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

Var (2x ± 5) is =________

If \(f(x)=\frac { 1 }{ 2 } \) ,\(E\left( { x }^{ 2 } \right) =\frac { 1 }{ 4 } \) then var(x) is _____________

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

The solution of sec²x tan y dx + sec²y tan x dy = 0 is _________

In (N, *), x * y = max(x, y), x, y \(\in \) N then 7 * (-7)

If * is defined by a * b = a² + b² + ab + 1, then (2 * 3) * 2 is _____________

The volume generated by the curve y² = 16x from x = 2 to x = 3 rotating about x - axis ......... cu. units

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

The area enclosed by the curve y² = 4x, the x-axis and its latus rectum is ________ sq.units.

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

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

lf u = (x-y)⁴+(y-z)⁴ +(z-x)⁴ then \(\sum { \frac { \partial u }{ \partial x } } \) = _____________

If u = log \(\sqrt { { x }^{ 2 }+{ y }^{ 2 } } \), then \(\frac { { \partial }^{ 2 }u }{ \partial { x }^{ 2 } } +\frac { { \partial }^{ 2 }u }{ { \partial y }^{ 2 } } \) is _____________

In LMV theorem, we have f'(x₁) = \(\frac { f(b)-f(a) }{ b-a } \) then a < x₁ _________

The critical points of the function f(x) = \((x-2)^{ \frac { 2 }{ 3 } }(2x+1)\) are __________

If x = cos θ + i sin θ, then xⁿ + \(\frac { 1 }{ { x }^{ n } } \) is ______

If a = cos α + i sin α, b = -cos β + i sin β then \(\left( ab-\frac { 1 }{ ab } \right) \) is _________

The points represented by 3 - 3i, 4 - 2i, 3 - i and 2 - 2i form _____ in the argand plane.

If zⁿ = \(cos\frac { n\pi }{ 3 } +isin\frac { n\pi }{ 3 } \), then z₁, z₂ ..... z₆ is _________

The value of (1+i)⁴ + (1-i)⁴ is __________

The least positive integer n such that \(\left( \frac { 2i }{ 1+i } \right) ^{ n }\) is a positive integer is ____________

If z = cos\(\frac { \pi }{ 4 } \) + i sin\(\frac { \pi }{ 6 } \), then ______

If \(\overset { \rightarrow }{ a } ,\overset { \rightarrow }{ b } ,\overset { \rightarrow }{ c } \) are three non - coplanar vectors, then \(\frac { \overset { \rightarrow }{ a } .\overset { \rightarrow }{ b } \times \overset { \rightarrow }{ c } }{ \overset { \rightarrow }{ c } \times \overset { \rightarrow }{ a } .\overset { \rightarrow }{ b } } +\frac { \overset { \rightarrow }{ b } .\overset { \rightarrow }{ a } \times \overset { \rightarrow }{ c } }{ \overset { \rightarrow }{ c } .\overset { \rightarrow }{ a } \times \overset { \rightarrow }{ b } } \) = _____________

The length of major and minor axes of 4x² + 3y² = 12 are ____________

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 __________

If the vectors \(a\overset { \wedge }{ i } +\overset { \wedge }{ j } +\overset { \wedge }{ k } \), \(\overset { \wedge }{ i } +b\overset { \wedge }{ j } +\overset { \wedge }{ k } \) and \(\overset { \wedge }{ i } +\overset { \wedge }{ j } +c\overset { \wedge }{ k } \) (a ≠ b ≠ c ≠ 1) are coplaner, then \(\frac { 1 }{ 1-a } +\frac { 1 }{ 1-b } +\frac { 1 }{ 1-c } =\) _____________

If \(\lambda \overset { \wedge }{ i } +2\lambda \overset { \wedge }{ j } +2\lambda \overset { \wedge }{ k } \) is a unit vector, then the value of λ is _____________

The two planes 3x + 3y - 3z - 1 = 0 and x + y - z + 5 = 0 are _____________

If \(\overset { \rightarrow }{ a } =\left| \overset { \rightarrow }{ a } \right| \overset { \rightarrow }{ e } \) then \(\overset { \rightarrow }{ e } .\overset { \rightarrow }{ e } \) is _____________

The area of the parallelogram having diagonals \(\overset { \rightarrow }{ a } =3\overset { \wedge }{ i } +\overset { \wedge }{ j } -2\overset { \wedge }{ k } \) and \(\overset { \rightarrow }{ b } =\overset { \wedge }{ i } -3\overset { \wedge }{ j } +\overset { \wedge }{ 4k } \) 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 __________

If e₁, e₂ are eccentricities of the ellipse \(\frac { { x }^{ 2 } }{ { a }^{ 2 } } +\frac { { y }^{ 2 } }{ { b }^{ 2 } } \) = 1 and the hyperbola \(\frac { { x }^{ 2 } }{ { a }^{ 2 } } +\frac { { y }^{ 2 } }{ { b }^{ 2 } } \) = 1 then 

If (1, -3) is the centre of the circle x² + y² + ax + by + 9 = 0 its radius is _________

The length of the diameter of a circle with centre (1, 2) and passing through (5, 5) is ____________

The director circle of the ellipse \(\frac { { x }^{ 2 } }{ 9 } -\frac { { y }^{ 2 } }{ 5 } =1\) is ____________

If x > 1, then \(2{ tan }^{ -1 }x+{ sin }^{ -1 }\left( \frac { 2x }{ 1+{ x }^{ 2 } } \right) \) ________

The equation 7x²- 6\(\sqrt { 3 } \) xy + 13y² - 4\(\sqrt { 3 } \) x - 4y - 12 = 0 represents ____________

If the distance between the foci is 2 and the distance between the direction is 5, then the equation of the ellipse is __________

The equation of the directrix of the parabola y²+ 4y + 4x + 2 = 0 is ___________

\(cot\left( \frac { \pi }{ 4 } -{ cot }^{ -1 }3 \right) \)

If \(4{ cos }^{ -1 }x+{ sin }^{ -1 }x=\pi \) then x is _____________

\(sin\left\{ 2{ cos }^{ -1 }\left( \frac { -3 }{ 5 } \right) \right\} =\) __________

The value of \({ cos }^{ -1 }\left( \cos\cfrac { 5\pi }{ 3 } \right) +sin^{ -1 }\left( \sin\cfrac{5\pi }{ 3 } \right) \) is ______________ 

If \(\rho\) (A) ≠ \(\rho\) ([AIB]), then the system is _____________

If ax² + bx + c = 0, a, b, c \(\in\) R has no real zeros, and if a + b + c < 0, then __________

If \(\rho\) (A) = r then which of the following is correct?

If \(\rho\) (A) = \(\rho\) ([A/B]) = number of unknowns, then the system is _________--

If the equation ax²+ bx+c = 0(a > 0) has two roots ∝ and β such that ∝ <- 2 and β > 2, then __________

The system of linear equations x + y + z = 2, 2x + y - z = 3, 3x + 2y + kz = has a unique solution if __________