Given the set \( P \) is the set of even
numbers between 15 and \( 25 . \) Label a
Venn diagram to represent the set \( \boldsymbol{P} \)
and indicate all the elements of set \( \boldsymbol{P} \)
in the Venn diagram.
B . \{16,20,24\}
c. \{16,18,20,22,24\}
D. None of these


Which of the following parameters does not characterise the thermodynamic
state of matter?
A. Temperature
B. Pressure
c. work
D. volume


The difference between an interior angle
of \( (n-1) \) sided regular polygon and an
interior angle of \( (n+1) \) sided regular
polygon is \( 9^{\circ} . \) Find the value of \( n \)
\( A \cdot 3 \)
B. 4
\( c .9 \)
D. 12


True or False
The radius of energy of Bohr's orbit is
equal to integral multiples of 0.529


A block kept on a rough surface starts sliding when the inclination of the surface is ' \( \theta \) ' with respect to the
horizontal. The coefficient of static
friction between the block and the
surface is:
\( A \cdot \sin \theta \)
B. \( \tan \theta \)
\( c \cdot \cos \theta \)
D. \( \sec \theta \)


If \( a, b, c \) are positive such that \( a b^{2} c^{3}= \)
64 then least value of \( \left(\frac{1}{a}+\frac{2}{b}+\frac{3}{c}\right) \)
is
\( A \cdot 6 \)
B. 2
\( c \cdot 3 \)
D. 32


Gold is extracted by hydrometallurgical process, based on its property:
A. of being electropositive
B. Of being less reactive
c. To form complexes which are water soluble
D. To form salts which are water soluble


Geometry of ammonia molecule and the
hybridisation of nitrogen involved in it
are:
A \( \cdot s p^{3} \) - hybridisation and tetrahedral geometry
B. \( s p^{3} \) - hybridisation and distorted tetrahedral geometry
C \( \cdot s p^{2} \) - hybridisation and trianguklar geometry
D. none of the above


Which one of the following is millet?
A. Triticum
B. Sorghum
c. oryza
D. None of the above


Two blocks are resting on ground with masses \( 5 k g \) and \( 7 k g . \) A string
connected them which goes over a massless pulley A. There is no friction between pulley an d string A. force \( \boldsymbol{F}= \)
\( 124 N \) is applied on pulley A.Find
acceleration of centre of mass of the
system of two masses \( \left(\operatorname{in} m / s^{2}\right) \)


Cellulose is a polymer of :
A. Glucose
B. Fructose
c. Ribose
D. sucrose


If \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\frac{1}{\boldsymbol{x}}+\mathbf{3} \boldsymbol{x}^{2} \) then \( \boldsymbol{y}= \)
A. \( \ln x+\frac{x^{3}}{2}+c \)
B. \( \ln x+3 x^{3}+c \)
c. \( \ln x+\frac{x^{3}}{3}+c \)
D. \( \ln x+x^{3}+c \)


Electric intensity due to an electric dipole varies with distance \( r \) as \( E \alpha r^{n}, \) where 'n"
is
A. -3
B. -2
c. -1
D. 0


Which one of the following pairs of geographical areas show maximum biodiversity in our country?
A. Sunderbans and Rann of Kutch
B. Eastern Ghats and west Bengal
c. Eastern Himalaya and Western Ghats
D. Kerala and Punjab


If \( \boldsymbol{A}=\mathbf{1}, \boldsymbol{B}=\mathbf{0} \) then the value of \( \overline{\boldsymbol{A}}+\boldsymbol{B} \)
in terms of Boolean algebra is
A . \( A \)
в. \( B \)
c. \( B+A \)
D. A.B


Evaluate: \( \int \frac{x d x}{(x-1)\left(x^{2}+1\right)} \)


Substances having same number of electrons but different mass is known
as:
A. isotopes
B. isobars
c. isotones
D. allotropes


The ratio of the value of \( g \) in Sl units to
CGS units is.
\( \mathbf{A} \cdot 10^{2}: 1 \)
B. 10: 1
\( c \cdot 10^{-1}: 1 \)
1
D. \( 10^{-2}: 1 \)


Centre of the hyperbola \( x^{2}+4 y^{2}+ \)
\( 6 x y+8 x-2 y+7=0 \) is
A \( .(1,1) \)
в. (0,2)
D. None of these


The coherence time will be
A \( .8 \times 10^{-8} s \)
В. \( 8 \times 10^{-9} s \)
c. \( 8 \times 10^{-10} s \)
D. \( 8 \times 10^{-11} s \)


Why should the battery key be pressed before the galvanometer key?


Write the name of the cell which is
generally used in transistors. Write the
reactions taking place at the anode and the cathode of this cell.


toppr
Q Type your question
\( A \)
and
\( B \)
\( c \)
and
\( D \)


Select the correct option(s) for an ideal
gas.
This question has multiple correct options
A. Most probable speed increases with increase in temperature
B. Fraction of particles moving with most probable speed increases with increase in temperature
C. Fraction of particles moving with most probable speed are more for \( C l_{2} \) than \( H_{2} \) under similar condition of \( T \)
\( P \& V \)
D. Most probable speed is more \( C l_{2} \) than \( H_{2} \) at same temperature


Check the commutativity and associativity of the following binary operation:
\( ^{\prime} *^{\prime} \) on \( N, \) defined by \( a * b=a^{b} \) for all
\( \boldsymbol{a}, \boldsymbol{b} \in \boldsymbol{N} \)


The surface density (mass/area) of a
circular disc of radius \( a \) depends on the
distance from the center of \( \rho(r)=A+ \)
Br. Find its moment of inertia about
the line perpendicular to the plane of the disc through its centre.


The torsional rigidity of a shaft is expressed by
A. Maximum torque it can transmit
B. Number of cycles it undergoes before failure
c. Elastic limit up to which it can resist torsion, shear and bending stresses
D. Torque required to produce a twist of one radian per unit length of shaft


Air pressure is usually highest when the
air is


For a quadratic function in standard
form, \( \boldsymbol{y}=\boldsymbol{a} \boldsymbol{x}^{2}+\boldsymbol{b} \boldsymbol{x}+\boldsymbol{c}, \) Find the axis of
symmetry.
A \( \cdot y=\frac{-b}{2 a} \)
в. \( x=\frac{-b}{2 a} \)
c. \( y=\frac{b^{2}-4 a c}{2 a} \)
D. None of these


Mark the CORRECT statements(s)
This question has multiple correct options
A. Direction of wave propagation is along the normal to wavefront.
B. For a point source of light, the shape of wavefront can be considered to be plane at very large
distance from the source.
C. A point source of light is placed at the focus of a thin spherical lens, then the shape of the wavefront for emerged light may be plane.
D. The shape of the wavefront for the light incident on a thin spherical lens (kept in vacuum) is plane, the shape of the wavefront corresponding to emergent light would be always spherical


\( X C l_{2}(\text { excess })+Y C l_{2} \rightarrow X C l_{4}+Y \downarrow \)
\( \boldsymbol{Y} \boldsymbol{O} \frac{\Delta}{>400^{0}} \frac{1}{2} \boldsymbol{O}_{2}+\boldsymbol{Y} \)
Ore of \( Y \) would be :
A. Siderite
B. Cinnabar
c. Malachite
D. Hornsilver


The general electronic configuration of the transition elements is:
\( \mathbf{A} \cdot(n-1) d^{10},(n+1) s^{2} \)
B \cdot \( (n-1) d^{1-10},(n+1) s^{1-2} \)
c. \( (n-1) d^{1-10}, n p^{6}, n s^{2} \)
D \cdot \( (n-1) d^{1-10}, n s^{1-2} \)


In Rutherford alpha particles scattering experiment, thin layer of which metal was used?
A. Aluminium
B. Gold
c. silver
D. zinç


Which of the following is/are soluble in
water?
A. Lower esters
B. Lower carboxylic acids
c. Lower alcohol
D. All of the above


Explain redox reaction of electrodes with example of denied cell.


Give the Molecular Orbital Energy
diagram of a) \( \left.N_{2} \text { and } b\right) O_{2} \). Calculate
the respective bond order. Write the
magnetic nature of \( N_{2} \) and \( O_{2} \)
molecules.


Independent assortment is absent in
case of
A. Genes located on the same chromosome
B. Genes located on homologous chromosomes
c. Genes located on nonhomologous chromosomes
D. All of the above


A \( 5-\mathrm{Kg} \) block is projected upwards with
an initial speed of \( 10 m s^{-1} \) from the
bottom of a plane inclined at \( 30^{0} \) with
horizontal. The coefficient of kinetic
friction between the block and the plane
is 0.2.
a. How far does move up the plane?
b. How long does it move up plane?
c. After what time from its projection does the block again come back to the bottom? With what speed does it arrive?


Atomic size of nickel, cobalt and iron is
in order of : \( \boldsymbol{F e}>\boldsymbol{C o}>\boldsymbol{N i} \)
A. True
B. False


Assertion
\( H_{2} S \) is more acidic than \( H_{2} O \)
Reason
\( H-S \) bond is more polar than \( H-O \)
bond.
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


Ammonia contains \( 82.65 \% N_{2} \) and
\( 17.65 \% H_{2} . \) If the law of constant
proportions is true, then the mass of zinc required to give 10 g ammonia will be:
A. 8.265 g
в. \( 0.826 \mathrm{g} \)
c. \( 82.65 \mathrm{g} \)
D. 826.5 \( g \)


The magnetic field inside a long straight solenoid carrying current:
A . Is zero
B. Decreases as we move towards its end
c. Increases as we move towards its end
D. Is same at all points


Evaluate \( \lim _{x \rightarrow 0} \frac{x^{3}}{\sin x^{2}} \)


The solution of differential equation
\( \boldsymbol{x}^{2} \boldsymbol{y} \boldsymbol{d} \boldsymbol{x}-\left(\boldsymbol{x}^{3}+\boldsymbol{y}^{3}\right) \boldsymbol{d} \boldsymbol{y}=\mathbf{0} \) is
A \( \cdot-\frac{1}{3} \frac{x^{3}}{y^{3}}+\log y=C \)
B. \( -\frac{1 x^{3}}{3 y^{3}}-\log y=C \)
\( ^{\mathbf{c}} \cdot \frac{x^{3}}{y^{3}}+\log y=C \)
D. None of these


Match the column:
Postulates Theory
p) Atoms are divisible into three
i. Dalton's subatomic particles \( \quad \) atomic theory
q) Discovery of the nucleus
i. Modern central positive charge) atomic theory
r) Atoms are indivisible
iii. Rutherford
s) Position of the electron
¡v. Neils Bohr
\( \mathbf{A} \cdot p \rightarrow i i, q \rightarrow i i i, r \rightarrow i, s \rightarrow i v \)
B \( \cdot p \rightarrow i, q \rightarrow i i, r \rightarrow i, s \rightarrow i i \)
\( \mathbf{c} \cdot p \rightarrow i i, q \rightarrow i, r \rightarrow i, s \rightarrow i i \)
D. \( p-i i i, q-i v, r-i i, s-i \)


If the probability of defective bolts is 0.1
the sum of the mean and standard
deviation for the distribution of
defective volts in a total of 500 bolts is \( (a+\sqrt{b}), \) then the value of \( a+b \) is


Drawing 4 queen cards from a well-
shuffled deck of 52 cards.
This activity is called an
A. measurement
B. experiment
c. event
D. sample


For parabola \( \boldsymbol{y}^{2}=\mathbf{8 4} \boldsymbol{x}, \) focal distance of
point (21,1764) is
A . 64
B. 84
\( c \cdot 24 \)
D. 42


Which of the following lanthanoid ions is diamagnetic?
\( \mathbf{A} \cdot S m^{2}+ \)
B. \( C e^{2} \)
\( \mathrm{c} \cdot Y b^{2} \)
D. \( E u^{2} \)


Evaluate
\( \boldsymbol{I}=\int \tan ^{-1}(\boldsymbol{x}) \boldsymbol{d} \boldsymbol{x} \)


Potential difference of \( 220-250 \mathrm{V} \) is
present between
A. Earth wire and neutral wire
B. Live wire and earth wire
c. Live wire and neutral wire
D. B and c both


The difference between the greatest and
the least values of the function \( f(x)= \) \( \int_{0}^{x}\left(a t^{2}+1+\cos t\right) d t, a>0, x \in[2,3] \)
is:
A \( \cdot \frac{19}{3} a+1+\sin 3-\sin 2 \)
в. \( \frac{18}{3} a+1+2 \sin 3 \)
c. \( \frac{18}{3} a-1+2 \sin 3 \)
D. none of these


A particle of mass \( \mathrm{m} \) is allowed to
oscillate near the minimum of a vertical
parabolic path having the equation \( x^{2}=4 a y . \) The time period of small
oscillation of the particle given by
A \( \cdot 2 \pi \sqrt{\frac{a}{g}} \)
B \( .2 \pi \sqrt{\frac{g}{2 a}} \)
\( \mathbf{C} \cdot 2 \pi \sqrt{\frac{a}{2 g}} \)
D. \( 2 \pi \sqrt{\frac{3 a}{2 g}} \)


\( \frac{d^{2} x}{d y^{2}}=-\frac{d^{2} y}{d x^{2}} \cdot\left(\frac{d x}{d y}\right)^{3} \)


How would short-term advantages differ from the advantages of using a longterm perspective in managing our resources?


A motor ship covers the distance of
\( 300 k m \) between two localities on a river
in 10 hours downstream and in 12
hours upstream. Find the flow velocity of the river assuming that these velocities are constant.
A. \( 2.0 \mathrm{km} / \mathrm{h} \)
B. 2.5 km/h
\( c .3 \mathrm{km} / \mathrm{h} \)
D. 3.5 km/h


White phosphorous \( \left(\boldsymbol{P}_{4}\right) \) has:
This question has multiple correct options
A. four \( P-P \) single bonds
B. four lone pair of electrons
C \( . P-P-P \) angle of \( 60^{\circ} \)
D. light \( P-P \) single bonds


Which of the following compounds has the highest boiling point?
A \( \cdot C H_{3} C H_{2} C H_{2} C l \)
B. \( C H_{3} C H_{2} C H_{2} C H_{2} C l \)
c. \( C H_{3} C H\left(C H_{3}\right) C H_{2} C l \)
D. \( \left(C H_{3}\right)_{3} C C l \)


Give a reason for your answer.


A body strikes the floor vertically with a velocity u and rebounds at the same
speed. The change in speed would be
\( A \cdot \mu \)
в. \( 2 \mu \)
\( c \cdot 3 \mu \)
D. zero


A thick wire has a
resistance than thin wire.
A. More
B. Less
c. Equal
D. \( A \) and \( B \)


If the variable a is of discrete type then
the frequency distribution can be represented by
A. scatter diagram
B. bar diagram
c. a pie chart


A black and a red die are rolled together. Find the conditional probability of
obtaining the sum 8 , given that the red die resulted in a number less than 4


Dimensional formula for Angular
momentum is:
A \( \cdot M L^{2} T^{-1} \)
B . \( M^{1} L^{3} T^{-1} \)
c. \( M^{1} L^{1} T^{-1} \)
D. \( M L^{3} T^{-2} \)


Adj \( \left(A d j\left[\begin{array}{cc}2 & -3 \\ 4 & 6\end{array}\right]\right)= \)
A \( \cdot\left[\begin{array}{cc}2 & -3 \\ 4 & 6\end{array}\right] \)
в. \( \left[\begin{array}{cc}6 & 3 \\ -4 & 2\end{array}\right] \)
с. \( \left[\begin{array}{cc}-6 & 3 \\ -4 & -2\end{array}\right] \)
D \( \cdot\left[\begin{array}{cc}-6 & -3 \\ 4 & -2\end{array}\right] \)


'Koroseal' is a long, chain polymer. When mixed with plasticizers, it forms an excellent plastic. Which one of the following is not the use of it?
A. For water-proofing
B. Lining material for tanks
c. In wire and cable insulation
D. For sun-shading


A solution is one molar in each of
\( N a C l, C d C l_{2}, Z n C l_{2} \) and \( P b C l_{2} . \) To
this, tin metal is added. Which of the
following is true? Given:
\( \boldsymbol{E}_{\boldsymbol{P b}^{2+} / \boldsymbol{P b}}^{\circ}=-\mathbf{0 . 1 2 6} \boldsymbol{V}, \boldsymbol{E}_{\boldsymbol{S n}^{2+} / \boldsymbol{S} n}^{\circ}= \)
\( -\mathbf{0 . 1 3 6} \boldsymbol{V} \)
\( \boldsymbol{E}_{\boldsymbol{C d}^{2+} / \boldsymbol{C d}}^{\circ}=-\mathbf{0 . 4 0} \boldsymbol{V}, \boldsymbol{E}_{Z n^{2+} / Z n}^{\circ}= \)
\( -\mathbf{0 . 7 6 3} \boldsymbol{V}, \boldsymbol{E}_{N a^{+} / N a}^{\circ}=-\mathbf{2 . 7 1} \boldsymbol{V} \)
A. \( S n \) can reduce \( N a^{+} \) to \( N a \)
B. \( S n \) can reduce \( Z n^{2+} \) to \( Z n \)
\( \mathrm{c} \cdot \operatorname{Sn} \) can reduce \( C d^{2+} \) to \( C d \)
D. \( S n \) can reduce \( P b^{2+} \) to \( P b \)


Which of the following statement(s) is/are incorrect?
This question has multiple correct options
A. Magnesium may be extracted by self reduction method.
B. Down's process is used to extract magnesium from sea water.
C. Magnalium is an alloy of magnesium
D. Formula of epsom salt is \( M g S O_{4} .6 H_{2} O \)


The phenomenon related to active water absorption is
A. Transpiration
B. Root pressure
c. osmotic pressure
D. Translocation


If \( \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{2} & -\mathbf{3} \\ \mathbf{- 4} & \mathbf{1}\end{array}\right], \) then adj \( \left(\mathbf{3} \boldsymbol{A}^{2}+\right. \)
\( 12 A) \) is equal to.
\( \mathbf{A} \cdot\left[\begin{array}{cc}72 & -84 \\ -63 & 51\end{array}\right] \)
В. \( \left[\begin{array}{ll}51 & 63 \\ 84 & 72\end{array}\right] \)
c. \( \left[\begin{array}{ll}51 & 84 \\ 63 & 72\end{array}\right] \)
D. \( \left[\begin{array}{cc}72 & -63 \\ -84 & 51\end{array}\right] \)


A vertical tree stands on a hill side that
makes an angle \( \alpha \) with the horizontal From a point directly up the hill from the tree, the angle of elevation of three top
is
\( \beta . \) From a point \( \mathrm{m} \mathrm{cm}, \) further up the
hill, the angle of depression of the tree top is \( \gamma \). If the tree is \( \mathrm{H} \mathrm{cm} \). tall, express
\( \mathrm{H} \) in terms of \( \boldsymbol{\alpha}, \boldsymbol{\beta}, \boldsymbol{\gamma} \)


In which of the following cases, change of colour can be an indication of extent
of the reaction?
\( ^{\mathrm{A}} \cdot_{S O_{2}(g)+\frac{1}{2}} O_{2}(g) \leftrightharpoons S O_{3}(g) \)
B. \( N_{2}(g)+3 H_{2}(g) \leftrightharpoons 2 N H_{3}(g) \)
c. \( 2 H I(g) \leftrightharpoons H_{2}(g)+I_{2}(g) \)
D. \( C(\text { graphite })+C O_{2}(g) \leftrightharpoons 2 C O(g) \)


Ball A is thrown up vertically with speed \( 10 \mathrm{m} / \mathrm{s} \) At the same instant another ball
B is released from rest at height


In gamma ray emission from a nucleus:
A. Both, the neutron number and the proton number change.
B. There is no change in the proton number and the neutron number.
C . Only the neutron number changes.
D. Only the proton number changes.


Which one of the following statements
is not correct?
A. The presence of moisture, nutrients and a large number of spores in the air are responsible for the rapid spreading of bread mold on slices of bread.
B. In binary fission, the organism divides to form two daughters.
C. Asexual reproduction involves gametes.
D. Asexual reproduction involves only one parent.


The Sl unit of the universal gravitational
constant \( G: \)
\( \mathbf{A} \cdot N m K g^{-2} \)
B. \( N m^{2} K g^{-2} \)
c. \( N m^{2} K g^{-1} \)
D. \( N m K g^{-1} \)


A square is inscribed in a circle of
radius \( 7 \mathrm{cm} \). Find the maximum area of
the square.
\( \mathbf{A} \cdot 98 \)
B. 89
c. 86
D. 96


Two identical rods are joined to form the shape of \( X \). the smaller angle between rods is \( \theta \). The moment of inertia of the
system about an axis passing through the point of intersection of the rod and perpendicular to their plane is
\( \mathbf{A} \cdot I \propto \theta \)
B. \( I \propto \sin ^{2} \theta \)
\( \mathbf{c} \cdot I \propto \cos ^{2} \theta \)
D. Independent of \( \theta \)


If \( \frac{\cos (\boldsymbol{A}-\boldsymbol{B})}{\cos (\boldsymbol{A}+\boldsymbol{B})}+\frac{\cos (\boldsymbol{C}+\boldsymbol{D})}{\cos (\boldsymbol{C}-\boldsymbol{D})}=\mathbf{0}, \) then
\( \tan A \tan B \tan C= \)
\( \mathbf{A} \cdot \tan D \)
B. \( \cot D \)
\( c .-\tan D \)
D. - cot \( D \)


What is the basic difference between
binary fission and budding?
A. In budding, the parents identity is lost, while in binary fission, it is maintained.
B. In binary fission, the parents identity is lost, while it is maintained in budding
C. There is a fusion of daughter cells in binary fission while in budding, genetically non-identical daughter cells are produced.
D. In binary fission, two dissimilar individuals (daughter cells) are formed while in budding, daughter and parent cells are similar.


\( A \) and \( B \) are two independent events.
The probability that both \( A \) and \( B \) occur is \( 1 / 6 \) and the probability that at least
one of them occurs is \( \frac{2}{3} . \) The probability of the occurrence of \( \boldsymbol{A}=\ldots \ldots \ldots \) if \( \boldsymbol{P}(\boldsymbol{A})= \)
\( 2 P(B) \)
\( A \cdot \frac{2}{9} \)
в. 4
\( c \cdot \frac{5}{9} \)
D. \( \frac{5}{18} \)


According to recent views, which is the
current representation of hydrated proton in aqueous solution?
\( \mathbf{A} \cdot H^{+} \)
B. \( H_{9} O_{5}^{+} \)
c. \( H_{9} O_{4}^{+} \)
D. \( H_{3} O^{+} \)


A ray of light travelling in water enters obliquely into glass. Does the light ray bend towards or away from the normal? Why?


Highest oxidation State of manganese in fluorides is \( +4\left(M n F_{4}\right) \) but highest
oxidation state in oxides is \( +7\left(M n_{2} O_{7}\right) \) because:
A. fluorine is more electronegative than oxygen
B. fluorine does not possess d-orbitals
c. fluorine stabilises lower oxidation state
D. in covalent compounds, fluorine can form single bond only while oxygen forms double bond


A bar magnet is placed with its North pole pointing North. Neutral point is at a distance 'd' from the center of magnet.
The net magnetic induction at the same
distance on the axial line of the magnet.
A \( \cdot 2 B_{H} \)
в. \( 3 B_{H} \)
\( c . B_{H} \)
D. \( 7 B \) н


In which of the configurations of a transistor, the power gain is highest?
A. Common base
B. Common emitter
c. common collector
D. Same in all the three


Name the following compounds according to the IUPAC system or
nomenclature:
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C O C H}\left(\boldsymbol{C}_{2} \boldsymbol{H}_{5}\right) \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{C l} \)


What is electromagnetic radiation?


Four children were asked to arrange forces due to rolling, static and sliding frictions in a decreasing order. Their arrangements are given below. Choose the correct arrangement in descending order:
A. rolling, static, sliding
B. rolling, sliding, static
c. static, sliding, rolling
D. sliding, static, rolling


If \( \bar{A} \) and \( \bar{B} \) two different physical quantities, Which of the following mathematical operations is/are valid.
A. \( \bar{A}+\bar{B} \)
в. \( \overline{A . \bar{B}} \)
c. \( \bar{A} \times \bar{B} \)
D. Both and (b) and (c)


A compound having the empirical
formula \( C_{3} H_{4} O, \) has a molecular
weight of \( 170 \pm 5 . \) The molecular
formula of the compound is:
A. \( C_{3} H_{4} O \)
в. \( C_{6} H_{8} O_{2} \)
\( \mathbf{c} \cdot C_{6} H_{12} O_{3} \)
D. \( C_{9} H_{12} O_{3} \)


The current flowing through an external
resistance of \( 2 \Omega \) is \( 0.5 A \) when it is
connected to the terminals of a cell. This
current reduces to 0.25 A when the
external resistance is \( 5 \Omega \). Use

Kirchhoff's laws to find e.m.f. of cell.
(Ans \( : E=1.5 V, r=1 \Omega) \)


A power transformer has 50 turns for
primary and 300 turns for secondary. What is turns ratio? How much is
secondary voltage with primary voltage of \( 230 V ? \)


For the zero order reaction \( \boldsymbol{A} \rightarrow \mathbf{2} \boldsymbol{B} \), the
rate constant is \( 2 \times 10^{-6} M \) min\( ^{-1} \). The
reaction is started with \( 10 M A \)
(i) What will be the concentration of \( A \)
after 2 days (ii) What is the initial halflife of the reaction
(iii) In what time, the reaction will
complete?


Number of oxygen molecules required for aerobic oxidation of one pyruvate is
A. 6
B. 8
c. 10
\( D \cdot 12 \)


The function \( f(x)=2-3 x+3 x^{2}- \)
\( x^{3}, x \varepsilon R \) is
A. neither increasing nor decreasing
B. increasing
c. decreasing
D. none of these


In the five-kingdom classification, Chlamydomonas and Chlorella have been included in which of the following group?
A. Plantae
B. Algae
c. Protista
D. Monera


Determine the contrapositve of each of the following statements:

It is necessary to be strong in order to be a sailor.


On dividing 0.46 by \( 15.374, \) the actual answer is \( 0.02992 . \) The correctly reported answer will be:
A. 0.03
B. 0.030
c. 0.029
D. 0.0299


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. \( A l, N a, M g, C a \)


Which of the following compounds contains \( \boldsymbol{S}=\boldsymbol{O} \) as well as \( \boldsymbol{S}=\boldsymbol{S} \)
bonds?
A. Sulphuric acid
B. Thiosulphuric acid
c. sulphurous acid
D. Thiosulphurous acid


If the arithmetic mean of \( n \) numbers of
a series is \( \bar{x} \) and sum of the first \( (n- \)
1) numbers is \( k, \) then which one of the following is the nth number of the series
\( ? \)
A . \( \bar{x}-n k \)
В . \( n \bar{x}-k \)
c. \( k \bar{x}-n \)
D. \( n k \bar{x} \)


The molar specific heat of the process
\( \boldsymbol{V} \propto \boldsymbol{T}^{4} \) for \( \boldsymbol{C} \boldsymbol{H}_{4} \) gas at room
temperature is:
\( A \cdot 4 R \)
B. 7R
\( c . \) зв
D. 8R


Which type of gate the following truth
table represents?
\( \begin{array}{lll}\text { Input } & \text { Input } & \text { Output } \\ A & B & Q \\ 0 & 0 & 1 \\ 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0\end{array} \)
\( \mathbf{A} \cdot \) NOT
B. AND
\( c \cdot \) OR
D. NAND


The simple interest on a certain sum at
\( 5 \% \) per annum for 3 years and 4 years differ by Rs. 42. The sum is:
A. Rs. 210
в. Rs. 280
c. \( R s .750 \)
D. Rs. 840


The radioactivity of certain radioactive
element drops to \( \left(\frac{1}{8}\right)^{\text {th }} \) of its initial
value in 30 second, its half life is:
A. 15 second
B. 5 second
c. 4 second
D. 10 second


The line joining the points (1,-2) and
(-3,4) is trisected; find the
coordinates of the points of trisection.


At constant pressure, the ratio of increase in volume of an ideal gas per degree rise in kelvin temperature to its original volume is (T= absolute temperature of the gas) is
A \( \cdot T^{2} \)
в. \( T \)
c. \( 1 / T \)
D. \( \frac{1}{T^{2}} \)


Equilibrium constant for an equilibrium reaction is \( 100 . \) Its forward reaction rate constant \( \boldsymbol{K}_{\boldsymbol{f}}=\mathbf{1 0}^{\mathbf{5}} . \) Its
backward reaction rate constant \( \boldsymbol{K}_{\boldsymbol{b}} \) is;
A \( \cdot 10^{2} \)
B. 10
\( c \cdot 10^{4} \)
D. \( 10^{3} \)


The equation \( 2 \cos ^{-1} x= \) \( \sin ^{-1}(2 x \sqrt{1-x^{2}}) \) is valid for all values
of \( x \) satisfying
A. \( -1 \leq x \leq 1 \)
в. \( 0 \leq x \leq 1 \)
c. \( 0 \leq x \leq 1 / \sqrt{2} \)
D. \( 1 / \sqrt{2} \leq x \leq 1 \)


What is the mass of neutron?
A \( \cdot 1.675 \times 10^{-24} g \)
В. \( 9.1 \times 10^{-31} k g \)
c. \( 1.675 \times 10^{-30} g \)
D. \( 9.1 \times 10^{-27} k g \)


Which of the following is a natural fabric?
A. Polythene
B. PVC
c. Nylon
D. Wool


Every electric appliance is marked with This question has multiple correct options
A. power
B. potential difference
c. charge
D. resistance


A system of vectors is said to be coplanar, if
I. Their scalar triple product is zero.
II. They are linearly dependent. Which of the following is true?
A. Onlyı
B. Only II
c. Both I and II
D. None of these


Pollutants directly emanating from human activities are.
A. Quantitative pollutants
B. Qualitative pollutants
c. Air pollutants
D. water pollutants


Titanium oxide is added in interior
paints for walls of rooms, halls and galleries to give:
\( A \). a whiter 'white'
B. a greener'green'
c. a redder'red
D. silver-white


The binding energy/nucleon of deuteron
\( \left(_{1} H^{2}\right) \) and the helium atom \( \left(_{2} H e^{4}\right) \) are
1.1 MeV and 7 MeV respectively. If the
two deuteron atoms fuse to form a
single helium atom, then the energy released is.
A \( .26 .9 \mathrm{MeV} \)
B . 25.8MeV
c. 23.6 Mev
D. \( 12.9 \mathrm{MeV} \)


A parallel plate capacitor having
capacitance \( C \) has two plates of same
area \( A \) and thickness t. The figure shows the charges available on the four
surfaces of the plates. The potential
difference V between the two plates is
given by:
A \( \cdot \frac{q_{2}-q_{3}}{2 C} \)
в. \( \frac{q_{2}-q_{3}}{C} \)
c. \( \frac{q_{1}-q_{4}}{2 C} \)
D. \( \frac{q_{1}-q_{4}}{C} \)


Fill in the blanks:
Value of gravitational constant (G) on moon is
A. Greater
B. Smaller
c. same
D. None


Which of the following is the natural method of hybridisation?
A. Interspecific hybridisation
B. Cross pollination
c. Somatic cell hybridisation
D. All of the above


A secondary school had 450 students in a certain year. \( 10 \% \) of the students were given admissions next year. Find the number of new students in the next
year


The cube as shown in Fig. has sides of
length \( \boldsymbol{L}=\mathbf{1 0 . 0} \mathrm{cm} . \) The electric field is
uniform, has a magnitude \( \boldsymbol{E}=\mathbf{4 . 0 0} \times \)
\( 10^{3} N C^{-1}, \) and is parallel to the \( x y- \)
plane at an angle of \( 37^{\circ} \) measured from
the \( +x-a x i s \) towards the \( +y-a x i s \)
The surfaces that have zero flux are
\( A \cdot S_{1} \) and \( S_{3} \)
B. \( S_{5} \) and \( S_{6} \)
\( c \cdot S_{2} \) and \( S_{4} \)
D. \( S_{1} \) and \( S_{1} \)


Depletion of ozone layer is mainly due to
A. Methane
B. Carbon dioxide
c. chloroflorocarbons
D. Nitrogen


The \( K E \) of the electron in an orbit of
radius \( r \) in hydrogen atom is : \( (e= \)
electric charge)
\( ^{A} \cdot \frac{e^{2}}{r^{2}} \)
в. \( \frac{e^{2}}{2 r} \)
\( c \cdot \frac{e^{2}}{r} \)
D. \( \frac{e^{2}}{2 r^{2}} \)


Simplify using laws of exponents:
\( \frac{100 \times 3^{3} \times 25 \times 32}{5^{2} \times 2^{4} \times 10} \)


\( N a_{2} C O_{3} \) is widely used in softening of hard water. If 1 L of hard water required
\( 0.0106 g \) of \( N a_{2} C O_{3}, \) The hardness in
ppm (parts per million i.e., \( 10^{6} \) ml) of
\( \boldsymbol{C a} \boldsymbol{C O}_{3} \) is:
A. 0.01 ppm \( C a C O_{3} \)
B. 0.10 ppm \( C a C O_{3} \)
c. 1.00 ppm \( C a C O_{3} \)
D. \( 10.00 \mathrm{ppm} \mathrm{CaCO}_{3} \)


Find the area of the region bounded by
the curve \( y^{2}=4 x \quad \) and the line \( x=3 \)


An industrial method for the
preparation of methanol is:
A. by catalytic reduction of carbon monoxide
B. by reacting methane with steam in presence of a catalyst
C . by reduction of \( H C H O \) with \( L i A l H_{4} \)
D. by reduction of \( H C H O \) with aqueous \( N a O H \)


A point source emits sound equally in all directions in a non-absorbing
medium. Two points \( P \) and \( Q \) are at
distance of \( 2 m \) and \( 3 m \) respectively from the source. The ratio of the
intensities of the wave at \( P \) and \( Q \) is:
A . 9: 4
B. 2: 3
\( c .3: 2 \)
D. 4: 9


State whether True or False, and correct
the statements if false:
(1) Kilometre is a multiple of metre.
A. True
B. False


The solution of the differential equation \( \sin y \frac{d y}{d x}=\cos y(1-x \cos y) \) is:
A \( \cdot \sec y=x+1+K e^{-x} \)
B. sec \( y=x+1+K e^{x} \)
c. sec \( y=x-1+K e^{x} \)
D. sec \( y=x-1+K e^{-x} \)


The intrinsic charge carrier density in germanium crystal at \( 300 K i s 2.5 \times \) \( 10^{13} / \mathrm{cm}^{3} . \) density in an n-type
germanium crystal at \( 300 \mathrm{K} \) be \( 5 \times \)
\( 10^{16} / c m^{3}, \) the hole density in this n-type
crystal at \( 300 \mathrm{K} \) would be
A \( \cdot 2.5 \times 10^{13} / \mathrm{cm}^{3} \)
В. \( 5 \times 10^{6} / c m^{3} \)
c \( \cdot 1.25 \times 10^{10} / \mathrm{cm}^{3} \)
D. \( 0.2 \times 10^{4} / c m^{3} \)


\( \mathbf{f} \overrightarrow{\boldsymbol{A}}=\widehat{\boldsymbol{j}}+\widehat{\boldsymbol{k}} \) and \( \overrightarrow{\boldsymbol{B}}=2 \hat{\boldsymbol{i}}-\widehat{\boldsymbol{j}}+\boldsymbol{4} \widehat{\boldsymbol{k}} \) then
the unit vector of \( \vec{A}+\vec{B} \) is
\( A \cdot \frac{3 i+5 \hat{k}}{\sqrt{24}} \)
B. \( \frac{3 \hat{i}-5 \vec{k}}{\sqrt{34}} \)
C. \( \frac{3 \hat{i}+5 \vec{k}}{\sqrt{34}} \)
D. None of these


The secretion of the sting of silk worm forms the silk fibre.
A . True
B. False


The phase difference between the particle at one compression and another particle in third compression is
\( A \cdot \pi \) radians
B. 2 \( \pi \) radians
c. \( 3 \pi \) radians
D. \( 4 \pi \) radians


Column Column II
(Carbohydrate)


Which one of the following has largest number of isomers?
\( (R= \) alkyl group,en = ethylenediamine)
\( \mathbf{A} \cdot\left[R u\left(N H_{3}\right)_{4} C l_{2}\right]^{+} \)
B . \( \left[\operatorname{Co}\left(N H_{3}\right)_{5} C l\right]^{2+} \)
c. \( \left[I r\left(P R_{3}\right)_{2} H(C O)\right]^{2} \)
D. \( \left[\operatorname{Co}(e n)_{2} C l_{2}\right] \)


If the flux of the electric field through a
closed surface is zero:
A. the electric field must be zero everywhere on the surface
B. the electric field must not be zero everywhere on the surface
C. the charge inside the surface must be zero
D. the charge in the vicinity of the surface must be zero


Find the inverse of the statement," If
\( \triangle A B C \) is equilateral, then it is
isosceles".
\( \mathbf{A} \cdot \) If \( \triangle A B C \) is isosceles, then it is equilateral
B. If \( \triangle A B C \) is not equilateral, then it is isosceles.
C. If \( \triangle A B C \) is not equilateral, then it is not isosceles.
D. If \( \triangle A B C \) is not isosceles, then it is not equilateral.


State the chemical property in each case on which the following uses of baking soda are based
(i) As an antacid
(ii) As a constituent of baking powder Give the chemical for baking soda


Figure shows the variation of the
internal energy \( U \) with density \( \rho \) of one
mole of an ideal monatomic gas for thermodynamic cycle ABCA. Here process \( A B \) is a part of rectangular
hyperbola
A. process AB is isothermal \& net work in cycle is done
on gas
B. process AB is isothermal \& net work in cycle is done by the gas
c. process AB is isobaric \& net work in cycle is done on the gas
D. process AB is adiabatic \& net work in cycle is done by
gas


Williamson's synthesis uses mechanism.
\( \mathbf{A} \cdot S_{N} 1 \)
B. \( S_{N} 2 \)
C . either \( S_{N} 1 \) or \( S_{N} 2 \)
D. none


According to Henry's law, the partial
pressure of \( \operatorname{gas}\left(\mathrm{P}_{\text {gas}}\right) \) is directly
proportional to mole fraction of gas in
dissolved state, i.e., \( \boldsymbol{P}_{\text {gas}}=\boldsymbol{K}_{\boldsymbol{H}} \cdot \boldsymbol{X}_{\boldsymbol{g a s}} \)
where \( K_{H} \) is Henry's constant. Now, choose the correct option(s). This question has multiple correct options
\( \mathbf{A} \cdot K_{H} \) is characteristic constant for a given gas-solvent system.
B. Higher is the value of \( K_{H} \), lower is the solubility of gas for a given partial pressure of gas.
\( \mathbf{C} \cdot K_{H} \) is temperature dependent
D. \( K_{H} \) increases with temperature.


Oxidation number of sodium in sodium
amalgam is:
\( A \cdot+2 \)
B. +1
\( c \cdot-2 \)
D. zero


limiting value of static friction is sliding friction.
A. less than
B. equal to
c. more than
D. less than or equal to


A water drop of radius 1.5 mm is falling from height \( 1 k m \) having drag constant 0.5 density of water drop is \( 1000 \mathrm{kg} / \mathrm{m}^{3} \)
and density of air is \( 1.29 \mathrm{kg} / \mathrm{m}^{3} \). Find the terminal velocity.
A. \( 8.7 \mathrm{m} / \mathrm{s} \)
B. \( 7.8 \mathrm{m} / \mathrm{s} \)
\( c .5 .6 m / s \)
D. \( 4.3 \mathrm{m} / \mathrm{s} \)


Find the coordinates of the foci, the
vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse \( \frac{x^{2}}{25}+\frac{y^{2}}{100}=1 \)


The value of \( \lim _{x \rightarrow 0} \frac{\sin \left(\pi \cos ^{2} x\right)}{x^{2}} \) is
A. \( -\pi \)
в. \( \frac{\pi}{2} \)
c. \( \pi \)
D. \( \frac{3 \pi}{2} \)


The order of -I effect of orbitals is:
В \( \cdot s p>s p^{2}>s p^{3} \)
\( \mathbf{c} \cdot s p^{2}>s p^{3}>s p \)
D. \( s p^{2}>s p>s p^{3} \)


Assertion
Energy can neither be created nor
destroyed.
Reason
Total energy of the universe is constant.
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


The mean distance between the Earth
and Sun as well as the distances within the solar system is represented by
A. light year
B. astronomical units
c. parsec
D. Angstrom


Which one of the following metals could not be obtained on electrolysis of aqueous solution of its salts?
\( A \cdot A g \)
в. мв
\( c \cdot c u \)
D. \( c o \)


Solve \( \int \frac{2 x}{\sqrt{1+x}} d x \)


In hot water bottles, water is used
because
A. its specific heat is low
B. its specific heat is highh
c. it is cheap
D. it is easily available


A lead bullet penetrates into a solid
object and melts. Assuming that \( 50 \% \) of its kinetic energy was used to heat it,
the initial speed of the bullet is (the
initial temperature of the bullet is \( 25^{\circ} \mathrm{C} \)
and its melting point is \( 300^{\circ} \mathrm{C} \) ). Latent
heat of fusion of lead \( =2.5 \times 10^{4} J / k g \) and specific heat capacity of lead \( = \) \( \mathbf{1 2 5 J} / \boldsymbol{k g}-\boldsymbol{K} \)
A. \( 100 \mathrm{m} / \mathrm{s} \)
в. \( \simeq 490 m / s \)
\( \mathrm{c} .520 \mathrm{m} / \mathrm{s} \)
D. \( 360 \mathrm{m} / \mathrm{s} \)


ff \( \Delta D E F \equiv \Delta B C A, \) write the part(s) of
\( \Delta B C A \) that correspond to \( \angle F \)


In which state, the lanthanide ions are
coloured?
This question has multiple correct options
A. Solid
B. Gas
c. Aqueous
D. Not coloured


Solve:
\( \boldsymbol{x}+\mathbf{7}-\frac{\mathbf{8} \boldsymbol{x}}{\mathbf{3}}=\frac{\mathbf{1 7} \boldsymbol{x}}{\mathbf{6}}-\frac{\mathbf{5} \boldsymbol{x}}{\mathbf{8}} \)


It was known by 1900 that the atom was not \( a_{\dots} \dots \dots \dots, \dots \) particle but contained at least one sub-atomic particle the
electron identified by J.J. Thomson
A. simple, divisible
B. complex, indivisible
c. simple, indivisible
D. complex, divisible


When electronic transition occur from
higher energy state to lower energy state with energy difference equal to \( \Delta \) E electron volts, the wavelength of the line emitted is approximately equal to:
A \( \cdot \frac{12395}{\Delta E} \times 10^{-10} \mathrm{m} \)
В \( \cdot \frac{12395}{\Delta E} \times 10^{10} \mathrm{m} \)
c. \( \frac{12395}{\Delta E} \times 10^{-10} \mathrm{cm} \)
D. \( \frac{12395}{\Delta E} \times 10^{10} \mathrm{cm} \)


Prerna invested Rs \( x \) for 6 months,
Ankita Rs 2400 for 10 months and
Pavneet Rs 3900 for 8 months. If Ankita
got Rs 6000 out of a total profit of Rs \( 19,200, \) then what is the money invested by Prerna in rupees?


Arrange the following elements in the order of their increasing non-metallic
character.
\( \boldsymbol{L} \boldsymbol{i}, \boldsymbol{O}, \boldsymbol{C}, \boldsymbol{B} \boldsymbol{e}, \boldsymbol{F} \)
A. \( O<F<C<B e<L i \)
в. \( L i<B e<C<O<F \)
c. \( F<O<C<B e<L i \)


For a real gas obeying vander Waal's equation a graph is plotted between
\( P V_{m}(y=a x i s) \) and \( P(x-a x i s) \) where
\( \boldsymbol{V}_{m} \) is molar volume. Find \( \boldsymbol{y}- \) intercept
of the graph.


Peak concentration of ozone occurs in
the atmosphere above a height of
\( A \cdot 10 \mathrm{km} \)
B. 15 km
c. \( 17 \mathrm{km} \)
D. 25 km


Which of the following statements are true about quartz?
A. it is pure crystalline form of silica.
B. it is a tetrahedral polymer of \( \boldsymbol{S} \boldsymbol{i} \boldsymbol{O}_{\boldsymbol{2}} \)
C. UV light can pass through quartz
A. A and B are correct
B. B and C are correct
c. A and C are correct
D. all are correct


PQR is a triangle. S is a point on the side
QR of \( \Delta \) PQR such that \( \angle \mathrm{PSR}=\angle \mathrm{QPR} / \)
Given \( \boldsymbol{Q} \boldsymbol{P}=\mathbf{8 c m}, P \mathrm{R}=\mathbf{6 c m} \) and \( \mathbf{S R}=\mathbf{3} \)
\( \mathrm{cm} \)
(I) Prove \( \Delta \mathrm{PQR} \sim \Delta \) SPR
(II) Find the length of QR and PS
areaof \( \Delta P Q R \)
(III) \( \frac{d r e a o f \Delta S P R}{a r e a o f} \)


The amount of electricity that can deposit \( 108 g \) of silver from silver nitrate solution is:
A. 1 ampere
B. 1 coulomb
c. 1 Faraday
D. 2 ampere


Use elements of set \( P=\{2,3\} \) to find the number of all possible ordered pairs.


What will be the displacement equation of the simple harmonic motion obtained by combining the motions? \( \boldsymbol{x}_{1}=\mathbf{2} \sin \boldsymbol{\omega} \boldsymbol{t}, \quad \boldsymbol{x}_{2}=\boldsymbol{4} \sin \left(\boldsymbol{\omega} \boldsymbol{t}+\frac{\boldsymbol{\pi}}{\boldsymbol{6}}\right) \)
and \( \quad x_{3}=6 \sin \left(\omega t+\frac{\pi}{3}\right) \)
A \( \cdot x=10.25 \sin (\omega t+\phi) \)
B \cdot \( x=10.25 \sin (\omega t-\phi) \)
C \( \cdot x=11.25 \sin (\omega t+\phi) \)
D \( \cdot x=11.25 \sin (\omega t-\phi) \)


Two vectors whose magnitudes are in ratio 1: 2 gives resultant of magnitude
30. If angle between these two vectors is
\( 120^{\circ}, \) then the magnitude of two vectors will be
A. \( 10 \sqrt{3}, 20 \sqrt{3} \)
3
B . \( 5 \sqrt{3}, 10 \sqrt{3} \)
D. \( 2 \sqrt{3}, 4 \sqrt{3} \)


Complete the following statements by selecting the correct alternative from
the choices given:

The geometry of \( X e F_{6} \) molecule and
the hybridization of \( X e \) atom in the
molecule is:
A. Distorted octahedral and \( s p^{3} d^{3} \)
B. Square planar and \( s p^{3} d^{2} \)
C. Pyramidal and \( s p^{3} \)
D. Octahedral and \( s p^{3} d^{3} \)


The daughter nucleus formed when \( ^{18} \boldsymbol{F} \) undergoes positron emission is:
\( \mathbf{A} \cdot 14 N \)
B. \( ^{16} O \)
\( \mathbf{c} \cdot^{18} \mathbf{O} \)
D. \( 19 F \)


The dotted line with label A on the graph
represents which of the following?
A. The amount of energy a reaction would need without an enzyme
B. The amount of energy a reaction would need with an enzyme
C. The speed of the reaction.
D. The amount of energy needed to start the reaction witt
an enzyme


Assertion
Two electrons in Helium are placed in only one shell while three electrons in
Lithium occupy two shells.
Reason
An orbit can have maximum \( 2 n^{2} \) of
electron so first orbital can have two
electron only.
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


Express \( 4 \frac{1}{8} \) as percent


Draw a structural formula for the
alkene(s) formed by treatment of each
haloalkane with sodium ethoxide in
ethanol.
Assume that elimination occurs by an
\( E_{2} \) mechanism.


In an A.C. circuit, the current flowing in
inductance is \( \boldsymbol{I}=\mathbf{5} \sin (\mathbf{1 0 0} \boldsymbol{t}-\boldsymbol{\pi} / \mathbf{2}) \)
amperes and the potential difference is
\( \boldsymbol{V}=\mathbf{2 0 0} \sin (\mathbf{1 0 0} \boldsymbol{t}) . \) The power
consumption is equal to
A. 1000 watt
B. 40 watt
c. 20 watt
D. zero


One gram sample of \( \boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{N} \boldsymbol{O}_{3} \) is
decomposed in a bomb calorimeter, the temperature of the calorimeter
increases by \( 6.12 K . \) The heat capacity of the system is \( 1.23 \mathrm{kJ} / \mathrm{g} / \) deg. What is the molar heat of decomposition for
\( N H_{4} N O_{3} ? \)
B. \( +398.1 k J / \) mol
c. \( -16.1 k J / \) mol
D. \( +602 k J / m o l \)


State whether given statement is true or false:
(a) \( N a_{2} H P O_{3} \) is Acid salt.


In the figure given \( \Delta A B C \) is a right
isosceles triangle with right angle at \( C \)
CD is a parallel to \( A B \) and \( B D=B A \). The
degree measure of \( \angle D B C \) equals:
A . \( 10^{\circ} \)
B . \( 15^{\circ} \)
\( c \cdot 20^{\circ} \)
D. 25


A rectangular loop carrying a current \( i \)
is situated near a long straight wire such that the wire is parallel to one of
the sides of the loop and is in the plane
of the loop. If steady current lis established in the wire as shown in fig.
the loop will
A. rotate about an axis parallel to the wire
B. move away from the wire
c. move toward the wire
D. remain stationary


If \( a^{2}+b^{2}+c^{2}=-2 \) and \( f(x)= \)
\( \left|\begin{array}{ccc}\mathbf{1}+\boldsymbol{a}^{2} \boldsymbol{x} & \left(\mathbf{1}+\boldsymbol{b}^{2}\right) \boldsymbol{x} & \left(\mathbf{1}+\boldsymbol{c}^{2}\right) \boldsymbol{x} \\ \left(\mathbf{1}+\boldsymbol{a}^{2}\right) \boldsymbol{x} & \mathbf{1}+\boldsymbol{b}^{2} \boldsymbol{x} & \left(\mathbf{1}+\boldsymbol{c}^{2}\right) \boldsymbol{x} \\ \left(\mathbf{1}+\boldsymbol{a}^{2}\right) \boldsymbol{x} & \left(\mathbf{1}+\boldsymbol{b}^{2}\right) \boldsymbol{x} & \mathbf{1}+\boldsymbol{c}^{\mathbf{2}} \boldsymbol{x}\end{array}\right| \) then
\( f(x) \) is a polynomial of degree
\( A \cdot \)
B.
\( c .3 \)
\( D \)


Assertion
\( \boldsymbol{x}=\mathbf{0} \) is point of minima of \( \boldsymbol{f} \)
Reason
\( f^{\prime}(0)=0 \)
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


The compound with more covalent character is :
A. \( \operatorname{SnCl}_{2} \)
в. \( \operatorname{Sn} C l_{4} \)
\( \mathbf{c} \cdot P b C l_{2} \)
\( \mathbf{D} \cdot P b C l_{4} \)


Fifteen joules of work is done on object A so that only its gravitational potential energy changes. Sixty joules of work is done on object B (same mass as object
A) so that only its gravitational potential energy changes. How many times does the height of object B change compared to the height change of object \( A, \) as result of the work done?
A. object B changes height four times as much as object
A changes height
B. Object B changes height sixteen times as much as object A changes height
c. object B changes height two times as much as object
A changes height
D. object B changes height less than two times as much as object A changes height (but not the same amount
E. object B changes height the same amount as object changes height


Which one is not a commercial energy?
A. coal
B. Animal power
C. Petroleum and natural gas
D. Electricity


An electric heater supplies heat to a
system at a rate of 120 W. If system
performs work at a rate of \( 80 \mathrm{J} s^{-1} \), the
rate of increase in internal energy is :
A. 30 J \( s^{-1} \)
B. 40 J \( s^{-1} \)
c. 50 \jmath \( s^{-1} \)
D. 60 J \( s^{-1} \)


Show that the function of \( \boldsymbol{y}= \)
\( A \sin 2 x+B \cos 2 x \) satisfies the
differential equation \( \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}+\boldsymbol{4} \boldsymbol{y}=\mathbf{0} \)


Find the number of molecule(s)/ion
having Lewis basic property from the following
\( \boldsymbol{H}_{2} \boldsymbol{O}, \boldsymbol{N} \boldsymbol{H}_{3}, \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{N} \boldsymbol{H}_{2}, \boldsymbol{R} \boldsymbol{O} \boldsymbol{H}, \boldsymbol{F} \boldsymbol{e} \boldsymbol{C l}_{3} \)


In the emission line spectra of hydrogen atom, how many lines can be accounted for by all possible electron transitions
between five lowest energy levels within the atom?
\( A \cdot 4 \)
B. 5
c. 10
D. 20


Which is not isoelectronic with the
other three?
A. \( C O \)
B. \( N O^{+} \)
\( c \cdot C N^{-} \)
D. \( O_{2} \)


Change in entropy is negative for:
A. Bromine\( (I) \rightarrow \) Bromine\( (g) \)
B \( \cdot C(s)+H_{2} O(g) \rightarrow C O(g)+H_{2}(g) \)
\( \mathbf{C} \cdot N_{2}(g, 10 a t m) \rightarrow N_{2}(g, 1 a t m) \)
D. \( F e(a t 400 K) \rightarrow F e(a t 300 K) \)


Photobromination of 2-methyl propane gives a mixture of 1-bromo-2-methyl propane and 2-bromo-2-methyl propane in the ratio:
A . 99:
B . 1: 99
\( c \cdot 1: \)
D. 3:


\( \ln \) an \( L C \) circuit the capacitor has
maximum charge \( q_{0} . \) The value of \( \left(\frac{d I}{d t}\right)_{\max }, \) where \( I \) is current in the circuit and \( t \) is time, is
\( ^{A} \cdot \frac{q_{0}}{L C} \)
в. \( \frac{q_{0}}{\sqrt{L C}} \)
c. \( \frac{q_{0}}{L C}-1 \)
D. \( \frac{q_{0}}{L C}+1 \)


Statement 1: Temperature of Real gases often changes when undergoing a free expansion under adiabatic condition
whereas that of an ideal gas does not.
Statement 2: First law of
thermodynamics holds for ideal gas only.
A. Statement 1 is true. Statement 2 is true and statement 2 is correct explanation for statement 1.
B. Statement 1 is true. Statement 2 is true and statement 2 is NOT correct explanation for statement 1.
c. Statement 1 is true. Statement 2 is false
D. Statement1 is false. Statement 2 is true


Calculate the molar conductivity of water at infinite dilution (in \( \mathrm{Sm}^{2} \mathrm{mol}^{-1} \) ).
( molar conductivity of hydrogen ions and the molar conductivity of hydroxide ions at infinite dilution are \( 349.6 \times 10^{-4} \mathrm{Sm}^{2} \)
\( \left.\mathrm{mol}^{-1} \text {and } 198.3 \times 10^{-4} \mathrm{Sm}^{2} \mathrm{mol}^{-1}\right) \)
A . 547.9
B. 647.9
c. \( 647.9 \times 10^{-4} \)
D. \( 547.9 \times 10^{-4} \)


Cork is a colloid of


A conducting rod of mass \( m \) and length
is free to move without friction on two
parallel long conducting rails, as shown below. There is a resistance \( R \) across
the rails. In the entire space around,
there is a uniform magnetic field \( \boldsymbol{B} \)
normal to the plane of the rod and rails.
The rod is given an impulsive velocity \( \boldsymbol{v}_{0} \) Finally, the initial energy \( \frac{1}{2} m v_{0}^{2} \)
A. Will be converted fully into heat energy in the resistor
B. Will enable rod to continue to move with velocity \( v_{0} \)
since the rails are frictionless
c. will be converted fully into magnetic energy due to induced current
D. Will be converted into the work done against the magnetic field


State True or False.
Lowering of vapour pressure is proportional to the mole fraction of the solute.
A. True
B. False


At what speed, the velocity head of a stream of water be equal to
\( 40 \mathrm{cm} \) of \( \mathrm{Hg} ? \)
B. \( 432.6 \mathrm{cms}^{-1} \)
c. \( 632.6 \mathrm{cms}^{-1} \)
D. \( 832.6 \mathrm{cms}^{-1} \)


Assertion
Stirring the liquid in thermal contact with the reservoir will convert the work
done into heat, is an irreversible
process.
Reason
If it is the reversible process it will violate the second law of
thermodynamics.
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


The rate law of reaction between the
substance \( \boldsymbol{A} \) and \( \boldsymbol{B} \) is given by \( \boldsymbol{r} \boldsymbol{a} \boldsymbol{t} \boldsymbol{e}= \)
\( \boldsymbol{K}[\boldsymbol{A}]^{n}[\boldsymbol{B}]^{m} . \) On doubling the
concentration of \( \boldsymbol{A} \) and making the volume of \( B \) half the ratio of new rate to
the earlier rate of reaction will be:
A \( \cdot \frac{1}{2^{n+m}} \)
в. \( m+n \)
\( \mathbf{c} \cdot 2^{n+m} \)
D. \( 2^{n-m-m-m} \)


When a ball is hit by a bat, forces acting on the ball are
A. muscular force
B. gravitational force
c. both A and B
D. neither A nor B


The type of collision is:
A . perfectly elastic
B. elastic
C . inelastic
D. perfectly inelastic


Otolith is formed of
A. carbohydrate
B. Magnesium
c. Lipid
D. Calcium cabonate


If \( \tan ^{-1} x+\tan ^{-1} y=\frac{\pi}{4}, x y<1, \) then
write the value of \( \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{x} \boldsymbol{y} \)


A uniform meter rule balances
horizontally on a knife-edge placed at the \( 60 \mathrm{cm} \) mark when a weight of \( 1 \mathrm{g} \) is suspended from one end. What is the weight of the rule?


