \\ ac+dc & dc+d^{2} \end{array}\right]$$
(c) $$\left[\begin{array}{cc} a^{3} & b^{3} \\ c^{3} & d^{3} \end{array}\right]$$
(d) None of these

Answer: (b) $$\left[\begin{array}{cc} b^{2}+bc & ab+bd \\ ac+dc & dc+d^{2} \end{array}\right]$$

Question 6.
If A = $$\left[\begin{array}{cc} 2x & 5 \\ 8 & x \end{array}\right]$$ = $$\left[\begin{array}{cc} 6 & -2 \\ 7 & 3 \end{array}\right]$$ then the value of x is
(a) 3
(b) ±3
(c) ±6
(d) 6

Question 7.
If A = $$\left[\begin{array}{cc} α & 0 \\ 1 & 1 \end{array}\right]$$ B = $$\left[\begin{array}{cc} 1 & 0 \\ 5 & 1 \end{array}\right]$$ where A² = B then the value of α is
(a) 1
(b) -1
(c) 4
(d) we cant calculate the value of α

Answer: (d) we cant calculate the value of α

Question 8.
If A = $$\left[\begin{array}{cc} 1 & 1 \\ 0 & 1 \end{array}\right]$$ B = $$\left[\begin{array}{cc} 0 & 1 \\ 1 & 0 \end{array}\right]$$ then AB =
(a) $$\left[\begin{array}{cc} 0 & 0 \\ 0 & 0 \end{array}\right]$$
(b) $$\left[\begin{array}{cc} 1 & 1 \\ 1 & 0 \end{array}\right]$$
(c) $$\left[\begin{array}{cc} 1 & 0 \\ 0 & 1 \end{array}\right]$$
(d) 10

Answer: (b) $$\left[\begin{array}{cc} 1 & 1 \\ 1 & 0 \end{array}\right]$$

Question 9.
If A = $$\left[\begin{array}{cc} 1 & 2 \\ 2 & 1 \end{array}\right]$$ then adj A =
(a) $$\left[\begin{array}{cc} 1 & -2 \\ -2 & 1 \end{array}\right]$$
(b) $$\left[\begin{array}{cc} 2 & 1 \\ 1 & 1 \end{array}\right]$$
(c) $$\left[\begin{array}{cc} 1 & -2 \\ -2 & -1 \end{array}\right]$$
(d) $$\left[\begin{array}{cc} -1 & 2 \\ -2 & -1 \end{array}\right]$$

Answer: (a) $$\left[\begin{array}{cc} 1 & -2 \\ -2 & 1 \end{array}\right]$$

Question 10.
If $$\left|\begin{array}{ll} x & 8 \\ 3 & 3 \end{array}\right|$$ = 0, the value of x is
(a) 3
(b) 8
(c) 24
(d) 0

Question 11.
If $$\left[\begin{array}{cc} 1-x & 2 \\ 18 & 6 \end{array}\right]$$ = $$\left[\begin{array}{cc} 6 & 2 \\ 18 & 6 \end{array}\right]$$ then x =
(a) ±6
(b) 6
(c) -5
(d) 7

Question 12.
A = [aij]m×n is a square matrix if
(a) m = n
(b) m < n
(c) m > n
(d) None of these

Question 13.
If A and B are square matrices then (AB)’ =
(a) B’A’
(b) A’B’
(c) AB’
(d) A’B’

Question 14.
A matrix A = [aij]m×n is said to be symmetric if
(a) aij = 0
(b) aij = aji
(c) aij = aij
(d) aij = 1

Question 15.
For any unit matrix I
(a) I² = I
(b) |I| = 0
(c) |I| = 2
(d) |I| = 5

Question 16.
$$\left|\begin{array}{lll} 3 & 4 & 5 \\ 0 & 2 & 3 \\ 0 & 0 & 7 \end{array}\right|$$ = A then |A| = ?
(a) 40
(b) 50
(c) 42
(d) 15

Question 17.
If a matrix is both symmetric matrix and skew symmetric matrix then
(a) A is a diagonal matrix
(b) A is zero matrix
(c) A is scalar matrix
(d) None of these

