By QB365 on 31 Dec, 2022
QB365 provides a detailed and simple solution for every Possible Questions in Class 12 Business Maths Subject - Important 1 Mark MCQ's, English Medium. It will help Students to get more practice questions, Students can Practice these question papers in addition to score best marks.
12th Standard
Business Maths and Statistics
Answer all the following Questions.
The rank of m x n matrix whose elements are unity is ________.
0
1
m
n
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 ________.
\(\frac { 1 }{ 4 } \)
\(\frac { 1 }{ 5 } \)
\(\frac { 1 }{ 6 } \)
\(\frac { 1 }{ 8 } \)
The rank of the matrix \(\left( \begin{matrix} 1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 4 & 9 \end{matrix} \right) \) is ________.
0
1
2
3
If \(\rho (A)\) = r then which of the following is correct?
all the minors of order r which does not vanish
A has at least one minor of order r which does not vanish
A has at least one (r+1) order minor which vanishes
all (r+1) and higher order minors should not vanish
ഽ2xdx is _______.
2x log 2 + c
2x + c
\(\frac { 2^{ x } }{ log2 } +c\)
\(\frac { log2 }{ { 2 }^{ x } } +c\)
ഽ\(\frac { { e }^{ x } }{ { e }^{ x }+1 } \) dx is _______.
log\(\left| \frac { { e }^{ x } }{ { e }^{ x }+1 } \right| +c\)
log\(\left| \frac { { e }^{ x }+1 }{ { e }^{ x } } \right| +c\)
log\(\left| { e }^{ x } \right| +c\)
log\(\left| { e }^{ x }+1 \right| +c\)
\(\int _{ 0 }^{ 1 }{ (2x+1) } dx\) is _______.
1
2
3
4
\(\int _{ 0 }^{ \frac { \pi }{ 3 } }\)tanx dx is _______.
log 2
0
log\(\sqrt { 2 } \)
2 log 2
Area bounded by the curve y = x (4 − x) between the limits 0 and 4 with x − axis is ________.
\(\frac{30}{3}\) sq.units
\(\frac{31}{2}\)sq.units
\(\frac{32}{3}\) sq.units
\(\frac{15}{2}\) sq.units
The demand function for the marginal function MR = 100 − 9x2 is ________.
100 − 3x2
100x − 3x2
100x − 9x2
100 + 9x2
For a demand function p, if \(\int \frac{d p}{p}=k \int \frac{d x}{x}\) then k is equal to ________.
\(\eta \)d
-\(\eta \)d
\(\frac{-1}{\eta_{d}}\)
\(\frac{1}{\eta_{d}}\)
Area bounded by y = \(\left| x \right| \) between the limits 0 and 2 is ________.
1sq.units
3 sq.units
2 sq.units
4 sq.units
The order and degree of the differential equation \(\left(\frac{d^{2} y}{d x^{2}}\right)^{\frac{3}{2}}-\sqrt{\left(\frac{d y}{d x}\right)}-4=0\) are respectively ______.
2 and 6
3 and 6
1 and 4
2 and 4
The complementary function of (D2+ 4)y = e2x is ______.
(Ax +B)e2x
(Ax +B)e−2x
A cos 2x + B sin 2x
Ae−2x+ Be2x
The complementary function of \(\frac { { d }^{ 3 }y }{ d{ x }^{ 3 } } -\frac { dy }{ dx } \) = 0 is ______.
A + Bex
(A + B) ex
(Ax + B) ex
Aex + B
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 ______.
\(f\left( \frac { y }{ x } \right) =k.x\)
\(xf\left( \frac { y }{ x } \right) =k\)
\(f\left( \frac { y }{ x } \right) =ky\)
\(yf\left( \frac { y }{ x } \right) =k\)
Δf(x) = _______.
f(x+ h)
f(x) − f(x+h)
f(x + h) − f(x)
f (x) − f(x−h)
If c is a constant then Δc = _______.
c
Δ
Δ2
0
For the given points (x0, y0) and (x1, y1) the Lagrange’s formula is _______.
\(y(x)=\frac{x-x_{1}}{x_{0}-x_{1}} y_{0}+\frac{x-x_{0}}{x_{1}-x_{0}} y_{1}\)
\(y(x)=\frac{x_{1}-x}{x_{0}-x_{1}} y_{0}+\frac{x-x_{0}}{x_{1}-x_{0}} y_{1}\)
\(y(x)=\frac{x-x_{1}}{x_{0}-x_{1}} y_{1}+\frac{x-x_{0}}{x_{1}-x_{0}} y_{0}\)
\(y(x)=\frac{x_{1}-x}{x_{0}-x_{1}} y_{1}+\frac{x-x_{0}}{x_{1}-x_{0}} y_{0}\)
If f (x)=x2 + 2x + 2 and the interval of differencing is unity then Δf (x) _______.
2x −3
2x +3
x + 3
x − 3
Value which is obtained by multiplying possible values of random variable with probability of occurrence and is equal to weighted average is called ________.
Discrete value
Weighted value
Expected value
Cumulative value
Probability which explains x is equal to or less than particular value is classified as ________.
discrete probability
cumulative probability
marginal probability
continuous probability
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 ________.
\(\sum { f(x) } \)
\(\sum[x+f(x)]\)
\(\sum { f(x)+x } \)
\(\sum { xp(x) } \)
If c is a constant in a continuous probability distribution, then p(x = c) is always equal to ________.
zero
one
negative
does not exist
If Z is a standard normal variate, the proportion of items lying between Z = –0.5 and Z = –3.0 is ________.
0.4987
0.1915
0.3072
0.3098
In turning out certain toys in a manufacturing company, the average number of defectives is 1%. The probability that the sample of 100 toys there will be 3 defectives is ________.
0.0613
0.613
0.00613
0.3913
Forty percent of the passengers who fly on a certain route do not check in any luggage. The planes on this route seat 15 passengers. For a full flight, what is the mean of the number of passengers who do not check in any luggage?
6.00
6.45
7.20
7.50
The weights of newborn human babies are normally distributed with a mean of 3.2 kg and a standard deviation of 1.1 kg. What is the probability that a randomly selected newborn baby weighs less than 2.0 kg?
0.138
0.428
0.766
0.262
A __________ of statistical individuals in a population is called a sample.
Infinite set
finite subset
finite set
entire set
In ________ the heterogeneous groups are divided into homogeneous groups.
Non-probability sample
a simple random sample
a stratified random sample
systematic random sample
_______ is a relative property, which states that one estimator is efficient relative to another.
efficiency
sufficiency
unbiased
consistency
Type I error is ______.
Accept H0 when it is true
Accept H0 when it is false
Reject H0 when it is true
Reject H0 when it is false.
Factors responsible for seasonal variations are ________.
Weather
Festivals
Social customs
All the above
Least square method of fitting a trend is ________.
Most exact
Least exact
Full of subjectivity
Mathematically unsolved
Which of the following Index number satisfy the time reversal test?
Laspeyre’s Index number
Paasche’s Index number
Fisher Index number
All of them
R is calculated using ________.
xmax - xmin
xmin - xmax
\(\overset{-}{x}\)max - \(\overset{-}{x}\)min
\(\overset{=}{x}\)max - \(\overset{=}{x}\)min
The Penalty in VAM represents difference between the first ________.
Two largest costs
Largest and Smallest costs
Smallest two costs
None of these
Solution for transportation problem using ________method is nearer to an optimal solution.
NWCM
LCM
VAM
Row Minima
In an assignment problem involving four workers and three jobs, total number of assignments possible are _______.
4
3
7
12
A type of decision –making environment is _______.
certainty
uncertainty
risk
all of the above
If the minor of a23 = the co-factor of a23 in |aij| then the minor of a23 is |ay| then the minor of a23 is ________
1
2
0
3
\(\int { { 3 }^{ x+2 } } \) dx = ______________ +c
\(\frac { { 3 }^{ x } }{ log3 } \)
\(\frac { 9\left( { 3 }^{ x } \right) }{ log3 } \)
\(\frac { 3.{ 3 }^{ x } }{ log3 } \)
\(\frac { { 3 }^{ x } }{ 9log3 } \)
The area lying above the X-axis and under the parabola y = 4x - x2 is ______ sq. units
\(\frac{16}{3}\)
\(\frac{8}{3}\)
\(\frac{32}{3}\)
\(\frac{64}{3}\)
The solution of \(\frac { dp }{ dt } \) = ke-t (k is a constant) is _____________
c-\(\frac { k }{ { e }^{ t } } \) = p
p = ket+c
t = log\(\left( \frac { c-p }{ k } \right) \)
t = logc p
The backward difference operator ∇ is ______________
Nepla
Alpha
Gamma
Delta
A probability distribution function is defined by \(F(x)\begin{cases} 0,\ x<0 \\ 1-{ e }^{ -x },\ x\ge 0 \end{cases}\) The probability density function is __________
\(f(x)\begin{cases} { 3e }^{ -3x },\quad x\ge 0 \\ 0,\quad x<0 \end{cases}\)
\(\\ f(x)\begin{cases} { 1-e }^{ -3x },\quad x\ge 0 \\ 0,\quad x<0 \end{cases}\)
\(f(X)=0\forall x\)
f(x) = 3e - 3x\(\infty\)
The marks second by 400 students in mathematics test were nolmally distributed, with mean 65. If 120 students got more marks above 85, the number of students securing between 45 and 65 is ____________
120
20
80
160
If α is the level of significance. then the confidence Co-efficient is
α
1
1-α
1+α
The multiplicative model bf the time series with the components T, S, C and I is __________
y = T + S x C x I
y = T x S x C x I
y = T + S x C + I
y = T + S + C + I
lf abasic feasible solution to a transportation problem contains less' than m + n - 1 allocations, it is called a_________basic feasible solution
Optimum
Degenerate
Non-degenerate
Balanced
Answers
1
\(\frac { 1 }{ 4 } \)
3
A has at least one minor of order r which does not vanish
\(\frac { 2^{ x } }{ log2 } +c\)
log\(\left| { e }^{ x }+1 \right| +c\)
2
log 2
\(\frac{32}{3}\) sq.units
100 − 3x2
\(\frac{-1}{\eta_{d}}\)
2 sq.units
2 and 6
A cos 2x + B sin 2x
A + Bex
\(f\left( \frac { y }{ x } \right) =k.x\)
f(x + h) − f(x)
0
\(y(x)=\frac{x-x_{1}}{x_{0}-x_{1}} y_{0}+\frac{x-x_{0}}{x_{1}-x_{0}} y_{1}\)
2x +3
Expected value
cumulative probability
\(\sum { xp(x) } \)
zero
0.3072
0.0613
6.00
0.138
finite subset
a stratified random sample
efficiency
Reject H0 when it is true
All the above
Most exact
Fisher Index number
xmax - xmin
Smallest two costs
VAM
3
all of the above
0
\(\frac { 9\left( { 3 }^{ x } \right) }{ log3 } \)
\(\frac{32}{3}\)
c-\(\frac { k }{ { e }^{ t } } \) = p
Nepla
\(f(x)\begin{cases} { 3e }^{ -3x },\quad x\ge 0 \\ 0,\quad x<0 \end{cases}\)
80
1-α
y = T x S x C x I
Non-degenerate