12th Math chapter 4 Bihar board with NCERT-Details & Highlights
| name of content | 12th Math chapter 4 full solution |
| content | Math objective type MCQ question with answer |
| name of subjects | class 12 Math |
| important for exam | Bihar board & other state board |
| pattern & Level | NCERT & State level question |
12th Math chapter 4 all objective solutions – download PDF
Question 1. Evaluate the determinant Δ=∣∣∣log3512log38log43log49∣∣∣
-
- (a) 152
(b) 12
(c) 143
(d) 6
- (a) 152
Answer: (a) 152
Direction (2 – 3): Evaluate the following determinants.
Question 2. ∣∣∣xx−75x+1∣∣∣
-
- (a) 3x2 + 4
(b) x(5x + 8)
(c) 3x + 4x2
(d) x(3x + 4)
- (a) 3x2 + 4
Answer: (b) x(5x + 8)
Question 3. ∣∣∣cos15∘sin75∘sin15∘cos75∘∣∣∣
-
- (a) 0
(b) 5
(c) 3
(d) 7
- (a) 0
Answer: (a) 0
Question 4. ∣∣∣∣∣2xyx2y2x2y22xyy22xyx2∣∣∣∣∣=
-
- (a) (x3 + y3)2
(b) (x2 + y2)3
(c) -(x2 + y2)3
(d) -(x3 + y3)2
- (a) (x3 + y3)2
Answer: (d) -(x3 + y3)2
Question 5. The value of ∣∣∣∣cos(α+β)sinα−cosα−sin(α+β)cosαsinαcos2βsinβcosβ∣∣∣∣ is independent of
-
- (a) α
(b) β
(c) α, β
(d) none of these
- (a) α
Answer: (a) α
Question 6. Let Δ=∣∣∣∣xx2x3yy2y3zz2z3∣∣∣∣, then the value of ∆ is
-
- (a) (x – y) (y – z) (z – x)
(b) xyz
(c) (x2 + y2 + z2)2
(d) xyz (x – y) (y – z) (z – x)
- (a) (x – y) (y – z) (z – x)
Answer: (d) xyz (x – y) (y – z) (z – x)
Question 7. The value of the determinant ∣∣∣∣αα2β+γββ2γ+αγγ2α+β∣∣∣∣=
-
- (a) (α + β)(β + γ)(γ + α)
(b) (α – β)(β – γ)(γ – α)(α + β + γ)
(c) (α + β + γ)2 (α – β – γ)2
(d) αβγ (α + β + γ)
- (a) (α + β)(β + γ)(γ + α)
Answer: (b) (α – β)(β – γ)(γ – α)(α + β + γ)
Question 8. Using properties of determinants, ∣∣∣∣∣111abca2−bcb2−cac2−ab∣∣∣∣∣=
-
- (a) 0
(b) 1
(c) 2
(d) 3
- (a) 0
Answer: (a) 0
Question 9. If a, b, c are the roots of the equation x3 – 3x2 + 3x + 7 = 0, then the value of ∣∣∣∣∣2bc−a2c2b2c22ac−b2a2b2a22ab−c2∣∣∣∣∣ is
-
- (a) 9
(b) 27
(c) 81
(d) 0
- (a) 9
Answer: (d) 0
Question 10. If ∣∣∣∣∣1+a2x(1+a2)x(1+a2)x(1+b2)x1+b2x(1+B2)x(1+c2)x(1+c2)x1+c2x∣∣∣∣∣, then f(x) is apolynomial of degree
-
- (a) 2
(b) 3
(c) 0
(d) 1
- (a) 2
Answer: (a) 2
Bihar Board 12th math chapter 4 most mcq solution
Question 11. ∣∣∣∣∣a2b22ab2aba2b2b22aba2∣∣∣∣∣ is equal to
-
- (a) a3 – b3
(b) a3 + b3
(c) (a3 – b3)2
(d) (a3 + b3)2
- (a) a3 – b3
Answer: (d) (a3 + b3)2
Question 12. If α, β, γ are in A.P., then ∣∣∣∣x−3x−2x−1x−4x−3x−2x−αx−βx−γ∣∣∣∣=
-
- (a) 0
(b) (x – 2)(x – 3)(x – 4)
(c) (x – α)(x – β)(x – γ)
(d) αβγ (α – β)(β – γ)2
- (a) 0
Answer: (a) 0
Question 13. ∣∣∣∣∣111a2+bcb2+cac2+aba3b3c3∣∣∣∣∣
-
- (a) -(a – b)(b – c)(c – a)(a2 + b2 + c2)
(b) (a – b)(b – c)(c – a)
(c) (a2 + b2 + c2)
(d) (a – b)(b – c)(c – a)(a2 + b2 + c2)
- (a) -(a – b)(b – c)(c – a)(a2 + b2 + c2)
Answer: (a) -(a – b)(b – c)(c – a)(a2 + b2 + c2)
Question 14. ∣∣∣∣∣(b+c)2(c+a)2(a+b)2a2b2c2bccaab∣∣∣∣∣=
-
- (a) (a – b)(b – c)(c – a)(a2 + b2 + c2)
(b) -(a – b)(b – c)(c – a)
(c) (a – b)(b – c)(c – a)(a + b + c)(a2 + b2 + c2)
(d) 0
- (a) (a – b)(b – c)(c – a)(a2 + b2 + c2)
Answer: (c) (a – b)(b – c)(c – a)(a + b + c)(a2 + b2 + c2)
Question 15. Find the area of the triangle with vertices P(4, 5), Q(4, -2) and R(-6, 2).
-
- (a) 21 sq. units
(b) 35 sq. units
(c) 30 sq. units
(d) 40 sq. units
- (a) 21 sq. units
Answer: (b) 35 sq. units
Question 16. If the points (a1, b1), (a2, b2) and(a1 + a2, b1 + b2) are collinear, then
-
- (a) a1b2 = a2b1
(b) a1 + a2 = b1 + b2
(c) a2b2 = a1b1
(d) a1 + b1 = a2 + b2
- (a) a1b2 = a2b1
Answer: (a) a1b2 = a2b1
Question 17. If the points (2, -3), (k, -1) and (0, 4) are collinear, then find the value of 4k.
-
- (a) 4
(b) 7/140
(c) 47
(d) 40/7
- (a) 4
Answer: (d) 40/7
Question 18. Find the area of the triangle whose vertices are (-2, 6), (3, -6) and (1, 5).
-
- (a) 30 sq. units
(b) 35 sq. units
(c) 40 sq. units
(d) 15.5 sq. units
- (a) 30 sq. units
Answer: (d) 15.5 sq. units
Question 19. If the points (3, -2), (x, 2), (8, 8) are collinear, then find the value of x.
-
- (a) 2
(b) 3
(c) 4
(d) 5
- (a) 2
Answer: (d) 5
Question 20. Using determinants, find the equation of the line joining the points (1, 2) and (3, 6).
-
- (a) y = 2x
(b) x = 3y
(c) y = x
(d) 4x – y = 5
- (a) y = 2x
Answer: (a) y = 2x
Question 21. Find the minor of the element of second row and third column in the following determinant ⎡⎣⎢261−30554−7⎤⎦⎥
-
- (a) 13
(b) 4
(c) 5
(d) 0
- (a) 13
Answer: (a) 13
BSEB 12th math chapter 4 objective solution
Question 22. If Δ=∣∣∣∣521302813∣∣∣∣, then write the minor of the element a23.
-
- (a) 7
(b) -7
(c) 4
(d) 8
- (a) 7
Answer: (a) 7
Question 23. A=⎡⎣⎢111bccaababc⎤⎦⎥
-
- (a) a(c2 – b2), b(a2 – c2), c(b2 – a2)
(b) a(c2 – b2), b(c2 – a2), c(b2 – a2)
(c) bc, ab, 2b
(d) None of these
- (a) a(c2 – b2), b(a2 – c2), c(b2 – a2)
Answer: (a) a(c2 – b2), b(a2 – c2), c(b2 – a2)
Question 24. A=⎡⎣⎢017253601⎤⎦⎥
-
- (a) 5, 16, 30
(b) 5, -16, -30
(c) 5, 16, -30
(d) -5, -16, -30
- (a) 5, 16, 30
Answer: (c) 5, 16, -30
Question 25. A=⎡⎣⎢2−31501−11−1⎤⎦⎥
-
- (a) -1, 4, 5
(b) -4, 5, -1
(c) 4, 5, 1
(d) -4, -5, 1
- (a) -1, 4, 5
Answer: (a) -1, 4, 5
Question 26. Find cofactors of a21 and a31 of the matrix A = [aij] = ⎡⎣⎢1433−55−262⎤⎦⎥
-
- (a) -16, 8
(b) -16, -8
(c) 16, 8
(d) 16, -8
- (a) -16, 8
Answer: (a) -16, 8
Question 27. Find the minor of 6 and cofactor of 4 respectively in the determinant Δ=∣∣∣∣147258369∣∣∣∣
-
- (a) 6, 6
(b) 6, -6
(c) -6, -6
(d) -6, 6
- (a) 6, 6
Answer: (d) -6, 6
Question 28. Find the cofactors of the element of third row and second column of the following determinant ∣∣∣∣111xyzy+zz+xx+y∣∣∣∣
-
- (a) x – y
(b) y – x
(c) x – z
(d) z – x
- (a) x – y
Answer: (b) y – x
Question 29. Find x, if ⎡⎣⎢112211x1−1⎤⎦⎥ is singular
-
- (a) 1
(b) 2
(c) 3
(d) 4
- (a) 1
Answer: (d) 4
Question 30. Find the value of x for which the matrix A=⎡⎣⎢3−x2−224−x−421−1−x⎤⎦⎥ is singular.
