Math Chapter Wise

EnglishEMRS PGT-2023

Q01.Let A = 0 0 -1 0 -1 0 -1 0 0 The only correct statement about the matrix A is:

AA= (–1)I, where I is a unit matrix BA–1/does not exist CA2 = I DA is a zero matrix

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EnglishEMRS PGT-2023

Q02.The system of equations: ax + y + z = α –1 x + αy + z = α –1 and x + y + αz = α –1 has no solution, if α is:

ANot –2 BEither –2 or 1 C–2 D1

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EnglishEMRS PGT-2023

Q03.If α and β are the roots of the equation x2 + x + 1 = 0 then 1 β α β α β equals:

A1 1 1 2 − − − B1 2/2 1 C1 1 1 2 − − D1 1/1 2

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EnglishEMRS PGT-2023

Q04.The matrix 3 0 0 0 4 0 0 0 5 is a:

AScalar matrix BSkew-symmetric matrix CSymmetric matrix DIdentity matrix

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EnglishBihar (TRE 2.0)-2023

Q05.The values of a and b in the equation 2a + b a - 2b 4 -3 = 5c -d 4c + 3d 11 24 are

Aa = -1, b = 2 Ba = -2, b = 1 Ca = 2, b = -1 DMore than one of the above ENone of the above

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EnglishBihar (TRE 2.0)-2023

Q06.If 1 0 3 0 A = and B = 0 2 0 4 then

AAB = BA BAB ≠ BA CA + B = B + A DMore than one of the above ENone of the above

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EnglishBihar (TRE 2.0)-2023

Q07.If A and B are invertible matrices of the same order, then

A(AB)-1 = (BA)-1 B(AB)-1 = B-1 A-1 C(AB)-1 = A-1 B-1 DMore than one of the above ENone of the above

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EnglishBihar (TRE 2.0)-2023

Q08.The number of possible matrices of order 3×3 with each entry 1 or 2 is

A18 B81 C512 DMore than one of the above ENone of the above

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EnglishBihar (TRE 2.0)-2023

Q09.If the area of a triangle with the vertices (-3, 0), (3, 0) and (0, k) is 9 sq. units, then the value of k is

A3 B-9 C9 DMore than one of the above ENone of the above

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EnglishBihar (TRE 2.0)-2023

Q10.If A is an invertible matrix of order 2, then det (A-1) is equal to

AImage/formula option A (see source) B1/det(A) C1 DMore than one of the above ENone of the above

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EnglishBihar (TRE 2.0)-2023

Q11.The value of 1 1 -2 3 4 5 -1 2 1 is

A-34 B-46 C44 DMore than one of the above ENone of the above

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EnglishBihar (TRE 2.0)-2023

Q12.For which value of x, will the matrix given below become singular? A = 8 x 0 4 0 2 12 6 0

A2 B4 C6 DMore than one of the above ENone of the above

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EnglishBihar (TRE 2.0)-2023

Q13.If ∆ ∆ ∆1 = 2 ax x 1 by y 1 cz z 1 and ∆ ∆ ∆2 = a b c x y z zy zx xy then

A∆1 = −∆2 B∆1 −∆2 = 0 C∆1 ≠ ∆2 DMore than one of the above ENone of the above

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EnglishEMRS TGT-2023

Q14.The rank of the matrix –1 2 5 2 –4 a – 4 1 –2 a +1 is:

A2, if a = 1 B3, if a = 2 C1, if a = –6 D1, if a = 6

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EnglishEMRS TGT-2023

Q15.If P'(x', y') is the reflection of the point P(x, y) on the x-axis, then the matrix which describe the reflection of point P(x, y), in the x-axis is:

A0 –1/–1 0 B–1 0/0 –1 C1 0/0 –1 D0 1/1 0

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EnglishEMRS TGT-2023

Q16.The matrix which describe the reflection of point P(x, y) through the origin is:

A0 –1/–1 0 B–1 0/0 –1 C1 0/0 –1 D0 1/1 0

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EnglishKVS PGT 2023

Q17.If the system of linear equations: x + y + kz = 4 x – 2y +2z = 3 3x + y – z = 5 are inconsistent, then the value of k is: b

A–1 B1 C0 D2

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EnglishKVS PGT 2023

Q18.The value of determinant 2 3 4 3 4 5 4 5 6 5 5 5 5 5 5 5 5 5 is:

A52 B0 C513 D59

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EnglishKVS PGT 2023

Q19.A matrix A = α β γ −α is such that A2 = I, then:

A1 + α2 + βγ = 0 B1 – α2 + βγ = 0 C1 – α2 – βγ = 0 D1 + α2 – βγ = 0

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EnglishKVS PGT 2023

Q20.If matrix A = 1 1 0 0 0 1 1 0 0 0 1 0 0 0 0 2, then Rank of the matrix (A - I) is:

A4 B2 C3 D1

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