MP Board Class 12th Maths Important Questions Chapter 4 Determinants

MP Board Class 12th Maths Important Questions Chapter 4 Determinants

MP Board Class 12th Maths Important Questions Chapter 4 Determinants

Important Questions

Very Short Answer Type Questions

Question 1.

Long Answer Type Questions

Question 1.
Prove that:

Question 2.
Prove that:

Solution:
Let ∆ =



∆ = (1 + a² + b² + c²). Proved.

Question 3.


= 2abc² [-a(a – b) + a (a + b)]
= 2²bc²[-a + b + a + b]
= 2a²bc².2b = 4a²b²c². Proved.

Question 4.
Solve the following determinant:

Question 6.
Prove that:

Solution:
Let



R.H.S. Proved.

Question 7.
Prove that:

c²?
Solution:

= a²b²c²[2 (1 + 1)]
= a²b²c².4 = 4a²b²c². Proved.

Question 8.
Solve the equation:

Question 9.

Solution:

⇒ (3a – x).1.(4x² – 0) = 0
⇒ 3a – x = 0, 4x² = 0
⇒ x = 3a, 0.

Question 10.
Prove that:

Solution:
Let ∆ =


= a² [7a + 3b – 6a – 3b]
= a²(a)
= a³. Proved.

Question 11.
Prove that:

Solution:
Let ∆


⇒ ∆ = 9y(x + y) [-x – y + x+ 2y]
⇒ ∆ = 9y² (x + y). Proved.

Question 12.
Prove that:

Solution:
Let



= (5x + 4) (x – 4) (2x – x – 4)
= (5x + 4) (x – 4) (x – 4)
= (5x + 4) (x – 4)². [∵(a – b)² = (b – a)²]
⇒ ∆ = (5x + 4) (4 – x)². Proved.

Question 13.
Prove that:

Solution:
Let ∆ =


= 2 (x + y) (x² – xy + y²)
⇒ ∆ = – 2(x² + y²). Proved.

Question 14.
Prove that:

Solution:
Let ∆ =

⇒ ∆ = (a – 1)² (a + 1 – 2)
⇒ ∆ = (a – 1)² (a – 1)
⇒ ∆ = (a – 1)³. Proved.

Question 15.
Prove that:

Solution:
Let ∆ =


= 9[x{(1 + y) (1 + 3z) – (1 + z)} – z{(x – y) – 0}]
= 9[x{1 + y + 3z + 3yz – 1 – z} – zx + zy]
= 9 [xy + 3xz + 3xyz – xz – zx + zy]
= 9 [3xyz + xy + yz + zx]. Proved.

Objective Type Questions:

Question 1.
Choose the correct answer:

Question 1.
If A is a square matrix of order 3 × 3, then value of |Adj. A| will be:
(a) |A|
(b) |A|²
(c) |A|³
(d) 3|A|
Answer:
(b) |A|²

Question 2.
If a, b, c are in Arithematic series, then value of determinant  will be:
(a) 0
(b) 1
(c) x
(d) 2x
Answer:
(a) 0

Question 3.

Question 4.
If ω is the cube roots of unitary, then
(a) 1
(b) 0
(c) ω
(d) ω²
Answer:
(b) 0

Question 5.

(a) a² + b² + c² – 3abc
(b) 0
(c) a³ + b³ + c³
(d) None of these
Answer:
(b) 0

Question 2.
Fill in the blanks:

Answer:

1. 3
2. -1
3. 27A
4. 0
5. 0

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