AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
The line \( x=y \) touches a circle at the
point \( (1,1) . \) If the circle also passes through the point (1,-3) then its radius is:
\begin{tabular}{l} 
A \( .3 \sqrt{2} \) \\
\hline
\end{tabular}
B. 3
c. \( 2 \sqrt{2} \)
D. 2
Subject: Maths
Using properties of determinants prove
that :
\( \left|\begin{array}{lll}\boldsymbol{x} & \boldsymbol{a} & \boldsymbol{a} \\ \boldsymbol{a} & \boldsymbol{x} & \boldsymbol{a} \\ \boldsymbol{a} & \boldsymbol{a} & \boldsymbol{x}\end{array}\right|=(\boldsymbol{x}+\mathbf{2} \boldsymbol{a})(\boldsymbol{x}-\boldsymbol{a})^{2} \)
Subject: Chemistry
In Ramsay - Rayleighs first method from
air, the correct statement is :
\( A \cdot O_{2} \) is removed as \( \mathrm{CO}_{2} \)
B. \( \mathrm{N}_{2} \) is removed as its oxide
c. oxygen is removed as \( \mathrm{CuO} \) and nitrogen is removed as \( \mathrm{Mg}_{3} \mathrm{N}_{2} \)
D. \( \mathrm{O}_{2} \) and \( \mathrm{N}_{2} \) are simultaneously removed as oxides of nitrogen
Subject: Chemistry
Assume that the decomposition of
\( H N O_{3} \) can be represented by the following equation
\( 4 H N O_{3}(g) \rightleftharpoons 4 N O_{2}(g)+ \)
\( \mathbf{2} \boldsymbol{H}_{\mathbf{2}} \boldsymbol{O}(\boldsymbol{g})+\boldsymbol{O}_{2}(\boldsymbol{g}) \)
The reaction approaches equilibrium at \( 400 K \) temperature and 30 atm pressure. At equilibrium partial
pressure of \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \) is \( \boldsymbol{2} \) atm.
Calculate \( \boldsymbol{K}_{c} \) in \( (\boldsymbol{m} \boldsymbol{o l} / \boldsymbol{L})^{3} \) at \( \boldsymbol{4} \boldsymbol{0} \boldsymbol{0} \boldsymbol{K} \)
\( (\text { Use }: \boldsymbol{R}=\mathbf{0 . 0 8 a t m}-\boldsymbol{L} / \boldsymbol{m o l}-\boldsymbol{K}) \)
\( A \cdot 4 \)
B. 8
\( c \cdot 16 \)
D. 32
Subject: Biology
Choose the correct order of the steps
involved in protein synthesis and
modification that takes place in several different locations throughout the cell.
I. Ribosome
II. Nucleus
III. Golgi apparatus
IV. Endoplasmic reticulum
A . ।, ॥, III and IV
B. ॥,।, IV and III
c. ॥ा, ॥, Iv and ।
D. ॥, I, III and IV
E . IV, III, II and I
Subject: Chemistry
Consider the following statements and arrange in the order of true/ false as
given in the codes
\( S_{1}: \) Argon is used in arc welding of metals or alloys to provide an inert atmosphere.
\( S_{2}: X e F_{2}, X e F_{4} \) and \( X e F_{6} \) are
colourless crystalline solids and sublime readily at \( 298 \mathrm{K} \)
\( \boldsymbol{S}_{3}: \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{2}, \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{4} \) and \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{6} \) are readily
hydrolysed.
\( S_{4}: \) Xenon fluorides react with fluoride
ion acceptor to form cationic species and fluoride ion donors to form fluoro
anions.
\( A \). FFFF
В. TFTF
c. \( \pi \pi \)
D. FTFT
Subject: Maths
If two sides of an isosceles \( \Delta \) are \( 3 \mathrm{cm} \)
and \( 8 \mathrm{cm}, \) then the length of the third side is :
\( \mathbf{A} \cdot 3 \mathrm{cm} \)
B. \( 8 \mathrm{cm} \)
\( c .3 \mathrm{cm} \) or \( 8 \mathrm{cm} \)
D. none
Subject: Physics
A charge \( q_{o} \) is distributed uniformly on a ring of radius R. A sphere of equal
radius R isconstructed with its centre
on the circumference of the ring. Find the electric flux through the surface of
the sphere.
A \( \cdot \frac{q_{0}}{3 \varepsilon_{0}} \)
в. \( \frac{q_{0}}{2 \varepsilon_{0}} \)
c. \( \frac{2 q_{0}}{\varepsilon_{0}} \)
D. \( \frac{4 q_{0}}{3 \varepsilon_{0}} \)
Subject: Chemistry
Neopentyl bromide, undergoes dehydrohalogenaton to give alkenes even though it has no hydrogen. This is due to:
A. \( E_{2} \) mechanism
B. \( E_{1} \) mechanism
C. Rearrangement of carbocations by \( E_{1} \) mechanism
D. \( E_{1} c B \) mechanism
E. \( E_{1} \) mechanism
Subject: Maths
What must be added to \( 7 z^{3}-11 z^{2}- \)
129 to \( \operatorname{get} 5 z^{2}+7 z-92 ? \)
A \( \cdot 7 z^{3}+16 z^{2}+7 z+37 \)
B . \( -7 z^{3}+16 z^{2}+7 z+37 \)
D. \( -7 z^{3}-7 z^{2}+7 z-37 \)
Subject: Physics
A diatomic molecule is formed by two
atoms which may be treated as mass
points \( m_{1}, \) and \( m_{2} \) joined by a massless rod of length r. Then, the moment of inertia of the molecule about an axis
passing through the centre of mass and perpendicular to rod is :
A. zero
B. \( \left(m_{1}+m_{2}\right) r^{2} \)
c. \( \frac{\left(m_{1}+m_{2}\right)}{m_{1} m_{2}} r^{2} \)
D. \( \left(\frac{m_{1} m_{2}}{m_{1}+m_{2}}\right) r^{2} \)
Subject: Chemistry
A mass of \( 0.65 g \) of zinc reacts completely with \( H C l \) to produce
hydrogen gas and a zinc chloride compound. The mass of the chlorine in the compound is \( 0.71 g \), what is the empirical formula of this compound?
(At. mass of \( Z n=65 g / \text { mol }) \)
\( \mathbf{A} \cdot Z n C l \)
в. \( Z n C l_{2} \)
c. \( Z n C l_{5} \)
D. \( Z n C l_{4} \)
Subject: Physics
Two bodies are projected vertically upwards from one point with the same initial velocity \( v_{0} . \) The second body is
projected \( t_{0} s \) after the first. How long after will the bodies meet?
A \( \cdot \frac{v_{0}}{2 g}+\frac{t_{0}}{2} \)
в. \( \frac{v_{0}}{g}+\frac{t_{0}}{2} \)
c. \( \frac{v_{0}}{g}+\frac{t_{0}}{4} \)
D. \( \frac{2 v_{0}}{g}+\frac{t_{0}}{2} \)
Subject: Physics
A toroid wound with 100 turns/m of wire
carries a current of \( 3 A \). The core of
toroid is made of iron having relative
magnetic permeability of \( \mu_{r}=5000 \) under given conditions. The magnetic field inside the iron is
\( \left(\text { Take } \mu_{o}=4 \pi \times 10^{-7} T m A^{-1}\right) \)
A \( .0 .15 T \)
в. \( 1.5 \times 10^{-2} T \)
c. \( 0.47 T \)
D. \( 1.88 T \)
Subject: Chemistry
\( F e C l_{3} \) on reaction with \( K_{4}\left[F e(C N)_{6}\right] \) in aqueous solution gives blue colour
These are separated by a
semipermeable membrane AB as
shown. Due to osmosis, there is:
