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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Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?
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2
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In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?
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3
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If C(n, 7) = C(n, 5), find n
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4
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A, B, C, D and E sit on five chairs all of which are facing north. C will sit only on the leftmost chair and B will not sit anywhere to the left of A. In how many ways they can be seated?
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5
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A fair coin is tossed 5 times. What is the probability of getting at least three heads on consecutive tosses?
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6
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From among the 36 students in a class, one leader and one class representative are to be appointed. In how many ways can this be done?
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7
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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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8
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12 person are seated at a round table. Number of ways of selecting 2 persons not adjacent to each other is
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9
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There are seven pairs of black shoes and five pairs of white shoes. They are all put into a box and shoes are drawn one at a time. To ensure that at least one pair of black shoes are taken out, what is the number of shoes required to be drawn out?
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10
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What is the probability of getting at least one six in a single throw of three unbiased dice?s
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