CUET · MATHS · PYQ PAPER 2023
The area of the region \(\left\{(x, y): y \geq x^2\right.\) and \(\left.y \leq|x|\right\}\) is
- A 2
- B 1
- C \(\frac{1}{2}\)
- D \(\frac{1}{3}\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{3}\)
Step-by-step Solution
Detailed explanation
Intersection points: \(x^2 = |x|\). For \(x \geq 0\), \(x^2 = x \Rightarrow x(x-1) = 0 \Rightarrow x = 0, x = 1\). Due to symmetry, Area \( = 2 \int_{0}^{1} (|x| - x^2) dx \) \( = 2 \int_{0}^{1} (x - x^2) dx \) \( = 2 \left[\frac{x^2}{2} - \frac{x^3}{3}\right]_{0}^{1} \)…
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
- A pair of dice is thrown until the sum of numbers appeared is a perfect square or a non-perfect square sum appeared five times in succession. If random variable \(X\) denotes the number of non perfect square sums appeared. then \(P(X>0)\) isCUET 2025 Medium
- Which of the following are normal equations to fit a straight line trend \(y=a+b x\) by the method of least squares?CUET 2025 Easy
- If a matrix has 8 elements then the possible order(s) it may have
(A) 8 x 1
(B) 5 x 3
(C) 6 x 2
(D) 2 x 4
Choose the correct answert from the option given below :CUET 2025 Easy - Mr. X purchased a house for ₹ 7,00,000 and made a down payment of ₹ 1,50,000 .
He repays the balance in 25 years by equal monthly installments as \(9 \%\) per annum compounded monthly. The equated monthly installment (EMM) is :
[Given that \((1.0075)^{-300}=0.106\) ]CUET 2025 Medium - The angle between the straight lines \(\frac{x+4}{2}=\frac{y+5}{5}=\frac{z+6}{3}\) and \(\frac{x-4}{10}=\frac{y-5}{2}=\frac{z-6}{-10}\) is:CUET 2023 Hard
- If \(y = x^2 \log_e x\), then \(\frac{d^2y}{dx^2}\) is equal to:CUET 2023 Easy
More PYQs from CUET
- Which of the following correctly expresses the equation for species- area relationships? Where( S=Species richness, A=Area, Z=slope of line (regression coefficient), C=Y- interceptCUET 2025 Medium
- An electron moves around the nucleus in a hydrogen atom of radius 0.05 nm with a velocity of \( 2 \times 10^6 \text{ m s}^{-1} \). The magnetic field produced at the centre of the nucleus is:CUET 2023 Medium
- In eukaryotes, RNA polymerase III transcribes:
(A) tRNA
(B) 5.8S rRNA
(C) 5srRNA
(D) snRNA
Choose the correct answer from the options given below:CUET 2025 Easy - If \(y=\sin ^{-1} x+\sin ^{-1} \sqrt{1-x^2}, x \in(-1,0)\), then \(\frac{d y}{d x}\) is equal toCUET 2025 Hard
- Ram can row a boat in still water at the rate of 6 km/hr. He finds that it takes him twice as long to row upstream of a river as to row downstream of the same river, then the speed of the current of the river isCUET 2025 Easy
- If \(A = \begin{vmatrix} a & d & l \\ b & e & m \\ c & f & n \end{vmatrix}\) and \(B = \begin{vmatrix} l & m & n \\ a & b & c \\ d & e & f \end{vmatrix}\), thenCUET 2023 Medium