` - ((d^2 y)/(dx^2))^(-1) ((dy)/(dx))^(-3)`
`((d^2 y)/(dx^2))^(-1) ((dy)/(dx))^(-2)`
`- ((d^2 y)/(dx^2)) ((dy)/(dx))^(-3)`
`((d^2 y)/(dx^2))^(-1)`
`3`
`2`
`1`
`0`
`1,2`
`2,1`
`1,4`
`4,1`
`(x^2 -2y^2) p^2-4pxy-x^2=0`
`(x^2-2y^2)p^2 + 4 pxy -x^2=0`
`(x^2+ 2y^2) p^2 - 4pxy-x^2=0`
`(x^2+ 2y^2) p^2 - 4 pxy+ x^2=0`
`x=y^2 + cy`
`x= 2cy^2`
`x= 2y^2 + cy`
None of the above
`y=xe^a + c`
`x=ye^a + c`
`y=lnx+c`
`x=lny+c`
`1, 2`
`2, 2`
`1, 3`
`1, 4`
`xy =C`
`y =Cx`
`x+y = C`
`x- y =C`
`y =xsin^(-1) a+ C`
`x =y sin^(-1) a+ C`
`y = x + xsin^(-1) a+ C`
`y = sin^(-1) a+ C`
`xy = x^4 + C`
`xy = y^4 + C`
`4xy = y^4 + C`
`3xy = y^3 + C`
`2`
`3`
`4`
`5`
`sin^(-1) y = sin^(-1) x + C`
`2sin^(-1) y = sqrt(1- x^2) + sin^(-1) x + C`
`2sin^(-1) y = xsqrt(1- x^2) + sin^(-1) x + C`
`2sin^(-1) y = x sqrt(1- x^2) + cos^(-1) x + C`
`2xy (dy)/(dx) = x^2 - y^2`
`2xy (dy)/(dx)= y^2 - x^2`
` 2xy (dy)/(dx) = x^2 + y^2`
` 2xy (dy)/(dx) = x^2 + y^2 = 0`
`1,1`
`2, 1`
`1, 2`
`2, 2`
Only I
Only II
Both I and II
Neither I nor II
`x = Cy`
`y^2 = Cx`
`x + xy -Cy =0`
None of these
`-1`
`1`
`2`
None of these
`1`
`-1`
`2`
None of these
`-1`
`1`
`-2`
None of these
` y = (x |x|)/2 + C`
` y = ( |x|)/2 + C`
` y = x^2/2 + C`
` y = x^3/2 + C`
` y = (1-e^(-2x))/2`
` y = (1+e^(-2x))/2`
`y = 1 + e^x`
`y = (1 + e^x)/2`
`0`
`1`
`2`
`3`
`y = cos x`
`y = sin x`
`y = sec x`
`y = cosec x`
Only 1
Only 2
Both 1 and 2
Neither 1 nor 2
`1`
`2`
`3`
`4`
`y + e^x = C`
`y - e^(-x) = C`
`y + e^(-x) = C`
`y - e^(x) = C`
` x [ 1 + ( (dy) /(dx))^2 ] = (d^2y)/(dx^2)`
`2x ((dy) /(dx)) (d^2y)/(dx^2) = 1+ ((dy) /(dx)) ^2`
`((dy) /(dx)) (d^2y)/(dx^2) = 1`
` ( (dy) /(dx))^2 + 1 = (d^2y)/(dx^2)`
`1`
`2`
`3`
Undefined
Only I
Only II
Both I and II
Neither I nor II
`(dy)/(dx) = y/x`
`(dy)/(dx) = x/y`
`(dy)/(dx) = -x/y`
None of these
`5`
`4`
`3`
`2`
`xy = C`
`x = Cy`
`x + y = C`
`x^2 + y^2 = C`
`y=e^(-x) + C`
`y=-e^(-x) + C`
`y = e^(x) + C`
`y = -e^(x) + C`
`(d^2y)/(dx^2)+y(dy)/(dx)+x = 0`
`(d^2y)/(dx^2)+y = 0`
`(d^2y)/(dx^2)-y = 0`
`(d^2y)/(dx^2)+x = 0`
`1, 1`
`1,2`
`2, 1`
`2, 1`
`6`
`3`
`2`
`1`
`(3, 2)`
`(2, 3/2)`
`(2, 4)`
`(2,2)`
`(d^2y)/(dx^2)+lamda^2y = 0`
`(d^2y)/(dx^2)-lamda^2y = 0`
`(d^2y)/(dx^2)+lamda^2y = 0`
None of these
a set of straight lines
a set of ellipses
a set of circles
None of these
`y =x- 1`
`4y =x^2`
`y = x`
`y =-x - 1`
`x + y = C`
`xy = C`
`C (x + y) = xy`
None of these
`sin y = C (1 -e^x)`
`cos y = C(1-e^x)`
`cot y = C (1 -e^x)`
