Math Chapter Wise

EnglishUP PCS (Pre) 2002

Q321.The equations x3 –2x2 –2x+1 = 0 and x4 –7x2 +1 = 0, have:

ANo common root BOne common root CTwo common root DThree common root

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EnglishUP PCS (Pre) 2002

Q322.If 1, Z1, Z2,........., Zn-1 are n, nth roots of unity, then (1–Z1)(1–Z2).......(1–Zn-1) is equal to:

A0 B1 Cn Dn2

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EnglishUP PCS (Pre) 2003

Q323.If the roots of the equation 2 x bx c 0 are two consecutive integers, then 2 b 4ac − − is equal to –

A0 B1 C2 D3

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EnglishUP PCS (Pre) 2003

Q324.If the equations 2 x x m 0 + + = + + = + + = + + = l and 2 x mx 0 + + = + + = + + = + + = l have a common root, then the value of m l is–

A0 B–1 C1 D2

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EnglishUP PCS (Pre) 2004

Q325.The number of real roots of 2 x 3 x 2 0 are–

A1 B2 C3 D4

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EnglishUP PCS (Pre) 2004

Q326.If α, β are the roots of the equation x2 +x+1=0, then the equation whose roots are α19,β17 is–

A2/x x 1 0 B2/x x 1 0 C2/x x 1 0 D2/x x 1 0

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EnglishUP PCS (Pre) 2005

Q327.If α, β, γ are the roots of the equation x3 +x2 +2x+1 = 0, the value of (α–2 + β–2 + γ–2) is:

A4 B3 C0 D2

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EnglishUP PCS (Pre) 2005

Q328.If one root of 5x2 + 13x + k = 0 is reciprocal of the other, then k is equal to:

A0 B3 C2 D5

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EnglishUP PCS (Pre) 2005

Q329.If the roots of the equation x3 + 3ax2 + 3bx+c = 0 are in G.P., then:

Ab = a3 c Bb3 = a3 c Cb3 = ac3 Db = ac

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EnglishUP PCS (Pre) 2006

Q330.The domain of the function [ [ ] ] () ' 2 4 x f x x 2 − = + where [x] represent the greatest integer function, is

A(–∞,–1)∪[–1,2] B(–∞,–2)∪[0,2] C(–∞,–2)∪[–1,2] DNone of the above

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EnglishUP PCS (Pre) 2006

Q331.If () = + g x 1 x and () () = + + f g x 3 2 x x then f(x) is

A1+x B2+x C1+2x2 D2+x2

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EnglishUP PCS (Pre) 2006

Q332.If all the coefficients of the polynomial f(x) are positive, then the equation f(x)=0 does not have:

Aa repeated root Ba negative root Ca positive root Dan imaginary root

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EnglishUP PCS (Pre) 2007

Q333.if α, β are real numbers and β ≠ 0 and α + iβ is a root of the equation x3 + qx2 + r = 0, then one of the roots is

A–α + iβ B2 α – q C–2 α – q Dnone of the above

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EnglishUP PCS (Pre) 2007

Q334.If sum of two roots of the equation x4 – 8x3 + 19x2 + 4λ x + 2 = 0 is 4, the value of λ is

A–3 B3 C2 D–4

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EnglishUP PCS (Pre) 2007

Q335.If roots of the equation ax2 + bx + c = 0 are in the ratio r: 1, then the value of () 2 r r +1 is

Abc/a Bca/b C2 ca b D2 bc a

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EnglishUP PCS (Pre) 2008

Q336.The sum of the fourth powers of the roots of x4 –x3 –7x2 +x+6 = 0 is

A1 B15 C19 D99

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EnglishUP PCS (Pre) 2008

Q337.Which of the following sets is finite?

AThe set of lines parallel to the x-axis. BThe set of numbers which are multiples of 5. CThe set of numbers which are solution of the equation x27 +26x18 -17x11 +7x3 -10 = 0 DThe set of circles through the origin (0, 0)

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EnglishUP PCS (Pre) 2008

Q338.The number of solutions in the set of real numbers of the equation 2 x + 5 x + 6 = 0is

Azero Bfour Ctwo Dinfinitely many

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EnglishUP PCS (Pre) 2008

Q339.If the sum of the roots of the equation ax2 +bx+c = 0 is equal to the sum of their cubes then

Aa3 +b3 =c3 Ba2 +b2 =3ac Cb2 –a2 =3ac Da3 +b3 =a+b

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EnglishUP PCS (Pre) 2009

Q340.Which one of the following does not have a solution in the set of integers?

Ax+6=0 B2x+4=0 Cx2 –4=0 D3x+7=0

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