{"id":19229,"date":"2022-06-03T13:30:18","date_gmt":"2022-06-03T08:00:18","guid":{"rendered":"https:\/\/mcq-questions.com\/?p=19229"},"modified":"2022-05-21T12:27:09","modified_gmt":"2022-05-21T06:57:09","slug":"mcq-questions-for-class-12-maths-chapter-4","status":"publish","type":"post","link":"https:\/\/mcq-questions.com\/mcq-questions-for-class-12-maths-chapter-4\/","title":{"rendered":"MCQ Questions for Class 12 Maths Chapter 4 Determinants with Answers"},"content":{"rendered":"

Students can access the NCERT MCQ Questions for Class 12 Maths Chapter 4 Determinants with Answers Pdf free download aids in your exam preparation and you can get a good hold of the chapter. Use MCQ Questions for Class 12 Maths with Answers<\/a> during preparation and score maximum marks in the exam. Students can download the Determinants Class 12 MCQs Questions with Answers from here and test their problem-solving skills. Clear all the fundamentals and prepare thoroughly for the exam taking help from Class 12 Maths Chapter 4 Determinants Objective Questions.<\/p>\n

Determinants Class 12 MCQs Questions with Answers<\/h2>\n

Students are advised to solve the Determinants Multiple Choice Questions of Class 12 Maths to know different concepts. Practicing the MCQ Questions on Determinants Class 12 with answers will boost your confidence thereby helping you score well in the exam.<\/p>\n

Explore numerous MCQ Questions of Determinants Class 12 with answers provided with detailed solutions by looking below.<\/p>\n

Question 1.
\nIf \\(\\left|\\begin{array}{rr}
\nx & 2 \\\\
\n18 & x
\n\\end{array}\\right|\\) = \\(\\left|\\begin{array}{rr}
\n6 & 2 \\\\
\n18 & 6
\n\\end{array}\\right|\\), then x is equal to
\n(a) 6
\n(b) \u00b16
\n(c) -6
\n(d) 6, 6<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) 6<\/p>\n<\/details>\n

\n

Question 2.
\nLet A be a square matrix of order 3 \u00d7 3. Then |kA| is equal to
\n(a) k|A|
\n(b) k\u00b2|A|
\n(c) k\u00b3|A|
\n(d) 3k|A|<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (c) k\u00b3|A|<\/p>\n<\/details>\n

\n

Question 3.
\nWhich of the following is correct?
\n(a) Determinant is a square matrix
\n(b) Determinant is a number associated to a matrix
\n(c) Determinant is a number associated to a square matrix
\n(d) None of these.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (c) Determinant is a number associated to a square matrix<\/p>\n<\/details>\n

\n

Question 4.
\nIf area of triangle is 35 sq. units with vertices (2, -6), (5, 4) and (k, 4). Then k is
\n(a) 12
\n(b) -2
\n(c) -12, -2
\n(d) 12, -2.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (d) 12, -2.<\/p>\n<\/details>\n

\n

Question 5.
\nIf A = \\(\\left[\\begin{array}{lll}
\na_{11} & a_{12} & a_{13} \\\\
\na_{21} & a_{22} & a_{23} \\\\
\na_{31} & a_{32} & a_{33}
\n\\end{array}\\right]\\) and Aij<\/sub> is co-factors of aij<\/sub>, then A is given by
\n(a) a11<\/sub>A31<\/sub> +a12<\/sub>A32<\/sub> + a13<\/sub>A33<\/sub>
\n(b) a11<\/sub>A11<\/sub> + a12<\/sub>A21<\/sub> + a13<\/sub>A33<\/sub>
\n(c) a21<\/sub>A11<\/sub> + a22<\/sub>A12<\/sub> + a23<\/sub>A13<\/sub>
\n(d) a11<\/sub>A11<\/sub> + a21<\/sub>A21<\/sub> + a31<\/sub>A31<\/sub><\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (d) a11<\/sub>A11<\/sub> + a21<\/sub>A21<\/sub> + a31<\/sub>A31<\/sub><\/p>\n<\/details>\n

\n

Question 6.
\nLet A be a non-singular matrix of order 3 \u00d7 3. Then |adj. A| is equal to
\n(a) |A|
\n(b) |A|\u00b2
\n(c) |A|\u00b3
\n(d) 3|A|<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) |A|\u00b2<\/p>\n<\/details>\n

\n

Question 7.
\nIf A is any square matrix of order 3 x 3 such that |a| = 3, then the value of |adj. A| is?
\n(a) 3
\n(b) \\(\\frac { 1 }{3}\\)
\n(c) 9
\n(d) 27<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (c) 9<\/p>\n<\/details>\n

\n

Question 8.
\nIf A is an invertible matrix of order 2, then det (A-1<\/sup>) is equal to
\n(a) det (A)
\n(b) \\(\\frac { 1 }{det(A)}\\)
\n(c) 1
\n(d) 0<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) \\(\\frac { 1 }{det(A)}\\)<\/p>\n<\/details>\n

\n

Question 9.
\nIf a, b, c are in A.P., then determinant
\n\"MCQ
\n(a) 0
\n(b) 1
\n(c) x
\n(d) 2x<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) 0<\/p>\n<\/details>\n

\n

Question 10.
\nIf x, y, z are non-zero real numbers, then the inverse of matrix A = \\(\\left[\\begin{array}{lll}
\nx & 0 & 0 \\\\
\n0 & y & 0 \\\\
\n0 & 0 & z
\n\\end{array}\\right]\\) is
\n\"MCQ<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer:
\n\"MCQ<\/p>\n<\/details>\n

\n

Question 11.
\nLet A = \"MCQ
\nwhere 0 \u2264 \u03b8 \u2264 2\u03c0 then
\n(a) Det (A) = 0
\n(b) Det (A) \u2208 (2, \u221e)
\n(c) Det (A) \u2208 (2, 4)
\n(d) Det (A) \u2208 [2, 4]<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (d) Det (A) \u2208 [2, 4]<\/p>\n<\/details>\n

\n

Question 12.
\nIf \\(\\left|\\begin{array}{rr}
\n2x & 5 \\\\
\n8 & x
\n\\end{array}\\right|\\) = \\(\\left|\\begin{array}{rr}
\n6 & -2 \\\\
\n7 & 3
\n\\end{array}\\right|\\), then value of ‘x’ is
\n(a) 3
\n(b) \u00b13
\n(c) \u00b16
\n(d) 6<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (c) \u00b16<\/p>\n<\/details>\n

\n

Question 13.
\nLet \u0394 = \\(\\left|\\begin{array}{lll}
\n\\mathbf{A} x & x^{2} & 1 \\\\
\nB y & y^{2} & 1 \\\\
\nC z & z^{2} & 1
\n\\end{array}\\right|\\) and \u03941<\/sub> = \\(\\left|\\begin{array}{rrr}
\n\\mathbf{A} & \\mathbf{B} & \\mathbf{C} \\\\
\n\\boldsymbol{x} & \\boldsymbol{y} & z \\\\
\nz \\boldsymbol{y} & z x & x y
\n\\end{array}\\right|\\), then
\n(a) \u03941<\/sub> = -\u0394
\n(b) \u0394 \u2260 \u03941<\/sub>
\n(c) \u0394 – \u03941<\/sub> = 0
\n(d) None of these<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (c) \u0394 – \u03941<\/sub> = 0<\/p>\n<\/details>\n

\n

Question 14.
\nIf x, y \u2208R, then the determinant:
\n\"MCQ
\nlies in the interval
\n(a) [-\u221a2, \u221a2]
\n(b) [-1, 1]
\n(c) [\u221a2, 1]
\n(d) [-1, \u221a2]<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) [-\u221a2, \u221a2]<\/p>\n<\/details>\n

\n

Question 15.
\nThe area of a triangle with vertices (-3, 0), (3, 0) and (0, k) is 9 sq. units. The value of \u2018k\u2019 will be:
\n(a) 9
\n(b) 3
\n(c) -9
\n(d) 6.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) 3<\/p>\n<\/details>\n

\n

Question 16.
\nIf A, B and C are angles of a triangle, then the determinant:
\n\\(\\left|\\begin{array}{ccc}
\n-1 & \\cos C & \\cos B \\\\
\n\\cos C & -1 & \\cos A \\\\
\n\\cos B & \\cos A & -1
\n\\end{array}\\right|\\) is equal to
\n(a) 0
\n(b) -1
\n(c) 1
\n(d) None of these.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) 0<\/p>\n<\/details>\n

