AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
An Arithmetic Series is defined as
\( \boldsymbol{f}(\boldsymbol{n})=\boldsymbol{a}+(\boldsymbol{n}-\mathbf{1}) \boldsymbol{d}, \boldsymbol{n} \in \boldsymbol{N}, \) prove
that A.M. of \( \boldsymbol{f}(\mathbf{1}) \) and \( \boldsymbol{f}(\boldsymbol{2 n}-\mathbf{1}) \) is \( \boldsymbol{f}(\boldsymbol{n}) \)
Subject: Maths
If \( A \) and \( B \) are two events, then which of
the following does not represent the
probability of at most one of \( A, B \) occurs.
\( \mathbf{A} \cdot 1-P(A \cap B) \)
B . \( P(\bar{A})-P(\bar{B})+-P(\bar{A}+\bar{B}) \)
\( \mathbf{c} \cdot P(\bar{A})+P(\bar{B})+-P(\bar{A} \cap \bar{B}) \)
\( \mathbf{D} \cdot P(A \cap \bar{B})+P(\bar{A} \cap \bar{B})-P(\bar{A} \cap \bar{B}) \)
Subject: Chemistry
Arrange the following sulphates of alkaline earth metals in order of decreasing thermal stability:
\( B e S O_{4}, M g S O_{4}, C a S O_{4}, S r S O_{4} \)
A \( \cdot B e S O_{4}>M g S O_{4}>C a S O_{4}>S r S O_{4} \)
в. \( \operatorname{SrSO}_{4}>\operatorname{Mg} S O_{4}>\operatorname{CaSO}_{4}> \)Ве\( S O_{4} \)
c. \( \operatorname{SrSO}_{4}>\operatorname{CaSO}_{4}>\operatorname{MgSO}_{4}>\operatorname{BeSO}_{4} \)
\( \mathrm{D} \cdot \operatorname{SrSO}_{4}>\operatorname{CaSO}_{4}>\operatorname{Be} \mathrm{SO}_{4}>\mathrm{MgSO}_{4} \)
Subject: Chemistry
A complex is represented as \( C o C l_{3} \)
\( X N H_{3} . \) Its 0.1 molal solution in water
shows \( \Delta T_{f}=0.558^{\circ} C . K_{f} \) of \( H_{2} O \) is
\( 1.86 \mathrm{K} / \mathrm{m} . \) Assuming \( 100 \% \) ionisation,
the number of \( N H_{3} \) molecules
associated with Co is:
Subject: Chemistry
Write down the number of \( 3 d \) electrons
in each of the following ions:
\( \boldsymbol{T} \boldsymbol{i}^{2+}, \boldsymbol{V}^{2+}, \boldsymbol{C} \boldsymbol{r}^{3+}, \boldsymbol{M} \boldsymbol{n}^{2+}, \boldsymbol{F} \boldsymbol{e}^{2+}, \boldsymbol{F} \boldsymbol{e}^{3+}, \boldsymbol{C} \boldsymbol{o} \)
and \( C u^{2+} . \) Indicate how would you
expect the five \( 3 d \) orbitals to be
occupied for these hydrated ions (octahedral).
Subject: Maths
In the figure, \( \boldsymbol{O} \) is the point of
intersection of two chords \( A B \) and \( C D \)
such that \( O B=O D \), then triangles
\( O A C \) and \( O D B \) are:
A. Equilateral but not similar
B. Isosceles but not similar
c. Equilateral and similar
D. Isosceles and similar
Subject: Maths
\( \int_{\pi / 6}^{\pi / 3} \frac{\sin ^{3} x}{\sin ^{3} x+\cos ^{3} x} d x= \)
A \( \cdot \frac{\pi}{2} \)
в.
\( c \cdot \frac{\pi}{12} \)
D. \( \frac{\pi}{6} \)
Subject: Physics
We consider the Thomson model of the
hydrogen atom in which the proton is distributed uniformly over a spherical volume of radius 0.25 angstrom. Applying the Bohr's condition in this model the ground state energy (in eV) of the electron will be close to :
A. \( -\frac{13.6}{4} \)
B . -13.6
c. \( -\frac{13.6}{2} \)
D. \( -2 \times 13.6 \)
Subject: Maths
The median of the following data is 525
Find the values of \( x \) and \( y \) if the total
frequency is 100
\begin{tabular}{|c|c|}
\hline Class Interval & Frequency \\
\hline \( 0-100 \) & 2 \\
\hline \( 100-200 \) & 5 \\
\hline \( 200-300 \) & \( x \) \\
\hline \( 300-400 \) & 12 \\
\hline \( 400-500 \) & 17 \\
\hline \( 500-600 \) & 20 \\
\hline \( 600-700 \) & \( \mathrm{Y} \) \\
\hline \( 700-800 \) & 9 \\
\hline \( 800-900 \) & 7 \\
\hline \( 900-1000 \) & 4 \\
\hline
\end{tabular}
Subject: Chemistry
If one-third of \( H I \) decomposes at a
particular temperature, \( \boldsymbol{K}_{c} \) for the equilibrium is:
\( \boldsymbol{H} \boldsymbol{I} \rightleftharpoons \boldsymbol{H}_{2}+\boldsymbol{I}_{2} \)
A . \( 1 / 16 \)
B. \( 1 / 4 \)
\( c \cdot 1 / 6 \)
D. \( 1 / 2 \)
Subject: Physics
An object \( 2.5 \mathrm{cm} \) high is placed at a
distance of \( 10 \mathrm{cm} \) from a concave
mirror of radius of curvature \( 30 \mathrm{cm} . \) The
size of the image is:
\( \mathbf{A} \cdot 9.2 \mathrm{cm} \)
в. \( 10.5 \mathrm{cm} \)
c. \( 5.6 \mathrm{cm} \)
D. \( 7.5 \mathrm{cm} \)
Subject: Physics
Two long thin charged rods with charge density \( \lambda \) each are placed parallel to each other at a distance d apart. The
force per unit length exerted on one rod by the other will bewhere \( \left(\boldsymbol{K}=\frac{\mathbf{1}}{\mathbf{4} \boldsymbol{\pi} \varepsilon_{0}}\right) \)
A \( \cdot \frac{K 2 \lambda}{d} \)
в. \( \frac{K 2 \lambda^{2}}{d} \)
c. \( \frac{K 2 \lambda}{d^{2}} \)
D. \( \frac{K 2 \lambda^{2}}{d^{2}} \)
Subject: Chemistry
\( \boldsymbol{H} \boldsymbol{C l O}, \boldsymbol{H} \boldsymbol{C l O}_{2}, \boldsymbol{H} \boldsymbol{C l} \boldsymbol{O}_{3}, \boldsymbol{H} \boldsymbol{C l O}_{4} \)
Arrange the given compound in order of increasing acidic strength
Subject: Chemistry
Consider the following elementary reaction,
\[
\mathbf{2 A}+\boldsymbol{B}+\boldsymbol{C} \rightarrow \boldsymbol{\text {Products.}}
\]
All reactant are present in the gaseous
state and reactant \( C \) is taken in excess.
What is the rate expression of the
reaction?
\( \mathbf{A} \cdot \) Rate\( =k[A]^{2}[B][C] \)
B . Rate\( =k[A]^{2}[B] \)
\( c \)
\[
\text {Rate}=k \frac{[A]^{2}[B]}{[C]}
\]
D. Rate\( =k[C]^{0} \)
Subject: Maths
In the figure given above, \( A D \) is a
straight line, \( O P \) perpendicular to \( A D \)
and 0 is the centre of both circles. If
\( \boldsymbol{O A}=\mathbf{2 0} \boldsymbol{c m}, \boldsymbol{O B}=\mathbf{1 5} \boldsymbol{c m} \) and \( \boldsymbol{O P}= \)
\( 12 \mathrm{cm} . \) what is \( A B \) equal to?
\( A \cdot 7 \mathrm{cm} \)
\( 3.8 \mathrm{cm} \)
\( c .10 \mathrm{cm} \)
\( 0.12 \mathrm{cm} \)
Subject: Physics
Assume that the number of hole-
electron pair in an intrinsic
semiconductor is proportional to
\( e^{\Delta E / 2 k T} . \) Here \( \Delta E= \) energy gap and
\( \boldsymbol{k}=\mathbf{8 . 6 2} \times \mathbf{1 0}^{\mathbf{5}} \boldsymbol{e V} / \boldsymbol{K} . \) The energy gap
for silicon is \( 1.1 e V . \) The ratio of electron
hole pairs at \( 300 K \) and \( 400 K \) is
\( \mathbf{A} \cdot e^{5.104 \times 10^{-8}} \)
B \( \cdot e^{-5} \)
\( c \cdot c \)
D. \( e^{2} \)
Subject: Chemistry
The heats of formation of
\( \boldsymbol{C}_{6} \boldsymbol{H}_{6}(l), \boldsymbol{H}_{2} \boldsymbol{O}(l), \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g}) \) are
11.70,-68.4 and \( -94.0 k c a l \)
respectively. Calculate the heat of combustion of benzene(l)
A . -780.9 kcal-780.9kcal
B. -680.9 kcal-780.9kcal
c. 580.9 kcal-780.9kcal
D. 480.9 kcal-780.9kcal
Subject: Chemistry
The relative reactivity of \( 1^{\circ} H, 2^{\circ} H \) and
\( 3^{\circ} H \) in bromination reaction has been
found to be 1: 82: 1600 respectively. In
the reaction the percentage yields of the products (A) and (B) are expected to be:
\( (A) \)
A . 99.4\%, 0.6\%
B . 50\%, 50\%
c. 0.6\%, 99.4\%
D. 80\%, 20\%
Subject: Maths
\( \int \frac{\sin 2 x}{\sin ^{2} x+2 \cos ^{2} x} d x= \)
A \( \cdot \log \left(1+\cos ^{2} x\right)+C \)
В \( \cdot \log \left(1+\tan ^{2} x\right)+C \)
\( \mathbf{c} \cdot-\log \left(1+\sin ^{2} x\right)+C \)
\( \mathbf{D} \cdot-\log \left(1+\cos ^{2} x\right)+C \)
Subject: Physics
The value of \( \left(n_{2}+n_{1}\right) \) and \( \left(n_{2}^{2}-n_{1}^{2}\right) \) for
\( H e^{+} \) ion in atomic spectrum are 4 and 8 respectively. The wavelength of emitted photon when electron jump
from \( n_{2} \) to \( n_{1} \) is:
\( ^{\mathbf{A}} \cdot \frac{32}{9} R_{H} \)
в. \( \frac{9}{32} R_{H} \)
c. \( \frac{9}{32 R_{H}} \)
D. \( \frac{32}{9 R_{H}} \)
Subject: Maths
The projection of the join of the points (3,4,2),(5,1,8) on the line whose d.c's \( \operatorname{are}\left(\frac{2}{7}, \frac{3}{7}, \frac{6}{7}\right) \) is
A. 7
B. \( \frac{31}{71} \)
\( \mathbf{c} \cdot \frac{42}{13} \)
\( D \cdot \frac{38}{138} \)
Subject: Maths
Solve \( \int \frac{1-\sqrt{x}}{1+\sqrt{x}} d x \)
A \( \cdot 3 \sqrt{x}+\frac{x}{2}-3 \log (1+\sqrt{x})+c \)
B \( 3 \sqrt{x}+3 \log (1+\sqrt{x})-\frac{1}{2} x+c \)
c. \( 3 \sqrt{x}-\frac{1}{2} x-3 \log (1+\sqrt{x})++c \)
D. \( 4 \sqrt{x}-x-4 \log (1+\sqrt{x})+c \)
Subject: Maths
\( \lim _{x \rightarrow 0^{-}}(\ln (\{x\}+|[x]|))^{\{x\}}, \) where \( \{\cdot\} \)
denotes fractional part function and \( [\cdot \) denotes greatest integer function, is
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot \ln 2 \)
D. \( \ln \frac{1}{2} \)
Subject: Biology
Arrange the direction of nerve
transmission in sequential order.
