datavorous/entrance-exam-dataset huggingface dataset:
In the given set of reactions.
the IUPAC name of product ' \( Y \) ' is

Options:
A N-Methylpropanamine
B N-lsopropylmethanamine
C Butan-2-amine
D N-Methylpropan-2-amine

The correct answer is:
N-Methylpropan-2-amine

Solution:
AgCN is a covalent compound, therefore, attacking side ofthe \( \mathrm{CN}^{-} \)is \( \mathrm{N} \), hence, the product thus formed is a secondary
amine. The reaction involved is,

Topic: Chemistry, Hydrogen, KCET, KCET 2015
In the manufacture of sulphuric acid by contact process, Tyndall box is used to

Options:
A filter dust particles
B remove impurities
C convert $\mathrm{SO}_{2}$ to $\mathrm{SO}_{3}$
D test the presence of dust particles

The correct answer is:
test the presence of dust particles

Solution:
In the manufacture of sulphuric acid by contact process, Tyndall box is used to test the presence of dust particles.

Topic: Chemistry, p Block Elements (Group 15, 16, 17 & 18), COMEDK, COMEDK 2013
In the mean and the median pertaining to a certain character of a population arc of the same value, the following is most likely to occur:

Options:
A a bi-modal distribution
B a T-shaped curve
C a skewed curve
D a normal distribution.

The correct answer is:
a normal distribution.

Solution:
The normal distribution is a symmetrical, bell-shaped distribution in which the mean, median and mode are all equal. It is a central component of inferential statistics. The standard normal distribution is a normal distribution represented in z scores. It always has a mean of zero and a standard deviation of one.
Related Theory
If one tail is longer than another, the distribution is skewed. These distributions are sometimes called asymmetric or asymmetrical distributions as they don't show any kind of symmetry. Symmetry means that one half of the distribution is a mirror image of the other half.

Topic: Biology, Organisms and Populations, NEET, NEET 2007
In the North East region of India, during the process of jhum cultivation, forests are cleared by burning and left for regrowth after a year of cultivation. How would you explain the regrowth of forest in ecological term?

Options:

None

Solution:
Forests that are cleared during jhum cultivation will show secondary succession. Since, soil is already present, the buried seeds open to germinate. New seeds will be brought into the area and new species will colonise the forest again due to wind dispersal and some other natural forces.

Topic: Biology, Ecosystem
In the order of ease of dehydration, which type of alcohol is the easiest to dehydrate?

Options:
A Primary alcohol
B Secondary alcohol
C Tertiary alcohol
D Aromatic alcohol

The correct answer is:
Tertiary alcohol

Solution:
Tertiary alcohols are the easiest to dehydrate among primary, secondary, and tertiary alcohols.

Topic: Chemistry, Alcohols Phenols and Ethers, NEET
In the order of increasing acid strength, which of the following correctly represents the acidity of alcohols?

Options:
A Primary < Secondary < Tertiary alcohols
B Tertiary < Secondary < Primary alcohols
C Secondary < Tertiary < Primary alcohols
D Primary = Secondary = Tertiary alcohols

The correct answer is:
Primary < Secondary < Tertiary alcohols

Solution:
Primary alcohols are generally more acidic than secondary alcohols, and secondary alcohols are more acidic than tertiary alcohols.

Topic: Chemistry, Alcohols Phenols and Ethers, NEET
In the peroxide effect, why is 1-bromopropane formed as the major product when HBr is added to propene?

Options:
A Formation of a primary free radical
B Formation of a secondary free radical
C Formation of a tertiary free radical
D Formation of a quaternary free radical

The correct answer is:
Formation of a secondary free radical

Solution:
In the peroxide effect, 1-bromopropane is formed as the major product because the secondary free radical formed in the mechanism is more stable than a primary free radical.

Topic: Chemistry, Hydrocarbons, NEET
In the reaction sequence
C6H5CHO→NaCN/HCl(X)→H2O/H⊕ Product, Product will be

Options:
A Optically inactive acid
B Optically inactive α -hydroxy acid
C Racemic mixture of two optically active α -hydroxy acids
D Racemic mixture of two optically active secondary alcohols

The correct answer is:
Racemic mixture of two optically active α -hydroxy acids

Solution:
In the reaction sequence racemic mixture of two optically active α -hydroxy acids

Topic: Chemistry, Aldehydes and Ketones, NEET
In the reaction sequence
C6H5CHO→NaCN/HCl[X]→H2O/H+/Δ Product
Product will be –

Options:
A Optically inactive acid
B Optically inactive α- hydroxy acid
C Racemic mixture of two optically active α- hydroxy acids
D Racemic mixture of two optically active secondary alcohols

The correct answer is:
Racemic mixture of two optically active α- hydroxy acids

Solution:
It is optically active compound but form raceme mixture.

Topic: Chemistry, Aldehydes and Ketones, NEET
In the reaction:
Which of the following compounds will be formed?

Options:
A

B

C

D

The correct answer is:

Solution:
In the cleavage of mixed ethers with two different alkyl groups, the alcohol and alkyl iodide that form depend on the nature of alkyl group.
A Caution
$\Rightarrow$ When primary or secondary alkyl groups are present, it is the lower alkyl group that forms alkyl iodide.

Topic: Chemistry, Alcohols Phenols and Ethers, NEET, NEET 2007
In the reduction of nitriles to primary amines, what is the impact of increasing the number of carbon atoms in the starting nitrile compound?

Options:
A Decreased yield of primary amine
B No effect on the reaction outcome
C Increased yield of primary amine
D Formation of secondary amines instead

The correct answer is:
Increased yield of primary amine

Solution:
Increasing the number of carbon atoms in the starting nitrile compound results in the ascent of the amine series, leading to the formation of primary amines with one more carbon atom.

Topic: Chemistry, Amines, NEET
In the synthesis of ethers via the Williamson ether synthesis, which type of alkyl halide leads to the exclusive formation of an alkene instead of an ether?

Options:
A Primary alkyl halide
B Secondary alkyl halide
C Tertiary alkyl halide
D Aromatic alkyl halide

The correct answer is:
Tertiary alkyl halide

Solution:
Tertiary alkyl halides, when used in the Williamson ether synthesis, lead to the exclusive formation of an alkene through elimination reactions.

Topic: Chemistry, Alcohols Phenols and Ethers, NEET
In the system of classification, which one of the following is NOT a family or order?

Options:
A Chlorophyta
B Leguminosae
C Angiospermae
D Sapindales

The correct answer is:
Angiospermae

Solution:
There are 7 major categories, namely, the kingdom, phylum, class, order, family, genus and species. Angiospermae is not a category. Angiospermae is a division under kingdom Plantae.

Topic: Biology, The Living World, NEET
In the treatment of waste water discharge, which treatment stage involves biological treatment?

Options:
A Primary treatment
B Secondary treatment
C Tertiary treatment
D Reverse osmosis stage

The correct answer is:
Secondary treatment

Solution:
During waste water treatment :
(a) Primary treatment involves physical process of removing the suspended matters.
(b) Secondary treatment involves biological treatment.
(c) Tertiary treatment involves the removal of phosphate, nitrate and sulphate.

Topic: Biology, Microbes in Human Welfare, JIPMER, JIPMER 2009
In throwing a six faced die, let $A$ be the event that an even number occurs, B be the event that an odd number occurs and $\mathrm{C}$ be the event that a number greater than 3 occurs. Which one of the following is correct?

Options:
A $\mathrm{A}$ and $\mathrm{C}$ are mutually exclusive
B $\mathrm{A}$ and $\mathrm{B}$ are mutually exclusive
C $\mathrm{B}$ and $\mathrm{C}$ are mutually exclusive
D $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ mutually exclusive.

The correct answer is:
$\mathrm{A}$ and $\mathrm{B}$ are mutually exclusive

Solution:
$A=\{2,4,6\}, B=\{1,3,5\}, C=\{4,5,6\}$
Hence, $A$ and $B$ are mutually exclusive.

Topic: Mathematics, Probability, NDA, NDA 2013 (Phase 1)
In throwing of two dice, the number of exhaustive events that ' 5 ' will never appear on any one of the dice is

Options:
A 5
B 18
C 25
D 36

The correct answer is:
25

Solution:
$\mathrm{n}(\mathrm{S})=6 \times 6=36$
$$
\begin{array}{|rrrr|r|r}
1,1 & 1,2 & 1,3 & 1,4 & 1,5 & 1,6 \\
2,1 & 2,2 & 2,3 & 2,4 & 2,5 & 2,6 \\
3,1 & 3,2 & 3,3 & 3,4 & 3,5 & 3,6 \\
4,1 & 4,2 & 4,3 & 4,4 & 4,5 & 4,6 \\
\hline 5,1 & 5,2 & 5,3 & 5,4 & 5,5 & 5,6 \\
\hline 6,1 & 6,2 & 6,3 & 6,4 & 6,5 & 6,6
\end{array}
$$
$\therefore \quad$ Required number of exhausistance events $=(6-1) \times(6-1)=5 \times 5=25$
$\therefore \quad$ Option (c) is correct.

Topic: Mathematics, Probability, NDA, NDA 2015 (Phase 1)
In throwing of two dice, what is the number of exhaustive events ?

Options:
A 6
B 12
C 36
D 18

The correct answer is:
36

Solution:
A dice has six faces. So, in throwing of two dice, the number of exhaustive events is $6 \times 6=36$.

Topic: Mathematics, Probability, NDA, NDA 2006 (Phase 2)
In tossing three coins at a time, what is the probability of getting at most one head?

Options:
A $\frac{3}{8}$
B $\frac{7}{8}$
C $\frac{1}{2}$
D $\frac{1}{8}$

The correct answer is:
$\frac{1}{2}$

Solution:
Possible samples are as follows $\{$ HHH, HTH, HHT, THH, TTH, THT, HTT, TTT\}
Let $A$ be the event of getting one head. Let $\mathrm{B}$ be the event of getting no head. Favourable outcome for
$A=\{T T H, T H T, H T T\}$
Favourable outcome for
$$
B=\{T T T\}
$$
Total no. of outcomes $=8$
$$
\therefore \quad P(A)=\frac{3}{8}, P(B)=\frac{1}{8}
$$
$\therefore$ Required probability $=$ Probability of getting one head
+ Probability of getting no head
$$
=P(A)+P(B)=\frac{3}{8}+\frac{1}{8}=\frac{4}{8}=\frac{1}{2}
$$

Topic: Mathematics, Probability, NDA, NDA 2010 (Phase 1)
In triangle $\mathrm{ABC}$, if $\frac{\sin ^{2} \mathrm{~A}+\sin ^{2} \mathrm{~B}+\sin ^{2} \mathrm{C}}{\cos ^{2} \mathrm{~A}+\cos ^{2} \mathrm{~B}+\cos ^{2} \mathrm{C}}=2$ then the
triangle is

Options:
A right-angled
B equilateral
C isosceles
D obtuse-angled

The correct answer is:
right-angled

Solution:
Given, $\frac{\sin ^{2} A+\sin ^{2} B+\sin ^{2} C}{\cos ^{2} A+\cos ^{2} B+\cos ^{2} C}=2$.
Let us take $\mathrm{A}=30^{\circ}, \mathrm{B}=60^{\circ}, \mathrm{C}=90^{\circ}$
$\frac{\sin ^{2} 30^{\circ}+\sin ^{2} 60^{\circ}+\sin ^{2} 90^{\circ}}{\cos ^{2} 30^{\circ}+\cos ^{2} 60^{\circ}+\cos ^{2} 90^{\circ}}$
$=\frac{\frac{1}{4}+\frac{3}{4}+1}{\frac{3}{4}+\frac{1}{4}+0}=\frac{1+1}{1}=\frac{2}{1}=2$
So, the given triangle is right-angled triangle.

Topic: Mathematics, Inverse Trigonometric Functions, NDA, NDA 2017 (Phase 2)
In vertebrates, the notochord is modified into

Options:
A Vertebral column
B Centrum of vertebrae
C Body of vertebrae
D Transverse process of vertebrae

The correct answer is:
Vertebral column

Solution:
The members of subphylum vertebrata possess notochord during the embryonic period. The notochord is replaced by a cartilaginous or bony vertebral column in the adult. Besides the basic chordate characters, vertebrates have a ventral muscular heart with two, three or four chambers, kidneys for excretion and osmoregulation and paired appendages which may be fins or limbs.

Topic: Biology, Animal Kingdom, NEET
In Werner's theory, what is the typical nature of the secondary valences?

Options:
A Ionizable and satisfied by neutral molecules
B Non-ionizable and satisfied by negative ions
C Ionizable and satisfied by negative ions
D Non-ionizable and satisfied by neutral molecules

The correct answer is:
Non-ionizable and satisfied by neutral molecules

Solution:
Secondary valences in Werner's theory are non-ionizable and are typically satisfied by neutral molecules.

Topic: Chemistry, Coordination Compounds, NEET
In what ratio does the line $\mathrm{y}-\mathrm{x}+2=0$ cut the line joining $(3,-1)$ and $(8,9) ?$

Options:
A $2: 3$
B $3: 2$
C $3:-2$
D $1: 2$

The correct answer is:
$2: 3$

Solution:
Let the point of intersection divide the line segment joining points, $(3,-1)$ and $(8,9)$ in $\mathrm{k}: 1$ ratio then:
The point is $\left(\frac{8 \mathrm{k}+3}{\mathrm{k}+1}, \frac{9 \mathrm{k}-1}{\mathrm{k}+1}\right)$
Since this point lies on the line $\mathrm{y}-\mathrm{x}+2=0$
We have, $\frac{9 \mathrm{k}-1}{\mathrm{k}+1}-\frac{8 \mathrm{k}+3}{\mathrm{k}+1}+2=0$
$=\frac{9 \mathrm{k}-1-8 \mathrm{k}-3}{\mathrm{k}+1}+2=0=\frac{\mathrm{k}-4}{\mathrm{k}+1}+2=0$
$=\mathrm{k}-4+2 \mathrm{k}+2=0=3 \mathrm{k}-2=0$
$\mathrm{k}=\frac{2}{3}: 1$ i.e. $2: 3$

Topic: Mathematics, Straight Lines, NDA, NDA 2007 (Phase 1)
In which disease does mosquito-transmitted pathogen cause chronic inflammation of lymphatic vessels?

Options:
A Ringworm diseases
B Ascariasis
C Elephantiasis
D Amoebiasis

The correct answer is:
Elephantiasis

Solution:
Elephantiasis, also known as lymphatic filariasis, is a very rare condition that’s spread by mosquitoes (Culex).
The most common symptom of elephantiasis is swelling of body parts. The swelling tends to happen in the: legs, genitals, breasts, arms.
The legs are the most commonly affected area. The swelling and enlargement of body parts can lead to pain and mobility issues. The skin is also affected and may be: dry, thick, ulcerated, darker than normal and pitted.
Some people experience additional symptoms, such as fever and chills. Elephantiasis affects the immune system. People with this condition are also at increased risk for a secondary infection.

Ascariasis is caused by the helminth Ascaris, commonly called a roundworm. Amoebiasis is caused by the pathogen Entamoeba histolytica. It causes a form of dysentery (also called amoebic dysentery). Both of these diseases are transmitted through contaminated food and water. Ringworm diseases are caused by fungi belonging to the genus Microsporum, Trichophyton, Epidermaphyton. They are transmitted through soil or personal items of infected people.

Topic: Biology, Human Health and Diseases, NEET, NEET 2018
In which of the following amino acids - $\mathrm{OH}$ group is present?
\begin{array}{cccc}
Lysine & Serine & Tyrosine & Valine \\
A & B & C & D
\end{array}

Options:
A A, B
B A, C
C $\mathrm{B}, \mathrm{C}$
D B, D

The correct answer is:
$\mathrm{B}, \mathrm{C}$

Solution:

Topic: Chemistry, Biomolecules, AP EAMCET, AP EAMCET 2023 (18 May Shift 2)
In which of the following aspect PCR is not leading over gene cloning ?

Options:
A Efficiency
B Less user's skill
C Error probability
D Less expensive

The correct answer is:
Error probability

Solution:
In Error probability aspect PCR is not leading over gene cloning. If standard PCR conditions do not yield the desired amplicon, PCR optimization is necessary to attain better results. The stringency of a reaction may be modulated such that the specificity is adjusted by altering variables (e.g., reagent concentrations, cycling conditions) that affect the outcome of the amplicon profile. For example, if the reaction is not stringent enough, many spurious amplicons will be generated with variable lengths. If the reaction is too stringent, no product will be produced. Troubleshooting PCR reactions may be a frustrating endeavor at times. However, careful analysis and a good understanding of the reagents used in a PCR experiment can reduce the amount of time and trials needed to obtain the desired results. Of all the considerations that impact PCR stringency, titration of Mg2+ and/or manipulating annealing temperatures likely will solve most problems. However, before changing anything, be sure that an erroneous result was not due to human error. Start by confirming all reagents were added to a given reaction and that the reagents were not contaminated.

Topic: Biology, Biotechnology - Principles and Processes, NEET
In which of the following cartilaginous ring support will not be observed?

Options:
A Secondary bronchi
B Trachea
C Initial bronchioles
D Respiratory bronchioles

The correct answer is:
Respiratory bronchioles

Solution:
Cartilaginous ring structures are found the tubes of the respiratory system to prevent its collapse. It is present in the trachea, two initial branches of bronchi along with the secondary and tertiary bronchi. The initial bronchioles also have it. The terminal bronchioles are not having any rings and they give rise to number of thing vascularized structures called alveoli. The terminal bronchi is also called as the respiratory bronchioles.

Topic: Biology, Breathing and Exchange of Gases, NEET
In which of the following cases a chemical reaction is possible?

Options:
A $\mathrm{ZnSO}_{4}(a q)$ is placed in a copper vessel
B $\mathrm{AgNO}_{3}$ solution is stirred with a copper spoon
C Conc. $\mathrm{HNO}_{3}$ is stored in a platinum vessel
D gold ornaments are washed with dil. $\mathrm{HCl}$

The correct answer is:
$\mathrm{AgNO}_{3}$ solution is stirred with a copper spoon

Solution:
A chemical reaction is possible when $\mathrm{AgNO}_{3}$ solution is stirred with copper spoon as copper has lesser positive value of standard electrode reduction potential as compared to Ag.
The reaction will be,
$2 \mathrm{AgNO}_{3}+\mathrm{Cu} \longrightarrow \mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}+2 \mathrm{Ag}$

Topic: Chemistry, Electrochemistry, KCET, KCET 2020
In which of the following chromosomal disorders do we observe the features like a long furrowed tongue and short stature?

Options:
A Down syndrome
B Klinefelter's syndrome
C Turner's syndrome
D Pater's syndrome

The correct answer is:
Down syndrome

Solution:
Syndrome	Chromosomal set up	Features
1. Down’s Syndrome (first described by Langdon Down In 1866)	Trisomy of Chromosome number 21	- Short statured with small round head. - Long and furrowed tongue. - Partially open mouth. - Physical, mental and psychomotor development retarded.
2. Klinefelter’s syndrome	Trisomy of sex chromosome (44 + XXY)	- Such males have some feminine features like gynaecomastia (development of breast), etc. - Sterile.
3. Turner’s syndrome	Monosomy of sex chromosome (44 + XO)	- Such females have rudimentary ovaries and lack other secondary sexual characters. - Sterile.

Topic: Biology, Principles of Inheritance and Variation, NEET
In which of the following locations are sacred groves found?

Options:
A Khasi and Jaintia Hills in Meghalaya
B Aravalli Hills of Rajasthan
C Sarguja, Chanda and Bastar areas of Madhya Pradesh
D All of the above

The correct answer is:
All of the above

Solution:
In many cultures, tracts of forest were set aside, and all the trees and wildlife within were venerated and given total protection. Such sacred groves are found in Khasi and Jaintia hills in Meghalaya; Aravalli hills in Rajasthan; Western Ghat regions of Karnataka and Maharashtra and the Sarguja, Chanda and Bastar areas of Madhya Pradesh. In Meghalaya, the sacred groves are the last refuges for a large number of rare and threatened plants.

Topic: Biology, Biodiversity and its Conservation, NEET
In which of the following method of biodiversity conservation, tracts of forest are set aside, and all the trees and wildlife within are venerated and given total protection?

Options:
A Sacred groves
B Botanical garden
C Biosphere reserves
D National park

The correct answer is:
Sacred groves

Solution:
India has also a history of religious and cultural traditions that emphasize the protection of nature. In many cultures, tracts of forest were set aside, and all the trees and wildlife within were venerated and given total protection. Such sacred groves are found in Khasi and Jaintia hills in Meghalaya, Aravalli hills of Rajasthan, Western Ghat regions of Karnataka and Maharashtra and the Sarguja, Chanda and Bastar areas of Madhya Pradesh. In Meghalaya, the sacred groves are the last refuges for a large number of rare and threatened plants.

Topic: Biology, Biodiversity and its Conservation, NEET
In which of the following reactions, standard reaction entropy changes $\left(\Delta S^{\circ}\right)$ is positive and standard Gibb's energy change $\left(\Delta G^{\circ}\right)$ decreases sharply with increasing temperature?

Options:
A $\mathrm{C}$ (graphite) $+\frac{1}{2} \mathrm{O}_2(g) \longrightarrow \mathrm{CO}(g)$
B $\mathrm{CO}(g)+\frac{1}{2} \mathrm{O}_2(g) \longrightarrow \mathrm{CO}_2(g)$
C $\mathrm{Mg}(s)+\frac{1}{2} \mathrm{O}_2(g) \longrightarrow \mathrm{MgO}(s)$
D $\frac{1}{2} \mathrm{C}$ (graphite) $+\frac{1}{2} \mathrm{O}_2(g) \longrightarrow \frac{1}{2} \mathrm{CO}_2(g)$

The correct answer is:
$\mathrm{C}$ (graphite) $+\frac{1}{2} \mathrm{O}_2(g) \longrightarrow \mathrm{CO}(g)$

Solution:
Among the given reactions only in the case of
$\mathrm{C} \text { (graphite) }+\frac{1}{2} \mathrm{O}_2(\mathrm{~g}) \longrightarrow \mathrm{CO}(\mathrm{g})$
entropy increases because randomness (disorder) increases. Thus, standard entropy change $\left(\Delta S^{\circ}\right)$ is positive.
Moreover, it is a combustion reaction and all the combustion reactions are generally exothermic, i.e., $\Delta H^{\circ}=-$ ve
We know that
$\begin{aligned}
& \Delta G^{\circ}=\Delta H^{\circ}-T \Delta S^{\circ} \\
& \Delta G^{\circ}=-v \mathrm{v}-T(+\mathrm{ve})
\end{aligned}$
Thus, as the temperature increases, the value of $\Delta G^{\circ}$ decreases.

Topic: Chemistry, Thermodynamics (C), NEET, NEET 2012 (Screening)
In which of the following, sporophylls may form distinct compact structures called strobili is found

Options:
A Selaginella and Fuucs
B Selaginella and Equisetum
C Fusus and Cycas
D Pteris and Polysiphonia

The correct answer is:
Selaginella and Equisetum

Solution:
The sporophytes bear sporangia that are subtended by leaf-like appendages called sporophylls. In some cases, sporophylls may form distinct compact structures called strobili or cones (Selaginella, Equisetum).

Topic: Biology, Plant Kingdom, NEET
In which of the following, this kind of vascular bundle can be seen?

Options:
A

Dicot stem

B

Monocot stem

C

Dicot leaf

D

Monocot leaf

The correct answer is:

Dicot stem

Solution:
A large number of vascular bundles are arranged in a ring; the ‘ring’ arrangement of vascular bundles is a characteristic of dicot stem. Each vascular bundle is conjoint, open, and with endarch protoxylem.

Topic: Biology, Anatomy of Flowering Plants, NEET
In which of the following, Tyndall effect is not observed?

Options:
A Smoke
B Emulsion
C Sugar solution
D Gold sol

The correct answer is:
Sugar solution

Solution:
Tyndall effect is not observed in sugar solution because it is a true homogeneous solution. Colloidal solutions show Tyndall effect.

Topic: Chemistry, Surface Chemistry, NEET
In which of the following will be observed the webbed neck condition?

Options:
A XXY
B XY
C XO
D XXX

The correct answer is:
XO

Solution:
The chromosomal disorder occurs when there is an addition or deletion of the chromosome in the individual. In case of trisomy of the 21st chromosome, Down's syndrome will be observed. Turner's syndrome is a type of chromosomal disorder occurring due to the loss of one X chromosome resulting in the genotype as 44+X or 44+XO.
Such females are characterized by stunted height and webbed-neck. They are sterile as ovaries are rudimentary and lack secondary sexual characteristics.
XXY condition is called Klinefelter's syndrome where an individual has an extra copy of X chromosome.

Topic: Biology, Principles of Inheritance and Variation, NEET
In which one of the following cases would you except to get a negative correlation?

Options:
A The ages of husbands and wives
B Shoe size and intelligence
C Insurance companies profits and the number of claims they have to pay
D Amount of rainfall and yield of crop

The correct answer is:
Insurance companies profits and the number of claims they have to pay

Solution:
By definition.

Topic: Mathematics, Statistics, NDA, NDA 2018 (Phase 2)
In which one of the following intervals is the function $\mathrm{f}(\mathrm{x})=\mathrm{x}^{2}-5 \mathrm{x}+6$ decreasing?

Options:
A $(-\infty, 2]$
B $[3, \infty]$
C $(-\infty, \infty)$
D $(2,3)$

The correct answer is:
$(-\infty, 2]$

Solution:
$\Rightarrow f^{\prime}(x)=x^{2}-5 x+6$
$\Rightarrow \quad f^{\prime}(x) < 0$
$\Rightarrow \quad 2 x-5 < 0$
$\Rightarrow \quad x < \frac{5}{2}$
Hence, $f(x)$ is decreasing in $(-\infty, 2.5]$

Topic: Mathematics, Application of Derivatives, NDA, NDA 2018 (Phase 2)