AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
If the heat of formation of \( N O_{2} \) is 'x'
\( \left[1 / 2 N_{2(g)}+O_{2(g)} \rightarrow N O_{2(g)}\right] \) the heat of
reaction \( N_{2(g)}+O_{2(g)} \rightarrow 2 N O_{(g)} \) is y
and the heat of reaction \( 2 N O_{(g)}+ \) \( O_{2(g)} \rightarrow 2 N O_{2(g)} \) is z, then:
A. \( 2 x+z=y \)
в. \( 2 y+z=x \)
c. \( 2 x-z=y \)
D. \( 2 z+x=y \)
Subject: Physics
A charged conducting sphere has diameter \( 2.4 m \) and surface charge
density \( 10 \mu C / m^{2} . \) Electric flux passing through its surface will be:-
A \( \cdot 8.17 \times 10^{7} \mathrm{Nm}^{2} / \mathrm{C} \)
В . \( 16 \times 10^{7} \mathrm{Nm}^{2} / \mathrm{C} \)
c. \( 1 \times 10^{6} \mathrm{Nm}^{2} / \mathrm{C} \)
D . \( 2.2 \times 10^{8} \mathrm{Nm}^{2} / \mathrm{C} \)
Subject: Chemistry
Two metallic oxides contain \( 27.6 \% \) and
\( 30 \% \) oxygen respectively. If the formula
of the first oxide is \( X_{3} O_{4}, \) that of the
second will be ?
A. \( X O \)
B. \( X O_{2} \)
\( \mathrm{c} \cdot \mathrm{X}_{2} \mathrm{O}_{5} \)
D. \( X_{2} O_{3} \)
Subject: Maths
IF \( f(x)=x^{2} \) for \( 0 \leq x \leq 1, \sqrt{x} \) for \( 1 \leq \) \( x \leq 2 \) then \( \int_{0}^{2} f(x) d x= \)
A \( \cdot \frac{4 \sqrt{2}}{3} \)
B. \( \frac{4 \sqrt{2}-1}{3} \)
c. \( \frac{\sqrt{2}}{3} \)
D.
Subject: Physics
A field of \( 100 \mathrm{Vm}^{-1} \) is directed at \( 30^{\circ} \mathrm{to} \)
positive x-axis. Find \( \left(V_{A}-V_{B}\right) \) if
\( O A=2 m \) and \( O B=4 m \)
A \( \cdot 100(\sqrt{3}-2) V \)
B . \( -100(2+\sqrt{3}) V \)
c. \( 100(2-\sqrt{3}) v \)
D \( \cdot 200(2+\sqrt{3}) v \)
Subject: Maths
Consider the following statements:
\( \frac{1}{22} \) can not be written as terminating decimal
2. \( \frac{2}{15} \) can be written as a terminating decimal
3. \( \frac{1}{16} \) can be written as a terminating decimal

Which of the statements given above is/are correct?
A. 1 only
B. 2 only
c. 1 and 3
D. 2 and 3
Subject: Chemistry
Assertion
lonization takes place in polar covalent
compounds
Reason
It involves transfer of electron from less
electronegative to more electronegative element to form charged species
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
The objects pictured above are coins moving around on a record player. The coins are not sliding on the record player surface. Which coins is moving faster and how many times faster it is moving than the other one? The space between each vertical line along the horizontal arrow is one-
seventh the radius of the circular record
player surface.
A. 1-three times faster than slowest
B. 3-five-seventh's faster than slowest
c. 3-five times faster than slowest
D. 1-five-seventh's faster than slowest
E. 2 -three-seventh's faster than slowest
Subject: Physics
A metal ball \( B_{1} \) (density \( 3.2 g / c c \) ) is dropped in water, while another metal
ball \( B_{2} \) (density \( 6.0 g / c c \) ) is dropped in
a liquid of density \( 1.6 g / c c \). If both the
balls have the same diameter and
attain the same terminal velocity, the ratio of viscosity of water to that of the liquid is
A . 2.0
B. 0.5
c. 4.0
D. Indeterminate due to insufficient dat
Subject: Maths
Two dice are thrown:
\( P \) is the event that the sum of the
scores on the uppermost faces is a
multiple of 6
\( Q \) is the event that the sum of the
scores on the uppermost faces is at
least 10
\( R \) is the event that same scores on both
dice.

Which of the following pairs is mutually exclusive?
A. \( P, Q \)
в. \( P, R \)
\( \mathbf{c} \cdot Q, R \)
D. None of these
Subject: Physics
Assertion
A conducting equilateral loop abc is
moved translationally with constant
speed \( \boldsymbol{v} \) in uniform inward magnetic
field \( B \) as shown. Then: \( V_{a}-V_{b}= \)
\( \boldsymbol{V}_{\boldsymbol{b}}-\boldsymbol{V}_{\boldsymbol{c}} \)
Reason
Point \( a \) is at higher potential than point
\( \boldsymbol{b} \)
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
Subject: Maths
If the roots of \( a x^{3}+b x^{2}+c x+d=0 \)
are in H.P., then the roots of \( d x^{3}-c x^{2}+ \)
\( b x-a=0 \) are in
A. A.P
в. с.
c. н.
D. A.G.P
Subject: Chemistry
Match the column I with column II and
mark the appropriate choice.
Column I
(A) \( 3 d \) -transition series
(i) Z=58 to Z=71
(B) Lanthanoid series
(ii) \( \mathrm{Z}=39 \) to \( \mathrm{Z}=48 \)
(C) Actinoid series
(iii) \( z=21 \) to \( z=30 \)
(D) 4d-transition series
(iv) \( z=90 \) to \( z=103 \)
\( A \cdot(A) \rightarrow(i),(B) \rightarrow(i i),(C) \rightarrow(i i i),(D) \rightarrow(i v) \)
B. (A) \( \rightarrow \) (ii), (B) \( \rightarrow \) (iii), (C) \( \rightarrow \) (iv), (D) \( \rightarrow \) (i)
C. \( (A) \rightarrow(\text { iii) },(B) \rightarrow(i),(C) \rightarrow(i v),(D) \rightarrow(\text { ii }) \)
D. \( (A) \rightarrow(\text { iv) },(B) \rightarrow(\text { iii) },(C) \rightarrow(i),(D) \rightarrow\text { (ii) } \)
Subject: Maths
The solution of \( y d x+x d y=d x+d y \) is:
A. \( x y=x+y+c \)
В \( \cdot x-y \frac{x}{y}+c=0 \)
c. \( x y-x+y=c \)
D. \( x+y \frac{x}{y}+c=0 \)
Subject: Physics
Prakash peddles a stationary bicycle, the pedals of which are attached to a
100 turn coil of area \( 0.1 m^{2} . \) The coil
rotates at half a revolution per second
and it is placed in a uniform magnetic field of \( 0.01 T \) perpendicular to the axis
of rotation of the coil. Determine the
maximum voltage generated in the coil.
Subject: Physics
For a particle in SHM, if the amplitude of the displacement is \( \alpha \) and the
amplitude of velocity is \( v, \) the amplitude of acceleration is
A \( . v \alpha \)
в. \( \frac{v^{2}}{\alpha} \)
c. \( \frac{v^{2}}{2 \alpha} \)
D. \( \underline{v} \)
Subject: Physics
The distance between earth and moon
is about \( 3.8 \times 10^{5} k m . \) At what point(s)
will the net gravitational force of earthmoon system be zero? [Given mass of
earth is 81 times the moon's mass)
\( \mathbf{A} \cdot 38 \times 10^{9} m \)
B . \( 38 \times 10^{7} m \)
c. \( 8 \times 10^{7} m \)
D. \( 3.8 \times 10^{7} m \)
Subject: Maths
\( \sin ^{-1} \mathbf{6} \boldsymbol{x}+\boldsymbol{\operatorname { s i n }}^{-1} \boldsymbol{6} \sqrt{\mathbf{3}} \boldsymbol{x}=-\boldsymbol{\pi} / 2 \) if \( \mathbf{x} \) is
equal to
A . - \( -1 / 12 \)
B. 1/6
\( c \cdot 1 / 12 \)
D. -1/6
Subject: Physics
An electron is projected from a distance
\( d \) and with initial velocity \( u \) parallel to a uniformly charged flat conducting plate
as shown. It strikes the plate after
travelling a distance \( \ell \) along the direction of projection. The surface
charge density of the conducting plate is equal to
A \( \cdot \frac{2 d \varepsilon_{0} m u^{2}}{e \ell^{2}} \)
B. \( \frac{2 d \varepsilon_{0} m u}{e \ell^{2}} \)
c. \( \frac{d \varepsilon_{0} m u^{2}}{e \ell} \)
D. \( \frac{d \varepsilon_{0} m u}{e l} \)
Subject: Chemistry
Predict product(s) in the following reaction:
\( \boldsymbol{C l}_{2}+\boldsymbol{O} \boldsymbol{H}^{-} \stackrel{\boldsymbol{h} o t}{\rightarrow} \)
This question has multiple correct options
A \( \cdot C l \)
в. \( C l O_{2} \)
c. \( O C l^{-} \)
D. \( C l O_{3}^{-} \)
Subject: Physics
The electrostatic potential due to the
charge configuration ot point \( P \) as
shown in figure for \( b<<a \) is
\( A \)
\[
\frac{2 q}{4 \pi \varepsilon_{0} a}
\]
B.
\[
\frac{2 q b^{2}}{4 \pi \varepsilon_{0} a^{3}}
\]
\( c \)
\[
\frac{q b^{2}}{4 \pi \varepsilon_{0} a^{3}}
\]
D. zero
Subject: Chemistry
\( L i^{2+} \) ion is in the excited state with
wave function of its electron being
denoted by the symbol \( \Psi_{3,1,0} \). How many radiations of different wavelength will
this \( L i^{2+} \) ion will emit upon de-
excitation?
A. zer
B. 6
\( c \)
\( D \)
Subject: Physics
Pick out the wrong statement from the following
A. The Sl unit of universal gravitational constant is \( N m^{2} k g^{-2} \)
B. The gravitational force is a conservative force
C. The force of attraction due to a hollow spherical shell of uniform density on a point mass inside it is zero
D. The centripetal acceleration of the satellite is equal to acceleration due to gravity
E . Gravitational potential energy \( =\frac{\text { gravitation potential }}{\text { mass of the body }} \)
Subject: Physics
Two spheres of masses \( m \) and \( M \) are
situated in air and the gravitational force between them is \( F \). The space
around the masses is now filled with a
liquid of specific gravity \( 3 . \) The gravitational force will now be
A \( .2 F \)
в. \( F \)
c. \( \frac{F}{3} \)
D. \( \frac{F}{9} \)
Subject: Chemistry
The correct IU PAC name of the
following alkane is:
\( \mathbf{A} \cdot 3,6- \) diethyl \( -2- \) methyloctane
B. \( 5- \) isopropyl -3 - ethyloctane
c. \( 3- \) ethyl \( -5- \) isopropyloctane
D. \( 3- \) isopropyl \( -6- \) ethyloctane.
Subject: Physics
A frog sits on the end of a long board of length \( L=10 c m . \) The board rests on
frictionless horizontal table. The frog wants to jump to the opposite end of the board. What is minimum take of speed
\( v \) in \( m s^{-1} \) relative to the ground that the frog follows to do the tricks?
[Assume that the board and frog have equal masses?]
A \( \cdot 2 \sqrt{5} m s^{-1} \)
B. \( 5 m s^{-1} \)
D. \( 10 \sqrt{2} \mathrm{ms}^{-1} \)
Subject: Maths
Statement-I: For every natural number \( \boldsymbol{n} \geq 2, \frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+\ldots \ldots+\frac{1}{\sqrt{n}}>\sqrt{\boldsymbol{n}} \)
Statement-2: For every natural number \( \boldsymbol{n} \geq \mathbf{2}, \sqrt{\boldsymbol{n}(\boldsymbol{n}+\mathbf{1})}<\boldsymbol{n}+\mathbf{1} \)
A. Statement-1 is true, Statement-2 is true; Statement- is a correct explanation for Statement-
B. Statement-1 is true, Statement-2 is false.
c. Statement- - is false, statement-2 is true
D. Statement-1 is true, Statement-2 is true; Statement- is not a correct explanation for Statement-
Subject: Maths
Argument and modulus of \( \frac{1+i^{2013}}{1-i} \) are respectively
A \( \cdot \frac{-\pi}{2} \) and 1
в. \( \frac{\pi}{2} \) and \( \sqrt{2} \)
c. 0 and \( \sqrt{2} \)
D \( \cdot \frac{\pi}{2} \) and 1
Subject: Physics
The dimension of universal gas
constant R are
A \( \cdot M^{2} L^{2} T^{-2} \)
B. \( M L^{2} T^{-2} \theta^{-1} \)
\( \mathbf{c} \cdot M^{2} L^{2} T^{-2} \theta^{-2} \)
D. \( M L T^{-2} \theta^{-2} \)
Subject: Maths
If \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\boldsymbol{x}^{-3} \) then \( \boldsymbol{y}= \)
A \( \cdot \frac{-1}{2 x^{2}}+c \)
B \( \cdot \frac{-x^{-4}}{4}+c \)
c. \( \frac{2}{x^{2}}+c \)
D. \( \frac{x^{-2}}{2}+c \)
Subject: Physics
Three charges \( \mathbf{q}_{1}=\mathbf{3} \mathbf{m} \mathbf{C}, \mathbf{q}_{2}=-\mathbf{3} \mathbf{m} \mathbf{C} \)
and \( q_{3} \) are kept at the vertices of a
triangle as shown in the figure. If the net
force acting on \( q_{1} \) is \( \bar{F} \), the charge \( q_{3} \) would have the magnitude \( \left(1+\frac{1}{n}\right)^{2} m C \)
So, \( n \) is:
\( \mathbf{A} \cdot \mathbf{8} \)
B. 4
\( c \cdot 1 \)
D. 16
Subject: Physics
A ball is dropped from height \( h \) and
another from \( 2 h . \) The ratio of time taken
by the two balls to reach ground is:
A. \( 1: \sqrt{2} \)
2 \( : \sqrt{2} \cdot \sqrt{2} \cdot \sqrt{2} \)
B. \( \sqrt{2}: 1 \)
c. 2: 1
D. 1: 2
Subject: Maths
In \( \triangle A B C, D \) is mid-point of \( A B, \) and \( E \) is
mid-point of BC. Calculate : \( D E \), if
\( \boldsymbol{A C}=\mathbf{6 . 4} \mathrm{cm} \)
A. \( 3.2 \mathrm{cm} \)
B. \( 3.3 \mathrm{cm} \)
\( c .4 .2 \mathrm{cm} \)
D. \( 2.6 \mathrm{cm} \)
Subject: Chemistry
Which of the statements about the
reaction below are incorrect?
\( 2 P b O(s)+C(s) \rightarrow 2 P b(s)+C O_{2}(g) \)
(a) Lead is getting reduced.
(b) Carbon dioxide is getting oxidised.
(c) Carbon is getting oxidised.
(d) Lead oxide is getting reduced.
A \( \cdot(a) \) and \( (b) \)
B. (a) and (c)
\( c \cdot(a),(b) \) and \( (c) \)
D. All
Subject: Physics
2 mole ideal He gas and 3 mole ideal \( H_{2} \)
gas at constant volume find out \( C_{v} \) of
mixture
A \( \cdot \frac{21 R}{10} \)
в. \( \frac{11 R}{10} \)
c. \( \frac{21 R}{5} \)
D. \( \frac{11 R}{5} \)
Subject: Maths
Find the perimeter of
(i) \( \Delta \mathrm{ABC} \)
(ii) rectangle BCDE.
\( \mathbf{A} \)
(i) \( -8 \frac{1}{60} \mathrm{cm}, \) (ii)- \( 5 \mathrm{cm} \)
3
(i) \( -5 c m, \) (ii) \( -10 \frac{1}{6} \mathrm{cm} \)
c. \( \left(\text { i) }-8 \frac{1}{60} \text { cm, (ii) }-10 \frac{1}{5} \) cm \right.
) . (i)- \( 8 \mathrm{cm}, \) (ii) \( -23 \mathrm{cm} \)
Subject: Chemistry
In the reaction,
\( \mathbf{2} \boldsymbol{H}_{2} \boldsymbol{S}+\boldsymbol{S} \boldsymbol{O}_{2} \rightarrow \mathbf{2} \boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{3} \boldsymbol{S} \)
mol each of \( S O_{2} \) and \( H_{2} S \) will give how much sulphur?
A. 1 mol
B. 3 mol
c. 1.5 mol
D. 2 mol
Subject: Physics
For the given combination of gates, if
the logic states of inputs \( A, B, C \) are as
follows \( \boldsymbol{A}=\boldsymbol{B}=\boldsymbol{C}=\mathbf{0} \) and \( \boldsymbol{A}=\boldsymbol{B}= \)
\( 1, C=0 \) then the logic states of
output D are
A. 0,0
B. 0,1
\( c \cdot 1,0 \)
D. 1
Subject: Chemistry
\( \boldsymbol{C O}+\boldsymbol{H}_{2} \rightarrow \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{O H} \)
Which catalyst is used in the above
reaction?
\( \mathbf{A} \cdot M n O_{2} \)
в. \( F e C l_{3} \)
c. \( P d C l_{2} \)
D. \( Z n O / C u O \)
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{ccc}\boldsymbol{x} & \mathbf{1} & -\boldsymbol{x} \\ \mathbf{0} & \mathbf{1} & -\mathbf{1} \\ \boldsymbol{x} & \mathbf{0} & \mathbf{7}\end{array}\right] \) and \( \operatorname{det}(\boldsymbol{A})= \)
\( \left|\begin{array}{ccc}\mathbf{3} & \mathbf{0} & \mathbf{1} \\ \mathbf{2} & \mathbf{- 1} & \mathbf{0} \\ \mathbf{0} & \mathbf{6} & \mathbf{7}\end{array}\right| \) then the value of \( \boldsymbol{x} \) is
A . -3
B. 3
\( c \cdot 2 \)
D. -8
E. -2
Subject: Physics
Rank the order of the magnitude of the momenta of the four objects pictured below, greatest first.
Masses are shown inside the
boundaries of the objects. Velocities are shown with the red arrows with the corresponding values.
A. Blue and yellow tie, green and purple and orange tie
B. Purple and orange tie, blue, yellow, green
c. Blue, purple and orange tie, green, yellow
D. Green and purple tie, orange, blue and yellow tie
E. Green, purple, and orange tie, blue and yellow tie
Subject: Chemistry
Given :
Oxidation:
\( H_{2} O_{2} \rightarrow O_{2}+2 H^{\oplus}+2 e^{-} \)
\( E^{\ominus}=-0.69 V \)
\( 2 F^{\ominus} \rightarrow F_{2}+2 e^{-} \)
\( E^{\ominus}=-2.87 V \)
Reduction:
\( H_{2} O_{2}+2 H^{\oplus}+2 e^{-} \rightarrow 2 H_{2} O \)
\( E^{\ominus}=-1.77 V \)
\( 2 I^{\ominus} \rightarrow I_{2}+2 e^{-} E^{\ominus}=-0.54 V \)
Which of the following statements is/are
correct?
This question has multiple correct options
A \( \cdot H_{2} O_{2} \) behaves as an oxidant for \( I^{\ominus} \)
B. \( H_{2} O_{2} \) behaves as a reductant for \( I_{2} \)
C. \( H_{2} O_{2} \) behaves as an oxidant for \( F^{\ominus} \)
D. \( H_{2} O_{2} \) behaves as a reductant for \( F_{2} \).
Subject: Physics
Piston cylinder device initially contains
\( 0.5 m^{3} \) of nitrogen gas at \( 400 k P a \) and
\( 27^{\circ} \mathrm{C} . \) An electric heater within the
device is turned on and is allowed to
pass a current of \( 2 A \) for 5 min from a
\( 120 V \) source. Nitrogen expands at
constant pressure and a heat loss of
\( 2800 J \) occurs during the process. \( \boldsymbol{R}= \) \( \frac{25}{3} k J / k m o l K . \) The final temperature of nitrogen is
\( \mathbf{A} \cdot 2.6^{\circ} \mathrm{C} \)
в. \( 56.6^{\circ} \mathrm{C} \)
c. \( 29.6^{\circ} \mathrm{C} \)
D. \( 5.67^{\circ} \mathrm{C} \)
Subject: Maths
A shopkeeper buys 15 identical articles
for Rs. 840 and pays sales-tax at the rate of \( 8 \% . \) He sells 6 of these articles at
Rs. 65 each and charges sales-tax at the same rate. Calculate the VAT paid by the
shopkeeper against the sale of these six articles.
A. Rs. 2.5 5
B. Rs.4.32
c. Rs. 7.52
D. Rs. 9.55
Subject: Physics
A \( 10 \mathrm{kg} \) block is pulled a along a frictional surface in the form of an are
of a circle of radius \( 10 \mathrm{m} \). The applied
force \( F \) is \( 200 \mathrm{N} \) as shown in figure If \( \mathrm{a} \)
block started from rest at \( \mathrm{P} \)
A. the velocity at Q would be \( 20 \mathrm{m} / \mathrm{s} \)
B. the velocity at Q would be \( 17 \mathrm{m} / \mathrm{s} \)
C. the velocity at \( Q \) would be \( 15.5 \mathrm{m} \).
D. the velocity at Q would be \( 18 \mathrm{m} / \mathrm{s} \)
Subject: Physics
Q Type your question.
100010
equilateral triangular body of side \( l \) This body is placed on a horizontal frictionless table (x-y plane) and is
hinged at point \( A \) so that it can move
without friction about the vertical axis
through \( A \). The body is set into
rotational motion on the table about
this axis with a constant angular
velocity \( \omega(a) \) Find the magnitude of the
horizontal force exerted by the hinge on
the body (b) At time \( T \), when side \( B C \) is
parallel to x-axis, force \( \boldsymbol{F} \) is applied on
\( B \) along \( B C \) (as in the figure). Obtain
the \( x \) -component and the \( y \) -component of the force exerted by the hinge on the body, immediately after time \( T \)
Subject: Physics
The conducting rod \( a b \), as shown in figure makes contact with metal rails
\( c a \) and \( d b . \) The apparatus is in a uniform
magnetic field of \( 0.800 T, \) perpendicular to the plane of the figure. In what
direction does the current flow in the
rod?
\( A \cdot b \) to \( a \)
B. a to
\( c . \) a to b and then b to a
D. a to
Subject: Chemistry
If the formula weight of \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) is 98 then the amount of acid present in 400 \( \mathrm{ml} \) of 0.1 molar solution of acid will be:
A. \( 2.45 g \)
B . \( 3.92 g \)
c. \( 4.90 g \)
D. \( 9.80 g \)
Subject: Maths
Prove that the eccentricity of the conic given by the general equation satisfies the relation \( \frac{e^{4}}{1-e^{2}}+4= \)
\( \frac{(a+b-2 h \cos \omega)^{2}}{\left(a b-h^{2}\right) \sin ^{2} \omega}, \) where \( \omega \) is the
angle between the axes.
Subject: Chemistry
Assertion
In the extraction of \( A g, \) complex
\( \boldsymbol{N} \boldsymbol{a}\left[\boldsymbol{A} \boldsymbol{g}(\boldsymbol{C} \boldsymbol{N})_{2}\right] \) is reacted with \( \boldsymbol{Z} \boldsymbol{n} \)
Reason
\( Z n \) is d-block transition metal.
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 and Reason is correct
Subject: Maths
If \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{S}, \) defined by \( \boldsymbol{f}(\boldsymbol{x})=\sin \boldsymbol{x}- \)
\( \sqrt{3} \cos x+1, \) in onto, then the interval
of \( \boldsymbol{S} \) is
A . [0.1]
B . [-1,1]
\( c \cdot[0,3] \)
D. [-1,3]
Subject: Chemistry
Complete the following chemical reactions. Classify the below into (a) hydrolysis, (b) redox and (c) hydration reactions.
(i) \( P b S(s)+H_{2} O_{2}(a q) \rightarrow \)
(ii) \( M n O_{4}^{-}(a q)+H_{2} O_{2}(a q) \rightarrow \)
(iii) \( \boldsymbol{C a O}(\boldsymbol{s})+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \rightarrow \)
(iv) \( A l C l_{3}(g)+H_{2} O(l) \rightarrow \)
\( (v) C a_{3} N_{2}(s)+H_{2} O(l) \rightarrow \)
Subject: Maths
For a random variable \( \boldsymbol{X} . \) If \( \boldsymbol{E}(\boldsymbol{X})=\mathbf{5} \)
and \( V(X)=6, \) then \( E\left(X^{2}\right) \) is equal to
A . 19
B. 31
c. 61
D. 11
Subject: Maths
If \( \phi(x)=\frac{1}{1+e^{-x}} \) then the value of
\( \boldsymbol{\phi}(\mathbf{5})+\boldsymbol{\phi}(\mathbf{4})+\ldots+\boldsymbol{\phi}(-\mathbf{3})+\boldsymbol{\phi}(-\mathbf{4})+ \)
\( \phi(-5) \)
\( \mathbf{A} \cdot \mathbf{5} \)
B. \( \frac{9}{2} \)
c. \( \frac{11}{2} \)
D. none of these
Subject: Biology
Choose the correct set.
\begin{tabular}{ll|l|l} 
& Column I & & Column \\
\hline I. & Gross primary productivity & A. & Total ass \\
II. & Secondary productivity & B. & Remains and does not situ \\
III. & Transducers & C. & Green ple \\
IV. & Foodweb & D. & Interlock \\
\hline
\end{tabular}
\( \mathbf{A} \)
।- \( A,\|-B,\|-C, I V-D \)
B. I-B, II-C. III-D, IV-A
C. \( \mid-\mathrm{C}, \) ।I- \( \mathrm{D}, \) III- \( \mathrm{A}, \mathrm{IV}-\mathrm{B} \)
D. \( |-A,||-C,|||-B, \mid V-D \)
Subject: Maths
The product of the d.cs of the line which makes equal angles with \( o x, o y, o z \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B. \( \sqrt{3} \)
c. \( \frac{1}{3 \sqrt{3}} \)
D. \( \frac{1}{\sqrt{3}} \)
Subject: Maths
Let \( f \) be a differentiable function
satisfying \( \boldsymbol{f}(\boldsymbol{x})+\boldsymbol{f}(\boldsymbol{y})+\boldsymbol{f}(\boldsymbol{z})+ \)
\( \boldsymbol{f}(\boldsymbol{x}) \boldsymbol{f}(\boldsymbol{y}) \boldsymbol{f}(\boldsymbol{z})=\mathbf{1 4} \) for all \( \boldsymbol{x}, \boldsymbol{y}, \boldsymbol{z} \in \boldsymbol{R} \)
Then
\( \mathbf{A} \cdot f^{\prime}(x)<0 \) for all \( x \in R \)
B . \( f^{\prime}(x)=0 \) for all \( x \in R \)
C \( \cdot f^{\prime}(x)>0 \) for all \( x \in R \)
D. none of these
Subject: Physics
Two billiard balls are rolling on a flat table. One has velocity components \( \boldsymbol{V}_{\boldsymbol{x}}=\mathbf{1} \boldsymbol{m} / \boldsymbol{s}, \boldsymbol{V}_{\boldsymbol{y}}=\sqrt{\mathbf{3}} \boldsymbol{m} / \boldsymbol{s} \) and the
other has component \( V_{x}=2 m / s \) and
\( V_{y}=2 m / s . \) If both the balls start moving from the same point the angle between their path is:
A \( .60^{\circ} \)
B . 45
\( c \cdot 22.5 \)
D. \( 15^{\circ} \)
Subject: Biology
Which of the following statement is/are
correct?
(A) All green plants can prepare their own food.
(B) Most animals are autotrophs.
(C) \( C O_{2} \) is not required for
photosynthesis.
(D) Oxygen is liberated during photosynthesis.
Choose the correct answer from the
options given below.
\( A \cdot(A) \) and \( (D) \)
B. (B) only
c. (B) and (C)
D. (A) and (B)
Subject: Chemistry
Plots for \( 2 s \) orbital are:
\( X, Y \) and \( Z \) are respectively
\( \mathbf{A} \cdot R, R^{2} \) and \( 4 \pi r^{2} R^{2} \)
B \( \cdot R^{2}, R \) and \( 4 \pi r^{2} R^{2} \)
\( \mathbf{C} \cdot 4 \pi r^{2} R^{2}, R^{2} \) and \( R \)
D \( \cdot R^{2}, 4 \pi r^{2} R^{2} \) and \( R \)
Subject: Chemistry
placed in the group 17 of the long from periodic table. Element with atomic
number 9 is placed above and with
atomic number 35 is placed below it.
Element with atomic number 16 is
placed left and with atomic number 18
is placed right to it. Which of the following statements are correct?
a) Valency of the element with atomic
number 18 is zero.
b) Elements with same valency will have atomic number 16,17 and 18
c) Valency of element with atomic
number 9,17 and 35 is one.
d) Element with atomic number 17 is
more electronegative than element with atomic number 16 and 35
\( A \cdot(a),(b) \) and \( (c) \)
B. (a), (c) and (d)
\( c \cdot(b),(c) \) and \( (d) \)
D. \( (a),(b) \) and \( (d) \)
Subject: Biology
Match the columns.
Column 1 1 Columr
A. Waste product of respiration
1. Resin
B. Waste product of \( \quad \) 2. \( \mathrm{CO}_{2} \) photosynthesis
3. Essential
\( \mathrm{C} \)
Leaves of \( 1 € \) flemon I
o oil
D. Stem of conifers 4. \( O_{2} \)
\( A \cdot A-2, B-4, C-1, D-3 \)
B. \( A-2, B-4, C-3, D-1 \)
C. \( A-4, B-2, C-3, D-1 \)
D. \( A-2, B-3, C-4, D-1 \)
Subject: Chemistry
According to the quantum mechanics, correct statements concerning the
electron in the hydrogen atom include
which of the following?
I. It moves in a definite orbit around the
nucleus.
II. It is associated with definite energy
levels.
III lit occupies a fixed position in space with reference to the nucleus
A. \( I \) only
B. II only
C. \( I \) and \( I I I \) only
D. II and III only
E. \( I, I I \) and \( I I I \)