The probability distribution of a random variable X is given below:
\(\begin{array}{lllll} X & 0 & 1 & 2 & 3 \\ P ( X ) & k & & \\ & & \frac{k}{2} & \frac{k}{4} & \frac{k}{8}\end{array}\)
then the value of \(P(X \leq 2)+P(X>2)\) is :

If \(y=x^{x \sin x}\) then \(\frac{d y}{d x}=\) ?

Let A = {1, 2, 3} Consider the relation R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)} Then R is:

If A and B are symmetric matrices of same order, then which of the following are correct?
(A) AB-BA is a skew-symmetric matrix.
(B) \(AB + BA\) is a skew-symmetric matrix.
(C) \(A B^T-B A^T\) is a skew-symmetric matrix.
(D) \(AB + BA\) is a symmetric matrix.
Choose the correct answer from the options given below :

For \(|x|<1\), if \(x=\cos \left(\frac{1}{a} \log y\right)\), then

Given that \(\sigma p_{0} q_{0} = 1000, \sigma p_{0} q_{0} = 1200, \sigma p_{0} q_{0} = 1350, \sigma p_{0} q_{0} = 1500\), where subscripts 0 and and 1 used for base year and current year respectively. The Paasche's Index number is :

The points of discontinuity of the function \(f\) defined by \(f(x)=\begin{cases} x + 2 & x \leq 1 \\x - 2 & 1 < x < 2\text { are: } \\0 & x \geq 2 \end{cases}\)

Which one of the following ligands forms a chelate?

'XO' type of sex determination is found in:

Answer the question on the basis of passage given below :
Formaldehyde is the first member of the aldehydic series. It is present in green leaves of plants where its presence is supposed to be due to the reaction of \(CO_2\) with water in the presence of sunlight and chlorophyll. Commercially, formaldehyde is obtained by the controlled oxidation of methane in the presence of molybdenum oxide (\(MoO\)) acting as a catalyst. Formaldehyde is a constituent of a number of polymers also called resins. These are non volatile solids or semi solids which are obtained directly from certain plants and can be synthesized in the laboratory.
Question: How is formalin useful?

The electric potential due to an electric dipole
(A) depends on r, where r is the magnitude of position vector \( \vec{r} \)
(B) depends on the angle between the position vector \( \vec{r} \) and the dipole moment vector \( \vec{p} \)
(C) falls off at long distances, as \( 1/r^2 \)
(D) does not depend upon the distance separating the charges
Choose the correct answer from the options given below:

The slope of the normal to the curve \(y^2=16 x\) at the point \((1,4)\) is :

In transmission of power from generation plants to users, transformers are used. Identify the correct reason to choose appropriate transformers.
(A) A step-up transformer is used at the generation plant and high voltages are transmitted.
(B) A step-down transformer is used at the generation plant and low voltages are transmitted.
(C) A step-up transformer lowers the current and hence loss due to joule heating is less.
(D) A step-down transformer lowers the current and hence loss due to joule heating is less.
Choose the correct answer from the options given below: