AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Assertion
\( \boldsymbol{L i I}+\boldsymbol{K} \boldsymbol{F} \rightarrow \boldsymbol{L} \boldsymbol{i} \boldsymbol{F}+\boldsymbol{K} \boldsymbol{I}: \) This
reaction is spontaneous in forward side.
Reason

The larger anion stabilizes larger cation
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
The equilibrium constant \( \boldsymbol{K}_{\boldsymbol{C}} \) for
\( A(g) \rightleftharpoons B(g) \) is 1.1
Which gas has a molar concentration greater than 1?
A. Both [A] and [B] > 1
B. only [A]
c. only [B]
D. Neither [A] or [B]
Subject: Physics
A particle is moving uniformly in a
circular path of radius 10 m. When it moves through a displacement \( 5 m \) then the magnitude of the corresponding angular displacement will be:
A \( \cdot 20^{\circ} \)
B . \( 30^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 90^{\circ} \)
Subject: Chemistry
Assertion
Avogram is equal to 1 amu.
Reason
Avogram is reciprocal of Avogadro's
number.
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
Consider a circle with unit radius. There
are seven adjacent sectors, \( S_{1}, S_{2}, S_{3} \ldots S_{7}, \) in the circle such that
their total area is \( \frac{1}{8} \) of the area of the circle. Further, the area of the jth sector
is twice that of the \( (j-1)^{t h} \) sector, for
\( j=2, \dots .7 \)
Find the area of the sector \( \boldsymbol{S}_{1} \)
\( \mathbf{A} \cdot \frac{3 \pi}{1016} \)
В. \( \frac{\pi}{508} \)
c. \( \frac{\pi}{1016} \)
D. \( \frac{\pi}{336} \)
Subject: Physics
A force vector applied on a mass is represented by \( \overrightarrow{\boldsymbol{F}}=\mathbf{6} \hat{\mathbf{i}}-\mathbf{8} \hat{\mathbf{8}}+\mathbf{1 0} \hat{\mathbf{k}} \) and
accelerates with \( 1 m / s^{2} \). what is the
mass of the body?
A. \( 10 \mathrm{kg} \)
B . \( 10 \sqrt{2} \mathrm{kg} \)
c. \( 2 \sqrt{10} \mathrm{kg} \)
D. 20 kg
Subject: Maths
If the roots of a quadratic expression
\( a x^{2}+b x+c \) are complex, then
A \( \cdot b^{2}<4 a c \)
В. \( b^{2}>4 a c \)
c. \( b^{2}=4 a c \)
\( \mathbf{D} \cdot a=0 \)
Subject: Physics
Atomic hydrogen is excited to the nth energy level.The maximum number of
spectral lines which it can emit while
returing to the ground state, is
A \( \cdot \frac{1}{2} n(n-1) \)
B . \( \frac{1}{2} n(n+1) \)
c. \( n(n+1) \)
D. \( n(n-1) \)
Subject: Chemistry
A gas expands from 1.5 to 6.5 L against a
constant pressure of 0.5 atm and during
this process the gas also absorbs \( 100 \mathrm{J} \) of heat. The change in the internal energy of
the gas is:
A. 153.3 J
в. 353.3 J
c. -153.3 J
D. -353.3 J
Subject: Physics
Q Type your question.
resistance of \( 12 \Omega \) are connected thick
conducting strips, as shown in the figure. A battery and a galvanometer (With a sliding jockey connected to it) are also available connections are to be made to
measure the unknown resistance \( \boldsymbol{X} \)
using the principle of Wheatstone bridge. Answer the following questions.
(a) Are there positive and negative terminals on the galvanometer
(b) copy the figure is your answer book and show the battery and the galvanometer (With jockey) connected at appropriate points.
