AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A ray of light travelling in a transparent medium falls on a surface separating the medium from air at an angle of
incidence \( 45^{\circ} . \) The ray undergoes total internal reflection. The possible value of
refractive index of the medium
with respect to air is
A \( \cdot 1.245 \)
B. 1.324
\( c \cdot 1.414 \)
D. 1.524
Subject: Physics
\( Y, K, \eta \) represent respectively the young's modulus, bulk modulus and
rigidity modulus of a body. If young's modulus is twice the bulk modulus,
then :
A \( . \eta=6 \mathrm{K} / 7 \)
в. \( \eta=7 \mathrm{K} / 9 \)
c. \( \eta=9 \) К/7
D. \( Y=18 K / 7 \)
Subject: Maths
A cistern 6 m long and 4 m wide
contains water up to the depth of 1 \( m 25 \) cm. The total area of the wet
surface is :
\( \mathbf{A} \cdot 49 m^{2} \)
B. \( 50 m^{2} \)
\( \mathrm{c} \cdot 53.5 \mathrm{m}^{2} \)
D. \( 55 m^{2} \)
Subject: Physics
An open knife edge of mass \( M \) is
dropped from a height \( h \) on a wooden
floor. If the blade penetrates distance in to the wood, the average resistance offered by the wood to the blade is
A. \( M g \)
в. \( M g\left(1+\frac{h}{s}\right) \)
c. \( \operatorname{Mg}\left(\frac{1-h}{s}\right) \)
D. \( M g\left(\frac{1+h}{s}\right)^{ } \)
Subject: Maths
In a class, 54 students are good in Hindi only, 63 students are good in Mathematics only and 41 students are good in English only. There are 18 students who are good in both Hindi and Mathematics. 10 students are good in all three subjects. What is the number of students who are good in Hindi and Mathematics but not in
English?
A . 18
в. 12
\( c \cdot 10 \)
\( D \)
Subject: Chemistry
Radius of 1st orbit of \( \boldsymbol{H} \) \& some orbit of
\( B e^{3+} \) is same. Energy of their orbit of
\( B e^{3+} \) is :
\( \mathbf{A} \cdot-54.4 e V \)
B. \( -13.6 e V \)
c. \( -108.8 e V \)
D. \( -27.2 e V \)
Subject: Maths
(Use a graph paper for this question.)
The daily pocket expenses of 200 students in a school are given below:
\[
\begin{array}{llll}
\text { Pocket } & \mathbf{0}- & \mathbf{5}- & \mathbf{1 0} \\
\text { expenses } & \mathbf{5} & \mathbf{1 0} & \mathbf{1 5}
\end{array}
\]
(in Rs)
Number of students
28
(frequency)
Draw a histogram representing the above distribution and estimate the
mode from the graph.
Subject: Physics
Five identical spaceships take off from Planet \( X \), and each passes by Planet \( Y \)
at a constant speed on its way to Planet
\( Z \). A science station on Planet \( Y \)
observes them passing by. At which of the following speeds spaceship would be observed to have the greatest length?
A \( \cdot 6 \times 10^{7} m / S \)
В. \( 9 \times 10^{7} m / S \)
c. \( 1 \times 10^{8} m / S \)
D. \( 1.5 \times 10^{8} \mathrm{m} / \mathrm{S} \)
E . \( 2 \times 10^{8} m / S \)
Subject: Physics
An ideal solenoid having 5000 turns \( / m \)
has an aluminium core and carries a
current of \( 5 A . \) If \( \chi_{A l}=2.3 \times 10^{-5}, \) then
the magnetic field developed at center will be
A. \( 0.031 T \)
\( T \)
в. \( 0.048 T \)
c. 0.0277
D. \( 0.050 T \)
Subject: Physics
The fission of a heavy nucleus gives, in
general, two smaller nuclei, two or three neutrons, some \( \beta- \) particles, and
some \( \gamma- \) radiation. It is always true
that the nuclei produced
A. have a total rest-mass that is greater than that of the original nucleus
B. have large kinetic energies that carry off the greater part of the energy released
c. travel in exactly opposite directions
D. have neutron-to-proton ratios that are too low for stability
E. have identical neutron-to
Subject: Physics
An object of mass \( \mathrm{m} \) is allowed to fall from rest along a rough inclined plane. The speed of the object on reaching the bottom of the plane is proportional to?
