Which of the following atoms does the electron configuration \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{2} \) represent?
A. An excited state \( C a \) atom
B. A ground state \( C a \) atom
c. An excited state \( S c \) atom
D. An excited state \( K \) atom


The triangle formed by the lines \( x- \)
\( 7 y+12=0,7 x+y-16=0 \) and
\( \mathbf{3} \boldsymbol{x}+\mathbf{4} \boldsymbol{y}=\mathbf{0} \) is right-angled triangle
A. True
B. False


Enumerate the salient features of
bryophytes.


Show that sequence of following \( n^{t h} \)
terms, are not in A.P. \( \frac{n}{n+1} \)


One of the following is an exception to the 'cell theory'.
A. Bacteria
B. Fungi
c. virus
D. Lichens


Identify the following substances which are underlined:
A dilute mineral acid which forms a
white precipitate when treated with barium chloride solution.


If \( A, B \) and \( C \) are three events, then
This question has multiple correct options
A \( . P(\text { exactly two of } A, B, C \text { occur }) \leq P(A \cap B)+P(B \cap \)
\( C)+P(C \cap A) \)
B \( . P(A \cup B \cup C) \leq P(A)+P(B)+P(C) \)
C. \( P(\text { exactly one of } A, B, C \text { occur }) \leq P(A)+P(B)+ \)
\( P(C)-P(B \cap C)-P(C \cap A)-P(A \cap B) \)
D. \( P(A \text { and at least one of } B, C \text { occurs }) \leq P(A \cap B)+ \)
\( P(A \cap C) \)


In birds, males carry two identical sex chromosomes \( (\mathrm{ZZ}) \) and females carry two different sex chromosomes \( (\mathrm{ZW}) . \) A
gene in parakeets called cinnamon is
sex-linked recessive on the \( z \)
chromosome.
If a cinnamon male is crossed with a
normal female, what percentage of the offspring will be cinnamon?
A. All of the males only
B. All of the females only
c. All of the offspring
D. None of the offspring


With of the following statements about
Euglena is correct?
A. Euglena is a flagellate organism.
B. Euglena when placed in continuous darkness, loses its photosynthetic activity and dies.
C. The pigments of Eugene are quite different from those of green plants.
D. Euglena is a marine protist.


For some constants \( a \) and \( b \) find the
derivative of
\( \left(a x^{2}+b\right)^{2} \)


\( 100 \mathrm{ml} \mathrm{CuSO}_{4} \) (aq) was electrolyzed using inert electrodes by passing 0.965 A till the \( p H \) of the resulting solution was \( 1 . \) The solution after electrolysis was
neutralized, treated with excess \( K I \)
and titrated with \( 0.04 \mathrm{M} N a_{2} S_{2} O_{3} \)
Volume of \( N a_{2} S_{2} O_{3} \) required was 35
ml. Assume no volume change
during electrolysis. If the initial
concentration \( (\mathrm{M}) \) of \( \mathrm{CuSO}_{4} \) was \( 64 \times \)
\( 10^{-x}, \) then what is the value of \( x ? \)


Complete the following equation:
\( \boldsymbol{C l}_{2}+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \)
A. \( H C l+H C l O \)
в. \( H C l+O_{2} \)
c. \( H C l O+O_{2} \)
D. None of the above


Which of the following triads does not follow Dobereiner's law of triads?
A. \( \mathrm{Li}, \mathrm{Na}, \mathrm{K} \)
B. Ca, Sr, Ba
c. вe, мg, са
D. Cu, Ag, Au


Which of the following is an random
experiment?
This question has multiple correct options
A. Rolling a pair of dice
B. Choosing 2 marbles from a jar
C. Choosing a number at random from 1 to 10
D. Tossing two coins


The ratio in which the line joining points (2,4,5) and (3,5,-4) divide YZ -plane is
\( \mathbf{A} \cdot-2: 3 \)
B. 2: 3
c. -3: 2
D. 3: 2


f \( l= \)
\( \lim _{n \rightarrow \infty} \sum_{r=2}^{n}\left((r+1) \sin \frac{\pi}{r+1}-r \sin \frac{\pi}{r}\right) \)
then find \( \{l\} . \) (where \{\} denotes the
fractional part function


Assertion
Ultrasonic waves are longitudinal waves of frequency grater than \( 20,000 H z \)
Reason
The maximum frequency of audible sound waves is \( 20,000 H z \)
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


Divides and write the quotient and the remainder.
\( \left(6 x^{5}-4 x^{4}+8 x^{3}+2 x^{2}\right) \div 2 x^{2} \)


In human being, secondary constrictions II are found on
A. \( x \) chromosome
B. Y chromosome
c. \( 13,14,15,21, \) 22 chromosome
D. 1,10,13,16 and \( Y \) chromosome


Which of the following is not malleable?
A. Sulphur
B. Selenium
c. Phosphorus
D. All of the above


If \( R s .64 \) amounts to Rs. 83.20 in 2 years
what will Rs.86 amount to in 4 years at
the same rate percent per annum?
\( A \cdot \) Rs 137.60
B. Rs 124.70
c. Rs 114.80
D. Rs 127.40


A plano-convex lens, when silvered at its plane surface is equivalent to a concave mirror of focal length \( 28 \mathrm{cm} \). When its
curved surface is silvered and the plane
surface is not silvered, it is equivalent
to a concave mirror of focal length 10 \( \mathrm{cm}, \) then the refractive index of the
material of the lens is:
\( \mathbf{A} \cdot \frac{9}{14} \)
B. \( \frac{14}{9} \)
c. \( \frac{17}{9} \)
D. None of these


In a Newton's Ring experiment, the diameter of the \( 20^{t h} \) dark ring was
found to be 5.82 mm and that the \( 10 t h \)
ring 3.36 mm. If the radius of the
planoconvex lens is \( 1 m, \) calculate the wavelength of light used


Prove that \( \frac{\tan \mathbf{A}}{\mathbf{1 + \operatorname { s e c } A}}-\frac{\tan A}{\mathbf{1 - \operatorname { s e c } A}}= \)
\( 2 \operatorname{cosec} A \)


What will be the ratio of \( C l^{35} \) and \( C l^{37} \)
respectively in ordinary chlorine if the atomic weight of chlorine is \( 35.5 ? \)
A . 1: 3
B. 3:
c. 1: 2
D. 2:


\( 4.28 \mathrm{g} \) of \( \mathrm{NaOH} \) is dissolved in water and the solution is made to 250 cc. What
will be the molarity of the solution?
A . 0.615 mol \( L^{-1} \)
B. 0.428 mol \( L^{-1} \)
c. 0.99 mol \( L^{-1} \)
D. 0.301 mol \( L^{-1} \)


Increase in the stability of the complex due to presence of multidentate ligands (which causes ring formation) is called chelation effect.
If true enter 1 , else enter 0 .


Pure water is a
of electricity.
A. good
B. badd
c. either could be possible
D. none of the above


For which colour is the fringe width minimum?
A . violet
B. red
c. green
D. yellow


Purine base of DNA molecule has
A. A and
B. c and T
c. A and a
D. None of the above


To determine the Young modulus of a wire, several measurements are taken.
In which row can the measurement not
be taken directly with the stated apparatus?
A. measurement: area of cross-section of wire apparatus : micrometer screw gauge
B. measurement: extension of wire ; apparatus: vernier scale
c. measurement: mass of load applied to wire ; apparatus : electronic balance
D. measurement: original length of wire ; apparatus metre rule


Assertion
\( A l(O H)_{3} \) is amphoteric in nature.
Reason
Al-O and O-H bonds can be broken with
equal ease in \( A l(O H)_{3} \)
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 table below shows the daily expenditure on food of 25 households in a locality.
Daily expenditure (in Rs.) \( \quad \) No. of households
\( 100-150 \)
150-200
200-250
250-300 2
300-350
Find the mean daily expenditure on food by a suitable method.
A . 211
B. 201
c. 215
D. 209


Differentiate between \( ^{\prime} Z Z^{\prime} \) and \( ^{\prime} X Y^{\prime} \)
type of sex-determination mechanisms.


State whether given statement is True or False

A reflective load is a load as it appears
to the source in the primary of a transformer.
A. True
B. False


Find out which of the following sequences are arithmetic progressions. For those which are arithmetic
progressions, find out the common
difference.10 \( +10+2^{5}, 10+2^{6}, 10+ \)
\( \mathbf{2}^{7}, \ldots . . \)


If the radius of a sphere is increased by \( 2 \mathrm{cm}, \) then its surface area increases by
\( 352 c m^{2} . \) The radius of the sphere before
the increase was
A. \( 3 \mathrm{cm} \)
B. \( 4 \mathrm{cm} \)
\( c .5 \mathrm{cm} \)
D. \( 6 \mathrm{cm} \)


Electric potential at a point \( P, r \) distance away due to a point charge \( q \) at \( A \) is \( V \) volts. If twice of this charge is distributed uniformly on the surface of a hollow sphere of radius \( 4 r \) with center
at point \( A, \) the potential at \( P \) now is :
\( A \cdot v \)
B. V/2
\( c \cdot v / 4 \)
D. v/8


Assertion (A): The principal amplitude
of complex number \( \boldsymbol{x}+\boldsymbol{i} \boldsymbol{x} \) is \( \frac{\boldsymbol{\pi}}{\boldsymbol{4}} \)
Reason (R): The principal amplitude of a
complex number \( \boldsymbol{x}+\boldsymbol{i} \boldsymbol{y} \) is \( \frac{\boldsymbol{\pi}}{\boldsymbol{4}} \) if \( \boldsymbol{y}=\boldsymbol{x} \)
A. Both A and R are true and R is the correct explanation of A
B. A is true R is false
c. A is false, R is true
D. Both A and R are false


Leaves of a healthy potted plant were coated with vaseline; will this plant remain healthy for long?


Describe the mass flow hypothesis for translocation of organic solutes (food) in plants. What is the major criticism against this hypothesis?


The passage of an electric current through a conducting solution causes:
A. mechanical effect
B. electrical effect
c. chemical effect
D. all of the above


Let \( f(x) \) be defined by \( f(x)= \) \( \left\{\begin{array}{cl}\sin 2 x & \text { if } 0<x \leq \frac{\pi}{6} \\ a x+b & \text { if } \frac{\pi}{6}<x \leq 1\end{array} . \text { The values of } a\right. \)
and \( b \) such that \( f \) and \( f^{\prime} \) are
continuous, are
A \( \cdot a=1, b=\frac{1}{\sqrt{2}}+\frac{\pi}{6} \)
в. \( a=\frac{1}{\sqrt{2}}, b=\frac{1}{\sqrt{2}} \)
c. \( _{a=1, b}=\frac{\sqrt{3}}{2}-\frac{\pi}{6} \)
D. None of these


The displacement of a particle
executing SMH is given by \( \boldsymbol{x}= \) \( 0.01 \sin 100 \pi(t+0.05) . \) The time
period is
A . 0.01 sec
B. 0.02 sec
c. \( 0.1 \mathrm{sec} \)
D. \( 0.2 \sec \)


A magnetic needle oscillates in a horizontal plane with a period T at a
place where the angle of dip is \( 60^{0} \) When the same needle is made to
oscillate in a vertical plane coinciding with the magnetic meridian, its period will be
A \( \cdot \frac{T}{\sqrt{2}} \)
B. T
c. \( \sqrt{2 T} \)
D. 2T


The instantaneous emf and current
equations of an RLC series circuit are \( e=200 \sin \left(\omega t-\frac{\pi}{6}\right) \)
\( i=20 \sin \left(\omega t+\frac{\pi}{6}\right) \)
The average power consumed per cycle is
A. zero
в. \( 2000 \mathrm{W} \)
c. \( 1000 W \)
D. \( 500 W \)


Imagine a new planet having the same density as that of the earth but it is 3
times bigger than the earth in size. If
the acceleration due to gravity on the
surface of the earth is \( g \) and that on the
new planet is \( g^{\prime} \), then what is the value of \( \frac{\boldsymbol{g}^{\prime}}{\boldsymbol{g}} \)


The vector equation \( \boldsymbol{r}=\boldsymbol{i}-\boldsymbol{2} \boldsymbol{j}-\boldsymbol{k}+ \)
\( t(6 j-k) \) represents a straight line
passing through the points:
A. (0,6,-1) and (1,-2,-1)
в. (0,6,-1) and (-1,-4,-2)
c. (1,-2,-1) and (1,4,-2)
D. (1,-2,-1) and (0,-6,1)


Fluorine does not show positive
oxidation states because:
A. it is most electronegative element
B. it forms only anions in ionic compounds
C. it cannot form multiple bonds
D. it shows non-bonded electron pair repulsion due to small size.


Draw a neat and labelled diagram of
suspended coil type moving coil galvanometer.


A broad source of light \( (1=680 \mathrm{nm}) \) illuminates normally two glass plates \( 120 \mathrm{mm} \) long that touch at end and are separated by a wire \( 0.048 \mathrm{mm} \) in diameter at the other end. The total
number of bright fringes that appear over the \( 120 \mathrm{mm} \) distance is:
A . 50
B. 100
\( c \cdot 141 \)
D. 400


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


Aluminium foil used for wrapping:
A. food
B. clothes
c. plastic
D. wires


Discuss the utility of systematics?


Sum to infinite terms the following series:
\( \mathbf{1}+\mathbf{5} \boldsymbol{x}^{2}+\mathbf{9} \boldsymbol{x}^{4}+\mathbf{1} \mathbf{3} \boldsymbol{x}^{\mathbf{6}}+\ldots .,|\boldsymbol{x}|<\mathbf{1} \)


Solve:
\( \int \frac{\cos x}{6+4 \sin x-\cos ^{2} x} d x \)


Stolonic budding is a characteristic of
A. Porifera and cnidaria
B. Scyphistoma cnidarians and porifera
C. Porifera and tunicates
D. Scyphistoma cnidarians and tunicates


A solid iron ball A of radius \( r \) collids
head on with another stationary solid iron ball \( B \) of radius \( 2 r . \) The ratio of
their speeds just after the collision \( (e=0.5) \) is:
A . 3
B. 4
\( c \cdot 2 \)
D.


The second law of thermodynamics
says that in a cyclic process
A. Work cannot be converted into heat
B. Heat cannot be converted into work
C. Work cannot be completely converted into heat
D. Heat cannot be completely converted into work


If \( n>0, \) prove that \( 2^{n}>1+n \sqrt{2^{n-1}} \)


Write about ocean thermal energy.


The amino acid containing mercaptan
unit is:
A. leucine
B. glutamine
c. cysteine
D. Iysine
E. isoleucine


A current of \( I \) ampere flows through a resistance \( R \) when connected across a
cell of emf \( E \) and internal resistance \( 1 \Omega \)
When \( R \) is increased by \( 50 \% \), the
current through the circuit is \( 0.8 A . \) The
value of \( \boldsymbol{R} \) is :
A . \( 1 \Omega \)
B. \( 1.5 \Omega \)
\( c .2 \Omega \)
D. 4\Omega


Whenever an object moves with a constant speed, its distance - time
graph is a
A. Parabola
B. Straight line, perpendicular to the time axis
c. straight line, parallel to the time axis
D. Straight line passing through origin


Graphite is used in making electrodes because :
A. It has high melting point
B. It a soft and slippery
c. It is a good conductor of electricity
D. none of these


Diamond and boron are soft non-metals.
A. True
B. False


Color of the four strips of carbon
resistor are respectively orange, green golden, silver. Then its resistance is :
\( \mathbf{A} \cdot 2.5 \pm 10 \% \) ohm
B. \( 3.5 \pm 5 \% \) ohm
c. \( 3.5 \pm 10 \% \) ohm
\( \mathbf{D} \cdot 350 \pm 10 \% \) ohm


The statements given below represent
the characteristics of nitrates of
different metals
(a) Nitrate of sodium liberates brown
coloured gas on strong heating.
(b) Nitrate of calcium liberates a pair of colourless gases on strong heating.
(c) Metallic silver can be obtained from
its nitrate on strong heating.
(d) Nitrate of potassium gives a solid product and a colourless gas on strong heating.
Which of the following options is
correct?
A. a and
B. c and d
c. only d
D. only b


One mole of diatomic ideal gas
undergoes a cyclic process \( A B C \) as shown in figure. The process BC is adiabatic. The temperatures at \( A, B \) and
\( \mathrm{C} \) are \( 400 K, 800 K \) and \( 600 K \)
respectively. Choose the correct
statement:
A. The change in internal energy in the process AB is \( -350 R \)
B. The change in internal energy in the process BC is \( -500 R \)
c. The change in internal energy in whole cyclin process is \( 250 R \)
D. The change in internal energy in the process CA is \( 700 R \)


If the percentage error in the edge of a cube is \( 1, \) then error in its volume is
A. \( 1 \% \)
B. 2\%
\( c .3 \% \)
D. none of these


Pitch is \( _{-}-_{-}-_{-}-_{-}-_{-} \) as frequency. Fill in the blank.
A. Same
B. Not the same
c. sometime same sometime different
D. All


Alkali metals dissolve in liquid \( N H_{3} \) then which of the following observation(s) is/are true?
A . \( H_{2} \) gas is liberated
B. Solution is blue due to the presence of solvated electrons
c. solution is conducting
D. All of the above


Which of the following bone structures protect the lungs in our body?
A. Rib cage
B. Skull
c. vertebral column
D. All of the above


Two infinitely long parallel plates of equal areas \( 6 \mathrm{cm}^{2} \) are separated by a distance of \( 1 \mathrm{cm} . \) While one of the plates has a charge of \( +10 n C \) and the other
has \( -10 n C . \) The magnitude of the
electric field between the plates, if \( \varepsilon_{0}= \) \( \frac{10^{-9}}{36 \pi} F / m \) is?
A. \( 0.6 \pi V / m \)
в. \( 6 \pi k V / m \)
c. \( 600 \pi k V / m \)
D. \( 60 \pi V / m \)
E . \( 6 \pi \)


Assertion: gases are characterised with
two coefficients of expansion
Reason: when heated both volume and
pressure increase with the rise in
temperature
A. Both assertion (A) and reason (R) are correct and \( \mathrm{R} \) gives the correct explanation
B. Both assertion (A) and reason (R) are correct but R doesnt give the correct explanation
c. \( A \) is true but \( R \) is false
D. A is false but R is true


If there is no rotation of plane-polarized light by a compound in a specific solvent, thought to be chiral, it may
mean that:
A. the compound may be a racemic mixture
B. the compound is certainly a chiral
c. the compound is certainly meso
D. there is no compound in the solvent


A ray of light takes grazing incidence on the first face of a prism and the
emergent ray is normal to the \( 2^{n d} \) face
of the prism. If \( \mathrm{D} \) is angle of deviation then the refracting angle of the prism is equal to
A \( \cdot 90^{\circ}-2 D \)
B. \( 90^{\circ}-D \)
c. \( 90^{\circ}-\frac{D}{2} \)
D. \( 180^{\circ}-2 D \)


The alternative name of glyptal is:
A. alkyl resin
B. phenol - formaldehyde resin
C. melamine- formaldehyde resin
D. melmac


Give the structural formula for 2 -methyl
propane.


A jeweller kept a diamond of mass \( 5.42 g m \) inside a box of mass \( .12 k g \) Find the combined mass of diamond
and box upto appropriate significant figures.


Solve: \( (x+y)^{2}+(x-y)^{2} \)
A \( \cdot 2 x^{2} \)
B.
c. \( 2 x^{2}+2 y^{2} \)
D. \( 2 y^{2} \)


Write the differential equation
representing the family of curves \( \boldsymbol{y}= \)
\( m x, \) where \( m \) is an arbitrary constant.


Assertion
Both \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3} \) and \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4} \) have the same
number of hydrogen atoms but \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4} \)
is a tribasic acid and \( H_{3} P O_{3} \) is a
dibasic acid
Reason
mole of \( H_{3} P O_{3} \) is neutralised by 2
moles of \( N a O H \) while 1 mole of \( H_{3} P O_{4} \)
is neutralised by 3 moles of \( N a O H \)
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


Number of longitudinal tracheal trunks in Cockroach is
A. Three pairs
B. Three
c. Two
D. Two pairs


In which of the following reactions,
\( \Delta \boldsymbol{H}>\boldsymbol{\Delta} \boldsymbol{U} ? \)
This question has multiple correct options
\( \mathbf{A} \cdot H_{2}(g)+I_{2}(g) \rightarrow 2 H I(g) \)
B \( \cdot P C l_{5}(g) \rightarrow P C l_{3}(g)+C l_{2}(g) \)
\( \mathbf{c} \cdot 2 H_{2} O_{2}(l) \rightarrow 2 H_{2} O(l)+O_{2}(g) \)
\( \mathbf{D} \cdot C(s)+O_{2}(g) \rightarrow C O_{2}(g) \)


Match the following.
\( \begin{array}{ll}\text { A. Incisors } & \text { 1. Grinding teeth } \\ \text { B. Canines } & \text { 2. Cracking teeth } \\ \text { C. Premolars } & \text { 3. Cutting teeth } \\ \text { D. Molars } & \text { 4. Tearing teeth }\end{array} \)
\( A \cdot A-2, B-4, C-1, D-3 \)
B. A- 2, B-1 , C-4, D-3
C \( . A-3, B-2, C-4, D-1 \)
D. A- 3, B-4, C-2, D-1


Express the following as percentages
\( \frac{126}{1050} \times 100 \)


A cell drives a current through a circuit
The e.m.f. of the cell is equal to the work done in moving unit charge:
This question has multiple correct options
A. from the positive to negative plate of the cell
B. from the positive plate back to the positive plate
C. from the negative plate back to the negative plate
D. from any point in the circuit back to the same point


The atomic number of natural
radioactive element is:
A. greater than 82
B. lesser than 82
c. not defined
D. at least 92


The average length of time required to complete a jury questionnaire is 40 minutes, with a standard deviation of 5 minutes. What is the probability that it will take a prospective juror between 35 and 45 minutes to complete the questionnaire?
A. About \( 68 \% \)
B. About \( 72 \% \)
c. About \( 76 \% \)
D. About \( 84 \% \)


Sl unit of weight is kilogram-force \( (K g f \)
).
A. True
B. False


Which of the following blood cells help in blood coagulation?
\( A \cdot \) RBCs
B. Lymphocytes
c. Thrombocytes
D. Basophils


A body of mass \( 300 \mathrm{kg} \) is moved
through \( 10 m \) along a smooth inclined
plane of an angle \( 30^{\circ} . \) The work done in moving the mass in joules is:
\( \left(g=9.8 m s^{-2}\right) \)
A. 9800
B. 14700
\( c .3450 \)
D. 4900


Which of the following is included in laws of refraction.
A. \( \angle i=\angle r \)
B. The incident ray, the reflected ray and normal at the point of incidence all lie in the same plane.
c. Both
D. None


The correct order of decreasing polarity
¡s:
\( \mathbf{A} \cdot H F>S O_{2}>H_{2} O>N H_{3} \)
B \( \cdot H F>H_{2} O>S O_{2}>N H_{3} \)
\( \mathbf{c} \cdot H F>N H_{3}>S O_{2}>H_{2} O \)
\( \mathbf{D} \cdot H_{2} O>N H_{3}>S O_{2}>H F \)


The investment of \( A \) is twice as that of \( B \)
and thrice as that of \( C . B \) invested for
twice the months than \( A \) and thrice the
months than
C. Who will earn the
highest profit


The equation of a parabola which passes through the intersection of a straight line \( x+y=0 \) and the circle \( x^{2}+y^{2}+4 y=0 \) is.
A \( \cdot y^{2}=4 x \)
В. \( y^{2}=x \)
c. \( y^{2}=2 x \)
D. None of these


On which of the following intervals is the function \( x^{100}+\sin x-1 \)
decreasing?
A \( \cdot\left(0, \frac{\pi}{2}\right) \)
в. (0,1)
c. \( \left(\frac{\pi}{2}, \pi\right) \)
D. None of the above.


The variation of magnetic susceptibility with the temperature of a ferromagnetic material can be plotted
as?
\( A \)
в.
\( c \)
D.


8
8
8
8


What is the energy required to move a body of mass \( \mathrm{m} \) from orbit of radius \( 2 \mathrm{r} \)
to \( 3 r ? \)


Hydraulic washing is based on the differences in
ore and gangue particles.
A. specific gravities
B. mass
c. type of material
D. none of these


If there was no \( C O_{2} \) in the atmosphere
the earth's temperature would be:
A. less than the present
B. same as present
c. higher than the present
D. dependent on \( O_{2} \) content of air


Let \( \boldsymbol{A}=\{\mathbf{9}, \mathbf{1 0}, \mathbf{1 1}, \mathbf{1 2}, \mathbf{1 3}\} \) and \( \boldsymbol{f}: \boldsymbol{A} \rightarrow \)
\( N \) be defined by \( f(n)= \) highest prime
factor of \( n, \) then its range is
A \( .\{13\} \)
в. \{3,5,11,13\}
c. \{11,13\}
D. \{2,3,5,11\}


Find the value of \( y-x \) from the
following equation \( \mathbf{2}\left[\begin{array}{cc}\boldsymbol{x} & \mathbf{5} \\ \mathbf{7} & \boldsymbol{y}-\mathbf{3}\end{array}\right]+\left[\begin{array}{cc}\mathbf{3} & \mathbf{- 4} \\ \mathbf{1} & \mathbf{2}\end{array}\right]=\left[\begin{array}{cc}\mathbf{7} & \mathbf{6} \\ \mathbf{1 5} & \mathbf{1 4}\end{array}\right] \)


Consider the following reaction:
The m-isomer of D and E is called:
A. Phthalic acid
B. Isophthalic acid
c. Terephthalic acid
D. None


Using Gausss law derive an expression
for the electric
field intensity at any point near a uniformly charged thin wire of charge/length as \( 1 \mathrm{C} / \mathrm{m} \)


The binding energies of nuclei \( X \) and \( Y \)
are \( \boldsymbol{E}_{1} \) and \( \boldsymbol{E}_{2}, \) respectively. Two atoms of \( X \) fuse to give one atom of \( Y \) and an energy \( Q \) is released. Then,
A \( \cdot Q=2 E_{1}-E_{2} \)
в. \( Q=E_{2}-2 E_{1} \)
c. \( Q<2 E_{1}-E_{2} \)
D. \( Q>E_{2}-2 E_{1} \)


What is the average of the first 300 terms of the given sequence?
\( \mathbf{1},-\mathbf{2}, \mathbf{3},-\mathbf{4}, \mathbf{5},-\mathbf{6}, \dots, \dots, \mathbf{n} .(-\mathbf{1})^{n+1} \)
A . -1
в. 0.5
\( c \cdot 0 \)
D. - 0.5


The water stored in an overhead tank
possesses energy


Given that:
\( \mathbf{2} C(s)+\mathbf{2} O_{2}(\boldsymbol{g}) \longrightarrow \mathbf{2} \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g}) ; \boldsymbol{\Delta} \boldsymbol{H}= \)
\( -787 k J \ldots(i) \)
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\frac{1}{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \longrightarrow \boldsymbol{H}_{2} \boldsymbol{O}(l) ; \boldsymbol{\Delta} \boldsymbol{H}= \)
\( -286 k J \ldots(i i) \)
\( \boldsymbol{C}_{2} \boldsymbol{H}_{2}(\boldsymbol{g})+\frac{5}{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \longrightarrow \boldsymbol{2} \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g})+ \)
\( \mathbf{3} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) \ldots . \)
\( \Delta H=-1301 k J \)
Heat formation of acetylene is:
B . \( +1802 k J \)
c \( .-800 k J \)
\( \mathbf{D} \cdot+228 k J \)


No current flows between two charged
bodies when connected if they have
same:
A. capacity
B. charge
c. potential
D. none of the above


A particle is executing simple harmonic motion (SHM) of amplitude \( A \), along the \( x \) -axis, about \( x=0 . \) When its potential Energy (PE) equals kinetic energy (KE), the position of the particle will be :
A \( \cdot \frac{A}{2} \)
в. \( \frac{A}{2 \sqrt{2}} \)
c. \( \frac{A}{\sqrt{2}} \)
D.


