AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
The solution of the equation \( \frac{d y}{d x}= \) \( \frac{x(2 \log x+1)}{\sin y+y \cos y} \) is
A \( y \sin y=x^{2} \log x+\frac{x^{2}}{y}+c \)
B \( \cdot y \cos y=x^{2}(\log x+1)+c \)
c. \( y \cos y=x^{2} \log x+\frac{x^{2}}{2}+c \)
D. \( y \sin y=x^{2} \log x+c \)
Subject: Maths
What does the shaded region represent in the figure given below?
A \( \cdot(P \cup Q)-(P \cap Q) \)
В . \( P \cap(Q \cup R) \)
\( \mathbf{c} \cdot(P \cap Q) \cap(P \cap R) \)
D \( \cdot(P \cap Q) \cup(P \cap R) \)
Subject: Physics
A block of mass \( 0.1 k g \) is held against a wall by applying a horizontal force on
\( \mathbf{5} N \) on it. If \( \mu_{s} \) between the wall and the
block is 0.5 the magnitude of the frictional force acting on the block is :
A . \( 0.98 N \)
B. \( 0.49 N \)
c. \( 4.9 N \)
D. \( 2.5 N \)
Subject: Physics
Assertion
Physically, if a dielectric with a high value of \( \mathrm{k} \) is placed in an electric field, the electric field will be greatly reduced
inside.
Reason
Dielectrics are very useful in modern electronics as it is possible to to precisely control their permittivity by doping them with other types of
materials.
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
The formula \( Y=3 B(1-2 \sigma) \) relates
young's modulus and bulk's modulus with poisson's ratio. A theoretical physicist derives this formula incorrectly as \( Y=3 B(1-4 \sigma) \)
According to this formula, what would be the theoretical limits of poisson's
ratio:
A. Poisson's ratio should be less than 1
B. Poisson's ratio should be less than 0.5
c. Poisson's ratio should be less than 0.25
D. Poisson's ratio should be less than 0
Subject: Biology
Which one of the following group of
codons is called as degenerate codons?
A. UAA, UAG and UGA
B. GUA, GUG, GCA and GCG
C . UUC, UUG, CCU, CAA and CUG
D. UUA and UUG, CUU, CUC and CUG
E . AAC, AAG, GAC and CGG
Subject: Biology
Study the graph which shows results of
three different experiments \( P, Q \) and \( R \)
In a few sentences, summarize what the
results of these experiments tell you
about the factors which limit
photosynthesis under different
environmental conditions?
A. In comparison with curve \( R \), curve P was limited by low temperature and low \( C O_{2} \) concentration, curve \( Q \) was limited by low \( C O_{2} \) concentration
B. In comparison with curve R, curve P was limited by high temperature and low \( C O_{2} \) concentration, curve \( Q \)
was limited by high \( C O_{2} \) concentration
C. In comparison with curve \( R \), curve P was limited by low temperature and high \( C O_{2} \) concentration, curve \( Q \) was
limited by high \( C O_{2} \) concentration.
D. None of the above
Subject: Physics
Magnetic field at point \( ^{\prime} \boldsymbol{P}^{\prime} \) due to given
current distribution is:
A \( \cdot \frac{\mu_{0} I}{4 \pi r}(1+\sqrt{2}) \odot \)
В \( \cdot \frac{\mu_{0} I}{2 \pi r}(1+\sqrt{2}) \odot \)
c. \( \frac{\mu_{0} I}{4 \pi r}(1+\sqrt{2}) \otimes \)
D. \( \frac{\mu_{0} I}{2 \pi r}(1+\sqrt{2}) \otimes \)
Subject: Physics
A monoatomic ideal gas \( \left(C_{V}=\frac{3}{2} R\right) \) is
allowed to expand adiabatically and reversibly from initial volume of \( 8 \mathrm{L} \) at
\( 300 \mathrm{K} \) to a volume of \( V_{2} \) at \( 250 \mathrm{K} . V_{2} \) is:
(Given \( \left.(4.8)^{1 / 2}=2.2\right) \)
A . \( 10.5 \mathrm{L} \)
B. 23 L
\( c .8 .5 \)
D. 50.5
Subject: Maths
Let \( A \) and \( B \) be events in a sample space \( S \) such that \( P(A)=0.5, P(B)= \) 0.4 and \( P(A \cup B)=0.6 . \) Observe the
following lists:
List I List I
\( P(A \cap B) \) a 0.4
\( P(A \cap \bar{B}) \) \( b \) 0.2
iii \( P(\bar{A} \cap B) \) 0.3
\( P(\bar{A} \cap \bar{B}) \)
The correct match of List I from List II is
A . i- a, ii-b, iii-c, iv- d
B. i-c, ii-b, iii- d, iv- a
c. i-c, ii-b, iii- a, iv- d
D. i-c, ii- a, iii-b, iv-
Subject: Physics
The saturated vapour pressure of water at \( 100^{0} \mathrm{C} \) is
A. \( 750 \mathrm{mm} \) o fHg
B. 760 mm of Hg
c. \( 76 \mathrm{mm} \) of \( \mathrm{Hg} \)
D. 7.6 mm of Hg
Subject: Physics
A ray of light is incident on a glass slab
of refractive index \( 1.52 . \) if the reflected
and refracted rays of light are mutually perpendicular to each other then the angle of incidence will be
A \( .90^{\circ} \)
B . \( 60^{\circ} \)
c. \( 56^{\circ} \) 40
D \cdot \( 19^{\circ} 58^{\prime} \)
Subject: Physics
The Young's modulus of a wire of length
\( L \) and radius \( r \) is \( Y \). If the length is
reduced to \( \frac{L}{2} \) and radius is \( \frac{r}{2}, \) then the Young's modulus will be
A \( \frac{Y}{2} \)
в. \( Y \)
\( c .2 Y \)
D. \( 4 Y \)
Subject: Physics
Using \( \varepsilon=-\frac{d \phi}{d t} \) and \( \varepsilon=i R \) find the
current in the loop after the external
field has stopped changing.
A \( \cdot \frac{d i}{d t}=-\left(\frac{2 R}{\mu_{0} \pi a}\right) \)
в. \( \frac{d i}{d t}=-\frac{R}{\mu_{0} a} \)
c. \( \frac{d i}{d t}=\frac{-2 R}{\mu_{0} a} i \)
D. \( \frac{d i}{d t}=\frac{-2 R}{3 \mu_{0} \pi a} \)
Subject: Physics
If two particles of masses \( m_{1} \) and \( m_{2} \)
move with velocities \( v_{1} \) and \( v_{2} \) towards
each other on a smooth horizontal
plane, what is the velocity of their
centre of mass.?
A \( \cdot V=\frac{m_{1} v_{1}+m_{2} v_{2}}{m_{1}+m_{2}} \)
B. \( V=\frac{m_{1} v_{1}-m_{2} v_{2}}{m_{1}+m_{2}} \)
\( \mathbf{c} \cdot V=\frac{m_{1} v_{1}+m_{2} v_{2}}{m_{1}-m_{2}} \)
D. \( V=\frac{m_{1} v_{1}-m_{2} v_{2}}{m_{1}-m_{2}} \)
Subject: Maths
\( \sum_{k=1}^{k=n} \tan ^{-1} \frac{2 k}{2+k^{2}+k^{4}}=\tan ^{-1}\left(\frac{6}{7}\right) \)
then the value of ' \( n \) ' is equal to
A . 2
B. 3
\( c \cdot 4 \)
D. 5
Subject: Maths
The number of solutions of
\( \sin ^{-1}\left(1+b+b^{2}+\ldots . \infty\right)+\cos ^{-1}(a- \)
\( \left.\frac{a^{2}}{3}+\frac{a^{3}}{9}+\ldots \infty\right)=\frac{\pi}{2} \)
\( A \)
B . 2
\( c .3 \)
\( D \)
Subject: Biology
Refer to the given dichotomous key and select the correct option regarding it.
I. \( (a) \) It is a seedless plant - Go to II
(b) It is a plant having seeds - Go to
\|\|
Il. (a) True stem, leaves and roots are absent - \( \mathbb{P} \)
(b) True stem, leaves and roots are present \( -[\boldsymbol{Q} \)
III. (a) Fruit is not formed and seeds are naked \( -\overline{\boldsymbol{R}} \)
(b) Fruits are formed and seeds are protected \( -\overline{\boldsymbol{S}} \)
A. P- Pteridium, Q - Ephedra, R - Lycopodium, S- Acer
B. P- selaginella, Q- Funaria, R - Cycas, S - Fern
c. P- - Marchantia, Q - Pteridium, R - Oryza, S - Thuja
D. P- -Riccia, Q - Azolla, R - Pinus, S - Brassica
Subject: Chemistry
Superoxides of alkali metals act as
oxidising agents while normal oxides are basic in nature. The oxide which is
paramagnetic in nature due to presence of unpaired electron is :
A. \( N a_{2} O_{2} \)
в. \( K O_{2} \)
\( \mathbf{c} \cdot N a_{2} O \)
D. \( K_{2} O_{2} \)
Subject: Physics
A particle is moving eastwards with a velocity of \( 5 m s^{-1} . \) In \( 10 s, \) the velocity changes to 5 ms \( ^{-1} \) northwards. The
average acceleration in time is:
A. Zero
B. \( 1 / \sqrt{2} \mathrm{ms}^{-2} \) towards north-west
C \( \cdot 1 / 2 m s^{-2} \) towards north-west
D. \( 1 / 2 m s^{-2} \) towards north
Subject: Physics
An uncharged parallel plate capacitor filled with a dielectric of dielectric
constant \( K \) is connected to an air filled
identical parallel capacitor charged to
potential \( V_{1} . \) If the common potential is
\( V_{2}, \) the value of \( K \) is
A. \( \frac{V_{1}-V_{2}}{V_{1}} \)
B. \( \frac{V_{1}}{V_{1}-V_{2}} \)
c. \( \frac{V_{2}}{V_{1}-V_{2}} \)
D. \( \frac{V_{1}-V_{2}}{V_{2}} \)
E \( \cdot \frac{V_{1}-V_{2}}{V_{1}+V_{2}} \)
Subject: Maths
Of the students in a college, it is known
that \( 60 \% \) reside in hostel and \( 40 \% \) are
day scholars.Previous year results report that \( 30 \% \) of all students who
reside in hostel attain 'A' grade and \( 20 \% \) of day scholars attain 'A' grade in their
annual examination. At the end of the
year, one student is chose at random
from the college and he has an 'A' grade, what is the probability that the student is a hostlier?
Subject: Physics
An ideal spring with spring constant \( k \) is hung from the ceiling and a block of mass \( M \) is attached to its lower end.
The mass is released with the spring initially unstretched. Then the maximum extension in the spring is (Given acceleration due to gravity \( =g) \)
A \( \cdot \frac{4 M g}{k} \)
в. \( \frac{2 M g}{k} \)
c. \( \frac{M g}{k} \)
D. \( \frac{M g}{2 k} \)
Subject: Chemistry
The reaction, \( \boldsymbol{X} \longrightarrow \boldsymbol{Y}(\text { Product }) \)
follows first order kinetics. In 40
minutes, the concentration of \( \boldsymbol{X} \)
changes from \( 0.1 ~ M \) to \( 0.025 M \), then
the rate of reaction when concentration
of \( \boldsymbol{X} \) is \( \mathbf{0 . 0 1} \boldsymbol{M} \) is:
A \( \cdot 1.73 \times 10^{-4} \mathrm{M} / \mathrm{min} \)
B . 3.47 \( \times 10^{-5} \mathrm{M} / \mathrm{min} \)
c. \( 3.47 \times 10^{-4} \mathrm{M} / \mathrm{min} \)
D. \( 1.73 \times 10^{-5} \mathrm{M} / \mathrm{min} \)
Subject: Chemistry
A gas expands against a constant external pressure of 2.00 atm, increasing its volume by \( 3.40 L \) Simultaneously, the system absorbs \( 400 J \) of heat from its surroundings.
What is \( \Delta E, \) injoules, for this gas?
\( \mathbf{A} \cdot-689 \)
в. -289
c. +400
D . +289
Subject: Physics
The adjacent sides of a paralleleogram \( \operatorname{are} \vec{A}=2 \hat{i}-3 \hat{j}+\hat{k} \quad \) and \( \quad \vec{B}= \)
\( -2 \hat{i}+4 \hat{j}-\hat{k} \) What is the area of the
parallelogram?
A. 4 units
B. 7units
c. \( \sqrt{5} \) units
D. \( \sqrt{8} \) units
Subject: Chemistry
Arrange the following in increasing order of their atomic radii.
\( \mathrm{Li}, \mathrm{Be}, \mathrm{Ne}, \mathrm{C}, \mathrm{B} \)
A. \( N e<C<B<B e<L i \)
в. \( L i>N e>C>B>B e \)
c. \( N e>C>B>B e>L i \)
D. \( L i>N e>B>C>B e \)
Subject: Physics
The value of numerical aperature of the objective lens of a microscope is \( 1.25 . \) If light of wavelength \( 5000 \dot{A} \) is used, the minimum separation between two points, to be seen as distinct, will be :
A \( .0 .24 \mu m \)
в. \( 0.48 \mu m \)
c. \( 0.12 \mu \) m
D. \( 0.38 \mu m \)
Subject: Chemistry
\( t_{1} \) for first order reaction is:
\( \overline{\mathbf{2}} \)
A. \( \frac{0.7}{k} \)
в. \( \frac{0.693}{k} \)
c. \( \frac{0.683}{k} \)
D. \( \frac{0.10}{k} \)
Subject: Chemistry
Assertion: The most important factor in determining the chemical properties of an element is the number of electrons
in the outermost shell.

Statement 2 : The number of electrons
in the outer shell determines the
bonding characteristics of the element.
A. Both Assertion and Reason are correct and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are correct and Reason is not the correct explanation of Assertion
c. Assertion is correct but Reason is not correct
D. Assertion is not correct but Reason is correct
E. Both the Assertion and Reason are not correct
Subject: Maths
The vertices of a triangle are 2,3,5)\( ,(-1,3,2),(3,5,-2), \) then the
angles are
\( \mathbf{A} \cdot 30^{\circ}, 30^{\circ}, 30^{\circ} \)
\( ^{\mathrm{B}} \cos ^{-1}\left(\frac{1}{\sqrt{5}}\right), 90^{\circ}, \cos ^{-1}\left(\frac{\sqrt{5}}{\sqrt{3}}\right) \)
c. \( 30^{\circ}, 60^{\circ}, 90^{\circ} \)
D \( \cdot \cos ^{-1}\left(\frac{1}{\sqrt{3}}\right), 90^{\circ}, \cos ^{-1}\left(\frac{\sqrt{2}}{\sqrt{3}}\right) \)
Subject: Maths
The position vectors of point \( A \) and \( B \) \( \operatorname{are} \hat{\boldsymbol{i}}-\hat{\boldsymbol{j}}+\boldsymbol{3} \hat{\boldsymbol{k}} \) and \( \boldsymbol{3} \hat{\boldsymbol{i}}+\boldsymbol{3} \hat{\boldsymbol{j}}+\boldsymbol{3} \hat{\boldsymbol{k}} \)
respectively. The equation of a plane is
\( r \cdot(5 \hat{i}+2 \hat{j}-7 \hat{k})+9=0 . \) The point \( A \)
and \( B \)
A. lie on the plane
B. are on the same side of the plane
c. are on the opposite side of the plane
D. None of these
Subject: Physics
When two waves of the same amplitude and frequency but having a phase difference of \( \phi \) travelling with the same speed in the same direction (positive \( x \) ) meets at a point then
A. their resultant amplitude will be twice that of a single wave but the frequency will be same
B. their resultant amplitude and frequency will both be twice that of a single wave
c. their resultant amplitude will depend on the phase angle while the frequency will be the same
D. the frequency and amplitude of the resultant wave will depend upon the phase angle
Subject: Maths
Given that \( x, y, z \) are positive real
numbers such that \( x y z=32 . \) The
minimum value of \( x^{2}+4 x y+4 y^{2}+ \)
\( 2 z^{2} \) is equal to
\( \mathbf{A} \cdot 64 \)
в. 256
c. 96
D. 216
Subject: Chemistry
Which of the following will not change the concentration of ammonia in the
equilibrium?
\( N_{2}(g)+3 H_{2}(g) \rightleftharpoons 2 N H_{3}(g) ; \Delta H= \)
\( -\boldsymbol{x} \boldsymbol{k} \boldsymbol{J} \)
A. increase of pressure
B. increase of temperature
c. decrease of volume
D. addition of catalyst
Subject: Maths
The values of \( x \) for which the angle
between the vectors \( a=x i-3 j-k \)
and \( b=2 x i+x j-k \) is acute, and the
angle between the vector \( b \) and the axis
of ordinates is obtuse, are
This question has multiple correct options
A . 1,2
в. -2,-3
c. all \( x<0 \)
D. all \( x>0 \)
Subject: Physics
The time period of a sound wave from a piano is \( 1.18 \times 10^{-3} s . \) Find its
frequency
\( \mathbf{A} \cdot 847.45 H z \)
в. \( 800 H z \)
\( \mathbf{c} .935 .55 H z \)
D. \( 1000 H z \)
Subject: Maths
\( O \) is the centre of the circle having
radius \( 5 \mathrm{cm} . O M \perp \) chord \( A B . \) If
\( \boldsymbol{O} \boldsymbol{M}=\mathbf{4} \mathrm{cm}, \) then the length of the
chord \( A B \) is
A. \( 6 \mathrm{cm} \)
B. \( 5 \mathrm{cm} \)
\( c \cdot 8 \mathrm{cm} \)
D. \( 10 \mathrm{cm} \)
Subject: Maths
The quadratic polynomial whose sum of
zeroes is 3 and product of zeroes is -2 is:
A \( \cdot x^{2}+3 x-2=0 \)
B . \( x^{2}-2 x+3=0 \)
c. \( x^{2}-3 x+2=0 \)
D. \( x^{2}-3 x-2=0 \)
Subject: Maths
\( \boldsymbol{P} \boldsymbol{Q} \boldsymbol{R} \boldsymbol{C} \) parallelogram, \( \boldsymbol{Q} \boldsymbol{M} \) is the
height form \( Q \) to \( R C \) and \( Q N \) is the
height from \( Q \) to \( P S \). If \( R C=12 \mathrm{cm} \)
and \( \boldsymbol{Q} \boldsymbol{M}=\mathbf{7 . 6 c m} . \) Find
(a) the area of the parallegram \( P Q R C \)
\( (b) Q N \) if \( P S=8 c m \)
Subject: Chemistry
The reaction \( N_{2} O_{5} \quad\left(\text { In } \quad C C l_{4}\right) \rightarrow \)
\( 2 N O_{2}+1 / 2 \quad O_{2}(g) \) is first order in
\( N_{2} O_{5} \) with rate constant \( 6.2 \times \)
\( 10^{-4} S^{-1} . \) What is the value of rate of
reaction when \( \left[\boldsymbol{N}_{\mathbf{2}} \boldsymbol{O}_{\boldsymbol{5}}\right]= \)
\( \begin{array}{lll}\mathbf{1 . 2 5} & \text { mole } & \boldsymbol{L}^{-1}\end{array} \)
\( \begin{array}{ll}\text { A } \cdot 7.75 \times 10^{-4} & L^{-1} S^{-1}\end{array} \)
B. \( 6.35 \times 10^{-3} \quad L^{-1} S^{-1} \)
\( \begin{array}{ll}\text { C. } 5.15 \times 10^{-5} & L^{-1} S^{-1}\end{array} \)
D. 3.85 \times 10 \( ^{-4} \quad L^{-1} S^{-1} \)
Subject: Maths
If \( y^{2}=a x^{2}+b x+c, \) where \( a, b, c \) are
constants, then \( y^{3} \frac{d^{2} y}{d x^{2}} \) is equal to.
