Math Chapter Wise

EnglishPGT 2003

Q261.2cosθ 1 0 0......0 1 2cosθ 1 0......0 0 1 2cosθ 1......0 0 0 1 2cosθ......0 0 0 0 0......0 Will be equal to

A0 Bsin nθ Csin(1) sin n θ + DNone of these

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EnglishPGT 2002

Q262.For what value of λ the equations x+y+z=1, x+2y+4z=λ, x+4y+10z=λ2 have a solution:

Aλ= 10 Bλ= –10 Cλ = 0 and λ=10 Dλ = 1 and λ = 2

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EnglishPGT 2002

Q263.The value of α for which the system of equations x+y+z=1, x+2y+4z= α, x+4y+10z = λ2 is consistent, are given by:

A1, 2 B1, –2 C–1, 3 DNone of these

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EnglishPGT 2002

Q264.If 2 3 a a 1 a b b 1 b c c 1 c + = 0 and the vectors A = (1, a, a2), B=(1,b,b2), C=(1,c,c2) are non coplanar, then the product abc=

A1 B–1 C2 D5

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EnglishPGT 2002

Q265.The Parameter, on which the value of the determinant 2 1 a a cos(p d)x cospx cos(p d)x sin(p d)x sinpx sin(p d)x − + does not depend upon, is:

Aa Bp Cd Dx

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EnglishPGT 2002

Q266.If A and B are 3× × ×3 matrices and |A| ≠0, then which of the following is true?

A|AB| = 0 ⇒|B|=0 B|AB|=0 ⇒ |B|=0 C|A+A|=2|A| DNone of these

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EnglishPGT 2000

Q267.If x y A z w = then Adj (Adj A) is equal to:

Ax y/z w B−w z/y x Cw z 1 y x xw yz − DNone of these

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EnglishPGT 2000

Q268.If 1 1 A 1 1 − = − and 1 1 B 1 1 = then the valueof AB is:

AZero B3 C1 DNone of these

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EnglishRajasthan TGT 2016

Q269.Degeneracy in transportation problem occurs, if (Matrix m × × ×n)

Aempty cells<(m+n–1) Bempty cells=(m+n+1) Cempty cells>(m+n–1) Dempty cells>(m+n+1)

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EnglishRajasthan TGT 2016

Q270.If all the elements of a 3× × ×3 matrix P are 1, then P2 –3P is

Aa null matrix Ban unit matrix Ca column matrix Da diagonal matrix

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EnglishRajasthan TGT 2016

Q271.If 0 1 A 1 0 =, then the matrix A is

Aidempotent matrix Bnilpotent matrix Cinvolutory matrix Dsingular matrix

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EnglishRajasthan TGT 2016

Q272.If Matrix x 1 2 2 A 3 x 1 2 3 3 x 1 − = − −, then the number of real values of x satisfying the equation d | A | 0 dx =, is

A0 B1 C2 D3

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EnglishRajasthan TGT 2015 UPPCS 1995

Q273.If cos x sinx 0 f(x) sin x cosx 0 0 0 1 − = then f(x) f(y) is equal to

A(x y) + f B(x y) − f C(x) f(y) + f D(x) F(y) − f

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EnglishRajasthan TGT 2015

Q274.If 3 4 A 1 1 − = − then n A is equal to

An n 4 3 (4) 1 (1) − B1 2n 4n 1 n 1 2n + − C1 3n 1 4n 1 n 1 n + − D1 2n 4n n 1 2n + − −

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EnglishRajasthan TGT 2015

Q275.If 1 1 1 A 2 1 0 1 0 0 − = − then 1 A− − is equal

AA B2/A C3/A D1 (A 2) 2 l −

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EnglishRajasthan TGT 2015 UPPCS (PRE) 2003

Q276.If x,y,z are positive numbers, then x x y y z z l log y log z log x 1 log z log x log y 1 equal to

A0 B3 Ce/log xyz De log (x y z) + +

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EnglishRajasthan TGT 2015

Q277.The system of equations x 2y 3z 1; + + = + + = + + = + + = 2x y 3z 2 + + = + + = + + = + + = and 5x 5y 9z 4 + + = + + = + + = + + = have

ANo solution BUnique solution CInfinite solutions DNone of these

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EnglishRajasthan TGT 2013

Q278.If A is square matrix of order n, then () adj adjA =

A() n 1 A − B()2 n 1 A − C() n 1 A + D()2 n 1 A +

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EnglishRajasthan TGT 2013

Q279.If the matrices ij ij ij 2×3 p×q 2×3 A= a,B= b,C= c and AB = C then (p, q) =

A(2, 3) B(3, 2) C(2, 2) D(3, 3)

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EnglishRajasthan TGT 2013

Q280.If [.] denotes the greatest integer and – 1 ≤ x < 0, 0 ≤ y < 1, 1 ≤ z < 2, then [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] x +1 y z x y +1 z x y z +1 = [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] x +1 y z x y +1 z = x y z +1

A[ ]/x B[ ]/y C[ ]/z D[ ] z 1 +

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