### 11th Standard Business Maths Study material & Free Online Practice Tests - View and download Sample Question Papers with Solutions for Class 11 Session 2019 - 2020 TN Stateboard

#### 11th Standard Business Maths - Operations Research Two Marks Questions - by Banumathi - Nilgiris Sep 21, 2019 - View & Download

• 1)

Draw the logic network for the following:
Activities C and D both follow A, activity E follows C, activity F follows D, activity E and F precedes B.

• 2)

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

 Activity: A B C D E F G H I J K Predecessor activity: - - - A B B C D F H,I F,G
• 3)

Construct a network diagram for the following situation:
A<D,E; B, D<F; C<G and B<H.

• 4)

Construct the network for the projects consisting of various activities and their precedence relationships are as given below:
A, B, C can start simultaneously A<F, E; B<D, C; E, D<G

• 5)

Construct the network for each the projects consisting of various activities and their precedence relationships are as given below:

 Activity A B C D E F G H I J K Immediate Predecessors - - - A B B C D E H,I F,G

#### 11th Standard Business Maths - Descriptive Statistics and Probability Two Marks Questions - by Banumathi - Nilgiris Sep 21, 2019 - View & Download

• 1)

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

• 2)

An aeroplane flies, along the four sides of a square at speeds of 100,200,300 and 400 kilometres per hour respectively. What is the average speed of the plane in its flight around the square.

• 3)

A die is thrown twice and the sum of the number appearing is observed to be 6. What is the conditional probability that the number 4 has appeared at least once?

• 4)

Suppose one person is selected at random from a group of 100 persons are given in the following

 Psychologist Socialist Democrate Total Men 15 25 10 50 Women 20 15 15 50 Total 35 40 25 100

What is the probability that the man selected is a Psychologist?

• 5)

A die is thrown. Find the probability of getting
(i) a prime number
(ii) a number greater than or equal to 3

#### 11th Standard Business Maths Unit 8 Financial Mathematics Two Marks Questions - by Banumathi - Nilgiris Sep 21, 2019 - View & Download

• 1)

The chairman of a society wishes to award a gold medal to a student getting highest marks in Business Mathematics. If this medal costs Rs 9,000 every year and the rate of compound interest is 15% what amount is to be deposited now.

• 2)

What is the amount of perpetual annuity of Rs 50 at 5% compound interest per year?

• 3)

Find the market value of 325 shares of amount Rs 100 at a premium of Rs 18.

• 4)

A man buys 500 shares of amount Rs 100 at Rs 14 below par. How much money does he pay?

• 5)

If the dividend received from 10% of Rs 25 shares is Rs 2000. Find the number of shares.

#### 11th Business Maths - Applications of Differentiation Two Marks Questions - by Banumathi - Nilgiris Sep 21, 2019 - View & Download

• 1)

The demand function for a commodity is $p={4\over x}$, where p is unit price. Find the instantaneous rate of change of demand with respect to price at p=4. Also interpret your result.

• 2)

The cost function of a firm is $C={1\over3}x^3-3x^2+9x$Find the level of output (x>0) when average cost is minimum

• 3)

Find the price elasticity of demand for the demand function x = 10 – p where x is the demand and p i the price. Examine whether the demand is elastic, inelastic or unit elastic at p = 6.

• 4)

Find the equilibrium price and equilibrium quantity for the following functions. Demand: x =100 – 2p and supply: x = 3p –50

• 5)

If f (x, y)  = 3x2 + 4y3 + 6xy - x3y3 + 7 then show that fxy (1,1) = 18.

#### 11th Business Maths - Differential Calculus Two Marks Questions - by Banumathi - Nilgiris Sep 21, 2019 - View & Download

• 1)

If $f(x)={ x }^{ 3 }-\frac { 1 }{ { x }^{ 3 } }$ then show that $f(x)+f\left( \frac { 1 }{ x } \right) =0$

• 2)

If $f(x)=\frac { x+1 }{ x-1 }$ ,then prove that f(f(x))=x

• 3)

Find the derivative of the following functions from first principles log (x+1)

• 4)

If $f\left( x \right) =\frac { 1 }{ 2x+1 } ,x\neq -\frac { 1 }{ 2 }$ then show that $f\left( f\left( x \right) \right) =\frac { 2x+1 }{ 2x+3 }$ provided that $x\neq -\frac { 3 }{ 2 }$

• 5)

Show that the function f(x) = 5x -3 is continous at x = +3

#### 11th Business Maths - Trigonometry Two Marks Question - by Banumathi - Nilgiris Sep 19, 2019 - View & Download

• 1)

Convert the following degree measure into radian measure 240o

• 2)

Convert the following degree measure into radian measure -320o

• 3)

Find the degree measure corresponding to the following radian measure.  -3

• 4)

Find the degree measure corresponding to the following radian measure.  $\frac { 11\pi }{ 18 }$

• 5)

Evaluate $\cot\left(\frac{-15\pi}{4}\right)$

#### 11th Business Maths - Analytical Geometry Two Marks Question - by Banumathi - Nilgiris Sep 19, 2019 - View & Download

• 1)

Find the equation of the following circles having the center ( 0,0) and radius 2 units

• 2)

Find the centre and radius of the circle x2 + y2 = 16

• 3)

Find the center and radius of the circle (x + 2) ( x - 5) + (y -2 ) ( y -1) = 0

• 4)

Find the equation of the circle whose centre is (-3, -2) and having circumferences 16$\pi$

• 5)

Find the equation of the circle on the line joining the points (1,0), (0,1) and having its centre on the line x + y= 1

#### 11th Business Maths - Algebra Two Marks Question - by Banumathi - Nilgiris Sep 19, 2019 - View & Download

• 1)

Verify that 8C4+8C3=9C4

• 2)

Evaluate the following expression.$\frac { 7! }{ 6! }$

• 3)

If four dice are rolled, find the number of possible outcomes in which atleast one die shows 2.

