12th Business Maths Monthly Test - 2 ( Numerical Methods )

St. Britto Hr. Sec. School - Madurai

12th Business Maths Monthly Test - 2 ( Numerical Methods )-Aug 2020

Time : 2.30 Hours

Part - A

Generic 2 - Answer All Question

Using Newton’s forward interpolation formula find the cubic polynomial.

x 0 1 2 3

f(x) 1 2 1 10

If f(x) = x²+ 3x than show that Δf(x) = 2x + 4

Using interpolation, find the value of f(x) when x = 15

x 3 7 11 19

f(x) 42 43 47 60

Find f(2.8) from the following table.

x 0 1 2 3

f(x) 1 2 11 34

Following are the population of a district

Year (x) 1881 1891 1901 1911 1921 1931

Population (y) Thousands 363 391 421 - 467 501

Using interpolation estimate the output of a factory in 1986 from the following data

Year 1974 1978 1982 1990

Output in 1000 tones 25 60 80 170

From the following table obtain a polynomial of degree y in x

x 1 2 3 4 5

y 1 -1 1 -1 1

Prove that
(1 + Δ)(1 - ∇) = 1

Find the missing figures in the following table

x 0 5 10 15 20 25

y 7 11 - 18 - 32

Evaluate Δ\(\left[ \frac { 1 }{ (x+1)(x+2) } \right] \) by taking ‘1’ as the interval of differencing

The area A of circle of diameter ‘d’ is given for the following values

D 80 85 90 95 100

A 5026 5674 6362 7088 7854

The population of a city in a censes taken once in 10 years is given below. Estimate
the population in the year 1955.

Year 1951 1961 1971 1981

Population in lakhs 35 42 58 84

Find f(0.5) if f(−1) = 202, f (0)= 175, f(1) = 82 and f(2) = 55

A second degree polynomial passes though the point (1,-1) (2,-1) (3,1) (4,5). Find the polynomial.

Find the missing entry in the following table

x 0 1 2 3 4

y_x 1 3 9 - 81

If u₀ = 560, u₁ = 556, u₂ = 520, u₄ = 385, show that u₃= 465

From the following data find y at x = 43 and x = 84

x 40 50 60 70 80 90

y 184 204 226 250 276 304

Using graphic method, find the value of y when x = 48 from the following data:

x 40 50 60 70

y 6.2 7.2 9.1 12

If y = x³− x²+ x − 1 calculate the values of y for x = 0,1,2,3,4,5 and form the forward differences table.

In an examination the number of candidates who secured marks between certain interval were as follows

Marks 0-19 20-39 40-59 60-79 80-99

No.of.candidates 41 62 65 50 17

Find the missing entries from the following

x 0 1 2 3 4 5

y = f(x) 0 - 8 15 - 35

Use Lagrange’s formula and estimate from the following data the number of workers
getting income not exceeding Rs. 26 per month

Income not exceeding (Rs) 15 25 30 35

No. of workers 36 40 45 48

The following data gives the melting point of a alloy of lead and zinc where ‘t’ is the temperature in degree c and P is the percentage of lead in the alloy

P 40 50 60 70 80 90

T 180 204 226 250 276 304

Find the melting point of the alloy containing 84 percent lead.

Using interpolation estimate the business done in 1985 from the following data

Year 1982 1983 1984 1986

Business done (in lakhs) 150 235 365 525

Using Lagrange’s interpolation formula find a polynomial which passes through the
points (0, –12), (1, 0), (3, 6) and (4,12).

If f (x) = e^ax then show that f(0), Δ(0), Δ² are in G.P

Find the value of f (x) when x = 32 from the following table

x 30 35 40 45 50

f(x) 15.9 14.9 14.1 13.3 12.5

The following data relates to indirect labour expenses and the level of output

Months Jan Feb Mar Apr May June

Units of output 200 300 400 640 540 580

Indirect labour
expenses (Rs) 2500 2800 3100 3820 3220 3640

Estimate the expenses at a level of output of 350 units, by using graphic method

If h = 1 then prove that (E⁻¹Δ)x³= 3x²− 3x + 1.

Evaluate ∆(log ax).

