AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
If the rms value of sinusoidal input to a full wave rectifier is \( \frac{v_{o}}{\sqrt{2}}, \) then the rms value of the rectifier's output is?
A \( \cdot \frac{v_{o}}{\sqrt{2}} \)
B. \( \frac{v_{o}^{2}}{\sqrt{2}} \)
c. \( \frac{v_{o}^{2}}{2} \)
D. \( \sqrt{2} V_{o}^{2} \)
E \( .2 V_{o}^{2} \)
Subject: Physics
A ball of mass \( 50 g m \) is dropped from a height \( h=10 m . \) It rebounds losing 75
percent of its kinetic energy. If it remains in contact with the ground for \( \Delta t=0.01 \) sec., the impulse of the
impact force is:
A. \( 1.3 N-s \)
B. \( 1.05 N-s \)
c. \( 1300 N-s \)
D. \( 015 N-s \)
Subject: Maths
The integrating factor of the differential equation \( 3 x \log _{e} x \frac{d y}{d x}+y=2 \log _{e} x \) is
given by:
A \( \cdot\left(\log _{e} x\right)^{2} \)
B. \( \log _{e}\left(\log _{e} x\right) \)
\( \mathbf{c} \cdot \log _{e} x \)
D. \( \quad\left(\log _{e} x\right)^{\frac{1}{3}} \)
Subject: Chemistry
select the correct statement \( (s): \)
This question has multiple correct options
\( \mathbf{A} \cdot \) When \( d_{x^{2}-y^{2}} \) or \( d_{x y} \) orbitals combine in parallel planes, then \( \delta \) or \( \delta \) molecular orbitals are formed.
B. When \( d_{x^{2}-y^{2}} \) or \( d_{x y} \) orbitals combine in parallel planes, then N.B.M.O. are formed.
C. When \( d_{y z} \) or \( d_{x z} \) orbitals combine in along the y-axis, then N.B.M.O. are formed.
D. No interaction is possible when \( p_{z} \) and \( d_{x z} \) orbitals overlap with collinear z-axis
Subject: Maths
Let \( S \) be the sample space of all \( 3 \times 3 \)
matrices with entries from the set
\( \{0,1\} . \) Let the events \( E_{1}= \)
\( \{A \in S: \operatorname{det} A=0\} \) and \( E_{2}= \)
\( \{A \in S: S u m \text { of entries of } A \text { is } 7\} \)
If a matrix is chosen at random from \( \boldsymbol{S} \)
then the conditional probability
\( \boldsymbol{P}\left(\boldsymbol{E}_{1} \mid \boldsymbol{E}_{2}\right) \) equals.
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{ll}x^{2}+k, & \text { when } x \geq 0 \\ -x^{2}-k, & \text { when } x<0\end{array} . \) If the \right.
function \( f(x) \) be continous at \( x=0 \)
then \( \boldsymbol{k}= \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. 1
c. 2
D. -
Subject: Maths
Solving \( \frac{\mathbf{2}}{\boldsymbol{x}}+\mathbf{3} \boldsymbol{y}=-\mathbf{3} \) and \( \boldsymbol{y}-\boldsymbol{4} \boldsymbol{x}=\frac{\mathbf{7}}{\mathbf{3}} \)
gives \( (\mathbf{x}, \mathbf{y}) \)
\( \mathbf{A} \cdot\left(-\frac{1}{2}, 3\right) \)
B \( \cdot\left(-1, \frac{1}{3}\right) \)
c. \( \left(-\frac{1}{2}, \frac{1}{3}\right) \)
D \( \cdot\left(-2, \frac{1}{3}\right) \)
Subject: Chemistry
Assertion
The standard unit for expressing the
mass of atom is amu.
Reason
amu is also called as avogram.
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
A particle of mass \( m \) and charge \( q \)
moving with velocity \( V \) enters Region
\( I I \) normal to the boundary as shown in
the figure. Region II has a uniform
magnetic field \( B \) perpendicular to the
plane of the paper. The length of the
Region \( \boldsymbol{I} \boldsymbol{I} \) is \( \ell \) Choose the correct
choice(s).

This question has multiple correct options
A. The particle enters Region III only if its velocity \( \mathrm{V}> \)
\( \frac{q \ell}{m} \)
B. The particle enters Region III only if its velocity \( \mathrm{V}< \)
\( \frac{q \ell}{m} \)
C. Path length of the particle in Region II is maximum when velocity \( \mathrm{V}=\frac{\mathrm{q} \ell \mathrm{B}}{\mathrm{m}} \)
D. Time spent in Region II is same for any velocity V as long as the particle returns to Region 1
Subject: Physics
A wooden plank rests in equilibrium on
two rocks on opposite sides of a narrow
stream. Three forces \( P, Q \) and \( R \) act on
the plank. How are the sizes of the
forces related?
\( \mathbf{A} \cdot \mathbf{P}+\mathbf{Q}=\mathbf{R} \)
B. \( P+R=Q \)
\( \mathbf{c} \cdot \mathrm{P}=\mathrm{Q}=\mathrm{R} \)
D. \( P=Q+R \)
Subject: Physics
If a slab of insulating material \( 4 \times \) \( 10^{-5} m \) thick is introduced between the
plates of a parallel plate capacitor, the distance between the plates has to be increased by \( 3.5 \times 10^{-5} m \) to restore the
capacity to original value. Then the dielectric constant of the material of
slab is :
\( A \cdot 8 \)
B. 6
c. 12
D. 10
Subject: Chemistry
Calculate the amount of \( N H_{3} \) and
\( N H_{4} C l \) required to prepare a buffer
solution of \( p H 9.0 \) when total
concentration of buffering reagents is \( 0.6 \operatorname{mol} L^{-} \cdot p K_{b} \) for \( N H_{3}= \)
\( 4.7, \log 2=0.30 \)
Subject: Physics
A force of \( 1 \mathrm{N} \) acts upon a mass of \( 1 \mathrm{kg} \) for 1 second and gives it a momentum \( P_{1} \) and kinetic energy \( E_{1} . \) The same
force acts upon the same mass for a displacement of \( 1 \mathrm{m} \) and gives it a
momentum \( P_{2} \) and kinetic energy \( E_{2} \) Then, which of the following is correct?
\( \mathbf{A} \cdot P_{1}=P_{2}, E_{1}=E_{2} \)
B. \( P_{1}>P_{2}, E_{1}>E_{2} \)
c. \( P_{1}<P_{2}, E_{1}<E_{2} \)
D. \( P_{1}>P_{2}, E_{1}<E_{2} \)
Subject: Maths
The image of the point (2,-1,1) by the
plane \( 3 x+4 y-5 z=0 \) is
A \( \cdot(-2,1,-1) \)
в. \( \left(\frac{2}{3}, \frac{-1}{4}, \frac{-1}{5}\right) \)
\( ^{\mathbf{C}} \cdot\left(\frac{59}{25}, \frac{-13}{25}, \frac{2}{5}\right) \)
D. none of these
Subject: Biology
Match the columns and find the correct
option.
(a) Munch
(i) Stomatal movement
(ii) Hastens fruit ripening by
(b) Darwin \( \quad \) volatiles
\( (c) \)
(iii) Growth of coleo towards light Cousins
(d) Levitt
(iv) Nature of enzymes
(v) Bidirectional traces in phloem
\( A \cdot a-i i i, b-i v, c-i, d-i i \)
B. a-iv, b-iii, c- i, d-i i
C. \( a-v, b- \) iii, c- ii, d- i
D. a- iii, b- i, c- iv, d- v
Subject: Maths
The area of a field in the shape of a
trapezium measure \( 1440 m^{2} . \) The perpendicular distance between its
parallel sides is \( 24 \mathrm{cm} . \) If the ratio of the parallel sides is \( 53, \) then the length of the longer parallel sides is
A. \( 75 \mathrm{m} \)
B. \( 45 \mathrm{m} \)
c. \( 120 \mathrm{m} \)
D. 60 m
Subject: Maths
If the projections ofthe line segment \( A B \)
on the \( y z \) -plane, \( z x \) -plane, \( x y \) -plane are \( \sqrt{160}, \sqrt{153}, 5 \) respectively, then the projection of \( A B \) on the \( z \) -axis is
A \( \cdot \sqrt{12} \)
B. \( \sqrt{13} \)
c. 12
D. 144
Subject: Chemistry
Draw structures of the following
derivatives.
(i) The 2,4 -dinitrophenylhydrazone of benzaldehyde
(ii) Cyclopropanone oxime
(iii) Acetaldehydedimethylacetal
(iv) The semicarbazone of
cyclobutanone
(v) The ethylene ketal of hexan-3-one
(vi) The methyl hemiacetal of formaldehyde
Subject: Maths
Prove that the triangle, whose position vectors of the vertices are \( 2 \hat{i}+4 \hat{j}- \) \( \hat{\boldsymbol{k}}, \boldsymbol{4} \hat{\boldsymbol{i}}+\mathbf{5} \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \) and \( \boldsymbol{3} \hat{\boldsymbol{i}}+\boldsymbol{6} \hat{\boldsymbol{j}}-\boldsymbol{3} \hat{\boldsymbol{k}} \)
respectively, is an isosceles right angled triangle.
Subject: Maths
\( A B C D \) is a parallelogram and \( P \) is a
point on the segment \( \overline{A D} \) dividing it internally in the ratio 3: 1 the line \( \overline{B P} \)
meets the diagonal \( \overline{A C} \) in \( Q . \) Then the
ratio \( \boldsymbol{A} \boldsymbol{Q}: \boldsymbol{Q} \boldsymbol{C} \) is
A .3: 4
B. 4: 3
c. 3: 2
D. 2 : 3
Subject: Maths
If \( \boldsymbol{f}(\boldsymbol{x})+\boldsymbol{f}(\boldsymbol{x}+\boldsymbol{4})=\boldsymbol{f}(\boldsymbol{x}+\boldsymbol{2})+\boldsymbol{f}(\boldsymbol{x}+ \)
6) then find the period of \( f(x) \)
Subject: Maths
Draw the histogram and use it to find the mode for the following frequency distribution.
House -
\[
\begin{array}{llll}
\text { Rent in } & \mathbf{4 0 0 0}- & \mathbf{6 0 0 0}- & \mathbf{8 0 0 0}- \\
\text { Rs. per } & \mathbf{6 0 0 0} & \mathbf{8 0 0 0} & \mathbf{1 0 0 0 0}
\end{array}
\]
month
Number
of
\[
200
\]
families
A . Rs. 8000
B. Rs. 8350
c. Rs. 8500
D. Rs. 8750
Subject: Biology
Assertion
Darwin's finches of Galapagos islands have different types of modified beaks according to their food habits.
Reason
Adaptive radiation, leads to
development of different functional
structure from a common ancestral
form.
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
Suppose that a function \( f \) satisfies the following conditions for all real values of
\( x \) and \( y \)
\( (i) f(x+y)=f(x) \cdot f(y) \)
\( (i i) f(x)=1+x g(x), \) where
\( \lim _{x \rightarrow 0} g(x)=1 . \) The value of \( \log f(8) \) is
Subject: Physics
The relationship between acceleration due to gravity \( (g) \) and universal
gravitational constant( \( G \) ) may be
represented as:
\( (M \text { and } R \) are the mass and radius of
the earth respectively
A. \( G=\frac{g M}{R^{2}} \)
В. \( g=\frac{G M}{R^{2}} \)
c. \( g=\frac{G}{R^{2}} \)
D. None of these
Subject: Physics
A uniform rod of length \( 60 \mathrm{cm} \) and mass
\( 6 k g \) is acted upon by two forces as shown in the diagram. The force exerted by \( 45 \mathrm{cm} \) part of the rod on \( 15 \mathrm{cm} \) part of
the rod is
A. \( 9 N \)
N
В. \( 18 N \)
c. \( 27 N \)
D. 30N
Subject: Physics
Two S.H.M.'s are represented by the relations \( \boldsymbol{x}=\mathbf{4} \sin (\mathbf{8 0} \boldsymbol{t}+\boldsymbol{\pi} / \mathbf{2}) \) and \( \boldsymbol{y}= \)
\( 2 \cos (60 t+\pi / 3) \)
The ratio of their time periods is
A . 2:
B. 1:
c. 4: 3
D. 3:
Subject: Physics
A skater of mass m standing on ice throws a stone of mass M with a velocity of \( V \) in a horizontal direction. The
distance over which the skater will move back (the coefficient of friction
between the skater and the ice is \( \mu \) ):
\( ^{\mathbf{A}} \cdot \frac{M^{2} V^{2}}{2 m \mu g} \)
в. \( \frac{M V^{2}}{2 m^{2} \mu g} \)
\( ^{\mathrm{c}} \cdot \frac{M^{2} V^{2}}{2 m^{2} \mu g} \)
D. \( \frac{M^{2} V^{2}}{2 m^{2} \mu^{2} g} \)
Subject: Physics
A container filled with liquid up to height \( h \) is place on a smooth horizontal
surface. The container is having a small hole at the bottom. As the liquid comes out from the hole, the container moves
in a backward direction with
acceleration \( a \) and finally, when all the liquid is drained out, it acquires a
