12th Class Mathematics Determinants Question Bank

done Assertion And Reason (MCQs) - Determinants Total Questions - 14

• question_answer1)

  Directions: (1 - 14)

  The following questions consist of two statements, one labelled as "Assertion [A] and the other labelled as Reason [R]". You are to examine these two statements carefully and decide if Assertion [A] and Reason [R] are individually true and if so, whether the Reason [R] is the correct explanation for the given Assertion [A]. Select your answer from following options.

  Assertion [A]: Minor of element 6 in the matrix is 3.

  Reason [R]: Minor of an element \[{{a}_{ij}}\] of a matrix is the determinant obtained by deleting its \[{{i}^{th}}\] row.

   
  A)
  Both A and R are individually true and R is the correct explanation of A. done clear
  B)
  Both A and R are individually true and R is not the correct explanation of A. done clear
  C)
  'A' is true but 'R' is false done clear
  D)
  'A' is false but 'R' is true done clear
  E)
  Both A and R are false. done clear
  View Solution play_arrow

• question_answer2)

  Assertion [A]: For two matrices A and B of order 3, \[\left| A \right|=3,\,\,\,\left| B \right|=-4\], then \[\left| 2AB \right|\] is \[-96\].

  Reason [R]: For a matrix A of order n and a scalar k, \[\left| kA \right|={{k}^{n}}\,\left| A \right|\].

  A)
  Both A and R are individually true and R is the correct explanation of A. done clear
  B)
  Both A and R are individually true and R is not the correct explanation of A. done clear
  C)
  'A' is true but 'R' is false done clear
  D)
  'A' is false but 'R' is true done clear
  E)
  Both A and R are false. done clear
  View Solution play_arrow

• question_answer3)

  Assertion (A): For a matrix  .

  Reason (R):   For  a  square  matrix  A,

  A)
  Both A and R are individually true and R is the correct explanation of A. done clear
  B)
  Both A and R are individually true and R is not the correct explanation of A. done clear
  C)
  'A' is true but 'R' is false done clear
  D)
  'A' is false but 'R' is true done clear
  E)
  Both A and R are false. done clear
  View Solution play_arrow

• question_answer4)

  Assertion [A]: For a square matrix of order 2 \[{{A}^{-1}}=\frac{1}{5}\,adj\,A,\]so \[\left| 2A \right|=20\].

  Reason [R]: For a square matrix of order n, \[{{A}^{-1}}=\frac{1}{\left| A \right|}\,adj\,A\] and \[\left| adj\,\,A \right|={{\left| A \right|}^{n-1}}\].

  A)
  Both A and R are individually true and R is the correct explanation of A. done clear
  B)
  Both A and R are individually true and R is not the correct explanation of A. done clear
  C)
  'A' is true but 'R' is false done clear
  D)
  'A' is false but 'R' is true done clear
  E)
  Both A and R are false. done clear
  View Solution play_arrow

• question_answer5)

  Assertion [A]: \[{{A}^{-1}}\]exists

  Reason [R]: \[R\left| A \right|=0\]

  A)
  Both A and R are individually true and R is the correct explanation of A. done clear
  B)
  Both A and R are individually true and R is not the correct explanation of A. done clear
  C)
  'A' is true but 'R' is false done clear
  D)
  'A' is false but 'R' is true done clear
  E)
  Both A and R are false. done clear
  View Solution play_arrow

• question_answer6)

  Assertion (A): Value of x for which the matrix  is singular is -5.

  Reason (R): A matrix A is singular if\[\left| A \right|\ne 0\].

  A)
  Both A and R are individually true and R is the correct explanation of A. done clear
  B)
  Both A and R are individually true and R is not the correct explanation of A. done clear
  C)
  'A' is true but 'R' is false done clear
  D)
  'A' is false but 'R' is true done clear
  E)
  Both A and R are false. done clear
  View Solution play_arrow

• question_answer7)

  Assertion [A]: adj A is a non-singular matrix.

  Reason [R]: A is non singular matrix.

