A charged oil drop is suspended in a
uniform field of \( 3 \times 10^{4} \mathrm{v} / \mathrm{m} \) so that it
neither falls nor rises. The charge on the drop will (Take the mass of the charge \( = \)
\( 9.9 \times 10^{-15} \mathrm{kg} \) and \( \mathrm{g}=10 \mathrm{m} / \mathrm{s}^{2} \)
A . \( 1.25 \times 10^{10} C \)
В. \( 2.5 \times 10^{10} C \)
c. \( 3.3 \times 10^{-18} \mathrm{C} \)
D. none


From the following identify the correct
ones.
This question has multiple correct options
A \( \cdot F e_{2} O_{3}+3 C O \rightarrow 2 F e+3 C O_{2} \)
в. \( Z n O+C \rightarrow Z n+C O \)
\( \mathbf{c} \cdot C a_{3}\left(P O_{4}\right)_{2}+C \rightarrow P \)
\( \mathbf{D} \cdot P b O+C \rightarrow P b \)


\( p H \) of saturated solution of silver salt of
monobasic acid \( H A \) is found ton be 9
Find the \( K_{s p} \) of sparingly soluble salt
\( A g A(s) \)
Given \( : \boldsymbol{K}_{\boldsymbol{a}}(\boldsymbol{H} \boldsymbol{A})=\mathbf{1 0}^{\mathbf{1 0}} \)
A \( \cdot 1.1 \times 10^{-9} \)
В. \( 1.1 \times 10^{-10} \)
\( c \cdot 10^{-12} \)
D. None of these


If six identical cells each having an emf
of \( 6 V \) are connected in parallel, the emf of the combination is
A . \( 1 v \)
B. 36V
\( c \cdot 1 / 6 v \)
D. \( 6 v \)


Drawing necessary ray diagram, prove with the help of prism that white light of Sun is mixture of different colours.


Let \( f(x)=\frac{\sqrt{x-2 \sqrt{x-1}}}{\sqrt{x-1}-1} \cdot x, \) then
This question has multiple correct options
B . \( f^{\prime}(3 / 2)=-1 \)
c. domain of \( f(x) \) is \( x \geq 1 \)
D. none of these


Which of the following is useful in maintaining the reproductive health?
A. Sex education
B. Birth control devices
c. Medical facilities
D. All of the above


Two wires if same material and area if
cross section but with length in the
ratio 5: 3 are streached by the same
force. The ratio of work done in two
cases is
A . 5: 8
B. 8: 5
\( c .5: 3 \)
D. 3: 5


A ball is dropped from a height \( h \) on a
floor of coefficient of restitution \( e \). The
total distance covered by the ball just before the second hit is
\( \mathbf{A} \cdot h\left(1-2 e^{2}\right) \)
B. \( h\left(1+2 e^{2}\right) \)
c. \( h\left(1-e^{2}\right) \)
\( D \cdot h e^{2} \)


Leaving the 3 middle stars apart, which shape is formed by the remaining 4 bright starts of the Orion?
A . Circle
B. Irregular circle
c. Triangle
D. Quadrilateral


A sphere of radius \( 3 \mathrm{cms} \) is dropped into a cylindrical vessel of radius \( 4 \mathrm{cms} \). If the sphere is submerged completely, then the height (in \( \mathrm{cm} \) ) to which the water rises, is
A . 2.35
B. 2.30
c. 2.25
D. 2.15


Which of the following is not true for a
species?
A. Variations occur among members of a species
B. Gene flow does not occur between the populations of a species
C. Members of a species can interbreed
D. None of the above


Select the correct statements.
This question has multiple correct options
A. Vapour may be condensed to liquid by the application of pressure.
B. To liquefy a gas one must lower the temperature below \( T_{c} \) and apply pressure.
C \( . \) At \( T_{c} \) there is no distinction between liquid and vapour
states
D. At the \( T_{c} \), density of liquid is very high as compared to its gaseous state.


A racing car has a uniform acceleration
of \( 4 m s^{-2} \) will it cover in \( 10 s \) after
start?


Explain why nitrogen is much less reactive than phosphorous?


Ecosystem of a pond is
A. Lotic
B. Lentic
c. Benthic
D. Xeric


If \( \Delta A B C \) is an equilateral triangle of side
\( a \) and \( \mathrm{D} \) is a point on \( B C \) such that \( B D=\frac{1}{3} B C \) then the prove that \( A D= \)
\( \frac{\sqrt{7} a}{3} \)


Growth of leaf primordia is
A. First apical then marginal
B. Only apical
c. only marginal
D. Lateral


The original colour of a salt is black. When it is heated its colour is changed from black to red. The salt may be:
A. zinc oxide
B. mercuric oxide
c. lead oxide
D. red lead


Find the mean deviation about the
mean for data.
\( \boldsymbol{x}_{i} \quad 5 \quad 10 \) 20 15
5 6 \( f_{i} \quad \) 7 \( \quad 4 \)


A mass of 1 kg carrying a charge of \( 2 C \)
is accelerated through a potential of \( 1 \mathrm{V} \) The velocity acquired by it is?
A \( \cdot \sqrt{2} m s^{-1} \)
B . \( 2 m s^{-1} \)
c. \( \frac{1}{\sqrt{2}} m s^{-1} \)
D. \( \frac{1}{2} m s^{-1} \)


Gravitational force between two point masses \( \mathrm{m} \) and \( \mathrm{M} \) separated by a distance \( r \) is \( F . \) Now if a point mass \( 3 \mathrm{m} \) is placed next to \( \mathrm{m} \), what will be the (a) force on M due to \( m,(b) \) total force on M?
A. \( F=4 F \)
B. \( F=5 F \).
\( \mathbf{c} \cdot F=6 F \)
\( \mathbf{D} \cdot F=7 F \)


The volume of a gas at \( 27^{\circ} \mathrm{C} \) and
2 atmospheric pressure is 2 litres. If the pressure is doubled and absolute
temperature is made half, the new volume of gas is
\( A \cdot 50 m \)
B. 500 m1
c. \( 1000 \mathrm{ml} \)
D. 2000 ml


Magnetic flux during time interval \( \tau \) varies through a stationary loop of
resistance \( \boldsymbol{R}, \) as \( \boldsymbol{\phi}_{\boldsymbol{B}}=\boldsymbol{a} \boldsymbol{t}(\boldsymbol{\tau}-\boldsymbol{t}) . \) Find
the amount of heat generated during
that time. Neglect the inductance of the
loop.
\( ^{\text {A }} \cdot \frac{a^{2} \tau^{3}}{R} \)
в. \( \frac{a^{2} \tau^{2}}{2 R} \)
c. \( \frac{a^{2} \tau^{3}}{3 R} \)
D. \( \frac{a^{2} \tau^{3}}{4 R} \)


What happens when concentrated
\( H N O_{3} \) comes in contact with skin?
Why?


The mixed anhydride of nitrogen is:
A. \( N_{2} O_{2}(2 N O) \)
в. \( N_{2} O_{4}\left(2 N O_{2}\right) \)
\( \mathrm{c} \cdot \mathrm{N}_{2} \mathrm{O}_{5} \)
D. \( N_{2} O_{2} \)


Choose the correct statement from the
following:
This question has multiple correct options
\( \mathbf{A} \cdot 50^{\circ} \mathrm{C} \) is equal to \( 122^{\circ} \mathrm{F} \)
B. A clinical thermometer cannot be sterilized using boiling water.
C. Unequal expansion causes cracks in the walls of the buildings.
D. Graphite is a bad conductor of heat.


The dimensions of the ratio \( \frac{\text { force } \times \text { distance }}{\text { power }} \) are
\( \begin{array}{lll}\mathbf{A} \cdot M & L^{o} & T^{o}\end{array} \)
\( \begin{array}{lll}\text { В. } M^{o} & L & T^{o}\end{array} \)
\( \begin{array}{lll}\mathrm{c} \cdot M^{2} & L & T^{0}\end{array} \)
\( \begin{array}{lll}\text { D. } M^{o} & L^{o} & T\end{array} \)


Sulfur dioxide can be anhydride for which of the following?
A. Sulfurous acid
B. Hyposulfurous acid
c. Sulfuric acid
D. Hydrosulfuric acid


A function \( f(x) \) defined as \( f(x)= \) \( \left\{\begin{array}{ll}\sin x, & x \text { is rational } \\ \cos x, & x \text { is irrational }\end{array} \) is continuous \right.
at
A \( \cdot x=n \pi+\frac{\pi}{4}, n \in I \)
В \( \cdot x=n \pi+\frac{\pi}{8}, n \in I \)
c. \( x=n \pi+\frac{\pi}{6}, n \in I \)
D・ \( x=n \pi+\frac{\pi}{3}, n \in I \)


Draw a labelled circuit diagram of a
potentiometer to measure internal resistance of a cell. Write the working formula. (Derivation not required)


Let \( \boldsymbol{S}=\{1,2,3, \ldots . ., 9\} . \) For \( \boldsymbol{k}= \)
\( \mathbf{1}, \mathbf{2}, \dots . ., \mathbf{5}, \) let \( N_{k} \) be the number of
subsets of \( S \), each containing five
elements out of which exactly \( k \) are odd
Then \( \boldsymbol{N}_{\mathbf{1}}+\boldsymbol{N}_{\mathbf{2}}+\boldsymbol{N}_{\mathbf{3}}+\boldsymbol{N}_{\mathbf{4}}+\boldsymbol{N}_{\mathbf{5}}= \)
A . 210
в. 252
c. 125
D. 126


Express 1.4191919 ..... in the form of \( \frac{p}{q} \)
where \( p \) and \( q \) are integer and \( q \neq 0 \)


Find the mean deviation about mean for
the following data.
\( \begin{array}{llll}\text { Class } & \mathbf{1 0}- & \mathbf{2 0}- & \mathbf{3 0}- \\ \text { interval } & \mathbf{1 9} & \mathbf{2 9} & \mathbf{3 9}\end{array} \)
Frequency 6


Arrange the following compounds in the decreasing order of acidic character.
I. Butane II. But-1-ene III. But-1-yne IV.Butan-1-ol
\( A \cdot(|I\rangle(\mid I)>(\| I)>(I V) \)
B. \( (\mid V)>(||)>(|||\rangle>(\mid) \)
\( c \cdot(\mid V)>(\| \mid)>(||>||) \)
\( D \cdot(|D>(\| \mid)>(\mid D)(\mid V) \)


The tube arising from the notch of the
kidney on the median side and connecting behind with the urinary bladder is


provides good heat and sound insulation.
A. Propylene
B. Styrofoam
c. Polythene
D. Acrylic


For a wave displacement amplitude is
\( 10^{-8} m, \) density for air \( 1.3 k g . m^{-3} \)
velocity in air \( 340 m^{-1} \) and frequency is
\( 2000 H z . \) The average intensity of wave
is
A \( \cdot 5.3 \times 10^{-4} \mathrm{Wm}^{-2} \)
B. \( 5.3 \times 10^{-5} \mathrm{Wm}^{-2} \)
c. \( 5.3 \times 10^{-8} \mathrm{Wm}^{-2} \)
D. \( 5.3 \times 10^{-6} \mathrm{Wm}^{-2} \)


Assertion
Gold sol is hydrophobic and multimolecular.
Reason
Gold sol is prepared by Bredig's arc method.
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 diseases caused by using mosquito repellents are
A. Blood related diseases
B. Fits
c. Bronchial diseases
D. Kidney related diseases


Length of female urethra is
\( A \cdot 15 \mathrm{cm} \)
B. 10 \( \mathrm{cm} \)
\( c \cdot 4 \mathrm{cm} \)
D. \( 2 \mathrm{cm} \)


The species though insignificant in number determines the existence of
many other species in a given
ecosystem
A. Extinct species
B. Endemic species
c. keystone species
D. sacred secies


In the figure, current through the \( 3 \Omega \)
resistor is 0.8 ampere, the potential
drop through \( 4 \Omega \) resistor is
A \( .9 .6 ~ V \)
B . \( 2.6 V \)
c. \( 4.8 V \)
D. \( 1.2 V \)


The resistivity of a potentiometer wire
is \( \rho \) and the area of cross section of the
wire is \( A . \) If the current flowing in the circuit is \( I \), then potential gradient will
be
A. \( I A \)
в. \( I A / \rho \)
c. \( I \rho / A \)
D. IA


What are the advantages of wind
energy?


If charges \( \boldsymbol{q} / 2 \) and \( 2 q \) are placed at the centre of face and at the corner of a
cube, then the total flux through the
cube will be:
A \( \cdot \frac{q}{2 \varepsilon_{0}} \)
в. \( \frac{q}{\varepsilon_{0}} \)
c. \( \frac{q}{6 \varepsilon_{0}} \)
D. \( \frac{q}{8 \varepsilon_{0}} \)


The probability distribution of a random variable is given below:
\[
\begin{array}{llll}
\boldsymbol{X}=\boldsymbol{x} & 0 & 1 & 2 \\
P(X= & 0 & K & 2 K
\end{array}
\]
\( 2 k \quad 3 K \)
\[
x)
\]
\[
\text { Then } \boldsymbol{P}(\mathbf{0}<\boldsymbol{X}<\mathbf{5})=
\]
A \( \cdot \frac{1}{10} \)
B. \( \frac{3}{10} \)
\( c \cdot \frac{8}{10} \)
D. \( \frac{7}{10} \)


If \( \hat{i}, \hat{j} \) and \( \hat{k} \) represents unit vectors
along the \( x, y \) and \( z- \) axes respectively
then find the value of angle \( \theta \) between the vectors \( \hat{i}+\hat{j}+\hat{k} \) and \( \hat{i}+\hat{j} \)


Solve for \( \boldsymbol{x} \)
\( \left|\begin{array}{ccc}1-x & 2 & 3 \\ 0 & x & 0 \\ 0 & 0 & x\end{array}\right|=0 \)
\( \mathbf{A} \cdot 1,0,0 \)
B. 1,1,0
c. 1,1,1
D. 0,0,0


Calculate the equilibrium concentration ratio of \( \boldsymbol{C} \) to \( \boldsymbol{A} \) if
equimolar ratio of \( A \) and \( B \) were
allowed to come to equilibrium at \( 300 K \)
\( \boldsymbol{A}(\boldsymbol{g})+\boldsymbol{B}(\boldsymbol{g}) \leftrightharpoons \boldsymbol{C}(\boldsymbol{g})+ \)
\( \boldsymbol{D}(\boldsymbol{g}) ; \quad \boldsymbol{\Delta} \boldsymbol{G}^{o}=-\boldsymbol{8} \boldsymbol{3} \boldsymbol{0} \boldsymbol{c a l} \)


\( \boldsymbol{E}_{\boldsymbol{n}}=-\frac{\mathbf{3 1 3 . 6}}{\boldsymbol{n}^{2}}, \) if the value of \( \boldsymbol{E}_{\boldsymbol{i}}= \)
-34.84 to which value ' \( n \) ' corresponds:
A . 2
B. 4
c. 1
D. 3


A radio capacitor of variable capacitance is made of \( n \) parallel plates each of area
\( A \) and separated from each other by a
distance \( d \). The alternate plates are connected together. The capacitance of
the combination is:
A \( \cdot \frac{n A \epsilon_{0}}{d} \)
в. \( \frac{(n-1) A \epsilon_{0}}{d} \)
c. \( \frac{(2 n-1) A \epsilon_{0}}{d} \)
D. \( \frac{(n-2) A \epsilon_{0}}{d} \)


The vector form of the equation of the
line passing through points (3,4,7) and (5,1,6) is
\( \mathbf{A} \cdot \vec{r}=(3 \hat{i}+4 \hat{j}-7 \hat{k})+\lambda(2 \hat{i}-3 \hat{j}+13 \hat{k}) \)
B \( \cdot \vec{r}=(3 \hat{i}+4 \hat{j}-7 \hat{k})+\lambda(8 \hat{i}+5 \hat{j}-\hat{k}) \)
C \( . \vec{r}=(3 \hat{i}+4 \hat{j}+7 \hat{k})+\lambda(2 \hat{i}-3 \hat{j}-\hat{k}) \)
D \( \cdot \vec{r}=(3 \hat{i}+4 \hat{j}-7 \hat{k})+\lambda(2 \hat{i}-3 \hat{j}-13 \hat{k}) \)


Specific heat of water is:
A. very low
B. medium
c. sometimes high and sometimes low
D. none of the above


Lead is considered as a major
pollutant.
A. water
B. air
c. soil
D. none of above


Match List I with List II and select the
correct option.
List 1
A. Adrenalin
1. Myxoedema
B.
2. Accelerates heart Hyperparathyroidism beat
C. Oxytocin
3. Salt-water balance
D. Hypothyroidism
4. Childbirth
E. Aldosterone
5. Demineralisation
A. A- 2, B- 5, C- 4, D-1, E-3
B. A- 3, B-4, C- 5, D-3, E-2
C. \( A-5, B-3, C-2, D-4, E-1 \)
D. \( A-2, B-3, C-4, D-5, E-1 \)
E . A- 5, B- 3, C- 4, D- 2, E-1


Derive an expression for intensity of electric field at a point broadside
position or an equatorial line of an electric dipole.


