CUET · MATHS · PYQ PAPER 2025
\(\int \frac{\sqrt{1-x}}{\sqrt{1+x}} d x=\alpha \sqrt{1-x^2}+\beta \sin ^{-1} x+C\), where \(C\) is an arbitrary constant, then which of the following are TRUE?
(A) \(\alpha=1\)
(B) \(\alpha=-1\)
(C) \(\beta=1\)
(D) \(\beta=-1\)
Choose the correct answer from the options given below :
- A (B) and (D) only
- B (A) and (C) only
- C (A) and (D) only
- D (B) and (C) only
Answer & Solution
Correct Answer
(B) (A) and (C) only
Step-by-step Solution
Detailed explanation
\(\int \frac{\sqrt{1-x}}{\sqrt{1+x}} d x = \int \frac{\sqrt{1-x}}{\sqrt{1+x}} \cdot \frac{\sqrt{1-x}}{\sqrt{1-x}} d x\) \(= \int \frac{1-x}{\sqrt{1-x^2}} d x\) \(= \int \frac{1}{\sqrt{1-x^2}} d x - \int \frac{x}{\sqrt{1-x^2}} d x\) \(= \sin^{-1} x - (-\sqrt{1-x^2}) + C\)…
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 a random variable \(X\) has the following probability distribution :
then Match List-I with List-IIX 0 1 2 3 4 P(X) k 2k 3k \(k^2\) \(6 k^2\)
Choose the correct answer from the options given below :List-I List-II (A) k (I) 3/7 (B) \(P(x<2)\) (II) \(6 / 49\) (C) \(P(X>3)\) (III) \(1 / 7\) (D) \(P(2 \leq X \leq 3)\) (IV) 22/49 CUET 2025 Hard - If \(A=\left[\begin{array}{cc}3 & 1 \\ -1 & 2\end{array}\right]\), then \(A^2-5 A+7 I=\)CUET 2023 Hard
- The value of \(\tan ^2\left(\sec ^{-1} 2\right)+\cot ^2\left(\operatorname{cosec}^{-1} 3\right)\) is:CUET 2023 Easy
- Let \(A=\left[\begin{array}{ll}2 & 3 \\ 1 & 2\end{array}\right]\) and \(B=\left[\begin{array}{cc}4 & -6 \\ -2 & 4\end{array}\right]\), then
(A) \(\operatorname{det}\left(A^T\right)=1\)
(B) \(A B=I\), where \(I\) is the identity matrix of order 2
(C) \(A^{-1}=\left[\begin{array}{cc}2 & -3 \\ -1 & 2\end{array}\right]\)
(D) \(\operatorname{adj}(B)=\left[\begin{array}{ll}4 & 2 \\ 6 & 4\end{array}\right]\)
Choose the correct answer from the options given below :CUET 2025 Hard - For \(x \in R -\{0\}\), the function \(f(x)=\frac{3}{x}+7\) is decreasing whenCUET 2025 Medium
- In which of the following intervals, the function \(f(x)=\frac{x}{\log x}\) is decreasing?CUET 2025 Hard
More PYQs from CUET
- Match List - I with List - II.
LIST I LIST II A. Anabaena I. Preparation of Ethanol B. Monascus purpureus II. Statins C. Saccharomyces cerevisiae III. Cyanobacteria D. Trichoderma polysporum IV. Cyclosporin A
Choose the correct answer from the options given below:CUET 2023 Medium - Identify the correct statements.
(A) The density of nuclear matter is independent of the size of the nucleus.
(B) Nuclear forces are charge independent and are non-central forces.
(C) The nuclides having the same mass number are called isotones.
(D) The mass of a nucleus can be less or more than the sum of the masses of nucleons present inside it.
Choose the correct answer from the options given below:CUET 2025 Hard - Elements of group-15, 16 and 17 form compounds with hydrogen with general formula MH3, H2M and HX (called hydrogen halides). Stability of these hydrides, along with M-H bond strength and basic nature decreases down the group. Boiling point of these hydrides mainly depends on the strength of their inter molecular forces.
Which of the following is liquid at \(20^{\circ} C\) ?
A. HCl
B. HI
C. HF
D. NH3
E. HBr
Choose the correct answer from the options given below:CUET 2023 Hard - Match (List I) with (List II)
(List I) (List II) A. \(\sin 2 x\) \(I.\) decreases from 1 to 0 in \(\left(0, \frac{\pi}{2}\right)\) B. \(\tan x\) \(II.\) decreases if \(x \in\left(0, \frac{\pi}{6}\right)\) C. \(\cos x\) \(III.\) increases from 0 to 1 in \(\left(0, \frac{\pi}{4}\right)\) D. \(\cos 3 x\) \(IV.\) is an increasing function in each quadrant
Choose the correct answer from the options given below:CUET 2023 Easy - Consider two lines \(l_1\) and \(l_2\) with cartesian equations \(\frac{x}{2}=\frac{1-y}{-2}=\frac{z}{1}\) and \(\frac{2 x-5}{16}=\frac{y-2}{-1}=\frac{z-5}{4}\) respectively. Which of the following is/are true?
(A) Direction ratio of \(l_1\) are \(2,2,1\)
(B) Direction cosines of \(l_1\) are \(\frac{2}{3}, \frac{-2}{3}, \frac{1}{3}\)
(C) Direction ratio of \(l_2\) are \(16,-1,4\)
(D) Angle between \(l_1\) and \(l_2\) is \(\cos ^{-1}\left(\frac{38}{3 \sqrt{273}}\right)\)
Choose the correct answer from the options given below:CUET 2025 Medium - The differential equation representing the family of curves \(y=A \cos (x+B)\), where \(A\) and \(B\) are arbitrary constants is :CUET 2023 Hard