\n

Question 17.
\nLet A be a square matrix all of whose entries are integers. Then which of the following is true?
\n(a) If det A = \u00b1 1, then A-1<\/sup> need not exist
\n(b) If det A = \u00b1 1, then A-1<\/sup> exists but all entries are not necessarily integers.
\n(c) If det A \u2260 \u00b1 1, then A-1<\/sup> exists and all its entries are non-integers
\n(d) If det A = \u00b1 1, then A-1<\/sup> exists and all its entries are integers.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (d) If det A = \u00b1 1, then A-1<\/sup> exists and all its entries are integers.
\nHint:
\nSince each entry of A is an integer,
\n\u2234 co-factor of each entry is also an integer.
\nHence, each entry of the adjoint is an integer.
\nAlso det A = \u00b1 1 and A-1<\/sup> = \\(\\frac { 1 }{det(A)}\\) (adj A).
\nHence, all entries of A-1<\/sup> are integers.<\/p>\n<\/details>\n

\n

Question 18.
\nThe number of values of ‘k\u2019 for which the linear equations:
\n4x + ky + 2z = 0
\nkx + 4y + z = 0
\n2x + 2y + z = 0
\npossesses a non-zero solution is
\n(a) 3
\n(b) 2
\n(c) 1
\n(d) zero.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) 2
\nHint:
\nThe system possesses non-zero solution
\nIf \\(\\left|\\begin{array}{lll}
\n4 & k & 2 \\\\
\nk & 4 & 1 \\\\
\n2 & 2 & 1
\n\\end{array}\\right|\\) = 0
\nIf 4(4 – 2) + k (k – 2) + 2(2k – 8) = 0
\nif = 8 – k\u00b2 + 2k + 4k – 16 = 0
\nif k\u00b2 – 6k + 8 = 0
\nif (k – 2)(k – 4) = 0
\nif k = 2 or 4
\nk = 2.<\/p>\n<\/details>\n

\n

Question 19.
\nIf A = \\(\\left[\\begin{array}{lll}
\n1 & \\alpha & 3 \\\\
\n1 & 3 & 3 \\\\
\n2 & 4 & 4
\n\\end{array}\\right]\\) is the adjoint of a 3 \u00d7 3 matrix A and |A| = 4 then \u03b1 is equal to
\n(a) 11
\n(b) 5
\n(c) 0
\n(d) 4<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) 11
\nHint:
\nHere |adj A| = |A|3-1<\/sup>
\n= |A|\u00b2 = 4\u00b2
\n= 16
\n\u21d2 1. (12 – 12) -\u03b1 (4 – 6)+ 3(4 – 6) = 16
\n\u21d2 2\u03b1 – 6 = 16
\n\u21d2 2\u03b1 = 22.
\nHence, \u03b1 = 11.<\/p>\n<\/details>\n

\n

Question 20.
\nIf \u03b1, \u00df \u2260 0 and f(x) = \u03b1” + \u00df” and
\n\"MCQ
\n= k (1 – \u03b1)\u00b2(1 – \u00df)\u00b2(\u03b1 – \u00df)\u00b2, then ‘4k\u2019 is equal to:
\n(a) \\(\\frac { 1 }{\u03b1\u00df}\\)
\n(b) 1
\n(c) -1
\n(d) \u03b1\u00df<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) 1
\nHint:
\n\"MCQ
\n= [(\u03b1 – 1) (\u00df\u00b2 – 1) – (\u03b1\u00b2 – 1) (\u00df – 1)]\u00b2
\n= (\u03b1 – 1)\u00b2(\u00df – 1)\u00b2(\u03b1 – \u00df)2.
\nHence, k = 1<\/p>\n<\/details>\n

