The function of meiosis I is to separate
A. Homologous chromosomes
B. Parental chromosomes
c. sister chromatids
D. cross overs


Solve the given pair of equations by substitution method:
\( \boldsymbol{x}+\boldsymbol{y}=\mathbf{0} \)
\( \boldsymbol{y}-\boldsymbol{x}=\boldsymbol{6} \)
A. (2,7)
(i)
в. (-3,3)
c. (4,9)
(年. (4,9)
D. (-6,2)


I. Sewage water treatment plants are setup for controlling water pollution.
II. BOD level increases after sewage treatment.
A. I and II are true
B. I and II are false
c. I is true and II is false
D. I is false and II is true


Number of digits expressing the significant number in 10.216 is :
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D.


In a \( \triangle A B C, \) measure \( \angle A=35^{0} \)
measure \( \angle B=65^{0}, \) find measure \( \angle C \)
A \( \cdot 60^{\circ} \)
В. \( 70^{\circ} \)
\( c .80^{\circ} \)
D. None of these


From a solid circular cylinder with height \( 10 c m \) and radius of the base
\( 6 c m, \) a right circular cone of the same height and same base is removed. Find the volume of the remaining solid. Also, find the whole surface area.


What will happen if one kidney is
removed from the body of a human
being?
A. Death due to poisoning
B. Uremia and death
c. Stoppage of urination
D. Nothing, the person will survive and remain normal, another kidney will become hypertrophied


Chlorine gas bleaches moist litmus
paper.
A . True
B. False


Let \( \boldsymbol{A}=\{\boldsymbol{x}, \boldsymbol{y}, \boldsymbol{z}\}, \boldsymbol{B}=\{\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}\} \) and \( \boldsymbol{f} \)
\( A \rightarrow B \) be defined by \( f(x)=a, f(y)= \)
\( \boldsymbol{b}, \boldsymbol{f}(\boldsymbol{z})=\boldsymbol{c} . \) This function is
A. surjective but not injective
B. injective but not surjective
c. bijective
D. none of these


When the piston of a pump is pulled up, the pressure inside
A. decreases
B. increases
c. remains same
D. none of the above


Which of the following is a singleton
set?
A. \( \{x:|x|=5, x \in N\} \)
B . \( \{x:|x|=6, x \in Z\} \)
c. \( \left(x: x^{2}+2 x+1=0, x \in N\right) \)
D. \( \left\{x: x^{2}=7, x \in N\right\} \)


The behavior of a body under zero resultant force is given by:
A. Newtons third law of motion
B. Newtons second law of motion
c. Newtons first law of motion
D. Newtons law of gravitation


To convert mechanical energy into
electrical energy, one can use
A. DC dynamo
B. AC dynamo
c. motor
D. (A) \& (B)


The area of the piston in hydraulic
machine are \( 10 \mathrm{cm}^{2} \) and \( 225 \mathrm{cm}^{2} \). The
force required on the smaller piston to support a load of \( 1000 N \) on the larger piston.
A \( .44 .44 \mathrm{N} \)
B. 55.55
c. 33.33 N
D. 4.44 N


Which of the following molecule/ion has a zero dipole moment?
A \( \cdot C l F_{3} \)
в. \( I C l_{2}- \)
c. \( S F_{4} \)
D. None of these


Zener diodes with breakdown voltage ranging over \( 2 \mathrm{V}-200 \mathrm{V} \) are
commercially available. Breakdown voltage of a zener diode
A. Increases with increasing doping concentration
B. Decreases with increasing doping concentration
C. Does not depend on doping concentration
D. May increases or decreases with increasing doping concentration


A conducting wheel rim in which there
we three conducting rods of each of
length \( l \) is rotating with constant
angular velocity \( \omega \) in a uniform
magnetic field Bas show in figure. The
induced potential difference between
its centre and rim will be :
\( \mathbf{A} \cdot B \omega l^{2} \)
B. \( \frac{3}{2} B \omega l^{2} \)
c. 0
D. \( \frac{B \omega l^{2}}{2} \)


Which of the following does NOT involve application of Methanol?
A. As a solvent
B. As an anti-freeze in pipelines
c. In consumable liquor
D. In Windshield washer fluid


\( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) is:
A. oxidising agent
B. both oxidising and reducing agent
C . reducing agent
D. none of the above


Cyathium inflorescence shows the
presence of
A. Similar type of flowers
B. One central male flower surrounded by a few female flowers
C. Few female flowers surrounded by a few male flowers
D. Achlamydeous flowers


H-bond is not present in:
A. water
B. glycerol
c. hydrogen fluoride
D. hydrogen sulphide


with horizontal floor. \( \mu_{s} \) and \( \mu_{k} \) are
coefficients of static and kinetic
frictions between the wiper and the floor. The wiper can not be used to wipe
the floor for \( \boldsymbol{\theta}<\boldsymbol{\theta}_{0} \) even if a large force
directed along the handle aiming
towards the centre is applied. Angle \( \theta_{0} \)
is given by:-
\( \mathbf{A} \cdot \cos ^{-1} \mu_{k} \)
\( \mathbf{B} \cdot \tan ^{-1} \mu_{s} \)
\( \mathbf{c} \cdot \tan -1 \mu_{k} \)
D. \( \cot ^{-1} \mu_{s} \)


A light ray falls on the air glass
interface at an angle of \( 30^{\circ} . \) What is the
angle of refraction for this rays? \( \left(n_{a g}=\frac{3}{2}\right) \)


Solve:
\( \left(y^{2}+10 y+24\right) \div(y+4) \)


In the core of nuclear fusion reactor, the
gas becomes plasma because of
A. strong nuclear force acting between the deuterons
B. Coulomb force acting between the deuterons
c. coulomb force acting between deuteron-electron pairs
D. the high temperature maintained inside the reactor \( \operatorname{cor} \)


Give an example for
(a) Non-narcotic analgesics
(b) Antiseptics
(c) Artificial sweetening agent.


Which is the longest phase of cell cycle?
\( \mathbf{A} \cdot \mathbf{G}_{1} \) phase
B. G_phase
c. Prophase
D. Telophase


If measure of one angle of linear pair is
\( 102^{\circ}, \) then the measure of second angle
is \( 78^{\circ} \)
A . True
B. False


Find the scalar and vector components
of the vector with initial point (2,1) and terminal point (-5,7)


Of which of the following colloidal systems, fog is an example :
A. liquid dispersed in gas
B. gas dispersed in gas
c. solid dispersed in gas
D. solid dispersed in liquid


The number of real solutions of the
equation \( e^{x}+x=0 \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. none of these


Find the value of :
\( 36 x^{2}+49 y^{2}+84 x y, \) when \( x=3, y=6 \)


The corresponding sides of two similar triangles are \( 4 \mathrm{cm} \) and \( 5 \mathrm{cm} \) respectively, find the ratio of the area of the first triangle to the area of the 2 nd triangle:


I nree points are located at the vertıces
of an equilateral triangle having each
side as \( \alpha . \) All the points move
simultaneously with speed \( u \) such that
first point continually heads for second,
the second for the third and the third for
the first. Time taken by the points to
meet at the centre is
A \( \cdot \frac{\alpha}{3 u} \)
B. \( \frac{2 \alpha}{3 u} \)
c. \( \frac{\alpha^{2}}{u^{3}} \)
\( D \cdot 3 \alpha \)
\( 2 u \)


Vitamin A is known as:
A. thiamine
B. pyridoxine
c. retinol
D. tocopherol


A conductor with a cavity is charged positively and its surface charge density is \( \sigma . \) If \( E \) and \( V \) represent the electric field and potential, then inside the cavity:
\( \mathbf{A} \cdot \) and \( V=0 \)
B. \( E=0 \) and \( V=0 \)
c. \( E=0 \) and \( \sigma= \) constant
D. \( V=0 \) and \( \sigma= \) constant
E . \( E=0 \) and \( V= \) constant


The IUPAC name of:
A. 2,3 -dimethylpentanoylchloride
B. 2,2 -dimethylpentanoylchloride
c. 3,3 -dimethylpentanoylchloride
D. 2,4 -dimethylpentanoylchloride


Two discs of the same material and
thickness have radii \( 0.2 m \) and \( 0.6 m \)
Their moments of inertia about their
axes will be in the ratio
A . 1: 81
B. 1: 27
\( c \cdot 1: 9 \)
D. 1: 3


f \( \mathrm{K} \) is the average kinetic energy per atom, find \( x, \) such that \( x=K \times 10^{23} \)


The cause of Brownian movement which
is not shown by true solutions or
suspensions is due to:
A. unbalanced bombardment of particles by molecules of the dispersion medium
B. attractive forces between dispersed phase and dispersion medium
c. larger size of the particles due to which they keep colliding and settling down
D. conversion currents formed in the so


A constant temperature, the
equilibrium constant \( \left(\boldsymbol{K}_{\boldsymbol{p}}\right) \) for the
decomposition reaction \( N_{2} O_{4} \rightleftharpoons 2 N O_{2} \)
is expressed by \( \boldsymbol{K}_{\boldsymbol{p}}=\left(\boldsymbol{4} \boldsymbol{x}^{2} \boldsymbol{p}\right) /\left(1-\boldsymbol{x}^{2}\right) \)
where \( p= \) pressure and \( x= \) extent of
decomposition. Which one of the following statements is true?
A. \( K_{p} \) increases with increase in \( \mathrm{p} \)
B. \( K_{p} \) increases with increase in \( x \)
C. \( K_{p} \) increases with decrease in \( x \)
D. \( K_{p} \) remains constant with change in p and \( x \)


The magnetic moment of a transition metal of \( 3 d \) -series is \( 6.92 B M . \) Its
electronic configuration will be:
A \( \cdot(3 d)^{4}(4 s)^{2} \)
B \( \cdot(3 d)^{5}(4 s)^{1} \)
\( c \cdot(3 d)^{10} \)
D. \( (3 d)^{5}(4 s)^{0} \)


Assertion
Pascal's law is the working principle of a hydraulic lift.
Reason
Pressure is thrust per unit area
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 difference in the densities of low-
density (LDP) and high-density polymers (HDP) is due to the fact that:
A. LDP are highly branched structures while HDP consists of closely packed linear molecules
B. LDP are linear chains while HDP are branched chains of polythene
c. both LDP and HDP are unbranched linear chains with different lengths
D. at high temperature, the density of polymer is reduced


Suppose \( A \) and \( B \) are two square
matrices of same order. If \( \boldsymbol{A}, \boldsymbol{B} \) are
symmetric matrices, then \( A B-B A \) is
A. A symmetric matrix
B. A skew symmetric
c. A scalar matrix
D. A triangular matrix


A spherical ball contracts in volume by \( 0.01 \% \) when subjected to a normal
uniform pressure of 100 atm. The Bulk
modulus of its material is
A . \( 1.01 \times 10^{11} \mathrm{Nm}^{-2} \)
В. \( 1.01 \times 10^{12} \mathrm{Nm}^{-2} \)
c. \( 1.01 \times 10^{10} N m^{-2} \)
D. \( 1.01 \times 10^{13} \mathrm{Nm}^{-2} \)


If \( y=\ln \sqrt{\tan x} \) then the value of \( \frac{d y}{d x} \) at \( x=\frac{\pi}{4} \) is
\( A \cdot \infty \)
B.
c.
D.


Shape of methane is with
bond angle \( 109.5^{\circ} \)
A . tetrahedral
B. pyramidal
c. bipyramidal
D. none of these


A beam of the plane polarized light
having flux \( 10^{-3} \) watt falls normally on a polarizer of a cross sectional area \( 3 \times \) \( 10^{-4} m^{2} . \) The polarizer rotates with an
angular frequency of 31.4 rad/s. The energy of the light passes through the polarizer per resolution will be
A \( \cdot 10^{-4} \) Joule
B. \( 10^{-3} \) Joule
c. \( 10^{-2} \) Joule
D. \( 10^{-1} \) Joule


Which of the following statements are
correct?
This question has multiple correct options
A. Ducts of sub-mandibular glands are Wharton's ducts.
B. Sub-maxillary glands are largest salivary glands.
C. Maximum saliva is produced by parotid gland.
D. VII cranial nerve suply to parotid salivary gland.


Choose the correct answer from the
alternatives given.
Study the graph and answer the
questions

In case of which soft drink was he
average annual sale maximum during
the period \( 1988-1993 ? \)
A. Pep-up only
B. Pep-up and Dew-drop
c. cool-sip only
D. Cool-sip and Pep-up


The quantity of heat generated in a
conductor depends on
A. square of the current \( \left(I^{2}\right) \)
B. resistance of the conductor \( (R) \)
c. time for which the mean flows \( (t) \)
D. \( I^{2} R t \)


Sea Gulls excrete salts through
A . Liver
B. Lungs
c. Urine
D. Nasal gland


The reaction responsible for the production of light energy from the sun will be:
A . fission
B. fusion
c. nuclear
D. none of these


Let \( A=\{1,2,3\} \) and \( B=\{a, b\} . \) Which
of the following subsets of \( A \times B \) is a
mapping from \( \boldsymbol{A} \) to \( \boldsymbol{B} \) This question has multiple correct options
A・ \( \{(1, a),(3, b),(2, a),(2, b)\} \)
В \( \cdot\{(1, b),(2, a),(3, a)\} \)
c. \( \{(1, a),(2, b)\} \)
D. none of these


A series LCR circuit contains
inductance \( 5 m H, \) capacitance \( 2 \mu F \) and resistance \( 10 \Omega \). If a frequency A.C. source is varied, what is the frequency at which maximum power is dissipated?
\( ^{\mathbf{A}} \cdot \frac{10^{5}}{\pi} H z \)
в. \( \frac{10^{-5}}{\pi} H z \)
c. \( \frac{2}{\pi} \times 10^{5} H z \)
D. \( \frac{5}{\pi} \times 10^{3} H z \)


\( \lim _{x \rightarrow \infty}\{\sqrt{x^{2}+\sqrt{x^{4}+1}}-\sqrt{2} x\} \)
\( A \cdot \alpha \)
B.
\( c \cdot 2 \)
D.


Which one is used as a biofertilizer?
A. Nostoc
B. Funaria
c. volvox
D. Rhizopus


The composition of malachite is:
A. \( C u F e S_{2} \)
в. \( C u C O_{3} \)
c. \( C u C O_{3} \cdot C u(O H)_{2} \)
D. \( C u(O H)_{2} \)


If a current of 1.5 ampere flows through a metallic wire for 3 hours, then how many electrons would flow through the wire?
A \( \cdot 2.25 \times 10^{22} \) electrons
B. \( 1.13 \times 10^{23} \) electrons
C \( \cdot 1.01 \times 10^{23} \) electrons
D. \( 4.5 \times 10^{23} \) electrons


The solubility product of \( B a S O_{4} \) is
\( 1.5 \times 10^{-9} . \) Find out the solubility in (i)
pure water and (ii) \( 0.1 M B a C l_{2} \) solution.


