CBSE Class 12 Mathematics Value and Properties of Determinant Worksheet Set A

Question. If A is a skew-symmetric matrix of order 3, then the value of |A| is
(a) 3
(b) 0
(c) 9
(d) 27
Answer : B

Question. If A is any square matrix of order 3x3 such that |A| = 3, then the value of |adj A| is
(a) 3/1
(b) 3
(c) 9
(d) 27
Answer : C

Question. The area of a triangle with vertices (−3,0), (3,0)and (0, k) is 9 sq. units. Then, the value of k will be
(a) 9
(b) 3
(c) -9
(d) 6
Answer : B

Question. For any square matrix A, AAT is a
(a) Unit matrix
(b) Symmetric matrix
(c) Skew symmetric matrix
(d) Diagonal matrix
Answer : B

Question. Which of the following is not true?
(a) Every skew-symmetric matrix of odd order is non-singular
(b) If determinant of a square matrix is non-zero, then it is non singular
(c) Adjoint of symmetric matrix is symmetric
(d) Adjoint of a diagonal matrix is diagonal
Answer : A

Question. If a matrix A is such that 3A³ + 2A² + 5A + I = O then its inverse is
(a) −(3A² + 2A + 5I)
(b) (3A² + 2A + 5I)
(c) (3A² − 2A + 5I)
(d) None of these
Answer : A

Question. If the order of matrix A is m x p and the order of B is p x n. Then the order of matrix AB is?
(a) m × n
(b) n × m
(c) n × p
(d) m × p
Answer : A

CASE STUDY QUESTIONS

1. Raja purchases 3 pens, 2 pencils and 1 mathematics instrument box and pays ₹ 41 to the shopkeeper. His friends, Daya and Anil purchases 2 pens, 1 pencil, 2 instrument boxes and 2 pens, 2 pencils and 2 mathematical instrument boxes respectively. Daya and Anil pays ₹ 29 and ₹ 44 respectively. Based on the above information answer the following:

Question. The cost of one pen is
(i) ₹ 2
(ii) ₹ 5
(iii) ₹ 10
(iv) ₹ 15
Answer : I

Question. The cost of one pen and one pencil is
(i) ₹ 5
(ii) ₹ 10
(iii) ₹ 15
(iv) ₹ 17
Answer : IV

Question. The cost of one pen and one mathematical instrument box is
(i) ₹ 7
(ii) ₹ 10
(iii) ₹ 15
(iv) ₹ 18
Answer : I

Question. The cost of one pencil and one mathematical instrumental box is
(i) ₹ 5
(ii) ₹ 10
(iii) ₹ 15
(iv) ₹ 20
Answer : IV

Question. The cost of one pen, one pencil and one mathematical instrumental box is
(i) ₹ 10
(ii) ₹ 15
(iii) ₹ 22
(iv) ₹ 25
Answer : III

2. The management committee of a residential colony decided to award some of its members (say x) for honesty, some (say y) for helping others and some others (say z) for supervising the workers to kept the colony neat and clean. The sum of all theawardees is 12. Three times the sum of awardees for cooperation and supervision added to two times the number of awardees for honesty is 33. The sum of the number of awardees for honesty and supervision is twice the number of awardeesfor helping.

Question. Value of x + y + z is
(a) 3
(b) 5
(c) 7
(d) 12
Answer : D

Question. Value of x − 2 y is
(a) z
(b) -z
(c) 2z
(d) -2z
Answer : B

Question. The value of z is
(a) 3
(b) 4
(c) 5
(d) 6
Answer : C

Question. The value of x + 2 y is
(a) 9
(b) 10
(c) 11
(d) 12
Answer : C

Question. The value of 2x + 3y + 5z is
(a) 40
(b) 43
(c) 50
(d) 53
Answer : B

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