CUET · MATHS · PYQ PAPER 2023
Find the area of the region bounded by the two parabolas \(y=x^2\) and \(y^2=x\) :
- A \(\frac{1}{2}\)
- B \(\frac{1}{3}\)
- C \(\frac{2}{3}\)
- D \(\frac{5}{3}\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{3}\)
Step-by-step Solution
Detailed explanation
Intersection points: \(x^4=x \Rightarrow x(x^3-1)=0 \Rightarrow x=0, 1\). Area \(A = \int_{0}^{1} (\sqrt{x} - x^2) dx\). \(A = \left[ \frac{2}{3}x^{3/2} - \frac{1}{3}x^3 \right]_{0}^{1}\).…
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
- Match List-l with List-ll
Choose the correct answer from the options given below :List-l (Parametric Equations) List-ll \(\frac{d y}{d x}\) (A) \(x=\frac{2}{t}, y=2 t\) (I) \(4 t^2\) (B) \(x=t^3, y=3 t+2\) (II) \(2(t+1)\) (C) \(x=\log t, y=2 t^2\) (III) \(-t^2\) (D) \(x=e^t, y=2 t e^t\) (IV) \(t^{-2}\) CUET 2025 Hard - A container contains 48 litres of buffalo milk. From this container 8 litres of buffalo milk was taken out and replaced with cow milk. This process was repeated further 3 more times. How much buffalo milk is there in the container now ?CUET 2023 Hard
- The value of \(\lambda\) for which the two vectors \((2 \hat{i}-\hat{j}+2 \hat{k})\) and \((3 \hat{i}+\lambda \hat{j}+\hat{k})\) are perpendicular, is :CUET 2025 Hard
- Which of the following statements is/are true?
(A) The vector sum of the three sides of a triangle in order is \(\vec{c}\)
b (B) The magnitude (r), direction ratios (a, b, c) and direction cosines (l, m, n) of any vector \(\vec{r}=a \hat{i}+b \hat{j}+c \hat{k}\) are related as \(l=\frac{a}{r}, m=\frac{b}{r}, n=\frac{c}{r}\)
(C) If θ is the angle between two vectors \(\vec{a}\) and \(\vec{b}\), then their cross product is given as \(\vec{a} \times \vec{b}=|\vec{a}||\vec{b}| \sin \theta\)
(D) The cross product of two vectors is commutative
Choose the correct answert from the option given below :CUET 2025 Easy - A random variable X denotes the number of sixes obtained in three throws of a die. Find the mean of the distributionCUET 2025 Easy
- Two cards are drawn simultaneously at random from a well shuffled pack of 52 Cards.
Let X be the random variable which denotes number of kings in the draw. Then the probability distribution of X isCUET 2025 Medium
More PYQs from CUET
- The Chelating ligand used for the estimation of hardness of water isCUET 2025 Medium
- On adding a small amount of boron to a silicon crystalCUET 2025 Easy
- An excess of potassium ions makes KCl crystal appear violet or liliac in colour since:
(A) Some of the anionic sites are occupied by an unpaired electron
(B)Some of the anionic sites are occupied by a pair of electrons
(C) There are vacancies at some anionic sites
(D)F-ntres are created which impart colour to the crystals.
Choose the correct answer from the options given below :CUET 2023 Easy - Which of the following statements are correct?
(A) A nucleus of mass number A has a radius R given by the expression \( R = R_0 A^{1/3} \)
(B) Volume of nucleus is proportional to mass number A
(C) The density of nucleus increases with the radius of nucleus.
(D) Density of nuclear matter does not depend on its mass number A
Choose the correct answer from the options given below:CUET 2025 Hard - The first restriction endonuclease to be isolated was :CUET 2023 Hard
- Samples of benzaldehyde and acetaldehyde can be distinguished by usingCUET 2023 Easy