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JEE Advanced

Functions

Mathematics

Previous Years Questions

Numerical

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Let the function $$f:(0,\pi ) \to R$$ be defined by $$f(\theta ) = {(\sin \theta + \cos \theta )^2} + {(\sin \theta - ...
JEE Advanced 2020 Paper 2 Offline
Let the function f : [0, 1] $$ \to $$ R be defined by$$f(x) = {{{4^x}} \over {{4^x} + 2}}$$Then the value of $$f\left( {...
JEE Advanced 2020 Paper 2 Offline
For a polynomial g(x) with real coefficients, let mg denote the number of distinct real roots of g(x). Suppose S is the ...
JEE Advanced 2020 Paper 1 Offline
Let f : [0, 2] $$ \to $$ R be the function defined by$$f(x) = (3 - \sin (2\pi x))\sin \left( {\pi x - {\pi \over 4}} \r...
JEE Advanced 2020 Paper 1 Offline
Let X be a set with exactly 5 elements and Y be a set with exactly 7 elements. If $$\alpha $$ is the number of one-one f...
JEE Advanced 2018 Paper 2 Offline

MCQ (Single Correct Answer)

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If the function f : R $$ \to $$ R is defined by f(x) = |x| (x $$-$$ sin x), then which of the following statements is TR...
JEE Advanced 2020 Paper 1 Offline
Let $${E_1} = \left\{ {x \in R:x \ne 1\,and\,{x \over {x - 1}} > 0} \right\}$$ and $${E_2} = \left\{ \matrix{ x \in...
JEE Advanced 2018 Paper 2 Offline
Let S = {1, 2, 3, .........., 9}. For k = 1, 2, .........., 5, let Nk be the number of subsets of S, each containing fiv...
JEE Advanced 2017 Paper 2 Offline
Let f1 : R $$ \to $$ R, f2 : [0, $$\infty $$) $$ \to $$ R, f3 : R $$ \to $$ R, and f4 : R $$ \to $$ [0, $$\infty $$) be ...
JEE Advanced 2014 Paper 2 Offline
The function $$f:[0,3] \to [1,29]$$, defined by $$f(x) = 2{x^3} - 15{x^2} + 36x + 1$$, is
IIT-JEE 2012 Paper 1 Offline
Match the statements given in Column I with the intervals/union of intervals given in Column II : ...
IIT-JEE 2011 Paper 2 Offline
Let f(x) = x2 and g(x) = sin x for all x $$\in$$ R. Then the set of all x satisfying $$(f \circ g \circ g \circ f)(x) = ...
IIT-JEE 2011 Paper 2 Offline

MCQ (More than One Correct Answer)

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Let $$f(x) = \sin \left( {{\pi \over 6}\sin \left( {{\pi \over 2}\sin x} \right)} \right)$$ for all $$x \in R$$ and g(...
JEE Advanced 2015 Paper 1 Offline
Let $$f:\left( { - {\pi \over 2},{\pi \over 2}} \right) \to R$$ be given by $$f(x) = {[\log (\sec x + \tan x)]^3}$$. T...
JEE Advanced 2014 Paper 1 Offline
For every pair of continuous function f, g : [0, 1] $$\to$$ R such that max {f(x) : x $$\in$$ [0, 1]} = max {g(x) : x $$...
JEE Advanced 2014 Paper 1 Offline
Let $$f:( - 1,1) \to R$$ be such that $$f(\cos 4\theta ) = {2 \over {2 - {{\sec }^2}\theta }}$$ for $$\theta \in \left(...
IIT-JEE 2012 Paper 2 Offline
Let $$f:(0,1) \to R$$ be defined by $$f(x) = {{b - x} \over {1 - bx}}$$, where be is a constant such that $$0 ...
IIT-JEE 2011 Paper 2 Offline

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