AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
If \( A^{-1}=\left[\begin{array}{ccc}3 & -1 & 1 \\ -15 & 6 & -5 \\ 5 & -2 & 2\end{array}\right] \) and \( B= \)
\( \left[\begin{array}{ccc}1 & 2 & -2 \\ -1 & 3 & 0 \\ 0 & -2 & 1\end{array}\right] \), then
\( (A B)^{-1}=? \)
Subject: Physics
In a transformer, in which the losses
may be neglected, the ratio of the primary voltage to secondary voltage is found to be \( 4: 1 . \) The ratio of the
primary to secondary turns and the ratio of the primary current to secondary current are respectively in
the ratio of :
\( A \cdot 4: 1 \& 1: 4 \)
B. \( 1: 4 \& 4: 1 \)
c. \( 4: 1 \& 4: 1 \)
D. \( 1: 4 \& 1: 4 \)
Subject: Maths
Number of permutation of 10 different objects taken all at a time in which particular 4 never comes together
A. \( 10 ! \times 4 \)
B. \( 10 !-4 \)
c. \( \frac{7 ! 6 !}{4 !} \)
D. \( 10 !-7 ! 4 ! \)
Subject: Chemistry
If \( \operatorname{CoO}(s)+H_{2}(g) \rightleftharpoons C o(s)+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}), \boldsymbol{K}_{1}=\boldsymbol{6} \boldsymbol{0} ; \boldsymbol{C} \boldsymbol{o} \boldsymbol{O}(\boldsymbol{s})+ \)
\( \boldsymbol{C O}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{C o}(s)+\boldsymbol{C O}_{2}, \boldsymbol{K}_{2}=180 \) then
the equilibrium constant of the
reaction \( \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{H}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{C} \boldsymbol{O}(\boldsymbol{g})+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \) will be -
\( A \cdot 0.44 \)
в. 0.1
c. 0.22
D. 0.33
Subject: Maths
The differential equation representing
the family of curves \( \boldsymbol{y}^{2}=\mathbf{2 c}(\boldsymbol{x}+\sqrt{\boldsymbol{c}}) \)
where \( c \) is a positive perimeter, is of
A. order 1 , degree 3
B. order 2 , degree 3
c. Degree 1 , order 2
D. None of these
Subject: Maths
For an A.P. given below find \( t_{20} \) and \( S_{10} \) \( \frac{1}{6}, \frac{1}{4}, \frac{1}{3}, \dots \)
A \( \cdot \frac{7}{4}, \frac{65}{12} \)
в. \( \frac{5}{4}, \frac{63}{12} \)
c. \( \frac{5}{4}, \frac{65}{12} \)
D. \( \frac{7}{4}, \frac{63}{12} \)
Subject: Maths
Points \( A, B, C \) and \( D \) are midpoints of
the sides of square \( J \) ETS. If the area of
JETS is 36 sq.cm, then the area of
\( A B C D \) is
A. 3 sq. cm
B. 7.5 sq. \( \mathrm{cm} \)
c. 9 sq. cm
D. 18 sq. cm
Subject: Physics
A rod of negligible mass having length
\( l=2 m \) is pivoted at its centre and two
masses of \( \boldsymbol{m}_{1}=\mathbf{6 k g} \) and \( \boldsymbol{m}_{2}=\mathbf{3 k g} \) are
hung from the ends as shown in figure.
(a) Find the initial acceleration of the
rod if it is horizontal initially
Subject: Maths
The diagonals of a parallelogram
\( A B C D \) intersect at \( O . A \) line through
intersect \( A B \) at \( X \) and \( D C \) at \( Y \). Identify
the correct option
A. \( O X=O Y \)
в. \( O X>O Y \)
c. \( O X<O Y \)
\( \cdot O X-O Y=0 \)
0
Subject: Physics
The equation \( \boldsymbol{y}=\boldsymbol{4}+\boldsymbol{2} \sin (\boldsymbol{6} \boldsymbol{t}-\boldsymbol{3} \boldsymbol{x}) \)
represents a wave motion with
This question has multiple correct options
A. amplitude 6 units
B. amplitude 2 units
c. wave speed 2 units
D. wave speed \( 1 / 2 \) units
Subject: Maths
If \( \cos A= \)
\( \boldsymbol{m} \cos \boldsymbol{B}, \boldsymbol{t h e n} \cot \frac{\boldsymbol{A}+\boldsymbol{B}}{\boldsymbol{2}} \cot \frac{\boldsymbol{B}-\boldsymbol{A}}{\boldsymbol{2}}= \)
A \( \cdot \frac{m-1}{m+1} \)
в. \( \frac{m+2}{m-2} \)
c. \( \frac{m+1}{m-1} \)
D. none of these
Subject: Chemistry
Which of the following represents the electronic configuration of a transition
elements?
A \( \cdot 1 s^{2}, 2 s^{2} p^{6} \dots . . n s^{2} p^{3} \)
B . \( 1 s^{2}, 2 s^{2} p^{6} \ldots . . n s^{2} p^{6} d^{3},(n+1) s^{2} \)
C \( \cdot 1 s^{2}, 2 s^{2} p^{6} \ldots n s^{2} p^{6} d^{10},(n+1) s^{2} p^{1} \)
D. \( 1 s^{2}, 2 s^{2} p^{6} \ldots . n s^{2} p^{6} \)
Subject: Physics
Two particle of equal masses have velocities \( \vec{V}_{1}=2 i m / s \) and the second particle has velocity \( 2 \hat{j} \) m/s. The first particle has an acceleration \( \overrightarrow{a_{1}}=(3 \hat{i}+ \)
\( \mathbf{3} \hat{\boldsymbol{j}}) \frac{m}{s^{2}} \) while the acceleration of the other particle is zero. The center of mass of the particle moves in a :
A . circle
B. parabola
c. straight line
D. ellipse
Subject: Maths
The value of \( c \) for which the area of the
figure bounded by the curve \( y=8 x^{2}- \)
\( x^{5}, \) the straight lines \( x=1 \) and \( x=c \) and the \( x- \) axis is equal to \( \frac{16}{3} \) is
\( A \cdot 2 \)
B . \( \sqrt{8-\sqrt{17}} \)
\( c .3 \)
D. -
Subject: Maths
Assertion
Let \( \boldsymbol{f} \) and \( \boldsymbol{g} \) be increasing and
decreasing function respectively from
\( [\mathbf{0}, \infty] \) to \( [\mathbf{0}, \infty] . \) Let \( h(\boldsymbol{x})=\boldsymbol{f}(\boldsymbol{g}(\boldsymbol{x})) . \) If
\( h(0)=0, \) then \( h(x) \) is always zero
Reason
\( h(x) \) is an increasing function of \( x \)
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
Match the Column-I with Column-II:
ColumnColumn-I (Process)
(a) \( \mathrm{Ni} \)
(p) Cracking of hydrocarbons
(b) \( A C l_{3} \)
(q) Fischer- - Tropsch process
(с) \( C o / A l_{2} O_{3} \)
(r) Hydrogenation of oil
(d) Zeolite
(s) Friedel-Crafts reaction
Subject: Physics
t is desired to measure the magnitude of field between the poles of a powerful loud speaker magnet. A small flat search coil of area \( 2 \mathrm{cm}^{2} \) with 25 closely
wound turns, is positioned normal to the field direction, and then quickly snatched out of the field region.
Equivalently, one can give it a quick \( 90^{\circ} \)
turn to bring its plane parallel to the field direction). The total charge flown in the coil (measured by a ballistic galvanometer connected to coil) is 7.5
mC. The combined resistance of the coil
and the galvanometer is \( 0.50 \Omega \) Estimate the field strength of magnet.
Subject: Maths
If \( \boldsymbol{\alpha}=\cos 10^{\circ}-\sin 10^{\circ}, \beta=\cos 45^{\circ}- \)
\( \sin 45^{\circ}, \gamma=\cos 70^{\circ}-\sin 70^{\circ} \) then the
descending order of \( \boldsymbol{\alpha}, \boldsymbol{\beta}, \boldsymbol{\gamma} \) is
\( \mathbf{A} \cdot \alpha, \beta, \gamma \)
в. \( \gamma, \beta, \alpha \)
c. \( \alpha, \gamma, \beta \)
\( \mathbf{D} \cdot \beta, \alpha, \gamma \)
Subject: Physics
Assertion
Free electrons always keep on moving in a conductor even when no magnetic
force act on them in a magnetic field
unless a current is passed through it.
Reason

The average velocity of free electron is
zero.
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
If at \( t=0, \) a travelling wave pulse on a string is described by the function. \( y=\frac{6}{x^{2}+3} . \) What will be the wave
function representing the pulse at
time \( t, \) if the pulse is propagating along positive \( x \) -axis with speed \( 4 \mathrm{m} / \mathrm{s} ? \)
A \( \cdot y=\frac{6}{(x+4 t)^{2}+3} \)
B. \( y=\frac{6}{(x-4 t)^{2}+3} \)
c. \( y=\frac{6}{(x-t)^{2}} \)
D. \( y=\frac{6}{(x-t)^{2}+12} \)
Subject: Maths
\( \int_{-3 \pi / 2}^{-\pi / 2}\left[(x+\pi)^{3}+\cos ^{2}(x+3 \pi)\right] d x \) is
equal to
\( \mathbf{A} \cdot\left(\pi^{4} / 32\right)+(\pi / 2) \)
B. \( \pi / 2 \)
\( \mathbf{c} \cdot(\pi / 4)-1 \)
\( \mathbf{D} \cdot\left(\pi^{4} / 32\right) \)
Subject: Maths
\( f \frac{1-\cos x}{\cos x(1+\cos x)}=\frac{\sin \alpha}{\cos x}-\frac{2}{1+\cos x} \)
then \( \boldsymbol{\alpha}= \)
A. \( \frac{\pi}{8} \)
B.
\( c \cdot \frac{\pi}{2} \)
\( D \)
Subject: Maths
Draw a triangle \( A B C \) with side \( B C= \)
\( \mathbf{6} c \boldsymbol{m}, \boldsymbol{A} \boldsymbol{B}=\mathbf{5} \boldsymbol{c m} \) and \( \angle \boldsymbol{A} \boldsymbol{B} \boldsymbol{C}=\mathbf{6 0}^{\boldsymbol{o}} \)
Then construct a triangle whose sides
\( \operatorname{are} \frac{3}{4} \) of the corresponding sides of the triangle \( \boldsymbol{A B C} \)
Subject: Chemistry
Match the physical property (in List I) with unit (in List II) :
\( \begin{array}{ll}\text { List-I } & \text { List-II } \\ \text { a) Viscosity } & \text { i) } \mathrm{Jm}^{-2} \\ \text {b) Surface tension } & \text { ii) } \mathrm{Nm}^{-1} \\ \text {c) Surface energy } & \text { iii) } \mathrm{Kg} \mathrm{m}^{-1} \mathrm{s}^{-1} \\ \text {d) Vapour pressure } & \text { iv) atm }\end{array} \)
A. a - iii, b-ii, c-i, d-iv
B. a-iv, b-ii, c-i, d-iii
c. a-i, b-iv, c-iii, d-ii
D. a-ii, b-iv, c-i, d-iii
Subject: Physics
Acceleration due to gravity on moon is
0.166 times than that on the earth. \( A \)
man weighing 60kg on earth would weigh \( _{\text {十一一一一一一一一一 }} \) on moon
A. \( 60 \mathrm{kg} \)
в. 30kg
c. \( 16.6 \mathrm{kg} \)
D. \( 10 \mathrm{kg} \)
Subject: Physics
In a Young's Double Slit experiment,
films of thickness \( t_{A} \) and \( t_{B} \) and
refractive indices \( \mu_{A} \) and \( \mu_{B} \) are placed in front of slits \( A \) and \( B \) respectively. If
\( \boldsymbol{\mu}_{A} \boldsymbol{t}_{A}=\boldsymbol{\mu}_{B} \boldsymbol{t}_{B}, \) then the central maxima
\( \operatorname{may} \)
This question has multiple correct options
A. not shift
B. shift forwards A
c. shift towards B
D. None of these
Subject: Maths
The lengths of two sides of a triangle are \( 7 \mathrm{cm} \) and \( 10 \mathrm{cm} . \) What is the possible
value range of the third side?
A. \( 3 \mathrm{cm}< \) third side \( <10 \mathrm{cm} \)
B. \( 7 \mathrm{cm}< \) third side \( <10 \mathrm{cm} \)
\( \mathrm{c} \cdot 3 \mathrm{cm}< \) third side \( <17 \mathrm{cm} \)
D. \( 7 \mathrm{cm}< \) third side
Subject: Chemistry
The solubility product \( \boldsymbol{K}_{s p} \) for \( \boldsymbol{B} \boldsymbol{i}_{2} \boldsymbol{S}_{3} \) is
\( 1.2 \times 10^{-98} . \) The solubility of \( B i_{2} S_{3} \) is
approximately:
A \( \cdot 1 \times 10^{-33} \)
В. \( 1 \times 10^{-20} \)
c. \( 1 \times 10^{-27} \)
D. \( 1 \times 10^{-24} \)
Subject: Chemistry
What would be the change in
the freezing point of \( H_{2} O \) in a solution
of \( 1 m N a C l(a q) ? \)
\( \mathbf{A} \cdot-1.86^{\circ} \mathrm{C} \)
B. \( -0.52^{\circ} \mathrm{C} \)
c. \( -3.72^{\circ} \mathrm{C} \)
D. \( 1.86^{\circ} \mathrm{C} \)
E \( .3 .72^{\circ} \mathrm{C} \)
Subject: Maths
Find the rate of interest when the
following are given. Principal \( =\boldsymbol{R} \boldsymbol{s} \boldsymbol{3} \mathbf{5 0} \) Time \( =\frac{\boldsymbol{2} \mathbf{1}}{\mathbf{2}} \) years
\( \boldsymbol{I}=\boldsymbol{R} \boldsymbol{s} \mathbf{1} \mathbf{4 0} \)
Subject: Maths
\( \ln a \Delta A B C, \) it is given that \( A B=A C \)
and the bisectors of \( \angle B \) and \( \angle C \)
intersect at \( 0 . \) If \( \mathrm{M} \) is a point on \( \mathrm{BO} \)
produced, prove that \( \angle M O C=\angle A B C \)
Subject: Chemistry
To stop bleeding from an injury ferric chloride can be applied Which comment about the statement is
justified?
A. It is not true, ferric chloride is a poison
B . It is true, \( F e^{3+} \) ions coagulate blood which is negatively charged so
C. It is not true, \( C l^{-} \) ions from positively charged sol profuse bleeding takes place
D. It is true, coagulation takes place because of formation of negatively charged sol with \( C l^{-} \) ions.
E. It is not true, ferric chloride is ionic and gets into blood stream
Subject: Maths
Let \( \boldsymbol{f}:(\boldsymbol{a}, \boldsymbol{b}) \rightarrow \boldsymbol{R} \) be a differentiable
function. Which of the following statements is/are true:
A \( \cdot \lim _{x \rightarrow a} f(x)=\infty \Rightarrow \lim _{x \rightarrow a}\left|f^{\prime}(x)\right|=\infty \)
B \( \cdot \lim _{x \rightarrow a} f^{\prime}(x)=\infty \Longrightarrow \lim _{x \rightarrow a} f(x)=\infty \)
c. \( \lim _{x \rightarrow a} f(x)=\infty \neq \lim _{x \rightarrow a}\left|f^{\prime}(x)\right|=\infty \)
D. \( \lim _{x \rightarrow a} f^{\prime}(x)=\infty \neq \lim _{x \rightarrow a} f(x)=\infty \)
Subject: Chemistry
Using molar concentrations what is
unit of \( K_{c} \) for the reaction
\( \mathbf{C H}_{3} \mathbf{O H}(\mathbf{g}) \rightleftharpoons \mathbf{C O}(\mathbf{g})+\mathbf{2} \mathbf{H}_{2}(\mathbf{g}) \)
\( A \cdot M^{-2} \)
B. \( \mathrm{M}^{2} \)
\( c \cdot M^{-1} \)
D.
Subject: Maths
If the line \( l x+m y+n=0 \) touches the
parabola \( \boldsymbol{y}^{2}=\mathbf{4} \boldsymbol{a} \boldsymbol{x}, \) prove that \( \boldsymbol{l} \boldsymbol{n}= \)
\( \boldsymbol{a} \boldsymbol{m}^{2} \)
Subject: Biology
Read the following five statements to \( \mathrm{E} \) ) and select the option with all
correct statements.
(A) Mosses and Lichens are the first
organisms to colonize bare rock.
(B) Selaginella is a homosporous
pteridophyte.
(C) Coralloid roots in Cycas have VAM.
(D) The main plant body in bryophytes is gametophytic whereas in pteridophytes it is sporophytic.
(E) In gymnosperms, male and female gametophytes are present within
sporangia located on sporophyte.
\( A \cdot(A),(D) \) and \( (E) \)
B. \( (B),(C) \) and \( (D) \)
c. \( (A),(C) \) and \( (D) \)
D. None of these
Subject: Maths
Simplify the expression \( \left(2 x^{4}-5 x^{4}\right)^{2} \)
and choose the correct option.
A . \( -21 x^{8} \)
В. \( -6 x^{8} \)
\( \mathrm{c} \cdot 9 x^{8} \)
D. \( 9 x^{16} \)
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{ll}\boldsymbol{a} & \boldsymbol{b} \\ \boldsymbol{0} & \boldsymbol{a}\end{array}\right] \) is \( \boldsymbol{n} \boldsymbol{t} \boldsymbol{h} \) root of \( \boldsymbol{I}_{2}, \) then
choose the correct statements.
(i) if \( n \) is odd, \( a=1, b=0 \)
(ii) if \( n \) is odd, \( a=-1, b=0 \)
(iii) if \( n \) is even, \( a=1, b=0 \)
(iv) if \( n \) is even, \( a=-1, b=0 \)
\( \mathbf{A} \cdot i, i i, i i i \)
B. \( i i, \) ii i \( i v \)
\( \mathbf{c} \cdot i, i i, i i i, i v \)
D. \( i, i i i, i v \)
Subject: Chemistry
Identify tthe compounds which are reduced and oxidised in the following
reaction.
\( \mathbf{3} N_{2} \boldsymbol{H}_{4}+\mathbf{2} \boldsymbol{B} \boldsymbol{r} \boldsymbol{O}_{3}^{-} \rightarrow \mathbf{3} \boldsymbol{N}_{2}+\mathbf{2} \boldsymbol{B} \boldsymbol{r}^{-}+ \)
\( \mathbf{6} \boldsymbol{H}_{2} \boldsymbol{O} \)
A \( \cdot N_{2} H_{4} \) is oxidised and \( B r O_{3}^{-} \) is reduced
B. \( B r O_{3}^{-} \) is oxidised and \( N_{2} H_{4} \) is reduced
C. \( B r O_{3}^{-} \) is both reduced and oxidised
D. This is not a redox reaction
Subject: Maths
Find the area bounded by the curves \( \boldsymbol{y}=\sqrt{1-\boldsymbol{x}^{2}} \) and \( \boldsymbol{y}=\boldsymbol{x}^{3}-\boldsymbol{x} . \) Also find
the ratio in which the y-axis divide this
area
A \( \cdot \frac{\pi}{2} ; \frac{\pi-1}{\pi+1} \)
В. \( \frac{\pi}{4} ; \frac{\pi-1}{\pi+1} \)
c. \( \frac{\pi}{2} ; \frac{\pi+1}{\pi-1} \)
D. None of these
Subject: Maths
If \( y=e^{x} \sin x, \) then find \( \frac{d y}{d x} \)
A \( \cdot e^{x}(\sin x+\cos x) \)
B . \( e^{x}(\sin x-\cos x) \)
\( \mathbf{c} \cdot e^{x} \sin x \)
D. None of these
Subject: Chemistry
Correct IUPAC nomenclature of given
compound is :
