Test Details

Differential Equations

Dec 12, 12:00 PM

120 minutes

Dec 13, 9:00 AM

100.0 marks

MCQ

50 questions

Ankush Kowale

skills in communication, listening, collaboration, adaptability, empathy and patience.

Class Details

Entrance

Maths

Physics

Biology

Chemistry

IIT-JEE/MHT-CET/NEET

Daily Online Quizz

12TH STD GURUKUL

Entrance

Maths

Physics

Biology

Chemistry

IIT-JEE/MHT-CET/NEET

Daily Online Quizz

With our unique teaching pedagogy, we have been able to help the students realize their dreams and get admission in to their desired institute for engineering or medical. The core pillars of our foundation are student-centric approach and feedback-driven mechanism.

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Question Text

Question 2 :
The solution of the differential equaton $3{e^x}\tan ydx + \left( {1 - {e^x}} \right){\sec ^2}ydy = 0$ is

Question 4 :
$\displaystyle \left ( x+y \right )\left ( dx-dy \right )= dx+dy.$

Question 6 :
Find the solution of $\displaystyle x\cos \frac{y}{x}\left ( y dx+x dy \right )=y \sin \frac{y}{x}\left ( x dy-y dx \right )$

Question 10 :
Solve the following differential equations : $ \dfrac {dy}{dx} = - \dfrac {y}{x} $

Question 12 :
Solution of $\dfrac { dy }{ dx } ={ 3 }^{ x+y }$ is

Question 15 :
Find the solution of $\displaystyle \frac{dy}{dx}+\frac{y}{x}=\frac{1}{\left ( 1+\log x+\log y \right )^{2}}$

Question 16 :
Solve $\displaystyle \left ( 4x+6y+3 \right )dx= \left ( 6x+9y+2 \right )dy$

Question 22 :
The solution of $y\, dx - x \,dy + \log \,x \,dx = 0$ is

Question 23 :
Let a solution $y = y(x)$ of the differential equation $e^{y}dy - (2 + \cos x) dx = 0$ satisfy $y(0) = 0$ then the value of $f\left (\dfrac {\pi}{2}\right )$ is equal to

Question 25 :
The slope of the tangent to the curve at a point $(x, y)$ on it is proportional to $(x-2)$. If the slope of the tangent to the curve at $(10, 9)$ on it is $3$. The equation of the curve is:

Question 27 :
The equation of the curve whose slope is $\displaystyle \frac{dy}{dx}= \frac{2y}{x}, \:x> 0, \:y> 0$ and passing through the point $y\left ( 1 \right )= 1$ is given by:

Question 28 :
The solution of the differential equation $ ({x^2} - {y^2})dx + 2xy\,dy = 0$

Question 29 :
The differential equation $\displaystyle \frac{\mathrm{d}\mathrm{y}}{\mathrm{d}\mathrm{x}}=\frac{\sqrt{1-\mathrm{y}^{2}}}{\mathrm{y}}$ determines a family of circles with:

Question 35 :
The solution of the differential equation $ydx+\left( x+{ x }^{ 2 }y \right) dy=0$ is

Question 36 :
Solve the given differential equation $\displaystyle \left ( xy^{2}+x \right )dx+\left ( yx^{2}+y \right )dy=0.$

Question 37 :
Solution of differential equation $\cfrac { dy }{ dx } \tan { y } =\sin { (x+y) } +\sin { (x-y) } $, is

Question 42 :
The equation of the curve which passes through the point $(2a,a)$ and for which the sum of the cartesian sub tangent and the abscissa is equal to the constant $a$, is :

Question 43 :
Let $\displaystyle f'\left ( x \right )= f\left ( x \right )$ where $\displaystyle f\left ( 0 \right )= 1.$ If $\displaystyle f\left ( x \right )+g\left ( x \right )= x^{2}$ then $\displaystyle \int_{0}^{1}f\left ( x \right )g\left ( x \right )dx$ is equal to:

Question 45 :
Find the solution of $\displaystyle \left ( x+y-1 \right )dy= \left ( x+y \right )dx.$

Question 46 :
Find the solution of $\displaystyle \frac{dy}{dx}-x\tan \left ( y-x \right )=1$

Question 47 :
The solution of the differential equation $(x+y)^2\displaystyle \frac{dy}{dx}=1$, satisfying the condition $y(1)=0$ is:

Question 50 :
At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production $P$ w.r.t. additional number of workers $x$ is given by $\frac{dP}{dx}=100-12\sqrt{x}$. If the firm employs 25 more workers, then the new level of production of items is:

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