AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
In damped oscillation mass is 1 kg and
spring constant \( =100 N / m, \) damping
coefficeint \( =0.5 \mathrm{kg} s^{-1} . \) If the mass
displaced by \( 10 \mathrm{cm} \) from its mean position then what will be the value of
its mechanical energy after 4 seconds?
A . \( 0.67 J \)
в. 0.067 Л
c. \( 6.7 J \)
D. \( 0.5 J \)
Subject: Maths
\( \boldsymbol{L} \boldsymbol{t}_{\boldsymbol{x} \rightarrow \mathbf{0}}=\frac{\sqrt{\mathbf{1}+\mathbf{x}}-\sqrt{\mathbf{1}+\mathbf{x}^{2}}}{\sqrt{\mathbf{1 - x}^{2}}-\sqrt{\mathbf{1 - x}}}= \)
\( A \)
B. -
\( c \cdot 0 \)
\( D \)
Subject: Physics
For which of the following dependence of
drift velocity \( v_{d} \) on electric field E is Ohm's law obeyed?
A \( \cdot v_{d} \propto E \)
B . \( v_{d}= \) constant
\( \mathbf{c} \cdot v_{d} \propto \sqrt{E} \)
D \( \cdot v_{d} \propto E^{2} \)
Subject: Maths
Applying Lagranges's MeanValue Theorem for a suitable function \( f(x) \) in
\( [0, h], \) we have \( f(h)+h f^{\prime}(\theta h), 0<\theta< \)
1. Then for \( f(x)=\cos x, \) the value of
\( \lim _{h \rightarrow 0^{+}} \theta \) is
A .
B. 0
\( c \cdot \frac{1}{2} \)
D.
Subject: Chemistry
The emf of a cell corresponding to the reaction,
\( Z n+2 H^{+}(a q .) \rightarrow Z n^{2+}(0.1 M)+ \)
\( H_{2}(g) 1 a t m \)
is 0.28 volt at \( 25^{\circ} \mathrm{C} \). Write the half-cell
reactions and calculate the \( p H \) of the
solution at the hydrogen electrode.
\( \boldsymbol{E}_{\boldsymbol{Z n}^{2+} / \boldsymbol{Z n}}^{\circ}=-\mathbf{0 . 7 6} \boldsymbol{v o l t} \) and \( \boldsymbol{E}_{\boldsymbol{H}^{+} / \boldsymbol{H}_{2}}^{\circ}=\boldsymbol{0} \)
Subject: Physics
In which of the following cases is the work done positive or zero or negative?
a) Work done by the porter on a suitcase in lifting it from the platform on to his head.
b) Work done by the force of gravity on suitcase as the suitcase falls from
porter's head.
c) Work done by the porter standing on platform with suitcase on his head.
d) Work done by force of gravity on a ball thrown up vertically up into the sky.
e) Work done by force applied by hands of a man swimming in a pond.
Subject: Chemistry
The hybridization of carbon atoms in
\( \boldsymbol{C}-\boldsymbol{C} \) single bond of \( \boldsymbol{C H} \equiv \boldsymbol{C}- \)
\( \boldsymbol{C H}=\boldsymbol{C H}_{2} \) is :
A \( s p^{3}-s p^{3} \)
is \( s s p^{3}-s p^{3} \)
B \( \cdot s p^{2}-s p^{3} \)
\( \mathbf{c} \cdot s p-s p^{2} \)
D. \( s p^{3}-s p \)
Subject: Physics
Two plane mirrors \( M_{1} \) and \( M_{2} \) are
inclined at angle \( \theta \) as shown in the
figure. A ray of light I, which is parallel
to \( M_{1} \) strikes \( M_{2} \) and after two
reflections, the ray 2 becomes parallel
to \( M_{2} . \) The angle \( \theta \) is
A. 0
B. 30
\( c \cdot 45 \)
D. 60
Subject: Maths
The coefficient of \( x^{53} \) in the following
expansions. \( \sum_{m=0}^{100} 100 C_{m}(x-3)^{100-m} \cdot 2^{m} \) is
A. \( ^{100} C_{47} \)
B. \( ^{100} C_{53} \)
\( \mathbf{c} .-_{100} 0_{53} \)
D. \( -100 C_{10} \)
Subject: Physics
A body falls from a height \( h=200 m \)
The ratio of distance travelled in each
\( 2 \sec \) during \( t=0 \) to \( t=6 \) sec of the
journey is
A. 1: 4: 9
B. 1: 2: 4
\( \mathrm{c} \cdot 1: 3: 5 \)
D. 1: 2: 3
Subject: Physics
The minimum energy required to dissociate \( A g B r \) bond in \( 0.6 e V . A \)
photographic flim is coated with a sliver bromide layer. Find the maximum
wavelength whose signature can be
recorded on the film
A. \( 207 n m \)
в. 702 \( n m \)
c. 207 \( A^{\circ} \)
D. 2070 \( n m \)
Subject: Maths
There are 50 marbles of 3 colors: blue
yellow and black The probability of picking up a blue marble is \( 3 / 10 \) and that of picking up a yellow marble is \( 1 / 2 \) The probability of picking up a black ball is
A \( .1 / 5 \)
B. 1/10
\( c \cdot 1 / 4 \)
D. \( 4 / 5 \)
Subject: Physics
The \( x \) -t graph of a particle undergoing simple harmonic motion is as shown in
the figure.

The acceleration of the particle at \( t= \)
is the
2
A \( \cdot \frac{\sqrt{3}}{32} \pi^{2} c m s^{-2} \)
B. \( -\frac{\pi^{2}}{32} c m s^{-2} \)
\( c \)
D.
Subject: Maths
Solve: \( |\cos x|=\cos x-2 \sin x \)
A \( \cdot x=(2 n+1) \pi+\frac{\pi}{4} \)
B \( \cdot x=(2 n+1) \pi+\frac{\pi}{2} \)
C \( \cdot x=2 n \pi+\frac{\pi}{4} \)
D \( \cdot x=2 n \pi+\frac{\pi}{2} \)
Subject: Physics
When a resistor of \( 11 \Omega \) is connected in
series with a electric cell. The current
following in it is \( 0.5 A . \) Instead when a resistor of \( 5 \Omega \) is connected to the same
electric cell in series, the current increases by \( 0.4 A . \) The internal resistance of the cell is
A. \( 1.5 \Omega \)
B. 2\Omega
\( c .2 .5 \Omega \)
D. 3.5\Omega
Subject: Chemistry
The weight of one hydrogen atom is:
\( \mathbf{A} \cdot 1.66 \times 10^{-27} k g \)
В. \( 2.66 \times 10^{-27} k g \)
C \( \cdot 1.76 \times 10^{-27} \mathrm{kg} \)
D. \( 1.66 \times 10^{-37} k g \)
Subject: Biology
Consider the following statements each with two blanks.
(i) Diaphragm contracts to help in
(1) \( _{--} \) while the contraction of
abdominal muscles helps in (2).
(ii). Vital capacity of trained athletes is
(3) than that of non-athletes
while the vital capacity of non-smokers
is \( -(4)_{-}- \) than that of smokers.
(iii) Alveolar \( \mathrm{PO}_{2} \) is \( ---(5) \) than
the venous \( \mathrm{PO}_{2} \) while arterial \( \mathrm{PO}_{2} \) is
(6) \( _{--} \) than the alveolar \( \mathrm{PO}_{2} \)
Which of the following options gives the correct fill ups for the respective blanks
numbers from (1) to (6) in the above
statements?
A. (1)-expiration,
(2)-inspiration (5)-higher, (6)-lower
B. (3)-higher, (4)-lower, (5)-lower, (6)-higher
c. (1)-inspiration, (2)-forced expiration, (3)-higher, (4)higher
D. (1)-expiration, (2)-forced expiration, (5)-higher, (6) lower
Subject: Maths
The radius of a sphere is \( 2 r, \) then its volume will be:
A \( \cdot \frac{4}{3} \pi r^{3} \)
В. \( 4 \pi r^{3} \)
c. \( \frac{8 \pi r^{3}}{3} \)
D. \( \frac{32}{3} \pi r^{3} \)
Subject: Physics
A student performs an experiment to determine the Young's modulus of a wire, exactly \( 2 \mathrm{m} \) long, by Searle's method. In a particular reading, the student measures the extension in the
length of the wire to be \( 0.8 m m \) with an
uncertainty of \( \pm 0.05 \mathrm{mm} \) at a load of exactly \( 1.0 k g . \) The student also
measures the diameter of the wire to be
\( 0.4 m m \) with an uncertainty of ±0.01
\( \mathrm{mm} . \) Take \( \mathrm{g}=9.8 \mathrm{m} / \mathrm{s}^{2} \) (exact). The
Young's modulus obtained from the reading is
в. \( (2.0 \pm 0.2) \times 10^{11} \mathrm{N} / \mathrm{m}^{2} \)
c. \( (2.0 \pm 0.1) \times 10^{11} \mathrm{N} / \mathrm{m}^{2} \)
D. \( (2.0 \pm 0.05) \times 10^{11} \mathrm{N} / \mathrm{m}^{2} \)
Subject: Chemistry
\( \boldsymbol{S} \boldsymbol{F}_{4} \stackrel{\text {hydrolysis}}{\boldsymbol{X}}+\boldsymbol{Y} \)
\( \boldsymbol{X}+\boldsymbol{H}_{2} \boldsymbol{S} \rightarrow \boldsymbol{Z} \)
Here, \( Z \) is :
\( A \cdot S O_{3} \)
B. colloidal sulphur
c. gaseous sulphur
D. solid sulphur
Subject: Maths
If \( \boldsymbol{x}=\boldsymbol{a} \boldsymbol{t}^{2}, \quad \boldsymbol{y}= \)
2at then \( \boldsymbol{d}^{2} \boldsymbol{y} / \boldsymbol{d} \boldsymbol{x}^{2}= \)
A \( \cdot \frac{-1}{t^{2}} \)
в. \( \frac{1}{t^{2}} \)
c. 0
D. \( \frac{1}{2 a^{3}} \)
Subject: Maths
If the four letter words (need not to
meaningful) are to be formed using the letter from the word "MEDITERRANEAN"
such that the first letter is \( R \) and the fourth letter is \( \mathrm{E} \), then the total number
of all such words is:
A . 110
B . 59
c. \( \frac{11 !}{(2 !)^{3}} \)
D. 56
Subject: Physics
Somewater at \( 0^{0} C \) is placed in a large
insulated vessel. The water vapour formed is pumped out continuously.The fraction of water that will ultimately
freeze is \( \frac{7}{8} . \) If the latent heat of vaporization is \( x \) times the latent heat
of fusion. Find out value of \( x \)
A. 5
B. 6
\( c \cdot 7 \)
D.
Subject: Physics
The C. M. of a uniform card board cut in
T shape as shown in figure is:
4. \( 4 \mathrm{cm} \) from A towards
B. \( 4 \mathrm{cm} \) from B towards
\( \mathrm{c} .3 \mathrm{cm} \) from \( \mathrm{B} \) towards \( \mathrm{A} \)
D. 3 cm from A towards
Subject: Chemistry
The type of overlapping in \( B r-F \) bond
in \( B r F_{3} \) molecule is:
A \( \cdot s p^{3}-p \)
B \( \cdot s p^{2}-p \)
\( \mathbf{c} \cdot s p^{3} d-p \)
\( \mathbf{D} \cdot s p^{3} d^{2}-p \)
Subject: Maths
Assertion(A): The minimum value
of \( 16 \cot x+9 \tan x \) is 3
Reason (R): For two positve real
numbers a and b, \( \boldsymbol{A} . \boldsymbol{M} \geq \boldsymbol{G} . \boldsymbol{M} \)
This question has multiple correct options
A. Both A and R are true and \( R \) is the correct explanation of A
B. Both A and R are true and R is not the correct explanation of
\( \mathrm{c} . \) A is true and \( \mathrm{R} \) is false
D. A is false and R is true
Subject: Physics
The resonant frequency of an L-C circuit
is
\( ^{\mathrm{A}} \cdot \frac{1}{2 \pi \sqrt{L C}} \)
в. \( \frac{1}{2 \pi} \sqrt{\frac{L}{C}} \)
c. \( \frac{1}{4 \pi} \sqrt{\frac{L}{C}} \)
D. \( \frac{1}{2 \pi} \sqrt{\frac{C}{L}} \)
Subject: Physics
A body projected vertically upwards
with a velocity u return to the starting point in 4 second \( . \) If \( g=10 m^{-2} \) the
value of \( u \) is \( \$ \$(m \mid s) \$ \$:- \)
A. 5
B. 20
\( c \cdot 40 \)
D. 10
Subject: Chemistry
Two Faraday of electricity is passed
through a solution of \( C u S O_{4} . \) The mass of copper deposited at the cathode is
at. mass of \( \mathrm{Cu}=63.5 \text { amu }) \)
\( A \cdot O g \)
в. \( 63.5 \mathrm{g} \)
\( c \cdot 2 g \)
D. 127 g
Subject: Maths
If \( \boldsymbol{P}(\boldsymbol{A})=\mathbf{0 . 8}, \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 5} \) and
\( P\left(\frac{B}{A}\right)=0.4 \) then \( P\left(\frac{A}{B}\right)=? \)
A .0 .32
B. 0.64
c. 0.16
D. 0.25
Subject: Chemistry
From the following data, calculate, bond
energy of the \( F_{2}^{-} \) ion
\( \boldsymbol{F e}(\boldsymbol{g}) \rightarrow \boldsymbol{2} \boldsymbol{F}(\boldsymbol{g}) ; \quad \boldsymbol{\Delta} \boldsymbol{H}^{o}= \)
\( \mathbf{1 5 6 . 9} \boldsymbol{k J} \)
II. \( \boldsymbol{F}^{-}(\boldsymbol{g}) \rightarrow \boldsymbol{F}_{2}(\boldsymbol{g}) \boldsymbol{e}^{-} ; \quad \boldsymbol{\Delta} \boldsymbol{H}^{o}= \)
\( \mathbf{3 3 3} \boldsymbol{k J} \)
III. \( \boldsymbol{F}_{2}^{-}(\boldsymbol{g}) \rightarrow \boldsymbol{F}_{2}(\boldsymbol{g}) \boldsymbol{e}^{-} ; \quad \boldsymbol{\Delta} \boldsymbol{H}^{o}= \)
\( \mathbf{2 9 0} \boldsymbol{k J} \)
A . \( 446.9 k J \)
в. \( 113.9 k J \)
c. \( 779.9 k J \)
D. \( 623.0 k J \)
Subject: Chemistry
When \( F e C r_{2} O_{4} \) (chromite) is reduced with Carbon in an electric-arc furnace:
A \( \cdot \) crand \( F e_{2} O_{3} \) are formed
B. Fe and \( C r_{2} O_{3} \) are formed
c. Fe and Cr (ferrochrome) are formed
D. \( F e C r O_{4} \) is formed
Subject: Physics
A car is being driven at a constant speed of \( 5 m / s \) by a force of \( 3 \times 10^{8} N \)
It takes 2 minutes to reach its
destination. What is the work done?
