AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A long solenoid of length \( L \) has a mean
diameter \( D . \) It has \( n \) layers of winding of
\( N \) turns each. If it carries a current \( I \)
the magnetic field at its centre will be.
A. Proportional to \( D \)
B. Inversely proportional to \( D \)
c. Independent of \( D \)
D. Proportional to L.
Subject: Physics
A satellite is changes it orbit from
radius of \( \mathrm{R} \) to radius of \( 2 \mathrm{R} \). If its initial
kinetic energy is \( K_{1} \) then calculate the
new kinetic energy.
A \( \cdot \frac{K_{1}}{4} \)
в. \( \frac{K_{1}}{2} \)
c. \( K_{1} \)
D. \( 2 K_{1} \)
E \( .4 K_{1} \)
Subject: Maths
Length of the latus rectum of the parabola \( \sqrt{\boldsymbol{x}}+\sqrt{\boldsymbol{y}}=\sqrt{\boldsymbol{a}} \) is
\begin{tabular}{l} 
A \( \cdot a \sqrt{2} \) \\
\hline
\end{tabular}
B. \( \frac{a}{\sqrt{2}} \)
\( c \)
D. 2a
Subject: Chemistry
Electrolysis of dilute aqueous \( \mathrm{NaCl} \) solution was carried out by passing 10 milli ampere current. The time required
to liberate 0.01 mol of \( \mathbf{H}_{2} \) gas at the
cathode is (1 Faraday \( =\mathbf{9 6 5 0 0 C} \) mol \( ^{-1} \) )
A \( \cdot 9.65 \times 10^{4} \mathrm{sec} \)
B . \( 19.3 \times 10^{4} \mathrm{sec} \)
c. \( 28.95 \times 10^{4} \) sec
D. \( 38.6 \times 10^{4} \mathrm{sec} \)
Subject: Maths
\( \cos ^{4} \theta-\sin ^{4} \theta+1 \) is equal to:
A \( \cdot 2 \cos e c^{2} \theta \)
B. \( -2 \cos e c^{2} \theta \)
c. \( \frac{2}{\tan ^{2} \theta} \)
D. \( \frac{2 \cot ^{2} \theta}{\cos e c^{2} \theta} \)
Subject: Chemistry
Equivalent weight of the underlined
\( 2 \underline{H}_{3} \boldsymbol{P} \boldsymbol{O}_{2} \longrightarrow \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4}+\boldsymbol{P} \boldsymbol{H}_{3} \)
A . 33
B. 24
\( c \cdot 42 \)
D. 31
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{cc}\cos \boldsymbol{\theta} & -\sin \boldsymbol{\theta} \\ \sin \boldsymbol{\theta} & \cos \boldsymbol{\theta}\end{array}\right], \) then \( \boldsymbol{A} \boldsymbol{A}^{\boldsymbol{T}} \)
equals
\( A \cdot\left[\begin{array}{cc}\cos 2 \theta & -\sin 2 \theta \\ \sin 2 \theta & \cos 2 \theta\end{array}\right] \)
B. \( \left[\begin{array}{cc}\cos ^{2} \theta & \sin ^{2} \theta \\ \sin ^{2} \theta & \cos ^{2} \theta\end{array}\right] \)
c. \( \left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right] \)
D. \( \left[\begin{array}{ll}0 & 0 \\ 0 & 0\end{array}\right] \)
Subject: Physics
On a long horizontally moving belt, a child runs to and fro with a speed \( 9 \mathrm{km} \)
\( \boldsymbol{h}^{-1}( \) with respect to the belt) between
his father and mother located \( 50 \mathrm{m} \)
apart on the moving belt. The belt moves
with a speed of \( 4 \mathrm{km} h^{-1} \). For an
observer on a stationary platform, the speed of the child running in the direction of motion of the belt is
\( A \cdot 4 \mathrm{km} h-1 \)
B. 5 km \( h-1 \)
c. \( 9 \mathrm{km} h-1 \)
D. 13 km \( h-1 \)
Subject: Physics
At two points separated by a distance of \( 3 \mathrm{cm}, \) the magnetic field strength due to a short magnet on its axial line are in the ratio 512:125. Then the distance of magnet from the first point is:
A. \( 8 \mathrm{cm} \)
B. \( 11 \mathrm{cm} \)
\( c \cdot 4 c m \)
D. 5cm
Subject: Chemistry
For given reaction:
\( \boldsymbol{C r}_{2} \boldsymbol{O}_{7}^{2-} \stackrel{\boldsymbol{H}^{+}}{\longrightarrow} \boldsymbol{C r}^{3} \)
Eq.wt of \( \boldsymbol{C r}_{2} \boldsymbol{O}_{7}^{2-} \) is:
A. mol. wt. \( / 6 \)
B. mol. wt./3
c. mol. wt. \( / 4 \)
D. mol. wt./1
Subject: Maths
The distance between the parallel planes given by the equations, \( \vec{r} .(2 \hat{i}- \) \( \mathbf{2} \hat{\mathbf{j}}+\hat{\boldsymbol{k}})+\mathbf{3}=\mathbf{0} \) and \( \vec{r} \cdot(\mathbf{4} \hat{\mathbf{i}}-\mathbf{4} \hat{\mathbf{j}}+ \)
\( \mathbf{2} \hat{\boldsymbol{k}})+\mathbf{5}=\mathbf{0} \) is -
A \( \cdot 1 / 2 \)
в. \( 1 / 3 \)
c. \( 1 / 4 \)
D. \( 1 / 6 \)
Subject: Physics
Suppose the object in figure shown is the brass plate of an outdoor sculpture.
If experiences shear forces as a result of
an earthquake. The frame is \( 0.80 m \) and
\( 0.50 c m \) thick. Calculate the shear
strain produced in this object if the
displacement x is 0.16mm (Shear
modulus=\( \left.3.5 \times 10^{10} P a\right) \)
Subject: Physics
Two samples \( A \) and \( B \) of same radioactive nuclide are prepared Sample A has twice the initial activity of sample B. For this situation, mark out the correct statement(s):
This question has multiple correct options
A. The half-lives of both the samples would be same
B. The half-lives of the samples are different
C. After each has passed through 5 half-lives, the ratio of activity of A to B is 2:
D. After each has passed through 5 half-lives, ratio of activities of A to B is 64:
Subject: Physics
The displacement time graphs of two particles \( A \) and \( B \) are straight lines
making angles of respectively \( 30^{\circ} \) and
\( 60^{\circ} \) with the time axis. If the velocity of
\( A \) is \( v_{A} \) and that of \( B \) is \( v_{B}, \) then the value of \( \frac{v_{A}}{v_{B}} \) is:
A \( \cdot \frac{1}{2} \)
в. \( \frac{1}{\sqrt{3}} \)
\( c \cdot \sqrt{3} \)
D.
Subject: Maths
Find the interval in which \( f(x)=x|x| \) is
differentiable.
\( A \cdot(-\infty, \infty) \)
В. \( (-\infty, 0) \cup(0, \infty) \)
\( c \cdot(0, \infty) \)
D. \( [0, \infty) \)
Subject: Physics
The pole strength of a bar magnet is 2 Am. If the field at poles are \( 0.2 \mathrm{T} \) and 0.22 T, then the force acting on the bar magnet is
consider field direction to be same
A. \( 0.4 \mathrm{N} \)
B. 0.04N
c. \( 0.44 \mathrm{N} \)
D. 0.8N
Subject: Physics
A tank is filled up to a height \( 2 \mathrm{H} \) with a
liquid and is placed on a platform of
height H from the ground. The distance
\( x \) from the ground where a small hole is
punched to get the maximum range
is
\( A \cdot H \)
B . \( 1.25 \mathrm{H} \)
c. \( 1.5 \mathrm{H} \)
D. 2
Subject: Maths
A class has three teachers Mr. X, Ms. Y
and Mrs. Z and six students
\( A, B, C, D, E, F . \) Number of ways in
which they can be seated in a line of 9
chairs, If bwteen any two teachers there are exactly two students, is
A. \( 18(6 !) \)
в. \( 12(6 !) \)
c. \( 24(6 !) \)
D. \( 6(6 !) \)
Subject: Maths
The absolute maximum and minimum
value of \( \boldsymbol{f}(\boldsymbol{x})=\sin \boldsymbol{x}+\cos \boldsymbol{x}, \boldsymbol{x} \in[\mathbf{0}, \boldsymbol{\pi}] \)
are respectively
A \( \cdot \sqrt{2},-1 \)
B. \( \sqrt{2}, 1 \)
c. \( \sqrt{2},-\sqrt{2} \)
D. \( \sqrt{3}, \sqrt{2} \)
Subject: Maths
f \( \boldsymbol{y}=\boldsymbol{a} \log |\boldsymbol{x}|+\boldsymbol{b} \boldsymbol{x}^{2}+\boldsymbol{x} \) has its
extremum values at \( x=-1 \) and \( x=2 \)
then the value of \( -2 a b \) is
Subject: Physics
The transverse displacement \( y(x, t) \) of \( a \)
wave on a string is given by \( y(x, t)= \) \( e^{\left(a x^{2}+b t^{2}+2 \sqrt{a b} x t\right)} . \) This represents a
A \( \cdot \) wave moving in -x direction with speed \( \sqrt{\frac{b}{a}} \)
B. standing wave of frequency \( \sqrt{b} \)
C standing wave of frequency \( \sqrt{\frac{1}{\sqrt{b}}} \)
D. wave moving in + x direction with \( \sqrt{\frac{a}{b}} \)
Subject: Physics
In a mass spectrometer used for measuring the masses of ions, the ions are initially accelerated by an electric potential V and then made to describe semicircular paths of radius R using a magnetic field B. If \( \mathrm{V} \) and \( \mathrm{B} \) are kept constant, the ratio ( \( \left.\frac{\text { Charge on the ion }}{\text { Mass of the ion }}\right) \) wil be proportional to
A \( -\frac{1}{R} \)
в. \( \frac{1}{R^{2}} \)
\( c \cdot R^{2} \)
D.
Subject: Chemistry
Assertion
Inert electrolytes like KCI \( , K N O_{3} \) are
used in salt bridge.
Reason
Salt bridge provides an electric contact between the two solutions without
allowing them to mix with each other
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
\( 250 m l \) of a sodium carbonate contains
\( 2.65 \operatorname{grams} N a_{2} C O_{3} . \) If \( 10 m l \) of that
solution is diluted to one litre, what is the concentration of the resultant
solution (mol wt. of \( \left.\boldsymbol{N a}_{2} \boldsymbol{C O}_{3}=\mathbf{1 0 6}\right) \)
\( \mathbf{A} \cdot 0.1 M \)
в. \( 0.001 M \)
c. \( 0.01 M \)
D. \( 10^{-4} M \)
Subject: Physics
The area of cross-section of the two
\( \operatorname{arms} \) of a hydraulic press are \( 1 \mathrm{cm}^{2} \) and
\( 10 \mathrm{cm}^{2} \) respectively(fig.). A force of \( 5 \mathrm{N} \) is applied on the water in the thinner
arm. What force should be applied
on the water in the thicker arm so that
the water may remain in equilibrium?
\( A \cdot 50 N \)
B. 60 N
c. 70 n
D. 80N
Subject: Maths
\( \frac{2 x+1}{(x-1)\left(x^{2}+1\right)}=\frac{A}{x-1}+ \)
\( \frac{B x+C}{x^{2}+1} \Rightarrow C= \)
A .
B. 1/2
\( c \cdot-1 / 2 \)
D. 5/2
Subject: Maths
If \( (x-a)^{2}+(y-b)^{2}=c^{2}, \) then prove
that \( \frac{\left[1+\left(\frac{d y}{d x}\right)^{2}\right]^{3 / 2}}{\frac{d^{2} y}{d x^{2}}} \) is a independent
of \( \boldsymbol{C} \)
Subject: Chemistry
Which of the following has higher
lattice energy \( -A l_{2} O_{3} \) or \( A l_{2} S e_{3} ? \)
A. \( A l_{2} O_{3}>A l_{2} S e_{3} \)
B . \( A l_{2} O_{3}<A l_{2} S e_{3} \)
c. \( A l_{2} O_{3}=A l_{2} S e_{3} \)
D. None of these
Subject: Maths
Given that tangent \( \overrightarrow{A B} \) is \( 4 \mathrm{cm} \) and radius \( \overline{C D} \) is \( 3 \mathrm{cm}, \) the length \( \overline{B C}=? \)
\( A \)
B. 2
\( c \)
\( D \cdot 4 \)
Subject: Chemistry
\( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3}+\boldsymbol{H}_{2} \boldsymbol{O} \leftrightharpoons \)
A \( \cdot H^{+}+N O_{3}^{2-} \)
B. \( H^{-}+N O_{3}^{+} \)
\( \mathrm{c} \cdot \mathrm{H}_{3} \mathrm{O}^{+}+\mathrm{NO}_{3} \)
D. \( H_{3} O^{-}+N O_{3}^{+} \)
Subject: Physics
Four particles each of mass \( \boldsymbol{m} \) are
placed at the corners of a square of side length \( l \). The radius of gyration of the system about an axis perpendicular to the square and passing through its
center is:
A \( \frac{l}{\sqrt{2}} \)
B. \( \frac{l}{2} \)
c. \( l \)
D. \( (\sqrt{2}) l \)
Subject: Biology
The domestic sewage in large cities
A. Is processed by aerobic and then anaerobic bacteria in the secondary treatment in sewage treatment plant \( (\mathrm{STPs}) \)
B. When treated in STPs does not really require the aeration step as the sewage contains adequate oxygen.
C. Has very high amounts of suspended solids and dissolved salts.
D. Has a high BOD as it contains both aerobic and anaerobic bacteria.
E. Is processed by anaerobic bacteria in the primary treatment and by aerobic bacteria in the secondary treatment in sewage treatment plant (STPs)
Subject: Maths
Rearrange the following steps of constructing a triangle when the base angle say \( \angle B \) and \( \angle C \) and its
perimeter \( \boldsymbol{B C}+\boldsymbol{C A}+\boldsymbol{A B} \) is given:
1. Draw perpendicular bisectors \( \boldsymbol{P Q} \) of
\( A X \) and \( R S \) of \( A Y \)
2. Draw a line segment, say \( X Y \) equal to \( B C+C A+A B \)
3. Let \( P Q \) intersect \( X Y \) at \( B \) and \( R S \)
intersect \( X Y \) at \( C . \) Join \( A-B \) and
\( A-C \)
4. Make \( \angle L X Y \) equal to \( \angle B \) and
\( \angle M Y X \) equal to \( \angle C \)
5. Bisect \( \angle L X Y \) and \( \angle M Y X \). Let these
bisectors intersect at a point \( \boldsymbol{A} \)
\( \mathbf{A} \cdot 1 \rightarrow 3 \rightarrow 5 \rightarrow 4 \rightarrow 2 \)
В. \( 2 \rightarrow 4 \rightarrow 5 \rightarrow 1 \rightarrow 3 \)
c. \( 5 \rightarrow 4 \rightarrow 3 \rightarrow 2 \rightarrow 1 \)
D. \( 2 \rightarrow 3 \rightarrow 5 \rightarrow 4 \rightarrow 1 \)
Subject: Maths
If \( \boldsymbol{A}=\{\mathbf{2}, \boldsymbol{3}\} \) and \( \boldsymbol{B}=\{1,2\}, \) then \( \boldsymbol{A} \times \)
\( B \) is equal to
A \( \cdot\{(2,1),(2,2),(3,1),(3,2)\} \)
B - \{(1,2),(1,3),(2,2),(2,3)\}
c. \{(2,1),(3,2)\}
D \( \cdot\{(1,2),(2,3)\} \)
Subject: Maths
The fees structure for one-day
admission to a swimming pool is as follows
Daily Admission Fees in Rs.
\( \begin{array}{lll}\text { Member } & \text { Children } & \text { Adult } \\ \text { Before 2.00 p.m. } & 20 & 30 \\ \text { After 2.00 p.m. } & 30 & 40 \\ \text { Non-Member } & & \\ \text { Before 2.00 p.m. } & 25 & 35 \\ \text { After 2.00 p.m. } & 40 & 50\end{array} \) Write the matrix that represents the
additional cost for non-membership.
Subject: Physics
Out of the following, select the correct
statements:
This question has multiple correct options
A. refractive index, frequency and deviation are maximum for red colour
B. if there were no atmosphere, the length of the day on the earth would increase
C. for greater value of \( \mu \), the angle of deviation increase
D. if the critical angle for the medium of a prism is \( \theta_{c} \) and the angle of prism is \( A \), there will be no emergent ray when \( A>2 \theta_{c} \)
Subject: Physics
Assertion
Absolute error may be negative or
positive.
Reason
Absolute error is the difference between
the real value and the measured value
of a physical quantity
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
divided into three parts \( A, B \) and \( C \) Piston I and II are connected by a rigid rod and can move without friction
inside the cylinder. Piston I is perfectly conducting while piston II is perfectly insulating. The initial state of \( \operatorname{gas}(\gamma= \)
1.5) present in each compartment \( \mathbf{A}, \mathbf{B} \)
and \( C \) is as shown. Now, compartment \( A \)
is slowly given heat through a heater \( H \) such that the final volume of \( C \) becomes \( \frac{4 V_{0}}{9} . \) Assume the gas to be ideal and find the heat supplied by the heater.
A \( .18 P_{o} V_{o} \)
B. \( 12 P_{o} V_{o} \)
\( \mathrm{c} \cdot 9 P_{o} V_{o} \)
D. \( 25 P_{o} V_{o} \)
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 \( t . \) Then the moment of
inertia of the dipole about the axis of
rotation is :
A \( \cdot \frac{4 t^{2} p E}{3 \pi^{2}} \)
в. \( \frac{1 t^{2} p E}{4 \pi^{2}} \)
c. \( \frac{2 t^{2} p E}{3 \pi^{2}} \)
D. \( _{4} \frac{t^{2} p E}{\pi^{2}} \)
Subject: Chemistry
The nature of \( \pi \) -bonds in perchlorate
ion is :
A \( . O(d \pi)-C l(p \pi) \)
в. \( O(p \pi)-C l(d \pi) \)
c. \( O(d \pi)-C l(d \pi) \)
D. \( O(p \pi)-C l(p \pi) \)
Subject: Chemistry
A magnesium ribbon is burnt in oxygen to give a white compound 'X' accompanied by emission of light. If the burning ribbon is now placed in an atmosphere of nitrogen, it continues to burn and forms a compound 'Y'. Write a balanced chemical equation when 'X' is dissolved in water.
\( \mathbf{A} \cdot 2 M g+O_{2} \rightarrow 2 M g O \)
В. \( 3 M g+N_{2} \rightarrow M g_{3} N_{2} \)
c. \( M g O+H_{2} O \rightarrow M g(O H)_{2} \)
D. \( M g+H_{2} O \rightarrow M g(O H)_{2} \)
Subject: Physics
A block of mass \( 0.1 \mathrm{kg} \) is held against a wall by applying a horizontal force of 5 N on the block. If the coefficient of friction
the block and the wall is \( 0.5, \) the
magnitude of the frictional force acting on the block is:
A. \( 2.5 \mathrm{N} \)
B. 0.98 N
c. \( 4.9 \mathrm{N} \)
D. 10 N
Subject: Chemistry
What is the maximum \( p H \) required to
prevent precipitation of \( Z n S \) in a
solution that is \( 0.01 M Z n C l_{2} \) and
saturated with \( 0.1 M H_{2} S ? \)
\( \left[\text { Given: } \boldsymbol{K}_{s p}(\boldsymbol{Z} \boldsymbol{n} \boldsymbol{S})=\mathbf{1 0}^{-\mathbf{2 1}}, \) for \right.
\( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{K} \boldsymbol{a}_{1} \times \boldsymbol{K} \boldsymbol{a}_{2}=\mathbf{1 0}^{-20} \)
Subject: Chemistry
The actinoids exhibit more number of
oxidation states in general than
lanthanoids because:
A. the \( 5 f \) orbitals are more buried than the 4 f orbitals
B. there is a similarity between \( 4 f \) and \( 5 f \) orbitals in their angular part of the wave function
C. the actinoids are more reactive than the lanthanoids
D. the \( 5 f \) orbitals extend further from the nucleus than
the \( 4 f \) orbitals
Subject: Chemistry
Blood-red colour in the detection of both
N and S in Lassaigne's extract is due to the formation of
\( \mathbf{A} \cdot F e(C N S)_{2} \)
в. \( F e(C N S)_{3} \)
c. \( K_{4}\left[F e(C N)_{6}\right] \)
D. \( K_{3}\left[F e(C N)_{6}\right] \)
Subject: Physics
Two particle execute \( S H M \) of same amplitude and frequency along the same straight line, They pass one another going in opposite direction each time their displacement is half of their amplitude. The phase difference between them is
A \( \cdot 0^{\circ} \)
B. \( 120^{\circ} \)
\( c \cdot 180^{\circ} \)
D. \( 135^{\circ} \)
Subject: Maths
State the following statement is True or
False

The sum of a natural number \( x \) and its
eciprocal is \( \frac{37}{6}, \) then the equation is \( \boldsymbol{x}+\frac{\mathbf{1}}{\boldsymbol{x}}=\frac{\mathbf{3 7}}{\mathbf{6}} \)
A. True
B. False
Subject: Biology
The DNA content of a diploid cell in the G1 phase of the cell cycle is measured If this DNA content is \( X \), then the DNA
content of the same cell at metaphase of meiosis I would be
\( A \cdot 0.5 x \)
B. 0.25 \( x \)
\( c \cdot x \)
D. \( 2 x \)
Subject: Physics
electric field is along negative \( x \) direction and it is constant. A particle having mass \( m \) and charge \( q \) is projected along \( x \) -direction with speed \( V_{0} . \) An additional force \( \overrightarrow{\boldsymbol{F}}=\overrightarrow{\boldsymbol{C}} \times \overrightarrow{\boldsymbol{V}} \) is
acting on the charge where \( \vec{V} \) is velocity vector and \( \vec{C} \) is a constant vector. The
charge comes out of region with speed \( \boldsymbol{V}_{0} \)
\( 2^{\text {as shown in figure, then the }} \)
magnitude of electric field is :
A \( \cdot \frac{3}{8} \frac{m V_{0}^{2}}{q d} \)
B. \( \frac{4}{3} \frac{m V_{0}^{2}}{q d} \)
c. \( \frac{8}{3} \frac{m V_{0}^{2}}{q d} \)
D. Can't be determined
Subject: Maths
The co-ordinates of the vertices \( A, B, C \)
of a triangle are \( (\mathbf{6}, \mathbf{3}),(-\mathbf{3}, \mathbf{5}),(\mathbf{4},-\mathbf{2}) \)
respectively and \( P \) is any point \( (x, y) \)
then the ratio of areas of triangles PBC and ABC is
A \( \cdot|x-y-2|: 7 \)
B \cdot | \( x+y+2 \mid: 7 \)
c. \( |x+y-2|: 7 \)
D. None of these
Subject: Chemistry
At \( 1100^{\circ} \mathrm{C} \), which reaction is
spontaneous to a maximum extent?
