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Maths NCERT Exemplar Solutions Class 11th Chapter Seven

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New answer posted

3 months ago

Maths NCERT Exemplar Solutions Class 11th Chapter Seven Exemplar Solution

The number of possible outcomes when a coin is tossed 6 times is:

(a) 36

(b) 64

(c) 12

(d) 32
0 Follower 3 Views

P
Payal Gupta

Contributor-Level 10

This is an Objective Type Questions as classified in NCERT Exemplar

W e     k n o w     t h a t     a     c o i n     h a s     H e a d     a n d     T a i l ( H , T ) ∴     W h e n     a     c o i n     i s     t o s s e d     6     t i m e s ,     t h e n     t h e P o s s i b l e     o u t c o m e = 2 6 = 6 4 H e n c e ,     t h e     c o r r e c t     o p t i o n     i s     ( b ) .

New answer posted

3 months ago

Maths NCERT Exemplar Solutions Class 11th Chapter Seven Exemplar Solution

If nC12 = nC8, then n is equal to:

(a) 20

(b) 12

(c) 6

(d) 30
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P
Payal Gupta

Contributor-Level 10

This is an Objective Type Questions as classified in NCERT Exemplar

G i v e n     t h a t : C 1 2 n = C 8 n ⇒                                     C n − 1 2 n = C 8 n                       [ ? C r n = C n − r n ] ⇒                                     n − 1 2 = 8 ⇒                                                         n = 8 + 1 2 = 2 0 H e n c e ,     t h e     c o r r e c t     o p t i o n     i s     ( a ) .

New answer posted

3 months ago

Maths NCERT Exemplar Solutions Class 11th Chapter Seven Exemplar Solution

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:

(i) No girls.

(ii) At least one boy and one girl.

(iii) At least three girls.
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P
Payal Gupta

Contributor-Level 10

This is a long answer type question as classified in NCERT Exemplar

W e     h a v e     4     g i r l s     a n d     7     b o y s     a n d     a     t e a m     o f     5     m e m b e r s     i s     t o     b e     s e l e c t e d . ( i ) I f     n o     g i r l     i s     s e l e c t e d ,     t h e n     a l l     t h e     5     m e m b e r s     a r e     t o     b e     s e l e c t e d               o u t     o f     7     b o y s     i . e .     C 5 7 = 7 ! 5 ! 2 ! = 7 * 6 . 5 ! 5 !   * 2 = 2 1     w a y s ( i i ) W h e n     a t l e a s t     o n e     b o y     a n d     o n e     g i r l     a r e     t o     b e     s e l e c t e d ,     t h e n             N u m b e r     o f     w a y s = C 1 4 * C 4 7 + C 2 4 * C 3 7 + C 3 4 * C 2 7 + C 4 4 * C 1 7                                       = 4 * 7 * 6 * 5 * 4 4 * 3 * 2 * 1 + 4 * 3 2 * 1 * 7 * 6 * 5 3 * 2 * 1 + 4 * 7 * 6 2 * 1 + 1 * 7                                       = 4 * 3 5 + 6 * 3 5 + 4 * 2 1 + 7 = 1 4 0 + 2 1 0 + 8 4 + 7 = 4 4 1     w a y s ( i i i ) W h e n     a t l e a s t     3     g i r l s     a r e     i n c l u d e d ,     t h e n               N u m b e r     o f     w a y s = C 3 4 * C 2 7 + C 4 4 * C 1 7                                       = 4 * 7 * 6 2 * 1 + 1 * 7 = 8 4 + 7 = 9 1     w a y s             H e n c e ,     t h e     r e q u i r e d     n u m b e r     o f     w a y s     a r e               ( i ) 2 1     w a y s                         ( i i ) 4 4 1     w a y s                 ( i i i ) 9 1     w a y s

New answer posted

3 months ago

Maths NCERT Exemplar Solutions Class 11th Chapter Seven Exemplar Solution

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 team be constituted?
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P
Payal Gupta

Contributor-Level 10

This is a long answer type question as classified in NCERT Exemplar

T o t a l     n u m b e r     o f     s t u d e n t s     i n     e a c h     c l a s s = 2 0 W e     h a v e     t o     s e l e c t     a t l e a s t     5     s t u d e n t s     f r o m     e a c h     c l a s s . W e     h a v e     t h e     f o l l o w i n g     c a s e s . ( i ) 5     s t u d e n t s     f r o m     X I     c l a s s     a n d     6     s t u d e n t s     f r o m     X I I     c l a s s ( i i ) 6     s t u d e n t s     f r o m     X I     c l a s s     a n d     5     s t u d e n t s     f r o m     X I I     c l a s s S o ,     n u m b e r     o f     w a y s     o f     s e l e c t i o n     o f     a     t e a m     o f     1 1     p l a y e r s                                                                                                     = C 5 2 0 * C 6 2 0 + C 6 2 0 * C 5 2 0 = 2 [ C 5 2 0 * C 6 2 0 ]             H e n c e ,     t h e     r e q u i r e d     w a y s     o f     s e l e c t i o n = 2 [ C 5 2 0 * C 6 2 0 ]

New answer posted

3 months ago

Maths NCERT Exemplar Solutions Class 11th Chapter Seven Exemplar Solution

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

(i) Include 2 particular players?

(ii) Exclude 2 particular players?
0 Follower 3 Views

P
Payal Gupta

Contributor-Level 10

This is a long answer type question as classified in NCERT Exemplar

G i v e n     t h a t     t h e     t o t a l     n u m b e r     o f     p l a y e r s = 1 6 W e     h a v e     t o     s e l e c t     1 1     p l a y e r s     o u t     o f     1 6     p l a y e r s . ( i ) I f     2     p l a y e r s     a r e     i n c l u d e d ,     t h e n     n u m b e r     o f     w a y s     o f     s e l e c t i o n = C 1 1 − 2 1 6 − 2 = C 9 1 4 ( i i ) I f     2     p l a y e r s     a r e     e x c l u d e d ,     t h e n     n u m b e r     o f     w a y s     o f     s e l e c t i o n = C 1 1 1 6 − 2 = C 1 1 1 4             H e n c e ,     t h e     r e q u i r e d     n u m b e r     o f     w a y s     o f     s e l e c t i o n     a r e               ( i ) C 9 1 4                         ( i i ) C 1 1 1 4

New answer posted

3 months ago

Maths NCERT Exemplar Solutions Class 11th Chapter Seven Exemplar Solution

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:

(i) They can be of any colour.

(ii) Two must be white and two red.

(iii) They must all be of the same colour.
0 Follower 4 Views

P
Payal Gupta

Contributor-Level 10

This is a long answer type question as classified in NCERT Exemplar

T o t a l     n u m b e r     o f     m a r b l e s = 6     w h i t e + 5     r e d = 1 1     m a r b l e s (i)Since,  we  have  to  draw  4  marbles  of  any  colour  from  the  11  marbles      ∴  Required  number  of  ways=C411 ( i i ) I f     2     m u s t     b e     w h i t e     a n d     2     m u s t     b e     r e d ,     t h e n     t h e     r e q u i r e d     n u m b e r     o f     w a y s = C 2 6 * C 2 5 ( i i i ) I f     a l l     t h e     4     m a r b l e s     a r e     o f     t h e     s a m e     c o l o u r ,     t h e n     t h e     r e q u i r e d     n u m b e r     o f     w a y s = C 4 6 + C 4 5                 H e n c e ,     t h e     r e q u i r e d     n u m b e r     o f     w a y s     a r e               ( i ) C 4 1 1               ( i i ) C 2 6 * C 2 5                 ( i i i ) C 4 6 + C 4 5

New answer posted

3 months ago

Maths NCERT Exemplar Solutions Class 11th Chapter Seven Exemplar Solution

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?
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P
Payal Gupta

Contributor-Level 10

This is a long answer type question as classified in NCERT Exemplar

Given  that  18  mice  were  placed  equally  in  two  experimental  groups  and o n e     c o n t r o l     g r o u p     i . e .     3     g r o u p s ∴     T h e     r e q u i r e d     n u m b e r     o f     a r r a n g e m e n t s = T o t a l     a r r a n g e m e n t s E q u a l l y     l i k e l y     a r r a n g e m e n t s                                                                                               = 1 8 ! 6 ! 6 ! 6 ! = 1 8 ! ( 6 ! ) 3 H e n c e ,     t h e     r e q u i r e d     a r r a n g e m e n t s = 1 8 ! ( 6 ! ) 3

