AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A transformer having efficiency of \( 75 \% \) is working on \( 220 V \) and \( 4.4 k W \) power supply. If the current in the secondary coil is \( 5 A . \) What will be the voltage
across secondary coil and the current in primary coil?
\( \mathbf{A} \cdot V_{s}=220 V, i_{p}=20 A \)
B. \( V_{s}=660 V, i_{p}=15 A \)
C . \( V_{s}=660 V, i_{p}=20 A \)
D. \( V_{s}=220 V, i_{p}=15 A \)
Subject: Physics
A rectangular block of mass \( M \) and
height \( a \) is resting on a smooth leve
surface. A force \( \boldsymbol{F} \) is applied to one
corner as shown in figure. At what point
should a parallel force \( 3 F \) be applied in
order that the block shall undergo pure translational motion? Assume normal
contact force between the block and
surface passes through the centre of
gravity of the block.
A \( \cdot \frac{a}{3} \) vertically above centre of gravity
B \cdot \( \frac{a}{6} \) vertically above centre of gravity
\( c . \) no such point exists
D. it is not possible
Subject: Chemistry
Match the catalysts to the correct
processes:
Catalyst \( \quad \) Process
A. \( T i C l_{3} \) ¡. Wacker process
ii. Ziegler - Natta
B. \( P d C l_{2} \quad \) polymerization
С. \( C u C l_{2} \)
iii. Contact process
D. \( V_{2} O_{5} \)
¡v. Deacon's process
\( A \cdot(A)-(i i i),(B)-(i i),(C)-(i v),(D)-(i) \)
B. (A) - (ii), (B) - (i), (C) - (iv), (D) - (iii)
C. \( (A)-(\text { ii) },(B)-(\text { iii) },(C)-(i v),(D)-(i) \)
D. (A) - (iii), (B) - (i), (C) - (ii), (D) - (iv)
Subject: Chemistry
Assertion
\( \mathbf{S}_{2} \boldsymbol{O}_{\mathbf{7}}^{\mathbf{2}-} \)
\( \& C r_{2} O_{7}^{2-} \) both exist.
Reason
Both have same valence electrons.
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 cylinder of length \( l \) and radius \( R \) is placed in a uniform electric field \( \boldsymbol{E} \)
parallel to the cylindrical axis. The total flux through the surface of the cylinder is given by
\( \mathbf{A} \cdot 2 \pi R^{2} E \)
в. \( \frac{\pi R^{2}}{E} \)
c. \( \pi\left(R^{2}-R l\right) E \)
\( D \)
Subject: Physics
Two particles of masses \( m_{1} \) and \( m_{2} \) in
projectile motion have velocities \( v_{1} \) and
\( v_{2} \) respectively at time \( t=0 . \) They
collide at time \( t_{0} . \) Their velocities
become \( v_{1}^{\prime} \) and \( v^{\prime}_{2} \) at time \( 2 t_{0} \) while
still moving in air. The value of
\( \left[\left(\boldsymbol{m}_{1} \boldsymbol{v}_{1}^{\prime}+\boldsymbol{m}_{2} \boldsymbol{v}_{2}^{\prime}\right)-\left(\boldsymbol{m}_{1} \boldsymbol{v}_{1}+\boldsymbol{m}_{2} \boldsymbol{v}_{2}\right)\right] \)
A . zero
в. \( \left(m_{1}+m_{2}\right) g t_{0} \)
c. \( 2\left(m_{1}+m_{2}\right) g t_{0} \)
D. \( \frac{1}{2}\left(m_{1}+m_{2}\right) g t_{0} \)
Subject: Physics
Assertion
Small liquid drops assume a spherical
shape.
Reason
Due to surface tension liquid drops tend to have minimum surface area.
