If x=at^2,y=2at then d^2y dx^2 = - Vidyadip

MCQ

If $\text{x}=\text{at}^2,\text{y}=2\text{at}$ then $\frac{\text{d}^2\text{y}}{\text{dx}^2}$=

A
$-\frac{1}{\text{t}^2}$
B
$\frac{1}{2\text{at}^3}$
C
$-\frac{1}{\text{t}^3}$
✓
$-\frac{1}{2\text{at}^3}$

✓

Answer

Correct option: D.

$-\frac{1}{2\text{at}^3}$

$\text{x}=\text{at}^2,\text{y}=2\text{at}$

$\frac{\text{dy}}{\text{dx}}=\frac{\frac{\text{dy}}{\text{dt}}}{\frac{\text{dx}}{\text{dt}}}=\frac{2\text{a}}{2\text{at}}$

$\frac{\text{d}}{\text{dx}}\Big(\frac{\text{dy}}{\text{dx}}\Big)=\frac{\frac{\text{d}}{\text{dt}}\Big(\frac{\text{dy}}{\text{dx}}\Big)}{\frac{\text{dx}}{\text{dt}}}=\frac{\frac{-1}{\text{t}^2}}{2\text{at}}=\frac{-1}{2\text{at}^3}$

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→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If $\left[\begin{array}{lll}x & -5 & -1\end{array}\right]\left[\begin{array}{lll}1 & 0 & 2 \\ 0 & 2 & 1 \\ 2 & 0 & 3\end{array}\right]\left[\begin{array}{l}x \\ 4 \\ 1\end{array}\right]=0$, then the value of $x$ is

Let $f(x)$ be an indefinite integral of $cos^3\,x.$
Statement $1\,:\,f(x)$ is a periodic function of period $\pi $

Statement $2\,:\,cos^3\,x$ is a periodic function.

If $A$ and $B$ are matrices of same order, then $\left(A B^{\prime}-B A^{\prime}\right)$ is a

The linear programming problem minimize Z = 3x + 2y subject to constraints $s x+y \geq 8,3 x+5 y \leq 15, x \geq 0$ and $y \geq 0$, has

If $f (a + b - x)$ $= f (x)$ , then $\int\limits_a^b {\,x.f\,(a + b - x)\,dx} $ $=$

For $\theta \in[0, \pi]$, let $f(\theta)=\sin (\cos \theta)$ and $g(\theta)=\cos (\sin \theta)$ Let $\alpha =\max _{0 \leq \theta \leq \pi} f(\theta), b=\min _{0 \leq \theta \leq \pi} f(\theta), c=\max _{0 \leq \theta \leq \pi} g(\theta)$ and $d =\max g(\theta)$. The correct inequalities satisfied by$a, b, c, d$ are

Let $P(3,2,3), Q(4,6,2)$ and $R(7,3,2)$ be the vertices of $\triangle \mathrm{PQR}$. Then, the angle $\angle \mathrm{QPR}$ is

Let $y=y(x)$ be the solution of the differential equation $d y=e^{a x+y} d x ; \alpha \in N$. If $y\left(\log _{e} 2\right)=\log _{e} 2$ and $y(0)=\log _{e}\left(\frac{1}{2}\right)$, then the value of $\alpha$ is equal to $.....$

The solution of the differential equation $xy\frac{{dy}}{{dx}} = \frac{{(1 + {y^2})(1 + x + {x^2})}}{{(1 + {x^2})}}$ is

If ${2^x} + {2^y} = {2^{x + y}}$, then ${{dy} \over {dx}} = $