Math Chapter Wise

EnglishRPSC PGT 2022

Q01.Value of integral ∫ ∫ 2 y 1 x x 0 0 1 e dxdy x is -

Ae Be –1 Ce – 2 D∞

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EnglishRPSC PGT 2022

Q02.The point on the curve y = x3 –3x + 2, where tangent is perpendicular to line y = 1 x, 3 is-

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

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EnglishRPSC PGT 2022

Q03.Double point of the curve x3 – y2 – 7x2 + 4y + 15x – 13 = 0 is-

A5, 2 3 − B() 3,2 C(3, 2) D(2, 3)

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EnglishDSSSB PGT 2021

Q04.The rate at which the radius of a sphere changes over time is 1 2π. When the radius is 5 cm, then the rate of change of the lightning surface area of the sphere will be:

A20 cm2//sec B10 cm2//sec C15 cm2//sec D5 cm2//sec

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EnglishDSSSB PGT 2021

Q05.The arm length of an equilateral triangle increases at a rate of 3 cm/sec. When the length of arm is 10 cm, then the area of triangle will increase by-

A10 cm2//sec B20 cm2//sec C15 cm2//sec D25 cm2//sec

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EnglishDSSSB PGT 2021

Q06.A particle moving in a straight line has displacement x feet in t second, where x = t3 +6t2 +15t. Then at the end of first second the velocity and acceleration of the particle will be-

A20 feet/sec2/and 12 feet/sec2 B30 feet/sec2/and 18 feet/sec2 C20 feet/sec2/and 18 feet/sec2 D30 feet/sec2/and 12 feet/sec2

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EnglishDSSSB PGT 2021

Q07.The arm length of a cube is 10 cm. If the error in measuring the length of arm is 0.08 cm, the approximate value of the error in the volume of the cube will be:

A24 cm3 B15 cm3 C8 cm3 D12 cm3

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EnglishDSSSB PGT 2021

Q08.The volume of a gas V = 600 P varies with the pressure according to Boyle's Law. If the pressure increases from P = 20 to P = 20.5, then the rate of change of volume with pressure will be:

A–1.42 B–1.44 C–1.45 D–1.46

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EnglishDSSSB PGT 2021

Q09.Let y2 = 4x be the coordinates of particle moving over an ellispe at a point where the growth rate of the ground is twice, then the rate of the Y-axis is

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

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EnglishJSSC PGT 2018

Q10.Revolving the circular area of radius 'R' through 360° ° ° about the x-axis, a complete torus is generated. The distance between the centre of the circle and the x-axis is 'd'. Then the surface area of the torus is:

A3π2/Rd B4π2/Rd Cπ2/Rd D2π2/Rd

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EnglishJSSC PGT 2018

Q11.Find the volume of the solid bounded by the following ellipsoid. 2 2 2 x y z + + = 1 4 9 49

A124 B176 C248 D312

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EnglishOPSC PGT 2017

Q12.What is the length of an arc of the curve y = 1– In (cos x) intercepted between x = 0 and x = π/4

AIn(2 1) BIn(2 2) C1 in 2 DNone of these

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EnglishDSSSB TGT 04-09-2021 Shift-I (Male)

Q13.Calculate the volume of sphere by triple integration?

A(8a3/π ) ÷ 3 B(4a3/π ) ÷ 3 C(2a3/π ) ÷ 3 D(a3/π ) ÷ 3

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EnglishHaryana PGT 2020

Q14.The volume of the solid generated by the revolution of the cardioid r = a (1 + cos θ) about the initial line is equal to:

A2πa3 B3 2 a 3 π C3 4 a 3 π D3 8 a 3 π

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EnglishUP PCS (Pre) 1997

Q15.The curvature of the curve xy = a2 at the point (a,a) is:

A5/2 1 2 a B3/ 2 1 2 a C1/2a D5/ 2/2 a

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EnglishUP PCS (Pre) 1997

Q16.The order and degree of the differential equation: 3/ 2 2 dy 1 dx r d y dx + =

A2,2 B2,6 C2,3 D1,6

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EnglishUP PCS (Pre) 1997

Q17.If a curve is given by rational algebraic equation, the tangents at the origin are obtained by:

AEquating to zero the highest degree terms BEquating to zero the lowest degree terms CEquating the coefficients of highest degree terms of x to zero DEquating to zero the coefficients of lowest degree terms of y

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EnglishUP PCS (Pre) 1997

Q18.The Cartesian formula for the radius of curvature is:

A3/ 2 2 dy 1 dx d y dx + ρ = B3/ 2 2 dy 1 dx d y dx − ρ = C2/3 2 dy 1 dx d y dx + ρ = DNone of these

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EnglishUP TGT-2016 (08-03-2019)

Q19.The centre of gravity of a semi-circular disc of radius 'a' is

A2a,0 π B3a,0 4 π C4a,0 3 π Da a, 2 2

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EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q20.(m,n) β =

A(m) (n) (mn) Γ + Γ Γ B(m) (n) (m n) Γ Γ Γ + C(m). (n) (m n) Γ Γ Γ − DNone of these

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