Comment

Add Comment

Year (x)	1881	1891	1901	1911	1921	1931
Population (y) Thousands	363	391	421	-	467	501

Year	1982	1983	1984	1986
Business done (in lakhs)	150	235	365	525

Months	Jan	Feb	Mar	Apr	May	June
Units of output	200	300	400	640	540	580
Indirect labour expenses (Rs)	2500	2800	3100	3820	3220	3640

InstaQB

Institutions

12th Standard English Medium

12th Standard Tamil Medium

11th Standard English Medium

11th Standard Tamil Medium

10th Standard English Medium

9th Standard English Medium

8th Standard English Medium

7th Standard English Medium

Class XII

Class XI

12Th Standard

11Th Standard

10Th Standard

9Th Standard

12th Business Maths Monthly Test - 2 ( Numerical Methods )

St. Britto Hr. Sec. School - Madurai

12th Business Maths Monthly Test - 2 ( Numerical Methods )-Aug 2020

Part - A

Generic 2 - Answer All Question

Using Newton’s forward interpolation formula find the cubic polynomial. x 0 1 2 3 f(x) 1 2 1 10

If f(x) = x2 + 3x than show that Δf(x) = 2x + 4

Using interpolation, find the value of f(x) when x = 15 x 3 7 11 19 f(x) 42 43 47 60

Find f(2.8) from the following table. x 0 1 2 3 f(x) 1 2 11 34

Following are the population of a district Year (x) 1881 1891 1901 1911 1921 1931 Population (y) Thousands 363 391 421 - 467 501

Using interpolation estimate the output of a factory in 1986 from the following data Year 1974 1978 1982 1990 Output in 1000 tones 25 60 80 170

From the following table obtain a polynomial of degree y in x x 1 2 3 4 5 y 1 -1 1 -1 1

Prove that (1 + Δ)(1 - ∇) = 1

Find the missing figures in the following table x 0 5 10 15 20 25 y 7 11 - 18 - 32

Evaluate Δ\(\left[ \frac { 1 }{ (x+1)(x+2) } \right] \) by taking ‘1’ as the interval of differencing

The area A of circle of diameter ‘d’ is given for the following values D 80 85 90 95 100 A 5026 5674 6362 7088 7854

The population of a city in a censes taken once in 10 years is given below. Estimate the population in the year 1955. Year 1951 1961 1971 1981 Population in lakhs 35 42 58 84

Find f(0.5) if f(−1) = 202, f (0)= 175, f(1) = 82 and f(2) = 55

A second degree polynomial passes though the point (1,-1) (2,-1) (3,1) (4,5). Find the polynomial.

Find the missing entry in the following table x 0 1 2 3 4 yx 1 3 9 - 81

If u0 = 560, u1 = 556, u2 = 520, u4 = 385, show that u3 = 465

From the following data find y at x = 43 and x = 84 x 40 50 60 70 80 90 y 184 204 226 250 276 304

Using graphic method, find the value of y when x = 48 from the following data: x 40 50 60 70 y 6.2 7.2 9.1 12

If y = x3 − x2 + x − 1 calculate the values of y for x = 0,1,2,3,4,5 and form the forward differences table.

In an examination the number of candidates who secured marks between certain interval were as follows Marks 0-19 20-39 40-59 60-79 80-99 No.of.candidates 41 62 65 50 17

Find the missing entries from the following x 0 1 2 3 4 5 y = f(x) 0 - 8 15 - 35

Use Lagrange’s formula and estimate from the following data the number of workers getting income not exceeding Rs. 26 per month Income not exceeding (Rs) 15 25 30 35 No. of workers 36 40 45 48

The following data gives the melting point of a alloy of lead and zinc where ‘t’ is the temperature in degree c and P is the percentage of lead in the alloy P 40 50 60 70 80 90 T 180 204 226 250 276 304 Find the melting point of the alloy containing 84 percent lead.

Using interpolation estimate the business done in 1985 from the following data Year 1982 1983 1984 1986 Business done (in lakhs) 150 235 365 525

Using Lagrange’s interpolation formula find a polynomial which passes through the points (0, –12), (1, 0), (3, 6) and (4,12).

If f (x) = eax then show that f(0), Δ(0), Δ2 are in G.P

Find the value of f (x) when x = 32 from the following table x 30 35 40 45 50 f(x) 15.9 14.9 14.1 13.3 12.5

The following data relates to indirect labour expenses and the level of output Months Jan Feb Mar Apr May June Units of output 200 300 400 640 540 580 Indirect labour expenses (Rs) 2500 2800 3100 3820 3220 3640 Estimate the expenses at a level of output of 350 units, by using graphic method

If h = 1 then prove that (E−1Δ)x3 = 3x2 − 3x + 1.

Evaluate ∆(log ax).

Comment

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Using Newton’s forward interpolation formula find the cubic polynomial.

x 0 1 2 3

f(x) 1 2 1 10

If f(x) = x²+ 3x than show that Δf(x) = 2x + 4

Using interpolation, find the value of f(x) when x = 15

x 3 7 11 19

f(x) 42 43 47 60

Find f(2.8) from the following table.

x 0 1 2 3

f(x) 1 2 11 34

Following are the population of a district

Year (x) 1881 1891 1901 1911 1921 1931

Population (y) Thousands 363 391 421 - 467 501

Using interpolation estimate the output of a factory in 1986 from the following data

Year 1974 1978 1982 1990

Output in 1000 tones 25 60 80 170

From the following table obtain a polynomial of degree y in x

x 1 2 3 4 5

y 1 -1 1 -1 1

Prove that
(1 + Δ)(1 - ∇) = 1

Find the missing figures in the following table

x 0 5 10 15 20 25

y 7 11 - 18 - 32

The area A of circle of diameter ‘d’ is given for the following values

D 80 85 90 95 100

A 5026 5674 6362 7088 7854

The population of a city in a censes taken once in 10 years is given below. Estimate
the population in the year 1955.

Year 1951 1961 1971 1981

Population in lakhs 35 42 58 84

Find the missing entry in the following table

x 0 1 2 3 4

y_x 1 3 9 - 81

If u₀ = 560, u₁ = 556, u₂ = 520, u₄ = 385, show that u₃= 465

From the following data find y at x = 43 and x = 84

x 40 50 60 70 80 90

y 184 204 226 250 276 304

Using graphic method, find the value of y when x = 48 from the following data:

x 40 50 60 70

y 6.2 7.2 9.1 12

If y = x³− x²+ x − 1 calculate the values of y for x = 0,1,2,3,4,5 and form the forward differences table.

In an examination the number of candidates who secured marks between certain interval were as follows

Marks 0-19 20-39 40-59 60-79 80-99

No.of.candidates 41 62 65 50 17

Find the missing entries from the following

x 0 1 2 3 4 5

y = f(x) 0 - 8 15 - 35

Use Lagrange’s formula and estimate from the following data the number of workers
getting income not exceeding Rs. 26 per month

Income not exceeding (Rs) 15 25 30 35

No. of workers 36 40 45 48

The following data gives the melting point of a alloy of lead and zinc where ‘t’ is the temperature in degree c and P is the percentage of lead in the alloy

P 40 50 60 70 80 90

T 180 204 226 250 276 304

Find the melting point of the alloy containing 84 percent lead.

Using interpolation estimate the business done in 1985 from the following data

Year 1982 1983 1984 1986

Business done (in lakhs) 150 235 365 525

Using Lagrange’s interpolation formula find a polynomial which passes through the
points (0, –12), (1, 0), (3, 6) and (4,12).

If f (x) = e^ax then show that f(0), Δ(0), Δ² are in G.P

Find the value of f (x) when x = 32 from the following table

x 30 35 40 45 50

f(x) 15.9 14.9 14.1 13.3 12.5

The following data relates to indirect labour expenses and the level of output

Months Jan Feb Mar Apr May June

Units of output 200 300 400 640 540 580

Indirect labour
expenses (Rs) 2500 2800 3100 3820 3220 3640

Estimate the expenses at a level of output of 350 units, by using graphic method

If h = 1 then prove that (E⁻¹Δ)x³= 3x²− 3x + 1.