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RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise

May 25, 2019 by Fazal Leave a Comment

You can Download RBSE Solutions for Class 12 Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Rajasthan Board RBSE Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise

Question 1.
Value of determinant
RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise is:
(a) 0
(b) 1
(c) -1
(d) none of these
Solution:
RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise
= cos 80° sin 10° – (- cos 109) sin 80°
= cos 80° sin 10° + cos 10° sin 80°
= sin (10° + 80°)
= sin 90° = 1
So, option (b) is correct.

Question 2.
Co-factors of first column of determinant
RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise
(a) -1, 3
(b) -1,- 3
(c)- 1, 20
(d) – 1,- 20
Solution:
RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise
Co-factor of a11
F11 = (- 1)2 M11
= 1 x (- 1) = – 1
Co-factor of a12
F21 = (-1)11 M21
= (- 1) × 20 = – 20
So, option (d) is correct.

Question 3.
If RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise , then the value of RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercisewill be :
(a) – 2∆
(b) 8∆
(c) -8∆
(d) -6∆
Solution:
RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise
So, option (c) is correct.

Question 4.
Which of the following determinant is identical to determinant
RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise :
RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise
Solution:
RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise
RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise
So, option (c) is correct.

Question 5.
Value of
RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise
(a) 0
(b) 1
(c) 1/2
(d) – 1/2
Solution:
RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise
= cos 50° cos 10° – sin 50° sin 10°
= cos (50° + 10°)
= cos 60° = \(\frac { 1 }{ 2 }\)
So, option (c) is correct.

Question 6.
Value of
RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise
(a) ab + bc + ca
(b) 0
(c) 1
(d) abc
Solution:
RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise

Question 7.
If ω is a cube root of unity, then value of
RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise
(a) ω2
(b) ω
(c) 1
(d) o
11 04 081
Solution:
RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise

Question 8.
If RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise , then x will be:
(a) 6
(b) 7
(c) 8
(d) 0
Solution:
RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise
⇒ (4 – 2)2 = (3x – 2) – (x + 6)
⇒ (2)2 = 3x – 2 – x – 6
⇒ 4 = 2x – 8
⇒ 4 + 8 = 2x
x = 6
So, option (a) is correct.

Question 9.
If RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise and F11, F12, F13, …, are the corresponding cofactors of a11, a12, a13, …, then which of the following is true :
(a) a12F12+ a22F22 + a32F32 = 0
(b) a12F12 + a22F22 + a32F32 ≠ ∆
(c) a12F12 + a22F22 + a32F32 = ∆
(d) a12F12 + a22F22 + a32F32 = – ∆.
Solution:
a12F12 + a22F22 + a32F32 = ∆
So, option (c) is correct.

Question 10.
Value of determinant
RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise
(a) x + y + z
(b) 2(x + y + z)
(c) 1
(d) 0
Solution:
RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise
So, option (d) is correct.

Question 11.
Solve the following equation :
RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise
Solution:
RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise
⇒ 1(9x – 48) – 2(36 – 42) + 3(32 – 7x) = 0
⇒ 9x – 48 + 12 + 96 – 21x =0
⇒ – 12x + 60 = 0
⇒ – 12x = -60
⇒ x = \(\frac { 60 }{ 12 }\) = -5
So, x = 5.

Question 12.
Find the value of determinant :
RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise
Solution:
RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise= 1(27 – 1) – 3(9 – 9) + 9(3 – 81)
= 26 – 0 – 702
= -676.

Question 13.
Find the value of determinant
RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise
Solution:
RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise

Question 14.
Prove that
RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise
Solution:
RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise
= a2b2c2 [- 1(1 – 1) – 1(-1 – 1) + 1(1 + 1)]
= a2b2c2 (0 + 2 + 2)
= 4a2b2c2 = R.H.S. Hence Proved.

Question 15.
Prove that x = 2 is a root of following equation. Also find its remaining roots :
RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise
Solution:
RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise
∵ R1 = R2
∴ Determinant will be zero.
∴ Root of equation is 2.
RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise

Question 16.
Prove that:
RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise
Solution:
RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise

Question 17.
Prove that
RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise .
Solution:
RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise
RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise
= (a + b + c)[(- b – c – a) (- c – a – b) – 0]
= (a + b + c)(b + c + a)(c + a + b)
= (a + b + c)3 = R.H.S.
Proved.

Question 18.
Prove that :
RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise
Solution:
RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise

Question 19.
Prove that:
RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise
Solution:
RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise
RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise
= (a – b) (b – c) [(b2 + c2 + bc) – (a2 + b2 + ab)]
= (a – b) (b – c) (b2 + c2 + bc – a2 – b2 – ab)
= (a – b)(b – c) [bc + c2 – a2 – ab]
= (a – b)(b – c) [bc – ab + c2 – a2 ]
= (a – b) (b – c) [b(c – a) + (c2 – a)]
= (a – b)(b – c)(c – a)(b + c + a)
= R.H.S. Proved.

Question 20.
Prove that:
RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise
Solution:
RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise
RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise

Question 21.
If a + b + c = 0, then solve:
RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise
Solution:
RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise
⇒ (-x) [(c – a) (a – c + x) – (b – c + x) (b – x – a)] = 0
⇒ (-x) [(ac – c2 + cx – a2 + ac – ax)
⇒ (b2 – bx – ab – bc + cx + ac – xb – x2 – ax)] = 0
= (-x) [x2 – (a2 + b2 – ab – bc – bc – ca)]= 0
If – x = 0, then x = 0
Now, if x2 = (a2 + b2 + c2 + bc – ab – ca) = 0 .
RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise
RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise

Question 22.
Prove that
RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise
Solution:
RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise

Question 23.
If p + q + r = 0, then prove that
RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise
Solution:
RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise

Question 24.
Prove that
RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise
Solution:
RBSE Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise

RBSE Solutions for Class 12 Maths

 

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