12th Standard EM Business Maths Study material & Free Online Practice Tests - View Model Question Papers with Solutions for Class 12 Session 2019 - 2020
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Business Maths Question Papers

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. Pofit 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 \(P[|\breve { \theta } -\theta |<\varepsilon ]\rightarrow 1\mu \quad as\quad n\rightarrow \infty ',\) for any positive \(\varepsilon \) then \(\breve { \theta } \) 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 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 \(\int { { e }^{ x }\left( { x }^{ 2 }+2x \right) dx } \)

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

  • 1)

    80% of students who do maths work during one study period, will do the maths work at the next study period. 30% of students who do english work during one study period, will do the english work at the next study period. Initially there were 60 students do maths work and 40 students do english work.
    Calculate,
    (i) The transition probability matrix
    (ii) The number of students who do maths work, english work for the next subsequent 2 study periods.

  • 2)

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

  • 3)

    The sum of three numbers is 6. If we multiplythe third number by 2 and add the first number to the result we get 7. By adding second and third numbers to three times the first number we get 12. Find the numbers using rank method

  • 4)

    A new transit system has just gone into operation in a city. Of those who use the transit system this year, 10% will switch over to using their own car next year and 90% will continue to use the transit system. Of those who use their cars this year, 80% will continue to use their cars next year and 20% will switch over to the transit system. Suppose the population of the city remains constant and that 50% of the commuters use the transit system and 50% of the commuters use their own car 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)

    Evaluate \(\int { { \left( logx \right) }^{ 2 } } dx\)

12th Business Maths - Operations Research - Two Marks Study Materials - by 8682895000 - View & Read

  • 1)

    What is transportation problem?

  • 2)

    Write mathematical form of transportation problem.

  • 3)

    what is feasible solution and non degenerate solution in transportation problem?

  • 4)

    What do you mean by balanced transportation problem?

  • 5)

    Consider the following pay-off (profit) matrix Action States

    Action States
    (s1) (s2) (s3) (s4)
    A1 5 10 18 25
    A2 8 7 8 23
    A3 21 18 12 21
    A4 30 22 19 15

    Determine best action using maximin principle.

12th Business Maths - Applied Statistics - Two Marks Study Materials - by 8682895000 - View & Read

  • 1)

    Fit a trend line by the method of freehand method for the given data

    Year 2000 2001 2002 2003 2004 2005 2006 2007
    Sales 30 46 25 59 40 60 38 65
  • 2)

    What is the need for studying time series?

  • 3)

    Define secular trend.

  • 4)

    Find the trend of production by the method of a five-yearly period of moving average for the following data:

    Year 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990
    Production(‘000) 126 123 117 128 125 124 130 114 122 129 118 123
  • 5)

    Write note on Fisher’s price index number

12th Business Maths - Sampling Techniques and Statistical Inference - Two Marks Study Materials - by 8682895000 - View & Read

  • 1)

    A server channel monitored for an hour was found to have an estimated mean of 20 transactions transmitted per minute. The variance is known to be 4. Find the standard error.

  • 2)

    The standard deviation of a sample of size 50 is 6.3. Determine the standard error whose population standard deviation is 6?

  • 3)

    What is sample?

  • 4)

    Define parameter

  • 5)

    In a sample of 400 population from a village 230 are found to be eaters of vegetarian items and the rest non-vegetarian items. Compute the standard error assuming that both vegetarian and non-vegetarian foods are equally popular in that village?

12th Business Maths - Probability Distributions - Two Marks Study Materials - by 8682895000 - View & Read

  • 1)

    In a family of 3 children, what is the probability that there will be exactly 2 girls?

  • 2)

    Determine the binomial distribution for which the mean is 4 and variance 3. Also find P(X=15).

  • 3)

    Write the conditions for which the poisson distribution is a limiting case of binomial distribution.

  • 4)

    Define Standard normal variate.

  • 5)

    Hospital records show that of patients suffering from a certain disease 75% die of it. What is the probability that of 6 randomly selected patients, 4 will recover?

12th Business Maths - Random Variable and Mathematical Expectation - Two Marks Study Materials - by 8682895000 - View & Read

  • 1)

    The discrete random variable X has the probability function

    X 1 2 3 4
    P(X=x) k 2k 3k 4k

    Show that k =0.1.

  • 2)

    Define random variable.

  • 3)

    What do you understand by continuous random variable?

  • 4)

    What are the properties of (i) discrete random variable and (ii) continuous random variable?

