AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
The area of cross-section of the two
arms of a hydraulic press are \( 1 \mathrm{cm}^{2} \) and
\( 10 \mathrm{cm}^{2} \) respectively (figure). A force of \( 50 \mathrm{N} \) is applied on the water in the thicker arm. What force should be
applied on the water in the thinner arm
so that the water may remain
in equilibrium?
A. 5 N
B. 10 N
\( c \cdot 25 N \)
D. 50 N
Subject: Physics
Masses \( 8,2,4,2 \mathrm{kg} \) are placed at the corners \( A, B, C, D \) respectively of a square ABCD of diagonal 80 cm. The distance of center of mass from A is:
A. 20 cm
B. 30cm
c. \( 40 \mathrm{cm} \)
D. 60cm
Subject: Physics
The absolute refractive index of glass
and water are \( 3 / 2 \) and \( 4 / 3, \) respectively. If the speed of light in glass is \( 2 \times 10^{8} \)
\( \mathrm{m} / \mathrm{s}, \) calculate the speed of light in :
(a) vacuum
(b) water
Subject: Chemistry
In which of the following reactions, \( \boldsymbol{K}_{\boldsymbol{p}} \)
is less than \( K_{C} ? \)
A \( \cdot N_{2} O_{4(g)} \rightleftharpoons 2 N O_{2(g)} \)
B. \( 2 H I_{(g)} \rightleftharpoons H_{2(g)}+I_{2(g)} \)
\( \mathrm{c} \cdot 2 S O_{2(g)}+O_{2(g)} \rightleftharpoons 2 S O_{3(g)} \)
D. \( N_{2(g)}+O_{2(g)} \rightleftharpoons 2 N O_{(g)} \)
Subject: Chemistry
Variation of equilibrium constant K for the reaction \( ; 2 A(s)+B(g) \rightleftharpoons \)
\( C(g)+2 D(g) \) is plotted against
absolute \( \mathrm{T} \) in figure as- \( \ln \boldsymbol{K} \boldsymbol{V} \boldsymbol{s}(\mathbf{1} / \boldsymbol{T}) \)
This question has multiple correct options
A. the forward reaction is exothermic
B. the forward reaction is endothermic
c. the slope of line is proportional to \( \Delta H \)
D. adding 'A' 'favours forward reaction
E. removing C favours forward reaction
Subject: Chemistry
At \( 27^{\circ} \mathrm{C} \) two moles of an ideal
monoatomic gas occupy a volume \( V \) The gas expands adiabatically to a
volume \( 2 \mathrm{V} \). Calculate the final
temperature of the gas.
A \( \cdot T_{f}=388.99 \mathrm{K} \)
в. \( T_{f}=288.99 \mathrm{k} \)
c. \( T_{f}=188.99 \mathrm{k} \)
D. \( T_{f}=588.99 \mathrm{K} \)
Subject: Physics
The electromagnetic waves travel with
A. the same speed in all media
B. the speed of sound in free space
C . the speed of light \( c=3 \times 10^{8} \mathrm{ms}^{-1} \) in solid medium
D. the speed of light \( c=3 \times 10^{8} \mathrm{ms}^{-1} \) in fluid medium
E. the speed of light \( c=3 \times 10^{8} m s^{-1} \) in free medium
Subject: Maths
In an acute angled triangle \( A B C \), the
minimum value of \( \tan ^{n} A+\tan ^{n} B+ \)
\( \tan ^{n} C . \) is
\( (\text { When } n \epsilon N, n>1) \)
A \( \cdot \frac{n}{3} \)
B. \( 3^{n} \)
c. \( \frac{n}{3}^{+1} \)
D. \( _{3} \frac{n}{2}-1 \)
Subject: Maths
Simplify \( \left(x^{2}-5\right)(x+5)+25 \)
A \( \cdot x^{2}(x+5)-5(x+5)+15 \)
B . \( x^{2}(x+5)-5(x-5)+25 \)
c. \( x^{2}(x+5)-5(x+5)+25 \)
D. \( x^{2}(x+5)-(x+5)+25 \)
Subject: Chemistry
A mixture of \( a \) mol of \( C_{3} H_{8} \) and \( b \) mol of
\( C_{2} H_{4} \) was kept is a container of \( V \) L
which exerts a pressure of 4.93 atm at temperature T. Mixture was burnt in
presence of \( O_{2} \) to convert \( C_{3} H_{8} \) and
\( C_{2} H_{4} \) into \( C O_{2} \) in the container at the
same temperature. The pressure of gases after the reaction and attaining the thermal equilibrium with atmosphere at temperature T was
found to be 11.08 atm.

