AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
In the reaction \( \boldsymbol{H}_{2} \boldsymbol{O}_{2}+\boldsymbol{2} \boldsymbol{K} \boldsymbol{I}+\boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
\( \rightleftharpoons 2 H_{2} O+I_{2}+K_{2} S O_{4}, \) the
concentration of lodine changes from 0
to \( 20^{-5} \) mol \( L^{-1} \) in 10 secs. Find the
average rate of the reaction.
A \( \cdot 20^{-7} \) molL \( ^{-1} \) sec \( ^{-1} \)
B. \( 20^{-4} \)mol\( L^{-1} \)sec\( ^{-1} \)
c. \( 20^{-5} \) molL \( ^{-1} \) sec \( ^{-1} \)
D. \( 20^{-6} \)molL\( ^{-1} \)sec\( ^{-1} \)
Subject: Chemistry
Which of the following is the correct chemical formula of sodium
phosphate?
A \( . \) NaPO \( _{4} \)
в. \( N a_{3}\left(P O_{4}\right)_{2} \)
c. \( N a_{2}\left(P O_{4}\right)_{2} \)
D. \( N a_{3} P O_{4} \)
Subject: Physics
A ray light travelling in the direction \( \frac{1}{2}(\hat{i}+\sqrt{3} \hat{j}) \) is incident on a plane mirror. After reflection, it travels along
the direction \( \frac{1}{2}(\hat{i}-\sqrt{3} \hat{j}) . \) What is the angle of incidence?
A . \( 30^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 75^{\circ} \)
Subject: Chemistry
Teflon (tetrafluoroethylene) is a black material used in non-stick pans for frying chips and vegetables. The oil or
butter does not stick at all. In the
process of manufacture, one of the
technical problems is:
A. to make teflon stick to the metal of the pan
B. to make teflon that is non-sticky
c. to make teflon
D. to cut a round sheet of teflon that exactly fits
Subject: Chemistry
Which of the following statement is true
for the complex, \( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4} \boldsymbol{B r}_{2}\right] \boldsymbol{N} \boldsymbol{O}_{2} ? \)
A. It shows ionisation, linkages and geometrical isomerism
B. It does not show optical isomerism because its cis and trans forms each have at least one plane of symmetry.
c. Its ionisation isomers cannot be differentiated by silver nitrate solution
D. (A) and
(B) both
Subject: Maths
Find the equation of the line in vector and in cartesion form that passes through the point with position vector \( \mathbf{2} \hat{\mathbf{i}}-\hat{\mathbf{j}}+\mathbf{4} \hat{\boldsymbol{k}} \) and is in the direction \( \hat{\mathbf{i}}+ \)
\( \mathbf{2} \hat{\boldsymbol{j}}-\hat{\boldsymbol{k}} \)
Subject: Maths
Find union of \( A \) and \( B \) by representing
using Venn diagram:
\( \boldsymbol{A}=\{\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}, \boldsymbol{d}\}, \boldsymbol{B}=\{\boldsymbol{b}, \boldsymbol{d}, \boldsymbol{e}, \boldsymbol{f}\} \)
\( \mathbf{A} \cdot\{a, b, c, d\} \)
B \( \cdot\{b, d, e, f\} \)
\( \mathbf{c} \cdot\{b, d\} \)
D. None of these
Subject: Physics
A beaker contains a liquid of density \( \rho \)
upto a height \( h \), such that \( P \) is the
atmospheric pressure and \( g \) is the acceleration due to gravity. Answer the following questions:
a) What is the pressure at the free surface of the liquid?
b) What is the pressure at the base of the beaker?
c) What is the lateral pressure at the base on the inner walls of beaker?
