If the following data is obtained from a simple random sample : 6, 7, 9, 10, 11, 17
Then the point estimate of population standard deviation is :

If \(x=t^4, y=t\), then \(\frac{d^2 y}{d x^2}\) is given by ______________

Which of the following is a vertex of the positive region bounded by the inequalities:
\(4 x+y \geq 80 ; \quad 2 x+y \geq 60 ; \quad x, y \geq 0\)

At what rate of interest will the present value of a perpetuity of Rs. 1000 payable at the end of every six months be Rs. 20000?

Let a pair of dice be thrown and the random variable X be the sum of numbers on the two dice. Then, Match List I with List II

LIST - I	LIST - II
A. \(P(X=2)\)	I. \(4 / 36\)
B. \(P(X=4)\)	II. \(5 / 36\)
C. \(P(X=5)\)	III. \(1 / 36\)
D. \(P(X=6)\)	Iv. \(3 / 36\)

Choose the correct answer from the options given below

If \(\tan ^{-1}(2 x)+\tan ^{-1}(3 x)=\frac{\pi}{4}\), then the value of \(x\) is:

The equation of tangent to the curve \(y=\sqrt{3 x-2}\) which is parallel to the line \(4 x-2 y+5=0\) is :

Aldehydes and ketones undergo

Match List - I with List - II.

List - I	List - II
(A) Citric acid	(I) Saccharomyces cerevisiae
(B) Ethanol	(II) Trichoderma polysporum
(C) Cyclosporin A	(III) Monascus purpureus
(D) Statins	(IV) Clostridium butylicum
	(V) Aspergillus niger

Choose the correct answer from the options given below:

If \(x=t^2\) and \(y=t^3\), then \(\frac{d y}{d x}=6\) at \(t=\)

A spherical ice ball is melting at the rate of \(100 \pi \mathrm{~cm}^3 / \mathrm{min}\). The rate at which its radius is decreasing when its radius is 15 cm, 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 \((3 / 5) \Delta_{\circ}\) and that of three \(t_{2 g}\) will decrease by \((2 / 5) \Delta_0\). The crystal field splitting \(\Delta_{ o }\) 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 ( \(\Delta_0>P\) ) or high spin ( \(\Delta_0<P\) ) 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.
Choose the correct order of the ligands in their increasing crystal field splitting:

Smack is chemically: