AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A particle starts \( S . H . M . \) from the
mean position. Its amplitude is \( A \) and
time period is \( T . \) At the time when its speed is half of the maximum speed, its displacement \( y \) is :
A \( \cdot \frac{A}{2} \)
B. \( \frac{A}{\sqrt{2}} \)
c. \( \frac{A \sqrt{3}}{2} \)
D. \( \frac{2 A}{\sqrt{3}} \)
Subject: Maths
The differential equation of the family of
curves
\( \frac{\boldsymbol{x}^{2}}{\boldsymbol{a}^{2}}+\frac{\boldsymbol{y}^{2}}{\boldsymbol{a}^{2}+\boldsymbol{\lambda}^{2}}=1 \) is \( (\boldsymbol{\lambda} \) is orbitary
constant)
A \( \cdot\left(x^{2}-a^{2}\right) y_{1}=x y \)
B . \( \left(x^{2}-a^{2}\right) y_{2}-x y=0 \)
C \( . x^{2} y_{2}-a^{2} y=0 \)
D. \( \left(x^{2}-a^{2}\right) y_{1}+x y=0 \)
Subject: Chemistry
A transition for \( H \) -atom from \( I I \) to \( I \)
orbit has same wavelength as from \( n^{t h} \)
orbit to \( 2^{n d} \) orbit for \( H e^{+} \) ion. The value
of \( ^{\prime} n^{\prime} \) is :
\( A \cdot 7 \)
B. 2
\( c .5 \)
D. 4
Subject: Physics
toppr OGII
Q Type your question_
opened, the piston moves slightly to the right, towards the tap.
What can be deducted about the
pressure of gas \( X ? \)
before opening after opening tap \( \operatorname{tap} \)
ess than pre than atmospheric \( \quad \) atmospheric pressure
\( \operatorname{mec} \)
more than atmospheric \( \quad \) atmospheric pressure \( \quad \) pressure
ore than less than atmospheric \( \quad \) atmospheric pressure
more than \( \quad \) same as atmospheric \( \quad \) atmospheric pressure ressurr
atmosphere
\( A \cdot A \)
B.
\( c . \)
\( D \)
Subject: Maths
if \( a, b, c \) are unequal what is the condition that the value of following determinat is zero \( \delta=\left|\begin{array}{lll}a & a^{2} & a^{3}+1 \\ b & b^{2} & b^{3}+1 \\ c & c^{2} & c^{3}+1\end{array}\right| \)
A \( .1+a b c=0 \)
B. \( a+b+c+1=0 \)
c. \( (a-b)(b-c)(c-a)=0 \)
D. None of these
Subject: Chemistry
Calculate the percentage ionization of
\( 0.01 \mathrm{M} \) acetic acid in \( 0.1 \mathrm{M} \) HCl. \( K_{a} \) of
acetic acid is \( 1.8 \times 10^{-5} \)
A . \( 0.18 \% \)
B. 0.018\%
c. \( 1.8 \% \)
D. 18\%
Subject: Physics
It takes time 8 min for light to reach from sun to the earth surface. If speed of
light is taken to be \( 3 \times 10^{8} \mathrm{m} s^{-1}, \) find
the order of magnitude of distance from the sun to the earth in km.
\( \mathbf{A} \cdot 10^{7} k m \)
B . \( 15 \times 10^{8} k m \)
\( \mathbf{c} \cdot 10^{8} k m \)
D. \( 10^{9} k m \)
Subject: Chemistry
When 100 J of heat is given to an ideal
gas it expands from \( 200 \mathrm{cm}^{3} \) to \( 400 \mathrm{cm}^{3} \) at a constant pressure of \( 3 \times \)
\( \mathbf{1 0}^{5} \) Pa. Then calculate \( : \boldsymbol{R}= \)
\( \left[\frac{25}{3} J / m o l-k\right] \) The molar heat capacity \( C_{p} \) at constant pressure when
the \( T=400 K \) is
A \( \frac{125}{3} J / m o l-K \)
в. \( \frac{125}{7} J / \) тод \( -K \)
c. \( \frac{125}{9} J / m o l-K \)
D. None of these
Subject: Maths
If \( f(x)=2 \tan ^{-1} x+ \)
\( \sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right), x>1, \) then \( f(5) \) is
equal to:
A . \( \pi \)
в.
\( \mathbf{c} \cdot 4 \tan ^{1}(5) \)
D. \( \tan ^{-1}\left(\frac{64}{155}\right) \)
Subject: Chemistry
Give the number of lone pairs in the central atoms of the following inter
halogen compounds \( \boldsymbol{A} \boldsymbol{X}, \boldsymbol{A} \boldsymbol{X}_{3}, \boldsymbol{A} \boldsymbol{X}_{5} \)
\( \boldsymbol{A} \boldsymbol{X}_{\mathbf{7}} \)
A . 3, 2, 1,
в. \( 3,2,1, \) о
c. 3,1,2,0
D. 3, 2, 2, 0
Subject: Maths
If \( \boldsymbol{I}=\int_{0}^{1} \frac{\boldsymbol{e}^{t}}{\mathbf{1}+\boldsymbol{t}} \) dt, then \( \boldsymbol{p}= \)
\( \int_{0}^{1} e^{t} \log (1+t) d t= \)
\( A \)
B. \( 2 I \)
c. \( e \log 2-I \)
D. none
Subject: Physics
Ice of mass 200 g at \( 0^{\circ} \mathrm{C} \) is converted to
water at \( 0^{\circ} \mathrm{C} \) in 8 minutes supplying
heat to it at a constant rate. Calculate
the time taken to raise the temperature of water to \( 100^{\circ} \mathrm{C} \) with heat provided at the same rate. (take the latent heat of
fusion of ice \( =336 J g^{-1 \circ} C^{-1} \) and
specific heat capacity of water \( = \) \( \left.4.2 J g^{-1 \circ} C^{-1}\right) \)
Subject: Physics
The frequency of oscillation of current in
the inductor is
\( \frac{1}{3 \sqrt{L C}} \)
3. \( \frac{1}{6 \pi \sqrt{L C}} \)
c. \( \frac{1}{\sqrt{L C}} \)
D. \( \frac{1}{2 \pi \sqrt{L C}} \)
Subject: Physics
The two adjacent sides \( \boldsymbol{O A}, \boldsymbol{O B} \) of parallelogram are \( 2 \hat{i}+4 \hat{j}-5 \hat{k} \) and \( \hat{i}+ \) \( 2 \hat{j}+3 \hat{k} . \) The unit vectors along the
diagonals of the parallelogram are given by
A \( \cdot \frac{(3 \hat{i}+6 \hat{j}-2 \hat{k})}{7} \)
B. \( \frac{(-\hat{i}-2 \hat{j}+8 \hat{k})}{\sqrt{69}} \)
\( \frac{(-3 \hat{i}-6 \hat{j}+2 \hat{k})}{7} \)
D. \( \frac{(\hat{i}+2 \hat{j}-8 \hat{k})}{\sqrt{69}} \)
Subject: Maths
A retailer gets a discount of \( 40 \% \) on the printed price of an article. The retailer sells it at the printed price. What is the gain or loss percent?
A. \( 12 \% \) gain
B. \( 12 \% \) loss
c. \( _{66} \frac{2}{3} \% \) gain
D. \( 66 \frac{2}{3} \% \) loss
Subject: Physics
A body moving along the positive \( x- \) axis
with uniform acceleration of \( -4 m s^{-2} \). Its
velocity at \( x=0 \) is \( 10 m s^{-1} \). The time
taken by the body to reach a point at \( x= \)
\( 12 \mathrm{cm} \) is:
A. \( (2 s) \)
B . \( (0.25 s) \)
c. \( (3 s) \)
D. \( (0.0125 s) \)
Subject: Physics
Choose the correct relation between
\( u, v \) and \( r \) for a spherical mirror, where
\( r \) is radius of curvature.
A \( \cdot r=\frac{2 u v}{u+v} \)
B. \( r=\frac{2}{u+v} \)
c. \( r=\frac{2(u+v)}{(u v)} \)
D. \( r=\frac{2 u v}{u-v} \)
Subject: Physics
A piece of iron of mass \( 2.0 \mathrm{kg} \) has a
thermal capacity of \( 966 J K^{-1} \). Find its
specific heat capacity in S.I. unit.
