AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A ball of mass \( 0.20 \mathrm{kg} \) falls freely from a certain height and rebounds elastically
with a speed of \( 40 \mathrm{ms}^{-1} . \) The change in momentum of the ball is:
A \( \cdot 4 k g m s^{-1} \)
B. \( 8 \mathrm{kg} \mathrm{ms}^{-1} \)
c. \( 16 k g m s^{-1} \)
D. \( 40 \mathrm{kg} \mathrm{ms}^{-1} \)
Subject: Maths
If \( 2 x+y=23 \) and \( 4 x-y=19 ; \) find
the values of \( x-3 y \) and \( 5 y-2 x \)
A. The values of \( x-3 y \) and \( 5 y-2 x \) are -20 and 31 respectively
B. The values of \( x-3 y \) and \( 5 y-2 x \) are 0 and 3 respectively
c. The values of \( x-3 y \) and \( 5 y-2 x \) are 14 and -9
respectively
D. The values of \( x-3 y \) and \( 5 y-2 x \) are 5 and 23 respectively
Subject: Maths
If
A, B are two independent events, \( P(A)=\frac{3}{4} \) and \( P(B)=\frac{5}{8}, \) then
\( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B})= \)
A \( \cdot \frac{3}{32} \)
в. \( \frac{29}{32} \)
c. \( \frac{15}{32} \)
D. \( \frac{5}{32} \)
Subject: Biology
Assertion
Tidal volume is the volume of air
inspired or expired with the normal breath.
Reason
Adult person contains 500 mL expired or inspired volumes of air with each
normal breath.
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
1 kg of a sample of water contains 222
\( \mathrm{mg} \) of \( \mathrm{CaCl}_{2} \) and \( 219 \mathrm{mg} \) of
\( M g\left(H C O_{3}\right)_{2} . \) Its permanent hardness and temporary hardness in ppm are respectively:
A .200,200
B . 200,150
c. 200,300
D. 150,220
Subject: Maths
ff \( A=\left[\begin{array}{ccc}-1 & 0 & 0 \\ 0 & x & 0 \\ 0 & 0 & m\end{array}\right] \) is a scalar matrix
then \( \boldsymbol{x}+\boldsymbol{m}= \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. -
\( c \cdot-2 \)
D. -3
Subject: Maths
In a \( \Delta A B C \) the sides b and \( c \) are given.
If there is an error \( \Delta A \) in measuring
angle \( A, \) then the error \( \Delta a \) in side a is
given by
\( ^{\text {A }} \cdot \frac{S}{2 a} \Delta A \)
в. \( \frac{2 S}{a} \Delta A \)
\( c \cdot b c \sin A \Delta A \)
D. none of these
Subject: Physics
An ultrasonic wave is sent from a ship towards the bottom of the sea. It is
found that the time interval between the
sending and receiving of the wave is 1.6
s. What is the depth of the sea, if the velocity of sound in the seawater is \( 1400 \mathrm{m} / \mathrm{s} ? \)
A. \( 1120 \mathrm{m} \)
B. 560 \( m \)
\( c \cdot 1400 m \)
D. 112 m
Subject: Physics
Radioactive material'A' has decay
constant \( ^{\prime} 8 \lambda^{\prime} \) and material 'B' has decay
constant \( ^{\prime} \lambda^{\prime} . \) Initially they have same
number of nuclei. After what time, the
ratio of number of nuclei of material 'B'
to that of 'A' will be \( \frac{1}{e} ? \)
A \( \cdot \frac{1}{\lambda} \)
в. \( \frac{1}{7 \lambda} \)
c. \( \frac{1}{8 \lambda} \)
D. \( \frac{1}{9 \lambda} \)
Subject: Maths
The principal value of
\( \cos ^{-1}\left[\frac{1}{\sqrt{2}}\left(\cos \left(\frac{9 \pi}{10}\right)-\sin \left(\frac{9 \pi}{10}\right)\right)\right] \) is
\( \mathbf{A} \cdot \frac{3 \pi}{20} \)
B. \( \frac{7 \pi}{200} \)
\( \mathbf{C} \cdot \frac{7 \pi}{10} \)
D. none of these
Subject: Physics
A high jumper can jump \( 2.0 \mathrm{m} \) on earth,
With the same effort how high will he be
able to jump on a planet whose density is one-third and radius one-fourth those
of the earth?
\( A \cdot 4 m \)
B. 8 m
\( c \cdot 18 m \)
D. 24 m
Subject: Biology
toppr
Q Type your question
This chart shows the relative
abundance of different groups of
echinoderms throughout geologic time.
The width of the band indicates the
number of species for each group.
Identify the time periods showed a
boom in all echinoderm groups?
A. Ordovician
B. Silurian
C. Mississippian
D. Permian
E . Jurassic
Subject: Physics
The base of a cylindrical vessel
measures \( 300 \mathrm{cm}^{2} \), water is poured into
it up to a depth of \( 6 \mathrm{cm} \). Calculate the pressure of water on the base of the
vessel. \( \left(\mathrm{g}=10 \mathrm{m} / \mathrm{s}^{2} ; \text { density of water }=\right. \)
\( 1000 k g / m^{3} \)
Subject: Physics
A river \( 10 m \) deep is flowing at \( 5 m / s \)
The shearing stress between horizontal layers of the river is \( (\boldsymbol{\eta}= \)
\( 10^{-3} \) SI units
\( \mathbf{A} \cdot 10^{-3} N / m^{2} \)
B. \( 0.8 \times 10^{-3} N / m^{2} \)
C. \( 0.5 \times 10^{-3} N / m^{2} \)
D. \( 1 \mathrm{N} / \mathrm{m}^{2} \)
Subject: Physics
Assertion: For the flow to be
streamlined, value of critical velocity should be as low as possible Reason: Once the actual velocity of flow of liquid becomes greater than the critical velocity, the flow becomes turbulent.
A. Both assertion and reason are true and reason is correct explanation of assertion
B. Both assertion and reason are true but reason is not the correct explanation of assertion.
c. Assertion is true but reason is false.
D. Both assertion and reason are false.
Subject: Physics
toppr
-०६
Q Type your question
the object's velocity as a function of
time. The data points are shown on the
graph below, along with a best-fit line that has been inserted to extrapolate data for the entirety of the object's
motion.

In using the graph to analyze the object's motion, several different
quantities about the best fit line can be
calculated.

Which quantities would be equal to the object's initial velocity, and to the object's displacement, during its slowing motion?
A. Initial Velocity: Slope
Displacement: Area under line
B. Initial Velocity: x-intercept
Displacement: Slope
c. Initial Velocity: y-intercept
Displacement: Area under line
D. Initial Velocity: Slope
Displacement: y-intercept
Subject: Maths
Solve the following problem graphically:
Minimise and Maximise
\( \boldsymbol{z}=\mathbf{3} \boldsymbol{x}+\mathbf{9} \boldsymbol{y} \)
Subject to the constraints:
\( \boldsymbol{x}+\mathbf{3} \boldsymbol{y} \leq \mathbf{6 0} \)
\( \boldsymbol{x}+\boldsymbol{y} \geq \mathbf{1 0} \)
\( \boldsymbol{x} \leq \boldsymbol{y} \)
\( \boldsymbol{x} \geq \mathbf{0}, \boldsymbol{y} \geq \mathbf{0} \)
Subject: Chemistry
The oxide of metal \( R \) can be reduced by
the metal \( P \) and metal \( R \) can reduce the
oxide of metal \( Q . \) Then the decreasing
order of the reactivity of metal \( P, Q \) and
\( R \) with oxygen is:
A. \( P>Q>R \)
в. \( P>R>Q \)
c. \( R>P>Q \)
D. \( Q>P>R \)
Subject: Chemistry
Consider the following statements and arrange in the order of true/false as
given in the codes:
\( S_{1}: \ln A B_{2} L_{2} \) type, the \( B A B \) bond angle will always be greater than normal tetrahedral \( (L \) is a lone pair)
\( S_{2}: \) Maleic acid has higher \( K_{a_{1}} \) value than fumaric acid due to
intramolecular hydrogen bonding.
\( S_{3}: \ln C l O_{3}^{-}, N H_{3} \) and \( X e O_{3}, \) the
hybridisation and the number of lone pair(s) on central atoms are same.
\( \mathbf{A} \cdot T T T \)
в. \( F T F \)
c. \( F T T \)
D. \( F F T \)
Subject: Chemistry
It necessary for electrode b to be
continuously replaced.
Reason
At the positive anode, oxygen gas is
formed and at high temperature of the
electrolysis cell it burns and oxidises away the carbon electrodes to form
toxic carbon monoxide or carbon
dioxide.
