Question - Using properties of determinants, prove the following: ------ = (a – b) (b – c) (c – a) (a + b + c)
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Question - Evaluate : -------
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Question - If y = 3 cos (log x) + 4 sin (log x), show that --------
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Question - Prove that tan^-1 -------------
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Question - Using the method of method of integration, find the area of the region bounded by the following lines:
3x – y – 3 = 0, 2x + y – 12 = 0, x – 2y – 1 = 0.
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Question - Find the particular solution of the following differential equation: ------
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Question - Question - Prove that -------
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Question - Using matrices solve the following system of linear equations:
x y 2z 7
3x 4y 5z 5
2x y 3z 12
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Question - A girl throws a cie. If she get a 5 OR 6, she tosses a coin three times and notes the number of heads. If she gets 1, 2, 3 OR 4, she tosses a coin two times and notes the number of heads obtained. If she obtained exactly two heads, what is the probability that she threw 1, 2, 3 OR 4 with the die?
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Question - Using differentials, find the approximate value of -------
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Question - Prove that sin^-1 --------------
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Question - Show that the height of a closed right circular cylinder of given surface and maximum volume, is equal to the diameter of its base.
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Question - Evaluate -------- 2x^2 + 5x dx as a limit of sum.
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Question - Evaluate : ----- sin x sin 2x sin 3x dx
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Question - If ------ are three vectors such that ------ Find. The value of ----------
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Question - Let A = R – {3} and B R – {1}. Consider the function f : A --- B defined by f(x) =-------. Show that f is one-one and onto and hence find f^-1.
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Question - If sin y = x sin (a + y), prove that ---------
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Question - manufacturer produces nuts and bolts. It takes 1 hours of work on machine A and 3 hours on machine B to product a package of nuts. It takes 3 hours on machine A and 1 hour on machine B to produce a package of bolts. He earns a profit of Rs. 17.50 per package on nuts and Rs. 7 per package of bolts. How many packages of each should be produced each day so as to maximize his profits if he operates his machines for at the most 12 hours a day? Form the above as a linear programming problem and solve it graphically.
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Question - Solve the following differential equation: -------------
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Question - How many times must a man toss a fair coin, so that the probability of having at least one head is more than 80%?
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