New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Functions question

2024 · 30 Jan · Shift 1 · Q59

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
Functions
2024 · 30 Jan · Shift 1 · Q59

Functions question

2024 · 30 Jan · Shift 1 · Q59

JEE MainMathematicsFunctionsNumerical+4 / −1

Let

\mathrm{A}=\{1,2,3, \ldots, 7\}

and let

\mathrm{P}(\mathrm{A})

denote the power set of

\mathrm{A}

. If the number of functions

f: \mathrm{A} \rightarrow \mathrm{P}(\mathrm{A})

such that

\mathrm{a} \in f(\mathrm{a}), \forall \mathrm{a} \in \mathrm{A}

is

\mathrm{m}^{\mathrm{n}}, \mathrm{m}

and

\mathrm{n} \in \mathrm{N}

and

\mathrm{m}

is least, then

\mathrm{m}+\mathrm{n}

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

More from Functions

If the domain of the function $f (x) = lo g_{e} (\frac{2 x + 3}{4 x ^{2} + x - 3}) + cos^{- 1} (\frac{2 x - 1}{x + 2})$ is $5 β - 4 α$ , then the value of $5 β - 4 α$ is equal to2024 · MCQ
If $f (x) = \frac{4 x + 3}{6 x - 4}, x e q \frac{2}{3}$ and $(f \circ f) (x) = g (x)$ , where $g : R - {\frac{2}{3}} \to R - {\frac{2}{3}}$ , then $(g o g o g) (4)$ is equal to2024 · MCQ
Let $f (x) = 1 + sin^{2} x sin^{2} x sin^{2} x cos^{2} x 1 + cos^{2} x cos^{2} x sin 2 x sin 2 x 1 + sin 2 x, x \in [\frac{π}{6}, \frac{π}{3}]$ …2023 · MCQ
Let $f : R - 0, 1 \to R$ be a function such that $f (x) + f (\frac{1}{1 - x}) = 1 + x$ . Then $f (2)$ is equal to2023 · MCQ
Let the sets A and B denote the domain and range respectively of the function $f (x) = \frac{1}{⌈ x ⌉ - x}$ , where $⌈ x ⌉$ denotes the smallest integer greater than or equal to $x$ . Then among the statements (S1) : $A \cap B = (1, \infty) - N$ …2023 · MCQ
Let $R = {a, b, c, d, e}$ and $S = {1, 2, 3, 4}$ . Total number of onto functions $f : R \to S$ such that $f (a) e q 1$ , is equal to …2023 · Numerical
If domain of the function $lo g_{e} (\frac{6 x ^{2} + 5 x + 1}{2 x - 1}) + cos^{- 1} (\frac{2 x ^{2} - 3 x + 4}{3 x - 5})$ is $(α, β) \cup (γ, δ]$ , then…2023 · Numerical
If $f (x) = \frac{( t a n 1 ^{\circ} ) x + l o g _{e} ( 123 )}{x l o g _{e} ( 1234 ) - ( t a n 1 ^{\circ} )}, x > 0$ , then the least value of $f (f (x)) + f (f (\frac{4}{x}))$ is :2023 · MCQ