AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Which of the hydrated species can exist?
I. \( \boldsymbol{H}_{\mathbf{5}} \boldsymbol{O}_{\mathbf{2}}^{+} \)
II. \( \boldsymbol{H}_{3} \boldsymbol{O}^{+} \)
III. \( \boldsymbol{H}_{3} \boldsymbol{O}_{2}^{-} \)
IV. \( \boldsymbol{H}_{7} \boldsymbol{O}_{3}^{+} \)
Select alternate from.
A. Il only
B. I and II
c. I, II and IV
D. I, II, II and IV
Subject: Chemistry
Consider the reaction: \( N_{2}+3 H_{2} \rightarrow \)
\( 2 N H_{3} . \) It is carried out at constant
temperature and pressure. If \( \Delta H \) and
\( \Delta U \) are the enthalpy and internal energy changes for the reaction respectively, then which of the following expression is true?
\( \mathbf{A} \cdot \Delta H>\Delta U \)
в. \( \Delta H<\Delta U \)
c. \( \Delta H=\Delta U \)
\( \mathbf{D} \cdot \Delta H=0 \)
Subject: Physics
toppr
Q Type your question
around the spool through which a mass
\( \mathrm{m} \) is hanging. There exists no friction at
point \( A, \) while the coefficient of friction
between spool and point \( B \) is \( \mu . \) The
angle between two surfaces is \( \theta \)
This question has multiple correct options
A. the magnitude of force on the spool at B in order to maintain equilibrium is \( m g \sqrt{\left(\frac{r}{R}\right)^{2}+\left(1-\frac{r}{R}\right)^{2}} \frac{1}{\tan ^{2} \theta} \)
B. the magnitude of force on the spool at \( B \) in order to maintain equilibrium is \( m g\left(1-\frac{r}{R}\right) \frac{1}{\tan \theta} \)
C. the maintain value of \( \mu \) for the system to remain in equilibrium is \( \frac{\cot \theta}{(R / r)-1} \)
D. the maintain value of \( \mu \) for the system to remain in equilibrium is \( \frac{\tan \theta}{(R / r)-1} \)
Subject: Chemistry
In which case mean free path is not
affected?
A \( \cdot H_{2} \) gas at \( 100^{\circ} \mathrm{C} \) and 1 atm is transferred into a vessel at \( 50^{\circ} \mathrm{C} \) and 0.5 atm
B. \( O_{2} \) gas at \( 200 K \) and \( 2 a t m \) is transferred into a vessel at \( 400 K \) and 1 atm
c. \( O_{2} \) gas is replaced by \( H_{2} \) gas keeping other variables constant
D. Medium is made more viscous
Subject: Chemistry
The highest bond length is \( \boldsymbol{C}-\boldsymbol{H}, \boldsymbol{C}- \)
\( \boldsymbol{O}, \boldsymbol{C}-\boldsymbol{C} \) and \( \boldsymbol{C}=\boldsymbol{C} \) is:
A. \( C-C \)
B. \( C-O \)
c. \( C-H \)
D. \( C=C \)
Subject: Chemistry
Assertion
\( E_{c e l l}^{0} \) is negative for electrolytic cell.
Reason
\( \triangle G^{0} \) is positive for electrolytic cell.
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: Maths
It is given that event \( A \& B \) are such \( \operatorname{that} \boldsymbol{P}(\boldsymbol{A})=\frac{\mathbf{1}}{\mathbf{4}}, \boldsymbol{P}\left(\frac{\boldsymbol{A}}{\boldsymbol{B}}\right)= \)
\( \frac{1}{2}, P\left(\frac{B}{A}\right)=\frac{2}{3}, \) then \( P(B)= \)
\( A \cdot \frac{1}{3} \)
B. \( \frac{2}{3} \)
\( c \cdot \frac{1}{2} \)
D.
