AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
A swimming pool was sufficiently
alkaline so that \( \mathrm{CO}_{2} \) absorbed from the
air produced in the pool a solution
which \( 2 \times 10^{-4} M \) in \( C O_{3}^{2-} M . \) If the
pool water was originally \( 4 \times 10^{-3} M \) in
\( M g^{2+}, 6 \times 10^{-4} M \) in \( C a^{2+} \) and \( 8 x \)
\( 10^{-7} M \) in \( F e^{2+}, \) then a precipitate
should form of:
\( \left(\boldsymbol{K}_{s p} \text { for } \boldsymbol{C a} \boldsymbol{C O}_{3}, \boldsymbol{M} \boldsymbol{g} \boldsymbol{C O}_{3}, \boldsymbol{F e} \boldsymbol{C O}_{3} \) are \right.
\( \mathbf{2 . 8} \times \mathbf{1 0}^{-\mathbf{9}}, \mathbf{3 . 5} \times \mathbf{1 0}^{-\mathbf{8}}, \mathbf{3}, \mathbf{2} \times \mathbf{1 0}^{-\mathbf{1 1}} \)
respectively
A . only \( M g C O_{3} \)
B . only \( C a C O_{3} \)
c. only \( F e C O_{3} \)
D. only \( M g C O_{3} \) and \( F e C O_{3} \)
E. \( M g C O_{3}, C a C O_{3} \) and \( F e C O_{3} \)
Subject: Physics
A solenoid is \( 2.0 \mathrm{m} \) long and \( 3.0 \mathrm{cm} \) in diameter. It has 5 layers of winding of 1000 turns each and carries a current of
5.0 A. What is the magnetic field at its centre?
A \( \cdot 1.5 \times 10^{-3} T \)
в. \( 1.5 \times 10^{-2} T \)
c. \( 1.5 \times 10^{-4} T \)
D. \( 2.5 \times 10^{-2} T \)
Subject: Chemistry
Identify \( X \) and \( Y \) in the following
reaction sequence \( \boldsymbol{X} \stackrel{\boldsymbol{Z} \boldsymbol{n}}{\boldsymbol{Y}} \boldsymbol{Y} \underset{\boldsymbol{Z} \boldsymbol{n}-\boldsymbol{H}_{2}}{\frac{\boldsymbol{O}_{\boldsymbol{2}}}{\boldsymbol{O}}}\left(\boldsymbol{C H}_{\boldsymbol{3}}\right)_{2} \boldsymbol{C O}+\boldsymbol{C H}_{2} \boldsymbol{O} \)
A. \( X=\left(C H_{3}\right)_{2} C_{\text {In }}^{C H} C H_{3}, Y=C H_{3} C H=C H C H_{3} \)
в. \( X=\left(C H_{3}\right)_{2} C H C H_{2} B r, Y=C H_{3} C H=C H C H_{3} \)
c. \( X=\left(C H_{3}\right)_{2} C B r C H_{2} B r, Y=\left(C H_{3}\right)_{2} C=C H_{2} \)
D. \( X=\left(C H_{3}\right)_{2} C(B r)-C H_{2} B r, Y=\left(C H_{3}\right)_{2} C=C H_{2} \)
Subject: Maths
Find the maximum value of \( g(f(x)) \) if \( f(x)=x+4 \) and
\( \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{6}-\boldsymbol{x}^{2} \)
A . -6
B. -4
\( c \cdot 2 \)
D. 4
E . 6
Subject: Maths
Which of the following is not an equivalence relation on \( Z \) ?
A \( . a R b \Leftrightarrow a+b \) is an even integer
B. \( a R b \Leftrightarrow a-b \) is an even integer
\( c \cdot a R b \Leftrightarrow a<b \)
D. \( a R b \Leftrightarrow a=b \)
Subject: Maths
Given \( \boldsymbol{A}=(\mathbf{1}, \mathbf{2}, \mathbf{5}), \boldsymbol{B}=(\mathbf{5}, \mathbf{7}, \mathbf{9}) \) and
\( C=(3,2,-1) . \) Find a until vector
normal to the plane of the triangle ABC.
