AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
Choose the pair of complementary angles.
A \( \cdot 30^{\circ}, 150^{\circ} \)
B. \( 76^{\circ}, 14^{\circ} \)
\( \mathbf{c} \cdot 65^{\circ}, 65^{\circ} \)
D. \( 120^{\circ}, 30^{\circ} \)
Subject: Maths
\( \frac{\boldsymbol{x}-\boldsymbol{y}}{\boldsymbol{x}}+\frac{1}{2}\left(\frac{\boldsymbol{x}-\boldsymbol{y}}{\boldsymbol{x}}\right)^{2}+\frac{1}{3}\left(\frac{\boldsymbol{x}-\boldsymbol{y}}{\boldsymbol{x}}\right)^{3}+ \)
\( \ldots= \)
\( \mathbf{A} \cdot \log _{e}(x+y) \)
B \( \cdot \log _{e} \frac{x}{y} \)
\( \mathbf{c} \cdot \log _{e}(x-y) \)
D \( \cdot \log _{e} \frac{y}{x} \)
Subject: Physics
The tension in a string holding a solid block below the surface of a liquid
(where \( \rho_{\text {liquid}}>\rho_{\text {block}} \) ) as in shown in
the figure is \( \boldsymbol{T} \) when the system is at rest.Then what will be the tension in the
string if the system has upward acceleration \( a \) ?
\( ^{\mathbf{A}} \cdot T\left(1-\frac{a}{g}\right) \)
в. \( T\left(1+\frac{a}{g}\right) \)
\( ^{\mathbf{c}} \cdot T\left(\frac{a}{g}-1\right) \)
D. \( \frac{a}{a} \)
Subject: Chemistry
The chemical reactions involved in
the extraction of metallic silver from
argentite is -
\( \mathbf{2} N \boldsymbol{a}\left[\boldsymbol{A} \boldsymbol{g}(\boldsymbol{C} \boldsymbol{N})_{2}\right]+\boldsymbol{Z} \boldsymbol{n} \rightarrow \)
\( \boldsymbol{N} \boldsymbol{a}_{2}\left[\boldsymbol{Z} \boldsymbol{n}(\boldsymbol{C} \boldsymbol{N})_{4}\right]+\boldsymbol{2} \boldsymbol{A} \boldsymbol{g} \downarrow \)
If the statement is true enter 1 else 0 .
Subject: Physics
Figure here shows the vertical cross-
section of a vessel filled with a liquid of
density \( \rho \)

The normal thrust per unit area on the
walls of the vessel at point \( P \) as shown
will be :
A \( . \) hog
в. Нр р
\( \mathbf{c} \cdot(H-h) \rho g \)
D \( \cdot(H-h) \) pgcos
Subject: Maths
The volume of a sphere of diameter \( 2 p \) cm is given by
A \( \cdot \pi p^{2} c m^{3} \)
В \( \cdot \pi p^{3} c m^{3} \)
\( \mathbf{c} \cdot 4 \pi p^{3} c m^{3} \)
D. \( \frac{4}{3} \pi p^{3} c m^{3} \)
Subject: Physics
A particular resistance wire has a resistance of 3.0 ohm per metre. The total resistance of three lengths of this wire each \( 1.5 \mathrm{m} \) long, joined in parallel
will be :
A \( .2 .5 \Omega \)
в. 3 \Omega
c. \( 4.5 \Omega \)
D. \( 1.5 \Omega \)
Subject: Physics
A particle with charge \( e \) and mass \( m \) moving along the X-axis with a uniform speed \( u \), enters a region where a
uniform electric field \( E \) is acting along
the Y-axis. The particle starts to move in a parabola. Its focal length (neglecting any effect of gravity) is :
\( ^{A} \cdot \frac{2 m u^{2}}{e E} \)
в. \( \frac{e E}{2 m u^{2}} \)
c. \( \frac{m u}{2 E} \)
D. \( \frac{m u^{2}}{2 e E} \)
Subject: Maths
If the common chord of the circle \( x^{2}+ \)
\( (y-\lambda)^{2}=16 \) and \( x^{2}+y^{2}=16 \)
subtend a right angle at the origin then \( \lambda \) is equal to
\( A \cdot 4 \)
B. \( 4 \sqrt{2} \)
\( c \cdot \pm 4 \sqrt{2} \)
\( D .8 \)
Subject: Maths
Suppose that on the interval [-2,4] the function \( f \) is differentiable, \( f(2)=1 \)
and \( |\boldsymbol{f}(\boldsymbol{x})| \leq \mathbf{5} . \) Find the bounding
function of \( \boldsymbol{f} \) on \( [-\mathbf{2}, \mathbf{4}], \) using LMVT.
A. \( y=-5 x-9 \) and \( y=5 x+11 \)
B. \( y=-5 x+9 \) and \( y=5 x+11 \)
c. \( y=5 x-9 \) and \( y=5 x-11 \)
D. \( y=5 x+9 \) and \( y=5 x-11 \)
Subject: Physics
A hemisphere and a solid cone of same
density have a common base. The
centre of mass of the common structure
coincides with the centre of the
common base. If \( \boldsymbol{R} \) is the radius of
hemisphere and \( h \) is height of the cone, then :
\( \mathbf{A} \cdot \frac{h}{R}=\sqrt{3} \)
B. \( \frac{h}{R}=\frac{1}{\sqrt{3}} \)
\( ^{\mathbf{C}} \cdot \frac{h}{R}=3 \)
D \( \cdot \frac{h}{R}=\frac{1}{3} \)
Subject: Physics
A particle experiences a positiondependent force given by
\[
\boldsymbol{F}(\boldsymbol{x})=-\boldsymbol{6} \boldsymbol{x}^{2}+\boldsymbol{4} \boldsymbol{x}+\boldsymbol{3} / \boldsymbol{x}^{2}
\]
where \( x \) is in meters and \( F \) is in
Newtons (units have been abbreviated).
At \( x=1 m, \) what is the potential energy
of the particle relative to the potential energy at the origin?
A . \( +5 J \)
в. \( +3 J \)
\( c .-3 J \)
D. \( -5 . J \)
E. Cannot be determined
Subject: Chemistry
In which of the following pair of reactions first reaction is spontaneous
while second reaction is non
spontaneous?
\( \mathbf{A} \cdot(\mathbf{i})-S H+H_{2} O \rightarrow H_{2} S+O H^{-} \)
(ii) \( N H_{2}^{-}+H_{2} O \rightarrow N H_{3}+O H^{-} \)
B. (i) - \( O R+H_{2} S O_{4} \rightarrow R O H+H S O_{4}^{-} \)
(ii) \( R^{-}+N H_{3} \rightarrow R H+N H_{2}^{-} \)
C . (i) \( C l^{-}+H F \rightarrow H C l+F^{-} \)
(ii) \( -O H+H C l \rightarrow H_{2} O+C l^{-} \)
D. \( \left(\text { i) }-O H+H B r \rightarrow H_{2} O+B r^{-}\right. \)
(ii) \( R O^{-}+N H_{3} \rightarrow R O H+N H_{2}^{-} \)
Subject: Chemistry
From 2 mg calcium \( 1.2 \times 10^{19} \) atoms
are removed. The number of \( g \) - atoms of calcium left is \( (\boldsymbol{C} \boldsymbol{a}=\mathbf{4 0}) \)
A \( .5 \times 10^{-5} \)
В. \( 2 \times 10^{-5} \)
c. \( 3 \times 10^{-5} \)
D. \( 5 \times 10^{-6} \)
Subject: Chemistry
The energies of activation for \( \boldsymbol{A}_{\mathbf{2}}+ \)
\( B_{2} \rightleftharpoons 2 A B \) are \( 180 k J \) mol \( ^{-1} \) forward
and \( 200 k J \) mol \( ^{-1} \) reverse reactions
respectively. The presence of catalyst lowers the activation energies of both
(forward and reverse) reactions \( \left(\boldsymbol{A}_{2}+\right. \)
\( B_{2} \rightleftharpoons 2 A B \) by \( 100 k J \) mol \( ^{-1} . \) The
magnitude of enthalpy change of the
reaction in the presence of catalyst will be \( \left(\text { in } \mathbf{k} \text { J } \boldsymbol{m} \boldsymbol{o} \boldsymbol{l}^{-1}\right) \)
A. 300
B. 120
c. 20
D. -20
Subject: Physics
An iron block of side \( 50 c m \times 8 c m \times \)
\( 15 c m \) has to be pushed along the floor.
The force required will be minimum
when the surface in contact with
ground is:
A. \( 8 c m \times 15 c m \) surface
B. \( 5 \mathrm{cm} \times 15 \mathrm{cm} \) surface
\( \mathrm{c} .8 \mathrm{cm} \times 5 \mathrm{cm} \) surface
D. force is same for all surfaces
Subject: Chemistry
When sodium acetate \( \left(\boldsymbol{C H}_{3} \boldsymbol{C O O N} \boldsymbol{a}\right) \)
is added to aqueous solution of acetic
\( \operatorname{acid}\left(\boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C O O H}\right) \)
A. the pH value become zero
B. pH value reamains unchanged
c. pH value deacreases
D. pH value increases
Subject: Chemistry
The major product obtained
when benzene reacts with
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{C I} \) in presence of
anhydrous \( A l C l_{3} \) is
\( A \)
B.
\( c \)
D. None of these
Subject: Physics
In a Zener regulated power supply a
Zener diode with \( V_{z}=6.0 V \) is used for
regulation. The load current is to be \( 4.0 m A \) and the unregulated input is
\( 10.0 V . \) What should be the value of
series resistor \( \boldsymbol{R}_{s} \)
Subject: Physics
If the radius of earth decreases by \( 10 \% \) the mass remaining unchanged, what will happen to the acceleration due to gravity?
A. Decreases by \( 19 \% \)
B. Increases by \( 19 \% \)
c. Decreases by more than \( 19 \% \)
D. Increases by more than \( 19 \% \)
Subject: Biology
TACAAAGGGTTTCAACCC if it is the
sequence of nucleotides in a DNA
strand, they predict the sequence of aminoacids found a protein formed from it.
A. Proline, pherrylalanine, , Iysine, methionine, glycine, valine
B. Methionine, pherrylalanine, glycine, valine, lysine proline
c. Valine, Glycine, proline, lysine, pherrylalanine, methionine
D. Methionine, pherrylalanine, proline, lysine, valine glycine
Subject: Chemistry
Identify the correct statement(s) about
orthoboric acid.
This question has multiple correct options
A. It has a layer structure in which planar \( B O_{3} \) units are joined by hydrogen bonds
B. Orthoboric acid \( \left(H_{3} B O_{3}\right) \) is a weak monobasic Lewis acid
c. on heating ortho-boric acid form meta-boric acid and on further heating to red hot,forms boric oxide anhdride
D. None of the above
Subject: Physics
Two unknown resistrance \( X \) and \( Y \) are
connected to left and right gaps of a meter bridge and the balancing point is obtained at \( 80 \mathrm{cm} \) from left. When a \( 10 \Omega \) resistance is connected in paralle to \( x \) the balance point is \( 50 \mathrm{cm} \) from left. The values of \( X \) and \( Y \) respectively are
\( A \cdot 40 \Omega, 9 \Omega \)
B. 30\Omega ,7.5\Omega
c. \( 20 \Omega, 6 \Omega \)
D. \( 10 \Omega, 3 \Omega \)
Subject: Maths
A terahedron has vertices \( \boldsymbol{P}(\mathbf{1}, \mathbf{2}, \mathbf{1}) \)
\( Q(2,1,3), R(-1,1,2) \) and \( O(0,0,0) \)
The angle between the faces OPQ and PQR is :
A \( \cdot \cos ^{-1}\left(\frac{9}{35}\right) \)
B. \( \cos ^{-1}\left(\frac{19}{35}\right) \)
c. \( \cos ^{-1}\left(\frac{17}{31}\right) \)
D. \( \cos ^{-1}\left(\frac{7}{31}\right) \)
Subject: Maths
In a battle \( 70 \% \) of the combatants lost
one eye, \( 80 \% \) an ear, \( 75 \% \) an arm, \( 85 \% \) a
leg, \( x \% \) lost all the four limbs the
minimum value of \( x \) is
A . 10
B. 12
c. 15
D.
Subject: Physics
The following bodies are made to roll up
(without slipping) the same inclined plane from a horizontal plane: (i) a ring of radius \( R, \) (ii) a solid cylinder of radius \( \frac{\boldsymbol{R}}{\mathbf{2}} \) and (iii) a solid sphere of radius \( \frac{R}{4} . \) If in each case, the speed of the centre of mass at the bottom of the
incline is same, the ratio of the
maximum heights they climb is:
A .4: 3: 2
B. 14: 15: 20
c. 10: 15: 7
D. 2: 3: 4
Subject: Maths
\( \boldsymbol{A} \cup(\boldsymbol{B} \cap \boldsymbol{C})=(\boldsymbol{A} \cup \boldsymbol{B}) \cap(\boldsymbol{A} \cup \boldsymbol{C}) \)
where \( \boldsymbol{A}= \)
\( \{1,2,4,5\}, B\{2,3,5,6\}, C= \)
\{4,5,6,7\} is \( A \cup(B \cap C)= \)
\( \{1,2, a, b, 6\} \) Find \( a+b \)
Subject: Chemistry
The kinetic energy of \( 2.8 g \) of nitrogen
\( \operatorname{gas} \operatorname{at} 127^{\circ} C \) is nearly
A \( .2 \times 249.3 J \)
В. \( 2 \times 200.4 J \)
C . \( 2 \times 25 J \)
D. \( 20.5 J \times 2 \)
Subject: Maths
\( \int\left\{\frac{(\log x-1)}{\left(1+(\log x)^{2}\right.}\right\}^{2} d x \) is equal to
A \( \frac{\log x}{(\log x)^{2}+1}+c \)
B. \( \frac{x}{x^{2}+1}+c \)
c. \( \frac{x e^{x}}{1+x^{2}}+c \)
D. \( \frac{x}{(\log x)^{2}+1}+c \)
Subject: Chemistry
The electrode with reaction:
\( \boldsymbol{C r}_{2} \boldsymbol{O}_{7}^{2-}(\boldsymbol{a q})+\mathbf{1 4 H}^{\oplus}(\boldsymbol{a q})+\boldsymbol{6} \boldsymbol{e}^{-} \rightarrow \)
\( 2 C r^{3+}(a q)+7 H_{2} O \) can be
represented as:
A \( \cdot P t \mid H^{\oplus}(a q), C r_{2} O_{7}^{2-}(a q) \)
B. \( P t \mid H^{\oplus}(a q), C r_{2} O_{7}^{2-(a q)}, C r^{3+}(a q) \)
C. \( P t_{H_{2}} \mid H^{\oplus}(a q), C r_{2} O_{7}^{2} \)
D. \( P t_{H_{2}} \mid H^{\oplus}(a q), C r_{2} O_{7}^{2-}(a q), C r^{3+}(a q) \)
Subject: Chemistry
The atomic masses of He and Ne are 4
and 20 a.m.u. respectively. The value of the de Broglie wavelength of He gas at
\( -73^{\circ} \mathrm{C} \) is \( \mathrm{M} \) times that of the de Broglie
wavelength of Ne at \( 727^{\circ} \mathrm{C} . \) M is:
Subject: Chemistry
For Adsorption phenomenon:
\( \mathbf{A} \cdot \Delta H=+v e, \Delta S=-v e \)
B . \( \Delta H=-v e, \Delta S=+v e \)
\( \mathbf{c} \cdot \Delta H=-v e, \Delta S=-v e \)
D. \( \Delta H=+v e, \Delta S=+v e \)
Subject: Chemistry
The voltage of the cell given below is
\( -0.46 V \)
\( \boldsymbol{P t}\left|\begin{array}{cc}\boldsymbol{N a H} \boldsymbol{S O}_{3} & \boldsymbol{N a}_{2} \boldsymbol{S O}_{3} \\ \boldsymbol{0 . 4} \boldsymbol{M} & \boldsymbol{6 . 4 4} \times \mathbf{1 0}^{-3} \boldsymbol{M}\end{array}\right|\left|\begin{array}{c}\boldsymbol{Z} \boldsymbol{n}^{2+} \\ \boldsymbol{0} . \boldsymbol{3} \boldsymbol{M}\end{array}\right| \)
Also, \( Z n^{2+}+2 e \rightarrow Z n(s) ; E^{o}= \)
\( -0.763 V \)
The value of \( \boldsymbol{K}_{2} \) where \( \boldsymbol{K}_{2}= \) \( \frac{\left[\boldsymbol{H}^{+}\right]\left[\boldsymbol{S O}_{3}^{2-}\right]}{\left[\boldsymbol{H} \boldsymbol{S O}_{3}^{-}\right]} \mathbf{i s} \)
A . \( 6.44 \times 10^{-8} \)
B. \( 5.43 \times 10^{-8} \)
c. \( 7.34 \times 10^{-8} \)
D. None of these
Subject: Physics
At constant pressure and at a temperature of \( 27^{0} \mathrm{C}, \) if the volume of a
given amount of gas is to be raised three times, the temperature to which the gas should be heated is
A \( \cdot 27^{0} \mathrm{c} \)
B. \( 625^{\circ} \) С
c. \( 627^{\circ} \) С
D. \( 273^{0} \mathrm{C} \)
Subject: Physics
A car runs at constant speed on a circular track of radius \( 100 \mathrm{m} \) taking
\( 62.8 \mathrm{s} \) on each lap. What is the average speed and average velocity on each complete lap? \( (\boldsymbol{\pi}=\mathbf{3 . 1 4}) \)
A. Velocity 10 \( \mathrm{m} / \mathrm{s} \), speed \( 10 \mathrm{m} / \mathrm{s} \)
B. Velocity zero, speed 10 m/s
c. Velocity zero, speed zero
D. Velocity 10 \( \mathrm{m} / \mathrm{s} \), speed zero
Subject: Maths
The radius of a spherical balloon increases from \( 7 \mathrm{cm} \) to \( 14 \mathrm{cm} \) as air is
being pumped into it. Find the ratio of
surface areas of the balloon in the two
cases.
A .1: 4
B . 4: 1
c. 1: 2
D. 2: 1
Subject: Physics
A body takes 10 minutes to cool from
\( 60^{\circ} \mathrm{C} \) to \( 50^{\circ} \mathrm{C} . \) The temperature of
surroundings is constant at \( 25^{\circ} \mathrm{C} \). Then, the temperature of the body after next
10 minutes will be approximately
A \( \cdot 43^{\circ} \mathrm{C} \)
В . \( 47^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 41^{\circ} C \)
D. \( 45^{\circ} \mathrm{C} \)
Subject: Physics
Assertion
Rainy clouds appear dark from below.
Reason

There is not sufficient light which can
be scattered by these clouds.
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
un treatment wırn cola water, an
element (A) reacts readily liberating a
colorless, odourless gas \( (\mathrm{B}) \) and \( \mathrm{a} \) solution (C). Lithium is reacted with (B)
yielding a solid product (D) which effervescence with water to give a
strongly basic solution (E). When \( C O_{2} \)
gas is bubbled through the solution \( (\mathrm{C}) \) a white ppt (F) is formed but this
redissolved forming solution (G) when
more \( C O_{2} \) is passed. The precipitate \( (F) \)
effervesced when moistened with conc.
\( H C l \) and give deep red coloration to the
Bunsen burner flame. (F) on heating
with an excess of carbon at \( 2000^{\circ} C \)
give (H).

Solid (H) on hydrolysis gives a gas, which on passing through ammonical
\( A g N O_{3} \) solution, yields:
A. white ppt
B. red ppt
C. no ppt
D. brown ppt
Subject: Maths
If \( p q=3, \) then \( p^{3} q^{4}+p^{4} q^{5}= \)
A \( \cdot 12 q \)
в. \( 7 p+9 q \)
c. \( 12 p+20 q \)
D. \( 96 p \)
E. \( 108 q \)
Subject: Maths
The area bounded by the \( y \) -axis, \( y= \) \( \cos x \) and \( y=\sin x \) when \( 0 \leq x \leq \frac{\pi}{2} \)
A \( \cdot 2(\sqrt{2}-1) \)
B. \( \sqrt{2}-1 \)
\( c \cdot \sqrt{2}+1 \)
D. \( \sqrt{2} \)
Subject: Physics
A screen is placed \( 2 \mathrm{m} \) away from a single narrow slit. The slit width if the first minimum lies \( 5 \mathrm{mm} \) on either side
of the central maximum is:
(wave length \( =5000 A^{\circ} \) )
A . \( 0.01 \mathrm{cm} \)
B. \( 0.02 \mathrm{cm} \)
\( c .0 .03 c m \)
D. \( 0.04 \mathrm{cm} \)
Subject: Physics
In X-ray spectrum, transition of an electron from an outer shell to an inner
shell gives a characteristics X-ray spectral line. If we consider the spectral
\( \operatorname{lines} K_{\beta}, L_{\beta}, M_{\alpha} \) then
A. \( K_{\beta} \) and \( L_{\beta} \) have a common inner shell
B. \( K_{\beta} \) and \( L_{\beta} \) have a common outer shell
c. \( L_{\beta} \) and \( M_{\alpha} \) have a common outer shel 1
D. \( L_{\beta} \) and \( M_{\alpha} \) have a common inner shell
Subject: Chemistry
The number of electrons involved in
electrode reaction by 1 coulomb charge is:
A \( \cdot 6.85 \times 10^{14} \)
B. \( 19.85 \times 10^{18} \)
c. \( 6.85 \times 10^{18} \)
D. \( 16.85 \times 10^{15} \)
Subject: Biology
Select the correct option:
Identify the types of vascular bundle in the figures (i) and (ii) and select the correct option.
conjoint
(A) Conjoint collateral - \( \quad \) bicollatera
(B) Conjoint bicollateral- - conjoint collateral
C) Conjoin Conjoin open
D) Conjoint collatera conjoint closed
\( A \)
B. B
\( c \cdot c \)
\( D \cdot D \)
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
Boltzmann's constant and \( \theta \) is
temperature. The dimension of \( \beta \) are.
A \( \cdot M^{0} L^{0} T^{0} \)
B. \( M^{-1} L^{-1} T^{-1} \)
\( \mathbf{c} \cdot M^{0} L^{2} T^{0} \)
D. \( M^{-1} L^{1} T^{2} \)
Subject: Maths
If \( f(x)= \) \( \left\{\begin{array}{cc}(\mathbf{1}+|\sin \boldsymbol{x}|)^{\frac{a}{|\sin |}} & ;-\frac{\pi}{6}<\boldsymbol{x}<\mathbf{0} \\ \boldsymbol{b} & ; \boldsymbol{x}=\mathbf{0} \\ \boldsymbol{e}^{\left(\frac{\tan 2 x}{\tan 3 x}\right)} & ; \mathbf{0}<\boldsymbol{x}<\frac{\pi}{\mathbf{6}}\end{array}\right. \)
is a continuous function on \( \left(-\frac{\pi}{6}, \frac{\pi}{6}\right) \)
then
A \( \cdot a=\frac{2}{3}, b=e^{2} \)
в. \( a=\frac{1}{3}, b=e^{1 / 3} \)
c. \( _{a=\frac{2}{3}, b=e^{2 / 3}} \)
D. \( a=e^{2 / 3}, b=\frac{2}{3} \)
Subject: Maths
Find the variance of the following distribution
\( \begin{array}{llll}\text { Class } & \mathbf{3 . 5}- & \mathbf{4 . 5}- & \mathbf{5 . 5 -} \\ \text { interval } & \mathbf{4 . 5} & \mathbf{5 . 5} & \mathbf{6 . 5}\end{array} \)
Frequency
14
Subject: Chemistry
Assertion
STATEMENT-1: An alcohol does not react
with \( C l^{-} \) ion in aqueous medium, but
reacts with concentrated \( H C I \) solution
to form alkyl chloride.
Reason
STATEMENT-2: The strong acid \( (\boldsymbol{H} \boldsymbol{C} \boldsymbol{I}) \) accelerates the removal of proton from
\( -O H \) group of alcohol
A. STATEMENT-1 is True, STATEMENT-2 is True STATEMENT-2 is a correct explanation for STATEMENT-
B. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1
C. STATEMENT-1 is True, STATEMENT-2 is False
D. STATEMENT-1 is False, STATEMENT-2 is True
Subject: Physics
Two sound speakers are driven in phase by an audio amplifier at frequency \( 600 H z . \) The speed of sound is \( 340 m / s \)
The speakers are on the \( y \) -axis, one at \( \boldsymbol{y}=+\mathbf{1 . 0 m} \) and the other at \( \boldsymbol{y}= \)
\( -1.0 m . \) A listener begins at \( y=0 \) and
walks along a line parallel to the \( y \) -axis
at a very large distance \( x \) away. How
many maxima can she possibly hear if she keeps walking in the same direction?
Subject: Maths
Chords \( M N \) and \( R S \) of a circle
intersect at \( \boldsymbol{P} \) outside the circle If
\( \boldsymbol{P N}=\mathbf{3} \boldsymbol{c m}, \boldsymbol{M} \boldsymbol{N}=\mathbf{5} \boldsymbol{c m}, \boldsymbol{P} \boldsymbol{R}=\boldsymbol{2} \boldsymbol{c m} \)
then the value of \( S R \) is equal to
\( \mathbf{A} \cdot 5 \mathrm{cm} \)
B. \( 8 \mathrm{cm} \)
c. \( 15 \mathrm{cm} \)
D. \( 10 \mathrm{cm} \)
Subject: Physics
The displacement of a particle performing linear S.H.M is given by \( \boldsymbol{x}= \) \( 6 \sin (3 \pi t-5 \pi / 6) \) metre. Find the time
at which the particle reaches the extreme position towards the left:
A. \( 5 / 9 \) secs
B . 4/9 secs
c. \( 1 / 9 \) secs
D. 7/9 secs
Subject: Physics
The nucleus \( ^{23} N e \) decays by \( \beta- \) emission into the nucleus \( ^{23} N a \). Write
down the \( \beta- \) decay equation and determine the maximum kinetic energy of the electrons emitted. Given,
\( \boldsymbol{m}\left(_{\mathbf{1 0}}^{23} \boldsymbol{N} \boldsymbol{e}\right)=\mathbf{2 2 . 9 9 4 4 6 6 a m u} \) and
\( \boldsymbol{m}\left(_{11}^{23} \boldsymbol{N a}\right)=22.989770 a m u . \) Ignore the
mass of antineutrino \( (\overline{\boldsymbol{v}}): \)
Subject: Physics
Air in a sealed syringe is slowly
compressed by moving the piston. The
temperature of the air stays the same. Which statement about the air is
correct?
A. The pressure of the air increases because its molecules now travel more slowly
B. The pressure of the air increases because the area of the syringe walls is now smaller.
C. The pressure of the air increases because its molecules now hit the syringe walls more frequently
D. The pressure of the air increases because its molecules now travel more quickly
Subject: Maths
Which of the following statement is true about a rational number \( \frac{-2}{3} ? \)
A . It lies to the left side of \( ^{\prime} 0^{\prime} \) on the number line
B. It lies to the right side of ' \( 0^{\prime} \) on the number line
c. It is not possible to represent on the number line.
D. It cannot be determined on which side the number lies
Subject: Physics
If the polarizing angle of a piece of glass
for green light is \( 54.74^{\circ}, \) then the angle of minimum deviation for an equilateral prism made of same glass is :
\( \left[\mathrm{GIVEN}, \tan 54.74^{\circ}=1.414\right] \)
A \( \cdot 45^{\circ} \)
B. 54.74
\( c \cdot 60 \)
\( D \cdot 30^{\circ} \)
Subject: Maths
If in the expansion of \( (1+y)^{n}, \) the
coefficient of \( 5^{t h}, 6^{t h} \) and \( 7^{t h} \) terms are
in A.P., then \( n \) is equal to:
A .7,11
в. 7,14
\( c \cdot 8,16 \)
D. none of the above
Subject: Maths
Assertion
The matrix \( \boldsymbol{A}=\left(\begin{array}{ccc}\mathbf{0} & \boldsymbol{a} & \boldsymbol{b} \\ -\boldsymbol{a} & \mathbf{0} & \boldsymbol{c} \\ -\boldsymbol{b} & -\boldsymbol{c} & \mathbf{0}\end{array}\right) \) is a
skew symmetric matrix.
Reason
A square matrix \( \boldsymbol{A}=\left(\boldsymbol{a}_{\boldsymbol{i} j}\right) \) of order \( \mathbf{m} \) is
said to be skew symmetric if \( \boldsymbol{A}^{\boldsymbol{T}}=-\boldsymbol{A} \)
A. Both (A) \& (R) are individually true \& (R) is correct explanation of (A),
B. Both (A) \&
(R) are individually true but (R) is not the correct (proper) explanation of (A).
C. (A)is true but (R) is false,
D. (A)is false but (R) is true.
Subject: Physics
A metal ball of radius \( 1 m m \) and density \( 10^{4} \mathrm{kg} \mathrm{m}^{-3} . \) falls freely in air through a height 'h' before falling in a tank full of
water. If on falling in water its velocity remains unchanged, then the value of h will be (Coefficient of viscosity of
water \( =10^{-3} \) Pa.s and \( g=10 m s^{-2} \)
A . \( 10 m \)
B. \( 15 \mathrm{m} \)
\( c .25 m \)
D. \( 20 m \)
Subject: Maths
The equations of line \( A B \) and line \( P Q \) are
\( y=-\frac{1}{2} x \) and \( y=2 x \) respectively. Find the
measure of angle \( \angle \mathrm{BOQ} \) which is formed by intersection of line \( A B \) and line PQ. (Point P and point A are in first and second quadrant respectively)
A \( \cdot 60^{\circ} \)
B. \( 150^{\circ} \)
\( c \cdot 90^{\circ} \)
D. \( 120^{\circ} \)
Subject: Physics
Vertical displacement of a plank with a body of mass \( m \) on it is varying according to law \( y=\sin \omega t+\sqrt{3} \cos \omega t \)
The minimum value of \( \omega \) for which the
mass just breaks off the plank and the moment it occurs first after \( t=0, \) are
given by
A. \( \sqrt{g / 2}, \frac{\sqrt{2}}{6} \frac{\pi}{\sqrt{g}} \)
в. \( \frac{g}{\sqrt{2}}, \frac{2}{3} \sqrt{\pi / g} \)
c. \( \sqrt{g / 2}, \frac{\pi}{3} \sqrt{2 / g} \)
D. \( \sqrt{2 g}, \sqrt{2 \pi / 3 g} \)
Subject: Maths
If \( \boldsymbol{A}-\boldsymbol{B}=\boldsymbol{\phi} \) and \( \boldsymbol{B}-\boldsymbol{A}=\boldsymbol{\phi}, \) then \( \mathbf{A} \)
and B are
A. Overlapping
B. Equivalent
c. Disjoint
D. Equal