AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
When hydrochloric acid is added to
cobalt nitrate solution at room
temperature, the following reaction takes place and the reaction mixture
becomes blue. On cooling the mixture, it
becomes pink. On the basis of this information mark the correct answer.
\( \left[\boldsymbol{C o}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right]_{(a q)}^{3+}+\boldsymbol{4} \boldsymbol{C l}_{(a q)}^{-} \rightleftharpoons \)
\( \left[\boldsymbol{C o C l}_{4}\right]_{(a q)}^{2-}+\boldsymbol{6} \boldsymbol{H}_{2} \boldsymbol{O}_{(l)} \)
A. \( \triangle H>0 \) for the reaction
B. \( \triangle H<0 \) for the reaction
c. \( \triangle H=0 \) for the reaction
D. The sign of \( \triangle H \) cannot be predicted on the basis of this information
Subject: Physics
A particle of mass \( m \) is moving along
\( x- \) axis with speed \( v \) when it collides
with a particle of mass \( 2 m \) initially at
rest. After the collision, the first particle
has come to rest and the second
particle has split into two equal-mass pieces that are shown in the figure. Which of the following statements correctly describes the speeds of the
two places? \( (\boldsymbol{\theta}>\mathbf{0}) \)
A. each piece moves with speed \( v \).
B. each piece moves with speed \( v / 2 \)
c. one of the piece moves with speed \( v / 2 \), the other moves with speed greater than \( v / 2 \).
D. each piece moves with speed greater than \( v / 2 \)
Subject: Chemistry
Natural rubber is not used in making
footwear for polar regions because:
A. natural rubber becomes soft at temperature lower \( \operatorname{than} 10^{\circ} C \)
B. natural rubber becomes brittle at temperature lower \( \operatorname{than} 10^{\circ} C \)
C . natural rubber melts at temperature lower than \( 10^{\circ} \mathrm{C} \)
D. natural rubber becomes stronger at temperature lower \( \operatorname{than} 10^{\circ} C \)
Subject: Physics
A steady flow of water passes along a
horizontal tube from a wide section \( \boldsymbol{X} \)
to the narrower section \( Y \), see figure.
Manometers are placed at \( P \) and \( Q \) at
the sections. Which of the statements
\( A, B, C, D \) is most correct?
A. water velocity at \( X \) is greater than \( Y \)
B. the manometer at \( P \) shows lower pressure than at \( Q \)
C. kinetic energy per \( m^{3} \) of water at \( X= \) kinetic energy per \( m^{3} \) at \( Y \)
D. the manometer at \( P \) shows greater pressure than at \( Y \)
Subject: Physics
A uniform solid cylinder of mass \( 5 k g \)
and radius \( 30 \mathrm{cm}, \) and free to rotate about its axis, receives an angular
impulse of \( 3 k g m^{2} s^{-1} \) initially followed
by a similar impulse after every 4 s.
What is the angular speed of the cylinder \( 30 s \) after the initial impulse?
The cylinder is at rest initially.
A. 100
в. 200
c. 300
D. 500
Subject: Physics
A series combination of two
capacitances of value 0.1 mu \( F \) and
\( 1 \mu F \) is connected with a source of voltage 500 volts. The potential difference in volts across the capacitor of value 0.1 mu \( F \) will be :
\( \mathbf{A} \cdot 50 \)
в. 500
c. 45.5
D. 454.5
Subject: Physics
Which of the following equations or principle is most suitable to solve given question.

A block of mass \( m \) remains at rest on a
table when a piece of paper is pulled out
from under it.
A. Newton's first law(law of inertia)
B. Newton's second law ( \( F_{n e t}=\mathrm{ma} \) )
c. Newton's third law (For every action there is an equal and opposite reaction)
D. Newton's law of universal gravitation
E. conservation of linear momentum
Subject: Maths
A man spends \( 80 \% \) of his income in
expenditure, with the increase in the cost of living his expenditure increases by \( 37 \frac{1}{2} \) and his income increases by \( 16 \frac{2}{3}, \) then the present percent saving is
A \( \cdot 1 \frac{2}{3} \)
B. \( 7 \frac{6}{5} \)
\( \mathrm{c} \cdot_{5} \frac{5}{7} \)
D. \( 9 \frac{3}{11} \)
Subject: Physics
The adjacent figure shows the crosssection of a long rod with its constant perpendicular to the plane of the paper It carries a constant current flowing
along its length \( B_{1}, B_{2}, B_{3} \) and \( B_{4} \)
respectively represent the length magnetic fields due to the current in the rod at point \( 1,2,3, \) and 4 lying at different separations from the centre 0 as shown in the figure. Which of the
following shall hold true.
A. \( B_{1}>B_{2} \neq 0 \)
В. \( B_{2}>B_{3} \neq 0 \)
c. \( B_{1}=B_{2}=B_{3}=0 \)
D. \( B_{3}>B_{4} \neq 0 \)
Subject: Maths
If \( A+B=225^{\circ}, \) then
\( \frac{\cot \boldsymbol{A}}{\mathbf{1}+\cot \boldsymbol{A}} \cdot \frac{\cot \boldsymbol{B}}{\mathbf{1}+\cot \boldsymbol{B}}= \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. -
\( c \cdot 0 \)
D. \( \frac{1}{2} \)
Subject: Physics
The wavelength of de broglie waves associated with a beam of protons of
kinetic energy \( 5 \times 10^{2} \mathrm{eV} \)
(Mass of each photon \( =\mathbf{1 . 6 7} \times \mathbf{1 0}^{-\mathbf{2 7}} \mathbf{K g} \)
\( \boldsymbol{h}=\mathbf{6 . 6 2} \times \mathbf{1 0}^{-\mathbf{3 4}} \mathbf{J s} \)
A. \( 2.42 \times 10^{-12} \mathrm{m} \)
B . \( 4.24 \times 10^{-12} \mathrm{m} \)
c. \( 1.82 \times 10^{-12} \mathrm{m} \)
D. \( 1.28 \times 10^{-12} \mathrm{m} \)
Subject: Maths
If \( \triangle_{1}, \triangle_{2} \) be the areas of two triangles with vertices \( (b, c),(c, a),(a, b), \) and \( \left(a c-b^{2}, a b-c^{2}\right),\left(b a-c^{2}, b c-\right. \)
\( \left.a^{2}\right),\left(c b-a^{2}, c a-b^{2}\right), \) then \( \frac{\triangle_{1}}{\triangle_{2}}= \)
\( (a+b+c)^{2} \)
A. True
B. False
Subject: Physics
An object \( 20 \mathrm{cm} \) from a concave mirror form an image, double the size of the object, on a screen. How far should the screen be placed from the mirror?
A. -40 cm
B. 40 cm
c. \( 20 \mathrm{cm} \)
D. -20 cm
E. 30 \( \mathrm{cm} \)
Subject: Physics
A straight line conductor of length
\( 0.4 m \) is moved with a speed of \( 7 m / s \) perpendicular to a magnetic filed of
intensity \( 0.9 W b / m^{2} . \) The induced e.m.f. across the conductor is
A . \( 5.04 V \)
B . \( 1.26 V \)
c. \( 2.52 V \)
D. 25.2 \( V \)
Subject: Chemistry
A compound has carbon, hydrogen, and oxygen in 3: 3: 1 atomic ratio. If the
number of moles in \( 1 g \) of the compound is \( 6.06 \times 10^{-3} \), the molecular formula of
the compound will be
\( A \cdot C_{3} H_{3} O \)
в. \( C_{6} H_{6} O_{2} \)
\( \mathbf{c} \cdot C_{9} H_{9} O_{3} \)
D. \( C_{12} H_{12} O_{4} \)
Subject: Physics
The circuit shown in the figure contains two diodes, each with a forward
resistance of \( 50 \Omega \) and with infinite
backward resistance. If the battery
voltage is \( 6 \mathrm{V} \), the current through the
\( 100-\Omega \) resistance is
A. zer
B. \( 0.02 A \)
c. \( 0.04 A \)
D. \( 0.046 A \)
Subject: Maths
In the given figure, if area of parallelogram \( A B E F \) is \( 96 \mathrm{cm}^{2} ; \) state
giving reason, the area of \( \triangle A D B \)
\( \mathbf{A} \cdot 48 \mathrm{cm}^{2} \)
B. \( 38 \mathrm{cm}^{2} \)
\( \mathrm{c} \cdot 58 \mathrm{cm}^{2} \)
\( \mathrm{D} \cdot 68 \mathrm{cm}^{2} \)
Subject: Chemistry
If you have a solution in equilibrium
containing \( C l^{-} \) ions and you added
NaCl to the solution, what is going to
happen?