Subject: Physics
Two conducting plates \( A \) and \( B \) are placed parallel to each other at a small
distance between them. Plate A is given
a charge \( q_{1} \) and plate \( B \) is given a
charge \( \boldsymbol{q}_{2} . \) Then :

This question has multiple correct options
A. the outer surfaces of \( A \) and \( B \) (not facing each other) get no charge
B. the inner surfaces of \( A \) and \( B \) (facing each other) get al the charge
C. the inner surfaces of \( A \) and \( B \) (facing each other) get equal and opposite charge of magnitude \( \left|\frac{q_{1}-q_{1}}{2}\right| \)
D. the outer surfaces of \( A \) and \( B \) (not facing each other) get charge of the same polarity and of magnitude
\( \frac{q_{1}+q_{2}}{2} \)
2
Subject: Maths
In a given \( A P ., \) if the p term is 'q'and the
\( q^{t h} \) tent is 'p', then its \( n^{t h} \) term is
\( \mathbf{A} \cdot p+q-n \)
B . \( p+q+n \)
C \( . p-q+n \)
D. \( p-q-n \)
Subject: Physics
Q Type your question
coll ana aırectea ınto the paper Is varying according to the relation \( \phi= \)
\( 6 t^{2}+7 t+1, \) where \( \phi \) is in milliweber
and \( t \) is in second. The magnitude of the
emf induced in the loop at \( t=2 s \) and
the direction of induce current through
\( \boldsymbol{R} \) are
8
A. 39 mV; right to left
B. 39 mV; left to right
c. \( 31 \mathrm{mV} ; \) right to left
D. 31 mV; left to right
Subject: Physics
Find the mismatch
A. Sky wave communication: Frequency upto 30 MHz
B. Line-of-sight communication: Frequency greater than \( 40 \mathrm{MHz} \)
C. Mobile telephony : Frequency range \( 800-950 \mathrm{kHz} \)
D. Facsimile : Static document
E. Ground wave propagation: Frequency less than a few МНz
Subject: Maths
The value of
\( \sin ^{-1}\left[\cos \left[\sin ^{-1}\left(\frac{1}{2} \tan \frac{\pi}{3}\right)\right]\right] \) is
\( \mathbf{A} \cdot 2 \tan ^{-1}(2-\sqrt{3}) \)
B \( \cdot 2 \tan ^{-1}(\sqrt{2}-1) \)
\( \mathbf{c} \cdot 2 \tan ^{-1}(\sqrt{2}+1) \)
D.
Subject: Physics
The equations of motion of a projectile
are given by \( \boldsymbol{x}=\mathbf{3 6} \boldsymbol{t m} \) and \( \mathbf{2} \boldsymbol{y}=\mathbf{9 6} \boldsymbol{t}- \)
\( 9.8 t^{2} \mathrm{m} . \) The angle of projection is
\( A \cdot \sin ^{-1}(4 / 5) \)
B. \( \sin ^{-1}(3 / 5) \)
\( c \cdot \sin ^{-1}(4 / 3) \)
\( D \cdot \sin ^{-1}(3 / 4) \)
Subject: Physics
Given a uniform electric field \( \overrightarrow{\boldsymbol{E}}=\mathbf{5} \times \)
\( \mathbf{1 0}^{3} \hat{\mathbf{i}} \mathbf{N} / \mathbf{C}, \) find the flux of this field
through a square of \( 10 \mathrm{cm} \) on a side whose plane is parallel to the \( \boldsymbol{Y}-\boldsymbol{Z} \)
plane. What would be the flux through the same square if the plane makes a
\( 30^{\circ} \) angle with the \( \$ \$ X \) -axis?
Subject: Physics
Two long thin parallel conductors of the
shape shown in figure above carry
direct currents \( I_{1} \) and \( I_{2} \). The separation
between the conductors is \( a \), the width
of the right-hand conductor is equal to \( b \)
With both conductors lying in one
plane, the magnetic interaction force between them reduced to a unit of their length is given as \( F_{1}=\frac{\mu_{0} I_{1} I_{2}}{x \pi b} \ln \frac{a+b}{a} \)
Find \( \boldsymbol{x} \)
Subject: Maths
Value of \( c \) using Rolle's theorem for
\( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{ll}\boldsymbol{x}^{2}+\mathbf{1} & , \mathbf{w h e n} \mathbf{0} \leq \boldsymbol{x} \leq \mathbf{1} \\ \mathbf{3}-\boldsymbol{x} & , \mathbf{w h e n} \mathbf{1}<\boldsymbol{x} \leq \mathbf{2}\end{array}\right. \)
\( A \)
B.
\( c \)
D. does notexis
Subject: Maths
If a line makes \( 45^{\circ}, 60^{\circ} \) with positive
direction of axes \( x \) and \( y \) then the
angles it makes with the \( z \) -axis is
A \( \cdot 30^{\circ} \)
В. \( 90^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 60^{\circ} \)
Subject: Chemistry
Assertion
Concentrated and not dilute \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
behaves as a dehydrating agent.
Reason
Concentrated sulphuric acid behaves
as a strong dehydrating agent as the hydration reaction is highly exothermic. It has strong affinity for water removing water molecules from other compounds
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
Using properties of determinants, prove
\[
\text { the following: }\left|\begin{array}{ccc}
\mathbf{1} & \mathbf{1} & \mathbf{1} \\
\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} \\
\boldsymbol{a}^{\mathbf{3}} & \boldsymbol{b}^{\mathbf{3}} & \boldsymbol{c}^{3}
\end{array}\right|=(\boldsymbol{a}-
\]
\( b)(b-c)(c-a)(a+b+c) \)
Subject: Chemistry
\( 60 \% \) of the first-order reaction was
completed in 60 min. The time taken for
reactants to decompose to half of their original amount will be:
\( \mathbf{A} \cdot \approx 30 \min \)
в. \( \approx 60 \) min
\( \mathbf{c} . \approx 90 \min \)
\( \mathbf{D} \cdot \approx 45 \min \)
Subject: Physics
The magnetic field due to a current carrying circular loop of radius \( 3 \mathrm{m} \) at a point on the axis at a distance of \( 4 \mathrm{m} \)
from the centre is \( 54 \mu T . \) What will be its
value at the centre of the loop?
A. \( 250 \mu T \)
в. \( 150 \mu T \)
c. \( 125 \mu T \)
D. \( 75 \mu T \)
Subject: Physics
Which one of the following statements
best describes the nature of the field
lines due to a bar magnet?
A. Field lines start from the north pole and end on the south pole. Any number of field lines can pass through a point
B. Field lines start from the north pole and end on the south pole. Only one field line passes through a point
C. Field lines are continuous lines passing inside and outside the magnet. Only one field line passes through a point
D. Field lines are continuous lines passing inside and outside the magnet. Any number of field lines can pass through a point
Subject: Physics
A rectangular loop carrying a current \( \boldsymbol{i}_{1} \) is situated near a long straight wire
carrying a steady current \( i_{2} . \) The wire is
parallel to one of the sides of the loop and is in the plane of the loop as shown in the figure. Then the current loop will
A. move away from the wire
B. move towards the wire
c. remain stationary
D. rotate about an axis parallel to the wirce
Subject: Chemistry
The rate of the reaction \( \boldsymbol{A}+\boldsymbol{B}_{2} \rightarrow \)
\( A B+B ; \) is directly proportional to the
concentration of \( A \) and independent of
concentration of \( B_{2} \), hence, rate law is:
\( \mathbf{A} \cdot k[A]\left[B_{2}\right] \)
\( \mathbf{B} \cdot k[A]^{2}\left[B_{2}\right] \)
c. \( k[A] \)
D. \( k\left[B_{2}\right] \)
Subject: Chemistry
The half-period T for the decomposition
of ammonia on tungsten wire was measured for different initial pressures
\( P \) of ammonia at \( 25^{\circ} \mathrm{C} \). Then:
\( P(m m \)
\( \begin{array}{llll}11 & 21 & 48 & 73\end{array} \)
Hg)
\( \mathrm{T}(\mathrm{sec}) \)
48 92
\[
\text { 210 } \quad 320
\]
This question has multiple correct options
A. Zero order reaction
B. First order reaction
C. Rate constant for reaction is 0.114 mol lit \( ^{-1} \) sec \( ^{-1} \)
D. Rate constant for reaction is 1.14 seconds
Subject: Maths
Find the derivative of the following functions (it is to be understood that
\( a, b, c, d, p, r \) and \( s \) are fixed non-zero constants and \( m \) and \( n \) are integers) \( \frac{\boldsymbol{a}}{\boldsymbol{x}^{4}}-\frac{\boldsymbol{b}}{\boldsymbol{x}^{2}}+\cos \boldsymbol{x} \)
Subject: Maths
If \( \int f(x) d x=f(x), \) then \( \int[j(x)]^{2} d x \) is
A \( \cdot \frac{1}{2}[f(x)]^{2} \)
B . \( [f(x)]^{3} \)
c. \( \frac{[f(x)]^{3}}{3} \)
D \cdot \( [f(x)]^{2} \)
Subject: Maths
Length of 40 bits of wire, correct to the nearest centimetre are given below. Calculate the variance.
\( \begin{array}{lllll}\text { Length } & 1- & 11- & 21- & 31- \\ \mathrm{cm} & 10 & 20 & 30 & 40\end{array} \)
No. of
bits \( \quad 2 \quad 3 \)
Subject: Physics
Find the magnitude of a charge which produces an electric field of strenght is
\( 18 \times 10^{3} N C^{-1} \) at a distance of \( 5 \mathrm{m} \) in
air.
A. \( 50 \mu c \)
B. \( 100 \mu c \)
\( c \cdot 25 \mu c \)
D. 250 \muc
Subject: Physics
n a coil of resistance \( 100 \Omega \), a current
is induced by changing the magnetic flux through it as shown in the figure.
The magnitude of change in flux through the coil is:
A \( .275 \mathrm{Wb} \)
В. \( 200 \mathrm{Wb} \)
\( c .225 W b \)
D. \( 250 \mathrm{Wb} \)
Subject: Chemistry
Calculate \( \Delta S_{r}^{o} \) at \( 298 K \) of
(a) \( N a(s)+\frac{1}{2} C l_{2}(g) \rightarrow N a C l(s) \)
\( \frac{1}{2} N_{2}(g)+2 H_{2}(g)+\frac{1}{2} C l_{2}(g) \rightarrow \)
\( N H_{4} C l(s) \)
(iii) \( C(\text { graphite }) \rightarrow C \) (Diamond)
The values of \( S^{o} \) of
\( N a, C l_{2}, N a C l, N H_{4} C l, N_{2}, H_{2} \)
diamond and graphite are
\( \mathbf{5 1}, \mathbf{2 2 3}, \mathbf{7 2}, \mathbf{9 5}, \mathbf{1 9 2}, \mathbf{1 3 1}, \mathbf{2 . 4 3}, \mathbf{5}, \mathbf{6 9} \mathbf{J K} \)
and \( m o l^{-1} \) respectively:
Subject: Physics
Find the value of wave number \( (\bar{V}) \) in
term of Rydberg's constant \( \left(R_{H}\right), \) when transition of electron takes place
between two levels of \( H e^{+} \) ion, whose
sum is 4 and difference is 2
A \( \cdot \frac{8}{9} R_{H} \)
В . \( \frac{32}{9} R_{H} \)
c. \( \frac{1}{9} R_{H} \)
D. none of these
Subject: Maths
The differential equation of the family of
curve \( \boldsymbol{y}^{2}=\mathbf{4} \boldsymbol{a}(\boldsymbol{x}+\boldsymbol{a}) \) is
A \( \cdot y^{2}=4 \frac{d y}{d x}\left(x+\frac{d y}{d x}\right) \)
B. \( \quad y^{2}\left(\frac{d y}{d x}\right)^{2}+2 x y \frac{d y}{d x}-y^{2}=0 \)
c. \( y^{2} \frac{d y}{d x}+4=0 \)
D. \( 2 y \frac{d y}{d x}+4 a=0 \)
Subject: Maths
Let \( \boldsymbol{f}= \)
\{(1,1),(2,3),(0,-1),(-1,-3)\} be a
function described by the formula \( f(x)=a x+b \) for some integers \( a, b \)
Determine \( a, b \)
A \( . a=2, b=-1 \)
В. \( a=1, b=0 \)
c. \( a=0, b=-1 \)
D. None of these
Subject: Maths
passing through a spot on a road for 100 periods each of 3 minutes and
summarised it in the table given below.
Find the mode of the data.
