Math Chapter Wise

EnglishTGT 1999

Q21.The chord of Curvature of the Curve P = f (r) (Polar form).

Af (r) Bf(r)/f '(r) C2f(r)/f '(r) D2f '(g)f '(r)

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EnglishPGT 2003

Q22.Find the position of the centroid of the arc of the semi–cardioid r=a (1+cos θ)

A, 5 5 a a B2 2, 5 5 a a C3 3, 5 5 a a D4 4, 5 5 a a

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EnglishPGT 2002

Q23.The length of the normal at the point (x, y) the curve x x a a 1 y a e e 2 − = + is:

A2 x acos a B2 x asin a C2 x asinh a D2 x acosh a

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EnglishPGT 2000

Q24.The value of the integral (((()))) 1 1 2 2 0 0 x y dxdy + ∫ ∫ ∫ ∫ is equal to:

A2/3 B0 C1/2 D1/3

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EnglishPGT 2000

Q25.The value of 2 1 1 1 x 0 y 0 xdzdxdy − ∫ ∫ ∫ ∫ ∫ ∫ ∫ ∫ ∫ ∫ ∫ ∫ is:

A8/35 B6/35 C3/35 D4/35

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EnglishRajasthan TGT 2015

Q26.If V is the region bounded by x 0, ≥ y 0, ≥ z 0, ≥ x y z 1, + + ≥ + + ≥ + + ≥ + + ≥ then 1 m 1 n 1 V x y z − − − − − − − − − − − − ∫ ∫ ∫ ∫ ∫ ∫ ∫ ∫ ∫ ∫ ∫ ∫ l dx dy dz is equal to

Am n (m n) l l + + Bm n (m n 1) l l + + − Cm n (m mn n) l l l + + Dm n m n) (m n) l l l + + + +

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EnglishRajasthan TGT 2015

Q27.Statement of Stoke's theorem is

AC S. ˆ F dr n.(F)dS = ∇ × ∫ ∫∫ BC S. ˆ (F) dr n.FdS ∇× = ∫ ∫∫ CC S. ˆ (F)dr n.FdS ∇ = ∫ ∫∫ DC S.. F dr (F) dS = ∇ × ∫ ∫∫

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EnglishRajasthan TGT 2013

Q28.For the curve y = f(x), curvature is equal to–

A3 2 2 2 2 dy d y 1 dx dx + B3 2 2 dy d y 1 dx dx + C() 3 2 2 2 2 dy d y dx 1 dx + D() 3 2 2 2 dy d y dx 1 dx +

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EnglishTGT 2011

Q29.The volume generated by rotating the arc 2 y 1 x = + = + enclosed between x = 0 and x = 4 around the x-axis is -

A8 3 π B49 3 π C65 3 π D76 3 π

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EnglishUP PCS (Pre) 1998

Q30.If the angle between the radius vector and the tangent at any point (r, θ) on the curve r = f (θ) is denoted by φ, then:

Adr cot r d φ = θ Bd cot r dr θ φ = Cd tan r dr θ φ = Ddr tan r d φ = θ

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EnglishUP PCS (Pre) 1994

Q31.The radius of curvature of the curve x y e at (0,1) is–

A2 B2 2 C1/2 D1/2 2

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EnglishUP PCS (Pre) 1995

Q32.For the curve r = f (θ) of the length of the polar sub-length at the point (r,θ) is–

A2 d r dr Bdr/d Cd r dr D1 d/r dr

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EnglishUP PCS (Pre) 1995

Q33.The value of the radius of curvature of the curve s = 4 a sin ψ ψ ψ at the (s, ψ ψ ψ) is–

A4a cos B4a sec C1 sec 4 D1 cos 4a

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EnglishUP PCS (Pre) 1995

Q34.If the area bounded by the curve y = f(x), x-axis and ordinates x = a, x = b is revolved about the x- axis then the volume generated is–

Ab 2 a x dy Bb 2 a y dx Cb a ds 2 y dx dx Db a ds 2 y dy dy

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EnglishUP PCS (Pre) 1996

Q35.2 2 x y 1 a b is revolved about its major and minor axes in turn. The ratio of the volumes of the solids of revolution thus obtained is:

Ab/a Ba/b C1 De/2

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EnglishUP PCS (Pre) 1996

Q36.The curve y = 4sinx – sin 2x at x = π/2, has value of ρ:

A5 5/4 B5/2 C5/4 DNone of these

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EnglishUP PCS (Pre) 1999

Q37.The radius of curvature of the curve y = x4 –4x3 –18x2 at (0, 0) is

A1/12 B1/24 C1/36 D1/48

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EnglishUP PCS (Pre) 2000

Q38.The length of the arc of the cycloid x = a (θ – sin θ), y = a (θ + cos θ) from θ = 0 to θ = 4π, is:

A4a B8a C16a D0

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EnglishUP PCS (Pre) 2000

Q39.The surface of the solid formed by the revolution about x-axis of the loop of the curve x = t2, 3 1 y t t 3 = − = − is:

Aπ B2π C3π D4π

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EnglishUP PCS (Pre) 2000

Q40.The area of the curve r = p (1 + cos θ) is:

A8p B1 p 2 π C3 p π D2 3 p 2 π

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