AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
An inductance \( L, \) a capacitance \( C \) and
a resistance \( \boldsymbol{R} \) may be connected to an
\( A C \) source of angular frequency \( \omega, \) in
three different combinations of \( \boldsymbol{R} \boldsymbol{C}, \boldsymbol{R} \boldsymbol{L} \)
and \( L C \) in series. Assume that \( \omega L= \) \( \frac{1}{\omega C} . \) The power drawn by the three
combinations are \( \boldsymbol{P}_{1}, \boldsymbol{P}_{2}, \boldsymbol{P}_{3} \)
respectively. Then,
\( \mathbf{A} \cdot P_{1}>P_{2}>P_{3} \)
B \( \cdot P_{1}=P_{2}<P_{3} \)
\( \mathbf{C} \cdot P_{1}=P_{2}>P_{3} \)
D \( \cdot P_{1}=P_{2}=P_{3} \)
Subject: Biology
Assertion
The water molecules are held together
from root cells to the vascular bundle
because of cohesive force.
Reason
Water does not ascend in the plant because of transpiration pull.
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: Biology
Assertion
Methane, component of green house gases, contributing to global warming
is about 20 percent.
Reason
Introduction of multi-point fuel
injection engines in automobiles has decreased methane content in the
exhausts.
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
A body oscillates with SHM according to
the equation \( \boldsymbol{x}=\mathbf{5 . 0} \cos (2 \pi t+\boldsymbol{\pi}) . \) At
time \( t=1.5 s, \) its displacement, speed
and acceleration respectively is:
B . \( 5,0,-20 \pi^{2} \)
c. \( 2.5,+20 \pi, 0 \)
D. \( -5.0,+5 \pi,-10 \pi^{2} \)
Subject: Maths
The curve \( y=a x^{3}+b x^{2}+c x+d \) has a
point on inflexion at \( x=1 \) then
\( \mathbf{A} \cdot a+b=0 \)
B . \( a+3 b=0 \)
c. \( 3 a+b=0 \)
D. \( 3 a+b=1 \)
Subject: Chemistry
Which of the following species are oxidised and reduced in the following (unbalanced) reaction?
\( \boldsymbol{C N}^{-}+\boldsymbol{O C l}^{-} \longrightarrow \boldsymbol{N}_{2}+\boldsymbol{H} \boldsymbol{C O}_{3}^{-}+ \)
\( C l^{-} \)
A. oxidized- \( C, N \) in \( C N^{-} \) ", reduced \( -O C l^{-} \)
B. Oxidized- \( N, C N^{-}, H C O_{3}^{-} ; N_{2} \) reduced \( -C O C l^{-} \)
C. oxidized- \( C, N, H C O_{3}^{-} ; N_{2} \) reduced \( -O C l^{-}, C N^{-} \)
D. None of these
Subject: Maths
Integrate the following functions with respect to t: \( \int \frac{\boldsymbol{d t}}{(\boldsymbol{6 t}-\mathbf{1})} \)
A \( \cdot \frac{1}{6} \ln (6 t-1)+C \)
B \( \cdot \ln (6 t-1)+C \)
c. \( -\ln (6 t-1)+C \)
D. \( -\frac{1}{6} \ln (6 t-1)+C \)
Subject: Maths
If \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \frac{1 . \cos x+5 \cos 3 x+\cos 5 x}{\cos 6 x+6 \cos 4 x+15 \cos 2 x+10} \) then
\( \boldsymbol{f}(\mathbf{0})+\boldsymbol{f}^{\prime}(\mathbf{0})+\boldsymbol{f}^{\prime \prime}(\mathbf{0})= \)
A \( \cdot \frac{1}{2} \)
B.
\( c \cdot-\frac{1}{2} \)
\( D \)
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{c}-2 \\ 4 \\ 5\end{array}\right] \) and \( B=\left[\begin{array}{lll}1 & 3 & -6\end{array}\right], \) then
verify that \( (A B)^{T}=B^{T} A^{T} \)
Subject: Physics
A wooden piece \( 5 N \) in weight and
\( 5 c m \times 3 c m \times 2 c m \) in size lies on
\( 5 c m \times 2 c m \) face. The pressure exerted
by it in \( N \) per \( c m^{2} \) is:
A. 150
B. 50
c. 0.5
D. 15
Subject: Physics
If \( R \) is radius of the earth and \( W \) is work
done in lifting a body from the ground to an altitude \( R \), the work which should be
done in lifting it further to twice that altitude is:
A \( \cdot \frac{W}{2} \)
B. \( W \)
c. \( \frac{W}{3} \)
D. \( 3 W \)
Subject: Maths
One Indian and four American men and
their wives are to be seated randomly around a circular table. Then the
conditional probability that the Indian man is seated adjacent to his wife given that each American man is seated adjacent to his wife is
A . \( 1 / 2 \)
B. \( 1 / 3 \)
\( c \cdot 2 / 5 \)
D. \( 1 / 5 \)
Subject: Physics
In the network shown, the sources of
emf \( 2 \vee, 12 \) V and 16 V are taken to be
ideal. Select incorrect statements from
the following:
This question has multiple correct options
A \( \cdot \) The potential drop across \( 4 \Omega \) is \( \frac{28}{13} \vee \)
B. The current through 2 v battery is \( \frac{17}{13} \) A, discharging.
C ' the current through 2 V battery is \( \frac{17}{13} \) A, charging.
D. The potential drop across \( 8 \Omega \) is \( \frac{60}{13} \vee \)
Subject: Physics
Two masses \( M_{1} \) and \( M_{2} \) are attached
to the end of a light string which passes
over a massless pulley attached to the
top of a double inclined smooth plane of
angles of inclination \( \boldsymbol{\alpha} \) and \( \boldsymbol{\beta} \). If \( \boldsymbol{M}_{\mathbf{2}}> \)
\( M_{1} \) and \( \beta>\alpha \) then the acceleration of
block \( M_{2} \) down the inclined will be:
A \( \cdot \frac{M_{2} g(\sin \beta)}{M_{1}+M_{2}} \)
В. \( \frac{M_{1} g(\sin \alpha)}{M_{1}+M_{2}} \)
\( c \)
D. Zero
Subject: Maths
The argument of the complex number
\( \sin \frac{6 \pi}{5}+i\left(1+\cos \frac{6 \pi}{5}\right) \) is
A \( \cdot \frac{6 \pi}{5} \)
в. \( \frac{5 \pi}{6} \)
c. \( \frac{9 \pi}{10} \)
D. \( \frac{2 \pi}{5} \)
Subject: Chemistry
The equation of the curve obtained by connecting all those points where the vapors of above mixture (all mixtures of
different composition are taken) just start forming will be
A \( \cdot P=P_{C}^{o}+\left(P_{B}^{o}-P_{C}^{o}\right) X_{B}^{l} \)
B . \( P=P_{B}^{o}+\left(P_{B}^{o}-P_{C}^{o}\right) X_{B}^{l} \)
\( ^{\mathrm{c}} \cdot p=\frac{P_{B}^{o} P_{C}^{o}}{X_{B}^{o}\left(P_{C}^{o}-P_{B}^{o}\right)+P_{B}^{o}} \)
D. \( P=\frac{P_{B}^{o} P_{C}^{o}}{X_{B}^{l}\left(P_{C}^{o}-P_{B}^{o}\right)+P_{B}^{o}} \)
Subject: Maths
Which one of the following is the unit vector perpendicular to both \( \overrightarrow{\boldsymbol{a}}=-\hat{\mathbf{i}}+ \) \( \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \) and \( \overrightarrow{\boldsymbol{b}}=\hat{\boldsymbol{i}}-\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} ? \)
A \( \cdot \frac{\hat{i}+\hat{j}}{\sqrt{2}} \)
в. \( \hat{k} \)
\( c \cdot \frac{\hat{j}+\hat{k}}{\sqrt{2}} \)
D. \( \frac{\hat{i}-\hat{\jmath}}{\sqrt{2}} \)
Subject: Maths
If \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{x \sin \frac{1}{x}, x \neq 0 \quad k \quad, x=0\right\} \) is
continuous at \( x=0, \) then the value of \( k \)
is
\( A \cdot 1 \)
B. - 1
c.
