A random variable X has the following probability distribution :

X	1	2	3	4	5	6	7
\(P(X)\)	C	2C	2C	3C	\(C^2\)	\(2 C^2\)	\(7 C^2+C\)

Then the value of C is :

The value of \(\left|\begin{array}{lll}265 & 240 & 219 \\ 240 & 225 & 198 \\ 219 & 198 & 181\end{array}\right|\) is

What is the mean of the numbers obtained on throwing a die having written \(1\) on three faces, \(2\) on two faces and \(5\) on \(1\) face?

Which of the following statements are correct?
(A) If \(\vec{a}\) and \(\vec{b}\) represent the adjacent sides of a triangle, then its area is \(\frac{1}{2}|\vec{a} \times \vec{b}|\)
(B) If \(\vec{a}\) and \(\vec{b}\) represent the adjacent sides of a parallelogram, then its area is \(|\vec{a} \times \vec{b}|\)
(C) \(|\vec{a} \times \vec{b}|=|\vec{a}||\vec{b}| \cos \theta\)
(D) If \(\vec{a}\) and \(\vec{b}\) represent the 'diagonals' of a parallelogram, then its area is \(\frac{1}{2}|\vec{a} \times \vec{b}|\)
Choose the correct answer from the options given below :

Integrating factor of \(\frac{dy}{dx} + y \cot x = 2x + x^2 \cot x\) (\(x \neq 0\)) is:

Which of the following terms are associated with a linear programming problem?
(A) Constraints
(B) Independent events
(C) Feasible region
(D) Objective function
Choose the correct answer from the options given below :

For \(A=\left[\begin{array}{lll}a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}\end{array}\right]\) if \(M_{i j}\) and \(A_{i j}\) are the minor and the cofactor of \(a_{i j}\) respectively, then \(|A|\) equals to :
(A) \(a_{11} A_{11}+a_{12} A_{12}+a_{13} A_{13}\)
(B) \(a_{21} A_{12}+a_{22} A_{22}+a_{23} A_{32}\)
(C) \(a_{11} M_{11}-a_{12} M_{12}+a_{13} M_{13}\)
(D) \(a_{11} M_{11}+a_{12} M_{12}+a_{13} M_{13}\)
Choose the correct answer from the options given below :

Which one of the following hormones is essential for maintenance of endometrium?

Read the passage carefully and answer the Questions
The term vitamin was coined from the word vital +amine since the earlier identifiedc ompounds had amino groups. Later work showed that most of them didn't contain amino groups. They are very essential for the body. They has to be taken various diet or in the form of medicines also.
Vitamins are classified into two groups depending upon their solubility in water or fat.
Fat soluble vitamins are soluble in fat and oils but insoluble in water. They are stored in liver and adipose (fat storing) tissues Water-soluble vitamins are soluble in water. These must be supplied regularly in diet because they are readily excreted in urine and cannot be stored in our body.
What are the sources of Vitamin C?

Match List-I with List-II

List-I (Complex ion)	List-II (Hybridisation)
(A) \(\left[ CoF _6\right]^{3-}\)	(I) \(d^2 s p^3\)
(B) \(\left[ Co ( CN )_4\right]^{2-}\)	(II) \(s p^3 d^2\)
(C) \(\left[ FeCl _4\right]^{-}\)	(III) \(s p^3\)
(D)\(\left[ Co \left( C _2 O _4\right)_3\right]^{3-}\)	(IV) \(d s p^2\)

Choose the correct answer from the options given below:

If \(\int \frac{d x}{(x-1)^{3 / 4}(x+2)^{5 / 4}}=\alpha[1-g(x)]^\beta+c\), where \(c\) is a constant of integration, then which of the
following are true?
(A) \(\alpha=\frac{2}{3}\)
(B) \(\beta=\frac{3}{4}\)
(C) \(3 \alpha+4 \beta=5\)
(D) \(g(x)=\frac{3}{x+2}\)
Choose the correct answer from the options given below:

Which of the following is a vertex of the positive region bounded by the inequalities:
\(4 x+y \geq 80 ; \quad 2 x+y \geq 60 ; \quad x, y \geq 0\)

The degree of the differential equation \(\left(1+\frac{d y}{d x}\right)^3=\left(\frac{d^2 y}{d x^2}\right)^2\) is: