A proton accelerated through potential difference V has de Broglie wavelength \(\lambda\). On doubling the potential, the de Broglie wavelength of the proton :

If a line makes angles \(\alpha, \beta\) and \(\gamma\) with positive \(x\)-axis, \(y\)-axis and \(z\)-axis respectively, then the value of \(\sin ^2 \frac{\alpha}{2} \cos ^2 \frac{\alpha}{2}+\sin ^2 \frac{\beta}{2} \cos ^2 \frac{\beta}{2}+\sin ^2 \frac{\gamma}{2} \cos ^2 \frac{\gamma}{2}\) is

Particular solution of the differential equation \(\log \left(\frac{d y}{d x}\right)=x+y\) given that when x = 0 y = 0 is:

A car starts from a point \(P\) at time \(t=0\) seconds and stops at \(Q\).
The distance \(x\), in meters, covered by it in \(t\) seconds is given by \(x(t)=t^3\left(3-\frac{t^2}{5}\right)\).
The distance between \(P\) and \(Q\) is:

The values of x and y in \(\left[\begin{array}{l}2 x+y \\ x+2 y\end{array}\right]=\left[\begin{array}{l}4 \\ 5\end{array}\right]\) are :

Consider \(f: R ^{+} \rightarrow[4, \infty)\) given by \(f(x)=x^2+4\)
(where \(R ^{+}\)is set of non negative real numbers) then \(f^{-1}(x)\) is :

The interval, on which the function \(f(x)=x^2 e^{-x}\) is increasing, is equal to:

The value of \(\int_0^{\frac{\pi}{2}} \frac{\sqrt{\cot x}}{\sqrt{\tan x}+\sqrt{\cot x}} d x\) is:

The correct arrangement of electromagnetic spectrum in decreasing order of wavelength is :

Read the following passage carefully and answer the given questions
The earthworm is referred to as the farmer's friend. This is because they help in the breakdown of complex organic matter as well as in loosening of soil. Similarly, decomposers break down complex organic matter into inorganic substances like carbon dioxide, water and nutrients and the process is called decomposition. Dead plant remains such as leaves, bark, flowers and dead remains of animals, including fecal matter, constitute detritus, which is the raw material for decomposition. Some of the steps in the process of decomposition are fragmentation, catabolism, leaching, humification etc.
The degradation of detritus into simpler inorganic substances by the bacterial and fungal enzymes is called as-

The self inductance of a coil is 200 \( \mu \)H, current changes by 1 A in 0.05 sec. What is the emf produced?

o-Nitrophenol is less soluble in water than p-nitrophenol because :

Match List - I with List - II.

List - I	List - II
A. Simple and face centred cubic	I. \(\text{a} = \text{b} = \text{c}\)
B. Cubic and rhombohedral	II. \(\alpha = \beta = \gamma = 90°\)
C. Cubic and tetragonal	III. have only two crystallographic angle of \(90°\)
D. Hexagonal and monoclinic	IV. belong to the same crystalline system

Choose the correct answer from the options given below :