AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Assertion
The solubility of salts of weak acids like phosphates decreases at lower pH.
Reason
This is because at lower \( \mathrm{pH} \), the
concentration of cations increases.
A. If both the assertion and reason are true and reason is the correct explanation of assertion.
B. If both the assertion and reason are true but reason is not the correct explanation of assertion
c. If assertion is true but reason is false.
D. If both assertion and reason are false
Subject: Chemistry
The wavelength associated with a golf ball weighing \( 200 \mathrm{g} \) and moving at a speed of \( 5 m h^{-1} \) is of the order:
B . \( 10^{-20} m \)
\( \mathbf{c} \cdot 10^{-30} m \)
D. \( 10^{-40} m \)
Subject: Maths
If \( 2 \tan ^{-1} x+\sin ^{-1} \frac{2 x}{1+x^{2}} \) is
independent of \( x, \) then
This question has multiple correct options
\( \mathbf{A} \cdot x>1 \)
B. \( x<-1 \)
c. \( 0<x<1 \)
D. \( -1<x<0 \)
Subject: Physics
Assertion
In desert area, days get hot fastly and the nights get cold fastly.
Reason
The specific heat capacity for air and land is less than of water.
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
what is the ratio of Youngs modulus \( \boldsymbol{E} \)
to shear modulus \( G \) in terms of
poissons ratio?
\( \mathbf{A} \cdot 2(1+\mu) \)
B . \( 2(1-\mu) \)
C \( \cdot \frac{1}{2}(1-\mu) \)
D \( \cdot \frac{1}{2}(1+\mu) \)
Subject: Physics
A circular disc rotates in a vertical
plane about a fixed horizontal axis which passes through a point \( X \) on the circumference of disc. When the centre
of the disc moves with speed \( v \), the
speed of the opposite end of the
diameter through \( \boldsymbol{X} \) is
A \( .2 v \)
B. \( \sqrt{2} v \)
\( c \)
D. \( v / 2 \)
Subject: Chemistry
NaOH is formed according to the following reaction:
\( 2 N a+\frac{1}{2} O_{2} \longrightarrow N a O_{2} \)
\( N a_{2} O+H_{2} O \longrightarrow 2 N a O H \)
To make 4 g \( N a O H, N a \) required is :
A . 4.6 g
в. 4.0 g
c. 2.3 g
D. 0.23 g
Subject: Chemistry
Air contains \( 79 \% N_{2} \) and \( 21 \% O_{2} \) by
volume. If the pressure is 750 of \( H g \), the
partial pressure of \( \boldsymbol{O}_{2} \) is:
A. 157.5 of \( H g \)
B. 175.5 of \( H g \)
c. 315.0 of \( H g \)
D. 257.5 of \( H g \)
Subject: Physics
An aeroplane starting from a point travels towards north-east with a
velocity of 400 kmph. Another aeroplane starting from the same point travels towards north west with a velocity of
\( 300 \mathrm{kmph} . \) The relative velocity of one aeroplane w.r.t. other is
A. \( 350 \mathrm{kmph} \)
в. \( 500 \mathrm{kmph} \)
c. \( 100 \mathrm{kmph} \)
D. \( 200 \mathrm{kmph} \)
Subject: Chemistry
A certain substance 'A' tetramerises in
water to the extent of \( 80 \% \). A solution of
2.5 g of \( A \) in 100 g of water lowers the
freezing point by \( 0.3^{\circ} \mathrm{C} \). The molar mass of \( A \) is:
A .122
B. 31
c. 244
D. 62
Subject: Physics
A certain color of light towards the purple end of the visible spectrum has a wave length of \( 420 n m \) in vacuum.

What is the frequency of this light? (The speed of light in a vacuum is \( 3.00 \times \) \( \left.10^{8} m / s\right) \)
A \( .126 \mathrm{Hz} \)
B. \( 1.26 \times 10^{11} \mathrm{Hz} \)
c. \( 7.1 \times 10^{14} \mathrm{Hz} \)
D. \( 1.4 \times 10^{15} \mathrm{Hz} \)
E . \( 1.4 \times 10^{6} \mathrm{Hz} \)
Subject: Physics
The total energy of the electron in the first excited state of hydrogen is
\( -3.4 e V . \) What is the kinetic energy of
the electron in this state?
A. +1.7 eV
B. +3.4 eV
c. \( +6.8 \mathrm{eV} \)
D. \( -13.4 \mathrm{eV} \)
Subject: Maths
For the equation given below, find the slope and the y-intercept:
\( \boldsymbol{x}=\mathbf{5} \boldsymbol{y}-\boldsymbol{4} \)
A \( \cdot \frac{1}{5} \) and \( \frac{4}{5} \)
B. \( \frac{4}{5} \) and \( \frac{4}{5} \)
c. \( \frac{4}{5} \) and \( \frac{1}{5} \)
D. \( \frac{1}{5} \) and \( \frac{1}{5} \)
Subject: Chemistry
Structure containing an amine group is
\( \mathbf{A} \cdot C H_{3}-C H_{2}-C H_{3} \)
в. \( C H_{3}-\underset{O}{\|}-O H \)
c. \( C H_{3}-O-C_{3} H_{7} \)
E . \( C H_{3}-C H_{2}-N H_{2} \)
Subject: Physics
Which of the following are responsible for a beam of light being separated into its seven components when it is passed through a prism?
1. Total internal reflection
2. The index of refraction of prism medium with respect to air varies with wavelength
3. The index of refraction of prism
medium with respect to air is independent of wavelength
4. Velocity of light in prism depends on wavelength.
A. 1 and 4 only
B. 2 and 4 only
c. 1 and 2 only
D. 2 and 3 only
Subject: Maths
f \( \boldsymbol{T} \boldsymbol{r}(\boldsymbol{A})=\boldsymbol{6}, \) then \( \boldsymbol{T} \boldsymbol{r}(\boldsymbol{4} \boldsymbol{A})= \)
\( A \cdot \frac{3}{2} \)
B. 2
c. 12
D. 24
Subject: Maths
In a Television game show, the prize money of Rs 1,00,000 is to be divided equally amongst the winners. Complete the following table and find whether the prize money given to an individual winner is directly or inversely proportional to the number of winners?
Number of winners
Prize for
each
\[
\begin{array}{rr}
50,000 \\
, 00,000
\end{array}
\]
winner (in Rs.)
Subject: Maths
If \( a+\frac{1}{a}=6 \) and \( a \neq 0 ; \) find \( a^{2}-\frac{1}{a^{2}} \)
\( \mathbf{A} \cdot \pm 24 \sqrt{3} \)
B. \( \pm 4 \sqrt{2} \)
\( c \cdot \pm 24 \sqrt{2} \)
D. \( \pm 4 \sqrt{3} \)
Subject: Physics
The bob of a pendulum of mass \( \mathrm{m} \) and length I and a charge of q is in the rest position in a uniform horizontal electric field of E. The tension in the string of the
pendulum is :
A . \( m g \)
в. \( q E \)
c. \( \left[(m g)^{2}+(q E)^{2}\right]^{1 / 2} \)
D \( \cdot\left[(m g)^{2}+(q E)^{2}\right]^{1 / 4} \)
Subject: Chemistry
\( B r C H_{2} C H_{2} C H_{2} B r \) reacts with Na in
the presence of ether at \( 100 \mathrm{C} \) to produce:
A \( \cdot B r C H_{2} C H=C H_{2} \)
B. \( C H_{2}=C=C H_{2} \)
c. cyclopropane
D. All of these
Subject: Physics
A rock is thrown vertically upward with
initial speed \( v_{0} . \) Assume a friction force
proportional to \( -v, \) where \( v \) is the
velocity of the rock and neglect the buoyant force exerted by air. Which of
the following is correct?
A. The acceleration of the rock is always equal to \( g \)
B. The acceleration of the rock is always equal to \( g \) only at the top of the flight
C. The acceleration of the rock is always less than \( g \)
D. The speed of the rock upon return to its starting point
is \( v_{0} \)
E. The rock can attain a terminal speed greater than \( v_{0} \) before it returns to its starting point
Subject: Chemistry
Heat of neutralization is least when
A. \( \mathrm{NaOH} \) is neutralised by \( \mathrm{CH}_{3} \mathrm{COOH} \)
B. NaOH is neutralised by HCI
C. \( \mathrm{NH}_{4} \mathrm{OH} \) is neutralised by \( \mathrm{CH}_{3} \mathrm{COOH} \)
D. \( \mathrm{NH}_{4} \mathrm{OH} \) is neutralised by \( \mathrm{HNO}_{3} \)
Subject: Maths
If \( A_{1}, A_{2}, \dots, A_{100} \) are sets such that \( \boldsymbol{n}\left(\boldsymbol{A}_{\boldsymbol{i}}\right)=\boldsymbol{i}+\boldsymbol{2}, \boldsymbol{A}_{1} \subset \boldsymbol{A}_{2} \subset \boldsymbol{A}_{3} \ldots \ldots . . \boldsymbol{A}_{100} \)
and \( \bigcap_{i=3}^{100} A_{i}=A, \) then \( n(A)= \)
\( A \cdot 3 \)
B. 4
\( c .5 \)
D. 6
Subject: Physics
A projectile is fired with the a speed \( u \)
at an angle \( \theta \) above the horizontal field. The coefficient of restitution be tween
the projectile and filed is e. Find the position from the starting point when the projectile will land at its second
collision
A \( \cdot \frac{e^{2} u^{2} \sin 2 \theta}{g} \)
B. \( \frac{\left(1+e^{2}\right) u^{2} \sin 2 \theta}{g} \)
\( ^{\mathbf{C}} \cdot \frac{\left(1+e^{2}\right) u^{2} \sin \theta \cos \theta}{g} \)
D. \( \frac{(1+e) u^{2} \sin 2 \theta}{g} \)
Subject: Physics
The capacity of a parallel plate capacitor with no dielectric substance
but with a separation of \( 0.4 \mathrm{cm} \) is \( 2 \mu F \)
If the separation is reduced to half and it is filled with a dielectric substance of
value \( 2.8, \) then the final capacity of the
capacitor is
A \( .11 .2 \mu F \)
в. \( 15.6 \mu F \)
c. \( 19.2 \mu F \)
D. 22.4 \( \mu F \)
Subject: Maths
The area of triangle formed by \( (0,0),(0, a) \) and \( (b, 0) \) is \( \ldots \)
\( \mathbf{A} \cdot a b \)
в. \( \frac{a b}{2} \)
c. \( \mid \frac{a b}{2} \)
D. \( |a b| \)
Subject: Maths
Express the following matrices as the sum of a symmetric and a skew symmetric matrix:
(i) \( \left[\begin{array}{cc}\mathbf{3} & \mathbf{5} \\ \mathbf{1} & -\mathbf{1}\end{array}\right] \)
(ii) \( \left[\begin{array}{ccc}6 & -2 & 2 \\ -2 & 3 & -1 \\ 2 & -1 & 3\end{array}\right] \)
(iii) \( \left[\begin{array}{ccc}\mathbf{3} & \mathbf{3} & -\mathbf{1} \\ -\mathbf{2}-\mathbf{2} & \mathbf{1} \\ -\mathbf{4}-\mathbf{5} & \mathbf{2}\end{array}\right] \)
(iv) \( \left[\begin{array}{cc}\mathbf{1} & \mathbf{5} \\ -\mathbf{1} & \mathbf{2}\end{array}\right] \)
Subject: Chemistry
Is there any changes in the
hybridisation of \( B \) and \( N \) atoms as a result of the following reaction.
\( \boldsymbol{B} \boldsymbol{F}_{3}+\boldsymbol{N} \boldsymbol{H}_{3} \rightarrow \boldsymbol{F}_{3} \boldsymbol{B}-\boldsymbol{N} \boldsymbol{H}_{3} ? \)
Subject: Physics
Two boys are holding a horizontal rod of length \( L \) and weight \( W \) through its two ends. If now one of the boys suddenly leaves he rod. what is the instantaneous
reaction force experienced by the other boy?
A \( \cdot \frac{W}{4} \)
в. \( \frac{W}{2} \)
c. \( \frac{3 W}{4} \)
D. \( W \)
Subject: Chemistry
Sodium salt \( (A) \) of a dibasic acid \( \stackrel{H C l}{\longrightarrow} \)
gas \( (B) \)
Clear solution of \( \operatorname{gas}(B) \) turns
\( K_{2} C r_{2} O_{7} \) to green and also lime water
milky. Identify \( (\boldsymbol{A}) \) and \( (\boldsymbol{B}) \)
A \( \cdot(A)-N a_{2} S O_{4} \)
\( (B)-S O_{2} \)
в. \( (A)-N a_{2} S O_{3} \)
\( (B)-S O_{3} \)
c. \( (A)-N a_{2} S O_{4} \)
\( (B)-S O_{3} \)
D \( \cdot(A)-N a_{2} S O_{3} \)
\( (B)-S O_{2} \)
Subject: Maths
\( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\frac{\boldsymbol{x}+\boldsymbol{y}+\mathbf{1}}{\mathbf{2} \boldsymbol{x}+\mathbf{2} \boldsymbol{y}+\mathbf{3}}, \) its solution is \( \boldsymbol{x}+ \)
\( y+\frac{k}{3}=c e^{3(x-2 y)}, \) what is \( k \)
\( A \)
B. 2
\( c \cdot 5 \)
D. 4
Subject: Chemistry
For the reaction \( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{I}_{2}(\boldsymbol{g}) \rightleftharpoons \)
\( 2 H I(g) K_{i}=66.9 \) at \( 350^{\circ} \mathrm{C} \) and \( K_{i}= \)
\( \mathbf{5 0 . 0} \) at \( 448^{\circ} \) C. The reaction has:
\( \mathbf{A} \cdot \Delta H=+v \)
в. \( \Delta H=- \) ve
c. \( \Delta H=z \) ro
D. none of the above
Subject: Chemistry
Two elements \( A \) and \( B \) form ideal
compounds of formula \( A B_{2} \) and \( A B_{4} \) When dissolved in \( 20.0 g \) of benzene 1.0 \( g \) of \( A B_{2} \) lowers freezing point by \( 2.3^{0} C \) whereas \( 1.0 g \) of \( A B_{4} \) lowers
freezing point by \( 1.3^{0} \mathrm{C} \). The \( K_{f} \) for
benzene is \( 5.4 . \) The atomic masses of \( A \)
and \( B \) are:
A .27,45
в. 42,25
c. 52,48
D. 48,52
Subject: Physics
The coefficient of linear expansion of
brass is \( 2 \times 10^{-5} C^{-1} . \) Find its (i)
coefficient of superficial expansion, (ii) coefficient of cubical expansion. Let \( x \) and \( y \) be the answers write \( (y- \)
\( \boldsymbol{x}) \times \mathbf{1 0}^{\mathbf{5}} \)
Subject: Maths
In the following figure, the radius of the
circle is \( 7 \mathrm{cm} \) and \( m(a r c R Y S)=30^{\circ} \)
find find:
\( \boldsymbol{A}(\boldsymbol{P} \boldsymbol{R} \boldsymbol{X} \boldsymbol{S}) \)
Subject: Chemistry
In which of the following reaction, the
value of \( \boldsymbol{K}_{\boldsymbol{P}} \) will be equal to \( \boldsymbol{K}_{\boldsymbol{C}}- \)
A \( \cdot N_{2}(g)+O_{2}(g) \rightleftharpoons 2 N O(g) \)
в. \( P C l_{5}(g) \rightleftharpoons P C l_{3}(g)+C l_{2}(g) \)
C. \( 2 N H_{3}(g) \rightleftharpoons N_{2}(g)+3 H_{2}(g) \)
\( \mathbf{D} \cdot 2 S O_{2}(g)+O_{2} \rightleftharpoons 2 S O_{3}(g) \)
Subject: Physics
\( A=3 \hat{i}+4 \hat{j} . \) Find a vector perpendicular to \( \vec{A} \) in the plane of \( \vec{A} \)
