Plus One Public Exam March 2019 One Mark Question Paper

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

50 x 1 = 50

The probability of drawing a spade from a pack of card is _________.

(a)

1/52

(b)

1/13

(c)

4/13

(d)

1/4

If median = 45 and its coefficient is 0.25, then the mean deviation about median is _________.

(a)

11.25

(b)

180

(c)

0.0056

(d)

Harmonic mean is better than other means if the data are for _________.

(a)

Speed or rates.

(b)

Heights or lengths.

(c)

Binary values like 0 and 1

(d)

Ratios or proportions.

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

(a)

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

(b)

(c)

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

(d)

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

The best measure of central tendency is _________.

(a)

Arithmetic mean

(b)

Harmonic mean

(c)

Geometric mean

(d)

Median

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

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

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

A invested some money in 10% stock at Rs.96. If B wants to invest in an equally good 12% stock, he must purchase a stock worth of _______.

(a)

Rs. 80

(b)

Rs. 115.20

(c)

Rs. 120

(d)

Rs. 125.40

10.

Rs. 5000 is paid as perpetual annuity every year and the rate of C.I 10 %. Then present value P of immediate annuity is _______.

(a)

Rs. 60,000

(b)

Rs. 50,000

(c)

Rs. 10,000

(d)

Rs. 80,000

11.

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

12.

Purchasing price of one share of face value 100 available at a discount of \(9\frac{1}{2}\%\) with brokerage \(\frac{1}{2}\%\) is ________.

(a)

Rs. 89

(b)

Rs. 90

(c)

Rs. 91

(d)

Rs. 95

13.

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

14.

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

(a)

dependent variable

(b)

independent variable

(c)

regressor

(d)

explanatory variable

15.

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

(a)

Negative

(b)

positive

(c)

Perfect positive

(d)

No correlation

16.

The demand function is always _______.

(a)

Increasing function

(b)

Decreasing function

(c)

Non-decreasing function

(d)

Undefined function

17.

Average cost is minimum when _______.

(a)

Marginal cost = Marginal revenue

(b)

Average cost = Marginal cost

(c)

Average cost = Marginal revenue

(d)

Average Revenue = Marginal cost

18.

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)

19.

If u = 4x² + 4xy + y² + 32 + 16 , then \(\frac { \partial ^{ 2 }u }{ \partial y\partial x } \) is equal to ________.

(a)

8x + 4y + 4

(b)

(c)

2y + 32

(d)

20.

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

(a)

(b)

(c)

(d)

21.

Network problems have advantage in terms of project _______.

(a)

Scheduling

(b)

Planning

(c)

Controlling

(d)

All the above

22.

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

23.

Which of the following is not correct?

(a)

Objective that we aim to maximize or minimize

(b)

Constraints that we need to specify

(c)

Decision variables that we need to determine

(d)

Decision variables are to be unrestricted

24.

The minimum value of the objective function Z = x + 3y subject to the constraints 2x + y ≤ 20, x + 2y ≤ 20, x > 0 and y > 0 is ______.

(a)

(b)

(c)

(d)

25.

In a network while numbering the events which one of the following statement is false?

(a)

Event numbers should be unique

(b)

Event numbering should be carried out on a sequential basis from left to right

(c)

The initial event is numbered 0 or 1

(d)

The head of an arrow should always bear a number lesser than the one assigned at the tail of the arrow

26.

If y = log x then y₂ = ________.

(a)

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

(b)

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

(c)

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

(d)

e²

27.

If the function f(x) is continuous at x = a if \(\lim _{ x\rightarrow a }{ f\left( x \right) } \) is equal to ________.

(a)

f(-a)

(b)

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

(c)

2f(a)

(d)

f(a)

28.

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

(a)

(b)

\(\infty\)

(c)

\(-\infty\)

(d)

\(\theta\)

29.

Which of the following function is neither even nor odd?

(a)

f(x) = x³ + 5

(b)

f(x) = x⁵

(c)

f(x) = x¹⁰

(d)

f(x) = x²

30.

The graph of the line y = 3 is _______.

(a)

Parallel to x-axis

(b)

Parallel to y-axis

(c)

Passing through the origin

(d)

Perpendicular to x-axis

31.

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

(a)

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

(b)

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

(c)

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

(d)

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

32.

If \(\tan A=\frac{1}{2}\) and \(\tan B=\frac{1}{3}\) then tan(2A + B) is equal to ______.

(a)

(b)

(c)

(d)

33.

\(\sec^{-1}\frac{2}{3}+cosec^{-1}\frac{2}{3}=\) ______.

