#### Term II Model Question Paper

11th Standard

Reg.No. :
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Time : 02:30:00 Hrs
Total Marks : 90
20 x 1 = 20
1. The value of x, if $\begin{vmatrix} 0 & 1 & 0 \\ x & 2 & x \\ 1 & 3 & x \end{vmatrix}=0$ is

(a)

0, - 1

(b)

0, 1

(c)

- 1, 1

(d)

- 1, - 1

2. If A is a square matrix of order 3, then |kA| is

(a)

k|A|

(b)

-k|A|

(c)

k3|A|

(d)

-k3|A|

3. If any three-rows or columns of a determinant are identical, then the value of the determinant is

(a)

0

(b)

2

(c)

1

(d)

3

4. The value of n, when nP2 = 20 is

(a)

3

(b)

6

(c)

5

(d)

4

5. The term containing x3 in the expansion of (x - 2y)7 is

(a)

3rd

(b)

4th

(c)

5th

(d)

6th

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

(a)

7/5

(b)

-7/5

(c)

5/7

(d)

-9/7

7. The degree measure of $\frac{\pi}{8}$ is

(a)

20o60'

(b)

22o30'

(c)

20o60'

(d)

20o30'

8. The value of $\frac{1}{cosec(-45^o)}$ is

(a)

$\frac{-1}{\sqrt2}$

(b)

$\frac{1}{\sqrt2}$

(c)

$\sqrt2$

(d)

$-\sqrt2$

9. The graph of y = ex intersect the y-axis at

(a)

(0,0)

(b)

(1,0)

(c)

(0,1)

(d)

(1,1)

10. If demand and the cost function of a firm are p= 2–x and c = 2x2 +2x +7 then its profit function is

(a)

x2 + 7

(b)

x2 - 7

(c)

- x2 + 7

(d)

- x2 - 7

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

(a)

1600

(b)

1000

(c)

1500

(d)

800

12. Example of contingent annuity is

(a)

(b)

An endowment fund to give scholarships to a student

(c)

Personal loan from a bank

(d)

All the above

13. 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

14. 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)

$(A\cup B)$

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 variable which influences the values or is used for prediction is called

(a)

Dependent variable

(b)

Independent variable

(c)

Explained variable

(d)

Regressed

17. The term regression was introduced by

(a)

R.A Fisher

(b)

Sir Francis Galton

(c)

Karl Pearson

(d)

Croxton and Cowden

18. 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

19. Network problems have advantage in terms of project

(a)

Scheduling

(b)

Planning

(c)

Controlling

(d)

All the above

20. 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

21. 7 x 2 = 14
22. Solve: $\begin{vmatrix}2& x&3\\4&1&6\\1&2&7 \end{vmatrix}=0$

23. Expand the following by using binomial theorem.$\left( x+\frac { 1 }{ y } \right) ^{ 7 }$

24. If 4(nC2) = (n+2)C3 , find n

25. Convert the following degree measure into radian measure 60o

26. Evaluate: $\underset { x\rightarrow 1 }{ lim } \frac { { x }^{ 3 }-1 }{ x-1 }$

27. A tour operator charges Rupees 136 per passenger with a discount of 40 paisa for each passenger in excess of 100. The operator requires at least 100 passengers to operate he tour. Determine the number of passenger that will maximize the amount of money the tour perator receives.

28. The total cost function for the production of x units of an item is given by c = 10 - 4x3 + 3x4 find the
(i) average cost, (ii) marginal cost (iii) marginal average cost.

29. 7 x 3 = 21
30. If A $= \begin{bmatrix} 1 & -1 \\2 & 3 \end{bmatrix}$ show that A2-4A+5I2 = 0 and also find A-1.

31. If $A=\left[ \begin{matrix} 2 & 4 \\ -3 & 2 \end{matrix} \right]$then, find A -1.

32. Find n, if $\frac{1}{9!}+\frac{1}{10!}=\frac{n}{11!}$

33. Solve: $\tan^{-1}2x+\tan^{-1}3x=\frac{\pi}{4}$

34. Express each of the following as the product of sine or cosine.
sinA+sin2A

35. Differentiate sin2 x with respect to x2.

36. Find the stationary value and the stationary points f(x)=x2+2x–5.

37. 7 x 5 = 35
38. Evaluate:$\begin{vmatrix} 1&a&a^2-bc\\1&b&b^2-ca\\1&c&c^2-ab \end{vmatrix}$

39. Solve by using matrix inversion method:
2x + 5y = 1
3x + 2y = 7

40. By the principle of mathematical induction, prove the following.
52n-1 is divisible by 24, for all $n\in N$ .

41. Draw the graph of the following function f(x) =16-x2

42. A company buys in lots of 500 boxes which is a 3 month supply. The cost per box is Rs 125 and the ordering cost in Rs 150. The inventory carrying cost is estimated at 20% of unit value.
(i) Determine the total amount cost of existing inventory policy
(ii) How much money could be saved by applying the economic order quantity?

43. Verify the relationship among AM, GM and HM for the following data

 X 7 10 13 16 19 22 25 28 f 10 22 24 28 19 9 12 16
44. For the given lines of regression 3X–2Y=5and X–4Y=7. Find
(i) Regression coefficients
(ii) Coefficient of correlation