AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
\( \operatorname{Let} \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{ll}\boldsymbol{x}+\boldsymbol{a} & ; \quad \boldsymbol{x}<0 \\ |\boldsymbol{x}-1| & ; \quad \boldsymbol{x} \geq 0\end{array}\right. \)
\( \boldsymbol{g}(\boldsymbol{x})=\left\{\begin{array}{ll}\boldsymbol{x}+\mathbf{1} & ; \text { if } \boldsymbol{x}<\mathbf{0} \\ (\boldsymbol{x}-\mathbf{1})^{2}+\boldsymbol{b} ; \boldsymbol{x} \geq \mathbf{0}\end{array}\right. \)
fgof is continuous \( (a>0), \) then
A \( . a=2, b=0 \)
В. \( a=2, b=1 \)
c. \( a=1, b=0 \)
D. \( a=1, b=1 \)
Subject: Chemistry
\( \boldsymbol{R}-\boldsymbol{O H} \stackrel{\boldsymbol{P B r}_{3}}{\boldsymbol{A}} \)
\( \boldsymbol{B} \frac{\text {Grignard reaction}}{\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{O}} \boldsymbol{C} \stackrel{\boldsymbol{H}^{+} / \boldsymbol{H}_{2} \boldsymbol{O}}{\boldsymbol{N}} \boldsymbol{D} \)
What are \( A, B, C \) and \( D \) are
respectively?
\( \mathbf{A} \cdot R-B r, R-M g-B r, R-C H_{2}-O-M g-B r, R- \)
\( C H_{2} C H_{2}-O H \)
B . \( R-B r, R-M g-B r, R-C H_{2}-O-C H_{2}-M g- \)
\( B r, R-C H_{2} C H_{2}-O H \)
c. \( R-B r, R-M g-B r, R-C H_{2}-C H_{2}-O-M g- \)
\( B r, R-C H_{2} C H_{2}-O H \)
D. \( R-B r, R-M g-B r, R-C H_{2}-C H_{2}-O-M g- \)
\( B r, R-C H_{2} O H \)
Subject: Physics
An electron is projected with velocity \( \mathbf{v}_{\mathbf{0}} \) in a uniform electric field \( \mathbf{E} \)
perpendicular to the field. Again it is projected with velocity vo perpendicular
to a uniform magnetic field B. If \( r_{1} \) is initial radius of curvature just after
entering in the electric field and \( \mathbf{r}_{2} \) is
initial radius of curvature just after entering in magnetic field then the ratio
\( \mathbf{r}_{1} / \mathbf{r}_{2} \) is equal to :
A \( \cdot \frac{\mathrm{Bv}_{0}^{2}}{\mathrm{E}} \)
в. \( \frac{\mathrm{B}}{\mathrm{E}} \)
c. \( \frac{\mathrm{Ev}_{0}}{\mathrm{B}} \)
D. \( \frac{\mathrm{Bv}_{0}}{\mathrm{E}} \)
Subject: Chemistry
In the reaction \( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}=\boldsymbol{C H}_{2} \frac{1 . \boldsymbol{H g}(\boldsymbol{O A c})_{2}, \boldsymbol{H}_{2} \boldsymbol{O}}{2 . N a B D_{4}} \)
the product obtained is:
\( \mathbf{A} \cdot \mathbf{C H}_{3} \mathbf{C H}_{2} \) СНОНСН \( _{2} \mathbf{D} \)
в. \( \mathrm{cH}_{3} \mathrm{CH}_{2} \mathrm{CHDCH}_{2} \mathrm{OH} \)
c. \( \mathrm{cH}_{3} \mathrm{CH}_{2} \mathrm{CD}(\mathrm{OH}) \mathrm{CH}_{3} \)
D. \( \mathrm{cH}_{3} \mathrm{CH}_{2} \mathrm{CD}_{2} \mathrm{CH}_{2} \) O
Subject: Physics
The force between two parallel conductors, each of length \( 50 \mathrm{cm} \) and
distant \( 20 \mathrm{cm} \) apart is \( 100 \mathrm{N} \). If the current in one conductor is double that
in another one then the values will
respectively be(Given \( \left.\mu_{0}=4 \pi \times 10^{-7}\right) \)
B. \( 50 A \) and \( 100 A \)
c. \( 10 A \) and \( 20 A \)
D. \( 5 A \) and \( 10 A \)
Subject: Physics
The moment of inertia of a uniform
circular disc of radius 'R' and mass 'M'
about an axis touching the disc at its diameter and normal to the disc is:
\( A \cdot M R^{2} \)
B . \( \frac{2}{5} \mathrm{MR}^{2} \)
\( \mathbf{c} \cdot \frac{3}{2} \mathbf{M} \mathbf{R}^{2} \)
D. \( \frac{1}{2} \mathrm{MR}^{2} \)
Subject: Chemistry
If \( 50 \% \) of \( C O_{2} \) converts to \( C O \) at the
following equilibrium:
\[
\frac{1}{2} C(s)+\frac{1}{2} C O_{2}(g) \rightleftharpoons C O(g)
\]
And the equilibrium pressure is 12 atm.
Calculate \( \boldsymbol{K}_{\boldsymbol{p}} \)
Subject: Maths
The area enclosed by the curves \( y= \)
\( \sin x+\cos x \) and \( y=|\cos x-\sin x| \) over
the interval \( \left[\mathbf{0}, \frac{\pi}{2}\right] \) is
A. \( 4(\sqrt{2}-1) \)
B. \( 2 \sqrt{2}(\sqrt{2}-1) \)
c. \( 2(\sqrt{2}+1) \)
D. \( 2 \sqrt{2}(\sqrt{2}+1) \)
Subject: Physics
The force exerted by a compression device is given by \( F(x)=k x(x-l) \) for
\( 0 \leq x \leq l, \) where \( l \) is the maximum
possible compression, \( x \) is the compression and \( k \) is the constant
Work done to compress the device by a distance \( d \) will be maximum when
A \( \cdot d=\frac{l}{4} \)
в. \( d=\frac{l}{\sqrt{2}} \)
\( c \cdot d=\frac{l}{2} \)
D. \( d=l \)
Subject: Maths
Find the \( 9 t h \) term in the expansion of
\( \left(3 x-\frac{1}{2 x}\right)^{8}, x \neq 0 \)
A \( \cdot \frac{256}{x^{8}} \)
в. \( \frac{\left(x^{8}\right)^{8}}{256} \)
c. \( \frac{1}{256 x^{8}} \)
D. \( 256 x^{8} \)
Subject: Chemistry
Bottles containing \( C_{6} H_{5} I \) and
\( C_{6} H_{5} C H_{2} I \) lost their original labels.
They are labelled \( A \) and \( B \) for testing. \( A \)
and B were separately taken in a test
tube and boiled with \( N a O H \) solution.
The end solution in each tube was made
acidic with dilute \( H N O_{3} \) and then
some \( A g N O_{3} \) solution was added.
Substance B gave a yellow precipitate. Which one of the following statements is true for this experiment?
A \( \cdot \) A was \( C_{6} H_{5} \)
B. A was \( C_{6} H_{5} C H_{2} I \)
c. в was \( C_{6} H_{5} I \)
D. Addition of \( H N O_{3} \) was unnecessary
Subject: Chemistry
A mixture of \( S O_{2} \) and \( O_{2} \) at 1
atmosphere in the ratio of 2: 1 is
passed through a catalyst at \( 1170^{\circ} \mathrm{C} \) for attainment of equilibrium. The exit
gas is found to contain \( 87 \% S O_{3} \) by
volume. Calculate \( \boldsymbol{K}_{\boldsymbol{p}} \) for the reaction, \( \boldsymbol{S O}_{2}(\boldsymbol{g})+\frac{1}{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{S} \boldsymbol{O}_{3}(\boldsymbol{g}) \)
Subject: Maths
Divide \( \left(\frac{\boldsymbol{y}}{\boldsymbol{6}}+\frac{\boldsymbol{2} \boldsymbol{y}}{\boldsymbol{3}}\right) \div\left(\boldsymbol{y}+\frac{\boldsymbol{2} \boldsymbol{y}-\mathbf{1}}{\boldsymbol{3}}\right) \)
Subject: Biology
A large quantity of urban sewage is drained to a nearby river. Which among the given conditions would happen after mixing of sewage into the river?
(i) BOD of receiving water body increases.
(ii) DO of receiving water body decreases.
(iii) It will not cause mortality among fishes and other aquatic creatures.
(iv) It will lead to nutrient enrichment of
receiving water body.
A. i, ii and iii
B. i, ii and iv
c. ii and iii
D. iii and iv
Subject: Physics
A billiard ball of mass \( M \) moving with
velocity \( v_{1} \) collides with another ball of
the same mass but at rest. If the
collision is elastic the angle of divergence after the collision is
A \( \cdot 0^{\circ} \)
B. \( 30^{\circ} \)
\( c \cdot 90^{\circ} \)
D. \( 45^{\circ} \)
Subject: Physics
A cnarge + \( \ell \) Is locatea somewnere
inside a vertical cone such that the
dept of the charge from the free surface
of the cone is \( H . \) It is formed that the
flux associated with the cone with thw
curved surface is \( \frac{3 Q}{5 \epsilon_{0}} \)

If the charge is raised vertically through a height \( 2 H \) then the flux through the curved surface is
\( \mathbf{A} \cdot \frac{3 Q}{5 \epsilon_{n}} \)
B. \( \frac{2 Q}{5 \epsilon_{n}} \)
\( c \cdot \frac{4 Q}{5 \epsilon_{n}} \)
D. Zero
Subject: Chemistry
Which yields isopropyl methyl ether as the major product with little or no by products?
A \( \cdot\left(C H_{3}\right)_{2} C H O^{-} N a^{+}+C H_{3} I \longrightarrow \)
в. \( C H_{3} O N a+\left(C H_{3}\right)_{2} C H I \)
c. \( \left(C H_{3}\right)_{2} C H O H+C H_{3} O H \stackrel{H_{2} S O_{4}}{\longrightarrow} \)
D. All three gives isopropyl methyl ether as the major product
Subject: Chemistry
Which of the following statements are true about quartz?
A. it is pure crystalline form of silica.
B. it is a tetrahedral polymer of \( \boldsymbol{S} \boldsymbol{i} \boldsymbol{O}_{\boldsymbol{2}} \)
C. UV light can pass through quartz
A. A and B are correct
B. B and C are correct
c. A and C are correct
D. all are correct
Subject: Maths
Find the value of :
\[
\begin{array}{l}
\cos \left[\frac{\pi}{6}+2 \tan ^{-1}(1)\right]+ \\
\sin \left[3 \sin ^{-1}\left(\frac{1}{2}\right)+2 \cos ^{-1}\left(\frac{1}{2}\right)\right]
\end{array}
\]
Subject: Physics
A particle of mass \( m_{1} \) is projected to
the right with a speed \( v_{1} \) onto a smooth
wedge of mass \( m_{2} \) which is
simultaneously projected due to the left
with a speed \( v_{2} \). Highest point on the wedge attained by the particle is \( \frac{\boldsymbol{m}_{2}\left(\boldsymbol{v}_{1}+\boldsymbol{v}_{2}\right)^{2}}{\boldsymbol{x} \boldsymbol{g}\left(\boldsymbol{m}_{1}+\boldsymbol{m}_{2}\right)} \cdot \) Find \( \boldsymbol{x} \)
Subject: Maths
In the system of equations \( \frac{12}{x+y}+ \) \( \frac{8}{x-y}=8 \) and \( \frac{27}{x+y}-\frac{12}{x-y}=3, \) the
values of \( x \) and \( y \) will be
A \( \cdot \frac{5}{3} \) and \( \frac{1}{3} \)
B. \( \frac{5}{2} \) and \( \frac{1}{2} \)
c. 2 and \( \frac{1}{3} \)
D. \( \frac{5}{4} \) and \( \frac{1}{4} \)
Subject: Physics
In the figure, the disc D does not slip on
the surface S. The pulley P has mass,
and the string does not slip on it. The
string is wound around the disc. Then,
which of the following statement(s) is/are true?
his question has multiple correct options
A. The acceleration of the block B is double the acceleration of the centre of \( D \)
B. The force of friction exerted by D on S acts to the left
c. The horizontal and the vertical sections of the string have the same tension
D. The sum of the kinetic energies of D and B is less than the loss in the potential energy of B as it moves down
Subject: Maths
The total cost \( C(x) \) associated with the
production of x units of an item is given
by \( C(x)=0.05 x^{3}-0.02 x^{2}+30 x+ \)
5000. Find the marginal cost when 3 units are produced, where by marginal
cost we mean the instantaneous rate of
change of total cost at any level of
output.
Subject: Physics
Derivation of second equation of motion
is:
\( \mathbf{A} \cdot d \theta=w d 2 t \)
B \( . d \theta=w d t \)
\( \mathbf{c} \cdot d \theta=w d 3 t \)
\( \mathbf{D} \cdot d \theta=w d t^{2} \)
Subject: Physics
A boy has two spare light bulbs in his drawer. One is marked \( 240 \mathrm{V} \) and \( 100 \mathrm{W} \)
and the other is marked \( 240 \mathrm{V} \) and \( 60 \mathrm{W} \)
He tries to decide which bulb should be
used and why??
A. The 60 W light bulb has more resistance and therefore burns more brightly
B. The 60W light bulb has less resistance and therefore burns less brightly
c. The 100 w bulb has more resistance and therefore burns more brightly
D. The 100 W bulb has less resistance and therefore burns less brightly
Subject: Chemistry
For the detection of phosphorus, the
organic compound after fusion with
\( N a_{2} O_{2} \) is extracted with water, boiled
with \( H N O_{3} \) and then ammonium
molybdate added to it. A yellow ppt. is obtained which is due to formation of :
A. ammonium sulphate
B. ammonium phosphomolybdate
c. ferric phosphate
D. disodium ammonium phosphate
Subject: Physics
The north poles of pole strengths, \( \boldsymbol{m}, \boldsymbol{9} \boldsymbol{m} \)
are kept apart by certain distance ' \( \boldsymbol{d} \) Find distance of null point from larger
pole
A \( .2 d / 4 \)
в. \( 2 d / 3 \)
c. \( 5 d / \)
D. \( 3 d / 2 \)
Subject: Maths
Trace of matrix \( \boldsymbol{A}^{k} \) is
\( \mathbf{A} \cdot 3^{k}+1+(-1)^{k} \)
B . \( 2^{k}+3^{k}-2 \)
c. \( 3^{k}-2^{k}+2 \)
\( \mathbf{D} \cdot 2^{k}+1 \)
Subject: Maths
If \( f(x)=\int_{0}^{x} t \sin t d t, \) then \( f^{\prime}(x) \) is
A \( \cdot \cos x+x \sin x \)
B. \( x \sin x \)
c. \( x \cos x \)
\( \mathbf{D} \cdot \sin x+x \cos x \)
Subject: Maths
If a particle \( A \) is moving along a straight line with velocity \( 3 m / s \) and another particle \( B \) has a velocity \( 5 m / s \)
at an angle of \( 60^{\circ} \) to the path of \( A, \) then
the velocity \( B \) relative to \( A \) is
A \( \cdot \sqrt{39} \mathrm{m} / \mathrm{s} \)
B . \( \sqrt{19} \mathrm{m} / \mathrm{s} \)
c. \( 19 m / s \)
D. None of these
Subject: Maths
The length of perpendicular from the
point (7,14,5) to the plane \( 2 x+4 y- \)
\( z=2 \) is
A \( \cdot 21 \sqrt{3} \)
is
B. \( 3 \sqrt{21} \)
c. \( \sqrt{321} \)
D. \( 5 \sqrt{2} \)
Subject: Chemistry
van't Hoff equation is
This question has multiple correct options
\( \mathbf{A} \cdot(d / d T) \ln K=-\Delta H / R T^{2} \)
B \( \cdot(d / d T) \ln K=+\Delta H / R T^{2} \)
\( \mathbf{c} \cdot(d / d T) \ln K=-\Delta H / R T \)
D \( \cdot K=A e^{\Delta H / R T} \)
Subject: Physics
When connected to the \( 220 \mathrm{V} \) mains
supply, the current in a toaster, a kettle, a lamp and a fan is \( 5.2 \mathrm{A}, 9.4 \mathrm{A}, 0.5 \mathrm{A} \) and 2.6A respectively. Which appliance has the greatest electrical resistance?
A. toaster
B. kettlein
c. lamp
D. fan
Subject: Chemistry
Match each coordination compound in List-I with an appropriate of characteristics from List-II. (en \( = \)
\( \boldsymbol{H}_{2} \boldsymbol{H} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{N} \boldsymbol{H}_{2} ; \) Atomic numbers:
\( \mathrm{Ti}=22, \mathrm{Cr}=24 ; \mathrm{Co}=27 ; \mathrm{Pt}=78) \)
List 1
Parama dexhil
\( A \)
4 \( \left[C r\left(N H_{3}\right)_{4} C l_{2}\right] C l \) and ionizatio
Diamag \( \operatorname{lex} \)
\( B \)
3 \( \left[T i\left(H_{2} O\right)_{3} C l\right]\left(N O_{3}\right)_{2} \)
2
and cis-trans
Parama \( \operatorname{exn} \)
\( c \)
\( \left[P t(e n)\left(N H_{3}\right) C l\right] N O_{3} \) 3 and cis-trans so ।
\( \left[C o\left(N H_{3}\right)_{4}\left(N O_{3}\right)_{2}\right] N O_{3} \) Diamagn
and exhib
ionizatior
isomerisr 4
Subject: Maths
\( \mathrm{If} \mathrm{A}=\left|\begin{array}{lll}\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} \\ \boldsymbol{x} & \boldsymbol{y} & \boldsymbol{z} \\ \boldsymbol{l} & \boldsymbol{m} & \boldsymbol{n}\end{array}\right| \) is a skew-symmetric
matrix then which of the following is
equal to \( x+y+z ? \)
A. \( a+b+c \)
B. \( l+m+n \)
\( \mathrm{c} \cdot-b-m \)
D. \( c-l-n \)
Subject: Physics
Two simple Harmonic Motions of
angular frequency 100 and 1000 rad \( S^{-1} \)
have the same displacement amplitude. The ratio of their maximum accelerations is :
A \( \cdot 1: 10^{3} \)
B \( \cdot 1: 10^{4} \)
c. 1: 10
D. \( 1: 10^{2} \)
Subject: Maths
If \( \boldsymbol{f}(\boldsymbol{x})+\mathbf{2} \boldsymbol{f}(\mathbf{1}-\boldsymbol{x})=\boldsymbol{x}^{2}+\boldsymbol{2} ; \forall \boldsymbol{x} \in \boldsymbol{R} \)
then \( f(x) \) is given by
A \( \cdot \frac{(x-1)^{2}}{3} \)
B. \( -\frac{(x-2)^{2}}{3} \)
c. \( x^{2}-1 \)
D. \( x^{2}-2 \)
Subject: Physics
If \( \lambda_{v}, \lambda_{x}, \lambda_{m} \) represents the wavelengths of vision, X-ray and microwaves
respectively then
A \( \cdot \lambda_{m}>\lambda_{x}>\lambda_{v} \)
в. \( \lambda_{m}>\lambda_{v}>\lambda_{x} \)
c. \( \lambda_{v}>\lambda_{x}>\lambda_{m} \)
D \( \cdot \lambda_{v}>\lambda_{m}>\lambda_{x} \)
Subject: Maths
In a \( \Delta A B C, D, E \) and \( F \) are respectively, the mid-points of BC, and
AB. If the lengths of side \( A B, B C \) and \( C A \) \( \operatorname{are} 7 \mathrm{cm}, 8 \mathrm{cm}, \) and \( 9 \mathrm{cm}, \) respectively
find the perimeter of \( \Delta D E F \)
Subject: Chemistry
Which reagent is used in
Rosenmund reduction?
\( \mathbf{A} \cdot H_{2} / P d-B a S O_{4} \)
\( \mathbf{B} \cdot L i A I H_{4} \)
\( \mathbf{c} \cdot N H_{2}-N H_{2} / K O H / C H_{2} O H-C H_{2} O H \)
\( \mathbf{D} \cdot Z n-H g / H C l \)
Subject: Maths
The sum of first 20 terms of \( \boldsymbol{A P} \) :
\( \mathbf{8}, \mathbf{3},-\mathbf{2}, \dots . . \) is:
\( \mathbf{A} \cdot-790 \)
B. -970
\( \mathbf{c} .-979 \)
D. -779
Subject: Maths
\( \boldsymbol{A}=(\mathbf{1},-\mathbf{1}, \mathbf{2}) \) and \( \boldsymbol{B}=(\mathbf{2}, \mathbf{3}, \mathbf{7}) \) are two
points. If \( \boldsymbol{P}, \boldsymbol{O} \) divide \( \boldsymbol{A B} \) in the ratios
2: 3,-2: 3 respectively then \( P_{x}+ \)
\( \boldsymbol{Q}_{\boldsymbol{y}}= \)
A \( \cdot \frac{-38}{5} \)
в. \( \frac{38}{5} \)
c. \( \frac{-2}{5} \)
D. \( \frac{-47}{6} \)
Subject: Physics
Assertion
If a gas container is placed in a moving
train, the temperature of gas will increase.
Reason
Kinetic energy of gas molecules will increase.
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
Assertion
Dielectric materials can be solids,
liquids, or gases.
Reason
Usage of dielectric depends on the application i.e.Industrial coatings such as parylene provide a dielectric barrier between the substrate and its
environment.
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
In a quadrilateral ABCD if \( \sin \left(\frac{A+B}{2}\right) \cos \left(\frac{A-B}{2}\right)+ \)
\( \sin \left(\frac{C+D}{2}\right) \cos \left(\frac{C-D}{2}\right)=2 \) then
\( \sum \cos \frac{A}{2} \cos \frac{B}{2} \) is equal to
\( \mathbf{A} \cdot \mathbf{0} \)
B. 6
\( c .3 \)
D.
Subject: Chemistry
The composition (by atoms) of compound \( A \) is \( 40 \% X \) and \( 60 \% \) Y. The composition (by atoms) of compound B is \( 25 \% \mathrm{X} \) and \( 75 \% \) Y. According to the law of multiple proportions, the ratio of the weight of element \( Y \) in compounds \( A \) and B is:
A . 1: 2
B . 2: 1
\( c \cdot 2: 3 \)
D. 3: 4
Subject: Physics
A planet revolves around the sun in an elliptical orbit of eccentricity e. If T is the time period of the planet, then the time spent by the planet between the ends of the minor axis and major axis close to the sun is
A \( \cdot \frac{T \pi}{2 e} \)
B \( \cdot T\left(\frac{2 e}{\pi}-1\right) \)
c. \( \frac{T e}{2 \pi} \)
D \( \cdot T\left(\frac{1}{4}-\frac{e}{2 \pi}\right) \)
Subject: Physics
\( \hat{\text { i }} \) and \( \hat{j} \) are unit vectors along along \( x \) and \( y- \) axis respectively. What is the magnitude and direction of the vectors \( \hat{\mathbf{i}}+\hat{\text { jand }} \hat{\boldsymbol{i}}-\hat{\boldsymbol{j}} \) ?What are the
components of a vector \( A=2 \hat{i}+3 \hat{j} \) along the directions of \( \hat{i}+\hat{j} \) and \( \hat{i}-\hat{j} \)
? [You may use graphical method]
Subject: Physics
A ball is initially moving with a velocity
\( 0.5 m s^{-1} . \) Its velocity decreases at a rate
of \( 0.05 m s^{-2} \). How much time will it take
to stop?
\( \mathbf{A} \cdot 5 s \)
в. \( 10 s \)
\( c .15 s \)
D. 20
Subject: Maths
\( \int \frac{x^{2}+x-1}{x^{2}+x-6} d x= \)
\( \mathbf{A} \cdot x+\log p+5|+\log | x-2 \mid+c \)
B . \( x-\log |x+3|+\log |x-2|+c \)
c. \( x-\log |x+3|-\log |x-2|+c \)
D. None of these
Subject: Chemistry
In what ratio \( \mathrm{Cl}_{17}^{37} \) and \( \mathrm{Cl}_{17}^{35} \) be present so
as to obtain \( \mathrm{Cl}_{17}^{35.5} ? \)
A .1: 2
B. 1:
\( c \cdot 1: 3 \)
D. 3:
Subject: Physics
What is the direction and magnitude of
the force on the positive charge \( +Q_{0} \) in
terms of the given quantities?
A \( \cdot \frac{-2 Q_{0}^{2}}{4 \pi \epsilon_{0} d^{2}} \)
B. \( \frac{-\sqrt{3} Q_{0}^{2}}{4 \pi \epsilon_{0} d^{2}} \)
\( c \)
\( D \)
Subject: Maths
If \( \boldsymbol{A}=\{1,2,3\} \) and \( \boldsymbol{B}=\{3,8\}, \) then
\( (\boldsymbol{A} \cup \boldsymbol{B}) \times(\boldsymbol{A} \cap \boldsymbol{B}) \) is
A \( \cdot\{(3,1),(3,2),(3,3),(3,8)\} \)
в. \{(1,3),(2,3),(3,3),(8,3)\}
\( c \cdot\{(1,2),(2,2),(3,3),(8,8)\} \)
D. \{(8,3),(8,2),(8,1),(8,8)\}
Subject: Chemistry
\( ^{35} C l \) and \( ^{37} C l \) are the two isotopes of
chlorine, in the ratio 3: 1 respectively. If
the isotope ratio is reversed the average atomic mass of chlorine will be:
\( \mathbf{A} \cdot 35.0 u \)
B. \( 35.5 u \)
c. \( 36.0 u \)
D. 36.5 \( u \)
Subject: Chemistry
The stability of dihalides of \( \boldsymbol{S} \boldsymbol{i}, \boldsymbol{G} \boldsymbol{e}, \boldsymbol{S} \boldsymbol{n} \)
and \( P b \) increases steadily in the
sequence?
A \( \cdot P b X_{2}<<\operatorname{Sn} X_{2}<<\operatorname{Ge} X_{2}<<\operatorname{Si} X_{2} \)
в. \( G e X_{2}<<\operatorname{Si} X_{2}<<\operatorname{SnX}_{2}<<P b X_{2} \)
c. \( S i X_{2}<<G e X_{2}<<P b X_{2}<<S n X_{2} \)
D. \( S i X_{2}<<G e X_{2}<<S n X_{2}<<P b X_{2} \)
Subject: Chemistry
\( \boldsymbol{p} \boldsymbol{H} \) of \( \boldsymbol{B} \boldsymbol{a}(\boldsymbol{O} \boldsymbol{H})_{2} \) solution is \( 12 . \) Its
solubility product is:
A \( \cdot 10^{-6} \)
В. \( 4 \times 10^{-6} \)
c \( .5 \times 10^{-7} \)
D. \( 5 \times 10^{-6} \)
Subject: Maths
The probability of \( A= \) Probability of \( B= \) Probability of \( \mathrm{C}=\frac{1}{4} \)
\( \boldsymbol{P}(\boldsymbol{A}) \cap \boldsymbol{P}(\boldsymbol{B}) \cap \boldsymbol{P}(\boldsymbol{C})=\mathbf{0} . \boldsymbol{P}(\boldsymbol{B} \cap \boldsymbol{C})= \)
0 and \( P(A \cap C)=\frac{1}{8} . P(A \cap B)=0 \) the
probability that atleast one of the events \( A, B, C \) exists is?
A \( \cdot \frac{5}{8} \)
в. \( \frac{37}{64} \)
\( c \cdot \frac{3}{4} \)
\( D \)
Subject: Maths
\( \operatorname{Let} A=\left[\begin{array}{ll}1 & 0 \\ 1 & 1\end{array}\right] . \) Then which of following
is not true?
This question has multiple correct options
A \( \cdot \lim _{n \rightarrow \infty} \frac{1}{n^{2}} A^{-n}=\left[\begin{array}{cc}0 & 0 \\ -1 & 0\end{array}\right] \)
B \( \lim _{n \rightarrow \infty} \frac{1}{n} A^{-n}=\left[\begin{array}{cc}0 & 0 \\ -1 & 0\end{array}\right] \)
\( ^{\mathrm{c}},_{A^{-n}}=\left[\begin{array}{cc}1 & 0 \\ -n & 1\end{array}\right] \forall n \neq N \)
D. none of these
Subject: Physics
A object is placed at \( 30 \mathrm{cm} \) on the principle axis of the convex lens from the lens and an image is formed \( 60 \mathrm{cm} \) from the lens. If focal length of the lens is \( 20 \mathrm{cm} \) then calculate the
magnification.
A . 0.5
B. 0.67
\( c \cdot 1.5 \)
D. 2.0
E. 3.0
Subject: Maths
Find the maximum value of \( \left|\begin{array}{ccc}\mathbf{1} & \mathbf{1} & \mathbf{1} \\ \mathbf{1} & \mathbf{1}+\sin \boldsymbol{\theta} & \mathbf{1} \\ \mathbf{1} & \mathbf{1} & \mathbf{1}+\cos \boldsymbol{\pi}\end{array}\right| \)
Subject: Maths
A sum of money invested at C.I. amounts to Rs. 800 in 3 years and to Rs.
840 in 4 years. The rate of interest per
annum is
A \( \cdot_{2} \frac{1}{2} \% \)
B . 4\%
c. \( 5 \% \)
D. \( 6 \frac{2}{3} \% \)
Subject: Physics
An aluminium rod has a breaking strain \( 0.2 \% . \) The minimum cross-sectional
area of the rod in \( m^{2} \) in order to support
a load of \( 10^{4} N \) is if (Young's modulus is
\( \mathbf{7} \times \mathbf{1 0}^{\mathbf{9}} \mathbf{N m}^{-\mathbf{2}} \mathbf{)} \)
\( \mathbf{A} \cdot 1.7 \times 10^{-4} \)
В. \( 1.7 \times 10^{-3} \)
c. \( 7.1 \times 10^{-4} \)
D. \( 1.4 \times 10^{-4} \)
Subject: Chemistry
Which statements is/ are correct?
This question has multiple correct options
A. When \( F e C l_{3} \) is added to excess of hot water, a
positively charged colloidal solution form
B. Amount of electrolyte required to cause coagulation is higher for lyophobic than Iyophillic colloids
C. High pressure is favaourable for physical as well as chemical adsorption
D. Physical and chemical adsorption both decrease entropy of universe
Subject: Chemistry
Justify that the following reactions are
redox reactions.
\( \mathbf{A} \cdot C u O(s)+H_{2}(g) \rightarrow C u(s)+H_{2} O(g) \)
B \( \cdot F e_{2} O_{3}(s)+3 C O(g) \rightarrow 2 F e(s)+3 C O_{2}(g) \)
\( \mathbf{c} \cdot 4 B C l_{3}(g)+3 L i A l H_{4}(s) \rightarrow 2 B_{2} H_{6}(s)+3 L i C l(s)+ \)
\( 3 A l C l_{3}(s) \)
D \( \cdot 2 K(s)+F_{2}(g) \rightarrow 2 K^{+} F^{-}(s) \)
Subject: Physics
A sings with a frequency \( (n) \) and \( B \) sings with a frequency \( 1 / 8 \) that of \( A \). If
the energy remains the same
and the amplitude of \( A \) is \( a \), then
amplitude of \( \boldsymbol{B} \) will be
A . \( 2 a \)
B. \( 8 a \)
c. \( 4 a \)
D.
Subject: Chemistry
Which of the following takes place in
discharge process at anode?
\( \mathbf{A} \cdot P b O_{2}+4 H^{+}+S O_{4}^{2-}+2 e^{-} \rightarrow P b S O_{4}+2 H_{2} O \)
B \( \cdot P b S O_{4}+2 H_{2} O \rightarrow P b O_{2}+4 H^{+}+S O_{4}^{2-}+2 e^{-} \)
\( \mathbf{c} \cdot P b S O_{4}+2 e^{-} \rightarrow P b+S O_{4}^{2} \)
\( \mathbf{D} \cdot P b S O_{4}+4 H_{2} O \rightarrow P b O_{2}+8 H^{+}+S O_{4}^{2-}+2 e^{-} \)