AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Compound \( C_{4} H_{8} O_{2} \) exists in various structures as shown:

Which statement(s) is/are correct?
(1)
(II)
\( (\mathrm{III}) \)
\( (\mathrm{IV}) \)
A. compounds land II give iodoform test: Compound gives white turbidity on heating with Lucas reagent while compound II reduces Tollens reagent
B. compound III gives silver mirror with \( \left[A g\left(N H_{3}\right)_{2}\right] \) and does not react with NaoBr
C. compound IV on acid hydrolysis gives \( C_{2} H_{5} \) COOH and MeOH
D. compound v on heating is decarboxylated to propane
Subject: Physics
A potential barrier of \( 0.3 \mathrm{V} \) exists across
a p-njunction. An electron with speed
\( 5 \times 10^{5} m / s e c \) approaches this p-n
junction from n-side, what will be its speed on entering the p-side?
A \( .4 .8 \times 10^{5} \mathrm{m} / \mathrm{sec} \)
В. \( 3.8 \times 10^{5} \mathrm{m} / \mathrm{sec} \)
c. \( 5.8 \times 10^{5} \mathrm{m} / \mathrm{sec} \)
D. \( 6.8 \times 10^{5} \mathrm{m} / \mathrm{sec} \)
Subject: Maths
The number of positive integral
solutions of the equation
\( \boldsymbol{x}_{1} \boldsymbol{x}_{2} \boldsymbol{x}_{3} \boldsymbol{x}_{4} \boldsymbol{x}_{5}=\mathbf{1 0 5 0} \) is
A. 1800
B. 1600
\( c \cdot 1400 \)
D. 1875
Subject: Physics
A flat curve on a highway has a radius
of curvature 400 m. A car goes around a
curve at a speed of \( 32 m / s . \) What is the minimum value of coefficient of friction
that will prevent the car from sliding? \( \boldsymbol{g}=\mathbf{9 . 8} \boldsymbol{m} / \boldsymbol{s}^{2} \boldsymbol{)} \)
Subject: Physics
One-fourth of a sphere of radius R is removed as shown in Fig. An electric field E exists parallel to the xy plane. Find the flux through the remaining curved part :
\( \mathbf{A} \cdot \pi R^{2} E \)
В. \( \sqrt{2} \pi R^{2} E \)
c. \( \pi R^{2} E / \sqrt{2} \)
D. none of these
Subject: Chemistry
Choose an incorrect statement.
\( \mathbf{A} \cdot \operatorname{In} C O_{2} \) molecule both \( \pi \) -bond's plane are
perpendicular of each other
B. \( C O_{2} \) is gas while \( S i O_{2} \) is solid
C \( \cdot \ln P_{4} \) molecule there are total six \( P-P \) linkage
D. In \( S_{8} \) molecule there are 16 lone pairs while in \( P_{4} \) molecule there are 8 lone pairs
Subject: Physics
\( 4.48 L \) of an ideal gas at S.T.P requires
12 calories to raise its temperature by
\( 15^{\circ} \mathrm{C} \) at constant volume. The \( C_{p} \) of the gas is:
A . 3 call \( l \)
в. 4 са \( l \)
c. \( 7 c a l \)
D. \( 6 c a l \)
Subject: Physics
Find the temperature at which the fundamental frequency of an organ pipe is independent of small variation in
temperature in terms of the coefficient of linear expansion \( (\alpha) \) of the material of the tube
A . \( 1 / 3 \alpha \)
B. \( 1 / 2 \alpha \)
c. \( 1 / 4 \alpha \)
D. \( 1 / 5 \alpha \)
Subject: Maths
Shamrao's income in \( 2015-16 \) after
paying all taxes is \( R s .6,40,000 . \) He pays \( R s .2000 \) per month for insurance
and \( 20 \% \) of his annual income into his
provident fund. He puts aside \( \boldsymbol{R} \boldsymbol{s} . \mathbf{5 0 0} \) per month for emergencies. How much
money does he have form yearly spending?
Subject: Maths
If \( m \) denotes the number of 5 digit numbers if each successive digits are in their descending order of magnitude and \( n \) is the corresponding figure. When the digits and in their ascending order of magnitude then \( (\boldsymbol{m}-\boldsymbol{n}) \) has the
value
A \( \cdot^{9} C_{4} \)
B . \( ^{9} C_{5} \)
\( \mathrm{c} \cdot^{10} \mathrm{C}_{3} \)
D. \( ^{9} C_{3} \)
Subject: Maths
Assertion \( (A): \sin ^{2} \theta+\sin ^{2}\left(\theta+60^{0}\right)+ \)
\( \sin ^{2}\left(\theta-60^{0}\right)=\frac{3}{2} \)
Reason \( (\mathrm{R}): \cos \alpha+\cos \left(120^{0}+\alpha\right)+ \)
\( \cos \left(120^{0}-\alpha\right)=0 \)
A. Both A and R are true and R is the correct explanation to A
B. Both A \& R are true but R is not the correct explanation to \( A \)
c. A is true, R is false
D. A is false, R is true
Subject: Maths
Water flows at the rate of \( 10 \mathrm{m} \) per min from cylindrical pipe \( 5 \mathrm{mm} \) in diameter How long will it take to fill up a conical vessel whose diameter at the base is 40
\( \mathrm{cm} \) and depth \( 24 \mathrm{cm} ? \)
A. 48 min 15 sec
B. 51 min 12 sec
c. 52 min 1 sec
D. 55 min
Subject: Maths
If \( \tan ^{-1} y=4 \tan ^{-1} x, \) then \( \frac{1}{y} \) is zero for
A \( . x=1 \pm \sqrt{2} \)
B. \( x=\sqrt{2} \pm \sqrt{3} \)
c. \( x=3 \pm 2 \sqrt{2} \)
D. all value of \( x \)
Subject: Chemistry
Which of the following properties are characteristic of lyophobic sols?
1. Low viscosity; 2. High viscosity; 3. Reversibility and 4. Coagulation by electrolytes at low concentration Select the correct answer using the
codes given below:
A. 2,3 and 4
B. 2 and 3 only
c. 1 and 4 only
D. 1 and 3 only
Subject: Chemistry
A bottle completely filled with conc.
\( H_{2} S O_{4} \) is left unstoppered for several
days and we observe spontaneous overflow of acid. It is due to
A. change in temperature
B. hygroscopic nature of \( H_{2} S O_{4} \)
C. absorption of air by \( H_{2} S O_{4} \)
D. dehydration of \( H_{2} S O_{4} \)
Subject: Chemistry
Stability of tetrabromides follows the
order:
A. \( \operatorname{SeBr}_{4}<\operatorname{Te} B r_{4}<\operatorname{PoBr}_{4} \)
B. \( \operatorname{SeBr}_{4}<\operatorname{PoBr}_{4}<\operatorname{TeBr} \)
\( \mathrm{c} \cdot \operatorname{PoBr}_{4}<\operatorname{Te} \mathrm{Br}_{4}<\operatorname{SeBr}_{4} \)
D. None of the these
Subject: Physics
In Young's double slit experiment width
sodium vapour lamp of wavelength 589 nm and the slits 0.589 mm apart, the
half angular width of the central maximum is
\( A \cdot \sin ^{-1}(0.01) \)
B. \( \sin ^{-1}(0.0001) \)
\( c \cdot \sin ^{-1}(0.001) \)
D. \( \sin ^{-1}(0.1) \)
Subject: Maths
The price of an article was increased by \( \boldsymbol{r} \% \). Later the new price was decreased by \( r \% \). If the latest price was Rs. 1 , then the original price was
A. Rs.
в.
Rs. \( \left(\frac{1-r^{2}}{100}\right) \)
c.
Rs. \( \frac{\sqrt{1-r^{2}}}{100} \)
D.
Rs. \( \frac{10000}{10000-r^{2}} \)
Subject: Physics
A uniform chain of length \( \pi r \) lies inside
a smooth semicircular tube \( A B \) of
radius \( r . \) Assuming a slightly
disturbance to start the chain in
motion, the velocity with which it will
emerge from the end \( \mathrm{B} \) of tube will be:
\( \sqrt[A \cdot]{g r\left(1+\frac{2}{\pi}\right)} \)
B. \( \sqrt{2 g r\left(\frac{2}{\pi}+\frac{\pi}{2}\right)} \)
c. \( \sqrt{g r(\pi+2)} \)
D. \( \sqrt{\pi g r} \)
Subject: Maths
The value of
\( \begin{array}{|ccc|}1 & \cos \alpha-\sin \alpha & \cos \alpha+\sin \alpha \\ 1 & \cos \beta-\sin \beta & \cos \beta+\sin \beta \\ 1 & \cos \gamma-\sin \gamma & \cos \gamma+\sin \gamma\end{array} \mid \)
A. \( \left|\begin{array}{ccc}1 & \cos \alpha & \sin \alpha \\ 1 & \cos \beta & \sin \beta \\ 1 & \cos \gamma & \sin \gamma\end{array}\right| \)
B. \( \left|\begin{array}{ccc}1 & \cos \alpha & \sin \alpha \\ 1 & \cos \beta & \sin \beta \\ 1 & \cos \gamma & \sin \gamma\end{array}\right| \)
\( \mathbf{c} \cdot\left|\begin{array}{lll}\cos \alpha & \cos \beta & 1 \\ \cos \beta & \cos \gamma & 1 \\ \cos \gamma & \cos \alpha & 1\end{array}\right| \)
D. \( \left|\begin{array}{ccc}1 & \cos \alpha & \sin \alpha \\ 1 & \cos \beta & \sin \beta \\ 1 & \cos \gamma & \sin \gamma\end{array}\right| \)
Subject: Physics
A given resistor cannot carry currents exceeding 20 A, without exceeding its maximum power dissipation ratings. By forced air cooling suppose that we increase the rate at which heat can be
carried by a factor of \( 2 . \) Now the maximum current that the resistor can
carry is
A. \( 10 A \)
В. \( 20 \sqrt{2} A \)
\( c \cdot 30 \sqrt{2} A \)
D. \( 40 A \)
Subject: Physics
Four \( 2 c m \times 2 c m \times 2 c m \) cubes of ice
are taken out from a refrigerator and
are put in \( 200 \mathrm{ml} \) of a drink at \( 10^{\circ} \mathrm{C} \)
(a) Find the temperature of the drink when thermal equilibrium is attained in
it.
(b) If the ice cubs do not do not melt
completely, find the amount melted.
Assume that no heat is lost to the
outside of the capacity. Density of ice
\( =900 k g / m^{3}, \) density of the drink \( = \)
\( 1000 k g / m^{3}, \) specific heat capacity of
the drink \( 4200 \mathrm{J} / \mathrm{kg}-\mathrm{K} \), latent heat of fusion of ice \( 3.4 \times 10^{5} J / k g \)
Subject: Physics
A square of side \( 3 \mathrm{cm} \) is located at a
distance \( 25 \mathrm{cm} \) from a concave mirror
of focal length \( 10 \mathrm{cm} \). The center of square is at the axis of the mirror and the plane is normal to axis of mirror. The
area enclosed by the image of the square is :
A \( \cdot 4 c m^{2} \)
в. \( 6 \mathrm{cm}^{2} \)
c. \( 16 \mathrm{cm}^{2} \)
D. \( 36 c m^{2} \)
Subject: Physics
Assertion: When radius of a circular wire
carrying current is doubled, its magnetic
moment becomes four times
Reason: Magnetic moment is
directly proportional to area of the loop
A. Both A and R are true and R is the correct explanation of A.
B. Both \( A \) and \( R \) are true and \( R \) is not correct explanation of A.
C. \( A \) is true, but \( R \) is false
D. A is false, but R is true
Subject: Biology
A cross between two tall garden pea plants produced all tall plants. The possible genotypes of the parents are
I) \( \pi, \) T
II) TT, Tt
III) \( T t, t \)
IV) \( \mathrm{Tt}, \mathrm{Tt} \)
A . ॥I, IV
B. I, IV
\( c \cdot 1,1 \)
D. II, III
Subject: Physics
Current passing through a coil of resistance R decreases uniformly as shown in the figure. If total amount of
charge q is passing through the coil
during a time interval \( t_{0} \) then what will
be the total amount of heat generated through it?
A \( \cdot \frac{3}{4} \frac{q^{2} R}{t_{0}} \)
в. \( \frac{4}{3} \frac{q^{2} R}{t_{0}} \)
c. \( \frac{q^{2}}{t_{R}} \)
D. \( \frac{q^{2} R^{2}}{t^{2}} \)
Subject: Chemistry
Which of the following are main requirements for vapour phase refining?
(i) Metal should form a volatile
compound with the reagent.
(ii) The volatile compound should be easily decomposable to give back pure
metal.
(iiii) Metal should be very reactive and form a stable compound with the
reagent.
A. (i), (ii) and (iii)
B. (i) and (ii)
c. (ii) and (iii)
D. (i) and (iii)
Subject: Physics
Water is flowing continuously from a
tap having an internal diameter \( 8 \times 10^{-3} \)
m. The water velocity as it leaves the tap is \( 0.4 \mathrm{m} \mathrm{s}^{-1} \). The diameter of the water
stream at a distance \( 2 \times 10^{-1} \mathrm{m} \) below
the tap is close to
\( A \cdot 5.0 \times 10^{-3} \mathrm{m} \)
B. 7.5 \( \times 10^{-3} \mathrm{m} \)
c. \( 9.6 \times 10^{-3} \mathrm{m} \)
D. 3.6 \( \times 10^{-3} \mathrm{m} \)
Subject: Chemistry
The specific gravity of the stainless steel spherical balls used in ball-
bearings are \( 10.2 . \) How many iron atoms are present in each ball of diameter 1
\( \mathrm{cm} \) if the balls contain 84 per iron by mass? The atomic mass of iron is 56
A \( \cdot 4.12 \times 10^{21} \)
B. \( 4.82 \times 10^{22} \)
D. None of these
Subject: Chemistry
The MRI (magentic resonance imaging) body scanners used in hospitals operate with \( 400 \mathrm{MHz} \) radio frequency energy. The wavelength corresponding to this radio frequency is:
A. \( 0.75 \mathrm{m} \)
B. 0.75 cm
c. \( 1.5 \mathrm{m} \)
D. \( 2 \mathrm{cm} \)
Subject: Maths
Lines \( P Q \) and \( R S \) intersect at \( O \). If
\( \angle P O S=2 \angle S O Q \) then the four angles
at \( \boldsymbol{O} \) are
В. \( 60^{\circ}, 60^{\circ}, 120^{\circ}, 120^{\circ} \)
c. \( 60^{\circ}, 90^{\circ}, 90^{\circ}, 120^{\circ} \)
D. \( 30^{\circ}, 60^{\circ}, 90^{\circ}, 180^{\circ} \)
Subject: Physics
A bullet of mass 2.5 g moving with a velocity of \( 500 m s^{-1}, \) enters a wooden
block and comes out of it with a velocity of \( 100 m s^{-1} . \) Find the work done by the
bullet while passing through the wooden block.
A. 100 J
B. 300 J
c. \( 500 \mathrm{J} \)
D. 800 J
Subject: Maths
Calculate the scalar product of the following vectors
Given two vectors \( \boldsymbol{a}= \)
\{-1,1,1\} and \( b=\{2,0,1\} . \) Find the
vector \( x \) if it is known that it is coplanar with the plane of the vectors a and b, is perpendicular to the vector
\( b, \) and \( a x=7 \)
Subject: Physics
Two lens of focal length \( f_{1} \) and \( f_{2} \) are kept in contact coaxially. The resultant power of combination will be
A. \( \frac{f_{1} f_{2}}{f_{1}-f_{2}} \)
в. \( \frac{f_{1}+f_{2}}{f_{1} f_{2}} \)
c. \( f_{1}+f_{2} \)
D. \( \frac{f_{1}}{f_{2}}+\frac{f_{2}}{f_{1}} \)
Subject: Physics
The temperature at which the reading of Fahrenheit thermometer will be double
that of a Centigrade thermometer is:
A \( \cdot 160^{\circ} \mathrm{C} \)
B. \( 180^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 32^{\circ} C \)
D. \( 100^{\circ} \mathrm{C} \)
Subject: Chemistry
The value of \( \boldsymbol{K}_{s p} \) is \( \boldsymbol{H} \boldsymbol{g} \boldsymbol{C l}_{2} \) at room
temperture is \( 4.0 \times 10^{-15} \). The
concentration of \( C l^{\ominus} \) ion in its
aqueous solution at saturation point is:
A \( \cdot 1 \times 10^{-5} \)
В. \( 2 \times 10^{-5} \)
c. \( 2 \times 10^{-15} \)
D. \( 8 \times 10^{-15} \)
Subject: Biology
Assertion
Capillary water is not readily available
to the plants as it lies below the level of
roots.
Reason
Gravitational water constitutes the only
water available to the plants.
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
\( \operatorname{Let} \overrightarrow{A B}=3 \hat{i}+\hat{j}-\hat{k} \) and \( \overrightarrow{A C}=\hat{i}- \)
\( \hat{j}+3 \hat{k} . \) If the point \( P \) on the line
segment \( B C \) is equidistant from \( A B \) and \( A C \) then \( \overrightarrow{A P} \) is
A \( \cdot 2 \hat{i}-\hat{k} \)
в. \( \hat{i}-2 \hat{k} \)
\( c \cdot 2 \hat{i}+\hat{k} \)
D. None of these
Subject: Chemistry
Out of \( \boldsymbol{S n C l}_{2}, \boldsymbol{N C O}^{-}, \boldsymbol{C S}_{2}, \boldsymbol{N O}_{2}^{+} \) and
\( S O_{2} \) select the one with linear
structure.
A. \( N C O^{-}, C S_{2}, N O_{2}^{+} \)
B. \( N C O^{-}, S n C l_{2}, N O_{2}^{+} \)
\( \mathrm{c} \cdot S O_{2}^{-}, C S_{2}, N O_{2}^{+} \)
D. None of these
Subject: Physics
A glass hemisphere of radius \( R \) and of
material having refractive index 1.5 is
silvered on its flat face as shown in
figure. A small object of height \( h \) is
located at a distance \( 2 R \) from the
surface of hemisphere as shown in figure. The final image will form.
A. At a distance of \( R \) from silvered surface, on the right side
B. On the object itself
C. At hemisphere surface
D. At a distance of \( 2 R \) from the silvered surface, on left
side
Subject: Maths
Simone and her three friends were
deciding how to pick the song they will \( \operatorname{sing} \) for their school's talent show. They
decide to roll a number cube.
The person with the lowest number chooses the song. If her friends rolled a
\( 6,5, \) and \( 2, \) what is the probability that Simone will get to choose the song?
A. \( \frac{1}{6} \)
B.
c. 0
D.
Subject: Physics
At a depth of \( 1000 \mathrm{m} \) in an ocean, what is the absolute pressure? Given density of sea water is \( 1.03 \times 10^{3} k g m^{-3}, g= \)
\( 10 m s^{-2} \)
A. 104 atm
B. 100 atm
c. 108 atm
D. 110 atm
Subject: Chemistry
Benzene and naphthalene form an ideal
solution at room temperature. For this process, the true statement(s) is(are):
This question has multiple correct options
A. \( \Delta G \) is positive
B . \( \Delta S_{\text {system}} \) is positive
C. \( \Delta S_{\text {surroundings}}=0 \)
D. \( \Delta H=0 \)
Subject: Physics
The moment of inertia of a circular of
mass \( M \) and radius \( R \) about an axis
passing through the center of mass is
10. The moment of inertia of
another circular disc of same mass and
thickness but half the density about the
same axis is
A \( \cdot \frac{I_{0}}{8} \)
B. \( \frac{I_{0}}{4} \)
\( c \cdot 8 I_{0} \)
D. \( 2 I_{0} \)
Subject: Chemistry
Which has the highest boiling point?
A. \( 0.1 \mathrm{M} \mathrm{Na}_{2} \mathrm{SO}_{4} \)
В. \( 0.1 M C_{6} H_{12} O_{6} \)
c. \( 0.1 \mathrm{M} \) М \( g \) Са\( _{2} \)
D. \( 0.1 \mathrm{M} \) Аl \( \left(\mathrm{NO}_{3}\right)_{3} \)
Subject: Chemistry
\( \Delta G^{o}(298 K) \) for the reaction \( \frac{1}{2} N_{2}+ \)
\( \frac{3}{2} H_{2} \stackrel{K_{1}}{\rightleftharpoons} N H_{3} \) is \( -16.5 \mathrm{kJ} \) mol\( ^{-1} . \) The
equilibrium constant \( \left(K_{1}\right) \) at \( 25^{\circ} C \)
\& the equilibrium constant \( K_{2} \) and \( K_{3} \)
for the following reactions are \( N_{2}+3 H_{2} \stackrel{K_{2}}{\rightleftharpoons} 2 N H_{3} \)
\( N H_{3} \stackrel{K_{3}}{\rightleftharpoons} \frac{1}{2} N_{2}+\frac{3}{2} H_{2} \)
A \( \cdot K_{1}=779.4, K_{2}=6.074 \times 10^{5} ; K_{3}=1.283 \times 10^{-3} \)
B . \( K_{1}=779.4, K_{2}=2.183 \times 10^{5} ; K_{3}=3.576 \times 10^{3} \)
C . \( K_{1}=124.4, K_{2}=6.074 \times 10^{5} ; K_{3}=2.34 \times 10^{3} \)
D. None of these
Subject: Chemistry
The complex formed by a pair of synapsed homologous chromosomes is called :Homologous chromosome are
paired and synapsed during zygotene stage of meiosis-I and known as
bivalent
Arrows numbered \( 4,8, \) and 12 can all be
A. NADH
B. ATP
\( c \cdot H_{2} \circ \)
D. \( F A D^{+} \) or \( F A D H_{2} \)
Subject: Chemistry
Type of Hybridisation of \( N \) and \( C- \)
\( N-C \) bond angle in \( \left(C H_{3}\right)_{3} N \) are
and \( _{-}--_{-}- \) respectively
\( \mathbf{A} \cdot s p^{3}, 108^{\circ} \)
B. \( s p^{2}, 120^{\circ} \)
c. \( s p^{3}, 109^{\circ} 28^{\prime} \)
D. \( s p^{2}, 117.5^{\circ} \)
Subject: Physics
In YDSE, if \( D \) equals distance of screen
and \( d \) is separation between the slit. The
distance of nearest point to the central maximum where intensity is same as that due to a single slit is equal to
A \( \cdot \frac{D \lambda}{d} \)
в. \( \frac{D \lambda}{2 d} \)
c. \( \frac{D \lambda}{3 d} \)
D. \( \frac{3 D \lambda}{d} \)
Subject: Chemistry
Which of the following complexes will show optical isomerism?
A \( \cdot\left[C r\left(N H_{3}\right)_{6}\right]^{2+} \)
B . \( \left[N i\left(H_{2} O\right)_{6}\right]^{2+} \)
c. \( \left[P t\left(N H_{3}\right)_{3} B r\right] N O_{3} \)
D. \( \left[C r(e n)_{3}\right] C l_{3} \)
Subject: Physics
A proton and electron are accelerated by same potential difference starting from
the rest have de-Broglie wavelength \( \lambda_{p} \)
and \( \lambda_{e} \)
A \( \cdot \lambda_{e}=\lambda_{p} \)
в. \( \lambda_{e}<\lambda_{p} \)
\( \mathbf{c} \cdot \lambda_{e}>\lambda_{p} \)
D. none of these
Subject: Maths
Determine the domain and range of the
following relations. \( \boldsymbol{S}=\{(\boldsymbol{a}, \boldsymbol{b}): \boldsymbol{b}=|\boldsymbol{a}-\mathbf{1}|, \boldsymbol{a} \in \boldsymbol{Z} \) and
\( |a| \leq 3\} \)
Subject: Maths
Praveen wanted to make a temporary shelter for her car, by making a box-like structure with tarpaulin that covers all
the four sides and the top of the car (with the front face as a flap which can be rolled up). Assuming that the stitching margins are very small, and therefore negligible, how much tarpaulin would be required to make the shelter of height 2.5 m, with base
dimensions \( 4 m \times 3 m ? \)
Subject: Maths
\( \mathbf{f} \boldsymbol{I}=\int \cot ^{-1}\left(\frac{\boldsymbol{a}^{2}-\boldsymbol{a} \boldsymbol{x}+\boldsymbol{x}^{2}}{\boldsymbol{a}^{2}}\right) \boldsymbol{d} \boldsymbol{x}, \) then
equals
\( \mathbf{A} \cdot_{x \tan ^{-1}}\left(\frac{x}{a}\right)-(x-a) \tan ^{-1}\left(\frac{x-a}{a}\right)+C \)
B \( \cdot \frac{a}{2} \log \left(2 a^{2}-2 a x+x^{2}\right)-\frac{a}{2} \log \left(x^{2}+a^{2}\right)+C \)
C \( \cdot x \tan ^{-1}\left(\frac{x}{a}\right)+(x-a) \tan ^{-1}\left(\frac{x-a}{a}\right)+\frac{a}{2} \log \left(2 a^{2}-\right. \)
\( \left.2 a x+x^{2}\right)+C \)
D. none of these
Subject: Chemistry
Assertion
Solubility on n-alcohols in water decreases with increase in molecular
weight.
Reason
The relative proportion of the hydrocarbon part in alcohols increases with increasing molecular weight which permits enhanced hydrogen bond with
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. Assertion is incorrect but Reason is correct
Subject: Chemistry
Assertion
Free chlorine is the Oxidising agent in aqua regia.
Reason It is present in high concentration as compared to nitric acid. Nitric acid reacts with HCl to form nitrosyl chloride
NOCI,chlorine and 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
Equipotential surfaces are shown in fig,
then the electric field strength will be
A . \( 100 \mathrm{Vm}-1 \) along \( \mathrm{X} \) -axis
B. \( 100 \mathrm{Vm}-1 \) along \( \mathrm{Y} \) -axis
c. \( 200 \mathrm{Vm}-1 \) at an angle \( 120^{\circ} \) wirh \( \mathrm{x} \) -axis
D. 50 Vm-1 at an angle \( 180^{\circ} \) wirh \( x \) -axis
Subject: Chemistry
Wave no. of a spectral line for a given
transition is \( x \mathrm{cm}^{-1} \) for \( H e^{+} \) then its
value for \( B e^{3+} \) for the same transition
is:
A. \( 4 x \mathrm{cm}^{-1} \)
B. \( x \mathrm{cm}^{-1} \)
c. \( \frac{x}{4} c m^{-1} \)
D. \( 2 x \mathrm{cm}^{-1} \)
Subject: Chemistry
The mineral carnallite contains
(i) \( _{--} \) and
(ii) metals.
(iii) \( _{---}- \) is purified by cupellation and (iv) purified by distillation.
A . (i) -calcium,
(ii)- zinc, (iii)- mercury, (iv)- - tin
B. (i)- calcium, (ii)- magnesium, (iii)- zinc, (iv)- - lead
c. (i)- potassium, (ii)- calcium, (iii)- copper, (iv)- mercury
D. (i)- magnesium, (ii)-potassium, (iii)- - silver, (iv) mercury
Subject: Maths
\( \boldsymbol{I}=\int \log [\boldsymbol{x}+\sqrt{\boldsymbol{x}^{2}+\boldsymbol{a}^{2}}] \boldsymbol{d} \boldsymbol{x} \)
\( \mathbf{A} \cdot x \log [x+\sqrt{x^{2}+a^{2}}]-\sqrt{x^{2}+a^{2}} \)
B \( \cdot x \log [x+\sqrt{x^{2}+a^{2}}]+x^{2}+a^{2} \)
C \( x \log [x+\sqrt{x^{2}+a^{2}}]+\sqrt{x^{2}+a^{2}} \)
D. \( x \log [x+\sqrt{x^{2}+a^{2}}]-x^{2}+a^{2} \)
Subject: Physics
The Speed of light in vacuum is:
A \( \cdot 2 \times 10^{10} \mathrm{m} / \mathrm{s} \)
B . \( 3 \times 10^{8} \mathrm{m} / \mathrm{s} \)
c. \( 4 \times 10^{5} \mathrm{m} / \mathrm{s} \)
D. \( 2 \times 10^{12} \mathrm{m} / \mathrm{s} \)
Subject: Maths
Assertion
If \( \alpha, \beta \) are the roots of the equation
\( 18\left(\tan ^{-1} x\right)^{2}-9 \pi \tan ^{-1} x+\pi^{2}=0 \)
\( \operatorname{then} \boldsymbol{\alpha}+\boldsymbol{\beta}=\frac{\boldsymbol{4}}{\sqrt{\mathbf{3}}} \)
Reason
\( \sec ^{2}\left(\cos ^{-1}\left(\frac{1}{4}\right)\right)+ \)
\( \operatorname{cosec}^{2}\left(\sin ^{-1}\left(\frac{1}{5}\right)\right)=41 \)
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. Assertion is incorrect but Reason is correct
Subject: Physics
The block of mass \( M \) moving on the
frictionless horizontal surface collides
with the spring of spring constant \( \boldsymbol{K} \)
and compresses it by length \( L \). The maximum moment of the block after
collision is
A \( \cdot \sqrt{M K} L \)
в. \( \frac{K L^{2}}{2 M} \)
c. zero
D. \( \frac{M L^{2}}{K} \)
Subject: Maths
Roots of quadratic equation \( 5 x^{2}- \) \( 22 x-15=0 \) are
A \( \cdot_{-5,} \frac{-3}{5} \)
в. \( _{5,} \frac{3}{5} \)
c. \( _{5}, \frac{-3}{5} \)
D. None of these
Subject: Chemistry
Which can act as buffer?
\( \mathbf{A} \cdot N H_{4} C l+N H_{4} O H \)
B \( \cdot C H_{3} C O O H+C H_{3} C O O N a \)
c. \( 40 \mathrm{mL} \) of \( 0.1 \mathrm{M} \mathrm{NaCN}+10 \mathrm{mL} \) of \( 0.1 \mathrm{M} \mathrm{HCl} \)
D. All of the above