MHT CET · Maths · Differentiation
If \(x=\mathrm{t}^2+\mathrm{t}+1, \mathrm{y}=\sin \left(\frac{\mathrm{t} \pi}{2}\right)+\cos \left(\frac{\mathrm{t} \pi}{2}\right)\), then \(\frac{\mathrm{dy}}{\mathrm{d} x}\) at \(\mathrm{t}=1\) is
- A \(\frac{\pi}{3}\)
- B \(\frac{-\pi}{4}\)
- C \(\frac{\pi}{2}\)
- D \(\frac{-\pi}{6}\)
Answer & Solution
Correct Answer
(D) \(\frac{-\pi}{6}\)
Step-by-step Solution
Detailed explanation
\( \frac{\mathrm{dx}}{\mathrm{dt}} = 2\mathrm{t}+1 \) \( \frac{\mathrm{dx}}{\mathrm{dt}} \Big|_{\mathrm{t}=1} = 2(1)+1=3 \)
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
- Radium decomposes at a rate proportional to the amount present. If half the orignal amount disappears in 1600 yrs, then the percentage loss in 100 years is \(\left(\right.\) Given \(\left.\log 2=0.6912 \& \mathrm{e}^{-0 \cdot 04320}=0 \cdot 9576\right)\)MHT CET 2020 Medium
- If \(f(x)=\cos (\log x)\), then \(f(x) \cdot f(y)-\frac{1}{2}\left(f\left(\frac{x}{y}\right)+f(x y)\right)\) has the valueMHT CET 2022 Medium
- If \(y=e^{4 x} \cos 5 x\), then \(\frac{d^{2} y}{d x^{2}}\) at \(x=0\) isMHT CET 2020 Easy
- The p. d. f. of a continuous random variable \(\mathrm{X}\) is given by
\(f(x)=\frac{1}{2} \quad\) if \(\quad 0 < x < 2\)
\(=0 \quad\) otherwise
and if \(a=P\left(X < \frac{1}{2}\right), b=P\left(X>\frac{3}{2}\right)\), then relation between \(a\) and \(b\) isMHT CET 2020 Easy - The equation of tangent to the curve \(y^{2}=a x^{2}+b\) at point \((2,3)\) is \(y=4 x-5\), then the values of \(a\) and \(\bar{b}\) areMHT CET 2010 Easy
- For the probability distribution
Then the \(\operatorname{Var}(\mathrm{X})\) is
(Given :
\(\left.(0.25)^2=0.0625,(0.35)^2=0 \cdot 1225,(0.45)^2=0 \cdot 2025\right)\)MHT CET 2024 Medium
More PYQs from MHT CET
- Which one of the following is the genetic material of bacteriophage \(\phi X 174\) ?MHT CET 2022 Hard
- Identify the product (A) obtained in the following reaction.
Phenol + concentrated Nitric acid \(\underset{\mathrm{H}_2 \mathrm{SO}_4}{\stackrel{\text { Concentrad }}{\longrightarrow}} \mathrm{A}\)MHT CET 2021 Medium - A magnetic needle of magnetic moment \(6 \times 10^{-2} \mathrm{Am}^2\) and moment of inertia \(9.6 \times 10^{-5} \mathrm{~kg} \mathrm{~m}^2\) performs simple harmonic motion in a magnetic field of 0.01 T . Time taken to complete 10 oscillations is [Take \(\pi=3 \cdot 14\) ]MHT CET 2024 Easy
- Electrons are accelerated through a potential difference of 16 kV . If the potential difference is increased to 64 kV , then de-Broglie wavelength associated with electron willMHT CET 2024 Easy
- Which among the following carbohydrates is a trisaccharide?MHT CET 2021 Medium
- In the circuit shown the ratio of quality factor and the bandwidth is
MHT CET 2023 Hard