The Greatest Integer Function \(f: R \rightarrow R\) given by \(f(x)=[x], x \in R\) and \([x]\) denotes the greatest integer less than or equal to \(x\) is :

If \(\frac{1}{|x|-3} \leq \frac{1}{2}\), then the value of \(x\) is:

A card is selected at random from a pack of 52 playing cards.The selected card is a queen.The probability that this card is a card of spade is :

If A is a skew-symmetric matrix of order 5 , then \(|a d j A|\) is equal to

Which of the following are the components of a time series?
(A) Cyclic component
(B) Regular component
(C) Seasonal component
(D) Economic component
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The particular solution of the differential equation \(x\left(1+y^2\right) d x-y\left(1+x^2\right) d y=0\), given that \(y(0)=1\) is :

Let \(\vec{a}=2 \hat{i}-\hat{j}, \vec{b}=-4 \hat{j}+\hat{k}\) and \(\vec{c}=\hat{i}+2 \hat{k}\). If \(\vec{d}\) is a vector perpendicular to both \(\vec{a}\) and \(\vec{b}\) such that \(\vec{c} \cdot \vec{d}=34\), then \(|\vec{d}|\) is equal to

A polaroid sheet is rotated between two crossed polarizers. The intensity of transmitted light would be maximum, when the angle between the axes of the first polarizer and the polaroid sheet is

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Werner in 1898, propounded his theory of coordination compounds. In coordination compounds metals show two types of linkages (valences)-primary and secondary. The primary valences are normally ionisable and are satisfied by negative ions. The secondary valences are non-ionisable. These are satisfied by neutral molecules or negative ions. The secondary valence is equal to the coordination number and is fixed for a metal. The ions or group bound by the secondary linkages to the metal have characteristic spatial arrangements corresponding to the different coordination numbers. Both double salts as well as complexes are formed by the combination of two or more stable compounds in stoichiometric ratio. However, they differ in the fact that double salts such as carnallite, Mohr's salt, potash alum etc. dissociate into simple ions completely when dissolved in water. But complex ions do not dissociate completely into simple ions.
Identify the correct formula of Mohr's salt and potash alum, respectively.

A and B throw a die alternatively till one of them gets 3 or 6 and wins the game. If B starts the game, then the probability of winning the game by A is

Identify the enzyme used for the isolation of genetic material from fungal cells.

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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/ion. 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.
The spin only magnetic moment of \(\left[ MnBr _4\right]^{2-}\) is 5.9 BM. Predict the geometry of the complex ion?

DNA fingerprinting techniques have the following steps. Arrange these
steps in the correct order.
(A) Digestion by restriction enzyme
(B) Transferring separated DNA fragments
(C) DNA-DNA hybridization
(D) Gel Electrophoresis
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