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A thin uniform metallic spherical shell of mass \(2m\) and radius \(R\) is half-filled with wax, and the amount of wax required has mass \(m.\) If it is completely filled, the amount of wax required is \(2m.\)  The sphere is filled with wax until the level is at a height \(h\) above the centre \(O.\) The centre-of-mass of the entire system varies as a function of \(h.\) Which, of the following, correctly represents the \(y\)-coordinate \((y_{\text{cm}})\) of centre-of-mass as a function of \(h?\)

1.		2.
3.		4.

A block of mass \(m\) is released on the inclined face of smooth wedge of equal mass \(m,\) which lies on a smooth horizontal plane. The system is initially at rest. When the block reaches the bottom of the wedge, and just before it hits the plane, it has a horizontal velocity component (w.r.t., ground) of \(v.\) The velocity of the wedge is:
         

1.	\(v\)	2.	\(2v\)
3.	\(\dfrac{v}{2}\)	4.	zero

320 mg of a sample of magnesium having a coating of its oxide required 20 mL of 0.1 M hydrochloric acid for the complete neutralisation of the latter. The composition of the sample is:
1. 87.5% Mg and 12.5% MgO
2. 12.5% Mg and 87.5% MgO
3. 80% Mg and 20% MgO
4. 20% Mg and 80% MgO 
 

\(P\) is the probability of finding the \(1s\) electron of a hydrogen atom in a spherical shell of infinitesimal thickness (dr) at a distance \(r\) from the nucleus. The volume of this shell is \(4\pi r^ 2 dr\).
The qualitative sketch of the dependence of \(P\) on \(r\) is:

1.		2.
3.		4.

Given below are two statements:

Statement 1:	The correct increasing order of ionic radii is  \(Mg^{2+}, < Na^+ < F^- < O^{2-} < C^{4-} \)
Statement 2:	All these species are isoelectronic.

 

1.	Statement 1 is correct, Statement 2 is incorrect
2.	Statement 2 is correct, Statement 1 is incorrect
3.	Both Statement 1 and Statement 2 are correct
4.	Both Statement 1 and Statement 2 are incorrect

Match List I with List II:

	List I: Orbital overlap		List II: Type of bond
(P)		(1)	\(p-d \pi^*\)
(Q)		(2)	\(d-d \sigma\)
(R)		(3)	\(p-d \pi\)
(S)		(4)	\(d-d \sigma^*\)

 

	P	Q	R	S
1.	2	1	3	4
2.	2	3	1	4
3.	4	2	1	1
4.	4	1	3	2

For independent processes at 300 K:
\(\begin{array}{|c|c|c|} \hline \text { Process } & \Delta \mathbf{H} / \mathbf{k J} \mathrm{mol}^{-1} & \Delta \mathbf{S} / \mathrm{J} \mathrm{K}^{-1} \\ \hline \text { A } & -25 & -80 \\ \hline \text { B } & -22 & 40 \\ \hline \text {C} & 25 & -50 \\ \hline \text { D } & 22 & 20 \\ \hline \end{array} \)  
How many of the above processes are non-spontaneous?
1. 2 processes
2. 3 processes
3. 1 process
4. 4 processes
 

Consider the given two statements:

Assertion (A):	Methanogens are placed under Archaebacteria
Reason (R):	Methanogens possess unique cell wall and membrane compositions distinct from eubacteria

Choose the correct option:

1.	Both (A) and (R) are True and (R) is the correct explanation of (A).
2.	Both (A) and (R) are True but (R) is NOT the correct explanation of (A).
3.	(A) is True but (R) is False.
4.	(A) is False but (R) is True.

Consider the given two statements:

Assertion (A):	Diatoms are completely decomposed after death and do not contribute to geological deposits.
Reason (R):	The cell wall of diatoms is made of silica and lacks sporopollenin.

Choose the correct option:

1.	Both (A) and (R) are True and (R) is the correct explanation of (A).
2.	Both (A) and (R) are True but (R) is NOT the correct explanation of (A).
3.	(A) is True but (R) is False.
4.	(A) is False but (R) is True.

With reference to the urinogenital system of a male frog, consider the following statements:

A.	Ureters function as urinogenital ducts.
B.	Vasa efferentia open into the cloaca directly.
C.	Testes are attached to kidneys by a fold of peritoneum.

Which of the statements given above are correct?

1.	A and B only	2.	B and C only
3.	A and C only	4.	A, B and C

Consider the following statements with reference to gymnosperms:

A.	Ovules are not enclosed by ovary walls.
B.	Endosperm is formed before fertilisation.
C.	Male and female cones may occur on the same plant or on different plants.
D.	Water is essential for fertilisation.

How many of the above statements are correct?

1.	One	2.	Two
3.	Three	4.	Four

Consider the following animals:
(a) Ascaris

(b) Wuchereria

(c) Ancylostoma

(d) Pheretima

(e) Nereis

(f) Hirudinaria

(g) Taenia
How many of the above are pseudocoelomates, as described in NCERT?

1.	Two	2.	Three
3.	Four	4.	Five

Which of the following features is directly relevant to the function of a flower in sexual reproduction?

1.	Arrangement of leaves on the stem
2.	Presence of brightly coloured corolla
3.	Position of flower on the plant axis
4.	Type of inflorescence

A student places a plant cell in a hypertonic solution and observes shrinkage of the protoplast away from the cell wall. When the same cell is transferred back to distilled water, the protoplast regains its original position.
Which conclusion is MOST consistent with interpretation of this experiment?

1.	The cell wall is selectively permeable
2.	The plasma membrane allows differential movement of substances
3.	Water enters the cell by active transport
4.	Cell wall controls osmotic behaviour of the cell

A eukaryotic cell loses all internal membranes but retains enzymes, ribosomes, and genetic material. Surprisingly, most biochemical reactions still occur.
Which limitation would most critically reduce overall cellular efficiency?

1.	Reduced protein synthesis
2.	Loss of temporal coordination of reactions
3.	Inability to transport metabolites
4.	Failure of transcription

A protein loses its biological activity following mild heating but regains function upon cooling.
Which inference is most consistent with this observation?

1.	Covalent bonds remain intact
2.	Primary structure is altered
3.	Denaturation is necessarily irreversible
4.	Active site geometry is permanently destroyed

A population of cells was analysed at a given instant. The following proportions were recorded:

State	Proportion (%)
State X	52
State Y	33
State Z	15

Further analysis showed that DNA content in State Z was exactly double that of State X.
Which inference is most justified?

1.	Cells spend the longest duration in DNA synthesis
2.	Chromosome number doubles in State Z
3.	State X represents the most time-consuming phase
4.	Cell division occurs predominantly in State Y