\( \mathbf{A} \cdot m^{0} \)
B. \( m \)
\( c \cdot m^{2} \)
D. \( m^{-1} \)
Subject: Chemistry
Which of the following pair of solutions
can we expect to be isotonic at the same temperature?
A . \( 0.1 \mathrm{M} \) NaCl and \( 0.1 \mathrm{M} \mathrm{Na}_{2} \mathrm{SO}_{4} \)
B. 0.1 M urea and 0.1 M Nacı
c. 0.1 M urea and 0.2 M \( M g C l_{2} \)
D. \( 0.1 \mathrm{M} \mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2} \) and \( 0.1 \mathrm{M} \mathrm{Na}_{2} \mathrm{SO}_{4} \)
Subject: Physics
A circular coil a carrying current
produces a magnetic field \( B_{0} \) at its
centre. This coil is made itself to 10
turns and the same current is set up in
it. The magnetic field \( B \) at its centre
would be
A. \( B=B_{0} \)
В. \( B=10 B_{0} \)
c. \( B=50 B_{0} \)
D. \( B=100 B_{0} \)
Subject: Maths
If \( A \) and \( B \) are two independent events such that \( \boldsymbol{P}(\boldsymbol{A})=\frac{1}{2} \) and \( \boldsymbol{P}(\boldsymbol{B})=\frac{1}{5} \)
then
This question has multiple correct options
A \( \cdot P(A \cup B)=\frac{3}{5} \)
в. \( P(A / B)=\frac{1}{2} \)
c. \( P(A / A \cup B)=\frac{5}{6} \)
D \cdot \( P\left(A \cap B / A^{\prime} \cup B^{\prime}\right)=0 \)
Subject: Chemistry
What weight of sodium nitrate will
separate when a saturated solution
containing 50 gram of water is cooled
from \( 50^{\circ} \mathrm{C} \) to \( 30^{\circ} \mathrm{C} \) ? The solubility of
\( N a N O_{3} \) at \( 50^{\circ} C \) and \( 30^{\circ} C \) is 114 g and 86 g respectively.
Subject: Physics
In a meter bridge circuit, resistance in
the left hand gap is \( 2 \Omega \) and an unknown resistance \( X \) is in the right hand gap as shown in Figure. The null point is found
to be \( 40 \mathrm{cm} \) from the left end of the wire.
What resistance should be connected to
\( x \) so that the new null point is \( 50 \mathrm{cm} \)
from the left end of the wire?
Subject: Maths
If \( a \) and \( b \) are real, then show that the
principal value of arg \( a \) is 0 or \( \pi \) according to \( a \) is positive or negative and that of arg \( b \) is \( \pi / 2 \) or \( -\pi / 2 \)
according to \( b \) is positive or negative.
Subject: Physics
Two drops of the same radius are falling are falling through air with a steady velocity of \( 5 \mathrm{cm} / \mathrm{s} \). If the two drops coalesce, the terminal velocity would be
A \( .10 \mathrm{cm} / \mathrm{s} \)
B. \( 2.5 \mathrm{cm} / \mathrm{s} \)
c. \( 5(4)^{1 / 3} c m / s \)
D. \( 5(3)^{1 / 3} \mathrm{cm} / \mathrm{s} \)
Subject: Physics
A body of mass \( 5 k g \) under the action of constant force \( \overrightarrow{\boldsymbol{F}}=\boldsymbol{F}_{\boldsymbol{x}} \hat{\boldsymbol{i}}+\boldsymbol{F}_{\boldsymbol{y}} \hat{\boldsymbol{j}} \) has
velocity at \( t=0 s \) as \( \vec{v}=(6 \hat{i}-2 \hat{j}) m / s \) and \( \operatorname{at} t=10 s \) as \( \vec{v}=+6 \hat{j} m / s . \) The
force \( \overrightarrow{\boldsymbol{F}} \) is:
A \( \cdot(-3 \hat{i}+4 \hat{j}) N \)
В \( \cdot\left(-\frac{3}{5} \hat{i}+\frac{4}{5} \hat{j}\right) N \)
c. \( (3 \hat{i}-4 \hat{j}) N \)
D \( \cdot\left(\frac{3}{5} \hat{i}-\frac{4}{5} \hat{j}\right) N \)
Subject: Physics
An object is placed on the principal axis of a concave mirror at a distance of 60
\( \mathrm{cm} . \) If the focal length of the concave mirror is \( 40 \mathrm{cm} \) then the magnification obtained is equal to:
\( A \cdot 2 \)
B. 1.5
\( c \cdot 3 \)
\( D \)
Subject: Maths
f \( \boldsymbol{A}=\{\mathbf{2}, \mathbf{3}, \mathbf{4}, \mathbf{5}, \mathbf{6}, \mathbf{7}\} \) and \( \boldsymbol{B}= \)
\( \{3,5,7,9,11,13\}, \) then find \( A-B \) and
\( \boldsymbol{B}-\boldsymbol{A} \)
Subject: Physics
A conducting rod of length \( l \) and mass
\( m \) is moving down a smooth inclined plane of inclination \( \theta \) with constant
velocity \( v . A \) current \( i \) is flowing in the conductor in a direction perpendicular to paper inwards, a vertically upwards magnetic field \( B \) exists in space. Then
magnitude of magnetic field \( B \) is :
A. \( \frac{m g}{i l} \sin \theta \)
в. \( \frac{m g}{i l} \tan \theta \)
c. \( \frac{m g \cos \theta}{i l} \)
D. \( \frac{m g}{\text {ilsint}} \)
Subject: Maths
The conjugate of a complex number is \( \frac{1}{i-1} . \) Then, that complex number is
A \( \cdot \frac{-1}{i+1} \)
B. \( \frac{1}{i-1} \)
c. \( \frac{-1}{i-1} \)
D. \( \frac{1}{i+1} \)
Subject: Chemistry
The solubility of \( C a F_{2} \) is \( 2 \times 10^{-4} \)
mole/litre. Its solubility product is:
A \( .2 .0 \times 10^{-4} \)
B . \( 4.0 \times 10^{-8} \)
c. \( 8.0 \times 8.0 \times 10^{-12} \)
D. \( 3.2 \times 10^{-11} \)
Subject: Chemistry
Compund \( (C) \) is :
\( A \)
\[
\begin{array}{c}
\mathrm{OH} \\
\mathrm{CH}_{3}-\mathrm{CH}-\mathrm{CH}_{2}-\mathrm{CH}-\mathrm{CH}_{3} \\
\mathrm{Cl}
\end{array}
\]
в. \( H O C H_{2}-C H_{2}-C H_{2}-C H_{2}-C H_{2}-C H_{2}-C l \)
\( c \)
\[
\mathrm{HO}-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\mathrm{CH}-\mathrm{CH}_{3}
\]
\( D \)
\[
\mathrm{HO}-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\underset{\mathrm{Cl}}{\mathrm{CH}}-\mathrm{CH}_{2}-\mathrm{CH}_{3}
\]
Subject: Physics
A block of mass \( m \) is connected to a
spring of force constant \( k . \) Initially the block is at rest and the spring has natural length. A constant force \( \boldsymbol{F} \) is applied horizontally towards right. The maximum speed of the block will be (there is no friction between block and
the surface)
A \( \cdot \frac{F}{\sqrt{2 m k}} \)
B. \( \frac{F}{\sqrt{m k}} \)
c. \( \frac{\sqrt{2} F}{\sqrt{m k}} \)
D. \( \frac{2 F}{\sqrt{m k}} \)
Subject: Chemistry
A lead storage cell is discharged which
causes the \( H_{2} S O_{4} \) electrolyte to
change from a concentration of \( 40 \% \) by weight (density \( =1.260 \) g/ml) to \( 28 \%, \) by weight. The original volume of
electrolyte was 1 L. Identify the correct
statement \( (s) \)
This question has multiple correct options
A. The overall cell reaction is : \( P b(s)+P b O_{2}(s)+ \) \( 2 H_{2} S O_{4}(a q) \rightarrow 2 P b S O_{4}(s)+2 H_{2} O(l) \)
