Recent questions tagged exemplar

A group consists of 4 girls and 7 boys.In how many ways can a team of 5 members be selected if the team has at least one boy and one girl

asked May 16, 2014 by sreemathi.v

1 answer

A group consists of 4 girls and 7 boys.In how many ways can a team of 5 members be selected if the team has no girls

asked May 15, 2014 by sreemathi.v

1 answer

A sports team of 11 students is to be constituted,choosing at least 5 from class XI and 6 from XII.If there are 20 students in each of these classes,in how many ways can the team be constituted?

asked May 15, 2014 by sreemathi.v

1 answer

In how many ways can a football team of 11 players be selected from 16 players?How many of them will exclude 2 particular players?

asked May 15, 2014 by sreemathi.v

1 answer

In how many ways can a football team of 11 players be selected from 16 players?How many of them will include 2 particular players?

asked May 15, 2014 by sreemathi.v

1 answer

A bag contains six white marbles and five red marbles.Find the number of ways in which four marbles can be drawn from the bag if they must all be of the same colour

asked May 15, 2014 by sreemathi.v

1 answer

A bag contains six white marbles and five red marbles.Find the number of ways in which four marbles can be drawn from the bag if two must be white and two red

asked May 15, 2014 by sreemathi.v

1 answer

A bag contains six white marbles and five red marbles.Find the number of ways in which four marbles can be drawn from the bag if they can be of any colour

asked May 15, 2014 by sreemathi.v

1 answer

$18$ mice were placed in two experimental groups and one control group,with all groups equally large.In how many ways can the mice be placed into three groups?

asked May 15, 2014 by sreemathi.v

1 answer

A convex polygon has 44 diagonals.Find the number of its sides

asked May 15, 2014 by sreemathi.v

1 answer

In an examination a student has to answer 4 questions out of 5 questions;questions 1 and 2 are compulsory.Determine the number of ways in which the student can make choice.

asked May 15, 2014 by sreemathi.v

1 answer

In a certain city,all telephone numbers have six digits,the first two digits always being 41 or 42 or 46 or 62 or 64.How many telephone numbers have all six digits distinct.

asked May 15, 2014 by sreemathi.v

1 answer

If 20 lines are drawn in a plane such that no two of them are parallel and no three are concurrent,in how many points will they intersect each other

asked May 15, 2014 by sreemathi.v

1 answer

Find the number of integers greater than 7000 that can be formed with the digits 3,5,7,8 and 9 where no digits are repeated

asked May 15, 2014 by sreemathi.v

1 answer

If $nC_{r-1}=36,nC_r=84$ and $nC_{r+1}=126$ then find $rC_2$

asked May 15, 2014 by sreemathi.v

1 answer

A box contain two white,three black and four red balls. In how many ways can three balls be drawn from the box,if atleast one black ball is to be includedin the draw

asked May 15, 2014 by sreemathi.v

1 answer

There are $10$ lamps in a hall.Each one of them can be switched on independently.Find the number of ways in which the hall can be illuminated.

asked May 15, 2014 by sreemathi.v

1 answer

There are 10 persons named $P_1,P_2,P_3.....P_{10}$.Out of 10 persons,5 person are to be arranged in a line such that in each arrangement $P_1$ must occur where as $P_4$ and $P_5$ do not occur.Find the number of such possible arrangement.

asked May 15, 2014 by sreemathi.v

1 answer

Find the number of different words that can be formed from the letters of the word TRIANGLE so that no vowels are together

asked May 15, 2014 by sreemathi.v

1 answer

Find the number of permutations of n distinct things taken r together in which 3 particular things must occur together.

asked May 15, 2014 by sreemathi.v

1 answer

A bag contains 5 black and 6 red balls.Determine the number of ways which 2 black and 3 red balls can be selected from the lot.

asked May 15, 2014 by sreemathi.v

1 answer

How many automobile license plates can be made if each plate contains two different letters followed by three different digits?

asked May 15, 2014 by sreemathi.v

1 answer

How many committee of five persons with a chairperson can be selected from 12 persons

asked May 15, 2014 by sreemathi.v

1 answer

We wish to select 6 persons from 8,but if the person A is chosen,then B must be chosen.In how many ways can selection be made?

asked May 15, 2014 by sreemathi.v

1 answer

Out of 18 points in a plane,no three are in the same line except five points which are collinear.Find the number of lines that can be formed joining the points

asked May 15, 2014 by sreemathi.v

1 answer

A candidate is required to answer 7 questions out of 12 questions,which are divided into two groups,each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. Find the number of different ways of doing questions.

asked May 15, 2014 by sreemathi.v

1 answer

If the letters of the word RACHIT are arranged in all possible ways as listed in dictionary.Then what is the rank of the word RACHIT?

asked May 14, 2014 by sreemathi.v

1 answer

Eight chairs are numbered 1 to 8. Two women and 3 men wish to occupy one chair each. First the women choose the chairs from amongst the chairs 1 to 4 and then men select from the remaining chairs. Find the total number of possible arrangements.

asked May 14, 2014 by sreemathi.v

1 answer

State whether the following statement is true or false. Justify. Let $P(n)$ be a statement and let $P(k) \Rightarrow P(k+1)$, for some natural number $k$, then $P(n)$ is true for all $n \in N$.

asked May 6, 2014 by thanvigandhi_1

0 answers

If $P(n) : 2n < n!, n \in N$, then $P(n)$ is true for all $n \geq $______ .

