If A and B are square matrix of order \(n \times n\), then \((A-B)^2\) is equal to
A. \(A^2-A B-B A+B^2\)
B. \(A^2-2 A B+B^2\)
C. \(A^2-2 B A+B^2\)
D. \(\quad A^2-B^2\)
E. \(A^2+2 A B+B^2\)
Choose the correct answer from the options given below:

Value of \(\mu(20)+\sigma(20)\) is (where \(\mu(n)\) is the Mobius function and \(o(n)\) is the sum of all positive divisors of \(n\) )

The integrating factor of the differential equation \(x \frac{d y}{d x}-y=2 x^2\) is :

If for the following data :

YEAR (X)	2000	2001	2002	2003	2004	2005	2006
PRODUCTION (iN TONNES) (Y)	40	45	46	42	47	50	46

the equation of the straight line trend is \(y=45.143+1.036(x-2003)\), then the trend value for the year 2004 is

The function \(f(x)=x^3+1\) is:

If \(x=a\left(\cos t+\log \tan \frac{t}{2}\right), y=a \sin t\), then value of \(\frac{d y}{d x}\) at \(t=\pi / 4\) is

If \(f(x) = \begin{cases} \frac{\sqrt{4+x}-2}{x}, & \text{if } x \neq 0 \\ k, & \text{if } x = 0 \end{cases}\) is continuous at \(x = 0\), then the value of k is:

In Sickle-cell anemia the substitution of amino acid in the globin protein results due to the single base substitution at the sixth codon of the \(\beta\)-globin gene from _________.

The value/s of \(\lambda\) for which the given system of equations will have infinitely many solutions \(x+y-6 z=0 ; \lambda x-y+2 z=0 ;-3 x+\lambda y+2 z=0\), is/are:

A point object is placed at a distance of 20 cm from a spherical lens of refractive index n=3/2 and the radius of curvature of each surface 10 cm. The distance of the image formed from the lens is

Why do light emitting diodes are preferred over conventional incandescent low power lamps?

Statins produced by the yeast variety is _______ which have been commercialised as blood-cholesterol lowering agents.

Read the passage carefully. Attempt the questions.
An overwhelming majority (99 per cent) of animals and nearly all plants cannot maintain a constant internal environment. Their body temperature changes with the ambient temperature. In aquatic animals, the osmotic concentration of the body fluids change with that of the ambient air and water osmotic concentration. These animals and plants are simply conformers. Considering the benefits of a constant internal environment to the organism, we must ask why these conformers had not evolved to become regulators. Recall the human analogy we used above; much as they like, how many people can really afford an air conditioner? Many simply 'sweat it out' and resign themselves to suboptimal performance in hot summer months. Very small animals are rarely found in polar regions. During the course of evolution, the costs and benefits of maintainin a constant internal environment are taken into consideration. Some species have evolved the ability to regulate, but only over a limited range of environmental conditions, beyond which they simply conform.
If the stressful external conditions are localised or remain only for a short duration, the organism has five other alternatives for survival.
Identify the statements which support the reason why small animals are rarely found in polar regions.
A. Small animals have larger surface area relative to their volume
B. Small animals have larger volume relative to their surface area
C. Shrews and humming birds are not found in polar region
D. Small animals have smaller surface area relative to their volume