Which of the following is the cell reaction that occurs when the following half-cells are combined?
\( \boldsymbol{I}_{2}+\boldsymbol{2} \boldsymbol{e}^{-} \rightarrow \boldsymbol{2} \boldsymbol{I}^{-}(\boldsymbol{1} \boldsymbol{M}) ; \boldsymbol{E}^{o}=+\boldsymbol{0 . 5 4} \mathbf{V} \)
\( \boldsymbol{B} \boldsymbol{r}_{2}+\boldsymbol{2} \boldsymbol{e}^{-} \rightarrow \boldsymbol{2} \boldsymbol{B} \boldsymbol{r}^{-}(\boldsymbol{1} \boldsymbol{M}) ; \boldsymbol{E}^{o}=+\mathbf{1} . \boldsymbol{0} \boldsymbol{9} \)
\( \mathbf{V} \)
A \( \cdot 2 B r^{-}+I_{2} \rightarrow B r_{2}+2 I^{-} \)
В \( \cdot I_{2}+B r_{2} \rightarrow 2 I^{-}+2 B r^{-} \)
c. \( 2 I^{-}+B r_{2} \rightarrow I_{2}+2 B r \)
D. \( 2 I^{-}+2 B r^{-} \rightarrow I_{2} B r_{2} \)


If \( \lim _{x \rightarrow \infty} f(x) \) exists and is finite and nonzero and if \( \lim _{x \rightarrow \infty}\left\{f(x)+\frac{3 f(x)-1}{f^{2}(x)}\right\}=3, \) then the
value of \( \lim _{x \rightarrow \infty} f(x) \) is
A . 2
B.
\( c \cdot-1 \)
D. 3


Energy gaps between the highest band and the lowest empty bands in elements \( A, B, C \) and \( D \) are 0,70,530 and \( 90 k J m o l^{-1} . \) Then
A. element A is metal
B. element C is insulator
c. element B and D can be semiconductors
D. all are correct conclusion about elements A, B, C and D


The effficiency of carnot cycle is given by:
\( \mathbf{A} \cdot\left(1-T_{2} / T_{1}\right) \)
B. \( \left(1+T_{2} / T_{1}\right) \)
c. \( \left(1-T_{1} / T_{2}\right) \)
D. \( \left(1-T_{2} \times T_{1}\right) \)


Sal and teak is the dominant species in which of the following forests :-
A. Tropical dry deciduous forests
B. Temperate deciduous forest
c. Temperate rain forest
D. None of the above


The World Nuclear Association
considers used fuel management to be
sustainable if it meets the following key
criteria:
A. It covers all the steps of used fuel management from the generation of used fuel up to and including final disposal in accordance with a well defined practical plan.
B. It proves to be feasible with a sustainable impact level
C. It protects human health and the environment and has no greater impact on the health of future generations than is allowed today.
D. It is able to demonstrate to a practicable extent that it is technically and economically viable.
E. All of the above


A random variable \( X \) takes the values
\( \mathbf{0}, \mathbf{1} \) and \( \mathbf{2} . \) If \( \boldsymbol{P}(\boldsymbol{X}=\mathbf{1})=\boldsymbol{P}(\boldsymbol{X}=\mathbf{2}) \) and
\( P(X=0)=0.4, \) then the mean value
of the random variable \( \boldsymbol{X} \) is
A . 0.2
B. 0.5
\( c .0 .7 \)
D. 0.9


Which is the short day plant from the following?
A. cotton
B. Rice
c. sugarcane
D. All of the above


The current in an ideal, long solenoid is varied at a uniform rate of \( 0.01 A / s . \) The solenoid has 2000 turns/m and its
radius is \( 6.0 \mathrm{cm} \)
(a) Consider a circle of
radius \( 1.0 \mathrm{cm} \) inside the solenoid with its axis coinciding with the axis of the solenoid. Write the change in the magnetic flux through this circle in 2.0 seconds.
(b) Find the electric field
induced at a point on the circumference of the circle.
(c) Find the electric field
induced at a point outside the solenoid
at a distance \( 8.0 \mathrm{cm} \) from its axis.


A particle is acted upon by a force of
constant magnitude which is always perpendicular to the velocity of the
particle. The motion of the particle takes place in a plane. It follows
A. its velocity is constant
B. its K.E. is constant
c. its acceleration is constant
D. it moves in a straight line


What is the mass of a lead atom?


Cells which help in rolling and unrolling of leaf lamina in grasses are
A. Complementary cells
B. Motor cells
c. Passage cells
D. Companion cells


How much time would it take to
distribute one Avogadro number of wheat grains, if \( 10^{10} \) grains are
distributed each second?


State True(1) or False(O)
A solid ball is exactly fitted inside the cubical box of side a. The volume of the
ball is \( \frac{4}{3} \pi a^{3} \)


Multiply:
\( \left(m^{2}-5\right) \times\left(m^{3}+2 m-2\right) \)


Urea on reacting with water gives:
A . \( N H_{3} \)
в. \( N_{2} O_{3} \)
c. \( H N O_{2} \)
D. \( H N O_{3} \)


\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left(\boldsymbol{3} \cos \left(\frac{\boldsymbol{\pi}}{\boldsymbol{6}}+\boldsymbol{x}^{0}\right)-\boldsymbol{4} \cos ^{3}\left(\frac{\boldsymbol{\pi}}{\boldsymbol{6}}+\boldsymbol{x}^{0}\right)\right. \)
A \( \cdot \cos \left(3 x^{0}\right) \)
B. \( \frac{\pi}{60} \sin \left(3 x^{0}\right) \)
c. \( \frac{\pi}{60} \cos \left(3 x^{0}\right) \)
D. \( -\frac{\pi}{60} \sin \left(3 x^{0}\right) \)


Pacemaker enzyme of EMP pathway is
A. Hexokinase
B. Pyruvate kinase
c. Enolase
D. Phosphofructokinase


Assume that blue flowered plant is dominant character over the white.
When a blue flowered plant is crossed
with its white flowered plant, the
progeny showed \( 50 \% \) of plants with blue flowers is with white flowers. The
genotypes of blue and white parents respectively are
\( A \cdot b b, b b \)
B. ВВ, Вь
\( c \cdot B B, b b \)
D. Bb, bb


Calculate inductive reactance of coil in
the following figure.


The volume strength of \( 3 N H_{2} O_{2} \) solution is:
A . \( 11.2 \mathrm{V} \)
B. \( 8.4 \mathrm{V} \)
c. \( 22.4 \mathrm{V} \)
D. 16.8 V


The reaction \( \boldsymbol{C H}_{3} \boldsymbol{C O O H}+ \)
\( C_{2} H_{5} O H \leftrightharpoons C H_{3} C O O C_{2} H_{5}+H_{2} O \)
can be made to proceed in the forward direction by:
A. increasing the temperature
B. sudden cooling of the reaction mixture
c. conducting the reaction in the presence of a small quantity of \( N a O H \)
D. taking excess of \( C_{2} H_{5} O H \) and \( C H_{3} C O O H \)


A sample of hydrogen gas contain 100 atoms. All the atoms are excited to the
same n excited state. The energy released by all the atoms is \( \frac{4800}{49} . R= \) \( 13.6 \mathrm{eV} \) ), as they come to the ground
state through various types of transition Then Find
A. maximum energy of the emitted photon will be less \( \operatorname{than} \frac{48}{49} R c h \)
B. Maximum energy of the emitted photon may be greater than \( \frac{48}{49} \) Rch
c. The value of \( n=6 \)
D. None of these


Which of the following compounds has highest boiling point?
A. Propan-1-ol
B. \( n \) - butane
c. chloroethane
D. Propanal


Which one of the following statements
is not correct?
A. Nickel forms \( N i(C O)_{4} \)
B. All the transition metals form monometallic carbonyl
c. \( N i(C O)_{4} \) is volatile and decomposes into Ni and \( c o \)
D. Transition metals form complexes


As the s-character of hybridized orbital decreases, the bond angle
A. Decreases
B. Increases
c. Does not change
D. become zero


Non-metals are poor conductors of heat, which are tend to:
A. be brittle
B. conduct an electrical current
c. have a shiny luster
D. be malleable
E. lose electrons


Voice is high pitched in
A. Aged persons
B. Adult males
c. Boys
D. Females


An organic compound having molecular mass 60 is found to contain \( C=20 \% \)
\( \boldsymbol{H}=\mathbf{6 . 6 7 \%} \) and \( \boldsymbol{N}=\mathbf{4 6 . 6 7} \%, \) while rest
is oxygen. On heating, it gives \( \boldsymbol{N} \boldsymbol{H}_{3} \) along with a solid residue. The solid residue gives violet colour with alkaline
copper sulphate solution. The compound is:
A \( \cdot C H_{3} N C O \)
в. \( C H_{3} C O N H_{2} \)
c. \( \left(N H_{2}\right)_{2} C O \)
D. \( C H_{3} C H_{2} C O N H_{2} \)


The attraction between molecules and
salt, when a salt is dissolved in water molecules, is :
A. atom- atom
B. molecule-molecule
c. molecule-ion
D. ion-ion
E. atom-ion


Transfer of electrons from one atom to
other atom takes place in:
A. covalent bond
B. ionic bond
c. co-ordinate covalent bond
D. none of these


For which of the following ideal gas
\( C_{V, m} \) is independent of temperature?
A. \( H e \)
в. \( H_{2} \)
c. \( C O \)
\( \mathrm{D} \cdot \mathrm{SO}_{2} \)


The volume that a gas occupies at \( 343 \mathrm{K} \) if its volume at \( -25^{0} \mathrm{C} \) is 7.5 litre is (The
process is isobaric)
A. 10.29 Itrs
B. 102.9 Itrs
c. 1.029 Itrs
D. 1029 Itrs


The wire shown in Fig, carries a current
of \( 10 A . \) Determine the magnitude of
magnetic field at the centre \( O \). Given
radius of the bent coil is \( 3 \mathrm{cm} \).


Starting with elemental phosphorus, \( \boldsymbol{P}_{4} \)
phosphoric acid can be prepared as
shown \( \boldsymbol{P}_{4}(s)+\mathbf{5} O_{2}(\boldsymbol{g}) \longrightarrow \boldsymbol{P}_{4} \boldsymbol{O}_{10}(s) \stackrel{\boldsymbol{H}_{2} O}{\longrightarrow} \)
\( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4} \)
A. True
B. False


Adjacent graph shows the variation of velocity of a rocket with time. Find the
time of burning of fuel from the graph
\( \left(g=10 m / s^{2}\right) \)
A \( .10 \mathrm{sec} \)
B. 110 sec
\( \mathrm{c} \cdot 120 \mathrm{sec} \)
D. Cannot be estimated from the graph


What is forbidden energy gap(Eg) or band gap?
A. Forbidden energy gap \( E_{g} \) is the difference of energy levels of conduction band and within conduction band
B. Forbidden energy gap \( E_{g} \) is the difference of energy levels of conduction band and valence band.
C. when there is no energy
D. conduction band


In organic compounds, halogens are estimated by :
A. Carius method
B. Liebig's method
c. Kjeldahl's method
D. Duma's method


Assertion
In the warmer liquid, the greater
number of molecules are energetic
enough to escape the surface during
evaporation.
Reason
Increase in temperature increases the
rate of evaporation.
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


Which of the following is mismatched?
A. Semicircular canals-inner ear
B. Utride and saccule - outer ear
c. Auditory canal - outer ear
D. ossicles - middle ear


\( \int_{-\pi}^{\pi} \sin m x \sin n x d x=? \)


The specific set of real numbers that lies between two conditional numbers \( a \)
and \( b \) is classified as
A . interval
B. break
c. double interval
D. equal interval


The motion of centre of mass depends
on
A. total external forces
B. total internal forces
c. sum of \( (a) \) and \( (b) \)
D. None of these


Consider the function \( \boldsymbol{f}(\boldsymbol{x}) \) which satisfying the functional equation:
\( 2 f(x)+f(1-x)=x^{2}+1, \forall x \in R \) and
\( \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{3} \boldsymbol{f}(\boldsymbol{x})+1 \)
The range of \( \phi(x)=g(x)+\frac{1}{g(x)+1} \) is
\( A \cdot[2, \infty) \)
B. \( [1, \infty) \)
\( c \cdot[-1, \infty) \)
D. \( R^{+} \)


Two bodies, \( A(\text { of } \operatorname{mass} 1 \mathrm{kg}) \) and \( \mathrm{B} \) (of mass \( 3 \mathrm{kg} \) ), are dropped from heights of
\( 16 \mathrm{m} \) and \( 25 \mathrm{m} \) respectively. The ratio of
the time taken by them to reach the ground is:-
A \( \cdot \frac{5}{4} \)
в. \( \frac{12}{5} \)
c. \( \frac{5}{12} \)
D. \( \frac{4}{5} \)


Evaluate \( : \int \frac{\log x}{x} d x \)


Assertion
Oxy hydrogen blow torch is used for
welding.
Reason
The temperature produced here is
above \( 2000^{\circ} \mathrm{C} \)
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


Assertion
When the electric current in a loop of wire changes, the changing current
creates a changing magnetic field.
Reason
Magnetic field lines of a circular loop of
wire is same as a magnet.
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 length of two wires are in the ratio
\( 3: 4 . \) Ratio of the diameters is 1: 2
young's modulus of the wires are in the
ratio \( 3: 2 ; \) If they are subjected to same
tensile force, the ratio of the elongation produced is
A . 1:
B. 1: 2
c. 2: 3
\( D \cdot 2: \)


The reaction that gives phenol as the
end product is/are:
This question has multiple correct options
\( \mathbf{A} \)
\( \sqrt{ }+\operatorname{conc.H}_{2} \operatorname{so}_{4} \frac{\text { Heat }}{\text { Fusion }}>\frac{\mathbf{H}^{+}}{\mathbf{H}_{2} \mathbf{O}} \)
B. \( \sqrt{\int}^{\mathrm{N} \mathrm{O}_{2}} \frac{\mathrm{NaNO}_{2}}{\mathrm{HCl}, 0^{\circ} \mathrm{C}} \)
\( c \)
\( y_{1}+\mathbf{k o H} \stackrel{300^{\circ} \mathbf{C}}{\longrightarrow} \stackrel{\mathbf{H C l}}{\longrightarrow} \)
\( \mathbb{P}+\mathrm{CH}_{3}-\mathrm{CH}=\mathrm{CH}_{2} \stackrel{\mathrm{H}^{+}}{\longrightarrow} \frac{\mathrm{O}_{2}}{\mathrm{KOH}}>\frac{\mathrm{H}^{+}}{ } \)


The equilibrium constants for the two complex formation are :
\( \boldsymbol{4} \boldsymbol{K}^{+}+\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{6}^{4-} \longrightarrow \)
\( \boldsymbol{K}_{4}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{6}\right] ; \boldsymbol{K}=\mathbf{3} . \boldsymbol{8} \times \mathbf{1 0}^{-\mathbf{3 8}} \)
\( \mathbf{3} \boldsymbol{K}^{+}+\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{\boldsymbol{6}}^{\boldsymbol{3}-} \longrightarrow \)
\( \boldsymbol{K}_{3}\left[\boldsymbol{F e}(\boldsymbol{C N})_{6}\right] ; \boldsymbol{K}=\mathbf{5} \times \mathbf{1 0}^{-18} \)
A \( \cdot K_{4} F e(C N)_{6} \) is more stable
B . \( K_{3} F e(C N)_{6} \) is more stable
c. both are equally stable
D. stability of complexes cannot be decrease


Find the length \( E C \)
\( s \)
D


Solve the following equation:
\( 2 \cos ^{2} x+4 \cos x=3 \sin ^{2} x \)


A bullet of mass \( 20 g \) is horizontally
fired with a velocity \( 150 \mathrm{ms}^{-1} \) from a
pistol of mass \( 2 k g . \) What is the recoil
velocity of the pistol?


The ellipse \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 \) cuts \( x \) axis at
A and y axis at \( \mathrm{B} \) and the line joining the focus \( \mathrm{S} \) and \( \mathrm{B} \) makes an angle \( \frac{3 \pi}{4} \) with x-axis. Then the eccentricity of the ellipse is
A. \( \frac{1}{\sqrt{2}} \)
в. \( \frac{1}{2} \)
c. \( \frac{\sqrt{3}}{2} \)
D. \( \frac{1}{3} \)


\( \left(2^{2}+4^{2}+6^{2}+\ldots \ldots+20^{2}\right)=? \)
A . 77
В. 1155
\( c .1540 \)
D. \( 385 \times 385 \)


A bar magnet oscillates with a
frequency of10 oscillations per minute. When another bar magnet is placed on its axis at a small distance, it oscillates
at 14 oscillations per minute. Now, the second bar magnet is turned so that poles are instantaneous, keeping the location same. The new frequency of oscillation will be
\( A \cdot 2 \) vibrations/min
B. 4 vibrations/min
c. 10 vibrations/min
D. 14 vibrations/min


Simplify the following.
\( b^{4} \div b^{5} \)


The radioactive isotope of hydrogen contains 2 neutrons.
A. True
B. False


Prove that \( (\operatorname{cosec} \theta-\cot \theta)^{2}=\frac{1-\cos \theta}{1+\cos \theta} \)


Sum of the fractions \( \frac{\mathbf{7}}{\mathbf{1 2}}, \frac{\mathbf{1 2}}{\mathbf{1 2}}, \frac{\mathbf{8}}{\mathbf{1 2}} \) is
equal to
A \( \cdot \frac{26}{12} \)
в. \( \frac{19}{12} \)
c. \( \frac{27}{12} \)
D. \( \frac{23}{12} \)


Which animal show did you see?


Find the \( 4^{t h} \) term from the end of the G.P. \( \frac{2}{27}, \frac{2}{9}, \frac{2}{3}, \dots \dots \dots, 162 \)


The number of isotopes of hydrogen are:
\( A \cdot 2 \)
B.
\( c \cdot 4 \)
D.


If \( \boldsymbol{x}=\mathbf{5} \) and \( \boldsymbol{y}=\mathbf{2} \) then \( \boldsymbol{x}-\mathbf{2} \boldsymbol{y}=\mathbf{9 . T h e} \)
contrapositive of this statement is
A. If \( x-2 y \neq 9 \) then \( x \neq 5 \) or \( y \neq 2 \)
B. If \( x-2 y \neq 9 \) then \( x \neq 5 \) and \( y \neq-2 \)
c. If \( x-2 y=9 \) then \( x=5 \) and \( y=-2 \)
D. none of these.


What stimulates the auditory nerve?
A. The movement of the three ear ossicles
B. The movement of stirrup
C. The movement of fluid in the cochlea
D. All of these


\( \lim _{x \rightarrow 0} \frac{\sin x}{x} \) is equal to:
\( A \cdot 2 \)
B. - -
\( c \)
D.


Let \( r^{t h} \) term of a series is given by, \( \boldsymbol{T}_{\boldsymbol{r}}= \) \( \frac{r}{1-3 r^{2}+r^{4}} \)
Then \( \lim _{n \rightarrow \infty} \sum_{r=1}^{n} T_{r} \) is
A \( \cdot \frac{3}{2} \)
в. \( \frac{1}{2} \)
\( c \cdot \frac{-1}{2} \)
D. \( \frac{-3}{2} \)


Boron has two stable isotopes, \( 10_{B(19 \%)} \)
and \( ^{11} \mathrm{B}(81 \%) . \) The atomic mass that
should appear for boron in the periodic table is


In the circuit shown in Figure the heat
produced in resistance R1 can be measured by
A. connecting both voltmeter and an ammeter in parallel to R1
B. both voltmeter in series with \( \mathrm{R} 1 \) and voltmeter in parallel to both R1 and R2
C. connecting ammeter in parallel to R1 and voltmeter in series with R1
D. connecting voltmeter in parallel to R1 and ammeter in series with R1


Explain why a charged balloon is
repelled by another charged balloon
whereas an uncharged balloon is attracted by another charged balloon?


Determine whether the following compound statements are true or false:
Delhi is in India and \( 2+2=4 \)
A . True
B. False


Polycyclic aromatic hydrocarbon are
formed from:
A. incomplete combustion of coal
B. incomplete combustion of oil and gas
C. incomplete combustion of organic substance
D. all of these


How many moles of helium are
produced when one mole of \( _{92}^{238} U \) disintegrates into \( _{82}^{206} \) Pb?


Evaluate \( \int \frac{x^{2}}{(x \sin x+\cos x)^{2}} d x \)
A. \( \frac{\sin x-x \cos x}{x \sin x+\cos x}+c \)
в. \( \frac{\cos x-x \sin x}{x \sin x+\cos x}+c \)
c. \( \frac{\cos x-x \sin x}{x \sin x-\cos x}+c \)
D. \( \frac{\sin x+x \cos x}{x \sin x+\cos x}+c \)


The intensity of magnetic induction field at the centre of a single turn circular coil of radius \( 5 \mathrm{cm} \) carrying of
0.9 A current is:
A . \( 36 \pi \times 10^{-7} \mathrm{T} \)
В . \( 9 \pi \times 10^{-7} T \)
\( \mathbf{c} \cdot 36 \pi \times 10^{-6} T \)
D. \( 9 \pi \times 10^{-6} T \)


Based on the following diagram, which colored bond(s) and corresponding number would exhibit the weakest
attractive forces for the structure?
A. Green (#3)
B. Red (#2)
c. Green (#3) and blue (#1)
D. Yellow (#4)


Which of the following is an example of fossil fuel?
A. Oxygen gas
B. Hydrogen Gas
c. Natural gas
D. Producer gas


The melting point of ice on Kelvin scale
is:
\( A \cdot O K \)
в. - -273 к
с. 273 к
D. 373 к


A body, initially at rest, is acted upon by four forces \( \boldsymbol{F}_{\mathbf{1}}=\hat{\boldsymbol{i}}+\widehat{\boldsymbol{k}}, \boldsymbol{F}_{2}=\mathbf{2} \hat{\boldsymbol{j}}+ \)
\( \mathbf{3} \widehat{k}, \boldsymbol{F}_{3}=\mathbf{3} \hat{\mathbf{i}} \) and \( \boldsymbol{F}_{4}=\mathbf{3} \hat{\mathbf{j}}-\mathbf{4} \hat{\mathbf{i}} . \) In which
plane will the body move?
A. x-y plane
B. x-z plane
c. \( y \) -z plane
D. none of these


What makes a balloon get inflated when
air is filled in it?


The resistance of wire is 5 ohm at \( 50 C \)
and 6 ohm at 100 C. The resistance of the
wire at \( 0 \mathrm{C} \) willbe
A. 2 ohm
B. 1 ohm
c. 4 ohm
D. 3 ohm


In the given figure, the current in the cell is
A . 33 A
в. 3.3 А
c. 0.33 A
D. 3.32 A


For the reaction, \( \boldsymbol{A B}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{A}(\boldsymbol{g})+\boldsymbol{B}(\boldsymbol{g}), \boldsymbol{A B} \) is \( \boldsymbol{3} \boldsymbol{3} \% \)
dissociated at a total pressure of \( \boldsymbol{P} \)
Therefore, \( P \) is related to \( K_{p} \) by one of
the following option:
A \( \cdot P=K_{p} \)
В. \( P=3 K_{p} \)
\( \mathbf{c} \cdot P=4 K_{p} \)
D. \( P=8 K_{p} \)


A metal ball is heated through a certain
temperature. Out of mass, radius, surface area and volume, which will
undergo largest percentage increase and which one the least?


In case of an orbiting satellite, if the radius of orbit is decreased
A . its \( K E \) decreases
B. its \( P E \) decreases
c. its \( M E \) is doubled
D. it stops moving in the orbit


Lines \( \mathrm{PQ} \) and RS intersect at \( 0 . \) If \( \angle P O R \)
is three times \( \angle R O Q, \) then \( \angle S O Q \) is
A \( \cdot 120^{\circ} \)
B. 150
\( c \cdot 135 \)
D. 45


Modern periodic table has
periods.
A. 7
B. 8
\( c \cdot 6 \)
\( D \)


Which does not lead to secondary succession?
A. All organisms that existed are lost
B. Where no living organisms ever existed
C. Abandoned crop field
D. Land affected by flood


The part labelled as A in the given image helps in
A. Removal of waste from the blood
B. Gaseous exchange
c. circulation of blood
D. None of the above


In a neuron, Schwann cells occur in
associated with
\( A \cdot A \times O n \)
B. Soma
c. Dendrite
D. Axon hillock


An Egg Seller distributes eggs to the shop in a city. The number of eggs he distributes for each shop has been recorded and the data obtained was
grouped into a class shown in the table
below. Find the mean using shortcut
method.
\begin{tabular}{|l|l|l|l|l|l|l|}
\hline Number of eggs & \( 0-30 \) & \( 30-60 \) & \( 60-90 \) & \( 90-120 \) & \( 150- \) 150 & \( 150- \) 180 \\
\hline Frequency & 40 & 26 & 38 & 12 & 25 & 30 \\
\hline
\end{tabular}
A. 91.5
B. 83.07
c. 87.34
D. 89.76


On an unbaked road, a cyclist
negotiating a bend of radius \( r \) at
velocity \( v \) must lean inwards by an
angle \( \theta \) equal to
A \( \cdot \tan ^{-1}\left(v^{2} / g\right) \)
B. \( \tan ^{-1}(g / v) \)
c. \( \tan ^{-1}\left(v^{2} / g r\right) \)
D. \( \tan ^{-1}\left(r g / v^{2}\right) \)


Select the incorrect statement among
the following.
\( A \cdot O_{3} \) is used as germicide for purification of air
B. \( \ln O_{3}, O-O \) bond length is identical with that of
molecular oxygen
C. \( O_{3} \) molecule is angular in shape
D. \( O_{3} \) is an oxidising agent


Which of the following metals is
obtained by the reduction of metal oxide using hydrogen gas?
A. \( C u \)
в. \( A l \)
c. \( M g \)
D. \( F e \)


Let \( \mathbf{f}: \boldsymbol{N} \rightarrow \boldsymbol{N}, \) where \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}+ \)
\( (-1)^{x-1}, \) then
A. \( f(x) \) is symmetric about \( x=1 \)
B. \( f(x) \) is symmetric about \( y=x \)
c. \( f(x) \) is not symmetric about \( y=x \)
D. \( f(x) \) is symmetric about \( x=a, a \in N \)


The resistance of \( 2 \Omega \) is connected
across one gap of a meter-bridge (length of the wire is \( 100 \mathrm{cm} \) ) and an unknown resistance greater than \( 2 \Omega \) is connected across the other gap. When the resistance are interchanged, the balance point shifts by 20cm. Neglecting any corrections, the unknown resistance is: \( (\text { in } \Omega) \)


\( A(1,-1,-1), B(2,1,-2) \) and \( C(-5,2,-6) \) are the
position vectors of the vertices of triangle \( A B C \) The length of the bisector
of its internal angle at \( A \) is:
A. \( \frac{\sqrt{10}}{4} \)
B. \( \frac{3 \sqrt{10}}{4} \)
c. \( \sqrt{10} \)
D. none


When 0.2 mole of ethane is burnt completely in a bomb calorimeter, the temperature of calorimeter system increased by \( 2 K \). What should be the
increase in temperature of the same calorimeter system, when 0.4 mole of
\( C H_{4} \) is burnt?
Given: \( \Delta_{C} U_{C_{2} H_{6}(g)}=-400 K c a l / m o l \)
and \( \Delta_{c} U_{C H_{4}(g)}=-200 K c a l / m o l \)
A . \( 2 K \)
в. 4 К
\( c \cdot 1 k \)
D. 3 K


If an error of \( 1^{\circ} \) is made in measuring
the angle of a sector of radius \( 30 \mathrm{cm} \) then the approximate error in its area is
A \( \cdot 450 \mathrm{cm}^{2} \)
В \( \cdot 25 \pi c m^{2} \)
\( \mathbf{c} \cdot 2.5 \pi c m^{2} \)
D. none of these


The acute angle \( \theta \) through which the coordinate axes should be rotated for
the point \( A(2,4) \) to attain the new
abscissa 4 is given by
A \( \cdot \tan \theta=\frac{3}{4} \)
В. \( \tan \theta=\frac{5}{6} \)
\( \mathbf{c} \cdot \tan \theta=\frac{7}{8} \)
D. None of these


Cochlea lodges
A. Helicotrema
B. Meibomian gland
C. Organ of Corti
D. Fenestra rotundus


\( \lim _{x \rightarrow \infty}\left(\frac{3 x^{2}+2 x+1}{x^{2}+x+2}\right)^{\frac{6 x+1}{3 x+2}} \) is equal to
\( A \cdot 3 \)
B. 9
\( c \)
D. none of these


One end of uniform wire of length \( L \) and of weight \( W \) is attached rigidly to a
point in the roof and a weight \( W_{1} \) is
suspended from the lower end. If \( \boldsymbol{A} \) is
the area of cross-section of the wire, the
stress in the wire at a height \( \frac{3 L}{4} \) from its lower end is:
A. \( \frac{W_{1}}{A} \)
\( ^{\text {В } \cdot} \frac{\left(W_{1}+\frac{W}{4}\right)}{A} \)
\( \frac{\left(W_{1}+\frac{3 W}{4}\right)}{A} \)
D. \( \frac{W_{1}+W}{A} \)


\( \boldsymbol{A}=\left[\begin{array}{lll}2 & 3 & 1 \\ 4 & 1 & 5 \\ 3 & 9 & 7\end{array}\right] . \) Then the additive
inverse of \( \boldsymbol{A} \) is:
\( A \)
\[
\left[\begin{array}{ccc}
-2 & -3 & 1 \\
4 & -1 & -5 \\
-3 & 9 & -7
\end{array}\right]
\]
B.
\[
\left[\begin{array}{ccc}
-2 & -3 & -1 \\
-4 & -1 & -5 \\
-3 & -9 & -7
\end{array}\right]
\]
\( c \)
\[
\left[\begin{array}{ccc}
2 & -3 & -1 \\
-4 & 1 & -5 \\
-3 & -9 & 7
\end{array}\right]
\]
D.
\[
\left[\begin{array}{ccc}
-2 & -3 & -1 \\
-4 & -1 & -5 \\
-3 & 9 & -7
\end{array}\right]
\]


If a resistance \( 5 \Omega \) is connected in the
left gap of a meter bridge and \( 15 \Omega \) in the other gap then position of balancing point is
\( A \cdot 10 \mathrm{cm} \)
B. 20 cm
c. \( 25 \mathrm{cm} \)
D. 75 cm


Integrate :
\( \int\left(x^{4}-x^{2}+1-\frac{2}{1+x^{2}}\right) d x \)


Electromagnets are used in which of the following?
A. Speaker
B. Motor
c. Generator
D. All of the above


\( \Delta H \) and \( \Delta S \) for the reaction,
\( \boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{O}(\boldsymbol{s}) \longrightarrow \boldsymbol{2} \boldsymbol{A} \boldsymbol{g}(\boldsymbol{s})+\frac{1}{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \)
are \( 30.56 k J m o l^{-1} \) and
\( 66.0 J K^{-1} \) mol \( ^{-1} \) respectively. Calculate the temperature at which free energy change for the reaction will be zero.
Predict whether the forward reaction
will be forward above or below this
temperature.


