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## MCQ (More than One Correct Answer)

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Let $$|M|$$ denote the determinant of a square matrix $$M$$. Let $$g:\left[0, \frac{\pi}{2}\right] \rightarrow \mathbb{R... JEE Advanced 2022 Paper 1 Online Let$$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

## 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 $$is the number of one-one f... JEE Advanced 2018 Paper 2 Offline ## MCQ (Single Correct Answer) More If the function f : R$$ \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}} &gt; 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

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