If A and B are two square matrices such that B=A-1 BA, then (A+B)2 is equal to
0
A2 + B2
A2 + 2AB+ B2
A + B
Solution of differential equation dy/dx = (1+y2) (1+x2)-1is
y-x=c(1+xy)
y+x=c(1+xy)
y+x=c(1-xy)
y-x=c(1-xy)
The solution of 3excos2ydx+(1-ex)cot y dy=0 is
Tan y=c(ex-1)3
Tan y=c(ex+1)3
Tan y=c(ex-1)2
Cos y=c(ex-1)3
The solution of (x+y+1) dy/dx=1 is
x+y+2=c ey
x-y+2=c ey
x+y-2=c ey
x+y+2=c e2y
The solution of (x+y+1)dx+(3x+4y+4)dy=0 is
x-2y-2=c ex/(2x+4y+4)
x+2y-3=c ex/(2x+4y+4)
x-2y+2=c ex/(2x+4y+4)
x = cos θ, y = sin 5θ ==>(1-x2) (d2y/dx2) - x(dy/dx) =
-5y
5y
25y
-25y
A= sin 780- sin 180+ cos 1320, B= cos 120+ cos 840+ cos 1320+ cos 1560 and C= (sin 750+sin 150)/ (sin 750+cos 150) then by arranging in the ascending order
C,A,B
B,A,C
A,C,B
A,B,C
The solution of (1+ex/y)dx+ex/y(1-x/y)dy=0 is
yey/x+x=c
yey/x-x=c
yey/x+y=c
The solution ofn(ex+1)y dy+(y+1)dx=0 is
ex+y=c(y+1)(ex+1)
ex+y=c(y+1)(ex-1)
ex+y=c(y-1)(ex+1)
ex+y=c(y-1)(ex-1)
The solution of (12x+5y-9)dx+(5x+2y-4)dy=0 is
6x2+5xy+y2+9x+4y=c
6x2+5xy+y2-9x-4y=c
6x2-5xy-y2-9x-4y=c
3x2+5xy+2y2-9x-4y=c
The radius of the circle r2-2√2r(cos θ + sin θ)-5=0 is
3
2
5
The solution of x cos(y/x)(y dx+x dy)=y sin y/x(x dy – y dx) is
C xy cos(2y/x)=1
C xy cos(x/y)=1
C xy cos(y/x)=1
C xy cos(y/x)=2
If x is real, then the minimum value of [(x2-x+1)/(x2+x+1)], is
1/3
1/2
1
A family of curves has the differential equation (xy)dy/dx = 2y2 - x2. Then the family of curves is
y2 = cx2 + x3
y2 = x2 + cx4
y2 = cx4 + x3
y2 = x + cx4
x2+y2=t+(1/t),x4+y4=t2+(1/t2)⇒x3y(dy/dx)=
-1
t
The solution of ex-y dx+ey-x dy=0 is
e2x-e2y=c
e2x+e2y=c
ex+ey=c
ex-ey=c
If a,b,c ≠ 0 and belong to the set { 0,1,2,3,................9 then log10[(a+10b+102c)/(10-4a+10-3b+10-2c)] is equal to
4
The line 4x + 6y + 9=0, touches the parabola y2=4x at the point
(-3, 9/4)
(3, -9/4)
(9/4, -3)
(-9/4, -3)
If the equation λx2 – 5xy + 6y2 + x -3y=0, represents a pair of straight lines, then their point of intersection is
(-3, -1)
(-1, -3)
(3, -1)
(1, 3)
The solution of excot y dx+(1-ex)cosec2ydy=0 is
(ex+1)cot y=c
(ex-1)cot y=c
(2ex-1)cot y=c
(ex-2)cot y=c
The solution of y dx-x dy+log x dx=0 is
y- log x-1=cx
x+log y+1=cx
y+log x+1=cx
y+log x-1=cx
The solution of extan y dx+(1-ex)sec2ydy=0 is
Tan y=c(1+ex)
Tan y=c(1-ex)
Tan y=c(1+ex)2
Cos y=c(1-ex)
If y=(x2-1)n, then (x2-1)yn+2+2xyn+1=
(n2+1)yn
(n2-1)yn
n(n2-1)yn
n(n+1)yn
The solution of x log x (dy/dx)+y=2 log x is
y log x=(log x)2-x+c
y log x=(log x)2+c
y log x=(log y)2+c
x log y=(log x)2+c
The curve represented by X= 2( cos t + sin t ), y=( cos t - sin t ) is
a circle
a parabola
an ellipse
hyperbola
The solution of (x2y3+x2)+(y2x3+y2)dy=0 is
(x3+1)(y3+1)=c
(x3-1)(y3-1)=c
(x3-1)(y3+1)=c
(x3+1)(y3-1)=c
The solution of y2 dx+(3xy-1)dy=0 is
xy3=y2+c
xy3=y2/2+c
xy3=y2/3+c
xy3=x2/2+c
If [x3/(2x-1)(x+2)(x-3)]=A+(B/[2x-1])+(C/[x+2])+(D/[x-3]) then A is equal to
-(1/50)
-(8/25)
27/25