AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
A gaseous mixture having 4 mole of \( H_{2} \)
and 6 mole of \( I_{2} \) on heating shows
equilibrium concentration of \( \boldsymbol{H} \boldsymbol{I} \) as \( \boldsymbol{2} \)
mole. If we start with 4 moles of \( H_{2} \) and
9 mole of \( I_{2} \) at the same temperature,
how many mole of \( \boldsymbol{H} \boldsymbol{I} \) will be formed?
Also calculate degree of dissociation of
\( H I \) at this temperature
Subject: Chemistry
Formation of metallic copper from the
sulphide ore in the commercial
metallurgical process involves:
A \( \cdot C u_{2} S+\frac{3}{2} O_{2} \rightarrow C u_{2} O+S O_{2} ; C u_{2} O+C \rightarrow 2 C u+C O \)
B. \( C u_{2} S+\frac{3}{2} O_{2} \rightarrow C u_{2} O+S O_{2} ; 2 C u_{2} O+C u_{2} S \rightarrow 6 C u+ \)
\( S O_{2} \)
c. \( C u_{2} S+2 O_{2} \rightarrow C u S O_{4} ; C u S O_{4}+C u_{2} S \rightarrow 3 C u+ \)
\( 2 S O_{2} \)
D. \( C u_{2} S+\frac{3}{2} O_{2} \rightarrow 2 C u+S O_{2} ; C u_{2} O+C O \rightarrow 2 C u+ \)
\( C O_{2} \)
Subject: Physics
When two infinitely long parallel wires
separated by a distance of \( 1 m, \) each carry a current of \( 3 A \), the force in newton/metre length experienced by each will be, \( \left(\operatorname{given} \mu_{0}=4 \pi \times 10^{-7} \mathrm{S.I}\right. \)
Units).
A. \( 2 \times 10^{-7} \)
B. \( 3 \times 10^{-7} \)
c \( .6 \times 10^{-7} \)
D. \( 18 \times 10^{-7} \)
Subject: Chemistry
Standard electrode potential for \( \mathrm{Fe} \)
electrode are given as \( F e^{++}+2 e^{-} \rightarrow F e \)
\( E^{0}=-0.44 V F e^{3+}+e^{-} \rightarrow F e^{++} E^{0}= \)
\( +0.77 V F e^{++}, F e^{+++} \) and Fe block are
kept together then:
A \( \cdot\left[F e^{+++}\right] \) decreases
B . \( \left[F e^{+++}\right] \) increases
C \( \cdot\left[F e^{++} F e^{+++}\right] \) remains unchanged
D. \( \left[F e^{++}\right] \) decreases
Subject: Maths
A cottage industry manufactures pedestal lamps and wooden shades, each requiring the use of a
grinding/cutting machine and a sprayer. It takes 2 hours
on grinding/cutting machine and 3
hours on the sprayer to manufacture a
pedestal lamp. It takes 1 hour on the grinding/cutting machine and 2 hours on the sprayer to manufacture a shade. On any day, the sprayer is available for
at the most 20 hours and the
grinding/cutting machine for at the
most 12 hours. The profit from the sale of a lamp is \( \boldsymbol{R} \boldsymbol{s} .5 \) and that from a shade is \( R s .3 . \) Assuming that
the manufacturer can sell all the lamps and shades that he produces, how should he schedule his daily production in order to maximise his profit?
Subject: Physics
one end has a small block of mass \( m \)
and charge \( q \) is attached at the other
end. The block rests over a smooth
horizontal surface. A uniform and
constant magnetic field \( B \) exists
normal to that plane of paper as shown in figure. An electric field \( \overrightarrow{\boldsymbol{E}}=\boldsymbol{E}_{0} \hat{\boldsymbol{i}}\left(\boldsymbol{E}_{\mathbf{0}}\right. \)
is a positive constant) is switched on at
\( \boldsymbol{t}=\mathbf{0} \) sec. The block moves on horizontal
surface without ever lifting off the
surface. Then the normal reaction
acting on the block is
A. Maximum at extreme position and minimum at mean position
B. Maximum at mean position and minimum at extreme position
C. is uniform throughout the motion
D. is both maximum and minimum at mean position
Subject: Physics
Fill in the blanks:
Magnification of convex mirror is in
range and of concave
mirror is in range
A \( (0,1),(-\infty, 0) \cup(1, \infty) \)
(1)
B . \( (-1,0),(-\infty, \infty) \)
c. \( (-\infty, \infty),(1, \infty) \)
D \( \cdot(-\infty, \infty),(-1,-\infty) \)
Subject: Maths
If \( \tan \theta+\tan \phi=a, \cot \theta+\cot \phi= \)
\( \boldsymbol{b}, \boldsymbol{\theta}-\boldsymbol{\phi}=\boldsymbol{\alpha} \neq \mathbf{0}, \) then
This question has multiple correct options
\( \mathbf{A} \cdot a b>4 \)
в. \( a b<4 \)
\( ^{\mathbf{c}} \tan ^{2} \alpha=\frac{a b(a b-4)}{(a+b)^{2}} \)
D \( \sec ^{2} \alpha=\frac{(a-b)^{2}+a^{2} b^{2}}{(a+b)^{2}} \)
Subject: Physics
Two towns \( A \) and \( B \) are connected by a regular bus service with a bus leaving in either direction every T minutes with same speed. A man cycling with speed of \( 20 \mathrm{km} / \mathrm{h} \) in the direction \( \mathrm{A} \) to \( \mathrm{B} \)
notices that a bus goes past him every
\( t_{1}=18 \) minutes in the direction of motion,
and every \( t_{2}=6 \) minutes in the opposite
direction. What is the period T of the bus service? Assume that velocity of cyclist is less than velocity of bus.
A. 4.5 minutes
B. 24 minutes
c. 9 minutes
D. 12 minutes
Subject: Chemistry
\( \triangle H \) of which of the following reaction is
zero?
\( \mathbf{A} \cdot H_{2}(g) \rightarrow 2 H^{+}(g)+2 e^{-} \)
B \( \cdot 2 H(g)+a q \rightarrow 2 H^{+}(a q)+2 e^{-} \)
\( \mathbf{c} \cdot 2 H(g) \rightarrow 2 H^{+}(g)+2 e^{-} \)
D \( \cdot H_{2}(g)+a q \rightarrow 2 H^{+}(a q)+2 e^{-} \)
Subject: Physics
A body moving with uniform acceleration travels a distance \( s_{n}= \)
\( (0.4 n+9.8) m \) in \( n^{t h} \) second. Initial
velocity of the body is \( \left(\operatorname{in} m s^{-1}\right) \)
A. 0.4
B. 10
\( c .3 .5 \)
D. 4
Subject: Maths
Two systems of rectangular axes have
the same origin. If a plane cuts them at
distance \( a, b, c \) and \( d, b^{\prime}, c^{\prime} \) from the
origin, then
A \( \cdot \frac{1}{a^{2}}-\frac{1}{b^{2}}-\frac{1}{c^{2}}-\frac{1}{a^{2}}-\frac{1}{b^{2}}-\frac{1}{c^{2}}=0 \)
B \( \cdot \frac{1}{a^{2}}-\frac{1}{b^{2}}-\frac{1}{c^{2}}-\frac{1}{a^{2}}-\frac{1}{b^{2}}+\frac{1}{c^{2}}=0 \)
c. \( \frac{1}{a^{2}}+\frac{1}{b^{2}}+\frac{1}{c^{2}}-\frac{1}{a^{2}}-\frac{1}{b^{2}}-\frac{1}{c^{2}}=0 \)
D \( \frac{1}{a^{2}}+\frac{1}{b^{2}}+\frac{1}{c^{2}}+\frac{1}{a^{2}}+\frac{1}{b^{2}}+\frac{1}{c^{2}}=0 \)
