datavorous/entrance-exam-dataset huggingface dataset:
What are the two functions of testes?

Options:
A Primary sex organ and endocrine gland
B Secondary sex organ and endocrine gland
C Primary sex organ and digestive gland
D Secondary sex organ and digestive gland

The correct answer is:
Primary sex organ and endocrine gland

Solution:
Testes performs dual functions as a primary sex organ as well as an endocrine glanD)

Topic: Biology, Chemical Coordination and Integration, NEET
What are the two types of lymphocytes present in our blood that carry out primary and secondary immune responses?

Options:
A Interferons
B B-lymphocytes and T-lymphocytes
C Antibodies
D Macrophages

The correct answer is:
B-lymphocytes and T-lymphocytes

Solution:
The primary and secondary immune responses are carried out with the help of two special types of lymphocytes present in our blood, i.e., B-lymphocytes and T-lymphocytes.

Topic: Biology, Human Health and Diseases, NEET
What are the unit vectors parallel to $x y$ -plane and perpendicular to the vector $4 \hat{i}-3 \hat{j}+\hat{k}$ ?

Options:
A $\pm(3 \hat{i}+4 \hat{j}) / 5$
B $\pm(4 \hat{i}+3 \hat{j}) / 5$
C $\pm(3 \hat{i}-4 \hat{j}) / 5$
D $\pm(4 \hat{i}-3 \hat{j}) / 5$

The correct answer is:
$\pm(3 \hat{i}+4 \hat{j}) / 5$

Solution:
A vector whose dot product with the vector $4 \hat{i}-3 \hat{j}+\hat{k}$ is zero and magnitude is 1 , will be the
required vectors. By taking option (a)
$\pm \frac{(3 \hat{i}+4 \hat{j})}{5} \cdot(4 \hat{i}-3 \hat{j}+\hat{k})=\frac{1}{5}(12-12)=0$
Hence, the vector given in option 'a' is the required vector.

Topic: Mathematics, Vector Algebra, NDA, NDA 2009 (Phase 2)
What are the units of standard enthalpy change, ∆r H?

Options:
A kJ
B kJ mol–1
C kJ/mol
D J

The correct answer is:
kJ mol–1

Solution:
Standard enthalpy change, ∆rH, is typically expressed in units of kJ mol–1, representing the enthalpy change per mole of substances specified by the equation.

Topic: Chemistry, Thermodynamics (C), NEET
What are the values of $p$ which satisfy the equation $\int_{0}^{P}\left(3 x^{2}+4 x-5\right) d x=p^{3}-2 ? \quad$

Options:
A $1 / 2$ and 2
B $-1 / 2$ and 2
C $1 / 2$ and $-2$
D $-1 / 2$ and $-2$

The correct answer is:
$1 / 2$ and 2

Solution:
Given equation,
$\int_{0}^{p}\left(3 x^{2}+4 x-5\right) d x=p^{3}-2$
$\Rightarrow\left[\frac{3 x^{3}}{3}+\frac{4 x^{2}}{2}-5 x\right]_{0}^{p}=p^{3}-2$
$\Rightarrow p^{3}+2 p^{2}-5 p=p^{3}-2$
$\Rightarrow 2 p^{2}-5 p+2=0$
$\Rightarrow 2 p^{2}-4 p-p+2=0$
$\Rightarrow 2 p(p-2)-1(p-2)=0$
$\Rightarrow(p-2)(2 p-1)=0$
$\Rightarrow p-2=0,2 p-1=0$
Hence the values of $p$ are $\frac{1}{2}$ and 2 .

Topic: Mathematics, Definite Integration, NDA, NDA 2008 (Phase 2)
What are the values of $x$ for which the two vectors
$\left(\mathrm{x}^{2}-1\right) \hat{\mathrm{i}}+(\mathrm{x}+2) \hat{\mathrm{j}}+\mathrm{x}^{2} \hat{\mathrm{k}}$ and $2 \hat{\mathrm{i}}-\mathrm{x} \hat{\mathrm{j}}+3 \hat{\mathrm{k}}$ are orthogonal?

Options:
A Noreal value of $x$
B $\mathrm{x}=\frac{1}{2}$ and $\mathrm{x}=-1$
C $\mathrm{x}=-\frac{1}{2}$ and $\mathrm{x}=1$
D $x=-1$ and $x=2$

The correct answer is:
$\mathrm{x}=-\frac{1}{2}$ and $\mathrm{x}=1$

Solution:
Ifvectors $\left(x^{2}-1\right) \hat{i}+(x+2) \hat{j}+x^{2} \hat{k}$ and $2 \hat{i}-x \hat{j}+3 \hat{k}$ are
orthogonal, then $2\left(x^{2}-1\right)-x(x+2)+3 x^{2}=0$
$\Rightarrow 2 x^{2}-2-x^{2}-2 x+3 x^{2}=0$
$\Rightarrow 4 \mathrm{x}^{2}-2 \mathrm{x}-2=0$
$\Rightarrow\left(2 \mathrm{x}^{2}-\mathrm{x}-1\right)=0$
$\Rightarrow(2 x+1)(x-1)=0$
$\Rightarrow \mathrm{x}=-\frac{1}{2}$ and $\mathrm{x}=1$

Topic: Mathematics, Vector Algebra, NDA, NDA 2006 (Phase 1)
What are the values of $(\mathrm{x}, \mathrm{y})$ satisfying the simultaneous
equations $\sin ^{-1} x+\sin ^{-1} y=\frac{2 \pi}{3}$ and $\cos ^{-1} x-\cos ^{-1} y=\frac{\pi}{3} ?$

Options:
A $(0,1)$
B $\left(\frac{1}{2}, 1\right)$
C $\left(1, \frac{1}{2}\right)$
D $\left(\frac{\sqrt{3}}{2}, 1\right)$

The correct answer is:
$\left(\frac{1}{2}, 1\right)$

Solution:
Given that
$\sin ^{-1} x+\sin ^{-1} y=\frac{2 \pi}{3}$ ...(i)
and $\cos ^{-1} x-\cos ^{-1} y=\frac{\pi}{3}$
$\Rightarrow \frac{\pi}{2}-\sin ^{-1} x-\frac{\pi}{2}+\sin ^{-1} y=\frac{\pi}{3}$
$\left[\right.$ since $\left.\cos ^{-1} x+\sin ^{-1} x=\frac{\pi}{2}\right]$
$\Rightarrow-\sin ^{-1} x+\sin ^{-1} y=\frac{\pi}{3}$ ...(ii)
On solving eq. (i) and (ii), we get
$2 \sin ^{-1} \mathrm{y}=\pi$ and $2 \sin ^{-1} \mathrm{x}=\frac{\pi}{3}$
$\Rightarrow \sin ^{-1} \mathrm{y}=\frac{\pi}{2}$ and $\sin ^{-1} \mathrm{x}=\frac{\pi}{6}$
Hence, $\mathrm{y}=\sin \frac{\pi}{2}$ and $\mathrm{x}=\sin \frac{\pi}{6}$
$\Rightarrow \mathrm{x}=\frac{1}{2}$ and $\mathrm{y}=1$

Topic: Mathematics, Inverse Trigonometric Functions, NDA, NDA 2006 (Phase 2)
What are $X$ and $Y$ in the following reaction?
Pent-2-ene $\underset{\text { (ii) } \mathrm{Zn}_{\mathrm{n} / \mathrm{H}_2 \mathrm{O}}}{\stackrel{\text { (i) } \mathrm{O}_3}{\longrightarrow}} X+Y$
\begin{array}{ll}\multicolumn{1}{c}{X} & \multicolumn{1}{c}{Y}
\end{array}

Options:
A $\mathrm{CH}_3 \mathrm{CHO}$ $\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{CHO}$
B $\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{CHO}$ $\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{CHO}$
C $\mathrm{CH}_3 \mathrm{CHO}$ $\left(\mathrm{CH}_3\right)_2 \mathrm{CO}$
D $\mathrm{CH}_3 \mathrm{CHO}$ $\mathrm{CH}_3 \mathrm{CHO}$

The correct answer is:
$\mathrm{CH}_3 \mathrm{CHO}$ $\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{CHO}$

Solution:

Topic: Chemistry, Hydrocarbons, AP EAMCET, AP EAMCET 2018 (22 Apr Shift 1)
What characteristic feature describes the spatial arrangement of ions/groups bound by secondary linkages in coordination compounds?

Options:
A It varies randomly
B It depends on the nature of the metal
C It corresponds to different coordination numbers
D It is always linear

The correct answer is:
It corresponds to different coordination numbers

Solution:
According to Werner's theory, the characteristic spatial arrangement of ions/groups bound by secondary linkages corresponds to different coordination numbers.

Topic: Chemistry, Coordination Compounds, NEET
What concept did Alfred Werner propose for metal ions in coordination compounds?

Options:
A Atomic number
B Primary valence and secondary valence
C Molecular weight
D Chemical reactivity

The correct answer is:
Primary valence and secondary valence

Solution:
Alfred Werner proposed the concept of primary valence and secondary valence for metal ions in coordination compounds.

Topic: Chemistry, Coordination Compounds, NEET
What conditions are necessary for the observation of the Tyndall effect, as mentioned in the paragraph?

Options:
A The diameter of dispersed particles is much smaller than the wavelength of light
B The refractive indices of dispersed phase and dispersion medium are similar
C The dispersion medium is opaque
D The refractive indices of dispersed phase and dispersion medium differ greatly in magnitude

The correct answer is:
The refractive indices of dispersed phase and dispersion medium differ greatly in magnitude

Solution:
According to the paragraph, the Tyndall effect is observed when the refractive indices of the dispersed phase and dispersion medium differ greatly in magnitude.

Topic: Chemistry, Surface Chemistry, NEET
What could be a possible reason for the sudden fish kill in the lake with an abundance of phytoplankton?

Options:
A The phytoplankton produced toxic chemicals.
B The phytoplankton depleted the oxygen in the water.
C Excessive sunlight caused a harmful algal bloom.
D The lake water was too acidic for fish survival.

The correct answer is:
The phytoplankton depleted the oxygen in the water.

Solution:
Correct Option is : (B)
The phytoplankton depleted the oxygen in the water.

Topic: Chemistry, Environmental Chemistry, NEET
What defines minerals suitable for metal extraction?

Options:
A Abundance
B Viability as ores
C Color
D Hardness

The correct answer is:
Viability as ores

Solution:
Only a few minerals, termed ores, are viable for extracting metals.

Topic: Chemistry, General Principles and Processes of Isolation of Metals, NEET
What determines the spatial arrangement of ions/groups bound by secondary linkages?

Options:
A It is fixed for all coordination compounds
B It depends on the nature of the ligands
C It corresponds to different coordination numbers
D It is always linear

The correct answer is:
It corresponds to different coordination numbers

Solution:
The spatial arrangement of ions/groups bound by secondary linkages corresponds to different coordination numbers in Werner's theory.

Topic: Chemistry, Coordination Compounds, NEET
What did Henry Moseley's work demonstrate about atomic number and atomic mass?

Options:
A Atomic number and atomic mass are unrelated.
B Atomic mass is more fundamental than atomic number.
C Atomic number is a more fundamental property than atomic mass.
D Atomic number and atomic mass are equal for all elements.

The correct answer is:
Atomic number is a more fundamental property than atomic mass.

Solution:
Henry Moseley showed that the atomic number is a more fundamental property of an element than its atomic mass.A plot of √v (where v is frequency of X-rays emitted) against atomic number (Z) gave a straight line and not the plot of vs atomic mass. He thereby showed that the atomic number is a more fundamental property of an element than its atomic mass

Topic: Chemistry, Classification of Elements and Periodicity in Properties, NEET
What distinction did Avogadro make between atoms and molecules in his proposal?

Options:
A Atoms and molecules are the same.
B Atoms cannot be combined.
C Atoms are larger than molecules.
D Atoms are smaller than molecules.

The correct answer is:
Atoms and molecules are the same.

Solution:
Avogadro made a distinction between atoms and molecules, which is now understandable, implying that he recognized that atoms and molecules are the same.

Topic: Chemistry, Some Basic Concepts of Chemistry, NEET
What distinguishes an open system from a closed system in thermodynamics?

Options:
A An open system has no boundaries, while a closed system has boundaries.
B An open system allows energy exchange, while a closed system does not.
C An open system allows both energy and matter exchange, while a closed system allows only energy exchange.
D An open system has fixed boundaries, while a closed system has flexible boundaries.

The correct answer is:
An open system allows both energy and matter exchange, while a closed system allows only energy exchange.

Solution:
The key distinction between open and closed systems is that open systems allow both energy and matter exchange with the surroundings, while closed systems only allow energy exchange.

Topic: Chemistry, Thermodynamics (C), NEET
What does "100 volume" hydrogen peroxide mean in terms of its oxygen production at STP?

Options:
A One milliliter of solution gives 100 mL of oxygen at STP
B One milliliter of solution gives 10 mL of oxygen at STP
C One milliliter of solution gives 50 mL of oxygen at STP
D One milliliter of solution gives 200 mL of oxygen at STP

The correct answer is:
One milliliter of solution gives 100 mL of oxygen at STP

Solution:
"100 volume" hydrogen peroxide means that one milliliter of the solution will give 100 mL of oxygen at standard temperature and pressure (STP).

Topic: Chemistry, Hydrogen, NEET
What does a positive value of standard electrode potential indicate?

Options:
A The species on the right is more stable than hydrogen gas.
B The species on the left is more stable than hydrogen gas.
C The species on the right is less stable than hydrogen gas.
D The species on the left is less stable than hydrogen gas.

The correct answer is:
The species on the right is more stable than hydrogen gas.

Solution:
If the standard electrode potential of an electrode is greater than zero (or positive) then its reduced form is more stable compared to hydrogen gas.

Topic: Chemistry, Electrochemistry, NEET
What does an equation of the first degree containing one arbitrary parameter passing through a fixed point represent?

Options:
A Circle
B Straight line
C Parabola
D Ellipse

The correct answer is:
Straight line

Solution:
From the given information, we have an equation of the first degree which contains one arbitraryparameter. Therefore the required equation represents a straight line

Topic: Mathematics, Straight Lines, NDA, NDA 2009 (Phase 1)
What does any deviation from the standard shape of ECG indicate?

Options:
A Normalcy
B Abnormality or disease
C Heart rate
D Cardiac cycle

The correct answer is:
Abnormality or disease

Solution:
Since ECGs obtained from different individuals have roughly the same shape for a given lead configuration, any deviation from this shape indicates a possible abnormality or disease.

Topic: Biology, Body Fluids and Circulation, NEET
What does E(cell) = Eo(cell) - 2.303RT / 2F log Kc provide a relationship between?

Options:
A Voltage and current
B Equilibrium constant and temperature
C Equilibrium constant and standard potential of the cell
D Temperature and pressure

The correct answer is:
Equilibrium constant and standard potential of the cell

Solution:
E(cell) = Eo(cell) - 2.303RT / 2F log Kcprovides a relationship between equilibrium constant and standard potential of the cell, as mentioned in the paragraph.

Topic: Chemistry, Electrochemistry, NEET
What does Eo(cell) represent?

Options:
A The cell's electromotive force
B The cell's equilibrium constant
C The cell's standard Gibbs energy
D The cell's charge passed

The correct answer is:
The cell's electromotive force

Solution:
Eo(cell) is the cell's electromotive force.

