Math Chapter Wise

EnglishKVS TGT 2017

Q21.1 2 d 1 (cos x) dx 1 x Where –

A1 x 1 B1 x 1 C1 x 1 D1 x 1/− < ≤

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EnglishKVS TGT 2017

Q22.The normal to a given curve is parallel to x– axis if–

Ady 0 dx Bdy 1 dx Cdx 1 dy Ddx 0 dy

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EnglishOPSC PGT 2017

Q23.Pole of a function is a point where the function becomes:

AMaximum BZero CUnbounded DDiscontinuous

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EnglishUP TGT 2021

Q24.The minimum value of 4 cosθ + 3 is

A–3 B–1 C0 D1

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EnglishUP TGT 2021

Q25.The angle of intersection of the curves y = 4 – x2 and y = x2 is

A–1 2 tan 7 B–1 4 2 tan 7 C–1 3 2 tan 7 D2/π

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EnglishUPPSC Polytechnic Lecturer 2021 (I)

Q26.The shortest distance between the parabola y=x2 and the straight line x–y=5 is-

A19 2 B2/8 C19/8 D19 2/8

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EnglishUP PGT 2021

Q27.The radius of curvature of the curve s = a log tan π ψ + 4 2 is –

Aa tanψ Ba secψ Ca sec2/ψ Da secψ tanψ

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EnglishUP PGT 2021

Q28.If the normal to curve y = f(x) at the point (a, b) makes an angle 3 4 π with the positive x axis then f'

A1 B–1 Ca/b Db/a

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EnglishUP PGT 2021

Q29.The line y = mx + 1 is a tangent to the parabola y2 = 4x, if

Am = 1 Bm = 2 Cm = –1 Dm = –2

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EnglishUP PGT 2021

Q30.Asymptotes of the curve x2 y2 = a2 (x2 + y2) are–

Ax = 0, y = 0 Bx = ± a, y = 0 Cx = 0, y = ± a Dx = ± a, y = ± a

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EnglishUP PGT 2021

Q31.If y = 4x – 5 is equation of the tangent to a curve y2 = ax3 + b at (2, 3), then (a, b) is equal to

A(2, 7) B(2, –7) C(–2, 7) D(–2, –7)

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EnglishUP PGT 2021

Q32.Sum of maximum and minimum values of 4(sin2 θ + cos4 θ) is

A3 B4 C5 D7

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EnglishUP PGT 2009 UPPSC GIC 2021

Q33.The function sinp θ cosq θ attains its maximum value, when-

A1 tan p / q − θ = B1 tan q / p − θ = C() 1 tan p / q − θ = D() 1 tan q / p − θ =

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EnglishUPPSC GIC 2021 UPPSC Ashram Paddhati 2021

Q34.When we expand sin 4 π θ + in powers of θ, the coefficient of 3 3! θ is-

A−1/2 B1/2 C−1/2 D1/2

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EnglishUP TGT 2021

Q35.If x is a real number, then the function f(x) = x3 + x2 + x + 1 has

Amaximum value at x = 0 Bminimum value at x = 1 Cmaximum value at x = –1 Dneither maximum nor minimum value

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EnglishUP TGT 2021

Q36.The tangent to the curve 2 3 2 2 2at 2at x =,y = 1+ t 1+ t at the point for which 1 t = 2, is

A13x – 16y = 2a B13x + 16y = 2a C13x – 8y = 4a D13x + 8y = 4a

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EnglishUP TGT 2021

Q37.For all real x, the minimum value of 2 1 – x + x 1+ x + x is

A0 B1/3 C1 D3

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EnglishUP TGT 2021

Q38.The point on the curve y2 = x, the tangent at which makes an angle π 4 with x- axis, is

A1 1 –, 4 2 B1 1, 4 2 C1 1 –,– 4 2 D1 1,– 4 2

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EnglishUP PGT 2011 UPPSC Ashram Paddhati 2021

Q39.If the function f(x) = a sinx + 1 3 sin3x has maximum value at x = π 3, the value of a is

A3 B1/3 C2 D1/2

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EnglishUPPSC Ashram Paddhati 2021 LT 2018

Q40.The equation of the tangent to the curve x = a(θ + sinθ), y = a(1 + cosθ) at the point θ = π 2, is

A2(x + y) = a(π + 4) B2(x – y) = a(π + 4) Cx + y = 0 Dx + y = aπ

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