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The domain of the function $$f(x)=\sin ^{-1}\left(\frac{x^{2}-3 x+2}{x^{2}+2 x+7}\right)$$ is:
JEE Main 2022 (Online) 29th July Evening Shift
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The function $$f(x)=x \mathrm{e}^{x(1-x)}, x \in \mathbb{R}$$, is :
JEE Main 2022 (Online) 28th July Evening Shift
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$$ \text { Let } f(x)=a x^{2}+b x+c \text { be such that } f(1)=3, f(-2)=\lambda \text { and } $$ $$f(3)=4$$. If $$f(0)+...
JEE Main 2022 (Online) 28th July Evening Shift
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Let $$\alpha, \beta$$ and $$\gamma$$ be three positive real numbers. Let $$f(x)=\alpha x^{5}+\beta x^{3}+\gamma x, x \in...
JEE Main 2022 (Online) 28th July Morning Shift
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Considering only the principal values of the inverse trigonometric functions, the domain of the function $$f(x)=\cos ^{-...
JEE Main 2022 (Online) 28th July Morning Shift
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The domain of the function $$f(x)=\sin ^{-1}\left[2 x^{2}-3\right]+\log _{2}\left(\log _{\frac{1}{2}}\left(x^{2}-5 x+5\r...
JEE Main 2022 (Online) 27th July Evening Shift
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Let $$f, g: \mathbb{N}-\{1\} \rightarrow \mathbb{N}$$ be functions defined by $$f(a)=\alpha$$, where $$\alpha$$ is the m...
JEE Main 2022 (Online) 27th July Morning Shift
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If the maximum value of $$a$$, for which the function $$f_{a}(x)=\tan ^{-1} 2 x-3 a x+7$$ is non-decreasing in $$\left(-...
JEE Main 2022 (Online) 26th July Evening Shift
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Let f : R $$\to$$ R be a continuous function such that $$f(3x) - f(x) = x$$. If $$f(8) = 7$$, then $$f(14)$$ is equal to...
JEE Main 2022 (Online) 26th July Morning Shift
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The number of bijective functions $$f:\{1,3,5,7, \ldots, 99\} \rightarrow\{2,4,6,8, \ldots .100\}$$, such that $$f(3) \...
JEE Main 2022 (Online) 25th July Evening Shift
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If the absolute maximum value of the function $$f(x)=\left(x^{2}-2 x+7\right) \mathrm{e}^{\left(4 x^{3}-12 x^{2}-180 x+3...
JEE Main 2022 (Online) 25th July Morning Shift
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The total number of functions, $$ f:\{1,2,3,4\} \rightarrow\{1,2,3,4,5,6\} $$ such that $$f(1)+f(2)=f(3)$$, is equal to...
JEE Main 2022 (Online) 25th July Morning Shift
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Let $${S_1} = \left\{ {x \in R - \{ 1,2\} :{{(x + 2)({x^2} + 3x + 5)} \over { - 2 + 3x - {x^2}}} \ge 0} \right\}$$ and $...
JEE Main 2022 (Online) 30th June Morning Shift
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The domain of the function $$f(x) = {{{{\cos }^{ - 1}}\left( {{{{x^2} - 5x + 6} \over {{x^2} - 9}}} \right)} \over {{{\l...
JEE Main 2022 (Online) 24th June Morning Shift
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The sum of absolute maximum and absolute minimum values of the function $$f(x) = |2{x^2} + 3x - 2| + \sin x\cos x$$ in t...
JEE Main 2022 (Online) 24th June Morning Shift
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For the function $$f(x) = 4{\log _e}(x - 1) - 2{x^2} + 4x + 5,\,x > 1$$, which one of the following is NOT correct?...
JEE Main 2022 (Online) 24th June Morning Shift
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Let $$f:R \to R$$ and $$g:R \to R$$ be two functions defined by $$f(x) = {\log _e}({x^2} + 1) - {e^{ - x}} + 1$$ and $$g...
JEE Main 2022 (Online) 25th June Morning Shift
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Let f(x) be a polynomial function such that $$f(x) + f'(x) + f''(x) = {x^5} + 64$$. Then, the value of $$\mathop {\lim }...
JEE Main 2022 (Online) 25th June Morning Shift
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Let f : R $$\to$$ R be defined as $$f(x) = {x^3} + x - 5$$. If g(x) is a function such that $$f(g(x)) = x,\forall 'x' \i...
JEE Main 2022 (Online) 25th June Morning Shift
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Let f : N $$\to$$ R be a function such that $$f(x + y) = 2f(x)f(y)$$ for natural numbers x and y. If f(1) = 2, then the ...
JEE Main 2022 (Online) 25th June Morning Shift
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Let f : R $$\to$$ R be defined as f (x) = x $$-$$ 1 and g : R $$-$$ {1, $$-$$1} $$\to$$ R be defined as $$g(x) = {{{x^2}...
JEE Main 2022 (Online) 26th June Evening Shift
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Let $$f(x) = 2{\cos ^{ - 1}}x + 4{\cot ^{ - 1}}x - 3{x^2} - 2x + 10$$, $$x \in [ - 1,1]$$. If [a, b] is the range of the...
JEE Main 2022 (Online) 26th June Morning Shift
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Let $$f(x) = {{x - 1} \over {x + 1}},\,x \in R - \{ 0, - 1,1\} $$. If $${f^{n + 1}}(x) = f({f^n}(x))$$ for all n $$\in$$...
JEE Main 2022 (Online) 26th June Morning Shift
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Let a function f : N $$\to$$ N be defined by $$f(n) = \left[ {\matrix{ {2n,} & {n = 2,4,6,8,......} \cr {n - 1,}...
JEE Main 2022 (Online) 28th June Morning Shift
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The domain of the function $${\cos ^{ - 1}}\left( {{{2{{\sin }^{ - 1}}\left( {{1 \over {4{x^2} - 1}}} \right)} \over \pi...
JEE Main 2022 (Online) 29th June Morning Shift
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The range of the function, $$f(x) = {\log _{\sqrt 5 }}\left( {3 + \cos \left( {{{3\pi } \over 4} + x} \right) + \cos \le...
JEE Main 2021 (Online) 1st September Evening Shift
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Let f : N $$\to$$ N be a function such that f(m + n) = f(m) + f(n) for every m, n$$\in$$N. If f(6) = 18, then f(2) . f(3...
JEE Main 2021 (Online) 31st August Evening Shift
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The domain of the function$$f(x) = {\sin ^{ - 1}}\left( {{{3{x^2} + x - 1} \over {{{(x - 1)}^2}}}} \right) + {\cos ^{ - ...
JEE Main 2021 (Online) 31st August Evening Shift
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Which of the following is not correct for relation R on the set of real numbers ?
JEE Main 2021 (Online) 31st August Morning Shift
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The domain of the function $${{\mathop{\rm cosec}\nolimits} ^{ - 1}}\left( {{{1 + x} \over x}} \right)$$ is :
JEE Main 2021 (Online) 26th August Evening Shift
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Let [t] denote the greatest integer less than or equal to t. Let f(x) = x $$-$$ [x], g(x) = 1 $$-$$ x + [x], and h(x) = ...
JEE Main 2021 (Online) 26th August Evening Shift
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Out of all patients in a hospital 89% are found to be suffering from heart ailment and 98% are suffering from lungs infe...
JEE Main 2021 (Online) 26th August Morning Shift
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Consider function f : A $$\to$$ B and g : B $$\to$$ C (A, B, C $$ \subseteq $$ R) such that (gof)$$-$$1 exists, then :...
JEE Main 2021 (Online) 25th July Evening Shift
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If [x] be the greatest integer less than or equal to x, then $$\sum\limits_{n = 8}^{100} {\left[ {{{{{( - 1)}^n}n} \over...
JEE Main 2021 (Online) 25th July Evening Shift
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Let N be the set of natural numbers and a relation R on N be defined by $$R = \{ (x,y) \in N \times N:{x^3} - 3{x^2}y - ...
JEE Main 2021 (Online) 27th July Evening Shift
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Let f : R $$\to$$ R be defined as $$f(x + y) + f(x - y) = 2f(x)f(y),f\left( {{1 \over 2}} \right) = - 1$$. Then, the va...
JEE Main 2021 (Online) 27th July Evening Shift
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Let g : N $$\to$$ N be defined asg(3n + 1) = 3n + 2,g(3n + 2) = 3n + 3,g(3n + 3) = 3n + 1, for all n $$\ge$$ 0. Then whi...
JEE Main 2021 (Online) 25th July Morning Shift
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If the domain of the function $$f(x) = {{{{\cos }^{ - 1}}\sqrt {{x^2} - x + 1} } \over {\sqrt {{{\sin }^{ - 1}}\left( {{...
JEE Main 2021 (Online) 22th July Evening Shift
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The number of solutions of sin7x + cos7x = 1, x$$\in$$ [0, 4$$\pi$$] is equal to
JEE Main 2021 (Online) 22th July Evening Shift
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Let [x] denote the greatest integer less than or equal to x. Then, the values of x$$\in$$R satisfying the equation $${[{...
JEE Main 2021 (Online) 22th July Evening Shift
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Let $$f:R - \left\{ {{\alpha \over 6}} \right\} \to R$$ be defined by $$f(x) = {{5x + 3} \over {6x - \alpha }}$$. Then ...
JEE Main 2021 (Online) 20th July Evening Shift
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Let [ x ] denote the greatest integer $$\le$$ x, where x $$\in$$ R. If the domain of the real valued function $$f(x) = \...
JEE Main 2021 (Online) 20th July Morning Shift
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Let f : R $$-$$ {3} $$ \to $$ R $$-$$ {1} be defined by f(x) = $${{x - 2} \over {x - 3}}$$.Let g : R $$ \to $$ R be give...
JEE Main 2021 (Online) 18th March Evening Shift
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If the functions are defined as $$f(x) = \sqrt x $$ and $$g(x) = \sqrt {1 - x} $$, then what is the common domain of the...
JEE Main 2021 (Online) 18th March Morning Shift
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The real valued function $$f(x) = {{\cos e{c^{ - 1}}x} \over {\sqrt {x - [x]} }}$$, where [x] denotes the greatest integ...
JEE Main 2021 (Online) 18th March Morning Shift
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Consider the function f : R $$ \to $$ R defined by $$f(x) = \left\{ \matrix{ \left( {2 - \sin \left( {{1 \over x}} \r...
JEE Main 2021 (Online) 17th March Evening Shift
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In a school, there are three types of games to be played. Some of the students play two types of games, but none play al...
JEE Main 2021 (Online) 17th March Morning Shift
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The inverse of $$y = {5^{\log x}}$$ is :
JEE Main 2021 (Online) 17th March Morning Shift
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Let A = {2, 3, 4, 5, ....., 30} and '$$ \simeq $$' be an equivalence relation on A $$\times$$ A, defined by (a, b) $$ \s...
JEE Main 2021 (Online) 16th March Evening Shift
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Let f be a real valued function, defined on R $$-$$ {$$-$$1, 1} and given by f(x) = 3 loge $$\left| {{{x - 1} \over {x +...
JEE Main 2021 (Online) 16th March Evening Shift
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The range of a$$\in$$R for which the function f(x) = (4a $$-$$ 3)(x + loge 5) + 2(a $$-$$ 7) cot$$\left( {{x \over 2}} \...
JEE Main 2021 (Online) 16th March Morning Shift
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Let [ x ] denote greatest integer less than or equal to x. If for n$$\in$$N, $${(1 - x + {x^3})^n} = \sum\limits_{j = 0}...
JEE Main 2021 (Online) 16th March Morning Shift
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The number of elements in the set {x $$\in$$ R : (|x| $$-$$ 3) |x + 4| = 6} is equal to :
JEE Main 2021 (Online) 16th March Morning Shift
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Let $$A = \{ 1,2,3,....,10\} $$ and $$f:A \to A$$ be defined as$$f(k) = \left\{ {\matrix{ {k + 1} & {if\,k\,is\,o...
JEE Main 2021 (Online) 26th February Evening Shift
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Let R = {(P, Q) | P and Q are at the same distance from the origin} be a relation, then the equivalence class of (1, $$-...
JEE Main 2021 (Online) 26th February Morning Shift
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Let x denote the total number of one-one functions from a set A with 3 elements to a set B with 5 elements and y denote ...
JEE Main 2021 (Online) 25th February Evening Shift
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A function f(x) is given by $$f(x) = {{{5^x}} \over {{5^x} + 5}}$$, then the sum of the series $$f\left( {{1 \over {20}}...
JEE Main 2021 (Online) 25th February Evening Shift
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Let f, g : N $$ \to $$ N such that f(n + 1) = f(n) + f(1) $$\forall $$ n$$\in$$N and g be any arbitrary function. Which ...
JEE Main 2021 (Online) 25th February Morning Slot
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Let f : R → R be defined as f (x) = 2x – 1 and g : R - {1} → R be defined as g(x) = $${{x - {1 \over 2}} \over {x - 1}}$...
JEE Main 2021 (Online) 24th February Morning Slot
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For a suitably chosen real constant a, let a function, $$f:R - \left\{ { - a} \right\} \to R$$ be defined by $$f(x) = {...
JEE Main 2020 (Online) 6th September Evening Slot
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If f(x + y) = f(x)f(y) and $$\sum\limits_{x = 1}^\infty {f\left( x \right)} = 2$$ , x, y $$ \in $$ N, where N is the s...
JEE Main 2020 (Online) 6th September Morning Slot
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If the minimum and the maximum values of the function $$f:\left[ {{\pi \over 4},{\pi \over 2}} \right] \to R$$, define...
JEE Main 2020 (Online) 5th September Morning Slot
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A survey shows that 73% of the persons working in an office like coffee, whereas 65% like tea. If x denotes the percenta...
JEE Main 2020 (Online) 5th September Morning Slot
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Let $$\mathop \cup \limits_{i = 1}^{50} {X_i} = \mathop \cup \limits_{i = 1}^n {Y_i} = T$$ where each Xi contains 10 ...
JEE Main 2020 (Online) 4th September Evening Slot
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A survey shows that 63% of the people in a city read newspaper A whereas 76% read newspaper B. If x% of the people read ...
JEE Main 2020 (Online) 4th September Morning Slot
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Let R1 and R2 be two relation defined as follows : R1 = {(a, b) $$ \in $$ R2 : a2 + b2 $$ \in $$ Q} and R2 = {(a, ...
JEE Main 2020 (Online) 3rd September Evening Slot
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Consider the two sets : A = {m $$ \in $$ R : both the roots of x2 – (m + 1)x + m + 4 = 0 are real} and B = [–3, 5). Wh...
JEE Main 2020 (Online) 3rd September Morning Slot
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Let f : R $$ \to $$ R be a function which satisfies f(x + y) = f(x) + f(y) $$\forall $$ x, y $$ \in $$ R. If f(1) = 2 an...
JEE Main 2020 (Online) 2nd September Evening Slot
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The domain of the function f(x) = $${\sin ^{ - 1}}\left( {{{\left| x \right| + 5} \over {{x^2} + 1}}} \right)$$ is (– $$...
JEE Main 2020 (Online) 2nd September Morning Slot
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If R = {(x, y) : x, y $$ \in $$ Z, x2 + 3y2 $$ \le $$ 8} is a relation on the set of integers Z, then the domain of R–1 ...
JEE Main 2020 (Online) 2nd September Morning Slot
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Let a – 2b + c = 1. If $$f(x)=\left| {\matrix{ {x + a} & {x + 2} & {x + 1} \cr {x + b} & {x + 3} &am...
