If \(\left|\begin{array}{ccc}x-2 & 1 & 2 \\ 1 & 2 x & 1 \\ -1 & 1 & 1\end{array}\right|=3\) then the values of x are:

For two events A and B. Match List I with List II

LIST-I	LIST-II
A. \(P(\bar{A} \cap \bar{B})=P(\bar{A}) \cdot P(\bar{B})\)	I. P(A/B) ≥ P(A)
B. \(A \subset B\) and \(P(B) \neq 0\)	II. P(A) = P(B)
C. P(AUB) = P(A) + P(B)	III. A and B are independent events
D. P(A/B) = P(B|A)	IV. A and B are mutually exclusive events

Choose the correct answer from the options given below:

The interval where the function \(f(x)=2 x^3-9 x^2+12 x+15\) is decreasing, is :

Three magnetic materials : (A) Paramagnetic, (B) Diamagnetic, (C) Ferromagnetic. The correct order of increasing magnetic susceptibility is :

Let A be a non-singular square matrix of order 3 and |adj A| = 5 then |A| is equal to

The integrating factor of differential equation \(\frac{d y}{d x}+y \tan x=\sec x\) is:

The minimum value of \(Z = 2x + y\) subjected to \(x + y ≥ 10, 2x + 3y ≤ 26, x, y ≥ 0\) is

A radioactive sample has a half life of 12 years. The fraction of sample that will decay in 24 years is :

Let \(*\) be a binary operation on set \(Q\) of rational numbers given by \(a * b=a+b+a b\).
Then identity element is:

Which of the following statements are TRUE?
(A) The variable \(t\) of \(t\)-distribution ranges from \(-\infty\) to \(\infty\).
(B) The probability curve of the \(t\)-distribution is symmetric about the line \(t=0\)
(C) The variance of the \(t\)-distribution is greater than one.
(D) As the number of degrees of freedom decreases, the \(t\)-distribution curve moves closer to the standard normal probability curve.
Choose the correct answer from the options given below :

"Answer the question on basis of passage given below:
\(G = \frac{\kappa A}{l}\)=k (both \(A\) and \(l\) are unity in their appropriate units in m or cm)
Molar conductivity of a solution at a given concentration is the conductance of the volume \(V\) of solution containing one mole of electrolyte kept between two electrodes with area of cross section \(A\) and distance of unit length (\(l\)). Therefore,
\(\Lambda_m = \frac{\kappa A}{l}\)
Since \(l = 1\) and \(A = V\) (volume containing 1 mole of electrolyte),
\(\Lambda_m = \kappa V\)
If the length \(l\) in the column of an electrolytic cell is halved and its area of cross-section is tripled, then conductance (\(G\)) would become:"

The electric potential due to an electric dipole
(A) depends on r, where r is the magnitude of position vector \( \vec{r} \)
(B) depends on the angle between the position vector \( \vec{r} \) and the dipole moment vector \( \vec{p} \)
(C) falls off at long distances, as \( 1/r^2 \)
(D) does not depend upon the distance separating the charges
Choose the correct answer from the options given below:

Match List - I with List - II.

List - I	List - II
(A) Aspergillus niger	(I) Butyric acid
(B) Saccharomyces cerevisiae	(II) Citric acid
(C) Clostridium butylicum	(III) Lactic acid
(D) Lactobacillus	(IV) Ethanol

Choose the correct answer from the options given below :