(a)

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

(b)

\(\frac{\pi}{2}\)

(c)

\(\pi\)

(d)

\(-\pi\)

34.

The value of \(\cos(-480^o)\) is ________.

(a)

\(\sqrt3\)

(b)

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

(c)

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

(d)

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

35.

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)

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

36.

The eccentricity of the parabola is _______.

(a)

(b)

(c)

(d)

37.

If the circle touches x axis, y axis and the line x = 6 then the length of the diameter of the circle is _______.

(a)

(b)

(c)

(d)

38.

Combined equation of co-ordinate axes is _______.

(a)

x²-y²= 0

(b)

x²+y²= 0

(c)

xy = c

(d)

xy = 0

39.

Length of the latus rectum of the parabola y² = - 25x is _______.

(a)

(b)

-5

(c)

(d)

-25

40.

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)

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

41.

Thirteen guests has participated in a dinner. The number of handshakes happened in the dinner is __________.

(a)

715

(b)

(c)

286

(d)

42.

The number of ways to arrange the letters of the word "CHEESE" is ______.

(a)

120

(b)

240

(c)

720

(d)

43.

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

(a)

(b)

2ⁿ- 1

(c)

n²

(d)

n² - 1

44.

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

(a)

(b)

(c)

(d)

45.

The number of diagonals in a polygon of n sides is equal to _______.

(a)

nC₂

(b)

nC₂ - 2

(c)

nC₂ - n

(d)

nC₂ - 1

46.

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

(a)

(b)

(c)

(d)

47.

If A and B are non-singular matrix then, which of the following is incorrect?

(a)

A² = I implies A^-1= A

(b)

I^-1 = I

(c)

If AX = B, then X = B^-1 A

(d)

If A is square matrix of order 3 then |adj A|= |A|²

48.

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

49.

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\(\triangle\)

50.

The co-factor of -7 in the determinant \(\begin{vmatrix} 2 & -3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & -7 \end{vmatrix}\) is________.

(a)

-18

(b)

(c)

-7

(d)

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Answers Key:

Multiple Choice Question

50 x 1 = 50

\(\frac{13}{52}\)=1/4

Mean deviation about median = co-eficient of mean deviation about median x Median
= 0.25 x 45
= 11.25

(a)
Speed or rates.

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

(a)
Arithmetic mean

(a)
functional relationship

(b)
two regression lines

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

\(x=\frac{12 \times 96}{10}=115.20\)

10.

\(P=\frac{a}{i}=\frac{5000}{0.1}=50,000\)

11.

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

12.

\(\text { M.V }=100-9 \frac{1}{2}+\frac{1}{2}=Rs.91\)

13.

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

14.

(a)
dependent variable

15.

(b)
positive

16.

(b)
Decreasing function

17.

(b)
Average cost = Marginal cost

18.

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

19.

\(\frac{\partial u}{\partial x} =8 x+4 y+4 \)
\(\frac{\partial^2 u}{\partial y \partial x} =4 \)

20.

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

21.

(d)
All the above

22.

(b)
Minimize total project duration

23.

(d)
Decision variables are to be unrestricted

24.

2x	+	y	=	20	x	+	y	=	20
x		0		10	x		0		20
y		20		0	y		20		0

Corner points	Z = x + 3y
(0, 0)	0
(0, 20)	60
(10, 0)	10

25.

(d)
The head of an arrow should always bear a number lesser than the one assigned at the tail of the arrow

26.

\(y_1=\frac{1}{x}, y_2=\frac{-1}{x^2}\)

27.

(d)
f(a)

28.

(a)
1

29.

f(-x) = -x³ + 5 ≠ f(x)

30.

(a)
Parallel to x-axis

31.

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

32.

\(\tan 2 A= \frac{2 \tan A}{1-\tan ^2 A}=\frac{2(1 / 2)}{1-1 / 4}=\frac{1}{3 / 4}=4 / 3 \)
\(\tan (2 A+B)= \frac{\tan 2 A+\tan B}{1-\tan 2 A \cdot \tan B}=\frac{\frac{4}{3}+\frac{1}{3}}{1-4 / 9} \)
\(=\frac{5 / 3}{5 / 9}=3 \)

33.

(b)
\(\frac{\pi}{2}\)

34.

\(\cos \left(-480^{\circ}\right) =\cos 480^{\circ}=\cos \left(360^{\circ}+120^{\circ}\right) \)
\(=\cos 120^{\circ}=\cos \left(180^{\circ}-60^{\circ}\right) \)
\(=-\cos 60^{\circ}=-1 / 2 \)

35.

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

36.