Reference no: EM131929885
Section A
Q.1 If the equation of line ab is (3-x)/1 = (y+2)/(-2)= (z-2)/4 then write the direction ratios of line parralal to above line
Q.2 If the Cartesian equation of a line is (3-x)/5 = (y+4)/7=(2z-6)/4 then find the vector equation for the line?
Q.3 Find the distance of the plane 3x-4y+12z =3 from origin?
Q.4 If x2/3 + y2/3 = a2/3 then find dy/dx?
Section B
Q.5 If 
then find [A'] ?
Q.6 write a unit vector in the direction of vetor PQ, where vector P and Q are the points ( 1,3,0) and (4,5,6) respectively?
Q.7 find the direction cosines of the line (x+2)/2 = (2y-7)/6 = (5-z)/6 also find the vector equation of the line through the point A(-1,2,3) and parallal to given line?
Q.8 Verify Rolle ‘s theorem for the function f(x) = sinx + cosx , x?[0,π/2
Section C
Q.9 The function
Is continuous on (0, 10) find the value of a and b?
Q.10 Find the points the curves 9y2 = x3 where the normal to the curve makes equal intercept on the axes?
OR
Find the approximate value of (3.02) upto 2 places of decimals where f(x) = 3x2 + 15x +3?
Q.11 - Solve the set of equation s
X+2y - 3z = -4
2x + 3y + 2z = 2
3x-3y-4z = 11.
Q.12 -Using properties of determinant show that 
= 9b2(a+b).
Q.13- Find the equation of plane which passing through the points (3,2,0) and contains the line
(x-3)/1 = (y-6)/5 = (z-4)/4 ?
Section D
Q.14 Find the distance of the points (-1,-5,-10) from the points of the intersection of the line r = 2i - j + 2k + λ(3i + 4j+12k) and the plane r.(i- j +k ) = 5
Q.15 - Find two positive numbers x and y such that x+y = 60 and xy3 ix maximum?
Q.16 A housewife wishes to mix together two kinds of food , X and Y in such a way that the mixture contains atleast 10 units of vitamin A, 12 units of vitamin B and 8 units of vitamin C. The vitamin contents of 1 kg of food are given below.
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Vitamin A
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Vitamin B
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Vitamin C
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Food X
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1
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2
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3
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Food y
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2
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2
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1
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1 kg of food X costs RS 6 and 1 kg 0f food Y costs Rs 10. Formulate the above problem as a linear programming problem and find the least cost of the mixture which will produce the diet graphically. what value will you like to attach with the problem?
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