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

Let \(L_1\) and \(L_2\) be two lines, represented as,
\(L_1: \vec{r}=\hat{i}+\hat{j}+\lambda(2 \hat{i}-\hat{j}+\hat{k})\) and \(L_2: \vec{r}=2 \hat{i}+\hat{j}-\hat{k}+\mu(4 \hat{i}-2 \hat{j}+2 \hat{k})\), where \(\lambda\) and \(\mu\) are scalars. Then which of the following are true?
(A)\(L_1\) is perpendicular to \(L_2\)
(B) \(L_1\) is parallel to \(L_2\)
(C) \(L_1\) passes through the point (1,1,0)
(D) \(L_2\) passes through the point (2,1,-1)
Choose the correct answer from the options given below:

Match List - I with List - II.

List - I	List - II
(A) \(\int_{-1}^1|x| d x\)	(I) 0
(B) \(\int_{-\pi / 2}^{\pi / 2} \sin x d x\)	(II) 2
(C) \(\quad \int_{-\pi / 2}^{\pi / 2} \cos x d x\)	(III) \(\pi / 4\)
(D) \(\quad \int_0^{\pi / 2} \sin ^2 x d x\)	(IV) 1

Choose the correct option from the ones given below :

The rate of change of area of a circle with respect to its circumference when radius is 6 cm, is

\(\int_0^{\pi / 2} \frac{\sin ^8 x}{\sin ^8 x+\cos ^8 x} d x\) is equal to

The area of region bounded by the curve \(y^2=4 a x\) and the straight line \(x=2 a, a>0\) in the first quardant is:

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 corner points of the bounded feasible region of the LPP: Maximise \(Z = x + y\) subject to constraints \(2x + 5y ≤ 100, 8x + 5y ≤ 200 x ≥ 0 y ≥ 0\) are

Rainbow is a phenomenon due to the combined effect of
(A) Interference
(B) Dispersion
(C) Reflection
(D) Refraction
(E) Scattering
Choose the correct answer from the options given below:

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 Characteristic of physical adsorption is that it is :

If \(f(x)=\left\{\begin{array}{ll}\frac{1-\tan x}{4 x-\pi} & x \neq \frac{\pi}{4} \\ k & x=\frac{\pi}{4}\end{array}\right.\) is continuous at \(x=\frac{\pi}{4}\), then the value of \(k\) is

Which of the following classes of compounds on hydrolysis yields carboxylic acids?
(A) RCN
(B) \(RCONH_{2}\)
(C) RCOCl
(D) RCOOR'
Choose the \textbf\{correct answer\} from the options given below:

Which of the following sugar is non-reducing?