QBManager

Permutation and Combination

119256 There are 10 points in a plane, out of these 10 points 6 are collinear. The number of triangles formed by joining these points is

1 120

2 150

3 100

4 180

Explanation:

C We have,
6 points are collinear
Number of triangle formed if all 10 point are non-
collinear is $^{10} C_{3}$ .
No. of triangles formed
$^{10} C_{3} -^{6} C_{3}$
$= 120 - 20$
$= 100$

SRM JEEE-2010

Permutation and Combination

119258 A polygon has 44 diagonals. The number of sides is

1 0

2 11

3 12

4 9

Explanation:

B Here,
Let the number of sides be $n$
$∴^{n} C_{2} - n = 44$
$\frac{n (n - 1)}{2} - n = 44$
$\Rightarrow n^{2} - n - 2 n = 88$
$\Rightarrow n^{2} - 3 n - 88 = 0$
$\Rightarrow (n - 11) (n + 8) = 0$
$\Rightarrow n = 11 (∵ n \neq 8)$
$∴ Number of sides = 11$
$∴$ Number of sides $= 11$

SRM JEEE-2013

Permutation and Combination

119259 930 Deepawali greeting cards are exchanged amongst the students of a class. If every student sends a card to every other student, then what is the number of students in the class?

1 31

2 29

3 43

4 24
[SRJMJEEE-2012]

Explanation:

A :We have,
Number of deepawali greeting cards $= 930$
Let the number of students in the class be $n$ .
$∴$ Number of cards send by $n$ students
$= n (n - 1)$
According to question,
$n (n - 1) = 930$
$n^{2} - n - 930 = 0$
$(n - 31) (n + 30) = 0$
$n = 31$
$∴ No. of students in class = 31 (∵ n \neq - 30)$

Permutation and Combination

119260 In a group of 8 girls, two girls are sisters. The
number of ways in which the girls can sit so
that two sisters are not sitting together is

1 4820

2 1410

3 2830

4 none of these

Explanation:

D Consider the arrangement by taking two girls
together as one and hence the 7 girls can now be
arranged in $7! = 5040$
$∴$ Total ways in which two girls sit together
$= 5040 \times 2 = 10080$
The required no. of ways $=$ the number of ways in which 8 girls can sit - the no. of ways in which two sisters are together
$= 8! - (2) 7! = 40320 - 2 \times 5040$
$= 40320 - 10080 = 30240$

SRM JEEE-2014

Permutation and Combination

119261 If the total number of $m$ elements subsets of the set $A = {a_{1}, a_{2}, a_{3}, \dots . a_{n}}$ is $λ$ times the number of 3 elements subsets containing $a_{4}$ , then $n$ is

1

(m - 1) λ

2

m λ

3

(m + 1) λ

4 0

Explanation:

B Here From set of $n$ element selecting a subset of $m$ element $=^{n} C_{m}$
Total number of subsets of $A$ each containing the element $a_{4} =^{n - 1} C_{m - 1}$
Thus, according to question, $^{n} C_{m} = λ .^{n - 1} C_{m - 1}$
$\Rightarrow \frac{n}{m} \cdot^{n - 1} C_{m - 1} = λ \cdot^{n - 1} C_{m - 1}$
$\Rightarrow λ = \frac{n}{m}$
$\Rightarrow n = m λ .$

BITSAT-2007

Permutation and Combination

119256 There are 10 points in a plane, out of these 10 points 6 are collinear. The number of triangles formed by joining these points is

1 120

2 150

3 100

4 180

Explanation:

C We have,
6 points are collinear
Number of triangle formed if all 10 point are non-
collinear is $^{10} C_{3}$ .
No. of triangles formed
$^{10} C_{3} -^{6} C_{3}$
$= 120 - 20$
$= 100$

SRM JEEE-2010

Permutation and Combination

119258 A polygon has 44 diagonals. The number of sides is

1 0

2 11

3 12

4 9

Explanation:

B Here,
Let the number of sides be $n$
$∴^{n} C_{2} - n = 44$
$\frac{n (n - 1)}{2} - n = 44$
$\Rightarrow n^{2} - n - 2 n = 88$
$\Rightarrow n^{2} - 3 n - 88 = 0$
$\Rightarrow (n - 11) (n + 8) = 0$
$\Rightarrow n = 11 (∵ n \neq 8)$
$∴ Number of sides = 11$
$∴$ Number of sides $= 11$

SRM JEEE-2013

Permutation and Combination

119259 930 Deepawali greeting cards are exchanged amongst the students of a class. If every student sends a card to every other student, then what is the number of students in the class?

