ExamSIDE
Questions
ExamSIDE.Com
Mathematics
Algebra
Complex Numbers
Quadratic Equation and Inequalities
Permutations and Combinations
Mathematical Induction and Binomial Theorem
Sequences and Series
Matrices and Determinants
Vector Algebra and 3D Geometry
Probability
Statistics
Mathematical Reasoning
Sets and Relations
Trigonometry
Trigonometric Functions & Equations
Properties of Triangle
Inverse Trigonometric Functions
Coordinate Geometry
Straight Lines and Pair of Straight Lines
Circle
Conic Sections
Calculus
Functions
Limits, Continuity and Differentiability
Differentiation
Application of Derivatives
Indefinite Integrals
Definite Integrals and Applications of Integrals
Differential Equations
Joint Entrance Examination
JEE Main
Chemistry
Physics
Mathematics
JEE Advanced
Physics
Chemistry
Mathematics
WB JEE
Physics
Chemistry
Mathematics
Graduate Aptitude Test in Engineering
GATE CSE
Discrete Mathematics
Programming Languages
Theory of Computation
Operating Systems
Digital Logic
Computer Organization
Database Management System
Data Structures
Computer Networks
Algorithms
Compiler Design
Software Engineering
Web Technologies
General Aptitude
GATE ECE
Signals and Systems
Network Theory
Control Systems
Digital Circuits
General Aptitude
Electronic Devices and VLSI
Analog Circuits
Engineering Mathematics
Microprocessors
Communications
Electromagnetics
GATE EE
Electric Circuits
Electromagnetic Fields
Signals and Systems
Electrical Machines
Engineering Mathematics
General Aptitude
Power System Analysis
Electrical and Electronics Measurement
Analog Electronics
Control Systems
Power Electronics
Digital Electronics
GATE ME
Engineering Mechanics
Machine Design
Strength of Materials
Heat Transfer
Production Engineering
Industrial Engineering
Turbo Machinery
Theory of Machines
Engineering Mathematics
Fluid Mechanics
Thermodynamics
General Aptitude
GATE CE
Engineering Mechanics
Strength of Materials Or Solid Mechanics
Structural Analysis
Construction Material and Management
Reinforced Cement Concrete
Steel Structures
Geotechnical Engineering
Fluid Mechanics and Hydraulic Machines
Hydrology
Irrigation
Geomatics Engineering Or Surveying
Environmental Engineering
Transportation Engineering
Engineering Mathematics
General Aptitude
GATE PI
Fluid Mechanics
Metrology
Theory of Machines
Engineering Mathematics
Heat Transfer
Machine Tools and Machining
Industrial Engineering
Engineering Mechanics
Strength of Materials
Thermodynamics
Machine Design
Casting
Joining of Materials
Metal Forming
GATE IN
Engineering Mathematics
Medical
NEET
Biology
Chemistry
Physics
NEW
New Website Launch
Experience the best way to solve previous year questions with
mock tests
(very detailed analysis),
bookmark your favourite questions
,
practice
etc...
VISIT NOW
JEE Main
Application of Derivatives
Mathematics
Previous Years Questions
START HERE
Numerical
More
If the tangent to the curve $$y=x^{3}-x^{2}+x$$ at the point $$(a, b)$$ is also tangent to the curve $$y = 5{x^2} + 2x -...
JEE Main 2022 (Online) 29th July Evening Shift
GO TO QUESTION
For the curve $$C:\left(x^{2}+y^{2}-3\right)+\left(x^{2}-y^{2}-1\right)^{5}=0$$, the value of $$3 y^{\prime}-y^{3} y^{\p...
JEE Main 2022 (Online) 27th July Evening Shift
GO TO QUESTION
A water tank has the shape of a right circular cone with axis vertical and vertex downwards. Its semi-vertical angle is ...
JEE Main 2022 (Online) 27th July Evening Shift
GO TO QUESTION
Let $$M$$ and $$N$$ be the number of points on the curve $$y^{5}-9 x y+2 x=0$$, where the tangents to the curve are para...
JEE Main 2022 (Online) 27th July Morning Shift
GO TO QUESTION
Let the function $$f(x)=2 x^{2}-\log _{\mathrm{e}} x, x>0$$, be decreasing in $$(0, \mathrm{a})$$ and increasing in $$(\...
JEE Main 2022 (Online) 26th July Morning Shift
GO TO QUESTION
A hostel has 100 students. On a certain day (consider it day zero) it was found that two students are infected with some...
