AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
Determine graphically the minimum value of the objective function \( Z=50 x+20 y \ldots(1) \)
subject to the constraints:
\( 2 x y \geq 5 \dots(2) \)
\( \mathbf{3} \boldsymbol{x}+\boldsymbol{y} \geq \mathbf{3} \dots(\mathbf{3}) \)
\( 2 x-3 y \leq 12 \dots(4) \)
\( \boldsymbol{x} \geq \mathbf{0}, \boldsymbol{y} \geq \mathbf{0} \ldots(\mathbf{5}) \)
Subject: Chemistry
The specific conductivity of \( N / 10 K C l \)
solution at \( 20^{\circ} \mathrm{C} \) is 0.0212 ohm \( ^{-1} \)
\( c m^{-1} \) and the resistance of the cell
containing this solution at \( 20^{\circ} \mathrm{C} \) is 55
ohm. The cell constant is:
A \( \cdot 3.324 \mathrm{cm}^{-1} \)
B. \( 1.166 \mathrm{cm}^{-1} \)
\( \mathbf{c} \cdot 2.372 \mathrm{cm}^{-1} \)
D. \( 3.682 \mathrm{cm}^{-1} \)
Subject: Maths
Let \( \boldsymbol{O A B C} \) be a parallelogram and \( \boldsymbol{D} \) the midpoint of \( \boldsymbol{O} \boldsymbol{A} \). The ratio in which
\( O B \) divides \( C D \) in the ratio
A .1: 2
B. 1: 3
\( c \cdot 1: 4 \)
D. 2: 1
Subject: Chemistry
The no. of cells which may be
constructed with different \( E_{c e l l}^{o} \) values
for the reaction
\( \boldsymbol{F} \boldsymbol{e}+\boldsymbol{2} \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{3}+} \rightarrow \boldsymbol{3} \boldsymbol{F} \boldsymbol{e}^{2+} \boldsymbol{i} \boldsymbol{s} \)
Subject: Chemistry
A sulphate of a metal (A) on heating evolves two gases \( (\mathrm{B}) \) and \( (\mathrm{C}) \) and an
oxide (D). Gas (B) turns \( K_{2} C r_{2} O_{7} \) paper
green while gas (C) forms a trimer in which there is no \( S-S \) bond.

Compound (D) with \( H C l \), forms a lewis
acid (E) which exists as a dimer.

Compounds \( (A),(B),(C),(D) \) and \( (E) \) are
respectively:
A \( \cdot \) FeSO\( _{4}, S O_{2}, S O_{3}, F e_{2} O_{3}, F e C l_{3} \)
в. \( A l_{2}\left(S O_{4}\right)_{3}, S O_{2}, S O_{3}, A l_{2} O_{3}, F e C l_{3} \)
c. FeS\( , S O_{2}, S O_{3}, \) FeSO\( _{4}, \) FeCl\( _{1} \)
D. FeS, \( S O_{2}, S O_{3}, F e_{2}\left(P O_{4}\right)_{3}, F e C l_{2} \)
Subject: Physics
A copper slab of mass \( 2 g \) contains \( 2 x \)
\( 10^{22} \) atoms. The charge on the nucleus
of each atom is \( 29 e . \) What fraction of
the electrons must be removed from the
sphere to give it a charge of \( +2 \mu C ? \)
A \( .58 \times 10^{22} \)
B. \( 1.25 \times 10^{13} \)
c. \( 2.16 \times 10^{11} \)
D. \( 2.16 \times 10^{-11} \)
Subject: Maths
A hemisphere bowl is made of steel of \( 0.25 \mathrm{cm} \) thickness. The inner radius of
the bowl is \( 5 \mathrm{cm} . \) The volume of steel
used is \( _{-}-_{-}-_{-}-_{-}-_{-} \cdot(\pi=\mathbf{3 . 1 4 1}) \)
\( \mathbf{A} \cdot 42.15 \mathrm{cm}^{3} \)
B . \( 41.52 \mathrm{cm}^{3} \)
c. \( 41.24 \mathrm{cm}^{3} \)
D. \( 40 \mathrm{cm}^{3} \)
Subject: Chemistry
The directing power of the groups
\( -N H_{2},-O C H_{3},-C_{6} H_{5} \quad \) and
\( N O_{2} \) follows the order
A. \( -N H_{2}>-O C H_{3}>-C_{6} H_{5}>-N O_{2} \)
B. \( -N O_{2}>-C_{6} H_{5}>-O C H_{3}>-N H_{2} \)
c. \( -O C H_{3}>-N H_{2}>-C_{6} H_{5}>-N O_{2} \)
D. \( -O C H_{3}>-N O_{2}>-N H_{2}>-C_{6} H_{5} \)
Subject: Maths
If \( C \) is the mid point of \( A B \) and \( P \) is any
point outside \( A B, \) then
\( \mathbf{A} \cdot \overline{P A}+\overline{P B}+\overline{P C}=0 \)
в. \( \overline{P A}+\overline{P B}+2 \overline{P C}=\overline{0} \)
c. \( \overline{P A}+\overline{P B}=\overline{P C} \)
D. \( \overline{P A}+\overline{P B}=2 \overline{P C} \)
Subject: Physics
A conducting rod of resistance is
moving with constant velocity \( v_{1} \) then
the force required to keep rod moving is
\( \frac{v B^{2} l^{2}}{R} \)
в. \( \frac{2 v B^{2} l^{2}}{R+r} \)
c. \( \frac{v B^{2} l^{2}}{R+r} \)
D. zer
Subject: Chemistry
Calculate the equilibrium constant for the reaction:
\( \boldsymbol{F} \boldsymbol{e}+\boldsymbol{C u} \boldsymbol{S O}_{4} \rightleftharpoons \boldsymbol{F} \boldsymbol{e} \boldsymbol{S O}_{4}+\boldsymbol{C u} \)
Given, \( \boldsymbol{E}_{\boldsymbol{F e} / \boldsymbol{F e}}^{\boldsymbol{o}}=\mathbf{0 . 4 4} \boldsymbol{V} ; \boldsymbol{E}_{\boldsymbol{C u} / \boldsymbol{C u}^{2+}}^{\boldsymbol{o}}= \)
\( -0.337 V \)
Subject: Maths
\( \int \frac{\cos x+\sin x}{\cos x-\sin x} d x \)
\( \mathbf{A} \cdot \log \sin (\pi / 4+x) \)
\( \mathbf{B} \cdot \log \sec (\pi / 4+x) \)
\( \mathbf{C} \cdot \log \cos (\pi / 4+x) \)
D \( \cdot \log \sec (\pi / 4-x) \)
Subject: Chemistry
Identify the functional group in Product
B?
\[
\sqrt{ }+\mathrm{NBS} \longrightarrow \mathrm{A}-\frac{(\mathrm{i}) \mathrm{Mg} / \mathrm{ether}}{(\mathrm{ii}) \mathrm{CO}_{2} / \mathrm{H}_{3} \mathrm{O}^{\oplus}}
\]
A. Ketone
B. Carboxylic acid
c. aldehyde
D. none
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 their de-
Broglie wavelengths when both move with equal velocities.
\( \mathbf{A} \cdot 1: 4 \)
B. 4: 1
c. 1: 2
\( D \cdot 2: 1 \)
Subject: Chemistry
Find the number of sesquioxide(s) from the following:
\( \boldsymbol{A l}_{2} \boldsymbol{O}_{3}, \quad \boldsymbol{C}_{3} \boldsymbol{O}_{2}, \quad \boldsymbol{C O}_{2}, \quad \boldsymbol{P b}_{2} \boldsymbol{O}_{3} \)
Subject: Physics
A tank \( 5 m \) high is half filled with water and then is filled to the top with oil of
density \( 0.85 g / c m^{3} . \) The pressure at the bottom of the tank, due to these
liquids is
\( \mathbf{A} \cdot 1.85 g / \mathrm{cm}^{2} \)
B. \( 89.25 g / c m^{2} \)
c. \( 462.5 g / c m^{2} \)
\( \mathbf{D} \cdot 500 g / c m^{2} \)
Subject: Physics
Two large thin metal plates are parallel and close to each other. On their inner
faces, the plates have surface charge
densities of opposite signs and
magnitude \( 27 \times 10^{-22} C \quad m^{-2} . \) The
electric field \( \overrightarrow{\boldsymbol{E}} \) in region II in between the plates is
\( \begin{array}{ll}\text { A } \cdot 4.25 \times 10^{-8} N & C^{-1}\end{array} \)
в. \( 6.28 \times 10^{-10} N \quad C^{-1} \)
\( \begin{array}{lll}\text { с. } 3.05 \times 10^{-10} N & C^{-1}\end{array} \)
\( \begin{array}{lll}\text { D } \cdot & 5.03 \times 10^{-10} N & C^{-1}\end{array} \)
Subject: Physics
Calculate the moment about the points \( \mathrm{C}(1,1,1) \) of a force \( 5 \mathrm{N} \). acting along the line \( \underset{A B}{\text { where } A, B \text { are the points }(2,3,4)} \) (3,5,6) respectively the distance being measured in \( \mathrm{m} \)
\( \mathbf{A} \cdot 5(-2 i+j) \)
B . \( 7(-2 i+j) \)
c. \( \frac{5}{3}(-2 i+j) \)
D. \( \frac{5}{3}(j) \)
Subject: Chemistry
In context of the lanthanoids, which of
the following statements is not correct?
A. There is a gradual decrease in the radii of the members with increasing atomic number in the series
B. All the members exhibit + 3 oxidation state
c. Because of similar properties the separation of lanthanoids is not easy
D. Availability of 4f electrons results in the formation of compounds in +4 state for all the members of the series
Subject: Maths
Show that the relation \( R \) defined in the
\( \operatorname{set} A \) of all polygons as \( R=\left\{\left(P_{1}, P_{2}\right):\right. \)
\( P_{1} \) and \( P_{2} \) have same number of sides
\}\( , \) is an equivalence relation. What is the set of all elements in \( A \) related to
the right angle triangle \( T \) with sides 3,4
and \( 5 ? \)
Subject: Chemistry
Which of the following factors are responsible for the increase in the rate
of a surface catalysed reaction?
I. A catalyst provides proper orientation for the reactant molecules to react
II. Heat of adsorption of reactants on a catalyst helps reactant molecules to.overcome activation energy
III. The catalyst increases the activation energy of the reaction
IV. Adsorption increases the local concentration of reactant molecules on
the surface of the catalyst Select the correct answer using the codes given below:
A . I and II
B. I and III
c. ।, ॥ land IV
D. I, II and III
Subject: Chemistry
Assertion
\( N_{2} \) molecule is highly unreactive.
Reason
\( \therefore N \ddot{:} N_{0}^{\circ}, N_{2} \) is unreactive since, bond
energy is very high.
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
Atomic masses of two isobars \( _{29}^{64} C u \) and
\( _{30}^{64} Z n \) are \( 63.9298 u \) and \( 63.9292 u \)
respectively. It can be concluded from this data that
A. both the isobars are stable
B. \( 64 Z n \) is radioactive, decaying to \( ^{64} C u \) through \( \beta- \) decay
C. \( ^{64} C u \) is radioactive, decaying to \( ^{64} Z n \) through \( \beta- \) decay
D. \( ^{64} C u \) is radioactive, decaying to \( ^{64} Z n \) through \( \gamma \) decay
Subject: Physics
Two resistors equal resisitances are joined in series and a current is passed through the combination. Neglect any
variation in resistance as the
temperature changes. In a given time interval
This question has multiple correct options
A. equal amounts of thermal energy must be produced in the resistors
B. unequal amount of thermal energy may be produced
c. the temperature must rise equally in the resistors
D. the temperature may rise equally in the resistors
Subject: Chemistry
Determine enthalpy change for,
\[
\boldsymbol{C}_{3} \boldsymbol{H}_{8}(\boldsymbol{g})+\boldsymbol{H}_{2}(\boldsymbol{g}) \longrightarrow \boldsymbol{C}_{2} \boldsymbol{H}_{6}(\boldsymbol{g})+
\]
\( \boldsymbol{C H}_{4}(\boldsymbol{g}) \) at \( 25^{\circ} \boldsymbol{C} \). using heat of
combustion values under standard
conditions.
\[
\begin{array}{llll}
\text { Compounds } & \boldsymbol{H}_{2}(\boldsymbol{g}) & \boldsymbol{C H}_{4}(\boldsymbol{g}) & \boldsymbol{C}_{2} \boldsymbol{H}_{\mathbf{6}} \\
\boldsymbol{\Delta H}^{\mathrm{o}} \text { in } & -285.8 & -890.0 & -1560.0
\end{array}
\]
kJ/mol
The standard heat of formation of
\[
C_{3} H_{8}(g) \text { is }-103.8 k J m o l^{-1}
\]
A. \( -55.7 k J \)
B . \( -75.5 k J \)
c. -55.7
D. None of these
Subject: Maths
Find the mode of the following
distribution
\begin{tabular}{llllll} 
Daily & \( 31- \) & \( 37- \) & \( 43- \) & \( 49- \) & 55 \\
Wages & 36 & 42 & 48 & 54 & 6 \\
No. of workers & 6 & 12 & 20 & 15 & 9 \\
\hline
\end{tabular}
\( \mathbf{A} \cdot 48.5 \)
B. 47.5
c. 46.2
D. 48.3
Subject: Biology
Assertion
Closed circulatory system is less efficient than open circulatory system.
Reason
The blood flow is slow in closed
circulatory system than in open circulatory system.
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
What will react with \( C H_{3} M g B r \)
followed by decomposition with \( \boldsymbol{H}_{3} \boldsymbol{O}^{\oplus} \)
to give \( 2^{\circ} \) alcohol.
A. \( C H_{2}=C H O H \)
в. \( C H_{3} C H O \)
\( c \)
D. None of these
Subject: Physics
A boy weighing \( 500 \mathrm{N} \) is standing on the ground wearing a pair of flat shoes. The area of contact of one shoe with the
ground is \( 100 \mathrm{cm}^{2} \). What will be the
pressure exerted by the boy on the ground if he stands on both feet?
A \( \cdot 25000 N / m^{2} \)
в. \( 50000 N / m^{2} \)
c. \( 2500 N / m^{2} \)
D. \( 5000 N / m^{2} \)
Subject: Maths
A sphere of radius \( r \) lies inside a cube
and touches each of the six sides of the
cube. Calculate the volume of the cube
in terms of \( r \)
A \( \cdot r^{3} \)
B \( .2 r^{3} \)
\( c \cdot 4 r^{3} \)
D. \( \frac{4}{3} \pi r^{3} \)
E \( .8 r^{3} \)
Subject: Chemistry
What is the trend of boiling points of
hydrides of \( \mathrm{N}, \mathrm{O}, \) and \( \mathrm{F} \) ?
A. Due to lower molecular masses \( N H_{3}, H_{2} O \) and HF have lower boiling points than those of the subsequent group member hydrides
B. Due to higher electronegativity of \( \mathrm{N}, \mathrm{O} \) and \( \mathrm{F} \) \( N H_{3}, H_{2} O \) and HF show hydrogen bonding and hence higher boiling points than the hydrides of their subsequent group members.
C. There is no regular trend in the boiling points of hydrides
D. Due to higher oxidation states of \( \mathrm{N}, \mathrm{O} \) and \( \mathrm{F} \), the boiling points of \( N H_{3}, H_{2} O \) and HF are higher than the hydrides of their subsequent group members.
