If F(x) is a distribution function of a random variable then the false statement is ____________

The sum of the mean and variance of a binomial distribution for 6 total is 2.16. Then the probability of success p =__________

A die is tossed 5 times. Getting an odd number is considered a success. Then the variance of distribution of number of success is _____________

In a binomial distribution,\(n=4,P(X=0)=\frac { 16 }{ 81 } \),then \(P(X=4)\) _____________

In a binomial distribution, if the mean is 8 and the variance is 6, then the number of trials is _____________

The random variable X has variance 4 and E(x²), then the mean of x is _____________

If F(x) is the probability distribution function then \(F\left( -\infty \right) \) is is _____________

The general solution of \(4\frac{d^2 y}{dx^2}\) + y = 0 is _________

The solution of \(\frac{dy}{dx}+y\) cot x = sin 2x is ___________

The number of commutative binary operations which can be defined on a set containing n elements is _________

A binary operation * is defined on the set of positive rational numbers Q⁺ by a*b = \(\frac { ab }{ 4 } \). Then 3 * \(\left( \frac { 1 }{ 5 } *\frac { 1 }{ 2 } \right) \) is _____________

Define * on Z by a * b = a + b + 1 ∀ a,b \(\in \) Z. Then the identity element of z is ________

The identity element in the group {R - {1},x} where a * b = a + b - ab is __________

The area of the ellipse \(\frac { { x }^{ 2 } }{ 9 } +\frac { { y }^{ 2 } }{ 4 } =1\) __________

The area bounded by the parabola y = x² and the line y = 2x is __________

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

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

The function -3x+12 is ________ function on R.

If the curves y = 2e^x and y = ae^-x intersect orthogonally, then a = _________

If B, B¹ are the ends of minor axis, F₁, F₂ are foci of the ellipse \(\frac { { x }^{ 2 } }{ 8 } +\frac { { y }^{ 2 } }{ 4 } \) = 1 then area of F₁BF₂B¹ is __________

The value of \({ \left| \overset { \rightarrow }{ a } +\overset { \rightarrow }{ b } \right| }^{ 2 }+{ \left| \overset { \rightarrow }{ a } -\overset { \rightarrow }{ b } \right| }^{ 2 }\) is _____________

The number of vectors of unit length perpendicular to the vectors \(\left( \overset { \wedge }{ i } +\overset { \wedge }{ j } \right) \) and \(\left( \overset { \wedge }{ j } +\overset { \wedge }{ k } \right) \)is __________

Let \(\overset { \rightarrow }{ a } \), \(\overset { \rightarrow }{ b } \)and \(\overset { \rightarrow }{ c } \)be three non- coplanar vectors and let  \(\overset { \rightarrow }{ p } ,\overset { \rightarrow }{ q } ,\overset { \rightarrow }{ r } \) be the vectors defined by the relations \(\overset { \rightarrow }{ P } =\frac { \overset { \rightarrow }{ b } \times \overset { \rightarrow }{ c } }{ \left[ \overset { \rightarrow }{ a } \overset { \rightarrow }{ b } \overset { \rightarrow }{ c } \right] } ,\overset { \rightarrow }{ q } =\frac { \overset { \rightarrow }{ c } \times \overset { \rightarrow }{ a } }{ \left[ \overset { \rightarrow }{ a } \overset { \rightarrow }{ b } \overset { \rightarrow }{ c } \right] } ,\overset { \rightarrow }{ r } =\frac { \overset { \rightarrow }{ a } \times \overset { \rightarrow }{ b } }{ \left[ \overset { \rightarrow }{ a } \overset { \rightarrow }{ b } \overset { \rightarrow }{ c } \right] } \) Then the value of \(\left( \overset { \rightarrow }{ a } +\overset { \rightarrow }{ b } \right) .\overset { \rightarrow }{ p } +\left( \overset { \rightarrow }{ b } +\overset { \rightarrow }{ c } \right) .\overset { \rightarrow }{ q } +\left( \overset { \rightarrow }{ c } +\overset { \rightarrow }{ a } \right) .\overset { \rightarrow }{ r } \)= ____________

The distance between the foci of a hyperbola is 16 and e = \(\sqrt { 2 } \). Its equation is ____________

If x < 0, y < 0 such that xy = 1, then tan^-1(x) + tan^-1(y) =_____