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### 11th Standard Business Maths Study material & Free Online Practice Tests - View Model Question Papers with Solutions for Class 11 Session 2020 - 2021 TN Stateboard [ Chapter , Marks , Book Back, Creative & Term Based Questions Papers - Syllabus, Study Materials, MCQ's Practice Tests etc..]

#### 11th Standard Business maths English Medium One Mark important Questions Book back and Creative - 2020 - by Question Bank Software - View & Read

• 1)

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

• 2)

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

• 3)

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

• 4)

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

• 5)

If any three rows or columns of a determinant are identical then the value of the determinant is ________.

#### 11th Standard Business Mathematics English Medium All Chapter Book Back and Creative One Marks Questions 2020 - by Question Bank Software - View & Read

• 1)

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

• 2)

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

• 3)

If nC3 = nC2, then the value of nC4 is _________

• 4)

The possible out comes when a coin is tossed five times _________.

• 5)

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

#### 11th Standard Business Mathematics English Medium All Chapter Book Back and Creative Two Marks Questions 2020 - by Question Bank Software - View & Read

• 1)

Suppose the inter-industry flow of the product of two sectors X and Y are given as under.

Production
Sector
Consumption
Sector
Domestic
demand
Gross
output
X Y
X 15 10 10 35
Y 20 30 15 65

Find the gross output when the domestic demand changes to 12 for X and 18 for Y.

• 2)

If $A=\begin{bmatrix} 1 & 2 \\ 4 & 2 \end{bmatrix}$ then show that |2A| = 4 |A|.

• 3)

Find the values of x if $\begin{vmatrix} 2 & 4 \\5 & 1 \end{vmatrix}=\begin{vmatrix} 2x & 4\\6 & x \end{vmatrix}.$

• 4)

Show that $\left[ \begin{matrix} 1 & 2 \\ 2 & 4 \end{matrix} \right]$is a singular matrix.

• 5)

Resolve into partial fractions for the following : $\frac{3 x+7}{x^2-3 x+2}$

#### 11th Standard Business Mathematics English Medium All Chapter Book Back and Creative Three Marks Questions 2020 - by Question Bank Software - View & Read

• 1)

Evaluate: $\begin{bmatrix} 3&-2&4\\2&0&1\\1&2&3 \end{bmatrix}$

• 2)

Show that $\begin{vmatrix}x+a &b&c \\a &x+b&c\\a&b&x+c \end{vmatrix}=x^2(x+a+b+c)$

• 3)

Using the properties of determinants, show that $\left| \begin{matrix} 2 & 7 & 65 \\ 3 & 8 & 75 \\ 5 & 9 & 86 \end{matrix} \right|$ = 0

• 4)

If $A=\left[ \begin{matrix} 2 & 4 \\ -3 & 2 \end{matrix} \right]$then, find A -1.

• 5)

How many numbers lesser than 1000 can be formed using the digits 5, 6, 7, 8 and 9 if no digit is repeated?

#### 11th Standard Business Mathematics English Medium All Chapter Book Back and Creative Five Marks Questions 2020 - by Question Bank Software - View & Read

• 1)

Prove that $\begin{vmatrix} {1\over a}&bc&b+c\\{1\over b}&ca&c+a\\{1\over c}&ab&a+b \end{vmatrix}=0$

• 2)

The sum of three numbers is 20. If we multiply the first by 2 and add the second number and subtract the third we get 23. If we multiply the first by 3 and add second and third to it, we get 46. By using matrix inversion method find the numbers.

• 3)

Use the product $\left[ \begin{matrix} 1 & -1 & 2 \\ 0 & 2 & -3 \\ 3 & -2 & 4 \end{matrix} \right] \left[ \begin{matrix} -2 & 0 & 1 \\ 9 & 2 & -3 \\ 6 & 1 & -2 \end{matrix} \right]$to solve the system of equations x - 2y + 2z = 1, 2y - 3z = 1, 3x - 2y + 4z = 2.

• 4)

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.

• 5)

Resolve into partial fractions for the following : $\frac{1}{\left(x^2+4\right)(x+1)}$

#### 11th Business Maths - Full Portion Five Marks Question Paper - by 8682895000 - View & Read

• 1)

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

• 2)

If$A=\begin{bmatrix}1&3&3\\1&4&3\\1&3&4 \end{bmatrix}$then verify that A (adj A) = |A| I and also find A-1.

• 3)

Let a, b and c denote the sides BC, CA and AB repectively of $\Delta$ ABC. If $\left| \begin{matrix} 1 & a & b \\ 1 & c & a \\ 1 & b & c \end{matrix} \right| =0$, then find the value of sin2 A + sin2B + sin2C.

• 4)

The sum of three numbers is 20. If we multiply the first by 2 and add the second number and subtract the third we get 23. If we multiply the first by 3 and add second and third to it, we get 46. By using matrix inversion method find the numbers.

• 5)

Show that the matrices $A=\left[ \begin{matrix} 1 & 3 & 7 \\ 4 & 2 & 3 \\ 1 & 2 & 1 \end{matrix} \right]$and $B=\left[ \begin{matrix} \frac { -4 }{ 35 } & \frac { 11 }{ 35 } & \frac { -5 }{ 35 } \\ \frac { -1 }{ 35 } & \frac { -6 }{ 35 } & \frac { 25 }{ 35 } \\ \frac { 6 }{ 35 } & \frac { 1 }{ 35 } & \frac { -10 }{ 35 } \end{matrix} \right]$are inverses of each other.

#### 11th Business Maths - Full Portion Three Marks Question Paper - by 8682895000 - View & Read

• 1)

Evaluate: $\begin{bmatrix} 3&-2&4\\2&0&1\\1&2&3 \end{bmatrix}$

• 2)

Without actual expansion show that the value of the determinant $\begin{vmatrix}5 &5^2 &5^3 \\5^2 & 5^3 & 5^4\\5^4&5^5&5^6 \end{vmatrix}$is zero.

• 3)

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

• 4)

Using co-factors of elements of  second column evaluate $\left| \begin{matrix} 6 & -1 & 5 \\ 3 & 0 & 4 \\ -2 & 7 & -3 \end{matrix} \right|$

• 5)

The technology matrix of an economic system of two industries is $\left[ \begin{matrix} 0.8 & 0.2 \\ 0.9 & 0.7 \end{matrix} \right]$ Test whether the system is viable as per Hawkins – Simon conditions.

#### 11th Business Maths - Full Portion Two Marks Question Paper - by 8682895000 - View & Read

• 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)

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

• 3)

Find the values of x if $\begin{vmatrix} 2 & 4 \\5 & 1 \end{vmatrix}=\begin{vmatrix} 2x & 4\\6 & x \end{vmatrix}.$

• 4)

Evaluate:$\left| \begin{matrix} 1 & 2 & 4 \\ -1 & 3 & 0 \\ 4 & 1 & 0 \end{matrix} \right|$

• 5)

Resolve into partial fractions for the following : $\frac{4 x+1}{(x-2)(x+1)}$

#### 11th Business Maths - Revision Model Question Paper 2 - by Question Bank Software - View & Read

• 1)

The inventor of input-output analysis is ________.

• 2)

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

• 3)

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

• 4)

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

• 5)

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

#### 11th Business Maths - Public Exam Model Question Paper 2019 - 2020 - by Question Bank Software - View & Read

• 1)

If A is 3 $\times$ 3 matrix and |A| = 4, then |A-1| 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 nC3 = nC2, then the value of nC4 is _________

• 4)

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

• 5)

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

#### 11th Business Maths - Operations Research Model Question Paper - by Question Bank Software - View & Read

• 1)

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

• 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 critical path analysis, the word CPM mean ______.

• 5)

Given an L.P.P maximize Z = 2x1 + 3x2 subject to the constrains x1 + x2 ≤ 1, 5x1 + 5x2 ≥ 0 and x1 ≥ 0, x2 ≥ 0 using graphical method, we observe ______.

#### 11th Business Maths - Correlation and Regression Analysis Model Question Paper - by Question Bank Software - View & Read

• 1)

The correlation coefficient is ________.

• 2)

The variable which influences the values or is used for prediction is called________.

• 3)

Scatter diagram of the variate values (X,Y) give the idea about ________.

• 4)

If regression co-efficient of Y on X is 2, then the regression co-efficient of X on Y is ________.

• 5)

Calculate the correlation coefficient from the following data
N = 9, ΣX = 45, ΣY = 108, ΣX2 = 285, ΣY2 = 1356, ΣXY = 597

#### 11th Business Maths - Descriptive Statistics and Probability Model Question Paper - by Question Bank Software - View & Read

• 1)

Which of the following is positional measure?

• 2)

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

• 3)

Harmonic mean is the reciprocal of _________.

• 4)

Median is same as _________.

• 5)

Harmonic mean is better than other means if the data are for _________.

#### 11th Business Maths - Financial Mathematics Model Question Paper - by Question Bank Software - View & Read

• 1)

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

• 2)

The Income on 7 % stock at 80 is _______.

• 3)

A invested some money in 10% stock at 96. If B wants to invest in an equally good 12% stock, he must purchase a stock worth of  _______.

• 4)

The present value of the perpetual annuity of Rs 2000 paid monthly at 10 % compound interest is _______.

• 5)

Example of contingent annuity is _______.

#### 11th Business Maths - Applications of Differentiation Model Question Paper - by Question Bank Software - View & Read

• 1)

The elasticity of demand for the demand function x = $\frac { 1 }{ p }$ is______.

• 2)

Relationship among MR, AR and ηd is ______.

• 3)

If u = 4x2 + 4xy + y2 + 32 + 16 , then $\frac { \partial ^{ 2 }u }{ \partial y\partial x }$ is equal to ________.

• 4)

If u = x3 + 3xy2 + y3 then  $\frac { \partial ^{ 2 }u }{ \partial y\partial x }$ is _______.

• 5)

if q = 1000 + 8p1 - p2 then, $\frac { \partial q }{ \partial { p }_{ 1 } }$ is _______.

#### 11th Business Maths - Differential Calculus Model Question Paper - by Question Bank Software - View & Read

• 1)

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

• 2)

The graph of y = ex intersect the y-axis at _______.

• 3)

Which one of the following functions has the property f (x) = $f\left( \frac { 1 }{ x } \right)$, provided $x \neq 0$

• 4)

The graph of f(x) = ex is identical to that of ________.

• 5)

$\lim _{ x\rightarrow 0 }{ \frac { { e }^{ x }-1 }{ x } } =$________.

#### 11th Business Maths - Trigonometry Model Question Paper - by Question Bank Software - View & Read

• 1)

The radian measure of 37o30' is ______.

• 2)

The value of $\sin(-420^o)$ is _______.

• 3)

The value of cos245o - sin245o is_______.

• 4)

The value of $\frac{3 \tan 10^{\circ}-\tan ^3 10^{\circ}}{1-3 \tan ^2 10^{\circ}}$ is _______,

• 5)

If $\alpha$ and $\beta$ be between 0 and $\frac{\pi}{2}$ and if $\cos(\alpha+\beta)=\frac{12}{13}$ and $\sin(\alpha-\beta)=\frac{3}{5}$ then $\sin2\alpha$ is  _____.

#### 11th Business Maths - Analytical Geometry Model Question Paper - by Question Bank Software - View & Read

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

• 3)

Length of the latus rectum of the parabola y2 = - 25x is _______.

• 4)

ax2 + 4xy + 2y2 = 0 represents a pair of parallel lines then 'a' is _______.

• 5)

The equation of the circle with centre (3,-4) and touches the x - axis is _______.

#### 11th Business Maths - Matrices And Determinants Important Questions - by Question Bank Software - View & Read

• 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)

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

• 4)

Which of the following matrix has no inverse

• 5)

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

#### 11th Business Maths - Algebra Important Questions - by Question Bank Software - View & Read

• 1)

If nC3 = nC2, then the value of nC4 is _________

• 2)

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

• 3)

There are 10 true or false questions in an examination. Then these questions can be answered in ______

• 4)

The value of (5C0 + 5C1) + (5C1 + 5C2) + (5C2 + 5C3) + (5C3 + 5C4) + (5C4 + 5C5 ) is ________

• 5)

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

#### 11th Business Maths - Half Yearly Model Question Paper 2019 - by Question Bank Software - View & Read

• 1)

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

• 2)

Which of the following matrix has no inverse

• 3)

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

• 4)

The possible out comes when a coin is tossed five times _________.

• 5)

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

#### 12th Business Maths - Term II Model Question Paper - by Kalaivani - Palani - View & Read

• 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 square matrix of order 3, then |kA| is________.

• 3)

If any three rows or columns of a determinant are identical then the value of the determinant is ________.

• 4)

The value of n, when nP2 = 20 is _______

• 5)

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

#### 11th Business Maths - Operations Research Three Marks Questions - by Question Bank Software - View & Read

• 1)

Solve the following LPP graphically. Maximize Z = 6x1 + 5x2 Subject to the constraints 3x1 + 5x2 ≤ 15, 5x1 + 2x2 ≤ 10 and x1,x2 ≥ 0

• 2)

Solve the following LPP graphically. Maximize Z =−x1 + 2x2
Subject to the constraints −x1 + 3x2 ≤ 10, x1 + x2 ≤ 6,x1 − x2 ≤ 2 and x1,x2 ≥ 0

• 3)

Solve the following LPP graphically. Minimize Z = x1 − 5x2 + 20
Subject to the constraints x1 − x2 ≥ 0,−x1 + 2x2 ≥ 2,x1 ≥ 3,x2 ≤ 4 and x1,x≥ 0.

• 4)

Solve the following LPP graphically. ∴ Maximize Z = 3x1 + 4x2  subject to the constraints x1 + x2 ≤ 4 and x1,x2 ≥ 0.

• 5)

Solve the following LPP graphically. Minimize$Z=-3{ x }_{ 1 }+4{ x }_{ 2 }$
Subject to the constraints ${ x }_{ 1 }+2{ x }_{ 2 }\le 8\quad ,{ 3x }_{ 1 }+{ 2x }_{ 2 }\le 12\quad and\quad \quad { x }_{ 1 }\ge 0,{ x }_{ 2 }\ge 2.$

#### 11th Business Maths - Correlation and Regression Analysis Three Marks Questions - by Question Bank Software - View & Read

• 1)

Calculate the correlation co-efficient for the following data.

 X 5 10 5 11 12 4 3 2 7 1 Y 1 6 2 8 5 1 4 6 5 2
• 2)

Calculate the coefficient of correlation between X and Y series from the following data.

 Description X Y Number of pairs of observation 15 15 Arithmetic mean 25 18 Standard deviation 3.01 3.03 Sum of squares of deviation from the arithmetic mean 136 138

Summation of product deviations of X and Y series from their respective arithmetic means is 122.

• 3)

A random sample of recent repair jobs was selected and estimated cost and actual cost were recorded.

 Estimated cost 300 450 800 250 500 975 475 400 Actual cost 273 486 734 297 631 872 396 457

Calculate the value of spearman’s correlation coefficient.

• 4)

The rank of 10 students of same batch in two subjects A and B are given below. Calculate the rank correlation coefficient.

 Rank of A 1 2 3 4 5 6 7 8 9 10 Rank of B 6 7 5 10 3 9 4 1 8 2
• 5)

The following table shows the sales and advertisement expenditure of a form

 Title Sales Advertisement expenditure(Rs.Cross) Mean 40 6 SD 10 1.5

Coefficient of correlation r = 0.9. Estimate the likely sales for a proposed advertisement expenditure of Rs. 10 crores.

#### 11th Business Maths - Descriptive Statistics and Probability Three Marks Questions - by Question Bank Software - View & Read

• 1)

Compared to the previous year the overhead expenses went up by 32% in 1995, they increased by 40% in the next year and by 50% in the following year. Calculate the average rate of increase in overhead expenses over the three years.

• 2)

From the following data compute the value of Harmonic Mean.

 Marks 10 20 30 40 50 No. of students 20 30 50 15 5
• 3)

Calculate the value of quartile deviation and its coefficient from the following data

 Roll No. 1 2 3 4 5 6 7 Marks 20 28 40 12 30 15 50
• 4)

A factory has 3 machines A1, A2, A3 producing 1000, 2000, 3000 screws per day respectively. A1 produces 1% defectives, A2 produces 1.5% and A3 produces 2% defectives. A screw is chosen at random at the end of a day and found defective. What is the probability that it comes from machines A1?

• 5)

X speaks truth 4 out of 5 times. A die is thrown. He reports that there is a six. What is the chance that actually there was a six?

#### 11th Business Maths - Financial Mathematics Three Marks Questions - by Question Bank Software - View & Read

• 1)

Find the amount of an ordinary annuity of 12 monthly payments of Rs 1, 500 that earns interest at 12% per annum compounded monthly. [(1.01)12 = 1.1262 ]

• 2)

A bank pays 8% per annum interest compounded quarterly. Find the equal deposits to be made at the end of each quarter for 10 years to have Rs 30,200? [(1.02)40 = 2.2080]

• 3)

A man buys 400 of Rs 10 shares at a premium of Rs 2.50 on each share. If the rate of dividend is 12%, then find
(i) his investment
(ii) annual dividend received by him
(iii) rate of interest received by him on his money

• 4)

Sundar bought Rs 4,500,12 % of Rs 10 shares at par. He sold them when the price rose to Rs 23 and invested the proceeds in Rs 25 shares paying 10% per annum at Rs 18. Find the change in his income.

• 5)

Find the amount of an annuity of Rs. 2000 payable at the end of every month for 5 years if money is worth 6% per annum compounded monthly.

#### 11th Business Maths - Applications of Differentiation Three Marks Questions - by Question Bank Software - View & Read

• 1)

Find the elasticity of demand in terms of x for the demand law $p={(a-bx)^{1\over 2}}.$ Also find the values of x when elasticity of demand is unity.

• 2)

Find the elasticity of supply for the supply law $x={p\over p+5}$ when p = 20 and interpret your result.

• 3)

Revenue function ‘R’ and cost function ‘C’ are R = 14x - x2 and C = x (x2 - 2). Find the
(i) average cost function
(ii) marginal cost function,
(iii) average revenue function and
(iv) marginal revenue function.

• 4)

Find the stationary value and the stationary points f(x) = x2 + 2x – 5.

• 5)

For the production function P = $4L^{ \frac { 3 }{ 4 } }K^{ \frac { 1 }{ 4 } }$ verify Euler’s theorem.

#### 11th Standard Business Maths - Operations Research Model Question Paper - by Kalaivani - Palani - View & Read

• 1)

The critical path of the following network is________.

• 2)

A solution which maximizes or minimizes the given LPP is called ______.

• 3)

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

• 4)

Which of the following is not correct?

• 5)

Network problems have advantage in terms of project _______.

#### 11th Standard Business Maths - Differential Calculus Three Marks Questions - by Question Bank Software - View & Read

• 1)

If $y=\sqrt { x } +\frac { 1 }{ \sqrt { x } }$ show that $2x\frac { dy }{ dx } +y=2\sqrt { x }$.

• 2)

Show that the function f(x) = [x] where [x] denotes the greatest integer function is discontinuous at all integral points

• 3)

Is the function defined by f(x) = x2 -sin x + 5 is continuous at x =$\pi$?

• 4)

Differentiate: $\sin ^{ -1 }{ \left( \sqrt { \cos { x } } \right) }$

• 5)

Differentiate: sin2 x + cos2 y = 1.

#### 11th Standard Business Maths - Trigonometry Three Marks Questions - by Question Bank Software - View & Read

• 1)

Find all other trigonometrical ratios if $\sin x=\frac{-2\sqrt6}{5}$ and x lies in III quadrant?

