CBSE[Delhi]_XII_Mathematics_2017_Set_III
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Q1
If a line makes angles 90˚and 60˚respectively with the positive direction of x and y axes, find the angle which it makes with the positive directions of zaxis.
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Q2Marks:1
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Q3
Determine the value of the constant ‘k’ so that the function:
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Q4
If A is a 3 x 3 invertible matrix, then what will be the value of k if det(A^{1}) = (det A)^{k}.
Marks:1Answer:
We know that

Q5
Prove that if E and F are independent events, then the events E and F’ are also independent.
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Q6
A small firm manufactures necklaces and bracelets. The total number of necklaces and bracelets that it can handle per day is at most 24. It takes one hour to make a bracelet and half an hour to make a necklace. The maximum number of hours available per day is 16. If the profit on a necklace is Rs.100 and that on a bracelet is Rs.300. Formulate an L.P.P. for finding how many of each should be produced daily to maximize the profit. It is being given that at least one of each must be produced.
Marks:2Answer:
Let the number of necklaces manufactured be x, and the number of bracelets manufactured be y.
Since the total number of items is at most 24,
x + y ≤ 24 …..(1)
A bracelet takes 1 hour to be manufactured and a necklace takes half an hour to be manufactured.
So, x bracelets take x hours to be manufactured and y necklaces take y/2 hours to be manufactured and maximum time available is 16 hours.
So,
The profit on one necklace is Rs.100 and the profit on one bracelet is Rs.300.
Let the profit be Z. Now, we wish to maximize the profit.
So,
Max Z = 100x + 300y ………(3)

Q7Marks:2
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Q8
Find the vector equation of the line passing through the point A (1, 2, 1) and parallel to the line 5x25=147y=35z.
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Q9
Show that the function f(x)=4x^{3}–18x^{2}+27x–7 is always increasing on R.
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Q10
The volume of a sphere is increasing at the rate of 3 cubic centimeters per second. Find the rate of increase of its surface area, when the radius is 2 cm.
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