AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A spherical capacitor consists of two
concentric spherical conductors, held in
position by suitable insulating
supports (Fig.). Show that the
capacitance of a spherical capacitor is
given by \( c=\frac{4 \pi \epsilon_{0} r_{1} r_{2}}{r_{1}-r_{2}} \)
where \( r_{1} \) and \( r_{2} \) are the radii of outer
and inner spheres, respectively.
Subject: Physics
Acceleration due to gravity as a
function of \( r \) is given by
A \( \cdot \frac{4}{3} \pi G r(A-B R) \)
B . \( 4 \pi G r(A-B R) \)
c. \( \frac{4}{3} \pi G r\left(A-\frac{3}{4} B R\right) \)
D \( \cdot \frac{4}{3} \pi G r\left(A-\frac{4}{3} B R\right) \)
Subject: Chemistry
Assertion
When small amount of acid or base is
added to pure water, its pH undergoes a change.
Reason
Addition of an acid or a base increases
the degree of ionisation of water.
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
A \( \cdot t^{2}+3,-t^{3}-1 \)
B. \( 4 t^{2}+3,-8 t^{2}-1 \)
\( \mathbf{C} \cdot t^{2}+3, t^{3}-1 \)
D. \( 16 t^{2}+3,-64 t^{3}-1 \)
Subject: Physics
A planet of mass \( m \) is moving in an elliptical orbit round the sun of mass
\( M . \) If the maximum and minimum
distances of the planet from the sun be
\( l_{1} \) and \( l_{2}, \) the angular momentum of
the planet about the sun will be
A \( \cdot m \frac{G M m}{\sqrt{\left(l_{1}+l_{2}\right)}} \)
в. \( m \sqrt{\frac{l_{1}+l_{2}}{G M l_{1} l_{2}}} \)
c. \( m \sqrt{\frac{2 G M l_{1} l_{2}}{\left(l_{1}+l_{2}\right)}} \)
\( D \)
Subject: Physics
In a p-njunction having depletion layer
of thickness \( 10^{-6} m \), the potential
across it is \( 0.1 \mathrm{V} \). The electric field is
A \( \cdot 10^{7} V / m \)
В \( \cdot 10^{-6} V / m \)
c. \( 10^{5} V / m \)
D. \( 10^{-5} V / m \)
Subject: Physics
A body is projected at an angle of \( 60^{\circ} \) with the horizontal. If its kinetic energy at maximum height is \( 10 \mathrm{J} \), then the height at which potential energy and kinetic energy have equal values (consider P.E. at the point of projection to be zero) is :
A. half of the maximum height
B. two third of the maximum height
c. one sixth of the maximum height
D. insufficient data to solve the problem.
Subject: Physics
A wire of length \( l \) carries a current \( i \) along x-axis. A magnetic field exits given by \( \boldsymbol{B}=\boldsymbol{B}_{0}(\hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}}) \boldsymbol{T} \). The
magnitude of the magnetic force acting on the wire is
A \( . i l B_{0} \)
в. \( \sqrt{3} B_{0} \) il
c. \( 2 i l B_{0} \)
D. \( \sqrt{2} B_{0} \) il
Subject: Chemistry
Among the electrolytes,
\( N a_{2} S O_{4}, C a C l_{2}, A l_{2}\left(S O_{4}\right)_{3} \) and
\( N H_{4} C l, \) the most effective coagulating
agent for \( S b_{2} S_{3} \) solution is:
A \( \cdot N a_{2} S O_{4} \)
в. \( C a C l_{2} \)
\( \mathbf{c} \cdot A l_{2}\left(S O_{4}\right) \)
D. \( N H_{4} C l \)
Subject: Physics
A solid sphere of mass \( M, \) radius \( R \) and having moment of inertia about an axis passing through the centre of mass as \( I, \) is recast into a disc of thickness \( t \)
whose moment of inertia about an axis
passing through its edge and perpendicular to its plane remains \( \boldsymbol{I} \)
Then, radius of the disc will be:
A \( \cdot \frac{2 R}{\sqrt{15}} \)
B. \( R \sqrt{\frac{2}{15}} \)
c. \( \frac{4 R}{\sqrt{15}} \)
D. \( \frac{R}{4} \)
Subject: Physics
An electron is taken from point \( A \) to
point \( B \) along the path \( A B \) in a uniform
electric field of intensity \( \boldsymbol{E}=\mathbf{1 0} \boldsymbol{V m}^{-1} \)
Side \( A B=5 m, \) and side \( B C=3 m \)
Then, the amount of work done on the
electron by us is :
A. 50 ev
B. 40 ev
c. - -50 ev
D. -40 eV
Subject: Chemistry
Consider the following statements
(i) Out of two \( -N H_{2} \) groups in semicarbazide only one is involved in formation of semicarbazones.