Subject: Chemistry
At \( 300 \mathrm{K} \) the standard enthalpies of
formation of \( C_{6} H_{5} C O O H_{(s)}, C O_{2(g)} \)
and \( H_{2} O_{(l)} \) are -408,-393 and -286
kJ \( m o l^{-1} \) respectively. Calculate the heat of combustion of benzoic acid at
constant volume.
B. +3199.75 kJ
D. -3199.75 k
Subject: Maths
If between any two quantities there be
inserted two arithmetic means \( \boldsymbol{A}_{1}, \boldsymbol{A}_{2} \)
two geometric means \( G_{1}, G_{2}: H_{1} H_{2}= \)
\( \boldsymbol{A}_{\mathbf{1}}+\boldsymbol{A}_{\mathbf{2}}: \boldsymbol{H}_{\mathbf{1}}+\boldsymbol{H}_{\mathbf{2}} \)
Subject: Maths
The angle subtended at the point (1,2,3) by the points \( P(2,4,5) \) and \( Q(3,3,1) \) is
A \( \cdot 90^{\circ} \)
B. \( 60^{\circ} \)
\( c \cdot 30^{\circ} \)
D. \( 0^{\circ} \)
\( E \cdot 45^{\circ} \)
Subject: Physics
The variation of the instantaneous
current (I) and the instantaneous emf(E) in a circuit is as shown in figure.
Which of the following statements is
correct?
A. The voltage lags behind the current by \( \pi / 2 \)
B. The voltage leads the current by \( \pi / 2 \)
c. The voltage and the current are in phase
D. The voltage leads the current by \( \pi \)
Subject: Chemistry
\( \boldsymbol{Y} \stackrel{\text {excess } H C l}{ } \boldsymbol{H} \boldsymbol{C} \equiv \boldsymbol{C} \boldsymbol{H} \stackrel{\boldsymbol{O}_{3} / Z n, \boldsymbol{H}_{2} \boldsymbol{O}}{\boldsymbol{N}} \boldsymbol{X} \)
\( X, Y \) respectively are :
A \( \cdot C O_{2}, C H_{3} C H C l \)
B. \( \mathrm{CO}_{2}, \quad_{\mathrm{Cl}}^{\mathrm{CH}_{2}-\mathrm{CH}_{2}} \mathrm{Cl} \)
\( c \)
\( \mathrm{H}_{\mathrm{O}}^{\mathrm{C}-\mathrm{C}}_{\mathrm{O}}^{-\mathrm{H},}, \mathrm{CH}_{3}-\mathrm{CHCl}_{2} \)
D.
\( \underset{\|}{\|}_{\mathrm{O}}^{\mathrm{C}-\mathrm{C}-\mathrm{H},} \underbrace{\mathrm{CH}_{2}-}_{\mathrm{O}} \frac{\mathrm{CH}_{2}}{\mathrm{Cl}} \mathrm{Cl} \)
Subject: Physics
Electrons of mass \( \mathrm{m} \) and charge e are accelerated through a potential difference V and strike the target. The
maximum speed of these electrons is
A \( \cdot \frac{e V}{m} \)
B. \( \frac{e V^{2}}{m} \)
c. \( \sqrt{\frac{e V}{m}} \)
D. \( \sqrt{\frac{2 e V}{m}} \)
Subject: Physics
Mid way between the two equal and similar charges, we placed the third equal and similar charge. Which of the following statements are correct, concerned to the equilibrium along the line joining the charges?
A. The third charge will experience a net force inclined to the line joining the charges.
B. The third charge is in a stable equilibrium.
c. The third charge is in an unstable equilibrium.
