The differential equation which represents the family of curves y=c1ec2xe, where c1 and c2 are arbitrary constants, is
y' =y2
y″ = y′ y
yy″ = y′
yy″ = y′
D.
yy″ = y′
y c1ec2x = …..(i)
y' = c1c2ec2x
y' = c2y.....(from (i) ....(ii)
y" = c2y' ....... (iii)
from (ii) & (iii)
Let f(x) = , then the value of is
0
does not exist
B.
does not exist
But is not defined on left hand side of - 3.
Hence, function is not defined.
The equation of the tangent to the curve y = x +4/x2, that is parallel to the x-axis, is
y= 0
y= 1
y= 2
y= 2
D.
y= 2
We have,
On differentiating w.r.t x, we get
since the tangent is parallel to X- axis, therefore
dy/dx = 0
⇒ x3 = 8
⇒ x = 2 abd y =3
If g(x) is a polynomial satisfying g(x) g(y) = g(x) + g(y) + g(xy) - 2 for all real x and y and g(2) = 5, then g(x) is
9
10
25
20
B.
10
Since, g(x) g(y) = g(x) + g(y) + g(xy) - 2
Now, at x = 0, y = 2, we get
g(0) g(2) = g(0) + g(2) + g(0) - 2
g(x) is given in a polynomial and by the relation given g(x) cannot be linear.
Let g(x) = x2 + k