MHT CET · Maths · Definite Integration
\(\int_{0}^{a} \sqrt{\frac{x}{a-x}} d x=\)
- A \(\left(\frac{\pi}{4}\right) a\)
- B \(-\pi a\)
- C \(2 \pi a\)
- D \(\left(\frac{\pi}{2}\right) a\)
Answer & Solution
Correct Answer
(D) \(\left(\frac{\pi}{2}\right) a\)
Step-by-step Solution
Detailed explanation
(C)
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
- If \(x \cdot \log _{\mathrm{e}}\left(\log _{\mathrm{e}} x\right)-x^2+\mathrm{y}^2=4(\mathrm{y}>0)\), then \(\frac{\mathrm{dy}}{\mathrm{d} x}\) at \(x=\mathrm{e}\) isMHT CET 2025 Medium
- The derivative of \(\tan ^{-1}\left(\frac{\sqrt{1+x}-\sqrt{1-x}}{\sqrt{1+x}+\sqrt{1-x}}\right)\) isMHT CET 2022 Medium
- If \(n(X)=700, n(A)=200, n(B)=300,\) \(n(A \cap B)=100\), where \(X\) is universal set and \(A\) and \(\mathrm{B}\) are subsets of \(\mathrm{X}\), then \(\mathrm{n}\left(\mathrm{A}^{\prime} \cap \mathrm{B}^{\prime}\right)=\)MHT CET 2020 Medium
- The difference between the maximum and minimum values of the objective function \(\mathrm{Z}=3 x+5 \mathrm{y}\), subject to the constraints \(x+3 \mathrm{y} \leqslant 60, x+\mathrm{y} \geqslant 10\), \(x-\mathrm{y} \leqslant 0, x, \mathrm{y} \geqslant 0\) isMHT CET 2025 Medium
- The angle between the lines \(\frac{x-1}{l}=\frac{y+1}{m}=\frac{z}{n}\) and \(\frac{x+1}{m}=\frac{y-3}{n}=\frac{z-1}{l}\), where \(l>\mathrm{m}>\mathrm{n}\) and \(\mathrm{l}, \mathrm{m}, \mathrm{n}\) are roots of the equation \(x^3+x^2-4 x-4=0\), isMHT CET 2025 Medium
- The domain of the definition of the function \(f(x)=\frac{1}{4-x^2}+\log _{10}\left(x^3-x\right)\) isMHT CET 2022 Hard
More PYQs from MHT CET
- Which of the following animal was selected by Morgan for studying linkage?MHT CET 2015 Medium
- The stopping potential for a photelectric emission process is 10 V . The maximum kinetic energy of the electrons ejected in the process is [Charge on electron \(\mathrm{e}=1.6 \times 10^{-19} \mathrm{C}\) ]MHT CET 2024 Easy
- If \(\int_{o}^{a} \frac{d x}{1+4 x^{2}}=\frac{\pi}{8}\), then \(a=\)MHT CET 2020 Medium
- 4 red balls and 5 green balls are selected from n balls. If the sum of both the selections is greater then \({ }^{n+1} C_4\) then the value of \(n\) is equal toMHT CET 2025 Medium
- The cumulative distribution function of a discrete random variable X is given by
Then \(\mathrm{E}\left(\mathrm{X}^2\right)=\)MHT CET 2024 Easy - The size of the real image produced by a convex lens of focal length \(\mathrm{F}\) is ' \(\mathrm{m}\) ' times the size of the object. The image distance from the lens isMHT CET 2023 Medium