A random variable X has the following probapality mass function?
X -2 3 1 P(X = x) \(\frac { \lambda }{ 6 } \) \(\frac { \lambda }{ 4 } \) \(\frac { \lambda }{ 12 } \) Then __________ 

A die is thrown 10 times. Getting a number greater than 3 is considered a success. The S.D of the number of successes is _________

If the mean and variance of a binomial variate are 2 and 1 respectively, the probability that X takes a value greater than one is equal to__________.

Var (2x ± 5) is =________

If \(f(x)={ Cx }^{ 2 }={ cx }^{ 2 },0 is the p.d.f, of x then c is _____________

Using y = vx, the differential equation \(\frac { dy }{ dx } =\frac { y }{ x+\sqrt { xy } } \) is reduced to ________.

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

The I.F of \(\frac{dy}{dx}-y\) tan x = cos x is _________

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

If a * b = a²b² - ab then 3 * (1 * 1)

\(\int _{ -\frac { \pi }{ 2 } }^{ \frac { \pi }{ 2 } }{ \frac { sinx }{ 2+cosx } dx= } \) __________

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

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

If is a homogeneous function of x and y of degree n, then \(x\frac { { \partial }^{ 2 }u }{ \partial { x }^{ 2 } } +y\frac { { \partial }^{ 2 }u }{ \partial x\partial y } \) = ...... \(\frac { { \partial }u }{ \partial { x } } \)

The cube root of 127 is ............

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

The function f(x) = x⁹ + 3x⁷+ 64 is increasing on ________

The least value of a when f f(x) = x² + ax + 1 is increasing on (1, 2) is __________

If x_r = \(cos\left( \frac { \pi }{ 2^{ r } } \right) +isin\left( \frac { \pi }{ 2^{ r } } \right) \) then x₁, x_2, x₃ ... x_∞ is _________

\(\frac { (cos\theta +isin\theta )^{ 6 } }{ (cos\theta -isin\theta )^{ 5 } } \) = ________

(1+i)³ = ______

The complex number z which satisfies the condition \(\left| \frac { 1+z }{ 1-z } \right| \) = 1 lies on _________

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

If \(\overset { \rightarrow }{ a } ,\overset { \rightarrow }{ b } ,\overset { \rightarrow }{ c } \) are mutually 丄^r unit vectors, then \(\left| \overset { \rightarrow }{ a } +\overset { \rightarrow }{ b } +\overset { \rightarrow }{ c } \right| \) is _______________ 

The distance from the origin to the plane \(\overset { \rightarrow }{ r } .\left( \overset { \wedge }{ 2i } -\overset { \wedge }{ j } +5\overset { \wedge }{ k } \right) =7\) is ______________ 

Th point of curve y = 2x² - 6x - 4 at which the targent is parallel to x - axis is __________

The point of contact of y² = 4ax and the tangent y = mx + c is _________

For any three vectors \(\overset { \rightarrow }{ a } ,\overset { \rightarrow }{ b } \) and \(\overset { \rightarrow }{ c } \), \(\left( \overset { \rightarrow }{ a } +\overset { \rightarrow }{ b } \right) .\left( \overset { \rightarrow }{ b } +\overset { \rightarrow }{ c } \right) \times \left( \overset { \rightarrow }{ c } +\overset { \rightarrow }{ a } \right) \) is _____________

If the work done by a force \(\overset { \rightarrow }{ F } =\overset { \wedge }{ i } +m\overset { \wedge }{ j } -\overset { \wedge }{ k } \) in moving the point of application from(1, 1, 1) to (3, 3, 3) along a straight line is 12 units, then m is _____________

The p.v, OP of a point P make angles 60^o and 45^o with X and Y axis respectively. The angle of inclination of  \(\overset { \rightarrow }{ OP } \) with z-axis is ___________

If \(\overset { \rightarrow }{ a } \) and \(\overset { \rightarrow }{ b } \) are two unit vectors, then the vectors \(\left( \overset { \rightarrow }{ a } +\overset { \rightarrow }{ b } \right) \times \left( \overset { \rightarrow }{ a } \times \overset { \rightarrow }{ b } \right) \) is parallel to the vector ___________

If y = 2x + c is a tangent to the circle x² + y² = 5, then c is __________

When the eccentricity of a ellipse becomes zero, then it becomes a __________

The value of \({ sin }^{ -1 }\left( cos\frac { 33\pi }{ 5 } \right) \) is________

If tan^-1(cot \(\theta\)) = 2\(\theta\), then\(\theta\) = _____________

y² - 2x - 2y + 5 = 0 is a _________

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

If p(x) = ax² + bx + c and Q(x) = -ax² + dx + c where ac ≠ 0 then p(x). Q(x) = 0 has at least _______ real roots.

For real x, the equation \(\left| \frac { x }{ x-1 } \right| +|x|=\frac { { x }^{ 2 } }{ |x-1| } \) has ________

Which of the following is/are correct?
(i) Adjoint of a symmetric matrix is also a symmetric matrix.
(ii) Adjoint of a diagonal matrix is also a diagonal matrix.
(iii) If A is a square matrix of order n and λ is a scalar, then adj(λA) = λⁿ adj(A).
(iv) A(adjA) = (adjA)A = |A| I

If A = \(\left[ \begin{matrix} 2 & 0 \\ 1 & 5 \end{matrix} \right] \) and B = \(\left[ \begin{matrix} 1 & 4 \\ 2 & 0 \end{matrix} \right] \) then |adj (AB)| = 

The distance between the planes x + 2y + 3z + 7 = 0 and 2x + 4y + 6z + 7 = 0

The equation of the circle passing through the foci of the ellipse  \(\frac{x^{2}}{16}+\frac{y^{2}}{9}=1\) having centre at (0, 3) is

The circle x² + y² = 4x + 8y +5 intersects the line 3x−4y = m at two distinct points if

The principal argument of (sin 40°+i cos 40°)⁵ is

According to the rational root theorem, which number is not possible rational zero of 4x⁷ + 2x⁴ - 10x³ - 5?