AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
3.2 moles of hydrogen iodide were heated in a sealed bulb at \( 444^{0} C \) till the
equilibrium state was reached. Its degree of dissociation at this temperature was found to be \( 22 \% \). The
number of moles of hydrogen iodide present at equilibrium are:
A .2 .496
B. 1.87
c. 2
D. 4
Subject: Maths
Suppose we define definite integral using the formula \( \int_{a}^{b} f(x) d x= \) \( \frac{b-a}{2}\{f(a)+f(b)\} . \) For more
accurate result, we have \( \int_{a}^{b} f(x) d x= \) \( \frac{b-a}{4}\{f(a)+f(b)+2 f(c)\}, \) when
\( c=\frac{a+b}{2} \cdot \) Also, let \( F(c)= \)
\( \frac{c-a}{2}\{f(a)+f(c)\}+ \)
\( \frac{b-c}{2}\{f(b)+f(c)\}, \) when \( c \epsilon(a, b) \)
(i) \( \int_{0}^{\pi / 2} \sin x d x \) equals
A \( \cdot \frac{\pi}{8}(1+\sqrt{2}) \)
в. \( \frac{\pi}{4}(1+\sqrt{2}) \)
c. \( \frac{\pi}{8 \sqrt{2}} \)
D. \( \frac{\pi}{4 \sqrt{2}} \)
Subject: Maths
\( f(x)=\left\{\begin{array}{cl}m x+1, & x \leq \frac{\pi}{2} \\ \sin x+n, & x>\frac{\pi}{2}\end{array} \) is \right.
continuous at \( x=\frac{\pi}{2}, \) then
A \( . m=1, n=0 \)
B. \( m=\frac{n \pi}{2}+1 \)
c. \( n=\frac{m}{2} \)
D. \( m=n=\frac{n \pi}{2} \)
Subject: Maths
Find the value of \( z \) in the given
equation \( \frac{z}{6}\left(\frac{3}{2}\right)-7=-2(3 z-4) \)
\( A \cdot-\frac{12}{5} \)
B. \( -\frac{4}{25} \)
c. \( \frac{4}{25} \)
D. \( \frac{12}{5} \)
Subject: Maths
The contrapositive of the statement 'If am not feeling well, then I will go to the
doctor' is:
A. If I am feeling well, then I will not go to the doctor
B. If / will go to the doctor, then I am felling well
c. If 1 will not go to the doctor, then I am feeling well
D. If I will go to the doctor, then I am not feeling well
Subject: Maths
Assertion
If mean \( \& \) median of an asymmetrical
distribution are 58 \& 61 respectively,
then Mode \( =\mathbf{6 7} \)
Reason
For an asymmetrical distribution Mode
\( =3 \) Median - 2 Mean
A. Both Assertion \&. Reason are individually true \& Reason is correct explanation of Assertion.
B. Both Assertion \& Reason are individually true but Reason is not the correct (proper) explanation of Assertion
c. Assertion is true Reason is false
D. Assertion is false Reason is true
Subject: Chemistry
When 1-pentyne \( (A) \) is treated with \( 4 N \)
alcoholic \( K O H \) at \( 175^{\circ} C, \) it is slowly
converted into an equilibrium mixture of \( 1.3 \% \) of 1 -pentyne \( (A), 95.2 \% \) 2-pentyne
\( (B) \) and \( 3.5 \% \) of 1,2 -pentadiene \( (C) . \) The
equilibrium was maintained at \( 174^{\circ} \mathrm{C} \)
Calculate \( \Delta G^{o} \) for the following
equilibria:
\( \boldsymbol{B} \rightleftharpoons \boldsymbol{A} ; \boldsymbol{\Delta} \boldsymbol{G}_{1}^{o}=? \)
\( \boldsymbol{B} \rightleftharpoons \boldsymbol{C} ; \boldsymbol{\Delta} \boldsymbol{G}_{2}^{o}=? \)
From the calculated values of \( \Delta G_{1}^{o} \) and
\( \Delta G_{2}^{o} \) indicate the order of stability of \( (A),(B) \) and \( (C) . \) Write a reasonable reaction mechanism showing all intermediates leading to \( (A),(B) \) and
\( (C) \)
Subject: Maths
The question is based on the Venn
Diagram. The circle stands for rural Triangle stands for educated, square
stands for hard-working and Rectangle stands for intelligent persons. The
number given represents a serial
number of the area

Which area represents " Intelligent hard-working and educated but not
rural" persons?
