Math Chapter Wise

EnglishUP PCS (Pre) 2009

Q341.The number of real solutions of the equation sin (ex) = 5x +5–x, is

A0 B1 C2 D4

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EnglishUP PCS (Pre) 2009

Q342.If the equations x3 +ax+1=0 and x4 +ax2 +1=0 have a common root, then the value of a is

A2 B–2 C1 D–1

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EnglishUP PCS (Pre) 2009

Q343.The set of real numbers x, satisfying x – 1 3 and x –1 1,is

A[2, 4] B[–∝, 2]∪[4, ∝] C[–2, 0]∪[2, 4] D[–4, 0]∪[1, 4]

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English

Q344.If the roots of the cubic equation 2x3 –3x2 – 5x+3=0 are in A.P., then one of the roots is

A1 B2 C1/2 D1/3

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English

Q345.If α,β,γ are the roots of the equation px3 + qx2 + rx + s=0, then α2 +β2 +γ2 is equal to

A2 q 2rs p − B2 q 2pr p − Cq2/–2pr D2 2 q p 2r +

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English(GIC) Lecturer, 2015

Q346.If one root of the equation x2 +px+12 = 0 is 4, with the equation x2 +px+q = 0 has equal roots, then the value of q is

A49/4 B4/49 C4 DNone of above

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English(GIC) Lecturer, 2015

Q347.The number of real solutions of the equation 2 2 3 3 x – = 3 – x – 9 x – 9 is equal to

A0 B1 C2 D3

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English(GIC) Lecturer, 2015

Q348.If α and β are roots of the equation x2 –x+1=0, then α2016 + β2016 is equal to

A2 B1 C–1 D–2

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English(GIC) Lecturer, 2015

Q349.If one root is rd 1 3 of the other of the equation 2 2 3x (1 4k)x (k 5) 0, Then the value of k is–

A78/7 B79/7 C79/8 DNone of the above

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EnglishTGT 2013

Q350.If x+2 and z–1 are two factors of equation x3 +10x2 +mx+n=0 then what will be the value of m and n:

A5 and –3 B17 and –8 C7 and –18 D23 and –19

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EnglishTGT 2003, 2013

Q351.If the roots of the equation x3 –12x2 + 39x–28 = 0 are in A.P. then the common difference of A.P. will be:

A12 B–12 C39 D3

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EnglishTGT 2013

Q352.If (2+i) is a root of equation x2 – ax+1=0. Then the value of a is

A2 B4 C1 D8

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EnglishTGT 2013

Q353.The graph of a linear equation in two variable will be:

AA circle BEquation of line CA parabola DAn ellipse

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EnglishUP PCS (Pre) 1997, PGT 2013

Q354.If α, β,γ, δ are the roots of equation x4 +px2 +qx+k=0, then the value of the product (()))((()))((()))((())), α + β + γ α + γ + δ α + β + δ β + γ + δ α + β + γ α + γ + δ α + β + δ β + γ + δ α + β + γ α + γ + δ α + β + δ β + γ + δ α + β + γ α + γ + δ α + β + δ β + γ + δ is

Ak B–k Cq D–q

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EnglishUP PCS (Pre) 1997, PGT 2013

Q355.The equation f(x)=x3 –x2 –8x+12=0 has double root α, then α is a root of:

Af"(x) = 0 Bf'(x)=0 Cf(x)+f"(x)=0 Dfx(x)+10=0

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EnglishUP PCS (Pre) 1997

Q356.The roots of the equation 3 2 x px qx r 0 + + + = + + + = + + + = + + + = are α, β and γ. The value of αβ + βγ + γαβ + βγ + γαβ + βγ + γαβ + βγ + γα is:

A–p Bq Cc DNone of these

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EnglishTGT 2010

Q357.Σ Σa2 (b–c) is equal to

Aa2 b – a2 c Ba2 b – a2 c–ab Ca2 (b– c) + b2 (c – a) + c2 (a – b) Da2 (b– c) + b2 (b –c) c2 (b– c)

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EnglishTGT 2010

Q358.If the roots of equation 2x2 + kx – 8 = 0 are equal and of opposite sign, then the value of k is.

A0 B– 2 C4 D8

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EnglishTGT 2010

Q359.If the sum of two roots of equation. x3 – 5x2 – 16x + 80 = 0 be zero, then all the roots are

A4, –4, 5 B5, –5, 4 C6,–6, 5 DNone of these

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EnglishTGT 2010

Q360.If α, β are the roots of the equation ax2 + bx + c = 0, then the equation, whose roots are 1 1 1, + + α + β α β α + β α β α + β α β α + β α β is

Aabx2 + (c2 + ab) x+ca = 0 Bacx2 + (a2 + b2) x+ bc = 0 Cbcx2 + (b2 + ac) x+ab = 0 DNone of these

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