How are Archea different from Bacteria
A. can form Methane
B. have different rRNA sequences
C. do not have peptidoglycan in their cell walls
D. all of these are correct


\( \sum_{r=1}^{50}\left[\frac{1}{49+r}-\frac{1}{2 r(2 r-1)}\right]= \)
A \( \cdot \frac{1}{50} \)
в. \( \frac{1}{99} \)
c. \( \frac{1}{100} \)
D. \( \frac{1}{101} \)


If \( 2 \sin \theta+1=0 \) and \( \sqrt{3} \tan \theta=1 \) then
find general value of \( \boldsymbol{\theta} \) is
\( ^{\mathrm{A}} \cdot_{n \pi \pm} \frac{\pi}{6} \)
в. \( \quad n \pi+(-1)^{n} \cdot \frac{7 \pi}{6} \)
c. \( _{2 n \pi+\frac{7 \pi}{6}} \)
D. \( 2 n \pi+\frac{11 \pi}{6} \)


Why are the energies different? Mass of \( _{20}^{42} C a=40.962278 u, \) mass of
proton \( =1.007825 u \)


What should be the charge on a sphere of radius \( 2 \mathrm{cm} \) so that when it is
brought in contact with another sphere of radius \( 5 \mathrm{cm} \) carrying a charge of \( 10 \mu C, \) there is no transfer of charge
between the spheres?


Electron microscope, the biggest innovation in microscopy was built on
principle of
A. wave nature of electrons
B. total internal reflection of light
c. thin film optical interference
D. light amplification by stimulated emission of radiation


\( \triangle A B C \) is congruent to \( \triangle F E D \)
\( A \). True
3. Falss


If \( \sin \alpha=\frac{1}{2}, \) then find value of \( 3 \sin \alpha- \)
\( 4 \sin ^{3} \alpha \)


When \( H_{2} O_{2} \) is added to ice cold
solution of acidified potassium
dichromate in ether and the contents
are shaken and allowed to stand?
A. A blue colour is obtained in ether due to formation of \( C r_{2}\left(S O_{4}\right)_{3} \)
B. A blue colour is obtained in ether due to formation of \( C r O_{5} \)
c. A blue colour is obtained in ether due to formation of \( C r O_{3} \)
D. Chromyl chloride is formed.


What are the products of the following reaction? \( \boldsymbol{C a} \boldsymbol{C O}_{3} \stackrel{\boldsymbol{\Delta}}{\longrightarrow} \)
A. \( C O+C O_{2} \)
в. \( C a O+C O \)
c. \( C O_{2}+C a_{2} O \)
D. \( C O_{2}+C a O \)


A hydrocarbon \( ^{\prime} \boldsymbol{A}^{\prime}\left(\boldsymbol{C}_{3} \boldsymbol{H}_{8}\right) \) on treatment
with chlorine in presence of sunlight
yielded compounds ' \( B^{\prime} \) as major
product. Reaction of \( ^{\prime} B^{\prime} \) with aqueous
KOH gave \( ^{\prime} C^{\prime} \) which on treatment with
concentrated \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) yielded \( ^{\prime} \boldsymbol{D}^{\prime} \)
Hydrogenation of \( ^{\prime} D^{\prime} \) gave back \( ^{\prime} A^{\prime} \). The sequence of reactions involved in above conversion is:
A. Substitution, Substitution, Addition, Dehydration
B. Substitution, Substitution, Dehydration, Addition
c. substitution, Dehydration, Addition, Addition
D. Addition, Substitution, Dehydration, Substitution


A polysaccharide is a polymer of
A. monosaccharides
B. disaccharides
c. both A and B
D. None of these


The wavelength \( \lambda_{e} \) of an electron and \( \lambda_{p} \) of a photon of same energy \( \boldsymbol{E} \) are
related by
\( A \cdot \lambda_{p} \propto \lambda_{e}^{2} \)
B . \( \lambda_{p} \propto \lambda_{e} \)
\( \mathbf{c} \cdot \lambda_{p} \propto \sqrt{\lambda_{e}} \)
D. \( \lambda_{p} \propto \frac{1}{\sqrt{\lambda_{e}}} \)


Can a body moving with a uniform
velocity be in equilibrium?
A. Yes, since the net force acting on it is zero.
B. No, as the acceleration of the body is zero.
C. No, as the velocity of the body is constant.
D. None of the above.


The treatment of benzene with
isobutene in the presence of sulphuric acid gives:
A. isobutyl benzene
B. t-butyl benzene
c. n-butyl benzene
D. no reaction


Calculate \( 10^{t h} \) term of the infinite series
\( 4,6,8, \dots \infty \)
A . 18
B. 20
c. 22
D. 26


An insurance company insured 2000 scooters and 3000 motor cycles. The
probability of an accident involving a scooter is 0.01 and that of a motor cycle
is \( 0.02 . \) An insured vehicle met with an
accident. Find the probability that the accidented vehicle was a motor cycle.


Identify which of the following system exhibit simple harmonic motion?
I. A simple pendulum with small deflection.
II. A mass attached to a spring
III. A ball bouncing up and down, in the absence of friction
A. I only
B. II only
c. III only
D. I and II only
E . I, II, and III


The atomic number of an element \( X \) is
34. Then it is present in period
A. 4th period and IVA group
B. 4 th period and VIA group
c. 4 th period and VIIA group
D. 5th period and VIA group


Primary treatment of sewage is also known as
A. Physical treatment
B. Chemical treatment
c. Biological treatment
D. All of the above


Which of the following models best describes the bonding within a layer of the graphite structure?
A. metallic bonding
B. ionic bonding
c. non-metallic covalent bonding
D. van der Waals forces


Two lenses have powers \( +D \) and \( -2 D \)
respectively. The power of combination is:
A . - D
\( B .+D \)
\( c \cdot-20 \)
\( D \cdot+2 D \)


expand:
\( 9(x-y)^{2}+6(y-x) \)


Graphite is used as a lubricant in machines because it has a very high melting point and also it :
A. is crystalline
B. has layer structure
c. is a giant molecule
D. is a liquid at room temperature


Pipe M and N running together can fill a cistern in 6 minutes. If \( \mathrm{M} \) takes 5
minutes less than \( \mathrm{N} \) to fill the cistern,
then the time in which \( \mathrm{N} \) alone can fill
the cistern will be
A . 15 min
B. 20 min
\( c .25 \) min
D. 10 min


What is the oxidation state of coloured
ion in \( \left[\boldsymbol{C u}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\right]^{2+} ? \)


Name the family in which nodulated
roots occur


Mark the statements which is true for
Braille system:
A. It makes up the letters of alphabets,punctuation marks
B. It has 64 dot patterns or characters
C. Dots are arranged in cells of 3 vertical rows of 2 dots each
D. All are true


For a point \( \boldsymbol{P} \) in the plane, let \( \boldsymbol{d}_{1}(\mathrm{P}) \) and
\( \boldsymbol{d}_{2} \)
(P) be the distances of the point
from the lines \( x-y=0 \) and \( x+y=0 \)
respectively. The area of the region consisting of all points P lying in the first quadrant of the plane and
satisfying \( 2 \leq d_{1}(P)+d_{2}(P) \leq 4, \) is
A .4
B. 6
c. 10
D. 16


Ruthen-ford used which of the following elements in his scattering experiment
A. Gold
B. Silver
c. Alluminum
D. Antimony


Standard molar heat of formation of
ethane \( C O_{2} \) and liquid water are -21.1
-94.1 and -68.3 kilo calorie. The value
of standard molar heat of combustion of
ethane will be:
\( \mathbf{A} \cdot-372 \) kcal
B . -272 kcal
c. -172 kcal
D. -472 kcal


Assertion
\( \boldsymbol{K}_{\boldsymbol{p}}=\boldsymbol{K}_{c} \) for all reactions. BECAUSE
Reason
\( \boldsymbol{K}_{\boldsymbol{p}} \) and \( \boldsymbol{K}_{\boldsymbol{c}} \) are interrelated by the
equation \( \boldsymbol{K}_{\boldsymbol{p}}=\boldsymbol{K}_{c}(\boldsymbol{R} \boldsymbol{T})^{\boldsymbol{\Delta} \boldsymbol{n}} \)
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


Evaluate \( \tan \left[\frac{1}{2} \cos ^{-1}\left(\frac{3}{\sqrt{11}}\right)\right] \)


Not all kinds of vibration in the material
bodies produce sensation of sound. True or false
A. True
B. False


Which is wrong about Krebs cycle?
A. It occurs in mitochondria
B. It starts with 6 carbon compound.
c. It is also called citric acid cycle
D. Glycolysis is linked to it through malic acid


Which of the following are equations for
the plane passing through the points
\( P(1,1,-1), Q(3,0,2) \) and \( R(-2,1,0) ? \)
A \( \cdot(2 \hat{i}-3 \hat{j}+3 \hat{k}) \cdot((x+2) \hat{i}+(y-1) \hat{j}+z \hat{k})=0 \)
B . \( x=3-t, y=-11 t, z=2-3 t \)
\( \mathbf{c} \cdot(x+2)+11(y-1)=3 x \)
D. \( (2 \hat{i}-\hat{j}+3 \hat{k}) \times(-3 \hat{i}+\hat{k}) \cdot((x+2) \hat{i}+(y-1) \hat{j}+z \hat{k})= \)
0


If number of electrons in an atom is 8
and number of protons is also 8 , then give the atomic number of atom and the
charge on the atom.
A. (i) Atomic number \( =8, \) (ii) Charge \( =0 \)
B. (i) Atomic number \( =4, \) (ii) Charge \( =0 \)
c. (i) Atomic number \( =8, \) (ii) Charge \( =+1 \)
D. (i) Atomic number \( =4, \) (ii) Charge \( =+1 \)


develops into embryo
A. Micropyle
B. Chalaza
c. zygote
D. Pollen grain


A charged particle of mass \( m \) and charge \( q \) is accelerated through a potential difference of \( V \) volt. It enters a
region of uniform magnetic field which is directed perpendicular to the direction of motion of the particle. The particle will move on a circular path of
radius given by
A \( \cdot \frac{V m}{q B^{2}} \)
B. \( \frac{2 V m}{q B^{2}} \)
c. \( \sqrt{\frac{2 V m}{q}} \cdot\left(\frac{1}{B}\right) \)
D. \( \sqrt{\frac{V m}{q}} \cdot\left(\frac{1}{B}\right) \)


prove the inequalities \( (n !)^{2} \leq \)
\( \boldsymbol{n}^{n}(\boldsymbol{n} !)<(2 \boldsymbol{n}) ! \) for all positive integers
\( \mathbf{n} \)


The equation \( x^{2}+9=2 y^{2} \) is an
example of which of the following
curves?
A. hyperbola
B. circle
c. ellipse
D. parabola
E. line


Locate the complex numbers \( z=x+ \)
iy such that
\( |z-i|=1, \arg \frac{z}{z+i}=\frac{\pi}{2} \)


\( \boldsymbol{C O}_{2}+\boldsymbol{N} \boldsymbol{H}_{3}+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \boldsymbol{X} \)
\( \boldsymbol{X}+\boldsymbol{N} \boldsymbol{a} \boldsymbol{C l} \rightarrow \boldsymbol{Y}+\boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{C l} \)
'Y' in the above reaction is:
\( \mathbf{A} \cdot N a_{2} C O_{3} \)
в. \( \left(N H_{4}\right)_{2} C O_{3} \)
c. \( N H_{4} H C O_{3} \)
D. \( N a H C O_{3} \)


Complete the following reaction
\( \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{O} \boldsymbol{H}+\boldsymbol{P} \boldsymbol{C l}_{5} \rightarrow \)


Aryl halides are less reactive towards
nucleophilic substitution reaction as compared to alkyl halides due to:
A. the formation of less stable carbonium ion
B. resonance stabilisation
c. larger carbon-halogen bond
D. inductive effect


Find the common difference \( d \) and write
three more terms.2,4,8,16,


\( 10 m l \) of hydrocarbon requires \( 55 m l \) of oxygen for complete combustion
producing \( 40 m l \) of \( C O_{2} . \) The formula of the hydrocarbon is :
A \( \cdot C_{4} H_{6} \)
в. \( C_{5} H_{10} \)
\( \mathbf{c} \cdot C_{4} H_{8} \)
D. \( C_{4} H_{10} \)


Which of the following is the land tortoise?
A. Trionyx
B. Testudo
c. chelone
D. Kachuga


Choose the correct answer from the
alternatives given. Active transport from outside to inside
of molecules across a membrane
requires:
A. cyclic AMP
B. acetyl chlorine
c. Атр
D. lecithin


produced by a sleep researcher studying the number of dreams people
recall when asked to record their
dreams for one week. Group \( \boldsymbol{X} \)
consisted of 100 people who observed
early bedtimes, and Group \( Y \) consisted
of 100 people who observed later
bedtimes. If a person is chosen at
random from those who recalled at least
1 dream, what is the probability that the
person belonged to Group \( Y ? \)
Dreams Recalled during One Week \begin{tabular}{|l|c|c|c|c|}
\hline & None & 1 to 4 & 5 or more & Total \\
\hline \hline Group X & 15 & 28 & 57 & 100 \\
\hline Group Y & 21 & 11 & 68 & 100 \\
\hline Total & 36 & 39 & 125 & 200 \\
\hline
\end{tabular}
\( A \)
\( \frac{68}{100} \)
B. \( \frac{79}{100} \)
\( c \)
\( \frac{79}{164} \)
D. \( \frac{16}{\text { ? }} \)


Dispersion of white light into its constituent colours occurs during:
A. Reflection at a plane mirror
B. Reflection at a concave mirror
c. Internal reflection inside a spherical drop of water
D. Refraction at the boundary of a transparent medium


A line through (-5,2) and (1,-4) is perpendicular to the line through \( (x,-7) \) and (8,7) Find the \( x \)
A . -4
B. -5
\( c .-6 \)
D. \( \frac{-19}{3} \)
E. none of these


\( \Delta G^{0} \) for the reaction \( 2 N O(g)+ \)
\( O_{2}(g) \rightarrow N_{2} O_{4}(g) \) at \( 298 \mathrm{k} \) and 1 atm
pressure, will be [given that the enthalpy of formation of \( \mathrm{NO}(\mathrm{g}) \) is
\( 90.5 k J m o l^{-1} \)
The enthalpy of formation of \( N_{2} O_{4}(g) \) is
\( 9.7 k J m o l^{-1} \)
The standard entropy of \( \mathrm{NO}(\mathrm{g}) \) is \( 210 J k^{-1}, O_{2}(g) \) is
\( 205 J k^{-1} m o l^{-1}, N_{2} O_{4}(g) \) is \( 304 J K^{-1} c \)
\( \exists: \)
B. \( -75.64 k J \)
c. \( -64.24 k J \)
D . \( -83.27 k J \)


Number of electrons transferred from
one atom to another during bond formation in SrS (Strontium Sulphide) is :
\( A \)
B. 2
\( c \cdot 3 \)
\( D \)


What are respiratory substrates?


The body of Tongue Worm Balanoglossus is differentiated into
A. Head, trunk and tail
B. Trunk and tail
c. Proboscis, collar and trunk
D. Proboscis and collar


Fill in the blanks with appropriate
words.
Ammonia is converted into urea in..........


Stability order of group IIIA (boron family) element is:
A \( \cdot G a^{+}<I n^{+}<T l^{+} \)
в. \( G a^{3+}>G a^{+} \)
c. both \( (A) \) and \( (B) \)
D. none of the above


An equilateral triangular loop is kept
near to a current carrying long wire as
shown in figure. Under the action of magnetic force alone, the loop
A. must move along positive or negative X-axis
B. must move in XY plane and not along X- of Y- axis
c. does not move
D. moves but which way we cannot predict


There are three closed containers in
which equal amount of gas are filled.
\( (\mathbf{I}) \)
\( (\mathbf{I I}) \)


A shopkeeper marks his goods \( 20 \% \) above cost price and allows a discount
of \( 15 \% . \) What percent does he gain or lose ?


Macula densa is found in
A. Internal ear
B. Kidney
c. Liver
D. spleen


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


The given figure represents a
multiplication operation, where each alphabet represents a different number,
then what is the value of \( A \)
\( A \cdot O \)
B. 3
\( c \cdot 2 \)
D. 4


When a fluid is in streamline flow, the
reason of viscous force acting between
its two layers is:
A. transport of energy from one layer to another
B. transport of linear momentum from one layer to another
c. same velocity of molecules
D. the variable density along the length of the tube


In a coil of resistance \( 100 \Omega \), a current is
induced by changing the magnetic flux through it as shown in the figure. The
magnitude of change in flux through
the coil is :
A. \( 275 \mathrm{Wb} \)
в. \( 200 \mathrm{Wb} \)
\( c \cdot 225 W b \)
D. \( 250 \mathrm{Wb} \)


In the nuclear reaction, \( 92 U^{238} \rightarrow 82 \)
\( P b^{208}, \) the number of \( \alpha \) and \( \beta \) particles
emitted are:
\( \mathbf{A} \cdot 7 \alpha, 5 \beta \)
B. \( 6 \alpha, 4 \beta \)
c. \( 4 \alpha, 3 \beta \)
D. \( 8 \alpha, 6 \beta \)


\( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{e} \) is:
A. pyramidal
B. trigonal planar
c. linear
D. bent (v-shaped)


Electrically charged drops of mercury fall from an altitude \( h \) into a spherical metal vessel of radius R. There is a
small opening in the upper part of the vessel. The mass of each drop is \( \mathrm{m} \), and the charge on the drop is Q. What will be
the number n of the last drop that can
still enter the sphere?


The value of \( k \) for which the function
\( f(x)=\frac{\left(e^{x}-1\right)^{4}}{\sin \left(\frac{x^{2}}{k^{2}}\right) \log \left\{1+\left(\frac{x^{2}}{2}\right)\right\}}, x \neq \)
\( \mathbf{0} ; \boldsymbol{f}(\mathbf{0})=\mathbf{8} \) may be continuous function
is
This question has multiple correct options
\( A \)
B. -
\( c \cdot 2 \)
\( D \cdot-2 \)


The boundaries of the plates, called weak zones, are also known as:
A. danger zones
B. seismic zones
c. colliding zones
D. none of the above


Another ion that would behave similar
to \( A l^{+3}(a q) \) in forming an acidic solution is:
A \( \cdot B e_{(a q)}^{2+} \)
В. \( B a_{(a q)}^{2+} \)
c. \( N a^{+} \)
\( \mathbf{D} \cdot T l^{+} \)


Which term of the A.P 5,9,13,17.... is 81?


Interhalogen compounds are ionic
A. True
B. False


Select the correct statement from the
following:
A. A diode can be used as a rectifier
B. A triode cannot be used as a rectifier
C. The current in a diode is always proportional to the applied voltage
D. The linear portion of the I-V characteristic of a triode is used for amplification without distortion


Find the equation of the circle whose center lies on the positive direction of \( y \) axis at a distance 6 from the origin and
whose radius is 4


For real values of \( x, \) the range of \( \frac{x^{2}+2 x+1}{X^{2}+2 x-1} \)
is
\( \mathbf{A} \cdot(-\infty, 0) \cup(1, \infty) \)
B \( \cdot\left[\frac{1}{2}, 2\right] \)
\( \mathbf{c} \cdot\left[-\infty, \frac{-2}{9}\right] \cup(1, \infty) \)
D. \( (-\infty,-6) \cup(-2, \infty) \)


The particle executing simple harmonic motion has a kinetic energy \( K_{0} \cos ^{2} \omega t \) The maximum values of the potential energy and the total energy are respectively
A. \( K_{0} \) and \( K_{0} \)
B. 0 and \( 2 K_{0} \)
c. \( \frac{K_{0}}{2} \) and \( K_{0} \)
D. \( K_{0} \) and \( 2 K_{0} \)


In Coulomb's law, the constant of
proportionality K has the units
\( \mathbf{A} \cdot N \)
в. \( N m^{2} \)
C. \( N C^{2} / m^{2} \)
D. \( N m^{2} / C^{2} \)


Acetic acid undergoes dimerisation, when dissolved in benzene (as shown in
figure) Molecular mass of acetic acid is found
to be 120 .

Which among the following relation is correct?
(where, \( \alpha= \) degree of association,
\( d= \) observed vapour density, \( D= \) Theoretical vapour density
\[
2 \mathrm{CH}_{3}-\mathrm{cooH} \rightleftharpoons \mathrm{cH}_{3}-\mathrm{c} \underbrace{\mathscr{J}}_{\mathrm{oH} \ldots \mathrm{o}}^{\mathrm{o} \ldots \mathrm{OH}}_{\mathscr{J}}^{\mathrm{c}-\mathrm{cH}_{3}}
\]
\( A \)
\[
\alpha=2\left(\frac{D-d}{d}\right)
\]
в.
\[
\alpha=2\left(\frac{D-d}{D}\right)
\]
c.
\[
\alpha=2\left(\frac{d-D}{d}\right)
\]
D.
\[
\alpha=\frac{2 d}{D-d}
\]


When light passes from one medium to another, the physical quantity that remains unchanged is
A. velocity
B. wavelength
C. frequency
D. None of these


What are the characteristics of the final
image formed by a compound microscope?


Which of the following is not a general characteristic of equilibria involving physical processes?
A. Equilibrium is possible only in a closed system at a given temperature.
B. The equilibrium is dynamic in nature
c. Measurable properties of the system keep changing
D. Equilibrium can be attained from both sides of the reaction


What happens during telophase?
A. Nuclear membrane is formed
B. Nucleolus appears
c. Astral rays disappear
D. All of the above


\( d \)
\( d \sigma \)
\( d \)
\( d \)


Self inductance \( L \) of long solenoid is
being proportional to the number of
turns \( N \) as-
A . \( N \)
В. \( N^{2} \)
c. \( N^{3} \)
D. \( N^{4} \)


Select the strongest oxidant oxoanion and weakest oxidant oxanion among
the following:
\( \boldsymbol{V} \boldsymbol{O}_{4}^{3-}, \boldsymbol{C r} \boldsymbol{O}_{4}^{2-}, \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4}^{2-}, \boldsymbol{F} \boldsymbol{e} \boldsymbol{O}_{4}^{2-} \)
A. Strongest: \( F e O_{4}^{2-} ; \) weakest \( : V O_{4}^{3} \)
B. Strongest: \( V O_{4}^{3-} \); weakest: \( F e O_{4}^{2} \)
c. Both are equally strong
D. None of these


The reducing agent in thermite process is:
A . \( A l \)
в. \( M g \)
c. \( F e \)
D. \( S \) i


Consider the following five graphs(note the axes carefully. Which of the following motion at constant speed?
A. Donly
B. D and E
\( c \cdot A, B \) and \( c \)
D. A and D


Write short notes on:
(a) Coelom
(b) Metamerism (c)
Notochord


\( \int x \sin ^{2} x d x \)
A. \( \frac{x^{2}}{4}-\frac{\cos 2 x}{3}+\frac{1}{8} \sin 2 x+c \)
B. \( \frac{x^{2}}{4}-\frac{x \sin 2 x}{4}-\frac{1}{8} \cos 2 x+c \)
C \( \frac{x^{2}}{4}+\frac{x \sin 2 x}{4}+\frac{1}{8} \cos 2 x+c \)
D. \( \frac{-x^{2}}{4}-\frac{\cos 2 x}{3}+\frac{1}{8} \cos 2 x+c \)


If \( \boldsymbol{a}>\mathbf{0}, \lim _{x \rightarrow \infty} \frac{[\boldsymbol{a} \boldsymbol{x}+\boldsymbol{b}]}{\boldsymbol{x}} \) is where [
denotes G.I.F.
\( \mathbf{A} \cdot \mathbf{0} \)
B.
c. \( [a] \)
\( D \cdot[b] \)


Photorespiration takes place in which of the following organelles?
A. Chloroplast and mitochondria
B. Mitochondria and peroxisome
c. Bundle sheath cells and chloroplasts
D. chloroplast, peroxisome and mitochondria.


Reactions that take place under the influence of electricity are called:
A. Electrolytic reaction
B. Hydrolytic reaction
c. condensation reaction
D. Photolytic reaction


A purse contains 4 copper coins and 3
silver coins. A second purse contains 6 copper coins and 4 silver coins. A purse is chosen randomly and a coin is taken out of it. What is the probability that it is a copper coin?
A \( \cdot \frac{41}{70} \)
B. \( \frac{31}{70} \)
c. \( \frac{27}{70} \)
D.


Electron transport chain occurs on:
A. Outer membrane of mitochondria
B. Inner membrane of mitochondria
c. Matrix of mitochondria
D. None of the above


In three dimensions, the coordinate
axes of a rectangular cartesian coordinate system are
A. three mutually parallel lines
B. three mutually perpendicular lines
c. two mutually perpendicular lines and any two parallel
D. None of these


\( \boldsymbol{x}=\mathbf{1}+\frac{\mathbf{1}}{\mathbf{2} \times \underline{\mathbf{1}}}+\frac{\mathbf{1}}{\mathbf{4} \times \underline{\mathbf{2}}}+\frac{\mathbf{1}}{\mathbf{8} \times \underline{\mathbf{3}}} \)
\( \mathbf{A} \cdot e^{1 / 2} \)
B \( \cdot e^{2} \)
\( c \)
\( D \cdot \frac{1}{1} \)


\( 0.001 M N H_{4} C l \) aqueous solution has
\( \mathbf{p H}: \)
A . 6.127
B. 7.126
c. 2.167
D. 1.267


An \( L C R \) series circuit with \( R=100 \Omega \)
is connected to a \( 200 \mathrm{V}, 50 \mathrm{Hz} \) a.c source. When only the capacitance is removed, the current leads the voltage
by \( 60^{\circ} . \) When only the inductance is removed, the current leads the voltage
by \( 60^{\circ} . \) The current in the circuit is :
A \( .2 A \)
в. \( 1 A \)
c. \( \frac{\sqrt{3}}{2} A \)
D. \( \frac{2}{\sqrt{3}} A \)


The contrapositive of \( \boldsymbol{p} \rightarrow(\sim \boldsymbol{q} \rightarrow \sim \boldsymbol{r}) \)
is
A \( \cdot(\sim q \wedge r) \rightarrow \sim p \)
в. \( (q \rightarrow r) \rightarrow \sim p \)
c. \( (q \vee \sim r) \rightarrow \sim p \)
D. none of these.


Find the value of \( \tan ^{-1}\left(\frac{1}{2} \tan 2 A\right)+ \)
\( \tan ^{-1}(\cot A)+\tan ^{-1}\left(\cot ^{3} A\right), \) for \( 0< \)
\( \boldsymbol{A}<\frac{\boldsymbol{\pi}}{\boldsymbol{4}} \)
\( \mathbf{A} \cdot-\pi / 2 \)
в. \( +\pi / 2 \)
c. \( -\pi \)
D. \( +\pi \)


The concentration of \( A g^{+} \) in a saturated
solution of \( A g_{2} C r O_{4} \) at \( 20^{0} C \) is \( 1.5 \times \)
\( 10^{-4} \)mol\( L^{-1} . \) The solubility product of
\( A g_{2} C r O_{4} \) at \( 20^{0} C \) is \( ? \)
B . \( 1.75 \times 10^{-10} \)
c. \( 3.0 \times 10^{-8} \)
D. \( 4.5 \times 10^{-10} \)


Presence of peroxide affects the addition of
\( A \cdot \) HBr
в. нс
c. \( H \)
D. All


In the figure, \( O P Q R \) is rhombus, three
of whose vertices lie on the circle with
centre \( \boldsymbol{O} \)
f the area of the rhombus is \( 32 \sqrt{3} c m^{2} \)
find the radius of the circle.


The graph between potential difference and current for a conductor is a straight line passing through the origin. Which law is illustrated by such a graph?
A. Law ofcombination of resistances
B. Henry's law
c. ohm'slaw
D. Joule's law ofheating


A convex lens of focal length \( 20 \mathrm{cm} \) is
cut into two equal parts so as to obtain
two plano convex lenses as shown in the fig (a). The two parts are then put in contact as shown in fig (b). The focal length of the combination is
A. zero
B . 5cm
c. \( 10 \mathrm{cm} \)
D. 20cm


Fill in the blanks with the help of options, given in the box.
I. In
(P) sketch of the solid, the measurements are kept proportional.
Il. \( \mathbf{A} \)
(Q) polygon has as many lines of symmetry as it has sides. III. \( \mathbf{A} \)
(R) is a skeleton-outline of
a solid that can be folded to make the
solid.
IV. While rectangle is a 2 -D figure,
(S) is a 3 -D figure.
A. P- Oblique, Q- Regular, R- Net, S- Cuboid
B. P- Isometric, Q- - Irregular, R- Net, S- Cuboid
c. P- oblique, Q- - Irregular, R- Net, S- Cuboid
D. P- Isometric, Q- Regular, R- Net, S- Cuboid


Assertion
Plastics are non-biodegradable.
Reason
As they cannot be decomposed by micro-organisms.
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 Reasn is correct


Haemoglobin shows maximum affinity
with
A. Carbon monoxide
B. Carbon dioxide
c. oxygen
D. Ammonia


At the magnetic poles of magnet, its attractive power is minimum
A. True
B. False


The displacement \( x \) of a particle varies
with time according to the relation \( x= \) \( \frac{a}{b}\left(1-e^{-b t}\right) . \) Which of the following
statements is incorrect?
A \( \cdot \) At \( t=\frac{1}{b}, \) the displacement of the particle is nearly \( \frac{2}{3}\left(\frac{a}{b}\right) \)
B. the velocity and acceleration of the particle at \( t=0 \) are \( a \) and \( -a b \) respectively
C . the particle cannot go beyond \( x=\frac{a}{b} \)
D. the particle will come back to its starting point at \( t \rightarrow \) \( \infty \)


\( 10 c m \) and \( 100 c m \) are placed on a
horizontal plane as shown in the Figure.
Outer loop is connected to a source of
unknown emf through a key K. If a
current of \( 2 A \) flows in the inner loop as
shown aside, when the key k is closed at
time \( t=0 s, \) then the emf of the source
sending a current \( I \), should be
[Take resistance of both wire per length
\( \left.\operatorname{as} 10^{-4} \Omega m^{-1}\right) \)
of unknow
\( \mathbf{A} \cdot 4 V \)
B. \( 4 t V \)
\( \mathbf{c} \cdot 04 \mathrm{t}^{2} \mathbf{V} \)
D. \( \left(0.4 t^{2}+4 t+4\right) V \)


A long charged cylinder of linear charged density \( \lambda \) is surrounded by a hollow co-axial conducting cylinder. What is the electric field in the space
between the two cylinders?


Which of the following is anodic
reaction:
\( \mathbf{A} \cdot S O_{4}^{2-}+H_{2} O \rightarrow H_{2} S O_{4}+1 / 2 O_{2}+2 e^{-} \)
\( \mathbf{B} \cdot H^{\oplus}+e^{-} \rightarrow 1 / 2 H_{2} \)
\( \mathbf{C} \cdot A g^{\oplus}+e^{-} \rightarrow A g \)
D. None of above


Assertion
Entropy is always constant for a closed
system.
Reason
Closed system is always reversible.
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


Urine is excreted out of the body
through
A . Pelvis
B. Ureter
c. Urinary bladder
D. Urethra


The specific conductance of a \( N / 10 \mathrm{KC} \)
solution at \( 18^{\circ} \mathrm{C} \) is \( 1.12 \times \)
\( 10^{-2} \) mho \( c m^{-1} . \) The resistance of the
solution contained in the cell is found to
be 65 ohms. Calculate the cell constant.
A \( \cdot 0.728 \mathrm{cm}^{-1} \)
B. \( 0.928 \mathrm{cm}^{-1} \)
c. \( 0.428 \mathrm{cm}^{-1} \)
D. \( 0.328 \mathrm{cm}^{-1} \)


The better reducing agent at \( 7100^{\circ} \mathrm{C} \) is:
A. \( C O \) (Ellingham diagram)
B. Coke
c. Both are equal
D. None of these


In the circuit shown, the value of
currents \( I_{1}, I_{2} \) and \( I_{3} \) are
' 3 A, \( \frac{-3}{2} A, \frac{9}{2} \),
3. \( \frac{9}{2} A, 3 \) A, \( \frac{-3}{2} \) A
c. \( 5 A, 4 A,-3 \) f
\( 7 A, \frac{5}{4} A, \frac{9}{2} A \)


Draw the electron dot diagram of \( \boldsymbol{C H}_{4} \)
and justify your answer.


During transcription, holoenzyme RNA polymerase binds to DNA sequence and DNA assumes a saddle like structure at
that point. The sequence is called as
\( A \). AAAT box
B. TATA box
\( c \cdot \operatorname{GGCC} \) box
D. CAAT box


\( H F \) can be prepared by the action of
\( H_{2} S O_{4} \) on \( N a F . \) Choose the correct
statement(s) for action of \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) on
Na Br.
This question has multiple correct options
A. \( H_{2} S O_{4} \) cannot react with \( N a B r \)
B. \( H B r \) cannot be prepared by the action of \( H_{2} S O_{4} \) on \( _{N a B r} \)
c. \( H_{2} S O_{4} \) oxidises \( H B r \) to form \( B r_{2} \)
D. \( S O_{2} \) gas is evolved


Out of the halogens, which one is the most powerful oxidizing agent?
A. bromine
B. fluorine
c. iodine
D. chlorine


If \( \boldsymbol{x}=\boldsymbol{a}(\boldsymbol{t}-\sin \boldsymbol{t}), \boldsymbol{y}=\boldsymbol{a}(\boldsymbol{1}-\cos \boldsymbol{t}) \)
find \( \boldsymbol{d} \boldsymbol{y} / \boldsymbol{d} \boldsymbol{x} \). at \( \boldsymbol{t}=\boldsymbol{\pi} \)


A body weighs \( 63 \mathrm{N} \) on the surface of the earth. What is the gravitational force (in
N) on it due to the earth at a height equal to half the radius of the earth?


Evaluate the following definite integral:
\( \int_{1}^{2} \frac{1}{x} d x \)


The self induction takes place when
magnetic flux through a coil:
A. Remains steady
B. Decreases
c. Increases
D. Either (B) or (C)


A body falls from the top of a building and reaches the ground \( 2.5 s \) later. How
high is the building? (Take \( g=10 m s^{-2} \)
A. 30.6 \( m \)
B. 31.25 \( m \)
c. 30 \( m \)
D. 25 m


Find the nature and order of the
interference at the point \( P \)
A \( \cdot 70^{t h} \) maxima
B. \( 80^{\text {th }} \) minima
\( \mathbf{c} \cdot 60^{t h} \operatorname{maxima} \)
\( D \cdot 70^{t h} \operatorname{minima} \)


Given that \( \cos 50^{\circ} 20^{\prime}=0.6388 \) and
\( \cos 50^{\circ} 42^{\prime}=0.6334, \) then the possible
value of \( \cos 50^{\circ} 20^{\prime} \) is
A .0 .6293
B. 0.6307
c. 0.6361
D. 0.6414


For an ideal step-down transformer, the
quantity which is constant for both the coils will be
A. current in the coils
B. voltage across the coils
c. resistance of coils
D. power in the coils


Alkaline earth metals have higher melting points than alkali metals.
If this is true enter 1 , if false enter 0 .


Rate of decomposition depends upon
A. Chemical composition of detritus
B. Temperature
c. Soil moisture and soil pH
D. All of these


A star initially has \( 10^{40} \) deuterons. It produces energy via the processes \( _{1} H^{2}+_{1} H^{2} \rightarrow_{1} H^{3}+p \) and \( _{1} H^{2}+_{1} \)
\( H^{3} \rightarrow_{2} H e^{4}+n . \) If the average power
radiated by the star is \( 10^{16} \mathrm{W} \), the deuteron supply of the star is exhausted in a time of the order of
[The mass of nuclei are as follows:
\( \boldsymbol{M}\left(\boldsymbol{H}^{2}\right)=\mathbf{2 . 0 1 4} \boldsymbol{a m} \boldsymbol{u}, \boldsymbol{M}(\boldsymbol{n})= \)
\( \mathbf{1 . 0 0 8 a m u} \)
\( M(p)=1.007 a m u, M\left(H e^{4}\right)= \)
\( 4.001 a m u\} \)
A \( \cdot 10^{6} s \)
B . \( 10^{8} \) s
\( c \cdot 10^{12} s \)
\( s \)
D. \( 10^{16} s \)


Reaction of ethyl chloride with sodium leads to (in the presence of dry ether):
A. ethane
B. propane
c. n-butane
D. n-pentane


Consider a sample of an equimolar mixture of He gas and Ne gas both at
\( 300 \mathrm{K} \) and 1 atmosphere.Assuming ideal behaviour which of the following quantities are equal for two samples? This question has multiple correct options
A. Root mean square speed of molecules
B. Mean translational kinetic energy of molecules
c. Number density of molecules
D. Kinetic energy of molecules


Maxwell introduced displacement current to remove the conceptual contradiction in
A. Gauss's law in electrostatics
B. Gauss's law in magnetism
c. Faraday's law
D. Ampere's law


Each chromosome composed of one chromatid in
A. Anaphase!
c. Metaphase!
D. Metaphase II


Who established that electric charge is quantised?
A. J.J. Thomson
B. William Crookes
c. R.A Millikan
D. Wilhelm Rontgen


\( \cos ^{-1}\left(\frac{\pi}{3}+\sec ^{-1}(-2)\right)= \)
\( A \cdot-1 \)
B.
\( c \cdot 0 \)
D. None of these


The heavy atom of hydrogen has neutrons.
A. 0
B.
\( c \cdot 2 \)
\( D \)


Which of the following are used in the formation of selenium dioxide along with water and elemental selenium?
A . Nitric acid
B. Sulfuric acid
c. sodium hydroxide
D. Quick lime


Answer the question based on following
ECG.

Which wave represents the ventricular
relaxation?


The total number of monohalogenated products formed by halogenation of 2,4,4 -trimethylhexane are:
A . 5
B. 7
\( c \cdot 6 \)
D. 8
\( E \)


Water gas is an equi-molar mixture of hydrogen and carbon monoxide. If 250
litres of water gas is burnt in air. Assuming both reactants and products are at same temperature and pressure,
the volume of \( O_{2} \) required is
\( 2 C O+O_{2} \rightarrow 2 C O_{2} ; 2 H_{2}+O_{2} \rightarrow \)
\( 2 H_{2} O \)
A. 250 litres
B. 125 litres
c. 75 litres
D. 500 litres


If the ratio of the sums of first of two
A.P.'s is \( (7 n+1):(4 n+27), \) find the ratio
of their \( m^{t h} \) terms.


Which of the following is produced only by plants?
A. Starch
B. Glycogen
c. cholesterol
D. Triglycerides


Hybridisation of carbon in \( \boldsymbol{C H}_{2}= \) \( \boldsymbol{C H}-\boldsymbol{C H}_{2} \) is:
\( A \cdot s p^{2} \)
в. \( s p \)
\( c \cdot s p^{3} \)
D. all of these


State your observation when Conc. nitric acid is heated in absence of copper gives:
A . yellow
B. brown
c. grey
D. black


Self-reduction of CuS to Cu can be
carried out in:
A. Bessemer converter
B. Pierce-Smith converter
c. both (a) and (b)
D. None of the above


The diagram shows the magnetic field around two bar magnets. Which
diagram shows the poles of the
magnets?
\( A \)
\( \mathbf{N} \quad \mathbf{S} \) \( \mathbf{N} \quad \mathbf{S} \)
B. \( \mathbf{N} \quad \mathbf{S} \) \( \mathrm{S} \)
\( c \)
\( \mathrm{S} \) \( \mathbf{N} \quad \mathbf{S} \)
\( D \)
\( \mathrm{S} \) \( \mathrm{S} \)


Check whether the probabilities \( \boldsymbol{P}(\boldsymbol{A}) \)
and \( P(B) \) are consistently defined \( \boldsymbol{P}(\boldsymbol{A})=\mathbf{0 . 5}, \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 4}, \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B})= \)
\( \mathbf{0 . 8} \)


Which of the following correctly represents the graphical relation between the angle of incidence \( \hat{\boldsymbol{i}} \) and the angle of reflection \( \hat{r} ? \)
A.
в.
\( c \)
D.


A body projected vertically up with a velocity 'u' attains a maximum height
H. If it is thrown up with velocity \( 2 u, \) it attains a maximum height of
\( A \cdot 8 H \)
B. 44
\( c . \) зн
D. 64


Explain the following giving a suitable
example for each.
(i) Aerosol
(ii) Emulsion
(iii) Micelle


Solve the following inequalities. \( \frac{2-5 x}{x+1}>2 \)


If \( \boldsymbol{A}=\{\mathbf{3}, \mathbf{6}, \mathbf{9}, \mathbf{1 2}, \mathbf{1 5}, \mathbf{1 8}\}, \boldsymbol{B}= \)
\( \{4,8,12,16,20\}, C= \)
\{2,4,6,8,10,12\} and \( D= \)
\( \{5,10,15,20,25\}, \) find
(i) \( \boldsymbol{A}-\boldsymbol{B} \)
(ii) \( B-C \)
(iii) \( C-D \)
(iv) \( D-A \)
\( (v) n(A-C) \)


We have to see an object in a dark room.
Then:
A. we have to light a torch on our eyes
B. we have to light a torch on the object
c. both can be done
D. we can't see the object through any of the above
processes


How many of the following are observed in the interphase nucleus?
Chromatid, Nucleosome, Centriole,
Nucleolus, Centromere, Kinetochore
A . Three
B. One
c. Four
D. Two


If \( \boldsymbol{y}=\boldsymbol{4}^{l o g_{2} \sec x}-\boldsymbol{9}^{l o g_{3} t a n x}, \) then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}= \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
c. 2
D. 3


Explain why dehydration of alcohols to form alkenes is always carried out with
conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4}, \) and not with conc. \( \boldsymbol{H} \boldsymbol{C l} \) or
\( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} ? \)


A \( 0.60 g \) sample consisting of only
\( C a C_{2} O_{4} \) and \( M g C_{2} O_{4} \) is heated at
\( 500^{\circ} \mathrm{C}, \) converting the two salts of
\( C a C O_{3} \) and \( M g C O_{3} . \) The sample then, weighs \( 0.465 g . \) If the sample had been
heated to \( 900^{\circ} \mathrm{C} \), where the products
are \( C a O \) and \( M g O, \) what would
the mixtures of oxides have weighed?
\( \mathbf{A} \cdot 0.12 g \)
B. \( 0.21 g \)
c. \( 0.252 g \)
D. \( 0.3 g \)


Two heater coils separately take 10 min and 5 min to boil a certain amount of
water. If both the coils are connected in
series, the time taken will be
A. 2.5 min
B. 3.33 min
c. 7.5 min
D. 15 min


Write the name of a different stage of
obtaining pure metal from its ore. Explain refining of copper by electrolysis with a diagram.


