CUET · MATHS · PYQ PAPER 2023
Let \(f:[-2,2] \rightarrow[-2,2]\) be a function defined by \(f(x)=x|x|\), then \(f\) is:
- A One-one but not onto
- B Onto but not one-one
- C Neither one-one nor onto
- D Bijective
Answer & Solution
Correct Answer
(D) Bijective
Step-by-step Solution
Detailed explanation
Let \(f(x_1) = f(x_2)\). Then \(x_1|x_1| = x_2|x_2|\). Since \(x|x|\) has the same sign as \(x\), \(x_1\) and \(x_2\) must have the same sign. If \(x_1, x_2 \ge 0\), \(x_1^2 = x_2^2 \implies x_1 = x_2\). If \(x_1, x_2 \(f\) is one-one. Let \(y \in [-2,2]\) (codomain). If…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from MATHS
- The value of \(\int_{\frac{-\pi}{2}}^{\pi / 2}\left(x^5+x^3 \cos x\right) d x\) is :CUET 2025 Easy
- \(\int \frac{e^{2 x}-e^{-2 x}}{e^{2 x}+e^{-2 x}} d x \) is equal to :CUET 2025 Hard
- Area (in sq. units) of the region bounded by the curve \(y^2=4 x\) y-axis and the line y = 3 isCUET 2025 Medium
- The angle between the line \(\vec{r}=(\hat{i}+2 \hat{j}-\hat{k})+\lambda(\hat{i}-\hat{j}+\hat{k})\) and the plane \(\vec{r} \cdot(2 \hat{i}-\hat{j}+\hat{k})=4\) is :CUET 2023 Easy
- If \(A\) is a square matrix of order 3 such that \(|A|=2\), then \(\operatorname{adj}(\operatorname{adj} A)\) is :CUET 2023 Hard
- If the mean of Binomial distribution is 5 and Variance is 3 then the value of \(p\) (probability of success) is :CUET 2023 Easy
More PYQs from CUET
- Which of the following is necessary to use to achieve half wave rectification of an alternating current?CUET 2023 Hard
- Mercury is the only liquid metal at room temperature due to:CUET 2023 Easy
- Match List - I with List - II
Choose the correct answer from the options given below:List - I List - II (A) \(\int_{-\pi / 2}^{\pi / 2} \sin ^5 x d x\) (I) \(\pi\) (B) \(\int_{-\pi / 2}^{\pi / 2}\left(x^3+\tan ^3 x+1\right) d x\) (II) \(\frac{\pi}{12}\) (C) \(\int_0^{\pi / 2} \frac{\cos ^5 x}{\cos ^5 x+\sin ^5 x} d x\) (III) \(\frac{\pi}{4}\) (D) \(\int_1^{\sqrt{3}} \frac{d x}{1+x^2}\) (IV) 0 CUET 2023 Easy - If the matrix A = \(\left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{array}\right]\), then \(A ^2\) is equal to:CUET 2023 Medium
- Amniocentesis is used to detect the :CUET 2023 Easy
- A voltage \( V = 200 \sin(400t) \) V AC source is connected to a series combination of an inductance 20 mH and resistance \( 6 \, \Omega \). The rms current in the AC circuit is:CUET 2025 Hard