AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A spring gun has a spring constant of
\( 80 N / m . \) The spring is compressed \( 12 \mathrm{cm} \) by a ball of mass \( 15 \mathrm{gm} \). How much is potential energy of the spring and what will be the velocity of the ball,
if the trigger is pulled:
A. \( 57.6 \mathrm{J}, 87.6 \mathrm{m} / \mathrm{s} \)
в. \( 67.6 \mathrm{J}, 97.6 \mathrm{m} / \mathrm{s} \)
c. \( 0.576 J, 76.8 \mathrm{m} / \mathrm{s} \)
D. none of these
Subject: Chemistry
The reagents \( X \) and \( Y \) are respectively:
A \( \cdot X=C H_{3} C O C l / A l C l_{3}, Y=K M n O_{4} / O H^{\Theta} / \Delta \)
(acidification)
B. \( X=C H_{3} C H_{2} C l / A l C l_{3}, Y=C r O_{3} / H^{+} / \Delta \)
C. \( X=C H_{3} C O C l / A l C l_{3}, Y=I_{2} / N a O H, \) (acidification)
D. \( X=K M n O_{4} / O H^{\Theta} / \Delta, \) (acidification), \( Y= \)
\( C H_{3} C H_{2} C l / A l C l_{3} \)
Subject: Chemistry
Statement \( 1: \ln \) an electrolytic cell, the anode becomes positive and the cathode becomes negative.
Statement 2: Anions migrate to the anode and cations migrate to the
cathode.
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: Physics
In the figure, the velocities are in ground frame and the cylinder is
performing pure rolling on the plank,
velocity of point \( ^{\prime} A^{\prime} \) would be :
\( A \cdot 2 V_{C} \)
В \( \cdot 2 V_{C}+V_{P} \)
\( \mathbf{c} \cdot 2 V_{C}-V_{P} \)
D \( \cdot 2\left(V_{C}-V_{P}\right) \)
Subject: Maths
Show that \( \triangle A B C \) is an isosceles
triangle, if the determinant \( \mid \begin{array}{ccc}\mathbf{1} & \mathbf{1} \\ \mathbf{1}+\cos \boldsymbol{A} & \mathbf{1}+\cos \boldsymbol{B} & \mathbf{1} \\ \cos ^{2} \boldsymbol{A}+\cos \boldsymbol{A} & \cos ^{2} \boldsymbol{B}+\cos \boldsymbol{B} & \mathbf{c o s}^{2}\end{array} \)
\( \mathbf{D} \)
Subject: Chemistry
Which of the following statements
is/are not correct?
This question has multiple correct options
A. The covalency of \( \mathrm{N} \) in \( \mathrm{HNO}_{3} \) is +5
B. \( H N O_{3} \) in the gaseous state has a trigonal planar structure
C. The oxidation state of \( \mathrm{N} \) in \( \mathrm{H} \mathrm{NO}_{3} \) is +4
D. Gold dissolves in \( H N O_{3} \) to form gold nitrate
Subject: Chemistry
The equilibrium constant for the reaction
\( \boldsymbol{C H}_{3} \boldsymbol{C O O H}(\boldsymbol{a q})+\boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{O H}(\boldsymbol{a q}) \Leftrightarrow \)
\( \boldsymbol{C H}_{3} \boldsymbol{C O O C}_{2} \boldsymbol{H}_{5}(\boldsymbol{a q})+\boldsymbol{H}_{2} \boldsymbol{O}(l) \) is 16
The initial concentration of each of
\( C H_{3} C O O H \) and \( C_{2} H_{5} O H \) is two (mole/lit). What is the concentration of
\( C H_{3} C O O C_{2} H_{5} \) at equilibrium in moles / lit?
A. 0.9
B. 0.6
\( c \cdot 1.6 \)
D. 0.7
Subject: Maths
Find the point \( (0, y) \) that is equidistant
from (4,-9) and (0,-2)
A \( \cdot\left(0,-\frac{93}{14}\right) \)
в. \( \left(\frac{93}{14}, 0\right) \)
\( ^{c} \cdot\left(0,-\frac{14}{93}\right) \)
D. \( \left(\frac{14}{93}, 0\right) \)
Subject: Chemistry
Which of the following is true?
A. The electron density in the xy-plane in 3d \( _{x y} \) orbital si
zero
B. The electron densities in the xy and xz-plane in 3d \( _{y z} \) orbital are zero
C. The electron density in the xy-plane in \( 3 d_{x}^{2} \) orbital is
zero
D. Pauli exclusion principle is followed by bosons which have integral spin
Subject: Maths
\( \int_{0}^{2 \pi} \sin ^{4} x d x \) is equal to
This question has multiple correct options
\( \mathbf{A} \cdot 2 \int_{0}^{\pi} \sin ^{4} x d c \)
B. \( 8 \int_{0}^{\frac{\pi}{4}} \sin ^{4} x d x \)
C \( \cdot 4 \int_{0}^{\frac{\pi}{2}} \cos ^{4} x d x \)
D. \( 3 \int_{0}^{\frac{2 \pi}{3}} \sin ^{4} x d x \)
Subject: Chemistry
A beam of specific kind of particles of
velocity, \( 2.1 \times 10^{7} m / s \) is scattered by
a gold \( (Z=79) \) nuclei. Find out specific charge (charge/mass) of this particle if this distance of closest approach is \( 2.5 \times 10^{-14} m ? \)
\( \mathbf{A} \cdot 4.84 \times 10^{7} C / k g \)
B . \( 4.84 \times 10^{-7} \mathrm{C} / \mathrm{kg} \)
c. \( 2.42 \times 10^{7} \mathrm{C} / \mathrm{kg} \)
\( \mathbf{D} \cdot 3 \times 10^{-12} C / k g \)
Subject: Chemistry
Which of the following alcohols is dehydrated most easily with conc.
\( \boldsymbol{H}_{2} \boldsymbol{S O}_{4} ? \)
A \( \cdot p-O_{2} N C_{6} H_{4} C H(O H) C H_{3} \)
в. \( p-C l C_{6} H_{4} C H(O H) C H_{3} \)
c. \( p-C H_{3} O C_{6} H_{4} C H(O H) C H_{3} \)
D. \( C_{3} H_{5} C H(O H) C H_{3} \)
Subject: Physics
Three forces
\( (\hat{i}+3 \hat{j}+\hat{k}), \frac{5}{7}(-2 \hat{i}+9 \hat{k}) \) and
\( 11(2 \hat{i}+\hat{j}+6 \hat{k}) \) are acting on a
particle. Calculate the work done in displacing the particle from point (4,-1,1) to point (11,6,8)
Subject: Maths
Following 10 observations are arranges in ascending order as follows. \( \mathbf{2}, \mathbf{3}, \mathbf{5}, \mathbf{9}, \boldsymbol{x}+\mathbf{1}, \boldsymbol{x}+\mathbf{3}, \mathbf{1 4}, \mathbf{1 6}, \mathbf{1 9}, \mathbf{2 0} \)
If the median of the data is 11 , find the
value of \( x \)
Subject: Maths
In a circle with centre \( \boldsymbol{O}, \boldsymbol{O} \boldsymbol{D} \perp \) chord
\( A B . \) If \( B C \) is the diameter, then which
of the following option is correct:
\( \mathbf{A} \cdot A C=B C \)
В \( . O D=B D \)
c. \( A C=2 \times O D \)
D. None of these
Subject: Physics
\( \mathbf{A} \)
1.05 \( m \) having negligible mass is
supported at its ends by two wires
of steel (wire \( A \) ) and aluminium (wire \( B \)
of equal lengths as shown in Fig. The cross-sectional areas of wires \( A \) and \( B \)
are \( 1.0 m m^{2} \) and \( 2.0 m m^{2}, \) respectively
At what point along the rod should a
mass \( m \) be suspended in order
to produce
(a) Equal stress in \( A \) and \( B \) and
(b) Equal strains in \( A \) and \( B \) ?
Subject: Maths
The lines \( 3 x+4 y=9 \) and \( 6 x+8 y+ \)
\( \mathbf{1 5}=\mathbf{0} \) are tangents to the same circle.
The radius of the circle is :-
A \( \cdot \frac{3}{10} \)
в. \( \frac{33}{20} \)
\( c \cdot \frac{33}{10} \)
D. \( \frac{33}{5} \)
Subject: Chemistry
The enthalpy of combustion of \( \mathrm{C}_{6} \mathrm{H}_{6}(l) \) is \( -3250 \mathrm{kJ} . \) When \( 0.39 \mathrm{g} \) of benzene is burnt in excess of oxygen in an open vessel, the amount of heat liberated is:
A. \( 16.25 \mathrm{KJ} \)
B. 33.50 KJ
c. 32.5 K
D. 65 K J
Subject: Chemistry
Select correct statement(s):
This question has multiple correct options
A. In graphite, only three electrons (out of four) are involved in \( \sigma \) bonding.
B. \( \pi- \) bonding electrons in graphite are delocalized over the whole structure.
C. Conduction of electricity in graphite is due to mobile electrons.
D. Diamond is insulator due to absence of mobile
electrons.
Subject: Maths
The number of solution of the equation \( \tan ^{-1}(x-1)+\tan ^{-1}(x)+\tan ^{-1}(x+ \)
1) \( =\tan ^{-1}(3 x) \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D. 4
Subject: Physics
A cylinder contains helium at 2.5
atmosphere pressure. Another identical cylinder contains argon at 1.5
atmosphere pressure at the same temperature. If both the gases are filled
in any one of the cylinders, the pressure of the mixture will be:
A. 1.5 atm
B. 2.5 atm
\( c \cdot 4 a t m \)
D. none of these
Subject: Physics
Two bodies of mass \( 4 \mathrm{kg} \) and \( 5 \mathrm{kg} \) are moving along east and north directions with velocities \( 5 m / s \) and \( 3 m / s \) respectively. Magnitude of the velocity of centre of mass of the system is:
\( ^{\mathrm{A}} \cdot \frac{25}{9} m / s \)
в. \( \frac{9}{25} m / s \)
c. \( \frac{41}{9} m / s \)
D. \( \frac{16}{9} m / s \)
Subject: Maths
A cricketer hits 120 runs in 150 balls
during a test match. \( 20 \% \) of the runs came in \( 6 s, 30 \% \) in \( 4 s, 25 \% \) in \( 2 s \) and
the rest in singles. How many runs did he score in singles?
A . 16
B. 4
c. 20
D. 30
Subject: Physics
The centre of gravity of a rod (of length
L), whose linear mass density varies as
the square of the distance from one end
is at:
A \( \cdot \frac{3 L}{5} \)
В \( \cdot \frac{2 L}{5} \)
c. \( \frac{L}{3} \)
D. \( \frac{3 L}{4} \)
Subject: Maths
\( f(x)=\left|\begin{array}{ccc}2 x & x^{2} & x^{3} \\ x^{2}+2 x & 1 & 3 x+1 \\ 2 x & 1-3 x^{2} & 5 x\end{array}\right| \)
then find \( \boldsymbol{f}^{\prime}(\mathbf{1}) \)
Subject: Physics
If the distance between the plates of a
parallel plate capacitor of capacity 10 \( \mu \) \( F \) is doubled. then new capacity will be :
\( \mathbf{A} \cdot 5 \mu F \)
в. \( 20 \mu F \)
c. \( 10 \mu F \)
\( \mathbf{D} \cdot 15 \mu F \)
Subject: Maths
If \( n(A)=m \) and \( n(B)=n ; \) then
\( \boldsymbol{n}(\boldsymbol{A} \times \boldsymbol{B})=\boldsymbol{m} \boldsymbol{n} \)
What is the value of \( n(A \times B)=m n \). if
\( \boldsymbol{m}=\boldsymbol{6} \) and \( \boldsymbol{n}=\boldsymbol{8} \)
Subject: Physics
The binding energies per nucleon for deuteron and helium are \( 1.1 \mathrm{MeV} \) and 7
MeV respectively. Calculate the energy released when two deuterons fuse to
form a helium nucleus.
A. 23.6 MeV
B. 25.8 MeV
c. \( 19.2 \mathrm{MeV} \)
D. 28.8 MeV
Subject: Maths
Let \( \mathbf{S}_{\mathbf{n}}=\sum_{\mathbf{k}=1}^{\mathbf{n}} \frac{\mathbf{n}}{\mathbf{n}^{2}+\mathbf{k} \mathbf{n}+\mathbf{k}^{2}} \) and \( \mathbf{T}_{\mathbf{n}}= \)
\( \sum_{\mathbf{k}=0}^{\mathbf{n}-1} \frac{\mathbf{n}}{\mathbf{n}^{2}+\mathbf{k} \mathbf{n}+\mathbf{k}^{2}} \) for \( \mathbf{n}=\mathbf{1}, \mathbf{2}, \mathbf{3}, \dots \)
Then, This question has multiple correct options
A \( \cdot \mathrm{S}_{\mathrm{n}}<\frac{\pi}{3 \sqrt{3}} \)
В \( \cdot \mathrm{s}_{\mathrm{n}}>\frac{\pi}{3 \sqrt{3}} \)
\( \mathrm{c} \cdot \mathrm{T}_{\mathrm{n}}<\frac{\pi}{3 \sqrt{3}} \)
D. \( \mathrm{T}_{\mathrm{n}}>\frac{\pi}{3 \sqrt{3}} \)
Subject: Physics
Electric current is due to flow of charge
carriers in the conductors. Which of the
following is/are correct?
This question has multiple correct options
A. The drift speed of charge carriers is a very small fraction of the mean thermal agitation speed of the same charge carriers
B. The number of charge carriers per unit volume is always the same as the number of atoms of the conductor per unit volume
C. The drift velocity is proportional to the electric field applied ordinarily
D. In an intrinsic semiconductor, the charge carriers are either electrons only or holes only; both of them may not participate in conduction
Subject: Chemistry
In a very ideal imaginary condition, a sample of ice was taken, and its osmotic pressure was found to be 0.274 \( \operatorname{atm} \) at \( 300 \mathrm{K} \) (density \( =1 \mathrm{g} / \mathrm{mL} \) ). Thus, number of water units attached to one
water unit is
\( A \cdot 4 \)
B. 3
\( c \cdot 6 \)
\( D .5 \)
Subject: Physics
A bucket tied to a string is lowered at a constant acceleration of \( g / 4 . \) If the mass of the bucket is \( M \) and is lowered
by a distance \( d \), the work done by the string will be (assume the string to be massless
A. \( 1 / 4 M g d \)
в. \( -4 / 3 \) М \( g d \)
c. \( -3 / 4 M g d \)
D. \( 4 / 3 M g d \)
Subject: Physics
If Planck's constant \( (h), \) surface tension
\( (s) \) and moment of inertia \( (I) \) are taken as fundamental quantities, then dimensions of linear momentum \( (p) \) will be given as:
\( \mathbf{A} \cdot h s^{2} I^{1 / 2} \)
B . \( h^{1 / 2} s^{1 / 2} I \)
c. \( h^{0} s^{1 / 2} I^{1 / 2} \)
D. None of these
Subject: Physics
Three identical wires are bent into
semi-circular arcs each of radius \( \boldsymbol{R} \)
These arcs are connected with each
other to form a closed mesh such that
one of them lies in x-y plane, one in \( y-z \) plane and the other in z-x plane as
shown in figure. In the region of space, a uniform \( \vec{B}=B_{0}(\hat{i}+\hat{j}) \) exists, whose magnitude increases at a constant rate
\( \boldsymbol{d} \boldsymbol{B} / \boldsymbol{d} \boldsymbol{t}=\boldsymbol{\alpha} . \) Calculate the magnitude of
emf induced in the mesh and mark
direction of flow of induced current in
the mesh.
Subject: Maths
If \( \boldsymbol{A}=\left(\boldsymbol{a}_{\boldsymbol{i} j}\right)_{\mathbf{3} \times \mathbf{3}} \) is a skew symmetric
matrix, then
This question has multiple correct options
\( \mathbf{A} \cdot a_{i i}=0 \forall i \)
B. \( A+A^{T} \) is a null matrix
c. \( |A|=0 \)
D. \( A \) is not invertible
Subject: Chemistry
\( \boldsymbol{C H}_{2}=\boldsymbol{C H}-\boldsymbol{C} \equiv \boldsymbol{N} \)
Hybridisation state of \( N \) atom is:
\( A \cdot s p^{3} \)
B . \( s p \)
\( c \cdot s p^{2} \)
D. none of the above
Subject: Chemistry
Choose the correct statement among
the following.
This question has multiple correct options
A. Radial distribution function
\( \mathbf{B} \cdot\left(\Psi^{24 \pi^{2}} d r\right) \)
C \( . \Psi(r) \Psi(\theta) \Psi(\Phi))=\Psi(x / y / z) \) is independent of \( \theta \) and \( \phi \)
D. '2p'orbital with quantum numbers.n=2,|=1,m=0,also shows angular dependence
Subject: Chemistry
Which of the following statement is
false?
A. Elements of \( n s^{2} n p^{6} \) electronic configuration lies in \( 1^{s t} \) to \( 6^{t h} \) period
B. Typical elements lies in \( 3^{r d} \) period
C. The seventh period will accommodate thirty two elements
D. Boron and silicon are diagonally related
Subject: Physics
The displacement of a particle is
described by \( \boldsymbol{x}=\boldsymbol{t}+\mathbf{2} \boldsymbol{t}^{2}+\mathbf{3} \boldsymbol{t}^{3}-\boldsymbol{4} \boldsymbol{t}^{4} \)
The acceleration at \( t=3 \sec \) is
A . +378 units
B. +374 units
c. -378 units
D. -374 units
Subject: Maths
\( \operatorname{Given} f(x)=\frac{[\{|x|\}] e^{x^{2}}\{[|x+\{x\}|]\}}{\left(e^{1 / x^{2}}-1\right) \operatorname{sgn}(\sin x)} \)
for \( \boldsymbol{x} \neq \mathbf{0} \)
\( =0, \) for \( x=0 \)
Where \( \{x\} \) is the fractional part
function; \( [x] \) is the step up function and
\( \operatorname{sgn}(x) \) is the signum function of \( x \) then,
\( \boldsymbol{f}(\boldsymbol{x}) \)
A. is continuous at \( x=0 \)
B. is discontinuous at \( x=1 \)
C. has a removable discontinuity at \( x=0 \)
D. has an irremovable discontinuity at \( x=0 \)
Subject: Maths
A point on the line \( \frac{\boldsymbol{x}-\mathbf{1}}{\mathbf{1}}=\frac{\boldsymbol{y}-\mathbf{2}}{\mathbf{2}}= \)
\( \frac{z+1}{3} \) at a distance \( \sqrt{6} \) from the origin
is
This question has multiple correct options
\( \mathbf{A} \cdot\left(\frac{-5}{7}, \frac{-10}{7}, \frac{13}{7}\right) \)
в. (1,2,-1)
\( ^{\mathbf{C}} \cdot\left(\frac{5}{7}, \frac{10}{7}, \frac{-13}{7}\right) \)
D. (-1,-2,1)
Subject: Physics
A spherical conducting shell of inner
radius \( r_{1} \) and outer radius \( r_{2} \) has a
charge \( Q \)
(a) A charge q is placed at the centre of the shell. What is the surface charge
density on the inner and outer surfaces of the shell?
(b) Is the electric field inside a cavity (with no charge) zero, even if the shell is not spherical, but has any irregular shape? Explain.
Subject: Chemistry
Assertion
Li \( F \) has more covalent character than
\( C s F \)
Reason
Lattice energy of \( C s F \) is less than that
of \( \boldsymbol{L} \boldsymbol{i} \boldsymbol{F} \)
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
Half litre each of three samples of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) labelled 10 volume, 15 volume and 20
volume are mixed and then diluted with
equal volume of water. The relative strength of resultant \( H_{2} O_{2} \) solution is:
A . 2.5
B. 5.0
c. 7.5
D. 10
Subject: Physics
Two man 'A' and 'B' are standing on opposite edge of a \( 6 \mathrm{m} \) long platform which is further kept on a smooth floor.
They starts moving towards each other and finally meet at the midpoint of platform. Find the displacement of platform. Find the displacement of platform if mass of \( A, B \) and platform \( \operatorname{are} 40 \mathrm{kg}, 60 \mathrm{kg} \) and \( 50 \mathrm{kg} \) respectively.
Subject: Physics
The wave number of first line of Balmer
series of hydrogen atom is \( 15200 \mathrm{cm}^{-1} \) What is the wave number of first line of
Balmer series of \( L i^{2+} \) ion.
A. \( 15200 \mathrm{cm}^{-1} \)
В. \( 136800 m^{-1} \)
c. \( 76000 \mathrm{cm}^{-1} \)
D. \( 13680 \mathrm{cm}^{-1} \)
Subject: Physics
Suppose India had a target of producing by \( 2020 \mathrm{AD}, 200,000 \mathrm{MW} \) of electric
power, ten percent of which was to be obtained from nuclear power plants. Suppose we are given that, on an average, the efficiency of utilization (i.e. conversion to electric energy) of thermal energy produced in a reactor was \( 25 \% . \) How much amount of
fissionable uranium would our country need per year by \( 2020 ? \) Take the
heat energy per fission of \( ^{235} U \) to be
about \( 200 \mathrm{MeV} \)
Subject: Maths
Two numbers are selected at random
(without replacement) from the first six positive integers. Let X denote the larger of the two numbers obtained. Find \( E(X) \)
A \( \cdot \frac{14}{3} \)
B. \( \frac{13}{3} \)
\( c \cdot \frac{12}{3} \)
D. \( \frac{11}{3} \)
Subject: Physics
The magnetic flux in a coil of 100 turns increases by \( 12 \times 10^{3} \) Maxwell in 0.2
second due to the motion of a magnet. The emf induced in the coil will be
\( A \cdot 6 v \)
B. \( 0.6 v \)
c. \( 0.06 v \)
D. 60 V
Subject: Maths
In the figure given, lines \( X Y \) and \( M N \)
intersect at \( 0 . \) If \( \angle P O Y=90^{\circ} \) and \( a: b= \)
\( 2: 3, \) then \( \angle X O N \) is equal to
A . \( 126^{\circ} \)
B . \( 30^{\circ} \)
\( c \cdot 90^{\circ} \)
D. \( 180^{\circ} \)
Subject: Maths
In the figure, \( A B=C D \) and \( \angle A= \)
\( \mathbf{9 0}^{\circ}=\angle D . \) Then
A. \( \Delta A B C \cong \Delta D B C \) by SAS postulate
B. \( \Delta A B C \cong \Delta D C B \) by RHS postulate
c. \( \Delta A B C \cong \Delta D B C \) by AAS postulate
D. \( \Delta A B C \cong \Delta D C B \) by SSS postulate
Subject: Physics
In a series \( L, R, C \) circuit which is
connected to ac source, when resonance
is obtained then net impedance Z will
be:
A \( . Z=R \)
B. \( \quad Z=\omega L-\frac{1}{\omega C} \)
\( \mathbf{c} \cdot Z=\omega L \)
D. \( z=\frac{1}{w C} \)
Subject: Maths
Evaluate the given integral. \( \int \sqrt{\frac{x}{1-x}} d x \)
\( A \cdot \sin ^{-1} \sqrt{x}+C \)
\( \mathbf{B} \cdot \sin ^{-1}[\sqrt{x}-\sqrt{x(1-x)}]+C \)
\( \mathbf{c} \cdot \sin ^{-1}[\sqrt{x(1-x)}]+C \)
D. \( \sin ^{-1} \sqrt{x}-\sqrt{x(1-x)}+C \)
Subject: Physics
A ray of light is incident at the glass-
water interface at an angle i. It merges
finally parallel to the surface of water.
Then, the value of \( \mu_{g} \) would be :
A \( \cdot(4 / 3) \sin i \)
B. \( 1 / \)sini
c. \( 4 / 3 \)
\( D \)
Subject: Chemistry
A binary liquid solution is prepared by mixing n-heptane and ethanol. Which one of the following statement is correct regarding the behavior of the solution?
A. The solution formed is an ideal solution
B. The solution is non-ideal, showing +ve deviation from Raoults Law
c. The solution is non-ideal, showing ve deviation from Raoults Law
D. n-heptane shows +ve deviation while ethanol shows ve deviation from Raoults Law
Subject: Chemistry
Which of the following solutions is more concentrated than the others?
A. \( 5.3 \mathrm{gm} \) of \( \mathrm{Na}_{2} \mathrm{CO}_{3} \) in \( 500 \mathrm{ml} \) solution
B. 5 gm of \( N a O H \) in 100 ml solution
c. 3.65 gm of \( H C l \) in 750 ml solution
D. 4.9 gm of \( H_{2} S O_{4} \) in \( 1000 \mathrm{ml} \) solution
Subject: Maths
Two events \( A \) and \( B \) are such that
\( \boldsymbol{P}(\boldsymbol{A})=\mathbf{0 . 2}, \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 3} \) and \( \boldsymbol{P}(\boldsymbol{A} \)
\( \boldsymbol{B})=\mathbf{0 . 5 . F i n d} \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B}) \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. 0.2
\( c .0 .3 \)
D. 0.5
Subject: Chemistry
Give the products formed on reductive
ozonolysis with LAH and oxidative
ozonolysis with \( \boldsymbol{H}_{2} \boldsymbol{O}_{2}, \) from the
compounds.
A. Propan-1,3-diol and propan-1,3-dioic acid
B. Propan-1,2-diol and propan-1,3-dioic acid
C. Propan-1,3-diol and propan-1,2-dioic acid
D. Propan-1,2-diol and propan-1,2-dioic acid
Subject: Physics
A particle undergoes SHM. When its displacement is \( 8 \mathrm{cm}, \) it has speed 3 \( \mathrm{m} / \mathrm{s} \) and a speed \( 4 \mathrm{m} / \mathrm{s} \) at displacement of \( 6 \mathrm{cm} . \) Find time period of oscillation.
A . \( 4 \pi \)
в. \( 6 \pi \)
c. \( 7 \pi \)
D. \( 8 \pi \)
Subject: Chemistry
Assertion
Lower parts of the ship or bridge is
coated with tar.
Reason
It is to increase rusting.
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
In solving LP problem : minimize \( \boldsymbol{z}= \) \( 6 x+10 y, \) subject to \( x \geq 6, y \geq 2,2 x+ \)
\( \boldsymbol{y} \geq \mathbf{1 0}, \boldsymbol{x} \geq \mathbf{0}, \boldsymbol{y} \geq \mathbf{0}, \) which constraints
are reduntant?
Subject: Maths
The determinant \( \Delta= \) \( \left|\begin{array}{ccc}a^{2}(1+x) & a b & a c \\ a b & b^{2}(1+x) & b c \\ a c & b c & c^{2}(1+x)\end{array}\right| \) is
divisible by
This question has multiple correct options
A. \( (x+3) \)
B \( \cdot(1+x)^{2} \)
\( c \cdot x^{2} \)
D. \( \left(x^{2}+1\right) \)
Subject: Chemistry
From the given reactions, which is a
redox reaction?
A \( \cdot C u(s)+H_{2} O(g) \rightarrow C u(s)+H_{2} O(l) \)
в. \( 2 C u(s)+O_{2}(g) \rightarrow 2 C u O(s) \)
c. \( C(s)+2 H_{2} \rightarrow C H_{4}(g) \)
D. \( 4 A l(s)+3 O_{2}(g) \rightarrow 2 A l_{2} O_{3}(s) \)
Subject: Maths
\( D L \) and \( B M \) are the height on sides
\( A B \) and \( A D \) respectively of parallelogram \( A B C D \) figure. If the area
of the parallelogram is \( 1470 \mathrm{cm}^{2} \) \( A B=35 \mathrm{cm} \) and \( A D=49 \mathrm{cm}, \) find the
ength of \( B M \) and \( D L \)
Subject: Biology
Many persons like to use asthma as an excuse for not being able to do well in sports. Try telling them about Down
Fraser, who was the first women to
break 60 sec in 100 m freestyle swimming. The first women to win four Olympic gold medals and the first swimmer to win the same event in three
consecutive Olympics was asthmatic. On the basis of the above passage,
answer the following question.
i) Describe her achievements in the
field of swimming.
Subject: Physics
A body is dropped from a height of \( 2 \mathrm{m} \) It penetrates into the sand on the
ground through a distance of \( 10 \mathrm{cm} \) before coming to rest. What is the retardation of the body in sand?
B. \( 196 \mathrm{ms}^{-2} \)
c. \( -196 \mathrm{ms}^{-2} \)
D. \( 9.8 \mathrm{ms}^{-2} \)
Subject: Chemistry
A cylinder of gas assumed to contain 11.2 \( k g \) of butane \( C_{4} H_{10} \). If a normal
family needs \( 20000 k J \) of energy per day. The cylinder will last: (Given that \( \Delta H \) for combustion of butane is -2658
kJ)
A . 20 days
B. 25 days
c. 26 days
D. 24 days
Subject: Physics
One half of a convex lens of focal length \( 10 \mathrm{cm} \) is covered with a black paper.can such a lens produce an image of a complete object placed at a distance of \( 30 \mathrm{cm} \) from the lens? Draw a ray
diagram to justify your answer. A \( 4 \mathrm{cm} \) tall object is placed perpendicular to its principal axis of a convex lens of focal length \( 20 \mathrm{cm} . \) The distance of the object from the lens is \( 15 \mathrm{cm} \). Find the nature, position and the size of the
image.
Subject: Physics
A particle of rest mass \( m_{0} \) is moving
with speed \( c / 2 . \) What is its momentum?
A \( \cdot \frac{m_{0}}{2} \)
в. \( \frac{1}{\sqrt{3}} m_{0} c \)
c. \( \frac{2}{\sqrt{3}} m_{0} c \)
D. none of the above