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

Which of the following is a statement?

Which one of the following is not a statement?

\(\int _{ 0 }^{ \frac { \pi }{ 2 } }{ \frac { sin \ x-cos \ x }{ 1+sin \ x cos \ x } dx= } \) ............

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

If u = sin-1 \(\left( \frac { { x }^{ 4 }+{ y }^{ 4 } }{ { x }^{ 2 }+{ y }^{ 2 } } \right) \) and f = sin u then f is a homogeneous function of degree ..................

If u = x^y + y^x then u_x + u_y at x = y = 1 is _____________

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

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

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?

For any value of \(n \in \mathbb{Z}, \int_{0}^{\pi} e^{\cos ^{2} x} \cos ^{3}[(2 n+1) x] d x\) is

The area between y² = 4x and its latus rectum is

If w (x, y) = x^y, x > 0, then \(\frac { \partial w }{ \partial x } \) is equal to

Which of the following is a discrete random variable?
I. The number of cars crossing a particular signal in a day
II. The number of customers in a queue to buy train tickets at a moment.
III. The time taken to complete a telephone call.

Let X represent the difference between the number of heads and the number of tails obtained when a coin is tossed n times. Then the possible values of X are

A rod of length 2l is broken into two pieces at random. The probability density function of the shorter of the two pieces is
\(f(x)=\left\{\begin{array}{ll} \frac{1}{l} & 0< x < l \\ 0 & l <x<2l \end{array}\right.\)
The mean and variance of the shorter of the two pieces are respectively.

If sin x is the integrating factor of the linear differential equation \(\frac { dy }{ dx } +Py=Q,\) then P is

The order and degree of the differential equation \(\sqrt { sinx } (dx+dy)=\sqrt { cos x } (dx-dy)\) 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 ?