# NCERT Solutions for Class 12 Maths Determinants Miscellaneous Exercise

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*NCERT Solutions** NCERT Solutions for Class 12 Maths* are not only the solutions of Maths exercise but it builds your foundation of other important subjects. Getting knowledge of depth concept of

*like Algebra, Calculus, Trigonometry, Coordinate Geometry help you to understand the concept of Physics and Physical Chemistry.*

**CBSE Class 12**^{th}Maths* CBSE Class 12^{th}* is an important school class in your life as you take some serious decision about your career. And out of all subjects, Maths is an important and core subjects. So

*is major role in your exam preparation as it has detailed chapter wise solutions for all exercise.*

**CBSE NCERT Solutions for Class 12**^{th}MathsAs we know that all the schools affiliated from CBSE follow the NCERT books for all subjects. You can check the **CBSE NCERT Syllabus**. Thus, * NCERT Solutions* helps the students to solve the exercise questions as given in

*.*

**NCERT Books**## NCERT Solutions for Class 12 Maths Determinants Miscellaneous Exercise

**NCERT Solutions for Class 12 Maths Determinants Miscellaneous ****Exercise****: Ques No 1.**

Prove that the determinant, is independent of θ.

**NCERT Solutions:**

Expanding along R_{1}, we get

Δ = x(-x^{2} – 1) – sinθ(-xsinθ – cosθ) + cosθ(-sinθ + xcosθ)

= -x^{3} – x + xsin^{2}θ + sinθcosθ – sinθcosθ + xcos^{2}θ

= -x^{3} – x + x(sin^{2}θ + cos^{2}θ) = -x3 – x + x

= -x3

= Independent of θ.

**NCERT Solutions for Class 12 Maths Determinants Miscellaneous ****Exercise****: Ques No 2.**

Without expanding the determinant, prove that

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**NCERT Solutions for Class 12 Maths Determinants Miscellaneous ****Exercise****: Ques No 3.**

Evaluate .

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**NCERT Solutions for Class 12 Maths Determinants Miscellaneous ****Exercise****: Ques No 4.**

If a, b and c are real numbers, and Show that either a + b + c = 0 or a = b = c.

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**NCERT Solutions for Class 12 Maths Determinants Miscellaneous ****Exercise****: Ques No 5.**

Solve the equation , a ≠ 0.

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**NCERT Solutions for Class 12 Maths Determinants Miscellaneous ****Exercise****: Ques No 6.**

Prove that .

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**NCERT Solutions for Class 12 Maths Determinants Miscellaneous ****Exercise****: Ques No 7.**

If A^{–1} = and B =, find (AB)^{-1}.

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**NCERT Solutions for Class 12 Maths Determinants Miscellaneous ****Exercise****: Ques No 8.**

Let A = , Verify that (i) [adj A]^{–1} = adj (A^{–1}) (ii) (A^{–1})^{–1} = A

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**NCERT Solutions for Class 12 Maths Determinants Miscellaneous ****Exercise****: Ques No 9.**

Evaluate.

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**NCERT Solutions for Class 12 Maths Determinants Miscellaneous ****Exercise****: Ques No 10.**

Evaluate

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Using properties of determinants in Exercises 11 to 15, prove that:

**NCERT Solutions for Class 12 Maths Determinants Miscellaneous ****Exercise****: Ques No 11.**

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**NCERT Solutions for Class 12 Maths Determinants Miscellaneous ****Exercise****: Ques No 12.**

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**NCERT Solutions for Class 12 Maths Determinants Miscellaneous ****Exercise****: Ques No 13.**

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**NCERT Solutions for Class 12 Maths Determinants Miscellaneous ****Exercise****: Ques No 14.**

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**NCERT Solutions for Class 12 Maths Determinants Miscellaneous ****Exercise****: Ques No 15.**

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**NCERT Solutions for Class 12 Maths Determinants Miscellaneous ****Exercise****: Ques No 16.**

Solve the system of equations

2/x + 3/y + 10/z = 4,

4/x – 6/y + 5/z = 1,

6/x + 9/y – 20/z = 2

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**NCERT Solutions for Class 12 Maths Determinants Miscellaneous ****Exercise****: Ques No 17.**

If a, b, c, are in A.P, then the determinant is

(A) 0

(B) 1

(C) x

(D) 2x

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**NCERT Solutions for Class 12 Maths Determinants Miscellaneous ****Exercise****: Ques No 18.**

If x, y, z are nonzero real numbers, then the inverse of matrix is

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**NCERT Solutions for Class 12 Maths Determinants Miscellaneous ****Exercise****: Ques No 19.**

Let A = , where 0 ≤ θ ≤ 2π. Then

(A) Det (A) = 0

(B) Det (A) ∈ (2, ∞)

(C) Det (A) ∈ (2, 4)

(D) Det (A) ∈ [2, 4]

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