\( A \cdot 12 \)
в. 10
\( c \)
\( D \)
Subject: Physics
Assertion
The ratio of inertial mass to
gravitational mass is equal to one.
Reason

The inertial mass and gravitational mass of a body are equivalent.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. If Assertion is incorrect but Reason is correct
Subject: Maths
If \( a=\cos 2 \alpha+i \sin 2 \alpha, b=\cos 2 \beta+ \)
\( i \sin 2 \beta \operatorname{then} \sqrt{\frac{a}{b}}+\sqrt{\frac{b}{a}}= \)
A. \( 2 i \sin (\alpha-\beta) \)
B. \( 2 i \sin (\alpha+\beta) \)
\( c \cdot 2 \cos (\alpha+\beta) \)
D. \( 2 \cos (\alpha-\beta) \)
Subject: Maths
Let \( \boldsymbol{f}: \boldsymbol{N} \rightarrow \boldsymbol{R} \) be such that \( \boldsymbol{f}(\mathbf{1})=\mathbf{1} \)
and \( \boldsymbol{f}(\mathbf{1})+\mathbf{2} \boldsymbol{f}(\mathbf{2})+\mathbf{3} \boldsymbol{f}(\boldsymbol{3})+\ldots+ \)
\( \boldsymbol{n} \boldsymbol{f}(\boldsymbol{n})=\boldsymbol{n}(\boldsymbol{n}+1) \boldsymbol{f}(\boldsymbol{n}), \) for all \( \boldsymbol{n} \in \)
\( N, n \geq 2, \) where \( N \) is the set of natural
numbers and \( R \) is the set of real
numbers. Then, the value of \( f(500) \) is
A. 1000
B. 500
c. \( \frac{1}{500} \)
D. \( \frac{1}{1000} \)
Subject: Maths
In a triangle \( A B C, \) the least value of \( \tan ^{2} \frac{A}{2}+\tan ^{2} \frac{B}{2}+\tan ^{2} \frac{C}{2} \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B.
\( c \cdot \sqrt{3} \)
D. \( \frac{2}{3} \)
Subject: Maths
If the integers \( m \) and \( n \) are chosen at
random from 1 to 100 , then the
probability that a number of the form
\( 7^{m}+7^{n} \) is divisible by 5 is
A \( \cdot \frac{1}{5} \)
B. \( \frac{1}{7} \)
\( c \cdot \frac{1}{4} \)
D. \( \frac{1}{49} \)
Subject: Chemistry
Which of the following is not correctly matched?
A . Acidic oxides \( -P_{2} O_{5}, N O_{2}, C l_{2} O_{7} \)
B. Basic oxides - \( N a_{2} O, C a O, M g O \)
c. Neutral oxides \( -C O_{2}, C O, B e O \)
D. Amphoteric oxides - \( Z n O, S n O, A l_{2} O_{3} \)
Subject: Physics
An inductor \( 2 / \pi \mathrm{F} \) and a resistor \( 100 / \pi \)
are connected in series across a source
of emf \( \mathbf{v}=\mathbf{1 0} \sin 100[\pi \mathrm{t}] . \) Here \( \mathrm{t} \) is in
second.
(a) find the impedance of the circuit find the energy dissipated in the circuit in 20 minutes.
Subject: Physics
A stone thrown upwards with speed attains maximum height h. Another
stone thrown upwards from the same point with speed \( 2 u \) attains maximum height H. What is the relation between h and H?
\( A \cdot 2 h=H \)
B. \( 3 h=H \)
\( c \cdot 4 h=H \)
\( D \cdot 5 h=H \)
Subject: Chemistry
Which of the following complex compounds will exhibit highest paramagnetic behaviour? \( (A t . N o . T i=22, C r=24, C o= \)
\( \mathbf{2 7}, \boldsymbol{Z} \boldsymbol{n}=\mathbf{3 0}) \)
\( \mathbf{A} \cdot\left[Z n\left(N H_{3}\right)_{6}\right]^{2+} \)
в. \( \left[T i\left(N H_{3}\right)_{6}\right]^{3+} \)
c. \( \left[C r\left(N H_{3}\right)_{6}\right]^{3} \)
D. \( \left[\operatorname{Co}\left(N H_{3}\right)_{6}\right]^{3+} \)
Subject: Chemistry
In the following sequence of reaction:
\( \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{B r} \frac{\boldsymbol{K O H}(\boldsymbol{a l} \boldsymbol{c})}{(\boldsymbol{A})} \stackrel{\boldsymbol{H B r}}{\longrightarrow} \)
\( (B) \frac{K O H(a q)}{(C)} \)
Subject: Maths
\( A B, B C \) and \( C D \) are the three consecutive
sides of a regular polygon. If \( \angle B A C= \)
\( 15^{\circ} . \) Find each interior angle of the
polygon.
A \( .147^{\circ} \)
B. 162
\( c \cdot 150 \)
D. \( 140^{\circ} \)
Subject: Chemistry
Observe the following statements:
1. The solubility of group \( V \) hydrides in
water decreases from \( N H_{3} \) to \( B i H_{3} \)
2. Phosphorous does not exhibit allotropy.
3. The stability of group V hydrides
decreases from \( N H_{3} \) to \( B i H_{3} \)
The correct statement(s) is/are:
A .2
B. 1 and 2
c. 1,2 and 3
D. 1 and 3
Subject: Chemistry
Consider the following cell reaction:
\[
\begin{array}{c}
2 F e(s)+O_{2}(g)+4 H^{+}(a q) \rightarrow \\
2 F e^{2+}(a q)+2 H_{2} O(l) ; E^{o}=1.67 V
\end{array}
\]
\( \mathbf{A t}\left[\boldsymbol{F} \boldsymbol{e}^{2+}\right]=\mathbf{1 0}^{-\mathbf{3}} \boldsymbol{M}, \boldsymbol{P}_{O_{2}}=\mathbf{0 . 1} \) atm
and \( p H=3, \) the cell potential at \( 25^{\circ} C \)
is:
A . 1.47
B. 1.77 V
c. \( 1.87 \mathrm{v} \)
D. 1.57 V
Subject: Chemistry
Which of the following alkenes on reductive ozonolysis will give a mixture of ketones?
