Question - Using properties of determinants, prove that: ----------
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Question - Differentiate x -------
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Question - Prove that tan^-1 -------------
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Question - Find the distance of the point (2, 12, 5) from the point of infersection of the line ----------------
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Question - Using the method of method of integration, find the area of the region bounded by the following lines:
3x â€“ y â€“ 3 = 0, 2x + y â€“ 12 = 0, x â€“ 2y â€“ 1 = 0.
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Question - Evaluate: -------
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Question - Assume that the chances of a patient having a heart attack is 40%. Assuming that a meditation and yoga course reduces the risk of heart attack by 30% and prescription of certain drug reduces its chance by 25%. At a time a patient can choose any one of the two options with equal probabilities. It is given that after going through one of the two options, the patient selected at random suffers a heart attack. Find the probability that the patient followed a course of meditation
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Question - Probabilities of solving problem independently by A and B are -------- respectively. If both try to solve the problem independently, find the probability that (i) the problem is solved (ii) exactly one of them solves the problem.
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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 - If y = Pe^ax + Q e^hx , show that ----------
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Question - 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 l_1.
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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 - Show that of all the rectangles inscribed in a given fixed circle, the square has the maximum area.
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Question - Using differentials, find the approximate value of -------
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Question - Suppose 5% of men and 0.25% of women have grey hair. A grey haired person is selected at random. What is the probability of this person being male? Assume that there are equal number of males and females.
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Question - Using properties of determinants, prove the following: -------------
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Question - Find a unit vector perpendicular to each of the vector -------
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Question - Prove that sin^-1 --------------
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