JEE Exam  >  JEE Notes  >  Chapter-wise Tests for JEE Main & Advanced  >  JEE Advanced (One or More Correct Option): Applications of Derivatives

JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced PDF Download

Q.1. If JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advancedthen A + B equals
(a)JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced
(b)JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced
(c)JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced
(d)JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced

Correct Answer is option (a)
JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced
Put t = cotx
JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced

Q.2. JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced
(a) JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced
(b) JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced
(c) JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced
(d) JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced

Correct Answer is option (a)
Put JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced Then 0 < θ < π
and JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced
JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced
JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced

Q.3. If JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advancedthen value of JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advancedis
(a) 0
(b)JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced
(c) √3
(d) None of these

Correct Answer is option (c)

JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced
Applying by parts on I1, we get
JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced


Q.4. If JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & AdvancedthenJEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advancedis equal to
(a) 3/5
(b) 1/5
(c) 1
(d) 2/5

Correct Answer is option (a)

JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced


Q.5. JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advancedthen which of the following is correct?
(a) K1 = K2 = 1
(B) K1 = -K2 = 1 
(C) K1 = K2 = -1
(D) K2 = 1 and K1 = -1

Correct Answer is option (b)

JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & AdvancedPutting cosx = t  and sin x = t respectively.
JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced
⇒ sec x – cosec x + c    Þ K= 1,  K2 = -1


Q.6. The value of JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advancedis
(a) 0
(b) 1
(c) 2
(d) π

Correct Answer is option (b)

JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced
On adding we get
JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced


Q.7. Let JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advancedwhere [.] denotes the greatest integer function, then the value of JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advancedis equal to
(a)JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced
(b) JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced
(c) 8/3
(d) 4/3

Correct Answer is option (a)

JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced
f(x) = -x2, x < - 1
1, -1 < x < 0
2, x = 0
1, 0 < x < 1
-x2, x > 1
f(x) is an even function.
JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced 


Q.8. If JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advancedand JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advancedthen the constants A and B are respectively
(a) JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced 
(b) JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced
(c) JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced
(d) JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced

Correct Answer is option (d)
JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced
∴ B = 0


Q.9. The value ofJEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & AdvancedThen (m, n) is

(a) (6, 260)
(b) (8, 280)

(c) (4, 240)
(d) none of these

Correct Answer is option (b)

JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced
JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced(a cos2θ + b sin2θ - (A)3 (b – a cos2θ - b sin2θ)4
sinθ cos θ dθ
JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced
Let sin θ= t  Þ cos θ dθ = dt
JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced
JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced


Q.10. Let f (x) be maximum and g (x) be minimum of {x | x |, x| x |} then JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced
(a) 1/12
(b) 1/3
(c) 2/3
(d) 7/12

Correct Answer is option (c)

JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced
JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced


Q.11. If f '(x) = JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advancedthen f(1) is equal to
(a) - log ( √2 - 1)  
(b) 1
(c) 1 + √2
(d) log (1 + √2)

Correct Answer is option (A, D)

JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced
Putting x = 0, f(0) = c so c =JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced
and f(1) = JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced
= log (1 + √2) = - log (√2 - 1)


Q.12. The value of JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advancedmust be same as
(a) JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced(e lies between 0 and 1)
(b) JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced(e lies between 0 and 1) 
(c) JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced (e is greater than 1) 
(d) JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced(e is greater than 1) 

Correct Answer is option (B, C)
JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced

if 0 < e < 1, JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & AdvancedSo,  (B) is correct
If e > 1, JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & AdvancedSo, (C) is correct. 


Q.13. If JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advancedthen
(a) A = 1/3
(b) B = -2
(c) A = 2/3
(d) B = -1

Correct Answer is option (A,B)

JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced


Q.14. If JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advancedthen
(a) A = 3/2
(b) B = 35/36
(c) C is indefinite
(d)JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced

Correct Answer is option (B, C, D)

JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced
We write 4ex + 6e-x = α(9ex -4e-x) + β(9e+ 4e-x)
So 9α + 9β = 4 -4α + 4β  = 6
JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced
JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced
JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advancedwhere δ is integration constant
JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced
On comparing with I = Ax + B ln (9e2x - 4) + C
JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advancedis indefinite


Q.15. If JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advancedthen I is equal to
(a) JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced
(b) JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced
(c) JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced
(d) JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced

Correct Answer is option (A, D)

We can write
JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced
Put JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advancedso that
JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced


Q.16. Which of the following options is/are correct? 
(a) JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advancedwhere {x} is fractional part of x .
(b) JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced
(c) JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced
(d) JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced

Correct Answer is option (B, C)

JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced
JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced
put x = cosθ ⇒ dx = - sinθ dθ
JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced


Q.17. If JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & AdvancedThen possible values of A and B are
(a) A = π/2, B = 0
(b) A = π/4, B = p/4sinα
(c) A = π/6, B = p/sinα
(d) A = π, B = p/sinα

Correct Answer is option (A, B)

JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced
JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced
Satisfy the last equation.


Q.18. Let JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advancedis natural number,  then
(a) 1n-2 > In
(b) n (ln-2 - In) = In-2
(c) JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced
(d) JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced

Correct Answer is option (A, B)
JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced
In =(n -1) In-2, -(n -1) In

nIn = (n -1) I n-2

n (ln-2 - In ) = In-2

Clearly In-2 > In
Also for JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced
0 < cos x< 1

So, cosn x < cosn-1x
⇒ In < In - 1
JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced


Q.19. The value of the integral I = JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advancedis
(a) JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced(a > 0, b > 0)
(b) JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced(a < 0, b < 0) 
(c) JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced(a = 1, b = 1)
(d) JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced

Correct Answer is option (A, B, C)
JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced


Q.20. The value of JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advancedis
(a) JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced
(b) 1
(c) π/4
(d) JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced

Correct Answer is option ( B, D)

Let JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced
JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced
JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced

The document JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced is a part of the JEE Course Chapter-wise Tests for JEE Main & Advanced.
All you need of JEE at this link: JEE
446 docs|930 tests

Top Courses for JEE

Explore Courses for JEE exam

Top Courses for JEE

Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Related Searches

Objective type Questions

,

JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced

,

mock tests for examination

,

past year papers

,

JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced

,

Semester Notes

,

video lectures

,

Extra Questions

,

MCQs

,

Free

,

pdf

,

study material

,

Exam

,

ppt

,

Previous Year Questions with Solutions

,

Viva Questions

,

Sample Paper

,

JEE Advanced (One or More Correct Option): Applications of Derivatives | Chapter-wise Tests for JEE Main & Advanced

,

Summary

,

practice quizzes

,

Important questions

,

shortcuts and tricks

;