CBSE Class 12th Mathematics Chapter 4 - Determinants Important Questions with Answers

You should focus on solving CBSE Class 12th Mathematics Chapter 4: Determinants important questions, especially to help you score high marks. By solving CBSE Class 12th Mathematics 4 questions, you will be solving exam-oriented questions only.

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Prepare thoroughly with the most important questions of CBSE Class 12th Mathematics Chapter 4 - Determinants. You can first cover the CBSE Class 12th Mathematics syllabus to understand the key topics and then start solving the CBSE Class 12th Mathematics Chapter 4 - Determinants Important Question to get a better understanding of your preparation level. Start practicing now.

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Question 1.

Find |AB|, if A =

[\begin{array}{rr} 0 & - 1 \\ 0 & 2 \end{array}]

and B =

[\begin{array}{ll} 3 & 5 \\ 0 & 0 \end{array}]

. (All India 2019)

Question 2.

If A =

[\begin{array}{ll} p & 2 \\ 2 & p \end{array}]

and |A³| = 125 then find the value of p. (All India 2019)

Question 3.

If A is a square matrix satisfying A’A = I, write the value of |A|. (All India 2019)

Question 4.

If A and B are square matrices of the same order 3, such that |A| = 2 and AB = 27. Write the value of |B|. (Delhi 2019)

Question 5.

Using properties of determinants, show that (All India 2019)

| \begin{array}{ccc} 3 a & - a + b & - a + c \\ - b + a & 3 b & - b + c \\ - c + a & - c + b & 3 c \end{array} |

= 3(a + 6 + c) (ab + be + ca)

Question 6.

Using properties of determinants, prove the following (Delhi 2019)

| \begin{array}{ccc} a + b + c & - c & - b \\ - c & a + b + c & - a \\ - b & - a & a + b + c \end{array} |

= 2(a + b) (b + c) (c + a)

Question 7.

Using properties of determinants, prove the following (Delhi 2019, 2012C, 2009)

| \begin{array}{ccc} a & b & c \\ a - b & b - c & c - a \\ b + c & c + a & a + b \end{array} |

= a³ + b³ + c³ – 3abc

Question 8.

Show that for the matrix A =

[\begin{array}{rrr} 1 & 1 & 1 \\ 1 & 2 & - 3 \\ 2 & - 1 & 3 \end{array}]

, A³ – 6A² + 5A + 11I = O. Hence, find A^-1. (All India 2019)

Question 9.

If A =

[\begin{array}{lll} 1 & 3 & 4 \\ 2 & 1 & 2 \\ 5 & 1 & 1 \end{array}]

, find A^-1. Hence solve the system of equations
x + 3y + 4z = 8
2x + y + 2z = 5
and 5x + y + z = 7. (All India 2019)

Question 10.

If A =

[\begin{array}{lll} 1 & 1 & 1 \\ 1 & 0 & 2 \\ 3 & 1 & 1 \end{array}]

, find A^-1. Hence, solve the system of equations x + y + z = 6, x + 2z = 7, 3x + y + z = 12. (Delhi 2019)

Question 1.

Using properties of determinants, prove that (CBSE 2018)

| \begin{array}{ccc} 1 & 1 & 1 + 3 x \\ 1 + 3 y & 1 & 1 \\ 1 & 1 + 3 z & 1 \end{array} |

= 9 (3xyz + xy + yz + zx).

Question 2.

Using properties of determinants, prove that (CBSE 2018C)

| \begin{array}{ccc} 5 a & - 2 a + b & - 2 a + c \\ - 2 b + a & 5 b & - 2 b + c \\ - 2 c + a & - 2 c + b & 5 c \end{array} |

= 12 (a + b + c) (ab + bc + ca).

Question 3.

Given A =

[\begin{array}{cc} 2 & - 3 \\ - 4 & 7 \end{array}]

, compute A and show that 2A^-1 = 9I – A (CBSE 2018)

Question 4.

If A =

[\begin{array}{ccc} 2 & - 3 & 5 \\ 3 & 2 & - 4 \\ 1 & 1 & - 2 \end{array}]

, A^-1. Use it to solve the system of equations 2x – 3y + 5z = 11, 3x + 2y – 4z = -5, x + y – 2z = -3. (CBSE 2018)

Question 5.

Given A =

[\begin{array}{lll} 5 & 0 & 4 \\ 2 & 3 & 2 \\ 1 & 2 & 1 \end{array}]

, B^-1 =

[\begin{array}{lll} 1 & 3 & 3 \\ 1 & 4 & 3 \\ 1 & 3 & 4 \end{array}]

, compute (AB)^-1. (CBSE 2018C)

Question 6.

Using properties of determinants, prove that (Delhi 2017: All India 2017)

| \begin{array}{ccc} x & x + y & x + 2 y \\ x + 2 y & x & x + y \\ x + y & x + 2 y & x \end{array} |

= 9y²(x + y).

Question 7.

If for any 2 × 2 square matrix A, A(adj A) =

[\begin{array}{ll} 8 & 0 \\ 0 & 8 \end{array}]

, then write the value of |A|. (All India 2017)

Question 8.

Determine the product of

[\begin{array}{ccc} - 4 & 4 & 4 \\ - 7 & 1 & 3 \\ 5 & - 3 & - 1 \end{array}]

[\begin{array}{ccc} 1 & - 1 & 1 \\ 1 & - 2 & - 2 \\ 2 & 1 & 3 \end{array}]

and then Use to solve the system of equations
x – y + z = 4
x – 2y – 2z = 9
and 2x + y + 3z = 1. (All India 2017, Delhi 2012C)

Question 9.

Use Products

[\begin{array}{rrr} 1 & - 1 & 2 \\ 0 & 2 & - 3 \\ 3 & - 2 & 4 \end{array}] [\begin{array}{rrr} - 2 & 0 & 1 \\ 9 & 2 & - 3 \\ 6 & 1 & - 2 \end{array}]

to solve the system equations
x – y + 2z = 1
2y – 3z = 1
and 3x – 2y + 4z = 2. (Delhi 2017, Foreign 2011)

Question 10.

Find the maximum value of (Delhi 2016)

| \begin{array}{ccc} 1 & 1 & 1 \\ 1 & 1 + \sin θ & 1 \\ 1 & 1 & 1 + \cos θ \end{array} |

Other CBSE Class 12th Mathematics Chapter Wise Questions

Three - dimensional Geometry

Continuity and Differentiability

Applications of Derivatives

Differential Equations

Inverse Trigonometric Functions

Relations and Functions

Applications of the Integrals

Linear Programming

Other CBSE Class 12th Subjects Important Questions

Political Science

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