Math Chapter Wise

EnglishTGT 1999

Q261.If sum of two roots of equation is x3 –3x2 –4x + 12 = 0 is zero. Then all the roots of the equations-

A4, 5, 3 B2, 3, 5 C2, –2, 3 D3, –3, 2

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EnglishTGT 1999

Q262.If α and β are roots of the equation ax2 +bx+c=0. Then a b a b β α + α + β + α + β + α + β + α + β + is equal to

A2/a B−2/a Ca/2 D−a/2

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EnglishTGT 1999

Q263.The domain of the function 1 f(x) x = will be

AIncreasing BDecreasing CConstant DData is insufficient

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EnglishPGT 2011

Q264.If α, β are the roots of the equation 4x2 +3x+7=0 then 1 1 + α β is equal to.

A7/3 B−7/3 C3/7 D−3/7

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EnglishPGT 2013

Q265.If a is a root of equation x3 +2x2 +gx+1 = 0, then 1 α will also be a root of this equation, when the value of g is-

A–1 B0 C1 D2

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EnglishPGT 2010

Q266.The number of roots of the equation 2 2 1 1 1 − = − − = − − = − − = − − − x x x is

Aone Btwo Czero Dinfinite

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EnglishPGT 2010

Q267.If the roots of the equation 2 y 2y 3 0 − + = − + = − + = − + = are α and β then α4 +β4 will be equal to

A16 8 3/+ B10 8 3 C13 12 2 D13 12 2/+

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EnglishPGT 2010

Q268.H.C.F. of x2 +2x–8 and x2 +x–12 will be

Ax–2 Bx–3 Cx+4 Dx+3

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EnglishPGT 2009

Q269.It the roots of the quadratic equation x2 + px + q = 0 are tan300 and tan150, respectively, then the value of 2 + q – p is

A2 B3 C0 D1

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EnglishPGT 2009

Q270.If the roots p and q of the equation lx2 + nx + n = 0 be in the ratio p: q then + + = + + = + + = + + = p q n q p l

A0 B2 n l Cn/l DNone of these

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EnglishPGT 2009

Q271.The product of any r consecutive natural number is always divisible by

Ar! Br2 Crn DNone of these

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EnglishPGT 2009

Q272.If α, β and γ are the roots of the equation x3 + px2 + qx + r = 0, then the value of 2 Σ Σα β α β α β is

A3r – pq B3p – rq C3r DNone of these

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EnglishPGT 2005

Q273.If α, β are the roots of the equation 2 2 3 0 − + = − + = − + = − + = x x then the value of (())) ((()) 4 4 2 2 − − α − + β − α − + β − α − + β − α − + β − is

A14/81 B−14/81 C22/81 D−22/81

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EnglishPGT 2005

Q274.One of the roots of the equation 3x2 +px+3=0; p>0 is square of the other, then p is equal to

A1/3 B1 C3 D2/3

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EnglishPGT 2005

Q275.The equation 1 1 4 1 + − − = − + − − = − + − − = − + − − = − x x x has

ANo solution BOne solution CTwo solution DMore than two solutions

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EnglishPGT 2004

Q276.Number of real solutions of the equation x2 + 8|x| + 8 = 0 is

A2 B4 C0 DNone of the above

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EnglishPGT 2004

Q277.If α, β and γ are roots of the equation x3 + ax2 + bx + a = 0 then the value of tan-1 α + tan-1 β + tan-1 γ will be

Anπ, b ≠ 1 B0 C1 Dπ, b ≠ 1

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EnglishPGT 2003

Q278.The equation ax3 +3bx2 +3cx+d=0 has two equal roots, then which statement is true?

A(bc–ad)2 =(b2 –ac)(c2 –bd) B(ac–bd)2 =(a2 –ac)(c2 –ad) C(bc–ad)2 =4(b2 –ac)(c2 –bd) D(ac–bd)2 =4(a2 –bc)(c2 –ad)

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EnglishPGT 2003

Q279.If a be a multiple root of order 3 of the equation x3 –bx2 +cx+d=0, then

A8 3 d a c = B8 3 d a c = − C8 3 d a c = DNone of the above

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EnglishPGT 2002

Q280.If the roots of the equations mx2 –4x+2(m+1)=0 are real, then:

Am ≤ 1 Bm ≥ – 2 Cm ≥–2 and m ≤ 1 Dm ≥1 or m ≤ –2

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