(ii) Cyclohexane froms cyanohydrin in good yield but \( 2,2,6- \)
trimethylcyclohexanone does not.
(iii) The \( \alpha- \)hydrogens in aldehydes
and ketones are acidic.
A. i and iii
B. ii and iii
c. i and i i
D. i, ii and iii
Subject: Physics
Two short dipoles are situated parallel
to each other separated by a distance \( x \)
The force of interaction is
A \( \cdot \) A force of attraction of \( \frac{2 K p_{1} p_{2}}{x^{4}} \)
B. A force of repulsion of \( \frac{2 K p_{\eta} p_{2}}{x^{4}} \)
C . A force of attraction of \( \frac{3 K p_{1} p_{2}}{x^{4}} \)
D. A force of repulsion of \( \frac{3 K p_{\eta} p_{2}}{x^{4}} \)
Subject: Maths
Arrange the ellipses in ascending order of their eccentricities when \( \angle S B S^{1} \) is
given, where \( S \& S^{1} \) are foci and \( B \) is
one end of the minor axis. For the four
ellipses \( \boldsymbol{A}, \boldsymbol{B}, \boldsymbol{C}, \boldsymbol{D} \angle \mathbf{S B S}^{1}= \)
\( \mathbf{2 0}^{\mathbf{0}}, \mathbf{6 0}^{\mathbf{0}}, \mathbf{3 0}^{\mathbf{0}}, \mathbf{9 0}^{\mathbf{0}} \)
\( A \cdot A, C, B, D \)
B. D, B, C, A
c. \( B, D, C, A \)
D. \( A, C, D, B \)
Subject: Biology
Match the enzymes in column I with
their respective biochemical reactions
in column II. Choose the correct
combination from.
Column I
(P)
(i) removal of phosphory Transaminases
acid group from a specific amino
(Q) Protein
(ii) removal of \( \alpha \) -amino group Kinases acid \( \quad \) from a specific amino
(R) Protein
(iii) addition of phosphoryl Phosphatases froup to a specific amino acid
\( (s) \)
(iv) interconversion of optical Dehydrogenases isomers
(v) oxidation and reduction of substrates
A. P-iv, Q-ii, R-iii, S-v
B. P-ii, Q-i, R-ii, S-iv
c. P-ii, Q-iii, R-i, S-v
D. P-v, Q-ii, R-iii, S-i
Subject: Chemistry
Yellow precipitate in the detection of phosphorous when an organic
compound is heated with \( N a_{2} O_{2} \) and
then boiled with conc. \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \) followed
by the addition of ammonium molybdate is due to the formation
of
A \( \cdot\left(N H_{4}\right)_{3} \cdot P O_{4} \cdot 12 M o O_{3} \)
B . \( \left(N H_{4}\right)_{3} \cdot P O_{4} \cdot 6 M o O_{3} \)
c. \( \left(N H_{4}\right)_{3} \cdot P O_{4} \cdot 12 M o O_{2} \)
D. \( \left(N H_{4}\right)_{3} P O_{4} \cdot 6 M o O_{2} \)
Subject: Maths
The differential equation by eliminating
\( \boldsymbol{a}, \boldsymbol{b} \) from \( (\boldsymbol{x}-\boldsymbol{a})^{2}+(\boldsymbol{y}-\boldsymbol{b})^{2}=\boldsymbol{r}^{2} \) is
\( \mathbf{A} \cdot\left(1-\left(y_{1}\right)^{2}\right)^{3}=r^{2}\left(y_{2}\right)^{2} \)
B . \( \left(1+\left(y_{1}\right)^{2}\right)^{3}=r^{2}\left(y_{2}\right)^{2} \)
C. \( \left(1+\left(y_{1}\right)^{2}\right)^{3}=r y^{2} \)
D. \( y_{1}^{2}=r y^{2} \)
Subject: Maths
Find the modulus, argument and the principal argument of the complex numbers.