(c) After appropriate connections are made, it is found that no deflection
takes place in the galvanometer when the sliding jockey touches the wire at a
distance of \( 60 \mathrm{cm} \) from \( A . \) Obtain the
value of the resistance of \( \boldsymbol{X} \)
Subject: Maths
If the position vector of a point \( \boldsymbol{R} \) which divides the line segment joining points \( P(\hat{i}+2 \hat{j}+\hat{k}) \) and \( Q(-\hat{i}+\hat{j}+\hat{k}) \) in the
ratio 2: 1 internally is \( -\frac{1}{3} \hat{i}+\frac{a}{3} \hat{j}+\hat{k} \)
What is the value of \( a ? \)
Subject: Maths
Find the Cartesian equation of the curve whose parametric equations are \( \boldsymbol{x}= \) \( \boldsymbol{t}^{2}+\boldsymbol{t}+\mathbf{1}, \boldsymbol{y}=\boldsymbol{t}^{2}-\boldsymbol{t}+\mathbf{1} \)
Subject: Biology
I ne aata glven in the table snows species richness of mosses, shrubs and trees calculated for one hectare
\( \left(10,000 m^{2}\right) \) of land every 50 years for
200 years based on a long running
ecological study.
\( \begin{array}{llll}\text { Year } & \text { Mosses } & \text { Shrubs } & \text { Trees } \\ 1800 & 16 & 2 & 0 \\ 1850 & 21 & 7 & 4 \\ 1900 & 10 & 5 & 3 \\ 1950 & 13 & 12 & 6 \\ 2000 & 17 & 28 & 14\end{array} \) The ecological process occurring
according to the data is
A. Evolution
B. Succession
c. Destabilization
D. Primary growth
E . Artificial selection
Subject: Physics
A body rests on a rough horizontal plane. A force is applied to the body directed towards the plane at an angle \( \emptyset \) with the vertical. The body can be moved along the plane
A. Only \( \emptyset \) is more than the angle of friction
B. Only \( \emptyset \) is less than the angle of friction
c. only \( \emptyset \) is equal to the angle of friction
D. For all values of
Subject: Physics
\( 1 \mathrm{kg} \) of water is supplied \( 630 \mathrm{kJ} \) of energy. Specific heat of water is 4200
J/kg \( ^{\circ} \) C.So calculate the rise in temperature of 1 kg water
A \( \cdot 40^{\circ} \mathrm{C} \)
B . \( 60^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 80^{\circ} \mathrm{C} \)
D. \( 150^{\circ} \mathrm{C} \)
Subject: Chemistry
What is the hybridization state of
cation part of solid \( \boldsymbol{P} \boldsymbol{C l}_{5} \) ?
A \( \cdot s p^{3} d^{2} \)
B \( \cdot s p^{2} \)
\( c \cdot s p^{3} \)
\( \mathrm{D} \cdot s p^{3} d \)
Subject: Maths
f the following function is continuous at \( x=\frac{\pi}{2}, \) then find \( a \) and \( b \) \( f(x)=\left\{\begin{array}{l}\frac{1-\sin ^{2} x}{3 \cos ^{2} x}, \text { if } x<\frac{\pi}{2} \\ a, \text { if } x=\frac{\pi}{2} \\ \frac{b(1-\sin x)}{(\pi-2 x)^{2}}, \text { if } x>\frac{\pi}{2}\end{array}\right. \)
Subject: Physics
Calculate the kinetic energy of 10 gram
of Argon molecules at \( 127^{\circ} \mathrm{C} \) [Universal gas constant \( \boldsymbol{R}= \) \( 8320 J / \) mol \( K . \) Atomic weight of Argon
\( =\mathbf{4 0} k \boldsymbol{g} / \boldsymbol{m o l}] \)
Subject: Chemistry
Butene when treated with chlorine at
about \( 500^{\circ} \mathrm{C} \) forms:
A \( \cdot \) МесН \( _{2} \) СНС। \( -\mathrm{cH}_{2} \mathrm{c} \)
B. Месн(С)-СН=СН \( _{2} \)
\( \mathrm{c} \cdot \mathrm{CICH}_{2} \mathrm{CH}_{2} \mathrm{CH}=\mathrm{CH}_{2} \)
D. \( \operatorname{Me} \mathrm{C}\left(\mathrm{Cl}_{2}\right) \mathrm{CH}=\mathrm{CH}_{2} \)
Subject: Chemistry
If the same element is forming oxides in different oxidation states, then, which
of the following statement is incorrect? This question has multiple correct options
A. Oxide will be neutral in nature in which element is in its highest oxidation state
B. Oxide will be highly acidic in nature in which element is in its highest oxidation state
c. oxide will be amphoteric in nature in which element is in its highest oxidation state
D. oxide will be highly basic in nature in which element is in its highest oxidation state
Subject: Chemistry
Balance the following equation by
oxidation number method.
\( \boldsymbol{F} \boldsymbol{e}_{2}\left(\boldsymbol{S} \boldsymbol{O}_{4}\right)_{3}+\boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{3}+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \)
\( \boldsymbol{F} \boldsymbol{e} \boldsymbol{S} \boldsymbol{O}_{4}+\boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
Subject: Chemistry
Boyle's law may be expressed as:
This question has multiple correct options
\( \mathbf{A} \cdot(d P / d V)_{T}=K / V \)
\( \mathbf{B} \cdot(d P / d V)_{T}=-K / V^{2} \)
\( \mathbf{c} \cdot(d P / d V)_{T}=-K / V \)
D. \( V \propto 1 / P \)
Subject: Maths
The lines \( 2 x-3 y=5 \) and \( 3 x-4 y=7 \)
are the diameters of a circle of area 154
square units. An equation of this circle is \( (\boldsymbol{\pi}=\mathbf{2 2} / \mathbf{7}) \)
A \( \cdot x^{2}+y^{2}+2 x-2 y=62 \)
B. \( x^{2}+y^{2}+2 x-2 y=47 \)
c. \( x^{2}+y^{2}-2 x+2 y=47 \)
D. \( x^{2}+y^{2}-2 x+2 y=62 \)
Subject: Maths
A kite is flying with the string inclined
at \( 75^{\circ} \) to the horizon. If the length of the
string is \( 25 m \), then height of the kite is :
A \( \cdot\left(\frac{25}{2}\right)(\sqrt{3}-1)^{2} \)
B. \( \left(\frac{25}{2}\right)\left(\frac{\sqrt{3}+1}{\sqrt{2}}\right) \)
c. \( \left(\frac{25}{2}\right)(\sqrt{3}+1)^{2} \)
D. \( \left(\frac{25}{2}\right)(\sqrt{6}+\sqrt{2}) \)
Subject: Physics
An electric dipole (dipole moment p) is placed in a uniform electric field in stable equilibrium position at rest. Now it is rotated by a small angle and released. The time after which it comes
to the equilibrium position again (for first time) is \( t . \) If the moment of inertia
of the dipole about the axis of rotation is \( x \frac{t^{2} p E}{\pi^{2}}, \) then \( x \) is:
\( A \)
B. 2
\( c \cdot 8 \)
\( D \)
Subject: Maths
toppr
Q Type your question
\( A_{1}= \) last digit of the product is not the
number 1,3,7 or 9
\( A_{2}= \) last digit of the product is among
the number 1,3,5,7 or 9
\( A_{3}= \) last digit of the product is among the number 1,3,7 or 9
\( A_{4}= \) last digit of Ihe product 'is among
the number 2,4,6 or 8
\( A_{5}= \) last digit of the product is the
number 5.
\( A_{6}= \) last digit of the product is the
number 0
\( A_{7}= \) last digit of the product is
1,2,3,4,6,7,8 or \( 9.0 n \) the basis of above information answer the following
questions. The chance that last digit of the product
is \( \boldsymbol{A}_{3} \)
\( ^{\mathrm{A}} \cdot\left(\frac{3}{5}\right)^{\prime} \)
B. \( \left(\frac{2}{5}\right)^{n} \)
\( ^{c} \cdot\left(\frac{2}{3}\right)^{n} \)
D. \( \left(\frac{4}{5}\right)^{\prime} \)
Subject: Chemistry
The gas phase decomposition of dimethyl ether follows first order kinetics:
\( \boldsymbol{C H}_{3}-\boldsymbol{O}-\boldsymbol{C H}_{3}(\boldsymbol{g}) \rightarrow \boldsymbol{C H}_{4}(\boldsymbol{g})+ \)
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{C} \boldsymbol{O}(\boldsymbol{g}) \)
The reaction is carried out in a constant
volume container at \( 50^{\circ} \mathrm{C} \) and has a
half life of 14.5 minutes. Initially, only
dimethyl ether is present at a pressure of 0.40 atm. What is the total pressure
of the system after 12 minutes? (Assume the ideal gas behaviour.)
A. 0.946 atm
B. 0.785 atm
\( c \cdot 0.777 \) atm
D. 0.749 atm
Subject: Physics
An a.c of \( 50 H z \) and \( 1 A \) peak value flow
in the primary coil of a transformer. The mutual inductance between primary
and secondary coils is \( 1.5 H . \) Then peak value of induced emf across secondary coil is
A. \( 75 \pi \) volt
B . \( 150 \pi \) volt
c. 225 volt
D. 300volt
Subject: Physics
A lift of mass \( 100 \mathrm{kg} \) starts moving from
rests in the upward direction. Fig shows
the variation if speed of the lift, \( \boldsymbol{T}_{1}, \boldsymbol{T}_{2} \)
and \( T_{3} \) stand for tension in the rope
form zero to two seconds, two to six
seconds, six to seven seconds
respectively then:
A \( \cdot T_{1}: T_{2}: T_{3}:: 1: 1: 1 \)
B. \( T_{1}: T_{2}: T_{3}:: 6: 5: 3 \)
\( \mathbf{c} \cdot T_{1}: T_{2}: T_{3}:: 3: 5: 6 \)
D. \( T_{1}: T_{2}: T_{3}:: 6: 5: 6 \)
Subject: Chemistry
Prussian blue has two types of iron with oxidation number as shown \( \prod_{\boldsymbol{F}}^{\boldsymbol{I I I}}[\stackrel{\boldsymbol{I I}}{\left.\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{\boldsymbol{6}}\right]}] \)
net charge on Prussian blue is - \( x \). The value of \( x \) is
Subject: Maths
Given right triangle \( \boldsymbol{R} \boldsymbol{S} \boldsymbol{T} \) in figure
calculate the length of \( \overline{S T} \), to the
nearest hundredth. (Use \( \cos 42^{0}= \)
\( \mathbf{0 . 7 4 3 2}) \)
\( \mathbf{A} \cdot 12.04 m m \)
B. \( 13.38 \mathrm{mm} \)
c. \( 16.21 \mathrm{mm} \)
D. 24.22 \( m m \)
E \( .26 .90 m m \)
Subject: Chemistry
Write half-reactions using electrons.
\( \boldsymbol{C r}_{2} \boldsymbol{O}_{2}^{\boldsymbol{7}-}+\boldsymbol{6} \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{2}+}+\mathbf{1 4} \boldsymbol{H}^{+} \longrightarrow \)
\( 2 C r^{3+}+6 F e^{3+}+7 H_{2} O \)
A. Oxidation : \( F e^{2+} \longrightarrow F e^{3+}+e^{-} \); Reduction:
\[
C r_{2} O_{2}^{7-}+14 H^{+}+6 e^{-} \longrightarrow 2 C r^{2+}+7 H_{2} O
\]
B. Oxidation: \( 3 F e^{2+} \longrightarrow 3 F e^{3+}+e^{-} \); Reduction:
\( \mathrm{Cr}_{2} \mathrm{O}_{2}^{7-}+14 \mathrm{H}^{+}+6 e^{-} \longrightarrow 2 \mathrm{Cr}^{2+}+7 \mathrm{H}_{2} \mathrm{O} \)
C. Oxidation : \( 2 F e^{2+} \longrightarrow 2 F e^{3+}+e^{-} \); Reduction:
\( \mathrm{Cr}_{2} \mathrm{O}_{2}^{7-}+14 \mathrm{H}^{+}+6 e^{-} \longrightarrow 2 \mathrm{Cr}^{2+}+7 \mathrm{H}_{2} \mathrm{O} \)
D. Oxidation: \( 3 F e^{2+} \longrightarrow F e^{3+}+3 e^{-} ; \) Reduction :
\( C r_{2} O_{2}^{7-}+14 H^{+}+3 e^{-} \longrightarrow 2 C r^{2+}+7 H_{2} O \)
Subject: Chemistry
In the reaction,
\( 4 H N O_{3}+P_{4} O_{10} \rightarrow 4 H P O_{3}+X ; \) the
product \( \boldsymbol{X} \) is
A. \( N_{2} O_{5} \)
в. \( N_{2} O_{3} \)
\( c \cdot N O_{2} \)
D. \( H_{2} O \)
Subject: Chemistry
What is the correct sequence of the increasing effectiveness of the following electrolyte for the coagulation of ferric hydroxide sol? \( \boldsymbol{K}_{4}\left[\boldsymbol{F} e(\boldsymbol{C} \boldsymbol{N})_{6}\right. \)
\( A l P O_{4} \)
\( \boldsymbol{C a} \boldsymbol{S O}_{4} \)
\( \boldsymbol{S} \boldsymbol{n} \boldsymbol{C l}_{4} \)
Select the correct answer using the codes given below:
\( A \cdot d, b, a, c \)
B. \( \mathrm{d}, \mathrm{c}, \mathrm{b} \),
\( c \cdot a, b, c, d \)
D. \( c, d, b, a \)
Subject: Physics
If the magnitude of its angular speed at
\( \boldsymbol{t}=\mathbf{3 . 0 s} \) is \( \boldsymbol{x} \boldsymbol{r} \boldsymbol{a} \boldsymbol{d} / \boldsymbol{s}, \) find \( \boldsymbol{2} \boldsymbol{x} \)
Subject: Maths
\( \mathbf{A}= \) the domain of \( \mathbf{f} \) where \( \mathbf{f}(\mathbf{x})=\log \mathbf{x}^{2} \)
and \( \mathbf{B}= \) the domain of \( \mathbf{g} \) where \( \mathbf{g}(\mathbf{x})= \) \( 2 \log x, \) then \( \mathbf{A}-\mathbf{B}= \)
\( A \cdot \phi \)
В \( \cdot(-\infty, 0) \)
c. \( (0, \infty) \)
D. (0,1)
Subject: Chemistry
Which of the following are correct about
mixture of two miscible liquids forming
azeotopes?
This question has multiple correct options
A. Has the lowest temperature at which the two liquids can exist in the liquid state
B. Has the lowest temperature attainable at which two liquids forms eutectic mixture
C. Eutectic point has found application to attain low melting point solids which are eutectic mixture
D. Composition of azeotrope and their b.pt. vary with the external pressure
Subject: Chemistry
The correct match between items of
List- I and List- II is:
List I
(A) Phenelzine
(P) Pyrimidine
(B) Chloroxylenol
(Q) Furan
(C) Uracil
(R) Hydrazine
(D) Rantitidine
(S) Phenol
\( A \)
\( (A)-(S) ;(B)-(R) ;(C)-(P) ;(D)-(Q) \)
B. \( (A)-(R) ;(B)-(S) ;(C)-(P) ;(D)-(Q) \)
C. \( (A)-(R) ;(B)-(S) ;(C)-(Q) ;(D)-(P) \)
\( D \cdot(A)-(S) ;(B)-(R) ;(C)-(Q) ;(D)-(P) \)
Subject: Physics
Thickness of a pencil measured by using a screw gauge (least count. \( 001 \mathrm{cm} \) ) comes out to be \( 0.802 \mathrm{cm} \). The
percentage error in the measurement is
A . \( 0.125 \% \)
B . \( 2.43 \% \)
c. \( 4.12 \% \)
D. 2.14\%
Subject: Chemistry
Assertion
On cooling, the brown colour of nitrogen dioxide disappears.
Reason
On cooling \( N O_{2} \) undergoes dimerisation resulting in the pairing of
odd electrons of \( N O_{2} \)
Read the above assertion and reason
and choose the corret option regarding
¡t.
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
If an equiconvex lens is cut into two
halves along (i) \( X O X^{\prime} \) and (ii) \( Y O Y^{\prime} \)
as shown in the figure. Let \( f, f^{\prime}, f^{\prime \prime} \) be the focal lengths of complete lens of each, in case (i) and of each half in case
(ii) respectively.
Choose the correct statement from the
following?
\( \mathbf{A} \cdot f^{\prime}=f, f^{\prime \prime}=f \)
B . \( f^{\prime}=2 f, f^{\prime \prime}=2 f \)
C. \( f^{\prime}=f, f^{\prime \prime}=2 f \)
D. \( f^{\prime}=2 f, f^{\prime \prime}=f \)
Subject: Maths
In the complex numbers, where \( i^{2}=-1 \)
what is the value of \( 5+6 i \) multiplied
by \( 3-2 i ? \)
A . 27
в. 27
c. \( 27+8 i \)
D. \( 15+8 i \)
E . \( 15-18 i \)
Subject: Chemistry
\( Z n C O_{3} \) is thermally more stable than
\( M g C O_{3}, \) because
A \( \cdot M g(O H)_{2} \) exhibits only properties while \( Z n(O H)_{2} \) is amphoteric
B. polarising action of \( Z n^{2+} \) with 18 -electron configuration on the anion is larger than that of \( M g^{2} \) with a noble-gas electron configuration and of same size and charge
c. both (a) and (b) are correct
D. none of the above is correct
Subject: Physics
A rod of mass \( \mathrm{M} \) kg and length \( \mathrm{L} \mathrm{m} \) is bent in the form of an equilateral
triangle as shown in figure. The moment of inertia of the triangle about a vertical axis perpendicular to the plane of the
triangle and passing through the centre (in units of \( \mathrm{kg} \boldsymbol{m}^{2} \) ) is?
A \( \cdot \frac{M L^{2}}{12} \)
B. \( \frac{M L^{2}}{54} \)
c. \( \frac{M L^{2}}{162} \)
D. \( \frac{M L^{2}}{108} \)
Subject: Physics
An equiconvex glass lens \( (i) \) has a focal
length \( f \) and power \( P . \) it is cut into symmetrical halves
\( (i i) \) by a plane containing the principle axis. The two pieces are recombined as shown in figure
\( (i i i) \) The power of new combination is:
(ii)
\( A \)
в. \( P / 2 \)
\( c .2 P \)
D. zero
Subject: Maths
The angle made by the tangent line at (1
3) on the curve \( y=4 x-x^{2} \) with \( O X \) is
A \( \cdot \tan ^{-1}(2) \)
B. \( \tan ^{-1}(1 / 3) \)
c. \( \tan ^{-1}(3) \)
D. \( \pi / 4 \)
Subject: Physics
Two identical sinusoidal waves each of
amplitude \( 5 m m \) with a phase difference of \( \frac{\pi}{2} \) are travelling in the same direction in a string. The amplitude of the resultant wave (in \( m m \) ) is:
A. zero
B. \( 5 \sqrt{2} \)
c. \( \frac{5}{\sqrt{2}} \)
D. 2.5
Subject: Maths
If \( \boldsymbol{f}(\boldsymbol{x})=\mathbf{1} \) for \( \boldsymbol{x}<\mathbf{0}=\mathbf{1}+\sin \boldsymbol{x} \) for
\( 0 \leq x<\pi / 2, \) then at \( x=0, \) then show
that the derivative \( f^{\prime}(x) \) does not exist.
Subject: Physics
A capacitor, as shown in figure has
square plates of length land are inclined
at an angle \( \theta \) with one another. For small
value of \( \theta, \) capacitance is given by:
\( ^{\mathbf{A}} \cdot \frac{\epsilon_{0} l^{2}}{d}\left(1-\frac{\theta l}{2 d}\right) \)
\( ^{\mathbf{B}} \cdot \frac{\epsilon_{0} l^{2}}{2 d}\left(1-\frac{\theta l}{d}\right) \)
c. \( \frac{\epsilon_{0} l^{2}}{d}\left(1+\frac{\theta l}{d}\right) \)
D \( \cdot \frac{\epsilon_{0} l^{2}}{2 d}\left(1+\frac{\theta l}{d}\right) \)
Subject: Maths
Let \( P(3,2,6) \) be point in space and \( Q \) be appoint on the line \( \vec{r}=(\hat{i}-\hat{j}+2 \hat{k})+ \)
\( \mu(-3 \hat{i}+\hat{j}+5 \hat{k}) . \) Then the value of \( \mu \) for which the vector \( \overrightarrow{P Q} \) is parallel to the
plane \( \boldsymbol{x}-\mathbf{4} \boldsymbol{y}+\mathbf{3} \boldsymbol{z}=\mathbf{1} \) is
A. \( 1 / 4 \)
B. - 1/4
c. \( 1 / 8 \)
D. \( -1 / 8 \)
Subject: Physics
If the energy \( (\boldsymbol{E}), \) velocity \( (\boldsymbol{v}) \) and force
\( (F) \) be taken as fundamental
quantities, then the dimensions of
mass will be
A. \( F v^{-2} \)
B. \( F v^{-1} \)
\( \mathbf{c} \cdot E v^{-2} \)
D. \( E v^{2} \)
Subject: Maths
The points \( (\boldsymbol{k}-\mathbf{1}, \boldsymbol{k}+\mathbf{2}),(\boldsymbol{k}, \boldsymbol{k}+ \)
1) \( ,(k+1, k) \) are collinear for
A. any value of \( k \)
B. \( k=-\frac{1}{2} \) only
c. no value of \( k \)
D. integral values of \( k \) only
Subject: Physics
What is the area of the plates of a 2 F parallel plate capacitor, given that the separation between the plates is 0.5 \( \mathrm{cm} ?[ \) You will realise from your answer
why ordinary capacitors are in the range of F or less. However, electrolytic capacitors do have a much larger capacitance (0.1 \( F \) ) because of very minute separation between the conductors.
Subject: Physics
A particle is moving along a circle such that it completes one revolution in 40 seconds. In 2 minutes 20 seconds, the
ratio \( \frac{\mid \text {displacement} \mid}{\text {distance}} \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot \frac{2}{7} \)
D. \( \frac{7}{11} \)
Subject: Chemistry
The osmotic pressure of a decimolar
solution of glucose at \( 30^{\circ} \mathrm{C} \) is :
\( \mathbf{A} \cdot 24.88 \mathrm{atm} \)
B. 2.488 atm
\( \mathbf{c} .0 .248 \mathrm{atm} \)
D. \( 189.09 \mathrm{cm} \)
Subject: Physics
Assertion
A disc rotates along the clockwise
direction and direction of angular velocity is upwards
Reason
The linear velocity of points on the disc
are directed towards the centre
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Physics
The initial number of atoms of a
radioactive element with half life 100
days, is \( 9.6 \times 10^{26} . \) The number of
atoms remaining undecayed after 500 days, will be
A \( \cdot 9.6 \times 10^{25} \)
B . \( 3.84 \times 10^{25} \)
\( \mathrm{c} \cdot 3 \times 10^{25} \)
D. \( 19.2 \times 10^{25} \)
Subject: Physics
A body dropped from a height \( h \) with an initial speed zero, strikes the ground with a velocity \( 3 k m / h \). Another body of
same mass dropped from the same
height \( h \) with an initial speed \( u= \)
\( 4 k m / h . \) Find the final velocity of
second mass, with which it strikes the
ground.
\( \mathbf{A} \cdot 3 k m / h \)
в. \( 4 \mathrm{km} / \mathrm{h} \)
\( \mathrm{c} .5 \mathrm{km} / \mathrm{h} \)
D. \( 6 \mathrm{km} / \mathrm{h} \)
Subject: Physics
A uniform metal disc of radius R is
taken and out of it, a disc of diameter \( \mathrm{R} \)
is cut-off from the end. The center of
mass of the remaining part will be:
A \( \cdot \frac{R}{4} \) from the cente
в. \( \frac{R}{3} \) from the centre
c. \( \frac{R}{5} \) from the cente
D. \( \frac{R}{6} \) from the center
Subject: Physics
Assertion
Kinematic equations are exact and are always correct.
Reason
The definitions of instantaneous
velocity and acceleration are true only for motion in which the magnitude and
direction of acceleration are constant
during the course of motion
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: Maths
If \( \sin ^{-1}\left(\frac{2 p}{1+p^{2}}\right)-\cos ^{-1}\left(\frac{1-q^{2}}{1+q^{2}}\right)= \)
\( \tan ^{-1}\left(\frac{2 x}{1+x^{2}}\right), \) then the value of \( x \) is equal to
A \( \cdot \frac{p+q}{1+p q} \)
в. \( \frac{p-q}{1-p q} \)
c. \( \frac{p-q}{p q-1} \)
D. \( \frac{p-q}{p q+1} \)
Subject: Physics
The resistors in parallel in the following
circuit are
\( \mathbf{A} \cdot R_{2} \quad \) and \( \quad R_{3} \)
\( \mathbf{B} \cdot R_{1} \quad \) and \( \quad R_{2} \)
\( \mathbf{C} \cdot R_{1} \quad \) and \( \quad R_{3} \)
\( \mathbf{D} \cdot\left(R_{1}+R_{2}\right) \quad \) with \( \quad R_{3} \)