The number of triangles that can be formed by choosing the vertices from a set of 12 points, seven of which lie on the same straight line, is
185
175
115
105
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1
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How many 4letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?
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2
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Ten participants are participating in a competition. In how many ways can the first three prizes be won?
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3
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One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is not a face card (Jack, Queen and King only)?
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4
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A, B, C, and D are four points, any three of which are noncollinear. Then, the number of ways to construct three lines each joining a pair of points so that the lines do not form a triangle is
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5
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In a simultaneous throw of two dice, what is the probability of getting a total of 7?
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6
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Find the probability that a leap year selected at random will contain 53 Sundays
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7
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A person tosses an unbiased coin. When head turns up, he gets Rs.8 and tail turns up he loses Rs.4. If 3 coins are tossed, what is probability that he gets a profit of Rs.12?
SolutionPerson will get profit of Rs 12 only when there is 2H (Head) and 1T (Tail) H + H + T = 12 8 + 8 + (4) = 12 Total outcome of 2 head and 1 tail = 2^{3} = 8 i.e (T, H, TH, HT, HH, HHT, HTH, THH) Total event with 2H and 1 T is 3 therfore probability = 3/8 
8
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It is required to seat 5 boys and 4 girls in a row so that the girls occupy the even places. How many such arrangements are possible?
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9
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A fiveletter word is to be formed from a group of 5 vowels and 4 consonants, using at least one vowel and at least one consonant. In how many ways the word having a greater number of consonants than vowels can be formed?
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10
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Find the number of ways in which mixed double tennis game can be arranged amongst 9 married couples if no husband and wife play in the same game
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