1 31

2 29

3 43

4 24
[SRJMJEEE-2012]

Explanation:

A :We have,
Number of deepawali greeting cards $= 930$
Let the number of students in the class be $n$ .
$∴$ Number of cards send by $n$ students
$= n (n - 1)$
According to question,
$n (n - 1) = 930$
$n^{2} - n - 930 = 0$
$(n - 31) (n + 30) = 0$
$n = 31$
$∴ No. of students in class = 31 (∵ n \neq - 30)$

Permutation and Combination

119260 In a group of 8 girls, two girls are sisters. The
number of ways in which the girls can sit so
that two sisters are not sitting together is

1 4820

2 1410

3 2830

4 none of these

Explanation:

D Consider the arrangement by taking two girls
together as one and hence the 7 girls can now be
arranged in $7! = 5040$
$∴$ Total ways in which two girls sit together
$= 5040 \times 2 = 10080$
The required no. of ways $=$ the number of ways in which 8 girls can sit - the no. of ways in which two sisters are together
$= 8! - (2) 7! = 40320 - 2 \times 5040$
$= 40320 - 10080 = 30240$

SRM JEEE-2014

Permutation and Combination

119261 If the total number of $m$ elements subsets of the set $A = {a_{1}, a_{2}, a_{3}, \dots . a_{n}}$ is $λ$ times the number of 3 elements subsets containing $a_{4}$ , then $n$ is

1

(m - 1) λ

2

m λ

3

(m + 1) λ

4 0

Explanation:

B Here From set of $n$ element selecting a subset of $m$ element $=^{n} C_{m}$
Total number of subsets of $A$ each containing the element $a_{4} =^{n - 1} C_{m - 1}$
Thus, according to question, $^{n} C_{m} = λ .^{n - 1} C_{m - 1}$
$\Rightarrow \frac{n}{m} \cdot^{n - 1} C_{m - 1} = λ \cdot^{n - 1} C_{m - 1}$
$\Rightarrow λ = \frac{n}{m}$
$\Rightarrow n = m λ .$

BITSAT-2007

Permutation and Combination

119256 There are 10 points in a plane, out of these 10 points 6 are collinear. The number of triangles formed by joining these points is

1 120

2 150

3 100

4 180

Explanation:

C We have,
6 points are collinear
Number of triangle formed if all 10 point are non-
collinear is $^{10} C_{3}$ .
No. of triangles formed
$^{10} C_{3} -^{6} C_{3}$
$= 120 - 20$
$= 100$

SRM JEEE-2010

Permutation and Combination

119258 A polygon has 44 diagonals. The number of sides is

1 0

2 11

3 12

4 9

Explanation:

B Here,
Let the number of sides be $n$
$∴^{n} C_{2} - n = 44$
$\frac{n (n - 1)}{2} - n = 44$
$\Rightarrow n^{2} - n - 2 n = 88$
$\Rightarrow n^{2} - 3 n - 88 = 0$
$\Rightarrow (n - 11) (n + 8) = 0$
$\Rightarrow n = 11 (∵ n \neq 8)$
$∴ Number of sides = 11$
$∴$ Number of sides $= 11$

SRM JEEE-2013

Permutation and Combination

119259 930 Deepawali greeting cards are exchanged amongst the students of a class. If every student sends a card to every other student, then what is the number of students in the class?

1 31

2 29

3 43

4 24
[SRJMJEEE-2012]

Explanation:

A :We have,
Number of deepawali greeting cards $= 930$
Let the number of students in the class be $n$ .
$∴$ Number of cards send by $n$ students
$= n (n - 1)$
According to question,
$n (n - 1) = 930$
$n^{2} - n - 930 = 0$
$(n - 31) (n + 30) = 0$
$n = 31$
$∴ No. of students in class = 31 (∵ n \neq - 30)$

Permutation and Combination

119260 In a group of 8 girls, two girls are sisters. The
number of ways in which the girls can sit so
that two sisters are not sitting together is

1 4820

2 1410

3 2830

4 none of these

Explanation:

D Consider the arrangement by taking two girls
together as one and hence the 7 girls can now be
arranged in $7! = 5040$
$∴$ Total ways in which two girls sit together
$= 5040 \times 2 = 10080$
The required no. of ways $=$ the number of ways in which 8 girls can sit - the no. of ways in which two sisters are together
$= 8! - (2) 7! = 40320 - 2 \times 5040$
$= 40320 - 10080 = 30240$

SRM JEEE-2014

Permutation and Combination

119261 If the total number of $m$ elements subsets of the set $A = {a_{1}, a_{2}, a_{3}, \dots . a_{n}}$ is $λ$ times the number of 3 elements subsets containing $a_{4}$ , then $n$ is

1

(m - 1) λ

2

m λ

3

(m + 1) λ

4 0

Explanation:

B Here From set of $n$ element selecting a subset of $m$ element $=^{n} C_{m}$
Total number of subsets of $A$ each containing the element $a_{4} =^{n - 1} C_{m - 1}$
Thus, according to question, $^{n} C_{m} = λ .^{n - 1} C_{m - 1}$
$\Rightarrow \frac{n}{m} \cdot^{n - 1} C_{m - 1} = λ \cdot^{n - 1} C_{m - 1}$
$\Rightarrow λ = \frac{n}{m}$
$\Rightarrow n = m λ .$

BITSAT-2007

Permutation and Combination

119256 There are 10 points in a plane, out of these 10 points 6 are collinear. The number of triangles formed by joining these points is

1 120

2 150

3 100

4 180

Explanation:

C We have,
6 points are collinear
Number of triangle formed if all 10 point are non-
collinear is $^{10} C_{3}$ .
No. of triangles formed
$^{10} C_{3} -^{6} C_{3}$
$= 120 - 20$
$= 100$

SRM JEEE-2010

Permutation and Combination

119258 A polygon has 44 diagonals. The number of sides is

1 0

2 11

3 12

4 9

Explanation:

B Here,
Let the number of sides be $n$
$∴^{n} C_{2} - n = 44$
$\frac{n (n - 1)}{2} - n = 44$
$\Rightarrow n^{2} - n - 2 n = 88$
$\Rightarrow n^{2} - 3 n - 88 = 0$
$\Rightarrow (n - 11) (n + 8) = 0$
$\Rightarrow n = 11 (∵ n \neq 8)$
$∴ Number of sides = 11$
$∴$ Number of sides $= 11$

SRM JEEE-2013

Permutation and Combination

119259 930 Deepawali greeting cards are exchanged amongst the students of a class. If every student sends a card to every other student, then what is the number of students in the class?

1 31

2 29

3 43

4 24
[SRJMJEEE-2012]

Explanation:

A :We have,
Number of deepawali greeting cards $= 930$
Let the number of students in the class be $n$ .
$∴$ Number of cards send by $n$ students
$= n (n - 1)$
According to question,
$n (n - 1) = 930$
$n^{2} - n - 930 = 0$
$(n - 31) (n + 30) = 0$
$n = 31$
$∴ No. of students in class = 31 (∵ n \neq - 30)$

Permutation and Combination

119260 In a group of 8 girls, two girls are sisters. The
number of ways in which the girls can sit so
that two sisters are not sitting together is

1 4820

2 1410

3 2830

4 none of these

Explanation:

D Consider the arrangement by taking two girls
together as one and hence the 7 girls can now be
arranged in $7! = 5040$
$∴$ Total ways in which two girls sit together
$= 5040 \times 2 = 10080$
The required no. of ways $=$ the number of ways in which 8 girls can sit - the no. of ways in which two sisters are together
$= 8! - (2) 7! = 40320 - 2 \times 5040$
$= 40320 - 10080 = 30240$

