AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
Two circles touch internally. The sum of their areas is \( 116 \pi \) sq. \( \mathrm{cm} \) and the
distance between their centers is \( 6 \mathrm{cm} \)
The radii of the given circles are
A. \( 8 \mathrm{cm} \& 20 \mathrm{cm} \)
B. \( 4 \mathrm{cm} \& 10 \mathrm{cm} \)
c. \( 6 \mathrm{cm} \) \& \( 8 \mathrm{cm} \)
D. \( 5 \mathrm{cm} \) \& \( 9 \mathrm{cm} \)
Subject: Physics
The coefficient of linear expansion of stee and brass are \( 11 \times 10^{-6} /^{\circ} \mathrm{C} \) and \( 19 \times \)
\( 10^{-6} /^{\circ} \mathrm{C} \) respectively. If their difference in
lengths at all temperatures has to kept constant at \( 30 \mathrm{cm} \), their lengths at \( 0 \mathrm{C} \)
should be:
A. \( 71.25 \mathrm{cm} \) and \( 41.25 \mathrm{cm} \)
B. 82 cm and 52 cm
c. \( 92 \mathrm{cm} \) and \( 62 \mathrm{cm} \)
D. 62.25 cm and 32.25 cm
Subject: Maths
Let \( \boldsymbol{A}=\{\mathbf{9}, \mathbf{1 0}, \mathbf{1 1}, \mathbf{1 2}, \mathbf{1 3}\} \) and \( \boldsymbol{f}: \boldsymbol{A} \rightarrow \)
\( N \) be defined by \( f(n)= \) highest prime
factor of \( n, \) then its range is
A \( .\{13\} \)
в. \{3,5,11,13\}
c. \{11,13\}
D. \{2,3,5,11\}
Subject: Physics
Find the terminal velocity of a steel ball of diameter \( 0.2 \mathrm{cm} \) when it falls through
a tube filled with glycerin. \( \left(\boldsymbol{g}=\mathbf{9 . 8 m} / \boldsymbol{s}^{2}\right. \)
,density of steel \( =8000 k g / m 63 \)
,density of glycerin \( =1.33 g / c m^{3}, \eta= \)
8.33 poise \( =0.833 N s / m^{2} \)
Subject: Physics
A person standing near the edge of the top of a building throws two balls \( A \) and
B. The ball \( A \) is thrown vertically
upward and \( B \) is thrown vertically downward with the same speed. The ball
\( A \) hits the ground with a speed \( v_{A} \) and
the ball \( B \) hits the ground with a speed
\( \boldsymbol{v}_{B} . \) We have:
В . \( v_{A}<v_{B} \)
c. \( v_{A}=v_{B} \)
D. the relation between \( v_{a} \) and \( v_{b} \) depends on height of the building above the ground
Subject: Maths
If \( 0<\alpha<\pi / 2 \) then the value of
\( \int_{0}^{\alpha} \frac{\boldsymbol{d} \boldsymbol{x}}{1-\cos \boldsymbol{x} \cos \boldsymbol{\alpha}} \) is
\( A \cdot \pi / \alpha \)
B . \( \pi / 2 \sin \alpha \)
c. \( \pi / 2 \cos \alpha \)
D. \( \pi / 2 \alpha \)
Subject: Chemistry
What will be \( p H \) of aqueous salt
solution of \( A B \) if \( p K_{a} \) of weak acid \( H A \)
is 4 and \( p K_{b} \) of weak base \( \mathrm{BOH} \) is \( 5 ? \)
\( \mathbf{A} \cdot \mathbf{5} \)
B. 7.5
\( c .6 .5 \)
D. 11.5
Subject: Chemistry
Group 16 elements have a lower value of first ionization enthalpy as compared to group 15 elements because:
A. half filled p-orbitals in group 15 elements are more stable
B. group 16 elements have smaller size than group 15 elements
c. group 16 elements contain double bond while group 15 elements have a triple bond
D. group 16 elements have more number of electrons in p-orbitals
Subject: Maths
\( \operatorname{Let} \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{cl}-\boldsymbol{x}^{3}+\log _{2} \boldsymbol{b}, & \mathbf{0} \leq \boldsymbol{x}<\mathbf{1} \\ \mathbf{3} \boldsymbol{x}, & \mathbf{1} \leq \boldsymbol{x} \leq \mathbf{3}\end{array}\right. \)
The set of real values of b for which \( f(x) \)
has smallest value at \( x=1 \), is?
A . (0,8]
B. \( [8, \infty) \)
c. \( [16, \infty] \)
\( D . \quad(0,16 \)
Subject: Maths
Find the middle term(s) in the
expansion of :
\( \left(\frac{p}{x}+\frac{x}{p}\right)^{9} \)
A \( \cdot \frac{126 x}{p}, \frac{126 p}{x} \)
В \( \cdot \frac{126}{p}, 126 x \)
\( ^{\mathrm{C}} \cdot \frac{160 x^{2}}{p}, \frac{162 x}{p^{2}} \)
D. None of these
Subject: Chemistry
An ion \( M^{3+} \) has electronic
configuration \( [\boldsymbol{A} \boldsymbol{r}] \boldsymbol{3} \boldsymbol{d}^{10} \boldsymbol{4} \boldsymbol{s}^{2} . \) Element \( \mathbf{M} \)
belongs to
A. s- block
B. p - block
c. \( d \) - block
D. f- bblock
Subject: Maths
The table below classifies 60 students
in a class according to their heights.
\begin{tabular}{ll} 
Height \( (\mathrm{cm}) \) & Number of students \\
\( 140-145 \) & 5 \\
\( 145-150 \) & 8 \\
\( 150-155 \) & 12 \\
\( 155-160 \) & 16 \\
\( 160-165 \) & 11 \\
\( 165-170 \) & 5 \\
\( 170-175 \) & 3 \\
\hline
\end{tabular} Find the median of the amount paid.
Subject: Physics
A stone falls freely from rest from a height \( h \) and it travels a distance \( \frac{9 h}{25} \) in the last second. The value of h is :
A . \( 145 \mathrm{m} \)
B. 100 \( m \)
c. \( 122.5 \mathrm{m} \)
D. 200 m
Subject: Physics
A short bar magnet has a magnetic moment of \( 0.39 J T^{-1} . \) The magnitude
and direction of the magnetic field produced by the magnet at a distance of \( 20 \mathrm{cm} \) from the centre of the magnet
on the equatorial line of the magnet is
A. 0.049 G, N-S direction
B. 4.9 G, S-N direction
c. 0.0195 G, S-N direction
D. \( 19.5 \mathrm{G} \), N-S direction
Subject: Chemistry
Identify the reaction during electrolytic reduction of alumina at cathode.
A \( \cdot 2 H_{2} O_{2} \rightarrow O_{2}+4 H^{+}+4 e^{-} \)
B. \( 3 F^{-} \rightarrow 3 F+3 e^{-} \)
c. \( A l^{+3}+3 e^{-} \rightarrow A l \)
D. \( 2 H^{+}+2 e^{-} \rightarrow H_{2} \)
Subject: Chemistry
What is the hybridisation of the metal in following complex?
\( \left[\boldsymbol{F e}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right]^{3+} \)
A \( \cdot d^{3} s p^{2} \)
в. \( d s p^{4} \)
\( \mathbf{c} \cdot d^{2} s p^{3} \)
D. None of these
Subject: Biology
Assertion
In barrier methods, ovum and sperms
are prevented from physical meetings.
Reason

Barrier methods are used during coitus, to prevent the entry of ejaculated semen into the female reproductive tract
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
In 1 L saturated solution of
\( A g C l\left[K_{s p}(A g C l)=1.6 \times 10^{10}\right], 0.1 \mathrm{mol} \)
of \( \boldsymbol{C u} \boldsymbol{C l}\left[\boldsymbol{K}_{s p}(\boldsymbol{C u} \boldsymbol{C l})=\mathbf{1 . 0} \times \mathbf{1 0}^{-\mathbf{6}}\right] \) is
added. The resultant concertraion of
\( A g^{+} \) in the solution is \( 1.6 \times 10^{-x} \). The
value of \( x \) is:
Subject: Maths
The points \( P, Q, R, S, T, U, A \) and \( B \) on
the number line are such that \( \boldsymbol{T} \boldsymbol{R}= \)
\( \boldsymbol{R S}=\boldsymbol{S U} \) and \( \boldsymbol{A P}=\boldsymbol{P Q}=\boldsymbol{Q B} . \) Name
the rational numbers represented by
\( \boldsymbol{P}, \boldsymbol{Q}, \boldsymbol{R}, \boldsymbol{S} \)
Subject: Chemistry
Enthalpy of polymerisation of ethylene, as represented by the reaction, \( \boldsymbol{n} \boldsymbol{C H}_{2}=\boldsymbol{C H}_{2} \rightarrow\left(-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\right) \boldsymbol{n} \)
is \( -100 \mathrm{kJ} \) per mole of ethylene. Given bond enthalpy of \( C=C \) bond is \( 600 \mathrm{kJ} \)
mol \( ^{-1} \), Determine enthalpy of \( C \) C bond (in \( \mathrm{kJ} \text { mol }) \)
A . 350
в. з23
c. 565
D. 453
Subject: Maths
\( \cos ^{-1}\left(\cos \left(\frac{-17 \pi}{5}\right)\right) \) is equal to
A. \( -\frac{17 \pi}{5} \)
в. \( \frac{3 \pi}{5} \)
\( c \cdot \frac{2 \pi}{5} \)
D. none of these
Subject: Maths
For any three sets, \( A B \) and \( C, B \backslash(A \cup \)
\( C) \) is:
\( \mathbf{A} \cdot(A \backslash B) \cap(A \backslash C) \)
B . \( (B \backslash A) \cap(B \backslash C) \)
c. \( (B \backslash A) \cap(A \backslash C) \)
D. \( (A \backslash B) \cap(B \backslash C) \)
Subject: Maths
Find the point of intersection of the following pair of lines, assuming that the vectors \( \vec{a} \) and \( \vec{b} \) are not parallel. \( \vec{r}=\gamma(\vec{b}+\vec{a}), \vec{r}=\mu(\vec{b}-\vec{a}) \)
A . origin
в. \( \vec{b}+\vec{a} \)
\( c \cdot 2 b \)
D. no intersection point
Subject: Maths
If \( l, m, n \) are d.c's of vector \( \overline{O P} \) then
maximum value of \( l \) mn is
A \( \cdot \frac{1}{\sqrt{3}} \)
B. \( \frac{1}{2 \sqrt{3}} \)
c. \( \frac{1}{3 \sqrt{3}} \)
D. \( \frac{2}{\sqrt{3}} \)
Subject: Chemistry
Which among the following is incorrect
of \( _{5} B \) in normal state?
A. \begin{tabular}{|c|c|c|c|c|}
\hline \( 2 s \) & \( 2 p \) & & \\
\hline\( \uparrow \uparrow \) & & \( \uparrow \) & \\
\hline
\end{tabular}
B. \begin{tabular}{|c|c|c|c|c|}
\hline \( 2 s \) & \multicolumn{3}{|c|} {\( 2 p \)} \\
\hline\( \uparrow \) & \( \uparrow \) & \( \uparrow \) & \multicolumn{2}{|c|} { Against aufbau principle as well as Hund's rule } \\
\hline
\end{tabular}
\( c \)
\begin{tabular}{c|c|c|c|}
\( 2 s \) & \multicolumn{2}{c} {\( 2 p \)} \\
\hline\( \uparrow \uparrow \) & \( \uparrow \) & & \\
\hline
\end{tabular} Violation of Pauli's exclusion
principle and not Hund's rule
D. \( 2 p \) \( 2 s \) \( \uparrow \downarrow \) \( : \quad \) Against aufbau principle
Subject: Physics
Two long parallel wires \( P \) and \( Q \) are held
perpendicular to the plane of the paper at a acceptance of \( 5 \mathrm{m} \) between them. If \( P \)
and \( Q \) carry currents of 2.5 and 5 amp
respectively in the same direction, then
the magnetic field at a point half way
between the wire is
\( \mathbf{A} \cdot \frac{\mu_{0}}{\pi} \)
B. \( \frac{\sqrt{3} \mu_{0}}{\pi} \)
\( c \cdot \frac{\mu_{0}}{2 \pi} \)
D. \( \frac{3 \mu_{0}}{2 \pi} \)
Subject: Physics
A solid cylindrical unchanged conductor of radius \( r \) and length \( l \) is placed in a region of space where a uniform electric field \( \vec{E} \) exits. The
electric field inside the conductor due
to the charge induced on its surface is :
A . \( \vec{E} \)
B . \( 2 \vec{E} \)
\( c \cdot-\vec{E} \)
D. \( -2 \vec{E} \)
Subject: Maths
If \( \boldsymbol{f}(\boldsymbol{x})=\frac{\boldsymbol{e}^{\boldsymbol{x}}}{\mathbf{1}+\boldsymbol{e}^{\boldsymbol{x}}}, \boldsymbol{A}=\int_{\boldsymbol{f}(-\boldsymbol{a})}^{f(\boldsymbol{a})} \boldsymbol{x} \boldsymbol{g}\{\boldsymbol{x}(\mathbf{1}- \)
\( \boldsymbol{x})\} \boldsymbol{d} \boldsymbol{x} \) and \( \boldsymbol{B}=\int_{\boldsymbol{f}(-\boldsymbol{a})}^{f(\boldsymbol{a})} \boldsymbol{g}\{\boldsymbol{x}(\boldsymbol{1}-\boldsymbol{x})\} \boldsymbol{d} \boldsymbol{x} \)
then \( \frac{B}{A} \) is equal to
\( A \cdot-1 \)
B . - -
\( c \cdot 2 \)
\( D \)
Subject: Chemistry
Write the IUPAC name of
\( \left[\boldsymbol{A} \boldsymbol{g}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{2}\right]\left[\boldsymbol{A} \boldsymbol{g}(\boldsymbol{C} \boldsymbol{N})_{2}\right] \) coordination
compound.
Subject: Chemistry
The angular momentum of an electron
in the \( 2^{n d} \) excited state ofa Helium ion
\( \left(\boldsymbol{H} \boldsymbol{e}^{+}\right) \) is:
A \( \cdot \frac{h}{2 \pi} \)
в. \( \frac{2 h}{2 \pi} \)
\( c \cdot \frac{3 h}{2 \pi} \)
D. \( \frac{4 h}{2 \pi} \)
Subject: Chemistry
Assertion
The \( 0-0 \) bond length in \( H_{2} O_{2} \) is shorter
than that of \( O_{2} F_{2} \)
Reason
\( H_{2} O_{2} \) has an open book-type structure.
Read the above assertion and reason
and choose the correct option regarding
¡t.
A. Assertion is true, Reason is true and Reason is correct explanation for Assertion
B. Assertion is true, Reason is true and Reason is NOT the
correct explanation for Assertion
c. Assertion is true, Reason is false
D. Assertion is false, Reason is true
Subject: Maths
\( \mathbf{5} \boldsymbol{x}^{\mathbf{3}}+\mathbf{5} \boldsymbol{x}^{\mathbf{2}}+\mathbf{4} \boldsymbol{x}+\mathbf{3}+\mathbf{4} \boldsymbol{x}^{\mathbf{2}}+\mathbf{5} \boldsymbol{x}= \)
A \( \cdot 9 x^{3}+4 x^{2}+4 x+5 \)
B . \( 5 x^{3}+5 x^{2}+9 x+4 \)
\( \mathbf{c} \cdot 5 x^{3}+9 x^{2}+9 x+3 \)
D. None of the above
Subject: Physics
The following truth table is for which
gate?
