The value of \(\int \frac{\cos x d x}{(1+\sin x)(2+\sin x)}\) is :

The solution of the differential equation \((x+1) \frac{d y}{d x}+1-2 e^{-y}=0 ; y(0)=0\) is

For a \(3 \times 3\) matrix \(A=\left[a_{i j}\right]\), whose element \(a_{i j}\) is given by \(a_{i j}=\sqrt{i^2+3 j}\), then what is element \(a_{31}\) ?

If A and B are two events such that \(P(A) \neq 0\) and \(P(A / B)=1\) then :

The value of \(\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\left(x^3+x \cos x+\tan ^5 x+1\right) d x\) is:

The value of \(\tan ^{-1} 1+\cos ^{-1}\left(-\frac{1}{2}\right)+\sin ^{-1}\left(-\frac{1}{2}\right)\) is

In a linear programming problem, the linear constraints are as follows :
\(x-3 y \geq 0, y \geq 0,0 \leq x \leq 6 \)
where \(z=x+2 y\)
Which of the following statement/s is/are correct ?
(A) The feasible region is not the first quadrant
(B) The feasible region is unbounded in the first quadrant
(C) The feasible region is bounded in the first quadrant
(D) The feasible region is a triangular region
(E) The maximum value of \(z\) is 10
Choose the correct answer from the options given below :

The area (in sq.units) of region bounded by \(y^2=9 x, x=2, x=4\) and the \(x\)-axis in the first quadrant is

The decreasing order of basicity of following amines in aqueous phase ;
(A) N, N-Dimethylmethamine
(B) Methanamine
(C) N-Ethylethanamine
(D) Phenylmethanamine
Choose the correct answer from the options given below :

The area bounded by \(x = 1, x = 2, xy = 1\) and x-axis is :

In Young's double slit experiment using monochromatic light of wavelength \(\lambda\), the intensity of light at a point on the screen where path difference is \(\lambda\), is 'T' units. What is the intensity of light at a point where path difference is \(\frac{\lambda}{4}\) ?

Which of the following are correct?
(A) A statistical hypothesis is a statement about the population parameter which may be true or false.
(B) In a statistical hypothesis testing procedure, a Type I error is made when the null hypothesis is accepted when it is false.
(C) In a statistical hypothesis testing procedure, a Type II error is made when the null hypothesis is rejected when it is true.
(D) The number of degrees of freedom of a statistic is the number of independent variates used to compute that statistic.
Choose the correct answer from the options given below :

Answer the question on basis of passage given below :
Adsorption is surface phenomenon and it differs from absorption which occurs throughout the body of the substance which absorbs. In physisorption the attractive forces are mainly van der Waal forces while in chemisorption actual bonding occurs between the particles of adsorbent and adsorbed more easily on the surface of a solid as compared to the gases which are liquified with difficulty. Adsorption increases with the increases in pressure and decreases as temperature is increased.
The ease with which the gases \(H _2, CH _4, CO _2 \backslash \& NH _3\) are adsorbed on the surface of charcoal is -