\n

Question 21.
\nThe system of linear equations:
\nx + \u03bby – z = 0
\n\u03bbr – y – z = 0
\nx + y – \u03bbz = 0
\nhas a non-trivial solution for
\n(a) Exactly one value of \u03bb
\n(b) Exactly two values of \u03bb
\n(c) Exactly three values of \u03bb
\n(d) Infinitely many values of \u03bb.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (c) Exactly three values of \u03bb
\nHint:
\nThe system AX = O has non-trivial solution if det A = 0
\ni.,e if \\(\\left|\\begin{array}{rrr}
\n1 & \\lambda & -1 \\\\
\n\\lambda & -1 & -1 \\\\
\n1 & 1 & -\\lambda
\n\\end{array}\\right|\\) = 0
\n\u21d2 (1)(\u03bb + 1) -\u03bb(-\u03bb\u00b2 + 1) + (-1)(\u03bb + 1) = 0
\n\u21d2 \u03bb + 1 + \u03bb\u00b3 – \u03bb – \u03bb – 1 = 0
\n\u21d2 \u03bb\u00b3 – \u03bb = 0
\n\u21d2 \u03bb(\u03bb\u00b2 – 1) = 0
\n\u21d2 \u03bb = 0, 1, -1.
\nHence, \u03bb = -1, 0, 1.<\/p>\n<\/details>\n

\n

Question 22.
\nLet on be a complex number such that 2\u03c9 + 1 = z, where z = \u221a-3
\nIf \\(\\left|\\begin{array}{ccc}
\n1 & 1 & 1 \\\\
\n1 & -\\omega^{2}-1 & \\omega^{2} \\\\
\n1 & \\omega^{2} & \\omega
\n\\end{array}\\right|\\) = 3k the k is equal to
\n(a) -1
\n(b) 1
\n(c) z
\n(d) -z<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (c) z
\nHint:
\n\"MCQ
\n[Operating R1<\/sub> \u2192 R1<\/sub> + R2<\/sub> + R3<\/sub>]
\n= 3[- \u03c9 (\u03c9\u00b2 + 1) – \u03c94<\/sup>]
\n= 3[- \u03c9\u00b3 – \u03c9 – \u03c9] = 3[- 1 – 2\u03c9]
\n= – 3(1 + 2\u03c9) = – 3z.
\nThus 3k = – 3z.
\nHence, k = -z.<\/p>\n<\/details>\n

\n

Question 23.
\nIf Sis the set of distinct values of \u2018h\u2019 for which the following system of linear equations:
\nx + y + z = 1,
\nx + ay + z = 1,
\nax + by + z = 1
\nhas no solution, then S is
\n(a) a finite set containing two or more elements
\n(b) a singleton
\n(c) an empty set
\n(d) an infinite set.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) a singleton
\nHint:
\nD = \\(\\left|\\begin{array}{lll}
\n1 & 1 & 1 \\\\
\n1 & a & 1 \\\\
\na & b & 1
\n\\end{array}\\right|\\) = 0
\n\u21d2 a – 1
\n\u21d2 x + y + z = 1
\nand x + by + z = 0.
\nThe planes are parallel
\n\u21d2 b = 1.
\nHence, S is a singleton.<\/p>\n<\/details>\n

\n

Question 24.
\nIf A = \\(\\left[\\begin{array}{rr}
\n2 & -3 \\\\
\n-4 & 1
\n\\end{array}\\right]\\), then adj. (3A\u00b2 + 12A) is equal to
\n\"MCQ<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer:
\n\"MCQ
\nHint:
\n\"MCQ<\/p>\n<\/details>\n

\n

Question 25.
\nIf the system of linear equations:
\nx + ky + 3z = 0
\n3x + ky – 2z = 0
\n2x + 4y – 3z = 0
\nhas a non zero solution (x, y, z), then \\(\\frac {xz}{y^2}\\) is equal to:
\n(a) -10
\n(b) 10
\n(c) -30
\n(d) 30<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) 10
\nHint:
\nThe given system has non-zero solution
\n\u21d2 \\(\\left|\\begin{array}{ccc}
\n1 & k & 3 \\\\
\n3 & k & -2 \\\\
\n2 & 4 & -3
\n\\end{array}\\right|\\)
\n\u21d2 1(-3k + 8)-k (-9 + 4) + 3 (12 – 2k) = 0
\n\u21d2 44 – 4k = 0
\n\u21d2 k = 11
\nLet z = \u03bb
\nThus x + 11 y = -3\u03bb
\nand 3x + 11 y = 2\u03bb
\n\"MCQ<\/p>\n<\/details>\n

