Tags Limits and Derivatives

Limits and Derivatives

Get insights from 93 questions on Limits and Derivatives, answered by students, alumni, and experts. You may also ask and answer any question you like about Limits and Derivatives

Follow Ask Question

Questions

Discussions

Active Users

Followers

New answer posted

a month ago

Limits and Derivatives Class 11th

The sum of the roots of the equation, $x + 1 - 2 l o g_{2} (3 + 2^{x}) + 2 l o g_{4} (10 - 2^{- x}) = 0,$ is :

0 Follower 2 Views

Vishal Baghel

Contributor-Level 10

$x + 1 - 2 l o g_{2} (3 + 2^{x}) + 2 l o g_{4} (10 - 2^{- x}) = 0$

$x + 1 + l o g_{2} [\frac{10 . 2^{x} - 1}{{(3 + 2^{x})}^{2}}] - x = 0$

${(2^{x})}^{2} - 14 . 2^{x} + 11 = 0$

2x + y

$x_{1} + x_{2} = l o g_{2} (49 - \frac{152}{4})$

$x_{1} + x_{2} = l o g_{2} 11$

0 0

New answer posted

3 months ago

Limits and Derivatives Ncert Solutions Maths class 11th

42. Find the derivative of the following functions:

(i)sin x cos x (ii) $s e c x$ (iii)5 sec x + 4 cosx

(iv) $c o s e c x$ (v)3cot x + 5 cosec x

(vi) $5 s i n x - 6 c o s x + 7$ (vii) $2 t a n x - 7 s e c x$

0 Follower 5 Views

alok kumar singh

Contributor-Level 10

(i) f(x)=sin x cos x

So, $f^{?} (x) = \underset{h ? 0}{l i m} \frac{f (x + h) ? f (x)}{h}$

$= \underset{h ? 0}{l i m} \frac{s i n (x + h) c o s (x + h) ? s i n x c o s x}{h}$

$= \underset{h ? 0}{l i m} \frac{1}{2 h} * [2 s i n (x + h) c o s (x + h) ? 2 s i n x c o s x]$

$= \underset{h ? 0}{l i m} \frac{1}{2 h} [s i n 2 (x + h) ? s i n 2 x]$

$= \underset{h ? 0}{l i m} \frac{1}{2 h} [2 c o s \frac{2 (x + h) + 2 x}{2} s i n \frac{2 (x + h) ? 2 x}{2}]$

$= \underset{h ? 0}{l i m} \frac{1}{h} [c o s (2 x + h) s i n h]$

$= \underset{h ? 0}{l i m} c o s (2 x + h) * \underset{h ? 0}{l i m} \frac{s i n h}{h}$

$= c o s (2 x + 0)$

$= c o s 2 x$

$(ii) f (x) = s e c x$

So, $f^{?} (x) = \underset{h ? 0}{l i m} \frac{f (x + h) ? f (x)}{h}$

$= \underset{h ? 0}{l i m} \frac{1}{h} [s e c (x + h) ? s e c x]$

$= \underset{h ? 0}{l i m} \frac{1}{h} [\frac{1}{c o s (x + h)} ? \frac{1}{c o s x}]$

$= \underset{h ? 0}{l i m} \frac{1}{h} [\frac{c o s x ? c o s (x + h)}{c o s (x + h) c o s x}]$

$= \underset{h ? 0}{l i m} \frac{1}{h} [\frac{? 2 s i n (\frac{x + x + h}{2}) s i n (\frac{x ? (x + h)}{2})}{c o s (x + h) c o s x}]$

$= \underset{h ? 0}{l i m} \frac{1}{h} [? \frac{2 s i n (\frac{2 x + h}{2}) s i n (? h / 2)}{c o s (x + h) c o s x}]$

$= \underset{h ? 0}{l i m} \frac{(? 1 s i n (\frac{2 x + h}{2})}{c o s (x + h) c o s x} * \underset{h ? 0}{l i m} (? 1) \frac{s i n h / 2}{h / 2}$

$= \frac{s i n x}{c o s x ? c o s x} * 1$

$= t a n x ? s e c x .$

(iii) Given f(x)=5 sec x+4 cosx.

So, $f^{?} (x) = \underset{h ? 0}{l i m} \frac{f (x + h) ? f (x)}{h}$

$\begin{array}{l} = \underset{h ? 0}{l i m} \frac{5 s e c (x + h) + 4 c o s (x + h) ? [5 s e c x + 4 c o s x]}{h} . \end{array}$

$= \underset{h ? 0}{l i m} \frac{5}{h} [s e c (x + h) ? s e c x] + \underset{h ? 0}{l i m} \frac{4}{h} [c o s (x + h) ? c o s x]$

$= \underset{h ? 0}{l i m} \frac{5}{h} [\frac{1}{c o s (x + h)} ? \frac{1}{c o s x}] + \underset{h ? 0}{l i m} \frac{4}{h} [? 2 s i n (\frac{x + h + x}{2}) s i n (\frac{x + h ? x}{2})]$

$= \underset{h ? 0}{l i m} \frac{5}{h} [\frac{c o s x ? c o s (x + h)}{c o s (x + h) (c o s x)}] + \underset{h ? 0}{l i m} \frac{4}{h} [? 2 s i n (\frac{2 x + h}{2}) s i n \frac{h}{2}]$

$= \underset{h ? 0}{l i m} \frac{5}{h} [? \frac{2 s i n (\frac{2 x + h}{2}) s i n (? h / 2)}{c o s (x + h) c o s x}] ? 4 \underset{h ? 0}{l i m} s i n (\frac{2 x + h}{2}) \underset{h ? 0}{l i m} \frac{s i n h / 2}{h / 2}$

$= \frac{s i n (\frac{2 x + 0}{2})}{c o s (x + 0) c o s x} * 1 ? 4 s i n (\frac{2 x}{2})$

$= 5 \frac{s i n x}{c o s x} ? \frac{1}{c o s x} ? 4 s i n x$

$= 5 t a n x ? s e c x ? 4 s i n x$

$(iv) Given f (x) = c o s e c x$

$f^{?} (x) = \underset{h ? 0}{l i m} \frac{f (x + h) ? f (x)}{h}$

$= \underset{h ? 0}{l i m} \frac{1}{h} [c o s e c (x + h) ? c o s e c x]$

$= \underset{h ? 0}{l i m} \frac{1}{h} [\frac{1}{s i n (x + h)} ? \frac{1}{s i n x}]$

$= \underset{h ? 0}{l i m} \frac{1}{h} [\frac{s i n x ? s i n (x + h)}{s i n (x + h) s i n x}]$

$= \underset{h ? 0}{l i m} \frac{1}{h} [\frac{2 c o s (\frac{x + x + h}{2}) s i n (\frac{x ? (x + h)}{2})]}{s i n (x + h) s i n x}]$

$= \underset{h ? 0}{l i m} \frac{1}{h} [\frac{2 c o s (\frac{x + x + h}{2}) s i n (\frac{x ? (x + h)}{2})}{s i n (x + h) s i n x}]$

$= \underset{h ? 0}{l i m} \frac{1}{h} [\frac{2 c o s (\frac{2 x + h}{2}) s i n (? h / 2)]}{s i n (x + h) s i n x}]$

$= \underset{h ? 0}{l i m} \frac{c o s (\frac{2 x + h}{2})}{s i n (x + h) s i n x} * \frac{(? 1) s i n (2)}{h / 2})$

$= \frac{c o s (\frac{2 x + 0}{2})}{s i n (x + 0) s i n x} * (? 1)$

$= ? \frac{c o s x}{s i n x} * \frac{1}{s i n x}$

$= ? c o t x ? c o s e c x$

(v) Given,f(x)=3 cot x+5cosecx.

So, $f^{?} (x) = \underset{h ? 0}{l i m} \frac{f (x + h) ? f (x)}{h}$ $= \frac{2}{c o s (x + 0) c o s x} * 1 + 7 s i n (\frac{2 x + 0}{2}) * (? 1)$

$= \underset{h ? 0}{l i m} 3 c o t (x + h) + 5 c o s e c (x + h) ? [3 c o t x + 5 c o s x)$

$_{h ? 0} \frac{3}{h} [c o t (x + h) ? c o t x] + \underset{h ? 0}{l i m}$

$= ? \frac{5}{h} [c o s e c (x + h) ? c o s e c x]$

$= \underset{h ? 0}{l i m} \frac{3}{h} [\frac{c o s (x + h)}{s i n (x + h)} ? \frac{c o s x}{s i n x}] + \underset{h ? 0}{l i m} \frac{5}{h} [\frac{1}{s i n (x + h)} ? \frac{1}{s i n x}]$

$= \underset{h ? 0}{l i m} \frac{3}{h} [\frac{c o s (x + h) s i n x ? c o s x s i n (x + h)}{s i n (x + h) s i n x}] + \underset{h ? 0}{l i m} \frac{5}{h} [\frac{s i n x ? s i n (x + h)}{s i n (x + h) s i n x}]$

$= \underset{h ? 0}{l i m} \frac{3}{h} [\frac{s i n (x ? (x + h))}{s i n (x + h) s i n x} + \underset{h ? 0}{l i m} \frac{5}{h} [\frac{2 c o s (\frac{x + x + h}{2}) s i n (\frac{x ? (x + h)}{2})}{s i n (x + h) s i n x}$

$= \underset{h ? 0}{l i m} \frac{3}{s i n (x + h) s i n x} * \underset{h ? 0}{l i m} (? 1) \frac{s i n h}{h} + \underset{h ? 0}{l i m} \frac{5}{h} [\frac{2 c o s (\frac{2 x + h}{2}) s i n (? h / 2)}{s i n (x + h) s i n x}$