SRM JEEE-2014

Permutation and Combination

119261 If the total number of $m$ elements subsets of the set $A = {a_{1}, a_{2}, a_{3}, \dots . a_{n}}$ is $λ$ times the number of 3 elements subsets containing $a_{4}$ , then $n$ is

1

(m - 1) λ

2

m λ

3

(m + 1) λ

4 0

Explanation:

B Here From set of $n$ element selecting a subset of $m$ element $=^{n} C_{m}$
Total number of subsets of $A$ each containing the element $a_{4} =^{n - 1} C_{m - 1}$
Thus, according to question, $^{n} C_{m} = λ .^{n - 1} C_{m - 1}$
$\Rightarrow \frac{n}{m} \cdot^{n - 1} C_{m - 1} = λ \cdot^{n - 1} C_{m - 1}$
$\Rightarrow λ = \frac{n}{m}$
$\Rightarrow n = m λ .$

BITSAT-2007

Permutation and Combination

119256 There are 10 points in a plane, out of these 10 points 6 are collinear. The number of triangles formed by joining these points is

1 120

2 150

3 100

4 180

Explanation:

C We have,
6 points are collinear
Number of triangle formed if all 10 point are non-
collinear is $^{10} C_{3}$ .
No. of triangles formed
$^{10} C_{3} -^{6} C_{3}$
$= 120 - 20$
$= 100$

SRM JEEE-2010

Permutation and Combination

119258 A polygon has 44 diagonals. The number of sides is

1 0

2 11

3 12

4 9

Explanation:

B Here,
Let the number of sides be $n$
$∴^{n} C_{2} - n = 44$
$\frac{n (n - 1)}{2} - n = 44$
$\Rightarrow n^{2} - n - 2 n = 88$
$\Rightarrow n^{2} - 3 n - 88 = 0$
$\Rightarrow (n - 11) (n + 8) = 0$
$\Rightarrow n = 11 (∵ n \neq 8)$
$∴ Number of sides = 11$
$∴$ Number of sides $= 11$

SRM JEEE-2013

Permutation and Combination

119259 930 Deepawali greeting cards are exchanged amongst the students of a class. If every student sends a card to every other student, then what is the number of students in the class?

1 31

2 29

3 43

4 24
[SRJMJEEE-2012]

Explanation:

A :We have,
Number of deepawali greeting cards $= 930$
Let the number of students in the class be $n$ .
$∴$ Number of cards send by $n$ students
$= n (n - 1)$
According to question,
$n (n - 1) = 930$
$n^{2} - n - 930 = 0$
$(n - 31) (n + 30) = 0$
$n = 31$
$∴ No. of students in class = 31 (∵ n \neq - 30)$

Permutation and Combination

119260 In a group of 8 girls, two girls are sisters. The
number of ways in which the girls can sit so
that two sisters are not sitting together is

1 4820

2 1410

3 2830

4 none of these

Explanation:

D Consider the arrangement by taking two girls
together as one and hence the 7 girls can now be
arranged in $7! = 5040$
$∴$ Total ways in which two girls sit together
$= 5040 \times 2 = 10080$
The required no. of ways $=$ the number of ways in which 8 girls can sit - the no. of ways in which two sisters are together
$= 8! - (2) 7! = 40320 - 2 \times 5040$
$= 40320 - 10080 = 30240$

SRM JEEE-2014

Permutation and Combination

119261 If the total number of $m$ elements subsets of the set $A = {a_{1}, a_{2}, a_{3}, \dots . a_{n}}$ is $λ$ times the number of 3 elements subsets containing $a_{4}$ , then $n$ is

1

(m - 1) λ

2

m λ

3

(m + 1) λ

4 0

Explanation:

B Here From set of $n$ element selecting a subset of $m$ element $=^{n} C_{m}$
Total number of subsets of $A$ each containing the element $a_{4} =^{n - 1} C_{m - 1}$
Thus, according to question, $^{n} C_{m} = λ .^{n - 1} C_{m - 1}$
$\Rightarrow \frac{n}{m} \cdot^{n - 1} C_{m - 1} = λ \cdot^{n - 1} C_{m - 1}$
$\Rightarrow λ = \frac{n}{m}$
$\Rightarrow n = m λ .$

BITSAT-2007