A: Polymethyl methacrylate is also
known as plexi glass.
R: PMMA is used in decorative articles.
\( A . \) Both \( A \) and \( R \) are correct and \( R \) is the correct explanation of the \( A \)
B. Both A and R are correct but R is not the correct explanation of the \( A \)
C. A is correct but R is in correct
D. A is incorrect but \( R \) is correct


The formation of ideal solution involves:
A. increase in entropy
B. increase in enthalpy
c. increase in free energy
D. increase in energy


Assertion
In leptosporangiate development sporangia are formed from a group of
initials
Reason
Eusporangiate development of sporangia starts from single initial
A. If both the assertion and the reason are true and the reason is a correct explanation of the assertion
B. If both the assertion and reason are true but the reason is not a correct explanation of the assertion
C. If the assertion is true but the reason is false
D. If both the assertion and reason are false


Greenhouse gases trap heat in the atmosphere which makes the Earth warmer. Which of these groups consists of greenhouse gases that cause most harm?
A. Methane, Carbon dioxide, Nitrous oxide
B. Nitrogen, Oxygen, Methane
c. Ozone, Carbon monoxide, Helium
D. Water vapour, Nitrogen, \( C F C s \)


Methanol is called as Marine Methanol
beacuse:
A. it is an essential compound for marine life
B. it is mostly obtained from deep sea bed
C. it is used as a marine fuel
D. it serves as a signal indicator for big ships on burning


How will you convent (i) chloroethane to
butane
(ii) Methylamine to methyl isocyanide?


Which part of distance-time graph
represent as increasing speed?
A . 20-40
B. 40-60
c. \( 60-80 \)
D. \( 80-100 \)


The combining of waves as they overlap
is known as
A. diffraction
B. interference
c. refraction
D. resonance


Wood charcoal is used in gas masks because it
A. has good smell
B. dissolves poisonous gases
c. adsorbs poisonous gases
D. reacts with poisonous gases


What is the conductivity of a semiconductor sample having electron concentration of \( 5 \times 10^{18} \quad m^{-3}, \) hole
concentration of \( 5 \times 10^{19} \quad m^{-3} \)
electron mobility of \( 2.0 m^{2} v^{-1} s^{-1} \) and
hole mobility of \( 0.01 m^{2} v^{-1} s^{-1} ? \)
(Take charge of electron as \( 1.6 \times \)
\( \left.10^{-19} C\right) \)
A \( \cdot 1.68(\Omega-m)^{-1} \)
в. \( 0.59(\Omega-m)^{-1} \)
c. \( 1.83(\Omega-m)^{-1} \)
D. \( 1.20(\Omega-m)^{-1} \)


Assertion
\( \int_{0}^{\pi / 4} \frac{\cos x+\sin x}{\cos ^{2} x+\sin ^{4} x} d x=\frac{\pi}{4}+ \)
\( \frac{1}{2 \sqrt{3}} \log (2+\sqrt{3})=I \)
Reason
\( \boldsymbol{I}=\int_{0}^{1} \frac{\boldsymbol{d} \boldsymbol{x}}{1-\boldsymbol{x}^{2}+\boldsymbol{x}^{4}} \)
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


Among the following compounds, which one is not responsible for the depletion of ozone layer?
A \( \cdot C H_{4} \)
в. \( C F C l_{3} \)
c. \( C H C l_{3} \)
D. \( C l_{2} \)


Find the distance between the following pairs of points:(-5,7),(-1,3)


Write the principal value of \( \cos ^{-1}\left(\frac{1}{2}\right)-2 \sin ^{-1}\left(-\frac{1}{2}\right) \)


The term 'bio-magnification' refers to
the
A. Increase in population size
B. Increase in the concentration of non-degradable pollutants as they pass through the food chains
C. Blowing up of environmental issues by man
D. Growth of organisation due to food consumption


Who came up with the idea of
evolution?
A. Mendel
B. Morgan
c. charles Darwin
D. None of these


Incorrect order of the value of \( \Delta_{0} \) for the
given complexes?
\( \mathbf{A} \cdot\left[\operatorname{Cr}\left(N H_{3}\right)_{6}\right]^{3+}<\left[\operatorname{Cr}(\operatorname{en})_{3}\right]_{3+} \)
B . \( \left[C o(e n)_{3}\right]^{+3}>\left[R h(e n)_{3}\right]^{+} \)
C \( \cdot\left[C o\left(H_{2} O\right)_{6}\right]^{+2}<\left[\operatorname{Co}\left(H_{2} O\right)_{6}\right]^{+} \)
D. \( \left[N i c l_{6}\right]^{4}-<\left[N i\left(H_{2} O\right)_{6}\right]^{+2} \)


Find the distance between \( \boldsymbol{x}+\boldsymbol{y}+\mathbf{1}= \)
0 and \( 2 x+2 y+5=0 \)


Gallium is in
room temperature.
A. plasma
B. liquid
c. solid
D. gaseous


The solution of the equation
\( z(z-2 i)=2(2+i) \) are
A. \( 3+i, 3-i \)
B. \( 1+3 i, 1-3 i \)
c. \( 1+3 i, 1-i \)
D. \( 1-3 i, 1+i \)


Study the bar graph representing the number of persons in various age
groups in a town shown in Fig. 23.9
Observe the bar graph and answer the
following questions:
What is the total number of persons
living in the town in the age-groups 10
15 and \( 60-65 ? \)


Prove that \( :=(a-b)(b-c)(c-a)(a+ \)
\( b+c) \)
\[
\begin{array}{ll}1 & a \\ 1 & b \\ 1 & c & a^{3}\end{array}
\]


A telegraph post has 5 arms, each arm is capable of four distinct positions including the position of rest. The total number of signals that can be made is:
A . 625
в. 1023
\( c \cdot 1024 \)
D. 930


For which value of \( a \) and \( b, \lim _{x \rightarrow 0} \frac{\sin 2 x}{x^{3}}+ \)
\( \boldsymbol{a}+\frac{\boldsymbol{b}}{\boldsymbol{x}^{2}}=\mathbf{0} \)
A \( \quad b=-2 \) and \( a=\frac{4}{3} \)
B. \( b=2 \) and \( a=\frac{4}{3} \)
c. \( _{b}=-2 \) and \( a=\frac{-4}{3} \)
D. None of these


The enthalpy change \( (\triangle \boldsymbol{H}) \) for the
reaction, \( \boldsymbol{N}_{2}(\boldsymbol{g})+\boldsymbol{3} \boldsymbol{H}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{2} \boldsymbol{N} \boldsymbol{H}_{3}(\boldsymbol{g}) \)
is \( -92.38 \mathrm{kJ} \) at \( 298 \mathrm{K} \). The internal energy
change \( \triangle \boldsymbol{U} \) at \( 298 \mathrm{K} \) is:
A \( .-92.38 \mathrm{kJ} \)
J. \( -92.38 \mathrm{JJ} \).
B. -87.42 kJ
c. - -97.34 k
D. - 89.9 kJ


On heating glycerol with excess amount of \( \boldsymbol{H} \boldsymbol{I}, \) the product formed is:
A. allyl iodide
B. isopropyl iodide
c. propylene
D. \( 1,2,3- \) triiodopropane


The number and position of some groups have been found to influence the
carcinogenic activity of polynuclear hydrocarbons. Which of the following groups are the above-mentioned
groups?
\( \mathbf{A} \cdot-C H_{3} \)
в. \( -O H \)
с. \( -O C H_{3} \)
D. All of the above


A man in a car at location \( Q \) on a
straight highway is moving with speed
v. He decides to reach a point P in a
field at a distance d from the
highway(point M) as shown in the
figure. Speed of the car in the field is half to that on the highway. What should
be the distance RM, so that the time
taken to reach P is minimum?


Nitesh
\& Jitesh invested Rs 15000 and
Rs 18000 respectively in a business If the total profit at the end of the year is Rs 8800 and Nitesh being an active
partner gets an additional \( 12.5 \% \) of the profit find the total profit of Nitesh in Rs


In Duma's method for estimation of
nitrogen, 0.25 g of an organic compound gave \( 40 \mathrm{mL} \) of nitrogen collected at 300 K temperature and 725 mm pressure. If the aqueous tension at \( 300 \mathrm{K} \) is \( 25 \mathrm{mm} \) the percentage of nitrogen in the compound is:
A . 16.76
B. 15.76
c. 17.36
D. 18.20


Which blood cells transport oxygen?
A. Red
B. White
c. Both A and B
D. None of the above


Very short answer type. Name the source gland and give one
main action of the following hormones:
parathormone


There are two candidates in an election.
\( 11 \% \) of the voters did not vote. 500 votes
were declared invalid. The elected
candidate got 3300 votes more than his opponent. If the elected candidate got
\( 48 \% \) of the total votes, how many votes did each candidate get ?


Prove that \( (1+i)^{4}\left(1+\frac{1}{i}\right)^{4}=16 \)


Simplify: \( \frac{\mathbf{6 x}^{2}+\mathbf{9 x}}{\mathbf{3 x}^{2}-\mathbf{1 2 x}} \)


If \( \cos (x+y)=y \sin x, \) then find \( \frac{d y}{d x} \)


0
0
meso:
\( A \)
B.
\( c \)
All of these


Which forms(s) of cyclohexane is/are free from angle strain?
A. Chair form
B. Boat form
c. Twist boat form
D. All of the above


If \( 2\left[\begin{array}{ll}3 & 4 \\ 5 & x\end{array}\right]+\left[\begin{array}{ll}1 & y \\ 0 & 1\end{array}\right]=\left[\begin{array}{cc}7 & 0 \\ 10 & 5\end{array}\right], \) find
\( (x-y) \)


The displacement \( (x) \) of a particle
starting from rest is given by \( \boldsymbol{x}=\mathbf{6} \boldsymbol{t}^{2}- \)
\( t^{3} . \) The time at which the particle will
attain zero velocity again is
A . 2
B. 4
\( c .6 \)
D.


Which of the substances \( A, B \) or \( C \) has
the highest specific heat? The
temperature vs time graph is shown
4
B
\( c \)
A have eaual specific


If \( a_{1}, a_{2}, \dots a_{n} \) are positive real numbers
whose product is a fixed number \( c \), then
the minimum value of \( \boldsymbol{a}_{1}+ \)
\( \boldsymbol{a}_{2}+, \dots \boldsymbol{a}_{\boldsymbol{n}-1}+\boldsymbol{2} \boldsymbol{a}_{\boldsymbol{n}} \)
A \( \cdot n(2 c)^{1 / n} \)
B . \( (n+1) c^{1 / n} \)
\( \mathbf{c} \cdot 2 n c^{1 / n} \)
D. \( (n+1)(2 c)^{1 / n} \)


The fusion process is possible at high temperature because at high
temperatures
A. the nucleus disintegrates
B. molecules disintegrate
c. atoms become ionised
D. the nuclei get sufficient energy so as to overcome the Coulomb repulsive force


ratio of carbon and oxygen in carbon dioxide molecule.
A . 2:
B. 3:
\( c \cdot 4: 2 \)
D. 1:


Find the coordinates of the point, which divides the line segment joining the points \( \boldsymbol{A}(\mathbf{2},-\mathbf{6}, \mathbf{8}) \) and \( \boldsymbol{B}(-\mathbf{1}, \mathbf{3},-\mathbf{4}) \)
externally in the ratio 1: 3


An electric dipole of momentum \( \vec{p} \) is placed in a uniform electric field. The
dipole is rotated through a very smal angle from equilibrium and is released. Prove that it executes simple harmonic motion with frequency \( f=\frac{1}{2 \pi} \sqrt{\frac{p E}{I}} \)
Where, \( I= \) moment of inertia of the
dipole.


Assertion
To unscrew a rusted nut, we need a
wrench with longer arm.
Reason
Wrench with longer arm reduces the
torque of the arm.
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


Water shortage is a problem faced only by people living in rural ares.
A. True
B. False


A steel wire when bent in the form of a
square encloses an area of \( 121 \mathrm{cm}^{2} . \) If
the same wire is bent in the form of a
circle, find the area of the circle.


Assertion
WBCs accumulate at the site of wounds
by diapedesis.
Reason
It is the squeezing of leucocytes from
the endothelium.
A. If both the assertion and the reason are true and the
reason is a correct explanation of the assertion
B. If both the assertion and reason are true but the reason is not a correct explanation of the assertion
C. If the assertion is true but the reason is false
D. If both the assertion and reason are false


Density of \( 2.03 M \) aqueous solution of
acetic acid is \( 1.017 g m L^{-1} \) molecular mass of acetic is \( 60 . \) Calculate the
molality of the solution.
A . 2.27
B. 1.27
c. 3.27
D. 4.27


If \( \lim _{x \rightarrow 0} \frac{x^{a} \sin ^{b} x}{\sin x^{c}} \) where \( a, b, c \epsilon R-\{0\} \)
exists and has non-zero value. Then
A \( \cdot a+c=b \)
B . \( a+b=c \)
\( \mathbf{c} \cdot a=b+c \)
D. \( a+b+c=0 \)


Find the integral \( \int \frac{2 x}{x\left(x^{2}+1\right)} d x \)


The perfect gas equation for 4 gram of hydrogen gas is:
\( \mathbf{A} \cdot P V=R T \)
B. \( P V=2 R T \)
\( ^{\mathbf{c}} \cdot_{P V}=\frac{1}{2} R T \)
D. \( P V=4 R T \)


If \( \vec{a}+\vec{b}+\vec{c}=0, \) then the angle \( \theta \) between \( \vec{b} \) and \( \vec{c} \) is given by
\( ^{\mathrm{A}} \cdot \cos \theta=\frac{a^{2}-b^{2}-c^{2}}{2 b c} \)
B. \( \cos \theta=\frac{b^{2}+c^{2}-a^{2}}{2 b c} \)
c. \( \cos \theta=\frac{a^{2}+b^{2}-c^{2}}{2 b c} \)
D. none of these


What happens when a nonpolar
material is subjected to external electric field.


When the starting point is provided then, which of the following conditions is going to change the \( K \) of an equilibrium?
A. Concentration of reactants
B. Pressure
c. concentration of products
D. Temperature


Find the ratio in which the line segment
joining the points \( P(x, 2) \) divides the line segment joining the points \( \boldsymbol{A}(\mathbf{1} \mathbf{2}, \mathbf{5}) \) and \( B(4,-3) . \) Also find the value of \( x \)


\( \tan ^{-1}\left[\frac{\cos x}{1+\sin x}\right] \) is equal to
A \( \cdot \frac{\pi}{4}-\frac{x}{2}, \) for \( x \epsilon\left(-\frac{\pi}{2}, \frac{3 \pi}{2}\right) \)
B. \( \frac{\pi}{4}-\frac{x}{2}, \) for \( x \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \)
\( ^{\mathbf{C}} \cdot \frac{\pi}{4}-\frac{x}{2}, \) for \( x \in\left(\frac{3 \pi}{2}, \frac{5 \pi}{2}\right) \)
D \( \cdot \frac{\pi}{4}-\frac{x}{2}, \) for \( x \in\left(-\frac{3 \pi}{2},-\frac{3 \pi}{2}\right) \)


The product \( 2^{\frac{1}{4}} \cdot 4^{\frac{1}{16}} \cdot 8^{\frac{1}{48}} \cdot 16^{\frac{1}{128}} \cdot \ldots \) to \( \infty \)
is equal to?
A .2
B. \( 2^{\frac{1}{2}} \)
c. 1
D. \( 2^{\frac{1}{4}} \)


Solve:
\( \lim _{n \rightarrow \infty}\left\{\frac{1}{n+1}+\frac{1}{n+2}+\ldots+\frac{1}{2 n}\right\}= \)
\( A \cdot \log 2 \)
B . \( \log 3 \)
\( c \)
D. \( \frac{\pi}{2} \)


Among the following complexes, the diamagnetic complexes are
\( (\boldsymbol{K}): \boldsymbol{K}_{3}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{6}\right] \)
\( (L):\left[\operatorname{Co}\left(N H_{3}\right)_{6}\right] C l_{3} \)
\( (M): N a_{3}\left[C o(\text {oxalate})_{3}\right] \)
\( (N):\left[N i\left(H_{2} O\right)_{6}\right] C l_{2} \)
\( (\boldsymbol{O}): \boldsymbol{K}_{2}\left[\boldsymbol{P} \boldsymbol{t}(\boldsymbol{C} \boldsymbol{N})_{4}\right. \)
\( (\boldsymbol{P}):\left[\boldsymbol{Z n}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right]\left(\boldsymbol{N} \boldsymbol{O}_{3}\right)_{2} \)
A. \( K, L, M, N \)
в. \( K, M, O, P \)
c. \( L, M, O, P \)
D. \( L, M, N, O \)


An insulated box containing monatomic ideal gas of molar mass \( \mathrm{M} \)
is moving with a uniform speed v. The box suddenly stops and consequently the gas acquires a new temperature. Calculate the change in the
temperature of the gas. Neglect heat absorbed by the box.
A \( \cdot \Delta T=2 \frac{M v^{2}}{3 R} \)
в. \( \Delta T=\frac{M v^{2}}{3 R} \)
\( ^{\mathbf{C}} \Delta T=3 \frac{M v^{2}}{3 R} \)
D. \( \quad \Delta T=4 \frac{M v^{2}}{3 R} \)


If \( 4,64, p \) re in GP find \( p \)
A \( \cdot 1024 \)
B. 2944
\( c .512 \)
D. 256


The full form of NAD is
A. Nicotine adenosine diphosphate
B. Nicotinamide adenosine dinucleotide
C. Nicotinamide adenine dinucleotide
D. Nicotinamide adenine diphosphate


Calculate the amount of heat energy
required to raise the temperature of \( 100 g \) of copper from \( 20^{\circ} C \) to \( 70^{\circ} C \) Specific heat capacity of copper:
\( \mathbf{3 9 0} \boldsymbol{J k g}^{-1} \boldsymbol{K}^{-1} \)
A . \( 195 . J \)
в. \( 3900 J \)
c. \( 1950 J \)
D. \( 390 J \)


Principle behind electric generator is
A. when a straight conductor is moved in the electric field, then current is induced in the conductor
B. when a circular loop is moved in electric field, then current is induced in the conductor.
C. when a straight conductor is moved in a magnetic field, the current is induced in the conductor.
D. none


During the formation of sodium chloride, sodium transfers one electron
to chlorine to attain the configuration of which noble gas?
A. Neon
B. Argon
c. Helium
D. Krypton


The length of the shortest chord of the circles \( \boldsymbol{x}^{2}+\boldsymbol{y}^{2}+\boldsymbol{2} \boldsymbol{g} \boldsymbol{x}+\boldsymbol{2} \boldsymbol{f} \boldsymbol{y}+\boldsymbol{c}=\boldsymbol{0} \)
which passes through the point \( (a, b) \) inside the circle


The set of all animals on the earth is a
A. Finite set
B. singleton set
c. Null set
D. Infinite set


\( M^{-2} \) configure is \( 1 s^{2} 2 s^{2} 2 p^{6}, \) then
\( M^{+2} \) configuration will be :
A \( \cdot 1 s^{2} \)
B. \( 1 s^{2} 2 s^{2} \)
C \( \cdot 1 s^{2} 2 s^{2} 2 p^{2} \)
D. \( 1 s^{2} 2 s^{2} 2 p^{4} \)


Divide the given polynomial by the given monomial:
\( \left(\frac{2}{3} a^{2} b^{2} c^{2}+\frac{4}{3} a b^{2} c^{2}\right) \div \frac{1}{2} a b c \)
A \( \cdot \frac{4}{3}(a b c+b c) \)
в. \( \frac{2}{3}(a b c+2 b c) \)
c. \( \frac{4}{3}(a b c+2 b c) \)
D. None


How \( C O_{2} \) controls fire?
A. forms a blanket around fire.
B. brings down temperature of the fuel.
C. Both A and B.
D. None of above.


Generally which ores are concentrated
by froth floatation method? Describe
this method.


Which of the following molecular orbitals has two nodal planes?
A \( \cdot \sigma 2 s \)
в. \( \pi 2 p_{y} \)
\( \mathbf{c} \cdot \pi^{*} 2 p_{y} \)
D. \( \sigma^{*} 2 p_{x} \)


The dentition of higher organisms corresponds to which of the following structure of cockroaches?
A. Labium
B. Mandibles
c. Labrum
D. Hypopahrynxx


The \( C-C \) bond energy in ethane is:
A . 341.11kJ/mole
B. 411.11kJ/mole
c. \( 141.11 \mathrm{kJ} / \mathrm{mol} \)
D. 313.11kJ/mole


Which of the following is not a disadvantage of building large dams for
generating hydro electric power?
A. Disturbance of the natural ecosystem in the surrounding forest area
B. Disruption of the plants and animals life
c. Displacement of people on a large scale.
D. None of the above


If \( A \) is in the 3 rd quadrant and \( B \) is in the
fourth quadrant and \( \cos A= \) \( -\frac{15}{17}, \cos B=\frac{4}{5} \) find the value of
\( \cos (\boldsymbol{A}+\boldsymbol{B}) \)
A \( \cdot-\frac{84}{85} \)
в. \( \frac{84}{85} \)
\( c \cdot-\frac{34}{85} \)
D. None of these


If \( \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{2} & \mathbf{3} \\ \mathbf{1} & -\mathbf{4}\end{array}\right] \) and \( \boldsymbol{B}=\left[\begin{array}{cc}\mathbf{1} & -\mathbf{2} \\ -\mathbf{1} & \mathbf{3}\end{array}\right] \)
then verify that \( (A B)^{-1}=B^{-1} A^{-1} \)


Solve the following pair of equations by
reducing them to a pair of linear
equations:
\( \frac{1}{(3 x+y)}+\frac{1}{(3 x-y)}= \)
\( \frac{3}{4}, \frac{1}{2(3 x+y)}-\frac{1}{2(3 x-y)}=\frac{-1}{8} \)
A \( . x=2, y=7 \)
в. \( x=5, y=0 \)
c. \( x=1, y=1 \)
D. \( x=2, y=3 \)


\( C_{3} H_{9} N \) represents:
A. A primary amine only
B. A secondary amine only
C . A tertiary amine only
D. Two primary, a secondary and a tertiary amine


Ohm's law is :
A. \( V I \)
B . \( I^{2} R \)
\( c . I R \)
D. \( R^{2} I \)


A particle is projected from ground with some initial velocity making an angle
\( 45^{\circ} \) with the horizontal. It reaches at
height of \( 7.5 \mathrm{m} \) above the ground while it travels a horizontal distance of \( 10 \mathrm{cm} \) from the point of projection. The initia speed of the projection is
\( A \cdot 5 m / s \)
B. \( 10 \mathrm{m} / \mathrm{s} \)
\( c \cdot 20 m / s \)
D. \( 40 \mathrm{m} / \mathrm{s} \)


\( x^{2}=x y \) is a relation which is:
A. Symmetric
B. Reflexive
c. Transitive
D. All of these


If \( 49 x^{2}-b=\left(7 x+\frac{1}{2}\right)\left(7 x-\frac{1}{2}\right), \) then
the value of \( b \) is
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( \frac{1}{\sqrt{2}} \)
\( c \cdot \frac{1}{4} \)
D.


The two adjacent sides of a
parallelogram, \( \vec{a}=2 i+4 j-5 k \) and \( \vec{b}=i+2 j+3 k, \) then find the unit
vector parallel to its diagonal.


Find the number of permutations that can be made with the letters of the word
PRAR'?
A . \( 4 ! \)
в. \( \frac{4 !}{2 !} \)
c. \( 2 ! \times 2 ! \)
D. none of these


Solid Ammonium carbamate
dissociates as:
\( N H_{2} C O O N H_{4}(s) \rightleftharpoons 2 N H_{3}(g)+ \)
\( \boldsymbol{C O}_{2}(\boldsymbol{g}) \)
In a closed vessel, solid ammonium
carbonate is in equilibrium with its dissociation products. At equilibrium, ammonia is added such that the partial
pressure of \( N H_{3} \) at new equilibrium
now equals the original total pressure. Calculate the ratio of total pressure at new equilibrium to that of original total
pressure.
A \( \cdot \frac{31}{27} \)
в. \( \frac{17}{7} \)
c. \( \frac{49}{29} \)
D. None of these


Complete proteins are not found in plants.
A. True
B. False


An electromagnetic wave passing through the space is given by equations \( \boldsymbol{E}=\boldsymbol{E}_{o} \sin (\boldsymbol{w} \boldsymbol{t}-\boldsymbol{k} \boldsymbol{x}), \boldsymbol{B}=\boldsymbol{B}_{0} \sin (\boldsymbol{w} \boldsymbol{t}- \)
\( k x) \) which of the following is true?
A \( \cdot E_{o} B_{0}=w k \)
в. \( E_{o} w=B_{o} k \)
c. \( E_{o} k=B_{o} w \)
D. \( E_{o} w k=B_{o} \)


Wool fibre can be obtain
from
A. sheep
B. goat
c. Ilama
D. all of these


Why do humans have two eyes?
a. The view field is increased up to \( 180^{\circ} \)
b. Better detection of faint objects
c. 3 dimensional view
d. More accurate estimation of distance
\( A \cdot a, b \) and \( d \)
B. c and d
\( c \cdot a, c \) and \( d \)
D. All of the above


The mean of 20 items of a data is 5 and
if each item is multiplied by 3 then the mean will be
A . 5
B. 10
c. 15
D. 20


We find it difficult to hear if we put
cotton in our ears. This is because
A. cotton damps the sound wave before reaching the ear drum
B. cotton creates a vacuum in the ear
c. cotton conducts the vibration to the ear drum
D. none of the above is true


Which of the following statement is NOT
true?
A. Lightning and spark from woolen clothing are essentially the same phenomena.
B. When you rub a plastic scale on your dry hair, it acquires a charge.
C. Charge acquired by a glass rod when it is rubbed with silk is called as negative charge.
D. Static charges are called so, because they do not move by themselves


The first four ionisation energy of an element are 191,578,872 and \( 5962 k c a l \)
mol \( ^{-1} \) respectively. The number of valence electrons is:


Ashok got the following marks in different subjects in a unit test,
20,11,21,25,23 and \( 14 . \) What is arithmetic mean of his marks?


Which of the following is true for
Thomson's model of the atom?
A. The radius of an electron can be calculated using Thomson's model
B. In an undisturbed atom, the electrons will be at their
equilibrium positions, where the attraction between the cloud of positive charge and the electrons balances their mutual repulsion
C. When the electrons are disturbed by collision, they will vibrate around their equilibrium positions and emit electromagnetic radiation whose frequency is of the order of magnitude of the frequency of electromagnetic radiation of a vibrating electron
D. Both
(B) and (C)


Find the maximum value of \( \left|\begin{array}{ccc}\mathbf{1} & \mathbf{1} & \mathbf{1} \\ \mathbf{1} & \mathbf{1}+\sin \boldsymbol{\theta} & \mathbf{1} \\ \mathbf{1} & \mathbf{1} & \mathbf{1}+\mathbf{c} \mathbf{o} \mathbf{s} \boldsymbol{\theta}\end{array}\right| \)


Resistance of a resistor at temperature
\( t^{\circ} \boldsymbol{C} \) is \( \boldsymbol{R}_{t}=\boldsymbol{R}_{0}\left(\mathbf{1}+\boldsymbol{\alpha} \boldsymbol{t}+\boldsymbol{\beta} \boldsymbol{t}^{2}\right), \) where \( \boldsymbol{R}_{0} \)
is the resistance at \( 0^{\circ} \mathrm{C} \). The
temperature coefficient of resistance at
temperature \( t^{\circ} C \) is
A \( \cdot \frac{\left(1+\alpha t+\beta t^{2}\right)}{\alpha+2 \beta t} \)
B. \( (\alpha+2 \beta t) \)
c. \( \frac{\alpha+2 \beta t}{\left(1+\alpha t+\beta t^{2}\right)} \)
D. \( \frac{\alpha+2 \beta t}{2\left(1+\alpha t+\beta t^{2}\right)} \)


Ethanoic acid + Ethanol
Isotopic oxygen of water will be present
with :
This question has multiple correct options
A. Ethanoic acid
B. Ethanol
c. After some time it will also be present in some molecules of ester
D. None of these


\( \lim _{x \rightarrow \pi / 2} \frac{\left(1-\tan \frac{x}{2}\right)}{\left(1+\tan \frac{x}{2}\right)} \frac{(1-\sin x)}{(\pi-2 x)^{3}} \) is equal
to -
A. 0
в. \( \frac{1}{32} \)
\( c \cdot \alpha \)
D.


Two boats approach a light house in mid-sea from opposite directions. The angles of elevation of the light house
from two boats are \( 30^{\circ} \) and \( 45^{\circ} \)
respectively. If the distance between two boats is \( 100 \mathrm{m}, \) find the height of the light house.


Let \( \sin \alpha, \) cos \( \alpha \) be the roots of the
equation \( x^{2}-b x+c=0 . \) Then which of
the following statements is / are correct?

This question has multiple correct options
A \( \cdot c \leq \frac{1}{2} \)
в. \( b \leq \sqrt{2} \)
c. \( c>\frac{1}{2} \)
D. \( b>\sqrt{2} \)


The vertices of a triangle are 2,3,5)\( ,(-1,3,2),(3,5,-2), \) then the
angles are
\( \mathbf{A} \cdot 30^{\circ}, 30^{\circ}, 30^{\circ} \)
\( ^{\mathrm{B}} \cos ^{-1}\left(\frac{1}{\sqrt{5}}\right), 90^{\circ}, \cos ^{-1}\left(\frac{\sqrt{5}}{\sqrt{3}}\right) \)
c. \( 30^{\circ}, 60^{\circ}, 90^{\circ} \)
D \( \cdot \cos ^{-1}\left(\frac{1}{\sqrt{3}}\right), 90^{\circ}, \cos ^{-1}\left(\frac{\sqrt{2}}{\sqrt{3}}\right) \)


\( \boldsymbol{f}: \boldsymbol{Q} \rightarrow \boldsymbol{Q} \) is defined by \( \boldsymbol{f}(\boldsymbol{x})=\mathbf{1 5} \boldsymbol{x}+\mathbf{7} \)
is
A . injective only
B. surjective only
c. bijective
D. neither injective nor surjective


Hydrogen chloride and \( S O_{2} \) are the side products in the reaction of ethanol with thionyl chloride. Which of the following is the main product in this reaction?
A. \( C_{2} H_{5} O C_{2} H_{5} \)
B. \( C_{2} H_{6} \)
c. \( C H_{3} C l \)
D \( \cdot C_{2} H_{5} C l \)


Why four-chambered heart is
beneficial?
A. It increases blood pressure.
B. It pumps blood to the lungs more often, so blood is better oxygenated.
C. It separates oxygenated and deoxygenated blood.
D. It lowers blood pressure and the threat of heart attacks.
E. It supplies the brain with more blood for cognition.


The equilibrium constant \( \left(\boldsymbol{K}_{c}\right) \) for the
reaction \( \boldsymbol{H} \boldsymbol{A}+\boldsymbol{B} \rightleftharpoons \boldsymbol{B} \boldsymbol{H}^{+}+\boldsymbol{A}^{-} \) is \( \mathbf{1 0 0} \)
If the rate constant for the forward
reaction is \( 10^{5} \), then rate constant for
the backward reaction is
A \( \cdot 10^{7} \)
B . \( 10^{3} \)
\( \mathbf{c} \cdot 10^{-3} \)
D. \( 10^{-5} \)


A block of mass \( m \) moving at a speed \( v \)
collides with another block of mass \( 2 m \)
at rest. The lighter block comes to rest after collision. What is the coefficient of
restitution.


What is the reason for the success of
monerans?
A. Eukaryotic nature and rigid cell wall
B. Absence of nucleus and other membrane bound organelles
C. Absence of vacuole and microscopic in nature
D. Rapid rate of cell division and metabolic diversity


Which of the following process is not a physical process of separation?
A . Levigation
B. Magnetic separation
c. Leaching
D. Froth fioatation


The tables show the resistance values
for three different resistors and the
currents through each resistor.
What is the ranking of the power
dissipated by each resistor, greatest
first?
\( \begin{array}{lc}\text { Current 1 } & \mathbf{2 I} \\ \text { Resistance 1 } & R \\ \text { Current 2 } & I \\ \text { Resistance 2 } & 2 R \\ \text { Current 3 } & I \\ \text { Resistance 3 } & 4 R\end{array} \)
A \( .3,2, \) and 1 tie
\( \mathbf{B} \cdot 3,2,1 \)
\( c \)
1,2,3
D. 1 and 3 tie, 2
E . All tie


In Fig. \( 1.35, \) a uniform bar of length I \( \mathrm{m} \) is supported at its end and loaded by a weight \( \mathrm{W} \) kgf at its middle. In
equilibrium, find the reactions \( \boldsymbol{R}_{1} \) and
\( R_{2} \) at the ends.


Match column - -I with column-II and
select the correct answer using the
codes given below:
Column-I Column
(A)
The rate of change \( \quad(p) \quad \) Accelera of momentum
The ratio of the total
(B) distance travelled to
(q) Velocity
the total time taken
\( (C) \)
The time rate of \( \quad \) (r) \( \quad \) Average
\( (r) \)
change of velocity \( \quad \) '(') \( \quad \) speed
Displacement per \( \quad(s) \quad \) Force
(D) \( \quad \) unit time
\( \mathbf{A} \cdot(A) \rightarrow(s),(B) \rightarrow(r),(C) \rightarrow(p),(D) \rightarrow(q) \)
B \( .(A) \rightarrow(p),(B) \rightarrow(r),(C) \rightarrow(q),(D) \rightarrow(s) \)
\( \mathbf{c} \cdot(A) \rightarrow(s),(B) \rightarrow(p),(C) \rightarrow(r),(D) \rightarrow(q) \)
D. \( (A) \rightarrow(q),(B) \rightarrow(r),(C) \rightarrow(p),(D) \rightarrow(s) \)


Show that the force on each plate of a parallel plate capacitor has
a magnitude equal to \( \left(\frac{1}{2}\right) \mathrm{QE} \), where \( \mathrm{Q} \) is
the charge on the capacitor, and E is the magnitude of electric field between the
plates. Explain the origin of the factor.


Simplify the following:
\( \frac{3-i}{2+i}+\frac{3+i}{2-i} \)


\( N O_{2} \) required for a reaction is produced
by the decomposition of \( N_{2} O_{5} \) in \( C C l_{4} \) as per the equation \( \mathbf{2} N_{2} O_{5}(g) \rightarrow 4 N O_{2}(g)+O_{2}(g) \)
The initial concentration of \( N_{2} O_{5} \) is
3.00 mol \( L^{-1} \) and it is 2.75 mol \( L^{-1} \)
after 30 minute. The rate of formation of
\( N O_{2} \) is :
в. \( 4.167 \times 10^{-3} \) mol \( L^{-1} \) min \( ^{-1} \)
c. \( 8.333 \times 10^{-3} \) mol \( L^{-1} \min ^{-1} \)
D. \( 1.667 \times 10^{-2} \) mol \( L^{-1} \min ^{-1} \)


Read the following statements carefully
(I) Energy transfer in the biotic world always proceeds from the autotrophs.
(II) Energy flow in undirectional
(III) Energy availability is maximum at the tertiary level
(IV) There is loss of energy from one
trophic level to that other.

Select the relevant statements for the
forest ecosystem.
\( \mathbf{A} \cdot \) ।, ॥ and \( 1 \mathbf{V} \)
B. I, II and III
c. ।, III and IV
D. II, III and IV


The radius of the earth is given \( 6.4 \times \)
\( 10^{6} m . \) What is the order of magnitude of
the size of the earth?
\( \mathbf{A} \cdot 10^{6} m \)
B . \( 6 \times 10^{6} \mathrm{m} \)
\( \mathbf{c} \cdot 10^{7} m \)
D . \( 5 \times 10^{6} m \)


The length and area of cross-section of a conductor are doubled, its resistance
is
A. unchanged
B. halvedd
c. doubled
D. quadrupled


Select the correct order of acidic nature
of non-metal oxide:
This question has multiple correct options
А. \( C O>C O_{2} \)
в. \( C O_{2}> \) СО
\( \mathrm{c} \cdot \mathrm{CO}_{2}>\mathrm{SiO}_{2} \)
D. \( C O_{2}< \) SiO \( _{2} \)


The genetic information in the body is encoded in the
A. Structural proteins
B. Enzymes
c. DNA
D. DNA and enzymes


Differentiate the following functions
with respect to \( x \)
\( (x \cos x)^{x}+(x \sin x)^{1 / x} \)


Which of the following is correct?
A. lodine is solid
B. Chlorine is insoluble in water.
C. lodine is more reactive than bromine.
D. Bromine is more reactive than chlorine.


Draw the diagram showing electroplating of a brass article silver and label the following:
a. Anode.
b. Electrolyte


The number of solutions of the
equation \( 1+x^{2}+2 x \sin \left(\cos ^{-1} y\right)=0 \)
is
\( A \)
B. 2
\( c \cdot 3 \)
\( D \cdot 4 \)


Find the number of spectral line in
Paschen series emitted by atomic \( \boldsymbol{H} \)
when electron excited from ground
state to \( 70^{t h} \) energy level return back.


Alpha particles that come closer to the nuclei
A. are deflected more
B. are deflected less
c. make more collision
D. are slowed down more


The diagram shows the speed-time
graph for a car. Which area represents the distance
traveled while the car is accelerating?
\( A \cdot X \)
B. \( X+Y \)
\( c . Y \)
D. \( Y-X \)


If the distance travel by a uniformly
accelerated particle in \( p \) th \( , q t \) and \( r t h \) second are \( a, b \) and \( c \) respectively. Then
A \( .(q-r) a+(r-p) b+(p-q) c=1 \)
B. \( (q-r) a+(r-p) b+(p-q) c=-1 \)
c. \( (q-r) a+(r-p) b+(p-q) c=0 \)
D. \( (q+r) a+(r+p) b+(p+q) c=0 \)


Dipole moment \( \propto \) diff.in \( e^{-} \) unity is
\( \boldsymbol{H} \boldsymbol{F}>\boldsymbol{H} \boldsymbol{C l}>\boldsymbol{H} \boldsymbol{B r}>\boldsymbol{H} \boldsymbol{I} \)
A. True
B. False


In an entrance test, there are multiple
choice questions. There are four possible options of which one is correct. The probability that a student knows
the answer to a question is \( 90 \% \). If he
gets the correct answer to a question, then the probability that he was guessing is
A \( \cdot \frac{1}{37} \)
B. \( \frac{36}{37} \)
\( c \cdot \frac{1}{4} \)
D. \( \frac{1}{49} \)


Which lenses are used in her
spectacles?


Two very long, straight wires carrying currents as shown in figure. Find all locations where the net magnetic field is zero
\( y=\sqrt{2} x \)
\( x \)
в. \( y=x \)
c. \( y=-x \)
D. \( y=-(x / 2) \)


\( 14 \mathrm{g} \) of nitrogen contains \( 3.01 \times 10^{23} \)
nitrogen molecules.
A. True
B. False


Assertion
Matter can neither be created nor
destroyed.
Reason
This is law of definite proportions.
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 heat capacity of a solid of mass 175
g is \( 315 \mathrm{J}^{\circ} \mathrm{C}^{-1} \). Calculate specific heat
capacity of solid.


is displaced from potassium bromide solution by
chlorine.
A. Potassium
B. Bromine
c. Both potassium and bromine
D. None of these


In an exothermic reaction if \( \mathrm{H} \) is the
enthalpy then activation energy is:
A. More than
B. Less than
c. Equal to the
D. None of the above


Which of the following is not a favourable condition for physical adsorption?
A. Higher critical temperature of adsorbate
B. Low temperature
c. High pressure
D. High temperature


Q Type your question
chord is attached to the object through
this hole The object is set into motion
with initial velocity of magnitude \( v_{0} \) at
right angle to the chord and at tehsame
time the chord is pulled through the
hole at uniform speed c m/s. Initially
object is at point \( \mathbf{A}\left(0, r_{0}\right) \) and at any
time I it is at point \( P(r \cos \theta, r \sin \theta) \)
Neglect the dimension of object Choose
CORRECT options(s)
This question has multiple correct options
A \( \cdot \) tension in the chord at any time t is \( \frac{m r_{0}^{2} v_{0}^{2}}{\left(r_{0}-c t\right)^{3}} \)
B. Tension in the chord at any time t is \( \frac{2 m_{0}^{2} v_{0}^{2}}{\left(r_{0}-c t\right)^{2}} \)
Condar speed of the object at any time is \( \frac{2 r_{0} v_{0}}{\left(r_{0}-c t\right)^{2}} \)
D. Angular speed of the object at any time t is \( \frac{r_{0} v_{0}}{\left(r_{0}-c t\right)^{2}} \)


n \( \Delta A B C, D E \| B C, A D=2.4 c m \)
\( A E=3.2 c m, C E=4.8 \mathrm{cm} . \) Find \( B D \)


Let \( T \) be the set of all triangles in a plane with \( \boldsymbol{R} \) a relation in \( \boldsymbol{T} \) given by
\( \left.\boldsymbol{R}=\left\{\left(\boldsymbol{T}_{1}, \boldsymbol{T}_{2}\right)\right\}: \boldsymbol{T}_{1} \text { congruent to } \boldsymbol{T}_{2}\right\} \)
Show that \( R \) is an equivalence relation.


The displacement-time graphs of two particles \( A \) and \( B \) are straight lines
making angles of respectively \( 30^{0} \) and
\( 60^{0} \) with the time axis. If the velocity of
\( A \) is \( v_{A} \) and that of \( B \) is \( v_{B}, \) then value of \( \frac{\boldsymbol{v}_{\boldsymbol{A}}}{\boldsymbol{v}_{\boldsymbol{B}}} \) is:
A. \( 1 / 2 \)
B. \( 1 / \sqrt{3} \)
\( c \cdot \sqrt{3} \)
D. \( 1 / 3 \)


What is the \( H^{+} \) ion concentration in
ammonium acetate solution?
\( \left(\boldsymbol{K}_{\boldsymbol{a}}=\mathbf{1 . 8} \times \mathbf{1 0}^{-\mathbf{5}}, \boldsymbol{K}_{\boldsymbol{b}}=\mathbf{1 . 8} \times \mathbf{1 0}^{-\mathbf{5}}, \boldsymbol{K}_{\boldsymbol{v}}\right. \)


In the following table the ecological
units are mentioned in the first column
vertically and their attributes are
mentioned horizontally Which of the following options is correct for
ecological units with their respective attributed indicated by \( A \) to \( P \)
Attributes Age of Age of Ecological \( \quad \) Age
Individual \( B \) Organism
Population \( E \)
I
Community
\( V \)
\( M \) Ecosystem
A . I-C II-B III-K IV-P
B. I-A II-G III-LIV-N
c. I-C II-A III-K IV-L
D. I-A II-B III-C IV-D


Under the action of a force, a \( 2 \mathrm{kg} \) body
moves such that its position \( ^{\prime} x^{\prime} \) in
meters as a function of time \( ^{\prime} t^{\prime} \) in
seconds given by: \( \boldsymbol{x}=\boldsymbol{t}^{2} / \mathbf{2} . \) The work
done by the force in the first 5 seconds is?


The standard reduction potentials \( \boldsymbol{E}^{\circ} \)
for \( \boldsymbol{O C l}^{-} / \boldsymbol{C l}^{-} \) and for \( \boldsymbol{C l}^{-} / \mathbf{1} / \mathbf{2 C l}_{2} \) are
\( 0.86 V \) and -1.10 volt respectively. The
\( \boldsymbol{E}^{\circ} \) value of \( \boldsymbol{O C l}^{-} / \mathbf{1} / \mathbf{2} \boldsymbol{C l}_{\mathbf{1}} \) will be \( \boldsymbol{?} \)
\( \mathbf{A} \cdot+1.96 V \)
B . \( -1.96 V \)
c. \( +0.24 V \)
D. \( -0.24 V \)


Which of the following does not have the dimensions of force?
A. Gravitational Potential gradient
B. Energy gradient
c. weight
D. Rate of change of momentummmmmm


The correct order of stability of
\( \boldsymbol{A l}^{+}, \boldsymbol{A l}^{+2}, \boldsymbol{A l}^{+\mathbf{3}} \mathbf{i s} \)
A \( \cdot A l^{+3}>A l^{+2}>A l^{+} \)
B. \( A l^{+2}>A l^{+3}>A l^{+} \)
c. \( A l^{+2}<A l^{+}>A l^{+} \)
D. \( A l^{+3}>A l^{+}>A l^{+} \)


Find a wrong number in the series:
9,19,37,75,149,297
A . 75
B. 37
c. 19
D. 149
E . 299


When steam is passed through red hot
coke:
A \( \cdot C O_{2} \) and \( H_{2} \) are obtained
B. \( C O \) and \( N_{2} \) are formed
c. \( C O \) and \( H_{2} \) are obtained
D. petrol gas is obtained


If \( \triangle A B C \cong \triangle R Q P, \angle A=80^{\circ}, \angle B= \)
\( 60^{\circ}, \) then the value of \( \angle P \) is
A . \( 60^{\circ} \)
В. \( 50^{\circ} \)
c. \( 40^{\circ} \)
D. \( 80^{\circ} \)


The volume of a solid cylinder is
\( 448 \pi \mathrm{cm}^{3} \) and height \( 7 \mathrm{cm} . \) Find its
lateral surface area and total surface
area.


Consider the statements about mono, di
and oligo saccharides:
I. These are crystalline solids.
II. These are soluble in cold water.
III. These are tasteless.
The incorrect statement(s) is/are:
A. only II
B. I, II and III
c. I and II only
D. I and III only


Fusion of the sulfonic acids with
sodium hydroxide initially gives the with the phenol being released by the subsequent addition of mineral acid.
A. phenate
B. sodium propanol
c. phenone
D. none of above


The value of \( 555 \times 193-555 \times 93 \) is
A .555,931
в. 1,210,321
c. 53,912
D. 55,500


The vector \( \boldsymbol{\alpha} \hat{\boldsymbol{i}}+\boldsymbol{2} \hat{\boldsymbol{j}}+\boldsymbol{\beta} \hat{\boldsymbol{k}} \) lies in the
plane of vectors \( \vec{b}=\hat{i}+\hat{j} \) and \( \vec{c}=\hat{j}+\hat{k} \) and bisects the angle between \( \vec{b} \) and \( \vec{c} \) Which one of the following gives
possible values of \( \boldsymbol{\alpha} \) and \( \boldsymbol{\beta} \)
A. \( \alpha=2, \beta=2 \)
2
в. \( \alpha=1, \beta=2 \)
c. \( \alpha=2, \beta=1 \)
D. \( \alpha=1, \beta=1 \)


The wavelength associated with an electron having kinetic energy is given by the expression:
\( \mathbf{A} \cdot h / \sqrt{2 m E} \)
в. \( 2 h / m E \)
c. \( 2 m h E \)
D. \( \frac{2 \sqrt{2 m E}}{h} \)


Vibrations, whose amplitudes of oscillation decrease with time, are
called:
A. free vibrations
B. forced vibrations
c. damped vibrations
D. sweet vibrations


A proton with kinetic energy \( 8 e V \) is moving in a uniform magnetic field. The kinetic energy of a deuteron moving in the same path in the same magnetic field will be:
A \( .2 e V \)
B. \( 4 e V \)
\( c .6 e V \)
D. \( 8 e V \)


\( \operatorname{Det}\left[\begin{array}{ccc}\mathbf{4 3} & \mathbf{1} & \mathbf{6} \\ \mathbf{3 5} & \mathbf{7} & \mathbf{4} \\ \mathbf{1 7} & \mathbf{3} & \mathbf{2}\end{array}\right]=\dots \)
\( A \)
B. - -
\( c \cdot 0 \)
\( D \)


Fuel gases containing hydrocarbons (ie.g. coke oven gas) are not preheated before burning, mainly because
A. the hydrocarbons crack thereby choking and fouling the heat transfer surface by carbon soot
B. it reduces its calorific value tremendously
c. it reduces its flame temperature tremendously
D. there are chances of explosion during preheating


Maximum value of \( \sin \theta+\cos \theta \) in
\( \left[0, \frac{\pi}{2}\right] \) is
A \( \cdot \sqrt{2} \)
B. 2
c. 0
D. \( -\sqrt{2} \)


\( \sigma \)
\( \delta \)
\( \dot{\theta} \)
\( \delta \)


is the deterioration
(destruction) of the earths land surfaces, often directly or indirectly as a result of mans activities and their
misuse of land resources.
A. Land pollution
B. Soil erosion
c. Deforestation
D. Enrichment of soil


The energy difference between the
ground state of an atom and its excited
state is \( 3 \times 10^{-19} J . \) What is the
wavelength of the photon required for this transition?
A \( .494 .5 \times 10^{-6} m \)
В. \( 3 \times 10^{-8} \mathrm{m} \)
c. \( 1.8 \times 10^{-7} \mathrm{m} \)
D. \( 6.6 \times 10^{-7} m \)


Gorilla like man with large head and
hands and protruding jaws is produced
due to
A. over-secretion of thyroxine
B. Over-secretion of growth hormone
C. Excess of vitamin C in diet
D. Excess secretion of TSH


In which part of stomach mainly digestion occurs?
A. Cardiac region
B. Fundic region
c. Pyloric region
D. All of the above


The line \( \frac{x-3}{2}=\frac{y-4}{5}=\frac{z-6}{7} \)
A . lies in \( 3 x+2 y+4 z-6=0 \)
B. is parallel to \( 2 x-5 y+3 z=0 \)
\( \mathbf{c} \cdot \) is \( \perp \) to \( 2 x-5 y+3 z=0 \)
D. passing through (1,2,3)


Evaluate \( \int_{0}^{2} \frac{6 x+3}{x^{2}+4} d x \)


The energy of electron in the ground state of hydrogen atom is \( -13.6 \mathrm{eV} \). The energy required for the transition from
\( \boldsymbol{n}=\mathbf{2} \) to \( \boldsymbol{n}=\mathbf{3} \) will be
A \( .2 e V \)
в. \( 4 e V \)
c. \( 1.89 e V \)
D. \( 2.89 e V \)


f \( \boldsymbol{\alpha}, \boldsymbol{\beta} \neq \mathbf{0}, \) and \( \boldsymbol{f}(\boldsymbol{n})=\boldsymbol{\alpha}^{n}+\boldsymbol{\beta}^{n} \) and
\( \left|\begin{array}{ccc}\mathbf{3} & \mathbf{1}+\boldsymbol{f}(\mathbf{1}) & \mathbf{1}+\boldsymbol{f}(\mathbf{2}) \\ \mathbf{1}+\boldsymbol{f}(\mathbf{1}) & \mathbf{1}+\boldsymbol{f}(\mathbf{2}) & \mathbf{1}+\boldsymbol{f}(\mathbf{3}) \\ \mathbf{1}+\boldsymbol{f}(\mathbf{2}) & \mathbf{1}+\boldsymbol{f}(\mathbf{3}) & \mathbf{1}+\boldsymbol{f}(\mathbf{4})\end{array}\right|= \)
\( \boldsymbol{K}(\mathbf{1}-\boldsymbol{\alpha})^{2}(\mathbf{1}-\boldsymbol{\beta})^{2}(\boldsymbol{\alpha}-\boldsymbol{\beta})^{2}, \) then \( \mathrm{K} \) is
equal to?
\( A \)
B.
\( c \cdot \alpha \beta \)
D. \( \frac{1}{\alpha} \)


A cylindrical vessel contains a liquid of
density \( \rho \) up to height \( h \). The liquid is
closed by a piston of mass \( m \) and area
of cross section \( A \). There is a small hole
at the bottom of the vessel. The speed \( v \)
with which the liquid comes out of the hole is
A \( \cdot \sqrt{2 g h} \)
B. \( \sqrt{2\left(g h+\frac{m g}{\rho A}\right)} \)
c. \( \sqrt{2\left(g h+\frac{m g}{A}\right)} \)
D. \( \sqrt{2 g h+\left(\frac{m g}{A}\right)} \)


What are the conditions for something
to be called as matter?


A source of wave produce 1 crest and 1 trough in 16 s. Find the frequency of the
wave
A . . \( 0625 \mathrm{Hz} \)
B. 16 \( \mathrm{Hz} \)
\( c \cdot 100 \)
D. онz


Sl unit of gravitational constant is:
A \( \cdot N^{2} m^{2} k g^{2} \)
в. \( N m k g^{2} \)
c. \( N^{2} m k g^{-2} \)
D. \( N m^{2} k g^{-2} \)


If \( A \) is a \( 2 \times 3 \) matrix and \( B \) is \( 3 \times 2 \)
matrix then the order of \( (A B)^{T} \) is equal
to the order of
\( \mathbf{A} \cdot A B \)
в. \( A^{T} B^{T} \)
\( c . \) ВА
D. All of these


How many grams of \( C O_{2} \) gas is dissolved in a 1 It bottle of carbonated
water if the manufacturer uses a
pressure of 2.4 atmosphere in the
bottling process at \( 25^{\circ} \mathrm{C} ? \) Given \( \boldsymbol{K}_{\boldsymbol{H}} \) of
\( C O_{2} \) water \( =29.76 \) atm/mole/l at \( 25^{\circ} \mathrm{C} \)
A . 3.52
B. 4.2
\( c .3 . \)
D. 2.5


A block \( A, \) whose weight is \( 200 N \), is
pulled up a slope of length \( 5 m \) by
means of a constant force \( \boldsymbol{F}(=\mathbf{1 5 0} \boldsymbol{N}) \)
as illustrated in Figure.
What is the work done by the force \( \boldsymbol{F} \) in
moving the block \( A, 5 m \) along the
slope?
A \( .450 J \)
B. \( 600 J \)
\( c .0 J \)
D. \( 750 J \)


True or False
Cathode rays can cast shadow of
opaque objects placed in their path.


Statement 1: Elemental iodine has a
higher boiling point than elemental bromine.

Statement 2 : lodine forms stronger covalent bonds than bromine.
A. Both Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement 1.
B. Both Statement 1 and Statement 2 are correct and Statement 2 is not the correct explanation of Statement 1.
c. Statement 1 is correct but Statement 2 is not correct
D. Statement 1 is not correct but statement 2 is correct
E. Both the Statement 1 and Statement 2 are not correct


\( \left|\begin{array}{cc}\boldsymbol{x}+\mathbf{1} & \boldsymbol{x}-\mathbf{1} \\ \boldsymbol{x}-\mathbf{3} & \boldsymbol{x}+\mathbf{2}\end{array}\right|=\left|\begin{array}{cc}\mathbf{4} & -\mathbf{1} \\ \mathbf{1} & \mathbf{3}\end{array}\right|, \) then write
the value of \( x \)


If \( 2 A+3 B=\left[\begin{array}{ccc}2 & -1 & 4 \\ 3 & 2 & 5\end{array}\right] \) and \( A+2 B= \)
\( \left[\begin{array}{ccc}5 & 0 & 3 \\ 1 & 6 & 2\end{array}\right] \) Then \( B \) is
A \( \cdot\left[\begin{array}{ccc}8 & -1 & 2 \\ -1 & 10 & -1\end{array}\right] \)
B. \( \left[\begin{array}{ccc}8 & 1 & 2 \\ -1 & 10 & -1\end{array}\right] \)
c. \( \left[\begin{array}{ccc}8 & 1 & -2 \\ -1 & 10 & -1\end{array}\right] \)
D. \( \left[\begin{array}{lll}8 & 1 & 2 \\ 1 & 10 & 1\end{array}\right] \)


Sodium metals are kept in kerosene oil
Why?


Using the properties of determinants,
find the value of
\( \left|\begin{array}{ccc}\mathbf{0} & \boldsymbol{a} & -\boldsymbol{b} \\ -\boldsymbol{a} & \boldsymbol{0} & -\boldsymbol{c} \\ \boldsymbol{b} & \boldsymbol{c} & \boldsymbol{0}\end{array}\right| \)


When both sides of the stem are
removed, and even after that it
continues to grow in diameter, then it is
due to the presence of
A. Pith
B. Apical meristem
c. Lateral meristem
D. Intercalary meristem


The diagonals of parallelogram are 48 and \( 30 c m \) find its area


What is scum and how is it formed?


\( \mathbf{f}\left[\begin{array}{ccc}\mathbf{1} & \mathbf{3} & \mathbf{0} \\ \mathbf{1} & \mathbf{0} & -\mathbf{2} \\ \mathbf{- 4} & \mathbf{- 4} & \mathbf{4}\end{array}\right]=\mathbf{A}+\mathbf{B} \) where \( \mathbf{A} \)
is symmetric matrix and B is skew-
symmetric, then \( \mathbf{A}-\mathbf{B} \) is equal to
\( \mathbf{A} \cdot\left[\begin{array}{ccc}1 & 1 & -4 \\ 3 & 0 & -4 \\ 0 & -2 & 4\end{array}\right] \)
B. \( \left[\begin{array}{lll}2 & 1 & 3 \\ -1 & 2 & 4 \\ 3 & -1 & 2\end{array}\right] \)
\( \mathbf{c} \cdot\left[\begin{array}{lll}0 & 1 & -1 \\ 2 & 3 & 4 \\ -4 & 1 & 2\end{array}\right] \)
D. \( \left[\begin{array}{ccc}2 & -3 & 0 \\ 0 & 1 & 2 \\ 2 & 4 & 0\end{array}\right] \)


At \( 700 K, K_{p}=0.140 \) for the reaction
\( \boldsymbol{C I F}_{3}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{C l F}(\boldsymbol{g})+\boldsymbol{F}_{2}(\boldsymbol{g}) \cdot \) Calculate
the equilibrium partial pressure of
\( C l F_{3}, C l F, \) and \( F_{2} \) if only \( C l F_{3} \) is
present initially, at a partial pressure of
1.47 atm.
A \( \cdot P_{C I F}=P_{F_{2}}=0.389 \) atm, \( P_{C I P_{3}}=1.08 \mathrm{atm} \)
B . \( P_{C I F}=0.45 \) at \( m, P_{F_{2}}=0.276 \) atm, \( P_{C l F_{3}}=2.30 \) at
C \( \cdot P_{C I F}=0.50 \) at \( m, P_{F_{2}}=0.389 \) at \( m, P_{C l F_{3}}=1.67 \) at \( m \)
D. \( P_{C I F}=P_{F_{2}}=0.678 \) atm, \( P_{C I F_{3}}=3.04 \mathrm{atm} \)


Out of the following oxides, the amphoteric oxide is:
A. \( F e_{2} O_{3} \)
B. \( A l_{2} O_{3} \)
c. \( P_{2} O_{5} \)
D. \( N_{2} \),


The population of a town grows at the
rate of \( 10 \% \) per year. Using differential equation, find how long will it take for the population to grow 4 times.