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
The degree and order of \( (2 x+ \)
\( \mathbf{3} \boldsymbol{y})\left(\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}\right)^{3}+\mathbf{7} \boldsymbol{x} \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}+\boldsymbol{y}=\boldsymbol{e}^{2 \boldsymbol{x}} \) are:
A .2,2
B. 1,3
\( c \cdot 1,2 \)
D. 2,
Subject: Maths
Let \( A \) and \( B \) be two events such that
\( \boldsymbol{P}\left(\boldsymbol{A} \cap \boldsymbol{B}^{\prime}\right)=\mathbf{0 . 2 0}, \boldsymbol{P}\left(\boldsymbol{A}^{\prime} \cap \boldsymbol{B}\right)=\mathbf{0 . 1 5} \)
\( P(A \text { and } B \text { both fail })=0.10 . \) Then
This question has multiple correct options
A. \( P(A / B)=11 / 14 \)
В . \( P(A)=0.7 \)
c. \( P(A \cup B)=0.9 \)
D. \( P(A / B)=1 / 2 \)
Subject: Maths
If the perimeter of a circle is \( 132 \mathrm{cm} \)
find its area.
A. 1356 sq. \( \mathrm{cm} \)
B. 1386 sq. \( \mathrm{cm} \)
c. 1340 sq. \( \mathrm{cm} \)
D. 1436 sq. \( \mathrm{cm} \)
Subject: Chemistry
Which of the following sets represent the
normal physical states of the elements
concerned at \( 25^{\circ} \mathrm{C} \) and one bar pressure,
with \( \Delta H^{\circ} \) (formation) \( =0 \)
\( \mathbf{A} \cdot C(\operatorname{diamond}), S_{8}(s), N a(s) \)
B. \( C(\text {diamond}) \) ), \( C(\text { graphite }), B r_{2}(I) \)
c. \( C(\text { graphite }), B r_{2}(g), P_{4}(\text { white }) \)
D. \( C(\text { graphite }), B r_{2}(I), I_{2}(s) \)
Subject: Physics
Choose the correct experiment to
demonstrate the transfer of heat by the
process of conduction.
A. Take two metal blocks of same size \& shape and heat one of them to a considerable temperature, then allow both the blocks to touch each other, after a while, you will see the other block gets heated due to contact
B. Take two metal blocks of same size \& shape and heat one of them to a considerable temperature, then keep the blocks separate, after a while you will see the other block gets heated due to contact.
C. Take two metal blocks of same size \& shape and heat one of them to a considerable temperature, then allow both the blocks to touch each other after the block get cooled down, after a while you will see the other block gets heated due to contact
D. None of above
Subject: Chemistry
The Gibbs free energy change for the reaction for which \( \Delta \boldsymbol{H}=-\mathbf{3 9 3 . 4 k J} \)
and \( \Delta S=-2.9 J K^{-1} \) mol \( ^{-1} \) at \( 298 \mathrm{K} \) is:
\( \mathbf{A} \cdot-352.5 k J \)
В. \( -392.5 k J \)
\( \mathbf{c} .+352.5 k J \)
D. \( +392.5 k J \)
Subject: Physics
\( \mathbf{A} \)
\( 0.5 \mathrm{kg} \) block slides from the point \( \mathrm{A} \) on a horizontal track with an initial speed \( 3 \mathrm{m} / \mathrm{s} \) towards a weightless horizontal spring of length \( 1 \mathrm{m} \) and force constant
2 N/m. The part AB of the Track is frictionless and the part BC has the coefficient of static and kinetic friction
as 0.22 and 0.20 respectively. If the distance \( A B \) and \( B D \) are \( 2 m \) and 2.14 m
respectively, find the total distance through which the block moves before it comes to rest completely.
\( \left(g=10 m / s^{2}\right) \)
Subject: Maths
If co-ordinates of a point \( P \) is (1,2,2) then unit vector along the position vector of the point \( P \) will be
A \( \cdot \frac{1}{3}(\hat{i}+2 \hat{j}+2 \hat{k}) \)
B . \( \hat{i}+2 \hat{j}+2 \hat{k} \)
c \( \cdot \frac{1}{3}(\hat{i}-2 \hat{j}-2 \hat{k}) \)
D. \( \frac{1}{\sqrt{3}}(\hat{i}+\hat{j}+\hat{k}) \)
Subject: Maths
If
\( D \) and \( E \) are the midpoint of the sides
\( A B \) of a triangle \( A B C, \) Prove that \( \boldsymbol{B E}+\overline{\boldsymbol{D C}}=\frac{\mathbf{3}}{\mathbf{2}} \overline{\boldsymbol{B} \boldsymbol{C}} \)
Subject: Maths
\( S \) and \( T \) are points on sides \( P R \) and \( Q R \)
of \( \triangle P Q R \) such that \( \angle P=\angle R T S . \) Show
that \( \triangle \boldsymbol{R} \boldsymbol{P} \boldsymbol{Q} \sim \triangle \boldsymbol{R} \boldsymbol{T} \boldsymbol{S} \)
Subject: Physics
In \( P-f \) curve the half power
frequencies are those at which
A \( \cdot P=\frac{P_{\max }}{\sqrt{2}} \)
B. \( P=\frac{P_{\text {max }}}{2} \)
c. \( \quad P=\frac{P_{\max }}{4} \)
D. \( P=P_{\max } \)
Subject: Physics
The acceleration \( \alpha \) of a particle moving with an velocity \( u \) varies with distance
\( x \) as \( a=k \sqrt{x} \) where \( k \) is a constant. Th
distance covered by the particle when its velocity become \( 3 u \) is given by
\( ^{\mathrm{A}} \cdot\left(\frac{3 u^{2}}{k}\right)^{2 / 3} \)
B. \( \left(3 k u^{2}\right)^{4 / 3} \)
\( ^{\mathrm{C}} \cdot\left(\frac{6 u^{2}}{k}\right)^{2 / 3} \)
D. \( \left(\frac{u^{2}}{3 k}\right)^{2 / 3} \)
Subject: Chemistry
For the reaction, \( \boldsymbol{S n O}_{2}(\boldsymbol{s})+\boldsymbol{2} \boldsymbol{H}_{2}(\boldsymbol{g}) \rightleftharpoons \)
\( \boldsymbol{S} \boldsymbol{n}(l)+\boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \) the equilibrium
mixture of steam and hydrogen
contained \( 45 \% \) and \( 24 \% H_{2} \) at \( 900 \mathrm{K} \)
and \( 1100 \mathrm{K} \) respectively. Calculate \( \boldsymbol{K}_{\boldsymbol{P}} \)
at both the temperatures. Generally should it be higher or lower temperatures for better reduction of
\( \boldsymbol{S} \boldsymbol{n} \boldsymbol{O}_{2} ? \)
\( \mathbf{A} \cdot \therefore K_{C_{2}}=1.03 \)
\( \mathbf{B} \cdot \therefore K_{C_{2}}=5.02 \)
\( \mathbf{c} \cdot \therefore K_{C_{2}}=15.01 \)
\( \mathbf{D} \cdot \therefore K_{C_{2}}=10.03 \)
Subject: Maths
For a real number r let \( [r] \) denote the
largest integer less than or equal to \( r \)
Let \( a>1 \) be a real number which is not
an integer, and let k be the smallest positive integer such that \( \left[\boldsymbol{a}^{k}\right]>[\boldsymbol{a}]^{k} \)
Then which of the following statements is always true?
A \( \cdot k \leq(2[a]+1)^{2} \)
B . \( k \leq([a]+1)^{4} \)
c. \( k<2^{[a]+1} \)
D. \( _{k \leq \frac{1}{a-[a]}}+1 \)
Subject: Physics
Calculate the velocity of a body of a mass 2 kg whose linear momentum is 5
N s.
A \( .2 .5 \mathrm{ms}^{-1} \)
B. \( 10 \mathrm{ms}^{-1} \)
c. \( 5 m s^{-1} \)
D. \( 2 m s^{-1} \)
Subject: Maths
Assertion
Show that the points \( (\boldsymbol{a}, \boldsymbol{a}),(-\boldsymbol{a},-\boldsymbol{a}) \)
and \( (-\sqrt{3} a, \sqrt{3} a) \) are the vertices of an
equilateral triangle.