A \( \cdot 1932 \mathrm{Jkg}^{-1} \mathrm{K}^{-1} \)
B . \( 241.5 \mathrm{Jkg}^{-1} \mathrm{K}^{-1} \)
c. \( 966 \mathrm{Jkg}^{-1} \mathrm{K}^{-1} \)
D. 483 Jkg\( ^{-1} K^{-1} \)
Subject: Physics
A particle of mass m strikes a horizontal smooth floor with a velocity u
making an angle \( \theta \) with the floor and rebounds with velocity v making an angle \( \phi \) with the floor. The coefficient of
restitution between the particle and the floor is e. Then
A. the impluse delivered by the floor to the body is \( m u(1-e) \sin \theta \)
B. \( \tan \phi=\operatorname{etan} \theta \)
c. \( v=u \sqrt{1-\left(1+e^{2}\right) \sin ^{2} \theta} \)
D. the ratio of the final kinetic energy to the initial kinetic energy is \( \cos ^{2} \theta+\operatorname{esin}^{2} \theta \)
Subject: Chemistry
Which of the following statements is
not correct?
A. The complexes \( \left[N i C l_{4}\right]^{2-} \) and \( \left[N i(C N)_{4}\right]^{2-} \) differ in th
B. The complexes \( \left[N i C l_{4}\right]^{2-} \) and \( \left[N i(C N)_{4}\right]^{2-} \) differ in th
C. The complexes \( \left[N i C l_{4}\right]^{2-} \) and \( \left[N i(C N)_{4}\right]^{2-} \) differ in \( g e \)
D. The complexes \( \left[N i C l_{4}\right]^{2-} \) and \( \left[N i(C N)_{4}\right]^{2-} \) differ in \( p r \)
Subject: Maths
In the figure given above, \( A B \) is paralle
to \( C D . \) If \( \angle D C E=x \) and \( \angle A B E=y \)
then what is \( \angle C E B \) equal to?
A \( \cdot y-x \)
в. \( \frac{(x+y)}{2} \)
c. \( x+y-(\pi / 2) \)
D. \( x+y-\pi \)
Subject: Maths
Find variance for following data:
\( \begin{array}{lllll}\text { Marks } & \mathbf{0}- & \mathbf{5}- & \mathbf{1 0}- & \mathbf{1 5}- \\ & \mathbf{4} & \mathbf{9} & \mathbf{1 4} & \mathbf{1 9}\end{array} \)
Frauency \( \quad 2 \quad 5 \quad 7 \) 3
\( A \cdot 7 \)
в. 55
c. 64
D. 78
Subject: Chemistry
As per observation (iii) LiH is more
stable than NaH, because:
A. Due to small size of \( L i^{+} \), the lattice energy of LiH is
greater
B. Due to greater size of \( H^{-} \), the lattice energy of LiH is greater
C. LiH is more covalent than NaH
D. Due to greater size of \( N a^{+} \), the lattice energy of NaH is greater
Subject: Physics
A rectangular copper coil is placed in uniform magnetic field of induction
\( 40 m T \) with its plane perpendicular to
the field. The area of the coil is
shrinking at a constant rate of \( 0.5 m^{2} s^{-1} \). The emf induced in the coil is
A . \( 10 \mathrm{mV} \)
в. \( 20 \mathrm{mV} \)
c. \( 80 m V \)
D. \( 40 \mathrm{mV} \)
Subject: Physics
The pole strength of \( 12 \mathrm{cm} \) long bar magnet is \( 20 \mathrm{A} \) m. The magnetic induction at a point \( 10 \mathrm{cm} \) away from the centre of the magnet on its axial line is \( \left[\frac{\boldsymbol{\mu}_{\boldsymbol{o}}}{\boldsymbol{4} \boldsymbol{\pi}}=\mathbf{1 0}^{-\boldsymbol{7}} \boldsymbol{H} \boldsymbol{m}^{-1}\right] \)
A \( .1 .17 \times 10^{-3} \mathrm{T} \)
В. \( 2.20 \times 10^{-3} \mathrm{T} \)
c. \( 1.17 \times 10^{-2} \mathrm{T} \)
D. \( 2.20 \times 10^{-2} \mathrm{T} \)
Subject: Chemistry
A compound has the following composition by weight: \( N a= \) \( \mathbf{1 8 . 6 0 \%}, \boldsymbol{S}=\mathbf{2 5 . 8 0 \%}, \boldsymbol{H}=\mathbf{4 . 0 2 \%} \) and
\( O=51.58 \% . \) Assuming that all the
hydrogen atoms in the compound are part of water of crystallization, the correct molecular formula of the
compound is:
A. \( N a_{2} S_{2} O_{3} \cdot 3 H_{2} O \)
в. \( N a_{2} S O_{4} \cdot 5 H_{2} O \)
c. \( N a_{2} S O_{4} \cdot 10 H_{2} O \)
D. \( N a_{2} S_{2} O_{3} \cdot 5 H_{2} O \)
Subject: Chemistry
No reaction occurs in which of the
following equations?