The mole fraction of \( C_{3} H_{8} \) in the
mixture is :
A .0 .25
в. 0.75
\( c \cdot 0.45 \)
D. 0.55
Subject: Physics
In the circuit shown in figure, ammeter
and voltmeter are ideal. If \( \boldsymbol{E}=\mathbf{4} \boldsymbol{V}, \boldsymbol{R}= \)
\( 9 \Omega \) and \( r=1 \Omega, \) then readings of
ammeter and voltmeter are
This question has multiple correct options
A \( \cdot A_{m}=1 A \)
B . \( A_{m}=2 A \)
c. \( V_{m}=3 V \)
D. \( V_{m}=4 V \)
Subject: Maths
Solve for \( x \) and \( y: \) \( \boldsymbol{x}+\boldsymbol{y}=\frac{\boldsymbol{7} \boldsymbol{\pi}}{\boldsymbol{4}}, \frac{\sin \boldsymbol{x}}{\cos \boldsymbol{y}}=-\sqrt{\boldsymbol{2}} \)
Subject: Chemistry
When dry \( C l_{2} \) gas is passed over dry
slaked lime, the product obtained is having the formula:
A. \( C a O \)
B. \( C a(O C l)_{2} \)
\( \mathrm{c} \cdot \mathrm{CaOCl} \)
D. \( C a C l_{2} O_{2} \)
Subject: Maths
Formulate the equations for the above problem. \( (x \text { and } y \text { are the number of units of } A \)
and \( B \) manufactured in a day
respectively)
A. \( 15 x+5 y \leq 10 ; 24 x+14 y \geq 1000 \)
B. \( 15 x+5 y \leq 600 ; 24 x+14 y \geq 1000 \)
c. \( 5 x+15 y \leq 600 ; 24 x+14 y \geq 1000 \)
D. \( 5 x+15 y \leq 10 ; 24 x+14 y \geq 1000 \)
Subject: Maths
If \( 2 x+3 y+4=0 \) is the perpendicular
bisector of the segment joining the points \( \boldsymbol{A}(\mathbf{1}, \mathbf{2}) \) and \( \boldsymbol{B}(\boldsymbol{a}, \boldsymbol{b}), \) then the
value of \( a+b \) is
A \( \cdot-\frac{81}{13} \)
B. \( -\frac{136}{13} \)
c. \( -\frac{135}{13} \)
D. \( -\frac{134}{5} \)
Subject: Chemistry
The ground state electronic configurations of the elements, U, \( \mathrm{V}, \mathrm{W} \) \( x \) and \( Y \) (these symbols do not have any
chemical significance) are as follows:
U \( 1 s^{2} 2 s^{2} 2 p^{3} \)
\( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{1} \)
W \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{2} \)
\( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{5} 4 s^{2} \)
\( Y 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{10} 4 s^{2} 4 p^{6} \)
Determine which sequence of elements
satisfy the following statements:
(i) Element forms a carbonate which is
not decomposed by heating
(ii) Element is most likely to form coloured ionic compounds
(iii) Element has largest atomic radius
(iv) Element forms only acidic oxide
A. vw y u
в. \( \vee \times Y \) w
c. \( v \) w \( Y x \)
D. \( v \times w u \)
Subject: Physics
A ray of light is incident on the plane mirror at rest. The mirror starts turning
at a uniform acceleration of \( \pi r a d / s^{2} \) about an axis in plane of mirror. The reflected ray, at the end of \( \frac{1}{4} s \) must have turned through
A \( .90^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 22.5^{\circ} \)
D. \( 11.25^{\circ} \)
Subject: Physics
A coil of area \( 80 \mathrm{cm}^{2} \) and number of
turns 50 is rotating about an axis perpendicular to a magnetic field of 0.05 Tesla at 2000 rotations per minute The maximum value of emf induced in
¡it will be
A . \( 200 \pi \) volt
в. \( \frac{10 \pi}{3} \) volt
c. \( \frac{4 \pi}{3} \) volt
D. \( \frac{2}{3} \) volt
Subject: Physics
A thin insulating ring of radius \( R \) has a
uniform linear charge density \( \lambda \). Now a
charge \( Q_{0} \) is placed at centre of this ring. The increment in the stretching
force of the wire due to the charge \( Q_{0} \)
is:
A. \( \frac{Q_{0} \lambda}{2 \pi \varepsilon_{\Omega}} \)
в. \( \frac{Q_{0} \lambda}{4 \pi \varepsilon_{0} R} \)
c. \( \frac{3 Q_{0} \lambda}{8 \pi \varepsilon_{0} R} \)
D. \( \frac{3 Q_{0} \lambda}{4 \pi \varepsilon_{0} R} \)
Subject: Chemistry
Which one of the following corresponds to a photon of highest energy?
A \( . \lambda=300 n m \)
В . \( v=3 \times 10^{8} s^{-1} \)
c. \( v=30 c m^{-1} \)
D . \( \varepsilon=6.626 \times 10^{-27} J \)
Subject: Chemistry
The compounds which have peroxo
linkage is/are
This question has multiple correct options
A \( \cdot H_{2} S_{2} O_{3} \)
в. \( H_{2} S O_{5} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{S}_{2} \mathrm{O}_{7} \)
D. \( H_{2} S_{2} O_{8} \)
Subject: Maths
If \( a_{1}, a_{2}, a_{3}, \dots a_{n} \in R \) then \( (x- \)
\( \left.a_{1}\right)^{2}+\left(x-a_{2}\right)^{2}+\ldots\left(x-a_{n}\right)^{2} \)
assumes least value at \( \boldsymbol{x}= \)
A \( \cdot a_{1}+a_{2}+a_{3}+\ldots+a_{n} \)
В . \( a_{n} \)
\( \mathbf{c} \cdot n\left(a_{1}+a_{2}+\ldots+a_{n}\right) \)
D. \( \frac{\left(a_{1}+a_{2}+\ldots+a_{n}\right)}{n} \)
Subject: Physics
A turn of radius \( 20 \mathrm{m} \) is banked for the
vehicles going at a speed of \( 36 k m / h \). If
the coefficient of static friction between
the road and the tyre is \( 0.4 . \) What are the possible speeds of a vehicle so that it neither slips down nor skids up?
\( \left(g=9.8 m / s^{2}\right) \)
A \( \cdot 2.2 m s^{-1} \leq v \leq 4.2 m s^{-1} \)
B. \( 4.2 m s^{-1} \leq v \leq 15 m s^{-1} \)
c. \( 15 m s^{-1} \leq v \leq 18.5 m s^{-1} \)
D. \( 15 \mathrm{ms}^{-1} \leq v \leq 22.5 \mathrm{ms}^{-1} \)
Subject: Maths
\( \left|\begin{array}{ccc}1+a & 1 & 1 \\ 1 & 1+b & 1 \\ 1 & 1 & 1+c\end{array}\right|= \)
\( \boldsymbol{X} \boldsymbol{a b c}\left(1+\frac{1}{\boldsymbol{a}}+\frac{1}{\boldsymbol{b}}+\frac{1}{c}\right) . \) Find the value
of \( \boldsymbol{X} \)
Subject: Physics
A perfectly reflecting mirror has an area
of \( 1 \mathrm{cm}^{2} \). Light energy is allowed to fall
on it for \( 1 h \) at the rate of \( 10 W / c m^{2} . \) The force that acts on the mirror is:
В. \( 6.7 \times 10^{-8} N \)
\( \mathrm{c} \cdot 1.34 \times 10^{-7} \mathrm{N} \)
D. 2.4 \( \times 10^{-4} N \)
Subject: Physics
A source of sound is travelling with a velocity \( 40 \mathrm{km} / \mathrm{hr} \) towards an observer and emits sound of frequency 2000 Hz. If velocity of sound is \( 1220 \mathrm{km} / \mathrm{hr} \), then what is the apparent frequency heard by an observer?
A. 2210 нᅩ
в. 1920 нz
c. 2068 Нz
D. 2086 Нz
Subject: Chemistry
The solubility of \( A g C N \) in a buffer solution of \( \boldsymbol{p} \boldsymbol{H}=\mathbf{3} \) is:
\( \left[\text { Given } \boldsymbol{K}_{s p} \text { of } \boldsymbol{A} \boldsymbol{g} \boldsymbol{C} \boldsymbol{N}=\mathbf{1 . 2} \times \mathbf{1 0}^{-\mathbf{6}} \) and \right.
\( \boldsymbol{K}_{a} \) for \( \boldsymbol{H} \boldsymbol{C} \boldsymbol{N}=\boldsymbol{4} . \boldsymbol{8} \times 10^{-10} . \) Assume
that no cyano complex is formed.
A \( \cdot a=1.67 \times 10^{-5} M \)
В. \( a=1.58 \times 10^{-5} M \)
C \( . a=1.51 \times 10^{-5} M \)
D. None of these
Subject: Chemistry
Henry's law constant for oxygen
dissolved in water is \( 4.34 \times 10^{4} \) atm at
\( 25^{C} . \) If the partial pressure of oxygen in air is 0.4 atm. Calculate the
concentration (in moles per litre) of the dissolved oxygen in water in
equilibrium with air at \( 25^{\circ} C \)
\( \mathbf{A} \cdot 5.11 \times 10^{-4} \)
В. \( 5.11 \times 10^{-3} \)
c. \( 9.2 \times 10^{-6} \)
D. \( 0.92 \times 10^{-6} \)
Subject: Maths
The value of "c" if the line \( \boldsymbol{x}+\mathbf{4} \boldsymbol{y}=\mathbf{9} \)
pases through \( (\mathbf{5}, \boldsymbol{c}) \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. - 1
c. 0
D. None of these
Subject: Chemistry
Assertion
An ideal gas is not expected to show any cooling on free expansion.
Reason
Ideal gas does not exist but is useful
concept.
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. Assertion is incorrect but Reason is correct
Subject: Physics
A planoconvex lens fits exactly into a planoconcave lens. Their plane surface are parallel to each other. If the lenses are made of different materials of
refractive indices \( \mu_{1} \) and \( \mu_{2} \) and \( R \) is
the radius of curvature of the curved
surface of the lenses, then focal length of combination is
A \( \cdot \frac{R}{\mu_{1}-\mu_{2}} \)
В. \( \frac{2 R}{\mu_{1}-\mu_{2}} \)
c. \( \frac{R}{2\left(\mu_{1}-\mu_{2}\right)} \)
D. \( \frac{R}{2-\left(\mu_{1}-\mu_{2}\right)} \)
Subject: Maths
The equation of the hyperbola whose foci are \( (\mathbf{6}, \mathbf{5}),(-\mathbf{4}, \mathbf{5}) \) and eccentricity \( \mathbf{5} / \mathbf{4} \) is?
