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New answer posted

a year ago

Maths Maths NCERT Exemplar Solutions Class 11th Chapter Thirteen

Kindly consider the following
$l i m_{x \to a} \frac{s i n x - s i n a}{\sqrt[]{x} - \sqrt[]{a}}$

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alok kumar singh

Contributor-Level 10

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

Sol:

$\begin{array}{l} G i v e n t h a t \underset{x \to a}{l i m} \frac{s i n x - s i n a}{\sqrt[]{x} - \sqrt[]{a}} \\ = \underset{x \to a}{l i m} \frac{s i n x - s i n a}{\sqrt[]{x} - \sqrt[]{a}} * \frac{\sqrt[]{x} + \sqrt[]{a}}{\sqrt[]{x} + \sqrt[]{a}} = \underset{x \to a}{l i m} \frac{(s i n x - s i n a) (\sqrt[]{x} + \sqrt[]{a})}{x - a} \\ = \underset{x \to a}{l i m} \frac{(2 c o s \frac{x + a}{2} . s i n \frac{x - a}{2}) (\sqrt[]{x} + \sqrt[]{a})}{x - a} [? s i n A - s i n B = 2 c o s \frac{A + B}{2} . s i n \frac{A - B}{2}] \\ = \underset{\frac{x - a}{2} \to 0}{l i m} (2 c o s \frac{x + a}{2} . \frac{s i n \frac{x - a}{2}}{2 * \frac{x - a}{2}}) (\sqrt[]{x} + \sqrt[]{a}) \\ = \underset{x \to a}{l i m} c o s (\frac{x + a}{2}) (\sqrt[]{x} + \sqrt[]{a}) [? \underset{\frac{x - a}{2} \to 0}{l i m} \frac{s i n \frac{x - a}{2}}{\frac{x - a}{2}} = 1] \\ T a k i n g, w e h a v e \\ = c o s (\frac{a + a}{2}) (\sqrt[]{a} + \sqrt[]{a}) = c o s a * 2 \sqrt[]{a} = 2 \sqrt[]{a} . c o s a \end{array}$

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New answer posted

a year ago

Maths Maths NCERT Exemplar Solutions Class 11th Chapter Thirteen

Kindly consider the following
$\underset{x \to 0}{l i m} \frac{s i n 2 x + 3 x}{2 x + t a n 3 x}$

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alok kumar singh

Contributor-Level 10

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

Sol:

$\begin{array}{l} G i v e n t h a t \underset{x \to 0}{l i m} \frac{s i n 2 x + 3 x}{2 x + t a n 3 x} \\ = \underset{x \to 0}{l i m} \frac{(\frac{s i n 2 x + 3 x}{2 x} * 2 x)}{(\frac{2 x + t a n 3 x}{3 x} * 3 x)} = \underset{x \to 0}{l i m} \frac{(\frac{s i n 2 x}{2 x} + \frac{3 x}{2 x}) * 2 x}{(\frac{2 x}{3 x} + \frac{t a n 3 x}{3 x}) * 3 x} \\ = \frac{(\underset{2 x \to 0}{l i m} \frac{s i n 2 x}{2 x} + \frac{3}{2})}{[\frac{2}{3} + \underset{3 x \to 0}{l i m} \frac{t a n 3 x}{3 x}]} * \frac{2}{3} [? \underset{x \to 0}{l i m} \frac{s i n x}{x} = 1] \\ = (\frac{1 + \frac{3}{2}}{\frac{2}{3} + 1}) * \frac{2}{3} [? \underset{x \to 0}{l i m} \frac{t a n x}{x} = 1] \\ = \frac{5 / 2}{5 / 3} * \frac{2}{3} = \frac{3}{2} * \frac{2}{3} = 1 \end{array}$

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New answer posted

a year ago

Maths Exemplar Solution

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

0 Follower 2 Views

alok kumar singh

Contributor-Level 10

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

Maths 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?

0 Follower 4 Views

Payal Gupta

Contributor-Level 10

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

Maths 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.

0 Follower 2 Views

Payal Gupta

Contributor-Level 10

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

Maths 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

0 Follower 3 Views

Payal Gupta

Contributor-Level 10

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

Maths 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.

0 Follower 2 Views

Payal Gupta

Contributor-Level 10

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

Maths 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.

0 Follower 2 Views

Payal Gupta

Contributor-Level 10

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

Maths 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.

0 Follower 2 Views

Payal Gupta

Contributor-Level 10

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

Maths 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.

0 Follower 5 Views

Payal Gupta

Contributor-Level 10

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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