Find union of \( A \) and \( B, \) and represent it
using Venn diagram:
\( \boldsymbol{A}=\{1,2,3,4,8,9\}, B=\{1,2,3,5\} \)


Prove that \( \sum_{r=0}^{n} 3^{r n} \mathbf{C}_{r}=4^{n} \)


Define metamerism.


Show that:
\[
\tan ^{-1}\left(\frac{\sqrt{1+x}-\sqrt{1-x}}{\sqrt{1+x}+\sqrt{1-x}}\right)=\frac{\pi}{4}
\]
\( \frac{1}{2} \cos ^{-1} x,-\frac{1}{\sqrt{2}} \leq x \leq 1 \)


The length, breadth and height of a cuboid are in the ratio 4: 2: 1 and its
total surface area is \( 1372 m^{2} \). Find the
dimensions of the cuboid.


Deduce an expression for the capacitance of a parallel plate
capacitor.


Carefully observe the given diagrams which indicates standard enthalpy of formation of different states of one mole
Mg and 2 mole Cl atom and match the
entries in column I and II provided.
Energy
(k) \( \quad \) state of Mg and \( C l_{2} \)
Energy (k.) States of Mg and C
Columnı


Energy potential from various sources
of sea is
commercial exploitation of same is
A. Small, difficult
B. Large, difficult
c. small, easy
D. Large, easy


A body is projected with a velocity \( u \). It
passes through a certain point above
the gound after \( t_{1} \) sec. The time after which the body passes through the same point during the return journey is:
A \( \cdot\left(\frac{u}{g}-t_{1}\right) \)
в. \( 2\left(\frac{u}{g}-t_{1}\right) \)
c. \( _{3}\left(\frac{u}{g}-t_{1}\right) \)
D. \( _{3}\left(\frac{u^{2}}{g^{2}}-t_{1}\right) \)


The volume of the greatest sphere that can be cut off from a cylindrical log of wood of base radius \( 1 \mathrm{cm} \) and height 5
\( \mathrm{cm} \) is :
A \( \cdot \frac{4}{3} \pi \)
в. \( \frac{10}{3} \pi \)
c. \( 5 \pi \)
D. \( \frac{20}{3} \pi \)


Answer the following question in one
word or one sentence or as per exact
requirement of the question. f \( \frac{\pi}{2}<x<\pi, \) then find \( \frac{d}{d x}(\sqrt{\frac{1+\cos 2 x}{2}}) \)


The important antioxidant used in food
is:
A. Внт
в. ВНС
c. Втх
D. All of the above


How many electrons make up a charge of \( 20 \mu C ? \)
A \( \cdot 1.25 \times 10^{14} \)
B. \( 2.23 \times 10^{14} \)
c. \( 3.25 \times 10^{14} \)
D. \( 5.25 \times 10^{14} \)


Two concentric circles are of radii \( 5 \mathrm{cm} \)
and \( 3 \mathrm{cm} . \) Find the length of the chord of the larger circle which touches the
smaller circle.
\( A \cdot 8 \mathrm{cm} \)
в. \( 4 \mathrm{cm} \)
\( c .3 \mathrm{cm} \)
D. \( 5 \mathrm{cm} \)


Find the solution set of \( \frac{3}{5} x-\frac{2 x-1}{3}> \)
1


A ball dropped from a point \( P \) crosses a
point \( Q \) in \( t \) second. if \( R \) and \( S \) are
points such that, \( P Q=Q R=R S \), the
time taken by the ball to travel from \( \boldsymbol{R} \)
to \( S \) is:
A. \( (\sqrt{2}-1) t \)
B . \( (\sqrt{3}-\sqrt{2}) t \)
c. \( \sqrt{3} t \)
D. \( (\sqrt{3}-1) t \)


Assertion
Death of companion cell leads to the death of sieve cells also.
Reason
Both companion and sieve are phloem
cells.
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


Find the amount and the compound
interest on \( R s .8000 \) at \( 5 \% \) per annum
for 2 years, compounded annually.


\( \boldsymbol{C H} \equiv \boldsymbol{C H} \frac{N \boldsymbol{H}_{4} O \boldsymbol{H}}{C u_{2} C l_{2}} \)
Product is-
A. \( C u-C \equiv C-C u \)
в. \( C H_{2}=C H-C \equiv C H \)
c. \( C H \equiv C-C u \)
D. \( C u-C \equiv C-N H_{4} \)


Compare the penetrating powers of \( \alpha, \beta \) and \( \gamma \) - radiations.
A \( \cdot \alpha>\beta>\gamma \)
v
в. \( \alpha<\beta<\gamma \)
c. \( \alpha>\gamma>\beta \)
D. \( \alpha<\gamma<\beta \)


The hybridizations of atomic orbitals of
nitrogen in \( N O_{2}^{+}, N O_{3}^{-} \) and \( N H_{4}^{+} \)
respectively are:
A \( \cdot s p, s p^{2} \) and \( s p^{3} \)
B \( \cdot s p^{2}, s p \) and \( s p^{3} \)
\( \mathbf{c} \cdot s p, s p^{3} \) and \( s p^{2} \)
D. \( s p^{2}, s p^{3} \) and \( s p \)


Cyclopropane rearranges to form
propene:
\( \triangle \rightarrow \boldsymbol{C H}_{2}-\boldsymbol{C H}=\boldsymbol{C H}_{2} \)
This follows first-order kinetics. The rate
constant is \( 2.714 \times 10^{-3} s e c^{-1} . \) The
initial concentration of cyclopropane is
\( 0.29 M . \) What will be the concentration
of cyclopropane after 100 sec?
A. \( 0.035 M \)
B. \( 0.22 M \)
c. \( 0.145 M \)
D. \( 0.0018 M \)


A ball is released from the top of a tower
of height h metres. It takes T seconds to reach the ground. What is the position
of the ball in \( T / 3 \) seconds?
A. \( h / 9 \) metres from the ground
B. \( 7 h / 9 m \) from the ground
c. \( 8 h / 9 \) metres from the ground
D. \( 17 h / 18 m \) from the ground


Draw the valence shell molecular orbital
diagram of oxygen molecule and predict
its magnetic nature


If \( 0<x<y, \) then the positive square
root of \( \boldsymbol{x}+\boldsymbol{y}-\boldsymbol{2} \sqrt{\boldsymbol{x} \boldsymbol{y}} \) is
\( \mathbf{A} \cdot \sqrt{x}+\sqrt{y} \)
В. \( \sqrt{x}-\sqrt{y} \)
c. \( \sqrt{y}-\sqrt{x} \)
D. \( -\sqrt{x}-\sqrt{y} \)


Mention any two occupational
respiratory disorders and their causes in human beings?


Assertion
If we bend an insulated conducting wire, the resistance of the wire
increases.
Reason
The drift velocity of electrons in bent
wire decreases.
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


toppr
Q Type your question
coefficient of viscosity \( \eta \) and density
\( \boldsymbol{\rho}\left(<\frac{\sigma}{2}\right) . \) If the length of the liquid
column is sufficiently long, the terminal
velocity attained by the ball is given by
(assume all pulleys to be mass-less and
string as mass-less and inextensible):
A \( \cdot \frac{2}{9} \frac{r^{2}(2 \sigma-\rho) g}{\eta} \)
B \( \cdot \frac{1}{9} \frac{r^{2}(\sigma-2 \rho) g}{\eta} \)
c. \( \frac{2}{9} \frac{r^{2}(\sigma-4 \rho) g}{\eta} \)
D.


n identical cells, each of emf \( \varepsilon \) and
internal resistance \( r, \) are joined in
series to form a closed circuit. One cell
\( A \) is joined with reversed polarity. The potential difference across each cell, except \( A \), is
A \( \cdot \frac{2 \varepsilon}{n} \)
в. \( \frac{n-1}{n} \)
c. \( \frac{n-2}{n} \)
D. \( \frac{2 n}{n-2} \)


f \( 2 f(x)+3 . f\left(\frac{1}{2}\right)=x^{2}-1 \) then find
\( f(x) \)


Let us consider the ionization of \( H C l \) in
the aqueous solution of \( \boldsymbol{C H}_{3} \) COOH.
\( \boldsymbol{C H}_{3} \boldsymbol{C O O H}+\boldsymbol{H C l} \rightleftharpoons \)
\( \boldsymbol{C H}_{3} \boldsymbol{C O O H}_{2}^{+}+\boldsymbol{C l}^{-} \)
Select the correct statement(s) among
the following:
This question has multiple correct options
A \( \cdot C l^{-} \) is the conjugate base of \( H C l \)
B. \( C H_{3} C O O H \) is the conjugate base of \( C H_{3} C O O H_{2}^{+} \)
C. \( C H_{3} C O O H_{2}^{+} \) is the conjugate base of \( C H_{3} \) COOH
D. \( C l^{-} \) is the conjugate base of \( C H_{3} C O O H \)


500 g of water at \( 100^{\circ} C \) is mixed with \( 300 \mathrm{g} \) at \( 30^{\circ} \mathrm{C} \). Find the temperature of the mixture. Specific heat of water \( = \) \( 4.2 J g^{-1} o C^{-1} \)
A \( .73 .8^{\circ} \mathrm{C} \)
B. \( 53.8^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 40^{\circ} \mathrm{C} \)
D. \( 60^{\circ} \mathrm{C} \)


See the diagram. Area of each plate is
\( 2.0 m^{2} \) and \( d=2 \times 10 \times 10^{-3} m . \)
charge of \( 8.85 \times 10^{-8} C \) is given to \( Q \)
Then the potential of \( Q \) becomes:
\( \mathbf{A} \cdot 13 V \)
B. 10v
c. \( 66.7 \mathrm{V} \)
D. \( 8.825 v \)


Line \( A B \) passes through point (1,2)
and intersects the positive \( x \) and \( y \) axes
at \( \boldsymbol{A}(\boldsymbol{a}, \boldsymbol{0}) \) and \( \boldsymbol{B}(\boldsymbol{0}, \boldsymbol{b}) \) respectively. If
the area of \( \triangle A O B \) is 1 unit the value of
\( (2 a-b)^{2} \) is
A .220
в. 240
c. 248
D. 284


Gametophyte and sporophyte are independent of each other in which of the following groups?
A. Pteridophytes
B. Angiosperms
c. Gymnosperms
D. Bryophytes


Which of the following is not an example of an emulsifying agent?
A. Proteins
B. Gums
c. soaps
D. Electrolytes


A student appears in an exam and is asked to measure the length of a side of a triangle. Which of the following
instruments is suitable for the
purpose?
A. Protactor
B. Microscope
c. Vernier callipers
D. Meter scale


If \( f(x)=\frac{\log \left(e^{x^{2}}+2 \sqrt{x}\right)}{\tan \sqrt{x}}, x \neq 0, \) then
the value of \( f(0) \) so that \( f \) is
continuous at \( x=0 \) is
A \( \cdot \frac{1}{2} \)
B. \( \sqrt{2} \)
\( c \cdot 2 \)
D. \( \frac{1}{\sqrt{2}} \)


If \( 6 \sin ^{2} \theta-\sin \theta=1 \) and \( 0 \leq \theta \leq \pi \)
calculate the value of \( \sin \theta \)
A \( \cdot \frac{1}{6} \)
B.
\( c \cdot \frac{1}{2} \)
D. 19
E . 30


Select the correct order of polarising
power of cation.
\( \mathbf{A} \cdot N a^{+}>M g^{+2}>A l^{+3}>S i^{+4} \)
B \( \cdot S i^{4+}>A l^{3+}>M g^{2+}>N a^{+} \)
\( \mathbf{C} \cdot A l^{3+}>M g^{2+} S i^{4+}>N a^{+} \)
D. \( M g^{2+}>A l^{3+}>S i^{4+}>N a^{+} \)


When a liquid taken in along cylindrical vessel of material with linear coefficient
of expansion \( (\alpha) \) is heated, the level of
liquid did not change. The volume coefficient of expansion of liquid is :
A \( \cdot \frac{\alpha}{3} \)
B. \( 3 \alpha \)
\( c \cdot a \)
D. \( \alpha^{3} \)


An ideal gas undergoes a quasi static, reversible process in which its molar
heat capacity \( C \) remains constant. If
during this process the relation of
pressure \( \boldsymbol{P} \) and volume \( \boldsymbol{V} \) is given by
\( P V^{n}= \) constant, then \( n \) is given by
(Here \( C_{P} \) ad \( C_{V} \) are molar specific heat
at constant pressure and constant volume, respectively):
\( ^{\mathrm{A}} \cdot_{n}=\frac{C-C_{P}}{C-C_{V}} \)
B. \( n=\frac{C_{P}-C}{C-C_{V}} \)
c. \( _{n}=\frac{C-C_{V}}{C-C_{P}} \)
D. \( _{n}=\frac{C_{P}}{C_{V}} \)


The \( 4^{t h} \) term of A.P is equal to 3 times
the first term and the \( 7^{t h} \) term excess
which the third term by 1. Find its \( n^{t h} \) term.
\( \mathbf{A} \cdot n+2 \)
B. \( 3 n+1 \)
c. \( (2 n+1) \)
D. \( 3 n+2 \)


In which of the following solvent it is possible to create acetylide ion?
\( A \)
AcOH
в. \( \mathrm{H}_{2} \mathrm{O} \)
c. \( (i-P r)_{2} N H \)
D. Acetone


What is the maximum speed at which a railway carriage can move without toppling over along a curve of radius \( R=200 m \) if the distance from the
centre of gravity of the carriage to the level of the rails is \( h=1.0 m \), the
distance between the rails is \( h=1.0 m \)
the distance between the rails is \( l= \)
\( 2.0 m \) and the rails are laid horizontally?
(Take \( \boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2} \) )
A \( \cdot 11.18 m s^{-1} \)
B. \( 22.36 m s^{-1} \)
c. \( 44.72 m s^{-1} \)
D. \( 74 m s^{-1} \)


An alternating voltage \( \boldsymbol{V}=\boldsymbol{V}_{0} \sin \omega \boldsymbol{t} \) is
applied across a circuit and as a result, a current \( \boldsymbol{I}=\boldsymbol{I}_{0} \sin \left(\boldsymbol{\omega} \boldsymbol{t}+\frac{\boldsymbol{\pi}}{2}\right) \) flows in it
The power consumed per cycle is
A . \( I_{0} V_{0} \)
в. \( 0.5 I_{0} V_{0} \)
c. \( 0.7 I_{0} V_{0} \)
D. \( 1.41 I_{0} V_{0} \)
\( E . \)


When glycerol is treated with excess of
\( \boldsymbol{H} \boldsymbol{I}, \) it produces:
A. 2-iodopropane
B. allyl iodide
c. propene
D. glycerol triiodide


Find the common difference of the A.P.
given below:
\( \mathbf{0 . 6}, \mathbf{1 . 7}, \mathbf{2 . 8}, \mathbf{3 . 9}, \ldots . \)


\( C u^{+} \) undergoes disproportionation to
\( C u \) and \( C u^{2+} \)
If true enter 1 , else enter 0 .
\( A \)


A long wire carries a current of \( 20 A \)
long the axis of a solenoid, the field due to the solenoid is 4 mT. The resultant
field at a point 3 mm from the solenoid
axis is :
A. \( 1.33 \mathrm{mT} \)
в. \( 4.2 \mathrm{mT} \)
c. \( 2.1 m T \)
D. \( 8.4 \mathrm{mT} \)


The temperature of a furnace is \( 2324^{\circ} \mathrm{C} \)
and the intensity is maximum in its
spectrum nearly at \( 12000 A^{\circ} . \) If the intensity in the spectrum of star is
maximum nearly at \( 4800 A^{\circ} \), then the
surface temperature of the star is :
A \( \cdot 8400^{\circ} \mathrm{C} \)
B. 6219 \( ^{\circ} \mathrm{C} \)
\( c \cdot 7200^{\circ} \mathrm{C} \)
D. \( 5900^{\circ} \mathrm{C} \)


A ball is thrown horizontally from the top of a tower \( 40 \mathrm{m} \) high. The ball strikes the ground at a point \( 80 \mathrm{m} \) from the
bottom of the tower. Find the angle that
the velocity vector makes with the horizontal just before the ball hits the
ground.
\( \mathbf{A} \cdot 45 m / s \)
в. \( 90 \mathrm{m} / \mathrm{s} \)
c. \( 37 m / s \)
D. \( 53 m / s \)


You are standing upright in a room in front of a vertical mirror. In this mirror,
you can see from your position, only the upper two- third part of your body. You
wish to see the full image of your body
in the mirror. Which combination of the
following three courses of action will achieve this? I. Move away from the mirror II. Move towards the mirror III.
Use a mirror whose height will allow you
to see your full image
A. I only
B. II only
c. III only
D. Either I or III


A train is running at \( 5 \mathrm{m} / \mathrm{s} \) and a man jumps out of it with a velocity \( 10 \mathrm{m} / \mathrm{s} \) in
a direction making an angle of \( 60^{\circ} \) with
the direction of the train. The velocity of the man relative to the ground is equal
to
A. \( 12.24 \mathrm{m} / \mathrm{s} \)
B. \( 11.25 \mathrm{m} / \mathrm{s} \)
c. \( 14.23 \mathrm{m} / \mathrm{s} \)
D. \( 13.23 \mathrm{m} / \mathrm{s} \)


In the given figure, the point \( P \) bisects \( A B \) and \( D C . \) Prove that \( \Delta A P C \cong \Delta B P D \)


What is a soap?


R.Q. would depend upon
A. Nature of enzymes
B. Nature of substrate
C. Amount of \( \mathrm{CO}_{2} \) released
D. Amount of \( \mathrm{O}_{2} \) utilised


Plastics being developed from ecofriendly renewable sources, plus some modern plastics are biodegradable is
one of the achievements of
A. Green revolution
B. Waste management
c. Revolution resource recovery
D. Green chemistry


A \( 1 \mathrm{m} \) long uniform beam is being
balanced as shown below. Calculate
force G.
A. 3.0 N
B. 4.5 \( \mathrm{N} \)
\( c \cdot 5.0 N \)
D. 6.0 N


Example of an intrinsic colloid is:
A \( \cdot A s_{2} S_{3} s o l \)
B. s sol
c. Egg albumin
D. \( \mathrm{Fe}\left(\mathrm{OH}_{2} \mathrm{sol}\right) \)


Acids combine with bases to form:
A. colour and gas
B. salt and water
c. water and heat
D. steam and crystals


State whether true or false.
The weight of a freely falling body from a very large height is always constant
A. True
B. False


6 th term of \( \frac{1}{4}, \frac{1}{2}, 1 \ldots \ldots \)


post a letter to my friend and do not receive a reply. It is known that one letter out of \( m \) letters do not reach its
destination. If it is certain that my friend will reply if he receives the letter If \( A \) denotes the event that my friend receives the letter and \( B \) that I get a
reply, then This question has multiple correct options
A \( \cdot P(B)=(1-1 / m)^{2} \)
B . \( P(A \cap B)=(1-1 / m)^{2} \)
c. \( P\left(A \mid B^{\prime}\right)=(m-1) /(2 m-1) \)
D. \( P(A \cup B)=(m-1) / m \)


Find the value of \( k \) so that the function \( f \)
is contiuous at the indicated point. \( f(x)=\begin{array}{ll}k x+1 & , x \leq \pi \\ \cos x & , x>\pi\end{array} \) at \( x=\pi \)


In a right \( \triangle A B C, \) right angled at \( C, M \)
is the mid point of the hypotenuse of
\( A B . C \) is joined to \( M \) produced to a
point \( D \) such that \( D M=C M . \) Point \( D \)
is joined to point \( \boldsymbol{B} \). Then
rhis question has multiple correct options
A. \( \triangle A M C \cong \triangle B M D \)
B. \( \angle D B C \) is a right angle
c. \( \triangle D B C \cong \triangle A C B \)
\( ^{\mathrm{D}} \cdot C M=\frac{1}{2} A B \)


Which of the following is incorrect for
glycolysis?
A. The end products of this process are \( C O_{2} \) and \( H_{2} O \)
B. IT produces ATP
c. It uses ATP
D. None of these.


Though there is only one electron in a hydrogen atom, the spectrum of hydrogen contains a number of lines. How do you explain this?


A rubber develops a force \( \boldsymbol{F}=(-2 x+ \)
1) \( N, \) (Where \( x \) is the extension in its
natural length in \( m \) ). Work done by the force when rubber is stretched from
\( \boldsymbol{x}=\mathbf{0} \) to \( \boldsymbol{x}=\mathbf{1} \boldsymbol{m} \) is :
A . \( 4 J \)
B. \( 8 J \)
c. \( Z \) ero
D. \( 10 J \)


A solution containing \( 0.122 \mathrm{kg} \) of
benzoic acid in \( 1 k g \) of benzene
(b.pt.353 K) boils at \( 354.5 K \)
Determine the apparent molar mass of benzoic acid (which dimerizes) in
the solution and the degree of
dimerization
Given: \( \Delta_{v a p} H_{1 m}(\text {benzene})= \)
\( \mathbf{3 9 4 . 5 7} \boldsymbol{J} \boldsymbol{g}^{-1} \)
A. 0.214 kg \( \mathrm{mol}^{-1}, 0.86 \)
в. 0.257 kg \( m o l^{-1}, 0.932 \)
c. \( 0.428 \mathrm{kg} \mathrm{mol}^{-1}, 0.956 \)
D. \( 0.454 \mathrm{kg} \mathrm{mol}^{-1}, 0.986 \)


A mass of \( 5 \mathrm{kg} \) is suspended from a spring of stiffness \( 46 \mathrm{kN} / \mathrm{m} . \) A dashpot is fitted between the mass and the
support with a damping ratio of 0.3.Calculate the critical damping coefficient in \( \mathrm{Ns} / \mathrm{m} \)
A . 939
B. 949
c. 959
D. 969


The increase in base area leads to
decrease in stability of an object
A. True
B. False


Which of the following is not a linear polynomial?
A \( . p(y)=8 y+6 \)
В. \( p(x)=8 y+2 x \)
c. \( p(x)=4+\frac{5 x}{x}+8 x^{\circ} \)
D. \( p(x)=4+5 x \)


A particle is moving along a circle such
that it completes one revolution in 40 seconds. In 2 minutes 20 seconds, the atio \( \frac{\mid \text {displacement} \mid}{\text {distance}} \) is?


Obtain: \( \int \frac{(3 x+2)}{(x+1)(x+2)(x-3)} d x \)


\( \ln \Delta A B C, \) if \( A B>B C \) then :
\( \mathbf{A} \cdot \angle C<\angle A \)
B . \( \angle C=\angle A \)
c. \( \angle C>\angle A \)
\( \mathbf{D} \cdot \angle A=\angle B \)


Write IUPAC names of the following coordination compounds.
a) \( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right] \boldsymbol{C l}_{3} \)
b) \( \boldsymbol{K}_{3}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{6}\right] \)
\( \boldsymbol{c} \boldsymbol{K}_{2}\left[\boldsymbol{P} \boldsymbol{d}(\boldsymbol{C l})_{4}\right. \)
d) \( \left[\boldsymbol{N} \boldsymbol{i}(\boldsymbol{C} \boldsymbol{o})_{4}\right] \)


The value of \( \square_{e q}^{\infty} \) for \( N H_{4} C l, \) NaOH and NaCl are respectively, 149.74,248.1 and \( 126.4 \Omega^{-1} c m^{2} e q u i v^{-1} . \) The value of \( \square_{e q}^{\infty} \)
of \( N H_{4} O H \) is
A . 371.44
B. 271.44
\( c \cdot 71.44 \)
D. Cannot be predicted from given data


Name the kind of mirror used to obtain
a virtual and enlarged image :
A. Concave Mirror
B. Convex Mirror
c. Plane Mirror
D. All of the above


One litre of \( C O_{2} \) ia passed through red hot coke. The volume become 1.4 litres
at same temperature and pressure The composition of product is
A. 0.8 litre of \( C O_{2} \) and 0.6 litre of \( C O \)
B. 0.7 litre of \( C O_{2} \) and 0.7 litre of \( C O \)
c. 0.6 litre of \( C O_{2} \) and 0.8 litre of \( C O \)
D. 0.4 litre of \( C O_{2} \) and 1.0 litre of \( C O \)


A coil is needed to operate an arc lamp of \( 150 \mathrm{V}, 50 \mathrm{Hz} \). The lamp of resistance of 5 ohms when running at 10 A. Find inductance of the choke coil, if the
same arc lamp is to be operated on 160 V, DC. What is the additional resistance
required?
A . \( 5 \Omega \)
B. \( 4.5 \Omega \)
c. \( 5.5 \Omega \)
D. 2.5\Omega


The product of the time period of a wave and its frequency is
A . Infinite
B. Zero
c. More than unity but less than infinity
D. Unity


\( Y \) and \( Z \) are, respectively:
A \( \cdot N_{2} O_{5} \) and \( H P O_{3} \)
B. \( N_{2} O_{4} \) and \( H P O_{3} \)
c. \( N_{2} O_{4} \) and \( H_{3} P O_{3} \)
D. \( N_{2} O_{3} \) and \( H_{3} P O_{4} \)


For \( \boldsymbol{y}=\boldsymbol{e}^{\boldsymbol{x}^{2} \cdot \sin \boldsymbol{x}} \) find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \)


Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube:
A .243
в. 3072
c. 11979
D. 19652


Assertion
In mammals, complex respiratory
system has developed.
Reason
Mammalian skin is impermeable to
gases.
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


Select correct statement for the lesser
number of oxidations states in \( 3 d- \)
series.
A. In the beginning of the series it can be due to the presence of too few electrons to loose or share.
B. Towards the end of the series, it can be ascribed to the presence of too many electrons and thus fewer empty orbitals to share electrons with the ligands.
\( \mathrm{c} . \) Both \( (\mathrm{A}) \) and \( (\mathrm{B}) \) are correct
D. None of the above is correct


When \( 75 \% \) of a number is added to 75
the result is the number again. The number is
A. 150
в. 200
c. 300
D. 225


Arrhenius bases produce what ion in solution?
A. Hydrogen ions
B. Hydroxide ions
c. water
D. Hydronium ions


In a series of radioactive decays, if a
nucleus of mass number 180 and
atomic number 72 decays into another nucleus of mass number 172 and
atomic number 69 , then the number of
\( \alpha \) and \( \beta \) particles released respectively
are
A .2,3
в. 2,2
c. 2,1
D. 2,0
E . 1,3


Meiotic division in zygote takes place in
A. Thallophyta
B. Angiosperms
c. Gymnosperms
D. Pteridophyta


A solution of caustic soda (NoOH) in
water or when fused,conducts electric current. What is the similarity in these two cases?


The symbol and formula for momentum
is
\( \mathbf{A} \cdot m, p v \)
в. \( p, m a \)
\( \mathbf{c} \cdot p, m v \)
D. \( M, m v \)


Excess atmospheric \( C O_{2} \) increases
green house effect as \( C O_{2} \)
A. Is opaque to infra-red rays
B. Is not opaque to infra-red rays
c. Precipitates dust in the atmosphere
D. Reduces atmospheric pressure


Which of the following is non-essential
in an ecosystem:-
A. \( C o_{2} \)
B. Grass
c. soil
D. Fungi


Solve \( \int(3 x-2) \sqrt{2 x^{2}-x+1} d x \)


A rectangular courtyard is \( 18 \mathrm{m} 72 \mathrm{cm} \) long and \( 13 \mathrm{m} 20 \mathrm{cm} \) broad. It is to be
paved with square tiles of the same
size. Find the least possible number of such tiles.


Which of the following pairs of isomers is not correctly matched with its type of isomerism?
A \( \cdot\left[C r\left(N H_{3}\right)_{6}\right]\left[C r(C N)_{6}\right] \) and
\( \left[C r\left(N H_{3}\right)_{4}(C N)_{2}\right]\left[C r\left(N H_{3}\right)_{2}(C N)_{4}\right] \) - coordination
isomerism
в. \( \operatorname{Co}\left[\left(N H_{3}\right)_{5} N O_{2}\right] C l_{2} \) and \( \left[C o\left(N H_{3}\right)_{5} O N O\right] C l_{2}- \) Linkage
isomerism
\( \mathbf{c} \cdot\left[\operatorname{Co}(p y)_{2}\left(H_{2} O\right)_{2} C l_{2}\right] C l \) and
\( \left[\cos (p y)_{-} 2\left(H_{-} 20\right) C_{-} 3\right] H_{-} 20 \$ \$- \) coordination
isomerism
D \cdot \( \left[P t\left(N H_{3}\right)_{4} B r_{2}\right] C l_{2} \) and \( \left[P t\left(N H_{3}\right)_{4} C l_{2}\right] B r_{2} \) -lonisation isomerism


The slope of a curve at each of its points is equal to the square of the abscissae of the point. Find the particular curve
through the point (-1,1) \( \mathbf{1}+\boldsymbol{y}=\boldsymbol{2} \boldsymbol{e}^{\boldsymbol{x}^{2} / \mathbf{2}} \)


Which one of the following plasma proteins is involved in the coagulation of blood?
A. Fibrinogen
B. Albumin
c. Serum amylase
D. Globulin


Match the elements of list I, which have differential equations, with elements of list II, which have solutions of
differential equations:
List I
\[
\text { A) } y y_{1}=\sec ^{2} x
\]
1) \( y \sec ^{2} x=\sec x+c \)
В) \( y_{1}=x \sec y \)
2) \( x y=\cos y+c \)
C) \( y_{1}+(2 y \tan x)=\sin x \)
3) \( x y=\sin x+c \)
D) \( x y_{1}+y=\cos x \)
\[
\text { 4) } y^{2}=2 \tan x+c
\]
\[
\text { 5) } x^{2}=2 \sin y+c
\]
Then, the correct order for \( \boldsymbol{A} \boldsymbol{B} \boldsymbol{C} \boldsymbol{D} \) is:
\( \mathbf{A} \cdot 3254 \)
B. 4123
c. 4513
D. 3512


A spring of spring constant k placed horizontally on a rough horizontal
surface is compressed against a block
of mass \( \mathrm{m} \) placed on the surface so as to store maximum energy in the spring. If the coefficient of friction between the
block and the surface is \( \mu, \) the potential
energy stored in the spring is:
A \( \cdot \frac{\mu^{2} m^{2} g^{2}}{k} \)
B. \( \frac{2 \mu^{2} g^{2}}{k} \)
\( ^{\mathrm{C}} \cdot \frac{\mu^{2} m^{2} g^{2}}{2 k} \)
D. \( \frac{3 \mu^{2} m g^{2}}{k} \)


In adjoining figure \( A B \) is a chord of a
circle and \( \angle A D B=45^{\circ}, \angle A C B \) will be:
A \( .45^{\circ} \)
B \( \cdot 60^{\circ} \)
\( c \cdot 90^{\circ} \)
D. \( 135^{\circ} \)


Absolute zero corresponds to:
A . \( -273 K \)
В. \( -273^{\circ} \mathrm{C} \)
c. \( 273^{\circ} \mathrm{F} \)
D. None of these


If \( A \) and \( B \) are skew-symmetric
matrices of the same order, prove that \( A B+B A \) is symmetric matrix.


Find the median of the following data.
\( 22 \quad 25 \) \( \mathbf{3 0} \) \( \boldsymbol{x} \quad \mathbf{1 4} \quad \mathbf{1 8} \)
\( \begin{array}{llll}f & 7 & ! 0 & 12\end{array} \) 16 5
A . 20
B. 19
c. 21
D. 22


In a certain region of space, electric field is along the z-direction throughout The magnitude of electric field is, however, not constant but increases
uniformly along the positive z-direction, at the rate of \( 10^{5} N C^{-1} \) per metre. What
are the force and torque experienced by a system having a total dipole moment equal to \( 10^{-7} \mathrm{Cm} \) in the negative zdirection?


Explain how silver is extracted from its
chief ore.


In the book 'Historia Naturalis' about
1000 medicinal plants were described, which was written by
A. Pliny
B. Linnaeus
c. cesalpino
D. Tippo


A relation which satisfies reflexive
symmetric and transitive is relation
A. an identity
B. a constant
c. an equivalence
D. None of these


The mean of 100 observations is 50 If
one of the observations which was 50 is
replaced by 150 the resulting mean will be
A . 51
B. 52
\( c .51 .5 \)
D. 53


Solve the following crossword puzzle with the clues given. Across:
2. Plantation prevents it.
5. Use should be banned to avoid soil
pollution.
6. Type of soil used for making pottery.
7. Living organism in the soil
Down:
1. In desert soil erosion occurs through.
2. Clay and loam are suitable for cereals
like.
3. This type of soil can hold very little
water
4. Collective name for layers of soil.


A rod has poisson's ratio \( 0.2 . \) If a rod
suffers a longitudinal strain of \( 2 \times 10^{-3} \)
then the percentage change in volume
is
\( \mathbf{A} \cdot+0.12 \)
в. -0.12
c. 0.28
D. -0.28


There is an auditorium with 35 rows of
seats. There are 20 seats in the first
row, 22 seats in the second row, 24 seats in the third row and so on. Find the
number of seats in the twenty-third row.


Which is correct statement about the
diborane structure?
A. All \( H B H \) bond angles are equal
B. All \( H-B \) bond lengths are equal
c. It has two three-centre- 2 -electron bonds
D. All hydrogen and boron atoms are in one plane


If \( \boldsymbol{B}=\left\{\boldsymbol{y} \mid \boldsymbol{y}^{2}=\boldsymbol{3} \boldsymbol{6}\right\} \) then the \( \operatorname{set} \boldsymbol{B} \) is a
set.
A. Empty
B. singleton
c. Infinite
D. None of the above


The cell in which the following reaction
occurs:
\( 2 F e_{(a q)}^{3+}+2 I_{(a q)}^{-} \rightarrow 2 F e_{(a q)}^{2+}+I_{2(s)} \) has
\( E_{c e l l}^{o}=0.236 V \) at \( 298 K \)
The equilibrium constant of the cell reaction is:
A. \( 6.69 \times 10^{-7} \)
B . \( 7.69 \times 10^{-7} \)
c. \( 9.69 \times 10^{7} \)
D. \( 6.69 \times 10^{7} \)


\( A \) and \( B \) are two events such that
\( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B})=\frac{\mathbf{3}}{\mathbf{4}}, \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})= \)
\( \frac{1}{4}, P(\bar{A})=\frac{2}{3} ; \operatorname{then} P(\bar{A} \cap B) \) is
A \( .1 / 12 \)
в. \( 5 / 12 \)
c. \( 4 / 9 \)
D. \( 1 / 3 \)


Electric field strength due to a point charge of \( 5 \mu C \) at a distance of \( 80 \mathrm{cm} \) front he charge is
A \( \cdot 8 \times 10^{4} N / C \)
в. \( 7 \times 10^{4} \mathrm{N} / \mathrm{C} \)
C \( .5 .55 \times 10^{4} N / C \)
D. \( 4 \times 10^{4} N / C \)


Show that the following statement is true by the method of contrapositive
\( p: \) If \( x \) is an integer and \( x^{2} \) is even then \( x \) is also even


Assertion
In nature chlorine does not exist in free
state.
Reason
Chlorine is highly electronegative element.
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


Priyanka has a recurring deposit account of Rs. 1000 per month at \( 10 \% \)
per annum. If she gets Rs. 5550 as
interest at the time of maturity, find the
total time for which the account was
held.


The maximum limit of nitrate in
drinking water is:
A. 50 ppm
B. 40 ppm
\( c .10 \mathrm{ppm} \)
D. 100 ppm


What will be the amount of heat
required to convert \( 50 g \) of ice at \( 0^{\circ} \mathrm{C} \) to
water at \( 0^{\circ} \mathrm{C} \) ?
A . 400 cal
B. 4000 cal
c. 3000 cal
D. 300cal


The value of \( c \) in the lagranges mean
value theorem for \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{3}, \boldsymbol{a}= \)
\( 1, h=\frac{1}{2} \) is
A \( \cdot \frac{1}{3} \)
в. \( \sqrt{\frac{19}{56}} \)
c. \( \sqrt{\frac{19}{3}}+2 \)
D. \( \sqrt{\frac{19}{3}}-2 \)


7th term of \( \frac{1}{2}, \frac{1}{4}, \frac{1}{6} \dots \dots \) is
\( A \cdot \frac{1}{10} \)
в. \( \frac{1}{12} \)
c. \( \frac{1}{14} \)
D. \( \frac{1}{16} \)


If \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) and \( \boldsymbol{g}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) are
functions defined by \( f(x)=3 x- \)
\( \mathbf{1} ; \boldsymbol{g}(\boldsymbol{x})=\sqrt{\boldsymbol{x}+\boldsymbol{6}}, \) then the value of \( (\boldsymbol{g} \circ \)
\( \left.\boldsymbol{f}^{-1}\right)(\mathbf{2 0 0 9}) \) is
A . 26
B . 29
c. 16
D. 15


During the electrolysis of carnallite,
\( M g C l_{2} \) is decomposed and not \( K C l \)
This is because of :
A . lower decomposition voltage of \( M g C l_{2} \) than that of \( K C l \)
B. reverse reaction \( M g C l_{2}+2 K \rightarrow M g+2 K C l \), if \( K C l \) i decomposed under other experimental condition
c. both \( A \) and \( B \)
D. none of the above


An element \( A \) (atomic mass \( =75 \) ) and
\( B \) (atomic mass \( =25 \) ) combine to form
a compound. The compound contains
\( 75 \% A \) by mass.The formula of the compound will be :
A \( . A_{2} B \)
в. \( A_{3} B \)
\( \mathrm{c} \cdot A B_{3} \)
D. \( A B \)


pH of saturated solution of \( C a(O H)_{2} \) is
9. the solubility product \( \left(K_{s p}\right) \) of
\( \boldsymbol{C a}(\boldsymbol{O H})_{2} \) is:
A \( .0 .5 \times 10^{-15} \)
В. \( 0.25 \times 10^{-10} \)
\( c \cdot 0.125 \times 10^{-15} \)
5
D. \( 0.5 \times 10^{10} \)


The main constituents of producer gas
are:
A. \( C O+N_{2} \)
в. \( C O+H_{2} \)
\( \mathrm{c} \cdot \mathrm{CO}+\mathrm{CO}_{2} \)
D. \( C O+C H_{4} \)


\( \ln (34)^{33} \) unit digit is 4


In a conference there are 11 mechanical
engineers and 7 metallurgical engineers. In how many ways can they be seated in a row such that all the
metallurgical engineers do not sit together?
A. \( 18 !-(12 ! \times 7 !) \)
B. \( ^{18} P_{4}-2 ! \)
\( \mathbf{c} \cdot^{18} P_{4} \times 11 \)
D. \( 18 !-11 ! \)


Cycas and ferns resemble each other in
possessing
A. Seeds
B. Ovules
c. Pollen tube
D. Circinate ptyxis and ramentata


Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}: \)
\( \mathbf{1 2} \boldsymbol{x}+\boldsymbol{y}-\boldsymbol{x}^{2}=\tan \boldsymbol{x}+\cos \boldsymbol{x} \)


A person wants to see two pillars from a distance of \( 11 \mathrm{km}, \) separately. The distance between the pillars must be approximately
A. 3.2m
B. \( 1 \mathrm{m} \)
c. \( 0.25 \mathrm{m} \)
D. 0.5 \( m \)


A charge q is accelerated through a potential difference V. It is then passed normally through a uniform magnetic field, where it moves in a circle of
radius r. The potential difference required to move it in a circle of radius
\( 2 r \) is?
A . 2 v
B. 4 v
c. \( 1 v \)
D. 3


Potentiometer wire Pq of length Im is
connected to a standard cell \( \boldsymbol{E}_{1} \) Another
cell of E2 of emf1.02v/s connected as
shown in the circuit diagram with a
resistance 'r' and with a switch 's'. With
the switch \( \mathrm{S} \) open, null position is
obtained at a distance of \( 51 \mathrm{cm} \) from
p,Calculate
A. Potential gradient of the wire.
B. emf of the cell
C. When switch S is closed, will null point moves towards p or \( Q ? \)
D. insufficient data


Which of the following is the most important factor in making lithium metal, the strongest reducing agent?
A. lonisation energy
B. Hydration enegy
c. Heat of sublimation
D. None of these


Which one of the following is the main process for extraction nickel in the pure form?
A. Vapour phase refining
B. zone refiningg
c. Electrolysis
D. Solvent extraction


The given quadratic equation have real roots and the roots are \( -2 \sqrt{3}, \frac{-\sqrt{3}}{2} \) \( \mathbf{2} \boldsymbol{x}^{2}+\mathbf{5} \sqrt{\mathbf{3}} \boldsymbol{x}+\mathbf{6}=\mathbf{0} \)
A. True
B. False


All given modifications belong to adventitious roots, except
A. Reproductive root of Asparagus
B. Storage roots of sweet potato
c. conical roots of carrot
D. Prop roots of banyan tree


A sphere of mass m moving with a constant velocity hits another
stationary sphere of the same mass. If \( e \) is the coefficient of restitution, then ratio of velocities of the two spheres after collision will be:
A \( \cdot \frac{(1-e)}{(1+e)} \)
в. \( \frac{(1+e)}{(1-e)} \)
c. \( \frac{(e-1)}{(e-1)} \)
D. \( \frac{(e+1)}{(e-1)} \)


All the oxygen in a 0.5434 sample of a pure oxide of iron is removed by
reduction in a stream of \( \boldsymbol{H}_{2} . \) The loss in
weight is 0.1210 g. Hence, formula of the iron oxide is \( (\boldsymbol{F e}=\mathbf{5 6}) \)
A. \( F e O \)
в. \( F e_{2} O_{3} \)
\( \mathrm{c} \cdot \mathrm{Fe}_{3} \mathrm{O}_{4} \)
D. \( \mathrm{FeO}_{2} \)


Multiple Answer Question Bohr's model could not explain the
spectra:
This question has multiple correct options
A. of electron species having more than one electron
B. in the presence of magnetic field
c. of metal atoms
D. in the presence of electric field


\( A B C D \) is a square. A point \( M \) is taken
on the side \( C D, K \) is the point of
intersection of side \( B C \) and the
bisector of the \( \angle B A M . \) Prove that
\( |\boldsymbol{M} \boldsymbol{A}|=|\boldsymbol{B} \boldsymbol{K}|+|\boldsymbol{D} \boldsymbol{M}| \)


No.of nodal planes in \( 3 d \) -orbitals are :
\( A \cdot 2 \)
B. 4
\( c \cdot 5 \)
D. 10


The \( x-t \) can be only?
A. Parallel to x-axis
B. Parallel to t-axis
C. Inclined with acute angle
D. Inclined with obtuse angle


A radius vector of a particle varies with time \( t \) as \( r=a t(1-\alpha t), \) where \( a \) is a
constant vector and \( \alpha \) is a positive
constant. Find the time interval \( \Delta t \)
taken by the particle to return to the initial points.
A \( \cdot \Delta t=\frac{3}{\alpha} \)
в. \( \Delta t=\frac{1}{2 \alpha} \)
c. \( \Delta t=\frac{2}{\alpha} \)
D. \( \Delta t=\frac{1}{\alpha} \)


An artificial satellite moving in a circular orbit around the earth has a
total \( (K . E .+P . E .) \) is \( E_{0} . \) Its potential
energy is
A. \( -E_{0} \)
в. \( 1.5 E_{0} \)
c. \( 2 E_{0} \)
D. \( E_{0} \)


A student connects four cells, each of internal resistance \( \frac{1}{4} \Omega, \) in series. One of the cells is incorrectly connected because its terminals are reversed. The
value of external resistance is \( 1 \Omega . \) If the
emf of each cell is 1.5 volt then current
in the circuit will be
A \( \cdot \frac{4}{3} A \)
B. 0
c. \( \frac{3}{4} \)
D. \( 1.5 A \)