B. A total of 2.0 moles of \( H_{2} S O_{4} \) is reacted
C. The total charge released from anode of the cell is \( 1.93 \times 10^{5} \) coulomb.
D. The mass of electrolytic solution has decreased.
Subject: Chemistry
i). State Raoult's Law.
ii). The vapour pressure of pure benzene at a certain temperature is 0.850 bar. \( A \) non-volatile non-electrolyte solid weighing 0.5 g when added to 39.0 gof benzene (molar mass 78 g \( m o l^{-1} \) ). Vapour pressure of the solution, then is
0.845 bar. What is the molar mass of
the solid substance?
Subject: Maths
Consider a differential equation of order
\( m \) and degree \( n . \) Which one of the following pairs is not feasible?
A \( \cdot(3,2) \)
В \( \cdot\left(2, \frac{3}{2}\right) \)
c. (2,4)
(年. \( (2,4)) \)
D. (2,2)
Subject: Physics
An ideal gas undergoes a quasi static, reversible process in which its molar
heat capacity \( C \) remains constant. If
during this process the relation of
pressure \( \boldsymbol{P} \) and volume \( \boldsymbol{V} \) is given by
\( P V^{n}= \) constant, then \( n \) is given by
(Here \( C_{P} \) ad \( C_{V} \) are molar specific heat
at constant pressure and constant volume, respectively):
\( ^{\mathrm{A}} \cdot_{n}=\frac{C-C_{P}}{C-C_{V}} \)
B. \( n=\frac{C_{P}-C}{C-C_{V}} \)
c. \( _{n}=\frac{C-C_{V}}{C-C_{P}} \)
D. \( _{n}=\frac{C_{P}}{C_{V}} \)
Subject: Physics
The fraction of a radioactive material
which remains active after time \( t \) is
\( \mathbf{9} / \mathbf{1 6} . \) The fraction which remains active after time \( t / 2 \) will be
A \( \cdot \frac{4}{5} \)
B. \( \frac{7}{8} \)
\( c \cdot \frac{3}{5} \)
D. \( \frac{3}{4} \)
Subject: Chemistry
Which equation in gaseous phase would be unaffected by an increase in pressure?
A. \( N_{2} O_{4} \rightleftharpoons 2 N O_{2} \)
B . \( N_{2}+O_{2} \rightleftharpoons 2 N O \)
c. \( N_{2}+3 H_{2} \rightleftharpoons 2 N H_{3} \)
D. \( c o+\frac{1}{2} O_{2} \rightleftharpoons C O_{2} \)
Subject: Physics
An object is kept at a distance of \( 16 \mathrm{cm} \) from a thin lens and the image formed is real. If the object is kept at a distance of \( 6 \mathrm{cm} \) from the same lens, the image formed is virtual. If the sizes, of the
images formed are equal, the focal length of the lens will be
\( \mathbf{A} \cdot 15 \mathrm{cm} \)
B. \( 17 \mathrm{cm} \)
\( \mathbf{c} \cdot 21 c m \)
D. \( 11 \mathrm{cm} \)
Subject: Physics
A car is moving in a straight line with speed \( 18 k m h^{-1} . \) It is stopped in \( 5 s \) by applying the brakes. Find : (i) the speed
of car in \( m s^{-1} . \) (ii) the retardation and
(iii) the speed of car after \( 2 s \) of applying
the brakes.
A \( .5 \mathrm{ms}^{-1} \)
B. \( 1 m s^{-1} \)
\( \mathbf{c} \cdot 3 m s^{-1} \)
D. none on these
Subject: Chemistry
Arrange the following in decreasing order of acidic strength.
I. Benzoic acid
II. 4 -nitrobenzoic acid
III. 3,4 -dinitrobenzoic acid
IV. 4-methoxy benzoic acid
\( A \cdot|||>||>|>\mid V \)
B. |||>|| > IV > |
c. \( \|>\| \backslash>\mid v>1 \)
D. |> || > || > IV
Subject: Physics
A ball of 100 g mass is thrown with a velocity of \( 100 m s^{-1} . \) The wavelength of
the de Broglie wave associated with the ball is about:
A. \( 6.63 \times 10^{-35} \mathrm{m} \)
В \( \cdot 6.63 \times 10^{-30} \mathrm{m} \)
c. \( 6.63 \times 10^{-33} \mathrm{cm} \)
D. \( 6.63 \times 10^{-33} \mathrm{m} \)
Subject: Chemistry
Solid calcium oxide reacts vigorously with water to form calcium hydroxide accompanied by liberation of heat. This process is called slaking of lime. Which among the following is (are) true about slaking of lime?
(i) It is an endothermic reaction
(ii) It is an exothermic reaction
(iii) The pH of the resulting solution will be more than seven
(iv) The pH of the resulting solution will be less than seven
A \( \cdot \) (i) and (ii)
B. (ii) and (iii)
c. (i) and (iv)
D. (iii) and (iv)
Subject: Physics
A uniform wire of resistance \( 100 \Omega \) its
melted and made in the form of uniform
wire, whose length is double that of the original. The resistance of the new wire
is
A \( .200 \sqrt{2} \Omega \)
B. \( 800 \Omega \)
c. \( 200 \Omega \)
D. \( 400 \Omega \)
Subject: Chemistry
0.5 Faraday of electricity was passed to deposit all the copper present in \( 500 \mathrm{m} \) of \( C u S O_{4} \) solution. What was the
molarity of this solution?
A. 1 м
B. 0.5 M
c. \( 0.25 \mathrm{M} \)
D. 2.5м
Subject: Maths
What is the multiplication of the numbers \( 1 \frac{1}{3} \times 3 \frac{1}{4} \times \frac{7}{8} ? \)
A \( \cdot 3 \frac{18}{24} \)
B \( \cdot_{2} \frac{19}{24} \)
c. \( _{3} \frac{19}{24} \)
D. \( _{2} \frac{18}{24} \)
Subject: Physics
Two identical buggies each of mass \( M \) moves one after due to inertia (without
friction) with the some velocity. A man
of mass \( m \) rides the rear buggy. At a certain moment, the manjumps into the front buggy with velocity relative to this buggy. Knowing that the mass of each buggy is equal to \( M \). Find the velocity with which the buggies will
move after that.
Subject: Physics
Assertion
It is harder to open and shut a door if we
apply force near the hinge
Reason
Torque is maximum if force is applied at the hinge of the door
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
Compared to K for the dissociation, \( 2 H_{2} S \rightleftharpoons 2 H^{+}+2 H S^{-}, \) then \( K \) for the
\( \boldsymbol{H}^{+}+\boldsymbol{H} \boldsymbol{S}^{-} \rightleftharpoons \boldsymbol{H}_{2} \boldsymbol{S} \) would have :
A \( \cdot \frac{1}{\sqrt{K}} \)
в. \( \frac{1}{K} \)
c. \( \frac{1}{K^{2}} \)
D. \( \frac{1}{K^{3}} \)
Subject: Physics
Lenses of power \( 3 D \) and \( -5 D \) are
combined to from a compound lens.An object is placed at a distance of \( 50 \mathrm{cm} \) from this lens. The position of its image will be; -
\( A \cdot-10 \mathrm{cm} \)
\( B .+10 \mathrm{cm} \)
\( c .-25 \mathrm{cm} \)
\( D \cdot+25 \mathrm{cm} \)
Subject: Physics
lce at \( 0^{\circ} C \) is added to \( 500 g \) of water at
\( 100^{\circ} \mathrm{C} \) degree. Ice is continually added to the system until it has all melted and no more ice will melt. What will be the
temperature of the water in the system?
A . 50
B . 25
c. 4.184
D.
E .
Subject: Chemistry
The Henr's law constant for \( \mathrm{N}_{2}, \mathrm{O}_{2} \) and
\( \mathrm{CO}_{2} \) in water are 1600,780 and 29 atm
M-1, respectively. Which of these gases has the highest concentration in a
sample of water at 25 degrees \( C \) when
the gas pressure over the water is 1.0 atm?
\( A \cdot N_{2} \)
B. 0,2
\( c \cdot c O_{2} \)
D. can't tell without more information about the samples
Subject: Physics
The dimension of angular momentum is
\( \mathbf{A} \cdot\left[M^{0} L^{1} T^{-1}\right] \)
B . \( \left[M^{1} L^{2} T^{-2}\right] \)
C \( \cdot\left[M^{1} L^{2} T^{-1}\right] \)
D \cdot \( \left[M^{2} L^{1} T^{-2}\right] \)
Subject: Maths
Study the following graph carefully and
answer the question given What was the difference between the
number of B type tyres manufactured in
\( \mathbf{1 9 9 4} \) and \( \mathbf{1 9 9 5} ? \)
A .1,00,000
B. 20,00,000
c. 10,00,000
D. 12,50,000
Subject: Chemistry
The oxidation potential of
\( Z n, C u, A g, H_{2} \) and \( N i \) are 0.76,-0.34
-0.80,0,0.55 volt respectively. Which of the following reaction will provide maximum voltage?
A. \( Z n+C u^{2+} \rightarrow C u+Z n^{2+} \)
B. \( Z n+2 A g^{+} \longrightarrow 2 A g+Z n^{2+} \)
c. \( H_{2}+C u^{2+} \rightarrow 2 H^{+}+C u \)
D. \( H_{2}+N i^{2+} \rightarrow 2 H^{+}+N i \)
Subject: Chemistry
Sodium sulphate is soluble in water,
whereas barium sulphate is sparingly
soluble because:
This question has multiple correct options
A. the hydration energy of sodium sulphate is more than its lattice energy
B. the lattice energy of barium sulphate is more than its hydration energy
C. the lattice energy has no role to play in solubility
D. the hydration energy of sodium sulphate is
less than its lattice energy
Subject: Physics
the specific heat capacity of liquid.
\( \mathbf{A} \cdot 0.3 \times 10^{3} J k g^{-1} K^{-1} \)
B \( \cdot 12 \times 10^{3} J k g^{-1} K^{-1} \)
C \( .3 \times 10^{3} \mathrm{Jkg}^{-1} \mathrm{K}^{-1} \)
\( \mathbf{D} \cdot 6 \times 10^{3} J k g^{-1} K^{-1} \)
Subject: Physics
The molar heat capacity in a process of diatomic gas if it does a work of \( \frac{Q}{4} \) when a heat of \( Q \) is supplied to it is
A \( \cdot \frac{2}{5}^{R} \)
в. \( \frac{5}{4} \) R
c. \( \frac{10}{3} \) R
D. \( \frac{6}{4} \) R
Subject: Physics
Two capacitors of \( 0.5 \mu F \) and \( 1 \mu F \) are connected in parallel across a battery. If the charge on \( 0.5 \mu F \) is \( 50 \mu C \), the charge
on the other capacitor is :
A. \( 100 \mu C \)
B. \( 50 \mu C \)
c. \( 25 \mu C \)
D. zero
Subject: Maths
If the \( (p+q)^{t h} \) term of a geometric
series is \( \mathrm{m} \) and the \( (p-q)^{t h} \) term is \( n \)
then the \( p^{t h} \) term is
\( \mathbf{A} \cdot(m n)^{1 / 2} \)
в. \( m \) n
\( c \cdot m+n \)
D. m-n
Subject: Maths
If the focal distance of an end of the
minor axis of any ellipse (referred to its axes as the axes of \( x \) and \( y \)
respectively) is \( k \) and the distance between the foci is \( 2 h, \) then its equation
is:
A \( \cdot \frac{x^{2}}{k^{2}}+\frac{y^{2}}{k^{2}+h^{2}}=1 \)
в. \( \frac{x^{2}}{k^{2}}+\frac{y^{2}}{h^{2}-k^{2}}=1 \)
c. \( \frac{x^{2}}{k^{2}}+\frac{y^{2}}{k^{2}-h^{2}}=1 \)
D. \( \frac{x^{2}}{k^{2}}+\frac{y^{2}}{h^{2}}=1 \)
Subject: Chemistry
A current of \( 965 A \) is passed for 100 sec
between inert electrodes in \( 500 m L \)
solution of \( 2 M C u S O_{4} . \) The molarity of solution after electrolysis would be:
(Assume no change in volume)
A \( .2 M \)
в. \( 1 M \)
c. \( 4 M \)
D. \( 0.5 M \)
Subject: Chemistry
A student prepared methanol in the laboratory by the addition of \( 266 g \) of \( C O \) and \( 60 g \) of \( H_{2}, \) as shown below. \( \boldsymbol{C O}(\boldsymbol{g})+\boldsymbol{H}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{O} \boldsymbol{H}(\boldsymbol{l}) \)
(a) Find out the limiting reagent
(b) Calculate the amount of methanol produced and the amount of excess reactant remaining after the completion of the reaction.
Subject: Chemistry
Which carboxylic acid \( (B) \) (Equivalent
weight \( \left.=52 g m e q^{-1}\right) \) loses \( C O_{2}, \) which
on heating gives an acid \( (\boldsymbol{C}) \)
(Equivalent weight \( =\mathbf{6 0} \) gm \( e q^{-1} \) )?
A \( \cdot R=C H_{3} \)
\[
\begin{array}{l}
C=C H_{3} C O O H \\
N . E .(E w)=52 \mathrm{gm} \mathrm{eq}^{-1}
\end{array}
\]
В. \( R=C H_{3} \)
\[
C=C H_{3}-C H_{2}-C O O H
\]
\[
\text { N.E. }(E w)=52 \text { gm } e q^{-1}
\]
\( \mathbf{c} \cdot R=C H_{3} \)
\[
\begin{array}{l}
C=C O O H \\
N \cdot E \cdot(E w)=52 \mathrm{gm} \mathrm{eq}^{-1}
\end{array}
\]
D. None of these
Subject: Maths
\( A B \| C D \) and \( A C M \) is a straight line
\( \angle B A C \) is equal to:
A \( \cdot 106^{\circ} \)
B. \( 108^{\circ} \)
\( \mathrm{c} \cdot 110^{\circ} \)
D. \( 109^{\circ} \)
Subject: Chemistry
The heat of hydrogenation of one double bond in cyclohexene is \( 28.6 \mathrm{kcal} \) mol \( ^{-1} \) and the heat of hydrogenation of benzene to cyclohexane is \( 50 \mathrm{kcal} \) mol \( ^{-1} \). What will be the resonance
stabilization energy of benzene?