Arrange the following in descending order of their role in soil erosion.
(i) Wind erosion
(ii) Chemical degradation
(ii) Physical degradation
(iv) Water erosion
\( \mathbf{A} \cdot \mathbf{i}, \) i, i ii, iv
B. iv, i, ii, iii
c. iv , iii, ii, i
D. iv, ii, iii, i


Classification of periodic table based on atomic number is given by:
A. Mendeleev's
B. Mosley
c. Both A and B
D. None of these


Which of the following statement is incorrect about the cell cycle?
A. It consists of mitosis and interphase
B. The cell's DNA replicates during G, phase
C. A cell can remain in Gi phase for weeks or much longe
D. Most proteins are formed throughout all subphases of interphase


At \( 373 \mathrm{k} \) the half-life period for the
thermal decomposition of \( N_{2} O_{5} \) is 4.6
sec and is independent of the initial
pressure of \( N_{2} O_{5} \). Calculate the specific rate constant of this
temperature.
\( \mathbf{A} \cdot K=0.1507 s^{-1} \)
В. \( K=0.3014 s^{-1} \)
C . \( K=0.1507 s^{-2} \)
D. \( K=0.3014 s^{-2} \)


Select correct statement.
A. In lead storage battery, galvanic cells are linked in series
B. Cathode and anode compartments are not separated in a battery as oxidizing agents and reducing agents both are solids
C. Recharging of storage battery is a non spontaneous process
D. All are correct statements


Walking fern belongs to the genus
A. Asplenium
B. Dryopteris
c. Pteris
D. Marsilea


Lymph flows in direction.
A. upwarddardpwardd
B. Downward
c. Frontward
D. Backward


In a circuit, \( 5 C \) of charge is passed
through a battery in 3 hours. The plates of the battery are maintained at the
potential difference of 12 V. Then, the amount of work done by a battery is:
A . 60 J
в. 180
c. 20
D. \( 6.48 \times 10^{5} \) 」


Will \( C a F_{2} \) be precipitated?
A. Yes
B. No
c. Data insufficient
D. None of these


Assertion
\( C l_{2} \) gas bleaches the articles
permanently.
Reason
\( C l_{2} \) is a strong reducing agent.
Read the above assertion and reason
and choose the correct option regarding
¡t.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The sum of the two digits of a two digit number is 12. The number obtained by interchanging the digits exceeds the given number by 18. Find the number.


In barley type of plant, the stomata open
A. For few hours during day
B. During night
c. Throughout day and night
D. Remains closed


Find the square root of 125 using repeated subtraction.


The phenomenon of electromagnetic induction was discovered by
A . Lenz
B. Maxwell
c. Fleming
D. Faraday


In which region of electromagnetic spectrum does the Balmer series lie?
A. UV
B. Visible
c. Infrared
D. Far infrared


Which organ is bypassed in foetal circulation?
A. Heart
B. Brain
c. Lung
D. Liver


Three right angled prisms of refractive
indices \( n_{1}, n_{2} \) and \( n_{3} \) are fixed together
using an optical glue as shown in figure. If a ray passes through the prisms without suffering any deviation,
then
A \( . n_{1}=n_{2}=n_{3} \)
B . \( n_{1}=n_{2} \neq n_{3} \)
c. \( 1+n_{1}=n_{2}+n_{3} \)
D. \( 1+n_{2}^{2}=n_{1}^{2}+n_{3}^{2} \)


I.F. of \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\frac{\boldsymbol{x}+\boldsymbol{y}+\mathbf{1}}{\boldsymbol{x}+\mathbf{1}} \) is:
A. \( \frac{1}{y+1} \)
в. \( \frac{1}{x+1} \)
c. \( \log (x+1) \)
D. \( \log (y+1) \)


A dipole of dipole moment \( \overrightarrow{\boldsymbol{p}} \) is kept along an electric field \( \overrightarrow{\boldsymbol{E}} \) such that \( \overrightarrow{\boldsymbol{E}} \) and \( \vec{p} \) are in the same direction. Find the work done in rotating the dipole by an angle \( \pi \)
A. \( W=3 E p \)
в. \( W=2 E p \)
c. \( W=4 \) Ер.
D. \( W=5 E p \)


If a thermometer reads freezing point of
water as \( 20^{\circ} \mathrm{C} \) and boiling point at
\( 150^{\circ} \mathrm{C} \) how much thermometer read
when the actual temperature is \( 60^{\circ} \mathrm{C} \)
\( \mathbf{A} \cdot 98^{\circ} C \)
B. \( 110^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 40^{\circ} \mathrm{C} \)
D. \( 60^{\circ} \mathrm{C} \)


What is the entropy change( \( \Delta S \) ) for adsorption?


Find the area enclosed between the
boundry of circle \( x^{2}+y^{2}=1 \) and the
line \( \boldsymbol{x}+\boldsymbol{y}=1 \) lying in the first
quadrant.


Among the following, density is highest for:
A. \( C H_{3} F \)
в. \( C H_{3} C l \)
\( \mathrm{c} \cdot C H_{3} B r \)
D. \( C H_{3} I \)


A cylinder contains helium at 2.5
atmosphere pressure. Another identical cylinder contains argon at 1.5
atmosphere pressure at the same temperature. If both the gases are filled
in any one of the cylinders, the pressure of the mixture will be:
A. 1.5 atm
B. 2.5 atm
\( c \cdot 4 a t m \)
D. none of these


Coal gas can be produced by:
A. carbonization
B. gasification
\( c . \) both a and \( b \)
D. none of above


When sugar is treated with sulphuric
acid, we get a very pure form of:
A. carbon
B. oxygen
c. water
D. hydrogen


In \( A C \) circuits choke is preferred to
resistors because
A. choke coil is cheap
B. voltage increase
c. energy is not wasted.
D. current increases


18 g glucose is added to 178.2 g of water the vapour pressure of water for this
aqueous solution at \( 100^{0} C \) is:
A. 704 torr
B. 759 torr
c. 7.6 torr
D. None of these


Toroid is
A. ring shaped closed solenopid
B. rectangular shaped solenoid
C. ring shaped open solenoid
D. square shaped solenoid


The instrument by which B.P. of man is determined is
A. Sphygmomanometer
B. Cardiograph
c. Ultrasound
D. stethoscope


Section-A Section-B
a) Incompressible liquid
e) Density constant
b) Turbulent flow
f) Stream lines
c) Tube of flow
g) Constant
d) Fluid flux rate in laminar
h) Reynold's no \( > \) flow 2000
\( A \cdot a-f ; b-e ; c-g ; d-h \)
B. \( a-e ; b-h ; c-f ; d-g \)
\( \mathbf{c} \cdot \mathrm{a}-\mathrm{g} ; \mathrm{b}-\mathrm{f} ; \mathrm{c}-\mathrm{e} ; \mathrm{d}-\mathrm{h} \)
D. \( a-h ; b-g ; c-e ; d-f \)


In cities like Bombay and Calcultta, the major air pollutants is/are:
A . ozone
B. carbon monoxide and oxides of sulphur
c. hydrocarbons and not air
D. algal spores and marsh gas


If \( \int_{0}^{1} \cot ^{-1}\left(1-x+x^{2}\right) d x= \)
\( \lambda \int_{0}^{1} \tan ^{-1} x d x, \) then \( \lambda \) is equal to
\( A \)
B. 2
\( c .3 \)
\( D \)


Show that if \( \left|\frac{z-3 i}{z+3 i}\right|=1, \) then \( z \) is a
real number.


In which kingdom are viruses placed?


Which of the following is correct IUPAC name of the given compound?
A. 2-cyclopropyl-butane
B. 1-Methyl-1-cyclopropyl-propane
c. 2-Propyl-butane
D. Propenyl-butane


Nails, horns, the scales on the back of a scaly anteater (pangolin) and the scales on the tail of rat are:
A. Derivative of keratinized epidermal material.
B. Homologous structures.
c. Both (A) and (B)
D. secretions from special skin glands


For which vitamin liver is not the source
\( ? \)
A. Vitamin - \( B_{2} \)
B. Vitamin - \( B_{1} \)
c. vitamin - \( B_{12} \)
D. Vitamin - \( H \)


A nucleus has charged of +50 e \( A \) proton is located at a distance of \( 10 \mathrm{m} \)
The potential at this point in volt will be-


The variance of the scores 2,4,6,8,10
is
\( A \cdot 2 \)
B. 4
\( c .6 \)
\( D \)


The density of \( 3 M \) solution of sodium
thiosulphate \( \left(N a_{2} S_{2} O_{3}\right) \) is \( 1.56 g / m L \)
Calculate
(i) amount of \( N a_{2} S_{2} O_{3} \) in \( \% \) w/w
(ii) mole fraction of \( N a_{2} S_{2} O_{3} \)
(iii) Molality of \( N a^{+} \) and \( S_{2} O_{3}^{2-} \) ions


If \( A_{2 \times 3}, B_{4 \times 3} \) and \( C_{2 \times 4} \) are three matrices then which of the following is/are defined?
A \( \cdot A C^{T} B \)
в. \( B^{T} C^{T} A \)
c. \( A B^{T} C \)
D. All of these


Without drawing exact triangles, state, giving reasons, whether the given pairs of triangle are congruent or not:
In \( \Delta A B C \) and \( \Delta P B C ; A B= \)
\( \boldsymbol{B P}, \boldsymbol{A C}=\boldsymbol{P C} \)


Carry out the following divisions \( 72 a^{3} b^{4} c^{5} \) by \( 8 a b^{2} c^{3} \)


Select the correct statement (s) about
the compound \( N O\left[B F_{4}\right] \)
This question has multiple correct options
A. It has \( 5 \sigma \) and \( 2 \pi \) bond
B. Nitrogen - oxygen bond length is higher than nitric oxide \( (N O) \)
C. It is a diamagnetic species
D. \( B F \) bond length in this compound is lower than in \( B F_{3} \)


Certain substance emits only the
wavelengths, \( \lambda_{1}, \lambda_{2}, \lambda_{3} \) and \( \lambda_{4} \) when it is at a high temperature. When this substance is at a colder temperature, it will absorb only the following wavelengths:
\( A \cdot \lambda_{1} \)
B. \( \lambda_{2} \)
\( c \cdot \lambda_{1} \) and \( \lambda_{2} \)
D. \( \lambda_{1}, \lambda_{2}, \lambda_{3} \) and \( \lambda_{4} \)


By eliminating \( \boldsymbol{\theta} \) from \( \boldsymbol{x}=\boldsymbol{a} \cos ^{2} \boldsymbol{\theta}, \boldsymbol{y}= \)
\( a \sin ^{2} \theta \) the expression is


In Bohr's model of hydrogen atom, let \( P E \) represent potential energy and \( T E \) the total energy. In going to a higher
orbit,
A. \( P E \) increases, \( T E \) decreases
B. \( P E \) decreases, \( T E \) increases
c. \( P E \) increases, \( T E \) increases
D. \( P E \) decreases, \( T E \) decreases


Represent with the help of neat diagrams hydrogen bonding if present
in the molecules of \( \boldsymbol{H} \boldsymbol{F}-\boldsymbol{H}_{2} \boldsymbol{O}, \boldsymbol{H} \boldsymbol{F} \)
\( -N H_{3}, \) aniline \( - \) aniline, \( H_{2} O \)
\( -\boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{O} \boldsymbol{H}, \boldsymbol{H}_{2} \boldsymbol{O}-\boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{O} \boldsymbol{C} \boldsymbol{H}_{3}, \boldsymbol{H}_{2} \boldsymbol{O} \)
\( -\boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4}, \boldsymbol{H}_{2} \boldsymbol{O}-\boldsymbol{N} \boldsymbol{a} \boldsymbol{C l} \)


Bond energies can be obtained by using
the following relation:
\( \Delta H(\text { reaction })=\sum \) Bond energy of
bonds, broken in the reactants \( -\sum \)
Bond energy of bonds, formed in the
products
Bond energy depends on three factors:
a. greater is the bond length, lesser is
the bond energy
b. bond energy increases with the bond
multiplicity
c. bond energy increases with the electronegativity difference between the
bonding atoms.
Arrange \( N-H, O-H \) and \( F-H \)
bonds in the decreasing order of bond
energy:
\( \mathbf{A} \cdot F-H>O-H>N-H \)
B \( . N-H>O-H>F-H \)
\( \mathbf{c} \cdot O-H>N-H>F-H \)
D . \( F-H>N-H>O-H \)


Solve:
\( \lim _{x \rightarrow} \frac{\sin (2+x)-\sin (2-x)}{x} \)


Tangents are drawn to the circle \( x^{2}+ \)
\( y^{2}=25 \) from the point \( (13,0) . \) Prove
that the angle between them is \( 2 \tan ^{-1}(5 / 12) \) and their equations are
\( 12 y+5 x+65=0 \) and \( 12 y-5 x- \)
\( \mathbf{6 5}=\mathbf{0} \)


Let \( \Delta= \)
\( \left|\begin{array}{ccc}\sin \theta \cos \phi & \sin \theta \sin \phi & \cos \theta \\ \cos \theta \cos \phi & \cos \theta \sin \phi & -\sin \theta \\ -\sin \theta \sin \phi & \sin \theta \cos \phi & 0\end{array}\right|, \) then
A. \( \Delta \) is independent of \( \theta \)
B. \( \Delta \) is independent of \( \phi \)
\( \mathrm{c} \cdot \Delta \) is a constant
D. none of these


Anabaena is an example for
A. Protista
B. Fungi
C . Bryophyte
D. Monera


Identify if a given sequence of numbers is an arithmetic progression or not.
a) \( 8,17,26,35, \dots \)
b) \( -4,-9,-16,-25, \)


Evaluate the following integrals:\( \int \frac{x+1}{\sqrt{x^{2}-x+1}} d x \)


Which of the following are examples of
the null
Set of all even prime numbers.
A. True
B. False


Balance the following equation taking place in basic solution.
\( \boldsymbol{F} \boldsymbol{e}(\boldsymbol{O} \boldsymbol{H})_{2}(\boldsymbol{s})+\boldsymbol{O}_{2}(\boldsymbol{g}) \longrightarrow \boldsymbol{F} \boldsymbol{e}(\boldsymbol{O} \boldsymbol{H})_{3}(\boldsymbol{s}) \)
A \( \cdot 4 \mathrm{Fe}(O H)_{2}(s)+2 H_{2} O(l)+O_{2}(g) \longrightarrow 4 \mathrm{Fe}(O H)_{3}(s) \)
B. \( 4 \mathrm{Fe}(\mathrm{OH})_{2}(s)+\mathrm{H}_{2} \mathrm{O}_{2}(l)+O_{2}(g) \longrightarrow 4 \mathrm{Fe}(\mathrm{OH})_{3}(s) \)
\( \mathbf{c} \cdot 4 F e(O H)_{3}(s)+2 H_{2} O(l)+O_{2}(g) \longrightarrow 4 F e(O H)_{3}(s) \)
D. None of these


If the earth expands suddenly to twice its diameter, what would be length of
the day?


Which of the following phenomena contributes significantly to the reddish appearance of the sun at sunrise or
sunset?
A. Dispersion of light
B. Scattering of light
c. Total internal reflection of light
D. Reflection of light from the earth


FHEMENT-1: \( \left[\lim _{x \rightarrow 0} \frac{\sin x}{x}\right]=0 \)
STATEMENT-2: For \( \boldsymbol{x} \in(-\boldsymbol{\delta}, \boldsymbol{\delta}), \) where \( \boldsymbol{\delta} \)
is positive and \( \delta \rightarrow 0, \tan x>x \)
A. STATEMENT-1 is True, STATEMENT-2 is True:
STATEMENT-2 is a correct explanation for STATEMENT
B. STATEMENT-1 is True, STATEMENT-2 is True:
STATEMENT-2 is not the correct explanation for STATEMENT-1
c. STATEMENT-1 is True, STATEMENT-2 is False
D. STATEMENT-1 is False, STATEMENT-2 is True


In an optical fibre
A. Core region is transparent, cladding is opaque.
B. Core region is opaque, cladding is transparent.
C. Both core and cladding regions are transparent.
D. Both core and cladding regions are opaque.


When a low flying aircraft passes over head, we sometimes notice a slight
shaking of the picture on our TV screen Identify the optical phenomenon behind ¡t.


Show that the lines \( \frac{x-1}{2}=\frac{y-2}{3}= \) \( \frac{z-3}{4} \) and \( 4 x-3 y+1=0=5 x- \)
\( 3 z+2 \) are interesting lines. Also find
point of intersection.


Evaluate:
\( \int[\sin (\log x)+\cos (\log x)] d x \)


In the circuit shown here, the ammeter
\( A \) reads \( 5 A \) and the voltmeter \( V \) reads
20V.Find the correct value of resistance


What is meant by shortsightedness?


With partial pressure of \( \boldsymbol{S O}_{3} \) and \( \boldsymbol{S O}_{2} \)
taken to be equal to \( 10^{-5} \) atm and 10 atm respectively then what must be the
partial pressure of \( \boldsymbol{O}_{2} \) so that the reaction may remain in equilibrium?
A . 10 atm
B. 0.01 atm
c. 100 atm
D. 0.1 atm


The energy of a particle executing simple harmonic motion is given by the equation \( \boldsymbol{E}=\boldsymbol{A} \boldsymbol{x}^{2}+\boldsymbol{B} \boldsymbol{v}^{2} \) where \( \boldsymbol{x} \) is the
displacement from mean position \( \boldsymbol{x}= \)
0 and \( v \) is the velocity of the particle at
\( x . \) Find the amplitude of \( S . H . M \)


Yellow colour in the flame denotes
A. outermost part
B. middle zone
c. innermost zone
D. none of these


The time period of the hour hand of a watch is
\( A \cdot 24 h \)
B. 12 \( h \)
\( c \cdot 1 h \)
D. 1 min


The molarity of \( C l^{-}(100 \mathrm{ml}) \) ions in the
solution after 0.2 moles \( H C l \) are mixed
with 0.1 moles \( C a C l_{2} \) solution?
A. 0.8 m
B. 0.04 М
\( c .0 .4 \mathrm{M} \)
D. 0.08 м


The \( p K_{a} \) of \( \mathrm{HCN} \) is \( 9.30 . \) The pH of a
solution prepared by mixing 2.5 moles
of KCN and 2.5 moles of HCN in water
and making up the total volume of 500 \( \mathrm{ml} \) is:
A . 9.30
B. 7.30
c. 10.30
D. 8.30


Assertion
The fungi are widespread in distribution and they even live on or inside other plants and animals.
Reason
Fungi are able to grow anywhere on land, water or on other organisms
because they have a variety of pigments, including chlorophyll, carotenoids, fucoxanthin and
phycoerythrin.
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


There are 6 Higher Secondary Schools, 8 High Schools and 13 Primary Schools in a town. Represent these data in the form
of \( 3 \times 1 \) and \( 1 \times 3 \) matrices.


Find the equation of the ellipse in the standard form whose distance between
foci is 2 and the length of latus rectum is \( \frac{15}{2} \)


Why zinc metal is used for
galvanisation?
A. zinc get corroded easily than iron
B. zinc does not corrode
c. corrosion constant of iron increase
D. All of the above


if \( \boldsymbol{y}=\boldsymbol{x}^{2}-\boldsymbol{9} \boldsymbol{x}+\mathbf{5} \) find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \)


Which one of the following systems has the smallest sized domains in its
dispersed phase?
A. Nanoemulsion
B. Coarse suspension
c. coarse emulsion
D. Microemulsion


The oxidation state of oxygen in \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \)
is:
\( A \cdot+1 \)
B. - -
\( c \cdot+2 \)
\( D \cdot-2 \)


The atomic mass of \( 7^{N^{15}} \) is 15.000108
a.m.u. and that is of \( 8^{\circ}^{16} 15.994915 \)
a.m.u. If the mass of a proton is 1.007825
a.m.u. then the minimum energy provided to remove the least tightly bound proton is
B. 12.13 Mev
c. 13.018 Mev
D. 12.13 ev


Large intestine absorbs
A. Digested food
B. Undigested food
c. water
D. Remaining enzymes


\( (X) \) on treatment with sodium
hydroxide followed by the addition of silver nitrate gives white precipitate at room temperature which is soluble in
\( N H_{4} O H .(X) \) can be:
\( A \). chlorobenzene
B. ethyl bromide
c. benzyl chloride
D. vinyl chloride


The figure below shows three steps \( (A, \)
B, \( C \) ) of Polymerase Chain Reaction
(PCR). Select the option giving
correct identification together with what it represents?
DNA
A . A - Denaturation at a temperature of about \( 50^{\circ} \mathrm{C} \)
B. C - Extension in the presence of heat stable DNA polymerase
C. A - Annealing with two sets of primers
D. B - Denaturation at a temperature of about \( 98^{\circ} \mathrm{C} \) separating the two DNA strands


In a chemical system, \( \boldsymbol{A}(s) \rightleftharpoons 2 \boldsymbol{B}(\boldsymbol{g})+ \)
\( 3 C(g), \) if partial pressure of \( C \) is
doubled, then partial pressure of \( \boldsymbol{B} \) will
be:
A. \( 2 \sqrt{2} \) times the original value
B. \( \frac{1}{2} \) times the original value
c. 2 times the original value
D. \( \frac{1}{2 \sqrt{2}} \) times the original value


Show that \( \frac{\sin 2 \alpha+\sin 2 \beta}{\cos 2 \alpha-\cos \beta}=\cot (\beta- \)
\( \boldsymbol{\alpha} \)


Which one of these are essential amino
acids?
A. Glutamic acid
B. Serine
c. Proline
D. Tryptophan


The excess of pressure inside a soap bubble is twice the excess pressure inside a soap bubble. The volume of the
first bubble is \( n \) times the volume of the
second where n is
A .0 .125
B. 0.250
c. 1
D.


Which of the following are measures of dispersion?
A. Standard Deviation,Median,Range
B. Standard Deviation,Mode,Range
c. standard Deviation, Variance,Range
D. Mean,Mode,Median


Let \( S=\{1,2, \ldots ., 20\} . \) A subset \( B \) of \( S \) is said to be "nice", if the sum of the elements of \( B \) is \( 203 . \) Then the
probability that a randomly chosen subset of \( S \) is "nice" is:
A \( \cdot \frac{6}{2^{20}} \)
в. \( \frac{5}{2^{20}} \)
c. \( \frac{4}{2^{20}} \)
D. \( \frac{7}{2^{20}} \)


Reverse bias applied to a p-njunction
diode
A. Lowers the potential barrier
B. Decreases the majority charge carriers
C. Raises the potential barrier
D. Change the mass of \( p \) -n junction diode


Crystalline form of carbon having 60 carbon atoms joined together is called:
A. polymer
B. buckminster fullerene
c. coal
D. diamond


Assertion
lodination of alkanes is carried out
under reflux conditions in the presence
of reducing agent. Because
Reason
lodination of alkanes take place
explosively.
A. Both Assertion and Reason are correct and the Reason is the correct explanation of the Assertion
B. Both Assertion and Reason are correct but the Reason is not the correct explanation of the Assertion
c. The Assertion is correct but the Reason is incorrect
D. Both Assertion and Reason are incorrect


Find the sum of first 15 terms of an A.P.
whose 5 th and 9 th terms are 26 and 42
respectively


Find the area of the triangle \( P Q R \) if coordinates of \( Q \) are (3,2) and the coordinates of mid-points of the sides through \( Q \) are (2,-1) and (1,2)


Which of the following statement
related to hysteresis loop is incorrect?
A. The curve of B against H for a ferromagnetic material is called hysteresis loop
B. The area of B-H curve is a measure of power dissipated per cycle per unit area of the specimen
C. Coercitivity is a measure of the magnetic field required to destroy the residual magnetism of ferromagnetic material
D. The retentivity of a specimen is the measure of magnetic field remaining in the specimen when the magnetising field is removed


A sample of compound is considered to
be optically pure:
A. if only one enantiomer is present
B. if only two enantiomer is present
C. if the compound is having recimic mixture
D. none of the above


Solve the following quadratic equation by factorization, the roots are \( \boldsymbol{x}^{2}-(\sqrt{\mathbf{3}}+\mathbf{1}) \boldsymbol{x}+\sqrt{\mathbf{3}}=\mathbf{0} \)
A . 3,1
в. \( \sqrt{2}, \)
c. \( \sqrt{3}, 1 \)
D. \( \sqrt{5}, \)


Bicuspid valve is present in the human heart in between which of the following?
A. Right atrium and right ventricle
B. Left atrium and left ventricle
c. Right and left atria
D. Left atrium and systemic aorta


Your external ear (pinna) is supported by
A. Bone
B. Cartilage
c. Tendon
D. capsule


Cells of the liver manufacture
A. Diastase
B. Amylase
c. Lipase
D. Insulin
E. None of the above


Find out the following squares by using the identities:
\( (10 m-9 n)^{2} \)


Deliquescent substances absorb moisture from the air \( \& \) changes into a solution.
A. True
B. False


Substance common in DNA and RNA is
A. Hexose sugar
B. Histamine
c. Thymine
D. Phosphate groups


Let \( \boldsymbol{P}(\boldsymbol{n})=11^{n+2}+12^{2 n+1}, \) then the
least value of the following which \( \boldsymbol{P}(\boldsymbol{n}) \)
is divisible by is
A . 19
B. 7
c. 133
D. none of these


A badminton player won 6 games and lost 4.The fraction of the games he won
is
\( A \cdot \frac{6}{4} \)
B. \( \frac{4}{6} \)
\( c \cdot \frac{6}{10} \)
D. \( \frac{5}{10} \)


Divide \( (10 x-25) \div(2 x-5) \)


\( \lim _{x \rightarrow 0} \frac{27^{x}-9^{x}-3^{x}+1}{\sqrt{2}-\sqrt{1+\cos x}}= \)
\( \mathbf{A} \cdot \mathbf{0} \)
B . \( 8 \sqrt{2}(\log 3)^{2} \)
c. \( 8(\log 3)^{2} \)
D.


The volume of \( 10 \mathrm{N} \) and \( 4 \mathrm{N} \) HCl required to make 1 L of 7 N HCl are:
A. \( 0.5 \mathrm{L} \) of \( 10 \mathrm{N} \) HCl and 0.4 Lof \( 4 \mathrm{N} \) HC (1)
B. 0.6 L of 10 N HCl and 0.6 L of 4 N HCI
c. 0.8 L of \( 10 \mathrm{N} \) HCl and \( 0.7 \mathrm{L} \) of \( 4 \mathrm{N} \) HC
D. 0.75 L of 10 N HCl and 0.4 L of 4 N HCI


When mango is placed in dilute aqueous solution of hydrochloric acid, it
A. shrinks
B. swells
c. bursts
D. nothing happens


Which of the following is true regarding
an \( N e \) atoms with a mass number of 20
and \( O^{2-} \) ion with a mass number of \( 16 ? \)
A. They contain the same number of protons
B. They contain the same number of neutrons
C. They contain the same number of protons plus netrons
D. The are isoelectronic
E. They are isomers


In a triangle \( A B C, D \) and \( E \) are the
midpoints of \( A B \) and \( A C . \) If the area of
\( \triangle A B C=60 \mathrm{sq.cm}, \) then the area of the
\( \triangle A D E \) is equal to
A . 15 sq.m
в. 20 sq.m
\( c .25 \mathrm{sq.m} \)
D. 30 sq.m


The total runs scored by two cricket players Arun and Bharath in 15
matches are 1050 and 900 with
standard deviation 4.2 and 3.0
respectively. Who is better run getter? Who is more consistent in
performance?


Which of the following facts regarding
bond order is not valid?
A. Bond order is given by the number of bonds between the two atoms in a molecule
B. With increase in bond order, bond enthalpy of the molecule decreases
C. Isoelectronic molecules and ions have identical bond
orders
D. With increase in bond order, bond length decreases


An advantage of excreting nitrogeneous
wastes in the form of uric acid is that
A. Uric acid can be excreted in almost solid form.
B. The formation of uric acid requires a great deal of energy.
C. Uric acid is the first metabolic breakdown products of acids.
D. Uric acid may be excreted through the lungs.


The length of an iron wire is \( L \) and area
of cross-section is \( A \). The increase in
length is \( l \) on applying the force \( F \) on its two ends. Which of the statement is
correct?
A. Increase in length is inversely proportional to its length
B. Increase in length is proportional to area of crosssection
C. Increase in length is inversely proportional to area of cross-section
D. Increase in length is proportional to Young's modulus


A Diwali rocket is ejecting \( 0.05 k g \) of
gases per second at a velocity of
\( 400 m s^{-1} . \) The repulsive force on the rocket is
A. 20 dyne
B. 20 newton
c. 20 kgwt
D. Sufficient data not given


Directions: In following quesiton, choose the missing term out of the given alternatives Reference:
\( A B C D E F G H I J K L M \)
N O P Q R ST U V W X Y Z
\( Z, X, V, T, R, \dots \dots \)
A. \( O, K \)
в. \( N, M \)
c. \( K, S \)
D. \( M, N \)
E . \( P, N \)


A circular loop carrying a current \( I \) is
placed in the \( x \) -y plane as shown in figure.An uniform magnetic field \( \vec{B} \) is oriented along the positive z-axis.The
loop tends to:
A. expand
B. contract
\( c . \) rotate about x-axis
D. rotate about y-axis


The law of conservation of momentum
is based on Newton's:
A. First law of motion
B. second law of motion
c. Third law of motion
D. law of gravitation


Which type of semi-conductor is formed
when a trivalent impurity is dopped in a pure semiconductor?


Magnetic lines form continuous closed loops. Why?


The law of the mean can also be put in
the form
\( \mathbf{A} \cdot f(a+h)=f(a)-h f^{\prime}(a+q h) 0<q<1 \)
B \( \cdot f(a+h)=f(a)+h f^{\prime}(a+q h) 0<q<1 \)
\( \mathbf{c} \cdot f(a+h)=f(a)+h f^{\prime}(a-q h) 0<q<1 \)
D. \( f(a+h)=f(a)-h f^{\prime}(a-q h) 0<q<1 \)


When the temperature is increased
from \( 0^{\circ} \mathrm{C} \) to \( 273^{\circ} \mathrm{C}, \) in what ratio the
average kinetic energy of molecules changes?
A.
B. 5
\( c \cdot 4 \)
\( D \cdot 2 \)


The electronic configuration of an element is \( 2,8,8,2 . \) This element is :
A. An alkali metal
B. An alkaline earth metal
c. A halogen
D. A noble gas


An angiosperm is different from a gymnosperm in the absence of
A. Vascular tissue
B. Ovary
\( c . \) seed
D. Naked ovule


\( N a H_{2} P O_{2} \) and \( N a H P O_{3} \) are acid
salts.
A. True
B. False


If \( A \) and \( B \) are two events such that
\( P(A)=\frac{3}{4} \) and \( P(B)=\frac{5}{8}, \) then
\( ^{\mathrm{A}} \cdot P(A \cup B) \geq \frac{3}{4} \)
в. \( P\left(A^{\prime} \cap B\right) \leq \frac{1}{4} \)
c. \( \frac{3}{8} \leq P(A \cap B) \leq \frac{5}{8} \)
D. All of the above


What compounds are identified as contributing to acid rain?
A. Carbon dioxide
B. Sulphur and nitrogen oxides
c. Mercury oxides
D. Phosphates


The current flowing through resistance
\( R \) if the rod \( M N \) moves toward left and
the rod \( M^{\prime} N^{\prime} \) moves toward the right is
\( A \)
\[
\frac{B l v}{R+(r / 2)}
\]
в. \( \frac{2 B l v}{R+r} \)
c. zero
\( D \)
\[
\frac{3 B l v}{2(R+r)}
\]


Which of the following is/are the factors on which angle of deviation depend?
A. Refractive index of the prism
B. Angle of the prism
c. Angle of refraction
D. Both A and B


On comparing the ratios \( \frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}} \) and \( \frac{c_{1}}{c_{2}} \)
find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident.
\( \mathbf{6} \boldsymbol{x}-\mathbf{3} \boldsymbol{y}+\mathbf{1 0}=\mathbf{0} ; \mathbf{2} \boldsymbol{x}-\boldsymbol{y}+\mathbf{9}=\mathbf{0} \)
A. Intersect at a point
B. Parallel
c. coincident
D. Data insufficient


Which of the following is Baeyer's reagent?
A. Alkaline \( K M n O_{4} \)
B. Acidic \( K_{2} C r_{2} O_{7} \)
c. Alkaline \( N a_{2} C r_{2} O_{7} \)
D. \( M n O_{2} \)


Two coherent monochromatic light
beams of intensities \( I \) and \( 4 I \) are
superposed. The maximum and minimum possible intensities in the resulting beam are:
A. \( 5 I \) and \( I \)
B. \( 5 I \) and \( 3 I \)
c. \( 9 I \) and \( I \)
D. \( 9 I \) and \( 3 I \)


The normal temperature of human body
is
A \( \cdot 27^{\circ} \mathrm{C} \)
В. \( 37^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 47^{\circ} C \)
D. \( 57^{\circ} \mathrm{C} \)


In
Fig., the length (in \( \mathrm{cm} \) ) of each side
has been indicated along the side. State
for each triangle whether it is scalene,
isosceles or equilateral:


Let \( \boldsymbol{S}=\{1,2,3, \ldots, 100\} . \) The number
of non-empty subsets \( \boldsymbol{A} \) of \( \boldsymbol{S} \) such
that the product of elements in \( \boldsymbol{A} \) is even is :-
A \( \cdot 2^{50}\left(2^{50}-1\right) \)
B . \( 2^{100}-1 \)
c. \( 2^{50}-1 \)
D. \( 2^{50}+1 \)


Nucleic acid was first isolated from pus
cells by
A. Friedrich Miescher
B. Altmann
c. waldeyer
D. Hoffmeister


Washing soda is:
A. \( N a_{2} C O_{3} \)
B. \( N a C l \)
c. \( N a_{2} C O_{3}, H_{2} O \)
D. \( N a_{2} S O_{4} \)


Most covalent halide of aluminium is :
A. Aluminium bromide
B. Aluminium fluoride
c. Aluminium iodide
D. Aluminium chloride


Draw the graphs of equations \( 2 x+y= \)
7 and \( 2 x+y=8 . \) If they intersect, write
the co-ordinates of the point of their intersection.


The following figure shown a logic gate
circuit with two input \( A \) and \( B \) output \( C \) The voltage waveforms of \( A, B \) and \( C \) are
as shown in second figure given. The logic gate is?
A. OR gate
B. AND gate
c. NAND gate
D. NOR gate


The event which cannot happen is
called
A . outcome
B. impossible event
c. frequency
D. none of these


When the price of chair was reduced by \( 20 \% \), the number of chairs sold
increased by \( 80 \% \), what was the effect on the sales rupees?
A . \( 34 \% \) increase
B. 44\% increase
c. \( 54 \% \) increase
D. 64\% increase


An electric dipole of length \( 2 \mathrm{cm}, \) when placed with its axis making an angle of \( 60^{\circ} \) with a uniform electric field,
experiences a torque of \( 6 \sqrt{3} \mathrm{Nm} \) Calculate the potential energy of the dipole, if it has a charge of \( \pm 2 \mathrm{nC} \)


There are many gas molecules \( N H_{3} \)
\( C O, C H_{4} \) and \( S O_{2} \) in a group once. They were discussing about who would be the better absorbed on charcoal. So they
decided to have the race among themselves to prove it as to who would be absorbed more in the same time.
Who do you think won?
A. \( C O \)
в. \( N H_{3} \)
\( \mathrm{c} \cdot C H_{4} \)
\( D \cdot S O_{2} \)


There is a right circular cone of height \( h \)
and vertical angle \( 60^{\circ} . \) A sphere when placed inside the cone, it touches the curved surface and the base of the cone.
The volume of sphere is
A \( \cdot \frac{4}{3} \pi h^{3} \)
В \( \cdot \frac{4}{9} \pi h^{3} \)
c. \( \frac{4}{27} \pi h^{3} \)
D. \( \frac{4}{81} \pi h^{3} \)


What is meant by the notation, \( \triangle G, \triangle S \)
and \( \triangle H ? \) Give the relationship between
them.


The moment of inertia of a non-
uniform semicircular wire having mass \( \mathrm{m} \) and radius \( \mathrm{r} \) about a line
perpendicular to the plane of the wire through the center is
\( \mathbf{A} \cdot m r^{2} \)
в. \( \frac{1}{2} m r^{2} \)
c. \( \frac{1}{4} m r^{2} \)
D. \( \frac{2^{2}}{5} \)


What are de-Broglie waves? Establish the de-Broglie wavelength equation.


Displacement between maximum
potential energy position and maximum kinetic energy position for a particle executing simple harmonic motion is


How many ordered pairs of \( (\mathrm{m}, \mathrm{n}) \) integers satisfy \( \frac{m}{12}=\frac{12}{n} ? \)
A . 30
B. 15
c. 12
D. 10


Particulate and gaseous pollutants along with harmless gases are released from the thermal power plants. Name the most widely used device of removing particulate pollutants from the air.
A. Electrostatic precipitator
B. Fabric filters
c. cyclone separators
D. None of the above


Solve the following:
\( \frac{4}{5}\left(x+\frac{5}{6}\right)+\frac{2}{3}\left(x-\frac{1}{4}\right)=1 \frac{1}{9} \)
A \( \cdot \frac{9}{14} \)
в. \( \frac{5}{12} \)
\( c \cdot \frac{3}{11} \)
D. \( \frac{7}{11} \)


\( \boldsymbol{A}=\{1,2,3,5\} \) and \( \boldsymbol{B}=\{\mathbf{4}, \mathbf{6}, \mathbf{9}\} \)
Define a relation \( \mathrm{R} \) from \( A \) to \( \mathrm{B} \) by \( \boldsymbol{R}= \)
\( \{(x, y): \text { the difference between } x \text { and } y \)
is odd, \( x \in A, y \in B\} . \) Write \( R \) in Roster
form


Correct naming of the given image is :
A . 2-methyl butene
B. 2-methylbut-2-ene
c. 2 -methylbut-1, 3-diene
D. 2-methyl-1,3 -butene


Write the balanced chemical equation for the following reaction and identify the type of reaction:

Nitrogen gas is treated with hydrogen gas in the presence of a catalyst at 773 \( \mathrm{K} \) to form ammonia gas.


Two equal positive charges are kept at points \( A \) and \( B . \) The electric potential at the points between \( A \) and \( B \) (excluding these points) is studied while moving
from \( A \) to \( B \). The potential
A. continuously increases
B. continuously decreases
c. increases then decreases
D. decreases then increases


The radius of the curved part of the wire is \( R, \) the linear parts are assumed to be
very long. Find the magnetic induction of the field at the point \( O \) if a currentcarrying wire has the shape shown in
figure above.
A \( \cdot B=\frac{3 \mu_{0}}{4} \frac{i}{R} \)
В. \( B=\frac{\mu_{0}}{2} \frac{i}{R} \)
c. \( _{B}=\frac{2 \mu_{0}}{3} \frac{i}{R} \)
D. \( B=\frac{\mu_{0}}{4} \frac{i}{R} \)


A sample of hydrogen gas \( \boldsymbol{H}_{2} \) is
irradiated by a light of \( \lambda=432.25 A \)
and all hydrogen after atomization gets excited to 3 rd orbit. Assuming no energy loss to the surroundings,
determine the bond energy of \( \boldsymbol{H}_{2} \) in \( \boldsymbol{k} \boldsymbol{J} \)


Find the value of \( 0.006 \div 0.06 \)
A . 0.01
в. 1.0
c. \( 0 . \)
D. 0.001


When two cylinder with different size like larger and smaller are kept together then though the pressure is same in both, still the force required is more for larger cylinder. Due to increase in which property?
A. Area
B. height
c. weight
D. volume


Let \( A, G \) and \( H \) be the \( A M, G M \) and \( H M \)
of two positive numbers a and b. The
quadratic equation whose roots are \( \boldsymbol{A} \)
and \( H \) is
This question has multiple correct options
\( \mathbf{A} \cdot A x^{2}-\left(A^{2}+G^{2}\right) x+A G^{2}=0 \)
B \( \cdot A x^{2}-\left(A^{2}+H^{2}\right) x+A H^{2}=0 \)
\( \mathbf{C} \cdot H x^{2}-\left(H^{2}+G^{2}\right) x+H G^{2}=0 \)
D. \( G x^{2}-\left(H^{2}+G^{2}\right) x+G H^{2}=0 \)


Q Type your question_
\( \mathbf{A} \)
\( B \)
\( c \)
\( D \)


prove that
\[
\begin{array}{l}
2 \tan ^{-1}\left[\tan \frac{\alpha}{2} \tan \left(\frac{\pi}{4}-\frac{\beta}{2}\right)\right]= \\
\tan ^{-1} \frac{\sin \alpha \cos \beta}{\cos \alpha+\sin \beta}
\end{array}
\]


\( A B C \) is an equilateral triangle of side a The value of \( \overrightarrow{A B} \cdot \overrightarrow{B C}+\overrightarrow{B C} \cdot \overrightarrow{C A}+ \)
\( \overrightarrow{C A} \cdot \overrightarrow{A B} \) is equal to
\( A \cdot \frac{3 a^{2}}{2} \)
B. \( 3 a^{2} \)
\( \mathrm{c} \cdot \frac{3 a^{2}}{2} \)
D. None of these


A spherical ball of radius \( 1 \times 10^{-4} m \)
and density \( 10^{4} k g / m^{3} \) falls freely under
gravity through a distance \( h \) before
entering a tank of water. If after entering the water the velocity of the ball does not change, find \( h \) in \( \mathrm{m} \) (Write
answer to nearest interger). (The
viscosity of water is \( 9.8 \times \) \( \left.10^{-6} N-s / m^{2}\right) \)


Spin only magnetic moment of the
compound \( \boldsymbol{H} \boldsymbol{g}\left[\boldsymbol{C o}(\boldsymbol{S} \boldsymbol{C} \boldsymbol{N})_{4}\right] \) is :
A \( \cdot \sqrt{3} \)
B. \( \sqrt{15} \)
c. \( \sqrt{24} \)
D. \( \sqrt{8} \)


When condensation product of hexamethylenediamine and adipic acid
is heated to \( 353 \mathrm{K}\left(80^{\circ} \mathrm{C}\right) \) in an
atmosphere of nitrogen for about \( 4-5 h \) the product obtained is:
A. Solid polymer of nylon 66
B. Liquid polymer of nylon 66
c. Gaseous polymer of nylon 66
D. Liquid polymer of nylon 6


As the angle of incidence is increased
for a ray incident on a reflecting surface, the angle between the incident and reflected rays ultimately approaches:
A. zero
В . \( 45^{\circ} \)
\( \mathrm{c} \cdot 90^{\circ} \)
D. \( 180^{\circ} \)


A body is projected vertically upwards with a velocity of \( 19.6 ~ m / s . \) The total time for which the body will remain in
the air is (Take \( \boldsymbol{g}=\mathbf{9 . 8 m} / \boldsymbol{s}^{2} \)
A . \( 4 s \)
B. \( 6 s \)
\( \mathrm{c} .9 \mathrm{s} \)
D. 12 s


The megaspore of a conifer, which is never released from the sporangium, divides by mitosis to produce a:
A. Male gametophyte
B. Female gametophyte
c. Multicellular embryo
D. Pollen grain


Decreasing order of rate of electrophilic aromatic substitution is:
A \( . a>b>c>d \)
в. \( a>c>b>d \)
c. \( b>a>c>d \)
D. \( b>c>a>d \)


Water pollution can be defined as:
A. Physical change in the properties of water
B. Chemical change in the properties of water
C. Biological change in the properties of water
D. All of the above


Oxy-haemoglobin dissociates into oxygen and deoxy-haemoglobin at
A \( \cdot \) Low \( O_{2} \) pressure in tissue
B. High \( O_{2} \) pressure in tissue
c. Equal \( O_{2} \) pressure inside and outside tissue
D. All times irrespective of \( O_{2} \) pressure


The common formula of Turn bull's blue
and Prussian blue is:
\( \mathbf{A} \cdot F e_{3}\left[F e(C N)_{6}\right]_{2} \)
\( \mathbf{B} \cdot F e_{3}\left[F e(C N)_{6}\right]_{3} \)
c. \( K F e\left[F e(C N)_{6}\right] \)
D. \( K_{4} F e_{2}\left[F e(C N)_{6}\right]_{2} \)


In the figure given, if \( D E \| B C \) and
\( \boldsymbol{A B}=\mathbf{5} \boldsymbol{x}-\mathbf{4}, \boldsymbol{B} \boldsymbol{D}=\mathbf{7} \boldsymbol{x}-\mathbf{5}, \boldsymbol{C} \boldsymbol{E}= \)
\( 5 x-3 \) and \( A D=3 x-2, \) find the value
of \( x \)
4
B.
c. \( \frac{7}{10} \)
" \( \frac{9}{10} \)


The quantity of heat absorbed by a
substance during the change of its state without rising its temperature is called latent heat.
A. True
B. False


Short Answer Type Question. Name the two extreme shapes of the
moon. When and at what intervals do
they occur?


