AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
To divide a line segment in the ratio \( p \) \( \boldsymbol{q}(\boldsymbol{p}, \boldsymbol{q} \text { are integers }) \) a ray \( \boldsymbol{A} \boldsymbol{X} \) is drawn
so that \( \angle B A X \) is an acute angle and
then mark points on ray \( A X \) at equal distances such that the minimum
number of points is:
\( \mathbf{A} \cdot p q \)
В. \( p+q-1 \)
c. \( p+q \)
D. Greater of \( p \) and \( q \)
Subject: Physics
\( n \) small drops of same size are charged
to \( V \) volts each. If they coalesce to form a signal large drop, then its potential will be :
A. \( V / n \)
в. \( V n \)
\( \mathbf{c} \cdot V n^{1 / 3} \)
\( \mathbf{D} \cdot V n^{2 / 3} \)
Subject: Physics
A glass prism of refractive index 1.5 is
immersed in water (refractive index
4/3). A light beam normally on the face
\( A B \) is totally reflected to reach on the
face \( B C \) if
A \( \cdot \sin \theta \geq \frac{8}{9} \)
В \( \cdot \frac{2}{3}<\sin \theta \geq \frac{8}{9} \)
\( ^{\mathbf{C}} \cdot \sin \theta \leq \frac{2}{3} \)
\( \mathrm{D} \cdot \sin \theta \leq \frac{8}{9} \)
Subject: Chemistry
Metal hydrides are ionic, covalent or
molecular in nature. Among \( L i H, N a H, K H, R b H \) and \( C s H, \) the
correct order of increasing ionic character is:
A \( . L i H>N a H>C s H>K H>R b H \)
в. \( L i H<N a H<K H<R b H<C s H \)
c. \( R b H>C s H>N a H>K H>L i H \)
D. \( N a H>C s H>R b H>L i H>K H \)
Subject: Maths
Simplify :
¡) \( \frac{-14 x^{8} y^{5}+21 x^{10} y-28 x^{7} y^{6}}{7 x^{7} y^{8}} \)
ii) \( \frac{15 a^{4} x^{8}-30 a^{7} x^{5}-45 a^{6} x^{6}}{20 a^{14} x^{5}} \)
iii) \( \frac{-60 x^{4} a^{5}-75 x^{3} a^{6}+8 x^{5} a^{4}}{-20 x^{8} a^{4}} \)
Subject: Physics
Figure shows a point \( \mathrm{P} \) near a long
conductor XY carrying a current 1. MN is a short current carrying conductor, kept at the point \( P, \) parallel to the conductor
\( \mathbf{X Y} \)
(i) What is the direction of magnetic
flux density 'B' at the point P due to the current flowing through XY?
(ii) What is the direction of the force
experienced by the conductor MN due to the current flowing through XY?
Subject: Chemistry
Kjeldahl's method cannot be used to estimate nitrogen for which of the following compounds?
A. \( C_{6} H_{5} N H_{2} \)
в. \( N H_{2}-C-N H_{2} \)
c. \( C_{6} H_{5} N O_{2} \)
D. \( C H_{3} C H_{2}-C \equiv N \)
Subject: Maths
The following table shows the ages of the patients admitted in a hospital during a year:
25- \( \quad 35 \)
\[
\begin{array}{lll}
\text { Agetin } & \text { 5- } & \text { 15- } \\
\text { years ) } & \text { 15 } & \text { 25 } & \text { 35 }
\end{array}
\]
Number
of patients
Find the mode and the mean of the data
given above. Compare and interpret the two measure of central tendency.
Subject: Physics
Three charges all of \( +q \) are brought
together so that they form an equilateral triangle, with a distance \( r \)
between them.