\( (\tan 1-i)^{2} \)
A. Modulus\( =\sec ^{2} 1, \operatorname{Arg}(z)=2 n \pi+(2- \)
\( \pi \) ), Principal \( \operatorname{Arg}(z)=(2-\pi) \)
B. Modulus = \( \operatorname{cosec}^{2} 1, \) Arg\( (z)=2 n \pi-(2- \)
\( \pi), \) Principal \( \operatorname{Arg}(z)=(-2-\pi) \)
C. Modulus\( =\sec ^{2} 1, \operatorname{Arg}(z)=2 n \pi-(2- \)
\( \pi), \) Principal \( \operatorname{Arg}(z)=(-2-\pi) \)
D. Modulus \( =\operatorname{cosec}^{2} 1, \) Arg\( (z)=2 n \pi+(2- \)
\( \pi), \) Principal \( \operatorname{Arg}(z)=(2-\pi) \)
Subject: Maths
\( \operatorname{Matrix} \boldsymbol{A}=\left[\begin{array}{ccc}\boldsymbol{x} & \boldsymbol{3} & \boldsymbol{2} \\ \boldsymbol{1} & \boldsymbol{y} & \boldsymbol{4} \\ \boldsymbol{2} & \boldsymbol{2} & \boldsymbol{z}\end{array}\right], \) if \( \boldsymbol{x} \boldsymbol{y} \boldsymbol{z}=\boldsymbol{6} \mathbf{0} \)
and \( 8 x+4 y+3 z=20, \) then \( A(a d j A) \)
is equal to
A. \( \left|\begin{array}{lll}64 & 0 & 0 \\ 0 & 64 & 0 \\ 0 & 0 & 64\end{array}\right| \)
B. \( \mid \begin{array}{ccc}68 & 0 & 0 \\ 0 & 68 & 0 \\ 0 & 0 & 68\end{array} \)
\begin{tabular}{l|lll}
38 & 0 & 0 \\
0 & 38 & 0 \\
0 & 0 & 38
\end{tabular}
D. \( \mid \begin{array}{ccc}32 & 0 & 0 \\ 0 & 32 & 0 \\ 0 & 0 & 32\end{array} \)
Subject: Chemistry
The concentration of \( N H_{3} \) solution
whose one litre can dissolve 0.10 mole
AgCl is:
\( \left[\boldsymbol{K}_{s p} \text { of } \boldsymbol{A} \boldsymbol{g} \boldsymbol{C l} \text { and } \boldsymbol{K}_{\boldsymbol{f}} \text { of } \boldsymbol{A} \boldsymbol{g}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{2}^{+}\right. \)
\( \operatorname{are} 10^{-10} M^{2} \) and \( 1.6 \times 10^{7} M^{-2} \)
respectively].
\( \mathbf{A} \cdot 2.5 M \)
B. \( 3.0 M \)
c. \( 2.8 M \)
D. none of these
Subject: Maths
\( \int(g(x)+1) \sin x d x \) is equal to
A \( \frac{e^{x}}{2}(\sin x-\cos x)+c \)
B. \( \frac{e^{2 x}}{5}(2 \sin x-\cos x)+c \)
c. \( \frac{e^{x}}{5}(\sin 2 x-\cos 2 x)+c \)
D. none of these
Subject: Maths
A square non-singular matrix A satisfies \( \boldsymbol{A}^{2}-\boldsymbol{A}+\boldsymbol{2} \boldsymbol{I}=\boldsymbol{0}, \) then \( \boldsymbol{A}^{-1}= \)
\( \mathbf{A} \cdot I-A \)
B \( \cdot \frac{1}{2}(I-A) \)
c. \( I+A \)
D \( \cdot \frac{1}{2}(I+A) \)
Subject: Physics
Four charges, all of the same magnitude, are placed at the four corners of a square. At the centre of the
square, the potential is \( \mathrm{V} \) and the field
is E. With suitable choices of the signs of the four charges, which of the following can be obtained? This question has multiple correct options
A. \( V=0, E=0 \)
B. \( V=0, E \neq 0 \)
c. \( V \neq 0, E=0 \)
D. \( V \neq 0, E \neq 0 \)
Subject: Physics
The \( I-V \) characteristics of a metal
wire at two different temperatures \( \left(T_{1}\right. \)
and \( T_{2} \) ) are given in the adjoining
figure. Here, we can conclude that:
\( A \cdot T_{1}>T_{2} \)
в. \( T_{1}<T_{2} \)
\( c \cdot T_{1}=T_{2} \)
D \( \cdot T_{1}=2 T_{2} \)
Subject: Physics
A bimetallic strip of steel and brass of length \( 10 \mathrm{cm}, \) initially at \( 15^{\circ} \mathrm{C}, \) is heated to \( 45^{\circ} \mathrm{C} \). What is the difference in length
between the two substances after they have been heated? The coefficient of
linear expansion for steel is \( 1.2 \times \) \( 10^{5} / C^{o}, \) and the coefficient of linear
expansion for brass is \( 1.9 \times 10^{5} / C^{o} \)
Subject: Maths
Express the following angles in degrees.
\( \begin{array}{ll}\text { (1) } & \left(\frac{5 \pi}{12}\right)^{\circ}\end{array} \)
(2) \( -\left(\frac{7 \pi}{12}\right)^{\circ} \)
(3) \( \frac{\pi}{3} \)
(4) \( \frac{5 \pi^{\circ}}{6} \)
(5) \( \frac{2 \pi^{\circ}}{9} \)
(6) \( \frac{7 \pi^{\circ}}{24} \)
Subject: Chemistry
\[
\boldsymbol{C H}_{3}-\boldsymbol{N H}_{2} \quad \boldsymbol{C H}_{3}-\boldsymbol{N H}-\boldsymbol{C H}_{3}
\]
\( \boldsymbol{C H}_{3}-\boldsymbol{N}-\boldsymbol{C H}_{3} \)
\( \boldsymbol{C H}_{3} \)
Compare boiling points of the given compounds:
Subject: Physics
Two billiard balls undergo a head-on collision. Ball 1 is twice as heavy as ball
2. Initially, ball 1 moves with a speed \( v \)
toward ball 2 which is at rest.
Immediately after collision, ball 1 travels at a speed of \( v / 3 \) in the same
direction. What type of collision has occured?
A. inelastic
B. elastic
c. completely inelastic
D. cannot be determined from the information giver
Subject: Maths
In a group of 400 people, 160 are
smokers and non-vegetarian, 100 are smokers and vegetarian and the remaining are non-smokers and vegetarian. The probabilities of getting a special chest disease are \( 35 \%,, 20 \% \)
and \( 10 \% \) respectively. A person is chosen from the group at random and is
found to be suffering from the disease. What is the probability that the selected person is a smoker and non-
vegetarian?