Subject: Maths
The slope of the tangent to the curve
\( \boldsymbol{y}=\boldsymbol{e}^{\boldsymbol{x}} \cos \boldsymbol{x} \) is minimum at \( \boldsymbol{x}=\boldsymbol{\alpha}, \boldsymbol{0} \leq \)
\( a \leq 2 \pi, \) then the value of \( \alpha \) is
A . 0
в. \( \pi \)
c. \( 2 \pi \)
D. \( \frac{3 \pi}{2} \)
Subject: Maths
\( f(a, b, c)=\left[\begin{array}{ccc}a & 0 & 0 \\ {[0.3 e m] 0} & b & 0 \\ {[0.3 e m] 0} & 0 & c\end{array}\right] \)
such that \( a b c \neq 0 \)
\( \operatorname{then} A^{-1}=\operatorname{diag}\left(\frac{1}{a}, \frac{1}{b}, \frac{1}{c}\right)= \)
\( \left[\begin{array}{ccc}\frac{1}{a} & 0 & 0 \\ {[0.3 e m] 0} & \frac{1}{b} & 0 \\ {[0.3 e m] 0} & 0 & \frac{1}{c}\end{array}\right] \)
Subject: Maths
\[
\operatorname{Let} f(x)=x+\frac{1}{2 x+\frac{1}{2 x+\frac{1}{2 x+\ldots . . \infty}}}
\]
Compute the value of \( \boldsymbol{f}(\mathbf{1 0 0}) \cdot \boldsymbol{f}^{\prime}(\mathbf{1 0 0}) \)
Subject: Physics
A magnetic field of \( 2 \times 10^{-2} T \) acts at
right angles to a coil of area \( 100 \mathrm{cm}^{2} \)
with 50 turns. The average emf induced in the coil is \( 0.1 V . \) When it is removed
from the field in \( t \) second, the value of \( t \)
is
A . \( 10 s \)
B. \( 0.1 s \)
c. \( 0.01 s \)
D. \( 1 s \)
Subject: Chemistry
Which of the following will show optical isomerism ?
\( \mathbf{A} \cdot\left[C u\left(N H_{3}\right)_{4}\right]^{2} \)
B \( \cdot\left[Z n C l_{4}\right]^{2} \)
\( \mathbf{c} \cdot\left[\operatorname{Cr}\left(C_{2} O_{4}\right)_{3}\right]^{3-} \)
D \( \cdot\left[\operatorname{Co}(C N)_{6}\right]^{3-} \)
Subject: Physics
Assertion
STATEMENT-1: Two particles undergo rectilinear motion along different straight lines. Then the centre of mass
of system of given two particles also always moves along a straight line.
Reason
STATEMENT-2: If direction of net
momentum of a system of particles having nonzero net momentum) is fixed, the centre of mass of given system moves along a straight line.
A. Statement-1 is True, Statement-2 is True; Statement- is a correct explanation for Statement-1
B. Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-
c. Statement- 1 is True, Statement- 2 is False
D. Statement-1 is False, Statement-2 is True
Subject: Maths
If \( f(1)=3 \) and \( f^{\prime}(1)=-\frac{1}{3} \) then the
derivative of \( \left(x^{11}+f(x)\right)^{-2} \) at \( x=1 \) is
A. \( -\frac{1}{2} \)
B. - -
c. 1
D. \( f^{\prime}(1) \)
Subject: Physics
A body of mass 'm' is raised from the surface of the earth to a height 'nR' (Rradius of earth). Magnitude of the change in the gravitational potential energy of the body is (g-acceleration due to gravity on the surface of earth)
A \( \cdot\left(\frac{n}{n+1}\right) m g R \)
B \( \cdot\left(\frac{n-1}{n}\right) m g R \)
c. \( \frac{m g R}{n} \)
D. \( \frac{m g R}{(n-1)} \)
Subject: Physics
Three identical bulbs are connected in
parallel with a battery. The current drawn from the battery is \( 6 A \). If one of
the bulbs gets fused, what will be the total current drawn from the battery?
