If the probability distribution of a random variable X is

then second moment about 0 i.e.,

X is a random variable with distribution given below

Then the value of k and variance are

The mean and variance of the random variable X which follows the following distribution are respectively

If X is a random variable with the following distribution

where p + q = 1 then the variance of X is

Which one of the following structural formulae of two organic compounds is correctly identified along with its related function?

Assertion : The only product of light reaction required in dark reaction are NADPH₂ and ATP  in C₄-plants.
Reason: Dark reaction occurs in night only.

A rectangle with sides 2m – 1 and 2n – 1 is divided into squares of unit length by drawing parallel lines as shown then number of rectangles possible with odd side lengths is

Using permutation or otherwise prove that is an integer, where n is a positive integer.

Find two values of k such that the points (2,-3), (3,0),(4,k) are collinear.

The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, the number of terms is

Here we used the concept of Arithmetic progression to find the number of terms in the given series. When we study Arithmetic Progression, which is associated with: There are two key formulas we encounter, those were nth term of AP and sum of the first n terms. So therefore the number of terms in this AP is 11.

The sum of all two digit numbers which when divided by 4 leaves 1 as remainder is

Here we used the concept of Arithmetic progression to find the number of terms in the given series. When we study Arithmetic Progression, which is associated with: There are two key formulas we encounter, those were nth term of AP and sum of the first n terms. So therefore the sum is 1210.

The value of current in the following diagrams is (diode assumed to be ideal one)

Three coins of unit radius are placed in an equilateral triangle as shown in the following figure The area of the equilateral triangle is

In Fig. is the potential barrier across a p-n junction, when no battery is connected across the junction:

The output of the given circuit in Fig.

A full wave rectifier along with the output is shown in fig. the contributions from the diode (2)are