velocity \( v . \) Neglect mass of the container. In this case
A. both \( a \) and \( v \) depend on \( h \)
B. only a depends on \( h \)
c. only \( v \) depends on \( h \)
D. neither \( a \) nor \( v \) depends on \( h \)
Subject: Physics
A uniform rod of mass \( 1 \mathrm{kg} \) is hanging from a thread attached at the midpoint of the rod. A block of mass \( m=3 \mathrm{kg} \) hangs at the left end of the rod and block of mass \( M \) hangs at the right side at \( 80 \mathrm{cm} \) from block \( m . \) If system is
in equilibrium. Calculate \( M \)
\( A \cdot 4 \) kg
в. 5 кв
\( c \cdot 6 \mathrm{kg} \)
\( D \cdot 8 \mathrm{kg} \)
E. 9 kg
Subject: Maths
If \( \boldsymbol{\alpha} \) and \( \beta \) are two different values of \( \boldsymbol{\theta} \)
lying between 0 and \( 2 \pi \) which satisfy
\( 3 \cos \theta+4 \sin \theta=6 . \) Find the value of
\( \sin (\alpha+\beta) \)
Subject: Physics
A fish is \( 10.0 \mathrm{cm} \) from the front surface
of a spherical fish bowl of radius
\( 20.0 \mathrm{cm}, \) as shown in the figure. The
walls of the bowl are thin,and their
effects can be neglected. As
observed from the point \( \boldsymbol{P}(\text { see figure }) \)
the fish is at a distance of:
A. \( 6.7 \mathrm{cm} \) from the surface and appears magnified in size
B. \( 8.6 \mathrm{cm} \) from the surface and appears magnified in size
c. \( 10.3 \mathrm{cm} \) from the surface and appears diminished in size
D. \( 11.4 \mathrm{cm} \) from the surface and appears diminished in size
Subject: Chemistry
The molecular formula of a
compound having a molecular weight of 92 and containing \( 30.5 \% \) of nitrogen
and \( 69.5 \% \) of oxygen by weight is:
A. \( N_{2} O_{4} \)
is
в. \( N O_{2} \)
\( \mathrm{c} \cdot N_{2} O_{3} \)
D. \( N_{2} \) O
Subject: Physics
In the figure shown, \( q \) is in coulomb and \( t \) in second. At time \( t=1 s \)
This question has multiple correct options
A \( \cdot V_{a}-V_{b}=4 V \)
в. \( V_{b}-V_{c}-1 V \)
C \( . V_{c}-V_{d}=16 V \)
D. \( V_{a}-V_{d}=20 V \)
Subject: Maths
The mean of the following distribution
is
15. Find the value of a
\( \begin{array}{lll}\text { C.I. } & \text { 5 } & \text { 10 }\end{array} \) 15 \( \mathbf{2 0} \) \( \mathbf{2 5} \)
Freq 6 a 6 5 10
Subject: Maths
Find the matrix \( A \) such that
\( \left[\begin{array}{cc}2 & -1 \\ 1 & 0 \\ -3 & 4\end{array}\right] A=\left[\begin{array}{cc}-1 & -8 \\ 1 & -2 \\ 9 & 22\end{array}\right] \)
Subject: Maths
The foci of an ellipse are \( S(-2,-3), S^{\prime}(0,1) \) and its \( e=\frac{1}{\sqrt{2}} \)
then the directrix corresponding to the
focus \( S^{\prime} \) is:
A. \( x+2 y-5=0 \)
B . \( x+2 y-9=0 \)
c. \( x+2 y-11=0 \)
D. none of these
Subject: Physics
The figure shows a particle ( carrying change \( +q \) ) at the origin. A uniform magnetic field is directed into the plane of the paper. The particle can be projected only in the plane of paper and along positive or negative \( x \) -or \( y \) -axis. The particle moves with constant speed and has to hit target located in the third quadrant. There are two direction of projections, which can make it possible, these are then
\( A \cdot+x \) and \( +y \)
B. \( +x \) and \( -y \)
\( c .-x \) and \( +y \)
D. - x and - y
Subject: Maths
In triangle \( A B C, \) medians \( A D \) and \( B E \) are drawn.lf \( \boldsymbol{A D}=\mathbf{4}, \angle \boldsymbol{D A B}=\frac{\boldsymbol{\pi}}{\mathbf{6}} \) and
\( \angle A B E=\frac{\pi}{3}, \) then the area of the
\( \triangle A B C \) is
A \( \cdot \frac{8}{3} \)
в. \( \frac{16}{3} \)
c. \( \frac{32}{3 \sqrt{3}} \)
D. \( \frac{64}{3} \)
Subject: Maths
The price of a table is \( R s .400 \) more than
that of a chair. If 6 tables and 6 chairs
together cost \( R s .4800, \) by what percent is the price of the chair less than that of the table ?
