Value of \(\tan ^{-1} 2+\tan ^{-1} 3+\tan ^{-1} 4\) is equal to:

Match List-I with List-II

List-I	List-II
(A) \(f ( x )=| x |\)	(I) Not differentiable at \(x=-2\) only
(B) \(f(x)=|x+2|\)	(II) Not differentiable at \(x=0\) only
(C) \(f(x)=\left|x^2-4\right|\)	(III) Not differentiable at \(x=2\) only
(D) \(f(x)=|x-2|\)	(IV) Not differentiable at \(x=2,-2\) only

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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

The shortest distance between the following lines :
\(\vec{r}=(\hat{i}+\hat{j}-\hat{k})+s(2 \hat{i}+\hat{j}+\hat{k})\)
\(\vec{r}=(\hat{i}+\hat{j}+2 \hat{k})+t(4 \hat{i}+2 \hat{j}+2 \hat{k})\), where \(s\) and \(t\) are scalars, is :

If \(A=\left[\begin{array}{l}-2 \\ -1 \\ -4\end{array}\right], B=\left[\begin{array}{lll}-1 & 2 & 3\end{array}\right]\), then the value of \(A^{\prime} B^{\prime}\) is

Which of the following are correct?
(A) Time series analysis does not help to understand the behavior of a variable in the past.
(B) Time series predict the future behavior of variable.
(C) Time series helps to plan future operations.
(D) The main aim of the time series analysis is to derive conclusions after arranging the time series in a systematic manner.
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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.
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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:

If three year moving averages for five data items given by \(16,18,20,10,21\) are \(x, y\) and \(z\) respectively, then :

The correct arrangement of electromagnetic spectrum in decreasing order of wavelength is :

The correct increasing reactivity order for SN2 reaction for the following compounds
(A) Benzyl Chloride
(B) Methyl Chloride
(C) Isopropyl Chloride
(D) Tertiary butyl Chloride
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Which one of the following infections is completely curable?

Identify the incorrect statement(s) from the following in the context of an electric current flowing through a conductor.
(A) The electrons suffer collisions with heavy fixed ions in the conductor
(B) The resistance of the given conductor depends on its temperature
(C) Resistance and resistivity both depend on the dimensions of the conductor
(D) When a potential difference V is applied across the conductor then V= IR
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