New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Functions question

2024 · 9 Apr · Shift 1 · Q55

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

PYQ Library
JEE Main
Mathematics
Functions
2024 · 9 Apr · Shift 1 · Q55

Functions question

2024 · 9 Apr · Shift 1 · Q55

JEE MainMathematicsFunctionsNumerical+4 / −1

If a function

f

satisfies

f(\mathrm{~m}+\mathrm{n})=f(\mathrm{~m})+f(\mathrm{n})

for all

\mathrm{m}, \mathrm{n} \in \mathbf{N}

and

f(1)=1

, then the largest natural number

\lambda

such that

\sum_{\mathrm{k}=1}^{2022} f(\lambda+\mathrm{k}) \leq(2022)^2

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

More from Functions

Let the range of the function $f (x) = \frac{1}{2 + s i n 3 x + c o s 3 x}, x \in R$ be $α$ . If $α$ and $β$ ar respectively the A.M. and the G.M. of $a$ and $b$ , then $\frac{α}{β}$ is equal to2024 · MCQ
Let $A = {(x, y) : 2 x + 3 y = 23, x, y \in N}$ and $B = {x : (x, y) \in A}$ . Then the number of one-one functions from $A$ to $B$ is equal to .2024 · Numerical
The function $f : N - {1} \to N$ ; defined by $n$ the highest prime factor of $n$ , is :2024 · MCQ
Let $f : R - {\frac{- 1}{2}} \to R$ and $g : R - {\frac{- 5}{2}} \to R$ be defined as $f (x) = \frac{2 x + 3}{2 x + 1}$ and $g (x) = \frac{∣ x ∣ + 1}{2 x + 5}$ . Then, the domain of…2024 · MCQ
If $f (x) = {2 + 2 x, 1 - \frac{x}{3}, - 1 \leq x < 0 0 \leq x \leq 3; g (x) = {- x, x, - 3 \leq x \leq 0 0 < x \leq 1$ , then range…2024 · MCQ
If the domain of the function $f (x) = cos^{- 1} (\frac{2 - ∣ x ∣}{4}) + {lo g_{e} (3 - x)}^{- 1}$ is $[- α, β) - {γ}$ , then $α + β + γ$ is equal to :2024 · MCQ
Let $A = {1, 2, 3, \dots, 7}$ and let $P (A)$ denote the power set of $A$ . If the number of functions $f : A \to P (A)$ such that $a \in f (a), \forall a \in A$ …2024 · Numerical
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