CUET · MATHS · PYQ PAPER 2023
Solution of differential equation \(\frac{d y}{d x}=\cos (x+y+3)\) is:
- A \(y=-\sin (x+y+3)+c\)
- B \(y=\sin (x+y+3)+c\)
- C \(y=2 \tan ^{-1}(x+c)-x-3\)
- D \(y=\frac{1}{2} \tan ^{-1}(x+c)+x+3\)
Answer & Solution
Correct Answer
(C) \(y=2 \tan ^{-1}(x+c)-x-3\)
Step-by-step Solution
Detailed explanation
\(v = x+y+3 \implies \frac{dv}{dx} = 1 + \frac{dy}{dx}\) \(\frac{dv}{dx} - 1 = \cos v\) \(\frac{dv}{1 + \cos v} = dx\) \(\int \frac{dv}{2 \cos^2 \left(\frac{v}{2}\right)} = \int dx\) \(\tan \left(\frac{v}{2}\right) = x + c\) \(\tan \left(\frac{x+y+3}{2}\right) = x + c\)…
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
- The area of the region bounded by the curves \(y=x^2+2, y=-x, x=0\) and x = 1 is :CUET 2023 Hard
- The function \(f(x)=\left\{\begin{array}{ll}\frac{\sin 2 x}{x}+\cos x & , \text { if } x \neq 0 \\ K & , \text { if } x=0\end{array}\right.\) is continuous at \(x = 0\) then the value of K is:CUET 2025 Easy
- A manufacturer can sell x items at a price of mp 3x + 5 each. The cost price of x items is ₹\(x^2\ + 5x.
If z is the number of items she should sell to get no profit and no loss, then:CUET 2023 Easy - For what value of \(\alpha\), the function \(f\) defined by \(f(x)=\left\{\begin{array}{ll}\alpha\left(x^2-2 x+1\right), & \text { if } x \leq 0 \\ 2 x+1, & \text { if } x>0\end{array}\right.\) is continuous at \(x=0\) ?CUET 2025 Easy
- If \(\vec{a}=2 \hat{j}-\hat{k}, \vec{b}=2 \hat{i}-3 \hat{j}+\hat{k}\) and \(\vec{c}=-\hat{i}+\hat{k}\) are three vectors, then the area (in sq, units) of the parallelogram whose diagonals are \((\vec{b}+\vec{c})\) and \((\vec{a}+\vec{c})\) isCUET 2025 Hard
- The point on the curve \(y^2=x\), where the tangent line makes an angle of \(\frac{\pi}{4}\) with x axis isCUET 2023 Easy
More PYQs from CUET
- The number of tangents to the curve \(x y-3 y+2=0\) having slope 2 is :CUET 2025 Easy
- In a Young's double slits experiment, the source is white light, one of the hole is covered by a red filter and another by a blue filter. In this case:CUET 2023 Hard
- Match List-I with List-II
Choose the correct answer from the options given below:List-I ( Terms) List-II (Examples) (A) Chromosomal disorder (I) Color Blindness (B) Incomplete dominance (II) Drosophila (C) Sex-linked recessive disorder (III) Antirrhinum (D) Male heterogamety (IV) Down's Syndrome CUET 2025 Hard - Two identical metal balls, A and B, with similar charges Q are suspended with insulating threads. They repel each other with a force F. Another identical uncharged metal ball C is first touched with metal ball A and then touched with metal ball B and finally removed. The new force of repulsion between A and B will beCUET 2025 Hard
- The matrix \(\left[\begin{array}{lll}2 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]\) is aCUET 2023 Medium
- Arrange the following compounds towards increasing \(S_{N}2\) reaction?
(A) n-Butyl bromide
(B) Isobutyl bromide
(C) Tertiary butyl bromide
(D) Sec-Butyl bromide
Choose the correct answer from the options given below:CUET 2025 Hard