Which of the following are correct?
(A) A statistical hypothesis is a statement about the population parameter which may be true or false.
(B) In a statistical hypothesis testing procedure, a Type I error is made when the null hypothesis is accepted when it is false.
(C) In a statistical hypothesis testing procedure, a Type II error is made when the null hypothesis is rejected when it is true.
(D) The number of degrees of freedom of a statistic is the number of independent variates used to compute that statistic.
Choose the correct answer from the options given below :

The minimum value of \(\left(x^2+\frac{250}{x}\right)\) is :

Consider the linear programming problem (LPP) :
Maximize \(Z=6 x+3 y\)
subject to the conditions
\(4 x+y \geq 80\)
\(x+5 y \geq 115\)
\(3 x+2 y \leq 150\)
\(x \geq 0, y \geq 0\)
In reference to the above LPP, which of the following are correct?
(A) The feasible region is bounded.
(B) The corner points of the feasible region are (15,20), (40,15) and (0,75).
(C) The maximum value of the objective function is 285.
(D) The LPP does not have optimal solution.
Choose the correct answer from the options given below :

The remainder when \(2^{340}\) is divided by 341 is :

In a village, there are three mohallas A, B and C. 60\% farmers in mohalla A believe in new technology of agriculture, while in B it is 70\% and in C is 80\%.
District agricultural officer selects a farmer at random and he found that the farmer believed in new technology of agriculture, then the probability that he belongs to mohalla B is:

Which of the following statements is true for \(f(x)=(x-1)^3(x-2)^2\)?
(A) f(x) decreases on \(\left(-\infty, \frac{8}{5}\right)\)
(B) f(x) increases on \(\left[\frac{8}{5}, 2\right]\)
(C) f(x) has point of inflection at x = 1
(D) f(x) decreases on \((2, \infty)\)
Choose the correct answer from the options given below:

If \(A\) is square matrix of order \(3 \times 3\) and \(|\operatorname{adj} A|=64\), then the value of \(|5 A|\) is

If \(A=\left[\begin{array}{cc}1 & 2 \\ 4 & -3\end{array}\right]\) and \(f(x)=2 x^2-4 x+5\), then \(f(A)\) is equal to

Read the passage carefully and answer the questions
The resistance ( \(R\) ) of an object is given by the expression \(R=\rho \frac{l}{A}\).
The inverse of \(R\) is called conductance and the inverse of \(\rho\) is called conductivity or specific conductance represented by \(\kappa\).
The conductivity depends upon the nature of the material (insulator, semiconductor or conductor) and the temperature of the substance.
Similarly, the conductance due to the ions present in the solution (ionic conductance) depends upon the nature of the electrolyte, size of ions, the nature of the solvent and the temperature.
Molar conductivity ( \(\Lambda_m\) ) of a solution at a given concentration is the conductance of volume \(V\) containing one mole of electrolyte kept between two electrodes of area \(A\) and unit distance apart. It is given by the expression \(\Lambda_m=\kappa V\).
Molar conductivity increases with decrease in concentration and when concentration approaches zero, it is called limiting molar conductivity.
The decrease is linear for a strong electrolyte. However, for a weak electrolyte the change is gradual at higher concentrations and sharp near zero concentration.
Using limiting molar conductivity values of strong electrolytes we can calculate the limiting molar conductivity of weak electrolytes using Kohlrausch law of independent migration of ions.
From molar conductivity and limiting molar conductivity we can determine the degree of dissociation \(\left(\frac{\Lambda_m}{\Lambda_m^0}\right)\) and the ionization constant of a weak acid.
Which of the following is an insulator?

If \(\left[\begin{array}{cc}2 x+1 & 5 x \\ 0 & y^2+1\end{array}\right]=\left[\begin{array}{cc}x+3 & 10 \\ 0 & 26\end{array}\right]\) , then the possible values of x + y are:

Question based on following passage:
Adsorption is the process of attracting and retaining the adsorbate molecules on the surface of adsorbent. It is of two types i.e. Physisrption and chemisorption. To increase the rate of reaction, the substance called 'catalyst' is added. Promotors enhance the activity of catalyst while poison decrease the catalyst activity. Solutions may be true solution, suspension and colloids. Colloids are heterogenous but quite stable. On the basis of nature of interaction, colloids may be Lyophilic or Lyophobic. On the basis of type of dispersed phase particles, there may be multimolecular colloids, macromlecular colloids and associated colloids. The congulation of colloids may be done by boiling, dialysis or by mixing oppositely charged sols.
Molybdenum used in Haber process, acts as a :

The projection of the vector \(\vec{a}=\hat{i}+2 \hat{j}-3 \hat{k}\) on the vector \(2 \hat{i}+6 \hat{j}+3 \hat{k}\) is:

"In the extraction of Al metal from Bauxite ore, the correct sequence of various processes involved is:
A. Heating the ore to remove volatile impurities.
B. Electrolysis of molten ore-mixture.
C. Leaching of alumina with concentrated NaOH.
D. Grading and crushing of big ore particles.
E. Mixing alumina with \(\text{CaF}_2\) or \(\text{Na}_3\text{AlF}_6\).
Choose the correct answer from the options given below:"