Book Online Demo
Check Your IQ
Try Test

Courses

Dropper NEET CourseDropper JEE CourseClass - 12 NEET CourseClass - 12 JEE CourseClass - 11 NEET CourseClass - 11 JEE CourseClass - 10 Foundation NEET CourseClass - 10 Foundation JEE CourseClass - 10 CBSE CourseClass - 9 Foundation NEET CourseClass - 9 Foundation JEE CourseClass -9 CBSE CourseClass - 8 CBSE CourseClass - 7 CBSE CourseClass - 6 CBSE Course
Offline Centres

Q.

Statement-1 : The equation x log x =2 - x is satified by at least one value of x lying between 1 and 2.

Statement 2 : The function ⨍ (x)=x log x is an increasing function in [1, 2] and g(x) = 2 – x is
a decreasing function in [1, 2] and the graphs represented by these functions intersect at a point in [1, 2]

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!
An Intiative by Sri Chaitanya

a

Statement-1 is false and the Statement-2 is true

b

Statement-1 is true and the Statement-2 is false

c

Statement-1 is true, Statement-2 is true and the Statement-2 is not the correct explanation of the Statement-1

d

Statement-1 is true, Statement-2 is true and the Statement-2 is true explanation of the Statement-1.

answer is A.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

let f(x)=x logx f'(x)=x.1x+logx.1=1+logx f(x) is increasing ⇒f'(x)>0 1+logx>0⇒logx>-1 x>e-1⇒x>1e x∈1,2is increasing g(x)=2-x g'(x)=-1 g(x) is always decreasing for x∈R f(x)=g(x) intersect atleast value x∈1,2

Watch 3-min video & get full concept clarity
Related Blogs
Get ₹ 1 crore* worth scholarship for JEE / NEET / Foundation
Result Producing online coaching for JEE/NEET of south India
Largest All India Test Series for JEE/NEET
Best Books for IIT JEE
Best Books for NEET
How to Join IIT after 10th
score_test_img

Get Expert Academic Guidance – Connect with a Counselor Today!

Related Blogs
Get ₹ 1 crore* worth scholarship for JEE / NEET / Foundation
Result Producing online coaching for JEE/NEET of south India
Largest All India Test Series for JEE/NEET
Best Books for IIT JEE
Best Books for NEET
How to Join IIT after 10th
whats app icon
Statement-1 : The equation x log x =2 - x is satified by at least one value of x lying between 1 and 2.Statement 2 : The function ⨍ (x)=x log x is an increasing function in [1, 2] and g(x) = 2 – x isa decreasing function in [1, 2] and the graphs represented by these functions intersect at a point in [1, 2]