• 4)

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

• 5)

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

#### 11th Business Maths - Matrices And Determinants Two Marks Question - by Banumathi - Nilgiris Sep 19, 2019 - View & Download

• 1)

The technology matrix of an economic system of two industries is$\begin{bmatrix} 0.6 & 0.9 \\ 0.20 & 0.80 \end{bmatrix}$ .Test whether the system is viable as per Hawkins-Simon conditions.

• 2)

Find the minors and cofactors of all the elements of the following determinants
$\begin{vmatrix}5&20\\ 0&-1 \end{vmatrix}$

• 3)

Solve: $\begin{vmatrix}2& x&3\\4&1&6\\1&2&7 \end{vmatrix}=0$

• 4)

Find |AB| if $A=\begin{bmatrix} 3&-1\\2&1 \end{bmatrix}and \begin{bmatrix} 3&0\\1&-2 \end{bmatrix}$

• 5)

If A $=\begin{bmatrix} 1 \\ -4\\3 \end{bmatrix}$ and  B = [-1 2 1], verify that (AB)T = BT. AT.

#### 11th Business Maths - Term 1 Five Mark Model Question Paper - by Banumathi - Nilgiris Sep 16, 2019 - View & Download

• 1)

If A = $\begin{bmatrix}3 & -1 & 1 \\ -15 & 6 & -5\\5 & -2 & 2 \end{bmatrix}$ then, find the Inverse of A.

• 2)

Solve by matrix inversion method: x - y + 2z = 3; 2x +Z = 1; 3x + 2y + z = 4.

• 3)

Find adjoint of $A=\left[ \begin{matrix} 1 & -2 & -3 \\ 0 & 1 & 0 \\ -4 & 1 & 0 \end{matrix} \right]$

• 4)

Resolve into partial fractions for the following:
$\frac { x+2 }{ (x-1)(x+3)^{ 2 } }$

• 5)

By the principle of mathematical induction, prove the following.
an-bn is divisible by a-b, for all $n\in N$ .

#### 11th Business Maths Quarterly Model Question Paper - by Banumathi - Nilgiris Sep 13, 2019 - View & Download

• 1)

The value of x if $\begin{vmatrix} 0 & 1 & 0 \\ x & 2 & x \\ 1 & 3 & x \end{vmatrix}=0$ is

• 2)

The value of the determinant ${\begin{vmatrix} a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & c \end{vmatrix}}^{2}$is

• 3)

The number of Hawkins-Simon conditions for the viability of an input - output analysis is

• 4)

If A and B are non-singular matrices then, which of the following is incorrect?

• 5)

If A = $\begin{vmatrix}cos \theta & sin \theta \\ -sin \theta&cons\theta \end{vmatrix}$ then |2A| is equal to

#### 11th Business Maths Unit 10 Operations Research Book Back Questions - by Banumathi - Nilgiris Sep 06, 2019 - View & Download

• 1)

Maximize: z=3x1+4x2 subject to 2x1+x2≤40, 2x1+5x2≤180, x1,x2≥0 in the LPP, which one of the following is feasible corner point?

• 2)

A solution which maximizes or minimizes the given LPP is called

• 3)

The minimum value of the objective function Z = x + 3y subject to the constraints 2x + y ≤20, x + 2y ≤ 20,x > 0 and y > 0 is

• 4)

In the context of network, which of the following is not correct

• 5)

The objective of network analysis is to

#### 11th Business Maths Unit 9 Correlation and Regression Analysis Book Back Questions - by Banumathi - Nilgiris Sep 06, 2019 - View & Download

• 1)

Example for positive correlation is

• 2)

If the values of two variables move in opposite direction then the correlation is said to be

• 3)

Correlation co-efficient lies between

• 4)

The variable whose value is influenced or is to be predicted is called

• 5)

The variable which influences the values or is used for prediction is called

#### 11th Business Maths Chapter 8 Descriptive Statistics and Probability Book Back Questions - by Banumathi - Nilgiris Sep 06, 2019 - View & Download

• 1)

When calculating the average growth of economy, the correct mean to use is?

• 2)

When an observation in the data is zero, then its geometric mean is

• 3)

The best measure of central tendency is

• 4)

Median is same as

• 5)

The median of 10,14,11,9,8,12,6 is

#### 11th Standard Business Maths - Financial Mathematics Book Back Questions - by Banumathi - Nilgiris Sep 04, 2019 - View & Download

• 1)

The dividend received on 200 shares of face value Rs.100 at 8% dividend value is

• 2)

What is the amount related is selling 8% stacking 200 shares of face value 100 at 50.

• 3)

The Income on 7 % stock at 80 is

• 4)

If ‘a’ is the annual payment, ‘n’ is the number of periods and ‘i’ is compound interest for Rs 1 then future amount of the annuity is

• 5)

An annuity in which payments are made at the beginning of each payment period is called

#### 11th Standard Business Maths Chapter 6 Applications of Differentiation Book Back Questions - by Banumathi - Nilgiris Sep 04, 2019 - View & Download

• 1)

Average fixed cost of the cost function C(x) = 2x3 +5x2 - 14x +21 is

• 2)

Marginal revenue of the demand function p= 20–3x is

• 3)

For the cost function C =$\frac { 1 }{ 25 } { e }^{ 25 }$, the marginal cost is

• 4)

Instantaneous rate of change of y = 2x2 + 5x with respect to x at x = 2 is

• 5)

If the average revenue of a certain firm is Rs 50 and its elasticity of demand is 2, then their marginal revenue is

#### 11th Standard Business Maths - Differential Calculus Book Back Questions - by Banumathi - Nilgiris Sep 03, 2019 - View & Download

• 1)

If f(x) = x2 - x + 1, then f (x + 1) is

• 2)

The graph of the line y = 3 is

• 3)

Which one of the following functions has the property f (x) = $f\left( \frac { 1 }{ x } \right)$

• 4)

The range of f(x) = |x|, for all $x\epsilon R$, is

• 5)

A function f(x) is continuous at x = a if $\lim _{ x\rightarrow a }{ f\left( x \right) }$ is equal to

#### 11th Standard Business Maths - Analytical Geometry - by Banumathi - Nilgiris Sep 02, 2019 - View & Download

• 1)

If m1 and m2 are the slopes of the pair of lines given by ax2+ 2hxy + by2 = 0, then the value of m1 + m2 is

• 2)

If the lines 2x - 3y - 5 = 0 and 3x - 4y - 7 = 0 are the diameters of a circle, then its centre is

• 3)

The locus of the point P which moves such that P is always at equidistance from the line x + 2y+ 7 = 0 is

• 4)

(1, - 2) is the centre of the circle x2 + y2 + ax + by - 4 = 0 , then its radius

• 5)

The length of the tangent from (4,5) to the  circle x2 +y2 = 16 is

#### 11th Standard Business Maths - Trigonometry - by Banumathi - Nilgiris Sep 02, 2019 - View & Download

• 1)

The degree measure of $\frac{\pi}{8}$ is

• 2)

The value of $\sin(-420^o)$ is

• 3)

The value of sec A sin(270o+A) is

• 4)

The value of cos245o-sin245o is

• 5)

The value of $\frac{2\tan30^o}{1+tan^230}$ is

#### 11th Standard Business Maths Unit 2 Algebra Book Back Questions - by Banumathi - Nilgiris Aug 31, 2019 - View & Download

• 1)

The value of n, when nP2 = 20 is

• 2)

The number of diagonals in a polygon of n seates is equal to

• 3)

The greatest positive integer which divide n(n + 1) (n + 2) (n + 3) for n $\in$ N is

• 4)

For all n > 0, nC1 + nC2 + nC3 + ... +nCn is equal to

• 5)

The middle term in the expansion of ${ \left( x+\frac { 1 }{ x } \right) }^{ 10 }$

#### 11th Standard Business Maths Unit 1 Matrices And Determinants Book Back Questions - by Banumathi - Nilgiris Aug 30, 2019 - View & Download

• 1)

If A = $\begin{vmatrix}cos \theta & sin \theta \\ -sin \theta&cons\theta \end{vmatrix}$ then |2A| is equal to

• 2)

If $\triangle=\begin{vmatrix} {a}_{11} & {a}_{12} & {a}_{13} \\ {a}_{21} & {a}_{22} & {a}_{23} \\ {a}_{31} & {a}_{32} & {a}_{33} \end{vmatrix}$ and Aij is cofactor of aij, then value of $\triangle$ is given by

• 3)

If $\begin{vmatrix} x & 2 \\ 8 &5 \end{vmatrix}=0$ then the value of x is

• 4)

If $\begin{vmatrix} 4 & 3 \\ 3 & 1 \end{vmatrix}=-5$ then value of $\begin{vmatrix} 20 & 15 \\ 15 & 5 \end{vmatrix}$ is

• 5)

If any three-rows or columns of a determinant are identical, then the value of the determinant is

#### 11th Standard Business Maths - Descriptive Statistics and Probability One Mark Question and Answer - by Banumathi - Nilgiris Aug 29, 2019 - View & Download

• 1)

Which of the following is positional measure?

• 2)

When calculating the average growth of economy, the correct mean to use is?

• 3)

When an observation in the data is zero, then its geometric mean is

• 4)

The correct relationship among A.M.,G.M.and H.M.is:

• 5)

Harmonic mean is the reciprocal of

#### 11th Standard Business Maths - Financial Mathematics One Mark Question with Answer Key - by Banumathi - Nilgiris Aug 29, 2019 - View & Download

• 1)

The dividend received on 200 shares of face value Rs.100 at 8% dividend value is

• 2)

What is the amount related is selling 8% stacking 200 shares of face value 100 at 50.

• 3)

A man purchases a stock of Rs 20,000 of face value 100 at a premium of 20%, then investment is

• 4)

A person brought a 9% stock of face value Rs 100, for 100 shares at a discount of 10%, then the stock purchased is

• 5)

The Income on 7 % stock at 80 is

#### 11th Business Maths - Applications of Differentiation One Mark Question with Answer - by Banumathi - Nilgiris Aug 28, 2019 - View & Download

• 1)

Average fixed cost of the cost function C(x) = 2x3 +5x2 - 14x +21 is

• 2)

Marginal revenue of the demand function p= 20–3x is

• 3)

If demand and the cost function of a firm are p= 2–x and c = 2x2 +2x +7 then its profit function is

• 4)

Relationship among MR, AR and ηd is

• 5)

For the cost function C =$\frac { 1 }{ 25 } { e }^{ 25 }$, the marginal cost is

#### 11th Standard Chapter 5 Differential Calculus One Mark Question and Answer - by Banumathi - Nilgiris Aug 27, 2019 - View & Download

• 1)

If f(x) = x2 - x + 1, then f (x + 1) is

• 2)

Let $f\left( x \right) =\begin{cases} { x }^{ 2 }-4x\quad ifx\ge 2 \\ x+2\quad ifx<2 \end{cases}$, then f(5) is

• 3)

For $f\left( x \right) =\begin{cases} { x }^{ 2 }-4x\quad ifx\ge 2 \\ x+2\quad ifx<2 \end{cases}$ then f(0) is

• 4)

If f(x) = $\frac{1-x}{1+x}$ then f(-x) is equal to

• 5)

The graph of the line y = 3 is

#### 11th Standard Chapter 4 Trigonometry - One Mark Questions and Answer - by Banumathi - Nilgiris Aug 27, 2019 - View & Download

• 1)

The degree measure of $\frac{\pi}{8}$ is

• 2)

The radian measure of 37o30' is

• 3)

If $\tan\theta=\frac{1}{\sqrt5}$ and $\theta$ lies in the first quadrant, then $\cos\theta$ is

• 4)

The value of $\sin15^o$ is

• 5)

The value of $\sin(-420^o)$ is

#### 11th Business Maths Chapter 3 Analytical Geometry One Mark Question Paper with Answer - by Banumathi - Nilgiris Aug 27, 2019 - View & Download

• 1)

If m1 and m2 are the slopes of the pair of lines given by ax2+ 2hxy + by2 = 0, then the value of m1 + m2 is

• 2)

The angle between the pair of straight lines x2 - 7xy + 4y2 = 0

• 3)

If the lines 2x - 3y - 5 = 0 and 3x - 4y - 7 = 0 are the diameters of a circle, then its centre is

• 4)

The x - intercept of the straight line 3x + 2y - 1 = 0 is

• 5)

The slope of the line 7x + 5y - 8 = 0 is

#### 11th Business Maths Algebra - One Mark Question with Answer Key - by Banumathi - Nilgiris Aug 26, 2019 - View & Download

• 1)

If nC3 = nC2, then the value of nC4 is

• 2)

The number of ways selecting 4 players out of 5 is

• 3)

The greatest positive integer which divide n(n + 1) (n + 2) (n + 3) for n $\in$ N is

• 4)

If n is a positive integer, then the number of terms in the expansion (x + a)n is

• 5)

For all n > 0, nC1 + nC2 + nC3 + ... +nCn is equal to

#### 11th Mathematics Matrices And Determinants One Mark Question Paper - by Banumathi - Nilgiris Aug 23, 2019 - View & Download

• 1)

The value of x if $\begin{vmatrix} 0 & 1 & 0 \\ x & 2 & x \\ 1 & 3 & x \end{vmatrix}=0$ is

• 2)

The value of $\begin{vmatrix} 2x+y & x & y \\ 2y+z & y & z \\ 2z+x & z & x \end{vmatrix}$ is

• 3)

The co-factor of -7 in the determinant $\begin{vmatrix} 2 & -3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & -7 \end{vmatrix}$ is

• 4)

If $\triangle=\begin{vmatrix} 1 & 2 & 3 \\ 3 & 1 & 2 \\ 2 & 3 & 1 \end{vmatrix}$ then $\begin{vmatrix} 3 & 1 & 2 \\ 1 & 2 & 3 \\ 2 & 3 & 1 \end{vmatrix}$ is

• 5)

The value of the determinant ${\begin{vmatrix} a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & c \end{vmatrix}}^{2}$is

#### 11th Business Maths Differential Calculus Model Question Paper - by Banumathi - Nilgiris Aug 20, 2019 - View & Download

• 1)

The graph of y = 2x2 is passing through

• 2)

Which one of the following functions has the property f (x) = $f\left( \frac { 1 }{ x } \right)$

• 3)

The range of f(x) = |x|, for all $x\epsilon R$, is

• 4)

A function f(x) is continuous at x = a if $\lim _{ x\rightarrow a }{ f\left( x \right) }$ is equal to

• 5)

If y = log x then y2 =

#### 11th Standard Business Maths First Mid Term Model Question Paper - by Banumathi - Nilgiris Aug 01, 2019 - View & Download

• 1)

The value of x if $\begin{vmatrix} 0 & 1 & 0 \\ x & 2 & x \\ 1 & 3 & x \end{vmatrix}=0$ is

• 2)

If A is a square matrix of order 3, then |kA| is

• 3)

If $\triangle=\begin{vmatrix} {a}_{11} & {a}_{12} & {a}_{13} \\ {a}_{21} & {a}_{22} & {a}_{23} \\ {a}_{31} & {a}_{32} & {a}_{33} \end{vmatrix}$ and Aij is cofactor of aij, then value of $\triangle$ is given by

