Consider the following L.P.P.
Minimize \(z=400 x+300 y\), subject to \(100 x+200 y \geq 12000,300 x+400 y \geq 20000,200 x+100 y \geq 15000\) and \(x, y \geq 0\). Then

A motorcycle has a scrap value of Rs. 22,500 after 15 years of its purchase.
If the annual depreciation charge is Rs. 8,500, then the original cost by linear method is :

If \(f: R \rightarrow R\) is defined by \(f(x)=x^2-3 x+2\) then \(f(f(x))\) is :

Let \(A\) be a non-singular matrix of order 3 and \(|A|=15\), then \(|\operatorname{adj} A|\) is equal to:

For what value of \(k\), the following system of equations has infinitely many solutions?
\(x+2 y=5\), \(3 x+k y=15\)

On a multiple choice examination with 4 possible answers (out of which one is correct)
for each of the five questions, the probability that a candidatewould get 4 or more correct answers just by guessing is:

Two percent of the bolts manufactured in a factory are found to be defective. Using the Poisson distribution, the probability that in a sample of 100 bolts chosen at random, exactly two will be defective, is : [Given \(e^{-2}=0.135\)]

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 complez 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 \(\Delta_{\circ}\) 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 \(\Delta_0\) 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 octabedral 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.
Which of the following relations is correct for the splitting of \(d\) orbitals in octahedral and tetrahedral crystal fields, considering same metal, the same ligands and metal-ligand distances?

Which of the following is NOT a disaccharide?

In which of the following interval the function \(f(x)=x^x, x>0\) is strictly increasing?

In a meeting, 70% of the members favour and 30% oppose a certain proposal.
A member is selected at random and we take X = 0 if he opposed, and X = 1 if he is in favour.
Then, E(X) is:

The electronic conductance depends on:
(A) The nature and structure of the metal
(B) Composition of metallic conductor
(C) The number of valence electrons per atom
(D) Temperature
(E) Number of ions
Choose the correct answer from the options given below:

The C-Br bond in bromobenzene as compared with C-Br bond in ethyl bromide is