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If 2nC3 : nC2 = 44 : 3, find n.
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If 16Cr = 16Cr + 2, find rC4.
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If α = mC2, then find the value of αC2.
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Two finite sets have m and n elements. The number of elements in the power set of first set is 48 more than the total number of elements in power set of the second set. Then, the values of m and n are:
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In a class of 175 students the following data shows the number of students opting one or more subjects. Mathematics 100; Physics 70; Chemistry 40; Mathematics and Physics 30; Mathematics and Chemistry 28; Physics and Chemistry 23; Mathematics, Physics and Chemistry 18. How many students have offered Mathematics alone?
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Suppose \[A_1 , A_2 , . . . , A_{30}\] are thirty sets each having 5 elements and \[B_1 , B_2 , . . . , B_n\] are n sets each with 3 elements. Let \[\cup^{30}_{i = 1} A_i = \cup^n_{j = 1} B_j = S\] and each element of S belong to exactly 10 of the \[A_i 's\]and exactly 9 of the\[B_j 's\] then n is equal to
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If \[x + iy = (1 + i)(1 + 2i)(1 + 3i)\],then x2 + y2 =
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Two finite sets have m and n elements. The number of subsets of the first set is 112 more than that of the second. The values of m and n are respectively
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If \[\frac{1 - ix}{1 + ix} = a + ib\] then \[a^2 + b^2\]
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From a group of 15 cricket players, a team of 11 players is to be chosen. In how many ways can this be done?
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How many different boat parties of 8, consisting of 5 boys and 3 girls, can be made from 25 boys and 10 girls?
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In how many ways can a student choose 5 courses out of 9 courses if 2 courses are compulsory for every student?
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In how many ways can a football team of 11 players be selected from 16 players? How many of these will
include 2 particular players?
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In how many ways can a football team of 11 players be selected from 16 players? How many of these will
exclude 2 particular players?
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There are 10 professors and 20 students out of whom a committee of 2 professors and 3 students is to be formed. Find the number of ways in which this can be done. Further find in how many of these committees:
a particular professor is included.
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There are 10 professors and 20 students out of whom a committee of 2 professors and 3 students is to be formed. Find the number of ways in which this can be done. Further find in how many of these committees:
a particular student is included.
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There are 10 professors and 20 students out of whom a committee of 2 professors and 3 students is to be formed. Find the number of ways in which this can be done. Further find in how many of these committees:
a particular student is excluded.
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How many different products can be obtained by multiplying two or more of the numbers 3, 5, 7, 11 (without repetition)?
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From a class of 12 boys and 10 girls, 10 students are to be chosen for a competition; at least including 4 boys and 4 girls. The 2 girls who won the prizes last year should be included. In how many ways can the selection be made?
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How many different selections of 4 books can be made from 10 different books, if
there is no restriction;
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