AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
Tangents are drawn to the circle \( x^{2}+ \)
\( y^{2}=25 \) from the point \( (13,0) . \) Prove
that the angle between them is \( 2 \tan ^{-1}(5 / 12) \) and their equations are
\( 12 y+5 x+65=0 \) and \( 12 y-5 x- \)
\( \mathbf{6 5}=\mathbf{0} \)
Subject: Maths
Let for \( \boldsymbol{a} \neq \boldsymbol{a}_{1} \neq \mathbf{0}, \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{a} \boldsymbol{x}^{2}+\boldsymbol{b} \boldsymbol{x}+ \)
\( c, g(x)=a_{1} x^{2}+b_{1} x+c_{1} \) and \( p(x)= \)
\( f(x)-g(x) \). If \( p(x)=0 \) only for \( x=-1 \)
and \( p(-2)=2, \) then the value of \( p(2) \) is
A . 3
B. 9
\( c \cdot 6 \)
D. 18
Subject: Maths
\( \operatorname{Let} \boldsymbol{D}_{1}=\left|\begin{array}{lll}\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{a}+\boldsymbol{b} \\ \boldsymbol{c} & \boldsymbol{d} & \boldsymbol{c}+\boldsymbol{d} \\ \boldsymbol{a} & \boldsymbol{b} & \boldsymbol{a}-\boldsymbol{b}\end{array}\right|, \quad \boldsymbol{D}_{2}= \)
\( \left|\begin{array}{ccc}\boldsymbol{a} & \boldsymbol{c} & \boldsymbol{a}+\boldsymbol{c} \\ \boldsymbol{b} & \boldsymbol{d} & \boldsymbol{b}+\boldsymbol{d} \\ \boldsymbol{a} & \boldsymbol{c} & \boldsymbol{a}+\boldsymbol{b}+\boldsymbol{c}\end{array}\right|, \) then the value of
\( \left|\frac{\boldsymbol{D}_{1}}{\boldsymbol{D}_{2}}\right|, \) where \( \boldsymbol{b} \neq \mathbf{0} \) and \( \boldsymbol{a} \boldsymbol{d} \neq \boldsymbol{b} \boldsymbol{c}, \) is
Subject: Maths
Assertion
\( (\sqrt{2}-1)^{n} \) can be expressed as \( \sqrt{N} \) \( \sqrt{N-1} \) for \( \forall N>1 \) and \( n \in N \)
Reason
\( (\sqrt{2}-1)^{n} \) can be written in the form \( \boldsymbol{\alpha}+\boldsymbol{\beta} \sqrt{\boldsymbol{2}} \forall, \boldsymbol{\alpha}, \boldsymbol{\beta} \) are integers \& n is a
positive integer.
A. Both Assertion \& Reason are individually true \& Reason is correct explanation of Assertion,
B. Both Assertion \& Reason are individually true but Reason is not the correct (proper) explanation of Assertion,
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true.
Subject: Maths
If a line passes through the point
\( P(1,2) \) makes an angle of \( 45^{\circ} \) with the x-axis and meets the line \( x+2 y-7= \)
0 in \( Q, \) then \( P Q \) equals-
A. \( \sqrt{3} \)
B. \( \frac{3 \sqrt{2}}{2} \)
\( c \cdot \frac{2 \sqrt{2}}{3} \)
D. \( \sqrt{2} \)
Subject: Chemistry
Rate constant for the decomposition of
ethylene oxide into \( C H_{4} \) and \( C O \) may
be described by the equation, \( \log \left[k\left(s^{-1}\right)\right]=14.34-\frac{1.25 \times 10^{4}}{T} \)
(a) What is the energy of activation of this reaction?
(b) What is the value of \( k \) at \( 670 K ? \)
Subject: Chemistry
As per Braun's principle, yield of Ammonia will be more in Haber's
process under conditions
\( \boldsymbol{L}=\operatorname{Low} ; \boldsymbol{H}=\operatorname{high} ; \boldsymbol{T}=\operatorname{Temp} ; \boldsymbol{P}= \)
Pressure)
A. \( L T ; L P \)
B. \( L T ; H P \)
c. \( H T ; H P \)
D. \( H T ; L P \)
Subject: Maths
Find \( \mathrm{BC} \), if \( \mathrm{AB}=7.2 \mathrm{cm} \)
A. \( 7.2 \mathrm{cm} \)
B. \( 7.1 \mathrm{cm} \)
\( c \cdot 0.72 \mathrm{cm} \)
D. \( 72 \mathrm{cm} \)
Subject: Maths
\( \cot ^{-1} 9+\operatorname{cosec}^{-1} \frac{\sqrt{41}}{4}=? \)
A \( \cdot \frac{\pi}{6} \)
в. \( \frac{\pi}{4} \)
\( c \cdot \frac{\pi}{3} \)
D. \( \frac{3 \pi}{4} \)
Subject: Maths
The solution of \( y \frac{d y}{d x}=1+y^{2} \) is:
A \( \cdot 2 x=\log \left[c\left(1+y^{2}\right)\right] \)
в. \( x=c y^{2} \)
c. \( c\left(1+y^{2}\right)=x \)
D \( \cdot 2 y=\log \left\{c\left(1+x^{2}\right)\right\} \)
Subject: Chemistry
Assertion
The pressure of a fixed amount of an ideal gas is proportional to its temperature
Reason
Frequency of collisions and their impact both increase in proportion to the
square root of temperature
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: Maths
Solve \( \left|\begin{array}{ccc}\mathbf{1} & \mathbf{1} & \mathbf{1} \\ \mathbf{1} & \mathbf{1}+\boldsymbol{x} & \mathbf{1} \\ \mathbf{1} & \mathbf{1} & \mathbf{1}+\boldsymbol{y}\end{array}\right| \)
\( A \)
B.
\( c \)
D. \( x y \)
Subject: Physics
A circular ring is fixed in a gravity free
space and one point of the ring is earthed. Now a magnet is placed along
axis of the ring at a distance from its
centre such that the nearer pole is north pole as shown in figure. A sharp impilse is applied on the magnet so that it
starts to move towards the ring. Then,
A. Initially magnet experiences an acceleration and then it retards to come to an instantaneous rest.
B. Magnet starts to oscillate about centre of the ring
C. Magnet continues to move along the axis with constant velocity
D. The magnet retards and comes to rest finally
Subject: Chemistry
Assertion
Ethanol is a weaker acid than phenol
Reason

Sodium ethoxide may be prepared by the reaction of ethanol with aqueous
NaOH
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
ff \( \boldsymbol{A}=\left[\begin{array}{cc}\cos \boldsymbol{x} & \sin \boldsymbol{x} \\ -\sin \boldsymbol{x} & \cos \boldsymbol{x}\end{array}\right], \) then find \( \boldsymbol{x} \)
satisfying \( \mathbf{0}<\boldsymbol{x}<\frac{\boldsymbol{\pi}}{\mathbf{2}} \) when \( \boldsymbol{A}+\boldsymbol{A}^{\boldsymbol{T}}=\boldsymbol{I} \)
Subject: Physics
A particle of mass \( 10 g \) is kept on the surface of a uniform sphere of mass
100 \( k g \) and radius \( 10 c m . \) Find the work
to be done against the gravitational force between them to take the particle far away from the
sphere
A \( \cdot 13.34 \times 10^{-10} \mathrm{J} \)
B . \( 13.33 \times 10^{-10} J \)
c. \( 6.67 \times 10^{-9} \mathrm{J} \)
D. \( 6.67 \times 10^{-10} J \)
Subject: Chemistry
\( \boldsymbol{O} \)
\( \boldsymbol{P h}-\boldsymbol{C H}_{2}-\stackrel{\|}{\boldsymbol{C}}-\boldsymbol{O H} \)
\( (A) \) is :
A. \( P h-C O_{2} H \)
в. \( P h-C H_{2}-O H \)
c. \( P h-C H_{3} \)
D.
Subject: Physics
The \( V-I \) graph for a conductor at
temperature \( T_{1} \) and \( T_{2} \) are shown in fig.
\( \left(T_{2}-T_{1}\right) \) is proportional to
A \( . \cos 2 \theta \)
B. \( \sin 2 \theta \)
c. \( \cot 2 \theta \)
D. \( \operatorname{Tan} 2 \theta \)
Subject: Maths
If the sum of \( 1+\frac{1+2}{2}+\frac{1+2+3}{3}+ \)
\( \ldots \) to \( n \) terms is \( S, \) then \( S \) is equal to
A \( \cdot \frac{n(n+3)}{4} \)
в. \( \frac{n(n+2)}{4} \)
c. \( \frac{n(n+1)(n+2)}{6} \)
D. \( n^{2} \)
Subject: Chemistry
On hydrolysis of sodium carbonate, the reaction takes place between?
A \( . N a^{+} \) and water
B. \( N a^{+} \) and \( O H^{-} \)
\( \mathrm{c} \cdot \mathrm{CO}_{3}^{2-} \) and water
D. \( C O_{3}^{2-} \) and \( H^{+} \)
Subject: Chemistry
\( \boldsymbol{C l O}^{-} \rightleftarrows \boldsymbol{C l O}_{3}^{-}+\boldsymbol{C l}^{-} \)
When the equation for the reaction represented above is balanced with
coefficients reduced to the lowest
whole-umber terms, correct statements
include which of the following?
I. The coefficient for \( C l^{-} \) is 4
II. The coefficient for \( C l O_{3}^{-} \) is 2
III. The coefficient for \( C l O^{-} \) is 3
A. I only
B. II only
C. III only
D. I and II only
E . I, II and III only
Subject: Physics
The correct value of dip angle at a place is
\( 45^{\circ} . \) If the dip circle is rotated by \( 45^{\circ} \) out of the meridian, then the tangent of the
angle of apparent dip at the place is :
A .
в. 0.5
c. \( \frac{1}{\sqrt{2}} \)
D. \( \sqrt{2} \)
Subject: Physics
Two point charges \( q_{1} \) and \( q_{2} \) are fixed at position vectors \( 4 \hat{i} \) and \( 3 \hat{j} \) respectively.
If a third charge \( q_{3} \) is in electrostatic equilibrium, then the position vector of
\( q_{3} \) may be :
This question has multiple correct options
A . \( 2 \hat{i}+1.5 \hat{j} \)
B . \( -2 \hat{i}+4.5 \hat{j} \)
c. \( 4 \hat{i}+3 \hat{j} \)
D. \( 3 \hat{i}+4 \hat{j} \)
Subject: Physics
In a resistance thermometer, the
resistances at \( 0^{\circ} \mathrm{C} \) and \( 100^{\circ} \mathrm{C} \) are 6.74
and 7.74 ohm respectively. The temperature corresponding to 6.53 ohm resistance is.
\( \mathbf{A} \cdot+53^{\circ} C \)
B. \( +21^{\circ} \mathrm{C} \)
\( \mathbf{c} .-53^{\circ} \mathrm{C} \)
D. \( -21^{\circ} \mathrm{C} \)
Subject: Chemistry
Which of the following is not correctly
matched?
\( \begin{array}{clc}\text { Complex ion } & \text { CFSE } \\ \text { a } & {\left[\operatorname{Co}\left(N H_{3}\right)_{6}\right]^{3+}} & 24 D q \\ \text { b } & {\left[\operatorname{Cr}\left(N H_{3}\right)_{6}\right]^{3+}} & 12 D q \\ \text { c } & {\left[F e F_{6}\right]^{3-}} & 4 D q \\ \text { d } & {\left[F e(C N)_{6}\right]^{3-}} & 20 D q\end{array} \)
Subject: Physics
The viscous force acting on a body falling under gravity in a viscous fluid will be
A \( \cdot \frac{6 \pi V}{\eta r} \)
в. \( \frac{6 \pi \eta r}{V} \)
c. \( 6 \pi \eta r V \)
D. \( \frac{r V}{6 \pi \eta} \)
Subject: Maths
If two events \( A \) and \( B \) such that \( P\left(A^{c}\right) \)
\( \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 4} \) and \( \boldsymbol{P}\left(\boldsymbol{A B}^{c}\right)=\mathbf{0 . 5}, \) then
\( \boldsymbol{P}\left[\boldsymbol{B} /\left(\boldsymbol{A} \cup \boldsymbol{B}^{c}\right)\right]= \)
A . 0.25
B. 0.50
c. 0.75
D. None of these
Subject: Chemistry
For which of the following reactions \( \boldsymbol{K}_{\boldsymbol{p}} \)
and \( K_{c} \) are not same?
A \( \left.\cdot H_{2}(g)+C l_{(} g\right) \rightleftharpoons 2 H C l(g) \)
B \( \cdot 2 S O_{3}(g) \rightleftharpoons 2 S O_{2}(g)+O_{2}(g) \)
c. \( N_{2}\left(g+O_{2} \rightleftharpoons 2 N O(g)\right. \)
D. None of these
Subject: Chemistry
\( Z n C O_{3} \) is thermally more stable than
\( M g C O_{3} \) because:
A. \( M g(O H)_{2} \) exhibits only basic properties while \( Z n(O H)_{2} \) is amphoteric
B. polarising action of \( Z n^{2+} \) with 18 -electron configuration on the anion is larger than that of \( M g^{2+} \) with a noble-gas electron configuration and of same size and charge
\( c . \) both
(a) and (b) are correct
D. none of the above is correct
Subject: Chemistry
\( C l_{2} \) gas is passed aqueous \( \mathrm{NaOH} \)
solution under given conditions
(a) \( C l_{2}+ \) NaOH (cold) \( \rightarrow \)
(b) \( C l_{2}+ \) NaOH (hot) \( \rightarrow \)
Equivalent mass of \( C l_{2} \) in \( (a) \) and \( (b) \) is
A. Equivalent mass of \( C l_{2} \) in (a) is \( 71.0 \mathrm{g} \) equivalent \( ^{-1} \)
Equivalent mass of \( C l_{2} \) in (b) is \( 42.6 \mathrm{g} \) equivalent \( ^{-1} \)
B. Equivalent mass of \( C l_{2} \) in (a) is \( 142.0 \mathrm{g} \) equivalent \( ^{-1} \)
Equivalent mass of \( C l_{2} \) in (b) is \( 85.2 \mathrm{g} \) equivalent \( ^{-1} \)
C. Equivalent mass of \( C l_{2} \) in (a) is \( 142.0 \mathrm{g} \) equivalent \( ^{-1} \)
Equivalent mass of \( C l_{2} \) in (b) is \( 42.6 \mathrm{g} \) equivalent \( ^{-1} \)
D. Equivalent mass of \( C l_{2} \) in (a) is 71.0 g equivalent \( ^{-1} \)
Equivalent mass of \( C l_{2} \) in (b) is 85.2 g equivalent \( ^{-1} \)
E. None of the above
Subject: Physics
Assertion
In some solids, the valence band is
completely filled while the next higher band separated by an energy gap of few electrons-volts is completely empty.
Reason
In insulators the energy band completely filled with electrons( the valence band) and above it is empty
band (the conduction band)
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
The capacitance of a parallel-plate
capacitor is \( C_{0} \) when the region
between the plates has air. This region
is now filled with a dielectric slab of
dielectric constant K. The capacitor is
connected to a cell emf \( \varepsilon_{1} \) and the slab
is taken out.
This question has multiple correct options
A. Charge \( \varepsilon C_{0}(K-1) \) flows through the cell
B. Energy \( \varepsilon^{2} C_{0}(K-1) \) is absorbed by the cell.
C. The energy stored in the capacitor is reduced by \( \varepsilon^{2} C_{0}(K-1) \)
D. The external agent has to do \( \frac{1}{2} \varepsilon^{2} C_{0}(K-1) \) amount of work to take the slab out.
Subject: Maths
\( \frac{0.86 \times 0.86 \times 0.86+0.14 \times 0.14 \times 0.1}{0.86 \times 0.86-0.86-0.14+0.14 \times 0.1} \)
is equal to
A . 1
B. 0
c. 2
D. 10
Subject: Maths
Let \( f \) be a function such that \( f(3)=1 \)
and \( f(3 x)=x+f(3 x-3) \) for all \( x \)
Then find the value of \( \boldsymbol{f}(\boldsymbol{3 0 0}) \)
A . 5500
B. 10100
\( c .5050 \)
D. 1,71,700
Subject: Maths
If a line \( A B \) makes an angle \( \theta \) with \( O X \)
and is at a distance of \( p \) units from the
origin, then the equation of \( A B \) is
A \( . x \sin \theta-y \cos \theta=p \)
B. \( x \cos \theta+y \sin \theta=p \)
\( \mathbf{c} . x \sin \theta+y \cos \theta=p \)
D. \( x \cos \theta-y \sin \theta=p \)
Subject: Physics
A semi-circular conducting ring acb of radius \( R \) moves with constant speed \( v \)
in a plane perpendicular to uniform
magnetic field \( B \) as shown in figure. Identify the correct statement
A \( \cdot V_{a}-V_{c}=B R v \)
В. \( V_{b}-V_{c}=B R v \)
c. \( V_{a}-V_{b}=0 \)
D. None of these
Subject: Maths
The vector equation of the plane which is at a distance of \( \frac{3}{\sqrt{14}} \) from the origin and the normal from the origin is \( 2 \hat{i}- \) \( \mathbf{3} \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \) is
A \( . \vec{r} .(2 \hat{i}-3 \hat{j}+\hat{k})=3 \)
B . \( \vec{r} .(\hat{i}+\hat{j}+\hat{k})=9 \)
c. \( \vec{r} .(\hat{i}+2 \hat{j})=3 \)
D. \( \vec{r} .(2 \hat{i}+\hat{k})=3 \)
Subject: Chemistry
Relation between hydrolysis constant and dissociation constant are given.
