MCQ Questions for Class 11 Engineering Maths Permutations And Combinations Quiz 14

What is the hundreds digits of ( 20 !-15!) ?

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0
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1
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2
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4
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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

$_{ }^{ n }{ { C }_{ r } }$

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$\left( \begin{matrix} 52 \\ 1 \end{matrix} \right)$
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$\left( \begin{matrix} 52 \\ 2 \end{matrix} \right)$
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$\left( \begin{matrix} 52 \\ 3 \end{matrix} \right)$
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$\left( \begin{matrix} 52 \\ 4 \end{matrix} \right)$

$n$ and

$r$ are positive integers such that

$r < n$ then

$^{n}C_{r}+^{n}C_{r-1}$ is equal to

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$^{2n}C_{2r-1}$
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$^{n+1}C_{r}$
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$^{n}C_{r+1}$
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$2^{n}C_{r}$

$x\epsilon N and C^{x-1_{4}}-C^{X-1}_{3}-\frac{5}{4}P^{x-2}_{2}< 0$ then x is equal to

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4,5,6,7,8,9,10
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3
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$3\leq x\leq 10$
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none of these

$m$ and

$n$ are positive integers more than or equal to

$2 , m > n ,$ then

$( m n ) !$ is divisible by

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$( m ! ) ^ { n }$
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$( n ! ) ^ { m }$
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$( m + n ) !$
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$( m - n ) !$

${ n }_{ C_ r }$ 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

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${ n+2 }_{ C_ r }$
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${ n+2 }_{ C_ r+1 }$
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${ n+2 }_{ C_ r }$
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${ n+2 }_{ C_ r+1 }$

$^{189}C_{35} + ^{189}C_{x} = ^{190}C_{x}$ , then

$x$ is equal to

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$34$
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$35$
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$36$
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$37$

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?

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$\ ^{52}C_{18}\times \ ^{35}C_{2}+\ ^{52}C_{19}\times \ ^{35}C_{1}+\ ^{52}C_{20}\times \ ^{35}C_{0}$
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$\ ^{52}C_{18}\times \ ^{35}C_{2}+\ ^{52}C_{19}\times \ ^{35}C_{1}+\ ^{52}C_{20}\times \ ^{35}C_{10}$
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$\ ^{52}C_{18}\times \ ^{35}C_{2}+\ ^{52}C_{19}\times \ ^{35}C_{1}+\ ^{52}C_{2}\times \ ^{5}C_{0}$
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$\ ^{52}C_{18}\times \ ^{35}C_{2}+\ ^{52}C_{9}\times \ ^{35}C_{10}+\ ^{52}C_{20}\times \ ^{5}C_{0}$

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?

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$2(\ ^{20}C_{3}\times \ ^{20}C_{7})$
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$2(\ ^{20}C_{5}\times \ ^{20}C_{6})$
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$2(\ ^{20}C_{4}\times \ ^{20}C_{8})$
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None of these

Explanation

A team of

$11$ students can be constituted in the following two ways

$i) 5$ student from class

$XI$ and

$6$ from

$XII$

$ii) 6$ student from class

$XI$ and

$5$ from

$XII$

$\therefore$ The required number of ways

$\Rightarrow \ ^{20}C_{5}\times \ ^{20}C_{6}+\ ^{20}C_{6}\times \ ^{20}C_{5}$

$\Rightarrow 2\left(\ ^{20}C_{5}\times \ ^{20}C_{6}\right)$

The number of five digit numbers in which digits decrease from left to right, is

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$^{9}C_{5}$
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$^{10}C_{5}$
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$2\times ^{10}C_{5}$
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$^{10}P_{5}$

$\dfrac {^{n}C_{r} + 4^{n}C_{r + 1} + 6^{n}C_{r + 2} + 4^{n}C_{r + 3} + ^{n}C_{r + 4}}{^{n}C_{r} + 3^{n}C_{r + 1} + 3^{n}C_{r + 2} + ^{n}C_{r + 3}} = \dfrac {n + k}{r + k}$ then the value of

$k$ is

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$1$
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$2$
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$4$
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$5$

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:

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$288$
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$306$
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$360$
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$310$

Explanation

(1) The number of four-digit numbers Strating with 5 is equal to

$6^3 = 216$
(2) Starting with 44 and 55 is equal to

$36\times 2 = 72$
(3) Starting with 433, 434 and 435 is equal to

$6\times 3 = 18$
(4) Remaining numbers are 4322, 4323, 4324, 4325 is equal to 4
so total number are

$716 + 72 + 18 + 4 = 310$

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

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Practice Class 11 Engineering Maths Quiz Questions and Answers

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

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Practice Class 11 Engineering Maths Quiz Questions and Answers

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