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New answer posted•a year ago

Exemplar Solution Limits and Derivatives

Kindly consider the following
$l i m_{x \to \frac{π}{6}} \frac{\sqrt[]{3} s i n x - c o s x}{x - \frac{π}{6}}$

2 Views|Posted a year ago

Asked by Alok Kumar Singh

Answered by

Alok Kumar Singh | Contributor-Level 10

a year ago

This is a Short Answer Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l} G i v e n t h a t \underset{x \to \frac{π}{6}}{l i m} \frac{\sqrt[]{3} s i n x - c o s x}{x - \frac{π}{6}} \\ = \underset{x \to \frac{π}{6}}{l i m} \frac{2 [\frac{\sqrt[]{3}}{2} s i n x - \frac{1}{2} c o s x]}{x - \frac{π}{6}} = \underset{x \to \frac{π}{6}}{l i m} \frac{2 [c o s \frac{π}{6} s i n x - s i n \frac{π}{6} c o s x]}{x - \frac{π}{6}} \\ = \underset{x \to \frac{π}{6}}{l i m} \frac{2 s i n (x - \frac{π}{6})}{x - \frac{π}{6}} [? s i n (A - B) = s i n A c o s B - c o s A s i n B] \\ = 2 \underset{x \to \frac{π}{6}}{l i m} \frac{s i n (x - \frac{π}{6})}{x - \frac{π}{6}} = 2.1 = 2 [? \underset{x \to 0}{l i m} \frac{s i n x}{x} = 1] \end{array}$

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New answer posted•a year ago

Exemplar Solution Maths NCERT Exemplar Solutions Class 11th Chapter Fourteen

State whether the following sentences are statements or not:

(a) The angles opposite to equal sides of a triangle are equal.

(b) The moon is a satellite of earth.

(c) May God bless you!

(d) Asia is a continent.

(e) How are you?

4 Views|Posted a year ago

Asked by Payal Gupta

Answered by

Payal Gupta | Contributor-Level 10

a year ago

This is an Objective Type Questions as classified in NCERT Exemplar

$\begin{array}{l} (a) I t i s a s t a t e m e n t . \\ (b) I t i s a s t a t e m e n t . \\ (c) I t i s n o t a s t a t e m e n t . \\ (d) I t i s a s t a t e m e n t . \\ (e) I t i s n o t a s t a t e m e n t . \end{array}$

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New answer posted•a year ago

Exemplar Solution Maths NCERT Exemplar Solutions Class 11th Chapter Fourteen

Which of the following statement is a conjunction?

(a) Ram and Shyam are friends.

(b) Both Ram and Shyam are tall.

(c) Both Ram and Shyam are enemies.

(d) None of the above.

2 Views|Posted a year ago

Asked by Payal Gupta

Answered by

Payal Gupta | Contributor-Level 10

a year ago

This is an Objective Type Questions as classified in NCERT Exemplar

$\begin{array}{l} L e t t h e t w o s t a t e m e n t s p a n d q b e s i m p l e s t a t e m e n t s . I f t h e y a r e c o n n e c t e d w i t h a n d . \\ T h e n, t h e r e s u l t i n g c o m p o u n d s t a t e m e n t p a n d q i s c a l l e d a c o n j u c t i o n o f p a n d q . \\ H e n c e, t h e c o r r e c t o p t i o n i s (d) . \end{array}$

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New answer posted•a year ago

Exemplar Solution Maths NCERT Exemplar Solutions Class 11th Chapter Fourteen

Which of the following is not a negation of “A natural number is greater than zero”

(a) A natural number is not greater than zero.

(b) It is false that a natural number is greater than zero.

(c) It is false that a natural number is not greater than zero.

(d) None of the above

3 Views|Posted a year ago

Asked by Payal Gupta

Answered by

Payal Gupta | Contributor-Level 10

a year ago

This is an Objective Type Questions as classified in NCERT Exemplar

$\begin{array}{l} T h e n e g a t i o n o f t h e g i v e n s t a t e m e n t i s f a l s e . i . e ., I t i s f a l s e t h a t a n a t u r a l n u m b e r i s n o t \\ g r e a t e r t h a n z e r o . \\ H e n c e, t h e c o r r e c t o p t i o n i s (c) . \end{array}$

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New answer posted•a year ago

Exemplar Solution Maths NCERT Exemplar Solutions Class 11th Chapter Fourteen

The negation of the statement “The product of 3 and 4 is 9” is

(a) It is false that the product of 3 and 4 is 9.

(b) The product of 3 and 4 is 12.

(c) The product of 3 and 4 is not 12.

(d) It is false that the product of 3 and 4 is not 9.

2 Views|Posted a year ago

Asked by Payal Gupta

Answered by

Payal Gupta | Contributor-Level 10

a year ago

This is an Objective Type Questions as classified in NCERT Exemplar

$\begin{array}{l} T h e n e g a t i o n o f t h e g i v e n s t a t e m e n t i s f a l s e . i . e ., I t i s f a l s e t h a t t h e p r o d u c t o f 3 a n d 4 i s 9 . \\ H e n c e, t h e c o r r e c t o p t i o n i s (a) . \end{array}$

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New answer posted•a year ago

Exemplar Solution Maths NCERT Exemplar Solutions Class 11th Chapter Fourteen

Which of the following is the conditional p → q?

(a) q is sufficient for p.

(b) p is necessary for q.

(c) p only if q.

(d) if q, then p.

2 Views|Posted a year ago

Asked by Payal Gupta

Answered by

Payal Gupta | Contributor-Level 10

a year ago

This is an Objective Type Questions as classified in NCERT Exemplar

$\begin{array}{l} W e k n o w t h a t p \to q i s s a m e a s p o n l y i f q . \\ H e n c e, t h e c o r r e c t o p t i o n i s (c) . \end{array}$

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New answer posted•a year ago

Exemplar Solution Maths NCERT Exemplar Solutions Class 11th Chapter Fourteen

The contrapositive of statement ‘If Chandigarh is capital of Punjab, then Chandigarh is in India’ is

(a) If Chandigarh is not in India, then Chandigarh is not the capital of Punjab.

(b) If Chandigarh is in India, then Chandigarh is capital of Punjab.

(c) If Chandigarh is not capital of Punjab, then Chandigarh is not in India.

(d) If Chandigarh is capital of Punjab, then Chandigarh is not in India.

2 Views|Posted a year ago

Asked by Payal Gupta

Answered by

Payal Gupta | Contributor-Level 10

a year ago

This is an Objective Type Questions as classified in NCERT Exemplar

$\begin{array}{l} L e t p : C h a n d i g a r h i s c a p i t a l o f P u n j a b . \\ a n d q : C h a n d i g a r h i s i n I n d i a . \\ \sim p : C h a n d i g a r h i s n o t t h e c a p i t a l o f P u n j a b . \\ \sim q : C h a n d i g a r h i s n o t i n I n d i a . \\ I f (\sim q), t h e n (\sim p) \\ i . e . I f C h a n d i g a r h i s n o t i n I n d i a, t h e n C h a n d i g a r h i s n o t t h e c a p i t a l o f P u n j a b . \\ H e n c e, t h e c o r r e c t o p t i o n i s (a) . \end{array}$

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New answer posted•a year ago

Exemplar Solution Maths NCERT Exemplar Solutions Class 11th Chapter Fourteen

The statement “If x² is not even, then x is not even” is converse of the statement

(a)  If x² is odd, then x is even.

(b) If x is not even, then x² is not even.

(c) If x is even, then x² is even.

(d) If x is odd, then x² is even.

5 Views|Posted a year ago

Asked by Payal Gupta

Answered by

Payal Gupta | Contributor-Level 10

a year ago

This is an Objective Type Questions as classified in NCERT Exemplar

$\begin{array}{l} L e t p : x^{2} i s n o t e v e n . \\ a n d q : x i s n o t e v e n . \\ S o, t h e c o n v e r s e o f t h e s t a t e m e n t p \to q i s q \to p \\ i . e . I f x i s n o t e v e n, t h e n x^{2} i s n o t e v e n . \\ H e n c e, t h e c o r r e c t o p t i o n i s (b) . \end{array}$

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New answer posted•a year ago

Exemplar Solution Maths NCERT Exemplar Solutions Class 11th Chapter Fourteen

The contrapositive of the statement “If p, then q”, is

(a) If q, then p.

(b) If p, then ~ q.

(c) If ~ q, then ~ p.

(d) If ~ p, then ~ q.

2 Views|Posted a year ago

Asked by Payal Gupta

Answered by

Payal Gupta | Contributor-Level 10

a year ago

This is an Objective Type Questions as classified in NCERT Exemplar

$\begin{array}{l} H e r e t h e s t a t e m e n t i s " I f p, t h e n q " \\ i . e . p \to q \\ C o n t r a p o s i t i v e o f t h e s t a t e m e n t p \to q i s (\sim q) \to (\sim p) \\ i . e . I f \sim q, t h e n \sim p . \\ H e n c e, t h e c o r r e c t o p t i o n i s (c) . \end{array}$

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New answer posted•a year ago

Exemplar Solution Maths NCERT Exemplar Solutions Class 11th Chapter Fourteen

The converse of the statement “If sun is not shining, then sky is filled with clouds” is

(a) If sky is filled with clouds, then the sun is not shining.

(b) If sun is shining, then sky is filled with clouds.

(c) If sky is clear, then sun is shining.

(d) If sun is not shining, then sky is not filled with clouds.

4 Views|Posted a year ago

Asked by Payal Gupta

Answered by

Payal Gupta | Contributor-Level 10

a year ago

This is an Objective Type Questions as classified in NCERT Exemplar

$\begin{array}{l} L e t p : S u n i s n o t s h i n i n g . \\ q : S k y i s f i l l e d w i t h c l o u d s . \\ S o, t h e c o n v e r s e o f t h e s t a t e m e n t p \to q i s q \to p . \\ i . e ., I f S k y i s f i l l e d w i t h c l o u d s, t h e n t h e S u n i s n o t s h i n i n g . \\ H e n c e, t h e c o r r e c t o p t i o n i s (a) . \end{array}$

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