\( \begin{array}{lll}A & B & Y=A+B \\ 0 & 0 & 0 \\ 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 1\end{array} \)
A. AND
B. OR
c. Nor
D. NAND
Subject: Physics
A proton moving with a constant speed passes through a region of space without any change in its speed. If \( \boldsymbol{E} \)
and \( B \) represent the electric and magnetic fields respectively, this region of space may have
a) \( \boldsymbol{B} \neq \mathbf{0}, \boldsymbol{E}=\mathbf{0} \)
b) \( \boldsymbol{B}=\mathbf{0}, \boldsymbol{E} \neq \mathbf{0} \)
c) \( B=0, E=0 \)
d) \( \boldsymbol{B} \neq \mathbf{0}, \boldsymbol{E} \neq \mathbf{0} \)
\( A \cdot a, b, c \) are true
B. b, c, dare true
\( c \cdot a, b, d \) are true
D. a, c, d are true
Subject: Physics
Two bodies, each of mass \( \mathrm{M} \), are kept
fixed with a separation 2 L. A particle of mass \( m \) is projected from the midpoint of the line joining their centres, perpendicular to the line. The gravitational constant is G. The correct statement(s) is (are).
A. The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is \( 4 \sqrt{\frac{G M}{L}} \)
B. The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is \( 2 \sqrt{\frac{G M}{L}} \)
C. The minimum initial velocity of the mass \( m \) to escape the gravitational field of the two bodies is \( \sqrt{\frac{2 G M}{L}} \)
D. The energy of the mass m remains constant
Subject: Biology
On the basis of following features, identify the correct tissue.
It is the covering or protective tissues in the animal body.

It forms a barrier to keep different body
systems separate.
The skin, the lining of the mouth, the
lining of blood vessels, lung alveoli and
kidney tubules are made up of this type
of tissue.
A. Epithelial tissue
B. Connective tissue
c. Muscular tissue
D. Nervous tissue
Subject: Physics
A particle starts from rest and moves with an acceleration of \( \boldsymbol{a}=\mathbf{2}+(\boldsymbol{t}- \)
2) \( \mid m / s^{2}, \) the velocity of the particle at
\( t=4 \sec \) is
\( A \cdot 2 m / s \)
B. \( 4 \mathrm{m} / \mathrm{s} \)
c. zero
D. \( 12 \mathrm{m} / \mathrm{s} \)
Subject: Chemistry
Read the given statements and select
the correct option:

Statement 1:Backing soda does not
taste sour.

Statement 2 :Bases are sour in taste
while acids are bitter in taste.
A. Both statements 1 and 2 are true statement 2 is correct explanation of statement 1.
B. Both statements 1 and 2 are true both statement 2 is not the correct explanation of statement 1
c. statements 1 is true and statement 2 is false
D. Both statements 1 and 2 are false
Subject: Physics
\( \ln \operatorname{an} L C R \) circuit as shown in figure,
both switches are open initially. Now
switch \( S_{1} \) is closed, \( S_{2} \) kept open. \( (q \) is
charge on the capacitor and \( 4 \tau=R C \) is
capacity time constant).
Which of the following statement is
correct?
A \( \cdot \operatorname{At} t=\frac{\tau}{2}, q=C V\left(1-e^{-1}\right. \)
B. Work done by the battery is half of the energy dissipated in the resistor
c. At \( t=\tau, q=C V / 2 \)
D. At \( t=2 \tau . q=C V\left(1-e^{-2}\right) \)
Subject: Chemistry
During the discharge of a lead storage
battery, the density of sulphuric acid
fell from 1.294 to \( 1.139 g m l^{-1} \)
Sulphuric acid of density \( 1.294 g m l^{-1} \)
is \( 39 \% \) by weight and that of density \( 1.139 g m l^{-1} \) is \( 20 \% \) by weight. The battery holds 3.5 L of the acid and the volume remained practically constant during the discharge. Find the number of ampere-hours for which the battery must has been used.

