Ask & Answer

Ask & Answer: India's Largest Education Community

1000+ExpertsQuick ResponsesReliable Answers

Your Question

Edit

Add relevant tags to get quick responses. Cancel Post

All Questions

New Question

9 months ago

Maths NCERT Exemplar Solutions Class 11th Chapter Thirteen Exemplar Solution

Kindly consider the following

$l i m_{x \to - 3} \frac{x^{3} + 27}{x^{5} + 243}$

0 Follower 3 Views

alok kumar singh

Contributor-Level 10

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

Sol:

$\begin{array}{l} G i v e n t h a t \underset{x \to - 3}{l i m} \frac{x^{3} + 27}{x^{5} + 243} \\ D i v i d i n g t h e n u m e r a t o r a n d denominator, b y x - 3 w e g e t \\ = \underset{x \to - 3}{l i m} \frac{\frac{x^{3} + {(3)}^{3}}{x - 3}}{\frac{x^{5} + {(3)}^{5}}{x - 3}} = \frac{\underset{x \to - 3}{l i m} (\frac{x^{3} - {(- 3)}^{3}}{x - 3})}{\underset{x \to - 3}{l i m} (\frac{x^{5} - {(- 3)}^{5}}{x - 3})} [? \underset{x \to a}{l i m} \frac{f (x)}{g (x)} = \frac{\underset{x \to a}{l i m} f (x)}{\underset{x \to a}{l i m} g (x)}] \\ = \frac{3 {(- 3)}^{3 - 1}}{5 {(- 3)}^{5 - 1}} [? \underset{x \to a}{l i m} \frac{x^{n} - a^{n}}{x - a} = n . a^{n - 1}] \\ = \frac{3 \times {(- 3)}^{2}}{5 \times {(- 3)}^{4}} = \frac{1}{5 \times 3} = \frac{1}{15} \end{array}$

0 0

New Question

9 months ago

Maths NCERT Exemplar Solutions Class 11th Chapter Thirteen Exemplar Solution

Kindly consider the following

$l i m_{x \to 0} \frac{\sqrt[]{1 + x^{3}} - \sqrt[]{1 - x^{3}}}{x^{2}}$

0 Follower 4 Views

alok kumar singh

Contributor-Level 10

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

Sol:

$\begin{array}{l} G i v e n t h a t \underset{x \to 0}{l i m} \frac{\sqrt[]{1 + x^{3}} - \sqrt[]{1 - x^{3}}}{x^{2}} \\ R a t i o n a l i z i n g t h e denominator, w e g e t \\ = \underset{x \to 0}{l i m} \frac{\sqrt[]{1 + x^{3}} - \sqrt[]{1 - x^{3}}}{x^{2}} \times \frac{\sqrt[]{1 + x^{3}} + \sqrt[]{1 - x^{3}}}{\sqrt[]{1 + x^{3}} + \sqrt[]{1 - x^{3}}} \\ = \underset{x \to 0}{l i m} \frac{(1 + x^{3}) - (1 - x^{3})}{x^{2} [\sqrt[]{1 + x^{3}} + \sqrt[]{1 - x^{3}}]} = \underset{x \to 0}{l i m} \frac{1 + x^{3} - 1 + x^{3}}{x^{2} [\sqrt[]{1 + x^{3}} + \sqrt[]{1 - x^{3}}]} \\ = \underset{x \to 0}{l i m} \frac{2 x^{3}}{x^{2} [\sqrt[]{1 + x^{3}} + \sqrt[]{1 - x^{3}}]} = \underset{x \to 0}{l i m} \frac{2 x}{\sqrt[]{1 + x^{3}} + \sqrt[]{1 - x^{3}}} = 0 \end{array}$

0 0

New Question

9 months ago

Diploma Engineering

What are the placements like for top Diploma in Engineering colleges in Mumbai?

0 Follower 4 Views

Aneena Abraham

Contributor-Level 10

Hi, please refer to the table below for the highest Return on Investment offered by the best Mumbai Diploma colleges for Engineering to their students in the form of placement package:

College Name	Tuition Fee	Annual Median Package
IIM Mumbai Placement	INR 15 lakh	INR 21.7 LPA
TISS Placement	INR 36,000 – INR 1.08 lakh	INR 1.5 LPA

0 0

New Question

9 months ago

Maths NCERT Exemplar Solutions Class 11th Chapter Thirteen Exemplar Solution

Kindly consider the following

$l i m_{x \to 3} \frac{x^{7} - 2 x^{5} - 1}{x^{3} + 3 x^{2} + 2}$

0 Follower 3 Views

alok kumar singh

Contributor-Level 10

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

Sol:

$\begin{array}{l} G i v e n t h a t \underset{x \to 1}{l i m} \frac{x^{7} - 2 x^{5} - 1}{x^{3} + 3 x^{2} + 2} [\frac{0}{0} f o r m] \\ = \underset{x \to 1}{l i m} \frac{x^{7} - x^{5} - x^{5} - 1}{x^{3} - x^{2} - 2 x^{2} + 2} = \underset{x \to 1}{l i m} \frac{x^{5} (x^{2} - 1) - 1 (x^{5} - 1)}{x^{2} (x - 1) - 2 (x^{2} - 1)} \\ D i v i d i n g t h e n u m e r a t o r a n d denominator b y (x - 1) w e g e t \\ = \underset{x \to 1}{l i m} \frac{x^{5} (\frac{x^{2} - 1}{x - 1}) - 1 (\frac{x^{5} - 1}{x - 1})}{x^{2} (\frac{x - 1}{x - 1}) - 2 (\frac{x^{2} - 1}{x - 1})} = \frac{\underset{x \to 1}{l i m} x^{5} (x + 1) - \underset{x \to 1}{l i m} (\frac{x^{5} - {(1)}^{5}}{x - 1})}{\underset{x \to 1}{l i m} x^{2} - 1 - 2 \underset{x \to 1}{l i m} (x + 1)} \\ = \frac{1 (2) - 5 . {(1)}^{5 - 1}}{1 - 2 (2)} = \frac{2 - 5}{1 - 4} = \frac{- 3}{- 3} = 1 \end{array}$

0 0

New Question

9 months ago

Indian Institute of Technology, BHU, Varanasi

What is the last date for IIT BHU Varanasi admission 2025?

0 Follower 6 Views

abhishek gaurav

Contributor-Level 9

The admission of IIT BHU Varanasi are handled through JoSAA for BTech and COAP for MTech, and they follow national exam timelines. The exact dates will depend on the schedules of these exams. Generally, final seat allotments close by August for most UG courses. Candidates are advised to track the official JoSAA or IIT BHU website regularly for exact deadlines.

0 0

New Question

9 months ago

Maths NCERT Exemplar Solutions Class 11th Chapter Thirteen Exemplar Solution

Kindly consider the following

$l i m_{x \to \sqrt[]{2}} \frac{x^{4} - 4}{x^{2} + 3 \sqrt[]{2} x - 8}$

0 Follower 3 Views

alok kumar singh

Contributor-Level 10

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

Sol:

$\begin{array}{l} G i v e n t h a t \underset{x \to \sqrt[]{2}}{l i m} \frac{x^{4} - 4}{x^{2} + 3 \sqrt[]{2} x - 8} \\ = \underset{x \to \sqrt[]{2}}{l i m} \frac{(x^{2} - 2) (x^{2} + 2)}{x^{2} + 4 \sqrt[]{2} x - \sqrt[]{2} x - 8} \\ = \underset{x \to \sqrt[]{2}}{l i m} \frac{(x + \sqrt[]{2}) (x - \sqrt[]{2}) (x^{2} + 2)}{x (x + 4 \sqrt[]{2}) - \sqrt[]{2} (x + 4 \sqrt[]{2})} \\ = \underset{x \to \sqrt[]{2}}{l i m} \frac{(x + \sqrt[]{2}) (x - \sqrt[]{2}) (x^{2} + 2)}{(x + 4 \sqrt[]{2}) (x - \sqrt[]{2})} = \underset{x \to \sqrt[]{2}}{l i m} \frac{(x + \sqrt[]{2}) (x^{2} + 2)}{(x + 4 \sqrt[]{2})} \\ T a k i n g, w e h a v e \\ = \frac{(\sqrt[]{2} + \sqrt[]{2}) (2 + 2)}{\sqrt[]{2} + 4 \sqrt[]{2}} = \frac{2 \sqrt[]{2} \times 4}{5 \sqrt[]{2}} = \frac{8}{5} . \end{array}$

0 0

New Question

9 months ago

Maths NCERT Exemplar Solutions Class 11th Chapter Fourteen Exemplar Solution

Form the biconditional statement $p \leftrightarrow q$ , where:

$i. p$ : The unit digit of an integer is zero.

It is divisible by 5.

$ii. p$ : A natural number $n$ is odd.

$q$ : Natural number $n$ is not divisible by 2.

$iii. p$ : A triangle is an equilateral triangle.

$q$ : All three sides of a triangle are equal.

0 Follower 8 Views

Payal Gupta

Contributor-Level 10

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

$\begin{array}{l} (i) p \leftrightarrow q : U n i t d i g i t o f a n integer i s z e r o i f a n d o n l y i f i t i s d i v i s i b l e b y 5 . \\ (i i) p \leftrightarrow q : A n a t u r a l n u m b e r i s o d d i f a n d o n l y i f i t i s n o t d i v i s i b l e b y 2 . \\ (i i i) p \leftrightarrow q : A t r i a n g l e i s a n e q u i l a t e r a l t r i a n g l e i f a n d o n l y i f a l l t h r e e s i d e s o f t r i a n g l e \\ a r e e q u a l . \end{array}$

0 0

New Question

9 months ago

School of Economics London School of Economics and Political Science

What is the application fee for international students at London School of Economics?

0 Follower 18 Views

Nishtha Sharma

Contributor-Level 10

London School of Economics application fee for international students for both UG and PG programme are listed below:

Type of Program	Deadline
UG	GBP 28.95 (INR 3,561.99)
PG	GBP 95 (INR 11,688)

0 0

New Question

9 months ago

West Bengal Design

When will the admissions for BDes courses at INSD Kolkata 2025 start?

0 Follower 1 View

Saurabh Khanduri

Contributor-Level 10

The admissions for BDes courses at INSD Kolkata for the year 2025 ar already open. Typically, admissions into INSD Kolkata starts at the beginning of May each year. Students who wishto apply for a BDes course at INSD Kolkata are advised to do so before the end of July.

0 0

New Question

9 months ago

Diploma Engineering

What are the top government Diploma in Engineering colleges in Mumbai?

0 Follower 2 Views

Aneena Abraham

Contributor-Level 10

Government Diploma Engineering colleges in Mumbai have limited seats with tough competition and admission are based on merit or counselling. Listed below are the top colleges with tuition fees -

Public/Government Colleges	Tuition Fee
ICTM Admission	INR 30,000
Veermata Jijabai Technological Institute Admission	INR 18,000 – INR 23,360
Government Polytechnic Admission	INR 18,000
SNDT College Admission	INR 45,420
TISS Admission	INR 1.08 lakh

Source: official site and may vary.

0 0

New Question

9 months ago

Maths NCERT Exemplar Solutions Class 11th Chapter Thirteen Exemplar Solution

Kindly consider the following

$l i m_{x \to 2} \frac{x^{2} - 4}{\sqrt[]{3 x - 2} - \sqrt[]{x + 2}}$

0 Follower 3 Views

alok kumar singh

Contributor-Level 10

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

Sol:

$\begin{array}{l} G i v e n t h a t \underset{x \to 2}{l i m} \frac{x^{2} - 4}{\sqrt[]{3 x - 2} - \sqrt[]{x + 2}} \\ R a t i o n a l i z i n g t h e denominator w e g e t \\ = \underset{x \to 2}{l i m} \frac{(x - 2) (x + 2)}{\sqrt[]{3 x - 2} - \sqrt[]{x + 2}} \times \frac{\sqrt[]{3 x - 2} + \sqrt[]{x + 2}}{\sqrt[]{3 x - 2} + \sqrt[]{x + 2}} \\ = \underset{x \to 2}{l i m} \frac{(x - 2) (x + 2) (\sqrt[]{3 x - 2} + \sqrt[]{x + 2})}{3 x - 2 - x - 2} \\ = \underset{x \to 2}{l i m} \frac{(x - 2) (x + 2) (\sqrt[]{3 x - 2} + \sqrt[]{x + 2})}{2 x - 4} \\ = \underset{x \to 2}{l i m} \frac{(x - 2) (x + 2) (\sqrt[]{3 x - 2} + \sqrt[]{x + 2})}{2 (x - 2)} = \underset{x \to 2}{l i m} \frac{(x + 2) (\sqrt[]{3 x - 2} + \sqrt[]{x + 2})}{2} \\ T a k i n g limits, w e h a v e \\ = \frac{(2 + 2) (\sqrt[]{6 - 2} + \sqrt[]{2 + 2})}{2} = \frac{4 (2 + 2)}{2} = 8 \end{array}$

0 0

New Question

9 months ago

Diploma Engineering

What are the top private Diploma in Engineering colleges in Mumbai?

