AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
During extraction of iron, which of the following reaction(s) exhibit development of elemental impurities in
iron?
This question has multiple correct options
A. \( C a O+S i O_{2} \rightarrow C a S i O_{3} \)
в. \( M n O_{2}+C \stackrel{\Delta}{\longrightarrow} M n+C O \)
\( \mathrm{c} \cdot \mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2} \stackrel{\Delta}{\longrightarrow} P_{4} \mathrm{O}_{10} \frac{\mathrm{C}}{\Delta} P_{4} \)
D. \( \operatorname{si} O_{2}+2 C \stackrel{\Delta}{\longrightarrow} S i+2 C O \uparrow \)
Subject: Chemistry
\( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{6}+\boldsymbol{H}_{2} \boldsymbol{O} \longrightarrow \boldsymbol{I}+\boldsymbol{A} \)
A. \( I: X e O_{3} \)
в. \( I: X e_{2} O_{5} F_{2} \)
c. \( I: X e_{2} O_{3} F_{6} \)
D. None of these
Subject: Maths
If \( 2 x-3 y=7 \) and \( (a+b) x-(a+b-3) y=4 a \)
\( +b \) represent coincident lines then a
and b satisfy the equation
\( A \cdot a+5 b=0 \)
B. \( 5 a+b=0 \)
\( c \cdot a-5 b=0 \)
D. \( 5 a-b=0 \)
Subject: Physics
A boy of height \( 1.5 \mathrm{m}, \) making move on a skateboard due east with velocity \( 4 \mathrm{m} \) s
\( -1, \) throws a coin vertically up with a
velocity of \( 3 \mathrm{m} \mathrm{s}^{-1} \) relative to himself.
a. Find the total displacement of the coin relative to ground till it comes to the hand of the boy.
b. What is the maximum height attained by the coin w.r.t to ground?
Subject: Physics
The velocity-time graph of a particle in one-dimensional motion is shown in the
figure. Which of the following formulae
is correct for describing the motion of
the particle over the time interval \( t_{1} \) to
\( t_{2} ? \)
A \( \cdot x\left(t_{2}\right)=x\left(t_{1}\right)+v\left(t_{1}\right)\left(t_{2}-t_{1}\right)+\left(\frac{1}{2}\right) a\left(t_{2}-t_{1}\right)^{2} \)
B \( \cdot v\left(t_{2}\right)=v\left(t_{1}\right)+a\left(t_{2}-t_{1}\right) \)
C \( \cdot v_{\text {average }}=\frac{\left(x\left(t_{2}\right)-x\left(t_{1}\right)\right)}{\left(t_{2}-t_{1}\right)} \)
D. \( a_{\text {average}}=\frac{\left(v\left(t_{t}\right)+v\left(t_{1}\right)\right)}{\left(t_{2}-t_{1}\right)} \)
Subject: Biology
Consider the following statements:
(i) Genus comprises a group of related species.
(ii) A taxon represents a taxonomic group of individual organism.
(iii) The family comprises a group of related genera.
(iv) Taxonomic category class includes related order.
A. (i), (ii) and (iv) are correct
B. (ii) and (iv) are correct
c. (i), (iii) and (iv) are correct
D. (ii), (iii) and (iv) are correct
Subject: Chemistry
A hydrogen like atom with atomic number \( Z \) is in higher excited state of quantum number 'n'. This excited state
atom can make a transition to the first
excited state by successively emitting two photons of energies \( 10 \mathrm{eV} \) and \( 68.2 \mathrm{eV} \) respectively. Alternatively the atom from the same the same excited
state can make a transition to the 2 nd
excited state by emitting two photons of energies \( 4.25 \mathrm{eV} \) and \( 5.95 \mathrm{eV} \) respectively Calculate the value of \( z \)
Subject: Maths
\( \boldsymbol{g}(\boldsymbol{x})=\lim _{m \rightarrow \infty} \frac{\boldsymbol{x}^{m} \boldsymbol{f}(\boldsymbol{x})+\boldsymbol{h}(\boldsymbol{x})+\boldsymbol{3}}{\boldsymbol{2} \boldsymbol{x}^{m}+\boldsymbol{4} \boldsymbol{x}+\mathbf{1}} \)
when \( x \neq 1 \) and \( g(1)=e^{3} \) such that
\( f(x), g(x) \) and \( h(x) \) are continuous function at \( \boldsymbol{x}=\mathbf{1} \) and \( \boldsymbol{f}(\mathbf{1})-\boldsymbol{h}(\mathbf{1})= \)
\( a(b-g(1)) \) then \( a+b \) is
Subject: Maths
Unit matrix is a diagonal matrix in which all the diagonal elements are unity. Unit matrix of order 'n' is denoted
by \( I_{n}(\text { or } I) \) i.e. \( A=\left[a_{i j}\right]_{n} \) is a unit
matrix when \( \boldsymbol{a}_{\boldsymbol{i} j}=\mathbf{0} \) for \( \boldsymbol{i} \neq \)
\( \boldsymbol{j} \boldsymbol{a} \boldsymbol{n} \boldsymbol{d} \boldsymbol{a}_{i j}=\mathbf{1} \)
A . True
B. False
Subject: Chemistry
Which of the following sets of quantum numbers is correct for an electron in \( 4 f \)
orbital?
\( A \cdot n=4,1=3, m=+4, s=+\frac{1}{2} \)
B. \( n=4,1=4, m=-4, s=+\frac{1}{2} \)
\( c \cdot n=4,1=3, m=+1, s=+\frac{1}{2} \)
D. \( n=4,1=2, m=2, s=+\frac{1}{2} \)
Subject: Chemistry
Q Type your question-
\( \mathbf{2} \boldsymbol{C H}_{3}-\boldsymbol{C} \equiv \boldsymbol{C}-\boldsymbol{H}+\boldsymbol{H} \boldsymbol{C} \equiv \)
\( \boldsymbol{C H} \frac{\text {Red hot}}{\text {tube}} ? \)
\( A \)
B.
\( c \)
\( D \)
Subject: Physics
toppr
-०६॥
Q Type your question_
placed the ends \( (X \text { and } Y) \) of each
object, near the north pole of the bar magnet and recorded his observations
in the table below.
End Y brought End X
Object brought near near
to N pole to N pole
N pole repelled \( \quad \) N pole attracted "
N pole
attracted \( \quad \) N pole repelled
\( \begin{array}{ll}\text { N pole } & \text { N pole remains } \\ \text { remains } & \text { stationary } \\ \text { stationary } & \end{array} \)
Which of the object(s) is/are the magnet?
Bar magnet Object
A. P only
\( c \)
D. P and R only
Subject: Physics
Two identical balls of equal masses \( A \)
and \( \mathrm{B} \) are lying on a smooth surface as shown in figure. Ball A hits the ball B
(which is at rest) with a velocity \( \mathbf{v}=16 \) \( \mathrm{m} / \mathrm{s} . \) What should be the minimum
value of coefficient of restitution
between \( A \) and \( B \) so that \( B \) just reaches
the highest point of inclined plane:
\( \left(g=10 m / s^{2}\right) \)
\( A \cdot \frac{2}{3} \)
B. \( \frac{1}{2} \)
\( c \cdot \frac{1}{3} \)
D.
Subject: Chemistry
0.01 mole of \( N a_{2} C_{2} O_{4} \) dissolve in
alkaline solution. This solution is
titrated with \( \mathrm{V} \mathrm{ml} \) 0.1 \( \boldsymbol{M} \boldsymbol{K} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4} \)
solution. Find out \( V \)
A .200
в. \( \frac{200}{3} \)
c. 40
D. \( \frac{100}{3} \)
Subject: Physics
Assertion
A piece of ice, with a stone frozen inside
it, floats on water in a beaker. When the
ice melts, the level of water in the
beaker decreases.
Reason
Density of stone is more than of water
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
\( A 5^{0} C \) rise is temperature is observed in
a conductor by passing a current, when the current is doubled, the rise in
temperature will be nearly
A \( \cdot 10^{0} \mathrm{C} \)
B . \( 16^{\circ} \mathrm{C} \)
\( c \cdot 20^{0} c \)
D. \( 12^{\circ} \mathrm{C} \)
Subject: Physics
The displacement of a particle along the
\( x \) -axis is given by \( x=a \sin ^{2} t . \) The motion
of the particle corresponds to
A. simple harmonic motion of frequency \( \omega / \pi \)
B. simple harmonic motion of frequency 3 \( \omega / 2 \pi \)
c. non simple harmonic motion
D. simple harmonic motion of frequency \( \omega / 2 \pi \)
Subject: Maths
Based on equations reducible to linear
equations Solve for \( x \) and \( y \frac{1}{3 x}-\frac{1}{7 y}=\frac{2}{3} ; \frac{1}{2 x}- \)
\( \frac{1}{3 y}=\frac{1}{6} \)
A. \( x=1 / 8, y=1 / 2 \)
в. \( x=1 / 3, y=1 / 6 \)
c. \( x=1 / 7, y=1 / 8 \)
D. \( x=1 / 5, y=1 / 7 \)
Subject: Maths
Fifteen coupons are numbered \( 1,2, \ldots . .15 \)
respectively. Three coupons are selected at random without replacement. The probability that the maximum number on the selected coupon is \( 9, \) is
A \( \cdot 4 / 65 \)
в. \( 3 / 65 \)
\( \mathrm{c} \cdot 1 / 13 \)
D. None of these
Subject: Physics
Assertion
The length of the day is slowly increasing.
Reason
The dominant effect causing a
slowdown in the rotation of the earth is
the gravitational pull of other planets in the solar system.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Maths
If the \( p^{t h}, q^{t h} \) and \( r^{t h} \) term of a G.P. are
a,b,c respectively, then \( a^{q-r} \cdot b^{r-p} \cdot c^{p-q} \)
is equal to
A.
B.
\( c \cdot a b c \)
D. par
Subject: Chemistry
\( A \) and \( B \) are two gases. A is identified
with the glass rod dipped in \( N H_{3} \) and \( B \) is identified with the glass rod dipped
in \( H C l . \) Then \( A \) and \( B \) are :
A. \( \mathrm{HCl}, \mathrm{NO}_{2} \)
в. \( \mathrm{HCl}, \mathrm{NH}_{3} \)
c. \( \mathrm{NH}_{3}, \mathrm{HCl} \)
D. \( \mathrm{NH}_{3}, \mathrm{SO}_{2} \)
Subject: Physics
In a metre bridge, the balancing point obtained at \( 40 \mathrm{cm} . \) If a resistance equa
that in the left gap is shunted across it
the new balancing point.
\( A \cdot 20 \mathrm{cm} \)
B. 25 cm
c. \( 30 \mathrm{cm} \)
D. 15 \( \mathrm{cm} \)
Subject: Chemistry
The correct relationship between the boiling points of very dilute solutions of \( A l C l_{3}\left(t_{1}\right) \) and \( C a C l_{2}\left(t_{2}\right), \) having the same molar concentration, is :
A \( \cdot t_{1}=t_{2} \)
В. \( t_{1}>t_{2} \)
c. \( t_{2}>t_{1} \)
D. \( t_{2} \geq t_{1} \)
Subject: Physics
The graph represents a current-voltage
behaviour of a water-voltmeter. Spot the
correct explanation:
A . Dissociation takes place till \( E_{1} \) and it obeys Ohm's law thereafter
B. Ohm's law is not valid for low voltage
c. Ohm's law is obeyed but only for potential difference larger than back emf
D. Electrolytes do not obey ohm's law
Subject: Maths
If \( \boldsymbol{\theta}+\boldsymbol{\phi}=\frac{\boldsymbol{\pi}}{\boldsymbol{4}}, \) then \( (\mathbf{1}+\tan \boldsymbol{\theta})(\mathbf{1}+ \)
\( \tan \phi) \) is equal to
A .
B. 2
\( c \cdot \frac{5}{2} \)
D.
Subject: Physics
The objective and eyepiece of an astronomical telescope are doubled convex lenses with refractive index 1.5
When the telescope is adjusted to infinity, the separation between the two lenses is \( 16 \mathrm{cm} \). If the space between
the lenses is now filled with water and again telescope is adjusted for infinity, then the present separation between the lenses is:
A. \( 8 \mathrm{cm} \)
в. 16 ст
\( c \cdot 24 c m \)
D. 32 ст
Subject: Maths
The length of the chord of the circle \( (x-3)^{2}+(y-5)^{2}=80 \) cut off by the
line \( 3 x-4 y-9=0 \) is
A . 16
B. 8
\( c \cdot \sqrt{96} \)
\( \mathbf{D} \cdot 2 \sqrt{96} \)
Subject: Maths
An ellipse with foci (2,2),(3,-5)
passes through \( (6,-1), \) then its semilatus rectum is:
\( A \cdot \frac{7}{2} \)
в. \( \frac{5}{2} \)
\( c \cdot \frac{9}{2} \)
D. \( \frac{11}{2} \)
Subject: Maths
\( \int_{0}^{1} \frac{\boldsymbol{d} \boldsymbol{x}}{\sqrt{1+\boldsymbol{x}-\sqrt{\boldsymbol{x}}}}= \)
\( A \cdot \frac{2 \sqrt{2}}{3} \)
B. \( \frac{4 \sqrt{2}}{3} \)
\( c \cdot \frac{8 \sqrt{2}}{3} \)
D. None of these
Subject: Maths
The term in dependent of \( x \) in \( \left(1+x+2 x^{3}\right)\left(\frac{3 x^{2}}{2}-\frac{1}{3 x}\right)^{9} \)
A \( \cdot \frac{25}{54} \)
в. \( \frac{17}{54} \)
\( c \cdot \frac{1}{6} \)
D. \( -\frac{17}{51} \)
Subject: Chemistry
Which one of the following is chloropicrin?
\( \mathbf{A} \cdot C C l_{3}-C\left(C H_{3}\right)_{2} \)
\( _{O H} \)
в. \( C C l_{3}-N O_{2} \)
c. \( C H C l_{2}-C H C l_{2} \)
D. \( C C l_{3} \) СНО
Subject: Maths
If \( y \) is a function of \( x, \) then \( \frac{d^{2} y}{d x^{2}}+ \) \( y \frac{d y}{d x}=0 . \) If \( x \) is a function of \( y, \) then the
equation becomes
A \( \cdot \frac{d^{2} x}{d y^{2}}+x \frac{d x}{d y}=0 \)
в. \( \frac{d^{2} x}{d y^{2}}+y\left(\frac{d x}{d y}\right)^{3}=0 \)
c. \( \frac{d^{2} x}{d y^{2}}-y\left(\frac{d x}{d y}\right)^{2}=0 \)
D \( \cdot \frac{d^{2} x}{d y^{2}}-x\left(\frac{d x}{d y}\right)^{2}=0 \)
Subject: Physics
A person moves \( 30 \mathrm{m} \) north, then \( 20 \mathrm{m} \) east, then \( 30 \sqrt{2} \) m south-west. His
displacement from the original position is:
A. 6 m south-west
B. 28 m south
c. \( 10 \mathrm{m} \) west
D. \( 15 \mathrm{m} \) east
Subject: Chemistry
Reaction \( 2 B a O_{2}(s) \rightleftharpoons 2 B a O(s)+ \)
\( O_{2}(g) ; \Delta H=+v e . \) At equilibrium
condition, Pressure of \( O_{2} \) is depends on
A. Increase mass of \( B a O_{2} \)
B. Increase mass of Bao
C. Increase temp. at \( E q^{m} \)
D. Increase mass of \( B a O_{2} \) and Bao both
Subject: Maths
Following table gives frequency distribution of time (in minutes) taken
by a person in watching T.V. on a day.
Time \( \quad \) 30 \( \quad 40 \quad 50 \quad 60 \) ne
in \( \min \)
\( \begin{array}{llll}\text { 40 } & \text { 50 } & \text { 60 } & \text { 70 }\end{array} \)
No. of 19
14
persons
Obtain modal time taken for watching a
T.V. by persons on a day.
A. \( 51.22 . \) minutes
B . 53.22 . minutes
c. 57.22 . minutes
D. \( 59.22 . \) minutes
Subject: Physics
Light of wavelength 589.3 nm is incident normally on a slit of width \( 0 . \) \( \mathrm{mm} . \) The angular width of the central diffraction maximum at a distance of
Im from the slit is
A \( \cdot 0.68 \)
В. \( 0.34^{\circ} \)
\( c .2 .05 \)
D. None of these
Subject: Physics
Assertion
Ultrasonic waves are longitudinal waves of frequency grater than \( 20,000 H z \)
Reason
The maximum frequency of audible sound waves is \( 20,000 H z \)
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 coil in the shape of an equilateral triangles of side I is suspended between the pole pieces of a permanent magnet such that \( \mathrm{B} \) is in plane of the coil. If due to a current i in the triangle, a torque \( \tau \) acts on it, the side I of the triangle is :
\( ^{\mathrm{A}} \cdot \frac{2}{\sqrt{3}}\left(\frac{\tau}{B i}\right)^{1 / 2} \)
в. \( \frac{2}{3}\left(\frac{\tau}{B i}\right) \)
\( ^{c} \cdot\left(\frac{\tau}{\sqrt{3} B i}\right)^{1 / 2} \)
D. \( \frac{1}{\sqrt{3}} \frac{\tau}{B i} \)
Subject: Maths
If one root of the equation \( x^{2}+p x+ \)
\( 12=0 \) is 4 while the equation \( x^{2}+ \)
\( p x+q=0 \) has equal roots, then one
value of \( q \) is
\( \mathbf{A} \cdot \mathbf{3} \)
в. 12
c. \( \frac{49}{4} \)
D. 4
Subject: Chemistry
The statements regarding preparations of ammonia is/are :
(i) Raw materials in cyanamide process are limestone, coke and nitrogen gas.
(ii) On heating nitrogen gas and \( \boldsymbol{C a}(\boldsymbol{O H})_{2}, \boldsymbol{N} \boldsymbol{H}_{3} \) is formed
(iii) In Haber's process \( 100 \% \) yield of
\( N H_{3} \) is possible at \( 500^{\circ} C \) and 250 atm
A. all are correct
B. i and ii
\( c \)
D. i and iii
Subject: Chemistry
The value of \( \wedge_{m}^{\infty} \) for \( K C l \) and \( K N O_{3} \) are
149.86 and \( 154.96 \Omega^{-1} c m^{2} m o l^{-1} \)
respectively. Also \( \lambda_{C l^{-}}^{\infty} \) is 71.44 ohm \( ^{-1} \mathrm{cm}^{2} \) mol \( ^{-1} \). The value of
\( \lambda_{N O_{3}^{-}}^{\infty} \) is :
A \( \cdot 76.54 \) ohm \( ^{-1} \mathrm{cm}^{2} \) mol \( ^{-1} \)
в. 133.08 ohm \( ^{-1} \mathrm{cm}^{2} \mathrm{mol}^{-1} \)
c. 37.7 ohm \( ^{-1} \mathrm{cm}^{2} \) mol \( ^{-1} \)
D. none of the above
Subject: Biology
Anaerobic respiration of
animals/humans produces
A. Glucose and \( \mathrm{O}_{2} \)
B. \( \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH} \) and \( \mathrm{CO}_{2} \)
C. Lactic acid and water
D. \( \mathrm{CO}_{2} \) and \( \mathrm{H}_{2} \mathrm{O} \)
Subject: Chemistry
Ethyl alcohol reacts with thionyl chloride to give:
A \( \cdot C H_{3} C H_{2} C l+H C l \)
в. \( C H_{3} C H_{2} C l+H_{2} O+S O_{2} \)
c. \( C H_{3} C H_{2} C l+H C l+S O_{2} \)
D. \( C H_{3} C H_{2} C l+S O_{2}+C l_{2} \)
Subject: Chemistry
If volume ratio of \( 0.02 M H C l \) and
\( 0.02 M B O H \) (a weak base) mixed to
make \( 200 \mathrm{mL} \) of buffer of \( p H=7 \) is
\( 2.23: X . \) The value of \( X \) is:
\( \boldsymbol{K}_{b} \) for \( \boldsymbol{B O H}=\mathbf{8 . 1} \times \mathbf{1 0}^{-\mathbf{8}} \)
\( A \)
B. 5
\( c \cdot 0.2 \)
D. 2.5
Subject: Chemistry
(i) Write the IUPAC name of the complex
\( \left[\boldsymbol{C r}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4} \boldsymbol{C l}_{2}\right] \boldsymbol{C l} \)
(ii) What type of isomerism is exhibited
by the complex \( \left[C o(e n)_{3}\right]^{3+} ? \) (en = ethane-1,2-diamine)
(iii) Why is \( \left[N i C l_{4}\right]^{2-} \) paramagnetic
but \( \left[N i(C O)_{4}\right] \) is diamagnetic?
(At. Nos. \( : \mathrm{Cr}=24, \mathrm{Co}=27, \mathrm{Ni}=28) \)
Subject: Maths
In figure points \( A, B, C \) and \( D \) are the
centre of four circles that each have a
radius of length one unit. If a point is
selected at random from the interior of
square ABCD.What is the probability
that the point will be chosen from the
shaded region?
A \( \cdot\left(1-\frac{\pi}{4}\right) \)
в. \( \left(1-\frac{\pi}{2}\right) \)
\( c \cdot\left(1-\frac{\pi}{6}\right) \)
D. \( \left(2-\frac{\pi}{4}\right) \)
Subject: Maths
Equation of the curve through the origin satisfying \( \boldsymbol{d} \boldsymbol{y}=(\sec \boldsymbol{x}+\boldsymbol{y} \tan \boldsymbol{x}) \boldsymbol{d} \boldsymbol{x} \) is:
A. \( y \sin x=x \)
B. \( y \cos x=x \)
\( \mathbf{c} \cdot y \tan x=x \)
D. none of these
Subject: Chemistry
Total vapour pressure of mixture of 1 mole of \( \boldsymbol{A}\left(\boldsymbol{P}_{A}^{0}=\mathbf{1 5 0 m m}\right) \) and 2 mole of
B \( \left(P_{B}^{0}=240 m m\right) \) is \( 200 m m . \) In this
case:
A. There is a positive deviation from Raoult's law
B. There is a negative deviation from Raoult's law
c. There is no deviation from Raoult's law
D. Molecular masses of A \& B are also required for calculating deviation
Subject: Maths
fe is the eccentricity of the ellipse \( \frac{x^{2}}{16}+\frac{y^{2}}{25}=1 \) and \( e_{2} \) is the eccentricity
of the hyperbola passing through the foci of the ellipse and \( e_{1} e_{2}=1, \) then equation of the hyperbola is
\( \stackrel{\mathbf{A}}{*} \frac{x^{2}}{9}-\frac{y^{2}}{16}=1 \)
в. \( \frac{x^{2}}{16}-\frac{y^{2}}{9}=-1 \)
c. \( \frac{x^{2}}{9}-\frac{y^{2}}{25}=1 \)
D. \( \frac{x^{2}}{25}-\frac{y^{2}}{9}=1 \)
Subject: Chemistry
Write nuclear reaction equations for:
(i) \( \alpha \) - decay of \( _{88}^{226} R a \)
(ii) \( \alpha \)
decay of \( _{94}^{242} P u\left(\text { iii) } \beta^{-} \text {- decay of }_{15}^{32} P\right. \)
(iv) \( \beta^{-} \) - decay of \( _{83}^{210} B i(v) \beta^{+}- \) decay of \( _{6}^{11} C \)
(vi) \( \beta^{+} \) - decay
of \( _{43}^{97} T c\left(\text { vii) Electron capture of } \frac{120}{54} X e\right. \)
Subject: Maths
The value of \( 2 \frac{1}{2} \times 10-4 \frac{1}{3} \times 10 \) is
A \( \cdot \frac{-3}{55} \)
в. \( \frac{3}{55} \)
c. \( \frac{55}{3} \)
D. \( \frac{-55}{3} \)
Subject: Maths
\( \operatorname{Let} n(A)=n . \) Then the number of all
relations on \( \boldsymbol{A} \) is
\( \mathbf{A} \cdot 2^{n} \)
B \( \cdot 2^{(n)} \)
c. \( 2^{n^{2}} \)
D. none
Subject: Maths
In a parallelgoram \( A B C D, P \) and \( Q \) are midpoints of \( B C \) and \( C D, a r(A P Q) \) will be \( _{\text {- }-\text { - }-\text { - of parallelogram }} \)
A. Equal
B. \( \frac{1}{8} \)
\( c \cdot \frac{1}{4} \)
D. \( \frac{3}{8} \)
Subject: Maths
The absolute minimum \& maximum
values of \( f(x)=\frac{x^{2}-3 x+4}{x^{2}+3 x+4} \) are
respectively
A \( \cdot \frac{1}{7} \) and 7
B. \( 5 \& 7 \)
c. \( \frac{1}{7} \& 1 \)
D. None of these
Subject: Maths
\( f(x)=x+2 \cos x \) is increasing in
A \( \cdot\left(0, \frac{\pi}{2}\right) \)
В \( \cdot\left(\frac{-\pi}{2}, \frac{\pi}{6}\right) \)
c. \( \left(\frac{\pi}{2}, \pi\right) \)
D. \( \left(\frac{-\pi}{2} \frac{\pi}{2}\right) \)
Subject: Chemistry
Lattice energy (numerical value) of choride of alkali metals is in order:
A . LiCI > NaCI>KCI> RbCI> Cscl
B. LiCI<NaCI<KCI<RbCI<CsCI
C. NaCI<KCI <LiCI <RbCI <CsC
D. NaCI<KCI<RbCI<CsCI<Lic
Subject: Chemistry
In the compound \( C o C l_{3} .5 N H_{3} \)
A. all the \( C l \) show primary valency only
B. Two \( C l \) show primary valency and one \( C l \) shows secondary valency
C. Two \( C l \) show primary valency and one \( C l \) shows primary valency as well as secondary valency
D. All the \( C l \) show secondary valency
Subject: Maths
Solve for \( x \) and \( y, \) if \( x+y=7 \) and \( 2 x+ \)
\( 3 y=18 \)
A \( . x=3, y=4 \)
в. \( x=2, y=5 \)
c. \( x=1, y=6 \)
D. \( x=4, y=3 \)
Subject: Physics
A particle of mass \( \mathrm{m} \) is attached to one
end of a massless spring of force
constant \( \mathrm{k}, \) lying on a frictionless horizontal plane. The other end of the spring is fixed. The particle starts moving horizontally from its equilibrium position at time \( t=0 \) with
an initial velocity \( u_{0} . \) When the speed of
the particle is \( 0.5 u_{0} . \) It collides elastically with a rigid wall. After this collision.
This question has multiple correct options
A. The speed of the particle when it returns to its equilibrium position is \( u_{0} \)
B. The time at which the particle passes through the equilibrium position for the first time is \( t=\pi \sqrt{\frac{m}{k}} \)
c. The time at which the maximum compression of the spring occurs is \( t=\frac{4 \pi}{3} \sqrt{\frac{m}{k}} \)
D. The time at which the particle passes through the equilibrium position for the second time is \( t= \) \( \frac{5 \pi}{3} \sqrt{\frac{m}{k}} \)
Subject: Chemistry
Let us consider the ionization of \( H C l \) in
the aqueous solution of \( \boldsymbol{C H}_{3} \) COOH.
\( \boldsymbol{C H}_{3} \boldsymbol{C O O H}+\boldsymbol{H C l} \rightleftharpoons \)
\( \boldsymbol{C H}_{3} \boldsymbol{C O O H}_{2}^{+}+\boldsymbol{C l}^{-} \)
Select the correct statement(s) among
the following:
This question has multiple correct options
A \( \cdot C l^{-} \) is the conjugate base of \( H C l \)
B. \( C H_{3} C O O H \) is the conjugate base of \( C H_{3} C O O H_{2}^{+} \)
C. \( C H_{3} C O O H_{2}^{+} \) is the conjugate base of \( C H_{3} \) COOH
D. \( C l^{-} \) is the conjugate base of \( C H_{3} C O O H \)
Subject: Maths
\( \operatorname{Let} f(x)=\left\{\begin{array}{l}\frac{\sin [x]}{[x]} ;[x] \neq 0 \\ 0 ;[x]=0\end{array}, \) then \right.
\( \lim _{x \rightarrow 0} f(x)= \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( \sin 1 \)
\( c \cdot 2 \)
D. does not exist
Subject: Chemistry
Both of the gas samples represented
above are at the same temperature and
pressure. The mass of \( \boldsymbol{H}_{2} \) in the one
liter container is 0.20 gram. The mass
of \( X \) in the two-liter container is 8
grams. The molecular weight of \( \boldsymbol{X} \) is :
A. \( 10 \mathrm{g} / \mathrm{mol} \)
B. 20 g/mol
c. 40 g/mol
D. \( 60 g / \) mol
E . 80 g/mol
Subject: Physics
A small sphere of radius \( r, \) falls from
rest in a viscous liquid. As a result, heat is produced due to viscous force. The rate of production of heat when the sphere attains its terminal velocity, is proportional to
A \( \cdot r^{5} \)
в. \( r^{3} \)
\( c \cdot r^{4} \)
D \( \cdot r^{2} \)
Subject: Maths
\( (\cos (\log x) d x= \)
\( \mathbf{A} \cdot x[\cos (\log x)-\sin (\log x)]+c \)
B. \( \frac{x}{2}[\cos (\log x)-\sin (\log x)]+c \)
c. \( \frac{\log x}{2}[\cos x+\sin x]+c \)
D \( \cdot \frac{x}{2}[\cos (\log x)+\sin (\log x)]+c \)
Subject: Physics
In the Ingen Hausz's experiment, the wax melts up to lengths \( 10 \mathrm{cm} \) and
\( 25 c m \) on two identical rods of different
materials. The ratio of thermal conductivities of the two materials is
A . 1: 6.25
B. 6.25: 1
c. \( 1: \sqrt{2.5} \)
D. 1: 2.5
Subject: Physics
negligible mass rests on a horizontal
plane as known. The diameter of the
base is \( a \) and the side of the cylinder
makes an angle \( \theta \) with the horizontal.
Water is then slowly poured into the
cylinder. The cylinder topples over when
the water reaches a certain height \( h \)
given by.
A \( . h=2 a \tan \theta \)
B \( \cdot h=a \tan ^{2} \theta \)
\( \mathbf{c} \cdot h=a \tan \theta \)
D. \( h=\frac{a}{2} \tan \theta \)