If the domain of the function $f(x) = \frac{1}{\sqrt{10+3x-x^2}} + \frac{1}{\sqrt{x+|x|}}$ is $(a, b)$, then $(1+a)^2 + b^2$ is equal to :

JEE Main 2025 · MathsMultiple choiceSingle correctEasyApplication

JEE Main 2 April 2025, Shift 2, Maths Q1

Question 1 of 75 in this shift, Maths question 1 of 25, Section A.

If the domain of the function

f(x) = \frac{1}{\sqrt{10+3x-x^2}} + \frac{1}{\sqrt{x+|x|}}

(a, b)

, then

(1+a)^2 + b^2

is equal to :

(1) $26$ Official answer
(2) $25$
(3) $29$
(4) $30$

Official answer

Option 1

NTA final key.

Chapter: Relations and Functions
Topic: Functions and Domain
Idea tested: Domain of 1/sqrt(f(x))

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Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 42 of the 174 JEE Main shifts held from 2017 to 2026.