### 12th Standard Business Maths Study material & Free Online Practice Tests - View Model Question Papers with Solutions for Class 12 Session 2019 - 2020 TN Stateboard [ Chapter , Marks , Book Back, Creative & Term Based Questions Papers - Syllabus, Study Materials, MCQ's Practice Tests etc..]

#### 12th Standard English Medium Business Maths Reduced Syllabus Annual Exam Model Question Paper - 2021 - by Sridevi - Sankarankoil - View & Read

• 1)

Which of the following is not an elementary transformation?

• 2)

If A is a singular matrix, then Adj A is.

• 3)

$\int _{ 0 }^{ 1 }{ (2x+1) } dx$ is

• 4)

$\int { { \left| x \right| }^{ 3 } }$dx = ________________ +c

• 5)

Area bounded by the curve y = x (4 − x) between the limits 0 and 4 with x − axis is

#### 12th Standard English medium Business Maths Reduced Syllabus Public Exam Model Question Paper With Answer Key - 2021 - by Sridevi - Sankarankoil - View & Read

• 1)

The rank of m×n matrix whose elements are unity is

• 2)

If A, B are two n x n non-singular matrices, then

• 3)

$\frac { sin5x-sinx }{ cos3x }$dx

• 4)

$\int { { a }^{ 3x+2 } }$ dx = _____________ +c

• 5)

For a demand function p, if ഽ$\frac{dp}{p}$ = k  ഽ$\frac{dx}{x}$ then k is equal to

#### 12th Standard English Medium Business Maths Reduced Syllabus Public Exam Model Question Paper - 2021 - by Sridevi - Sankarankoil - View & Read

• 1)

if $\rho (A)\neq \rho (A,B),$ then the system is

• 2)

If A is a singular matrix, then Adj A is.

• 3)

$\frac { sin2x }{ 2sinx } dx$ is

• 4)

The anti-derivative of f(x) = $\sqrt { x } +\frac { 1 }{ \sqrt { x } }$ is ___________ +c

• 5)

Area bounded by the curve y = e−2x between the limits 0 ≤ x ≤ ∞ is

#### 12th Standard English Medium Business Maths Reduced Syllabus Creative Five Mark Question with Answerkey - 2021(Public Exam ) - by Sridevi - Sankarankoil - View & Read

• 1)

Show that the equations x−4y+7z=14,3x+8y−2z=13,7x−8y+26z =5 are inconsistent.

• 2)

Investigate for what values of ‘a’ and ‘b’ the following system of equations x+y+z=6,x+2y+3z=10, x+2y+az = b have
(i) no solution
(ii) a unique solution
(iii) an infinite number of solutions.

• 3)

Show that the following system of equations have unique solution:
x+y+z=3,x+2y+3z=4,x+4y+9z = 6 by rank method.

• 4)

An amount of Rs.5,000/- is to be deposited in three different bonds bearing 6%, 7% and 8% per year respectively. Total annual income is Rs.358/-. If the income from first two investments is 70/- more than the income from the third, then find the amount of investment in each bond by rank method.

• 5)

Two types of soaps A and B are in the market. Their present market shares are 15% for A and 85% for B. Of those who bought A the previous year, 65% continue to buy it again while 35% switch over to B. Of those who bought B the previous year, 55% buy it again and 45% switch over to A. Find their market shares after one year and when is the equilibrium reached?

#### 12th Standard English Medium Business Maths Reduced Syllabus Creative Three Mark Question with Answerkey - 2021(Public Exam ) - by Sridevi - Sankarankoil - View & Read

• 1)

Show that the equations 2x - Y + z = 7, 3x +y- 5z = 13, x +y + z = 5 are consistent and have a unique solution.

• 2)

Solve: 2x - 3y - 1 = 0, 5x + 2y - 12 = 0 by Cramer's rule.

• 3)

Two products A and B currently share the market with shares 60% and 40% each respectively. Each week some brand switching latees place. Of those who bought A the previous week 70% buy it again whereas 30% switch over to B. Of those who bought B the previous week, 80% buy it again whereas 20% switch over to A. Find their shares after one week and after two weeks.

• 4)

If f' (x) = 3x2 - $\frac { 2 }{ { x }^{ 3 } }$ and f(1) = 0, find f(x)

• 5)

Find the area under the demand curve xy = 1 bounded by the ordinates x = 3, x = 9 and x-axis

#### 12th Standard English Medium Business Maths Reduced Syllabus Creative Two Mark Question with Answerkey - 2021(Public Exam ) - by Sridevi - Sankarankoil - View & Read

• 1)

Find the rank of the matrix $\left[ \begin{matrix} 7 & -1 \\ 2 & 1 \end{matrix} \right]$

• 2)

Solve: x + 2y = 3 and 2x + 4y = 6 using rank method.

• 3)

For what value of x, the matrix
$A=\left| \begin{matrix} 1 & -2 & 3 \\ 1 & 2 & 1 \\ x & 2 & -3 \end{matrix} \right|$ is singular?

• 4)

Evaluate $\int { { a }^{ 3{ log }_{ a }x } } dx$

• 5)

Evaluate ∫ tan2x dx

#### 12th Standard English Medium Business Maths Reduced Syllabus Creative one Mark Question with Answerkey - 2021(Public Exam ) - by Sridevi - Sankarankoil - View & Read

• 1)

The value of $\left| \begin{matrix} { 5 }^{ 2 } & { 5 }^{ 3 } & { 5 }^{ 4 } \\ { 5 }^{ 3 } & { 5 }^{ 4 } & { 5^{ 5 } } \\ { 5 }^{ 4 } & { 5 }^{ 5 } & { 5 }^{ 6 } \end{matrix} \right|$

• 2)

If A is a singular matrix, then Adj A is.

• 3)

$\int { \frac { 2 }{ { \left( { e }^{ x }+{ e }^{ -x } \right) }^{ 2 } } }$ dx = ____________ +c

• 4)

The anti-derivative of f(x) = $\sqrt { x } +\frac { 1 }{ \sqrt { x } }$ is ___________ +c

• 5)

The value of the integral $\int _{ 0 }^{ \frac { \pi }{ 2 } }{ \frac { { \sqrt { cosx } } }{ \sqrt { cosx } +\sqrt { sinx } } } dx=\quad$

#### 12th Standard English Medium Business Maths Syllabus Five Mark Important Questions with Answer key - 2021(Public Exam ) - by Sridevi - Sankarankoil - View & Read

• 1)

Find k, if the equations x+y+z=7,x+2y+3z=18,y+kz=6 are inconsistent

• 2)

Investigate for what values of ‘a’ and ‘b’ the following system of equations x+y+z=6,x+2y+3z=10, x+2y+az = b have
(i) no solution
(ii) a unique solution
(iii) an infinite number of solutions.

• 3)

An automobile company uses three types of Steel S1, S2 and S3 for providing three different types of Cars C1, C2 and C3. Steel requirement R (in tonnes) for each type of car and total available steel of all the three types are summarized in the following table.

 Types of Steel Types of Car Total Steel available C1 C2 C3 S1 3 2 1 28 S2 1 1 2 13 S3 2 2 2 14

Determine the number of Cars of each type which can be produced by Cramer’s rule.

• 4)

A new transit system has just gone into operation in Chennai. Of those who use the transit system this year, 30% will switch over to using metro train next year and 70% will continue to use the transit system. Of those who use metro train this year, 70% will continue to use metro train next year and 30% will switch over to the transit system. Suppose the population of Chennai city remains constant and that 60% of the commuters use the transit system and 40% of the commuters use metro train this year.
(i) What percent of commuters will be using the transit system after one year?
(ii) What percent of commuters will be using the transit system in the long run?

• 5)

The subscription department of a magazine sends out a letter to a large mailing list inviting subscriptions for the magazine. Some of the people receiving this letter
already subscribe to the magazine while others do not. From this mailing list, 60% of those who already subscribe will subscribe again while 25% of those who do
not now subscribe will subscribe. On the last letter it was found that 40% of those receiving it ordered a subscription. What percent of those receiving the current
letter can be expected to order a subscription?

#### 12th Standard English Medium Business Maths Reduced Syllabus Annual Exam Model Question Paper with Answer Key - 2021 - by Sridevi - Sankarankoil - View & Read

• 1)

In a transition probability matrix, all the entries are greater than or equal to

• 2)

The rank of an n x n matrix each of whose elements is 2 is

• 3)

The value of $\int _{ \frac { \pi }{ 2 } }^{ \frac { \pi }{ 2 } }{ cosx }$ dx is

• 4)

The value of $\int _{ 0 }^{ \frac { \pi }{ 2 } }{ cosx } { e }^{ sinx }dx=$

• 5)

Area bounded by the curve y = $\frac{1}{x}$ between the limits 1 and 2 is

#### 12th Standard English Medium Business Maths Syllabus Five Mark Important Questions - 2021(Public Exam ) - by Sridevi - Sankarankoil - View & Read

• 1)

Show that the equations x−4y+7z=14,3x+8y−2z=13,7x−8y+26z =5 are inconsistent.

• 2)

Investigate for what values of ‘a’ and ‘b’ the following system of equations x+y+z=6,x+2y+3z=10, x+2y+az = b have
(i) no solution
(ii) a unique solution
(iii) an infinite number of solutions.

• 3)

An amount of Rs.5,000/- is to be deposited in three different bonds bearing 6%, 7% and 8% per year respectively. Total annual income is Rs.358/-. If the income from first two investments is 70/- more than the income from the third, then find the amount of investment in each bond by rank method.

• 4)

Solve by Cramer’s rule x+y+z=4,2x−y+3z=1,3x+2y−z = 1

• 5)

A total of Rs 8,500 was invested in three interest earning accounts. The interest rates were 2%, 3% and 6% if the total simple interest for one year was Rs 380 and the amount ,invested at 6% was equal to the sum of the amounts in the other two accounts, then how much was invested in each account? (use Cramer’s rule).

#### 12th Standard English Medium Business Maths Syllabus Three Mark Important Questions with Answer key - 2021(Public Exam ) - by Sridevi - Sankarankoil - View & Read

• 1)

Show that the equations 2x+y=5,4x+2y=10 are consistent and solve them.

• 2)

Show that the equations 2x - Y + z = 7, 3x +y- 5z = 13, x +y + z = 5 are consistent and have a unique solution.

• 3)

Evaluate $\int { \frac { { 8 }^{ 1+x }+{ 4 }^{ 1-x } }{ { 2 }^{ x } } } dx$

• 4)

Evaluate $\int _{ 1 }^{ 2 }{ \frac { log\quad x }{ { x }^{ 2 } } } dx$

• 5)

The marginal cost function is MC = 300 ${ x }^{ \frac { 2 }{ 5 } }$ and fixed cost is zero. Find out the total cost and average cost functions.

#### 12th Standard English Medium Business Maths Reduced Syllabus Three Mark Important Questions - 2021(Public Exam ) - by Sridevi - Sankarankoil - View & Read

• 1)

Find the rank of the matrix A = $\left( \begin{matrix} 1 & 1 & 1 \\ 3 & 4 & 5 \\ 2 & 3 & 4 \end{matrix}\begin{matrix} 1 \\ 2 \\ 0 \end{matrix} \right)$

• 2)

Solve the equations 2x + 3y = 7, 3x + 5y = 9 by Cramer’s rule.

• 3)

A total of Rs 8,600 was invested in two accounts. One account earned $4\frac { 3 }{ 4 } %$% annual interest and the other earned $6\frac { 1 }{ 2 } %$annual interest. If the total interest for one year was Rs 431.25, how much was invested in each account? (Use determinant method).

• 4)

Find the rank of the following matrices
$\left( \begin{matrix} 1 & 2 & -1 \\ 2 & 4 & 1 \\ 3 & 6 & 3 \end{matrix}\begin{matrix} 3 \\ -2 \\ -7 \end{matrix} \right)$

• 5)

Integrate the following with respect to x.
$\frac { 1 }{ x{ \left( logx \right) }^{ 2 } }$

#### 12th Standard English medium Business Maths Reduced Syllabus Two Mark Important Questions with Answer key - 2021(Public Exam ) - by Sridevi - Sankarankoil - View & Read

• 1)

Find the rank of the following matrices.
$\left( \begin{matrix} 5 & 6 \\ 7 & 8 \end{matrix} \right)$

• 2)

Evaluate $\int { \sqrt { 2x+1dx } }$

• 3)

Integrate the following with respect to x.
(3 + x)(2 − 5x)

• 4)

Integrate the following with respect to x.
(4x + 2) $\sqrt { { x }^{ 2 }+x+1 }$

• 5)

Evaluate the following
$\int _{ 0 }^{ \infty }{ { e }^{ -mx } } { x }^{ 6 }dx$

#### 12th Standard English Medium Business Maths Reduced Syllabus Two Mark Important Questions - 2021(Public Exam ) - by Sridevi - Sankarankoil - View & Read

• 1)

Evaluate $\int { \sqrt { 2x+1dx } }$

• 2)

Evaluate $\int { \left( { x }^{ 3 }+7 \right) \left( x-4 \right) dx }$

• 3)

Integrate the following with respect to x.

$\frac { 8x+13 }{ \sqrt { 4x+7 } }$

• 4)

Evaluate $\int { \frac { cos2x }{ { sin }^{ 2 }{ xcos }^{ 2 }x } dx }$

• 5)

Evaluate ഽ$\sqrt { { x }^{ 2 }-16 }$dx

#### 12th Standard English Medium Business Maths Reduced Syllabus One mark Important Questions with Answer key - 2021(Public Exam ) - by Sridevi - Sankarankoil - View & Read

• 1)

IfA =$\left( \begin{matrix} 1 \\ 2 \\ 3 \end{matrix} \right)$  then the rank of AAT is

• 2)

If $\rho (A)=\rho (A,B)$the number of unknowns, then the system is

• 3)

In a transition probability matrix, all the entries are greater than or equal to

• 4)

$\frac { sin5x-sinx }{ cos3x }$dx

• 5)

$\frac { { e }^{ x } }{ \sqrt { { 1+e }^{ x } } }$dx is

#### 12th Standard English Medium Business Maths Reduced Syllabus One Mark Important Questions - 2021(Public Exam ) - by Sridevi - Sankarankoil - View & Read

• 1)

The rank of the unit matrix of order n is

• 2)

The rank of the diagonal matrix$\left( \begin{matrix} 1 & & \\ & 2 & \\ & & -3 \end{matrix}\\ \quad \quad \quad \quad \quad \quad \quad \begin{matrix} 0 & & \\ & 0 & \\ & & 0 \end{matrix} \right)$

• 3)

ഽ2xdx is

• 4)

$\frac { { e }^{ x } }{ \sqrt { { 1+e }^{ x } } }$dx is

• 5)

The marginal revenue and marginal cost functions of a company are MR = 30 − 6x and MC = −24 + 3x where x is the product, then the profit function is

#### 12th Standard Business Maths English Medium Free Online Test Book Back One Mark Questions - by Sridevi - Sankarankoil - View & Read

• 1)

If A=(1 2 3), then the rank of AAT is

• 2)

For the system of equations x+2y+3z=1, 2x+y+3z=25x+5y+9z =4

• 3)

$\frac { 1 }{ { x }^{ 3 } }$dx is

• 4)

Area bounded by the curve y = x (4 − x) between the limits 0 and 4 with x − axis is

• 5)

The degree of the differential equation $\frac { { d }^{ 4 }y }{ { dx }^{ 4 } } { -\left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) }^{ 4 }+\frac { dy }{ dx } =3$

#### 12th Standard Business Maths English Medium Free Online Test Book Back 1 Mark Questions with Answer Key - by Sridevi - Sankarankoil - View & Read

• 1)

The rank of m×n matrix whose elements are unity is

• 2)

ഽ2xdx is

• 3)

Area bounded by the curve y = e−2x between the limits 0 ≤ x ≤ ∞ is

• 4)

The order and degree of the differential equation $\sqrt { \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } } =\sqrt { \frac { dy }{ dx } +5 }$ are respectively

• 5)

Δf(x) =

#### 12th Standard Business Maths English Medium Free Online Test Book Back One Mark Questions - Part Two - by Sridevi - Sankarankoil - View & Read

• 1)

if T=$_{ B }^{ A }\left( \begin{matrix} \overset { A }{ 0.4 } & \overset { B }{ 0.6 } \\ 0.2 & 0.8 \end{matrix} \right)$ is a transition probability matrix, then at equilibrium A is equal to

• 2)

$\frac { sin2x }{ 2sinx } dx$ is

• 3)

Area bounded by the curve y = $\frac{1}{x}$ between the limits 1 and 2 is

• 4)

The order and degree of the differential equation ${ \left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) }^{ \frac { 1 }{ 2 } }-\sqrt { \frac { dy }{ dx } } -4=0$ are respectively

• 5)

E ≡

#### 12th Standard Business Maths English Medium Free Online Test Book Back 1 Mark Questions with Answer Key - Part Two - by Sridevi - Sankarankoil - View & Read

• 1)

If A= $\begin{pmatrix} 2 & 0 \\ 0 & 8 \end{pmatrix}$,then $\rho (A)$ is

• 2)

$\frac { sin5x-sinx }{ cos3x }$dx

• 3)

If the marginal revenue function of a firm is MR = ${ e }^{ \frac { -x }{ 10 } }$, then revenue is

• 4)

The differential equation ${ \left( \frac { dx }{ dy } \right) }^{ 3 }+2{ y }^{ \frac { 1 }{ 2 } }$ = x is

• 5)

If h = 1, then Δ(x2) =

#### 12th Standard Business Maths English Medium Free Online Test Book Back One Mark Questions - Part Three - by Sridevi - Sankarankoil - View & Read

• 1)

Rank of a null matrix is

• 2)

$\int _{ 0 }^{ \infty }{ { x }^{ 4 }{ e }^{ -x } }$dx is

• 3)

Area bounded by y = $\left| x \right|$ between the limits 0 and 2 is

• 4)

The solution of the differential equation $\frac { dy }{ dx } =\frac { y }{ x } +\frac { f\left( \frac { y }{ x } \right) }{ f'\left( \frac { y }{ x } \right) }$ is

• 5)

For the given data find the value of Δ3y0 is

 x 5 6 9 11 y 12 13 15 18

#### 12th Standard Business Maths English Medium Free Online Test Book Back 1 Mark Questions with Answer Key - Part Three - by Sridevi - Sankarankoil - View & Read

• 1)

$\left| { A }_{ n\times n } \right|$=3 $\left| adjA \right|$ =243 then the value n is

• 2)

$\Gamma \left( \frac { 3 }{ 2 } \right)$

• 3)

The area bounded by the parabola y2 = 4x bounded by its latus rectum is

• 4)

Which of the following is the homogeneous differential equation?

• 5)

If f (x)=x+ 2x + 2 and the interval of differencing is unity then Δf (x)

#### 12th Standard Business Maths English Medium Free Online Test Creative 1 Mark Questions - by Sridevi - Sankarankoil - View & Read

• 1)

For what value of k, the matrix $A=\left( \begin{matrix} 2 & k \\ 3 & 5 \end{matrix} \right)$ has no inverse?

