If \(x, y, z\) are all distinct and \(\left|\begin{array}{lll}x & x^2 & 1+x^3 \\ y & y^2 & 1+y^3 \\ z & z^2 & 1+z^3\end{array}\right|=0\), then the value of \(x y z\) is :

Pipe A and B can fill a tank in 15 hours and 20 hours respectively. Pipe C can empty the tank in 25 hours. Pipes A, B and C work together but pipe C is closed after 10 hours, then the time taken by pipe A and B to fill the remaining tank is:

The function \(f(x)=x^3+3 x^2+4 x+4, x \in R\) (set of real numbers):

The total cost function is given by \(C(x)=\frac{1}{3} x^3-5 x^2+30 x-15\) and selling price per unit is Rs. 6. The profit is maximum if the value of x is:

If \(u=\sin ^{-1}\left(\frac{2 x}{1+x^2}\right)\) and \(v=\tan ^{-1} x, x \in(-1,1)\), then \(\frac{d u}{d v}\) is equal to:

The area of a triangle whose vertices are (-3,0), (3, 0) and (0, k) is 6. Then the value (or the values) of k will be:

For the given five values 15, 24, 18, 33, 42, the three-year moving averages are :

A very long straight wire carries a current (I) directed along positive Y-axis. A point charge +Q moves with velocity (v) along X -axis. The direction of force on the charge at point (5,0,0) m is

The ratio of intensities of two waves is 16:1. If these two are superimposed, What is the ratio of maximum and minimum intensities?

A boat 10 m high floating at a uniform speed of 13 meters per minute \(( m / min )\) away from a lamp post 15 m high.
Then the rate at which the length of shadow of the boat increases is :

Calculate the separation of two points on moon that can be resolved using 600 cm telescope. Given distance of moon from earth \(= 3.8 \times 10^{10}\) cm. The wavelength most sensitive to eye is \(5.5 \times 10^{-5}\) cm.

Match List I with List II

LIST I	LIST II
A. Multimolecular colloids	I. Nitro cellulose
B. Macromolecular colloids	II. Sulphur molecule
C. Associated colloids	III. Nylon
D. Colloidion	IV. Soaps

Choose the correct answer from the options given below:

Answer the question on basis of passage given below :
The noble gases have closed shell electronic configuration and are monatomic gases under normal conditions. The low boiling points of lighter noble gases are due to the weak dispersion forces between the atoms and the absence of other inter atomic interaction. The direct reaction of xenon with fluorine leads to
of compounds with oxidation numbers +2, +4 and +6.
XeF4 reacts violently with water to give XeO3. The compound of Xenon exhibit stereoisomerism and their geometries can be deduced considering the total number of electrons in the valence shell.
Argon is used in arc welding because it has