The area enclosed between the graph of \(y=x^3\) and the lines \(x=0, y=1, y=8\) is

Let L be the set of all lines in a plane and R be the relation on set L defined by \(R=\left\{\left(L_1, L_2\right) : L_1 \perp L_2\right\}\). Then R is
(A) an equivalence Relation
(B) a symmetric Relation
(C) not a transitive Relation
(D) a reflexive Relation
Choose the correct answer from the options given below :

The solution of the differential equation \(\frac{d y}{d x}-\frac{y}{x}=2 \log _e x\)

If \(A, B\) are symmetric matrices of the same order, then \(A B-B A\) is a :

Consider the following statements :
(A) \(\int_{-a}^a f(x) d x=2 \int_0^a f(x) d x\) if \(f(-x)=-f(x)\)
(B) \(\int_a^b f(x) d x=\int_a^b f(t) d t\)
(C) \(\int_0^a f(x) d x=\int_0^a f(x-a) d x\)
(D) \(\int_a^b f(x) d x=\int_a^b f(a+b-x) d x\)
Choose the correct answer from the options given below :

The function \(f(x)=x+\frac{1}{x}\) has

Area bounded by the curve \(y=\cos ^{-1} x\) and the lines \(x=0, x=1\) is:

Match List - I with List - II.

LIST I (Use of transgenic animal)	LIST II (Work done)
A. Emphysema	I. Polio vaccine
B. Human alpha-lactalbumin	II. Rosie
C. Transgenic mice	III. Toxin sensitive transgenic animal
D. Chemical safety testing	IV. α-1-antitrypsin

Choose the correct answer from the options given below:

The ratio of magnetic fields at the centre of a current carrying a circular loop of radius 16 cm and at a point on its axis at a distance r from its centre is 125 : 64. The value of r is

The straight line \(\frac{x+2}{3} = \frac{z-3}{-2}, y=2\) is

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:

Two point charges of 2 C each are separated from each other by a distance of 1 m in water (K = 80). The force between the charges is:

Question based on following passage :
Adsorption is the process of attracting and retaining the adsorbate molecules on the surface of adsorbent. It is of two types i.e. Physisrption and chemisorption. To increase the rate of reaction, the substance called 'catalyst' is added. Promotors enhance the activity of catalyst while poison decrease the catalyst activity. Solutions may be true solution, suspension and colloids. Colloids are heterogenous but quite stable. On the basis of nature of interaction, colloids may be Lyophilic or Lyophobic. On the basis of type of dispersed phase particles, there may be multimolecular colloids, macromlecular colloids and associated colloids. The congulation of colloids may be done by boiling, dialysis or by mixing oppositely charged sols.
The best coagulating agent for \(Fe(OH)_3\) solution is :