Assertion
On going away from a point charge or a small electric dipole, electric field decreases at the same rate in both the
cases.
Reason
Electric field is inversely proportional to
square of distance from the charge or on electric dipole.
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.


How many obligate taxonomic categories are common between man
and housefly?
A \( . \) A) One
B. B) Two
c. c) Three
D. D) Four


The difference between the maximum
and the minimum observations in the
data is
A. class interval
B. frequency
c. cumulative frequency
D. range


\( \ln \beta \) decay.
A. Atomic number decreased by one
B. Mass number decreases by one
C. Proton number remains the same
D. Neutron number decreases by one


During dispersion of light, the least dispersed light is :
A . violet
B. green
c. yellow
D. red


Which of the following is the hormone secreted by juxtaglomerular cells of kidney which stimulates the formation
of RBC?
A. cholecystokinin
B. Erythropoietin
c. secretin
D. All of the above


If the \( 3 r d \) and the \( 9 t h \) terms of an \( A P \)
are 4 and -8 respectively, which term of this is zero?


Assertion
Consider two functions \( \boldsymbol{f}(\boldsymbol{x})=\mathbf{1}+ \)
\( e^{\cot ^{2} x} \) and \( g(x)=\sqrt{2|\sin x|-1}+ \)
\( \frac{1-\cos 2 x}{1+\sin ^{4} x} \)
Statement I: The solution of the
equation \( f(x)=g(x) \) is given by \( x= \) \( (2 n+1) \frac{\pi}{2}, \forall n \in I \)
Reason
Statement II: If \( f(x) \leq k \) and \( g(x) \leq k \)
(where \( k \in \boldsymbol{R} \) ), then solutions of the
equation \( f(x)=g(x) \) is the solution
corresponding to the equation \( f(x)=k \)
A. Statement I is true, Statement II is also true Statement II is the correct explanation of Stateme
B. Statement I is true, Statement II is also true Statement II is not the correct explanation of statement
c. Statement lis true, Statement II is false
D. Statement lis false, Statement II is true


What is the product of the reaction?
\( \mathbf{A} \)
\( B \)
\( \mathbf{C} \)
\( D \)


Oxygen is divalent, Sulphur exhibits valency 2,4 and 6 due to :
A. lower E.N
B. presence of d-orbitals
c. S-being bigger atom
D. ionisation energy is less


The equation of a wave disturbance is
given as : \( \boldsymbol{y}= \) \( 0.02 \cos \left(\frac{\pi}{2}+50 \pi t\right) \cos (10 \pi x), \) where
\( x \) and \( y \) are in meters and \( t \) in seconds.
Choose the wrong statement:
A. Antinode occurs at \( X=0.3 m \)
B. The wavelength is \( 0.2 \mathrm{m} \).
c. The speed of the constituent waves is \( 4 m / s \)
D. Node occurs at \( X=0.15 \mathrm{m} \)


Consider the following compounds
1. sulphur dioxide
2. hydrogen peroxide
3. ozone
Among these compounds, those which can act as bleaching agents would include :
A. \( I \) and \( I I I \)
B. II and III
c. \( I \) and \( I I \)
D. \( I \), II and \( I I I \)


A thin plank of mass \( M \) and length \( l \) is
pivoted at one end. The plank is
released at \( 60^{\circ} \) from the vertical.What
is the magnitude and direction of the force on the pivot when the plank is horizontal?


The vertical height of an almirah is \( 2 m \)
its base is a square of side length \( 0.4 m \)
and its mass is \( 200 k g . \) The maximum height from the floor at which a
horizontal force \( 490 N \) should be
applied on the almirah so that it does not tilt is:
A. \( 0.6 m \)
в. \( 0.8 m \)
\( c .1 m \)
D. \( 1.2 m \)


What is the best way to carry out the
following transformation? \( 1- \)pentyne\( \longrightarrow \) pentanal
A. \( H g S O_{4} / H_{2} S O_{4} \)
B. \( H_{2} / \)Lindlar's catalyst; \( O_{3} ; Z n . H_{2} O \)
c. \( H I O_{4} / H_{2} O \)
D. \( B H_{3} ; H_{2} O_{2} / N a O H \)


Factors of \( (\boldsymbol{a}+\boldsymbol{b})^{3}-(\boldsymbol{a}-\boldsymbol{b})^{3} \) are
A \( \cdot 2 a b\left(3 a^{2}+b^{2}\right) \)
B . \( a b\left(3 a^{2}+b^{2}\right) \)
c. \( 2 b\left(3 a^{2}+b^{2}\right) \)
D. \( 3 a^{2}+b^{20} \)


A shopkeeper buys 15 identical articles for Rs. 840 and pays sales-tax at the rate of \( 8 \% . \) He sells 6 of these articles at
Rs. 65 each and charges sales-tax at the same rate. Calculate the VAT paid by the shopkeeper against the sale of these six articles.
A . \( R s 4.32 \)
в. \( R s 0 \)
c. \( R s 12 \)
D. Rs1.12


Magnetite does not contain \( M g ? \)
A. True
B. False


A \( 100 c m \) long thin tube (sealed at both
ends) lies horizontally, in the middle
\( 0.1 m \) containing mercury and the two ends containing air at standard atmospheric pressure. If the tube is turned to a vertical position, by what amount will the mercury be displaced?


f \( \log 1001=3.000434 \), find the number of digits in \( 1001^{101} \)


The coefficient of \( t^{50} \) in
\( \left(1+t^{2}\right)^{25}\left(1+t^{25}\right)\left(1+t^{40}\right)\left(1+t^{45}\right)(1 \)
is
A \( \cdot 1+\sqrt[25]{5} \)
B. \( 1+^{25} C_{5}+^{25} C_{7} \)
\( \mathbf{C} \cdot 1+^{25} C_{7} \)
D. None of these


Find the tenth term of \( G . P .5,25,125 \)


The matrix \( \left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right] \) is the matrix reflection in the line
\( \mathbf{A} \cdot x=1 \)
B . \( x+y=1 \)
c. \( y=1 \)
D. \( x=y \)


\( \frac{\sqrt{3}}{\frac{1}{4}} \)


Match the columns
\begin{tabular}{ll|l|l}
& A & B \\
a. & green plastic covering & 1. & live wire \\
\hline b. & black plastic covering & 2. & neutral wire \\
c. & red plastic covering & 3. & earth wire
\end{tabular}
A. a-2, b-3, c-1
B. \( a-1, b-2, c-3 \)
c. \( a-3, b-1, c-2 \)
D. \( a-3, b-2, c-1 \)


A tube of flow is shown in the figure.
A. The fluid particles must be accelerated from \( A \) to \( B \)
B. Fluid particles may accelerate from \( A \) to \( B \)
C. The fluid particles must be decelerated from \( A \) to \( B \)
D. The fluid particles may be decelerated from \( B \) to \( A \)


In order to increase the sensitivity of a moving coil galvanometer:
A. the magnetic field should be increased
B. the suspension wire should be made stiff.
c. the area of the coil should be reduced
D. the number of turns in the coil should be reduced


Solve \( 6 \sin ^{2} x+2 \sin ^{2} 2 x=5 \)


Assertion
\( C e^{4+} \) is good analytical reagent.
Reason
\( C e^{4+} \) has the tendency to change to
\( C e^{3+} \)
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. Both Assertion and Reason are incorrect


Which of the following statement is true
for the reaction, \( \boldsymbol{H}_{2}+\boldsymbol{B} \boldsymbol{r}_{2} \rightarrow \boldsymbol{2} \boldsymbol{H} \boldsymbol{B} \boldsymbol{r} \)
The rate law is \( \frac{\boldsymbol{d} \boldsymbol{x}}{\boldsymbol{d} \boldsymbol{t}}=\boldsymbol{k}\left[\boldsymbol{H}_{2}\right]\left[\boldsymbol{B} \boldsymbol{r}_{2}\right]^{1 / 2} \)
A. order of reaction is 1.5
B. molecularity of the reaction is 2
c. by increasing the concentration of \( B r_{2} \) four times the rate of reaction is doubled
D. all the above are correct


For the given circuit, select the correct
alternative(s)
This question has multiple correct options
A. The equivalent capacitance between points \( 1 \& 2 \) is
\( \frac{15 C}{11} \)
B. The equivalent capacitance between points \( 3 \& 6 \) is \( \frac{5 C}{3} \)
C. The equivalent capacitance between points \( 1 \& 3 \) is \( \frac{15 C}{14} \)
D. The equivalent capacitance between points 3 \& 5 is
\( \frac{14 C C}{15} \)


A cylindrical vessel filled with water up to a height of \( 2 \mathrm{m} \) stands on a horizontal plane. The side wall of the vessel is a plugged circular hole touching the bottom. Find the minimum diameter of
the hole so that the vessel begins to move on the floor if the plug is removed. The coefficient of friction between the
bottom of the vessel and the plane is 0.4
and the total mass of water plus vessel
is \( 100 \mathrm{kg} \)


The atomicity of phosphorus is \( X \) and
the P-P-P bond angle is Y. What are X
and Y?

If answers are 2 and \( 90, \) represent as 290]


From the following the metals that cannot be obtained by electrolysis of the aqueous solution of their salts are:
A \( . A g \)
в. \( C u \)
c. \( M g \)
D. \( A l \)


Which one is the correct statement?
\( \mathbf{A} \cdot(+) \) tartaric acid and meso tartaric acid are tautomers
B. \( (+) \) tartaric acid and meso tartaric acid are diastereoisomers
C. \( (+) \) tartaric acid and \( (-) \) tartaric acid are diastereoisomers
D. \( (+) \) tartaric acid and meso tartaric acid are
enantiomers


Which one correctly determines the
\( \operatorname{sex} ? \)
A. \( x 0 \) condition in Turner's syndrome determines female \( \operatorname{sex} \)
B. Homozygous XX produce male in Drosophila
C. Homozygous zz determine female sex in birds
D. \( \times 0 \) determines male sex in Grasshopper


A capacitor of capacitance \( 1 \mu F \) is
charged to a potential of \( 1 V . \) It is
connected in parallel to an indicator of
inductance \( 10^{-3} \) H. The maximum
current that will flow in the circuit has
the value
A. \( \sqrt{1000} \mathrm{mA} \)
в. \( 1 \mathrm{mA} \)
\( c \cdot 1 \mu A \)
D. \( 1000 \mathrm{mA} \)


Name the scientists who have
contributed to the following.
(i) Reverse transcription.
(ii) Photorespiration.
(iii) Principle of limiting factors.
(iv) Photolysis of water


A planet revolves round the sun in an
elliptical orbit of semi minor and major
axes \( x \) and \( y \) respectively. Then the time period of revolution is proportional to:
A. \( \quad(x+y)^{\frac{3}{2}} \)
в. \( \quad(y-x)^{\frac{3}{2}} \)
c. \( \quad_{x} \frac{3}{2} \)
D. \( \frac{3}{y^{\frac{3}{2}}} \)


When the switch of an electric bell is
pushed
A. Flow of the current stops through the electromagnet in the bell
B. Current starts to flow through the electromagnet
c. voltage decreases in the current flowing through the electromagnet
D. None of the above


The RBC transports \( \mathrm{CO}_{2} \) in the form of
A. Bicarbonate ions
B. Carbonic acid.
c. oxyhaemoglobin.
D. Carboxyhaemoglobin.


As compared to \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{5}, \boldsymbol{H}_{2} \boldsymbol{S}_{2} \boldsymbol{O}_{8} \)
A. Has two peroxy linkage
B. Liberates \( I_{2} \) from \( K I \) slowly and thus kinetics of oxidation of \( K I \) by \( S_{2} O_{8}^{2-} \) can be studied
c. Has different oxidation number
D. Reacts with \( K M n O_{4} \)


In the argand diagram, the complex number z is in the fourth
quadrant, then \( \bar{z},-z, \overline{-z} \) are
respectively are in quardrants
В . 1,2,3
c. 3,2,1
D. 2,1,


Electromagnetic induction is the
phenomenon of converting - ........... energy into electrical energy.


Water table may go down if the water is not sufficiently replenished. This may happen due to which of the following reason/(s)?
A. Increasing population
B. Increasing industries
c. Agricultural activities
D. All of the above


In roots, lateral branches grow from.
A. Epiblema
B. Pericycle
c. cortex
D. Endodermis


Select the correct one from the given
options:
Blue of color of sky is due to
of light by in air.
1. absorption, sol particles
2. scattering, sol particles
3. absorption, oxygen
4. scattering, oxygen


Loss of upper fertile layer of soil is known as
A. Pedogenesis
B. Podosolization
c. soil erosion
D. None of the above


The dimensions of self inductance are
\( \mathbf{A} \cdot\left[M L T^{-2} A^{-2}\right] \)
В \( \cdot\left[M L^{2} T^{-1} A^{-2}\right] \)
\( \mathbf{c} \cdot\left[M L^{2} T^{-2} A^{-2}\right] \)
D \( \cdot\left[M L^{2} T^{-1} A^{-1}\right] \)


Total charge required for the oxidation of two moles \( M n_{3} O_{4} \) in to \( M n O_{4}^{2-} \) in
presence of alkaline medium is:
A. \( 5 F \)
в. 10F
c. २०
D. None of these


The reaction between \( C O_{2} \) and \( a \)
Grignard regent will yield :
A. An alkyl magnesium halide.
B. an alcohol
c. magnesium carbonate.
D. a carboxylic acid


Blue,green,yellow and yellow is the color band on the resistor,find its resistance?
\( \mathbf{A} \cdot\left(75 \times 10^{4}\right) \Omega \pm 5 \% \)
B . \( \left(65 \times 10^{4}\right) \Omega \pm 5 \% \)
C \( \cdot\left(52 \times 10^{4}\right) \Omega \pm 5 \% \)
D. \( \left(65 \times 10^{4}\right) \Omega \pm 10 \% \)


Gobar gas is a:
A. solid fuel
B. liquid fuel
C . primary fuel
D. secondary fuel


What is the value of \( \lim _{x \rightarrow 0} \frac{\sin x}{\tan 3 x} \)
A \( \cdot \frac{1}{4} \)
B. \( \frac{1}{3} \)
\( c \cdot \frac{1}{2} \)
D.


During a doorbell ringing
A. Current always flows in the circuit
B. Electromagnet is always present
C. Striker is always in contact with metal gong
D. Striker always repeatedly hits metal gong


The oxidation state(s) of \( C l \) in \( C a O_{2} C l_{2} \)
(bleaching powder) is/are:
\( A \cdot+1 \) only
B. - - ' only
\( c \cdot+1 \) and -1
D. none of these


Which equation in gaseous phase would be unaffected by an increase in pressure?
A. \( N_{2} O_{4} \rightleftharpoons 2 N O_{2} \)
B . \( N_{2}+O_{2} \rightleftharpoons 2 N O \)
c. \( N_{2}+3 H_{2} \rightleftharpoons 2 N H_{3} \)
D. \( c o+\frac{1}{2} O_{2} \rightleftharpoons C O_{2} \)


Determine of \( U \) is
A . 13
B. 15
\( c .3 \)
D. 2


The initial internal energy of the gas in
container 'A', if the containers were at
room temperature \( 300 \mathrm{K} \) initially-
A . 1406.25 cal
в. 1000 cal
c. 2812.5 cal
D. none of these


In the following sequence of reactions Toluene \( \frac{K M n O_{4}}{\longrightarrow} A \frac{S O C l_{2}}{B G O_{4}} B \frac{H_{2} / P d}{C} C \)
then product \( \boldsymbol{C} \) is:
A \( \cdot C_{6} H_{5} \) СООН
в. \( C_{6} H_{5} C H_{3} \)
\( \mathrm{c} \cdot C_{6} H_{5} C H_{2} O H \)
D. \( C_{6} H_{5} C H O \)


The wave carries
A. Power
B. Energy
C. Displacement
D. Work


A uniform but time varying magnetic field is present in a circular region of radius R. The magnetic field is perpendicular and into the plane of the loop and the magnetic of field is increasing at a constant rate \( \alpha . \) There is
a straight conducting rod of length \( 2 \mathrm{R} \) placed as shown in figure. The magnitude of induced emf across the rod is
This question has multiple correct options
\( \mathbf{A} \cdot 60^{\circ} \)
B. \( 90^{\circ} \)
\( c \cdot 30^{\circ} \)
D. \( 20^{\circ} \)


Write the IUPAC name of the following
amine.
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C H}-\boldsymbol{N H}_{2}-\boldsymbol{C}=\mathbf{0}- \)
\( \boldsymbol{O} \boldsymbol{H} \)


Spindle fibres are attached to kinetochores of chromosomes in?
A. Metaphase
B. Anaphase
c. Telophase
D. 1 and 2


Consider a particle initially moving with
a velocity of \( 5 m s^{-1} \) starts decelerating
at a constant rate of \( 2 m s^{-2} \). Find the
distance travelled in the third second.


A chord of a circle of radius \( 6 \mathrm{cm} \)
subtends an angle of \( 60^{\circ} \) at the centre
of the circle. The area of the minor
segment is (use \( \pi=3.14) \)
A \( \cdot 6.54 \mathrm{cm}^{2} \)
в. \( 0.327 \mathrm{cm}^{2} \)
c. \( 7.25 \mathrm{cm}^{2} \)
D. 3.27 \( c m^{2} \)


Assertion
SO is a bleaching agent.
Reason
Nascent oxygen causes bleaching.
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


IUPAC name of the tertiary butyl alcohol
is:
A. 1-butanol
B. 2-butanol
c. 2-methyl-1-propanol
D. 2-methyl-2-propanol


Which is the correct IUPAC name for
\( \boldsymbol{C H}_{3}-\boldsymbol{C} \boldsymbol{H}-\boldsymbol{C} \boldsymbol{H}_{2}-\boldsymbol{B} \boldsymbol{r}: \)
\( \boldsymbol{C}_{2} \boldsymbol{H}_{5} \)
A. 1-Bromo-2-ethylpropane.
B. 1-Bromo-2-ethyl-2-methylethane.
c. 1 -Bromo-2-methylbutane
D. 2-Methyl-1-bromobutane


The number of significant figures in
0.00386 is :
A. 5
B. 3
\( c \cdot 6 \)
\( D \)


Assertion
Alcohols are dehydrated to hydrocarbons in presence of acidic
zeolite.
Reason
Zeolites are porous catalyst.
A. If both (A) and (R) are true and (R) is the correct explanation of (A).
B. If both (A) and (R) are true, but (R) is not the correct explanation of \( (A) \)
c. If (A) is correct, but (R) is incorrect.
D. If (A) and (R) are both incorrect


Arrange the following in increasing energy levels:
\( A \cdot 5 p<4 d<3 p<4 f<5 d<6 s \)
\( B .3 p<4 d<5 p<6 s<4 \)
\( c \cdot 3 p<4 d<5 p<4 f<6 s \)
D. \( 3 p<4 d<5 p<4 f<6 p \)


Carbon dioxide in the expired air is more than that in inspired air because
A. It is absorbed at the alveolar surface
B. It is released at the alveolar surface
c. Both A and B
D. None of these


When a bomb calorimeter is used to
determine the heat of reaction, which
property of the system under investigation is most likely to remain
constant?
A. Number of molecules
B. Pressure
c. Temperature
D. volume


The negative of the statement "lf a
number is divisible by 15 then it is divisible by 5 or \( 3 " \)
A. if a number is divisible by 15 then it is not divisible by and 3
B. a number is divisible by 15 and it is not divisible by 5 o
3
c. a number is divisible by 15 or it is not divisible by 5 and
3
D. a number is divisible by 15 and it is not divisible by 5 and 3


The value of \( \lim _{x \rightarrow 3} \frac{\left(x^{3}+27\right) \log _{e}(x-2)}{x^{2}-9} \) is
\( \mathbf{A} \cdot \mathbf{9} \)
B. 18
c. 27
D.


Bond present between two residues of carbohydrate is
A. Amide
B. Phosphodiester
c. Glycosidic
D. Hydrogen bond


Ordinary light passes through two polarizing filters. The filters have been rotated so that their polarizing axes are
oriented at \( 90^{\circ} \) to each other, and no
light gets through both of them. By adding a third polarizing filter so that there are three in a row, how might
one cause light to pass through the three filters?
A. Orient the third filter so that its polarizing axis is
in front of the first
B. Orient the third filter so that its polarizing axis is rotated \( 45^{\circ} \) counter-clockwise relative to the seconds and place it in back of the second
C. Orient the third filter so that its polarizing axis is rotated \( 45^{\circ} \) clockwise relative to the first and place it in between the two filters
D. Orient the third filter so that its polarizing axis is rotated \( 90^{\circ} \) clockwise relative to the first and place it in front of the first
E. Both A and B will work to allow light through


Anhydrous \( A l C l_{3} \) is a covalent
compound. From the data given below,
predict whether it would remain covalent or become ionic in an aqueous
solution.
(lonisation energy of \( \boldsymbol{A} \boldsymbol{L}= \) \( \mathbf{5 1 3 7} \boldsymbol{K J} \quad \boldsymbol{m o l}^{-1} \mathbf{)} \)
\( \Delta \boldsymbol{H} \) hydration for \( \boldsymbol{A} \boldsymbol{l}^{3+}= \)
\( -4665 K J m o l^{-1} \)
\( \Delta H \) hydration for \( C l^{-}= \)
\( -381 K J m o l^{-1} \)
A. lonic
B. Covalent
c. Partially ionic
D. Partially covalent


The urine under normal conditions does
not contain glucose because
A. The normal blood sugar is fructose.
B. Glucose of blood is not filtered in the glomerulus
c. Glucose in glomerular filtrate is reabsorbed in the uriniferous tubules
D. Glucose in glomerular filtrate is converted into glycogen.


What concentration of \( \boldsymbol{F}- \)
\( \boldsymbol{C H}_{2} \boldsymbol{C O O H},\left(\boldsymbol{K}_{a}=\mathbf{2 . 6} \times \mathbf{1 0}^{-3}\right) \) is
needed so that \( \left[\boldsymbol{H}^{+}\right]=\mathbf{2} \times \mathbf{1 0}^{-\mathbf{3}} \) ?
в. \( 2.6 \times 10^{-3} M \)
c. \( 5.2 \times 10^{-3} M \)
D. \( 3.53 \times 10^{-3} M \)


Assertion
If there is no external torque acting on a body about its center of mass, then the velocity of the center of mass remains constant.
Reason
The linear momentum of an isolated
system remains constant.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is incorrect but Reason is correct
D. Both Assertion and Reason are incorrect


A sum of money is rounded off to the nearest rupee. The probability that the round off error is at least ten paisa is \( \frac{9 k}{100} . \) The value of \( k \) is


In a Wheatstone bridge, three resistances \( P, Q \) and \( R \) are connected in the three arms and the fourth arm is
formed by two resistances \( S_{1} \) and \( S_{2} \) connected in parallel. The condition for the bridge to be balanced will be
A \( \cdot \frac{P}{Q}=\frac{R\left(S_{1}+S_{2}\right)}{2 S_{1} S_{2}} \)
в. \( \frac{P}{Q}=\frac{R}{S_{1}+S_{2}} \)
c. \( \frac{P}{Q}=\frac{2 R}{S_{1}+S_{2}} \)
D. \( \frac{P}{Q}=\frac{R\left(S_{1}+S_{2}\right)}{S_{1} S_{2}} \)


Eliminate \( x \) from equations
\( \sin (a+x)=2 b \) and \( \sin (a-x)=2 c \)
A \( \cdot \frac{(b+c)^{2}}{\sin ^{2} a}-\frac{(b-c)^{2}}{\cos ^{2} a}=1 \)
B. \( \frac{(b+c)^{2}}{\sin ^{2} a}+\frac{(b+c)^{2}}{\cos ^{2} a}=1 \)
\( ^{C} \cdot \frac{(b+c)^{2}}{\sin ^{2} a}+\frac{(b-c)^{2}}{\cos ^{2} a}=1 \)
D. \( \frac{(b+c)^{2}}{\sin ^{2} a}+\frac{(b-c)^{2}}{\cos ^{2} a}=-1 \)


Draw a diagram showing the external features of a fish and label any two
parts


a) What is ecological secession?
b) Represent an ideal pyramid of number in a grassland ecosystem.
c) Name the two types of nutrient cycles with an example each.


Consider the following statements (A) and (B) and identify the correct answer given below:
Statement A: Positive values of packing fraction implies a large value of binding energy Statement B: The difference between
the mass of the nucleus and the mass
number of the nucleus is called the
packing fraction
A. A and B are correct
B. A and B are false
c. A is true, B is false
D. A is false, B is true


Numerous shinning ovules on swollen placentae with axile placentation are found in
A. Lagenaria
B. Lycopersicon
c. Lactuca
D. All of the above


Evaluate: \( \int \sqrt[9]{x^{-8}} d x \)
A \( \cdot 9 x^{\frac{1}{9}}+c \)
\( c \)
B \( .9 x^{8}+c \)
c. \( x^{\frac{1}{9}}+c \)
D. \( x^{\frac{8}{9}}+c \)


\( A \stackrel{C O}{\longrightarrow} \) Chlorine \( \stackrel{S O_{2}}{\longrightarrow} \)
B. Identify
\( A \) and \( B \)


Shape and hybridization of \( I F_{5} \)
respectively are
A. trigonal bipyramidal, \( s p^{3} d \)
B. see-saw, \( s p^{3} d \)
C . square pyramidal, \( s p^{3} d^{2} \)
D. pentagonal pyramidal, sp \( ^{3} d^{3} \)


A particle of mass in oscillates with
simple harmonic motion between two
points \( x_{1} \) and \( x_{2}, \) the equilibrium
position being a Its potential energy is plotted on the graph. Which of the
following curve represents the phenomenon?
A
(a)
B.
c.
D.


Find the square root of following surds:
\( \mathbf{5}+\sqrt{\mathbf{2 1}} \)


Faces of the cube are in shape of
A. Square
B. Rectangle
c. circle
D. Triangle


Two parallel wires each of length \( 10 c m \)
are \( 0.5 \mathrm{cm} \) apart. A film of water is
formed between them. If the surface
tension of water is \( 0.072 N / m, \) then the work done in on increasing the distance between the wires by 1 mm is
A . \( 1.44 \times 10^{-5} \mathrm{J} \)
в. \( 1.72 \times 10^{-5} \mathrm{J} \)
c. \( 1.44 \times 10^{-4} J \)
D. \( 1.72 \times 10^{-4} J \)


Assertion
Insulin is antagonistic to glucagon.
Reason
It is an anabolic hormone.
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 long solenoid has 1000 turns. When a
current of \( 4 A \) flows through it, the
magnetic flux linked with each turn of
the solenoid is \( 4 \times 10^{-3} \) Wh. The self-
inductance of the solenoid is:
A. 4 н
в. 3 н
\( c .2 H \)
D. 1


Show that
\( \tan ^{-1}\left(\frac{1}{2}\right)+\tan ^{-1}\left(\frac{1}{3}\right)=\frac{\pi}{4} \)


What will be the height of image when an object of 2 mm is placed at a
distance \( 20 \mathrm{cm} \) infront of the axis of a
convex mirror of radius of curvature
\( 40 \mathrm{cm} ? \)
A \( .20 \mathrm{mm} \)
B. \( 10 \mathrm{mm} \)
\( c .6 m m \)
D. \( 1 \mathrm{mm} \)


Assertion
The compressive strength of a typical brittle material is significantly higher than its tensile strength.
Reason
In compression force between the
molecules increases.
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 particle of mass \( 0.1 k g \) executes \( S H M \)
under a force \( \boldsymbol{F}=(-10 x) N . \) Speed of
particle at mean position is \( 6 m / s \). Then amplitude of oscillations is
A. \( 0.6 m \)
B. \( 0.2 m \)
\( c \cdot 0.4 m \)
D. \( 0.1 m \)


Which of the following is the correct decreasing order of the strengths of four fundamental forces of nature?
A. Electromagnetic force >weak nuclear force>gravitational force>strong nuclear force.
B. Strong nuclear force>weak nuclear force>electromagnetic force>gravitational force
c. Gravitational force>electromagnetic force>strong nuclear force>weak nuclear force
D. strong nuclear force>electromagnetic force>weak nuclear force>gravitational force


Which of the following sets have both heterocyclic compounds?
A. Phenol and Furane
B. Furan and Thiophene
c. Thiophene and Phenol
D. Furan and Aniline


Which of the following devices does not make use of solar energy directly?
A. Solar panels
B. Solar furnaces
c. solar cells
D. Dry cells


Divide the polynomial \( 2 x^{4}-4 x^{3}- \)
\( 3 x-1 \) by \( (x-1) \) and verify the
remainder with zero of the divisor.


