AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
The equilibrium constant of a reaction at \( 298 K \) is \( 5 \times 10^{-3} \) and at \( 1000 K \) is
\( 2 \times 10^{-5} . \) What is the sign of \( \Delta H \) for
the reaction?
\( \mathbf{A} \cdot \Delta H \) is \( +v e \)
B. \( \Delta H \) is -ve
\( \mathbf{c} \cdot \Delta H \propto 0 \)
D. \( \Delta H \) is \( \pm v e \)
Subject: Physics
The velocity of light in air is \( 3 \times \)
\( 10^{8} m s^{-1} \) and that in water is \( 2.2 \times \)
\( 10^{8} m s^{-1} . \) The polarising angle of
incidence is:
A . 45
B. \( 50^{\circ} \)
c. \( 53.74^{\circ} \)
D. \( 63^{\circ} \)
Subject: Physics
The number of \( U^{238} \) nuclei in a rock
sample is equal to the number of \( \mathrm{Pb}^{206} \)
atoms. The half-life of \( \mathrm{U}^{238} \) is \( 4.5 \times 10^{9} \)
years.The age of the rock is
A \( \cdot 4.5 \times 10^{9} y \)
B. \( 9 \times 10^{9} y \)
C. \( 13.5 \times 10^{9} y \)
D. \( 18 \times 10^{9} y \)
Subject: Chemistry
Where among the following metal
complexes the one which exhibits optical activity is: \( (A A= \) bidentate
ligand; \( X= \) monodentate ligand
A \( \cdot \operatorname{cis}-\left[M A_{4} X_{2}\right] \)
B . trans - [M A \( _{4} X_{2} \) ]
c. \( \operatorname{cis}-\left[M(A A)_{2} X_{2}\right] \)
D. \( \operatorname{trans}-\left[M(A A)_{2} X_{2}\right] \)
Subject: Maths
The term independent of \( x \) in \( (2 x- \) \( \left.\frac{1}{2 x^{2}}\right)^{12} \) is
\( \mathbf{A} \cdot-^{12} C_{3} \cdot 2^{6} \)
B. \( -^{12} C_{5} .2^{2} \)
c. \( 12 C_{6} \)
D. \( ^{12} C_{4} .2^{4} \)
Subject: Chemistry
A mixture containing 2 moles of \( N_{2} \) and
3 moles of \( \boldsymbol{H}_{2} \) gas is brought to equilibrium in a 3 L vessel.lf the molar
concentration of \( N H_{3} \) at equilibrium is
\( 1 / 3 \) mol/L, calculate the \( K_{c} \) for the
formation of \( \boldsymbol{N} \boldsymbol{H}_{2} \cdot \boldsymbol{N}_{2}(\boldsymbol{g})+\boldsymbol{3} \boldsymbol{H}_{2}(\boldsymbol{g}) \rightleftharpoons \)
\( \mathbf{2} \boldsymbol{N} \boldsymbol{H}_{3}(\boldsymbol{g}) \)
Subject: Chemistry
The energy required to break one mole
\( C l-C l \) bonds in \( C l_{2} \) is \( 242 K J m o l^{-1} \)
The longest wavelength of light capable of breaking a single \( C l-C l \) bond is:
\( A .594 n m \)
B. 640 nm
\( c .700 n m \)
D. 494 ит
Subject: Maths
In the given figure, \( \angle \boldsymbol{X}= \)
\( \mathbf{6 2}^{\circ}, \angle \boldsymbol{X} \boldsymbol{Y} \boldsymbol{Z}=\mathbf{5 4}^{\boldsymbol{o}} . \ln \triangle \boldsymbol{X} \boldsymbol{Y} \boldsymbol{Z} \) If YO and
ZO are the bisectors of \( \angle X Y Z \) and
\( \angle X Z Y \) respectively find \( \angle O Z Y \) and
\( \angle Y O Z \)
Subject: Chemistry
The percentage volume of \( C_{3} H_{8} \) in a
mixture of \( C_{3} H_{8}, C H_{4} \) and \( C O \) is 36.5
The volume of \( C O_{2} \) produced when 100
mL of mixture is burnt in excess of \( \boldsymbol{O}_{2} \)
is:
A . \( 273 \mathrm{mL} \)
B. \( 183 \mathrm{mL} \)
\( c .173 \mathrm{mL} \)
D. \( 193 \mathrm{mL} \)
Subject: Physics
The angular velocity of the earth's rotation about its axis is \( \omega . \) An object
weighed by a spring balance gives the same reading at the equator as at height \( h \) above the poles, the value of \( h \)
will be:
\( ^{\mathrm{A}} \cdot \frac{\omega^{2} R^{2}}{g} \)
В. \( \frac{\omega^{2} R^{2}}{2 g} \)
c. \( \frac{2 \omega^{2} R^{2}}{g} \)
D. \( \frac{2 \omega^{2} R^{2}}{3 g} \)
Subject: Maths
If \( R \) is the relation 'less than' from \( A= \)
\{1,2,3,4,5\} to \( B=\{1,4\}, \) the set of
ordered pairs corresponding to \( R \), then the inverse of \( \boldsymbol{R} \) is
A \( \cdot\{(3,1),(3,2),(3,3)\} \)
в. \{(4,1),(4,2),(4,3)\}
c. \{(4,3),(4,4),(4,5)\}
D. \{(1,3),(2,4),(3,5)\}
Subject: Chemistry
An organic compound 'A' produces a gas with brisk effervescence when
sodium bicarbonate is added to it. The
compound 'A' contains same number of carbons as in ethane. The compound 'A' reacts with ethanol to form a sweet
smelling compound 'C' in presence
of conc. \( H_{2} S O_{4} . A \) and \( C \) respectively are
A. ethanoic acid and ethyl ethanoate
B. methanoic acid and ethyl methanoate
c. ethanoic acid and sodium ethanoate
D. methanoic acid and sodium methanoate
Subject: Physics
The fraction of atoms of radioactive
element that decays in 6 days is \( 7 / 8 \) The fraction that decays in 10 days will
be
A. \( \frac{77}{88} \)
в. \( \frac{71}{80} \)
c. \( \frac{31}{32} \)
D. \( \frac{15}{16} \)
Subject: Maths
Write the degree of the differential
equation \( \boldsymbol{x}\left(\frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}\right)^{3}+\boldsymbol{y}\left(\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}\right)^{4}+\boldsymbol{x}^{3}= \)
\( \mathbf{0} \)
Subject: Maths
A hemispherical container with radius \( 6 \mathrm{cm} \) contains \( 325 \mathrm{ml} \) of milk. Calculate
the volume of milk that is needed to fill
the container completely. \( (\pi=3.142) \)
A. \( 147.45 \mathrm{ml} \)
B. \( 127.45 \mathrm{ml} \)
c. \( 137.45 \mathrm{ml} \)
D. None
Subject: Maths
If the roots of cubic equation \( a x^{3}+ \)
\( b x^{2}+c x+d=0 \) are in G.P., then
В \( \cdot c a^{3}=b d^{3} \)
\( \mathbf{c} \cdot a^{3} b=c^{3} d \)
D. \( a b^{3}-c d^{3} \)
Subject: Physics
A coil with 100 turns has an inductance
of \( 0.05 H \) and \( 0.02 A \) current is passed
through it. Flux linked with the coil is
A \( \cdot 10^{-2} W b \)
В \( \cdot 10^{-3} W b \)
\( \mathbf{c} \cdot 10^{-4} W b \)
D. \( 10^{-5} W b \)
Subject: Chemistry
State True or False.
In the purification of bauxite ore as a preliminary step in the production of \( A l \)
\( \left.[\boldsymbol{A l}](\boldsymbol{O H})_{4}\right]^{-} \) can be converted to
\( A l(O H)_{3} \) by passing \( C O_{2} \) through it.
Subject: Chemistry
The energy required to convert all atoms
presents in \( 1.2 g \) magnesium to \( M g^{2+} \)
ions if \( I E . \) and \( I E_{2} \) of magnesium are \( 120 \mathrm{kJ} \) mol \( ^{-1} \) and \( 240 \mathrm{kJ} \) mol\( ^{-1} \)
respectively:
A. \( 18 \mathrm{kJ} \)
J
в. 36 к
c. 360 k.
D. 24 kJ
Subject: Maths
If \( \omega \) is cube root of unity, then \( \boldsymbol{\Delta}=\left|\begin{array}{cccc}\boldsymbol{x}+\mathbf{1} & \boldsymbol{\omega} & \boldsymbol{\omega}^{2} \\ \boldsymbol{\omega} & \boldsymbol{x}+\boldsymbol{\omega}^{2} & \mathbf{1} \\ \boldsymbol{\omega}^{2} & \boldsymbol{1} & \boldsymbol{x}+\boldsymbol{\omega}\end{array}\right|= \)
\( \mathbf{A} \cdot x^{3}+1 \)
B. \( x^{3}+\omega \)
c. \( x^{3}+\omega^{2} \)
D. \( x^{3} \)
Subject: Physics
If you have several \( 2.0 \mu F \) capacitors,
each capable of withstanding 200 volts without breakdown how would you
assemble a combination having minimum number of capacitors and of given equivalent capacitance which capable of withstanding 1000 volts
\( (A) 0.40 \mu F \)
(B) \( 1.2 \mu F, \) capable of withstanding
\( \mathbf{1 0 0 0} \) volts.
Subject: Maths
State True or False:
On subtracting \( \boldsymbol{x}^{\mathbf{3}}-\mathbf{4} \boldsymbol{x}-\mathbf{1} \) from \( \mathbf{3} \boldsymbol{x}^{\mathbf{3}}- \)
\( x^{2}+6, \) the answer is \( 2 x^{3}-x^{2}+4 x+7 \)
A. True
B. False
Subject: Physics
An oscillating circuit contains an inductor of inductance \( 10^{-6} \mathrm{H} \) and two
capacitor each of capacitance \( 5 \times 10^{-6} \)
farad connected in parallel. Then the
resonance frequency of the circuit is
A \( \cdot \frac{10^{5}}{2 \pi} \)
B. \( \frac{10^{5}}{\pi} \)
c. \( \frac{3 \times 10^{5}}{2 \pi} \)
D. \( \frac{\sqrt{2 \times 10^{5}}}{\pi} \)
Subject: Physics
A charge of \( -1 C \) contains \( n \) electrons,
then \( \boldsymbol{n}=? \)
A \( \cdot 6.25 \times 10^{-20} \)
B . \( 6.25 \times 10^{19} \)
c. \( 6.25 \times 10^{18} \)
D. \( 6.25 \times 10^{-19} \)
Subject: Physics
manometer M as shown. The stopcock S
controls the flow of air \( A B \) is dipped into
a liquid whose surface tension is \( \sigma . \) On
opening the stopcock for a while a bubble is formed at \( \mathrm{B} \) and the
manometer level is recorded showing a
difference h in the levels in the two
arms if \( P \) be the density of manometer liquid and \( r \) the radius of curvature of
the bubble then the surface tension \( \sigma \) of
the liquid is given by
\( \mathbf{A} \cdot \rho h r g \)
B. 2 phrg
c. 4 phrg
D. \( \frac{r h \rho g}{4} \)
Subject: Maths
ЭТАТЕМЕNT-1 \( : \lim _{x \rightarrow \alpha} \frac{\sin (f(x))}{x-\alpha}, \) where
\( f(x)=a x^{2}+b x+c, \) is finite and non-
zero, then \( \lim _{x \rightarrow \alpha} \frac{\frac{e^{\frac{1}{f(x)}}-1}{\frac{1}{f(x)}} \text { does not }}{e^{\frac{1}{f(x)}+1}} \)
exist. STATEMENT-2 : \( \lim _{x \rightarrow \alpha} \frac{f(x)}{x-\alpha} \) can take
finite value only when it takes \( \frac{0}{0} \) form.
A. STATEMENT-1 is True, STATEMENT-2 is True STATEMENT-2 is a correct explanation for STATEMEN
B. STATEMENT-1 is True, STATEMENT-2 is True STATEMENT-2 is NOT a correct explanation fo STATEMENT-1
C. STATEMENT-1 is True, STATEMENT-2 is False
D. STATEMENT-1 is False, STATEMENT-2 is True
Subject: Maths
A right circular cone has a base radius of \( r \) and a height of \( h . \) If the radius decrease by 20 percent and the height increase by 10 percent, which of the following is the resulting percent change in the volume of the cone?
A . \( 10 \% \) decrease
B. 12\% decrease
c. 18.4\% decrease
D. \( 29.6 \% \) decrease
Subject: Chemistry
Assertion
STATEMENT 1 (Assertion)- The oxidizing
power is maximum for \( \boldsymbol{H} \boldsymbol{C l O}_{4} \) and
least for HCIO.
Reason
STATEMENT 2 (Reason)-With increase
in oxidation number of chlorine,the
thermal stability of the anion of the oxyacid increases.
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: Physics
Find whether \( \alpha \) - decay or any of the \( \beta- \) decay are allowed for \( _{89}^{226} A c \) Given
masses are:
\( M\left(_{89}^{226} A c\right)=226.028356 a m u \)
\( M\left(_{87}^{222} F r\right)=222.017415 a m u \)
\( M\left(_{90}^{226} T h\right)=226.017388 a m u \)
\( M\left(_{88}^{226} R a\right)=226.025406 a m u \)
\( M\left(_{2}^{4} H e\right)=4.002603 a m u \)
Subject: Physics
A batsman hits a cricket ball which
then rolls on a level ground. After
covering a short distance, the ball
comes to rest. The ball slows to a stop
because:
A. the batsman did not hit the ball hard enough
B. velocity is proportional to the force exerted on the ball
C. there is a force on the ball opposing the motion
D. there is no unbalanced force on the ball, so the ball
would want to come to rest
Subject: Chemistry
\( 25 g \) hydrocarbon of burning with
excess of air produces \( 88 g C O_{2} \) and \( 9 g \)
water. Mass of \( C \) and \( H \) in the
hydrocarbon is:
A. \( C=24 g, H=1 g \)
в. \( C=20 g, H=5 g \)
c. \( C=18 g, H=7 g \)
D. \( C=19 g, H=6 g \)
Subject: Physics
Two spherical bodies of masses \( 2 M \)
and \( M \) and of radii \( 3 R \) and \( R \)
respectively are held at a distance \( 16 R \)
from each other in free space. When they are released, the start approaching
each other due to the gravitational force of attraction, then find
(a) the ratio of their accelerations
during their motion
(b) their velocities at the time of
impact.
Subject: Maths
The equation of hyperbola whose coordinates of the foci are (±8,0) and
the lenght of latus rectum is 24 units, is
A \( \cdot 3 x^{2}-y^{2}=48 \)
в. \( 4 x^{2}-y^{2}=48 \)
c. \( x^{2}-3 y^{2}=48 \)
D. \( x^{2}-4 y^{2}=48 \)
Subject: Chemistry
\( Q \) туре уоит question
в \( \frac{\mathrm{CH}_{3} \mathrm{OH}}{\mathrm{CH}_{3} \mathrm{ONa}} \mathrm{CH}_{3}-\underbrace{\mathrm{I}}_{\mathrm{C}-\mathrm{CH}_{2}}^{\mathrm{CH}_{3}} \frac{\mathrm{H}_{2} \mathrm{O}^{18}}{\mathrm{H}^{+}} \)
\( \begin{array}{cc}\mathbf{C H}_{3} & \mathbf{C H}_{3} \\ \mathbf{C H}_{3}-\mathbf{C}-\mathbf{C H}_{2}, \mathbf{C H}_{3}-\mathbf{C}-\mathbf{C H}_{2} \\ \mid & \mid \\ \mathbf{O H}_{\mathbf{1 8}} \mathbf{O} \mathbf{H} & \mathbf{O H}\end{array} \)
\( \mathrm{CH}_{3}-\frac{\mathrm{CH}_{3}}{\mathrm{C}-\mathrm{CH}_{2}, \mathrm{CH}_{3}-\mathrm{C}-\mathrm{CH}_{2}} \underbrace{\mathrm{CH}_{3}}_{\mathrm{Is}} \mathrm{OH}_{18} \mathrm{OH}_{\mathrm{OH}}^{1 \mathrm{d}} \)
Subject: Maths
The value of
\( \frac{18^{3}+7^{3}+3.18 .7 .25}{3^{6}+6.243 .2+15.81 .4+20.27 .8+15.9 .16+6.3 .32+64} \)
\( A \cdot 4 \)
\( B .3 \)
\( c \cdot 2 \)
D.
Subject: Physics
Consider the following nuclear
reactions:
\( 238 M \longrightarrow_{y}^{x} N+2_{2}^{4} H e \)
\( 92^{B} M \)
\( \boldsymbol{y}^{\boldsymbol{x}} \boldsymbol{N} \longrightarrow_{\boldsymbol{B}}^{\boldsymbol{A}} \boldsymbol{L}+\boldsymbol{2} \boldsymbol{\beta}^{+} \)
the number of neutrons present in the
element ' \( L^{\prime} \) is:
A .142
в. 144
c. 140
D. 146
Subject: Maths
\( A(1,3) \) and \( B(7,5) \) are two opposite
vertices of a square. The equation of a side through \( \boldsymbol{A} \) is
A. \( x+2 y-7=0 \)
В. \( x-2 y+5=0 \)
c. \( 2 x+y-5=0 \)
D. None of these
Subject: Maths
ABCD is a trapezium with \( A B \) and \( C D \) parallel. If \( \mathrm{AB}=\mathbf{6}, \mathrm{BC}=\mathbf{5}, \mathrm{CD}=\mathbf{3}, \mathrm{DA}=\mathbf{4} \)
\( A=90^{\circ} \) the area of \( A B C D \) is?
A .27
B. 12
c. 18
D. 15
Subject: Maths
If \( y= \)
\( (x+\sqrt{x^{2}-a^{2}})^{n} \quad \) then \( \quad\left(x^{2}-a^{2}\right)\left(\frac{d y}{d x}\right. \)
A \( \cdot n^{2} y \)
B. \( -n^{2} y \)
\( c \cdot n y^{2} \)
D \cdot \( n^{2} y^{2} \)
Subject: Physics
Assertion
In a free fall, weight of a body becomes
effectively zero.
Reason
Acceleration due to gravity acting on a body having free fall is zero.
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
A laser used to weld detached retains
emits light with a wavelength 652 nm in
pulses that are of \( 20 m s \) duration. The average power during each pulse is \( 0.6 W . \) The energy in each pulse and in a single photon are :
A \( .7 .5 \times 10^{15} e V, 2.7 e V \)
В . \( 6.5 \times 10^{16} e V, 2.9 e V \)
\( c \cdot 6.5 \times 10^{16} e V, 2.7 e V \)
\( V \)
D. \( 7.5 \times 10^{16} e V, 1.9 e V \)
Subject: Chemistry
Select incorrect statement about
hydrides of group 15 elements:
A. The central atom in the hydride is \( s p^{2} \) hybridised.
B. \( N H_{3} \) readily form \( N H_{4}^{+} \) salts with \( H^{+} ; P H_{4}^{+} \) salts are formed with \( H^{+} \) under anhydrous condition.
C. The tetrahedron is distorted due to repulsion between the lone pair of electrons and the bond pairs.
D. The bond energy of the M-H bond decreases from \( N H_{3} \) to \( B i H_{3} \) because of increase in the size of the element.
Subject: Physics
A heat engine receives 150 Joules of
heat energy and performs 70 Joules of work. If heat loss in the surrounding is zero. Find out by what value does the internal energy of the system change?
A . \( 0 . J \)
B. \( 40 J \)
c. \( 80 J \)
D. \( 120 J \)
E . \( 150 J \)
Subject: Maths
The area of a circle is 314 sq. \( \mathrm{cm} \) and area of its minor sector is 31.4 sq. cm.
Find the area of its major sector.
A \( .282 .6 \mathrm{cm}^{2} \)
в. \( 200.6 \mathrm{cm}^{2} \)
\( \mathbf{c} \cdot 180.04 \mathrm{cm}^{2} \)
D. 1220.09cm \( ^{2} \)
Subject: Physics
The frequency of a fork is 500 Hz. The
velocity of sound in air is \( 350 \mathrm{ms}^{-1} \). The
distance through which sound travels
by the time the fork makes 125 vibrations is
\( \mathbf{A} \cdot 87.5 m \)
B. \( 700 m \)
c. \( 1400 m \)
D. \( 1.75 m \)
Subject: Chemistry
Name the law or principle to which the following observations confirm:
(1) When water is added to a \( 1.0 M \)
aqueous solution of acetic acid, the
number of hydrogen ion \( \left(\boldsymbol{H}^{+}\right) \)
increases.
(2) When 9650 coulombs of electricity is passed through a solution of copper sulphate, \( 3.175 g \) of copper is deposited on the cathode (atomic weight of \( \boldsymbol{C u}= \)
63.5)
(3) When ammonium chloride is added
to a solution of ammonium hydroxide, the concentration of hydroxyl ions
decreases.
Subject: Chemistry
Balance the following equation:
\( \boldsymbol{C u}(\boldsymbol{s})+\boldsymbol{A} \boldsymbol{u}^{\oplus} \longrightarrow \boldsymbol{A u}(\boldsymbol{s})+\boldsymbol{C u}^{2+} \)
\( \mathbf{A} \cdot C u(s)+2 A u^{\oplus} \longrightarrow A u(s)+C u^{2+} \)
B \( \cdot C u(s)+2 A u^{\oplus} \longrightarrow 2 A u(s)+C u^{2+} \)
\( \mathbf{c} \cdot 2 C u(s)+A u^{\oplus} \longrightarrow 2 A u(s)+2 C u^{2+} \)
D \( \cdot 2 C u(s)+A u^{\oplus} \longrightarrow 2 A u(s)+C u^{2+} \)
Subject: Physics
A dipole is placed in a shell as shown
Find the electric flux emerging out of
the shell and in a hypothetical sphere of
radius r as shown.
A. \( \frac{2 q}{8} \)
В \( \cdot \frac{q}{\varepsilon_{0}}, \frac{-q}{\varepsilon_{0}} \)
c. \( \frac{-q}{\varepsilon_{0}}, \frac{q}{\varepsilon_{0}} \)
0.0
Subject: Maths
A scooter going to the east at 10
\( \mathrm{m} / \mathrm{s} \) turns right through an angle of \( 90^{\circ} \)
If the speed of the scooter remains unchanged in taking this turn, the change in the velocity of the scooter is:
A. 20 \( \mathrm{m} / \mathrm{s} \) in south-west direction
B. zero
c. \( 10.0 \mathrm{m} / \mathrm{s} \) in south direction
D. 14.14 m/s in south-western direction
Subject: Chemistry
Study the given figure carefully.
Which of the following reactions explains the above change most appropriately?
A. \( Z n S O_{4}+C u \rightarrow C u S O_{4}+Z n \)
в. \( C u S O_{4}+F e \rightarrow F e S O_{4}+C u \)
c. FeSO\( _{4}+C u \rightarrow \) CuSO\( _{4}+ \) Fe
D. \( C u S O_{4}+Z n \rightarrow Z n S O_{4}+C u \)
Subject: Maths
State whether the following statements are true of false. Justify.
(i) For an arbitrary binary operation \( * \) on as \( \operatorname{set} N, a * a=a \forall a \epsilon N \)
(ii) If \( * \) is a commutative binary
operation on \( N, \) then \( a *(b * c)=(c * \)
\( b) * a \)
A. True
B. False
Subject: Chemistry
Find out \( \mathrm{B} \) in the given process.
A \( \cdot \operatorname{Na}\left[A l(O H)_{4}\right. \)
в. \( N a O H \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{SO}_{4} \)
D. \( A l_{2} O_{3} \)
Subject: Chemistry
The number of coulombs necessary to deposit \( 1 ~ g \) of potassium metal (molar mass \( 39 g m o l^{-1} \) ) from \( K^{+} \) ions is:
A \( \cdot 96500^{\circ} \mathrm{C} \)
B . \( 1.93 \times 10^{50} C \)
\( \mathbf{c} \cdot 1237^{\circ} \mathrm{C} \)
D. 2474 \( ^{\circ} \mathrm{C} \)
Subject: Physics
The variation of PE of a simple harmonic
oscillator is as shown. Then force
constant of the system is (PE 'U' is in
joules, displacement \( ^{\prime} x^{\prime} \) is in \( \mathrm{mm} \) )
A. \( 100 \mathrm{N} / \mathrm{m} \)
B. \( 150 \mathrm{N} / \mathrm{m} \)
c. \( \frac{200}{3} \mathrm{N} / \mathrm{m} \)
D. \( 300 \mathrm{N} / \mathrm{m} \)
Subject: Maths
Let \( A, B, C \) be the subsets of the
universal set \( X \) Let \( A^{\prime} B^{\prime} C^{\prime} \) denote their
complements in X Then which of below
corresponds to the shaded portion in
the given figure
\( \mathbf{A} \cdot A^{\prime} \cap B \cap C \)
B \( \cdot A \cap B^{\prime} \cap C \)
c. \( A \cap B \cap C^{\prime} \)
\( \mathbf{D} \cdot A^{\prime} \cap B^{\prime} \cap C \)
Subject: Physics
a distance \( L \) in front of the centre of a
mirror of width \( d \), hung vertically on a
wall. A man walks in front of the mirror
along a line parallel to the mirror at a
distance \( 2 L \) from it as shown in the
figure. The greatest distance over which
he can see the image of the light source
in the mirror is :
\( \mathbf{A} \cdot d / 2 \)
B. \( d \)
c. \( 2 d \)
D. \( 3 d \)
Subject: Physics
A smooth inclined plane having angle of
inclination \( 30^{\circ} \) with horizontal has a
mass 2.5 kg held by a sprang which is fixed at the upper end as shown in figure. If the mass is taken \( 2.5 \mathrm{cm} \) up along the surface of the inclined plane,
the tension in the spring reduces to zero
If the mass is then released, the angular frequency of oscillation in radian per second is:
A. 0.707
В. 7.07
c. 1.414
D. 14.14
Subject: Chemistry
The electronic configuration of the
starting and ending elements of fourth
period are:
\( \mathbf{A} \cdot 4 s^{1} \) and \( 3 d^{10} 4 s^{2} 4 p^{6} \)
B \( \cdot 4 s^{1} \) and \( 4 s^{2} 3 d^{10} \)
C \( .4 s^{2} 3 d^{1} \) and \( 4 s^{2} 4 p^{6} \)
D. \( 4 s^{2} 3 d^{1} \) and \( 4 s^{2} 3 d^{10} \)
Subject: Chemistry
For the reaction of one-mole zinc dust
with one more sulphuric acid in a bomb
calorimeter, \( \Delta U \) and \( w \) correspond to:
[Hint: In bomb calorimeter, \( \boldsymbol{w}= \)
\( \mathbf{0}, \mathbf{\Delta} \boldsymbol{U}=\boldsymbol{q}(-\boldsymbol{v} e)] \)
A. \( \Delta U, 0, W=0 \)
в. \( \Delta U<0, W<0 \)
c. \( \Delta U>0, W=0 \)
D. \( \Delta U>0, W>0 \)
Subject: Physics
The lowest pressure (the best vaccum) that can be created in laboratory at \( 20^{\circ} \mathrm{C} \) is \( 10^{-10} \mathrm{mm} \) of \( \mathrm{Hg} \). At this
pressure, the number of ideal gas
molecules per \( c m^{3} \) will be
A. \( 3.22 \times 10^{12} \)
B . \( 1.61 \times 10^{12} \)
c. \( 3.29 \times 10^{6} \)
D. \( 3.22 \times 10^{5} \)
Subject: Chemistry
Among \( N a, H g, S, P t \) and graphite, which can be used as electrodes in
electrolytic cells having aqueous solutions?
A. \( H g \) and \( P t \)
в. \( H g, P t \) and graphite
c. \( N a \) and \( S \)
D. \( N a, H g \) and \( S \)
Subject: Physics
The speed of light in two media I and I
are \( 2.2 \times 10^{8} m / s \) and \( 2.4 \times 10^{8} m / s \)
respectively. The critical angle for light refracting from I to II medium will be
A \( \sin ^{-1}\left(\frac{12}{11}\right) \)
(i) \( \left(\frac{1}{1}\right)(1)^{\frac{1}{11}} \)
\( \mathbf{B} \cdot \sin ^{-1}\left(\frac{11}{12}\right) \)
\( \mathbf{c} \cdot \sin ^{-1}\left(\frac{12}{24}\right) \)
\( \mathbf{D} \cdot \sin ^{-1}\left(\frac{12}{21}\right) \)
Subject: Chemistry
Assuming all volumes measured at the same temperature and pressure, state the volume ratio of the reactants and
products when acetylene (ethyne) burning in oxygen to give carbon dioxide and steam.
A .1: 5: 4: 2
B. 2: 5: 2: 2
\( c \cdot 2: 5: 4: 1 \)
D. 2: 5: 4: 2
Subject: Physics
In a gravity free space, a man of mass \( M \) standing at a height \( h \) above the floor throws a stone of mass \( \boldsymbol{m} \)
downwards with a speed \( u . \) When the stone reaches the floor, distance of the
man above the floor will be :
\( A \cdot h \)
B. \( 2 h \)
c. \( _{h}-\frac{2 m h}{M} \)
D. \( \frac{m h}{M}+h \)
Subject: Maths
\( \boldsymbol{x}=\boldsymbol{3} \cos \boldsymbol{\Theta}, \boldsymbol{y}=\boldsymbol{3} \sin \boldsymbol{\Theta}, \boldsymbol{t h e n} \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=? \)
\( A \cdot-\cot \theta \)
B. \( -\sin \theta \)
\( c \cdot \sin \Theta \)
D. \( \tan \theta \)
Subject: Maths
Examine if Rolles theorem is applicable to any of the following functions. Can you say some thing about the
converse of Rolles theorem from these
example?
(i) \( \boldsymbol{f}(\boldsymbol{x})=[\boldsymbol{x}] \) for \( \boldsymbol{x} \in[\mathbf{5}, \boldsymbol{9}] \)
(ii) \( \boldsymbol{f}(\boldsymbol{x})=[\boldsymbol{x}] \) for \( \boldsymbol{x} \in[-\boldsymbol{2}, \boldsymbol{2}] \)
(iii) \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}-1 \) for \( \boldsymbol{x} \in[\mathbf{1}, \boldsymbol{2}] \)
Subject: Chemistry
The magnetic moment of complex ion is
2.83 BM. The complex ion is :
\( \mathbf{A} \cdot\left[V\left(H_{2} O\right)_{6}\right]^{3+} \)
B . \( \left[\operatorname{Cr}\left(\text { Ha }_{2} \text { O }\right)_{6}\right]^{3} \) '
c. \( \left[C u(C N)_{4}\right]^{2} \)
\( \mathbf{D} \cdot\left[M n C l_{4}\right]^{2} \)