CUET · MATHS · PYQ PAPER 2023
Two curves \(x^3-3 x y^2+2=0\) and \(3x^2 y-y^3=2\) :
- A Touch each other
- B Cut at right angle
- C Cut at an angle \(\frac{\pi}{3}\)
- D Cut at an angle \(\frac{\pi}{4}\)
Answer & Solution
Correct Answer
(B) Cut at right angle
Step-by-step Solution
Detailed explanation
\(m_1 = \frac{d}{dx}(x^3-3 x y^2+2=0)\) \(3x^2 - 3y^2 - 6xy \frac{dy}{dx} = 0 \Rightarrow m_1 = \frac{x^2 - y^2}{2xy}\) \(m_2 = \frac{d}{dx}(3x^2 y-y^3=2)\) \(6xy + 3x^2 \frac{dy}{dx} - 3y^2 \frac{dy}{dx} = 0 \Rightarrow m_2 = \frac{6xy}{3y^2 - 3x^2} = \frac{2xy}{y^2 - x^2}\)…
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 matrix \(\left[\begin{array}{lll}0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{array}\right]\) is a
(A) Null matrix
(B) Unit matrix
(C) Symmetric matrix
(D) Skew-symmetric matrix
Choose the correct answer from the options given below:CUET 2025 Hard - The general solution of the differential equation \(\frac{d y}{d x}=x y+x+y+1\) isCUET 2025 Hard
- If the tangent to the curve \(y^2 + 3x - 7 = 0\) at the point (h, k) is parallel to the line x - y = 4, then the value of k is:CUET 2023 Medium
- Match List-l with List-ll
Where \(R\) is set of real numbers
Choose the correct answer from the options given below :List-l List-ll (A) \(f: R \rightarrow R\) s.t \(f(x)=x^4\) is (I) one-one, Into (B) \(f: R \rightarrow[0, \infty)\) s.t \(f(x)=x^4\) is (II) many-one, into (C) \(f:[0, \infty) \rightarrow R\) s.t \(f(x)=x^4\) is (III) one-one, onto (D) \(f:[0, \infty) \rightarrow[0, \infty)\) s.t \(f(x)=x^4\) is (IV) many-one, onto CUET 2025 Medium - If \(A=\left[\begin{array}{ll}x & 3 \\ 2 & y\end{array}\right], \quad B=\left[\begin{array}{cc}2 y & 1 \\ 3 & x\end{array}\right]\) and \(A+2 B=\left[\begin{array}{cc}6 & 5 \\ 8 & -2\end{array}\right]\), then the value of \((x, y)\) is:CUET 2023 Medium
- Two charged particles, placed at a distance d apart in vacuum, exert a force F on each other. Now, each of the charges is doubled. To keep the force unchanged, the distance between the charges should be changed to :CUET 2024 Easy
More PYQs from CUET
- When \(CuSO_4\) solution is electrolysed using platinum electrodes, which of the following is true ?CUET 2023 Easy
- Match List I with List - II.
List - I List - II (A) Pollination by water (I) Honey bee (B) Chasmogamous and Cleistogamous flowers (II) Zostera (C) Pollination by wind (III) Oxalis (D) Pollinating agent (IV) Maize
Choose the correct answer from the options given below :CUET 2023 Easy - The electrochemical cells \(Zn \left| Zn ^{2+} \| Cu ^{2+}\right| Cu\) and \(Fe ^{-} Fe ^{2+} \| Cu ^{2+} \mid Cu\) are connected in series. What will be the net emf of the cell at \(25^{\circ} C\) ? Given: \(E ^{\circ}\) of \(Zn ^{2+} \mid Zn =-0.76 V ; \quad E ^{\circ}\) of \(Cu ^{2+} \mid Cu =+0.34 V ; \quad E ^{\circ}\) of \(Fe ^{2+} \mid Fe =-0.41 V\)CUET 2023 Easy
- The function \(f(x)=2 x^3-3 x^2-12 x+4\) has:
(A) two points of local maxima.
(B) two points of local minima.
(C) one local maxima and one local minima.
(D) no local maxima or local minima.CUET 2023 Hard - If A and B are skew-symmetric matrices, then which of the following is not true?CUET 2025 Medium
- Match List-l with List-ll
List-l (Microbes) List-II (Products or uses) (A). Trichoderma polysporum (I). Blood cholesterol lowering agent (B). Streptococcus (II). Citric acid (C). Aspergillus niger (III). Clot buster to remove blood clots (D). Monascus purpureus (IV). Cyclosporin A
Choose the correct answer from the options given below:CUET 2025 Easy