\n

Fill in the blanks<\/span><\/p>\n

Question 1.
\nIf \\(\\left|\\begin{array}{ll}
\nx & 2 \\\\
\n8 & x
\n\\end{array}\\right|\\) = \\(\\left|\\begin{array}{ll}
\n3 & 2 \\\\
\n9 & 6
\n\\end{array}\\right|\\), then the value of x is ……………..<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: \u00b14
\nHint:
\n\\(\\left|\\begin{array}{ll}
\nx & 2 \\\\
\n8 & x
\n\\end{array}\\right|\\) = \\(\\left|\\begin{array}{ll}
\n3 & 2 \\\\
\n9 & 6
\n\\end{array}\\right|\\)
\n\u21d2 x\u00b2 – 16 = 18 – 18
\n\u21d2 x\u00b2 = 16
\n\u21d2 x = \u00b14.<\/p>\n<\/details>\n

\n

Question 2.
\nLet A be a 3 x 3 determinant and |A| = 7. Then the value of |2A| is ……………….<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: 56
\nHint:
\n|2A| = 2\u00b3 |A| = 8 x 7 = 56.<\/p>\n<\/details>\n

\n

Question 3.
\nIf A = \\(\\left[\\begin{array}{ll}
\n1 & 2 \\\\
\n4 & 2
\n\\end{array}\\right]\\) Then the value of k = ……………
\nif |2A| = k|A|<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: 4
\nHint:
\nif |2A| = 2\u00b2|A| = 4|A|
\nk = 4<\/p>\n<\/details>\n

\n

Question 4.
\nIf A is a skew-symmetric matrix of order 3, then det A = ……………..<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: 0.<\/p>\n<\/details>\n

\n

Question 5.
\nThe value of \\(\\left[\\begin{array}{ccc}
\n102 & 18 & 36 \\\\
\n1 & 3 & 4 \\\\
\n17 & 3 & 6
\n\\end{array}\\right]\\) is ……………..<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: 0
\nHint:
\n\u0394 = 6\\(\\left|\\begin{array}{ccc}
\n17 & 3 & 6 \\\\
\n1 & 3 & 4 \\\\
\n17 & 3 & 6
\n\\end{array}\\right|\\) = 6(0) = 0<\/p>\n<\/details>\n

\n

Question 6.
\nIf \u0394 = \\(\\left|\\begin{array}{ll}
\n1 & a \\\\
\n1 & b
\n\\end{array}\\right|\\), then minor of \u2018b\u2019 is ………………<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: 1<\/p>\n<\/details>\n

\n

Question 7.
\nMinor of \u2018d\u2019 is = \\(\\left|\\begin{array}{ll}
\na & c \\\\
\nb & d
\n\\end{array}\\right|\\), is ………………<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: a<\/p>\n<\/details>\n

\n

Question 8.
\nA square matrix A has inverse if and only if A is ………………<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: Invertible.<\/p>\n<\/details>\n

\n

Question 9.
\nCo-factor of \u2018b\u2019 in \\(\\left|\\begin{array}{ll}
\na & c \\\\
\nb & d
\n\\end{array}\\right|\\) is ……………<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: -c<\/p>\n<\/details>\n

\n

Question 10.
\nIf \u0394 = \\(\\left|\\begin{array}{lll}
\n1 & 2 & 3 \\\\
\n2 & 0 & 1 \\\\
\n5 & 3 & 8
\n\\end{array}\\right|\\) then minor of a22<\/sub> is …………….<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: -7<\/p>\n<\/details>\n

\n

We believe the knowledge shared regarding NCERT MCQ Questions for Class 12 Maths Chapter 4 Determinants with Answers Pdf free download has been useful to the possible extent. If you have any other queries regarding CBSE Class 12 Maths Determinants MCQs Multiple Choice Questions with Answers, feel free to reach us via the comment section and we will guide you with the possible solution.<\/p>\n","protected":false},"excerpt":{"rendered":"

Students can access the NCERT MCQ Questions for Class 12 Maths Chapter 4 Determinants with Answers Pdf free download aids in your exam preparation and you can get a good hold of the chapter. Use MCQ Questions for Class 12 Maths with Answers during preparation and score maximum marks in the exam. Students can download …<\/p>\n

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