11th Public Exam March 2019 Important One Mark Test

Download Tamil Nadu 11th Standard Business Maths and Statistics question papers, model tests, one-mark questions, important questions, and public exam papers in PDF format. Free study materials and answer keys for TN State Board students.

Questions:

Multiple Choice Question

120 x 1 = 120

Probability that at least one of the events A, B occur is _________.

(a)

\(P(A\cup B)\)

(b)

\(P(A\cap B)\)

(c)

P(A/B)

(d)

\((A\cup B)\)

The probability of obtaining an even prime number on each die, when a pair of dice is rolled is _________.

(a)

1/36

(b)

(c)

1/3

(d)

1/6

If the outcome of one event does not influence another event then the two events are _________.

(a)

Mutually exclusive

(b)

Dependent

(c)

Not disjoint

(d)

Independent

If two events A and B are dependent then the conditional probability of P(B/A) is _________.

(a)

\(P(A)P(B/A)\)

(b)

\(\frac { P(A\cap B) }{ P(B) } \)

(c)

\(\frac { P(A\cap B) }{ P(A) } \)

(d)

\(P(A)P(A/B)\)

The two events A and B are mutually exclusive if _________.

(a)

\(P\left( A\cap B \right) =0\)

(b)

\(P\left( A\cap B \right) =1\)

(c)

\(P\left( A\cup B \right) =0\)

(d)

\(P\left( AUB \right) =1\)

If Q₁ = 30 and Q₃ = 50, the coefficient of quartile deviation is _________.

(a)

(b)

(c)

(d)

0.25

The first quartile is also known as _________.

(a)

median

(b)

lower quartile

(c)

mode

(d)

third decile

If the mean of 1,2,3,.......n is\(\frac { 6n }{ 11 } \), then the value of n is _________.

(a)

(b)

(c)

(d)

The median of 10,14,11,9,8,12,6 is _________.

(a)

(b)

(c)

(d)

10.

The correct relationship among A.M.,G.M.and H.M.is: ________.

(a)

A.M.

(b)

G.M.≥A.M.≥H.M.

(c)

H.M.≥G.M.≥A.M.

(d)

A.M.≥G.M.≥H.M.

11.

The geometric mean of two numbers 8 and 18 shall be _________.

(a)

(b)

(c)

(d)

11.08

12.

The harmonic mean of the numbers 2,3,4 is _________.

(a)

\(\frac { 12 }{ 13 } \)

(b)

(c)

\(\frac { 36 }{ 13 } \)

(d)

\(\frac { 13 }{ 36 } \)

13.

The best measure of central tendency is _________.

(a)

Arithmetic mean

(b)

Harmonic mean

(c)

Geometric mean

(d)

Median

14.

When calculating the average growth of economy, the correct mean to use is?

(a)

Weighted mean

(b)

Arithmetic mean

(c)

Geometric mean

(d)

Harmonic mean

15.

Which of the following is positional measure?

(a)

Range

(b)

Mode

(c)

Mean deviation

(d)

Percentiles

16.

If Cov(x, y) = –16.5, \({ \sigma }_{ x }^{ 2 }=2.89,{ \sigma }_{ y }^{ 2 }\) = 100. Find correlation coefficient ________.

(a)

-0.12

(b)

0.001

(c)

-1

(d)

-0.97

17.

The coefficient of correlation describes ________.

(a)

the magnitude and direction

(b)

only magnitude

(c)

only direction

(d)

no magnitude and no direction

18.

The term regression was introduced by ________.

(a)

R.A Fisher

(b)

Sir Francis Galton

(c)

Karl Pearson

(d)

Croxton and Cowden

19.

The person suggested a mathematical method for measuring the magnitude of linear relationship between two variables say X and Y is ________.

(a)

Karl Pearson

(b)

Spearman

(c)

Croxton and Cowden

(d)

Ya Lun Chou

20.

If two variables moves in decreasing direction then the correlation is ________.

(a)

positive

(b)

negative

(c)

perfect negative

(d)

no correlation

21.

Scatter diagram of the variate values (X,Y) give the idea about ________.

(a)

functional relationship

(b)

regression model

(c)

distribution of errors

(d)

no relation

22.

If X and Y are two variates, there can be atmost ________.

(a)

One regression line

(b)

two regression lines

(c)

three regression lines

(d)

more regression lines

23.

When one regression coefficient is negative, the other would be ________.

(a)

Negative

(b)

Positive

(c)

Zero

(d)

None of them

24.

The regression coefficient of X on Y ________.

(a)

b_xy = \(\frac { N\Sigma dxdy-(\Sigma dx)(\Sigma dy) }{ N\Sigma dy^{ 2 }-(\Sigma dy)^{ 2 } } \)

(b)

b_yx = \(\frac { N\Sigma dxdy-(\Sigma dx)(\Sigma dy) }{ N\Sigma dy^{ 2 }-(\Sigma dy)^{ 2 } } \)

(c)

b_xy= \(\frac { N\Sigma dxdy-(\Sigma dx)(\Sigma dy) }{ N\Sigma dx^{ 2 }-(\Sigma dx)^{ 2 } } \)

(d)

b_y=\(\frac { N\Sigma xy-(\Sigma x)(\Sigma y) }{ \sqrt { N\Sigma { x }^{ 2 }-(\Sigma x)^{ 2 }\times \sqrt { N\Sigma y^{ 2 }-(\Sigma y)^{ 2 } } } } \)

25.