a) Cyton
b) Axon
c) Dendron
d) Nerve terminal
\( A \cdot c, a, b, d \)
в. \( a, c, b, d \)
\( c \cdot c, a, d, b \)
D. \( \mathrm{c}, \mathrm{b}, \mathrm{a}, \mathrm{d} \)
Subject: Chemistry
A sample consisting of 1 mol of a
monoatomic perfect gas \( \left(C_{v}=\frac{3}{2} R\right) \) is
taken through the cycle as shown:
\( \Delta H \) for the overall cycle is :
A \( \cdot+5.67 \times 10^{3} J \)
B \( .-5.67 \times 10^{3} J \)
c. \( -11.34 \times 10^{3} J \)
\( D \)
Subject: Physics
\( I \) is the moment of inertia of a thin
square plate about an axis passing through opposite corners of plate. The moment of inertia of same plate about an axis perpendicular to the plane of plate and passing through its centre is :
A \( \cdot \frac{I}{2} \)
в. \( \frac{I}{\sqrt{2}} \)
\( c \cdot \sqrt{2} I \)
D. \( 2 I \)
Subject: Maths
The lower limit of the modal class of the
following data is :
\( \begin{array}{lllll} & 0 & 10 & 20 & 30 \\ \text { c.l. } & - & - & - & - \\ & 10 & 20 & 30 & 40\end{array} \)
Frequency \( \quad 5 \quad 8 \quad \) 13 \( \quad \) 7
A . 10
B. 30
c. 20
D. 50
Subject: Maths
If the radius of a sphere is increased by \( 2 \mathrm{cm}, \) then its surface area increases by
\( 352 c m^{2} . \) The radius of the sphere before
the increase was
A. \( 3 \mathrm{cm} \)
B. \( 4 \mathrm{cm} \)
\( c .5 \mathrm{cm} \)
D. \( 6 \mathrm{cm} \)
Subject: Maths
Solve the systems of equations:
\( \frac{\boldsymbol{x}-\mathbf{2}}{\mathbf{4}}+\frac{\boldsymbol{y}+\mathbf{1}}{\mathbf{3}}=\mathbf{2} ; \frac{\boldsymbol{x}+\mathbf{1}}{\mathbf{7}}+\frac{\boldsymbol{y}-\mathbf{3}}{\mathbf{2}}= \)
\( \frac{1}{2} \)
A \( \cdot(6,2) \)
в. (2,2)
c. (2,3)
(年. (2,3,3)
D. (3,4)
Subject: Physics
The \( X-Z \) plane separates two media
\( A \) and \( B \) of refractive indices \( \mu_{A}=1.5 \)
and \( \mu_{B}=2 . \) A ray of light travels from
\( A \) to \( B \), its direction in two media are
given by unit vectors. \( \hat{\boldsymbol{u}}_{\boldsymbol{A}}=\boldsymbol{a} \hat{\boldsymbol{i}}+\boldsymbol{b} \hat{\boldsymbol{j}} \) and
\( \hat{\boldsymbol{u}}_{B}=\boldsymbol{c} \hat{\boldsymbol{i}}+\boldsymbol{d} \hat{\boldsymbol{j}} \) respectively, then :
\( ^{A} \cdot \frac{a}{c}=\frac{4}{3} \)
B. \( \frac{a}{c}=\frac{3}{4} \)
c. \( \frac{b}{d}=\frac{4}{3} \)
D. \( \frac{b}{d}=\frac{3}{4} \)
Subject: Physics
There is some change in length when a 33000N tensile force is applied on a steel rod of the area of cross section
\( \mathbf{1 0}^{-3} \mathbf{m}^{2} . \) The change in temperature required to produce the same elongation if the steel rod is heated is:
(The modulus of elasticity is \( 3 x \) \( 10^{11} N m^{-2} \) and coefficient of linear
expansion of steel is \( 1.1 \times 10^{-5} 0 C^{-1} \) )
A \( \cdot 20^{\circ} \)
В. \( 15^{\circ} \mathrm{C} \)
\( \mathrm{c} \cdot_{10^{0}} \mathrm{C} \)
D. \( 0^{0} C \)
Subject: Physics
The speed of a body moving with uniform acceleration is \( u . \) This speed is
doubled while covering a distance \( S \)
When it covers an additional distance \( \boldsymbol{S} \)
its speed would become?
A \( \cdot \sqrt{3} u \)
B. \( \sqrt{5} u \)
c. \( \sqrt{11} u \)
D. \( \sqrt{7} u \)
Subject: Maths
\( \lim _{x \rightarrow 0} \frac{\int_{0}^{x}\left(t^{2}+e^{t^{2}}\right)^{\frac{1}{1-\cos t}}}{\left(e^{x}-1\right)} d t \) is equal to
A \( \cdot e^{4} \)
B \( \cdot e^{2} \)
\( c \cdot e^{3} \)
\( D \)
Subject: Physics
Two magnetic poles each of magnetic pole strength \( 16 A m \) are placed at a distance of \( 2 m \) apart. Find magnetic force acting on each pole.
A \( \cdot 4 \times 10^{-7} N \)
В. \( 16 \times 10^{-7} N \)
c. \( 32 \times 10^{-7} N \)
D. \( 64 \times 10^{-7} N \)
Subject: Chemistry
Among
\( \boldsymbol{P b S}, \boldsymbol{C u S}, \boldsymbol{H} \boldsymbol{g} \boldsymbol{S}, \boldsymbol{M n S}, \boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{S}, \boldsymbol{N i S} \)
and \( \operatorname{Sn} S_{2}, \) the total number of black
coloured sulphides are:
\( A \cdot 6 \)
B. 7
\( c \cdot 8 \)
D.
Subject: Maths
If \( \cos ^{2} x+\cos ^{2} 2 x+\cos ^{2} 3 x=1, \) then
A \( x=(2 n+1) \frac{\pi}{4}, n \in I \)
в. \( _{x}=(2 n+1) \frac{\pi}{2}, n \in I \)
c. \( _{x=n \pi \pm} \frac{\pi}{6}, n \in I \)
D. None of these
Subject: Physics
In a hydrogen like atom, when an electron jumps from the M-shell to the L-shell, the wavelength of emitted radiation is \( \lambda \). If an electron jumps from
N-shell to the L-shell, the wavelength of emitted radiation will be?
A \( \cdot \frac{27}{20} \lambda \)
в. \( \frac{16}{25} \lambda \)
c. \( \frac{20}{27} \lambda \)
D. \( \frac{25}{16} \lambda \)
Subject: Maths
Find the non-zero roots of the equation \( \boldsymbol{\Delta}=\left|\begin{array}{ccc}\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{a} \boldsymbol{x}+\boldsymbol{b} \\ \boldsymbol{b} & \boldsymbol{c} & \boldsymbol{b} \boldsymbol{x}+\boldsymbol{c} \\ \boldsymbol{a} \boldsymbol{x}+\boldsymbol{b} & \boldsymbol{b} \boldsymbol{x}+\boldsymbol{c} & \boldsymbol{c}\end{array}\right|=0 \)
Subject: Maths
Evaluate:
\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left\{\cos ^{-1}\left(\frac{\boldsymbol{4} \boldsymbol{x}^{\boldsymbol{3}}}{\mathbf{2 7}}-\boldsymbol{x}\right)\right\} \)
\( ^{A} \cdot \frac{4}{\sqrt{9-x^{2}}} \)
В. \( \frac{1}{\sqrt{9-x^{2}}} \)
c. \( \frac{-3}{\sqrt{9-x^{2}}} \)
D. \( \frac{-1}{\sqrt{9-x^{2}}} \)
Subject: Chemistry
The correct sequence of decreasing acidity is:
\( \mathbf{A} \cdot\left(C H_{3}\right)_{3} C O H>\left(C H_{3}\right)_{2} C H O H>C_{2} H_{5} O H> \)
\( C H_{3} O H \)
B \( \cdot C H_{3} O H>C_{2} H_{5} O H>\left(C H_{3}\right)_{2} C H O H> \)
\( \left(C H_{3}\right)_{3} C O H \)
\( \mathbf{c} \cdot C_{2} H_{5} O H>C H_{3} O H>\left(C H_{3}\right)_{3} C O H> \)
\( \left(C H_{3}\right)_{2} C H O H \)
\( \mathbf{D} \cdot\left(C H_{3}\right)_{2} C H O H>\left(C H_{3}\right)_{3} C O H>C_{2} H_{5} O H> \)
\( C H_{3} O H \)
Subject: Chemistry
Mathematical relation for conversion of
Temperature from Celsius scale to
Fahrenheit scale is:
A \( \cdot F=\frac{5}{9} C+32 \)
B . \( C=\frac{9}{5} F+32 \)
c. \( F=\frac{9}{5} C+32 \)
D. \( F=\frac{9}{5} C-32 \)
Subject: Maths
Consider the following:
1. \( \sin ^{-1} \frac{4}{5}+\sin ^{-1} \frac{3}{5}=\frac{\pi}{2} \)
2. \( \tan ^{-1} \sqrt{3}+\tan ^{-1} 1=-\tan ^{-1}(2+ \)
\( \sqrt{\mathbf{3}}) \)
Which of the above is/are correct?
A. 1 only
B. 2 only
c. Both 1 and 2
D. Neither 1 nor 2
Subject: Chemistry
Two reactions, \( A \rightarrow \) Products and \( B \rightarrow \)
Products, have rate constants \( k_{A} \) and
\( k_{B} \) at temperature \( T \) and activation
energies \( \boldsymbol{E}_{\boldsymbol{A}} \) and \( \boldsymbol{E}_{\boldsymbol{B}} \) respectively. If
\( k_{A}>k_{B} \) and \( E_{A}<E_{B} \) and assuming
that collision frequency for both the
reactions is same, then:
This question has multiple correct options
A. At higher temperature \( k_{A} \) will be greater than \( k_{B} \)
B. At lower temperature \( k_{A} \) and \( k_{B} \) will be close to each other in magnitude
C . As temperature rises, \( k_{A} \) and \( k_{B} \) will be close to each other in magnitude
D. At lower temperature \( k_{A}>k_{B} \)
Subject: Maths
If \( \left(x^{3 / 2}-x y^{1 / 2}+x^{1 / 2} y-y^{3 / 2}\right) \) is
divided by \( \left(x^{1 / 2}-y^{1 / 2}\right), \) the quotient is:
\( \mathbf{A} \cdot x+y \)
в. \( x-y \)
C \( \cdot x^{1 / 2}-y^{1 / 2} \)
D. \( x^{2}-y^{2} \)
Subject: Biology
Match list I with list II and select the
correct option.
\( \begin{array}{llll} & \text { List I } & & \text { List II } \\ \text { A. } & \text { Gemmules } & \text { 1. } & \text { Agave } \\ \text { B. } & \text { Leaf-buds } & \text { 2. } & \text { Penicillum } \\ \text { C. } & \text { Bulbil } & \text { 3. } & \text { Water hyacinth } \\ \text { D. } & \text { Offset } & \text { 4. } & \text { Sponges } \\ \text { E. } & \text { Conidia } & \text { 5. } & \text { Bryophyllum }\end{array} \)
\( \mathbf{A} \)
\( A-4, B-5, C-1, D-3, E-2 \)
2
B. A- \( 4, B-3, C-2, D-1, E-5 \)
C. \( A-3, B-5, C-4, D-2, E-1 \)
D. \( A-4, B-1, C-5, D-3, E-2 \)
E. \( A-3, B-5, C-4, D-1, E-2 \)
Subject: Physics
A thin uniform square lamina of side \( a \)
is placed in the \( X Y \) plane with its sides
parallel to \( X \) and \( Y \) axes and with its
centre coinciding with the origin. Its moment of inertia about an axis
passing through a point on the \( Y \) axis at
a distance \( y=2 a \) and parallel to \( X \)
axis is equal to its moment of inertia
about an axis passing through a point on the \( X \) axis at a distance \( x=d \) and
perpendicular to \( X Y \) plane. The value of
\( \boldsymbol{d} \) is:
A \( \cdot \frac{7}{3} a \)
B. \( \sqrt{\frac{47}{12}} a \)
c. \( \frac{9}{5} a \)
D. \( \sqrt{\frac{51}{12}} a \)
Subject: Maths
Compute \( \boldsymbol{P}(\boldsymbol{A} \mid \boldsymbol{B}), \) if \( \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 5} \) and
\( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})=\mathbf{0 . 3 2} \)
\( \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 5} \)
Subject: Chemistry
When \( F e S O_{4} \) is added in the sodium
extract the compound formed is?
A . only \( N a_{4}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right] \)
B. only \( \mathrm{Fe}(\mathrm{OH})_{2} \)
c. only \( N a_{2} S O_{4} \)
D. Mixture of these three
Subject: Maths
Mean deviation of
\( \mathbf{7}, \mathbf{1 0}, \mathbf{1 0}, \mathbf{1 5}, \mathbf{1 0}, \mathbf{8}, \mathbf{8}, \mathbf{7}, \mathbf{3}, \mathbf{2}, \mathbf{1 0} \) through
mean is
A . 3.14
B. 8
\( c \cdot \frac{4}{5} \)
D. None of these
Subject: Chemistry
Which one of the following reactions
represents the oxidising property of
\( \boldsymbol{H}_{2} \boldsymbol{O}_{2} ? \)
\( \mathbf{A} \cdot 2 K M n O_{4}+3 H_{2} O_{4}+5 H_{2} O_{2} \rightarrow K_{2} S O_{4}+ \)
\[
2 M n S O_{4}+8 H_{2} O+5 O_{2}
\]
B.
\[
2 K_{3}\left[F e(C N)_{6}\right]+2 K O H+H_{2} O_{2} \rightarrow 2 K_{4}\left[F e(C N)_{6}\right]+
\]
\( 2 H_{2} O+O_{2} \)
\( \mathbf{c} \cdot P b O_{2}+H_{2} O_{2} \rightarrow P b O+H_{2} O+O_{2} \)
D. \( 2 K I+H_{2} S O_{4}+H_{2} O_{2} \rightarrow K_{2} S O_{4}+I_{2}+2 H_{2} O \)
Subject: Maths
If \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) and \( \boldsymbol{g}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) are defined
by \( f(x)=2 x+3 \) and \( g(x)=x^{2}+7 \)
then the values of \( x \) such that
\( g(f(x))=8 \) are:
A . 1,2
в. -1,2
c. -1,-2
D. 1,-2
Subject: Physics
The value of gravitational constant \( \boldsymbol{G} \) in Meter-Kilogram-Second system is \( 6.67 \times 10^{-11} N-m^{2} k g^{-2} . \) What will be
its value in centimetre gram
second system.
A. \( 6.67 \times 10^{-5} \)
В. \( 6.67 \times 10^{-9} \)
\( \mathbf{c} \cdot 6.67 \times 10^{-8} \)
D. \( 6.67 \times 10^{-13} \)
Subject: Physics
A long wire carries a current \( 5 A \). The
energy stored in the magnetic field
inside a volume \( 1 \mathrm{mm}^{3} \) at a distance
10cm from the wire is
A \( \cdot \frac{\pi}{4} \times 10^{-13} J \)
В \( \cdot \frac{\pi}{2} \times 10^{-13} J \)
C . \( \pi \times 10^{-13} \mathrm{J} \)
D. \( \frac{\pi}{8} \times 10^{-13} \mathrm{J} \)
Subject: Maths
\( \boldsymbol{R}_{1}= \)
\( \{(\boldsymbol{a}, \boldsymbol{a}),(\boldsymbol{a}, \boldsymbol{b}),(\boldsymbol{a}, \boldsymbol{c}),(\boldsymbol{b}, \boldsymbol{c}),(\boldsymbol{c}, \boldsymbol{a}),(\boldsymbol{b}, \boldsymbol{b}) \)
Subject: Physics
An object is placed on the surface of a smooth inclined plane of inclination \( \boldsymbol{\theta} \). It
takes timer to reach the bottom. If the
same object h allowed to slide down a
rough inclined plane of inclination \( \boldsymbol{\theta} \), it takes time \( n t \) to reach the bottom, where \( n \) is a number greater than 1 . The coefficient of friction \( \mu \) is given by
A \( \cdot \mu=\tan \theta\left(1-\frac{1}{n^{2}}\right) \)
B \cdot \( \mu=\cos \theta\left(1-\frac{1}{n^{2}}\right) \)
c. \( _{\mu}=\tan \theta \sqrt{1-\frac{1}{n^{2}}} \)
D. \( \mu=\cos \theta \sqrt{1-\frac{1}{n^{2}}} \)
Subject: Chemistry
Which of the following carbonyl compounds is most polar?
A. \( C_{2} H_{5}-\stackrel{I}{C}-C_{2} H_{5} \)
B. \( \quad o \)
\( C H_{3}-C-C H_{3} \)
c.
\[
C H_{3}-C-H
\]
D.
\[
H-C-H
\]
Subject: Physics
One mole of an ideal monoatomic gas is heated a constant pressure of one
atmosphere from \( 0^{\circ} C \) to \( 100^{\circ} \mathrm{C} \). Then
the work done by gas is
\( \mathbf{A} \cdot 6.56 J \)
В. \( 8.32 \times 10^{2} J \)
c. \( 12.48 \times 10^{2} J \)
D. \( 20.8 \times 10^{2} J \)
Subject: Chemistry
Which of the following statement(s) is
(are) true?
This question has multiple correct options
A \( \cdot \) Ionisation energy \( \alpha \frac{1}{\text { Screening effect }} \)
B. The first ionization energies of Be and Mg are more than ionization energies of \( B \) and \( A I \) respectively.
C. Atomic and ionic radii of Niobium and Tantalum are
almost same.