A. Blue color formation in side \( x \)
B. Blue color formation in side Y.
c. Blue colour formation in both of the sides \( x \) and
D. No blue colour formation
Subject: Maths
Divide the following and write your answer in lowest terms: \( \frac{3 x^{2}-x-4}{9 x^{2}-16} \div \) \( \frac{4 x^{2}-4}{3 x^{2}-2 x-1} \)
A \( \frac{3 x+1}{4(3 x+4)} \)
В. \( \frac{3 x-1}{4(3 x+4)} \)
c. \( \frac{3 x+1}{4(3 x-4)} \)
D. None of these
Subject: Maths
Construct a quadrilateral \( \boldsymbol{A B N V} \) where \( \boldsymbol{A} \boldsymbol{V}=\mathbf{7} \boldsymbol{c m}, \boldsymbol{B} \boldsymbol{A}=\mathbf{8} \boldsymbol{c m}, \boldsymbol{B} \boldsymbol{N}= \)
\( \mathbf{1 0} c \boldsymbol{m}, \boldsymbol{N} \boldsymbol{V}=\mathbf{5} \boldsymbol{c m} \) and \( \boldsymbol{B} \boldsymbol{V}=\mathbf{1 1} \boldsymbol{c m} \)
Then, the perimeter of \( \Delta B N V \) is
\( \mathbf{A} \cdot 26 \mathrm{cm} \)
B. \( 24 \mathrm{cm} \)
c. \( 28 \mathrm{cm} \)
D. \( 22 \mathrm{cm} \)
Subject: Physics
A tank is filled with water of density 1 g \( c m^{-3} \) and oil of density \( 0.9 \mathrm{g} \mathrm{cm}^{-3} . \) The height of water layer is \( 100 \mathrm{cm} \) and of the oil layer is \( 400 \mathrm{cm} . \) If \( g=980 \mathrm{cm} s^{-2} \) then the velocity of efflux from an opening in the bottom of the tank is :
B . \( \sqrt{900 \times 980} \mathrm{cms}^{-1} \)
c. \( \sqrt{1000} \times 980 c \mathrm{cms}^{-1} \)
D. \( \sqrt{92 \times 980} \mathrm{cms}^{-1} \)
Subject: Physics
A uniform, horizontal beam of light is incident upon a prism as shown in the fig. The prism is in the shape of a
quarter cylinder of radius \( R=5 c m, \) and has a refractive index \( \frac{2}{\sqrt{3}} . \) A patch on the table for a distance \( x \) from the
cylinder is unilluminated. The value of \( x \)
is
A . \( 2.5 \mathrm{cm} \)
в. 5 ст
\( c \cdot 5 \sqrt{3} \mathrm{cm} \)
D. \( 10 \mathrm{cm} \)
Subject: Maths
Given the set \( P \) is the set of even
numbers between 15 and \( 25 . \) Label a
Venn diagram to represent the set \( \boldsymbol{P} \)
and indicate all the elements of set \( \boldsymbol{P} \)
in the Venn diagram.
B . \{16,20,24\}
c. \{16,18,20,22,24\}
D. None of these
Subject: Physics
A railway carriage has its centre of gravity at a height of \( 1 m \) above the rails
which are \( 1.5 m \) apart.The maximum
safe speed at which it could travel round an unbanked curve of radius
\( 100 m \) is
\( \mathbf{A} \cdot 12 m / s \)
в. \( 18 \mathrm{m} / \mathrm{s} \)
c. \( 22 m / s \)
D. \( 27 m / s \)
Subject: Chemistry
\( 2 \mathrm{g} \) benzoic acid \( \left(C_{6} H_{5} C O O H\right) \)
dissolved in 25 g of benzene shoes a depression in freezing point equal to 1.62 K. Molal depression constant for benzene is \( 4.9 \mathrm{K} \mathrm{kg} \) mol\( ^{-1} . \) What is the percentage association of acid if it
forms dimer in solution?
