AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A tension of \( 20 N \) is applied to a copper
wire of cross sectional area \( 0.01 c m^{2} \)
Young's Modulus of copper is \( 1.1 \times \)
\( 10^{11} N / m^{2} \) and Poisson's ratio is 0.32
The decrease in cross sectional area of
the wire is:
\( \mathbf{A} \cdot 1.16 \times 10^{-6} \mathrm{cm}^{2} \)
В. \( 1.16 \times 10^{-5} \mathrm{m}^{2} \)
c. \( 1.16 \times 10^{-4} m^{2} \)
D. \( 1.16 \times 10^{-3} \mathrm{cm}^{2} \)
Subject: Physics
If the number of electric lines of force
emerging out of a closed surface is \( 1000, \) then the charge enclosed by the surface is
A \( \cdot 8.854 \times 10^{-9} C \)
В. \( 8.854 \times 10^{-4} C \)
c. \( 8.854 \times 10^{-1} C \)
D. \( 8.854 C \)
Subject: Maths
\( \int \frac{d\left(x^{2}+1\right)}{\sqrt{x^{2}+2}} \) is equal to
A \( \cdot 2 \sqrt{x^{2}+2}+k \)
B . \( \sqrt{x^{2}+2}+k \)
\( \left(\frac{1}{x^{2}+2}\right)^{\frac{3}{2}}+k \)
D. none of these
Subject: Physics
An alternating voltage \( \boldsymbol{E}= \) \( \mathbf{5 0} \sqrt{\mathbf{2}} \sin (\mathbf{1 0 0} t) \boldsymbol{V} \) is connected to a
1 \( \mu F \) capacitor through an ac ammeter. What will be the reading of the ammeter?
A . \( 10 \mathrm{mA} \)
B. \( 5 m A \)
c. \( 5 \sqrt{2} \) mA
D. \( 10 \sqrt{2} \mathrm{mA} \)
Subject: Maths
Which of the following equations has two distinct real roots ?
A \( \cdot 2 x^{2}-3 \sqrt{2} x+\frac{9}{4}=0 \)
В. \( x^{2}+x-5=0 \)
c. \( x^{2}+3 x+2 \sqrt{2}=0 \)
D. \( 5 x^{2}-3 x+1=0 \)
Subject: Physics
A liquid of density \( \rho_{1} \) is flowing through
a tube of varying cross-section. A manometer containing a liquid of
density \( \rho_{2} \) is connected to the tube as shown. The area of cross section of the
tube at points \( A \) and \( B \) are \( a_{1} \) and \( a_{2} \)
respectively. The rate of flow of the liquid through the tube is
A \( \cdot a_{1} a_{2} \sqrt{\frac{2 \rho_{2} g h}{\rho_{1}\left(a_{2}^{2}-a_{1}^{2}\right)}} \)
в. \( \quad a_{1} a_{2} \sqrt{\frac{2 g h}{\rho_{1}\left(a_{2}^{2}-a_{1}^{2}\right)}} \)
c. \( \frac{a_{1}}{a_{2}} \sqrt{\frac{2 \rho_{2} g h}{\rho_{1}\left(a_{2}^{2}-a_{1}^{2}\right)}} \)
D. \( a_{1} a_{2} \sqrt{\frac{2 \rho_{1} g h}{\rho_{2}\left(a_{2}^{2}-a_{1}^{2}\right)}} \)
Subject: Physics
Consider the situation shown in figure.
The elevator is going up with an acceleration of \( 2.00 m / s^{2} \) and the focal
ength of the mirror is \( 12.0 \mathrm{cm} . \) All the
surfaces are smooth and pulley is light.
The mass-pulley system is released from rest (with respect to the elevator)
at \( t=0 \) when the distance of \( B \) from
the mirror is \( 42.0 \mathrm{cm} \). Find the distance
between the image of the block \( B \) and
the mirror at \( t=0.200 s . \) Take \( g= \)
\( 10 m / s^{2} \)
Subject: Maths
Three girls Reshma, Salma and Mandip are playing a game by standing on a circle of radius \( 5 \mathrm{m} \) drawn in a park.
Reshma throws a ball to Salma. Salma
to Mandip, Mandip to Reshma. If the distance between Reshma and Salma
and between Salma and Mandip is \( 6 \mathrm{m} \) each, what is the distance
between Reshma and Mandip?
\( \mathbf{A} \cdot 4.8 \mathrm{m} \)
B. \( 9.6 \mathrm{m} \)
\( c \cdot 2.4 m \)
D. \( 7.2 \mathrm{m} \)
Subject: Chemistry
Assertion
\( Z n C O_{3}(s) \) is soluble in \( N H_{3}(a q) \) but
\( \operatorname{Zn} S(s) \) is not
Reason
Solubility product \( \left(K_{s p}\right) \) for \( Z n S \) is
much smaller than for \( Z n C O_{3} \) and a
saturated solution of \( Z n S \) does not
produce a large enough \( \left[Z n^{2+}\right] \) for the
complex ion to form
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
Solve the following pair of simultaneous equations:
\( 4 x+\frac{3}{y}=1 ; 3 x-\frac{2}{y}=5 \)
A. \( x=-6, y=7 \)
в. \( x=-3, y=1 \)
c. \( x=1, y=-1 \)
D. \( x=2, y=0 \)
Subject: Chemistry
Assertion
\( \boldsymbol{S}_{3} \boldsymbol{O}_{\boldsymbol{6}}^{2-}(\text { trithionate }) \) has \( \boldsymbol{S}-\boldsymbol{S} \) bond
Reason
It is a conjugate base of \( \boldsymbol{H} \boldsymbol{S}_{3} \boldsymbol{O}_{\boldsymbol{6}}^{-} \)
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 wire of cross section \( A \) is stretched
horizontally between two clamps
located \( 2 l m \) apart. A weight \( W k g \) is suspended from the mid-point of the wire.If the Young's modulus of the
material is \( Y, \) the value of extension \( x \)
is
\( ^{\mathrm{A}} \cdot\left(\frac{W l}{Y A}\right)^{1 / 3} \)
\( \mathbf{B} \cdot\left(\frac{Y A}{W I}\right)^{1 / 3} \)
c. \( \frac{1}{l}\left(\frac{W l}{Y A}\right)^{2 / 3} \)
\( ^{\mathrm{D}} \cdot\left(\frac{W}{Y A}\right)^{2 / 3} \)
Subject: Chemistry
One millimole \( O_{2} \) gas is dissolved in
\( \mathbf{5 4 0 0} \mathrm{ml} \) water at \( 25^{\circ} \mathrm{C} \). Calculate the
Henry's law constant \( \boldsymbol{K}_{\boldsymbol{H}} \) for this
solution. \( p_{O_{2}}=2 \times 10^{-8} \) bar.
Subject: Maths
Find the values of \( K \) so that the
quadratic equations \( x^{2}+2(K-1) x+ \)
\( K+5=0 \) has atleast one positive root
A. \( k \leq-1 \)
B. \( k \leq 1 \)
c. \( k \geq-1 \)
D. \( -1 \leq k \leq 1 \)
Subject: Maths
The average weight of 15 Oarsmen in a
boat is increased by \( 1.6 \mathrm{kg} \) when one of the crew, who weigh \( 42 \mathrm{kg} \) is replaced
by a new man. Find the weight of the new man (in kg).
A . 65
B. 66
c. 43
D. 67
Subject: Maths
The slope of tangent to the curve \( x= \) \( \boldsymbol{t}^{2}+\mathbf{3} \boldsymbol{t}-\mathbf{8}, \boldsymbol{y}=\mathbf{2} \boldsymbol{t}^{2}-\boldsymbol{2} \boldsymbol{t}-\mathbf{5} \) at the
point (2,-1) is :
A \( \cdot \frac{22}{7} \)
B. \( \frac{6}{7} \)
c. -6
D. None of these
Subject: Physics
\( A \) 2kg body and 3kg body are moving along the X-axis. At a particular instant the \( 2 \mathrm{kg} \) body is \( 1 \mathrm{m} \) from the origin and
has the velocity of \( 3 m s^{-1} \) and \( 3 k g \) body is \( 2 \mathrm{m} \) from the origin and has a velocity
of \( -1 m s^{-1} . \) The position of the center of mass of the system is:
\( A \cdot 1 m \)
B. 1.6m
c. \( 2.2 \mathrm{m} \)
D.
Subject: Maths
An article is marked at Rs. \( 500 . \) The
wholesaler sells it to a retailer at \( 20 \% \)
discount and charges sales-tax on the remaining price at 12.5\%. The retailer, in turn, sells the article to a customer at
its marked price and charges sales-tax at the same rate. Calculate:
(i) the price paid by the customer
(ii) the amount of VAT paid by the retailer.
A . (i) Rs. 662.50
(ii) Rs. 11.50
B . (i) Rs. 562.50
(ii) Rs. 12.50
c. (i) Rs. 472.50
(ii) Rs. 13.50
D. (i) Rs. 410.50
(ii) Rs. 14.50
Subject: Physics
In Youngs double slit experiment, the fringes are displaced by a distance \( x \)
when a glass plate of one refractive index 1.5 is introduced in the path of one of the beams. When this plate in replaced by another plate of the same thickness, the shift of fringes is \( (3 / 2) x \) The refractive index of the second plate
is
A . 1.75
в. 1.50
c. 1.25
D. 1.00
Subject: Maths
The possible value of \( \boldsymbol{\theta} \in(\mathbf{0}, \boldsymbol{\pi}) \) such
\( \operatorname{that} \sin (\theta)+\sin (4 \theta)+\sin (7 \theta)=0 \) are
A \( \cdot \frac{2 \pi}{9}, \frac{\pi}{4}, \frac{4 \pi}{9}, \frac{\pi}{2}, \frac{3 \pi}{4}, \frac{8 \pi}{9} \)
В. \( \frac{\pi}{4}, \frac{5 \pi}{12}, \frac{\pi}{2}, \frac{2 \pi}{3}, \frac{3 \pi}{4}, \frac{8 \pi}{9} \)
С \( \cdot \frac{2 \pi}{9}, \frac{\pi}{4}, \frac{\pi}{2}, \frac{2 \pi}{3}, \frac{3 \pi}{4}, \frac{35 \pi}{36} \)
D. \( \frac{2 \pi}{9}, \frac{\pi}{4}, \frac{\pi}{2}, \frac{2 \pi}{3}, \frac{3 \pi}{4}, \frac{8 \pi}{9} \)
Subject: Chemistry
When acetone and chloroform are
mixed together, which of the following
observations is correct?
\( (\mathbf{A}) \)
A. A-A and B-B interactions are stronger than A-B interactions
B. A-A and B-B interactions are weaker than A-B
interactions
C. A-A and B-B interactions are equal
D. The liquid form separate layers and are immiscible
Subject: Physics
\( 10 \mathrm{kg} \) of a metals melted and recast into a cylinder of diameter \( 6 \mathrm{mm} \) and \( 25 \mathrm{cm} \)
long. Find the density of the cylinder. If this cylinder is again melted and recast into 7 equal sized cubes find the density
of each cube. Whet do you infer about densities found?
Subject: Chemistry
The correct order of strength of H-bond
in the following compound:
\( \mathbf{A} \cdot H_{2} O>H_{2} O_{2}>H F>H_{2} S \)
B \( \cdot H F>H_{2} O_{2}>H_{2} O>H_{2} S \)
\( \mathbf{c} \cdot H F>H_{2} O>H_{2} S>H_{2} O_{2} \)
\( \mathbf{D} \cdot H F>H_{2} O>H_{2} O_{2}>H_{2} S \)
Subject: Maths
n given figure, \( A B C \) is a right triangle
right-angled at B. AD and CE are the two
medians drawn from A and C
respectively. IF \( \boldsymbol{A C}=\mathbf{5} c \boldsymbol{m} \) and \( \boldsymbol{A} \boldsymbol{D}= \)
\( \frac{3 \sqrt{5}}{2} c m, \) find the length of \( C E \)
Subject: Physics
A transformer consists of 500 turn in
the primary coil and 10 turns in a
secondary coil with the load of \( 10 \Omega \) Find out current in the primary coil when the voltage across the secondary
coil is \( \mathbf{5 0} \boldsymbol{V} \)
A . \( 5 A \)
в. \( 1 A \)
\( c \cdot 10 A \)
D. \( 2 A \)
Subject: Maths
If \( R \) be a relation defined from \( A= \)
\{1,2,3,4\} to \( B=\{1,3,5\}, \) i.e. \( (a, b) \in \)
\( R \) iff \( a<b \) then \( R o R^{-1} \) is
A \( \cdot\{(1,3),(1,5),(2,3),(2,5),(3,5),(4,5)\} \)
B・ \( \{(3,1),(5,1)(3,2),(5,2),(5,3),(5,4)\} \)
c. \{(3,3),(3,5),(5,3),(5,5)\}
D \( \cdot\{(3,3),(3,4),(4,5)\} \)
Subject: Physics
A particle of mass \( m \) initially moving
with speed \( v . A \) force acts on the particle \( \boldsymbol{f}=\boldsymbol{k} \boldsymbol{x} \) where \( \boldsymbol{x} \) is the distance travelled
by the particle and \( k \) is constant. Find the speed of the particle when the work done by the force equals \( W \)
A \( \cdot \sqrt{\frac{k}{m}+v^{2}} \)
B. \( \sqrt{\frac{2 W}{m}+v^{2}} \)
c. \( \sqrt{\frac{2 W}{k}+v^{2}} \)
D. \( \sqrt{\frac{W}{2 m}+v^{2}} \)
Subject: Physics
The change in the P.E., when a body of mass \( m \) is displaced from Earth's surface to a vertical height equal to radius of earth \( (\mathrm{g}= \) acceleration due to gravity on earth surface) is:
A \( \cdot \frac{m g R}{2} \)
в. \( \frac{2 m g R}{3} \)
c. \( \frac{3 m g R}{4} \)
D. \( \frac{m g R}{3} \)
Subject: Physics
In a thermo-nuclear reaction, \( 10^{-3} \mathrm{Kg} \) of
Hydrogen is converted into \( 0.99 \times 10^{-3} \)
kg of Helium. If the efficiency of the generator is \( 50 \% \), the electrical energy
generated in KWH is
A \( \cdot 10^{5} \)
B . \( 1.5 \times 10^{5} \)
c. \( 1.25 \times 10^{5} \)
D. \( 1.3 \times 10^{5} \)
Subject: Chemistry
The composition of turbid suspension
(B) and the white precipitate (C) are respectively.
A \( \cdot \operatorname{Sn} C l_{2}, \operatorname{Sn}(O H)_{2} \)
в. \( \operatorname{Sn}(O H) C l, \quad N a_{2} Z n O_{2} \)
c. \( \operatorname{Sn}(O H) C l, \operatorname{Sn}(O H)_{2} \)
D. \( \operatorname{Sn}(O H) C l, \) SnCl \( _{4} \)
Subject: Maths
If \( n(A)=1000, n(B)=500 \) and if
\( \boldsymbol{n}(\boldsymbol{A} \cap \boldsymbol{B}) \geq 1 \) and \( \boldsymbol{n}(\boldsymbol{A} \cup \boldsymbol{B})=\boldsymbol{p}, \) then
A. \( 500 \leq p \leq 1000 \)
B . \( 1001 \leq p \leq 1498 \)
c. \( 1000 \leq p \leq 1498 \)
D. \( 999 \leq p \leq 1499 \)
E . \( 1000 \leq p \leq 1499 \)
Subject: Physics
A particle experience a constant acceleration for 20 sec. after starting
from rest, it travels adistance \( s_{1} \) in first
\( 10 \sec \) and a distance \( s_{2} \) in next 10 sec
then
A \( \cdot s_{2}=s_{1} \)
В. \( s_{2}=2 s_{1} \)
\( \mathbf{c} \cdot s_{2}=3 s_{1} \)
D. \( s_{2}=0.5 s_{1} \)
Subject: Physics
A proton and an \( \alpha- \) particle enter a
uniform magnetic field perpendicular with the same speed. If proton takes \( 20 \mu s \) to make 5 revolution, then the
periodic time for the \( \alpha \) -particle would
be:
\( A \cdot 5 \mu s \)
в. \( 8 \mu s \)
c. \( 10 \mu s \)
D. \( 12 \mu s \)
Subject: Maths
If the point \( P(k-1,2) \) is equidistant
from the points \( \boldsymbol{A}(\boldsymbol{3}, \boldsymbol{k}) \) and \( \boldsymbol{B}(\boldsymbol{k}, \boldsymbol{5}) \)
then how many values of \( k \) are
obtained?

Write \( 0, \) if the value cannot be
determined
Subject: Chemistry
Match the List-I with List-II and select
the correct answer using the codes
given below the lists.
List

List II
A. Coagulation \( \quad \) 1. Scattering
B. Lyophilization 2. Washing of precipitates
C. Peptization
3. Purification of colloids
D. Tyndall effect \( \quad \) 4. Electrolyte
A. A- \( 4 ; \) B-3; C-2; D-1
B. A-2; B-1; C-3; D-4
c. \( A-3 ; B-1 ; C-2 ; D-4 \)
D. A-4; B-3; C-1; D-2
Subject: Chemistry
\( K_{2} S O_{4} \cdot A l_{2}\left(S O_{4}\right)_{3} \cdot 24 H_{2} O \) and
\( \left(N H_{4}\right)_{2} S O_{4} \cdot A l_{2}\left(S O_{4}\right)_{3} \cdot 24 H_{2} O \) are:
A. isotopes
B. allotropes
c. isomorphous
D. isomers
Subject: Chemistry
The electronic arrangements of four elements i, ii, iii, iv are:
(iii) \( 1 s^{2} 2 s^{2} 2 p^{5} \) (iv)
(i) \( 1 s^{2} \) (ii) \( 1 s^{2} 2 s^{2} 2 p^{2} \) \( 1 s^{2} 2 s^{2} 2 p^{6} \)
The tendency to form ionic bond is maximum in:
\( A \)
B. i i
c. iii
\( D . \) iv
Subject: Chemistry
Primary and secondary valency of \( P t \) in
\( \left[\boldsymbol{P t}(\boldsymbol{e n})_{2} \boldsymbol{C l}_{2}\right] \boldsymbol{C l}_{2} \) are:
\( A \cdot 2,4 \)
в. 2,
\( c \cdot 6,6 \)
D. 4,2
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{rr}\mathbf{2} & -\mathbf{3} \\ -\mathbf{4} & \mathbf{1}\end{array}\right], \) then ad
\( \left(3 A^{2}+12 A\right) \) is equal to:
A. \( \left[\begin{array}{ll}51 & 63 \\ 84 & 72\end{array}\right] \)
B. \( \left[\begin{array}{ll}51 & 84 \\ 63 & 72\end{array}\right] \)
c. \( \left[\begin{array}{cc}72 & -63 \\ -84 & 51\end{array}\right] \)
D. \( \left[\begin{array}{cc}72 & -84 \\ -63 & 51\end{array}\right] \)
Subject: Maths
A point on the parabola \( y^{2}=18 x \) at
which the ordinate increases at twice
the rate of the abscissa is
A. (2,6)
(年) (2,6)
в. (2,-6)
\( ^{\mathrm{c}} \cdot\left(\frac{9}{8},-\frac{9}{2}\right) \)
D \( \cdot\left(\frac{9}{8}, \frac{9}{2}\right) \)
Subject: Physics
Two balls of equal masses are thrown upwards along the same vertical line at
an interval of 2 seconds with the same
initial velocity of \( 39.2 m s^{-1} . \) The total
time of flight of each ball, if they collide at a certain height, and the collision is perfectly inelastic, will be
A. \( 5 s \) and \( 3 s \)
B. \( 10 s \) and \( 6 s \)
c. \( 5 \sqrt{15 s} \) and \( 3 \sqrt{15 s} \)
D. \( (5+\sqrt{15}) s \) and \( (3+\sqrt{15}) s \)
Subject: Chemistry
A carbon sample from the frame of
picture gives 7 counts of \( C^{14} \) per minute
per gram of carbon. If freshly cut wood
gives 15.3 counts of \( C^{14} \) per minute,
calculate the age of frame. \( \left(t_{1 / 2} \text { of } C^{14}=\right. \) 5570 years
A . 6286 years
B. 5527 years
c. 5570 years
D. 4570 years
Subject: Physics
A small metal sphere falls from a
height \( h \) onto a plane surface strikes it with velocity \( v \) and rebounds. If \( e \) is the coefficient of restitution:
a) the height to which it rebounds after
\( n \) collisions is \( e^{n} h \)
b) the height to which it rebound after 3
collisions is \( e^{6} h \)
c) the velocity with which it rebounds after 4 collisions is \( e^{4} v \)
d) the velocity with which it strikes the surface for the second collision is \( e v \)
A. Only a and b are correct
B. Only b and c are correct
c. \( b, c \) and \( d \) are correct
D. a, b and c are correct
Subject: Physics
A ball is thrown upwards from the top of
a tower \( 40 m \) high with a velocity of 10 \( m / s \). Find the time when it strikes
the ground. Take \( \boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{\mathbf{2}} \)
A. \( 4 s \)
B. \( 6 s \)
\( c \cdot 3 s \)
D. \( 7 s \)
Subject: Physics
A policeman on duty detects a drop of \( 10 \% \) in the pitch of the horn of a moving car as it crosses him. If the velocity of sound is \( 330 m / s, \) the speed of the car
will be
\( \mathbf{A} \cdot 36.7 m / \)sec
в. \( 17.3 \mathrm{m} / \mathrm{sec} \)
\( \mathbf{c} .25 \mathrm{m} / \mathrm{sec} \)
D. \( 27 \mathrm{m} / \mathrm{sec} \)
Subject: Chemistry
Which of the following ions would have the minimum coagulating value for sol obtained on peptizing \( \boldsymbol{S n}(\boldsymbol{O} \boldsymbol{H})_{4} \) by
little \( N a O H \) solution?
A \( \cdot C l \)
B. \( S O_{4}^{2-} \)
\( c \cdot K^{+} \)
D. \( B a^{2+} \)
Subject: Physics
Q Type your question
volume. This is strictly true only if there are no external influences. A gas
column under gravity, for example, does not have uniform density (and
pressure). As you might expect, its density decreases with height. The precise dependence is given by the socalled law of atmospheres
\( \boldsymbol{n}_{2}=\boldsymbol{n}_{1} \exp \left[-\boldsymbol{m} \boldsymbol{g}\left(\boldsymbol{h}_{2}-\boldsymbol{h}_{1}\right) / \boldsymbol{k}_{B} \boldsymbol{T}\right] \)
where \( n_{2}, n_{1} \) refer to number density at
heights \( h_{2} \) and \( h_{1} \) respectively. Use this
relation to derive the equation for sedimentation equilibrium of a suspension in a liquid column:
\( \boldsymbol{n}_{2}=\boldsymbol{n}_{1} \exp \left[-\boldsymbol{m} \boldsymbol{g} \boldsymbol{N}_{\boldsymbol{A}}\left(\boldsymbol{\rho}-\boldsymbol{\rho}^{\prime}\right)\left(\boldsymbol{h}_{2}-\right.\right. \)
\( \left.\left.\boldsymbol{h}_{1}\right) /(\boldsymbol{\rho} \boldsymbol{R} \boldsymbol{T})\right] \)
where \( \rho \) is the density of the suspended
particle and \( \rho^{\prime} \) that of surrounding
medium. \( \left[\mathrm{N}_{A} \) is Avogadro's number, and \right. \( \mathrm{R} \) the universal gas constant. [Hint : Use Archimedes principle to find
the apparent weight of the suspended particle.]
Subject: Maths
Given, \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{cl}\tan 4 x \times \cos 3 x & x \neq 0 \\ x & x=0\end{array} . \text { If } f \) is \right.
continuous at \( \boldsymbol{x}=\mathbf{0}, \) then \( \boldsymbol{k}= \)
\( A \cdot 0 \)
B. 4
c. \( \frac{4}{3} \)
D.
Subject: Physics
Two students ordered tea in a
restaurant and wanted for a friend who
was to join them shortly. One of them poured hot tea in his cup and mixed cold milk in it and the other poured hot tea but mixed the cold milk only after
the friend came after five minutes. Now
the temperature of the cup of tea of the
A. Second student is higher
B. Both student is same
c. First student is higher
D. First student is less by \( 20 \mathrm{c} \) that of the second student
Subject: Chemistry
Identify \( \boldsymbol{x}, \boldsymbol{y} \) and \( \boldsymbol{z} \) for the following metallurgical process:
Metal sulphide \( \stackrel{x}{\rightarrow} \) Metal oxide \( \stackrel{y}{\rightarrow} \)
Impure metal
\( x, y \) and \( z \) are respectively:
A. roasting, smelting, electrolysis
B. roasting, calcination, smelting
c. calcination, auto-reduction, basemerisation
D. None of the above
Subject: Maths
If \( \cdot \) donotes fractional part of \( x, \) then
\( \lim _{x \rightarrow 3+}\{x\}^{2} \frac{\sin (x-3)}{(x-3)} \) is equal?
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( \frac{1}{2} \)
\( c \cdot \frac{1}{3} \)
\( D \)
Subject: Maths
The sum of the series \( ^{20} C_{0}+^{20} C_{1}+ \)
\( ^{20} C_{2}+\ldots+^{20} C_{10} \) is
A \( 2^{20} \)
0
B . \( 2^{19} \)
C \( \cdot 2^{19}+\frac{1}{2} \cdot 20 C_{10} \)
D - \( 2^{19}-\frac{1}{2} \cdot 2^{0} C_{10} \)
Subject: Physics
In a mixture of gases, the average number of degrees of freedom per molecule is \( 6 . \) The rms speed of the molecules of the gas is \( c . \) The velocity of
sound in the gas is
A \( \cdot \frac{c}{\sqrt{2}} \)
в. \( \frac{3 c}{4} \)
c. \( \frac{2 c}{3} \)
D. \( \frac{c}{\sqrt{3}} \)
Subject: Maths
Using Rolle's theorem, the equation \( \boldsymbol{a}_{0} \boldsymbol{x}^{\boldsymbol{n}}+\boldsymbol{a}_{1} \boldsymbol{x}^{\boldsymbol{n}-1}+\ldots+\boldsymbol{a}_{\boldsymbol{n}}=\mathbf{0} \) has
atleast one root between 0 and \( 1, \) if
A \( \cdot \frac{a_{0}}{n}+\frac{a_{1}}{n-1}+\ldots .+a_{n-1}=0 \)
в. \( \frac{a_{0}}{n-1}+\frac{a_{1}}{n-2}+\ldots+a_{n-2}=0 \)
c. \( n a_{0}+(n-1) a_{1}+\ldots .+a_{n-1}=0 \)
D. \( \frac{a_{0}}{n+1}+\frac{a_{1}}{n}+\ldots .+a_{n}=0 \)
Subject: Physics
The refractive index \( (\mu) \) of glass is found to have the values
1.49,1.50,1.52,1.54 and 1.48
Calculate absolute error is each
measurement
A \( \cdot \Delta n_{5}=1.51-1.48=+0.03 \)
B . \( \Delta n_{4}=1.51-1.54=-0.03 \)
C \( . \Delta n_{3}=1.51-1.52=-0.01 \)
D. All of these
Subject: Biology
Given below are the three statements
each with two blanks. Select the option
which correctly fills up the blank in any two statements. (A) Each seminiferous
tubule is lined on Its inside by two types of cells called_(i)_and_(ii).
(B) The seminiferous tubules open into the \( (\mathrm{i})_{-} \) through \( (\mathrm{i} \mathrm{i}) \)
(C) The enlarged end of penis called the \( \underline{\text { (i) }} \) is covered by a loose fold of skin called the \( (\text { ii }) \)
A. (A)-(i)spermatogonia,(ii) follicular cells
(B)-(i) vas deferens,
(ii) urethral meatus
B. (B)-(i) vasa efferentia, (ii) rete testis
(C)-(i) glans penis
(ii) foreskin
C. (A)-(i) spermatogonia,
(ii) Sertoli cells
(C)-(i) urethral meatus,
(ii) scrotum
D. (A)-(i) spermatocytes, (ii) oogonia
(B)-(i) rete testis, (ii) vasa efferentia
Subject: Chemistry
Order of magnitude of density of
Uranium nucleous is: \( \left[\boldsymbol{m}_{\boldsymbol{p}}=\mathbf{1 . 6 7} \times\right. \)
\( \left.\mathbf{1 0}^{-\mathbf{2 7}} \mathbf{k g}\right] \)
A \( \cdot 10^{20} \mathrm{kgm}^{3} \)
В . \( 10^{17} \mathrm{kgm}^{3} \)
\( \mathbf{c} \cdot 10^{14} \mathrm{kgm}^{3} \)
D. \( 10^{11} \mathrm{kgm}^{3} \)
Subject: Physics
A wire of uniform cross-section has a
resistance of \( R \). If it is drawn to three
times the length, but the volume remains constant, what will be its
resistance?
\( \mathbf{A} \cdot 3 R \Omega \)
B. \( 5 R \Omega \)
\( \mathbf{c} .7 R \Omega \)
D. \( 9 R \Omega \)
Subject: Maths
toppr LoGin
Q Type your question
to Rs. \( 50,000 . \) The data about the
number of persons in various
categories is as under:

Monthly \( \quad \) Number of Cars income
(in rupees) 2 More than
30,001
40,000 If 400 50 25
\( 40,001- \)
50,000 \( 100 \quad 300 \) 125
Find the probability that a person
selected at random in the income slab
\( 40,001-50,000 \) have more than 2
cars.
A. 0.125
B. 0.225
c. 0.325
D. None of thesee
Subject: Chemistry
A, \( \mathrm{B}, \mathrm{C} \) are three elements with atomic numbers, Z-1, Z, and Z+1 respectively. B is an inert gas.
Identify the group to which \( A \) and \( C \) belong.
A. Alkali metal, Alkaline earth metal
B. Halogen, Alkali metal
c. Inert gas, Alkali metal
D. Halogens, Inert gas
Subject: Maths
\( \operatorname{Given} \vec{A}=2 \hat{i}-\hat{j}+2 \hat{k} ; \vec{B}=-\hat{i}-2 \hat{j}+ \)
\( \mathbf{2} \hat{\boldsymbol{k}} \)
The unit vector of \( \vec{A}-\vec{B} \)
A \( \frac{\hat{k}}{\sqrt{10}} \)
в. \( \frac{3 \hat{\imath}}{\sqrt{10} \bar{\imath}} \)
c. \( \frac{3 \hat{i}+\hat{j}}{\sqrt{10}} \)
D. \( \frac{-3 \hat{i}+\hat{k}}{\sqrt{10}} \)
Subject: Chemistry
The standard reduction potential of two reactions are given. \( \boldsymbol{A} \boldsymbol{g} \boldsymbol{C l}_{(s)}+\boldsymbol{e}^{-} \rightarrow \boldsymbol{A} \boldsymbol{g}_{(s)}+\boldsymbol{C l}_{(a q)}^{-} ; \boldsymbol{E}^{\ominus}= \)
\( \mathbf{0 . 2 2 V} \)
(i)
\( \boldsymbol{A} \boldsymbol{g}_{(a q)}^{+}+\boldsymbol{e}^{-} \rightarrow \boldsymbol{A} \boldsymbol{g}_{(s)} ; \boldsymbol{E}^{\ominus}=\mathbf{0 . 8 0 V} \)
The solubility product of \( A g C l \) under standard conditions of temperature is:
A \( .1 .6 \times 10^{-5} \)
В. \( 1.5 \times 10^{-8} \)
c. \( 3.2 \times 10^{-10} \)
D. \( 1.5 \times 10^{-10} \)