Self Studies

Permutations an...

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  • Question 1
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    If f(x)=1x+x2x3+....x15+x16+x17f(x)=1-x+x^2-x^3+....-x^{15}+x^{16}+x^{17}, then the coefficient of x2x^2 in f(x1)f(x-1) is?

  • Question 2
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    Replace the question mark (?) with the correct option.

  • Question 3
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    Let 5<n1<n2<n3<n45 < n_1 < n_2 < n_3 < n_4 be integers such that n1+n2+n3+n4=35n_1+n_2+n_3+n_4=35. The number of such distinct arrangements (n1,n2,n3,n4)(n_1, n_2, n_3, n_4).

  • Question 4
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    If p:q:r=1:2:3  thenp:q:r=1:2:3\;then 5p2+q2+r2\sqrt {5{p^2} + {q^2} + {r^2}} is equal to: 

  • Question 5
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    Area of the triangle formed by (x1,y1),(x2,y2),(3y2,(2y1))(x_{1,}y_{1}),(x_{2},y_{2}), (3y_{2},(-2y_{1}))

  • Question 6
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    77 boys and 88 girls have to sit in a row on 1515 chairs numbered from 11 to 1515 then?

  • Question 7
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    A is a set containing n elements. A  subset P of A is chosen. The set A is reconstructed by replacing the element of P.A subset Q of A is again chosen. The number of way of choosing P and Q so that P Q =ϕ\phi is :- 

  • Question 8
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    A box contains 5 pairs of shoes. If 4 shoes are selected, then the number of ways in which exactly one pair of shoes obtained is :

  • Question 9
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    There are locks and matching keys. If all the locks and keys are to be perfectly matched, find the maximum number of trails required to open a lock.

  • Question 10
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    Find the area of the triangle formed by the mid points of sides of the triangle whose vertices are (2,1)(2, 1), (2,3)(-2, 3), (4,3)(4, -3).

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