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

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

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

Answer

Answer: (c) I – A

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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

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

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

Answer

Answer: (b) \(\frac{π}{3}\)

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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

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

Answer

Answer: (a) 3

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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

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

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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

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

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

Answer

Answer: (b) 8

---

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

Answer

Answer: (c) -5

---

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

Answer

Answer: (a) m = n

---

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

Answer

Answer: (a) B’A’

---

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

Answer

Answer: (b) a_ij = a_ji

---

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

Answer

Answer: (a) I² = I

---

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

Answer

Answer: (c) 42

---

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

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

Answer

Answer: (a) square matrix

---

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

Answer

Answer: (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

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

Answer

Answer: (d) None of these

---

Question 22.
If A = [a_ij]_2×2 where a_ij = 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

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

Answer

Answer: (a) skew symmetric 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

Answer

Answer: (d) m × n

---

Question 25.
If matrix A = [a_ij]_2×2 where a_ij = {\(_{0 if i = j}^{1 if i ≠ j}\) then A² is equal to
(a) I
(b) A
(c) O
(d) None of these

Answer

Answer: (a) I

---

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

Answer

Answer: (b) symmetric matrix

---

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

Answer

Answer: (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

Answer

Answer: (c) 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

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

Answer

Answer: (c) 2, 2

---

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

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

Answer

Answer: (d) 4

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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

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

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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

Answer

Answer: (a) 2I

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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

Answer

Answer: (b) 5I – A

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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

Answer: (b) n × m matrix

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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

Answer: (d) any a and b

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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

Answer

Answer: (b) 2I – A

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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

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

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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

Answer

Answer: (c) Both (a) and (b)

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