AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A capacitors is charged to store an
energy \( U . \) The charging battery is disconnected. An identical capacitor is now connected to the first capacitor in
parallel. The energy in each of the capacitors is
A \( \cdot \frac{U}{2} \)
в. \( \frac{3 U}{2} \)
c. \( U \)
D. \( \frac{U}{4} \)
Subject: Maths
If \( A=\left|\begin{array}{cc}0 & 1 \\ 2 & 4\end{array}\right|, B=\left|\begin{array}{cc}-1 & 1 \\ 2 & 2\end{array}\right| \)
\( c=\left|\begin{array}{cc}1 & 0 \\ 1 & 0\end{array}\right|, \) then \( 2 A+3 B-C= \)
A \( \cdot\left|\begin{array}{cc}-4 & 5 \\ 9 & 14\end{array}\right| \)
в. \( \left|\begin{array}{cc}4 & 3 \\ 9 & 10\end{array}\right| \)
с. \( \left|\begin{array}{cc}4 & -5 \\ 9 & 14\end{array}\right| \)
О \( \cdot\left|\begin{array}{cc}-4 & 5 \\ 14 & 9\end{array}\right| \)
Subject: Physics
The equation of the standing wave in a string clamped at both ends, vibrating in its third harmonic is given by \( \boldsymbol{y}=\mathbf{0 . 4} \sin (\mathbf{0 . 3 1 4} \boldsymbol{x}) \cos (\mathbf{6 0 0} \boldsymbol{\pi} \boldsymbol{t}) \) where
\( x \) and \( y \) are in \( \mathrm{cm} \) and \( t \) in sec.
a) the frequency of vibration is \( 300 H z \)
b) the length of the string is \( 30 \mathrm{cm} \)
c) the nodes are located at \( x= \)
\( \mathbf{0}, \mathbf{1 0 c m}, \mathbf{3 0 c m} \)
A. Only a is true
B. a, b are true
\( c . b, c \) are true
D. a, b, care true
Subject: Physics
A body when acted upon by a force of
10 \( k g f \), gets displaced by \( 0.5 m \) normal to the force. Calculate the work done by
the force, when the displacement is in the direction of force.
A . \( 5 . J \)
в. \( 500 J \)
c. \( 0.5 J \)
D. \( 50 J \)
Subject: Chemistry
Radius of \( 2 n d \) shell of \( H e^{+} \) (where \( a_{0} \)
Bohr radius)
A \( .3 a_{0} \)
в. \( a_{0} \)
c. \( \frac{3}{2} a_{0} \)
D. \( 2 a_{0} \)
Subject: Physics
A material of \( 0.25 \mathrm{cm}^{2} \) cross sectional
area is placed in a magnetic field of strength \( (H) 1000 A m^{-1} . \) Then the
magnetic flux produced is:
[Susceptibility of material is 314 and
Permeability of free space, \( \mu_{0}=4 \pi \times \)
\( 10^{-7} H m^{-1} \)
A . \( 8.33 \times 10^{-8} \mathrm{Wb} \)
В. \( 1.84 \times 10^{-6} \mathrm{Wb} \)
\( \mathbf{c} \cdot 9.87 \times 10^{-6} \mathrm{Wb} \)
D. \( 3.16 \times 10^{-8} \mathrm{Wb} \)
Subject: Maths
Using integration find the area of the triangular region whose sides have the
equations \( \boldsymbol{y}=\mathbf{2} \boldsymbol{x}+\mathbf{1}, \boldsymbol{y}=\mathbf{3} \boldsymbol{x}+\mathbf{1} \) and
\( \boldsymbol{x}=\mathbf{4} \)
Subject: Maths
Which of the following equations are not
quadratic?
\( \mathbf{A} \cdot x(2 x+3)=x+2 \)
B \( \cdot(x-2)^{2}+1=2 x-3 \)
\( \mathbf{c} \cdot y(8 y+5)=y^{2}+3 \)
D. \( y(2 y+15)=2\left(y^{2}+y+8\right) \)
Subject: Maths
If \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R}, \boldsymbol{g}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) are defined by
\( \boldsymbol{f}(\boldsymbol{x})=\mathbf{5} \boldsymbol{x}-\mathbf{3}, \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{x}^{2}+\mathbf{3}, \) then
\( \left(g o f^{-1}\right)(3)= \)
A \( \cdot \frac{25}{3} \)
в. \( \frac{111}{25} \)
c. \( \frac{9}{25} \)
D. \( \frac{25}{111} \)
Subject: Biology
In a DNA molecule distance between
two bases is
\( \mathbf{A} \cdot 2 n m / 20 \stackrel{\circ}{A} \)
B \( \cdot 0.2 n m / 2 \stackrel{\circ}{A} \)
c. \( 3.4 n m / 34^{\circ} \)
D. \( 0.34 n m / 3.4^{\circ} \)
Subject: Maths
5 pencils and 7 pens together cost Rs.
\( \mathbf{5 0}, \) whereas \( \mathbf{7} \) pencils and \( \mathbf{5} \) pens together cost Rs. \( 46 . \) The cost of one pencil is
A. Rs.
в. Rs.
c. Rs.
D. Rs.
Subject: Physics
The resultant of two forces \( P \) and \( Q \) is \( R \)
If \( Q \) is doubled and when \( Q \) is reversed \( R \) is again doubled. Show that \( P: Q: \)
\( \boldsymbol{R}=\sqrt{\mathbf{2}}: \sqrt{\mathbf{3}}: \sqrt{\mathbf{2}} \)
Subject: Physics
A car is moving with speed \( 10 m / s \) on a
circle path of radius \( 2 m \). If speed is
increasing at the rate of \( 10 m / s^{2} . \) The acceleration of car is
\( \mathbf{A} \cdot \sqrt{26} m / s^{2} \)
B . \( 10 \sqrt{26} \mathrm{m} / \mathrm{s}^{2} \)
\( \mathbf{c} \cdot 5 \sqrt{26} m / s^{2} \)
D. \( 10 \sqrt{13} \mathrm{m} / \mathrm{s}^{2} \)
Subject: Physics
Three different objects \( m_{1}, m_{2} \) and \( m_{3} \)
are allowed to fall from rest and from
the same point \( \boldsymbol{O} \) along three different
frictionless paths. The speeds of the three objects, on reaching the ground will be in the ratio of
\( \mathbf{A} \cdot m_{1}: m_{2}: m_{3} \)
B. 1: 1: 1
c. \( m_{1}: 2 m_{2}: 3 m_{3} \)
D. \( \frac{1}{m_{1}}: \frac{1}{m_{2}}: \frac{1}{m_{3}} \)
Subject: Maths
\( f^{n} P_{r}=^{n} P_{r+1} \) and \( ^{n} C_{r}=^{n} C_{r-1}, \) then
the values of \( n \) and \( r \) are:
A \( \cdot r, 3 \)
B. 3,2
c. 4,2
D. 3,4
Subject: Chemistry
When \( \mathbf{S O}_{2} \) is passed through acidified
solution of \( \mathbf{H}_{2} \mathbf{S} \)
A \( \cdot \mathrm{H}_{2} \mathrm{SO}_{3} \) is formed
B. \( \mathrm{H}_{2} \mathrm{SO}_{4} \) is formed
c. sulphur is precipitated
D. \( \mathrm{H}_{2} \mathrm{SO}_{5} \) is formed
Subject: Physics
A reversible engine converts one-sixth of the heat input into work. When the temperature of the sink is reduced by
\( 62^{\circ} \mathrm{C}, \) the efficiency of the and sink are
A \( \cdot 80^{\circ} \mathrm{C}, 37^{\circ} \mathrm{C} \)
в. \( 95^{\circ} \mathrm{C}, 28^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 90^{\circ} C, 37^{\circ} C \)
D . \( 99^{\circ} C, 37^{\circ} C \)
Subject: Maths
\( A 2 \times 2 \) matrix whose elements \( a_{i j} \) are
given by \( a_{i j}=i-j \) is
\( \mathbf{A} \cdot\left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right] \)
B. \( \left[\begin{array}{cc}0 & -1 \\ 1 & 0\end{array}\right] \)
\( \mathbf{c} \cdot\left[\begin{array}{cc}-1 & 0 \\ 0 & 1\end{array}\right] \)
D. \( \left[\begin{array}{cc}0 & 1 \\ -1 & 0\end{array}\right] \)
Subject: Chemistry
Choose the correct option regarding change in oxidation number of the underlined atom in the following
conversion.
\( \boldsymbol{H}_{2} \underline{\boldsymbol{S}} \boldsymbol{O}_{5}+\boldsymbol{2} \boldsymbol{K} \boldsymbol{I} \rightarrow \boldsymbol{K}_{2} \boldsymbol{S} \boldsymbol{O}_{4}+\boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{I}_{2} \)
\( A \cdot 2 \)
B. 3
\( c \)
D. No Change
Subject: Maths
\( \lim _{x \rightarrow 0}\left\{(1+x)^{\frac{2}{x}}\right\} \) (where \{\} denotes the
fractional part of \( x \) ) is equal to:
A \( \cdot e^{2}-7 \)
B \( \cdot e^{2} \)
c. \( e^{7}-7 \)
D. limit does not exist
Subject: Physics
Some physical quantities are given in list 1. The related units are given in list
2. Match the correct pairs
List 1 List 2
a) Magnetic Field Intensity \( W b m^{-1} \)
e)
) Magnetic Flux f) \( W b m^{-2} \)
b)
c Potential Magnetic \( W b \)
c) g)
h) \( A m^{-1} \)
d) Magnetic Induction
A. \( a-e, b-f, c-g, d-h \)
B. a-h, b-g, c-e, d-f
c. a-h, b-e, c-g, d-f
D. a-f, b-g, c-e, d-h
Subject: Maths
For all positive integers \( \mathbf{w} \) and \( \mathbf{y}, \) where \( \mathbf{w}>\mathbf{y}, \) let the operation \( \otimes \) be defined by \( \mathbf{w} \otimes \mathbf{y}=\frac{\mathbf{2}^{w+y}}{\mathbf{2}^{w-y}} . \) For how many positive
integers \( \mathbf{w} \) is \( \mathbf{w} \otimes \mathbf{1} \) equal to \( \mathbf{4} \) ?
A. None
B. One
c. Two
D. Four
E. More than four
Subject: Chemistry
In which of the following octahedral complexes of Co (atomic number 27),
will the magnitude of \( \Delta_{\mathrm{o}} \) be the highest?
\( \mathbf{A} \cdot\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+} \)
B . [Co(NH3) \( _{6} \) ] \( ^{3} \)
c. \( \left[\mathrm{Co}(\mathrm{CN})_{6}\right]^{3-} \)
D \( \cdot\left[\mathrm{Co}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right]^{3} \)
Subject: Chemistry
The ratio of heats liberated at \( 298 K \)
from the combustion of one kg of coke and by burning water gas obtained from kg of coke is:
Given: Enthalpies of combustion of
\( C, C O \) and \( H_{2} \) as
\( 393.5 k J, 285 k J, 285 k J \) respectively
all at \( 298 K . \) (Assume coke to be \( 100 \% \)
carbon).
A .0 .69: 1 \)
B. 0.96: 1
c. 0.79: 1
D. 0.86: 1
Subject: Physics
Ine v-I grapn ror a conauctor at
temperature \( T_{1} \) and \( T_{2} \) are as shown in
the fig. The term \( \left(T_{2}-T_{1}\right) \) is
proportional to
A \( \cdot \frac{\sin 2 \theta}{\sin ^{2} \theta} \)
B. \( \frac{\cot 2 \theta}{\sin ^{2} \theta} \)
c. \( \frac{\cos 2 \theta}{\sin 2 \theta} \)
D. \( \frac{\tan 2 \theta}{\sin ^{2} \theta} \)
Subject: Chemistry
When electronic transition occur from
higher energy state to lower energy state with energy difference equal to \( \Delta \) E electron volts, the wavelength of the line emitted is approximately equal to:
A \( \cdot \frac{12395}{\Delta E} \times 10^{-10} \mathrm{m} \)
В \( \cdot \frac{12395}{\Delta E} \times 10^{10} \mathrm{m} \)
c. \( \frac{12395}{\Delta E} \times 10^{-10} \mathrm{cm} \)
D. \( \frac{12395}{\Delta E} \times 10^{10} \mathrm{cm} \)
Subject: Physics
A short linear object of length \( \boldsymbol{I} \) lies
along the axis mirror of focal length \( \boldsymbol{F} \)
at a distance u form the of the mirror.
The size of the image is approximately equal to:
\( ^{\mathbf{A}} \cdot\left(\frac{u-f}{f}\right)^{1 / 2} \)
\( ^{\mathrm{B}} \cdot_{I}\left(\frac{u-f}{f}\right)^{2} \)
\( ^{\mathrm{c}} \cdot\left(\frac{f}{u-f}\right)^{1 / 2} \)
D. \( _{I}\left(\frac{f}{u-f}\right) \)
Subject: Physics
You work is a material testing lab and
your bess tells you to increase the
temperature of a sample by \( 40.0^{\circ} \mathrm{C} \) The only thermometer you can find at your
workbench reads in \( ^{\circ} \boldsymbol{F} \). If The initial
temperature of the sample is \( 68.2^{\circ} F \)
What is its temperature in \( ^{\circ} \boldsymbol{F} \), when the
desired temperature increase has been achieved?
Subject: Physics
\( \boldsymbol{R} \) that carries a charge uniformly
distributed throughout its volume. The
volume charge density is \( \rho . \) A Gaussian
sphere of radius \( a \) is imagined that is
concentric to the charged sphere.

If \( a>R, \) what is the charge enclosed in
the Gaussian surface?
\( \mathbf{A} \cdot Q_{e n c}=4 \pi \rho R^{2} \)
\( ^{\mathbf{B}} Q_{e n c}=\frac{4}{3} \pi \rho a^{3} \)
\( \mathbf{c} \cdot Q_{e n c}=4 \pi \rho a^{2} \)
\( \mathrm{D} \)
\( E \cdot Q_{e n c}=\pi \rho a^{2} \)
Subject: Maths
Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \)
\( \boldsymbol{y}=\frac{1}{\boldsymbol{x}^{2}-\boldsymbol{2} \boldsymbol{x}+\boldsymbol{3}} \)
Subject: Chemistry
Which one of the following platinum complexes is used in cancer
chemotherapy?
\( A \cdot \operatorname{cis}-\left[P t C l_{2}\left(N H_{3}\right)_{2}\right. \)
B. trans \( -\left[P t C l_{2}\left(N H_{3}\right)\right] \)
\( \mathrm{c} \cdot\left[P t\left(N H_{3}\right)_{4}\right]^{2+} \)
\( \mathbf{D} \cdot\left[P t C l_{4}\right]^{2-} \)
Subject: Maths
The following table shows the heights
\( (c m) \) of 50 girls of class \( X \) of a school
\( \begin{array}{ll}\text { Height }(\mathrm{cm}) & \text { Number of girls } \\ 120-130 & 2 \\ 130-140 & 8 \\ 140-150 & 12 \\ 150-160 & 20 \\ 160-170 & 8 \\ & \\ \text {Total} & 50\end{array} \)
Find the mean of the above data by step
deviation method.
Subject: Maths
Find the total surface area of a hollow
cylinder of internal radius \( 3 \mathrm{cm} \) thickness \( 1 \mathrm{cm} \) and height \( 14 \mathrm{cm} \)
\( A \cdot 330 \mathrm{cm}^{3} \)
B. \( 660 \mathrm{cm}^{2} \)
c. \( 990 \mathrm{cm}^{2} \)
D. \( 1320 \mathrm{cm}^{2} \)
Subject: Chemistry
'A' represents central atom, 'B' number of bond pairs and 'E' number of lone
pairs. Then the one having \( \boldsymbol{A} \boldsymbol{B}_{\mathbf{5}} \boldsymbol{E} \)
formula is
A \( \cdot P C l_{5} \)
в. \( S F_{6} \)
c. \( B C l_{3} \)
D. \( C l F_{5} \)
Subject: Physics
Assertion: The clouds in sky generally appear to be whitish.

Reason: Diffraction due to clouds is
efficient in equal measure at all wavelengths.
A. If both assertion and reason are true but the reason is the correct explanation of assertion
B. If both assertion and reason are true but the reason is not the correct explanation of assertion
c. If assertion is true but reason is false
D. If both the assertion and reason are false
E. If reason is true but assertion is false
Subject: Chemistry
About phosphorous acid \( \left(\boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3}\right) \)
which of the following statements is/are true?

This question has multiple correct options
A. Hybridization of P is the same as the hybridization of N in \( H N O_{3} \)
B. It is a dibasic acid
c. It is a reducer acid
D. Hybridization of P is the same as that of \( x \) e in \( X e O_{4} \)
Subject: Chemistry
Fifty millilitre of a mixture of \( \mathrm{CO} \) and
\( C H_{4} \) was exploded with \( 85 \mathrm{ml} \) of \( O_{2} \). The
volume of \( C O_{2} \) produced was 50
ml.Calculate the percentage composition of the gaseous mixture.
A . 20\%
B. 40\%
c. 60\%
D. 80\%
Subject: Physics
Light in certain cases may be considered as a stream of particles called photons. Each photon has a linear nomentum \( \frac{h}{\lambda} . \) where \( h \) is the Planck's
constant and \( \lambda \) is the wavelength of the
light.A beam of light of wavelength \( \lambda \) is incident on a plane mirror at an angle of incidence \( \theta \). Calculate the change in
linear momentum of photon as the beam is reflected by the mirror
Subject: Physics
From a tower of height \( \boldsymbol{H}, \) a particle is thrown vertically upwards with a speed
\( u . \) The time taken by the particle, to hit the ground, is \( n \) times that taken by it to reach the highest point of its path.
The relation between \( \boldsymbol{H}, \boldsymbol{u} \) and \( \boldsymbol{n} \) is:
A \( \cdot 2 g H=n u^{2}(n-2) \)
B . \( g H=(n-2) u^{2} \)
C \( \cdot 2 g H=n^{2} u^{2} \)
D. \( g H=(n-2)^{2} u^{2} \)
Subject: Maths
Find the mean
\begin{tabular}{lccccc} 
Age (yrs) & 7 & 8 & 9 & 10 & 11 \\
No. of Students & 5 & 6 & 4 & 12 & 7 \\
\hline
\end{tabular}
\( A \cdot 9.3 \)
B. 8.7
C. 11.9
\( D \cdot 5.2 \)
Subject: Physics
The number of quanta of radiation of frequency \( 4.98 \times 10^{14} s^{-1} \) required to
melt 100 g of ice are (latent heat of melting of ice is 33 joule per \( g \) ):
A \( \cdot 10^{20} \)
B. \( 10^{2} \)
\( c \cdot 10^{24} \)
D. \( 6.023 \times 10^{21} \)
Subject: Maths
ff \( y=\tan \left(\frac{5}{2} \pi t+\frac{\pi}{6}\right) \) then find the
value of \( \frac{\boldsymbol{a} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{t}} \) at \( \boldsymbol{t}=\mathbf{0} \)
Subject: Maths
The general solution of the differential equation \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\boldsymbol{e}^{\boldsymbol{y}+\boldsymbol{x}}+\boldsymbol{e}^{\boldsymbol{y}-\boldsymbol{x}} \) is
A \( \cdot e^{-y}=e^{x}-e^{-x}+c \)
B . \( e^{-y}=e^{-x}-e^{x}+c \)
\( \mathbf{c} \cdot e^{-y}=e^{x}+e^{-x}+c \)
D. \( e^{y}=e^{x}+e^{-x}+c \)
where \( c \) is an arbitrary constant
Subject: Physics
An intense stream of water of cross
sectional area A strikes a wall at an
angle \( \theta \) with the normal to the wall and
returns back elastically. If the density of
water is \( \rho \) and its velocity is \( v \), then the
force exerted on the wall will be :
A. \( 2 A v \rho \cos \theta \)
B. \( 2 A v^{2} \rho \cos \theta \)
c. \( 2 A v^{2} \rho \)
D. 2Av
Subject: Physics
The increase in energy of a metal bar of length 'L' and cross-sectional area 'A'
when compressed with a load 'M' along its length is (Y = Young's modulus of the material of metal bar)
\( ^{\mathbf{A}} \cdot \frac{F L}{2 A Y} \)
в. \( \frac{F^{2} L}{2 A Y} \)
c. \( \frac{F L}{A Y} \)
D \( \cdot \frac{F^{2} L^{2}}{2 A Y} \)
Subject: Chemistry
Calculate value of \( ^{\prime} \ln \left(K_{e q}\right)^{\prime} \) for the
reaction at \( 250 \mathrm{K} \)
\( N_{2} O_{4}(g) \rightleftharpoons 2 N O_{2}(g) \)
Given: \( \boldsymbol{H}_{f}^{0}\left(\left(\boldsymbol{N} \boldsymbol{O}_{2}\right) \boldsymbol{g}\right)= \)
\( +40.407 k J / m o l \)
\( \boldsymbol{H}_{f}^{0}\left(\left(\boldsymbol{N}_{2} \boldsymbol{O}_{4}\right) \boldsymbol{g}\right)=+\mathbf{7 0 k} \boldsymbol{J} / \boldsymbol{m o l} \)
\( \boldsymbol{S}_{\boldsymbol{r}}^{\boldsymbol{0}}=\mathbf{1 0 J} \boldsymbol{K}^{-\mathbf{1}} \)
A .4
B . - -
\( c \cdot 1.2 \)
D. -1.2
Subject: Physics
Assertion (A): Corpuscular theory fails in explaining the velocity of light in air
to water.

Reason (R) : According to corpuscular theory, light should travel faster in denser media than in rarer media.
A. A and R are true R is correct explanation for A
B. A and R are true R is not correct explanation for A
c. A is true but R is false
D. A is false but R is true
Subject: Chemistry
One gas bleaches the colour of the
flowers by reduction, while the other by oxidation. The gases are:
A. \( N H_{3} \) and \( S O_{3} \)
B. CO and Cu
\( \mathrm{c} \cdot \mathrm{SO}_{2} \) and \( \mathrm{Cl}_{2} \)
D. \( H_{2} S \) and \( M n C l_{2} \)
Subject: Chemistry
Electrolysis of dilute aqueous NaCl solution was carried out by passing 10 mA current. The time required to
liberate 0.01 moles of \( H_{2} \) gas at the cathode is
A \( \cdot 9.65 \times 10^{4} s \)
B . \( 19.3 \times 10^{4} s \)
c. \( 28.95 \times 10^{4} s \)
D. \( 38.6 \times 10^{4} s \)
Subject: Chemistry
Which one is not true about \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} ? \)
A. It is composed of \( 2 \mathrm{H}, 1 \mathrm{S} \) and 40 atoms.
B. Its molar mass is 98 g/mol.
C. It is composed of one molecules \( H_{2} \), one atom S and two molecules \( O_{2} \)
D. Its relative molecular mass is 98
Subject: Chemistry
\( P \) in \( P C l_{5} \) has \( s p^{3} d \) hybridisation which of the following statement is wrong
about \( \boldsymbol{P C l}_{5} \) structure?
A. Two \( P-C l \) bonds are stronger and three \( P-C l \) bonds are weaker
B. Two \( P-C l \) bonds are axial and larger than three \( P \) Cl equatorial bonds
C . \( P C l_{5} \) has trigonal bipyramidal geometry with nonpolar nature
D. All of these
Subject: Physics
Photon having the energy equivalent to the binding energy of 4th state of \( \boldsymbol{H} \boldsymbol{e}^{+} \) atom is used to eject an electron from the metal surface of work function 1.4
eV. If electrons are further accelerated
through the potential difference of \( 4 \mathrm{V} \) then determine the minimum value of
de-Broglie wavelength associated with the electron.
в. 2.5 А \( ^{\text {о }} \)
\( c \cdot 7.6 A^{\circ} \)
D. \( 10 A^{\circ} \)
Subject: Physics
Three particles of masses \( 50 g, 100 g \)
and \( 150 g \) are placed at the vertices of
an equilateral triangle of side \( 1 m \) (as
shown in the figure). The \( (x, y) \) coordinates of the centre of mass will
be :
\( ^{\mathbf{A}} \cdot\left(\frac{7}{12} m, \frac{\sqrt{3}}{8} m\right) \)
B \( \cdot\left(\frac{\sqrt{3}}{4} m, \frac{5}{12} m\right) \)
\( ^{\mathbf{c}} \cdot\left(\frac{7}{12} m, \frac{\sqrt{3}}{4} m\right) \)
D. \( \left(\frac{\sqrt{3}}{8} m, \frac{7}{12} m\right) \)
Subject: Maths
The number of real solutions of the
equation \( \left(\frac{\mathbf{9}}{\mathbf{1 0}}\right)^{\boldsymbol{x}}=-\mathbf{3}+\boldsymbol{x}-\boldsymbol{x}^{2} \) is
A .2
B.
\( c \cdot 0 \)
D. None of these
Subject: Maths
A man goes 100 m North then 100 m
East and then 20 m North and then \( 100 \sqrt{2} \) m South West. Find the displacement
\( \mathbf{A} \cdot 20 m \) west
B. \( 20 \mathrm{m} \) East
c. \( 20 m \) North
D. \( 20 m \) south
Subject: Maths
The \( L S A \) (lateral surface area) of a cube
of side \( 1 \mathrm{cm} \) is
\( \mathbf{A} \cdot 16 \mathrm{cm}^{2} \)
B. \( 4 \mathrm{cm}^{2} \)
\( \mathbf{c} \cdot 2 c m^{2} \)
D. \( 1 \mathrm{cm}^{2} \)
Subject: Chemistry
The water table is:
A. the upper level of an underground surface in which the soil or rocks are permanently saturated with water.
B. the upper level of an underground surface in which the soil or rocks are unsaturated with water.
C. the lower level of an underground surface in which the soil or rocks are permanently saturated with water.
D. the lower level of an underground surface in which the soil or rocks are unsaturated with water.
Subject: Maths
In a triangle \( A B C, \angle A+\angle B=144^{\circ} \) and \( \angle A \)
\( +\angle C=124^{\circ} \)
Calculate each angle of the triangle.
A \( \cdot A=88^{\circ}, B=56^{\circ} \) and \( C=36 \)
B. A \( =78^{\circ}, B=66^{\circ} \) and \( C=36^{\circ} \)
C. \( A=58^{\circ}, B=86^{\circ} \) and \( C=36^{\circ} \)
D. \( A=88^{\circ}, B=26^{\circ} \) and \( C=66^{\circ} \)
Subject: Chemistry
For which one of the following gaseous equilibrium will an increase in pressure increase the yield of the product:
A \( \cdot 2 H I \rightleftharpoons H_{2}+I_{2} \)
в. \( 2 S O_{2}+O_{2} \rightleftharpoons 2 S O_{3} \)
c. \( H_{2} O+C O \rightleftharpoons H_{2}+C O_{2} \)
D. \( H_{2}+B r_{2} \rightleftharpoons 2 H B r \)
Subject: Maths
Prove that \( 2 \tan ^{-1} \frac{1}{2}-\tan ^{-1} \frac{1}{7}=\frac{\pi}{4} \)
Prove that \( 3 \sin ^{-1} x=\sin ^{-1}(3 x- \)
\( \left.4 x^{3}\right), x \in\left[\frac{-1}{2}, \frac{1}{2}\right] \)
Subject: Physics
Binding energy per nucleon versus
mass number curve for nuclei is
shown in the figure. \( A, B, C \) and \( D \) are
four muclei indicated on the curve. The
process that would release energy is
he process that
\( \mathbf{A} \cdot C \rightarrow 2 D \)
B . \( A \rightarrow C+D \)
\( \mathbf{c} \cdot A \rightarrow 2 C \)
D. \( B \rightarrow C+D \)
Subject: Chemistry
Assertion
Bond angle in \( P F_{3} \) greater than the
bond angle in \( \boldsymbol{P H}_{3} \)
Reason
Electrons in \( P F_{3} \) are displaced towards
more electro-negative \( \boldsymbol{F}, \) in \( \boldsymbol{P}-\boldsymbol{F} \) bond
A. Statement 1 is True, statement 2 is True; statement 2 is a correct explanation for statement 1.
B. Statement 1 is True, statement 2 is True; statement 2 is not a correct explanation for statement 1
c. statement 1 is True, statement 2 is False
D. Statement 1 is False, statement 2 is True
Subject: Maths
The middle term in the expansion of \( \left(1-\frac{1}{x}\right)^{n}(1-x)^{n}, \) is
A \( \cdot^{2 n} C_{n} \)
в. \( ^{-2 n} C_{n} \)
\( \mathrm{c} .^{-2 n} C_{n-1} \)
D. none of these
Subject: Chemistry
An aqueous solution of \( 2 \% \) non-volatile
solute exerts a pressure of 1.004 bar at the normal boiling point of the solvent.
What is the molecular mass of the
solute?
A \( .23 .4 \mathrm{gmol}^{-1} \)
B . \( 41.35 \mathrm{gmol}^{-1} \)
c. \( 10 \mathrm{gmol}^{-1} \)
D. 20.8 gmol-
Subject: Maths
Prove the following:
\( \left|\begin{array}{llll}\boldsymbol{x} & \boldsymbol{a} & \boldsymbol{a} & \boldsymbol{a} \\ \boldsymbol{a} & \boldsymbol{x} & \boldsymbol{a} & \boldsymbol{a} \\ \boldsymbol{a} & \boldsymbol{a} & \boldsymbol{x} & \boldsymbol{a} \\ \boldsymbol{a} & \boldsymbol{a} & \boldsymbol{a} & \boldsymbol{x}\end{array}\right|=(\boldsymbol{x}+\boldsymbol{3} \boldsymbol{a})(\boldsymbol{x}-\boldsymbol{a})^{3} \)
Subject: Maths
For \( 2 \geq r \geq n,\left(\begin{array}{c}r \\ n\end{array}\right)+2\left(\begin{array}{c}r-1 \\ n\end{array}\right)+\left(\begin{array}{c}r-2 \\ n\end{array}\right) \)
A \( \cdot\left(\begin{array}{c}r-1 \\ n+1\end{array}\right) \)
B \( \cdot 2\left(\begin{array}{c}r+1 \\ n+1\end{array}\right) \)
\( \mathbf{c} \cdot 2\left(\begin{array}{c}r \\ n+1\end{array}\right) \)
D. \( \left(\begin{array}{c}r \\ n+1\end{array}\right) \)
Subject: Maths
If \( \hat{\boldsymbol{i}}+\widehat{\boldsymbol{j}}, \widehat{\boldsymbol{j}}+\widehat{\boldsymbol{k}}, \hat{\boldsymbol{i}}+\widehat{\boldsymbol{k}} \) are the position
vectors of the vertices of a \( \Delta A B C \)
taken in order, then \( \angle A \) is equal to
A \( \cdot \frac{\pi}{2} \)
в.
c.
D.
E \( \cdot \frac{\pi}{3} \)