Download App

CONTINUITY AND DIFFERENTIABILITY — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSCONTINUITY AND DIFFERENTIABILITY1 Mark
MCQ
If $x = t^2, y = t^3,$ then $\frac{\text{d}^2\text{y}}{\text{dx}^2} =$
  • A
    $\frac{3}{2}$
  • ✓
    $\frac{3}{4\text{t}}$
  • C
    $\frac{3}{2\text{t}}$
  • D
    $\frac{3\text{t}}{2}$
✓

Answer

Correct option: B.
$\frac{3}{4\text{t}}$
$\text{x}=\text{t}^2$
$\Rightarrow\frac{\text{dx}}{\text{dt}} = 2\text{t}$
$\text{y}=\text{t}^3$
$\Rightarrow\frac{\text{dy}}{\text{dt}} = 3\text{t}^2$
$\Rightarrow\frac{\text{dy}}{\text{dx}} = \frac{3\text{t}^2}{2\text{t}} = \frac{3\text{t}}{2}$
Hence, $\frac{\text{d}^2\text{y}}{\text{dx}^2} = \frac{3}{4\text{t}}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from CONTINUITY AND DIFFERENTIABILITY→CONTINUITY AND DIFFERENTIABILITY — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

The value of $ \left( {{{\tan }^{ - 1}}\pi + {{\tan }^{ - 1}}\left( {\frac{1}{\pi }} \right)} \right) + {\tan ^{ - 1}}\sqrt 3 - {\sec ^{ - 1}}( - 2)$ is equal to
  1. $ \frac{{ - \pi }}{3}$
  2. $ \frac{{ \pi }}{6}$
  3. $ \frac{{ 2 \pi }}{3}$
  4. $ \pi$
→
Choose the correct answer in Exercise:
The value of $\int^{1}_{0}\tan^{-1}\bigg(\frac{2\text{x}-1}{1+\text{x}-\text{x}^{2}}\bigg)\text{dx}$ is
  1. 1
  2. 0
  3. -1
  4. $\frac{\pi}{4}$
→
Find the area enclosed by the parabola $y^2=x$ and the line $y+x=2$ and the $x$-axis.
→
If $\text{f}(\text{x})=\sqrt{\text{x}^2+6\text{x}+9},$ then f'(x) is equal to:
  1. 1 for x < -3
  2. -1 for x < -3
  3. 1 for all $\text{x}\in\text{R}$
  4. None of these.
→
If $A$ and $B$ are square matrices of order $n \times n$ such that, $A^{2 }− B^{2 }= (A − B)(A + B),$ then of the following will always be true?
→
If $\int\frac{1}{5+4\sin\text{x}}\text{ dx}=\text{A}\tan^{-1}\Big(\text{B}\tan\frac{\pi}{2}+\frac{4}{3}\Big)+\text{C},$ then:
  1. $\text{A}=\frac{2}{3},\text{B}=\frac{5}{3}$
  2. $\text{A}=\frac{1}{3},\text{B}=\frac{2}{3}$
  3. $\text{A}=-\frac{2}{3},\text{B}=\frac{5}{3}$
  4. $\text{A}=\frac{1}{3},\text{B}=-\frac{5}{3}$
→
The distance of the point (-3, 4, 5) from the origin:
  1. 50
  2. $5\sqrt{2}$ 
  3. 6
  4. None of these 
→
The solution set of the inequation $3 x+5 y<7$ is
→
The direction ratios of a line parallel to z -axis are:
→
Choose the correct answers from the given four options: If $x = t^2, y = t^3,$ then $\frac{\text{d}^2\text{y}}{\text{dx}^2}$ is:
→