Math Chapter Wise

EnglishHaryana PGT 2019

Q41.A normal to y = (x–1)2 at x = 2 also passes through the point:

A(0, 4) B(0, 0) C(4, 0) D(1, 2)

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EnglishUKPSC Lecturer (Mains) 2020

Q42.The angle between the curves 6y = –x2 + 7 and y = x3 is:

Aπ / 4 Bπ /3 Cπ / 2 Dπ

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EnglishHaryana PGT 2019

Q43.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

Q44.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

Q45.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

Q46.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

Q47.The minimum value of (5 +)(2 +) 1+ x x x is:

A4 B5 C9 D10

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EnglishUKPSC Lecturer (Mains) 2020

Q48.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

Q49.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

Q50.If xy = c2 then the maximum value of ax + by -

A2abc B2c ab C2c ab D2c abc

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EnglishTGT 2004

Q51.The slope of the tangent to the curve represented by x=t2 +3t–8 and y=2t2 –2t–5 at the point (2,–1) is

A7/6 B6/7 C8/5 D– 1 2

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EnglishUP PCS (Pre) 1997

Q52.The orthogonal trajectories of the family of curves xy=c2 are:

A2 2 2 2x 3y a − = B2 2 2 2x 3y a + = C2 2 2 x y a + = D2 2 2 x y a − = Where a is a constant

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EnglishUP PCS (Pre) 2001

Q53.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

Q54.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

Q55.If x is real, the maximum value of is:

A41 B1 C17/7 D1/4

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EnglishUK SSSC LT 2020

Q56.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

Q57.Number of asymptotes of the curve x2 y2 = a2 (x2 + y2) is:

A3 B1 C4 D2

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EnglishHaryana PGT 2018

Q58.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

Q59.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

Q60.The function f defined by f(x) = x1/x has a maximum at:

Aloge2 Be C2 D1

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