Download App

STD 12 - 9. differential equations — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 9. differential equations1 Mark
MCQ
Differential equation of $y = \sec ({\tan ^{ - 1}}x)$ is
  • A
    $(1 + {x^2})\frac{{dy}}{{dx}} = y + x$
  • B
    $(1 + {x^2})\frac{{dy}}{{dx}} = y - x$
  • ✓
    $(1 + {x^2})\frac{{dy}}{{dx}} = xy$
  • D
    $(1 + {x^2})\frac{{dy}}{{dx}} = \frac{x}{y}$
✓

Answer

Correct option: C.
$(1 + {x^2})\frac{{dy}}{{dx}} = xy$
c
(c) $y = \sec ({\tan ^{ - 1}}x)$

$\frac{{dy}}{{dx}} = \sec ({\tan ^{ - 1}}x)\tan ({\tan ^{ - 1}}x)\,.\,\frac{1}{{1 + {x^2}}}$$ = \frac{{xy}}{{1 + {x^2}}}$

==> $(1 + {x^2})\frac{{dy}}{{dx}} = xy$.

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 STD 12 - 9. differential equations→STD 12 - 9. differential equations — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

Let $S$ be the sample space of all $3 \times 3$ matrices with entries from the set $\{0,1\}$. Let the events $E _1$ and $E _2$ be given by

$E_1=\{A \in S: \operatorname{det} A=0\} \text { and }$ $E_2=\{A \in S: \text { sum of entries of } A \text { is } 7\}.$ If a matrix is chosen at random from $S$, then the conditional probability $P\left(E_1 \mid E_2\right)$ equals. . . . . . . .

→
The area bounded by the curve $y = x,$ $x -$ axis and ordinates $x = - 1$ to $x = 2$ is
→
$\int\limits_a^b {} \, [x] \,dx + \int\limits_a^b {} \, [ - x] \,dx$

where $[. ]$ denotes greatest integer function is equal to :

→
If $P(x, y, z)$ moves such that $x = 0, z = 0$ then the locus of $P$ is the line whose $d.cs$ are:
→
Choose the correct answer from the given four options.
Let $\text{f}:\text{R}-\Big\{\frac{3}{5}\Big\}\rightarrow\ \text{R}$ be defined by $\text{f}(\text{x})=\frac{3\text{x}+2}{5\text{x}-3}.$ Then,
→
Let $O$ be the origin. Let $\overline{ OP }= x \hat{ i }+ y \hat{ j }-\hat{ k }$ and $\overline{ OQ }=-\hat{ i }+2 \hat{ j }+3 x \hat{ k }, x , y \in R , x >0,$ be such that $|\overline{ PQ }|=\sqrt{20}$ and the vector $\overline{ OP }$ is perpendicular to $\overline{ OQ }$. If $\overline{ OR }=3 \hat{ i }+ z \hat{ j }-7 \hat{ k }, z \in R ,$ is coplanar with $\overline{ OP }$ and $\overline{ OQ },$ then the value of $x ^{2}+ y ^{2}+ z ^{2}$ is equal to ...... .
→
If the point of minima of the function, $f(x) = 1 + a^2x -x^3 $ satisfy the inequality $\frac{{{x^2} + x + 2}}{{{x^2} + 5x + 6}} < 0$, then $'a'$ must lie in the interval
→
A relation $R$ is defined from $\{2, 3, 4, 5\}$ to $\{3, 6, 7, 10\}$ by $: xRy \Leftrightarrow x$ is relatively prime to $y.$ Then, domain of $R$ is:
→
The radius of a circular plate is increasing at the rate of $0.01\ cm/\sec$. The rate of increase of its area when the radius is $12\ cm,$ is :
→
If $\mathrm{A}$ and $\mathrm{B}$ are two events such that $\mathrm{P}(\mathrm{A}) \neq 0$ and $\mathrm{P}(\mathrm{B} | \mathrm{A})=1,$ then.
→