Hofmann bromamide degradation
reaction is shown by:
A \( . A r N H_{2} \)
в. \( A r C O N H_{2} \)
c. \( A r N O_{2} \)
D. \( A r C H_{2} N H_{2} \)


Sodium phenoxide when heated with
\( C O_{2} \) under pressure at \( 125^{0} C \)
gives
A. Salol
B. Salicylaldehyde
c. Sodium benzoate
D. Sodium salcylate


A current of 9.65 A is passed through
\( 100 \mathrm{ml} \) NaCl solution containing sufficient \( N a C l \) for 100 s. What will be
the \( p H \) of the resulting solution?
Assume \( 100 \% \) current efficiency and
constancy of the volume of solution.


Figure shows the electric field lines
around an electric dipole. Which of the arrows best represents the electric field
at point P?
\( A \)
3.
\( c \)
D


Magnification produced by plane mirror
is \( +1 . \) It means:
A. Image formed by plane mirror is greater than size of the object
B. Image formed by plane mirror is erect and of same size as the object
C. Image formed by plane mirror is smaller than size of object and is virtual
D. None


Calculate \( E^{\ominus} \) for the reactions:
\( Z n Y^{2-}+2 e^{-} \rightleftharpoons Z n(s)+Y^{4-} \) is the
completely deprotonated anion of EDTA. The formation constant for
\( Z n Y^{2-} \) is \( 3.5 \times \)
\( \mathbf{1 0}^{\mathbf{1 6}} \mathbf{a n d} \boldsymbol{E}^{\ominus} \operatorname{for} \boldsymbol{Z} \boldsymbol{n} \rightarrow \boldsymbol{Z} \boldsymbol{n}^{\mathbf{2}+}+\mathbf{2} \boldsymbol{e}^{-} \)
is \( 0.76 \mathrm{V} \)
A . \( -1.25 V \)
B. \( 0.48 V \)
\( c .+0.68 V \)
D. \( -0.27 V \)


Oxidation number of \( \boldsymbol{O} \) in \( \boldsymbol{O}_{3} \)
\( A \cdot+1 \)
B. - -
\( c \cdot 0 \)
\( D \cdot+2 \)
\( E \cdot+3 \)


Many properties of an element and its compounds can be predicted from the position of that an element in the periodic table. What property could not be predicted this way?
A. The acidic or basic nature of its oxide
B. The formula of its oxide
C. The number of isotopes it has
D. Its metallic or non-metallic properties


'P-protein' is a constituent of
A. Sieve tube elements
B. xylem parenchyma
c. Parenchyma
D. Pericycle


Explain sex determination in human beings.


Which of the following ions has same number of unpaired electrons as those present in \( V^{3+} \) ion?
A \( \cdot F e^{3} \)
B. \( N i^{2} \)
c. \( M n^{2} \)
D. \( C r^{3} \)


Two identical containers \( A \) and \( B \) with
frictionless pistons contain the same ideal gas at the same temperature and
the same volume \( V \). The mass of \( \operatorname{gas} \) in \( A \)
is \( m_{A} \) and that in \( B \) is \( m_{B} . \) The gas in
each cylinder is now allowed to expand isothermally to the same final volume \( 2 V \)
The changes in the pressure in \( A \) and \( B \)
are found to be \( \triangle p \) and \( 1.5 \triangle p \)
respectively. Then
\( \mathbf{A} \cdot 4 m_{A}=9 m_{B} \)
в. \( 2 m_{A}=3 m_{B} \)
\( \mathbf{c} \cdot 3 m_{A}=2 m_{B} \)
D. \( 9 m_{A}=4 m_{B} \)


The terminalization process starts in
A. Leptotene
B. Zygotene
c. Diplotene
D. Diakinesis


A wheel, starting from rest, rotates with a uniform angular acceleration of
2rads \( ^{-2} \). The number of rotations it
performs in the tenth second is
\( A \cdot 3 \)
B. 6
\( c \cdot 9 \)
D. 12


Corresponding to a given temperature,
there is a wavelength \( \lambda_{m}, \) for which the
intensity of heat radiations is
A. maximum
B. constant
c. zero
D. minimum


Nerve impulse is a
A. Physical process
B. Chemical process
C . Effected process
D. Electron-chemical process


Match the column and select the
correct option from the following.
\( \begin{array}{llll} & \text { List I } & & \text { List II } \\ \text { A } & \text { Anomocytic } & 1 & \text { Parallel } \\ \text { B } & \text { Anisocytic } & 2 & \text { cross } \\ \text { C } & \text { Diacytic } & 3 & \text { Unequal } \\ \text { D } & \text { Paracytic } & 4 & \text { Irregular }\end{array} \)
A \( \cdot A-4, B-3, C-2, D-1 \)
B. A- \( 4, \) B- \( 2, \) C- \( 3, \) D-
c. \( A-4, B-3, C-1, D-2 \)
D. A- 3, B- 4, C- 2, D-


The reaction which will not occur during the formation of chloroform from
\( C_{2} H_{5} O H \) and \( C a O C l_{2} \) is:
A. addition
B. oxidation
c. chlorination
D. hydrolysis


There is an electric field E in x-direction.
If the work done on moving a charge of \( 0.2 \mathrm{C} \) through a distance of \( 2 \mathrm{m} \) along a
line making an angle \( 60^{\circ} \) with \( x \) -axis is
4 J, then what is the value of E?
A. \( \sqrt{3} \) N/C
B. 4 N/C
c. \( 5 \mathrm{N} / \mathrm{c} \)
D. 20 N/C


Assertion: The heat of vaporization of
water and the heat of fusion of water is
numerically different. Reason: When water freezes or
vaporizes, its chemical composition remains unchanged.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
E. Both Assertion and Reason are incorrect


Solve the following equations:
\( \sqrt{4 x^{2}-7 x-15}-\sqrt{x^{2}-3 x}= \)
\( \sqrt{x^{2}-9} \)


A highly rigid cubical block A of small mass \( \mathrm{M} \) and side \( \mathrm{L} \) is fixed rigidly on to
another cubical block \( \mathrm{B} \) of the same
dimensions and of low modulus of
rigidity \( \eta \) such that the lower face of \( A \)
completely covers the upper face of B. The lower face of B is rigidly held on a
horizontal surface. A small force F is
applied perpendicular to one of a sides faces of A. After the force is withdrawn, block A executes small oscillations, the
time period of which is given by
\( \mathbf{A} \cdot 2 \pi \sqrt{M \eta L} \)
в. \( 2 \pi \sqrt{M \eta / L} \)
c. \( 2 \pi \sqrt{M L / \eta} \)
D. \( 2 \pi \sqrt{M / \eta L} \)


A proton and \( \alpha \) -particle are accelerated through the same potential difference. The ratio of their de-Broglie wavelength
will be
A .1:
B. 1: 2
\( c \cdot 2: \)
D. \( 2 \sqrt{2}: 1 \)


Observe the figure and find the
perimeter of the quadrilateral \( \boldsymbol{A P B O} \)
where \( ^{\prime} P^{\prime} \) is any exterior point, and
\( O A=7 \mathrm{cm} A P=24 \mathrm{cm},^{\prime} O^{\prime} \) is the
centre


A student conducted an experiment and obtained three values during three
repetitive trials: \( 1.65,1.68,1.71 . \) Later the student discovered that the true
value was \( 2.37 . \) In contrast to the rea
value, the experimental results should be characterized as:
A. not accurate and not precise
B. accurate but not precise
c. not accurate but precise
D. accurate and precise
E . accurate, precise, but unreliable


Two short magnets of equal dipole
moments \( M \) are fastened
perpendicularly at their centres as given in the figure. The magnitude of
the magnetic field at a distance \( d \) from
the centre on the bisector of the right angle is
A. \( \frac{\mu_{0} m}{4 \pi d^{3}} \)
в. \( \frac{\mu_{0} \sqrt{2} M}{4 \pi d^{3}} \)
c. \( \frac{\mu_{0} 2 \sqrt{2} M}{4 \pi d^{3}} \)
D. \( \frac{\mu_{0} 2 M}{4 \pi d^{3}} \)


If \( F \) is the force between two bodies of
masses \( m_{1} \) and \( m_{2} \) at certain
separation, then the force between \( \sqrt{2} m_{1} \) and \( \sqrt{3} m_{2} \) at same separation
is:
A \( \cdot \sqrt{6} F \)
в. \( \sqrt{26} F \)
\( c .6 F \)
D. \( \sqrt{216} F \)


The Radius of curvature of two surfaces
of a convex lens are \( 10 \mathrm{cm} \) and \( 20 \mathrm{cm} \)
respectively. The refrective index of glass is 1.5 then determine focal length of the lens.


Which of the following has highest
mass?
A. 50 g of iron
B. 5 moles of nitrogen gas
c. \( 1 \mathrm{g} \) atom of silver
D. \( 5 \times 10^{23} \) atoms of carbon


Solve:
\( \cos ^{-1}(\cos x)=\pi+x, \) then \( x \) belongs
to
В. \( (\pi, 2 \pi) \)
D. None of these


The total number of terms in the
expansion of \( (x+a)^{100}+(x-a)^{100} \)
after simplification is
A .202
B. 51
\( c .50 \)
D. 49


The most direct malonic ester synthesis of the 3-phenyl propanoic acid would involve the use of :
A. \( C_{6} H_{5} C H_{2} C H_{2} C H_{2} C l \)
в. \( C_{6} H_{5} C H_{2} C H_{2} C l \)
c. \( C_{6} H_{5} C H_{2} C l \)
D. \( C l C H_{2} C O O H \)


The heat of combustion of ethyne \( C_{2} H_{4} \)
gas at \( 298^{\circ} \) is \( -1411.3 K J . \) Calculate
the heat of reaction at constant value
and at \( 298 K . R=8.314 J / k / \) mol


An object will not turn when:
A. The forces are acting on it at different positions
B. Every forces is creating different turning effects
C. Every moment has the same amplitude
D. All the forces are acting at its centre of gravity


From a normal pack of cards, a card is drawn at random. Find the probability of getting a jack or a king.
A \( \cdot \frac{2}{52} \)
в. \( \frac{1}{52} \)
c. \( \frac{2}{13} \)
D. \( \frac{1}{26} \)


Find a transformation of the polygon
that does result in at least one type of
symmetry. Draw the image and list the coordinates of the vertices of the larger
shape. How do you know the diagram
has symmetry?


Which one of the following is not a redox reaction?
A. \( C a C O_{3} \rightarrow C a O+C O_{2} \)
В. \( 2 H_{2}+O_{2} \longrightarrow 2 H_{2} O \)
\( ^{\mathrm{c}} \cdot_{N a+H_{2} O} \rightarrow N a O H+\frac{1}{2} H_{2} \)
D. \( _{M n C l_{3}} \rightarrow M n C l_{2}+\frac{1}{2} C l_{2} \)


A sphere of brass released in a long liquid column attains a terminal speed
\( \boldsymbol{v}_{0} . \) If the terminal speed attained by sphere of marble of the same radius
and released in the same liquid in \( n v_{0} \) then the value of \( n \) will be (Given : The
specific gravities of brass, marbles and
the liquid are 8.5,2.5 and 0.8 respectively \( ) \)
A \( \cdot \frac{5}{17} \)
в. \( \sqrt{\frac{17}{77}} \)
c. \( \frac{11}{31} \)
D. \( \frac{17}{5} \)


Glycogen, a naturally occurring polymer stored in animals is a:
A. monosaccharide
B. disaccharide
c. trisaccharide
D. polysaccharide


Rate of disappearance of the reactant \( \mathbf{A} \) at two different temperature is given by \( \boldsymbol{A} \rightleftharpoons \boldsymbol{B} \)
\( \frac{-d[A]}{d t}=\left(2 \times 10^{-2} S^{-1}\right)[A]-4 \times \)
\( \mathbf{1 0}^{-\mathbf{3}} \boldsymbol{S}^{-\mathbf{1}}[\boldsymbol{B}] ; \mathbf{3 0 0} \boldsymbol{K} \)
\( \frac{-d[A]}{d t}=\left(4 \times 10^{-2} S^{-1}\right)[A]-16 \times \)
\( \mathbf{1 0}^{-4} \boldsymbol{S}^{-1}[\boldsymbol{B}] ; \mathbf{4 0 0} \boldsymbol{K} \)
Calculate heat of reaction in the given temperature range, when equilibrium is
set up.
A. \( 8.03 \mathrm{kJ} \)
B. 16.06 k
c. 32.12 k
D. None of these


The first electro-chemical was invented
by:
A. Luigí Galvani
B. Alessandro Volta
c. Deniel.
D. Lechanche


Fill in the blank spaces by choosing the correct words from the list given below:
List : yellow spot, principal focus, less, shutter, more.

The small but very light sensitive area on the retina is called
A. yellow spot
B. principal focus
c. shutter
D. none of the above


A solid insulating sphere of radius \( \boldsymbol{R} \) is
given a charge \( Q \). If at a point inside the
sphere the potential is 1.5 times the potential at the surface, this point will
be:
A. at a distance of \( 2 R / 3 \) form the centre
B. at the centre
c. at a distance of \( 2 R / 3 \) form the surface
D. data insufficient


Which of the following hydroxides is
most basic?
\( \mathbf{A} \cdot \operatorname{Be}(O H)_{2} \)
B. \( B a(O H)_{2} \)
\( \mathbf{c} \cdot C a(O H)_{2} \)
D. \( M g(O H)_{2} \)


A cylinder contains gas at a pressure of 2.5 atm. Due to leakage, the pressure falls to 2 atm, after sometime. The percentage
of the gas which is leaked out is
A . 40
B. 15
c. 20
D. 25


An \( \alpha \) -particle and a proton are
accelerated from rest by a potential difference of \( 100 V . \) After this, their de
Broglie wavelengths are \( \lambda_{\alpha} \) and \( \lambda_{p} \)
respectively. The ratio \( \lambda_{p} / \lambda_{\alpha}, \) to the nearest integer, is:


Corundum is mineral of Al.
A . silicate
B. oxide
c. double salt
D. sulphate


\( C O_{2} \) gas along with solid (Y) is obtained when sodium salt (X) is
heated. \( (X) \) is again obtained when \( C O_{2} \)
gas is passed into aqueous solution of
(Y). Identify \( (X) \) and \( (Y) \) respectively.
A. \( N a_{2} C O_{3}, N a_{2} O \)
в. \( N a_{2} C O_{3}, \) NaOH
с. \( N a H C O_{3}, N a_{2} C O_{3} \)
D. \( N a_{2} C O_{3}, N a H C O_{3} \)


Which of the following has no lone pair
over the central atom?
A \( . N H_{3} \)
в. \( P H_{3} \)
\( \mathrm{c} \cdot B F_{3} \)
D. \( P C l_{3} \)


Find 4 consecutive even numbers
whose sum is 356


Four cells, each of emf \( E \) and internal
resistance \( r, \) are connected in series
across an external resistance \( \boldsymbol{R} \). By
mistake one of the cells is connected in
reverse. Then the current in the external
circuit is:
A \( \cdot \frac{2 E}{4 r+R} \)
в. \( \frac{3 E}{4 r+R} \)
c. \( \frac{3 E}{3 r+R} \)
D. \( \frac{2 E}{3 r+R} \)


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


A spherical \uparrow ole of radius \( \mathbf{R} / \mathbf{2} \) is
excavated from \( \mathbf{t} \uparrow \) e asteroid of mass
M as shown in fig. T Me gravitational
acceleration at a point on t \( \uparrow \mathbf{e} \)
surf ace of \( \mathbf{t} \uparrow \mathbf{e} \) asteroid just above \( \mathbf{t} \uparrow \)
excavation is :
A. GM/R \( ^{2} \)
B. \( \mathrm{GM} / 2 \mathrm{R}^{2} \)
c. \( \mathrm{GM} / 8 \mathrm{R}^{2} \)
D. \( 7 \mathrm{gW} 8 \mathrm{R}^{2} \)


Calculate the \( p H \) of the solution to the
nearest integer.


In the presence of a catalyst, the heat evolved or absorbed during the reaction:
A . increaases
B. decreases
c. remains unchanged
D. may increase or decrease


When potassium perchlorate is heated,a gas is evolved.lt can also be
obtained by heating:
This question has multiple correct options
A \( \cdot K C l O_{3} \)
в. \( K_{2} C r_{2} O_{7} \)
\( c \cdot s O_{2} \)
D. all of these


Name the following alkyl groups:


If principal quantum number \( n=5, \) then the total number of orbitals present in a given stationary state is:
A .24
B. 25
\( c \cdot 26 \)
D. 27


The size of an object as perceived by an eye depends primarily on
A. actual size of the object
B. intensity of light
c. aperture of the pupil
D. size of the image formed on the retina


Fill in the blanks with suitable units of
measurements.
The distance I walk in 10 minutes is
about one


What do you understand by the antiparallel arrangement of DNA strands?


Write the electronic configuration of Elements with an electron sextet, e.g.
\( \boldsymbol{O}, \boldsymbol{S}, \boldsymbol{e t c} \)


On the basis of the atomic model
Rutherford concluded that:
A. atoms consist of predominantly empty spaces
B. atoms consist of central nucleus containing positively charged particles
c. whole of the atomic mass is concentrated in the nucleus
D. all are correct


Prove that
\( \int \frac{x^{2}}{x^{6}+1} d x \)


Give the electron configuration of the given metal (atom/ions)
\( F e O_{4}^{2-}(\text { ferrate ion }) \)
\( \mathbf{A} \cdot[A r] 3 s^{2} \)
B . \( [A r] 4 s^{2} \)
c. \( [A r] 3 d^{2} \)
D. none of these


The segment \( A B \) of wire carrying current
\( I_{1} \) is placed perpendicular to a long
straight wire carrying current \( \boldsymbol{I}_{2} \) as
shown in figure.The magnitude of force experienced by the straight wire \( A B \) is
A \( \cdot \frac{\mu_{o} I_{1} I_{2}}{2 \pi} 1 n 3 \)
В. \( \frac{\mu_{o} I_{1} I_{2}}{2 \pi} 1 n 2 \)
c. \( \frac{2 \mu_{o} I_{1} I_{2}}{2 \pi} \)
D. \( \frac{\mu_{o} I_{1} I_{2}}{2 \pi} \)


If \( (\boldsymbol{m}+\mathbf{1})^{t h},(\boldsymbol{n}+\mathbf{1})^{t h} \) and \( (\boldsymbol{r}+\mathbf{1})^{t h} \)
terms of an A.P. are in G.P and \( \boldsymbol{m}, \boldsymbol{n}, \boldsymbol{r} \)
are in H.P., then ratio of the first term of
the A.P. to its common difference in
terms of \( n \) is
\( A \cdot \frac{n}{2} \)
B. \( -\frac{n}{2} \)
\( c \cdot \frac{n}{3} \)
D. \( -\frac{n}{3} \)


The device used for producing electric current is called a:
A. generator.
B. galvanometer.
c. ammeter.
D. motor


A hydrogen atom \( \left(\operatorname{mass}=1.66 \times 10^{-27}\right. \)
kg, ionization potential = \( 13.6 e V \) ), moving with a velocity of \( 6.24 \times \) \( 10^{4} m s^{-1} \) makes a completely inelastic
head-on collision with another
stationary hydrogen atom. Both atoms are in the ground state before collision.
Up to what state either of one atom may
be excited?


Evaluate:
\( \int_{-1}^{1} x e^{x^{2}} d x \)


What is nutrition? Describe nutrition in
a moeba. (Draw diagram)


From the discharge tube experiment, it was concluded that:
A. mass of proton is in fraction
B. matter contains electrons
c. nucleus contains positive charge
D. positive rays are heavier than protons


What does the Big Bang Theory say?
A. All of the matter in the Universe exploded from a tiny, dense point
B. Two galaxies collided causing a big bang
C. The universe was created in its current location
D. The universe is collapsing and getting smaller.


A coil of area \( A \), turns \( N \) and carrying current \( i \) is placed with its face parallel to the lines of magnetic induction \( B \)
The work done in rotating the coil
through an angle of \( 180^{0} \) is
\( \mathbf{A} \cdot i N A B \)
в. 2 iNA \( B \)
c. \( \frac{i N A B}{2} \)
D. Zero


When a person walks on a rough
Surface
A. the frictional force exerted by the surface keeps him moving.
B. normal reaction of the force applied by the man on the surface keeps him moving.
C. the force applied by the man keep him moving.
D. weight of the man keeps him moving.


Equivalent mass of a trivalent metal is
\( 32.7 . \) Molecular mass of its oxide is:
A . 244.2
B. 68.2
c. 166.3
D. 103.7


In which of the following pair of reactions first reaction is spontaneous
while second reaction is non
spontaneous?
\( \mathbf{A} \cdot(\mathbf{i})-S H+H_{2} O \rightarrow H_{2} S+O H^{-} \)
(ii) \( N H_{2}^{-}+H_{2} O \rightarrow N H_{3}+O H^{-} \)
B. (i) - \( O R+H_{2} S O_{4} \rightarrow R O H+H S O_{4}^{-} \)
(ii) \( R^{-}+N H_{3} \rightarrow R H+N H_{2}^{-} \)
C . (i) \( C l^{-}+H F \rightarrow H C l+F^{-} \)
(ii) \( -O H+H C l \rightarrow H_{2} O+C l^{-} \)
D. \( \left(\text { i) }-O H+H B r \rightarrow H_{2} O+B r^{-}\right. \)
(ii) \( R O^{-}+N H_{3} \rightarrow R O H+N H_{2}^{-} \)


What is a chemical change?
A. Change in size, shape
B. Change from one substance to another new substance
C. Change in temperature from lower to higher
D. None of above


When an external voltage \( V \) is applied across a semiconductor diode such
that \( p- \) side is connected to the positive
terminal of the battery and \( n- \) side to the negative terminal, it is said to be
\( A \). reverse biased.
B. forward biased
c. bias free.
D. None of these


Find the mean height of 30 players
using direct method:
\begin{tabular}{|l|l|l|l|l|l|l|}
\hline Height(cm) & 100 & 120 & 150 & 160 & 170 & 180 \\
\hline Number of players & 3 & 6 & 2 & 5 & 10 & 4 \\
\hline
\end{tabular}
A \( .151 \mathrm{cm} \)
B. \( 149 \mathrm{cm} \)
\( \mathbf{C} \cdot 148 \mathrm{cm} \)
D. \( 150 \mathrm{cm} \)


The viruses which can cause bacterial
diseases are called
A. Slime moulds
B. Smuts
c. Bacteriophages
D. Bacteriomosaics


The emf induced in the circuit is :
\( \mathbf{A} \cdot 2 \pi a^{2} B_{0} \)
B . \( \pi a^{2} B_{0} \)
c. \( \frac{a^{2} B_{0}}{2} \)
D. \( \frac{\pi a^{2} B_{0}}{2} \)


0
0
0
\( \frac{0}{0} \)


The G.M. of first n natural numbers is
A \( \cdot \frac{n+1}{2} \)
в. \( (n !)^{n} \)
\( \mathbf{c} \cdot(n !)^{1 / n} \)
D. None of these


If \( A \) is a square matrix of order 3 such
that \( |\boldsymbol{a} \boldsymbol{d} \boldsymbol{j} \cdot \boldsymbol{A}|=\boldsymbol{3} \boldsymbol{6}, \) find \( |\boldsymbol{A}| \)


\( 5 \% \) income of \( A \) is equal to \( 15 \% \) income of \( \mathrm{B} \) and \( 10 \% \) income of \( \mathrm{B} \) is equal to \( 20 \% \) income of \( C . \) If the income of \( C \) is
Rs.2000, then find the total income of \( A \)
B and C.


Which of the following is in the form of
A.P.?
в. \( 0,3,2,1,-2 \ldots \)
c. 4,5,7,10,14
D. \( -2,2,-2,2,-2 \dots \)


Match column I with column II:
List List II
Magnus energy Pascal's Law
Loss of Archimedes' Energy
Pressure is same at same \( \quad \) Viscous force level in a liquid
Lifting of Hydraulic Machines
\( \mathbf{A} \cdot \mathbf{B} \rightarrow 4, \mathbf{C} \rightarrow 2, D \rightarrow 1, A \rightarrow 1 \)
B. \( A \rightarrow 4, B \rightarrow 3, C \rightarrow 1, D \rightarrow 1 \)
C. \( \mathrm{C} \rightarrow 4, \mathrm{A} \rightarrow 2, \mathrm{B} \rightarrow 1, \mathrm{D} \rightarrow 1 \)
D . \( D \rightarrow 4, A \rightarrow 2, B \rightarrow 1, C \rightarrow 1 \)


Let the sum of the series \( \frac{1}{1^{3}}+ \) \( \frac{1+2}{1^{3}+2^{3}}+\ldots . .+\frac{1+2+\ldots .+n}{1^{3}+2^{3}+\ldots . .+n^{3}} \)
upto \( n \) terms be \( S_{n}, n=1,2,3, \dots . . \)
Then \( S_{n} \) cannot be greater than
This question has multiple correct options
A \( \cdot \frac{1}{2} \)
B.
c. 2
D. 4


Which of the following plants in Brassicaceae family have two stamens in flower?
A. Raphanus
B. Nasturtium
c. coronopus
D. Brassica


If \( a-b=7, a b=8, \) find \( a^{2}+b^{2} \)


If \( f(x)=\max \left\{\sin x, \cos x, \frac{1}{2}\right\}, \) then the
area of the region bounded by the
curves \( \boldsymbol{y}=\boldsymbol{f}(\boldsymbol{x}), \boldsymbol{x}- \) axis \( \boldsymbol{y}- \) axis and
\( \boldsymbol{x}=2 \pi \) is
\( ^{\mathbf{A}} \cdot\left(\frac{5 \pi}{12}+3\right) \cdot \) sq.unit
в. \( \left(\frac{5 \pi}{12}+\sqrt{2}\right) \). sq.unit
c. \( \left(\frac{5 \pi}{12}+\sqrt{3}\right) \cdot \) sq.unit
D \( \cdot\left(\frac{5 \pi}{12}+\sqrt{2}+\sqrt{3}\right) \cdot \) sq.unit


Argyrol is a:
A. Ferric oxide sol
B. Silver sol
c. Gold sol
D. Arsenic sol


Both soap and detergent are some type of salts. What is the difference between them? Describe in brief the cleansing
action of soap. Why do soaps not form lather in hard water? List two problems that arise due to the use of detergents
instead of soaps.


A thick shell with inner radius \( R \) and
outer radius \( 3 R \) has a uniform charge
density \( \sigma c / m^{3} . \) It has a spherical cavity of radius \( R \) as shown in the figure. the
electric field at the centre of the cavity is
A . zero
в. \( 2 \sigma R / \varepsilon_{0} \)
c. \( 3 \sigma R / 4 \varepsilon_{0} \)
D. \( 7 \sigma R / 12 \varepsilon_{0} \)


A swimming pool is \( 24 \mathrm{m} \) long and \( 15 \mathrm{m} \) broad When a number of men dive into
the bath the height of water rises by 1
\( \mathrm{cm} \) If the average volume of water displaced by each man be \( 0.1 m^{3} \) how
many men are there in the bath?
\( A \cdot 32 \)
B. 36
c. 42
D. 46


Evaluate \( \int\left(\frac{x^{2}+3 x+4}{\sqrt{x}}\right) d x \)


Which of the following is polar aprotic solvent?
A. DMSO
B. Crown ether
c. DMF
D. All of these


Identify the category of drug which is used to relieve pain.
A. Analgesic
B. Antibiotic
c. Anticoagulant
D. Antidiuretic


Akhtar, Kiran and Rahul were riding in a motorcar that was moving with a high velocity on an expressway when an insect hit the windshield and got stuck on the windscreen. Akhtar and Kiran
started pondering over the situation. Kiran suggested that the insect
suffered a greater change in momentum as compared to the change in momentum of the motorcar(because
the change in the velocity of the insect was much more than that of the
motorcar). Akhtar said that since the
motorcar was moving with a larger
velocity, it exerted a larger force on the insect. And as a result the insect died.
Rahul while putting an entirely new explanation said that both the motorcar and the insect experienced the same force and a change in their momentum. Comment on these suggestions.


Assertion
Boron always forms covalent bond.
Reason
The small size of \( B^{3+} \) favours
formations of covalent bond.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A \( 40 \mathrm{cm} \) long wire having a mass \( 3.2 \mathrm{gm} \)
and area of c.s \( 1 \mathrm{mm}^{2} \) is stretched
between the support \( 40.05 \mathrm{cm} \) apart. In its fundamental mode. It vibrate with a
frequency \( 1000 / 64 H z . \) Find the young's
modulus of the wire.
A \( \cdot 1 \times 10^{9} \mathrm{Nm}^{2} \)
B . \( 2 \times 10^{9} \mathrm{Nm}^{2} \)
c. \( 1 \times 10^{8} \mathrm{Nm}^{2} \)
D. \( 4 \times 10^{9} \mathrm{Nm}^{2} \)


Which term of the following sequence \( \mathbf{2}, \mathbf{2} \sqrt{\mathbf{2}}, \mathbf{4}, \ldots \) is \( \mathbf{1 2 8} ? \)


If three lines are chosen at random,
prove that they are just likely as not to denote the sides of a possible triangle.


If the terminal of a gold-leaf electroscope is grounded by touching it with a finger,
A. the gold leaves spread apart in a 'v"
B. the gold leaves close together.
c. there is no effect on the gold leaves.
D. None of the above


\( \angle H A C \)


The simplification of \( \cos (A+ \)
\( B) \cos (A-B) \) is equivalent to:
A \( \cdot \sin ^{2} A-\sin ^{2} B \)
B. \( \cos ^{2} B-\sin ^{2} A \)
\( \mathbf{c} \cdot \cos ^{2} A-\cos ^{2} B \)
D. \( \cos 2 A \cdot \sin 2 B \)


If \( \frac{1}{2}\left(e^{y}-e^{-y}\right)=x, \) prove that
\( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\frac{1}{\sqrt{\boldsymbol{x}^{2}+\mathbf{1}}} \)


Assertion
\( P h-C H_{3} O \) undegoes nitration faster
\( \operatorname{than} \boldsymbol{P h}-\boldsymbol{S}-\boldsymbol{C H}_{3} \)
Reason
\( \boldsymbol{C H}_{3} \boldsymbol{O}- \) group has greater -I effect then \( \boldsymbol{C H}_{3}-\boldsymbol{S}- \) group.
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 \( f(x)=2, g(x)=x^{2}, h(x)=2 x, \forall x \in \)
\( \boldsymbol{R} \) then find \( (\boldsymbol{f}(\boldsymbol{g}(\boldsymbol{h}(\boldsymbol{x})))) \)


In which of the following compound three chlorine atoms are present?
A. Phosgene
B. Dichloromethane
c. DDT
D. chlroform


Which of the following sulphides can
not be reduced to metal by \( H_{2} \) at about
\( \mathbf{1 0 0 0}^{\circ} \mathbf{C} ? \)
A. Нg S
в. \( P b S \)
с. \( B i_{2}, S_{3} \)
D. All of these


If \( y=e^{x} \sin x, \) then find \( \frac{d y}{d x} \)
A \( \cdot e^{x}(\sin x+\cos x) \)
B . \( e^{x}(\sin x-\cos x) \)
\( \mathbf{c} \cdot e^{x} \sin x \)
D. None of these


toppr
5
Q Type your question
\( B \)
\( \mathbf{C} \)
\( D \)


The surface of a table is smoother as
compared to that of a road. This is due
to:
A. irregularities in the surface of road
B. polishing of the table
c. a road surface may have more dust as compared to table
D. all of the above


A Funtion \( f \) is defined as \( f(x)= \) \( \frac{x^{2}-4 x+3}{x^{2}-1} \) for \( x \neq 1,=2 \) for \( x=1 \) Is
the function continuous at \( x=1 . ? \)
A . True
B. False


The structure shows:
A. geometrical isomerism
B. optical isomerism
c. geometrical and optical isomerism
D. tautomerism


The reaction \( : \boldsymbol{C a} \boldsymbol{C O}_{3}(\boldsymbol{g}) \rightleftharpoons \)
\( \boldsymbol{C a O}(s)+\boldsymbol{C O}_{2}(\boldsymbol{g}), \) would proceed to
completion if the reaction vessel is
connected to bottle containing \( K O H \)
solution or carried out in open vessel. If true enter \( 1, \) if false enter 0


An electric bulb has a rated power of \( 50 W \) at \( 100 V . \) If it is used on an \( A C \)
source \( 200 V, 50 H z, \) a choke has to be
used in series with it. This choke should
have an inductance of
\( \mathbf{A} \cdot 0.01 m H \)
в. \( 1 m H \)
\( c .0 .1 H \)
D. \( 1.1 H \)


The hormone used as an oral
contraceptive is:
A. Aldosterone
B. Cortisone
c. Progesterone
D. Testosterone


If \( \boldsymbol{P}\left(\boldsymbol{E}_{\boldsymbol{k}}\right) \propto \boldsymbol{k} \) for \( \boldsymbol{0} \leq \boldsymbol{k} \leq \boldsymbol{n}, \) then
\( \lim _{n \rightarrow \infty} \sum_{k=0}^{n} P\left(E_{k} \mid A\right) \) equals
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( 1 / 2 \)
c. \( 1 / 6 \)
\( D \)


\( x \)
\( d \)
\( d \)
\( d x \)


Why \( N_{2} \) have double valency \( 3,5 ? \)


The ratio between the number of carbon
atoms and nitrogen atoms in melamine molecule is
A .1: 2
B . 2: 1
c. 2: 3
D. 3: 2


In which book Bentham and Hooker
proposed their classification?
A. Genera Plantarum
B. Species Plantarum
c. Historia Plantarum
D. Historia Nature


Assertion
One faraday of electric charge deposits
weight equal to the electrochemical
equivalent of the substance.
Reason
One faraday deposits one mole of the
substance.
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


Find the value of \( x \)


To reduce the resonant frequency in an
LCR series circuit with a generator
A. the generator frequency should be reduced.
B. another capacitor should be added in parallel to the first.
C. the iron core of the inductor should be removed.
D. dielectric in the capacitor should be removed


\( A B C D \) is a cyclic quadrilateral such
that \( A B \) is a diameter of the circle
circumscribing it and \( \angle A D C=140^{\circ} \)
then \( \angle B A C \) is equal to
\( A \cdot 80 \)
B. \( 50^{\circ} \)
\( c \cdot 40^{\circ} \)
D. \( 30^{\circ} \)


Which among the following oxides of nitrogen on dissolution in water produces an acid which can act as both oxidising and reducing agents?
A . \( N O \)
B. \( N_{2} O_{3} \)
c. \( N_{2} O_{5} \)
D. \( N O_{2} \)


Consider the points \( \boldsymbol{P}(\mathbf{2},-\mathbf{4}) ; \boldsymbol{Q}(\mathbf{4},-\mathbf{2}) \boldsymbol{a} \boldsymbol{n} \boldsymbol{d} \boldsymbol{R}(\mathbf{7}, \mathbf{1}) . \) The
points P,Q,R
A. form an equilateral triangle
B. form a right angled triangle
c. form an isosceles triangle which is not equilateral
D. are collinear


In Korper-Kappe theory,
A. Korper refers to mantle and kappe to body
B. Korper is cortex while kappe is cap
C. Korper is calyptrogen while kappe is rest of the mreistem
D. Korper is equivalent to corpus and kappe to tunica


Let \( \boldsymbol{A}=\{1,2,3,4,5,6\} . \) Let \( R \) be a relation on \( A \) defined by \( R=\{(a, b) \)
\( a, b \in A, b \text { is exactly divisible by a }\} \) Find
the range of \( R \)


\( (3-\sqrt{7})(3+\sqrt{7})= \)
\( \mathbf{A} \cdot \mathbf{4} \)
B . 2
\( c \cdot 6 \)
D. 8


The instability of the nucleus can be due to various cause.An unstable
nucleus emits radiations if possible to transform into less unstable state.Then
the cause and the result can be
This question has multiple correct options
A. a nucleus of excess nucleons is \( \alpha \) active
B. an excited nucleus of excess protons is \( \beta^{-} \) active
C. an excited nucleus of excess protons is \( \beta^{+} \) active
D. an nucleus of excess neutrons is \( \beta^{-} \) active


A voltmeter has a resistance of \( G \) ohms
and range \( V \) volts. The value of
resistance required in series to convert
it into voltmeter of range \( n V \) is
A \( . n G \)
в. \( G / n \)
c. \( G /(n-1) \)
D. \( (n-1) G \)


\( \ln a \Delta A B C, \) if \( \cos A \cos B \cos C=\frac{\sqrt{3}-1}{8} \)
and \( \sin A \sin B \sin C=\frac{3+\sqrt{3}}{8}, \) then
The value of \( \tan A \tan B+\tan B \tan C+ \)
\( \tan C \tan A \) is


Which compound on heating alone
does not form \( O_{2} ? \)
A \( . K C l O_{4} \)
B. \( K M n O_{4} \)
c. \( K N O_{3} \)
D. \( N H_{4} N O_{2} \)


(a) Obtain an expression for the energy stored in a solenoid of self-inductance
\( L^{\prime} \) when the current though it grows from zero to \( ^{\prime} I^{\prime} \)
(b) A square loop MNOP of side \( 20 \mathrm{cm} \) is placed horizontally in a uniform magnetic field acting vertically downwards as shown in the figure. The loop is pulled with a constant velocity of \( 20 \mathrm{cm} s^{-1} \) till it goes out of the field
(i) Depict the direction of the induced current in the loop as it goes out of the field. For how long would the current in the loop persist?
(ii) Plot a graph showing the variation of magnetic flux and induced emf as a function of time.
\[
x \times x \times x \times x \times x
\]


Three condensers are connected as
shown in series. If the insulated plate of
\( C_{1} \) is at \( 45 V \) one plate of \( C_{3} \) is earthed
find the p.d between the plate of \( C_{2} \)
A . \( 10 V \)
B . \( 20 V \)
\( c .30 V \)
D. \( 45 V \)


Find the derivative of
\( \frac{2}{x+1}-\frac{x^{2}}{3 x-1} \)


Give reasons for the following:
Hydrogen chloride gas cannot be dried over quick lime.


The diagram alongside shows the
refraction of a ray of light from air to a liquid. Angle of incidence is :
A . \( 30^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 90 \)
D. 60


For the ellipse \( 12 x^{2}+4 y^{2}+24 x- \)
\( \mathbf{1 6} \boldsymbol{y}+\mathbf{2 5}=\mathbf{0} \)
A. centre is (-1,2)
B. Length of axes are \( \sqrt{3} a n d 1 \)
\( ^{\mathrm{c}} \cdot_{\text {eceentricity is }} \sqrt{\frac{2}{3}} \)
D. All of these


Which one of the following is smallest in size ?
A . \( N^{-3} \)
B. \( O^{-2} \)
\( c \cdot F^{-} \)
D. \( N a^{\text {t }} \)


Which of the following are the examples of atmospheric pressure?
A. Fountain bottle
B. Ping pong funnel
c. Million dollar bet
D. All of the above


Rest mass energy of an electron is 0.54
MeV. If velocity of the electron is \( 0.8 \mathrm{C} \) then its kinetic energy will be:
A. \( 0.36 \mathrm{MeV} \)
B. 0.41 Mev
c. 0.48 Mev
D. 1.32 MeV


Which of the following acts as a biological catalyst?
A. Lipids
B. Proteins
c. carbohydrages
D. Nucleic acids


Which of the following alcohols is the least soluble in water?
A. Ethanol
B. 1-Propanol
c. 1-Butanol
D. 1-Pentanol


The correct set of carbonate ore is:
(a) Magnesite
(b) Siderite
(c) Zincite
(d) Argentite
\( A \cdot a, b \)
B. a, d
\( c \cdot c, d \)
\( D \cdot b, c \)


If \( |x|<1 \) then the coefficient of \( x^{n} \) in
expansion of \( \left(1+x+x^{2}+x^{3} \dots\right)^{2} \) is
\( A \)
B . \( n-1 \)
\( \mathbf{c} \cdot n+2 \)
\( \mathbf{D} \cdot n+1 \)


A sphere of mass \( M \) and radius \( r \)
shown in the figure, slips on rough
horizontal plane. At some instant it has
translational velocity \( v_{0} \) and rotational
velocity about centre \( \boldsymbol{v}_{\mathbf{0}} / 2 \boldsymbol{r} . \) The
percentage change of translational
velocity after the sphere start pure
rolling:
A. \( 14.28 \% \)
B . \( 7.14 \% \)
c. \( 21.42 \% \)
D. None


Which is the anhydride of orthosilicic
acid?
\( A \cdot s i \)
B. Sio
\( \mathrm{c} \cdot \operatorname{si0}_{2} \)
D. \( \operatorname{si} 0_{3} \)


Convert the following ratio to
percentage
4: 5


According to lac operon concept, an
operator gene combines with
A. Co-repressor to switch off transcription of structural gene
B. Inducer gene to switch on structural gene transcription
C. Repressor gene to switch off transcription of structural gene
D. Regulator protein to switch on structural gene transcription
E. Regulator protein to switch off structural gene transcription


Density of equilibrium mixture of \( N_{2} O \)
and \( N O_{2} \) at 1 atm and 384 Kis
\( 1.84 g / d m^{3} . \) Equilibrium constant of the following reaction is:
\( N_{2} O_{4} \rightleftharpoons 2 N O_{2} \)
A. 1.98 atm
B. 2.09 atm
c. 2.36 atm
D. 1.48 atm


f \( 2 x+y=9 \) and \( 3 x-y=6 \) then find
the value of \( x \)


The eccentricity of the hyperbola whose latus-return is 8 and length of the conjugate axis is equal to half the distance between the foci, is
A \( \cdot \frac{4}{3} \)
B. \( \frac{4}{\sqrt{3}} \)
c. \( \frac{2}{\sqrt{3}} \)
D. None of these


Integrate the following \( \int \frac{x^{2}}{(x \sin x+\cos x)^{2}} d x \)


An electric heater of power 3 kW is used for one minute.Find the energy supply by the heater.


Which of the following are correct for the given diagram?
This question has multiple correct options
A. \( \Delta H_{3}=\Delta H_{1}+\Delta H_{2} \)
В. \( \Delta H_{1}=0 \)
C. \( \Delta H_{2}=\left(C_{\text {calorimeter}}+C_{\text {produt} t}\right) \times\left(T_{1}-T_{2}\right) \)
D. \( \Delta H_{2}=\left(C_{\text {clorimeter}}+C_{\text {produc} t}\right) \times\left(T_{2}-T_{1}\right) \)


The D.E whose solution in \( y=c e^{x} \) is?
A \( \cdot y_{1}=y^{2} \)
В. \( y_{2}=y_{1} \)
c. \( y_{1}=y \)
D. \( y_{1}+y=0 \)


Calculate mean deviation about
median
\begin{tabular}{lllll}
Scores & 145 & 155 & 165 & 175 \\
Frequency & 4 & 6 & 10 & 18 \\
\hline
\end{tabular}
A. 11.56
B. 6.66
c. 11.25
D. 10.56


\( \operatorname{Let} \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}} \boldsymbol{F}(\boldsymbol{x})=\frac{\boldsymbol{e}^{\boldsymbol{s} \boldsymbol{m} \boldsymbol{x}}}{\boldsymbol{x}}, \boldsymbol{x}>\mathbf{0} \)
\( \int_{1}^{4} \frac{\mathbf{3}}{\boldsymbol{x}} \boldsymbol{e}^{s \boldsymbol{m} \boldsymbol{x}^{3}} \boldsymbol{d} \boldsymbol{x}=\boldsymbol{F}(\boldsymbol{k})-\boldsymbol{F}(1), \) then one
of the possible values of \( k \) is
A . 16
B. 62
c. 64
D. 15


solve \( \boldsymbol{a}^{\boldsymbol{7}}+\frac{\mathbf{1}}{\boldsymbol{a}^{\boldsymbol{9}}}=? \)


Median of the following freq. dist.
\( \boldsymbol{x}_{i} \quad \boldsymbol{3} \quad \boldsymbol{6} \) \( \mathbf{1 2} \) \( \mathbf{1 0} \)
\( f_{i} \quad 3 \quad 4 \quad 2 \) 13
\( A \cdot 7 \)
B. 10
c. 8.5
D. None of these


Given below are some points, with thei
\( \boldsymbol{P}(\mathbf{4}, \mathbf{3}), \boldsymbol{Q}(-\mathbf{3}, \mathbf{2}), \boldsymbol{R}(\mathbf{5}, \mathbf{1}), \boldsymbol{S}(\mathbf{0},-\mathbf{4}) \)
What is the \( x- \) coordinate of point \( P \)
\( ? \)


In case of a real and inverted image, the magnification created by the mirror is
A. positive
B. negative
c. unity
D. infinity


Balance the following equations by ion
electron method:
\( \boldsymbol{C l}_{2}+\boldsymbol{I O}_{3}^{-}+\boldsymbol{O H}^{-} \rightarrow \boldsymbol{I} \boldsymbol{O}_{4}^{-}+\boldsymbol{C l}^{-}+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O} \)


Commercial product "Agar" which is used in " ice creams" and to grow microbes in the laboratory is extracted from
A. Laminaria and Ploysiphonia
B. Porphyra and Sargassumm
c. Gelidium and Gracilaria
D. Marchantia and Polytrichum


For the adsorption of a gas on a solid, the plot of \( \log (x / m) \) versus log \( P \) linear with slope equal to:
\( A \cdot K \)
B. \( \log k \)
c.
D.


Define the following terms:
Kinetic energy.


By what number should \( \left(\frac{-2}{3}\right)^{-3} \) be divided so that the quotient may be \( \left(\frac{4}{27}\right)^{-2} \)


(a) In an experiment Griffith introduced heat-killed S-strain bacteria
Streptococcus into a mouse along with live R-strain bacteria. The mouse died
but the scientist recovered living \( \mathrm{S} \) strain bacteria from the dead mouse
Explain the conclusion Griffith arrived at after the experiment.
(b) Explain MacLeod, McCarty and Averys work that followed Griffith's experiment. State the conclusion they arrived at.


a flywheel is in the form of a solid circular wheel of mass \( 72 \mathrm{kg} \) and radius \( 50 \mathrm{cm} \) and it makes 70 r.p.m. then the energy of revolution is:
A. 245534 J
B. 24000 J
c. 4795000
D. 4791600 J


Match the columns
\begin{tabular}{lll|l}
Column I & \multicolumn{3}{c} { Column II } \\
a & Arachis & 1. & Swollen placenta \\
b & Cichorium & 2. & Epicalyx \\
c & Lilium & 3. & Fasciculate tuberous root \\
d & Physalia & 4. & Geocarpy \\
& 5. & Bulbils
\end{tabular}
\( \mathbf{A} \)
\( a-4, b-3, c-2, d-5 \)
B. \( a-4, b-1, c-2, d-3 \)
\( \mathrm{C} \cdot \mathrm{a}-5, \mathrm{b}-4, \mathrm{c}-3, \mathrm{d}- \)
D. \( a-4, b-3, c-5 \) \( d- \)


Which of the following is the resulting product at anode when electrolysis of a dilute solution of sodium chloride
occurs?
A. Sodium
B. Hydrogen
c. Chlorine
D. oxygen
E . Peroxide


The energy of first excited state of \( L i^{2+} \)
will be:
A . 13.6 ev
B. 27.2 ev
c. 30.6 ev
D. 40.8 ev


Represent the galvanic cell in which the reaction takes place. \( \boldsymbol{Z} \boldsymbol{n}(\boldsymbol{s})+\boldsymbol{C u}^{2+}(\boldsymbol{a q}) \rightarrow \boldsymbol{Z} \boldsymbol{n}^{2+}(\boldsymbol{a q})+ \)
\( \boldsymbol{C u}(\boldsymbol{s}) \)


When an inert atmosphere is needed for a metallurgical process, nitrogen is frequently used. However, in the
reduction of \( T i C l_{4} \) by magnesium,
helium is used. This is because \( N_{2} \) can
combine with


Which combination will give the strongest covalent bond?
A \( \cdot K^{+} \) and \( C l^{-} \)
B. \( K^{+} \) and \( O^{2} \)
c. \( C a^{2+} \) and \( C l^{-} \)
D. \( C a^{2+} \) and \( O^{2} \)


In the stress -strain curve shown, the
metal is
A. Highly Ductile
B. Highly Brittle
c. Highly magnetic
D. Highly chargeable


An increase in pressure in the reaction
\( 2 H I(g) \rightleftharpoons H_{2}(g)+I_{2}(g) \) would :
A. produce more \( I^{-}(a q) \)
B. produce more \( H_{2} \)
c. not effect the system
D. drive it to the right


\( f(x)=\cot ^{-1}\left(\frac{x^{x}-x^{-x}}{2}\right) \) then \( f^{1}(1)= \)
\( \mathbf{A} \cdot-\log 2 \)
B. \( \log 2 \)
\( c \cdot 1 \)
D. -


Construct a \( \triangle A B C \) in which \( A B= \)
\( \mathbf{5} c \boldsymbol{m} \cdot \angle \boldsymbol{B}=\mathbf{6 0}^{\circ} \) altitude \( \boldsymbol{C} \boldsymbol{D}=\mathbf{3} \boldsymbol{c m} \)
Construct a \( \triangle A Q R \) similar to \( \triangle A B C \)
such that side of \( \triangle A Q R \) is 1.5 times
that of the corresponding sides of
\( \triangle \boldsymbol{A} \boldsymbol{C} \boldsymbol{B} \)


Animals which have well developed echolocation system like that of bats
are
A. Wild cats
B. Beavers
c. Primates
D. Whales and dolphins
E. Hedgehogs


Illustrate a condition in which :
Electric field is not zero but potential is
zero


The main constituents of dettol are:
A. chloramphenicol and glycerol
B. 2-3\% solution of iodine in alcoho
c. \( 0.2 \% \) solution of pheno
D. chloroxylenol and terpineol


\( 0.4 g \) of \( \mathrm{NaOH} \) is present in one litre of
the solution shows that \( \boldsymbol{H}^{+} \)
concentration of the solution is?


For making atom bomb, what else is
needed except \( U^{235} ? \)
A. neutron
B. proton
C . electron
D. meson


The branch of science that deals with
the study of universe is called:
A. Anthropology
B. Astronomy
c. Geology
D. Universe


Two homogenous spheres \( A \) and \( B \) of
masses \( m \) and \( 2 m \) having radii \( 2 a \) and
\( a \) respectively are placed in touch. The distance of centre of mass from first
sphere is:
\( A \)
B . \( 2 a \)
\( c .3 a \)
D. \( 3 a / 2 \)


Solve :
\( \int \frac{u}{v} d x \)


\( \mathbf{f} \mathbf{3}\left[\begin{array}{ll}\mathbf{4} & \mathbf{2} \\ \mathbf{1} & \mathbf{3}\end{array}\right]-\mathbf{2}\left[\begin{array}{cc}-\mathbf{2} & \mathbf{1} \\ \mathbf{3} & \mathbf{2}\end{array}\right]+\left[\begin{array}{ll}\boldsymbol{x} & -\mathbf{4} \\ \mathbf{3} & \boldsymbol{y}\end{array}\right]= \)
0 then \( (x, y)= \)
\( \mathbf{A} \cdot(165) \)
В. \( (5 ~ 16) \)
c. \( (-16-5) \)
\( \mathbf{D} \cdot(-5-16) \)


What is the volume occupied by \( 3 X \) molecules of \( C O ? \)
\( A \cdot v \)
B. 3v
c. v/3
D. \( 6 v \)


Which of the following statement is
correct?
A. Cell membrane is involved only in exosmosis
B. Cell membrane is involved only in endosmosis.
c. Cell membrane is involved both in exosmosis and endosmosis
D. None of the above.


The equation of line with slope \( \frac{5}{4} \) nd passing through (8,4)


The waves related to tele-
communication are
A. infrared
B. visible light
c. microwaves
D. ultraviolet rays


The order of reactivities of methyl
halides in the formation of Grignard
reagent is :
A. \( C H_{3} I>C H_{3} B r>C H_{3} C l \)
в. \( C H_{3} C l>C H_{3} B r>C H_{3} I \)
c. \( C H_{3} B r>C H_{3} C l>C H_{3} I \)
D. \( C H_{3} B r>C H_{3} I>C H_{3} C l \)


A body of mass \( 5 \mathrm{kg} \) undergoes a change in speed from 30 to \( 40 \mathrm{m} / \mathrm{s} \). Its
momentum would increase by:
A. \( 50 \mathrm{kgm} / \mathrm{s} \)
B. \( 75 \mathrm{kgm} / \mathrm{s} \)
c. \( 150 \mathrm{kgm} / \mathrm{s} \)
D. \( 350 \mathrm{kgm} / \mathrm{s} \)


Chemically inert halide of sulphur is:
A \( \cdot S C l_{2} \)
в. \( S F_{2} \)
c. \( S F_{4} \)
D. \( S F_{6} \)


Which of the following has maximum hydrogen bonding?
A. Ethyl amine
B. Ammonia
c. Ethanol
D. Diethyl ether


Find the magnitude of a charge which produces an electric field of strenght is
\( 18 \times 10^{3} N C^{-1} \) at a distance of \( 5 \mathrm{m} \) in
air.
A. \( 50 \mu c \)
B. \( 100 \mu c \)
\( c \cdot 25 \mu c \)
D. 250 \muc


If \( \tan 2 A=\cot (A-18), \) where \( 2 A \) is an
acute angle, then find the value of \( \boldsymbol{A} \)


The brain capacity of Homo erectus was
about
\( \mathbf{A} \cdot 650 c . c \)
B . 900 c.c.
c. 1500 c.c.
D. 1400 c.c.


How can we get compound X back from
Y? Name the process.
A. Saponification
B. Esterification
c. Carbonification
D. Hydrogenation


Poor conductors of electricity is/are:
A. Silver
B. Aluminium
c. Pure water
D. copper


\( A \) and \( B \) are seeking admission into
IIT. If the probability for \( A \) to be
selected is 0.5 and that both to be
selected is \( 0.3, \) them is it possible that,
the probability of \( B \) to be selected is 0.9
\( ? \)


Differentiate between Starch and
Glucose.


Determine the force acting on a body if the velocity of the body is changed from \( 5 m s^{-1} \) to10 \( m s^{-1} \) in 2 s. The density
and the volume of the object are \( \mathbf{5 0 0 0 k g} \boldsymbol{m}^{-3} \boldsymbol{a n d} \quad \mathbf{0 . 0 0 5} \boldsymbol{m}^{3} \)
\( \mathbf{A} \cdot 100 \mathrm{N} \)
B. 65.5 N
c. \( 32.5 \mathrm{N} \)
D. 62.5 N


In the potentiometer arrangement
shown, the driving cell D has emf E and
internal resistance r. The cell C, whose
emf is to be measured, has emf E/2 and
internal resistance 2r. The
potentiometer wire is \( 100 \mathrm{cm} \) long. If balance is obtained, the length \( \boldsymbol{A} \boldsymbol{J}=\boldsymbol{l} \)
This question has multiple correct options
\( \mathbf{A} \cdot l=50 \mathrm{cm} \)
\( \mathrm{B}, \quad \mid>50 \mathrm{cm} \)
C. balance will be obtained only if resistance of AB is \( >r \)
D. balance cannot be obtained


The decomposition of \( \boldsymbol{K} \boldsymbol{C l} \boldsymbol{O}_{3} \) to \( \boldsymbol{K} \boldsymbol{C l} \)
and \( O_{2} \) on heating is an example of :
A. intermolecular redox change
B. intramolecular redox change
c. disproportionation or auto redox change
D. None of the above


A metal surface is illuminated by light
of two different wavelengths \( 248 n m \)
and \( 310 n m . \) The maximum speeds of
the photoelectrons corresponding to
these wavelengths are \( u_{1} \) and \( u_{2} \)
respectively. If the ratio \( u_{1}: u_{2}=2: 1 \)
and \( h c=1240 e V n m, \) the work
function of the metal is nearly:
\( \mathbf{A} \cdot 3.7 \mathrm{eV} \)
B. \( 3.2 e V \)
c. \( 2.8 e V \)
D. \( 2.5 e V \)


Show that \( \left|\begin{array}{ccc}\mathbf{1} & \mathbf{1} & \mathbf{1} \\ \boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} \\ \boldsymbol{a}^{2} & \boldsymbol{b}^{2} & \boldsymbol{c}^{2}\end{array}\right|=(\boldsymbol{a}-\boldsymbol{b})(\boldsymbol{b}- \)
\( c)(c-a) \)


Which of the following statements are
correct?
This question has multiple correct options
A. The process of producing a hard coating of iron nitride on the surface of steel is called nitriding.
B. The process of producing a thin coating of iron carbide on the surface of mild steel is called case hardening.
C. Quenched steel is produced by healing steel to redness and allowing it to cool slowly.
D. Stainless steel is produced by heating wrought iron in molten chromium,


At \( 27^{\circ} C \) a gas is compressed suddenly such that its pressure becomes \( \left(\frac{1}{8}\right) \) th of original pressure. Final temperature will be \( (\gamma=5 / 3) \)
\( \mathbf{A} \cdot 450 K \)
B. \( 300 K \)
c. \( -142^{\circ} \mathrm{C} \)
D. \( 327^{\circ} \)


The metal used as a catalyst in the hydrogenation of oils is:
A. sodium
B. nickel
c. mercury
D. manganese


A charge ' \( q \) ' is placed exactly mid way between two charges 'Q' and ' \( Q \) ' separated by a distance \( 2 r \) in air. The
force on the charge ' \( q \) ' is :
A. \( \frac{2 Q}{4 \pi \epsilon_{0} r^{2}} \)
в. \( \frac{Q}{4 \pi \epsilon_{0} r^{2}} \)
c. \( Z e r o \)
D. \( \frac{5 Q}{4 \pi \epsilon_{0} r^{2}} \)


Find the domain on which the function
\( f(x)=2 x^{2}-5 \) and \( g(x)=5 x-2 \) are
equal
A \( \cdot_{3,-\frac{1}{2}} \)
в. \( -3,-\frac{1}{2} \)
c. \( _{3, \frac{1}{2}} \)
D. \( _{-3, \frac{1}{2}} \)


Find the ratio of speed of B with \( \mathbf{A} \) \( \left(i . e \frac{V_{B}}{V_{A}}\right) \) when all collisions end :
\( A \)
B. 2
\( c \cdot 3 \)
\( D \)


A transition metal complex adopts \( t_{2} g^{4} e g^{2} \) configuration. The nature of ligand surrounding the ion is :-
A. Strong field
B. weak field
c. neutral
D. \oplus \( \oplus \)vefield