A \( .15 \times 10^{8} J \)
B . \( 18 \times 10^{10} J \)
c. \( 6 \times 10^{10} J \)
D . \( 10 \times 10^{8} J \)
Subject: Physics
An engine operates by taking n moles of
an ideal gas through the cycle ABCDA
shown in figure. The thermal efficiency
of the engine is :

Take \( C_{v}=1.5 \mathrm{R}, \) where \( \mathrm{R} \) is gas constant
4.0 .32
3.0 .24
\( c \cdot 0.15 \)
2
Subject: Maths
Solve \( \int x \sin ^{2} x d x \)
A \( \cdot \frac{(x-1)}{2}\left(x-\frac{\cos 2 x}{2}\right)+C \)
в. \( \frac{(x-1)}{2}\left(x-\frac{\sin 2 x}{2}\right)+C \)
c. \( \frac{(x+1)}{2}\left(x-\frac{\sin 2 x}{2}\right)+C \)
D. None of these
Subject: Physics
If a simple pendulum of length L has maximum angular displacement \( \boldsymbol{\theta} \) then the maximum kinetic energy of the
bob of mass \( \mathrm{m} \) is
A \( \cdot \frac{1}{2} m(L / g) \)
В. \( m g L(1-\cos \theta) \)
c. \( (m g L \sin \theta) / 2 \)
D. \( m g / 2 L \)
Subject: Chemistry
For the gas phase reaction,
\[
\boldsymbol{P} \boldsymbol{C l}_{5(g)} \rightleftharpoons \boldsymbol{P} \boldsymbol{C l}_{3(g)}+\boldsymbol{C l}_{2(g)}
\]
Which of the following conditions are
correct?
\( \begin{array}{lll}\text { A. } \triangle H<0 & \text { and } & \Delta S<0\end{array} \)
B. \( \triangle H>0 \) and \( \Delta S<0 \)
c. \( \Delta H=0 \) and \( \Delta S<0 \)
\( \begin{array}{lll}\text { D. } \triangle H>0 & \text { and } & \Delta S>0\end{array} \)
Subject: Chemistry
Consider the following statements are arrange in the order of true/false as given in the codes. Select the correct
arrangement.
\( S_{1}: \) Ammonia on heating with concentrated solution of sodium
hypochlorite gives nitrogen gas.
\( S_{2}: \) The phosphine gas dissolves in
water in presence of sunlight and produces phosphonium hydroxide like ammonium hydroxides.
\( S_{3}: \) Barium azide on heating gives pure
nitrogen gas.
\( S_{4}: \) The oxo-acids of phosphorus in which phosphorus has lower oxidation state less than +5 contain either \( \boldsymbol{P}-\boldsymbol{P} \)
or \( P-H \) bonds but not both in addition
to \( P=O \) and \( P-O H \) bonds.
A. TF TT
B. F FTT
c. тт T \( F \)
D. TFTF
Subject: Chemistry
REACTANT(S) \( \quad \) PRODUCT(S)
Magnesium + Oxygen 一
\[
\begin{array}{l}
\text { Magnesium Oxide }+\text { Oxygen } \\
\begin{array}{ll}
48.6 g & +50.0 g \longrightarrow 80.6 g \\
+ & ?
\end{array}
\end{array}
\]
Predict the mass of oxygen that will be left over after the reaction of 48.6 grams of magnesium with 50.0 grams of oxygen.
A . 20.6
в. 19.6
\( c \cdot 18 \)
D. 17.6
Subject: Chemistry
Among the electrolytes
\( N a_{2} S O_{4}, C a C l_{2}, A l_{2}\left(S O_{4}\right)_{3} \) and
\( N H_{4} C l, \) the most effective coagulation
agent for \( \boldsymbol{S b}_{2} \boldsymbol{S}_{3} \) sol is:
\( \mathbf{A} \cdot N a_{2} S O_{4} \)
в. \( C a C l_{2} \)
c. \( _{A l_{2}}\left(S O_{4}\right)_{3} \)
D. \( N H_{4} C l \)
Subject: Chemistry
Statement I: In the kinetic theory of gases, collisions between gas particles and the walls of the container are
considered elastic.

Statement II: Gas molecules are
considered pointlike, volumeless
particles with no intermolecular forces
and in constant, random motion.
A. Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement 1
B. Both the Statement 1 and Statement 2 are correct and Statement 2 is not the correct explanation of Statement 1
c. Statement 1 is correct but Statement 2 is not correct
D. Statement 1 is not correct but Statement 2 is correct
E. Both the Statement 1 and Statement 2 are not correct
Subject: Physics
A sample of gas in a box is at pressure
\( P_{0} \) and temperature \( T_{0} . \) If number of
molecules is doubled and total kinetic
energy of the gas kept constant then final temperature and pressure will be
\( \mathbf{A} \cdot T_{0} \cdot P_{0} \)
в. \( T_{0} .2 P_{0} \)
c. \( \frac{T_{0}}{2} .2 P_{0} \)
D. \( \frac{T_{0}}{2} \cdot P_{0} \)
Subject: Physics
Two cells of same emf \( E \) but different
internal resistances \( r_{1} \) and \( r_{2} \) are
connected in series with an external
resistance \( R \). The potential drop across
the first cell is zero. Then \( \boldsymbol{R} \) is
A \( \cdot r_{1}+r_{2} \)
В. \( r_{1}-r_{2} \)
c. \( r_{2}-r_{1} \)
D. \( r_{1} r_{2} \)
Subject: Biology
When a cross is made between a tall
plant with yellow seeds (Tt Yy) and a tall plant with green seeds (Tt yy), what is true regarding the proportions of phenotypes of the offsprings in \( F 1 \) generation? Proportion of Tall and Green Proportion of Dwarf and Green
A \( \cdot \frac{3}{8} \frac{1}{8} \)
в. \( \frac{2}{8} \frac{1}{8} \)
c. \( \frac{1}{8} \frac{3}{8} \)
D. \( \frac{2}{8} \frac{2}{8} \)
Subject: Chemistry
Assertion
In cyanide process for the extraction of gold and silver from their native ores,
the cyanide solution acts as a reducing agent to reduce the gold and silver compounds present in the ores into the metallic states.
Reason
In the extraction of gold and silver, the cyanide solution acts as complexing reagent in the presence of air and form their respective soluble complexes.
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
Calculate the standard deviation of the
following data
\( \boldsymbol{x} \quad \boldsymbol{3} \quad \boldsymbol{8} \quad \mathbf{1 3} \quad \mathbf{1 7} \quad \boldsymbol{2 3} \)
\( \begin{array}{llllll}f & 7 & 10 & 15 & 10 & 8\end{array} \)
Subject: Maths
n figure, chords \( \overline{P Q} \) and \( \overline{R S} \) intersect
at \( \mathrm{T} . \) If \( \boldsymbol{m} \angle \boldsymbol{R}=\mathbf{5 0}^{\boldsymbol{o}} \) and \( \boldsymbol{m} \angle \boldsymbol{P}=\mathbf{4 6}^{\boldsymbol{o}} \)
the number of degrees in minor arc PR
is
\( A \cdot 84 \)
B. 168
\( c \cdot 42 \)
D. 130
E. cannot be determine
Subject: Maths
Consider the complex numbers \( z= \) \( \frac{(1-i \sin \theta)}{(1+i \cos \theta)} . \) The value of \( \theta \) for which \( z \) is
purely imaginary are-
A \( \cdot n \pi-\frac{\pi}{4}, n \epsilon I \)
В \( \cdot n \pi+\frac{\pi}{4}, n \epsilon I \)
c. \( n \pi, n \epsilon I \)
D. No real values of \( \theta \)
Subject: Chemistry
Assertion
Following is not a suitable technique for
the preparation of shown alkane
product.
\[
\mathbf{2} \boldsymbol{H}_{3} \boldsymbol{C}-\underset{\boldsymbol{C} \boldsymbol{H}_{3}}{\boldsymbol{C}-\boldsymbol{C l}}+\boldsymbol{N a} \frac{\boldsymbol{T} \boldsymbol{H} \boldsymbol{F}}{\boldsymbol{H e a t}} \boldsymbol{H}_{3} \boldsymbol{C}-
\]
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{3} \)
\[
\begin{array}{l}
c-C-C H_{3} \\
C H_{3} C H_{3}
\end{array}
\]
Reason
Above mentioned reaction involves a
highly unstable tertiary carbanion
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 wrong but reason is correct
Subject: Maths
\( \cos ^{-1}\left[\cos \left(\left(-\frac{17}{15}\right) \pi\right)\right] \) is equal to
A \( \cdot \frac{17 \pi}{15} \)
в. \( \frac{13 \pi}{15} \)
\( c \cdot \frac{3 \pi}{15} \)
D. \( -\frac{17 \pi}{15} \)
Subject: Physics
The frequency of oscillation of current in
the inductance is
A \( \cdot \frac{1}{3 \sqrt{L C}} \)
в. \( \frac{1}{6 \pi \sqrt{L C}} \)
c. \( \frac{1}{\sqrt{L C}} \)
D. \( \frac{1}{3 \pi \sqrt{L C}} \)
Subject: Maths
What is the value of \( x \) for the following
equations: \( x-5 y=10 \) and \( x+y=4 ? \)
(Use cross multiplication method)
\( \mathbf{A} \cdot x=5 \)
B. \( x=4 \)
c. \( x=3 \)
D. \( x=2 \)
Subject: Maths
Consider two events \( A \) and \( B \) of an
experiment where \( P(A \cap B)=\frac{1}{4} \) and \( P(B)=\frac{1}{2}, \) then \( P(A) \) cannot exceed
\( A \cdot \frac{1}{2} \)
B. \( \frac{2}{3} \)
\( c \cdot \frac{3}{4} \)
D.
Subject: Chemistry
The binding energy of \( e^{-} \) in the ground
state of the hydrogen atom is \( 13.6 e V \) The energies required to eject out an
electron from three lowest states of \( \mathrm{He}^{+} \)
atom will be (in eV):
A . 13.6,10.2,3.4
в. 13.6,3.4,1.5
c. 13.6,27.2,40.8
D. 54.4,13.6,6
Subject: Physics
In SHM match the following
Column I
a) Maximum velocity
e) \( 1 / 2 \mathrm{M} \)
\( \omega^{2} A^{2} \)
b) Maximum acceleration
f) \( 1 / 4 \mathrm{M} \)
\( \omega^{2} A^{2} \)
c) Maximum Force
g) \( A \omega \)
d) Maximum total energy
h) \( \omega^{2} A \)
¡) \( \boldsymbol{m} \boldsymbol{\omega}^{2} \boldsymbol{A} \)
A. a-g, b-h, c-i, d-e
B. a-h, b-g, c-i, d-e
c. \( a-g, b-h, c-f, d-e \)
D. a-g, b-i, c-h, d-f
Subject: Physics
Two identical balls each of mass in are
moving in opposite direction with a speed v. if they collide elastically maximum potentail energy stored in the ball is :
A. 0
в. \( \frac{1}{2} m v^{2} \)
\( \mathrm{c} \cdot m v^{2} \)
\( \mathbf{D} \cdot 2 m v^{2} \)
Subject: Maths
Suppose \( \boldsymbol{E}_{1}, \boldsymbol{E}_{2}, \boldsymbol{E}_{3} \) be three mutually
exclusive events such that \( \boldsymbol{P}\left(\boldsymbol{E}_{i}\right)=\boldsymbol{p}_{i} \)
for \( \boldsymbol{i}=\mathbf{1}, \mathbf{2}, \mathbf{3} \)
\( \operatorname{then} P\left(E_{1} \cap E_{2}^{\prime}\right)+P\left(E_{2} \cap E_{3}^{\prime}\right)+ \)
\( \boldsymbol{P}\left(\boldsymbol{E}_{3} \cap \boldsymbol{E}_{1}^{\prime}\right) \) equals
A \( \cdot p_{1}\left(1-p_{2}\right)+p_{2}\left(1-p_{3}\right)+p_{3}\left(1-p_{1}\right) \)
В. \( p_{1} p_{2}+p_{2} p_{3}+p_{3} p_{1} \)
c. \( p_{1}+p_{2}+p_{3} \)
D. None of these
Subject: Maths
\( \begin{array}{ccc}\sin ^{2} x & \cos ^{2} x & 1 \\ \cos ^{2} x & \sin ^{2} x & 1 \\ -10 & 12 & 2\end{array} \mid= \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( 12 \cos ^{2} x-10 \sin ^{2} x \)
