AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A thin prism of angle \( 5^{\circ} \) is placed at a
distance of \( 10 \mathrm{cm} \) from object. What is the distance of the image from object?
(Given \( \mu \) of prism \( =1.5 \) )
A \( \cdot \frac{\pi}{8} c m \)
в. \( \frac{\pi}{12} \mathrm{cm} \)
c. \( \frac{5 \pi}{36} c m \)
D. \( \frac{\pi}{7} c m \)
Subject: Physics
A curved section of a rod is banked for a
speed \( v \). If there is no friction between
road and tyres of the car, then:
A. car is more likely to slip at speeds higher than \( v \) than speeds lower than \( v \)
B. car cannot remain in static equilibrium on the curved section
c. car will not slip when moving with speed \( v \)
D. None of the above
Subject: Physics
Assertion
Nuclear fusion are made at very high
temperature, \( \boldsymbol{i} \boldsymbol{e}_{\bullet}, \boldsymbol{1} \boldsymbol{0}^{\boldsymbol{7}} \boldsymbol{K} \)
Reason
Nuclear fusion reactions are exoergic.
\( \mathbf{A} \cdot S \) is correct but \( E \) is wrong
B. \( S \) is wrong but \( E \) is correct
C. Both \( S \) and \( E \) are correct and \( E \) is correct explanation
of \( S \)
D. Both \( S \) and \( E \) are correct but \( E \) is not correct
explanation of \( S \)
Subject: Physics
A proton is moving with velocity \( 10^{4} m / s \) parallel to the magnetic field of
intensity 5 tesla.The force on the proton
is
A. \( 8 \times 10^{15} N \)
B . \( 10^{4} N \)
c. \( 1.6 \times 10^{-19} N \)
D. zero
Subject: Chemistry
For a first order reaction, if \( \boldsymbol{K}_{\mathbf{1}}: \boldsymbol{K}_{\mathbf{2}}: \boldsymbol{K}_{\mathbf{3}} \)
is \( 1: 2: 3, \) then which of the following
statement(s) is/are incorrect? \( \left([\boldsymbol{A}]_{\mathbf{0}}=\right. \)
\( \mathbf{1} \boldsymbol{M}) \)
A. At time \( t_{\infty} \), [C] is \( 2 / 3 \) M.
B . \( [B]_{t}>[C]_{t} \)
C. When \( [A]_{t}=1 / 2 M, \) then \( [D]=1 M \)
D・ \( [A]_{t}+\frac{\left[B l_{t}\right.}{2}+\frac{[C]_{t}}{2}+\frac{\left[D_{l t}\right.}{4}=1 M \)
Subject: Maths
\( \frac{\tan ^{2} \theta}{1+\sec \theta}+1 \) equals to
\( A \cdot \tan \theta \)
B. \( \frac{1}{\cos \theta} \)
\( \mathbf{c} \cdot \sec \theta-1 \)
\( \mathbf{D} \cdot \sec \theta+\tan \theta \)
Subject: Physics
What is the magnitude of angular
velocity of the stick plus puck after the collision?
A \( \cdot \frac{6 v_{i}}{5 l} \)
в. \( \frac{5 v_{i}}{6 l} \)
c. \( \frac{v_{i}}{l} \)
D. \( \frac{v_{i}}{\sqrt{2} i} \)
Subject: Chemistry
Assertion
\( O_{3} \) and \( N O_{2}^{-} \) are isoelectronic.
Reason
Bond angles of \( \boldsymbol{O}_{3} \) and \( \boldsymbol{N} \boldsymbol{O}_{2}^{-} \) are \( \mathbf{1 1 6 . 8}^{\circ} \)
and \( 115^{\circ} \) respectively.
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
An object of length \( 6 \mathrm{cm} \) is placed on
the principle axis of a concave mirror of focal length \( f \) at a distance of 4 f. The length of the image will be
A \( .2 \mathrm{cm} \)
в. \( 12 \mathrm{cm} \)
\( \mathrm{c} .4 \mathrm{cm} \)
D. \( 1.2 \mathrm{cm} \)
Subject: Maths
If \( A \) and \( B \) be two finite sets such that
the total number of subsets of A is 960
more than the total number of subsets
of \( \mathrm{B}, \) then \( n(A)-n(B) \) (where \( n(x) \)
denotes the number of elements in set
\( x \) ) is equal to?
Subject: Chemistry
Which of the following oxo-acids of sulphur has more than one oxidation
state of
oxygen?
A \( \cdot H_{2} S_{2} O_{3} \)
в. \( H_{2} S_{2} O_{4} \)
c. \( H_{2} S_{2} O_{6} \)
D. \( H_{2} S_{2} O_{8} \)
Subject: Chemistry
The wavelength of radiation emitted, when in \( H e^{+} \) electron falls from infinity
to ground state would be:
\( \left(R=1.097 \times 10^{7} m^{-1}\right) \)
A \( .2 .2 \times 10^{-8} m \)
th
B. 2.2 \( \times 10^{-9} \mathrm{m} \)
c. \( 120 m \)
D. \( 22 \times 10^{7} \mathrm{m} \)
Subject: Maths
\( \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{1} & \mathbf{2} \\ \mathbf{3} & \mathbf{2} \\ \mathbf{- 1} & \mathbf{0}\end{array}\right], \boldsymbol{B}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{3} & \mathbf{2} \\ \mathbf{4} & \mathbf{- 1} & \mathbf{3}\end{array}\right], \) then
order of \( A B \) is
A. \( 2 \times 2 \)
в. \( 3 \times 3 \)
\( c \cdot 1 \times 3 \)
D. \( 3 \times 2 \)
Subject: Biology
Choose the correct statement among
the following.
A. Atrioventricular node is the pacemaker that generates action potential and initiates the atrial systole
B. During each cardiac cycle the lub sound is due to closure of semilunar valves
C. Stroke volume in each cardiac cycle is approximately 170 ml of blood.
D. QRS complex in an ECG indicates depolarisation of ventricles
E. The opening between right atrium and right ventricle is guarded by bicuspid valve.
Subject: Physics
A simple pendulum is suspended from
the ceiling of a car accelerating
uniformly on a horizontal road. If the
acceleration is \( a_{0} \) and the length of the
pendulum is \( l \), find the time period of
small oscillations about the mean
position
\( \mathbf{A} \)
B.
\( ^{\mathrm{C}} 2 \pi \frac{\sqrt{l}}{\left(a_{0}^{2}+g^{2}\right)^{1 / 4}} \)
D. \( \pi \frac{\sqrt{l}}{\left(a_{0}^{2}+g^{2}\right)^{1 / 4}} \)
Subject: Physics
A glass flask of volume \( 200 \mathrm{cm}^{3} \) is just
filled with mercury at \( 20 C \). The amount of
mercury that will overflow when the
temperature of the system is raised to \( 100 C \) is: \( \gamma_{\text {glass}}=1.2 \times 10^{-5} / C^{\circ}, \gamma_{\text {mercury}}= \)
\( 1.8 \times 10^{-4} / C^{\circ} \)
A \( .2 .15 \mathrm{cm}^{3} \)
В. \( 2.69 c m^{3} \)
\( c .2 .52 c m^{3} \)
D. \( 2.25 \mathrm{cm}^{3} \)
Subject: Physics
The amplitude of oscillation of a particle is 0.05 m.lf its period is 1.57 s. Then the velocity at the mean position
is
\( A \cdot 0.1 \mathrm{m} / \mathrm{s} \)
B. \( 0.2 \mathrm{m} / \mathrm{s} \)
\( c \cdot 0.3 \mathrm{m} / \mathrm{s} \)
D. \( 0.5 \mathrm{m} / \mathrm{s} \)
Subject: Maths
If \( \boldsymbol{y}=\frac{\boldsymbol{x}^{4}+\boldsymbol{4}}{\boldsymbol{x}^{2}-\boldsymbol{2} \boldsymbol{x}+\boldsymbol{2}} \) then find \( \left.\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}\right|_{\boldsymbol{x}=\frac{1}{2}} \)
Subject: Physics
A body is allowed to fall on the ground
from a height \( h_{1} . \) If it is rebound to a
height \( h_{2} \) then the coefficient of
restitution is:
\( \mathbf{A} \cdot \frac{\mathrm{h}_{2}}{\mathrm{h}_{1}} \)
B. \( \sqrt{\frac{h_{2}}{h_{1}}} \)
\( \mathbf{c} \cdot \frac{h_{1}}{h_{2}} \)
D. \( \sqrt{\frac{\mathrm{h}_{1}}{\mathrm{h}_{2}}} \)
Subject: Physics
A small bead of mass m moving with
velocity v gets threaded on a stationary semicircular ring of mass \( \mathrm{m} \) and radius R kept on a horizontal table. The ring can freely rotate about its centre. The bead comes to rest relative to the ring. What will be the final angular velocity of
the system?
A. \$\$displaystyle \{vyl《R\$\$
B. \$\$|displaystyle(2v)|(R)\$\$
c. \$\$ ldisplaystyle \{v)|(2R) \$\$
D. \$\$ldisplaystyle \{3v)|(R)\$\$
Subject: Maths
if \( \alpha \) and \( \beta \) are angles in the first quadrant, \( \tan \alpha=\frac{1}{7}, \sin \beta=\frac{1}{\sqrt{10}}, \) then
using the formula \( \sin (A+B)= \)
\( \sin A \cos B+\cos A \sin B, \) one can find
the value of \( (\boldsymbol{\alpha}+\mathbf{2} \boldsymbol{\beta}) \) to be
\( A \cdot 0^{\circ} \)
B. 45
\( c \cdot 60 \)
\( D \cdot 90^{\circ} \)
Subject: Physics
The magnetic field \( \overline{\boldsymbol{d} \boldsymbol{B}} \) due to a small
current element dl at a distance \( \vec{r} \) and
carrying current 'i' is
A \( \left.\cdot \frac{\mu_{0}}{d B}=\frac{\frac{d \bar{d}}{4 \pi} i}{r}\right) \)
В \( \cdot \frac{ }{d B}=\frac{\mu_{0}}{4 \pi} i^{2}\left(\frac{\overline{d l} \times \bar{r}}{r^{2}}\right) \)
\( ^{\mathbf{C}} \cdot \frac{\mu_{0}}{d B}=\frac{\frac{\mu}{4 \pi} i^{2}}{r} \)
D \( \cdot \frac{\mu_{0}}{d B} i\left(\frac{\overline{d l} \times \bar{r}}{r^{3}}\right) \)
Subject: Physics
A wire is bent in the form of a circular
arc with a straight portion \( \boldsymbol{A B} \)

Magnetic induction at \( O \) when current
is flowing in the wire, is
\( ^{\text {A } \cdot} \frac{\mu_{0}}{2^{r}}(\pi-\theta+\tan \theta) \)
в. \( \frac{\mu_{0} I}{2 \pi r}(\pi+\theta-\tan \theta) \)
c. \( \frac{\mu_{0} I}{2 \pi r}(\pi-\theta+\tan \theta) \)
D. \( \frac{\mu_{0} I}{2 \pi_{r}}(-\tan \theta+\pi-\theta) \)
Subject: Maths
Find the coefficient of \( x^{-7} \) in the
expansion of \( \left(\boldsymbol{a} \boldsymbol{x}-\frac{\mathbf{1}}{\boldsymbol{b} \boldsymbol{x}^{2}}\right)^{11} \)
\( \begin{array}{ll}\text { A. } & ^{11} C_{5}\end{array} \)
В. \( ^{10} C_{4} \)
c. \( ^{11} C_{4} \)
D. \( ^{10} C_{5} \)
Subject: Physics
Pitch of the helical path described by the particle is :
A. \( \frac{2 \pi m v_{0}}{B_{0} q} \)
В. \( \frac{\sqrt{3} \pi m v_{0}}{2 B_{0} q} \)
c. \( \frac{\pi m v_{0}}{B_{0} q} \)
D. \( \frac{2 \sqrt{3} \pi m v_{0}}{B_{0} q} \)
Subject: Chemistry
Assertion
When a metal is treated with
cone.H \( N O_{3} \) it generally yields a
nitrate, \( N O_{2} \) and \( H_{2} O \)
Reason
Conc. \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \) reacts with metal and
first produces a metal nitrate and
nascent hydrogen. The nascent
hydrogen then further reduces \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \)
to \( N O_{2} \)
A. If both Assertion and Reason are correct and Reason is the correct explanation of Assertion
B. If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion
C. If Assertion is correct but Reason is incorrect
D. If Assertion is incorrect but Reason is correct
Subject: Physics
In the experimental set up of metre
bridge shown in the figure, the null
point is obtained at a distance of \( 40 \mathrm{cm} \)
from A. If a \( 10 \Omega \) resistor is connected in
series with \( R_{1}, \) the null point shifts by
10cm. The resistance that should be
connected in parallel with \( \left(\boldsymbol{R}_{1}+\mathbf{1 0}\right) \boldsymbol{\Omega} \)
such that the null point shifts back to its initial position is?
A. \( 40 \Omega \)
в. \( 60 \Omega \)
\( c .20 \Omega \)
D. \( 30 \Omega \)
Subject: Physics
150 g of ice is mixed with 100 g of water at temperature \( 80^{\circ} \mathrm{C} \). The latent heat of
ice is 80 cal/g and the specific heat of
water is 1 cal/g \( -^{\circ} C \). Assuming no heat loss to the environment, the amount of
ice which does not melt is
A. \( 100 \mathrm{g} \)
B. 08
c. \( 150 g \)
D. 50
Subject: Chemistry
Assertion
Natural rubber becomes stiff by the vulcanization with sulphur
Reason
Sulphur forms cross links at the reactive sites of double bonds in
vulcanization.
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
Assertion: A series combination of cells
is used when their internal resistance
is much smaller than the external
resistance
Reason: It follows from the relation \( \boldsymbol{I}= \) \( \frac{n E}{R+n r}, \) where the symbols have their standard meaning.
A. Both (A) and (R) are true and (R) is the correct explanation of A
B. Both (A) and (R) are true but (R) is not the correct explanation of A
c. (A) is true but (R) is false
D. (A) is false but (R) is true
Subject: Chemistry
The heat of combustion of \( C H_{4}(g), C \)
(graphite) and \( H_{4}(g) \) are respectively \( -20 k . c a l,-40 k . c a l \) and \( -10 k . c a l . \) The heat
of formation of \( \mathrm{CH}_{4} \) is
A. \( -40 K \). cal
в. \( +40 K . c a l \)
c. \( -80 K . c a l \)
D. \( +80 K . c a l \)
Subject: Chemistry
Identify all the possible monochloro structural isomers expected to be
formed on free radical
monochlorination of
\( \left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{C H C H}_{2} \boldsymbol{C H}_{3} \)
In the given molecule, there are four
different types of hydrogen atoms. Replacement of these hydrogen atoms will give the following?
\( \mathbf{A} \cdot\left(C H_{3}\right)_{2} C H C H_{2} C H_{2} C l \)
B \( \cdot\left(C H_{3}\right)_{2} C H C H(C l) C H_{3} \)
\( \mathbf{c} \cdot\left(C H_{3}\right)_{2} C(C l) C H_{2} C H_{3} \)
D. \( C H_{3} C H\left(C H_{2} C l\right) C H_{2} C H_{3} \)
Subject: Physics
The charge on a body is +1 C. Find the number of electrons in excess or deficit
on the body.
A \( \cdot 6.25 \times 10^{1} \) coulomb
B. \( 6.25 \times 10^{-18} \) coulomb
c. \( 6.25 \times 10^{-1} \) coulomb
D. \( 6.25 \times 10^{18} \) coulomb
Subject: Maths
In a diagram of \( \Delta A B C \) and \( \Delta D E F \)
below, \( \boldsymbol{B C} \cong \boldsymbol{E} \boldsymbol{F}, \angle \boldsymbol{B} \cong \angle \boldsymbol{E} \) and \( \angle \boldsymbol{A} \cong \)
\( \angle D . \) Which method can be used to prove
\( \Delta A B C \cong \Delta D E F ? \)
A. AAA congruence
B. SAS congruence
C. AAS congruence
D. SSS congruence
Subject: Maths
In a quadrilateral \( P Q R S, \overrightarrow{P Q}= \) \( \vec{a}, \overrightarrow{Q R}=\vec{b}, \overrightarrow{S P}=\vec{a}-\vec{b} . M \) is the mid-
point of \( Q R \) and \( X \) is a point on \( S M \) such that \( \overrightarrow{S X}=\frac{4}{5} S \vec{M}, \) then \( \overrightarrow{P X} \) is
A \( \cdot \frac{1}{5} \overrightarrow{P R} \)
В. \( \frac{3}{5} \overrightarrow{P R} \)
c. \( \frac{2}{5} \overrightarrow{P R} \)
D. None of these
Subject: Physics
When a current of \( (2.50 \pm 0.5) A \)
flows through a wire, it develops a
potential difference of \( (20 \pm 1) V . \) The
resistance of the wire is :
A. \( (8 \pm 2) \Omega \)
в. \( (10 \pm 3) \Omega \)
c. \( (18 \pm 4) \Omega \)
D. \( (20 \pm 6) \Omega \)
Subject: Physics
Consider a thin target \( \left(10^{-2} \mathrm{m} \) square \right.
\( \left.10^{-3} m \text { thickness }\right) \) of sodium, which
produces a photo-current of \( 100 \mu A \) when a light of intensity \( 100 W / m^{2}(\lambda=660 n m) \) falls on it.
Find the probability that a photoelectron is produced when a photon strikes a sodium atom.
[ Take density of \( \left.\boldsymbol{N} \boldsymbol{a}=\mathbf{0 . 9 7} \boldsymbol{k} \boldsymbol{g} / \boldsymbol{m}^{3}\right] \)
Subject: Chemistry
State True or False.
In an electrode concentration cell, the
cell reaction \( \mathrm{Zn}\left(\mathrm{C}_{1}\right) \rightarrow \mathrm{Zn}\left(\mathrm{C}_{2}\right) \) will be
spontaneous if \( \mathbf{c}_{1}>\mathbf{c}_{2} \)
A. True
B. False
Subject: Maths
Which among the following is/are not
correct?
This question has multiple correct options
A. The ratios of the areas of two similar triangles is equal to the ratio of their corresponding sides.
B. The areas of two similar triangles are in the ratio of the corresponding altitudes.
C. The ratio of area of two similar triangles are in the ratio of the corresponding medians.
D. If the areas of two similar triangles are equal, then the triangles are congruent
Subject: Chemistry
Assertion
Nitric acid stains the skin
Reason
Nitric acid reacts with proteins to form yellow nitrated products is formed when the acid contacts epithelial cells of skin
giving it a stain.
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 solid sphere of radius r made of a soft material of bulk modulus K is
surrounded by a liquid in a cylindrical container.A massless piston of area a floats on the surface of the liquid, covering entire cross section of
cylindrical container. When a mass m is placed on the surface of the piston to compress the liquid, the fractional decrement in the radius of the sphere, \( \left(\frac{d r}{r}\right), \) is?
A \( \cdot \frac{m g}{3 K a} \)
в. \( \frac{m g}{K a} \)
с. \( \frac{K a}{m g} \)
D. \( \frac{K a}{3 m g} \)
Subject: Physics
A string of negligible thickness is
wrapped several times around a
cylinder kept on a rough horizontal
surface. A man standing at a distance \( l \)
from the cylinder holds one end of the string and pulls the cylinder towards him (fig). There is no slipping anywhere. The length of the string passed through the hand of the man while the cylinder reaches his hands is
\( A \)
B . \( 2 l \)
\( c .3 l \)
D. \( 4 l \)
Subject: Physics
Energy of all molecules of a monatomic
gas having a volume \( V \) and pressure \( P \) is \( \frac{3}{2} P V . \) The total translational kinetic energy of all molecules of a diatomic
gas at the same volume and pressure is
A \( \cdot \frac{1}{2} P V \)
в. \( \frac{3}{2} P V \)
c. \( \frac{5}{2} P V \)
D. 3 PV
Subject: Chemistry
A qualitative analysis test for \( M n^{2+} \)
involves its oxidation to \( M n O_{4}^{-} \) in
acidic solution by sodium bismuthate,
\( N a B i O_{3} . \) The bisulphate ion is reduced
to \( B i^{3 i} . \) What is a balanced equation for
this test?
A \( \cdot B i O_{3}^{-2}+M n^{2+}+H^{+} \rightarrow M n O_{4}^{-}+B i^{3+}+H_{2} O \)
B. \( 5 B i O_{3}^{-}+2 M n^{2+}+7 H^{+} \rightarrow 2 M n O_{4}^{-}+5 B i^{3+}+7 O H \)
C. \( 5 B i O_{3}^{-}+2 M n^{2+}+14 H^{+} \rightarrow 2 M n O_{4}^{-}+5 B i^{3+}+7 H_{2} O \)
D. None of these
Subject: Maths
Find the values of \( x \) and \( y \) in the given
triangles, where \( \angle A=70^{\circ}, \angle B= \)
\( \mathbf{3 6}^{\circ}, \angle \boldsymbol{D}=\mathbf{6 8}^{\circ} \) and \( \angle \boldsymbol{F}=\mathbf{5 6}^{\circ} \)
A \( . x=103, y=80 \)
B . \( x=105, y=75 \)
C \( . x=105, y=87 \)
Subject: Maths
\( \boldsymbol{f}=\{(\boldsymbol{3}, \boldsymbol{4}),(\boldsymbol{4}, \boldsymbol{3})\} \boldsymbol{g}=\{(\boldsymbol{3}, \boldsymbol{7}),(\boldsymbol{4}, \boldsymbol{8})\} \)
Find \( \boldsymbol{f}-\boldsymbol{g} \)
Subject: Chemistry
The cylindrical shape of alkynes is due
to:
\( \mathbf{A} \cdot \) three \( \sigma C-C \) bonds
B. three \( \pi C-C \) bonds
C. two \( \sigma C-C \) and two \( \pi C-C \) bonds
D. one \( \sigma C-C \) and two \( \pi C-C \) bonds
Subject: Physics
Two vectors \( \overrightarrow{\boldsymbol{A}}=\mathbf{2} \hat{\mathbf{i}}+\hat{\boldsymbol{j}} \) and \( \overrightarrow{\boldsymbol{B}}=\boldsymbol{a} \hat{\boldsymbol{i}}- \)
\( 2 \hat{j} \) are perpendicular to each other. The value of a is
A.
B. 2
\( c \cdot 3 \)
D. 4
Subject: Maths
Two aeroplanes I and II bomb a target in succession. The probabilities of I and I scoring a hit correctly are 0.3 and 0.2 respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the second plane is
A . 0.06
в. \( \frac{7}{22} \)
\( c .0 .2 \)
D. 0.7
Subject: Maths
A invested Rs 76000 in a business After
few months B joined him with Rs 57000 At the end of the year the total profit
was divided between them in the ratio
of 2: 1 After how many months did \( B \) join?
\( A \cdot 4 \)
B. 8
\( c \cdot 9 \)
D. None of these
Subject: Maths
The sum of 100 terms of the series. \( 9+ \)
\( \mathbf{0 9}+.009 . \) will be?
\( ^{\mathbf{A}} \cdot_{1}-\left(\frac{1}{10}\right)^{100} \)
B. \( 1+\left(\frac{1}{10}\right)^{106} \)
\( ^{\mathrm{c}} \cdot_{1-}\left(\frac{1}{10}\right)^{106} \)
D. \( _{1+}\left(\frac{1}{10}\right)^{100} \)
Subject: Physics
Concave and convex lenses, each have
the same focal length \( 20 \mathrm{cm} \) and they
are put in contact to form a
combination lens. This combination
lens is used to view an object of \( 5 \mathrm{cm} \)
length, kept at a distance \( 20 \mathrm{cm} \) from
the lens combination. As compared to
the object the image will be
A. Magnified and inverted.
B. Reduced and erect.
C. of the same size as the object and erect.
D. of the same size as the object but inverted.
Subject: Chemistry
The correct reactivity order of alcohols towards \( \boldsymbol{H}-\boldsymbol{X} \) will be:
(I) \( \boldsymbol{C H}_{2}=\boldsymbol{C H}-\boldsymbol{O H} \)
(II) \( \boldsymbol{C H}_{2}=\boldsymbol{C H}-\boldsymbol{C H}_{2} \boldsymbol{O H} \)
(III) \( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{O H} \)
\( (\mid V) C H_{3}-C H-C H_{3} \)
a \( ^{1} \)
A \( , I I>I>I I I>I V \)
\( V \)
B. \( I V>I I I>I I>I \)
c. \( I I>I V>I>I I I \)
D. \( I I>I V>I I I>I \)
Subject: Maths
Using properties of determinants, prove
the following:
\( \left(\begin{array}{ccc}\mathbf{1} & \boldsymbol{x} & \boldsymbol{x} \\ \mathbf{2} \boldsymbol{x} & \boldsymbol{x}(\boldsymbol{x}-\mathbf{1}) & \boldsymbol{x}(\boldsymbol{x} \boldsymbol{x} \\ \mathbf{3} \boldsymbol{x}(\mathbf{1}-\boldsymbol{x}) & \boldsymbol{x}(\boldsymbol{x}-\mathbf{1})(\boldsymbol{x}-\mathbf{2}) & \boldsymbol{x}(\boldsymbol{x}+\mathbf{1})\end{array}\right. \)
\( 6 x^{2}\left(1-x^{2}\right) \)
Subject: Chemistry
\( \boldsymbol{B} \boldsymbol{e} \boldsymbol{C l}_{2}+\boldsymbol{L} \boldsymbol{i} \boldsymbol{A} \boldsymbol{l} \boldsymbol{H}_{4} \longrightarrow \boldsymbol{X}+\boldsymbol{L} \boldsymbol{i} \boldsymbol{C l}+ \)
\( \boldsymbol{A l C l}_{3} \)
A. \( X \) is lithium hydride
B. \( X \) is \( B e H_{2} \)
c. \( X \) is \( B e C l_{2} \cdot 2 H_{2} O \)
D. \( X \) is \( L i H \)
Subject: Maths
\( f(x)=\left|\begin{array}{ccc}\sin x & \cos x & \tan x \\ x^{3} & x^{2} & x \\ 2 x & 1 & 1\end{array}\right|, \) then
\( \lim _{x \rightarrow 0} \frac{f(x)}{x^{2}} \) is
\( A \)
B. 3
\( c \cdot 1 \)
D. zero
Subject: Physics
Assertion
Balmer series lies in the visible region of electromagnetic spectrum.
Reason \( \frac{1}{\lambda}=R\left[\frac{1}{2^{2}}-\frac{1}{n^{2}}\right], \) where \( n=3,4,5 \)
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
The electron is present in the -1.51 eV
energy state. Find the angular momentum of the electron.
A. \( \frac{h}{\pi} \)
в. \( \frac{h}{2 \pi} \)
c. \( \frac{3 h}{2 \pi} \)
D. \( \frac{2 h}{\pi} \)
E. none of these
Subject: Physics
A police inspector in a jeep is chasing a pickpocket on a straight road. The jeep is going at a maximum speed \( v \) (assume uniform). The pickpocket rides on the motorcycle of a waiting friend
when the jeep is at a distance \( d \) away
and the motorcycle starts with a constant acceleration \( a \). What should
be the speed of the jeep so that the
pickpocket will be caught?
A \( \cdot v \geq \sqrt{\frac{3}{2} a d} \)
B. \( v \geq \sqrt{2 a d} \)
C \( . v \geq \sqrt{6 a d} \)
D. \( v>2 a d \)
Subject: Physics
Q Type your question
\( \left(p+\frac{a}{V^{2}}\right)(V-b)=R T \)
undergoes the quasi-static cyclic
process which is shown in the p-V
diagram. The net heat absorbed by the gas in this process is:
\( ^{A} \cdot \frac{1}{2}\left(p_{1}-p_{2}\right)\left(V_{1}-V_{2}\right) \)
B \( \cdot \frac{1}{2}\left(p_{1}+p_{2}\right)\left(V_{1}-V_{2}\right) \)
c. \( \frac{1}{2}\left(p_{1}+\frac{a}{V_{1}^{2}}-p_{2}-\frac{a}{V_{2}^{2}}\right)\left(V_{1}-V_{2}\right) \)
\( \cdot \frac{1}{2}\left(p_{1}+\frac{a}{V_{1}^{2}}+p_{2}+\frac{a}{V_{2}^{2}}\right)\left(V_{1}-V_{2}\right) \)
Subject: Chemistry
\( 100 \mathrm{ml} \) of liquid \( \mathrm{A} \) and \( 25 \mathrm{ml} \) of liquid \( \mathrm{B} \) is mixed to give a solution which does not obey Raoult's law. The volume of the
solution:
A. will be 125 \( \mathrm{m} \) ।
B. can be > or < than 125 \( \mathrm{m} \)
c. can be greater than, equal to or less than \( 125 \mathrm{m} \)
D. will be less than 125 \( \mathrm{m} \) ।
Subject: Physics
A convex lens makes a real image \( 4 \mathrm{cm} \) long on a screen.When the lens is
shifted to a new position without disturbing object or the screen, we again get a real image on the screen which is \( 9 \mathrm{cm} \) long. The length of the
object must be :
A . \( 2.25 \mathrm{cm} \)
B. \( 6 \mathrm{cm} \)
\( c .6 .50 \mathrm{cm} \)
D. \( 36 \mathrm{cm} \)