Which of the following solutions at the
same temperature will be isotonic?
A. \( 3.42 \mathrm{g} \) of cane sugar in one litre water and \( 0.18 \mathrm{g} \) of glucose in one litre water
B. 3.42 of cane sugar in one litre water and 0.18 g of glucose in 0.1 litre water
c. \( 3.42 \mathrm{g} \) of cane sugar in one litre water and \( 0.585 \mathrm{g} \) of NaCl in one litre water
D. 3.42 g of cane sugar in one litre water and 1.17 g of NaCl in one litre water


Female gametophyte of angiosperm is
A . 7 celled
B. 8 celled
c. 11 celled
D. 5 celled


Assertion : When a particle moves in a
circle with a uniform speed, its velocity and acceleration both changes.

Reason : The centripetal acceleration in circular motion is dependent on angular velocity of the body.
A. If both Assertion and Reason are true and the Reason is the correct explanation of the Assertion
B. If both Assertion and Reason are true but the Reason i not the correct explanation of the Assertion
c. If Assertion is true statement but Reason is false
D. If both Assertion and Reason are false statements


The decreasing fugacity order of the following compounds is:
i. \( \boldsymbol{P h} \boldsymbol{S O}_{3}^{\ominus} \boldsymbol{i} \boldsymbol{i} . \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{S O}_{3}^{\ominus} \)
ii \( i . C_{2} H_{5} C O O^{\ominus} \) iv. \( C_{N} \)
\( \boldsymbol{v} . \boldsymbol{O} \boldsymbol{H} \)
A \( \cdot(v)>(i v)>(i i i)>(i i)>(i) \)
B. \( (i)>(i i)>(i i i)>(i v)>(v) \)
c. \( (i v)>(v)>(i i i)>(i i)>(i) \)
D. \( (i)>(i i)>(i i i)>(v)>(i v) \)


What is an ecological pyramid?
Compare the pyramids of energy, biomass and numbers.


The plates of a parallel plate capacitor
have an area of \( 90 \mathrm{cm}^{2} \) each and are
separated by \( 2.5 m m . \) The capacitor is
charged by a 400 volt supply. How much electrostatic energy is stored by the capacitor?
A \( .2 .55 \times 10^{-6} J \)
В. \( 1.55 \times 10^{-6} J \)
c. \( 8.15 \times 10^{-6} J \)
D. \( 5.5 \times 10^{-6} J \)


State True or False:
Dynamo output can be coupled to a transformer.
A. True
B. False


Solve
\( y-12=-5 \)


The line through \( A(-2,3) \) and \( B(4, b) \) is
perpendicular to the line \( 2 x-4 y=5 \)
Find the value of \( |\boldsymbol{b}| \)


Standard E.M.F. experienced by the person with dental filling is:
A . \( +3.89 V \)
B . \( 2.89 V \)
c. \( 0.93 V \)
D. \( +0.43 V \)


Which one of the following is used to make 'non-stick' cookware?
A. Polystyrene
B. PVC
c. Polyethylene terephthalate
D. Polytetra fluoroethylene


If \( x^{2}+a x+b \) is an integer for every
integer \( \boldsymbol{x} \) then
A. \( a \) is always an integer but b need not be an integer
B. \( b \) is always an integer but a need not be an integer
\( \mathrm{c} \cdot a+b \) is always an integer
D. none of these


\( \boldsymbol{A l}+\boldsymbol{N} \boldsymbol{O}_{\mathbf{2}}^{-} \rightarrow \boldsymbol{A l}(\boldsymbol{O} \boldsymbol{H})_{4}^{-}+\boldsymbol{N} \boldsymbol{H}_{3} \)
The oxidizing agent for this reaction
is
A . \( A l \)
в. \( N \)
\( c \cdot O \)
D. both \( A \) and \( B \)


The minimum resistance that can be
obtained by connecting 5 resistance of \( \frac{1}{4} \Omega \) each is
A \( \cdot \frac{4}{5} \Omega \)
в. \( \frac{4}{\Omega} \)
\( c .20 \Omega \)
D. \( 0.05 \Omega \)


Assertion: An isosceles \( \Delta \) is right angled.
Reason \( : \angle A=\angle B=45^{\circ} \) and \( \angle C= \)
\( \mathbf{9 0}^{\circ} \)
Which of the following statement is
true?
A. A is true and \( \mathrm{R} \) is the correct explanation of
B. A is true and R is not the correct explanation of
c. A is false
D. None of these


Find the reduced form of the expression \( \frac{20 u^{3} v^{2}-15 u^{2} v}{10 u^{4} v+30 u^{3} v^{3}} \)
A \( \cdot \frac{5 u v}{40 u^{7} v^{4}} \)
в. \( \frac{2 v-1}{u+2 u v^{2}} \)
c. \( \frac{4 u v-3}{2 u^{2}+6 u v^{2}} \)
D. \( \frac{2 u v-3 u v^{2}}{u^{2}+6} \)


The resistivity of the conductors is of
the order of
A \( \cdot 10^{8} \Omega m \)
B . \( 10^{-8} \Omega m \)
\( \mathbf{c} \cdot 10^{8} \Omega \)
D. \( 10^{-8} \Omega \)


Wave motion happens due to
A. propagation of energy
B. propagation of matter
C. propagation of both energy and matter
D. None of these.


A top of mass \( m=1.0 \mathrm{kg} \) and
moment of inertia relative to its own
axis \( I=4.0 g m^{2} \) spins with an angular
velocity \( \omega=310 \) rad/s. Its point of rest
is located on a block which is shifted in
a horizontal direction with a constant
acceleration \( \boldsymbol{w}=\mathbf{1 . 0} \boldsymbol{m} / \boldsymbol{s}^{2} . \) The
distance between the point of rest and the centre of inertia of the top equals
\( l=10 \mathrm{cm} . \) If the angular velocity of
precession \( \omega^{\prime} \) is \( x \) find the value of \( 10 x \)


(2R,4S)-2,4-Dichloropentane and \( (2 S, 4 R)-2,4 \) -dichloropentane are:
A. diastereomers
B. constitutional isomers
c. enantiomer
D. identical


If the 9 th term of an A.P is 35 and 19 th
is \( 75, \) then its 20 th term will be
\( \mathbf{A} \cdot 78 \)
B. 79
c. 80
D. 81


Indian rose wood tree is common name
of
A. Acacia
B. Shorea
c. Dalbergia
D. Eucalyptus


When spheres are raised to the same
temperature
A .1: 32: 243
B . 1: 8: 27
c. 1: 16: 128
D. 1: 4: 9


\( \frac{\sqrt{2}}{\frac{5}{2}} \)


The oxidation number of \( S \) in \( N a_{2} S_{4} O_{6} \)
is :
A . +2.5
B. +2 and +3 (two \( S \) have +2 and other two have +3 )
\( \mathrm{c} \cdot+2 \) and +3 (three \( S \) have +2 and one \( S \) has +3
D. +5 and 0 (two S have +5 and the other two \( S \) have 0 )


\( 3 \mathrm{g} \) of salt of molar mass 30 is dissolved in 250 g of water. The molality of a solution is \( x \) M. The value of \( 10 x \) is


Pure water is a \( -=------ \) conductor of
electricity.
A. good
B. bad
c. semi
D. none of the above


Out of \( 1 M B a C l_{2} \) and \( 1 M A l C l_{3}, \) which
one has higher freezing point and why?


\( \left(\begin{array}{lll}\mathbf{7} & \mathbf{1} & \mathbf{5} \\ \mathbf{8} & \mathbf{0} & \mathbf{0}\end{array}\right)\left(\begin{array}{l}\mathbf{2} \\ \mathbf{3} \\ \mathbf{1}\end{array}\right)+\mathbf{5}\left(\begin{array}{l}\mathbf{1} \\ \mathbf{0}\end{array}\right) \) is equal to
A \( \cdot\left(\begin{array}{l}16 \\ 27\end{array}\right. \)
B. \( \left(\begin{array}{l}27 \\ 16\end{array}\right. \)
c. \( \left(\begin{array}{l}15 \\ 16\end{array}\right. \)
D. \( \left(\begin{array}{l}16 \\ 15\end{array}\right. \)


In how many rears will a sum of Rs. 800
at \( 10 \% \) per annum compound interest, compounded semiannually becomes
Rs. \( 926.10 ? \)
A. 1 year
B. 3 years
c. 2 years
D. \( 1 \frac{1}{2} \) years


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


A student was carrying out a Grignard reaction between \( P h M g B r \) and ethyl
benzoate. She ran out of anhydrous ether just after the Grignard reagent was made. Which of the following solvents can still used to dissolve the
ethyl benzoate for its reaction with
already formed \( \boldsymbol{P h} M \boldsymbol{g} \boldsymbol{B r} \)
A. acetone
B. ethyl acetate
c. absolute alcohol
D. benzene


Electric charge is uniformly distributed along a long straight wire of a radius of 1 mm. The Charge per cm length of the wire is Q coulomb. Another cylindrical surface
of radius \( 50 \mathrm{cm} \) and length \( 1 \mathrm{m} \) symmetrically encloses the wire as shown in fig. The total flux passing through the cylindrical surface
is
A \( \cdot \frac{Q}{\epsilon_{0}} \)
в. \( \frac{100 Q}{\epsilon_{0}} \)
c. \( \frac{10 Q}{\pi \epsilon_{0}} \)
D. \( \frac{100 Q}{\pi \epsilon_{0}} \)


If \( 9.2 \mathrm{cm} \) is the diameter of a circle then
its radius is
A \( .4 .1 \mathrm{cm} \)
в. \( 4.6 \mathrm{cm} \)
c. \( 4.8 \mathrm{cm} \)
D. \( 4.3 \mathrm{cm} \)


Which of the following statement is true for Iymph?
A. WBC and serum
B. All components of blood expect RBCs and some proteins
c. RBCs WBCs and plasma
D. RBCs proteins and platelets


Which of the following is not directly
formed from DNA?
A. DNA
B. Protein
c. \( m \) RNA
D. t RNA


Atomic number is
A. the total number of protons present in the nucleus of an atom.
B. an atom of each element having a definite combining capacity.
C. the electrons present in the outermost shell of an atom.
D. an outermost-shell, which had eight electrons.


why does the sky sometimes appear white?


Food is stored in Rhizopus/ Cystopus
Fungi as
A. Protein and steroids
B. Sugar and oil
c. Protein and starch
D. Glycogen and oil


Ethylamine is?
A. \( C H_{3}-C H_{2}-C H_{3} \)
в. \( C H_{3}-\underset{O}{\|}-O H \)
c. \( C H_{3}-O-C_{3} H_{7} \)
D. \( C H_{3}-C-C H_{3} \)
I
O
E \( \cdot C H_{3}-C H_{2}-N H_{2} \)


Sum of the probabilities of all the elementary events of an experiment is
\( \mathbf{A} \cdot \mathbf{0} \)
B. 0.2
c. 1
D. 0.8


In the electronic structure of \( \mathrm{H}_{2} \mathrm{SO}_{4} \), the
total number of shared electrons is:
A . 20
B . 16
c. 12
D. 8


For \( B e, Z_{e f f}=1.95 \) and for \( \boldsymbol{B} \boldsymbol{e}^{\boldsymbol{x}+}, \boldsymbol{Z}_{\boldsymbol{e f f}}=\mathbf{2 . 3 0 .} \) Hence, ion is:
\( \mathbf{A} \cdot B e^{+} \)
в. \( B e^{2} \)
\( \mathbf{c} \cdot B e^{3+} \)
D. \( B e \)


What will a deposit of Rs. 5,500 at \( 8 \% \)
compounded quarterly interest be worth, if left in the bank for 10 years?


The collector supply voltage in \( \mathrm{CE} \) transistor amplifier is \( 10 V . \) The base
current is \( 10 \mu A \) in the absence of the
signal voltage and the voltage between the collector and the emitter is \( 4 V \). The
current gain \( (\beta) \) of a transistor is 200
then the value of the load resistance \( \boldsymbol{R}_{\boldsymbol{L}} \)
\( \mathbf{A} \cdot 2 k \Omega \)
в. \( 1 k \Omega \)
\( c .3 k \Omega \)
D. \( 4 k \Omega \)


Sewer gas is a complex mixture of:
A. toxic and nontoxic gases
B. toxic gases
c. nontoxic gases
D. inert gases


The points \( \boldsymbol{A}(\mathbf{2}, \mathbf{9}), \boldsymbol{B}(\boldsymbol{a}, \mathbf{5}), \boldsymbol{C}(\mathbf{5}, \mathbf{5}) \) are
the vertices of a triangle \( A B C \) right
angled at B. find the value of \( ^{\prime} a^{\prime} \) and
hence the area of \( \Delta A B C \)


Which of the following is an occupational respiratory disease
A. A)diptheria
B. B) pneumonia
c. \( \mathrm{c} \) tuberculosis
D. D) asbestosis


The central equation of the quantum theory is the Schrodinger equation. If true enter 1 , else enter 0 .


