Math Chapter Wise

EnglishHaryana PGT 2019

Q41.If the curves x = y2 and xy = k intersect at right angle, then:

A8k2 = 3 B8k2 = 1 C8k2 = 5 D8k2 = –1

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EnglishUKPSC Lecturer (Mains) 2020

Q42.The maximum value of the function y = sin x (1 + cos x), 0 2π x ≤ is:

A3 3/4 B2 3/5 C3 3 D2

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EnglishUKPSC Lecturer (Mains) 2020

Q43.The semi-vertical angle of right circular cone of given surface area and maximum volume is:

A-1 2 sin 3 B-1 2 sin 3 C-1 3 sin 4 D-1 1 sin 3

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EnglishUKPSC Lecturer (Mains) 2020

Q44.Given that x + y = 20 and P = x2 y3. Then P is maximum when?

Ax= 6, y =14 Bx= 15, y =5 Cx= 12, y =8 Dx= 8, y =12

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EnglishUKPSC Lecturer (Mains) 2020

Q45.The minimum value of (5 +)(2 +) 1+ x x x is:

A4 B5 C9 D10

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EnglishUKPSC Lecturer (Mains) 2020

Q46.The absolute maximum of function g(t) =8t –t4 on the interval [–2, 1] is:

A0 B31/8 C–32 D7

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EnglishUP PCS (Pre) 1996 UKPSC Lecturer (Mains) 2020

Q47.If () () 2n 2m+1 dy = x – a. x – b dx, where n and m are positive integers and a > b, then which of the following is true for the function y?

AMaxima at x = a BMinima at x = a CMaxima at x = b DMinima at x = b

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EnglishTGT 2001

Q48.If xy = c2 then the maximum value of ax + by -

A2abc B2c ab C2c ab D2c abc

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EnglishUP PCS (Pre) 2001

Q49.A particle moves in a straight line according to the equation x=4t3 +2t+5 where x is in meters and t in seconds. The average acceleration of the 4th second is:

A84 meter/sec2 B96 meter/sec2 C194 meter/sec2 D110 meter/sec2

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EnglishHaryana PGT 2019

Q50.The point lying on y2 = 8x and at a minimum distance from x2 + (y + 6)2 = 1 will be

A(2, –4) B(2, 4) C(18, –12) D(8, 8)

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EnglishHaryana PGT 2019

Q51.If x is real, the maximum value of is:

A41 B1 C17/7 D1/4

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EnglishUK SSSC LT 2020

Q52.Slope of normal to the curve x = a cos3 θ, y = a sin3 θ at the point θ = π/4:

A1 B–1 C0 D3

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EnglishHaryana PGT 2020

Q53.Number of asymptotes of the curve x2 y2 = a2 (x2 + y2) is:

A3 B1 C4 D2

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EnglishHaryana PGT 2018

Q54.If the parametric equation of a curve is given by x = et cost, y = et sint, then the tangent to the curve at the point π t = 4 makes with the axis of x the angle:

Aπ B4/π C2/π D6/π

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EnglishHaryana PGT 2018

Q55.If f(x) = |x2 – 25| for all x ∈ R. The total number of points on R at which f attains a local extremum (minimum or maximum) is:

AFour BThree CTwo DOne

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EnglishHaryana PGT 2018

Q56.The function f defined by f(x) = x1/x has a maximum at:

Aloge2 Be C2 D1

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EnglishHaryana PGT 2018

Q57.The radii of curvature at the origin for the curve 3 3 x + y = 3axy are each equal to:

Aa/2 Ba/3 C2a/3 D3a/2

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EnglishHaryana PGT 2018

Q58.On the interval [0, 1] the function x25 (1 – x)75 takes its maximum value at the point:

A0 B1/3 C1/2 D1/4

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EnglishHaryana PGT 2018

Q59.The point of inflexion on the curve () 2 y = x x + 1 is:

A() 3, 2 3 ± B1 1, 3 2 2 ± C1 3, 2 2 2 ± D1 4, 3 2 3 ±

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EnglishUKPSC GIC 2018

Q60.The minimum value of 3x4 – 2x3 – 6x2 + 6x + 1 = 0 in the interval (0, 2) is

A1 B1/2 C2 D3

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