Skip to main content
Back to FUNCTIONS

JEE MATHEMATICS MCQ: FUNCTIONS

1 Medium
1 of 1
Analyzing +4 | -1
If Q denotes the set of all rational numbers and f(pq)=p2−q2f\left( {\frac{p}{q}} \right) = \sqrt {{p^2} - {q^2}} for any pq∈Q\frac{p}{q} \in {\cal Q}, then observe the following statements.

I. f(pq)f\left( {\frac{p}{q}} \right) is real for each pq∈Q\frac{p}{q} \in {\cal Q}.

II.f(pq)f\left( {\frac{p}{q}} \right) is a complex number for each pq∈Q\frac{p}{q} \in {\cal Q}.

Which of the following is correct?
View answer and explanation
Correct option: C
I is false, II is true
The correct answer is C (I is false, II is true) because if p < q, then the square root of a negative number results in a complex number, making statement I false and statement II true.

More Questions from FUNCTIONS

Practice All Chapter MCQs →
If f:(−∞,2]⟶(−∞,4]f:(-\infty, 2] \longrightarrow(-\infty, 4], where f(x)=x(4−x)f(x)=x(4-x), then f−1(x)f^{-1}(x) is given by: If g(f(x))=∣sin⁡x∣g(f(x))=|\sin x| and f(g(x))=(sin⁡x)2f(g(x))=(\sin \sqrt{x})^2, then Let f:(2,  3)→(0,  1)f:\left( {2,\;3} \right) \to \left( {0,\;1} \right) be defined by f(x)=x−[x]f\left( x \right) = x - \left[ x \right], then f−1(x){f^{ - 1}}\left( x \right) equals Let f:R→Rf: R \rightarrow R be defined as f(x)=x4f(x)=x^4, Choose the correct answer. Which of the following functions are odd functions Let f(x)=(x+1)2−1(x≥−1)f(x)=(x+1)^2-1(x \geq-1). Then the set S={x:f(x)=f−1(x)}S=\left\{x: f(x)=f^{-1}(x)\right\} contains
Type at least 2 characters or jump directly:
🩺 NEET MCQs 🔬 JEE MCQs 🎯 JEE College Predictor Study guides 📊 Dashboard
🔓

Save your learning progress

Sign in with a free account to save your practice answers and quiz results, then return to them when you revise.

Continue with Free Account →