The direction ratios of the perpendicular from the point \((1,0,1)\) to the plane \(x-y+z=0\) are :

If \(A=\left[\begin{array}{cc}-2 & 3 \\ 1 & 2\end{array}\right]\) and \(B=\left[\begin{array}{cc}-1 & 0 \\ 2 & 3\end{array}\right]\), then \((3 A+2 B)^{\prime}\) is:

The area (in sq. units) of the region \(\left\{(x, y): 3 x^2 \leq y \leq|x|\right\}\) is equal to :

The non-negative remainder when \(7^{30}\) is divided by 5 is :

The area bounded by the curve \(y=-x|x|\), the \(x\)-axis and the ordinates \(x=-1\) and \(x=1\) is given by:

The planes 2x - y + 4z = 5 and \(5 x-\frac{5}{2} y+10 z=6\) are

The condition on \(a\) and \(b\), such that for \(y=\frac{a}{x}-\frac{b}{x^2}, \frac{d y}{d x}=0\) at \(x=1\) is :

Arrange the following in the increasing order of their solubility in n-octane on the basis of their solute-solvent interaction:
(A) KCI
(B) CH3OH
(C) CH3CN
(D) Cyclohexane
Choose the correct answer from the options given below:

Which of the following is a statistic?

A 400 pF capacitor is charged by a 200 V supply. It is then disconnected from the supply and is connected to another uncharged 400 pF capacitor. The electrostatic energy lost in the process is

Match the electromagnetic waves in Column-I with production methods in Column-II

Column-I (Electromagnetic Waves)	Column-II (Production Methods)
(A) Microwaves	(I) LC oscillator
(B) Infrared	(II) Magnetron
(C) X-rays	(III) Vibration of atoms/molecules
(D) Radio waves	(IV) Bombarding large atomic number metal target with fast-moving electrons

Choose the correct answer from the options given below :

If the optimal value of the objective function \(z=p x+y\) of an L.P.P occurs at two corner points \((2,11)\) and \((4,5)\) of its bounded feasible region, then its optimal value is

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