Math Chapter Wise

EnglishUPPSC GDC 2021

Q21.The order of the differential equation- 2 x x x ∆ y + 3∆y – 3y = x, is

A1 B2 C3 D4

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EnglishUPPSC GDC 2021 UKPSC Lecturer (Mains) 2020

Q22.The rate of convergence of Newton-Raphson method is:

ACubic BFourth order CLinear DQuadratic

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EnglishUP Higher Asst. Prof. 2021

Q23.Using Runge-Kutta method of order 4 for the following initial value problem () 2 2 dy x y,y 1 0 dx = + = the value of y(1.1) shall be

A0.110 B0.117 C0.119 D0.101

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EnglishUP Higher Asst. Prof. 2021

Q24.Using Euler's modified method. the value of y(0.02) for the differential equation () 2 dy x y,y 0 1 dx = + = and taking h = 0.01 is.

Ay(0.02) = 1.2020 By(0.02) = 1.0250 Cy(0.02) = 1.0201 Dy(0.02) = 1.0203

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EnglishUP Higher Asst. Prof. 2021

Q25.Solution of the initial value problem u' = –2tu2 u(0) = 1 with h = 0.2 on the interval [0, 1] is

Au(0.2)= u1= 0.8615241 Bu(0.2)= u1= 0.7615241 Cu(0.2)= u1= 0.9615241 Du(0.2)= u1= 0.5615241

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EnglishUPPSC GDC 2021

Q26.If y (0) = 3, y (1) = 10, y(2) = 18, y(3) = 30 and y(4) = 50, then value of ∆ ∆ ∆4 y(0) is

A0 B– 1 C1 D2

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EnglishUPPSC GDC 2021

Q27.If n is an integer, then the value of Pn (– 1), where Pn (x) denotes Legendre's polynomial, is

A0 B(– 1)n C1 Dn 1 2 n

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EnglishUPPSC GDC 2021

Q28.Simpson's three-eighth rule of integration can be applied when the range of integration [a, b] is divided into a number of subintervals which must be multiple of

A2 B3 C4 D8

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EnglishUPPSC GDC 2021

Q29.Which relation is NOT correct?

A() () E 1 2 E 1 + δ = µ − B2 1 4 δ µ = + C1/ 2 E µ + δ = D1/2 E δ = ∇

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EnglishUPPSC GDC 2021

Q30.Let f1(x) = 4, f2(x) = x3 and f3 (x) = 1 + Ax + Bx2. If f3 (x) is orthogonal to f1 (x) and f2 (x) on the interval (–2, 2). Then

AA = 0, B = 1 BA = 0, B = 0 CA = 0, B = 3 4 DA = 0, B = – 3 4

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EnglishUPPSC GDC 2021

Q31.If Pn(x) denotes Legendre's polynomial, then the value of P'n+1 (x) – xP'n(x) is equal to

A(n + 1) Pn (x) Bn2 CPn(x) DP'n(x)

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EnglishUKPSC Lecturer (Mains) 2020

Q32.Solution of L.P.P.: Max. z = 3x1 + 4x2 Subject x1 –x2 ≤–1 –x1 + x2≤0 and x1, x2≥0 is:

Ax1 = 2, x3 = 3 Bx1 = 1, x2 = 2 Cx1 = 0, x2 = 1 DNon-existent

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EnglishUKPSC Lecturer (Mains) 2020

Q33.For a set of two linear equations with four variables, the maximum number of basic solutions is:

A2 B4 C6 D8

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EnglishUK SSSC LT 2020

Q34.The value of ((()) 2 3 x E ∆ is:

A2x B3x C4x D6x

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EnglishUK SSSC LT 2020

Q35.Which of the following option is correct for the relationship between E and ∇ ∇ ∇?

AE–1/≡ 1 – ∇ BE ≡ 1 + ∇ CE–1/≡ 1 + ∇ DNone of the above

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EnglishUKPSC GIC 2018

Q36.If f(x) be a polynomial of degree n in x, then which is correct?

A∆n f(x) = 0 B∆n+1 f(x) = 0 C∆n–1 f(x) = 0 DNone of these

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EnglishUKPSC GIC 2018

Q37.The missing value in the following table: x: 0 1 2 3 4 y: 1 3 9 - 81

A35 B31 C30 D27

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EnglishUKPSC GIC 2018

Q38.The value of 2 x x 2 x ∆ Ee e. E ∆ e is

Aex Be–x Cex+h Dex–h

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EnglishUKPSC GIC 2018

Q39.Which of the following interpolation formula can be used for equal and unequal intervals?

ANewton-Gregory formula BBessel's formula CSterling's formula DLagrange's formula

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EnglishUKPSC Lecturer (Mains) 2020 UKPSC GIC 2018

Q40.The cubic polynomial which takes the following values: x: 0 1 2 3 f(x): 1 2 1 10

Ax3 – 7x2 + 7x + 1 Bx3 + 7x2 + 6x + 1 C2x3 – 7x2 + x + 1 D2x3 – 7x2 + 6x + 1

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