A. \( \frac{-13 i+9 j-7 k}{\sqrt{(299)}} \)
в. \( \frac{13 i-9 j+7 k}{\sqrt{(299)}} \)
c. \( \frac{-15 i+16 j-5 k}{\sqrt{(506)}} \)
D. \( \frac{15 i-16 j+5 k}{\sqrt{(506)}} \)
Subject: Physics
A particle is moving with a constant speed \( v \) in a circle of radius \( R \). What is
the magnitude of average acceleration after half revolution?
\( ^{\text {A }} \cdot \frac{v^{2}}{2 R} \)
в. \( \frac{2 v^{2}}{\pi R} \)
c. \( \frac{v^{2}}{R} \)
D. \( \frac{v^{2}}{\pi R} \)
Subject: Physics
toppr
Q Type your question
the velocity of man with respect to
ground any how remains constant)
Plank is placed on smooth horizontal
surface. The man, while running
whistles with frequency \( f_{0} . \) A detector
(D) placed on plank detects frequency.
The man jumps off with same velocity (w.r.t. to ground) from point \( \mathrm{D} \) and slides on the smooth horizontal surface
[Assume coefficient of friction between
man and horizontal is zero]. The speed
of sound in still medium is \( 330 \mathrm{m} / \mathrm{s} \)
Answer following questions on the basis of above situations. Choose the correct
plot between the frequency detected by detector versus position of the man relative to detector:
\( A \)
B.
\( c \)
\( D \)
Subject: Maths
The set of values of \( x \) for which
\( \tan ^{-1} \frac{x}{\sqrt{1-x^{2}}}=\sin ^{-1} x \) holds is
A. \( R \)
в. (-1,1)
\( \mathbf{c} \cdot[0,1] \)
D. [-1,0]
Subject: Physics
What is the value of \( \frac{d P}{P} \) for adiabatic expansion of the gas?
A \( \cdot \gamma \frac{d V}{V} \)
B. \( -\frac{d V}{V} \)
c. \( \frac{d V}{V} \)
D. \( -\gamma \frac{d V}{V} \)
Subject: Physics
The Young's modulus of a material is
\( 2 \times 10^{11} N / m^{2} \) and its elastic limit is
\( 1.8 \times 10^{8} N / m^{2} . \) For a wire of \( 1 m \) length
of this material, the maximum elongation achievable is
\( \mathbf{A} \cdot 0.2 m m \)
в. \( 0.3 m m \)
\( c .0 .4 m m \)
D. \( 0.5 m m \)
Subject: Chemistry
An unknown compound \( A \) dissociates
at \( 500^{\circ} \mathrm{C} \) to give products as follows\( \boldsymbol{A}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{B}(\boldsymbol{g})+\boldsymbol{C}(\boldsymbol{g})+\boldsymbol{D}(\boldsymbol{g}) \)
Vapour density of the equilibrium mixture is 50 when it dissociates to the
extent to \( 10 \% \). What will be the
molecular weight of compound \( \boldsymbol{A} \) ?
A. 120
в. 130
\( c \cdot 134 \)
D. 140
Subject: Chemistry
Order of size of \( s p, s p^{2} \) and \( s p^{3} \) orbitals
is:
A \( \cdot s p^{3}<s p^{2}<s p \)
B \( . s p<s p^{2}<s p^{3} \)
c. \( s p^{2}<s p<s p^{3} \)
D. \( s p^{2}<s p^{3}<s p \)
Subject: Physics
Determine the volume contraction of a
solid copper cube, \( 10 \mathrm{cm} \) on an edge, when subjected to a hydraulic pressure of \( 7.0 \times 10^{6} \) Pa. (Bulk modulus of
copper, \( \left.\boldsymbol{B}=\mathbf{1 4 0} \times \mathbf{1 0}^{\mathbf{9}} \boldsymbol{P a}\right) \)
Subject: Physics
The magnifying power of a telescope with tube length \( 60 \mathrm{cm} \) is \( 5 . \) What is the
focal length of its eye piece?