• 2)

Prove that $\sin^2\frac{\pi}{6}+\cos^2\frac{\pi}{3}-\tan^2\frac{\pi}{4}=-\frac12$

• 3)

Prove that$\left\{1+\cot x-\sec\left(\frac{\pi}{2}+x\right)\right\}\left\{1+\cot x+\sec\left(\frac{\pi}{2}+x\right)\right\}=2\cot x$

• 4)

Write $\tan ^{ -1 }{ \left( \frac { 1 }{ \sqrt { { x }^{ 2 }-1 } } \right) } ,\left| x \right| >1$ in the simplest form.

• 5)

Prove that $\frac{\sin(x+y)}{\sin(x-y)}=\frac{\tan x+\tan y}{\tan x-\tan y}$

#### 11th Business Maths - Analytical Geometry Three Marks Questions - by Question Bank Software - View & Read

• 1)

A point moves so that its distance from the point (-1, 0) is always three times its distance from the point (0, 2). Find its locus.

• 2)

Find the equation of a circle of radius 5 whose centre lies on X-axis and passes through the point (2, 3).

• 3)

Find the equation of a circle whose diameters are 2x - 3y + 12 = 0 and x + 4y - 5 = 0 and area is 154 square units.

• 4)

Find the condition that the straight lines y=m1x+C1, y=m2x+C2, and y=m3x+C3 may meet at a point?

• 5)

Find the locus of a point such that the sum of its distances from the points (0, 2) and (0, -2) is 6.

#### 11th Business Maths Algebra Three Marks Questions - by Question Bank Software - View & Read

• 1)

Resolve into partial factors:$\frac { x+4 }{ ({ x }^{ 2 }-4)(x+1) }$

• 2)

Solve : $\frac { (2x+1)! }{ (x+2)! } .\frac { (x-1)! }{ (2x-1)! } =\frac { 3 }{ 5 }$

• 3)

How may different numbers between 100 and 1000 can be formed using the digits 0, 1,2,3,4, 5, 6 assuming that in any number, the digits are not repeated.

• 4)

There are 6 gentlemen and 4 ladies to line at a round table. In how many ways can they seat themselves so that no two ladies together?

• 5)

In how many ways can n prizes be given to n boys, when a boy may receive any number of prizes?

#### 11th Business Maths - Matrices And Determinants Three Marks - by Question Bank Software - View & Read

• 1)

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

• 2)

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

• 3)

Write the minors and co-factors of the elements of $\begin{vmatrix}5 & 3 \\-6 & 2\end{vmatrix}$

• 4)

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

• 5)

Find the inverse of $\begin{bmatrix}-1 & 5 \\-3 & 2 \end{bmatrix}$.

#### 11th Business Maths - Correlation and Regression Analysis Model Question Paper - by Kalaivani - Palani - View & Read

• 1)

Example for positive correlation is______.

• 2)

Correlation co-efficient lies between ______.

• 3)

The correlation coefficient from the following data N = 25, ΣX = 125, ΣY = 100, ΣX2 = 650, ΣY2 = 436, ΣXY = 520 ________.

• 4)

From the following data, N = 11, ΣX = 117, ΣY = 260, ΣX2 = 1313, ΣY2 = 6580, ΣXY = 2827 the correlation coefficient is ________.

• 5)

The variable which influences the values or is used for prediction is called________.

#### 11th Business Maths - Descriptive Statistics and Probability Model Question Paper - by Kalaivani - Palani - View & Read

• 1)

Which of the following is positional measure?

• 2)

The best measure of central tendency is _________.

• 3)

The geometric mean of two numbers 8 and 18 shall be _________.

• 4)

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

• 5)

The first quartile is also known as _________.

#### 11th Business Maths - Financial Mathematics Model Question Paper - by Kalaivani - Palani - View & Read

• 1)

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

• 2)

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

• 3)

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

• 4)

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

• 5)

Example of contingent annuity is _______.

#### 11th Business Maths - Applications of Differentiation Model Question Paper - by Kalaivani - Palani - View & Read

• 1)

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

• 2)

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

• 3)

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

• 4)

If u = x3 + 3xy2 + y3 then  $\frac { \partial ^{ 2 }u }{ \partial y\partial x }$ is _______.