JEE Main 2020 (Online) 9th January Evening Slot
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If A = {x $$ \in $$ R : |x| < 2} and B = {x $$ \in $$ R : |x – 2| $$ \ge $$ 3}; then :
JEE Main 2020 (Online) 9th January Evening Slot
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Let ƒ : (1, 3) $$ \to $$ R be a function defined by $$f(x) = {{x\left[ x \right]} \over {1 + {x^2}}}$$ , where [x] denot...
JEE Main 2020 (Online) 8th January Evening Slot
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Let ƒ(x) = xcos–1(–sin|x|), $$x \in \left[ { - {\pi \over 2},{\pi \over 2}} \right]$$, then which of the following is ...
JEE Main 2020 (Online) 8th January Morning Slot
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The inverse function of f(x) = $${{{8^{2x}} - {8^{ - 2x}}} \over {{8^{2x}} + {8^{ - 2x}}}}$$, x $$ \in $$ (-1, 1), is :...
JEE Main 2020 (Online) 8th January Morning Slot
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If g(x) = x2 + x - 1 and (goƒ) (x) = 4x2 - 10x + 5, then ƒ$$\left( {{5 \over 4}} \right)$$ is equal to:...
JEE Main 2020 (Online) 7th January Morning Slot
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For x $$ \in $$ (0, 3/2), let f(x) = $$\sqrt x $$ , g(x) = tan x and h(x) = $${{1 - {x^2}} \over {1 + {x^2}}}$$. If $$\p...
JEE Main 2019 (Online) 12th April Morning Slot
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Let f(x) = loge(sin x), (0 < x < $$\pi $$) and g(x) = sin–1 (e–x ), (x $$ \ge $$ 0). If $$\alpha $$ is a positive ...
JEE Main 2019 (Online) 10th April Evening Slot
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Let f(x) = ex – x and g(x) = x2 – x, $$\forall $$ x $$ \in $$ R. Then the set of all x $$ \in $$ R, where the function h...
JEE Main 2019 (Online) 10th April Morning Slot
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Let f(x) = x2 , x $$ \in $$ R. For any A $$ \subseteq $$ R, define g (A) = { x $$ \in $$ R : f(x) $$ \in $$ A}. If S = [...
JEE Main 2019 (Online) 10th April Morning Slot
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The domain of the definition of the function $$f(x) = {1 \over {4 - {x^2}}} + {\log _{10}}({x^3} - x)$$ is
JEE Main 2019 (Online) 9th April Evening Slot
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If the function ƒ : R – {1, –1} $$ \to $$ A defined by ƒ(x) = $${{{x^2}} \over {1 - {x^2}}}$$ , is surjective, then A i...
JEE Main 2019 (Online) 9th April Morning Slot
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Let $$\sum\limits_{k = 1}^{10} {f(a + k) = 16\left( {{2^{10}} - 1} \right)} $$ where the function ƒ satisfies ƒ(x + y) ...
JEE Main 2019 (Online) 9th April Morning Slot
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Let $$f(x) = \int\limits_0^x {g(t)dt} $$ where g is a non-zero even function. If ƒ(x + 5) = g(x), then $$ \int\limits_0...
JEE Main 2019 (Online) 8th April Evening Slot
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Let ƒ(x) = ax (a > 0) be written as ƒ(x) = ƒ1 (x) + ƒ2 (x), where ƒ1 (x) is an even function of ƒ2 (x) is an odd fun...
JEE Main 2019 (Online) 8th April Evening Slot
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If $$f(x) = {\log _e}\left( {{{1 - x} \over {1 + x}}} \right)$$, $$\left| x \right| < 1$$ then $$f\left( {{{2x} \over...
JEE Main 2019 (Online) 8th April Morning Slot
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If the function f given by f(x) = x3 – 3(a – 2)x2 + 3ax + 7, for some a$$ \in $$R is increasing in (0, 1] and decreasin...
JEE Main 2019 (Online) 12th January Evening Slot
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Let a function f : (0, $$\infty $$) $$ \to $$ (0, $$\infty $$) be defined by f(x) = $$\left| {1 - {1 \over x}} \right|$$...
JEE Main 2019 (Online) 11th January Evening Slot
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Let fk(x) = $${1 \over k}\left( {{{\sin }^k}x + {{\cos }^k}x} \right)$$ for k = 1, 2, 3, ... Then for all x $$ \in $$ R,...
JEE Main 2019 (Online) 11th January Morning Slot
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Let f : R $$ \to $$ R be defined by f(x) = $${x \over {1 + {x^2}}},x \in R$$. Then the range of f is :
JEE Main 2019 (Online) 11th January Morning Slot
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Let N be the set of natural numbers and two functions f and g be defined as f, g : N $$ \to $$ N such that f(n) = $$\lef...
JEE Main 2019 (Online) 10th January Evening Slot
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Let A = {x $$ \in $$ R : x is not a positive integer}. Define a function $$f$$ : A $$ \to $$ R as...
JEE Main 2019 (Online) 9th January Evening Slot
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For $$x \in R - \left\{ {0,1} \right\}$$, Let f1(x) = $$1\over x$$, f2 (x) = 1 – x and f3 (x) = $$1 \over {1 - x}$$ be...
JEE Main 2019 (Online) 9th January Morning Slot
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Let N denote the set of all natural numbers. Define two binary relations on N as R = {(x, y) $$ \in $$ N $$ \times $$ N ...
JEE Main 2018 (Online) 16th April Morning Slot
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Let f : A $$ \to $$ B be a function defined as f(x) = $${{x - 1} \over {x - 2}},$$ Where A = R $$-$$ {2} and B = R $$-$...
JEE Main 2018 (Online) 15th April Evening Slot
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Consider the following two binary relations on the set A = {a, b, c} : R1 = {(c, a), (b, b), (a, c), (c, c), (b, c), (a...
JEE Main 2018 (Online) 15th April Morning Slot
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The function f : N $$ \to $$ N defined by f (x) = x $$-$$ 5 $$\left[ {{x \over 5}} \right],$$ Where N is the set of natu...
JEE Main 2017 (Online) 9th April Morning Slot
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Let f(x) = 210.x + 1 and g(x)=310.x $$-$$ 1. If (fog) (x) = x, then x is equal to :
JEE Main 2017 (Online) 8th April Morning Slot
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The function $$f:R \to \left[ { - {1 \over 2},{1 \over 2}} \right]$$ defined as $$f\left( x \right) = {x \over {1 + {x^2...
JEE Main 2017 (Offline)
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If $f(x)+2 f\left(\frac{1}{x}\right)=3 x, x \neq 0$, and $\mathrm{S}=\{x \in \mathbf{R}: f(x)=f(-x)\}$; then $\mathrm{S}...
JEE Main 2016 (Offline)
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Let P = {$$\theta $$ : sin$$\theta $$ $$-$$ cos$$\theta $$ = $$\sqrt 2 \,\cos \theta $$} and Q = {$$\theta $$ : sin$$\t...
JEE Main 2016 (Online) 10th April Morning Slot
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For x $$ \in $$ R, x $$ \ne $$ 0, Let f0(x) = $${1 \over {1 - x}}$$ and fn+1 (x) = f0(fn(x)), n = 0, 1, 2, . . . . Th...
JEE Main 2016 (Online) 9th April Morning Slot
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The domain of the function f(x) = $${1 \over {\sqrt {\left| x \right| - x} }}$$ is
AIEEE 2011
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For real x, let f(x) = x3 + 5x + 1, then
AIEEE 2009
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Let $$f\left( x \right) = {\left( {x + 1} \right)^2} - 1,x \ge - 1$$ Statement - 1 : The set $$\left\{ {x:f\left( x \ri...
AIEEE 2009
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Let $$f:N \to Y$$ be a function defined as f(x) = 4x + 3 where Y = { y $$ \in $$ N, y = 4x + 3 for some x $$ \in $$ N }...
AIEEE 2008
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The largest interval lying in $$\left( { - {\pi \over 2},{\pi \over 2}} \right)$$ for which the function $$f\left( x \...
AIEEE 2007
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A function is matched below against an interval where it is supposed to be increasing. Which of the following pairs is i...
AIEEE 2005
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A real valued function f(x) satisfies the functional equation f(x - y) = f(x)f(y) - f(a - x)f(a + y) where a is given co...
AIEEE 2005
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Let $$f:( - 1,1) \to B$$, be a function defined by $$f\left( x \right) = {\tan ^{ - 1}}{{2x} \over {1 - {x^2}}}$$, then...
AIEEE 2005
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The graph of the function y = f(x) is symmetrical about the line x = 2, then
AIEEE 2004
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The domain of the function $$f\left( x \right) = {{{{\sin }^{ - 1}}\left( {x - 3} \right)} \over {\sqrt {9 - {x^2}} }}$$...
AIEEE 2004
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If $$f:R \to S$$, defined by $$f\left( x \right) = \sin x - \sqrt 3 \cos x + 1$$, is onto, then the interval of $$S$$ is...
AIEEE 2004
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The range of the function f(x) = $${}^{7 - x}{C_{x - 3}}$$ is
AIEEE 2004
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Domain of definition of the function f(x) = $${3 \over {4 - {x^2}}}$$ + $${\log _{10}}\left( {{x^3} - x} \right)$$, is
AIEEE 2003
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If $$f:R \to R$$ satisfies $$f$$(x + y) = $$f$$(x) + $$f$$(y), for all x, y $$ \in $$ R and $$f$$(1) = 7, then $$\sum\li...
AIEEE 2003
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A function $$f$$ from the set of natural numbers to integers defined by $$$f\left( n \right) = \left\{ {\matrix{ {{{n...
AIEEE 2003
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The function $$f\left( x \right)$$ $$ = \log \left( {x + \sqrt {{x^2} + 1} } \right)$$, is
AIEEE 2003
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The domain of $${\sin ^{ - 1}}\left[ {{{\log }_3}\left( {{x \over 3}} \right)} \right]$$ is
AIEEE 2002
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Numerical
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For $$\mathrm{p}, \mathrm{q} \in \mathbf{R}$$, consider the real valued function $$f(x)=(x-\mathrm{p})^{2}-\mathrm{q}, x...
JEE Main 2022 (Online) 28th July Morning Shift
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The number of functions $$f$$, from the set $$\mathrm{A}=\left\{x \in \mathbf{N}: x^{2}-10 x+9 \leq 0\right\}$$ to the s...
JEE Main 2022 (Online) 27th July Evening Shift
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Let $$f(x)=2 x^{2}-x-1$$ and $$\mathrm{S}=\{n \in \mathbb{Z}:|f(n)| \leq 800\}$$. Then, the value of $$\sum\limits_{n \...
JEE Main 2022 (Online) 27th July Morning Shift
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The sum of the maximum and minimum values of the function $$f(x)=|5 x-7|+\left[x^{2}+2 x\right]$$ in the interval $$\lef...
JEE Main 2022 (Online) 25th July Evening Shift
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Let $$f(x)$$ be a quadratic polynomial with leading coefficient 1 such that $$f(0)=p, p \neq 0$$, and $$f(1)=\frac{1}{3}...
JEE Main 2022 (Online) 25th July Evening Shift
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The number of points where the function $$f(x) = \left\{ {\matrix{ {|2{x^2} - 3x - 7|} & {if} & {x \le - 1} \cr ...
JEE Main 2022 (Online) 24th June Morning Shift
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The number of one-one functions f : {a, b, c, d} $$\to$$ {0, 1, 2, ......, 10} such that 2f(a) $$-$$ f(b) + 3f(c) + f(d...
JEE Main 2022 (Online) 24th June Morning Shift
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Let $$f:R \to R$$ be a function defined by $$f(x) = {\left( {2\left( {1 - {{{x^{25}}} \over 2}} \right)(2 + {x^{25}})} \...
JEE Main 2022 (Online) 25th June Morning Shift
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Let f : R $$\to$$ R satisfy $$f(x + y) = {2^x}f(y) + {4^y}f(x)$$, $$\forall$$x, y $$\in$$ R. If f(2) = 3, then $$14.\,{{...
