CUET · MATHS · PYQ PAPER 2023
The function \(f(x)=\frac{x-1}{x\left(x^2-1\right)}, x \neq 1, f(1)=1\), is discontinuous at:
- A Exactly one point
- B Exactly two points
- C Exactly three points
- D No point
Answer & Solution
Correct Answer
(C) Exactly three points
Step-by-step Solution
Detailed explanation
\(f(x)=\frac{x-1}{x(x-1)(x+1)} = \frac{1}{x(x+1)}\) for \(x \neq 1\). Discontinuities occur where the denominator is zero for the simplified form or where the function definition changes. \(x(x+1)=0 \implies x=0, x=-1\). At \(x=1\):…
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
- A small company manufactures necklaces and bracelets. The combined number of necklaces and bracelets it can handle per day is at the most 24 .A bracelet takes 1 hour to make and a necklace takes half hour to be made.Maximum number of hours available per day is 16 .If the number of necklaces and bracelets made per day is \(x\) and \(y\)
respectively then the time constraint for the L.P.P.is :CUET 2023 Hard - \(\int_0^{\frac{\pi}{2}} \frac{\cos x}{(1+\sin x)(2+\sin x)} d x=\)CUET 2023 Hard
- The acute angle between the lines \(\vec{r}=(4 \hat{i}-\hat{j})+\lambda(2 \hat{i}+\hat{j}-3 \hat{k})\) and \(\frac{x-1}{1}=\frac{y+1}{-3}=\frac{z-2}{2}\) isCUET 2025 Easy
- Consider a closed cylinder of radius \(r\) with a fixed surface area. The volume of the cylinder is maximum when its height is :CUET 2025 Medium
- Which of the following statements is/are correct?
(A) \(|x|\) is continuous everywhere in its domain.
\((B)|x|\) is differentiable everywhere in its domain.
(C) \([x]\) is continuous at every integral point.
\((D)[x]\) is discontinuous at every integral point.
Choose the correct answer from the options given below :CUET 2023 Easy - The degree of the differential equation \(\left(1+\frac{d y}{d x}\right)^3=\left(\frac{d^2 y}{d x^2}\right)^2\) is:CUET 2023 Hard
More PYQs from CUET
- The capacity of a parallel plate capacitor does not depend on :CUET 2023 Hard
- The resistance of a given carbon resistor is \(3.6 \times 10^6 \Omega \pm 5 \%\). What are the sequence of colour strips on the resistor?CUET 2023 Hard
- A pair of dice is thrown 7 times. If getting a total of 7 is considered a success, the probability of exactly 6 successe, is:CUET 2023 Easy
- A galvanometer has a resistance of 8 \( \Omega \). It is shunted by a wire of resistance 2 \( \Omega \). If the total current is 2 A, the current passing through the shunt isCUET 2023 Medium
- Arrange the following electromagnetic waves in the increasing order of their energy.
(A) Ultraviolet rays
(B) Infrared rays
(C) Microwaves
(D) X-rays
(E) Gamma rays
Choose the correct answer from the options given below:CUET 2025 Medium - The equation of the normal to the curve \(y=4 x^3+2 \sin x\) at \((0,3)\) is :CUET 2023 Hard