AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
The median of the following items \( \mathbf{2 5}, \mathbf{1 5}, \mathbf{2 3}, \mathbf{4 0}, \mathbf{2 7}, \mathbf{2 5}, \mathbf{2 3}, \mathbf{2 5} \) and \( \mathbf{2 0} \) is
A .27
B . 40
c. 25
D. 23
Subject: Chemistry
\( X e F_{2} \) reacts with \( P F_{5} \) to give:
A. \( X e F_{6} \)
\( \mathbf{B} \cdot[X e F]^{+}\left[P F_{6}\right]^{-} \)
c. \( x e F_{4} \)
\( \mathbf{D} \cdot\left[P F_{4}\right]^{+}\left[X e F_{3}\right]^{-} \)
Subject: Physics
Figure shows a potentiometer with a cell of \( 2.0 \mathrm{V} \) and internal resistance 0.40
\( \Omega \) maintaining a potential drop across
the resistor wire AB. A standard cell
which maintains a constant emf of 1.02
V gives a balance point at \( 67.3 \mathrm{cm} \)
length of the wire. The standard cell is
then replaced by a cell of unknown emf
E and the balance point, similarly turns out to be at \( 82.3 \mathrm{cm} \), length of the wire. Then the E is
\( A \cdot 1 V \)
B. 1.25 \( v \)
\( c \cdot 1.5 v \)
D. \( 1.75 \mathrm{v} \)
Subject: Biology
Consider the following statements:
(a) In leguminous plants, leaf base becomes swollen, called pulvinus.
(b) The fleshy leaves of onion and garlic
store food
(c) In Alstonia, leaves show alternate
phyllotaxy.
(d) The lamina in Australian acacia
become green and synthesize food.
Of the above statements.
A \( \cdot(b) \) and
(d) are correct
B. (a) and
(c) are correct
c. (a) and (b) are correct
D. (b) and
(c) are correct
E . (a) and
(d) are correct
Subject: Chemistry
The ions \( M g^{+2} \) and \( P O_{4}^{-3} \) combine to
form compounds:
\( \mathbf{A} \cdot M g_{3}\left(P O_{4}\right)_{2} \)
в. \( M g_{2}\left(P O_{4}\right)_{2} \)
c. \( M g_{2}\left(P O_{4}\right)_{3} \)
D. \( M g_{3}\left(P O_{4}\right)_{3} \)
Subject: Chemistry
A heat engine carries one mole of an
ideal mono-atomic gas around the cycle
as shown in figure, the amount of heat
added in the process \( A B \) and heat
removed in the process \( C A \) are:
A \( \cdot q_{A B}=450 R \) and \( q_{C A}=-450 R \)
B . \( q_{A B}=450 R \) and \( q_{C A}=-225 R \)
\( \mathbf{c} \cdot q_{A B}=450 R \) and \( q_{C A}=-375 R \)
\( \mathbf{D} \cdot q_{A B}=375 R \) and \( q_{C A}=-450 R \)
Subject: Maths
The system of linear equations:
\( \boldsymbol{\lambda} \boldsymbol{x}+\boldsymbol{2} \boldsymbol{y}+\boldsymbol{2} \boldsymbol{z}=\mathbf{5} \)
\( 2 \lambda x+3 y+5 z= \)
\( 4 x+\lambda y+6 z=10 \) has
A. no solution when \( \lambda=2 \)
B. a unique solution when \( \lambda=-8 \)
c. infinitely many solutions when \( \lambda=2 \)
D. no solution when \( \lambda=8 \)
Subject: Physics
A light rigid rod of length \( \boldsymbol{L}=\frac{8}{5} \mathrm{m} \)
hinged at one end has a bob of mass \( \mathrm{m} \)
attached to its other end. Find speed (in
\( \mathrm{m} / \mathrm{s} \) ) of bob at the lowest point when rod is released from vertical position.