JEE Main 2022 (Online) 30th June Morning Shift
GO TO QUESTION
Let $$f(x) = |(x - 1)({x^2} - 2x - 3)| + x - 3,\,x \in R$$. If m and M are respectively the number of points of local mi...
JEE Main 2022 (Online) 25th June Evening Shift
GO TO QUESTION
Let l be a line which is normal to the curve y = 2x2 + x + 2 at a point P on the curve. If the point Q(6, 4) lies on the...
JEE Main 2022 (Online) 28th June Morning Shift
GO TO QUESTION
The number of distinct real roots of the equation 3x4 + 4x3 $$-$$ 12x2 + 4 = 0 is _____________....
JEE Main 2021 (Online) 27th August Morning Shift
GO TO QUESTION
A wire of length 36 m is cut into two pieces, one of the pieces is bent to form a square and the other is bent to form a...
JEE Main 2021 (Online) 26th August Morning Shift
GO TO QUESTION
Let f : [$$-$$1, 1] $$ \to $$ R be defined as f(x) = ax2 + bx + c for all x$$\in$$[$$-$$1, 1], where a, b, c$$\in$$R suc...
JEE Main 2021 (Online) 17th March Evening Shift
GO TO QUESTION
Let a be an integer such that all the real roots of the polynomial 2x5 + 5x4 + 10x3 + 10x2 + 10x + 10 lie in the interva...
JEE Main 2021 (Online) 26th February Evening Shift
GO TO QUESTION
If the curves x = y4 and xy = k cut at right angles, then (4k)6 is equal to __________.
JEE Main 2021 (Online) 25th February Evening Shift
GO TO QUESTION
The minimum value of $$\alpha $$ for which the equation $${4 \over {\sin x}} + {1 \over {1 - \sin x}} = \alpha $$ has a...
JEE Main 2021 (Online) 24th February Morning Slot
GO TO QUESTION
Let AD and BC be two vertical poles at A and B respectively on a horizontal ground. If AD = 8 m, BC = 11 m and AB = 10 m...
JEE Main 2020 (Online) 6th September Morning Slot
GO TO QUESTION
If the lines x + y = a and x – y = b touch the curve y = x2 – 3x + 2 at the points where the curve intersects the x-axi...
JEE Main 2020 (Online) 5th September Evening Slot
GO TO QUESTION
Let the normal at a point P on the curve y2 – 3x2 + y + 10 = 0 intersect the y-axis at $$\left( {0,{3 \over 2}} \right)$...
JEE Main 2020 (Online) 8th January Morning Slot
GO TO QUESTION
MCQ (Single Correct Answer)
More
Let $$f(x)=3^{\left(x^{2}-2\right)^{3}+4}, x \in \mathrm{R}$$. Then which of the following statements are true? $$\mathr...
JEE Main 2022 (Online) 29th July Morning Shift
GO TO QUESTION
If the minimum value of $$f(x)=\frac{5 x^{2}}{2}+\frac{\alpha}{x^{5}}, x>0$$, is 14 , then the value of $$\alpha$$ is eq...
JEE Main 2022 (Online) 28th July Morning Shift
GO TO QUESTION
Let $$f(x) = \left\{ {\matrix{ {{x^3} - {x^2} + 10x - 7,} & {x \le 1} \cr { - 2x + {{\log }_2}({b^2} - 4),} & {x...
JEE Main 2022 (Online) 26th July Morning Shift
GO TO QUESTION
The curve $$y(x)=a x^{3}+b x^{2}+c x+5$$ touches the $$x$$-axis at the point $$\mathrm{P}(-2,0)$$ and cuts the $$y$$-axi...
JEE Main 2022 (Online) 25th July Morning Shift
GO TO QUESTION
Let $$f(x) = 4{x^3} - 11{x^2} + 8x - 5,\,x \in R$$. Then f :
JEE Main 2022 (Online) 30th June Morning Shift
GO TO QUESTION
If xy4 attains maximum value at the point (x, y) on the line passing through the points (50 + $$\alpha$$, 0) and (0, 50 ...
JEE Main 2022 (Online) 30th June Morning Shift
GO TO QUESTION
Let $$\lambda x - 2y = \mu $$ be a tangent to the hyperbola $${a^2}{x^2} - {y^2} = {b^2}$$. Then $${\left( {{\lambda \o...