The direction cosines of the normal to
the plane \( 5 y+4=0 \) are?
A \( \cdot 0, \frac{-4}{5}, 0 \)
в. 0,1,0
c. 0,-1,0
D. None of these


A large insulated sphere of radius \( r \)
charged with \( Q \) units of electricity is placed in contact with a small insulated uncharged sphere of radius \( r^{\prime} \) and is
then separated. The charge on the smaller sphere will now be:
A \( \cdot \frac{Q\left(r^{\prime}+r\right)}{r^{\prime}} \)
в. \( \frac{Q\left(r^{\prime}+r\right)}{r} \)
c. \( \frac{Q r}{\left(r^{\prime}+r\right)} \)
D. \( \frac{Q_{r}^{\prime}}{\left(r^{\prime}+r\right)} \)


Assertion
If the angles of the base of the prism are
equal, then in the position of minimum deviation, the refracted ray will pass parallel to the base of prism.
Reason
In the case of minimum deviation, the
angle of incidence is equal to the angle
of emergence.
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 activity of a radioactive substance
is \( R_{1} \) at time \( t_{1} \) and \( R_{2} \) at time \( t_{2}\left(>t_{1}\right) \)
Its decay constant is \( \lambda \). Then
A \( . R_{1} t_{1} \)
B \( \cdot R_{2}=R_{1} e^{\lambda\left(t_{1}-t_{2}\right)} \)
c. \( \frac{R_{1}-R_{2}}{t_{2}-t_{1}}= \) constant
D. \( R_{2}=R_{1} e^{\lambda\left(t_{2}-t_{1}\right)} \)


The identity elements with respect to multiplication in integers is
A .
B. - -
c. 0
D. none


The voltage across \( \boldsymbol{Q} \) is
7.60
\( \mathbf{A} \cdot 20 V \)
B. \( \frac{\sqrt{1350}}{10} V \)
c. \( 5.5 V \)
D. \( \frac{\sqrt{9524}}{10} V \)


Gravitational force is the weakest force
in nature. Explain.


Coordination compounds have great
importance in biological systems. In
this context which of the
following statement(s) is/are incorrect?
A. Chlorophyll is a green pigment in plants and contains calcium
B. Haemoglobin is the red pigment of blood and contains iron
C. Cyanocobalamin is \( B_{12} \) and contains cobalt
D. Carboxypeptidase A is an enzyme and contains zinc


The heat capacity of a certain amount
of a particular gas at constant pressure
is greater than that at constant volume by \( 29.1 \mathrm{J} / \mathrm{K} . \) Match the items given in
Column I with the items given in Column II.
List 1
If the gas is monatomic, heat capacity at constant volume

If the gas monatomic, heat capacity at constant pressure
If the gas is rigid diatomic, heat capacity at constant pressure
If the gas is vibrating diatomic, heat capacity at constant pressure
\( \mathbf{A} \cdot A \rightarrow 2, B \rightarrow 3, C \rightarrow 4, D \rightarrow 1 \)
B. \( \mathrm{B} \rightarrow 1, \mathrm{C} \rightarrow 3, \mathrm{D} \rightarrow 4, \mathrm{A} \rightarrow 1 \)
C. \( \mathrm{C} \rightarrow 1, \mathrm{D} \rightarrow 3, \mathrm{A} \rightarrow 4, \mathrm{B} \rightarrow 1 \)
D. \( D \rightarrow 1, A \rightarrow 3, B \rightarrow 4, C \rightarrow 1 \)


Which scientist experimentally proved the existence of electromagnetic wave.
A. Marconi
B. Hertz
c. мaxwell
D. S.C.Bose


The number of amino acids in insulin is:
A . 2
B. 574
\( c \cdot 51 \)
D. 5733


If \( \boldsymbol{a}>\mathbf{0} \) and \( \int_{0}^{a}[\boldsymbol{f}(\boldsymbol{x})+\boldsymbol{f}(-\boldsymbol{x})] \boldsymbol{d} \boldsymbol{x}= \)
\( \int_{-a}^{a} \phi(x) d x \) then one of the possible
values of \( \phi(x) \) can be
A \( \cdot f(-x) \)
B . \( -f(x) \)
c. \( \frac{1}{2} f(x) \)
D. none of these


Hot milk is easier to drink from a bowl
than from a glass. Mention the reason.


Compare the focussing in a camera with the focussing in a human eye.


If \( \theta \) is the angle between the lines whose vector equations are \( \overrightarrow{\boldsymbol{r}}=\boldsymbol{3} \overrightarrow{\boldsymbol{i}}+\boldsymbol{2} \overrightarrow{\boldsymbol{j}}+ \)
\( 4 \vec{k}+\lambda(\vec{i}+2 \vec{j}+2 \vec{k}) \) and \( \vec{r}=5 \vec{i} \)
\( 2 \vec{k}+\mu(3 \vec{i}+2 \vec{j}+6 \vec{k}) ; \lambda \) and \( \mu \) being
parameters, then
This question has multiple correct options
\( ^{\mathbf{A}} \cdot \cos \theta=\frac{19}{21} \)
B. \( \sin \theta=\frac{19}{21} \)
\( ^{\mathbf{C}} \sin \theta=\frac{4 \sqrt{5}}{21} \)
D. \( \cos \theta=\frac{4 \sqrt{5}}{21} \)


Cobalt-60 is used to irradiate tumors
with \( \gamma \) -rays
\( _{27}^{60} C o \longrightarrow_{28}^{60} N i+_{-1}^{0} e+\gamma \)
Which is responsible for destroying cancer-cells?
A \( \cdot \gamma- \) rays
В. \( \alpha- \)rays
\( \mathbf{c} \cdot \beta-r a y s \)
D. None of these


If \( \alpha \) and \( \beta \) are the roots of \( a x^{2}+b x+ \)
\( c=0, \) then the quadratic equation
whose roots are \( \frac{1}{\alpha} \) and \( \frac{1}{\beta} \) is
A \( \cdot a x^{2}+b x+c=0 \)
B. \( b x^{2}+a x+c=0 \)
c. \( c x^{2}+b x+a=0 \)
D. \( c x^{2}+a x+c=0 \)


Which letter orbital corresponds to \( l= \)
2?
A.
B.
\( c \cdot d \)
D.
E.


Which of the following statements is
correct with respect to the property of elements with increase in atomic
number in the carbon family (group 14)?
A. Their metallic character decreases
B. The stability of +2 oxidation state increases.
c. Their ionization energy increases.
D. Their atomic size decreases


What is slaked lime?


In human beings the blood goes to the
heart in one cycle once. Is it true or
false?


Which of the following reactions takes place at anode?
A. Reduction
B. Oxidation
c. Decomposition
D. Dissolution


The sum of the coefficients in the first
three terms of the expansion of \( \left(x^{2}-\frac{2}{x}\right)^{m} \) is equal to \( 97 . \) Find the term of the expansion containing \( \boldsymbol{x}^{4} \)


When a solid sphere moves through a liquid the liquid opposes is the motion
with a force the magnitude of the force depends upon the coefficient of viscosity of the liquid the radius of the
sphere find the expression of force using dimension formula:
A \( \cdot v t=\frac{2(d-\rho) g r^{2}}{8 \eta} \)
B. \( v t=\frac{(d-\rho) g r^{2}}{6 \eta} \)
c. \( v t=\frac{2(d-\rho) g r^{2}}{9 \eta} \)
\( V t=\frac{(d-\rho) g r^{2}}{9 \eta} \)


Which of the following statements is
false?
A \( \cdot \) At temperature equal to \( \frac{a}{R b} \) (where a and b are vander Waal's constant). real gases obey ideal gas laws over an appreciable range of pressure
B. Most probable speed of a gas is always greater than its average speed
C. Dalton's law of partial pressure is not valid for reacting gases
D. A gas cannot be liquified above its critical temperature


The freezing point of one molal \( N a C l \)
solution assuming \( N a C l \) to be \( 100 \% \) dissociated in water is:
[Molal depression constant is \( 1.86] \)
A \( .-2.72^{2} C \)
В. \( -3.72^{2} C \)
c. \( 2.72^{2} C \)
D. \( 3.72^{2} C \)


\( f \tan ^{-1} \frac{x-1}{x-2}+\tan ^{-1} \frac{x+1}{x+2}=\frac{\pi}{4}, \) then
find the value of \( x \)


The ' \( C^{\prime} \) shaped structure of alimentary
canal is
A. Stomach
B. Oesophagus
c. Duodenum
D. Vermiform appendix


Draw a line \( P Q=12.5 \mathrm{cm} . \) Divide it 7
equal parts.


Bacteria are examples of
A. Protistan cells
B. Eukaryotic cells
c. Animal cells
D. Prokaryotic cells


Which is the most effective method of
separating mixtures of miscible volatile liquids?
A. Fractional distilliation
B. Simple distillation
c. chromatography
D. Filtration


What is standard deviation of the set of
observations \( 32,28,29,30,31 ? \)
A . 1.6
B. \( \sqrt{2} \)
\( c \cdot 2 \)
D. none of these


If the roots of the equation \( p x^{2}+q x+ \)
\( r=0 \) are in the ratio \( =l: m \)
\( \left(l^{2}+m^{2}\right) p r+l m\left(2 p r-q^{2}\right)=0 \)


The volume of blood each ventricle
pumps out during a cardiac cycle is
about
A . 70 \( \mathrm{ml} \)
B. 5000 ml
c. \( 71 \mathrm{ml} \)
D. 1200 m!


Milk curdles when lemon juice is added.
This is :
A. evaporation
B. coagulation
c. reversible
D. photochemical change


Sulphur sol contains:
A. discrete \( S \) -atoms
B. discrete \( S \) -molecules
C. large aggregates of \( S \) -molecules
D. water dispersed in solid sulphur


The vapour pressure of two liquids 'P and 'Q' are 80 and 60 torr, respectively.
The total vapour pressure of solution obtained by mixing 3 mole of \( P \) and 2 mole of Q would be:
A. 68 torr
B. 140 torr
c. 72 torr
D. 20 torr


Which of the following statements is
wrong?
A. Mean free path varies inversely with the number of molecules per unit volume of gas.
B. The time spent during a collision is appreciable and attraction among molecules give rise to force.
C. Mean free path is independent of the temperature or pressure in a sample of gas in a container of fixed volume
D. If \( \lambda \) is mean free path, the \( \lambda \propto T \) at constant \( P \) and \( \lambda \propto \)
\( \frac{1}{P} \) at constant \( T \)


ff \( \mathbf{5} \boldsymbol{A}=\left(\begin{array}{cc}\mathbf{3} & \mathbf{- 4} \\ \mathbf{4} & \boldsymbol{x}\end{array}\right) \) and \( \boldsymbol{A} \boldsymbol{A}^{\boldsymbol{T}}= \)
\( A^{T} A=I, \) then the value of \( x, \) is
\( A \cdot 3 \)
B. -3
\( c \cdot 2 \)
D. - 2


A copper coin was electroplated with Zn and then heated at high temperature until there is a change in colour. What will be the resulting colour?
A. White
B. Black
c. Silver
D. Golden


Which among ice and water has the higher specific heat capacity?
A . Ice
B. Water
\( c \cdot \) both \( A \& B \)
D. none of the above


Organic molecules always contain:
A. hydrogen
B. oxygen
c. carbon
D. sulfur
E. nitrogen


What happens when \( S O_{2} \) is passed
through acidified \( K_{2} C r_{2} O_{7} \) solution?


f \( \boldsymbol{A}=(-\mathbf{3}, \mathbf{2}, \mathbf{5}), \boldsymbol{B}=(-\mathbf{3}, \mathbf{4}, \mathbf{5}) \) and
\( C=(-3,4,7) \) are the position vectors
of vertices of \( \Delta A B C \) then its
circumcentre is
A. (-3,3,5)
(年 \( \cdot(-3,3,5) \)
В. (-3,3,6)
c. (-3,4,6)
a
D. (-3,4,7)


If K.E. of an electron, \( \alpha- \) particle and a
proton are represented by \( \boldsymbol{E}_{1}, \boldsymbol{E}_{2} \) and \( \boldsymbol{E}_{3} \) respectively (provided all these have same de Broglie wavelength) then
A \( . E_{1}=E_{2}=E_{3} \)
в. \( E_{1}>E_{2}>E_{3} \)
c. \( E_{1}>E_{3}>E_{2} \)
D. \( E_{2}>E_{3}>E_{1} \)


In the rhombus \( A B C D, A C \) and \( B D \) are the diagonals. If the diagonals are \( 16 \mathrm{cm} \) and \( 12 \mathrm{cm} . \) Find the length of each of its sides.
\( A \cdot 10 \mathrm{cm} \)
B. 12 \( \mathrm{cm} \)
\( c \cdot 9 \mathrm{cm} \)
D. \( 8 \mathrm{cm} \)


The value of ' \( m_{s} \) ' for an electron
spinning in clock-wise direction is and for anti-clockwise
direction is


Wand X are \( _{\text {- - }} \), respectively.
\( A \cdot O_{3} \) and \( P_{4} O_{6} \)
B. \( O_{2} \) and \( P_{4} O_{6} \)
\( \mathrm{c} \cdot \mathrm{O}_{2} \) and \( P_{4} \mathrm{O}_{1} \)
D. \( O_{3} \) and \( P_{4} O_{1} \)


An inclined plane makes an angle \( 30^{\circ} \)
with horizontal. A groove OA=5cm cut on the plane makes an angle \( 30^{0} \) with \( 0 x \)
A short smooth cylinder is free ti slide down the groove under the influence of gravity. the time taken by the cylinder to
reach from \( A \) to 0 is \( \left(g=10 m / s^{2}\right) \)
\( \mathbf{A} \cdot 4 s \)
в. \( 10 s \)
c. \( 2 s \)
D. \( 5 s \)


Let \( y=e^{\sqrt{x}} \) then find \( \frac{d y}{d x} \)


Which polymer among the following polymers does NOT soften on heating?
A. Bakelite
B. Polythene
c. Polystyrene
D. PVC


If a concave lens of very large focal
length \( 100 \mathrm{cm} \) is placed in contact with the convex lens, find the shifting of the image


Which of the following reaction(s) can be used for the preparation of alkyl halides?
(I) \( C H_{3} C H_{2} O H+H C l \quad \) anh. \( Z n C l_{2} \)
(II) \( C H_{3} C H_{2} O H+H C l \rightarrow \)
\( (\| I)\left(C H_{3}\right)_{3} C O H+H C l \rightarrow \)
\( (\mathrm{IV})\left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{C H O H}+\boldsymbol{H C l} \stackrel{\boldsymbol{a n h . Z n C l}_{2}}{\longrightarrow} \)
\( \mathbf{A} \cdot(I V) \) only
B. (III) and (IV) onlyyy y
c. \( (I),(I I I) \) and \( (I V) \) only
D. \( (I) \) and \( (I I) \) only


What are the different ways in which
glucose is oxidised to provide energy in various organism?


Which of the following pair is incorrectly matched?
A. Van Arkel method - Zirconium
B. Krolls process - Titanium
c. Froth Floatation - Cerussite
D. Distillation - zinç


Convert the following ratio into
percentage:
\( \frac{\mathbf{5 4 6}}{\mathbf{6 0 0}} \)


The predominant antibody in saliva is
A . \( \lg G \)
B. \( \lg A \)
c. \( \lg \) m
D. IgD


The oxidation states of \( S \) atoms in
\( S_{4} O_{6}^{2-} \) from left to right respectively
are:
\( \boldsymbol{O}-\underbrace{\boldsymbol{O}}{\boldsymbol{S}}-\boldsymbol{S}-\boldsymbol{S}-\underset{\boldsymbol{V}}{\|}^{\boldsymbol{O}}-\boldsymbol{O}^{-} \)
\( A \cdot+6,0,0,+6 \)
B. +3,1,+1,+3
\( c \cdot+5,0,0,+5 \)
D. None of above


The \( \Delta H \) for the reaction at \( 0^{\circ} \mathrm{C} \)
\( Z n+2 A g C l \rightarrow Z n C l_{2}+2 A g \)
is -52.05 kcal. If the e.m.f. of the cell is
1.015 volt, the temperature coefficient of
the cell at \( 0^{\circ} \mathrm{C} \) in \( V /^{o} C \) is:
A . \( -4.311 \times 10^{-4} \)
В . \( 2.388 \times 10^{-4} \)
c. \( 4.311 \times 10^{-4} \)
D. \( 4.311 \times 10^{-5} \)


In Searle's experiment to find Young's
modulus, the diameter of wire is
measured as \( D=0.05 \mathrm{cm}, \) the length of
wire is \( L=125 c m, \) and when a weight,
\( \boldsymbol{m}=20 k g \) is the put, extension in wire
was found to be \( 0.100 \mathrm{cm} \). Find the
maximum permissible error in Young's modulus \( (Y) \)


A force \( F \) is related to the position of \( a \)
particle by the relation \( \boldsymbol{F}=\left(\mathbf{1 0} \boldsymbol{x}^{2}\right) \boldsymbol{N} \)
The work done by the force when the particle moves from \( x=2 m \) to \( x=4 \) m is
A \( \cdot \frac{56}{3} J \)
в. \( 560 J \)
c. \( \frac{560}{3} J \)
D. \( \frac{3}{560} J \)


The indicator used in the titration of a
strong acid and a strong base is/are :
This question has multiple correct options
A. phenolphthalein
B. methyl orange
c. alizarin yellow
D. red litmus


What is the main difference between
electromagnetic wave theory and
Planck's quantum theory?
A. According to electromagnetic wave theory, the energy is emitted or absorbed continuously whereas according to Planck's quantum theory, energy is emitted or absorbed discontinuously,i.e. in certain definite packets called 'Quanta'
B. According to electromagnetic wave theory, energy is emitted or absorbed discontinuously, i.e., in certain definite packets called 'Quanta' whereas according to Planck's quantum theory, the energy is emitted or absorbed continuously
C. According to electromagnetic wave theory, the energy is emitted or absorbed continuously whereas according to Planck's quantum theory, energy is emitted or absorbed continuously,i.e. in certain definite packets called 'Quanta'
D. According to electromagnetic wave theory, the energy is emitted or absorbed discretely whereas according to Planck's quantum theory, energy is emitted or absorbed discontinuously, i.e., in certain definite packets called'Quanta'


A force acting on a particle varies with
the displacement \( x \) as \( F=a x-b x^{2} \)
Where \( a=1 N / m \) and \( b=1 N / m^{2} \)
The work done by this force for the first
one meter \( (F \text { is in newtons, } x \) is in
meters is:
A \( \cdot \frac{1}{6} J \)
в. \( \frac{2}{6} J \)
c. \( \frac{3}{6} J \)
D. None of these


\( C_{6} H_{5} C \equiv N \) and \( C_{6} H_{5} N \equiv C \) are
which type of isomers?
A. Position
B. Functional
c. Tautomerism
D. Linkage


Define a scalar matrix.


Solutions of copper sulphate, iron
sulphate and zinc sulphate are prepared and marked I, II and III respectively. Few pieces of aluminium are added to each solution. After some
time a change will be observed in:
A. I and II
B. Il and III
c. III and
D. all the three


Which of the following statement are
correct?
This question has multiple correct options
A. Orthophosphoric acid is used as a stabilizer for \( H_{2} O_{2} \)
B. Orthophosphoric acid is used for making phosphorus and phosphates.
C. Orthophosphoric acid is used preparation of \( H B r \) in the laboratory.
D. Orthophosphoric acid is a tribasic acid.


Explain what is galvanization. What purpose is served by it?


\( \int e^{x}\left(\frac{2+\sin 2 x}{1+\cos 2 x}\right) d x= \)
A \( \cdot e^{x} \cot x+c \)
B \( \cdot 2 e^{x} \sec ^{2} x+c \)
\( \mathbf{c} \cdot e^{x} \cos 2 x+c \)
D. \( e^{x} \tan x+c \)


The equation of a transverse wave
travelling on a rope is given by \( \boldsymbol{y}= \)
\( 10 \sin \pi(0.01 x-2 \pi t) \) where \( y \) and \( x \) are
in \( c m \) and \( t \) in seconds. The maximum
transverse speed of a particle in the rope is about.
A. \( 63 \mathrm{cm} / \mathrm{s} \)
B. \( 75 \mathrm{cm} / \mathrm{s} \)
c. \( 100 \mathrm{cm} / \mathrm{s} \)
D. \( 121 \mathrm{cm} / \mathrm{s} \)


In which one of the following compounds, the oxidation number of sulphur is the least
\( A \cdot S O_{2} \)
в. \( S O_{3} \)
\( \mathbf{c} \cdot N a_{2} S O_{4} \)
D. \( H_{2} S O_{4} \)


\( \begin{array}{ll}\text { Appearance } & \begin{array}{l}\text { Reaction } \\ \text { with } \\ \text { dilute }\end{array} \\ & \boldsymbol{H C l}\end{array} \)
Unknown
metal #1 Dissolved
with
bubbles
of clear
gas Dull gray
solid with
white oxide
coating of
\( D \)
Unknow \( _{1 \# 2}^{\text {าown }} \) metal Solid;
lustrous,
smooth
silver-gray
surface No
reaction bub
of
gas
Identify the orange gas produced on the
addition of dilute \( H N O_{3} \) to unknown
metal #2.
\( \mathbf{A} \cdot C l_{2} \)
B. \( H_{2} \)
\( c \cdot O_{2} \)
D. \( C O_{2} \)
E \( . N O_{2} \)


In above figure, a candle is placed in
front of the plane mirror. Points \( A, B, C, D \) and E are marked as shown in the
figure. Find out the possible point where image is formed.
\( A \cdot A \)
B. В
\( c \cdot c \)
\( D \cdot D \)
E.


A solid conducting sphere of radius \( 2 R \)
carrying charge \( Q \) is surrounded by two
point charges \( Q \) and \( 2 Q \) as shown in the
figure. The electric field at point \( \boldsymbol{P} \) due
to the induced charge on conducting
sphere is
A \( \cdot \frac{7}{16} \frac{K Q}{R^{2}} \) towards right
B \( \cdot \frac{1}{8} \frac{K Q}{R^{2}} \) towards right
\( \mathrm{C} \cdot \frac{\mathrm{KQ}}{\mathrm{R}^{2}} \) towards right
D. Zero


The line \( \mathbf{L} \) given by \( \frac{\mathbf{x}}{\mathbf{5}}+\frac{\mathbf{y}}{\mathbf{b}}=\mathbf{1} \) passes
through the point \( (13,32) . \) If the line \( \mathbf{K} \) is parallel to L and has the equation \( \frac{\mathbf{x}}{\mathbf{c}}+\frac{\mathbf{y}}{\mathbf{3}}=\mathbf{1}, \) then the distance between
\( \mathbf{L} \) and \( \mathbf{K} \) is
A. \( \sqrt{17} \)
в. \( \frac{17}{\sqrt{15}} \)
c. \( \frac{23}{\sqrt{17}} \)
D. \( \frac{23}{\sqrt{15}} \)


Which of the following state of an ecosystem helps it to avoid changes?
A. Homeostasis
B. Shortage of components
c. Deficiency of light
D. Imbalance


How meiosis differs from mitosis?


Which of the following is safest way to protect yourself from lightning?
A. Run to an open field
B. Open an umbrella for cover
c. Take shelter under trees
D. Squat low on ground


Write short note on catenation.


The temperature-entropy diagram of a reversible engine cycle is given in the figure. Its efficiency is-
\( A \cdot \frac{1}{2} \)
B. \( \frac{1}{4} \)
\( c \cdot \frac{1}{3} \)
D. 2


Two particles of mass \( 1 k g \) and \( 0.5 k g \) are moving in the same direction with
speed of \( 2 m / \) sec and \( 6 m / \)sec
respectively on a smooth horizontal surface. Find the speed of centre of mass of the system


Anastral mitosis can be traced in
A. Invertebrates
B. Vertebrates
c. Both A and B
D. Plant cells


Match column I and column II and
select the correct answer using the
codes given below:


Find the distance between the pairs of points whose cartesian coordinates are (2,3,-1),(2,6,2)
A. \( 3 \sqrt{2} \)
B. \( 2 \sqrt{3} \)
\( c \cdot 5 \sqrt{2} \)
D. \( 2 \sqrt{5} \)


Q Type your question
IOr \( 1.00 \times 10 \). \( \kappa g \) or oxygen gas at two
different temperatures.
(a) What does the dotted plot signify?
(b) Which is true \( : T_{1}>T_{2} \) or \( T_{1}<T_{2} ? \)
(c) What is the value of PV / T where the
curves meet on the y-axis?
(d) If we obtained similar plots for
\( 1.00 \times 10^{-3} k g \) of hydrogen, would we
get the same value of PV/T at the point
where the curves meet on the y-axis? If
not, what mass of hydrogen yields the
same value of PV/T (for low pressure
high temperature region of the plot)?
(Molecular mass of \( \boldsymbol{H}_{2}=\mathbf{2 . 0 2} \boldsymbol{u}, \) of
\( O_{2}=32.0 u, R=8.31 J m o l^{-1} K^{-1} . \)


A converging lens of focal length \( 15 \mathrm{cm} \) and a converging mirror of focal length
\( 20 c m \) are placed with their principal
axis coinciding. A point source \( S \) is
placed on the principal axis at a
distance of \( 12 \mathrm{cm} \) from the lens as
shown in the figure. It is found that the final beam comes out parallel to the principal axis. Find the separation between the mirror and the lens.


When the following bodies of same radius starts rolling down on same inclined plane, identify the decreasing order of their time of descent:
I) Solid cylinder
II) Hollow cylinder
III) Hollow sphere
IV) Solid sphere
A. \( I V, I, I I I, I I \)
в. \( I I, I I I, I, I V \)
c. \( I, I V, I I I, I I \)
D. II, III, IV,


Which one of the following is a compound?
A. The black residue left when sugar is charred
B. Nitrogen gas
c. Air
D. carbon dioxide


Anhydrous \( A l C l_{3} \) is covalent. from the
data given below Lattice Energy \( =5137 \mathrm{KJ} \) mol\( ^{-1} \)
\( \triangle \boldsymbol{H} \) hydration \( \boldsymbol{A l}^{3+}= \)
\( -4665 K J / m o l^{-1} \)
\( \triangle \boldsymbol{H} \) hydration \( \boldsymbol{C l}^{-}= \)
\( -381 K J / m o l^{-1} \)
Identify the correct statement-
A. It will remain covalent in aqueous solution
B. The solution will consists of \( A I^{3+} \) and \( C I^{-} \)
c. The solution will consists of hydrate \( A I^{3+} \) and \( C I^{-} \)
D. None of these


The electricity produced by creating photo electrons is called:
A. Photoelectricity
B. Static electricity
c. Thermal electricity
D. Piezoelectricity


What tube is used by both the digestive and respiratory systems?
A. Esophagus
B. Larynx
c. Pharynx
D. None of these.


Find the position of center of mass of
the uniform planner section shown in
figure with respect to the origin (0)


Given that carbon \( 14\left(C_{14}\right) \) decays at a
constant rate in such a way that it
reduces to \( 50 \% \) in 5568 years. Find the age of an old wooden piece in the carbon
is only \( 12 \frac{1}{2} \% \) of the original.


Which of the following is not a unit of time?
A. Mean solar day
B. Lunar Month
C. Calendar year
D. Light year


The sum of mole fractions of solute and
solvent of a solution is equal to:
A. number of moles of solute
B. number of moles of solvent
c. number of mole of solution
D. unity


\( f\left(a-b=3 \text { and } a b=10, \text { find } a^{3}-b^{3}=\right. \)


How many numbers can be formed by using all the digits 1,2,3,4,3,2,1 so that the odd digits always occupy the odd places?
A . 16
B. 17
c. 18
D. 20


In the figure,two 4 -digit numbers are to be formed by filling the places with digits. The number of different ways in which the places can be filled by digits so that the sum of the numbers formed
is also a 4 -digit number and in no place the addition is with carrying, is
\( \mathbf{A} \cdot 55^{4} \)
B. 220
\( c \cdot 45^{4} \)
D. none of these


\( 4_{1} H^{1} \rightarrow_{2} H e^{4}+2_{+1} e^{0}+ \)energy
Energy released in this process is [lt is
\( \operatorname{given} 4_{1} H^{1}=4.031300 \mathrm{amu},_{2} H e^{4}= \)
\( \left.4.0026603 \text { amu, } 2_{1} e^{0}=0.01098 \text { amu }\right] \)
A . 14 Mev
B. 16.45 Mev
c. 37.2 Mev
D. \( 32.7 \mathrm{Mev} \)


Hydrogen bomb is based on
A. controlled chain reaction
B. uncontrolled chain reaction
c. nuclear fusion
D. nuclear fission


Which of the following is not in uniform
motion?
A. A bullet travelling with a constant speed in a straight line
B. A swinging pendulum
c. The earth rotating about its axis
D. Both B \& C


\( \operatorname{Let} z=\frac{(1+i)^{2}}{a-i},(a>0) \) and \( |z|=\sqrt{\frac{2}{5}} \)
then \( \bar{z} \) is equal to
A. \( -\frac{1}{5}-\frac{3 i}{5} \)
в. \( \frac{1}{5}+\frac{3 i}{5} \)
\( c \cdot \frac{3}{5}-\frac{1 i}{5} \)
D. \( -\frac{3}{5}+\frac{1 i}{5} \)


Explain the working of a diode as a half wave rectifier.


Vexillum is found in
A . Rosaceae
B. Papilionaceae
c. Cruciferae
D. Solanaceae


Assertion
It is possible to accelerate even if you are travelling at constant speed.
Reason
In the uniform circular motion, even if the particle has the constant speed, it
has an acceleration.
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


If 7 times the \( 7^{t h} \) term of an \( A . P \geq 11 \)
times its \( 11^{t h} \) term, then find its \( 18^{t h} \)
term.


Marks obtained by four students are \( : 25,35,45,55 . \) The average deviations from the mean is
A . 10
B. 9
c. 7
D. none of these


Potential energy of a current loop placed inside some magnetic field does not depend upon magnetic moment of the
loop.Enter 1 if True and 0 if False.


The position of an object moving along \( x \) -axis is given by \( x=a+b t^{2}, \) where \( a= \)
\( 8.5 \mathrm{m} \) and \( \mathrm{b}=2.5 \mathrm{m} \mathrm{s}^{-2} \) and \( \mathrm{t} \) is
measured in seconds. The
instantaneous velocity of the object at \( t \)
\( =2 \operatorname{sis} \)
A \( \cdot 5 \mathrm{m} s^{-1} \)
B. \( 10 \mathrm{m} s^{-1} \)
c. \( 15 \mathrm{m} \mathrm{s}^{-1} \)
D. 20 \( \mathrm{m} \mathrm{s}^{-1} \)


Find the area of the figure bounded by the following curves
\( y=\sin x_{2}, y=2 x / \pi \)


The imaginary roots of the equation \( \left(x^{2}+2\right)^{2}+8 x^{2}=6 x\left(x^{2}+2\right) \) are
A. \( 1+i \)
в. \( 2 \pm i \)
c. \( -1 \pm i \)
D. noneofthese


If \( [A] \neq 0 \) then which of the following is
not true?
A \( \cdot\left(A^{2}\right)^{-1}=\left(A^{-1}\right)^{2} \)
B. \( \left(A^{\prime}\right)^{-1}=\left(A^{-1}\right)^{\prime} \)
\( \mathbf{c} \cdot A^{-1}=|A|^{-1} \)
D. None of these


The first four terms of an \( A . P . \) whose
first term is 2 and the common
difference is 2 are:
B. 2,4,8,16
\( \mathrm{c} .2,4,6,8 \)
D. 2,5,8,11


Heat is transmitted from higher to lower
temperature through actual mass motion of the molecules in
A. conduction
B. convection
c. radiation
D. None of these


From a point in the interior of an equilateral triangle, perpendiculars are drawn on the three sides. The lengths of the perpendiculars are \( 14 \mathrm{cm}, 10 \mathrm{cm} \) and \( 6 \mathrm{cm} \)

The area of the triangle is \( 300 \sqrt{m} \mathrm{cm}^{2} \)
where \( m \) is


In the given reaction, (A) is:
is
A. \( C H_{3} C H O \)
в. \( C H_{3} C H_{2} \) ОН
c. \( C H_{2}=C H_{2} \)
D.
\[
\begin{array}{l}
C H_{2}-O H \\
C H_{2}-O H
\end{array}
\]


The vector equation of the plane passes through the points \( A \& B \) with position vector \( 2 \hat{i}+\hat{j}-\hat{k} \&-\hat{i}+3 \hat{j}+4 \hat{k} \)
respectively \( \& \) Ler to the plane \( \bar{r} \cdot(\hat{i}-2 \hat{j}+4 \hat{k})=10 \) is
A \( \cdot \bar{r} \cdot(18 \hat{i}+17 \hat{j}-3 \hat{k})=49 \)
B . \( \bar{r} .(18 \hat{i}-17 \hat{j}-3 \hat{k})+22=0 \)
c. \( \bar{r} .(18 \hat{i}+17 \hat{j}+4 \hat{k})=25 \)
D・ \( \bar{r} .(18 \hat{i}+17 \hat{j}+4 \hat{k})=24 \)


The temperature of the slag zone in the
metallurgy of iron using the blast furnace is:
\( 1.800-1000^{\circ} C \)
\( 2.500-700^{\circ} C \)
\( 3.1200-1500^{\circ} \mathrm{C} \)
Select the correct one from the given options.


An organic compound was used with sodium metal and extracted with
distilled water. On adding freshly
prepared \( F e S O_{4} \) solution followed by
the addition of \( F e C l_{3} \) and dil. \( H C l \)
produced a greenish blue solution. \( 0.30 \mathrm{g} \) of the organic compound after Kjeldahlisation evolved a gas \( (\boldsymbol{X}) \)
which was passed on \( 100 \mathrm{ml} \) of \( 0.1 \mathrm{M} \)
\( H_{2} S O_{4} . \) The excess of acid required 20
\( \mathrm{ml} \) of \( 0.5 \mathrm{M} \) NaOH for neutralization.
The organic compound which suitably fits into the above data is:
\( A \)
\( C H_{3}-C-N H_{2} \)
в. \( C_{6} H_{5}-\stackrel{\|}{C}-N H_{2} \)
c. \( H_{2} N-C-N H_{2} \)
D. \( H_{2} N-\stackrel{\|}{C}-N H_{2} \)


Light is a form of energy that causes sensation of warmth or coldness
A. True
B. False


What are the peculiarities of the series
\( \boldsymbol{C H}_{4}, \boldsymbol{C}_{2} \boldsymbol{H}_{6}, \boldsymbol{C}_{3} \boldsymbol{H}_{8}, \boldsymbol{C}_{4} \boldsymbol{H}_{10}-_{--}-_{-} \) etc?
Write the general formula of these compounds.


A negatively charged ion is known as
A. anion
B. cation
c. positron
D. non of these


Explain why you can hear two people talking even when they walk around a
corner.


Find \( \mathbf{S}, \) where \( \boldsymbol{S}=\frac{[\boldsymbol{n}(\boldsymbol{n}+\mathbf{1})(\boldsymbol{2} \boldsymbol{n}+\mathbf{1})]}{\mathbf{6}} \)
and \( n=20 \)
A . 2780
в. 2870
c. 1460
D. 1870


If \( \angle A \) and \( \angle B \) are acute angles such
that \( \cos A=\cos B, \) then show that \( \angle \boldsymbol{A}=\angle \boldsymbol{B} \)


Study the four statements, a-d, given
below and select the two correct ones
out of them.
(a) Definition of biological species was
given by Ernst Mayr.
(b) Photoperiod does not affect reproduction in plants.
(c) Binomial nomenclature system was
given by R.H. Whittaker.
(d) In unicellular organisms
reproduction is synonymous with growth.
\( A \cdot \) a and \( b \)
B. b and c
c. \( c \) and \( d \)
D. a and d


Which of the following is the strongest reducing agent in aqueous medium?
\( \mathbf{A} \cdot M g \)
в. \( N a \)
\( c \cdot L i \)
D. \( C a \)


Write the names of two important substances used in the preparation of
soap?


Place the elements of the following sets
in the proper location on the given Venn
diagram.
\( \boldsymbol{U}=\{\mathbf{5}, \mathbf{6}, \mathbf{7}, \mathbf{8}, \mathbf{9}, \mathbf{1 0}, \mathbf{1 1}, \mathbf{1 2}, \mathbf{1 3}\} \)
\( M=\{5,8,10,11\}, N=\{5,6,7,9,10\} \)


Assertion: Diborane has two types
of hydrogens.

Reason : By methylation only four hydrogen atoms of diborane are substituted forming \( M e_{4} B_{2} H_{2} \)
A. Both Assertion and Reason are true and Reason is correct explanation of Assertion
B. Both Assertion and Reason are true and Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true


The main waste which passes into the dialysing solution of a dialysis machine is
A. Cellulose
B. Glucose
c. water
D. urea


Equation of plane parallel to z-axis.
\( \mathbf{A} \cdot a x+b y+d=0 \)
B. \( b x+c z+d=0 \)
c. \( b y+c z+d=0 \)
D. None of these


Forests are called the lungs of the earth.
Why?


Telomerase is an enzyme which is a
A. simple protein
B. RNA
c. Ribonucleoprotein
D. Repetitive DNA


A body of mass \( m \) is moving with constant velocity v along a line parallel to x-axis. The angular momentum with respect to origin.
A. Remains constant
B. Is zero
c. Goes on decreasing
D. Goes on increasing


Yellow brittle solid (A) gives a colourless \( \operatorname{gas}(B) \) on heating in air. \( B \) on heating in the
presence of oxygen gives gas \( \mathrm{C} \). \( \mathrm{C} \) is dissolved in D to form E. E on dilution
with water gives
D. B when dissolved in alkali 'F' gives
salt G.
From the above information answer the
following questions.

Write the balanced equations for \( B \) to G.
A. \( S O_{2}+2 N a O H \rightarrow N a_{2} S O_{3}+H_{2} O \)
в. \( 2 S O_{2}+O_{2} \rightarrow 2 S O_{3} \)
\( \mathrm{c} \cdot \mathrm{SO}_{2}+\mathrm{H}_{2} \mathrm{SO}_{4} \rightarrow \mathrm{H}_{2} \mathrm{S}_{2} \mathrm{O}_{7} \)
D. \( H_{2} S_{2} O_{7}+H_{2} O \rightarrow 2 H_{2} S O_{4} \)


In the complex \( \left[\boldsymbol{F e}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right]^{3+} \)
\( \left[\boldsymbol{F e}(\boldsymbol{S C N})_{6}\right]^{3-},\left[\boldsymbol{F e}\left(\boldsymbol{C}_{2} \boldsymbol{O}_{4}\right)_{3}\right]^{3-} \) and
\( \left[\boldsymbol{F} e C l_{6}\right]^{3-}, \) more stability is shown by :
\( \mathbf{A} \cdot\left[F e\left(H_{2} O\right)_{6}\right]^{3} \)
в. \( \left[F e(S C N)_{6}\right]^{-3} \)
\( \mathbf{c} \cdot\left[F e\left(C_{2} O_{4}\right)_{3}\right]^{3-} \)
D. \( \left[F e C l_{6}\right]^{3-} \)


Newland could classify elements only
upto:
A. copper
B. chlorine
c. calcium
D. chromium


A ray of white light is incident on a
spherical Water drop whose center is
as shown below when observed from the
opposite side, the emergent light
A. will be white and will emerge without deviating
B. will be internally reflected
C. will split into different colors such that the angles of deviation will be different for different colors
D. will split into different colors such that the angles of deviation will be same for all colors


In the known interhalogen compounds, the maximum number of halogen atom
is:


Photorespiration and photosynthesis both require
A. Organic fuel
B. Chlorophyll
c. cytochromes
D. Energy


Find \( \frac{d y}{d x} \)
\( \left(x^{3}-2 y^{3}\right) d x+3 x y^{2} d y=0 \)


Prove that: \( \left|\begin{array}{ccc}\boldsymbol{b}+\boldsymbol{c} & \boldsymbol{a} & \boldsymbol{b} \\ \boldsymbol{c}+\boldsymbol{a} & \boldsymbol{c} & \boldsymbol{a} \\ \boldsymbol{a}+\boldsymbol{b} & \boldsymbol{b} & \boldsymbol{c}\end{array}\right|=(\boldsymbol{a}+\boldsymbol{b}+ \)
\( c)(a-c)^{2} \)


True multicellularity occurs only in
A. Animals
B. Eukaryotes
c. Plants and animals
D. Plants, animals and protists
E. Plants, animals and fungi


Which of the following are true for the first order reaction?
This question has multiple correct options
A \( \cdot t_{3 / 4}=2 t_{1 / 2} \)
B . \( t_{15 / 16}=4 t_{1 / 2} \)
C \( \cdot t_{15 / 16}=3 t_{3 / 4} \)
D. \( t_{7 / 8}=2 t_{3 / 4} \)


Any heavenly body having light of its own is called a
A. nebulae
B. star
c. comet
D. meteorite


On passing one faraday of electricity through a dilute solution of an acid, the
volume of hydrogen obtained at NTP
is
A. \( 22400 m L \)
B. \( 1120 m L \)
c. \( 2240 m L \)
D. \( 11200 m L \)


Sea water contains
oxygen which is utilized by plants and animals for respiration.
A . pure
B. dissolved
c. unutilized
D. free


Two angles of triangle \( A B C \) are \( 85^{\circ} \) and
\( 65^{\circ} \) while the two angles of another
triangle DEF are \( 30^{\circ} \) and \( 65^{\circ} . \) Which of the statements is correct?
A. \( \triangle \) ABC is similar to \( \triangle \) DEF
B. \( \triangle \) ABC is congurent to \( \triangle \) DEF
c. \( \triangle \) ABC is equal to \( \triangle \) DEF
D. None of these


Bubble gum contains
A. thiokol rubber
B. styrene - butadiene rubber
C. isobutylen - isoprene rubber
D. acrylonitrile - butadiene rubber


In each of the following two polynomials
find the value of \( a, \) if \( x+a \) is a factor.
\( x^{4}-a^{2} x^{2}+3 x-a \)


For the equilibrium, \( \boldsymbol{H}_{2}+\boldsymbol{I}_{2} \leftrightharpoons \mathbf{2 H} \boldsymbol{I} \)
which of the following will effect the equilibrium constant?
A. Pressure change
B. Concentration change
c. catalyst
D. Temperature change


Find the value of \( k \) so that the line \( 2 x- \)
\( k y-7=0 \) may be parallel to \( 3 x+ \)
\( 4 y+7=0 \)


Robin wants to shove rubber pipe up a plastic tap. The problem is that the pipe's diameter is smaller than that
required to secure a tight fit. So Robin switches on a half-dryer on and pointed it towards the pipe. He found that now the pipe fitted in easily. Why is this so?
A. The pipe expanded due to the hot air, and then contracted back again
B. the tap got deformed because of the hot air
c. The hot air caused adhesion between rubber and plastic.
D. none of the above


The ratio of the peak current through the capacitor and supply is known-as:
A. Resonance current
B. Dynamic resistance
c. Q-factor
D. None of the above


Starch is stored in
A. Chromoplasts
B. Amyloplasts
c. chloroplasts
D. Both B and C


Subtract the following with the help of
numberline:
\( (-2)-7 \)


Which of the following undergoes hydrolysis very easily?
A \( \cdot \mathrm{NCl}_{3} \)
в. PCls
c. \( \mathrm{AsCl}_{3} \)
D. BiCla


Which is multiplied by temperature in the equation which calculates free
energy?
A. Positive \( \Delta H \)
B. Negative \( \Delta H \)
c. Positive \( \Delta G \)
D. Negative \( \Delta G \)
E. Positive \( \Delta S \)


State the properties and uses of a Junction Diode.


Respiratory rate in new born baby is
A. Equal to an adult
B. Less than an adult
c. More than an adult
D. None of the above


When the body of the animal can be divided into identical halves in only one
plane then it is termed as
A. Asymmetry
B. Bilateral symmetry
C. Radial symmetry
D. Biradial symmetry


What type of placentation is seen in tomato and gurhal?
A. Axile
B. Free central and axile
c. Axile and marginal
D. Marginal basal


An AP consists of 50 terms of which 3 rd
term is 12 and the last term is \( 106 . \) Find
the 29 th term.


If the given planes \( a x+b y+c z+d= \)
0 and \( a x+b y+c z+d=0 \) be
mutually perpendicular, then
A \( \cdot \frac{a}{a}=\frac{b}{b}=\frac{c}{c} \)
В \( \cdot \frac{a}{a}+\frac{b}{b}+\frac{c}{c}=0 \)
c. \( a a+b b+c c+d d=0 \)
D. \( a a+b b+c c=0 \)


Lead in the atmosphere can cause
A. Brain damage
B. Breathlessness
c. Itching eyes
D. Respiratory ailments


The digestion in amoeba can be defined
as
A. Intracellular
B. Extracellular
c. secretory
D. Both A and B


Deduce the expression for the the equivalent resistance of three resistors
connected in Parallel.


A voltmeter of reading up to \( 1000 m V \) is calibrated by a potentiometer. An emf of \( 1.08 V \) is balanced across \( 5.4 m \) length
of the wire. When voltmeter reading is \( 0.9 V, \) the balancing length is \( 4.55 m \)
The error in the voltmeter reading is:
A. -0.01mV
B. 0.5 mv
c. \( 0.25 \mathrm{mv} \)
D. No error


A stone is thrown in a vertically upward
direction with a velocity of \( 5 m s^{-1} . \) If the acceleration of the stone during its motion is \( 10 m s^{-2} \) in the downward
direction, what will be the height attained by the stone and how much time will it take to reach there?


\( \boldsymbol{f}: \boldsymbol{R} \longrightarrow \boldsymbol{R} \operatorname{are} \boldsymbol{g}: \boldsymbol{R} \longrightarrow \boldsymbol{R} \) are defined
by \( f(x)=2 x+3 \) and \( g(x)=x^{2}+7 \)
then the values of \( x \) for which \( f[g(x)]= \)
25 are
\( A \cdot \pm 1 \)
в. ±2
\( c .\pm 3 \)
\( \mathrm{D} \cdot \pm 4 \)


According to figure, find the values of
angles \( x, y \) and \( z \)


What causes the global warming?
A. Burning of fossil fuels
B. Deforestation
c. Industrialization
D. All of the above


An object moves with constant acceleration. Which of the following
expression is also constant.
A \( \cdot \frac{d|\vec{v}|}{d t} \)
B. \( \mid \frac{d \vec{v}}{d t} \)
c. \( \frac{d\left(v^{2}\right)}{d t} \)
\( \frac{d\left(\frac{\vec{v}}{\sqrt{\mid 1}}\right)}{d t} \)


Explain the relationship between CFCs and ozone in the stratosphere.


Give the main postulates of Bohr's model of an atom.


In the energy band diagram of a
material shown below, the open circles and filled circles denote holes and
electrons respectively. The material is:
A. an n-type semiconductor
B. a p-type semiconductor
\( c . \) an insulator
D. a meta


The motion of the arm of a fast bowler
while bowling is an example of nonuniform circular motion.

State whether given statement is True/False?
A. True
B. False


When an electron in hydrogen atom jumps from the excited state to the ground state, how would the de-Broglie wavelength associate with the electron
change? Justify your answer


Estimate the lowering of vapour pressure due to the solute (glucose) in
a \( 1.0 \mathrm{M} \) aqueous solution at \( 100^{\circ} \mathrm{C} \)
A . 10 torr
B. 18 torr
c. 13.45 torr
D. 24 torr


Give chemical equations of the
following conversions:
(i) Diethyl ether from Ethanol
(ii) Ethanol from Diethyl ether
(iii) Ethyl acetate from Ethanol
(iv) Ethanol from Glucose


Two vectors \( \vec{A} \) and \( \vec{B} \) of magnitude 2
units and 1 unit, respectively are directed along the \( x \) -axis and \( y \) axis. Their resultant \( \vec{A}+\vec{B} \) is directed
along the line:
A. \( y-2 x=0 \)
в. \( 2 y-x=0 \)
c. \( y+x=0 \)
D. \( y-x=0 \)


toppr
Q Type your question
\( (\mathbf{E}) \)
\( A \)
\( B \)
\( c \)
\( D \)


The value of relative permittivity of air
is
A \( \cdot 8.854 \times 10^{-12} C^{2} N^{-1} m^{-2} \)
B. \( 9 \times 10^{9} C^{2} N^{-1} m^{-2} \)
c. 1
D. \( 8.854 \times 10^{12} \)


A stress \( 10^{7} \) Pa produces a strain of \( 4 x \)
\( 10^{-3} . \) The energy stored per unit volume
of the body \( \left(\operatorname{in} \mathrm{J} . \mathrm{m}^{-3}\right) \) is
\( A \cdot 2 \times 10^{3} \)
B. \( 2 \times 10^{4} \)
c. \( 2.5 \times 10^{10} \)
D. \( 0.8 \times 10^{4} \)


The self-inductance of an air core
solenoid of 100 turns is 1 m \( H \). The self-
inductance of another Solenoid of 50
turns (with the same length and crosssectional area) with a core having relative permeability 500 is
A . \( 125 \mathrm{mH} \)
B. 24 mH
c. \( 60 \mathrm{mH} \)
D. 30 mH
E. \( 45 \mathrm{mH} \)


Write a chemical equation for burning
of lanthanoids \( (\text { ln }) \) in oxygen.


The histogram shows that the level of
diabetic (in mg per dl) of 105
children. How many children have a leve
of diabetic between \( 60-80 \)
A . 20
B. 15
\( c .25 \)
D. 35


Product (s) of \( Z- \)scheme which is/are
utilise in calvin cycle, is/are:
A. only \( A T P \)
B. \( A T P, N A D P H \) and \( O_{2} \)
c. \( A T P \) and \( N A D P H \)
D. only \( O_{2} \)


A ball of mass \( 200 g \) is thrown with a
speed \( 20 m s^{-1} \). The ball strikes a bat
and rebounds along the same line at a
speed \( 40 m s^{-1} \) Variation of the
interaction force, as long as the ball remains in contact with the bat, is as
shown in Fig. Average force exerted by
the bat on the ball is:
\( .5000 N \)
\( N \)
в. 2000N
\begin{tabular}{l}
\( c .2500 N \) \\
\hline
\end{tabular}
D. \( 6000 N \)


Perform the division \( \left(a^{4}-a^{3}+a^{2}-\right. \)
\( a+1) \div\left(a^{3}-2\right) \)


If \( \cos ^{-1} \lambda+\cos ^{-1} \mu+\cos ^{-1} \gamma=3 \pi \)
then find the value of \( \lambda \mu+\mu \gamma+\gamma \lambda \)
A . 1
B . 2
\( c .3 \)
D. 4


A person drawn a card from a pack of 52 cards, replaces it \( \& \) shuffles the pack. He continues doing this till the draws a spade. The probability that he will fail exactly the first two times is
A \( \cdot \frac{1}{64} \)
в. \( \frac{9}{64} \)
c. \( \frac{36}{64} \)
D. \( \frac{60}{64} \)


Senescence and death are essential in
the function of
A. Sieve tubes
B. Companion cells
c. Both A and B
D. xylem and sclerenchyma cells


A cell of emf \( E \) and internal resistance \( r \)
is connected across a resistance \( r \). The
potential difference between the terminals of the cell must be
A. \( E \)
B. \( E / 2 \)
c. \( E / 4 \)
D. \( 3 E / 2 \)


A rectangle polygon of \( n \) sides is
constructed. No. of ways 3 vertices be
selected so that no two vertices are
consecutive is
\( \mathbf{A} \cdot^{n} C_{3}-n(n-4) \)
B . \( ^{n} C_{3}-n-n(n-4) \)
C. \( ^{n} C_{3}+n-n(n-4) \)
D. \( ^{n} C_{3}+n(n-4) \)


Action of hydrogen iodide on anisole
gives:
A. phenol and iodomethane
B. iodobenzene and methanol
c. phenol and methanol
D. iodobenzene and iodomethane


Complete the following reaction:
\( \mathrm{HC} \equiv \mathrm{CH}_{H_{2} S O_{4}}^{H g_{2}^{2+}}(\boldsymbol{A}) \stackrel{\mathcal{O}}{\rightarrow}(\boldsymbol{B}) \)


The value of \( \frac{\cos \left(90^{\circ}-A\right)}{1+\sin \left(90^{\circ}-A\right)}+ \)
\( \frac{1+\sin \left(90^{\circ}-A\right)}{\cos \left(90^{\circ}-A\right)} \) is equal to:
A \( \frac{2}{\cos A} \)
в. \( \frac{2}{\sin A} \)
c. \( \frac{2}{\sec A} \)
D. \( \frac{2}{\operatorname{cosec} A} \)


Calculate the average income of workers using direct method.
\begin{tabular}{|l|l|l|l|l|l|}
\hline Workers & 4 & 6 & 8 & 10 & 12 \\
\hline Weekly income & 300 & 500 & 700 & 800 & 900 \\
\hline
\end{tabular}
A. 10 rupees
B. 9 rupees
c. 8 rupees
D. 7 rupees


Find the degree of each algebraic
expression \( \boldsymbol{p} \boldsymbol{q}+\boldsymbol{p}^{2} \boldsymbol{q}-\boldsymbol{p}^{2} \boldsymbol{q}^{2} \)


What percent of Rs.150 is Rs.30?
A . 5\%
B. 20\%
c. 30\%
D. 45\%


Assertion: In a cavity within a
conductor, the electric field is zero.
Reason: Charges in a conductor reside
only at its surface.
A. If both assertion and reason are true but the reason is
the correct explanation of assertion.
B. If both assertion and reason are true but the reason is not the correct explanation of assertion.
C. If assertion is true but reason is false.
D. If both the assertion and reason are false.
E. If reason is true but assertion is false.


Which theory explains all the characteristics of light?


Ribosomes are the site for
A. DNA replication
B. Transcription
c. Translation
D. Translocation
E . Repression


Equal masses of oil and water are given equal amounts of heat. Then which of the following statement is true?
A. Temperature rise in oil is less than temperature rise in water.
B. Temperature rise in oil is more than temperature rise in water.
c. Temperature rise in oil is equal to the temperature rise in water
D. None of these.


What compounds are used in reaction of ester preparation?
A. An organic acid and an aldehyde
B. An alcohol and an aldehyde
c. An acid and a ketone
D. Two alcohols
E. An alcohol and an organic acid


Prove that the line \( 5 x-2 y-1=0 \) is
mid-parallel to the lines \( 5 x-2 y-9= \)
0 and \( 5 x-2 y+7=0 \)


Why are some organic compounds purified by distillation at low pressure?
A. They have low boiling points
B. They have high boiling points
c. They are highly volatile
D. They dissociate before reaching their boiling points


If the vectors \( \bar{a}=2 i+j-k \) and \( \bar{b}= \)
\( i+j+k, \) then find the angle between
its.
A \( \cdot \sin ^{-1} \frac{\sqrt{2}}{3} \)
B. \( \cos ^{-1} \frac{\sqrt{2}}{3} \)
c. \( \cos ^{-1} \frac{2}{\sqrt{3}} \)
D. \( \sin ^{-1} \frac{2}{\sqrt{3}} \)


Which group of organisms possesses a protein rich layer called pellicle?
A. Chrysophytes
B. Euglenoids
c. Dinoflagellates
D. Slime moulds
E. Protozoans


Pressures insides two soap bubbles are
1.01 and 1.02 atmospheres. Ratio
between their volumes is :-
A . 102:10
B . \( (102)^{3}:(101)^{3} \)
\( c \cdot 8: \)
D. 2:


In an electric field, if an amino acid migrate towards cathode, the pH of solution is said to be
A. Less than PI
B. More than Pl
c. Equal to PI
D.


Leaching is a process of :
A. reduction
B. concentration
C . refining
D. oxidation
E. none of these


Compute \( 100 \times P(A \mid B), \) if \( P(B)=0.5 \)
and \( P(A \cap B)=0.32 \)


Which structures are found in
mycoplasmas, spirochaetes and
rickettsias?
A. DNA
B. RNAA
c. Ribosomes
D. All of the above


Which of the following graphs represents the correct variation of
capacitive reactance \( \boldsymbol{X}_{C} \) with
frequency \( \nu ? \)
\( A \)
B.
c.
D.


\( C_{6} H_{5} N_{2} C l \stackrel{H B F_{4}}{\longrightarrow} X \frac{C u}{N a N O_{2}} Y \)
Find out \( Y \) in this reaction.
A \( \cdot C_{6} H_{5} N O_{2} \)
в. \( C_{6} H_{6} \)
c. \( C_{6} H_{5} N H_{2} \)
D. \( C_{6} H_{5} C l \)


How is human male represented?
A. \( x x \)
B. xo
c. \( x y \)
D. YY


Which of the following is an experimental observation that would support calling a compound "aromatic"?
A. A pungent odor.
B. Substitution reactions (as opposed to addition reactions) with \( B r_{2} \) and \( F e B r_{3} \)
C. A total of (2n+2) pi electrons anywhere in the molecule
D. A pale, purple color.


A body of volume \( V \) and density \( \rho \) is initially submerged in a liquid of density \( \rho^{\prime} . \) If it lifted through a height \( h \) in the liquid, its potential energy will:
A . increase by \( h V\left(\rho-\rho^{\prime}\right) g \)
B. decrease by \( h V\left(\rho-\rho^{\prime}\right) g \)
C . increase by \( h V_{\rho g / \rho} \)
D. decrease by \( h V_{\rho g / \rho} \)


Which statement BEST describes why
work is a path function
A. You finish at a different place
B. You start at a different place
C. The amount of work varies depending on which path you take to get to the destination
D. The amount of work is the same whichever path you take to get to the destination
E. Work is not a path function, it is a state function


\( A B C \) is an equilateral triangle with \( O \) as its centre, \( \vec{F}_{1}, \vec{F}_{2} \) and \( \vec{F}_{3} \) represent three forces acting along the sides \( A B, B C \) and \( A C \) respectively. If the
total torque about \( O \) is zero then the
magnitude of \( \vec{F}_{3} \) is?
A \( \frac{F_{1}+F_{2}}{2} \)
\( \mathbf{B} \cdot 2\left(F_{1}+F_{2}\right) \)
\( c \cdot F_{1}+F_{2} \)
D. \( F_{1}-F_{2} \)


In good-quality microscopes, lens combinations are used for the objective and eyepiece instead of single lenses.
A. True
B. False


If velocity of a particle at a position os \( \operatorname{given} \operatorname{as} v^{2}=2 x, \) then the acceleration
of particle is [where \( x \) is metre and \( v \) in \( \mathrm{m} / \mathrm{s}] \)
A \( \cdot 4 m / s^{2} \)
в. \( 0.5 m / s^{2} \)
\( \mathbf{c} \cdot 2 m / s^{2} \)
D. \( 1 m / s^{2} \)


The equation \( \sqrt{(x-2)^{2}+y^{2}}+ \)
\( \sqrt{(x+2)^{2}+y^{2}}=5 \) represents
A . a circle
B. ellipse
c. line segment
D. an empty set


With a neat circuit diagram, explain the working of a single stage \( C E \) amplifier. Draw the frequency response curve and discuss the results.


The reflected and refracted rays are
observed to be perpendicular to each other, when ray of light is incident at an
angle of \( 60^{\circ} \) on a transparent block. The refractive index of that block is:
\( A \cdot \frac{3}{2} \)
B. \( \frac{1}{2} \)
c. \( \frac{2}{\sqrt{3}} \)
D. \( \sqrt{3} \)


Find the equation of the line having an
inclination \( 60^{\circ} \) with the positive direction of \( X \) axis and cut off an
intercept of 4 on the positive side of \( Y \)
axis.