D. Metallic and covalent radii of potassium are \( 2.3 A^{\circ} \)
and \( 2.03 A^{\circ} \) respectively.
Subject: Maths
If \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{3}+\boldsymbol{b} \boldsymbol{x}^{2}+\boldsymbol{a} \boldsymbol{x} \) satisfies the
conditions of Rolles theorem on [1,3] with \( c=2+\frac{1}{\sqrt{3}} \) then \( (a, b)= \)
\( \mathbf{A} \cdot(11,6) \)
В \( \cdot(11,-6) \)
c. (-6,11)
D. (6,11)
Subject: Maths
The probability of a man hitting a target in one trial is \( \frac{1}{4} . \) The chances of hitting the target at least once in \( n \) trials exceeds \( \frac{2}{3}, \) then the value of \( n \) equals
\( A \cdot 2 \)
B. 4
\( c \cdot 6 \)
D. 8
Subject: Physics
Two plane mirrors \( A \) and \( B \) are aligned parallel to each other, as shown in the figure A light ray is incident at an angle
\( 30^{\circ} \) at a point just inside one end of \( A \) The plane of incidence coincides with
the plane of the figure The maximum
number of times the ray undergoes reflections (including the first one ) before it emerges out is
\( A \cdot 30 \)
B. 3
\( c \cdot 32 \)
\( D \cdot 34 \)
Subject: Physics
\( \mathbf{A} \)
\( 13 N \) weight and a \( 12 N \) weight are
connected by massless string over a
mass less friction less pulley, The \( 13 N \) weight has a downward acceleration with magnitude equal to that of a freely falling body time
A . 1
B. 1/12
c. \( 1 / 13 \)
D. \( 1 / 25 \)
Subject: Maths
The sum \( 1+\frac{2}{x}+\frac{4}{x^{2}}+\frac{8}{x^{3}}+ \)
\( \ldots(u p t o \infty), x \neq 0, \) is finite if
A \( \cdot|x|<2 \)
В . \( |x|>2 \)
c \( \cdot|x|<1 \)
D . \( 2|x|<1 \)
Subject: Chemistry
In vinyl acetylene \( \boldsymbol{C H} \equiv \boldsymbol{C}-\boldsymbol{C H}= \)
\( C H_{2} \) type of overlapping in \( \left(C_{2} \sigma C_{3}\right) \)
bond is :
\( \mathbf{A} \cdot s p^{2}-s p \)
B. \( s p-s p^{2} \)
\( \mathbf{c} \cdot s p^{3}-s p^{3} \)
D. \( s p^{3}-s p^{2} \)
Subject: Chemistry
If very small amount of phenolphthalein is added to 0.15 mol litre \( ^{-1} \) solution
of sodium benzoate, what fraction of the
indicator will exist in the coloured
form? State any assumption that you make.
\( K_{a}(\text { Benzoic acid })=6.2 \times \)
\( \mathbf{1 0}^{-\mathbf{5}}, \boldsymbol{K}_{\boldsymbol{w}}\left(\boldsymbol{H}_{\mathbf{2}} \boldsymbol{O}\right)=\mathbf{1} \times \mathbf{1 0}^{-\mathbf{1 4}} \)
\( \boldsymbol{K}_{l n} \) (Phenolphthalein) \( \mathbf{3} . \mathbf{1 6} \times \mathbf{1 0}^{-\mathbf{1 0}} \)
Subject: Chemistry
Given the following bond dissociation
enthalpies \( \left(k J . m o l^{-1}\right) \)
\( \boldsymbol{P} \equiv \boldsymbol{P}-\mathbf{4 9 0}, \boldsymbol{P}-\boldsymbol{P}-\mathbf{2 0 9}, \boldsymbol{N} \equiv \boldsymbol{N}- \)
\( \mathbf{9 4 6}, N-N-160 \)
Compare the enthalpy changes for the
process
(i) \( 2 P_{2}(g) \longrightarrow P_{4}(g) \)
(ii) \( 2 N_{2}(g) \longrightarrow N_{4}(g) \)
Choose the correct option.
A \( \cdot P_{4} \) is feasible but \( N_{4} \) is not feasible
B. \( P_{4} \) is not feasible but \( N_{4} \) is feasible
c. Both \( P_{4} \) and \( N_{4} \) are feasible
D. Both \( P_{4} \) and \( N_{4} \) are not feasible.