Math Chapter Wise

EnglishKVS TGT 2017

Q81.For expressing the vector 26 x 12 2 as a linear combination of the vectors 1 1 C 1, 1 2 1 C 1, 0 3 0 C 0, 1 as 1 2 3 C C C where,, in that order are –

A7, 9, 19 B9, 7, 19 C19, 9, 7 D7, 19, 9

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EnglishOPSC PGT 2017

Q82.Cramer's rule is used to solve:

AAn integral BA system of linear equations CAn algebraic equation DNone of these

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EnglishOPSC PGT 2017

Q83.Jacobi's method requires the coefficient matrix in system of equations to be:

ASymmetric BHermitian CSparse DDiagonally dominant

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EnglishOPSC PGT 2017

Q84.When performing Gaussian elimination, the pivot represents the:

ALargest element in column BLargest element in row CLargest element in matrix DDiagonal element

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EnglishOPSC PGT 2017

Q85.A norm on a vector space X is a function, whose range is a set of:

ARational numbers BPositive real numbers CReal numbers DNon-negative real numbers

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EnglishOPSC PGT 2017

Q86.Given a vector space X with a subspace M. The co-dimension of M is the:

Ag.c.d. of dimension of X and M BNumber of functions from X to M CDimension of quotient space X/M DDimension of largest normed subspace of X

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EnglishOPSC PGT 2017

Q87.A bounded (linear) operator from X to Y is a linear transformation T:X → → → Y such that the operator norm T is:

AFinite BZero CInfinite DUnity

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EnglishOPSC PGT 2017

Q88.The dual of a + a′ ′ ′b = a + b is:

Aa(a b) ab Ba(a b) a b Ca(a b) ab Da (a b) ab

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EnglishUPPSC GDC 2021

Q89.The order of sylow 3-subgroup of a group of order 12 is

A2 B3 C2 or 4 D4

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EnglishUPPSC GDC 2021

Q90.Let p be a prime number, then f (x) = xp – 1∈ Q [x] has splitting field Q (α), if

Ap 1 and 1 α = α = Bp 1 and 1 α ≠ α = Cp 1 and 1 α ≠ α ≠ DNone of the above

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EnglishUPPSC GDC 2021

Q91.If all vertices are of degree at least 3, then the largest number of vertices in a graph with 35 edges is

A25 B23 C21 D27

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EnglishUPPSC GDC 2021

Q92.If two bounded lattices A and B are complemented, then which of the following is complemented?

AA – B BA + B CA × B DAll of the above

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EnglishUPPSC GDC 2021

Q93.Let Q be the field of rational numbers. Then over Q, 2 + 3 is algebraic of degree

A2 B3 C4 D6

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EnglishUPPSC GDC 2021

Q94.For all a, b in Boolean algebra, the value of (a + b) a' b' is

Aa B1 Ca + b D0

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EnglishUPPSC GDC 2021

Q95.The dimension of Lie group SL (n, C) is

An2 Bn2/– 1 C2 (n2/– 1) D2n2

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EnglishUPPSC GDC 2021 UPPSC Polytechnic Lecturer 2021(II)

Q96.If p is a prime number, then any group of order 2p has a normal subgroup of order

Ap – 1 Bp Cp +1 D() 1 p 1 2 +

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EnglishUPPSC Polytechnic Lecturer 2021 (I)

Q97.The number of regions contained in a connected planar graph having 6 vertices and 7 edges is-6

A6 B4 C11 D3

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EnglishUPPSC Polytechnic Lecturer 2021 (I)

Q98.A simple graph with 10 vertices and 5 components can not have more than-

A2 edges B5 edges C10 edges D15 edges

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EnglishUPPSC Polytechnic Lecturer 2021 (I)

Q99.The maximum number of edges in a simple graph with 9 vertices is-

A9 B8 C36 D45

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EnglishUPPSC Polytechnic Lecturer 2021 (I)

Q100.If x=a+b satisfies the congruence relation () ≡ 4x 3 mod15, then which of the following is true?

AIf a=4, then b is multiple of 12 BIf a=4, then b is multiple of 15 CIf a=12, then b is multiple of 15 DIf a=10, then b is multiple of 15

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