Q21. The order of the differential equation- 2 x x x ∆ y + 3∆y – 3y = x, is
A 1
B 2
C 3
D 4
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Correct answer: 2
English UPPSC GDC 2021 UKPSC Lecturer (Mains) 2020
Q22. The rate of convergence of Newton-Raphson method is:
A Cubic
B Fourth order
C Linear
D Quadratic
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Correct answer: Quadratic
English UP 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
A 0.110
B 0.117
C 0.119
D 0.101
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Correct answer: 0.110
English UP 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.
A y(0.02) = 1.2020
B y(0.02) = 1.0250
C y(0.02) = 1.0201
D y(0.02) = 1.0203
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Correct answer: y(0.02) = 1.0201
English UP 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
A u(0.2)= u1= 0.8615241
B u(0.2)= u1= 0.7615241
C u(0.2)= u1= 0.9615241
D u(0.2)= u1= 0.5615241
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Correct answer: u(0.2)= u1= 0.9615241
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
A 0
B – 1
C 1
D 2
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Correct answer: 1
Q27. If n is an integer, then the value of Pn (– 1), where Pn (x) denotes Legendre's polynomial, is
A 0
B (– 1)n
C 1
D n 1 2 n
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Correct answer: (– 1)n
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
A 2
B 3
C 4
D 8
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Correct answer: 3
Q29. Which relation is NOT correct?
A () () E 1 2 E 1 + δ = µ −
B 2 1 4 δ µ = +
C 1/ 2 E µ + δ =
D 1/2 E δ = ∇
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Correct answer: 1/ 2 E µ + δ =
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
A A = 0, B = 1
B A = 0, B = 0
C A = 0, B = 3 4
D A = 0, B = – 3 4
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Correct answer: A = 0, B = – 3 4
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)
B n2
C Pn(x)
D P'n(x)
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Correct answer: (n + 1) Pn (x)
English UKPSC 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:
A x1 = 2, x3 = 3
B x1 = 1, x2 = 2
C x1 = 0, x2 = 1
D Non-existent
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Correct answer: Non-existent
English UKPSC Lecturer (Mains) 2020
Q33. For a set of two linear equations with four variables, the maximum number of basic solutions is:
A 2
B 4
C 6
D 8
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Correct answer: 6
Q34. The value of ((()) 2 3 x E ∆ is:
A 2x
B 3x
C 4x
D 6x
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Correct answer: 6x
Q35. Which of the following option is correct for the relationship between E and ∇ ∇ ∇?
A E–1/≡ 1 – ∇
B E ≡ 1 + ∇
C E–1/≡ 1 + ∇
D None of the above
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Correct answer: E–1/≡ 1 – ∇
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
D None of these
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Correct answer: ∆n+1 f(x) = 0
Q37. The missing value in the following table: x: 0 1 2 3 4 y: 1 3 9 - 81
A 35
B 31
C 30
D 27
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Correct answer: 31
Q38. The value of 2 x x 2 x ∆ Ee e. E ∆ e is
A ex
B e–x
C ex+h
D ex–h
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Correct answer: ex
Q39. Which of the following interpolation formula can be used for equal and unequal intervals?
A Newton-Gregory formula
B Bessel's formula
C Sterling's formula
D Lagrange's formula
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Correct answer: Lagrange's formula
English UKPSC 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
A x3 – 7x2 + 7x + 1
B x3 + 7x2 + 6x + 1
C 2x3 – 7x2 + x + 1
D 2x3 – 7x2 + 6x + 1
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Correct answer: 2x3 – 7x2 + 6x + 1