A pendulum is suspended from the roof of a rail road car. When the car is
moving on a circular track the pendulum inclines.
A. Forward
B. Rearward
c. Towards the centre of the path
D. Away from the centre of the path


Weight of an object on moon will be
A. One third of it's value on earth
B. Same as on earth
c. 100 times it's value on eartg
D. One sixth of its value on earth


Look at the classification table below.
Which of the following sets of headings is correct?
II
oil snow wind
paint rayon oxygen
A. I-gas, II-liquid, III- solid
B . I-liquid, II-gas, III-solid
c. \( I \) -liquid, \( I I \) -solid, \( I I I- \) gas
D. I-solid, II-gas, III-liquid


Find the compound interest if Principal\( =R s .4000, \) Rate\( =6 \% \)
Time \( =3 \) years compounded annually


Equation of the plane passing through a point with position vector \( 3 \hat{i}-3 \hat{j}+\hat{k} \)
\& normal to the line joining the points with position vectors \( 3 \hat{i}+4 \hat{j}-\hat{k} \& \) \( \mathbf{2} \hat{\mathbf{i}}-\hat{\boldsymbol{j}}=\mathbf{5} \hat{\boldsymbol{k}} \) is
\( \mathbf{A} \cdot \bar{r} \cdot(-\hat{i}-5 \hat{j}+6 \hat{k})+18=0 \)
B \( \cdot \bar{r} \cdot(\hat{i}-5 \hat{j}+6 \hat{k})=22 \)
c. \( \bar{r} .(\hat{i}+5 \hat{j}-6 \hat{k})+18=0 \)
D \( \cdot \bar{r} .(-\hat{i}+5 \hat{j}+6 \hat{k})+12=0 \)


All the electrons in a sample of the hydrogen atom are excited to \( n=7 \) level. The number of emission spectral lines possible are:
A \( \cdot 12 \)
B. 15
\( c \cdot 2 \)
D. 18


At. N.T.P. \( 28 ~ g m ~ o f ~ N i t r o g e n ~ o c c u p i e s \)
22.4 liters. What is the mass of 5.6 liters
of nitrogen at \( 38 \mathrm{cm} \) of Hg pressure and
\( 273^{0} \mathrm{C} \) temperature?
This question has multiple correct options
A. \( 7 \mathrm{gm} \)
B. 48 gm
\( c \cdot 1.75 \mathrm{gm} \)
D. 1.5 gm


There will be no force experienced if
A. two parallel wires carry currents in the same direction
B. two parallel wires carry currents in the opposite direction
C. a positive charge is projected between the pole pieces of a bar magnet
D. a positive charge is projected along the axis of a solenoid carrying current


The interval in which the function \( \mathbf{f}(\mathbf{x})=\mathbf{x}+\mathbf{e}^{-\mathbf{x}}+\tan \frac{\boldsymbol{\pi}}{\mathbf{1 2}} \) is increasing
is
\( A \cdot(-\infty, 0) \)
B. \( (1, \infty) \)
\( c \cdot(-1, \infty) \)
D. \( (0, \infty) \)


Eimplify: \( \boldsymbol{i}^{\mathbf{9}} \)


The plane side of a plano-convex lens is silvered and the lens then acts as a
concave mirror of \( 30 \mathrm{cm} \) focal length. The refractive Index of the lens is \( \frac{3}{2} \)
Find the radius of the curvature of the
lens.
\( \mathbf{A} \cdot 20 \mathrm{cm} \)
B. \( 30 \mathrm{cm} \)
\( \mathbf{c} \cdot 40 \mathrm{cm} \)
D. \( 25 \mathrm{cm} \)


To find the n-factor in the following chemical changes. \( \boldsymbol{K}_{2} \boldsymbol{C r}_{2} \boldsymbol{O}_{7} \stackrel{\boldsymbol{H}^{+}}{\rightarrow} \boldsymbol{C r}^{3+} \)


State and explain coulomb's inverse
square law


The monomer \( (G=M e \text { or } C l) \) when
treated with Zieglar - Natta catalyst undergo polymerisation as shown in the figure. The Zieglar-Natta catalyst is:
\( \mathbf{A} \cdot T i C l_{4} \)
в. \( R_{3} A l \)
c. \( R_{3} A l / T i C l_{4} \)
D. \( R_{3} B / T i C l_{4} \)


Two light waves of intensities \( ^{\prime} I_{1}^{\prime} \) and \( ^{\prime} I_{2}^{\prime} \) having same frequency pass through
same medium at a time in same
direction and interfere. The sum of the
minimum and maximum intensities is
\( \mathbf{A} \cdot\left(I_{1}+I_{2}\right) \)
B \( \cdot 2\left(I_{1}+I_{2}\right) \)
C \( \cdot\left(\left(\sqrt{I}_{1}+\sqrt{I}_{2}\right)\right) \)
D. \( \left(\left(\sqrt{I}_{1}-\sqrt{I}_{2}\right)\right) \)


The specie among the following which can act as an acid and a base is
A \( . H S O_{4}^{-} \)
B. \( S O_{4}^{2-} \)
c. \( H_{3} O^{+} \)
D. \( C l \)


To protect tooth decay we are advised to brush our teeth regularly. The nature of the toothpaste commonly used is:
A . acidic
B. basic
c. netural
D. corrosive


The properties that have increasing values with increase in atomic number
for the elements of 1A are?
I. Ionization energy (potential)
I. Atomic radius
III. Atomic mass
A. I only
B. III only
c. I and II only
D. Il and III only
E . ।, ॥।, and III


If \( 6.022 \times 10^{23} \) molecules of urea are
present in 100 ml of its solution, then
calculate the concentration of the
solution (Molecular mass of urea \( =\mathbf{6 0} \) )


Law of mass action cannot be applied
to:
A. decomposition of gaseous \( H I \)
B. decomposition of gaseous \( P C l_{5} \)
C. transition of Rhombic Sulphur to Monoclicnic sulphur
D. decomposition of Calcium carbonate


Last step in biogas production is carried out by
A. Decomposer microbes
B. Fermentative microbes
c. Methanogens
D. Thermoacidophiles


Arrange the following in the increasing order of basic strength:
¡)Aniline
ii)p-nitroaniline
iii)p-toluidine
A. is iis iii
B. iiciciii
D. iii <iisi


Solve: \( \left(\tan ^{-1} x\right)^{2}+\left(\cot ^{-1} x\right)^{2}=\frac{5 \pi^{2}}{8} \)


An electron make transition from orbit
number \( N \) to \( P^{t h} \) orbit in \( H- \) atom and
emit the photon of wavelength \( (\lambda) . \) In
orbit \( \boldsymbol{P}, \) velocity of electron in \( \boldsymbol{H}- \) atom is maximum. Which of the following wavelength \( (\lambda) \) is not possible?
(Where \( 1 / R=912 A) \)
\( \mathbf{A} \cdot 1216 \stackrel{\circ}{A} \)
B . 972.8 A
\( c \cdot 1026^{\circ} \)
D. 3973 h


\[
\boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{6} \stackrel{\text {Complete } \boldsymbol{H} \boldsymbol{y} \text {drolysis}}{\boldsymbol{P}}+
\]
other product
\[
\begin{array}{l}
\downarrow \boldsymbol{O H}^{-} / \boldsymbol{H}_{2} \boldsymbol{O} \\
\boldsymbol{Q} \\
\downarrow
\end{array}
\]
slow disproportionation in \( O H^{-} / H_{2} O \)
Products
Under ambient conditions, the total
number of gases released as products in the final step of the reaction scheme
shown below is:
A . 0
B. 1
\( c \cdot 2 \)
D. 3


Structure of RNA can be studied by
A. Feulgen
B. Toluene blue
c. x-ray crystallography
D. chromatography


Differentiate the following function with
respect to \( x \) \( \frac{1}{\sin x} \)


State whether the following statement is True or False.

The product of three odd numbers is odd.
A. True
B. False


Very pure hydrogen \( (99.9 \%) \) can be made by which of the following
processes?
A. Reaction of methane with steam
B. Mixing natural hydrocarbons of high molecular weight
c. Electrolysis of water
D. Reaction of salt like hydrides with water


The equation of motion of a particle executing SHM is \( \left(\frac{d^{2} x}{d t^{2}}\right)+k x=0 . \) The time period of the particle will be ?
A \( \cdot \frac{2 \pi}{\sqrt{k} \pi} \)
в. \( 2 \pi \)
\( c \cdot 2 \pi k \)
D. \( 2 \pi \sqrt{k} \)


\( \int \frac{3.2^{x}-2.3^{x}}{2^{x}} d x= \)
A \( \cdot 3 x+\frac{2(1.5)^{x}}{\log (1.5)}+c \)
B. \( 3 x-\frac{2(1.5)^{x}}{\log (1.5)}+c \)
\( \mathbf{c} \cdot 3 x-2(1.5)^{x} \log 1.5+c \)
D. \( 3 x+2 \log 1.5(1.5)^{x}+c \)


Which of the following statement about enzyme inhibitors is incorrect?
A. A competitive inhibitor binds the active site of the enzyme
B. An allosteric inhibitor binds a site on the active site of the enzyme.
C. A noncompetitive inhibitor binds a site other than the active site
D. Noncompetitive inhibition cannot be completely overcomes by the addition of more substrate.


The area between the curve \( y^{2}=9 x \) and
the line \( y=3 x \) is
A \( \cdot \frac{1}{3} \) sq. units
B. \( \frac{8}{3} \) sq. units
c. \( \frac{1}{2} \) sq, units
D. \( \frac{1}{5} \) sq. units


One point electric charge \( Q \) is placed at
the point \( P . A \) closed surface is placed
near the point \( P . \) The electrical flux
passing through a closed surface will be
\( \mathbf{A} \cdot Q \epsilon_{0} \)
В . \( \epsilon_{0} / Q \)
\( c \cdot Q / \epsilon_{0} \)
D. zero


When the separation between the two charges is increased the electric
potential energy of the charges
A. Increases
B. Decreases
c. Remains unchanged
D. May increase or decrease


The minimum number of gates required to realise the expression \( Z= \) \( D A B C+D \overline{A B C} \) is
A. One
B. Two
c. Eight
D. Five


If the polynomial \( 3 x^{2}-x^{3}-3 x+5 \) is
divided by another polynomial \( \boldsymbol{x}-\mathbf{1}- \)
\( x^{2}, \) the remainder comes out to be 3
then quotient polynomial is
\( \mathbf{A} \cdot 2-x \)
B. \( 2 x-1 \)
c. \( 3 x+4 \)
D. \( x-2 \)


Assertion: A soft iron core is used in a
moving coil galvanometer to increase the strength of magnetic field Reason: From soft iron more number of
the magnetic lines of force passes
A. Both A and R are true and R is the correct explanation of A
B. Both A and R are true and R is not correct explanation of
c. A is true, but R is false
D. A is false, but R is true


Assertion
Transcription unit is often monocistronic in eukaryotes and polycistronic in prokaryotes.
Reason
Exons do not appear in mature RNA,
introns appear in mature RNA.
A. Assertion and Reason are true, Reason is correct explanation of Assertion.
B. Assertion and Reason are true, Reason is not the correct explanation of Assertion
C. Assertion is true, Reason is false.
D. Assertion is false, Reason is true.


(a) Name two oxoacids of sulphur.
(b) (i) How will you manufacture ammonia by Haber process?
(ii) Write any two uses of inert gases.


When \( 2 s-2 s, 2 p-2 p \) and \( 2 p-2 s \)
orbitals overlap, the bond strength decreases in the order:
A \( \cdot p-p>s-s>p-s \)
В. \( p-p>p-s>s-s \)
c. \( s-s>p-p>p-s \)
D. \( s-s>p-s>p-p \)


The angle of reflection is given by the
angle :
A. NOQ
B. QOB
c. PON
D. AOP


Ethyl alcohol is mainly manufactured by :
A. destructive distillation of wood
B. hydrogenation of \( C O \)
c. fermentation of molasses
D. calalytic oxidation of ethane


Two wires of the same material and
Iength but diameter in the ratio 1: 2 are stretched by the same force. The ratio of
potential energy per unit volume for the two wires when stretched will be :
A . 1:
B. 2:
\( c \cdot 4: 1 \)
D. 16: 1


\( \mathbf{A}=(\mathbf{1}, \mathbf{1}, \mathbf{4}) \) and \( \mathbf{B}=(\mathbf{5},-\mathbf{3}, \mathbf{4}) \) are two
points. If the points \( P, Q \) are on the line
\( A B \) such that \( A P=P Q=Q B \) then \( P Q= \)
A \( \cdot 2 \sqrt{2} \)
в. 4
c. \( \sqrt{\frac{32}{9}} \)
D. \( \sqrt{2} \)


Equal torques are applied about a central axis on two rings of same mass and same thickness but made up of different materials. If ratio of their
densities is 4: 1 then the ratio of their
angular acceleration will be :
A . 4: 1
B. 1: 16
\( c \cdot 8: 1 \)
D. 1: 12


Find the coordinates of the point where the diagonals of the parallelogram formed by joining the points (-2,-1) (1,0),(4,3) and (1,2) meet.
A . (5,1)
в. (1,1)
c. (1,5)
(年. (1,5)
D. \( (1,1-) \)


The general solution of \( \tan x-\sin x= \)
\( 1-\tan x \sin x \)
A \( \cdot x=n \pi+\frac{\pi}{4} \)
\( x=n \pi+(-1)^{n}\left(-\frac{\pi}{2}\right) \)
В \( \cdot x=\frac{n \pi}{4}-\frac{\pi}{4} \)
\( x=n \pi+(-1)^{n}\left(-\frac{\pi}{2}\right) \)
C \( \cdot x=n \pi+\frac{\pi}{4} \)
D. \( x=n \pi+\frac{\pi}{6} \)
\( x=n \pi+(-1)^{n}\left(-\frac{\pi}{2}\right) \)


A square \( A B C D \) is divided equally into
5 rectangles. The perimeter of each
rectangle is \( 60 \mathrm{cm} . \) Find the perimeter
of the square.
A. \( 120 \mathrm{cm} \)
B. \( 100 \mathrm{cm} \)
c. \( 25 \mathrm{cm} \)
D. \( 60 \mathrm{cm} \)


There should be a full stop at the end of a symbol for units.
A. True
B. False


A choke coil has negligible resistance.
The alternating potential drop across it is 220 volts and the current is \( 5 \mathrm{mA} \). The
power consumed is
A \( \cdot 220 \times \frac{5}{1000} W \)
в. \( \frac{220}{5} W \)
c. zero
D. \( 2.20 \times 5 W \)


Which endocrine gland is associated with kidneys?
A. Thyroid
B. Pancreas
c. Adrenal
D. Pineal