\( \mathbf{A} \cdot 30 \mathrm{cm} \)
B. \( 20 \mathrm{cm} \)
c. \( 10 \mathrm{cm} \)
\( \mathbf{D} \cdot 40 \mathrm{cm} \)
Subject: Chemistry
The equilibrium constant for the
reaction \( \boldsymbol{C O}(\boldsymbol{g})+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \rightleftharpoons \)
\( \boldsymbol{C O}_{2}(\boldsymbol{g})+\boldsymbol{H}_{2}(\boldsymbol{g}) \) is \( \mathbf{7 . 3} \) at \( \mathbf{4 5 0}^{\circ} \boldsymbol{C} \) \&1
atm pressure. The initially
concentration of water \( \operatorname{gas} C O \& H_{2} \) in
equimolar ratio \( \& \) steam are 2 moles \( \& \) 5 moles respectively. The number of moles of \( C O, H_{2}, C O_{2} \& H_{2} O \) (vapour) at equilibrium are
\( \boldsymbol{n}_{C O_{2}}=\mathbf{0 . 9 2 8}, \boldsymbol{n}_{\boldsymbol{H}_{2}}=\mathbf{1 . 9 2 8}, \boldsymbol{n}_{C O}= \)
\( \mathbf{0 . 0 7 2}, \boldsymbol{n}_{\boldsymbol{H}_{2}} \boldsymbol{o}=\mathbf{4 . 0 7 2} \)
If true enter 1 , else enter 0 .
A.
Subject: Maths
Calculate \( \frac{1}{x_{1}^{3}}+\frac{1}{x_{2}^{3}}, \) where \( x_{1} \) and \( x_{2} \)
are roots of the equation \( 2 x^{2}-3 a x- \)
\( \mathbf{2}=\mathbf{0} \)
Subject: Chemistry
The standard enthalpy of formation of water liquid is \( 285.76 \mathrm{kJ} \) at \( 298 \mathrm{K} \)
Calculate the value at \( 373 \mathrm{K} \). The molar
heat capacities at constant pressure
\( \left(C_{P}\right) \) in the given temperature range of
\( \boldsymbol{H}_{2}(\boldsymbol{g}), \boldsymbol{O}_{2}(\boldsymbol{g}) \) and \( \boldsymbol{H}_{2} \boldsymbol{O}(l) \) are
respectively 38.83,29.16 and 75.312 \( \$ \$ J K^{\wedge}\{1\} \operatorname{mol}^{\prime}\{1\} \)
A \( \cdot \Delta H_{373}^{\circ}\left(H_{2} O,(l)\right)=-284.11 k J \)
B. \( \Delta H_{3^{\prime 3}}\left(H_{2} O,(l)\right)=+284.11 k J \)
C . \( \Delta H_{373}^{\circ}\left(H_{2} O,(l)\right)=28.411 k J \)
D. None of these
Subject: Maths
If \( p \) is the length of the perpendicular from the origin on the line \( \frac{x}{a}+\frac{y}{b}=1 \)
and \( a^{2}, p^{2}, b^{2} \) are in A.P. then \( a b \) is equal
to
This question has multiple correct options
A \( \cdot p^{2} \)
B \( \cdot \sqrt{2} p^{2} \)
c. \( -\sqrt{2} p^{2} \)
D. \( 2 p^{2} \)
Subject: Chemistry
Assertion
Dil. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) can convert into a normal
salt.
Reason
Sulphuric acid is dibasic acid. On neutralizing with a base it forms acid salt and normal salt
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
Two people carry a heavy electric motor
(M) by placing it on a board \( 2.0 \mathrm{m} \) long
that weighs 200 N. one person A lifts at one end with a force of \( 400 \mathrm{N} \). and the
other \( \mathrm{B} \) lifts the opposite end with a force of 600 N. The distance from \( A \)
where the centre of gravity of the motor
is located is
\( A \cdot 1 m \)
B. 1.25 m
\( c \cdot 0.8 m \)
D. \( 0.75 \mathrm{m} \)
Subject: Chemistry
Permutit is the trade name of a mixture
of:
A. hydrated silicates of \( C a \) and \( M g \)
B. hydrated silicates of \( A l \) and \( N a \)
C. hydrated aluminates of \( C a \) and \( N a \)
D. hydrated aluminates of \( M g \) and \( N a \)
Subject: Chemistry
The products of the following reactions is(are):
\( \mathbf{C}_{2} \mathbf{H}_{5} \mathbf{B} \mathbf{r}+\mathbf{2} \mathbf{N} \mathbf{a}+\mathbf{C} \mathbf{H}_{3} \mathbf{B} \mathbf{r} \stackrel{d r y e t h e r}{\rightarrow} ? \)
A. ethane
B. propane
c. butane
D. ethane, propane and butane
Subject: Physics
If \( \boldsymbol{v}=\frac{\boldsymbol{A}}{\boldsymbol{t}}+\boldsymbol{B} \boldsymbol{t}^{2}+\boldsymbol{C} \boldsymbol{t}^{3} \) where \( \mathbf{v} \) is
velocity, t is time and \( A, B \) and \( C \) are constant then the dimensional formula
of B is?
\( \mathbf{A} \cdot\left[M^{0} L T^{0}\right] \)
\( \mathbf{B} \cdot\left[M L^{0} T^{0}\right] \)
\( \mathbf{c} \cdot\left[M^{0} L^{0} T\right] \)
\( \mathbf{D} \cdot\left[M^{0} L T^{-3}\right] \)
Subject: Chemistry
The IUPAC name of A and B are,
repectively:
A. Potassium tetracyanonickelate (II), potassium tetrachloronickelate (II)
B. Tetracyanopotassiumnickelate (II) teterachlorpotassiumnickelate (II)
C. Tetracyanornickel (II), tetrachloronickel (II)
D. Potassium tetracyanonickel (II), potassium tetrachloronickel (II)
Subject: Maths
If \( y=\frac{1}{2 x^{2}+3 x+1} \) then \( \frac{d^{2} y}{d x^{2}} \) at \( x= \)
-2 is :
\( A \cdot \frac{38}{27} \)
в. \( -\frac{38}{27} \)
c. \( \frac{27}{38} \)
D. None
Subject: Physics
A thin horizontal disc of radius \( R= \)
\( 10 \mathrm{cm} \) is located within a cylindrical
cavity filled with oil whose viscosity \( \boldsymbol{\eta}=\mathbf{0 . 0 8} \boldsymbol{P} \) (figure shown above). The
clearance between the disc and the
horizontal planes of the cavity is equal
to \( h=1.0 m m . \) Find the power
developed by the viscous forces acting on the disc when it rotates with the
angular velocity \( \omega=60 \mathrm{rad} / \mathrm{s} \). The end
effects are to be neglected. Round off to closest integer.
Subject: Physics
A solid cube is subjected to a pressure
of \( \left(5 \times 10^{5} \quad N / m^{2}\right) . \) Each side of the
cube is shortened by then volumetric strain and Bulk modulus of the cube are
\( \begin{array}{ll}\text { A. } 0.03,5 \times 10^{5} & \text { N } / m^{2}\end{array} \)
B. \( 0.03,1.67 \times 10^{7} \quad N / m^{2} \)
C. \( 3,1.67 \times 10^{-7} \quad N / m^{2} \)
D. \( 0.01,1.67 \times 10^{7} \quad N / m^{2} \)
Subject: Physics
If a system is displaced from its equilibrium position and released, it
moves according to the equation \( \ddot{\boldsymbol{\theta}}=-\frac{\boldsymbol{I}^{2}}{\boldsymbol{k} \boldsymbol{l}} \boldsymbol{\theta} \)
where \( I, \) k and I are constants. It will
oscillate with a frequency:
\( ^{A} \cdot \sqrt{\frac{I^{2}}{k l}} \)
в. \( 2 \pi \sqrt{\frac{k l}{I^{2}}} \)
\( ^{\mathrm{c}} \cdot \frac{1}{2 \pi} \sqrt{\frac{I^{2}}{k l}} \)
D. \( \frac{1}{2 \pi} \sqrt{\frac{k l}{I^{2}}} \)
Subject: Physics
Two satellites of earth, \( S_{1} \) and \( S_{2} \), are
moving in
the same orbit. The mass of \( S_{1} \) is four
times the
mass of \( S_{2} \). Which one of the following
statements is true?
A. The kinetic energies of the two satellites are
equal
B. The time period of \( S_{1} \) is four times that of \( S_{2} \)
c. The potential energies of earth and satellite in
the two cases are equal
D. \( S_{1} \) and \( S_{2} \) are moving with the same speed
Subject: Chemistry
Given the correct order of initials T or \( F \)
for the following statements. Use T if the statement is true and \( F \) it is false.
Statement-1: \( \pi \) bond is formed by
sidewise overlapping of \( \boldsymbol{d}_{\boldsymbol{x}^{2}-\boldsymbol{y}^{2}} \) and \( \boldsymbol{p}_{\boldsymbol{y}} \)
orbital along x-axis. Statement-2: Zig-zag geometry would be suggested for the \( \left[\boldsymbol{I}(\boldsymbol{C} \boldsymbol{N})_{2}\right]^{-} \)
A. T,
в. F,
c. न, न
D. F,
Subject: Chemistry
The density of \( 3 M \) solution of sodium
thiosulphate \( \left(N a_{2} S_{2} O_{3}\right) \) is \( 1.56 g / m L \)
Calculate
(i) amount of \( N a_{2} S_{2} O_{3} \) in \( \% \) w/w
(ii) mole fraction of \( N a_{2} S_{2} O_{3} \)
(iii) Molality of \( N a^{+} \) and \( S_{2} O_{3}^{2-} \) ions
Subject: Physics
For four particles \( A, B, C \& D, \) the velocities of one with respect to other are given as \( \bar{V}_{D C} \) is \( 20 \mathrm{m} / \mathrm{s} \) towards north, \( \bar{V}_{B C} \) is \( 20 \mathrm{m} / \mathrm{s} \) towards east and
\( \bar{V}_{B A} \) is \( 20 \mathrm{m} / \mathrm{s} \) towards south. Then \( \overline{\boldsymbol{V}}_{D A} \) is:
A. \( 20 \mathrm{m} / \mathrm{s} \) towards north
B. 20 \( \mathrm{m} / \mathrm{s} \) towards south
c. \( 20 \mathrm{m} / \mathrm{s} \) towards east
D. 20 \( \mathrm{m} / \mathrm{s} \) towards west.
Subject: Physics
A man who is standing at a point \( x \) between two parallel walls as shown in the diagram, fires a starting pistol. He hears the first echo after 0.6 s and
another one after \( 0 . \) s.

How long after firing the pistol will he hear the next echo?
A \( .1 .2 \mathrm{s} \)
B . 1.4
\( c \cdot 1.6 s \)
D. 2.4 s
Subject: Chemistry
At \( 400 \mathrm{K}, \) the half-life of a sample of a gaseous compound initially at 56.0 \( k P a \) is 340 s. When the pressure is 28.0
\( k P a, \) the half-life is 170 s. The order of
the reaction is:
A. 0
B. 2
\( c \)
D. \( 1 / 2 \)
Subject: Maths
The volume of a largest sphere that can be cut from cylindrical log of wood of
base radius \( 1 m \) and height \( 4 m \) is:
A \( \cdot \frac{8}{3} \pi m^{3} \)
в. \( \frac{10}{3} \pi m^{3} \)
c. \( \frac{16}{3} \pi m^{3} \)
D. \( \frac{4}{3} \pi m^{3} \)
Subject: Maths
The value of \( \mathbf{1 0 0 0}\left[\frac{\mathbf{1}}{\mathbf{1 \times 2}}+\frac{\mathbf{1}}{\mathbf{2} \times \mathbf{3}}+\frac{\mathbf{1}}{\mathbf{3} \times \mathbf{4}}+\dots+\overline{\mathbf{9} c}\right. \)
is equal to
A. 1000
в. 999
\( c .1001 \)
D. \( \frac{1}{990} \)
Subject: Biology
Assertion
In ECG graph of heart, pulse 'R' is the peak point
Reason
It shows the atrial depolarisation which takes 0.2 seconds.
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
Which of the following reactions led to the discovery of neutrons?
