Find the equations of the tangent and normal to the curve x = a sin³θ, y = b cos³θ at
Find the equation of tangent and normal to the curve x = 1 – cos θ, y = θ – sin θ at θ =
Find the equations of the normal to the curve x² = 4y which passes through the point (1, 2).
Find the equation of tangent to the curve 4x² + 9y² = 36 at the point (3 cos θ, 2 sin ).
Find the equations of the tangent and the normal, to the curve 16x² + 9y² = 145 at the point where x₁ = 2 and y₁ > 0.
P speaks truth in 70% of the cases and Q in 80% of the cases. In what percent of cases are they likely to agree
in stating the same fact ?
Assume that each born child is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls ? Given that :
(i) the youngest is a girl.
(ii) atleast one is a girl.
Show that the relation S in the set R of real numbers defined as S = {(a, b) : a, b ∈ R and a ≤ b³} is neither reflexive nor symmetric nor transitive.
Let f : N → N be defined as
for all n ∈ N. State whether the function f is
bijective. Justify your answer.
Find the general solution of the differential equation (1 + tan y)(dx – dy) + 2xdy = 0.