c. \( 12 \sin ^{2} x-10 \cos ^{2} x-2 \)
D. \( 10 \sin 2 x \)
Subject: Maths
A ball is drawn at random from a box
containing 10 red, 30 white, 20 blue and
15 orange marbles. The probability of a ball drawn is red, white or blue \( \ldots \)
A \( \cdot \frac{1}{3} \)
B. \( \frac{3}{5} \)
\( c \cdot \frac{2}{3} \)
D. \( \frac{4}{5} \)
Subject: Physics
fixed plane inclined at angle \( \boldsymbol{\theta} \) with
horizontal. A light string is tied to the cylinder at the right most point, and a
mass \( m \) hangs from the string, as
shown in. Assume that the coefficient of
friction between the cylinder and the
inclined plane is sufficiently large to
prevent slipping. For the cylinder to
remain static, the value of m is
\( A \cdot \frac{M \sin \theta}{1-\sin \theta} \)
B. \( \frac{M \cos \theta}{1+\sin \theta} \)
\( c \cdot \frac{M \sin \theta}{1+\sin \theta} \)
D. \( \frac{M \cos \theta}{1-\sin \theta} \)
Subject: Chemistry
Ortho-nitrophenol is less soluble in
water than para and meta-nitrophenols
because:
A. o- nitrophenol is more volatile in steam than those of \( \mathrm{m}- \) and \( \mathrm{p}- \) isomers.
B. o- nitrophenol shows intramolecular \( H \) -bonding.
C. o-nitrophenol shows intermolecular \( H \) -bonding.
D. none of these
Subject: Biology
Biologists believe that the current DNA
\( \rightarrow \mathrm{RNA} \rightarrow \) Protein system is the result of a long period of evolution because
A. The transcription of DNA to mRNA and translation of mRNA into proteins consists of many steps.
B. DNA replication is complicated but relatively error-free and the current system is very complex and precise
c. Evidence indicates that RNA preceded DNA as the genetic material
D. All of the above
Subject: Chemistry
Identify the products.
\[
\underset{\mathrm{Me}}{\longrightarrow} \underbrace{\Gamma=\mathrm{O}+2 \mathrm{Me}-\equiv-\mathrm{H} \frac{\mathrm{M}_{\mathrm{CO}}}{_{\mathrm{MCOH}}}^{+}}_{(\mathrm{B})}(\mathrm{C})
\]
Subject: Physics
Three concentric spherical metallic shells \( A, B \) and \( C \) of \( \operatorname{radii} a, b \) and \( c(a< \) \( b<c) \) have charge densities \( \sigma,-\sigma \) and
\( \sigma \) respectively. If the shells \( A \) and \( C \) are
at the same potential then the relation between \( a, b \) and \( c \) is :
A \( a+b+c=0 \)
0
B . \( a+c=b \)
\( \mathbf{c} \cdot a+b=c \)
\( \mathbf{D} \cdot a=b+c \)
Subject: Physics
Q Type your question
unırormiy aıstrıbutea tnrougnout ırs
volume

Which of the following expressions
gives the electric field strength at point
\( P, \) a point that lies inside the sphere
and is a distance \( r \) from the center of
the sphere?
\( ^{\mathrm{A}} \cdot_{E}=\frac{Q r}{4 \pi \epsilon_{0} R^{3}} \)
B. \( \quad E=\frac{Q}{4 \pi \epsilon_{0} r^{2}} \)
c. \( E=0 \) (Point \( P \) is inside of a conductor.
'D \( \quad E=\frac{3 Q r}{4 \pi \epsilon_{0} R^{3}} \)
\( E=\frac{3 Q}{4 \pi \epsilon_{0} r^{3}} \)
Subject: Chemistry
Which among the following is a bi-
dentate ligand?
written as bipy
\( \mathbf{A} \cdot C H_{3} C O O^{-} \)
\( \mathbf{B} \cdot: O C N^{-} \)
\( \mathbf{c} \cdot: N C O^{-} \)
\( \begin{array}{cc}\mathbf{D} \cdot C H_{3}-C_{\|}-C H=C & -C H_{3} \\ : O & : O:\end{array} \)