A manufacturing company makes two types of teaching aids A and B

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 Multiple Choice QuestionsLong Answer Type

311.

Show that lines:
straight r with rightwards arrow on top space equals space straight i with hat on top space plus straight j with hat on top space plus straight k with hat on top space plus space straight lambda open parentheses straight i with hat on top minus straight j with hat on top space plus space straight k with hat on top close parentheses
straight r with rightwards arrow on top space equals space 4 straight j with hat on top space plus space 2 straight k with hat on top space plus space straight mu open parentheses 2 straight j with hat on top minus straight j with hat on top plus 3 straight k with hat on top close parentheses space are space coplanar.
Also, find the equation of the plane containing these lines. 

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 Multiple Choice QuestionsShort Answer Type

312.

Find the value of p, so that the lines:
are perpendicular to each other. Also find the equations of a line passing through a point (3, 2, -4) and parallel to line l1.

126 Views

 Multiple Choice QuestionsLong Answer Type

313.

Find the equation of the plane through the line of intersection of the planes x + y + z = 1 and 2x + 3y + 4z = 5 which is perpendicular to the plane x- y + z = 0. Also find the distance of the plane obtained above, from the origin.

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314.

A manufacturing company makes two types of teaching aids A and B of Mathematics for class XII. Each type of A requires 9 labour hours of fabricating and 1 labour hour for finishing. Each type of B requires 12 labour hours for fabricating and 3 labour hours for finishing. For fabricating and finishing, the maximum labour hours available per week are 180 and 30 respectively. The company makes a profit of 80 on each piece of type A and 120 on each piece of type B. How many pieces of type A and type B should be manufactured per week to get a maximum profit? Make it as an LPP and solve graphically. What is the maximum profit per week?


Let x be the number of pieces manufactured of type A and y be the number of pieces manufactured of type B. Let us summarize the data given in the problem as follows:

Product Time for Fabricating (in hours) Time for Finishing (in hours) Maximum labour hours available
Type A 9 1 180
Type B 12 3 30
Maximum Profit (in Rupees) 80 120  

Thus, the mathematical form of above LPP is
Maximize Z = 80x+120y
subject to
9 straight x plus 12 straight y less or equal than 180
straight x plus 3 straight y less or equal than 30
Also, we have straight x greater or equal than 0 comma space space straight y greater or equal than 0
Let us now find the feasible region, which is the set of all points whose coordinates satisfy all constraints. 
Consider the following figure. 


Thus, the feasible region consists of the points A, B and C.
The values of the objective function at the corner points are given below in the following table:
Points Value of Z
A(12, 6) Z = 80 x 12 + 120 x 6 = Rs. 1680
B(0, 10) Z = 80 x 0 +120 x 10 = Rs. 1200
C(20, 0) Z = 80 x 20 + 120 x 0 = Rs.1600

Clearly,Z is maximum at x=12 and y=6 and the maximum profit is Rs.1680.
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 Multiple Choice QuestionsShort Answer Type

315.

Find the Cartesian equation of the line passes through the point (-2, 4, -5) and is parallel to the line fraction numerator straight x plus 3 over denominator 3 end fraction equals fraction numerator 4 minus straight y over denominator 5 end fraction equals fraction numerator straight z plus 8 over denominator 6 end fraction.

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316.

Find the vector equation of the line passing through the point A(1, 2, –1) and parallel to the line 5x – 25 = 14 – 7y = 35z.

1145 Views

317.

Find the shortest distance between the lines.

r = (4i^ -j^) + λ (i^ - j^ + 2k^) + μ (2i^ + 4j^-5k)^


 Multiple Choice QuestionsLong Answer Type

318.

Find the distance of the point (-1,-51-10) from the point of intersection of the line r = 2i^ -j^ + 2k^ + λ (3i^ + 4j^ + 2k^) and the plane r. (i^-j^ + k^) = 5


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319.

Find the shortest distance between the following lines:

x - 31 = y - 5-2 = z - 71 and x + 17 = y + 1-6 = z + 11 


320.

Find the point on the line x + 23 = y + 12 = z - 32 at a distance 3 2 from the point
(1, 2, 3).


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