A. The reaction will shift to the left to compensate for the increased concentration of \( C l^{-} \) ions
B. The reaction will become unbalanced and stay unbalanced
C. Le Chatelier's principle says that nothing will happen
D. More \( N a^{+} \) ions will be made so that concentrations of
\( N a^{+} \) and \( C l^{-} \) even out
E . Equilibrium will be restored
Subject: Chemistry
Which of the following order for bond angles is correct?
A. \( B F_{3}<N F_{3}<C l F_{3}<P F_{3} \)
B. \( B F_{3}<N F_{3}<P F_{3}<C l F_{3} \)
c. \( C l F_{3}<P F_{3}<N F_{3}<B F_{3} \)
D. \( B F_{3} \approx N F_{3}<P F_{3}<C l F_{3} \)
Subject: Physics
If \( g \) on the surface of the Earth is
\( 9.8 m s^{-2}, \) its value at a height of
\( 6400 k m \) is: (Radius of the Earth \( = \)
\( 6400 k m) \)
A. \( 4.9 \mathrm{ms}^{-2} \)
В. \( 9.8 \mathrm{ms}^{-2} \)
c. \( 2.45 \mathrm{ms}^{-2} \)
D. \( 19.6 \mathrm{ms}^{-2} \)
Subject: Chemistry
\( F e C r_{2} O_{4}(\text { Chromite }) \) is a good source
of chromium and its compound like
\( N a_{2} C r O_{4} \) and \( N a_{2} C r_{2} O_{7} \)
I. \( \boldsymbol{F e} \boldsymbol{C r}_{2} \boldsymbol{O}_{4}+\boldsymbol{N a O H}+\boldsymbol{a i r} \longrightarrow \)
\( (\boldsymbol{A})+\boldsymbol{F} \boldsymbol{e}_{2} \boldsymbol{O}_{3} \)
II. \( (\boldsymbol{A})+(\boldsymbol{B}) \longrightarrow \boldsymbol{N} \boldsymbol{a}_{2} \boldsymbol{C r}_{2} \boldsymbol{O}_{7} \)
\( \mathrm{III} . N a_{2} C r_{2} O_{7}+X \stackrel{\triangle}{\longrightarrow} C r_{2} O_{3} \)
IV. \( \boldsymbol{C r}_{2} \boldsymbol{O}_{3}+\boldsymbol{Y} \stackrel{\Delta}{\longrightarrow} \boldsymbol{C r} \)
Compounds \( (A) \) and \( (B) \) are:
A \( \cdot N a_{2} C r O_{4}, H_{2} S O_{4} \)
в. \( N a_{2} C r_{2} O_{7}, H C l \)
c. \( N a_{2} C r O_{6}, H_{2} S O_{4} \)
D. \( N a_{4}\left[F e(O H)_{6}\right], H_{2} S O_{4} \)
Subject: Chemistry
Calculate the molar conductivity of water at infinite dilution (in \( \mathrm{Sm}^{2} \mathrm{mol}^{-1} \) ).
( molar conductivity of hydrogen ions and the molar conductivity of hydroxide ions at infinite dilution are \( 349.6 \times 10^{-4} \mathrm{Sm}^{2} \)
\( \left.\mathrm{mol}^{-1} \text {and } 198.3 \times 10^{-4} \mathrm{Sm}^{2} \mathrm{mol}^{-1}\right) \)
A . 547.9
B. 647.9
c. \( 647.9 \times 10^{-4} \)
D. \( 547.9 \times 10^{-4} \)
Subject: Maths
Adjacent sides of a parallelogram are \( 5 c m \) and \( 3.5 \mathrm{cm} . \) One of its diagonals is
\( 6.5 \mathrm{cm} . \) Then what is the area of
parallelogram?
A. \( 8 \sqrt{3} \mathrm{cm}^{2} \)
В. \( 9 \sqrt{3} \mathrm{cm}^{2} \)
\( \mathbf{c} \cdot 10 \sqrt{3} \mathrm{cm}^{2} \)
D. \( 12 \sqrt{3} \mathrm{cm}^{2} \)
Subject: Maths
For the measures of central tendency,
of the following is not true.
A. \( Z=3 M-2 \bar{x} \)
в. \( 2 \bar{x}+Z=3 M \)
c. \( 2 \bar{x}-3 M=-Z \)
D. \( 2 \bar{x}=Z-3 M \)
Subject: Maths
The range of \( \boldsymbol{f}(\boldsymbol{x})=\mathbf{1 0}+|\boldsymbol{x}+\mathbf{4}| \) is
A. \( (0, \infty) \)
)
B. \( [10, \infty) \)
c. \( (-\infty, 10] \)
\( D \cdot(-\infty, \infty) \)
Subject: Biology
Fermentation is represented by the
equation
A \( \cdot C_{6} H_{12} O_{6}+6 O_{2} \stackrel{\text {light}}{\rightarrow} 6 C O_{2}+H_{2} O+673 k c a l \)
B . \( C_{6} H_{12} O_{6}+\rightarrow 2 C_{2} H_{5} O H+2 C O_{2}+18 k c a l \)
c. \( 6 C O_{2}+12 H_{2} O \stackrel{\text { Chlorophyll }}{\longrightarrow} C_{6} H_{12} O_{6}+6 H_{2} O+6 O_{2} \)
D. \( 6 C O_{2}+6 H_{2} O \rightarrow C_{6} H_{12} O_{6}+6 O_{2} \)
Subject: Chemistry
Choose the correct answer form the
alternatives given.

All alkali halides are soluble in water
except LiF. The low solubility of LiF in
water is due to its
(i) the low
solubility of Csl is due to
(ii).
LiF is soluble in
A. (i)-low lattice enthalpy (ii)-large hydration enthalpy
(iii)-polar solvents
B. (i)-high lattice enthalpy
(ii)-smaller hydration enthalpy (iii)-non-polar solvents
C . (i)-high hydration enthalpy (ii)-high lattice enthalpy
(iii)-non-polar solvents
D. (i)-smaller high hydration enthalpy (ii)-lattice enthalpy (iii)-polar solvents
Subject: Biology
Which of the following is the correct representation of organisation levels in living beings?
A. Subcellular \( \rightarrow \) Cellular \( \rightarrow \) Individual \( \rightarrow \) Community Population
B. Atomic \( \rightarrow \) Molecular \( \rightarrow \) Subcellular \( \rightarrow \) Cellular \( \rightarrow \) Tissue \( \rightarrow \) Organ system \( \rightarrow \) Individual
c. Individual \( \rightarrow \) Population \( \rightarrow \) organ system \( \rightarrow \) Tissue \( \rightarrow \) Cellular \( \rightarrow \) Molecular \( \rightarrow \) Atomic
D. Atomic \( \rightarrow \) Molecular \( \rightarrow \) Tissue \( \rightarrow \) Individual \( \rightarrow \) Ecosystem \( \rightarrow \) Community
Subject: Maths
The probabilities that three men hit a target are \( 1 / 6,1 / 4 \) and \( 1 / 3 . \) Each man
shoots once at the target. What is the probability that exactly one of them hits the target?