Subject: Maths
The area enclosed between the curves
\( \boldsymbol{y}=\boldsymbol{x}^{3} \) and \( \boldsymbol{y}=\sqrt{\boldsymbol{x}} \) is, (in square
units):
A \( \cdot \frac{5}{3} \)
в.
c. \( \frac{5}{12} \)
D. \( \frac{12}{5} \)
Subject: Physics
If velocity of a particle at a position os \( \operatorname{given} \operatorname{as} v^{2}=2 x, \) then the acceleration
of particle is [where \( x \) is metre and \( v \) in \( \mathrm{m} / \mathrm{s}] \)
A \( \cdot 4 m / s^{2} \)
в. \( 0.5 m / s^{2} \)
\( \mathbf{c} \cdot 2 m / s^{2} \)
D. \( 1 m / s^{2} \)
Subject: Physics
If a body is projected with a velocity of
\( 9.8 m / s \) making an angle of \( 45^{\circ} \) with the horizontal, then the range of the
projectile is (Take \( \boldsymbol{g}=\mathbf{9 . 8} \boldsymbol{m} / \boldsymbol{s}^{2} \) )
\( \mathbf{A} \cdot 39.2 m \)
в. \( 9.8 m \)
\( \mathrm{c} .4 .9 \mathrm{m} \)
D. \( 19.6 m \)
Subject: Physics
A loop of magnetic moment \( \overrightarrow{\boldsymbol{M}} \) is placed in the orientation of unstable equilibrium position in uniform magnetic field \( \vec{B} \). The external work
done in rotating it through an angle \( \theta \) is
A. \( -M B(1-\cos \theta) \)
B. \( -M B(\cos \theta) \)
\( \mathbf{c} \cdot M B \cos \theta \)
D. \( M B(1-\cos \theta) \)
Subject: Maths
Let \( X \) and \( Y \) be two random variables.
The relationship \( \boldsymbol{E}(\boldsymbol{X} \boldsymbol{Y})=\boldsymbol{E}(\boldsymbol{x}) \cdot(\boldsymbol{Y}) \)
holds.
A. Always
B. If \( E(X+Y)=E(X)+E(Y) \) is true
c. If \( X \) and \( Y \) are independent
D. If \( X \) can be obtained from \( Y \) by a linear transformation
Subject: Physics
An object, \( 1 m \) tall, is put in front of a
plane mirror at a distance of 0.2 m.The
size of the image formed is:
A. \( 0.2 m \)
в. \( 0.5 m \)
\( \mathrm{c} .0 .1 \mathrm{m} \)
D. \( 1 m \)
Subject: Chemistry
Assertion
A substance that can either act as an
acid or a base is called ampholyte.
Reason
Bisulphide ion \( \left(\boldsymbol{H} \boldsymbol{S}^{-}\right) \) and bicarbonate
ion \( \left(H C O_{3}^{-}\right) \) are ampholytes.
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
The conditions favourable for the
reaction: \( 2 S O_{2}(g)+O_{2}(g) \rightleftharpoons \)
\( 2 S O_{3}(g) ; \triangle H^{\circ}=-198 K J \) are
A. low temperature,high pressure
B. any value of T and P
c. low temperature and low pressure
D. high temperature and high pressure
Subject: Maths
Given, \( |\vec{a}|=|\vec{b}|=1 \) and \( |\vec{a}+\vec{b}|=\sqrt{3} .1 \)
\( \vec{c} \) be a vector such that \( \vec{c}-\vec{a}-2 \vec{b}= \) \( \mathbf{3}(\overrightarrow{\boldsymbol{a}} \times \overrightarrow{\boldsymbol{b}}), \) then \( \overrightarrow{\boldsymbol{c}} . \overrightarrow{\boldsymbol{b}} \) is equal to
A \( \cdot-\frac{1}{2} \)
в. \( \frac{1}{2} \)
\( c \cdot \frac{3}{2} \)
D.
Subject: Chemistry
Which of the following mixtures in aqueous solution acts as a buffer?