Evaluate the definite integral:
\( \int_{0}^{\pi / 2} \cos x d x \)


Maximum number of teeth found in
placental mammals is
A . 32
B. 54
\( c \cdot 44 \)
D. 22


Solve:
\( 2.5 x-6+7.5 x-24=0 \)


We consider the Thomson model of the
hydrogen atom in which the proton is distributed uniformly over a spherical volume of radius 0.25 angstrom. Applying the Bohr's condition in this model the ground state energy (in eV) of the electron will be close to :
A. \( -\frac{13.6}{4} \)
B . -13.6
c. \( -\frac{13.6}{2} \)
D. \( -2 \times 13.6 \)


Tick the correct answer.
The major constituent of atmosphere by percent is
A. Nitrogen
B. Oxygen
c. Carbon dioxide
D. None of these


What is half-life of a reaction? Derive
formula for finding out half-life from
first order rate reaction.


if \( 1+x^{2}=\sqrt{3} x, \) then \( , \prod_{n=1}^{24}\left(x^{n}+\frac{1}{x^{n}}\right) \)
is equal to:


Write name of any two green house
gases.


The number of cycles an oscillator completes in each second is called its
A. Frequency
B. Velocity
c. Amplitude
D. Angular velocity


Let a sequence be defined by \( a_{1}= \)
\( \mathbf{1}, \boldsymbol{a}_{\mathbf{2}}=\mathbf{1} \) and \( , \boldsymbol{a}_{\boldsymbol{n}}=\boldsymbol{a}_{\boldsymbol{n}-\mathbf{1}}+\boldsymbol{a}_{\boldsymbol{n}-\mathbf{2}} \) for al
\( \boldsymbol{n}>2 \)
find \( \frac{\boldsymbol{a}_{\boldsymbol{n}+1}}{\boldsymbol{a}_{\boldsymbol{n}}} \) for \( \boldsymbol{n}=\mathbf{1}, \boldsymbol{2}, \boldsymbol{3}, \boldsymbol{4} \)


Which of the following acid is used as a dehydrating and drying agent?
A . Acetic acid
B. Hydrochloric acid
c. Nitric acid
D. Sulphuric acid


The reaction/method that does not give an alkane is:
A. Catalytic hydrogenation of alkenes
B. Hydrolysis of alkylmagnesium bromide
c. Kolbe's electrolytic method
D. Dehydrohalogenation of an alkyl halide


When ethyl bromide is heated with
silver nitrate the product obtained is:
A. ethyl nitrite
B. ethyl nitrate
c. nitropropane
D. none of the above


The uncertainty in the position of an electron \( \left(\text { mass }=\mathbf{9 . 1} \times \mathbf{1 0}^{-\mathbf{2 8}} \mathbf{g}\right) \)
moving with a velocity of \( 3.0 \times \) \( 10^{4} c m^{-1} \) accurate up to \( 0.011 \%, \) will
be:
A . \( 1.92 \mathrm{cm} \)
B. 7.68 ст
c. \( 0.175 \mathrm{cm} \)
D. \( 3.84 \mathrm{cm} \)


toppr \( E \)
Q Type your question.
0
\( A \)
\( \begin{array}{lll}A & B & Y \\ 0 & 0 & 1\end{array} \)
010
101
в. \( A B \cdot Y \)
\( 0 \quad 0 \quad 1 \)
0.11
101
c.
\( A B Y \)
00
011
101
110
D. \( A B Y \)
00.1
011


Triangle PAB is formed by three
tangents to circle 0 and \( \angle A P B=40^{\circ} \)
then angle AOB
A . \( 45^{\circ} \)
B. \( 50^{\circ} \)
\( c \cdot 60^{\circ} \)
D. 70


Area of a square 625 sq m Then the measure of its side is
A. \( 15 \mathrm{m} \)
B. 25
\( c \cdot 20 m \)
D. 24


A boat moves with a speed of \( 5 k m / h \) relative to water in a river flowing with a speed of \( 3 k m / h \) and a width of \( 1 k m \) The minimum time taken around a
round trio is
\( \mathbf{A} \cdot 5 \) minutes
B. 20 minutes
c. 30 minutes
D. 60 minutes


Hydrogen halide with the highest boiling point is:
\( \mathbf{A} \cdot H F \)
в. \( H B r \)
c. \( H C l \)
D. \( H I \)


In a right angled triangle, if one of the
other two angles is \( 35^{\circ} \), find the
remaining angle.


Polysaccharide monomers are linked by
A. Peptide bonds
B. Glycosidic bonds
c. Hydrogen bonds
D. Phosphodiester bonds


Controlled oxidation of methanol gives?
A. methanoic acid
B. methanal
c. carbon dioxide and water
D. methane


A body starts from rest with uniform
acceleration. If its velocity after \( n \)
seconds is \( v \) then assuming straight line motion, its displacement in the last two seconds is:
A . \( v n \)
B. \( \frac{2 v(n-1)}{n} \)
c. \( \frac{2 v(n+1)}{n} \)
D. \( \frac{v}{n} \)


The highest boiling point is for:
A. \( C_{2} H_{5} O H \)
в. \( C_{2} H_{5} C l \)
\( \mathbf{c} \cdot C_{2} H_{6} \)
D. \( C H_{3} O C C H_{3} \)


Partial roasting of chalcopyrite
produces
A \( \cdot C u_{2} S \) and Feo
B. \( C u_{2} O \) and FeO
c. cus and \( F e_{2} O_{3} \)
D. \( C u_{2} O \) and \( F e_{2} O_{3} \)


Calculate the electrostatic force of
attraction between a proton and an electron in a hydrogen atom. The radius of the electron orbit is \( 0.05 \mathrm{nm} \) and
charge on the electron is \( 1.6 \times 10^{-9} C \)


The molecular mass of \( K_{2} C O_{3} \) is :
\( A \cdot 1284 \)
B. 112
\( c \cdot 116 u \)
D. 122 u
E. None of these


Insert five numbers between 4 and 8 so
that the resulting sequence is an \( \boldsymbol{A} . \boldsymbol{P} \)


\( \int\left(\frac{x^{6}-1}{x^{2}+1}\right) d x \)


Which are the scientific names of
cockroaches?
A. Periplaneta americana and Blatta indica
B. Periplaneta orientalis and Blatta americana
C. Periplaneta americana and Blatta orientalis
D. Both A and B


Match the following with correct
answers.
(a) Toucan bird I Modified teeth
(b) Siberian bird II Silver white
mane
(c) Macaque \( \quad \) II Long beak
(d) Macaque \( \quad \) IV Migrate to India during winter
A . a- -II, b- -I, c- II, d- -IV
B. a- III, b- -IV, c-1, d- -I
c. a-।, b- II, c- -II, d-IV
D. a- -V, b- |II, c- ||, d- | -


Differentiate with respect to \( x \) :
\( \log \left\{\cot \left(\frac{\pi}{4}+\frac{x}{2}\right)\right\} \)


Which of the following cannot be ferromagnetic?

This question has multiple correct options
A . alloys
B. solids
c. liquids
D. gases


A solid compound 'X' on heating gives
\( C O_{2} \) gas and a residue. The residue
mixed with water forms 'Y'. On passing
an excess of \( C O_{2} \) through 'Y' in water, a clear solution 'Z' is obtained. On boiling
Z', compound 'X' is reformed. The compound 'X' is :
A \( \cdot C a\left(H C O_{3}\right)_{2} \)
в. \( C a C O_{3} \)
c. \( N a_{2} C O_{3} \)
D. \( K_{2} C O_{3} \)


Which of the following possesses potential energy?
A. Moving vehicle on the road
B. A running athlete
c. Stone on the road
D. A stretched rubber band


Express the following angles in radian
measure:
i) \( 520^{\circ} \)
ii) \( -310^{\circ} \)
iii) \( 630^{\circ} \)
iv) \( -22^{\circ} 30^{\prime} \)


Bauxite is an oxide mineral of:
A. barium
B. boron
C. bismuth
D. aluminium


The binding energy of an electron in the ground state of an atom is equal to \( 24.6 e V . \) Find the energy required to
remove both the electrons from the
atom.
\( \mathbf{A} \cdot 79 e V \)
B. 89 eV
\( \mathbf{c} \cdot 99 e V \)
\( \mathbf{D} \cdot 69 \mathrm{eV} \)


Find the value of:
\( \left(\frac{1+i}{1-i}\right)^{40} \)


Let \( A, B, C, D \) be (not necessarily square) real matrices such that \( \boldsymbol{A}^{\boldsymbol{T}}= \)
\( \boldsymbol{B} \boldsymbol{C} \boldsymbol{D} ; \boldsymbol{B}^{T}=\boldsymbol{C} \boldsymbol{D} \boldsymbol{A} ; \boldsymbol{C}^{T}=\boldsymbol{D} \boldsymbol{A} \boldsymbol{B} \) and
\( D^{T}=A B C \)
for the matrix \( S=A B C D \), consider the
two statements.
\( \boldsymbol{S}^{3}=\boldsymbol{S} \)
\( \| S^{2}=S^{4} \)
A. II is true but not
B. I is true but not I
c. Both I and II are true
D. Both I and II are false.


Name 2 Fungi causing food poisoning?


Solve the equation \( \frac{2}{2-x}+\frac{1}{2}- \) \( \frac{4}{x(2-x)}=0 \)


Assertion
Parallax method is used for measuring
distances of nearby stars only.
Reason
With increase of distance of star,
parallactic angle becomes too small to be measured accurately.
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 major greenhouse gas is
A. сFC
в. \( C O_{2} \)
c. \( \mathrm{c} \)
D. NO


The oxidation number of phosphorus in \( \boldsymbol{B} \boldsymbol{a}\left(\boldsymbol{H}_{2} \boldsymbol{P} \boldsymbol{O}_{2}\right)_{2} \) is:
\( A \cdot+3 \)
B. +2
\( c \cdot+1 \)
D. -


A light ray passing through a thin prism suffers a deviation \( \delta \). Now the prism is
cut into two halves symmetrically in the vertical direction. The deviation for the
same ray will be
\( A \cdot \frac{\delta}{2} \)
B.
c. \( 2 \delta \)
D.


The equation of an incident wave travelling along +X direction is given by \( \boldsymbol{y}=\boldsymbol{A} \sin (\boldsymbol{2} \boldsymbol{t}-\mathbf{5} \boldsymbol{x}) . \) This wave gets
reflected at a rigid boundary. The equation of the reflected wave is
A \( . y=\operatorname{Asin}(2 t-5 x) \)
B. \( y=\operatorname{Asin}(2 t-5 x+\pi) \)
c. \( y=\operatorname{Asin}(2 t+5 x+\pi) \)
D. \( y=\operatorname{Asin}(2 t-5 x+\pi / 2) \)


For a series LCR circuit at resonance,
the statement which is not true is
A. Peak energy stored by a capacitor = peak energy stored by an inductor
B. Average power = apparent power
C. Wattless current is zero
D. Power factor is zero


The surface area of a sphere is given by the formula
A \( \cdot 4 \pi r^{2} \)
в. \( 4 \pi r \)
\( \mathrm{c} \cdot 2 \pi r^{2} \)
D. \( \frac{1}{2} \pi r^{2} \)


Enzymes increase the rate of reactions
by
A. Increasing the free energy of activation.
B. Decreasing the energy of activation.
C. Changing the equilibrium constant of the reaction.
D. Increasing the free energy change of the reaction.


Rolling friction varies with velocity. This
statement is :
A . True
B. False


Two positive point charges of unequal magnitude are placed at a certain distance apart. A samll positive test charge is placed at null point, then:
A. Charge is in equilibrium.
B. A test charge is in stable equilibrium
c. The test charge is in neutral equilibrium
D. The test charge is in unstable equilibrium


In the galvanic cell :
\( Z n / Z n^{2+}\left(C_{1}\right) \| C u^{2+}\left(C_{2}\right) / C u \)
\( \boldsymbol{E}_{c e l l}-\boldsymbol{E}_{c e l l}^{o}=+\mathbf{0 . 0 5 9 1} \boldsymbol{V} . \) The value of
\( \frac{C_{1}}{C_{2}} \) at \( 298 K \) is:
A \( \cdot 10^{-1} \)
B. \( 10^{2} \)
\( c \cdot 10^{-2} \)
D. 10


A small circular loop of conducting wire
has radius \( a \) and carries current \( I \). It is
placed in a uniform magnetic field \( \boldsymbol{B} \) perpendicular to its plane such that
when rotated slightly about its
diameter and replaced, it starts performing simple harmonic motion of time period \( T . \) If the mass of the loop is
\( m \) then:
\( ^{\mathbf{A}} \cdot_{T}=\sqrt{\frac{2 m}{I B}} \)
в. \( T=\sqrt{\frac{\pi m}{I B}} \)
\( ^{\mathrm{c}} \cdot T=\sqrt{\frac{2 \pi m}{I B}} \)
D \( \cdot T=\sqrt{\frac{\pi m}{2 I B}} \)


Given \( \frac{\pi}{2}<\alpha<\pi, \) then the expression \( \sqrt{\frac{1-\sin \alpha}{1+\sin \alpha}}+\sqrt{\frac{1+\sin \alpha}{1-\sin \alpha}}= \)
A \( \frac{1}{\cos \alpha} \)
B. \( -\frac{2}{\cos \alpha} \)
c. \( \frac{2}{\cos \alpha} \)
D. None of these


The term phylum in taxonomy was given by
A. John Roy
B. G. L. Cuvier
c. c. L. Linnaeus
D. Lamark


Find \( \int \frac{x^{4}+1}{x\left(x^{2}+1\right)^{2}} \)


In air, a charged soap bubble of radius 'r' is in equilibrium having outside and inside pressures being equal. The charge on the bubble is
\( (\epsilon= \) permittivity of free space Tesurface tension of soap solution)
A \( \cdot 4 \pi r^{2} \sqrt{\frac{2 T \epsilon_{0}}{r}} \)
В. \( 4 \pi r^{2} \sqrt{\frac{4 T \epsilon_{0}}{r}} \)
c. \( _{4 \pi r^{2}} \sqrt{\frac{6 T \epsilon_{0}}{r}} \)
D. \( 4 \pi r^{2} \sqrt{\frac{8 T \epsilon_{0}}{r}} \)


A rectangular copper coil is placed in uniform magnetic field of induction
\( 40 m T \) with its plane perpendicular to
the field. The area of the coil is
shrinking at a constant rate of \( 0.5 m^{2} s^{-1} \). The emf induced in the coil is
A . \( 10 \mathrm{mV} \)
в. \( 20 \mathrm{mV} \)
c. \( 80 m V \)
D. \( 40 \mathrm{mV} \)


A mixture of sand and sulphur is
seprated by
A. Fractional crystallization from aqueous medium
B. Dissolving in \( C S_{2} \) and filtering.
c. Sublimation
D. Fractional distillation


An isolated parallel plate capacitor is charged upto a certain potential difference. When a \( 3 m m \) thick slab is
introduced between the plates then in order to maintain the same potential difference, the distance between the
plates is increased by \( 2.4 m m \). Find the dielectric constant of the slab. (Assume
charge remains constant)
A. 5
в. 10
\( c \cdot 2.5 \)
D. 7.5