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Faculty of Science, B.Sc. (Fourth Semester) EXAMINATION, Summer - 2020, (CBCS Pattern), MATHEMATICS, Paper Il, (Algebra and Trigonometry), MCQ, , (Thursday, 25-03-2021) Time: 12.00 PM to 01.00, PM, , Time: 1 Hr. Max. Marks: 40, , , , Note: 1. All questions are compulsory., 2. Each question carry one marks., 3. All the symbols have their usual meanings., , 1. Let a be any square matrix in which all non-diagonal entries are zero then, the, matrix 4 is, , called as..., a) Scalar Matrix b) Diagonal Matrix, c) Both (a) and (b) d) None of these., , 2. Which of the following property doesn’t satisfied by the matrices?, a) Matrix addition is commutative. b) Matrix multiplication is, commutative., c) Matrix addition is associative. d) Matrix multiplication is associative., , 3. What will be the order of matrix 48, if 4 =[a,],., and 8 =|),, a) mxa b) oxp, Cc) pxa d) None of these., , 4. In what condition the two matrices 4 and 8 are said to be conformable for, multiplication 4s ?, a) If the product 48 is defined. b) If the product 48 is not defined., , c) Either (a) or (b) d) None of these., , 5. If 4 be any square matrix of order mx », then what is order of 4?, a) mxn b) axm, Cc) axa d) mxm, , W Edit with WPS Office

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(2), , 6. If 4 and & denote the transpose of 4 and s, then which of the following is, correct?, , a) (A)J=A b) (kA) = 4’, kis any scalar., c) (ABY=B8'A d) All of these., , 7. A square matrix 4 is said to be Nilpotent matrix if, a) A=A b) A'=A, c) A’ =0 d) a’ =/, , 8. If 4 be any n—square matrix then choose the correct statement., , a) A= (adj A) =|Al/, b) (ad A): a =alr,, , c) Both (a) and (b) d) None of these., 9. A square matrix 4 is said to be Symmetric matrix if, , a) A=A b) A =A, , c) A=-A d) a’ =!, , 10. Let 4 be any square matrix such that |4|+0, then 4 is said to be, , a) Singular Matrix b) Non-Singular Matrix, Cc) Identity Matrix d) None of these., , 11. A non-zero matrix 4 is said to be rank of order r, if, , a) Ahas at least one non-zero minor of order + b) Every minor of order + +1 is, zero., c) Both (a) and (b) d) None of these., , 12. Which of the following are elementary row operations?, a) The interchange of any two distinct rows of a matrix., b) The multiplication of any row by a fixed non zero scalar., c) The addition to the elements of a row, a fixed scalar multiple of the, corresponding elements of another row., d) All of the above., , 13. The number of non-zero rows in the row echelon form of a matrix 4 is known as, a) Rank of A b) Row Rank of 4, c) Column Rank of 4 d) None of these., , 14. If Abe any square matrix such that any two rows or columns of 4 identical, then, a) |al=o b) |al=o, , c) |4l=1 d) None of these., , W Edit with WPS Office

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15. The row rank of amatrix 4=|2 -4 9|]is, , 1 2 3, a) 2 b)1, c)0 d)3, , 16. Choose the correct statement of the following., a) Every matrix is column equivalent to a column echelon matrix., b) Every matrix is row equivalent to a row echelon matrix., c) Identity matrix are always in row reduced echelon form., d) All of the above., , 17. Which of the following statement is incorrect., a) The elementary operations do not alter the rank of a matrix., b) The elementary operations do alter the rank of a matrix., c) Interchange of a pair of rows does not change the rank of the matrix., d) None of these above., , 18. If Ais the null matrix, then the rank of matrix Ais, a) Can't determine b) Zero, c) Non zero d) None of these., , 19. If A and 8 arenon-singular matrices of same order, then adj( AB) =, a) A -adj(B) b) B -adj(A), C) adj(A)- adj (8) d) None of these., , 20. A square matrix 4 is said to be Hermitian matrix if, a) Ao =A b) a°=-A, , c) A #A d) A°#-A, , 21.1f ax =8 is asystem of m linear equations in » unknowns, then which of the, following statement is correct?, , a) The system of equations is always consistent., , b) The system of equations always has unique solution., , c) If system of equations has a solution, then it is said to be consistent., , d) None of these., , 22. Let ax =o is ahomogeneous system of equations in » unknowns. If x, and x, are two solutions of this system, then which of the following is true?, , a) x, + x, is also a solution of ax =o b) Ax, is also solution of ax =o for any, scalar 4., c) Ax, + Ax, is also a solution of ax =0 d) All of the above., , W Edit with WPS Office

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(4), , 23. The two systems of linear equations in same number of unknowns over the field, F are said to be equivalent if, , a) Every solution of either system is a solution of the other., , b) They have the same solution set., , c) Both (a) and (b), , d) None of these., , 24. Let ax =8 is anon-homogeneous system of » linear equations in » unknowns, have a unique solution, if, a) Ais non-singular b) (A) =n, , c) [also d) All of the above, , 25. Let ax =o bea system of m homogeneous equations in n unknowns. Let r be, the rank of the system. Then the system has_ unique solution if, , a) A(A)=r=n b) (A) #r=n, cC) AA)=rz#n d) A A)=r>n, 26. The roots of the characteristic’s equation |4—Ai|=0 are called, a) Characteristics roots b) Eigen values, c) Proper values d) All of the above, 1 0 0, , 27. The characteristics roots of the matrix 4=| 3 1 0] are, —-7 § 1, , a) 1,1,1 b) 1,2,2, c) 1,2,1 d) 0,0,1, , -2 -1, 28. The characteristics equation of the matrix 4 -| é is, , a) 4 -2A-3 b)# -2A+3, c) 4 +2A-3 d) 4 +2A4+3, , 1 2 1, 29. For what value of /, the system : L:| = | has infinitely many solutions?, ALLY, , a) A=6 b)A=6e, c) A=3 d) A=3, 30. The system of equations x+3y—2z=0; 2x-y+4z=0and x-11y+14z=0 has, a) Unique solution b) No solution, c) Infinitely many solution d) None of the above, , W Edit with WPS Office