match List - I with List - II

List - I	List - II
(A) Equations of line through (5, -4, 6) with direction ratios 3, 7, 2	(I) \(\frac{x+3}{5}=\frac{y+7}{-4}=\frac{z+2}{6}\)
(B) Equations of line through (3, 7, 2) with direction ratios 5, -4, 6	(II) \(\frac{x-3}{5}=\frac{y-7}{-4}=\frac{z-2}{6}\)
(C) Equations of line through (-5, 4, -6) with direction ratios 3, 7, 2	(III) \(\frac{x-5}{3}=\frac{y+4}{7}=\frac{z-6}{2}\)
(D) Equations of line through (-3, -7, -2) with direction ratios 5, -4, 6	(IV) \(\frac{x+5}{3}=\frac{y-4}{7}=\frac{z+6}{2}\)

Choose the correct answert from the option given below :

If E and F are independent events associated with an experiment, then which one of the following statements is correct?

In the month of January, the number of cases diagnosed of influenza epidemic are given in the following table:

Date	1	2	3	4	5	6	7
Number of cases	2	0	5	12	20	27	46

The 3-day moving averages are:

If the interval in which the function \(f(x)=\frac{x}{x^2+1}\) is strictly increasing is \((-a, a)\), then \(a\) is equal to

If \(a\) and \(b\) are the order and degree of the differential equation
\(\frac{\left[1+\left(\frac{d y}{d x}\right)^2\right]^{\frac{3}{2}}}{\frac{d^2 y}{d x^2}}=K \text { respectively, then }\)
the value of \(a+2 b\) is :

Two dice are thrown simultaneously. If X denotes the number of sixes, then the variance of X is:

The region represented by the system of inequalities \(x \geq 0 ; y \geq 0\),
\(2 x+y \geq 8\) and \(x+2 y \geq 10\) is :

Read the passage carefully and answer the questions:
The degeneracy of the \(d\) orbitals has been removed due to ligand electron-metal electron repulsions in the octahedral complex to yield three orbitals of lower energy, \(t_{2 g}\) set and two orbitals of higher energy, \(e_g\) set. This splitting of the degenerate levels due to the presence of ligands in a definite geometry is termed as crystal field splitting and the energy separation is denoted by \(\Delta_0\). Thus energy of the two \(e_g\) orbitals will increase by \((3 / 5) \Delta_0\) and that of three \(t_{2 g}\) will decrease by \((2 / 5) \Delta_0\). The crystal field splitting \(\Delta_0\) depends upon the field produced by the ligand and charge on the metal ion. Some ligands are able to produce strong fields, in which case the splitting will be large, whereas others produce weak fields and consequently result in small splitting of \(d\) orbitals. Relative magnitude of crystal field splitting energy \(\Delta_{\circ}\) and pairing energy, \(P\) (energy required for electron pairing in a single orbital) determine the formation of low spin ( \(\Delta_{\circ}>P\) ) or high spin ( \(\Delta_{\circ}<P\) ) complex. In tetrahedral coordination entity formation, the \(d\)-orbital splitting is inverted and is smaller as compared to the octahedral field splitting. The crystal field theory attributes the colour of the complex to \(d-d\) transition of the electron. The colour of the coordination compounds depends on the crystal field splitting. In the absence of ligand, crystal field splitting does not occur and hence the substance is colourless
What will be the crystal field splitting energy for tetrahedral \(\left[ CoCl _4\right]^{2-}\) if its value for octahedral \(\left[ CoCl _6\right]^{4-}\) is \(18,000 cm^{-1}\) ?

Match List-l with List-ll

List-l (Evolutionary stages of man)	List-II (Features)
(A) Dryopethicus	(I) Brain capacity 900 cc
(B) Australopithecines	(II) Hairy and walked like gorillas
(C) Homo habilis	(III) Brain capacity 650-800 cc
(D) Homo erectus	(IV) Lived in east African grasslands

Choose the correct answer from the options given below:

The function \(f: R \rightarrow R , f(x)=x^2\) is

Two nuclei with mass numbers A and B have density ratios of :

The set of positive integers less than 50 forming the equivalence class of 6 modulo 9 is given by :

The minimum value of the objective function \(Z=x+2 y\) of an L.P.P. subject to constraints
\(2 x+y \geq 3, \frac{x}{2}+2 y \geq 6, x \geq 0, y \geq 0\) is