The correlation coefficient ________.

(a)

r = ±\(\sqrt { { b }_{ xy }\times { b }_{ yx } } \)

(b)

r = \(\frac { 1 }{ { b }_{ xy }\times { b }_{ yx } } \)

(c)

r = b_xy x b_yx

(d)

r = ±\(\sqrt { \frac { 1 }{ { b }_{ xy }\times { b }_{ yx } } } \)

26.

The present value of the perpetual annuity of Rs. 2000 paid monthly at 10 % compound interest is _______.

(a)

Rs. 2,40,000

(b)

Rs. 6,00,000

(c)

Rs. 20,40,000

(d)

Rs. 2,00,400

27.

An annuity in which payments are made at the beginning of each payment period is called _______.

(a)

Annuity due

(b)

An immediate annuity

(c)

perpetual annuity

(d)

none of these

28.

If ‘a’ is the annual payment, ‘n’ is the number of periods and ‘i’ is compound interest for Rs. 1 then future amount of the annuity is _______.

(a)

A = \(\frac{a}{i}(1+i)(1+i)^n-1]\)

(b)

A = \(\frac{a}{i}[(1+i)^n-1]\)

(c)

P = \(\frac{a}{i}\)

(d)

P = \(\frac{a}{i}(1+i)[1-(1+i)^{-n}]\)

29.

The annual income on 500 shares of face value Rs.100 at 15% is _______.

(a)

Rs. 7,500

(b)

Rs. 5,000

(c)

Rs. 8,000

(d)

Rs. 8,500

30.

A person brought 100 shares of 9% stock of face value Rs. 100, at a discount of 10%, then the stock purchased is _______.

(a)

Rs. 9000

(b)

Rs. 6000

(c)

Rs. 5000

(d)

Rs. 4000

31.

The brokerage paid by a person on the sale of 400 shares of face value Rs.100 at 1% brokerage ________.

(a)

Rs. 600

(b)

Rs. 500

(c)

Rs. 200

(d)

Rs. 400

32.

If a man received a total dividend of Rs. 25,000 at 10% dividend rate on a stock of face value Rs.100, then the number of shares purchased.

(a)

3500

(b)

4500

(c)

2500

(d)

300

33.

The dividend received on 200 shares of face value Rs.100 at 8% is ________.

(a)

Rs. 1600

(b)

Rs. 1000

(c)

Rs. 1500

(d)

Rs. 800

34.

The variable whose value is influenced (or) is to be predicted is called ________.

(a)

dependent variable

(b)

independent variable

(c)

regressor

(d)

explanatory variable

35.

The correlation coefficient is ________.

(a)

r(X, Y) = \(\frac { { \sigma }_{ x }{ \sigma }_{ y } }{ cov(x,y) } \)

(b)

r(X, Y) = \(\frac { cov(x,y) }{ { \sigma }_{ x }{ \sigma }_{ y } } \)

(c)

r(X, Y) = \(\frac { cov(x,y) }{ { \sigma }_{ y } } \)

(d)

r(X, Y) = \(\frac { cov(x,y) }{ { \sigma }_{ x } } \)

36.

The correlation coefficient from the following data N = 25, ΣX = 125, ΣY = 100, ΣX² = 650, ΣY²= 436, ΣXY = 520 ________.

(a)

0.667

(b)

-0.006

(c)

-0.667

(d)

0.70

37.

If r(X,Y) = 0 the variables X and Y are said to be ______.

(a)

Positive correlation

(b)

Negative correlation

(c)

No correlation

(d)

Perfect positive correlation

38.

If the values of two variables move in opposite direction then the correlation is said to be ______.

(a)

Negative

(b)

Positive

(c)

Perfect positive

(d)

No correlation

39.

Example for positive correlation is______.

(a)

Income and expenditure

(b)

Price and demand

(c)

Repayment period and EMI

(d)

Weight and Income

40.

If R = 5000 units / year, C₁ = 20 paise , C₃ = Rs. 20 then EOQ is _______.

(a)

5000

(b)

100

(c)

1000

(d)

200

41.

if q = 1000 + 8p₁ - p₂ then, \(\frac { \partial q }{ \partial { p }_{ 1 } } \) is _______.

(a)

-1

(b)

(c)

1000

(d)

1000 - p₂

42.

The demand function is always _______.

(a)

Increasing function

(b)

Decreasing function

(c)

Non-decreasing function

(d)

Undefined function

43.

A company begins to earn profit at _______.

(a)

Maximum point

(b)

Breakeven point

(c)

Stationary point

(d)

Even point

44.

If u = \({ e }^{ { x }^{ 2 } }\) then \(\frac { \partial u }{ \partial x } \) is equal to _______.

(a)

\({ 2x }e^{ { x }^{ 2 } }\)

(b)

\({ e }^{ { x }^{ 2 } }\)

(c)

\({2 e }^{ { x }^{ 2 } }\)

(d)

45.

If f(x,y) is a homogeneous function of degree n, then \(x\frac { \partial f }{ \partial x } +y\frac { \partial f }{ \partial y } \) is equal to ________.

(a)

(n–1)f

(b)

n(n–1)f

(c)

(d)

46.

The maximum value of f(x) = sinx is ________.

(a)

(b)

\(\frac { \sqrt { 3 } }{ 2 } \)

(c)

\(\frac { 1 }{ \sqrt { 2 } } \)

(d)

\(-\frac { 1 }{ \sqrt { 2 } } \)

47.

Profit P(x) is maximum when ________.

(a)

MR = MC

(b)

MR = 0

(c)

MC = AC

(d)

TR = AC

48.

Instantaneous rate of change of y = 2x² + 5x with respect to x at x = 2 is _________.

(a)

(b)

(c)

(d)

49.

Relationship among MR, AR and η_d is ______.

(a)

\({ n }_{ d }=\frac { AR }{ AR-MR } \)

(b)

η_d = AR - MR

(c)

MR = AR = η_d

(d)

\(AR=\frac { MR }{ {ηd } } \)

50.

The elasticity of demand for the demand function x = \(\frac { 1 }{ p } \) is______.

(a)

(b)

(c)

\(-\frac { 1 }{ p } \)

(d)

\(\infty \)

51.

If the demand function is said to be inelastic, then _______.

(a)

|η_d| > 1

(b)

|η_d| = 1

(c)

|η_d| < 1

(d)

|η_d| = 0

52.

Marginal revenue of the demand function p = 20–3x is _______.

(a)

20–6x

(b)

20–3x

(c)

20+6x

(d)

20+3x

53.

Average fixed cost of the cost function C(x) = 2x³ +5x² - 14x +21 is _______.

(a)

\(\frac { 2 }{ 3 } \)

(b)

\(\frac { 5}{ x } \)

(c)

\(\frac { 14 }{ x } \)

(d)

\(\frac { 21 }{ x } \)

54.

Given an L.P.P maximize Z = 2x₁ + 3x₂ subject to the constrains x₁ + x₂ ≤ 1, 5x₁ + 5x₂≥ 0 and x₁ ≥ 0, x₂ ≥ 0 using graphical method, we observe ______.

(a)

No feasible solution

(b)

unique optimum solution

(c)

multiple optimum solution

(d)

none of these

55.

In critical path analysis, the word CPM mean ______.

(a)

Critical path method

(b)

Crash project management

(c)

Critical project management

(d)

Critical path management

56.

Network problems have advantage in terms of project _______.

(a)

Scheduling

(b)

Planning

(c)

Controlling

(d)

All the above

57.

The objective of network analysis is to ________.

(a)

Minimize total project cost

(b)

Minimize total project duration

(c)

Minimize production delays, interruption and conflicts

(d)

All the above

58.

In the context of network, which of the following is not correct?

(a)

A network is a graphical representation

(b)

A project network cannot have multiple initial and final nodes

(c)

An arrow diagram is essentially a closed network

(d)

An arrow representing an activity may not have a length and shape

59.

The maximum value of the objective function Z = 3x + 5y subject to the constraints x > 0 , y > 0 and 2x + 5y ≤ 10 is ______.

(a)

(b)

(c)

(d)

60.

A solution which maximizes or minimizes the given LPP is called ______.

(a)

a solution

(b)

a feasible solution

(c)

an optimal solution

(d)

none of these

61.

Maximize: z = 3x₁+ 4x₂ subject to 2x₁+ x₂≤ 40, 2x₁+ 5x₂≤ 180, x₁, x₂≥ 0. In the LPP, which one of the following is feasible corner point?

(a)

x₁ = 18, x₂= 24

(b)

x₁= 15, x₂= 30

(c)

x₁= 2.5, x₂= 35

(d)

x₁= 20.5, x₂= 19

62.

The critical path of the following network is________.

(a)

1 – 2 – 4 – 5

(b)

1 – 3 – 5

(c)

1 – 2 – 3 – 5

(d)

1 – 2 – 3 – 4 – 5

63.

\(\frac{d}{dx}(a^x)=\) ________.

(a)

\(\frac { 1 }{ x\log e^a}\)

(b)

a^a

(c)

x log_e^a

(d)

a^xlog_e^a

64.

If y = x and z = \(\frac{1}{x}\) then \(\frac{dy}{dz}=\)________.

(a)

x²

(b)

(c)

-x²

(d)

\(-\frac{1}{x^2}\)

65.

\(\frac{d}{dx}(\frac{1}{x})\) is equal to ________.

(a)

\(-\frac{1}{x^2}\)

(b)

\(-\frac{1}{x}\)

(c)

log x

(d)

\(\frac{1}{x^2}\)

66.

For what value of x, f(x) = \(\frac{x+2}{x-1}\) is not continuous?

(a)

-2

(b)

(c)

(d)

-1

67.

\(\lim _{ x\rightarrow \infty }{ \frac { \tan { \theta } }{ \theta } } =\)________.

(a)

(b)

\(\infty\)

(c)

\(-\infty\)

(d)

\(\theta\)

68.

The range of f(x) = |x|, for all \(x\in R\), is ________.

(a)

(0, \(\infty \))

(b)

(0, \(\infty \))

(c)

(-\(\infty \), \(\infty \))

(d)

(1, \(\infty \))

69.

If f(x) = 2^x and get g(x) = \(\frac{1}{2^x}\) then (fg)(x) is ________.

(a)

(b)

(c)

4^x

(d)

\(\frac{1}{4^x}\)

70.

The graph of y = 2x² is passing through _______.

(a)

(0,0)

(b)

(2,1)

(c)

(2,0)

(d)

(0,2)

71.

If f(x) = \(\frac{1-x}{1+x}\) then f(-x) is equal to _______.

(a)

-f(x)

(b)

\(\frac{1}{f(x)}\)

(c)

\(-\frac{1}{f(x)}\)

(d)

f(x)

72.

If f(x) = x² - x + 1, then f (x + 1) is _______.

(a)

x²

(b)

(c)

(d)

x² + x + 1

73.

\(\left(\frac{\cos x}{cosec x}\right)-\sqrt{1-\sin^2x}\sqrt{1-\cos^2x}\) is _______.

(a)

cos²x-sin²x

(b)

sin²x-cos²x

(c)

(d)

74.

\(\sin\left(\cos^{-1}\frac{3}{5}\right)\) is _____.

(a)

\(\frac{3}{5}\)

(b)

\(\frac{5}{3}\)

(c)

\(\frac{4}{5}\)

(d)

\(\frac{5}{4}\)

75.

\(\tan\left(\frac{\pi}{4}-x\right)\) is _______.

(a)

\(\left(\frac{1+\tan x}{1-\tan x}\right)\)

(b)

\(\left(\frac{1-\tan x}{1+\tan x}\right)\)

(c)

1-tan x

(d)

1+tan x

76.

If \(\alpha\) and \(\beta\) be between 0 and \(\frac{\pi}{2}\) and if \(\cos(\alpha+\beta)=\frac{12}{13}\) and \(\sin(\alpha-\beta)=\frac{3}{5}\) then \(\sin2\alpha\) is _____.

(a)

\(\frac{16}{15}\)

(b)

(c)

\(\frac{56}{65}\)

(d)

\(\frac{64}{65}\)

77.

The value of \(\frac{3 \tan 10^{\circ}-\tan ^3 10^{\circ}}{1-3 \tan ^2 10^{\circ}}\) is _______,

(a)

\(\frac{1}{\sqrt3}\)

(b)

\(\frac{1}{2}\)

(c)

\(\frac{\sqrt3}2\)

(d)

\(\frac{1}{\sqrt2}\)

78.

The value of \(\frac{2\tan30^o}{1+tan^230}\) is _____.

(a)

\(\frac12\)

(b)

\(\frac{1}{\sqrt3}\)

(c)

\(\frac{\sqrt{3}}{2}\)

(d)

\(\sqrt3\)

79.

The value of 1 - 2sin²45^o is _______.

(a)

(b)

\(\frac{1}{2}\)

(c)

\(\frac14\)

(d)

80.

The value of cos²45^o- sin²45^o is_______.

(a)

\(\frac{\sqrt3}{2}\)

(b)

\(\frac{1}{2}\)

(c)

(d)

\(\frac{1}{\sqrt{2}}\)

81.

The value of sin 15^o cos 15^o is ______.

(a)

(b)

\(\frac{1}{2}\)

(c)

\(\frac{\sqrt3}{2}\)

(d)

\(\frac{1}{4}\)

82.

The value of \(\sin(-420^o)\) is _______.

(a)

\(\frac{\sqrt3}{2}\)

(b)

\(-\frac{\sqrt3}{2}\)

(c)

\(\frac{1}{2}\)

(d)

\(\frac{-1}{2}\)

83.

If \(\tan\theta=\frac{1}{\sqrt5}\) and \(\theta\) lies in the first quadrant, then \(\cos\theta\) is _______.

(a)

\(\frac{1}{\sqrt6}\)

(b)

\(\frac{-1}{\sqrt6}\)

(c)

\(\frac{\sqrt5}{\sqrt6}\)

(d)

\(\frac{-\sqrt5}{\sqrt6}\)

84.

The degree measure of \(\frac{\pi}{8}\) is ______.

(a)

20^o60^'

(b)

22^o30^'

(c)

20^o60^'

(d)

20^o30^'

85.

The distance between directrix and focus of a parabola y² = 4ax is _______.

(a)

(b)

(c)

(d)

86.

The eccentricity of the parabola is _______.

(a)

(b)

(c)

(d)

87.

The equation of the circle with centre (3,-4) and touches the x - axis is _______.

(a)

(x - 3)² +(y - 4)² = 4

(b)

(x - 3)² +(y + 4)² = 16

(c)

(x-3)²+ (y- 4)²= 16

(d)

x²+y²= 16

88.

ax² + 4xy + 2y² = 0 represents a pair of parallel lines then 'a' is _______.

(a)

(b)

-2

(c)

(d)

-4

89.

If the centre of the circle is (-a, -b) and radius is \(\sqrt{a^2-b^2}\), then the equation of circle is _______.

(a)

x²+y²+2ax+2by+2b²= 0

(b)

x²+y²+2ax +2by-2b²= 0

(c)

x² +y² - 2ax - 2by - 2b² = 0

(d)

x² + y - 2ax - 2by + 2b² = 0

90.

The centre of the circle x² + y - 2x + 2y - 9 = 0 is _______.

(a)

(1,1)

(b)

(-1,-1)

(c)

(-1,1)

(d)

(1, -1)

91.

The focus of the parabola x² = 16y is _______.

(a)

(4,0)

(b)

(-4,0)

(c)

(0,4)

(d)

(0,-4)

92.

If kx² + 3xy - 2y²= 0 represent a pair of lines which are perpendicular then k is equal to _______.

(a)

1/2

(b)

-1/2

(c)

(d)

-2

93.

The locus of the point P which moves such that P is at equidistance from their coordinate axes is _______.

(a)

\(y={1\over x}\)

(b)

y = -x

(c)

y = x

(d)

\(y=-{1\over x}\)

94.

If the lines 2x - 3y - 5 = 0 and 3x - 4y - 7 = 0 are the diameters of a circle, then its centre is _______.

(a)

(-1, 1)

(b)

(1,1)

(c)

(1, -1 )

(d)

(-1, -1)

95.

The angle between the pair of straight lines x² - 7xy + 4y² = 0 _______.

(a)

\(tan^{-1}\left(1\over 3\right)\)

(b)

\(tan^{-1}\left(1\over 2\right)\)

(c)

\(tan^{-1}\left(\sqrt{33}\over 5\right)\)

(d)

\(tan^{-1}\left(5\over\sqrt{33}\right)\)

96.

The number of permutation of n different things taken r at a time, when the repetition is allowed is ________.

(a)

rⁿ

(b)

n^r

(c)

\(\frac { n! }{ (n-r)! } \)

(d)

\(\frac { n! }{ (n+r)! } \)

97.

Number of words with or without meaning that can be formed using letters of the word "EQUATION" , with no repetition of letters is _____.

(a)

(b)

(c)

(d)

98.

The total number of 9 digit number which have all different digit is ________.

(a)

10!

(b)

(c)

9\(\times\)9!

(d)

10\(\times\)10!

99.

The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is _________.

(a)

(b)

(c)

(d)

100.

If \(\frac { kx }{ (x+4)(2x-1) } =\frac { 4 }{ x+4 } +\frac { 1 }{ 2x-1 } \) then k is equal to _______.

(a)

(b)

(c)

(d)

101.

The constant term in the expansion of \({ \left( x+\frac { 2 }{ x } \right) }^{ 6 }\) is _______

(a)

156

(b)

165

(c)

162

(d)

160

102.

For all n > 0, nC₁ + nC₂ + nC₃ + ... +nC_n is equal to _______

(a)

(b)

2ⁿ- 1

(c)

n²

(d)

n² - 1

103.

The greatest positive integer which divide n(n + 1) (n + 2) (n + 3) for n \(\in\) N is ________.

(a)

(b)

(c)

(d)

104.

The number of ways selecting 4 players out of 5 is _______.

(a)

(b)

(c)

(d)

105.

If nC₃ = nC₂, then the value of nC₄ is _______.

(a)

(b)

(c)

(d)

106.

If \(\begin{vmatrix} 4 & 3 \\ 3 & 1 \end{vmatrix}=-5\) then value of \(\begin{vmatrix} 20 & 15 \\ 15 & 5 \end{vmatrix}\) is ________.

(a)

-5

(b)

-125

(c)

-25

(d)

107.

If \(\triangle=\begin{vmatrix} {a}_{11} & {a}_{12} & {a}_{13} \\ {a}_{21} & {a}_{22} & {a}_{23} \\ {a}_{31} & {a}_{32} & {a}_{33} \end{vmatrix}\) and A_ij is cofactor of a_ij, then value of \(\triangle\) is given by ________.

(a)

a₁₁ A₃₁ + a₁₂ A₃₂ + a₁₃ A₃₃

(b)

a₁₁ A₁₁ + a₁₂A₂₁ + a₁₃ A₃₁

(c)

a₂₁ A₁₁ + a₂₂ A₁₂ + a₂₃ A₁₃

(d)

a₁₁ A₁₁ + a₂₁ A₂₁ + a₃₁ A₃₁

108.

If A = \(\begin{vmatrix}cos \theta & sin \theta \\ -sin \theta&cons\theta \end{vmatrix},\) then |2A| is equal to ________.

(a)

4 cos 2 \(\theta\)

(b)

(c)

(d)

109.

If A is a square matrix of order 3 and IAI = 3 then | adj A| is equal to ________.

(a)

(b)

(c)

(d)

110.

If A is 3 \(\times\) 3 matrix and |A| = 4, then |A^-1| is equal to ________.

(a)

\({{1}\over{4}}\)

(b)

\({{1}\over{16}}\)

(c)

(d)

111.

If A is an invertible matrix of order 2, then det (A^-1) be equal to ________.

(a)

det (A)

(b)

\({{1}\over{det(A)}}\)

(c)

(d)

112.

If A \(=\begin{pmatrix} -1 & 2 \\ 1 & -4 \end{pmatrix}\) then A (adj A) is ________.