This question has multiple correct options
\( \mathbf{A} \cdot I^{\ominus}+F e^{2+} \longrightarrow \)
B . \( F_{2}+2 N a C l \longrightarrow \)
\( \mathbf{c} \cdot C l_{2}+2 N a F \longrightarrow \)
D \( \cdot I_{2}+2 N a B r \longrightarrow \)
Subject: Maths
\( \cos \theta+\frac{1}{3} \cos ^{3} \theta+\frac{1}{5} \cos ^{5} \theta+\ldots= \)
\( \mathbf{A} \cdot \log (\tan \theta) \)
B. \( \log (\cot \theta) \)
\( ^{\mathbf{c}} \cdot \log \left(\tan \frac{\theta}{2}\right) \)
D. \( \log \left(\cot \frac{\theta}{2}\right) \)
Subject: Physics
The refractive index of the material of a
prism is \( \sqrt{2} \) and the angle of the prism
is \( 30^{\circ} . \) One of the two refracting surface of the prism is made a mirror inwards, by silver coating. A beam of monochromatic light entering the prism from the other face will retrace its path (after reflection from the silvered surface) if its angle of incidence on the prism is?
A . \( 30^{\circ} \)
B . \( 60^{\circ} \)
c. zero
D. \( 45^{\circ} \)
Subject: Chemistry
Phenol reacts with \( P C l_{5} \), the main
product is:
\( A \)
\[
\mathrm{Ph}-\mathrm{O}-\underbrace{\mathrm{O}}_{\mathrm{Cl}}^{\mathrm{l}}-\mathrm{Cl}
\]
B.
\[
\mathrm{Ph}-\mathrm{O}-\underset{\mathrm{C}}{\mathrm{P}}^{\mathrm{O}}-\mathrm{O}-\mathrm{Ph}
\]
\( c \)
\[
\mathrm{Ph}--\mathrm{O}-\begin{array}{c}
\mathrm{O} \\
\mathrm{P} \\
\mathrm{OPh}
\end{array}-\mathrm{O}-\mathrm{Ph}_{\mathrm{h}}
\]
D. none of thes
Subject: Maths
How that the points \( \boldsymbol{P}(-\boldsymbol{2}, \boldsymbol{3}, \boldsymbol{5}), \boldsymbol{Q}(\boldsymbol{1}, \boldsymbol{2}, \boldsymbol{3}) \) and \( \boldsymbol{R}(\boldsymbol{7}, \boldsymbol{0},-\boldsymbol{1}) \)
are collinear.
Subject: Chemistry
Assertion
When \( A g N O_{3} \) is treated with excess of
potassium iodide, colloidal particles
gets attracted towards anode.
Reason
Precipitate adsorb common ions (excess) and thus, become charged.
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: Chemistry
A complex whose IUPAC name is not
correctly written is :
\( \mathbf{A} \cdot F e\left(\sigma-C_{5} H_{5}\right)_{2}, \) Bis \( \left(\eta^{5} \text { -cyclopentadienyl liron }(0)\right. \)
B. \( C r\left(C_{6} H_{6}\right)_{2}, \) Bis \( \left(\eta^{5} \) -benzene)chromium(o) \right.
\( \mathbf{c} \cdot\left[C o C l_{2}\left(H_{2} O\right)_{4}\right] C l .2 H_{2} O \)
Tetraaquadichlorocobalt(III)chloride-2-water
D. \( \left[Z n(N C S)_{4}\right]^{2-} \), Tetrathiocyanato-N-zincate(II)ion
Subject: Maths
Enter 1 if true else 0 . If \( \vec{a}=\hat{i}+\hat{j}+\hat{k}, \vec{b}=4 \hat{i}-2 \hat{j}+3 \hat{k} \) and
\( \overrightarrow{\boldsymbol{c}}=\hat{\boldsymbol{i}}-\boldsymbol{2} \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \)
then \( 2 \hat{i}-4 \hat{j}+4 \hat{k} \) a vector of
magnitude 6 units which is parallel to the vector \( 2 \vec{a}-\vec{b}+3 \vec{c} \)
Subject: Chemistry
Given the following molar conductivity
at infinite dilution and \( 25^{\circ} \mathrm{C} \)
\( \mathrm{HCl}: \wedge_{m}^{\infty}=426.2 \mathrm{S} \mathrm{cm}^{2} \mathrm{mol}^{-1} \mathrm{KCl}: \wedge_{m}^{\infty}= \)
\( 114.42 \mathrm{S} \mathrm{cm}^{2} \mathrm{mol}^{-1} \mathrm{CH}_{3} \mathrm{COOK}: \wedge_{m}^{\infty}= \)
\( 149.86 \mathrm{s} \mathrm{cm}^{2} \mathrm{mol}^{-1} \)
The molar conductance at infinite
dilution and \( 25^{\circ} \mathrm{C}, \) for acetic acid
solution is:
A. \( 390.76 \mathrm{Scm}^{2} \mathrm{mol}^{-1} \)
B . \( 461.86 \mathrm{Scm}^{2} \mathrm{mol}^{-1} \)
c. \( 289.63 \mathrm{Scm}^{2} \mathrm{mol}^{-1} \)
D. \( 172.94 \mathrm{Scm}^{2} \mathrm{mol}^{-1} \)
Subject: Physics
The displacement of a particle is given by \( \boldsymbol{y}=\boldsymbol{a}+\boldsymbol{b} \boldsymbol{t}+\boldsymbol{c} \boldsymbol{t}^{2}-\boldsymbol{d} \boldsymbol{t}^{4} . \) The initial
velocity and acceleration, respectively,
are
A \( . b,-4 d \)
В. \( -b, 2 c \)
c. \( b, 2 c \)
D. \( 2 c,-4 d \)
Subject: Maths
ff \( x_{i}=a_{i} b_{i} c_{i}, i=1,2,3 \) are three-digit
positive integers such that each \( x_{i} \) is a
multiple of \( 19, \) then for some integer \( n \) prove that \( \left|\begin{array}{lll}\boldsymbol{a}_{1} & \boldsymbol{a}_{2} & \boldsymbol{a}_{3} \\ \boldsymbol{b}_{1} & \boldsymbol{b}_{2} & \boldsymbol{b}_{3} \\ \boldsymbol{c}_{1} & \boldsymbol{c}_{2} & \boldsymbol{c}_{3}\end{array}\right| \) is divisible
by 19
Subject: Physics
A uniform circular disc placed on a
rough horizontal surface has initially
velocity \( v_{0} \) and an angular velocity \( \omega_{0} \) as
shown in the figure. The disc comes to
rest after moving some distance in the direction of motion. Then \( \frac{v_{0}}{r \omega_{0}} \) is
A . \( 1 / 2 \)
B.
\( c \cdot 3 / 2 \)
D. 2
Subject: Maths
Find \( \boldsymbol{F}(\boldsymbol{x}) \) from the \( \operatorname{given} \boldsymbol{F}^{\prime}(\boldsymbol{x}) \)
\( \boldsymbol{F}^{\prime}(\boldsymbol{x})=\mathbf{4} \boldsymbol{x}+\mathbf{1} \) and \( \boldsymbol{F}(-1)=\mathbf{2} \)
Subject: Chemistry
An isolated box, equally partitioned
contains two ideal gases \( A \) and \( B \) as
shown

When the partition is removed, the gases mix. The changes in enthalpy \( (\Delta H) \) and entropy \( (\Delta S) \) in the process, respectively, are:ositive, zero
A. Zero, positive
B. zero, negative
c. Positive, zero
D. Negative, zero
Subject: Physics
A force \( F=\left(3 x^{2}+2 x-7\right) N \) acts on a
\( 2 k g \) body as a result of which the body gets displaced from \( \boldsymbol{x}=\mathbf{0} \) to \( \boldsymbol{x}=\mathbf{5} \boldsymbol{m} \)
The work done by the force will be:
A . \( 5 . J \)
B. \( 70 J \)
\( \mathrm{c} .115 \mathrm{J} \)
D. \( 270 J \)
Subject: Maths
Let \( A \) be the sum of the first 20 terms
and \( B \) be the sum of the first 40 terms
of the series \( 1^{2}+2.2^{2}+3^{2}+2.4^{2}+ \)
\( 5^{2}+2.6^{2}+\ldots . . \) If \( B-2 A=100 \lambda, \) then
\( \lambda \) is equal to
\( \mathbf{A} \cdot 464 \)
в. 496
c. 232
D. 248
Subject: Physics
Two points \( A \) and \( B \) are located in diametrically opposite directions of a
point charge of \( +2 \mu \mathrm{C} \) at distances \( 2 \mathrm{m} \) and \( 1 \mathrm{m} \) respectively from it. The potential difference between \( A \) and \( B \) is
A. \( 3 \times 10^{3} \vee \)
В. \( 6 \times 10^{4} \mathrm{V} \)
\( \mathbf{c} \cdot-9 \times 10^{3} \mathbf{v} \)
D. \( -3 \times 10^{3} \mathrm{v} \)
Subject: Physics
Two organ (open) pipes of lengths 50 \( \mathrm{cm} \) and \( 51 \mathrm{cm} \) produce 6 beats/s. Then the speed of sound is nearly
\( A \cdot 300 \mathrm{ms}^{-1} \)
B. 306 \( \mathrm{ms}^{-1} \)
c. \( 303 \mathrm{ms}^{-1} \)
D. 350 \( \mathrm{ms}^{-1} \)
Subject: Chemistry
n homogenous catalytic reactions,
there are three alternative paths \( A, B \) and \( C \) (shown in figure). Which one of the following indicates the relative ease with which the reaction can take place?
\( \mathbf{A} \cdot A>B>C \)
в. \( C>B>A \)
c. \( B>C>A \)
D. \( A=B=C \)
Subject: Chemistry
In solid state \( \boldsymbol{P} \boldsymbol{C l} \boldsymbol{l}_{5} \) is a:
A. covalent solid
B. octahedral structure
C . ionic solid with \( \left[P C l_{6}\right]^{+} \) octahedral and \( \left[P C l_{4}\right]^{-} \) tetrahedral
D. ionic solid with \( \left[P C l_{4}\right]^{+} \) tetrahedral and \( \left[P C l_{6}\right] \) octahedral
Subject: Chemistry
Match each set of hybrid orbitals from
LIST-I with complex(es) given in LIST-II.
\( \begin{array}{ll}\text { LIST-I } & \text { LIST -II } \\ \text { P. } d s p^{2} & \text { 1. }\left[F e F_{6}\right]^{4-} \\ \text { Q. } s p^{3} & \text { 2. }\left[T i\left(H_{2} O\right)_{3} C l_{3}\right] \\ \text { R. } s p^{3} d^{2} & \text { 3. }\left[\operatorname{Cr}\left(N H_{3}\right)_{6}\right]^{3+} \\ \text { s.d }^{2} s p^{3} & \text { 4. }\left[F e C l_{4}\right]^{2-} \\ & \text { 5. }\left[N i(C O)_{4}\right] \\ & \text { 6. }\left[N i(C N)_{4}\right]^{2-}\end{array} \) The correct option is:
A. \( P \rightarrow 5 ; Q \rightarrow 4,6 ; R \rightarrow 2,3 ; S \rightarrow 1 \)
в. \( P \rightarrow 5,6 ; Q \rightarrow 4 ; R \rightarrow 3 ; S \rightarrow 1,2 \)
c. \( P \rightarrow 6 ; Q \rightarrow 4,5 ; R \rightarrow 1 ; S \rightarrow 2, \),
D. \( P \rightarrow 4,6 ; Q \rightarrow 5,6 ; R \rightarrow 1,2 ; S \rightarrow 3 \)
Subject: Chemistry
A current of \( 4.0 A \) is passed for 5 hours through \( 1 L \) of \( 2 M \) solution of nickel
nitrate using two nickel electrodes. The molarity of the solution at the end of the electrolysis will be:
\( \mathbf{A} \cdot 1.6 M \)
в. \( 1.2 M \)
c. \( 2.5 M \)
D. \( 2.0 M \)
Subject: Maths
If a line has the direction ratios
4,-12,18 then find its direction
cosines.
