AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A body is sliding down an inclined plane (angle of inclination \( 45^{\circ} \) ). If the coefficient of friction is 0.5 and \( g= \)
\( 9.8 m / s^{2}, \) then the downward
acceleration of the body in \( m / s^{2} \) is:
A \( \cdot \frac{4.9}{\sqrt{2}} \)
B. \( 4.9 \sqrt{2} \)
C. \( 19.2 \sqrt{2} \)
D. 4.9
Subject: Physics
When light is incident on a glass block at polarizing angle
a) reflected ray is plane polarized
b) reflected and refracted rays are perpendicular
c) reflected and refracted rays are
partially polarized
d) refracted ray is partially polarised
\( A \cdot a, c \) and \( d \) are correct
B. a, b and d are correct
\( c \cdot b, c \) and \( d \) are correct
D. a, b and c are correct
Subject: Physics
A body is projected with some initial velocity \( u \) at angle \( \frac{\pi}{7} \) with the horizontal. At what angle should
another body be thrown so that the
horizontal range in both cases is the
same?
A. \( \frac{\pi}{2} \)
в. \( \frac{5 \pi}{14} \)
c. \( \frac{4 \pi}{7} \)
D. \( \frac{6 \pi}{7} \)
Subject: Physics
A particle of unit mass undesgro one
dimension motion. Such that its
verocity varies accordingly to \( v(x)= \)
\( \beta \vec{x}^{2} \pi, \) where \( \beta \) and \( n \) are constant and \( x \)
is the position of the particle. The accelerationx is the position of the particle. The accelerationof the particle
a function of \( x, \) is given by
A. \( -2 n \beta^{2} x^{-} 2 n-1 \)
B . \( -2 n \beta^{2} x^{-4 n-1} \)
C \( .-2 \beta^{2} x^{-2 n+1} \)
D. \( -2 n \beta^{2} e^{-} 4 n+1 \)
Subject: Chemistry
\( \boldsymbol{E}^{\circ} \) for \( \boldsymbol{M}^{2+}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{2} \boldsymbol{e}^{-} \rightarrow \boldsymbol{M}(\boldsymbol{s}) \)
(where \( M=C a, S r \text { or } B a) \) is nearly
constant.
Subject: Physics
A wire of uniform cross section is hanging vertically and due to its own weight its length changes. There is a point 'C' on the wire such that change in length AC is equal to the change in length BC. Points \( A, B \) and \( C \) are shown in the figure. Find \( \frac{\boldsymbol{A C}}{\boldsymbol{B C}} \)
A \( \cdot \sqrt{2}-1 \)
B. \( \frac{\sqrt{2}-1}{\sqrt{2}+1} \)
c. \( \frac{\sqrt{2}+1}{\sqrt{2}-1} \)
D. None of these
Subject: Maths
The arithmetic mean (average) of the first \( n \) positive integers is
A \( \cdot \frac{n}{2} \)
в. \( \frac{n^{2}}{2} \)
c. \( n \)
D. \( \frac{n-1}{2} \)
E \( \cdot \frac{n+1}{2} \)
Subject: Physics
A pin which is \( 2 \mathrm{cm} \) long is placed at a distance of \( 16 \mathrm{cm} \) from a convex lens.
Assuming it to be perpendicular to the principal axis, find the position of the image if the focal length of the lens is 12
\( \mathrm{cm} \)
A . \( 48 \mathrm{cm} \)
B. 24 \( \mathrm{cm} \)
c. \( 12 \mathrm{cm} \)
D. None of these
Subject: Physics
A ball is released from the top of a tower
of height h metres. It takes T seconds to reach the ground. What is the position of the ball in \( T / 3 \)
seconds?
A. h/9 metre from the ground
B. 7h/9 metre from the ground
c. \( 8 \mathrm{h} / 9 \) metre from the ground
D. 17h/18 metre from the ground
Subject: Chemistry
If \( C O_{2} \) is passed into waste water
containing \( C r O_{7}^{2-} \) (yellow) then:
A. Solution turns green due to formation of \( C r^{3} \)
B. Solution turns blue due to formation of \( C r O_{5} \)
C. Solution turns orange due to formation of \( C r_{2} O_{7}^{2} \)
D. No effect takes place
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 determine the magnification of the obtained image.
\( A \cdot 2 \)
B. - -
\( c \cdot 2.5 \)
D. -2.5
Subject: Chemistry
Which of the following reduction
reactions are actually employed in
commerical extraction of metals?
This question has multiple correct options
\( \mathbf{A} \cdot F e_{2} O_{3}+2 A l \rightarrow A l_{2} O_{3}+2 F e \)
B. \( C r_{2} O_{3}+2 A l \rightarrow A l_{2} O_{3}+2 C r \)
\( \mathbf{c} \cdot 2 N a\left[A u(C N)_{2}\right]+Z n \rightarrow N a_{2}\left[Z n(C N)_{4}\right]+2 A u \)
\( \mathbf{D} \cdot C u_{2} S+P b \rightarrow C u+P b S \downarrow \)
Subject: Physics
The height of water in a capillary tube of
radius \( 2 c m \) is \( 4 c m . \) What should be the
radius of capillary, if the water rises to \( 8 c m \) in tube?
A \( .1 \mathrm{cm} \)
в. \( 0.1 \mathrm{cm} \)
\( c .2 c m \)
D. \( 4 c m \)
Subject: Chemistry
IUPAC name for \( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right]^{2+} \) is:
A. hexammoniacobaltate(II) ion
B. hexaamminecobaltate(II) ion
c. hexammoniacobalt(II) ion
D. hexaamminecobalt(II) ion
Subject: Maths
\( f\left|\begin{array}{ccc}6 i & -3 i & 1 \\ 4 & 3 i & -1 \\ 20 & 3 & i\end{array}\right|=x+i y \) then
A \( . x=3, y=1 \)
B. \( x=1, y=3 \)
c. \( x=0, y=3 \)
D. \( x=0, y=0 \)
Subject: Maths
\( A \) line cuts the \( x \) -axis at \( A(7,0) \) and the y-axis at \( B(0,-5), \) A variable line \( P Q \) is
drawn perpendicular to \( A B \) cutting the
x-axis at \( \boldsymbol{P} \) and the \( y \) -axis at in \( \boldsymbol{Q} \)

If \( A Q \) and \( B P \) intersect at \( R, \) the locus
of \( \boldsymbol{R} \) is
A \( \cdot x^{2}+y^{2}+7 x-5 y=0 \)
B . \( x^{2}+y^{2}-7 x+5 y=0 \)
c. \( 5 x-7 y=35 \)
D. None of these
Subject: Physics
When a lens of refractive index \( n_{1} \)
is placed in a liquid of refractive index
\( n_{2}, \) the lens looks to be disappeared
only, if
A \( \cdot n_{1}=n_{2} / 2 \)
в. \( n_{1}=3 n_{2} / 4 \)
c. \( n_{1}=n_{2} \)
D. \( n_{1}=5 n_{2} / 4 \)
Subject: Maths
Investigate the behaviour of the
function \( \boldsymbol{y}=\left(\boldsymbol{x}^{3}+\boldsymbol{4}\right)(\boldsymbol{x}+\mathbf{1})^{3} \) and
construct its graph. How many
solutions does the equation \( \left(x^{3}+\right. \)
4)\( (x+1)^{3}=c \) possess?
Subject: Chemistry
Identify \( (X),(Y) \) and \( (Z) \) in the given
reaction.
\( C H_{3} C H O \frac{K_{2} C r_{2} O_{7}}{H_{2} S O_{4}}(X) \stackrel{P C l_{5}}{ } \)
\( (Y) \frac{C_{6} H_{6}}{a n h . A l C l_{3}}(Z): \)
\( \mathbf{A} \cdot(X)=H C O O H, \quad(Y)=C O C l_{2}, \quad(Z)=C_{6} H_{5} C l \)
B \( \cdot(X)=C H_{3} C O O H, \quad(Y)=C H_{3} C O C l, \quad(Z)= \)
\( C_{6} H_{5} C O C H_{3} \)
\( \mathbf{c} \cdot(X)=C H_{3} C O O H, \quad(Y)=C H_{3} C H_{2} C H_{2} C l, \quad(Z)= \)
\( C_{6} H_{5} C H_{2} C H_{2} C H_{3} \)
\( \mathbf{D} \cdot(X)=C H_{3} C O C H_{3}, \quad(Y)=C H_{3} C H(C l) C H_{3}, \quad(Z)= \)
\( C_{6} H_{5} C O C H_{3} \)
Subject: Chemistry
Correct order of boun angle of the
following is?
A. \( C l O_{2}>O C l_{2}>O F F_{2} \)
в. \( O F_{1}>O C l_{2}>C l_{2} O \)
c. \( O C l_{2}>C l O_{2}>O F_{2} \)
D. \( O C l_{2}>O F_{2}>C l O_{2} \)
Subject: Maths
In a factory there are three types of
Machines \( M_{1}, M_{2} \) and \( M_{3} \) which produces \( 25 \%, 35 \% \) and \( 40 \% \) of the
total products respectively. \( M_{1}, M_{2} \) and
\( M_{3} \) produces \( 2 \%, 4 \% \) and \( 5 \% \) defective
products, respectively. What is the percentage of non-defective products?
A . \( 89 \% \)
B. \( 97.1 \% \)
c. \( 96.1 \% \)
D. \( 86.1 \% \)
Subject: Chemistry
\begin{tabular}{ll|l|l} 
& Column I & & Column II \\
a. & Enthalpy & p. & Intrinsic property \\
b. & Temperature & q. & Path function \\
c. & Free energy & r. & Function \( U, P, V \) \\
d. & Work & s. & State function
\end{tabular}
\( \mathbf{A} \cdot(a-r, s),(b-p, s),(c-r, s),(d-q) \)
\( \mathbf{B} \cdot(a-r),(b-s),(c-r, s),(d-q, r) \)
\( \mathbf{C} \cdot(a-r, s),(b-r),(c-p, s),(d-q) \)
D \( .(a-q),(b-p, s),(c-s),(d-q, s) \)
Subject: Chemistry
Match List I (Substances) with List-II
(Processes employed in the
manufacture of the substance) and
select the correct option.
List - (Substances)
A. Sulphuric acid
1. Haber's process
B. Steel
2. Bessemer's
process
c. Sodium hydroxide \( \quad 3 \). Leblanc process
D. Ammonia
A. \( A-1, B-4, C-2, D-3 \)
в. \( A-1, B-2, C-3, D-4 \)
c. \( A-4, B-3, C-2, D-1 \)
D. \( A-4, B-2, C-3, D-1 \)
Subject: Physics
A hollow smooth uniform sphere \( A \) of mass m rolls without sliding on a smooth horizontal surface. It collides
head on elastically with another stationary smooth solid sphere \( B \) of the same mass \( \mathrm{m} \) and same radius. The
ratio of kinetic energy of \( B \) to that of \( A \) just after the collision is :
\( A \cdot 1: 1 \)
в. 2: 3
\( c .3: 2 \)
D. 4: 3
Subject: Chemistry
IUPAC name of \( \left(\mathbf{C H}_{3}\right)_{2} \mathbf{C H}- \)
\( \mathbf{C H}\left(\mathbf{C H}_{3}\right)_{2} \)
A. 1,1,2,3 -Tetra ethyl ethane
B. 1,2, - -Diisopropyl ethane
c. 2,3 -Dimethyl butane
D. 2, 3, 3-Trimethyl butane
Subject: Physics
There exist uniform magnetic and electric fields of magnitudes \( 1 T \) and \( \mathbf{1} \boldsymbol{V} / \boldsymbol{m}, \) respectively, along positive \( \boldsymbol{y}- \)
axis. A charged particle of mass \( 1 k g \) and charge \( 1 C \) is having velocity 1 \( m / s \) along \( x \) -axis and is at origin at \( \boldsymbol{t}=\mathbf{0} . \) Then, the coordinates of the
particle at time \( \pi s \) will be
A. (0,1,2)\( m \)
в. \( \left(0,-\pi^{2},-2\right) m \)
c. \( \left(2, \pi^{2} / 2,2\right) m \)
D・ \( \left(0, \pi^{2} / 2,2\right) m \)
Subject: Maths
For a \( \Delta A B C, A B=4 \mathrm{mm}, B C=5 \)
\( \mathrm{mm} \) and \( \boldsymbol{A C}=\mathbf{6} \) mm. If \( \boldsymbol{\Delta} \boldsymbol{A} \boldsymbol{B} \boldsymbol{C} \cong \)
\( \Delta D E F, \) then \( E F=_{-}- \)
\( \mathbf{A} \cdot 4 \mathrm{mm} \)
B. \( 6 \mathrm{mm} \)
\( c .5 \mathrm{mm} \)
D. cannot be determined
Subject: Chemistry
Ethylamine is?
A. \( C H_{3}-C H_{2}-C H_{3} \)
в. \( C H_{3}-\underset{O}{\|}-O H \)
c. \( C H_{3}-O-C_{3} H_{7} \)
D. \( C H_{3}-C-C H_{3} \)
I
O
E \( \cdot C H_{3}-C H_{2}-N H_{2} \)
Subject: Biology
Assertion
Higher yields in case of bell pepper can
be achieved by growing them in carbon dioxide enriched green houses.
Reason
In the case of bell pepper, due to higher
intracellular \( \mathrm{CO}_{2} \) concentration in
bundle sheath cells RuBisCo mainly
acts as carboxylating enzyme.
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
Find the mode of the data given below:
\begin{tabular}{|l|c|c|c|c|c|}
\hline Class & \( 20-29 \) & \( 30-39 \) & \( 40-49 \) & \( 50-59 \) & \( 60-69 \) \\
\hline Frequency & 15 & 20 & 50 & 30 & 10 \\
\hline
\end{tabular}
Subject: Chemistry
Which of the following gives, on ozonolysis, both aldehydes and
ketones?
A. \( M e_{2} C=C H M e \)
В. \( M e_{2} C=C M e_{2} \)
\( \mathbf{c} \cdot \operatorname{meCH}_{2}-C(M e)=C M e_{2} \)
D. \( \operatorname{Me} C H(M e)-C H=C H M e \)
Subject: Physics
A string of length \( 1 \mathrm{m} \) and linear mass density \( 0.01 \mathrm{kg} / \mathrm{m} \) is stretched to a tension of 100 N. When both ends of the
string are fixed, the three lowest
frequencies for standing wave are \( \boldsymbol{n}_{1}, \boldsymbol{n}_{2} \) and \( \boldsymbol{n}_{3} . \) Then
A \( \cdot n_{3}=5 n_{1}=f_{3}=125 \mathrm{H} \)
B . \( f_{3}=5 f_{1}=n_{2}=125 \mathrm{Hz} \)
C \( . f_{3}=n_{2}=3 f_{1}=150 \mathrm{Hz} \)
D. \( n_{2}=\frac{f_{1}+f_{2}}{2}=75 \mathrm{Hz} \)
Subject: Physics
A polarizer and an analyzer are oriented so that the maximum amount of lights
is transmitted. Fraction of its
maximum value is the intensity of the
transmitted light reduced when the
analyzer is rotated through (intensity of
incident light \( =\boldsymbol{I}_{\boldsymbol{o}} \boldsymbol{)} \)
a) \( 30^{\circ} \) b) \( 45^{\circ} \)
c) \( 60^{\circ} \)
A \( .0 .375 I_{0}, 0.25 I_{0}, 0.125 I_{0} \)
B. \( 0.25 I_{0}, 0.375 I_{0}, 0.125 I_{0} \)
C \( \cdot 0.125 I_{0}, 0.25 I_{0}, 0.0375 I_{0} \)
D. \( 0.125 I_{0}, 0.375 I_{0}, 0.25 I_{0} \)
Subject: Chemistry
Prostaglandin \( E_{1} \) 1 is a compound produced by the body to regulate a variety of processes including blood clotting, fever, pain and inflammation.
How many \( s p^{2} \) hybridised carbon atoms
are present in compound 1?
