If a matrix has 8 elements then the possible order(s) it may have
(A) 8 x 1
(B) 5 x 3
(C) 6 x 2
(D) 2 x 4
Choose the correct answert from the option given below :

If the lines \(\frac{1-x}{3}=\frac{3 y-6}{k}=\frac{3-z}{-2}\) and \(\frac{1-x}{2 k}=\frac{y-5}{3}=\frac{6-z}{5}\) are perpendicular, then \(k\) is equal to :

If \(A\) and \(B\) are independent events such that \(P(A \mid B)=\frac{1}{3}\) and \(P(B)=\frac{1}{2}\), then the value of \(P(A \cap B)\) is equal to :

If \(a, b\) and \(c\) are positive real numbers, then
Match List-I with List-II

List-I (Expression)	List-II (The Least value of the expression)
(A) \((a+b)(b+c)(c+a)\)	(I) \(8 a b c\)
(B) \((a+b+c)(a b+b c+c a)\)	(II) \(9 a^2 b^2 c^2\)
(C) \(\left(a^2+b^2+c^2\right)\left(a b^2+b c^2+c a^2\right)\)	(III) \(9 a b c\)
(D) \((a+b)^2(b+c)^2(c+a)^2\)	(IV) \(64 a^2 b^2 c^2\)

Choose the correct answer from the options given below:

A car starts from a point at time \(t = 0\) seconds and stops at Q.
The distance \(x\) in meters covered by it in \(t\) seconds is given by
\(x = t^2 \left( 2 - \frac{t}{3} \right)\).
The time taken by it to reach Q is:

An edge of a variable cube is increasing at the rate of 3 cm/s. How fast is the volume of the cube increasing when the edge is 10 cm long?

If \(f(x)=\left\{\begin{array}{ll}\frac{\tan \left(\frac{\pi}{4}-x\right)}{\cot 2 x}, & x \neq \frac{\pi}{4}, \\ 2 K+1, & x=\frac{\pi}{4},\end{array}\right.\) is continuous at \(x=\frac{\pi}{4}\), then the value of \(K\) is equal to

Let \(X\) denote the number of tails in two tosses of a coin. If the mean and the variance of \(X\) are \(\mu\) and \(\sigma^2\) respectively, then \(\mu+\sigma^2\) is equal to:

The electric potential at a point in an electric field is \( 8 \times 10^4 \text{ V} \). The work done to bring a point charge \( 5 \times 10^{-9} \text{ C} \) from infinity to this point is:

The properties which depend on the number of solute particles irrespective of their nature relative to the total number of particles in the solution are called colligative properties. These are relative lowering of vapour pressure of the solvent, depression of freesing point of the solvent, elevation of boiling point of the solvent and osmotic pressure of the solution. All of these properties help in calculating the observed molar mass of the solute.
Determination of osmotic pressure is considered best for the determination of molecular mass of the solute.
The binary liquid mixtures which show negative deviation from Raoult's law are :
(A) n-hexane and n-heptone
(B) phenol and acetone
(C) ethanol and acetone
(D) chloroform and acetone
(E) benzene and toluene
Choose the correct answer from the options given below :

Typical embryo sac at maturity is:

Which of the following is NOT a basic step in the genetic modification of an organism?

In the circuit diagram shown in the figure, the resistance \( R_1 = 10 \, \Omega \), \( R_2 = 15 \, \Omega \) and E= 20 V. When the switch S is closed, the ratio of \( i_1 \) to \( i_3 \) will be: