AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
If \( \boldsymbol{A}\left(\mathbf{1}, \boldsymbol{p}^{2}\right), \boldsymbol{B}(\mathbf{0}, \mathbf{1}) \) and \( \boldsymbol{C}(\boldsymbol{p}, \mathbf{0}) \) are the
coordinates of three points, then the
value of \( p \) for which the area of the
triangle \( A B C \) is minimum is
A \( \cdot \frac{1}{\sqrt{3}} \)
B. \( -\frac{1}{\sqrt{3}} \)
c. \( \frac{1}{\sqrt{2}} \) or \( -\frac{1}{\sqrt{3}} \)
D. none
Subject: Physics
When slightly different weights are placed on the two pans of a beam balance, the beam comes to rest at an
angle with the horizontal. The beam is supported at a single point \( P \) by a pivot. Then which of the following statement(s) is/are true?
nonzero at the equilibrium position
B. The whole system does not continue to rotate about \( P \) because it has a large moment of inertia
c. The centre of mass of the system lies below P.
D. The centre of mass of the system lies above P.
Subject: Maths
A vector \( n \) of magnitude 8 units is
inclined to \( x \) -axis at \( 45^{0}, y \) -axis at \( 60^{\circ} \)
and at an acute angle with \( z \) -axis. If a
plane passes through a point \( (\sqrt{2},-1,1) \) and is normal to \( \vec{n}, \) find its
equation in vector form
A \( \cdot r .(\sqrt{2} i+j+k)=2 \)
B . r. \( (\sqrt{2} i+j+k)=4 \)
c. \( r .(\sqrt{2} i-j+k)=2 \)
D \cdot r. \( (\sqrt{2} i-j+k)=4 \)
Subject: Chemistry
General electron configuration of d-block
elements is:
\( \mathbf{A} \cdot n s^{2} n p^{6} n d^{1-10} \)
B \( \cdot(n-1) d^{1-10} n s^{0-2} n p^{0-6} \)
\( \mathbf{c} \cdot(n-1) d^{1-10} n s^{1-2} \)
\( \mathbf{D} \cdot n d^{1-9} n s^{0-2} \)
Subject: Chemistry
The magnetic momentum of
\( \boldsymbol{K}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{5}(\boldsymbol{N} \boldsymbol{O})\right] \) is:
A. \( 1.73 B M \)
В. \( 5.47 B M \)
\( \mathrm{c} .6 .9 \mathrm{BM} \)
D. zero
Subject: Maths
The position vectors of the points \( A, B, C \) and \( D \) are \( 3 \hat{i}-2 \hat{j}-\hat{k}, 2 \hat{i}+ \)
\( \mathbf{3} \hat{\boldsymbol{j}}-\mathbf{4} \hat{\boldsymbol{k}},-\hat{\mathbf{i}}+\hat{\boldsymbol{j}}+\mathbf{2} \hat{\boldsymbol{k}} \) and \( \mathbf{4} \hat{\boldsymbol{i}}+\mathbf{5} \hat{\boldsymbol{j}}+\boldsymbol{\lambda} \hat{\boldsymbol{k}} \)
respectively. If the points \( A, B, C \) and \( D \)
lie on a plane, find the value of \( \lambda \)
Subject: Maths
Sand is pouring from a pipe at the rate of \( 12 \mathrm{cm}^{3} / \mathrm{s} \). The falling sand forms a cone on the ground in such a way that
the height of the cone is always onesixth of the radius of the base. How fast
is the height of the sand cone increasing when the height is \( 4 \mathrm{cm} \)
Subject: Maths
Evaluate:
\( \int \frac{x}{\sqrt{\left(1-x^{2}\right)} \cos ^{2} \sqrt{\left(1-x^{2}\right)}} d x \)
A \( \cdot \tan \sqrt{1-x^{2}} \)
\( \mathbf{B} \cdot-\tan \sqrt{1-x^{2}} \)
c. \( -\tan \left(1-x^{2}\right) \)
D. \( -\sec ^{2} \sqrt{1-x^{2}} \)
Subject: Chemistry
For the \( 1^{s t} \) order reaction, \( A(g) \rightarrow \)
\( \mathbf{2} \boldsymbol{B}(\boldsymbol{g})+\boldsymbol{C}(\boldsymbol{s}), \boldsymbol{t}_{\mathbf{1} / \mathbf{2}}=\mathbf{2 4} \) min. The
reaction is carried out taking a certain mass of 'A' enclosed in a vessel
in which it exerts a pressure of \( 400 \mathrm{mm} \) Hg. The pressure of the reaction mixture after the expiry of 48 min will be:
\( A \cdot 700 \mathrm{mm} \)
B. 600 mm
c. \( 500 \mathrm{mm} \)
D. \( 1000 \mathrm{mm} \)
Subject: Maths
If \( \sin ^{4} \theta+\cos ^{4} \theta=1-\frac{1}{2} f(\theta) \) then
\( f\left(\frac{\pi}{4}\right)= \)
\( A \)
B.
\( c \cdot 1 / 2 \)
D. \( 1 / 4 \)
Subject: Physics
The values of \( L, C \) and \( R \) in an \( L-C- \)
\( R \) series circuit are \( 4 m H, 40 p F \) and
100 \( \Omega \) respectively. The quality factor of the current is
A . 10
B. 100
\( c \cdot 1000 \)
D. 10,000
Subject: Physics
An uncharged capacitor of capacitance \( 4 \mu F, \) a battery of emf 12 volt and a resistor of \( 2.5 ~ M \Omega \) are connected
in series. The time after which \( v_{c} \) ?
\( 3 v_{R}=0.693 \)
A. 6.93 sec
B. \( 13.86 \mathrm{sec} \)
c. \( 20.52 \mathrm{sec} \)
D. none of these
Subject: Physics
A conducting bar with mass \( \mathrm{m} \) and
length L slides over horizontal rails that
are connected to a voltage source. The
voltage source maintains a constant
current I in the rails and bar, and a
constant, uniform, vertical magnetic field \( \vec{B} \) fills the region between the rails (as shown in fig). Find the magnitude and direction of the net force on the
conducting bar. Ignore friction, air resistance and electrical resistance :
A. ILB, to the right
B. ILB, to the left
c. \( 21 L \) B, to the right
D. 2ILB, to the left
Subject: Physics
What is the limit of temperatures human body can achieve?
\( \mathbf{A} \cdot 25^{\circ} C \) to \( 42^{\circ} C \)
B . \( 35^{\circ} \mathrm{C} \) to \( 42^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 35^{\circ} C \) to \( 62^{\circ} C \)
D. \( 5^{\circ} C \) to \( 42^{\circ} C \)
Subject: Physics
Seema's uncle was advised by his doctor to have an MRI
(Magnetic Resonance Imaging) scan of his brain. Her uncle felt it to be
expensive and wanted to postpone it. When Seema learnt about this, she took
the help of her family and
also approached the doctor, who also offered a substantial discount. She
then convinced her uncle to undergo the
test to enable the doctor to know
the condition of his brain. The
information thus obtained greatly helped the doctor to treat him properly. Based on the above paragraph, answer the question. Assuming that MRI test was performed using a magnetic field of \( 0.1 \mathrm{T} \), find the minimum and maximum values of
the force that the magnetic field could exert on a proton moving with a speed of
\( \mathbf{1 0}^{4} \mathbf{m} / \mathbf{s} \)

Given charge of proton \( =1.6 \times 10^{-19} \mathrm{C} \)
Subject: Physics
A charged parallel plate capacitor of
distance
(d) has \( U_{0} \) energy. A slab of
dielectric constant (K) and thickness
(d) is then introduced between the
plates of the capacitor. The new energy of the system is given by:
A \( . \) к \( U_{0} \)
B. \( K^{2} U_{0} \)
\( c \cdot \frac{U_{0}}{K_{0}} \)
D. \( \frac{U_{0}}{K^{2}} \)
Subject: Physics
Null point with \( 1 V \) cell comes out to be \( 55 \mathrm{cm} \) and with \( R=10 \Omega \) it is \( 50 \mathrm{cm} \)
What is the internal resistance of the
cell?
A . \( 0.5 \Omega \)
В. \( 0.4 \Omega \)
\( c .1 \Omega \)
D. \( 0.2 \Omega \)
Subject: Maths
\( \operatorname{Let} f(x)=\frac{\ln (1+x \tan x)}{4 x}, x \neq 0 \) is
continuous at \( \boldsymbol{x}=\mathbf{0}, \) then \( \boldsymbol{f}(\mathbf{0}) \) must be
equal to
A . 1
B. 0
\( c .3 \)
D.
Subject: Maths
\( f(\vec{a}, \vec{b} \text { are the position vectors of } A, B \) respectively, find the position vector of a point \( C \) in \( A B \) produced such that \( A C= \) \( 3 \mathrm{AB} \) and that a point \( \mathrm{D} \) in BA produced such that \( \mathrm{BD}=2 \mathrm{BA} \)
Subject: Physics
The equation of wave in string is \( y= \) \( 20 \sin \frac{\pi x}{2} \cos 40 \pi t \) in metre. The speed
of the wave is
A. Zero
в. \( 80 \mathrm{m} / \mathrm{s} \)
c. \( 320 m / s \)
D. \( 160 \mathrm{m} / \mathrm{s} \)
Subject: Maths
\( \mathbf{f} \boldsymbol{A}=\left[\begin{array}{lll}\mathbf{0} & \mathbf{1} & \mathbf{2} \\ \mathbf{1} & \mathbf{2} & \mathbf{3} \\ \mathbf{3} & \boldsymbol{a} & \mathbf{1}\end{array}\right] \) and \( \boldsymbol{A}^{-\mathbf{1}}= \)
\( \left[\begin{array}{ccc}1 / 2 & -1 / 2 & 1 / 2 \\ -4 & 3 & c \\ 5 / 2 & -3 / 2 & 1 / 2\end{array}\right] \)
then
A \( a=2, c=1 / 2 \)
2
В. \( a=1, c=-1 \)
c. \( a=-1, c=1 \)
D. \( a=1 / 2, c=1 / 2 \)
Subject: Chemistry
The molar conductivities at infinite
dilution of \( K C l, K N O_{3} \) and \( A g N O_{3} \) at
\( \mathbf{2 9 8} \boldsymbol{K} \) are
0.01499 mho \( m^{2} m o l^{-1}, 0.01250 m h o r \)
and 0.01334 mho \( m^{2} m o l^{-1} \)
respectively. What is the molar
conductivity of \( A g C l \) infinite dilution at
this temperature?
Subject: Chemistry
The state of hybridization of \( C_{2}, C_{3}, C_{5} \)
and \( C_{6} \) of the hydrocarbon is in the
following sequence:
A \( \cdot s p, s p^{2}, s p^{3} \) and \( s p^{2} \)
B . \( s p, s p^{3}, s p^{2} \) and \( s p^{3} \)
\( \mathbf{c} \cdot s p^{3}, s p^{2}, s p^{2} \) and \( s p \)
D. \( s p, s p^{2}, s p^{2} \) and \( s p^{3} \)
Subject: Maths
In the \( \Delta A B C, A=(1,3,-2) \) and \( G(-1,4, \)
2) is the centroid of the triangle. If D is the mid point of \( \mathrm{BC} \) then \( \mathrm{AD}= \)
A \( \cdot \frac{\sqrt{21}}{2} \)
B. \( \frac{3 \sqrt{21}}{2} \)
\( c \cdot \sqrt{21} \)
D. \( \frac{63}{2} \)
Subject: Chemistry
For the reaction:
\( 4 A l(s)+3 O_{2}(g)+6 H_{2} O+ \)
\( \boldsymbol{4} \stackrel{\theta}{\boldsymbol{O}} \boldsymbol{H} \rightarrow \boldsymbol{4}\left[\boldsymbol{A l}(\boldsymbol{O} \boldsymbol{H})_{4}\right]^{\oplus} \)
\( \boldsymbol{E}_{c e l l}^{\ominus}=\mathbf{2 . 7 3} \boldsymbol{V} \)
If \( \boldsymbol{\Delta}_{f} \boldsymbol{G}^{\ominus}[\stackrel{\oplus}{\boldsymbol{O}} \boldsymbol{H}]=-\mathbf{1 5 7} \boldsymbol{k} \boldsymbol{J} \boldsymbol{m o l}^{-1} \)
\( \boldsymbol{\Delta}_{f} \boldsymbol{G}^{\ominus}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)=-\mathbf{2} \mathbf{3} \mathbf{7} . \mathbf{2} \boldsymbol{k} \boldsymbol{J} \boldsymbol{m o l}^{-1} \)
The value of \( \Delta_{f} G^{\ominus}\left[A l(O H)_{4}\right]^{\ominus} \) is:
[free energy of formation of \( \left(A l(O H)_{4}^{\ominus}\right] \)
A \( \cdot \Delta_{f} G^{\ominus}\left[A l(O H)_{4}\right]^{\ominus}=+3.50 \times 10^{3} k J m o l^{-} \)
в. \( \Delta_{f} G^{\ominus}\left[A l(O H)_{4}\right]^{\ominus}=+2.40 \times 10^{3} k J \) тог\( ^{-} \)
c. \( \Delta_{f} G^{\ominus}\left[A l(O H)_{4}\right]^{\ominus}=-1.30 \times 10^{3} k J m o l^{-1} \)
D. None of these
Subject: Chemistry
Given standard electrode potentials:
\( \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{3}+}+\boldsymbol{3} \boldsymbol{e}^{-} \longrightarrow \boldsymbol{F} \boldsymbol{e} ; \boldsymbol{E}^{\boldsymbol{o}}=-\mathbf{0 . 0 3 6} \boldsymbol{v o l} \boldsymbol{t} \)
\( \boldsymbol{F} \boldsymbol{e}^{2+}+\boldsymbol{2} \boldsymbol{e}^{-} \longrightarrow \boldsymbol{F} \boldsymbol{e} ; \boldsymbol{E}^{o}=-\mathbf{0 . 4 4 0} \boldsymbol{v o l t} \)
The standard electrode potential \( E^{o} \) for \( \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{3}+}+\boldsymbol{e}^{-} \longrightarrow \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{2}+} \) is:
A. 0.476 volt
B. 0.404 volt
c. 0.440 volt
D. 0.772 volt
Subject: Chemistry
Identify \( X, Y \) and \( Z \) in the given
reaction
\( \boldsymbol{C H}_{2}=\boldsymbol{C H}_{2} \frac{\boldsymbol{B r}_{2}}{\boldsymbol{C C l}_{4}} \boldsymbol{X} \frac{\boldsymbol{N a C N}}{(\boldsymbol{2} \text { moles })} \)
\( Y \stackrel{\boldsymbol{L i A l H}_{4}}{\longrightarrow} \boldsymbol{Z} \)
\( \mathbf{A} \cdot X=C H_{2} B r C H_{2} B r, Y=C H_{3} C H_{2} C H_{2} C N \)
B . \( X=C H_{2} B r C H_{2} B r, Y=C H_{3} C H_{2} C N \)
\( \mathbf{c} \cdot X=C H_{3} C H_{2} B r, Y=C H_{3} C H_{2} C N \)
D. \( X=C H_{2} B r C H_{2} B r, Y=N C C H_{2} C H_{2} C N \)
Subject: Maths
The angles of a pentagon are in the ratio \( 4: 8: 6: 4: 5 . \) Find each angle of
the pentagon.
A \( \cdot 40^{\circ}, 160^{\circ}, 120^{\circ}, 80^{\circ} \)and \( 100^{\circ} \)
B . \( 60^{\circ}, 160^{\circ}, 120^{\circ}, 80^{\circ} \) and \( 100^{\circ} \)
c. \( 80^{\circ}, 160^{\circ}, 120^{\circ}, 80^{\circ} \) and \( 100^{\circ} \)
D. \( 30^{\circ}, 160^{\circ}, 120^{\circ}, 80^{\circ} \) and \( 100^{\circ} \)
Subject: Physics
If the potential energy of two molecules is given by, \( U=\frac{A}{r^{12}}-\frac{B}{r^{6}} \) then at
equilibrium position, its potential energy is equal to:
A \( \cdot \frac{A^{2}}{4 B} \)
B. \( -\frac{B^{2}}{4 A} \)
c. \( \frac{2 B}{A} \)
D. 3A
Subject: Physics
A hypothetical planet has density \( \rho \) radius \( \mathrm{R} \), and surface gravitational acceleration \( g \). If the radius of the
planet were doubled, but the planetary density stayed the same, find the acceleration due to gravity at the planet's surface.
A \( .4 g \)
в. \( 2 g \)
\( c . g \)
D. \( g / 2 \)
Subject: Chemistry
Arrange the following in the increasing order of solubility in water:
¡) \( \boldsymbol{C}_{\boldsymbol{6}} \boldsymbol{H}_{\boldsymbol{5}} \boldsymbol{N} \boldsymbol{H}_{\boldsymbol{2}} \)
ii) \( \left(C_{2} H_{5}\right)_{2} N H \)
iii) \( \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{N} \boldsymbol{H}_{2} \)
A. is iis iii
B. iisisiii
\( c . \) iiisisi
D. iii <iisi
Subject: Maths
If \( A \) and \( B \) are acute angles such that
\( \sin A=\sin ^{2} B, 2 \cos ^{2} A=3 \cos ^{2} B \)
then
This question has multiple correct options
\( A \cdot A=\frac{\pi}{6} \)
B. \( A=\frac{\pi}{2} \)
c. \( B=\frac{\pi}{4} \)
D. \( B=\frac{\pi}{3} \)
Subject: Physics
A particle
(A) is dropped from a height and another particle(B) is thrown in horizontal direction with speed of 5 m/sec from the same height. The
correct statement is?
A. Both particles will reach at ground simultaneously
B. Both particles will reach at ground with same speed
c. Particle (A) will reach at ground first with respect is particle (B)
D. Particle (B) will reach at ground first with respect to particle (A)
Subject: Biology
Assertion
The proton gradient is broken down due
to the movement of protons across the
membrane channel of the \( F_{0} \) of the
ATPase
Reason
It is the breakdown of proton gradient
that leads to release of energy.
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 and Reason are correct
Subject: Maths
If the arithmetic mean of \( n \) numbers of
a series is \( \bar{x} \) and sum of the first \( (n- \)
1) numbers is \( k, \) then which one of the following is the nth number of the series
\( ? \)
A . \( \bar{x}-n k \)
В . \( n \bar{x}-k \)
c. \( k \bar{x}-n \)
D. \( n k \bar{x} \)
Subject: Physics
In resonance tube exp. we find \( l_{1}= \)
\( 25.0 \mathrm{cm} \) and \( l_{2}=75.0 \mathrm{cm} . \) If there is no
error in frequency, what will be maximum permissible error in speed of
sound. (Take \( \left.f_{0}=325 H z\right) \)
\( \boldsymbol{V}=\mathbf{2} \boldsymbol{f}_{0}\left(\boldsymbol{l}_{2}-\boldsymbol{l}_{1}\right) \)
A. \( v=(329 \pm 1.3) \mathrm{m} / \mathrm{s} \)
B. \( v=(326 \pm 1.3) \mathrm{m} / \mathrm{s} \)
c. \( v=(325 \pm 1.4) \mathrm{m} / \mathrm{s} \)
D. \( v=(325 \pm 1.3) \mathrm{m} / \mathrm{s} \)
Subject: Physics
Assertion
In photoelectron emission the velocity of electron ejected from near the surface is larger than that coming from interior of metal.
Reason
The velocity of ejected electron will be
zero
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. If Assertion is incorrect but Reason is correct
Subject: Physics
A car taken a turn along a curved road
of radius \( 40 \mathrm{m} \) and the angle of banking
of the road is \( 45^{\circ} . \) At what maximum
speed can the car be driven so that it may not skid. \( \left(\boldsymbol{g}=\mathbf{1 0} \boldsymbol{m s}^{-2}\right) \)
A \( \cdot 20 m s^{-1} \)
B. \( 10 \mathrm{ms}^{-1} \)
c. \( 5 m s^{-1} \)
D. \( 1 \mathrm{ms}^{-1} \)
Subject: Chemistry
The value closest to the thermal velocity of a Helium atom at room temperature
\( (300 \mathrm{K}) \) in \( m s^{-1} \) is \( :\left[k_{B}=1.4 \times\right. \)
\( \left.\mathbf{1 0}^{-\mathbf{2 3}} \boldsymbol{J} / \boldsymbol{K} ; \boldsymbol{m}_{\boldsymbol{H} e}=\mathbf{7} \times \mathbf{1 0}^{-\mathbf{2 7}} \boldsymbol{k} \boldsymbol{g}\right] \)
A \( \cdot 1.3 \times 10^{4} \)
B . \( 1.3 \times 10^{3} \)
c. \( 1.3 \times 10^{5} \)
D. \( 1.3 \times 10^{2} \)
Subject: Physics
Q Type your question
and radius \( 20 \mathrm{cm} . \) A steady pull of \( 25 \mathrm{N} \)
is applied on the cord as shown in the
figure. The fly wheel is mounted on a horizontal axle with frictionless
bearings. Find the workdone by the pull when \( 2 \mathrm{m} \) of the cord is unwound.
A. 30
3. 40
c. 50
)
Subject: Physics
Four point charges \( -\mathrm{Q},-\mathrm{q}, 2 \mathrm{q} \) and \( 2 \mathrm{Q} \) are placed, one at each corner of the square The relation between \( Q \) and \( q \) fo which
the potential at the centre of the square is zero, is
A. \( Q=q \)
B. \( Q=\frac{1}{q} \)
c. \( Q=-q \)
D. \( Q=-\frac{1}{q} \)
Subject: Maths
If the lines \( \frac{x-1}{2}=\frac{y+1}{3}=\frac{z}{5 t-1} \)
and \( \frac{\boldsymbol{x}+\mathbf{1}}{\mathbf{2} \boldsymbol{s}+\mathbf{1}}=\frac{\boldsymbol{y}}{\mathbf{2}}=\frac{\boldsymbol{z}}{\mathbf{4}} \) are parallel to
each other, then value of s,t will be
A \( \cdot_{6,} \frac{5}{7} \)
B. \( \frac{1}{2}, 1 \)
c. \( _{3,} \frac{5}{7} \)
D. \( 4, \frac{7}{10} \)
Subject: Physics
A point ' \( O^{\prime} \) marked on the surface of a
glass sphere of diameter \( 20 \mathrm{cm} \) is
viewed through glass from the position
directly opposite to the point ' \( O \) '. If the
refractive index of the glass is \( 1.5, \) find the position of the image formed. Also, draw the ray diagram for the formation
of the image.
Subject: Maths
If \( t_{3}=15, S_{10}=120 \) then the tenth
term of the series i:
A \( \cdot 6 \frac{3}{5} \)
B. \( s_{5}^{3} \)
\( c \cdot_{6} \frac{4}{5} \)
D. \( _{6} \frac{3}{4} \)
Subject: Physics
Four equal charges \( Q \) are placed at the
removing a charge \( -Q \) from its centr
A . zero
B. \( \frac{\sqrt{2} \mathrm{Q}^{2}}{4 \pi \epsilon_{0} \mathrm{a}} \)
c. \( \frac{\sqrt{2} \mathrm{Q}^{2}}{\pi \epsilon_{0} \mathrm{a}} \)
D. \( \frac{Q^{2}}{2 \pi \epsilon_{0} a} \)
Subject: Physics
Relation between wavelength of photon and electron of same energy is
\( \mathbf{A} \cdot \lambda_{p h}>\lambda_{e} \)
\( \mathbf{B} \cdot \lambda_{p h}<\lambda_{e} \)
\( \mathbf{c} \cdot \lambda_{p h}=\lambda_{e} \)
D. \( \frac{\lambda_{c}}{\lambda_{p h}}= \) constant
Subject: Physics
A road is 8 m wide. Its radius of
curvature is \( 40 \mathrm{m} \). The outer edge is
above the lower edge by distance of 1.2 \( m . \) The most suited velocity on the
road is nearly:
\( \mathbf{A} \cdot 5.7 m s^{-1} \)
B. \( 8 m s^{-1} \)
c. \( 36.1 \mathrm{ms}^{-1} \)
D. \( 9.7 \mathrm{ms}^{-1} \)
Subject: Chemistry
The molecular formula of Baking soda
is:
A. \( N a H C O_{3} \)
в. \( N a H C O_{3} .6 H_{2} O \)
\( \mathbf{c} \cdot N a_{2} C O_{3} \)
D. \( N a_{2} C O_{3} .10 H_{2} O \)
Subject: Physics
Normal temperature of a human body is
\( 98.4^{\circ} \mathrm{F} \). Its value in Celsius scale is
\( \mathbf{A} \cdot 32^{\circ} C \)
В. \( 37^{\circ} \mathrm{C} \)
\( c \cdot 28^{\circ} C \)
D. \( 48^{\circ} \mathrm{C} \)
Subject: Maths
The median of given observations arranged in ascending order in \( 25 . \) Find
the value of \( p \) \( \mathbf{1 1}, \mathbf{1 3}, \mathbf{1 5}, \mathbf{1 9}, \boldsymbol{p}+\mathbf{2}, \boldsymbol{p}+\mathbf{4}, \mathbf{3 0}, \mathbf{3 5}, \mathbf{3 9}, \mathbf{4 6} \)
A . 22
B . 24
\( c \cdot 21 \)
D. 26
Subject: Maths
A man walks in a horizontal circle round
the foot of a pole which is inclined to the
vertical. The foot of the pole is at the
centre of the circle. The greatest and least angles which the pole subtends at his eye are \( \tan ^{-1}\left(\frac{9}{5}\right) \) and \( \tan ^{-1}\left(\frac{6}{5}\right) \)
respectively and when he is midway between the corresponding positions, the angle is \( \theta \). If the man's height be neglected, find the length of the pole.
Subject: Chemistry
A chemist has synthesized a greenish yellow gaseous compound of chlorine and oxygen and finds that its density is
\( 7.71 g / L \) at \( 36^{0} C \) and 2.88 atm. Then molecular formula of the compound will
be:
A \( \cdot C l O_{3} \)
в. \( C l O_{2} \)
c. \( C l O \)
D. \( C l_{2} O_{2} \)
Subject: Physics
A remote - sensing satellite of earth revolves in a circular orbit at a height of
\( 0.25 \times 10^{6} \mathrm{m} \) above the surface of earth
If earth's radius is \( 6.38 \times 10^{6} m \) and
\( g=9.8 m s^{-2}, \) then the orbital speed of
the satellite is:
\( \mathbf{A} \cdot 6.67 k m s^{-1} \)
B . \( 7.76 \mathrm{km} \mathrm{s}^{-1} \)
c. \( 8.56 k m s^{-1} \)
D. \( 9.13 \mathrm{km} \mathrm{s}^{-1} \)
Subject: Maths
For a real number \( \boldsymbol{y},[\boldsymbol{y}] \) denotes the
greatest integer less than or equal to \( y \) then \( f(x)=\frac{\tan (\pi[x-\pi])}{1+[x]^{2}} \) is
A. discontinuous at some \( x \)
B. continuous at all \( x \), but \( f^{\prime}(x) \) does not exist for same \( x \)
\( \mathbf{C} \cdot f^{\prime}(x) \) exists for all \( x \) but \( f^{\prime}(x) \) does not exist
D. \( f^{\prime}(x) \) exists for all \( x \)
Subject: Physics
The escape velocity from the earth for a rocket is \( 11.2 \mathrm{km} / \mathrm{s} \) ignoring air resistance. The escape velocity of \( 10 \mathrm{mg} \) grain of sand from the earth will be
\( \mathbf{A} \cdot 0.112 \mathrm{km} / \mathrm{s} \)
B. \( 11.2 \mathrm{km} / \mathrm{s} \)
c. \( 1.12 \mathrm{km} / \mathrm{s} \)
D. \( 0.0112 \mathrm{kms}^{-1} \)
Subject: Biology
If egg of an organism has \( 10 p g \) of DNA in its nucleus. How much DNA would a
diploid cell of same organism have in
\( G_{2} \) phase of meiosis?
A . \( 10 p g \)
B. \( 5 p g \)
\( \mathrm{c} \cdot 2 p g \)
D. \( 40 p g \)
Subject: Chemistry
At \( 27^{\circ} \mathrm{C} \) it was observed in the
hydrogenation of a reaction, the
pressure of \( \boldsymbol{H}_{2}(\boldsymbol{g}) \) decreases from 10 atm to 2 atm in 10 min. Calculate the
rate of reaction in \( \mathrm{M} \) min\( ^{-1} \) (Given \( \mathrm{R}= \)
\( \left.0.08 L \operatorname{atm} K^{-1} m o l^{-1}\right) \)
A. 0.02
2
B. 0.03
\( c .0 .04 \)
D. 0.05
Subject: Maths
If the tangent \( P Q \) and \( P R \) are drawn to
the circle \( x^{2}+y^{2}=a^{2} \) from the point
\( P\left(x_{1}, y_{1}\right), \) then the equation of the
circumcircle of \( \triangle \boldsymbol{P Q R} \) is
A \( \cdot x^{2}+y^{2}-x x_{1}-y y_{1}=0 \)
B . \( x^{2}+y^{2}+x x_{1}+y y_{1}=0 \)
c. \( x^{2}+y^{2}-2 x x_{1}-2 y y_{1}=0 \)
D. None of these
Subject: Physics
A vector \( \vec{A} \) of length 10 units makes an angle of \( 60^{\circ} \) with a vector \( \vec{B} \) of length 6
units. Find the magnitude of the vector difference \( \vec{A}-\vec{B} \& \) the angle it makes with vector \( \vec{A} \).
A \( \cdot 2 \sqrt{19}, \tan ^{-1}\left(\frac{3 \sqrt{3}}{7}\right) \)
в. \( \sqrt{19}, \tan ^{-1}\left(\frac{3 \sqrt{3}}{7}\right) \)
c. \( 2 \sqrt{19}, \tan ^{-1}\left(\frac{\sqrt{3}}{7}\right) \)
D. \( \sqrt{19}, \tan ^{-1}\left(\frac{\sqrt{3}}{7}\right) \)
Subject: Maths
If \( a=e^{i \alpha}, b=e^{i \beta}, c=e^{i \gamma} \) and \( \cos \alpha+ \)
\( \cos \beta+\cos \gamma=0=\sin \alpha+\sin \beta+ \)
\( \sin \gamma, \) then prove the following
\( a+b+c=0 \)
Subject: Chemistry
The oxidation numbers of phosphorus in \( B a\left(H_{2} P O_{2}\right)_{2} \) and xenon in
\( N a_{4} X e O_{6} \) respectively are:
\( A \cdot+3 \) and +4
B. +2 and +6
\( c \cdot+1 \) and +8
D. -1 and -6
Subject: Physics
An athlete completes half a round of a
circular track of radius, \( \boldsymbol{R} \). Then, the
displacement and distance covered by the athlete are
\( \mathbf{A} \cdot 2 R \) and \( \pi R \)
B. \( \pi R \) and \( 2 R \)
c. \( R \) and \( 2 \pi R \)
D. \( 2 \pi R \) and \( R \)
Subject: Physics
Electric ield on the axis of small electric dipole at a distance \( r \) is \( \vec{E}_{1} \) and \( \vec{E}_{2} \) at \( a \) distance \( 2 \mathrm{r} \) on a line of perpendicular dissector. Then
\( ^{\mathbf{A}} \cdot \vec{E}_{2}=-\frac{\vec{E}_{1}}{8} \)
В \( \quad \vec{E}_{2}=-\frac{\vec{E}_{1}}{16} \)
\( \mathbf{c} \cdot \underset{E_{2}}{\overrightarrow{4}}=-\frac{\vec{E}_{1}}{_{1}} \)
D \( \quad \vec{E}_{2}=\frac{\vec{E}_{1}}{8} \)
Subject: Chemistry
What is the empirical formula of vanadium oxide, if 2.74 g of metal oxide contains 1.53 g of metal? (Atomic mass: \( \boldsymbol{V}=\mathbf{5 2}, \boldsymbol{O}=16) \)
\( A \cdot V_{2} O_{3} \)
B. VO
\( c \cdot V_{2} O_{5} \)
D. \( V_{2} O_{7} \)