[Note : Sketch shown is of an electrolytic
cell used in the extraction of
aluminium]
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
Evaluate: \( \lim _{x \rightarrow 1} \frac{x^{\frac{-2}{3}}-1}{x^{\frac{-3}{4}}-1} \)
A \( \cdot \frac{5}{9} \)
B. \( \frac{9}{5} \)
\( c \cdot \frac{8}{9} \)
\( D \)
Subject: Maths
Two events \( A \) and \( B \) are such that
\( P(A)=\frac{1}{4}, P(B)=\frac{1}{2} \) and \( P(B \mid A)=\frac{1}{2} \)
Consider the following statements
\( (I) P(\bar{A} \mid \bar{B})=\frac{3}{4} \)
\( (I I) A \) and \( B \) are mutually exclusive
\( (I I I) P(\bar{A} \mid \bar{B})+P(A \mid \bar{B})=1 \)
Then
A. Only I is correct
B. Only I and II are correct
c. only \( I \) and \( I I I \) are correct
D. only II and III are correct
Subject: Chemistry
What is the electronic configuration of elements of \( I I I \) rd group
A \( \cdot 1 s^{2}, 2 s^{2} 2 p s^{3} \)
В \( \cdot 1 s^{2}, 2 s^{2} 2 p^{6}, 3 s^{2} 3 p^{1} \)
C \( \cdot 1 s^{2}, 2 s^{2} 2 p^{6} \)
D. \( 1 s^{2}, 2 s^{2} 2 p^{6}, 3 s^{1} \)
Subject: Physics
Sound waves are passing through two routes-one in straight path and the other along a semicircular path of
radius \( r \) and are again combined into one pipe and superposed as shown in
the figure. If the velocity of sound waves in the pipe is \( v, \) then frequencies of
resultant waves of maximum
amplitude will be integral multiples of
\( A \)
в. \( \frac{v}{r(\pi-1)} \)
c. \( \frac{2 v}{r(\pi-1)} \)
D. \( \frac{v}{r(\pi+1)} \)
Subject: Physics
If the kinetic energy of the moving
particle is \( \boldsymbol{E} \), then the de Broglie wavelength is
A \( \cdot \lambda=\frac{h}{\sqrt{2 m E}} \)
B. \( \lambda=\frac{\sqrt{2 m E}}{h} \)
c. \( \lambda=h \sqrt{2 m E} \)
D. \( \lambda=\frac{h}{E \sqrt{2 m}} \)
Subject: Maths
The figure formed by four points \( 1+ \)
\( 0 i ;-1+0 i, 3+4 i \) and \( \frac{25}{-3-4 i} \) on the argand plane is
A. parallelogram but not a rectangle
B. a trapesium which is not equilateral
c. cyclic quadrilateral
D. none of these
Subject: Chemistry
Identify \( \mathrm{W}, \mathrm{X}, \mathrm{Y}, \) and \( \mathrm{Z} \) respectively in the given reactions. \( \boldsymbol{C a C O}_{3} \stackrel{\triangle}{\rightarrow} \boldsymbol{W}+\boldsymbol{X} \)
\( \boldsymbol{W}+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \boldsymbol{Y} \)
\( \boldsymbol{Y}+\boldsymbol{Z} \rightarrow \boldsymbol{N} \boldsymbol{a} \boldsymbol{O} \boldsymbol{H}+\boldsymbol{C a C O}_{3} \)
A. \( C a O, C O_{2}, C a C O_{3}, N a_{2} C O_{3} \)
в. \( C O_{2}, \) Са\( (O H)_{2}, C a(H C O)_{3}, N a H C O_{3} \)
c. \( C a O, C O_{2}, C a(O H)_{2}, N a_{2} C O_{3} \)
D. \( C O_{2}, C a O, H_{2} C O_{3}, N a_{2} C O_{3} \)
Subject: Chemistry
The d-electron configurations of \( \boldsymbol{C r}^{2+}, \boldsymbol{M n}^{2+}, \boldsymbol{F} \boldsymbol{e}^{2+} \) and \( \boldsymbol{C o}^{2+} \) are
\( d^{4}, d^{5}, d^{6} \) and \( d^{7} \) respectively. Which one
of the following will exhibit minimum paramagnetic behaviour? (Atomic numbers of \( \mathrm{Cr}=\mathbf{2 4}, \boldsymbol{M n}= \)
\( \mathbf{2 5}, \mathbf{F e}=\mathbf{2 6}, \mathbf{C o}=\mathbf{2 7}) \)
\( \mathbf{A} \cdot\left[M n\left(H_{2} O\right)_{6}\right]^{2+} \)
в. \( \left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2} \)
c. \( \left[\operatorname{Co}\left(H_{2} O\right)_{6}\right]^{2+} \)
D \( \cdot\left[C r\left(H_{2} O\right)_{6}\right]^{2} \)
Subject: Chemistry
The increase order for the value of \( e / m \) (charge to mass ratio) for electron \( (e) \) proton \( (p) ; \) neutron \( (n) \) and alpha particle \( (\alpha) \) is:
A \( \cdot e<p<n<\alpha \)
в. \( n<p<e<\alpha \)
c. \( n<p<\alpha<e \)
D. \( n<\alpha<p<e \)
Subject: Physics
Displacement of a particle of mass \( 2 k g \) moving in a straight line varies with
time at \( s=\left(2 t^{3}+2\right) m . \) Impulse of the
force acting on the particle over a time interval between \( t=0 \) and \( t=1 s \) in
A. \( 10 N-s \)
В. \( 12 \mathrm{N}-\mathrm{s} \)
c. \( 8 N-s \)
D. \( 6 N-s \)
Subject: Physics
Brown, Red and Orange coloured bands
on a Carbon resistor are followed by silver band. The value of resistor is
\( \mathbf{A} \cdot 320 \Omega \pm 5 \% \)
B . \( 12 k \Omega \pm 5 \% \)
c. \( 320 \Omega \pm 10 \% \)
D. \( 12 k \Omega \pm 10 \% \)
Subject: Physics
Assertion
A current continues to flow in
superconducting coil even after switch
is off.
Reason
Superconducting coils show Meissner effect
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
For the following reaction, select the
statement that best describes the
change.
\( \boldsymbol{R} \boldsymbol{C H}_{2} \boldsymbol{O H}+ \)
\( \boldsymbol{P C C} \quad\left[\boldsymbol{C _ { 5 }} \boldsymbol{H}_{5} \boldsymbol{N} \boldsymbol{H}^{+} \boldsymbol{C l} \boldsymbol{C r} \boldsymbol{O}_{3}^{-}\right] \longrightarrow \)
A. The alcohol is oxidized to an acid, and the \( C r(V I) \) is reduced
B. The alcohol is oxidized to an aldehyde, and the \( C r(V I) \) is reduced
c. The alcohol is reduced to an aldehyde, and the \( \operatorname{Cr}(I I I) \) is oxidized
D. The alcohol is oxidized to a keton, and the \( C r(V I) \) is reduced
Subject: Physics
Two point charges each of \( 1 C \)
separated by 1 m distance experience a
force of \( 5.6 \times 10^{9} N \) in vacuum. How
much force is experienced by them if they are immersed in water., keeping the distance of separation between them same?
\( \boldsymbol{K}=\mathbf{8 0} \) for water.
Subject: Physics
A tiny mirror M is fixed on a piece of
cardboard placed on a table. The cardboard is illuminated by light from a bulb. The position of eye with respect to
position of bulb is shown in Fig. as \( A, B \)
\( \mathrm{C} \) and \( \mathrm{D} . \) In which of the shown figure, the light will be visible to eye?
This question has multiple correct options
\( A \cdot A \)
B. B
\( c \cdot c \)
\( D \)
Subject: Physics
Which of the following statements contains a reference to displacement?
I. The town is a five mile drive along the
winding country road.
II. The town sits at an altitude of \( 940 \mathrm{m} \)
III. The town is ten miles north, as the
crow flies.
A. I only
B. III only
c. I and III only
D. II and III only
E . I, II, and III
Subject: Chemistry
\( P C l_{2} \rightleftharpoons P C l_{3}+C l_{2} \) in the reversible
reaction the moles of \( \boldsymbol{P C l}_{2}, \boldsymbol{P C l}_{3} \) and
\( C l_{2} \) are \( a, b \) and \( c \) respectively and total
pressure is \( \boldsymbol{P} \) then value of \( \boldsymbol{K}_{\boldsymbol{p}} \)
is
A \( \cdot \frac{b c}{a} R T \)
в. \( \frac{b}{(a+b+c)} P \)
c. \( \frac{b c P}{a(a+b+c)} \)
D. \( \frac{c}{(a+b+c)} P \)
Subject: Chemistry
Dipole moment of \( C O \) is very small
\( (0.1 D) \) (in-spite of the larger difference in electronegativity between \( C \text { and } O) \) and negative end of the dipole lies near
the less electronegative \( C \) -atom. It is
due to:
A. occupation of anti-bonding molecular orbitals
B. occupation of empty \( d \) - orbitals
c. occupation of lone-pairs
D. occupation of the lone pairs as well as empty \( d- \) orbitals
Subject: Chemistry
The standard heat of combustion of
solid boron is equal to:
\( A \cdot \Delta H_{f}^{\circ}\left(B_{2} O_{3}\right) \)
B \( \cdot 1 / 2 \Delta H_{f}^{\circ}\left(B_{2} O_{3}\right) \)
\( \mathrm{c} \cdot 2 \Delta H_{f}^{\circ}\left(B_{2} O_{3}\right) \)
D. \( 6 / 2 \Delta H_{f}^{\circ}\left(B_{2} O_{3}\right) \)
Subject: Maths
If the \( A . M \) is twice the \( G . M . \) of the
numbers \( a \) and \( b \), then \( a: b \) will be
This question has multiple correct options
A \( \cdot \frac{2-\sqrt{3}}{2+\sqrt{3}} \)
B. \( \frac{2+\sqrt{3}}{2-\sqrt{3}} \)
c. \( \frac{\sqrt{3}-2}{\sqrt{3}+2} \)
D. \( \frac{\sqrt{3}+2}{\sqrt{3}-2} \)
Subject: Maths
\( \int \sin x \log (\sec x+\tan x) d x=f(x)+ \)
\( \boldsymbol{x}+\boldsymbol{c} \) then \( \boldsymbol{f}(\boldsymbol{x})= \)
A \( \cdot \cos x \log (\sec x+\tan x)+c \)
B. \( \sin x \log (\sec x+\tan x)+c \)
c. \( -\cos x \log \sec x+\tan x)+c \)
D. - \( \cos x \log \sec x+c \)
Subject: Chemistry
A 0.001 molal solution of a complex
represented as \( P t\left(N H_{3}\right)_{4} C l_{4} \) in water had freezing point depression of
\( \mathbf{0 . 0 0 5 3 ^ { \circ }} \mathbf{C .} \) Given, \( \boldsymbol{K}_{f} \) for \( \boldsymbol{H}_{2} \boldsymbol{O}= \)
1.86 Kmolality \( ^{-1} \). Assuming 100\%
ionisation of the complex, write the ionisation nature and formula of
complex
A \( \cdot P t\left[\left(N H_{3}\right)_{4} C l_{2}\right] C l_{2} \rightarrow P t\left[\left(N H_{3}\right)_{4} C l_{2}\right]^{2+} 2 C l \)
B . \( P t\left[\left(N H_{3}\right)_{4} C l_{2}\right] C l_{2} \rightarrow P t\left[\left(N H_{3}\right)_{4} C l_{2}\right]^{+} C l \)
c. \( P t\left[\left(N H_{3}\right)_{4} C l_{2}\right] C l_{2} \rightarrow 2 P t\left[\left(N H_{3}\right)_{4} C l_{2}\right]^{+} C l \)
D. \( P t\left[\left(N H_{3}\right)_{4} C l_{2}\right] C l_{2} \rightarrow P t\left[\left(N H_{3}\right)_{4} C l_{2}\right]^{3+} 3 C l \)
Subject: Chemistry
\( O_{3}(g) \) is a powerful oxidising agent. The given equations,
\( \boldsymbol{S}+\mathbf{3} \boldsymbol{O}_{3}+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4}+\boldsymbol{3} \boldsymbol{O}_{2} \)
represent oxidation of \( S \) in the
presence of moisture to \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
Subject: Maths
If
\( \frac{n}{^{n} C_{r}+4^{n} C_{r+1}+6^{n} C_{r+2}+4^{n} C_{r+3}+^{n} C} \)
\( \frac{\boldsymbol{r}+\boldsymbol{k}}{\boldsymbol{n}+\boldsymbol{k}}, \) then the value of \( \boldsymbol{k} \) equals
A . 1
B. 2
\( c \cdot 4 \)
D. None of these
Subject: Maths
n an automobile factory, certain parts are to be fixed into the chassis in a
section before it moves into another
section. On a given day, one of the three persons \( A, B \) and \( C \) carries out this task. \( A \) has \( 45 \% \) chance, \( B \) has \( 35 \% \)
chance and \( C \) has \( 20 \% \) chance of doing
the task. The probability that \( A, B \) and
\( C \) will take more than the allotted time is \( \frac{1}{6}, \frac{1}{10} \) and \( \frac{1}{20} \) respectively. If it is found that the time taken is more than
the allotted time, what is the probability that \( A \) has done the task?
Subject: Physics
Choose the mirror image of the word above:
ANS43Q12
(1) AHZA EOT S
(2) \( \sin \varepsilon \) 오 2 ИА
(3) 2ИA£AOSI
(4) ド \( S O A \varepsilon \) АИ 2
\( A \)
B. 2
\( c \cdot 3 \)
\( D \)
Subject: Physics
Two spherical conductors \( A \) and \( B \) of
radii \( 1 \mathrm{mm} \) and \( 2 \mathrm{mm} \) separated by a distance of \( 5 \mathrm{cm} \) and are uniformly charged. If the spheres are connected by a conducting wire then in equilibrium condition, the ratio of the magnitude of
the electric fields at the surfaces of
spheres \( A \) and \( B \) is:
A . 4: 1
B. 1: 2
c. 2: 1
D. 1: 4
Subject: Biology
Match the columns and choose the
correct option.
\( (a) \)
\( (b) \)
\( (c) \)
\( (e) \)
\( (d) \)
\( \mathbf{A} \cdot a-3, b-5, c-4, d-1, e-2 \)
B \( \cdot a-2, b-5, c-1, d-3, e-4 \)
\( \mathbf{c} \cdot a-2, b-4, c-1, d-3, e-5 \)
D \( . a-3, b-1, c-5, d-2, e-4 \)
E \( . a-5, b-4, c-2, d-1, e-3 \)
Subject: Maths
For any two real numbers \( \theta \phi, \) we define \( \theta R \phi \) if and only if \( \sec ^{2} \theta-\tan ^{2} \phi=1 \)
The relation \( \boldsymbol{R} \) is
A. Reflexive but not transitive
B. Symmetric but not reflexive
c. Both reflexive and symmetric but not transitive
D. An equivalence relation
Subject: Physics
A cyclist riding the bicycle at a speed of \( 14 \sqrt{3} m s^{-1}, \) takes a turn around a circular of radius \( 20 \sqrt{3} m, \) without
skidding. Given \( g=9.8 m s^{-2}, \) what is
his inclination to the vertical?
A . \( 30^{\circ} \)
B. \( 90^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 60^{\circ} \)
Subject: Maths
A large group of students took a test in Physics and the final grades have a mean of 70 and a standard deviation of
10. If we can approximate the distribution of these grades by a normal distribution, what percent of the
students should fail the test (grades \( < \)
60)\( ? \)
A . 15.21
в. 23.2
c. \( 15.87 \% \)
D. 16.23
Subject: Chemistry
For the reaction \( 2 S O_{2}+O_{2} \rightleftharpoons 2 S O_{3} \)
the units of \( \boldsymbol{K}_{c} \) is:
A. litre/mole
B . mole /litre
c. \( \left(\text {mol litre}^{-1} \text {) }^{2}\right. \)
D. (liter mole \( ^{-1} \) ) \( ^{2} \)
Subject: Physics
The radioactivity of a sample is \( \boldsymbol{R}_{1} \) at a
time \( T_{1} \) and \( R_{2} \) at a time \( T_{2} \). If the half-
life of the specimen is \( T, \) the number of atoms that have disintegrated in the
\( \operatorname{time}\left(T_{2}-T_{1}\right) \) is equal to
\( \frac{\boldsymbol{n}\left(\boldsymbol{R}_{1}-\boldsymbol{R}_{2}\right) \boldsymbol{T}}{\ln 4} . \) Here \( \boldsymbol{n} \) is some integral
number. What is the value of \( n \) ?
Subject: Maths
\( R_{1} \) and \( R_{2} \) are the reminders when the
polynomial \( a x^{3}+3 x^{2}-3 \) and \( 2 x^{3}- \)
\( 5 x+2 a \) are divided by \( (x-4) \)
respectively. If \( 2 R_{1}-R_{2}=0, \) then find
the value of a
A \( \cdot a=\frac{1}{6} \)
в. \( _{a=\frac{1}{3}} \)
c. \( _{a=\frac{1}{7}} \)
D. \( a=\frac{1}{5} \)
Subject: Chemistry
Cinnabar \( (H g S) \) is heated in air, it is
first converted into which
is then reduced to on further
heating
A. \( H g O, H g \)
в. \( H g O, H g_{2} O \)
\( \mathbf{c} \cdot H g_{2} O, H g \)
D. \( H g_{2} O, H g O \)
Subject: Maths
If \( g(x)=\frac{5 x-3}{2 x^{2}-11-6}, \) what is the
sum of all the real numbers that are not
in the domain of \( g(x) ? \)
A . -2
B. 0.5
\( c \cdot 2 \)
D. 5.5
E . 6.5
Subject: Physics
Assertion
When the current in a coil changes, it
induces a back emf in the same coil
Reason

Emf is a measure of the inertia of the
coil against the change of current through it.
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
The hydrolysis constant of the salts NaA and NaB [of two weak acids HA and HB]
\( \operatorname{are} 10^{-8} \) and \( 10^{-10} \) respectively. If the
dissociation constant \( K_{a} \) of weak acid
\( \mathrm{HC} \) is \( 10^{-5}, \) then decreasing order of the acid strength would be -
\( \mathbf{A} \cdot \) НВ>НС>НА
В. НА>НВ>нс
c. нВ>НА>нс
D. None of these
Subject: Physics
A circular loop of radius \( 0.3 \mathrm{cm} \) lies
parallel to a much bigger circular loop of radius \( 20 \mathrm{cm} . \) The centre of the small
loop is on the axis of the bigger loop. The distance between their centres is \( 15 \mathrm{cm} \)
If a current of \( 2.0 A \) flows through the smaller loop, then flux liked with bigger loop is:
A \( \cdot 6 \times 10^{-11} \) weber
В. \( 3.3 \times 10^{-11} \) weber
c. \( 6.6 \times 10^{-9} \) weber
D. \( 9.1 \times 10^{-11} \) weber
Subject: Physics
Pressure depends on distance as, \( \boldsymbol{P}= \) \( \frac{\boldsymbol{\alpha}}{\boldsymbol{\beta}} \exp \left(-\frac{\boldsymbol{\alpha} \boldsymbol{z}}{\boldsymbol{k} \boldsymbol{\theta}}\right), \) where \( \boldsymbol{\alpha}, \boldsymbol{\beta} \) are
constants, \( z \) is distance, \( k \) is Boltzman's
constant and \( \theta \) is temperature. The
dimensions of \( \beta \) are
\( \mathbf{A} \cdot\left[M^{0} L^{0} T^{0}\right] \)
B \( \cdot\left[M^{-1} L^{-1} T-1\right] \)
\( \mathbf{c} \cdot\left[M^{0} L^{2} T^{0}\right] \)
D \cdot \( \left[M^{-1} L^{1} T^{2}\right] \)
Subject: Physics
A metal rod having \( \boldsymbol{\alpha}=\mathbf{1 0} \times \mathbf{1 0}^{-\mathbf{6}} /^{\circ} \boldsymbol{C} \)
has a length of \( 250 \mathrm{cm} \) at \( 40^{\circ} \mathrm{C} \). The
temperature at which it can be shortened by \( 1 \mathrm{mm} \)
\( \mathbf{A} \cdot 80^{\circ} \mathrm{C} \)
в. \( -40^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 0^{\circ} C \)
D. \( 40^{\circ} \mathrm{C} \)
Subject: Maths
Let \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{2} & \mathbf{4} \\ \mathbf{3} & \mathbf{2}\end{array}\right], \boldsymbol{B}=\left[\begin{array}{cc}\mathbf{1} & \mathbf{3} \\ -\mathbf{2} & \mathbf{5}\end{array}\right] \) and
\( \boldsymbol{C}=\left[\begin{array}{cc}\mathbf{- 2} & \mathbf{5} \\ \mathbf{3} & \mathbf{4}\end{array}\right] . \) Find:
\( \boldsymbol{A}+\mathbf{2} \boldsymbol{B} \)