0 Follower 4 Views

Aneena Abraham

Contributor-Level 10

Private colleges generally have higher tuition fees as compared to government colleges with more seats available and admission based merit basis.

Listed below are the top private Diploma Engineering colleges in Mumbai with tuition fees -

Private Colleges	Tuition Fee
K J Somaiya School of Engineering Admission	INR 20,000
Alamuri Ratnamala Institute of Engineering and Technology Admission	INR 18,000 – INR 79,450
Theem College of Engineering Admission	INR 18,000
B.P. Marine Academy Belapur Admission	INR 16 lakh
K J Somaiya Polytechnic College Admission	INR 18,000

Source: official site and may vary.

Hope this helps!

0 0

New Question

9 months ago

Maths NCERT Exemplar Solutions Class 11th Chapter Thirteen Exemplar Solution

Kindly consider the following

$l i m_{x \to 1} \frac{x^{4} - \sqrt[]{x}}{\sqrt[]{x} - 1}$

0 Follower 2 Views

alok kumar singh

Contributor-Level 10

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

Sol:

$\begin{array}{l} G i v e n t h a t \underset{x \to 1}{l i m} \frac{x^{4} - \sqrt[]{x}}{\sqrt[]{x} - 1} \\ = \underset{x \to 1}{l i m} \frac{\sqrt[]{x} [{(x)}^{7 / 2} - 1]}{\sqrt[]{x} - 1} \\ D i v i d i n g t h e n u m e r a t o r a n d denominator b y x - 1 \\ = \underset{x \to 1}{l i m} \frac{\frac{\sqrt[]{x} [{(x)}^{7 / 2} - {(1)}^{7 / 2}]}{x - 1}}{\frac{{(x)}^{1 / 2} - {(1)}^{1 / 2}}{x - 1}} \\ = \underset{x \to 1}{l i m} \frac{\frac{{(x)}^{7 / 2} - {(1)}^{7 / 2}}{x - 1}}{\frac{{(x)}^{1 / 2} - {(1)}^{1 / 2}}{x - 1}} \times \underset{x \to 1}{l i m} \sqrt[]{x} [? \underset{x \to a}{l i m} f (x) . g (x) = \underset{x \to a}{l i m} f (x) . \underset{x \to a}{l i m} g (x)] \\ = \frac{\frac{7}{2} {(1)}^{7 / 2 - 1}}{\frac{1}{2} {(1)}^{1 / 2 - 1}} \times \sqrt[]{1} = \frac{7 / 2}{1 / 2} = 7 . \end{array}$

0 0

New Question

9 months ago

Engineering Engineering in Mumbai

What is the eligibility criteria for admission to Diploma in Engineering in Mumbai?

0 Follower 4 Views

Aneena Abraham

Contributor-Level 10

Hi,

To get admission to diploma in engineering colleges in Mumbai, a candidate must have passed Class 10 from a recognised board with Mathematics and Science as compulsory subjects with an aggregate of 50-60% marks

There will be no entrance and admission is purely based on Class 12 merit.

Source: Official site and may vary.

0 0

New Question

9 months ago

Maths NCERT Exemplar Solutions Class 11th Chapter Fourteen Exemplar Solution

Rewrite each of the following statements in the form of conditional statements:

i. The square of an odd number is odd.

ii. You will get a sweet dish after the dinner.

iii. You will fail if you do not study.

iv. The unit digit of an integer is 0 or 5 if it is divisible by 5.

v. The square of a prime number is not prime.

vi. 2b = a + c if a, b, and c are in A.P.

