12th Standard English Medium Business Maths Reduced Syllabus One mark Important Questions with Answer key - 2021(Public Exam )

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Questions:

Multiple Choice Question

50 x 1 = 50

Lagrange’s interpolation formula can be used for _______.

(a)

equal intervals only

(b)

unequal intervals only

(c)

both equal and unequal intervals

(d)

none of these.

∇ ≡ _______.

(a)

1+E

(b)

1 - E

(c)

1− E⁻¹

(d)

1+ E⁻¹

A type of decision –making environment is _______.

(a)

certainty

(b)

uncertainty

(c)

risk

(d)

all of the above

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

(a)

(b)

(c)

(d)

The solution for an assignment problem is optimal if _______.

(a)

each row and each column has no assignment

(b)

each row and each column has atleast one assignment

(c)

each row and each column has atmost one assignment

(d)

each row and each column has exactly one assignment

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

(a)

Exactly one

(b)

at least one

(c)

at most one

(d)

none of these

The Penalty in VAM represents difference between the first ________.

(a)

Two largest costs

(b)

Largest and Smallest costs

(c)

Smallest two costs

(d)

None of these

In a degenerate solution number of allocations is _______.

(a)

equal to m+n–1

(b)

not equal to m+n–1

(c)

less than m+n–1

(d)

greather than m+n–1

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

(a)

\(\frac { 2{ v }^{ 2 } }{ 1+v } dv=\frac { dx }{ x } \)

(b)

\(\frac { 2{ v }^{ 2 } }{ 1+v } dv=-\frac { dx }{ x } \)

(c)

\(\frac { 2{ v }^{ 2 } }{ 1-v } dv=\frac { dx }{ x } \)

(d)

\(\frac { 1+v }{ 2{ v }^{ 2 } } dv=-\frac { dx }{ x } \)

10.

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

(a)

x = v y

(b)

y = v x

(c)

y = v

(d)

x = v

11.

The complementary function of (D²+ 4)y = e^2x is ______.

(a)

(Ax +B)e^2x

(b)

(Ax +B)e^−2x

(c)

A cos 2x + B sin 2x

(d)

Ae^−2x+ Be^2x

12.

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

(a)

\(y=\frac { dy }{ dx } +\frac { dy }{ dx } -{ \left( \frac { dy }{ dx } \right) }^{ 3 }\)

(b)

\(y={ \left( \frac { dy }{ dx } \right) }^{ 3 }=x\frac { dy }{ dx } -\frac { dy }{ dx } \)

(c)

\(\frac { dy }{ dx } +y={ \left( \frac { dy }{ dx } \right) }^{ 3 }-x\frac { dy }{ dx } \)

(d)

\(\frac { { d }^{ 3 }y }{ d{ x }^{ 3 } } =0\)

13.

\(\overset {-}{X}\) chart is a ________.

(a)

attribute control chart

(b)

variable control chart

(c)

neither Attribute nor variable control chart

(d)

both Attribute and variable control chart

14.

A typical control charts consists of ________.

(a)

CL, UCL

(b)

CL, LCL

(c)

CL, LCL, UCL

(d)

UCL, LCL

15.

Which of the following Index number satisfy the time reversal test?

(a)

Laspeyre’s Index number

(b)

Paasche’s Index number

(c)

Fisher Index number

(d)

All of them

16.

Consumer price index are obtained by: ________.

(a)

Paasche’s formula

(b)

Fisher’s ideal formula

(c)

Marshall Edgeworth formula

(d)

Family budget method formula

17.

The value of ‘b’ in the trend line y = a + bx is ________.

(a)

Always positive

(b)

Always negative

(c)

Either positive or negative

(d)

Zero

18.

Least square method of fitting a trend is ________.

(a)

Most exact

(b)

Least exact

(c)

Full of subjectivity

(d)

Mathematically unsolved

19.

Type II error is ______.

(a)

Accept H₀ when it is wrong

(b)

Accept H₀ when it is true

(c)

Reject H₀ when it is true

(d)

Reject H₀ when it is false

20.

An estimator is a sample statistic used to estimate a ______.

(a)

population parameter

(b)

biased estimate

(c)

sample size

(d)

census

21.

The method of obtaining the most likely value of the population parameter using statistic is called ______.

(a)

estimation

(b)

estimator

(c)

biased estimate

(d)

standard error.

22.

Errors in sampling are of ______.

(a)

Two types

(b)

three types

(c)

four types

(d)

five types

23.

In ________ the heterogeneous groups are divided into homogeneous groups.

(a)

Non-probability sample

(b)

a simple random sample

(c)

a stratified random sample

(d)

systematic random sample

24.

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

(a)

5040

(b)

5400

(c)

4500

(d)

5540

25.

If f (x) is a continuous function and a < c < b, then \(\int_{a}^{c} f(x) d x+\int_{c}^{b} f(x) d x\) is _______.

(a)

\(\int_{a}^{b} f(x) d x-\int_{a}^{c} f(x) d x\)

(b)

\(\int_{a}^{c} f(x) d x-\int_{a}^{b} f(x) d x\)

(c)

\(\int_{a}^{b} f(x) d x\)

(d)

26.

\(\int _{ -1 }^{ 1 }{ { x }^{ 3 }{ e }^{ { x }^{ 4 } } } \) dx is _______.

(a)

(b)

2\(\int _{ -1 }^{ 1 }{ { x }^{ 3 }{ e }^{ { x }^{ 4 } } } \)dx

(c)

(d)

\({ e }^{ { x }^{ 4 } }\)

27.

ഽ\(\frac { { e }^{ x } }{ \sqrt { { 1+e }^{ x } } } \) dx is _______.

(a)

\(\frac { { e }^{ x } }{ \sqrt { { 1+e }^{ x } } } +c\)

(b)

\(2\sqrt { 1+{ e }^{ x } } +c\)

(c)

\(\sqrt { 1+{ e }^{ x } } +c\)

(d)

\({ e }^{ x }\sqrt { 1+{ e }^{ x } } +c\)

28.

\(\int \frac{\sin 5 x-\sin x}{\cos 3 x} d x\) is _______.

(a)

−cos 2x + c

(b)

−cos 2x + c

(c)

\(-\frac14\)cos2x + c

(d)

−4cos2x + c

29.

If the area to the left of a value of z (z has a standard normal distribution) is 0.0793, what is the value of z?

(a)

-1.41

(b)

1.41

(c)

-2.25

(d)

2.25

30.

Let z be a standard normal variable. If the area to the right of z is 0.8413, then the value of z must be: ________.

(a)

1.00

(b)

-1.00

(c)

0.00

(d)

-0.41

31.

Cape town is estimated to have 21% of homes whose owners subscribe to the satelite service, DSTV. If a random sample of your home in taken, what is the probability that all four home subscribe to DSTV?

(a)

0.2100

(b)

0.5000

(c)

0.8791

(d)

0.0019

32.

A statistical analysis of long-distance telephone calls indicates that the length of these calls is normally distributed with a mean of 240 seconds and a standard deviation of 40 seconds. What proportion of calls lasts less than 180 seconds?

(a)

0.214

(b)

0.094

(c)

0933

(d)

0.067

33.

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?

(a)

0.819

(b)

0.242

(c)

0.286

(d)

0.533

34.

Which of the following cannot generate a Poisson distribution?

(a)

The number of telephone calls received in a ten-minute interval

(b)

The number of customers arriving at a petrol station

(c)

The number of bacteria found in a cubic feet of soil

(d)

The number of misprints per page

35.

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 ________.

(a)

0.5443

(b)

0.4543

(c)

0.5543

(d)

0.4573

36.

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

(a)

(2/3)⁶

(b)

(2/3)⁵(1/3)

(c)

(1/3)⁶

(d)

4(2/3)⁶

37.

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 ________.

(a)

240/729

(b)

489/729

(c)

496/729

(d)

251/729

38.

If X ~ N(μ, σ²), the maximum probability at the point of inflexion of normal distribution is ________.