\( \mathbf{A} \cdot 33 \frac{1}{3} \% \)
в. \( 50 \% \)
\( \mathbf{c} \cdot 66 \frac{2}{3} \% \)
D. None of these
Subject: Chemistry
Use the bond energies to estimate \( \Delta \boldsymbol{H} \) for this reaction:
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{O}_{2}(\boldsymbol{g}) \longrightarrow \boldsymbol{H}_{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \)
\begin{tabular}{|c|c|}
\hline Bond & Bond energy \\
\hline \( \mathrm{H}-\mathrm{H} \) & \( 436 \mathrm{kJ} \mathrm{mol}^{-1} \) \\
\hline \( 0-0 \) & \( 142 \mathrm{kJ} \mathrm{mol}^{-1} \) \\
\hline \( 0=0 \) & \( 499 \mathrm{kJ} \mathrm{mol}^{-1} \) \\
\hline \( \mathrm{H}-0 \) & \( 460 \mathrm{k} \mathrm{mol}^{-1} \) \\
\hline
\end{tabular}
A. \( -127 k J \)
\( J \)
в. \( -109 k J \)
c. \( -400 k J \)
D. \( -800 k J \)
Subject: Chemistry
Match List-I with List-II.
List - 1
a) Red lead
p) Lead monoxide
b) Litharge
q) An ore of lead
c) Galena
r) An ore of tin
d) Cassiterite
s) Minium
A \( \cdot a-r ; b-s ; c-p ; d-q \)
B. \( a-r ; b-q ; c-r ; d-p, q \)
c. \( a-s ; b-p ; c-q ; d-r \)
D. a-r; b-s; c-q; ;d-p
Subject: Physics
Mass of the earth is:
A \( \cdot \frac{4}{3} \pi R^{3}(A-B R) \)
B \( \cdot 4 \pi R^{3}(A-B R) \)
\( ^{\mathbf{C}} \cdot \frac{4}{3} \pi R^{3}\left(A-\frac{3}{4} B R\right) \)
D \( \cdot 4 \pi R^{3}\left(A-\frac{3}{4} B R\right) \)
Subject: Physics
\( 4.00 \mathrm{cm} \) contains air compressed by a piston of mass \( m=13.0 \mathrm{kg} \) which can slide freely in the cylinder. The entire arrangement is immersed in a water
bath whose temperature can be controlled. The system is initially in
equilibrium at temperature \( t=20^{\circ} C \)
The initial height of the piston above the
bottom of the cylinder is \( h_{i}=4.00 \mathrm{cm} \)
The temperature of the water bath is
gradually increased to a final
temperature \( t_{f}=100^{\circ} \mathrm{C} . \) Calculate the
final height \( h_{f} \) of the piston.
\( \mathbf{A} \cdot 25.09 \mathrm{cm} \)
B. \( 5.09 \mathrm{cm} \)
c. \( 15.09 c m \)
D. \( 10.09 \mathrm{cm} \)
Subject: Physics
The mass of \( \mathrm{O}_{2} \) molecule is 16 times that
\( \mathrm{H}_{2} \) molecule. The rms velocity of \( \mathrm{O}_{2} \)
molecule at room temperature \( \mathrm{C}_{r m s} \). The
rms velocity of \( \mathrm{H}_{2} \) molecule at the same
temperature will be:
A \( \cdot \frac{C_{r m s}}{16} \)
в. \( \frac{C_{r m s}}{4} \)
\( \mathbf{c} \cdot 4 C_{r m s} \)
D. \( 16 C_{r m} \)
Subject: Chemistry
\( 2 H_{2} S(g)+3 O_{2}(g) \rightarrow 2 S O_{2}(g)+ \)
\( 2 H_{2} O(g)+ \) heat
Which quantity is increased when the volume of the system is decreasing?
I. Rate of reaction
Il. Equilibrium concentration of
reactants
III. Value of \( \boldsymbol{K}_{e q} \)
A . I only
B. III only
c. I and II only
D. II and III only
E . I, II, and III
Subject: Maths
Negation of " \( 2+3=5 \) and \( 8<10 " \) is
A \( .2+3 \neq 5 \) and \( <10 \)
B. \( 2+3=5 \) and \( 8 \Varangle 10 \)
\( c \cdot 2+3 \neq 5 \) or \( 8 \Varangle 10 \)
D. None of the above
Subject: Physics
An ideal monatomic gas expands to twice its volume. If the process is isothermal, the magnitude of work done
by the gas is \( W_{i} . \) If the process is adiabatic, the magnitude of work done
by the gas is \( W_{a} . \) Which of the following
is true?
A \( . W_{i}=W_{a}>0 \)
в. \( W_{i}>W_{a}=0 \)
c. \( W_{i}>W_{a}>0 \)
D. \( W_{a}=W_{i}=0 \)
Subject: Physics
A jet airplane is travelling at a speed of \( 500 \mathrm{km} / \mathrm{h} \) ejects its products of combustion with a speed of \( 1500 \mathrm{km} / \mathrm{h} \) relative to the jet plane. The speed of the latter with respect to an observer on the
ground is:
\( \mathbf{A} .1500 \mathrm{km} / \mathrm{h} \)
B. 2000 km/h
\( c \cdot 1000 \mathrm{km} / \mathrm{h} \)
D. \( 500 \mathrm{km} / \mathrm{h} \)
Subject: Maths
Prove that \( \left|\begin{array}{lll}\boldsymbol{a}+\boldsymbol{b} & \boldsymbol{b} & \boldsymbol{c} \\ \boldsymbol{b}+\boldsymbol{c} & \boldsymbol{c} & \boldsymbol{a} \\ \boldsymbol{c}+\boldsymbol{a} & \boldsymbol{a} & \boldsymbol{b}\end{array}\right|=\mathbf{3} \boldsymbol{a} \boldsymbol{b} \boldsymbol{c}-\boldsymbol{1} \)
\( \boldsymbol{a}^{3}-\boldsymbol{b}^{3}-\boldsymbol{c}^{3} \)
Subject: Physics
the horizontal and vertical components
of the force exerted on the beam at the
wall
A. Horizontal component is \( 500 N \) towards left and vertical component \( 75 N \) downwards
B. Horizontal component is \( 500 N \) towards right and vertical component \( 75 N \) upwards
C. Horizontal component is \( 625 N \) towards left and vertical component \( 150 N \) upwards
D. Horizontal component is \( 625 N \) towards right and vertical component \( 150 N \) downwards
Subject: Maths
Show that the function \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \cot ^{-1}(\sin x+\cos x) \) is decreasing on
\( \left(0, \frac{\pi}{4}\right) \) and increasing on \( \left(\frac{\pi}{4}, \frac{\pi}{2}\right) \)
Subject: Chemistry
In a volume of \( 5 d m^{3}, 26 \) moles of pure \( A \)
and 4 moles of pure \( B \) were placed. At
equilibrium 1 mol of \( C \) was present.
Calculate \( K_{c} \) for the reaction, \( \boldsymbol{A}+\boldsymbol{2} \boldsymbol{B} \rightleftharpoons \boldsymbol{C} \)
Subject: Maths
The area of the region between the curve
\( \boldsymbol{y}=\boldsymbol{x}^{3} \) and the lines \( \boldsymbol{y}=-\boldsymbol{x} \) and \( \boldsymbol{y}=\mathbf{1} \)
is:
A. 5 sq. units
B. \( \frac{4}{5} \) sq. units
c. \( \frac{5}{4} \) sq. units
D. \( \frac{3}{5} \) sq. units
Subject: Chemistry
The \( \Delta H \) value at \( 360 \mathrm{K} \) for the reaction:
\( \boldsymbol{F} \boldsymbol{e}_{2} \boldsymbol{O}_{3(s)}+\boldsymbol{3} \boldsymbol{H}_{2(\boldsymbol{g})} \rightarrow \boldsymbol{2} \boldsymbol{F} \boldsymbol{e}_{(s)}+\boldsymbol{3} \boldsymbol{H}_{2} \boldsymbol{O}_{(l)} \)
given that \( \Delta \boldsymbol{H}_{300}=-33.29 k J m o l^{-1} \)
and \( C_{p} \) for \( F e_{2} O_{3(s)}, F e_{(s)}, H_{2} O(l) \) and \( \boldsymbol{H}_{2(\boldsymbol{g})} \) are \( \mathbf{1 0 3 . 8}, \mathbf{2 5 . 1}, \mathbf{7 5 . 3} \) and \( \mathbf{2 8 . 8} \)
\( \boldsymbol{J} \boldsymbol{K}^{-1} \boldsymbol{m} \boldsymbol{o l}^{-1}, \) is:
A \( .-28.1 k J m o l^{-1} \)
B. 28.1 kJmol-
\( \mathbf{c} .85 .9 k J m o l^{-1} \)
D. \( -85.9 ~ k J m o l^{-1} \)
Subject: Chemistry
n-Butane \( \left(C_{4} H_{10}\right) \) is produced by
monobromination of \( C_{2} H_{6} \) followed by
Wurtz reaction. Calculate the volume of
ethane at STP required to produce 55 g of \( n \) -butane. The bromination takes
place with \( 90 \% \) yield and the Wurtz reaction with \( 85 \% \) yield.
A . 27.75 느
B . 55.5 느
c. 111
D. 5.55
Subject: Chemistry
Statement 1: Substances with hydrogen
bonding tend to have unusually low boiling points. Statement 2: Extra energy is necessary to break the hydrogen bonds.
A. Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement 1
B. Both the Statement 1 and Statement 2 are correct, but Statement 2 is not the correct explanation of Statement 1.
c. statement 1 is correct, but statement 2 is not correct
D. Statement 1 is not correct, but Statement 2 is correct
Subject: Chemistry
Assertion
\( 1 M \) solution of \( K C l \) has greater
osmotic pressure than \( 1 M \) solution of
glucose at the same temperature.
Reason
In solution \( K C l \) dissociates to produce more number of particles.
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 which species does the specifed atom have an incomplete outer shell?
A. \( B F_{3} \) (B)
B. \( C H_{3}^{-}(\mathrm{C}) \)
\( \mathrm{c} \cdot F_{2} \mathrm{O}(\mathrm{F}) \)
D. \( H_{2} O^{+}(0) \)
Subject: Physics
A straight conductor of uniform cross-
section carries a current \( I . \) If \( s \) is the
specific charge of an electron, the momentum of all the free electrons per unit length of the conductor, due to
their drift velocity only is
A . \( 1 s \)
в. \( \sqrt{\frac{I}{s}} \)
c. \( \frac{I}{s} \)
\( ^{\mathrm{D} \cdot}\left(\frac{I}{s}\right)^{2} \)
Subject: Maths
8 players compete in a tournament, every one plays everyone else just once. The winner of a game gets \( 1, \) the loser 0 or each gets \( \frac{1}{2} \) if the game is drawn. The
final result is that every one gets a different score and the player playing placing second gets the same as the total of four bottom players.The total
score of all the players is
A .28
в. 21
\( c \cdot 20 \)
D. 22
Subject: Physics
The incident intensity on a horizontal surface at sea level from the sun is
about \( 1 k W m^{-2} \). Find the ratio of this
pressure to atmospheric pressure \( \boldsymbol{p}_{0} \)
(about \( \left.1 \times 10^{5} P a\right) \) at sea level.
[Assuming that \( 50 \% \% \) of this intensity is reflected and \( 50 \% \% \text { is absorbed }] \)
A \( .5 \times 10^{-11} \)
B. \( 4 \times 10^{-8} \)
c. \( 6 \times 10^{-12} \)
D. \( 8 \times 10^{-11} \)
Subject: Physics
The equation of a wave is given by \( \boldsymbol{y}= \) \( 10 \sin \left[\frac{2 \pi t}{30}+\alpha\right] . \) If the displacement is
\( 5 c m \) at \( t=0, \) then the total phase at
\( t=7.5 s \) will be
A \( \cdot\left(\frac{2 \pi}{3}\right) r a d \)
В. \( \left(\frac{2 \pi}{5}\right) \) rad
c. \( \left(\frac{\pi}{3}\right) \) rad
D. \( \left(\frac{\pi}{2}\right) \) rad