D. The third charge will experience a net force perpendicular to the line joining the charges.
Subject: Maths
\( \frac{\boldsymbol{x}+\boldsymbol{4}}{\boldsymbol{2}}+\frac{\boldsymbol{x}-\boldsymbol{3}}{\boldsymbol{3}}=\frac{\boldsymbol{x}+\boldsymbol{2}}{\boldsymbol{4}}+\frac{\boldsymbol{x}+\boldsymbol{3}}{\boldsymbol{5}}, \) find
the value of \( x \)
Subject: Maths
The equations of a line are given by \( \frac{\mathbf{4}-\boldsymbol{x}}{\mathbf{3}}=\frac{\boldsymbol{y}+\mathbf{3}}{\mathbf{3}}=\frac{\boldsymbol{z}+\mathbf{2}}{\mathbf{6}} . \) Write the
direction cosines of a line parallel to this line.
Subject: Maths
The image of the point (1,6,3) in the \( \operatorname{line} \frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3} \) is
A. (1,0,7)
в. (1,3,5)
c. (2,4,6)
D. (-1,-6,-3)
Subject: Maths
The value of \( \left(1+i x+i^{2} x^{2}+i^{3} x^{3}+\right. \)
\( \ldots \text { to } \infty) \times \)
\( \left(1-i x+i^{2} x^{2}-i^{3} x^{3}+\ldots . t o \infty\right) \) is
A. Imaginary
B. a positive real
c. a negative real
D. equal to zero
Subject: Physics
A \( 50 W, 100 V \) lamp is to be connected to an AC mains of \( 200 \mathrm{V}, 50 \mathrm{Hz} \). What capacitor is essential to be put in series with the lamp?
A \( \cdot \frac{25}{\sqrt{2}} \mu F \)
в. \( \frac{50}{\pi \sqrt{3}} \mu F \)
c. \( \frac{50}{\sqrt{2}} \mu F \)
D. \( \frac{100}{\pi \sqrt{3}} \mu F \)
Subject: Chemistry
Equivalent conductivity of acetic acid at infinite dilution is \( 390.7 \mathrm{mho} \mathrm{cm}^{2} \mathrm{gm} \)
equiv and for \( 0.1 \mathrm{M} \) acetic acid is 5.2
mho \( c m^{2} \) gm.equiv \( ^{2} \). Calculate degree
of dissociation, \( \boldsymbol{H}^{+} \) ion concentration
and dissociation constant of the acid.
Subject: Biology
Select suitable name for the process
\( \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}+2 \mathrm{ADP}+\mathrm{Pi} 2 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}+\mathrm{CO}_{2}+ \)
2ATP
A. Photorespiration.
B. Lactate fermentation
c. Aerobic respiration
D. Alcoholic fermentation
Subject: Maths
Eccentricity of the hyperbola whose
asymptotes are given by \( 3 x+2 y+ \)
\( \mathbf{5}=\mathbf{0} \) and \( \mathbf{2} \boldsymbol{x}+\mathbf{3} \boldsymbol{y}+\mathbf{5}=\mathbf{0} \) is
A \( \cdot \sqrt{2} \)
B. \( \frac{3}{2} \)
\( c \cdot 2 \)
D. None of these
Subject: Physics
A body of mass 5 kg undergoes a change in speed from 20 to \( 0.20 \mathrm{m} / \mathrm{s} \)
The momentum of the body would
A. increase by \( 99 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
B. decrease by \( 99 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
c. increase by \( 101 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
D. decrease by \( 90 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
Subject: Maths
Find what straight lines are represented by the following equation and determine the angles between them. \( \boldsymbol{y}^{3}-\boldsymbol{x} \boldsymbol{y}^{2}-\mathbf{1 4} \boldsymbol{x}^{2} \boldsymbol{y}+\boldsymbol{2 4} \boldsymbol{x}^{3}=\mathbf{0} \)
Subject: Physics
An electric circuit is composed of three
conducting rods \( M O, O N \) and \( P Q \) as
shown in figure. The resistance of the
rods per unit length is \( \lambda \). The rod \( P Q \)
slides, as shown in the figure, at a constant velocity \( v, \) keeping its tilt
angle relative to \( O N \) and \( N=M O \)
fixed \( 45^{\circ} . \) At each instance, the circuit
is closed. The whole system is embedded in a uniform magnetic field
\( B, \) which is directed perpendicularly into the page. Compute the timedependent induced electric current induced in the rods?
Subject: Physics
An ideal fluid is flowing in a tube of varying cross-section. At some point the radius of the tube is \( r \) and the velocity
of flow is \( v \). The velocity of flow at
another point, where the radius is \( r / 2 \)
is
A.
в. \( \frac{v}{2} \)
\( c \cdot 2 v \)
D. \( 4 v \)
Subject: Maths
Construct a \( \triangle A B C \) with \( A B= \)
\( \mathbf{3} c m, B C=4 c m \) and \( A C=5 c m \) and
find \( \boldsymbol{m} \angle \boldsymbol{A} \boldsymbol{C} \boldsymbol{B}=\boldsymbol{?} \)
A .37
B. 53
\( c \cdot 60^{\circ} \)
D. \( 90^{\circ} \)
Subject: Maths
The differential equation which
represents the family of curves \( \mathbf{y}= \)
\( \mathbf{c}_{1} \mathbf{e}^{\mathbf{c}_{2} \mathbf{x}} \) where \( \mathbf{c}_{1} \) and \( \mathbf{c}_{2} \) are arbitrary
constants, is:
A \( \cdot y^{\prime}=y^{2} \)
B. \( \mathrm{y}^{\prime \prime}=\mathrm{y}^{\prime} \mathrm{y} \)
\( \mathbf{C} \cdot \mathbf{y y}^{\prime \prime}=\mathbf{y}^{\prime} \)
D・yy" = (y') 2
Subject: Physics
With reference to the figure shown, if the coefficient of friction at the
surfaces is 0.42 , then the force
required to pull out the \( 6.0 k g \) block with
an acceleration of \( 1.50 m / s^{2} \) will be :
A \( .36 N \)
в. 24 N
\( c .84 N \)
D. \( 51 N \)
Subject: Chemistry
At \( 1400 K, K_{c}=2.5 \times 10^{-3} \) for reaction
\( \boldsymbol{C H}_{4}(\boldsymbol{g})+\mathbf{2} \boldsymbol{H}_{2} \boldsymbol{S}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{C} \boldsymbol{S}_{2}(\boldsymbol{g})+ \)
\( 4 H_{2}(g) . \) At \( 10.0 L \) reaction vessel at
\( 1400 \mathrm{K} \) contains 2.00 mole of \( \mathrm{CH}_{4}, 3.0 \)
mol of \( \mathrm{CS}_{2}, 3.0 \) mole of \( \mathrm{H}_{2} \) and 4.0 mole
of \( \mathrm{H}_{2} \mathrm{S} \). Then
A. this reaction is at equilibrium with above concentrations
B. the reaction will proceed in forward direction to reach equilibrium
c. the reaction will proceed in backward direction to each equilibrium
D. the information is insufficient to decide the direction of progress of reaction
Subject: Chemistry
A coordination complex of type \( M X_{2} Y_{2} \)
(M-metal ion; \( X, Y \) -monodentate ligands), can have either a tetrahedral
or a square planar geometry. The maximum number of possible isomers in these two cases are respectively:
A \( \cdot 1 \) and 2
B. 2 and1
c. 1 and 3
D. 3 and 2
Subject: Physics
The energy gap of silicon is 1.14 eV.The
maximum wavelength at which silicon starts energy absorption, will be \( \left(h=6.62 \times 10^{-34} J s, c=3 \times 10^{8} m / s\right) \)
A \( \cdot 10.888 \AA \)
B \( \cdot 108.88 \AA \)
\( c \cdot 1088.8 \AA \)
D \( \cdot 10888 \) 能
Subject: Physics
A permanent magnet has the shape of a sufficiently thin disc magnetized along