• 2)

$\int { \left( x-1 \right) } { e }^{ -x }$ dx = __________ +c

• 3)

The area bounded by y = 2x - x2 and X-axis is _________ sq. units

• 4)

The differential equation $\left( \frac { dx }{ dy } \right) ^{ 2 }+5y^{ \frac { 1 }{ 3 } }$=x is

• 5)

E2.f(x) =

#### 12th Standard Business Maths English Medium Free Online Test Creative One Mark Questions with Answer Key - by Sridevi - Sankarankoil - View & Read

• 1)

The rank of an n x n matrix each of whose elements is 2 is

• 2)

If $\int { \frac { { 2 }^{ \frac { 1 }{ x } } }{ { x }^{ 2 } } } dx=k{ 2 }^{ \frac { 1 }{ x } }$ +c, then k is

• 3)

The area of the region bounded by the ellipse

• 4)

The differential equation of all circles with centre at the origin is

• 5)

∇f(x+ 3h)

#### 12th Standard Business Maths Applications of Matrices and Determinants English Medium Free Online Test One Mark Questions with Answer Key 2020 - 2021 - by Sridevi - Sankarankoil - View & Read

• 1)

The rank of m×n matrix whose elements are unity is

• 2)

The rank of the unit matrix of order n is

• 3)

IfA =$\left( \begin{matrix} 1 \\ 2 \\ 3 \end{matrix} \right)$  then the rank of AAT is

• 4)

The rank of the diagonal matrix$\left( \begin{matrix} 1 & & \\ & 2 & \\ & & -3 \end{matrix}\\ \quad \quad \quad \quad \quad \quad \quad \begin{matrix} 0 & & \\ & 0 & \\ & & 0 \end{matrix} \right)$

• 5)

In a transition probability matrix, all the entries are greater than or equal to

#### 12th Standard Business Maths Differential Equations English Medium Free Online Test One Mark Questions 2020 - 2021 - by Sridevi - Sankarankoil - View & Read

• 1)

The degree of the differential equation $\frac { { d }^{ 4 }y }{ { dx }^{ 4 } } { -\left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) }^{ 4 }+\frac { dy }{ dx } =3$

• 2)

The order and degree of the differential equation ${ \left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) }^{ \frac { 1 }{ 2 } }-\sqrt { \frac { dy }{ dx } } -4=0$ are respectively

• 3)

If y=cx + c− c3 then its differential equation is

• 4)

The differential equation of y = mx + c is (m and c are arbitrary constants)

• 5)

Solution of $\frac { dy }{ dx }$ + Px = 0

#### 12th Standard Business Maths Differential Equations English Medium Free Online Test One Mark Questions with Answer Key 2020 - 2021 - by Sridevi - Sankarankoil - View & Read

• 1)

The order and degree of the differential equation $\sqrt { \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } } =\sqrt { \frac { dy }{ dx } +5 }$ are respectively

• 2)

The integrating factor of the differential equation $\frac{dx}{dy}+Px=Q$

• 3)

The complementary function of (D2+ 4)y = e2x is

• 4)

The particular integral of the differential equation f(D)y = eax where f(D) = (D−a)2

• 5)

The differential equation of all circles with centre at the origin is

#### 12th Standard Business Maths English Medium Free Online Test Creative 1 Mark Questions - Part Two - by Sridevi - Sankarankoil - View & Read

• 1)

The value of $\left| \begin{matrix} { 5 }^{ 2 } & { 5 }^{ 3 } & { 5 }^{ 4 } \\ { 5 }^{ 3 } & { 5 }^{ 4 } & { 5^{ 5 } } \\ { 5 }^{ 4 } & { 5 }^{ 5 } & { 5 }^{ 6 } \end{matrix} \right|$

• 2)

$\int { { \left| x \right| }^{ 3 } }$dx = ________________ +c

• 3)

The area unded by the curves y = 2x, x = 0 anx=2 is________sq.units.

• 4)

The amount present in a radio active element disintegrates at a rate proportional to its amount. The differential equation corresponding to the above statement is (k is negative).

• 5)

∆f(x + 3h)

#### 12th Standard Business Maths English Medium Free Online Test Creative One Mark Questions with Answer Key - Part Two - by Sridevi - Sankarankoil - View & Read

• 1)

If $\left| \begin{matrix} 2x & 5 \\ 8 & x \end{matrix} \right| =\left| \begin{matrix} 6 & -2 \\ 7 & 3 \end{matrix} \right|$ then x =

• 2)

$\int { \frac { 2 }{ { \left( { e }^{ x }+{ e }^{ -x } \right) }^{ 2 } } }$ dx = ____________ +c

• 3)

The area of the region bounded by the line 2y = -x + 8, X - axis and the lines x = 2 and x = 4 is ________ sq.units.

• 4)

The differential equation satisfied by all the straight lines in xy plane is

• 5)

Δ can be defined as Δf(x) =f(x + h) -f(x) where h is the __________ interval of spacing

#### 12th Standard Business Maths English Medium Free Online Test Creative 1 Mark Questions - Part Three - by Sridevi - Sankarankoil - View & Read

• 1)

If A is a singular matrix, then Adj A is.

• 2)

$\int { \frac { 2 }{ { \left( { e }^{ x }+{ e }^{ -x } \right) }^{ 2 } } }$ dx = ____________ +c

• 3)

The area enclosed by the curve y = cos2x in [0,$\pi$] the lines x=0, x=$\pi$ and the X-axis is ________sq.units.

• 4)

If y = k.eλx then its differential equation where k is arbitrary constant is

• 5)

If c is a constant, then Δc =

#### 12th Standard Business Maths English Medium Free Online Test Creative One Mark Questions with Answer Key - Part Three - by Sridevi - Sankarankoil - View & Read

• 1)

If A, B are two n x n non-singular matrices, then

• 2)

$\int { { e }^{ x } }$ f(x) + f' (x) dx = _____________ +c

• 3)

The area of the region bounded by the line y = 3x + 2, the X-axis and the ordinates x = - 1 and x = 1is_________ sq. units.

• 4)

The differential equation obtained by eliminating a and b from y = a e3x + b e-3x is

• 5)

Δ(f(x) + g(x)) = ________

#### 12th Standard Business Maths English Medium Free Online Test Creative 1 Mark Questions - Part Four - by Sridevi - Sankarankoil - View & Read

• 1)

$\int { { 3 }^{ x+2 } }$ dx = ______________ +c

• 2)

The area of the region bounded by the curve y2 = 2y - x and the y-axis _____ sq. units

• 3)

The differential equation formed by eliminating A and B from y = ex (A cos x + B sin x) is

• 4)

Δ(f(x) + g(x)) = ________

• 5)

V(4X+3) is

#### 12th Standard Business Maths English Medium Free Online Test Creative One Mark Questions with Answer Key - Part Four - by Sridevi - Sankarankoil - View & Read

• 1)

$\int _{ 1 }^{ e }{ log } x$ dx = ______________ +c

• 2)

If the marginal cost function MC = 2 - 4x, then the cost function is

• 3)

The degree of the differential equation $\sqrt { 1+\left( \frac { { d }y }{ dx } \right) ^{ \frac { 1 }{ 3 } } } =\frac { { d }^{ 2 }y }{ dx^{ 2 } }$ is

• 4)

The P.I. of the differential equation f(D)y = eax where f(D)=(D-a) g(D), g(a) ≠0 is _____

• 5)

If c is a constant, then Δc =

#### 12th Standard Business Maths English Medium Free Online Test Creative 1 Mark Questions - Part Five - by Sridevi - Sankarankoil - View & Read

• 1)

$\int { \frac { { x }^{ 5 }-{ x }^{ 4 } }{ { x }^{ 3 }-{ x }^{ 2 } } }$dx = __________ +c

• 2)

If MR = 15 - 8x, then the revenue function is

• 3)

The degree and order of $\frac { { d }^{ 2 }y }{ dx^{ 2 } } -6\sqrt { \frac { dy }{ dx } }$=0 are

• 4)

E [c.f(x)] = ___________ where c is a constant

• 5)

If $f(x)=\begin{cases} \frac { A }{ x } ,\quad 1<x<{ e }^{ 3 } \\ 0,\quad otherwise \end{cases}$ is a p.d.f. of a continuous random variable. X then P(X≥e)

#### 12th Standard Business Maths English Medium Free Online Test Creative One Mark Questions with Answer Key - Part Five - by Sridevi - Sankarankoil - View & Read

• 1)

The value of $\int _{ 0 }^{ \frac { \pi }{ 2 } }{ cosx } { e }^{ sinx }dx=$

• 2)

If MR = 15 - 8x, then the revenue function is

• 3)

In (x2-y2)dy=2xy dx, if we put y=vx, then the equation is transformed into

• 4)

The value of Δ ex is

• 5)

If F(x) is the probability distribution function, then F(- ∞) is_______.

#### 12th Standard Business Maths Applications of Matrices and Determinants English Medium Free Online Test One Mark Questions 2020 - 2021 - by Sridevi - Sankarankoil - View & Read

• 1)

If A=(1 2 3), then the rank of AAT is

• 2)

if T=$_{ B }^{ A }\left( \begin{matrix} \overset { A }{ 0.4 } & \overset { B }{ 0.6 } \\ 0.2 & 0.8 \end{matrix} \right)$ is a transition probability matrix, then at equilibrium A is equal to

• 3)

If $\rho (A)$ =r then which of the following is correct?

• 4)

If the rank of the matrix  $\left( \begin{matrix} \lambda & -1 & 0 \\ 0 & \lambda & -1 \\ -1 & 0 & \lambda \end{matrix} \right)$  is 2. Then $\lambda$ is

• 5)

if $\rho (A)=\rho (A,B)$ then the system is

#### 12th Standard Business Maths Integral Calculus – I English Medium Free Online Test One Mark Questions 2020 - 2021 - by Sridevi - Sankarankoil - View & Read

• 1)

$\frac { 1 }{ { x }^{ 3 } }$dx is

• 2)

$\frac{logx}{x}$dx , x > 0 is

• 3)

$\sqrt { { e }^{ x } }$ dx is

• 4)

$\frac { { e }^{ x } }{ { e }^{ x }+1 }$ dx

• 5)

$\frac { { 2x }^{ 3 } }{ 4+{ x }^{ 4 } }$dx is

#### 12th Standard Business Maths Integral Calculus – I English Medium Free Online Test 1 Mark Questions with Answer Key 2020 - 2021 - by Sridevi - Sankarankoil - View & Read

• 1)

ഽ2xdx is

• 2)

$\frac { sin5x-sinx }{ cos3x }$dx

• 3)

$\frac { { e }^{ x } }{ \sqrt { { 1+e }^{ x } } }$dx is

• 4)

ഽe2x[2x2 + 2x]dx

• 5)

$\frac { dx }{ \sqrt { { x }^{ 2 }-{ 36 } } }$ is

#### 12th Standard Business Maths Integral Calculus – II English Medium Free Online Test One Mark Questions 2020 - 2021 - by Sridevi - Sankarankoil - View & Read

• 1)

Area bounded by the curve y = x (4 − x) between the limits 0 and 4 with x − axis is

• 2)

