AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x})=\cos \boldsymbol{x} \) and \( \boldsymbol{g}(\boldsymbol{x})=[\boldsymbol{x}+\mathbf{2}] \)
where [.] denotes the greatest integer function. Then, \( (g o f)^{\prime}\left(\frac{\pi}{2}\right) \) is?
\( \mathbf{A} \cdot \mathbf{1} \)
B.
c. -1
D. Does not exist
Subject: Physics
A cube of side \( 20 \mathrm{cm} \) is kept in a region
as shown in the figure. An electric field
\( \vec{E} \) exists in the region such that the
potential at a point is given by \( \boldsymbol{V}= \)
\( 10 x+5, \) where \( V \) is in volt and \( x \) is in \( m \)
Find the electric flux through the cube
Subject: Chemistry
\( \boldsymbol{R} \boldsymbol{C O C l}+\boldsymbol{H}_{2} \stackrel{\boldsymbol{P d}-\boldsymbol{B a S O}_{4}}{\boldsymbol{R} \boldsymbol{C H} \boldsymbol{O}}+ \)
HCl. The reaction is known as:
A. Rosenmund reduction
B. Stephen's reaction
c. Wolff-Kishner reduction
D. Clemmensen's reduction
Subject: Chemistry
Assertion
Finely divided iron does not form ferric chloride with hydorchloric acid.
Reason
Hydrochloric acid produces hydrogen gas with iron.
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 number of moles of \( \boldsymbol{C} \boldsymbol{O}_{2} \) produced
when 3 moles of \( H C l \) react with excess
of \( \boldsymbol{C a} \boldsymbol{C O}_{3}, \) is:
\( \mathbf{A} \cdot \mathbf{1} \)
в. 1.5
\( c \cdot 2 \)
D. 2.5
Subject: Maths
Given \( : \boldsymbol{u}=\mathbf{1}+\boldsymbol{i} \sqrt{\mathbf{3}} \) and \( \boldsymbol{v}=\sqrt{\mathbf{3}}+\boldsymbol{i} \)
Calculate \( \frac{u^{3}}{v^{4}} \)
A \( \cdot(1 / 4)-i \sqrt{1 / 4} \)
B. \( (3 / 4)-i \sqrt{3} / 4 \)
c. \( (1 / 4)-i \sqrt{3} / 4 \)
D. none of these
Subject: Maths
If the roots of the equation \( x^{2}+p x+ \)
\( c=0 \) are (2,-2) and the roots of the
equation \( \boldsymbol{x}^{2}+\boldsymbol{b} \boldsymbol{x}+\boldsymbol{q}=\mathbf{0} \) are \( (-\mathbf{1},-\mathbf{2}) \)
then the roots of the equation \( x^{2}+ \)
\( b x+c=0 \) are
A \( .-3,-2 \)
в. -3,2
c. 1,-4
D. -5,1
Subject: Chemistry
The given graph shows the vapor pressure curves for some liquids.
Liquids \( A, B, C \) and \( D \) respectively
are:
A. diethyl ether, acetone, ethyl alcohol, water
B. acetone, ethyl alcohol, diethyl ether, water
c. water, ethyl alcohol, acetone, diethyl ether
D. ethyl alcohol, acetone, diethyl ether, water
Subject: Maths
In a circle with center \( 0, \) central angle \( A O B \) has a measure of \( \frac{5 \pi}{4} \) radians. The area of the sector formed by central
angle \( A O B \) is what fraction of the area
of the circle?