\( A \cdot \hat{k} \)
B. \( -3 \hat{i}-4 \hat{j} \)
c. \( 4 \hat{j}-3 \hat{i} \)
D. \( 4 \hat{i}-3 \hat{j} \)
Subject: Physics
Pressure depends on distance as, \( \mathbf{p}= \) \( \frac{\boldsymbol{\alpha}}{\boldsymbol{\beta}} \exp \left(-\frac{\boldsymbol{\alpha} \mathbf{z}}{\mathbf{k} \boldsymbol{\theta}}\right), \) where \( \boldsymbol{\alpha}, \boldsymbol{\beta} \) are constants
\( \mathbf{z} \) is distance, \( \mathbf{k} \) is Boltzman's constant
and \( \theta \) is temperature. The dimension of
\( \beta \) are
\( \mathbf{A} \cdot \mathbf{M}^{o} \mathrm{L}^{o} \mathrm{T}^{o} \)
B. \( \mathrm{M}^{-1} \mathrm{L}^{-1} \mathrm{T}^{-1} \)
c. \( \mathrm{M}^{\circ} \mathrm{L}^{2} \mathrm{T}^{\circ} \)
D. \( \mathrm{M}^{-1} \mathrm{L}^{1} \mathrm{T}^{2} \)
Subject: Maths
The heights of trees in a forest are given as follows. Draw a histogram to represent the data.
\( \begin{array}{llll}\text { Heights } & \mathbf{1 6}- & \mathbf{2 1}- & \mathbf{2 6}- \\ \text { in } & \mathbf{2 0} & \mathbf{2 5} & \mathbf{3 0} \\ \text { metre } & & & \end{array} \)
Number
of trees
10
15
25
Subject: Maths
The straight lines \( \mathbf{x}+\mathbf{2 y}-\mathbf{9}=\mathbf{0}, \mathbf{3 x}+ \)
\( 5 y-5=0 \) and \( a x+b y-1=0 \) are
concurrent if the straight line \( 22 x- \)
\( 35 y-1=0 \) passes through the point
\( A \cdot(a, b) \)
в. \( (b, a) \)
c. \( (-a, b) \)
D. (-a,-b)
Subject: Maths
The equation of the straight line which is perpendicular to \( 7 x-8 y=6 \) and
passing through (-4,5) is
A. \( 8 x+7 y=3 \)
в. \( 7 x+8 y=3 \)
c. \( 8 x-7 y=3 \)
D. \( 7 x-8 y=3 \)
Subject: Physics
\( A \gamma \) ray photon produces an electron positron pair. If the rest mass energy of electron is 0.51 Mev and the total
kinetic energy of electron - positron pair is \( 0.78 M e V \) then the energy of \( \gamma- \) ray
photon is \( M e v \) is
A . 0.78
в. 1.8
c. 1.28
D. 0.28
Subject: Physics
In resonance tube experiment, the velocity of sound is given by \( \boldsymbol{v}= \)
\( 2 f_{0}\left(l_{1}-l_{1}\right) . \) We found \( l_{1}=25.0 c m \) and
\( l_{2}=75.0 c m . \) If there is no error in
frequency, what will be the maximum
permissible error in the speed of sound? \( \left(\text {Take} f_{0}=\mathbf{3 2 5 H z}\right) \)
Subject: Chemistry
\( \boldsymbol{A}+\boldsymbol{B} \rightleftharpoons \boldsymbol{C}+\boldsymbol{D}, \boldsymbol{K}_{c} \) for this reaction is
10. If 1,2,3,4 mole/litre of \( A, B, C \) and
\( D \) respectively are present in a
container at \( 25^{\circ} C, \) the direction of
reaction will be
A. From left to right
B. From right to left
c. Reaction is at equilibriumm
D. Unpredictable
Subject: Chemistry
The total number of cyclic isomers
possible for a hydrocarbon with the
molecular formula \( C_{4} H_{6} \) is:
\( A \cdot O \)
B.