(a)

\(\begin{pmatrix} -4 & -2 \\ -1 & -1 \end{pmatrix}\)

(b)

\(\begin{pmatrix} 4 & -2 \\ -1 & 1 \end{pmatrix}\)

(c)

\(\begin{pmatrix} 2 & 0 \\ 0 & 2 \end{pmatrix}\)

(d)

\(\begin{pmatrix} 0 & 2 \\ 2 & 0 \end{pmatrix}\)

113.

Which of the following matrix has no inverse.

(a)

\(\begin{pmatrix} -1 & 1 \\ 1 &-4 \end{pmatrix}\)

(b)

\(\begin{pmatrix} 2 & -1 \\ -4 &2 \end{pmatrix}\)

(c)

\(\begin{pmatrix} cos\ a & sin\ a \\ -sin\ a & cos\ a \end{pmatrix}\)

(d)

\(\begin{pmatrix} sin\ a & cos\ a \\ -cos\ a & sin\ a \end{pmatrix}\)

114.

The inventor of input-output analysis is ________.

(a)

Sir Francis Galton

(b)

Fisher

(c)

Prof. Wassily W. Leontief

(d)

Arthur Cayley

115.

The number of Hawkins-Simon conditions for the viability of an input - output analysis is ________.

(a)

(b)

(c)

(d)

116.

The inverse matrix of \(\begin{pmatrix} \frac { 1 }{ 5 } & \frac { 5 }{ 25 } \\ \frac { 2 }{ 5 } & \frac { 1 }{ 2 } \end{pmatrix}\) is ________.

(a)

\({{7}\over{30}}\begin{pmatrix} \frac { 1 }{ 2 } & \frac { 5 }{ 12 } \\ \frac { 2 }{ 5 } & \frac { 4 }{ 5 } \end{pmatrix}\)

(b)

\({{7}\over{30}}\begin{pmatrix} \frac { 1 }{ 2 } & \frac { -5 }{ 12 } \\ \frac { -2 }{ 5 } & \frac { 1 }{ 5 } \end{pmatrix}\)

(c)

\({{30}\over{7}}\begin{pmatrix} \frac { 1 }{ 2 } & \frac { 5 }{ 12 } \\ \frac { 2 }{ 5 } & \frac { 4 }{ 5 } \end{pmatrix}\)

(d)

\({{30}\over{7}}\begin{pmatrix} \frac { 1 }{ 2 } & \frac { -5 }{ 12 } \\ \frac { -2 }{ 5 } & \frac { 4 }{ 5 } \end{pmatrix}\)

117.

adj (AB) is equal to ________.

(a)

adj A adj B

(b)

adj A^T adj B^T

(c)

adj B adj A

(d)

adj B^T adj A^T

118.

The value of the determinant \({\begin{vmatrix} a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & c \end{vmatrix}}^{2}\)is ________.

(a)

abc

(b)

(c)

a²b²c²

(d)

-abc

119.

If \(\triangle=\begin{vmatrix} 1 & 2 & 3 \\ 3 & 1 & 2 \\ 2 & 3 & 1 \end{vmatrix}\) then \(\begin{vmatrix} 3 & 1 & 2 \\ 1 & 2 & 3 \\ 2 & 3 & 1 \end{vmatrix}\) is ________.

(a)

\(\triangle\)

(b)

-\(\triangle\)

(c)

3\(\triangle\)

(d)

-3\(\triangle\)

120.

The value of \(\begin{vmatrix} 2x+y & x & y \\ 2y+z & y & z \\ 2z+x & z & x \end{vmatrix}\) is ________.

(a)

xyz

(b)

x+y+z

(c)

2x+2y+2z

(d)

Visit QB365-SLMS - https://www.qb365.in/slms/

Answers Key:

Multiple Choice Question

120 x 1 = 120

(a)
\(P(A\cup B)\)

A = {(2, 2)}, n(S) = 36; P(A) = 1/36

(d)
Independent

(b)
\(P\left( A\cap B \right) =1\)

(d)
0.25

(b)
lower quartile

\(\bar{x}=\frac{1+2+3+.....n}{n}\)
\(\frac{6n}{11}=\frac{n(n+)}{2n}\)
2 x 6n = 11n x 11
12n - 11n = 11 \(\Rightarrow\) n = 11

6, 8, 9, 10, 11, 12, 14
\(\therefore \) Median = 10

10.

(d)
A.M.≥G.M.≥H.M.

11.

GM = \(\sqrt{8 \times 18} = \sqrt{144} = 12\)

12.

\(H.M=\frac{n}{ \frac { 1 }{ a }+ \frac { 1 }{ b }+\frac { 1 }{ a }}=\frac{3}{ \frac { 1 }{ 2 }+ \frac { 1 }{ 3 }+\frac { 1 }{ 4 }}\)
\(=\frac{3}{ \frac {6+4+3}{2}}=\frac{3}{ \frac {13}{12}}=\frac{36}{13}\)

13.

(a)
Arithmetic mean

14.

15.

(d)
Percentiles

16.

\(r =\frac{\operatorname{cov}(x, y)}{\sigma_x \sigma_y} \)
\(=\frac{-16.5}{\sqrt{2.89 \times 100}}=\frac{-16.5}{17}=-0.97\)

17.

