11th Business Maths Important 2 mark Question Paper

St. Britto Hr. Sec. School - Madurai

11th Business Maths Important 2 mark Question Paper-Aug 2020

Time : 1.30 Hours

Part - A

Generic 2 - Answer All Question

Find the focus, equation of the directrix, vertrix and length of latus sections of the parabola x²=6y.

Show that 10P₃ = 9 P₃ + 3. 9P₂

Draw a network diagram for the project whose activities and their predecessor relationships are given below

Activity A B C D E F

Predecessor activity - - D A B C

Activity	A	B	C	D	E	F
Predecessor activity	-	-	D	A	B	C

If the production of a firm is given by p = 4LK - L² + K² , L>0, K>0, prove that \(L\frac { \partial p }{ \partial L } +k\frac { \partial p }{ \partial k } =2p\)

ResoIve into partial fractions :\(\frac { 12x-17 }{ (x-2)(x-1) } \)

Evaluate : 5P₃ and P(8, 5)

Determine whether the following functions are odd or even?
\(f(x)=log({ x }^{ 2 }+\sqrt { { x }^{ 2 } } +1)\)

A fruit grower can use two typ~s of fertilizers in his garden, brand P and brand Q. The amounts (in Kg) of nitrogen, phosphoric acid, potash and chlorine in a bag of each brand are given in the table. Tests indicate that the garden needs atIeast 240 kgs of phosphoric acid, at least 270 kg of potash and atmost 310 kg of chlorine. If the grower wants to minimize the amount of nitrogen added to the garden, formulate the above as mathematical LPP.

If f(x) = \(\frac{x-1}{x+1}\), 0\(-\frac{1}{x}\)

A bag contains 5 white and 3 black balls. Two balls are drawn at random one after the other without replacement. Find the probability that both balls drawn are black.

A demand function is given by xpⁿ= k where n and k are constants. Prove that elasticity of demand is always constant.

Find \(\frac{dy}{dx}\) at (1, 1) to the curve 2x² + 3xy + 5y² = 10.

Letu = x cos y + y cos x. Verify \(\frac { { \partial }^{ 2 }u }{ { \partial x }\partial y } +\frac { { \partial }^{ 2 }u }{ { \partial y }{ \partial x } } \)

Evaluate
\(\cos\left[\tan^{-1}\left(\frac34\right)\right]\)

Find the values of each of the following trigonometric ratios. \(cosec { \left( { 1125 }^{ o } \right) } \)

Find the number of permutations of English vowels A, E, I, 0, U taking two at a time?

How many triangles can be formed by joining the vertices of a hexagon?

A cash prize of Rs 1,500 is given to the student standing first in examination of Business Mathematics by a person every year. Find out the sum that the person has to deposit to meet this expense. Rate of interest is 12% p.a

Find the values of each of the following trigonometric ratios.
sin15^o

If y=1+1/x, show that y is a strictly decreasing function for all real values of x(x\(\neq\)0).

Express the following as sum or difference
2cos3\(\theta\)cos\(\theta\)

Find the quadrants in which the terminal sides of the following angles lie.
-320^o

If nP_r = 360, find n and r.

Find the first quartile and third quartile for the given observations
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22

let u= x²y³ cos \(\left( \frac { x }{ y } \right) \) by using Euler’s theorem show that \(x.\frac { \partial u }{ \partial x } +y.\frac { \partial u }{ \partial y } =5u\)

The total cost function for the production of x units of an item is given by c = 10 - 4x³ + 3x⁴ find the
(i) average cost, (ii) marginal cost (iii) marginal average cost.

Evaluate\(\cos\left[\frac{\pi}{3}-\cos^{-1}\left(\frac{1}{2}\right)\right]\)

Find n if 25 C_n+5 = 25 C_2n-1.

Evaluate:\(\left| \begin{matrix} x & x+1 \\ x-1 & x \end{matrix} \right| \)

For the production function P = 3(L)^0.4 (K)^0.6, find the marginal productivities of labour (L) and capital (K) when L = 10 and K = 6. [use; (0.6)^0.6 = 0.736, (1.67)^0.4 = 1.2267]

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11th Business Maths Important 2 mark Question Paper

St. Britto Hr. Sec. School - Madurai

11th Business Maths Important 2 mark Question Paper-Aug 2020

Part - A

Generic 2 - Answer All Question

Find the focus, equation of the directrix, vertrix and length of latus sections of the parabola x2=6y.