Area bounded by the curve y = $\frac{1}{x}$ between the limits 1 and 2 is

• 3)

The marginal revenue and marginal cost functions of a company are MR = 30 − 6x and MC = −24 + 3x where x is the product, then the profit function is

• 4)

If the marginal revenue MR = 35 + 7x − 3x2, then the average revenue AR is

• 5)

For the demand function p(x), the elasticity of demand with respect to price is unity then

#### 12th Standard Business Maths Integral Calculus – II English Medium Free Online Test 1 Mark Questions with Answer Key 2020-2021 - by Sridevi - Sankarankoil - View & Read

• 1)

Area bounded by the curve y = e−2x between the limits 0 ≤ x ≤ ∞ is

• 2)

If the marginal revenue function of a firm is MR = ${ e }^{ \frac { -x }{ 10 } }$, then revenue is

• 3)

The demand function for the marginal function MR = 100 − 9x2 is

• 4)

The producer’s surplus when the supply function for a commodity is P = 3 + x and x0 = 3 is

• 5)

If MR and MC denote the marginal revenue and marginal cost and MR − MC = 36x − 3x2 − 81 , then the maximum profit at x is equal to

#### 12th Standard Business Maths Numerical Methods English Medium Free Online Test One Mark Questions 2020 - 2021 - by Sridevi - Sankarankoil - View & Read

• 1)

Δ2y0 =

• 2)

E ≡

• 3)

If c is a constant then Δc =

• 4)

If ‘n’ is a positive integer Δn[ Δ-n​ ​​​​​​f(x)]

• 5)

For the given points (x0, y0) and (x1,y1) the Lagrange’s formula is

#### 12th Standard Business Maths Random Variable and Mathematical expectation English Medium Free Online Test One Mark Questions with Answer Key 2020 - 20 - by Sridevi - Sankarankoil - View & Read

• 1)

Demand of products per day for three days are 21, 19, 22 units and their respective probabilities are 0.29, 0.40, 0.35. Profit per unit is 0.50 paisa then expected profits for three days are

• 2)

Given E(X) = 5 and E (Y) = -2, then E(X – Y) is

• 3)

A formula or equation used to represent the probability distribution of a continuous random variable is called

• 4)

Which of the following is not possible in probability distribution?

• 5)

A discrete probability distribution may be represented by

#### 12th Standard Business Maths Numerical Methods English Medium Free Online Test One Mark Questions with Answer Key 2020 - 2021 - by Sridevi - Sankarankoil - View & Read

• 1)

Δf(x) =

• 2)

If m and n are positive integers then ΔmΔnf(x) =

• 3)

E f (x)=

• 4)

∇ f(a) =

• 5)

Lagrange’s interpolation formula can be used for

#### 12th Standard Business Maths Random Variable and Mathematical expectation English Medium Free Online Test One Mark Questions 2020 - 2021 - by Sridevi - Sankarankoil - View & Read

• 1)

Value which is obtained by multiplying possible values of random variable with probability of occurrence and is equal to weighted average is called

• 2)

Probability which explains x is equal to or less than particular value is classified as

• 3)

A variable that can assume any possible value between two points is called

• 4)

If X is a discrete random variable and p(x) is the probability of X, then the expected value of this random variable is equal to

• 5)

If c is a constant, then E(c) is

#### 12th Standard Business Maths Probability Distributions English Medium Free Online Test One Mark Questions 2020 - 2021 - by Sridevi - Sankarankoil - View & Read

• 1)

Normal distribution was invented by

• 2)

If Z is a standard normal variate, the proportion of items lying between Z = –0.5 and Z = –3.0 is

• 3)

The parameters of the normal distribution $f(x)=\left( \frac { 1 }{ \sqrt { 72\pi } } \right) \frac { { e }^{ -(x-10)^{ 2 } } }{ 72 } -\infty <X<\infty$

• 4)

An experiment succeeds twice as often as it fails. The chance that in the next six trials, there shall be at least four successes is

• 5)

The average percentage of failure in a certain examination is 40. The probability that out of a group of 6 candidates atleast 4 passed in the examination are:

#### 12th Standard Business Maths Probability Distributions English Medium Free Online Test One Mark Questions with Answer Key 2020 - 2021 - by Sridevi - Sankarankoil - View & Read

• 1)

If X ~N(9,81) the standard normal variate Z will be

• 2)

A manufacturer produces switches and experiences that 2 per cent switches are defective. The probability that in a box of 50 switches, there are atmost two defective is :

• 3)

If for a binomial distribution b(n,p) mean = 4 and variance = 4/3, the probability, P(X ≥ 5) is equal to :

• 4)

Which of the following cannot generate a Poisson distribution?

• 5)

The starting annual salaries of newly qualified chartered accountants (CA’s) in South Africa follow a normal distribution with a mean of  Rs.180,000 and a standard deviation of Rs. 10,000. What is the probability that a randomly selected newly qualified CA will earn between Rs.165,000 and Rs.175,000 per annum?

#### 12th Standard Business Maths Sampling techniques and Statistical Inference English Medium Free Online Test One Mark Questions 2020 - 2021 - by Sridevi - Sankarankoil - View & Read

• 1)

A ________ may be finite or infinite according as the number of observations or items in it is finite or infinite.

• 2)

A finite subset of statistical individuals in a population is called __________

• 3)

Which one of the following is probability sampling

• 4)

In ___________ the heterogeneous groups are divided into homogeneous groups.

• 5)

___________ is a relative property, which states that one estimator is efficient relative to another.

#### 12th Standard Business Maths Sampling techniques and Statistical Inference English Medium Free Online Test 1 Mark Questions with Answer Key 2020-2021 - by Sridevi - Sankarankoil - View & Read

• 1)

A __________ of statistical individuals in a population is called a sample.

• 2)

Any statistical measure computed from sample data is known as ____________

• 3)

Errors in sampling are of

• 4)

An estimator is a sample statistic used to estimate a

• 5)

If probability $P[|\hat{\theta}-\theta|<\varepsilon] \rightarrow 1$ as $n \rightarrow \infty$for any positive $\varepsilon$ then $\hat{\theta}$ is said to _____________ esitimator of $\theta$.

#### 12th Standard Business Maths Applied Statistics English Medium Free Online Test One Mark Questions 2020 - 2021 - by Sridevi - Sankarankoil - View & Read

• 1)

A time series is a set of data recorded

• 2)

Least square method of fitting a trend is

• 3)

The component of a time series attached to long term variation is trended as

• 4)

Another name of consumer’s price index number is:

• 5)

Laspeyre’s index = 110, Paasche’s index = 108, then Fisher’s Ideal index is equal to:

#### 12th Standard Business Maths Applied Statistics English Medium Free Online Test One Mark Questions with Answer Key 2020 - 2021 - by Sridevi - Sankarankoil - View & Read

• 1)

A time series consists of

• 2)

The component of a time series attached to long term variation is trended as

• 3)

Another name of consumer’s price index number is:

• 4)

Laspeyre’s index = 110, Paasche’s index = 108, then Fisher’s Ideal index is equal to:

• 5)

Consumer price index are obtained by:

#### 12th Standard Business Maths Operations Research English Medium Free Online Test One Mark Questions 2020 - 2021 - by Sridevi - Sankarankoil - View & Read

• 1)

The transportation problem is said to be unbalanced if _________

• 2)

Number of basic allocation in any row or column in an assignment problem can be

• 3)

Solution for transportation problem using __________method is nearer to an optimal solution.

• 4)

If number of sources is not equal to number of destinations, the assignment problem is called____________

• 5)

The solution for an assignment problem is optimal if

#### 12th Standard Business Maths Operations Research English Medium Free Online Test One Mark Questions with Answer Key 2020 - 2021 - by Sridevi - Sankarankoil - View & Read

• 1)

In a non – degenerate solution number of allocations is

• 2)

The Penalty in VAM represents difference between the first ________

• 3)

In an assignment problem the value of decision variable xij is _________

• 4)

The purpose of a dummy row or column in an assignment problem is to

• 5)

In an assignment problem involving four workers and three jobs, total number of assignments possible are

#### 12th Standard Business Maths English Medium Free Online Test 1 Mark Questions 2020 - by Sridevi - Sankarankoil - View & Read

• 1)

IfA =$\left( \begin{matrix} 1 \\ 2 \\ 3 \end{matrix} \right)$  then the rank of AAT is

• 2)

If $\left| \begin{matrix} 2x & 5 \\ 8 & x \end{matrix} \right| =\left| \begin{matrix} 6 & -2 \\ 7 & 3 \end{matrix} \right|$ then x =

• 3)

$\Gamma (1)$ is

• 4)

If ∫ x sin x dx = - x cos x + α then α = __________ +c

• 5)

The particular integral of the differential equation $\frac { d^{ 2 }y }{ { dx }^{ 2 } } -5\frac { dy }{ dx }$+6y=e5x is _______

#### 12th Standard Business Maths English Medium Free Online Test One Mark Questions with Answer Key 2020 - by Sridevi - Sankarankoil - View & Read

• 1)

The rank of the unit matrix of order n is

• 2)

$\frac { { 2x }^{ 3 } }{ 4+{ x }^{ 4 } }$dx is

• 3)

∫ (1-x) $\sqrt { x }$ dx = ______________+c

• 4)

The demand and supply functions are given by D(x)= 16 − x2 and S(x) = 2x2 + 4 are under perfect competition, then the equilibrium price x is

• 5)

The area of the region bounded by y = x + 1, the X-axis and the lines x = 0,x = 1 is___________.

#### 12th Standard Business Maths English Medium Free Online Test 1 Mark Questions 2020 - Part Two - by Sridevi - Sankarankoil - View & Read

• 1)

if $\rho (A)\neq \rho (A,B),$ then the system is

• 2)

$\frac { dx }{ \sqrt { { x }^{ 2 }-{ 36 } } }$ is

• 3)

∫ x cos x dx = ____________ +c.

• 4)

The demand and supply function of a commodity are P(x) = (x − 5)2 and S(x)= x2 + x + 3 then the equilibrium quantity x0 is

• 5)

The area below the demand curve p =f(x) and above the line p =Po is________.