\( c \cdot 2 \)
D. 3
\( E \cdot 4 \)
\( F .5 \)
\( G \cdot 6 \)
\( \mathrm{H} \cdot 7 \)
1. 8
J. 9
Subject: Biology
Match the following and choose the
correct option:
(A) Adipose tissue
(i) Nose
(B) Stratified epithelium
(ii) Blood
(C) Hyaline cartilage
(iii) Skin
(D) Fluid connective tissue
(iv) Fat storage
\( A \cdot A-(i) ; B-(i i), C-(i i i) ; D-(i v) \)
B. A- (iv); B- (iii), C- (i); D- (ii)
C \( . \) A- (iii); B- (i), C- (iv); D- (ii)
D. A- (ii); B- (i), C- (iv); D- (iii)
Subject: Maths
The value of \( \Delta=\left|\begin{array}{llll}1^{2} & 2^{2} & 3^{2} & 4^{2} \\ 2^{2} & 3^{2} & 4^{2} & 5^{2} \\ 3^{2} & 4^{2} & 5^{2} & 6^{2} \\ 4^{2} & 5^{2} & 6^{2} & 7^{2}\end{array}\right| \)
equals to
\( \mathbf{A} \cdot \mathbf{0} \)
B \( \cdot 1^{2}+2^{2}+3^{2}+4^{2}+\ldots+7^{2} \)
\( c \cdot 1 \)
D. -
Subject: Physics
Two inclined friction less tracks, one
gradual and the other steep meet at \( \boldsymbol{A} \)
from where two stones are allowed to
slide down from rest, one on each track.
Will the stones reach the bottom at the
same time? Will they reach there with
the same speed? Explain. Given \( \boldsymbol{\theta}_{\mathbf{1}}= \)
\( \mathbf{3 0}^{0}, \boldsymbol{\theta}_{2}=\mathbf{6 0}^{0}, \) and \( \boldsymbol{h}=\mathbf{1 0} \boldsymbol{m}, \) what are
the speeds and times taken by the two
stones ?
Subject: Chemistry
The molecular formula of the first
member of alkenynes and its name is
given by the set:
A \( \cdot C_{3} H_{2}, \) Alkene
B. \( C_{5} H_{6} \), Pent-1-en-3-yne
C. \( C_{6} H_{8} \), Hex-1-en-5-yne
D. \( C_{4} H_{4}, \) But-1-en-3-yne
Subject: Physics
A thin uniform square plate \( A B C D \) of
side \( a \) and mass \( m \) is suspended in a
vertical plane as shown in the figure.
\( A E \) and \( B F \) are two massless
inextensible strings. The line \( A B \) is
horizontal. The tension in \( A E \) just after
\( B F \) is cut will be
A \( \cdot \frac{2 m g}{5} \)
в. \( m g \)
c. \( \frac{2 m g}{7} \)
D. \( \frac{3 m g}{5} \)
Subject: Physics
An LCR series circuit is
under resonance. If \( I_{m} \), is current
amplitude, \( V_{m} \) is voltage amplitude, \( R \) is the resistance, \( Z \) is the impedance,
\( X_{L} \) is the inductive reactance and \( X_{C} \)
is the capacitive reactance, then
\( ^{\mathrm{A}} \cdot_{I_{m}}=\frac{Z}{V_{m}} \)
в. \( _{I_{m}}=\frac{V_{m}}{X_{L}} \)
\( \mathbf{c} \cdot_{I_{m}}=\frac{V_{m}}{X_{C}} \)
D. \( _{I_{m}}=\frac{V_{m}}{R} \)
Subject: Chemistry
During the discharge of a lead storage
battery, the density of \( 40 \% H_{2} S O_{4} \) by weight fell from 1.225 to 0.98 (which is \( 20 \% \) by weight). The change in
molarities of \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) is:
\( A \cdot 6 M \)
в. \( 5 M \)
\( c .3 M \)
D. None of these
Subject: Maths
If \( \boldsymbol{y}^{2}=\boldsymbol{P}(\boldsymbol{x}) \) is a polynomial of degree
3, then \( 2 \frac{d}{d x}\left(y^{3} \frac{d^{2} y}{d x^{2}}\right) \) is equal to
A \( \cdot P(x)+P^{\prime}(x) \)
в. \( P(x) P^{\prime}(x) \)
c. \( P(x) P^{\prime \prime \prime}(x) \)
D. a constant
Subject: Maths
An analysis of monthly wages paid to workers in two firms \( A \) and \( B \) belonging to the same industry gives the following results :
Firm
A
No.of wage earners 586
Mean of monthl wages Rs
5253
Variance of the distribution
(i) Which firm \( A \) or \( B \) pays larger
amount as monthly wages?
