If \(A=\left[\begin{array}{ccc}a & 4 & -5 \\ d & b & -6 \\ 5 & e & c\end{array}\right]\) is a skew symmetric matrix, then value of \(a+b+c+d+e\) is equal to

\(\int \frac{\sin x-x \cos x}{x(x+\sin x)} d x=\) (where \(C\) is an arbitrary constant)

If the corner points of the bounded feasible region for a linear programming problem (LPP) are (0, 2), (3, 0), (6, 0), (6, 8) and (0, 5), then which of the following are correct for the objective function \(Z=4 x+6 y \) ?
(A) The minimum value of the objective function occurs at (0, 2) and (3, 0) only.
(B) The minimum value of the objective function occurs at the mid-point of the line segment joining the points (0, 2) and (3, 0) only.
(C) The minimum value of the objective function occurs at every point of the line segment joining the points (0, 2) and (3,0).
(D) The difference between the maximum value and minimum value of the objective function is 60.
Choose the correct answer from the options given below :

If \(A\) is a square matrix of order 3 such that \(|A|=3\) then \(|\operatorname{adj}(\operatorname{adj} A)|\) is equal to:

Which of the following statements are correct?
(A) Direction ratios of the line \(\frac{x-1}{2}=\frac{y+2}{3}=\frac{z-3}{4}\) are 2, 3, 4
(B) Direction ratios of the line \(\frac{x-1}{2}=\frac{2-y}{7}=\frac{2 z-1}{6}\) are 2, -7, 3
(C) Direction cosines of z axis are 0, 1, 0
(D) Direction ratios of the line joining the point (1, 2, -3) and (4, 5, 6) are 1, 1, 3
(E) Direction cosines of a line which makes equal angles with the coordinate axes are \(\frac{1}{3}, \frac{-1}{3}, \frac{1}{3}\)
Choose the correct answer from the options given below:

For the following probability distribution,

X	1	2	3	4
p(x)	\(\frac{1}{10}\)	\(\frac{1}{5}\)	\(\frac{3}{10}\)	\(\frac{2}{5}\)

The value of \(E\left(X^2\right)-[E(X)]^2\)

Given that the value of a determinant of order three is zero; which one of the following is not correct?

Ferromagnetic material core used for transformer must have

Genetically modified organisms have been useful in many ways. Which one
of the following statements is not correct in the case of GMO plants?

How many haploid cells will be formed after first meiotic division of one primary spermatocyte ?

We have four aqueous solution labelled as :
(A) 0.1 M NaCl
(B) 0.01 M NaCl
(C) \(0.01 M BaCl _2\)
(D) 0.01 M Sucrose
Choose the correct increasing order of Van't Hoff factor from the options given below :

For the given \(5\) values, \(15, 18, 21, 27, 39;\) the three year moving averages are:

Which of the following statements is INCORRECT?