$= \frac{3}{s i n x ? s i n x} * (? 1) + 5 \underset{h00New answer posted 3 months ago Limits and Derivatives Ncert Solutions Maths class 11th 29. Kindly consider the following 0 Follower 2 Views Follow Characters 0 /2500 Disclaimer: Please note that external links or URLs are not allowed. Non adherence will lead to removal of the comment Cancel Post A alok kumar singh Contributor-Level 10 29. Given, f (x) = (x - a 1) (x - a 2)… (x - a n)So, \underset{x \to a_{1}}{l i m} f (x) = \underset{x \to a_{1}}{l i m} (x - a_{1}) \underset{x \to a_{1}}{l i m} (x - a_{2}) ? \underset{x \to a_{1}}{l i m} (x - a^{n}) = (a 1 - a 1) (a 1 - a 2) … (a 1 - a n) = 0 (a 1 - a 2) … (a 1 - a n) = 0 And \underset{x \to a}{l i m} f (x) = \underset{x \to a}{l i m} (x - a_{1}) \underset{x \to a}{l i m} (x - a_{2}) \dots \underset{x \to a}{l i m} (x - a n) = (a - a 1) (a - a 2) … (a - a n) 00New answer posted 3 months ago Limits and Derivatives Ncert Solutions Maths class 12th 17. Kindly consider the following 0 Follower 2 Views Follow Characters 0 /2500 Disclaimer: Please note that external links or URLs are not allowed. Non adherence will lead to removal of the comment Cancel Post A alok kumar singh Contributor-Level 10 17. Kindly go through the solution = = \underset{x \to 0}{l i m} \frac{2 s i n^{2} x}{2 s i n^{2} \frac{x}{2}} = \frac{\underset{x \to 0}{l i m} {(\frac{s i n x}{x})}^{2} * x^{2}}{\underset{x \to 0}{l i m} {(\frac{s i n^{} \frac{x}{2}}{\frac{x}{2}})}^{2} {\frac{x}{2}}^{2}} = \frac{{(1)}^{2} * x^{2} * 4}{{(1)}^{2} * x^{2}} = 4 00New answer posted 4 months ago Limits and Derivatives Limits and Derivatives 18. \underset{x \to 0}{l i m} \frac{a x + x c o s x}{b s i n x} 0 Follower 5 Views Follow Characters 0 /2500 Disclaimer: Please note that external links or URLs are not allowed. Non adherence will lead to removal of the comment Cancel Post A alok kumar singh Contributor-Level 10 18. \underset{x ? 0}{l i m} \frac{a x + x c o s x}{b s i n x} = \underset{x ? 0}{l i m} \frac{x (a + c o s x)}{b s i n x} = \frac{1}{b} * \frac{(a + c o s 0)}{1} = \frac{a + 1}{b} 00 View All 2 AnswersNew answer posted 4 months ago Limits and Derivatives Limits and Derivatives Kindly consider the following 73. \frac{x}{s i n^{n} x} 0 Follower 2 Views Follow Characters 0 /2500 Disclaimer: Please note that external links or URLs are not allowed. Non adherence will lead to removal of the comment Cancel Post A alok kumar singh Contributor-Level 10 73. Given, f (x) = \frac{x}{s i n^{n} x} So, f?(x) = \frac{(s i n^{x} x \frac{d x}{d x}) - (x \frac{d}{d x} s i n^{x} x)}{{(s i n^{x} x)}^{2}} = \frac{s i n^{x} x - x \cdot n {(s i n x)}^{x - 1} \frac{d}{d x} s i n x}{{(s i n x)}^{2 x}} = \frac{{(s i n x)}^{n} - x \cdot x {(s i n x)}^{n - 1} \cdot c o s x}{{(s i n x)}^{2 n}} = \frac{{(s i n x)}^{n - 1} [s i n x - n x \cdot c o s x]}{{(s i n x)}^{2 n}} = \frac{s i n x - n \cdot x \cdot c o s x}{{(s i n x)}^{2 n - (n - 1)}} = \frac{s i n x - n x c o s x}{{(s i n x)}^{n + 1}} 00New answer posted 4 months ago Limits and Derivatives Limits and Derivatives Kindly consider the following 72. (x + sec x) (x - tan x 0 Follower 2 Views Follow Characters 0 /2500 Disclaimer: Please note that external links or URLs are not allowed. Non adherence will lead to removal of the comment Cancel Post A alok kumar singh Contributor-Level 10 72. Given, f (x) = (x + sec x) (x tan x) So, f?(x) = (x + see x) \frac{d}{d x} (x - t a n x) + (x - t a n x) \frac{d}{d x} (x + s e c x) . = (x + s e c x) (\frac{d x}{d x} - \frac{d}{d x} t a n x) + (x - t a n x) (\frac{d x}{d x} + \frac{d}{d x} s e c x) Let g(x) = tan x. So, g?(x) = = \underset{h \to 0}{l i m} \frac{1}{h} [t a n (x + h) - t a n x] = \underset{h \to 0}{l i m} \frac{1}{h} [\frac{s i n (x + h)}{c o s (x + h)} - \frac{s i n x}{c o s x}] = \underset{h \to 0}{l i m} \frac{1}{h} [\frac{s i n (x + h) c o s x - s i n x c o s (x + h)}{c o s (x + h) c o s x}] = \underset{h \to 0}{l i m} \frac{1}{h} [\frac{s i n (x + h - x)}{c o s (x + h) c o s x}] = \underset{h \to 0}{l i m} \frac{1}{c o s (x + h) c o s x} * \underset{h \to 0}{l i m} \frac{s i n h}{h} = \frac{1}{c o s^{2} x} = s e c^{2} x . _____ (2) And P(x) = see x. = \underset{h \to 0}{l i m} \frac{s e c (x + h) - s e c x}{h} = \underset{h \to 0}{l i m} \frac{1}{h} [\frac{1}{c o s (x + h)} - \frac{1}{c o s x}] = \underset{h \to 0}{l i m} \frac{1}{h} [\frac{c o s x - c o s (x + h)}{c o s (x + h) c o s x}] = \underset{h \to 0}{l i m} \frac{1}{h} [\frac{- 2 s i n (\frac{x + x + h}{2}) s i n (\frac{x - (x + h)}{2})}{c o s (x + h) c o s x}] = \frac{s i n x}{c o s^{2} x} = tan x sec x. ____ (3) Putting (2) and (3) in (1) we get, f ?(x) = (x + sec x) (1 - sec 2 x) + (x - tan x) (1 + tan x sec x) 00New answer posted 4 months ago Limits and Derivatives Limits and Derivatives Kindly consider the following 71. \frac{x}{1 + t a n x} 0 Follower 2 Views Follow Characters 0 /2500 Disclaimer: Please note that external links or URLs are not allowed. Non adherence will lead to removal of the comment Cancel Post A alok kumar singh Contributor-Level 10 71. Given, f (x) = \frac{x}{1 + t a n x} = \frac{x}{1 + \frac{s i n x}{c o s x}} = \frac{c o s x \cdot x}{c o s x + s i n x} S o, f^{'} (x) = \frac{(c o s x + s i n x) \frac{d}{d x} (x \cdot c o s x) - (x \cdot c o s x) \frac{d}{d x} (c o s x + s i n x)}{{(c o s x + s i n x)}^{2}} = \frac{(c o s x + s i n x) (- x s i n x + c o s x) - (- x \cdot s i n x c o s x + x c o s^{2} x)}{{(c o s x + s i n x)}^{2}} = \frac{- x c o s x s i n x + c o s^{2} x - x s i n^{2} x + s i n x c o s x + x s i n x c o s x - x c o s^{2} x}{{(c o s x + s i n x)}^{2}} = \frac{c o s^{2} x + s i n x c o s x - x (s i n^{2} x + c o s^{2} x)}{{(c o s x + c s i n x)}^{2}} Dividing numerator and denominator by cos2x we get, = \frac{\frac{c o s^{2} x}{c o s^{2} x} + \frac{s i n x}{c o s x} \cdot \frac{c o s x}{c o s x} - x \frac{1}{c o s^{2} x}}{{(\frac{c o s x}{c o s x} + \frac{s i n x}{c o s x})}^{2}} = \frac{1 + t a n x - x s e c^{2} x}{{(1 + t a n x)}^{2}} 00New answer posted 4 months ago Limits and Derivatives Limits and Derivatives Kindly consider the following 70. \frac{x^{2} c o s (\frac{π}{4})}{s i n x} 0 Follower 2 Views Follow Characters 0 /2500 Disclaimer: Please note that external links or URLs are not allowed. Non adherence will lead to removal of the comment Cancel Post A alok kumar singh Contributor-Level 10 70. Given, f (x) = \frac{x^{2} c o s (\frac{π}{4})}{s i n x} = \frac{x^{2}}{s i n x} * c o s \frac{π}{4} So, f? (x) = = c o s \frac{π}{4} [\frac{2 \cdot x s i n x - x^{2} c o s x}{s i n^{2} x}] = x c o s \frac{π}{4} [\frac{2 s i n x - x c o s x}{s i n^{2} x}] . 00New answer posted 4 months ago Limits and Derivatives Limits and Derivatives Kindly consider the following 69. \frac{4 x + 5 s i n x}{3 x + 7 c o s x} 0 Follower 3 Views Follow Characters 0 /2500 Disclaimer: Please note that external links or URLs are not allowed. Non adherence will lead to removal of the comment Cancel Post A alok kumar singh Contributor-Level 10 69. Given, f (x) = \frac{4 x + 5 s i n x}{3 x + 7 c o s x} So, f^{'} (x) = \frac{(3 x + 7 c o s x) \frac{d}{d x} (4 x + 5 s i n x) - (4 x + 5 s i n x) \frac{d}{d x} (3 x + 7 c o s x)}{{(3 x + 7 c o s x)}^{2}} = \frac{(3 x + 7 c o s x) (4 x + 5 c o s x) - (4 x + 5 s i n x) (3 - 7 s i n x)}{{(3 x + 7 c o s x)}^{2}} \begin{array}{l} \underline{= x + x x + x +^{} x - x + x x - x + 35 s i n^{2} x} \\ {(3 x + 7 c o s x)}^{2} \end{array} = \frac{15 x c o s x + 28 c o s x + 28 x s i n x - 15 s i n x + 35 (c o s^{2} x + s i n^{2} x)}{{(3 x + 7 c o s x)}^{2}} = \frac{35 + 15 x c o s x + 28 c o s x + 28 x s i n x - 15 s i n x}{{(3 x + 7 c o s x)}^{2}} 00❮ 12345678910 ❯Taking an Exam? Selecting a College? Get authentic answers from experts, students and alumni that you won't find anywhere else Sign Up on Shiksha On Shiksha, get access to 65k Colleges 1.2k Exams 688k Reviews 1800k Answers .write-a-review-widget h2.tbSec2 {
border-bottom: none;
padding: 0 0 16px;
margin: 0px;
font-size: 16px;
line-height: 1.5;
font-weight: 600;
}
.write-a-review-widget .link-btn {
text-align: center;
}
.static-widget{
margin-bottom: 16px;
box-shadow: 0 2px 2px 0 rgb(0 0 0 / 16%), 0 0 0 1px rgb(0 0 0 / 8%);
background: #fff;
padding: 12px 12px 16px;
}
.button {
display: inline-block;
cursor: pointer;
font-weight: 600;
text-align: center;
vertical-align: middle;
-webkit-user-select: none;
-moz-user-select: none;
-ms-user-select: none;
user-select: none;
background-color: transparent;
border: 1px solid transparent;
padding: 0 10px;
font-size: .875rem;
height: 34px;
line-height: 32px;
border-radius: 2px;
outline: 0;
white-space: nowrap;
min-width: 90px;
text-transform: capitalize;
}
a.button--orange {
background-color: #f37921;
border-color: #f37921;
color: #fff;
} Share Your College Life Experience Write a Review Community Guidelines User Points System Questions Discussions Tagsvar GA_currentPage = "TAG DETAIL PAGE";
var ga_user_level = "Non-Logged In";
function LazyLoadAnADesktopCallback(){
$LAB
.script('//js.shiksha.ws/public/js/build/ajax-api.1e2339.js',
'//js.shiksha.ws/public/js/build/ana_desktop.d666ad.js',
'//js.shiksha.ws/public/js/build/quesDiscPosting.8361d6.js',
'//js.shiksha.ws/public/js/build/jquery.tinyscrollbar.min.v5.dc5c57.js',
'//js.shiksha.ws/public/js/build/bottomStickyRegistrationLayer.c9e9a3.js')
.wait(function(){
LazyLoadCallBackTDP();
prepareClickDataTDP();
});
}var getcHostName = "https://www.shiksha.com/resources/college-comparison";1234 Compare Remove All CompareCollege Comparison Cancel Ok.ana-posting-overlay{position: fixed;left: 0;right: 0;top: 0;bottom: 0;background: rgba(0,0,0,.4);z-index: 10000;}
.ana-posting-iframe-bx{z-index: 10000;width: 1022px;height: 630px;max-height:100%;max-width:100%;position: fixed;margin: 0 auto;box-sizing: border-box;top: 50%;left: 50%;transform: translate(-50%,-50%);overflow: hidden;border-radius: 8px;}
a#closeAnAPopup {background: #fff;border-radius: 1000px;height: 30px;width: 30px;text-align: center;font-size: 12px;right: -12px;top: -12px;box-shadow: 0px 2px 4px 0px rgba(0,0,0,0.8);}
.ana-posting-close{top: -3px;right: 3px;font-size: 20px !important;color: #666 !important;cursor: pointer;margin: 0 auto;position: absolute;}
.ana-posting-iframe{border: none;height: 100%;width: 100%;}
.hide{display: none;}
body.freeze{position: fixed;width:100%;overflow:hidden}
@media screen and (max-width:767px) {
.ana-posting-iframe-bx{width: 100%; height: 100%;}
.ana-posting-overlay{background:#fff}
}×// Attach window click event handler for GA tracking
if(typeof loadNewHomePageWidget == 'function'){
loadNewHomePageWidget('/shiksha/loadAjaxForm/abroadtab','hmpgrdsn_tababroad');
}This website uses Cookies and related technologies for the site to function correctly and securely, improve & personalise your browsing experience, analyse traffic, and support our marketing efforts and serve the Core Purpose. By continuing to browse the site, you agree to Privacy Policy and Cookie Policy . OKGet our experts to answer your questions within 24 Hrs Ask Question Shiksha About Us Management Team Careers Shiksha Authors Colleges Client login Advertise with us Add Colleges Contact Us Others FAQs Grievances Notices / Summons Privacy Sitemap Terms & Conditions Our Group Infoedge.in Naukri.com Naukri Campus Naukrigulf 99acres.com Jeevansathi.com AmbitionBox.com Naukri Learning Job Hai MBA : MBA Home Top MBA Colleges MBA Colleges Executive MBA Colleges MBA Exams Engineering : Engineering Top Engineering Colleges Engineering Colleges Engineering Exams JEE Main JEE Advanced Medicine : NEET NEET PG AIIMS PG JIPMER PG PGIMER Exam Top Medical Colleges Medical Colleges Medical Exams Other Courses : Animation B Com B Sc BBA CA Fashion & Textile Design Hotel Management Law Mass Communication MBBS MCA M.Tech BCA Pharmacy M Sc Study Abroad : Study Abroad Home BTech abroad MBA abroad MS abroad GRE GMAT SAT IELTS TOEFL Sarkari Exams : SSC CGL IBPS PO SBI PO NDA UPSC Civil Services Exam IES SSC CHSL AFCAT IBPS CWE RRB SSC JE CDS SBI Clerk IBPS Clerk Resources : Careers after 12th Courses After 12th Education Boards Ask a Question Discussions Write a college review Articles Shiksha Ask & Answer App Education Trends Important Updates : XAT 2026 Exam CAT Form Correction 2025 CAT Syllabus 2025 CAT Score vs Percentile CAT 2025 JEE Main 2026 Trigonometric Table NEET 2026 JEE Main PYQ Chemical Bonding and Molecular Structure XAT Registration 2026 MCC NEET UG Counselling 2025 Trade Marks belong to the respective owners. Copyright © 2025 Info edge India Ltd. All rights reserved.try{ overlayViewsArray.push(new Array('common/calendardiv','calendardivId')); }catch(e){ }try{ overlayViewsArray.push(new Array('network/commonOverlay','addRequestOverlay')); }catch(e){ }window.dataLayer = window.dataLayer || [];
function gtag(){dataLayer.push(arguments);}
gtag('js', new Date());

gtag('config', 'G-F0XEJFWK9T');// added for switch tracking of search results on and off
var track_search_results_flag = "1";
var facebook_channel_path = "https://www.shiksha.com/public/channel.html";

function proceedToPostQuestionFromHome(objForm,id){
objForm.setAttribute("method",'get');
objForm.setAttribute("action",'https://ask.shiksha.com/messageBoard/MsgBoard/postQuestionFromCafeForm');
objForm.submit();
}try{ jsb9eraseCookie("jsb9Track");
var prevWindowOnunload = window.onbeforeunload; window.onbeforeunload = function(){ try{ if(typeof(prevWindowOnunload) == "function") { prevWindowOnunload.call(); } jsb9onUnloadTracking(); }catch(e){ } }
function jsb9onUnloadTracking() { jsb9eraseCookie("jsb9Track"); var date = new Date(); var presentTime = date.getTime(); var presentUrl = window.location.href; jsb9createCookie("jsb9Track",presentTime+"|"+presentUrl,5); } var date = new Date(); jsb9TrackEndTime = date.getTime(); function jsb9TrackTime() { var jsb9date = new Date(); jsb9TrackFinalLoad=jsb9date.getTime(); if(typeof(jsb9TrackVal) == "string") { var cookieArr = jsb9TrackVal.split('|'); var prevTime = cookieArr[0]; var refererUrl = cookieArr[1]; var jsb9Iframe = document.createElement('div');jsb9Iframe.style.cssText='height:0px;overflow:hidden;'; jsb9Iframe.id = 'jsb9Div'; var style = 'border:0;width:0;height:0;display:none'; var jsb9ServerTime = 319.28205490112; var presentUrl = window.location.href; var customTrack = ""; for(var i in jsb9recordTimes) { customTrack += "|"+i+":"+jsb9recordTimes[i]; } var data = presentUrl+"|"+refererUrl+"|"+prevTime+"|"+jsb9TrackStartTime+"|"+jsb9TrackEndTime+"|"+jsb9TrackFinalLoad+"|"+jsb9ServerTime+customTrack; jsb9Iframe.innerHTML = '<iframe border="0" height=0 widht=0 style="visibility: hidden" src="https://track.99acres.com/images/zero.gif?data='+data+'"></iframe>';
document.body.appendChild(jsb9Iframe); } } }catch(e){ }var shikshaProduct = 'anaDesktopV2';/**
* Method loads all required scripts for Unified Registration
* callback function is loadRequiredDataForUnifiedRegistrationProcess
* callback API will be alwys called either file is already loaded or not
*/
function initForUnifiedRegistration()
{
LazyLoad.loadOnce([
'//js.shiksha.ws/public/js/build/ajax-api.1e2339.js'
],loadRequiredDataForUnifiedRegistrationProcess,null,null,true);
}

/*
Function which put values into global vars. like is_ldb user or cross btn click
*/

function loadRequiredDataForUnifiedRegistrationProcess()
{
/* ajax to set if user register or not START */
//checkLdbUser();
/* ajax to set if user register or not END */
/* set variable to check whether user has clicked unified overlay or not*/
unified_form_overlay1_cancel_clicked = getCookie('is_unified_overlay1_clicked');
unified_form_overlay2_cancel_clicked = getCookie('is_unified_overlay2_clicked');
unified_form_overlay3_cancel_clicked = getCookie('is_unified_overlay3_clicked');
/* set Form submit url for diff types of overlays */
if(typeof(arr_unified) !== 'undefined') {
ShikshaUnifiedRegistarion.url_unified = ShikshaUnifiedRegistarion.ajaxUrlHelper(arr_unified);
}
if($('homepagePromotionCarousel')) {
//if($('questionText')) { $('questionText').value = 'Make an informed career choice, ask the expert now!';}
}
// showResetPasswordLayer();
}
/* UNIFIED REGISTRATION APIs END */$j = $.noConflict();var lazyLoadJsFiles = []
function lazyLoadJsFilesInParallel() {
if(lazyLoadJsFiles.length > 0) {
LazyLoad.loadOnce(lazyLoadJsFiles,function(){},null,null,true);
}
}

function LazyLoadAnAContactUsCallback(){
$LAB.script('//js.shiksha.ws/public/js/build/quesDiscPosting.8361d6.js').wait(function(){
LazyLoadAnAContactUs();
});
}

