AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
The other end of the diameter through
the point (-1,1) on the circle \( x^{2}+ \) \( y^{2}-6 x+4 y-12=0 \) is :
\( \mathbf{A} \cdot(-7,5) \)
B. (-7,-5)
c. (7,-5)
D. (7,5)
Subject: Physics
This question has Statement I and Statement II. Of the four choices given
after the Statements, choose the one
that best describes the two Statements.
Statement - I: A point particle of mass
\( m \) moving with speed \( v \) collides with
stationary point particle of mass \( M . \) If the maximum energy loss possible is \( \operatorname{given} \operatorname{as} f\left(\frac{1}{2} m v^{2}\right) \) then \( f= \)
\( \left(\frac{m}{M+m}\right) \)
Statement - II: Maximum energy loss occurs when the particles get stuck together as a result of the collision.
A. Statement I is true, Statement II is true, Statement II is not a correct explanation of Statement!
B. Statement I is true, Statement II is false.
c. Statement l is false, Statement II is true
D. Statement I is true, Statement II is true, Statement II is correct explanation of Statement
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x})=(\boldsymbol{x}+\mathbf{1})^{2}-\mathbf{1},(\boldsymbol{x} \geq-\mathbf{1}) . \) Then
the \( \operatorname{set} S=\left\{x: f(x)=f^{-1}(x)\right\} \) is
Subject: Maths
Using elementary tranormtion, find the
\[
\text { inverse of }\left[\begin{array}{ccc}
\mathbf{1} & \mathbf{3} & -\mathbf{2} \\
-\mathbf{3} & \mathbf{0} & -\mathbf{5} \\
\mathbf{2} & \mathbf{5} & \mathbf{0}
\end{array}\right]
\]
Subject: Physics
A series LCR circuit is tuned to resonance
If the angular frequency of the applied AC voltage at resonance is \( \omega \), the impedance
of the circuit then is:
A \( \cdot R+\omega L+\left(\frac{1}{\omega C}\right) \)
B.
c. \( \sqrt{R^{2}+\omega L+\left(\frac{1}{\omega C}\right)^{2}} \)
D. \( \sqrt{R^{2}+\left(\omega L-\frac{1}{\omega C}\right)^{2}} \)
Subject: Physics
A solid hemisphere is just pressed
below the liquid, the value of \( \frac{F_{1}}{F_{2}} \) is
(where \( F_{1} \) and \( F_{2} \) ) are the hydrostatic
force acting on the curved and flat
surfaces of the hemisphere)(Neglect atmospheric pressure)
A \( \cdot \frac{1}{2} \)
B. 2 3
\( c \cdot \frac{1}{3} \)
D. None of these
Subject: Maths
If \( \theta \) is the angle between two lines
whose d.c.s are \( l_{1}, m_{1}, n_{1} \) and \( l_{2}, m_{2}, n_{2} \)
then the d.cs of one of the angular bisectors of the two lines are
\( ^{\text {A }} \cdot \frac{l_{1}+l_{2}}{2}, \frac{m_{1}+m_{2}}{2}, \frac{n_{1}+n_{2}}{2} \)
B. \( \frac{l_{1}+l_{2}}{2 \cos \left(\frac{\theta}{2}\right)}, \frac{m_{1}+m_{2}}{2 \cos \left(\frac{\theta}{2}\right)}, \frac{n_{1}+n_{2}}{2 \cos \left(\frac{\theta}{2}\right)} \)
c. \( \frac{l_{1}+l_{2}}{\cos \left(\frac{\theta}{2}\right)}, \frac{m_{1}+m_{2}}{\cos \left(\frac{\theta}{2}\right)}, \frac{n_{1}+n_{2}}{\cos \left(\frac{\theta}{2}\right)} \)
D. \( \frac{l_{1}+l_{2}}{2 \sin \left(\frac{\theta}{2}\right)} \frac{m_{1}+m_{2}}{2 \sin \left(\frac{\theta}{2}\right)} \frac{n_{1}+n_{2}}{2 \sin \left(\frac{\theta}{2}\right)} \)
Subject: Biology
Assertion
Androgens stimulate muscular growth.
Reason

Androgens produce anabolic effects on protein and carbohydrate metabolism.
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: Chemistry
Peroxonitrous acid is an unstable
intermediate formed in the oxidation of
\( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{2} \) by \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \)
"Peroxonitrous acid has the same
formula as nitric acid, \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \)
Answer whether the above statement is
true or false.lf true enter 1 , else 0
Subject: Maths
In given figures sides \( A B \) and \( A C \) and
median \( A D \) of a triangle \( A B C \) are
respectively proportional to sides \( \boldsymbol{P Q} \)
and \( P R \) and median \( P M \) of another
triangle \( P Q R . \) Show that \( \triangle A B C \sim \)
\( \triangle \boldsymbol{P} \boldsymbol{Q} \boldsymbol{R} \)
Subject: Physics
A small ring of mass \( m \) is connected
with a particle of same mass by an ideal string \( \& \) the whole system is released as shown in figure. Coefficient of friction between ring \( A \) and wire is 3/5. Ring A will start sliding when connecting string will make an angle \( (5 \times x)^{0} \) with the vertical. Find \( x \)
(particle is free to move and ring can slide only)
Subject: Physics
Let \( m_{P} \) be the mass of a proton, \( m_{n} \) the
mass of a neutron, \( M_{1} \) the mass of a
\( 20 \mathrm{Ne} \) nucleus and \( M_{2} \) the mass of a
10
\( _{20}^{40} C a \) nucleus. Then This question has multiple correct options
A. \( M_{2}=2 M_{1} \)
В . \( M_{2}>2 M_{1} \)
c. \( M_{2}<2 M_{1} \)
D. \( M_{1}<10\left(m_{n}+m_{p}\right) \)
Subject: Maths
If \( A B=A \) and \( B A=B, \) then
This question has multiple correct options
\( \mathbf{A} \cdot A^{2} B=A^{2} \)
B. \( B^{2} A=B^{2} \)
c. \( A B A=A \)
D. \( B A B=B \)
Subject: Chemistry
Which one is the general formula of
monohydric alcohols?
A. \( C_{n} H_{2 n-2} O H \)
в. \( C_{n+1} H_{2 n} O H \)
c. \( C_{2 n} H_{2 n+2} 2 O H \)
D. \( C_{n} H_{2 n} O H \)
Subject: Physics
ENERGY OF AN ORBITING SATELLITE
A comet orbits the sun in a highly elliptical orbit. Which of the following quantities remains constant throughout its orbit?
(i) Linear speed
(ii) Angular speed (iii) Angular momentum (iv) Kinetic energy
(v) Potential energy (vi)Total energy
\( A \cdot(i),(\text { ii) },( \text { iii) } \)
B. (iii), (iv), (v)
c. (iii) and (vi)
D. (ii), (iii) and (vi)
Subject: Chemistry
The ratio of the mass of \( C-12 \) atom to
that of an atom of element \( X \) (whose
atomicity is four) is \( 1: 9 . \) The molecular mass of element X is :
A \( \cdot 480 \mathrm{gmol}^{-1} \)
в. 432 gmol-\( ^{-1} \)
c. \( 36 g m o l^{-1} \)
D. \( 84 ~ g m o l^{-1} \)
Subject: Chemistry
For the reaction \( \boldsymbol{P} \boldsymbol{C l}_{5}_{5} \rightleftharpoons \boldsymbol{p} \boldsymbol{C l}_{3(g)}+ \)
\( C l_{2(g)}, \) the forward reaction at constant
temperature is favoured by:
A. introducing an inert gas at constant volume
B . introducing \( C l_{2} \) at constant volume
C . introducing \( P C l_{5} \) at constant volume
D. reducing the volume of the container
Subject: Maths
What is the angle between \( \vec{A} \) and the resultant of \( (\overrightarrow{\boldsymbol{A}}+\overrightarrow{\boldsymbol{B}}) \) and \( (\overrightarrow{\boldsymbol{A}}-\overrightarrow{\boldsymbol{B}}) \)
\( \mathbf{A} \cdot 0^{\circ} \)
B \( \cdot \tan ^{-1}\left(\frac{A}{B}\right) \)
\( ^{\mathbf{c}} \cdot \tan ^{-1}\left(\frac{B}{A}\right) \)
D. \( \tan ^{-1}\left(\frac{A-B}{A+B}\right) \)
Subject: Physics
A swimmer wishes to cross a \( 500 \mathrm{m} \)
wide river flowing at \( 5 \mathrm{km} / \mathrm{h} \). His speed with respect to water is \( 3 \mathrm{km} / \mathrm{h} \). (a) If he
heads in a direction making an angle \( \theta \)
with the flow, find the time he takes to
cross the river.(b) Find the shortest
possible time to cross the river.
Subject: Maths
In the given \( \Delta A B C, \) if \( A B=A C \) and
\( B D=D C, \) then \( \angle A D C= \)
\( \mathbf{A} \cdot 60^{\circ} \)
B. \( 120^{\circ} \)
\( \mathbf{c} \cdot 90^{\circ} \)
D. \( 45^{\circ} \)
Subject: Maths
\( f \sum_{i=1}^{10}\left(x_{i}-15\right)= \)
12 and \( \sum_{i=1}^{10}\left(x_{i}-15\right)^{2}=18 \) then the
S.D. of observations \( \boldsymbol{x}_{1}, \boldsymbol{x}_{2} \ldots \ldots . . \boldsymbol{x}_{10} \) is
A \( \cdot \frac{2}{5} \)
B. \( \frac{3}{5} \)
\( c \cdot \frac{4}{5} \)
D. None of these
Subject: Biology
Identify the correct order of appearance of the following organisms on the
surface of earth.
I. Eukaryotes
II. Heterotrophic organisms
III. Metazoa
IV. Photosynthetic organisms
\( \mathbf{A} \cdot\|, 1,1 V,\| 1 \)
В. ॥, ।, ॥I, IV
c. ॥, IV, ।, ॥ा
D. IV, I, II, III
E . \( \mathrm{IV}, \) ।।, ।, ॥ा
Subject: Chemistry
\( \boldsymbol{H}-\boldsymbol{C} \equiv \boldsymbol{C}-\boldsymbol{H}+ \)
\( \boldsymbol{H}_{2} \frac{P d-B a S O_{4} / Q u i n o l i n e}{ } \boldsymbol{A} \stackrel{\boldsymbol{H} C l}{\longrightarrow} \)
\( \boldsymbol{B} \stackrel{\boldsymbol{a q} \cdot \boldsymbol{K} \boldsymbol{O} \boldsymbol{H}}{\longrightarrow} \boldsymbol{C} \)
Here, \( C \) is :
A. propane
B. ethanol
c. ethyne
D. ethylene
Subject: Physics
If an object is placed at a distance \( \mathrm{R} \)
from the pole of first surface, then the real image is formed at a distance \( \mathrm{R} \)
from the pole of the second surface. The refractive index \( \mu \) of the sphere is given
by
A . 1.5
B. 2
\( c \cdot \sqrt{2} \)
D. none of these
Subject: Chemistry
What is the cell reaction occurring in
Daniell cell (galvanic cell)?
\( \mathbf{A} \cdot C u(s)+Z n S O_{4}(a q .) \rightarrow C u S O_{4}(a q .)+Z n(s) \)
B \( \cdot Z n(s)+C u S O_{4}(a q .) \rightarrow C u(s)+Z n S O_{4}(a q .) \)
\( \mathbf{c} \cdot N i(s)+Z n S O_{4}(a q .) \rightarrow N i S O_{4}(a q .)+Z n(s) \)
\( \mathbf{D} \cdot 2 N a(s)+C d S O_{4}(a q .) \rightarrow N a_{2} S O_{4}(a q .)+C d(s) \)
Subject: Chemistry
Match the correct pairs of isomers with their examples.
A)Ionisation \( \left.P t\left(N H_{3}\right)_{2} C l_{2}\right]\left[P t\left(N H_{3}\right)_{4}\right] \)
\( \left[P t C l_{4}\right. \)
B) Linkage \( \left[C r\left(N H_{3}\right)_{6}\right]\left[C o(C N)_{6}\right] \& \)
\( \left[C o\left(N H_{3}\right)_{6}\left[C r(C N)_{6}\right]\right. \)
C)Coordination \( \left[\operatorname{Co}\left(N H_{3}\right)_{5}\left(N O_{2}\right)\right] C l_{2} \& \)
\( \left[\operatorname{Co}\left(N H_{3}\right)_{5}(O N O)\right] C l_{2} \)
DPolymerisation \( \left[\mathrm{Co}\left(\mathrm{SO}_{4}\right)\left(\mathrm{NH}_{3}\right)_{5}\right] \mathrm{Br} \& \)
\( \left[\operatorname{Col} \operatorname{Br}\left(N H_{3}\right)_{5}\right] S O_{4} \)
\( A \cdot A->a, B->b, C->c, D \rightarrow d \)
B. \( A->b, B->a, C->d, D \rightarrow C \)
\( c \cdot A->d, B->c, C->b, D \rightarrow a \)
D. \( A->d, B->b, C->c, D \rightarrow a \)
Subject: Maths
If \( y=\log _{10}(\sin x), \) then \( \frac{d y}{d x} \) equals to:
A \( \cdot \sin x \log _{10} e \)
B. \( \cos x \log _{10} e \)
C. \( \cot x \log _{10} e \)
D. \( \cot x \)
Subject: Physics
A planet revolves about the sun in elliptical orbit. The arial velocity \( \left(\frac{\boldsymbol{d} \boldsymbol{A}}{\boldsymbol{d} \boldsymbol{t}}\right) \)
of the planet is \( 4.0 \times 10^{16} m^{2} / s . \) The
least distance between planet and the sun is \( 2 \times 10^{12} \mathrm{m} . \) Then the maximum
speed of the planet in \( \mathrm{km} / \mathrm{s} \) is
\( A \cdot 10 \)
B. 20
\( c \cdot 40 \)
D. none of these
Subject: Chemistry
Concentration of \( A g^{+} \) ions in a
saturated solution of \( A g_{2} C r O_{4} \) at \( 20^{\circ} \mathrm{C} \)
is \( 1.5 \times 10^{-4} \) mol \( L^{-1}, \) At \( 20^{0} C, \) the
solubility product of \( A g_{2} C r O_{4} \) is:
A. \( 5.6 \times 10^{-12} \)
B . \( 1.68 \times 10^{-10} \)
c. \( 5.6 \times 10^{-11} \)
D. \( 1.68 \times 10^{-11} \)
Subject: Maths
Find the values of \( c \) that satisfy the
Rolle's theorem for integrals on [-2,1]
\( \boldsymbol{f}(\boldsymbol{t})=\boldsymbol{2} \boldsymbol{t}-\boldsymbol{t}^{3}-\boldsymbol{t}^{2} \)
This question has multiple correct options
\( ^{\mathrm{A}} \cdot_{c}=\frac{1+\sqrt{7}}{-3} \)
B. \( c=\frac{1-\sqrt{7}}{-3} \)
\( c_{c}=\frac{-1+\sqrt{7}}{-3} \)
D. \( c=\frac{-1-\sqrt{7}}{-3} \)
Subject: Maths
Find a vector \( \overrightarrow{\boldsymbol{v}} \) which is co-planar with the vectors \( \vec{a}=\hat{i}-2 \hat{j}+\hat{k} \) and \( \vec{b}=\hat{i}- \)
\( \hat{\boldsymbol{j}}+2 \hat{\boldsymbol{k}} \) and is orthogonal to the vector \( \vec{c}=-2 \hat{i}+\hat{j}+\hat{k} . \) It is given that the projection of \( \overrightarrow{\boldsymbol{v}} \) along the vector \( \hat{\boldsymbol{i}}-\hat{\boldsymbol{j}}+ \)
\( \hat{k} \) is equal to \( 16 \sqrt{3} \)
\( \mathbf{A} \cdot 6 \hat{j}-12 \hat{k} \)
B . \( 12 \hat{i}-6 \hat{j}+30 \hat{k} \)
c. \( 9(\hat{i}-\hat{j}+\hat{k}) \)
D. None of these
Subject: Physics
A ring consisting of two parts \( A D B \) and
\( A C B \) of same conductivity k carries an amount of heat H. The ADB part is now
replaced with another metal keeping
the temperatures \( T_{1} \) and \( T_{2} \) constant. The heat carried increases to 2 H. What
should be the conductivity of the new
ADB part? Given \( \frac{A C B}{A D B}=3 \)
A \( \cdot \frac{7}{3} k \)
B. 2k
c. \( \frac{5}{2} k \)
\( D . \) 3k
Subject: Chemistry
An ideal gas \( \left(C_{v}=\frac{3}{2} R\right) \) is maintained
in a vessel of volume \( 83 \times 10^{-4} m^{3} \) at
pressure \( 1.6 \times 10^{6} N m^{-2} \) and
temperature \( 300 K . \) If \( 2.49 \times 10^{4} J \)
heat is given to this vessel, then its
final temperature will be
\( \mathbf{A} \cdot 600 K \)
B. \( 625 K \)
\( \mathbf{c} .650 K \)
D. \( 675 K \)
Subject: Maths
\( \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{5} & \mathbf{5} \boldsymbol{\alpha} & \boldsymbol{\alpha} \\ \mathbf{0} & \boldsymbol{\alpha} & \mathbf{5} \boldsymbol{\alpha} \\ \mathbf{0} & \mathbf{0} & \mathbf{5}\end{array}\right] ; \) If \( \left|\boldsymbol{A}^{2}\right|=\mathbf{2 5}, \) then
\( |\boldsymbol{\alpha}|= \)
A . 5
B \( .5^{2} \)
\( c \cdot 1 \)
\( D \)
\( \therefore \)
Subject: Physics
Figure below shows two paths that may
be taken by a gas to go from a state \( \boldsymbol{A} \)
to a state \( c \)
In process \( A B, 400 J \) of heat is added to
the system and in process \( B C, 100 J \) of
heat is added to the system. The heatt
absorbed by the system in the process
\( A C \) will be
A . \( 500 J \)
B . \( 460 J \)
c. \( 300 J \)
D. \( 380 J \)
Subject: Chemistry
In the following (unbalanced) reaction:
\( \boldsymbol{I}^{-}+\boldsymbol{O}_{3} \longrightarrow \boldsymbol{O}_{2}+\boldsymbol{I}_{2} \)
What is oxidising agent?
\( A \cdot O_{3} \)
B . \( I^{-} \)
c. None
D. Both
Subject: Chemistry
The IUPAC name of the compound is:
\[
\begin{array}{c}
\mathbf{B r}-\mathbf{C H}_{2}-\mathbf{C H}-\mathbf{C O}-\mathbf{C H}_{2}-\mathbf{C H}_{2}-\mathbf{C H}_{\mathbf{3}} \\
\mathbf{C O N H}_{2}
\end{array}
\]
A. 2 - Bromo methyl- 3 - oxo hexanamide
B. 1- Bromo - 2 - amido-3 - oxo - hexane
c. 1 - Bromo - 2 - amido - n- propyl ketone
D. 3 - Bromo - 2 -proponyl - propanamide
Subject: Chemistry
Calcium carbonate decomposes on heating according to the following equation.
\( \boldsymbol{C a} \boldsymbol{C O}_{3}(\boldsymbol{s}) \rightleftharpoons \boldsymbol{C a O}(\boldsymbol{s})+\boldsymbol{C O}_{2}(\boldsymbol{g}) \)
How many moles of \( C O_{2} \) will be
obtained by decomposition of 50 g \( \boldsymbol{C a C O}_{3} ? \)
A. \( \frac{3}{2} \)
в. \( \frac{5}{2} \)
\( c \cdot \frac{1}{2} \)
D.
Subject: Chemistry
Which of the following reactions does
not show the correct products of the
reaction?
\( \mathbf{A} \cdot C H_{3}-C H=C H_{2} \frac{H B r}{\text {Peroxide}} C H_{3}-C H_{2}-C H_{2} B r \)
B \( \cdot C H_{3}-C H=C H_{2} \frac{H C l}{\text {Peroxide}} C H_{3}-C H_{2}-C H_{2} C l \)
C. \( \quad B r \)
\[
C H_{3}-C H=C H_{2} \stackrel{H B r}{\longrightarrow} C H_{3}-C H-C H_{3}
\]
D. \( C H_{3}-C H=C H_{2} \stackrel{H C l}{\longrightarrow} C H_{3}-C H-C H_{3} \)
\( C l \)
Subject: Chemistry
According to Bohr's theory, the energy in
the \( n^{t h} \) orbit is \( \boldsymbol{E}_{\boldsymbol{n}}= \)
\( \frac{-\mathbf{2 . 1 7 6} \times \mathbf{1 0}^{-\mathbf{1 8}} \times Z^{2}}{\mathbf{n ^ { 2 }}} J . \) The longest
wavelength of light that will be needed to remove an electron from the 3 rd orbit
of \( H e^{+} \) ion is:
A \( \cdot \lambda=2055 A^{\circ} \)
B . \( \lambda=2154 A^{\circ} \)
c. \( \lambda=2164 A^{\circ} \)
D . \( \lambda=2004 A^{\circ} \)
Subject: Chemistry
Dry \( N_{2} \) was passed successively
through a solution of solute \( A_{2} B \) in
water at \( 27^{\circ} C \) and then through pure
water. The loss in mass of solution was
\( 2.5 \mathrm{g} \) and that of pure water was \( 0.04 \mathrm{g} \) Find the degree of dissociation of salt
\( A_{2} B \) when solution of \( A_{2} B \) has same concentration as \( 1.86 \% \) (mass/vol)
solution of urea at \( 27^{\circ} C . \) Assume
molarity is equal to molality. Divide answer by 10 and write the nearest integer.
Subject: Chemistry
Which one is the general formula of
monohydric alcohols?
A. \( C_{n} H_{2 n} O H \)
в. \( C_{n+1} H_{2 n} O H \)
c. \( C_{2 n} H_{2 n+2} \) OH
D. \( C_{n} H_{2 n+1} O H \)
Subject: Physics
Two blocks of mass \( m_{1} \) and \( m_{2} \) are
connected by a non deformed light spring on a horizontal table. The coefficient of friction between the
blocks and table is \( \mu \). The minimum
force applied on block 1 which will move the block 2 also is given as \( \mu g\left(m_{1}+\frac{m_{2}}{x}\right) . \) Find \( x \)
Subject: Chemistry
Fluorobenzene \( \left(C_{6} H_{5} F\right) \) can be
synthesized in the laboratory:
A. By heating phenol with \( H F \) and \( K F \)
B. From aniline by diazotization, followed by heating the diazonium salt with \( H B F_{4} \)
c. By direct fluorination of benzene with \( F_{2} \) gas
D. By reacting bromobenzene with \( N a F \) solution
Subject: Physics
Four charges are placed at the
circumference of the dial of a clock as
shown in figure. If the clock has only
hour hand, then the resultant force on a
positive charge \( q_{0} \) placed at the centre,
points in the direction which shows the
time as :-
A . 1: 30
B. 7:30
\( c \cdot 4: 30 \)
D. 10: 30
Subject: Chemistry
The heat of combustion of ethanal
determined in a bomb calorimeter is
\( -670.48 K \) Cals mole\( ^{-1} \) at \( 25^{\circ} \) C.What
is \( \Delta H \) at \( 25^{\circ} C \) for the reaction:
A . \( -335.24 K \) Cals
В. -671.08 КСа\( l s \)
c. \( -670.48 K \) Cals.
D. +670.48 KCals.
Subject: Physics
In the adjoining potentiometer circuit, the resistance of uniform cross section
the potentiometer wire \( A B \) of Length \( 1 \mathrm{m} \)
is \( 10 \Omega . \) When the variable resistance \( R= \)
\( 10 \Omega, \) the balance point is obtained for length I as shown. If the variable resistance is doubled, the new balance
length is
\( A \)
B. \( 1.5 l \)
\( c \cdot 2 l \)
\( D \)
\( \mathbf{?} \)
Subject: Physics
A force of 50 dynes is acted on a body of mass \( 5 g \) which is at rest for an interval
of \( 3 s, \) then impulse is:
A. \( 0.15 \times 10^{-13} \mathrm{Ns} \)
В. \( 0.98 \times 10^{-3} N s \)
\( \mathrm{c} \cdot 1.5 \times 10^{-3} \mathrm{Ns} \)
D. \( 2.5 \times 10^{-3} N s \)
Subject: Maths
\( \int_{0}^{1} \frac{\boldsymbol{d} \boldsymbol{x}}{(1+\boldsymbol{x}) \sqrt{\left(\boldsymbol{2}+\boldsymbol{x}-\boldsymbol{x}^{2}\right)}}=\frac{\mathbf{1}}{\boldsymbol{k}} \sqrt{\mathbf{2}} . \) Finc
the value of \( k \)
Subject: Maths
If \( \left|\begin{array}{lll}a & a^{3} & a^{4}-1 \\ b & b^{3} & b^{4}-1 \\ c & c^{3} & c^{4}-1\end{array}\right|=0 \) and \( a, b, c \) are all
distinct, then \( a b c(a b+b c+c a) \) is
equal to
A. \( a+b+c \)
B. abc
\( c \cdot 0 \)
D. none of these
Subject: Maths
At the college entrance examination each candidate is admitted or rejected according to whether he has passed or failed the tests. Of the candidate who
are really capable, \( 80 \% \) pass the test and of the incapable, \( 25 \% \) pass the test. Given that \( 40 \% \) of the candidates are
really capable, then the proportion of capable college students is about
A . \( 68 \% \)
B. 70\%
c. \( 73 \% \)
D. 75\%
Subject: Maths
The equation of the line passing through \( (-4,3), \) parallel to the \( 3 x+ \) \( \mathbf{7} \boldsymbol{y}+\mathbf{6}=\mathbf{0} \)
A. \( 3 x+7 y-9=0 \)
B. 3x+7y+9=0
c. \( 3 x+7 y+3=0 \)
D. 3x+7y+12=0
Subject: Chemistry
Molecular shape of \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{3}^{+}, \boldsymbol{S} \boldsymbol{F}_{3}^{+} \) and
\( \boldsymbol{C} \boldsymbol{F}_{3}^{+} \) are
A. the same with 2,1 and 0 lone pairs of electrons respectively
B. different with 2, 1 and 0 lone pairs of electrons respectively
c. different with 0,1 and 2 lone pairs of electrons respectively
D. the same with 2,0 and 1 lone pairs of electrons respectively
Subject: Physics
Equal volume of two immiscible liquids of densities \( \rho \) and \( 2 \rho \) are filled in a vessel as shown in the figure. Two small \( \boldsymbol{h} \quad \boldsymbol{3 h} \)
holes are punched at depths \( \frac{-}{2} \) and \( \frac{1}{2} \)
from the surface of lighter liquid. If \( v_{1} \)
and \( v_{2} \) are the velocities of efflux at
these two holes, then \( v_{1} / v_{2} \) is
\( ^{A} \cdot \frac{1}{2 \sqrt{2}} \)
B. \( \frac{1}{2} \)
\( c \cdot \frac{1}{4} \)
D. \( \frac{1}{\sqrt{2}} \)
Subject: Chemistry
Predict which of the following reaction
(s) has a positive entropy change?
।. \( \boldsymbol{A} \boldsymbol{g}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{C l}(\boldsymbol{a} \boldsymbol{q}) \rightarrow \boldsymbol{A} \boldsymbol{g} \boldsymbol{C l}(\boldsymbol{s}) \)
II. \( \boldsymbol{N} \boldsymbol{H}_{\boldsymbol{4}} \boldsymbol{C l}(\boldsymbol{s}) \rightarrow \boldsymbol{N} \boldsymbol{H}_{\boldsymbol{3}}(\boldsymbol{g})+\boldsymbol{H} \boldsymbol{C l}(\boldsymbol{g}) \)
III. \( 2 N H_{3}(g) \rightarrow N_{2}(g)+3 H_{2}(g) \)
A . I and II
в. ॥
c. ॥ and III
D. I
Subject: Biology
The diagram shows a section through
the human heart. Which blood vessels
carry blood to and from the lungs?
A. Blood to lungs - 1 , Blood from lungs - 3
B. Blood to lungs - 1, Blood from lungs - 4
C. Blood to lungs - 2, Blood from lungs - 3
D. Blood to lungs - 2, Blood from lungs - 4
Subject: Maths
The differential equation by eliminating \( A \) and \( B \) from \( y=A x^{3}+B x^{2} \) is
\( ^{\mathbf{A}} \cdot_{x^{2}}\left(\frac{d^{2} y}{d x^{2}}\right)+4 x\left(\frac{d y}{d x}\right)+6 y=0 \)
в. \( x^{2}\left(\frac{d^{2} y}{d x^{2}}\right)-4 x\left(\frac{d y}{d x}\right)-6 y=0 \)
c. \( x^{2}\left(\frac{d^{2} y}{d x^{2}}\right)-4 x\left(\frac{d y}{d x}\right)+6 y=0 \)
D \( x^{2}\left(\frac{d^{2} y}{d x^{2}}\right)-5 x\left(\frac{d y}{d x}\right)+6 y=0 \)
Subject: Maths
Roots of the equation \( \boldsymbol{x}^{3}-(\boldsymbol{a}+\boldsymbol{b}+ \)
\( c) x^{2}+(a b+b c+c a) x-a b c=0 \)
\( x^{2}+2 x+7=0 \) and \( a x^{2}+b x+c=0 \)
have a common root, where \( a, b, c \in R, \) can
be
A .4,8,28
В. 1,2,7
c. 1,4,36
D. None of the above
Subject: Physics
An air bubbles starts rising from the bottom of a lake. Its diameter is \( 3.6 \mathrm{mm} \)
at the bottom and \( 4 \mathrm{mm} \) at the surface.
The depth of the lake is \( 2.5 \mathrm{m} \) and the temperature at the surface is \( 40^{\circ} \mathrm{C} \) then
temperature at the bottom is :
A \( \cdot 25^{\circ} \mathrm{C} \)
в. 20 \( ^{\circ} \) С
\( c \cdot 15^{0} c \)
D. \( 12^{0} \mathrm{C} \)
Subject: Maths
In an examination \( A \) got \( 25 \% \) marks
more than \( \mathrm{B}, \mathrm{B} \) got \( 10 \% \) less than \( \mathrm{C} \) and \( \mathrm{C} \)
got \( 25 \% \) more that \( D \). If \( D \) got 320 marks out of \( 500, \) the marks obtained by \( A \)
were:
A . 450
B. 405
\( c .360 \)
D. 400
Subject: Physics
The radius of a black hole \( \left(R_{B}\right) \) and its
Schwarzschild radius \( \left(R_{S}\right) \) are related
as:
A \( \cdot R_{B}>R_{S} \)
B \( . R_{B} \geq R_{S} \)
\( \mathbf{c} \cdot R_{B} \leq R_{S} \)
D. \( R_{B}=R_{S}=\infty \)
Subject: Chemistry
Consider the following equilibrium in a closed container \( N_{2} O_{4}(g) \rightleftharpoons 2 N O_{2}(g) \)
At a fixed temperature, the volume of the reaction container is halved. For this
change, which of the following statements held true regarding the
equilibrium constant \( \left(\boldsymbol{K}_{\boldsymbol{p}}\right) \) and degree
of dissociation \( (\alpha): \)
A. Neither \( K_{p} \) nor \( \alpha \) changes
B. Both \( K_{p} \) and \( \alpha \) -changes
C. \( K_{p} \) changes, but \( \alpha \) does not change
D. \( K_{p} \) does not change, but \( \alpha \) -changes
Subject: Physics
The initial velocity of a particle is \( u \) (at
\( t=0 \) ) and the acceleration \( a \) is given by
\( \boldsymbol{f} \boldsymbol{t} \)
Which of the following relations is
valid?
A \( \cdot v=u+f t^{2} \)
B . \( v=u+f t^{2} / 2 \)
\( \mathbf{c} \cdot v=u+f t \)
D. \( v=u \)