A \( \cdot_{6} C^{14}+_{1} p^{1} \rightarrow_{7} N^{14}+_{0} n^{1} \)
B. \( _{4} B e^{9}+_{2} H e^{4} \rightarrow_{6} C^{12}+_{0} n^{1} \)
\( \mathbf{c} \cdot_{5} B^{11}+_{1} D^{2} \rightarrow_{6} C^{11}+_{0} n^{1} \)
D. \( _{4} B e^{8}+_{2} H e^{4} \rightarrow_{6} C^{11}+_{0} n^{1} \)
Subject: Physics
Three ants on the floor of a moving bus along a straight line with a uniform speed of \( 2 \mathrm{cm} / \mathrm{s} \) also moves with the
same velocity with respect to the ground along the straight line. Then
A. The collection of three ants can be considered as a rigid body with respect to the bus frame of reference
B. The collection of three ants can be considered as a rigid body with respect to the ground frame of reference
c. The collection of three ants is not a rigid body, since they are moving
D. The first ant can be considered as a rigid body, while the others are moving relative to first ant
Subject: Chemistry
Which of the following is an example of a disproportionation reaction?
A. \( C a C O_{3} \rightarrow C a O+C O_{2} \)
в. \( 2 H C u C l_{2} \rightarrow C u+C u^{2+}+4 C l^{-}+2 H^{+} \)
c. \( P C l_{5} \rightarrow P C l_{3}+C l_{2} \)
D. \( 2 H_{2} S+S O_{2} \rightarrow 2 H_{2} O+3 S \)
Subject: Physics
A student measure the thickness of an
object by three different instruments and gets the result as \( 0.5 \mathrm{cm}, 0.50 \mathrm{cm} \) \( 0.500 \mathrm{cm} . \) State the one which is more
accurate.
A . \( 0.5 \mathrm{cm} \)
B. \( 0.50 \mathrm{cm} \)
c. \( 0.500 \mathrm{cm} \)
D. All the measurements are equally accurate.
Subject: Chemistry
In the following reaction \( ; x A \rightarrow y B \) \( \log _{10}\left[-\frac{\boldsymbol{d}[\boldsymbol{A}]}{\boldsymbol{d} \boldsymbol{t}}\right]=\log _{10}\left[\frac{\boldsymbol{d}[\boldsymbol{B}]}{\boldsymbol{d} \boldsymbol{t}}\right]+\mathbf{0 . 3 0 1 0} \)
'A' and 'B' respectively can be:
A. n-Butane and Iso-butane
B. \( C_{2} H_{4} \) and \( C_{4} H_{8} \)
c. \( N_{2} O_{4} \) and \( N O_{2} \)
D. \( C_{2} H_{2} \) and \( C_{6} H_{6} \)
Subject: Maths
The value of \( b \) for which the function
\( f(x)=\sin x-b x+c \) is a strictly
decreasing function \( \forall x \in R \)
A. \( b \in(-1,1) \)
в. \( b \in(-\infty, 1) \)
C. \( b \in(1, \infty) \)
D. \( b \in[1, \infty) \)
Subject: Physics
The proportional limit of steel is \( 8 x \) \( 10^{8} N / m^{2} \) and its Young's modulus is
\( \mathbf{2} \times \mathbf{1 0}^{11} \mathbf{N} / \mathbf{m}^{2} . \) The maximum
elongation, a one metre long steel wire can be given without exceeding the proportional limit is
\( A \cdot 2 m m \)
B. \( 4 \mathrm{mm} \)
\( \mathrm{c} \cdot 1 \mathrm{mm} \)
D. 8 mm
Subject: Physics
A small magnet M is allowed to fall
through a fixed horizontal conducting ring R. Let \( g \) be the acceleration due to gravity. The acceleration of M will be This question has multiple correct options
A. \( <g \) when it is above \( R \) and moving towards \( R \)
B. > g when it is above R and moving towards R
c. < g when it is below R and moving away from R
D. \( >g \) when it is below \( R \) and moving away from \( R \)
Subject: Chemistry
Two structure of \( H_{2} O_{2} \) are drawn below.
Identify the phase \( (X) \) and \( (Y) \) of \( H_{2} O_{2} \)
\( \mathbf{A} \cdot(X) \) is the structure of \( H_{2} O_{2} \) in gas phase and \( (Y) \) in solid phase
B. \( (X) \) is structure of \( H_{2} O_{2} \) in solid phase and \( (Y) \) in gas phase
c. \( (X) \) and \( (Y) \) are structures of \( H_{2} O_{2} \) in gas phase
D. \( (X) \) and \( (Y) \) are structures of \( H_{2} O_{2} \) in solid phase
Subject: Physics
When a transverse plane wave traverses a medium, individual particles execute periodic motion given by the equation \( \boldsymbol{y}=\mathbf{0 . 2 5} \cos (2 \pi \boldsymbol{t}-\boldsymbol{\pi} \boldsymbol{x}) . \) The phase
difference for two positions of same particle which are occupied by time intervals 0.4 second apart is
A \( .144^{\circ} \)
B. \( 135^{\circ} \)
\( \mathrm{c} \cdot 72^{\circ} \)
D. \( 108^{\circ} \)
Subject: Maths
The number \( \frac{13}{15} \) is correctly represented
on number line
\( A \)
\( \begin{array}{cccccc}< & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ \frac{1}{15} & & & \frac{13}{15} & \frac{15}{15} & \frac{17}{15}\end{array} \)
B. \( \begin{array}{ccccccc}\langle 1 & & 1 & 1 & 1 & 1 & 1 \\ 10 & & \frac{13}{15} & \frac{14}{15} & \frac{15}{15} & \frac{16}{15} & \frac{17}{15}\end{array} \)
\( c \)
\( \begin{array}{lllllllll}\nwarrow_{1} & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ \frac{2}{15} & \frac{3}{15} & \frac{4}{15} & & \frac{13}{15} & \frac{14}{15} & \frac{15}{15} & \frac{16}{15} & \cdots & .\end{array} \)
D. \begin{tabular}{ccccccccc}
\hline 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\
\( \frac{14}{15} \) & \( \frac{15}{15} \) & \( \frac{16}{15} \) & \( \frac{17}{15} \) & \( \frac{18}{15} \) & \( \frac{6}{15} \) & \( \frac{13}{15} \) & \( \cdot \) & \( \cdot \)
\end{tabular}
Subject: Maths
Elements of a matrix \( A \) of order \( 10 \times 10 \)
are defined as \( a_{i j}=w^{i+j} \) (where \( w \) is
cube root of unity), then trace \( (A) \) of the
matrix is
\( A \cdot \omega \)
B.
\( c \cdot \omega^{2} \)
D.
Subject: Maths
Evalaute the integral \( \int_{0}^{\pi} x f(\sin x) d x \)
\( \mathbf{A} \cdot 2 \pi \)
\( ^{\mathbf{B}} \cdot \pi \int_{0}^{\pi / 2} f(\cos x) d x \)
\( ^{\mathbf{c}} \cdot_{\pi} \int_{0}^{\pi} f(\cos x) d x \)
D. \( \pi \int_{0}^{\pi} f(\sin x) d x \)
Subject: Maths
A solution of the equation \( 5 \sin ^{2} x+ \)
\( 3 \sin x \cos x-3 \cos ^{2} x=2 \) is
This question has multiple correct options
A \( \cdot_{2 \pi+\tan ^{-1} \frac{-3+\sqrt{69}}{6}} \)
B. \( \quad 7 \pi+\tan ^{-1} \frac{-3-\sqrt{69}}{6} \)
c. \( \tan ^{-1} \frac{-3+\sqrt{69}}{6}-\pi \)
D. \( \tan ^{-1} \frac{-3-\sqrt{69}}{6}-5 \pi \)
Subject: Chemistry
The molality of \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) solution is \( \boldsymbol{9} \). The
weight of the solute in \( 1 \mathrm{kg} H_{2} S O_{4} \) solution is:
A . \( 900.0 \mathrm{g} \)
в. \( 469 \mathrm{g} \)
c. \( 882.0 \mathrm{g} \)
D. \( 9.0 \mathrm{g} \)
Subject: Chemistry
Which of the following reactions is/ are
not intermolecular redox reaction?
