datavorous/entrance-exam-dataset huggingface dataset:
Which of the following function is inverse function

Options:
A $f(x)=\frac{1}{x-1}$
B $f(x)=x^2$ for all $x$
C $f(x)=x^2, \quad x \geq 0$
D $f(x)=x^2, x \leq 0$

The correct answer is:
$f(x)=\frac{1}{x-1}$

Solution:
For finding inverse of any function, function should be bijective. Since $f(x)=\frac{1}{x-1}$ is bijective function.

Topic: Mathematics, Functions, JEE Main
Which of the following function is invertible

Options:
A $f(x)=2^x$
B $f(x)=x^3-x$
C $f(x)=x^2$
D None of these

The correct answer is:
$f(x)=2^x$

Solution:
A function is invertible if it is one-one and onto.

Topic: Mathematics, Functions, JEE Main
Which of the following function is not continuous at x=0?

Options:
A fx=1+2x1x,x≠0=e2,x=0
B fx=sin⁡x-cos⁡x,x≠0=-1,x=0
C fx=e1x-1e1x+1,x≠0=-1,x=0
D fx=e5x-e2xsin⁡3x,x≠0=1,x=0

The correct answer is:
fx=e1x-1e1x+1,x≠0=-1,x=0

Solution:
Given fx
e1/x-1e1/x+1x≠0-1x=0
R.H.L. limx→0+1-e-1/x1+e-1/x=1≠f0

Topic: Mathematics, Continuity and Differentiability, JEE Main
Which of the following function or activity is not affected by smooth muscles in human?

Options:
A Transportation of food through the digestive tract
B Transport of gametes through the genital duct
C Transportation of urine through the ureter and bladder
D Chewing and swallowing of food through buccal cavity.

The correct answer is:
Chewing and swallowing of food through buccal cavity.

Solution:
Transportation of food by peristalsis through the digestive tract, transport of gametes through genital tract and transportation of urine through ureter and ureter is mainly controlled by contraction and relaxation of non-striated smooth muscles. Chewing and swelling of food involves striated and skeletal voluntary muscles.

Topic: Biology, Locomotion and Movement, NEET
Which of the following functional groups is generally least reactive towards nucleophilic substitution reactions?

Options:
A Amide
B Ester
C acid chloride
D Acid Anhydride

The correct answer is:
Amide

Solution:
Reactivity order

R-cO||-Cl>R-cO||-o-cO||-R>R-cO||-OR>R-cO||-NH2

Reactivity for nucleophilic in decreasing order.

Topic: Chemistry, Carboxylic Acid Derivatives, JEE Main
Which of the following functions from $\mathrm{Z}$ into $\mathrm{Z}$ are bijective?

Options:
A
$f(x)=x^3$

B
$\mathrm{f}(\mathrm{x})=\mathrm{x}+2$

C
$\mathrm{f}(\mathrm{x})=2 \mathrm{x}+1$

D
$f(x)=x^2+1$

The correct answer is:
$\mathrm{f}(\mathrm{x})=\mathrm{x}+2$

Solution:
The function $f(x)=x+2$ is one-one as for $x_1, x_2 \in Z$. Consider, $\mathrm{f}\left(\mathrm{x}_1\right)=\mathrm{f}\left(\mathrm{x}_2\right)$
$$
\Rightarrow x_1+2=x_2+2 \Rightarrow x_1=x_2
$$
Also, let $y \in$ codomain of $f=Z$ such that $y=f(x)$ $\Rightarrow \mathrm{y}=\mathrm{x}+2 \Rightarrow \mathrm{x}=\mathrm{y}-2 \in \mathrm{Z}$ for all $\mathrm{y} \in \mathrm{Z}$
$\therefore \mathrm{f}$ is onto. Hence, $\mathrm{f}(\mathrm{x})=\mathrm{x}+2$ is bijective.

Topic: Mathematics, Relations and Functions (Class 11)
Which of the following functions is carried out by cytoskeleton in a cell?

Options:
A Transportation
B Nuclear division
C Protein synthesis
D Motility

The correct answer is:
Motility

Solution:
An elaborate network of filamentous proteinaceous structures consisting of microtubules (of tubulin protein), microfilaments (of actin or myosin proteins) and intermediate filaments present in the cytoplasm is collectively referred to as the cytoskeleton. The cytoskeleton in a cell are involved in many functions such as mechanical support, motility, maintenance of the shape of the cell.

Topic: Biology, Cell - The Unit of Life, NEET, NEET 2023 (All India)
Which of the following functions is differentiable at $x=0$ ?

Options:
A $\cos (|x|)+|x|$
B $\cos (|x|)-|x|$
C $\sin (|x|)+|x|$
D $\sin (|x|)-|x|$

The correct answer is:
$\sin (|x|)-|x|$

Solution:
(a) We have,
$f(x)=\cos |x|+|x|$
$=\left\{\begin{array}{cc}\cos (-x)+(-x), & x < 0 \\ \cos (x)+x, & x \geq 0\end{array}\right.$
$= \begin{cases}\cos x-x, & x < 0 \\ \cos x+x, & x \geq 0\end{cases}$
$\therefore f^{\prime}(x)= \begin{cases}-\sin x-1, & x < 0 \\ -\sin x+1, & x \geq 0\end{cases}$
$\therefore f^{\prime}\left(0^{-}\right)=-1$ and $f^{\prime}\left(0^{+}\right)=1$
$\Rightarrow f^{\prime}\left(0^{-}\right) \neq f^{\prime}\left(0^{+}\right)$
So, it is not differentiable at $x=0$.
(b) We have,
$$
\begin{aligned}
f(x) &=\cos |x|-|x| \\
&=\left\{\begin{array}{rr}
\cos (-x)-(-x), & x < 0 \\
\cos (x)-x, & x \geq 0
\end{array}\right.\\
&= \begin{cases}\cos x+x, & x < 0 \\
\cos x-x, & x \geq 0\end{cases} \\
\therefore f^{\prime}(x) &= \begin{cases}-\sin x+1, & x < 0 \\
-\sin x-1, & x \geq 0\end{cases} \\
\therefore f^{\prime}\left(0^{-}\right) &=1 \text { and } f^{\prime}\left(0^{+}\right)=-1
\end{aligned}
$$
So, it is not differentiable at $x=0$.

Topic: Mathematics, Continuity and Differentiability, JEE Main
Which of the following functions is injective?

Options:
A fx=x2+3,  x∈-∞, ∞
B fx=x+1,  x∈2, ∞
C fx=x-4x-5,  x∈∞, 5
D fx=4x2+3x-54+3x+5x2,  x∈ -∞, ∞

The correct answer is:
fx=x+1,  x∈2, ∞

Solution:
The function fx=x2+3,  x∈-∞, ∞ is not injective as f1=f-1 but 1≠-1 .
The function fx=x-4x-5,  x∈-∞, 5 is not injective as f4=f5 but 4≠5
The function fx=4x2+3x-54+3x+5x2,  x∈  -∞, ∞ is not injective as f0=f-2741 but 0≠-2741
For the function, fx=x+1, x∈2, ∞
Let fx=fy,  x,y∈2, ∞⇒x+1=y+1
⇒x+1=y+1
⇒x=y
So, f is an injective

Topic: Mathematics, Functions, JEE Main
Which of the following functions is inverse of itself

Options:
A $f(x)=\frac{1-x}{1+x}$
B $f(x)=5^{\log x}$
C $f(x)=2^{x(x-1)}$
D None of these

The correct answer is:
$f(x)=\frac{1-x}{1+x}$

Solution:
$f \circ f(x)=f(f(x))=f\left(\frac{1-x}{1+x}\right)=\frac{1-\frac{1-x}{1+x}}{1+\frac{1-x}{1+x}}=x, \forall x$
$\therefore f \circ f=I \Rightarrow f$ is the inverse of itself.

Topic: Mathematics, Functions, JEE Main
Which of the following functions is inverse of itself?

Options:
A \( f(t)=\frac{(1-t)}{(1+t)} \)
B \( f(t)=\frac{\left(1-t^{2}\right)}{\left(1+t^{2}\right)} \)
C \( f(t)=4^{\log t} \)
D \( f(t)=2^{t} \)

The correct answer is:
\( f(t)=\frac{(1-t)}{(1+t)} \)

Solution:
Let y=ft ∴t=f-1y
Now, y=ft=1 - t1 + t⇒y+ty=1-t
⇒t+ty=1-y⇒t=1-y1+y
i.e., f-1y=1 - y1 + y or f-1t=1 - t1+ t
Thus, this function is inverse of itself.

Topic: Mathematics, Functions, JEE Main
Which of the following functions is/are identical to $|x-2|$ ?

Options:
A $f(x)=\sqrt{x^2-4 x+4}$
B $g(x)=|x|-|2|$
C $h(x)=\frac{|x-2|^2}{|x-2|}$
D $t(x)=\left|\frac{x^2-x-2}{x+1}\right|$

The correct answer is:
$f(x)=\sqrt{x^2-4 x+4}$

Solution:
$\begin{aligned}
& f(x)=\sqrt{x^2-4 x+4}=\sqrt{(x-2)^2}=|x-2| \\
& g(x)=|x|-|2|=|x|-2== \begin{cases}-x-2, & x \lt 2 \\
x-2, & x \geq 2\end{cases} \\
&
\end{aligned}$
Thus $g(x)$ is not same as $|x-2|$
$h(x)=\frac{|h-2|^2}{|x-2|}=|x-2|, x \neq 2 \text {. }$
This is not same as $|x-2|$ as $h(x)$ has domain $R-\{2\}$
$t(x)=\left|\frac{x^2-x-2}{x+1}\right|=\left|\frac{(x-2)(x+1)}{x+1}\right|=|x-2|, x \neq-1 \text {. }$
Thus $t(x)$ is not same as $|x-2|$ as $t(x)$ has domain $R-\{-1\}$.

Topic: Mathematics, Functions, JEE Main
Which of the following functions satisfies all conditions of the Rolle’s theorem in the intervals specified?

Options:
A fx=x13,x∈-2,3
B fx=sin⁡x,x∈-π,π6
C fx=ln⁡x2+abxa+b, x∈a,b,0<a<b
D fx=ex2-x,x∈0,4

The correct answer is:
fx=ln⁡x2+abxa+b, x∈a,b,0<a<b

Solution:
fx=x13 is not differentiable at x=0
For fx=sin⁡x, f-π≠fπ6
For fx=ln⁡x2+abxa+b
fa=fb=ln⁡1=0
Also, it is continuous in a,b and differentiable in a,b. Hence, Rolle’s Theorem is applicable.
For fx=ex2-x, f0≠f4

Topic: Mathematics, Application of Derivatives, JEE Main
Which of the following given below can liberate Br2 from KBr?
F2,Cl2,I2 and Conc.H2SO4

Options:
A F2,Cl2,I2 and Conc.H2SO4
B Cl2,I2 and Conc.H2SO4
C F2,Cl2,I2
D F2,Cl2 and Conc.H2SO4

The correct answer is:
F2,Cl2 and Conc.H2SO4

Solution:
I2 cannot liberate Br2 from KBr, since I2 is weaker oxidant than Br2.
F2 and Cl2 , being stronger oxidants than Br2 , can liberate Br2 from KBr.
F2+2KBr→2KF+Br2
Cl2+2KBr→2KCl+Br2
Reaction of conc. H2SO4 with KBr forms HBr. HBr is a strong reducing agent so it reduces H2SO4 to form a mixture of SO2 and Br2 .
KBr+H2SO4→HBr+KHSO4
KHSO4+KBr→HBr+K2SO4
HBr so formed reduces H2SO4 .
H2SO4+2HBr→SO2+2H2O+Br2

Topic: Chemistry, p Block Elements (Group 15, 16, 17 & 18), JEE Main
Which of the following gives a positive test with ninhydrin?

Options:
A Starch
B Egg albumin
C Polyvinyl chloride
D Cellulose

The correct answer is:
Egg albumin

Solution:
Ninhydrin test is a test of amino acids. Egg albumin contains protein which is a natural polymer of amino acids which will show positive ninhydrin test

Topic: Chemistry, Biomolecules, JEE Main, JEE Main 2024 (05 Apr Shift 1)
Which of the following gives a reversible operation?

Options:
A
B
C
D

The correct answer is:

Solution:
A logic gate gives the reversible operation if we can recover input data from the output.

For example, a NOT gate gives the reversible operation because we always know that the input is the reverse of the output.

For the given logic gate, let the input is X.

So, the output, Y=X+X¯=X¯ (NOT gate)

Topic: Physics, Semiconductors, JEE Main, JEE Main 2020 (07 Jan Shift 1)
Which of the following gives aldol condensation reaction

Options:
A $\mathrm{C}_6 \mathrm{H}_5 \mathrm{OH}$
B

C

D

The correct answer is:

Solution:
Although both $\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{COCH}_3$ and $\left(\mathrm{CH}_3\right)_3 \mathrm{CCOCH}_3$ contain a-hydrogen, yet $\left(\mathrm{CH}_3\right)_3 \mathrm{CCOCH}_3$ does not undergo Aldol condensation due to steric hindrance

Topic: Chemistry, Aldehydes and Ketones, JEE Main
Which of the following gives ketone on oxidation

Options:
A $\left(\mathrm{CH}_3\right)_3 \mathrm{COH}$
B $\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{CH}_2 \mathrm{OH}$
C $\left(\mathrm{CH}_3\right)_2 \mathrm{CHCH}_2 \mathrm{OH}$
D $\mathrm{CH}_3 \mathrm{CHOHCH}_3$

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

Solution:

Topic: Chemistry, Alcohols Phenols and Ethers, JEE Main
Which of the following gives ketone on oxidation ?

Options:
A (CH3)3COH
B CH3CH2CH2OH
C (CH3)2CHCH2OH
D CH3CHOHCH3

The correct answer is:
CH3CHOHCH3

Solution:
CH3CHOHCH3 gives ketone on oxidation
CH3-CH| OH-CH3â[O]CH3-C||O-CH3

Topic: Chemistry, Alcohols Phenols and Ethers, JEE Main
Which of the following gives positive Libermann-nitroso test?

Options:
A 2-butanamine
B N-ethyl-2-pentanamine
C N-methylpiperidine
D N, N-dimethylcyclohexylamine

The correct answer is:
N-ethyl-2-pentanamine

Solution:
2 o amine will give positive nitrosamine test.

Topic: Chemistry, Amines, JEE Main
Which of the following gives propyne on hydrolysis

Options:
A $\mathrm{Al}_4 \mathrm{C}_3$
B $\mathrm{Mg}_2 \mathrm{C}_3$
C $\mathrm{B}_4 \mathrm{C}$
D $\mathrm{La}_4 \mathrm{C}_3$

The correct answer is:
$\mathrm{Mg}_2 \mathrm{C}_3$

Solution:
Propyne can be prepared by the hydrolysis of magnesium carbide
$\mathrm{Mg}_2 \mathrm{C}_3+4 \mathrm{H}_2 \mathrm{O} \rightarrow \mathrm{CH}_3 \mathrm{C} \equiv \mathrm{CH}+2 \mathrm{Mg}(\mathrm{OH})_2$

Topic: Chemistry, p Block Elements (Group 13 & 14), JEE Main
Which of the following gives the molarity of a 17.0% by mass solution of sodium acetate, CH 3 COONa FM = 82.0 amu in water? Given the density is 1.09 g/mol .

Options:
A 2.26×10-6M
B 0.207 M
C 2.07 M
D 2.26 M

The correct answer is:
2.26 M

Solution:
17.0% solution of CH 3 COONa means that 100âg solution contain 17âg of CH 3 COONa .
Moles of CH 3 COONaâ=â 17âg 82.0âgâ mol â1 â=â 17 82.0 âmol
Volume of 100âg solution =Mass of solutionDensity of solution
=â 100âg 1.09âgâ mol â1 â=â 100 1.09 mL
So molarity of solution =â Molesâofâsolute Literâofâsoln.
=  17 82.0 mol 100 1.09 ×10 −3  L
= 2.259 M = 2.26 M

Topic: Chemistry, Some Basic Concepts of Chemistry, JEE Main
Which of the following glands is large sized at birth but reduces in size with ageing?

Options:
A
Pineal

B
Pituitary

C
Thymus

D
Thyroid

The correct answer is:
Thymus

Solution:
The thymus is a lobed organ that is located near the heart and beneath the breastbone. It is quite large at the time of birth but keeps reducing in size with age and by the time puberty is attained it reduces to a very small size. While the size of pineal gland (located at brain), pituitary gland (in brain), thyroid (located in front of neck) remains constant in size since birth.

Topic: Biology, Human Health and Diseases
Which of the following graph correctly represents the variation of molar conductance (Δm) with dilution for a strong electrolyte?

Options:
A
B
C
D

The correct answer is:

Solution:
On dilution the molar conductance of the electrolyte solution will increase exponentially.

Topic: Chemistry, Electrochemistry, JEE Main
Which of the following graph represent Boyles law?

Options:
A
B
C
D All of these

The correct answer is:
All of these

Solution:
As per Boyles law
PV=constant
PV=constant 1V2
log⁡P=-log⁡V+log⁡(constant)

Topic: Chemistry, States of Matter, JEE Main
Which of the following graph represents uniform motion

Options:
A

B

C

D

The correct answer is:

Solution:
A body is said to be in uniform motion if it covers equal distances in equal intervals of time i.e., moving with a constant speed. The distance-time graph which shows a straight line and the speed-time graph which shows a straight line parallel to time-axis represent uniform motion.

Topic: Physics, Motion In One Dimension, JEE Main
Which of the following graphs are correct for velocity of e- in an orbit vs Z, 1n and n?

Options:
A (i), (ii)
B (ii), (iv)
C (i), (ii), (iii)
D (i), (ii), (iv)

The correct answer is:
(i), (ii), (iv)

Solution:
As velocity of e- in an orbit vn∝Z∝1n .
It means plots (i), (ii) and (iv) are correct while (iii) is incorrect.

Topic: Chemistry, Structure of Atom, JEE Main
Which of the following graphs correctly represents the variation ββ=-dVdPT/V of with P for an ideal gas at constant temperature?

Options:
A
B
C
D

The correct answer is:

Solution:
As PV=RT
So P × dV + V × dP = 0
or dVdPr=VP
or Î²=dVdPrV=1P
Hence, Plot in (A) is correct.

Topic: Chemistry, Thermodynamics (C), JEE Main
Which of the following graphs correctly represents the variation of β = − 1 V   dV dP with P for an ideal gas at constant temperature?

Options:
A
B
C
D

The correct answer is:

Solution:
PV = Constant
On differentiating both sides, we get
PdV + VdP = 0
PdV = -VdP
dVdP=-VP
1 P  = − 1 V   dV dP  = β
Since β=1P ; inverse relation result into rectangular hyperbola.

Topic: Chemistry, States of Matter, JEE Main
Which of the following graphs correctly represents the variation of ββ=-dVdPTV with P for an ideal gas at constant temperature?

Options:
A
B
C
D

The correct answer is:

Solution:
As PV = RT
So P.dV + V.dP = 0
or dVdP=-VP
or β=-dVdPTV=1P
Hence plot in A is correct.

Topic: Chemistry, States of Matter, JEE Main
Which of the following graphs is inconsistent with ideal gas behaviour ?

Options:
A
B
C
D

The correct answer is:

Solution:
P∝1V
P=nRTV

Topic: Chemistry, States of Matter, JEE Main
Which of the following graphs represent Boyle's law

Options:
A

B

C

D

The correct answers are:
,

Solution:
According to Boyle's Law $P V=$ constant, at constant temperature either $P$ increases or $V$ increases both (b) \& (c) may be correct.

Topic: Chemistry, States of Matter, JEE Main
Which of the following graphs represents the motion of a particle moving with constant velocity?

Options:
A graphs (i) and (iii)
B graphs (i) and (iv)
C graphs (i) and (ii)
D graph (i)

The correct answer is:
graphs (i) and (iv)

Solution:
For the graphs (i) and (iv), slope is constant, hence the velocity is constant.

Topic: Physics, Motion In One Dimension, JEE Main
Which of the following graphs represents $y=2|x-2|-|x+1|+x ?$

Options:
A

B

C

D

The correct answer is:

Solution:
It can be seen that
$f(x)= \begin{cases}5 & \text { if } x \leq-1 \\ 3-2 x & \text { if }-1 \leq x \leq 2 \\ 2 x-5 & \text { if } x \geq 2\end{cases}$

Topic: Mathematics, Functions, JEE Main
Which of the following graphs shows most significant deviation from ideal gas behaviour?

Options:
A
B
C
D

The correct answer is:

Solution:
For ideal gas,
PV=nRT
PT=nRV
So expected graph when PT is plotted against V will be

Topic: Chemistry, States of Matter, JEE Main
Which of the following group of plants exhibit more species diversity?

Options:
A Angiosperms
B Algae
C Bryophytes
D Fungi

The correct answer is:
Angiosperms

Solution:
Fungi belong to a different kingdom and are not considered plants as they are not photosynthetic and cell wall is made of chitin. These groups ae mainly saprophytic and some are parasitic. Many of the fungi contribute as decomposers in the food chain.
Sub division Angiosperms of the plant kingdom show the highest diversity among all the plant groups and also the most evolved. One of the reasons for it is the development of the reproductive structure called flower. Algae and bryophytes are the simpler non-vascular group of the plant kingdom.

Topic: Biology, Biodiversity and its Conservation, NEET
Which of the following halide is $2^{\circ}$

Options:
A Isopropyl chloride
B Isobutyl chloride
C n-propyl chloride
D n-butyl chloride

The correct answer is:
Isopropyl chloride

Solution:

Topic: Chemistry, Haloalkanes and Haloarenes, JEE Main
Which of the following halides cannot be hydrolysed ?

(I) TeF 6 (II) SF 6 (III) NCl 3 (IV) NF 3

Choose the correct code :

Options:
A III and IV
B I, II and III
C I, II and IV
D II and IV

The correct answer is:
II and IV

Solution:
In SF6, S sterically hindered by six fluorine atoms hence, attack of H2O molecule will not occur. NF3 is not hydrolysed due to absence of vacant orbital either on N of F atom.
TeF6 is hydrolysed due to large size of Te.
NCl 3 + 4 H 2 O → NH 4 OH + 3 HOCl TeF 6 + 6 H 2 O → 6 HF + H 6 TeO 6 Telluric acid

Topic: Chemistry, p Block Elements (Group 15, 16, 17 & 18), JEE Main
Which of the following halides is most acidic

Options:
A $\mathrm{PCl}_3$
B $\mathrm{BiCl}_3$
C $\mathrm{SbCl}_3$
D $\mathrm{CCl}_4$

The correct answer is:
$\mathrm{PCl}_3$

Solution:
Because phosphorous is most electronegative element out of $P, B i, S b$ and $C$.

Topic: Chemistry, p Block Elements (Group 15, 16, 17 & 18), JEE Main
Which of the following halides will be most reactive in SN1 reaction and SN2 reactions, respectively

Options:
A (I), (II)
B (II), (I)
C (I), (III)
D (III), (I)

The correct answer is:
(III), (I)

Solution:
(I) 1° allylic halide have less steric hindrance, so it is more reactive for SN2 reaction.
(III) 3° allylic halide gives most stable tertiary allylic carbonium ion so most reactive towards SN1 reaction.

Topic: Chemistry, Haloalkanes and Haloarenes, JEE Main
Which of the following halogen oxides is used for the estimation of carbon monoxide in automobile exhaust gases?

Options:
A \( \mathrm{Cl}_{2} \mathrm{O}_{7} \)
B \( \mathrm{I}_{2} \mathrm{O}_{5} \)
C \( \mathrm{ClO}_{2} \)
D \( \mathrm{BrO}_{3} \)

The correct answer is:
\( \mathrm{I}_{2} \mathrm{O}_{5} \)

Solution:
Iodine pentoxide oxidizes CO to carbon dioxide and reduces itself to iodine. And the iodine released is reacted with Na2S2O3 to estimate the amount of iodine is released and from that amount of carbon monoxide can be estimated. The reactions are as follows.

5CO+I2O5→5CO2+I2I2+2Na2S2O3→2NaI+Na2S4O6

Topic: Chemistry, p Block Elements (Group 13 & 14), JEE Main
Which of the following has acidic hydrogen

Options:
A Ethyne
B Ethene
C Ethane
D Benzene

The correct answer is:
Ethyne

Solution:
$2 \mathrm{CH} \equiv \mathrm{CH}+2 \mathrm{Na} \rightarrow 2 \mathrm{CH} \equiv \mathrm{C}^{-} \mathrm{Na}^{+}+\mathrm{H}_2$
Reaction with sodium metal shows that hydrogen is acidic.

Topic: Chemistry, Hydrocarbons, JEE Main
Which of the following has an ester linkage?

Options:
A Nylon-6, \( 6 \)
B Dacron
C PVC
D Bakelite

The correct answer is:
Dacron

Solution:
The ester linkage in which two groups are linked by ester (-COO-). When a carboxylic acid and an alcohol react, a water molecule is removed, and an ester molecule is formed. Because of this ester formation, this bond is known as an ester linkage.

When a diacid is condensed with dialcohol, the polymer obtained contains ester linkage. Terylene or dacron is formed from ethylene glycol and terephthalic acid. It has ester linkages present in the structure.

Nylon-6,6 is a polyamide, Bakelite has ether linkage. While PVC is polyvinyl chloride.

Topic: Chemistry, Polymers, JEE Main
Which of the following has an optical isomer ?

Options:
A
$\left[\mathrm{CO}\left(\mathrm{NH}_3\right)_3 \mathrm{Cl}\right]^{+}$

B
$\left[\mathrm{CO}(\text { en })\left(\mathrm{NH}_3\right)_2\right]^{2+}$

C
$\left[\mathrm{CO}\left(\mathrm{H}_2 \mathrm{O}\right)_4(\mathrm{en})\right]^{3+}$

D
$\left[\mathrm{CO}(\mathrm{en})_2\left(\mathrm{NH}_3\right)_2\right]^{3+}$

The correct answer is:
$\left[\mathrm{CO}(\mathrm{en})_2\left(\mathrm{NH}_3\right)_2\right]^{3+}$

Solution:
It is an octahedral complex of the type $\left[\mathrm{M}(\mathrm{AA})_2 \mathrm{X}_2\right]$
Where AA is bidentate ligand.

Topic: Chemistry, Coordination Compounds, JEE Main, JEE Main 2009
Which of the following has an optical isomer ?

Options:
A
$\left[\mathrm{CO}\left(\mathrm{NH}_3\right)_3 \mathrm{Cl}\right]^{+}$

B
$\left[\mathrm{CO}(\text { en })\left(\mathrm{NH}_3\right)_2\right]^{2+}$

C
$\left[\mathrm{CO}\left(\mathrm{H}_2 \mathrm{O}\right)_4(\mathrm{en})\right]^{3+}$

D
$\left[\mathrm{CO}(\mathrm{en})_2\left(\mathrm{NH}_3\right)_2\right]^{3+}$

The correct answer is:
$\left[\mathrm{CO}(\mathrm{en})_2\left(\mathrm{NH}_3\right)_2\right]^{3+}$

Solution:
It is an octahedral complex of the type $\left[\mathrm{M}(\mathrm{AA})_2 \mathrm{X}_2\right]$
Where AA is bidentate ligand.

Topic: Chemistry, Coordination Compounds, JEE Main
Which of the following has chiral structure

Options:
A

B $\mathrm{CH}_3-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}_3$
C

D $\mathrm{CH}_3-\mathrm{CHOH}-\mathrm{CH}_2 \mathrm{CH}_3$

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

Solution:
Chiral structure is that in which one carbon atom is attached to 4 different atoms or groups.

Topic: Chemistry, General Organic Chemistry, JEE Main
Which of the following has density greater than water

Options:
A $L i$
B $\mathrm{Na}$
C K
D $R b$

The correct answer is:
$R b$

Solution:
$\mathrm{Li}, \mathrm{Na}, \mathrm{K}$ are lighter than water but $R b$ is heavier than water.

Topic: Chemistry, s Block Elements, JEE Main
Which of the following has greatest reducing power

Options:
A $\mathrm{HI}$
B $\mathrm{HBr}$
C $\mathrm{HCl}$
D $\mathrm{HF}$

The correct answer is:
$\mathrm{HI}$

Solution:
HI is the strongest reducing agent among halogen acids because of lowest bond dissociation energy.

Topic: Chemistry, p Block Elements (Group 15, 16, 17 & 18), JEE Main
Which of the following has highest boiling point?

Options:
A $1 \%$ urea solution
B $1 \%$ sucrose
C $1 \%$ NaCl solution
D $1 \% \mathrm{CaCl}_{2}$ solution

The correct answer is:
$1 \% \mathrm{CaCl}_{2}$ solution

Solution:
The elevation in boiling point is given by
$\Delta T_{b}=i \times k_{b} \times m$
West, $\Delta T_{B}=$ Elevation in boiling point
$i=$ Van't Voff factor
$K_{b}=$ molal boiling point constant
$m=$ molality of solution. (it is same fore
all, acconding to question)
Therefore, Elevation in boiling paint is directly proportional to the number of species present in the solution (van't Ueff factor)
(i) $0.1 \mathrm{M} \mathrm{NaCl} \Rightarrow i=2$, since NaCl is ionic and if will dessociate into $\mathrm{Na}^{+}$and $\mathrm{Cl}^{-}$in aqueals solution
(ii) $0.1 \mathrm{M}$ suchose $\Rightarrow$ it will not dissociate in aqueous solution, since it is covalent in nuture.
(iio) $0.1 \mathrm{M} q \mathrm{ucose} \Rightarrow$ it will not dissociate in aqueous solution, since it is coualent in nature.
(iv) $0.1 \mathrm{M}$ urea $\Rightarrow$ it will not dissociate in aqueous solution, since it is covalent in nature.
Therefore, Nacl will have highest boiling point because it is ionic and will have highest number of solute particles.

Topic: Chemistry, Chemical Bonding and Molecular Structure, JEE Main