AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A man is \( 180 \mathrm{cm} \) tall and his eyes are
10cm below the top of his head. In order
to see his entire height right from toe to head, he uses a plane mirror kept at a distance of \( 1 \mathrm{m} \) from him. The minimum
length of the plane mirror required is :
A . \( 180 \mathrm{cm} \)
B. \( 90 \mathrm{cm} \)
\( \mathbf{c} .85 \mathrm{cm} \)
D. \( 170 \mathrm{cm} \)
Subject: Chemistry
Unit of ionic mobility is
\( \mathbf{A} \cdot m^{2} \sec ^{-1} v o l t^{-1} \)
B. \( m \) sec\( ^{-1} \)
\( \mathrm{c} \cdot m \sec ^{-1} \)volt
D. \( m \) sec \( ^{-1} \) volt \( ^{1} \)
Subject: Chemistry
The equilibrium constant for the
reaction is 9.40 at \( 900^{\circ} C \)
\( \boldsymbol{S}_{2}(\boldsymbol{g})+\boldsymbol{C}(s) \rightleftharpoons \boldsymbol{C} \boldsymbol{S}_{2}(\boldsymbol{g}) \)
Calculate the pressure of two gases at
equilibrium, when 1.42 at \( m \) of \( S_{2} \) and
excess of \( C(s) \) come to equilibrium.
Subject: Maths
f a plane passes through the point (1,1,1) and is perpendicular to the line \( \frac{x-1}{3}=\frac{y-1}{0}=\frac{z-1}{4} \) then its
perpendicular distance from the origin is
A \( \cdot \frac{3}{4} \)
B. \( \frac{4}{3} \)
\( c \cdot \frac{7}{5} \)
D.
Subject: Maths
The number of solutions of the equation
\( \mathbf{2}\left(\boldsymbol{\operatorname { S i n }}^{-1} \boldsymbol{x}\right)^{2}-\mathbf{5} \operatorname{Sin}^{-1} \boldsymbol{x}+\mathbf{2}=\mathbf{0} \) is
A .
в.
\( c \cdot 2 \)
\( D \)
Subject: Physics
Two charges \( +q \) and \( -q \) are placed at a distance a in a uniform electric field.
The dipole moment of the combination is \( 2 q a(\cos \theta \hat{i}+\sin \theta \hat{j}), \) where, \( \theta \) is the
angle between the direction of the field and the line joining the charges. Which of the following statement(s) is are correct?
This question has multiple correct options
A. The torque exerted by the field on the dipole vanishes
B. The net force on the dipole vanishes
c. The torque is independent of the choice of coordinates
D. The net force is independent of a
Subject: Physics
The charge on a parallel plate capacitor
is varying as \( \boldsymbol{q}=\boldsymbol{q}_{0} \sin (2 \pi n t) . \) The
plates are very large and close together. neglecting the edge effects, the displacement current through the capacitor is:
\( ^{\text {A. }} \frac{q}{\varepsilon_{0}} \)
в. \( \frac{q_{0}}{\varepsilon_{0}} \sin 2 \pi n t \)
\( \mathbf{c} \cdot 2 \pi n q_{0} \cos 2 \pi n t \)
\( \stackrel{\mathrm{D}}{\cdot} \frac{2 \pi n q_{0}}{\varepsilon_{0}} \cos 2 \pi n t \)
Subject: Chemistry
Assertion: The buffer HCOOH/HCOONa
will have pH lesser than 7 . Reason: Conjugate base of a weak acid is a strong base.
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false
Subject: Biology
Q Type your question_ \( \sqrt{0} \)
a uructure
\begin{tabular}{c|cc} 
& Characters & Monocot root & Dicot root \\
(i) & Vascular bundle & Polyarch i.e., more than 6 vascular bundles & Diarch to hexarch i.e., \( 2-6 \) vascular bundles \\
(ii) & Cambium & Absent & Present, so secondary growth occurs \\
(iii) & Pith & Poorly developed & Well developed large pith \\
& & Gives rise & \\
(iv) & Activity of pericycle & to secondary roots and cork cambium & Gives rise to lateral roots only \\
\hline
\end{tabular} dentify the incorrect differences and
select the correct option.
A. (i) and (iii)
B. (i) and (iv)
C . (iii) and (iv)
D. (ii) and (iii)
Subject: Chemistry
Base strength of -
\( (i) H_{3} C C H_{2} \)
\( (i i) H_{2} C=C H \)
and \( (\boldsymbol{i} \boldsymbol{i} \boldsymbol{i}) \boldsymbol{H}-\boldsymbol{C} \equiv \boldsymbol{C} \)
is in the order of :
\( A \cdot(\text { i) }>(\text { iii })>(\text { ii }) \)
B. (i) > (ii) > (iii)
\( c . \) (ii) > (i) > (iii)
D. (iii) > (ii) > (i)
Subject: Chemistry
Which of the following products are not correctly matched in the given
reactions?
A \( \cdot C_{2} H_{5} O C H_{3}+H B r \frac{373 K}{\longrightarrow} C_{2} H_{5} O H+C H_{3} B r \)
B . \( C_{2} H_{5} O C_{2} H_{5}+2 H I \rightarrow C_{2} H 5 I+C_{2} H_{5} O H \)
C \( \cdot C_{2} H_{5} O C_{2} H_{5}+H C C l \stackrel{\text {Exess}}{\text {Cold}}\left[\left(C_{2} H_{5}\right)_{2} O^{+} H\right] C l \)
D. \( \left(C H_{3}\right)_{3} C O C_{2} H_{5} \stackrel{H I}{\longrightarrow}\left(C H_{3}\right)_{3} C I+C_{2} H_{5} O H \)
Subject: Physics
A posıtively chargea partıcle or cnarge
\( q^{\prime} \) enters in a uniform magnetic field 'B
directed inward and is deflected a
distance \( \boldsymbol{y}_{0} \) after traveling a distance
shown in the figure. Then
the pe
use coos FathER30DAY
\( A \)
UPGRADE NOWI
B.
\( c \)
D.
\( E \)
Subject: Physics
The fissionable material used in a
breeder reactor is
A \( \cdot 92 \mathrm{U}^{235} \)
55
В \( \cdot \) g \( _{9} \mathrm{Pu}^{239} \)
\( \mathrm{c} \cdot_{90} \mathrm{Th}^{234} \)
D. \( c^{12} \)
Subject: Maths
The coefficient of \( t^{50} \) in
\( \left(1+t^{2}\right)^{25}\left(1+t^{25}\right)\left(1+t^{40}\right)\left(1+t^{45}\right)(1 \)
is
A \( \cdot 1+\sqrt[25]{5} \)
B. \( 1+^{25} C_{5}+^{25} C_{7} \)
\( \mathbf{C} \cdot 1+^{25} C_{7} \)
D. None of these
Subject: Physics
The magnetic field at the center of the
circular loop as shown in figure, when a
single wire is bent to form a circular
loop and also extends to form straight sections, is :
\( ^{\text {A }} \cdot \frac{\mu_{0} I}{2 R} \odot \)
\( ^{\text {В }} \cdot \frac{\mu_{0} I}{2 R}\left(1+\frac{1}{\pi \sqrt{2}}\right) \odot \)
c. \( \frac{\mu_{0} I}{2 R}\left(1-\frac{1}{\pi \sqrt{2}}\right) \otimes \)
\( \stackrel{\mathrm{D}}{\frac{\mu_{0}}{R}}\left(1-\frac{1}{\pi \sqrt{2}}\right) \otimes \)
Subject: Maths
Find solution of following inequality, also show it graphically:
\[
\boldsymbol{x}+\mathbf{3} \leq \mathbf{5}, \boldsymbol{x} \in \boldsymbol{Z}
\]
\( A \)
\begin{tabular}{rrrrrrrrrr}
\hline-3 & -2 & -1 & 0 & 1 & 2 & 3 & 4 & 5 & 6
\end{tabular}
B.
\begin{tabular}{rrrrrr}
\hline & & & & & & \\
\hline-2 & -1 & 0 & 1 & 2 & 3
\end{tabular}
\( c \)
\( \underbrace{\longleftarrow}_{-2}-1 \quad_{0} \quad_{1} \quad_{2} \quad_{1} \)
\( D \)
\begin{tabular}{rrrrrr}
\hline & 1 & 1 & & & 1 \\
-2 & -1 & 0 & 1 & 2 & 3
\end{tabular}
Subject: Maths
A man buys two cycles for a total cost of Rs. \( 900 . \) By selling one cycle at a loss of \( 20 \% \) and the other at a profit of \( 25 \%, \) he makes a profit of Rs. 90 on the whole transaction. Find the cost price of each
cycle.
A . Rs. 200; Rs. 500
B. Rs. 300; Rs. 600
c. Rs. 400; Rs. 700
D. Rs. 500; Rs. 800
Subject: Chemistry
Statement 1: Lanthanides have much
less tendency to form complexes than
actinides.

Statement 2: Compared to actinides, the lanthanides have relatively larger size of atoms and less nuclear charge.
A. Statement 1 is True, statement 2 is True, statement 2 is a correct explanation of statement 1.
B. Statement 1 is True, statement 2 is True, statement 2 is not a correct explanation of statement 1
c. Statement 1 is true, Statement 2 is False
D. Statement 1 is False, Statement 2 is True
Subject: Chemistry
Find the heat transferred to the
water, when the temperature of a 20 gram sample of water is increased from
\( 10^{\circ} \mathrm{C} \) to \( 30^{\circ} \mathrm{C} ? \)
A. 400 calories
B. 600 calories
c. 20 calories
D. 200 calories
E. 30 calories
Subject: Chemistry
Which of the following is known as fusion mixture?
A. mixture of \( N a_{2} C O_{3}+N a H C O_{3} \)
в. \( N a_{2} C O_{3}+10 H_{2} O \)
c. mixture of \( K_{2} C O_{3}+N a_{2} C O_{3} \)
D. \( N a H C O_{3} \)
Subject: Physics
A wave is travelling on a string with the frequency 4 cycles per second, and its speed is 0.08 meters per second. Calculate the wavelength of the wave?
A . \( 0.25 \mathrm{m} \)
B. \( 0.55 m \)
c. \( 3.125 \mathrm{m} \)
D. \( 0.02 \mathrm{m} \)
E. 12.55 m
Subject: Physics
A straight wire of finite length carrying
current I subtends an angle of \( 60^{\circ} \) at
point \( P \) as shown. The magnetic field at
P is:
\( ^{\mathrm{A}} \cdot \frac{\mu_{0} I}{2 \sqrt{3} \pi x} \)
B. \( \frac{\mu_{0} I}{2 \pi x} \)
c. \( \frac{\sqrt{3} \mu_{0} I}{2 \pi x} \)
D. \( \frac{\mu_{0} I}{3 \sqrt{3} \pi x} \)
Subject: Chemistry
One litre of a sample of hard water \( (d=1 \)
\( g / m L \) contains 136 mg of \( C a S O_{4} \) and
\( 190 \mathrm{mg} \) of \( M g C l_{2} . \) What is the total
hardness of water in terms of \( C a C O_{3} ? \)
A. 100 ppm
B. 200 ppm
c. 300 ppm
D. None of the above
Subject: Chemistry
Calculate the pH of \( 0.1 \mathrm{M} \) solution of \( (\mathrm{i}) \)
\( N a H C O_{3}, \) (ii) \( N a_{2} H P O_{4} \) and (iii)
\( N a H_{2} P O_{4} \)
Given that:
\( \boldsymbol{C O}_{2}+\boldsymbol{H}_{2} \boldsymbol{O} \rightleftharpoons \boldsymbol{H}^{+}+\boldsymbol{C} \boldsymbol{O}_{3}^{2-} ; \boldsymbol{K}_{1}= \)
\( 4.2 \times 10^{-7} \mathrm{M} \)
\( \boldsymbol{H} \boldsymbol{C O}_{3}^{-} \rightleftharpoons \boldsymbol{H}^{+}+\boldsymbol{C} \boldsymbol{O}_{3}^{2-} ; \boldsymbol{K}_{2}=\boldsymbol{4} . \boldsymbol{8} \times \)
\( 10^{-11} \mathrm{M} \)
