Consider the LPP, Min \(Z=3 x-2 y\) subject to the conditions
\(
\begin{array}{l}
4 x+3 y \geq 12 \\
4 x+y \geq 4 \\
x \geq 0, y \geq 0
\end{array}
\)
then which of the following is correct?

If the sum and difference of squares of mean and variance of a Binomial distribution is \(\frac{225}{256}\) and \(\frac{63}{256}\) respectively, the \(P(X \geq 2)\) is :

The number of all possible matrices of order \(3 \times 3\) with each entry 2 or 3 is:

Area (in sq. units) of the region bounded by the curves \(y = - 1, y = 2 x = y^3\) and \(x = 0\) is

Two ropes are tied along the two diagonals of a cubic room. Ropes are inclined to each other at :

Consider \(z=x+3 y\) subject to the constraints \(2 x+3 y \geq 6,2 x+y \leq 8, x \geq 0, y \geq 0\). The minimum value of \(z\) is :

The coordinates of the point where the line \(\frac{x-3}{2}=\frac{y-4}{-3}=\frac{z-1}{5}\) crosses \(X Y\) plane is :

Read the passage carefully and answer the Questions:
According to Valence Bond theory, the metal atom or ion under the influence of ligands can use its ( \(n-1\) )d, \(n s, n p\) or \(n s, n p, n d\) orbitals for hybridisation to yield a set of equivalent orbitals of definite geometry such as octahedral, tetrahedral, square planar and so on. These hybridised orbitals are allowed to overlap with ligand orbitals that can donate electron pairs for bonding. While the VB theory, to a larger extent, explains the formation, structures and magnetic behaviour of coordination compounds, it suffers from the many shortcomings. The Crystal field theory (CFT) is an electrostatic model which considers the metal-ligand bond to be ionic arising purely from electrostatic interactions between the metal ion and the ligand. The five \(d\) orbitals in an isolated gaseous metal atom/ion have same energy, i.e., they are degenerate. This degeneracy is maintained if a spherically symmetrical field of negative charges surrounds the metal atom/lon. However, when this negative field is due to ligands in a complex, it becomes asymmetrical and the degeneracy of the \(d\) orbitals is lifted. It results in splitting of the \(d\) orbitals. The pattern of splitting depends upon the nature of the crystal field.
Which of the following is not true about the limitations of VBT:

A radioactive sample decays 7/8 times its initial quantity in 21 minutes. The half life of the sample will be

Assume P, Q, R and W are matrices of order \(3 \times 3, a \times 4, b \times c\) and \(d \times a\) respectively. If PQ + WR is well is well defined, find the value of ab + cd

If \(x=-1\) and \(x=-2\) are the extreme points of \(f(x)=\alpha \log |x|+\beta x^2+x\) then

Benzene ring in phenol is expected to give the characteristic substitution or replacement reactions i.e. halogenation, nitration, sulphonation, alkylation etc. In these reactions, the attacking reagent is electrophile. The phenolic group activates the ortho and para positions in the ring due to conjugation. Disubstitution reactions are quite fast as the electron density in the ring has increased considerably. Phenols do not respond to nucleophilic substitution reactions as it is influenced by phenolic group.
Picric acid is very strong acid due to presence of:"

Match List I with List II.

LIST I	LIST II
A. Down's Syndrome	I. Absence of a copy of X chromosome
B. Klinefelter's Syndrome	II. Presence of additional copy of X chromosome
C. Turner's Syndrome	III. Mutation in X chromosome
D. Colour blindness	IV. Trisomy of 21st chromosome

Choose the correct answer from the options given below: