datavorous/entrance-exam-dataset huggingface dataset:
What is a keystone species?

Options:
A A species which makes up only a small proportion of the total biomass of a community, yet has a huge impact on the community's organization and survival.
B A common species that has plenty of biomass, yet has a fairly low impact on the community's organization.
C A rare species that has minimal impact on the biomass and on other species in the community.
D A dominant a large proportion of the biomass and which affects many other species.

The correct answer is:
A species which makes up only a small proportion of the total biomass of a community, yet has a huge impact on the community's organization and survival.

Solution:
Keystone species are those species which has significant and disproportionately large influence on the community structure and characteristics. It has often considerably low abundance and biomass as compared to dominant species. Removal of such species causes serious disruption in structure and function of community.

Topic: Biology, Organisms and Populations, AIIMS, AIIMS 2008
What is a keystone species?

Options:
A A species which adds upto only a small proportion of the total biomass of a community, yet has a huge impact on the communityâs organization and survival.
B A common species that has plenty of biomass, yet has a fairly low impact on the community’s organization
C A rare species that has minimal impact on the biomass and on other species in the community
D A dominant species that constitutes a large proportion of the biomass and which affects many other species.

The correct answer is:
A species which adds upto only a small proportion of the total biomass of a community, yet has a huge impact on the community’s organization and survival.

Solution:
Species having a much greater influence on community characteristics, relative to their low abundance or biomass are called keystone species, e. g., in tropical forests, figs are keystone species. Removal of these species causes serious disruption in the functioning of the community.

Topic: Biology, Biodiversity and its Conservation, NEET
What is a thermochemical equation?

Options:
A An equation that describes a chemical reaction.
B An equation that specifies the physical state of a substance.
C A balanced chemical equation together with the value of its ∆rH.
D An equation that represents the temperature dependence of a reaction.

The correct answer is:
A balanced chemical equation together with the value of its ∆rH.

Solution:
A thermochemical equation is a balanced chemical equation that includes the value of the standard enthalpy change (∆rH) for the reaction.

Topic: Chemistry, Thermodynamics (C), NEET
What is a tonoplast?

Options:
A Outer membrane of mitochondria
B Inner membrane of chloroplast
C Membrane boundary of the vacuole of plant cells
D Cell membrane of a plant cell.

The correct answer is:
Membrane boundary of the vacuole of plant cells

Solution:
The vacuole is the membrane-bound space found in the cytoplasm. The vacuole is bound by a single membrane called tonoplast.

Topic: Biology, Cell - The Unit of Life, NEET
What is a vector of unit length orthogonal to both the vectors $\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}$ and $2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}-\hat{\mathrm{k}} ?$

Options:
A $\frac{-4 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}-\hat{\mathrm{k}}}{\sqrt{26}}$
B $\frac{-4 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+\hat{\mathrm{k}}}{\sqrt{26}}$
C $\frac{-3 \hat{i}+2 \hat{j}-\hat{k}}{\sqrt{14}}$
D $\frac{-3 \hat{i}+2 \hat{j}+\hat{k}}{\sqrt{14}}$

The correct answer is:
$\frac{-4 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+\hat{\mathrm{k}}}{\sqrt{26}}$

Solution:
$\begin{aligned} \vec{A}=\hat{i}+\hat{j}+\hat{k} \\ \vec{B}=2 \hat{i}+3 \hat{j}-\hat{k} \\ \vec{A} \times \vec{B}=\left|\begin{array}{lll}\hat{i} & \hat{j} & \hat{k} \\ 1 & 1 & 1 \\ 2 & 3 & -1\end{array}\right| \\=& \hat{i}(-1-3)-\hat{j}(-1-2)+\hat{k}(3-2) \\ &=-4 \hat{i}+3 \hat{j}+\hat{k} \end{aligned}$
Vector of unit length orthogonal to both the vectors $\vec{A}$ and $\vec{B}$
$=\frac{\vec{A} \times \vec{B}}{|\vec{A} \times \vec{B}|}$
$=\frac{-4 i+3 j+k}{\sqrt{16+9+1}}=\frac{-4 \hat{i}+3 \hat{j}+\hat{k}}{\sqrt{26}}$

Topic: Mathematics, Vector Algebra, NDA, NDA 2016 (Phase 1)
What is $\int \mathrm{a}^{\mathrm{x}} \mathrm{e}^{\mathrm{x}} \mathrm{dx}$ equal to ?

Options:
A $\frac{\mathrm{a}^{\mathrm{x}} \mathrm{e}^{\mathrm{x}}}{\ell \mathrm{na}}+\mathrm{c}$
B $\mathrm{a}^{\mathrm{x}} \mathrm{e}^{\mathrm{x}}+\mathrm{c}$
C $\frac{\mathrm{a}^{\mathrm{x}} \mathrm{e}^{\mathrm{x}}}{\ell \mathrm{n}(\mathrm{ae})}+\mathrm{c}$
D None of the above
where $\mathrm{c}$ is the constant of integration.

The correct answer is:
$\frac{\mathrm{a}^{\mathrm{x}} \mathrm{e}^{\mathrm{x}}}{\ell \mathrm{n}(\mathrm{ae})}+\mathrm{c}$

Solution:
Let $I=\int \underset{I}{a^{x}} e^{x} d x$
$I=a^{x} \int e^{x} d x-\int a^{x} \ell n a e^{x} d x$
$\mathrm{I}=\mathrm{a}^{\mathrm{x}} \mathrm{e}^{\mathrm{x}}-\ell \mathrm{n} \mathrm{a} \int \mathrm{a}^{\mathrm{x}} \mathrm{e}^{\mathrm{x}} \mathrm{dx}$
$\mathrm{I}=\mathrm{a}^{\mathrm{x}} \mathrm{e}^{\mathrm{x}}-\ln \mathrm{a} .(\mathrm{I})$
$\Rightarrow(1+\ln \mathrm{a}) \mathrm{I}=\mathrm{a}^{\mathrm{x}} \mathrm{e}^{\mathrm{x}} .$
$\Rightarrow \mathrm{I}=\frac{\mathrm{a}^{\mathrm{x}} \mathrm{e}^{\mathrm{x}}}{\ell \mathrm{n}(\mathrm{ae})}+\mathrm{c}(\because \ell \mathrm{n} \mathrm{e}=1)$

Topic: Mathematics, Indefinite Integration, NDA, NDA 2012 (Phase 2)
What is an active site in an enzyme?

Options:
A The substrate
B The pocket or crevice into which the substrate fits
C The amino acid sequence
D The secondary structure

The correct answer is:
The pocket or crevice into which the substrate fits

Solution:
An active site of an enzyme is a crevice or pocket into which the substrate fits.

Topic: Biology, Biomolecules (B), NEET
What is an endangered species? Give an example of an endangered plant and animal species each.

Options:

None

Solution:
An endangered species is a population of organisms, which is facing a high risk of becoming extinct in near future due to
(i) Its number is very low.
(ii) It is threatened by the continuously changing changing environment.
(iii) It is facing predator threat.
An endangered plant species is Venus fly trap.
An endangered animal species is Siberian tiger.

Topic: Biology, Biodiversity and its Conservation
What is an example of "competitive release"?

Options:
A Species expand their range dramatically when a competing species is removed
B Competition occurs between unrelated species for the same resource
C Interference competition reduces the feeding efficiency of one species
D Competitive exclusion occurs only when resources are abundant

The correct answer is:
Species expand their range dramatically when a competing species is removed

Solution:
Competitive release is when a species whose distribution is restricted to a small geographical area because of the presence of a competitively superior species, is found to expand its distributional range dramatically when the competing species is experimentally removed.

Topic: Biology, Organisms and Populations, NEET
What is an incomplete ecosystem? Explain with the help of suitable example.

Options:

None

Solution:
An ecosystem is comprised of biotic and a biotic components. Abiotic components include light, air, water, temperature, humidity etc., while biotic factor comprises all living organisms. An is limited absent ecosystem incomplete is any component (either abiotic or biotic). For example the profundal and benthic zone in an aquatic ecosystem.

Topic: Biology, Ecosystem
What is another term for the central atom/ion in a coordination entity?

Options:
A Primary valence
B Secondary valence
C Lewis acid
D Coordination entity

The correct answer is:
Coordination entity

Solution:
The central atom/ion in a coordination entity is also referred to as a coordination entity.

Topic: Chemistry, Coordination Compounds, NEET
What is another term for the central atom/ion in a coordination entity?

Options:
A Primary valence
B Secondary valence
C Lewis acid
D Coordination entity

The correct answer is:
Lewis acid

Solution:
The central atom/ion in a coordination entity is also referred to as a Lewis acid.

Topic: Chemistry, Coordination Compounds, NEET
What is /are the critical points $(\mathrm{s})$ of the function $\mathrm{f}(\mathrm{x})=$ $\mathrm{x}^{2 / 3}(5-2 \mathrm{x})$ on the interval $[-1,2] ?$

Options:
A 1 only
B 0,1
C $\frac{3}{2}$ only $\quad$
D $0, \frac{3}{2}$

The correct answer is:
1 only

Solution:
$\mathrm{f}(\mathrm{x})=\mathrm{x}^{2 / 3}(5-2 \mathrm{x})$
or, $f(x)=5 x^{2 / 3}-2 x^{5 / 3}$
differentiating both the sides.
$\mathrm{f}^{\prime}(\mathrm{x})=5 \times \frac{2}{3} \mathrm{x}^{-1 / 3}-2 \times \frac{5}{3} \mathrm{x}^{2 / 3}$
or, $\mathrm{f}^{\prime}(\mathrm{x})=\frac{10}{3}\left(\mathrm{x}^{-1 / 3}-\mathrm{x}^{2 / 3}\right)$
To get the critical value. $\mathrm{f}^{\prime}(\mathrm{x})=0$
so, $\mathrm{x}^{-1 / 3}-\mathrm{x}^{2 / 3}=0 \Rightarrow \mathrm{x}^{-1 / 3}(1-\mathrm{x})=0$
$\Rightarrow 1-x=0$ as $x^{-1 / 3} \neq 0$
or, $\mathrm{x}=1$ is the only value in the interval $[-1,2]$

Topic: Mathematics, Application of Derivatives, NDA, NDA 2007 (Phase 1)
What is arg (bi) where $\mathrm{b}>0$ ?

Options:
A 0
B $\frac{\pi}{2}$
C $\pi$
D $\frac{3 \pi}{2}$

The correct answer is:
$\frac{\pi}{2}$

Solution:
$\arg ($ bi $) \tan ^{-1}\left(\frac{\mathrm{b}}{0}\right)=\tan ^{-1}(\infty)=\frac{\pi}{2}(\because \mathrm{b}>0)$

Topic: Mathematics, Complex Number, NDA, NDA 2008 (Phase 1)
What is bond dissociation enthalpy?

Options:
A The enthalpy changes when two atoms combine to form a molecule.
B The enthalpy changes when one mole of covalent bonds in a gaseous covalent compound is broken to form products in the gas phase.
C The enthalpy change when a solid substance sublimes at a constant temperature and under standard pressure.
D The enthalpy change when a substance is heated at constant volume.

The correct answer is:
The enthalpy changes when one mole of covalent bonds in a gaseous covalent compound is broken to form products in the gas phase.

Solution:
Bond dissociation enthalpy specifically refers to the energy required to break one mole of covalent bonds in a gaseous covalent compound to form products in the gas phase.

Topic: Chemistry, Thermodynamics (C), NEET
What is $\mathrm{C}(\mathrm{n}, \mathrm{r})+2 \mathrm{C}(\mathrm{n}, \mathrm{r}-1)+\mathrm{C}(\mathrm{n}, \mathrm{r}-2)$ equal to?

Options:
A $\mathrm{C}(\mathrm{n}+1, \mathrm{r})$
B $\mathrm{C}(\mathrm{n}-1, \mathrm{r}+1)$
C $\mathrm{C}(\mathrm{n}, \mathrm{r}+1)$
D $\mathrm{C}(\mathrm{n}+2, \mathrm{r})$

The correct answer is:
$\mathrm{C}(\mathrm{n}+2, \mathrm{r})$

Solution:
$C(n, r)+2 C(n, r-1)+C(n, r-2)$
$={ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}}+2\left({ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}-1}\right)+{ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}-2}$
$={ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}}+{ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}-1}+{ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}-1}+{ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}-2}$
$\quad\left(\because{ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}}+{ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}-1}={ }^{\mathrm{n}+1} \mathrm{C}_{\mathrm{r}}\right)$
$={ }^{\mathrm{n}+1} \mathrm{C}_{\mathrm{r}}+{ }^{\mathrm{n}+1} \mathrm{C}_{\mathrm{r}-1}$
$={ }^{\mathrm{n}+2} \mathrm{C}_{\mathrm{r}}$
$=\mathrm{C}(\mathrm{n}+2, \mathrm{r})$

Topic: Mathematics, Binomial Theorem, NDA, NDA 2018 (Phase 1)
What is $\int\left(\frac{1}{\cos ^{2} x}-\frac{1}{\sin ^{2} x}\right) \mathrm{dx}$ equal to?

Options:
A $2 \operatorname{cosec} 2 x+c$
B $-2 \cot 2 \mathrm{x}+\mathrm{c}$
C $2 \sec 2 x+c$
D $-2 \tan 2 x+c$
where $\mathrm{c}$ is the constant of integration.

The correct answer is:
$2 \operatorname{cosec} 2 x+c$

Solution:
Let $\mathrm{I}=\int\left(\frac{1}{\cos ^{2} \mathrm{x}}-\frac{1}{\sin ^{2} \mathrm{x}}\right) \mathrm{d} \mathrm{x}$
$=\int\left(\sec ^{2} \mathrm{x}-\operatorname{cosec}^{2} \mathrm{x}\right) \mathrm{dx}$
$=\int \sec ^{2} \mathrm{x} \mathrm{d} \mathrm{x}-\int_{\mathrm{c}} \operatorname{cosec}^{2} \mathrm{x} \mathrm{d} \mathrm{x}$
$=\tan \mathrm{x}+\cot \mathrm{x}+\mathrm{c}$
$=\tan \mathrm{x}+\frac{1}{\tan \mathrm{x}}+\mathrm{c}=\frac{\tan ^{2} \mathrm{x}+1}{\tan \mathrm{x}}+\mathrm{c}=\frac{\sec ^{2} \mathrm{x}}{\tan \mathrm{x}}+\mathrm{c}$
$=\frac{2}{2 \sin \mathrm{x} \cos \mathrm{x}}+\mathrm{c}=\frac{2}{\sin 2 \mathrm{x}}+\mathrm{c}=2 \operatorname{cosec} 2 \mathrm{x}+\mathrm{c}$

Topic: Mathematics, Indefinite Integration, NDA, NDA 2012 (Phase 2)
What is $\int \frac{a+b \sin x}{\cos ^{2} x} d x$ equal to?

Options:
A $a \sec x+b \tan x+c$
B $a \tan x+b \sec x+c$
C $a \cot x+b \operatorname{cosec} x+c$
D $a \operatorname{cosec} x+b \cot x+c$

The correct answer is:
$a \tan x+b \sec x+c$

Solution:
Consider $\int \frac{a+b \sin x}{\cos ^{2} x} d x=\int\left(\frac{a}{\cos ^{2} x}+\frac{b \sin x}{\cos ^{2} x}\right) d x$
$=\int\left(a \sec ^{2} x+b \tan x \sec x\right) d x=a \tan x+b \sec x+c$

Topic: Mathematics, Indefinite Integration, NDA, NDA 2009 (Phase 2)
What is $\int \frac{e^{x}(1+x)}{\cos ^{2}\left(x e^{x}\right)} d x$ equal to?

Options:
A $x e^{x}+c$
B $\cos \left(x e^{x}\right)+c$
C $\tan \left(x e^{x}\right)+c$
D $x \operatorname{cosec}\left(x e^{x}\right)+c$
Where $\mathrm{c}$ is a constant of integration.

The correct answer is:
$\tan \left(x e^{x}\right)+c$

Solution:
Let $\mathrm{I}=\int \frac{\mathrm{e}^{\mathrm{x}}(1+\mathrm{x})}{\cos ^{2}\left(\mathrm{xe}^{\mathrm{x}}\right)} \mathrm{dx}$
Put, $x e^{x}=t \Rightarrow e^{x}(1+x) d x=d t$
$\therefore \quad \mathrm{I}=\int \frac{\mathrm{dt}}{\cos ^{2} \mathrm{t}}=\int \mathrm{sec}^{2} \mathrm{tdt}=\tan \mathrm{t}+\mathrm{c}$
where ' $\mathrm{c}$ ' is a constant of integration. $=\tan \left(\mathrm{xe}^{\mathrm{x}}\right)+\mathrm{c}$

Topic: Mathematics, Indefinite Integration, NDA, NDA 2010 (Phase 2)
What is $\frac{\sin 5 x-\sin 3 x}{\cos 5 x+\cos 3 x}$ equal to?

Options:
A $\sin x$
B $\cos x$
C $\tan x$
D $\cot \mathrm{x}$

The correct answer is:
$\tan x$

Solution:
$\begin{aligned} & \frac{\sin 5 x-\sin 3 x}{\cos 5 x+\cos 3 x} \\ & \sin c-\sin d=2 \cos \left(\frac{\mathrm{c}+\mathrm{d}}{2}\right) \sin \left(\frac{\mathrm{c}-\mathrm{d}}{2}\right) \\ & \cos c-\cos d=2 \cos \left(\frac{\mathrm{c}+\mathrm{d}}{2}\right) \cos \left(\frac{\mathrm{c}-\mathrm{d}}{2}\right) \end{aligned}$
$$
\begin{array}{l}
\begin{array}{l}
\therefore \frac{\sin 5 x-\sin 3 x}{\cos 5 x+\cos 3 x}=\frac{2 \cos \left(\frac{5 x+3 x}{2}\right) \sin \left(\frac{5 x-3 x}{2}\right)}{2 \cos \left(\frac{5 x+3 x}{2}\right) \cos \left(\frac{5 x-3 x}{2}\right)} \\

Topic: Mathematics, Trigonometric Ratios & Identities, NDA, NDA 2018 (Phase 1)
What is $\frac{\sin \theta+1}{\cos \theta}$ equal to?

Options:
A $\frac{\sin \theta+\cos \theta-1}{\sin \theta+\cos \theta+1}$
B $\frac{\sin \theta+\cos \theta+1}{\sin \theta+\cos \theta-1}$
C $\frac{\sin \theta-\cos \theta-1}{\sin \theta+\cos \theta+1}$
D $\frac{\sin \theta-\cos \theta+1}{\sin \theta+\cos \theta-1}$

The correct answer is:
$\frac{\sin \theta-\cos \theta+1}{\sin \theta+\cos \theta-1}$

Solution:
Consider $\frac{1+\sin \theta}{\cos \theta}=\frac{1+\frac{2 \tan \frac{\theta}{2}}{1+\tan ^{2} \frac{\theta}{2}}}{\frac{1-\tan ^{2} \frac{\theta}{2}}{1+\tan ^{2} \frac{\theta}{2}}}$
$\left(\because \sin 2 \theta=\frac{2 \tan \theta}{1+\tan ^{2} \theta}\right.$ and $\left.\cos 2 \theta=\frac{1-\tan ^{2} \theta}{1+\tan ^{2} \theta}\right)$
$=\frac{\left(1+\tan \frac{\theta}{2}\right)^{2}}{\left(1-\tan \frac{\theta}{2}\right)\left(1+\tan \frac{\theta}{2}\right)}$
$=\frac{1+\tan \frac{\theta}{2}}{1-\tan \frac{\theta}{2}}=\frac{\cos \frac{\theta}{2}+\sin \frac{\theta}{2}}{\cos \frac{\theta}{2}-\sin \frac{\theta}{2}}$
Multiplied and divide by $2 \sin \frac{\theta}{2}$ $=\frac{2 \sin \frac{\theta}{2} \cos \frac{\theta}{2}+2 \sin ^{2} \frac{\theta}{2}}{2 \sin \frac{\theta}{2} \cos \frac{\theta}{2}-2 \sin ^{2} \frac{\theta}{2}}$
$=\frac{\sin \theta+1-\cos \theta}{\sin \theta-1+\cos \theta}$
$(\because \sin 2 \theta=2 \sin \theta \cos \theta$ and
$\left.\cos 2 \theta=1-2 \sin ^{2} \theta\right)$

Topic: Mathematics, Trigonometric Ratios & Identities, NDA, NDA 2010 (Phase 2)
What is $\frac{\cot 224^{\circ}-\cot 134^{\circ}}{\cot 226^{\circ}+\cot 316^{\circ}}$ equal to ?

Options:
A $-\operatorname{cosec} 88^{\circ}$
B $-\operatorname{cosec} 2^{\circ}$
C $-\operatorname{cosec} 44^{\circ}$
D $-\operatorname{cosec} 46^{\circ}$

The correct answer is:
$-\operatorname{cosec} 2^{\circ}$

Solution:
$\frac{\cot 224^{\circ}-\cot 134^{\circ}}{\cot 226^{\circ}+\cot 316^{\circ}}$
$=\frac{\cot \left(180^{\circ}+44^{\circ}\right)-\cot \left(180^{\circ}-46^{\circ}\right)}{\cot \left(180+46^{\circ}\right)+\cot \left(270^{\circ}+46\right)^{\circ}}$
$=\frac{\cot 44^{\circ}+\cot 46^{\circ}}{\cot 46^{\circ}-\tan 46^{\circ}}=\frac{\tan 46^{\circ}+\tan 44^{\circ}}{\tan 44^{\circ}-\tan 46^{\circ}}$
$=\frac{\sin \left(46^{\circ}+44^{\circ}\right)}{\sin \left(44^{\circ}-46^{\circ}\right)}=-\operatorname{cosec} 2^{\circ}$

Topic: Mathematics, Trigonometric Ratios & Identities, NDA, NDA 2014 (Phase 1)
What is causing the decline of commercially important species of marine fish populations around the world?

Options:
A Alien species invasions
B Co:extinctions
C Habitat loss and fragmentation
D Over:exploitation

The correct answer is:
Over:exploitation

Solution:
Many marine fish populations around the world are over harvested, endangering the continued existence of some commercially important species due to over:exploitation.

Topic: Biology, Biodiversity and its Conservation, NEET
What is common to Lantana, Eichhomia and African catfish?

Options:
A All are endangered species of India.
B All are key stone species.
C All are mammals found in India.
D All the species are neither threatened nor indigenous species of India.

The correct answer is:
All the species are neither threatened nor indigenous species of India.

Solution:
Lantana, Eichhomia and African catfish, all the species are neither threatened nor indigenous species of India.

Topic: Biology, Biodiversity and its Conservation, NEET
What is common to Lantana, Eichhornia and African catfish?

Options:
A
All are endangered species of India

B
All are key stone species

C
All are mammals found in India

D
All the species are neither threatened nor indigenous species of India.

The correct answer is:
All the species are neither threatened nor indigenous species of India.

Solution:
All the three above mentioned species are neither threatened nor indigenous species of India, Lantana Eichhornia (water hyacinth) and African catfish (Clarias gariepinus) all are alien (exotic species) that are invasive and also have an harmful impact resulting in extinction of the indigenous species.

Topic: Biology, Biodiversity and its Conservation
What is common to Lantana, Eichhornia and African catfish?

Options:
A All are endangered species of India
B All are key stone species
C All are mammals found in India
D All the species are not indigenous species of India

The correct answer is:
All the species are not indigenous species of India

Solution:
Non-native or alien species are often introduced inadvertently for their economic and other uses. They often become invasive and drive away from the local species. These species are considered to be the second major cause of extinction of species (the first being habitat destruction). Water Hyacinth (Eichhornia crassipes) was introduced in Indian water to reduce pollution. It has clogged water bodies including wetlands at many places, resulting in the death of several aquatic plants and animals. Lantana camara has replaced many species in forest of U.P. and M.P. African catfish, Clarias gariepinus, has been illegally introduced for aquaculture in India. It is threatening native Catfishes (e.g., Clarias bacterachus) of Indian rivers.

Topic: Biology, Biodiversity and its Conservation, NEET
What is correct regarding ecological succession?

Options:
A The decrease in biodiversity at each transitional level.
B Primary succession is faster than secondary succession.
C Change to environmental condition extreme to mesic.
D The climax community is most stable with the environment as the niche and food web complexity is less.

The correct answer is:
Change to environmental condition extreme to mesic.

Solution:
Both hydrarch and xerarch successions lead to medium water conditions (mesic) – neither too dry (xeric) nor too wet (hydric).

Topic: Biology, Ecosystem, NEET
What is $\cos 20^{\circ}+\cos 100^{\circ}+\cos 140^{\circ}$ equal to?

Options:
A 2
B 1
C $1 / 2$
D 0

The correct answer is:
0

Solution:
$\cos 20^{\circ}+\cos 100^{\circ}+\cos 140^{\circ}$
$=\left(\cos 140^{\circ}+\cos 20^{\circ}\right)+\cos 100^{\circ}$
$=2 \cos \left(\frac{160^{\circ}}{2}\right) \cdot \cos \left(\frac{120^{\circ}}{2}\right)+\cos 100^{\circ}$
$=2 \cdot \cos 80^{\circ} \cdot \frac{1}{2}+\cos 100^{\circ}$
$=2 \cos \left(\frac{180^{\circ}}{2}\right) \cdot \cos \left(\frac{20^{\circ}}{2}\right)$
$=2 \cos 90^{\circ} \cdot \cos 10^{\circ}$
$=2 \times 0 \times \cos 10^{\circ}=0$

Topic: Mathematics, Trigonometric Ratios & Identities, NDA, NDA 2014 (Phase 1)
What is $\frac{\sin \theta}{\operatorname{cosec} \theta}+\frac{\cos \theta}{\sec \theta}$ equal to?

Options:
A 1
B $\frac{1}{2}$
C $\frac{1}{3}$
D 2

The correct answer is:
1

Solution:
$\frac{\sin \theta}{\operatorname{cosec} \theta}+\frac{\cos \theta}{\sec \theta}=\frac{\sin \theta}{\frac{1}{\sin \theta}}+\frac{\cos \theta}{\frac{1}{\cos \theta}}=\sin ^{2} \theta+\cos ^{2} \theta=1$

Topic: Mathematics, Trigonometric Ratios & Identities, NDA, NDA 2012 (Phase 1)
What is DNA?

Options:
A Deoxyribonucleic acid
B Ribonucleic acid
C Polymer of ribonucleotides
D Polymer of deoxyribonucleotides

The correct answer is:
Deoxyribonucleic acid

Solution:
DNA stands for Deoxyribonucleic Acid and it is the most abundant genetic material found in living systems.

Topic: Biology, Molecular Basis of Inheritance, NEET
What is $\frac{\mathrm{d} \sqrt{1-\sin 2 \mathrm{x}}}{\mathrm{dx}}$ equal to, where $\frac{\pi}{4} < \mathrm{x} < \frac{\pi}{2}$ ?

Options:
A $\cos x+\sin x$
B $-(\cos x+\sin x)$
C $\pm(\cos x+\sin x)$
D None of the above

The correct answer is:
$\cos x+\sin x$

Solution:
For $\frac{\pi}{4} < x < \frac{\pi}{2}$
$\quad \sqrt{1-\sin 2 x}=\left(\sin ^{2} x+\cos ^{2} x+2 \sin x \cdot \cos x\right)^{1 / 2}$
$=(\sin x-\cos x)$
$\therefore \quad$ Differentiation $=\cos x+\sin x$

Topic: Mathematics, Application of Derivatives, NDA, NDA 2018 (Phase 2)
What is $\frac{\mathrm{d}^{2} \mathrm{x}}{\mathrm{dy}^{2}}$ equal to?

Options:
A $-\left(\frac{d^{2} y}{d x^{2}}\right)^{-1}\left(\frac{d y}{d x}\right)^{-3}$
B $\left(\frac{d^{2} y}{d x^{2}}\right)^{-1}\left(\frac{d y}{d x}\right)^{-2}$
C $-\left(\frac{d^{2} y}{d x^{2}}\right)\left(\frac{d y}{d x}\right)^{-3}$
D $\left(\frac{d^{2} y}{d x^{2}}\right)^{-1}$

The correct answer is:
$-\left(\frac{d^{2} y}{d x^{2}}\right)\left(\frac{d y}{d x}\right)^{-3}$

Solution:
Let $\mathrm{y}=\mathrm{f}(\mathrm{x}) \Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}}=\mathrm{f}^{1}(\mathrm{x}) \Rightarrow \frac{\mathrm{dx}}{\mathrm{dy}}=\frac{1}{\mathrm{f}^{\prime}(\mathrm{x})}$
$\frac{d^{2} x}{d y^{2}}=\frac{\frac{-d}{d y} f^{\prime}(x)}{\left(f^{\prime}(x)\right)^{2}}$
$\frac{-d}{d y} f^{\prime}(x)$
$\frac{d y}{\left(f^{\prime}(x)\right)^{2}}=\frac{\frac{-d}{d y}\left(\frac{d y}{d x}\right) \cdot \frac{d x}{d x}}{\left(f^{\prime}(x)\right)^{2}}=\frac{\frac{-d}{d x}\left(f^{\prime}(x)\right) \cdot \frac{d x}{d y}}{\left(\frac{d y}{d x}\right)^{2}}$
$\Rightarrow \frac{-f^{\prime}(x) \cdot \frac{d x}{d y}}{\left(\frac{d y}{d x}\right)^{2}}=\frac{-\left(\frac{d^{2} y}{d x^{2}}\right)}{\left(\frac{d y}{d x}\right)^{3}}=\frac{-d^{2} y}{d x^{2}}\left(\frac{d y}{d x}\right)^{-3}$

Topic: Mathematics, Differential Equations, NDA, NDA 2017 (Phase 1)