Which is the correct formula for \( M g C l_{2} \)
\( ? \)
A \( \cdot K_{h}=\frac{K_{w}}{K_{a}} \)
в. \( K_{h}=\frac{K_{w}}{K_{b}} \)
\( ^{\mathrm{c}} \cdot_{K_{h}}=\frac{K_{w}}{K_{a} \times K_{b}} \)
D. \( _{K_{w}}=\frac{K_{h}}{K_{b}} \)
Subject: Physics
Find the amount of heat supplied to decrease the volume of an ice water
mixture by \( 1 \mathrm{cm}^{3} \) without any change in
temperature. \( \left(\rho_{\text {ice}}=0.9 \rho_{\text {water}}, L_{\text {ice}}=\right. \)
\( \mathbf{8 0} \) cal \( / \mathbf{g m} \)
A . 360 call
B. 500 call
c. 720 call \( l \)
D. none of these
Subject: Maths
\( y+x^{2}=\frac{d y}{d x} \) has the solution:
A \( \cdot y+x^{2}+2 x+2=c \cdot e^{x} \)
B. \( y+x+2 x^{2}+2=c . e^{x} \)
C \( \cdot y+x+x^{2}+2=c \cdot e^{2 x} \)
D. \( y^{2}+x+x^{2}+2=c . e^{2 x} \)
Subject: Chemistry
The compounds \( \left[\boldsymbol{P t C l}_{2}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\right] \boldsymbol{B r}_{2} \)
and \( \left[\boldsymbol{P t B r}_{2}\left(\boldsymbol{N H}_{3}\right)_{4}\right] \boldsymbol{C l}_{2} \) constitute a
pair of:
A. coordination isomers
B. linkage isomers
c. ionisation isomers
D. optical isomers
Subject: Chemistry
Q Type your question
\( \boldsymbol{L} \)
(A) Polystyrene, Bakelite,
Teflon, PVC
(B) Polythene, Polystyrene,
Bakelite, PVC
(C) PVC, \( \quad \) Polythene
Polystyrene, Bakelite
(D) PVC, \( \quad \) Teflon
Melamine, Bakelite
Choose your answer from \( A, B, C \) and \( D \)
and enter accordingly.
Subject: Physics
A small cube of mass 'm' slides down a
circular path of radius 'R' formed from a arge block of mass 'M' as shown in
figure 'M' rests on a table and both blocks move without friction. The blocks
are initially at rest and 'm' starts from
the top of the path. Find the velocity 'v' of the cube as it leaves the block. Initially
the line joining \( \mathrm{m} \) and the centre is horizontal.
Subject: Chemistry
Which is correct for any kind of
species?
\( \mathbf{A} \cdot\left(E_{2}-E_{1}\right)>\left(E_{3}-E_{2}\right)>\left(E_{4}-E_{3}\right) \)
B \( \cdot\left(E_{2}-E_{1}\right)<\left(E_{3}-E_{2}\right)<\left(E_{4}-E_{3}\right) \)
\( \mathbf{C} \cdot\left(E_{2}-E_{1}\right)=\left(E_{3}-E_{2}\right)=\left(E_{4}-E_{3}\right) \)
D \( \cdot\left(E_{2}-E_{1}\right)=1 / 4\left(E_{3}-E_{2}\right)=1 / 9\left(E_{4}-E_{3}\right) \)
Subject: Physics
Assuming \( \boldsymbol{g}_{(m o o n)}=\left(\frac{1}{6}\right) g_{e a r t h} \) and
\( D_{(m o o n)}=\left(\frac{1}{4}\right) D_{e a r t h} \) where \( g \) and \( D \)
are the acceleration due to gravity and diameter respectively, the escape velocity from the moon is:
A \( \cdot \frac{11.2}{24} k m s^{-1} \)
B . \( 11.2 \times \sqrt{24} \mathrm{kms}^{-1} \)
c. \( \frac{11.2}{\sqrt{24}} k m s^{-1} \)
D. \( 11.2 \times 24 \mathrm{kms}^{-1} \)
Subject: Maths
In the given figure, \( A B C \) is a triangle,
side \( \mathrm{CB} \) is produced to \( \mathrm{E} \) and \( \angle \boldsymbol{A}: \angle \boldsymbol{B} \)
\( \angle C=2: 1: 3 . \) Find \( \angle D B E, \) if DB is
perpendicular to AB.
A \( \cdot 66^{\circ} \)
B . \( 46^{\circ} \)
\( c \cdot 60^{\circ} \)
D. none of the above
Subject: Physics
In an earth satellite moving in a circular orbit, a piece of metal weighing \( 16 g \) (on the earth) is weighed by a spring balance while the metal is suspended in water. If the relative density of the
metal is \( 8, \) what weight will be
recorded?
A. \( -2 g \)
B. zero
\( c \cdot 2 g \)
D. 14 g
Subject: Chemistry
a) Assign the position of the element having outer electronic configuration in the periodic table
(i) \( n s^{2} n p^{4} \) for \( n=3 \)
\( (n-1) d^{2} n s^{2} \) for \( n=4 \)
b) The size of \( N a^{+} \) cation is smaller
than \( N a . \) Explain
Subject: Physics
Two bodies are thrown simultaneously from a tower with same initial velocity \( v_{0} \)
one vertically upwards, the other vertically downwards. The distance between the two bodies after time t is
\( \mathbf{A} \cdot 2 v_{0} t+\frac{1}{2} g t^{2} \)
B. \( 2 v_{0} \)
C. \( v_{0} t+\frac{1}{2} g t^{2} \)
D. \( v_{0} \)
Subject: Maths
Number of points of focal minima of the functions \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}+\frac{\mathbf{1}}{\boldsymbol{x}^{2}}-\mathbf{8} \boldsymbol{x}-\frac{\boldsymbol{8}}{\boldsymbol{x}}+ \)
7 are
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D.
Subject: Maths
If \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x} \) and \( \boldsymbol{g}(\boldsymbol{x})=|\boldsymbol{x}|, \) then \( \boldsymbol{f}(\boldsymbol{x})+ \)
\( g(x) \) is equal to
\( \mathbf{A} \cdot \mathbf{0} \)
B . \( 2 x \)
\( \mathbf{c} \cdot 2 x \) if \( x \geq 0 \)
D. \( 2 x \) if \( x \leq 0 \)
Subject: Physics
Read the following statements.
a. Ozone in found mostly in the
stratosphere
b. Ozone layer lies \( 55-75 \) kms above the surface of the earth.
c. 0 zone absorbs ultraviolet radiation
from the Sun
d. Ozone layer has no significance for life on the earth.
Which set of the statements is correct?
A. a and c
B. b and d
\( c . \) b and \( c \)
D. a and d
Subject: Maths
Choose the correct answer from the
alternatives given.
The simple interest on a sum of money
is \( \frac{1}{16} \) of the sum. If the number of years is numerically equal to the rate percent per annum, then the rate percent per annum is
\( A \cdot 3 \frac{1}{3} \)
в. \( 6 \frac{2}{3} \)
\( c \cdot 2 \frac{1}{2} \)
\( D \cdot 7 \frac{1}{2} \)
Subject: Physics
\( N=2.5 \times 10^{3} \) wire turns are uniformly
wound on a wooden toroidal core of very
small cross-section. A current \( I \) flows
through the wire. If the ratio \( \eta \) of the magnetic induction inside the core to that at the centre of the toroid is \( x \times \)
\( 10^{2} . \) Find \( x \)
Subject: Chemistry
The statements regarding ozone
i) It oxidises \( C l_{2} \) to \( H C l \)
ii) It oxidises \( P b S \) to \( P b S O_{4} \)
iii) It oxidises \( \boldsymbol{K}_{4}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{6}\right] \) to
\( \boldsymbol{K}_{3}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{6}\right] \)
The correct combination is:
A. All are correct
B. (ii) and (iii) are correct
c. only (ii) is correct
D. Only (iii) is correct
Subject: Chemistry
Which of the following statements is incorrect?
A. It is not possible to compress a gas at a temperature below \( T_{c} \)
B. At a temperature below \( T_{c} \), the molecules are close enough for the attractive forces to act, and condensation occur
C. No condensation takes place above \( T_{c} \)
D. The kinetic energy of the gas molecules is higher above \( T_{c} \), and the attraction between them decreases
Subject: Physics
The relation between \( \left[\in_{0}\right] \) and \( \left[\mu_{0}\right] \) is
A \( \cdot\left[\mu_{0}\right]=\left[\epsilon_{0}\right][L]^{2}[T]^{-2} \)
B . \( \left[\mu_{0}\right]=\left[\epsilon_{0}\right][L]^{-2}[T]^{2} \)
C \( \cdot\left[\mu_{0}\right]=\left[\epsilon_{0}\right]^{-1}[L]^{2}[T]^{-2} \)
D \( \cdot\left[\mu_{0}\right]=\left[\epsilon_{0}\right]^{-1}[L]^{-2}[T]^{2} \)
Subject: Physics
At which depth, we get the necessary temperature for OTEC in the ocean?
\( A \cdot O m \) to \( 20 m \)
B. 100 m to 300 m
c. \( 400 \mathrm{m} \) to \( 600 \mathrm{m} \)
D. 700 \( \mathrm{m} \) to \( 900 \mathrm{m} \)
Subject: Physics
Assertion
If the current in a solenoid is reversed in
direction while keeping the same magnitude, the magnetic field energy stored in the solenoid decreases.
Reason

Magnetic field energy density is proportional to square of current
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
In Boolean algebra, \( \boldsymbol{A}+\boldsymbol{B}=\boldsymbol{Y} \) implies
that
A. sum of \( A \) and \( B \) is \( Y \).
B. \( Y \) exists when \( A \) exists or \( B \) exists or both \( A \) and \( B \) exist
c. \( Y \) exists only when \( A \) and \( B \) both exist
D. \( Y \) exists when \( A \) or \( B \) exist but not when both \( A \) and \( B \) exist
Subject: Physics
A water hose of cross sectional area 4
\( \mathrm{cm}^{2} \) is used to fill a 30 Iit vessel. If it
takes 1 minute to fill that vessel, the speed at which water leaves the hose is:
\( \mathbf{A} \cdot 250 \mathrm{cms}^{-1} \)
B. \( 62.5 \mathrm{cms}^{-1} \)
c. \( 125 \mathrm{cms}^{-1} \)
D. \( 500 \mathrm{cms}^{-1} \)
Subject: Chemistry
A photon of wavelength \( 4 \times 10^{-7} \mathrm{m} \)
strikes on the metal surface, the work
function of the metal is 2.13 eV.

Calculate the energy of the photon (eV)
(ii) the kinetic energy of the emission and (iii) the velocity of the photoelectrons \( (1 e V= \) \( \left.1.6020 X 10^{-23} J\right) \)
Subject: Biology
Which statement is correct for blood
pressure
A. The instrument by which we can measure B.P. is called stethoscope
B. Normal B.P. of the healthy person is \( 140 / 80 \mathrm{mm} \) Hg.
C. Diastolic pressure that shows the state of heart relaxation.
D. Systolic pressure limit is 140 \( \mathrm{mm} \mathrm{Hg} \)
Subject: Physics
A conducting sphere of radius \( \boldsymbol{R} \) having
charge \( q \) is joined to another
conducting sphere of radius \( 2 R \) having
charge \( -2 q . \) The charge flowing between them will be
\( \mathbf{A} \cdot \mathbf{q} \)
в. \( \frac{2 q}{3} \)
c. \( \frac{q}{3} \)
D. \( \frac{4 q}{3} \)
Subject: Physics
The de-Broglie wavelength \( \left(\boldsymbol{\lambda}_{B}\right) \) associated with the electron orbiting in the second excited state of hydrogen atom is related to that in the ground
state \( \left(\lambda_{G}\right) \) by :
A \( \cdot \lambda_{B}=\lambda_{G} / 3 \)
B . \( \lambda_{B}=\lambda_{G} / 2 \)
\( \mathbf{c} \cdot \lambda_{B}=2 \lambda_{G} \)
D. \( \lambda_{B}=3 \lambda_{G} \)
Subject: Physics
Two drops of same radius are falling through air with steady speed \( 2^{\frac{1}{3}} m / s . \) If the two drops coalesce, what would be
the terminal speed in \( m / s ? \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. 4
\( c \cdot 2 \)
D.