CBSE[Delhi]_XII_Mathematics_2017_Set II
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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 z-axis.
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Q2Marks:1View Answer
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Q3
If A is a 3 x 3 invertible matrix, then what will be the value of k if det(A-1) = (det A)k.
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We know that
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Q4
Determine the value of the constant ‘k’ so that the function:
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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.
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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)
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Q7
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Q8
Show that all the diagonal elements of a skew symmetric matrix are zero.
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Q9Marks:2View Answer
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Q10
Show that the function f(x)=4x3–18x2+27x–7 is always increasing on R.
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