New answer posted

3 months ago

Maths NCERT Exemplar Solutions Class 11th Chapter Seven Exemplar Solution

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

[Hint: Polygon of n sides has (nC2 – n) number of diagonals.]
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P
Payal Gupta

Contributor-Level 10

This is a short answer type question as classified in NCERT Exemplar

  G i v e n     t h a t     q u e s t i o n     n u m b e r     1     a n d     2     a r e     c o m p u l s o r y . ∴     T h e     r e m a i n i n g     q u e s t i o n s     a r e     5 − 2 = 3 L e t     n     b e     t h e     n u m b e r     o f     s i d e s     i n     a     p o l y g o n . Since,  Polygon  of  n  sides  has  (C2n−n)  number  of  diagonals ∴ C 2 n − n = 4 4 = n ! 2 ! ( n − 2 ) ! − n = 4 4 ⇒ n ( n − 1 ) ( n − 2 ) ! 2 . ( n − 2 ) ! − n = 4 4         ⇒ n ( n − 1 ) 2 − n = 4 4 ⇒ n 2 − n − 2 n 2 = 4 4             ⇒ n 2 − 3 n = 8 8             ⇒ n 2 − 3 n − 8 8 = 0 ⇒ n 2 − 1 1 n + 8 n − 8 8 = 0             ⇒ n ( n − 1 1 ) + 8 ( n − 1 1 ) = 0 ⇒ ( n − 1 1 ) ( n + 8 ) = 0           ∴     n = 1 1     a n d     n = − 8                 [ ? n ≠ − 8 ] S o ,     n = 1 1 H e n c e ,     t h e     r e q u i r e d     n u m b e r     o f     s i d e s = 1 1 .

New answer posted

3 months ago

Maths NCERT Exemplar Solutions Class 11th Chapter Seven Exemplar Solution

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

Contributor-Level 10

This is a short answer type question as classified in NCERT Exemplar

  G i v e n     t h a t     q u e s t i o n     n u m b e r     1     a n d     2     a r e     c o m p u l s o r y . ∴     T h e     r e m a i n i n g     q u e s t i o n s     a r e     5 − 2 = 3 T o t a l     n u m b e r     o f     q u e s t i o n s     t o     b e     a t t e m p t e d = 4     q u e s t i o n s     1     a n d     2     a r e     c o m p u l s o r y . S o     o n l y     2     q u e s t i o n s     a r e     t o     b e     d o n e     o u t     o f     3     q u e s t i o n s T h e r e f o r e     n u m b e r     o f     w a y s = C 2 3 = C 3 − 2 3 = C 1 3 = 3           [ ? C r n = C n − r n ] H e n c e ,     t h e     r e q u i r e d     n u m b e r     o f     w a y s = 3 .

New answer posted

3 months ago

Maths NCERT Exemplar Solutions Class 11th Chapter Seven Exemplar Solution

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?
0 Follower 3 Views

P
Payal Gupta

Contributor-Level 10

This is a short answer type question as classified in NCERT Exemplar

  I f     f i r s t     t w o     d i g i t s     i s     4 1 ,     t h e n     t h e     r e m a i n i n g     4     d i g i t s     c a n     b e     a r r a n g e d     i n     P 4 8     w a y s                                                   = 8 ! ( 8 − 4 ) ! = 8 ! 4 ! = 8 * 7 * 6 * 5 * 4 ! 4 ! = 1 6 8 0 S i m i l a r l y     f i r s t     t w o     d i g i t s     c a n     b e     4 2     o r     4 6     o r     6 2     o r     6 4 . ∴     T o t a l     n u m b e r     o f     t e l e p h o n e     n u m b e r s     h a v e     a l l     d i g i t s     d i s t i n c t = 5 * 1 6 8 0 = 8 4 0 0 H e n c e ,     t h e     r e q u i r e d     t e l e p h o n e     n u m b e r s = 8 4 0 0 .

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