Reason
Using the distance formula we can show that the sides are equal.
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
Assertion
Cathode rays get deflected towards the
negative plate of electric field.
Reason
Cathode rays are negatively charged.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct.
Subject: Physics
Two planets have masses \( M_{1} \) and \( M_{2} \)
and radii \( \boldsymbol{R}_{1} \) and \( \boldsymbol{R}_{2} \) respectively. Then
the time periods of near surface satellite of the two planets will be equal if
A. \( M_{1} R_{2}^{2}=M_{2} R_{1}^{2} \)
B. \( M_{1} R_{2}^{3}=M_{2} R_{1}^{3} \)
\( \mathbf{c} \cdot M_{1}^{2} R_{2}=M_{2}^{2} R_{1} \)
D. \( M_{1} R_{1}^{3}=M_{2} R_{2}^{3} \)
Subject: Maths
If \( x=t^{3}+t+5 \& y=\sin t \) then
\( \frac{d^{2} y}{d x^{2}}= \)
A. \( \frac{\left(3 t^{2}+1\right) \sin t+6 t \cos t}{\left(3 t^{2}+1\right)^{3}} \)
B. \( \frac{\left(3 t^{2}+1\right) \sin t+6 t \cos t}{\left(3 t^{2}+1\right)^{2}} \)
c. \( \frac{\left(3 t^{2}+1\right) \sin t+6 t \cos t}{\left(3 t^{2}+1\right)^{2}} \)
D. \( \frac{c o s t}{3 t^{2}+1} \)
Subject: Maths
If \( S_{n}=\sum_{n}^{r=0} \frac{1}{n C_{r}} \) and \( t_{n}=\sum_{n}^{r=0} \frac{r}{n C_{r}} \)
then \( \frac{t_{n}}{S_{n}} \) is equal to
A \( \cdot \frac{1}{2} n \)
в. \( \frac{1}{2} n-1 \)
\( c \cdot n-1 \)
D. \( \frac{2 n-1}{2} \)
Subject: Maths
If the area bounded by the curve \( |\boldsymbol{y}|= \)
\( \sin ^{-1}|x| \) and \( x=1 \) is \( a(\pi+b), \) then
the value \( a-b \) is:
A \( . \)
B. 2
\( c \cdot 3 \)
D. 4
Subject: Maths
\begin{tabular}{|ccc} 
If \( \boldsymbol{f}(\boldsymbol{x})= \) & \\
\( \mathbf{1} \) & \( \boldsymbol{x} \) & \( \boldsymbol{x}+ \) \\
\( \boldsymbol{2} \boldsymbol{x} \) & \( \boldsymbol{x}(\boldsymbol{x}-\mathbf{1}) \) & \( (\boldsymbol{x}+ \) \\
\( \boldsymbol{3} \boldsymbol{x}(\boldsymbol{x}-\mathbf{1}) \) & \( \boldsymbol{x}(\boldsymbol{x}-\mathbf{1})(\boldsymbol{x}-\mathbf{2}) \) & \( (\boldsymbol{x}+\mathbf{1}) \boldsymbol{x} \)
\end{tabular}
then \( f(100) \) is equal to?
\( \mathbf{A} \cdot \mathbf{0} \)
B. 1
\( c \cdot 100 \)
D \( .-100 \)
Subject: Physics
In the electric field due to a point
charge \( \boldsymbol{q}, \) a test charge is carried from
\( A \) to the points \( B, C, D \) and \( E \) lying on
the same circle around \( q \). The work done
is
A. the least along \( A B \)
B. the least along \( A D \)
C. zero along any one of the paths \( A B, A D, A C \) and \( A E \)
D. the least along \( A E \).
Subject: Chemistry
A sample of neon gas is contained by a closed 5-liter vessel. The temperature of
container is \( 25^{\circ} \mathrm{C} \) and pressure is 1.5 atmospheres (R is equal to \( 0.08 \mathrm{L} \) \( \operatorname{atm} / \operatorname{mol} \mathrm{K} \)
Find the expressions which is equal to the molar quantity of gas in the sample?
A \( \frac{(1.5)(5.0)}{(0.08)(25)} \)
B. \( \frac{(0.08)(25)}{(1.5)(5.0)} \)
c. \( \frac{(1.5)(25)}{(0.08)(5.0)} \)
D. \( \frac{(0.08)(298)}{(1.5)(5.0)} \)
E \( \frac{(1.5)(5.0)}{(0.08)(298)} \)
Subject: Maths
If \( y=\tan ^{-1}\left(\frac{a \cos x-b \sin x}{b \cos x+a \sin x}\right) \) then
\( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=? \)
\( A \cdot \frac{a}{b} \)
B. \( \frac{-b}{a} \)
c.
D. -
Subject: Maths
From (1,4) you travel \( 5 \sqrt{2} \) units by making \( 135^{0} \) angles with positive \( x \) axis (anticlockwise) and then 4 units by
making \( 120^{0} \) angle with positive \( x \) -axis (clockwise) to reach Q. Find co-
ordinates of point \( Q \)
A \( \cdot(+6,9-2 \sqrt{3}) \)
в. \( (-6,9-2 \sqrt{3}) \)
c. \( (-6,9+2 \sqrt{3}) \)
D. \( (+6,9+2 \sqrt{3}) \)
Subject: Chemistry
\( A B, A_{2} \) and \( B_{2} \) are diatomic molecules
If the bond enthalpies of \( A_{2}, A B \& B_{2} \) are in the ratio 1: 1: 0.5 and enthalpy of
formation of \( A B \) from \( A_{2} \) and \( B_{2} \) is -100
kJ/mol \( ^{-1} \). What is the bond enthalpy of
\( \boldsymbol{A}_{2} \)
A. \( 400 \mathrm{kJ} / \mathrm{mol} \)
B. 300 kJ/mole
c. \( 500 \mathrm{kJ} / \mathrm{mole} \)
D. 900 kJ/mole
Subject: Maths
A function \( f(x)=\sqrt{1-2 x}+x \) is
defined from \( D_{1} \rightarrow D_{2} \) and is onto. If
the set \( D_{1} \) is its complete domain then
the set \( D_{2} \) is
A \( \cdot\left(-\infty, \frac{1}{2}\right] \)
в. \( (-\infty, 2) \)
\( \mathbf{c} \cdot(-\infty, 1) \)
D \( \cdot(-\infty, 1] \)
Subject: Maths
A solid cylinder of glass whose diameter
is \( 1.5 \mathrm{m} \) and height \( 1 \mathrm{m} \) is melted and recasted into a sphere, then the radius of the sphere is
\( A \cdot 1 m \)
B. \( 0.75 \mathrm{m} \)
c. \( 1.25 \mathrm{m} \)
D. \( 1.5 \mathrm{m} \)
Subject: Biology
Assertion
The process of filtration takes place in malpighian corpuscles
Reason
The total blood pressure is very high in glomerular capillaries
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
Vertical displacement of a plank with a
body of mass ' \( m \) ' on it is varying
according to law \( \boldsymbol{y}=\sin (\boldsymbol{\omega} \boldsymbol{t})+ \)
\( \sqrt{3} \cos (\omega t) . \) The minimum value of \( \omega \) for
which the mass just breaks off the plank and the moment this occurs first
\( \operatorname{after} t=0 \) are given by \( (y \) is positive
vertically upwards):
A \( \cdot \sqrt{\frac{g}{2}}, \sqrt{\frac{2}{g}} \frac{\pi}{6} \)
В \( \cdot \frac{g}{\sqrt{2}} \frac{2}{3}, \sqrt{\frac{\pi}{g}} \)
