Two variants of the CAT paper are to be given to 12 students. In how many ways can the students be placed in two rows of six each so that there should be no identical variants side by side and that the students sitting one behind the other should have the same variant. Find the number of ways this can be done
2 x 12C6 x (6!)2
2 x 6! x 6!
2 x 12C6 x 6!
None of these
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Six boys and 4 girls are to be seated in two separate rows with five chairs each, such that two particular girls are always together and all the girls are not in the same row. In how many ways can they be seated?
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2
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Seven different objects must be divided among three people. In how many ways can this be done if one or two of them must get no objects?
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3
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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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4
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A five-letter 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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5
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If A and B are two independent events with P(A) = 3/5 and P(B) = 4/9 , then P(A' ∩ B' ) equals
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6
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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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7
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How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated
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8
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9
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If four dice are thrown together, then what is the probability that the sum of the numbers appearing on them is 25 ?
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10
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Four letters are selected from the word “CAPAME” and are rearranged to form four letter words. How many words can be formed?
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