JEE Main 2022 (Online) 24th June Morning Shift
GO TO QUESTION
If the tangent at the point (x1, y1) on the curve $$y = {x^3} + 3{x^2} + 5$$ passes through the origin, then (x1, y1) do...
JEE Main 2022 (Online) 24th June Morning Shift
GO TO QUESTION
The surface area of a balloon of spherical shape being inflated, increases at a constant rate. If initially, the radius ...
JEE Main 2022 (Online) 24th June Morning Shift
GO TO QUESTION
Let $$\lambda$$$$^ * $$ be the largest value of $$\lambda$$ for which the function $${f_\lambda }(x) = 4\lambda {x^3} - ...
JEE Main 2022 (Online) 24th June Evening Shift
GO TO QUESTION
The slope of normal at any point (x, y), x > 0, y > 0 on the curve y = y(x) is given by $${{{x^2}} \over {xy - {x^2}{y^2...
JEE Main 2022 (Online) 24th June Evening Shift
GO TO QUESTION
If the angle made by the tangent at the point (x0, y0) on the curve $$x = 12(t + \sin t\cos t)$$, $$y = 12{(1 + \sin t)^...
JEE Main 2022 (Online) 25th June Evening Shift
GO TO QUESTION
Water is being filled at the rate of 1 cm3 / sec in a right circular conical vessel (vertex downwards) of height 35 cm a...
JEE Main 2022 (Online) 25th June Evening Shift
GO TO QUESTION
Consider a cuboid of sides 2x, 4x and 5x and a closed hemisphere of radius r. If the sum of their surface areas is a con...
JEE Main 2022 (Online) 26th June Evening Shift
GO TO QUESTION
Let S be the set of all the natural numbers, for which the line $${x \over a} + {y \over b} = 2$$ is a tangent to the cu...
JEE Main 2022 (Online) 26th June Morning Shift
GO TO QUESTION
The sum of the absolute minimum and the absolute maximum values of the function f(x) = |3x $$-$$ x2 + 2| $$-$$ x in the ...
JEE Main 2022 (Online) 26th June Morning Shift
GO TO QUESTION
Let $${{dy} \over {dx}} = {{ax - by + a} \over {bx + cy + a}}$$, where a, b, c are constants, represent a circle passing...
JEE Main 2022 (Online) 27th June Morning Shift
GO TO QUESTION
A wire of length 22 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into an ...
JEE Main 2022 (Online) 29th June Morning Shift
GO TO QUESTION
The number of real roots of the equation $${e^{4x}} + 2{e^{3x}} - {e^x} - 6 = 0$$ is :
JEE Main 2021 (Online) 31st August Morning Shift
GO TO QUESTION
A box open from top is made from a rectangular sheet of dimension a $$\times$$ b by cutting squares each of side x from ...
JEE Main 2021 (Online) 27th August Evening Shift
GO TO QUESTION
A wire of length 20 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into a r...
JEE Main 2021 (Online) 27th August Morning Shift
GO TO QUESTION
Let 'a' be a real number such that the function f(x) = ax2 + 6x $$-$$ 15, x $$\in$$ R is increasing in $$\left( { - \inf...
JEE Main 2021 (Online) 20th July Morning Shift
GO TO QUESTION
The maximum value of $$f(x) = \left| {\matrix{ {{{\sin }^2}x} & {1 + {{\cos }^2}x} & {\cos 2x} \cr {1 + ...
JEE Main 2021 (Online) 16th March Evening Shift
GO TO QUESTION
Let slope of the tangent line to a curve at any point P(x, y) be given by $${{x{y^2} + y} \over x}$$. If the curve inter...
JEE Main 2021 (Online) 26th February Evening Shift
GO TO QUESTION
Let A1 be the area of the region bounded by the curves y = sinx, y = cosx and y-axis in the first quadrant. Also, let A2...
JEE Main 2021 (Online) 26th February Evening Shift
GO TO QUESTION
The maximum slope of the curve $$y = {1 \over 2}{x^4} - 5{x^3} + 18{x^2} - 19x$$ occurs at the point :
JEE Main 2021 (Online) 26th February Morning Shift
GO TO QUESTION
The minimum value of $$f(x) = {a^{{a^x}}} + {a^{1 - {a^x}}}$$, where a, $$x \in R$$ and a > 0, is equal to :
JEE Main 2021 (Online) 25th February Evening Shift
GO TO QUESTION
If the curves, $${{{x^2}} \over a} + {{{y^2}} \over b} = 1$$ and $${{{x^2}} \over c} + {{{y^2}} \over d} = 1$$ intersect...
