AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Which of the following is not a true
statement about detergents?
A. Anionic detergents are sodium salts of sulphonated long chain alcohols or hydrocarbons.
B. Cationic detergents are quarternary ammonium salts of amines with acetates, chlorides or bromides as
ions.
C. Non-ionic detergents do not contain any ion in their constitution.
D. Detergents containing branched hydrocarbon chains are biodegradable.
Subject: Maths
\( \operatorname{Let} \boldsymbol{f}(\boldsymbol{x})=\mathbf{1}+\mathbf{2} \boldsymbol{x}^{2}+\mathbf{2}^{2} \boldsymbol{x}^{\boldsymbol{4}}+\ldots \ldots+ \)
\( 2^{10} x^{20} . \) Then \( f(x) \) has
A. more than one minimum
B. exactly one minimum
c. at least one maximum
D. none of these
Subject: Maths
State the following statement is True or
False
The digit at ten's place of a two digit number exceeds the square of digit at units place \( (x) \) by 5 and the number formed is \( 61, \) then the equation is
\( \mathbf{1 0}\left(\boldsymbol{x}^{2}+\mathbf{5}\right)+\boldsymbol{x}=\mathbf{6 1} \)
A. True
B. False
Subject: Maths
\( \cos ^{-1}\left(\cos \left(\frac{7 \pi}{5}\right)\right) \) is equal to
\( A \cdot \frac{3 \pi}{5} \)
B. \( \frac{2 \pi}{5} \)
\( c \cdot \frac{-7 \pi}{5} \)
D. \( \frac{7 \pi}{5} \)
E \( \cdot \frac{-2 \pi}{5} \)
Subject: Maths
Consider the line \( x=\sqrt{3} y \) and the
circle \( x^{2}+y^{2}=4 \)
What is the area of the region in the first quadrant enclosed by the y-axis, the line \( x=\sqrt{3} \) and the circle?
A \( \cdot \frac{2 \pi}{3}+\frac{\sqrt{3}}{2} \)
B \( \cdot \frac{\pi}{2}-\frac{\sqrt{3}}{2} \)
c. \( \frac{\pi}{3}-\frac{1}{2} \)
D. None of the above
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{lll}\mathbf{0} & \mathbf{0} & \mathbf{1} \\ \mathbf{0} & \mathbf{1} & \mathbf{0} \\ \mathbf{1} & \mathbf{0} & \mathbf{0}\end{array}\right], \) then
This question has multiple correct options
A. AdjA is zero matrix
B.
\[
A d j A=\left[\begin{array}{ccc}0 & 0 & -1 \\ 0 & -1 & 0 \\ -1 & 0 & 0\end{array}\right]
\]
\( \mathbf{c} \cdot A^{-1}=A \)
D. \( A^{2}=I \)
Subject: Physics
If the equations of alternating voltage and alternating current in an A.C. circuit
\( \operatorname{are} \boldsymbol{E}=\boldsymbol{E}_{0} \sin \omega \boldsymbol{t} \) volt and \( \boldsymbol{I}= \)
\( I_{0} \sin (\omega t-\pi / 2) \) ampere
respectively. The power loss in the circuit will be
A . zero
в. \( \frac{E_{0} I_{0}}{\sqrt{2}} \)
c. \( \frac{E_{0} I_{0}}{2} \)
D. \( \frac{E I}{\sqrt{2}} \)
Subject: Maths
If \( 8 \tan A=15, \) then the value of \( \frac{\sin A-\cos A}{\sin A+\cos A} \) is:
A \( \cdot \frac{7}{23} \)
в. \( \frac{11}{23} \)
c. \( \frac{13}{23} \)
D. \( \frac{17}{23} \)
Subject: Chemistry
The boiling points of methanol, water
and dimethyl ether are \( 338 \mathrm{K}, 373 \mathrm{K} \) and
\( 307.5 \mathrm{K} \) respectively.Which one of the following statements gives the best explanation for these wide variations in
b.p.?
A. The molecular mass increases from water (18) to methanol
(32) to diethyl ether (74)
B. The extent of intermolecular H-bonding decreases from water to methanol and it is absent in ether
c. The extent of intramolecular H-bonding decreases from ether to methanol to water.
D. The density of water is greater than that of methanol which is in turn less than dimethyl ether
Subject: Chemistry
Assertion
The aqueous solution of \( F e C l_{3} \) is basic
in nature.
Reason
FeCl \( _{3} \) hydrolyses in 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. Reason is correct but Assertion is incorrect
D. Both Assertion and Reason are incorrect
Subject: Physics
Brass scale of a Barometer gives
correct reading at \( 0^{\circ} \mathrm{C} \). coefficient of
linear expansion of brass is \( 18 \times \) \( 10^{-6} /^{-6} \mathrm{C} . \) If the barometer reads
\( 76 \mathrm{cm} \) at \( 20^{\circ} \mathrm{C}, \) the correct reading is
\( \left(\gamma_{\mathrm{Hg}}=18 \times 10^{-5} / 0 \mathrm{C}\right) \)
A. \( 76.426 \mathrm{cm} \)
B. \( 75.7 \mathrm{cm} \)
c. \( 76.2736 \mathrm{cm} \)
D. \( 76.264 \mathrm{cm} \)
Subject: Physics
The average distance between Earth and the Sun is \( 1.496 \times 10^{8} k m \) and the
speed of light coming from the Sun is \( 3 \times 10^{8} m / s . \) How much time will it
take for Sun's rays to reach Earth?
A. 3 min
B. \( 498.66 s \)
c. \( 8 \min 30 s \)
D. \( 554 s \)
Subject: Chemistry
The reaction, \( \boldsymbol{A}+\boldsymbol{O} \boldsymbol{H}^{-} \rightarrow \) Products
obeys rate law expression as:
\( \frac{-\boldsymbol{d}[\boldsymbol{A}]}{\boldsymbol{d} \boldsymbol{t}}=\boldsymbol{k}[\boldsymbol{A}]\left[\boldsymbol{O H}^{-}\right] \)
If initial concentrations of \( [A] \) and
\( \left[\boldsymbol{O} \boldsymbol{H}^{-}\right] \) are \( \boldsymbol{0 . 0 0 2} \boldsymbol{M} \) and \( \boldsymbol{0 . 3} \boldsymbol{M} \)
respectively and if it take 30 sec for \( 1 \% \)
\( A \) to react at \( 25^{\circ} \mathrm{C} \), calculate the rate
constant for the reaction.
Subject: Chemistry
\( \boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{A} \boldsymbol{X}+\boldsymbol{B} \boldsymbol{Y} \longrightarrow \boldsymbol{H} \boldsymbol{A}+\boldsymbol{O} \boldsymbol{Y}+ \)
\( \boldsymbol{X}_{2} \boldsymbol{B} \)
In the above-unbalanced redox
reaction, the oxidation number of \( \boldsymbol{X} \) is
-2 and neither \( X \) nor water is involved
in the redox process. If the above reaction is balanced with
the smallest whole-number
coefficients, the sum of the
stoichiometric coefficients of all the
compounds is :
\( A \cdot 9 \)
B. 8
\( c .7 \)
D. 6
Subject: Physics
In hydrogen atom the electron is
making \( 6.6 \times 10^{15} \) rev/s around the
nucleus of radius 0.53 A. The magnetic field produced at the centre of the orbit is nearly
A. \( 0.12 W b / m^{2} \)
в. \( 1.2 \mathrm{Wb} / \mathrm{m}^{2} \)
c. \( 12 W b / m^{2} \)
D. \( 120 W b / m^{2} \)
Subject: Physics
A step up transformer operates on a
\( 230 V \) line and supplies to a load \( 2 A \)
The ratio of primary to secondary
windings is \( 1: 25 . \) Determine the
primary current.