A . 28.6 kcal mol-1
B. 55.0 kcal mol-1
c. 85.8 kcal \( m o l^{-1} \)
D. 35.8 kcal mol-1
Subject: Maths
If \( 2 \vec{a}+3 \vec{b}-5 \vec{c}=\overrightarrow{0}, \) then ratio in which
\( \vec{c} \) divides \( \overrightarrow{A B} \) is
A. 3: 2 internally
B. 3: 2 externally
c. 2: 3 internally
D. 2: 3 externally
Subject: Maths
\( \mathbf{f}\left[\begin{array}{ccc}\mathbf{1} & \mathbf{3} & \mathbf{0} \\ \mathbf{1} & \mathbf{0} & -\mathbf{2} \\ \mathbf{- 4} & \mathbf{- 4} & \mathbf{4}\end{array}\right]=\mathbf{A}+\mathbf{B} \) where \( \mathbf{A} \)
is symmetric matrix and B is skew-
symmetric, then \( \mathbf{A}-\mathbf{B} \) is equal to
\( \mathbf{A} \cdot\left[\begin{array}{ccc}1 & 1 & -4 \\ 3 & 0 & -4 \\ 0 & -2 & 4\end{array}\right] \)
B. \( \left[\begin{array}{lll}2 & 1 & 3 \\ -1 & 2 & 4 \\ 3 & -1 & 2\end{array}\right] \)
\( \mathbf{c} \cdot\left[\begin{array}{lll}0 & 1 & -1 \\ 2 & 3 & 4 \\ -4 & 1 & 2\end{array}\right] \)
D. \( \left[\begin{array}{ccc}2 & -3 & 0 \\ 0 & 1 & 2 \\ 2 & 4 & 0\end{array}\right] \)
Subject: Maths
Let \( f: N \rightarrow N \) be defined by \( f(n)= \) \( \left\{\begin{array}{l}\frac{n+1}{2}, \text { if } \mathrm{n} \text { is odd } \\ \frac{n}{2}, \text { if } \mathrm{n} \text { is even }\end{array}\right\} \) for all \( n \in N \)
State whether the function \( f \) is bijective.
Justify your answer
Subject: Physics
A liquid has a volume \( V_{1} \) at
temperature \( \theta_{1} \). The temperature is
increased to \( \theta_{2} \). If \( \gamma \) is the coefficient of
cubic expansion, the increase in
volume is given by
A \( \cdot V_{1} \gamma\left(\theta_{2}-\theta_{1}\right) \)
в. \( V_{1} \gamma \theta_{2} \)
c. \( V_{1}+V_{1} \gamma \theta_{2} \)
D. \( V_{1}\left[1+\gamma\left(\theta_{2}-\theta_{1}\right]\right. \)
Subject: Maths
If \( A \) and \( B \) are two non singular matrices of the same order such that
\( B^{r}=I, \) for some positive integer \( r>1 \)
\( \operatorname{then} \boldsymbol{A}^{-1} \boldsymbol{B}^{r-1} \boldsymbol{A}-\boldsymbol{A}^{-1} \boldsymbol{B}^{-1} \boldsymbol{A}= \)
A . \( I \)
B. \( 2 I \)
\( c \cdot O \)
D. \( -I \)
Subject: Chemistry
The \( \boldsymbol{K}_{s p} \) of \( \boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{C r} \boldsymbol{O}_{4}, \) AgCI, \( \boldsymbol{A g B r} \) and \( \boldsymbol{A g} \)
are respectively, \( 1.1 \times 10^{-12}, 1.8 \times \)
\( 10^{-10}, 5.0 \times 10^{-13}, 8.3 \times 10^{-17} . \) Which
one of the following salts will
precipitate last if \( A g N O_{3} \) solution is added to the solution containing equal
moles of NaCl, NaBr, Nal and \( N a_{2} C r O_{4} \)
\( ? \)
A . Agc
в. Аgвт
\( \mathbf{c} \cdot A g_{2} C r O_{4} \)
D. Agl