Math Chapter Wise

EnglishUP PCS (Pre) 2007

Q381.IF A is non-singular real matrix, then–

At/A A Bt/A A 0 C2/A.t A D2 t t A.A A

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EnglishUP PCS (Pre) 2007

Q382.Inverse matrix of 2 3 4 2 is–

A2 4 1 3 2 8 B2 4 1 3 2 8 C2 3 1 4 2 8 D2 3 1 4 2 8

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EnglishUP PCS (Pre) 2008

Q383.If 0 1 2 A = 3 5 4 and 8 9 7 B = 3 2 1 then

AAB does not exist. BAB is a 2×2 matrix CAB is a 3×3 matrix DAB is a 3×2 matrix

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EnglishUP PCS (Pre) 2008

Q384.Let 0 1 A = -1 0 and 1 0 B = 0 1 consider the statements: I. AB = 0 II. BA = 0 III. AB = A IV. BA = B Then the number of true statements is

Aone Btwo Cthree Dfour

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EnglishUP PCS (Pre) 2008

Q385.A necessary and sufficient condition that a square matrix A possesses an inverse is that

AA is null matrix BA is not a null matri CA 0 = DA 0/≠

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EnglishUP PCS (Pre) 2008

Q386.If B is a non-zero 3× × ×1 matrix and A is a non-zero 1× × ×3 matrix and if r denotes the rank of AB then

Ar = 0 Br ≤1 Cr >1 Dr >2

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EnglishUP PCS (Pre) 2008

Q387.The rank of matrix 1 1 1 A = 2 3 4 4 9 16 is

Acannot be found B1 C2 D3

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EnglishUP PCS (Pre) 2008

Q388.If A = 1 3 3 4 and A2 +KA–5I=0, then K is equal to

A–5 B3 C7 D4

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EnglishUP PCS (Pre) 2008

Q389.The system of equation is 2x+3y+z = a, x+2y+3z = b, 3x+y+2z = c

Ais inconsistent. Bhas infinitely many solutions Chas a unique solution Dhas trivial solution

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EnglishUP PCS (Pre) 2009

Q390.The identify element in the multiplicative group of the set of matrices α cosα -sinα A =, sinα cosα Where α is a real number, is

A1 0/0 0 B1 0/0 1 C0 1/1 0 DNone of the above

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EnglishUP PCS (Pre) 2009

Q391.If A, B are symmetric matrices of the same order, then (AB–BA) is

Asymmetric Bskew symmetric Cunit matrix Dnull matrix

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EnglishUP PCS (Pre) 2009

Q392.The diagonal elements of a skew symmetric matrix are all

Anon-zero Bzero (0) Cone (1) Dzero or one both

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EnglishUP PCS (Pre) 2009

Q393.If a 0 0 A= 0 b 0 0 c c then the eigen values of Adj A are

Abc, ca, ab B1 1 1,, a b c C1 1 1,, bc ca ab Db+c, c+a, a+b

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EnglishUP PCS (Pre) 2009

Q394.The inverse of the square matrix- cos α -sin α A = sin α cos α is

A-sin α cos α/-cos α sin α Bcos α sin α/-sin α cos α Ccos α sin α/sin α cos α Dsin α cos α 0/0 -cos α sin α

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EnglishUP PCS (Pre) 2009

Q395.If 2 3 a a a +1 b b b +1 = 0 c c c +1 and ≠ 2 1 a a 1 b b 0 1 c c then the value of abc is

A-1 B0 C1 DNone of the above

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EnglishUP PCS (Pre) 2009

Q396.For what values of λ, the equations x+y+z = 1, x+2y+4z = λ, x+4y+10z =λ2 have a solution?

Aλ= 1 only Bλ= 0 only Cλ=1 and λ=0 both Dλ= 1 and λ=2 both

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EnglishUP PCS (Pre) 2009

Q397.If a matrix X satisfies 1 3 1 0 X 0 1 0 1 = then X is equal to

A1 3/0 1 B1 0/3 1 C−1 3/0 1 D−1 0/3 1

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EnglishUP PCS (Pre) 2009

Q398.If 1 1 A 2 1 − = −, a 1 B b 1 = − and (A+B)2 = A2 + B2, then the values of a and b are respectively

A1, 4 B1, 2 C4, 2 D2, 1

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EnglishUP PCS (Pre) 2009

Q399.If 1 2 3 A 4 2 5 − = − and 2 3 B 4 5 2 1 = then

AAB, BA exist and are equal. BAB, BA exist, but they are not equal CAB exists and BA does not exist DAB does not exist and BA exists

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EnglishUP PCS (Pre) 2009

Q400.Inverse of the matrix 2 k 3 5 will not exist if k is equal to

A5/6 B6/5 C3/10 D10/3

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