Subject: Physics
The path difference between two waves \( \boldsymbol{y}_{1}=\boldsymbol{a}_{1} \sin \left(\boldsymbol{\omega} \boldsymbol{t}-\frac{\boldsymbol{2} \boldsymbol{\pi} \boldsymbol{x}}{\boldsymbol{\lambda}}\right) \) and \( \boldsymbol{y}_{2}= \)
\( \boldsymbol{a}_{2} \cos \left(\boldsymbol{\omega} \boldsymbol{t}-\frac{\boldsymbol{2} \boldsymbol{\pi} \boldsymbol{x}}{\boldsymbol{\lambda}}+\boldsymbol{\phi}\right) \)
\( ^{A} \cdot \frac{\lambda}{2 \pi}[\phi+\pi / 2] \)
в. \( \frac{\lambda}{2 \pi}[\phi] \)
c. \( \frac{\lambda}{2 \pi}[\phi-\pi / 2 \)
D. \( \frac{2 \pi}{\lambda}[\phi \)
Subject: Maths
If \( (\boldsymbol{w}-\overline{\boldsymbol{w}} \boldsymbol{z}) /(1-\boldsymbol{z}) \) is purely real where
\( \boldsymbol{w}=\boldsymbol{\alpha}+\boldsymbol{i} \boldsymbol{\beta}, \boldsymbol{\beta} \neq \mathbf{0} \) and \( \boldsymbol{z} \neq \mathbf{1}, \) then set
of the values of \( z \) is
\( \mathbf{A} \cdot z:|z|=1 \)
B . \( z: z=\bar{z} \)
c. \( z: z \neq 1 \)
D \( \cdot z:|z|=1, z \neq 1 \)
Subject: Biology
Match the species with type of wood
(a) Tectona grandis
(b) Cedrus deodara
(c) Shorea robusta
(d) Dalbergia sisso
(e) Softwood
(f) Hardwood
A. a-e, b-f, c-f, d-e
B. a-e, b-e, c-f, d-f
c. a-f, b-e, c-f, d-f
D. a-f, b-e, c-e, d-f
Subject: Physics
A copper rod and a steel rod maintain a difference in their lengths constant=10
\( \mathrm{cm} \) at all temperatures. If their
coefficients of expansion are \( 1.6 \times \) \( 10^{-5} K^{-1} \) and \( 1.2 \times 10^{-5} K^{-1}, \) then the
length of the Cu rod is
A. \( 40 \mathrm{cm} \)
B. 30 cm
c. \( 32 \mathrm{cm} \)
D. 24 cm
Subject: Maths
In a triangle \( A B C, \angle A-\angle B=30^{\circ} \) and \( \angle A \)
\( \angle C=42^{\circ} ; \) find angle \( A \)
A \( \cdot A=84^{\circ} \)
B \( \cdot A=64 \)
C \( \cdot A=95 \)
D. \( A=92^{\circ} \)
Subject: Physics
When a bar of iron \( 50.0 \mathrm{cm} \) long at \( 15^{\circ} \mathrm{C} \) is heated in a furnace, it becomes
\( 50.4 \mathrm{cm} . \) If the coefficient of linear
expansion of iron is \( 1.1 \times 10^{-5} C^{o-1} \)
find the temperature of furnace.
Subject: Chemistry
At \( 500 \mathrm{K}, \) equilibrium constant, \( \boldsymbol{K}_{c} \) for
the following reaction is 5
\( \frac{1}{2} \boldsymbol{H}_{2(g)}+\frac{1}{2} \boldsymbol{I}_{2(g)} \rightleftharpoons \boldsymbol{H} \boldsymbol{I}_{(g)} \)
What would be the equilibrium
constant \( \boldsymbol{K}_{c} \) for the reaction:
\( \mathbf{2} \boldsymbol{H} \boldsymbol{I}_{(g)} \rightleftharpoons \boldsymbol{H}_{2(g)}+\boldsymbol{I}_{2(g)} ? \)
A .0 .04
B. 0.4
\( c \cdot 25 \)
D. 2.
Subject: Chemistry
Which of the following complex/ion has highest C-O bond length?
\( \mathbf{A} \cdot\left[V(C O)_{6}\right]^{-} \)
в. \( F e(C O)_{5} \)
c. \( N i(C O)_{4} \)
D. \( \left[M n(C O)_{6}\right]^{+} \)
Subject: Physics
A body is projected vertically upward with speed \( 10 m / s \) and other at same time with same speed in downward
direction form the top of a tower. The
magnitude of acceleration of first body with respect to second is \( \{\text { take } g= \)
\( \left.10 m / s^{2}\right\} \)
A. zero
B . \( 5 m / s^{2} \)
c. \( 10 m / s^{2} \)
D. \( 20 m / s^{2} \)
Subject: Maths
Let \( f \) be a real function given by \( f(x)= \) \( \sqrt{x-2} . \) Find the following.
(i) \( \boldsymbol{f} \circ \boldsymbol{f} \)
(ii) \( \boldsymbol{f} \circ \boldsymbol{f} \circ \boldsymbol{f} \)
(iii) \( (f \circ f \circ \)
\( \boldsymbol{f}(\mathbf{3 8}) \)
(iv) \( \boldsymbol{f}^{2} \)
Also, show that \( \boldsymbol{f} \circ \boldsymbol{f} \neq \boldsymbol{f}^{2} \)
Subject: Chemistry
\( \boldsymbol{O H} \)
\( \boldsymbol{C H}_{3}-\dot{\boldsymbol{C}}-\boldsymbol{C H}_{2}-\stackrel{\boldsymbol{O}}{\boldsymbol{C}}-\boldsymbol{C H}_{3} \)
\( \boldsymbol{H} \)
The IUPAC name of the compound is
A. 2 - Hydroxypentan - 4 - one
B. 4 - Hydroxypentan - 2 - one
c. 4 - oxopentan -2 - ol
D. 2 - oxopentan \( -4- \) o
Subject: Physics
For two structures namely \( S_{1} \) with \( n_{1}= \) \( \sqrt{45 / 4} \) and \( n_{2}=3 / 2, \) and \( S_{2} \) with \( n_{1}= \)
\( 8 / 5 \) and \( n_{2}=7 / 5 \) and taking the refractive index of water to be \( 4 / 3 \) and
that of air to be \( 1, \) the correct option is
are
This question has multiple correct options
A. NA of \( S_{1} \) immersed in water is the same as that of \( S_{2} \)
immersed in a liquid of refractive index \( \frac{16}{3 \sqrt{15}} \)
B. NA of \( S_{1} \) immersed in liquid of refractive index \( \frac{6}{\sqrt{15}} \)
same as that of \( S_{2} \) immersed in water
C. NA of \( S_{1} \) placed in air is the same as that of \( S_{2} \)
immersed in a liquid of refractive index \( \frac{4}{\sqrt{15}} \)
D. NA of \( S_{1} \) placed in the air is the same as that of \( S_{2} \) placed in water
Subject: Physics
Two coils have self-inductance \( \boldsymbol{L}_{\mathbf{1}}=\mathbf{4} \)
\( \boldsymbol{m} \boldsymbol{H} \) and \( \boldsymbol{L}_{2}=\mathbf{1} \boldsymbol{m} \boldsymbol{H} \) respectively. The
currents in the two coils are increased
at the same rate. At a certain instant of
time both coils are given the
same power. If \( i_{1} \) and \( i_{2} \) are the currents
in the two coils, at that instant of time
respectively, then the value of \( \left(i_{1} / i_{2}\right) \) is
A \( \cdot \frac{1}{8} \)
в. \( \frac{1}{4} \)
\( c \cdot \frac{1}{2} \)
D.
Subject: Chemistry
The given figure shown the Maxwell
distribution of molecular speeds of gas
at three different temperatures \( \boldsymbol{T}_{1}, \boldsymbol{T}_{2} \)
and \( T_{3} . \) The correct order of temperature
is :
\( \mathbf{A} \cdot T_{1}>T_{2}>T_{3} \)
В. \( T_{1}>T_{3}>T_{2} \)
\( \mathbf{c} \cdot T_{3}>T_{2}>T_{1} \)
D. \( T_{2}>T_{3}>T_{1} \)
Subject: Chemistry
The ratio of number of moles of
\( K M n O_{4} \) and \( K_{2} C r_{2} O_{7} \) required to
oxidise \( 0.1 \mathrm{mol} \mathrm{Sn}^{+4} \) in acidic medium:
A .6: 5
B. 5: 6
c. 1: 2
D. 2: 1
Subject: Chemistry
If \( \boldsymbol{K}_{s p} \) for \( \boldsymbol{H} \boldsymbol{g} \boldsymbol{S} \boldsymbol{O}_{4} \) is \( \boldsymbol{6} . \boldsymbol{4} \times 10^{-5}, \) then
solubility of this substance in mole per
\( m^{3} \) is:
A. \( 8 \times 10^{-3} \)
В. \( 6.4 \times 10^{-5} \)
c. \( 8 \times 10^{-6} \)
D. None of these
Subject: Physics
The magnitude of electric field at different points along the length of the rod is given by
A \( \cdot \frac{V_{o}}{L^{2}}(L-X) \)
B. \( \frac{V_{o}}{(L+X)} \)
c. \( \frac{V_{o}}{L} \)
D. \( \frac{V_{o}}{2 L} \)
Subject: Maths
f \( a, b, c \in R^{+} \) and \( 2 b=a+c, \) then
check the nature of roots of equation \( \boldsymbol{a} \boldsymbol{x}^{2}+\boldsymbol{2} \boldsymbol{b} \boldsymbol{x}+\boldsymbol{c}=\mathbf{0} \)
Subject: Maths
Find the direction cosine \( l, \boldsymbol{m}, \boldsymbol{n} \) of line
which are connected by the relations \( \boldsymbol{l}+\boldsymbol{m}+\boldsymbol{n}=\mathbf{0} . \boldsymbol{2 m} \boldsymbol{n}+\boldsymbol{2} \boldsymbol{m} \boldsymbol{l}-\boldsymbol{n l}=\mathbf{0} \)
Subject: Chemistry
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{O} \boldsymbol{H} \frac{c o \boldsymbol{c} \boldsymbol{c} \boldsymbol{H}_{2} \boldsymbol{S O}_{4}}{170^{\circ} \boldsymbol{C}} \)
\( \boldsymbol{A} \quad \frac{\boldsymbol{C l}_{2}}{500^{\circ} \boldsymbol{C}} \boldsymbol{B} \)
\( A \) and \( B \) are:
A \( \cdot A: C H_{3} C H_{2} C H_{3}, \quad B: C H_{3} C H_{2} C H_{2} C l \)
B. \( A: C H_{3} C H=C H_{2}, \quad B: C H_{2} C l C H=C H_{2} \)
c. \( A: C H_{2}=C H_{2}, \quad B: C H_{3} C H_{2} C l \)
D. \( A: C H_{3} C H_{2} C H_{3}, \quad B: C H_{3} C H=C H_{2} \)
Subject: Maths
Two circles of radii \( 10 \mathrm{cm} \) and \( 8 \mathrm{cm} \)
intersects each other and the length of
the common chord is \( 12 \mathrm{cm} \), find the
distance between their centers.
A. \( 2 \mathrm{cm} \)
в. \( (8+2 \sqrt{7}) \) ст
\( c .8 \mathrm{cm} \)
D. \( 2 \sqrt{7} \) cm
Subject: Maths
The value of
\( \int_{-\pi / 2}^{\pi / 2}\left(\operatorname{psin}^{3} x+q \sin ^{4} x+r \sin ^{5} x\right) \) does
not depend on
\( A \cdot p, q, r \)
B. p, ronly
c. ponly
D. \( q \), ronly
Subject: Chemistry
When Mg is burnt in air and they are
decomposed by \( \boldsymbol{H}_{2} \boldsymbol{O}, \boldsymbol{M} \boldsymbol{g} \boldsymbol{O}, \boldsymbol{M} \boldsymbol{g}_{3} \boldsymbol{N}_{2} \)
changing to \( M g(O H)_{2} \) and \( N H_{3} \). If
true enter 1 , else enter 0
Subject: Chemistry
Assertion: Both reactions are Lewis
acid-base reactions?
¡. \( \boldsymbol{N} \boldsymbol{H}_{3}+\boldsymbol{B} \boldsymbol{F}_{3} \longrightarrow \boldsymbol{H}_{3} \boldsymbol{N}-\boldsymbol{B} \boldsymbol{F}_{3} \)
ii. \( \boldsymbol{M} \boldsymbol{g}+\boldsymbol{S} \longrightarrow \boldsymbol{M} \boldsymbol{g}^{2+}+\boldsymbol{S}^{2-} \)
Reason: Lewis acid-base reaction
involve the donation of lone pair electrons from base to acid. This
donation results in a coordinate bond.
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
E. Both Assertion and Reason are incorrect
Subject: Physics
The \( 6 V \) Zener diode is shown in figure
has negligible resistance and a knee
current of \( 5 m A \). The minimum value of
\( R(i n \Omega) \) so that the voltage across it
does not fall below \( 6 V \) is
A. 40
в. 60
\( c \cdot 72 \)
D. 80
\( E .120 \)
Subject: Physics
A sphere \( P(\text { emissivity }=1 \) ) of radius
\( 2 R \) and and another sphere \( Q \) (emissivity \( =1 / 2 \) ) of radius \( R \) are
placed in vacuum at some distance. There are no other objects. The temperature of the sphere \( Q \) is
maintained at \( 200 K \) by the means of a
heater. A fraction \( 1 / 32 \) of the power
emitted by the sphere \( Q \) falls on the sphere \( P \). If the equilibrium
temperature of the sphere \( \boldsymbol{P} \) is \( 10 \boldsymbol{T} \) (in
\( K \) ), find the value of \( T: \)
Subject: Chemistry
What will be the emf for the given cell :
\( P t\left|H_{2}\left(P_{1}\right)\right| H^{+}(a q)\left|H_{2}\left(P_{2}\right)\right| P t \)
\( ^{\text {A } \cdot} \frac{R T}{F} \log \frac{P_{1}}{P_{2}} \)
в. \( \frac{R T}{2 F} \log \frac{P_{1}}{P_{2}} \)
c. \( \frac{R T}{F} \log \frac{P_{2}}{P_{1}} \)
D. noneofthese
Subject: Physics
Two wheels \( A \) and \( B \) are released from
rest from points \( X \) and \( Y \) respectively
on an inclined plane as shown in figure. Which of the following statement(s) is/are incorrect?
This question has multiple correct options
A. Wheel \( B \) takes twice as much time to roll from \( Y \) to \( Z \) than that of wheel \( A \) from \( X \) to \( Z \)
B. At point \( Z \) velocity of wheel \( A \) is four times that of wheel \( B \)
c. Acceleration of the wheel \( A \) is four times that of wheel
\( B \)
D. Both wheel take same time to arrive at point \( Z \).
Subject: Maths
STATEMENT-1: If a and b are positive and \( [x] \) denotes the greatest integer
less than or equal to \( x, \) then \( \lim _{x \rightarrow 0^{+}} \frac{x}{a}\left[\frac{b}{x}\right]=\frac{b}{a} \)
STATEMENT-2: \( \lim _{x \rightarrow \infty} \frac{\{x\}}{x} \rightarrow 0, \) where \( \{x\} \)
denotes the fractional part of \( x \)
A. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-
B. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1
C. STATEMENT-1 is True, STATEMENT-2 is False
D. STATEMENT-1 is False, STATEMENT-2 is True
Subject: Chemistry
(a) An organic compound (A) of
molecular formula \( C_{2} H_{4} O \) is prepared
by the reduction of compound (B) of
molecular formula \( C_{2} H_{3} N \) dissolved in
ether, with \( S n C l_{2} \) and \( H C l . \) Compound
(A) reduces Tollen's reagent. When a
drop of conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) is added to
compound (A), it polymerises to give a cyclic compound
(C). Identify (A), (B) and (C). Explain the reactions?
(b) Ionic conductance at infinite dilution of \( A l^{3+} \) and \( S O_{4}^{2-} \) are 189 ohm \( ^{-1} \mathrm{cm}^{2} \) gm.equiv \( ^{-1} \) and
160 ohm \( ^{-1} \mathrm{cm}^{2} \) gm.equiv \( ^{-1} \). Calculate
equivalent and molar conductance of the electrolytes at infinite dilution?
Subject: Physics
The diameter of a brass rod is \( 4 m m \) and
Youngs modulus of brass is \( 9 \times \) \( 10^{10} N / m^{2} \) The force required to stretch
it by \( 0.1 \% \) of its length is
A. \( 360 \pi N \)
Then
в. \( 36 N \)
c. \( 144 \pi \times 10^{3} N \)
D. \( 36 \pi \times 10^{5} N \)
Subject: Maths
Equation of the curve whose polar sub \( \operatorname{tangent} r^{2} \frac{d \theta}{d r} \) is constant
A. \( r(\theta+c)+k=0 \)
B \( \cdot r^{2}(\theta+c)=2 k \)
c. \( r(\theta-c)=k^{2} \)
D. \( r \theta=c \)
Subject: Physics
In moving from \( A \) to \( B \) along an electric
field line, the electric field does \( 1.28 \times \)
\( 10^{-18} J \) of work on an electron. If \( \phi_{1}, \phi_{2} \)
are equipotential surface, then
potential difference \( V_{E}-V_{D} \) is equal
to:
A. -8 volt
B. +8 volt
\( c \). zero
D. 64 volt
Subject: Physics
An aeroplane is flying from city \( A \) to \( B \) along path 1. The path 1 is a circular arc whose centre coincides with the centre
of the earth. Another aeroplane is flying along path 2 from \( A \) to \( B \). The path 2 is
circular arc whose centre is at \( \mathrm{C} \). O is
the centre of the earth. Then
A. The distance travelled by \( 1^{s t} \) aeroplane is greater than that of \( 2^{n d} \) aeroplane
B. The distance travelled by \( 1^{\text {st}} \) aeroplane is less than that of \( 2^{n d} \) aeroplane
c. The displacement of both aeroplane is different
D. None of these
Subject: Chemistry
Slaked lime is obtained when water is
added to:
A \( \cdot \operatorname{CaSO}_{4} \cdot \frac{1}{2} \mathrm{H}_{2} \mathrm{O} \)
в. \( C a C l_{2} \)
\( c \cdot C a O \)
D. \( C a C O_{3} \)
Subject: Chemistry
Which of the following expressions is
correct?
\( \boldsymbol{A} \cdot \ldots_{p}=K_{c}\left(\frac{R T}{\sum n}\right)^{\Delta n} \)
\( \mathrm{B} \cdot \quad K_{p}=K_{x}\left(\frac{P}{\sum n}\right)^{\Delta n} \)
\( \mathrm{C} \cdot_{p}=K_{n}\left(\frac{P}{\sum n}\right)^{\Delta n-1} \)
\( \mathrm{D} \cdot_{p}=K_{c}\left(\frac{P}{\sum n}\right)^{-\Delta n+1} \)
Subject: Biology
In the given diagram of a leg of
cockroach, parts have been indicated by
alphabets. Select the answer in which
these alphabets have been
correctly matched with the parts which
they indicate.
A. A- Coxa; B- Tibia; C- Tarsus; D- Femur; E- Trochanter
B. A- Coxa; B- Femur; C- - Trochanter
D- Tarsus; E- Tibia
C. A- Coxa; B- Tarsus; C- Femur; D- Tibia; E- Trochanter
D. A- Coxa; B- Trochanter; C- Femur; D- Tibia; E- Tarsus
Subject: Maths
What is the area of the region bounded by \( \mathrm{X} \) -axis, the curve \( \boldsymbol{y}=\boldsymbol{f}(\boldsymbol{x}) \) and the two ordinates \( x=\frac{1}{2} \) and \( x=1 ? \)
A \( \cdot \frac{5}{12} \) sq unit
B. \( \frac{5}{6} \) sq unit
c. \( \frac{7}{6} \) sq unit
D. 2 sq unit
Subject: Chemistry
Which one of the following is the correct set with respect to molecule,
hybridization and shape?
A. \( B e C l_{2}, s p^{2} \), linear
B . \( B e C l_{2}, s p^{2}, \) triangular planar
c. \( B C l_{3}, s p^{2} \), triangular planar
D. \( B C l_{3}, s p^{3} \), tetrahedral