Show that 10P3 = 9 P3 + 3. 9P2

Draw a network diagram for the project whose activities and their predecessor relationships are given below Activity A B C D E F Predecessor activity - - D A B C

If the production of a firm is given by p = 4LK - L2 + K2 , L>0, K>0, prove that \(L\frac { \partial p }{ \partial L } +k\frac { \partial p }{ \partial k } =2p\)

ResoIve into partial fractions :\(\frac { 12x-17 }{ (x-2)(x-1) } \)

Evaluate : 5P3 and P(8, 5)

Determine whether the following functions are odd or even? \(f(x)=log({ x }^{ 2 }+\sqrt { { x }^{ 2 } } +1)\)

If f(x) = \(\frac{x-1}{x+1}\), 0\(-\frac{1}{x}\)

A bag contains 5 white and 3 black balls. Two balls are drawn at random one after the other without replacement. Find the probability that both balls drawn are black.

A demand function is given by xpn= k where n and k are constants. Prove that elasticity of demand is always constant.

Find \(\frac{dy}{dx}\) at (1, 1) to the curve 2x2 + 3xy + 5y2 = 10.

Letu = x cos y + y cos x. Verify \(\frac { { \partial }^{ 2 }u }{ { \partial x }\partial y } +\frac { { \partial }^{ 2 }u }{ { \partial y }{ \partial x } } \)

Evaluate \(\cos\left[\tan^{-1}\left(\frac34\right)\right]\)

Find the values of each of the following trigonometric ratios. \(cosec { \left( { 1125 }^{ o } \right) } \)

Find the number of permutations of English vowels A, E, I, 0, U taking two at a time?

How many triangles can be formed by joining the vertices of a hexagon?

A cash prize of Rs 1,500 is given to the student standing first in examination of Business Mathematics by a person every year. Find out the sum that the person has to deposit to meet this expense. Rate of interest is 12% p.a

Find the values of each of the following trigonometric ratios. sin15o

If y=1+1/x, show that y is a strictly decreasing function for all real values of x(x\(\neq\)0).

Express the following as sum or difference 2cos3\(\theta\)cos\(\theta\)

Find the quadrants in which the terminal sides of the following angles lie. -320o

If nPr = 360, find n and r.

Find the first quartile and third quartile for the given observations 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22

let u= x2y3 cos \(\left( \frac { x }{ y } \right) \) by using Euler’s theorem show that \(x.\frac { \partial u }{ \partial x } +y.\frac { \partial u }{ \partial y } =5u\)

The total cost function for the production of x units of an item is given by c = 10 - 4x3 + 3x4 find the (i) average cost, (ii) marginal cost (iii) marginal average cost.

Evaluate\(\cos\left[\frac{\pi}{3}-\cos^{-1}\left(\frac{1}{2}\right)\right]\)

Find n if 25 Cn+5 = 25 C2n-1.

Evaluate:\(\left| \begin{matrix} x & x+1 \\ x-1 & x \end{matrix} \right| \)

For the production function P = 3(L)0.4 (K)0.6, find the marginal productivities of labour (L) and capital (K) when L = 10 and K = 6. [use; (0.6)0.6 = 0.736, (1.67)0.4 = 1.2267]

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Tamilnadu Stateboardszs - Class

Find the focus, equation of the directrix, vertrix and length of latus sections of the parabola x²=6y.

Show that 10P₃ = 9 P₃ + 3. 9P₂

Draw a network diagram for the project whose activities and their predecessor relationships are given below

Activity A B C D E F

Predecessor activity - - D A B C

If the production of a firm is given by p = 4LK - L² + K² , L>0, K>0, prove that \(L\frac { \partial p }{ \partial L } +k\frac { \partial p }{ \partial k } =2p\)

Evaluate : 5P₃ and P(8, 5)

Determine whether the following functions are odd or even?
\(f(x)=log({ x }^{ 2 }+\sqrt { { x }^{ 2 } } +1)\)

A demand function is given by xpⁿ= k where n and k are constants. Prove that elasticity of demand is always constant.

Find \(\frac{dy}{dx}\) at (1, 1) to the curve 2x² + 3xy + 5y² = 10.

Evaluate
\(\cos\left[\tan^{-1}\left(\frac34\right)\right]\)

Find the values of each of the following trigonometric ratios.
sin15^o

Express the following as sum or difference
2cos3\(\theta\)cos\(\theta\)

Find the quadrants in which the terminal sides of the following angles lie.
-320^o

If nP_r = 360, find n and r.

Find the first quartile and third quartile for the given observations
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22

let u= x²y³ cos \(\left( \frac { x }{ y } \right) \) by using Euler’s theorem show that \(x.\frac { \partial u }{ \partial x } +y.\frac { \partial u }{ \partial y } =5u\)

The total cost function for the production of x units of an item is given by c = 10 - 4x³ + 3x⁴ find the
(i) average cost, (ii) marginal cost (iii) marginal average cost.

Find n if 25 C_n+5 = 25 C_2n-1.

For the production function P = 3(L)^0.4 (K)^0.6, find the marginal productivities of labour (L) and capital (K) when L = 10 and K = 6. [use; (0.6)^0.6 = 0.736, (1.67)^0.4 = 1.2267]