Math Chapter Wise

EnglishTGT 2010

Q361.If x,y and z are real and different, then the equation u = x2 +4y2 +9z2 +12yz –4zx –2xy is always

Azero Bnon-negative Cnon-positive DNone of these

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EnglishTGT 2009

Q362.If 1 is a root of equation ax2 +bx+c=0, then-

Aa = 1 Bb = 1 Cc = 1 Da + b + c = 0

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EnglishTGT 2009

Q363.If the quadratic equation px2 – 2x + 2 = 0 has real linear factor, the value of p will be

A1 p 2 ≤ B1 p 2 > Cp = 1 Dp = 2

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EnglishTGT 2009

Q364.If x 2 e y 1 y, = + + = + + = + + = + + the y=

Ax x e e 2 − + Bx x e e 2 − Cex/+ e-x Dex/– e-x

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EnglishTGT 2009

Q365.The number of root of the quadratic equation 8 sec2 θ – 6 sec θ + 1 = 0 will be

AInfinite B1 C2 D0

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EnglishTGT 2009

Q366.If one root of equation ax2 + bx + c = 0 is square of another root then-

Aa3 + bc (b+c) = 3abc Bb3 + ac (a+c) = 3abc Cc3 + ab (a+b) = 3abc DNone of these

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EnglishTGT 2009

Q367.If tanα and tanβ are roots of quadratic equation x2 – px + q = 0. Then the value of sin2 (α+β) will be;

AP2 /P2 + (1–q)2 BP2 /P2 +q2 Cq2 /P2 + (1–q)2 DP2//(P+q)2

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EnglishTGT 2005

Q368.The difference of roots of quadratic equation x2 -6x+6=0 is-

A0 B6 C12 D18

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EnglishTGT 2005

Q369.In a quadratic equation x2 2 +px+q = 0, taken coefficient of x 17 instead of 13 by which obtained roots are –2 & –15. Therefore, what is orginal roots of the equation?

A2, 15 B10, 3 C–10, –3 D–2, 15

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EnglishTGT 2005

Q370.If x is real and K=(x2 –x+1)/x2 +x+1, then-

A1 3 K ≤ B3/K ≥ C1 3 K ≤ DNone of these

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EnglishTGT 2005

Q371.If a and b are roots of equation (x–a)(x–b)=c, ≠ c 0. Then the roots of (x–α)(x–β)=c, ≠ c 0 will be

Aa, c Bb, c Ca, b Da + c, b + c

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EnglishTGT 2005

Q372.The number of solutions of the equation |x2 |–3|x|+2=0 will be:

A4 B1 C3 D2

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EnglishTGT 2004

Q373.If 7 and 2 are the roots of x 3 7 2 x 2 7 6 x = 0, then the third root is

A14 B1/2 C–9 D+9

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EnglishTGT 2004

Q374.In using Newton–Raphson method for finding the roots of an equation, the original curve is being replaced by

AA line through the origin BA line joining two points on either side of x- axix CA line joining two points on either side of y- axis DA tangent to the curve

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EnglishTGT 2004

Q375.If one root of x2 – 12x +3k = 0 is square of the other, then the value of k is

A12 B9 C6 D3

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EnglishTGT 2004

Q376.If α, β, γ, δ be the roots of x4 –x3 + 2x2 +x+ 1 = 0 then the value of (α2 +1)(β2 + 1) (γ2 + 1) (2 1 δ +) is

A0 B2 C1 D4

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EnglishTGT 2004

Q377.If ax2 +bx +c = 0 (a ≠ 0) has no real roots (a, b, c being real's) and if a + b + c < 0, the sign of c is

Apositive BNegative Ccannot be determined Dboth positive and negative

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EnglishTGT 2003

Q378.The value of k for which the quadratic equation kx2 + 1= kx +3x –11x2 has real and equal roots are

A(–11, –3) B(5, 7) C(5, –7) DNone of these

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EnglishTGT 2003

Q379.The equation (cos p–1) x2 + (cos p)x+ sin p = 0 in the variable x, has real roots. The p can take any value in the interval:

A(0, 2π) B(–π, 0) C, 2 2 π − D0, 2 π

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EnglishTGT 2003

Q380.The set of values of p for which the roots of the equation 3x2 +2x+p(p–1) = 0 are of opposite sign is

A(–∞, 0) B(0,1) C(1, ∞) D(0, ∞)

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