IIT JEE & NEET Question Bank with Solution: HSC Matrices Solved textual MCQs : Maharashtra Board

2. Matrices

This MCQs are based on the Mathematics Part I Textbook of Maharashtra (click here for reference).
For more questions with explanation of Matrices (click matrices).

Q.1. The inverse of an invertible symmetric matrix is

(A) symmetric

(B) non-symmetric

(D) diagonal matrix

Q.2. Let a, b, c $element of$ R be all non-zero and satisfy $a cubed space plus space b cubed space plus space c cubed space equals space 2.$ If the matrix A = $open square brackets table row a b c row b c a row c a b end table close square brackets$ satisfies $A to the power of T space A space equals space I comma$ then a value of abc can be:

(A) $negative 1 third$

(B) $1 third$

(D) 3

Q.3. If the elements of matrix A are the reciprocals of elements of matrix $open square brackets table row 1 omega cell omega squared end cell row omega cell omega squared end cell 1 row cell omega squared end cell 1 cell omega squared end cell end table close square brackets$ , where $omega$ is complex cube root of unity, then

(A) $A to the power of negative 1 end exponent$ does not exist

(B) $A to the power of negative 1 space end exponent space equals space I$

(D) $A to the power of negative 1 end exponent space equals space A$

Q.4. For a $2 space cross times space 2$ matrix A, if A (adj A) = $open square brackets table row 10 0 row 0 10 end table close square brackets$ , then determinant A equals

(A) 20

(B) 10

(D) 40

Q.5. If $A to the power of negative 1 space end exponent equals space minus space 1 half open square brackets table row 1 cell negative 4 end cell row cell negative 1 end cell 2 end table close square brackets$ , then A =

(A) $open square brackets table row 2 4 row cell negative 1 end cell 1 end table close square brackets$

(B) $open square brackets table row 2 4 row 1 cell negative 1 end cell end table close square brackets$

(D) $open square brackets table row 2 4 row 1 1 end table close square brackets$

Q.6. If the matrices A = $open square brackets table row 1 1 2 row 1 3 4 row 1 cell negative 1 end cell 3 end table close square brackets$ , B = adj A and C = 3A, then $fraction numerator open vertical bar a d j space B close vertical bar over denominator open vertical bar C close vertical bar end fraction$ is equal to

(A) 16

(B) 2

(C) 8

(D) 72

Q.7. If $A equals open square brackets table row 1 2 row 3 4 end table close square brackets$ , adj $A equals open square brackets table row 4 a row cell negative 3 end cell b end table close square brackets$ , then the values of a and b are.

(A) a = - 2, b = 1

(B) a = 2, b = 4

(D) a = 1, b = - 2

Q.8. If $F space open parentheses alpha close parentheses equals space open square brackets table row cell cos space alpha end cell cell negative sin space alpha end cell 0 row cell sin space alpha end cell cell cos space alpha end cell 0 row 0 0 1 end table close square brackets$ , where $alpha space element of space R$ , then $open square brackets F space open parentheses alpha close parentheses close square brackets to the power of negative 1 end exponent$ =

(A) $F open parentheses negative alpha close parentheses$

(B) $F space open parentheses alpha to the power of negative 1 end exponent close parentheses$

(D) None of these

Q.9. If A is a square matrix of order 2 and A(adjA) = $open square brackets table row 10 0 row 0 10 end table close square brackets$ , then $open vertical bar A close vertical bar$ =

(A) 10

(B) 100

(D) 0

Q.10. If the inverse of matrix A = $open square brackets table row 1 2 x row 4 cell negative 1 end cell 7 row 2 4 cell negative 6 end cell end table close square brackets$ does not exist, then x =

(A) -3

(B) 0

(D) 3

Q.11. If $A space equals space open square brackets table row lambda 1 row cell negative 1 end cell cell negative lambda end cell end table close square brackets$ , then $A to the power of negative 1 end exponent$ does not exist if $lambda$ =

(A) 0

(B) $plus-or-minus space 1$

(D) 3

Q.12. If $A space equals space open square brackets table row cell cos space alpha end cell cell negative sin space alpha end cell row cell sin space alpha end cell cell cos space alpha end cell end table close square brackets$ ,then $A to the power of negative 1 end exponent space equals$

(A) $open square brackets table row cell fraction numerator 1 over denominator cos space alpha end fraction end cell cell fraction numerator negative 1 over denominator sin space alpha end fraction end cell row cell fraction numerator 1 over denominator sin space alpha end fraction end cell cell fraction numerator 1 over denominator cos space alpha end fraction end cell end table close square brackets$

(B) $open square brackets table row cell cos space alpha end cell cell sin space alpha end cell row cell negative sin space alpha end cell cell cos space alpha end cell end table close square brackets$

(C) $open square brackets table row cell negative cos space alpha end cell cell sin space alpha end cell row cell negative sin space alpha end cell cell cos space alpha end cell end table close square brackets$

(D) $open square brackets table row cell negative cos space alpha end cell cell sin space alpha end cell row cell sin space alpha end cell cell negative cos space alpha end cell end table close square brackets$

Q.13.The inverse of $A space equals space open square brackets table row 0 1 0 row 1 0 0 row 0 0 1 end table close square brackets$ is

(A) I

(B) A

(D) -I

Q.14. The inverse of $open square brackets table row 0 1 row 1 0 end table close square brackets$ is

(A) $open square brackets table row 1 1 row 1 1 end table close square brackets$

(B) $open square brackets table row 0 1 row 1 0 end table close square brackets$

(D) None of these

Q.15. If $A space equals space open square brackets table row 1 2 row 2 1 end table close square brackets$ and A (adj A) = k I, then the value of k is.

(A) 1

(B) - 1

(D) - 3

Q.16. If $A space equals space open square brackets table row 2 cell negative 4 end cell row 3 1 end table close square brackets$ , then the adjoin of matrix A is .

(A) $open square brackets table row cell negative 1 end cell 3 row cell negative 4 end cell 1 end table close square brackets$

(B) $open square brackets table row 1 4 row cell negative 3 end cell 2 end table close square brackets$

(D) $open square brackets table row cell negative 1 end cell cell negative 3 end cell row cell negative 4 end cell 2 end table close square brackets$

Q.17. If $A space equals space open square brackets table row 1 2 row 3 4 end table close square brackets$ and A (adj A) = k I, then the value of k is.

(A) 2

(B) - 2

(D) -10

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Saturday, September 4, 2021

HSC Matrices Solved textual MCQs : Maharashtra Board

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