Question - A speaks truth in 60% of the cases, while B in 90% of the cases. In what percent of cases are they likely to contradict each other in stating the same fact? In the cases of contradiction do you think, the statement of B will carry more weight as he speaks truth in more number of cases than A?
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Question - A school wants to award its students for the values of Honesty, Regularity and Hard work with a total cash award of Rs 6,000. Three times the award money for Hard work added to that given for honesty amounts to Rs 11,000. The award money given for Honesty and Hard work together is double the one given for Regularity. Represent the above situation algebraically and find the award money for each value, using matrix method. Apart from these values, namely, Honesty, Regularity and Hard work, suggest one more value which the school must include for awards.
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Question - If the sum of the lengths of the hypotenuse and a side of a right triangle is given, show
that the area of the triangle is maximum, when the angle between them is 60°.
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Question - An experiment succeeds thrice as often as it fails. Find the probability that in the next
five trials, there will be at least 3 successes.
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Question - Consider the binary operation * on the set {1,2,3,4,5} defined by a * b = min {a,b}. Write the operation table of the operation *.
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Question - ---------- find the value of x.
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Question - There are three coins. One is a two-headed coin (having head on both faces), another
is a biased coin that comes up heads 75% of the times and third is also a biased coin
that comes up tails 40% of the times. One of The three coins is chosen at random and
tossed, and it shows heads. What is the probability that it was the two-headed coin?
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Question - If x = cost (3-2 cos^2 t) and y = sin t (3-2 sin^2 t), find the value of -------------
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Question - Find the particular solution of the differential equation log ----- 3x + 4y, given that y = 0 when x = 0.
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Question - Find the equations of the tangent and normal to the --------at the point-----
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Question - The scalar product of the vector ------- with a unit vector along the sum of vectors --------- is equal to one. Find the value of A and hence find
the unit vector along ------
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Question - Evaluate : -------
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Question - There are three coins. One is a two-headed coin (having head on both faces), another is a biased coin that comes up heads 75% of the times and third is also a biased coin that comes up tails 40% of the times. One of The three coins is chosen at random and
tossed, and it shows heads. What is the probability that it was the two-headed coin?
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Question - Find the value of ‘a’ for which the function f defined as
-------------
is continuous at x = 0.
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Question - If y = log ------------
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Question - Show that the differential equation 2ye^x/y dx + (y – 2x e^x/y) dy = 0 is homogeneous. Find the particular solution of this differential equation, given that x = 0 when y = 1.
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Question - A cooperative society of farmers has 50 hectares of land to grow two crops A and B. The profits from crops A and B per hectare are estimated as Rs 10,500 and Rs 9,000 respectively. To control weeds, a liquid herbicide has to be used for crops A and B at the rate of 20 litres and 10 litres per hectare, respectively. Further not more than 800 litres of herbicide should be used in order to protect fish and wildlife using a pond which collects drainage from this land. Keeping in mind that the protection of fish and other wildlife is more important than earning profit, how much land should be allocated to each crop so as to maximize the total profit? Form an LPP from the above and solve it graphically. Do you agree with the message that the protection of wildlife is utmost necessary to preserve the balance in environment?
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Question - If y = 3 cos (log x) + 4 sin (log x), show that --------
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Question - Prove that----------
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Question - A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of machine time and 3 hours of craftsman’s time in its making while a cricket bat takes 3 hours of machine time and 1 hour of craftsman’s time. In a day, the factory has the availability of not more than 42 hours of machine time and 24 hours of craftsman’s time.
If the profit on a racket and on a bat is Rs20 and Rs10 respectively, find the number of tennis rackets and crickets bats that the factory must manufacture to earn the maximum profit. Make it as an L.P.P and solve graphically.
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