• a)
    1
  • b)
    – 1
  • c)
    0
  • d)
    none of these
Correct answer is option 'C'. Can you explain this answer?

JEE Question

Vikas Saini
Mar 12, 2020
Santosh sahoo discovers sin90* as zero LOL.sin90* is not perfact 1 in limits,it is slightly less than 1,so it is zero in GIF and LHL and RHL has cos 

Khaja Moinuddin
May 01, 2020

Option A is correct answer

Vishwajeet Dhumal
Apr 08, 2020
We have to find the the greatest integer part of the value [sinx]. we know that sin pi/2 = 1 but since the limit is approaching pi/2 but is not completely pi/2, therefore we can conclude by the rules of greatest integer function that the value of function greater than 0 and slightly less than 1 is always zero(only if it is the greatest integer function).

Option C is correct answer

Suresh Kumar
May 12, 2020

Because sinx is less less than x sinx is belong in 1to 0 so g.i.f. of this is 0

By putting pie/2 in box of sinx it will be less than 1 so box value will be zero

Harsh Gujalwar
May 27, 2020
The ans must be zero as theta tends to pie hence sin theta tend to 1 but never equal to 1 hence gif is 0

Harun Shankar
May 21, 2020
At exactly x=1 without limits step of sinx is 1 but limit x tends to means it approaches to not equal to
then the value is always less than 1 if we apply step function it is zero

Amar Kumar
Oct 21, 2020
Zero is correct answer

Rocky Srk
Mar 29, 2020
Sinx has value a little less then 1 in limit... here sinx is under integral function [ ] so option C is correct...

Amal Krishnan
Jul 02, 2020
[sin90]=[1]=0

Suraj Jangid
Oct 13, 2020
Option (c),0 is correct answer

Sagar Naik
Apr 17, 2020
Bez it is in greatest integer function.....[sinx]

Shweta Singh
May 09, 2020
Π/2=90• which is equal to 0

Ramesh Sinha
Jul 31, 2020
A is the correct answer

Aishwary Omar
Apr 21, 2020

Amrit Raj Garg
Aug 04, 2020
Boom bam ye sab choro jake P.U.B.G khelo

Shubham Choudhary
May 02, 2020
With the observation of graph of Sin X we can see that
limit X tends to pie/2+ and X tends to pie/2- is less than one so it's gif is zero

As differentiation of sin X becomes cos X and cos π/2 =0

Santosh Sahoo
Apr 01, 2019
Sin pi by 2 = sin90degree = 0
so the option c is correct......l hope you understand

Armesha Sharma
May 25, 2020
Why do u mean by cos???

Sahil Deshwal
Sep 27, 2020
As limit tends sinx becomes approx equal to 1 but not equal to 1 . hence[<1]=0>

Bhukya Nithin
May 16, 2020
When we consider the value of sin[pi/2] it gets in between 0 and 1.
And we know that, [ ] this bracket indicates the greatest integer function.
therefore,when we consider the both left hand limit and right hand limit they both equal each other to 0.
that's why 0 is the correct answer.

Vidya Aasthaanam
Jun 11, 2020
Ans is 0 because x->pie÷2 therfore sinx->1 but not 1 exact it near 1 but not 1 and then apply greatest integer ans is 0

Nilimesh Nayak
Jul 20, 2020
The value of sinπ\2 not accurate 1.Because the value of X is less than or equal to 1andgrater than or _1.

Manoj Patel
Jun 11, 2020
Value of sin90 is not equal to one it is less than one so GIF function of less than one is 0

Aman Tiwari
Jul 06, 2020
Since it's value at left and right limit less than 1 so integral part will be 0 at both limt

Sahil Yadav
Mar 28, 2020
Sin(π\2)=1 so, option A is correct answer

Mahalakshmi Maha
Apr 25, 2020
Actually sinπ/2 is 1, but the question is greatest integer function of sinx i.e, [sinx] and the value is not exactly 1 as limit approaches π/2 and not exactly π/2. So it is to be considered as 0 by the greatest integer function rule. So answer is 0. Option C is correct.

Shubham Nayan
May 19, 2020
In these types of questions we have to consider g.i.f .As sinx is approaching 1 i.e it is less than 1, the answer will be 0.But if the whole limit would have been in the gif the answer would be 1.

Taranjeet Singh
Jun 12, 2020
As limit x approaches to π\2.now put value in (sinx) from R.H.L then we get + sin π/2 and from L.H. L side we get -sinπ/2. And at 0 we simply get sinπ/2 and we also know that sin 90 is zero so in above all three values become 0 from R. H. L & L. H. L also it is 0 at x= 0.hence

Sarvesh Gaikwad
May 26, 2020
Answer is C BECAUSE SINX IS LESS THAN 1 AND BOX OR GREATEST INTEGER FUNCTION OF LESS THAN 1 IS ZERO

Rahul Kumar
Jun 14, 2020
LHL :- h => 0 [Sin(π/2 - h)] = limh => 0 [Cosh]
so,
Cosh => 1 so, it's become zero.
RHL :- h=> 0 [sin ( π/2 + h)] = lim h=>0 [Cosh]
here h tending to zero means cosh tending to. 1so it's also zero.
so zero answer

Shan Mukherjee
Apr 12, 2020
Sin(x) tending to 90° means either greater than 90° or less then 90° in both the cases it will less the zero according to it's graph
hence gif of any number less the one is absolute zero.
good question

C Ramamohanreddy
Apr 21, 2020
The question really mean that if x approach 90*then sinx approach what, yes it approach 1,but not exactly 1,it may be 0.99 something ,you may think it may be 1.01 but sin value doesn't exceed 1.so G.I.F of less than one is zero

Sontosh Dey
Apr 15, 2020
Yes option c is correct

Raghav Shukla
May 09, 2020
Just see limit is in greatest integer function , since range of sinx is -1 to 1
.From graph you can see when you see left hand limit you got a number less than 1 whose greatest integer is zero(0) similarly when you see right hand limit you got a number less than 1 whose greatest integer is zero(0)
SINCE RHL=LHL=0
SO LIMIT OF FUNCTION EXISTS AT pi/2 and equal to zero(0)

Ankit Singh
Apr 14, 2020
Option c is the correct answer

Bibhabasu Dutta
Jul 26, 2020
No bro correct answer is D

Srihasa Bathula
Aug 06, 2020
Sinπ/2= sin180/2

sin90 =0

Jayanthan Ips
Dec 07, 2020
Option a is th correct answer

Nitesh Pal Pal
Dec 10, 2020
[sinx] is zero at pi/2+ (at GIF)
[sinx]is zero at pi/2-(at LIF)
hence , LIF=GIF (it is a continuous)
So, zero is the answer..
the figures shows parabolic nature..
..

Lt sin x .... that is simply take derivative of sin x...
derivative of sin x is cos x...
now put value of x
cos π/2 = 0..
hence correct option is C
that is 0

Step values of any rational number is an integer. sin (pi/2) value is 1. As x tends to pi/2 on LHS and RHS sin x is less than 1. so step value is 0.

Konduru Premsai
Apr 28, 2020
D) As RHL not equal to LHL.

Anibesh Behera
Dec 02, 2020
Ans is Zero . option C

Deekshita Meduri
Nov 11, 2020
From periodicity it's right
and
sin x equal to 0

Yes because differentiation of sinx is cosx

Evil Beings
Jul 16, 2020
This is the greatest integer funtions which always shows the smallest integral value of the function inside

Ravi Teja
Mar 30, 2020
As [ ]is not given as g.i.f ans may be opt A
even if [ ]is given as g.i.f then limit does not exists....

Keshav Aggarwal
Jun 22, 2020
Correct answer is c by drawing its graph and make some transformations u will get ur result c option

Deepak Yadav
May 21, 2020
Since it is approaching towards pi/2 not exact pi/2 so the value is not exact 1

GIF of 1 is 0

sin pi/2 = 1

Deepak Kumar
Jun 20, 2020
As x approach the 1/2
and when we put the value of x in the question
ie.
sinx
put x=1/2
sin1/2=0
so option c is the correct answer of this question

Bandari Veeresham
Jun 29, 2020
Here as the x tends to pi by 2 function tends to 1 but not equals to 1 so the graph lies between y=0 and 1
in this greatest integer function is 0 Hence answer is 0

Neet Aspirant
Nov 03, 2020
Take the first derivative of sinx which is equal to cosx.
Then substitute x=pi/2 to get the answer =cospi/2=0

Harsh Srivastava
Jun 28, 2020
Because this is greatest integer fnc the value will become zero till π/2 at π/2 it will become one hence answer is 0

Its Kings Club
May 25, 2020
It is not an indeterminate form so limit will be applied directly.
sin90 is 0