\( \mathbf{A} \cdot C H_{3} C H=C H C H_{3} \)
в. \( \left(C H_{3}\right)_{2} C=C H C H_{3} \)
\( \mathbf{c} \cdot\left(C H_{3}\right)_{2} C=C\left(C H_{3}\right)_{2} \)
D. None of these
Subject: Maths
A die is tossed twice. Getting an odd number is termed a success. The
probability distribution of number of successes \( (X) \) is formed. Then its mean,
variance are
A \( \cdot 1, \frac{1}{2} \)
B. \( \frac{1}{2}, 1 \)
c. \( \frac{1}{2}, \frac{1}{2} \)
D. 1,1
Subject: Chemistry
A sample of \( 0.16 g C H_{4} \) was subjected
to the combustion at \( 27^{\circ} C \) in a bomb
calorimeter. The temperature of the
calorimeter. The temperature of the
calorimeter system (including water)
was found to rise by \( 0.5^{\circ} \mathrm{C} \). Calculate
the heat of combustion of methane at
(i) constant volume and
(ii) constant pressure. the thermal capacity of calorimeter system is
\( 17.0 k J K^{-1} \) and \( R= \)
\( 8.314 J K^{-1} m o l^{-1} \)
Subject: Maths
Assertion
Odd in favour of an event \( A \) are \( 2: 1 \& \)
odd in favour of \( A \cup B \) are 3: 1 then
\( \frac{1}{12} \leq P(B) \leq \frac{3}{4} \)
Reason
If \( \boldsymbol{A} \cap \boldsymbol{B} \subset \boldsymbol{A} \) then \( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B}) \leq \boldsymbol{P}(\boldsymbol{A}) \)
A. Both Assertion \& Reason are individually true \& Reason is correct explanation of Assertion
B. Both Assertion \& Reason are individually true but Reason is not the , correct (proper) explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
Subject: Physics
A small block oscillates back and forth
on a smooth concave surface of radius
R. Find the time period of small oscillations.
A \( \cdot \pi \sqrt{\frac{2 R}{g}} \)
в. \( 2 \pi \sqrt{\frac{R}{3 g}} \)
c. \( 2 \pi \sqrt{\frac{2 R}{3 g}} \)
D. \( 2 \pi \sqrt{\frac{R}{g}} \)
Subject: Physics
Three particles, each of mass \( 1 g m \) and carrying a charge \( q, \) are suspended from a common point by insulated massless string, each \( 100 \mathrm{cm} \) long. If
the particles are in equilibrium and are located at the corner of an equilateral
triangle of side length 3 cm. Calculate
the charge \( q \) on each particle. (Take \( g= \)
\( \left.10 m / s^{2}\right) \)
Subject: Physics
Three ammeters \( A, B \) and \( C \) of
resistances \( \boldsymbol{R}_{\boldsymbol{A}}, \boldsymbol{R}_{\boldsymbol{B}} \) and \( \boldsymbol{R}_{\boldsymbol{C}} \)
respectively are joined as shown. When
some potential difference is applied
across the terminals \( T_{1} \) and \( T_{2}, \) their
readings are \( I_{A}, I_{B} \) and \( I_{C} \) respectively
This question has multiple correct options
\( \mathbf{A} \cdot I_{A}=I_{B} \)
B \( \cdot I_{A} R_{A}+I_{B} R_{B}=I_{C} R_{C} \)
\( \mathbf{C} \cdot \frac{I_{A}}{I_{C}}=\frac{R_{C}}{R_{A}} \)
D. \( \frac{I_{B}}{I_{C}}=\frac{R_{C}}{R_{A}+R_{B}} \)
Subject: Chemistry
What is the basic formula for starch?
\( \mathbf{A} \cdot\left(C_{6} H_{12} O_{6}\right)_{n} \)
В \( \cdot\left(C_{6} H_{10} O_{5}\right)_{n} \)
\( \mathrm{c} \cdot\left(C_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right) \)
D \( \cdot\left(C_{6} H_{12} O_{4}\right)_{n} \)
Subject: Chemistry
Assertion
In the present form of periodic table, the period number corresponds to the
highest principal quantum number of the elements in the period.
Reason
Elements having similar outer electronic configurations in their atoms
belong to same period.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Chemistry
Let a light of wavelength \( \lambda \) and intensity
\( \boldsymbol{I}^{\prime} \) strikes a metal surface to emit \( \boldsymbol{x} \)
electrons per second. Average energy of each electron is ' \( y^{\prime} \) unit. What will
happen to ' \( x \) ' and ' \( y \) ' when
(a) \( \lambda \) is halved
(b) intensity \( I \) is doubled?
Subject: Chemistry
The isotopes \( U^{238} \) and \( U^{235} \) occur in nature in the ratio \( 140: 1 . \) Assuming that at the time of earth formation, they were present in equal ratio, the estimated age of the age of earth will be :
(The half-life period of \( U^{238} \) and \( U^{235} \) are \( 4.5 \times 10^{9} \) and \( 7.13 \times 10^{8} \) years
respectively.)
A. \( 6.04 \times 10^{9} \) years
B. \( 6.25 \times 10^{9} \) years
c. \( 6.59 \times 10^{9} \) years
D. non of these
Subject: Maths
Different words being formed by
arranging the letters of the word "INTERMEDIATE".All the words obtained
are written in the form of a dictionary, If vowels \( \& \) consonants occupy their original places, then the number of permutations is
A \( \cdot \frac{6 !}{2 !} \times \frac{6 !}{2 !} \)
в. \( \frac{6 !}{3 !} \times \frac{6 !}{2 !} \)
c. \( \frac{6 ! \times 6 !}{3 ! 2 ! 2 !} \)
D. None of these
Subject: Physics
A rubber ball of mass 250 g hits a wall normally with a velocity \( 10 m s^{-1} \) and bounces back with a velocity of \( 8 m s^{-1} . \) The impluse is \( -\dots-\dots--N \) s.
A. -0.5
в. +0.5
c. -4.5
D. +4.5
Subject: Chemistry
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{5} \boldsymbol{S O}_{4}\right] \boldsymbol{B r} \) and
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{5} \boldsymbol{B r}\right] \boldsymbol{S} \boldsymbol{O}_{4} \) are a pair of
isomers.
A . ionisation
B. ligand
c. coordination
D. hydrate
Subject: Chemistry
Which of the following statements is
true for \( \boldsymbol{I} \boldsymbol{O}_{2} \boldsymbol{F}_{2}^{-} ? \)
A. The electrons are located at the corners of a trigonal bipyramidal but one of the equatorial pairs is unshared
B. It has \( s p^{3} d \) hybridisation and is \( T \) - shaped
C . Its structure is analogous to \( S F_{4} \)
D. (A) and
(C) both
Subject: Chemistry
Assertion : The heavier p-block
elements do not form strong \( \pi \) bonds.
Reason: The heavier elements of \( \mathrm{p} \)
block form \( d \pi-d \pi \) bonds.
A. Both A and R are true and R is the correct explanation of \( A \)
B. Both A and R are true but R is not the correct explanation of A
c. A is true but R is false.
D. A is false but R is true.
Subject: Chemistry
Acid hydrolysis of ester in first order reaction and rate constant is given by \( \boldsymbol{k}=\frac{\mathbf{2 . 3 0 3}}{\boldsymbol{t}} \log \frac{\boldsymbol{V}_{\infty}-\boldsymbol{V}_{0}}{\boldsymbol{V}_{\infty}-\boldsymbol{V}_{t}} \) where \( \boldsymbol{V}_{0}, \boldsymbol{V}_{t} \)
and \( V_{\infty} \) are the volume of standard
NaOH required to neutralise acid
present at a given time, if ester is \( 50 \% \) neutralised then:
A. \( V_{\infty}=V_{t} \)
B \( \cdot V_{\infty}=\left(V_{t}-V_{0}\right) \)
\( \mathbf{c} \cdot V_{\infty}=\left(2 V_{t}-V_{0}\right) \)
D. \( V_{\infty}=\left(2 V_{t}+V_{0}\right) \)
Subject: Chemistry
When \( 10 \mathrm{ml} \) of \( H_{2} \) and \( 12.5 \mathrm{ml} \) of \( C l_{2} \) are
allowed to react,the final mixture
contains under the same conditions.
A. 22.5 ml of \( H C l \)
B. 12.5 ml of \( H C l \)
c. \( 20 \mathrm{ml} \) of \( \mathrm{HCl} \)
D. 2.5 \( \mathrm{ml} \) of \( \mathrm{Cl}_{2} \) and \( 20 \mathrm{ml} \) HCl
Subject: Biology
A list of animals is given below. Identify the animals with open circulatory system and choose the correct answer.
(A) Squid
(B) Cockroach
(C) Earthworm
(D) Prawn
(E) Silverfish
(F) Snail
\( A \cdot B, D, F \)
B. A, B, D, F
c. \( \mathrm{c}, \mathrm{D}, \mathrm{E}, \mathrm{G} \)
D. B, D, E, F
E. \( A, B, D, F, G \)
Subject: Maths
A biased coin is tossed twice.The
probability of head is twice the tail.The PDF of number of heads is
\( \begin{array}{llll}\mathbf{x} & \mathbf{0} & \mathbf{2} & \mathbf{2}\end{array} \)
\( p(x) \quad \frac{a}{d} \quad \frac{b}{d} \quad \frac{c}{d} \)
then values of \( a, b, c, d \) are
A. \( a=1, b=2, c=3, d=4 \)
В. \( a=1, b=4, c=4, d=9 \)
c. \( a=1, b=4, c=4, d=10 \)
D. \( a=1, b=2, c=1, d=4 \)
Subject: Physics
An object starts from rest, and moves under the acceleration \( \overrightarrow{\boldsymbol{a}}=\mathbf{4} \hat{\mathbf{i}} \). Its
position after \( 3 s \) is given by \( \vec{r}= \) \( (7 \hat{i}+4 \hat{j}) . \) What is its initial position?
Subject: Physics
Identify the wrong statement.
A. Current loop is equivalent to a magnetic dipole
B. Magnetic dipole moment of a planar loop of area \( A \) carrying current \( l \) is \( l^{2} A \)
C. Particles like proton, electron carry an intrinsic magnetic moment
D. The current loop (magnetic moment \( m \) ) placed in a uniform magnetic field, \( B \) experiences a torque \( \tau= \) \( m \times B \)
E. Ampere's circuit law is not independent of Biot Savart's law
Subject: Maths
If \( A=\left[\begin{array}{ll}\alpha & 2 \\ 2 & \alpha\end{array}\right] \) and \( \left|A^{3}\right|=125 \) then \( \alpha \) is
\( \mathbf{A} \cdot \pm 1 \)
B. =2
\( c .\pm 3 \)
D. ±5
Subject: Maths
Classify the following function \( \boldsymbol{f}(\boldsymbol{x}) \)
defined in \( R \rightarrow R \) as injective,
surjective, both or none:
\( \boldsymbol{f}(\boldsymbol{x})=\left(\boldsymbol{x}^{2}+\boldsymbol{x}+\mathbf{5}\right)\left(\boldsymbol{x}^{2}+\boldsymbol{x}-\boldsymbol{3}\right) \)
A. only injective
B. Only surjective
c. Neither injective not surjective
D. Both injective and surjective.
Subject: Physics
In a meniscus of radius \( r, \) with excess
pressure \( p \) in atmospheric pressure \( p_{0} \) the force experienced
A \( \cdot\left(p-p_{0}\right) \pi r^{2} \)
в. \( \left(p-p_{0}\right) 2 \pi r \)
c. \( p \pi r^{2} \)
D. \( p_{0} 2 \pi r \)
Subject: Maths
\( \operatorname{Let} z=x+i y \& \operatorname{amp}\left(e^{z^{2}}\right)=\operatorname{amp} \)
\( \left(e^{(z+i)}\right) . \) If \( y=(x) \) is a function, then
\( \boldsymbol{y}(\mathbf{3}) \) is equal to
A \( \cdot \frac{1}{2} \)
в. \( \frac{1}{3} \)
\( c \cdot \frac{1}{4} \)
D.
Subject: Maths
ff \( \left[\begin{array}{cc}1 & 2 \\ 3 & -5\end{array}\right], \) then \( A^{-1} \) is equal to
\( ^{\mathbf{A}} \cdot\left[\begin{array}{cc}\frac{5}{11} & \frac{2}{11} \\ \frac{3}{11} & -\frac{1}{11}\end{array}\right] \)
в. \( \left[\begin{array}{rr}-\frac{5}{11} & -\frac{2}{11} \\ -\frac{3}{11} & -\frac{1}{11}\end{array}\right] \)
\( ^{\mathbf{C}} \cdot\left[\begin{array}{cc}\frac{5}{11} & \frac{2}{11} \\ \frac{3}{11} & \frac{1}{11}\end{array}\right] \)
D. \( \left[\begin{array}{ll}5 & 2 \\ 3 & -1\end{array}\right] \)
Subject: Chemistry
The radii of two of the first four Bohr's
orbits of the hydrogen atom are in the
ratio \( 1: 4 . \) The energy difference
between them may be:
A. either \( 12.09 e V \) or \( 3.4 e V \)
B. either \( 2.55 e V \) or \( 10.2 e V \)
c. either \( 13.6 e V \) or \( 3.4 e V \)
D. either \( 3.4 e V \) or \( 0.85 e V \)
Subject: Chemistry
Which of the following statement is
wrong about the reaction?
A. At lower temperature, the reaction is kinetically controlled and o/p directive effects of the \( (M e) \) group operate
B. At a higher temperature, the reaction is thermodynamically controlled, and longer reaction times are employed for equilibrium to be reached. The most stable form of m-toulene sulphonic acid is obtained
C. \( (M e-) \) group is activated by +1 effect, and \( o-, p- \) directing
D. \( (M e-) \) group is deactivating by hyperconjugation and is \( m- \) directing
Subject: Physics
The equation of a travelling wave is given by \( \boldsymbol{y}=\mathbf{1 0} \cos \left[\frac{\boldsymbol{\pi} \boldsymbol{t}}{\mathbf{3}}+\boldsymbol{\alpha}\right] . \) If the
displacement is \( 10 \mathrm{cm} \) at \( t=0, \) then the
total phase at \( t=1.5 s \) will be
A \( \cdot\left(\frac{2 \pi}{3}\right) r a d \)
в. \( (2 \pi) \) rad
c. \( \left(\frac{\pi}{3}\right) r a d \)
D. \( \left(\frac{2 \pi}{6}\right) r a d \)
Subject: Maths
The shortest distance between the line \( y \)
\( -x=1 \) and the curve \( x=y^{2} \) is :
A \( \cdot \frac{2 \sqrt{3}}{8} \)
B. \( \frac{3 \sqrt{5}}{8} \)
c. \( \frac{\sqrt{3}}{4} \)
D. \( \frac{3 \sqrt{2}}{8} \)
Subject: Physics
Two identical circular loops of metal wire are lying on a table without
touching each other. Loop - \( A \) carries a
current which increases with time. In
response, the loop-B
A. remains stationary
B. is attracted by the loop \( A \)
c. is repelled by the loop \( A \)
D. rotates about its \( C M \) with \( C M \) fixed
E. none of these
Subject: Maths
Let \( C \) be the circle with centre at (1,1)
and radius \( =1 . \) If \( T \) is the circle
centered at \( (0, y), \) passing through origin and touching the circle \( C \)
externally, then the radius of \( T \) is equal
to :
A \( \cdot \frac{\sqrt{3}}{\sqrt{2}} \)
B. \( \frac{\sqrt{3}}{2} \)
\( c \cdot \frac{1}{2} \)
D.
Subject: Chemistry
Assertion
Noble gases are considered unreactive
elements.
Reason
Group 18 elements have complete octet
except Helium.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Physics
A card sheet divided into squares each of size \( 1 \mathrm{mm}^{2} \) is being viewed at a
distance of \( 9 \mathrm{cm} \) through a magnifying glass (a converging lens of focal length \( 9 \mathrm{cm} \) ) held close to the eye.

In order to view the squares distinctly with the maximum possible magnifying
power.
(a) What is the magnification produced by the lens? How much is the area of each square in the virtual image?
