If [x3/(2x-1)(x+2)(x-3)]=A+(B/[2x-1])+(C/[x+2])+(D/[x-3]) then A is equal to
A. 1/2
B. -(1/50)
C. -(8/25)
D. 27/25
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
A. 1
B. 2
C. 3
D. 4
The solution of x log x (dy/dx)+y=2 log x is
A. y log x=(log x)2-x+c
B. y log x=(log x)2+c
C. y log x=(log y)2+c
D. x log y=(log x)2+c
The solution of (x2y3+x2)+(y2x3+y2)dy=0 is
A. (x3+1)(y3+1)=c
B. (x3-1)(y3-1)=c
C. (x3-1)(y3+1)=c
D. (x3+1)(y3-1)=c
The solution of y2 dx+(3xy-1)dy=0 is
A. xy3=y2+c
B. xy3=y2/2+c
C. xy3=y2/3+c
D. xy3=x2/2+c
The solution of excot y dx+(1-ex)cosec2ydy=0 is
A. (ex+1)cot y=c
B. (ex-1)cot y=c
C. (2ex-1)cot y=c
D. (ex-2)cot y=c
The solution of (x+y+1) dy/dx=1 is
A. x+y+2=c ey
B. x-y+2=c ey
C. x+y-2=c ey
D. x+y+2=c e2y
The solution of x cos(y/x)(y dx+x dy)=y sin y/x(x dy – y dx) is
A. C xy cos(2y/x)=1
B. C xy cos(x/y)=1
C. C xy cos(y/x)=1
D. C xy cos(y/x)=2
A family of curves has the differential equation (xy)dy/dx = 2y2 - x2. Then the family of curves is
A. y2 = cx2 + x3
B. y2 = x2 + cx4
C. y2 = cx4 + x3
D. y2 = x + cx4
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
A. C,A,B
B. B,A,C
C. A,C,B
D. A,B,C
The solution of extan y dx+(1-ex)sec2ydy=0 is
A. Tan y=c(1+ex)
B. Tan y=c(1-ex)
C. Tan y=c(1+ex)2
D. Cos y=c(1-ex)
If the equation λx2 – 5xy + 6y2 + x -3y=0, represents a pair of straight lines, then their point of intersection is
A. (-3, -1)
B. (-1, -3)
C. (3, -1)
D. (1, 3)
If A and B are two square matrices such that B=A-1 BA, then (A+B)2 is equal to
A. 0
B. A2 + B2
C. A2 + 2AB+ B2
D. A + B
The solution of y dx-x dy+log x dx=0 is
A. y- log x-1=cx
B. x+log y+1=cx
C. y+log x+1=cx
D. y+log x-1=cx
The solution of (12x+5y-9)dx+(5x+2y-4)dy=0 is
A. 6x2+5xy+y2+9x+4y=c
B. 6x2+5xy+y2-9x-4y=c
C. 6x2-5xy-y2-9x-4y=c
D. 3x2+5xy+2y2-9x-4y=c
The solution of (x+y+1)dx+(3x+4y+4)dy=0 is
A. x-2y-2=c ex/(2x+4y+4)
B. x+2y-3=c ex/(2x+4y+4)
C. x-2y-2=c ex/(2x+4y+4)
D. x-2y+2=c ex/(2x+4y+4)
Solution of differential equation dy/dx = (1+y2) (1+x2)-1is
A. y-x=c(1+xy)
B. y+x=c(1+xy)
C. y+x=c(1-xy)
D. y-x=c(1-xy)
The line 4x + 6y + 9=0, touches the parabola y2=4x at the point
A. (-3, 9/4)
B. (3, -9/4)
C. (9/4, -3)
D. (-9/4, -3)
The solution of 3excos2ydx+(1-ex)cot y dy=0 is
A. Tan y=c(ex-1)3
B. Tan y=c(ex+1)3
C. Tan y=c(ex-1)2
D. Cos y=c(ex-1)3
The solution of (1+ex/y)dx+ex/y(1-x/y)dy=0 is
A. yey/x+x=c
B. yey/x-x=c
C. yey/x+y=c
D. yey/x+x=c
The solution ofn(ex+1)y dy+(y+1)dx=0 is
A. ex+y=c(y+1)(ex+1)
B. ex+y=c(y+1)(ex-1)
C. ex+y=c(y-1)(ex+1)
D. ex+y=c(y-1)(ex-1)
The curve represented by X= 2( cos t + sin t ), y=( cos t - sin t ) is
A. a circle
B. a parabola
C. an ellipse
D. hyperbola