\( \begin{array}{ll}\text { No. of cars } & \text { Frequency } \\ 0-10 & 7 \\ 10-20 & 14 \\ 20-30 & 13 \\ 30-40 & 12 \\ 40-50 & 20 \\ 50-60 & 11 \\ 60-70 & 15 \\ 70-80 & 8\end{array} \)
A. \( 44 . \)
B. 45.8
c. \( 46 . \)
D. 42
Subject: Maths
\( p^{t h} \) term of the series \( \left(3-\frac{1}{n}\right)+\left(3-\frac{2}{n}\right)+\left(3-\frac{3}{n}\right) \dots \dots \)
will be
\( A \cdot 3+\frac{p}{n} \)
B \( \cdot 3-\frac{p}{n} \)
c. \( 3+\frac{n}{p} \)
D. \( 3-\frac{n}{p} \)
Subject: Maths
The envelope of a family of curves is a
curve \( f(x, y, c)=0 \) whose equation is
obtained by eliminating the parameter \( c \) from \( f(x, y, c)=0 \) and \( \frac{\partial f}{\partial c}=0 \)
where \( \frac{\partial f}{\partial c} \) is the differential coefficient of f with respect to c, treating x and y as constants. Moreover, the envelope of the family of normals to a curve is known as the evolute of the curve. The envelope of the family of straight lines whose sum of intercepts on the axes is 4 is:
A \( \cdot \sqrt{x}+\sqrt{y}=2 \)
в. \( (x-y)^{2}-8(x+y)+16=0 \)
c. \( (x-y)^{2}=4(x+y) \)
D. \( (x+y)^{2}=4(x-y) \)
Subject: Physics
If the acceleration due to gravity at the
surface of the earth is \( g \), the work done
in slowly lifting a body of mass \( m \) from
the earth's surface to a height \( \boldsymbol{R} \) equal to the radius of the earth is
\( ^{\mathrm{A}} \cdot \frac{m g R}{2} \)
в. \( 2 m g R \)
\( \mathrm{c} \cdot m g R \)
D. \( _{m g} \frac{R}{4} \)
Subject: Maths
A triangle and a parallelogram have the
same base and the same area. If the
sides of the triangle are \( 26 \mathrm{cm}, 28 \mathrm{cm} \) and \( 30 \mathrm{cm}, \) and the parallelogram stands on the base \( 28 \mathrm{cm}, \) find the height of the parallelogram.
Subject: Chemistry
To determine whether a water solution
of \( N a_{2} S_{2} O_{3} \) at room temperature is
supersaturated, one can :
A. heat the solution to its boiling point
B. add water to the solution
c. add a crystal of \( N a_{2} S_{2} O_{3} \) to the solution
D. acidify the solution
E. cool the solution to its freezing point
Subject: Chemistry
A neutral atom of an element has \( 2 \mathrm{K}, 8 \mathrm{L} \)
\( 9 \mathrm{M} \) and \( 2 \mathrm{N} \) electrons
The total number of p-electron are :
\( \mathbf{A} \cdot \mathbf{6} \)
B. 12
c. 18
D. 24
Subject: Maths
Assertion
f \( n>1 \) then Statement - 1 :
\( \int_{0}^{\infty} \frac{\boldsymbol{d} \boldsymbol{x}}{\mathbf{1}+\boldsymbol{x}^{n}}=\int_{0}^{1} \frac{\boldsymbol{d} \boldsymbol{x}}{\left(\mathbf{1}-\boldsymbol{x}^{n}\right)^{1 / n}} \)
Reason
Statement
-2: \( \int_{a}^{b} f(x) d x=\int_{a}^{b} f(a+ \)
\( \boldsymbol{b}-\boldsymbol{x}) d \boldsymbol{x} \)
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 the expansion of \( (1+x)^{n}, \) the \( 5^{t h} \)
term is 4 times the \( 4^{t h} \) term and the \( 4^{t h} \)
term is 6 times the \( 3^{r d} \) term. than \( n= \)
\( A \cdot 9 \)
B. 10
\( c \cdot 11 \)
D. 12
Subject: Physics
Two vectors of equal magnitude have a resultant equal to either of them. Then, the angle between them will be \( 2 \pi / 3 \)
radians. The angle in degrees is:
A \( .30^{\circ} \)
B. \( 120^{\circ} \)
\( c \cdot 60 \)
D. \( 45^{\circ} \)
Subject: Chemistry
\( \boldsymbol{C u} \boldsymbol{S O}_{4} \) is paramagnetic while \( \boldsymbol{Z} \boldsymbol{n} \boldsymbol{S} \boldsymbol{O}_{4} \)
is diamagnetic because:
A. \( C u^{2+} \) ion has \( 3 d^{9} \) configuration while \( Z n^{2+} \) ion has \( 3 d^{10} \) configuration
B. \( C u^{2+} \) ion has \( 3 d^{5} \) configuration while \( Z n^{2+} \) ion has \( 3 d^{6} \) configuration.
\( \mathrm{c} \cdot \mathrm{Cu}^{2+} \) has half filled orbitals while \( Z n^{2+} \) has fully filled orbitals
D. \( C u S O_{4} \) is blue in colour while \( Z n S O_{4} \) is white
Subject: Physics
Dip circle is not set into magnetic meridian and the angle at which it is inclined to the magnetic meridian is
unknown. \( \delta^{\prime} \) and \( \delta^{\prime \prime} \) are apparent dips at a place in which dip circle is kept in transverse positions. The dip is:
\( \mathbf{A} \cdot \cot \delta=\cot \delta^{\prime}+\cos \delta^{\prime \prime} \)
B. \( \tan ^{2} \delta^{\prime}=\tan \delta^{\prime}+\tan ^{2} \delta^{\prime \prime} \)
\( \mathbf{c} \cdot \cos ^{2} \delta=\cos ^{2} \delta^{\prime}+\cos ^{2} \delta^{\prime \prime} \)
D. \( \cot ^{2} \delta=\cot ^{2} \delta^{\prime}+\cot ^{2} \delta^{\prime \prime} \)
Subject: Physics
An electric dipole moment \( \vec{P}=(2.0 \hat{i}+ \) \( 3.0 \hat{j}) \mu \) is placed in a uniform electric field \( \overrightarrow{\boldsymbol{E}}=(\mathbf{3 . 0 \hat { \boldsymbol { i } }}+\mathbf{2 . 0 \hat { \boldsymbol { k } }}) \times \mathbf{1 0}^{\mathbf{5}} \mathbf{N} \boldsymbol{C}^{-\mathbf{1}} \)
This question has multiple correct options
A . The torque that \( \vec{E} \) exerts on \( \mathrm{P} \) is \( (0.6 \hat{i}-0.4 \hat{j}-0.9 \hat{k}) \)
\( \mathrm{Nm} \)
B. The potential energy of the dipole is 0.9 J
c. The potential energy of the dipole is 0.6
D. If the dipole is rotated in the electric field, the maximum potential energy of the dipole is 1.3
Subject: Biology
enzymes have heme as a
prosthetic group.
(i) Catalase
(ii) Carboxypeptidase
(iii) Succinic dehydrogenase
(iv) Peroxidase
\( A \). (i) only
B. (i) and (ii) only
c. (ii) and (iii) only
D. (iii) and (iv) only
E. (i) and (iv) only
Subject: Chemistry
\( \boldsymbol{A}^{+} \boldsymbol{B}^{-}+\boldsymbol{C}^{+} \boldsymbol{D}^{-} \longrightarrow \boldsymbol{A}^{+} \boldsymbol{D}^{-}+\boldsymbol{C}^{+} \boldsymbol{B}^{-} \)
Identify the above generalized type of
reaction:
A. Chemical replacement reaction
B. Chemical double decomposition reaction
c. Chemical displacement reaction
D. Chemical combination reaction
Subject: Maths
If \( f(x)=\ln \left(x^{2}-x+2\right) ; R^{+} \rightarrow R \) and
\( \boldsymbol{g}(\boldsymbol{x})=\{\boldsymbol{x}\}+\mathbf{1} ;[\mathbf{1}, \mathbf{2}] \rightarrow[\mathbf{1}, \mathbf{2}], \) where
\( \{x\} \) denotes fractional part of \( x \). Find
the domain and range of \( f(g(x)) \) when defined.
Subject: Chemistry
From the list of compounds given below, identify the compounds which can give only two position isomers:
(a) Hexane
(b) Pentene
(c) Heptyne
(d) Propanol
(e) Pentanone
\( \mathbf{A} \cdot a, d \) and \( b \)
B. \( b, d \) and \( e \)
\( \mathbf{c} \cdot e, a \) and \( c \)
D. \( b, c \) and \( d \)
Subject: Maths
If the differential equation representing the family of all circles touching \( x- \) axis at the origin is \( \left(x^{2}-y^{2}\right) \frac{d y}{d x}= \)
\( \boldsymbol{g}(\boldsymbol{x}) \boldsymbol{y}, \) then \( \boldsymbol{g}(\boldsymbol{x}) \) equals:
A \( \cdot \frac{1}{2} x \)
в. \( 2 x^{2} \)
c. \( 2 x \)
D. \( \frac{1}{2} x^{2} \)
Subject: Physics
A monkey standing on the ground wants to climb to the top of a vertical pole 13 \( \mathrm{m} \) tall. He climbs \( 5 \mathrm{m} \) in \( 1 \mathrm{s} \) and then
slips downwards \( 3 \mathrm{m} \) in the next second
He again climbs \( 5 \mathrm{m} \) in \( 1 \mathrm{s} \) and slips by \( 3 \mathrm{m} \) in the next second as so on. How much time will the monkey take to reach the top of the pole?
\( \mathbf{A} \cdot 7 \sec \)
B. 9 sec
c. 11 sec
D. 13 sec
Subject: Physics
Find the value of an inductance which
should be connected in series with a
capacitor of \( 5 \mu F, \) a resistance of \( 10 \Omega \)
and an ac source of \( 50 H z \) so that the
power factor of the circuit is unity.
A \( \cdot \frac{20}{\pi^{4}} \)
в. \( \frac{20}{\pi^{2}} \)
c. \( \frac{20}{\pi^{3}} \)
D. \( \frac{20}{\pi^{5}} \)
Subject: Chemistry
How many grams of sucrose must be
added to \( 320 g \) of water to lower the
vapour pressure by \( 1.5 m m H g \) at \( 25^{\circ} C \)
\( ? \)
(Given: The vapour pressure of water at
\( 25^{\circ} \mathrm{C} \) is \( 23.8 \mathrm{mm} \) Hg and molar mass
of sucrose is \( 324.3 g / m o l \) )
A. \( 21.5 g \)
в. \( 140 g \)
c. \( 363.36 g \)
D. \( 160.12 g \)
Subject: Physics
The region between two concentric
spheres of radii a and \( b(>a) \)
contains volume charge density \( \rho(r)= \)
\( C \)
\( \boldsymbol{r} \)
where \( C \) is a constant and \( r \) is the
radial distance, as shown in figure. A
point charge \( q \) is placed at the origin, \( r= \)
O.Find the value of \( C \) for which the
electric field in the region between
the spheres is constant (i.e., r
independent)
Subject: Maths
Given n real numbers \( a_{1}, a_{2}, \dots a_{n}, \) the
value of \( x \) for which sum of the square of
all the deviations is least is
A \( \cdot a_{1}+a_{2}+\ldots+a_{n} \)
В - \( 2\left(a_{1}+a_{2}+\ldots+a_{n}\right) \)
c. \( a_{1}^{2}+a_{2}^{2}+\ldots a_{n}^{2} \)
D. \( \frac{a_{1}+a_{2}+\ldots+a_{n}}{n} \)
Subject: Maths
For the parabola \( \boldsymbol{y}^{2}+\mathbf{8} \boldsymbol{x}-\mathbf{1 2} \boldsymbol{y}+\mathbf{2 0}= \)
\( \mathbf{0} \)
This question has multiple correct options
A. vertex is (2,6)
B. Focus is (0.6)
c. Latusrectum 4
D. Axis \( y=6 \)
Subject: Physics
A magnet makes 40 oscillation per minute at a place having magnetic intensity of \( 0.1 \times 10^{-5} \) Tesla. At another
place it takes 2.5 sec to complete one oscillation. The value of earth's
horizontal field at that place is
A \( .0 .76 \times 10^{-6} T \)
В. \( 0.18 \times 10^{-6} T \)
\( \mathbf{c} \cdot 0.09 \times 10^{-6} T \)
D. \( 0.36 \times 10^{-6} T \)
Subject: Maths
\( \mathrm{f} f_{0}^{\pi / 3} \frac{\cos }{3+4 \sin x} d x= \)
\( K \log \frac{(3+2 \sqrt{3})}{3} \) then \( K \) is
A \( \cdot \frac{1}{2} \)
B.
\( c \cdot \frac{1}{4} \)
D.
Subject: Physics
The position vector of a particle is \( \vec{r}= \) \( \boldsymbol{a}[\cos \omega \boldsymbol{t} \hat{\boldsymbol{i}}+\sin \omega \boldsymbol{t} \hat{j}] . \) The velocity of the
particle is
A. parallel to position vector
B. directed towards origin
c. directed away from origin
D. perpendicular to position vector
Subject: Chemistry
Amongst the primary alkyl halides the order of reactivity is:
\( \boldsymbol{C H}_{3} \boldsymbol{X}>\boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{X}>\boldsymbol{C}_{3} \boldsymbol{H}_{7} \boldsymbol{X}, \) etc.
Subject: Physics
A projectile is thrown into space so as to have the maximum possible
horizontal range equal to \( 400 m \). Taking
the point of projection as the origin, the coordinates of the point where the
velocity of the projectile is minimum
are:
\( \mathbf{A} \cdot(400,100) \)
в. (200,100)
c. (400,200)
D. (200,200)