1
JEE Advanced 2020 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1
Consider the rectangles lying the region
$$\left\{ {(x,y) \in R \times R:0\, \le \,x\, \le \,{\pi \over 2}} \right.$$ and $$\left. {0\, \le \,y\, \le \,2\sin (2x)} \right\}$$
and having one side on the X-axis. The area of the rectangle which has the maximum perimeter among all such rectangles, is
$$\left\{ {(x,y) \in R \times R:0\, \le \,x\, \le \,{\pi \over 2}} \right.$$ and $$\left. {0\, \le \,y\, \le \,2\sin (2x)} \right\}$$
and having one side on the X-axis. The area of the rectangle which has the maximum perimeter among all such rectangles, is
2
JEE Advanced 2017 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1
By approximately matching the information given in the three columns of the following table.
Let f(x) = x + loge x $$-$$ x loge x, x$$ \in $$(0, $$\infty $$)
Column 1 contains information about zeroes of f(x), f'(x) and f"(x).
Column 2 contains information about the limiting behaviour of f(x), f'(x) and f"(x) at infinity.
Column 3 contains information about increasing/decreasing nature of f(x) and f'(x).
Let f(x) = x + loge x $$-$$ x loge x, x$$ \in $$(0, $$\infty $$)
Column 1 contains information about zeroes of f(x), f'(x) and f"(x).
Column 2 contains information about the limiting behaviour of f(x), f'(x) and f"(x) at infinity.
Column 3 contains information about increasing/decreasing nature of f(x) and f'(x).
Column - 1 | Column - 2 | Column - 3 | |
---|---|---|---|
(i) | f(x) = 0 for some $$x \in (1,{e^2})$$ | (i) $$\mathop {\lim }\limits_{x \to \infty } \,f(x) = 0$$ | f is increasing in (0, 1) |
(ii) | f'(x) = 0 for some $$x \in (1,e)$$ | $$\mathop {\lim }\limits_{x \to \infty } \,f(x) = - \infty $$ | f is decreasing in (e, $${e^2}$$) |
(iii) | f'(x) = 0 for some $$x \in (0,1)$$ | $$\mathop {\lim }\limits_{x \to \infty } \,f'(x) = - \infty $$ | f' is increasing in (0, 1) |
(iv) | f'(x) = 0 for some $$x \in (1,e)$$ | $$\mathop {\lim }\limits_{x \to \infty } \,f'(x) = 0$$ | f' is decreasing in (e, $${e^2}$$) |
Which of the following options is the only INCORRECT combination?
3
JEE Advanced 2017 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1
By approximately matching the information given in the three columns of the following table.
Let f(x) = x + loge x $$-$$ x loge x, x$$ \in $$(0, $$\infty $$)
Column 1 contains information about zeroes of f(x), f'(x) and f"(x).
Column 2 contains information about the limiting behaviour of f(x), f'(x) and f"(x) at infinity.
Column 3 contains information about increasing/decreasing nature of f(x) and f'(x).
Let f(x) = x + loge x $$-$$ x loge x, x$$ \in $$(0, $$\infty $$)
Column 1 contains information about zeroes of f(x), f'(x) and f"(x).
Column 2 contains information about the limiting behaviour of f(x), f'(x) and f"(x) at infinity.
Column 3 contains information about increasing/decreasing nature of f(x) and f'(x).
Column - 1 | Column - 2 | Column - 3 | |
---|---|---|---|
(i) | f(x) = 0 for some $$x \in (1,{e^2})$$ | (i) $$\mathop {\lim }\limits_{x \to \infty } \,f(x) = 0$$ | f is increasing in (0, 1) |
(ii) | f'(x) = 0 for some $$x \in (1,e)$$ | $$\mathop {\lim }\limits_{x \to \infty } \,f(x) = - \infty $$ | f is decreasing in (e, $${e^2}$$) |
(iii) | f'(x) = 0 for some $$x \in (0,1)$$ | $$\mathop {\lim }\limits_{x \to \infty } \,f'(x) = - \infty $$ | f' is increasing in (0, 1) |
(iv) | f'(x) = 0 for some $$x \in (1,e)$$ | $$\mathop {\lim }\limits_{x \to \infty } \,f'(x) = 0$$ | f' is decreasing in (e, $${e^2}$$) |
Which of the following options is the only CORRECT combination?
4
JEE Advanced 2017 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1
By approximately matching the information given in the three columns of the following table.
Let f(x) = x + loge x $$-$$ x loge x, x$$ \in $$(0, $$\infty $$)
Column 1 contains information about zeroes of f(x), f'(x) and f"(x).
Column 2 contains information about the limiting behaviour of f(x), f'(x) and f"(x) at infinity.
Column 3 contains information about increasing/decreasing nature of f(x) and f'(x).
Let f(x) = x + loge x $$-$$ x loge x, x$$ \in $$(0, $$\infty $$)
Column 1 contains information about zeroes of f(x), f'(x) and f"(x).
Column 2 contains information about the limiting behaviour of f(x), f'(x) and f"(x) at infinity.
Column 3 contains information about increasing/decreasing nature of f(x) and f'(x).
Column - 1 | Column - 2 | Column - 3 | |
---|---|---|---|
(i) | f(x) = 0 for some $$x \in (1,{e^2})$$ | (i) $$\mathop {\lim }\limits_{x \to \infty } \,f(x) = 0$$ | f is increasing in (0, 1) |
(ii) | f'(x) = 0 for some $$x \in (1,e)$$ | $$\mathop {\lim }\limits_{x \to \infty } \,f(x) = - \infty $$ | f is decreasing in (e, $${e^2}$$) |
(iii) | f'(x) = 0 for some $$x \in (0,1)$$ | $$\mathop {\lim }\limits_{x \to \infty } \,f'(x) = - \infty $$ | f' is increasing in (0, 1) |
(iv) | f'(x) = 0 for some $$x \in (1,e)$$ | $$\mathop {\lim }\limits_{x \to \infty } \,f'(x) = 0$$ | f' is decreasing in (e, $${e^2}$$) |
Which of the following options is the only CORRECT combination?
Questions Asked from Application of Derivatives (MCQ (Single Correct Answer))
Number in Brackets after Paper Indicates No. of Questions
JEE Advanced 2020 Paper 1 Offline (1)
JEE Advanced 2017 Paper 1 Offline (3)
JEE Advanced 2016 Paper 1 Offline (1)
JEE Advanced 2013 Paper 2 Offline (2)
IIT-JEE 2012 Paper 2 Offline (2)
IIT-JEE 2008 Paper 1 Offline (1)
IIT-JEE 2007 (4)
IIT-JEE 2005 Screening (1)
IIT-JEE 2004 Screening (2)
IIT-JEE 2003 Screening (2)
IIT-JEE 2002 Screening (2)
IIT-JEE 2001 Screening (3)
IIT-JEE 2000 Screening (5)
IIT-JEE 1999 (1)
IIT-JEE 1998 (2)
IIT-JEE 1997 (1)
IIT-JEE 1995 Screening (3)
IIT-JEE 1994 (2)
IIT-JEE 1987 (2)
IIT-JEE 1986 (1)
IIT-JEE 1983 (4)
JEE Advanced Subjects
Physics
Mechanics
Units & Measurements
Motion
Laws of Motion
Work Power & Energy
Impulse & Momentum
Rotational Motion
Properties of Matter
Heat and Thermodynamics
Simple Harmonic Motion
Waves
Gravitation
Electricity
Optics
Modern Physics
Chemistry
Physical Chemistry
Some Basic Concepts of Chemistry
Structure of Atom
Redox Reactions
Gaseous State
Equilibrium
Solutions
States of Matter
Thermodynamics
Chemical Kinetics and Nuclear Chemistry
Electrochemistry
Solid State & Surface Chemistry
Inorganic Chemistry
Periodic Table & Periodicity
Chemical Bonding & Molecular Structure
Isolation of Elements
Hydrogen
s-Block Elements
p-Block Elements
d and f Block Elements
Coordination Compounds
Salt Analysis
Organic Chemistry
Mathematics
Algebra
Quadratic Equation and Inequalities
Sequences and Series
Mathematical Induction and Binomial Theorem
Matrices and Determinants
Permutations and Combinations
Probability
Vector Algebra and 3D Geometry
Complex Numbers
Trigonometry
Coordinate Geometry
Calculus