If \(A=\left[\begin{array}{ll}1 & 2 \\ 4 & 5\end{array}\right]\) then
Match List-I with List-II

List-I	List-II
(A) \(\operatorname{det}(A)\)	(I) \(-\frac{1}{3}\)
(B) \(\operatorname{det}\left(A^{-1}\right)\)	(II) \(- 12\)
(C) \(\operatorname{det}(2 A)\)	(III) \(- 3\)
(D) \(\operatorname{det}\left( 3 A ^T\right)\)	(IV) \(- 27\)

Choose the Correct answer from the options given below :

The unit vector in the direction of \(\vec{a}+\vec{b}\) if \(\vec{a}=2 \hat{i}-\hat{j}+2 \hat{k} \& \vec{b}=-\hat{i}+\hat{j}-\hat{k}\) is:

The solution set of the linear constraints \(x-2 y \geq 0,2 x-y \leq-4, x \geq 0\) and \(y \geq 0\) is

Area lying between the curves \(y^2=9 x\) and \(y=3 x\) is:

\(\tan ^{-1} \frac{1}{\sqrt{3}}-\sin ^{-1} \frac{1}{2}\) is equal to :

For the given values 27, 35, 42, 45, 51, 34, 43; the five yearly moving averages are:

The term of the perpetuity is:

Which one of the following is a result of convergent evolution?

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 animal which is NOT a conformer.

In an AC generator, a 100 turns coil of area \( 0.10 \text{ m}^2 \) rotates at 50 Hz in a uniform magnetic field of 0.01 T. The maximum voltage generated in the coil is:

Match List I with List II.

LIST I	LIST II
A. Conida	I. Bryophyllum
B. Binary fission	II. Agave
C. Adventitious buds	III. Penicillium
D. Bulbil	IV. Amoeba

Choose the correct answer from the options given below:

Which of the following process does not occur at the interface of phases?

The interval in which the function f given by \(f(x)=x^3+\frac{1}{x^3}, x \neq 0\) is increasing: