AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
\( \boldsymbol{p} \boldsymbol{H} \) of a \( \boldsymbol{0 . 0 1} \boldsymbol{M} \) solution \( \left(\boldsymbol{K}_{\boldsymbol{a}}=\boldsymbol{6 . 6} \times\right. \)
\( \left.10^{-4}\right) \) is:
A . 7.6
B. 8
c. 2.6
D.
Subject: Physics
When a photon of energy \( 7 e V \) is made incident on a metal then the emitted
electron is stopped by a stopping potential of \( -5.5 V . \) The work function
of metal will be :
A. \( -1.5 e V \)
B. \( 1.5 e V \)
c. \( 12.5 e V \)
D. \( 37.5 e V \)
Subject: Physics
The temperature (T) of one mole of an ideal gas varies with its volume (V) as \( \boldsymbol{T}=-\boldsymbol{\alpha} \boldsymbol{V}^{3}+\beta \boldsymbol{V}^{2}, \) where \( \boldsymbol{\alpha} \) and \( \boldsymbol{\beta} \) are
positive constants. The maximum pressure of gas during this process is
A \( \cdot \frac{\alpha \beta}{2 R} \)
B. \( \frac{\beta^{2} R}{4 \alpha} \)
c. \( \frac{(\alpha+\beta) R}{2 \beta^{2}} \)
D. \( \frac{\alpha^{2} R}{2 \beta} \)
Subject: Physics
A body of mass 5 kg undergoes a change in speed from 30 to \( 40 \mathrm{m} / \mathrm{s} \). Its momentum would increase by :
A. \( 50 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
B. 75 kg m/s
c. \( 150 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
D. 350 kg m/s
Subject: Physics
A particle of mass \( m \) is in a uni-
directional potential field where the potential energy of a particle depends
on the \( x \) -coordinate given by \( \phi_{x}= \)
\( \phi_{0}(1-\cos a x) \&^{\prime} \phi_{0}^{\prime} \) and \( ^{\prime} a^{\prime} \) are
constants. Find the physical
dimensions of \( ^{\prime} \boldsymbol{a}^{\prime} \& \boldsymbol{\phi}_{0} \)
A \( \cdot L^{-1}, M^{1} L^{2} T^{-2} \)
B . \( L^{-2}, M^{1} L^{3} T^{-2} \)
C \( \cdot L^{-1}, M^{0} L^{2} T^{-1} \)
D. None of these
Subject: Maths
If \( z=\frac{\sqrt{3}}{2}+\frac{i}{2}(i=\sqrt{-1}), \) then \( (1+ \)
\( \left.i z+z^{5}+i z^{8}\right)^{9} \) is equal to
A . -1
B. 1
c. 0
D \( \cdot(-1+2 i)^{9} \)
Subject: Chemistry
After black and white photographic film has been developed, unreacted silver bromide is removed by reaction with
sodium thiosulfate.
\( A g B r+2 N a_{2} S_{2} O_{3} \rightarrow 4 N a^{+}+ \)
\( \boldsymbol{B} \boldsymbol{r}^{-}+\left[\boldsymbol{A} \boldsymbol{g}\left(\boldsymbol{S}_{2} \boldsymbol{O}_{3}\right)_{2}\right]^{3-} \)
What is the function of the thiosulfate
ion?
A. To make the silver ions soluble
B. To oxidise the silver ions
c. To reduce the bromine
D. To reduce the silver ions
Subject: Maths
The value of \( (x- \)
\( \left(x+\frac{1}{2}-\frac{\sqrt{3}}{2} i\right)\left(x+\frac{1}{2}+\frac{\sqrt{3}}{2} i\right) \)
A. \( x^{3}+x^{2}+x 1 \)
B . \( x^{3}-1 \)
c. \( x^{3}+1 \)
D. \( x^{3}-x^{2}+x+1 \)
Subject: Physics
A charge of \( 5 \times 10^{-10} C \) is given to a
metal cylinder of length \( 10 \mathrm{m}, \) placed in air. The electric intensity at a distance of \( 0.2 \mathrm{m} \) from its axis is :
A. \( 4.5 \vee / \) m
B. \( 45 \mathrm{V} / \mathrm{m} \)
c. \( 450 \mathrm{V} / \mathrm{m} \)
D. \( 100 \mathrm{v} / \mathrm{m} \)
Subject: Maths
There are two small boxes \( A \) and \( B \). \( \ln A \)
there are 9 white beads and 8 black
beads.
\( \ln B \) there are 7 white and 8 black
beads. We want to take a bead from a
box.
(a) What is the probability of getting a white bead from each box?
(b) \( A \) white bead and a black bead are
added to box \( B \) an then a bead is taken
from it.

What is probability of getting a white bead from it.
Subject: Biology
Find out the correct order of succession
levels in xerarch.
A. Lichen, moss stage, annual herb stage, perennial herb stage, shrub stage, forest
B. Annual herb stage, perennial herb stage, lichen moss stage, shrub stage, forest
C. Perennial herb stage, annual herb stage, lichen moss stage, shrub stage, forest
D. Shrub stage, forest, annual herb stage, perennial herb stage, lichen moss stage
E. Forest, shrub stage, annual stage, perennial herb stage, lichen moss stage
Subject: Physics
\( 1 k g \) of water at \( 20^{\circ} C \) is, mixed with
\( 800 g \) of water at \( 80^{\circ} \mathrm{C} \). Assuming that no heat is lost to the
surroundings, calculate the final temperature of the mixture:
A \( \cdot 24.44^{\circ} \mathrm{C} \)
B . \( 46.67^{\circ} \mathrm{C} \)
c. \( 44.44^{\circ} \mathrm{C} \)
D. \( 54.44^{\circ} \mathrm{C} \)
Subject: Chemistry
\( \boldsymbol{K}_{a 1}, \boldsymbol{K}_{a 2} \) and \( \boldsymbol{K}_{a 3} \) are the respective
ionisation constants for the following reactions;
\( \boldsymbol{H}_{2} \boldsymbol{S} \rightleftharpoons \boldsymbol{H}^{+} \boldsymbol{H} \boldsymbol{S}^{-} \)
\( \boldsymbol{H} \boldsymbol{S}^{-} \rightleftharpoons \boldsymbol{H}^{+} \boldsymbol{S}^{2-} \)
\( \boldsymbol{H}_{2} \boldsymbol{S} \rightleftharpoons \mathbf{2} \boldsymbol{H}^{+} \boldsymbol{S}^{2-} \)
The correct relationship between
\( \boldsymbol{K}_{a 1}, \boldsymbol{K}_{a 2} \) and \( \boldsymbol{K}_{a 3} \) is:
В. \( K_{a 3}=K_{a 1}+K_{a 2} \)
C \( . K_{a 3}=K_{a 1}-K_{a 2} \)
D. \( K_{a 3}=K_{a 1} / K_{a} \)
Subject: Maths
\( X, Y \) are mid-points of opposite sides
\( A B \) and \( D C \) of a parallelogram
\( A B C D . A Y \) and \( D X \) are joined
ntersecting in \( \mathrm{P} ; C X \) and \( B Y \) are
joined intersecting in Q. What is \( \boldsymbol{P X Q Y} \) ?
A. Rectangle
B. Rhombus
C. Parallelogram
Dauare
Subject: Maths
If head means one and tail means two
then coefficients of quadratic equation
\( a x^{2}+b x+c=0 \) are chosen by tossing
three fair coins. The probability that roots of the equation are imaginary is
A \( \cdot \frac{5}{8} \)
B. \( \frac{3}{8} \)
\( c \cdot \frac{7}{8} \)
D.
Subject: Maths
The unit vectors orthogonal to \( -i+ \) \( 2 j+2 k \) and making equal angles with
\( x \) and \( y \) axis are
A \( \cdot \pm \frac{1}{3}(2 \bar{i}+2 \bar{j}-\bar{k}) \)
B. \( _{\pm \frac{1}{3}(\bar{i}+\bar{j}-\bar{k})} \)
c. \( \pm \frac{1}{3}(2 \bar{i}-2 \bar{j}-\bar{k}) \)
D. \( \pm \frac{1}{4}(\bar{i}+\bar{j}-\bar{k}) \)
Subject: Physics
A horizontal plane supports a fixed vertical cylinder of radius \( R \) and a particle is attached to the cylinder by a horizontal thread \( A B \) as shown in
figure. A horizontal velocity \( \boldsymbol{v}_{0} \) is
imparted to the particle, normal to the thread, then during subsequent motion:
A. Angular momentum of particle about \( O \) remain constant
B. Angular momentum of particle about \( B \) remains constant
c. Momentum of particle remains constant
D. Kinetic energy of particle remains constant
Subject: Physics
A mass ' \( m^{\prime} \) moves with velocity \( v= \) \( \sqrt{3} m / s \) and collides with another mass
\( 2 m \) initially at rest. After collision first mass move with velocity \( \frac{v}{\sqrt{3}} \) in the
direction perpendicular to initial
direction of motion. Speed of second mass (in \( \mathrm{m} / \mathrm{s} \) ) after collision is
Subject: Chemistry
Assertion
Specific gravity is dimensionless.
Reason
Specific gravity is density of a
substance measured w.r.t. density of
water at \( 4^{\circ} C \)
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
How many grams of carbon dioxide gas is dissolved in a 1 L bottle of carbonated
water if the manufacturer uses a
pressure of 2.4 atm in the bottling
process at \( 25^{\circ} \mathrm{C} ? \)

Given: \( K_{H} \) of \( C O_{2} \) in water \( =29.76 \)
\( \operatorname{atm} /(\operatorname{mol} / L) \) at \( 25^{\circ} \mathrm{C} \)
A. \( 3.88 \mathrm{g} \)
B. 4.90 g
c. \( 5.33 \mathrm{g} \)
D. 3.52 g
Subject: Maths
f \( x, y z \) are all different and if \( \left|\begin{array}{lll}\boldsymbol{x} & \boldsymbol{x}^{\boldsymbol{2}} & \boldsymbol{1}+\boldsymbol{x}^{\boldsymbol{3}} \\ \boldsymbol{y} & \boldsymbol{y}^{\boldsymbol{2}} & \boldsymbol{1}+\boldsymbol{y}^{\boldsymbol{3}} \\ \boldsymbol{z} & \boldsymbol{z}^{\boldsymbol{2}} & \boldsymbol{1}+\boldsymbol{z}^{\boldsymbol{3}}\end{array}\right|=0 \) then \( \mathbf{x y z}= \)
A . -1
B.
\( c . \)
D. ±1
Subject: Chemistry
Which of the following compounds
cannot be prepared singly by the Wurtz
reaction?
\( \mathbf{A} \cdot C_{2} H_{6} \)
B. \( \left(C H_{3}\right)_{2} C H C H_{3} \)
\( \mathbf{c} \cdot C H_{3} C H_{2} C H_{2} C H_{3} \)
D. All of the above can be prepared
Subject: Chemistry
Identify the unknown compounds.
\( \mathbf{A} \cdot A \rightarrow C H_{3} C O C l, B \rightarrow C_{6} H_{5} C l, C \rightarrow N a C N \)
B \( \cdot A \rightarrow C H_{3} C l, B \rightarrow C_{6} H_{5} C H_{2} C l, C \rightarrow K C N \)
\( \mathbf{C} \cdot A \rightarrow C H_{4}, B \rightarrow C_{6} H_{5} C H_{2} C l, C \rightarrow A g C N \)
\( \mathbf{D} \cdot A \rightarrow C H_{3} C l, B \rightarrow C_{6} H_{5} C O C l, C \rightarrow K C N \)
Subject: Chemistry
(a) Complete the following equations:
(i) \( C r_{2} O_{7}^{2-}+2 O H^{-} \rightarrow \)
\( M n O_{4}^{-}+4 H^{+}+3 e^{-} \rightarrow \)
(b) Account for the following:
(i) \( Z n \) is not considered as a transition
element.
(ii) Transition metals form a larger number of complexes.
(iii) The \( E^{0} \) value for the \( M n^{3+} / M n^{2+} \)
couple is much more positive than that for \( \boldsymbol{C r}^{3+} / \boldsymbol{C r}^{2+} \) couple.
Subject: Maths
Find the point on the curve \( 4 x^{2}+ \) \( a^{2} y^{2}=4 a^{2}, 4<a^{2}<8 \) that is farthest
from the point \( (\mathbf{0},-\mathbf{2}) \)
A \( .(0,0) \)
в. (0,1)
\( c \cdot(0,2) \)
D. (0,3)
Subject: Chemistry
\( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) turns acidified \( \boldsymbol{T} \boldsymbol{i} \boldsymbol{O}_{2} \) solution to
orange coloured pertitanic acid \( \left[\boldsymbol{H}_{2} \boldsymbol{T} \boldsymbol{i} \boldsymbol{O}_{4}\right] \)
A. True
B. False
Subject: Maths
If \( \mathbf{f}(\boldsymbol{\theta})=\sin ^{99} \boldsymbol{\theta} \cos ^{94} \boldsymbol{\theta} ; \boldsymbol{\theta} \in\left(-\frac{\boldsymbol{\pi}}{2}, \frac{\boldsymbol{\pi}}{2}\right) \)
attains a maximum at \( \boldsymbol{\theta} \) equals
A \( \cdot \tan ^{-1} \sqrt{\frac{94}{99}} \)
B. \( \tan ^{-1} \sqrt{\frac{99}{94}} \)
c.
D.
Subject: Physics
A particle is an oscillating simple
harmonically with angular frequency \( \omega \)
and amplitude \( A \). It is at a point \( (A) \) at \( a \)
certain instant (shown in the figure). At
this instant, it is moving towards mean
position (B). It takes time \( t \) to reach mean position (B). If the time period of oscillation is \( T, \) the average speed
between \( A \) and \( B \) is :
A. \( \frac{A \sin \omega t}{t} \)
B. \( \frac{A \cos \omega t}{t} \)
c. \( \frac{A \sin \omega t}{T} \)
D. \( A \cos \omega t \)
Subject: Physics
Consider the following statements about acceleration due to gravity on earth and mark the correct
statement(s):
A. The value of \( g \) is constant throughout
в. \( g^{\prime}=g\left(1-\frac{d}{r}\right) \)
\( \mathrm{c} . g \) is slightly less (by about \( 1 \% \) ) when distance \( <200 \mathrm{m} \)
D. \( g \) is slightly greater when distance \( <200 m \)
Subject: Physics
A person brings amass of \( 1 k g \) from
infinity to a point A Initially, the mass was at rest but it moves at a speed of \( 3 m / s \) as it reaches A. The work done by
the person on the mass is \( -5.5 J \) The
gravitational potential at \( \boldsymbol{A} \) is
A. \( -1 J / k g \)
в. \( -4.5 J / k g \)
\( \mathbf{c} .-5.5 J / k g \)
D. \( -10 J / k g \)
Subject: Maths
The General solution for the equation \( (2 \sqrt{x y}-x) d y+y d x=0 \) is?
A \( \cdot y=c e^{-\sqrt{x / y} / y} \)
B \( \cdot y=c e^{\sqrt{y / x}} \)
C \( \cdot x=c e^{\sqrt{y / x}} \)
D. None of these
Subject: Maths
If vectors \( \bar{b}, \bar{c}, \bar{d} \) are not coplanar then
prove that \( (\overline{\boldsymbol{a}} \times \overline{\boldsymbol{b}}) \times(\overline{\boldsymbol{c}} \times \overline{\boldsymbol{d}})+(\overline{\boldsymbol{a}} \times \overline{\boldsymbol{c}}) \times(\overline{\boldsymbol{d}} \times \)
\( \vec{b})+(\bar{a} \times \bar{d}) \times(\bar{b} \times \bar{c}) \) is parallel to \( \bar{a} \)
Subject: Maths
Lines \( l \) and \( m \) and two circles lie in a
plane. If \( l \) passes through the centers of the two circles and if \( m \) is parallel to \( l \)
which of the following could NOT be the number of points at which \( m \) intersects the circles?
\( \mathbf{A} \cdot \mathbf{0} \)
B. 1
\( c \cdot 3 \)
D. 4
E . 5
Subject: Maths
\( \int\left(1+x-x^{-1}\right) e^{x+x^{-1}} d x \) is equal to
A \( \cdot(x+1) e^{x+x^{-1}}+C \)
B . \( (x-1) e^{x+x^{-1}}+C \)
c. \( x e^{x+x^{-1}}+C \)
D. \( x e^{x+x^{-1}} x+C \)
Subject: Physics
Two sources of sound \( S_{1} \) and \( S_{2} \)
produce sound waves of same frequency \( 660 H z . \) A listener is moving
from source \( S_{1} \) towards \( S_{2} \) with a
constant speed \( u \) m/ \( s \) and he hears
10 beats/s. The velocity of sound is
\( 330 m / s . \) Then, \( u \) equals:
A \( .2 .5 \mathrm{m} / \mathrm{s} \)
в. \( 15.0 \mathrm{m} / \mathrm{s} \)
\( c .5 .5 m / s \)
D. \( 10.0 \mathrm{m} / \mathrm{s} \)
Subject: Biology
Assertion
Each molecule of NADPH and two ATP
are required for the fixation of one
molecule of \( \boldsymbol{C O}_{2} \)
Reason
Three molecule of NADPH and two ATP
are required the for fixation of one
molecule of \( \boldsymbol{C O}_{2} \)
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
In a closed circuit the e.m.f. and internal
resistance of the generator are \( \boldsymbol{E} \) and \( \boldsymbol{r} \)
respectively. If the external resistance
in the circuit is \( R \), then the Ohm's law
has the form:
\( ^{\mathrm{A}} \cdot_{I}=\frac{E}{(R+r)} \)
в. \( I=\frac{E}{R} \)
c. \( _{I=\frac{E}{r}} \)
D. \( _{I}=\frac{E}{R-r} \)
Subject: Chemistry
Assertion \( (A): \) Moist \( C l_{2} \) bleaches the
vegetable colouring matter Reason \( (\mathrm{R}): \mathrm{Cl}_{2} \) is a strong reducing
agent.
A. A and R are true, R is correct explanation of A
B. A and R are true,R is not correct explanation of A
c. A is true, but R is false
D. A is false, but R is true
Subject: Chemistry
\( M g \) forms \( M g(I I), \) because of:
A. The oxidation state of \( M g \) is +2
B. Difference between \( I . P_{1} \) and \( I . P_{2} \) is greater than 16.0 \( e v \)
c. There are only two electrons in the outermost energy level of \( M g \)
D. Difference between \( I . P_{1} \) and \( I . P_{2} \) is less than 11 ev
Subject: Physics
A bullet of mass \( m \) is being fired from a
stationary gun of mass \( M . \) If the
velocity of the bullet is \( v, \) the velocity of
the gun is
A \( \cdot \frac{M v}{m+M} \)
B. \( \frac{m v}{M} \)
c. \( \frac{(M+m) v}{M} \)
D. \( \frac{M+m}{M v} \)
Subject: Chemistry
Assertion
Plastics are non-biodegradable.
Reason
As they cannot be decomposed by micro-organisms.
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 Reasn is correct
Subject: Physics
The maximum power dissipated by external resistance \( \mathrm{R} \) by a cell of an external emf \( \mathrm{E} \) and internal resistance is \( \frac{E^{2}}{4 R} \) which is obtained for
\( A \cdot R<r \)
B. \( R>r \)
\( c \cdot R=r \)
D. any value of R.
Subject: Maths
Solve the inequality with absolute value
\( -3|-2 x+4|<=4 \)
\( ^{A} \cdot\left(-\infty, \frac{7}{3}\right) \)
B \( \cdot\left(\frac{7}{3},+\infty\right) \)
\( ^{c} \cdot\left(\frac{7}{3},+\frac{7}{3}\right) \)
D \( \cdot\left(0, \frac{7}{3}\right) \)
E \( .(-\infty,+\infty) \)
Subject: Physics
For a particle executing simple
harmonic motion, the displacement x is given by \( \boldsymbol{x}= \) Acoswt. Identify the graph
which represents the variation of
potential energy (U) as a function of
time \( t \) and displacement \( x \)
A . ।, II
B. ॥, ॥॥
\( c \cdot 1,1 v \)
D. II, IV
Subject: Biology
Match the following Columns I, II with III.
\begin{tabular}{lll} 
Column I (Common name) & Column II (Roman numerical designation) & Column III (Activation product) \\
A. & & \\
Prothrombin & 1.1 & (i) Convertin \\
B. & & \\
Proconvertin & 2. \( \mathrm{V} \) & (ii) Fibrin \\
Cibrinogen & 3. II & (iii) \\
D. & & Thrombin \\
Proaccelerin & 4. VII & (iv) \\
\hline
\end{tabular}
\( A \)
A- 3- (iii), B- 4- (i), C-1- (ii), D- 2- (iv)
B. D- 4- (ii), B- 3- (iii) C- 2- (iv), A- - 1- (i)
c. \( c-3- \) (iii), A- \( 4- \) (ii), B- \( 1- \) (iv), D- \( 2- \) (i)
D. A- 3- (iii),C- 4- (i), D- 2- (ii), B- 1- (iv)
Subject: Physics
Three positive charge each of magnitude \( Q \) are placed at the corner of the equilateral tringle. The value of charges placed at the centroid of the triangle such that system must be in equilibrium is
\( ^{A} \cdot \frac{+Q}{\sqrt{3}} \)
в. \( \frac{-Q}{\sqrt{3}} \)
c. \( \frac{-2 Q}{\sqrt{3}} \)
D. \( \frac{+2 Q}{\sqrt{3}} \)
Subject: Physics
Four masses (each of \( \mathrm{m} \) ) are placed at the vertices of a regular pyramid (triangular base) of side 'a'. Find the work done by the system while taking them apart so that they form the pyramid of side '2a'
\( ^{\text {A }} \cdot \frac{3 G m^{2}}{a} \)
в. \( -\frac{3 G m^{2}}{a} \)
c. \( -\frac{2 G m^{2}}{a} \)
D. \( \frac{2 G m^{2}}{a} \)
Subject: Maths
A sphere fits exactly inside a right
circular cone with base area \( 154 \mathrm{cm}^{2} \)
as shown.What is the radius of the
sphere if the height and slant height of
the cone are integers?
\( \mathbf{A} \cdot 21 / 4 \mathrm{cm} \)
B. \( 41 / 2 \mathrm{cm} \)
\( \mathbf{c} \cdot 6 \mathrm{cm} \)
D. \( 51 / 4 \mathrm{cm} \)
Subject: Physics
A car moving with a speed of 25 ms \( ^{-1} \) takes a U-turn in 5 seconds, without
changing its speed. The average acceleration during these 5 seconds is
\( \mathbf{A} \cdot 5 m s^{-2} \)
B. \( 10 m s^{-2} \)
c. \( 2.5 m s^{-2} \)
D. \( 7.5 \mathrm{ms}^{-2} \)
Subject: Physics
Three particles, each having a charge of
\( 10 C \) are placed at the corners of an
equilateral triangle of side \( 10 \mathrm{cm} \). The
electrostatic potential energy of the system is :
A . \( 100 J \)
В. \( 27 \times 10^{12} J \)
c. 0
\( D \cdot \infty \)
Subject: Maths
Solve the following:
\( \frac{2 x-3}{2 x-1}=\frac{3 x-1}{3 x+5} \)
A \( \cdot 1 \frac{2}{3} \)
в. \( 5 \frac{2}{3} \)
\( c \cdot_{7} \frac{2}{3} \)
D. \( 2 \frac{2}{3} \)
Subject: Chemistry
At \( 30^{\circ} C, \) the solubility of
\( A g_{2} C O_{3}\left(K_{s p}=8 \times 10^{-2}\right) \) will be
maximum in:
A. 0.05 M \( \mathrm{Na}_{2} \mathrm{CO}_{3} \)
B. \( 0.05 M A g N O_{3} \)
c. Pure water
D. \( 0.05 N H_{3} \)
Subject: Maths
Factorize:
\( a^{2}-(2 a+3 b)^{2} \)
\( \mathbf{A} \cdot-3(a+b)(a+3 b) \)
B \( \cdot 3(a+b)(a+3 b) \)
\( \mathbf{c} \cdot-3(a-b)(a-3 b) \)
D. \( 3(a+b)(a-3 b) \)
Subject: Chemistry
The hybrid orbitals used by Phosphorus
n the formation of \( \mathbf{P C l}_{5} \) are :
\( A \cdot s p^{3} \)
B \( \cdot \operatorname{sp}^{2} \)
c. \( d s p^{2} \)
\( D \cdot s p^{3} d \)
Subject: Maths
The construction of \( \Delta E F G \) when
\( F G=3 c m \) and \( m \angle G=60^{\circ} \) is possible
when difference of \( E F \) and \( E G \) is equal
to:
A . \( 3.2 \mathrm{cm} \)
B. \( 3.1 \mathrm{cm} \)
\( \mathrm{c} .3 \mathrm{cm} \)
D. 2.8 \( c m \)
Subject: Chemistry
\( 100 g \) of liquid \( A \) (molar mass \( \left.140 g m o l^{-1}\right) \) was dissolved in \( 1000 g \) of liquid B (molar mass \( 180 g \) mol\( ^{-1} \) ). The
vapour pressure of pure liquid B was
found to be 500 torr. Calculate the
vapour pressure of pure liquid \( A \) and its vapour pressure in the solution if the
total vapour pressure of the solution is
475 torr.
Subject: Maths
ff \( f(x) \) be a polynomial function
satisfying \( f(x) f\left(\frac{1}{x}\right)=f(x)+f\left(\frac{1}{x}\right) \) and
\( \boldsymbol{f}(\mathbf{4})=\mathbf{6 5} . \) Then, find \( \boldsymbol{f}(\boldsymbol{6}) \)
Subject: Biology
You remove four fresh tobacco leaves of
similar size and age. Leave "leaf \( 1 " \) as it is, smear "leaf \( 2^{\prime \prime} \) with vaseline on the
upper surface, "leaf \( 3^{\prime \prime} \) on the lower
surface and "leaf \( 4 " \) on both the
surfaces. Hang the leaves for a few hours and you observe that leaf 1 wilts
the most, leaf 2 has wilted, leaf 3 wilted
less than leaf 2 and leaf 4 remains
fresh. Which of the following conclusion is most logical?
A. Tobacco leaf has more stomata on the upper surface
B. Tobacco leaf has more stomata on the lower surface
c. Stomata are equally distributed in upper and lower surfaces
D. No conclusion on stomatal distribution can be drawn from this experiment
Subject: Maths
If \( 0<x<1000 \) and \( \left[\frac{x}{2}\right]+\left[\frac{x}{3}\right]+ \)
\( \left[\frac{x}{5}\right]=\frac{31}{30} x \) where \( [x] \) is the greatest
integer less than or equal to \( x \), the number of possible values of \( x \) is
A . 34
B. 32
\( c .33 \)
D. 30
Subject: Physics
A sphere of radius \( r \) has a volume density of charge \( \rho=k r . \) Find the
electric field intensity at the surface of
the sphere.
A. \( \frac{4 \pi k R^{4}}{3 \epsilon_{0}} \)
в. \( \frac{k R}{3 \epsilon_{0}} \)
c. \( \frac{4 \pi k R}{\epsilon_{0}} \)
D. \( \frac{k R^{2}}{4 \epsilon_{0}} \)
Subject: Chemistry
Consider the following statements.
I Pig iron is malleable and ductile.
Il : Pig iron can be melted to produce cast iron of desired shapes.
III : Wrought iron is obtained by heating pig iron with iron oxide in a furnace.
Which of the statement(s) given above is/are correct?
A. I only
B. I and II
c. ॥ and III
D. III only
Subject: Maths
Differentiate the following w.r.t. \( x \)
\( \sin ^{2} \sqrt{x} \)
A \( \cdot \frac{1}{2 \sqrt{x}} \sin (3 \sqrt{x}) \)
B. \( \frac{1}{\sqrt{x}} \sin (2 \sqrt{x}) \)
c. \( \frac{1}{2 \sqrt{x}} \sin (2 \sqrt{x}) \)
D. \( \frac{1}{2 \sqrt{x}} \sin (4 \sqrt{x}) \)
Subject: Physics
A charged oil drop is suspended in a
uniform field of \( 3 \times 10^{4} \mathrm{v} / \mathrm{m} \) so that it
neither falls nor rises. The charge on the drop will (Take the mass of the charge \( = \)
\( 9.9 \times 10^{-15} \mathrm{kg} \) and \( \mathrm{g}=10 \mathrm{m} / \mathrm{s}^{2} \)
A . \( 1.25 \times 10^{10} C \)
В. \( 2.5 \times 10^{10} C \)
c. \( 3.3 \times 10^{-18} \mathrm{C} \)
D. none
Subject: Maths
If \( \boldsymbol{m} \tan \left(\boldsymbol{\theta}-\mathbf{3 0}^{\circ}\right)=\boldsymbol{n} \tan \left(\boldsymbol{\theta}+\mathbf{1 2 0}^{\circ}\right) \)
then \( \frac{m-n}{m+n} \) is equal to
A \( .2 \cos 2 \theta \)
B. \( 2 \sin ^{2} \theta \)
c. \( 1 /(8 \cos 2 \theta) \)
D. \( 1 /(8 \sin 2 \theta) \)
Subject: Physics
Inside a railway car a plumb bob (a heavy mass suspended by a thread) is suspended from the roof and a helium filled balloon is tied by a string to the
floor of the car. When the railway car accelerates to the right, then
A. Both the plumb bob and balloon move to the left
B. Both the plumb bob and balloon move to the right
c. Plumb bob moves to the left and the balloon moves to the right
D. Plumb bob moves to the right and the balloon moves to the left
Subject: Physics
If \( 10 g \) of the ice at \( 0^{0} C \) is mixed with
\( 10 g \) of water at \( 10^{0} C, \) then the final
temperature of the mixture will be :
\( \mathbf{A} \cdot 5^{0} C \)
B. \( 0^{\circ} \mathrm{C} \)
c. \( 100 K \)
D. \( 40^{\circ} \mathrm{C} \)
Subject: Physics
A uniform thin rod of Length L and Mass M is bent at the middle point 0
Consider an axis passing through its middle point 0 and perpendicular to the plane of the bent rod. The moment of inertia about this axis is:
A \( \cdot \frac{2}{3} m L^{2} \)
B. \( \frac{1}{3} m L^{2} \)
c. \( \frac{1}{12} m L^{2} \)
D. Dependent on \( \theta \)