AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
\( \left|\begin{array}{cc}\boldsymbol{x}+\mathbf{1} & \boldsymbol{x}-\mathbf{1} \\ \boldsymbol{x}-\mathbf{3} & \boldsymbol{x}+\mathbf{2}\end{array}\right|=\left|\begin{array}{cc}\mathbf{4} & -\mathbf{1} \\ \mathbf{1} & \mathbf{3}\end{array}\right|, \) then write
the value of \( x \)
Subject: Maths
Let \( \boldsymbol{f}:(1,2) \rightarrow \mathbb{R} \) satisfies the
inequality \( \frac{\cos (2 x-4)-33}{2}<f(x)<\frac{x^{2}|4 x-8|}{x-2} \mid \forall x \in \)
\( (1,2) . \) then find \( \lim _{x \rightarrow 2^{-}} f(x) \)
Subject: Physics
A ball resting on a tray attached to a spring is made to oscillate vertically, such that the fixed end of the spring is attached to the ground. If the spring is compressed and let go, the ball will execute SHM until
A. the ball is in contact with the spring
B. the ball occasionally loses contact with the spring
c. the ball loses contact with the spring beyond the mean position
D. the ball loses contact with the spring beyond the extreme position
Subject: Chemistry
For a reaction, where the \( \Delta G^{o}= \)
\( -553.91 k J \) and 2 electrons are
transferred, what will be the \( E_{c e l l}^{o} \) of the reaction?
A . \( -2.87 V \)
В. \( -0.00287 V \)
c. \( 0.00287 V \)
D. \( 2.87 V \)
Subject: Physics
A potentiometer wire of length 10 m and resistance \( 30 \Omega \) is connected in
series with a battery of emf \( 2.5 V \) internal resistance \( 5 \Omega \), and an external
resistance \( \boldsymbol{R} \). If the fall of potential
along the potentiometer wire is \( \mathbf{5 0} \mu V \boldsymbol{m} \boldsymbol{m}^{-1}, \) then the value of \( \boldsymbol{R} \) is
found to be \( 23 n \Omega \). What is \( n ? \)
Subject: Maths
Given, matrix \( \boldsymbol{A}=\left[\begin{array}{l}\mathbf{3} \\ \mathbf{2}\end{array}\right] \) and \( \boldsymbol{B}=\left[\begin{array}{l}-\mathbf{2} \\ -\mathbf{1}\end{array}\right] \)
find the matrix \( X \) such that \( X-A=B \)
\( A \cdot\left[\begin{array}{l}0 \\ 0\end{array}\right] \)
в. \( \left[\begin{array}{l}1 \\ 1\end{array}\right] \)
\( c \cdot\left[\begin{array}{l}4 \\ 0\end{array}\right] \)
D. \( \left[\begin{array}{l}1 \\ -1\end{array}\right. \)
Subject: Chemistry
Assertion
In the Contact process, sulphur trioxide vapours are absorbed in concentrated
sulphuric add and not in water to obtain sulphuric acid.
Reason Directly dissolving sulphur trioxide in water is not possible due to highly exothermic nature of the reaction.
Acidic vapors are formed. Oleum is reacted with water to form conc.
sulphuric ac
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
Time period depends on Gravitational constant (G),plank constant, (h) and speed of light (c), then \( \mathrm{T} \) is proportional
to
\( ^{\mathrm{A}} \cdot \frac{G^{1 / 2} h^{1 / 2}}{C^{3 / 2}} \)
B. \( \frac{G^{1 / 2} h}{C^{5 / 2}} \)
\( ^{\mathrm{C}} \cdot \frac{G h^{1 / 2}}{C^{5 / 2}} \)
\( ^{\mathrm{D} \cdot \frac{G^{1 / 2} h^{1 / 2}}{C^{5 / 2}}} \)
Subject: Biology
Match the following and choose the correct combination from the options
given
\( \begin{array}{llll} & \text { Column I } & & \text { Column II } \\ \text { A } & \text { DDT } & 1 & \text { N0 }_{x} \text { , CO } \\ \text { B } & \text { PAN } & 2 & \text { Smog } \\ \text { C } & \text { Acid rain } & 3 & \begin{array}{l}\text { Biological } \\ \text { magnification }\end{array} \\ \text { D } & \begin{array}{l}\text { Global } \\ \text { warming }\end{array} & 4 & \text { so }_{2}\end{array} \)
A. A- \( 4, \) B- \( 3, \) C- \( 2, \) D-
B. A-1, B- 3, C- 2, D-4
c. \( A-2, B-3, C-4, D-1 \)
D. A- 3, B-2, C-4
Subject: Maths
The G.M. of n positive terms \( \boldsymbol{x}_{1}, \boldsymbol{x}_{2}, \ldots . . . \boldsymbol{x}_{n} \)
is
в. \( \frac{1}{n}\left(x_{1} \times x_{2} \times \ldots . . \times x_{n}\right) \)
C. \( \left(x_{1} \times x_{2} \times \ldots . \times x_{n}\right)^{1 / n} \)
D. none of these
Subject: Physics
Two-point charge \( +3 \mu C a n d+8 \mu C \)
each other with a force of \( 40 N \). If a
charge of \( -5 \mu C \) is added to each of them,then the force between them will
become:
A . \( -10 N \)
в. \( +10 N \)
\( \mathrm{c} \cdot+20 N \)
D . \( -20 N \)
Subject: Physics
A charge q exists at a distance or \( \mathrm{R} \)
from a spherical concave mirror of
mass of radius of curvature R, Let
mirror subtends a half angle \( \theta=30^{\circ} \) at
the angle.
Flux passing through the mirror is
\( A \)
B. \( \frac{q \sin ^{2} 30^{\circ}}{\varepsilon_{0}} \)
c. \( \frac{q \sin ^{2} 30}{2 \varepsilon_{0}} \)
D. \( \frac{q \sin ^{2} 15^{\circ}}{2 \varepsilon_{0}} \)
Subject: Chemistry
Silver is removed electrolytically from
\( 200 m L \) of a \( 0.1 N \) solution of \( A g N O_{3} \)
by a current of 0.1 A. How long will it take to remove half of the silver from the solution?
A . \( 0.1 s \)
B. \( 100 s \)
\( \mathbf{c} .965 s \)
D. \( 9650 s \)
Subject: Chemistry
The following reactions take place in the blast furnace in the preparation of impure iron.Identify the reaction pertaining to the formation of the slag.
A \( \cdot 2 C(s)+O_{2}(g) \rightarrow 2 C O(g) \)
B. \( F e_{2} O_{3}(s)+3 C O(g) \rightarrow 2 F e(\ell)+3 C O_{2}(g) \)
c. \( C a C O_{3}(s) \rightarrow C a O(s)+C O_{2}(g) \)
D. \( \operatorname{CaO}(s)+\operatorname{Si} O_{2}(s) \rightarrow \operatorname{CaSiO}_{3}(s) \)
Subject: Maths
f \( \boldsymbol{I}=\int \frac{\boldsymbol{d} \boldsymbol{x}}{(1+\sin \boldsymbol{x})^{4}}= \)
\( \frac{-\boldsymbol{A}}{\mathbf{4} \mathbf{9} \mathbf{9} \mathbf{2}}\left(\frac{\mathbf{1}}{\mathbf{7}} \boldsymbol{u}^{\mathbf{7}}+\frac{\mathbf{3}}{\mathbf{5}} \boldsymbol{u}^{\mathbf{5}}+\boldsymbol{u}^{\mathbf{3}}+\boldsymbol{u}\right)+\boldsymbol{C} \)
where \( u=\frac{1-2 \sin x}{1+\sin x} \) then \( A \) is equal
Subject: Chemistry
The internal energy of air in a room of
volume \( 50 \mathrm{m}^{3} \) at atmospheric pressure
will be
A \( \cdot 2.5 \times 10^{7} \) erg
B . 2.5 \( \times 10^{7} \) Joule
c. \( 5.255 \times 10^{7} \) Joule
D. \( 1.25 \times 10^{7} \) Joule
Subject: Physics
Two large vertical and parallel metal plates having a separation of \( 1 \mathrm{cm} \) are
connected to a DC voltage source of potential difference \( X . \) A proton is released at rest midway between the two plates. It remains at rest in the air then \( X \) is:
A \( \cdot 1 \times 10^{-5} V \)
В. \( 1 \times 10^{-7} V \)
c. \( 1 \times 10^{-9} V \)
D. \( 1 \times 10^{-10} V \)
Subject: Physics
A1 \( \mu F \) capacitor and a \( 2 \mu F \) capacitor
are connected in series across a \( 1200 \mathrm{V} \)
supply line. The charged capacitors are
disconnected from the line and from
each other and reconnected with
terminals of like sign together. Find the final charge on each and the voltage
across them:
A \( \cdot \frac{1600}{13} V \)
В. \( \frac{1600}{32} V \)
c. \( \frac{1600}{3} V \)
D. \( \frac{160}{3} V \)
Subject: Maths
A circular disc of area \( A_{1} \) is given with
its radius as diameter of a circular disc
of area \( A_{2} \) is cut out of it. The area of the
remaining disc is denoted by \( A_{3} . \) Then
\( \mathbf{A} \cdot A_{1} A_{3}<16 A_{2}^{2} \)
B. \( A_{1} A_{3}>16 A_{2}^{2} \)
\( \mathbf{c} \cdot A_{1} A_{3}=16 A_{2}^{2} \)
D. \( A_{1} A_{3}>2 A_{2}^{2} \)
Subject: Physics
An \( L-C-R \) series circuit has a
maximum current of \( 5 A . \) If \( L=0.5 H \)
and \( C=8 \mu F, \) then the angular
frequency of \( \boldsymbol{A} \boldsymbol{C} \) voltage is :
A. 500 rad/s
B. 5000 rad/s
c. 400 rad/s
D. \( 250 \mathrm{rad} / \mathrm{s} \)
Subject: Physics
Two towns \( T_{1} \) and \( T_{2} \) are connected by
a regular bus service. A
scooterist moving from \( \boldsymbol{T}_{1} \) to \( \boldsymbol{T}_{2} \) with
speed of \( 20 k m h^{-1} \) notices that a bus
goes past it every 21 minutes in the
direction of his motion and every 7
minutes in the opposite direction. If a
bus leaves in either direction every \( t \)
minutes, the period \( t \) is
A . 1.5 minute
B. 9.5 minute
c. 6 minute
D. 10.5 minute
Subject: Physics
(a) Write the relation between object
distance \( (u), \) image distance \( (v) \) and
focal distance \( (\boldsymbol{f}) \) of a spherical lens.
(b) What is magnification?
(c) The refractive index of glass with respect to air is \( \frac{3}{2} \) and the refractive index of water with respect to air is \( \frac{4}{3} . \) If the speed of light in air is \( 3 \times 10^{8} m / s \)
find the speed of light in (i) glass, (ii) water
Subject: Chemistry
If \( 3- \) hexanone is reacted with
\( N a B H_{4} \) followed by hydrolysis with
\( D_{2} O, \) the product will be :
\( \mathbf{A} \cdot C H_{3} C H_{2} C H(O H) C H_{2} C H_{2} C H_{3} \)
B. \( C H_{3} C H_{2} C D(O H) C H_{2} C H_{2} C H_{3} \)
c. \( C H_{3} C H_{2} C H(O D) C H_{2} C H_{2} C H_{3} \)
D. \( C H_{3} C H_{2} C D(O D) C H_{2} C H_{2} C H_{3} \)
Subject: Chemistry
From the given reactions which is a
redox reaction?
This question has multiple correct options
\( \mathbf{A} \cdot C u O(s)+H_{2}(g) \rightarrow C u(s)+H_{2} O(l) \)
B \( \cdot 2 C u(s)+O_{2}(g) \rightarrow 2 C u O(s) \)
\( \mathbf{c} \cdot C(s)+2 H_{2}(g) \rightarrow C H_{4}(g) \)
D. \( 4 A l(s)+3 O_{2}(g) \rightarrow 2 A l_{2} O_{3}(s) \)
Subject: Maths
Find the \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \) by implicit differentiation
\( \boldsymbol{x}^{2}-\mathbf{8} \boldsymbol{x} \boldsymbol{y}+\boldsymbol{y}^{2}=\boldsymbol{8} \)
Subject: Physics
In a Zener regulated power supply of a
Zener diode with \( V_{2}=6 V \) is used for
regulation. The load current is to be \( 4 m A \) and the unregulated input is \( 10 V \)
The value of series resistor \( \boldsymbol{R}_{\boldsymbol{S}} \) is
(Assume \( \left.\boldsymbol{I}_{z}=\mathbf{5} \boldsymbol{I}_{L}\right) \)
A. less than \( 5 \Omega \)
B. Infinite
c. greater than \( 100 \Omega \)
D. zero
Subject: Chemistry
A graph is plotted between \( E_{\text {cell}} \) and \( \log _{10}\left[\frac{Z n^{2+}}{C u^{2+}}\right] \) The curve was linear with
intercept
on \( E_{\text {cell}} \) axis equal to 1.10 V. Calculate \( E_{\text {cell}} \)
for
\( \left.Z n\right|_{0.1 M} ^{Z n^{2+}}||_{0.01 M}^{C u^{2+}} \mid C u \)
A . 1.07
B. 1.129 v
c. \( 0.059 v \)
D. 0.0295 V
Subject: Chemistry
The value of the ionic product constant
for water \( \left(\boldsymbol{K}_{\boldsymbol{w}}\right) \) at \( \mathbf{6 0}^{\circ} \mathbf{C} \) is \( \mathbf{9 . 6} \times \mathbf{1 0}^{\mathbf{1 4}} \boldsymbol{M}^{\mathbf{2}} \)
What is the \( \left[\boldsymbol{H}_{3} \boldsymbol{O}^{+}\right] \) of a neutral
aqueous solution at \( 60^{\circ} \mathrm{C} \) and an
aqueous sol ion with a \( \mathrm{pH}=7.0 \) at \( 60^{\circ} \)
respectively?
A . \( 3.1 \times 10^{-7} \) acidic
B. \( 3.1 \times 10^{-7} \) neutral
c. \( 3.1 \times 10^{-8} \) basic
D. \( 3.1 \times 10^{-7} \) basic
Subject: Physics
Two different liquids are flowing in two tubes of equal radius. The ratio of
coefficient of viscosity of liquids is 52:
49 and the ratio of their densities is
\( 15.6: 1, \) then the ratio of their critical
velocities will be:
A . 0.068
B. 0.68
\( c \cdot 6.8 \)
\( D \cdot 68 \)
Subject: Chemistry
Which of the following statement is
correct?
A. Cathode is negative terminal both in galvanic and electrolytic cells
B. Anode is positive terminal both in galvaniv and electrolytic cells
C. Cathode is negative terminal in an electrolytic cell whereas anode is negative terminal in a galvanic cell
D. Anode is negative terminal in an electrolytic cell whereas cathode is positive terminal in galvanic cell
Subject: Physics
The half life of a radioactive substance
is 20 minutes. The approximate time
interval \( \left(\mathrm{t}_{2}-\mathrm{t}_{1}\right) \) between the time \( \mathrm{t}_{1} \)
when \( \frac{1}{3} \) of it had decayed and \( t_{2} \) when \( \frac{2}{3} \) of it had decayed is :
\( A \cdot 7 \min \)
B. 14 min
\( c .20 \mathrm{min} \)
D. 28 min
Subject: Chemistry
Which one of the following reaction conditions are used for preparing diethyl ether from ethyl alcohol?
A. \( H I / 200^{\circ} C \)
в. Сопс.Н\( _{2} S O_{4} / 140^{\circ} C \)
c. \( N a O H / 70^{\circ} C \)
D. \( N a O C_{2} H_{5} / 27^{\circ} C \)
Subject: Chemistry
The butter of tin is represented by:
A. \( S n C l_{2} .5 H_{2} O \)
в. \( \operatorname{Sn} C l_{2} \)
\( \mathrm{c} \cdot \operatorname{Sn} C l_{4} \)
D. \( S n C l_{4} .5 H_{2} O \)
Subject: Maths
The antiderivative of \( \frac{x+\left(\cos ^{-1} 3 x\right)^{2}}{\sqrt{1-9 x^{2}}} \) is
A \( \cdot C-\frac{1}{9}\left[\sqrt{1-9 x^{2}}+\left(\cos ^{-1} 3 x\right)^{3}\right] \)
B. \( C+\frac{1}{9}\left[\sqrt{1-9 x^{2}}+\left(\cos ^{-1} 3 x\right)^{2}\right. \)
c. \( c-\frac{1}{3}\left[\left(1-9 x^{2}\right)^{3 / 2}+\left(\cos ^{-1} 3 x\right)^{3}\right. \)
D. none of these
Subject: Physics
A telescope is used to resolve two stars
separated by \( 4.6 \times 10^{-6} \) rad. If the wavelength of light used is \( 5460 A \) what should be the aperture of the objective of the telescope?
A. \( 0.1488 \mathrm{m} \)
B. 0.567 m
\( c \cdot 1 m \)
D. 2 \( m \)
Subject: Maths
\( \int \frac{x^{3}-1}{x^{3}+x} d x \) is equal to
\( \mathbf{A} \cdot x-\log x+\log \left(x^{2}+1\right)-\tan ^{-1} x+c \)
B. \( x-\log x+\frac{1}{2} \log \left(x^{2}+1\right)-\tan ^{-1} x+c \)
c. \( x+\log x+\frac{1}{2} \log \left(x^{2}+1\right)+\tan ^{-1} x+c \)
D \( x+\log x-\frac{1}{2} \log \left(x^{2}+1\right)-\tan ^{-1} x+c \)
Subject: Physics
Figure shows the circular motion of a
particle. The radius of the circle, the
period, sense of revolution and the initial position are indicated in the
figure. The simple harmonic motion of
the \( x \) - projection of the radius vector of the rotating particle P is
A \( \cdot x=2 \cos \left[2 \pi t+\frac{\pi}{4}\right. \)
B・ \( x=2 \sin \left[2 \pi t+\frac{\pi}{4}\right] \)
c. \( x=2 \sin \left[2 \pi t-\frac{\pi}{4}\right] \)
D. \( x=2 \cos \left[2 \pi t-\frac{\pi}{4}\right] \)
Subject: Physics
A fricionless wire \( A B \) is fixed on
sphere of radius R. A very small particle slips on the wire. The journey from \( A \) to \( B \) is performed in time
A .2 Rg \( \cos \theta \)
B. \( 2 \sqrt{R g} \cos \theta \)
\( c \cdot 2 \sqrt{\frac{R}{g}} \)
\( 0.2 \sqrt{\frac{9}{2}} \)
Subject: Physics
The specific heat of a gas in a polytropic process is given by
A. \( \frac{R}{\gamma-1}+\frac{R}{N-1} \)
в. \( \frac{R}{1-\gamma}+\frac{R}{1-N} \)
c. \( \frac{R}{\gamma-1}-\frac{R}{N-1} \)
D. \( \frac{R}{1-\gamma}-\frac{R}{1-N} \)
Subject: Chemistry
When \( H_{2} O \) is shaken with an acidified
solution of \( K_{2} C r_{2} O_{7} \) in the presence of ether, the ethereal layer turns blue due to the formation of :
A. \( C r_{2} O_{3} \)
B. \( C r O_{5} \)
\( \mathrm{c} \cdot \mathrm{Cr} \mathrm{O}_{4}^{-} \)
D. none of these
Subject: Physics
A homogeneous ball (mass \( =\boldsymbol{m} \) ) of
ideal black material at rest is
illuminated with a radiation having a set of photons (wavelength \( =\lambda \) ), each
with the same momentum and the
same energy. The rate at which photons fall on the ball is n. The linear
acceleration of the ball is:
\( A \cdot m \lambda / n h \)
B. \( n h / m \lambda \)
c. \( n h /(2 \pi)(m \lambda) \)
D. \( 2 p m \lambda / n h \)
Subject: Chemistry
Which of the following cell
representations is/are correct?
This question has multiple correct options
\( \left.\mathbf{A} \cdot P l, H_{2}(1 b a r)|H C I(a q)| C l_{2}(1 b a r)\right) P t \)
B . \( H g\left|H g_{2} C l_{2}(S)\right| H C l(a q) \mid H_{2}(1 b a r), P t \)
\( \mathbf{c} \cdot A t|A g C l(s)| K C I(a q)\left|H g_{2}(s)\right| H g \)
D \( \cdot P t_{3} H_{2}(1 b a r)|H l| A u l(s) \mid A \mu \)
Subject: Chemistry
The anhydride of \( \mathbf{H C l O}_{4} \) is:
A \( \cdot \mathrm{ClO}_{4} \)
в. \( \mathrm{Cl}_{2} \mathrm{O}_{7} \)
\( \mathrm{c} \cdot \mathrm{ClO}_{2} \)
D. \( \mathrm{ClO}_{3} \)
Subject: Chemistry
Which of the following statements is not correctly showing the trend of the properties mentioned?
A. \( C H_{3} C H_{2} O H>C H_{3} C H_{2} C H_{2} O H> \)
\( C H_{3} C H_{2} C H_{2} C H_{2} O H \)
B . \( C H_{3} C H_{2} O H>C H_{3} C H_{2} C H_{2} O H> \)
\( C H_{3} C H_{2} C H_{2} C H_{2} O H \)
(Boilingpoint)
c. \( C H_{3} C H_{2} C H_{2} O H>C H_{3} C H-C H_{2} O H> \)
\( C H_{3} \)
\( C H_{3} \)
\( C H_{3}-C_{I}^{\prime}-O H \)
Boiling point
D. \( \quad C H_{3} \)
\[
C H_{3}-C_{C H_{3}}^{L}-O H<C H_{3} C H-C H_{2} O H
\]
\( C H_{3} C H_{2} C H_{C} H_{2} O H \)
Subject: Maths
In rectangle \( A B C D, \) diagonal \( B D=26 \mathrm{cm} \) and cotangent of angle \( A B D=1.5 . \) Flnd the area and the perimeter of the rectangle ABCD
A. Area = 436 sq. cm and perimeter = \( 11 \sqrt{13} \mathrm{cm} \)
B. Area = 842 sq. cm and perimeter = \( 15 \sqrt{13} \mathrm{cm} \)
c. Area \( =312 \) sq. \( \mathrm{cm} \) and perimeter \( =20 \sqrt{13} \mathrm{cm} \)
D. Area = 231 sq. cm and perimeter = \( 12 \sqrt{13} \mathrm{cm} \)
Subject: Physics
In hydrogen atom, an electron makes transition from \( n=3 \) to \( n=2 \) state in
time interval of \( 1.2 \times 10^{-8} \) s. Calculate
the average torque (in \( \mathrm{Nm} \) ) acting on the electron during this transition.
A . \( 1.055 \times 10^{-26} \)
В. \( 4.40 \times 10^{-27} \)
c. \( 1.7 \times 10^{-26} \)
D. \( 8.79 \times 10^{-27} \)
Subject: Physics
The pressure of a certain mass of gas at \( 27^{0} \mathrm{Cis} 84 \mathrm{cm} \) of Hg. If \( 25 \% \) of the gas is
now introduced into the same vessel at
the same temperature, the final pressure of the gas will be in cm of Hg
A . 105
B. 100
\( c \cdot 95 \)
D. 90
Subject: Chemistry
Which of the following conditions are correct for real solutions showing negative deviation from Raoult's law?
A \( \cdot \Delta H_{M i x}<0 ; \Delta V_{M i x}>0 \)
B. \( \Delta H_{M i x}>0 ; \Delta V_{M i x}>0 \)
c. \( \Delta H_{M i x}>0 ; \Delta V_{M i x}<0 \)
D. \( \Delta H_{M i x}<0 ; \Delta V_{M i x}<0 \)
Subject: Chemistry
In this ladder, symbols of elements are jumbled up. Rearrange these symbols of elements in the increasing order of their atomic number in the periodic table
\( \mathrm{Ca} \)
B. H, He, Li, B, Be, C, N, O, F, Ne, Na, Mg, Al, S, P, Si, CI, Ar, K \( \mathrm{c} \)
c. H, He, Li, Be, B, C, N, O, F, Na, Ne, Mg, Al, S, P, s, Cl, Ar, K. \( \mathrm{Ca} \)
D. H, He, Li, Be, B, C, N, O, F, Ne, Na, Mg, Al, si, P, s, cl, Ar. \( c \)
Subject: Maths
Solve the equation \( 3 \sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right)- \)
\( 4 \cos ^{-1}\left(\frac{1-x^{2}}{1+x^{2}}\right)+2 \tan ^{-1}\left(\frac{2 x}{1-x^{2}}\right)=\frac{\pi}{3} \)
Subject: Chemistry
A metal nitrate gives black ppt. with \( \mathrm{Kl} \) and on adding excess of Kl it gives orange colour. It is:
A \( \cdot \mathrm{Hg}^{+} \)
B. Bit \( ^{3} \)
\( c \cdot \operatorname{sn}^{+} \)
D. \( P b^{+2} \)
Subject: Physics
A hot body, obeying Newton's law of cooling is cooled down from its peak
value \( 80^{\circ} C \) to an ambient temperature of \( 30^{\circ} C . \) It takes 5 minutes in cooling
down from \( 80^{\circ} \mathrm{C} \) to \( 40^{\circ} \mathrm{C} \). How much
time will it take to cool down from
\( 62^{\circ} \mathrm{C} \) to \( 32^{\circ} \mathrm{C} ? \)
(Given \( \ln 2=0.693, \ln 5=1.609) \)
A. 9.6 minutes
B. 3.75 minutes
c. 8.6 minutes
D. 6.5 minutes
Subject: Maths
\( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{8} \\ \mathbf{9} & \mathbf{4}\end{array}\right] \boldsymbol{B}=\left[\begin{array}{ll}\mathbf{6} & \mathbf{7} \\ \mathbf{3} & \mathbf{5}\end{array}\right] \) Find \( \boldsymbol{A}+\boldsymbol{B} \)
Subject: Physics
One \( \mathrm{Kg} \) of a diatomic gas is at a pressure of \( 8 \times 10^{4} \mathrm{N} / \mathrm{m}^{2} . \) The density
of the gas is \( 4 \mathrm{kg} / \mathrm{m}^{3} . \) The energy of the gas due to its thermal motion will be
B . \( 5 \times 10^{4} \) 」
c. \( 6 \times 10^{4} \) 」
D. \( 7 \times 10^{4} \) 」
Subject: Physics
A wire \( 1 m \) long has cross-section
\( 1 m m^{2} \) and \( Y=1.2 \times 10^{11} P a . \) Find the
work done in stretching it by \( 2 m m \)
A . 2.4
B. 0.24J
c. 0.024J
D. 1.2.
Subject: Chemistry
Then equilibrium constant for the
reaction is:
For the following reactions, equilibrium constants are indicated on the arrow
\[
\begin{array}{l}
\mathrm{H}_{3} \mathrm{PO}_{4} \stackrel{K_{1}}{\Leftrightarrow} \mathrm{H}^{+}+\mathrm{H}_{2} \mathrm{PO}_{4} \\
\mathrm{H}_{2} \mathrm{PO}_{4}^{*} \Leftrightarrow \mathrm{H}^{*}+\mathrm{HPO}_{4}^{-2} \\
\mathrm{HPO}_{4}^{-2} \stackrel{K_{3}}{\Leftrightarrow} \mathrm{H}^{+}+\mathrm{PO}_{4}^{-3}
\end{array}
\]
Then equilibrium constant for the reaction
\[
\mathrm{H}_{3} \mathrm{PO}_{4} \Leftrightarrow \quad 3 \mathrm{H}^{+}+\mathrm{PO}_{4}^{3} \text { will be }
\]
\( \mathbf{A} \cdot K_{1}+K_{2}+K_{3} \)
B . \( \sqrt{K_{1} K_{2} K_{3}} \)
\( \mathbf{c} \cdot K_{1} \times K_{2} \times K_{3} \)
D. \( \frac{1}{K_{1} K_{2} K_{3}} \)
Subject: Physics
Suppose a particle \( a \) of charge \( 2 e \) and
\( \operatorname{mass} 2 m_{e}\left(m_{e} \) being mass of electron) \right.
revolves around the proton in nearest allowed circular orbit of radius r. If the
radius of first Bohr orbit for the electron
is \( A_{0}, \) then the relation between \( r \) and
\( a_{0} \) is
A. \( a_{0}=4 r \)
\( r \)
B . \( a_{0}=8 r \)
c. \( a_{0}=2 r \)
D. \( a_{0}=\frac{r}{4} \)
Subject: Chemistry
Q Type your question-
account for this effect we define a
quantity called the Van't Hoff factor
given by :
\[
\boldsymbol{i}=
\]
Actual number of particles in solution Number of formula units initiall
\( i=1 \) (for non-electrolytes)
\( i>1 \) (for non-electrolytes, undergoing dissociation) \( i<1 \) (for solutes, undergoing dissociation)

Answer the following questions:
A solution of benzoic acid is dissolved
in benzene such that it undergoes
molecular association and its molar
mass approaches 244. The benzoic molecules will exist as:
A . Dimer
B. Monomer
C. Tetramer
D. Trimer
Subject: Maths
The direction cosines of the vectors \( 2 \vec{i}+\vec{j}-2 \vec{k} \) is equal to
A \( \cdot \frac{2}{3}, \frac{1}{3},-\frac{2}{3} \)
B. \( \frac{2}{3}, \frac{1}{3}, \frac{2}{3} \)
c. \( \frac{1}{3}, \frac{2}{3},-\frac{2}{3} \)
D. \( \frac{2}{3}, \frac{2}{3}, \frac{1}{3} \)
Subject: Chemistry
For the galvanic cell, \( \boldsymbol{A} \boldsymbol{g} \mid \boldsymbol{A} \boldsymbol{g} \boldsymbol{C l}(\boldsymbol{s}), \boldsymbol{K} \boldsymbol{C l}(\mathbf{0} . \boldsymbol{2} \boldsymbol{M}) \| \boldsymbol{K} \boldsymbol{B r}(\mathbf{0 . 0 0 1} \)
Calculate the emf generated and assign correct polarity to each electrode for the spontaneous process after taking into
account the cell reaction at \( 25^{\circ} C \).
Given, \( \boldsymbol{K}_{s p A g C l}=\mathbf{2 . 8} \times \)
\( \mathbf{1 0}^{-\mathbf{1 0}} ; \mathbf{K}_{s p A g B r}=\mathbf{3 . 3} \times \mathbf{1 0}^{-\mathbf{1 3}} \)
Subject: Physics
The ratio of the value of \( G \) in \( S \) l units to
CGS units is
\( \mathbf{A} \cdot 10^{3}: 1 \)
B \( \cdot 10^{2}: 1 \)
\( \mathbf{c} \cdot 10^{-2}: 1 \)
D. \( 10^{-3}: 1 \)
Subject: Physics
A resistor \( R \) on inductance \( 0.2 H \) and a
capacitor of capacitance \( C \) are
connected in series. A sinusoidal
voltage of \( r m s \) value \( 200 V \) is applied across the combination using a fixed
frequency oscillator. If the rms value of current through the circuit is \( 2.828 A \) and the inductive and capacitive reactances are \( 3 R \) and \( 2 R \) respectively. Calculate (i) resistance of the resistance of the resistor
(ii) frequency of \( A C \) (iii) capacitance of the capacitor.
\( \begin{array}{ll}\text { A. } & (500 \Omega, 119.3 H z, 13.3 \mu F)\end{array} \)
B. \( \quad(50 \Omega, 119.3 H z, 13.3 \mu F) \)
C. \( \quad(50 \Omega, 1193 H z, 133 \mu F) \)
D. \( \quad(50 \Omega, 0.1193 H z, 133 \mu F) \)
Subject: Maths
If the lateral surface area of a cube is
\( 1600 \mathrm{cm}^{2} \) then its edge is
\( \mathbf{A} \cdot 15 \mathrm{cm} \)
B. \( 18 \mathrm{cm} \)
\( c .20 \mathrm{cm} \)
D. \( 24 \mathrm{cm} \)