maths 6markers

8/2/2019 maths 6markers

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TUTORIALS FOR SCIENCE & COMMERCE

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9717335481,9312441580

Q. Given that A =

321

121

211

find A-1

. Hence using A-1

solve the system of equations:

xy + z = 4, x2y2z = 9, 2x + y + 3z = 1

OR

Using elementary transformation find the inverse of matrix:

423

320

211

Q. Using integration find the area of the region enclosed between the circles x2 + y2 = 4 and

(x2)2 + y2 = 1

Q. A manufacturer has three machines I, II, III installed in his factory. Machines I and II are

capable of being operated for at most 12 hours where as machine III must be operated for

at least 5 hours a day. She produces only two items M and N each requiring the use of all

the three machines. The number of hours required for producing I unit of each of M and

N on the three machines are given as :

Items No. of hrs required on machines

I II III

M

N

1

2

2

1

1

1.25

She makes a profit of Rs 600 and Rs 400 on items M and N resp. How many of each item

should she produce so as to maximize her profit assuming that she can sell all the items

that she produced? What will be the maximum profit?

Q. Find the equation of plane passing through the point (1,1,1) and containing the line

kjikjir 5353 . Also show that the plane contains the line

kjikjir 5252


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Q. Evaluate 0

1

2111sin dxxxxx

Q.A point on the hypotenuse of a triangle is at distance a and b from the sides of thetriangle. Show that the minimum length of the hypotenuse is ( a

2/3+ b

2/3)

3/2.

OR

An open toped box is to be constructed by removing equal squares from each corner of a

3 metre by 8 metre rectangular sheet of aluminium and folding up the sides. Find the

volume of the largest such box.

Q. Assume that the chances of a patient having a heart attack is 40%. It is also assumed thata meditation and yoga course reduce the risk of heart attack by 30% and prescription of

certain drugs reduces its chance by 25%. At a time a patient can choose any one of two

options with equal prob. It is given that after going through one of two options the patient

selected at random suffers a heart attack. Find the prob. that the patient followed a course

of meditation and yoga.

Q.. Using matrices, solve the following system of equations:

2x

3y + 5z = 11; 3x + 2y

4z = -5; x + y

2z = -3.

Q.. Find the distance of the point (-1,-5,-10) from the point of intersection of the line

r=^^^

22 kji +(^^^

243 kji ) and the plane

r. (^^^

kji ) = 5.

Q. Prove that the radius of the right circular cylinder of greatest curved surface area

which can be inscribed in a given cone is half of that of the cone.

OR

Show that the height of the cylinder of maximum volume that can be inscribed in a


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sphere of radius R is3

2R. Also find the maximum volume.

Q.. Evaluate: 2

0

sinlog

dxx OR Find: dxxx )cottan(

Q.. Find the area of the region bounded by the curves y = x2 + 2, y = x, x = 0 and x =3.

Q.. An insurance company insured 2000 scooter drivers, 4000 car drivers and 6000 truck

drivers. The probability of an accident involving a scooter driver, car driver and a

truck driver is 0.01, 0.03 and 0.15 respectively. one of the insured person meets with

an accident. What is the probability that he is a car driver?

Q. There is a factory located at each of the two places P and Q. From these locations, a

certain commodity is delivered to each of these depots situated at A, B and C. The

weekly requirements of the depots are respectively 5, 5 and 4 units of the commodity

while the production capacity of the factories at P and Q are respectively 8 and 6

units. The cost of transportation per unit is given below. How many units should be

transported from each factory to each depot in order that the transportation cost is minimum.

Formulate the above LPP mathematically and then solve it.

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