
Which of the following is/are true about A',B',C'andD' ? A. Order of atomic radii: \( B' < A' < D' < C' \)
B. Order of metallic character: \( B' < A' < D' < C' \)
C. Size of the element: \( D' < C' < B' < A' \)
D. Order of ionic radii: \( B^{+} < A^{+} < D^{+} < C^{+} \)
Choose the correct answer from the options given below:
To determine which statements are true about elements A', B', C', and D', we refer to the periodic trends:
Let's evaluate each option:
Thus, the correct answer is: A, B, and D only.
Analysis of each statement:
Statement A: Order of atomic radii \(B' < A' < D' < C'\). The atomic radii decrease from left to right in a period and increase from top to bottom in a group. This order is correct.
Statement B: Order of metallic character \(B' < A' < D' < C'\). Metallic character decreases from left to right in a period and increases from top to bottom in a group. This order aligns with the general trend, so this statement is correct.
Statement C: Size of the element \(D' < C' < B' < A'\). This statement would be correct if we consider ionic sizes and periodic trends, but based on the provided context, this order does not match general atomic radius trends. This statement is incorrect.
Statement D: Order of ionic radii \(B^+ < A^{++} < D^{++} < C^{++}\). Ionic radii depend on the effective nuclear charge and the number of electrons lost. This order is correct based on typical ionic sizes across groups and periods.
Thus, the correct answer is: A, B, and D only.

Given below are two statements:
Statement (I):
are isomeric compounds.
Statement (II):
are functional group isomers.
In the light of the above statements, choose the correct answer from the options given below:
If the domain of the function \( f(x) = \frac{1}{\sqrt{3x + 10 - x^2}} + \frac{1}{\sqrt{x + |x|}} \) is \( (a, b) \), then \( (1 + a)^2 + b^2 \) is equal to:
A point particle of charge \( Q \) is located at \( P \) along the axis of an electric dipole 1 at a distance \( r \) as shown in the figure. The point \( P \) is also on the equatorial plane of a second electric dipole 2 at a distance \( r \). The dipoles are made of opposite charge \( q \) separated by a distance \( 2a \). For the charge particle at \( P \) not to experience any net force, which of the following correctly describes the situation?

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Choke coil is simply a coil having a large inductance but a small resistance. Choke coils are used with fluorescent mercury-tube fittings. If household electric power is directly connected to a mercury tube, the tube will be damaged.
Reason (R): By using the choke coil, the voltage across the tube is reduced by a factor \( \frac{R}{\sqrt{R^2 + \omega^2 L^2}} \), where \( \omega \) is the frequency of the supply across resistor \( R \) and inductor \( L \). If the choke coil were not used, the voltage across the resistor would be the same as the applied voltage.
In light of the above statements, choose the most appropriate answer from the options given below: