# CBSE 12th Mathematics Board Exam 2020: Important Questions & Answers from Chapter 4 - Determinants

Check important questions and answers for Class 12th Mathematics Board Examination 2020 from Chapter 4 -Determinants.

*Determinants*

The Central Board of Secondary Education, CBSE has scheduled the CBSE Class 12th Mathematics Examination 2020 on March 17, 2020. The students who will be appearing for the upcoming examination can go through the list of important questions and answers for Chapter 4 - Determinants. These questions are strictly based on the latest CBSE pattern prescribed by the Board for Class 12th Mathematics Examination 2020.

**Question 1- **If a_{1}, a_{2}, a_{3}_{,} ..., a_{r}_{ }is in GP, then prove that the given determinant is independent of *r*.

**Answer: **R_{1} and R_{2} are identical.

**Question 2-** Show that the points (a + 5, a - 4), (a - 2, a + 3) and (a, a) do not lie on a straight line for any value if a.

**Answer: **7/2 ≠ 0

This means that the given points form a triangle and do not lie in a straight line.

**Question 3- **Show that △ABC is an isosceles triangle if the determinant

**Answer: **** **cos A = cos C or cosB = cos C or cosB = cos A

This means ABC is an isosceles triangle.

**Question 4-** Find the value of x, if:

**Answer: **x = -12, 0

**Question 5- **Find the value of θ satisfying following:

**Answer:**

**Question 6- **If the coordinates of the vertices of an equilateral triangle with sides of length ‘a’ are (x_{1},y_{1}), (x_{2},y_{2}) and (x_{3},y_{3}), then

**Question 7- **Solve:

**Answer: **(a + b + c)^{3}

**Question 8- **Find the value of A^{-1 }if:

Using A^{-1}, solve the system of linear equations x - 2y = 10, 2x - y - z = 8 and - 2y + z = 7.

**Answer:** * x* = 0, *y* = - 5 and *z* = - 3

**Question 9- **Using matrix method, solve the system of equations 3*x* + 2*y* - 2*z* = 3, *x* + 2*y* + 3*z* = 6 and 2*x* - *y* + *z* = 2.

**Answer:*** x *= 1, *y* = 1 and *z* = 1

**Question 10- **Find *BA* and use this to solve the system of equations *y* + 2*z* = 7, *x* - y = 3 and 2*x* + 3*y* + 4*z* = 17.

**Answer: ***x* = 2, *y* = - 1 and *z* = 4

The above-mentioned questions are based on the NCERT textbook, previous year papers and sample papers. This article will help the students in the last minute preparation before the examination. The students appearing for the CBSE Class 12th Mathematics Examination can also go through the link mentioned below:

**CBSE 12th Maths Board Exam 2020: Chapter-wise Important Questions & Answers**

**CBSE 12th Maths Board Exam 2020: Important Multiple Choice Questions (MCQs) with Answers**