Answer: (b) A is zero matrix

Question 18.
The matrix P = $$\left[\begin{array}{ccc} 0 & 0 & 4 \\ 0 & 4 & 0 \\ 4 & 0 & 0 \end{array}\right]$$ is
(a) square matrix
(b) diagonal matrix
(c) unit matrix
(d) None of these

Question 19.
If A and B are two matrices of the order 3 × m and 3 × n, respectively, and m = n, then the order of matrix (5A – 2B) is
(a) m × 3
(b) 3 × 3
(c) m × n
(d) 3 × n

Question 20.
If A = $$\frac{1}{π}$$ $$\left[\begin{array}{cc} \sin ^{-1}(x \pi) & \tan^{1}\left(\frac{x}{\pi}\right) \\ \sin ^{-1}\left(\frac{x}{\pi}\right) & \cot ^{-1}(\pi x) \end{array}\right]$$
B = $$\frac{1}{π}$$ $$\left[\begin{array}{cc} \cos ^{-1}(x \pi) & \tan ^{-1}\left(\frac{x}{\pi}\right) \\ \sin ^{-1}\left(\frac{x}{\pi}\right) & -\tan ^{-1}(\pi x) \end{array}\right]$$
then A – B equal to
(a) I
(b) O
(c) 1
(d) $$\frac{3}{2}$$ I

Answer: (d) $$\frac{3}{2}$$ I

Question 21.
For any two matrices A and B, we have
(a) AB = BA
(b) AB ≠ BA
(c) AB = 0
(d) None of these

Question 22.
If A = [aij]2×2 where aij = i + j, then A is equal to
(a) $$\left[\begin{array}{cc} 1 & 2 \\ 3 & 4 \end{array}\right]$$
(b) $$\left[\begin{array}{cc} 2 & 3 \\ 3 & 4 \end{array}\right]$$
(c) $$\left[\begin{array}{cc} 1 & 1 \\ 2 & 2 \end{array}\right]$$
(d) $$\left[\begin{array}{cc} 1 & 2 \\ 1 & 2 \end{array}\right]$$

Answer: (b) $$\left[\begin{array}{cc} 2 & 3 \\ 3 & 4 \end{array}\right]$$

Question 23.
If A and B are matrices of same order, then (AB’ – BA’) is a
(a) skew symmetric matrix
(b) null matrix
(c) symmetric matrix
(d) unit matrix

Question 24.
If A is matrix of order m × n and B is a matrix such that AB’ and B’A are both defined, then order of matrix B is
(a) m × m
(b) n × n
(c) n × m
(d) m × n

Question 25.
If matrix A = [aij]2×2 where aij = {$$_{0 if i = j}^{1 if i ≠ j}$$ then A² is equal to
(a) I
(b) A
(c) O
(d) None of these

Question 26.
The matrix $$\left[\begin{array}{ccc} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 0 \end{array}\right]$$ is a
(a) identity matrix
(b) symmetric matrix
(c) skew symmetric matrix
(d) None of these

Question 27.
A square matrix A = [aij]n×n is called a diagonal matrix if aij = 0 for
(a) i = j
(b) i < j
(c) i > j
(d) i ≠ j

Question 28.
The matrix A = $$\left[\begin{array}{cc} 0 & 1 \\ 1 & 0 \end{array}\right]$$ is a
(a) unit matrix
(b) diagonal matrix
(c) symmetric matrix
(d) skew symmetric matrix

Question 29.
If P = $$\left[\begin{array}{ccc} i & 0 & -i \\ 0 & -i & i \\ -i & i & 0 \end{array}\right]$$ and Q = $$\left[\begin{array}{cc} -i & i \\ 0 & 0 \\ i & -i \end{array}\right]$$ then PQ is equal to
(a) $$\left[\begin{array}{cc} -2 & 2 \\ 1 & -1 \\ 1 & -1 \end{array}\right]$$
(b) $$\left[\begin{array}{cc} 2 & -2 \\ -1 & 1 \\ -1 & 1 \end{array}\right]$$
(c) $$\left[\begin{array}{cc} 2 & -2\\ -1 & 1 \end{array}\right]$$
(d) $$\left[\begin{array}{ccc} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}\right]$$

