CUET Mathematics 2024 - If y=x (a+y), then d y/d x is : | PYQs + Solutions

CUET Mathematics 2024

Calculus

Medium

$\frac{\sin ^{2} a}{\sin (a+y)}$

$\frac{\sin (a+y)}{\sin ^{2} a}$

$\frac{\sin (a+y)}{\sin a}$

$\frac{\sin ^{2}(a+y)}{\sin a}$

✅ Correct Option: 4

Related questions:

For the differential equation $\left(x \log _{e} x\right) d y=\left(\log _{e} x-y\right) d x$

(A) Degree of the given differential equation is $1$ .

(B) It is a homogeneous differential equation.

(C) Solution is $2y \log _{\mathrm{e}} \mathrm{x}+A=\left(\log _{\mathrm{e}} \mathrm{x}\right)^{2}$ , where $A$ is an arbitrary constant

(D) Solution is $2 y \log _{e} x+A=\log _{e}\left(\log _{e} x\right)$ , where $A$ is an arbitrary constant

Choose the correct answer from the options given below :

The degree of the differential equation $\left(1-\left(\frac{d y}{d x}\right)^{2}\right)^{\frac{3}{2}}=k \frac{d^{2} y}{d x^{2}}$ is :

Choose the correct answer from the options given below:

List-I	List-II
(A) Integrating factor of $x \, dy - (y + 2x^2) \, dx = 0$	(I) $\frac{1}{x}$
(B) Integrating factor of $(2x^2 - 3y) \, dx = x \, dy$	(II) $x$
(C) Integrating factor of $(2y + 3x^2) \, dx + x \, dy = 0$	(III) $x^2$
(D) Integrating factor of $2x \, dy + (3x^3 + 2y) \, dx = 0$	(IV) $x^3$

CUET Mathematics 2024 PYQs