\( \boldsymbol{H}_{2} \boldsymbol{P} \boldsymbol{O}_{4} \rightleftharpoons \boldsymbol{H}^{+}+\boldsymbol{H}_{2} \boldsymbol{P} \boldsymbol{O}_{4}^{-} ; \boldsymbol{K}_{1}=\mathbf{7 . 5} \times \)
\( 10^{-3} \mathrm{M} \)
\( \boldsymbol{H}_{2} \boldsymbol{P} \boldsymbol{O}_{4}^{-} \rightleftharpoons \boldsymbol{H}^{+}+\boldsymbol{H} \boldsymbol{P} \boldsymbol{O}_{4}^{2-} ; \boldsymbol{K}_{2}= \)
\( \mathbf{6} \cdot \mathbf{2} \times \mathbf{1} \mathbf{0}^{-\mathbf{8}} \mathbf{M} \)
\( \boldsymbol{H} \boldsymbol{P} \boldsymbol{O}_{4}^{2-} \rightleftharpoons \boldsymbol{H}^{+}+\boldsymbol{P} \boldsymbol{O}_{4}^{3-} ; \boldsymbol{K}_{3}=\mathbf{1 . 0} \times \)
\( 10^{-12} \mathrm{M} \)
Subject: Physics
Two protons attract each other when the distance between them is
A \( \cdot 10^{-18} \mathrm{m} \)
m \( \mathrm{r}^{-18} \mathrm{m}^{-} \)
B. \( 10^{-20} \mathrm{m} \)
\( \mathbf{c} \cdot 10^{-15} \mathrm{m} \)
D. \( 10^{-22} \mathrm{m} \)
Subject: Physics
If the displacement, velocity and acceleration of particle in \( S H M \) are
\( \mathbf{1} \boldsymbol{c m}, \mathbf{1} \boldsymbol{c m} / \boldsymbol{s e c} \) and \( \mathbf{1} \boldsymbol{c m} / \boldsymbol{s e c}^{\mathbf{2}} \)
respectively its time period (in secs) will be:
A . \( \pi \)
B. \( 0.5 \pi \)
\( c .2 \pi \)
D. \( 1.5 \pi \)
Subject: Physics
A cell of emf \( 4.5 ~ V \) is connected to a
junction diode whose barrier potential is \( 0.7 V . \) If the external resistance in the
circuit is \( 190 \Omega \), the current in the circuit is
\( \mathbf{A} \cdot 20 m A \)
B. \( 2 m A \)
\( c .23 m A \)
D. 200 mA
Subject: Maths
An equation that defines \( y \) as a function
of \( x \) is given. Solve for \( y \) in terms of \( x \)
and replace \( y \) with the function notation
\( \boldsymbol{f}(\boldsymbol{x}) \)
\( \boldsymbol{x}-\boldsymbol{2} \boldsymbol{y}=\mathbf{1 8} \)
A \( \cdot f(x)=\frac{1}{2} x-18 \)
B \( \cdot f(x)=\frac{1}{2} x-9 \)
c. \( f(x)=-x+9 \)
D. \( f(x)=-\frac{1}{2} x+9 \)
Subject: Physics
A body is dropped from a certain height.
When it loses \( U \) amount of its energy it
acquires a velocity' \( v^{\prime} . \) The mass of the
body is:
A \( \cdot 2 U / v^{2} \)
B \( \cdot 2 v / U^{2} \)
c. \( 2 v / U \)
D. \( U^{2} / 2 v \)
Subject: Chemistry
The van dar Waal's parameters for
gases \( W, X, Y \) and \( Z \) are:
\( \begin{array}{lll}\text { Gas } & \mathrm{a}\left(\mathrm{atm} l^{2} / \mathrm{mol}^{2}\right) & \mathrm{b}(\mathrm{l} / \mathrm{mol}) \\ \mathrm{w} & 4.0 & 0.027 \\ \mathrm{x} & 8.0 & 0.030 \\ \mathrm{Y} & 6.0 & 0.032 \\ \mathrm{z} & 12.0 & 0.027\end{array} \)
Which one of these gases has the
highest critical temperature?
\( A \cdot w \)
B. \( x \)
\( c \)
\( D . z \)
Subject: Maths
An exterior angle of a triangle is \( 105^{\circ} \) and its two interior opposite angles are equal. Each of these equal angles is
A. \( _{37} \frac{1^{0}}{2} \)
в. \( _{52} \frac{1^{0}}{2} \)
c. \( _{72} \frac{1^{0}}{2} \)
D. 75
Subject: Physics
A particle of mass m begins to slide down a fixed smooth sphere from the top with negligible initial velocity. What is its tangential acceleration when it breaks off the sphere?
A \( \cdot \frac{2 g}{3} \)
B. \( \frac{\sqrt{5} g}{3} \)
\( c \cdot g \)
D. \( \frac{g}{3} \)
Subject: Physics
The escape velocity from the earth is
\( 11 k m s^{-1} . \) The escape velocity from a
planet having twice the radius and same mean density as that of earth is
\( \mathbf{A} \cdot 5.4 \mathrm{kms}^{-1} \)
B . \( 11 k m s^{-1} \)
\( \mathbf{c} \cdot 22 k m s^{-1} \)
D. None of the above
Subject: Physics
A potentiometer circuit shown in the
figure is set up to measure emf of cell \( \mathrm{E} \)
As the point P moves from X to Y, the
galvanometer G shows deflection
always in one direction, but the
deflection decreases continuously until Y is reached. The balance point between
\( X \) and \( Y \) maybe obtained by
A. Decreasing the resistance \( R \) and decreasing \( v \)
B. Decreasing the resistance R and increasing
C. Increasing the resistance \( R \) and increasing \( v \)
D. Increasing the resistance \( R \) and decreasing
Subject: Chemistry
\( 40 m l \) of ammonia gas, taken in an
audiometer tube, was subjected to
sparks till the volume did not further
change. The volume was found to
increase by 40 ml. 40 ml of oxygen gas
then mixed and the mixture was further
exploded. The gases remained were 30 ml. Deduce the formula of ammonia.
(Ammonia contain \( N \) and \( H \) only).
Subject: Chemistry
At \( 25^{\circ} C, \Delta H_{f}\left(H_{2} O, I\right)= \)
\( -56700 J / \) mol and energy of
ionization of \( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{I})=\mathbf{1 9 0 5 0} \boldsymbol{J} / \)moll
the reversible EMF at \( 25^{\circ} \mathrm{C} \) of the cell is
\( 414 \times 10^{-x}, \) then the value of \( x \) is \( ? \)
\( \boldsymbol{P t}\left|\boldsymbol{H}_{2}(\boldsymbol{g})(\boldsymbol{1} \boldsymbol{a} \boldsymbol{t m})\right| \boldsymbol{H}^{+} \| \boldsymbol{O} \boldsymbol{H}^{-} \mid \boldsymbol{O}_{2}(\boldsymbol{g})(\boldsymbol{1} \)
if at \( 26^{\circ} \mathrm{C} \) the emf increase by 0.001158
\( \mathbf{V} \)
Ans in \( \mathrm{V} \)
Subject: Maths
If \( \boldsymbol{x}+\frac{\mathbf{1}}{\boldsymbol{x}}=\mathbf{2}, \) then what is the value of
\( \boldsymbol{x}^{64}+\boldsymbol{x}^{121} ? \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. - -
Subject: Chemistry
which of the following pairs of nitrates gives the same gaseous products on thermal decomposition? This question has multiple correct options
A. \( K N O_{3} \) and \( P b\left(N O_{3}\right)_{2} \)
в. \( K N O_{3} \) and \( N a N O_{3} \)
c. \( P b\left(N O_{3}\right)_{2} \) and \( C u\left(N O_{3}\right)_{2} \)
D. \( \operatorname{NaNO}_{3} \) and \( \operatorname{Ca}\left(N O_{3}\right)_{2} \)
Subject: Physics
If \( E=16 \) volts, \( r=4 \Omega \) and distance of
balance point \( P \) from end \( A \) is \( 90 \mathrm{cm} \)
then the value of \( X \) is
A . \( 3 \Omega \)
B. \( 6 \Omega \)
\( c .9 \Omega \)
D. \( 12 \Omega \)
Subject: Physics
If \( 200 \mathrm{J} \) of heat is added during the time
interval from \( \mathrm{B} \) to \( \mathrm{C} \), the specific heat of
the substance is.
A \( \cdot 200 J / k g^{o} C \)
в. \( 100 \mathrm{J} / \mathrm{kg}^{\circ} \mathrm{C} \)
c. \( 60 J / k g^{o} C \)
D. \( 17 J / k g^{o} C \)
ह \( \cdot 1.67 \mathrm{J} / \mathrm{kg}^{\circ} \mathrm{C} \)
Subject: Maths
The acute angle between two lines such
that the direction cosines \( l, \boldsymbol{m}, \boldsymbol{n} \) of each of them satisfy the equation \( l+ \)
\( \boldsymbol{m}+\boldsymbol{n}=\mathbf{0} \) and \( l^{2}+\boldsymbol{m}^{2}-\boldsymbol{n}^{2}=\mathbf{0} \) is
\( A \cdot 30 \)
B . 45
\( c \cdot 60 \)
D. \( 15^{\circ} \)
Subject: Maths
Prove using PMI: \( \frac{1}{1.2 .3}+\frac{1}{2.3 .4}+ \)
\( \frac{1}{\mathbf{3 . 4 . 5}}+\ldots+\frac{1}{n(n+1)(n+2)}= \)
\( \frac{n(n+3)}{4(n+1)(n+2)} \)
Subject: Chemistry
Two isomers of a compound
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{3} \boldsymbol{C l}_{3}\right]\left(\boldsymbol{M} \boldsymbol{A}_{3} \boldsymbol{B}_{3} \text { type }\right) \) are
shown in the figures. The isomers can
be classified as:
\( (\mathbf{i}) \)
A. (i) fac-isomers
(ii) mer-isomer
B. (i) optical-isomer
(ii) trans-isomer
C. (i) mer-isomer
(ii) fac-isomer
D. (i) trans-isomer
(ii) cis-isomer.
Subject: Maths
Let \( P, Q, R \) and \( S \) be the points on the plane with position vectors \( (-2 i-j), 4 i \) \( (3 i+3 j) \) and \( (-3 i+2 j) \) respectively. The quadilateral PQRS must be a
A. Parallelogram, which is neither a rhombus nor a rectangle
B. Square
c. Rectangle, but not a square
D. Rhombus, but not a square
Subject: Physics
An \( \alpha- \) particle and a proton have their
masses in the ratio 4: 1 and charges
in the ratio 2: 1

Find ratio of de-Broglie wavelengths
when both have equal momentum.
\( \mathbf{A} \cdot 2: 1 \)
B. 1: 1
\( \mathbf{c} \cdot 4: 1 \)
D. 1: 4
E .1: 4
Subject: Chemistry
The molecular electronic configuration
of \( B e_{2} \) is:
A \( \cdot \sigma 1 s^{2}, \sigma^{*} 1 s^{2}, \sigma 2 s^{2}, \sigma^{*} 2 p^{2} \)
B . \( \sigma 1 s^{2}, \sigma 2 s^{2} \)
C. \( \sigma 1 s^{2}, \sigma^{*} 1 s^{2}, \sigma 2 s^{2}, \sigma^{*} 2 s^{2} \)
D. none of the above
Subject: Physics
Unpolarized light of intensity \( \boldsymbol{I}_{\mathbf{0}} \) is incident on a polarizer and the emerging light strikes a second polarizing filter with its axis at
\( 45^{\circ} \) to that of the first. The intensity of
the emerging beam:
A \( \cdot \frac{I o}{2} \)
в. \( \frac{\text { Io }}{4} \)
\( c \cdot I_{o} \)
D. \( \frac{\text { Io }}{3} \)
Subject: Physics
Assertion
A biconvex lens of focal length \( 10 \mathrm{cm} \) is split into two equal parts by a plane parallel to its principle axis.The focal length of each part will be \( 20 \mathrm{cm} \)
Reason

Focal length depends on the radii of curvature of two surfaces.
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
The value of
\( \frac{(1.5)^{2}+(4.7)^{3}+(3.8)^{3}-3 \times 1 .}{(1.5)^{2}+(4.7)^{2}+(3.8)^{2}-1.5 \times 4.7-4} \)
\( A \cdot 8 \)
B. 9
c. 10
\( D \)
Subject: Chemistry
Assertion
Aqueous solution of the compound
\( \mathrm{CoCl}_{3} \cdot 4 N \mathrm{H}_{3} \) when treated with excess
of \( A g N O_{3}, 1 \) mole of \( A g C l \) is
precipitated.
Reason
The compound \( C o C l_{3} .4 N H_{3} \) has six
primary valencies and one secondary valency.
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
A carbon compound contains \( 12.8 \% \) of carbon; \( 2.1 \% \) of hydrogen and \( 85.1 \% \) of bromine. The molecular mass of
compound is \( 187.9 . \) Calculate the molecular formula of the compound (Atomic mass \( \mathrm{H}=1.008, \mathrm{C}=12, \mathrm{Br}= \)
79.9)
A \( . C H_{3} B r \)
в. \( C H_{2} B r_{2} \)
\( \mathbf{c} \cdot C_{2} H_{4} B r_{2} \)
D. \( C_{2} H_{3} B r_{3} \)
Subject: Chemistry
In the following, equilibrium partial
pressure of \( N H_{3}, N_{2} \) and \( H_{2} \) gasses are 4,1 and 2 atm respetively at \( 300 \mathrm{K} \)
what is value of \( \boldsymbol{K}_{\boldsymbol{p}} \) ?
\( N_{2}(g)+3 H_{2}(g) \rightleftharpoons 2 N H_{3}(g) \)
Subject: Physics
Four divers of the same weight dive from four different heights \( 10 \mathrm{m}, 9 \mathrm{m}, 12 \) \( m \) and \( 8 m \) as shown here. The diver
from which height will have the highest
kinetic energy on hitting the water below?
A . 10 meters
B. 9 meters
c. 12 meters
D. 8 meters
Subject: Maths
If \( z_{1} \) and \( z_{2} \) are two non zero complex
numbers such that \( \left|z_{1}+z_{2}\right|=\left|z_{1}\right|+ \)
\( \left|z_{2}\right| \) then \( \arg z_{1}-\arg z_{2} \) is equal to
A. \( -\pi \)
в. \( \frac{\pi}{2} \)
\( c \cdot-\frac{\pi}{2} \)
D.
Subject: Maths
If \( \boldsymbol{f}(\boldsymbol{a})=\boldsymbol{a}^{2}, \boldsymbol{\phi}(\boldsymbol{a})=\boldsymbol{b}^{2} \) and \( \boldsymbol{f}^{\prime}(\boldsymbol{a})= \)
\( \mathbf{3} \phi^{\prime}(\boldsymbol{a}) \) then \( \lim _{x \rightarrow 0} \frac{\sqrt{\boldsymbol{f}(\boldsymbol{x})}-\boldsymbol{a}}{\sqrt{\boldsymbol{\phi}(\boldsymbol{x})}-\boldsymbol{b}} \) is
\( \mathbf{A} \cdot b^{2} / a^{2} \)
в. \( b / a \)
c. \( 2 b / a \)
D. None of these
Subject: Maths
The odds against A solving a problem are 8 to 6 and the odds in favour of \( B \)
solving the same problem 14 to \( 12 . \) The probability of solving the problem if they both try independently is
A \( \cdot \frac{67}{91} \)
в. \( \frac{5}{21} \)
c. \( \frac{4}{21} \)
D.
Subject: Maths
If \( \boldsymbol{P}(\boldsymbol{A})=\mathbf{0 . 8} \) and \( \boldsymbol{P}(\boldsymbol{B} \mid \boldsymbol{A})=\mathbf{0 . 4}, \) Find
\( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B}) \)
Subject: Physics
A conducting wheel rim in which there
we three conducting rods of each of
length \( l \) is rotating with constant
angular velocity \( \omega \) in a uniform
magnetic field Bas show in figure. The
induced potential difference between
its centre and rim will be :
\( \mathbf{A} \cdot B \omega l^{2} \)
B. \( \frac{3}{2} B \omega l^{2} \)
c. 0
D. \( \frac{B \omega l^{2}}{2} \)
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{rr}4 & \boldsymbol{x}+\mathbf{2} \\ \mathbf{2} \boldsymbol{x}-\mathbf{3} & \boldsymbol{x}+\mathbf{1}\end{array}\right] \) is symmetric
then \( x= \)
\( A \cdot 3 \)
B. 5
\( c \cdot 2 \)
D. 4
Subject: Physics
The magnetic induction in vacuum at a plane surface of a uniform isotropic magnetic is equal to \( B \), the vector \( \vec{B} \)
forming an angle \( \alpha \) with the normal of the surface. The permeability of the
magnetic is equal to \( \mu \). Find the
magnitude of the magnetic induction
\( B^{\prime} \) in the magnetic in the vicinity of its surface.
Subject: Chemistry
Which can act as buffer?
A \( . N H_{4} C l+H C l \)
в. \( C H_{3} C O O H+H_{2} C O_{3} \)
c. \( 40 \mathrm{ml} \) of \( 0.1 \mathrm{M} \mathrm{NaCN}+20 \mathrm{ml} \) of \( 0.1 \mathrm{M} \mathrm{HCN} \)
D. \( N a C l+N a O H \)
Subject: Physics
A particle moves in the xy-plane with constant acceleration a directed along the negative y-axis. The equation of path of the particle has the form \( y= \) \( b x-c x^{2}, \) where \( b \) and \( c \) are positive
constants. The velocity \( v \) of the particle at the origin of coordinates will be
A \( \cdot \sqrt{\frac{a}{2 c}\left(1+b^{2}\right)} \)
в. \( \sqrt{\frac{a}{4 c}\left(1+b^{2}\right)} \)
c. \( \sqrt{\frac{3 a}{2 c}\left(1-b^{2}\right)} \)
D. none of these
Subject: Maths
If \( \boldsymbol{E} \) and \( \boldsymbol{F} \) are independent events such
that \( \boldsymbol{P}(\boldsymbol{E})=\mathbf{0 . 7} \) and \( \boldsymbol{P}(\boldsymbol{F})=\mathbf{0 . 3}, \) then \( \mathrm{P} \)
\( (\boldsymbol{E} \cap \boldsymbol{F}) \)
A . 0.4
B.
c. 0.21
D. None
Subject: Physics
A closed surface in the shape of a cube
is placed in a uniform electric field \( \boldsymbol{E} \)
along one of the sides of the cube as
shown here. The length of the side is \( l \)
The total electric flux through two
faces 1 and 2 is:
A . zero
B. \( -E l^{2} \)
\( c \cdot 2 E l^{2} \)
D. \( \frac{E l^{2}}{2} \)
Subject: Maths
Simplify:
\( 10 a^{2}-15 b^{2}+20 c^{2} \)
A \( \cdot 5\left(2 a^{2}-3 b^{2}+4 c^{2}\right) \)
B. \( 5\left(2 a-3 b^{2}+4 c^{2}\right) \)
C. \( 5\left(10 a^{2}-3 b^{2}+4 c^{2}\right) \)
D. \( 5\left(2 a^{2}+3 b^{2}+4 c^{2}\right) \)
Subject: Chemistry
Which one of the following shows maximum paramagnetic character?
\( \mathbf{A} \cdot\left[F e(C N)_{6}\right]^{3-} \)
в. \( \left[F e(C N)_{6}\right]^{4-} \)
\( \mathbf{c} \cdot\left[\operatorname{Cr}\left(H_{2} O\right)_{6}\right]^{3+} \)
D \( \cdot\left[C u\left(H_{2} O\right)_{6}\right]^{2+} \)