Answer: (b) $$\left[\begin{array}{cc} 2 & -2 \\ -1 & 1 \\ -1 & 1 \end{array}\right]$$

Question 30.
For what values of x and y are the following matrices equal
A = $$\left[\begin{array}{cc} 2x+1 & 3y\\ 0 & y^{2}-5y \end{array}\right]$$ B = $$\left[\begin{array}{cc} x+3 & y^{2}+2 \\ 0 & -6 \end{array}\right]$$
(a) 2, 3
(b) 3, 4
(c) 2, 2
(d) 3, 3

Question 31.
Find x, y, z and w respectively such that
$$\left[\begin{array}{cc} x-y & 2x+z\\ 2x-y & 2x+w \end{array}\right]$$ = $$\left[\begin{array}{cc} 5 & 3 \\ 12 & 15 \end{array}\right]$$
(a) 7, 2, 1, 1
(b) 7, 5, 3, 8
(c) 1, 2, 5, 6
(d) 6, 3, 2, 1

Answer: (a) 7, 2, 1, 1

Question 32.
If $$\left[\begin{array}{cc} x-y & 2x+z\\ 2x-y & 3z+w \end{array}\right]$$ = $$\left[\begin{array}{cc} -1 & 5 \\ 0 & 13 \end{array}\right]$$ then the value of w is
(a) 1
(b) 2
(c) 3
(d) 4

Question 33.
If A and B are 2 × 2 matrices, then which of the following is true?
(a) (A + B)² = A² + B² + 2AB
(b) (A – B)² = A² + B² – 2AB
(c) (A – B)(A + B) = A² + AB – BA – B²
(d) (A + B) (A – B) = A² – B²

Answer: (c) (A – B)(A + B) = A² + AB – BA – B²

Question 34.
If A = $$\left[\begin{array}{cc} 1 & 2\\ 3 & 4 \end{array}\right]$$ then A2 – 5A is equal to
(a) 2I
(b) 3I
(c) -2I
(d) null matrix

Question 35.
If A = $$\left[\begin{array}{ccc} 2 & 2 & 1 \\ 1 & 3 & 1 \\ 1 & 2 & 2 \end{array}\right]$$ then A³ – 7A² + 10A =
(a) 5I + A
(b) 5I – A
(c) 5I
(d) 6I

Question 36.
If A is a m × n matrix such that AB and BA are both defined, then B is an
(a) m × n matrix
(b) n × m matrix
(c) n × n matrix
(d) m × m matrix

Answer: (b) n × m matrix

Question 37.
If A = $$\left[\begin{array}{ccc} 1 & 0 & 0 \\ 0 & 1 & 0 \\ a & b & -1 \end{array}\right]$$ then (A – I) (A + I) = 0 for
(a) a = b = 0 only
(b) a = 0 only
(c) b = 0 only
(d) any a and b

Answer: (d) any a and b

Question 38.
If A = $$\left[\begin{array}{cc} 1 & 1\\ 0 & 2 \end{array}\right]$$ then A8 – 28 (A – I)
(a) I – A
(b) 2I – A
(c) I + A
(d) A – 2I

Question 39.
The inverse of A = $$\left|\begin{array}{ll} 2 & 3 \\ 5 & k \end{array}\right|$$ will not be obtained if A has the value
(a) 2
(b) $$\frac{3}{2}$$
(c) $$\frac{5}{2}$$
(d) $$\frac{15}{2}$$

Answer: (d) $$\frac{15}{2}$$

Question 40.
If $$\left[\begin{array}{cc} a+b & 2\\ 5 & ab \end{array}\right]$$ = $$\left[\begin{array}{cc} 6 & 2 \\ 5 & 8 \end{array}\right]$$ then find the value of a and b respectively
(a) 2, 4
(b) 4, 2
(c) Both (a) and (b)
(d) None of these