  • 5)

    Find the expected value for the random variable of an unbiased die

12th Business Maths - Numerical Methods - Two Marks Study Materials - by 8682895000 - View & Read

  • 1)

    Construct a forward difference table for the following data

    x 0 10 20 30
    y 0 0.174 0.347 0.518
  • 2)

    Construct a forward difference table for y = f(x) = x3+2x+1 for x = 1,2,3,4,5

  • 3)

    Using interpolation estimate the business done in 1985 from the following data

    Year 1982 1983 1984 1986
    Business done (in lakhs) 150 235 365 525
  • 4)

    Using interpolation, find the value of f(x) when x = 15

    x 3 7 11 19
    f(x) 42 43 47 60
  • 5)

    Find the missing figures in the following table

    x 0 5 10 15 20 25
    y 7 11 - 18 - 32

12th Business Maths - Differential Equations - Two Marks Study Materials - by 8682895000 - View & Read

  • 1)

    Solve: \(\frac { dy }{ dx } \) = y sin 2x
     

  • 2)

    Solve the following differential equations: \(\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } +16y=0\)

  • 3)

    Find the order and degree of the following differential equations.
    \(\frac { { d }^{ 3 }y }{ d{ x }^{ 3 } } =0\)

  • 4)

    Find the differential equation of the following
    x2 + y2 = a2

  • 5)

    Write down the order and degree of the following differential equations.
    \(\left( \frac { dy }{ dx } \right) ^{ 3 }-4\left( \frac { dy }{ dx } \right) \)+y=3ex

12th Business Maths - Integral Calculus II - Two Marks Study Materials - by 8682895000 - View & Read

  • 1)

    Find the area of the region bounded by the parabola \(y=4{ - }x^{ 2 }\) , x −axis and the lines x = 0, x = 2

  • 2)

    If the marginal revenue function for a commodity is MR = 9 − 4x2 . Find the demand function.

  • 3)

    The marginal cost function of a commodity is given by MC = \(\frac { 14000 }{ \sqrt { 7x+4 } } \) and the fixed cost is Rs.18,000.Find the total cost and average cost.

  • 4)

    Calculate consumer’s surplus if the demand function p = 122 − 5x − 2x2 and x = 6

  • 5)

    For the marginal revenue function MR = 6 − 3x2 − x3 , Find the revenue function and demand function.

12th Business Maths - Integral Calculus I - Two Marks Study Materials - by 8682895000 - View & Read

  • 1)

    Integrate the following with respect to x.

    \(\frac { 8x+13 }{ \sqrt { 4x+7 } } \)

  • 2)

    Integrate the following with respect to x.
    \(\frac { { x }^{ 3 } }{ x+2 } \)

  • 3)

    Evaluate \(\int { \frac { { 5+5e }^{ 2x } }{ { e }^{ x }+{ e }^{ -x } } dx } \)

  • 4)

    Evaluate \(\int { \frac { x }{ { x }^{ 2 }+1 } dx } \)

  • 5)

    Integrate the following with respect to x.
    \(\frac { { e }^{ 2x } }{ { e }^{ 2x }-2 } \)

12th Business Maths - Applications of Matrices and Determinants - Two Marks Study Materials - by 8682895000 - View & Read

  • 1)

    Find the rank of the matrix \(\begin{pmatrix} 1 & 5 \\ 3 & 9 \end{pmatrix}\)
     

  • 2)

    Find the rank of the matrix \(\begin{pmatrix} -5 & -7 \\ 5 & 7 \end{pmatrix}\)

  • 3)

    Show that the equations 3x−2y=6, 6x−4y=10 are inconsistent

  • 4)

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

  • 5)

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

12th Business Maths - Full Portion Two Marks Question Paper - by 8682895000 - View & Read

  • 1)

    Show that the equations 3x−2y=6, 6x−4y=10 are inconsistent

  • 2)

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

  • 3)

    Evaluate \(\int { \frac { 1 }{ \sqrt { x+2 } -\sqrt { x-2 } } } dx\)

  • 4)

    Evaluate \(\int { \left( 2sinx-5cos \right) dx } \)

  • 5)

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

12th Business Maths - Full Portion Three Marks Question Paper - by 8682895000 - View & Read

  • 1)

    Show that the equationsx+y=5, 2x+y=8 are consistent and solve them.

  • 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 =\(\left( \begin{matrix} -2 & 1 & 3 \\ 0 & 1 & 1 \\ 1 & 3 & 4 \end{matrix}\begin{matrix} 4 \\ 2 \\ 7 \end{matrix} \right) \)

  • 4)

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

  • 5)

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

12th Business Maths - Full Portion Five Marks Questions - by 8682895000 - View & Read

  • 1)

    Find k, if the equations x+2y−3z= −2,3x−y−2z=1,2x+3y−5z=k are consistent.

  • 2)

    Show that the equations5x+3y+7z=4,3x+26y+2z=9,7x+2y+10z =5 are consistent and solve them 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)

    In a market survey three commodities A, B and C were considered. In finding out the index number some fixed weights were assigned to the three varieties in each of the commodities. The table below provides the information regarding the consumption of three commoditiesaccording to the three varieties and also the total weight received by the commodity

    Commodity Variety Variety Total weight
    I II III
    A 1 2 3 11
    B 2 4 5 21
    C 3 5 6 27

    Find the weights assigned to the three varieties by using 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 Business Maths - Public Exam Model Question Paper 2019 - 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 \(\left| \begin{matrix} 2x & 5 \\ 8 & x \end{matrix} \right| =\left| \begin{matrix} 6 & -2 \\ 7 & 3 \end{matrix} \right| \) then x =

  • 3)

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

  • 4)

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

  • 5)

    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

12th Business Maths - Integral Calculus – II Model Question Paper - by Sridevi - Sankarankoil - View & Read

  • 1)

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

  • 2)

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

  • 3)

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

  • 4)

    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.

  • 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.

View all

TN Stateboard Education Study Materials

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

Probability Distributions

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

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