Which one of the following property of light does not support wave theory of light
A. Light obeys laws of reflection and refraction
B. Light waves get polarised
c. Light shows photoelectric effect
D. Light shows interference


A liquid drop placed on a horizontal plane has a near spherical shape (slightly flattened due to gravity). Let \( \boldsymbol{R} \) be the radius of its largest horizontal section. A small disturbance causes the
drop to vibrate with frequency \( v \) about
its equilibrium shape. By dimensional analysis the ratio \( \frac{v}{\sqrt{\frac{\sigma}{\rho R^{3}}}} \) can be (Here
\( \sigma \) is surface tension, \( \rho \) is density, \( g \) is
acceleration due to gravity, and \( k \) is an arbitrary dimensionless constant).
\( ^{\mathrm{A}} \cdot \frac{k \rho g R^{2}}{\sigma} \)
в. \( \frac{k \rho R^{2}}{g \sigma} \)
c. \( \frac{k \rho R^{3}}{g \sigma} \)
D. \( \frac{k \rho}{g \sigma} \)


Let \( f: X \rightarrow Y \) be a function defined by
\[
f(x)=a \sin \left(x+\frac{\pi}{4}\right)+b \cos x+c \text { If }
\]
is both one-one and onto, then find the
\( \operatorname{sets} X \) and \( Y \)
A \( x \in\left[-\frac{\pi}{2}-\alpha, \frac{\pi}{2}-\alpha\right] \) and \( Y \in[c-r, c+r] \) where \( \alpha \)
\[
\tan ^{-1}\left(\frac{a+b \sqrt{2}}{a}\right) \text { and } r=\sqrt{a^{2}+\sqrt{2} a b+b^{2}}
\]
в. \( X \in\left[-\frac{\pi}{1}-\alpha, \frac{\pi}{1}-\alpha\right] \) and \( Y \in[c-r, c+r] \) where \( \alpha \)
\[
\tan ^{-1}\left(\frac{a+b \sqrt{2}}{a}\right) \text { and } r=\sqrt{a^{2}+\sqrt{2} a b+b^{2}}
\]
c. \( x \in\left[-\frac{\pi}{4}-\alpha, \frac{\pi}{4}-\alpha\right] \) and \( Y \in[c-r, c+r] \) where \( \alpha= \)
\[
\tan ^{-1}\left(\frac{a+b \sqrt{2}}{a}\right) \text { and } r=\sqrt{a^{2}+\sqrt{2} a b+b^{2}}
\]
D. \( X \in\left[-\frac{\pi}{8}-\alpha, \frac{\pi}{8}-\alpha\right] \) and \( Y \in[c-r, c+r] \) where \( \alpha= \)
\[
\tan ^{-1}\left(\frac{a+b \sqrt{2}}{a}\right) \text { and } r=\sqrt{a^{2}+\sqrt{2} a b+b^{2}}
\]


Using the digits 0,2,4,6,8 not more than once in any number, the number of 5 digited numbers that can be formed
is
A . 16
B. 24
\( c \cdot 120 \)
D. 96


Draw a ray diagram showing the formation of the image by a point object on the principal axis of a spherical convex surface separating
two media of refractive indices \( n_{1} \) and
\( n_{2}, \) when a point source is kept in
rarer medium of refractive index \( n_{1} \) Derive the relation between object and image distance in terms of refractive index of the medium and
radius of curvature of the surface.
Hence obtain the expression for lens-
maker's formula in the case of
thin convex lens.


In the atmosphere which colour of light gets scattered the least?


A cell of emf \( 4.5 ~ V \) is connected to a
junction diode whose barrier potential is \( 0.7 V . \) If the external resistance in the
circuit is \( 190 \Omega \), the current in the circuit is
\( \mathbf{A} \cdot 20 m A \)
B. \( 2 m A \)
\( c .23 m A \)
D. 200 mA


CO is practically non-polar since:
A. the \( \sigma \) -electron drift from \( C \) to \( O \) is almost nullified by the \( \pi \) -electron drift from \( O \) to \( C \)
B. the \( \sigma \) -electron drift from \( O \) to \( C \) is almost nullified by the \( \pi \) -electron drift from \( C \) to \( O \)
C. the bond moment is low
D. there is a triple bond between \( C \) and \( O \)


Solve \( \left(x^{2}+3 x\right)(2 x+3)-16 \frac{2 x+3}{x^{2}+3 x} \)


The graph below shows the momentum
of an object with respect to time. The
object is initially travelling in the positive direction. Which section has
the greatest magnitude of force acting on the object?
\( A \)
в.
c. 5
D. 283
E. 3 \& 5


Solve :
\( \int \frac{d x}{x^{2}+8 x+20} \)


Find the external work done by the system in kcal, when 20 kcal of heat is
supplied to the system the increase in the internal energy is \( 8400 J(J= \) \( 4200 J / k c a l) \)
A . \( 16 ~ k c a l l \)
B. 18 kcall
c. 20 k call \( l \)
D. 19 kcall \( l \)


In given figure the diagonal BD of a parallelogram ABCD intersects the
segment AE at the point \( F \), where E is
any point on the side BC. Prove that
\( \boldsymbol{D} \boldsymbol{F} \times \boldsymbol{E} \boldsymbol{F}=\boldsymbol{F} \boldsymbol{B} \times \boldsymbol{F} \boldsymbol{A} \)


A fruit seller bought mangoes at \( \boldsymbol{R} \boldsymbol{s} \boldsymbol{9 0} \)
per dozen and sold them at a loss of 8
percent. How much will a customer pay for:
i) one mango
ii) 40 mangoes


Cycas revoluta is popularly known as
A. Sago palm
B. Royal palm
c. Date palm
D. Sea palm


For a system to be in equilibrium, the torques acting on it must balance. This is true only if the torques are taken
about
A. the centre of the system
B. the centre of mass of the system
c. any point on the system


Write degree of the differential equation \( \frac{d^{2} y}{d x^{2}}+x\left(\frac{d y}{d x}\right)^{2}=2 x^{2} \log \left(\frac{d^{2} y}{d x^{2}}\right) \)


Fill in the blanks so as to make the
following statements true:
A ray stands on a line, then the sum of the two adjacent angles so formed is


In hypothetical reaction, \( \boldsymbol{A}_{2}+\boldsymbol{B}_{2} \longrightarrow \)
\( 2 A B, \) follows the mechanism as given
below:
\( A_{2} \rightleftharpoons A+A \quad \) (fast reaction)
\( A+B_{2} \longrightarrow A B+B \quad \) (slow reaction)
\( A+B \longrightarrow A B \quad \) (fast reaction)
Give the rate law and order of reaction.


toppr
Q Type your question.
4
B.
\( c \)
\( D \)


What is the minimum \( p H \) required to
prevent the precipitation of \( Z n S \) in a
solution that is \( 0.01 M Z n C l_{2} \) and
saturated with \( 0.10 M H_{2} S ? \)
\( \left(\boldsymbol{K}_{s p} \boldsymbol{o} \boldsymbol{f} \boldsymbol{Z} \boldsymbol{n} \boldsymbol{S}=\mathbf{1 0}^{-21}, \boldsymbol{K}_{\boldsymbol{a}_{1}} \times\right. \)
\( \left.\boldsymbol{K}_{a_{2}} \boldsymbol{o} \boldsymbol{f} \boldsymbol{H}_{2} \boldsymbol{S}=\mathbf{1 0}^{-20}\right) \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. 4


If \( \boldsymbol{X}=\left\{4^{n}-3 n-1: n \in N\right\} \) and
\( \boldsymbol{Y}=\{\mathbf{9}(\boldsymbol{n}-\mathbf{1}): \boldsymbol{n} \in \boldsymbol{N}\}, \) where \( \mathrm{N} \) is
the set of natural numbers, then \( \boldsymbol{X} \cup \boldsymbol{Y} \)
is equal to:
A. \( Y \)
B. \( N \)
c. \( Y-x \)
D. \( x \)


Choose the correct criteria to prove that two triangles are congruent:
Criteria:
A) All three corresponding sides are
congruent.
B) Two angles and the side between
them are congruent.
C) Two angles and a non-included side
are congruent.
D) Two sides and the angle between
them are congruent. For the given congruency theorem which option is suitable.
1) SSS (side-side-side) =
2) SAS (side-angle-side) =
3) AAS (angle-angle-side) =
4) ASA (angle-side-angle) ) =


The change in the gravitational potential energy when a body of mass \( \mathrm{m} \) is raised to a height \( n R \) above the surface of the Earth is (Here R is the
radius of the earth)
A \( \cdot\left(\frac{n}{n+1}\right) \) mgR
в. \( \left(\frac{n}{n-1}\right) \) тg \( R \)
c. \( n m g R \)
D. \( \frac{m g R}{n} \)


\( 60 \mathrm{mL} \) of a mixture of equal volume of
\( C l_{2} \) and an oxide of chlorine was heated
and then cooled back to the original temperature. The resulting gas mixture was found to have a volume of \( 75 \mathrm{mL} \). On
treatment with caustic soda solution, the volume contracted to 15 mL. Assume
that all measurements are made at the
same \( \mathrm{T} \) and \( \mathrm{P.} \) Deduce the simplest
formula for oxide of \( C l_{2} \) and calculate
its molar mass. The oxide of \( C l_{2} \) on
heating decomposes quantitatively to
\( O_{2} \) and \( C l_{2} . \) If the molar mass is \( x \)
\( \mathrm{gm} / \mathrm{mol}, \) then find the nearest integral
value of \( \boldsymbol{x} \)


Assertion
The \( p- \) isomer of dichlorobenzene has
higher melting point than o - and \( m- \) isomer
Reason
\( p- \) isomer is symmetrical and thus shows more closely packed structure
A. Assertion is true, Reason is true and Reason is correct explanation for Assertion
B. Assertion is true, Reason is true and Reason is NOT the correct explanation for Assertion
c. Assertion is true, Reason is false
D. Assertion is false, Reason is true


Animal that can change its colour is
A. Planaria
B. Octopus
c. Leech
D. Hydra


A wire of resistance 10.0 ohm is
stretched so as to increase its length by \( 20 \% \). Its resistance then would be:
A. 10.0 ohm
B. 12.0 ohm
c. 14.4 ohm
D. 10.2 ohm


Asthma may be attributed to
A. Bacterial infection of the lungs
B. Allergic reaction of the mast cells in the lungs
C. Inflammation of the trachea
D. Accumulation of fluid in the lungs


Find the friction force.


Sir Julian Huxley (1940) proposed the
term
A. New systematics
B. Natural selection
c. Phylogeny
D. Taxonomy


Copper pyrites, \( C u F e S_{2}, \) is the important source of copper. 10 g of it was leached with dil. \( H_{2} S O_{4} \) and solution diluted to 1 L
\( 10 \mathrm{mL} \) of this solution required \( 10 \mathrm{mL} \) of
0.02 \( \mathrm{M} \mathrm{KMnO}_{4} \) in acidic solution. What
is \% of \( F e \) in \( C u F e S_{2} ? \)


For an elastic material
\( \mathbf{A} \cdot Y>\eta \)
в. \( Y<\eta \)
c. \( Y \eta=1 \)
D. \( Y=\eta \)


Which of the following laws are conserved, if the areal acceleration is
zero
A. Law of conservation of angular velocity
B. Law of conservation of angular momentum
c. Law of conservation of angular acceleration
D. Law of conservation of angular displacement


A high school had 1200 students
enrolled in 2003 and 1500 students in
\( 2006 . \) If the student population \( P ; \) grows as a linear function of time \( t, \) where \( t \) is
the number of years after 2003
(a) How many students will be enrolled
in the school in \( 2010 ? \)
(b) Find a linear function that relates
the student population to the time \( t \)


A golfer swings a golf club so that the end of the club is moving \( 30 \mathrm{m} / \mathrm{s} \) when it strikes the ball. The radius of the
circular path for the end of the club (which includes the club and the
golfer's arms ) is \( 1.8 \mathrm{m} \)
What is the centripetal acceleration of
the end of the club as it strikes the
ball?
\( \mathbf{A} \cdot 500 m / s^{2} \)
B. \( 1.7 \mathrm{m} / \mathrm{s}^{2} \)
\( \mathbf{c} \cdot 0.06 m / s^{2} \)
D. \( 54 \mathrm{m} / \mathrm{s}^{2} \)
E . \( 0 \mathrm{m} / \mathrm{s}^{2} \)


The atomic number of astatine which
belongs to the sixth period is:
A . 53
B. 54
\( c \cdot 85 \)
D. 86


Which one of the following statements
is false?
A. Photochemical smog causes irritation in eyes
B. London smog is a mixture of smoke and fog
C. Photochemical smog results in the formation of PAN
D. London smog is oxidising in nature