  A)
  Both A and R are individually true and R is the correct explanation of A. done clear
  B)
  Both A and R are individually true and R is not the correct explanation of A. done clear
  C)
  'A' is true but 'R' is false done clear
  D)
  'A' is false but 'R' is true done clear
  E)
  Both A and R are false. done clear
  View Solution play_arrow

• question_answer8)

  Assertion [A]: For a square matrix\[A,\,{{\left( 2A \right)}^{-1}}=\frac{1}{2}{{A}^{-1}}\].

  Reason [R]: For any matrix A and scalar k, kA is a matrix obtained by multiplying each element of A by k.

  A)
  Both A and R are individually true and R is the correct explanation of A. done clear
  B)
  Both A and R are individually true and R is not the correct explanation of A. done clear
  C)
  'A' is true but 'R' is false done clear
  D)
  'A' is false but 'R' is true done clear
  E)
  Both A and R are false. done clear
  View Solution play_arrow

• question_answer9)

  Assertion : \[\left| AA' \right|=0\]

  Reason: A is skew matrix.

  A)
  Both A and R are individually true and R is the correct explanation of A. done clear
  B)
  Both A and R are individually true and R is not the correct explanation of A. done clear
  C)
  'A' is true but 'R' is false done clear
  D)
  'A' is false but 'R' is true done clear
  E)
  Both A and R are false. done clear
  View Solution play_arrow

• question_answer10)

  Assertion: \[\left| P \right|=O\]

  Reason : Determinant of skew symmetric matrix is O.

  A)
  Both A and R are individually true and R is the correct explanation of A. done clear
  B)
  Both A and R are individually true and R is not the correct explanation of A. done clear
  C)
  'A' is true but 'R' is false done clear
  D)
  'A' is false but 'R' is true done clear
  E)
  Both A and R are false. done clear
  View Solution play_arrow

• question_answer11)

  Assertion [A]: For a matrix \[A={{\left[ {{a}_{ij}} \right]}_{3}}\], if det. (adj A) = 49 then det\[\left( A \right)\text{ }=\text{ }\pm 7\].

  Reason [R]: For a square matrix A of order n, \[\left| adj\,\,A \right|={{\left| A \right|}^{n-1}}\].

   
  A)
  Both A and R are individually true and R is the correct explanation of A. done clear
  B)
  Both A and R are individually true and R is not the correct explanation of A. done clear
  C)
  'A' is true but 'R' is false done clear
  D)
  'A' is false but 'R' is true done clear
  E)
  Both A and R are false. done clear
  View Solution play_arrow

• question_answer12)

  Assertion: \[adj\,\,\left( adj\,\,A \right)={{\left( \det \,\,A \right)}^{n-2}}\,A\].

  Reason: \[\left| adj\,\,A \right|={{\left| A \right|}^{n-1}}\].

  A)
  Both A and R are individually true and R is the correct explanation of A. done clear
  B)
  Both A and R are individually true and R is not the correct explanation of A. done clear
  C)
  'A' is true but 'R' is false done clear
  D)
  'A' is false but 'R' is true done clear
  E)
  Both A and R are false. done clear
  View Solution play_arrow

• question_answer13)

  Assertion : If \[{{\left| A \right|}^{2}}=25\] then \[\left| A \right|=\pm \frac{1}{5}\]

  Reason: \[\left| AB \right|=\left| A \right|\,\,\,\left| B \right|\]

  A)
  Both A and R are individually true and R is the correct explanation of A. done clear
  B)
  Both A and R are individually true and R is not the correct explanation of A. done clear
  C)
  'A' is true but 'R' is false done clear
  D)
  'A' is false but 'R' is true done clear
  E)
  Both A and R are false. done clear
  View Solution play_arrow

• question_answer14)

  Assertion [A]: Value of k for which area of the triangle with vertices (1, 1), (0, 2), (k, 0) is 3 sq. units are 4 and 8.

  Reason [R]: Area of the triangle with vertices \[\left( {{x}_{1}},\,{{y}_{1}} \right),\,\left( {{x}_{2}},\,{{y}_{2}} \right)\left( {{x}_{3}},\,{{y}_{3}} \right)\]  is

  A)
  Both A and R are individually true and R is the correct explanation of A. done clear
  B)
  Both A and R are individually true and R is not the correct explanation of A. done clear
  C)
  'A' is true but 'R' is false done clear
  D)
  'A' is false but 'R' is true done clear
  E)
  Both A and R are false. done clear
  View Solution play_arrow