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

12th Standard

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Time : 01:00:00 Hrs
Total Marks : 50

Part-A

Multiple Choice Questions

50 x 1 = 50
1. If A =$\left( \begin{matrix} 1 \\ 2 \\ 3 \end{matrix} \right)$ then the rank of AAT is

(a)

0

(b)

1

(c)

2

(d)

3

2. If $\rho (A)=\rho (A,B)$ then the system is

(a)

Consistent and has infinitely many solutions

(b)

Consistent and has a unique solution

(c)

consistent

(d)

inconsistent

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

(a)

2

(b)

1

(c)

0

(d)

3

4. $\int \frac{\sin 5 x-\sin x}{\cos 3 x} d x$ is

(a)

−cos 2x + c

(b)

−cos 2x + c

(c)

$-\frac14$cos2x + c

(d)

−4cos2x + c

5. $\frac { { e }^{ x } }{ \sqrt { { 1+e }^{ x } } }$ 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)

${ e }^{ x }\sqrt { 1+{ e }^{ x } } +c$

6. $\int _{ -1 }^{ 1 }{ { x }^{ 3 }{ e }^{ { x }^{ 4 } } }$ dx is

(a)

1

(b)

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

(c)

0

(d)

${ e }^{ { x }^{ 4 } }$

7. 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)

0

8. 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

9. 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)

5

(b)

2

(c)

3

(d)

19

10. 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)

$\frac { { d }^{ 3 }y }{ d{ x }^{ 3 } } =0$

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

(a)

(Ax +B)e2x

(b)

(Ax +B)e−2x

(c)

A cos 2x + B sin 2x

(d)

Ae−2x+ Be2x

12. 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

13. 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)

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

14. ∇ ≡

(a)

1+E

(b)

1 - E

(c)

1− E−1

(d)

1+ E−1

15. 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.

16. Given $E(X)=5 \text { and } E(Y)=-2, \text { then } E(X-Y)$ is

(a)

3

(b)

5

(c)

7

(d)

-2

17. 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

18. A probability density function may be represented by:

(a)

table

(b)

graph

(c)

mathematical equation

(d)

both (b) and (c)

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

(a)

E(X)

(b)

V(X)

(c)

0

(d)

E(X)-X

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

(a)

non-negative

(b)

negative

(c)

one

(d)

zero

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

(a)

zero

(b)

one

(c)

minimum

(d)

maximum

22. 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 +∞

23. 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

24. 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)

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

25. 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

26. 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

27. 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

28. 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

29. 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

30. 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

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. 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

33. 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

34. 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

35. Errors in sampling are of

(a)

Two types

(b)

three types

(c)

four types

(d)

five types

36. 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.

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

(a)

population parameter

(b)

biased estimate

(c)

sample size

(d)

census

38. 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

39. Least square method of fitting a trend is

(a)

Most exact

(b)

Least exact

(c)

Full of subjectivity

(d)

Mathematically unsolved

40. 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

41. Consumer price index are obtained by:

(a)

Paasche’s formula

(b)

Fisher’s ideal formula

(c)

Marshall Edgeworth formula

(d)

Family budget method formula

42. 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

43. A typical control charts consists of

(a)

CL, UCL

(b)

CL, LCL

(c)

CL, LCL, UCL

(d)

UCL, LCL

44. $\overset {-}{X}$ 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

45. 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

46. 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

47. 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

48. 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

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

(a)

4

(b)

3

(c)

7

(d)

12

50. A type of decision –making environment is

(a)

certainty

(b)

uncertainty

(c)

risk

(d)

all of the above