\( \mathrm{E}_{1} \)
\( A \)
B. 2
\( c \cdot 3 \)
\( D \)
Subject: Maths
\( \int e^{2 x}\left(\frac{1+\sin 2 x}{1+\cos 2 x}\right) d x \) is equal to
A \( \cdot e^{2 x} \tan x+C \)
B . \( e^{2 x} \cot x+C \)
\( ^{\mathrm{c}} \cdot \frac{e^{2 x} \tan x}{2}+C \)
\( ^{\mathrm{D} \cdot \frac{e^{2 x} \cot x}{2}}+C \)
Subject: Maths
If \( (\cos \theta+i \sin \theta)(\cos 2 \theta+i \sin \theta) \)
\( (\cos n \theta+i \sin n \theta)=1, \) then the value
of \( \boldsymbol{\theta} \) is
A \( \cdot \frac{2 m \pi}{n(n+1)} \)
B. \( 4 m \pi \)
c. \( \frac{4 m \pi}{n(n+1)} \)
D. \( \frac{m \pi}{n(n+1)} \)
Subject: Physics
Charges are placed on the vertices of a square as shown. Let \( \vec{E} \) be the electric
field and V the potential at the centre. If the charges on \( A \) and \( B \) are interchanged with those on D and
respectively, then
A. \( \bar{E} \) changes, v remains unchanged
B. \( \bar{E} \) remains unchanged, v changed
c. both \( \vec{E} \) and \( v \) change
D. \( \vec{E} \) and v remain unchange
Subject: Maths
Consider the functions defined
implicitly by the equation \( \mathbf{y}^{3}-\mathbf{3 y}+ \) \( \mathbf{x}=\mathbf{0} \) on various intervals in the real line. If \( \boldsymbol{x} \in(-\infty,-2) \cup(2, \infty), \) the
equation implicitly defines a unique real valued differentiable function \( \mathbf{y}= \)
\( \mathbf{f}(\mathbf{x}) . \) If \( \boldsymbol{x} \in(-\mathbf{2}, \mathbf{2}), \) the equation
implicitly defines a unique real valued differentiable function \( \mathbf{y}=\mathbf{g}(\mathbf{x}) \) satisfying \( \mathbf{g}(\mathbf{0})=\mathbf{0} \)
\( \int_{-1}^{1} \mathbf{g}^{\prime}(\mathbf{x}) \boldsymbol{d} \boldsymbol{x}= \)
A \( \cdot 2 g(-1) \)
B. 0
c. \( -2 g(1) \)
D. \( 2 \mathrm{g}(1) \)
Subject: Chemistry
The stability of dihalides of \( \boldsymbol{S} \boldsymbol{i}, \boldsymbol{G} \boldsymbol{e} . \boldsymbol{S} \boldsymbol{n} \)
and \( P b \) increases steadily in the
sequence:
A. \( P b X_{2}<\operatorname{SnX}_{2}<\operatorname{GeX}_{2}<\operatorname{SiX}_{2} \)
в. \( G e X_{2}<\operatorname{Si} X_{2}<\operatorname{SnX}_{2}<P b X_{2} \)
c. \( \operatorname{si} X_{2}<\operatorname{Ge} X_{2}<\operatorname{Pb} X_{2}<\operatorname{SnX}_{2} \)
D. \( \operatorname{SiX}_{2}<\operatorname{GeX}_{2}<\operatorname{SnX}_{2}<P b X_{2} \)
Subject: Chemistry
The \( \boldsymbol{E}^{o} \) for, \( \boldsymbol{M} \boldsymbol{n}^{4+}+\boldsymbol{2} \boldsymbol{e} \rightarrow \boldsymbol{M} \boldsymbol{n}^{2+} \) is
equal to:
A . 1.23 v
B. 2.46 V
c. \( 0.56 v \)
D. -0.56
Subject: Maths
In the given figure, \( O A C B \) is a
quadrant of a circle. The radius \( \boldsymbol{O A}= \)
\( 3.5 \mathrm{cm}, O D=2 \mathrm{cm} . \) Calculate the area
of the shaded portion.
A \( \cdot 6.225 \mathrm{cm}^{2} \)
В \( \cdot 6.25 \mathrm{cm}^{2} \)
c. \( 6.116 \mathrm{cm}^{2} \)
D. \( 4.25 \mathrm{cm}^{2} \)
Subject: Chemistry
Acetophenone cannot be prepared
easily starting from:
A \( \cdot C_{6} H_{5} C H_{3} \)
B . \( C_{6} H_{6} \)
\( \mathbf{c} \cdot C_{6} H_{5} C H(O H) C H_{3} \)
D. \( C_{6} H_{5} C \equiv C H \)
Subject: Chemistry
Monomer used to prepare orlon
is
\( \mathbf{A} \cdot H_{2} C=C H-C l \)
B \( \cdot F_{2} C=C F_{2} \)
\( \mathbf{c} \cdot H_{2} C=C H C N \)
D. \( H_{2} C=C(C l)-C H=C H_{2} \)
Subject: Physics
In a city, electricity costs \( \$ 0.12 \) per kilowatt-hour. A bulb of 150-watt
operates for 5 hours. Calculate the cost
of electricity which is consumed by the bulb.
A. \( \$ 0.009 \)
в. \$0.09
c. \( \$ 0.90 \)
D. \$9.00
E. \( \$ 90.00 \)
Subject: Physics
If 10 g of ice at \( 0^{\circ} \mathrm{C} \) mixes with 10 g of water at \( 10^{\circ} \mathrm{C} \), then the final
temperature \( t \) is given by
A \( \cdot(10 \times 80)+10(t-0)=10(10-t) \)
в. \( 10 \times 80=10(10-t)+10(t-0) \)
\( \mathbf{c} \cdot t=5^{\circ} C \)
D. \( t=0^{\circ} \mathrm{C} \)
Subject: Maths
\( \mathbf{1}+\mathbf{4}+\mathbf{1 0}+\mathbf{1 9}+\ldots \frac{\mathbf{3} \boldsymbol{n}^{2}-\mathbf{3} \boldsymbol{n}+\mathbf{2}}{\mathbf{2}}= \)
A \( \cdot \frac{n^{2}\left(n^{2}+1\right)}{2} \)
B \( \cdot \frac{n\left(n^{2}+1\right)}{2} \)
c. \( \frac{n^{2}(n+1)}{2} \)
D. \( \left\{\frac{n(n+1)}{2}\right\}^{2} \)
Subject: Physics
Two particle A and B are initially at a
distance x. Initial velocity of particles \( \mathbf{A} \) and \( \mathrm{B} \) are \( 10 \mathrm{m} / \mathrm{s} \) and 25
\( \mathrm{m} / \mathrm{s} \) respectively in the direction shown in figure and their constant
accelerations are \( 1 m / s^{2} \) and \( 2 m / s^{2} \) respectively in the direction shown in figure.What should be the minimum
value of \( x, \) so that these particle can just avoid collision:
\( ^{\mathbf{A}} \cdot \frac{125}{2} m \)
в. \( \frac{75}{2} \) г
c. \( \frac{75}{4} \) m
D. \( \frac{125}{4} m \)
Subject: Maths
On multiplying 137592 by the smallest number \( _{--}-_{-}- \) the product is a perfect cube, the cube root of this perfect cube number is
A \( \cdot 7 \times 13^{2}, 546 \)
В. \( 7 \times 13^{3}, 546 \)
c. \( 5 \times 13,546 \)
D. \( 7 \times 13^{4}, 546 \)
Subject: Chemistry
The reaction \( \boldsymbol{C H}_{3} \boldsymbol{C O O H}+ \)
\( C_{2} H_{5} O H \leftrightharpoons C H_{3} C O O C_{2} H_{5}+H_{2} O \)
can be made to proceed in the forward direction by:
A. increasing the temperature
B. sudden cooling of the reaction mixture
c. conducting the reaction in the presence of a small quantity of \( N a O H \)
D. taking excess of \( C_{2} H_{5} O H \) and \( C H_{3} C O O H \)
Subject: Maths
The probability that a student is not a swimmer is \( \frac{1}{5} . \) Then the probability that out of five students, four are swimmers
is
\( ^{\mathbf{A}} \cdot_{^{5}} C_{4}\left(\frac{4}{5}\right)^{4} \frac{1}{5} \)
\( ^{\mathrm{B}}\left(\frac{4}{5}\right)^{4} \frac{1}{5} \)
\( ^{\mathbf{c}} \cdot_{^{5}} C_{1} \frac{1}{5}\left(\frac{4}{5}\right)^{4} \)
D. none of these.
Subject: Maths
\( \int \frac{\boldsymbol{x}^{3 / 2}+\boldsymbol{x}^{5 / 2}+\boldsymbol{x}}{\boldsymbol{x}^{2}+\boldsymbol{2} \boldsymbol{x}^{1 / 2}+\boldsymbol{x}+1} \boldsymbol{d} \boldsymbol{x} \) equals
A. \( \frac{2}{3} x^{3 / 2}+x-\tan ^{-1} x^{1 / 4}+C \)
B. \( \frac{2}{3} x^{5 / 2}-x+\tan ^{-1} x^{1 / 2}+C \)
C. \( \frac{2}{3} x^{1 / 2}-x-\tan ^{-1} x^{1 / 4}+C \)
D. \( \frac{2}{3} x^{3 / 2}-x+\tan ^{-1} x^{1 / 4}+C \)
Subject: Chemistry
Arrange the following compounds in order of their Molar conductance:
(।) \( \boldsymbol{K}\left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{O}_{2}\right)_{4}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{2}\right] \)
\( (\|)\left[\boldsymbol{C r}(\boldsymbol{O} \boldsymbol{N} \boldsymbol{O})_{3}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{3}\right] \)
\( (\|\|)\left[\boldsymbol{C r}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right] \boldsymbol{C l}_{3} \)
\( (\mathrm{IV}) M g\left[C r\left(N O_{2}\right)_{5}\left(N H_{3}\right)\right] \)
\( A \cdot\|<I<I V<\| 1 \)
B. II IV \( <1<11 \)
c. \( \|<1=1 V<\| \)
D. IV <III <II<I
Subject: Biology
In the event of global warming, which one of the following is most likely to
occur?
A. Existing plant and animal communities will move North in response to warming.
B. Agriculture in the prairie provinces will be redeveloped on soils of the Canadian Shield
c. The anticipated rise in sea level will be caused primarily by the melting of polar ice caps
D. The decomposition of organic matter in the unfrozen surface layer of polar soils will increase
Subject: Chemistry
How many following oxyacids have peroxy linkage? \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{3}, \boldsymbol{H}_{2} \boldsymbol{S}_{2} \boldsymbol{O}_{8}, \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{2}, \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{5}, \boldsymbol{H} \boldsymbol{l} \boldsymbol{l} \)
Subject: Maths
Which of the following relations are functions from \( A=\{1,4,9,16\} \) to \( B=\{-1 \) \( \mathrm{~ 2 , ~ - 3 , ~ - 4 , ~ 5 , ~ 6 ~ \} . ~ I n ~ c a s e ~ o f ~ a ~ f u n c t i o n , ~ w r i t e ~} \)
down its range.
\( f_{1}=\{(1,-1),(4,2),(9,-3),(16,-4)\} \)
Subject: Physics
The areal velocity and the angular momentum of the planet are related by which of the following relations?
(where \( m_{p} \) is the mass of the planet)
A \( \cdot \frac{\Delta \bar{A}}{\Delta t}=\frac{\bar{L}}{2 m_{p}} \)
B \( \cdot \frac{\Delta \bar{A}}{\Delta t}=\frac{\bar{L}}{m_{p}} \)
\( \mathbf{C} \cdot \underset{\Delta t}{\frac{\Delta \bar{A}}{\Delta t}}=\frac{2 \bar{L}}{m_{p}} \)
D. \( \frac{\Delta \bar{A}}{\Delta t}=\frac{\bar{L}}{\sqrt{2 m_{p}}} \)
Subject: Chemistry
Select the correct order of \( C-0 \) bond
order in mixed phosphine carbonyl
complex:
\( \mathbf{A} \cdot\left[\left(P h_{3} P\right)_{3} M o(C O)_{3}\right]>\left[\left(P h_{2} P C l\right)_{3} M o(C O)_{3}\right]> \)
\( \left(P h P C l_{2}\right)_{3} M o(C O)_{3} \)
\( \mathbf{B} \cdot\left[\left(P h_{3} P\right)_{3} M o(C O)_{3}\right]>\left[\left(P h_{2} P C l\right)_{3} M o(C O)_{3}\right]< \)
\( \left(P h P C l_{2}\right)_{3} M o(C O)_{3} \)
\( \mathbf{C} \cdot\left[\left(P h_{3} P\right)_{3} M o(C O)_{3}\right]=\left[\left(P h_{2} P C l\right)_{3} M o(C O)_{3}\right]> \)
\( \left(P h P C l_{2}\right)_{3} M o(C O)_{3} \)
\( \mathbf{D} \cdot\left[\left(P h_{3} P\right)_{3} M o(C O)_{3}\right]<\left[\left(P h_{2} P C l\right)_{3} M o(C O)_{3}\right]> \)
\( \left(P h P C l_{2}\right)_{3} M o(C O)_{3} \)
Subject: Physics
In the figure shown, the spherical body
and block, each have a mass \( m \). The
moment of inertia of the spherical body
about centre of mass is \( 2 m R^{2} . \) The
spherical body rolls without slipping on the horizontal surface. The ratio of
kinetic energy of the spherical body to that of block is:
\( A \cdot \frac{1}{3} \)
B. \( \frac{1}{2} \)
\( c \cdot \frac{2}{3} \)
\( D \)
Subject: Maths
The length of the chord \( x+y=3 \)
intercepted by the circle \( x^{2}+y^{2}- \)
\( 2 x-2 y-2=0 \) is
A \( \cdot \frac{7}{2} \)
B. \( \frac{3 \sqrt{3}}{2} \)
c. \( \sqrt{14} \)
D. \( \frac{\sqrt{7}}{2} \)
Subject: Physics
Q Type your question
indices of refraction are given for water
and for air. The angle the light ray makes with the normal in air is shown.
What angle does the light ray make with the normal as it approaches the
boundary from the water?
The angles in the drawing are not
necessarily drawn with accurate
measurements.
\( A \cdot 30.0^{\circ} \)
B \( \cdot 29.7^{\circ} \)
c. \( 33.1^{\circ} \)
D \( .58 .5^{\circ} \)
\( E \)
Subject: Physics
If a car is moving at a velocity \( v \) in a circular road with coefficient of friction
\( \mu \) and banking angle \( \theta \). Find the radius of the road such that friction force
doesn't act on the car in the radial
direction.
A \( \cdot_{r}=\frac{v^{2}}{g \tan \theta} \)
в. \( \quad r=\frac{\sqrt{v}}{g \tan \theta} \)
\( ^{\mathrm{c}} \cdot_{r}=\sqrt{\frac{v^{2}}{g \tan \theta}} \)
D. \( r=\frac{v^{2}}{\sqrt{g}} \)
Subject: Physics
A \( 300,000 k g \) commercial airlines is flying through the air with \( 150,000 N \) of
thrust.

For airplanes traveling at high speeds,
the drag force is related to the velocity by the following equation
\[
\boldsymbol{F}_{\text {drag}}=-\boldsymbol{b v}^{2}
\]
where drag force is opposite to the direction of the velocity. If the drag constant \( b \) is \( 3 k g / m \) and the
airplane is moving at \( 200 m / s, \) how would you describe its motion?
A. In equilibrium (cruising at constant speed)
B. Nearequilibrium, positive acceleration
c. Near equilibrium, negative acceleration
D. Greatly accelerating during takeoff
E. Greatly slowing down during landing
Subject: Chemistry
Ortho-xylene on ozonolysis followed by reductive hydrolysis gives:
A. \( C H O-C H O \) and \( C H_{3}-C O O H \)
в. \( C H_{3}-C O-C O-C H_{3}, C H O-C H O \) and \( C H_{3}- \)
\( C O-C H O \)
c. \( C H_{3}-C O-C O-C H_{3} \) and \( C H O-C H O \)
D. \( C H_{3}-C O-C O-C H_{3}, C H_{3}-C O-C H O \) and
\( C H O-C H O \)