11th Business Maths Important 5 mark Question Paper

St. Britto Hr. Sec. School - Madurai

11th Business Maths Important 5 mark Question Paper-Aug 2020

Time : 2.00 Hours

Part - A

Generic 5 - Answer All Question

a bank pays 8% interest compounded quarterly. Determine the equal deposits to be made at the end of each quarter for 3 years so as to receive Rs.300 at the end of 3 years.

Resolve into partial factors : \(\frac { { x }^{ 2 }+x+1 }{ { x }^{ 2 }+2x+1 } \)

The first of three urns contains 7 White and 10 Black balls, the second contains 5 White and 12 Black balls and third contains 17 White balls and no Black ball. A person chooses an urn at random and draws a ball from it. And the ball is found to be White. Find the probabilities that the ball comes from
(i) the first urn
(ii) the second urn
(iii) the third urn

A company manufactures two models of voltage stabilizers viz., ordinary and autocut. All components of the stabilizers are purchased from outside sources, assembly and testing is carried out at company’s own works. The assembly and testing time required for the two models are 0.8 hour each for ordinary and 1.20 hours each for auto-cut. Manufacturing capacity 720 hours at present is available per week. The market for the two models has been surveyed which suggests maximum weekly sale of 600 units of ordinary and 400 units of auto-cut. Profit per unit for ordinary and auto-cut models has been estimated at Rs 100 and Rs 150 respectively. Formulate the linear programming problem.

Calculate the earliest start time, earliest finish time, latest start time and latest finish time of each activity of the project given below and determine the critical path of the project and duration to complete the project.

Activity 1-2 1-3 1-5 2-3 2-4 3-4 3-5 3-6 4-6 5-6

Duration (in week) 7 6 11 3 9 2 4 9 6 3

By the principle of mathematical induction, prove the following.
1+4+7+.....+(3n-2)=\(\frac { n(3n-1) }{ 2 } \) , for all \(n\in N\).

A furniture dealer deals only two items viz., tables and chairs. He has to invest Rs.10,000/- and a space to store atmost 60 pieces. A table cost him Rs.500/– and a chair Rs.200/–. He can sell all the items that he buys. He is getting a profit of Rs.50 per table and Rs.15 per chair. Formulate this problem as an LPP, so as to maximize the profit.

Find D₆,D₈,P₇ and P₂₀ for the data 57, 58, 61, 42, 38, 65, 72, 66.

Find the value of p for which the straight lines 8px+(2-3p)y+1 = 0 and px +8y -7 =0 are perpendicular to each other.

Using the following information you are requested to (i) obtain the linear regression of Y on X (ii) Estimate the level of defective parts delivered when inspection expenditure amounts to Rs.28,000 ΣX=424, ΣY=363, ΣX² =21926, ΣY² =15123, ΣXY=12815, N=10. Here X is the expenditure on inspection, Y is the defective parts delivered.

If tan A - tan B = x and cot B - cot A = y, prove that cot (A - B) = \(\frac { 1 }{ x } +\frac { 1 }{ y } \)

Show that the function f(x) = |x| is not differentiable at x = 0.

Solve the following linear programming problem graphically.
Maximize Z = 3x₁ + 5x₂ subject to the constraints x₁+x₂≤6, x₁≤4; x₂≤5, and x₁, x₂ ≥0

If cosec A + sec A = cosec B + sec B, prove that cot\(\left( \frac { A+B }{ 2 } \right) \)=tanA tanB

A firm manufactures two products A and B on which the profits earned per unit are Rs. 3 and Rs. 4 respectively. Each product is processed on two machines M₁ and M₂. Product A requires one minute of processing time on M₁ and two minutes on M₂, While B requires one minute on M₁ and one minute on M₂. Machine M₁ is available for not more than 7 hrs 30 minutes while M₂ is available for 10 hrs during any working day. Formulate this problem as a linear programming problem to maximize the profit.

By the principle of Mathematical Induction, prove that 1 + 3 + 5 …+ (2n–1) = n², for all n∈N.

What is the maximum slope of the tangent to the curve y = - x³ + 3x² + 9x - 27 and at what point is it?

