Area bounded by \(x=\frac{y^2}{4}\) and its latus rectum is:

The integral value of \(k\) for which the system of linear equations
\(\begin{array}{l}k x+y+2 z=0 \\k y=x-3 z \\2 x+y+k z=0\end{array}\)
has a non-zero solution is :

The general solution of the differential equation \(\frac{d y}{d x}=e^{x+y}\) is :

The points on the ellipse \(\frac{x^2}{9}+\frac{y^2}{25}=1\) at which the tangents are parallel to the \(x\)-axis are:

If \(f(x)=2 x^3-15 x^2+36 x+1, x \in[1,5]\), then the absolute minimum value of \(f(x)\) is:

Probability distribution of random variable \(X\) is

X	-2	-1	0	1	2
P(X)	2/11	1/11	4/11	3/11	1/11

Then the value of \(E(X)\) is

If \(|\vec{a}|=1,|\vec{b}|=2,|2 \vec{a}+\vec{b}|=2 \sqrt{3}\) then \(|\vec{a}-\vec{b}|\) is :

Which of the following statements are correct in reference to the linear programming problem (LPP):
Maximize \(Z =5 x +2 y, Z =5 x +2 y, Z =5 x +2 y\)
subject to the following constraints
\(3 x+5 y \leq 15,5 x+2 y \leq 10, x \geq 0, y \geq 0\)
(A) The LPP has a unique optimal solution at \((2,0)\) only.
(B) The feasible region is bounded with corner points \((0,0),(2,0),(20 / 19,45 / 19)\) and \((0,3)\).
(C) The optimal value is unique, but there are an infinite number of optimal solutions.
(D) The feasible region is unbounded.
Choose the correct answer from the options given below:

Nucleophilic addition will be most favoured in:

If \(\frac{d}{d x}\left(2 \frac{d^2 y}{d x^2}\right)^3=7\), then the sum of order and degree of the differential equation is:

Which of the following are the components of a time series?
(A) Cyclic component
(B) Regular component
(C) Seasonal component
(D) Economic component
Choose the correct answer from the options given below:

Match List - I with List - II.

List - I (Process)	List - II (Metal)
A. Electrolytic reduction	I. Iron
B. Bessemerization	II. Zinc
C. Smelting	III. Aluminium
D. Reduction from oxide	IV. Copper

Choose the correct answer from the options given below:

Read the passage carefully and answer the questions
The osmotic pressure is one of the four colligative properties which depends on the number of particles of solute in the solution, irrespective of their nature. The osmotic pressure is equal to the product of concentration, gas constant and temperature. It is the most commonly used property for the determination of the molar mass of biomolecules. In many situations, the molecules get dissociated or associated when they are dissolved in a solvent, thereby changing the number of molecules in the solution. As a result, an abnormal molecular mass is obtained. The extent of dissociation or association is given by van't Hoff factor (i), which is the ratio of normal molar mass to abnormal molar mass. It is related with the degree of association or ionization. The introduction of van't Hoff factor in the osmotic pressure equation modifies the equation.
How is the osmotic pressure of a concentrated solution related to the osmotic pressure of a dilute solution of the same substance at a given temperature?