InstaQB

Home
Institutions
- Institutions
  
  Polytechnic Colleges
  
  Medical Colleges
  
  Arts & Science Colleges
  
  Universities
  
  Engineering Colleges
  
  Agricultural Colleges
  
  Research Institute
  
  Law Colleges
  
  Audiology and Speech Colleges
  
  Business & Management colleges
  
  Nursing colleges
  
  Hotel Management institutes
  
  Aeronautical Colleges
  
  Bachelor's Degree
Syllabus
Courses
Stateboard
- 12th Standard English Medium
  
  Maths
  
  Physics
  
  Chemistry
  
  Biology
  
  Computer Science
  
  Business Maths
  
  Economics
  
  Commerce
  
  Accountancy
  
  History
  
  Computer Applications
  
  Computer Technology
  12th Standard Tamil Medium
  
  உயிரியல்
  
  கணினி பயன்பாடுகள்
  
  கணினி அறிவியல்
  
  வணிகக் கணிதம்
  
  வணிகவியல்
  
  பொருளியல்
  
  கணிதவியல்
  
  வேதியியல்
  
  இயற்பியல்
  
  கணினி தொழில்நுட்பம்
  
  வரலாறு
  
  கணக்குப்பதிவியல்
  11th Standard English Medium
  
  Maths
  
  Commerce
  
  Economics
  
  Biology
  
  Business Maths
  
  Accountancy
  
  Computer Science
  
  Physics
  
  Chemistry
  
  Computer Applications
  
  History
  
  Computer Technology
  
  Bio - Zoology
  11th Standard Tamil Medium
  
  கணிதவியல்
  
  உயிரியல்
  
  பொருளியல்
  
  இயற்பியல்
  
  வேதியியல்
  
  வணிகக் கணிதம்
  
  கணினி அறிவியல்
  
  கணக்குப்பதிவியல்
  
  வணிகவியல்
  
  கணினி பயன்பாடுகள்
  10th Standard English Medium
  
  Mathematics
  
  Science
  
  Social Science
  
  9th Standard English Medium
  
  Mathematics
  
  Science
  
  Social Science
  
  8th Standard English Medium
  
  Mathematics
  
  Science
  
  Social Science
  7th Standard English Medium
  
  Mathematics
  
  Science
  
  Social Science
ICSE/ISC
- Class XII
  
  Mathematics
  
  Physics
  
  Accountancy
  
  Biology
  
  History
  
  Geography
  
  Psychology
  
  chemistry
  
  Economics
  
  Computer Science
  
  Political Science
  
  Business Studies
  Class XI
  
  Accountancy
  
  Chemistry
  
  Mathematics
  
  Biology
  
  Geography
  
  Physics
  
  History
CBSE
- 12Th Standard
  
  Physics
  
  Chemistry
  
  Maths
  
  Biology
  
  History
  
  Economics
  
  Commerce
  
  Geography
  
  Socialogy
  
  Business Studies
  
  Computer Science
  
  Biotechnology Class
  
  Political Science
  
  Home Science
  11Th Standard
  
  Physics
  
  Chemistry
  
  Maths
  
  Biology
  
  History
  
  Economics
  
  Commerce
  
  Socialogy
  
  Business Studies
  
  Geography
  
  Home Science
  
  Computer Science
  
  Biotechnology Class
  
  Political Science
  10Th Standard
  
  Physics
  
  Chemistry
  
  Biology
  
  Mathematics
  
  Economics
  
  Geography
  
  History & Civics
  
  Computer Application
  9Th Standard
  
  Physics
  
  Chemistry
  
  Biology
  
  mathematics
  
  Computer Application
  
  Economics
  
  Geography
  
  History & Civics

12th Maths Weekly Test - 4 (Ordinary Differential Equations)

St. Britto Hr. Sec. School - Madurai

12th Maths Weekly Test - 4 (Ordinary Differential Equations)-Aug 2020

Time : 1.00 Hours

Part - A

Multiple Choice Question - Answer All Question

The order and degree of the differential equation\(\left[(\frac{d^2y}{dx^2})+(\frac{dy}{dx})\right]^\frac{1}{2}=\frac{d^3y}{dx^3 }\) are

1,2
2,1
3,2
2,3

The solution of sec²x tan y dx+sec²y tan x dy=0 is

tan x+tan y =c
sec x+sec y=c
tan x tan y=c
sec x-sec y =c

The solution of (x² -ay)dx=(ax-y² )dy is

y=x² +y² -a(x+y)
x² - y² + x - ay = 0
x³ +y² =3ayx+c
(x² -ay)(ax-y² )=0

The I.F. of cosec x\(\frac{dy}{dx}\) ysec² x=0 is

e^{sec x}
e^{tan x}
e^{sec x tan x}
e^sec2 x

The general solution of 4 \(\frac{d^2y}{dx^2}\)+y=0 is

y = e^{\(\frac{\pi}{2}\)} [A cos \(\frac{x}{2}\)+B sin \(\frac{x}{2}\)]
y = e^{\(\frac{\pi}{2}\)} [A cos \(\frac{x}{2}\)-B sin \(\frac{x}{2}\)]
y = Acos \(\frac{x}{2}\)+Bsin\(\frac{x}{2}\)
t = Ae^{\(\frac{x}{2}\)}+Be^{\(\frac{-\pi}{2}\)}

The I.F of y log y\(\frac{dx}{dy}\)+ x - log y = 0 is

log(log y)
log y
\(\frac{1}{log y}\)
\(\frac{1}{log (log\space y)}\)

The order and degree of y'+(y")² =(x+y")² are _________.