A . \( 8.8 A \)
B . \( 12.5 A \)
c. \( 25 A \)
D. \( 50 A \)
Subject: Chemistry
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{O H} \frac{\text {SOCI}_{2} \boldsymbol{P}_{\boldsymbol{y} \boldsymbol{r i d i n e}}}{\boldsymbol{\}} \)
Ethanol
What will be the major organic product of the reaction?
Subject: Chemistry
Latent heat of vaporization of liquid at
\( \mathbf{5 0 0} \boldsymbol{K} \) and \( \mathbf{1} \) atm pressure is \( 10 \mathrm{kcal} / \) mol. What is the change in internal energy when 3 moles of the liquid is vaporized at the same
temperature?
A . \( 27 \mathrm{kcal} \)
B. \( 7 k c a l \)
c. 33 k call \( l \)
Subject: Physics
The position \( x \) of a particle with respect
to time \( t \) along \( x- \) axis is given by \( x= \)
\( 9 t^{2}-t^{3} \) where \( x \) is in metres and \( t \) in
seconds. What will be the position of this particle when it achieves
maximum speed along the \( +x \)
direction?
A . \( 24 m \)
в. 32 т
\( \mathrm{c} .54 \mathrm{m} \)
D. \( 81 m \)
Subject: Physics
A long straight wire of circular crosssection is made of a non-magnetic material. The wire is of radius a.The
wire carries a current \( I \) which is
uniformly distributed over its cross-
section. The energy stored per unit length in the magnetic field contained within the wire is
\( \mathbf{A} \cdot u=\frac{\mu_{0} I^{2}}{8 \pi} \)
B. \( U=\frac{\mu_{0} I^{2}}{16 \pi} \)
\( ^{\mathbf{C}} \cdot U=\frac{\mu_{0} I^{2}}{4 \pi} \)
D. \( U=\frac{\mu_{0} I^{2}}{2 \pi} \)
Subject: Physics
\( 150 g \) of ice is mixed with \( 100 g \) of water
at temperature \( 80^{\circ} \mathrm{C} \). The latent heal of
ice is 80 cal \( / g \) and the specific heat of
water is 1 cal \( / g^{\circ} \) C. Assuming no heat loss to the environment, the amount of
ice which does not melt is :
A. \( 100 g \)
в. \( 0 g \)
c. \( 150 g \)
D. \( 50 g \)
Subject: Physics
A converging lens of focal length \( f \) is
used as simple microscope. If the least distance of distinct version of the
observer is \( D \) and the lens is held close
to the eye, the magnifying power of the lens is
A. \( D / 2 f \)
B. \( f / D \)
c. \( \frac{D}{f}-1 \)
D. \( D / f \)
Subject: Biology
Which of these are examples of evolution by anthropogenic action?
(i) Adaptive radiation of marsupials of
Australia.
(ii) Appearance of antibiotic resistant
microbes.
(iii) Evolution of finches in Galapagos islands.
(iv) Appearance of dark winged moth in England during post industrialisation period.
(v) Convergent evolution of placental mammals in Australia.
A. (i) and (ii)
B. (v) only
c. (ii) only
D. (ii) and (iv) only
E. (iii) and (v) only
Subject: Maths
For \( x, t \in R \) let
\( \boldsymbol{p}_{1}(\boldsymbol{x})=(\sin t) \boldsymbol{x}^{2}-(2 \cos \boldsymbol{t}) \boldsymbol{x}+\sin \boldsymbol{t} \)
be a family of quadratic polynomials in \( x \) with variable co efficients. Let \( A(t)= \) \( \int_{0}^{1} p_{t}(x) d x . \) Which of the following
statements are true?
(I) \( A(t)<0 \) for all \( t \)
(II) \( A(t) \) has infinitely many critica points.
(III) \( A(t)=0 \) for infinitely many t.
(IV) \( A^{\prime}(t)<0 \) for all \( t \)
A. (I) and (II) only
B. (II) and (III) only
C. (III) and (IV) only
\( D \cdot(I V) \) and (1) only
Subject: Chemistry
In the reaction, \( \boldsymbol{C r} \boldsymbol{O}_{\boldsymbol{5}}+\boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \rightarrow \)
\( \boldsymbol{C r}_{2}\left(\boldsymbol{S O}_{4}\right)_{3}+\boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{O}_{2}, \) one mole of
\( C r O_{5} \) will liberate how many moles of
\( O_{2} ? \)
A. \( 5 / 2 \)
B. 5/4
\( c \cdot 9 / 2 \)
D. None of the above
Subject: Maths
A point is moving on \( y=4-2 x^{2} \). The \( x \)
coordinate of the point is decreasing at the rate of 5 units per second. Then the rate at which y-coordinate of the point
is changing when the point is at (1,2)
is.
A . 5 units/sec
B. 10 units/sec
c. 15 units/sec
D. 20 units/sec
Subject: Physics
A body is projected horizontally from the top of a tower with initial velocity
\( 18 m s^{-1} . \) It hits the ground at angle \( 45^{\circ} \)
What is the vertical component of velocity when strikes the ground?
B. \( 18 m s^{-1} \)
\( \mathrm{D} \cdot 9 \mathrm{ms}^{-1} \)
Subject: Physics
A parachutist with total weight \( 75 k g \) drops vertically onto a sandy ground with a speed of \( 2 m s^{-1} \) and comes to a
halt over a distance of 0.25 m. The
average force from the ground on her is close to
\( \mathbf{A} \cdot 600 N \)
в. \( 1200 N \)
c. \( 1350 N \)
D. \( 1950 N \)
Subject: Physics
A cylindrical vessel of cross-sectional area, \( s \), is left out in the rain in which
water is falling vertically downward
with the velocity, \( v, \) in the still air. When the wind starts blowing in North-East
direction with velocity, \( v, \) the rate of collection of water in the vessel is
A . \( v . s \)
В. \( \sqrt{2} v . s \)
c. \( 2 v . s \)
D. \( 2 \sqrt{2} v . s \)
Subject: Physics
The displacement \( x \) of a particle varies
with time \( t \) as \( x=a e^{-\alpha t}+b e^{\beta t}, \) where
\( a, b, \alpha \) and \( \beta \) are positive constants. The velocity of the particle will
A. be independent of \( \alpha \) and \( \beta \)
B. drop to zero when \( \alpha=\beta \)
c. go on decreasing with time
D. go on increasing with time
Subject: Maths
What will be the area of the field
\( A B G F E A ? \)
\( \mathbf{A} \cdot 7225 m^{2} \)
B. \( 8225 \mathrm{m}^{2} \)
\( c \cdot 6225 m^{2} \)
D. \( 6725 m^{2} \)
Subject: Physics
A transparent cube contains a small air bubble. Its apparent is \( 2 \mathrm{cm} \) when seen
through one face and \( 5 \mathrm{cm} \) when seen through other face. If the refractive
index of the material of the cube is 1.5
the real length of the edge of cube must
be
A. \( 7 \mathrm{cm} \)
B. \( 7.5 \mathrm{cm} \)
c. \( 10.5 \mathrm{cm} \)
D. \( \frac{14}{3} \mathrm{cm} \)
Subject: Physics
The instantaneous potential difference
between points \( A \) and \( B \) is :
A \( \cdot 8 \sin \left(50 \pi t+37 \frac{\pi}{180}\right) \)
B \( \cdot 8 \sin \left(50 \pi t-37 \frac{\pi}{180}\right) \)
c. \( 10 \sin (50 \pi t) \)
D. \( 10 \cos (50 \pi t) \)
Subject: Maths
\( A B C \) is a triangle, the point \( P \) is on side \( B C \) such that \( 3 \overrightarrow{B P}=2 \overrightarrow{P C} \), the
point \( Q \) is on the line \( \overrightarrow{C A} \) such that \( 4 \overrightarrow{C Q}=\overrightarrow{Q A} . \) If \( R \) is the common point of \( \overrightarrow{A P} \& \overrightarrow{B Q}, \) then the ratio in which the line joining \( \boldsymbol{C} \boldsymbol{R} \) divides \( \overrightarrow{\boldsymbol{A}} \boldsymbol{B} \) is
A .2: 5
B. 3: 8
c. 4: 1
D. 6: 1
Subject: Physics
Each of the resistors shown in Figure
has resistance \( R \). Find the equivalent
resistance between \( A \) and \( B \)
\( ^{A} \cdot \frac{7 R}{4} \)
в. \( \frac{5 R}{4} \)
c. \( \frac{9 R}{4} \)
D. \( \frac{11}{4} \)
Subject: Chemistry
When \( 4 A \) of current is passed through a \( \mathbf{1} . \mathbf{0} \boldsymbol{L}, \mathbf{0 . 1 0} \boldsymbol{M} \boldsymbol{F} \mathbf{e}^{\mathbf{3}+}(\mathbf{a q}) \) solution for \( \mathbf{1} \boldsymbol{h} \)
it is partly reduced to \( F e(s) \) and partly
of \( F e^{2+}(a q) \)
Identify the correct statement(s).
This question has multiple correct options
A. 0.10 mole of electrons are required to convert all \( F e^{3+} \) to \( F e^{2} \)
B. 0.025 mol of \( F e(s) \) will be deposited.
c. 0.075 mol of iron remains as \( F e^{2} \)
D. 0.050 mol of iron remains as \( F e^{2} \)
Subject: Chemistry
Select the correct IUPAC name for \( \left[\left(\mathrm{NH}_{3}\right.\right. \)
\( \left.\mathrm{T}_{4} \mathrm{Co}(\mathrm{OH})\left(\mathrm{NH}_{2}\right) \mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4}\right]^{4+} \)
A. \( \mu \text { -Amido- } \mu \text { -hydroxidobis (tetraammine cobalt }(4+)) \)
in
B. \( \mu \) -Amido- \( \mu \) -hydroxidobis (tetraarnmine cobalt(III)) ion
c. \( \mu \) -t-Amido- \( \mu \) -hydroxidobis (tetraarnmine cobaltate
\( (4+)) \) ion
D. \( \mu \) -Amido- \( \mu \) -hydroxidobis (tetraarnmine cobaltate (III))) ion
Subject: Physics
For a given prism \( \theta \) and \( \delta \) are angular dispersion and deviation correct
relation is
\( \mathbf{A} \cdot \theta \propto \delta \)
B \( \cdot \theta \propto \frac{1}{\delta} \)
c. \( \theta \propto \delta^{2} \)
D. \( \theta \alpha \propto \frac{1}{\delta^{2}} \)
Subject: Chemistry
Match the four starting materials (P, Q,
R, S) given in List I with the corresponding reaction schemes (I, II, III, IV) provided in List II and select the correct answer using the code given below the lists.
A. P-1, Q- 4, R- 2, S- 3
B. P- 3, Q-1,R- 4, S-2
c. \( P-3, Q-4, R-2, S-1 \)
D. P- \( 4,0-1, R-3, S-2 \)
Subject: Maths
\( \int \frac{3 x+1}{(x-1)^{2}(x+3)} d x= \)
A. \( \log \left|\frac{x-1}{x+3}\right|-\frac{1}{x-1}+c \)
в. \( \frac{1}{2} \log \left|\frac{x-1}{x+3}\right|-\frac{1}{x-1}+c \)
c. \( \frac{1}{2} \log \left|\frac{x-1}{x+3}\right|+\frac{1}{x+1}+c \)
D. \( \frac{1}{2} \log \left|\frac{x+1}{x-3}\right|+\frac{1}{x+1}+c \)
Subject: Maths
A cylinder and \( a \) cone have equal bases.
The height of the cylinder is \( 3 \mathrm{cm} \) and
the area of its base is \( 100 \mathrm{cm}^{2} \). The cone
is placed upon the cylinder. Volume of
the solid figure so formed is \( 500 \mathrm{cm}^{3} \)
Find the total height (in \( c m \) ) of the
figure.
Subject: Physics
A metal wire of linear mass density of
\( 9.8 g m \) is stretched with a tension of
10 kg \( -w t \) betweentwo rigid supports 1
metre apart. The wire passes at its middle point between the poles of aper magnet and it vibrates in resonance when carrying an alternating current of frequency \( n \).The frequency nof the alternating source is
\( \mathbf{A} \cdot 50 H z \)
в. \( 100 H z \)
c. \( 200 H z \)
D. \( 25 H z \)
Subject: Chemistry
Following are the thermochemical
reactions:
\( \boldsymbol{H}_{2}+\frac{1}{2} \boldsymbol{O}_{2} \rightarrow \boldsymbol{H}_{2} \boldsymbol{O} ; \boldsymbol{\Delta} \boldsymbol{H}=-\boldsymbol{6} \boldsymbol{8} . \boldsymbol{3} \boldsymbol{9} \)
kcal/mol
\( \boldsymbol{K}+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \boldsymbol{K} \boldsymbol{O} \boldsymbol{H}(\boldsymbol{a} \boldsymbol{q})+ \)
\( \frac{1}{2} H_{2} ; \Delta H=-48.0 \mathrm{kcal} / \mathrm{mol} \)
\( K O H+H_{2} O \rightarrow K O H(a q) ; \Delta H= \)
\( -14.0 \mathrm{kcal} / \mathrm{mol} \)
The heat of formation (in kcal/mol) of
KOH is:
A. \( -68.39+48-14.0 \)
B. \( -68.39-48.0+14.0 \)
c. \( +68.39-48.0+14 . \)
D. \( +68.39+48.0-14.0 \)
Subject: Maths
The equation of the plane containing the line \( \frac{x+1}{-3}=\frac{y-3}{2}=\frac{z+2}{1} \)
and the point (0,7,-7) is
A. \( x+y+z=0 \)
в. \( x+y+z=2 \)
c. \( x+y+z=1 \)
D. None of these
Subject: Chemistry
\( \boldsymbol{N} \boldsymbol{i}\left|\boldsymbol{N} \boldsymbol{i}^{2+} \| \boldsymbol{C} \boldsymbol{u}^{2+}\right| \boldsymbol{C} \boldsymbol{u} \)
The standard EMF of the above cell is
\( 0.59 \mathrm{V} . \) The standard electrode potential (reduction potential) of the copper electrode is 0.34 V. Calculate the
standard electrode potential of nicke
electrode.
A . \( -0.5 V \)
B. \( 0.25 V \)
c. \( 0.93 V \)
D. - \( 0.25 V \)
Subject: Chemistry
Gypsum on heating gives:
This question has multiple correct options
\( ^{\mathbf{A}} \cdot \operatorname{CaSO}_{4} \cdot \frac{1}{2} H_{2} O \)
B \( \cdot C a S O_{4} \)
\( \mathbf{c} \cdot C a O \)
\( \mathbf{D} \cdot C a S+O_{2} \)
Subject: Maths
If the standard deviation of \( n \)
observations \( x_{1}, x_{2}, \dots, x_{n} \) is 4 and
another set of \( n \) observations
\( \boldsymbol{y}_{1}, \boldsymbol{y}_{2}, \dots, \boldsymbol{y}_{n} \) is \( 3 . \) The standard deviation
of \( n \) observations \( x_{1}-y_{1}, x_{2}- \)
\( \boldsymbol{y}_{2}, \dots, \boldsymbol{x}_{\boldsymbol{n}}-\boldsymbol{y}_{n} \) is
A . 1
в. \( \frac{2}{\sqrt{3}} \)
\( c .5 \)
D. data insufficient
Subject: Physics
A car starts from rest and accelerates
uniformly over a time of 5.21 seconds
for a distance of \( 110 \mathrm{m} . \) Determine the acceleration of the car.
\( \mathbf{A} \cdot 8.10 m / s / s \)
В. \( 8.1 m / s / s \)
c. \( 8.0 m / s / s \)
D. \( 7.10 m / s / s \)
Subject: Physics
A resistance of \( \mathrm{R} \Omega \) draws current from
a potentiometer as shown in the figure.
The potentiometer has a total
resistance \( R_{0} \Omega . \) A voltage \( V \) is supplied
to the potentiometer. Derive an
expression for the voltage across \( \mathrm{R} \) when the sliding contact is in the
middle of the potentiometer.
Subject: Physics
If a dip circle is placed in a vertical
plane at an angle of \( 30^{\circ} \) to the magnetic meridian, the dip needle makes an angle of \( 45^{\circ} \) with the horizontal. The real
dip at that place is?
A \( \cdot \tan ^{-1}(\sqrt{3} / 2) \)
B. \( \tan ^{-1}(\sqrt{3}) \)
C \( \cdot \tan ^{-1}(\sqrt{3} / \sqrt{2}) \)
D \cdot \( \tan ^{-1}(2 / \sqrt{3}) \)
Subject: Maths
\( \ln \) a \( \Delta A B C, i f \angle A=\angle B+ \)
\( \angle C \) then \( \angle A=\dots \dots \dots \)
A . \( 60^{\circ} \)
B . \( 45^{\circ} \)
\( c .90^{\circ} \)
D. none
Subject: Chemistry
Soap was never actually discovered but instead gradually evolved from crude mixtures of alkaline and fatty material
Up to \( 1800, \) soap was believed to be a mechanical mixture of fat and alkali,
then Chevreul, a French chemist showed that soap formation, was actually a chemical reaction.
Which one of the following follows from
the above statement?
A. Chevreul discovered the process of soap making
B. Alkaline and fatty material, both being natural material, their mixture which is used as soap is still natural materials mixture
c. Soap is a natural product, whose existence was later established
D. Crude mixing of alkaline and fatty material in early days was actually chemical process of formation of soap
Subject: Physics
Biogas is a mixture of:
\( \mathbf{A} \cdot S O_{2}+H_{2} S \)
B \( \cdot O_{2}+C O_{2}+O_{3} \)
\( \mathbf{c} \cdot C O_{2}+C H_{4}+N_{2}+H_{2} S \)
D. \( N O_{2}+H_{2}+C O_{2} \)
Subject: Chemistry
Passing \( \boldsymbol{H}_{2} \boldsymbol{S} \) gas into a mixture of \( M n^{2+}, N i^{2+}, C u^{2+} \) and \( H g^{2+} \) ions in
an acidified aqueous solution precipitates.
A. CuS and Hgs
B. MnS and cus
c. Mns and Nis
D. Nis and Hgs
Subject: Physics
if \( L=2.331 c m, B=2.1 c m, \) then \( L+B= \)
A. \( 4.431 \mathrm{cm} \)
в. \( 4.43 \mathrm{cm} \)
c. \( 4.5 \mathrm{cm} \)
D. \( 4.2 \mathrm{cm} \)
Subject: Chemistry
What are the conditions for an ideal
solution which obeys Raoult's law over
the entire range of concentration?
A \( \cdot \Delta_{m i x} H=0, \Delta_{m i x} V=0, P_{\text {Total}}=p_{A}^{o} x_{A}+p_{B}^{o} x_{B} \)
B. \( \Delta_{\operatorname{mix}} H=+v e, \Delta_{\operatorname{mix}} V=0, P_{\text {Total}}=p_{A}^{o} x_{A}+p_{B}^{o} x_{B} \)
C. \( \Delta_{\operatorname{mix}} H=0, \Delta_{\operatorname{mix}} V=+v e, P_{\text {Total}}=p_{A}^{\circ} x_{A}+p_{B}^{o} x_{B} \)
D. \( \Delta_{\text {mix}} H=0, \Delta_{\text {mix}} V=0, P_{\text {Total}}=p_{B}^{o} x_{B} \)
Subject: Physics
A person decides to use his bath tub
water to generate electric power to run a 40 watt bulb. The bath tub is located at a height of \( 10 \mathrm{m} \) from the ground \& it
holds 200 litres of water. If we install a
water driven wheel generator on the
ground, at what rate should the water
drain from the bath tub to light bulb? How long can we keep the bulb on, if the bath tub was full initially? The
efficiency of generator is \( 90 \% .(g= \)
\( 10 m / s^{-2} \)
Subject: Chemistry
The oxidation of oxalic acid by acidified
\( K M n O_{4} \) is an example of
autocatalysis. It is due to which of the following?
A. \( S O_{4}^{2-} \)
в. \( M n O_{4}^{2} \)
\( \mathbf{c} \cdot M n^{2+} \)
D. \( K^{\oplus} \)
Subject: Chemistry
Give IUPAC name of the following compound:
\( \boldsymbol{C H} \equiv \boldsymbol{C}-\boldsymbol{C}\left(\boldsymbol{C H}_{3}\right) \)
A. 3,3 - dimethylpropyne
B. 3,3-dimethylbutyne
c. 2,2-dimethylbut-3-yne
D. None of these
Subject: Chemistry
Densities of diamond and graphite are
\( 3.5 \mathrm{g} / \mathrm{mL} \) and \( 2.3 \mathrm{g} / \mathrm{mL} \)
\( \boldsymbol{C}(\text {diamond}) \rightleftharpoons \boldsymbol{C}(\text {graphite}) \)
\( \boldsymbol{\Delta}_{r} \boldsymbol{H}=-\mathbf{1 . 9} \mathbf{k J} / \mathrm{mole} \)
Favourable conditions for formation of
diamond are:
A. high pressure and low pressure
B. low pressure and high temperature
c. high pressure and high temperature
D. low pressure and low temperature
Subject: Maths
For \( \boldsymbol{x} \in \boldsymbol{R}, \) let \( [\boldsymbol{x}] \) denotes the greatest integer \( \leq x \), then the value of \( \left[-\frac{1}{3}\right]+ \) \( \left[-\frac{1}{3}-\frac{2}{100}\right]+\ldots+\left[-\frac{1}{3}-\frac{99}{100}\right] \) is
A. -100
B. -123
c. -135
D. -153
Subject: Maths
Construct a \( \triangle X Y Z \) such that:
\( \boldsymbol{Y} \boldsymbol{Z}=\mathbf{5} \boldsymbol{c m}, \angle \boldsymbol{Z} \boldsymbol{Y} \boldsymbol{X}=\mathbf{3 0}^{\boldsymbol{o}} \) and
\( \angle Y Z X=75^{\circ} \)
Subject: Maths
Consider the function \( f \) defined by \( f(x) \)
\( =x-x(x), \) where \( x \) is a positive
veriable,and (x) denotes the integral part of \( x \) and show that it is
discontinuous for intergral values of x,and continuous for all others. Is the function periodic? If periodic,what is its
period? Draw its graph.
Subject: Maths
Given \( \boldsymbol{A}=\{\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}, \boldsymbol{d}, \boldsymbol{e}, \boldsymbol{f}, \boldsymbol{g}, \boldsymbol{h}\} \) and \( \boldsymbol{B}= \)
\( \{a, e, i, o, u\} \)
then \( B-A \) is equal to
A \( \cdot\{i, o, u\} \)
в. \( \{a, b, c\} \)
c. \( \{c, d, e\} \)
D. \( \{a,, i, z\} \)
Subject: Chemistry
What osmotic pressure would the 1.25 molal sucrose solution exhibit at \( 25^{\circ} \mathrm{C} \) ?
(The density of this solution is 1.34 \( g / m L \)
\( \mathbf{A} \cdot 28.70 \mathrm{atm} \)
B. 30.22 atm
c. 21.72 atm
D. 24.55 atm
Subject: Maths
f \( \boldsymbol{m}=-\mathbf{1} \mathbf{9} \) and \( \boldsymbol{n}=\mathbf{2 3}, \) the value of
\( 25 m^{2}+40 m n+16 n^{2} \) is
\( A \cdot 9 \)
в. -9
\( c .1 \)
D. 3