20 + Interview Questions in NUMERICAL METHODS IN GENERAL AWARENESS Page 1 InterviewSolution

1.	E is a _____(a) shifting operator (b) Displacement operator (c) 1 + ∆ (d) all of these (e) none of these
Answer» (d) all of these

Discussion

2.	For the given points (x0 , y0 ) and (x1, y1 ) the Lagrange’s formula is ______(a) y(x) = (x - x1)/(x0 - x1)y0 + (x - x0)/(x1 - x0)y1(b) y(x) = (x1 - x)/(x0 - x1)y0 + (x - x0)/(x1 - x0)y1(c) y(x) = (x - x1)/(x0 - x1)y1 + (x - x0)/(x1 - x0)y0(d) y(x) = (x1 - x)/(x0 - x1)y1 + (x - x0)/(x1 - x0)y0
Answer» (a) y(x) = (x - x₁)/(x₀ - x₁)y₀ + (x - x₀)/(x₁ - x₀)y₁

Discussion

3.	∇ f(a) = ______ (a) f(a) + f(a – h) (b) f(a) – f(a + h) (c) f(a) – f(a – h) (d) f(a)
Answer» (c) f(a) – f(a – h)

Discussion

4.	If f(x) = x2 + 2x + 2 and the interval of differencing is unity then ∆ f(x) _______ (a) 2x – 3 (b) 2x + 3 (c) x + 3 (d) x – 3
Answer» (b) 2x + 3 f(x) = 2x² + 2x + 2 h = 1 ∆f(x) = (x + 1)² + 2(x + 1) + 2 – x² – 2x – 2 = x² + 2x + 1 +2x + 2 + 2 – x² – 2x – 2 = 2x + 3

4.

If f(x) = x2 + 2x + 2 and the interval of differencing is unity then ∆ f(x) _______ (a) 2x – 3 (b) 2x + 3 (c) x + 3 (d) x – 3

Answer»

(b) 2x + 3

f(x) = 2x² + 2x + 2

h = 1

∆f(x) = (x + 1)² + 2(x + 1) + 2 – x² – 2x – 2

= x² + 2x + 1 +2x + 2 + 2 – x² – 2x – 2

= 2x + 3

Discussion

5.	If h = 1 then prove that (E-1 ∆) x3 = 3x2 – 3x + 1.
Answer» h = 1 To prove (E^-1 ∆) x³ = 3×2 – 3x + 1 L.H.S = (E^-1 ∆) x³ = E^-1 (∆x³ ) = E^-1 [(x + h)³ – x³ ] = E^-1 ( x + h)³ – E^-1 (x³) = (x – h + h)³ – (x – h)³ = x³ (x – h)³ But given h = 1 So(E^-1 ∆) x³ = x³ - (x – 1)³ = x³ – [x³ - 3x² + 3x – 1] = 3x² – 3x + 1 = RHS

5.

If h = 1 then prove that (E-1 ∆) x3 = 3x2 – 3x + 1.

Answer»

h = 1

To prove (E^-1 ∆) x³ = 3×2 – 3x + 1

L.H.S = (E^-1 ∆) x³ = E^-1 (∆x³ )

= E^-1 [(x + h)³ – x³ ]

= E^-1 ( x + h)³ – E^-1 (x³)

= (x – h + h)³ – (x – h)³

= x³ (x – h)³

But given h = 1

So(E^-1 ∆) x³ = x³ - (x – 1)³

= x³ – [x³ - 3x² + 3x – 1]

= 3x² – 3x + 1

= RHS

Discussion

6.	If c is a constant then ∆c = ______ (a) c (b) ∆ (c) ∆2(d) 0
Answer» The correct answer is : (d) 0

Discussion

7.	If h = 1, then ∆(x2) = ________ (a) 2x (b) 2x – 1 (c) 2x + 1(d) 1
Answer» (c) 2x + 1 ∆(x² ) = (x + h)²– x² = (x + 1)² – x² = 2x + 1

7.

If h = 1, then ∆(x2) = ________ (a) 2x (b) 2x – 1 (c) 2x + 1(d) 1

Answer»

(c) 2x + 1

∆(x² ) = (x + h)²– x² = (x + 1)² – x² = 2x + 1

Discussion

8.	∇ = _______ (a) 1 + E (b) 1 – E (c) 1 – E-1 (d) 1 + E-1
Answer» The correct answer is : (c) 1 – E^-1

Discussion

9.	Evaluate (log ax)
Answer» \(\triangle\)log ax = log a a (x + h) - log ax = log [a(x + h)/ax] = log(1 + h/x)

9.

Evaluate (log ax)

Answer»

\(\triangle\)log ax = log a a (x + h) - log ax

= log [a(x + h)/ax]

= log(1 + h/x)

Discussion

10.	E = ______ (a) 1 + ∆ (b) 1 – ∆ (c) 1 + ∇ (d) 1 – ∇
Answer» (a) 1 + Δ E = 1 + ∆

10.

E = ______ (a) 1 + ∆ (b) 1 – ∆ (c) 1 + ∇ (d) 1 – ∇

Answer»

(a) 1 + Δ

E = 1 + ∆

Discussion

11.	E f(x) = _______ (a) f(x – h) (b) f(x) (c) f(x + h) (d) f(x + 2h)
Answer» (c) f(x + h)

11.

E f(x) = _______ (a) f(x – h) (b) f(x) (c) f(x + h) (d) f(x + 2h)

Answer»

(c) f(x + h)

Discussion

12.	If m and n are positive integers then ∆m ∆n f(x) = _______ (a) ∆m + n f(x) (b) ∆m f(x)(c) ∆n f(x) (d) ∆m - n f(x)
Answer» The correct answer is : (a) ∆^{m + n}f(x)

Discussion

13.	E-n f(x) is ______ (a) f(x + nh) (b) f(x – nh)(c) f(-nh) (d) f(x – n)
Answer» The correct answer is : (b) f(x – nh)

Discussion

14.	If f(x) = x2 + 3x then show that ∆f(x) = 2x + 4
Answer» f(x) = x² + 3 x ∆f(x) = f(x + h) – f(x) = (x + h)² + 3(x + h) – x² – 3x = x² + 2xh + h² + 3x + 3h – x² – 3x = 2xh + 3h + h² Put h = 1, ∆f(x) = 2x + 4

14.

If f(x) = x2 + 3x then show that ∆f(x) = 2x + 4

Answer»

f(x) = x² + 3 x

∆f(x) = f(x + h) – f(x)

= (x + h)² + 3(x + h) – x² – 3x

= x² + 2xh + h² + 3x + 3h – x² – 3x

= 2xh + 3h + h²

Put h = 1, ∆f(x) = 2x + 4

Discussion

15.	∆f(x) = _______ (a) f(x + h) (b) f(x) – f(x + h) (c) f(x + h) – f(x) (d) f(x) – f(x – h)
Answer» (c) f(x + h) – f(x) ∆f(x) = f(x + h) – f(x)

15.

∆f(x) = _______ (a) f(x + h) (b) f(x) – f(x + h) (c) f(x + h) – f(x) (d) f(x) – f(x – h)

Answer»

(c) f(x + h) – f(x)

∆f(x) = f(x + h) – f(x)

Discussion

16.	If ‘n’ is a positive integer ∆n [∆-n f(x)] _______ (a) f(2x) (b) f(x + h) (c) f(x) (d) ∆ f(2x)
Answer» The correct answer is : (c) f(x)

Discussion

17.	Match the following(a) ∆f(x)(i) 2x + 1(b) E2 f(x)(ii) 1 + ∆(c) E(iii) f(x + h) – f(x)(d) ∆x2 , h = 1(iv) f(x + 2h)
Answer» (a) – (iii), (b) – (iv), (c) – (ii), (d) – (i)

Discussion

18.	∆4 y3 = _______ (a) (E – 1)4 y3 (b) (E3 – 1) y3 (c) (E – 1)3 y0(d) (E – 1)4 y0
Answer» (a) (E – 1)⁴ y₃

Discussion

19.	Say true or false 1. ∇y2 = y1 – y0 2. ∇2 yn = ∇yn – ∇yn + 1 3. When 5 values are given, the polynomial which fits the data is of degree 4 4. E ∆ = ∆ E 5. f(2) + ∆f(2) = f(3)
Answer» 1. False 2. True 3. True 4. True 5. True

19.

Say true or false 1. ∇y2 = y1 – y0 2. ∇2 yn = ∇yn – ∇yn + 1 3. When 5 values are given, the polynomial which fits the data is of degree 4 4. E ∆ = ∆ E 5. f(2) + ∆f(2) = f(3)

Answer»

1. False

2. True

3. True

4. True

5. True

Discussion

20.	Fill in the blanks. 1. The two methods of interpolation are _______ and _______ 2. If values of x are not equidistant we use _______ method. 3. ∆(f(x) + g(x)) = ______ 4. ∆k yn = ______ 5. The first three terms in Newton’s method will give a ________ interpolation.
Answer» 1. graphical method, algebraic method 2. Lagrange’s method 3. ∆f(x) + ∆g(x) 4. ∆^k-1 y_{n + 1} – ∆^{k - 1} y_n 5. Parabolic

20.

Fill in the blanks. 1. The two methods of interpolation are ___ and _ 2. If values of x are not equidistant we use _ method. 3. ∆(f(x) + g(x)) = 4. ∆k yn = 5. The first three terms in Newton’s method will give a ____ interpolation.

Answer»

1. graphical method, algebraic method

2. Lagrange’s method

3. ∆f(x) + ∆g(x)

4. ∆^k-1 y_{n + 1} – ∆^{k - 1} y_n

5. Parabolic

Discussion

Explore topic-wise InterviewSolutions in .

E is a _____(a) shifting operator (b) Displacement operator (c) 1 + ∆ (d) all of these (e) none of these

For the given points (x0 , y0 ) and (x1, y1 ) the Lagrange’s formula is ______(a) y(x) = (x - x1)/(x0 - x1)y0 + (x - x0)/(x1 - x0)y1(b) y(x) = (x1 - x)/(x0 - x1)y0 + (x - x0)/(x1 - x0)y1(c) y(x) = (x - x1)/(x0 - x1)y1 + (x - x0)/(x1 - x0)y0(d) y(x) = (x1 - x)/(x0 - x1)y1 + (x - x0)/(x1 - x0)y0

∇ f(a) = ______ (a) f(a) + f(a – h) (b) f(a) – f(a + h) (c) f(a) – f(a – h) (d) f(a)

If f(x) = x2 + 2x + 2 and the interval of differencing is unity then ∆ f(x) _______ (a) 2x – 3 (b) 2x + 3 (c) x + 3 (d) x – 3

If h = 1 then prove that (E-1 ∆) x3 = 3x2 – 3x + 1.

If c is a constant then ∆c = ______ (a) c (b) ∆ (c) ∆2(d) 0

If h = 1, then ∆(x2) = ________ (a) 2x (b) 2x – 1 (c) 2x + 1(d) 1

∇ = _______ (a) 1 + E (b) 1 – E (c) 1 – E-1 (d) 1 + E-1

Evaluate (log ax)

E = ______ (a) 1 + ∆ (b) 1 – ∆ (c) 1 + ∇ (d) 1 – ∇

E f(x) = _______ (a) f(x – h) (b) f(x) (c) f(x + h) (d) f(x + 2h)

If m and n are positive integers then ∆m ∆n f(x) = _______ (a) ∆m + n f(x) (b) ∆m f(x)(c) ∆n f(x) (d) ∆m - n f(x)

E-n f(x) is ______ (a) f(x + nh) (b) f(x – nh)(c) f(-nh) (d) f(x – n)

If f(x) = x2 + 3x then show that ∆f(x) = 2x + 4

∆f(x) = _______ (a) f(x + h) (b) f(x) – f(x + h) (c) f(x + h) – f(x) (d) f(x) – f(x – h)

If ‘n’ is a positive integer ∆n [∆-n f(x)] _______ (a) f(2x) (b) f(x + h) (c) f(x) (d) ∆ f(2x)

Match the following(a) ∆f(x)(i) 2x + 1(b) E2 f(x)(ii) 1 + ∆(c) E(iii) f(x + h) – f(x)(d) ∆x2 , h = 1(iv) f(x + 2h)

∆4 y3 = _______ (a) (E – 1)4 y3 (b) (E3 – 1) y3 (c) (E – 1)3 y0(d) (E – 1)4 y0

Say true or false 1. ∇y2 = y1 – y0 2. ∇2 yn = ∇yn – ∇yn + 1 3. When 5 values are given, the polynomial which fits the data is of degree 4 4. E ∆ = ∆ E 5. f(2) + ∆f(2) = f(3)

Fill in the blanks. 1. The two methods of interpolation are _______ and _______ 2. If values of x are not equidistant we use _______ method. 3. ∆(f(x) + g(x)) = ______ 4. ∆k yn = ______ 5. The first three terms in Newton’s method will give a ________ interpolation.

Fill in the blanks. 1. The two methods of interpolation are ___ and _ 2. If values of x are not equidistant we use _ method. 3. ∆(f(x) + g(x)) = 4. ∆k yn = 5. The first three terms in Newton’s method will give a ____ interpolation.