-
- (a) 0, 1
(b) 1, 3
(c) 0, 3
(d) 3, 2
- (a) 0, 1
Answer: (c) 0, 3
Question 31. For what value of x, matrix [6−x3−x41] is a singularmatrix?
-
- (a) 1
(b) 2
(c) -1
(d) -2
- (a) 1
Answer: (b) 2
Question 32. If for the non-singular matrix A, A2 = I, then find A-1.
-
- (a) A
(b) I
(c) O
(d) None of thes - e
- (a) A
Answer: (a) A
Important most mcq notes 12th math chapter 4
Question 33. If the equation a(y + z) = x, b(z + x) = y, c(x + y) = z have non-trivial solutions then the value of 11+a+11+b+11+c is
-
- (a) 1
(b) 2
(c) -1
(d) -2
- (a) 1
Answer: (b) 2
Question 34. A non-trivial solution of the system of equations x + λy + 2z = 0, 2x + λz = 0, 2λx – 2y + 3z = 0 is given by x : y : z =
-
- (a) 1 : 2 : -2
(b) 1: -2 : 2
(c) 2 : 1 : 2
(d) 2 : 1 : -2
- (a) 1 : 2 : -2
Answer: (d) 2 : 1 : -2
Question 35. If 4x + 3y + 6z = 25, x + 5y + 7z = 13, 2x + 9y + z = 1, then z = ________
-
- (a) 1
(b) 3
(c) -2
(d) 2
- (a) 1
Answer: (d) 2
Question 36. If the equations 2x + 3y + z = 0, 3x + y – 2z = 0 and ax + 2y – bz = 0 has non-trivial solution, then
-
- (a) a – b = 2
(b) a + b + 1 = 0
(c) a + b = 3
(d) a – b – 8 = 0
- (a) a – b = 2
Answer: (a) a – b = 2
Question 37. Solve the following system of equations x – y + z = 4, x – 2y + 2z = 9 and 2x + y + 3z =1.
-
- (a) x = -4, y = -3, z = 2
(b) x = -1, y = -3, z = 2
(c) x = 2, y = 4, z = 6
(d) x = 3, y = 6, z = 9
- (a) x = -4, y = -3, z = 2
Answer: (b) x = -1, y = -3, z = 2
Question 38. If the system of equations x + ky – z = 0, 3x – ky – z = 0 & x – 3y + z = 0 has non-zero solution, then k is equal to
-
- (a) -1
(b) 0
(c) 1
(d) 2
- (a) -1
Answer: (c) 1
Question 39. If the system of equations 2x + 3y + 5 = 0, x + ky + 5 = 0, kx – 12y – 14 = 0 has non-trivial solution, then the value of k is
-
- (a) -2, 125
(b) -1, 15
(c) -6, 175
(d) 6, −125
- (a) -2, 125
Answer: (c) -6, 175
Question 40. If ∣∣∣2x85x∣∣∣=∣∣∣67−23∣∣∣, then the value of x is
-
- (a) 3
(b) ±3
(c) ±6
(d) 6
- (a) 3
Answer: (c) ±6
Question 41. 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
- (a) 9
Answer: (b) 3
Question 42. The number of distinct real roots of ∣∣∣∣sinxcosxcosxcosxsinxcosxcosxcosxsinx∣∣∣∣=0 in the interval −π4≤x≤π4 is
-
- (a) 0
(b) 2
(c) 1
(d) 3
- (a) 0
Answer: (c) 1
Question 43.
-
- (a) 0
(b) -1
(c) 2
(d) 3
- (a) 0
Answer: (a) 0
Question 44. The value of the determinant ∣∣∣∣xx+2yx+yx+yxx+2yx+2yx+yx∣∣∣∣ is
-
- (a) 9x2 (x + y)
(b) 9y2 (x + y)
(c) 3y2 (x + y)
(d) 7x2 (x + y)
- (a) 9x2 (x + y)
Answer: (b) 9y2 (x + y)
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| SL.N. | Subject name with solutions |
| 01 | Physics |
| 02 | Chemistry |
| 03 | Biology |
| 04 | Math |
| 05 | Hindi |
| 06 | English |