A. \( M g O+C \rightarrow M g+C O \)
B. \( Z n O+C \rightarrow Z n+C O \)
c. \( M g O+Z n \rightarrow M g+Z n O \)
D. \( Z n O+M g \rightarrow M g O+Z n \)
Subject: Maths
Solve the differential equation: \( y d x- \)
\( \boldsymbol{x} \boldsymbol{d} \boldsymbol{y}+\boldsymbol{3} \boldsymbol{x}^{2} \boldsymbol{y}^{2} \boldsymbol{e}^{\boldsymbol{x}^{3}} \boldsymbol{d} \boldsymbol{x} \)
A \( \cdot \frac{x}{y}=e^{x^{3}}+c \)
В. \( -\frac{x}{y}=e^{x^{-3}}+c \)
c. \( -\frac{x}{y}=e^{x^{3}}+c \)
D. \( \frac{x}{y}=e^{x^{-3}}+c \)
Subject: Physics
The electron present in excited state of
\( H e^{\oplus \text { ion shows separation on collision }} \)
with an electron having 2.5 eV energy. What will be the minimum value of \( n \) for
this electrons of \( H e^{\oplus} \) ion?
A .4
B. 5
\( c \cdot 6 \)
D. 3
Subject: Physics
Assertion
A wire bent into an irregular shape with
the points \( P \) and \( Q \) fixed. If a current \( I \)
passed through the wire, then the area
enclosed by the irregular portion of the
wire increases.
Reason
Opposite currents carrying wires repel
each other
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
If 10 g of a sample of water contains 16.2 gof \( \boldsymbol{C a}\left(\boldsymbol{H} \boldsymbol{C O}_{3}\right)_{2}, \) then the hardness of
water is:
A. 200 ppm
B. 300 ppm
c. 60 ppm
D. 100 ppm
Subject: Chemistry
The longest wavelength of \( \boldsymbol{H} \boldsymbol{e}^{+} \) in Paschen series is ' \( m \) ' then shortest
wavelength of \( B e^{3+} \) in Paschen series
in terms of ' \( m \) ' is:
A \( \cdot \frac{7}{64} m \)
в. \( \frac{5}{36} m \)
c. \( \frac{64}{7} \) m
D. \( \frac{53}{8} m \)
Subject: Maths
If \( \sum_{n=1}^{5} \frac{1}{n(n+1)(n+2)(n+3)}=\frac{k}{3} \)
then k is equal to?
A \( \frac{55}{336} \)
в. \( \frac{17}{105} \)
c. \( \frac{19}{112} \)
D.
Subject: Physics
A can is taken out from a refrigerator at
\( 0^{\circ} \mathrm{C} . \) The atmospheric temperature is
\( 25^{\circ} \mathrm{C} . \) If \( t_{1} \) is the time taken to heat from
\( 0^{\circ} \mathrm{C} \) to \( 5^{\circ} \) and \( t_{2} \) is the time taken from
\( 10^{\circ} \mathrm{C} \) to \( 15^{\circ} \mathrm{C}, \) then
A \( \cdot t_{1}>t_{2} \)
в. \( t_{1}<t_{2} \)
c \( \cdot t_{1}=t_{2} \)
D. There is no relation
Subject: Chemistry
\( C l_{2} \) gas is obtained by various reaction
select the reactions from the
following(s):
This question has multiple correct options
A. \( K M n O_{4}+ \) conc.HCl \( \triangleq \)
B . \( K C l+K_{2} C r_{2} O_{7}+ \) conc.H \( _{2} S O_{4} \stackrel{\Delta}{\longrightarrow} \)
c. \( M n O_{2}+ \) conc.HCl \( \Delta \)
D. \( K C l+F e_{2}\left(S O_{4}\right)_{3} \rightarrow \)
Subject: Maths
Time period \( T \) of a simple pendulum of length \( l \) is given by \( T=2 \pi \sqrt{\frac{l}{g}} . \) If the length is increased by \( 2 \% \), then an approximate change in the time period
is
A . \( 2 \% \)
B . \( 1 \% \)
c. \( \frac{1}{2} \% \)
D. None of these
Subject: Maths
If the roots of the equation
\( (x-a)(x-b)+(x-b)(x-c)+ \)
\( (x-c)(x-a)=0 \) are equal, then
\( a^{2}+b^{2}+c^{2} \) is equal to
\( \mathbf{A} \cdot a+b+c \)
B . \( 2 a+b+c \)
c. \( 3 a b c \)
D. \( a b+b c+c a \)
E \( . a b c \)
Subject: Physics
If the uncertainty in the position of proton is \( 6 \times 10^{-8} m, \) then the
minimum uncertainty in its speed will
be:
A \( \cdot 1 \mathrm{cms}^{-1} \)
В. \( 0.52 \mathrm{ms}^{-1} \)
\( \mathbf{c} \cdot 1 \mathrm{mms}^{-1} \)
D. \( 100 \mathrm{ms}^{-1} \)
Subject: Physics
toppr \( E \)
\( Q \) тур
Note: the rate-flow vectors are not drawn
to scale. Identify the case(es) in which the
effective current through the conductor is the highest.
\( \mathbf{A} \)
\[
\begin{array}{l}
\odot 5 \mathrm{c} / \mathrm{s} \\
5 \mathrm{c} / \mathrm{s} \longleftrightarrow
\end{array}
\]
в.
\[
\Leftrightarrow 9 \mathrm{c} / \mathrm{s}
\]
\[
1 \mathrm{c} / \mathrm{s} \longleftrightarrow
\]
\( c \)
\[
\begin{array}{l}
\Leftrightarrow 7 \mathrm{c} / \mathrm{s} \\
3 \mathrm{c} / \mathrm{s} \longleftrightarrow(\oplus)
\end{array}
\]
D
\[
\Leftrightarrow 1 \mathrm{C} /
\]
\[
\text { 9 C/s } \longleftarrow
\]
Subject: Maths
The \( 4 t h \) term from the end in the
expansion of \( \left(\frac{x^{3}}{2}-\frac{2}{x^{2}}\right)^{7} \) is
A . \( 35 x \)
B. \( 70 x^{2} \)
\( c \cdot 35 x^{2} \)
D. \( 70 x \)
Subject: Chemistry
Which of the following metal sulphides
has maximum solubility in water?
\( \mathbf{A} \cdot C d S\left(K_{s p}=36 \times 10^{-30}\right) \)
B \( \cdot \operatorname{Fe} S\left(K_{s p}=11 \times 10^{-20}\right) \)
\( \mathbf{c} \cdot H g S\left(K_{s p}=32 \times 10^{-54}\right) \)
D. \( Z n S\left(K_{s p}=11 \times 10^{-22}\right) \)
Subject: Maths
Let \( z \) be a complex number such that the imaginary part of z is nonzero and a \( =z^{2}+z+1 \) is real. Then a cannot take
the value
A . -1
B. \( \frac{1}{3} \)
\( c \cdot \frac{1}{2} \)
D. \( \frac{3}{4} \)