• 4)

The number of permutation of n different things taken r at a time, when the repetition is allowed is

• 5)

The distance between directrix and focus of a parabola y2 = 4ax is

#### 11th Standard Business Maths Chapter 4 Trigonometry Sample Question Paper - by Banumathi - Nilgiris Jul 31, 2019 - View & Download

• 1)

The degree measure of $\frac{\pi}{8}$ is

• 2)

If $\tan\theta=\frac{1}{\sqrt5}$ and $\theta$ lies in the first quadrant, then $\cos\theta$ is

• 3)

The value of sin 15o cos 15o is

• 4)

The value of sec A sin(270o+A) is

• 5)

If sin A+ cos A=1, then sin 2A is equal to

#### 11th Standard Business Maths Chapter 3 Analytical Geometry Important Question Paper - by Banumathi - Nilgiris Jul 26, 2019 - View & Download

• 1)

If m1 and m2 are the slopes of the pair of lines given by ax2+ 2hxy + by2 = 0, then the value of m1 + m2 is

• 2)

The angle between the pair of straight lines x2 - 7xy + 4y2 = 0

• 3)

If the lines 2x - 3y - 5 = 0 and 3x - 4y - 7 = 0 are the diameters of a circle, then its centre is

• 4)

The distance between directrix and focus of a parabola y2 = 4ax is

• 5)

The equation of directrix of the parabola y2 = - x is

#### 11th Standard Business Maths Unit 2 Algebra Important Question Paper - by Banumathi - Nilgiris Jul 24, 2019 - View & Download

• 1)

If nC3 = nC2, then the value of nC4 is

• 2)

The value of n, when nP2 = 20 is

• 3)

The number of ways selecting 4 players out of 5 is

• 4)

If nPr = 720 (nCr), then r is equal to

• 5)

The possible out comes when a coin is tossed five times

#### 11th Business Maths - Unit 1 Model Question Paper - by Banumathi - Nilgiris Jul 18, 2019 - View & Download

• 1)

The value of x if $\begin{vmatrix} 0 & 1 & 0 \\ x & 2 & x \\ 1 & 3 & x \end{vmatrix}=0$ is

• 2)

If $\triangle=\begin{vmatrix} 1 & 2 & 3 \\ 3 & 1 & 2 \\ 2 & 3 & 1 \end{vmatrix}$ then $\begin{vmatrix} 3 & 1 & 2 \\ 1 & 2 & 3 \\ 2 & 3 & 1 \end{vmatrix}$ is

• 3)

The value of the determinant ${\begin{vmatrix} a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & c \end{vmatrix}}^{2}$is

• 4)

Which of the following matrix has no inverse

• 5)

The Inverse of matrix of$\begin{pmatrix} 3 & 1 \\ 5 & 2\end{pmatrix}$ is

• 1)

Prove that $\left| \begin{matrix} x & sin\theta & cos\theta \\ -sin\theta & -x & 1 \\ cos\theta & 1 & x \end{matrix} \right|$ is independent of $\theta$

• 2)

Using matrix method, solve x+2y+z=7, x+3z = 11 and 2x-3y =1.

• 3)

if A=$\left[ \begin{matrix} cos\ \alpha & sin\ \alpha \\ -sin\ \alpha & \ cos\ \alpha \ \end{matrix} \right]$ is such that AT = A-1, find $\alpha$

• 4)

Verify that A(adj A) = (adj A) A = IAI·I for the matrix A = $\begin{bmatrix}2 & 3 \\-1 & 4\end{bmatrix}$

• 5)

Solve: 2x+ 5y = 1 and 3x + 2y = 7 using matrix method.

#### 11th Standard Business Maths Public Exam March 2019 Important One Mark Test - by Basky Mar 15, 2019 - View & Download

• 1)

The value of $\begin{vmatrix} 2x+y & x & y \\ 2y+z & y & z \\ 2z+x & z & x \end{vmatrix}$ is

• 2)

If $\triangle=\begin{vmatrix} 1 & 2 & 3 \\ 3 & 1 & 2 \\ 2 & 3 & 1 \end{vmatrix}$ then $\begin{vmatrix} 3 & 1 & 2 \\ 1 & 2 & 3 \\ 2 & 3 & 1 \end{vmatrix}$ is

• 3)

The value of the determinant ${\begin{vmatrix} a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & c \end{vmatrix}}^{2}$is

• 4)

• 5)

The inverse matrix of $\begin{pmatrix} \frac { 1 }{ 5 } & \frac { 5 }{ 25 } \\ \frac { 2 }{ 5 } & \frac { 1 }{ 2 } \end{pmatrix}$ is

#### Plus One Business Maths Public Exam March 2019 One Mark Question Paper - by Basky Mar 12, 2019 - View & Download

• 1)

The co-factor of -7 in the determinant $\begin{vmatrix} 2 & -3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & -7 \end{vmatrix}$ is

• 2)

If $\triangle=\begin{vmatrix} 1 & 2 & 3 \\ 3 & 1 & 2 \\ 2 & 3 & 1 \end{vmatrix}$ then $\begin{vmatrix} 3 & 1 & 2 \\ 1 & 2 & 3 \\ 2 & 3 & 1 \end{vmatrix}$ is

• 3)

• 4)

If A and B are non-singular matrices then, which of the following is incorrect?

• 5)

If A is a square matrix of order 3 and IAI = 3 then | adj A| is equal to

#### 11th Standard Business Maths Public Exam March 2019 Important One Mark Questions - by Basky Mar 12, 2019 - View & Download

• 1)

The value of x if $\begin{vmatrix} 0 & 1 & 0 \\ x & 2 & x \\ 1 & 3 & x \end{vmatrix}=0$ is

• 2)

If $\triangle=\begin{vmatrix} 1 & 2 & 3 \\ 3 & 1 & 2 \\ 2 & 3 & 1 \end{vmatrix}$ then $\begin{vmatrix} 3 & 1 & 2 \\ 1 & 2 & 3 \\ 2 & 3 & 1 \end{vmatrix}$ is

• 3)

The value of the determinant ${\begin{vmatrix} a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & c \end{vmatrix}}^{2}$is

• 4)

If A is a square matrix of order 3, then |kA| is

• 5)

• 1)

The technology matrix of an economic system of two industries is$\begin{bmatrix} 0.50 & 0.30 \\ 0.41 & 0.33 \end{bmatrix}$. Test whether the system is viable as per Hawkins Simon conditions.

• 2)

Find the minors and cofactors of all the elements of the following determinants.
$\begin{bmatrix} 1&-3&2\\4&-1&2\\3&5&2 \end{bmatrix}$

• 3)

Find |AB| if $A=\begin{bmatrix} 3&-1\\2&1 \end{bmatrix}and \begin{bmatrix} 3&0\\1&-2 \end{bmatrix}$

• 4)

If A $=\begin{bmatrix} 1 \\ -4\\3 \end{bmatrix}$ and  B = [-1 2 1], verify that (AB)T = BT. AT.

• 5)

Using the property of determinant, evaluate $\begin{vmatrix} 6 &5 &12 \\ 2 & 4 &4 \\2 & 1 & 4 \end{vmatrix}.$

#### 11th Standard Business Maths Public Exam March 2019 Important 5 Marks Questions - by Basky Mar 12, 2019 - View & Download

• 1)

Evaluate:$\begin{vmatrix} 1&a&a^2-bc\\1&b&b^2-ca\\1&c&c^2-ab \end{vmatrix}$

• 2)

If A = $\begin{bmatrix}1 & 1 & 1 \\ 3 & 4 & 7\\1 & -1 & 1 \end{bmatrix}$ verify that A ( adj A ) = ( adj A ) A = |A| I3.

• 3)

Solve by using matrix inversion method: x - y + z = 2; 2x- y = 0 , 2y - z = 1.

• 4)

Without expanding show that $\Delta =\left| \begin{matrix} { cosec }^{ 2 }\theta & { cot }^{ 2 }\theta & 1 \\ { cot }^{ 2 }\theta & { cosec }^{ 2 }\theta & -1 \\ 42 & 40 & 2 \end{matrix} \right| =0$

• 5)

If $A=\left[ \begin{matrix} 1 & tan\quad x \\ -tan\quad x & \quad \quad \quad 1 \end{matrix} \right]$, then show that ATA-1=$\left[ \begin{matrix} cos\quad 2x & -sin2x \\ sin\quad 2x & cos2x \end{matrix} \right] .$

• 1)

The value of x if $\begin{vmatrix} 0 & 1 & 0 \\ x & 2 & x \\ 1 & 3 & x \end{vmatrix}=0$ is

• 2)

If any three-rows or columns of a determinant are identical, then the value of the determinant is

• 3)

The value of n, when nP2 = 20 is

• 4)

13 guests have participated in a dinner. The number of handshakes happened in the dinner is

• 5)

The eccentricity of the parabola is

#### 11th Standard Business Maths Public Exam March 2019 Model Test Question Paper - by Basky Mar 04, 2019 - View & Download

• 1)

If A and B are non-singular matrices then, which of the following is incorrect?

• 2)

If any three-rows or columns of a determinant are identical, then the value of the determinant is

• 3)

The term containing x3 in the expansion of (x - 2y)7 is

• 4)

If $\frac { kx }{ (x+4)(2x-1) } =\frac { 4 }{ x+4 } +\frac { 1 }{ 2x-1 }$ then k is equal to

• 5)

The focus of the parabola x2 = 16y is

• 1)

The value of $\begin{vmatrix} 2x+y & x & y \\ 2y+z & y & z \\ 2z+x & z & x \end{vmatrix}$ is

• 2)

The inverse matrix of $\begin{pmatrix} \frac { 1 }{ 5 } & \frac { 5 }{ 25 } \\ \frac { 2 }{ 5 } & \frac { 1 }{ 2 } \end{pmatrix}$ is

• 3)

The value of $\begin{vmatrix} 5 & 5 & 5 \\ 4x & 4y & 4z \\ -3x & -3y & -3z \end{vmatrix}$is

• 4)

If A is 3 x 3 matrix and |A|= 4, then |A-1| is equal to

• 5)

If any three-rows or columns of a determinant are identical, then the value of the determinant is

• 1)

The number of Hawkins-Simon conditions for the viability of an input - output analysis is

• 2)

The inventor of input-output analysis is

• 3)

The possible out comes when a coin is tossed five times

• 4)

Number of words with or without meaning that can be formed using letters of the word "EQUATION" , with no repetition of letters is

• 5)

The double ordinate passing through the focus is

• 1)

The number of Hawkins-Simon conditions for the viability of an input - output analysis is

• 2)

Which of the following matrix has no inverse

• 3)

If nC3 = nC2, then the value of nC4 is

• 4)

Number of words with or without meaning that can be formed using letters of the word "EQUATION" , with no repetition of letters is

• 5)

The slope of the line 7x + 5y - 8 = 0 is

• 1)

• 2)

If A is an invertible matrix of order 2, then det (A-1) be equal to

• 3)

The value of n, when nP2 = 20 is

• 4)

The last term in the expansion of (3 +$\sqrt{2}$ )8 is

• 5)

If kx2 + 3xy - 2y2 = 0 represent a pair of lines which are perpendicular then k is equal to

#### 11th Stateboard Maths Analytical Geometry Important Questions - by Basky Feb 15, 2019 - View & Download

• 1)

The angle between the pair of straight lines x2 - 7xy + 4y2 = 0

• 2)

The slope of the line 7x + 5y - 8 = 0 is

• 3)

If kx2 + 3xy - 2y2 = 0 represent a pair of lines which are perpendicular then k is equal to

• 4)

The length of the tangent from (4,5) to the  circle x2 +y2 = 16 is

• 5)

The focus of the parabola x2 = 16y is

• 1)

The inverse matrix of $\begin{pmatrix} \frac { 1 }{ 5 } & \frac { 5 }{ 25 } \\ \frac { 2 }{ 5 } & \frac { 1 }{ 2 } \end{pmatrix}$ is

• 2)

Which of the following matrix has no inverse

• 3)

The term containing x3 in the expansion of (x - 2y)7 is

• 4)

The number of permutation of n different things taken r at a time, when the repetition is allowed is

• 5)

If kx2 + 3xy - 2y2 = 0 represent a pair of lines which are perpendicular then k is equal to

• 1)

If A $=\begin{pmatrix} -1 & 2 \\ 1 & -4 \end{pmatrix}$ then A (adj A) is

• 2)

The value of $\begin{vmatrix} x & x^2 & -yz & 1 \\ y & y^2 & -zx & 1 \\ z & z^2 & -xy &1 \end{vmatrix}$ is

• 3)

The number of ways selecting 4 players out of 5 is

• 4)

The value of (5Co + 5C1) + (5C1 + 5C2) + (5C2 + 5C3) + (5C3 + 5C4) + (5C4 + 5C5 ) is

• 5)

(1, - 2) is the centre of the circle x2 + y2 + ax + by - 4 = 0 , then its radius

• 1)

Correlation co-efficient lies between

• 2)

The variable whose value is influenced or is to be predicted is called

• 3)

When one regression coefficient is negative, the other would be

• 4)

The lines of regression intersect at the point

• 5)

Cov(x,y)=–16.5, ${ \sigma }_{ x }^{ 2 }=2.89,{ \sigma }_{ y }^{ 2 }$=100. Find correlation coefficient

• 1)

The critical path of the following network is

• 2)

In a network while numbering the events which one of the following statement is false?

• 3)

In the given graph the coordinates of M1 are

• 4)

The maximum value of the objective function Z = 3x + 5y subject to the constraints x > 0 , y > 0 and 2x + 5y ≤10 is

• 5)

The objective of network analysis is to

• 1)

Suppose the inter-industry flow of the product of two industries are given as under.

 Production sector Consumption sector Domestic demand Total output X Y X 30 40 50 120 Y 20 10 30 60

Determine the technology matrix and test Hawkin's -Simon conditions for the viability of the system. If the domestic demand changes to 80 and 40 units respectively, what should be the gross output of each sector in order to meet the new demands.

• 2)

An amount of Rs. 5000 is put into three investment at the rate of interest of 6%, 7% and 8% per annum respectively. The total annual income is Rs. 358. If the combined income from the first two investment is Rs. 70 more than the income from the third, find the amount of each investment by matrix method.

• 3)

Resolve into partial fractions for the following:
$\frac { x-2 }{ (x+2)(x-1)^{ 2 } }$

• 4)

Using binomial theorem, find the value of ${ \left( \sqrt { 2 } +1 \right) }^{ 5 }+{ \left( \sqrt { 2 } -1 \right) }^{ 5 }$

• 5)

Show by the principle of mathematical induction that 23n–1 is a divisible by 7, for all n∈N.

• 1)

If $\triangle=\begin{vmatrix} 1 & 2 & 3 \\ 3 & 1 & 2 \\ 2 & 3 & 1 \end{vmatrix}$ then $\begin{vmatrix} 3 & 1 & 2 \\ 1 & 2 & 3 \\ 2 & 3 & 1 \end{vmatrix}$ is

• 2)

If any three-rows or columns of a determinant are identical, then the value of the determinant is

• 3)

The number of ways to arrange the letters of the word "CHEESE" is

• 4)

The number of permutation of n different things taken r at a time, when the repetition is allowed is

• 5)

The x - intercept of the straight line 3x + 2y - 1 = 0 is

#### 12th Standard Business Maths Important Question Paper - by S.B.O.A. Matric and Hr Sec School Oct 01, 2018 - View & Download

• 1)

If $\triangle=\begin{vmatrix} 1 & 2 & 3 \\ 3 & 1 & 2 \\ 2 & 3 & 1 \end{vmatrix}$ then $\begin{vmatrix} 3 & 1 & 2 \\ 1 & 2 & 3 \\ 2 & 3 & 1 \end{vmatrix}$ is

• 2)

The inverse matrix of $\begin{pmatrix} \frac { 1 }{ 5 } & \frac { 5 }{ 25 } \\ \frac { 2 }{ 5 } & \frac { 1 }{ 2 } \end{pmatrix}$ is

• 3)

The value of $\begin{vmatrix} 5 & 5 & 5 \\ 4x & 4y & 4z \\ -3x & -3y & -3z \end{vmatrix}$is

• 4)

If any three-rows or columns of a determinant are identical, then the value of the determinant is

• 5)

The number of ways selecting 4 players out of 5 is

• 1)

The value of x if $\begin{vmatrix} 0 & 1 & 0 \\ x & 2 & x \\ 1 & 3 & x \end{vmatrix}=0$ is

• 2)

The value of the determinant ${\begin{vmatrix} a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & c \end{vmatrix}}^{2}$is

• 3)

• 4)

The number of Hawkins-Simon conditions for the viability of an input - output analysis is

• 5)

The Inverse of matrix of$\begin{pmatrix} 3 & 1 \\ 5 & 2\end{pmatrix}$ is

• 1)

The co-factor of -7 in the determinant $\begin{vmatrix} 2 & -3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & -7 \end{vmatrix}$ is

• 2)

If $\triangle=\begin{vmatrix} 1 & 2 & 3 \\ 3 & 1 & 2 \\ 2 & 3 & 1 \end{vmatrix}$ then $\begin{vmatrix} 3 & 1 & 2 \\ 1 & 2 & 3 \\ 2 & 3 & 1 \end{vmatrix}$ is

• 3)

The value of the determinant ${\begin{vmatrix} a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & c \end{vmatrix}}^{2}$is

• 4)

If $\triangle=\begin{vmatrix} {a}_{11} & {a}_{12} & {a}_{13} \\ {a}_{21} & {a}_{22} & {a}_{23} \\ {a}_{31} & {a}_{32} & {a}_{33} \end{vmatrix}$ and Aij is cofactor of aij, then value of $\triangle$ is given by

• 5)

If nC3 = nC2, then the value of nC4 is

• 1)

If m1 and m2 are the slopes of the pair of lines given by ax2+ 2hxy + by2 = 0, then the value of m1 + m2 is

• 2)

The angle between the pair of straight lines x2 - 7xy + 4y2 = 0

• 3)

If the lines 2x - 3y - 5 = 0 and 3x - 4y - 7 = 0 are the diameters of a circle, then its centre is

• 4)

The locus of the point P which moves such that P is at equidistance from their coordinate axes is

• 5)

The locus of the point P which moves such that P is always at equidistance from the line x + 2y+ 7 = 0 is

• 1)

The value of n, when nP2 = 20 is

• 2)

The number of ways selecting 4 players out of 5 is

• 3)

The greatest positive integer which divide n(n + 1) (n + 2) (n + 3) for n $\in$ N is

• 4)

If n is a positive integer, then the number of terms in the expansion (x + a)n is

• 5)

For all n > 0, nC1 + nC2 + nC3 + ... +nCn is equal to

• 1)

If $\tan\theta=\frac{1}{\sqrt5}$ and $\theta$ lies in the first quadrant, then $\cos\theta$ is

• 2)

The value of 1-2sin245o is

• 3)

The value 4cos340o-3cos40o is

• 4)

The value of $\frac{2\tan30^o}{1+tan^230}$ is

• 5)

If $\sin A=\frac{1}{2}$ then $4\cos^3A-3\cos A$ is

• 1)

The angle between the pair of straight lines x2 - 7xy + 4y2 = 0

• 2)

If the lines 2x - 3y - 5 = 0 and 3x - 4y - 7 = 0 are the diameters of a circle, then its centre is

• 3)

The x - intercept of the straight line 3x + 2y - 1 = 0 is

• 4)

If the centre of the circle is (-a, -b) and radius $\sqrt{a^2-b^2}$then the equation of circle is

• 5)

Combined equation of co-ordinate axes is

• 1)

The value of x if $\begin{vmatrix} 0 & 1 & 0 \\ x & 2 & x \\ 1 & 3 & x \end{vmatrix}=0$ is

• 2)

The value of the determinant ${\begin{vmatrix} a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & c \end{vmatrix}}^{2}$is

• 3)

The number of Hawkins-Simon conditions for the viability of an input - output analysis is

• 4)

Which of the following matrix has no inverse

• 5)

The Inverse of matrix of$\begin{pmatrix} 3 & 1 \\ 5 & 2\end{pmatrix}$ is

• 1)

The value of x if $\begin{vmatrix} 0 & 1 & 0 \\ x & 2 & x \\ 1 & 3 & x \end{vmatrix}=0$ is

• 2)

• 3)

If A = $\begin{pmatrix} a & b \\ c & d \end{pmatrix}$such that ad - bc $\neq$ 0 then A-1 is

• 4)

The Inverse of matrix of$\begin{pmatrix} 3 & 1 \\ 5 & 2\end{pmatrix}$ is

• 5)

If A and B are non-singular matrices then, which of the following is incorrect?