#### +1 Public Model Exam 2019

11th Standard

Reg.No. :
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Time : 02:30:00 Hrs
Total Marks : 90
20 x 1 = 20
1. The number of Hawkins-Simon conditions for the viability of an input - output analysis is

(a)

1

(b)

3

(c)

4

(d)

2

2. 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)

$\begin{pmatrix} sin\ a & cos\ a \\ -cos\ a & sin\ a \end{pmatrix}$

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

(a)

2

(b)

3

(c)

4

(d)

5

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

(a)

7!

(b)

3!

(c)

8!

(d)

5!

5. The slope of the line 7x + 5y - 8 = 0 is

(a)

7/5

(b)

-7/5

(c)

5/7

(d)

-9/7

6. 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)

$y=-{1\over x}$

7. The value of $cosec^{-1}\left(\frac{2}{\sqrt{3}}\right)$ is

(a)

$\frac{\pi}{4}$

(b)

$\frac{\pi}{2}$

(c)

$\frac{\pi}{3}$

(d)

$\frac{\pi}{6}$

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

(a)

1

(b)

2

(c)

3

(d)

4

9. A 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)

10. If y = x and z = $\frac{1}{x}$ then $\frac{dy}{dz}=$

(a)

x2

(b)

1

(c)

-x2

(d)

$-\frac{1}{x^2}$

11. The elasticity of demand for the demand function x = $\frac { 1 }{ p }$ os

(a)

0

(b)

1

(c)

$-\frac { 1 }{ p }$

(d)

$\infty$

12. 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)

nf

(d)

f

13. Market 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

14. 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)

20,40,000

(d)

Rs 2,00,400

15. 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.

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

(a)

1/36

(b)

0

(c)

1/3

(d)

1/6

17. 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

18. 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

19. 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

20. 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

21. 7 x 2 = 14
22. Evaluate$\left| \begin{matrix} 1 & 3 & 4 \\ 102 & 18 & 36 \\ 17 & 3 & 6 \end{matrix} \right|$

23. Evaluate the following using binomial theorem:(101)4

24. Find the acute angle between the lines 2x - y + 3 = 0 and x + y + 2 = 0.

25. Evaluate$\cos\left[\frac{\pi}{3}-\cos^{-1}\left(\frac{1}{2}\right)\right]$

26. Find $\frac{dy}{dx}$ if x = at2, y = 2at

27. Find the maximum and minimum values of x3-6x2+7

28. Find the number of shares which will give an annual income of Rs 3,600 from 12% stock of face value Rs 100.

29. A die is thrown twice and the sum of the number appearing is observed to be 6. What is the conditional probability that the number 4 has appeared at least once?

30. From the following data calculate the correlation coefficient Σxy=120, Σx2=90, Σy2=640

31. A retired person has Rs. 70,000 to invest and two types of bonds are available in the market for investment. First type of bond yields an annual income of 8% on the amount invested and the second type yields 10% per annum. As per norms, he has to invest a minimum of Rs. 10,000 in the first type and not more than Rs.30,000 in the second type. How should he plan his investment, so as to get maximum returns after one year of investment? Formulate the above as LPP.

32. 7 x 3 = 21
33. The technology matrix of an economic system of two industries is $\left[ \begin{matrix} 0.8 & 0.2 \\ 0.9 & 0.7 \end{matrix} \right]$ Test whether the system is viable as per Hawkins – Simon conditions.

34.  Find the middle terms in the expansion of ${ \left( { 2x }^{ 2 }-\frac { 3 }{ { x }^{ 3 } } \right) }^{ 10 }$

35. Find the locus of a point such that the sum of its distances from the points (0, 2) and (0, -2) is 6.

36. Convert the following into the product of trigonometric functions
cos55+ sin 55o

37. Verify the existence of the function $f(x)=\begin{cases} 5x-4if\quad 0 at x=1 38. The production function for a commodity is P = 10L + 0.1 L2 +15K-0.2K2 +2KL where L is labour and K is Capital. (i) Calculate the marginal products of two inputs when 10 units of each of labour and Capital are used (ii) If 10 units of capital are used, what is the upper limit for use of labour which a rational producer will never exceed? 39. A man wishes to pay back his depts of Rs.3783 due after 3 years by 3 equal yearly instalments. Find the amount of each instalments,money being worth 5% p.a. compounded annually 40. Calculate Quartile deviation and Coefficient of Quartile deviation of the following data.  Marks: 0 10 20 30 40 50 60 70 No. of students: 150 142 130 120 72 30 12 4 41. Calculate the correlation co-efficient from the below data:  X 1 2 3 4 5 6 7 8 9 Y 9 8 10 12 11 13 14 16 5 42. Construct the network for the projects consisting of various activities and their precedence relationships are as given below:  Immediate Predecessor A B C D E F G H I Activity B C D,E,F G I H J K L 43. 7 x 5 = 35 1. Two commodities A and B are produced such that 0.4 tonne of A and 0.7 tonne of B are required to produce a tonne of A. Similarly 0.1 tonne of A and 0.7 tonne of B are needed to produce a tonne of B. Write down the technology matrix. If 6.8 tonnes of A and 10.2 tonnes of B are required, find the gross production of both of them. 2. Resolve into partial fractions for the following: \(\frac { x+2 }{ (x-1)(x+3)^{ 2 } }$

1. Using the principle of mathematical induction, prove that 1.3 + 2.32 + 3.33 + ... + n.3n =$\frac { (2n-1){ 3 }^{ n+1 }+3 }{ 4 } for\quad all\quad n\in N$

2. If the equation ax2 +5xy -6y2 +12x + 5y +c = 0 represents a pair of perpandicular straight lines, find a and c.

1. Prove that $\frac{\cos4x+\cos3x+\cos2x}{\sin4x+\sin3x+\sin2x}=\cot3x$

2. Prove that (sin 3x + sin x) sin x + (cos 3x - cos x) cos x = 0.

1. Draw the graph of the following function f(x)=e-2x

2. Find the stationary values and stationary points for the function f(x) = 2x3 +9x2 +12x+1

1. The total revenue (TR) for commodity x is $TR=12x+{x^2\over2}-{x^3\over 3}$S.T. at the highest point of average revenue (AR), AR = MR

2. a bank pays 8% interest compounded quarterly. Determine the equal deposits to be made at the end of each quarter for 3 years so as to receive Rs.300 at the end of 3 years.

1. Compute upper Quartiles, lower Quartiles, D4 and P60, P75 from the following data

 CI 10-20 20-30 30-40 40-50 50-60 60-70 70-80 Frequency 12 19 5 10 9 6 6
2. Calculate correlation coefficient for the following data.

 X 25 18 21 24 27 30 36 39 42 48 Y 26 35 48 28 20 36 25 40 43 39
1. A project schedule has the following characteristics

 Activity 1-2 1-3 2-4 3-4 3-5 4-9 5-6 5-7 6-8 7-8 8-10 9-10 Time 4 1 1 1 6 5 4 8 1 2 5 7

Construct the network and calculate the earliest start time, earliest finish time, latest start time and latest finish time of each activity and determine the Critical path of the project and duration to complete the project.

2. Reshma wishes to mix two types of food P and Q in such a way that the Vitamin contents of the mixture contain at least 8 units of vitamin A and 11 units of vitamin B. Food P costs Rs.60/kg and Food Q costs Rs.80/kg. Food P contains 3 units 1 kg of vitamin A and 5 units 1 kg of vitamin B while food Q contains 4 units 1 kg of vitamin A and 2 units 1 kg of vitamin B. Determine the minimum cost of the mixture.