Subject: Physics
A ring of mass \( m \) and radius r rolls on an inclined plane. A torque is produced in the ring due to
A. mgsin\theta and the radius of the ring
B. the perpendicular distance between the force and the point of contact and the force \( m g \) acting on it
c. the perpendicular distance between the force and the point of contact and the normal force acting on the object
D. the perpendicular distance between the force and the point of contact and the force \( m g \sin \theta \) acting on it
Subject: Physics
A steel ball of diameter \( \boldsymbol{d}=\mathbf{3 . 0} \boldsymbol{m m} \)
starts sinking with zero initial velocity in olive oil whose viscosity is \( \eta= \)
\( 0.90 P . \) How soon after the beginning of
motion will the velocity of the ball differ from the steady-state velocity by \( \boldsymbol{\eta}=\mathbf{1 . 0 \%} ? \)
Subject: Physics
Two long, thin, parallel conductors, separated by a distance d carry
currents \( i_{1} \) and \( i_{2} . \) The force acting on unit length of any one conductor is \( \mathrm{F} \) :
This question has multiple correct options
A . F is attractive, if \( i_{1} \) and \( i_{2} \) flow in the same directions
B. F is attractive, if \( i_{1} \) and \( i_{2} \) flow in the opposite directions
c. F is the same for both conductors
D. F is the different for the two conductors
Subject: Chemistry
A solution containing \( 10.2 g \) per glycerin per liter of a solution is found to be
isotonic with \( 2 \% \) solution of glucose molar mass \( 180 . \) Calculate the molar
mass glycerin.
A. 97.89 g/mol
в. 183.24 g/mol
c. \( 91.8 \mathrm{g} / \mathrm{mol} \)
D. None of these
Subject: Chemistry
The vapour pressure of two miscible liquids \( (A) \) and \( (B) \) are 300 and 500 mm of Hg respectively. In a flask, 10 moles of
(A) is mixed with 12 moles of \( (\mathrm{B}) \)
However, as soon as (B) is added, (A)
starts polymerising into a completely insoluble solid. The polymerization follows first-order kinetics. After 100
minutes, 0.525 moles of a solute is dissolved which arrests the
polymerisation completely. The final vapour pressure of the solution is 400 \( \mathrm{mm} \) of Hg. The rate constant of the
polymerisation reaction is Assume negligible volume change on
mixing and polymerisation and ideal behaviour for the final solution:
A \( .1 .0 \times 10^{-4} \)
В. \( 3.0 \times 10^{-4} \)
c. \( 2.0 \times 10^{-4} \)
D. None of these
Subject: Chemistry
Assertion
Displacement reactions of chlorine, bromine and iodine using fluorine are not generally carried out in aqueous Solution.
Reason
Fluorine being highly reactive attacks
water and displaces the oxygen of
water.
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
If \( H \) is harmonic mean between \( P \) and
\( Q . \) Then the value of \( \frac{\boldsymbol{H}}{\boldsymbol{P}}+\frac{\boldsymbol{H}}{\boldsymbol{Q}} \) is
\( A \cdot 2 \)
в. \( \frac{P Q}{P+Q} \)
c. \( \frac{P+Q}{P Q} \)
D. None of these
Subject: Biology
Read the given statements and select
the correct option
Statement 1: Ethylene is a gaseous hormone.
Statement 2 : Ethylene causes climacteric ripening of fruits.
A. Both statements 1 and 2 are correct
B. Statement 1 is correct but statement 2 is incorrect
c. Statement 1 is incorrect but statement 2 is correct
D. Both statements1 and 2 are incorrect
Subject: Maths
Solve the following pair of equations by
reducing them to a pair of linear
equations:
\( \frac{1}{(3 x+y)}+\frac{1}{(3 x-y)}= \)
\( \frac{3}{4}, \frac{1}{2(3 x+y)}-\frac{1}{2(3 x-y)}=\frac{-1}{8} \)
A \( . x=2, y=7 \)
в. \( x=5, y=0 \)
c. \( x=1, y=1 \)
D. \( x=2, y=3 \)
Subject: Chemistry
According to Rutherford, the electron revolves around the nucleus in definite
orbits but :
A. Rutherford did not specify the number of orbits and the number of electrons in each orbit
B. Rutherford did specify the number of orbits and the number of electrons in each orbit
C. Rutherford did not specify the number of orbits and the number of protons in each orbit
D. Rutherford did not specify the number of orbits and the number of neutrons in each orbit
Subject: Physics
A body of mass \( \mathrm{m} \) is placed on earth surface which is taken from earth
surface to a height of \( \boldsymbol{h}=\mathbf{3} \boldsymbol{R} \) then
change in gravitational potential energy is:
\( ^{A} \cdot \frac{m g R}{4} \)
в. \( \frac{2}{3} m g R \)
c. \( \frac{3}{4} m g R \)
D. \( \frac{m g R}{2} \)
Subject: Physics
\( A \) and \( B \) are two identical spherical
charged bodies which repel each other with force \( F, \) kept at a finite distance apart A third uncharged sphere of the same size is brought in contact with sphere \( \mathrm{B} \) and removed. It is then kept at mid-point of \( A \) and \( B \) find the magnitude of force on \( \mathbf{C} \)
\( A \cdot F / 2 \)
B. F/8
\( c \cdot F \)
D. zero
Subject: Chemistry
The energy required to brake one mole
of \( C l-C l \) bonds in \( C l_{2} \) is
\( 242 k j m o l^{-1} . \) The longest wavelength
of light capable of breaking single \( C l \)
\( C l \) bond is:
\( \left(c=3 \times 10^{8} m s^{-} 1 \text { and } N_{A}=6.02 \times\right. \)
\( \left.10^{23} m o l^{-1}\right) \)
A . \( 494 n m \)
В. 594 пт
\( c .640 n m \)
D. 700 nm
Subject: Maths
Solve the differential equation : \( \boldsymbol{y}+ \)
\( \boldsymbol{x} \frac{d \boldsymbol{y}}{d \boldsymbol{x}}=\boldsymbol{x}-\boldsymbol{y} \frac{d \boldsymbol{y}}{d \boldsymbol{x} \boldsymbol{x}} \)
Subject: Maths
\( \operatorname{Let} f(x)=\left\{\begin{array}{ll}x, & \text { if } x \text { is irrational } \\ 0, & \text { if is rational }\end{array}\right. \)
then fis
A. Continuous everywhere
B. Discontinuous everywhere
c. continuous only at \( x=0 \)
D. continuous at all rational numbers
Subject: Maths
n Fig., the side \( Q R \) of \( \triangle P Q R \) is produced
to a point \( S \) If the bisectors of \( \angle P Q R \) and \( \angle P R S \)
meet at point \( T, \) then prove that \( \angle \mathrm{QTR}=\frac{1}{2} \angle \mathrm{QPR} \)
Subject: Chemistry
The following reaction is used for the
preparation of oxygen gas in the laboratory \( 2 K C l O_{3}(s) \frac{\text {Heat}}{\text {Catalyst}} 2 K C l(s)+3 O_{2}(g) \)
Which of the following statement is correct about the reaction?