Determine the electrostatic potential
energy needed to bring the system together from infinity:
\( A \)
B. \( \frac{3 q^{2}}{4 \pi \epsilon_{0} r} \)
c. \( \frac{5 q^{2}}{4 \pi \epsilon_{0} r} \)
D. \( \frac{7 q^{2}}{4 \pi \epsilon_{0} r} \)
Subject: Physics
Pis a point on an equipotential surface
S. The field at Pis E.
This question has multiple correct options
A. E must be perpendicular to s in all cases
B. E will be perpendicular to S only if S is a plane surface.
C. E cannot have a component along a tangent to S.
D. E may have a nonzero component along a tangent to if \( \mathrm{S} \) is a curved surface.
Subject: Physics
The area of cross section of a steel wire
\( \left(y=2 \times 10^{11} N / m^{2}\right) \) is \( 0.1 c m^{2} . \) The
force required to double its length will
be:
A \( \cdot 2 \times 10^{12} N \)
В. \( 2 \times 10^{11} N \)
C . \( 2 \times 10^{10} N \)
D. \( 2 \times 10^{6} N \)
Subject: Maths
The expression \( \sin 27^{\circ} \cos 57^{\circ} \sin 87^{\circ} \)
simplifies to
A \( \cdot \frac{\sin 9^{\circ}}{4} \)
B. \( \frac{\cos 9^{\circ}}{4} \)
c. \( \frac{\sin 9^{\circ}}{2} \)
D. \( \frac{\cos 9^{\circ}}{2} \)
Subject: Chemistry
Gas \( A \) is formed on the hydrolysis of
calcium cyanamide. The gas can turn moist litmus paper blue and forms a brown precipitate with Nessler's
reagent. The gas, \( \boldsymbol{A} \) is:
A \( \cdot N_{2} \)
B. NO
\( c \cdot N O_{2} \)
D. \( N H_{3} \)
Subject: Maths
Draw a circle with centre \( O \) and radius
\( 4 \mathrm{cm} . \) Take point \( \boldsymbol{A} \) such that \( \boldsymbol{d}(\boldsymbol{O}, \boldsymbol{A})= \)
\( 9 \mathrm{cm} . \) Draw tangents from point \( \boldsymbol{A} \)
Subject: Maths
Assertion
If vectors \( a \) and \( c \) are non collinear then
the lines \( r=6 a-c+\lambda(2 c-a) \) and
\( \boldsymbol{r}=\boldsymbol{a}-\boldsymbol{c}+\boldsymbol{\mu}(\boldsymbol{a}+\boldsymbol{3} \boldsymbol{c}) \) are coplanar
Reason
There exist \( \lambda \) and \( \mu \) such that the two
values of \( r \) become same.
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
An electromagnetic wave radiates outwards from a dipole antenna, with
\( E_{0} \) as the amplitude of its electric field
vector. The electric field \( E_{0} \) which
transports significant energy from the source falls off as
A \( \cdot \frac{1}{r^{3}} \)
B. \( \frac{1}{r^{2}} \)
\( c \cdot \frac{1}{r} \)
D. remains constant
Subject: Chemistry
Assertion
Two sugar units joined by \( 1,2- \)
glycosidic bond in sucralose.
Reason
It contains \( C_{1} \) -glucose and \( C_{2} \) -fructose
glycosidic 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. Both Assertion and Reason are incorrect
Subject: Chemistry
Select the correct I.U.P.A.C name for
\( \left[\boldsymbol{P t}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\right]\left[\boldsymbol{P t C l}_{4}\right]: \)
A. Tetraammineplatinum(II) tetrachloridoplatinate(II)
B. Tetraammineplatinate(II) tetrachloridoplatinate(II)
C. Tetraammineplatinate(II) tetrachloridoplatinum(II)
D. All are correct
Subject: Maths
The probability distribution of a random
variable \( \boldsymbol{X} \) is given below:
\[
\boldsymbol{X}=\boldsymbol{x} \quad 0 \quad 1 \quad 2 \quad 3
\]
\( P(X=x) \quad \frac{1}{10} \quad \frac{2}{10} \quad \frac{3}{10} \)
\[
\begin{array}{r}
\frac{4}{10} \\
\hline 0
\end{array}
\]
Then the variance of \( \boldsymbol{X} \) is
\( A \)
B. 2
\( c \cdot 3 \)
D. 4
Subject: Chemistry
Bond energies can be obtained by using
the following relation:
\( \Delta H(\text { reaction })=\sum \) Bond energy of
bonds, broken in the reactants \( -\sum \)
Bond energy of bonds, formed in the
products
Bond energy depends on three factors:
a. greater is the bond length, lesser is
the bond energy
b. bond energy increases with the bond
multiplicity
c. bond energy increases with the electronegativity difference between the
bonding atoms.