A. \( H N O_{3}+K N O_{3} \)
в. \( H_{2} S O_{4}+K_{2} S O_{4} \)
c. \( N H_{4} O H+N H_{4} C l \)
D. \( C H_{3} \) СООН \( + \) NaCl
Subject: Maths
The angles of a triangle are \( (2 x+ \) \( \left.30^{\circ}\right),\left(3 x-110^{\circ}\right) \) and \( \left(\frac{5}{2} x+20^{\circ}\right), \) find
the value of \( x \)
A \( \cdot 16^{\circ} \)
В. \( 32^{\circ} \)
\( c \cdot 40^{\circ} \)
\( D \cdot 50^{\circ} \)
Subject: Maths
ff \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) defined by \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{2} \boldsymbol{x}+\mathbf{5} \)
if \( \boldsymbol{x}>\mathbf{0} ; \boldsymbol{f}(\boldsymbol{x})=\mathbf{3} \boldsymbol{x}-\mathbf{2}, \) if \( \boldsymbol{x} \leq \mathbf{0}: \) then \( \boldsymbol{f} \)
is
A . a function
B. one one
c. onto
D. one-one and onto
Subject: Chemistry
A cell with two electrodes, one of grey
tin and the other white tin, both dipped
in solution of \( \left(N H_{4}\right)_{2} S n C l_{6} \) showed
zero e.m.f. at \( 18^{\circ} \mathrm{C} \). What conclusion may
be drawn from this?
A. The e.m.f. developed at the electrode-solution phase boundary cancels the normal e.m.f.
B. Grey tin being non-metallic ceases to provide a reversible electrode reaction
C. Electrode surface develops a protective layer and the cell develops a very large internal resistance
D. The Gibbs energy change of the cell becomes zero
Subject: Chemistry
Which of the following reactions does
not occur?
A \( \cdot F_{2}+2 C l^{-} \rightarrow 2 F^{-}+C l_{2} \)
B. \( C l_{2}+2 F^{-} \rightarrow 2 C l^{-}+F_{2} \)
c. \( B r_{2}+2 I^{-} \rightarrow 2 B r^{-}+I_{2} \)
D. \( C l_{2}+2 B r^{-} \rightarrow 2 C l^{-}+B r_{2} \)
Subject: Chemistry
The partial pressure of \( \boldsymbol{O}_{2} \) in air is 0.21 at \( m \) at sea level. If aquatic life
requires a concentration of \( \boldsymbol{O}_{2} \) at least
4.16 \( m g / \) litre, will the aquatic life
sustain in sea level lake. \( \boldsymbol{K}_{\boldsymbol{H}} \) for \( \boldsymbol{O}_{2} \) is \( 1.3 \times 10^{-3} \) mol / litre - atm.
A. 0.82 mg/litre
в. \( 0.87 \mathrm{mg} / \) litre
c. 0.95 mg/litre
D. \( 0.9 \mathrm{mg} / \) litre
Subject: Physics
A toroid with mean radius \( r_{0} \) and
diameter \( 2 a \) has \( N \) turns carrying current I. What is the magnetic field B inside the toroid?
A \( \cdot \frac{\mu_{0} N I}{2 \pi r_{0}} \)
В. \( \frac{\mu_{0} N I}{2 \pi\left(r_{0}+a\right)} \)
c. \( \frac{\mu_{0} N I}{\pi\left(r_{0}+a\right)} \)
D. zero
Subject: Maths
If \( \boldsymbol{y}=\sqrt{\boldsymbol{x}}+\sqrt{\boldsymbol{y}+\sqrt{\boldsymbol{x}+\sqrt{\boldsymbol{y}+\ldots \infty}}} \)
then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}= \)
A \( \cdot \frac{y^{2}-x}{2 y^{3}-2 x y-1} \)
В. \( \frac{x^{2}-x}{2 x^{3}-2 x y-1} \)
C. \( \frac{x^{2}-x}{2 x^{3}-2 x y^{2}-1} \)
D. None of these
Subject: Chemistry
When moderate amount of sodium
metal is dissolved in liquid \( N H_{3} \) at low
temperature, which one of the following \( \operatorname{occur}(s) ? \)