The charging and discharging reactions are as follows:
\( P b+S O_{4}^{2-} \rightarrow P b S O_{4}+2 e^{-}(\text {charging }) \)
\( P b O_{2}+4 H^{\oplus}+S O_{4}^{2-}+2 e^{-} \rightarrow P b S O_{4}+ \)
\( 2 H_{2} O(\text { discharging }) \)
Subject: Maths
n Fig. \( \boldsymbol{A D} \perp \boldsymbol{C D} \) and \( \boldsymbol{C B} \perp \boldsymbol{C D .} \) If
\( A Q=B P \) and \( D P=C Q, \) prove that
\( \angle D A Q=\angle C B P \)
Subject: Maths
A vector is inclined at \( \frac{\pi}{4} \) rad with \( x \) -axis
\( \& \frac{\pi}{3} \) rad with \( y \) -axis then find angle of vector with z-axis.
\( ^{A} \cdot \frac{2 \pi}{3} r a d \)
в. \( \frac{5 \pi}{3} \) rad
c. \( \frac{\pi}{4} \) rad
D. \( \frac{\pi}{2} \) rad
Subject: Maths
Let \( a=2 \hat{i}+\hat{j}+\hat{k}, b=\hat{i}+2 \hat{j}-\hat{j} \) an a
unit vector \( \hat{c} \) be coplanar. If \( \hat{c} \) is perpendicular to \( a \), then \( c \) is equal to
\( \mathbf{A} \cdot(-\hat{j}+\hat{k}) \)
B. \( \pm \frac{1}{\sqrt{2}}(-\hat{j}+\hat{k}) \)
\( ^{\mathrm{C}} \pm \frac{1}{\sqrt{2}}(\hat{j}+\hat{k}) \)
D. None of these
Subject: Maths
If \( n \geq 1 \) is any integer, \( d(n) \) denotes
the number of positive factors of \( n, \) then
for any prime number \( \mathbf{p}, \mathbf{d}\left(\mathbf{d}\left(\mathbf{d}\left(\mathbf{p}^{7}\right)\right)\right)= \)
A .
B . 2
\( c \cdot 3 \)
D. 4
Subject: Physics
An elevator platform is going up at a
speed \( 20 \mathrm{ms}^{-1} \) and during its upward motion a small ball of 50 g mass falling
in downward direction strikes the
platform elastically at a speed \( 5 \mathrm{ms}^{-1} \) Find the speed (in \( \mathrm{ms}^{-1} \) ) with which the
ball rebounds:
Subject: Physics
For a circuit, \( L, C \) and \( R \) represent the
inductance, capacitance and resistance. Then, the dimensional
formula for \( C^{2} L R \) is
\( \mathbf{A} \cdot[M L T] \)
B . \( \left[M^{0} L^{0} T I^{0}\right] \)
c. \( \left[M^{2} L^{2} T^{0} I^{0}\right. \)
D \cdot \( \left[M^{0} L^{0} T^{3} I^{0}\right] \)
Subject: Biology
Assertion
Emphysema is a chronic disorder in which alveolar walls are damaged.
Reason

Emphysema is closely related to cigarette smoking.
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
A sample of gas has a volume of 0.2 litres measured at 1 atm pressure and
\( 0^{\circ} \mathrm{C} . \) At the same pressure, at \( 273^{\circ} \mathrm{C} \)
its volume will become:
A. 0.1 litre
B. 0.4 litre
c. 0.8 litre
D. 0.6 litre
Subject: Maths
The distance between the lines \( 4 x+ \)
\( 3 y=11 \) and \( 8 x+6 y=15 \) is :
\( A \cdot \frac{7}{2} \)
B. \( \frac{7}{3} \)
\( c \cdot \frac{7}{5} \)
D. \( \frac{7}{10} \)
Subject: Chemistry
An athlete is given 180 g of glucose \( \left(C_{6} H_{12} O_{6}\right) \) He utilises \( 50 \% \) of the energy due to internal combustion in
the body.In order to avoid storage of energy in the body.Calculate the mass of water he would need to perspire.Given enthalpy of combustion of glucose is
\( -2800 K J m o l^{-1} \)
Subject: Maths
ff \( \boldsymbol{D}_{\boldsymbol{r}}=\left|\begin{array}{ccc}\boldsymbol{r}-\mathbf{1} & \boldsymbol{n} & \boldsymbol{6} \\ (\boldsymbol{r}-\mathbf{1})^{2} & \boldsymbol{2} \boldsymbol{n}^{2} & \boldsymbol{4} \boldsymbol{n}-\boldsymbol{2} \\ (\boldsymbol{r}-\mathbf{1})^{3} & \boldsymbol{3} \boldsymbol{n}^{3} & \boldsymbol{3} \boldsymbol{n}^{2}-\boldsymbol{3} \boldsymbol{n}\end{array}\right| \)
then \( \sum_{r=1}^{n} D_{r}= \)
\( A \)
B.
c. \( \frac{n(n-1)}{2}-r^{2} \)
D. \( 2 n-n^{2} \)
Subject: Physics
A screen is placed \( 90 \mathrm{cm} \) from an object The image of the object on the screen is formed by convex lens at two different locations separated by \( 20 \mathrm{cm} \) Determine the focal length of the lens
(b) suppose the object has a size of 10 \( \mathrm{cm}, \) and in one case the image is half of its size. Determine image size when lens is displaced to second position
Subject: Chemistry
\( " \boldsymbol{N}<\boldsymbol{P}<\boldsymbol{A} \boldsymbol{s}^{\prime \prime} \)
Above order is incorrect for:
A. Electropositivity
B. Covalent radii
c. Size of \( M^{3} \)
D. Acidic nature of \( M_{2} O_{3} \) type oxide
Subject: Chemistry
The conversion of ozone into oxygen is
exothermic. Under what conditions is
ozone the most stable?
\( \mathbf{2} \boldsymbol{O}_{3}(\boldsymbol{g}) \rightleftharpoons \mathbf{3} \boldsymbol{O}_{2}(\boldsymbol{g}) \)
A. At low pressure and low temperature
B. At high pressure and high temperature
C. At high pressure and low temperature
D. At low pressure and high temperature
Subject: Physics
\( \begin{array}{ll}\text { Column } A & \text { Column B } \\ \text { a) Force } & \text { i) } f \times t \\ \text { b) Momentum } & \text { ii) } m \times a \\ \text { c) Impulse } & \text { iii) } m \times v\end{array} \)
\( \mathbf{A} \cdot a-i i i, b-i i, c-i \)
B . \( a-i i, b-i i i, c-i \)
c. \( a-i, b-i i, c-i i i \)
D. \( a-i i i, b-i, c-i i \)
Subject: Chemistry
The correct order of melting points of
hydrides of group 16 elements is:
\( \mathbf{A} \cdot H_{2} S>H_{2} S e>H_{2} T e \)
B. \( H_{2} S<H_{2} S e<H_{2} T e \)
\( \mathbf{c} \cdot H_{2} S>H_{2} S e<H_{2} T e \)
\( \mathbf{D} \cdot H_{2} S<H_{2} S e>H_{2} T e \)
Subject: Physics
In a Wheatstone bridge \( P=10 \Omega, Q=20 \Omega \)
\( \mathrm{R}=30 \Omega \). The value of 'S' in order that no
current flows through the galvanometer
is :
A . \( 15 \Omega \)
B. \( 45 \Omega \)
\( c \cdot 30 \Omega \)
D. \( 60 \Omega \)
Subject: Maths
If \( \lim _{x \rightarrow 0}\left(\frac{\sin 2 x}{x^{3}}+a+\frac{b}{x^{2}}\right)=0 \) then
the value of \( 3 a+b \) is
A . 2
B. -2
\( c \cdot-1 \)
D.
Subject: Chemistry
Avogadro number is equal to:
\( \mathbf{A} \cdot 6.023 \times 10^{21} \)
B . \( 6.023 \times 10^{22} \)
C \( \cdot 6.023 \times 10^{23} \)
D. \( 6.023 \times 10^{24} \)
Subject: Chemistry
Express the rate for the following reaction in terms of concentration of
reactants and products.
\( 5 B r^{-}(a q)+B r O_{3}^{-}(a q)+6 H^{+} \rightarrow \)
\( \mathbf{3} \boldsymbol{B} \boldsymbol{r}_{2}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{3} \boldsymbol{H}_{2} \boldsymbol{O}(l) \)
Subject: Physics
An electron of mass \( M_{e}, \) initially at rest moves through a certain distance in a uniform electric field in time \( t_{1} . A \)
proton of mass \( M_{p}, \) also initially at rest,
takes time \( t_{2}, \) to move through an equal distance in this uniform electric field.
Neglecting the effect of gravity, the ratio \( t_{2} / t_{1} \) is nearly equal to?
A . 1
в. \( \sqrt{\frac{M_{p}}{M_{e}}} \)
c. \( \sqrt{\frac{M_{e}}{M_{p}}} \)
D. 1836
Subject: Maths
If the area of a triangle is 81 square \( \mathrm{cm} \) and its perimeters is \( 27 \mathrm{cm} \), them its in
radius is
A. \( 6 \mathrm{cm} \)
B. 3 \( \mathrm{cm} \)
c. \( 1.5 \mathrm{cm} \)
D. none of these
Subject: Maths
ff \( x_{1}, x_{2}, \dots, x_{n} \) are \( ^{\prime} n^{\prime} \) positive real
numbers; then \( A . M \geq G . M \geq H . M \)
\( \frac{x_{1}+x_{2}+x_{3}+\ldots+x_{n}}{n} \geq\left(x_{1} x_{2} x_{3} \ldots x_{n}\right)^{n} \geq \)
\( \frac{n}{\frac{1}{x_{1}}+\frac{1}{x_{2}}+\frac{1}{x_{3}}+\ldots+\frac{1}{x_{n}}} \) equality occurs when
numbers are same using this concept.Here equality occurs numbers are of same.Using this concept answer the following f \( a>0, b>0, c>0 \) and the minimum
value of \( a\left(b^{2}+c^{2}\right)+b\left(c^{2}+a^{2}\right)+ \)
\( c\left(a^{2}+b^{2}\right) \) is \( \lambda a b c, \) then \( \lambda \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c .3 \)
D.
Subject: Physics
The number of radioactive nuclei that
were present after \( 7 h \) is
\( A \cdot 2 \times 10^{4} \)
B . \( 1.25 \times 10^{8} \)
c. \( 1.875 \times 10^{6} \)
D. \( 1.25 \times 10^{4} \)
Subject: Maths
The equation of the straight line passing through the point of intersection of the straight lines \( \frac{x}{a}= \) \( \frac{\boldsymbol{y}}{\boldsymbol{b}}=1 \) and \( \frac{\boldsymbol{x}}{\boldsymbol{b}}+\frac{\boldsymbol{y}}{\boldsymbol{a}}=\mathbf{1} \) and having
infinite slopes is
Subject: Physics
A ray of light is incident at the glass-
water interface at an angle \( i \). It merges finally parallel to the surface of the water. Then, the value of \( \mu_{g} \) would
be(where \( \mu_{g} \) is the refractive index of glass with respect to water)
A \( \cdot(4 / 3) \sin i \)
B. 1/ \( \sin i \)
\( c \cdot 4 / 3 \)
\( D \)
Subject: Physics
A object starts from rest at \( t=0 \) and
accelerates at a rate given by \( a=6 t \)
What is its displacement at any time \( t ? \)
A \( \cdot t^{2} \)
в. \( t^{3} \)
\( c \cdot 3 t^{2} \)
D. \( 3 t^{3} \)