Exemplar Solution

a year ago

This is a True or False Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l} L e t u s c o n s i d e r a A . P, a, a + d, a + 2 d, \dots \\ ∴ a_{2} + a_{4} = a + d + a + 3 d = 2 a + 4 d = 2 a_{3} \\ \Rightarrow a_{3} = \frac{a_{2} + a_{4}}{2} \\ \frac{a_{2} + a_{4}}{2} = \frac{a + 2 d + a + 4 d}{2} = \frac{2 a + 6 d}{2} = a + 3 d = a_{4} \\ H e n c e, t h e g i v e n s t a t e m e n t i s T r u e . \end{array}$

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New answer posted•a year ago

If some or all of  $n$ objects are taken at a time, the number of combinations is $2^{n} - 1$ .

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Exemplar Solution Maths NCERT Exemplar Solutions Class 11th Chapter Nine

a year ago

This is a True or False Type Questions as classified in NCERT Exemplar

$\begin{array}{l} W h e n s o m e o r a l l o b j e c t s, t a k e n a t a t i m e, t h e n t h e n u m b e r o f s e l e c t i o n w i l l b e \\ {}_{n}{C_{1}} + {}_{n}{C_{2}} + {}_{n}{C_{3}} + \dots + {}_{n}{C_{n}} = 2^{n} - 1 [? {}_{n}{C_{0}} + {}_{n}{C_{1}} + {}_{n}{C_{2}} + {}_{n}{C_{3}} + \dots + {}_{n}{C_{n}} = 2^{n}] \\ H e n c e, t h e g i v e n s t a t e m e n t i s' T r u e' . \end{array}$

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New answer posted•a year ago

Every progression is a sequence but the converse, i.e., every sequence is also a progression, need not necessarily be true.

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a year ago

This is a True or False Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l} L e t u s c o n s i d e r a s e q u e n c e o f p r i m e n u m b e r s 2, 3, 5, 7, 11, \dots \\ I t i s c l e a r t h a t t h i s p r o g r e s s i o n i s a s e q u e n c e b u t s e q u e n c e i s n o t a p r o g r e s s i o n \\ b e c a u s e i t d o e s n o t f o l l o w a s p e c i f i c p a t t e r n . \\ H e n c e, t h e g i v e n s t a t e m e n t i s T r u e . \end{array}$

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New answer posted•a year ago

In a steamer, there are stalls for 12 animals, and there are horses, cows, and calves (not less than 12 each) ready to be shipped. They can be loaded in 312 ways.

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Exemplar Solution Maths NCERT Exemplar Solutions Class 11th Chapter Nine

a year ago

This is a True or False Type Questions as classified in NCERT Exemplar

$\begin{array}{l} T h e r e a r e 3 t y p e s o f a n i m a l s h o r s e s, c o w s a n d c a l v e s n o t l e s s t h a n 12 e a c h . \\ S o, n u m b e r o f w a y s o f l o a d i n g = 3^{12} \\ H e n c e, t h e g i v e n s t a t e m e n t i s' T r u e' . \end{array}$

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New answer posted•a year ago

State whether the statements are True or False:

Two sequences cannot be in both A.P. and G.P. together.

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a year ago

This is a True or False Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l} L e t u s c o n s i d e r a G . P, a, a r a n d a r^{2} \\ I f i t i s i n A . P t h e n a r - a \neq a r^{2} - a r \\ H e n c e, t h e g i v e n s t a t e m e n t i s T r u e . \end{array}$

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New answer posted•a year ago

In the permutations of  $n$ things, $r$  taken together, the number of permutations in which $m$ particular things occur together is $n - m P_{r} - m \times r P m$ .

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a year ago

This is a True or False Type Questions as classified in NCERT Exemplar

$\begin{array}{l} A r r a n g e m e n t o f n t h i n g s, r t a k e n a t a t i m e i n w h i c h m t h i n g s o c c u r t o g e t h e r . \\ S o, n u m b e r o f o b j e c t e x c l u d i n g m o b j e c t = (r - m) \\ H e r e, w e f i r s t a r r a n g e (r - m + 1) o b j e c t \\ ∴ N u m b e r o f a r r a n g e m e n t s = (r - m + 1)! \\ m o b j e c t s c a n b e a r r a n g e d i n m! w a y s \\ S o, t h e r e q u i r e d n u m b e r o f a r r a n g e m e n t s = (r - m + 1)! \times m! \\ H e n c e, t h e g i v e n s t a t e m e n t i s' F a l s e' . \end{array}$

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New answer posted•a year ago

Three letters can be posted in five letterboxes in 35 ways.

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a year ago

This is a True or False Type Questions as classified in NCERT Exemplar

$\begin{array}{l} G i v e n t h a t 3 l e t t e r s a r e t o b e p o s t e d i n 5 l e t t e r b o x e s \\ ∴ Required n u m b e r o f w a y s = 5^{3} = 125 \\ H e n c e, t h e g i v e n s t a t e m e n t i s' F a l s e' \end{array}$

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New answer posted•a year ago

There are 12 points in a plane of which 5 points are collinear, then the number of lines obtained by joining these points in pairs is ¹²C₂ - ⁵C₂.

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Exemplar Solution Maths NCERT Exemplar Solutions Class 11th Chapter Nine

a year ago

This is a True or False Type Questions as classified in NCERT Exemplar

$\begin{array}{l} Required n u m b e r o f l i n e s = {}_{12}{C_{2}} - {}_{5}{C_{2}} + 1 \\ H e n c e, t h e g i v e n s t a t e m e n t i s' F a l s e' \end{array}$

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New answer posted•a year ago

The sum of terms equidistant from the beginning and end in an A.P. is equal to . .

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Exemplar Solution Maths NCERT Exemplar Solutions Class 11th Chapter Nine

a year ago

This is a Fill in the blanks Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l} L e t A . P b e a, a + d, a + 2 d, a + 3 d, \dots, a + (n - 1) d \\ T a k i n g f i r s t a n d l a s t t e r m \\ a_{1} + a_{n} = a + a + (n - 1) d = 2 a + (n - 1) d \\ T a k i n g second a n d second l a s t t e r m \\ a_{2} + a_{n - 1} = (a + d) + [a + (n - 2) d] = 2 a + (n - 1) d = a_{1} + a_{n} \\ T a k i n g t h i r d f r o m t h e b e g i n n i n g a n d t h i r d f r o m t h e e n d \\ a_{3} + a_{n - 2} = (a + 2 d) + [a + (n - 3) d] = 2 a + (n - 1) d = a_{1} + a_{n} \\ F r o m t h e a b o v e p a t t e r n, w e o b s e r v e t h a t t h e s u m o f t e r m s equidistant f r o m t h e b e g i n n i n g \\ a n d t h e e n d i n a n A . P i s e q u a l t o t h e [f i r s t t e r m + l a s t t e r m] \\ H e n c e, t h e c o r r e c t v a l u e o f t h e f i l l e r i s [f i r s t t e r m + l a s t t e r m] . \end{array}$

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New answer posted•a year ago

For $a, b, c$ to be in G.P., the value of $\frac{a - b}{b - c}$ is equal to . .

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