AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
kept in two identical vessels, which are
placed in a freezer that extracts heat
from them at the same rate causing
each liquid to transform into a solid.
The schematic figure shows the
temperature T vs time t plot for the two
materials. We denote the specific heat
in the liquid states to be \( C_{L 1} \) and \( C_{L 2} \)
for materials 1 and 2 respectively, and
latent heats of fusion \( U_{1} \) and \( U_{2} \)
respectively. Choose the correct option.
A. \( C_{L 1}>C_{L 2} \) and \( U_{1}<U_{2} \)
B. \( C_{L 1}>C_{L 2} \) and \( U_{1}>U_{2} \)
\( \mathbf{c} \cdot C_{L 1}<C_{L 2} \) and \( U_{1}>U_{2} \)
D. \( C_{L 1}<C_{L 2} \) and \( U_{1}<U_{2} \)
Subject: Biology
Q Type your question_
木政
,
Classification of representative
mammals.
\( \begin{array}{lll}\text { Kingdom } & \text { Animalia } & \text { Animalia } \\ \text { Phylum } & \text { Chordata } & \text { Chordata } \\ \text { Class } & \text { Mammalia } & \text { Mammalia } \\ \text { Order } & \text { Cetacea } & \text { Carnivora } \\ \text { Family } & \text { Mysticeti } & \text { Felidae } \\ \text { Genus } & \text { Balenopora } & \text { Felis } \\ \text { Species } & \text { B. physaius } & \text { F. catus } \\ \text { Common name } & \text { Blue Whale } & \text { Cat }\end{array} \)
\( A \)
Family
B. Kingdom
c. Species
D. Order
E. Class
Subject: Chemistry
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{X}+\boldsymbol{K O H}(\boldsymbol{a l} \boldsymbol{c}) \rightarrow \)
\( \boldsymbol{C H}_{2}=\boldsymbol{C H}_{2}+\boldsymbol{K} \boldsymbol{X}+\boldsymbol{H}_{2} \boldsymbol{O} \)
These type of reactions are called
A. addition reactions
B. substitution reactions
c. elimination reactions
D. molecular rearrangement
Subject: Chemistry
The resistance of two electrolytes \( X \) and
Y were found to be 45 and 100
respectively when equal volumes
of both the solutions were taken in the
same cell in two different experiments.
If equal volumes of these solutions are mixed in the same cell, what will be the
conductance of the mixture?
\( A \cdot 0.032 \mathrm{mho} \)
B. 0.048 mho
c. 0.026 mho
D. 0.016 mho
Subject: Maths
Given an angle \( \theta, \) which of the following angles cannot be obtained by using the method of construction of angle bisectors?
\( A \cdot \frac{\theta}{2} \)
в. \( \frac{\theta}{4} \)
\( c \cdot \frac{\theta}{6} \)
\( D \cdot \frac{\theta}{8} \)
Subject: Chemistry
On addition of \( \operatorname{conc} . H_{2} S O_{4} \) to a
chloride salt, colourless fumes are
evolved but in case of iodide salt, violet
fumes come out. This is because:
A. \( H_{2} S O_{4} \) reduces HI to \( I_{2} \)
B. \( H I \) is of violet colour
C. \( H I \) gets oxidised to \( I_{2} \)
D. \( H I \) changes to \( H I O_{3} \)
Subject: Physics
A uniform vertical field \( E \) is established
between two parallel plates. In this field, a small conducting sphere of mass \( \boldsymbol{M} \)
is suspended from a string of length \( l \). If the sphere is given a charge \( +q \) (statcoulomb) and if lower plate is charged
positively, the period of the simple pendulum is:
A \( .2 \pi \sqrt{l / g} \)
\( ^{\mathrm{B}} \cdot 2 \pi \sqrt{\frac{l}{\left(g+\frac{q E}{m}\right)}} \)
c.
\[
\sqrt[2 \pi]{\frac{l}{\left(g-\frac{q E}{m}\right)}}
\]
\( D \)
\[
\sqrt{\frac{l}{\left(\frac{q E}{m}-g\right)}}
\]
Subject: Chemistry
Which are correct statements?
This question has multiple correct options
\( \mathbf{A} \cdot\left[A g\left(N H_{3}\right)_{2}\right]^{+} \) is linear with sp hybridised \( A g^{+} \) ion.
B. \( N i C l_{4}^{2-}, V O_{4}^{3-} \) have tetrahedral geometry.
\( \mathbf{C} \cdot\left[C u\left(N H_{3}\right)_{4}\right]^{2+},\left[P t\left(N H_{3}\right)_{4}\right]^{2+} \) and \( \left[N i(C N)_{4}\right]^{2-} \) have
\( d s p^{2} \) hybridisation of the metal ion.
D. \( F e(C O)_{5} \) have bipyramidal structure with \( d s p^{3} \) hybridised iron.
Subject: Physics
Particle 1 experiences a perfectly elastic
collision with a stationary particle
2. Determine their mass ratio, if after a head-on collision the particles fly apart in the opposite directions with equal
velocities.
A \( \cdot \frac{2}{3} \)
B. \( \frac{3}{2} \)
\( c \cdot \frac{1}{3} \)
D. 3
Subject: Maths
A school has a hall which is 22 m long and \( 15.5 m \) broad. A carpet is laid
inside the hall leaving all around a margin of \( 75 \mathrm{cm} \) from the walls. Find the
area of the carpet and the area of the
strip left uncovered. If the width of the carpet is \( 82 \mathrm{cm}, \) find the cost at the rate
of \( \boldsymbol{R} \boldsymbol{s} \boldsymbol{6} \boldsymbol{0} \) per meter
Subject: Maths
\( \operatorname{Given} \boldsymbol{F}(\boldsymbol{x})=\left[\begin{array}{ccc}\cos \boldsymbol{x} & -\sin \boldsymbol{x} & \mathbf{0} \\ \sin \boldsymbol{x} & \cos \boldsymbol{x} & \boldsymbol{0} \\ \boldsymbol{0} & \boldsymbol{0} & \boldsymbol{1}\end{array}\right] \)
\( \boldsymbol{x} \in \boldsymbol{R} \) Then prove \( \boldsymbol{y}, \boldsymbol{F}(\boldsymbol{x}+\boldsymbol{y})= \)
\( \boldsymbol{F}(\boldsymbol{x}) \boldsymbol{F}(\boldsymbol{y}) \)
Subject: Maths
The mean weight of 500 male students in a certain college is 151 pounds and the standard deviation is 15 pounds. Assuming the weights are normally distributed, find the approximate number of students weighing.
(i) between 120 and 155 pounds,
\[
\begin{array}{llll}
z & 0.2667 & 2.067 & 2.2667 \\
& & & \\
\text { Area } & 0.1026 & 0.4803 & 0.4881
\end{array}
\]
(ii) more than 185 pounds.
Subject: Maths
The ratio in which the surface \( x^{2}+ \)
\( y^{2}+z^{2}=25 \) divides the line joining
(0,1,2) and (3,4,5) is \( \frac{a \pm \sqrt{b}}{c} \) then \( \boldsymbol{a}+\boldsymbol{b}+\boldsymbol{c}= \)
Subject: Maths
Solve: \( 4 x+\frac{6}{y}=15 \) and \( 6 x-\frac{8}{y}= \)
\( \mathbf{1 4} \)
A. \( x=2 ; y=3 \)
В. \( x=3 ; y=2 \)
c. \( x=1 ; y=5 \)
D. \( x=4 ; y=1 \)
Subject: Maths
How much more than \( 2 x^{2}+4 x y+2 y^{2} \)
is \( 5 x^{2}+10 x y-y^{2} ? \)
State True or False: The answer is \( 3 x^{2}+ \)
\( 6 x y-3 y^{2} \)
A . True
B. False
Subject: Chemistry
The hybridisation of central and terminal carbon atoms is
are respectively
\( \mathbf{A} \cdot s p \) and \( s p \)
B. \( s p^{2} \) and \( s p^{2} \)
c. \( s p \) and \( s p^{2} \)
D. \( s p^{2} \) and \( s p \)
Subject: Chemistry
Which of the following statements
is/are correct?
This question has multiple correct options
\( \mathbf{A} \cdot \) Solid \( P C l_{5} \) exists as tetrahedral \( P C l_{4}^{+} \) and octahedral
\( P C l_{6}^{-} \) ions.
B. Solid \( P B r_{5} \) exists as \( P B r_{4}^{+} B r^{-} \)
C. Solid \( N_{2} O_{5} \) exists as \( N O_{3}^{-} \) and \( N O_{2}^{+} \)
D. Oxides of phosphorus \( P_{2} O_{3} \) and \( P_{2} O_{5} \) exist as
monomers.
Subject: Maths
If \( a, b, c \) are distincts \( \& w(\neq 1) \) is a cube of unity then minimum value of
\( \boldsymbol{x}=\left|\boldsymbol{a}+\boldsymbol{b} \boldsymbol{w}+\boldsymbol{c} \boldsymbol{w}^{2}\right|+\left|\boldsymbol{a}+\boldsymbol{b} \boldsymbol{w}^{2}+\boldsymbol{c} \boldsymbol{w}\right| \)
A \( \cdot 2 \sqrt{3} \)
B. 3
\( c \cdot 4 \sqrt{2} \)
D.
Subject: Maths
The function \( \boldsymbol{f}(\boldsymbol{x})=\int_{0}^{x} \boldsymbol{e}^{-\boldsymbol{x}^{2} / 2}\left(\boldsymbol{x}^{2}-\right. \)
\( 3 x+2) d x \) is maximum at \( x= \)
\( A \)
B. 2
\( c \cdot 3 \)
D. 4
Subject: Physics
Hot water cools from \( 60^{\circ} \mathrm{C} \) to \( 50^{\circ} \mathrm{C} \) in
the first 10 minutes and to \( 42^{\circ} C \) in the
next 10 minutes. The temperature of the surroundings is :
A \( \cdot 25^{\circ} \mathrm{C} \)
B . \( 10^{\circ} \mathrm{C} \)
\( \mathrm{c} \cdot 15^{\circ} \mathrm{C} \)
D. \( 20^{\circ} \mathrm{C} \)
Subject: Physics
A long spring when stretched by \( x c m \)
has a potential energy \( v . \) On increasing the stretching to \( n x c m, \) the potential energy stored in the spring will be
A \( . n v \)
B . \( n^{2} v \)
\( c \cdot n v^{3} \)
D. \( n v^{-2} \)
Subject: Physics
A particle moves in a circle of radius
1.0 \( c m \) with a speed given by \( v=2 t \)
where \( v \) is in \( c m / s \) and \( t \) in
seconds. Find the radial acceleration of
the particle at \( t=1 s: \)
\( \mathbf{A} \cdot 2.0 \mathrm{cms}^{-2} \)
B. \( 3.0 \mathrm{cms}^{-2} \)
c. \( 4.0 \mathrm{cms}^{-2} \)
D. \( 5.0 \mathrm{cms}^{-2} \)
Subject: Physics
If the lattice constant of this
semiconductor is decreased, then
which of the following is correct? (where
\( \boldsymbol{E}_{c} \) is conduction bandwidth, \( \boldsymbol{E}_{\boldsymbol{g}} \) is Band
gap and \( E_{v} \) is valence bandwidth)
A \( \cdot \) All \( \mathrm{E}_{\mathrm{c}}, \mathrm{E}_{\mathrm{g}}, \mathrm{E}_{\mathrm{V}} \) decrease
B. All E \( _{c}, E_{g}, \) Ev increase
c. \( \mathrm{E}_{c} \), and \( \mathrm{E}_{\mathrm{v}} \) increase but \( \mathrm{E}_{\mathrm{g}} \) decreases
D. E \( _{c} \), and Ev, decrease Eg increases
Subject: Maths
The area of the region described by
\( A=(x, y): x^{2}+y^{2} \leq 1 \) and \( y^{2} \leq 1-x \)
is:
A \( \cdot \frac{\pi}{2}+\frac{4}{3} \)
В \( \cdot \frac{\pi}{2}-\frac{4}{3} \)
c. \( \frac{\pi}{2}-\frac{2}{3} \)
D. \( \frac{\pi}{2}+\frac{2}{3} \)
Subject: Biology
Match the columns and find the correct
combination:
\begin{tabular}{llll} 
& \multicolumn{2}{l} { I } \\
a & Auxin & II & \\
b & Cytokinin & 2. & Inhibitor of growth \\
c & Gibberellin & 3. & Apical dominance \\
d & Ethylene & 4. & Epinasty \\
& Abscisic & 5. & Induces amylase synthesis
\end{tabular}
\( A \)
\( a-3, b-1, c-5, d-4, e-2 \)
B. \( a-4, b-5, c-1, d-3, e-2 \)
c. \( a-2, b-1, c-5, d-3, e-4 \)
D. \( a-3, b-1, c-5, d-2, e-4 \)
E. \( a-4, b-1, c-5, d-3, e-2 \)
Subject: Maths
Solve the following pairs of linear (simultaneous) equation by the method of elimination by substitution: \( 2 x+ \)
\( \mathbf{3} \boldsymbol{y}=\mathbf{8}, \mathbf{2} \boldsymbol{x}=\mathbf{2}+\mathbf{3} \boldsymbol{y} \)
A \( \cdot x=2, y=\frac{3}{2} \)
в. \( x=3, y=5 \)
c. \( _{x}=\frac{5}{2}, y=1 \)
D. \( x=\frac{3}{2}, y=4 \)
Subject: Physics
the car is moving towards east with a speed of \( 25 \mathrm{km} / \mathrm{h} \). To the driver of the
car, a bus appears to move towards north with a speed of \( 25 \sqrt{3} k m / h . \) What
is the actual velocity of the bus?
A \( \cdot 50 k m / h, 30^{\circ} \) east of north
B. \( 50 k m / h, 30^{\circ} \) north of east
\( \mathrm{c} \cdot 25 k m / h, 30^{\circ} \) east of north
D. \( 25 k m / h, 30^{\circ} \) north of east
Subject: Maths
If \( \overrightarrow{\boldsymbol{a}}=\hat{\boldsymbol{i}}+\boldsymbol{2} \hat{\boldsymbol{j}}+\boldsymbol{3} \hat{\boldsymbol{k}}, \overrightarrow{\boldsymbol{b}}=\boldsymbol{2} \hat{\boldsymbol{i}}+\boldsymbol{3} \hat{\boldsymbol{j}}+ \)
\( \hat{\boldsymbol{k}}, \overrightarrow{\boldsymbol{c}}=\mathbf{3} \hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}+\boldsymbol{2} \hat{\boldsymbol{k}} \) are vectors
satisfying \( \boldsymbol{\alpha} \overrightarrow{\boldsymbol{a}}+\boldsymbol{\beta} \overrightarrow{\boldsymbol{b}}+\boldsymbol{\gamma} \overrightarrow{\boldsymbol{c}}=-\boldsymbol{3}(\hat{\boldsymbol{i}}-\hat{\boldsymbol{k}}), \) then the
ordered triplet \( (\boldsymbol{\alpha}, \boldsymbol{\beta}, \boldsymbol{\gamma}) \) is
В . (-2,-1,1)
c. (-2,1,1)
D. (2,1,1)
Subject: Physics
A neutron moving with a speed \( v \) makes
a head on collision with a hydrogen atom in ground state kept at rest. The minimum kinetic energy of neutron for which inelastic collision will take place
is
A . \( 10.2 e V \)
B. 20.4eV
c. \( 12.1 e V \)
D. \( 16.8 e V \)
Subject: Physics
The equation of the progressive wave is \( \boldsymbol{y}=\boldsymbol{a} \sin 2 \pi\left(\boldsymbol{n} \boldsymbol{t}-\frac{\boldsymbol{x}}{\mathbf{5}}\right) . \) The ratio of
maximum particle velocity to wave velocity is
A \( \cdot \frac{\pi a}{5} \)
в. \( \frac{2 \pi a}{5} \)
c. \( \frac{3 \pi a}{5} \)
D. \( \frac{4 \pi a}{5} \)
Subject: Chemistry
Find the minimum uncertainty in the
position of proton when \( u_{p r o t o n}=0.01 \times \) speed of light.