\( \mathbf{A} \cdot 6 A \)
в. \( 2 A \)
\( c .4 A \)
D. \( 8 A \)
Subject: Chemistry
When \( 20 g \) of \( C a C O_{3} \) were put into 10
litre flask and heated to \( 800^{\circ} \mathrm{C}, 35 \% \) of
\( \mathrm{CaCO}_{3} \) remained unreacted at
equilibrium. \( K_{P} \) for decomposition of
\( \boldsymbol{C a C O}_{3} \) is:
A. 1.145 atm
B. 0.145 atm
c. 2.145 atm
D. 3.145 atm
Subject: Maths
The point \( P \) is on the \( y \) -axis. If \( P \) is equidistant from (1,2,3) and (2,3,4)
then \( \boldsymbol{P}_{\boldsymbol{y}}= \)
A \( \cdot \frac{15}{2} \)
B. 15
c. 30
D. \( \frac{3}{2} \)
Subject: Maths
Find solution of following inequality, also show it graphically.
\( \boldsymbol{x}-\mathbf{5} \geq-\mathbf{7}, \boldsymbol{x} \in \boldsymbol{R} \)
\( A \)
\( \begin{array}{cccccc} & 1 & 1 & 1 & & & 1 \\ -2 & -1 & 0 & 1 & 2 & 3\end{array} \)
B.
\begin{tabular}{lllllll}
\hline-2 & -1 & 0 & 1 & 2 & 3
\end{tabular}
\( c \)
\begin{tabular}{lllllll} 
& & & & & & & \( \bullet \) \\
\hline-3 & -2 & -1 & 0 & 1 & 2 & 3 & 4
\end{tabular}
\( D \)
\( \longleftrightarrow \)\begin{tabular}{ccccccc} 
& & & & & \( \rightarrow \) & \( \rightarrow \) \\
\hline-2 & -1 & 0 & 1 & 2 & 3 & 4
\end{tabular}
Subject: Maths
Let \( \boldsymbol{f} \) be a function satisfying
\( \boldsymbol{f}(\boldsymbol{x}+\boldsymbol{y})=\boldsymbol{f}(\boldsymbol{x}) \boldsymbol{f}(\boldsymbol{y}) \) for all \( \boldsymbol{x} \) and \( \boldsymbol{y} \)
and \( \boldsymbol{f}(\mathbf{0})=\boldsymbol{f}^{\prime}(\mathbf{0})=\mathbf{1} \) then
This question has multiple correct options
A. \( f \) is differentiable for all \( x \)
B . \( f^{\prime}(x)=f(x) \)
\( \mathbf{c} \cdot f(x)=e^{x} \)
D. \( f \) is continuous for all \( x \)
Subject: Chemistry
1 mol benzene \( \left(P_{\text {benzene }}^{o}=42 \mathrm{mm}\right) \) and 2 mol toluene \( \left(P_{\text {toluene}}^{o}=36 \mathrm{mm}\right) \) will have
This question has multiple correct options
A. total pressure of 38 mm.
B. mole fraction of vapour of benzene above liquid mixture is \( 7 / 19 \)
c. positive deviation from Raoult's law
D. negative deviation from Raoult's law
Subject: Physics
A charged oil drop is suspended in
uniform field of \( 3 \times 10^{4} V / m \) so that it
neither falls nor rises. The charge on the drop will be:
(Take the mass of the charge \( =\mathbf{9 . 9} \times \)
\( \left.10^{-15} \mathrm{kg} \text { and } g=10 m / s^{2}\right) \)
A . \( 3.3 \times 10^{-18} \mathrm{C} \)
B. \( 3.2 \times 10^{-18} \mathrm{C} \)
c. \( 1.6 \times 10^{-18} \mathrm{C} \)
D. \( 4.8 \times 10^{-18} \mathrm{C} \)
Subject: Physics
A hammer weighing \( 3 \mathrm{kg}, \) moving with a velocity of \( 10 \mathrm{m} / \mathrm{s} \), strikes against the head of a spike and drives it into a block of wood. If the hammer comes to rest in
\( 0.025 s, \) the average (retarding) force acting on the spike will be
A . 600 N
B. -600 N
c. \( 1200 \mathrm{N} \)
D. -1200 N
Subject: Physics
A cylindrical rod magnet has a length of \( 5.0 \mathrm{cm} \) and a diameter of \( 1.0 \mathrm{cm} . \) It has a
uniform magnetization of \( 5.3^{*} 10^{3} \mathrm{A} / \mathrm{m} \) What is its magnetic dipole moment?
A . 20.8 \( m J T^{-1} \)
B . \( 10.8 m J T^{-1} \)
\( \mathbf{c} \cdot 5.8 m J T^{-1} \)
D. 30.8mJT"
Subject: Physics
The distance between two planets of
masses \( \mathrm{M} \) and \( 4 \mathrm{M} \) is 'a' what is the
gravitational potential at a point on a line joining them of which the gravitational intensity is zero?
\( \mathbf{A} \cdot-\frac{9 G M}{r} \)
B. \( -\frac{5 G M}{a} \)
\( \mathbf{c} \cdot-\frac{3 G M}{a} \)
D. \( -\frac{7 G M}{a} \)
Subject: Maths
Assertion
Let \( \boldsymbol{f}: \boldsymbol{X} \rightarrow \boldsymbol{Y} \) be a function defined by \( f(x)=2 \sin \left(x+\frac{\pi}{4}\right)-\sqrt{2} \cos x+c \)
Statement I: For set \( \boldsymbol{X}, \boldsymbol{x} \in\left[\mathbf{0}, \frac{\boldsymbol{\pi}}{\mathbf{2}}\right] \cup \)
\( \left[\pi, \frac{3 \pi}{2}\right], f(x) \) is one-one function
Reason Statement II: \( \boldsymbol{f}^{\prime}(\boldsymbol{x}) \geq \mathbf{0}, \boldsymbol{x} \in\left[\mathbf{0}, \frac{\boldsymbol{\pi}}{\mathbf{2}}\right] \)
A. Statementl is true, statement II is also true:
Statement II is the correct explanation of Statement
B. Statement I is true, Statement II is also true:
Statement II is not the correct explanation of Statement
c. Statement I is true, Statement II is false
D. Statement l is false, Statement II is true
Subject: Maths
For the curve \( f(x)=\frac{1}{1+x^{2}}, \) let two
points on it be \( \boldsymbol{A}(\boldsymbol{\alpha}, \boldsymbol{f}(\boldsymbol{\alpha})), \boldsymbol{B}\left(-\frac{1}{\boldsymbol{\alpha}}, \boldsymbol{f}\left(-\frac{1}{\boldsymbol{\alpha}}\right)\right)(\boldsymbol{\alpha}>\mathbf{0}) \)
Find the minimum area bounded by
the line segments \( 0 A, O B \) and \( f(x) \) where 'O' is the origin.
A \( \cdot \frac{(\pi-1)}{2} \)
в. \( \frac{\pi}{2} \)
c. \( \frac{(\pi-2)}{2} \)
D. Maximum area is always infinitt
Subject: Maths
f \( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B})=\mathbf{0 . 8}, \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})=\mathbf{0}, \mathbf{3} \)
\( \operatorname{then} P(\bar{A})+P(\bar{B})= \)
A . 0.3
в. 0.5
\( c .0 . \)
D. 0.9
Subject: Maths
Following are the car parking charges near railway station upto
\( 4 \mathrm{hrs} \quad \) Rs 60
\( \mathbf{8} \) hrs \( \quad \boldsymbol{R} \boldsymbol{s} \mathbf{1 0 0} \)
\( \mathbf{1 2} \) hrs \( \quad \boldsymbol{R} \boldsymbol{s} \mathbf{1 4 0} \)
\( \mathbf{2 4} \) hrs \( \quad \boldsymbol{R} \boldsymbol{s} \mathbf{1 8 0} \)
Check if the parking charges are in direct proportion to the parking time.
Subject: Physics
For the same two projectiles, after \( 3 s \) from the initial launch, what will be the
difference between the two projectiles
speeds? The previous problem's text:
A projectile is fired 30.0 degrees above
the horizontal with speed \( \left|\boldsymbol{v}_{1}\right|=\mathbf{4 0 m} / \boldsymbol{s} \)
and a second one 60.0 degrees above
the horizontal with speed \( \left|\boldsymbol{v}_{2}\right|=\mathbf{3 0 m} / \boldsymbol{S} \)
simultaneously. After 2 seconds, how far apart will the two projectiles be? Assume no air
resistance and that they are fired from the same spot, and that each moves independent of the outer projectile. Take \( \boldsymbol{g}=\mathbf{9 . 8 1 m} / \boldsymbol{s}^{2} \)
A. \( 10 \mathrm{m} / \mathrm{s} \)
B. \( 15.4 m / s \)
c. \( 20.5 m / s \)
D. \( 30.0 \mathrm{m} / \mathrm{s} \)
E . \( 35.9 \mathrm{m} / \mathrm{s} \)
Subject: Physics
Two \( S H M \) are represented by equation
\( \boldsymbol{x}_{1}=\mathbf{4} \sin \left(\boldsymbol{\omega} \boldsymbol{t}+\mathbf{3 7}^{\boldsymbol{o}}\right) \) and \( \boldsymbol{x}_{2}= \)
\( 5 \cos (\omega t) . \) The phase difference between
them is
A \( .37^{\circ} \)
B . \( 127^{\circ} \)
\( c \cdot 53^{\circ} \)
D. \( 143^{\circ} \)
Subject: Physics
During \( \beta- \) decay (beta minus), the
emission of antineutrino particle is supported by which of the following statement(s)?
This question has multiple correct options
A. Angular momentum conservation holds good in any nuclear reaction
B. Linear momentum conservation holds good in any nuclear reaction
C. The KE of emitted \( \beta- \)particle is varying continuously
to a maximum value
D. None of the above
Subject: Chemistry
Assertion
Anhydrous sulphuric acid has very high viscosity.
Reason
\( H- \) bonding makes it viscous.
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: Maths
If \( \vec{a}+\vec{b} \perp \vec{a} \) and \( |\vec{b}|=\sqrt{2}|\vec{a}| \), then?
\( \mathbf{A} \cdot(2 \vec{a}+\vec{b}) \| \vec{b} \)
B . \( (2 \vec{a}+\vec{b}) \perp \vec{b} \)
c. \( (2 \vec{a}-\vec{b}) \perp \vec{b} \)
D. \( (2 \vec{a}+\vec{b}) \perp \vec{a} \)
Subject: Maths
Evaluate \( : \int \frac{1}{\sqrt{(x-1)(x-2)}} d x \)
A.
\[
\begin{array}{l}\text { B. } \log \left|\left(x-\frac{3}{2}\right)+\sqrt{x^{2}-3 x+2}\right|+C \\ \text { c. } \log \left(\left(x-\frac{3}{2}\right)+\sqrt{x^{2}-3 x+2}\right)+C \\ \text { D. } & =\log \left|\left(x-\frac{3}{2}\right)+\sqrt{x^{2}+3 x+2}\right|+C\end{array}
\]
Subject: Physics
A point charge \( +Q \) having mass \( m \) is fixed on horizontal smooth surface.
