CUET · MATHS · PYQ PAPER 2023
If \(x=\log t^2\) and \(y=(\log t)^2\) then \(\frac{d^2 y}{d x^2}\) is:
- A 2
- B \(\frac{1}{2}\)
- C \(\frac{\log t}{t}\)
- D \(\frac{4 \log t-4}{t^6}\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
\( x = 2 \log t \) \( \frac{dx}{dt} = \frac{2}{t} \) \( \frac{dy}{dt} = 2 (\log t) \cdot \frac{1}{t} = \frac{2 \log t}{t} \) \( \frac{dy}{dx} = \frac{dy/dt}{dx/dt} = \frac{2 \log t / t}{2 / t} = \log t \)…
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 \(x=4 t^2, y=8 t\), then \(\frac{d^2 y}{d x^2}\) is:CUET 2023 Hard
- \(\int \frac{\cos 2 x-\cos 2 \alpha}{\cos x-\cos \alpha} d x\) is equal toCUET 2025 Easy
- Choose the correct answer
A. \(\sin ^{-1} x+\cos ^{-1} x=\frac{\pi}{2}, x \in[-1,1]\)
B. \(\cos ^{-1}(-x)=-\cos ^{-1} x, x \in[-1,1]\)
C. \(\sin ^{-1} x+\cos ^{-1} x=\frac{\pi}{2}, x \in(-1,1)\) only
D. \(\tan ^{-1} x+\cot ^{-1} x=\frac{\pi}{2}, x \in R\)
E. \(\tan ^{-1} x+\tan ^{-1} y=\tan ^{-1}\left(\frac{x+y}{1-x y}\right), x y<1\)
Choose the correct answer from the options given below:CUET 2023 Hard - A box contains 10 balls, each marked with one of the digits 0 to 9 .
If four balls are drawn successively with replacement from the box,
then the probability that none is marked with the digit \(0\) is :CUET 2025 Easy - If \(\left|\begin{array}{cc}2 & 3-x \\ x & 1\end{array}\right|=0\), then the values of x are:CUET 2023 Easy
- If \(A=\left[\begin{array}{cc}3 & 1 \\ -1 & 2\end{array}\right]\), then \(A^2-5 A+7 I=\)CUET 2023 Hard
More PYQs from CUET
- The general solution of the differential equation \(\frac{d y}{d x}+\sqrt{\frac{1-y^2}{1-x^2}}=0\) is :CUET 2023 Medium
- Consider the differential equation, \(x \frac{d y}{d x}=y\left(\log _e y-\log _e x+1\right)\), then which of the following are true?
(A) It is a linear differential equation
(B) It is a homogenous differential equation
(C) Its general solution is \(\log _e\left(\frac{y}{x}\right)=C x\), where \(C\) is constant of integration
(D) Its general solution is \(\log _e\left(\frac{x}{y}\right)=C_y\), where \(C\) is constant of integration
(E) If \(y(1)=1\), then its particular solution is \(y=x\)
Choose the correct answer from the options given below:CUET 2025 Medium - Choose the incorrect statements from the options given below:
(A) S I unit of inductive reactance and capacitive reactance is Ohm
(B) Inductive reactance acting like resistance, stops the dc and ac both
(C) Inductive reactance and capacitive reactance both are proportional to frequency of ac supply,
(D) There is no power consumption in pure capacitive reactance.
Choose the correct answer from the options given below:CUET 2025 Medium - Pipe A can independently empty a half-filled tank in 3 hours whereas pipe B can alone fill the same tank in 4 hours, when the tank is completely empty. In how much time.CUET 2023 Easy
- Which molecule serves as the genetic material in most organisms?CUET 2023 Hard
- Which of the following are correct?
(A) The function \(f(x)=3 x+12\) is increasing on \(R\).
(B) The function \(f(x)=e^{2 x}\) is decreasing on \(R\).
(C) The function \(f(x)=x^2-x+1\) is neither increasing nor decreasing on \((-1,1)\).
(D) The function \(f(x)=x^3-3 x^2+4 x\) is increasing on \(R\).
Choose the correct answer from the options given below :CUET 2025 Hard