A \( \cdot \frac{5}{8} \)
B. \( \frac{8}{5} \)
c. \( \frac{16}{5} \)
D. \( \frac{4}{5} \)
Subject: Maths
The solution of \( \frac{d y}{d x}+\frac{x^{2}}{y^{2}}=0 \) is:
A \( \cdot x^{2}+y^{2}=c \)
B . \( x^{2}-y^{2}=c \)
c. \( x^{3}-y^{3}=c \)
D. \( x^{3}+y^{3}=c \)
Subject: Physics
In a series L-C circuit, if \( L=10^{-3} \mathrm{H} \) and
\( C=3 \times 10^{-7} F \) is connected to a
\( 100 V-50 H z \) a.c. source, the
impedance of the circuit is
A \( \cdot \frac{10^{5}}{3 \pi}-10 \pi \)
В. \( 0.1 \pi-3 \times 10^{-5} \pi \)
\( ^{\mathbf{C}} \cdot \frac{10^{5}}{3 \pi}-\frac{\pi}{10} \)
D. None of these
Subject: Chemistry
Which of the following statement
regarding solubility of ethers in water is
true?
A. Ethers are sparingly soluble in water due to the formation of hydrogen bond with water.
B. Ethers are highly soluble in water due to the formation of hydrogen bond with water.
C. Ethers are sparingly soluble in water as they cannot form hydrogen bond with water.
D. Ethers are highly soluble in water as they are polar in nature.
Subject: Chemistry
Assertion (A): The basic nature of VA
group hy-drides decreases from ammonia to bismuthine.
Reason (R): Availability of lone pair on the cen-tral atom in hydrides decreases
down the group.
A. Both (A) and (R) are true and
(R) is the correct
explanation of (A)
B. Both (A) and (R) are true and (R) is not the
correct explanation of (A)
\( c . \) (A) is true and
(R) is false
D. (A) is false but (R) is true
Subject: Maths
Given a square matrix \( \boldsymbol{A}=\left[\boldsymbol{a}_{\boldsymbol{g}}\right], \) where
\( a_{g}=\hat{i}^{2}-\hat{j}^{2} . \) Then matrix \( A \) is a unit
matrix or null matrix or a symmetric matrix a skew symmetric matrix. Select with a reason.
Subject: Biology
In the resting state of the neural
membrane, diffusion due to
concentration gradients, if allowed
would drive
A. \( N a^{+} \) into the cell
B. \( N a^{+} \) out of the cell
c. \( K^{+} \) into the cell
D. \( K^{+} \) and \( N a^{+} \) out of the cell
Subject: Physics
Consider an iron rod of length 1 metre
and cross-section \( 1 \mathrm{cm}^{2} \) with a Young's
modulus of \( 10^{12} \) dyne \( c m^{-2} . \) We wish to
calculate the force with which the two
ends must be pulled to produce an elongation of \( 1 \mathrm{mm} \). It is equal to:
Subject: Maths
If \( \bar{a}, \bar{b}, \bar{c} \) are the vertices of a triangle \( A B C, \) then \( |\bar{a} \times \bar{b}+\bar{b} \times \bar{c}+\bar{c} \times \bar{a}|= \)
A. Area of the triangle \( \Delta A B C \)
B. Two times area of the triangle \( \Delta A B C \)
C. Three times area of the triangle \( \Delta A B C \)
D. Four times area of the triangle \( \Delta A B C \)
Subject: Chemistry
Assertion
All \( \boldsymbol{F}-\boldsymbol{S}-\boldsymbol{F} \) angles in \( \boldsymbol{S} \boldsymbol{F}_{4} \) is greater
than \( 90^{\circ} \) but lesser than \( 180^{\circ} \)
Reason
The lone pair-bond pair repulsion is stronger than bond pair-bond pair repulsion.
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 air bubble of volume \( v_{0} \) is released by
a fish at a depth h in a lake. The bubble rises to the surface. Assume constant
temperature and standard atmospheric pressure \( P \) above the lake. The volume of
the bubble just before reaching the surface is (d is the density of water)
\( \mathbf{A} \cdot v_{0}+\frac{h g d}{P} \)
B. \( \frac{v_{0}(P+h g d)}{P} \)
c. \( \frac{v_{0}}{P}+h g d \)
D. \( \left(v_{0}+v_{0} d g\right) \)
Subject: Chemistry
Consider the following \( E^{0} \) values:
\( E_{F e^{3+} / F e^{2+}}^{0}=+0.77 V ; E_{S n^{2+} / S n}^{0}=-0.14 V \)
Under standard conditions the EMF for
the reaction
\( S n_{(s)}+2 F e_{(a q)}^{3+} \rightarrow 2 F e^{2+}_{(a q)}+S n_{(a q)}^{2+} \) is :
A . \( 1.68 \mathrm{v} \)
B . \( 1.40 \mathrm{V} \)
c. \( 0.91 v \)
D. \( 0.63 \mathrm{v} \)
Subject: Physics
If the activity of 108 Ag is 3 micro curie, the number of atoms present in it are \( \lambda=0.005 \mathrm{sec}^{-1} \)
A. \( 2.2 \times 10^{7} \)
B. 2.2 \( \times 10^{6} \)
c. \( 2.2 \times 10^{5} \)
D. 2.2 \times 10 \( ^{4} \)
Subject: Physics
Mass \( m_{1} \) hits and sticks with \( m_{2} \) while
sliding horizontally with velocity \( v \) along the common line of centres of the three
\[
\text { equal masses }\left(\boldsymbol{m}_{1}=\boldsymbol{m}_{2}=\boldsymbol{m}_{3}=\boldsymbol{m}\right)
\]
Initially masses \( m_{2} \) and \( m_{3} \) are stationary and the spring is unstretched. Minimum kinetic energy of
\( m_{2} \) is \( y m v^{2} / 36 . \) Find \( y \)
Subject: Physics
When a hydrogen atom emits a photon in going from \( n=5 \) to \( n=1 \), its recoil
speed is almost
\( \mathbf{A} \cdot 10^{-4} m / s \)
B . \( 2 \times 10^{-2} \mathrm{m} / \mathrm{s} \)
c. \( 4 m / s \)
D. \( 8 \times 10^{-2} \mathrm{m} / \mathrm{s} \)
Subject: Physics
The nuclear reaction \( n+_{5}^{10} B \rightarrow_{3}^{7} L i+_{2}^{4} \)
He is observed to occur even when very
slow-moving neutrons \( \left(M_{n}=\right. \) 1.0087amu \( ) \) strike a boron atom at
rest. For a particular reaction in which \( \boldsymbol{K}_{n}=\mathbf{0}, \) the helium \( \left(\boldsymbol{M}_{\boldsymbol{H} e}=\right. \)
\( 4.0026 a m u) \) is observed to have a
speed of \( 9.30 \times 10^{6} m s^{-1} . \) Determine
(a) the kinetic energy of the lithium
\( \left(M_{L i}=7.0160 a m u\right) \) and
(b) the \( Q \)
value of the reaction.
Subject: Physics
a material of bulk modulus B
is surrounded by an incompressible liquid in a cylindrical container. \( \mathbf{A} \) massless piston of area A floats on the surface of the liquid. The magnitude
of fractional change in the radius of the sphere \( \left(\frac{\boldsymbol{d} \boldsymbol{R}}{\boldsymbol{R}}\right) \) when a mass \( \mathrm{M} \) is placed slowly on the piston to compress the liquid is:
A \( \cdot \frac{M g}{3 A B} \)
в. \( \frac{M g}{A B} \)
\( \mathrm{c} \cdot \frac{3 M g}{A B} \)
D. None of these
Subject: Maths
Let a function \( \boldsymbol{f}(\boldsymbol{x})= \)
a relation between \( b \) and \( c \) such that
\( \lim _{x \rightarrow 1} f(x) \) exists is
B. \( 3 b+2 c-1=0 \)
c. \( 3 b-2 c-1=0 \)
D. \( b-2 c+1=0 \)
Subject: Physics
A convex refracting surface of radius of
curvature \( 20 \mathrm{cm} \) separates two media of refractive indices \( 4 / 3 \) and \( 1.60 . \) An
object is placed in the first medium \( (\mu=4 / 3) \) at a distance of \( 200 \mathrm{cm} \) from
the refracting surface. The position of
the image formed is
A . \( 120 \mathrm{cm} \)
B. 240 cm
\( c .100 \mathrm{cm} \)
D. 60 cm
Subject: Chemistry
The density of a gas \( A \) is twice that of \( B \)
Molar mass of \( A \) is half that of \( B \). The
ratio of partial pressure of \( \boldsymbol{A} \) to \( \boldsymbol{B} \) is:
A. \( 1 / 4 \)
B. \( 1 / 2 \)
\( c \cdot 4 / 1 \)
D. 2/1
Subject: Maths
\( \sec ^{-1} x+\tan ^{-1} x \) is real if
\( \boldsymbol{x} \boldsymbol{\epsilon}(-\infty,-\boldsymbol{a}] \cup[\boldsymbol{b}, \infty) \)
Find the value of \( a+b \)
A . -1
B. 0
c.
D.
Subject: Maths
The area lying in the first quadrant inside the circle \( x^{2}+y^{2}=12 \) and
bounded by the parabolas \( \boldsymbol{y}^{2}= \)
\( 4 x, x^{2}=4 y \) is:
A \( \cdot\left(\frac{\sqrt{2}}{3}+\frac{3}{2} \sin ^{-1} \frac{1}{3}\right) \)
B \( \cdot 4\left(\frac{\sqrt{2}}{3}+\frac{3}{2} \sin ^{-1} \frac{1}{3}\right) \)
\( ^{c} \cdot\left(\frac{\sqrt{2}}{3}+\frac{3}{2} \sin ^{-1} \frac{1}{3}\right) \)
D. none of these
Subject: Physics
A container contains 0.25 kg of a liquid at its boiling temperature. If the latent heat of fusion for the liquid is 500 Joules/kg and the latent heat of
vaporization for the liquid is 1000 Joules/Kg. How much heat must be
added to the liquid to boil all of the liquid away?
A \( .125 \mathrm{J} \)
J.
в. \( 2000 J \)
c. \( 4000 J \)
D. \( 0.50 J \)
E . \( 250 J \)
Subject: Chemistry
In which of the following cases, pH is
greater than \( 7 ? \)
A. \( 50 m l \) of \( 0.01 M H C l+50 m l \) of \( 0.1 M \) NaCl
B . \( 50 m l \) of \( 0.1 M H_{2} S O_{4}+50 m l \) of \( 0.2 M \) NaOH
\( \mathrm{c} .50 \mathrm{ml} \) о \( 6.0 .1 \mathrm{M} \mathrm{CH}_{3} \mathrm{COOH}+50 \mathrm{ml} \) о \( 0.1 \mathrm{M} \) КОН
D. \( 50 m l \) of \( 0.1 M H N O_{3}+50 m l \) of \( 0.1 M N H_{3} \)
Subject: Chemistry
The specific heat of copper is \( 0.385 \mathrm{J} / \mathrm{g} \)
\( ^{o} C \) ). If 34.2 g of copper, initially at \( 25^{\circ} \mathrm{C} \)
absorbs \( 4.689 \mathrm{kJ} \), what will be the final
temperature of the copper?
A . \( 25.4^{\circ} \mathrm{C} \)
B . \( 27.8^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 356^{\circ} \mathrm{C} \)
D. \( 381^{\circ} \mathrm{C} \)
Subject: Maths
If \( 2 f(\sin x)+f(\cos x)=x, \) then
\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}} \boldsymbol{f}(\boldsymbol{x}) \) is
\( \mathbf{A} \cdot \sin x+\cos x \)
B. 2
c. \( \frac{1}{\sqrt{1-x^{2}}} \)
D. none of these
Subject: Maths
Find the values of the following determinants where \( i=\sqrt{-1} \)
\( (i)\left|\begin{array}{cc}2 i & -3 i \\ i^{3} & -2 i^{5}\end{array}\right| \)
\( (i i)\left|\begin{array}{cc}\mathbf{1}+\mathbf{3} i & \boldsymbol{i}-\mathbf{2} \\ \boldsymbol{i}+\mathbf{2} & \mathbf{1}-\mathbf{3} i\end{array}\right| \)
Subject: Maths
The domain of \( \boldsymbol{f}(\boldsymbol{x})=\sqrt{\mathbf{2 5}-\boldsymbol{x}^{2}} \) is
\( \mathbf{A} \cdot(-\infty,-5) \)
B. \( (5, \infty) \)
c . [-5,5]
D. \( [-\infty, \infty] \)
Subject: Maths
\( \left[\begin{array}{cc}1 & 1 \\ 0 & 1\end{array}\right]\left[\begin{array}{cc}1 & 2 \\ 0 & 1\end{array}\right]\left[\begin{array}{cc}1 & 3 \\ 0 & 1\end{array}\right] \ldots \ldots\left[\begin{array}{cc}1 & n \\ 0 & 1\end{array}\right]= \)
\( A \cdot 27 \)
3.26
\( c .376 \)
D. 378
Subject: Physics
A false balance has equal arms. An
object weights \( \boldsymbol{w}_{1} \) when placed in one
pan and \( w_{2} \) when placedin the other pan. Then weight w of the object is
в. \( \frac{w_{1}+w_{2}}{2} \)
\( ^{\mathbf{c}} \cdot\left(\frac{w_{1}^{2}+w_{2}^{2}}{2}\right)-1 \)
\( \mathbf{D} \cdot \sqrt{w_{1}^{2}+w_{2}^{2}} \)
Subject: Maths
\( \operatorname{Points} \boldsymbol{A}(\boldsymbol{3}, \boldsymbol{2}, \boldsymbol{4}), \boldsymbol{B}\left(\frac{\boldsymbol{3} \boldsymbol{3}}{\boldsymbol{5}}, \frac{\boldsymbol{2} \boldsymbol{8}}{\boldsymbol{5}}, \frac{\boldsymbol{3} \boldsymbol{8}}{\boldsymbol{5}}\right), \) and
\( C(9,8,10) \) are given. The ratio in which
\( B \) divides \( \overline{A C} \) is
A . 5: 3
B . 2: 1
c. 1: 3
D. 3: 2
Subject: Physics
Two copper spheres, \( A \) and \( B \), are identical in all respect but A carries a charge of \( -3 \mu C \) whereas \( B \) Is charged
to \( +1 \mu C \). The two spheres are brought together until they touch and then separated by some distance. Which of the following statements is true concerning the electrostatic force \( \boldsymbol{F} \) between the spheres?
A. \( F=0 \) as one of the spheres is uncharged
B. \( F=0 \) as both the spheres are uncharged
c. \( F \) is attractive
D. F is repulsive
Subject: Physics
A bullet of mass m traveling at velocity v strikes a block of mass \( 2 \mathrm{m} \) that is
attached to a rod of length \( \mathrm{R} \). The bullet collides with the block at a right angle and gets stuck in the block. The rod is free to rotate. What is the centripetal acceleration of the block after the
collision?
A \( \cdot v^{2} / R \)
B . \( (1 / 2) v^{2} / R \)
C \( \cdot(1 / 3) v^{2} / R \$ \)
D. \( (1 / 9) v^{2} / R \)
Subject: Chemistry
Hybridisation state of \( X e \) in \( X e F_{2} \)
\( X e F_{4}, \) and \( X e F_{6} \) respectively are:
\( \mathbf{A} \cdot s p^{2}, s p^{3} d, s p^{3} d^{2} \)
B . \( s p^{3} d, s p^{3} d^{2}, s p^{3} d^{3} \)
c. \( s p^{3} d^{2}, s p^{3} d, s p^{3} d^{3} \)
D \( \cdot s p^{2}, s p^{3}, s p^{3} d \)
Subject: Maths
Prove that \( \operatorname{at} x=2, \) limits of function
does not exist \( \boldsymbol{f}(\boldsymbol{n})= \)
\( \left\{\begin{array}{ccc}x^{2}+x+1 & \text { if } & x \geq \\ n & \text { if } & x<2\end{array}\right\} \)
Subject: Physics
A pulley fixed to a rigid support carries a rope whose one end is tied to a ladder
with a man and the other end to the
counterweight of mass \( M . \) The man of
mass \( m \) climbs up a distance \( h \) with
respect to the ladder and then stops. If the mass of the rope and the friction in
the pulley axle are negligible, find the displacement of the centre of mass of
this system.
Subject: Physics
A ray of light incident parallel to the base PQ of an isosceles right-angled
triangular prism PQR suffers two
successive total internal reflections at
the faces \( \mathrm{PQ} \) and \( \mathrm{QR} \) before reversed in
direction as shown. If the
refractive index of the material of the
prism is \( \mu, \) then find the value of \( \mu \)
Subject: Physics
Radiations of intensity \( 0.5 W / m^{2} \) are
striking a metal plate. The pressure on the plate is
A \( \cdot 0.166 \times 10^{-8} \mathrm{N} / \mathrm{m}^{2} \)
B . \( 0.332 \times 10^{-8} \mathrm{N} / \mathrm{m}^{2} \)
c. \( 0.111 \times 10^{-8} \mathrm{N} / \mathrm{m}^{2} \)
D. \( 0.083 \times 10^{-8} N / m^{2} \)
Subject: Chemistry
Which of the following is a physical change?
a) Hammering of a red hot iron rod to
make a flat sheet.
b) Formation of ice by cooling of water.
c) Rising up of water vapors from sea to
make clouds.
d) Heating of charcoal in air to high temperature till it begins to flow.
\( A \cdot a, b \) and \( c \)
B. b, cand d
c. \( c, \) d and a
D. \( d, \) a and \( b \)
Subject: Maths
Find the value of \( f \) in \( \frac{1}{f}=\frac{1}{u}+\frac{1}{v}, \) when
\( \boldsymbol{u}=\mathbf{1 5} \) and \( \boldsymbol{v}=\mathbf{1 0} \)
A . -6
в. \( \frac{1}{6} \)
\( c \cdot 6 \)
D. \( -\frac{1}{6} \)
Subject: Chemistry
A solution which is \( 10^{-3} M \) each in
\( M n^{2+}, F e^{2+}, Z n^{2+} \) and \( H g^{2+} \) is treated
with \( 10^{-16} M \) sulphide ion. If \( K_{s p} \) of \( M n S, F e S, Z n S \) and \( H g S \) are
\( 10^{-13}, 10^{-18}, 10^{-24} \) and \( 10^{-53} \)
respectively, which one will precipitate first?
A. FeS
в. \( M g S \)
c. Нg S
D. ZnS
Subject: Maths
The value of \( \left(\sin \frac{\pi}{8}+\right. \)
\( \left.i \cos \frac{\pi}{8}\right)^{8}\left(\sin \frac{\pi}{8}-i \cos \frac{\pi}{8}\right)^{8} \) is
\( A \cdot-1 \)
B.
\( c \)
\( D \cdot 2 \)
Subject: Maths
Solve: \( 4 x+\frac{6}{y}=15 \) and \( 6 x-\frac{8}{y}= \)
\( \mathbf{1 4} \)
Hence, find 'a' if \( \boldsymbol{y}=\boldsymbol{a} \boldsymbol{x}-\boldsymbol{2} \)
A \( \cdot x=1, y=6 \) and \( a=3 \frac{2}{5} \)
B. \( x=3, y=12 \) and \( a=7 \frac{6}{5} \)
c. \( _{x}=3, y=2 \) and \( a=1 \frac{1}{3} \)
D. \( x=12, y=16 \) and \( a=4 \frac{31}{3} \)
Subject: Chemistry
In which of the following cells, use of salt bridge to eliminate liquid junction potential is not necessary?
A \( \cdot P t H_{2}(g)|H C l| A g C l(s) \mid A g \)
B . \( H g\left|H g_{2} C l_{2}(s)\right| K C l \)saturated\( |H C l(a q)| H_{2}(g) P t \)
c. \( Z n\left|Z n S O_{4} \| C u S O_{4}\right| C u \)
D. \( Z n\left|Z n S O_{4}\right| F e^{3+}(a q), F e^{2+}(a q) \mid P t \)
Subject: Physics
A uniform ladder of length \( 5 m \) is placed
against the wall as shown in the figure.
If coefficient of friction \( \mu \) is the same for
both the walls, what is the minimum
value of \( \mu \) for it not to slip?
A \( \cdot \mu=\frac{1}{2} \)
B. \( \mu=\frac{1}{4} \)
\( c \cdot_{\mu}=\frac{1}{3} \)
D. \( \mu=\frac{1}{5} \)
Subject: Chemistry
Air contains \( 21 \% \) of oxygen by volume.
Calculate the volume of such air
required for the complete combustion
of \( 700 \mathrm{cm}^{3} \) of ethylene \( \left(C_{2} H_{4}\right) \) at \( 15^{\circ} \mathrm{C} \)
and 756 mm pressure.
Subject: Physics
A spring of spring constant \( \boldsymbol{K} \) is fixed at
one end has a small block of mass \( m \)
and charge \( q \) is attached at the other
end. The block rests over a smooth
horizontal surface. A uniform and
constant magnetic field \( B \) exists
normal to the plane of the paper as
shown in the figure. An electric field \( \overrightarrow{\boldsymbol{E}}=\boldsymbol{E}_{0} \hat{\boldsymbol{i}}\left(\boldsymbol{E}_{0} \text { is a positive constant }\right) \) is
switched on at \( t=0 \) sec. The block
moves on the horizontal surface without
ever lifting off the surface. Where is the normal reaction acting on the block
maximum?
Subject: Chemistry
Perchloric acid is prepared by the action of concentrated sulphuric acid
on:
A \( \cdot \mathrm{NaClO}_{4} \)
в. \( \mathrm{KClO}_{3} \)
c. \( \left.\operatorname{ca}\left(\mathrm{ClO}_{3}\right) \mathrm{lO}_{3}\right) \)
D. Bac
Subject: Chemistry
AgBr dissolved in \( N a_{2} S_{2} O_{3} .1 \) mol of
AgBr is dissolved in \( x \) mol of \( N a_{2} S_{2} O_{3} \) What is the value of \( x ? \)
\( A \)
B. 0.5
\( c \cdot 0.3 \)
D. 1.5
Subject: Chemistry
The inner transition elements are the
elements in which last electrons enters
into:
\( A \cdot(n-1) \) d-orbitals
B. (n-2) f-orbitals
C. \( (n-1) \) d-orbitals and \( (n-1) \) f-orbitals
D. \( (n-1) \) d-orbitals and ns orbitals
Subject: Chemistry
What will happen if the pH of the
solution of \( 0.001 \mathrm{M} M g\left(N O_{3}\right)_{2} \) solution
is adjusted to \( \boldsymbol{p} \boldsymbol{H}=\mathbf{9} ? \)
\( \left[\text { Given that }: \boldsymbol{K}_{s p} \text { of } M g(\boldsymbol{O} \boldsymbol{H})_{2}=\mathbf{8 . 9} \times\right. \)
\( \mathbf{1 0}^{-12} \) )
A. ppt will take place
B. ppt will not take place
c. solution will be saturated
D. none of the above
Subject: Physics
A spherometer has 10 threads per \( \mathrm{cm} \) and its circular scale has 50 divisions.
The least count of the instrument is
A . \( 0.01 \mathrm{cm} \)
B. \( 0.02 \mathrm{cm} \)
c. \( 0.002 \mathrm{cm} \)
D. \( 0.2 \mathrm{cm} \)
Subject: Maths
Find the projection of the vector \( \hat{\mathbf{i}}+ \) \( \mathbf{3} \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \) on the vector \( \mathbf{7} \hat{\boldsymbol{i}}-\hat{\boldsymbol{j}}+\boldsymbol{8} \hat{\boldsymbol{k}} \)
Subject: Maths
A point \( Q \) at a distance 3 from the point \( P(1,1,1) \) lying on the line joining the points \( \boldsymbol{A}(\mathbf{0},-\mathbf{1}, \mathbf{3}) \) and \( \boldsymbol{P}, \) has the
coordinates
This question has multiple correct options
A \( \cdot(2,3,-1) \)
В. (4,7,-5)
D. (-2,-5,7)
Subject: Chemistry
Sodium hydroxide reacts with \( S O_{2} \) in aqueous medium to give:
A. \( \operatorname{NaHSO}_{3} \)
в. \( N a_{2} S_{2} O_{3} \)
\( \mathbf{c} \cdot \operatorname{NaH} S O_{4} \)
D. \( N a_{2} S O_{3} \)
Subject: Physics
A \( 2 V \) battery, a \( 990 \Omega \) resistor and a
potentiometer of \( 2 m \) length,all are connected in series of the resistance of
potentiometer wire is \( 10 \Omega \), then the potential gradient of the potentiometer wire is
A \( \cdot 0.05 V m^{-1} \)
B \( .0 .5 V m^{-1} \)
c. \( 0.01 V m^{-1} \)
D. \( 0.001 V m^{-1} \)
Subject: Physics
An object is placed in front of a spherical mirror whose 2 times magnified images is formed on the screen. Then choose the
CORRECT option:
A. Mirror is concave \( \mathrm{m}=+2 \)
B. Mirror is concave \( m=-2 \)
c. Mirror is convex \( \mathrm{m}=+2 \)
D. Mirror is convex \( \mathrm{m}=-2 \)
Subject: Physics
A uniform disc of mass \( m \) and radius \( R \)
is pivoted at the point \( P \) and is free to
rotate in a vertical plane. The center \( C \) of the disc is initially in a horizontal position with \( P \) as shown in the figure.
It is released from this position, then its
angular acceleration when the line \( \boldsymbol{P C} \)
is inclined to the horizontal at an angle
\( \theta \) is:
A \( \cdot \frac{2 g \cos \theta}{3 R} \)
B. \( \frac{g \sin \theta}{2 R} \)
c. \( \frac{2 g \sin \theta}{R} \)
D. \( \frac{2 g \sin \theta}{3 R} \)
Subject: Maths
The equation of the line farthest from (-5,-4) belonging to the family of \( \operatorname{lines}(2+\lambda) x+(3 \lambda+1) y+2(2+ \)
\( \lambda)=0, \) where \( \lambda \) is a variable parameter
is
A. \( 3 x+4 y+6=0 \)
в. \( 3 x+4 y+3=0 \)
c. \( 4 x+3 y+3=0 \)
D. \( 4 x+3 y-3=0 \)
Subject: Maths
If the line \( h x+k y=1 \) touches \( x^{2}+ \)
\( y^{2}=a^{2}, \) then the locus of the point \( (h \)
k) is a circle of radius
\( A \cdot a \)
B.
\( c \cdot \sqrt{a} \)
D. \( \frac{1}{\sqrt{a}} \)
Subject: Physics
mass m carrying charge \( q . \) The bead
freely move on the smooth fixed ring
placed on a smooth horizontal plane. In
the same plane a charge \( +Q \) has also
been fixed as shown. The potential at
the point \( \boldsymbol{P} \) due to \( +\boldsymbol{Q} \) is \( \boldsymbol{V} \). The velocity
with which the bead should projected
from the point \( P \) so that is can complete
a circle should be greater than
A \( \cdot \sqrt{\frac{6 q V}{m}} \)
B. \( 4 \sqrt{\frac{q V}{m}} \)
c. \( \sqrt{\frac{3 q V}{m}} \)
D. \( \sqrt{\frac{7 q V}{2 m}} \)
Subject: Physics
A ball of mass 'm' is projected from the
ground with a speed 'u' at an angle ' \( \alpha \) with the horizontal. The magnitude of
the change in momentum of the ball over a time interval from begining till it strikes the ground again is
A \( \cdot \frac{m u \sin \alpha}{2} \)
B. \( 2 m u \cos \alpha \)
c. \( \frac{m u \cos \alpha}{2} \)
D. \( 2 m u \sin \alpha \)