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1.If A=(2 3 4 ),B=( 7 8 9 ) and C=( 4 3 7 ) be any three matrices which of the following products is defined?
A)AB
B)BA
C)BC
D)ABC
2. According to the cramer's rule, the given system of
linear equations will have a unique solution if and only if
A)D≠0
B)D=0,D1≠0,D2 ≠0,D3 ≠0
C)D=0,D1=0,D2 =0,D3 =0
D)D≠0,D1=0,D2 =0,D3 =0
3.if A=( ) be any input coefficient matrix,what is the value
corresponding Liontief's technology matrix?
4.In which interval is the function f(x)=4x-2x2 increasing?
A)(-∞,1)
B) (1,∞)
C) (2,∞)
D) (3,∞)
5.What is the degree of the differential equation.......?
B) 3
C) 2
D) 1
6.If 'a' be the geometric mean between 1 and 100 then what is the value of a^2?
A)10
C)100
D)101
7.If 'V' be the original cost 'S' the scrap value 'n' the
number of years of estimated life and 'r%' be the compound rate of depreciation
of a machinery per annum then which of the following is applied to find the
scrap value of the machine.
8.What is the amount of an annuity of Rs.70 a year for 4
years at 5 percent per annum?
C)Rs.403
D)Rs.406
9.In a simplex tableau, the optimum solution will be
obtained if the entries of the last rows are
A)All negative
B)All positive
C)positive and negative
D)All zero
10.If 2x+4y=15 and 4x+y=9 are any two lines of regressions
then what types of correlation is between the variables x and y?
A)Positive
B)Negative
C)Zero
D)Cannot be estimated
11.What is the probability of getting 53 Fridays in a
non-leap year?
C)1/7
D)2/7
12. Given is the input-output coefficient matrix. A(0.6 0.7)
(0.3 0.2)
i) what type of the model does the given coefficient matrix
represent? 1
ii) write its corresponding leontif’s technology matrix. 1
iii) write the determinant of leonitif’s matrix. 1
iv) Is the leontif’s matrix singular or non-singular ? 1
v)Is the model represented by the above matrix viable as per
Howkin’s-simon condition ? 1
13. solve the following system by using gauss elimination
method : 5
3x-y+z=2
-15x+6y-5z=5
5x-2y+2z=1
14. the demand function for a certain commodity is given by
P=200-80Q where 0≤ P≤ 25. Determine the price or
price intervals where the demand is unit elastic ,inelastic or elastic. 2+1+1+1
15. A function f(x) is defined as f(x) =
I) Is the function increasing or decreasing at x=1? 1
ii) What are the turning point of the function? 1
iii)At which point does it have maximum value? 1
iv) At which point does it have minimum value? 1
v)What is its point of inflection? 1
16.a water tank is being filled up with water . The rate of
increase of volume of water at any time ’t’
is given by dv/dt =0.2(100-t) where v is measured in liters and time is
measured in seconds. (v=0 when t=0)
i) Find the volume of water filled up in the tank in
‘t’ seconds. 2
ii)Find the volume of water filled up in 10seconds. 1
iii)How much time will it require to fill up the whole tank
if the total capacity of the tank is 100 liters?2
17.Using simplex method, maximize F=15x+20y subject to the constraints
3x+y≤ 12,
x+2y≤ 12x,y≥ 0 5
18.A bag contains 6 white,5 blue and 4 yellow marbles. Three
marbles are drawn out of the bag randomly one after another without
replacement.
i)Find the probability that all three are white marbles. 1
ii)Find the probability that first is white second is blue
and the third is yellow marble. 2
iii)Find the probability of getting third yellow marble. 2
19.A random variable X has the following probability distribution.
| x | 1 | 3 | 5 | 7 | 9 | 11 |
|---|---|---|---|---|---|---|
| P(x) | 0.1 | 0.2 | k | 0.2 | 0.1 | 0.3 |
Find the value of k and E(x). 1+1
b)If 30% of the mobile sets produced by a manufacturing
company are defective, find the probability that out of 3 mobile sets selected
at random. 1+1+1
(i)no mobile set is defective
(ii)one is defective
(iii)All three are defective.
Group C 3 x 8=24
20.(a)Find the area bounded by the curveX2-5x+6=y and the x-axis of coordinates. 2
b)The marginal cost of repair of a machine is given by MC=20t+150,where t is the age of the machine (in years) and Marginal cost being paid(in Rs.)per year.
i)Find the total cost of repair after 4 years, if fixed cost is considered as zero. 2
ii)How many are necessary for the total cost of repair to be Rs.1000? 2
c)Show that the function f(x)=X3-6x2+48x+150 has neither maximum nor minimum value. 2
21. a)A man is appointed to a salary of Rs.5,000 with an yearly increase of 5% of the salary of the previous year. How much salary does he receive during the eighth year? 2
b)Find the difference between simple interest and compound interest on Rs.1500 for 3 years at 6% p.a. 3
c)Find the present value of an annuity of Rs.1200 per year for 5 years at 9% p.a. 3
22)In the following table, the heights and weights of a child during first six years of his/her life are given.
| Heights(in cm)(x) | 30 | 40 | 50 | 60 | 70 | 80 |
|---|---|---|---|---|---|---|
| Weights (in kg)(y) | 10 | 12 | 13 | 16 | 18 | 22 |
a)Find the weight of the child corresponding to the height 85 cm. 5
b)Are the heights and weights correlated or not? 1
c)What types of correlation do you find between them? 1
d)How strong is the correlation between them ? 1
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