New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Functions question

2024 · 1 Feb · Shift 2 · Q31

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

PYQ Library
JEE Main
Mathematics
Functions
2024 · 1 Feb · Shift 2 · Q31

Functions question

2024 · 1 Feb · Shift 2 · Q31

JEE MainMathematicsFunctionsMCQ+4 / −1

If the domain of the function

f(x)=\frac{\sqrt{x^2-25}}{\left(4-x^2\right)}+\log _{10}\left(x^2+2 x-15\right)

is

(-\infty, \alpha) \cup[\beta, \infty)

, then

\alpha^2+\beta^3

is equal to :

A
140
B
175
C
125
D
150

More from Functions

Consider the function $f : R \to R$ defined by $f (x) = \frac{2 x}{1 + 9 x ^{2}}$ . If the composition of $f, 10 times (f \circ f \circ f \circ \dots \circ f) (x) = \frac{2 ^{10} x}{1 + 9 α x ^{2}}$ …2024 · Numerical
Let $A = {1, 3, 7, 9, 11}$ and $B = {2, 4, 5, 7, 8, 10, 12}$ . Then the total number of one-one maps $f : A \to B$ , such that $f (1) + f (3) = 14$ , is :2024 · MCQ
If $S = {a \in R : ∣2 a - 1∣ = 3 [a] + 2 {a}}$ , where $[t]$ denotes the greatest integer less than or equal to $t$ and ${t}$ represents the fractional part of $t$ , then $72 \sum_{a \in S} a$ is equal to .2024 · Numerical
Let $f, g : R \to R$ be defined as : $f (x) = ∣ x - 1∣ and g (x) = {e^{x}, x + 1, x \geq 0 x \leq 0.$ Then the function $f (g (x))$ is2024 · MCQ
The function $f (x) = \frac{x ^{2} + 2 x - 15}{x ^{2} - 4 x + 9}, x \in R$ is2024 · MCQ
If the function $f (x) = (\frac{1}{x})^{2 x}; x > 0$ attains the maximum value at $x = \frac{1}{e}$ then :2024 · MCQ
Let $f (x) = \frac{1}{7 - s i n 5 x}$ be a function defined on $R$ . Then the range of the function $f (x)$ is equal to :2024 · MCQ
If the range of $f (θ) = \frac{s i n ^{4} θ + 3 c o s ^{2} θ}{s i n ^{4} θ + c o s ^{2} θ}, θ \in R$ is $\frac{α}{β}$ , then the sum of the infinite G.P., whose first term is 64 and the common ratio is $\frac{α}{β}$ …2024 · Numerical