(b) What is the angular magnification (magnifying power) of the lens?
(c) Is the magnification in
(a) equal to the magnifying power in (b)? Explain:
Subject: Chemistry
A solid body of constant heat capacity \( 1 J /^{\circ} C \) is being heated by keeping it in contact with reservoirs in two ways:
(i) Sequentially keeping in contact with 2 reservoirs such that each reservoir
supplies same amount of heat
(ii) Sequentially keeping in contact with 8 reservoirs such that each
reservoir supplies same amount of heat
In both the cases body is brought from
initial temperature of \( 100^{\circ} \mathrm{C} \) to a final
temperature of \( 200^{\circ} \mathrm{C} \). Entropy change
of the body in two cases respectively is :
A. \( \ln 2,4 \ln 2 \)
B. \( \ln 2, \ln 2 \)
c. \( \ln 2,2 \ln 2 \)
D. \( 2 \ln 2,8 \ln 2 \)
Subject: Chemistry
The increasing order of acidic strength in the following acids.
\( \boldsymbol{C l C H}_{2} \boldsymbol{C O O H}, \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C O O H}, \boldsymbol{C l C} \)
and \( C H_{3} C O O H \) is:
A \( \cdot\left(C H_{3}\right)_{2} C H C O O H<C H_{3} C H_{2} C O O H< \)
\( \mathrm{ClCH}_{2} \mathrm{CH}_{2} \mathrm{COOH}<\mathrm{CH}_{3} \mathrm{COOH}<\mathrm{ClCH}_{2} \mathrm{COOH} \)
в. \( C H_{3} C H_{2} C O O H<\left(C H_{3}\right)_{2} C H C O O H< \)
\( \mathrm{ClCH}_{2} \mathrm{CH}_{2} \mathrm{COOH}<\mathrm{CH}_{3} \mathrm{COOH}<\mathrm{ClCH}_{2} \mathrm{COOH} \)
c. \( \left(C H_{3}\right)_{2} C H C O O H<C H_{3} C H_{2} \) СООН\( < \)
\( \mathrm{ClCH}_{2} \mathrm{CH}_{2} \mathrm{COOH}<\mathrm{ClCH}_{2} \mathrm{COOH}<\mathrm{CH}_{3} \mathrm{COOH} \)
D. \( \left(C H_{3}\right)_{2} C H C O O H<C l C H_{2} C H_{2} C O O H< \)
\( C H_{3} C H_{2} C O O H<C H_{3} C O O H<C l C H_{2} C O O H \)
Subject: Physics
The dimensions of \( \frac{\alpha}{\beta} \) in the equation \( \boldsymbol{F}=\frac{\boldsymbol{\alpha}-\boldsymbol{t}^{2}}{\beta \boldsymbol{v}^{2}}, \) where \( \boldsymbol{F} \) is force, \( \boldsymbol{v} \) is
velocity and \( t \) is time, is :
\( \mathbf{A} \cdot\left[M L T^{-1}\right] \)
B . \( \left[M L^{-1} T^{-2}\right] \)
\( \mathbf{c} \cdot\left[M L^{3} T^{-4}\right] \)
\( \mathbf{D} \cdot\left[M L^{2} T^{-4}\right] \)
Subject: Maths
f \( x, y, z \) are different and \( \left|\begin{array}{lll}\boldsymbol{x} & \boldsymbol{x}^{2} & \boldsymbol{1}+\boldsymbol{x}^{2} \\ \boldsymbol{y} & \boldsymbol{y}^{2} & \boldsymbol{1}+\boldsymbol{y}^{2} \\ \boldsymbol{z} & \boldsymbol{z}^{2} & \boldsymbol{1}+\boldsymbol{z}^{2}\end{array}\right|=\mathbf{0} \) then prove that
\( \mathbf{1}+\boldsymbol{x} \boldsymbol{y} \boldsymbol{z}=\mathbf{0} \)