Math Chapter Wise

EnglishUP PCS (Pre) 1995 & 1999

Q321.The matrices A, B, C are such that the addition and multiplication occuring in the statements given below are valid. The incorrect statement is:

A(A+B)+C= A+(B+C) B(AB)C =A(BC) CA(B+C) = AB+AC DAB = AC⇒B=C

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EnglishUP PCS (Pre) 1999

Q322.If A and B are square matrices of the same order such that A2 = I = B2 I being the unit matrix, then:

A, B, Cis true Dnone of

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EnglishUP PCS (Pre) 1999

Q323.The rank of the matrix 0 3 1 2 4 0 3 6 9 12 0 5 10 15 20 is

Azero B1 C2 D3

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EnglishUP PCS (Pre) 1999

Q324.The determinant 1 0 0 2 a a 2 1 1 is zero for:

Aevery value of a Ba = 1 only Ca = 0 only Da = 0, 1 only

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EnglishUP PCS (Pre) 1999

Q325.The value of the determinant 1 2 3 4 1 3 6 10 1 4 10 20 1 5 15 35 is:

A0 B1 C10 D49

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EnglishUP PCS (Pre) 1999

Q326.The diagonal elements of a skew-symmetric matrix are

Azero elements Bnon-zero elements Cunit elements Dzero and unit elements both

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EnglishUP PCS (Pre) 1999

Q327.The system of linear equations x+2y+3z = kx, 3x+y+2z = ky, 2x+3y+z = kz has a non–zero solution when k equals

A2 B4 C6 D8

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EnglishUP PCS (Pre) 1999

Q328.If 0 1 2 1 2 3 A = 0, B = -2, C = 1 3 1 1 2 are matrices, then the order of (5A–3B) C is:

A5×1 B2×1 C3×1 Dmatrix does not exist

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EnglishUP PCS (Pre) 2000

Q329.The value of the determinant 1 2 3 47 1 3 6 10 1 4 10 20 1 5 15 a is

A1050 B105 C40 D35

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EnglishUP PCS (Pre) 2000

Q330.If 1 1 A 1 1 − = − and 1 2 B 3 2 = are two matrices, then:

AAB is non-singular BBA is non-singular CAB = BA DAB ≠ BA

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EnglishUP PCS (Pre) 2000

Q331.The rank of the matrix 1 2 3 2 4 1 1 2 7 − − − − is:

A1 B2 C3 D4

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EnglishUP PCS (Pre) 2000

Q332.If A and B are matrices of the same order, then (A + B)2 = A2 + B2 + 2AB is possible if

AAB = I BBA = I CAB = BA DNone of the above

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EnglishUP PCS (Pre) 2001

Q333.The value of the determinant 3 5 1 7 9 16 1 4 5 30 1 14 6 20 50 1 is:

Azero B1 C5 D70

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EnglishUP PCS (Pre) 2001

Q334.If 0 1 0 -2 1 3 A = and B = 2 3 1 2 1 -1 are two matrices then:

AAB exists but BA does not exist BBA exists but AB does not exist CAB and BA exist and AB=BA DAB and BA exist but AB≠BA

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EnglishUP PCS (Pre) 2001

Q335.The inverse of the matrix cos θ sin θ -sin θ cos θ is:

Acos θ -sin θ/sin θ cos θ Bcos θ sin θ/sin θ -cos θ Ccos θ sin θ/-sin θ cos θ D-cos θ sin θ/sin θ cos θ

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EnglishUP PCS (Pre) 2001

Q336.If 0 1 A = 1 2 and 1 B = 2 then AB is equal to:

A1/4 B0/5 C5/2 D2/5

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EnglishUP PCS (Pre) 2001

Q337.If ω is a cube root of unity then the value of the determinant: 2 a b c a b c a b c ω is:

Aa3 +b3 +c3 –3abc Ba3 –b3 –c3 –3abc Ca3 –b3 +c3 +3abc DNone of these

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EnglishUP PCS (Pre) 2001

Q338.The rank of the matrix 1 -3 2 -3 9 -6 2 -6 4 is equal to:

Azero B1 C2 D3

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EnglishUP PCS (Pre) 2001

Q339.If 1 A = 2 and B =[2,3] are two matrices then (AB)–1 is:

A2 0/0 1 B3 5/0 1 C1 4/2 0 Ddoes not exist

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EnglishUP PCS (Pre) 2002

Q340.If I3 is the identity matrix of order 3, then [I3]–1 is equal to

A0 BI3 C2I3 D3I3

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