This question has multiple correct options
A. Blue colored solution is obtained
B. \( N a^{+} \) ions are formed in the solution
C . Liquid \( N H_{3} \) becomes good conductor of electricity
D. Liquid \( N H_{3} \) remains diamagnetic.
Subject: Maths
The function \( \mathbf{f}(\mathbf{x})=\frac{\cos \mathbf{3} \boldsymbol{x}-\cos \mathbf{4} \boldsymbol{x}}{\boldsymbol{x} \sin \mathbf{2} \boldsymbol{x}} \) for
\( \neq \mathbf{0}, \mathbf{f}(\mathbf{0})=\frac{\mathbf{7}}{\mathbf{4}} \mathbf{a t} \boldsymbol{x}=\mathbf{0}, \) is
This question has multiple correct options
A. Continuous
B. discontinuous
c. left continuous
D. right continuous
Subject: Chemistry
acts as the
cathode.
\( \mathbf{A} \cdot Z n(s) \)
B. \( C u^{2+}(a q) \)
\( \mathbf{c} \cdot Z n^{2+}(a q) \)
\( \mathbf{D} \cdot C u(s) \)
E \( . H_{2} O \)
Subject: Chemistry
Assertion
Reduciton potential value of \( \left(\boldsymbol{E}^{\circ}\right) \) of \( \mathbf{0} \)
benzoquine (I) is greater than pbezoquinone (II)
Reason
Two adjacent (C=0) groups in (I)
destablise (I) relative to (II).
o-benzoquinone p-benzoquinone
\( (\mathrm{I}) \)
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
The line represented by the equation \( \boldsymbol{y}=-\boldsymbol{2} \boldsymbol{x}+\boldsymbol{6} \) is the perpendicular
bisector of the line segment AB. If A has the coordinates \( (7,2), \) what are the
coordinates for B ?
A. (3,0)
(年) (3,0),(0,0)
в. (4,0)
c. (6,2)
(年. \( 6,2,2,6) \)
D. (5,6)
Subject: Maths
The function \( \mathbf{f}(\mathbf{x})=\mathbf{2} \log (\mathbf{x}-\mathbf{3})- \)
\( x^{2}+6 x+3 \) increases in the interval
A . (3,4)
в. \( (-\infty, 2) \)
\( c \cdot(3, \infty) \)
D. None ot these
Subject: Physics
The figure below shows a pattern of two
fishes. Write the mapping rule for the
rotation of Image A to Image B.
A. Image B has to be rotated by 90 degrees anticlockwise to map with image \( A \)
B. Image B should first have a mirror reflection and then be rotated to map with image \( A \)
C. The width of image B should be reduced by 1 unit ( square in the graph shown) and then rotated by 90 degrees to map with image \( A \)
D. The width of image B should be increased by 1 unit square in the graph shown) and then rotated by 90 degrees to map with image \( A \)
Subject: Physics
The figure shows three circuits I, II and
III which are connected to a \( 3 V \) battery.
If the powers dissipated by the
configurations \( \boldsymbol{I}, \boldsymbol{I} \boldsymbol{I} \) and \( \boldsymbol{I} \boldsymbol{I} \boldsymbol{I} \) are \( \boldsymbol{P}_{1}, \boldsymbol{P}_{2} \)
and \( P_{3} \) respectively, then :
\( \mathbf{A} \cdot P_{1}>P_{3}>P_{2} \)
В \( \cdot P_{2}>P_{1}>P_{3} \)
\( \mathbf{c} \cdot P_{1}>P_{2}>P_{3} \)
\( \mathbf{D} \cdot P_{3}>P_{2}>P_{1} \)
Subject: Chemistry
When one mole of each of the following complex is treated with an excess of
\( A g N O_{3} \).which will give maximum
amount of \( \boldsymbol{A} \boldsymbol{g} \boldsymbol{C l} \) ?
\( \mathbf{A} \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{6}\right] C l_{3} \)
в. \( \left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5} \mathrm{Cl}\right] \mathrm{Cl}_{2} \)
\( \mathbf{c} \cdot\left[\operatorname{Co}\left(N H_{3}\right) C l_{2}\right] C l \)
D. \( \left[C o\left(N H_{3}\right)_{3} C l_{3}\right] \)
Subject: Maths
A building has 8 right cylindrical pillars whose cross sectional diameter is \( 1 \mathrm{m} \)
and whose height is \( 4.2 \mathrm{m} \). Find the expenditure to paint these pillars at the
rate of Rs.24 per \( \boldsymbol{m}^{2} \)
A . Rs.2534.40
B. Rs.2506.13
c. Rs.2610.9
D. Rs.2514.5
Subject: Maths
If \( \boldsymbol{A} \) satisfies the equation \( \boldsymbol{x}^{3}-\mathbf{5} \boldsymbol{x}^{2}+ \)
\( 4 x+k I=0, \) then \( A^{-1} \) exists if
A. \( k \neq-1 \)
в. \( k \neq 0 \)
c. \( k \neq 1 \)
D. none of these
Subject: Physics
A sinusoidal progressive wave is generated in a string. It's equation is given by \( y=(2 m m) \sin (2 \pi x- \)
\( \mathbf{1 0 0} \pi \boldsymbol{t}+\boldsymbol{\pi} / \mathbf{3}) . \) The time when particle
at \( x=4 m \) first passes through mean
position, will be
A \( \cdot \frac{1}{150} \sec \)
в. \( \frac{1}{12} \) sec
c. \( \frac{1}{300} \) sec
D. \( \frac{1}{100} \) sec
Subject: Physics
A sphere of solid material of specific
gravity 8 has a concentric spherical cavity and just sinks in water. The ratio
of radius of cavity to that of outer
radius of the sphere must be
\( \mathbf{A} \cdot 4^{1 / 3} \)
\( ^{\text {В } \cdot \frac{5^{1 / 3}}{2}} \)
c. \( \frac{9^{1 / 3}}{2} \)
D. \( \frac{3^{1 / 3}}{2} \)
Subject: Chemistry
\( \boldsymbol{H}-\boldsymbol{F} \) form stronger bond than
\( \boldsymbol{H}_{2} \boldsymbol{O}[\because \boldsymbol{E} \boldsymbol{N} \boldsymbol{o} \boldsymbol{f} \boldsymbol{F}>\boldsymbol{O} \& \boldsymbol{H} \text { bond } \boldsymbol{\alpha} \)
\( \boldsymbol{E} \boldsymbol{N}] \) still heat of vapourisation of \( \boldsymbol{H} \boldsymbol{F} \)
is lower than that of pure water. Why?
Subject: Chemistry
Select incorrect statement.
A. Mellitic acid is benzene hexa-carboxylic acid.
B. \( P b \) dissolves in conc. \( H C l \) forming \( P b C l_{2} \)
C \( . P b \) dissolves in hot \( N a O H \) forming \( N a_{2}\left[P b(O H)_{6}\right] \)
D. Diamond is unreactive but graphite forms \( (C H)_{n} \) with
\( F_{2} \)
Subject: Chemistry
If the bond dissociation energies of \( \boldsymbol{X} \boldsymbol{Y} \)
\( X_{2} \) and \( Y_{2} \) (all diatomic molecules) are
in the ratio of 1: 1: 0.5 and \( \Delta_{1} H \) for the
formation of \( X Y \) is \( -200 k J \) mol\( ^{-1} . \) The
bond dissociates energy of \( X_{2} \) will be:
A \( .100 \mathrm{kJ} \mathrm{mol}^{-1} \)
в. 200 kJ mol-
c. \( 800 k J \) mol \( ^{-1} \)
D. \( 400 \mathrm{kJ} \mathrm{mol}^{-1} \)
Subject: Maths
Using properties of determinants, prove
the following:
\( \left|\begin{array}{ccc}a^{2} & b c & a c+c^{2} \\ a^{2}+a b & b^{2} & a c \\ a b & b^{2}+b c & c^{2}\end{array}\right|=4 a^{2} b^{2} c^{2} \)
Subject: Physics
Angular momentum of a planet of mass \( m \) orbiting around sun is \( J \). Areal velocity of its radius vector will be:
A \( \cdot \frac{J}{2 M} \)
в. \( \frac{J}{M} \)
c. \( \frac{m}{2 J} \)
D. \( \frac{1}{2 m J} \)
Subject: Chemistry
Consider the cell:
\( \boldsymbol{C d}(\boldsymbol{s})\left|\boldsymbol{C} \boldsymbol{d}^{2+}(\mathbf{1} . \boldsymbol{0} \boldsymbol{M}) \| \boldsymbol{C} \boldsymbol{u}^{2+}(\mathbf{0 . 1} \boldsymbol{M})\right| \boldsymbol{C} \)
If we wish to make a cell with a more
positive voltage using the same substance, we should:

This question has multiple correct options
A \( \cdot \) increase both \( \left[C d^{2+}\right] \) and \( \left[C u^{2+}\right] \) to 2.0 M
B. decrease the \( \left[C d^{2+}\right] \) to \( 0.1 \mathrm{M} \)
c. increase the \( \left[C u^{2+}\right] \) to \( 1.0 \mathrm{M} \)
D. decrease both the \( \left[C d^{2+}\right] \) and \( \left[C u^{2+}\right] \) to 0.01 M
Subject: Maths
A dishonest dealer sells his goods at
cost price but uses \( 20 \% \) less weight.
What is his profit or loss \( \% ? \)
\( \mathbf{A} \cdot 22.5 \% \)
B . \( 12.5 \% \)
c. \( 25 \% \)
D. 50\%
Subject: Physics
A rectangular loop of sides \( a \) and \( b \) is
placed in \( \boldsymbol{x}-\boldsymbol{y} \) plane. A uniform but
time varying magnetic field of strength \( \vec{B}=20 t \hat{i}+10 t^{2} \hat{j}+50 \hat{k} \) is present in
the region. The magnitude of induced
emf in the loop at time \( t \) is :
A. \( 20+20 t \)
B . 20
\( c .20 t \)
D. zero
Subject: Physics
A steel rod is clamped at its two ends and rests on a fixed horizontal base. The
rod is in natural length at \( 20^{\circ} \mathrm{C} \). Find the longitudinal strain developed in the
rod if the temperature rises to \( 50^{\circ} \mathrm{C} \)
Coefficient of linear expansion of steel
\( =1.2 \times 10^{-6} /^{\circ} \mathrm{C} \)
A \( .3 .6 \times 10^{-4} \)
B . \( 3.6 \times 10^{-5} \)
\( \mathbf{c} \cdot 6 \times 10^{-4} \)
D. \( 2.4 \times 10^{-5} \)
Subject: Maths
If \( x>0 \) and \( \cos ^{-1}\left(\frac{12}{x}\right)+ \)
\( \cos ^{-1}\left(\frac{35}{x}\right)=\frac{\pi}{2}, \) then \( x \) is
\( A \cdot 7 \)
B. 39
c. 37
D. -37
Subject: Chemistry
Consider the reaction: \( C l_{2}+2 K I \rightarrow \)
\( \boldsymbol{I}_{2}+2 \boldsymbol{K} \boldsymbol{C l} \)
Which species will be reduced at the cathode?
A \( \cdot C l_{2} \)
В. \( I_{2} \)
c. \( I^{-} \)
D. \( C l \)
Subject: Physics
A broadcasting centre broadcasts at 300 metre band. A capacitor of capacitance \( 2.5 \mu \mathrm{F} \) is available. The value of the inductance required for resonant circuit is nearly
A \( \cdot 1 \times 10^{-4} \mathrm{H} \)
В. \( 1 \times 10^{-8} \mathrm{H} \)
c. \( 1 \times 10^{-6} H \)
D. \( 1 \times 10^{-2} H \)
Subject: Physics
Show dimensionally that the frequency
(a) of transverse wanes in a string of
length / and mass per unit length \( \boldsymbol{m} \)
under a tension T is given by, \( \boldsymbol{n}= \) \( \boldsymbol{k} \sqrt{\boldsymbol{T}} / \boldsymbol{l} \sqrt{\boldsymbol{m}} \)
Subject: Physics
Four similar charges each of magnitude
\( Q \) are placed at the four comers of a
square of side 'a'. The intensity of the
electric field at the intersection of the
diagonal is
A. 0
в. \( \frac{Q}{4 \pi \varepsilon_{0} a^{2}} \)
c. \( \frac{4 Q}{4 \pi \varepsilon_{0} a^{2}} \)
D. \( \frac{Q}{8 \pi \varepsilon_{0} a^{2}} \)
Subject: Biology
In the pelvic girdle of man \( A, B, C, D \) and
E respectively represents
A. A-Pubis, B-Acetabulum, C-llium, D-Ischium, E-Pubic symphysis
B. A-llium, B-Acetabulum, C-Pubis, D-Ischium, E-Pubic
symphysis
C. A-lschium, B-Acetabulum, C-Pubis, D-llium, E-Pubic symphysis
D. A-llium, B-Pubis, C-Acetabulum, D-Pubic symphysis E-lschium
E. A-llium, B-Acetabulum, C-Pubic symphysis, D-Ischium, E-Pubis
Subject: Physics
A stone is thrown upwards with a
velocity \( 50 m g^{-1} \). Another stone is
simultaneously thrown downwards from the same location with a velocity
\( 50 m s^{-1} . \) When the first stone is at the
highest point, the relative velocity of the
second stone w.r.t. the first stone is:
A. Zero
B. \( 50 m s^{-1} \)
c. \( 100 \mathrm{ms}^{-1} \)
D. \( 150 \mathrm{ms}^{-1} \)
Subject: Physics
Assertion
At absolute zero semiconductors
behaves as the ideal insulator.
Reason
In semiconductor electron vibration
happen at room temperature. But at
very low-temperature electron can not
get energy and so it can not vibrate. and
so current can not pass,so
semiconductor act as an insulator.
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 particle is projected horizontally from
the top of a tower with a velocity \( v_{0} . \) If \( v \)
be its velocity at any instant, then the radius of curvature of the path of the particle at that instant is directly proportional to
\( \mathbf{A} \cdot v^{3} \)
B \( \cdot v^{2} \)
c.
D. \( \frac{1}{v} \)
Subject: Maths
If \( \boldsymbol{A}=\{\boldsymbol{p}, \boldsymbol{q}, \boldsymbol{r}, \boldsymbol{s}\}, \boldsymbol{B}=\{\boldsymbol{r}, \boldsymbol{s}, \boldsymbol{t}, \boldsymbol{u}\}, \) then
\( \boldsymbol{A} / \boldsymbol{B} \) is:
\( A \cdot(p, q) \)
\( B \cdot\{r, s\} \)
c. \( \{t, u\} \)
D. \( \{p, q, t, u\} \)
Subject: Physics
Two identical containers connected by a
fine capillary tube contain air at N.T.P. if one of those containers is immersed in
pure water, boilling under normal pressure then new pressure is
\( A .76 \mathrm{cm} \) of \( \mathrm{Hg} \)
B. 152 \( \mathrm{cm} \) of \( \mathrm{Hg} \)
c. \( 57 \mathrm{cm} \) of \( \mathrm{Hg} \)
D. 87.76 cm of Hg
Subject: Physics
Two copper wires having the length in ratio 4: 1 and their radii ratio as 1: 4
are stretched by the same force. Then the ratio of the longitudinal strain in the two will be
\( \mathbf{A} \cdot 1: 16 \)
B. 16: 1
\( \mathbf{c} \cdot 1: 64 \)
D. 64: 1
Subject: Maths
If \( \boldsymbol{A} \times \boldsymbol{B}= \)
\( \{(3, a),(3,-1),(3,0),(5, a),(5,-1),(5 \)
find \( \boldsymbol{A} \)
A \( \cdot\{a, 5\} \)
в. \( \{a,-1\} \)
c. \{0,5\}
D. \{3,5\}
Subject: Chemistry
Assertion
With the help of redox titration, we can determine the the concentration of
unknown solution using a standard
solution of known concentration
Reason

We can determine the unknown
concentration using the formula:
\( \boldsymbol{N}_{\mathbf{1}} \boldsymbol{V}_{\mathbf{1}}=\boldsymbol{N}_{\mathbf{2}} \boldsymbol{V}_{\mathbf{2}} \)
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
An \( \alpha- \) particle of energy 5 MeV is
scattered through \( 180^{\circ} \) by a fixed
uranium nucleus. The distance of
closest approach is of the order of
A \( \cdot 10^{-12} \mathrm{cm} \)
B . \( 10^{-10} \mathrm{cm} \)
\( c \cdot 1 A \)
D. \( 10^{-15} \mathrm{cm} \)
Subject: Maths
\( \int \frac{\boldsymbol{d x}}{\left(x^{2}+1\right)\left(x^{2}+4\right)}= \)
A \( \cdot \frac{1}{3} \tan ^{-1} x-\frac{1}{3} \tan ^{-1} \frac{x}{2}+c \)
B - \( \frac{1}{3} \tan ^{-1} x+\frac{1}{3} \tan ^{-1} \frac{x}{2}+c \)
c. \( \frac{1}{3} \tan ^{-1} x-\frac{1}{6} \tan ^{-1} \frac{x}{2}+c \)
\( \mathbf{D} \cdot \tan ^{-1} x-2 \tan ^{-1} \frac{x}{2}+c \)
Subject: Maths
Assertion
\( (A): \frac{\tan 3 x-\tan 2 x}{1+\tan 3 x \tan 2 x}=1 \Rightarrow x= \)
\( n \pi+\frac{\pi}{4}, n \in l \)
Reason
\( (R): \tan x \) is not defined at \( x=n \pi+ \)
\( \frac{\pi}{2}, n \in l \)
A. Both (A) and (R) are individually true and (R) is the correct explanation of (A)
B. Both (A) and (R) are individually 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: Physics
A vector \( \vec{A}=2 \hat{i}+3 \hat{j}+6 \hat{k} \) makes an
angle of \( \beta \) with positive direction of \( x- \) axis. \( \beta \) is equal to:
A \( \cdot \tan ^{-1} \frac{2}{7} \)
B. \( \sin ^{-1} \frac{2}{7} \)
\( c \cdot \cos ^{-1} \frac{2}{7} \)
D. \( \cos ^{-1} \frac{4}{7} \)
Subject: Chemistry
At \( 50 \mathrm{C} \), liquid \( N H_{3} \) has ionic product is
\( 10^{-30} . \) How many amide \( \left(N H_{2^{-}}\right) \) ions
are present per \( m m^{3} \) in pure liquid \( N H_{3} ?\left(\operatorname{take} N_{A}=6 \times 10^{23}\right) \)
Subject: Physics
A taut string for which \( \mu=5.00 \times \)
\( 10^{-2} k g / m \) is under a tension of \( 80.0 \mathrm{N} \)
How much power must be supplied to the string to generate sinusoidal waves at a frequency of \( 60.0 \mathrm{Hz} \) and an
amplitude of \( 6.00 \mathrm{cm} ? \)