#### 12th Standard Business Maths English Medium Free Online Test One Mark Questions with Answer Key 2020 - Part Two - by Sridevi - Sankarankoil - View & Read

• 1)

If the number of variables in a non- homogeneous system AX = B is n, then the system possesses a unique solution only when

• 2)

$\int _{ 0 }^{ 1 }{ (2x+1) } dx$ is

• 3)

The given demand and supply function are given byD(x) = 20 − 5x and S(x) = 4x + 8 if they are under perfect competition then the equilibrium demand is

• 4)

If the marginal cost function MC = 2 - 4x, then the cost function is

• 5)

The complementary function of (D2+ 4)y = e2x is

#### 12th Standard Business Maths English Medium Free Online Test 1 Mark Questions 2020 - Part Three - by Sridevi - Sankarankoil - View & Read

• 1)

If $\rho (A)$ =r then which of the following is correct?

• 2)

If f (x) is a continuous function and a < c < b ,then $\int _{ a }^{ c }{ f(x) } dx+\int _{ c }^{ b }{ f(x) } dx$ is

• 3)

The value of $\int _{ -3 }^{ 2 }{ |x+1| } dx$ is______.

• 4)

The complementary function of $\frac { { d }^{ 3 }y }{ d{ x }^{ 3 } } -\frac { dy }{ dx }$ = 0 is

• 5)

The solution of $\frac { dy }{ dx }$ =ex-y is

#### 12th Standard Business Maths English Medium Free Online Test One Mark Questions with Answer Key 2020 - Part Three - by Sridevi - Sankarankoil - View & Read

• 1)

if $\left| A \right| \neq 0,$ then A is

• 2)

If f (x) is a continuous function and a < c < b ,then $\int _{ a }^{ c }{ f(x) } dx+\int _{ c }^{ b }{ f(x) } dx$ is

• 3)

$\int _{ 1 }^{ 4 }{ f\left( x \right) } dx,$ where f(x) =  $\begin{cases} 7x+3\quad if\quad 1\le x\le 3 \\ 8x\quad if\quad 3\le x\le 4 \end{cases}$ is _____________.

• 4)

The marginal cost function is MC = 100 $\sqrt x$. find AC given that TC  = 0 when the out put is zero is

• 5)

Profit = Total revenue - __________.

#### 12th Standard Business Maths English Medium Free Online Test 1 Mark Questions 2020 - Part Four - by Sridevi - Sankarankoil - View & Read

• 1)

If $\rho (A)=\rho (A,B)$the number of unknowns, then the system is

• 2)

$\int _{ 0 }^{ 1 }{ (2x+1) } dx$ is

• 3)

Lagrange’s interpolation formula can be used for

• 4)

E[X-E(X)]2 is

• 5)

If X is a continuous random variable. then P(X≥a)= _________.

#### 12th Standard Business Maths English Medium Free Online Test One Mark Questions with Answer Key 2020 - Part Four - by Sridevi - Sankarankoil - View & Read

• 1)

IfA =$\left( \begin{matrix} 1 \\ 2 \\ 3 \end{matrix} \right)$  then the rank of AAT is

• 2)

$\frac { { 2x }^{ 3 } }{ 4+{ x }^{ 4 } }$dx is

• 3)

If MR and MC denotes the marginal revenue and marginal cost functions, then the profit functions is

• 4)

If y=cx + c− c3 then its differential equation is

• 5)

If m and n are positive integers then ΔmΔnf(x) =

#### 12th Standard Business Maths English Medium Free Online Test 1 Mark Questions 2020 - Part Five - by Sridevi - Sankarankoil - View & Read

• 1)

if $\left| A \right| \neq 0,$ then A is

• 2)

If f (x) is a continuous function and a < c < b ,then $\int _{ a }^{ c }{ f(x) } dx+\int _{ c }^{ b }{ f(x) } dx$ is

• 3)

$\int _{ 0 }^{ 1 }{ \frac { 1 }{ 2x-3 } }$ dx = ____________

• 4)

When x0 = 5 and p0 = 3 the consumer’s surplus for the demand function pd = 28 − x2 is

• 5)

The are bounded by the demand curve xy = 1, the X-axis, x = 1 and x = 2 is ________

#### 12th Standard Business Maths English Medium Free Online Test One Mark Questions with Answer Key 2020 - Part Five - by Sridevi - Sankarankoil - View & Read

• 1)

The system of equations 4x+6y=5, 6x+9y=7 has

• 2)

Cramer’s rule is applicable only to get an unique solution when

• 3)

If f (x) is a continuous function and a < c < b ,then $\int _{ a }^{ c }{ f(x) } dx+\int _{ c }^{ b }{ f(x) } dx$ is

• 4)

The given demand and supply function are given byD(x) = 20 − 5x and S(x) = 4x + 8 if they are under perfect competition then the equilibrium demand is

• 5)

The area bounded by the parabola y2 = 4x bounded by its latus rectum is

#### 12th Standard Business Maths English Medium Free Online Test 1 Mark Questions 2020 - Part Six - by Sridevi - Sankarankoil - View & Read

• 1)

The value of $\int _{ 2 }^{ 3 }{ f(5-x) } dx-\int _{ 2 }^{ 3 }{ f(x) } dx$ is

• 2)

The marginal cost function is MC = 100 $\sqrt x$. find AC given that TC  = 0 when the out put is zero is

• 3)

If sec2 x is an integrating factor of the differential equation $\frac { dy }{ dx }$ + Py Q then P =

• 4)

The solution of $\frac { dy }{ dx }$ =ex-y is

• 5)

Lagrange’s interpolation formula can be used for

#### 12th Standard Business Maths English Medium Free Online Test One Mark Questions with Answer Key 2020 - Part Six - by Sridevi - Sankarankoil - View & Read

• 1)

if $\left| A \right| \neq 0,$ then A is

• 2)

If n > 0, then $\Gamma$(n) is

• 3)

Area bounded by y = ex between the limits 0 to 1 is

• 4)

A homogeneous differential equation of the form  $\frac { dy }{ dx }$ = f$\left( \frac { y }{ x } \right)$ can be solved by making substitution,

• 5)

Lagrange’s interpolation formula can be used for

#### 12th Standard Business Maths English Medium Free Online Test One Mark Questions with Answer Key 2020 - Part Seven - by Sridevi - Sankarankoil - View & Read

• 1)

Cramer’s rule is applicable only to get an unique solution when

• 2)

$\Gamma (n)$ is

• 3)

If the marginal revenue of a firm is constant, then the demand function is

• 4)

If cos x is an I.F. of $\frac { dy }{ dx }$+Py=Q then P is ______

• 5)

Lagrange’s interpolation formula can be used for

#### 12th Standard Business Maths English Medium Free Online Test 1 Mark Questions 2020 - Part Seven - by Sridevi - Sankarankoil - View & Read

• 1)

$\int _{ 2 }^{ 4 }{ \frac { dx }{ x } }$ is

• 2)

$\int { \frac { { e }^{ log\sqrt { x } } }{ x } }$ dx = ________________ +c

• 3)

Area bounded by y = x between the lines y = 1, y = 2 with y = axis is

• 4)

The are bounded by the demand curve xy = 1, the X-axis, x = 1 and x = 2 is ________

• 5)

The particular integral of the differential equation is $\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } -8\frac { dy }{ dx }$+16y = 2e4x

#### 12th Standard Business Maths English Medium Free Online Test 1 Mark Questions 2020 - Part Eight - by Sridevi - Sankarankoil - View & Read

• 1)

The system of linear equations x+y+z=2,2x+y−z=3,3x+2y+k =4 has unique solution, if k is not equal to

• 2)

Using the factorial representation of the gamma function, which of the following is the solution for the gamma function $\Gamma$(n) when n = 8

• 3)

The demand and supply function of a commodity are P(x) = (x − 5)2 and S(x)= x2 + x + 3 then the equilibrium quantity x0 is

• 4)

The P.I. of $\frac { d^{ 2 }y }{ { dx }^{ 2 } } -6\frac { dy }{ dx } +9y$=e3x is ______

• 5)

If we have f(x)=2x, 0$\le$x$\le$1, then f (x) is a

#### 12th Standard Business Maths English Medium Free Online Test One Mark Questions with Answer Key 2020 - Part Eight - by Sridevi - Sankarankoil - View & Read

• 1)

The system of linear equations x+y+z=2,2x+y−z=3,3x+2y+k =4 has unique solution, if k is not equal to

• 2)

Using the factorial representation of the gamma function, which of the following is the solution for the gamma function $\Gamma$(n) when n = 8

• 3)

The profit of a function p(x) is maximum when

• 4)

A homogeneous differential equation of the form  $\frac { dy }{ dx }$ = f$\left( \frac { y }{ x } \right)$ can be solved by making substitution,

• 5)

The integrating factor of (1+x2)$\frac { dy }{ dx }$+xy = (1+x2)3 is

#### 12th Standard Business Maths English Medium Free Online Test 1 Mark Questions 2020 - Part Nine - by Sridevi - Sankarankoil - View & Read

• 1)

$\left| { A }_{ n\times n } \right|$=3 $\left| adjA \right|$ =243 then the value n is

• 2)

If f (x) is a continuous function and a < c < b ,then $\int _{ a }^{ c }{ f(x) } dx+\int _{ c }^{ b }{ f(x) } dx$ is

• 3)

The marginal cost function is MC = 100 $\sqrt x$. find AC given that TC  = 0 when the out put is zero is

• 4)

Which of the following is the homogeneous differential equation?

• 5)

∇ = ______________

#### 12th Standard Business Maths English Medium Free Online Test One Mark Questions with Answer Key 2020 - Part Nine - by Sridevi - Sankarankoil - View & Read

• 1)

Cramer’s rule is applicable only to get an unique solution when

• 2)

The value of $\int _{ 2 }^{ 3 }{ f(5-x) } dx-\int _{ 2 }^{ 3 }{ f(x) } dx$ is

• 3)

$\int { \frac { { x }^{ 5 }-{ x }^{ 4 } }{ { x }^{ 3 }-{ x }^{ 2 } } }$dx = __________ +c

• 4)

The demand function for the marginal function MR = 100 − 9x2 is

• 5)

Integrating factor of $\frac { dy }{ dx } +\frac { 1 }{ xlogx } y=\frac { 2 }{ x^{ 2 } }$ is ______

#### 12th Standard Business Maths English Medium Free Online Test 1 Mark Questions 2020 - Part Ten - by Sridevi - Sankarankoil - View & Read

• 1)

$\frac { { e }^{ x } }{ { e }^{ x }+1 }$ dx

• 2)

For a demand function p, if ഽ$\frac{dp}{p}$ = k  ഽ$\frac{dx}{x}$ then k is equal to

• 3)

The area below the demand curve p =f(x) and above the line p =Po is________.

