The function \(f(x)=x^2 e^{-2 x}\) increases on

The side of an equilateral triangle increases at the rate of \(3 cm / sec\), then the rate at which the area of the triangle increases when the side is 4 cm , is :

If A and B square matrices of order 3 such that |A|= -1, |B|= 5, then the value of |2AB| is:

The area bounded by the curve \(y =\sin x\) between \(x =0\) and \(x =2 \pi\) is

The number of arbitrary constants in the general solution of a differential equation with degree 1 and order 3, is

The interval on which the function \(f(x)=x^4-\frac{x^3}{3}\) is strictly decreasing, is :

For the differential equation \((x+y) d y+(x-y) d x=0\), which of the following is/are correct?
(A) Differential equation is homogeneous
(B) Order of differential equation is 1
(C) Integrating factor of differential equation is \(e ^{ x }\)
(D) Degree of the equation is not defined
Choose the correct answer from the options given below:

A' can run 1 km in 5 minutes 20 seconds and 'B' can run the same distance in 6 minutes. How many meters start can 'A' give 'B' in a kilometer race so that they finish the race together?

Match List-l with List-II

List-l (Type of solution)	List-II (Example)
(A) solid in solid	(I) Camphor in \(N_2\)
(B) solid in gas	(II) Cu in Au
(C) gas in solid	(III) Hg in Na
(D) liquid in solid	(IV) \(H_2\) in Pd

Choose the correct answer from the options given below :

Read the passage carefully and answer the Questions
The concentration dependence of the rate of a reaction is called the differential rate equation. It is not always convenient to determine the instantaneous rate, as it is measured by calculating the slope of the tangent at point 't' in the concentration vs time plot. This makes it difficult to determine the rate and hence the order of the reaction. This difficulty is overcome by integrating the differential rate equation. This integrated rate equation gives a direct relation between concentrations at different times and the rate constant. The integrated rate equations are different for the reactions having different reaction orders.
A reaction is first order in A and second order in B. If the concentration of B is doubled its initial concentration and A is reduced to 3/4th of its initial concentration, the new rate of the reaction is

The electric field and magnetic field of a plane electromagnetic wave propagating in vacuum are expressed as
\(E_x=E_0 \sin (k z-\omega t)\)
\(B_y=B_0 \sin (k z-\omega t)\)
Which of the following statements are correct?
(A). The wave is propagating along the z- direction.
(B). The electric field Ex and magnetic field By are perpendicular to each other and perpendicular to the z direction.
(C) The electric and magnetic fields Ex and By are perpendicular to each other, and parallel to the direction of propagation.
(D) k is related to the wave length À of the wave by the usual equation \(k = A / 2 Tt\)
Choose the correct answer from the options given below:

In Young's double slit experiment, the light has a frequency \( 12 \times 10^{14} \text{ Hz} \) and the distance between the centres of adjacent fringes is 0.8 mm. If the screen is 1.6 m away, what is the distance between the slits? (Take speed of light \( c = 3 \times 10^8 \text{ m s}^{-1} \))

Oral pills used by females for contraception consists of combination of: