AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
The hydrogen ion concentration of a 10
-8 M \( H C l \) aqueous solution at \( 298 \mathrm{K} \) is:
\( \left[\text { Given that: } \boldsymbol{K}_{\boldsymbol{w}}=10^{-14}\right] \)
A . \( 1.0 \times 10^{-6} \) М
В. \( 1.0525 \times 10^{-7} \) М
c. \( 9.525 \times 10^{-8} \) М
D. \( 1.0 \times 10^{-8} \) М
Subject: Physics
If \( 100 \mathrm{J} \) of heat is needed to completely
change the substance from a solid to a
liquid state, what is the heat of fusion
for the substance?
A \( \cdot 1,000 \mathrm{J} / \mathrm{kg} \)
B. \( 100 \mathrm{J} / \mathrm{kg} \)
\( c \cdot 50 J / k g \)
D. 20 J/kg
E. 5 J/kg
Subject: Physics
Which of the following is the unit vector perpendicular to \( \vec{A} \) and \( \vec{B} \) ?
\( A \cdot \frac{\widehat{A} \times \widehat{B}}{A B \sin \theta} \)
B. \( \frac{\widehat{A} \times \widehat{B}}{A B \cos \theta} \)
c. \( \frac{\vec{A} \times \vec{B}}{A B \sin \theta} \)
D. \( \frac{\vec{A} \times \vec{B}}{A B \cos \theta} \)
Subject: Physics
Match the columns
i. amount of light entering into eye
a. rodes controlled by
ii. colour sensing cells
b. cones
iii.cells helping in vision in dim light
c. iris
d.
iv.junction of optic nerve and retina \( \quad \) blindspot
\( A \cdot i-a, i i-b, i i i-c, i v-d \)
B. \( i-d, i i-c, i i i-b-i v-a \)
\( \mathbf{C} \cdot \mathbf{i}-\mathrm{c}, \mathrm{i} \mathbf{i}-\mathrm{b}, \mathrm{i} \) ii-a, \( \mathrm{iv}-\mathrm{d} \)
D. i-b,ii-a,iii-c,iv-b
Subject: Physics
Charges -q and +q are fixed at the ends of a light rod of length \( l \). The rod is clamped at one end with axis of the dipole along the electric field. The rod is slightly displaced and then released, Neglecting gravity find the time period of small oscillations. Mass of charges is
meach.
\( ^{\mathbf{A}} \cdot_{2 \pi} \sqrt{\frac{m l}{q E}} \)
в. \( \quad 2 \pi \sqrt{\frac{m l}{3 q E}} \)
\( ^{\mathbf{c}} \cdot_{2 \pi} \sqrt{\frac{m l}{2 q E}} \)
D. \( 2 \pi \sqrt{\frac{2 m l}{q E}} \)
Subject: Physics
A polarizer -analyser set is adjusted such that the intensity of light coming out of the analyser is just \( 10 \% \) of the original intensity. Assuming that the polarizer-analyser set does not absorb any light, the angle by which the analyser need to be rotated further to
reduce the output intensity to be zero, is:
A . \( 90^{\circ} \)
в. \( 71.6^{\circ} \)
c. \( 18.4^{\circ} \)
D. \( 45^{\circ} \)
Subject: Chemistry
The upper stratosphere consisting of
the ozone layer protects us from the sun's radiation that falls in the
wavelength region of:
A. \( 600-750 \mathrm{nm} \)
B. \( 0.8-1.5 \mathrm{nm} \)
\( c .400-550 \mathrm{nm} \)
\( m \)
D. 200 - 315 nm
Subject: Physics
Calculate thermal capacity of solid of mass \( 0.8 ~ k g \) and specific heat capacity
of \( 0.4 J / g^{o} C \)
\( \mathbf{A} \cdot 160 J^{\circ} C^{-1} \)
B. \( 320 J^{\circ} C^{-1} \)
c. \( 640 J^{\circ} C^{-1} \)
D. \( 960 J^{\circ} \mathrm{C}^{-1} \)
Subject: Physics
To get from one office to another, one travels as follows (with all angles
measured clockwise from the West) \( 2 m \)
at \( 180^{\circ}, 0.5 m \) at \( 150^{\circ}, \) and \( 1 m \) at \( 30^{\circ} \) How far will a person be from his starting point? \( (\text { in } m) \)
A . 1.5
B. 1.43
\( c .1 \)
D. 1.96
Subject: Chemistry
Arrange the following elements in increasing order of their size.
Be, Ca, Ba, Ra
A. Be <Ca<Ba<Ra
B. \( \mathrm{Ca}<\mathrm{Be}<\mathrm{Ba}<\mathrm{Ra} \)
c. \( \mathrm{Be}<\mathrm{Ca}<\mathrm{Ra}<\mathrm{Ba} \)
D. None of these
Subject: Maths
\( P \) is a point on the X-axis.lt is equidistant from the points (2,6) and \( (-4,0) . \) The co-ordinates of \( P \) are
A. \( P(-2,0) \)
в. \( P(2,0) \)
c. \( P(-6,0) \)
D. \( P(6,0) \)
Subject: Chemistry
If in solvent, n simple molecules of solute combine to form an associated
molecule, \( x \) is degree of association the
Van't Hoff's factor \( ^{\prime} \boldsymbol{i}^{\prime} \) is equal to:
A \( \cdot \frac{1}{1-n x} \)
в. \( \frac{1-x+n x}{1} \)
c. \( \frac{1-x+\frac{x}{n}}{1} \)
D. \( \frac{x}{\frac{n}{1}-1+x} \)
Subject: Physics
A laser beam of pulse power \( 10^{12} W \) is
focussed on an object of area \( 10^{-4} \mathrm{cm}^{2} \)
The energy flux in \( W / c m^{2} \) at the point of focus is
A \( \cdot 10^{4} \)
B. \( 10^{8} \)
\( \mathbf{c} \cdot 10^{16} \)
D. \( 10^{20} \)
Subject: Biology
Which is the correct sequence of the
components of a reflex arc?
A. Receptors - Muscle - Sensory neuron - Motor neuron Spinal cord
B. Receptors - Motor neuron - Spinal cord - Sensory neuron - Muscle
C. Receptors - Spinal cord - Sensory neuron - Motor neuron- Muscle
D. Receptors - Sensory neuron - Spinal cord - Motor neuron - Muscle
Subject: Maths
If \( [\overrightarrow{\boldsymbol{a}} \overrightarrow{\boldsymbol{b}} \overrightarrow{\boldsymbol{c}}]=1 \) then \( \frac{\overrightarrow{\boldsymbol{a}} \cdot \overrightarrow{\boldsymbol{b}} \times \overrightarrow{\boldsymbol{c}}}{\overrightarrow{\boldsymbol{c}} \times \overrightarrow{\boldsymbol{a}} \cdot \overrightarrow{\boldsymbol{b}}}+\frac{\overrightarrow{\boldsymbol{b}} \cdot \overrightarrow{\boldsymbol{c}} \times \overrightarrow{\boldsymbol{a}}}{\overrightarrow{\boldsymbol{a}} \times \overrightarrow{\boldsymbol{b}} \cdot \overrightarrow{\boldsymbol{c}}}+ \)
\( \frac{\vec{c} \cdot \vec{a} \times \vec{b}}{\vec{b} \times \vec{c} \cdot \vec{a}} \) is equal to
\( A \cdot 3 \)
B. 1
\( c \cdot-1 \)
D. None of these
Subject: Chemistry
The bond length of \( C-O \) bond in
carbon monoxide is \( 1.128 \$ \$\{ \) buildrel \( \mathrm{~ I l c i r c ~ l o v e r ~ \{ m a t h r m \{ A \} \} \$ \$ . ~ T h e ~} \)
\( C-O \) bond in \( F e(C O)_{5} \) is:
Subject: Physics
A body colls from \( 70^{\circ} \mathrm{C} \) to \( 60^{\circ} \mathrm{C} \) in 10
minutes when kept in air at \( 30^{\circ} \mathrm{C} \). In the next ten minutes its temprature will fall
A . Below \( 50^{\circ} \mathrm{C} \)
В. \( \operatorname{To} 50^{\circ} \mathrm{C} \)
c. To above \( 52.5^{\circ} \mathrm{C} \)
D. To any of the above depending on its specific heat
Subject: Maths
The angle made by the tangent at any
point on the curve \( \boldsymbol{x}=\boldsymbol{a}(\boldsymbol{t}+ \)
\( \sin t \cos t), y=a(1+\sin t)^{2} \) with \( x \) -axis
is
A \( \cdot \frac{\pi}{2} \)
B. \( \frac{\pi}{4} \)
c. \( _{\pi+\frac{t}{2}} \)
D. \( \frac{\pi}{4}+\frac{t}{2} \)
Subject: Chemistry
If certain decomposition reaction found to obey equation in term of partial pressure (P) of reactant : \( \frac{\boldsymbol{a}-\boldsymbol{p}^{2}}{\boldsymbol{p}^{2}}=\boldsymbol{b k t} \)
what is order of reaction if \( a, b \) and \( k \)
are constant (t represents time)?
\( A \cdot 3 \)
B. 6
\( c \cdot 2 \)
\( D \)
Subject: Maths
The value of 'c' in Rolle's theorem for the
function \( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{c}\boldsymbol{x}^{2} \cos \left(\frac{1}{\boldsymbol{x}}\right), \boldsymbol{x} \neq \mathbf{0} \\ \mathbf{0}, \boldsymbol{x}=\mathbf{0}\end{array}\right. \)
the interval [-1,1] is?
A \( \cdot \frac{-1}{2} \)
B. \( \frac{1}{4} \)
\( c \cdot 0 \)
D. Non-existent in the interval
Subject: Maths
Consider \( \boldsymbol{x}=\mathbf{4} \tan ^{-1}\left(\frac{\mathbf{1}}{\mathbf{5}}\right), \boldsymbol{y}= \)
\( \tan ^{-1}\left(\frac{1}{70}\right) \) and \( z=\tan ^{-1}\left(\frac{1}{99}\right) \)
What is \( x \) equal to?
A \( \cdot \tan ^{-1}\left(\frac{60}{119}\right) \)
в. \( \tan ^{-1}\left(\frac{120}{119}\right) \)
\( ^{\mathbf{c}} \cdot \tan ^{-1}\left(\frac{90}{169}\right) \)
D. \( \tan ^{-1}\left(\frac{170}{169}\right) \)
Subject: Chemistry
Some of the following metals
are obtained by electrolysis of their fused salts.
\( A l, N a, C u, A g, M g, C a \)
These metals are:
A. \( C u, A g \)
в. \( A l, N a, C u \)
c. \( A g, M g, C a \)
D. \( A l, N a, M g, C a \)
Subject: Biology
The graph illustrates the data obtained
from reactions of an enzyme with its specific substrate at various
temperatures and at pH 6 Based on the data, what would be the
result if the experiment is carried out at
\( \mathbf{5}^{\circ} \boldsymbol{C} ? \)
A. No prediction would be valid
B. An amount of product equal to that at \( 20^{\circ} \mathrm{C} \) would be formed
c. An amount of product equal to that at the optimum temperature would be formed
D. An amount of product equal to that at \( 60^{\circ} \mathrm{C} \) would be formed
E. Little or no product would be formed
Subject: Physics
An upright object is placed at a
distance in front of a converging lens equal to twice the focal length \( 20 \mathrm{cm} \) of
the lens. On the other side there is a
concave mirror of focal length \( 15 \mathrm{cm} \)
separated from thelens by a distance of
70 cm. Then select the correct
statements from the following
his question has multiple correct options
A. Magnification for the system is \( 1 / 2 \)
B. Magnification for the system is
c. Final image by the system will real and at distance of \( 80 \mathrm{cm} \) from centre of curvature of spherical mirror
ification for the system is \( +1 / 2 \)
Subject: Maths
If \( (x, y, z) \neq(0,0,0) \) and \( (\hat{i}+\hat{j}+ \)
\( \mathbf{3} \hat{\boldsymbol{k}}) \boldsymbol{x}+(\mathbf{3} \hat{\boldsymbol{i}}-\mathbf{3} \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}}) \boldsymbol{y}+(-\mathbf{4} \hat{\mathbf{i}}+ \)
\( \mathbf{5} \hat{\boldsymbol{j}}) z=\boldsymbol{\lambda}(\boldsymbol{x} \hat{\boldsymbol{i}}+\boldsymbol{y} \hat{\boldsymbol{j}}+\boldsymbol{z} \hat{\boldsymbol{k}}), \) then the value
of \( \lambda \) will be
A \( .-2,0 \)
B. 0,-2
c. -1,0
D. 0,-1
Subject: Physics
Assertion
Angle of repose is equal to the angle of
limiting friction.
Reason
When the body is just at the point of motion, the force of friction in this stage
is called limiting friction
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
Assertion: The equivalent resistance between the points \( X \) and \( Y \) in the figure
is 10
Reason: According to Wheatstone bridge, points \( A \) and \( C \) have the same
potential.
A. Both (A) and (R) are true and (R) is the correct explanation of
B. Both (A) and (R) are true but (R) is not the correct explanation of
C. (A) is true but (R) is false
D. (A) is false but (R) is true
Subject: Chemistry
Rutherford's scattering formula fails for very small scattering angles because:
This question has multiple correct options
A. the gold foil is very thin
B. the kinetic energy of \( \alpha \) -particles is very high
C. the full nuclear charge of the target atom is partially screened by its electron
D. there is strong repulsive force between the \( \alpha \) -particles and nucleus of the target
Subject: Physics
Source and observer start moving simultaneously along \( x \) and \( y \) -axis
respectively. The speed of source is
twice the speed of observer, \( V_{0} . \) If the
ratio of observed frequency to frequency
of the source is \( 0.75, \) find the velocity of
sound
A \( \cdot \frac{11}{\sqrt{5}} v_{0} \)
B. \( \frac{17}{\sqrt{5}} v_{0} \)
c. \( \frac{16}{\sqrt{5}} v_{0} \)
D. \( \frac{19}{\sqrt{5}} v_{0} \)
Subject: Chemistry
The \( K_{a} \) value of ammonium ion
\( \left(N H_{4}+\right) \) is \( 5.6 \times 10^{-10}, \) the \( K_{b} \) value of
\( \operatorname{ammonia} N H_{3}=1.8 \times 10^{-5}, \) then
A. Ammonia is more strongly basic than ammonium is acidic
B. Ammonia is weaker basic than ammonium is acidic
c. Both a and \( b \)
D. Data insufficient
Subject: Chemistry
Pauling scale Linus Pauling: Phenomenon of electronegativity Relative electronegativities of two atoms in a molecule
\( \boldsymbol{E} \boldsymbol{N}(\boldsymbol{X})-\boldsymbol{E} \boldsymbol{N}(\boldsymbol{Y})=\mathbf{0 . 1 0 2}(\triangle \mathbf{1} / 2) . \mathbf{1} \)
0.02 is conversion factor between \( k J \)
and eV is:
Subject: Maths
If \( A \) satisfies the equation \( x^{3}-5 x^{2}+ \)
\( 4 x+\lambda=0, \) then \( A^{-1} \) exists if
A. \( \lambda \neq 1 \)
B. \( \lambda \neq 2 \)
c. \( \lambda \neq-1 \)
D. \( \lambda \neq 0 \)
Subject: Chemistry
How will the lowering of temperature affect the chemical equilibrium in the
system \( : 2 N O+O_{2} \rightleftharpoons 2 N O_{2}, \Delta H<0 \)
This question has multiple correct options
A. Relative concentration of products and reactants does not change
B. Relative concentration of products and reactants change
c. Equilibrium is shifted to the lefttt
D. Equilibrium is shifted to the right
Subject: Chemistry
Which of the following statements
is/are correct?
This question has multiple correct options
A. The bleaching action of chlorine is due to oxidation and so permanent, while the bleaching action of sulphurdioxide is due to reduction and so temporary.
B. \( H I \) cannot be prepared by heating an ionic iodide with conc. \( H_{2} S O_{4}, \) but \( H C l \) can be prepared by the same
way.
C. The oxidising power of halogens follow the order:
\( C l_{2}>F_{2}>B r_{2}>I_{2} \)
D. On reaction of \( X e F_{2} \) with water, no redox change
takes place.
Subject: Physics
A large tank is filled with water (density
\( \rho \), upto height h. Water is coming out from section (4). Fluid pressure at
section (3) is:
(Given \( : A_{2}=A_{4}=2 A_{3} \) and
\( \boldsymbol{A}_{2}, \boldsymbol{A}_{3}, \boldsymbol{A}_{4}<<\boldsymbol{A}_{1} ; \) atmospheric
pressure \( =P_{0} . \) Assume water to be nonviscous and incompressible.
A. \( P_{0}+\rho g h \)
в. \( P_{0}-\rho g h \)
\( c \)
D. \( P_{0}-3 \rho g h \)
Subject: Physics
An electrical cable of copper has just one wire of radius \( 9 \mathrm{mm} \). Its resistance
is \( 5 \Omega .6 \) different well-insulated copper wires each of radius \( 3 \mathrm{mm} \) replace this single copper wire of the cable. The total resistance of the cable will now be
equal to
A . \( 7.5 \Omega \)
B. \( 45 \Omega \)
c. \( 90 \Omega \)
D. 270\Omega
Subject: Maths
A ladder \( 10 \mathrm{m} \) long rests against a vertical wall with the lower end on the
horizontal ground. The lower end of the ladder is pulled along the ground away
from the wall at the rate of \( 3 c m / s \) The
height of the upper end while it is descending at the rate of \( 4 \mathrm{cm} / \mathrm{s} \), is
A. \( 4 \sqrt{3} m \)
В. \( 5 \sqrt{3} m \)
c. \( 5 \sqrt{2} m \)
D. \( 6 m \)
Subject: Chemistry
After electrolysis of a sodium chloride
solution with inert electrodes for a
certain period of time, \( 600 m L \) of the
solution was left which was found to be
\( 1 N \) in \( N a O H . \) During the same period
\( 31.75 g \) of copper was deposited in the copper voltameter in series with the
electrolytic cell. Calculate the percentage theoretical yield of \( N a O H \) obtained.
Subject: Physics
\( \operatorname{Let} \rho(r)=\frac{Q r}{4 \pi R^{4}} \) be the charge density
distribution of a solid sphere of radius \( R \) and total charge \( Q . \) Find the magnitude of electric field at a point \( \boldsymbol{P} \)
inside the sphere at a distance \( r_{1} \) from
the centre of the sphere.
A \( \cdot \frac{Q}{4 \pi^{2} \epsilon_{6} r_{1}^{2}} \)
в. \( \frac{Q r_{1}^{2}}{4 \pi^{2} \epsilon_{\epsilon} R^{4}} \)
c. \( \frac{Q r_{1}^{2}}{16 \pi \epsilon_{1} R^{4}} \)
D. 0
Subject: Physics
The balancing point in a meter bridge is \( 44 \mathrm{cm} . \) If the resistances in the
are gaps are inchanged the new balance point is
A. \( 44 \mathrm{cm} \)
B. 56 \( \mathrm{cm} \)
c. \( 50 \mathrm{cm} \)
D. 22 \( \mathrm{cm} \)
Subject: Physics
Four charges \( +\boldsymbol{Q},-\boldsymbol{Q},+\boldsymbol{Q},-\boldsymbol{Q} \) are
placed at the corners of a square taken order. At the centre of the square:
A. \( E=0, V=0 \)
B. \( E=0, V \neq 0 \)
c. \( E \neq 0, V=0 \)
D. \( E \neq 0, V \neq 0 \)
Subject: Chemistry
\( 0.6 \mathrm{g} \) of an organic compound when dissolved in 21.7 g water freezes at 272.187 K. The molar mass of the
organic compound is close to:
\( \left(K_{f} \text { of water is } 1.86 \) deg/molality; \right. freezing point is \( 273 \mathrm{K} \) )
A. \( 61 \mathrm{g} \) mol \( ^{-1} \)
B. \( 63 \mathrm{g} \) mol \( ^{-1} \)
\( \mathbf{c} \cdot 65 \mathrm{g} m o l^{-1} \)
D. \( 67 \mathrm{g} \) mol \( ^{-1} \)
Subject: Physics
If a electric flux leaving and entering
from closed surface are \( \phi \) and \( \phi \)
respectively, then the charge associated with closed surface will be
A \( \cdot \frac{\phi_{2}-\phi_{1}}{\varepsilon_{0}} \)
B. \( \frac{\phi_{1}+\phi_{2}}{\varepsilon_{0}} \)
c. \( \frac{\phi_{1}-\phi_{2}}{\varepsilon_{0}} \)
D \( \cdot \varepsilon_{0}\left(\phi_{2}-\phi_{1}\right) \)
Subject: Physics
A uniform field of \( 30 \mathrm{mT} \) exists in the \( +x \)
direction. A particle of charge +ve and
\( \operatorname{mass} 1.67 \times 10^{-27} \mathrm{kg} \) is projected
through the field in the \( +Y \) direction with
a speed of \( 4.8 \times 10^{6} m / s \)
(a) Find the force on the charged particle in magnitude and direction
(b) Find the force if the particle were negatively charged.
(c) Describe the nature of path followed by the particle in both the cases.
Subject: Physics
Match the following
a) step up transformer
d) turns ratio
is 1
e) \( \mathrm{Ns}>\mathrm{Np} \)
b) step down transformer
c) Ideal transformer
f) \( \mathrm{Np}>\mathrm{Ns} \)
A. a-f, b-e, c-d
B. a-e, b-d, c-f
c. a-d, b-e, c-f
D. a-e, b-f, c-d
Subject: Chemistry
Among the given compounds, the compound which is most susceptible to
a nucleophilic attack at the carbonyl
group is:
A \( \cdot C H_{3} C O C l \)
в. \( C H_{3} C H O \)
\( \mathbf{c} \cdot C H_{3} C O O C H_{3} \)
D. \( C H_{3} \) СООСОСН\( _{3} \)
Subject: Chemistry
State whether True or False.
Ozone is the oxidising agent in the following reaction:
\( \boldsymbol{O}_{3}(\boldsymbol{g})+\boldsymbol{H}_{2} \boldsymbol{O}_{2}(l) \rightarrow \boldsymbol{H}_{2} \boldsymbol{O}(l)+ \)
\( \mathbf{2} \boldsymbol{O}_{\mathbf{2}}(\boldsymbol{g}) \)
Subject: Maths
Let \( \boldsymbol{f}, \boldsymbol{g} \) and \( \boldsymbol{h} \) be functions from \( \boldsymbol{R} \) to \( \boldsymbol{R} \)
Show that
(i) \( (\boldsymbol{f}+\boldsymbol{g}) \boldsymbol{o} \boldsymbol{h}=\boldsymbol{f} \boldsymbol{o} \boldsymbol{h}+\boldsymbol{g} \boldsymbol{o} \boldsymbol{h} \)
(ii) \( (\boldsymbol{f} \cdot \boldsymbol{g}) \boldsymbol{o} \boldsymbol{h}=(\boldsymbol{f} \boldsymbol{o} \boldsymbol{h}) \cdot(\boldsymbol{g} \boldsymbol{o} \boldsymbol{h}) \)
Subject: Physics
in which two infinitely long static line charges of constant positive line charge
density \( \lambda \) are kept parallel to each other.
In their resulting electric field, point
charges \( \boldsymbol{q} \) and \( -\boldsymbol{q} \) are kept in
equilibrium between them. The point
charges are confined to move in the \( x \)
direction only. If they are given a small
displacement about their equilibrium positions, then the correct statement(s) is (are)
A. Both charges execute simple harmonic motion.
B. Both charges will continue moving in the direction of their displacement
c. Charge \( +q \) executes simple harmonic motion while charge \( -q \) continues moving in the direction of its displacement.
D. Charge \( -q \) executes simple harmonic motion while charge \( +q \) continues moving in the direction of its displacement
Subject: Maths
"If Tom buys a red skateboard then
Amanda buys green in-line skates".
Which statement below is logically equivalent?
A. If Amanda does not buy green in-line skates then Tom does not buy a red skateboard
B. If Tom does not buy a red skateboard then Amanda does not buy green in-line skates
C. If Amanda buys green in-line skates then Tom buys a red skateboard
D. If Tom buys a red skateboard then Amanda does not buy green in-line skates
Subject: Maths
\( f(x-1)(x+2)(x-3)=A+ \)
\( \frac{B}{(2 x-1)}+\frac{C}{(x+2)}+\frac{D}{(x-3)} \) then
\( \mathbf{A}= \)
A \( \cdot \frac{1}{2} \)
B. \( \frac{-1}{50} \)
\( c \cdot \frac{-8}{25} \)
D. \( \frac{27}{25} \)
Subject: Chemistry
Match list I with list II and select the
correct answer using the codes given
below the lists.
List - I List- 1
1.
Heavy
water
2. Temporary
hard
water
\( A \)
Bicarbonates of
\( M g \) and \( C a \) in
water
B. No foreign ions in
water
3. Softwater
permanent
hard
water
\( A \cdot 1-C, 2-D, 3-B, 4-A \)
B. \( 1- \) B, \( 2-A, 3-C, 4-D \)
\( c \cdot 1-B, 2-D, 3-C, 4-A \)
D. \( 1-C, 2-A, 3-B, 4-C \)
Subject: Maths
ff \( \Delta=\left|\begin{array}{lll}a r g z_{1} & a r g z_{2} & a r g z_{3} \\ a r g z_{2} & a r g z_{3} & a r g z_{1} \\ a r g z_{3} & a r g z_{1} & a r g z_{2}\end{array}\right|, \) the \( , \Delta \)
is divided by:
A \( \cdot \arg \left(z_{1}+z_{2}+z_{3}\right) \)
B \( \cdot \arg \left(z_{1} \cdot z_{2} \cdot z_{3}\right) \)
C \( \cdot\left(a r g z_{1}+a r g z_{2}+\arg z_{3}\right) \)
D. N.O.T
Subject: Physics
Match the terms in column I with those
of column II
\( \begin{array}{ll}\text { Column - I } & \text { Column - II } \\ \text { i. Electric fuse } & \text { A. Chemical effect } \\ \text { ii. Relay } & \text { B. Electric discharge } \\ \text { iii. CFL } & \text { C. Magnetic effect } \\ \text { iv. Button cell } & \text { D. Heating effect }\end{array} \)
iii-A, iv-D
\( A \cdot \) i-C, ii-B,
B. i-B, ii-A, iii-C, iv-D
c. i-D, ii-C, iii-B, iv-A
D. i-D, ii-B, iii-C, iv-D
Subject: Physics
The differential equation representing the SHM of a particule is \( \frac{\mathbf{9} d^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{t}^{2}}+\boldsymbol{4} \boldsymbol{Y}= \)
0.The time period of the particle is fiven
by
A \( \frac{\pi}{3} \sec \)
в. \( \pi \) sec
\( ^{\mathrm{c}} \cdot \frac{2 \pi}{3} s e c \)
D. \( 3 \pi s e c \)
Subject: Physics
Two resistors of resistances \( 2 \Omega \) and \( 6 \Omega \)
are connected in parallel. This
combination is then connected to a
battery of emf \( 2 \mathrm{V} \) and internal
resistance \( 0.5 \Omega . \) What is the current
flowing through the battery?
A. 4 A
в. \( \frac{4}{3} A \)
c. \( \frac{4}{17} A \)
D. 1A
Subject: Chemistry
When 0.1 mole of solid NaOH is added
in \( 1 \mathrm{L} \) of \( 0.1 \mathrm{M} N H_{3} \) (aq) then which
statement is going to be wrong?
\( \left(\boldsymbol{K}_{\boldsymbol{b}}=\mathbf{2} \times \mathbf{1 0}^{-\mathbf{5}}, \log \mathbf{2}=\mathbf{0 . 3}\right) \)
A. degree of dissociation of \( N H_{3} \) approaches to zero
B. Change in pH would be 1.85
c. concentration of \( \left[N a^{+}\right]=0.1 M,\left[N H_{3}\right],= \) \( 0.1 M,\left[O H^{-}\right]=0.2 M \)
D. on addition of \( O H^{-}, K_{b} \) of \( N H_{3} \) does not changes
Subject: Maths
A square of side \( a \) lies above the \( x \) -axis
and has one vertex at the origin. The side passing through it makes an angle \( \left(0<\alpha<\frac{\pi}{4}\right) \) with the positive direction of \( x \) -axis. The equation of its diagonal not through the origin
A \( \cdot y(\cos \alpha-\sin \alpha)-x(\sin \alpha-\cos \alpha)=a \)
B \cdot \( y(\cos \alpha+\sin \alpha)+x(\sin \alpha-\cos \alpha)=a \)
c. \( y(\cos \alpha+\sin \alpha)+x(\sin \alpha+\cos \alpha)=a \)
D・ \( y(\cos \alpha+\sin \alpha)+x(\cos \alpha-\sin \alpha)=a \)
Subject: Physics
If a rubber ball is taken down to a \( 100 \mathrm{m} \) deep lake, its volume decreases by \( 0.1 \% \)
If \( \boldsymbol{g}=\mathbf{1 0} \quad \boldsymbol{m} / \boldsymbol{s}^{2} \) then the bulk modulus
of elasticity for rubber, in \( \mathrm{N} / \mathrm{m}^{2} \), is
A \( \cdot 10^{8} \)
B . \( 10^{\text {9 }} \)
c. \( 10^{11} \)
D. \( 10^{10} \)
Subject: Physics
A square aluminium rod is \( 1 \mathrm{m} \) long and \( 5 \mathrm{mm} \) on edge. What must be the radius of another aluminium rod whose length
is \( 1 \mathrm{m} \) and which has the same
resistance as the previous rod?
A. \( 5.0 \mathrm{mm} \)
B. 4.2 mm
\( c .2 .8 \mathrm{mm} \)
D. \( 1.4 \mathrm{mm} \)
Subject: Chemistry
The charge on one mole electron is:
A . \( 1.6 \times 10^{-19} \mathrm{C} \)
B. \( 96500 C \)
\( c \cdot 6.02 \times 10^{-23} C \)
\( C \)
D. \( 1.6 \times 10^{-23} C \)