(a)
the magnitude and direction

18.

(b)
Sir Francis Galton

19.

(a)
Karl Pearson

20.

(a)
positive

21.

(a)
functional relationship

22.

(b)
two regression lines

23.

(a)
Negative

24.

(a)
b_xy = \(\frac { N\Sigma dxdy-(\Sigma dx)(\Sigma dy) }{ N\Sigma dy^{ 2 }-(\Sigma dy)^{ 2 } } \)

25.

(a)
r = ±\(\sqrt { { b }_{ xy }\times { b }_{ yx } } \)

26.

\(P =\frac{\frac{a}{i}}{k} \)
\(=\frac{\frac{2000}{0.1}}{12}=2,40,000\)

27.

(a)
Annuity due

28.

(b)
A = \(\frac{a}{i}[(1+i)^n-1]\)

29.

Income \(=500 \times 100 \times \frac{15}{100}=7,500\)

30.

If F.V = 100, Investment = 90
FV 10,000,
Investment \(= \frac{ 90 \times 10,000}{100} = 9000\)

31.

Brokerage = 100 x 400 x \(\frac{1}{100}=400\)

32.

\(25,000=\frac{x\times 100\times10}{100}\Rightarrow x=2500\)

33.

Investment = 200 x 100 x \(\frac{8}{100}\)= Rs. 1600

34.

(a)
dependent variable

35.

(b)
r(X, Y) = \(\frac { cov(x,y) }{ { \sigma }_{ x }{ \sigma }_{ y } } \)

36.

\(r =\frac{N \Sigma X Y-\Sigma X \Sigma Y}{\sqrt{N \Sigma X^2-(\Sigma X)^2} \sqrt{N \Sigma Y^2-(\Sigma Y)^2}} \)
\(=\frac{25(520)-(125)(100)}{\sqrt{25(650)-(125)^2} \sqrt{25(436)-(100)^2}} \)
= 0.667

37.

38.

(a)
Negative

39.

(a)
Income and expenditure

40.

\(E O Q=\sqrt{\frac{2 C_3 R}{C_1}}=\sqrt{\frac{2 \times 20 \times 5000}{20}}=1000\)

41.

(b)
8

42.

(b)
Decreasing function

43.

(b)
Breakeven point

44.

(a)
\({ 2x }e^{ { x }^{ 2 } }\)

45.

46.

(a)
1

47.

(a)
MR = MC

48.

dy/dx = 4x + 5
At x = 2, dy/dx = 13

49.

(a)
\({ n }_{ d }=\frac { AR }{ AR-MR } \)

50.

\(\eta_d=-\frac{p}{x} \frac{d x}{d p}=\frac{-p}{\frac{1}{p}}\left(\frac{-1}{p^2}\right)=1\)

51.

(a)
|η_d| > 1

52.

R = px = 20x- 3x²
M.R = dR/dx = 20 - 6x

53.

(d)
\(\frac { 21 }{ x } \)

54.

Since there is no common area between the lines x₁ + x₂ ≤ 1 and 5x₁ + 5x₂≥ 0

55.

(a)
Critical path method

56.

(d)
All the above

57.

(b)
Minimize total project duration

58.

(d)
An arrow representing an activity may not have a length and shape

59.

(b)
15

60.

61.

Since x₁ = 2.5, x₂ = 35 satisfies all the Constraints

62.

63.

(d)
a^xlog_e^a

64.

\(\frac{d y}{d x}=1, \frac{d z}{d x}=\frac{-1}{x^2} \quad \frac{d y}{d z}=-x^2\)

65.

(a)
\(-\frac{1}{x^2}\)

66.

(b)
1

67.

(a)
1

68.

(b)
(0, \(\infty \))

69.

\((f g) x=2^x \frac{1}{2^x}=1\)

70.

(a)
(0,0)

71.

\(f(x) = \)\(\frac{1-x}{1+x} = \frac {1} {f(x)}\)

72.

\(f(x+1) =(x+1)^2-(x+1)+1 \)
\(=x^2+2 x+1-x-1+1 \)
\(=x^2+x+1 \)

73.

cos x sin x - cos x sin x = 0

74.

\(\sin \left(\cos ^{-1} \frac{3}{5}\right)=\sin \left(\sin ^{-1} \frac{4}{5}\right)=4 / 5\)

75.

\(\tan (\pi / 4-x)=\frac{\tan \pi / 4-\tan x}{1+\tan \pi / 4 \tan x}=\frac{1-\tan x}{1+\tan x}\)

76.

\(\cos (\alpha+\beta)=\frac{12}{13} \Rightarrow \sin (\alpha+\beta)=\frac{5}{13} \)
\(\sin (\alpha-\beta)=3 / 5 \Rightarrow \cos (\alpha-\beta)=4 / 5 \)
\(\sin 2 \alpha=\sin ((\alpha+\beta)+(\alpha-\beta)) \)
\(= \sin (\alpha+\beta) \cos (\alpha-\beta) +\cos (\alpha+\beta) \sin (\alpha-\beta) \)
\(= \frac{5}{13} \cdot \frac{4}{5}+\frac{3}{5} \cdot \frac{12}{13}=\frac{56}{65}\)

77.