its axis. The radius of the disc is \( \boldsymbol{R}= \)
1.0 \( c m . \) Evaluate the magnitude of a
molecular current \( I^{\prime} \) flowing along
the rim of the disc if the magnetic induction at the point on the axis of the disc, lying at a distance \( \boldsymbol{x}=\mathbf{1 0} \boldsymbol{c m} \)
from its centre, is equal to \( B=30 \mu T \)
Subject: Maths
\( \int \frac{1}{\left(x^{2}-1\right)\left(x^{2}+2\right)} d x= \)
A. \( \frac{1}{3}\left[\frac{1}{2} \log \left|\frac{x+1}{x-1}\right|-\frac{1}{\sqrt{2}} \tan ^{-1} \frac{x}{\sqrt{2}}\right]+c \)
B \( \cdot \frac{1}{3}\left[\frac{1}{2} \log \left|\frac{x-1}{x+1}\right|+\frac{1}{\sqrt{2}} \tan ^{-1} \frac{x}{\sqrt{2}}\right]+c \)
c. \( \frac{1}{3}\left[\frac{1}{2} \log \left|\frac{x-1}{x+1}\right|-\frac{1}{\sqrt{2}} \tan ^{-1} \frac{x}{\sqrt{2}}\right]+c \)
D. \( \frac{1}{3}\left[\frac{1}{3} \log \left|\frac{x-1}{x+1}\right|-\frac{1}{2 \sqrt{2}} \tan ^{-1} \frac{x}{\sqrt{2}}\right]+c \)
Subject: Maths
Four equal circles each of radius \( a \)
units touch one another. the area
enclosed between them in square units,
is \( \left(\operatorname{take} \pi=\frac{22}{7}\right) \)
\( A \cdot 3 a^{2} \)
B. \( \frac{6 a^{2}}{7} \)
c. \( \frac{41 a^{2}}{7} \)
D. \( \frac{a^{2}}{7} \)
Subject: Chemistry
When \( M n O_{2} \) is fused with \( \mathrm{KOH} \) and \( O_{2} \)
what is the product formed and its
colour?
A. Mno - colourless
B . \( K M n O_{4} \) - purple
C. \( K_{2} M n O_{4} \) - dark green
D. \( M n O_{3} \) - black
Subject: Chemistry
The IUPAC name of \( \boldsymbol{K}_{3} \boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{6} \) is:
A. potassium hexacyanoferrate(II)
B. potassium hexacyanoferrate(III)
c. potassium hexacyanoiron(II)
D. tripotassium hexacyanoiron(II)
Subject: Physics
The radius of the first orbit of the \( e^{-} \) of a
hydrogen atom is \( 5.3 \times 10^{11} m \), what is
the radius of its second orbit.?
A. \( 3.12 \times 10^{-10} \mathrm{m} \)
В. \( 2.12 \times 10^{-10} \mathrm{m} \)
c. \( 4.12 \times 10^{-10} \mathrm{m} \)
D. \( 5.12 \times 10^{-10} \mathrm{m} \)
Subject: Maths
Let \( \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{5} & \mathbf{8} \\ \mathbf{8} & \mathbf{1 3}\end{array}\right] \) then show that \( \boldsymbol{A} \)
satisfies the equation \( x^{2}-18 x+1= \)
\( \mathbf{0} \)
Subject: Maths
Let \( x_{1}, x_{2}, \ldots . . x_{n} \) be \( n \) observations and
\( \bar{X} \) be their arithmetic mean. The
formula for the standard deviation is
given by
A \( \cdot \sum_{i=1}^{n}\left(x_{i}-\bar{X}\right)^{2} \)
B \( \cdot \frac{1}{n} \sum_{i=1}^{n}\left(x_{i}-\bar{X}\right)^{2} \)
c. \( \sqrt{\frac{1}{n} \sum_{i=1}^{n}\left(x_{i}-\bar{X}\right)^{2}} \)
D. \( \sqrt{\frac{1}{n} \sum_{i=1}^{n} x_{i}^{2}+\bar{X}^{2}} \)