A \( \cdot 11 / 72 \)
B. 21/72
c. \( 31 / 72 \)
D. 3/4
Subject: Maths
If \( y_{1}(x) \) is a solution of the differential equation \( \frac{d y}{d x}+f(x) y=0, \) then \( a \) solution of differential equation \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}+ \)
\( \boldsymbol{f}(\boldsymbol{x}) \boldsymbol{y}=\boldsymbol{r}(\boldsymbol{x}) \) is
A \( \cdot \frac{1}{y(x)} \int y_{1}(x) r(x) d x \)
B. \( y_{1}(x) \int \frac{r(x)}{y_{1}(x)} d x \)
c. \( f r(x) y_{1}(x) d x \)
D. None of these
Subject: Physics
Assertion
The direction of induced emf is always
such as to oppose the change that causes it.
Reason
Conservation of energy applies to know the direction of induced emf.
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
A projectile is fired with a velocity at
right angle \( \theta \) to the slope which is
inclined at an angle \( \theta \) with the horizontal. The expression for the range \( \boldsymbol{R} \) along the incline is:
\( ^{\mathbf{A}} \cdot \frac{2 v^{2}}{g} \sec \theta \)
B \( \cdot \frac{2 v^{2}}{g} \tan \theta \)
\( ^{\mathrm{c}} \cdot \frac{2 v^{2}}{g} \sec \theta \tan \theta \)
D \( \cdot \frac{2 v^{2}}{g} \tan ^{2} \theta \)
Subject: Chemistry
Arrange the following in increasing
order of their nucleophilicity in a polar
aprotic solvent.
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{O}^{-}, \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{S}^{-}, \boldsymbol{C H}_{3} \boldsymbol{C S}_{2} \)
A \( \cdot C H_{3} C S_{2}^{-}<C H_{3} C H_{2} O^{-}<C H_{3} C H_{2} S^{-} \)
в. \( C H_{3} C H_{2} O^{-}<C H_{3} C S_{2}^{-}<C H_{3} C H_{2} S^{-} \)
c. \( C H_{3} C H_{2} S^{-}<C H_{3} C S_{2}^{-}<C H_{3} C H_{2} O \)
D. None of these
Subject: Physics
Find the ratio of magnetic dipole moment to angular momentum in a hydrogen like atom:
A \( \cdot \frac{e}{m} \)
B. \( \frac{e}{2 m} \)
c. \( \frac{e}{3 m} \)
D. \( \frac{2 e}{m} \)
E \( \cdot \frac{3 e}{m} \)
Subject: Physics
Two identical glass bulbs are
interconnected by a thin glass tube. A
gas is filled in these bulbs at N.T.P. If
one bulb is placed in ice and another bulb is placed in hot bath, then the pressure of the gas becomes 1.5 times.
The temperature of hot bath will be
\( \mathbf{A} \cdot 100^{\circ} C \)
B. \( 182^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 256^{\circ} \mathrm{C} \)
D. \( 546^{\circ} \mathrm{C} \)
Subject: Physics
The volume of a sphere is \( 1.76 \mathrm{cm}^{3} . \) The
volume of 25 such spheres taking into account the significant figure is:
A \( \cdot 0.44 \times 10^{2} c m^{3} \)
В. \( 44.00 \mathrm{cm}^{3} \)
\( c \cdot 44.0 c m^{3} \)
D. \( 44 \mathrm{cm}^{3} \)
Subject: Physics
The distance of Neptune and Saturn
from the sun are nearly \( 10^{13} \mathrm{m} \) and \( 10^{12} \) \( \mathrm{m} \) respectively. Assuming that they move in circular orbits, their periodic times would be in the ratio of
A . 10
в. 100
c. \( 10 \sqrt{10} \)
D. 1000
Subject: Maths
The product of \( -3 x y z, 6 x^{2} y z^{3}, \) and
\( -4 x^{3} z^{2} \) is
\( \mathbf{A} \cdot 64 x^{6} y^{2} z^{6} \)
B. \( -64 x^{6} y^{2} z^{6} \)
C \( .-42 x^{6} y^{2} z^{6} \)
D. \( 72 x^{6} y^{2} z^{6} \)
Subject: Chemistry
Assertion: Diborane has two types
of hydrogens.

Reason : By methylation only four hydrogen atoms of diborane are substituted forming \( M e_{4} B_{2} H_{2} \)
A. Both Assertion and Reason are true and Reason is correct explanation of Assertion
B. Both Assertion and Reason are true and Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
Subject: Physics
An arrow is placed at a distance of 25 \( \mathrm{cm} \) from a diverging mirror of focal length \( 20 \mathrm{cm} . \) Find the image distance.
A . \( 12.1 \mathrm{cm} \)
B. \( 13.1 \mathrm{cm} \)
\( c .11 .1 c m \)
D. \( 14.2 \mathrm{cm} \)
Subject: Chemistry
The following reaction is known to occur in the human body:
\( \boldsymbol{C O}_{2}+\boldsymbol{H}_{2} \boldsymbol{O} \rightleftharpoons \boldsymbol{H}_{2} \boldsymbol{C O}_{3} \rightleftharpoons \boldsymbol{H}^{+}+ \)
\( \boldsymbol{H} \boldsymbol{C O}_{\mathbf{3}}^{-} \)
If \( C O_{2} \) escapes from the system
A . pH will decrease
B. \( H^{+} \) ion concentration will decrease
c. \( H_{2} C O_{3} \) concentration will be unaltered
D. The forward reaction will be promoted
Subject: Maths
The lines \( (a+b) x+(a-b) y-2 a b= \)
\( \mathbf{0},(\boldsymbol{a}-\boldsymbol{b}) \boldsymbol{x}+(\boldsymbol{a}+\boldsymbol{b}) \boldsymbol{y}-\boldsymbol{2} \boldsymbol{a} \boldsymbol{b}=\boldsymbol{0} \) and
\( x+y=0 \) forms an isosceles triangle
whose vertical angle is
A \( \cdot \frac{\pi}{2} \)
B. \( \mid \tan ^{-1}\left(\frac{2 a b}{a^{2}-b^{2}}\right) \)
c. \( \mid \tan ^{-1}\left(\frac{a}{b}\right) \)
D・ \( 2 \mid \tan ^{-1}\left(\frac{\mathrm{a}}{b}\right) \)
Subject: Chemistry
Which of the following eletrolyte will have maximum flocculation value for
\( \boldsymbol{F} \boldsymbol{e}(\boldsymbol{O} \boldsymbol{H})_{3} \) sol?
A . \( N a C l \)
в. \( N a_{a} S \)
\( \mathrm{c} \cdot\left(N H_{4}\right)_{3} P O_{4} \)
D. \( K_{2} S O_{4} \)
Subject: Maths
Verify Lagrange's mean value theorem for the following function on the indicated interval. In each case find a
point \( ^{\prime} c^{\prime} \) in the indicated interval as
stated by the Lagrange's mean value theorem:
\( \boldsymbol{f}(\boldsymbol{x})=\sin \boldsymbol{x}-\sin 2 \boldsymbol{x}-\boldsymbol{x} \) on \( [\mathbf{0}, \boldsymbol{\pi}] \)
Subject: Maths
Prove that:
\( \tan ^{-1}\left(\frac{6 x-8 x^{3}}{1-12 x^{2}}\right) \)
\( \tan ^{-1}\left(\frac{4 x}{1-4 x^{2}}\right)=\tan ^{-1} 2 x ;|2 x|< \)
\( \frac{1}{\sqrt{3}} \)
Subject: Physics
The driver of an express train travelling
at a speed of \( v_{1} \) sees on the same track
at distance \( d \) in front of him a goods
train travelling in the same direction at
a speed \( v_{2} \) such that \( v_{1}>v_{2} \)
Immediately he applies brakes to his
express train producing retardation \( a \) to avoid collision. Then
\( ^{\mathbf{A}} \cdot_{a}<\frac{v_{1}^{2}-v_{2}^{2}}{2 d} \)
В. \( _{a<\frac{\left(v_{1}-v_{2}\right)^{2}}{2 d}} \)
c. \( _{a>} \frac{\left(v_{1}-v_{2}\right)^{2}}{2 d} \)
D. \( _{a>} \frac{v_{1}^{2}-v_{2}^{2}}{2 d} \)
Subject: Physics
The resistance of an ammeter is \( 13 \Omega \)
and its scale is graduated for a current upto 100 amps. After and additional shunt has been connected to this
ammeter it becomes possible to
measure currents upto 750 amperes by this meter. The value of shunt-
resistance is-
A \( .2 K \Omega \)
B. 20\Omega
\( c .2 \Omega \)
D. \( 0.2 \Omega \)
Subject: Maths
Find \( : A^{2} \) if
\( \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{3} & \mathbf{2} \\ -\mathbf{5} & \mathbf{1} & \mathbf{0} \\ \mathbf{1} & \mathbf{2} & \mathbf{5}\end{array}\right] \)
Subject: Maths
\( \boldsymbol{A}=(-1,2,-\mathbf{3}), \boldsymbol{B}=(\mathbf{5}, \mathbf{0},-\mathbf{6}), \boldsymbol{C}= \)
(0,4,-1) are the vertices of a triangle.
The d.c's of the internal bisector of \( \angle \mathrm{BAC} \)
are?
\( ^{\mathbf{A}} \cdot\left(\frac{25}{\sqrt{714}}, \frac{-8}{\sqrt{714}}, \frac{-5}{\sqrt{714}}\right) \)
в. \( \left(\frac{5}{\sqrt{74}}, \frac{6}{\sqrt{74}}, \frac{8}{\sqrt{74}}\right) \)
\( ^{\mathbf{C}} \cdot\left(\frac{25}{\sqrt{714}}, \frac{8}{\sqrt{714}}, \frac{5}{\sqrt{714}}\right) \)
D. \( \left(\frac{-5}{\sqrt{74}}, \frac{6}{\sqrt{74}}, \frac{-8}{\sqrt{74}}\right) \)
Subject: Physics
Two coaxial coils are very close to each
other and their mutual inductance is 5
\( \mathrm{mH} \). If a current \( 50 \sin 500 r \) is passed in
one of the coils then the peak value of induced e.m.f. in the secondary coil will
be?
A . \( 5000 v \)
в. \( 500 v \)
\( c .150 v \)
D. 125v
Subject: Maths
Find the mean for the following distribution
\( \begin{array}{lllll}\text { Marks } & \begin{array}{l}10- \\ 20\end{array} & \begin{array}{l}20- \\ 30\end{array} & \begin{array}{l}\text { 30- } \\ 40\end{array} & \begin{array}{l}\text { 40- } \\ 50\end{array}\end{array} \)
Frequency 6 8 13
Subject: Physics
Critical angle for certain medium is
\( \sin ^{-1}(0.6) . \) The polarizing angle of that
medium is :
A \( \cdot \tan ^{-1}(1.5) \)
В \( \cdot \tan ^{-1}(0.8) \)
c. \( \tan ^{-1}(1.6667) \)
D. \( \tan ^{-1}(0.667) \)
Subject: Physics
A body of mass \( 10 \mathrm{kg} \) dropped from a height \( 20 \mathrm{m}, \) acquires a velocity of 10 \( \mathrm{m} / \mathrm{s} \) after falling through a distance of 20 \( \mathrm{m} \). What is the work done by the air resistance on the body?
A. 750 J
B. 1000
c. 1500
D. 2000 J
Subject: Physics
A body of mass travels in a straight line with a velocity \( v=k x^{3 / 2} \) where \( k \) is a
constant. The work done in displacing the body from \( x=0 \) to \( x \) is proportional
to:
\( \mathbf{A} \cdot x^{1 / 2} \)
B. \( x^{2} \)
c. \( x^{3} \)
D. \( x^{5 / 2} \)
Subject: Maths
The cartesian equation of a line is \( \frac{\boldsymbol{x}+\mathbf{3}}{\mathbf{2}}=\frac{\boldsymbol{y}-\mathbf{5}}{\mathbf{4}}=\frac{\boldsymbol{z}+\mathbf{6}}{\mathbf{2}} \) find the vector
equation of the line?
Subject: Physics
Two simple harmonic motions are given
by
\( \boldsymbol{x}_{1}=\boldsymbol{a} \sin \omega \boldsymbol{t}+\boldsymbol{a} \cos \omega t \) and
\( \boldsymbol{x}_{2}=\boldsymbol{a} \sin \omega \boldsymbol{t}+\frac{\boldsymbol{a}}{\sqrt{\mathbf{3}}} \cos \boldsymbol{\omega} \boldsymbol{t} \)
The ratio of the amplitudes of first and
second motion and the phase difference between them are respectively
A \( \cdot \sqrt{\frac{3}{2}} \) and \( \frac{\pi}{12} \)
B. \( \frac{\sqrt{3}}{2} \) and \( \frac{\pi}{12} \)
c. \( \frac{3}{\sqrt{2}} \) and \( \frac{\pi}{12} \)
D. \( \sqrt{\frac{3}{2}} \) and \( \frac{\pi}{6} \)
Subject: Chemistry
What is the role of conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) in the
given reaction?
\( \boldsymbol{C u} \boldsymbol{S O}_{4} \cdot \boldsymbol{5} \boldsymbol{H}_{2} \boldsymbol{O} \frac{\operatorname{Conc.H}_{2} \boldsymbol{S O}_{4}}{\longrightarrow} \boldsymbol{C u} \boldsymbol{S} \boldsymbol{O}_{4}+ \)
\( \mathbf{5} \boldsymbol{H}_{2} \boldsymbol{O} \)
A . Dilute acid
B. Dehydrating agent
c. Non-volatile acid
D. Oxidising agent
Subject: Chemistry
The phosphorus present in an organic compound of mass 75 g is oxidized to phosphoric acid by heating with fuming nitric acid. The phosphoric acid so obtained is precipitated as \( M g N H_{4} P O_{4}, \) which on ignition is
converted into \( M g_{2} P_{2} O_{7} \). If the mass of
Mg2P207 is 50 g, the percentage composition of phosphorus present in the sample of the organic compound is:
A . 19.5
в. 18.
\( c \cdot 20 \)
D. 18.6
Subject: Physics
Th - 230 undergoes a series of
radioactive decay processes resulting
in \( B i-214 \) being the final product.
What was the sequence of the
processes that occurred?
\( \mathbf{A} \cdot \alpha, \alpha, \alpha, g, \beta \)
в. \( \alpha, \alpha, \alpha, \alpha, \beta \)
\( \mathbf{c} \cdot \alpha, \alpha, \beta, \beta \)
\( \mathbf{D} \cdot \alpha, \beta, \beta, \beta, \gamma \)
Subject: Physics
(a) Which physical quantity has its \( \mathrm{S} \) I unit \( (1) \mathrm{Cm}(2) \mathrm{N} / \mathrm{C} \)
(b) Two point charges \( q \) and \( -q \) is placed at a distance \( 2 a \) apart. Calculate the
electric field at a point \( P \) is situated at a distance r along the perpendicular bisector of the line joining the charges. What is the electric field when \( r>> \) a?
Also, give the direction of electric field
w.r.t. electric dipole moment?
Subject: Chemistry
Consider the following three halides:
(i) \( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C l} \)
(ii) \( \boldsymbol{C H}_{2}=\boldsymbol{C H}-\boldsymbol{C l} \)
(iii) \( C_{6} H_{5}-C l \)
Arrange C-Cl bond length of these compounds in decreasing order.
A. i > ii > ii i
c. iii > ii > i
D. ii > iii >