JEE Main 2021 (Online) 25th February Morning Slot
GO TO QUESTION
If the curve y = ax2 + bx + c, x$$ \in $$R, passes through the point (1, 2) and the tangent line to this curve at origin...
JEE Main 2021 (Online) 24th February Evening Slot
GO TO QUESTION
Let $$f:R \to R$$ be defined as$$f(x) = \left\{ {\matrix{ { - 55x,} & {if\,x < - 5} \cr {2{x^3} - 3{x^2}...
JEE Main 2021 (Online) 24th February Evening Slot
GO TO QUESTION
For which of the following curves, the line $$x + \sqrt 3 y = 2\sqrt 3 $$ is the tangent at the point $$\left( {{{3\sqrt...
JEE Main 2021 (Online) 24th February Evening Slot
GO TO QUESTION
If the tangent to the curve y = x3 at the point P(t, t3) meets the curve again at Q, then the ordinate of the point whic...
JEE Main 2021 (Online) 24th February Morning Slot
GO TO QUESTION
The function f(x) = $${{4{x^3} - 3{x^2}} \over 6} - 2\sin x + \left( {2x - 1} \right)\cos x$$ :
JEE Main 2021 (Online) 24th February Morning Slot
GO TO QUESTION
If the tangent to the curve, y = f (x) = xloge x, (x > 0) at a point (c, f(c)) is parallel to the line-segment joinin...
JEE Main 2020 (Online) 6th September Evening Slot
GO TO QUESTION
The set of all real values of $$\lambda $$ for which the function $$f(x) = \left( {1 - {{\cos }^2}x} \right)\left( {\lam...
JEE Main 2020 (Online) 6th September Evening Slot
GO TO QUESTION
The position of a moving car at time t is given by f(t) = at2 + bt + c, t > 0, where a, b and c are real numbers grea...
JEE Main 2020 (Online) 6th September Morning Slot
GO TO QUESTION
If x = 1 is a critical point of the function f(x) = (3x2 + ax – 2 – a)ex , then :
JEE Main 2020 (Online) 5th September Evening Slot
GO TO QUESTION
Which of the following points lies on the tangent to the curve x4ey + 2$$\sqrt {y + 1} $$ = 3 at the point (1, 0)?...
JEE Main 2020 (Online) 5th September Evening Slot
GO TO QUESTION
If the point P on the curve, 4x2 + 5y2 = 20 is farthest from the point Q(0, -4), then PQ2 is equal to: ...
JEE Main 2020 (Online) 5th September Morning Slot
GO TO QUESTION
The area (in sq. units) of the largest rectangle ABCD whose vertices A and B lie on the x-axis and vertices C and D lie ...
JEE Main 2020 (Online) 4th September Evening Slot
GO TO QUESTION
The minimum value of 2sinx + 2cosx is:
JEE Main 2020 (Online) 4th September Evening Slot
GO TO QUESTION
If the surface area of a cube is increasing at a rate of 3.6 cm2/sec, retaining its shape; then the rate of change of it...
JEE Main 2020 (Online) 3rd September Evening Slot
GO TO QUESTION
The function, f(x) = (3x – 7)x2/3, x $$ \in $$ R, is increasing for all x lying in :
JEE Main 2020 (Online) 3rd September Morning Slot
GO TO QUESTION
The equation of the normal to the curve y = (1+x)2y + cos 2(sin–1x) at x = 0 is :
JEE Main 2020 (Online) 2nd September Evening Slot
GO TO QUESTION
Let f : (–1, $$\infty $$) $$ \to $$ R be defined by f(0) = 1 and f(x) = $${1 \over x}{\log _e}\left( {1 + x} \right)$$, ...
JEE Main 2020 (Online) 2nd September Evening Slot
GO TO QUESTION
If p(x) be a polynomial of degree three that has a local maximum value 8 at x = 1 and a local minimum value 4 at x = 2; ...
JEE Main 2020 (Online) 2nd September Morning Slot
GO TO QUESTION
If the tangent to the curve y = x + sin y at a point (a, b) is parallel to the line joining $$\left( {0,{3 \over 2}} \ri...
JEE Main 2020 (Online) 2nd September Morning Slot
GO TO QUESTION
Let P(h, k) be a point on the curve y = x2 + 7x + 2, nearest to the line, y = 3x – 3. Then the equation of the normal t...
JEE Main 2020 (Online) 2nd September Morning Slot
GO TO QUESTION
A spherical iron ball of 10 cm radius is coated with a layer of ice of uniform thickness the melts at a rate of 50 cm3/m...
JEE Main 2020 (Online) 9th January Morning Slot
GO TO QUESTION
A 2 m ladder leans against a vertical wall. If the top of the ladder begins to slide down the wall at the rate 25 cm/sec...
JEE Main 2019 (Online) 12th April Morning Slot
GO TO QUESTION
If m is the minimum value of k for which the function f(x) = x$$\sqrt {kx - {x^2}} $$ is increasing in the interval [0,3...
JEE Main 2019 (Online) 12th April Morning Slot
GO TO QUESTION
If the tangent to the curve $$y = {x \over {{x^2} - 3}}$$ , $$x \in \rho ,\left( {x \ne \pm \sqrt 3 } \right)$$, at a p...
JEE Main 2019 (Online) 10th April Evening Slot
GO TO QUESTION
A spherical iron ball of radius 10 cm is coated with a layer of ice of uniform thickness that melts at a rate of 50 cm3 ...
JEE Main 2019 (Online) 10th April Evening Slot
GO TO QUESTION
A water tank has the shape of an inverted right circular cone, whose semi-vertical angle is $${\tan ^{ - 1}}\left( {{1 \...
JEE Main 2019 (Online) 9th April Evening Slot
GO TO QUESTION
If the tangent to the curve, y = x3 + ax – b at the point (1, –5) is perpendicular to the line, –x + y + 4 = 0, then whi...
JEE Main 2019 (Online) 9th April Morning Slot
GO TO QUESTION
Let S be the set of all values of x for which the tangent to the curve y = ƒ(x) = x3 – x2 – 2x at (x, y) is parallel to...
JEE Main 2019 (Online) 9th April Morning Slot
GO TO QUESTION
If ƒ(x) is a non-zero polynomial of degree four, having local extreme points at x = –1, 0, 1; then the set S = {x $$ \i...
JEE Main 2019 (Online) 9th April Morning Slot
GO TO QUESTION
The height of a right circular cylinder of maximum volume inscribed in a sphere of radius 3 is
JEE Main 2019 (Online) 8th April Evening Slot
GO TO QUESTION
Given that the slope of the tangent to a curve y = y(x) at any point (x, y) is $$2y \over x^2$$. If the curve passes th...
JEE Main 2019 (Online) 8th April Evening Slot
GO TO QUESTION
Let ƒ : [0, 2] $$ \to $$ R be a twice differentiable function such that ƒ''(x) > 0, for all x $$ \in $$ (0, 2). If $$...
JEE Main 2019 (Online) 8th April Morning Slot
GO TO QUESTION
If S1 and S2 are respectively the sets of local minimum and local maximum points of the function, ƒ(x) = 9x4 + 12x3 – 3...
JEE Main 2019 (Online) 8th April Morning Slot
GO TO QUESTION
The tangent to the curve y = x2 – 5x + 5, parallel to the line 2y = 4x + 1, also passes through the point :
JEE Main 2019 (Online) 12th January Evening Slot
GO TO QUESTION
Let f(x) = $${x \over {\sqrt {{a^2} + {x^2}} }} - {{d - x} \over {\sqrt {{b^2} + {{\left( {d - x} \right)}^2}} }},\,\,$$...
JEE Main 2019 (Online) 11th January Evening Slot
GO TO QUESTION
If y(x) is the solution of the differential equation $${{dy} \over {dx}} + \left( {{{2x + 1} \over x}} \right)y = {...
JEE Main 2019 (Online) 11th January Morning Slot
GO TO QUESTION
The maximum value of the function f(x) = 3x3 – 18x2 + 27x – 40 on the set S = $$\left\{ {x\, \in R:{x^2} + 30 \le 11x} ...
JEE Main 2019 (Online) 11th January Morning Slot
GO TO QUESTION
The tangent to the curve, y = xex2 passing through the point (1, e) also passes through the point
JEE Main 2019 (Online) 10th January Evening Slot
GO TO QUESTION
The shortest distance between the point $$\left( {{3 \over 2},0} \right)$$ and the curve y = $$\s...
JEE Main 2019 (Online) 10th January Morning Slot
GO TO QUESTION
If $${{dy} \over {dx}} + {3 \over {{{\cos }^2}x}}y = {1 \over {{{\cos }^2}x}},\,\,x \in \left( {{{ - \pi } \over 3...
JEE Main 2019 (Online) 10th January Morning Slot
GO TO QUESTION
Let M and m be respectively the absolute maximum and the absolute minimum values of the function, f(x) = 2x3 $$-$$ 9x2 ...
JEE Main 2018 (Online) 16th April Morning Slot
GO TO QUESTION
If $$\beta $$ is one of the angles between the normals to the ellipse, x2 + 3y2 = 9 at the points (3 cos $$\theta $$, $$...
JEE Main 2018 (Online) 15th April Morning Slot
GO TO QUESTION
If a right circular cone, having maximum volume, is inscribed in a sphere of radius 3 cm, then the curved surface area (...
JEE Main 2018 (Online) 15th April Morning Slot
GO TO QUESTION
A tangent to the curve, y = f(x) at P(x, y) meets x-axis at A and y-axis at B. If AP : BP = 1 : 3 and f(1) = 1, then the...
JEE Main 2017 (Online) 9th April Morning Slot
GO TO QUESTION
The function f defined by f(x) = x3 $$-$$ 3x2 + 5x + 7 , is :
JEE Main 2017 (Online) 9th April Morning Slot
GO TO QUESTION
The tangent at the point (2, $$-$$2) to the curve, x2y2 $$-$$ 2x = 4(1 $$-$$ y) does not pass through the point : ...
JEE Main 2017 (Online) 8th April Morning Slot
GO TO QUESTION
Let C be a curve given by y(x) = 1 + $$\sqrt {4x - 3} ,x > {3 \over 4}.$$ If P is a point on C, such that the tangent...
JEE Main 2016 (Online) 10th April Morning Slot
GO TO QUESTION
The minimum distance of a point on the curve y = x2−4 from the origin is :
JEE Main 2016 (Online) 9th April Morning Slot
GO TO QUESTION
If the tangent at a point P, with parameter t, on the curve x = 4t2 + 3, y = 8t3−1, t $$ \in $$ R, meets the curve again...
JEE Main 2016 (Online) 9th April Morning Slot
GO TO QUESTION
Consider : f $$\left( x \right) = {\tan ^{ - 1}}\left( {\sqrt {{{1 + \sin x} \over {1 - \sin x}}} } \right),x \in \left(...
JEE Main 2016 (Offline)
GO TO QUESTION
A wire of length $$2$$ units is cut into two parts which are bent respectively to form a square of side $$=x$$ units and...
JEE Main 2016 (Offline)
GO TO QUESTION
Let $$f(x)$$ be a polynomial of degree four having extreme values at $$x=1$$ and $$x=2$$. If $$\mathop {\lim }\limits_{...
JEE Main 2015 (Offline)
GO TO QUESTION
If $$f$$ and $$g$$ are differentiable functions in $$\left[ {0,1} \right]$$ satisfying $$f\left( 0 \right) = 2 = g\left...
JEE Main 2014 (Offline)
GO TO QUESTION
The intercepts on $$x$$-axis made by tangents to the curve, $$y = \int\limits_0^x {\left| t \right|dt,x \in R,} $$ whic...
JEE Main 2013 (Offline)
GO TO QUESTION
A line is drawn through the point $$(1, 2)$$ to meet the coordinate axes at $$P$$ and $$Q$$ such that it forms a triang...
AIEEE 2012
GO TO QUESTION
A spherical balloon is filled with $$4500\pi $$ cubic meters of helium gas. If a leak in the balloon causes the gas to e...
AIEEE 2012
GO TO QUESTION
Let $$a,b \in R$$ be such that the function $$f$$ given by $$f\left( x \right) = In\left| x \right| + b{x^2} + ax,\,x \n...
AIEEE 2012
GO TO QUESTION
The shortest distance between line $$y-x=1$$ and curve $$x = {y^2}$$ is
AIEEE 2011
GO TO QUESTION
For $$x \in \left( {0,{{5\pi } \over 2}} \right),$$ define $$f\left( x \right) = \int\limits_0^x {\sqrt t \sin t\,dt.} $...
AIEEE 2011
GO TO QUESTION
Let $$f:R \to R$$ be a continuous function defined by $$$f\left( x \right) = {1 \over {{e^x} + 2{e^{ - x}}}}$$$ Stateme...
AIEEE 2010
GO TO QUESTION
Let $$f:R \to R$$ be defined by $$$f\left( x \right) = \left\{ {\matrix{ {k - 2x,\,\,if} & {x \le - 1} \cr ...
AIEEE 2010
GO TO QUESTION
The equation of the tangent to the curve $$y = x + {4 \over {{x^2}}}$$, that is parallel to the $$x$$-axis, is
AIEEE 2010
GO TO QUESTION
Given $$P\left( x \right) = {x^4} + a{x^3} + b{x^2} + cx + d$$ such that $$x=0$$ is the only real root of $$P'\,\left( ...
AIEEE 2009
GO TO QUESTION
Let $$f\left( x \right) = x\left| x \right|$$ and $$g\left( x \right) = \sin x.$$ Statement-1: gof is differentiable at ...
AIEEE 2009
GO TO QUESTION
How many real solutions does the equation $${x^7} + 14{x^5} + 16{x^3} + 30x - 560 = 0$$ have?
AIEEE 2008
GO TO QUESTION
Suppose the cubic $${x^3} - px + q$$ has three distinct real roots where $$p>0$$ and $$q>0$$. Then which one of t...
AIEEE 2008
GO TO QUESTION
If $$p$$ and $$q$$ are positive real numbers such that $${p^2} + {q^2} = 1$$, then the maximum value of $$(p+q)$$ is
AIEEE 2007
GO TO QUESTION
A value of $$c$$ for which conclusion of Mean Value Theorem holds for the function $$f\left( x \right) = {\log _e}x$$ on...
AIEEE 2007
GO TO QUESTION
The function $$f\left( x \right) = {\tan ^{ - 1}}\left( {\sin x + \cos x} \right)$$ is an incresing function in
AIEEE 2007
GO TO QUESTION
A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides havi...
AIEEE 2006
GO TO QUESTION
The function $$f\left( x \right) = {x \over 2} + {2 \over x}$$ has a local minimum at
AIEEE 2006
GO TO QUESTION
If the equation $${a_n}{x^n} + {a_{n - 1}}{x^{n - 1}} + ........... + {a_1}x = 0$$ $${a_1} \ne 0,n \ge 2,$$ has a positi...
AIEEE 2005
GO TO QUESTION
The normal to the curve $$x = a\left( {\cos \theta + \theta \sin \theta } \right),y = a\left( {\sin \theta - \theta \...
AIEEE 2005
GO TO QUESTION
A spherical iron ball $$10$$ cm in radius is coated with a layer of ice of uniform thickness that melts at a rate of $$5...
AIEEE 2005
GO TO QUESTION
Area of the greatest rectangle that can be inscribed in the ellipse $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}}...
AIEEE 2005
GO TO QUESTION
The normal to the curve x = a(1 + cos $$\theta $$), $$y = a\sin \theta $$ at $$'\theta '$$ always passes through the fix...
AIEEE 2004
GO TO QUESTION
If $$2a+3b+6c=0$$, then at least one root of the equation $$a{x^2} + bx + c = 0$$ lies in the interval
AIEEE 2004
GO TO QUESTION
A function $$y=f(x)$$ has a second order derivative $$f''\left( x \right) = 6\left( {x - 1} \right).$$ If its graph pass...
AIEEE 2004
GO TO QUESTION
A point on the parabola $${y^2} = 18x$$ at which the ordinate increases at twice the rate of the abscissa is
AIEEE 2004
GO TO QUESTION
If the function $$f\left( x \right) = 2{x^3} - 9a{x^2} + 12{a^2}x + 1,$$ where $$a>0,$$ attains its maximum and minim...
AIEEE 2003
GO TO QUESTION
If $$2a+3b+6c=0,$$ $$\left( {a,b,c \in R} \right)$$ then the quadratic equation $$a{x^2} + bx + c = 0$$ has
AIEEE 2002
GO TO QUESTION
The maximum distance from origin of a point on the curve $$x = a\sin t - b\sin \left( {{{at} \over b}} \right)$$ $$y = ...
AIEEE 2002
GO TO QUESTION
Joint Entrance Examination
JEE Main
JEE Advanced
WB JEE
Graduate Aptitude Test in Engineering
GATE CSE
GATE ECE
GATE EE
GATE ME
GATE CE
GATE PI
GATE IN
Medical
NEET
CBSE
Class 12