D. 2
Subject: Chemistry
A substance A decomposes in solution following the first order kinetics. Flask contains 1 L of 1 M solution of \( A \) and flask
II contains \( 100 \mathrm{mL} \) of \( 0.6 \mathrm{M} \) solution
After \( 8 \mathrm{hr} \), the concentration, of \( \mathrm{A} \) in the flask I becomes 0.25 M. What will be the
time for the concentration of \( A \) in flask
to become 0.3 M?
A . \( 0.4 \mathrm{hr} \)
B. 2.4 hr
c. \( 4.0 \mathrm{hr} \)
D. Unpredictable as rate constant is not given
Subject: Physics
The length of a metal wire is \( L_{1} \) when
the tension is \( T_{1} \) and \( L_{2} \) when the
tension is \( T_{2} . \) The unstretched length of
wire is :
A \( \cdot \frac{L_{1}+L_{2}}{2} \)
в. \( \sqrt{L_{1} L_{2}} \)
c. \( \frac{T_{2} L_{1}-T_{1} L_{2}}{T_{2}-T_{1}} \)
D. \( \frac{T_{2} L_{1}+T_{1} L_{2}}{T_{2}+T_{1}} \)
Subject: Maths
If \( \boldsymbol{x}^{2}+\boldsymbol{y}^{2}=\boldsymbol{2} \) and \( \boldsymbol{y}_{2}=\boldsymbol{A} \boldsymbol{y}^{-3} \) then \( \mathbf{A}= \)
A . -2
B. -
\( c \cdot 0 \)
\( D \)
Subject: Chemistry
\( \mathbf{2} \boldsymbol{A}+\boldsymbol{B} \rightarrow \boldsymbol{C}+\boldsymbol{D} \)
In this reaction, if we double the
concentration of \( A, \) reaction rate
become two times. And in another
experiment, we double the
concentration of \( A \) and \( B \), reaction rate
again become two times. What is the
order of this reaction?
A
B. 3
\( c \cdot 2 \)
D. 1.5
Subject: Chemistry
Find the forward \( \Delta_{r} U^{\circ} \) at \( 300 K \) for the
reaction \( 4 H C l(g)+O_{2}(g) \rightarrow \)
\( 2 C l_{2}(g)+2 H_{2} O(g) \) Assume all gases
are ideal. Given \( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) \rightarrow \)
\( 2 H C l(g) \Delta_{r} H_{300}^{\circ}=-184.5 k J / m o l \)
\( \mathbf{2} \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{O}_{2}(\boldsymbol{g}) \rightarrow \mathbf{2} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \)
\( \boldsymbol{\Delta}_{r} \boldsymbol{H}_{300}^{\circ}=-\mathbf{4 8 3 k J} / \) mol (Use \( \mathrm{R}=\mathbf{8 . 3} \)
J/mole)
A . 111.5 kJ/mole
B. -109.01 kJ/mole
c. -111.5 kJ/mole
D. None
Subject: Chemistry
Some of alkali metal salts are coloured
\( N a_{2} C r O_{4}- \) yellow, \( K M n O_{4}- \) pink
\( K_{2} M n O_{4} \) -green. It is due to:
A. cations are coloured ions
B. anions are coloured ions
c. both \( A \) and \( B \)
D. none of the above
Subject: Chemistry
Among the oxides of nitrogen:
\( N_{2} O_{3}, N_{2} O_{4} \) and \( N_{2} O_{5} ; \) the
molecule(s) having nitrogen-nitrogen bond is/are:
A. Only \( N_{2} O_{5} \)
B. \( N_{2} O_{3} \) and \( N_{2} O_{4} \)
c. \( N_{2} O_{3} \) and \( N_{2} O_{5} \)
D. \( N_{2} O_{4} \) and \( N_{2} O_{5} \)
Subject: Chemistry
Which of the following reactions proceed in forward direction with an
increase in temperature?
\( \mathbf{A} \cdot H_{2}(g)+I_{2}(g) \rightleftharpoons 2 H I(g)+3000 c a l \)
B \( \cdot N_{2}(g)+O_{2}(g) \rightleftharpoons 2 N O(g)-43200 c a l \)
\( \mathbf{c} \cdot N_{2}(g)+3 H_{2}(g) \rightleftharpoons 2 N H_{3}(g)+22400 c a l \)
\( \mathbf{D} \cdot C(g)+O_{2}(g) \rightleftharpoons C O_{2}(g)+94300 c a l \)
Subject: Chemistry
Salt \( A \) commonly used in bakery products, on heating, gets converted into another salt \( B \) which itself is used
for removal of hardness of water and a
\( \operatorname{gas} C \) is evolved. The gas \( C \) when
passed through lime water turns it
milky. Identify \( A, B \) and \( C \).
A. Salt \( A \), which is sodium bicarbonate; Salt \( B \) is sodium carbonate; \( C \) is \( C O_{2} \) gas
B. Salt A, which is sodium carbonate; Salt \( B \) is sodium bicarbonate; \( C \) is \( H_{2} \) gas
c. salt \( A, \) which is sodium bicarbonate; Salt \( B \) is sodium carbonate; \( C \) is \( H_{2} \) gas
D. None of these
Subject: Chemistry
\( (\mathbf{1}) \boldsymbol{C}_{6} \boldsymbol{H}_{5}-\stackrel{\mathbf{0}}{\boldsymbol{C}}-\boldsymbol{C}_{\mathbf{6}} \boldsymbol{H}_{\mathbf{5}} \)
\( (2) C_{6} H_{5}-C H O \)
\( (\mathbf{3}) \boldsymbol{p}-\boldsymbol{C} \boldsymbol{H}_{3}-\boldsymbol{C}_{6} \boldsymbol{H}_{4}-\boldsymbol{C} \boldsymbol{H} \boldsymbol{O} \)
\( (4) p-C H_{3} O-C_{6} H_{4}-C H O \)
Correct order for nucleophilic addition reaction.
A \( .2>1>3>4 \)
4 \( 4>1>3>1>3>1>3>2 \) 4
в. \( 4>3>2>1 \)
c. \( 2>3>4>1 \)
D. \( 4>2>3>1 \)
Subject: Physics
For a normal eye, in case of an adult, the
least distance of distinct vision is:
A. 5 to \( 8 \mathrm{cm} \)
B. 10 to \( 15 \mathrm{cm} \)
c. 20 to \( 25 \mathrm{cm} \)
D. 30 to \( 35 \mathrm{cm} \)
Subject: Maths
The radius of the base of a cone is
increasing at the rate of \( 3 \mathrm{cm} / \mathrm{minute} \) and the altitude is decreasing at the rate of \( 4 \mathrm{cm} / \mathrm{minute} . \) The rate of change
of lateral surface when the radius is
\( \mathbf{7} c \boldsymbol{m} \) and altitude \( \mathbf{2 4 c m} \) is
A \( .54 \pi c m^{2} / \) min
B. \( 7 \pi c m^{2} / \) min
\( \mathbf{c} \cdot 27 c m^{2} / \min \)
D. none of these
Subject: Maths
\( n \stackrel{L t}{\rightarrow} \infty \)
\( \left\{\frac{\sqrt{\mathbf{1}}+\sqrt{\mathbf{2}}+\sqrt{\mathbf{3}}+\ldots+\sqrt{\boldsymbol{n}}}{\boldsymbol{n} \sqrt{\boldsymbol{n}}}\right\}= \)
\( A \cdot O \)
B.
\( c \cdot 2 / 3 \)
D. 3/2
Subject: Physics
A leaky capacitor \( 10 \Omega / 60^{\circ} \) is
connected in series with a \( 10 \Omega \)
resistance. Find the overall impedance.
Fig. 26.42
A. \( 10 \Omega \)
B. \( 10 \sqrt{2} \) ?
\( \mathrm{c} \cdot 15 \Omega \)
D. \( 10 \sqrt{3} \Omega \)
Subject: Chemistry
Specific heat at constant volume of a monoatomic gas is 0.75 cal/g. 1 mole of this gas requires 3 cal of heat to raise the temperature of 1 mole of this gas.
The heat required to raise the
temperature through \( 1^{\circ} \mathrm{C} \) of 1 -mole gas
at constant pressure is:
A. 5
B. 6
\( c \cdot 3 \)
D.
Subject: Chemistry
The pair of molecules forming strongest hydrogen bonds are:
A. \( \operatorname{SiH}_{4} \) and \( \operatorname{SiF}_{4} \)
в. \( C H_{3} C O C H_{3} \) and \( C H C l_{3} \)
c. \( C H_{3} C O O H \) and \( H C O O H \)
D. \( H_{2} O \) and \( H_{2} \)
Subject: Physics
A body is sliding down an inclined plane having coefficient of friction \( 0.5 . \) If the normal reaction is twice that of the
resultant downward force along the
incline, the angle between the inclined plane and horizontal is
A \( \cdot 15^{\circ} \)
B . \( 30^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 60^{\circ} \)
Subject: Maths
The value of \( \sum_{r=1}^{n} r\left(^{n} C_{r}+^{r} P_{r}\right) \) is
A \( \cdot n \cdot 2^{n-1}-1 \)
B . \( n \cdot 2^{n-1}+(n+1) ! \)
C \( \cdot n \cdot 2^{n-1}+(n+1) !-1 \)
D. \( n^{2}+n+5 \)
Subject: Maths
A particle is moving with a velocity of \( \boldsymbol{v}=\left(\mathbf{3}+\mathbf{6} \boldsymbol{t}+\mathbf{9} \boldsymbol{t}^{2}\right) \boldsymbol{m} / \boldsymbol{s} . \) This
displacement of the particle in the interval \( t=5 s \) to \( t=8 s \) is
\( \mathbf{A} \cdot 1287 m \)
в. \( 1285 \mathrm{m} \)
c. \( 1280 m \)
D. \( 1290 m \)
Subject: Chemistry
\( \boldsymbol{N} \boldsymbol{i}\left|\boldsymbol{N} \boldsymbol{i}^{2+}(\boldsymbol{1} . \boldsymbol{0} \boldsymbol{M}) \| \boldsymbol{A} \boldsymbol{u}^{3+}(\mathbf{1} . \boldsymbol{0} \boldsymbol{M})\right| \boldsymbol{A} \boldsymbol{u} \)
(where \( \boldsymbol{E}^{o} \) for \( \boldsymbol{N} \boldsymbol{i}^{2+} / \boldsymbol{N} \boldsymbol{i} \) is \( -\mathbf{0 . 2 5} \) and \( \boldsymbol{V} \)
and \( E^{o} \) for \( A u^{3+} / A u \) is \( 0.150 V \) ). What
is the emf of the cell?
A \( .+0.4 V \)
в. \( -1.75 V \)
\( \mathrm{c} .+1.25 \mathrm{V} \)
D. \( +1.75 V \)
Subject: Physics
A vertical column of liquid \( h_{0} \) long at \( 0^{\circ} C \)
balances another column of same liquid
at \( t^{o} C . \) If \( r \) is the absolute expansion of
that liquid, height of second liquid column is :
\( \mathbf{A} \cdot h_{0}(1-r t) \)
в. \( \frac{h_{0}}{(1-r t)} \)
c. \( h_{0}(1+r t) \)
D. \( \frac{h_{0}}{1+r t} \)
Subject: Maths
Volume of the box of outer dimensions
\( 22 \mathrm{cm} \times 12 \mathrm{cm} \times 9 \mathrm{cm} \)
A \( \cdot 2276 \mathrm{cm}^{3} \)
B. 2500 \( c m^{3} \)
c. \( 2600 \mathrm{cm}^{3} \)
D. 2376 \( c m^{3} \)
Subject: Physics
The amount of work done in lifting a
mass ' \( m \) ' from the surface of the earth
to height \( 2 R \) is
A. \( 2 m g R \)
в. \( 3 m g R \)
c. \( \frac{3}{2} m g R \)
D. \( \frac{2}{3} m g R \)
Subject: Maths
If \( f(x y)=f(x) . f(y) \forall x, y \in R \) If the
function is continuous at one point \( \boldsymbol{x}= \)
\( a, \) then \( f(x) \) is:
A. continuous for all \( x \in R-\{0\} \)
B. continuous forall \( x \in R \)
c. discontinuous on
D. continuous at \( x=0 \)
Subject: Physics
\( \mathrm{cm} \) and having a resistance of 0.2 ohm
is allowed to slide over two paralle
thick metallic rails with uniform
velocity of \( 0.2 \mathrm{m} / \mathrm{s} \) as shown in the
figure. The rails are situated in a
horizontal plane. If the horizontal
component of earth's magnetic field is
\( 0.3 \times 10^{-4} \mathrm{T} \) and a steady state current
of \( 3 \mu A \) is induced through the rod. The
angle of dip will be :
A \( \cdot \tan ^{-1}\left(\frac{3}{4}\right) \)
B. \( \tan ^{-1}\left(\frac{1}{\sqrt{3}}\right) \)
\( \mathbf{c} \cdot \tan ^{-1}(\sqrt{3}) \)
D \( \tan ^{-1}\left(\frac{1}{3}\right) \)
Subject: Maths
If \( \boldsymbol{y}=\log _{e}\left(\frac{\boldsymbol{x}^{2}}{e^{2}}\right), \) then \( \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}} \) equals
\( A \cdot-\frac{1}{x} \)
B. \( -\frac{1}{x^{2}} \)
c. \( \frac{2}{x^{2}} \)
D. \( -\frac{2}{x^{2}} \)
Subject: Chemistry
Predict product (s) in the following reaction,
\( \boldsymbol{P}+\boldsymbol{O H}^{-} \rightarrow \boldsymbol{P r o d u c t s} \)
This question has multiple correct options
A \( . P H_{3} \)
B \( \cdot P O_{4}^{2} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{PO}_{2} \)
D. \( P O_{2}^{-} \)
Subject: Chemistry
The degree of dissociation of \( N_{2} O_{4} \) into
\( N O_{2} \) at 1 atmosphere and \( 40^{\circ} C \) is 0.25
Calculate its \( \boldsymbol{K}_{\boldsymbol{p}} \) at \( \boldsymbol{4} \boldsymbol{0}^{\circ} \boldsymbol{C} \)
Subject: Physics
Two parallel wires \( 1 m \) apart carry
currents of \( 1 A \) and \( 3 A \) respectively in
opposite directions. The force per unit length acting between these two wires is
A \( .6 \times 10^{-7} \mathrm{Nm}^{-1} \) repulsive
B. \( 6 \times 10^{-7} \mathrm{Nm}^{-1} \) attractive
c. \( 6 \times 10^{-5} \mathrm{Nm}^{-1} \)repulsive
D. \( 6 \times 10^{-5} \mathrm{Nm}^{-1} \) attractive
Subject: Maths
Evaluate \( \left(x^{3}+2 x^{2}+3 x\right) \div 2 x \)
A \( \cdot\left(x^{2}+2 x-3\right) \div 2 \)
B. \( \left(x^{2}-2 x+3\right) \div 2 \)
c. \( \left(x^{2}+2 x+3\right) \div 2 \)
D. \( \left(x^{2}+x+3\right) \div 2 \)
Subject: Chemistry
Which of the following is not a redox reaction?
A. \( M g+N_{2} \rightarrow M g_{3} N_{2} \)
B . \( M n O_{4}^{-}+C_{2} O_{4}^{2-} \rightarrow M n^{2+}+C O_{2} \)
c. \( C u S O_{4}+K I \rightarrow 2 C u I+I_{2}+K_{2} S O_{4} \)
D. \( A g C l+N H_{3} \rightarrow\left[A g\left(N H_{3}\right)_{2}\right] C l \)
Subject: Chemistry
A gas can never be liquefied at?
A. \( T=T_{C} \) and \( P=P_{C} \)
в. \( T<T_{C} \) and \( P=P_{C} \)
c. \( T<T_{C} \) and \( P<P_{C} \)
D. \( T>T_{C} \) and \( P>>P_{C} \)
Subject: Maths
If \( M \) denotes the maximum value of
\( \left(1+\sec ^{-1} x\right)\left(1+\cos ^{-1} x\right) \& m \)
denotes the maximum value of
\( \left(1+\operatorname{cosec}^{-1} x\right)\left(1+\sin ^{-1} x\right), \) then
\( \left[\frac{M}{m}\right] \) is (where [.] denotes greatest integer function)
Subject: Physics
A uniform solid sphere of mass \( \mathrm{M} \) and
radius \( R \) is kept on the horizontal
surface.

Find potential energy of the solid
sphere
A \( \cdot \frac{m g R}{2} \)
в. тg R
\( c \cdot \frac{m g R}{4} \)
D. \( \frac{2 m g}{B} \)
Subject: Chemistry
In alkyl halides, the homologous series of alkyl halide is represented as:
A. \( C_{n} H_{2 n+1} X \)
в. \( C_{n} H_{2 n+4} X \)
c. \( C_{n} H_{2 n+3} X \)
D. \( C_{n} H_{Z n+2} X \)
Subject: Physics
A force \( -F \widehat{k} \) acts on \( 0, \) the origin of the
coordinate system.The torque about the point (1,-1) is
A \( . F(\hat{i}-\hat{j}) \)
B . \( -F(\hat{i}+\widehat{j}) \)
C \( . F(\hat{i}+\widehat{j}) \)
D . \( -F(\hat{i}-\widehat{j}) \)
Subject: Chemistry
Which of the following configuration
can form a diatomic molecule?
\( \mathbf{A} \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{2} \)
B \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{4} \)
\( \mathbf{C} \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{5} \)
D. \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} \)
E \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{1} \)
Subject: Maths
A pole of height 20 ft has a shadow of length \( 11.55 \mathrm{ft} \) at a particular instant of
time. Find the angle of elevation (in degree) of the sun at this point of time.
\( \mathbf{A} \cdot 90 \)
B. 60
\( c \cdot 30^{\circ} \)
D. 45
Subject: Physics
A physical quantity \( x \) is calculated from the relation \( x=\frac{a^{2} b^{3}}{c \sqrt{d}} . \) If the percentage
error in \( a, b, c \) and \( d \) are \( 2 \%, 1 \%, 3 \% \) and \( 4 \% \), respectively, what is the percentage
error in \( x \) ?
Subject: Physics
Match the columns
\( \mathbf{A} \)
\( B \)
(1) Speed of
(a) 4.3 light years away from light earth
(2) Light year
(b) \( 300,000 \mathrm{km} / \mathrm{s} \)
(3) Sun
(c) Nearest star
(4) Alpha
(d) distance travelled by light in Centauri \( \quad \) one year
(e) 18 light minutes away from the Earth
A. \( 1-d \) 2-d, \( 3-a, 4-e \)
B. \( 1-a, 2-b, 3-c, 4-e \)
\( \mathbf{C} \cdot 1-\mathrm{d}, 2-\mathrm{b}, 3-\mathrm{e}, 4-\mathrm{c} \)
D. \( 1-b, 2-d, 3-c, 4-a \)
Subject: Physics
Current of \( \frac{50}{\pi} H z \) frequency is passing through an A.C circuit having series combination of resistance \( \boldsymbol{R}=\mathbf{1 0 0} \mathbf{\Omega} \)
and inductor \( L=1 H, \) then phase
difference between voltage and current
is
A \( \cdot 60^{\circ} \)
B. \( 30^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 90^{\circ} \)
Subject: Maths
Evaluate \( \frac{\cos 45^{0}}{\sec 30^{0}+\operatorname{cosec} 30^{0}} \)
A. \( \frac{\sqrt{2}}{\sqrt{3}+1} \)
B. \( \frac{\sqrt{3}}{2 \sqrt{2}+2 \sqrt{6}} \)
c. \( \frac{\sqrt{2}}{\sqrt{2}+1} \)
D. \( \frac{\sqrt{2}}{\sqrt{3}+2} \)
Subject: Physics
\( \mathrm{KE}= \)
\( \mathbf{A} \cdot \operatorname{mgh} \)
\( \mathbf{B} \cdot m v^{2} \)
\( \mathbf{c} \cdot \frac{1}{2} m g h \)
D \( \cdot \frac{1}{2} m v^{2} \)
Subject: Chemistry
IUPAC name of \( \boldsymbol{C} \boldsymbol{H}_{3}-\boldsymbol{O}-\underset{\boldsymbol{I}}{\boldsymbol{C} \boldsymbol{H}_{3}} \boldsymbol{H}-\boldsymbol{C} \boldsymbol{H}_{3} \)
is
A. 3-Methoxy propane
B. 2-Methyl methoxy ethane
c. 1-Methoxy-1-methyl ethane
D. Methoxy isopropane
Subject: Chemistry
HOTS
The various types of hydrides and
examples of each type are given below:
Hydride type Compound A Electron deficient
B Saline \( \quad \) ii \( \quad \boldsymbol{C H}_{4} \)
C Electron-precise iii \( \quad N H_{3} \)
D Interstitial \( \quad \) iv \( \quad B_{2} H_{6} \)
E Electron rich
\( \mathbf{v} \quad \mathbf{C r H} \)
Choose the correct matching from the
code given below:
\( A \cdot(A)-(i i),(B)-(i v),(C)-(v),(D)-(i i i),(E)-(i) \)
B. (A)-(iv), (B) - (i), (C) - (ii), (D) - (v), (E) - (iii)
\( c \cdot(A)-(i v),(B)-(i i i),(C)-(v),(D)-(i i),(E)-(i) \)
\( D \cdot(A)-(v),(B)-(i i i),(C)-i(v),(D)-(i i),(E)-(i) \)
Subject: Physics
A coil of 100 turns and 5 square
centimeter is placed in a magnetic field
\( \mathrm{B}=0.2 \mathrm{T} . \) The normal to the plane of the coil makes an angle of 60 with the direction of the magnetic field. The magnetic flux linked with the coil is :
A \( \cdot 5 \times 10^{-3} \mathrm{wb} \)
B. \( 5 \times 10^{-5} \mathrm{wb} \)
\( c \cdot 10^{-2} w b \)
D. \( 10^{-4} \mathrm{wb} \)
Subject: Physics
Positive and negative point charges of equal magnitude are kept at \( \left(0,0 \frac{a}{2}\right) \) and \( \left(0,0 \frac{-a}{2}\right), \) respectively. The work done by the electric field when another
positive point charge is moved from \( (-a, 0,0) \) to \( (0, a, 0) \) is:
A. positive
B. negative
c. zero
D. depends on the path connecting the initial and final positions
Subject: Physics
\( \mathbf{A} \)
\( 2 k g \) mass starts from rest on an
inclined smooth surface with
inclination \( 30^{\circ} \) and length 2 m. How much will it travel before coming into rest on a horizontal frictional surface
with frictional coefficient of 0.25
\( A \cdot 4 M \)
B. 6 M
\( c \cdot 8 M \)
\( D \cdot 2 M \)
Subject: Maths
For \( \left(\boldsymbol{\theta}_{1}, \boldsymbol{\theta}_{2}, \boldsymbol{\theta}_{3}, \ldots \ldots \boldsymbol{\theta}_{n}\right) \boldsymbol{\epsilon}(\mathbf{0}, \boldsymbol{\pi} / 2) \) if
\( \ln \left(\sec \theta_{1}-\tan \theta_{1}\right)+\ln \left(\sec \theta_{2}-\right. \)
\( \left.\tan \theta_{2}\right)+\ldots . \ln \left(\sec \theta-\tan \theta_{n}\right)+\ln \pi= \)
0 then find the value of \( \cos \left[\left(\sec \theta_{1}+\right.\right. \)
\( \left.\tan \theta_{1}\right)\left(\sec \theta_{2}+\tan \theta_{2}\right) \dots . .\left(\sec \theta_{n}+\right. \)
\( \left.\tan \theta_{n}\right) \)
Subject: Chemistry
Which physical properties of \( \boldsymbol{N} \boldsymbol{H}_{3} \)
enable separation of \( \boldsymbol{N} \boldsymbol{H}_{3} \) from a
mixture of \( \boldsymbol{N} \boldsymbol{H}_{3}, \boldsymbol{N}_{2} \) and \( \boldsymbol{H}_{2} ? \)
A. Ammonia is easily liquefied
B. Ammonia is highly soluble
c. Both A and B
D. None of these