A \( \cdot \frac{-1}{4} \)
в. \( \frac{-1}{6} \)
c. \( \frac{-3}{4} \)
D. \( \frac{-1}{8} \)
Subject: Maths
The law of the mean can also be put in
the form
\( \mathbf{A} \cdot f(a+h)=f(a)-h f^{\prime}(a+q h) 0<q<1 \)
B \( \cdot f(a+h)=f(a)+h f^{\prime}(a+q h) 0<q<1 \)
\( \mathbf{c} \cdot f(a+h)=f(a)+h f^{\prime}(a-q h) 0<q<1 \)
D. \( f(a+h)=f(a)-h f^{\prime}(a-q h) 0<q<1 \)
Subject: Physics
Two identical charges of magnitude \( +\mathrm{Q} \) are fixed as shown.A third charge - \( Q \)
is placed mid way between them at point P. Then small displacements of - Q are made in the directions indicated by
arrows. The -Q is stable with respect to displacement .
\( \odot \) (out of the What is and
A . I and III
B. I and
c. ॥ and \( I V \)
D. III and \( v \)
E. stable for any small displacement
Subject: Physics
Assertion
When an object is placed between two plane parallel mirrors, then all the images found are of equal intensity.
Reason

In case of plane parallel mirrors, only two images are possible.
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: Biology
Choose the correct answer from the
alternatives given.

Which of the following represents the pulmonary circulation as the blood flows from
the right ventricle?
A. Pulmonary trunk \( \rightarrow \) pulmonary veins \( \rightarrow \) pulmonary capillaries \( \rightarrow \) pulmonary arteries
B. Pulmonary arteries \( \rightarrow \) pulmonary capillaries \( \rightarrow \) pulmonary trunk \( \rightarrow \) pulmonary veins
c. Pulmonary capillaries \( \rightarrow \) pulmonary trunk \( \rightarrow \) pulmonary arteries \( \rightarrow \) pulmonary veins
D. Pulmonary trunk \( \rightarrow \) pulmonary arteries \( \rightarrow \) pulmonary capillaries \( \rightarrow \) pulmonary veins
Subject: Chemistry
List List - II
A) Polystyrene
\( p \)
Condensation polymer
B) Polythene Thermoplastic polymer
C) Nylon- 6,6
r) Polyamide
D) Terylene
s) Addition
polymer
A \( \cdot(a-q, s),(b-q, s),(c-p, q, r),(d-p) \)
B. \( (a-p),(b-s),(c-p, r),(d-p, q) \)
\( c \cdot(a-s),(b-q),(c-p, r),(d-q) \)
D. \( (a-q),(b-s),(c-r),(d-p, q) \)
Subject: Physics
\( \ln \) an \( A C \) circuit, the potential across an inductance and resistance joined in series are respectively \( 16 V \) and \( 20 V \)
The total potential difference across the circuit is
\( \mathbf{A} \cdot 20.0 V \)
B . \( 25.6 V \)
c. \( 31.9 V \)
D. 33.6 \( V \)
Subject: Chemistry
Action of \( \boldsymbol{P C l}_{5} \) on \( \boldsymbol{S O}_{2} \) chiefly yields:
A \( . P O C l_{3} \)
в. \( P_{4} S_{3} \)
c. \( s O_{2} C l_{2} \)
D. \( S O_{3} \)
Subject: Maths
\( " * " \) is said to be commutative in \( A \) for
all \( a, b \epsilon A \)
A \( . a+b=b+a \)
B. \( a * b=b * a \)
\( c \cdot a-b=b-a \)
\( a \)
D. \( a * b \neq b * a \)
Subject: Chemistry
Hard water when passed through ion
exchange resin containing \( R C O O H \) group, becomes free from :
A \( \cdot C l \)
B. \( S O_{4}^{-2} \)
\( \mathrm{c} \cdot \mathrm{H}_{3} \mathrm{O}^{+} \)
D. \( C a^{+2} \)
Subject: Biology
Which group represent micronutrients?
A. Mn, Zn, Fe, B, CI, Ni
B. \( c, \mathrm{S}, \mathrm{O}, \mathrm{N}, \mathrm{K}, \mathrm{Ca} \)
\( c \cdot \) са, Мg, к, ऽ,
D. C, H, Fe, Mn, Си, Мо
Subject: Chemistry
Which pair of statements about
diamond and graphite is correct?
A. Diamond and graphite are both pure carbon. They are both macromolecules
B. Diamond and graphite can both be used as electrodes Graphite is also used as a lubricant
c. Diamond has covalent bonds. Graphite has ionic bonds
D. Diamond is hard with a high melting point. Graphite is soft with a low melting point.
Subject: Physics
Volume of a liquid when compressed by additional pressure of \( 10^{5} N / m^{2} \) is 196
cc and when compressed by a pressure of \( 1.5 \times 10^{5} N / m^{2}, \) the volume is \( 194 c c \)
The bulk modulus of the liquid is:
A \( \cdot 10^{5} N / m^{2} \)
B . \( 1.5 \times 10^{6} \)
c. \( 5 \times 10^{5} N / m^{2} \)
D. \( 5 \times 10^{6} N / m^{2} \)
Subject: Maths
Find the second term of the binomial
expansion of \( \left(\sqrt[13]{\boldsymbol{a}}+\frac{\boldsymbol{a}}{\sqrt{\boldsymbol{a}^{-1}}}\right)^{m}, \) if \( \boldsymbol{C}_{3}^{\boldsymbol{m}} \)
\( C_{2}^{m}=4: 1 \)
Subject: Chemistry
Which of the following statement is
true?
A . Cold and very diluted \( H N O_{3} \) forms \( N H_{4} N O_{3} \) with \( Z n \) or \( S n \)
B. Concentrated \( H N O_{3} \) forms \( H_{2} S n O_{3} \) with \( S n \)
C . Cold and concentrated \( H N O_{3} \) forms \( N O_{2} \) with \( C u \)
D. All the above statements are correct
Subject: Chemistry
Chromium compound widely used in the
tanning of leather is:
\( \mathbf{A} \cdot C r_{2} O_{7} \)
B. \( C r_{2} O_{2} C l_{2} \)
\( \mathrm{c} \cdot \mathrm{Cr}_{2} \mathrm{O}_{3} \)
D. \( K_{2} S O_{4} C r_{2}\left(S O_{4}\right)_{3} 24 H_{2} O \)
Subject: Maths
The length of the latus rectum of the parabola \( \boldsymbol{x}=\boldsymbol{a} \boldsymbol{y}^{2}+\boldsymbol{b} \boldsymbol{y}+\boldsymbol{c} \) is \( \frac{\boldsymbol{k}}{\boldsymbol{a}} . \) Find \( \boldsymbol{k} \)
Subject: Maths
\( \left|\begin{array}{ccc}\mathbf{1} & \mathbf{1} & \mathbf{1} \\ \boldsymbol{p} & \boldsymbol{q} & \boldsymbol{r} \\ \boldsymbol{p} & \boldsymbol{q} & \boldsymbol{r}+\mathbf{1}\end{array}\right| \) is equal to
A \( \cdot q-p \)
B. \( q+p \)
\( c \cdot q \)
\( D \)
Subject: Maths
f \( \int \frac{x^{2}}{(x \sin x+\cos x)^{2}} d x= \)
\( \frac{f(x)}{x \sin x+\cos x}+\tan x+c, \) then
A \( \cdot f(x)=\frac{x}{\cos x} \)
B. \( f(x)=\frac{\cos x}{x} \)
c. \( f(x)=-\frac{x}{\cos x} \)
D. none of these
Subject: Maths
Let \( f \) be a function which is continuous
and differentiable for all real \( x \). If
\( \boldsymbol{f}(\mathbf{2})=-\mathbf{4} \) and \( \boldsymbol{f}^{\prime}(\boldsymbol{x}) \geq \mathbf{6} \) for all \( \boldsymbol{x} \in \)
\( [2,4], \) then
\( \mathbf{A} \cdot f(4)<8 \)
B \( \cdot f(4) \geq 8 \)
\( \mathbf{c} \cdot f(4) \geq 12 \)
D. none of these
Subject: Chemistry
In the following equilibrium:
\( N_{2} O_{4}(g) \rightleftharpoons 2 N O_{2}(g) \)
when 5 mole of each are taken and
temperature is kept at \( 298 K \), the total
pressure was found to be 20 bar.
given: \( \Delta G_{f}^{o} N O_{2}=100 k J, G_{f}^{o} N_{2} O_{4}= \)
\( \mathbf{5 0 k J} \)
(i) Find \( \Delta G \) of the reaction at \( 298 K \)
(ii) Find the direction of the reaction.
Subject: Chemistry
Amongst \( L i C l, R b C l, B e C l_{2} \) and
\( M g C l_{2}, \) the compounds with the
greatest and the least ionic character
respectively are:
\( \mathbf{A} \cdot L i C l \) and \( R b C l \)
в. \( R b C l \) and \( B e C l_{2} \)
c. \( M g C l_{2} \) and \( B e C l_{2} \)
D. \( R b C l \) and \( M g C l_{2} \)
Subject: Physics
An electric dipole of dipole moment \( \mathrm{p} \) and rotational inertia I is allowed to
oscillate about its equilibrium position in a uniform electric field E. Then, for
small amplitudes the frequency of oscillation will be
A \( \cdot \sqrt{p E / I} \)
в. \( \sqrt{I / p E} \)
c. \( \frac{1}{2 \pi} \sqrt{p E / I} \)
D. \( 2 \pi \sqrt{p E / I} \)
Subject: Maths
Find 'c', so that \( \boldsymbol{f}^{\prime}(\boldsymbol{c})=\frac{\boldsymbol{f}(\boldsymbol{b})-\boldsymbol{f}(\boldsymbol{a})}{\boldsymbol{b}-\boldsymbol{a}} \)
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{e}^{\boldsymbol{x}} \) at \( \boldsymbol{a}=\mathbf{0}, \boldsymbol{b}=\mathbf{1} \)
Subject: Maths
From \( 2012-2016, \) the amount (in crores)
spent on natural gas \( \mathrm{N} \) and electricity \( \mathrm{E} \) by Indian residents can be described by the following expressions, where t is the number of years since 2012 Gas spending model, \( \mathrm{N}=2.13 t^{2}-4.21 t+37.40 \)
Electricity spending model, \( \mathrm{E}=-0.209 t^{2}+5.393 t+307.735 \)
What is the total amount A spent on
natural gas and electricity by Indian residents from 2012 to 2016?
A. \( 1.467 t^{2}+7.423+121.721 \)
1
B. \( 1.339 t^{2}-8.729 t+76.245 \)
c. \( 1.01 t^{2}+7.083+97.83 \)
D. \( 1.921 t^{2}+1.183 t+345.135 \)
Subject: Maths
The marks scored by two students
\( M, N \) in a class are given below. Find
the mean using direct method.
\begin{tabular}{|l|l|l|l|l|l|}
\hline\( M \) & 98 & 88 & 87 & 90 & 70 \\
\hline\( N \) & 50 & 65 & 80 & 95 & 100 \\
\hline
\end{tabular}
A. 65 marks
B. 70 marks
C. 85 marks
D. 90 marks