• 4)

If X is a discrete random variable., then which of the following is correct?

• 5)

In a Poisson distribution mean is 25, then S.D is

#### 12th Standard Business Maths English Medium Free Online Test One Mark Questions with Answer Key 2020 - Part Ten - by Sridevi - Sankarankoil - View & Read

• 1)

Cramer’s rule is applicable only to get an unique solution when

• 2)

$\int _{ 2 }^{ 4 }{ \frac { dx }{ x } }$ is

• 3)

If MR and MC denote the marginal revenue and marginal cost and MR − MC = 36x − 3x2 − 81 , then the maximum profit at x is equal to

• 4)

The area bounded by the curve y = 4ax and the lines y2 = 2a and Y-axis is _______ sq. units.

• 5)

The variable separable form of $\frac { dy }{ dx } =\frac { y(x-y) }{ x(x+y) }$ by taking y vx and $\frac { dy }{ dx } =v+x\frac { dv }{ dx }$

#### 12th Standard Business Maths English Medium Model 5 Mark Creative Questions (New Syllabus 2020) - by Sridevi - Sankarankoil - View & Read

• 1)

For what values of k, the system of equations kx+ y+z = 1,x+ ky+z= 1,x+ y+kz= 1 have
(I) Unique solution
(ii) More than one solution
(iii) no solution

• 2)

Evaluate ഽ x3 sin (x4) dx

• 3)

The marginal cost function of a commodity in a firm is 2 + e3x where X is the output. Find the total cost and average cost function if the fixed cost is Rs. 500.

• 4)

The rate of increase in the cost Cof ordering holding as the size q of the order increases is given by the differential equation $\frac { dc }{ dq } =\frac { { c }^{ 2 }+2cq }{ { q }^{ 2 } }$. Find the relationship between c and q if c = 1 when q = 1.

• 5)

From the data, find the number of students whose height is between 80 cm and 90 em

 Height in cm (x) 40-60 60-80 80 - 100 100-120 120-140 No. of. students (y) : 250 120 100 70 50

#### 12th Standard Business Maths English Medium Model 5 Mark Book Back Questions (New Syllabus 2020) - by Sridevi - Sankarankoil - View & Read

• 1)

Find k, if the equations x+y+z=7,x+2y+3z=18,y+kz=6 are inconsistent

• 2)

A total of Rs 8,500 was invested in three interest earning accounts. The interest rates were 2%, 3% and 6% if the total simple interest for one year was Rs 380 and the amount ,invested at 6% was equal to the sum of the amounts in the other two accounts, then how much was invested in each account? (use Cramer’s rule).

• 3)

Find k if the equations x+y+z=1,3x−y−z=4,x+5y+5z=k are inconsistent.

• 4)

Integrate the following with respect to x.
$\frac { { 3x }^{ 2 }-2x+5 }{ { \left( x-1 \right) }\left( x^{ 2 }+5 \right) }$

• 5)

Evaluate $\int _{ 1 }^{ e }{ logx }$ dx

#### 12th Standard Business Maths English Medium Sample 5 Mark Creative Questions (New Syllabus 2020) - by Sridevi - Sankarankoil - View & Read

• 1)

Using determinants, find the quadratic defined by fix) = ax2 + bx + c if f(1) = 0,f(2) = - 2 and f(3) = -6.

• 2)

Evaluate ഽ sin (log x) + cos (log x) dx

• 3)

The marginal cost C' (x) and marginal revenue R' (x) are given by C' (x) = 20 +$\frac{x}{20}$ and R' (x) = 30. The fixed cost is Rs.200. Determine the maximum profit.

• 4)

The net profit p and quantity x satisfy the differential equation $\frac { dp }{ dx } =\frac { 2{ p }^{ 3 }-{ x }^{ 3 } }{ 3x{ p }^{ 2 } }$. Find the relationship between the net profit and demand given that p = 20, when x = 10.

• 5)

From the data, find the number of students whose height is between 80 cm and 90 em

 Height in cm (x) 40-60 60-80 80 - 100 100-120 120-140 No. of. students (y) : 250 120 100 70 50

#### 12th Standard Business Maths English Medium Sample 5 Mark Book Back Questions (New Syllabus 2020) - by Sridevi - Sankarankoil - View & Read

• 1)

Find k, if the equations x+y+z=7,x+2y+3z=18,y+kz=6 are inconsistent

• 2)

Show that the following system of equations have unique solution:
x+y+z=3,x+2y+3z=4,x+4y+9z = 6 by rank method.

• 3)

The price of 3 Business Mathematics books, 2 Accountancy books and one Commerce book is Rs840. The price of 2 Business Mathematics books, one Accountancy book and one Commerce book is Rs 570. The price of one Business Mathematics book, one Accountancy book and 2 Commerce books is Rs 630. Find the cost of each book by using Cramer’s rule.

• 4)

The subscription department of a magazine sends out a letter to a large mailing list inviting subscriptions for the magazine. Some of the people receiving this letter already subscribe to the magazine while others do not. From this mailing list, 45% of those who already subscribe will subscribe again while 30% of those who do not now subscribe will subscribe. On the last letter, it was found that 40% of those receiving it ordered a subscription. What percent of those receiving the current letter can be expected to order a subscription?

• 5)

Find k if the equations x+y+z=1,3x−y−z=4,x+5y+5z=k are inconsistent.

#### 12th Standard Business Maths English Medium Important 5 Mark Creative Questions (New Syllabus 2020) - by Sridevi - Sankarankoil - View & Read

• 1)

For what values of k, the system of equations kx+ y+z = 1,x+ ky+z= 1,x+ y+kz= 1 have
(I) Unique solution
(ii) More than one solution
(iii) no solution

• 2)

Evaluate $\int { \frac { { x }^{ 7 } }{ { x }^{ 5 }+1 } } dx$

• 3)

Evaluate $\int _{ 0 }^{ \frac { \pi }{ 4 } }{ sin } 3xsin\ 2x\ dx$

• 4)

Find the area of the region bounded by the parabola y2 = 4x and the line 2x - Y = 4.

• 5)

Solve: (D2 + 14D + 49)y = e-7x + 4.

#### 12th Standard Business Maths English Medium Important 5 Mark Book Back Questions (New Syllabus 2020) - by Sridevi - Sankarankoil - View & Read

• 1)

Show that the equations x+y+z=6,x+2y+3z=14,x+4y+7z =30 are consistent
and solve them.

• 2)

Investigate for what values of ‘a’ and ‘b’ the following system of equations x+y+z=6,x+2y+3z=10, x+2y+az = b have
(i) no solution
(ii) a unique solution
(iii) an infinite number of solutions.

• 3)

The price of three commodities X,Y and Z are x,y and z respectively Mr.Anand purchases 6 units of Z and sells 2 units of X and 3 units of Y. Mr.Amar purchases a unit of Y and sells 3 units of X and 2units of Z. Mr.Amit purchases a unit of X and sells 3 units of Y and a unit of Z. In the process they earn Rs.5,000/-, Rs.2,000/- and`5,500/- respectively Find the prices per unit of three commodities by rank method.

• 4)

An automobile company uses three types of Steel S1, S2 and S3 for providing three different types of Cars C1, C2 and C3. Steel requirement R (in tonnes) for each type of car and total available steel of all the three types are summarized in the following table.

 Types of Steel Types of Car Total Steel available C1 C2 C3 S1 3 2 1 28 S2 1 1 2 13 S3 2 2 2 14

Determine the number of Cars of each type which can be produced by Cramer’s rule.

• 5)

Two types of soaps A and B are in the market. Their present market shares are 15% for A and 85% for B. Of those who bought A the previous year, 65% continue to buy it again while 35% switch over to B. Of those who bought B the previous year, 55% buy it again and 45% switch over to A. Find their market shares after one year and when is the equilibrium reached?

#### 12th Standard Business Maths English Medium Model 3 Mark Creative Questions (New Syllabus) 2020 - by Sridevi - Sankarankoil - View & Read

• 1)

If $\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0 \end{matrix} \right] \left[ \begin{matrix} x \\ y \\ z \end{matrix} \right] =\left[ \begin{matrix} 2 \\ -1 \\ 3 \end{matrix} \right]$ find x,y and z

• 2)

Evaluate ഽ sin3 x cos x dx

• 3)

Find the area bounded by one arc of the curve y = sin ax and the x-axis.

• 4)

Solve: (x+y)2$\frac { dy }{ dx }$=1

• 5)

Estimate the population for the year 1995.

 year (x) 1961 1971 1981 1991 2001 population in thousands (y) 46 66 81 93 101

#### 12th Standard Business Maths English Medium Model 3 Mark Book Back Questions (New Syllabus) 2020 - by Sridevi - Sankarankoil - View & Read

• 1)

Find the rank of the matrix $\left( \begin{matrix} 0 & -1 & 5 \\ 2 & 4 & -6 \\ 1 & 1 & 5 \end{matrix} \right)$

• 2)

The total cost of 11 pencils and 3 erasers is Rs 64 and the total cost of 8 pencils and 3 erasers is Rs 49. Find the cost of each pencil and each eraser by Cramer’s rule.

• 3)

Find the rank of the matrix A =$\left( \begin{matrix} 4 & 5 & 2 \\ 3 & 2 & 1 \\ 4 & 4 & 8 \end{matrix}\begin{matrix} 2 \\ 6 \\ 0 \end{matrix} \right)$

• 4)

Evaluate $\int { \frac { { ax }^{ 2 }+bx+v }{ \sqrt { x } } dx }$

• 5)

Evaluate $\int { \frac { 7x-1 }{ { x }^{ 2 }-5x+6 } dx }$

#### 12th Standard Business Maths English Medium Sample 3 Mark Creative Questions (New Syllabus) 2020 - by Sridevi - Sankarankoil - View & Read

• 1)

Show that the equations x + 2y = 3, Y - z = 2, x +y + z = 1 are consistent and have infinite sets of solution.

• 2)

Evaluate $\int { \frac { cos2x-cos2\alpha }{ cosx-cos\alpha } } dx$

• 3)

Find the area under the demand curve xy = 1 bounded by the ordinates x = 3, x = 9 and x-axis

• 4)

Solve: (x2-yx2)dy + (y2+xy2)dx=0

• 5)

Find the number of men getting wages between Rs.30 and Rs.35 from the following table.

 Wages (x) 20 - 30 30 - 40 40 - 50 50 - 60 No. of men (y) 9 30 35 42

#### 12th Standard Business Maths English Medium Sample 3 Mark Book Back Questions (New Syllabus) 2020 - by Sridevi - Sankarankoil - View & Read

• 1)

Find the rank of the matrix A = $\left( \begin{matrix} 1 & 1 & 1 \\ 3 & 4 & 5 \\ 2 & 3 & 4 \end{matrix}\begin{matrix} 1 \\ 2 \\ 0 \end{matrix} \right)$

• 2)

A total of Rs 8,600 was invested in two accounts. One account earned $4\frac { 3 }{ 4 } %$% annual interest and the other earned $6\frac { 1 }{ 2 } %$annual interest. If the total interest for one year was Rs 431.25, how much was invested in each account? (Use determinant method).

• 3)

Find the rank of the matrix A =$\left( \begin{matrix} 4 & 5 & 2 \\ 3 & 2 & 1 \\ 4 & 4 & 8 \end{matrix}\begin{matrix} 2 \\ 6 \\ 0 \end{matrix} \right)$

• 4)

Evaluate $\int { \frac { { 2x }^{ 2 }-14x+24 }{ x-3 } dx }$

• 5)

Integrate the following with respect to x.
$\frac { { e }^{ 3x }+{ e }^{ 5x } }{ { e }^{ x }+{ e }^{ -x } }$

#### 12th Standard Business Maths English Medium Important 3 Mark Creative Questions (New Syllabus) 2020 - by Sridevi - Sankarankoil - View & Read

• 1)

Show that the equations x + 2y = 3, Y - z = 2, x +y + z = 1 are consistent and have infinite sets of solution.

• 2)

If f' (x) = 3x2 - $\frac { 2 }{ { x }^{ 3 } }$ and f(1) = 0, find f(x)

• 3)

Find the area bounded by one arc of the curve y = sin ax and the x-axis.

• 4)

Form the differential equation for $\frac { { x }^{ 2 } }{ { a }^{ 2 } } +\frac { { y }^{ 2 } }{ { b }^{ 2 } }$=1 where a & b are arbitrary constants.

• 5)

Show that the equation of the curve whose slope at any point is equal to y + 2x and which passes through the origin is y=2(ex-x-1).

#### 12th Standard Business Maths English Medium Important 3 Mark Book Back Questions (New Syllabus) 2020 - by Sridevi - Sankarankoil - View & Read

• 1)

Find the rank of the matrix A =$\left( \begin{matrix} 0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & 1 & 1 \end{matrix}\begin{matrix} 1 \\ 2 \\ 3 \end{matrix} \right)$

• 2)

At marina two types of games viz., Horse riding and Quad Bikes riding are available on hourly rent. Keren and Benita spent Rs 780 and Rs 560 during the month of May.

 Name Number of hours Total amount spent (in Rs) Horse Riding Quad Bike Riding Keren 3 4 780 Benita 2 3 560

Find the hourly charges for the two games (rides). (Use determinant method).

• 3)

Find the rank of the following matrices
$\left( \begin{matrix} 2 & -1 & 1 \\ 3 & 1 & -5 \\ 1 & 1 & 1 \end{matrix} \right)$

• 4)

Evaluate $\int { \frac { { ax }^{ 2 }+bx+v }{ \sqrt { x } } dx }$

• 5)

Evaluate $\int { \frac { { x }^{ 2 }+{ 5x }^{ 2 }-9 }{ x+2 } dx}$

#### 12th Standard Business Maths English Medium Model 2 Mark Creative Questions (New Syllabus) 2020 - by Sridevi - Sankarankoil - View & Read

• 1)

Solve: 2x + 3y = 4 and 4x + 6y = 8 using Cramer's rule.

• 2)

Evaluate $\int { x } \sqrt { x+2 } dx$

• 3)

Find the demand function for which the elasticity of demand is 1

• 4)

Form the differential equation of family of rectangular hyperbolas whose asymptotes are the Co-ordinate axes.

• 5)

When h = 1, find Δ (x3).

#### 12th Standard Business Maths English Medium Model 2 Mark Book Back Questions (New Syllabus) 2020 - by Sridevi - Sankarankoil - View & Read

• 1)

Find the rank of the matrix A =$\left( \begin{matrix} 1 & -3 \\ 9 & 1 \end{matrix}\begin{matrix} 4 & 7 \\ 2 & 0 \end{matrix} \right)$

• 2)

If f ' (x) = 8x3 − 2x and f (2)= 8, then find f (x)

• 3)

Integrate the following with respect to x.
2cos x − 3sin x + 4sec2 x − 5cosec2x

• 4)

Evaluate ഽ$\frac { dx }{ \sqrt { { 4x }^{ 2 }-9 } }$

• 5)

If $\int _{ 1 }^{ a }{ { 3 }x^{ 2 } }$ dx = -1, then find the value of a ( a ∈ R ).

#### 12th Standard Business Maths English Medium Sample 2 Mark Creative Questions (New Syllabus) 2020 - by Sridevi - Sankarankoil - View & Read

• 1)

Solve: x + 2y = 3 and 2x + 4y = 6 using rank method.

• 2)

If f'(x) = 8x3 -2x2, f(2) = 1, find f(x)

• 3)

The marginal cost at a production level of x units is given by C '(x) = 85+$\frac{375}{x^2}$. Find the cost of producing 10 in elemental units after 15 units have been produced?

• 4)

Solve: x dy +y dx = 0

• 5)

When h = 1, find Δ (x3).

#### 12th Standard Business Maths English Medium Sample 2 Mark Book Back Questions (New Syllabus) 2020 - by Sridevi - Sankarankoil - View & Read

• 1)

Find the rank of the matrix A =$\left( \begin{matrix} 1 & -3 \\ 9 & 1 \end{matrix}\begin{matrix} 4 & 7 \\ 2 & 0 \end{matrix} \right)$

• 2)

If f ' (x) = 8x3 − 2x and f (2)= 8, then find f (x)

• 3)

Integrate the following with respect to x.
(4x + 2) $\sqrt { { x }^{ 2 }+x+1 }$

• 4)

Evaluate $\int _{ \frac { \pi }{ 6 } }^{ \frac { \pi }{ 3 } }{ sinx }$ dx

• 5)

Evaluate the following
$\Gamma$ $\left( \frac { 9 }{ 2 } \right)$

#### 12th Standard Business Maths English Medium Important 2 Mark Creative Questions (New Syllabus) 2020 - by Sridevi - Sankarankoil - View & Read

• 1)

Solve: 2x + 3y = 4 and 4x + 6y = 8 using Cramer's rule.

• 2)

If f'(x) = 8x3 -2x2, f(2) = 1, find f(x)

• 3)

If the marginal revenue for a commodity is MR = 9 - 6x2 + 2x, find the total revenue function.

• 4)

Form the differential equation of family of rectangular hyperbolas whose asymptotes are the Co-ordinate axes.

• 5)

If f(0) = 5, f(1) = 6, f(3) = 50, find f(2) by using Lagrange's formula.

#### 12th Standard Business Maths English Medium Important 2 Mark Book Back Questions (New Syllabus) 2020 - by Sridevi - Sankarankoil - View & Read

• 1)

Find the rank of the matrix A = $\left( \begin{matrix} 1 & 2 & 3 \\ 2 & 3 & 4 \\ 3 & 5 & 7 \end{matrix} \right)$

• 2)

Evaluate $\int { \left( { x }^{ 3 }+7 \right) \left( x-4 \right) dx }$

• 3)

Evaluate $\int { \sqrt { 1+sin2x\quad dx } }$

• 4)

Evaluate ഽ$\frac { dx }{ \sqrt { { x }^{ 2 }+25 } }$

• 5)

Using second fundamental theorem, evaluate the following:
$\int _{ 0 }^{ 1 }{ { e }^{ 2x } } dx$

#### 12th Standard Business Maths English Medium Model 1 Mark Creative Questions (New Syllabus) 2020 - by Sridevi - Sankarankoil - View & Read

• 1)

If $\left| \begin{matrix} 2x & 5 \\ 8 & x \end{matrix} \right| =\left| \begin{matrix} 6 & -2 \\ 7 & 3 \end{matrix} \right|$ then x =

• 2)

$\int { { 3 }^{ x+2 } }$ dx = ______________ +c

• 3)

$\int { \frac { { x }^{ 5 }-{ x }^{ 4 } }{ { x }^{ 3 }-{ x }^{ 2 } } }$dx = __________ +c

• 4)

$\int _{ 1 }^{ 4 }{ f\left( x \right) } dx,$ where f(x) =  $\begin{cases} 7x+3\quad if\quad 1\le x\le 3 \\ 8x\quad if\quad 3\le x\le 4 \end{cases}$ is _____________.

• 5)

The area of the region bounded by the line y = 3x + 2, the X-axis and the ordinates x = - 1 and x = 1is_________ sq. units.

#### 12th Standard Business Maths English Medium Model 1 Mark Book Back Questions (New Syllabus) 2020 - by Sridevi - Sankarankoil - View & Read

• 1)

If the rank of the matrix  $\left( \begin{matrix} \lambda & -1 & 0 \\ 0 & \lambda & -1 \\ -1 & 0 & \lambda \end{matrix} \right)$  is 2. Then $\lambda$ is

• 2)

if $\frac { { a }_{ 1 } }{ x } +\frac { { b }_{ 1 } }{ y } ={ c }_{ 1 },\frac { { a }_{ 2 } }{ x } +\frac { { b }_{ 2 } }{ y } ={ c }_{ 2 },{ \triangle }_{ 1= }\begin{vmatrix} { a }_{ 1 } & { b }_{ 1 } \\ { a }_{ 2 } & { b }_{ 2 } \end{vmatrix};\quad { \triangle }_{ 2 }=\begin{vmatrix} { b }_{ 1 } & { c }_{ 1 } \\ { b }_{ 2 } & { c }_{ 2 } \end{vmatrix}{ \triangle }_{ 3 }=\begin{vmatrix} { c }_{ 1 } & { a }_{ 1 } \\ { c }_{ 2 } & a_{ 2 } \end{vmatrix}$ then (x,y) is

• 3)

$\sqrt { { e }^{ x } }$ dx is

• 4)

If f (x) is a continuous function and a < c < b ,then $\int _{ a }^{ c }{ f(x) } dx+\int _{ c }^{ b }{ f(x) } dx$ is

• 5)

$\int _{ 0 }^{ \infty }{ { x }^{ 4 }{ e }^{ -x } }$dx is

#### 12th Standard Business Maths English Medium Sample 1 Mark Creative Questions (New Syllabus) 2020 - by Sridevi - Sankarankoil - View & Read

• 1)

The rank of m×n matrix whose elements are unity is

• 2)

For the system of equations x+2y+3z=1, 2x+y+3z=25x+5y+9z =4

• 3)

If $\left| \begin{matrix} 2x & 5 \\ 8 & x \end{matrix} \right| =\left| \begin{matrix} 6 & -2 \\ 7 & 3 \end{matrix} \right|$ then x =

• 4)

$\Gamma (n)$ is

• 5)

If ∫ x sin x dx = - x cos x + α then α = __________ +c

#### 12th Standard Business Maths English Medium Sample 1 Mark Book Back Questions (New Syllabus) 2020 - by Sridevi - Sankarankoil - View & Read

• 1)

The rank of the matrix  $\left( \begin{matrix} 1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 4 & 9 \end{matrix} \right)$ is

• 2)

If the number of variables in a non- homogeneous system AX = B is n, then the system possesses a unique solution only when

• 3)

$\frac { sin2x }{ 2sinx } dx$ is

• 4)

$\frac { dx }{ \sqrt { { x }^{ 2 }-{ 36 } } }$ is

• 5)

Using the factorial representation of the gamma function, which of the following is the solution for the gamma function $\Gamma$(n) when n = 8

#### 12th Standard Business Maths English Medium Important 1 Mark Creative Questions (New Syllabus) 2020 - by Sridevi - Sankarankoil - View & Read

• 1)

If $\left| \begin{matrix} 2x & 5 \\ 8 & x \end{matrix} \right| =\left| \begin{matrix} 6 & -2 \\ 7 & 3 \end{matrix} \right|$ then x =

• 2)

If $\int { \frac { 1 }{ \left( x+2 \right) \left( { x }^{ 2 }+1 \right) } }$ dx = a log $\left| 1+{ x }^{ 2 } \right|$ +b tan-1 x + $\frac { 1 }{ 5 } log\left| x+2 \right|$ +c then

• 3)

∫ e3 log x (x4 +1)-1 dx = ____________ +c

• 4)

$\int { \frac { 1 }{ 1+sinx } }$ dx = ____________ +c

• 5)

$\int _{ 1 }^{ 4 }{ f\left( x \right) } dx,$ where f(x) =  $\begin{cases} 7x+3\quad if\quad 1\le x\le 3 \\ 8x\quad if\quad 3\le x\le 4 \end{cases}$ is _____________.

#### 12th Standard Business Maths English Medium Important 1 Mark Book Back Questions (New Syllabus) 2020 - by Sridevi - Sankarankoil - View & Read

• 1)

if T=$_{ B }^{ A }\left( \begin{matrix} \overset { A }{ 0.4 } & \overset { B }{ 0.6 } \\ 0.2 & 0.8 \end{matrix} \right)$ is a transition probability matrix, then at equilibrium A is equal to

• 2)

If $\rho (A)=\rho (A,B)$the number of unknowns, then the system is

• 3)

$\frac { sin5x-sinx }{ cos3x }$dx

• 4)

If $\int _{ 0 }^{ 1 }{ f(x) } dx=1,\int _{ 0 }^{ 1 }{ xf(x) } dx=a$ and $\int _{ 0 }^{ 1 }{ { x }^{ 2 }f(x) } dx={ a }^{ 2 }$, then $\int _{ 0 }^{ 1 }{ { (a-x) }^{ 2 } } f(x)$ is

• 5)

Area bounded by y = x between the lines y = 1, y = 2 with y = axis is

#### 12th Standard Business Maths One Mark important Questions Book back and Creative - 2020 - by Sridevi - Sankarankoil - View & Read

• 1)

For the system of equations x+2y+3z=1, 2x+y+3z=25x+5y+9z =4

• 2)

Cramer’s rule is applicable only to get an unique solution when

• 3)

For what value of k, the matrix $A=\left( \begin{matrix} 2 & k \\ 3 & 5 \end{matrix} \right)$ has no inverse?

• 4)

If A, B are two n x n non-singular matrices, then

• 5)

$\int _{ 0 }^{ 1 }{ \sqrt { { x }^{ 4 }({ 1-x) }^{ 2 } } } dx$ is

#### 12th Standard Business Mathamatics English Medium All Chapter Book Back and Creative One Marks Questions 2020 - by Sridevi - Sankarankoil - View & Read

• 1)

The rank of the diagonal matrix$\left( \begin{matrix} 1 & & \\ & 2 & \\ & & -3 \end{matrix}\\ \quad \quad \quad \quad \quad \quad \quad \begin{matrix} 0 & & \\ & 0 & \\ & & 0 \end{matrix} \right)$

• 2)

For the system of equations x+2y+3z=1, 2x+y+3z=25x+5y+9z =4

• 3)

If $\left| \begin{matrix} 2x & 5 \\ 8 & x \end{matrix} \right| =\left| \begin{matrix} 6 & -2 \\ 7 & 3 \end{matrix} \right|$ then x =

• 4)

If A, B are two n x n non-singular matrices, then

• 5)

$\frac { dx }{ \sqrt { { x }^{ 2 }-{ 36 } } }$ is

#### 12th Standard Business Mathamatics English Medium All Chapter Book Back and Creative Two Marks Questions 2020 - by Sridevi - Sankarankoil - View & Read

• 1)

Find the rank of the matrix $\left( \begin{matrix} 5 & 3 & 0 \\ 1 & 2 & -4 \\ -2 & -4 & 8 \end{matrix} \right)$

• 2)

Find the rank of the following matrices
$\left( \begin{matrix} 1 & -1 \\ 3 & -6 \end{matrix} \right)$

• 3)

Find the rank of the matrix $\left( \begin{matrix} 2 & -4 \\ -1 & 2 \end{matrix} \right)$

• 4)

If A and B are non-singular matrices, prove that AB is non-singular.

• 5)

Evaluate $\int { \frac { x }{ \sqrt { { x }^{ 2 }+1 } } dx }$

#### 12th Standard Business Mathamatics English Medium All Chapter Book Back and Creative Three Marks Questions 2020 - by Sridevi - Sankarankoil - View & Read

• 1)

Find the rank of the matrix A = $\left( \begin{matrix} 1 & 1 & 1 \\ 3 & 4 & 5 \\ 2 & 3 & 4 \end{matrix}\begin{matrix} 1 \\ 2 \\ 0 \end{matrix} \right)$

• 2)

Find the rank of the following matrices
$\left( \begin{matrix} 3 & 1 & -5 \\ 1 & -2 & 1 \\ 1 & 5 & -7 \end{matrix}\begin{matrix} -1 \\ -5 \\ 2 \end{matrix} \right)$

• 3)

If $\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0 \end{matrix} \right] \left[ \begin{matrix} x \\ y \\ z \end{matrix} \right] =\left[ \begin{matrix} 2 \\ -1 \\ 3 \end{matrix} \right]$ find x,y and z

• 4)

Solve: 2x + 3y = 5, 6x + 5y= 11

• 5)

Evaluate $\int { { e }^{ x }\left( { x }^{ 2 }+2x \right) dx }$

### TN Stateboard Education Study Materials

#### 12th Standard Business Maths English Medium Reduced Syllabus 2020 - 2021 - by QB Admin Jan 23, 2021 Jan 23, 2021

Reduced Syllabus and Chapters for 12th Standard Business Maths English Medium

### TN Stateboard Updated Class 12th Business Maths Syllabus

#### Applications of Matrices and Determinants

Rank of a Matrix - Cramer’s Rule - Transition Probability Matrices

#### Integral Calculus – I

Indefinite Integrals - Definite Integrals

#### Integral Calculus – II

The Area of the region bounded by the curves - Application of Integration in Economics and Commerce

#### Differential Equations

Formation of ordinary differential equations - First order First-degree Differential Equations - Second Order First Degree linear differential equations with constant coefficient

#### Numerical Methods

Finite differences - Interpolation

#### Random Variable and Mathematical Expectation

Random Variable - Mathematical Expectation

Distributions

#### Sampling techniques and Statistical Inference

Sampling - Estimation - Hypothesis testing

#### Applied Statistics

Time Series Analysis - Index Numbers - Statistical Quality control

#### Operations Research

Transportation Problem - Assignment Problems - Decision theory

#### TN StateboardStudy Material - Sample Question Papers with Solutions for Class 12 Session 2019 - 2020

Latest Sample Question Papers & Study Material for class 12 session 2019 - 2020 for Subjects Maths, Chemistry, Physics, Biology, Computer Science, Economics, Commerce, Accountancy, History, Computer Applications, Computer Technology, English, உயிரியல், கணினி பயன்பாடுகள், கணினி அறிவியல், வணிகக் கணிதம், வணிகவியல், பொருளியல், கணிதவியல், வேதியியல், இயற்பியல், கணினி தொழில்நுட்பம், வரலாறு, கணக்குப்பதிவியல் in PDF form to free download [ available question papers ] for practice. Download QB365 Free Mobile app & get practice question papers.

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