Topic: Chemistry, Electrochemistry, NEET
What does IUPAC stand for in the context of Coordination Chemistry nomenclature?

Options:
A International Union of Pure and Applied Chemistry
B International Organization for Standardization (ISO)
C International Atomic Energy Agency (IAE
A)
D International Chemical Society (ICS)

The correct answer is:
International Union of Pure and Applied Chemistry

Solution:
IUPAC stands for the International Union of Pure and Applied Chemistry, which provides recommendations for coordination chemistry nomenclature.

Topic: Chemistry, Coordination Compounds, NEET
What does knowledge of molecular structure help in understanding and predicting?

Options:
A Properties of inorganic compounds
B Properties of organic compounds
C Properties of gases
D Properties of metals

The correct answer is:
Properties of organic compounds

Solution:
Knowledge of fundamental concepts of molecular structure helps in understanding and predicting the properties of organic compounds.

Topic: Chemistry, General Organic Chemistry, NEET
What does Nernst's equation represent for the electrode reaction involving Mn+(aq) and M(s)?

Options:
A The standard hydrogen electrode potential for the reaction
B The concentration of solid M in the reaction
C The gas constant R value for the reaction
D The Faraday constant F value for the reaction

The correct answer is:
The standard hydrogen electrode potential for the reaction

Solution:
Nernst's equation represents the electrode potential at any concentration measured with respect to the standard hydrogen electrode for the electrode reaction involving Mn+(aq) and M(s).

Topic: Chemistry, Electrochemistry, NEET
What does STP stand for in the context of gases?

Options:
A Standard Test Parameters
B Standard Temperature and Pressure
C Specific Thermal Properties
D Standard Testing Procedures

The correct answer is:
Standard Temperature and Pressure

Solution:
STP stands for Standard Temperature and Pressure.

Topic: Chemistry, States of Matter, NEET
What does the decreasing standard electrode potential imply as we go from top to bottom in the series?

Options:
A The reducing power of the species on the left increases.
B The oxidizing power of the species on the left increases.
C The reducing power of the species on the right increases.
D Both B and C

The correct answer is:
Both B and C

Solution:
The paragraph explains that as we go from top to bottom in the series, the standard electrode potential decreases and with this, decreases the oxidising power of the species on the left and increases the reducing power of the species on the right hand side of the reaction.

Topic: Chemistry, Electrochemistry, NEET
What does the differential equation $y \frac{d y}{d x}+x=a$ (where $a$ is a constant) represent? $\quad$

Options:
A A set of circles having centre on the Y-axis
B A set of circles having centre on the $X$ -axis
C A set of ellipses
D A pair of straight lines

The correct answer is:
A set of circles having centre on the $X$ -axis

Solution:
Given differential equation is
$\frac{y d y}{d x}+x=a$
$\Rightarrow \quad y d y+x d x=a d x$
Integrate on both sides, we get
$$
\int y d y+\int x d x=\int a d x
$$
$\Rightarrow \quad \frac{y^{2}}{2}+\frac{x^{2}}{2}=a x+c$
where $c$ is a constant of integration. $\Rightarrow \quad y^{2}+x^{2}-2 a x=c$
This represents a circle whose centre is on the $X$ -axis.

Topic: Mathematics, Differential Equations, NDA, NDA 2011 (Phase 1)
What does the differential equation $y \frac{d y}{d x}+x=k$ (where k
is a constant) represents?

Options:
A A family of circles having centre on the y-axis.
B A family of circles having centre on the $\mathrm{x}$ -axis.
C A family of circles touching the $\mathrm{x}$ -axis
D A family of ellipses.

The correct answer is:
A family of circles having centre on the $\mathrm{x}$ -axis.