• 5)

if q = 1000 + 8p1 - p2 then, $\frac { \partial q }{ \partial { p }_{ 1 } }$ is _______.

#### 11th Standard Business Maths - Operations Research Two Marks Questions - by Question Bank Software - View & Read

• 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 Question Bank Software - View & Read

• 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

 Title 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 Question Bank Software - View & Read

• 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 Question Bank Software - View & Read

• 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 Question Bank Software - View & Read

• 1)

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

• 2)

If $f(x)=\frac { x+1 }{ x-1 }$ ,x ≠ 0 then prove that f(f(x)) = x

• 3)

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

• 4)

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

• 5)

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

#### 11th Business Maths - Term 1 Model Question Paper - by Kalaivani - Palani - View & Read

• 1)

The inventor of input-output analysis is ________.

• 2)

The possible out comes when a coin is tossed five times _________.

• 3)

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

• 4)

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

• 5)

The graph of y = 2x2 is passing through _______.

#### 11th Business Maths - Trigonometry Two Marks Question - by Question Bank Software - View & Read

• 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 Question Bank Software - View & Read

• 1)

Find the equation of the following circles having the centre (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 Question Bank Software - View & Read

• 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 Question Bank Software - View & Read

• 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 Question Bank Software - View & Read

• 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 Question Bank Software - View & Read

• 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 matrix 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 Question Bank Software - View & Read

• 1)

Maximize: z = 3x1 + 4x2 subject to 2x+ x≤ 40, 2x1+ 5x≤ 180, x1, x≥ 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 Question Bank Software - View & Read

• 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 Question Bank Software - View & Read

• 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 Question Bank Software - View & Read

• 1)

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

• 2)

What is the amount related is selling 8% stack 200 shares of face value Rs 100 at Rs 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 Question Bank Software - View & Read

• 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 Question Bank Software - View & Read

• 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) = $f\left( \frac { 1 }{ x } \right)$, provided $x \neq 0$

• 4)

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

• 5)

If the 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 Question Bank Software - View & Read

• 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 Question Bank Software - View & Read

• 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 Question Bank Software - View & Read

• 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 ${ \left( x+\frac { 1 }{ x } \right) }^{ 10 }$ is _______

#### 11th Standard Business Maths Unit 1 Matrices And Determinants Book Back Questions - by Question Bank Software - View & Read

• 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 Question Bank Software - View & Read

• 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 Question Bank Software - View & Read

• 1)

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

• 2)

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

• 3)

A man purchases a stock of Rs 20,000 of face value Rs 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 Question Bank Software - View & Read

• 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 Question Bank Software - View & Read

• 1)

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

• 2)

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

• 3)

If $f\left( x \right) =\begin{cases} { x }^{ 2 }-4x\quad ifx\ge 2 \\ x+2\quad ifx<2 \end{cases}$ 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 Question Bank Software - View & Read

• 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 Question Bank Software - View & Read

• 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 Question Bank Software - View & Read

• 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 Question Bank Software - View & Read

• 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 Question Bank Software - View & Read

• 1)

The graph of y = 2x2 is passing through _______.

• 2)

Which one of the following functions has the property f (x) = $f\left( \frac { 1 }{ x } \right)$, provided $x \neq 0$

• 3)

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

• 4)

If the 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 Question Bank Software - View & Read

• 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 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 Question Bank Software - View & Read

• 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 Question Bank Software - View & Read

• 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 Question Bank Software - View & Read

• 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 Question Bank Software - View & Read

• 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 matrix of $\begin{pmatrix} 3 & 1 \\ 5 & 2\end{pmatrix}$ is ________.

#### 11th Standard Business Maths Public Exam March 2019 Important Creative 3 Mark Questions and Answers - by Basky - View & Read

• 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 - View & Read

• 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)

adj (AB) is equal to ________.

• 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 - View & Read

• 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)

adj (AB) is equal to ________.

• 4)

If A and B are non-singular matrix 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 - View & Read

• 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 square matrix of order 3, then |kA| is________.

• 5)

adj (AB) is equal to ________.

#### 11th Standard Business Maths Public Exam March 2019 Important Creative Questions and Answers - by Basky - View & Read

• 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 - View & Read

• 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 = $\left[ \begin{matrix} cos\quad 2x & -sin2x \\ sin\quad 2x & cos2x \end{matrix} \right] .$

#### Plus One Business Maths Public Exam Official Model Question Paper 2019 - by Basky - View & Read

• 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)

Thirteen guests has 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 - View & Read

• 1)

If A and B are non-singular matrix 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 _______.

#### Plus One Business Maths Matrices And Determinants Important Questions - by Basky - View & Read

• 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 $\times$ 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 ________.

#### 11th Standard Business Maths 3rd Revision Test Question Paper 2019 - by Basky - View & Read

• 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 _______.

#### 11th Standard Business Maths Public Exam Important Questions and Answers 2019 - by Basky - View & Read

• 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 _______.

#### 11th Standard Business Maths Model Revision Test Question Paper 2019 - by Basky - View & Read

• 1)

adj (AB) is equal to ________.

• 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 - View & Read

• 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 _______.

#### 11th Standard Business Maths First Revision Question Paper - by Basky - View & Read

• 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 _______.

#### 11th Standard Business Maths Half Yearly Model Question Paper - by Basky - View & Read

• 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 (5C0 + 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 _______.

#### 11th Business Maths Correlation and Regression Analysis Important Questions - by Basky - View & Read

• 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)

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

#### Operations Research Important Questions - 11th Business Maths - by Basky - View & Read

• 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 ________.

#### 11th Business Maths 5 Marks Revision Test - by Basky - View & Read

• 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 $n \in N$.

#### 11th Business Maths Half Yearly Model Question Paper 1 - by Basky - View & Read

• 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 - View & Read

• 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 _______

#### 11th Business Mathematics Important One Mark Question Paper - by Basky - View & Read

• 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)

adj (AB) is equal to ________.

• 4)

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

• 5)

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

#### 11th Business Mathematics Term I Model Question Paper - by Basky - View & Read

• 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 _________

#### Business Mathematics Important Question Paper 1 In 11th - by Basky - View & Read

• 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 _______.

#### Algebra Important Question In 11th Business Mathematics - by Basky - View & Read

• 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 _______

#### Trignometry Important Question Paper In 11th Business Mathematics - by Basky - View & Read

• 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 ________.

#### Analytical Geometry Important Question Paper In 11th Business Mathematics - by Basky - View & Read

• 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 is $\sqrt{a^2-b^2}$, then the equation of circle is _______.

• 5)

Combined equation of co-ordinate axes is _______.

### TN Stateboard Education Study Materials

#### 11th Stateboard Business Maths 2019 - 2020 Academic Monthly Syllabus - by Question Bank Software Aug 13, 2019 Aug 13, 2019

Business Maths 2019 - 2020 Academic Monthly Syllabus

### TN Stateboard Updated Class 11th Business Maths Syllabus

#### Matrices and Determinants

Determinants-Inverse of a Matrix-Input-Output Analysis

#### Algebra

Partial Fractions-Permutations-Combinations-Mathematical Induction-Binomial Theorem-Analytical Geometry-Locus-System of Straight Lines-Pair of Straight Lines-Circles-Conics

#### Analytical Geometry

Locus-System of Straight Lines-Pair of Straight Lines-Circles-Conics

#### Trigonometry

Trigonometric Ratios-Trigonometric Ratios of Compound Angles-Transformation Formulae-Inverse Trigonometric Functions

#### Differential Calculus

Functions and their Graphs-Limits and Derivatives-Differentiation Techniques

#### TN StateboardStudy Material - Sample Question Papers with Solutions for Class 11 Session 2020 - 2021

Latest Sample Question Papers & Study Material for class 11 session 2020 - 2021 for Subjects Maths, Commerce, Economics, Biology, Accountancy, Computer Science, Physics, Chemistry, Computer Applications , History , Computer Technology, தமிழ், English in PDF form to free download [ available question papers ] for practice. Download QB365 Free Mobile app & get practice question papers.

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