(ii) Which firm \( A \) or \( B \) shows greater variability in individual wages?
Subject: Physics
Which one of the following is a possible nuclear reaction?
A \( \cdot \frac{10}{5} B+_{2}^{4} H e \rightarrow_{7}^{13} N+_{1}^{1} H \)
B \( \cdot \frac{23}{13} \mathrm{Na}+_{1}^{1} \mathrm{H} \rightarrow_{20}^{20} \mathrm{Ne}+_{2}^{4} \mathrm{He} \)
C \( \cdot \frac{239}{11} \mathrm{Np} \rightarrow_{94}^{239} \mathrm{Pu}+\beta^{-}+\bar{v} \)
D. \( \frac{11}{7} N+_{1}^{1} H \rightarrow_{6}^{12} C+\beta^{-}+v \)
Subject: Chemistry
Which of the following properties of halogens increases with the increasing atomic number?
(I) lonization energy,
(II) Ionic radius,
(III) The bond energy of the \( \boldsymbol{X}_{2} \)
molecule,
(IV) Enthalpy of vaporisation.
A. IV
B. ।,॥
c. ॥।,V
D. I,II, III
Subject: Maths
f \( \vec{a} \) and bare unit vectors and \( \theta \) is the
angle between them, show that \( \sin \frac{\boldsymbol{\theta}}{\mathbf{2}}=\frac{\mathbf{1}}{\mathbf{2}}|\overrightarrow{\boldsymbol{a}}-\overrightarrow{\boldsymbol{b}}| ? \)
Subject: Physics
A concave lens of focal length \( 20 \mathrm{cm} \) placed in contact with a plane mirror acts as a convex mirror of focal length
\( A \cdot 10 \mathrm{cm} \)
B. 40 \( \mathrm{cm} \)
\( c \cdot 60 \mathrm{cm} \)
D. 20 cm
Subject: Physics
The dimensions of \( \frac{\alpha}{\beta} \) in the equation \( \boldsymbol{F}=\frac{\boldsymbol{\alpha}-\boldsymbol{t}^{2}}{\beta \boldsymbol{v}^{2}}, \) where \( \mathrm{F} \) is the force, \( \mathrm{v} \) is
velocity and t is time, is
A \( \cdot\left[M L T^{-1}\right] \)
В \( \cdot\left[M L^{-1} T^{-2}\right] \)
c. \( \left[M L^{3} T^{-4}\right] \)
D・ \( \left[M L^{2} T^{-4}\right] \)
Subject: Maths
The formula of students t-distribution
is
A \( \cdot t=\frac{s}{\sqrt{n}} \)
в. \( t=\frac{|\bar{X}-\mu|}{s} \)
c. \( \quad t=\frac{|\bar{X}-\mu|}{\frac{s}{\sqrt{n}}} \)
D. \( \quad t=\frac{\sqrt{n}}{s} \)
Subject: Maths
The area bounded by the parabola \( \boldsymbol{x}= \)
\( y^{2} \) and the line \( y=x-6 \) is
A \( \cdot \frac{125}{3} \) sq. units
B. \( \frac{125}{6} \) sq. units
c. \( \frac{125}{4} \) sq. units
D. \( \frac{115}{3} \) sq. units
Subject: Physics
Velocity of a particle of mass \( 2 \mathrm{kg} \) varies with time \( t \) according to the equation \( \overrightarrow{\boldsymbol{v}}=(2 \boldsymbol{t} \hat{\boldsymbol{i}}+\boldsymbol{4} \hat{\boldsymbol{j}}) \boldsymbol{m} / \boldsymbol{s} . \) Here \( \boldsymbol{t} \) is in seconds.
