Download App

Continuity and Differentiability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsContinuity and Differentiability1 Mark
MCQ
If $a x^2+2 h x y+b y^2=1$, then $\frac{d y}{d x}$ equals
  • A
    $\frac{h x+b y}{a x+h y}$
  • B
    $\frac{a x+h y}{h x+b y}$
  • C
    $\frac{a x+h x}{h y+b y}$
  • ✓
    $\frac{-(a x+h y)}{h x+b y}$
✓

Answer

Correct option: D.
$\frac{-(a x+h y)}{h x+b y}$
(d) : Given, $a x^2+2 h x y+b y^2=1$
Differentiating w.r.t. $x$, we get
$
2 a x+2 h\left(x \frac{d y}{d x}+y\right)+2 b y \frac{d y}{d x}=0 \Rightarrow \frac{d y}{d x}=-\left(\frac{a x+h y}{h x+b y}\right)
$

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

$\text{The value of}\ \hat{\text{i}}\cdot(\hat{\text{j}}\times\hat{\text{k}})+\hat{\text{j}}\cdot(\hat{\text{i}}\times\hat{\text{k}})+\hat{\text{k}}\cdot(\hat{\text{i}}\times\hat{\text{j}})\ \text{is}$
→
Let $g (x)$ be an antiderivative for $f (x)$. Then $ln \,\left( {1 + {{\left( {g(x)} \right)}^2}} \right)$ is an antiderivative for
→
Choose the correct answer from the given four option.The degree of the differential equation $\Big(\frac{\text{d}^2\text{y}}{\text{d}\text{x}^2}\Big)+\Big(\frac{\text{d}\text{y}}{\text{d}\text{x}}\Big)^2-\sin\Big(\frac{\text{d}\text{y}}{\text{d}\text{x}}\Big)$ is:
→
If $A$ and $B$ are non $-$ zero square matrices of the same order such that $AB = 0,$ then
→
Let $f : X \rightarrow Y$ be a function such that $f(x) = \sqrt{x - 2} + \sqrt{4 - x} ,$ then the set of $X$ and $Y$ for which $f(x)$ is both injective as well as surjective, is-
→
A box contains coupons labelled $1,2,3, \ldots, n$. A coupon is picked at random and the number $x$ is noted. The coupon is put back into the box and a new coupon is picked at random. The new number is $y$.Then, the probability that one of the numbers $x, y$ divides the other is (in the options below $[r]$ denotes the largest integer less than or equal to $r$)
→
Let $f\left( x \right) = x\left| x \right|\,,\,g\left( x \right) = \sin \,x$ and $h\left( x \right) = \left( {gof} \right)\left( x \right)$. Then
→
Lety = $f(x) =\left[ \begin{array}{l}
\,\,\,\,{e^{ - \,\,\,\frac{1}{{{x^2}}}}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,if\,\,\,\,\,x\,\,\,\, \ne \,\,\,0\\
\,\,\,\,0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,if\,\,\,\,x\,\,\,\, = \,\,\,0
\end{array} \right.$ Then which of the following can best represent the graph of $y = f(x)$ ?
→
If $A=\left[\begin{array}{ll}1 & 0 \\ 2 & 1\end{array}\right], B=\left[\begin{array}{ll}x & 0 \\ 1 & 1\end{array}\right]$ and $A=B^2$, then $x$ equals
→
If the function $f(x)=k x^3-9 x^2+9 x+3$ is monotonically increasing in every interval, then: 
→