None of these
`(d^2y)/(dx^2)+4y = 0`
`x(dy)/(dx)+y = x^3`
`(x-y)^2(dy)/(dx) = 9`
`cos^2x (dy)/(dy)+y = tanx`
`xy = C`
`x = Cy`
`y =Cx`
None of these
`1`
`2`
`-1`
Does not exist
`cosx cosy = sqrt3/2`
`sinx sin y = sqrt3/2`
`sinx sin y = 1/2`
`cosx cos y = 1/2`
`3`
`2`
`2/3`
Not defined
`sin^(-1)y+sin^(-1)x = C`
`sin^(-1)y-sin^(-1)x = C`
`2sin^(-1)y+sin^(-1)x = C`
`2sin^(-1)y-sin^(-1)x = C`
`(d^3y)/(dx^3) = 0`
`(d^2x)/(dy^2) = C`
`(d^3x)/(dy^3) = 1`
`(d^3y)/(dx^3) = C`
`2`
`1`
`-2`
`-1`
A set of circles having .centre on the Y-axis
A set of circles hav•ng centre on the X-axis
A set of ellipses
A pair of straight lines
`1`
`2`
`4`
`8`
`y^2 = In [C^2(e^x + 1)^2 ]`
`dy= In [C(e^x + 1)]`
`y^2 = In [C(e^x + 1)]`
None of the above
`(x^2-y^2)(dy)/(dx) = 2xy`
`(x^2+y^2)(dy)/(dx) = 2xy`
`(dy)/(dx) = (x^2+y^2)`
`xdx+ydy = 0`
Family of straight lines through the origin
Family of circles with their centres at the origin
Family of parabolas with their vertices at the origin
Family of straight lines having slope 1 and not passing through the origin
`y = 2-xy'`
`X = 2yy'`
`xy = y'`
`X = yy'`
`(1 + e^x)tan y = c`
`(1 + e^x)^3 tan y = c`
`(1 + e^x)^2 tan y = c`
`(1 + e^x) sec^2 y = c`
`yy'- 2xyy' + y^2 = 0`
`yy'(yy'+2x)+y^2 = 0`
`yy'(yy'-2x)+y^2 = 0`
`yy'-2xyy'+y = 0`
Cirle
Straight line
Parabola
Ellipse
`y - C = sin (x + y)`
`x - C =sin (x + y)`
`y- C = tan (x + y)`
None of these
`3 ,2`
`4, 3`
`4 ,2`
`3 ,3`
`yx^2+2x = 2Cy`
`y^2x+2y = 2Cx`
`y^2x^2+2x = 2Cy`
None of these
Rectangular hyperbola
Strai!Jlt line passing through origin
Parabola whose vertex is at origin
Circle whose centre is at origin
`-1`
`0`
`1`
`2`
`x =log t`
`x = Ce^t`
`e^x = t`
`x = sqrt t`
`y (1-x) = x^2`
`y^2(1+x^2) = x^4`
`y^2 = (x+1)^2`
`y = x^2`
`y = x^2/2+x+C`
`log(y+1) = x^2/2+x+C`
`y = x^2+x+C`
`log(y+1) = x^2+x+C`
`2 ,1`
`2 , 5`
`2 , 5/6`
`1 , 1/3`
`(dQ)/(dt) =-Q`
`(dQ)/(dt) = -KQ , K < 0`
`(dQ)/(dt) = -KQ , K > 0`
`(dQ)/(dt) = Q`
`2 log (x + y) = C(y- x)`
`(y- x) + log (x + y) = C``
`(y/x)+[log(y/x)] = C`
None of these
`y = -1+e^(t^2//2)`
`y = 1+e^(t^2//2)`
`y = -t`
`y = t`
`x^2(d^2y)/(dx^2)-2x(dy)/(dx)+2y = 0`
`x^2(d^2y)/(dx^2)-y((dy)/(dx))^2+2 = 0`
`(1-x^2)(d^2y)/(dx^2)-(y(dy)/(dx))^2 = 0`
None of these
`4`
`3`
`2`
`1`
`y = xcosx`
`ycosx = x`
`xy = cosx`
`ysinx = x`
`y + tan (x + y) = C`
`y-tan{(x+y)/2} = C`
`y+tan{(x+y)/2} = C`
`y +tan{(x-y)/2} =C`
`-5`
`0`
`0.01`
`(10)^(-1)`
`1`
`2`
`3`
`4`