By Mathematical Induction, prove that 1²+2²+3²+……….+ n²\(=\frac{n(n+1)(2n+1)}{6}\), for all n∈N.

By the principle of mathematical induction, prove the following.
1.2+2.3+3.4+.....+n(n+1)=\(\frac { n(n+1)(n+2) }{ 3 } \), for all \(n\in N\).

If the equation ax² +5xy -6y² +12x + 5y +c = 0 represents a pair of perpandicular straight lines, find a and c.

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Activity	1-2	1-3	1-5	2-3	2-4	3-4	3-5	3-6	4-6	5-6
Duration (in week)	7	6	11	3	9	2	4	9	6	3

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12th Standard Tamil Medium

11th Standard English Medium

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11th Business Maths Important 5 mark Question Paper

St. Britto Hr. Sec. School - Madurai

11th Business Maths Important 5 mark Question Paper-Aug 2020

Part - A

Generic 5 - Answer All Question

a bank pays 8% interest compounded quarterly. Determine the equal deposits to be made at the end of each quarter for 3 years so as to receive Rs.300 at the end of 3 years.

Resolve into partial factors : \(\frac { { x }^{ 2 }+x+1 }{ { x }^{ 2 }+2x+1 } \)

By the principle of mathematical induction, prove the following. 1+4+7+.....+(3n-2)=\(\frac { n(3n-1) }{ 2 } \) , for all \(n\in N\).

Find D6,D8,P7 and P20 for the data 57, 58, 61, 42, 38, 65, 72, 66.

Find the value of p for which the straight lines 8px+(2-3p)y+1 = 0 and px +8y -7 =0 are perpendicular to each other.

If tan A - tan B = x and cot B - cot A = y, prove that cot (A - B) = \(\frac { 1 }{ x } +\frac { 1 }{ y } \)

Show that the function f(x) = |x| is not differentiable at x = 0.

Solve the following linear programming problem graphically. Maximize Z = 3x1 + 5x2 subject to the constraints x1+x2≤6, x1≤4; x2≤5, and x1, x2 ≥0

If cosec A + sec A = cosec B + sec B, prove that cot\(\left( \frac { A+B }{ 2 } \right) \)=tanA tanB

By the principle of Mathematical Induction, prove that 1 + 3 + 5 …+ (2n–1) = n2, for all n∈N.

What is the maximum slope of the tangent to the curve y = - x3 + 3x2 + 9x - 27 and at what point is it?

By Mathematical Induction, prove that 12+22+32+……….+ n2\(=\frac{n(n+1)(2n+1)}{6}\), for all n∈N.

By the principle of mathematical induction, prove the following. 1.2+2.3+3.4+.....+n(n+1)=\(\frac { n(n+1)(n+2) }{ 3 } \), for all \(n\in N\).

If the equation ax2 +5xy -6y2 +12x + 5y +c = 0 represents a pair of perpandicular straight lines, find a and c.

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By the principle of mathematical induction, prove the following.
1+4+7+.....+(3n-2)=\(\frac { n(3n-1) }{ 2 } \) , for all \(n\in N\).

Find D₆,D₈,P₇ and P₂₀ for the data 57, 58, 61, 42, 38, 65, 72, 66.

Solve the following linear programming problem graphically.
Maximize Z = 3x₁ + 5x₂ subject to the constraints x₁+x₂≤6, x₁≤4; x₂≤5, and x₁, x₂ ≥0

By the principle of Mathematical Induction, prove that 1 + 3 + 5 …+ (2n–1) = n², for all n∈N.

What is the maximum slope of the tangent to the curve y = - x³ + 3x² + 9x - 27 and at what point is it?

By Mathematical Induction, prove that 1²+2²+3²+……….+ n²\(=\frac{n(n+1)(2n+1)}{6}\), for all n∈N.

By the principle of mathematical induction, prove the following.
1.2+2.3+3.4+.....+n(n+1)=\(\frac { n(n+1)(n+2) }{ 3 } \), for all \(n\in N\).

If the equation ax² +5xy -6y² +12x + 5y +c = 0 represents a pair of perpandicular straight lines, find a and c.