\(\frac{3 \tan 10^{\circ}-\tan ^3 10^{\circ}}{1-3 \tan ^2 10^{\circ}} =\tan 3(10) =\tan 30^{\circ}=\frac{1}{\sqrt{3}} \)

78.

\(\frac{2 \tan 30^{\circ}}{1+\tan ^2 30^{\circ}} =\sin 2\left(30^{\circ}\right)=\sin 60^{\circ}=\frac{\sqrt{3}}{2} \)

79.

1 - 2sin²45^o= cos 2(45^o)
= cos 90^o = 0

80.

cos²45^o- sin²45^o = cos 2(45^o)
= cos 90^o = 0

81.

\(\frac{1}{2}\left(2 \sin 15^{\circ} \cos 15^{\circ}\right) =\frac{1}{2} \sin 2\left(15^{\circ}\right)=\frac{1}{2} \sin 30^{\circ} =\frac{1}{2} \times \frac{1}{2}=\frac{1}{4}\)

82.

\(\sin \left(-420^{\circ}\right) =-\sin 420^{\circ}=-\sin (360+60) =-\sin 60^{\circ}=\frac{-\sqrt{3}}{2} \)

83.

\(\sec \theta =\sqrt{1+\tan ^2 \theta}=\sqrt{1+\frac{1}{5}}=\sqrt{\frac{6}{5}} \)

84.

\(\frac{\pi}{8}=\frac{180^{\circ}}{8}=22 \frac{1}{2}^{\circ}=22^{\circ} 30^{\prime}\)

85.

(b)
2a

86.

(d)
1

87.

(b)
(x - 3)² +(y + 4)² = 16

88.

\(h^2-a b=0\)
\(4-2 a=0 \Rightarrow a=2\)

89.

\((x+a)^2+(y+b)^2=a^2-b^2\)
\(x^2+a^2+2 a x+y^2+b^2+2 b y=a^2-b^2\)

90.

C(- g, -f)

91.

(0, a), a = 4

92.

\(a+b=0 \Rightarrow k-2=0\)

93.

94.

95.

96.

(b)
n^r

97.

98.

The ninth digit cannot be filled with zero
Ninth place can be filled in 9 ways
Eighth place can be filled in 9 ways
Seventh place can be filled in 8 ways and so on No. of ways
= 9 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2
= 9 x 9!

99.

The number of parallelograms = 4C₂ x 3C₂

100.

Equality coefficient of x in the numerator
kx = 4 (2n) + 1 (x)
kx = 9x

101.

\(t_{r+1} =6 C_r n^{6-r}\left(\frac{2^r}{x^r}\right) \)
\(=6 C_r x^{6-2 r} 2^r \)
\(6-2 r =0 = r =3 \)
\(t_{r+1} =6 C_3 2^3=160 \)

102.

nC₀+ nC₁ + nC₂ + nC₃ + ... +nC_n = 2n and nC₀ = 1

103.

Since if n = 1 then (1) (2) (3) (4) = 24 is divisible by = 24

104.

No. of ways = 5C₄ = 5C₁ = 5

105.

x + y = n
3 + 2 = 5 = n
nC₄ = 5C₄ = 5C₁ = 5

106.

\(\left|\begin{array}{cc} 20 & 15 \\ 15 & 5 \end{array}\right|=5 \times 5\left|\begin{array}{ll} 4 & 3 \\ 3 & 1 \end{array}\right|\)
\(=5 \times 5 \times-5\)
\(=-125\)

107.

(Corresponding co-factor)

108.

\(|A|=\cos ^2 \theta+\sin ^2 \theta=1\)
\(|2 A|=2^2(1)=4\)

109.

(Since \(|\operatorname{adj} A|=|A|^{n-1} n=3\) ))
\(=|3|^2=9\)

110.

(Since \(\left|A^{-1}\right|=\frac{1}{|A|}\))

111.

(b)
\({{1}\over{det(A)}}\)

112.

\(|A|=4-2=2\)
\(A(\operatorname{adj} A)=|A| I=\left(\begin{array}{ll} 2 & 0 \\ 0 & 2 \end{array}\right)\)

113.

\(\text {Since }|A|=4-4=0\)

114.

115.

(d)
2

116.

\(A=\left(\begin{array}{cc} \frac{4}{5} & \frac{-5}{12} \\ \frac{-2}{5} & \frac{1}{2} \end{array}\right)\)
\(|A|=\frac{2}{5}-\frac{1}{6}=\frac{12-5}{30}=\frac{7}{30}\)
\(A^{-1}=\frac{1}{|A|} \text { adjA }=\frac{30}{7}\left(\begin{array}{ll} \frac{1}{2} & \frac{5}{12} \\ \frac{2}{5} & \frac{4}{5} \end{array}\right)\)

117.

118.

119.

(b)
-\(\triangle\)

120.

\(\left|\begin{array}{ccc} 2 x+y & x & y \\ 2 y+z & y & z \\ 2 z+x & z & x \end{array}\right| \quad c_1 \rightarrow c_1-c_3\)
\(\left|\begin{array}{ccc} 2 x & x & y \\ 2 y & y & z \\ 2 z & z & x \end{array}\right|=0 \ \text {Since } c_1 \sim c_3\)