Another point charge having magnitude \( +2 Q \& \) mass \( 2 m \) is projected horizontally towards the charge \( +\mathrm{Q} \) from the distance with velocity \( V_{0} \) Force applied by floor on the fixed charge in horizontal direction, when distance between charges becomes 'd'
A \( \cdot \frac{2 K Q^{2}}{d^{2}} \)
B. \( \frac{K Q^{2}}{d^{2}} \)
c. zero
D. none
Subject: Maths
If \( \boldsymbol{A}=\{\boldsymbol{x}: \boldsymbol{x} \in \boldsymbol{W}, \boldsymbol{3} \leq \boldsymbol{x}<\mathbf{6}\}, \boldsymbol{B}= \)
\{3,5,7\} and \( C=\{2,4\} ; \) find \( :(A- \)
\( \boldsymbol{B}) \times \boldsymbol{C} \)
Subject: Physics
Electric charges -q, -q, -q and 3q are
placed at the corners of a square ABCD
of length/as shown in figure. The magnitude of electric dipole moment of
the system is
\( A \cdot \sqrt{2 q} \)
B. 9
\( c \cdot 2 q \)
D. \( 2 \sqrt{2} q l \)
Subject: Maths
\( \Delta A B C \) is an isosceles right triangle
with area \( P . \) The radius of the circle that
passes through the point \( A, B \) and \( C \) is:
\( A \cdot \sqrt{P} \)
B. \( \sqrt{\frac{P}{2}} \)
c. \( \frac{\sqrt{P}}{2} \)
D. \( \sqrt{2 P} \)
Subject: Maths
The distance of the point (1,-5,9) from the planer. \( (\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\boldsymbol{k}})=\mathbf{5} \)
measured long the line \( r=\hat{i}+\hat{j}+\hat{k} \) is
A \( 3 \sqrt{5} \)
5
B. \( 10 \sqrt{3} \)
\( c \cdot 5 \sqrt{3} \)
D. \( 3 \sqrt{10} \)
Subject: Maths
State which quadrants or on which axis do the following points line?
1. \( \boldsymbol{A}(-\mathbf{3}, \mathbf{2}) \)
2. \( B(5,3) \)
3. \( C(0,4) \)
4. \( \boldsymbol{D}(-\mathbf{3}, \mathbf{0}) \)
Subject: Physics
The work function for tungsten and
sodium are \( 4.5 e V \) and \( 2.3 e V \)
respectively. If threshold wavelength \( \lambda \) for sodium is \( 5460 A \), the value of \( \lambda \) for
tungsten is
\( \mathbf{A} .5893 \hat{A} \)
в. 10683 ,
c. 2791 ,
D. 528 月
Subject: Chemistry
The elements undergoing reduction and oxidation during the reaction,
\( \left(N H_{4}\right)_{2} C r_{2} O_{7} \rightarrow N_{2}+C r_{2} O_{3}+ \)
\( 4 H_{2} O \) are respectively:
\( A \cdot N \) and \( C r \)
B. Crand N
c. \( \mathrm{N} \) and 0
D. Crand 0
Subject: Maths
If \( A=\{1,3,5,7\} \) and \( B=\{1,2,3,4,5,6,7, \)
83, then the number of one-to-one functions from A into B is
A \( \cdot 1340 \)
B. 1860
\( c \cdot 1430 \)
D. 1880
E . 1680
Subject: Maths
If \( A \) and \( B \) are two non-empty sets
having n elements in common, then what is the number of common
elements in the sets \( A \times B \) and \( B \times A ? \)
\( A \cdot n \)
B \( \cdot n^{2} \)
\( c \cdot 2 n \)
D. zero
Subject: Physics
A particle is executing simple harmonic
motion of amplitude \( A . \) At a distance \( x \) from the centre, a particle moving towards the extreme position receives a blow in the direction of motion which
instantaneously doubles the velocity. Its
new amplitude will be
A. \( A \)
B. \( \sqrt{A^{2}-x^{2}} \)
c. \( \sqrt{2 A^{2}-3 x^{2}} \)
D. \( \sqrt{4 A^{2}-3 x^{2}} \)
Subject: Chemistry
Write Chemical equation when \( X e F_{4} \) disproportionates to \( \mathrm{Xe}(0) \) and \( \boldsymbol{X} e(\boldsymbol{V} \boldsymbol{I}) \)
compounds through \( X e(I I) \) and \( \boldsymbol{X} \boldsymbol{e}(\boldsymbol{V} \boldsymbol{I} \boldsymbol{I} \boldsymbol{I}) \)
Subject: Physics
When a voltage \( V_{s}=200 \sqrt{2} \sin (\omega t+ \)
\( \left.15^{\circ}\right) V \) is applied to an ac circuit, the
current in the circuit is found to be \( i= \)
\( 2 \sin [\omega t+(\pi / 4)] A . \) If the average power
consumed in the circuit is \( x \sqrt{6} W \). Find
\( \boldsymbol{x} \)
Subject: Chemistry
The molar specific heat of oxygen at
constant pressure \( \mathrm{C}_{p}=7.03 \mathrm{cal} / \mathrm{mol}^{o} \mathrm{C} \)
and \( \mathrm{R}=8.31 \mathrm{J} / \mathrm{mol}^{o} \mathrm{C} \). the amount of
heat taken by 5 mol of oxygen when
heated at constant volume from \( 10^{\circ} \mathrm{C} \) to
\( 20^{\circ} \mathrm{C} \) will be approximately
A \( .25 \mathrm{cal} \)
B. 50 cal
c. \( 250 c a l \)
D. 500 call
Subject: Chemistry
Consider two sealed jars of equal volume. One contains 2 g of hydrogen at \( 200 \mathrm{K} \) and the other contains \( 28 \mathrm{g} \) of nitrogen at \( 400 \mathrm{K} \). The gases in the two jars will have
A. the same pressure
B. the same average kinetic energy.
c. the same number of molecules
D. the same average molecular speed
Subject: Biology
Assertion
Peptidyl transfer site is contributed by larger sub-unit of ribosome
Reason
The enzyme peptidyl transferase is contributed by both \( 23 S \) and 16 S ribosomal sub-units
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: Maths
The equation of motion of a body falling under gravity is given by \( \frac{d v}{d t}=g- \) \( \frac{g}{\lambda^{2}} v^{2} . \) The Velocity as a function of time
is? given that \( \boldsymbol{v}=\mathbf{0} \boldsymbol{t}=\mathbf{0} \)
A \( \cdot v=\lambda^{2} \tan h^{-1} \frac{g t}{\lambda} \)
B. \( v=\lambda \cot h^{-1} \frac{g t}{\lambda} \)
c. \( v=\lambda \tan h^{-1} \frac{g t}{\lambda} \)
D. \( v=\lambda \cot ^{2} h^{-1} \frac{g t}{\lambda} \)
Subject: Physics
Two identical blocks \( A \) and \( B \) connected
by a massless string are placed on a frictionless horizontal plane. A bullet having same mass moving with
a speed u strikes block \( \mathrm{B} \) from behind as shown. If the bullet gets embedded into the block \( \mathrm{B} \), then find the impulse on A due to tension in the string.
A \( \cdot \frac{m}{3} \)
в. \( \frac{2 m u}{3} \)
\( c \cdot \frac{m u^{2}}{3} \)
Subject: Maths
A player tosses two fair coins. He wins Rs. \( 5 /- \) if two heads occur, \( R s .2 /- \) if one head occurs and \( R s .1 /- \) if no head
occurs. Then his expected gain is
A \( \cdot \) Rs. \( \frac{8}{3} \)
в. \( \operatorname{Rs} . \frac{7}{3} \)
c. \( R s .2 .5 \)
D. Rs.1.5
Subject: Chemistry
Find the oxidation number of nitrogen in each case:
\( N \) in \( N H_{3}, N H_{2} O H, N a N_{3} \) and
\( N H_{4} N O_{2} \)
\( \mathbf{A} \cdot_{-3,-1,-\frac{1}{3},+3 \&-3} \)
B. \( _{-3,-2,-\frac{1}{3},+1} \)
D. None of the above
Subject: Physics
Assertion
Dust particles generally settle down in a
closed room.
Reason
The terminal velocity is inversely proportional to the square of their radii.
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
Which of the following processes will be
at equilibrium?
This question has multiple correct options
A. Water maintained at \( 233 \mathrm{K} \) in a closed container.
B. Sulphur dioxide being released in atmosphere at 298
K.
C. Heating calcium carbonate at \( 773 \mathrm{K} \) in a closed kiln.
D. Formation of ammonia at \( \left(300^{\circ} \mathrm{C}\right) \) temperature.
Subject: Chemistry
\( \mathbf{N H}_{3} \) on burning in oxygen gives:
A. \( \mathrm{NOandH}_{2} \mathrm{O} \)
B. \( N O_{2} \) and \( H_{2} O \)
c. \( \mathrm{N}_{2} \) and \( \mathrm{H}_{2} \mathrm{O} \)
D. \( \mathrm{N}_{2} \mathrm{OandH}_{2} \)
Subject: Chemistry
Best method of form aromatic iodide is:
\( \mathbf{A} \cdot A r N_{2}^{+}+H I \rightarrow \)
B. \( R N H_{2}+I_{2} \rightarrow \)
\( \mathbf{c} \cdot A r N_{2}^{+}+K I \rightarrow \)
D. \( A r N_{2}^{+}+P I_{3} \rightarrow \)
Subject: Physics
A boat moves with a speed of \( 5 k m / h \) relative to water in a river flowing with a speed of \( 3 k m / h \) and a width of \( 1 k m \) The minimum time taken around a
round trio is
\( \mathbf{A} \cdot 5 \) minutes
B. 20 minutes
c. 30 minutes
D. 60 minutes
Subject: Maths
\( A \equiv(1,2) \) and \( B \equiv(7,10) \) are two points. If \( \boldsymbol{P}(\boldsymbol{x}, \boldsymbol{y}) \) is a point such that
\( \angle A P B=60^{\circ} \) and area of \( \Delta A P B \) is
maximum, then which of the following is (are) TRUE?
This question has multiple correct options
A. \( P \) lies on any line perpendicular to \( A B \)
B. \( P \) lies on the perpendicular bisector of \( A B \)
c. \( P \) lies on the line \( 3 x+4 y=36 \)
D. Radius of circumcircle of \( \Delta P A B \) is 10 units
Subject: Chemistry
For the gaseous reaction \( 2 A+B \rightarrow \)
\( C+D, \) the rate is given by \( k[A][B] . \) The
volume of the container containing the reaction mixture is suddenly reduced to one-fourth of its original volume. with respect to the original rate, now the rate would be:
A \( \cdot \frac{1}{16} \) times the original rate
B . \( \frac{1}{8} \) times the original rate
c. 16 times the original rate
D. 8 times the original rate
Subject: Biology
Consider statements a-c about
pollution.
(a) To control air pollution all Delhi buses were asked to run on unleaded
petrol by the end of 2002
(b) Electrostatic precipitator can
remove \( 99 \% \) of particulate matter from
thermal power plant exhaust.
(c) It is possible to estimate amount of organic matter in sewage water by measuring BOD. Of the statements.
\( A \cdot b \) and \( c \) correct
B. a alone correct
c. b alone correct
D. c alone correct
E. a and b correct
Subject: Physics
Two children are at the opposite end of an iron pipe. One struks the end of the pipe with a stone. Calculate the ratio of the time taken by sound waves in air and in iron to reach the other child. Use
speed of sound in (i) air \( =344 m s^{-1} \)
and
(ii) iron \( =\mathbf{5 1 3 0 m s}^{-1} \)