A \( \cdot-\frac{2}{11},-\frac{6}{11},-\frac{9}{11} \)
B. \( -\frac{2}{11}, \frac{6}{11},-\frac{9}{11} \)
c. \( \frac{2}{11},-\frac{6}{11}, \frac{9}{11} \)
D. \( \frac{2}{11}, \frac{6}{11}, \frac{9}{11} \)
Subject: Maths
The number of permutations of the letters of the word "ENGINEERING" is
A \( \cdot \frac{11 !}{3 ! ! ! !} \)
в. \( \frac{11 !}{(3 ! 2 !)^{2}} \)
c. \( \frac{11 !}{(3 !)^{2} \cdot 2 !} \)
D. \( \frac{11 !}{3 !(2 !)^{2}} \)
Subject: Chemistry
Ratio of radii of \( \mathrm{K}, \mathrm{L}, \mathrm{M} \) shells of hydrogen atom is :
A. 1: 2: 3
B . \( 1: \frac{1}{4}: \frac{1}{9} \)
c. 1: 4: 9
D. \( 1: \frac{1}{2}: \frac{1}{3} \)
Subject: Maths
If \( \boldsymbol{\alpha}, \boldsymbol{\beta}, \boldsymbol{\gamma} \in[\mathbf{0}, \boldsymbol{2} \boldsymbol{\pi}], \) then the sum of all
possible values of \( \alpha, \beta, \gamma \) if \( \sin \alpha= \) \( -\frac{1}{\sqrt{2}}, \cos \beta=-\frac{1}{2}, \tan \gamma=-\sqrt{3}, \) is
A \( \cdot \frac{22 \pi}{3} \)
B. \( \frac{21 \pi}{3} \)
c. \( \frac{20 \pi}{3} \)
D. \( 8 \pi \)
Subject: Maths
If \( y=\sin ^{-1}\left(x^{2}\right) \) then find \( \frac{d y}{d x} \) using first
principle.
A. \( \frac{2 x}{\sqrt{1-x^{4}}} \)
в. \( \frac{2}{\sqrt{1-x^{2}}} \)
c. \( \frac{x}{\sqrt{1-x^{4}}} \)
D. \( -\frac{1}{\sqrt{1-x^{4}}} \)
Subject: Physics
Assertion
The force exerted by the fluid is due to
the collisions of molecules with their
surroundings.
Reason
The normal force exerted by the fluid
particles on the walls of the container
results pressure.
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 incorrect but Reason is correct
D. Both Assertion and Reason are incorrect
Subject: Physics
A particle of mass \( \mathrm{m} \) is performing simple harmonic motion along line AB with amplitude 2 a with centre of oscillation as \( 0 . \) At time \( t=0 \) particle is
at point \( C(O C=a) \) and is moving towards B with velocity \( \boldsymbol{v}=\boldsymbol{a} \sqrt{\mathbf{3}} \mathrm{m} / \mathrm{s} \)
The equation of motion can be given by This question has multiple correct options
A. \( x=2 a(\sin t+\sqrt{3} \cos t) \)
B \cdot \( x=2 a \sin \left(t+\frac{\pi}{6}\right) \)
c. \( x=a(\sin t+\sqrt{3} \cos t) \)
D. \( x=a(\sqrt{3} \sin t+\cos t) \)
Subject: Physics
If the pressure difference between the two points of a horizontal pipe is
\( 0.1 p_{a t m}, \) then the velocity water flow in the pipe is :
в. \( \sqrt{20} \mathrm{ms}^{-1} \)
\( \mathrm{c} \cdot 10 \mathrm{ms}^{-1} \)
D. \( 14 \mathrm{ms}^{-1} \)
Subject: Maths
If the straight line \( a x+b y+p=0 \) and
\( x \cos \alpha+y \sin \alpha=p \) enclosed an angle
of \( \frac{\pi}{4} \) and the line \( x \sin \alpha-y \cos \alpha=0 \)
meets them at the same point, then
\( a^{2}+b^{2} \) is
A .4
B. 3
\( c \cdot 2 \)
D.
Subject: Chemistry
The volume of the water needed to
dissolve 1 g of \( B a S O_{4}\left(K_{s p}=1.1 \times\right. \)
\( \left.10^{-10}\right) \) at \( 25^{\circ} C \) is:
A . 820 litre
B. 450litre
c. 205 litre
D. none of these
Subject: Maths
If \( k=\tan 25^{\circ} \) then find \( \frac{k-1}{k+1}+\frac{k+1}{k-1} \)
A. 2 \( \operatorname{cosec} 130^{\circ} \)
B . 2 \( \operatorname{cosec} 45^{\circ} \)
c. \( 2 \sec 130^{\circ} \)
D. \( 2 \sec 400^{\circ} \)
Subject: Physics
A drop of liquid is broken down into 27 identical liquid drops. If the terminal
velocity of original liquid drop is \( V_{T} \) then find the terminal velocity of the new liquid drop thus formed.
A \( \cdot \frac{V_{T}}{3} \)
в. \( \frac{V_{T}}{9} \)
c. \( \frac{V_{T}}{27} \)
D. \( \frac{9 V_{T}}{9} \)
Subject: Physics
A plano-concave lens is made of glass of refractive index 1.5 and the radius of
curvature of its curved face is \( 100 \mathrm{cm} \)
What is the power of the lens?
A \( .+0.5 D \)
в. \( -0.5 D \)
\( c .2 D \)
D. \( +2 D \)
Subject: Chemistry
Calculate the pH of \( 0.1 M \) solution of
\( N H_{4} O C N . K_{b} \) for \( N H_{3} \) is \( 1.75 \times 10^{-5} \)
and \( K_{a} \) for \( H O C N \) is \( 3.3 \times 10^{-4} \)
Subject: Physics
Find the amount of work done by friction and gravity till the chain leaves the table, if the hanging part is pulled gently and released
A \( \cdot \frac{5 m g \ell}{18} \)
в. \( \frac{18 m g \ell}{5} \)
c. \( \frac{m g \ell}{5} \)
D. \( \frac{m g \ell}{18} \)
Subject: Chemistry
Given, \( C_{\text {graphite }}+O_{2}(g) \rightarrow \)
\( \boldsymbol{C O}_{2}(\boldsymbol{g}) ; \boldsymbol{\Delta}_{r} \boldsymbol{H}^{o}=-\boldsymbol{3} \boldsymbol{9} \boldsymbol{3} . \boldsymbol{5} \boldsymbol{k} \boldsymbol{J} \boldsymbol{m o l}^{-1} \)
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\frac{1}{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{H}_{2} \boldsymbol{O}(l) ; \boldsymbol{\Delta}_{r} \boldsymbol{H}^{o}= \)
\( -285.8 k J m o l^{-1} \)
\( \boldsymbol{C O}_{2}(\boldsymbol{g})+\boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) \rightarrow \boldsymbol{C} \boldsymbol{H}_{4}(\boldsymbol{g})+ \)
\( \mathbf{2} \boldsymbol{O}_{\mathbf{2}}(\boldsymbol{g}) ; \boldsymbol{\Delta}^{r} \boldsymbol{H} \mathbf{6} \boldsymbol{o}=+\mathbf{8} \mathbf{9 0 . 3} \boldsymbol{k} \boldsymbol{J} \boldsymbol{m o l}^{-1} \)
Based on the above thermochemical
wquations, the value of Delt\( a_{r} H^{o} \) at
\( 298 K \) for the reaction,
\( \boldsymbol{C}_{(g r a p h i t e)}+\mathbf{2} \boldsymbol{H}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{C} \boldsymbol{H}_{4}(\boldsymbol{g}) \) will be:
A. \( -78.8 k J \) mol \( ^{-1} \)
B. \( +144.0 k J \) mol \( ^{-1} \)
c. \( +74.8 k J \) mol \( ^{-1} \)
D. - 144.0kJ mol \( ^{-1} \)