A. 1 -Bromo-3-chlorocyclohex-4-ene.
B. 3-Bromo-5-chlorocyclohex-1-ene.
c. 4 -Bromo-6-chlorocyclohex-1-ene.
D. 5-Bromo-3-chlorocyclohex-1-ene.
Subject: Physics
The coil is rotated in a clockwise
direction in the magnetic field at a
constant rate to induce a current in the
wire. If the direction of rotation of the
coil is reversed and coil remains
rotating at the same constant rate, Identify the correct statement.
A. The current in the coil will reverse its direction
B. The current in the coil will stop flowing
c. The current in the coil will continue to flow in the same direction as before
D. The current in the coil will decrease steadily
E. The current in the coil will increase steadily
Subject: Physics
A p-type semiconductor is made from a silicon specimen by doping on a
average one indium atom per \( 5 \times 10^{7} \)
silicon atoms. If the number density of
atoms in the silicon specimen is \( 5 \times \) \( 10^{26} \) atoms \( / m^{3}, \) then the number of
acceptor atoms in silicon per cubic centimeter will be:
A \( .2 .5 \times 10^{30} \)
В. \( 1.0 \times 10^{13} \)
c. \( 1.0 \times 10^{15} \)
D. \( 2.5 \times 10^{36} \)
Subject: Chemistry
A catalyst lower the activation energy of
a reaction from \( 20 \mathrm{kJ} \) mole \( ^{-1} \) to \( 10 \mathrm{kJ} \)
mol \( ^{-1} \). The temperature at which the uncatalysed reaction will have the same rate as that of the catalyzed at 27
\( o C \) is:
A \( \cdot-123^{\circ} C \)
B. \( 327^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 150^{\circ} \mathrm{C} \)
\( \mathrm{D} \cdot+23^{\circ} \mathrm{C} \)
Subject: Physics
An object of mass \( m \) and velocity \( v_{0} \)
strikes a rigid uniform rod of length \( l \)
and mass \( m_{r} . \) The rod is hanging by a frictionless pivot from the ceiling. Immediately after striking the rod, the object continues forward but its speed
reduces to \( \frac{v_{0}}{2} . \) The moment of inertia of
the rod about its centre of mass is
\( I_{C M}=\frac{1}{2} m_{r} l^{2} . \) For the collision to be
inelastic:
A. the rod and object are of equal mass
B. the rod is either heavier or lighter than the object
c. the rod is of negligible mass
D. none of these
Subject: Chemistry
One of the reaction that takes place to
producing steel from iron ore is the reduction of iron(III) oxide by carbon
monoxde to give iron metal and \( C O_{2} \) \( \boldsymbol{F} \boldsymbol{e} \boldsymbol{O}(\boldsymbol{s})+\boldsymbol{C O}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{F} \boldsymbol{e}(\boldsymbol{s})+ \)
\( \boldsymbol{C O}_{2}(\boldsymbol{g}) ; \boldsymbol{K}_{\boldsymbol{p}}=\mathbf{0 . 2 6 5} \)
What are the equilibrium partial
pressures of \( C O \) and \( C O_{2} \) at \( 1050 K \) if
the initial partial pressures are: \( \boldsymbol{p}_{C O}= \)
1.4 atm and \( p_{C O_{2}}=0.80 a t m ? \)
Subject: Chemistry
For gaseous reaction, rate \( \boldsymbol{k}[\boldsymbol{A}][\boldsymbol{B}] . \) If volume of container is reduced to \( 1 / 4 \) of initial, then the rate of reaction will be
times of initial.
A . \( 1 / 8 \)
B. 8
c. \( 1 / 16 \)
D. 16
Subject: Chemistry
How many milli moles of sucrose should
be dissolved in 500 gms of water so that the difference between the boiling point and freezing point of the solution
becomes \( 103.57^{\circ} \mathrm{C} ?\left(K_{f}=\right. \)
\( \mathbf{1} . \mathbf{8 6}^{\circ} \boldsymbol{C} / \boldsymbol{m}, \boldsymbol{K}_{\boldsymbol{b}}=\mathbf{0 . 5} \mathbf{2}^{\boldsymbol{o}} \boldsymbol{C} / \boldsymbol{m} \)
A. 500 moles
B. 90 mmoles
c. 1330 mmoles
D. 1330 moles
Subject: Maths
Prove \( : 1^{2}+\left(1^{2}+2^{2}\right)+ \)
\( \left(1^{2}+2^{2}+3^{2}\right)+\ldots \) upto \( n \) terms \( = \)
\( \frac{n(n+1)^{2}(n+2)}{12} \)
Subject: Chemistry
Tetrahedral complexes are formed:
I : where the central metal has a low
oxidation state
II : where ligands are weak field
III : where the electronic configuration of the central metal is \( , d^{0}, d^{5} \) or \( d^{10} \)
A . I, II, III only correct
B. I, I I only correct
c. ॥, Ill only correct
D. III only correct
Subject: Chemistry
\( \boldsymbol{R} \boldsymbol{C O C l}+\boldsymbol{H}_{2} \stackrel{\boldsymbol{P d}+\boldsymbol{B a S O}_{4}}{\longrightarrow} \boldsymbol{A} \stackrel{\boldsymbol{H C N}}{\longrightarrow} \boldsymbol{B} \stackrel{\boldsymbol{H}_{3} \boldsymbol{O}}{\longrightarrow} \)
\( C \)
In the reaction sequence \( A, B \) and \( C \) are given by the set:-
\( \begin{array}{llll}\text { A. } R C H O, & R C H(O H) C N, & R C H(O H) C H_{2} N H_{2}\end{array} \)
в. \( R C H O, \quad R C H(O H) C N, \quad R C H(O H) C O O H \)
\( c \)
\( \mathrm{RCHO} \)
D. \( R C H O, \quad R-C H_{2}-C N, \quad R-C H_{2}-C O O H \)
Subject: Physics
A candle placed \( 25 \mathrm{cm} \) from a lens forms
an image on a screen placed \( 75 \mathrm{cm} \) on the other side of the lens. The focal
length and type of the lens should be?
A. \( +18.75 \mathrm{cm} \) and convex lens
B. \( -18.75 \mathrm{cm} \) and concave lens
c. \( +20.25 \mathrm{cm} \) and convex lens
D. \( -20.25 \mathrm{cm} \) and concave lens
Subject: Maths
If the line joining the points (-1,2,3),(2,-1,4) is perpendicular to the line joining the points \( (x,-2,4),(1,2,3) \) then \( x= \)
\( \mathbf{A} \cdot \mathbf{3} \)
B. 10
\( c \cdot \frac{-3}{10} \)
D. \( \frac{-10}{3} \)
Subject: Physics
Assertion
In alpha decay of different radioactive nuclides, the energy of alpha particles has been compared. It is found that as the energy of alpha particle increases the half-life of the decay goes on decreasing.
Reason
More is the energy in any decay process, more is the probability of decaying the nuclide which leads to faster rate of
decay.
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 series AC circuit containing an inductor \( (20 \mathrm{mH}), \) a capacitor \( (120 \mu F) \) and a resistor \( (60 \Omega) \) is driven by an \( A C \) source of \( 24 \mathrm{V} / 50 \mathrm{Hz} \). The energy dissipated in the circuit in 60 s is :
A \( \cdot 2.26 \times 10^{3} J \)
В . \( 3.39 \times 10^{3} J \)
c. \( 5.65 \times 10^{2} J \)
D. \( 5.17 \times 10^{2} J \)
Subject: Maths
Match the following:
\( \begin{array}{ll}\text { List - I } & \text { List - II } \\ \text { a) Angular velocity } & \text { e) null vector } \\ \text { b) Power } & \text { f) Scalar } \\ \text { c) If } \overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}=\overrightarrow{\mathrm{A}}-\overrightarrow{\mathrm{B}} \text { then } \overrightarrow{\mathrm{B}} \text { is } & \text { g) unit vector } \\ \mathrm{d}) \frac{\vec{A}}{|\vec{A}|} & \text { h) axial vector }\end{array} \)
\( \mathbf{A} \cdot \mathbf{a} \rightarrow \mathbf{f} ; \mathbf{b} \rightarrow \mathbf{h} ; \mathbf{c} \rightarrow \mathbf{e} ; \mathrm{d} \rightarrow \mathbf{f} \)
B \( \cdot a \rightarrow h ; b \rightarrow f ; c \rightarrow g ; d \rightarrow e \)
\( \mathbf{C} \cdot \mathbf{a} \rightarrow \mathbf{g} ; \mathbf{b} \rightarrow \mathbf{e} ; \mathbf{c} \rightarrow \mathbf{h} ; \mathbf{d} \rightarrow \mathbf{f} \)
\( \mathbf{D} \cdot \mathbf{a} \rightarrow \mathbf{h} ; \mathbf{b} \rightarrow \mathbf{f} ; \mathbf{c} \rightarrow \mathbf{e} ; \mathbf{d} \rightarrow \mathbf{g} \)
Subject: Chemistry
A coordination compound X gives pale
yellow colour with \( A g N O_{3} \) solution while its isomer Y gives white
precipitate with \( B a C l_{2} . \) Two
compounds are isomers of \( \operatorname{CoBr} \boldsymbol{S O}_{4} \)
\( \mathbf{5} N \boldsymbol{H}_{3} . \) What could be the possible
formula of \( X \) and \( Y ? \)
A \( \cdot X=\left[\operatorname{Co}\left(N H_{3}\right)_{5} S O_{4}\right] B r, Y=\left[\operatorname{Co}\left(N H_{3}\right)_{5} B r\right] S O_{4} \)
B . \( X=\left[C o\left(N H_{3}\right)_{5} B r\right] S O_{4}, Y=\left[C o\left(N H_{3}\right)_{5} S O_{4}\right] B r \)
c. \( X=\left[\operatorname{Co}\left(N H_{3}\right)_{5} B r\left(S O_{4}\right)\right], Y=\left[\operatorname{CoBr}\left(S O_{4}\right)\left(N H_{3}\right)_{5}\right. \)
D. \( X=\left[\operatorname{Co}(B r)_{5} N H_{3}\right] S O_{4}, Y=\left[\operatorname{CoBr}\left(S O_{4}\right)\right] N H_{3} \)
Subject: Chemistry
Marshalls acid is prepared by the
electrolytic oxidation of \( H_{2} S O_{4} \) as
\( 2 H_{2} S O_{4} \rightarrow H_{2} S_{2} O_{8}+2 H^{\oplus}+2 e^{-} \)
Oxygen and hydrogen are byproducts. In
such Electrolysis 2.24 L of \( H_{2} \) amd \( 0.56 \mathrm{L} \)
\( O_{2} \) were produced at STP. The weight of
\( H_{2} S_{2} O_{8} \) formed is:
A \( .9 .7 g \)
в. \( 19.4 g \)
c. \( 14.55 g \)
D. \( 29.1 g \)
Subject: Physics
In a transformer, coefficient of mutual
inductance between primary and secondary coil is \( 0.2 \mathrm{H} \). When current changes by 5 Na in the primary, then:
the induced era in the secondary will be
A. \( 0.5 \mathrm{v} \)
B. 1
\( c \cdot 1.5 v \)
D. 2.0