The value of \(\left|\begin{array}{ccc}1 & x & y \\ 1 & x+y & y \\ 1 & x & x+y\end{array}\right|\) is

A boat can row at the speed of \(16 km / hr\) in still water. If the river is flowing at \(8 km / hr\), and it takes 8 hours for a round trip, then the distance between the two places is :

The solution set of the inequation \(|2 x-3| \leq 4\) is

If a person rides his motorbike \(x km\) at 30 km per hour, he has to spend ₹ 3 per kilometer on petrol; if he rides \(y km\) at a faster speed of 40 km per hour, the petrol cost increases to ₹ 4 per kilometer. If he has ₹ 100 to spend on petrol and wishes to find the maximum distance he can travel within one hour, then linear programming problem (LPP) formulation is:

If \(y=x^{x \sin x}\) then \(\frac{d y}{d x}=\) ?

Which one of the following set of constraints represents the shaded region given below?

Match List-I with List-II

List-I	List-II
(A) The vectors \(\lambda \hat{i}+\hat{j}+2 \hat{k}\) and \(\hat{i}+\lambda \hat{j}+\hat{k}\) are perpendicular if \(\lambda\) is equal to	(I) 1
(B) The vectors \(3 \hat{i}+6 \hat{j}-\hat{k}\) and \(2 \hat{i}+\lambda \hat{j}-2 \hat{k}\) are collinear if \(\lambda\) is equal to	(II) -1
(C) The number of vectors of unit-length which are perpendicular to both the vectors \(\vec{a}=\hat{i}+\hat{j}+2 \hat{k}\) and \(\vec{b}=3 \hat{i}-\hat{j}+5 \hat{k}\) is	(III) \(2 / 3\)
(D) If \(|\vec{a}|=1\) and \(\vec{a}+\vec{b}=\overrightarrow{0}\), then \(|\vec{b}|\) is equal to	(IV) 2

Choose the correct answer from the options given below :

Self Inductance of coil causes :

ELISA is based on the principles of:

Which of the following is not an expression of Dalton's law of partial pressures?

Read the passage carefully and answer the Questions
Carboxylic acids are the earliest organic compounds isolated from nature. These are also known as organic acids but are weaker acids as compared to mineral acids. However, they are more acidic than alcohols and phenols because of greater resonance stabilization of the parent acid and its conjugate base. The acidic strength is determined by the \(K _a\), which is called the acidity constant. The greater the value of \(K _a\), the greater the tendency of the acid to ionize and hence the stronger the acid. The acidic strength of the saturated aliphatic carboxylic acid depends upon the inductive effect and its position with respect to - COOH groups. Electron -donating substituents tend to decrease whereas electron-withdrawing substituents tend to increase the acidic strength. The acidic strength of the aromatic carboxylic acid, on the other hand depends upon both the inductive effect and the resonance effect of the substituents.
Which of the following groups when attached directly does not increase the acidity of the carboxylic acid?

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, \(t_2\), 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 ( \(\Delta_{\circ}>P\) ) 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 \(18,000 cm^{-1}\) ?

Solution of the differential equation \(\frac{d y}{d x}=1+x+y+x y\) are :