(a)

\({ \left( \frac { 1 }{ \sqrt { 2\pi } } \right) }^{ { e }^{ \frac { 1 }{ 2 } } }\)

(b)

\({ \left( \frac { 1 }{ \sqrt { 2\pi } } \right) }^{ { e }^{ \left( -\frac { 1 }{ 2 } \right) } }\)

(c)

\({ \left( \frac { 1 }{ \sigma \sqrt { 2\pi } } \right) }^{ { e }^{ \left( \frac { 1 }{ 2 } \right) } }\)

(d)

\({ \left( \frac { 1 }{ \sqrt { 2\pi } } \right) }\)

39.

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

(a)

0.4987

(b)

0.1915

(c)

0.3072

(d)

0.3098

40.

A discrete probability function p(x) is always non-negative and always lies between ________.

(a)

0 and \(\infty \)

(b)

0 and 1

(c)

–1 and +1

(d)

–∞ and +∞

41.

In a discrete probability distribution the sum of all the probabilities is always equal to ________.

(a)

zero

(b)

one

(c)

minimum

(d)

maximum

42.

A discrete probability function p(x) is always ________.

(a)

non-negative

(b)

negative

(c)

one

(d)

zero

43.

E[X-E(X)] is equal to ________.

(a)

E(X)

(b)

V(X)

(c)

(d)

E(X)-X

44.

A probability density function may be represented by ________.

(a)

table

(b)

graph

(c)

mathematical equation

(d)

both (b) and (c)

45.

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

(a)

discrete random variable

(b)

continuous random variable

(c)

discrete sample space

(d)

random variable

46.

Given E(X)=5 and E(Y)=−2, then E(X−Y) is ________.

(a)

(b)

(c)

(d)

-2

47.

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 ________.

(a)

(b)

(c)

(d)

48.

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

(a)

(b)

(c)

(d)

49.

If \(\rho (A)=\rho (A,B)\) the number of unknowns, then the system is______.

(a)

Consistent and has infinitely many solutions

(b)

Consistent and has a unique solution

(c)

consistent

(d)

inconsistent

50.

If A =\(\left( \begin{matrix} 1 \\ 2 \\ 3 \end{matrix} \right) \) then the rank of AA^Tis ________.

(a)

(b)

(c)

(d)

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Answers Key:

Multiple Choice Question

50 x 1 = 50

(d)
all of the above

(b)
3

(d)
each row and each column has exactly one assignment

(a)
Exactly one

(d)
\(\frac { 1+v }{ 2{ v }^{ 2 } } dv=-\frac { dx }{ x } \)

10.

(a)
x = v y

11.

12.

(a)
\(y=\frac { dy }{ dx } +\frac { dy }{ dx } -{ \left( \frac { dy }{ dx } \right) }^{ 3 }\)

13.

(b)
variable control chart

14.

15.

16.

(d)
Family budget method formula

17.

18.

(a)
Most exact

19.

(a)
Accept H₀ when it is wrong

20.

(a)
population parameter

21.

(a)
estimation

22.

(a)
Two types

23.

24.

(a)
5040

25.

26.

27.

(b)
\(2\sqrt { 1+{ e }^{ x } } +c\)

28.

(a)
−cos 2x + c

29.

(a)
-1.41

30.

(b)
-1.00

31.

(d)
0.0019

32.

(d)
0.067

33.

(b)
0.242

34.

(b)
The number of customers arriving at a petrol station

35.

(a)
0.5443

36.

(d)
4(2/3)⁶

37.

38.

39.

40.

(b)
0 and 1

41.

(b)
one

42.

(a)
non-negative

43.

44.

(d)
both (b) and (c)

45.

(b)
continuous random variable

46.

47.

(b)
2

48.

49.

(b)
Consistent and has a unique solution

50.

(b)
1

12th Standard English Medium Business Maths Reduced Syllabus One mark Important Questions with Answer key - 2021(Public Exam )

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Std: 12th Standard - Business Maths and Statistics

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Questions:

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Answers Key:

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