asked May 6, 2014 by thanvigandhi_1

1 answer

Choose the correct answer if $x^n-1 $ is divisible by $ x - k$, then the least positive integral value of $k$ is

asked May 6, 2014 by thanvigandhi_1

0 answers

Choose the correct answer for all $n \in N, 3.5^{2n+1}+2^{3n+1}$ is divisible by

asked May 6, 2014 by thanvigandhi_1

1 answer

Choose the correct answer if $10^n+3.4^{n+2}+k$ is divisible by 9 for all $n \in N$, then the least positive integral value of $k$ is

asked May 6, 2014 by thanvigandhi_1

0 answers

Prove that number of subsets of a set containing $n$ distinct elements is $2^n$, for all $ n \in N$ by using principle of mathematical induction.

asked May 6, 2014 by thanvigandhi_1

0 answers

Prove that, $ \large\frac{1}{n+1}$$+ \large\frac{1}{n+2}$$+...+\large\frac{1}{2n}$$ > \large\frac{13}{24}$, for all natural numbers $n > 1$ by using principle of mathematical induction.

asked May 6, 2014 by thanvigandhi_1

0 answers

Show that $ \large\frac{n^5}{5}$$+\large\frac{n^3}{3}$$+\large\frac{7n}{15}$ is a natural number for all $n \in N$ by using the principle of mathematical induction.

asked May 6, 2014 by thanvigandhi_1

0 answers

Prove that, $ \sin \theta + \sin 2\theta + \sin 3\theta+...+ \sin n\theta = \large\frac{\Large\frac{\sin n \theta}{2} \sin \Large\frac{(n+1)}{2} \theta}{\sin \Large\frac{\theta}{2}}$, for all $ n \in N$ by using principle of mathematical induction.

asked May 6, 2014 by thanvigandhi_1

0 answers

Prove that, $ \cos \theta, \cos 2\theta \cos 2^2\theta....\cos 2^{n-1} \theta = \large\frac{\sin 2^n \theta}{2^n \sin \theta}$, for all $n \in N$ by using the principle of mathematical induction.

asked May 6, 2014 by thanvigandhi_1

0 answers

Prove that for all $n \in N$ \[\] $\cos \alpha+ \cos ( \alpha + \beta ) + \cos ( \alpha + 2 \beta )+...+ \cos ( \alpha + (n-1) \beta )$ \[\] $ = \large\frac{ \cos \bigg( \alpha + \bigg( \Large\frac{n-1}{2} \bigg) \beta \bigg) \sin \bigg( \Large\frac{n \beta}{2} \bigg)}{\sin \Large\frac{\beta}{2}}$ by using principle of mathematical induction.

asked May 6, 2014 by thanvigandhi_1

0 answers

A sequence $d_1, d_2, d_3...$ is defined by letting $d_1=2$ and $d_k=\large\frac{d_{k-1}}{k}$ for all natural numbers $k \geq 2$. Show that $d_n = \large\frac{2}{n!}$ for all $n \in N$ by using principle of mathematical induction.

asked May 6, 2014 by thanvigandhi_1

0 answers

A sequence $b_0, b_1, b_2...$ is defined by letting $b_0=5$ and $b_k=4+b_{k-1}$ for all natural numbers $k $. Show that $b_n = 5+4n$ for all natural number $n$ using mathematical induction.

asked May 6, 2014 by thanvigandhi_1

0 answers

A sequence $a_1, a_2, a_3...$ is defined by letting $a_1=3$ and $a_k=7a_{k-1}$ for all natural numbers $k \geq 2$. Show that $a_n = 3.7^{n-1}$ for all natural numbers by using principle of mathematical induction.

asked May 6, 2014 by thanvigandhi_1

0 answers

Prove the following statement by the principle of mathematical induction : \[\] $1+5+9+...+(4n-3)=n(2n-1)$ for all natural numbers $n$.

asked May 5, 2014 by thanvigandhi_1

1 answer

Prove the following statement by the principle of mathematical induction : \[\] $1+2+2^2+...+2^n=2^{n+1}-1$ for all natural numbers $n$.

asked May 5, 2014 by thanvigandhi_1

0 answers

Prove the following statement by the principle of mathematical induction : \[\] $2+4+6+...+2n=n^2+n$ for all natural numbers $n$.

asked May 5, 2014 by thanvigandhi_1

0 answers

Prove the following statement by the principle of mathematical induction : \[\] $ \sqrt n <\large\frac{1}{\sqrt 1}$$+\large\frac{1}{\sqrt 2}$$+...+\large\frac{1}{\sqrt n}$, for all natural numbers $n \geq 2$.

asked May 5, 2014 by thanvigandhi_1

0 answers

Prove the following statement by the principle of mathematical induction : \[\] $2n < (n+2)!$ for all natural number $n$.

asked May 5, 2014 by thanvigandhi_1

0 answers

Prove the following statement by the principle of mathematical induction : \[\] $n^2 < 2^n$ for all natural numbers $n \geq 5$.

asked May 5, 2014 by thanvigandhi_1

0 answers

Prove the following statement by the principle of mathematical induction : \[\] $n(n^2+5)$ is divisible by 6, for each natural number $n$.

asked May 5, 2014 by thanvigandhi_1

0 answers

Prove the following statement by the principle of mathematical induction : \[\] $n^3-n$ is divisible by 6, for each natural number $n \geq 2$.

asked May 5, 2014 by thanvigandhi_1

0 answers

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