Find the impulse imparted to the particle in the time interval from \( t=0 \)
to \( t=2 s \)
A \( \cdot 8 \hat{i} N-s \)
В. \( 10 \hat{i} N-s \)
c. \( 12 \hat{i} N-s \)
D. \( 16 \hat{i} N-s \)
Subject: Chemistry
A metal \( M \) of molar mass 96 g \( m o l^{-1} \) reacts with fluorine to form a salt that
can be represented as \( M F_{x} \). In order to determine \( x .9 .18 \mathrm{g} \) of the sample of the salt is dissolved in 100 g of water and its boiling point was determined to be
\( 374.38 \mathrm{K} \). What is the value of \( x \) ?
Given: \( \boldsymbol{K}_{\boldsymbol{b}}(\boldsymbol{w} \boldsymbol{a} \boldsymbol{t e r})=\mathbf{0 . 5 1 2} \boldsymbol{K} \boldsymbol{k g m o l}^{-1} \)
Assume complete dissociation of salt
A . \( x=2 \)
в. \( x=4 \)
c. \( x=5 \)
D. \( x=7 \)
Subject: Physics
Let \( F \) be the force acting on a particle
having position vector \( r \) and \( \tau \) be the torque of this force about the origin.
Then
A. \( r . \tau=0 \) and \( F . \tau \neq 0 \)
B. \( r . \tau \neq 0 \) and \( F . \tau=0 \)
c. \( r . \tau \neq 0 \) and \( F . \tau \neq 0 \)
D. r. \( \tau= \) O and \( F . \tau=0 \)
Subject: Maths
\( \operatorname{Given} f(x)\left\{\begin{array}{ll}|x-2|+\lambda & \text { if } x \leq 2 \\ x^{2}+1 & \text { if } x>2\end{array}\right. \)
If \( f(x) \) has a local minimum at \( x=2 \)
then which of the following is most appropriate
A. \( \lambda \leq 5 \)
в. \( \lambda \geq 5 \)
c. \( \lambda \leq 0 \)
D. \( \lambda \geq 0 \)
Subject: Physics
The freezing point on a thermometer is
marked as \( 20^{\circ} \) and the boiling point as
\( 150^{\circ} . \) A temperature of \( 60^{\circ} \mathrm{C} \) on this thermometer will be read as
A \( \cdot 40^{\circ} \)
B . \( 65^{\circ} \)
\( \mathrm{c} \cdot 98^{\circ} \)
D. \( 110^{\circ} \)
Subject: Chemistry
In the given square \( P, Q, R, S \) with atomic number is written are
metalloids. About this the 4 statements
are given below. Select the correct
option of the true statements.
(a) Element after square \( P \) is a non-
metal
(b) Square \( R \) represents metalloid
(c) Element just before square \( R \) is a metalloid
\( (d) \) Element just before square \( S \) is a non-metal
\( A \cdot(a),(b) \) and \( (c) \)
в. \( (a),(b) \) and \( (d) \)
c. \( (b) \) and \( (c) \)
D. \( (a),(b),(c) \) and \( (d) \)
Subject: Physics
If a source is transmitting an electromagnetic wave of frequency \( 8.2 \times 10^{6} H z, \) then the wavelength of
the electromagnetic waves transmitted from the source will be:
A . \( 36.6 m \)
в. \( 40.5 \mathrm{m} \)
c. 42.3 m
D. \( 50.9 m \)
Subject: Physics
A driver takes \( 0.20 s \) to apply the brakes after he sees a need for it. This is called
the reaction time of the driver. If he is
driving a car at a speed of \( 54 k m / h \) and the brakes causes a deceleration of
\( 6.0 m / s^{2}, \) find the distance traveled by
the car after he sees the need to put the
brakes on.
A . \( 18.63 m \)
в. \( 20 m \)
c. 26.85 m
D. 27.67m