A. It is a decomposition reaction and endothermic in nature
B. It is a combination reaction
c. It is a decomposition reaction and accompanied by release of heat
D. It is a photochemical decomposition reaction and exothermic in nature
Subject: Maths
The distance of point \( \boldsymbol{P}\left(\boldsymbol{x}_{1}, \boldsymbol{y}_{1}, \boldsymbol{z}_{1}\right) \) to
the plane \( a x+b y+c z+D=0 \) is
given by
A \( \cdot \frac{\left|a x_{1}+b y_{1}+c z_{1}-d\right|}{\sqrt{a+b+c}} \)
B. \( \frac{\left|a x_{1}+b y_{1}+c z_{1}\right|}{\sqrt{a^{2}+b^{2}+c^{2}}} \)
c. \( \frac{\left|a x_{1}+b y_{1}+c z_{1}-d\right|}{\sqrt{a^{2}+b^{2}+c^{2}}} \)
D. None of these
Subject: Chemistry
IUPAC name of DDT is:
A. \( 1,1^{\prime}-(2,2,2-\text { Trichloroethane- } 1,1-\text { diyl }) \) bis \( (4- \) chlorobenzene)
B. p, p-dichloro diphenyl trichloro ethene
C. \( p, p \) -dichloro diphenyl trichloro benzene
D. p, p-tetra chloro ethane
Subject: Chemistry
An aqueous solution of aniline of concentration \( 0.24 M \) is prepared. What
concentration of sodium hydroxide is needed in this solution so that
anilinium ion concentration remains at
\( 1 \times 10^{-8} M ? \)
\( \left(\boldsymbol{K}_{\boldsymbol{a}} \text { for } \boldsymbol{C}_{\boldsymbol{6}} \boldsymbol{H}_{\boldsymbol{5}} \boldsymbol{N} \boldsymbol{H}_{\boldsymbol{3}}^{+}=\boldsymbol{2} . \boldsymbol{4} \times \boldsymbol{1} \boldsymbol{0}^{-\boldsymbol{5}} \boldsymbol{M}\right) \)
Subject: Chemistry
\( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) is treated with marble, it
releases which
A \( \cdot C O_{2}, \) turns lime water milky
B. \( H_{2} \), burns with a pop sound
c. \( O_{2} \), rekindles a burning spirit
D. none of the above
Subject: Physics
A rod bent in right angle along its centre
line, is placed on a rough horizontal
fixed cylinder of radius \( R \) as shown in
fig. Mass of rod is \( 2 m \) and rod is in
equilibrium. Assume that friction force
on rod at \( A \) and \( B \) are equal in
magnitude

This question has multiple correct options
A. Normal force applied by cylinder on rod at \( A \) is \( 3 m g / 2 \)
B. Normal force applied by cylinder on rod at \( B \) must be zero
C. Friction force acting on rod at \( B \) is upward
D. Normal force applied by cylinder on rod at \( A \) is \( \mathrm{mg} \)
Subject: Physics
A disc rotates about its axis of
symmetry in a horizontal plane at a steady rate of 3.5 revolutions per second. A coin placed at a distance of \( 1.25 \mathrm{cm} \) from the axis of rotation
remains at rest on the disc. The
coefficient of friction between the coin
and the disc is :
A. 0.5
B. 0.3
\( c . \) о.
D. 0.60
Subject: Physics
Masses of three wires of the same
metal are in the ratio 1: 2: 3 and their
lengths in the ratio \( 3: 2: 1 . \) Electrical
resistances of these wires will be in the
ratio
A. 1: 2: 3
B. 3: 2: 1
c. 1: 6: 27
D. 27: 6: 1
Subject: Physics
If \( \overline{\boldsymbol{F}} \) is the force and \( \bar{r} \) is the radius
vector, then the torque is :
A \( \cdot \bar{r} \times \bar{F} \)
в. \( \bar{r} \bar{F} \)
c. \( |\bar{r}| .|\bar{F}| \)
D \( \cdot \frac{|\bar{r}|}{|\bar{F}|} \)
Subject: Chemistry
The correct order for the increasing
extent of hydrolysis is:
\( \mathbf{A} \cdot P O_{4}^{3-}<H P O_{4}^{2-}<H_{2} P O_{4}^{-} \)
B. \( H_{2} P O_{4}^{-}<H P O_{4}^{2-}<P O_{4}^{3-} \)
\( \mathbf{c} \cdot H P O_{4}^{2-}<P O_{4}^{3-}<H_{2} P O_{4}^{-} \)
D \( \cdot P O_{4}^{3-}<H_{3} P O_{4}^{-}<H P O_{4}^{2-} \)
Subject: Physics
What is the mass of one atom of \( C-12 \)
in grams?
\( \mathbf{A} \cdot 1.992 \times 10^{-23} \mathrm{gm} \)
B . \( 1.989 \times 10^{-23} \mathrm{gm} \)
C \( \cdot 1.892 \times 10^{-23} \mathrm{gm} \)
D. \( 1.965 \times 10^{-23} \mathrm{gm} \)
Subject: Chemistry
Select the correct statement \( (s) \)
A. \( \mathrm{HCl} \) and \( \mathrm{HF} \) do not from free radical easily due to larger bond-energy
B. HI with a minimum bond energy is every reactive and
instead from \( \mathrm{I}_{2} \)
C. Both (a) and (b)
D. None of the above
Subject: Physics
A particle is moving in a potential region given by \( U=K\left(x^{2}+y^{2}+z^{2}\right) \)
The force acting on the particle is given by:
A . \( -2 K(x \hat{i}+y \hat{j}+z \hat{k}) \)
B . \( K(x \hat{i}+y \hat{j}+z \hat{k}) \)
c. \( \frac{K}{2}(x \hat{i}+y \hat{j}+z \hat{k}) \)
D. \( K\left(x^{2} \hat{\imath}+y^{2} \hat{\jmath}+z^{2} \hat{k}\right) \)
Subject: Maths
Assertion
If \( \boldsymbol{P}(\boldsymbol{A} / \boldsymbol{B})=\boldsymbol{P}(\boldsymbol{B} / \boldsymbol{A}) \cdot \mathbf{A}, \mathrm{B} \) are two non
mutually exclusive events then
\( \boldsymbol{P}(\boldsymbol{A})=\boldsymbol{P}(\boldsymbol{B}) \)
Reason
For non mutually exclusive events
\( (A \cap B) \neq \phi \) and \( P(A / B)= \)
\( \frac{\boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})}{\boldsymbol{P}(\boldsymbol{B})}, \boldsymbol{P}(\boldsymbol{B} / \boldsymbol{A})=\frac{\boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})}{\boldsymbol{P}(\boldsymbol{A})} \)
A. Both Assertion \& Reason are individually true \& Reason is correct explanation of Assertion
B. Both Assertion \& Reason are individually true but Reason is not the , correct (proper) explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
Subject: Chemistry
The two compounds \( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C} \|_{2}-\boldsymbol{C H}_{2}- \)
\( \boldsymbol{C H}_{3} \) and \( \boldsymbol{C H}_{3}-\stackrel{\boldsymbol{O} \|}{\boldsymbol{C}}-\underbrace{\boldsymbol{C H}_{3}}_{\mid \boldsymbol{C H}_{3}}-\boldsymbol{C H}_{3} \)
may be considered as:
A. position isomers
B. metamers
c. stereoisomers
D. tautomers
Subject: Maths
\( \mathbf{f} \boldsymbol{A}=\left[\begin{array}{ccc}-\mathbf{1} & \mathbf{2} & \mathbf{0} \\ -\mathbf{1} & \mathbf{1} & \mathbf{1} \\ \mathbf{0} & \mathbf{1} & \mathbf{0}\end{array}\right], \) Show that
\( \boldsymbol{A}^{2}=\boldsymbol{A}^{-1} \)
Subject: Maths
Evaluate the following definite integrals as limit of sums.
\( \int_{a}^{b} x d x \)
A \( \cdot b^{2}+a^{2} \)
B. \( \frac{b^{2}-a^{2}}{2} \)
c. \( a^{2}-b^{2} \)
D. \( a^{2}+b^{2} \)
Subject: Physics
The magnetic field intensity due to a solenoid at end point \( \boldsymbol{P} \) is :
A. \( \mu_{0} n I \)
в. \( \frac{\mu_{0} n I}{2} \)
c. \( \frac{\mu_{0} n I}{2}(\cos \theta-\cos \phi) \)
D. \( \frac{\mu_{0} n I}{2}(\sin \theta-\sin \phi) \)
Subject: Chemistry
For combustion of 1 mole of benzene at
\( 25^{0} C, \) the heat of reaction at constant
pressure is - 780.9 kcal. What will be the
heat of reaction at constant volume?
\( \boldsymbol{C}_{\boldsymbol{6}} \boldsymbol{H}_{\boldsymbol{6}(\boldsymbol{I})}+\boldsymbol{7} \frac{1}{2} \boldsymbol{O}_{2(\boldsymbol{g})} \rightarrow \boldsymbol{6} \boldsymbol{C} \boldsymbol{O}_{2(\boldsymbol{g})}+ \)
\( \mathbf{3} \boldsymbol{H}_{2} \boldsymbol{O}_{(l)} \)
A . -781.8 kcal
в. -780.0 kcal
c. +781.8 kcal
D. +780.0 kcal
Subject: Chemistry
(a) Number of compounds which are aromatic \( =\boldsymbol{w} \)
(b) Number of compounds which are
non-aromatic \( =x \)
(c) Number of compounds which are
anti-aromatic \( =\boldsymbol{y} \)
(d) Number of compounds which are readily undergo Dimerization at room
temperature \( =z \)
Sum of \( \boldsymbol{w} \) \( v+x+y+z= \)
Subject: Maths
Factorise the expressions and divide
them as directed.5pq \( \left(p^{2}-q^{2}\right) \div \)
\( \mathbf{2} p(\boldsymbol{p}+\boldsymbol{q}) \)
A \( \cdot \frac{5}{2} q(p-q) \)
в. \( \frac{3}{2} p q \)
c. \( \frac{5}{2} q(p+q) \)
D \( \cdot \frac{2}{5} q(p q) \)
Subject: Physics
The \( x \) and \( y \) coordinates of a particle at
any time \( t \) are given by \( x=2 t+4 t^{2} \) and
\( \boldsymbol{y}=\mathbf{5} \boldsymbol{t}, \) where \( \mathbf{x} \) and \( \mathbf{y} \) are in meter and \( \boldsymbol{t} \)
in second. The acceleration of the
particle at \( t=5 s \) is:
A. \( 40 \mathrm{ms}^{-2} \)
B . \( 20 \mathrm{ms}^{-2} \)
\( c \cdot 8 m s^{-2} \)
D. zero
Subject: Physics
In the adjoining diagram \( \boldsymbol{R}_{1}= \) \( \mathbf{1 0 \Omega}, \boldsymbol{R}_{2}=\mathbf{2 0 \Omega}, \boldsymbol{R}_{3}=\mathbf{4 0 \Omega}, \boldsymbol{R}_{4}=\mathbf{8 0 \Omega} \)
and \( V_{A}=5 V, V_{B}=10 V, V_{C}= \)
\( 20 V, V_{D}=15 V . \) The current in the
resistance \( \boldsymbol{R}_{1} \) will be
A. 0.4 A towards 0
B. 0.4 A away from 0
\( c . \) 0.6 A towards 0
D. 0.6 A away from 0
Subject: Physics
Two balls are dropped from the same
height from places \( A \) and \( B \). The body at
\( B \) takes two seconds less to reach the
ground at \( B \) strikes the ground with a
velocity greater than at \( A \) by \( 10 m / s \) The product of the acceleration due to gravity at the two places \( A \) and \( B \) is:
A . 5
B . 25
c. 125
D. 12.5
Subject: Maths
The area of a triangle is computed using the formula \( S=\frac{1}{2} b c \sin A . \) If the relative errors made in measuring b, \( c \) and calculating \( \mathrm{S} \) are respectively 0.02
0.01 and 0.13 the approximate error in \( A \) when \( A=\pi / 6 \) is
A . 0.05 radians
B. 0.01 radians
c. 0.05 degree
D. 0.01 degree
Subject: Physics
A non-zero external force acts on a
system of particles. The velocity and acceleration of the centre of mass are
found to be \( v_{0} \) and \( a_{C} \) respectively at
any instant \( t . \) It is possible that
(i) \( \boldsymbol{v}_{\mathbf{0}}=\mathbf{0}, \boldsymbol{a}_{\boldsymbol{C}}=\mathbf{0} \)
(ii) \( \boldsymbol{v}_{0} \neq \mathbf{0}, \boldsymbol{a}_{C}=\mathbf{0} \)
(iii) \( \boldsymbol{v}_{0}=\mathbf{0}, \boldsymbol{a}_{C} \neq \mathbf{0} ;(\text { iv }) \boldsymbol{v}_{\mathbf{0}} \neq \mathbf{0}, \boldsymbol{a}_{C} \neq \mathbf{0} \)
Then
A. (iii) and (iv) are true
B. (i) and (ii) are true
\( c . \) (i) and (iii) are true
D. (i), (iii) and (iv) are true
Subject: Maths
Find the value of \( \boldsymbol{X} \)
\( \mathbf{A} \cdot 60^{\circ} \)
B. \( 70^{\circ} \)
\( \mathbf{c} \cdot 80^{\circ} \)
\( \mathbf{D} \cdot 90^{\circ} \)
Subject: Physics
For an LCR circuit, the power transferred
from the driving source to the driven
oscillator is \( \boldsymbol{P}=\boldsymbol{I}^{2} \boldsymbol{Z} \) cos \( \boldsymbol{p} \) Then
A. the power factor \( \cos \phi>0, P>0 \)
B. the driving force can give no energy to the oscillator (P \( =0 \) ) in some cases.
C. the driving force cannot syphon Out (P \( <0 \) ) the energy out of oscillator.
D. all of these.
Subject: Maths
\( \frac{x^{3}}{x^{2}-x+2}=x+k-\left[\frac{x+2}{x^{2}-x+2}\right] \Rightarrow \)
\( \mathbf{k}= \)
\( \mathbf{A} \cdot \mathbf{4} \)
B . 2
\( c \cdot 1 \)
\( D \)
Subject: Maths
The value of the integral \( \int_{-\pi}^{\pi}(\cos a x- \) \( \sin b x)^{2} d x, \) where \( a \) and \( b \) are integers,
is
A \( .2 \pi(1+a+b) \)
B. 0
c. \( \pi \)
D. \( 2 \pi \)
Subject: Maths
Identify the type of set \( \boldsymbol{A}=\{\boldsymbol{x} \mid \boldsymbol{x} \epsilon \boldsymbol{R}, \boldsymbol{2} \leq \boldsymbol{x} \leq \boldsymbol{3}\} \)
A. Finite Set
B. Infinite Set
c. Null set
D. singleton set
Subject: Chemistry
The aufbau principle is violated in
\( 2 s \)
\[
2 p x \quad 2 p y \quad 2 p z
\]
This question has multiple correct options
\( \mathbf{A} \)
\( \uparrow \downarrow \quad \uparrow \downarrow \)
B.
\( \uparrow \)
\( \uparrow \downarrow \)
\[
\uparrow
\]
c.
\( \uparrow \downarrow \)
\( \uparrow \)
\( \uparrow \)
D.
\( \uparrow \downarrow \quad \uparrow \downarrow \)
Subject: Physics
Assertion
If an object is submerged in fluid at rest, the fluid exerts a force on its
surface.
Reason
The force exerted by the fluid at rest has to be parallel to the surface in contact
with it.
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