A coin is tossed 6 times. The probability that tail appears odd number of times is:

If the matrix \(A=\left[\begin{array}{ccc}0 & -3 & x+y \\ 3 & x-2 y & 5 \\ -6 & -5 & 0\end{array}\right]\) is skew-symmetric then values of \(x\) and \(y\) respectively are :

Which of the following statement(s) is/are TRUE?
(A) Skew symmetric matrix of even order is always symmetric
(B) Skew symmetric matrix of odd order is non-singular
(C) Skew symmetric matrix of odd order is singular
(D) Skew symmetric matrix is always square matrix
Choose the correct answer from the options given below:

A balloon which always remains spherical, has a variable diameter, \(\frac{3}{2}(5 x+7)\). Then the rate of change of its volume with respect to x is

If \(A\) is any event associated with sample space and If \(E_1, E_2, E_3\) are mutually exclusive and exhaustive events. Then which of the following are true?
(A) \(P(A)=P\left(E_1\right) P\left(E_1 \mid A\right)+P\left(E_2\right) P\left(E_2 \mid A\right)+P\left(E_3\right) P\left(E_3 \mid A\right)\)
(B) \(P(A)=P\left(A \mid E_1\right) P\left(E_1\right)+P\left(A \mid E_2\right) P\left(E_2\right)+P\left(A \mid E_3\right) P\left(E_3\right)\)
(C) \(P\left(E_i \mid A\right)=\frac{P\left(A \mid E_i\right) P\left(E_i\right)}{\sum_{i=1}^3 P\left(A \mid E_i\right) P\left(E_i\right)}, i=1,2,3\)
(D) \(P\left(A \mid E_i\right)=\frac{P\left(E_i \mid A\right) P\left(E_i\right)}{\sum_{i=1}^3 P\left(E_i \mid A\right) P\left(E_i\right)}, i=1,2,3\)
Choose the correct answer from the options given below:

The function \(f(x)=|x-1|\) is strictly increasing in the interval.

The shortest distance between lines \(\frac{-x-3}{4}=\frac{y-6}{3}=\frac{z}{2}\) and \(\frac{-x-2}{4}=\frac{y}{1}=\frac{z-7}{1}\) is :

Of the incident solar radiation, less than _______ of it is photosynthetically active radiation (PAR).

For a maximizing LPP, the constraints are:

Which of the following are correct?
(A) The probability curve in t-distribution is symmetric about the line \(t =0\).
(B) t-axis is an asymptote of the curve.
(C) The variable t of t-distribution ranges from \(-\infty\) to \(\infty\).
(D) As the number of degrees of freedom increases, the t-distribution curve moves closer to the binomial distribution.
Choose the correct answer from the options given below :

The volume of a cube is increasing at a rate of 9 cubic centimeter per second. Then rate of change of surface area when the length of an edge is 10 centimeter is:

Identify the enzyme which is used to isolate genetic material from the bacterial cells.

The chromosome numbers in the gamete of fruit fly is: