Q20Written answer
Given find BA and use this to solve the system of
equations y + 2z = 7, x – y = 3, 2x + 3y + 4z = 17.
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NCERT Exemplar · Class 12 · Maths
Chapter 4: Determinants
Practice each question, then open the answer or worked solution.
Questions
20 questionsQ21Written answer
If a + b + c ¹ 0 and then prove that a = b = c.
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Q22Written answer
Prove that is divisible by a + b + c and find the quotient.
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Q23Written answer
If x + y + z = 0, prove that
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Objective Type Questions (M.C.Q.)
Choose the correct answer from given four options in each of the Exercises from 24 to 37.
Q24Written answer
If then, value of x is
(A) 3 (B) ± 3 (C) ± 6 (D) 6
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Option (C) ± 6
From the given,
On equating the determinants, we have
2x2 – 40 = 18 + 14
2x2 = 72
x2 = 36
Thus, x = ± 6
Q25Written answer
The value of determinant
(A) a3 + b3 + c3 (B) 3 bc (C) a3 + b3 + c3 – 3abc (D) none of these
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Option (C) a3 + b3 + c3 – 3abc
Given,
Q26Written answer
The area of a triangle with vertices (–3, 0), (3, 0) and (0, k) is 9 sq. units. The value of k will be
(A) 9 (B) 3 (C) – 9 (D) 6
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Option (B) 3
We know that, the area of a triangle with vertices (x1, y1), (x2, y2) and (x3, y3) is given by
Q27Written answer
The determinant equals
(A) abc (b–c) (c – a) (a – b) (B) (b–c) (c – a) (a – b)
(C) (a + b + c) (b – c) (c – a) (a – b) (D) None of these
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Option (D)
Q28Written answer
The number of distinct real roots of = 0 in the interval -π/4 ≤ x ≤ π/4 is
(A) 0 (B) 2 (C) 1 (D) 3
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Option (C) 1
Q29Written answer
If A, B and C are angles of a triangle, then the determinant is equal to
(A) 0 (B) -1 (C) 1 (D) None of these
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Option (A) 0
