AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
The mass of a box measured by a
grocer's balance is 2.3 kg.two gold pieces of masses \( 20.15 g \) and \( 20.17 g \)
are added to the box. The total mass of
the box is:
A . \( 2.30 \mathrm{kg} \)
в. \( 2.340 \mathrm{kg} \)
c. \( 2.34 \mathrm{kg} \)
D. \( 2.3 \mathrm{kg} \)
Subject: Chemistry
The \( \boldsymbol{K}_{s p}\left(\mathbf{2 5}^{o} \boldsymbol{C}\right) \) of sparingly salt
\[
\boldsymbol{X} \boldsymbol{Y}_{2}(\boldsymbol{s}) \text { is } \boldsymbol{3} . \mathbf{5 6} \times \mathbf{1 0}^{-5}\left(\boldsymbol{m o l} \quad \boldsymbol{L}^{-1}\right)^{3}
\]
and at \( 30^{\circ} \mathrm{C} \),the vapour pressure of its saturated solution in water is \( 31.78 \mathrm{mm} \)
of Hg.Calculate the enthalpy change of the reaction.( write your answer to
nearest integer)
\[
\boldsymbol{X} \boldsymbol{Y}_{2}(\boldsymbol{s}) \rightleftharpoons \boldsymbol{X}^{2+}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{2} \boldsymbol{Y}^{\ominus}(\boldsymbol{a} \boldsymbol{q})
\]
Given : Vapour pressure of pure water \( =31.82 \mathrm{mm} \) of \( \mathrm{Hg} \)
Subject: Chemistry
Choose the correct statement about the
industrial preparation of hydrogen from
water gas \( \left(C O+H_{2}\right) \)
\( \mathbf{A} \cdot H_{2} \) is removed through occlussion with \( P d \)
B. \( C O \) and \( H_{2} \) are fractionally separated using differences in their densities
C. \( C O \) is removed by absorption in \( a q . C u_{2} C l_{2} \) solution
D. \( C O \) is oxidised to \( C O_{2} \) with steam in the presence of a
catalyst followed by absorption of \( C O_{2} \) in alkali
Subject: Physics
Two conducting spheres of radii \( r_{1} \) and
\( r_{2} \) are charged to the same surface
charge density. The ratio of electric
fields near their surface is :
A \( \cdot r_{1}^{2} / r_{2}^{2} \)
B . \( r_{2}^{2} / r_{1}^{2} \)
\( \mathbf{c} \cdot r_{1} / r_{2} \)
D. 1: 1
Subject: Physics
A massive ball moving with speed \( \mathbf{v} \)
collides head-on with a tiny ball at rest having a very small mass as compared to the first ball. If the collision is elastic,
then immediately after the impact, the second ball will move with a speed approximately equal to
\( A \)
B. 2v
\( c \cdot v / 2 \)
D. \( \infty \)
Subject: Maths
If \( \vec{r} \times \vec{b}=\vec{c} \times \vec{b} \& \vec{r}, \vec{a}=0 \) where
\( \overrightarrow{\boldsymbol{a}}=\boldsymbol{2} \hat{\boldsymbol{i}}+\boldsymbol{3} \hat{\boldsymbol{j}}-\hat{\boldsymbol{k}}, \overrightarrow{\boldsymbol{b}}= \)
\( \mathbf{3} \hat{\mathbf{i}}-\hat{\boldsymbol{j}}-\boldsymbol{k}, \overrightarrow{\boldsymbol{c}}=\hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \) then \( \overrightarrow{\boldsymbol{r}} \)
A \( \cdot 2(\hat{i}-\hat{j}+\hat{k}) \)
B \( \cdot 2(\hat{i}+\hat{j}-\hat{k}) \)
c. \( 2(-\hat{i}+\hat{j}+\hat{k}) \)
D. \( 2(\hat{i}+\hat{j}+\hat{k}) \)
Subject: Maths
n fig sides QP and RQ of \( \Delta \) PQR are produced to the points \( \mathrm{S} \) and \( \mathrm{T} \)
respectively. If \( \angle S P R=105^{\circ} \angle P Q T= \)
\( 110^{\circ} \) then find \( \angle P R Q \)
\( A \cdot 35 \)
B. \( 70^{\circ} \)
\( c .105 \)
0.140
Subject: Chemistry
The temperature maintained in contact
tower during the manufacture of sulphuric acid is :
A \( \cdot 450-500^{\circ} \mathrm{C} \)
в. \( 350-400^{\circ} \mathrm{C} \)
c. \( 300-350^{\circ} \mathrm{C} \)
D. \( 250-300^{\circ} \mathrm{C} \)
Subject: Maths
The complete solution set of \( |2 x-3|+ \)
\( |\boldsymbol{x}+\mathbf{5}| \leq|\boldsymbol{x}-\mathbf{8}| \) is
\( A \cdot\left[-5, \frac{3}{2}\right] \)
B \( \cdot(-\infty,-5] \)
\( \mathbf{c} \cdot\left[\frac{3}{2}, \infty\right] \)
\( \mathbf{D} \cdot(-\infty,-5] \cup\left[\frac{3}{2}, \infty\right] \)
Subject: Physics
A body moving with a constant acceleration travels the distances \( 3 m \)
and 8 m respectively in \( 1 ~ s \) and \( 2 s \)
Calculate the acceleration of the body.
\( \mathbf{A} \cdot 2 m s^{-2} \)
B. \( 3 m s^{-2} \)
c. \( 4 m s^{-2} \)
D. \( 5 m s^{-2} \)
Subject: Physics
A harmonically moving transverse wave on a string has a maximum particle velocity and acceleration of \( 3 \mathrm{m} / \mathrm{s} \) and
\( 90 \mathrm{m} / \mathrm{s}^{2} \) respectively. Velocity of the wave is \( 20 \mathrm{m} / \mathrm{s} \). Find the waveform.
A \( \cdot y=(10 \mathrm{cm}) \sin \left(30 t \pm \frac{3}{2} x+\phi\right) \)
B. \( y=(20 c m) \sin \left(30 t \pm \frac{3}{2} x+\phi\right) \)
c. \( y=(10 \mathrm{cm}) \sin \left(60 t \pm \frac{3}{2} x+\phi\right) \)
D. \( y=(20 \mathrm{cm}) \sin \left(60 t \pm \frac{3}{2} x+\phi\right) \)
Subject: Physics
Assertion
Thermonuclear fusion reactions may
become the source of unlimited power
for the mankind.
Reason
A single fusion event involving isotopes
of hydrogen produces more energy than energy from nuclear fission of \( \frac{235}{93} U \)
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 spool of mass \( M \) and radius \( 2 R \) lies on an inclined plane as shown in figure. A light thread is wound around the connecting tube of the spool and its free
end carries a weight of mass \( m \). The
value of \( m \) so that system is in equilibrium is
\( A \cdot 2 M \sin \alpha \)
B. \( M \sin \alpha \)
\( c .2 M \tan \alpha \)
D. \( M \tan \alpha \)
Subject: Physics
An object is placed in front of a thin convex lens of focal length \( 30 \mathrm{cm} \) and a plane mirror is placed \( 15 \mathrm{cm} \) behind the lens. If the final image of the object coincides with the object, the distance of the object from the lens is :
\( A \cdot 60 \mathrm{cm} \)
B. 30 cm
c. \( 15 \mathrm{cm} \)
D. 25 cm
Subject: Physics
A car is moving with a speed of \( 30 m / s \)
on a circular path on a radius \( 500 m \). It
is increasing at the rate of \( 2 m / s e c^{2} \) What is the acceleration of the car?
\( \mathbf{A} \cdot 9.8 m / s e c^{2} \)
B. \( 2.7 m / s e c^{2} \)
c. \( 2.4 m / s e c^{2} \)
D. \( 1.8 m / s e c^{2} \)
Subject: Chemistry
Which of the following is compound \( X \) of
the synthesis?
\( A \)
в.
\( \mathrm{c} \cdot \begin{array}{c}^{o H} \\ \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}-\mathrm{CH}_{2} \mathrm{Br}\end{array} \)
D.
\[
C H_{3} C H_{2} C H-C H_{2}
\]
\( O B r \)
\( _{O H} \)
Subject: Biology
Q Type your question
blood. Study the same and answer the
following questions
(i) Name the blood vessels labelled 1
and 2
(ii) State the function of blood vessels
labelled 5 and 8
(iii) What is the importance of the blood
vessel labelled 6?
(iv) Which blood vessel will contain a
high amount of glucose after a meal?
(v) Draw a diagram of the different
blood cells as seen in an amino acids
smear of human blood.
Subject: Maths
\( \mathbf{f} \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{2} & \mathbf{- 3} \\ \mathbf{5} & \mathbf{0} & \mathbf{2} \\ \mathbf{1} & \mathbf{- 1} & \mathbf{1}\end{array}\right], \boldsymbol{B}= \)
\( \left[\begin{array}{ccc}\mathbf{3} & \mathbf{- 1} & \mathbf{2} \\ \mathbf{4} & \mathbf{2} & \mathbf{5} \\ \mathbf{2} & \mathbf{0} & \mathbf{3}\end{array}\right], \boldsymbol{C}=\left[\begin{array}{ccc}\mathbf{4} & \mathbf{1} & \mathbf{2} \\ \mathbf{0} & \mathbf{3} & \mathbf{2} \\ \mathbf{1} & \mathbf{- 2} & \mathbf{3}\end{array}\right], \) Then
Compute \( (\boldsymbol{A}+\boldsymbol{B}) \) and \( (\boldsymbol{B}-\boldsymbol{C}) . \) Also
verify that \( \boldsymbol{A}+(\boldsymbol{B}-\boldsymbol{C})=(\boldsymbol{A}+\boldsymbol{B})- \)
\( C \)
Subject: Chemistry
Assertion
The balancing of chemical equations is based on the law of conservation of
mass.
Reason
Total mass of reactants is equal to total
mass of products.
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. Assertion is incorrect but Reason is correct
Subject: Maths
The function \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \frac{\log (1+a x)-\log (1-b x)}{x} \) is not
defined at \( x=0 . \) The value which
should be assigned to \( f \) at \( x=0 \) so that
it is continuous there, is
A \( . a-b \)
B. \( a+b \)
\( \mathbf{c} \cdot \log a+\log b \)
D. none of these
Subject: Physics
The percentage change in the acceleration of the earth towards the
sun from a total eclipse of the sun to the
point where the moon is on a side of earth directly opposite to the sun is:
\( r_{1} \) is the distance of earth from sun, \( r_{2} \)
is the distance of earth from moon
A \( \cdot \frac{M_{s}}{M_{m}} \frac{r_{2}}{r_{1}} \times 100 \)
B. \( \frac{M_{s}}{M_{m}}\left(\frac{r_{2}}{r_{1}}\right)^{2} \times 100 \)
\( ^{\mathbf{C}} 2\left(\frac{r_{1}}{r_{2}}\right)^{2} \frac{M_{m}}{M_{s}} \times 100 \)
\( ^{\mathrm{D}}\left(\frac{r_{1}}{r_{2}}\right)^{2} \frac{M_{s}}{M_{m}} \times 100 \)
Subject: Physics
The distance between them at time \( t \) is:
A \( \cdot \sqrt{(200)^{2}+(100)^{2}} m \)
B. \( \sqrt{(200-4 t)^{2}+(100-2 t)^{2}} m \)
c. \( [(200-4 t)+(100-2 t)] m \)
D. \( \sqrt{(200-2 t)^{2}+(100-4 t)^{2}} m \)
Subject: Maths
If, is continuous at \( x=2, \) find the value
of \( k \)
\( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{ll}\frac{\boldsymbol{x}^{3}+\boldsymbol{x}^{2}-\mathbf{1 6} \boldsymbol{x}+\mathbf{2 0}}{(\boldsymbol{x}-\mathbf{2})^{2}}, & \boldsymbol{x} \neq \mathbf{2} \\ \boldsymbol{k}, & \boldsymbol{x}=\mathbf{2}\end{array}\right. \)
Subject: Chemistry
The pH of the solution obtained by mixing \( 100 \mathrm{ml} \) of a solution of \( \mathrm{pH}=3 \) with \( 400 \mathrm{ml} \) of a solution of \( \mathrm{pH}=4 \) is :
A. \( 3-\log 2.8 \)
B. \( 7-\log 2.8 \)
c. \( 4-\log 2.8 \)
D. \( 5-\log 2.8 \)
Subject: Maths
Find \( \boldsymbol{P} \boldsymbol{M} \)
\( \mathbf{A} \cdot 3 c m \)
\( \mathbf{B} \cdot 4 c m \)
\( \mathbf{c} \cdot 5 c m \)
D. \( 8 \mathrm{cm} \)
Subject: Maths
The direction cosines of the line which
is perpendicular to the lines with direction cosines proportional to
(1,-2,-2)\( \&(0,2,1) \) are
\( ^{\mathrm{A}} \cdot\left(\frac{2}{3},-\frac{1}{3}, \frac{2}{3}\right) \)
в. \( \left(\frac{2}{3}, \frac{1}{3}, \frac{2}{3}\right) \)
c. \( \left(\frac{2}{3}, \frac{1}{3}, \frac{-2}{3}\right) \)
D. \( \left(\frac{-2}{3}, \frac{1}{3}, \frac{2}{3}\right) \)
Subject: Maths
For a certain type of computers, the length of time between charges of the
battery is normally distributed with a
mean of 50 hours and a standard
deviation of 15 hours. John owns one of
these computers and wants to know the
probability that the length of time will
be between 50 and 70 hours.
A .0 .4082
B. 0.4025
c. 0.4213
D. 0.4156
Subject: Maths
If \( D \) is a point on side \( A B \) of \( A B C \) and \( D E \) is a line through D meeting \( A C \) at \( E \) such that \( \Delta A D E \sim \Delta A C B . \) Then \( A B \)
AD is equal to
A . AE. AC
B. AC. DE
c. AE. BC
D. AB. BC
Subject: Maths
If \( \boldsymbol{f}(\boldsymbol{x})= \)
\[
\left\{\begin{array}{cc}
\frac{x^{2}}{2}, & \text { if } 0 \leq x \leq 1 \\
2 x^{2}-3 x+\frac{3}{2}, & \text { if } 1<x \leq 2
\end{array},\text { Show }\right.
\]
that \( f \) is continuous at \( x=1 \)
Subject: Maths
Let the three digit numbers \( A 28,3 B 9 \)
and \( 62 C, \) where \( A, B, C \) are integers
between 0 and 9 , be divisible by a fixed integer \( k, \) Show that the determinant \( \left|\begin{array}{lll}\boldsymbol{A} & \boldsymbol{3} & \boldsymbol{6} \\ \boldsymbol{8} & \boldsymbol{9} & \boldsymbol{C} \\ \boldsymbol{2} & \boldsymbol{B} & \boldsymbol{2}\end{array}\right| \) is also divisible by the
same integer \( \boldsymbol{k} \)
Subject: Physics
In Figure circuit section, \( A B \) absorbs
energy at a rate of 50W when a current
\( =1.0 \mathrm{A} \) passes through it in the indicated direction. What is the
potential difference between \( A \) and \( B \) ?