c. \( \sqrt{\frac{g}{2}} \frac{\pi}{3}, \sqrt{\frac{2}{g}} \)
D. \( \sqrt{2 g}, \sqrt{\frac{2 \pi}{3 g}} \)
Subject: Physics
A coil of inductance \( 300 \mathrm{mH} \) and
resistance \( 2 \Omega \) is connected to a source
of voltage 2 V. The current reaches half of its steady state value in
A . \( 0.05 \mathrm{s} \)
B. 0.1 s
c. \( 0.105 \mathrm{s} \)
\( D \cdot 0.3 \mathrm{s} \)
Subject: Chemistry
Determine the oxidation state of Cr in
\( \left[\boldsymbol{C r}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4} \boldsymbol{C l}_{2}\right] \boldsymbol{C l} \)
\( A \cdot+3 \)
B . - -
\( c \cdot+2 \)
\( D \cdot+4 \)
Subject: Maths
Calculate the values of the
determinants:
\( \left|\begin{array}{cccc}\mathbf{0} & \mathbf{1} & \mathbf{1} & \mathbf{1} \\ \mathbf{1} & \boldsymbol{b}+\boldsymbol{c} & \boldsymbol{a} & \boldsymbol{a} \\ \mathbf{1} & \boldsymbol{b} & \boldsymbol{c}+\boldsymbol{a} & \boldsymbol{b} \\ \mathbf{1} & \boldsymbol{c} & \boldsymbol{c} & \boldsymbol{a}+\boldsymbol{b}\end{array}\right| \)
Subject: Physics
On a rainy day, a raindrop falls from very high clouds and faces retardation due to air. This retardation is directly proportional to the instantaneous speed of the drop and proportionality constant is given as \( \alpha . \) An expression for the
distance travelled \( s \) by the drop in time \( t \)
is: (given acceleration due to gravity \( = \)
\( \boldsymbol{g} \)
A. \( s=\frac{g}{\alpha^{2}}\left(e^{-\alpha t}-1\right)+\frac{g}{\alpha} t \)
в. \( _{s}=\frac{g t}{\alpha} \)
c. \( _{s}=\frac{g}{\alpha^{2}}\left(e^{-\alpha t}-1\right) \)
D. \( _{s}=\frac{g t}{\alpha^{2}}+\frac{g}{\alpha}\left(e^{-\alpha t}-1\right) \)
Subject: Maths
For any two events \( A \) and \( B \)
\( \mathbf{A} \cdot P(A)+P(B)>P(A \cap B) \)
B \( \cdot P(A)+P(B)<P(A \cap B) \)
\( \mathbf{c} \cdot P(A)+P(B) \geq P(A \cap B) \)
D \( . P(A)+P(B) \leq P(A \cap B) \)
Subject: Physics
A chain \( A B \) of length \( l \) is lying in a
smooth horizontal tube so that a
fraction \( h \) of its length \( l \), hangs freely
and touches the surface of the table
with its end B. At a certain moment,
the end \( A \) of the chain is set free. The
velocity of end \( A \) of the chain, when it
slips out of tube, is:
A \( \cdot h \sqrt{\frac{2 g}{l h}} \)
в. \( \sqrt{2 g h \times \log _{e}\left(\frac{l}{h}\right)} \)
c. \( \sqrt{2 g l \times \log _{e}\left(\frac{l}{h}\right)} \)
D \( \cdot \frac{1}{h l} \sqrt{2 g} \)
Subject: Chemistry
What product is formed when
cyclohexanone is oxidised?
