AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
Choose the correct criteria to prove that two triangles are congruent:
Criteria:
A) All three corresponding sides are
congruent.
B) Two angles and the side between
them are congruent.
C) Two angles and a non-included side
are congruent.
D) Two sides and the angle between
them are congruent. For the given congruency theorem which option is suitable.
1) SSS (side-side-side) =
2) SAS (side-angle-side) =
3) AAS (angle-angle-side) =
4) ASA (angle-side-angle) ) =
Subject: Physics
Monochromatic light is incident on a pair of narrow slits a distance of \( 0.1 \mathrm{mm} \)
apart. A series of
bright and dark fringes are observed on a screen a distance of \( 2.0 \mathrm{m} \) away. The
distance between
adjacent bright fringes is \( 8.0 \mathrm{mm} \) What is the path difference between the
light waves from the two slits that meet
at the second
order dark fringe?
A \( \cdot 2.0 \times 10^{-7} \mathrm{m} \)
В. \( 4.0 \times 10^{-7} \mathrm{m} \)
\( \mathbf{c} \cdot 6.0 \times 10^{-7} m \)
7
Subject: Physics
Charges \( 1 \mu C \) are placed at each of the four corners of a square of side \( 2 \sqrt{2} m \)
The potential at the point of intersection of the diagonals is \( _{-}-_{-}-_{-}(K=9 \times \)
\( \left.\mathbf{1 0}^{\mathbf{9}} \boldsymbol{S} \boldsymbol{I} \text { unit }\right) \)
\( \mathbf{A} \cdot 18 \times 10^{3} V \)
в. \( 1800 \mathrm{V} \)
\( \mathbf{c} \cdot 18 \sqrt{2} \times 10^{3} V \)
D. None of these
Subject: Maths
Convert in \( \frac{\boldsymbol{p}}{\boldsymbol{q}} \) form:
(i) \( 0 . \overline{47} \)
(ii) \( 0 . \overline{001} \)
(iii) \( 0 . \overline{9} \)
(iv) \( 2.3 \overline{5} \)
Subject: Physics
\( _{3} L i^{7}+_{1} H^{2} \rightarrow_{4} B e^{8}+_{o} n^{1}+Q \)
Mass of \( _{3} L i^{7}=7.01823 a m u \)
Mass of \( _{1} H^{2}=2.01474 a m u \)
Mass of \( _{4} B e^{8}=8.00785 a m u \)
Mass of \( _{o} n^{1}=1.00899 a m u \)
Then, the value of Q is
A. 5 MeV
в. \( 10 \mathrm{MeV} \)
c. 15 MeV
D.
Subject: Maths
Solve: \( \boldsymbol{x}(\boldsymbol{3} \boldsymbol{x}+\mathbf{1 4})+\boldsymbol{8} \)
A \( \cdot(x+4)(3 x+2) \)
в. \( (x+2)(x+4) \)
c. \( (x-4)(x+6) \)
D. \( (x-2)(4 x+5) \)
Subject: Chemistry
For the reaction \( C_{2} H_{5} O H+B r^{-} \leftrightharpoons \)
\( C_{2} H_{5} B r+O H^{-}, \) equilibrium will shift
to the right on:
A. exposing the system to light
B. adding an alkali
c. adding an acid
D. adding \( C_{2} H_{5} B r \)
Subject: Physics
There is no resistance in the inductive
circuit. Kirchhoff's voltage law for the
circuit is
A \( \cdot V+L \frac{d i}{d t}=0 \)
B. \( v=L \frac{d i}{d t} \)
\( ^{\mathbf{C}} \cdot V-L^{2} \frac{d i}{d t}=0 \)
D. None of these
Subject: Chemistry
What does the exponential factor
represent?
A. The total number of reactants in a reaction.
B. The amount of energy needed to start a chemical reaction.
C. The fraction of reactants that have approached the activation energy hill and made it over per number of attempts.
D. The fraction of reaction energy given off per unit of time.
E. The fraction of products that have approached the activation energy hill and made it over per number of attempts.
Subject: Physics
(a) Two identical vessels \( A \) and \( B \)
containing equal volume of water are placed in sun. The outer surface of one vessel A is blackened, while of other
vessel B is polished. Thermometer \( \boldsymbol{T}_{1} \)
and \( T_{2} \) are used to measure the
temperature of vessel \( A \) and \( B \) respectively. Which thermometer will
record a higher temperature? Give a reason for your answer
(b) If the two vessels \( A \) and \( B \) as
described in part (a) are filled with
boiling water and placed inside the room, which thermometer will show a
higher temperature after 15 minutes? Give a reason for your answer
Subject: Biology
During lactic acid fermentation
A \( \cdot O_{2} \) is used, \( C O_{2} \) is liberated
B. Neither \( O_{2} \) is used nor \( C O_{2} \) liberated
\( \mathrm{c} \cdot O_{2} \) is not used, \( C O_{2} \) is liberated
D. \( O_{2} \) is used, \( C O_{2} \) is not liberated
Subject: Physics
Two short bar magnets with magnetic moments 400 ab \( A c m^{2} \) and \( 800 a b A \)
\( c m^{2} \) are placed with their axis in the same straight line with similar poles facing each other and with their centres
at \( 20 \mathrm{cm} \) apart from each other. Then
the force of repulsion is:
Disclaimer: No option as 0.08 dyne was
given in the original paper.
A. 12 dyne
B. 6 dyne
c. 0.08 dyne
D. 150 dyne
Subject: Maths
The metallic cuboid \( 100 \mathrm{cm} \times 80 \mathrm{cm} \times \)
\( 64 \mathrm{cm} \) is recast into a cube. The surface
area of the cube is
A \( \cdot 19200 \mathrm{cm}^{2} \)
B. \( 31600 \mathrm{cm}^{2} \)
c. \( 38400 \mathrm{cm}^{2} \)
D. \( 25600 \mathrm{cm}^{2} \)
Subject: Physics
A conduction loop of area \( 5 \mathrm{cm}^{2} \) is
placed in a magnetic field which varies sinusoidally with time as \( B= \)
\( 0.2 \sin 300 t . \) The normal to the coil
makes an angle of \( 60^{\circ} \) with the field. The emf induced at \( t=(\pi / 900) \) s is?
A \( .7 .5 \times 10^{-3} \mathrm{v} \)
B. zero
c. \( 15 \times 10^{-3} v \)
D. \( 20 \times 10^{-3} \mathrm{V} \)
Subject: Chemistry
The equilibrium constant for the reaction:
\( N_{2}(g)+O_{2}(g) \rightleftharpoons 2 N O(g) \) at \( 2000 \mathrm{K} \) is
\( 4 \times 10^{4} \)
In presence of catalyst the equilibrium is established ten times faster at the
same temperature
What is the value of equilibrium constant in presence of catalyst?
A \( \cdot 40 \times 10^{-4} \)
B . \( 4 \times 10^{-4} \)
c. \( 4 \times 10^{4} \)
D. None
Subject: Chemistry
A buffer solution is prepared in which the concentration of \( N H_{3} \) is \( 0.30 M \) and
the concentration of \( N H_{4}^{+} \) is \( 0.20 M . \) If
the equilibrium constant, \( \boldsymbol{K}_{\boldsymbol{b}} \) for \( \boldsymbol{N} \boldsymbol{H}_{3} \)
equals \( 1.8 \times 10^{-5}, \) what is the pH of
this solution? \( (\log 2.7=0.433) \)
A . 9.08
B. 9.43
c. 11.72
D. 8.73
Subject: Chemistry
The free energy of the formation of \( ^{\prime} N O^{\prime} \)
is \( 78 k J / m o l \) at the temperature of an
automobile engine \( (1000 K) . \) What is
the \( K_{C} \) equilibrium constant for this
reaction at \( 1000 K \)
\( \frac{1}{2} N_{2}(g)+\frac{1}{2} O_{2}(g) \rightleftharpoons N O(g) \)
A . \( 8.4 \times 10^{-5} \)
В. \( 7.1 \times 10^{-9} \)
c. \( 4.2 \times 10^{-10} \)
D. \( 1.7 \times 10^{-19} \)
Subject: Physics
If the density of a planet is double than
that of the earth and the radius is 1.5
times that of the earth, the acceleration
due to gravity on the surface of the planet is
\( A \)
\( \frac{3}{4} \) times that on the surface of earth
B. 3 times that on the surface of earth
c. \( \frac{4}{3} \) times that on the surface of earth
D. 6 times that on the surface of earth
Subject: Chemistry
Assertion
The -As=As- linkage present in arsphenamine (a sulpha drugs) resemles the -N=N-linkage present is
azo dyes.
Reason
The first antibacterial agent, prontosil resembles in structure to the
compound salvarsan.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Physics
An electric toaster draws \( 8 A \) current in
a \( 220 V \) circuit. It is used for \( 2 h r . \) What
is the cost of operating the toaster if the
\( \operatorname{cost} \) of electrical energy is
Rs. \( 4.5 / k W h ? \)
A. \( R s .9 .50 \)
B. Rs. 25.50
c. \( R s .14 .84 \)
D. Rs. 15.84
Subject: Chemistry
List- List-II
A) \( H_{3} P O_{2} \)
1) Tribasic
B) \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3} \)
2) Mono
basic
C) \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4} \)
3
Tetrabasic
D) \( \boldsymbol{H}_{4} \boldsymbol{P}_{2} \boldsymbol{O}_{6} \)
4) Di-
basic
The correct match is :
A \( . \) A-3, \( B \) -2, \( c-1, D-5 \)
B. A-2, B-4, C-1, D-3
c. \( A-2, B-5, C-3, D-4 \)
D. A-1, B-2, C-3, D-4
Subject: Maths
If \( \boldsymbol{A}=(\boldsymbol{6}, \boldsymbol{7}, \boldsymbol{8}, \boldsymbol{9}), \boldsymbol{B}=(\boldsymbol{4}, \boldsymbol{6}, \boldsymbol{8}, \boldsymbol{1 0}) \) and
\( \boldsymbol{C}=\{\boldsymbol{x}: \boldsymbol{x} \boldsymbol{\epsilon} \boldsymbol{N}: \boldsymbol{2}<\boldsymbol{x} \leq 7\} ; \) find :
\( \boldsymbol{A}-(\boldsymbol{B} \cup \boldsymbol{C}) \)
Subject: Physics
The mass of oxygen gas (in Kilo grams) occupying a volume of 11.2 litre at a temperature \( 27^{0} \mathrm{C} \) and a pressure of \( 76 \mathrm{cm} \)
of mercury is :
(Molecular weight of oxygen \( =32 \) )
A. 0.001456
B. 0.01456
c. 0.1456
D. 1.1456
Subject: Biology
Which is the correct sequence of the
components of a reflex arc?
A. Receptors \( \rightarrow \) muscles \( \rightarrow \) sensory neuron \( \rightarrow \) motor neuron \( \rightarrow \) spinal cord
B. Receptors \( \rightarrow \) motor neuron \( \rightarrow \) spinal cord \( \rightarrow \) sensory neuron \( \rightarrow \) muscle
C. Receptors \( \rightarrow \) spinal cord \( \rightarrow \) sensory neuron \( \rightarrow \) motor neuron \( \rightarrow \) muscle
D. Receptors \( \rightarrow \) sensory neuron \( \rightarrow \) spinal cord \( \rightarrow \) motor neuron \( \rightarrow \) muscle
Subject: Maths
f \( m \) and \( n \) are the order and degree of
the differential equation \( \left(\frac{d^{2} y}{d x^{2}}\right)^{5}+4 \frac{\left(\frac{d^{2} y}{d x^{2}}\right)^{3}}{\left(\frac{d^{2} y}{d x^{2}}\right)}+\frac{d^{2} y}{d x^{2}}=x^{2}-1 \)
then
A \( . m=3, n=3 \)
B. \( m=2, n=6 \)
\( \mathrm{c} \cdot m=3, n=5 \)
Subject: Chemistry
If aqueous solution of \( A l_{2}\left(S O_{4}\right)_{3} \) is
mixed with \( N a_{2} C O_{3} \) which of the
following will be one the products?
A \( \cdot A l_{2}\left(C O_{3}\right)_{3} \)
В \( \cdot A l(O H)_{3} \)
c. \( _{A l}\left(H C O_{3}\right)_{3} \)
D. \( _{N a A l_{2}}\left(C O_{3}\right)_{2} \)
Subject: Maths
The following pair of linear equations consistent. State true and false:
\( \boldsymbol{x}+\mathbf{3} \boldsymbol{y}=\mathbf{1 1} ; \mathbf{2}(\mathbf{2} \boldsymbol{x}+\mathbf{6} \boldsymbol{y})=\mathbf{2 2} \)
A. True
B. False
Subject: Chemistry
Arrange the following compounds in increasing order of their boiling points.
I. \( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{B r} \)
II. \( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{B r} \)
III. \( \left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{C H} \boldsymbol{C H}_{2} \boldsymbol{B r} \)
IV. \( \left(\boldsymbol{C H}_{3}\right)_{3} \boldsymbol{C B r} \)
A. \( I I<I<I I I<I V \)
в. \( I I I<I<I V<I I \)
c. \( I V<I I I<I I<I \)
II \( I<I V<I I I<I I \)
1
Subject: Physics
The dimensions of \( \frac{a}{b} \) in the equation \( P=\frac{a-t^{2}}{b x}, \) where \( P \) is pressure, \( x \) is
distance and \( t \) is time, are
A \( \cdot\left[M^{2} L T^{-3}\right] \)
в. \( \left[M T^{-2}\right] \)
\( \mathbf{c} \cdot\left[L T^{-3}\right] \)
\( \mathbf{D} \cdot\left[M L^{3} T^{-1}\right] \)
Subject: Physics
(a) Distinguish with the help of a suitable diagram, the difference in the
behaviour of a conductor and a
dielectric placed in an external electric field. How does polarised dielectric modify the original external field?
(b) A capacitor of capacitance \( C \) is charged fully by connecting it to a battery of emf E. It is then disconnected from the battery. If the separation between the plates of the capacitor is now doubled, how will the following change?
(i) Charge stored by the capacitor.
(ii) Field strength between the plates.
(iii) Energy stored by the capacitor. Justify your answer in each case.
Subject: Chemistry
When \( H_{2} S \) is passed into aqueous \( S O_{2} \)
\( \mathbf{A} \cdot H_{2} S \) is converted to yellow precipitate of sulphur.
B. \( S O_{2} \) is converted to yellow precipitate of sulphur.
C . a clear solution of \( H_{2} S O_{4} \) is formed.
D. \( S O_{2} \) as well as \( H_{2} S \) are converted into a yellow precipitate of sulphur
Subject: Chemistry
The rate constant of a reaction
increases by 3 times for every \( 10^{0} C \) rise in temperature uniformly, in the range
of \( 20^{\circ} \mathrm{C} \) to \( 80^{\circ} \mathrm{C} \). If the rate constant at
\( 30^{\circ} \mathrm{C} \) is \( \mathrm{K}, \) then what is its value at
\( 60^{0} C ? \)
\( A \cdot 9 K \)
в. 27К
\( c \cdot 6 k \)
D. 81K
Subject: Maths
A bag contains 4 white and 2 black balls and another bag contains 3 white and 5 black balls. If one ball is drawn from
each bag, then the probability that one ball is white and one ball is black is
A \( \cdot \frac{5}{24} \)
в. \( \frac{13}{24} \)
\( c \cdot \frac{1}{4} \)
D. \( \frac{2}{3} \)
Subject: Chemistry
For the cell \( \boldsymbol{M} / \boldsymbol{M}^{+} \| \boldsymbol{X}^{-} / \boldsymbol{X}, \boldsymbol{E}_{M^{+} / M}^{\circ}= \)
0.44 and \( E_{X / X^{-}}^{\circ}=0.33 V . \) From the data it can be deduced that \( M+X \rightarrow \)
\( M^{+}+X^{-} \) is spontaneous.
A. \( M+X \rightarrow M^{+}+X^{-} \) is spontaneous
В. \( E_{\text {Сец}}=0.77 V \)
c. \( E_{\text {Cell }}=-0.77 V \)
D. None
Subject: Maths
Find the median class of the following
distribution.
\( \begin{array}{ll} \text { Weight }\operatorname{(in} k g) & \text { Number of students } \\ 45-47 & 7 \\ 47-49 & 5 \\ 49-51 & 8 \\ 51-53 & 12 \\ 55-57 & 2 \\ 57-59 & 10\end{array} \)
Subject: Maths
The perimeter of two similar triangles
\( \triangle A B C \) and \( \triangle D E F \) are \( 36 \mathrm{cm} \) and 24
\( \mathrm{cm} \) respectively. If \( D E=10 \mathrm{cm}, \) then
\( A B \) is :
A . \( 12 \mathrm{cm} \)
B. \( 20 \mathrm{cm} \)
c. \( 15 \mathrm{cm} \)
D. \( 18 \mathrm{cm} \)
Subject: Physics
The magnetic field at the origin due to a current element \( i . \vec{d} l \) placed at a
position \( \vec{r} \) is This question has multiple correct options
A \( \frac{\mu_{0} i}{4 \pi} \frac{\overrightarrow{d l} \times \vec{r}}{r^{3}} \)
В. \( \frac{\mu_{0} i}{4 \pi} \frac{\vec{r} \times \vec{d} l}{r^{3}} \)
\( ^{\mathrm{C}}-\frac{\mu_{0} i}{4 \pi} \frac{\vec{r} \times \vec{d} l}{r^{3}} \)
D. \( -\frac{\mu_{0} i}{4 \pi} \frac{\vec{d} l \times \vec{r}}{r^{3}} \)
Subject: Maths
The circumference of the front wheel of
a cart is \( 30 \mathrm{ft} \) long and that of the back wheel is 36 ft long. What is the distance travelled by the cart when the front wheel has done five more revolutions
than the rear wheel?
A \( .20 f t \)
B. 25 ft
c. \( 750 f t \)
D. \( 900 f t \)
Subject: Physics
A man' \( A^{\prime} \) stands at the position shown
in the figure and a second man \( ^{\prime} B^{\prime} \)
approaches the mirror along the line perpendicular to it which passes through its centre. AT the moment when
\( A^{\prime} \) and \( ^{\prime} B^{\prime} \) first sec each other in the
mirror, the distance of \( B \) from the mirror is:
Subject: Chemistry
Calculate pH at which \( M g(O H)_{2} \) begin to precipitate form a solution
containing \( 0.1 \mathrm{M} M g^{2+} \) ions.
\( \boldsymbol{K}_{s p} \) of \( \boldsymbol{M} \boldsymbol{g}(\boldsymbol{O} \boldsymbol{H})_{2}=\mathbf{1} \times \mathbf{1 0}^{-11} \)
Subject: Chemistry
In Millikan's oil drop experiment, the charge of three oil drops \( X, Y, \) and \( Z \) have been found to be 2,0.04 and 0.8 respectively. What could be the probable charge of an electron and the number of electrons attached to these
oil drops?
A. \( 0.04 \mathrm{C}, 50,1,20 \)
B. \( 0.04 \mathrm{C}, 50,2,20 \)
c. \( 0.8 c, \) २०, 15, 50
D. 0.8, 1, 50, 23
Subject: Maths
The value of \( ^{10} \boldsymbol{C}_{1}+^{10} \boldsymbol{C}_{2}+^{10} \boldsymbol{C}_{3}+\ldots+ \)
\( ^{10} \mathrm{C}_{9} \) is
A \( .2^{10} \)
B . \( 2^{11} \)
\( c \cdot 2^{10}-2 \)
D. \( 2^{10}-1 \)
Subject: Physics
In the Bohr model of a \( \pi- \) mesic atom,
a \( \pi- \) meson of mass \( m_{\pi} \) and of the
same charge as the electron is in a
circular orbit of radius ' \( r^{\prime} \) about the
nucleus with an orbital angular momentum \( h / 2 \pi . \) If the radius of a
nucleus of atomic number \( Z \) is given by \( \boldsymbol{R}=\mathbf{1 . 6} \times \mathbf{1 0}^{-15} \boldsymbol{Z}^{\frac{1}{3}} \boldsymbol{m}, \) then the limit
on \( Z \) for which \( \left(\epsilon_{0} h^{2} / \pi m e^{2}=\right. \) \( \left.0.53 A \text { and } m_{\pi} / m_{e}=264\right) \pi- \) mesic
atoms might exist is
\( \mathbf{A} \cdot<105 \)
B \( .>105 \)
\( \mathbf{c} .<37 \)
\( \mathbf{D} \cdot>37 \)
Subject: Maths
Let the matrix \( A \) and \( B \) be defined as
\( A=\left|\begin{array}{ll}\mathbf{3} & \mathbf{2} \\ \mathbf{2} & \mathbf{1}\end{array}\right| \) and \( \boldsymbol{B}=\left|\begin{array}{ll}\mathbf{3} & \mathbf{1} \\ \mathbf{7} & \mathbf{3}\end{array}\right| \) then the
value of \( \operatorname{Det.}\left(2 A^{9} B^{-1}\right), \) is
\( A \cdot 2 \)
в.
\( c \cdot-1 \)
\( D .-2 \)
Subject: Chemistry
Assertion
\( H_{2} S O_{4} \) is a strong acid
Reason
\( H_{2} S O_{4} \) undergoes almost complete ionization in aqueous solution.
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 standing wave is produced on a string
fixed at one end and free at other. The
length of the string must be an
A \( \cdot \) odd integral multiple of \( \frac{\lambda}{4} \)
B. integral multiple of \( \frac{\lambda}{2} \)
c. integral multiple of \( \lambda \)
D. integral multiple of \( \frac{\lambda}{4} \)
Subject: Physics
If \( \bar{v}, v_{r m s} \) and \( v_{p} \) represent the mean
speed, root mean square and most probable speed of the molecules in an ideal monoatomic gas at temperature
\( T \) and if \( m \) is mass of the molecule,
then
A \( \cdot v_{p}<\bar{v}<v_{r m} \)
B. No molecule can have a speed greater than \( \sqrt{2 v_{r m s}} \)
C. No molecule can have a speed less than \( v_{p} / \sqrt{2} \)
D. None of the above
Subject: Chemistry
Which of the following compounds will given racemic mixture on nucleophilic
substitution by \( O H^{\ominus} \) ion?
(a) \( \boldsymbol{C H}_{3}-\boldsymbol{C H}-\boldsymbol{B r} \)
\( \boldsymbol{C}_{2} \boldsymbol{H}_{5} \)
\( \boldsymbol{1} \)
\( \boldsymbol{B} \)
(b) \( \boldsymbol{C H}_{3}-\underset{C_{2} \boldsymbol{H}_{5}}{\boldsymbol{C}}-\boldsymbol{C H}_{3} \)
(c) \( \boldsymbol{C H}_{3}-\underset{\boldsymbol{C}_{2} \boldsymbol{H}_{5}}{\boldsymbol{C} \boldsymbol{H}}-\boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{B} \boldsymbol{r} \)
в. \( (a),(b),(c) \)
c. \( (b),(c) \)
(n)
D. \( (a),(c) \)
Subject: Chemistry
\( ^{210} 84^{\circ} \mathrm{o} \longrightarrow_{82}^{206} \mathrm{Pb}+_{2}^{4} \mathrm{He} \)
In this reaction, predict the position of group of \( P o \) in periodic table when lead
is in the \( I V A \) group:
A . IIA
в. \( I V B \)
c. \( V I A \)
D. \( V I B \)
Subject: Physics
A radioactive sample decays by \( 63 \% \) of its initial value in \( 10 s . \) It would have
decayed by \( 50 \% \) of its initial value in
\( \mathbf{A} \cdot 7 s \)
в. 14 s
c. \( 0.7 s \)
D. \( 1.4 s \)
Subject: Physics
A uniform solid right circular cone of
base radius \( \mathrm{R} \) is joined to a uniform
solid hemisphere of radius \( R \) and of the
same density, as shown. The centre of
mass of the composite solid lies at the
centre of base the cone. The height of
the cone is
\( \mathbf{A} \cdot 1.5 \mathrm{R} \)
B. \( \sqrt{3} \) R
\( c \cdot 3 R \)
D. \( 2 \sqrt{3} \) R
Subject: Maths
If \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) defined by \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2} \) is
A. one-one but not onto
B. onto but not one-one
c. bijective
D. neither one-one nor onto
Subject: Physics
Two thin lenses have combined power of 10 \( D \). When separated by \( 20 \mathrm{cm} \) their
equivalent power is 6.25 D.Their
individual powers in \( D \) are
A . 3.5 and 6.5
B. 5 and 5
c. 7.5 and 2.5
D. 9.0 and 1
Subject: Chemistry
The volume of perhydrol which on
decomposition gives 1.5 lit of \( O_{2} \) gas at
STP is:
\( \mathbf{A} \cdot 25 \mathrm{ml} \)
B. \( 15 \mathrm{ml} \)
c. \( 10 \mathrm{ml} \)
D . 20 m
Subject: Physics
A 2 -dimensional bent rod is made out of
a material with uniform density.
Its center of mass is located at which
position coordinate? Refer to the
diagram of the bent rod and ignore the
rod's thickness in your calculations.
\( \mathbf{A} \cdot(0,0) \)
B \( \cdot\left(\frac{w}{4}, \frac{l}{4}\right) \)
c. \( \left(\frac{w}{3}, \frac{l}{3}\right) \)
D \( \cdot\left(\frac{w}{2}, \frac{l}{2}\right) \)
E \( \cdot\left(\frac{w^{2}}{2(l+w)}, \frac{l^{2}}{2(l+w)}\right) \)
Subject: Maths
Check whether the vector \( 4 \hat{\mathbf{i}}+\mathbf{1 3} \hat{\mathbf{j}}- \)
\( 18 \hat{k} \) is a linear combination of the vectors \( \hat{i}-2 \hat{j}+3 \hat{k} \) and \( 2 \hat{i}+3 \hat{j}-4 \hat{k} \)
Subject: Maths
The image of the point (1,6,3) in the \( \operatorname{line} \frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3} \) is?
A. (1,0,7)
в. (7,0,1)
c. (2,7,0)
D. (-1,-6,-3)
Subject: Chemistry
If the ionization energy for hydrogen atom is \( 13.6 e V \), then the ionization energy for \( \boldsymbol{H} \boldsymbol{e}^{+} \) ion should be:
A . \( 13.6 e V \)
B. \( 6.8 e V \)
c. \( 54.4 e V \)
D. \( 72.2 e V \)
Subject: Maths
\( \boldsymbol{a}=\mathbf{2} \overline{\mathbf{i}}+\overline{\boldsymbol{k}}, \overline{\boldsymbol{b}}=\mathbf{3} \overline{\boldsymbol{j}}+\mathbf{4} \overline{\boldsymbol{k}}, \overline{\boldsymbol{c}}=\mathbf{8} \overline{\mathbf{i}}-\mathbf{3} \overline{\boldsymbol{j}} \)
and \( \bar{a} \) is expressed as a linear combination of \( \bar{b} \) and \( \bar{c} \) then \( \bar{a}= \)
A \( \cdot \frac{1}{2}(\bar{b}+\bar{c}) \)
B \( \cdot \frac{1}{3}(\bar{b}+\bar{c}) \)
c. \( \frac{1}{4}(\bar{b}+\bar{c}) \)
D. \( \frac{1}{4}(\bar{b}-\bar{c}) \)
Subject: Physics
A truck is moving along frictionless rail track at a speed of \( 18 m / s \).The mass of
the truck is \( 8000 k g \).If it starts raining,what will be the speed of the
compartment when it has collected water equal to \( 1000 k g \)
A. \( 3 m / s \)
в. \( 6 m / s \)
\( \mathrm{c} \cdot 8 \mathrm{m} / \mathrm{s} \)
D. \( 16 m / s \)
Subject: Chemistry
Balance the following equations by ion
electron method:
\( \boldsymbol{C l}_{2}+\boldsymbol{I O}_{3}^{-}+\boldsymbol{O H}^{-} \rightarrow \boldsymbol{I} \boldsymbol{O}_{4}^{-}+\boldsymbol{C l}^{-}+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O} \)
Subject: Physics
Assertion
The refractive index of a prism depends only on the kind of glass of which it is made of and the colour of light.
Reason
The refractive index of a prism depends on the refracting angle of the prism and the angle of minimum deviation.
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
Assume that the chances of a patient having a heart attack are \( 40 \% \). It is also assumed that a meditation and yoga
course reduce the risk of heart attack
by \( 30 \% \) and the prescription of certain drugs reduces its chances by \( 25 \% \). At a time a patient can choose any one of the two options the patient selected at random suffers a heart attack. Find the
probability that the patient followed a course of meditation and yoga?
Subject: Biology
The process of glycolysis can be
represented as
A. \( C_{6} H_{12} O_{6} \rightarrow 2 C_{3} H_{4} O_{3}+4 H \)
B. \( C_{6} H_{12} O_{6}+6 C O_{2} \rightarrow 6 C O_{2}+6 H_{2} O \)
\( \mathrm{c} \cdot 6 H_{2} O+6 C O_{2} \rightarrow C_{6} H_{12} O_{6}+6 O_{2} \)
D. None of the above