AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
\( \boldsymbol{Y} \stackrel{\boldsymbol{N a}}{\longleftrightarrow} \boldsymbol{X} \stackrel{\boldsymbol{c o n c . H}_{2} \boldsymbol{S O}_{4}, \boldsymbol{4 1 3} \boldsymbol{K}}{\longrightarrow}\left(\boldsymbol{C}_{2} \boldsymbol{H}_{5}\right)_{2} \boldsymbol{O} \)
What are \( X \) and \( Y \) in the above reactions
\( ? \)
\( \mathbf{A} \cdot X-H_{3} C O H, Y-H_{3} C O N a \)
B \( \cdot X-C_{4} H_{9} O H, Y-C_{4} H_{9} O N a \)
\( \mathbf{c} \cdot X-C_{2} H_{5} O H, Y-C_{2} H_{5} O N a \)
D. \( X-C_{3} H_{7} O H, Y-C_{3} H_{7} O N a \)
Subject: Physics
When \( 1 F \) of electricity is passed
through acidulated water, \( O_{2} \) evolved is:
A \( \cdot 11.2 d m^{3} \)
B. \( 5.6 d m^{3} \)
c. \( 1.0 d m^{3} \)
D. \( 22.4 d m^{3} \)
Subject: Physics
A \( 0.5 m \) long solenoid of \( 10 t u r n s / c m \)
has area of cross-section \( 1 \mathrm{cm}^{2} \)
Calculate the voltage induced across its
ends if the current in the solenoid is
charged from \( 1 A \) to \( 2 A \) in \( 0.1 s \)
Subject: Chemistry
Fluorocarbons are effective scavengers
for ozone due to:
A. photolytic reaction of \( O_{2} \) producing \( C l \) radicals
B. photolytic decomposition of \( O_{3} \) producing \( O \) radicals
C. photolytic decomposition of \( O_{3} \) by \( C l \) radicals into \( O_{2} \)
D. photolytic production of oxides of nitrogen
Subject: Physics
A coil has an inductance of \( 0.7 ~ H \) and is
joined in series with a resistance of
220\Omega. When an alternating emf of \( 220 V \) at \( 50 ~ c p s \) is applied to it, then the
wattless component of the current in the circuit is (take \( 0.7 \pi=2.2) \)
\( \mathbf{A} \cdot 5 A \)
B. \( 0.5 A \)
\( \mathbf{c} \cdot 0.7 A \)
D. \( 7 A \)
Subject: Physics
A mass \( m_{1} \) of a substance of specific
heat capacity \( c_{1} \) at temperature \( t_{1} \) is
mixed with a mass \( m_{2} \) of other
substance of specific heat capacity \( c_{2} \)
at a lower temperature \( t_{2} . \) Deduce the
expression for the temperature of the mixture. State the assumption made, if
any.
A \( \cdot \frac{m_{1} t_{1}+m_{2} t_{2}}{m_{1}+m_{2}} \)
В. \( \frac{m_{1} t_{1}+m_{2} t_{2}}{m_{1} c_{1}+m_{2} c_{2}} \)
\( \mathbf{c} \cdot \frac{m_{1} c_{1}+m_{2} c_{2}}{m_{1}+m_{2}} \)
D. \( \frac{m_{1} c_{1} t_{1}+m_{2} c_{2} t_{2}}{m_{1} c_{1}+m_{2} c_{2}} \)
Subject: Physics
Two small balls \( A \) and \( B \) are made of
same material. \( \boldsymbol{A} \) is solid but \( \boldsymbol{B} \) is
hollow. These are connected by an ideal spring and this whole system is kept
over a smooth plank such that center of mass of two balls coincide with mid
point of the plank. Initially the spring is
compressed by certain amount and the plank is in horizontal position. Now we
release the system. Then:
A. Plank will rotate clock wise
B. Plank will rotate anti clock wise
c. Plank will not rotate
D. It will depend upon string constant
Subject: Chemistry
Assertion
The order of densities of the various
allotropes of phosphorus is as follows:
black phosphorus, red phosphorus, white phosphorus.
Reason
As tendency of polymerisation increases, the compactness of substance also increases.
