Mathematics Tes...

Let y = y(x) be the solution of the differential equation

0 < x < 2.1, with y(2) = 0. Then the value of dy/dx at x = 1 is equal to :

The area bounded by the curve 4y² = x²(4 – x)(x – 2) is equal to :

Let y = y(x) be the solution of the differential equation

cosx (3sinx + cosx + 3)dy =
                (1 + y sinx (3sinx + cosx + 3))dx,

A function f, defined for all x, y ∈ R is such that f(1) = 2 ; f(2) = 8 and f(x + y) – kxy = f(x) + 2y² ; Where k is some constant ; then value of f(x) and k are :

(where [.] denotes greatest integer function)

If p : 5 is not greater than 2 and

   q : Jaipur is capital of Rajasthan, 

are two statements. Then negation of statement p ⇒ q is the statement

The set of values of 'λ' for which equation sin⁴x + cos⁴x = λ has a solution, is :-

Let 2p + 3q + 4r = 15 and if the expression p³q⁵r⁷ takes the maximum value, then p : q : r is equal to (where p, q, r ∈ R⁺) -