Arrange \( N-H, O-H \) and \( F-H \)
bonds in the decreasing order of bond
energy:
\( \mathbf{A} \cdot F-H>O-H>N-H \)
B \( . N-H>O-H>F-H \)
\( \mathbf{c} \cdot O-H>N-H>F-H \)
D . \( F-H>N-H>O-H \)
Subject: Maths
Write minors and cofactors of the
elements of the following determinants:
\( (i)\left|\begin{array}{cc}2 & -4 \\ 0 & 3\end{array}\right| \)
\( (i i)\left|\begin{array}{ll}a & c \\ b & d\end{array}\right| \)
\( (i i i)\left|\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right| \)
\( (i v)\left|\begin{array}{ccc}1 & 0 & 4 \\ 3 & 5 & -1 \\ 0 & 1 & 2\end{array}\right| \)
Subject: Maths
\( f(a+b+c=0, \) then one root of \( \left|\begin{array}{ccc}\boldsymbol{a}-\boldsymbol{x} & \boldsymbol{c} & \boldsymbol{b} \\ \boldsymbol{c} & \boldsymbol{b}-\boldsymbol{x} & \boldsymbol{a} \\ \boldsymbol{b} & \boldsymbol{a} & \boldsymbol{c}-\boldsymbol{x}\end{array}\right|=0 \) is
\( A \cdot a+b \)
B.
\( c \cdot b+c \)
D. atca
Subject: Maths
The number \( x \) was multiplied by 0.5 and
the product divided by \( 3 . \) The result was
squared and 1 added to it. The final result was \( 50 . \) What was the value of
number \( \boldsymbol{x} \) ?
A .42
B. 30
\( c \cdot 24 \)
D. 18
Subject: Chemistry
The correct statement(s) about \( C r^{2+} \)
and \( M n^{3+} \) is(are):
[Atomic numbers of \( \mathbf{C r}=\mathbf{2 4} \) and \( \mathbf{M n}= \)
This question has multiple correct options
A. \( C r^{2+} \) is a reducing agent
B. \( M n^{3+} \) is an oxidizing agent
c. Both \( C r^{2+} \) and \( M n^{3+} \) exhibit \( d^{4} \) electronic configuration
D. When \( C r^{2+} \) is used as a reducing agent, the chromium ion attains \( d^{5} \) electronic configuration
Subject: Physics
A diver at a depth of \( 12 m \) in water \( \left(\mu=\frac{4}{3}\right) \) sees the sky in a cone of semi-vertical angle of :
\( ^{\mathbf{A}} \cdot \sin ^{-1}\left(\frac{4}{3}\right) \)
B \( \cdot \tan ^{-1}\left(\frac{4}{3}\right) \)
\( ^{c} \cdot \sin ^{-1}\left(\frac{3}{4}\right) \)
D. \( 90^{\circ} \)
Subject: Physics
Two sources \( A \) and \( B \) are sounding notes of frequency \( 660 \mathrm{Hz} \) A listener moves from \( A \) to \( B \) with a constant
velocity \( u . \) If the speed of sound is
\( 330 \mathrm{m} / \mathrm{s} \) what must be the value of \( u \)
so that he hears 8 beats per second?
A \( .2 .8 \mathrm{m} / \mathrm{s} \)
в. \( 2 m / s \)
c. \( 3.0 \mathrm{m} / \mathrm{s} \)
D. \( 3.5 \mathrm{m} / \mathrm{s} \)
Subject: Physics
A uniform but time varying magnetic
field \( \mathrm{B}=\boldsymbol{K}_{1} \boldsymbol{K}_{2} \boldsymbol{t} \) where \( \boldsymbol{K}_{1} \& \boldsymbol{K}_{2} \) are
positive constants and t is time (in seconds), is applied perpendicular to the plane of a circular loop of radius a and resistance R.Find the total charge (in coulomb) that will pass through any point of the loop by the time \( \mathrm{B} \)
becomes zero. [Given a \( =2 \mathrm{m}, \mathrm{R}=\pi \Omega, K_{1} \) \( =2 T] \)
Subject: Physics
A square wire frame of side \( a \) is placed
a distance \( b \) away from a long straight
conductor carrying current \( I \). The frame
has resistance \( R \) and self inductance \( L \)
The frame is rotated by \( 180^{\circ} \) about \( 00^{\prime} \)
as shown in figure. Find the electric charge flown through the frame.
\( ^{A} \cdot \frac{2 \mu_{0} i a^{2}}{2 \pi R b} \)
В. \( \frac{\mu_{0} i}{2 \pi R} \log _{e} \frac{b+a}{b-a} \)
c. \( \frac{\mu_{0} i a}{2 \pi R} \log _{e} \frac{b+a}{b-a} \)
D. none of thes
Subject: Maths
If \( f(x) \) is a function such that \( f^{\prime \prime}(x)+ \)
\( \boldsymbol{f}(\boldsymbol{x})=\mathbf{0} \) and \( \boldsymbol{g}(\boldsymbol{x})=[\boldsymbol{f}(\boldsymbol{x})]^{2}+\left[\boldsymbol{f}^{\prime}(\boldsymbol{x})\right]^{2} \)
and \( g(3)=8, \) then \( g(8)= \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. 3
\( c .5 \)
D. 8
Subject: Physics
A block of mass \( 0.18 k g \) is attached to a
spring of force constant \( 2 N m^{-1} \). The
coefficient of friction between the block
and the floor is \( 0.1 . \) Initially, the block is at rest and the spring is un-stretched. An impulse is given to the block as shown in Fig. The block slides a distance of \( 0.06 m \) and comes to rest for
the first time. The initial velocity of the block in \( m s^{-1} \) is \( V=N / 10 . \) Then N is :
\( A \)
B.
\( c \)
D.
Subject: Maths
A box contains 6 pens, 2 of which are
defective. Two pens are taken randomly
from the box. If r.v. \( X: \) Number of
defective pens obtained, then standard deviation of \( \boldsymbol{X}= \)
\( ^{\mathrm{A}}: \pm \frac{4}{3 \sqrt{5}} \)
B. \( \frac{8}{3} \)
\( c \cdot \frac{16}{45} \)
D. \( \frac{4}{3 \sqrt{5}} \)
Subject: Physics
\( \vec{A}, \vec{B} \) and \( \vec{C} \) satisfy the relations, \( \vec{A} \cdot \vec{B}=0 \) and \( \vec{A} \cdot \vec{C}=0, \) then \( \vec{A} \) is
parallel to
A . \( \vec{B} \)
в. \( \vec{c} \)
c. \( \vec{B} \times \vec{C} \)
D. 高广
Subject: Maths
Calculate the median from the following distribution
\( \begin{array}{lllll}\text { Class } & \begin{array}{l}5- \\ 10\end{array} & \begin{array}{l}10 \\ 15\end{array} & \begin{array}{l}15- \\ 20\end{array} & 2\end{array} \) \( 20- \)
25
Frequency \( \quad 4 \quad \) 7
10
Subject: Maths
\( f(x)=\left\{\begin{array}{cc}1-\cos x & x \neq 0 \\ x & \\ k & x=0\end{array}\right\} \)
continuous at \( x=0, \) then the value of \( k \)
is:
A . 0
\( B \cdot \frac{1}{2} \)
\( c \cdot \frac{1}{4} \)
\( D \cdot-\frac{1}{2} \)
Subject: Maths
Evalaute the integral \( \int_{0}^{1} \sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right) d x \)
A \( \cdot \frac{\pi}{4}-\log 2 \)
B \( \cdot \frac{\pi}{2}+\log 2 \)
c. \( \frac{\pi}{2}-\log 2 \)
D. \( \frac{\pi}{4}+\log 2 \)
Subject: Physics
Six particles each of mass \( m \) are placed
at the corners of a regular hexagon of
edge length \( a \). If a point mass \( m_{0} \) is
placed at the centre of the hexagon, then the net gravitational force on the
point mass \( \boldsymbol{m}_{0} \) is :
A \( \cdot \frac{6 G m^{2}}{a^{2}} \)
в. \( \frac{6 G m m_{0}}{a^{2}} \)
c. zero
D. none of these
Subject: Physics
A particle suspended from a fixed point, by a light inextensible thread of length is projected horizontally from its lowest position with velocity \( \sqrt{\frac{\mathbf{7 g L}}{\mathbf{2}}} . \) The thread will slack after swinging through
an angle \( \theta, \) such that \( \theta \) equal
A \( .30^{\circ} \)
B. \( 135^{\circ} \)
\( c \cdot 120^{\circ} \)
D. \( 150^{\circ} \)
Subject: Maths
If the vectors \( a \hat{i}+\hat{j}+\hat{k}, \hat{i}+b \hat{j}+\hat{k} \) and
\( \hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}+\boldsymbol{c} \hat{\boldsymbol{k}}(\boldsymbol{a} \neq \boldsymbol{b} \neq \boldsymbol{c} \neq 1) \) are coplanar
then the value of \( \frac{1}{1-a}+\frac{1}{1-b}+ \) \( \frac{1}{1-c} \) is equal to
A . 1
B.
\( c \cdot 2 \)
D. none of these
Subject: Chemistry
Which of the following statements is
correct?
This question has multiple correct options
A. \( S O_{2} \) is anhydride of sulphurous acid.
B. \( S O_{2} \) acts as only oxidising agent.
c. The coloured matter lost colour on exposure to \( S O_{2} \) can regain colour on exposure to atmosphere
D. \( S O_{2} \) can get reduced to sulphur.
Subject: Maths
\( A B C \) is a triangle right-angled at \( B \)
and \( D \) is a point on \( B C \) produced
\( (B D>B C), \) such that \( B D=2 D C \)
Which one of the following is correct?
A. \( A C^{2}=A D^{2}-3 C D^{2} \)
B. \( A C^{2}=A D^{2}-2 C D^{2} \)
c. \( A C^{2}=A D^{2}-4 C D^{2} \)
D. \( A C^{2}=A D^{2}-5 C D^{2} \)
Subject: Physics
A man of mass \( \mathrm{M} \) stands at one end of a
plank of lenght L which lies at rest on a frictionless surface. The man walk to
the other end of the plank. If the mas of the plank is \( \frac{M}{3}, \) the distance that the man moves relative to the ground is
A. \( \frac{3 L}{4} \)
в. \( \frac{L}{4} \)
c. \( \frac{4 L}{5} \)
D. \( \frac{L}{3} \)
Subject: Physics
An object approaches a convergent lens from the left of the lens with a
uniform speed \( 5 \mathrm{m} s^{-1} \) and stops at the
focus. The image:
A. moves away from the lens with an uniform speed 5 m
B. moves away from the lens with an uniform acceleration
c. moves away from the lens with a non-uniform acceleration
D. moves towards the lens with a non-uniform acceleration.
Subject: Chemistry
The reaction: \( O C l^{-}+I^{-} \stackrel{O H^{-}}{\longrightarrow} O I^{-}+ \)
\( C l^{-} \) takes place in following steps:
(i) \( O C l^{-}+H_{2} O \stackrel{K_{1}}{\kappa_{2}} H O C l+O H^{-} \)
(fast)
(ii) \( I^{-}+H O C l \stackrel{K_{3}}{\longrightarrow} H O l+C l^{-} \) (slow)
\( \left(\text { iii) } O H^{-}+H O I_{K_{2}^{\prime}}^{K_{1}^{\prime}} H_{2} O+O I^{-}(\text {fast })\right. \)
The rate of expression in terms of rate of
consumption of \( I^{-} \) is :
A \( \cdot \frac{-d I}{d t}=K \cdot \frac{[O C l] \mid I}{\int_{O H} \mid}^{-} \)
B. \( \frac{d I \text { - }}{d t}=K \cdot \frac{[O C l][I]}{[O H]^{2}} \)
c. \( \frac{d I}{d t}=K \cdot \frac{(O C l)^{2} I}{[\rho H]} \)
D. None of these
Subject: Chemistry
\( C O_{2} \) and \( S i O_{2} \) is a solid or gas?
A. \( C O_{2} \) gas and \( S i O_{2} \) solid
B. \( C O_{2} \) solid and \( S i O_{2} \) gas
c. \( C O_{2} \) gas and \( S i O_{2} \) gas
D. \( C O_{2} \) solid and \( S i O_{2} \) solid
Subject: Chemistry
Which of the following will form an ideal
solution?
A \( \cdot C_{2} H_{5} O H \) and water
B. \( H N O_{3} \) and water
c. \( C H C l_{3} \) and \( C H_{3} C O C H_{3} \)
D. \( C_{6} H_{6} \) and \( C_{6} H_{5} C H_{3} \)
Subject: Physics
List List - II
a. Temperature of water e. \( 273 \mathrm{K} \)
at the bottom of a lake
b. \( \gamma_{r} \) of water is - ve f. \( 277 \mathrm{K} \)
between
c. \( \gamma_{r} \) of water is positive
g. above 277
\( k \)
d. Temperature of water
h. \( 273 \mathrm{K} \) and
just below ice layer in \( 277 \mathrm{K} \)
a Lake
\( A \cdot a-g, b-h, c-e, d-f \)
B. a-h, b-e, c-f, d-g
c. a-e, b-f, c-g, d-h
D. a-f, b-h, c-g, d-e
Subject: Chemistry
The complex ion \( \left[\boldsymbol{F e}(\boldsymbol{C N})_{\boldsymbol{6}}\right]^{\boldsymbol{4}-} \) contains:
\( \mathbf{A} \cdot s p^{3} d^{2} \) hybrid orbitals with octahedral structure
B. total 104 electrons on \( F e^{+2} \)
C. six sigma Bonds
D. total of 36 electrons on \( F e^{2+} \) ions.
Subject: Biology
The four figures \( (A, B, C \text { and } D) \) given
below represent four different types of animals tissues. Which one of these is
correctly identified in the given options along with its correct location and function?
A. Tissue-
B- Glandular epithelium; Location- Intestine; Function- Secretion
B. Tissue C- Collagen fibres; Location- Cartilage; Function- Attach bone to bone
c. Tissue D- Smooth muscle tissue; Location- Heart:
Function- Heart contraction
D. Tissue A- Columnar epithelium; Location- Nephron; Function- Secretion and absorption
Subject: Maths
If \( \cos ^{-1}\left(\frac{x}{2}\right)+\cos ^{-1}\left(\frac{y}{3}\right)=\theta, \) if \( 9 x^{2}- \)
\( 12 x y \cos \theta+4 y^{2}=m \sin ^{2} \theta . \) Find \( m . \)
Subject: Physics
Match the following A
\( \mathbf{A} \)
1-b, 2-c, 3-a, 4-d
B. \( 1-c, 2-d, 3-b, 4-a \)
c. \( 1-a, 2-c, 3-b, 4-d \)
D. \( 1-c, 2-a, 3-d, 4-b \)
Subject: Chemistry
For which of the following reactions will the equilibrium mixture contain an
appreciable concentration of both reactants and products?
A \( \cdot C l_{2}(g) \rightleftharpoons 2 C l(g) ; K_{c}=6.4 \times 10^{-39} \)
B. \( C l_{2}(g)+2 N O(g) \rightleftharpoons 2 N O C l(g) ; K_{c}=3.7 \times 10^{8} \)
c. \( C l_{2}(g)+2 N O(g) \rightleftharpoons 2 N O_{2} C l(g) ; K_{c}=1.8 \)
D. \( H_{2}(g)+I_{2}(g) \rightleftharpoons 2 H I(g) . K_{c}=49 \)
Subject: Physics
An alpha particle collides elastically with a stationary nucleus and
continues moving at an angle of \( 60^{\circ} \) with respect to the original direction of motion. The nucleus recoils at an angle
of \( 30^{0} \) with respect to this direction Mass number of the nucleus is :
A. 3
B. 4
\( c \cdot 6 \)
D. 8
Subject: Physics
Illuminating the surface of a certain metal alternately with light of
wavelength \( \lambda_{2}=0.54 \mu m \) and \( \lambda_{2}= \)
\( 0.54 \mu m, \) it was found that the
corresponding maximum velocities of photo electrons have a ratio \( \eta=2, \) Find the work function of that metal.
A \( .6 .99 e V \)
B. \( 1.9 e V \)
c. \( 7.53 e V \)
D. \( 1.88 e V \)
Subject: Maths
The domain of the function \( \boldsymbol{f}(\boldsymbol{x})= \) \( \sin ^{-1}\left(\log _{2}\left(\frac{x^{2}}{2}\right)\right) \) is
A. [-2,-1)\( \cup(1,2] \)
B. (-2,-1]\( \cup[1,2] \)
c. [-2,-1]\( \cup[1,2] \)
D. (-2,-1)\( \cup(1,2) \)
Subject: Chemistry
\( \mathbf{2} \boldsymbol{H}+\boldsymbol{C u O} \rightarrow \boldsymbol{X}+\boldsymbol{Y} \)
The compound \( X \) and \( Y \) are:
A. \( H_{2} O, C u \)
в. \( H_{2}, \) Си \( O \)
\( c . \) both \( A \) and \( B \)
D. none of the above
Subject: Maths
Assertion
Triangles on the same base and between the same parallel lines are
equal in area.
Reason
The distance between two parallel lines
is same everywhere.
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: Chemistry
From the following chemical reactions determine the relative Bronsted-Lowery acid strengths (strongest to weakest). \( \boldsymbol{H} \boldsymbol{C l O}_{4}(\boldsymbol{s o l})+\boldsymbol{C H}_{3} \boldsymbol{C O O H}(l) \longrightarrow \)
\( \boldsymbol{C H}_{3} \boldsymbol{C}(\boldsymbol{O H})_{2}^{+}(\boldsymbol{s o l})+\boldsymbol{C l O}_{\boldsymbol{4}}^{-}(\boldsymbol{a q}) \)
\( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4}(\boldsymbol{s} \boldsymbol{o l})+\boldsymbol{C H}_{3} \boldsymbol{C O O H}(l) \rightleftharpoons \)
\( \boldsymbol{C H}_{3} \boldsymbol{C}(\boldsymbol{O H})_{2}^{+}(\boldsymbol{s o l})+\boldsymbol{C l O}_{4}^{-}(\boldsymbol{s o l}) \)
A \( \cdot H C l O_{4}>C H_{3} C(O H)_{2}^{+}>H_{2} S O_{4} \)
в. \( H C l O_{4}>C H_{3} C O O H>H_{2} S O_{4} \)
c. \( H C l O_{4}>H_{2} S O_{4}>C H_{3} C(O H)_{2}^{+} \)
D. \( H C l O_{4}>H_{2} S O_{4}>C H_{3} C O O H \)
Subject: Chemistry
For the given pair of \( S_{N} 2 \) reaction, the
first product occurs with larger rate
constant.
\[
\bigwedge_{\mathrm{Br}}+\mathrm{HO}^{-} \longrightarrow \sim_{\mathrm{Y}} \mathrm{Br}+\mathrm{HO}^{-} \rightarrow
\]
Subject: Maths
The binomial distribution whose mean
is 9 and the variance is 2.25 is
\( ^{\mathbf{A}} \cdot\left(12, \frac{1}{2}, \frac{1}{2}\right) \)
B \( \cdot\left(12, \frac{2}{3}, \frac{1}{3}\right) \)
\( ^{\mathbf{c}} \cdot\left(12, \frac{5}{6}, \frac{1}{6}\right) \)
D. \( \left(12, \frac{3}{4}, \frac{1}{4}\right) \)
Subject: Physics
A potentiometer wire of length \( L \) and a
resistance \( r \) are connected in series
with a battery of e.m.f. \( \boldsymbol{E}_{0} \) and \( \mathbf{a} \)
resistance \( r_{1} . \) An unknown e.m.f. \( \boldsymbol{E} \) is
balanced at a length \( l \) of the
potentiometer wire. The e.m.f. \( \boldsymbol{E} \) will be
given by:
A \( \cdot \frac{L E_{0} r}{\left(r+r_{1}\right) l} \)
в. \( \frac{L E_{0} r}{l r_{1}} \)
\( \mathbf{c} \cdot \frac{E_{0} r}{\left(r+r_{1}\right)} \cdot \frac{l}{L} \)
D. \( \frac{E_{0} l}{L} \)
Subject: Chemistry
For the elements:
\( \boldsymbol{C l}, \boldsymbol{B r}, \boldsymbol{F}, \boldsymbol{A l}, \boldsymbol{C}, \boldsymbol{L} \boldsymbol{i}, \boldsymbol{C s} \) \& \( \boldsymbol{X} \boldsymbol{e} \)
Choose the best option. The element having 8 electrons in the outermost shell is:
A. \( X e \)
в. \( C s \)
\( c \cdot B r \)
D. \( C \)
Subject: Physics
A coil of radius \( \pi \) meters, 100 turns
carries a current of \( 3 A \). The magnetic induction at a point on its axis at a distance equal to \( \sqrt{3} \) times its radius from its centre is :
A. \( 7.2 \times 10^{-6} \mathrm{Wbm}^{-2} \)
в. \( 7.4 \times 10^{-6} \mathrm{Wbm}^{-2} \)
c. \( 7.5 \times 10^{-6} \mathrm{Wbm}^{-2} \)
D. \( 7.83 \times 10^{-6} \mathrm{Wbm}^{-2} \)
Subject: Chemistry
\( 1 \mathrm{cc} \) of \( 0.1 \mathrm{N} H C l \) is added to \( 999 \mathrm{cc} \)
solution of \( N a C l . \) The \( p H \) of the
resulting solution will be:
A. 7
B. 3
\( c \cdot 4 \)
D.
Subject: Physics
Three identical capacitors, each of capacitance \( C, \) are connected in series
with a battery of emf \( V \) and get fully charged. Now, the battery is removed and the capacitors are connected in
parallel with positive terminals are one point and negative terminals at other point. Then, the common potential will be :
A. \( V \)
в. \( 3 V \)
c. \( \frac{V}{3} \)
D.
Subject: Physics
If the mass of the earth increases by \( 80 \% \) and radius of the earth increases
by \( 40 \% \) then the percentage charge in acceleration due to gravity on the surface of radius of earth is (where \( g_{s}=\frac{G M}{R^{2}}, M= \) mass of earth and \( R= \) radius of earth \( \} \) )
A. zero
B . \( +8.16 \% \)
c. \( -8.16 \% \)
D. \( 160 \% \)