In the figure shown, plank is
being pulled to the right with a constant
speed v. If the cylinder does not slip then
This question has multiple correct options
A. the speed of the centre of mass of the cylinder is \( 2 v \)
B. the speed of the centre of mass of the cylinder is zero
c. the angular velocity of the cylinder is \( v / R \)
D. the angular velocity of the cylinder is zero


True or False.
Nonmetals are less dense and have low
melting and boiling points.


Find the equation of parabola with focus (5,0) and vertex (5,3)
A \( \cdot y=12(x-5)^{2}-3 \)
B . \( y-3=-(x-5)^{2} \)
c. \( y=\frac{(x-5)^{2}}{12}-3 \)
D. \( y=-\frac{(x-5)^{2}}{12}+3 \)


Cycloalkanes are isomeric with
A. Alkenes
B. Alkanes
c. Alkynes
D. Arenes


The angle of the prism is \( 30^{\circ} . \) The rays
incident at \( 60^{\circ} \) at one refracting face
suffer a deviation of \( 30^{\circ} . \) Then, the angle
of emergence is :
A \( \cdot 0^{\circ} \)
B. \( 30^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 90^{\circ} \)


Compare reactivity towards nucleophilic addition reaction?
A.
\[
H-C-H
\]
c.
\[
C H_{3}-C-C H_{3}
\]
D.
\[
C H_{3}-C H_{2}-C-H
\]


What is the nature of the graph: \( y= \)
\( -4 x^{2}+6 \)
A. parabola not passing through origin
B. Hyperbola not passing through origin
c. Ellipse not passing through origin
D. it is not a conic


A ball is dropped from a height h. If the coefficient of restitution be e, then the
body rebounds to a height of
\( \mathbf{A} \cdot e h \)
B \( \cdot e^{2} h \)
\( c \cdot e^{3} h \)
D. \( e^{4} h \)


The branch of science which deals with
nature and natural phenomena is called
A. Sociology
B. Biology
c. civics
D. Physics


What is the difference between galvanic cell and electrolytic cell?
A. In galvanic cell, electrical energy is produced while in electrolytic cell electrical energy is consumed
B. In galvanic cell, anode is (-) ve while in electrolytic cell anode is \( (+) \) ve
c. In galvanic cell, cathode is \( (+) \) ve while in electrolytic cell anode is \( (-) v e \)
D. All are correct


Determine the molecular formula of an
oxide of iron in which the mass per cent
of iron and oxygen are 69.9 and 30.1 respectively.


Which of the following is a noncombustible substance?
A. coke
B. Diamond
c. coal
D. woodd


Algae growing on animal bodies and shells are called
A. Epizoic
B. Epiphytic
c. sea Lettuce
D. Parasitic
E. Coenobia


Balance the following equation in basic medium by ion-electron method and oxidation number methods and identify
the oxidising agent and the reducing
agent
\( \boldsymbol{C l}_{2} \boldsymbol{O}_{7}(\boldsymbol{g})+\boldsymbol{H}_{2} \boldsymbol{O}_{2}(\boldsymbol{a} \boldsymbol{q}) \rightarrow \boldsymbol{C l O}_{2}^{-}(\boldsymbol{a q})+ \)
\( \boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{H}^{+} \)


If ocean thermal energy is made
feasible and cheaper, it has
tremendous potential because:
A. Potential energy in oceans is immense
B. Ocean waves are very strong
c. Most of the solar energy is incident on the ocean surface
D. A lot of heat energy is trapped in the land mass below the oceans


Compare vitamin (Part I) with its
deficiency disease (Part II)
Part I Part II
A. Vitamin - \( B_{12} \)
1.Sterility
B. Vitamin- \( B_{6} \) 2. Haemorrhagic condition
\( \begin{array}{ll}\text { C. Vitamin }-E & \text { 3. Pernicious anaemia }\end{array} \)
Vitamin - \( K \quad \) 4. Skin disease
\( D \)
A \( \cdot \) A- \( -1 ; \) B-2; \( c-3 ; D-4 \)
c. \( A-3 ; B-4 ; C-1 ; D-2 \)
D. A-3; B-4; C-2; D-1


A device for producing highly intense and coherent (wave in same phase) beam of light is called
A. laser
B. maser
c. search light
D. none of these


If \( V_{B}=5 V \), then the maximum value of \( R \)
so that the voltage \( V \) is above the knee
point voltage, should be
\( A \cdot 0.7 \times \Omega \)
в. 4.3 К.
\( c \cdot 5 K \Omega \)
D. 5.7 к.


A monoatomic gas at pressure \( P_{1} \) and
volume \( V_{1} \) is compressed adiabatically to \( \frac{1}{8} \) th of its original volume. What is the final pressure of the gas
\( A \cdot 64 P_{1} \)
в. \( P_{1} \)
\( c \cdot 16 P_{1} \)
D. \( 32 P_{1} \)


Process that produces soap from fats is called as:
A. acidification
B. saponification
c. hydrolysis
D. condensation


For the principal value:
\( \sin ^{-1}\left(-\frac{\sqrt{\mathbf{3}}}{\mathbf{2}}\right)+\cos ^{-1}\left(\frac{\sqrt{\mathbf{3}}}{\mathbf{2}}\right) \)


Petiole is modified into tendril in
A. Gloriosa
B. Passiflora
c. Nepenthes
D. Luffa


Which of the following is not unity of charge?
A. Faraday
B. Fahrenheit
c. coulumb
D. Ampere/ Second


For the equilibrium system
\( 2 H X(g) \rightleftharpoons H_{2}(g)+X_{2}(g) \)
the equilibrium constant is \( 1.0 \times 10^{-5} \)
What is the concentration of \( \mathrm{HX} \) if the
equilibrium concentration of \( \boldsymbol{H}_{2} \) and
\( X_{2} \) are \( 1.2 \times 10^{-3} M, \) and \( 1.2 \times 10^{-4} M \)
respectively?
A \( \cdot 12 \times 10^{-4} M \)
В. \( 12 \times 10^{-3} M \)
c. \( 12 \times 10^{-2} M \)
D. \( 12 \times 10^{-1} M \)


Form the differential equation of the family of curves represented by the equation(a being the parameter). \( (x-a)^{2}+2 y^{2}=a^{2} \)


Given that \( \sqrt{3} \) is an irrational number, prove that \( (2+\sqrt{3}) \) is an irrational
number.


A particle is projected vertically upwards and it attains maximum
height \( \boldsymbol{H} . \) If the ratio of times to attain
height \( h(h<H) \) is \( 1 / 3, \) then \( h \) equals
\( A \cdot 2 / 3 H \)
B. 3H
c. 5/9. म
D. 3/.


What is the bond order of \( N O \)
molecule?
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
c. 2.5
D. 3


Which among the following belong to Auxin?
\( A \cdot \mid A A, I B A, C K \)
в. \( G A_{3}, 2,4-D, \) IA \( A \)
c. IAA, IBA, NAA
D. \( 2,4-D, I A A, A B A \)


The sales of Dove in 2010 was by what
percent less than the sales of Dove in
\( 2007 ? \)
A. \( 40 \% \)
3. \( 60 \% \)
\( c .70 \% \)
\( 0.50 \% \)


Not more than one oxidation state is
show by:
\( \mathbf{A} \cdot M n \)
в. \( C r \)
c. \( F e \)
D. \( S c \)


In \( \triangle A B C, \) if \( a, b, c \) are in \( A . P . \) then \( \cot \frac{\boldsymbol{A}}{2} \cot \frac{\boldsymbol{C}}{2}= \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 3 \)
D.


Two masses \( M_{1} \) and \( M_{2} \) at an infinite
distance from each other and initially at rest, start interacting gravitationally. Find their velocity of approach when they are distances apart.


Write the product and mechanism for given reactions. \( C_{6} H_{5}-C H_{2}-C H O \stackrel{D i l N a O H}{\longrightarrow}(D) \)


Thermal neutrons are those which
A. are at very high temperature
B. move with high velocities
C. have kinetic energies similar to those of the surroundings molecules
D. are at rest


If \( A, B \) and \( C \) are mutually exclusive and exhaustive events, then \( \boldsymbol{P}(\boldsymbol{A})+ \)
\( P(B)+P(C) \) equals to
A \( \cdot \frac{1}{3} \)
B. 1
\( c .0 \)
D. Any value between 0 and 1


If \( a=3, b=4, c=5 \) each one of \( \vec{a}, \vec{b} \)
and \( \vec{c} \) is perpendicular to the sum of the remaining then \( |\overrightarrow{\boldsymbol{a}}+\overrightarrow{\boldsymbol{b}}+\overrightarrow{\boldsymbol{c}}| \)
A \( \cdot \frac{5}{\sqrt{2}} \)
B. \( \frac{2}{\sqrt{5}} \)
\( c \cdot 5 \sqrt{2} \)
D. \( \sqrt{5} \)


Two parallel rail tracks run north-south.
Train \( A \) moves north with a speed of
\( 54 k m h^{-1} \) and train \( B \) moves south
with a speed of \( 90 \mathrm{kmh}^{-1} \). The relative
speed of \( B \) with respect to \( A \) is:
\( \mathbf{A} \cdot 40 \mathrm{ms}^{-1} \) (towards north)
B. \( 40 \mathrm{ms}^{-1} \) (towards south)
C \( .10 \mathrm{ms}^{-1} \) (towards north)
D. \( 10 \mathrm{ms}^{-1} \) (towards south)


Arrangement of ovules on the placentae developed from central axis of ovary is
A. Parietal placentation
B. Basal placentation
c. Marginal placentation
D. Axile placentation


The potential difference between the
wire and the cylinder produces an
electric field of \( 2 \times 10^{4} V m^{-1} \) at a
distance of \( 1.2 \mathrm{cm} \) from the wire
\( \mathbf{A} \cdot 360 V \)
B. \( 180 V \)
\( c \cdot 200 V \)
D. \( 240 V \)


Solve the following equation and check
your results:
\( 2 x-1=14-x \)


What are the number of signification numbers in \( 0.00034800 ? \) How much is
one astronomical unit in meters?


In the given figure, electric lines of force
diagram is shown. Then:
A \( \cdot E_{A}<E_{B} \)
В. \( E_{A}>E_{B}>E_{C} \)
\( \mathbf{c} \cdot E_{C}>E_{B} \)
\( \mathbf{D} \cdot E_{A}=E_{B}=E_{C} \)


Find the correct match
A. ii and iv
B. i and ii
C . iv only
D. i and iii


Select the correct statement about
muscular disorder.
A. Accumulation of urea and creatine in joints
B. An overdose of vitamin D causes osteoporosis
C. Rapid contraction of skeletal muscles causes dystrophy
D. Failure of neuromuscular transmission in myasthenia gravis can prevent normal swallowing


Reduce the equation \( x+2 y-6=0 \) to
slope-intercept form and find its slope
and \( \boldsymbol{y}- \) intercept.


toppr
Q туре your question
perpendicular to the plane of the
triangle. The base of the triangle AB has
a resistance \( 1 \Omega \) while the other two
sides have resistance \( 2 \Omega \) each. The
magnitude of potential difference between the points \( A \) and \( B \) will be
\( 4 \cdot 0.4 \)
\( (\mathrm{A}) \)
8. 0.6 v
\( (\mathrm{B}) \)
c. \( 1.2 v \)
\( (C) \)
D. Non
\( (\mathrm{D}) \)


\( 0.25 M \) solution of pyridium chloride
\( C_{5} H_{6} N^{+} C l^{-} \) was found to have a \( p H \)
of \( 2.699 . \) What is \( p K_{b} \) for pyridine,
\( \boldsymbol{C}_{\mathbf{5}} \boldsymbol{H}_{\mathbf{5}} \boldsymbol{N} ? \)


A ray of monochromatic light in
incident on one refracting face of a
prism of angle \( 75^{\circ} . \) If passes through the prism and is incident on the other face at the critical angle. If refactive index of the material of the prism is \( \sqrt{2} \) the angle of incidence on the first face
of the prism is
A \( \cdot 30^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 0^{\circ} \)


If \( x^{2}+2 x y+2 y^{2}=1, \) then \( \frac{d y}{d x} \) at the
point where \( y=1 \) is equal to:
A .
B. 2
\( c \cdot-1 \)
D. -
\( E \)


Chlorine water is usually stored in dark coloured bottles why?


Consider the following statement. When jumping from some height, you should bend your knees as you come to rest instead of keeping your legs stiff. Which of the following relations can be useful
in explaining the statement? where symbols have their usual meaning.
A \( \cdot \Delta P_{1}=-\Delta P_{2} \)
B. \( \Delta E=-\Delta P E+K E=0 \)
c. \( F \Delta t=-m \Delta F \)
D. \( \Delta x \propto \Delta F \)


Does Euclid's fifth postulate imply the existence of parallel lines? Explain.


What is meant by consumers in an
ecosystem?


The atomic weight of uranium isotope, which is equally fissionable is :
A . 235
в. 238
c. 234
D. 236


Thrice the square of a natural number decreased by 4 times the number is
equal to 50 more than the number. The number is
\( A \cdot 4 \)
B. 5
\( c \cdot 6 \)
D. 10


The largest leaf belongs to
A. Nerium
B. Nicotiana
c. victoria
D. Rafflesia


Consider the function \( \boldsymbol{f}(\boldsymbol{x})= \) \( \left\{\begin{array}{cl}\frac{\tan k x}{x}, & x<0 \\ 3 x+2 k^{2}, & x \geq 0\end{array} . \) What is the non- \right.
zero value of k for which the function is
continuous at \( \boldsymbol{x}=\mathbf{0} ? \)
A . \( 1 / 4 \)
B. \( 1 / 2 \)
c. 1
D.


Space between body wall and alimentary canal lined by mesoderm is
A. Pseudocoelom
B. Acoelom
c. Haemocoel
D. coelom


Which part of lens in human eye is helpful in adjustment of focal length?
A. Cornea
B. Mucus
c. ciliary body
D. conjunctiva


A wire has a diameter of \( 0.2 m m \) and a
length of \( 50 \mathrm{cm} . \) The specific resistance
of it's material is \( 40 \times 10^{-6} \) ohmcm.
The current through it, when a potential difference of \( 2 V \) is applied across it, is
\( \mathbf{A} \cdot 3 \cdot 14 A \)
B . \( 31.4 A \)
c. \( 0.314 A \)
D. \( 0.0314 A \)