AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be a differentiable
function for all values of \( x \) and has the
peoperty that \( f(x) \) and \( f^{\prime}(x) \) have opposite signs for all values of \( x \). Then
A. \( f(x) \) is an increasing function
B. \( f(x) \) is a decreasing function
C \( \cdot f^{2}(x) \) is a decreasing function
D. \( |f(x)| \) is an increasing function
Subject: Maths
The vectors \( \hat{\boldsymbol{i}}+\boldsymbol{2} \hat{\boldsymbol{j}}+\boldsymbol{3} \hat{\boldsymbol{k}}, \boldsymbol{2} \hat{\boldsymbol{i}}-\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \) and
\( \mathbf{3} \hat{\mathbf{i}}+\hat{\boldsymbol{j}}+\mathbf{4} \hat{\boldsymbol{k}} \) are so placed that the end
point of one vector is the starting point of the next vector. Then the vectors are :
A. Not coplanar
B. Coplanar but cannot form a triangle
c. coplannar but can form a triangle
D. coplanar and can form a right angled triangle
Subject: Physics
541
negligible resistance and radius \( a \). It is
hinged at the center of the ring and
rotated about this point in clockwise
direction with a uniform angular
velocity \( \omega . \) There is a uniform magnetic
field of strength \( B \) pointing inward and
\( r \) is a stationary resistance. Then
This question has multiple correct options
A. current through \( r \) is zero
B. current through \( r \) is \( \left(2 B \omega a^{2}\right) / 5 r \)
c. direction of current in external resistance \( r \) is from
center to circumference
D. direction of current in external resistance \( r \) is from
circumference to center
E. answer required
Subject: Chemistry
Average atomic weight of boron is 10.10 and boron exists in two isotopic forms
\( B^{10} \) and \( B^{11} . \) The percentage abundance
of \( B^{10} \) is?
A . \( 10 \% \)
B. \( 90 \% \)
c. \( 50 \% \)
D. 20\%
Subject: Maths
Area of a rhombus is \( 256 \mathrm{cm}^{2} \). One of
the diagonal is twice of the other diagonal. The sum of the diagonals is:
\( \mathbf{A} \cdot 38 \mathrm{cm} \)
в. \( 48 \mathrm{cm} \)
c. \( 28 \mathrm{cm} \)
D. \( 56 \mathrm{cm} \)
Subject: Physics
The nature of image of a candle flame located \( 40 \mathrm{cm} \) from a concave spherical mirror is real, inverted and magnified
four times. Then the radius of curvature
of the mirror is:
\( A .32 \mathrm{cm} \)
B. \( 64 \mathrm{cm} \)
c. \( 48 \mathrm{cm} \)
D. \( 80 \mathrm{cm} \)
Subject: Maths
Three vectors \( \vec{A}, \vec{B} \) and \( \vec{C} \) are as shown in figure. If magnitude of \( \vec{A} \) is \( 4 \mathrm{m} \) and \( \vec{A}+\vec{B}+\vec{C}=0, \) then the magnitude of \( \vec{B} \) and \( \vec{C} \) are respectively
A. \( 4 m, 4 m \)
в. \( 4 \sqrt{3} m, 4 \sqrt{3} m \)
c. \( 4 m, 4 \sqrt{3} m \)
D. \( 4 \sqrt{3} m, 4 m \)
Subject: Maths
The value of \( (a+b)^{2}-2(a-b)^{2}+ \)
\( (a-b)(a+b) \) is
A \( \cdot 4 a b-b^{2} \)
B . \( 2 a b-b^{2} \)
\( c \cdot 3 a b-b^{2} \)
D. \( 6 a b-2 b^{2} \)
Subject: Physics
Two force point charges \( +q \) and \( +4 q \)
are a distance \( \ell \) apart. A third charge \( q_{1} \)
is so placed that the entire system is in equilibrium. Find the location,
magnitude and sign of the third charge.
This question has multiple correct options
A \( \cdot q_{1}=\frac{4}{9} q \)
B. \( q_{1}=\frac{-4}{9} q \)
\( \mathbf{C} \cdot q_{1} \) is to be placed at a distance \( \ell / 3 \) from \( q \)
D. \( q_{1} \) is to be placed at a distance \( \frac{2 \ell}{3} \) from \( 4 q \)
Subject: Maths
A family is going to a theme park having \( t \) members in the family. Each ticket costs \( \$ 80, \) and the number of
tickets needs to be bought can be
calculated from the expression \( t^{2}- \)
\( 4 t-90=6 \) when \( t>0 . \) What is the
total cost of the theme park tickets that
the family paid?
A. \( \$ 640 \)
B. \( \$ 800 \)
c. \( \$ 960 \)
D. \( \$ 1,120 \)
Subject: Physics
In a photoelectric effect, the anode
potential is plotted against the plate
current
A. A and B will have different intensities while B and
will have different frequencies
B. B and C will have different intensities while A and will have different frequencies
C. \( A \) and \( B \) will have different intensities while \( A \) and \( C \) will have equal frequencies
D. A and B will have equal intensities while B and C will have different frequencies
Subject: Chemistry
Water gas is an equi-molar mixture of hydrogen and carbon monoxide. If 250
litres of water gas is burnt in air. Assuming both reactants and products are at same temperature and pressure,
the volume of \( O_{2} \) required is
\( 2 C O+O_{2} \rightarrow 2 C O_{2} ; 2 H_{2}+O_{2} \rightarrow \)
\( 2 H_{2} O \)
A. 250 litres
B. 125 litres
c. 75 litres
D. 500 litres
Subject: Chemistry
\( 2 C+O_{2}=2 C O . \) The rate of
disappearance of \( \boldsymbol{C} \) is \( 2 \times \)
\( 10^{-3} \) mol \( L^{-1} \) sec \( ^{-1} \). What is the
instantaneous rate of the reaction?
A. \( 2 \times 10^{-3} \)
В. \( 1 \times 10^{-3} \)
c. \( 4 \times 10^{-3} \)
D. None of these
Subject: Maths
A variable point \( \boldsymbol{P} \) on the ellipse of eccentricity is joined to the foci \( S \) and
\( s^{\prime} . \) The eccentricity of the locus of the in
cetre of the triangle \( P S S^{1} \) is
A \( \cdot \sqrt{\frac{2 e}{1+e}} \)
B. \( \sqrt{\frac{e}{1+e}} \)
c. \( \sqrt{\frac{1-e}{1+e}} \)
D. \( \frac{e}{2(1+e)} \)
Subject: Maths
If \( z=\sqrt{\frac{1-i}{1+i}}, \) then arg \( z= \)
A. \( \frac{\pi}{4}, \frac{\pi}{2} \)
B. \( -\frac{\pi}{4}, \frac{\pi}{2} \)
c. \( \frac{3 \pi}{4}, \pi \)
D. \( -\frac{\pi}{4}, \frac{3 \pi}{4} \)
Subject: Maths
The position vectors of the points \( A, B, C \) are respectively (1,1,1)\( ;(1,-1,2) ;(0,2,-1) \)
Find a unit vector parallel to the plane determined by ABC \& perpendicular to the vector (1,0,1)
A \( \cdot \pm \frac{1}{3 \sqrt{3}}(i+5 j-k) \)
B . \( \pm(i+5 j-k) \)
\( \mathbf{c} \cdot \pm(-i-5 j-k) \)
D \( : \pm \frac{1}{3 \sqrt{3}}(-i-5 j-k) \)
Subject: Physics
By applying a force \( \boldsymbol{F}=(\mathbf{3} \boldsymbol{x} \boldsymbol{y}-\mathbf{5} \boldsymbol{z}) \boldsymbol{j}+ \)
\( 4 z k \) a particle is moved along the path
\( \boldsymbol{y}=\boldsymbol{x}^{2} \) from point \( (\boldsymbol{0}, \boldsymbol{0}, \boldsymbol{0}) \) to the point
\( (2,4,0) . \) The work done by the \( F \) on the particle is (all values are in SI units)
\( A \)
в. \( \frac{140}{5} J \)
c. \( \frac{232}{5} J \)
D.
Subject: Chemistry
The reaction between \( N O \) and \( C l_{2} \) takes place in the following two steps:
\( \boldsymbol{I} \cdot \boldsymbol{N} \boldsymbol{O}+\boldsymbol{C l}_{2}_{k_{2} \atop f a t}^{k_{1}} \boldsymbol{N O C l}_{2} \)
II. \( N O C l_{2}+N O \frac{k_{3}}{s l o w} \geq 2 N O C l \)
The rate law of overall reaction, \( 2 N O+ \)
\( C l_{2} \longrightarrow 2 N O C l, \) can be given by:
A \( \cdot \) Rate \( =k[N O]^{2}\left[C l_{2}\right] \)
B・Rate \( =k[N O]\left[C l_{2}\right] \)
c. Rate \( =k[N O C l][N O \)
D・Rate \( =k[N O]\left[C l_{2}\right]^{2} \)
Subject: Maths
The area of coloured paper required to completely cover a solid cubical box of
\( \operatorname{edge}^{\prime} x^{\prime} \) units is :
A \( \cdot 4 x^{2} \)
В. \( 5 x^{2} \)
\( c \cdot 6 x^{2} \)
\( D \cdot 8 x^{2} \)
Subject: Physics
If \( f_{0}=5 c m, \lambda=600 A^{0}, a=1 \mathrm{cm} \) for \( \mathrm{a} \)
microscope, then what will be its resolving power
A \( .11 .9 \times 10^{5} / m \)
B . \( 10.9 \times 10^{5} / m \)
c. \( 10.9 \times 10^{4} / m \)
D. \( 10.9 \times 10^{3} / m \)
Subject: Chemistry
Match the List I with the List II.
A. \( A-i v, B-i, C- \) ii, D - iii
B. A - v, B - i, C - ii, D - iii
C. \( A-i v, B-i, C- \) iii, \( D-i i \)
D. \( A-i, B-i v, C- \) ii, \( D \) -iii
Subject: Chemistry
Which of the following is an acid-base
neutralization reaction?
\( \mathbf{A} \cdot A g^{+}(a q)+C l^{-} \rightarrow A g C l(a q) \)
B \( \cdot C_{5} H_{12}(s)+8 O_{2}(g) \rightarrow 5 C O_{2}(g)+6 H_{2} O(l) \)
\( \mathbf{C} \cdot N H_{3}(s)+H_{2} O(s) \leftrightharpoons N H_{4}^{+}(s)+O H^{-}(s) \)
D. \( H C_{2} H_{3} O_{2}(l)+O H^{-}(a q) \rightarrow H_{2} O(O)+C_{2} H_{3} O_{2}^{-}(a q) \)
E \( \cdot C a C O_{3}(s) \rightarrow C a O(s)+C O_{2}(g) \)
Subject: Physics
Which of the following units can be
used to express G?
\( A \cdot N K g^{-2} \)
B. \( \mathrm{Nm}^{-2} \mathrm{Kg}^{2} \)
\( \mathrm{C} \cdot \mathrm{Nm}^{2} \mathrm{Kg}^{-2} \)
D. \( \mathrm{Nm}^{-2} \mathrm{Kg}^{-3} \)
Subject: Physics
toppr
Q Type your question
decay products of the neutron.
Therefore, considering the decay of a
neutron as a two-body decay process, it
was predicted theoretically that the kinetic energy of the electron should be a constant. But experimentally, it was observed that the electron kinetic
energy has a continuous spectrum. Considering a three-body decay
process, i.e. \( \boldsymbol{n} \rightarrow \boldsymbol{p}+\boldsymbol{e}^{-}+\overline{\boldsymbol{v}}_{e}, \) around
1930, Pauli explained the observed
electron energy spectrum. Assuming
the anti-neutrino \( \left(\bar{v}_{e}\right) \) to be massless
and possessing negligible energy, and
the neutron to be at rest, momentum
and energy conservation principles are
applied. From this calculation, the maximum kinetic energy of the electron
is \( 0.8 \times 10^{6} e V . \) The kinetic energy
carried by the proton is only the recoil
energy. What is the maximum energy of the
anti-neutrino?
A. Zero
B. Much less than \( 0.8 \times 10^{6} e V \).
C . Nearly \( 0.8 \times 10^{6} \mathrm{eV} \)
D. Much larger than \( 0.8 \times 10^{6} e V \)
Subject: Physics
Below is a chart describing the
parameters of 5 metal wires:
\begin{tabular}{lll} 
Wire & Length \( (\boldsymbol{m}) \) & Diameter \( (\boldsymbol{m m}) \) \\
1 & 1 & 0.5 \\
2 & 1 & 1 \\
4 & 2 & 0.5 \\
5 & 2 & 1 \\
\hline 6 & 2 & 2 \\
\hline
\end{tabular} Assuming all of the wires are made
from the same material, rank these
wires from highest to lowest resistance.
A. 4,5,6,1,3,2
B. 3,2,1,6,5,4
C. 4,1,5,2,6,3
D. 1,4,2,5,3,6
E. 4,5,6,1,2,3
Subject: Maths
Coffee is coming out from a conical filter, with height and diameter both \( 25 \mathrm{cm} \) into a cylindrical coffee pot with
diameter \( 15 \mathrm{cm} . \) The constant rate at
which coffee comes out from the filter
into the pot is \( 100 \mathrm{cm}^{3} / \) min. The rate in
cm / min at which the level in the pot is rising at the instance when the coffee in the pot is \( 10 \mathrm{cm} \), is
A \( \cdot \frac{9}{16 \pi} \)
В \( \cdot \frac{25}{9 \pi} \)
c. \( \frac{5}{3 \pi} \)
D. \( \frac{16}{9 \pi} \)
Subject: Chemistry
\( \ln \) a \( S_{N} 2 \) substitution reaction of the type \( \boldsymbol{R}-\boldsymbol{B r}+\boldsymbol{C l}^{-} \stackrel{D M \boldsymbol{F}}{\rightarrow} \boldsymbol{R}-\boldsymbol{C l}+ \)
\( B r^{-} \) Which one of the following has the
highest relative rate?
\( A \)
(1)
в. \( C H_{3} C H_{2} B r \)
c. \( C H_{3}-C H_{2}-C H_{2} B r \)
D.
(4)
\[
\begin{array}{c}
\mathrm{cH}_{3}-\mathrm{cH}-\mathrm{cH}_{2} \mathrm{Br} \\
\mathrm{CH}_{3}
\end{array}
\]
Subject: Chemistry
\( \mathbf{0 . 0 0 1} \) molal solution of \( \left[\boldsymbol{P t}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4} \boldsymbol{C l}_{4}\right] \)
in water had a freezing point depression
of \( 0.0054 \quad^{o} C . \) If \( K_{f} \) for water is 1.80 the correct formula of the compound is :
\( \mathbf{A} \cdot\left[P t\left(N H_{3}\right)_{4} C l_{3}\right] C l \)
\( ^{\mathbf{B}} \cdot\left[P t\left(N H_{3}\right)_{4} C l_{4}\right] \)
c. \( \left[P t\left(N H_{3}\right)_{4} C l_{2}\right] C l_{2} \)
D. \( \left[P t\left(N H_{3}\right)_{4} C l\right] C l_{3} \)
Subject: Maths
The ratio between the length and
breadth of a rectangular garden is 5: 3
If the perimeter of the garden is 160
meters, what will be the area of \( 5 m \)
wide road around its outside?
A. \( 600 m^{2} \)
B. \( 1200 m^{2} \)
\( \mathrm{c} \cdot 900 m^{2} \)
D. \( 1000 m^{2} \)
Subject: Physics
Assertion: Material used in the
construction of a standard resistance is
constantan or manganin Reason : Temperature coefficients of constantan and Magnanin are very
small
A. Both (A) and (R) are true and
(R) is the correct explanation of (A)
B. Both (A) and (R) are true but (R) is not the correct explanation of \( (A) \)
c. (A) is true but (R) is false
D. (A) is false but (R) is true
Subject: Maths
When \( a \) is real number then \( (z+ \)
\( \boldsymbol{a})(\overline{\boldsymbol{z}}+\boldsymbol{a})= \)
A. \( |z-a| \)
B. \( z^{2}+a^{2} \)
c. \( |z+a|^{2} \)
D. \( z^{2}-a^{2} \)
Subject: Physics
The momentum P and kinetic energy E of a body of mass \( \mathrm{m} \) are related as :
A \( . P=\sqrt{2 m E} \)
B. \( P=\frac{1}{2} m E \)
\( ^{\mathrm{c}} \cdot_{P}=\frac{2 m}{E} \)
D. \( P=2 m E \)
Subject: Chemistry
Assertion
Bohr proposed that angular momentum of electron in an orbit is quantized.
Reason

Debroglie derived that \( : m u r=n \frac{h}{2 \pi} \)
Read the above assertion and reason
and choose the correct option regarding
¡t.
A. Statement is correct but Explanation is wrong.
B. Statement is wrong but Explanation is correct
C. Both Statement and Explanation are correct and Explanation is the correct explanation for Statement.
D. Both Statement and Explanation are correct but Explanation is not the correct explanation for Statement
Subject: Maths
If \( \boldsymbol{\alpha} \leq 2 \sin ^{-1} \boldsymbol{x}+\cos ^{-1} \boldsymbol{x} \leq \boldsymbol{\beta}, \) then
A \( \cdot \alpha=\frac{\pi}{2}, \beta=\frac{\pi}{2} \)
B. \( \quad \alpha=\frac{\pi}{2}, \beta=\frac{3 \pi}{2} \)
c. \( \alpha=0, \beta=\pi \)
Subject: Physics
A solenoid is \( 1.5 m \) long and its inner
diameter is \( 4.0 \mathrm{cm} \). It has 3 layers of
winding's of 1000 turns each and carries a current of 2.0 amperes.The magnetic flux for a cross-section of the solenoid is nearly.
A . \( 4.1 \times 10^{-5} \) weber
B. \( 5.2 \times 10^{-5} \) weber
c. \( 6.31 \times 10^{-3} \) weber
D . \( 2.5 \times 10^{-7} \) weber
Subject: Physics
A particle of mass M is moving in a
horizontal circle of radius R with
uniform speed \( V \). when it moves from one point to a diametrically opposite point, its
A. kinetic energy changes by \( M V^{2} / 4 \)
B. momentum does not change
c. momentum changes by 2 MV
D. kinetic energy changes by \( M V^{2} \)
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x})=\mathbf{4} \boldsymbol{x}-\mathbf{3} . \) If \( \boldsymbol{f}(\boldsymbol{a})=\mathbf{9} \) and
\( f(b)=5, \) then calculate \( f(a+b) \)
\( \mathbf{A} \cdot \mathbf{5} \)
B. 7
c. 14
D. 16
E . 17
Subject: Physics
The frequencies of four sound waves are given below. Which of these sound
waves can be used to measure the
depth of sea by the echo method?
\( A \cdot 15,000 \mathrm{Hz} \)
B. 10 kHz
c. \( 50 \mathrm{kHz} \)
D. \( 10,000 \mathrm{Hz} \)
Subject: Chemistry
Choose the correct statement(s) for
froth flotation process, which is used for
the concentration of sulphide ore.
a) It is based on the difference in the
ability of different minerals to become
wet.
b) It uses sodium ethyl xanthate,
\( C_{2} H_{5} O C S_{2} N a \) as collector.
c) It uses \( N a C N \) as a depressant in the
mixture of \( Z n S \) and \( P b S, \) where \( Z n S \)
forms soluble complex and \( P b S \) forms
froth.
(a) and (b) are correct
A. only
B. Only (b) and (c) are correct
c. only (a) and (c) are correct
D. All statements are correct
Subject: Chemistry
A tangent drawn on the curve obtained by plotting concentration of product mole \( L^{-1} \) ) of the first-order reaction vs
time (min) at the point corresponding
to time minute takes an angle to \( 30^{\circ} \)
with concentration axis Hence the rate
of formations of product after 20 minutes will be:
A. 0.580 mole \( L^{-1} \) min \( ^{-1} \)
B. 1.723 mole \( L^{-1} \) min \( ^{-1} \)
c. 0.290 mole \( L^{-1} \) min \( ^{-1} \)
D. 0.866 mole \( L^{-1} \) min \( ^{-1} \)
Subject: Physics
The magnification of an object placed in front of a convex lens of focal length
\( 20 \mathrm{cm} \) is \( +2 . \) To obtain a magnification
of \( -2, \) the object has to be moved a distance equal to:
\( \mathbf{A} \cdot 10 \mathrm{cm} \)
B. \( 20 \mathrm{cm} \)
c. \( 30 \mathrm{cm} \)
D. \( 40 \mathrm{cm} \)
Subject: Maths
In Figure \( 5, \) rectangle \( A B C D \) is
inscribed in a circle. If the radius of the
circle is 2 and \( \overline{C D}=2, \) find the area of
the shaded region.
A. 0.36
3. 0.47
7
\( c .0 .57 \)
D. 0.707
\( =0.86 \)
Subject: Biology
Given below are some characteristics of
vessels and tracheids.
(i) Multicellular with wide lumen
(ii) Dead cells
(iii) Cell walls are lignified
(iv) Discontinues lumen due to
presence of end walls
(v) Long, cylindrical tube-like structure
(vi) Elongated cells with tapering ends Categorize the above characteristics
with vessels \( (x) \) and tracheids \( (y) \) and select the correct option.
A. \( x-(i),(\text { (i), (iii) }),(v), Y-(i \text { i) }, \) (iii), (iv), (vi)
B. X-(i), (iii), (vi), Y- (ii), (iii), (iv), (v)
c. \( x-(i),(\text { iv }),(v), Y-(\text { ii), (iv) },(v),(v i) \)
D. \( x-(i),(\text { ii) },(v),(v i), Y-(i), \) (iii), (iv), (vi)
Subject: Maths
Assertion
The equation \( 4 x^{3}-9 x^{2}+2 x+1=0 \)
has atleast one real root in (0,1)
Reason
If 'f' is a continuous function such that
\( \int_{a}^{b} f(x)=0, \) the the equation \( f(x)=0 \) has atleast one real root in \( (a, b) \)
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
Tow monochromatic coherent source of
wavelength \( 5000 A \) are placed along the
line normal to the screen as shown in
the figure.
(a) Determine the condition for maxima
at the point \( \boldsymbol{P} \)
(b) Find the order of the centre bright
fringe if \( \boldsymbol{d}=\mathbf{0 . 5} \boldsymbol{m m}, \boldsymbol{D}=\mathbf{1} \boldsymbol{m} \)
Subject: Physics
Q Type your question
thin-walled hollow sphere of radius \( \mathrm{R} \)
and mass M as shown. The hollow
sphere is fixed in position and the only
force on the point mass is the
gravitational attraction of the hollow
sphere. There is a very small hole in the
hollow sphere through which the point mass falls as shown. The velocity of a
point mass when it passes through point \( P \) at a distance \( R / 2 \) from the
centre of the sphere is?
A \( \cdot \sqrt{\frac{2 G M}{3 R}} \)
в. \( \sqrt{\frac{5 G M}{3 R}} \)
c. \( \sqrt{\frac{25 G M}{24 R}} \)
Subject: Physics
Currents of \( 10 A, 2 A \) are passed through two parallel wires \( A \) and \( B \) respectively in opposite directions. If the wire A is infinitely long and the length of the wire B is \( 2 m, \) the force on the conductor \( B \)
which is situated at \( 10 \mathrm{cm} \)
distance from A will be
\( \mathbf{A} \cdot 8 \times 10^{-5} N \)
B . \( 5 \times 10^{-5} N \)
c. \( 8 \pi \times 10^{-7} N \)
D. \( 4 \pi \times 10^{-7} N \)
Subject: Chemistry
If you dilute \( 25.0 \mathrm{mL} \) of \( 1.5 \mathrm{M} H C l \) to \( 500 \mathrm{mL}, \) then the molar concentration of
each ions becomes \( \boldsymbol{Y} \times \mathbf{1 0}^{-\mathbf{3}} \boldsymbol{M} . \) Here \( \boldsymbol{Y} \)
is:
Subject: Maths
Let \( E^{e} \) denotes the complement of an
event \( E . \) If \( E, F, G \) are pairwise
independent events with \( P(G)>0 \) and
\( \boldsymbol{P}(\boldsymbol{E} \cap \boldsymbol{F} \cap \boldsymbol{G})=\mathbf{0 .} \) Then, \( \boldsymbol{P}\left(\boldsymbol{E}^{e} \cap \boldsymbol{F}^{e} \mid \boldsymbol{G}\right) \)
equals
\( \mathbf{A} \cdot P\left(E^{e}\right)+P\left(F^{e}\right) \)
B . \( P\left(E^{e}\right)-P\left(F^{e}\right) \)
\( \mathbf{c} \cdot P\left(E^{e}\right)-P(F) \)
D. \( P(E)-P\left(F^{e}\right. \)
Subject: Chemistry
Two weak acid solutions \( H A_{1} \) and \( H A_{2} \)
each with the same concentration and
having pKa values 3 and 5 are placed in contact with hydrogen electrode \( (1 \mathrm{atm} \) \( 25^{0} C \) ) and are interconnected through a salt bridge. Find emf of the cell.
A \( .+0.059 \mathrm{V} \)
B. 0.059
c. \( 0.0295 \mathrm{v} \)
D. 0.118 V
Subject: Maths
\( \mathbf{f} \mathbf{a}^{2}+\boldsymbol{b}^{2}+\boldsymbol{c}^{2}=-\mathbf{2} \) and \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left|\begin{array}{ccc}\mathbf{1}+\boldsymbol{a}^{2} \boldsymbol{x} & \left(\mathbf{1}+\boldsymbol{b}^{2}\right) \boldsymbol{x} & \left(\mathbf{1}+\boldsymbol{c}^{2}\right) \boldsymbol{x} \\ \left(\mathbf{1}+\boldsymbol{a}^{2}\right) \boldsymbol{x} & \mathbf{1}+\boldsymbol{b}^{2} \boldsymbol{x} & \left(\mathbf{1}+\boldsymbol{c}^{2}\right) \boldsymbol{x} \\ \left(\mathbf{1}+\boldsymbol{a}^{2}\right) \boldsymbol{x} & \left(\mathbf{1}+\boldsymbol{b}^{2}\right) \boldsymbol{x} & \mathbf{1}+\boldsymbol{c}^{2} \boldsymbol{x}\end{array}\right| \)
Then, \( f(x) \) is a polynomial of degree
A .2
B. 3
\( c .4 \)
\( D \)
Subject: Physics
The temperature coefficient of
resistance of platinum is \( \boldsymbol{\alpha}=\mathbf{3 . 9 2} \times \)
\( 10^{-1} K^{-1} \) at \( 20^{\circ} C . \) Find the
temperature at which the increase in the resistance of platinum wire is \( 10 \% \)
of its value at \( 20^{\circ} C \)
A \( .40 .5^{\circ} \mathrm{C} \)
в. \( 45.5^{\circ} \mathrm{C} \)
c. \( 48.5^{\circ} \mathrm{C} \)
D. \( 43.5^{\circ} \mathrm{C} \)
Subject: Chemistry
In the reaction \( : \boldsymbol{C l}_{2}+\boldsymbol{O H}^{-} \rightarrow \boldsymbol{C l}^{-}+ \)
\( \boldsymbol{C l O}_{\boldsymbol{4}}^{-}+\boldsymbol{H}_{2} \boldsymbol{O} ? \)
A. Chlorine is oxidised
B. Chlorine is reduced
C. Chlorine is oxidised as well as reduced
D. Chlorine is neither oxidised nor reduced
Subject: Maths
Let \( \rho \) be a relation defined on \( N, \) the set
of natural numbers, as
\( \boldsymbol{\rho}=\{(\boldsymbol{x}, \boldsymbol{y}) \in \boldsymbol{N} \times \boldsymbol{N}: \mathbf{2} \boldsymbol{x}+\boldsymbol{y}=\mathbf{4 1}\} \)
then
A. \( \rho \) is an equivalence relation
B. \( \rho \) is only reflexive relation
c. \( \rho \) is only symmetric relation
D. \( \rho \) is not transitive
Subject: Maths
A value of \( \theta \) for which \( \frac{2+3 i \sin \theta}{1-2 i \sin \theta} \) is
purely imaginary, is:
\( ^{\mathrm{A}} \cdot \sin ^{-1}\left(\frac{1}{\sqrt{3}}\right) \)
в. \( \frac{\pi}{3} \)
\( \mathbf{c} \cdot \cos ^{-1} \sqrt{-} 1 \)
D. Noneofthese
Subject: Physics
Two infinitely long current carrying
conductors \( X \) and \( Y \) are kept parallel to
each other, \( 24 \mathrm{cm} \) apart in vacuum
They carry currents of \( 5 \mathrm{A} \) and \( 7 \mathrm{A} \) respectively, in the same direction, as shown in Figure above. Find the position
of a neutral point, i.e. a point where
resultant magnetic flux density is zero.
(Ignore earth's magnetic field)
Subject: Maths
Let \( \overrightarrow{\boldsymbol{a}}=\hat{\boldsymbol{i}}+2 \hat{\boldsymbol{j}} \) and \( \overrightarrow{\boldsymbol{b}}=\boldsymbol{2} \hat{\boldsymbol{i}}+\hat{\boldsymbol{j}} \)
\( |\vec{a}|=|\vec{b}| \) ? Are the vectors \( \vec{a} \) and \( \vec{b} \)
equal?
Subject: Physics
From a complete ring of mass \( M \) and
radius \( R, \) a \( 30^{\circ} \) sector is removed. The
moment of inertia of the incomplete
ring about an axis passing through the
centre of the ring and perpendicular to the plane of the ring is
\( ^{A} \cdot \frac{9}{12} M R^{2} \)
\( ^{\text {В }} \frac{11}{12}^{M R^{2}} \)
\( ^{\mathrm{c}} \cdot \frac{11.3}{12} M R^{2} \)
D. \( M R^{2} \)
Subject: Chemistry
From among the elements, choose the
following:
\( \mathrm{Cl}, \mathrm{Br}, \mathrm{F}, \mathrm{O}, \mathrm{Al}, \mathrm{C}, \mathrm{Li}, \mathrm{Cs} \) and \( \mathrm{Xe} \)
The element whose oxide is amphoteric.
Subject: Physics
Two glass plates are \( 10 \mathrm{cm} \) long. At one
end, a piece of paper of 0.02 mm
thickness is placed to make a wedge as
shown in the figure. Find the separation
between the two fringes. Assume \( \lambda= \)
\( \mathbf{5 0 0} \boldsymbol{n m} \)
A \( \cdot 1.25 \times 10^{-3} \mathrm{m} \)
B. 1.5 nm
\( c .2 .5 n m \)
D. none of the above
Subject: Physics
Three measurement are made as
\( 18.425 \mathrm{cm} 7.21 \mathrm{cm} \) and \( 5.0 \mathrm{cm} . \) The
addition should be written as then:
A. \( 30.635 \mathrm{cm} \)
B . \( 30.64 c m \)
c. \( 30.63 c m \)
D. \( 30.6 \mathrm{cm} \)