0 Follower 2 Views

Payal Gupta

Contributor-Level 10

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

$\begin{array}{l} (i) I f p, t h e n q \Rightarrow I f t h e n u m b e r i s o d d, t h e n i t s s q u a r e i s o d d n u m b e r . \\ (i i) q i f p \Rightarrow I f t a k e t h e d i n n e r, t h e n y o u w i l l g e t s w e e t d i s h . \\ (i i i) p o n l y i f q \Rightarrow I f y o u d o n o t s t u d y, t h e n y o u w i l l f a i l . \\ (i v) p i s s u f f i c i e n t f o r q \Rightarrow I f a n integer i s d i v i s i b l e b y 5, t h e n i t s u n i t d i g i t s a r e 0 a n d 5 . \\ (v) q i s n e c e s s a r y f o r p \Rightarrow I f a n y n u m b e r i s p r i m e, t h e n i t s s q u a r e i s n o t p r i m e . \\ (v i) q i m p l i e s p \Rightarrow I f a, b, c a r e i n A . P t h e n 2 b = a + c . \end{array}$

0 0

New Question

9 months ago

Maths NCERT Exemplar Solutions Class 11th Chapter Thirteen Exemplar Solution

Kindly consider the following

$\underset{x \to a}{l i m} \frac{{(2 + x)}^{\frac{5}{2}} - {(a + 2)}^{\frac{5}{2}}}{(x - a)}$

0 Follower 2 Views

alok kumar singh

Contributor-Level 10

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

Sol:

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

0 0

New Question

9 months ago

Maths NCERT Exemplar Solutions Class 11th Chapter Thirteen Exemplar Solution

Kindly consider the following

$l i m_{x \to 1} \frac{{(1 + x)}^{6} - 1}{{(1 + x)}^{2} - 1}$

0 Follower 6 Views

alok kumar singh

Contributor-Level 10

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

Sol:

$\begin{array}{l} G i v e n t h a t \underset{x \to 0}{l i m} \frac{{(1 + x)}^{6} - 1}{{(1 + x)}^{2} - 1} \\ D i v i d i n g t h e n u m e r a t o r a n d denominator b y x, w e g e t \\ = \underset{x \to 0}{l i m} \frac{\frac{{(1 + x)}^{6} - 1}{x}}{\frac{{(1 + x)}^{2} - 1}{x}} \\ P u t 1 + x = y \Rightarrow x = y - 1 \\ = \underset{y - 1 \to 0}{l i m} \frac{\frac{y^{6} - {(1)}^{6}}{y - 1}}{\frac{y^{2} - {(1)}^{2}}{y - 1}} = \frac{\underset{y \to 1}{l i m} \frac{y^{6} - {(1)}^{6}}{y - 1}}{\underset{y \to 1}{l i m} \frac{y^{2} - {(1)}^{2}}{y - 1}} [\underset{x \to a}{l i m} \frac{f (x)}{g (x)} = \frac{\underset{x \to a}{l i m} f (x)}{\underset{x \to a}{l i m} g (x)}] \\ = \frac{6 . {(1)}^{6 - 1}}{2 . {(1)}^{2 - 1}} = \frac{6}{2} = 3 [\underset{x \to a}{l i m} \frac{x^{n} - a^{n}}{x - a} = n . a^{n - 1}] \end{array}$

0 0

New Question

9 months ago

Indian Institute of Technology, BHU, Varanasi

Which courses are offered by IIT BHU Varanasi?

0 Follower 11 Views

abhishek gaurav

Contributor-Level 9

IIT BHU Varanasi offers BTech, MTech, BPharma, MPharma, MSc, BArch, and PhD programmes. These courses span disciplines like Engineering, Science, Architecture, and Humanities. Dual-degree options are also available. The institute is affiliated with Banaras Hindu University.

0 0

New Question

9 months ago

Maharashtra Diploma

How many Diploma in Engineering colleges are there in Mumbai?

0 Follower 3 Views

Aneena Abraham

Contributor-Level 10

Hi,

There are about 90+ best Diploma in Engineering colleges in Mumbai of which 60+ colleges are owned privately, 10+ colleges are owned by the government, and 3 colleges are owned by semi-government institutions.

Admissions to majority of these colleges are based on merit. ICTM, VJTI, K J Somaiya School of Engineering, Government Polytechnic and B.P. Marine Academy Panvel are the top Diploma colleges in Mumbai for Engineering.

0 0

New Question

9 months ago

Institute of Technology, Nirma University Institute of Technology, Nirma University Placement

What is the trend of the highest package provided at the Institute of Technology, Nirma University?

0 Follower 5 Views