The differential equation associated with the family of concentric circles having their centres at the origin is _________.

The general solution of x \(\frac{dy}{dx}\) = y is _________.

The differential equation corresponding to xy = c² where c is an arbitrary constant is ________.

The transformation y = vx reduces \(\\ \\ \\ \frac { dy }{ dx } =\frac { x+y }{ 3x } \) __________ 

If cosx is an integrating factor of the differential equation \(\frac{dy}{dx}+Py= Q\), then P = ___________

In (S, *), is defined by x * y = x where x, y \(\in \) S, then

Let p: Kamala is going to school
q: There are 20 students in the class. Then Kamala is not going to school or there are 20 students in the class is represented by

Which of the following is a contradiction?

\(\int _{ a }^{ b }{ f(x) } dx=\) ..............

The area enclosed by the curve y = \(\frac { { x }^{ 2 } }{ 2 } \) , the x - axis and the lines x = 1, x = 3 is __________

The value of \(\int _{ \frac { \pi }{ 2 } }^{ \frac { \pi }{ 2 } }{ \sqrt { \frac { 1-cos2x }{ 2x } } } \) dx is __________

If u = \((\frac{y}{x})\) then x \(x\frac { \partial u }{ \partial x } +y\frac { \partial u }{ \partial y } \) = .....................

The approximate value of (627)^\(\frac14\) is ................

If f(x, y, z) = sin (xy) + sin (yz) + sin (zx) then f_xx is _____________

If log_e4 = 1.3868, then log_e4.01 = _____________

The equation of the tangent to the curve y = x²-4x+2 at (4, 2) is __________

In the set Q define a⊙b = a+b+ab. For what value of y, 3⊙(y⊙5) = 7?

The value of \(\int _{ -1 }^{ 2 }{ |x|dx } \) is

If \(f(x)=\int_{0}^{x} t \cos t d t, \text { then } \frac{d f}{d x}=\)

If \(u(x, y)=e^{x^{2}+y^{2}}\),then \(\frac { \partial u }{ \partial x } \) is equal to

If X is a binomial random variable with expected value 6 and variance 2.4, then P(X = 5) is 

A pair of dice numbered 1, 2, 3, 4, 5, 6 of a six-sided die and 1, 2, 3, 4 of a four-sided die is rolled and the sum is determined. Let the random variable X denote this sum. Then the number of elements in the inverse image of 7 is

The integrating factor of the differential equation \(\frac { dy }{ dx } +y=\frac { 1+y }{ \lambda } \) is

What is the value of the limit \(\lim _{x \rightarrow 0}\left(\cot x-\frac{1}{x}\right) \text { is }\) 

The abscissa of the point on the curve \(f\left( x \right) =\sqrt { 8-2x } \) at which the slope of the tangent is -0.25 ?