CBSE Questions for Class 11 Engineering Maths Permutations And Combinations Quiz 14 - MCQExams.com

What is the hundreds digits of ( 20 !-15!) ? 
  • 0
  • 1
  • 2
  • 4
  • 5
$$\left( \begin{matrix} 51 \\ 3 \end{matrix} \right) +\left( \begin{matrix} 50 \\ 3 \end{matrix} \right) +\left( \begin{matrix} 49 \\ 3 \end{matrix} \right) +\left( \begin{matrix} 48 \\ 3 \end{matrix} \right) +\left( \begin{matrix} 47 \\ 3 \end{matrix} \right) +\left( \begin{matrix} 47 \\ 4 \end{matrix} \right) $$ is equal to (where $$\left( \begin{matrix} n \\ r \end{matrix} \right) $$ denotes $$_{  }^{ n }{ { C }_{ r } }$$
  • $$\left( \begin{matrix} 52 \\ 1 \end{matrix} \right) $$
  • $$\left( \begin{matrix} 52 \\ 2 \end{matrix} \right) $$
  • $$\left( \begin{matrix} 52 \\ 3 \end{matrix} \right) $$
  • $$\left( \begin{matrix} 52 \\ 4 \end{matrix} \right) $$
If $$n$$ and $$r$$ are positive integers such that $$r < n$$ then $$^{n}C_{r}+^{n}C_{r-1}$$ is equal to
  • $$^{2n}C_{2r-1}$$
  • $$^{n+1}C_{r}$$
  • $$^{n}C_{r+1}$$
  • $$2^{n}C_{r}$$
If $$x\epsilon N and C^{x-1_{4}}-C^{X-1}_{3}-\frac{5}{4}P^{x-2}_{2}< 0$$ then x is equal to 
  • 4,5,6,7,8,9,10
  • 3
  • $$3\leq x\leq 10$$
  • none of these
If  $$m$$  and  $$n$$  are positive integers more than or equal to  $$2 , m > n ,$$  then  $$( m n ) !$$  is divisible by
  • $$( m ! ) ^ { n }$$
  • $$( n ! ) ^ { m }$$
  • $$( m + n ) !$$
  • $$( m - n ) !$$
If $${ n }_{ C_ r }$$ denotes the number of combinations of n things taken r at a time, then the expression + $${n}_{C_r-1} + 2 \times {n}_{C_r}$$ equals 
  • $${ n+2 }_{ C_ r }$$
  • $${ n+2 }_{ C_ r+1 }$$
  • $${ n+2 }_{ C_ r }$$
  • $${ n+2 }_{ C_ r+1 }$$
If $$^{189}C_{35} + ^{189}C_{x} = ^{190}C_{x}$$, then $$x$$ is equal to
  • $$34$$
  • $$35$$
  • $$36$$
  • $$37$$
In a village, there are $$87$$ families of which $$52$$ families have at most $$2$$ children. In a rural development programme, $$20$$ families are to be helped chosen for assistance, of which at least $$18$$ families must have at most $$2$$ children. In how many ways can the choice be made?
  • $$\ ^{52}C_{18}\times \ ^{35}C_{2}+\ ^{52}C_{19}\times \ ^{35}C_{1}+\ ^{52}C_{20}\times \ ^{35}C_{0}$$
  • $$\ ^{52}C_{18}\times \ ^{35}C_{2}+\ ^{52}C_{19}\times \ ^{35}C_{1}+\ ^{52}C_{20}\times \ ^{35}C_{10}$$
  • $$\ ^{52}C_{18}\times \ ^{35}C_{2}+\ ^{52}C_{19}\times \ ^{35}C_{1}+\ ^{52}C_{2}\times \ ^{5}C_{0}$$
  • $$\ ^{52}C_{18}\times \ ^{35}C_{2}+\ ^{52}C_{9}\times \ ^{35}C_{10}+\ ^{52}C_{20}\times \ ^{5}C_{0}$$
A sports team of $$11$$ students is to be constituted, choosing at least $$5$$ from class $$XI$$ and at least $$5$$ from class $$XII$$. If there are $$20$$ students in each of these classes, in how many ways can the teams be constituted?
  • $$2(\ ^{20}C_{3}\times \ ^{20}C_{7})$$
  • $$2(\ ^{20}C_{5}\times \ ^{20}C_{6})$$
  • $$2(\ ^{20}C_{4}\times \ ^{20}C_{8})$$
  • None of these
The number of five digit numbers in which digits decrease from left to  right, is 
  • $$^{9}C_{5}$$
  • $$^{10}C_{5}$$
  • $$2\times ^{10}C_{5}$$
  • $$^{10}P_{5}$$
If $$\dfrac {^{n}C_{r} + 4^{n}C_{r + 1} + 6^{n}C_{r + 2} + 4^{n}C_{r + 3} + ^{n}C_{r + 4}}{^{n}C_{r} + 3^{n}C_{r + 1} + 3^{n}C_{r + 2} + ^{n}C_{r + 3}} = \dfrac {n + k}{r + k}$$ then the value of $$k$$ is
  • $$1$$
  • $$2$$
  • $$4$$
  • $$5$$
The number of four -digit numbers strictly grater than $$4321$$ that can be formed using the digits $$0,1,2,3,4,5$$ (repetition of digits is allowed) is:
  • $$288$$
  • $$306$$
  • $$360$$
  • $$310$$
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