Solution:
Given differential equation is $\mathrm{y} \frac{\mathrm{dy}}{\mathrm{dx}}+\mathrm{x}=\mathrm{k}$
$$
\begin{array}{l}
\Rightarrow \quad y \frac{d y}{d x}=k-x \\
\Rightarrow \quad y d y=(k-x) d x
\end{array}
$$
Integrate on both side, we get
$$
\int \mathrm{ydy}=\int(\mathrm{k}-\mathrm{x}) \mathrm{d} \mathrm{x}
$$
$$
\begin{array}{l}
\Rightarrow \quad \frac{\mathrm{y}^{2}}{2}=\mathrm{kx}-\frac{\mathrm{x}^{2}}{2}+\mathrm{c} \\
\Rightarrow \mathrm{x}^{2}+\mathrm{y}^{2}-2 \mathrm{kx}-\mathrm{c}=0
\end{array}
$$
Which represents a family of circles whose centre lies on the $\mathrm{x}$ -axis.

Topic: Mathematics, Differential Equations, NDA, NDA 2010 (Phase 2)
What does the equation "The universe = The system + The surroundings" represent?

Options:
A A fundamental law of thermodynamics
B The definition of a closed system
C The relationship between the universe, system, and surroundings
D An equation for calculating thermodynamic properties

The correct answer is:
The relationship between the universe, system, and surroundings

Solution:
This equation represents the relationship between the universe, system, and surroundings in thermodynamics.

Topic: Chemistry, Thermodynamics (C), NEET
What does the equation $x^{3} y+x y^{3}-x y=0$ represent?

Options:
A A pair of straight lines only
B A pair of straight lines and a circle
C A rectangular hyperbola only
D A rectangular hyperbola and a circle

The correct answer is:
A pair of straight lines and a circle

Solution:
$\begin{array}{ll}\text { Given equation } \\ x^{3} y+x y^{3}-x y & =0\end{array}$
$\Rightarrow x y\left(x^{2}+y^{2}\right)=x y$
$\Rightarrow x y\left(x^{2}+y^{2}-1\right)=0$
$\Rightarrow x^{2}+y^{2}=1, x y=0$
Above equations represent a pair of straight lines and a circle.

Topic: Mathematics, Pair of Lines, NDA, NDA 2008 (Phase 2)
What does the equation $x d y=y d x$ represent?

Options:
A A family of circles
B A family of parabolas
C A family of hyperbolas
D A family of straight lines

The correct answer is:
A family of straight lines

Solution:
Given equation is $x d y=y d x$ By separating the variable we get
$\frac{d y}{y}=\frac{d x}{x}$
On integrating both sides, we get
$\int \frac{d y}{y}=\int \frac{d x}{x}$
$\Rightarrow \log y=\log x+\log c$
$\Rightarrow y=c x$
It represents a family of straight lines.

Topic: Mathematics, Differential Equations, NDA, NDA 2009 (Phase 2)
What does the following diagram represent?

Options:
A Sewage Treatment
B Secondary Treatment
C Primary Treatment
D Both

The correct answer is:
Both

Solution:
The diagram represents secondary treatment, which is a part of sewage treatment.

Topic: Biology, Microbes in Human Welfare, NEET
What does the formation of turbidity in the Lucas test indicate?

Options:
A Presence of a primary alcohol
B Presence of a secondary alcohol
C Presence of a tertiary alcohol
D Presence of an aromatic alcohol

The correct answer is:
Presence of a tertiary alcohol

Solution:
The formation of turbidity in the Lucas test indicates the presence of a tertiary alcohol.

Topic: Chemistry, Alcohols Phenols and Ethers, NEET
What does the negative sign in the expression E⊖(Zn2+/Zn) = − 0.76 V mean?

Options:
A It means that H is more reactive than zinc. When the zinc electrode will be connected to Standard Hydrogen Electrode , Zn will get reduced and H+will get oxidized.
B It means that Zn and H will both get reduced when connected to the standard hydrogen electrode.
C It means that Zn is more reactive than hydrogen. When the zinc electrode will be connected to Standard Hydrogen Electrode , Zn will get oxidized and H+will get reduced.
D The negative sign has no significance.

The correct answer is:
It means that Zn is more reactive than hydrogen. When the zinc electrode will be connected to Standard Hydrogen Electrode , Zn will get oxidized and H+will get reduced.

Solution:
Correct Option is : (C)
It means that Zn is more reactive than hydrogen. When the zinc electrode will be connected to Standard Hydrogen Electrode , Zn will get oxidized and H+will get reduced.

Topic: Chemistry, Electrochemistry, NEET
What does the negative sign in the expression $E_{\mathrm{Zn}{ }^{2+} / \mathrm{Zn}}^{\ominus}=-0.76 \mathrm{~V}$ mean?

Options:

None

Solution:
Greater negative reactivity of standard reduction potential shows that zinc metal is more reactive than hydrogen. When zinc electrode will be connected to standard hydrogen electrode. $\mathrm{Zn}$ will get oxidised and $\mathrm{H}^{+}$will get reduced.
Thus, zinc electrode will act as the anode of the cell and hydrogen electrode will act as the cathode of the cell.

Topic: Chemistry, Electrochemistry
What does the positive or negative sign on boundary surface diagrams represent?

Options:
A Charge distribution
B Bond strength
C Atomic number
D Molecular weight

The correct answer is:
Charge distribution

Solution:
The positive and negative signs on boundary surface diagrams do not represent charge but instead indicate the sign (phase) of the orbital wave function.

Topic: Chemistry, Chemical Bonding and Molecular Structure, NEET
What does the primary valence represent in Werner's theory?

Options:
A The number of ligands
B The number of secondary valences
C The coordination number
D The metal's charge

The correct answer is:
The number of secondary valences

Solution:
The primary valence in Werner's theory represents the number of secondary valences for a metal.

Topic: Chemistry, Coordination Compounds, NEET
What does the secondary valence represent in Werner's theory?

Options:
A The number of ligands
B The number of primary valences
C The coordination number
D The metal's charge

The correct answer is:
The coordination number

Solution:
The secondary valence in Werner's theory represents the coordination number for a metal in coordination compounds.

Topic: Chemistry, Coordination Compounds, NEET
What does the series
$1+3^{-\frac{1}{2}}+3+\frac{1}{3 \sqrt{3}}+\ldots$ represents?

Options:
A AP
B GP
C $\mathrm{HP}$
D None of the above series

The correct answer is:
None of the above series

Solution:
Given series is $1+\frac{1}{\sqrt{3}}+3+\frac{1}{3 \sqrt{3}}+\ldots .$
Consider $\frac{\mathrm{a}_{2}}{\mathrm{a}_{1}}=\frac{1}{\sqrt{3}}, \frac{\mathrm{a}_{3}}{\mathrm{a}_{2}}=\frac{3}{1 / \sqrt{3}}, \frac{\mathrm{a}_{4}}{\mathrm{a}_{3}}=\frac{1 / 3 \sqrt{3}}{3}$
Also find $a_{2}-a_{1}=\frac{1}{\sqrt{3}}-1=\frac{1-\sqrt{3}}{\sqrt{3}}$
$a_{3}-a_{2}=3-\frac{1}{\sqrt{3}}=\frac{3 \sqrt{3}-1}{\sqrt{3}}$
$a_{4}-a_{3}=\frac{1}{3 \sqrt{3}}-3=\frac{1-9 \sqrt{3}}{3 \sqrt{3}}$
Thus, $\frac{a_{2}}{a_{1}} \neq \frac{a_{3}}{a_{2}} \neq \frac{a_{4}}{a_{3}}$
and $\mathrm{a}_{2}-\mathrm{a}_{1} \neq \mathrm{a}_{3}-\mathrm{a}_{2} \neq \mathrm{a}_{4}-\mathrm{a}_{3}$
Hence, Given series is neither A.P., GP. nor H.P.

Topic: Mathematics, Sequences and Series, NDA, NDA 2012 (Phase 1)