1,1
1.2
2,1
2,2

The differential equation corresponding to xy=c² where c is an arbitrary constant is ________.

xy"+x=0
y"=0
xy'+y=0
xy"-x=0

The population p of a certain bacteria decreases at a rate proportional to the population p. The differential equation corresponding to the above statement is __________.

\(\frac{dp}{dt}=\frac{k}{p}\)
\(\frac{dp}{dt}=kt\)
\(\frac{dp}{dt}=kp\)
\(\frac{dp}{dt}=-kp\)

The solution of log \(\left(\frac{dy}{dx}\right)\)=ax+by is______.

\(\frac{e^{ax}}{a}+\frac{e^{-by}}{b}+c = 0\)
ae^ax -be^-by +c=0
ae^x +be^y =k
be^ax +ae^-by =k

The general solution of x \(\frac{dy}{dx}\)=y is _________.

y=cx
x²+y²=c
x²-y²=c
y=c^x

The differential equation of x² y = k is _________.

\(x^2\frac{dy}{dx}=0\)
\(x^2\frac{dy}{dx}+y=0\)
\(x\frac{dy}{dx}+2y=0\)
\(y\frac{dy}{dx}+2x=0\)

The I.F. of (1+y²)dx=(tan^-1 y-x)dy is ________.

e^tan-1 y
e^tan-1 x
tan^-1 y
tan^-1 x

The order and degree of the differential equation \(\frac{d^2y}{dx^2}+\left(\frac{dy}{dx}\right)^{1/3}+ x^{\frac{1}{4}}\) = 0 are respectively

2,3
3,3
2,6
2,4

The differential equation representing the family of curves y = Acos(x + B), where A and B are parameters, is

\(\frac{d^2y}{dx^2}-y=0\)
\(\frac{d^2y}{dx^2}+y=0\)
\(\frac{d^2y}{dx^2}=0\)
\(\frac{d^2x}{dy^2}=0\)

The order and degree of the differential equation \(\sqrt{sin\ x}\)(dx + dy) = \(\sqrt{cos\ x}\)(dx − dy)

1,2
2,2
1,1
2,1

The differential equation of the family of curves y = Ae^x + Be^-x , where A and B are arbitrary constants is

\(\frac{d^2y}{dx^2}+y=0\)
\(\frac{d^2y}{dx^2}-y=0\)
\(\frac{dy}{dx}+y=0\)
\(\frac{dy}{dx}-y=0\)

The general solution of the differential equation\(\frac{dy}{dx}=\frac{y}{x}\) is

xy = k
y = k log x
y = kx
log y = kx

The solution of \(\frac{dy}{dx}\)+ p(x)y=0 is

y = ce ^{∫ pdx}
y = ce ^{− ∫ pdx}
x = ce ^{− ∫ pdy}
x = ce ^{∫ pdy}

The integrating factor of the differential equation \(\frac{dy}{dx}+y=\frac{1+y}{λ}\) is

\(\frac{x}{e^λ}\)
\(\frac{e^λ}{x}\)
λe^x
e^x

The degree of the differential equation y y(x) = 1 + \(\frac{dy}{dx}+\frac{1}{1.2}\left(\frac{dy}{dx}\right)^2+\frac{1}{1.2.3}\left(\frac{dy}{dx}\right)^3\) + . . . . is

2
3
1
4

If p and q are the order and degree of the differential equation y =\(\frac{dy}{dx}+x^3\left(\frac{d^2y}{dx^2}\right)+xy=cosx,\)when

p < q
p = q
p > q
p exists and q does not exist

The solution of the differential equation \(\frac{dy}{dx}=2xy\) is

\(y=Ce^{x^2}\)
y= 2x² +C
\(y=Ce^{-x^2}\) + C
y = x² +C

The general solution of the differential equation log \(\left(\frac{dy}{dx}\right)\) = x + y is

e^x+e^y =C
e^x+e^-y =C
e^-x+e^y =C
e^-x+e^-y =C

The solution of the differential equation \(\frac{dy}{dx}=\frac{y}{x}+\frac{ϕ\left(\frac{y}{x}\right)}{ϕ'\left(\frac{y}{x}\right)}\) is

\(xϕ\left(\frac{y}{x}\right)=k\)
\(ϕ\left(\frac{y}{x}\right)=kx\)
\(yϕ\left(\frac{y}{x}\right)=k\)
\(ϕ\left(\frac{y}{x}\right)=ky\)

If sin x is the integrating factor of the linear differential equation \(\frac{dy}{dx}\) + Py = Q, Then P is

log sin x
cos x
tan x
cot x

The number of arbitrary constants in the particular solution of a differential equation of third order is

3
2
1
0

Integrating factor of the differential equation \(\frac{dy}{dx}=\frac{x+y+1}{x+1}\) is

\(\frac{1}{x+1}\)
x+1
\(\frac{1}{\sqrt{x+1}}\)
\({\sqrt{x+1}}\)

P is the amount of certain substance left in after time t. If the rate of evaporation of the substance is proportional to the amount remaining, then

P=Ce^kt
P=Ce^-kt
P=Ckt
Pt=C

If the solution of the differential equation \(\frac{dy}{dx}=\frac{ax+3}{2y+f}\) represents a circle, then the value of a is

2
-2
1
-1

Comment

Add Comment

Tamilnadu Stateboardszs - Class