A. НООС\( \cdot\left(C H_{2}\right)_{4} \cdot \)СООН
в. \( C H_{3} C H_{2} C O O H \)
c. \( C H_{3}\left(C H_{2}\right)_{4} \cdot C O O H \)
D. None of the above
Subject: Physics
To find out degree of freedom, the correct expression is :
A \( \cdot f=\frac{2}{\gamma-1} \)
B. \( f=\frac{\gamma+1}{2} \)
\( ^{\mathbf{C}} f=\frac{2}{\gamma+1} \)
D. \( f=\frac{1}{\gamma+1} \)
Subject: Maths
\( \left[5\left\{\left(\frac{1}{8}\right)^{\frac{-1}{3}}+\left(\frac{1}{27}\right)^{\frac{-1}{3}}\right\}\right]^{\frac{1}{2}} \)
\( \mathbf{A} \cdot 5 \)
B. \( \sqrt{13} \)
\( \mathbf{c} .25 \)
D. 13
Subject: Physics
In YDSE, find the missing wavelength at \( \boldsymbol{y}=\boldsymbol{d}, \) where symbols have their usual meaning (take \( D>>d \) ).
\( ^{\mathrm{A}} \cdot \frac{d^{2}}{D} \)
B. \( \frac{2 d^{2}}{7 D} \)
c. \( \frac{3 d^{2}}{D} \)
D. \( \frac{d^{2}}{3 D} \)
Subject: Physics
The velocity time graph of a body
moving in a straight line is shown in the figure. The displacement and distance traveled by the body in 8 s are
A. \( 12 \mathrm{m}, 20 \mathrm{m} \)
B. \( 14 \mathrm{m}, 12 \mathrm{m} \)
\( c \cdot 16 m, 20 m \)
D. \( 12 \mathrm{m} .16 \mathrm{m} \)
Subject: Chemistry
The wavelength of first line of the Lymen
series for hydrogen is \( 1216 A^{\circ} . \) The wavelength for the first line of this
series for a 10 time ionised sodium
atom \( (z=11) \) will be :
A \( \cdot 1000 A^{\circ} \)
B . \( 100 A^{\circ} \)
c. \( 10 A^{\circ} \)
D. \( 1 A^{\circ} \)
Subject: Chemistry
In the formation of sulphur trioxide by
the contact process \( 2 S O_{2}(g)+ \)
\( O_{2}(g) \rightarrow 2 S O_{3}(g) \)
The rate of reaction is expressed as \( -\frac{d\left(O_{2}\right)}{d t}= \)
\( 2.5 \times 10^{-4} \) mol
\( L^{-1} \sec ^{-1} \) The rate of disappearance of
\( \left(\boldsymbol{S O}_{2}\right) \) will be:
A. \( 5 \times 10^{-4} \) molL \( ^{-1} S^{-1} \)
В. \( -1.25 \times 10^{-4} \) тод \( L^{-1} S^{-1} \)
c. \( 3.75 \times 10^{-4} \) molL \( ^{-1} S^{-1} \)
D. \( 50.0 \times 10^{-4} \) molL \( ^{-1} S^{-1} \)
Subject: Physics
A cell of e.m.f. \( \varepsilon \) and internal resistance
is used to send current to an external resistance R. The total resistance of
circuit,
A \( \cdot \frac{R r}{(R+r)} \)
в. \( \frac{R+r}{2} \)
\( c \cdot R r \)
D. \( R+r \)
Subject: Physics
Graph of position of image versus
position of point object from a convex lens is shown. Then, focal length of the
lens is
A. \( 0.50 \pm 0.05 \mathrm{cm} \)
B. \( 0.50 \pm 0.10 \mathrm{cm} \)
\( c .5 .00 \pm 0.05 c m \)
D. \( 5.00 \pm 0.10 \mathrm{cm} \)
Subject: Chemistry
During estimation of nitrogen in the organic compound by Kjeldahls method, the ammonia evolved from 0.5 g of the compound in Kjeldahls estimation of nitrogen, neutralised 10 mL of 1 IM
\( H_{2} S O_{4} . \) Find out the percentage of nitrogen in the compound?
A . 14\%
в. 28\%
c. 56\%
D. 68\%
Subject: Maths
A car travels \( 40 \mathrm{km} \mathrm{s} \) in 30 mins. If the
speed of bus remains same, how far can
it travel in 3 hrs?
A. \( 120 \mathrm{km} \)
B. \( 80 \mathrm{km} \)
\( c .240 k m \)
D. None of these
Subject: Physics
If four atoms of hydrogen combine to
form an \( 2^{4} H e \) atom, then the amount of
energy released is :
A. \( 26.7 \mathrm{MeV} \)
в. \( 25.3 \mathrm{MeV} \)
\( \mathrm{c} .22 \mathrm{MeV} \)
D. \( 24.5 \mathrm{MeV} \)
Subject: Physics
toppr
Q Type your question-
\( F_{2} . \) The object weighs \( 10 \mathrm{N} \). There is
negligible friction between the rods and
cords. Angle \( \boldsymbol{\theta} \) is \( \mathbf{9 0}^{\circ} \)

Which row of the table gives an angle \( \theta \)
of \( 90^{\circ} ? \)
\( F_{1} / N \)
\( 6 . \)
4.0
8.0
8.0
\( A \)
B. B
\( c \)
D
Subject: Physics
An infinitely long wire is kept along z-
axis from \( z=-\infty \) to \( z=+\infty, \) having
uniform linear charge density \( \frac{10}{9} n C / m . \) The electric field \( \vec{E} \) at point \( (6 \mathrm{cm}, 8 \mathrm{cm}, 10 \mathrm{cm}) \) will be:
\( A \cdot(160 i+120 j+200 k) N / C \)
B. (200 k) N/C
\( c \cdot(160 i+120 j) N / c \)
D. \( (120 \mathrm{i}+160 \mathrm{j}) \mathrm{N} / \mathrm{C} \)
Subject: Chemistry
Given that:
\( \boldsymbol{C}(\text {graphite})+\boldsymbol{O}_{2}(\boldsymbol{g}) \longrightarrow \)
\( \boldsymbol{C O}_{2}(\boldsymbol{g}) ; \quad \boldsymbol{\Delta} \boldsymbol{H}=-\boldsymbol{3} \boldsymbol{9} \boldsymbol{3} \cdot \boldsymbol{7} \boldsymbol{k} \boldsymbol{J} \)
Calculate the quantity of graphite (in
\( \mathrm{gm} \) ) that must be burnt to evolve
\( 5000 k J \) of heat.
A. 152.8
B. 15.2
c. 200
D. None of these
Subject: Chemistry
For how long current of \( 3 \mathrm{A} \) has to passed through \( A g N O_{3} \) solution to coat a
metal surface of \( 80 \mathrm{cm}^{2} \) area and
thickness of \( 5 \times 10^{-4} c m . \) The density of
silver is \( 10.5 \mathrm{gm} / \mathrm{cm}^{3} \)
Subject: Physics
The potential difference in open circuit for a cell is \( 2.2 \mathrm{V} \). When a \( 4 \Omega \) resistor is
connected between its two electrodes
the potential difference becomes \( 2 \mathrm{V} \) The internal resistance of the cell will be
A . \( 1 \Omega \)
B. \( 0.2 \Omega \)
\( c .2 .5 \Omega \)
D. \( 0.4 \Omega \)
Subject: Maths
The product of two middle terms in the
expansion of \( \left(\frac{3 x^{2}}{2}-\frac{1}{3 x}\right)^{9} \) is
\( ^{\mathrm{A}} \cdot\left(^{9} C_{4}\right)^{2} \cdot \frac{x^{9}}{512} \)
в. \( -9_{C_{4}} .^{9} C_{5}, \frac{x^{8}}{512} \)
c. \( _{-9}^{\text {g }} q_{4} .^{9} C_{5} \). \( \frac{x^{9}}{512} \)
D・ \( _{9} C_{4} .^{9} C_{5}, \frac{x^{9}}{256} \)
Subject: Physics
A substance of mass \( 49.53 g \) occupies
\( 1.5 \mathrm{cm}^{3} \) of volume. The density of the
substance (in \( g c m^{-3} \) ) with correct number of significant figures is :
A. 3.3
B. 3.302
c. 3.30
D. 3.300