Assertion
(A): Steel is more elastic than
rubber.
Reason (R): Under a given deforming force, steel is deformed less than rubber.
A) Both Assertion and Reason are true and the reason is correct explanation of
the assertion
B)Both Assertion and Reason are true,
but reason is not correct explanation of the assertion
C) Assertion is true, but the reason is
false
D) Assertion is false, but the reason is
true
\( A \cdot A \)
B. B
\( c \cdot c \)
\( D \cdot D \)


Find the discriminant of the following quadratic equations and hence determine the nature of the roots of the
equation:
\( \frac{1}{4} x^{2}-2 x+1=0 \)


The value of E for elements are as
follows:
\( \boldsymbol{F} \boldsymbol{e}^{+\mathbf{2}}+\boldsymbol{2} \boldsymbol{e} \rightarrow \boldsymbol{F} \boldsymbol{e} ; \boldsymbol{E}^{\boldsymbol{o}}=\mathbf{0 . 4 4} \boldsymbol{V} \)
\( \boldsymbol{F} \boldsymbol{e}^{+\mathbf{3}}+\mathbf{1} \boldsymbol{e} \rightarrow \boldsymbol{F} \boldsymbol{e}^{+\mathbf{2}} ; \boldsymbol{E}^{\boldsymbol{o}}=+\mathbf{0 . 7 7} \boldsymbol{V} \)
\( \boldsymbol{S} \boldsymbol{n}^{+\mathbf{4}}+\boldsymbol{2} \boldsymbol{e} \rightarrow \boldsymbol{S} \boldsymbol{n}^{+2} ; \boldsymbol{E}^{\boldsymbol{o}}=+\mathbf{0 . 1 3} \boldsymbol{V} \)
\( \boldsymbol{I}_{2}+\boldsymbol{2} \boldsymbol{e} \rightarrow \boldsymbol{2} \boldsymbol{I} ; \boldsymbol{E}^{o}=+\mathbf{0 . 5 4} \boldsymbol{V} \)
\( \boldsymbol{C r}^{3+}+\boldsymbol{3} \boldsymbol{e} \rightarrow \boldsymbol{C r} ; \boldsymbol{E}^{o}=\mathbf{0 . 7 4} \boldsymbol{V} \)
Based on the above data correct
statements are:

This question has multiple correct options
A. Strongest reducing agent is \( C r^{3+} \)
B. Strongest oxidising agent is \( F e^{3} \)
\( \mathbf{c} \cdot S n^{+4} \) can oxidise \( I \)
D. \( S n^{+3} \) can oxidise \( I \)


If A's salary is \( 50 \% \) more than B's, then
by what percent B's salary is less than A's salary?
A . 32\%
B. 33\%
\( \mathbf{c} \cdot 33 \frac{1}{3} \% \)
D. 42\%


Select wrong statement from the following:
Electromagnetic waves
A. are transverse
B. travel with same speed in all media
c. travel with the speed of light
D. are produced by accelerating charge


Fill up the blanks in the following paragraph by selecting the correct
option.
The movement of air into and out of the
lungs is carried out by creating a
(i) \( _{--}- \) between the lungs and the atmosphere. Inspiration can occur if intra-pulmonary pressure is
(ii) than the atmospheric pressure. Expiration takes place when the intra-pulmonary pressure is
(iii) \( _{---} \) than the atmospheric pressure. Inspiration is initiated by the
(iv) \( _{--} \) of diaphragm which
\( (v) \)
the volume of thoracic
chamber in the anteroposterior axis.
A. (i) concentration gradient (ii) less (iii) higher (iv) relaxation (v)increases
B. (i) concentration gradient (ii) higher (iii) less (iv) contraction (v)decreases
c. (i) pressure gradient (ii) higher (iii) less (iv) relaxation
(v)decreases
D. (i) pressure gradient (ii) less (iii) higher (iv) contraction (v) increases


State Newlands law of Octaves.


In heart cells, which one a second
messenger that speeds up muscle contraction in response to adrenaline
A . cAMP
B. сGMP
c. GтР
D. ATP
E. AMP


In what ways is the bar graph better
than pictography.


Which of the following represents an infra-red wavelength?
A \( \cdot 10^{-4} \mathrm{cm} \)
B. \( 10^{-5} \mathrm{cm} \)
\( \mathrm{c} \cdot 10^{-6} \mathrm{cm} \)
D. \( 10^{-7} \mathrm{cm} \)


Modes of controlling pollution in large
cities include :
A. less use of insecticides
B. proper disposal of organic wastes, sewage and industrial effluents
c. shifting of factories out of the residential area
D. all of the above


Certain force acting on a \( 20 \mathrm{kg} \) mass
changes its velocity from \( 5 m s^{-1} \) to
\( 2 m s^{-1} . \) Calculate the work done by the
force.


Q Type your question
Based on the graphs, how does the
motion between the two objects differ?
Frequency
II. Angular Frequency
III. Period
IV. Amplitude
V. Phase Constant
A . I and II
B. I, II, and III
C. I and III
\( D \)
E. All of them (I - v )


Sugar is soluble in water due to:
A. High solvation energy.
B. Ionic character of sugar.
C. High conductivity character of sugar.
D. Hydrogen bond formation with water.


If \( f(x) \) and \( g(x) \) are both continuous at
\( x=c \) then which of the following is/are
always continuous at \( x=c ? \)
This question has multiple correct options
A. \( f(x)+g(x) \)
B. \( (f(x)-g(x)) \times f(x) \)
c. \( g(x) \times f(x) \)
D. \( \frac{f(x)-g(x)}{g(x)} \)


Polaroid glass is used in sun glasses
because
A. It reduces the light intensity to half on account of polarisation
B. It is fashionable
c. It has good colour
D. It is cheaper


Stilt roots are reported from
A. Pandanus
B. Radish
c. Mango-ginger
D. Bryophyllum


Assertion
The inductive reactance limits
amplitude of the current in a purely inductive circuit
Reason
The inductive reactance is independent
of the frequency of the current
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The order and degree of the differential
equation \( y^{\prime}+\left(y^{\prime \prime}\right)^{2}=\left(x+y^{\prime \prime}\right)^{2} \) are:
A .2,1
в. 1,1
\( c \cdot 2,2 \)
D. 1,2


Which of the following have dipole
moment?

This question has multiple correct options
A. nitrobenzene
B. p-chloronitrobenzene
c. m-dichlorobenzene
D. o-dichlorobenzene


2.16 grams of \( \mathrm{Cu} \), on reaction with
\( H N O_{3}, \) followed by ignition of the
nitrate, gave 2.7 g of copper oxide. In another experiment 1.15 g of copper oxide, upon reaction with hydrogen, gave 0.92 g of copper. This data illustrate the law of:
A. multiple proportions
B. definite proportions
c. reciprocal proportions
D. conservation of mass


The pH values of certain familiar substances are given below
\( \begin{array}{ll}\text { Substance } & \text { pH value } \\ \text { Blood } & 7.4 \\ \text { Baking soda } & 8.2 \\ \text { Vinegar } & 2.5 \\ \text { Household ammonia } & 12\end{array} \)
Analyse the data in the table and answer the following questions
a) Which substances are acidic in
nature?
b) Which substances are basic in
nature?


Composition of azurite mineral is:
A \( \cdot C u C O_{3} \cdot C u O \)
в. \( C u\left(H C O_{3}\right)_{2} . C u(O H)_{2} \)
\( \mathrm{c} \cdot 2 \mathrm{Cu} \mathrm{CO}_{3} \cdot \mathrm{Cu}(\mathrm{OH})_{2} \)
D. None of these


Degree of a constant term of a
polynomial is
A .
B. 0
\( c \cdot 2 \)
D. Not defined


A body starts from rest and moves with
a uniform acceleration. The ratio of the
distance covered in the \( n^{t h} \) sec to the
distance covered in \( n \) sec is:
A \( \cdot \frac{2}{n}-\frac{1}{n^{2}} \)
B. \( \frac{1}{n^{2}}-\frac{1}{n} \)
C \( \cdot \frac{2}{n^{2}}-\frac{1}{n} \)
D. \( \frac{1}{n}-\frac{1}{n^{2}} \)


Both a short day plant and a long day
plant can produce flower
simultaneously in a given place. Explain.


Insert 17 arithmetic means between \( 3 \frac{1}{2} \) and \( -41 \frac{1}{2} \)


Rate of formation of \( \boldsymbol{S} \boldsymbol{O}_{3} \) according to
the reaction \( 2 S O_{2}+O_{2} \rightarrow \)
\( \mathbf{2 S O}_{3} \quad \) is \( \quad \mathbf{1 . 6} \times \mathbf{1 0}^{-\mathbf{3}} \mathbf{k g} \quad \mathbf{m i n}^{-\mathbf{1}} \)
Hence rate at which \( S O_{2} \) reacts is:
A . \( 1.6 \times 10^{-3} \mathrm{kg} \) min \( ^{-1} \)
В. \( 8.0 \times 10^{-4} k g \) min\( ^{-1} \)
c. \( 3.2 \times 10^{-3} k g \) min\( ^{-1} \)
D. \( 1.28 \times 10^{-3} \mathrm{kg} \) min\( ^{-1} \)


Heat capacity is amount of heat required to raise its temperature by
\( \mathbf{A} \cdot 1^{\circ} C \)
в. \( 1 K \)
c. Both
D. None


toppr
Q Type your question
from the bottom of the vessel.
The correct system of water flowing out
is :
\( A \)
B.
\( c \)
\( D \)


The expression
\( (\sqrt{2 x^{2}+1}+\sqrt{2 x^{2}-1})^{6}+ \)
\( \left(\frac{2}{\sqrt{2 x^{2}+1}+\sqrt{2 x^{2}-1}}\right)^{6} \) is a
polynomial of degree
\( A \cdot 6 \)
B. 8
c. 10
D. 12


Write short notes on synergic bonding.


Specific resistance of a wire depends on the
A. Length of the wire
B. Area of cross-section of the wire
c. Resistance of the wire
D. Material of the wire


A river/ lake with an inflow of domestic
sewage rich in organic waste may result in
A. Death of fish due to lack of oxygen
B. Drying of the river/ake very soon due to algal bloom
c. Increase population of aquatic food web organisms
D. An increased production of fish due to biodegradable nutrients


Write about rain-water harvesting and its advantages.


Explain what will happen to a plant cell, if it is kept in a solution having higher water potential.


A coil of self inductance \( 2 \cdot 5 H \) and
resistance \( 20 \Omega \) is connected to a
battery of emf 120V having internal
resistance of \( 5 \Omega \). Find the current in the
circuit in steady state.


The IUPAC name of the given compound
is:
A. 2,4 -butanedione
B. ethoxy ethanone
C. ethanoic diketone
D. acetic anhydride


A npn transistor is connected in
common emitter configuration in a given amplifier. A load resistance of \( 800 \Omega \) is connected in the collector
circuit and the voltage drop across it is
\( 0.8 V . \) If the current amplification factor
is 0.96 and the input resistance of the circuit is \( 192 \Omega \), the voltage gain and the power gain of the amplifier will respectively be
A .4,3.84
в. 3.69,3.84
\( c \cdot 4,4 \)
D. 4.3 .69


Area of a square is \( (100 \pm 2) m^{2} . \) Its
side is:
A. \( (10 \pm 1) m \)
в. \( (10 \pm 0.1) m \)
c. \( (10 \pm \sqrt{2}) m \)
D. \( 10 \pm \sqrt{2} \% \)


find the sum of the first 20 even natural
numbers.
A . 400
в. 410
c. 420
D. 430


A body is projected with some initial velocity \( u \) at angle \( \frac{\pi}{7} \) with the horizontal. At what angle should
another body be thrown so that the
horizontal range in both cases is the
same?
A. \( \frac{\pi}{2} \)
в. \( \frac{5 \pi}{14} \)
c. \( \frac{4 \pi}{7} \)
D. \( \frac{6 \pi}{7} \)


The most powerful chlorinating agent is :
A \( \cdot \mathrm{PCl}_{3} \)
в. \( \mathrm{Cl}_{2} \mathrm{O} \)
c. \( \mathrm{PCl}_{5} \)
D. \( \mathrm{ClO}_{2} \)


\[
C H_{3} O-C H=C H-N O_{2}
\]
ne
\( C H_{2}=C H-N O_{2} \) \( C H_{2}=C H-C l \)
\[
C H_{2}=C H_{2}
\]
Which of the following is the correct order of \( C=C \) bond lengths among
these compounds?
A \( I>I I>I I I>I V \)
\( V \)
в. \( I V>I I I>I I>I \)
c. \( I>I I I>I I>I V \)
D. \( I I>I I I>I>I V \)


For the reaction \( \boldsymbol{P C l}_{3}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) \rightleftharpoons \)
\( \boldsymbol{P C l}_{5}(\boldsymbol{g}) \) the value of \( \boldsymbol{K}_{c} \) at \( 250^{\circ} \boldsymbol{C} \) is 26
The value of \( \boldsymbol{K}_{\boldsymbol{p}} \) at this temperature will
be:
A . 0.61
B. 0.57
c. 0.83
D. 0.46


Loop of Henle is part of
A. Uriniferous tubule
B. Seminiferous tubule
c. Neuron
D. Muscle fibres


The noble gas which can form more number of compounds is :
A . Ne
в. не
c. \( x_{e} \)
\( D \cdot A \)


If 3 coins are tossed simultaneously,
the probability of 2 heads and 1 tail is:
A \( \cdot \frac{5}{8} \)
B. \( \frac{1}{8} \)
\( c \cdot \frac{3}{8} \)
D. \( \frac{7}{8} \)


Enzymatic filters are used for removing
A. Nitrogen pollutants
B. Chloride pollutants
c. Hydrocarbons
D. Lead


Assertion
When a battery is short-circuited, the
terminal voltage is zero.
Reason
In the situation of a short-circuit, the
current is zero
A. Both Assertion and Reason are correct and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct.


Among \( K O_{2}, A l O_{2}^{-}, B a O_{2} \) and \( N O_{2}^{+} \)
unpaired electron is present in:
A. \( K O_{2} \) only
B. \( N O_{2}^{+} \) and \( B a O_{2} \)
c. \( K O_{2} \) and \( A l O_{2}^{-} \)
D. \( B a O_{2} \) only


If both \( \alpha, \beta \) and \( 6 x^{2}+11 x+3=0 \) are
real roots of the equation then
A. both \( \cos ^{-1} \alpha \) and \( \cos ^{-1} \beta \) are real
B. both \( \operatorname{cosec}^{-1} \alpha \) and \( \cos ^{-1} \beta \) are real
C. both \( \cot ^{-1} \alpha \) and \( \cot ^{-1} \beta \) are real
D. none of these


A person standing between a pair of tall and wide cliffs claps his hands. He hears the first two echoes at 2 sec and 3
sec respectively. If the speed of sound is \( 330 \mathrm{m} / \mathrm{sec}, \) then
A. Separation between the cliffs is \( 825 \mathrm{m} \)
B. The time of third echo is 5 second
C. every third echo is the loudest
D. after the second echo,none is formed


\( \frac{x}{x} \)


What is true for E. coli with lac-z gene?
A. They cannot synthesize permease.
B. They cannot synthesize functional beta galactosidase.
C. They cannot synthesize transacetylase.
D. They cannot transport lactose from the medium into the cell.


Mass of a planet is \( 5 \times 10^{24} \mathrm{kg} \) and
radius is \( 6.1 \times 10^{6} \mathrm{m} . \) The energy
needed to send a 2 kg body into space from its surface, would be.
A. 9 joule
B. 18 joule
C. \( 2.2 \times 10^{8} \) joule
D. \( 1.1 \times 10^{8} \) joul


A perfectly reflecting mirror has an area
of \( 1 \mathrm{cm}^{2} \). Light energy is allowed to fall
on it for \( 1 h \) at the rate of \( 10 W / c m^{2} . \) The force that acts on the mirror is:
В. \( 6.7 \times 10^{-8} N \)
\( \mathrm{c} \cdot 1.34 \times 10^{-7} \mathrm{N} \)
D. 2.4 \( \times 10^{-4} N \)


How does the internal energy of the system change?
A. Increases
B. Decreases
c. Remains Same
D. cannot be predicted


State the following statement is True or
False

If the starting and end points of a vector are collinear, it is known as a unit
vector
A. True
B. False


A \( 10 V \) cell of negligible internal
resistance is connected in parallel
across a battery of emf \( 200 \mathrm{V} \) and
internal resistance \( 38 \Omega \) as shown in the
figure. Find the value of current in the
circuit.


Find union of \( A \) and \( B \) by representing
using Venn diagram:
\( \boldsymbol{A}=\{1,2,3,4,8,9\}, B=\{1,2,3,5\} \)
\( \mathbf{A} \cdot\{1,2,3,4,5,8,9\} \)
B . \{1,2,3\}
\( \mathbf{c} \cdot\{1,2,3,4,8,9\} \)
D. None of these


Choose the quadratic equation in \( \boldsymbol{p} \)
whose solutions are 1 and 7
A \( \cdot p^{3}-p x+6=0 \)
B . \( p^{2}-p x+6=0 \)
c. \( p^{2}-8 p+7=0 \)
D. \( p^{2}-5 p+7=0 \)


Complete hydrolysis of starch gives:
A. glucose and galactose in equimolar amounts
B. galactose and fructose in equimolar amounts
c. glucose only
D. glucose and fructose in equimolar amount


Which one of the following reactions is not associated with the Solvay process of manufacture of sodium carbonate?
A \( . \) NaCl \( +N H_{4} C O_{3} \rightarrow N a H C O_{3}+N H_{4} C l \)
в. 2 NaOH \( +C O_{2} \rightarrow \) Na\( _{2} \) CO \( _{3}+H_{2} \) O
c. \( 2 N a H C O_{3} \rightarrow N a_{2} C O_{3}+H_{2} O+C O_{2} \)
D. \( N H_{3}+H_{2} C O_{3} \rightarrow N H_{4} H C O_{3} \)


State Henry's law.


Name the anomalous pairs


Atomic hydrogen is used as:
A. rocket propolent
B. liquid fule
C. fire extinguisher
D. none of these


Let \( \omega=-\frac{1}{2}+i \frac{\sqrt{3}}{2}, \) then the value of the
determinant
\( \left|\begin{array}{ccc}1 & 1 & 1 \\ 1 & -1-\omega^{2} & \omega^{2} \\ 1 & \omega^{2} & \omega^{4}\end{array}\right|, \) is
This question has multiple correct options
\( A .3 \omega \)
В. \( 3 \omega(\omega-1) \)
\( c \cdot 3 \omega^{2} \)
D. \( 3(-2 \omega-1) \)


The diagram gives information about
blood pressures in various parts of the circulatory system during the cardiac cycle. At which point \( a, b, c \) or \( d, \) does
the semi-lunar valve of the aorta close?
\( A \)
B.
\( c \cdot d \)
\( D \)


If the centroid of the tetrahedron
\( O A B C, \) where \( A, B, C \) are given by \( (\alpha, 5,6),(1, \beta, 4),(3,2, \gamma) \) respectively
be \( 1,-1,2, \) then value of \( \alpha^{2}+\beta^{2}+\gamma^{2} \)
equals
A \( \cdot \alpha^{2}+\beta^{2} \)
B. \( \gamma^{2}+\beta^{2} \)
c. \( \alpha^{2}+\gamma^{2} \)
D. None of these


Dolly sheep was obtained by
A. Cloning the udder cell (somatic cell) fused with 6 enucleated oocyte
B. Cloning of gametes
C. Tissue culture
D. None of the above


Ethyl mercaptan is prepared by the reaction of the following, followed by hydrolysis:
A \( \cdot C_{2} H_{5} M g B r+S O_{2} \)
B. \( C_{2} H_{5} M g B r+S \)
c. \( C_{2} H_{5} M g B r+C S_{2} \)
D. \( C_{2} H_{5} M g B r+H_{2} S \)


If \( \boldsymbol{A}=[\mathbf{1}], \) then the order of the matrix
is
\( \mathbf{A} \cdot 1 \times 1 \)
в. \( 2 \times 1 \)
c. \( 1 \times 2 \)
D. None of these


ff \( \boldsymbol{A}=\left[\begin{array}{cc}\boldsymbol{6} & \boldsymbol{2} \\ \boldsymbol{5} & \boldsymbol{-} \boldsymbol{4}\end{array}\right] \) and \( \boldsymbol{B}=\left[\begin{array}{cc}\mathbf{1} & \boldsymbol{2} \\ -\boldsymbol{5} & \boldsymbol{1}\end{array}\right], \) find
a matrix \( X \) such that \( 2 A+3 B- \)
\( \mathbf{5} \boldsymbol{X}=\mathbf{0} \)


Value of the determinant \( \left|\begin{array}{ccc}\boldsymbol{x} & \boldsymbol{y} & \boldsymbol{z} \\ \boldsymbol{p} & \boldsymbol{q} & \boldsymbol{r} \\ \boldsymbol{y} \boldsymbol{z} & \boldsymbol{z} \boldsymbol{x} & \boldsymbol{x} \boldsymbol{y}\end{array}\right| \)
is equal to
A \( \cdot x^{p}\left(z^{2}-y^{2}\right)+q y\left(x^{2}-z^{2}\right)+r z\left(-x^{2}+y^{2}\right) \)
В . \( x^{p^{p}\left(z^{2}-y^{2}\right)+q y\left(x^{2}-z^{2}\right)+r z\left(x^{2}-y^{2}\right)} \)
C. \( x^{p}\left(z^{2}-y^{2}\right)+q y\left(-x^{2}+z^{2}\right)+r z\left(-x^{2}+y^{2}\right) \)
D.


\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left(\frac{\mathbf{3} \boldsymbol{x}+\boldsymbol{4}}{\mathbf{2} \boldsymbol{x}-\mathbf{3}}\right) \)
A \( \cdot \frac{17}{(2 x-3)^{2}} \)
B \( \cdot \frac{1}{(2 x-3)^{2}} \)
c. \( \frac{-1}{(2 x-3)^{2}} \)
D. \( \frac{-17}{(2 x-3)^{2}} \)


The formula of the complex tris (ethylene diamine) cobalt (III) sulphate is:
A \( \cdot\left[\operatorname{Co}(e n)_{2} S O_{4}\right] \)
в. \( \left[\operatorname{Co}(e n)_{3} S O_{4}\right] \)
\( ^{\mathbf{c}}:\left[C o(e n)_{3}\right]_{2} S O_{4} \)
D \( \cdot\left[C o(e n)_{3}\right]_{2}\left(S O_{4}\right)_{3} \)


If \( \boldsymbol{\alpha} \boldsymbol{\epsilon}\left(\mathbf{0}, \frac{\boldsymbol{\pi}}{\mathbf{2}}\right), \) then the value of
\( \tan ^{-1}(\cot \alpha)-\cot ^{-1}(\tan \alpha)+ \)
\( \sin ^{-1}(\sin \alpha)-\cos ^{-1}(\cos \alpha) \) is equal to
A \( .2 \alpha \)
B . \( \pi+\alpha \)
\( c \cdot 0 \)
D. \( \pi-2 \alpha \)


Assertion
Tyrosine behave as a acidic at \( \boldsymbol{p} \boldsymbol{H}=\mathbf{7} \)
Reason
\( p K_{a} \) of phenol is more than 7
Select the correct option.
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 cricket ball of mass 120 g is moving with a velocity of \( 12 m s^{-1} \), it turns back
and move with a velocity of \( 20 m s^{-1} \) when hit by a bat. Find the impulse and the force, if the force acts for 0.02 s.


Assertion
Galvanized iron does not rust.
Reason
Zn has a more negative electrode
potential than Fe.
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


A body of mass 5 kg undergoes a change in speed from 20 to \( 0.20 \mathrm{m} / \mathrm{s} \)
The momentum of the body would
A. increase by \( 99 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
B. decrease by \( 99 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
c. increase by \( 101 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
D. decrease by \( 90 \mathrm{kg} \mathrm{m} / \mathrm{s} \)


Light of wavelength 520 mm passing
through a double slit, produces
interference pattern of relative intensity
versus angular position \( \theta \) as shown in the figure. Find the separation
between the slits.


A steel wire of length \( 60 \mathrm{cm} \) and area of
\( \operatorname{cross} \operatorname{section} 10^{-6} m^{2} \) is joined with an
aluminium wire of length \( 45 \mathrm{cm} \) and
area of cross section \( 3 \times 10^{-6} m^{2} . \) The
composite string is stretched by a tension of \( 80 N . \) Density of steel is
\( 7800 k g m^{-3} \) and that of aluminium is
\( 2600 k g m^{-3} . \) The minimum frequency of tuning fork, which can produce standing wave in it with node at the joint is
A. \( 357.3 \mathrm{Hz} \)
В. \( 375.3 \mathrm{Hz} \)
\( \mathbf{c} .337 .5 \mathrm{Hz} \)
D. \( 325.5 \mathrm{Hz} \)


The girth of the stem or root increases
due to?
A. Apical meristem
B. Cambium
c. Inter catary meristem
D. Epidermis


Zener-diode is used in.
A. Amplification
B. Rectification
C. Oscillator in producing oscillations
D. Volatge regulation


\( O \) is the centre of the circle. If chord \( A B \)
chord \( C D, \) then value of \( x \) is equal to
4.70
3.50
\( c \cdot 55 \)
) . 45


Which of the following represents type(s) of environmental pollution
A. Air pollution
B. water pollution
c. soil pollution
D. All of the above


\( \ln C_{3} \) plants, the first stable product of photosynthesis during dark reaction is
A. 3-phosphoglyceric acid
B. Phosphoglyceraldehyde
c. Malic acid
D. Oxaloacetic acid


Carbon atoms in compound \( \left(C N_{4}\right) C_{2} \)
are:
A. sp hybridizes
B \( \cdot s p^{2} \) hybridized
c. \( s p \& s p^{2} \) hybridized
D. \( s p, s p^{2} \& s p^{3} \) hybridized


Select the best statement for the
situation above:
A. This mixture given an optical rotation of zero
B. Will rotate plane polarised light in clockwise direction
C. Will rotate plane polarised light in anticlockwise direction
D. None of the above statement is true


Is there any changes in the
hybridisation of \( B \) and \( N \) atoms as a result of the following reaction.
\( \boldsymbol{B} \boldsymbol{F}_{3}+\boldsymbol{N} \boldsymbol{H}_{3} \rightarrow \boldsymbol{F}_{3} \boldsymbol{B}-\boldsymbol{N} \boldsymbol{H}_{3} ? \)


In a potato race 20 potatoes are placed in a line at intervals of 4 metres with
the first potato 24 metres from the
starting point. A contestant is required to bring the potatoes back to the starting place one at a time. How far would he run in bringing back all the potatoes?
A . \( 2340 \mathrm{m} \)
B. 2480 m
\( c .2540 \mathrm{m} \)
D. 2230 m


cost of one apple is 3 times the cost of
an orange. If price of 3 apples is 72 then price of 6 oranges will be Rs.
A .24
B. 36 6
c. 48
D. 72


Assertion
A tube light emits white light.
Reason
Emission of light in a tube takes place
at a very high temperature.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which of the following is NOT a quadratic polynomial?
\( \mathbf{A} \cdot p(x)=16-4 x \)
в. \( p(x)=13-x \)
C \( \cdot p(x)=12 x^{3}-x \)
D. All of the above


At what depth (in terms of the radius of earth) the acceleration due to gravity will be \( \frac{2 g}{5} ? \)


\( \boldsymbol{f}(\boldsymbol{x})\left\{\begin{aligned}=& \frac{\left|\boldsymbol{x}^{2}-\boldsymbol{x}\right|}{\boldsymbol{x}^{2}-\boldsymbol{x}}, \quad \boldsymbol{x} \neq \boldsymbol{0}, \boldsymbol{x} \neq \mathbf{1} \\=& \boldsymbol{x}=\mathbf{0} \\=-\mathbf{1}, & \boldsymbol{x}=\mathbf{1} \end{aligned} \) Discus \right.
its continuity in \( 0<x \leq 1 \)
This question has multiple correct options
A. continuous at \( x=0 \)
B. dis-continuous at \( x=1 \)
c. dis-continuous at \( x=0 \)
D. continuous at \( x=1 \)


Which of the following has the smallest
size ?
\( \mathbf{A} \cdot I^{-} \)
B. \( S^{2-} \)
\( c \cdot O^{2} \)
D. \( C l \)


Find the \( 7^{t h} \) term from the last in the G.P
\( 2,4,8,16, \dots 60 \) terms


\( \sqrt{\sqrt[3]{125+\sqrt{24}}} \) is equal to
\( A \cdot \sqrt{5}-1 \)
B. \( \sqrt{3}+\sqrt{2} \)
c. \( \sqrt{3}+1 \)
D. \( \sqrt{5}+\sqrt{2} \)