This question has multiple correct options
\( \mathbf{A} \cdot P b O_{2}+H_{2} O \rightarrow P b O+H_{2} O_{2} \)
B \( \cdot 2 K C l O_{3} \rightarrow 2 K C l+3 O_{2} \)
\( \mathbf{C} \cdot\left(N H_{4}\right)_{2} C r_{2} O_{7} \rightarrow N_{2}+C r_{2} O_{3}+4 H_{2} O \)
D. \( N H_{4} N O_{2} \rightarrow N_{2}+2 H_{2} O \)
Subject: Maths
\( \mathbf{f} \boldsymbol{u}_{\boldsymbol{r}}=\boldsymbol{a}_{\boldsymbol{r}} \boldsymbol{x}+\boldsymbol{b}_{\boldsymbol{r}} \boldsymbol{y}+, \boldsymbol{c}_{\boldsymbol{r}}=\mathbf{0}(r=1,2,3 \)
be the three sides of a triangle them the equations of the circumcircle of this triangle is \( \mid \begin{array}{ccc}\frac{\mathbf{1}}{\boldsymbol{u}_{1}} & \frac{\mathbf{1}}{\boldsymbol{u}_{2}} & \frac{\mathbf{1}}{\boldsymbol{u}_{3}} \\ \boldsymbol{a}_{2} \boldsymbol{a}_{3}-\boldsymbol{b}_{2} \boldsymbol{b}_{3} & \boldsymbol{a}_{3} \boldsymbol{a}_{1}-\boldsymbol{b}_{3} \boldsymbol{b}_{1} & \boldsymbol{a}_{1} \boldsymbol{a}_{2}-\boldsymbol{b}_{4} \\ \boldsymbol{a}_{2} \boldsymbol{b}_{3}+\boldsymbol{a}_{3} \boldsymbol{b}_{2} & \boldsymbol{a}_{3} \boldsymbol{b}_{1}+\boldsymbol{a}_{1} \boldsymbol{b}_{3} & \boldsymbol{a}_{1} \boldsymbol{b}_{2}+\boldsymbol{a}_{2}\end{array} \)
\( =0 \)
Subject: Physics
Center of mass of 3 particle \( 10 k g, 20 k g \) and \( 30 k g \) is at \( (0,0,0,) . \) Where shoud a
particle of mass \( 40 k g \) be placed so that the combination centre of mass will be at
(3,3,3)
A. (0,0,0)
)
в. (7.5,7.5,7.5)
c. (1,2,3)
D. (4,4,4)
Subject: Chemistry
The number of \( \sigma \) and \( (\pi) \) bonds present
in the sulphuric acid molecule are:
\( \mathbf{A} \cdot 6 \sigma 2 \pi \)
B. \( 6 \sigma \) \( 0 \pi \)
\( \mathbf{c} \cdot 2 \sigma 4 \pi \)
D. \( 2 \sigma 2 \pi \)
Subject: Maths
Let \( \bar{a}, \bar{b}, \bar{c} \) be vectors of length 3,4,5 respectively. Let \( \bar{a} \) be perpendicular to \( \bar{b}+\bar{c}, \bar{b} t o \bar{c}+\bar{a} \) and \( \bar{c} \) to \( \bar{a}+ \)
b. \( \operatorname{Then}|\bar{a}+\bar{b}+\bar{c}| \) is equals to:
A \( \cdot 2 \sqrt{5} \)
B. \( 2 \sqrt{2} \)
с. \( 10 \sqrt{5} \)
।
D. \( 5 \sqrt{2} \)
Subject: Maths
If the sum of the roots of the quadratic
equation \( a x^{2}+b x+c=0 \) is equal to
the sum of the square of their reciprocals, then \( \frac{a}{c}, \frac{b}{a} \) and \( \frac{c}{b} \) are in
A . GP
в. нР
c. АGР
D. AP
Subject: Physics
Two concentric and coplanar circular
coils have radii \( a \) and \( b(>>a) \) as
shown in figure. Resistance of the inner coil is \( R \) Current in the outer coil is
increased from 0 to \( i \), then find the total
charge circulating the inner coil :
\( ^{\text {A }} \cdot \frac{\mu_{0} \pi a^{2} i}{2 R b} \)
в. \( \frac{2 \mu_{0} \pi a^{2}}{2 R b} \)
c. \( \frac{\mu_{0} \pi a^{2} i}{4 R b} \)
D. \( \frac{\mu_{0} \pi a^{3} i}{4 R b} \)