A \( \cdot \frac{(x-1)^{2}}{16}-\frac{(y-5)^{2}}{9}=1 \)
В. \( \frac{x^{2}}{16}-\frac{y^{2}}{9}=1 \)
c. \( \frac{(x-1)^{2}}{16}-\frac{(y-5)^{2}}{9}=-1 \)
D. \( \frac{(x-1)^{2}}{4}-\frac{(y-5)^{2}}{9}=1 \)
Subject: Maths
If \( f \) and \( g \) are two functions such that
\( (f g)(x)=(g f)(x) \) for all \( x . \) Then \( f \) and
\( g \) may be defined as
A \( \cdot f(x)=\sqrt{x}, g(x)=\cos x \)
B . \( f(x)=x^{3}, g(x)=x+1 \)
\( \mathbf{c} \cdot f(x)=x-1, g(x)=x^{2}+1 \)
D. \( f(x)=x^{m}, g(x)=x^{n} \) where \( m, n \) are unequal integers
Subject: Maths
Add the following algebraic expressions:
(i) \( 2 x^{2}+3 x+5,3 x^{2}-4 x-7 \)
(ii) \( x^{2}-2 x-3, x^{2}+3 x+1 \)
(iii) \( 2 t^{2}+t-4,1-3 t-5 t^{2} \)
(iv) \( \boldsymbol{x y}-\boldsymbol{y} \boldsymbol{z}, \boldsymbol{y} \boldsymbol{z}-\boldsymbol{x} \boldsymbol{z}, \boldsymbol{z} \boldsymbol{x}-\boldsymbol{x} \boldsymbol{y} \)
\( (v) a^{2}+b^{2}, b^{2}+c^{2}, c^{2}+a^{2}, 2 a b+ \)
\( 2 b c+2 c a \)
Subject: Maths
Forty persons were examined for their Haemoglobin \% in blood (in mg per 100
\( \mathrm{ml} \) ) and the results were grouped as
below:
Determine modal value of Haemoglobin \( \% \) in blood of persons.
Haemoglobins 5
\[
\%(\mathrm{mg} /
\]
13. -14 100mI)
No. of Persons
A. \( 3.71 \mathrm{mg} / 100 \mathrm{ml} \)
B. \( 14.71 \mathrm{mg} / 100 \mathrm{ml} \)
c. \( 15.71 \mathrm{mg} / 100 \mathrm{ml} \)
D. \( 16.71 \mathrm{mg} / 100 \mathrm{ml} \)
Subject: Chemistry
Electronic configuration of chlorine is :
A \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{1} 3 p^{6} \)
B . \( 1 s^{2} 2 s^{2} 2 p^{5} 3 s^{2} 3 p^{6} \)
c. \( 1 s^{2} 2 s^{2} 2 p^{6} 4 s^{2} 4 p^{5} \)
D. \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{5} \)
Subject: Physics
Two uniformly charged plates are pictured above, with four evenly spaced points shown along a horizontal lines between the plates.What is the correct
rank of strength of the electric field at the points, greatest first?
A. 1,2,3,4
B. 4, 3, 2,1
C. The electric field strength is the same at all points
D. 1 and 4 tie, 2 and 3 tie
\( \mathrm{E} \cdot 2 \) and 3 tie, 1 and 4 tie
Subject: Maths
If \( a, b, c \) and \( d \) are in \( G P, \) then \( (a+b+ \)
\( \boldsymbol{c}+\boldsymbol{d})^{2} \) is equal to:
\( \mathbf{A} \cdot(a+b)^{2}+(c+d)^{2}+2(b+c)^{2} \)
B. \( (a+b)^{2}+(c+d)^{2}+2(a+c)^{2} \)
\( \mathbf{C} \cdot(a+b)^{2}+(c+d)^{2}+2(b+d)^{2} \)
D. \( (a+b)^{2}+(c+d)^{2}+(b+c)^{2} \)
E \( \cdot(a+b)^{2}+(c+d)^{2}+(b-c)^{2} \)
Subject: Physics
In the shown figure the magnitude of
acceleration of centre of mass of the
system is \( \left(\boldsymbol{g}=\mathbf{1 0 m} \boldsymbol{s}^{-\mathbf{2}}\right) \)
A \( \cdot 4 m s^{-2} \)
B. \( 10 \mathrm{ms}^{-2} \)
c. \( 2 \sqrt{2} \mathrm{ms}^{-2} \)
\( D \cdot 5 m s^{-2} \)
Subject: Chemistry
Which of the following oxoacids of phosphorous is a reducing agent and a monobasic acid as well
A \( \cdot H_{4} P_{2} O_{5} \)
в. \( H P O_{3} \)
\( \mathrm{c} \cdot H_{3} P O_{3} \)
D. \( H_{3} P O_{2} \)
Subject: Maths
\( \left|\begin{array}{ccc}\mathbf{0} & \boldsymbol{p}-\boldsymbol{q} & \boldsymbol{p}-\boldsymbol{r} \\ \boldsymbol{q}-\boldsymbol{p} & \boldsymbol{0} & \boldsymbol{q}-\boldsymbol{r} \\ \boldsymbol{r}-\boldsymbol{p} & \boldsymbol{r}-\boldsymbol{q} & \boldsymbol{0}\end{array}\right| \) is equal to
A. \( p+q+r \)
B.
c. \( p-q-r \)
\( \mathbf{D} \cdot-p+q+r \)
Subject: Maths
A plane \( \pi \) makes intercept 3 and 4
respectively on z-axis and x-axis. If \( \pi \) is
parallel to y-axis, then its equation is
A. \( 3 x+4 z=12 \)
B. \( 3 z+4 x=12 \)
c. \( 3 y+4 z=12 \)
D. \( 3 z+4 y=12 \)
Subject: Physics
Assertion
For good conductors, the \( \boldsymbol{I}-\boldsymbol{V} \) graph is
a perfect straight line inclined to current axis.
Reason
By Ohm's law, voltage across the ends of a conductor is directly proportional to the resistance of the conductor.
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
The negative Zn pole of Daniel cell,
sending a constant current through a circuit, decreases in mass by 0.13 g in 30 minutes. If the chemical equivalent of Zn and Cu and 32.5 and 31.5 respectively, the increase in the mass of the positive Cu pole in this time is :
A. 0.180 g
B. 0.141g
c. \( 0.126 \mathrm{g} \)
D. 0.242
Subject: Maths
If \( f(x)=\left|\begin{array}{ccc}a & -1 & 0 \\ a x & a & -1 \\ a x^{2} & a x & a\end{array}\right|, \) by using
properties of determinants, find the
value \( \boldsymbol{f}(\mathbf{2 x})-\boldsymbol{f}(\boldsymbol{x}) \)
Subject: Physics
A charged particle \( A \) of charge \( q=2 C \)
has velocity \( \boldsymbol{v}=\mathbf{1 0 0} \boldsymbol{m} / \boldsymbol{s} . \) When it
passes through point \( A \) and has
velocity in the direction shown, the strength of magnetic field at point \( B \)
due to this moving charge is \( (r=2 m) \)
A \( .2 .5 \mu T \)
B. \( 5.0 \mu T \)
c. \( 2.0 \mu T \)
D. none of these
Subject: Maths
Find the value(s) of the parameter'a' (a
9) for each of which the area of the
figure bounded by the straight line \( y= \) \( \frac{a^{2}-a x}{1+a^{4}} \& \) the parabola \( y= \)
\( \frac{x^{2}+2 a x+3 a^{2}}{1+a^{4}} \) is the greatest
A \( \cdot a=2^{1 / 4} \)
В . \( a=5^{1 / 4} \)
c. \( a=7^{1 / 4} \)
Subject: Biology
Assertion
Death of companion cell leads to the death of sieve cells also.
Reason
Both companion and sieve are phloem
cells.
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 \( 2=10^{m} \) and \( 3=10^{n} \) then find the
value of 0.15
A \( \cdot 10^{n-m-1} \)
B . \( 10^{n-m+1} \)
c. \( 10^{n-m-2} \)
D. \( 10^{n-m}-m \)
Subject: Maths
Solve: \( \frac{\sin ^{3} \frac{x}{2}-\cos ^{3} \frac{x}{2}}{2+\sin x}=\frac{\cos x}{3} \)
A. \( x=(2 n+1) \frac{\pi}{2}, n \epsilon z \)
B \( \cdot x=(4 n+1) \frac{\pi}{2}, n \epsilon z \)
C \( \cdot x=(4 n+1) \frac{\pi}{4}, n \epsilon z \)
D \( \cdot x=(2 n+1) \frac{\pi}{4}, n \epsilon z \)
Subject: Chemistry
Anisole on reaction with chloromethane
in presence of anhydrous \( A l C l_{3} \) gives
A. o-methyl anisole and p-methoxy anisole
B. p-methyl anisole and p-methoxy anisole
c. o-methyl anisole and p-methyl anisole
D. o-methoxy acetphenone and p-methoxy acetophenone
Subject: Physics
\( A B C \) is an equilateral triangle with \( O \) as its centre, \( \vec{F}_{1}, \vec{F}_{2} \) and \( \vec{F}_{3} \) represent three forces acting along the sides \( A B, B C \) and \( A C \) respectively. If the
total torque about \( O \) is zero then the
magnitude of \( \vec{F}_{3} \) is?
A \( \frac{F_{1}+F_{2}}{2} \)
\( \mathbf{B} \cdot 2\left(F_{1}+F_{2}\right) \)
\( c \cdot F_{1}+F_{2} \)
D. \( F_{1}-F_{2} \)
Subject: Chemistry
\( \boldsymbol{C a} \boldsymbol{C O}_{3}+\boldsymbol{S i O}_{2} \rightarrow \)
A \( \cdot C a O+\operatorname{Si} C O_{3} \)
в. \( \mathrm{CaSiO}_{3}+\mathrm{SiO}_{2} \)
c. \( C a S i O_{3}+C a O \)
D. \( \mathrm{CaSiO}_{3}+\mathrm{CO}_{2} \)
Subject: Maths
n the following figure, \( \boldsymbol{O A}=\boldsymbol{O C} \) and
\( A B=B C . \) Prove that
\( \angle A O B=90^{\circ} \)
ii) \( \Delta A O D \cong \Delta C O D \)
iii) \( \boldsymbol{A} \boldsymbol{D}=\boldsymbol{C} \boldsymbol{D} \)
Subject: Maths
If order of matrix \( A \) is \( 4 \times 3 \) and order of
matrix \( B \) is \( 3 \times 5 \) then order of matrix
\( \boldsymbol{B}^{\prime} \boldsymbol{A}^{\prime} \) is:
\( \mathbf{A} \cdot 5 \times 2 \)
B. \( 4 \times 5 \)
\( \mathbf{c} \cdot 5 \times 4 \)
D. \( 3 \times 2 \)
Subject: Physics
A body is projected vertically upward
with a velocity of \( 10 m s^{-1} \). It reaches maximum height \( h \) at time \( t . \) In time \( \frac{t}{2} \) the height covered is
A \( \cdot \frac{h}{2} \)
в. \( \frac{2}{5} h \)
\( c \cdot \frac{3}{4} h \)
D. \( \frac{5}{8} h \)
Subject: Physics
A balloon is going upwards with velocity \( 12 \mathrm{m} / \mathrm{s} \). It releases a packet when it is a height of \( 65 \mathrm{m} \) from the ground. How much time will the packet take to reach the ground if \( g=10 m / s^{2} \)
A. 5 second
B. 6 second
c. 7 second
D. 8 second
Subject: Maths
Assertion
Consider two functions \( \boldsymbol{f}(\boldsymbol{x})=\mathbf{1}+ \)
\( e^{\cot ^{2} x} \) and \( g(x)=\sqrt{2|\sin x|-1}+ \)
\( \frac{1-\cos 2 x}{1+\sin ^{4} x} \)
Statement I: The solution of the
equation \( f(x)=g(x) \) is given by \( x= \) \( (2 n+1) \frac{\pi}{2}, \forall n \in I \)
Reason
Statement II: If \( f(x) \leq k \) and \( g(x) \leq k \)
(where \( k \in \boldsymbol{R} \) ), then solutions of the
equation \( f(x)=g(x) \) is the solution
corresponding to the equation \( f(x)=k \)
A. Statement I is true, Statement II is also true Statement II is the correct explanation of Stateme
B. Statement I is true, Statement II is also true Statement II is not the correct explanation of statement
c. Statement lis true, Statement II is false
D. Statement lis false, Statement II is true
Subject: Biology
Assume the cell has a diploid number of
4. If the above chromosomes are in the
tetrad or bivalent stage of meiosis, which statement below is correct about
the events of anaphase I?
A. Two of the tetrads will go to one cell, and two will go to the other
B. Sister chromatids will break apart and each will go in one of four cells
c. one member of each homologous pair will go into each of the two cells
D. The tetrads will separate but each new cell will still be diploid since each chromosome has two chromatids
Subject: Physics
Net magnetic field at the centre ofthe
circle 0 due to a current carrying
loop as shown in figure is \( \left(\boldsymbol{\theta}<\mathbf{1 8 0}^{\circ}\right) \)
A. zero
B. perpendicular to paper inwards
C. perpendicular to paper outwards
D. is perpendicular to paper inwards if \( \theta \leq 90^{\circ} \) and
perpendicular to paper outwards if \( 90^{0} \leq \theta<180^{\circ} \)
Subject: Physics
A circular loop of wire is in the same
place as an infinitely long wire carrying a constant current i. Four possible motion of the loop are marked by \( \mathrm{N}, \mathrm{E}, \mathrm{W} \)
and \( \mathrm{S} \) as shown.
A clockwise current is induced in the
loop when loop is pulled towards
\( A \)
B.
\( c \cdot w \)
\( D \)
Subject: Physics
A large hollow metal sphere of radius has a small opening at the top through which drops of mercury each of radius \( r \) and charged to a potential V fall into the
sphere and the potential becomes \( V^{\prime} \)
after \( \mathrm{N} \) drops fall into it. Then:
A. \( \mathrm{V}^{\prime}<\mathrm{V} \) for any value of \( \mathrm{N} \)
B. \( \mathrm{V}^{\prime}=\mathrm{V} \) for \( \mathrm{N}=1 \)
c. \( \mathrm{v}^{\prime}=\mathrm{v} \) for \( \mathrm{N}=\frac{\mathrm{R}}{\mathrm{r}} \)
D
Subject: Physics
constant \( \mathrm{k} \) are attached horizontally at the two ends of a uniform horizontally
rod \( A B \) of length \( \ell \) and mass \( m \). The rod
is pivoted at its centre 'O' and can rotate
freely in horizontal plane. The other ends
of the two spring are fixed to rigid supports as shown in figure. The rod is gently pushed through a small angle and released. The frequency of resulting
oscillation is:
\( \mathbf{A} \cdot \frac{1}{2 \pi} \sqrt{\frac{6 k}{m}} \)
B \( \cdot \frac{1}{2 \pi} \sqrt{\frac{2 k}{m}} \)
\( \mathbf{C} \cdot \frac{1}{2 \pi} \sqrt{\frac{k}{m}} \)
D. \( \frac{1}{2 \pi} \sqrt{\frac{3 k}{m}} \)
Subject: Chemistry
Balance the following equations by ion electron method:
\( \boldsymbol{I}_{2}+\boldsymbol{O H}^{-} \rightarrow \boldsymbol{I} \boldsymbol{O}_{3}^{-}+\boldsymbol{I}^{-}+\boldsymbol{H}_{2} \boldsymbol{O} \)
Subject: Chemistry
Naphthalene, a white solid used to
make moth balls has a vapour pressure
of \( 0.10 \mathrm{mm} \) Hg at \( 27^{\circ} \mathrm{C} . \) Hence
\( \boldsymbol{K}_{\boldsymbol{p}} \) and \( \boldsymbol{K}_{\boldsymbol{c}} \) for the equilibrium are:
\( \mathbf{C}_{\mathbf{1 0}} \mathbf{H}_{\mathbf{8}}(\mathbf{s}) \rightleftharpoons \mathbf{C}_{\mathbf{1 0}} \mathbf{H}_{\mathbf{8}}(\mathbf{g}) \)
A. 0.10,0.10
B . \( 0.10,4.1 \times 10^{-3} \)
c. \( 1.32 \times 10^{-4}, 5.34 \times 10^{-6} \)
D. \( 5.36 \times 10^{-6}, 1.32 \times 10^{-4} \)