A \( .10 V \)
в. \( 50 V \)
\( c \cdot 20 V \)
D. 30V
Subject: Maths
The mean score of 1000 students for an
examination is 34 and standard
deviation is 16
(i) How many candidates can be
expected to obtain marks between 30
and 60 assuming the normality of the distribution and
(ii) Determine the limits of the marks of
the central \( 70 \% \) of the candidates
\( \{P[0<z<0.25]=0.0987 ; P[0<z< \)
1.63 \( ]=\mathbf{0 . 4 4 8 4} ; P[\mathbf{0}<\boldsymbol{z}<\mathbf{1 . 0 4}]= \)
\( \mathbf{0 . 3 5}\} \)
Subject: Chemistry
Among the following outermost configuration of metals which shows the highest oxidation state?
A \( \cdot 3 d^{3} 3 s^{2} \)
B . \( 3 d^{5} 4 s^{1} \)
\( \mathbf{c} \cdot 3 d^{5} \mathbf{4} s^{2} \)
D. \( 3 d^{4} 4 s^{2} \)
Subject: Physics
Two perfectly elastic particles \( A \) and \( B \) of equal masses travelling along the
line joining them with velocity \( 15 \mathrm{ms}^{-1} \)
and \( 10 \mathrm{ms}^{-1} \) respectively collide. Their velocities after the elastic collision will
be \( \left(\text { in } m s^{-1}\right) \) respectively
A. 20 and 5
B. 10 and 15
\( c \cdot 25 \) and 20
D. 0 and 25
Subject: Maths
The number of reflexive relation in \( \operatorname{set} A \)
\( =\{a, b, c\} \) is equal to
A \( \cdot 2^{9} \)
B \( \cdot 2^{4} \)
\( c \cdot 2^{7} \)
D. \( 2^{\text {6 }} \)
Subject: Physics
Two blocks of masses \( 10 k g \) and \( 4 k g \) are connected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulsive force
gives a velocity of \( 14 m s^{-1} \) to the
heavier block in the direction of the
lighter block. The velocity of centre of mass of the system at that moment is
A \( .30 m s^{-1} \)
B. \( 20 m s^{-1} \)
\( \mathrm{c} \cdot 10 \mathrm{ms}^{-1} \)
\( \mathbf{D} \cdot 5 m s^{-1} \)
Subject: Chemistry
1 L of a hydrogen weighs as much as 1 L
of \( C O_{2} . \) The molecular formula of the
hydrocarbon is :
A \( \cdot C_{3} H_{8} \)
в. \( C_{2} H_{6} \)
\( \mathbf{c} \cdot C_{2} H_{4} \)
D. \( C_{3} H_{6} \)
Subject: Chemistry
Consider the following processes.
\( \begin{array}{ll} & \boldsymbol{\Delta} \boldsymbol{H}(\boldsymbol{k} \boldsymbol{J} / \boldsymbol{m o l}) \\ 1 / 2 A \rightarrow B & +150 \\ 3 B \rightarrow 2 C+D & -125 \\ E+A \rightarrow 2 D & +350\end{array} \)
For \( \boldsymbol{B}+\boldsymbol{D} \rightarrow \boldsymbol{E}+\mathbf{2} \boldsymbol{C}, \boldsymbol{\Delta} \boldsymbol{H} \) will be:
A . 325 kJ/mol
B. 525 kJ/mol
c. -175 kJ.mol
D. -325 kJ/mol
Subject: Physics
Assertion (A): Fragments produced in
the fission of \( U^{235} \) are radioactive
Reason (R) : The fragments have abnormally high proton to neutron ratio
A. Both A and R are true and R is correct explanation of A
B. Both A and R are true and R is not correct explanation of
c. \( A \) is true but \( R \) is false
D. A is false but R is true
Subject: Maths
For two data sets, each of size of \( 5, \) the
variances are given to be 4 and 5 and the corresponding means are given to be 2 and \( 4, \) respectively. The variance of the combined data set is :
A \( \cdot \frac{11}{2} \)
B. 6
c. \( \frac{13}{2} \)
D.
Subject: Chemistry
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C l} \stackrel{N a C N}{\longrightarrow} \boldsymbol{X} \stackrel{\boldsymbol{P t} / \boldsymbol{H}_{2}}{\longrightarrow} \)
\( \boldsymbol{Y} \frac{\text {Acetic}}{\text {anhydride}} \boldsymbol{Z} \)
In the above sequence, \( Z \) is:
A. \( C H_{3} C H_{2} C H_{2} N H C O C H_{3} \)
в. \( C H_{3} C H_{2} C H_{2} N H_{2} \)
c. \( C H_{3} C H_{2} C H_{2} C O N H C H_{3} \)
D. \( C H_{3} C H_{2} C H_{2} C O N H C O C H_{3} \)
Subject: Maths
The value of \( \sum_{i=1}^{10} r(i) \) is equal to
A \( \cdot \log \left[2-\frac{k}{H}\right] \)
в. \( 5 R\left[2+\frac{11 k}{H}\right] \)
c. \( _{5 R}\left[2-\frac{11 k}{H}\right] \)
D. \( 4 R\left[2-\frac{11 k}{H}\right. \)
Subject: Physics
Velocity of particle moving along a
straight line at any time \( t \) is given by \( v=\cos \left(\frac{\pi}{3} t\right) . \) The distance travelled by the particle in the first two seconds is equal to
A \( \cdot \frac{\sqrt{3}}{2 \pi} \)
B. \( \frac{3 \sqrt{3}}{2 \pi} \)
\( c \cdot \frac{3 \sqrt{3}}{\pi} \)
D. zero
Subject: Physics
\( \operatorname{mass} m=2 k g \) are connected to the
ends of an ideal spring having force
constant \( \boldsymbol{k}=\mathbf{1 0 0 0} \boldsymbol{N m}^{-1} . \) System of
these blocks and spring is placed on a rough floor. Coefficient of friction
between blocks and floor is \( \mu=0.5 \)
Block B is pressed towards left so that
spring gets compressed.
Initial minimum compression \( \boldsymbol{x}_{\mathbf{0}} \) of
spring such that block A leaves contact
with the wall when system is released is:
\( \mathbf{A} \cdot 3 \mathrm{cm} \)
B. \( 4 \mathrm{cm} \)
\( \mathbf{c} .5 \mathrm{cm} \)
D. \( 6 \mathrm{cm} \)
Subject: Chemistry
In which of the following pairs of
carbanion, the first one is more stable
than the second?
A \( \cdot \stackrel{\ominus}{C} F_{3}, C C l_{3} \)
B. \( H C=\stackrel{\ominus}{C}, H_{2} C=\stackrel{\ominus}{C H} \)
\( c \)
D. \( \left(C H_{3}\right)_{3} \stackrel{\ominus}{C}, H_{3} C-\stackrel{\ominus}{C} H_{3} \)
Subject: Physics
The pendulum bob has a speed of \( 3 \mathrm{m} / \mathrm{s} \)
at its lowest position. The pendulum is \( 0.5 \mathrm{m} \) long. The speed of the bob, when
the bob makes an angle of \( 60^{\circ} \) to the vertical will be \( \left(\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2}\right) \)
\( A \cdot 1 \mathrm{m} / \mathrm{s} \)
B. \( 1.5 \mathrm{m} / \mathrm{s} \)
\( c \cdot 3 m / s \)
D. \( 2 \mathrm{m} / \mathrm{s} \)
Subject: Physics
Assertion
In a decay process of a nucleus, the
mass of products is less than that of
the parent.
Reason
The rest mass energy of the products must be less than that of the parent
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
For the reactions, \( \boldsymbol{A} \rightleftharpoons \boldsymbol{B}, \boldsymbol{B} \rightleftharpoons \boldsymbol{C}, \boldsymbol{C} \rightleftharpoons \)
D, equilibrium constants are
\( \boldsymbol{K}_{1}, \boldsymbol{K}_{2}, \boldsymbol{K}_{3} \) respectively
What is the value of the equilibrium constant for \( \boldsymbol{A} \rightleftharpoons \boldsymbol{D} ? \)
\( \mathbf{A} \cdot K_{1}, K_{2}, K_{3} \)
в. \( K_{1} \times K_{2} \times K_{3} \)
c. \( K_{1} K_{2} / 3 \)
D. None of these
Subject: Chemistry
Relative molecular mass is the ratio of
A. the average mass of one molecule of an element or compound to of the mass of an atom of carbon-12
B. the average mass of one molecule of an element or compound to one twelfth of the mass of an atom of carbon-12
C. the average mass of one molecule of an element or compound to one fifth of the mass of an atom of carbon-12
D. the average mass of one molecule of an element or compound to one twelfth of the mass of an atom of carbon-16
Subject: Maths
If \( \boldsymbol{f} \) satisfies \( |\boldsymbol{f}(\boldsymbol{u})-\boldsymbol{f}(\boldsymbol{\nu})| \leq|\boldsymbol{u}-\boldsymbol{\nu}| \) for
\( \boldsymbol{u}, \boldsymbol{\nu} \in[\boldsymbol{a}, \boldsymbol{b}] \)
then the maximum value of \( \left|\int_{a}^{b} f(x) d x-(b-a) f(a)\right| \) is?
A \( \cdot \frac{b-a}{2} \)
в. \( \frac{(b-a)^{2}}{2} \)
c. \( (b-a)^{2} \)
D. None of these
Subject: Maths
The points \( \boldsymbol{A}(\boldsymbol{a}, \boldsymbol{b}+\boldsymbol{c}), \boldsymbol{B}(\boldsymbol{b}, \boldsymbol{c}+\boldsymbol{a}) \) and
\( \boldsymbol{C}(\boldsymbol{c}, \boldsymbol{a}+\boldsymbol{b}) \) are:
A. collinear
B. doesn'tt lie in the same plane
c. doesn't lie on the same line
D. nothing can be said
Subject: Maths
If \( \boldsymbol{y}=[\boldsymbol{x}+\sqrt{\boldsymbol{x}^{2}-\mathbf{1}}]^{15}+ \)
\( [x-\sqrt{x^{2}-1}]^{15}, \) then \( \left(x^{2}-1\right) \frac{d^{2} y}{d x^{2}}+ \)
\( x \frac{d y}{d x} \) is equal to
A . \( 125 y \)
B . \( 225 y^{2} \)
c. \( 225 y \)
D. \( 224 y^{2} \)
Subject: Maths
If the equation \( \sin ^{-1}\left(x^{2}+x+1\right)+ \)
\( \cos ^{-1}(a x+1)=\frac{\pi}{2} \) has exactly two
distinct solutions then value of \( a \)
could not be

This question has multiple correct options
\( A \cdot-1 \)
B.
\( c \)
\( D \)
Subject: Physics
The work performed (in J) to make a
hoop out of a steel band of length \( l= \)
\( 2.0 m, \) width \( h=6.0 \mathrm{cm}, \) and thickness
\( \boldsymbol{\delta}=\mathbf{2 . 0} \boldsymbol{m m} \) is \( \boldsymbol{x} \times \mathbf{1 0}^{\mathbf{1}} \boldsymbol{J} . \) The process
is assumed to proceed within the elasticity range of the material. Find the
value of \( \boldsymbol{x} \)
Subject: Maths
The order and degree of the differential equation \( \sqrt{\frac{\boldsymbol{d y}}{\boldsymbol{d} \boldsymbol{x}}}-4 \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}-\boldsymbol{7} \boldsymbol{x}=\boldsymbol{0} \) are
A. 1 and \( 1 / 2 \)
B. 2 and 1
c. 1 and 1
D. 1 and 2
Subject: Maths
Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}, \) when \( \boldsymbol{y}=\boldsymbol{3} \tan \boldsymbol{x}+ \)
\( \boldsymbol{5} \log _{\boldsymbol{a}} \boldsymbol{x}+\sqrt{\boldsymbol{x}}-\boldsymbol{3} \boldsymbol{e}^{\boldsymbol{x}}+\frac{\boldsymbol{1}}{\boldsymbol{x}} \)
Subject: Chemistry
When \( 100 g \) of saturated solution is
evaporated at \( 50^{\circ} \mathrm{C}, 50 \mathrm{g} \) of solid is left over. Find the solubility of the
substance at \( 50^{\circ} \mathrm{C} \)
A . 100
B. 50
c. 75
D. 25
Subject: Physics
If the work done in stretching a wire by
1 \( m m \) is \( 2 J, \) the work necessary for
stretching another wire of same
material but with double radius of
cross-section and half the length by
1 mm is:
\( \mathbf{A} \cdot 16 J \)
B. \( 8 J \)
c. \( 4 J \)
D \( \frac{1}{4} J \)
Subject: Maths
The position vectors of three points are \( \mathbf{2} \overrightarrow{\boldsymbol{a}}-\overrightarrow{\boldsymbol{b}}+\mathbf{3} \overrightarrow{\boldsymbol{c}}, \overrightarrow{\boldsymbol{a}}-\mathbf{2} \overrightarrow{\boldsymbol{b}}+\boldsymbol{\lambda} \overrightarrow{\boldsymbol{c}} \) and \( \boldsymbol{\mu} \overrightarrow{\boldsymbol{a}}-\mathbf{5} \overrightarrow{\mathbf{b}} \)
where \( \vec{a}, \vec{b}, \vec{c} \) are non coplanar vectors then the points are collinear when
A \( \cdot \lambda=-2, \mu=\frac{9}{4} \)
B. \( \lambda=-\frac{9}{4}, \mu=2 \)
c. \( \lambda=\frac{9}{4}, \mu=-2 \)
D. None of these
Subject: Physics
Assertion
The focal length of a lens does not
depend on the medium in which it is submerged
Reason \( \frac{1}{\boldsymbol{f}}=\frac{\boldsymbol{\mu}_{2}-\boldsymbol{\mu}_{1}}{\boldsymbol{\mu}_{1}}\left(\frac{1}{\boldsymbol{R}_{1}}-\frac{1}{\boldsymbol{R}_{2}}\right) \)
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. Assertion is incorrect but Reason is correct
Subject: Physics
A plane progressive wave of frequency \( 25 H z, \) amplitude \( 2.5 \times 10^{-5} m \) and
initial phase zero moves along the negative x-direction with a velocity of
\( 300 m s^{-1} . A \) and \( B \) are two points \( 6 m \)
a part on the line of propagation of the wave. At any instant the phase difference between \( A \) and \( B \) is \( \Theta \). The
maximum difference the displacement of the particles at \( A \) and \( B \) is \( \Delta, \) then This question has multiple correct options
\( \mathbf{A} \cdot \Theta=\pi \)
B \( \cdot \Theta=0 \)
c. \( \Delta=0 \)
D. \( \Delta=5 \times 10^{-5} m \)
Subject: Maths
If \( u, v, w \) are non-coplanar vector and
\( \boldsymbol{p}, \boldsymbol{q} \) are real numbers, then the equality \( [\mathbf{3 u} \boldsymbol{p v} \boldsymbol{p w}]-[\boldsymbol{p v} \boldsymbol{w} \boldsymbol{q} \boldsymbol{w}]-[\mathbf{2 w} \boldsymbol{q} \boldsymbol{v} \boldsymbol{q} \boldsymbol{u}]= \)
\( \mathbf{0} \) holds for
A. Exactly two values of \( (p, q) \)
B. More than but not all values of \( (p, q) \)
c. All values of \( (p, q) \)
D. Exactly one values of \( (p, q) \)