If \(\cos ^{-1} \sqrt{3} x+\cos ^{-1} x=\frac{\pi}{2}\), then the value of \(x\) is :

\(I=\int a^{5 x+3} d x\) is :

The value of \(\tan \left(\cos ^{-1} x\right)\) is:

The value of the determinant \(\left|\begin{array}{ccc}a+1 & b & c \\ a & b+1 & c \\ a & b & c+1\end{array}\right|\) is :

Which one of the following inequalities is redundant for the shaded feasible region (ABCDA) shown below?

In a game of billiards, A can give B 15 points in 60 and A can give C 20 points in 60.
How many points can B give C in a game of 90?

Match List-I with List-II

List-I	List-II
(A) \(f ( x )=| x |\)	(I) Not differentiable at \(x=-2\) only
(B) \(f(x)=|x+2|\)	(II) Not differentiable at \(x=0\) only
(C) \(f(x)=\left|x^2-4\right|\)	(III) Not differentiable at \(x=2\) only
(D) \(f(x)=|x-2|\)	(IV) Not differentiable at \(x=2,-2\) only

Choose the correct answer from the options given below:

If \(\left|\begin{array}{cc}2 x & 2 \\ 4 & x\end{array}\right|=10\), then \(x\) is:

The force between two small charged spheres having charges of \( 0.2 \, \mu\text{C} \) and \( 0.6 \, \mu\text{C} \) placed 0.6 m apart in air will be:

Two thin lenses of focal lengths \( f_1 \) and \( f_2 \) are in contact and coaxial. The power of the combination is:

A transistor is operated in common emitter configuration at \(V_c = 3V\) such that a change in the base current from \(50 \mu A\) to \(250 \mu A\) produces a change in the collector current from 5 mA to 20 mA. The current gain is :

Answer the question on the basis of passage given below :
A colloid is a heterogeneous system in which a substance is dispersed (dispersed phase) as fine particles in another substance called dispersion medium.
Their particle size is intermediate between that of pure solutions (less than 1 nm ) and suspensions (greater than 1000 nm ).
They are known for interesting properties such as enormous surface area, Tyndall effect, Brownian motion etc.
They are widely used in industries and day to day life.
Some prominent uses of colloids are those in smoke precipitators, purification of water, medicines, cleansers etc.
Stability of a colloid is intermediate between that of a solution and suspension. This stability can be attributed to _____________
A. Presence of charge on the particles of dispersed phase.
B. Prolonged mechanical stirring.
C. Solvation by the dispersion medium.
D. Brownian Motion.
E. Dialysis
Choose the correct answer from the options given below :

Observed and calculated values for the standard electrode potentials \(\left(M^{2+} \rightarrow M\right)\) are shown in the figure above.
Based on the data shown, which of the following statements are true?
(A) Cu is not able to liberate \(H _2\) from acid.
(B) Zn is not able to liberate \(H _2\) from acid.
(C) An increase in the sum of the first and second ionization enthalpies leads to lessnegative \(E^{\circ}\) values.
(D) Only oxidising acids react with Cu.
Choose the correct answer from the options given below: