What will be the value of ( n )-factor ( \left( \mathrm{n}_{\mathrm{f}} \right) ) or valence factor of P in ( \mathrm{Ca}_{3} \mathrm{P}_{2} ) and ( \mathrm{H}_{3} \mathrm{PO}_{4} ) respectively for the following change:

[ \mathrm{Ca}_{3} \mathrm{P}_{2} \rightarrow \mathrm{H}_{3} \mathrm{PO}_{4} ]

(A) 10, 5
(B) 4, 8
(C) 16, 8
(D) 3, 3

$f(x)$ is a real-valued function defined as

$$f(x) = \left[\log_{\sqrt{2}}\left(\sin\left(\ln\left(\frac{\sqrt{4-x^{2}}}{1-x}\right)\right) + \cos\left(\ln\left(\frac{\sqrt{4-x^{2}}}{1-x}\right)\right)\right)\right]$$

where [.] denotes the greatest integer function.

Then which of the following statements are true?

A. The number of integers in the domain of $f(x)$ is 2.
B. The number of integers in the domain of $f(x)$ is 3.
C. The range of $f(x)$ is the set of all non-positive integers $\cup {1}$.
D. The range of $f(x)$ is the set of all positive integers.

The yellow-green pigment is found in
Option 1) Rhodophyta

Option 2) Chlorophyta

Option 3) Phaeophyta

Option 4) Xanthophyta

If ( |z| = 1 ) and ( z \neq \pm 1 ), then all the values of ( \frac{z}{1 - z^{2}} ) lie on:

A. A line not passing through the origin
B. ( |z| = \sqrt{2} )
C. The X-axis
D. The Y-axis

A trader marks his goods such that he can make a 32% profit after giving a 12% discount. However, a customer availed a 20% discount instead of 12%. What is the new profit percentage of the trader?

Option 1) 20%
Option 2) 44%
Option 3) 30%
Option 4) 28.8%

What is a solution?

India gained independence in ______.
Option 1) 1946
Option 2) 1947
Option 3) 1948
Option 4) 1949

Which of the following is/are correct for 17 g/L of H₂O₂ solution?
A. Volume strength is 5.6 at 273 K and 1 atm.
B. Molarity of solution is 0.5 M.
C. 1 mL of this solution gives 2.8 mL O₂ at 273 K and 2 atm.
D. The normality of the solution is 2 N.

If tangents are drawn from points on the hyperbola (\frac{x^{2}}{4}-\frac{y^{2}}{9}=1) to the circle (x^{2}+y^{2}=4), then the locus of the mid-point of the chord of contact is

A (x^{2}+y^{2}=\frac{x^{2}}{9}-\frac{y^{2}}{4})
B (\left(x^{2}+y^{2}\right)^{2}=\frac{x^{2}}{4}-\frac{y^{2}}{9})
C (\left(x^{2}+y^{2}\right)^{2}=16\left(\frac{x^{2}}{4}-\frac{y^{2}}{9}\right))
D (\left(x^{2}+y^{2}\right)^{2}=9\left(\frac{x^{2}}{9}-\frac{y^{2}}{4}\right))

The cambial activity is maximum in spring and minimum in winter season respectively.

Which of the following is true?

Option 1) A median is a line joining the vertex to the midpoint of any side.
Option 2) A median always lies inside the triangle.
Option 3) The point of intersection of medians is known as the centroid.
Option 4) A centroid always lies inside the triangle.

Which of the following are the isotopes of hydrogen?

1. Deuterium
2. Tritium
3. Heavy water
4. Hydrates

Given ( \mathrm{A}=\left[\begin{array}{ll}p & 0 \ 0 & 2\end{array}\right], \mathrm{B}=\left[\begin{array}{cc}0 & -q \ 1 & 0\end{array}\right], \mathrm{C}=\left[\begin{array}{cc}2 & -2 \ 2 & 2\end{array}\right] ) and ( \mathrm{BA}=\mathrm{C}^{2} ), find the values of ( p ) and ( q ).

A) ( p=-8, q=-6 )
B) ( p=-8, q=-4 )
C) ( p=8, q=4 )
D) ( p=8, q=6 )

Find the coordinates of the points which bisect the line segment joining the points P(4, 2, -6) and Q(10, -16, 6).

Which of the following are true according to Dalton’s Atomic Theory?

(i) Atoms can neither be created nor destroyed in a chemical reaction.
(ii) Atoms of different elements have different masses and chemical properties.
(iii) Atoms can be broken down into smaller parts like protons, electrons, and neutrons.
(iv) Atoms of an element have variable chemical properties depending on the chemical reactions.
(v) The relative number and kinds of atoms vary in a given compound.
(vi) Atoms combine in the ratio of small whole numbers to form compounds.

Option 1) i, iii, v

Option 2) vi, ii, i

Option 3) i, ii, vi

Option 4) iv, v, vi

Compare and contrast nervous and hormonal mechanisms for control and coordination in animals.

Nervous mechanisms involve the rapid transmission of signals through the nervous system using neurons. This allows for quick responses to stimuli, enabling organisms to react swiftly to changes in their environment. The effects of nervous control are usually short-lived and specific to particular areas.

In contrast, hormonal mechanisms involve the release of hormones into the bloodstream, which can affect various tissues and organs throughout the body. This system typically operates more slowly than the nervous system, with responses often taking minutes to hours to manifest. However, hormonal effects can be long-lasting and more widespread, influencing growth, metabolism, and overall homeostasis.

In summary, the nervous system provides fast and localized responses, while the hormonal system offers slower but more prolonged and widespread effects. Both systems work together to ensure proper control and coordination in animals.

If getting a number greater than 4 on a fair die is considered a success, then the variance of the distribution of success on tossing a die five times is:

A) (\frac{5}{4})
B) (\frac{10}{9})
C) (\frac{2}{3})
D) (\frac{1}{3})

Interest paid on debentures and long-term loans and advances will result in cash from financing activities.

Option 1) Inflow

Option 2) Outflow

Option 3) Either inflow or outflow

Option 4) None of these

Identify the correct option that refers to 'Van der Waals forces'.
Option 1) Intermolecular forces.

Option 2) Intramolecular forces.

Option 3) Atomic forces.

Option 4) Molecular forces.

S1: The Supreme Court judges are recommended by the Chief Justice and the Cabinet ministry. S2: The judges of the Supreme Court change every 5 years, as and when the government changes. Select the option that is correct from the following:
Option 1) S1: True; S2: True; S2 is the reason for S1
Option 2) S1: True; S2: True; S2 and S1 are independent
Option 3) S1: True; S2: False
Option 4) S1: False; S2: True