Subject: Chemistry
Identify the compounds \( A, B \) and \( C \)
(i) \( \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{O} \boldsymbol{H} \quad \boldsymbol{P C l}_{5} \quad \boldsymbol{A} \quad \boldsymbol{K} \boldsymbol{C} \boldsymbol{N} \)
(ii) \( \boldsymbol{C}_{6} \boldsymbol{H}_{5} \boldsymbol{C O O H} \quad \boldsymbol{S O C l}_{2}, \boldsymbol{A} \quad \boldsymbol{N H}_{3} \)
Subject: Physics
A block of mass \( 3 k g \) is released from
the rest at top of the inclined plane. If length and height of the inclined plane is \( 6 \mathrm{m} \) and \( 4 \mathrm{m} \) respectively. Calculate its speed at the bottom of inclined plane. Assume the force of friction 16 \( \mathrm{N} \)
on the block is a constant.
A. \( 2 \mathrm{m} / \mathrm{s} \)
B. 3 \( \mathrm{m} / \mathrm{s} \)
\( c \cdot 4 m / s \)
\( D \cdot 5 m / s \)
E. \( 6 \mathrm{m} / \mathrm{s} \)
Subject: Physics
An object moving with a speed of 6.25 \( \mathrm{m} / \mathrm{s}, \) is decelerated at a rate given by \( \frac{d v}{d t}=-2.5 \sqrt{v} \) where \( v \) is the instantaneous speed. The time taken by the object, to come to rest, would be then
\( \mathbf{A} \cdot 2 s \)
B . \( 4 s \)
c. \( 8 s \)
D. \( 1 s \)
Subject: Physics
You have to design a compound microscope with objective lens of focal length \( 1 \mathrm{cm} . \) The object should be placed at \( \ldots . . . \) distance from the lens.
\( A \cdot 8 m m \)
B. \( 11 \mathrm{mm} \)
c. \( 22 \mathrm{mm} \)
D. \( 2 \mathrm{cm} \)
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{cc}-\mathbf{1} & \mathbf{2} \\ \mathbf{3} & \mathbf{4}\end{array}\right] \) and \( \boldsymbol{B}=\left[\begin{array}{cc}\mathbf{3} & -\mathbf{2} \\ \mathbf{1} & \mathbf{5}\end{array}\right] \)
\( \mathbf{2} \boldsymbol{A}+\boldsymbol{B}+\boldsymbol{X}=\mathbf{0}, \) then the matrix \( \boldsymbol{X} \) is
A. \( \left[\begin{array}{ll}1 & 2 \\ 7 & 13\end{array}\right] \)
B. \( \left[\begin{array}{cc}-1 & 2 \\ 7 & -13\end{array}\right] \)
\( \mathbf{c} \cdot\left[\begin{array}{cc}-1 & -2 \\ 7 & 13\end{array}\right] \)
D. \( \left[\begin{array}{cc}-1 & -2 \\ -7 & -13\end{array}\right] \)
Subject: Maths
The \( G . M . \) of the numbers
\( \mathbf{3}, \mathbf{3}^{2}, \mathbf{3}^{3}, \dots, \mathbf{3}^{n} \) is
A \( \cdot \frac{2}{n} \)
в. \( \frac{n-1}{2} \)
c. \( \frac{n}{3} \)
D. \( \frac{n+1}{2} \)
Subject: Maths
Relation \( \boldsymbol{R} \) in the set \( \boldsymbol{Z} \) of all integers
defined as \( \boldsymbol{R}= \)
\[
\{(x, y):(x-y) \text { is an integer }\}
\]
enter 1 -reflexive and transitive but not
symmetric 2-reflexive only 3-Transitive only 4-Equivalence
5-None
Subject: Physics
The frequencies of two sound sources are \( 256 \mathrm{Hz} \) and \( 260 \mathrm{Hz}, \) At \( \mathrm{t}=0, \) the intensity of sound is maximum. Then
the phase differance at the time \( t=1 / 16 \)
sec will be
A. zero
в. \( \pi \)
c. \( \pi / 2 \)
D. \( \pi / 4 \)
Subject: Chemistry
When \( N a N O_{3} \) is heated in a closed
vessel, \( O_{2} \) is liberated and \( N a N O_{2} \) is left behind. At equilibrium:
A. addition of \( N a N O_{2} \) favours reverse reaction
B. addition of \( N a N O_{3} \) favours forward reaction
c. increasing temperature favours forward reaction
D. increasing pressure favours forward reaction
Subject: Physics
A wire loop \( P Q R S \) formed by joining
two semi-circular wires of radii \( \boldsymbol{R}_{1} \) and
\( R_{2} \) carries a current \( I \) as shown in the
following diagram. The magnetic
induction at the centre \( O \) is
A \( \cdot \frac{\mu_{0} I}{4 R_{1}} \)
в. \( \frac{\mu_{0} I}{4 R_{2}} \)
c. \( \frac{\mu_{0}}{4 \pi} I\left(\frac{1}{R_{1}}-\frac{1}{R_{2}}\right) \)
D \( \cdot \frac{\mu_{0}}{4} I\left(\frac{1}{R_{1}}+\frac{1}{R_{2}}\right) \)
Subject: Chemistry
The correct order of energy of orbitals in
octahedral complex is:
A \( \cdot d_{x^{2}-y^{2}}=d_{z^{2}}>d_{x y}=d_{y z} \)
В . \( d_{z^{2}}>d_{x y}>d_{x^{2}-y} \)
c. \( d_{z^{2}}=d_{x y}>d_{x^{2}-y^{2}} \)
D. \( d_{x^{2}-y^{2}}>d_{x y}>d_{y z} \)
Subject: Maths
Area of the region bounded by \( \boldsymbol{y}=|\boldsymbol{x}| \)
and \( \boldsymbol{y}=\mathbf{1}-|\boldsymbol{x}| \) is
A \( \cdot \frac{1}{3} \) sq. units
B. 1 sq. units
c. \( \frac{1}{2} \) sq. unit
D. 2 sq. units
Subject: Maths
A triangle has vertices at \( (\mathbf{6}, \mathbf{7}),(\mathbf{2},-\mathbf{9}) \)
and \( (-4,1) . \) Find the slope of its sides.
A \( \cdot \frac{11}{7},-13,-\frac{1}{4} \)
в. \( \frac{11}{7}, 13,-\frac{1}{4} \)
c. \( \frac{11}{7},-13, \frac{1}{4} \)
D. None of these
Subject: Physics
The position of a particle along \( x \) -axis at
time \( t \) is given by \( x=1+t-t^{2} \). the
distance travelled by the particle on first 2 second is
A. \( 1 \mathrm{m} \)
B. 2 \( m \)
c. \( 2.5 \mathrm{m} \)
D. 3 \( m \)
Subject: Maths
Let \( S_{1}, S_{2}, \dots . S_{n} \) be squares such that
for each \( n \geq 1, \) the length of a side of \( S_{n} \) equals the length of the diagonal of
\( S_{n+1} . \) If the length of a side of \( S_{1} \) is \( 10 \mathrm{cm}, \) then the least value of \( n \) for
which the area of \( S_{n} \) less than 1 sq \( c m \)
A. 7
B. 8
c. 9
D. 10
Subject: Physics
If a metallic sphere gets cooled from
\( 62^{\circ} \mathrm{C} \) to \( 50^{\circ} \mathrm{C} \) in \( 10 \mathrm{min} \) and in the next
10 min gets cooled to \( 42^{\circ} \mathrm{C} \), then the temperature of the surroundings is
A \( \cdot 30^{\circ} \mathrm{C} \)
B . \( 36^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 26^{\circ} C \)
D. \( 20^{\circ} \mathrm{C} \)
Subject: Chemistry
In a photoemissive cell with executing wavelength \( \lambda \), the fastest electron has to speed v. If the exciting wavelength is changed to \( \frac{3 \lambda}{4}, \) the speed of the fastest emitted electron will be:
\( ^{\mathrm{A}} v\left(\frac{3}{4}\right)^{1 / 2} \)
в. \( _{v}\left(\frac{4}{3}\right)^{1 / 2} \)
\( ^{\mathrm{c}} \cdot \operatorname{lessthan} v\left(\frac{4}{3}\right)^{1 / 2} \)
D. greater than \( v\left(\frac{4}{3}\right)^{1 / 2} \)
Subject: Maths
Show that:
\( \int_{-a}^{a} f(x) d x=2 \int_{0}^{a} f(x) d x, \) if \( f(x) \) is an
even function. \( \boldsymbol{I}=\mathbf{0}, \) if \( \boldsymbol{f}(\boldsymbol{x}) \) is an odd
function.
Subject: Physics
When an ac source of voltage \( \boldsymbol{V}= \)
\( V_{0} \sin 100 t \) is connected across a
circuit, the phase difference between
the voltage \( V \) and current lin the circuit
is observed to be \( \pi / 4, \) as shown in
figure. If the circuit consists
possibly only of RC or RL or LC in series,
find possible values of two elements.
A \( . R=1 k \Omega, C=10 \mu F \)
B. \( R=1 k \Omega, C=1 \mu F \)
c. \( R=1 k \Omega, L=10 m H \)
D. \( R=10 k \Omega, L=10 m H \)
Subject: Chemistry
The freezing point of equimolal aqueous solution will be highest for :
A. \( C_{6} H_{5} N H_{3} C l \)
в. \( C a\left(N O_{3}\right)_{2} \)
c. \( L a\left(N O_{3}\right)_{3} \)
D. \( C_{6} H_{12} O_{6} \)
Subject: Maths
If \( \bar{a}=\bar{i}+\bar{j}+t \bar{k} \) and \( \bar{b}=\bar{i}+2 \bar{j}+3 \bar{k} \)
then the value of \( t \) for which \( \bar{a}+\bar{b} \) and
\( \bar{a}-\bar{b} \) are perpendicular is
\( A \ldots \pm 2 \)
В. \( \pm 2 \sqrt{2} \)
\( \mathbf{c} \cdot \pm 2 \sqrt{3} \)
\( \mathrm{D} \cdot \pm 3 \)
Subject: Physics
Six particles situated at the corners of a regular hexagon of side \( a \) move at a
constant speed \( v \). Each particle maintains a direction towards the
particle at the next corner. Calculate the time the particles will take to meet each other.
A \( \cdot \frac{2 a}{3 v} \)
в. \( \frac{v}{a} \)
c. \( \frac{2 a}{v} \)
D. \( \frac{a}{3 v} \)
Subject: Chemistry
Dual behaviour of the matter proposed by de Broglie led to the discovery of electron microscope often used for the highly magnified images of biological molecules and other types of material. If the velocity of the electrons in this
microscope is \( 1.6 \times 10^{6} m s^{-1} \)
calculate de Broglie wavelength associated with this electron.
A. 325 pm
B. 455 pm
C. \( 474 \mathrm{pm} \)
D. 526 pm
Subject: Chemistry
Which two orbitals are located along the
axis, and not between the axis?
\( \mathbf{A} \cdot d_{x^{2}-y^{2}}, d_{z^{2}} \)
B . \( d_{x y}, p_{z} \)
\( \mathbf{c} \cdot d_{y z}, p_{x} \)
D. \( d_{y z}, d_{x^{2}-y^{2}} \)
Subject: Physics
A planet in its elliptical orbit has the
farthest distance from the sun(r, \( ) \)
equal to three times its nearest
distance from the sun(r \( _{2} \) ). Will the
orbital speed of the planet be different
at those points?
A. Orbital velocity at nearest point will be twice that at farthest point
B. orbital velocity at nearest point will be thrice that at farthest point
c. orbital velocity at farthest point will be thrice that at nearest point
D. orbital velocity will be same, since no other force acts on the planet
Subject: Chemistry
Match List-I (Compounds) with List-I
(Oxidation states of Nitrogen) and
select answer using the codes
given below the lists.
\begin{tabular}{llll} 
List - 1 & & List - II \\
\hline\( (a) \) & \( \mathrm{NaN}_{3} \) & (1) & +5 \\
\( (b) \) & \( \mathrm{N}_{2} \mathrm{H}_{2} \) & (2) & +2 \\
\( (c) \) & \( \mathrm{NO} \) & (3) & \( -\frac{1}{3} \) \\
\( (d) \) & \( \mathrm{N}_{2} \mathrm{O}_{5} \) & (4) & -1
\end{tabular}
\( A \)
\( a-3 \quad b-4 \quad c-2 \)
\( \begin{array}{llll}\text { В. } a-4 & b-3 & c-2 & d-1\end{array} \)
\( d-2 \)
2 \( c-1 \) \( b-4 \)
c. \( a-3 \)
\( \begin{array}{llll}\text { D. } a-4 & b-3 & c-1 & d-2\end{array} \)
Subject: Physics
The specific resistance of the material
of a wire is \( \rho, \) its volume is \( 3 m^{3} \) and its
resistance is \( 3 \Omega \). The length of the wire will be
A \( \cdot \frac{\sqrt{1}}{\rho} \)
B. \( \frac{3}{\sqrt{\rho}} \)
c. \( \frac{1}{\rho} \sqrt{3} \)
D. \( \rho \sqrt{\frac{1}{3}} \)
Subject: Physics
After falling from rest through a height
\( h, \) a body of mass \( m \) begins to raise a body of mass \( M(M>m) \) connected to
it through a pulley. Find the fraction of kinetic energy lost when the body of mass \( M \) is jerked into motion.
A \( \cdot \frac{M}{M+m} \)
в. \( \frac{M}{M-m} \)
c. \( \frac{2 M}{M+m} \)
D. \( \frac{M}{2(M+m)} \)
Subject: Maths
The donations given to an orphanage home by the students of different classes of a secondary school are given below.
\( \begin{array}{ll}\text { Class } & \text { Donation by each } \\ & \text { students }(\text { in } R s)\end{array} \) No. of
students
donated
\( _{5} \) vı vıl 7 vııl 10 Ix 15 \( x \) 20
Find the mean, median and mode of the
data
A. Rs.11.26, Median = Rs.10; Mode = Rs.10
B. \( R s .1 .26, \) Median \( =R s .10 ; \) Mode \( =R s .10 \)
c. \( R s .11 .26, \) Median \( =R s .20 ; \) Mode \( =R s .10 \)
D. None of these
Subject: Physics
and that of an ideal Voltmeter is
infinite. A Voltmeter and an Ammeter
are connected in the circuit as shown.
Resistance of ammeter is say \( \boldsymbol{R} / \mathbf{1} \mathbf{0} \) and
that of Voltmeter is \( 10 R \). Then:
A. Percentage error in the reading of Ammeter (compared to that measured, if both Ammeter and voltmeter were ideal) is \( 1.0 \% \)
B. Percentage error in the reading of voltmeter is \( 10.0 \% \)
c. Both (a) and
(b) are correct
D. Both
(a) and
(b) are wrong
Subject: Physics
The radius of hollow metallic sphere is \( r \) If the potential difference between its surface and a at a distance \( 3 r \) from its
centre is v then the electric field
intensity at a distance of \( 3 r \) its centre is:
A. v/2r
B. \( \vee / 3 \) r
c. \( \vee / 4 r \)
D. V/6
Subject: Maths
When \( x=2, \) the value of the
expression \( 4 x^{2}+\frac{9}{x^{2}}-12 \) is:
A \( \cdot \frac{25}{4} \)
в. \( \frac{-4}{25} \)
c. \( \frac{4}{25} \)
D. \( \frac{-25}{4} \)
Subject: Physics
In an ac circuit, \( \mathrm{V} \) and I are given by \( \boldsymbol{V}=\mathbf{1 5 0} \sin (\mathbf{1 5 0} \boldsymbol{t}) \boldsymbol{V} \boldsymbol{a n d} \boldsymbol{I}= \)
\( 150 \sin \left(150 t+\frac{\pi}{3}\right) A \)
The power dissipated in the circuit is
A . \( 106 \mathrm{w} \)
B. 150 \( \mathrm{w} \)
c. \( 5625 \mathrm{w} \)
D. zero