Math Chapter Wise

EnglishPGT 2002

Q281.Let P(x) = a0+a1x2 +a2x4 +.....+anx2n be a polynomial in the real variable x with 0<aa<a1<a2<......<an. The function P(x) has:

Aneither a max, nor a minimum Bonly one max. Conly one max. and one minimum. DNone of these

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EnglishPGT 2000

Q282.If α, β, γ, δ be the roots of x4 +6x2 –5x+4=0. Then (α+β+γ) (β+γ+δ)(γ+α+β) (δ+α+β) is:

A6 B–5 C–4 DNone of these

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EnglishPGT 2000

Q283.The Condition that one root of the equation (1+m2)x2 +2cmx+(c2 –a2)=0 is reciprocal of the other is:

A1+m2 = cm B2 c a 1 m = + C1+m2 = c2 –a2 D1+m2 +2c = 0

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EnglishPGT 2000

Q284.The number of the solution of equation- sin(ex)=5x + 5–x is

AOne BZero CInfinite DNone of these

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EnglishPGT 2000

Q285.For the equation |x2 |+|x|–6=0:

AThere are four distinct roots. BThere are only three distinct root. CThere is only two distinct root. DThere is only one root

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EnglishPGT 2000

Q286.If,, α β γ α β γ α β γ α β γ are root of x3 –7x2 +5x–2=0 the value of 1 1 1 + + αβγ αγ αβγ αγ αβγ αγ αβγ αγ is:

A7/5 B7/4 C7/3 D7/2

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EnglishRajasthan TGT 2016

Q287.The nth divided difference of a polynomial of degree 'n' is

Aa variable Ba constant Calways zero DNone of these

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EnglishRajasthan TGT 2015

Q288.If a,b are the roots of 2 x px 1 0 + + = + + = + + = + + = and c,d are the roots of 2 x + + + qx + + + 1 0 = then the value of (a c) − − (b c) − − (a d) + + (b d) + + is

A−2 2/p q B−2 2/q p C2 2 p q + D2pq

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EnglishRajasthan TGT 2015

Q289.If the ratio of the roots of the equation 2 ax bx c 0 is r, then 2 (r 1) r + is equal to

A2 a bc B2 b ca C2 c ab D1/abc

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EnglishRajasthan TGT 2015

Q290.For x = 6, the value of the polynomial 4 3 2 x 5x 5x 5x 2 − − − + − − − + − − − + − − − + is equal to

A2 B–12 C1296 D8

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EnglishRajasthan TGT 2015

Q291.The roots of the equation 3 x 18x 35 0 − − = − − = − − = − − = are

Aall real and equal Ball real and distrinct Call complex Done real and two complex conjugate

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EnglishRajasthan TGT 2015

Q292.The number of all most negative roots in 9 8 3 x 5x x 7x 2 0 + − + + = + − + + = + − + + = + − + + = is

A1 B4 C2 D3

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EnglishRajasthan TGT 2013

Q293.If α1, α2, α3,......... αn are the roots of the equation n n-1 n-2 1 2 n-1 n n x + P x + P x +........ + P x + P = 0,P 0, then the value of 1 2 3 n 1 1 1 1 + + +...........+ α is-

An 1 n P − Bn 1 n P − CPn–1 D–Pn–1

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EnglishRajasthan TGT 2013

Q294.The roots of the equation x3 – 15x – 126 = 0, are

A6,3 2 3i, 3 2 3i + − − B6,3 2 3i, 3 2 3i − − − C6, 3 2 3i, 3 2 3i − − − + D6, 3 2 3i, 3 2 3i − − − − +

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EnglishRajasthan TGT 2011

Q295.If the polynomial 4 3 f(x) 2x kx 75k = + − = + − = + − = + − is divided by x, the remainder is 150, then the value of k will be

A–2 B–1 C1 D2

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EnglishRajasthan TGT 2011

Q296.If the roots of the equation x3 –12x2 +39x–28= 0 are in A.P., then difference between two of its roots is

A1 B2 C3 D3

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EnglishRajasthan TGT 2011

Q297.If x2 –3x+2 is a factor of x4 –px2 +q, then

Ap 5,q 2 = Bp 5,q 4 = Cp 5,q 4 = − = − Dp 5,q 4 = − =

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EnglishRajasthan TGT 2011

Q298.The number of real roots of the equation 8 4 2 2x 3x x 7 0 + + + = + + + = + + + = + + + = is

A2 B4 C6 D0

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EnglishJharkhand TGT 2017

Q299.An equation of 4th degree is given as 2x4 – 15x3 +35x2 –30x+8=0. It is known that the roots of this equation are in geometric progression. The roots of this equation are

A(1,2,4,8) B(1/2, 1,2,4) C(2,4,8,16) D1 1,,1,2 4 2

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EnglishJharkhand TGT 2017

Q300.If 1, ω, ω2 are the cube roots of unity then (a+b)(aω+bω2)(aω2 +bω)=

A0 B1 Ca+b Da3/+ b3

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