Math Chapter Wise

EnglishUP PGT 2004,2016 UKPSC GIC 2018 Rajsthan TGT 2013

Q61.If the line ax + by + c = 0 is normal to the curve xy = 1, then

Aa > 0, b > 0 Ba >0, b < 0 Ca < 0, b < 0 DNone of these

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EnglishUKPSC GIC 2018

Q62.If the tangent to the curve 3y3 = kx2 + x3 at the point k k, 2 2 passes through the point (1, 1), then the value of k is

A0 B1 C–1 D2

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EnglishNVS PGT 10-06-2019

Q63.If A is the area formed by the positive x-axis, and the normal and tangent to the circle x2 + y2 = 4 at (((()))) 1, 3, then A 3 equals:

A4 B2 C2/3 D1

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EnglishNVS PGT 10-06-2019

Q64.If a, b, c are non-negative real numbers, then the minimum value of a b c b c c a a b + + + + + + + + + + + + + + is

A3/2 B1 C2 D5/2

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EnglishKVS PGT 23-12-2018

Q65.If the curve 2 ay x 7 + = + = and 3 x y =, cut orthogonally at (1,1), then the value of a is:

A1 B0 C6 D–6

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EnglishKVS PGT 23-12-2018

Q66.f(x) sinx cos2x,(x 0) = + > = + > = + > = + > has minima for x=

An 2 π B() 3 n 1 2 + π C() 2n 1 2 + π Dnπ

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EnglishKVS PGT 23-12-2018

Q67.The equation of the tangent at the point P(t), where t is any parameter, to the parabola 2 y 4ax = is:

A2 y xt at = + B2 yt x at = + Cy tx = Da y tx t = +

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EnglishUP PGT-2016 (02-02-2019)

Q68.If line ax+by+c=0 is a normal to the curve xy=4, then

Aa< 0, b < 0 Ba > 0, b > 0 Ca > 0, b < 0 Da < 0, b = 0

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EnglishUP PGT-2016 (02-02-2019)

Q69.Maximum value of the function 2 1 2x x f(x) 3 + − + − = is equal to

A3 B9 C27 D81

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EnglishUP PGT-2016 (02-02-2019)

Q70.If 2y=x+3 is a tangent line to the curve y3 = ax2 +b at the point (1,2), then 3b–5a is equal to

A0 B2 C3 D4

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EnglishUP PGT-2016 (02-02-2019)

Q71.The least possible value of 'a' for which the function f(x)=x2 +ax+1 may be increasing in the interval [1, 2] is

A2 B1 C0 D–2

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EnglishLT 2018

Q72.If a hyperbola, whose parametric equations are x=ct, c y, t = meets any circle with centre at (0,0) in our points, determined by the parametric values t1, t2, t3 and t4, then the value of t1.t2.t3.t4 is

Ac2 B–c2 C–1 D1

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EnglishLT 2018

Q73.If x+2y=8, then the maximum value of xy is

A20 B16 C24 D8

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EnglishLT 2018

Q74.The equation of the tangent at 2 π θ = θ = to the curve ((())) ((()) x a sin,y a 1 cos = θ + θ = + θ = θ + θ = + θ = θ + θ = + θ = θ + θ = + θ is

Ax y a 2 2 π − = + Ba x y 2 π − = Cx y a 2 2 π + = + Da x y 2 π + =

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EnglishDSSSB TGT (SECTION-B) 28 DEC 2014

Q75.The function y= f(x) has a relative minima where

Af(x) 0 and f (x) 0 Bf (x) 0 andf (x) 0 Cf (x) 0 andf (x) 0 Df (x) 0 and f (x) 0

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EnglishDSSSB TGT (SECTION-B) 28 DEC 2014

Q76.The local maximum values of the function 4 3 2 f(x) 3x 4x 12x 2 = + − + = + − + = + − + = + − + are

A1 B2 C–2 D0

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EnglishSECTION B PGT TIER-I 31.11.2014

Q77.The maximum value of sin x + cos x is–

A2 B1 C2 D0

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EnglishSECTION B PGT TIER-I 31.11.2014

Q78.Which of the following function is decreasing on 0, 2?

Asin 2x Btan x Ccos x Dcos 3x

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EnglishSECTION B PGT TIER-I 31.11.2014

Q79.The two curves 3 2 x 3xy 2 0 and 2 3 3x y y 2 − =

Atouch each other Bcut at right angle Ccut at an angle π/3 Dcut at an angle π/4

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EnglishSECTION B PGT TIER-I 31.11.2014

Q80.If x is real, the minimum value of 2 x 8x 17 is

A–1 B0 C1 D2

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