A \( \cdot 3.15 \times 10^{3} m \)
В. \( 13.2 \times 10^{-14} \mathrm{m} \)
c. \( 6.6 \times 10^{-14} m \)
D. \( 1.05 \times 10^{-14} m \)
Subject: Physics
A plank of mass \( M \) is suspended
horizontally by using two wires as shown in the figure.They have same length \( (L) \) and same cross sectional
\( \operatorname{area}(A) . \) Their Young's modulus are \( Y_{1} \)
and \( Y_{2} \) respectively. The elastic
potential energy of the system will be
\( A \)
\[
\frac{2 M^{2} g^{2} L}{A\left(Y_{1}+Y_{2}\right)}
\]
в.
\[
\frac{m^{2} g^{2} L}{A\left(Y_{1}+Y_{2}\right)}
\]
\( c \)
\[
\frac{m^{2} g^{2} L}{2 A\left(Y_{1}+Y_{2}\right)}
\]
D.
\[
\frac{M^{2} g^{2} L\left(Y_{1}+Y_{2}\right)}{2 A Y_{1} Y_{2}}
\]
Subject: Physics
Assertion
The capacitive reactance limits the amplitude of the current in a purely capacitive circuit
Reason
Capacitive reactance is proportional to
the frequency and the capacitance
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
A ball is projected vertically upwards. Its speed at half of maximum height is \( 20 m / s . \) The maximum height attained by it is [Take \( \left.\boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} / \boldsymbol{s}^{2}\right] \)
A . 35 m
в. 15 т
\( c .25 m \)
D. \( 40 m \)
Subject: Chemistry
Match the column:
Column-I Column-II
(p) Complex having lowest
(a) \( \left[F e(C O)_{4}\right]^{2-} \quad \) bond length of CO ligand
(q) Follow Sidgwick's rule of
(b) \( \left[V(C O)_{6}\right]^{-} \quad \) E.A.N.
(r) Synergic bonding is
(c) \( K\left[P t C l_{3}\left(C_{2} H_{4}\right)\right] \) involved in complex/ion
\( (d) \)
(s) Complex having highest \( \left[F e\left(H_{2} O\right)_{5} N O\right] S O_{4} \) bond length of CO ligand
(t) Oragnometallic compound
\( \mathbf{A} \cdot(\mathrm{a}) \mathrm{q}, \mathrm{r}, \mathrm{s}, \mathrm{t} ;(\mathrm{b}) \mathrm{p}, \mathrm{q}, \mathrm{r}, \mathrm{t} ;(\mathrm{c}) \mathrm{r}, \mathrm{r} ;(\mathrm{d}) \mathrm{r} \)
B. (a)s,t; (b) p,q,r,t; (c) r; (d) r
C. \( (a) q, s, t ;(b) q, r, t ;(c) r, t ;(d) r \)
D. \( (a) q, r, t ;(b) q, r, t ;(c) r \)
Subject: Chemistry
The electronic configuration of \( \mathrm{Cu}^{+2} \) is:
A \( \cdot(A r) 4 s^{3} 3 d^{10} \)
B . \( (A r) 4 s^{3} 3 d^{10} \)
c. \( (A r) 3 d^{9} \)
D \cdot \( (A r) 4 s^{2} 3 d^{7} \)
Subject: Maths
\( \int \cos x \log \left(\tan \frac{x}{2}\right) d x= \)
\( A \cdot \sin x \log |\tan x|-x+c \)
B. \( -\sin x \log \left|\tan \frac{x}{2}\right|+x+c \)
\( \mathbf{c} \cdot-\sin x \log \left|\tan \frac{x}{2}\right|-x+c \)
\( \mathbf{D} \cdot \sin x \log \left|\tan \frac{x}{2}\right|-x+c \)
Subject: Maths
Find the surface area of a cone
\( \mathbf{A} \cdot 8635 m^{2} \)
\( \mathbf{B} \cdot 86.35 m^{2} \)
c. \( 0.8635 m \)
\( \mathbf{D} \cdot 8.635 m^{2} \)
Subject: Chemistry
A cationic colloidal electrolyte forms
micelles at \( 10^{-4} \) M concentration in
water. If \( 1 \mathrm{mm}^{3} \) solution contains \( 10^{12} \)
micelle structure, then the number of
cations involved in one micelle is:
A . 20
B . 40
c. 60
D. 80
Subject: Maths
Let \( M \) and \( m \) be respectively the
absolute maximum and the absolute
minimum values of the function,
\( f(x)=2 x^{3}-9 x^{2}+12 x+5 \) in the
interval \( [0,3] . \) Then \( M-m \) is equal to.
A . 1
B. 5
\( c \cdot 4 \)
D. 9
Subject: Chemistry
Bond energy of \( \boldsymbol{C l}_{2}, \boldsymbol{B r}_{2} \) and \( \boldsymbol{I}_{2} \) follow
the order:
A. \( C l_{2}>B r_{2}>I_{2} \)
в. \( B r_{2}>C l_{2}>I_{2} \)
c. \( I_{2}>B r_{2}>C l_{2} \)
D. \( I_{2}>C l_{2}>B r_{2} \)
Subject: Maths
If \( G \) and \( G^{\prime} \) be the centroids of the
triangles \( A B C \) and \( A^{\prime} B^{\prime} C^{\prime} \) respectively, then \( \overrightarrow{\boldsymbol{A A}^{\prime}}+\overrightarrow{\boldsymbol{B B}^{\prime}}+\overrightarrow{\boldsymbol{C C}^{\prime}}= \)
A \( \cdot \frac{2}{3} \overrightarrow{G G^{\prime}} \)
в. \( \overrightarrow{G G^{\prime}} \)
\( \mathbf{c} \cdot 2 \overrightarrow{G G^{\prime}} \)
\( \mathbf{D} \cdot 3 \overrightarrow{G G^{\prime}} \)
Subject: Chemistry
In the first order reaction \( 75 \% \) of the
reactant disappeared in 1.388 hrs Calculate the rate constant of the
reaction:
A \( \cdot 1 s^{-1} \)
- \( ^{-1} \)
B. \( 2.8 \times 10^{-4} s^{-1} \)
c. \( 17.2 \times 10^{-3} s^{-1} \)
D. \( 1.8 \times 10^{-3} s^{-1} \)
Subject: Physics
If impulse \( I \) varies with time \( t \) as
\( f\left(k g m s^{-1}\right)=20 t^{2}-40 t . \) The change in
momentum is minimum at
\( \mathbf{A} \cdot t=1 s \)
B . \( t=2 s \)
c. \( _{t=\frac{1}{2} s} \)
D. \( t=\frac{3}{2} s \)
Subject: Chemistry
Which of the following is a disproportionation reaction?
A \( \cdot C u_{2} O+2 H^{+} \rightarrow C u+C u^{2+}+H_{2} O \)
B \( \cdot 2 C r O_{4}^{2-}+2 H^{+} \rightarrow C r_{2} O_{7}^{2-}+H_{2} O \)
\( \mathrm{c} \cdot \mathrm{CaCO}_{3}+2 \mathrm{H}^{+} \rightarrow \mathrm{Ca}^{2+}+\mathrm{H}_{2} \mathrm{O}+\mathrm{CO}_{2} \)
D. \( C r_{2} O_{7}^{2-}+2 O H^{-} \rightarrow 2 C r O_{4}^{2-}+H_{2} O \)
Subject: Physics
In Young's double slit experiment, the
two slits act as coherent sources of
equal amplitude \( A \) and wavelength \( \lambda \). In
another experiment with the same set up the two slits are same of equal amplitude of wavelength \( \lambda \) but are
incoherent. The ratio of intensity of light at the mid point of the screen in the first to the second case is?
A . 4: 1
B . 2: 1
\( c \cdot 1: 1 \)
D. 1: 2
Subject: Chemistry
The final product obtained in the reaction is:
\[
\mathrm{H}_{3}-\langle\bigcirc\rangle-\mathrm{O} \mathrm{CH}_{3}+\mathrm{HBr} \longrightarrow
\]
\( A \)
в.
\( c \)
\[
\mathrm{cH}_{3}(\bigcirc)-\mathrm{O} \sqrt{\bigcirc}-\mathrm{cH}_{3}
\]
D. none of these
Subject: Physics
A uniform magnetic field of 1.5 T exists in a cylindrical region of radius \( 10.0 \mathrm{cm} \) its direction parallel to the axis along east to west. A wire carrying current of \( 7.0 \mathrm{A} \) in the north to south direction passes through this region. What is the magnitude and direction of the force on the wire if,(a) the wire intersects the axis,(b) the wire is turned from N-S to northeast-northwest direction,(c) the
wire in the N-S direction is lowered from
the axis by a distance of \( 6.0 \mathrm{cm} \) ?
Subject: Maths
Let \( \vec{a} \) and \( \vec{b} \) be two unit vectors such that \( |\vec{a}+\vec{b}|=\sqrt{3} . \) If \( \vec{c}=\vec{a}+2 \vec{b}+ \)
\( \mathbf{3}(\overrightarrow{\boldsymbol{a}} \times \overrightarrow{\boldsymbol{b}}), \) then \( \mathbf{2}|\overrightarrow{\boldsymbol{c}}| \) is equal to
A . \( \sqrt{55} \)
в. \( \sqrt{37} \)
c. \( \sqrt{43} \)
D. \( \sqrt{51} \)
Subject: Maths
If \( \boldsymbol{a}+\boldsymbol{b}=\mathbf{7} \boldsymbol{a} \boldsymbol{n} \boldsymbol{d} \boldsymbol{a} \boldsymbol{b}=\boldsymbol{6}, \boldsymbol{f} \boldsymbol{i} \boldsymbol{n} \boldsymbol{d} \boldsymbol{a}^{2}-\boldsymbol{b}^{2} \)
\( \mathbf{A} \cdot \pm 35 \)
B. ±12
\( c .\pm 22 \)
\( \mathrm{D} \cdot \pm 39 \)
Subject: Maths
\( G(1,1,-2) \) is the centroid of the
triangle \( A B C \) and \( D \) is the mid point of
\( \boldsymbol{B C} \cdot \) If \( \boldsymbol{A}=(-1,1,-4), \) then \( \boldsymbol{D}= \)
\( ^{\mathbf{A}} \cdot\left(\frac{1}{2}, 1, \frac{-5}{2}\right) \)
в. (5,1,2)
c. (-5,-1,-2)
D. (2,1,-1)
Subject: Physics
A circular coil of wire carries a current.
\( P Q \) is a part of a very long wire carrying
a current and passing close to the circular coil. If the direction of currents
are those as shown in the Figure, what
is the direction of force acting on \( P Q ? \)
A. Parallel to \( P Q \), towards \( P \)
B. Parallel to \( P Q \), towards \( Q \)
C. At right angles to \( P Q \), towards right
D. At right angles to \( P Q \), towards left
Subject: Chemistry
In a mixture of gases, the volume
content of a gas is \( 0.06 \% \) at STP.
Calculate the number of molecules of
the gas in 1 L of the mixture.
A. \( 1.613 \times 10^{23} \)
В. \( 6.023 \times 10^{23} \)
c. \( 1.61 \times 10^{27} \)
D. \( 1.61 \times 10^{19} \)
Subject: Chemistry
How many of the following oxides are basic oxides?
\( \boldsymbol{C O}_{2}, \boldsymbol{S n O}_{2}, \boldsymbol{P b O}, \boldsymbol{P b O}_{2}, \boldsymbol{P b}_{3} \boldsymbol{O}_{4}, \boldsymbol{A l}_{2} \boldsymbol{O}_{3} \)
Subject: Physics
Assertion
The size and shape of the rigid body remains unaffected under the effect of
external forces.
Reason
The distance between two particles remains constant in a rigid body
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
\( K_{h} \) values for
\( \boldsymbol{A} \boldsymbol{r}(\boldsymbol{g}), \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g}), \boldsymbol{H} \boldsymbol{C} \boldsymbol{H} \boldsymbol{O}_{(\boldsymbol{g})} \) and \( \boldsymbol{C} \boldsymbol{H}_{4}(\boldsymbol{g}) \)
are \( 40.39,1.67,1.83 \times 10^{-5} \) and 0.413
respectively. The order of their increasing solubility is:
A. \( H C H O<C H_{4}<C O_{2}<A r \)
в. \( H C H O<C O_{2}<C H_{4}<A r \)
c. \( A r<C O_{2}<C H_{4}<H C H O \)
D. \( A r<C H_{4}<C O_{2}<H C H O \)
Subject: Chemistry
In a \( 500 \mathrm{ml} \) capacity vessel \( C O \) and \( C l_{2} \)
are mixed to form \( C O C l_{2} \) at
equilibrium, it contains 0.2 moles of
\( C O C l_{2} \) and 0.1 mole each of \( C O \) and
\( C l_{2} . \) The equilibrium constant \( K_{c} \) for
reaction
\( \boldsymbol{C O}+\boldsymbol{C l}_{2} \leftrightharpoons \boldsymbol{C O C l}_{2}, \) is :
A . 20
B. 15
\( c \cdot 10 \)
D. 5
Subject: Physics
Figure shows a container having liquid
of variable density.The density of liquid \( \operatorname{varies} \operatorname{as} \rho=\rho_{0}\left(4-\frac{3 h}{h_{0}}\right) \) Here \( h_{0} \) and
\( \rho_{0} \) are constants and h is measured
from bottom of the container. A solid
block of small dimensions whose
density is \( \frac{5}{2} \rho_{0} \) and mass \( m \) is released from bottom of the tank. Prove that the
block will execute simple harmonic
motion. Find the frequency of oscillation
\( ? \)
Subject: Chemistry
An aqueous solution containing a nonvolatile solute is heated in an open
vessel till the boiling point is reached. Thereafter, the boiling is continued and the temperature and the vapour
pressure of the solution are recorded at
\( 5 \min , 10 \) min, and 15 min. The
corresponding temperatures and
pressures are \( \boldsymbol{T}_{5}, \boldsymbol{T}_{10}, \boldsymbol{T}_{15} \) and
\( P_{5}, P_{10}, P_{15}, \) respectively.
The correct relationship among them is:
A \( \cdot T_{5}<T_{10}<T_{15} \) and \( P_{5}=P_{10}=P_{15} \)
B . \( T_{5}=T_{10}=T_{15} \) and \( P_{5}=P_{10}=P_{15} \)
C \( \cdot T_{5}=T_{10}=T_{15} \) and \( P_{5}<P_{10}<P_{15} \)
D. \( T_{5}<T_{10}<T_{15} \) and \( P_{5}<P_{10}<P_{15} \)
Subject: Physics
on by a spring with spring constant \( k \)
and a weak frictional force of constant
magnitude \( f \). The block is pulled a
distance \( x_{0} \) from equilibrium position and then released. It oscillates many
times and ultimately comes to rest. Find the number of cycles the mass oscillates before coming to rest:
\( ^{\text {A }} \cdot \frac{1}{4}\left[\frac{k x_{0}}{f}-1\right] \)
в. \( \frac{1}{2}\left[\frac{k x_{0}}{f}-1\right] \)
c. \( \frac{1}{3}\left[\frac{k x_{0}}{f}-1\right] \)
D. none of the above
Subject: Chemistry
The colour of halogens progressively
deepens from fluorine to iodine
because:
A. halogens of higher atomic number absorb light of longer wavelength since the difference in energy between the ground state and excited state decreases as the atomic number increases
B. fluorescence and phosphorescence become more intense as the atomic numbers of halogen increases
C. the standard electrode potential increases from \( I_{2} \) to \( F_{2} \)
D. halogens of higher atomic number absorb light of shorter wavelength since the difference in energy between the ground state and excited state increases as the atomic number increases