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: Chemistry
A black compound of manganese reacts with a halogen acid to give greenish yellow gas. When excess of this gas
reacts with \( N H_{3} \) an unstable trihalide
is formed. In this process, the oxidation state of nitrogen changes from
A. 0 to -3
B. -3 to 0
\( \mathbf{c} \cdot-3 \) to +5
D. -3 to +3
Subject: Chemistry
Equilibrium constant for the given reaction is \( K=10^{20} \) at temperature
\( \mathbf{3 0 0} \boldsymbol{K} \)
\( \boldsymbol{A}(s)+\mathbf{2} \boldsymbol{B}(\boldsymbol{a} \boldsymbol{q} .) \rightleftharpoons \mathbf{2} \boldsymbol{C}(\boldsymbol{s})+\boldsymbol{D}(\boldsymbol{a} \boldsymbol{q} .) \)
\( \boldsymbol{K}=\mathbf{1} \mathbf{0}^{\mathbf{2 0}} \)
The equilibrium concentration of B
starting with a mixture of 1 mol \( / \) lit of A and \( 1 / 3 m o l / l i t \) of \( B \) at \( 300 K \) is
в. \( 2 \times 10^{-1} \)
c. \( 2 \times 10^{-11} \)
D. \( 10^{-10} \)
Subject: Chemistry
These questions consist of two statements each, printed as assertion and reason. While answering these questions you are required to choose anyone of the following five responses.
Assertion: Ozone is powerful oxidising
agent in comparison to \( \boldsymbol{O}_{\mathbf{2}} \)

Reason: Ozone is diamagnetic but \( \boldsymbol{O}_{2} \)
is paramagnetic.
A. If both assertion and reason are true and the reason is correct explanation of the assertion
B. If both assertion and reason are true but reason is not correct explanation of the assertion
c. If the assertion is true but reason is false
D. If both the assertion and reason are false
E. If the assertion is false but the reason is true
Subject: Physics
Statement 1:If \( \vec{A} \cdot \vec{B}=\vec{B} \cdot \vec{C} \) then \( \vec{A} \) may
not always be equal to \( \overrightarrow{\boldsymbol{C}} \) Statement 2: The dot product of two vector involves cosine of the angle
between the two vectors.
A. a) Statement- - is false, Statement- 2 is true
B. b) Statement-1 is true, Statement-2 is true, Statement
2 is a correct explanation for statement-
c. c) Statement- - is true, Statement-2 is true; Statement
2 is not a correct explanation for statement-
D. d) Statement-1 is true, Statement-2 is false
Subject: Chemistry
If the value of Avogadro number is \( 6.023 \times 10^{23} \) mol \( ^{-1} \) and the value of
Boltzmann constant is \( 1.380 \times \)
\( 10^{-23} J K^{-1}, \) then the number of
significant digits in the calculated value of the universal gas constant is :
A .4
B. 5
\( c \cdot 3 \)
D. 2
Subject: Biology
Assertion
ADH and RAAS work in response to low
blood volume and blood pressure.
Reason
ANF works in response to high blood
volume and blood pressure.
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
Figure shows two flasks connected to each other. The volume of the flask 1 is
twice that of flask 2. The system is filled with an ideal gas at temperature \( 100 \mathrm{K} \) and \( 200 \mathrm{K} \) respectively in the flasks. If the mass of the gas in \( 1 \mathrm{m} \), then what is the mass of the gas in flask 2 in equilibrium?
A . \( m \)
в. \( \frac{m}{2} \)
c. \( \frac{m}{4} \)
D. \( \frac{m}{8} \)
Subject: Chemistry
\( 0.53 \mathrm{g} \) of substance gave \( 1.158 \mathrm{g} \) of \( B a S O_{4} \) by Carius method. Calculate the
percentage of sulphur.
A . \( 42.10 \% \)
B . \( 23.3 \% \)
c. \( 32.03 \% \)
D. 30\%
Subject: Physics
Q Type your question-
to two ideal voltmeters \( V_{1} \& V_{2} \)
Assume that a voltmeter reads \( \Delta V= \)
\( -\int_{a}^{b} \vec{E} \cdot d \vec{\ell} \) between its terminals. A time varying magnetic field \( B(t) \) exists in a circular region of radius a and it is
directed into the plane of the figure
\( B(t)=B_{0} t \) where \( B_{0} \) is a positive
constant of proper dimensions and t is
the time. The emf induced in the circuit
is :
\( A \cdot 2 \pi a^{2} B_{0} \)
В \( \cdot \pi a^{2} B_{0} \)
c. \( \frac{a^{2} B_{0}}{2} \)
D・ \( \pi a^{2} B_{0} \)
Subject: Chemistry
Spectroscopy is:
A. the study of heat changes in a chemical reaction.
B. the use of the absorption, emission, or scattering of electromagnetic radiation by matter to study the matter or the chemical processes it undergoes.
C. the mathematical description of the motion and interaction of subatomic particles. It incorporates quantization of energy, wave-particle duality, the uncertainty principle, and their relationship to chemical processes.
D. none of the above
Subject: Maths
The radius of a sphere is changing at the rate of \( 0.1 \mathrm{cm} / \) sec. The rate of its
surface area when the radius is \( 200 \mathrm{cm} \)
is
A \( \cdot 8 \pi c m^{2} / \) sec
В . \( 12 \pi c m^{2} / \) sec
c. \( 160 \pi c m^{2} / \) sec
D. \( 200 \pi c m^{2} / \) sec
Subject: Maths
If \( \vec{a}, \vec{b}, \vec{c} \) are position vectors of the vertices \( A, B, C \) of a triangle \( A B C \)
show that the area of the triangle \( A B C \) is \( \frac{1}{2}[\vec{a} \times \vec{b}+\vec{b} \times \vec{c}+\vec{c} \times \vec{a}] . \) Also deduc
the condition for collinearity of the
points \( A, B \) and \( C \)
Subject: Physics
What was the average speed of the cyclist for the past hour when he travels at a constant \( 25 k m / h r \) for 30 minutes,
coasts for 15 minutes at a constant
\( 20 \mathrm{km} / \mathrm{hr} \) and then pedals at a
constant \( 40 \mathrm{km} / \mathrm{hr} \) for another 15
minutes?
A. \( 27.5 \mathrm{km} / \mathrm{hr} \)
B. \( 25 \mathrm{km} / \mathrm{hr} \)
c. \( 22.5 \mathrm{km} / \mathrm{hr} \)
D. \( 30 \mathrm{km} / \mathrm{hr} \)
E . \( 32.5 \mathrm{km} / \mathrm{hr} \)
Subject: Physics
Two wires \( A \) and \( B \) of same length are made of same material. The figure represents the load F versus extension
\( \Delta x \) graph for the two wires. Then:
A. the cross sectional area of A is greater than that of B.
B. the elasticity of B is greater than that of A.
C. the cross-sectional area of B is greater than that of A.
D. the elasticity of A is greater than that of B.
Subject: Maths
If \( \left|\begin{array}{lll}a & a^{3} & a^{4}-1 \\ b & b^{3} & b^{4}-1 \\ c & c^{3} & c^{4}-1\end{array}\right|=0 \) and \( a, b, c \) are all
distinct then \( a b c(a b+b c+c a) \) is equal
to
A \( . a+b+c \)
в. \( a b c \)
c. 0
D. none of these
Subject: Maths
For the function \( f(x)=e^{\cos x}, \) Rolle's
theorem is
A \( \cdot \) applicable, when \( \frac{\pi}{2} \leq x \leq \frac{3 \pi}{2} \)
B. applicable, when \( 0 \leq x \leq \frac{\pi}{2} \)
C . applicable, when \( 0 \leq x \leq \pi \)
D. applicable, when \( \frac{\pi}{4} \leq x \leq \frac{\pi}{2} \)
Subject: Maths
Let \( y=\left(1+x^{2}\right) \tan ^{-1}(x-x) \) and
\( f(x)=\frac{1}{2 x} \frac{d y}{d x}, \) then \( f(x)+\cot ^{-1} x \) is
equal to
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( \frac{\pi}{2} \)
c. \( -\frac{\pi}{2} \)
D.
Subject: Maths
Let \( \boldsymbol{f}: \mathbb{R} \rightarrow \mathbb{R} \) defined by \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \frac{a x^{2}+a x+b}{a x+b} \) then
A. \( f \) is many one
B. \( f \) is one-one
c. \( f \) is onto
D. range of \( f \) is not a single-tone set
Subject: Chemistry
Assertion
Water in liquid state is more stable
than ice at room temperature.
Reason
Water in liquid form has higher entropy
than ice.
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: Maths
In the given figure, if \( P Q R S \) is a
rectangle which one is true?
\( \mathbf{A} \cdot A r \Delta(A P S)=A r \Delta(Q R B) \)
B. \( P A=R B \)
\( \mathbf{c} \cdot A r(P Q S)=A r(Q R S) \)
D. All of the above
Subject: Chemistry
It has \( d^{2} s p^{2} \) hybridisation. \( \left(N H_{4}\right)_{2} C r_{2} O_{7} \) on heating gives a gas /vapour, which is also produced in significant quantity by:
(I) heating \( \boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{C l} \)
(II) heating \( C u S O_{4} 5 H_{2} O \)
(III) heating \( B a\left(N_{3}\right)_{2} \)
(IV) treating \( N a N O_{3} \) with \( Z n \) in basic medium.
A. Only III
B. ।, IV
c. only IV
D. ॥, II
Subject: Physics
A vessel \( A \) has volume \( V \) and vessel \( B \)
has volume \( 2 V \) Both contain some
water which has a constant volume.The
pressure in the space above water is \( p_{a} \)
for vessel \( \boldsymbol{A} \) and \( \boldsymbol{p}_{\boldsymbol{b}} \) for vessel \( \boldsymbol{B} \) ?
A \( \cdot p_{a}=p_{b} \)
в. \( p_{a}=2 p_{b} \)
\( \mathbf{c} \cdot p_{b}=2 p_{a} \)
\( \mathbf{D} \cdot p_{b}=4 p_{a} \)
Subject: Maths
The slope of a curve at each of its points is equal to the square of the abscissae of the point. Find the particular curve
through the point (-1,1) \( \mathbf{1}+\boldsymbol{y}=\boldsymbol{2} \boldsymbol{e}^{\boldsymbol{x}^{2} / \mathbf{2}} \)
Subject: Maths
Let the function \( f(x)=\sin x+\cos x \)
be defined in \( [0,2 \pi], \) then \( f(x) \)
A \( \cdot \) increases in \( \left(\frac{\pi}{4}, \frac{\pi}{2}\right) \)
B. decreases in \( \left[\frac{\pi}{4}, \frac{5 \pi}{4}\right] \)
C . increases in \( \left[0, \frac{\pi}{4}\right] \cup[\pi, 2 \pi] \)
D. decreases in \( \left[0, \frac{\pi}{4}\right) \cup\left(\frac{\pi}{2}, 2 \pi\right] \)
Subject: Physics
In Young's double slit experiment, one of the slit is wider than another, so that
amplitude of the light from one slit is
double of that from other slit. If \( \boldsymbol{I}_{m} \) be
the maximum intensity, the resultant intensity I when they interfere at phase difference \( \phi \) is given by
A \( \cdot \frac{I_{m}}{9}(4+5 \cos \phi) \)
в. \( \frac{I_{m}}{3}\left(1+2 \cos ^{2} \frac{\phi}{2}\right) \)
c. \( \frac{I_{m}}{5}\left(1+4 \cos ^{2} \frac{\phi}{2}\right) \)
D. \( \frac{I_{m}}{9}\left(1+8 \cos ^{2} \frac{\phi}{2}\right) \)
Subject: Physics
Two spherical soap bubbles of radii \( a \)
and \( b \) in vacuum coaleasce under
isothermal conditions. The resulting bubbles has a radius given by:
A \( \cdot \frac{(a+b)}{2} \)
B. \( \frac{a b}{a+b} \)
c. \( \sqrt{a^{2}+b^{2}} \)
\( \mathbf{D} \cdot a+b \)
Subject: Biology
What are \( P, Q, R, S \) in the given figure?
A. P- -Right ventricle, Q - Left ventricle, R - Right atrium
- Left atrium
B. P- Right atrium, Q - Left atrium, R - Right ventricle, S Left ventricle
c. P-Right ventricle, Q - Left atrium, R - Right atrium, S Left ventricle
D. P- -Right atrium, Q- Right ventricle, R - Left atrium, S Left ventricl
Subject: Physics
Consider a transparent hemisphere \( (n=2) \) in front of which a small object
is placed in air \( (n=1) \) as shown.
Consider a ray starting from \( \boldsymbol{O} \) which strikes the spherical surface at grazing
incidence \( (\boldsymbol{i}=\mathbf{9 0 ^ { \circ }}) . \) Taking \( \boldsymbol{x}=\boldsymbol{R}, \) what
will be the angle (from normal) at which
the ray may emerge from the plane
surface.
\( \mathbf{A} \cdot 90 \)
В. \( 0^{\circ} \)
\( c .30 \)
\( D \cdot 60 \)
Subject: Maths
If 0 is the origin and \( A_{n} \) is the point
with coordinates \( (\boldsymbol{n}, \boldsymbol{n}+\mathbf{1}) \) then
\( \left(O A_{1}\right)^{2}+\left(O A_{2}\right)^{2}+\ldots+\left(O A_{7}\right)^{2} \) is
equal to
Subject: Maths
A straight line L through the point (3,-2) is inclined at an angle 60 to the line \( \sqrt{\mathbf{3}} x+y=1 . \) If \( L \) also intersects
the \( x \) -axis, the equation of \( L \) is
A \( \cdot y+\sqrt{3} x+2-3 \sqrt{3}=0 \)
B . \( y-\sqrt{3} x+2+3 \sqrt{3}=0 \)
c. \( \sqrt{3} y-x+3+2 \sqrt{3}=0 \)
D. \( \sqrt{3} y+x-3+2 \sqrt{3}=0 \)
Subject: Physics
Figure show the lines of equipotentials
in the region. The potentials are shown with the equipotentials. If electric
intensities are \( E_{P} \) and \( E_{S}, \) then
\( \mathbf{A} \cdot E_{P}=E_{S} \)
В. \( E_{P}>E_{S} \)
\( \mathbf{c} \cdot E_{S}>E_{P} \)
D. \( E_{P}-E_{S}=0 \)
Subject: Physics
Figure shows three spherical shells in
separate situations, with each shell having the same uniform positive net
charge. Points 1,4 and 7 are at the same radial distances from the centre
of the their respective shells; so are
points 2,5 and \( 8 ; \) and so are points 3,6 and \( 9 . \) With the electric potential taken equals to zero at an infinite distance,
choose correct statement.
A. Point 3 has highest potential
B. Point 1,4 and 7 are at same potential
C. Point 3 has lowest potential
D. Point 5 and 8 are at same potential
Subject: Biology
Nucleosome contains
\( \mathbf{A} \cdot H_{2} A, H_{2} B, H_{3}, H_{4} \)
\( \mathbf{B} \cdot H_{3}, H_{4} \)
\( \mathbf{c} \cdot H_{2} A, H_{2} B, H_{3} \)
D. \( H_{1}, H_{2} A, H_{2} B, H_{3} \)
Subject: Physics
The surface energy of a liquid drop is \( \boldsymbol{E} \)
It is sprayed into 1000 equal droplets.
The work done in spraying is
\( \mathbf{A} \cdot 999 E \)
в. \( 99 E \)
\( \mathrm{c} .9 \mathrm{E} \)
D. \( E \)
Subject: Maths
If the lines given by \( 3 x+2 k y=2 \) and
\( \mathbf{2} \boldsymbol{x}+\mathbf{5} \boldsymbol{y}+\mathbf{1}=\mathbf{0} \) are parallel, then the
value of \( k \) is
A \( \cdot \frac{-5}{4} \)
B. \( \frac{2}{5} \)
c. \( \frac{15}{4} \)
D. \( \frac{3}{2} \)
Subject: Physics
The moments of inertia of a thin square
plate \( A B C D \) of uniform thickness
about an axis passing through the
centre \( \boldsymbol{O} \) and perpendicular to the plate
are
This question has multiple correct options
\( \mathbf{A} \cdot I_{1}+I_{2} \)
B. \( I_{3}+I_{4} \)
c. \( I_{1}+I_{3} \)
D. \( I_{2}+I_{3} \)
Subject: Chemistry
Which of the following molecules has the shortest carbon-carbon single bond length?
A. \( C H_{2}=C H-C-C H_{3} \)
в. \( C H_{2}=C H-C=N \)
c. \( C H_{2}=C H-C=O \)
D. \( C H_{2}=C H-C H=C H_{2} \)
Subject: Physics
A mass \( M \) is lowered with the help of a
string by a distance \( x \) at a constant
acceleration \( g / 2 . \) The work done by the string will be
A. \( M g x \)
в. \( -\frac{M g x}{2} \)
c. \( \frac{1}{2}^{M g x^{2}} \)
D. \( M g x^{2} \)
Subject: Maths
For \( \tan ^{-1}\left(\frac{1-x}{1+x}\right), 0 \leq x \leq 1 \)
What is the sum of the smallest and the
largest values of function.
A \( \cdot \frac{\pi}{4} \)
в. \( \frac{\pi}{2} \)
c. \( \frac{3 \pi}{4} \)
D. \( \frac{3 \pi}{2} \)
Subject: Physics
A capacitor of capacitance \( 10 \mu F \) is
charged a potential \( 50 V \) with a battery. The battery is now disconnected and an additional charge \( 200 \mu C \) is given to the positive plate of the capacitor. The potential difference across the
capacitor will be :
A . \( 50 V \)
B. \( 80 V \)
\( \mathbf{c} \cdot 100 V \)
D. \( 60 V \)
Subject: Chemistry
A drop of a solution (volume \( =0.05 m l \) )
contains \( 6 \times 10^{-7} \) mole of \( H^{+} \)
If the rate of disappearance of \( \boldsymbol{H}^{+} \) is
\( 6.0 \times 10^{5} \) mol \( L^{-1} s^{-1} \)
How long will it take for the \( H^{+} \) in the
drop to disappear?
A \( .8 .0 \times 10^{-8} \mathrm{s} \)
B . \( 2.0 \times 10^{-8} \) s
c. \( 6.0 \times 10^{-6} \mathrm{s} \)
D. \( 2.0 \times 10^{-2} \mathrm{s} \)
Subject: Physics
A tank has a small hole at its bottom of
area of cross-section a. Liquid is being
poured in the tank at the rate \( V m^{3} / s \) the maximum level of liquid in the container will be(Area of \( \operatorname{tank} A) \)
A. \( \frac{V}{g a A} \)
в. \( \frac{V^{2}}{2 g a^{2}} \)
c. \( \frac{V^{2}}{g A a} \)
D. \( \frac{V^{2}}{2 g a A} \)
Subject: Chemistry
From the experimental data, the compositions are found as barium = \( 58.81 \% \), sulfur \( =13.73 \% \), and oxygen \( = \)
\( 27.46 \% . \) Predict the empirical formula of the compound.
A. \( B a S O_{4} \)
в. \( B a S_{2} O \)
c. \( B a_{2} S O_{3} \)
D. \( B a S_{2} O_{4} \)
E \( . B a_{2} \mathrm{SO}_{4} \)
Subject: Maths
Examine the Rolles theorem is
applicable to the followng function. Find the number of points the following function is not continous?
\( \boldsymbol{f}(\boldsymbol{x})=[\boldsymbol{x}] \) for \( \boldsymbol{x} \boldsymbol{\epsilon}[\boldsymbol{2}, \boldsymbol{2}] \)
Subject: Maths
The distance between the origin and the centroid of the tetrahedron whose vertices are \( (\mathbf{0}, \mathbf{0}, \mathbf{0}) \)
\( (a, 0,0),(0, b, 0),(0,0, c) \) is?
A \( \cdot \sqrt{a^{2}+b^{2}+c^{2}} \)
B. \( \frac{\sqrt{a^{2}+b^{2}+c^{2}}}{2} \)
c. \( \frac{\sqrt{a^{2}+b^{2}+c^{2}}}{4} \)
D. \( 4 \sqrt{a^{2}+b^{2}+c^{2}} \)
Subject: Maths
\( \boldsymbol{E}_{1}=\frac{\boldsymbol{x}^{2}}{\boldsymbol{a}^{2}}+\frac{\boldsymbol{y}^{2}}{\boldsymbol{b}^{2}}-\mathbf{1}=\mathbf{0},(\boldsymbol{a}>\boldsymbol{b}) \) and
\( \boldsymbol{E}_{2}=\frac{\boldsymbol{x}^{2}}{\boldsymbol{k}^{2}}+\frac{\boldsymbol{y}^{2}}{\boldsymbol{b}^{2}}-\mathbf{1}=\mathbf{0},(\boldsymbol{k}<\boldsymbol{b}) \boldsymbol{E}_{2} \) is
inscribed in \( E_{1} . \) If \( E_{1} \) and \( E_{2} \) have same
eccentricities then length of minor axis
of \( \boldsymbol{E}_{2}=\boldsymbol{p}\left(\mathrm{LLR} \text { of } \boldsymbol{E}_{1}\right) \) then \( \boldsymbol{p}=? \)
A \( \cdot \frac{1}{2} \)
B. 1
\( c \cdot \frac{2}{3} \)
D.
Subject: Maths
The middle term in the expansion of \( (1+x)^{2 n} \) is
This question has multiple correct options
A. \( \frac{1 \cdot 3 \cdot 5 \ldots(2 n-1)}{n !} 2^{n} \cdot x^{n} \)
в. \( \frac{1 \cdot 3 \cdot 5 \ldots(2 n-1)}{n !} 2^{n} \cdot x^{n} x^{n} \)
c. \( ^{2 n} C_{n} \)
D. \( 2 n C_{n}-1 x^{n-1} \)
Subject: Maths
The position vector of the vertices of a triangle \( A B C \) are \( \hat{i}, \hat{j}, \hat{k} \) then the
position vector of its orthocentre is
\( \mathbf{A} \cdot \hat{i}+\hat{j}+\hat{k} \)
B . \( 2(\hat{i}+\hat{j}+\hat{k}) \)
c \( \cdot \frac{1}{3}(\hat{i}+\hat{j}+\hat{k}) \)
D \( \cdot \frac{1}{\sqrt{3}}(\hat{\imath}+\hat{j}+\hat{k}) \)
Subject: Maths
An Incomplete rrequency alstrıbution IS
given below Median value is \( 46, \) the
missing frequency is
\( \begin{array}{lll}\text { Variate } & \text { Frequency } \\ 10-20 & 12 \\ 20-30 & 30 \\ 30-40 & ? \\ 40-50 & 65 \\ 50-60 & 45 \\ 60-70 & 25 \\ 70-80 & 18 \\ \text { Total } & 229\end{array} \)
A . 33
B. 35
\( c \cdot 34 \)
D. 2
Subject: Maths
The direction ratios of \( \overrightarrow{A B} \) are (-2,2,1)
If \( \boldsymbol{A}=(\mathbf{4}, \mathbf{1}, \mathbf{5}) \) and \( l(\mathbf{A B})=\mathbf{6} \) units, find
the coordinates of \( \boldsymbol{B} \).
Subject: Physics
Figure gives a speed-time graph of a particle in motion along a constant direction. Three equal
intervals of time are shown. In which
interval is the average acceleration greatest in magnitude ? In which
interval is the average speed greatest? Choosing the positive direction as the constant direction of motion, give the
signs of \( \mathbf{v} \) and a in the three intervals.
What are the accelerations at the points \( A, B, C \) and \( D ? \)
Subject: Chemistry
\( A+2 B \rightarrow C+D \) the equilibrium
constant is:
A \( \cdot \frac{[C][D]}{[A][B]^{2}} \)
в. \( \frac{[C][D]}{[A][B]} \)
\( ^{\mathbf{c}} \frac{[A][B]^{2}}{[C][D]} \)
D. \( \frac{[A][C]}{[B][D]} \)
Subject: Maths
The solution of \( \frac{d y}{d x}=\frac{x+x^{2}}{y+y^{2}} \) is:
A \( \cdot x^{3}-y^{3}-y^{2}-x^{2}=c \)
B . \( 2\left(x^{3}-y^{3}\right)+3\left(x^{2}-y^{2}\right)=c \)
c. \( x^{2}+y^{2}+x+y=c \)
D. \( x^{2} y+x y^{2}=c \)
Subject: Chemistry
Assertion
An aqueous solution of ammonium
acetate can act as a buffer.
Reason
Acetic acid is a weak acid and
\( N H_{4} O H \) is a weak base.
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
How many moles of \( C O_{2} \) are in 1.53 g
\( C O_{2} ? \)
A. \( 1.807 \times 10^{-24} \)
4 \( 47 \times 10^{77} \) ?
В. \( 3.476 \times 10^{-2} \)
c. \( 1.717 \times 10^{-2} \)
D. \( 1.204 \times 10^{24} \)
E . \( 2.414 \times 10^{-1} \)
Subject: Physics
The potential gradient along the length of a uniform wire is 10 volt/m \( B \) and \( C \)
are two points at \( 30 \mathrm{cm} \) and \( 60 \mathrm{cm} \) in a scale fitted along the wire. The pd between B and C is
A . \( 3 V \)
B. \( 0.4 V \)
\( c .7 V \)
D. \( 4 V \)
Subject: Physics
A circular table has a radius of \( 1 \mathrm{m} \) and
mass 20 kg. It has 4 legs of 1 m each
fixed symmetrically on its circumference. The maximum weight which can be placed anywhere on this
table without toppling it is :
A \( .84 .3 \mathrm{kg} \)
в. \( 34.8 \mathrm{kg} \)
c. \( 48.3 \mathrm{kg} \)
D. \( 43.8 \mathrm{kg} \)