JEE Main 2022 (Online) 26th June Evening Shift
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Let f : R $$\to$$ R be a function defined by $$f(x) = {{2{e^{2x}}} \over {{e^{2x}} + e}}$$. Then $$f\left( {{1 \over {10...
JEE Main 2022 (Online) 27th June Morning Shift
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Let [t] denote the greatest integer $$\le$$ t and {t} denote the fractional part of t. The integral value of $$\alpha$$ ...
JEE Main 2022 (Online) 27th June Evening Shift
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Let S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Define f : S $$\to$$ S as $$f(n) = \left\{ {\matrix{ {2n} & , & {if\,n = 1,2...
JEE Main 2022 (Online) 27th June Evening Shift
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Let f(x) and g(x) be two real polynomials of degree 2 and 1 respectively. If $$f(g(x)) = 8{x^2} - 2x$$ and $$g(f(x)) = 4...
JEE Main 2022 (Online) 29th June Evening Shift
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Let c, k $$\in$$ R. If $$f(x) = (c + 1){x^2} + (1 - {c^2})x + 2k$$ and $$f(x + y) = f(x) + f(y) - xy$$, for all x, y $$\...
JEE Main 2022 (Online) 29th June Morning Shift
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The number of 4-digit numbers which are neither multiple of 7 nor multiple of 3 is ____________.
JEE Main 2021 (Online) 31st August Evening Shift
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If A = {x $$\in$$ R : |x $$-$$ 2| > 1}, B = {x $$\in$$ R : $$\sqrt {{x^2} - 3} $$ > 1}, C = {x $$\in$$ R : |x $$-$...
JEE Main 2021 (Online) 27th August Morning Shift
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Let S = {1, 2, 3, 4, 5, 6, 7}. Then the number of possible functions f : S $$\to$$ S such that f(m . n) = f(m) . f(n) fo...
JEE Main 2021 (Online) 27th July Morning Shift
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Let A = {n $$\in$$ N | n2 $$\le$$ n + 10,000}, B = {3k + 1 | k$$\in$$ N} an dC = {2k | k$$\in$$N}, then the sum of all t...
JEE Main 2021 (Online) 27th July Evening Shift
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Let A = {0, 1, 2, 3, 4, 5, 6, 7}. Then the number of bijective functions f : A $$\to$$ A such that f(1) + f(2) = 3 $$-$$...
JEE Main 2021 (Online) 22th July Evening Shift
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If f(x) and g(x) are two polynomials such that the polynomial P(x) = f(x3) + x g(x3) is divisible by x2 + x + 1, then P(...
JEE Main 2021 (Online) 18th March Evening Shift
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If a + $$\alpha$$ = 1, b + $$\beta$$ = 2 and $$af(x) + af\left( {{1 \over x}} \right) = bx + {\beta \over x},x \ne 0$$,...
JEE Main 2021 (Online) 24th February Evening Slot
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Suppose that a function f : R $$ \to $$ R satisfies f(x + y) = f(x)f(y) for all x, y $$ \in $$ R and f(1) = 3. If $$\sum...
JEE Main 2020 (Online) 6th September Evening Slot
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Set A has m elements and set B has n elements. If the total number of subsets of A is 112 more than the total number of ...
JEE Main 2020 (Online) 6th September Morning Slot
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Let A = {a, b, c} and B = {1, 2, 3, 4}. Then the number of elements in the set C = {f : A $$ \to $$ B | 2 $$ \in $$ f(A)...
JEE Main 2020 (Online) 5th September Evening Slot
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The number of distinct solutions of the equation $${\log _{{1 \over 2}}}\left| {\sin x} \right| = 2 - {\log _{{1 \over ...
JEE Main 2020 (Online) 9th January Morning Slot
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Let X = {n $$ \in $$ N : 1 $$ \le $$ n $$ \le $$ 50}. If A = {n $$ \in $$ X: n is a multiple of 2} and B = {n $$ \in $$ ...
JEE Main 2020 (Online) 7th January Evening Slot
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