function loadJsFilesInParallel(){
$j(document).trigger('labLoadedJs');
$LAB
.script("//js.shiksha.ws/public/js/build/AutoSuggestor.512dd5.js")
.wait(function(){
if(SHOW_AUTOSUGGESTOR_JS){
autosuggestorInstanceCheck = setInterval(function(){
var fileLoaded = false;
try{
var aso = new AutoSuggestor();
fileLoaded = true;
} catch(e) {
fileLoaded = false;
}
if(fileLoaded){
clearInterval(autosuggestorInstanceCheck);
if(typeof(initializeAutoSuggestorInstance) == 'function') {
initializeAutoSuggestorInstance();
}
if(typeof(initializeAutoSuggestorInstanceSearchV2) == 'function') {
try {
initializeAutoSuggestorInstanceSearchV2('{"suggestionContainerClass":"search-college-layer","bucketCount":4,"searchVersion":"2","tabPressedHandler":"handleAutoSuggestorTabPressed","enterPressedHandler":"handleAutoSuggestorEnterPressedSearch","mouseClickedHandler":"handleAutoSuggestorMouseClickedSearch","navigationKeysHandler":"handleNavigationKeysHandler","objectName":"autoSuggestorInstanceSearch","searchBoxId":"searchby-college","suggestionContainerId":"search-college-layer","typeAhead":0,"suggestionType":"course_and_institute","suggestionCount":8,"autoSuggestorUrl":"\/search\/AutoSuggestorV2\/getSuggestionsFromSolr\/","isMobileSearch":false,"showGrouping":1,"getTrendingSuggestions":1}');
initializeAutoSuggestorInstanceSearchV2('{"suggestionContainerClass":"search-college-layer","bucketCount":4,"searchVersion":"2","tabPressedHandler":"handleAutoSuggestorTabPressedCareers","enterPressedHandler":"handleAutoSuggestorEnterPressedCareers","mouseClickedHandler":"handleAutoSuggestorEnterPressedCareers","objectName":"autoSuggestorInstanceCareer","searchBoxId":"searchby-career","suggestionContainerId":"search-career-layer","getTrendingSuggestions":1,"typeAhead":0,"disableCache":1,"suggestionType":"career","suggestionCount":8}');
initializeAutoSuggestorInstanceSearchV2('{"suggestionContainerClass":"search-college-layer","bucketCount":4,"searchVersion":"2","tabPressedHandler":"handleAutoSuggestorTabPressedQuestion","enterPressedHandler":"handleAutoSuggestorEnterPressedQuestion","mouseClickedHandler":"handleAutoSuggestorEnterPressedQuestion","mouseClickedHandlerLastElement":"handleAutoSuggestorEnterPressedAskQuestion","askNewQuestionURL":"https:\/\/ask.shiksha.com","mouseClickedHandlerCTA":"handleAutoSuggestorEnterPressedCTA","backKeyHandler":"handleAutoSuggestorBackKeyPressedQuestion","objectName":"autoSuggestorInstanceQuestion","searchBoxId":"searchby-question","suggestionContainerId":"search-question-layer","removeExactMatch":1,"suggestionType":"question","suggestionCount":8,"isMobileSearch":false,"autoSuggestorUrl":"\/search\/AutoSuggestorV2\/getSuggestionsFromSolr\/","showGrouping":1,"getTrendingSuggestions":1}');
initializeAutoSuggestorInstanceSearchV2('{"suggestionContainerClass":"search-college-layer","bucketCount":4,"searchVersion":"2","tabPressedHandler":"handleAutoSuggestorTabPressedExams","enterPressedHandler":"handleAutoSuggestorEnterPressedExams","mouseClickedHandler":"handleAutoSuggestorEnterPressedExams","backKeyHandler":"handleAutoSuggestorBackKeyPressedExams","objectName":"autoSuggestorInstanceExam","searchBoxId":"searchby-exam","suggestionContainerId":"search-exam-layer","suggestionType":"exam","suggestionCount":8,"autoSuggestorUrl":"\/search\/AutoSuggestorV2\/getSuggestionsFromSolr\/","showGrouping":1,"getTrendingSuggestions":1}');
tagsASConfig = '{"suggestionContainerClass":"search-college-layer","bucketCount":4,"searchVersion":"2","enterPressedHandler":"handleAutoSuggestorEnterPressedTags","mouseClickedHandler":"handleAutoSuggestorEnterPressedTags","objectName":"autoSuggestorInstanceForTags","searchBoxId":"tagSearch","suggestionContainerId":"tagSearch_container","typeAhead":0,"suggestionType":"tag","suggestionCount":10,"autoSuggestorUrl":"\/Tagging\/TaggingDesktop\/getAutoSuggestor","showGrouping":1,"disableCache":1,"removePartialMatch":0}';
initializeAutoSuggestorInstanceSearchV2(tagsASConfig);
initializeAutoSuggestorInstanceSearchV2('{"suggestionContainerClass":"search-college-layer","searchVersion":"2","enterPressedHandler":"handleAutoSuggestorEnterPressedTags","mouseClickedHandler":"handleAutoSuggestorEnterPressedTags","objectName":"autoSuggestorInstanceForTagsQDP","searchBoxId":"tagSearchQDP","suggestionContainerId":"tagSearchQDP_container","typeAhead":0,"suggestionType":"tag","suggestionCount":6,"autoSuggestorUrl":"\/Tagging\/TaggingDesktop\/getAutoSuggestor","showGrouping":1,"disableCache":1,"callBackFunctionAfterBuildingSuggestionContainer":"showSuggestedTags","callBackFunctionOnInputKeysPressed":"showSuggestedTags"}');
}
catch(e) {
console.log(e);
}
}
if(typeof(initializeAutoSuggestorInstancesForCollgeReviews) == 'function') {
initializeAutoSuggestorInstancesForCollgeReviews();
}
if(typeof(initializeAutoSuggestorInstancesForCampusConnect) == 'function') {
initializeAutoSuggestorInstancesForCampusConnect();
}

if(typeof(initializeAutoSuggestorInstanceAlt) == 'function') {
initializeAutoSuggestorInstanceAlt();
}
}
},1000);
}
});
LazyLoadAnADesktopCallback();
}
(function(g,b,d){var c=b.head||b.getElementsByTagName("head"),D="readyState",E="onreadystatechange",F="DOMContentLoaded",G="addEventListener",H=setTimeout;
function f(){ loadJsFilesInParallel(); /*if(typeof CTACallBackSearch == 'function') CTACallBackSearch();*/} H(function(){if("item"in c){if(!c[0]){H(arguments.callee,25);return}c=c[0]}var a=b.createElement("script"),e=false;a.onload=a[E]=function(){if((a[D]&&a[D]!=="complete"&&a[D]!=="loaded")||e){return false}a.onload=a[E]=null;e=true;f()};
a.src="//js.shiksha.ws/public/js/LAB.min.js";c.insertBefore(a,c.firstChild)},0);if(b[D]==null&&b[G]){b[D]="loading";b[G](F,d=function(){b.removeEventListener(F,d,false);b[D]="complete"},false)}})(this,document);lazyLoadCss('//css.shiksha.ws/public/css/build/socialSharingInner.min.5de709.css');var reset_password_token = '';
var reset_usremail = '';
var reset_password = '';
var usergroup = '';

//var registration_context = '';
var user_logged_in_pref_data = "";
var userInfo = null;
var firstTimePageLoad = true;var serviceWorker = "service-worker.js";
if ('serviceWorker' in navigator && typeof serviceWorker == 'string' && serviceWorker.length > 0 && typeof registerServiceWorker == 'function') {
registerServiceWorker(serviceWorker);
}
/* function to bind autosuggestor */
if(typeof(bindAutoSuggestorEvents) == 'function'){
bindAutoSuggestorEvents();
}
/* responsible for showing GNB sub-menu on mouse hover */
if(typeof(activateGnbMouseOver) == 'function'){
activateGnbMouseOver();
}
var homepageMiddlePanel, instituteDetailPageClass, cookieDomain = '.shiksha.com';
$j(document).ready(function(){
shikshaOnreadyEventPC();
getSocialSharingLayer();
});
$j(window).on('load',function(){
shikshaOnloadEventPC();
if(typeof isUserLoggedIn !='undefined' && isUserLoggedIn && typeof getPredictorList != 'undefined' && typeof getPredictorList == 'function'){
getPredictorList();
}
});window.pushNotiConf = {
deviceType : 'desktop'
};
if(document.getElementById("pushNotificationContainer") != null){
var d = new Date();
var dStr = d.getDate()+''+d.getMonth()+''+d.getFullYear()+'v10';
var randomId = Math.floor(Math.random() * 100);

var loadNotificationSDK = function() {
var obj = document.createElement('script');
/* obj.src = 'https://localshiksha.com/public/js/shikshaPushNotification.js?'+dStr+randomId;*/
obj.src = '//js.shiksha.ws/public/js/build/shikshaPushNotification.b0fa7c.js?'+dStr+randomId;
obj.async = true;
document.head.appendChild(obj);
};

var helperObj = document.createElement('script');
/* helperObj.src = 'https://localshiksha.com/pwa/public/js/push-notification-helpers.js?'+dStr;*/
helperObj.src = '//js.shiksha.ws/pwa/public/push-notification-helpers.js?'+dStr+randomId;
helperObj.async = true;
document.head.appendChild(helperObj);

if (typeof helperObj.onload == 'object') {
helperObj.onload = function(e) {
console.log('notification helper sdk loaded');
loadNotificationSDK();
};
} else {
loadNotificationSDK();
}
if(typeof gaTrackEventCustom == 'function'){
window.phpGATrack = gaTrackEventCustom;
}
}setTimeout(function(){if(typeof loadViewsOnPageLoad == 'function'){loadViewsOnPageLoad();} },2000);var multiLocationCourses = [0];if(shikshaProduct=='CMSExam'){
var elem = document.getElementById("cookieAdSlot-d");
elem.parentNode.removeChild(elem);
}facebook Twitter Google +if (document.addEventListener){
document.addEventListener('mouseup', handleShareLayerHide, false);
} else if (document.attachEvent){
document.attachEvent('onmouseup', handleShareLayerHide);
}

function handleShareLayerHide(e)
{
var target = (e && e.target) || (event && event.srcElement);
var obj = $('socialLayer');
if(target!=obj){
obj.style.display='none';
}
}×//Load website tour
$j(document).ready(function(){
window.contentMapping = {"Filters":"Filter rankings by publisher, exams, location, specialization etc.","DEB":"Download details of eligibility, admissions, fees, infra etc.","Shortlist":"Save your shortlist, get updates, college recommendations etc.","Compare":"Compare colleges on ranking, placements, reviews, fees etc.","Reviews":"Get honest reviews from students who studied in this college","Questions":"Get answers from the students currently studying in this college","Institute":"View college details, courses offered & recommendations","Course":"View course details, admission process & insights","Exam":"View Exam Detail","QuestionSearch":"Now you can also search from 5 lakh+ answered questions","DownloadGuide":"Get all details offline, receive important updates & more.","QuestionPapers":"Get prep tips & previous years question papers."};
initializeWebsiteTour('cta','anaDesktopV2',contentMapping);
});
lazyLoadCss('//css.shiksha.ws/public/css/build/quesDiscPosting.min.99ce37.css');}{l i m}$

Need guidance on career and education? Ask our experts

Your Question

Limits and Derivatives

Questions

Discussions

Active Users

Followers

All

Discussions

Unanswered Questions

Share Your College Life Experience