If \(\left|\begin{array}{cc}2 & 3-x \\ x & 1\end{array}\right|=0\), then the values of x are:

If \(A=\left[\begin{array}{ccc}0 & x^2-6 & -3 \\ -x & 0 & -8 \\ x^2-2 x & 8 & 0\end{array}\right]\) is a skew symmetric matrix, then the value(s) of \(x\) is/ are -
(A) 3
(B) -3
(C) -2
(D) -1
Choose the correct answer from the options given below :

If A is a square matrix of order 3 and \(|A|=-5\), then \(|3 A|\) is equal to

The straight line \(\frac{x+3}{3}=\frac{y+2}{4}=\frac{z+1}{0}\) is

If the binomial distribution \(X \sim B(n, p)\) has mean 3 and variance \(\frac{3}{2},(p+q)=1\), then which of the following is/are TRUE?
(A) \(q=\frac{1}{2}, n=6\)
(B) \(P(X \leq 5)=\frac{63}{64}, p=\frac{1}{2}\)
(C) \(q=\frac{1}{3}, p=\frac{2}{3}\)
(D) \(P(X=4)=\frac{15}{64}, n=6\)
Choose the correct answer from the options given below:

The differential coefficient of \(\log _e\left[\log _e\left(\log _e x^5\right)\right]\) with respect to \(x\) is:

A swimmer's speed in still water is \(6 km / hr\). He swims between two points in a river and returns back to the starting point. He took 24 minutes more to cover the distance

The least non-negative remainder when \(2^{101}\) is divided by \(5\) is:

Choose the correct statement for the collision theory of chemical reactions

Which of the following electrolytes will have maximum coagulating value for \(\text{AgI/Ag}^{+}\) sol?

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.
Conformers have not evolved to become regulators because:

At any instant t the values of voltage applied and the current through a series LCR circuit are given as : \( V = \frac{1}{\sqrt{2}} \sin(100\pi t) \text{ V}, I = \frac{1}{\sqrt{2}} \sin(100\pi t + \frac{\pi}{3}) \text{ A} \). The average power consumed in the circuit is given by :

If the mass of a proton is \( m_p = 1.007825 \text{ u} \) and the mass of the neutron is \( m_n = 1.008665 \text{ u} \), the mass defect in the formation of \( {}_{3}^{7}\text{Li} \) nucleus is: (take the mass of Lithium nucleus as \( M_{Li} = 7.000000 \text{ u} \))