Suppose \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) is differentiable
function satisfying \( \boldsymbol{f}(\boldsymbol{x}+\boldsymbol{y})=\boldsymbol{f}(\boldsymbol{x})+ \)
\( \boldsymbol{f}(\boldsymbol{y})+\boldsymbol{x} \boldsymbol{y}(\boldsymbol{x}+\boldsymbol{y}) \) for every \( \boldsymbol{x}, \boldsymbol{y} \in \boldsymbol{R} \) if
\( f^{\prime}(0)=0, \) then which of the following hold(s) good?
This question has multiple correct options
\( A . f \) is an odd function
B. \( f \) is a bijective mapping
c. \( f \) has a minima but no maxima
D. \( f \) has an inflection point


What is the formula for electric power?
A \( \cdot P=I^{2} R t \)
B . \( P=\frac{w}{t} \)
c. \( P=V I \times t \)
D. \( P=v Q \)


Let \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{ccc}x & \text { if } & x \text { is rational } \\ 2-x & \text { if } & x \text { is irrational }\end{array} \) Then \right.
fof \( (x) \) is continuous
A. everywhere
B. no where
c. at all irrational \( x \)
D. at all rational \( x \)


Assertion
The centre of mass of a body may lie where there is no mass
Reason
Centre of mass of a body is a point, where the whole mass of the body is
supposed to be concentrated
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


Two thin long parallel wires separated by a distance \( b \) are carrying a current \( I \) ampere each. The magnitude of the force per unit length exerted by one wire on the other is
A \( \frac{\mu_{0} I^{2}}{b^{2}} \)
в. \( \frac{\mu_{0} I^{2}}{2 \pi b} \)
c. \( \frac{\mu_{0} I}{2 \pi b} \)
D. \( \frac{\mu_{0} I}{2 \pi b^{2}} \)


Eka-aluminium forms chloride of the
type :
A \( \cdot E_{2} C l \)
в. \( E C l_{3} \)
\( \mathbf{c} \cdot E_{2} C l_{3} \)
D. \( E_{3} C l_{4} \)


If Kinetic energy is expressed as \( m v^{2} / 2 \) for a particle undergoing uniform velocity motion, How is the kinetic energy expressed in case of the same particle, if it was rotating:
A \( \cdot m \omega^{2} / 2 \)
B. \( I \omega^{2} / 2 \)
c. \( m V^{2} / 2 \)
D. \( I V^{2} / 2 \)


In optical instruments, the lenses are used to form images by :
A. reflection
B. refraction
c. dispersion
D. scattering


Light of wavelength 488 nm is produced by an argon laser which is used in the photoelectric effect. When light from this spectral line is incident on the emitter, the stopping (cut-off) potential of photoelectrons is 0.38 V. Find the work function(in eV) of the
material from which the emitter is
made.


When \( K_{2} C r_{2} O_{7} \) is treated with \( H_{2} O_{2} \)
then:
This question has multiple correct options
A. in strong acidic medium deep blue-violet complex \( C r O\left(O_{2}\right)_{2} \) is formed
B. in less acidic medium violet, coloured complex \( \left[\mathrm{CrO}\left(\mathrm{O}_{2}\right)(\mathrm{OH})\right]^{-} \) is formed
C . in alkaline medium \( \left[\mathrm{Cr}\left(\mathrm{O}_{2}\right)_{4}\right]^{3-} \) is formed
D. in ammonical solution \( \left(N H_{3}\right)_{3} C r O_{4} \) dark red-brown compound is formed.


The atomic radius of hydrogen atom is:
\( A \cdot 25 \mathrm{pm} \)
B. 30 pm
c. \( 53 \mathrm{pm} \)
D. \( 43 \mathrm{pm} \)


\( 4 \mathrm{CR}=\mathrm{AB} \)
If the above statement is true then
mention answer as 1 , else mention 0 if
false


A minimum value of \( \sin x \cos 2 x \) is
\( A \cdot 1 \)
B. - 1
c. \( -\frac{2}{3 \sqrt{6}} \)
D. None of these


Differentiation gives us the instantaneous rate of change of one variable with respect to another
A. True
B. False


Apply laws of exponents and simplify. \( \left(3^{0} \times 2^{5}\right)+5^{0} \)


Explain the preparation of Gold Sol by Bredig's arc method?


Number of elements needed for healthy growth and development of plants is
A . 16
B . 24
\( c .34 \)
D. 10


In which of the following situations, is there a risk factor for children of
incurring erythroblastosis foetalis?
A. Mother is Rh-ve and father is Rh-ve
B. Mother is Rh-ve and father is Rh +ve
c. Mother is Rh tve and father is Rh +ve
D. Mother is Rh \( + \) ve and father is Rh-ve


A point source of light is placed at the
bottom of a water lake. If the area of the
illuminated circle on the surface is
equal to 3 times the square of the lake. The refractive index of water is
A. \( \sqrt{\pi+1} \)
B. \( \sqrt{\frac{\pi}{3}+1} \)
c. \( \frac{\pi}{3}+1 \)
D. \( \frac{\pi}{4}+1 \)


A horizontal aluminium rod of diameter
\( 4.8 \mathrm{cm} \) projects \( 5.3 \mathrm{cm} \) from a wall. \( 1200 \mathrm{kg} \) object is suspended from the end of the rod. The shear modulus of
aluminium is \( 3.0 \times 10^{10} N / m^{2} \)
Neglecting the mass of the rod, find the
shearing stress on the rod.
A \( .6 .5 \times 10^{6} N m^{-2} \)
В. \( 9.5 \times 10^{6} \mathrm{N} \mathrm{m}^{-2} \)
c. \( 8.5 \times 10^{6} \mathrm{N} \mathrm{m}^{-2} \)
D. \( 7.5 \times 10^{6} \mathrm{N} \mathrm{m}^{-2} \)


The region represented by the inequation system \( \boldsymbol{x}, \boldsymbol{y} \geq \mathbf{0}, \boldsymbol{y} \leq \mathbf{6}, \boldsymbol{x}+ \)
\( y \leq 3 \) is
A. Unbounded in first quadrant
B. Unbounded in first and second quadrants
C. Bounded in first quadrant
D. None of the above


A car of mass \( m \) starts moving so that its velocity varies according to the law \( \boldsymbol{v}=\boldsymbol{\beta} \sqrt{\boldsymbol{s}}, \) where \( \boldsymbol{\beta} \) is a constant, and \( \boldsymbol{s} \) is
the distance covered. The total work
performed by all the forces which are acting on the car during the first \( t \) seconds after the beginning of motion is:
\( \mathbf{A} \cdot m \beta^{4} t^{2} / 8 \)
B \( \cdot m \beta^{2} t^{4} / 8 \)
\( \mathbf{c} \cdot m \beta^{4} t^{2} / 4 \)
\( \mathbf{D} \cdot m \beta^{2} t^{4} / 4 \)


Ethers on hydrolysis gives:
A. esters
B. alcohols
c. aldehydes
D. alkanes


The axes being inclined at an angle of
\( 60^{\circ}, \) the inclination of the straight line
\( \boldsymbol{y}=2 \boldsymbol{x}+\mathbf{5} \) with \( \mathbf{x} \) -axis is
\( A \cdot 30 \)
B . \( \tan ^{-1}(\sqrt{3} / 2) \)
\( c \cdot \tan ^{-1} 2 \)
D. \( 60^{\circ} \)


Solve the differential equation \( y e^{\frac{x}{y}} d x=\left(x e^{\frac{x}{y}}+y^{2}\right) d y(y \neq 0) \)


How is ethanol produced by
fermentation?
A. Using anaerobic conditions at \( 30^{\circ} \mathrm{C} \)
B. Using anaerobic conditions at \( 450^{\circ} \mathrm{C} \)
C . Using steam at \( 30^{\circ} \mathrm{C} \)
D. Using steam at \( 450^{\circ} \mathrm{C} \)


Relation to another coordinate system
\( \mathbf{S}_{2} \) (denoted by double primes) having an acceleration \( -\overline{\mathbf{g}}, \) and coincident with
the original coordinate system \( \mathbf{S}_{0} \) at
\( \mathbf{t}=\mathbf{0}, \) the equation of the object
becomes
A \( \cdot 0=-\mathrm{m} \overline{\mathrm{g}}-\mathrm{b} \overline{\mathrm{v}}^{\prime \prime} \)
B. \( m\left(\frac{d \vec{v}^{\prime \prime}}{d t}\right)=0 \)
\( ^{\mathrm{c}} m\left(\frac{d \overrightarrow{v^{\prime \prime}}}{d t}\right)=-b v^{\vec{\eta}}-b g t \)
\( ^{\mathrm{D}} \cdot_{m}\left(\frac{d \overrightarrow{v^{\prime \prime}}}{d t}\right)=-b v^{\vec{\eta}}+b g t \)


Assertion
\( H_{2} S \) reacts with oxygen under standard
conditions in acid medium to give \( \boldsymbol{H}_{2} \boldsymbol{O} \)
and sulphur.
Reason
\( \boldsymbol{E}_{\boldsymbol{H}^{+} / \boldsymbol{O}_{2} / \boldsymbol{P t}}>\boldsymbol{E}_{\boldsymbol{H}^{+} / \boldsymbol{H}_{2} \boldsymbol{S} / \boldsymbol{S}}^{\boldsymbol{o}} \)
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


\( 40 \mathrm{ml} \) of ammonia gas was taken in a eudiometer tube and subjected to sparks till the volume did not further
change. The volume was found to increase by \( 40 \mathrm{ml} .40 \mathrm{ml} \) of oxygen gas then mixed and the mixture was further
exploded. The gases remaining were 30
ml. Deduce the formula of ammonia.
(Ammonia contains \( N \) and \( H \) only)


The term Darwin's finches was given to Galapagos finches by
A. Huxley
B. spencer
c. wallace
D. Lank


Find \( \int \frac{d x}{\sqrt{9+8 x-x^{2}}} \)


What are the effects of acid rain ?


What effect does branching of an alkane chain has on its boiling point?


Paracetamol is a/an
A . antipyratic
B. analgesic
\( c . \) both a and \( b \)
D. None of the above


If two mirrors are inclined at some
angle \( \theta . \) An object is placed between the mirrors and there are 5 images formed
for an object, then \( \theta \) is may be
A \( \cdot 45^{\circ} \)
B. \( 53^{\circ} \)
\( c \cdot 63^{\circ} \)
D. \( 75^{\circ} \)


Which of the following is the most
accurate instrument?
A. A scale whose least count is \( 0.1 \mathrm{cm} \)
B. A vernier caliper in which 10 vernier divisions coincide with 9 main scale divisions whose main scale is millimetre scale.
C. A microscope in which 50 vernier divisions coincide with 49 main scale divisions whose main scale is millimetre scale.
D. A microscope in which 50 vernier divisions coincide with 49 main scale divisions and in the main scale
there are 20 divisions in \( 1 \mathrm{cm} \)


Diameter of plano-convex lens is \( 6 \mathrm{cm} \)
and thickness at the centre is \( 3 \mathrm{mm} \). If
speed of light in material of lens is \( 2 x \)
\( 10^{8} m / s, \) the focal length of the lens is:
A. \( 20 \mathrm{cm} \)
B. 30 cm
c. \( 10 \mathrm{cm} \)
D. \( 15 \mathrm{cm} \)


Lead storage cell is a secondary cell.
If true enter 1 , else enter 0


Zinc can displace silver from
\( \left[\boldsymbol{A} \boldsymbol{g}(\boldsymbol{C} \boldsymbol{N})_{2}\right]^{-} \)
If true enter 1 , else enter 0 .


Define homologous series.
A. Compound with same melting point
B. Compound which are stereo isomers
C. Compounds which have different parameters
D. Compound with same general formula


The work done by the frictional force at the instant of pure rolling is
\( ^{\text {A }} \cdot \frac{\mu m g a t^{2}}{2} \)
B. \( \mu \) mgat \( ^{2} \)
\( \mathrm{c},_{\mu m g} \frac{a t^{2}}{\alpha} \)
D. zero


The IUPAC name of given compound is :
A. Heptan-4-one
B. Heptan-4-ol
c. Heptan- 4 -a
D. Heptan-4-ane


Which of the following is the correct graph showing \( \boldsymbol{V}-\boldsymbol{I} \) characteristics
for an ideal \( P N \) junction diode?


The nature of the image of a candle flame located \( 40 \mathrm{cm} \) from a concave
mirror is real, inverted and magnitude
four times. Then the radius of curvature
of the mirror is:
\( \mathbf{A} \cdot 32 c m \)
B. \( 64 \mathrm{cm} \)
\( \mathbf{c} \cdot 48 c m \)
D. \( 80 \mathrm{cm} \)


1 mol benzene \( \left(P_{\text {benzene }}^{o}=42 \mathrm{mm}\right) \) and 2 mol toluene \( \left(P_{\text {toluene}}^{o}=36 \mathrm{mm}\right) \) will have
This question has multiple correct options
A. total pressure of 38 mm.
B. mole fraction of vapour of benzene above liquid mixture is \( 7 / 19 \)
c. positive deviation from Raoult's law
D. negative deviation from Raoult's law


Find the hydrocarbon for which volume
of oxygen required is 1.5 times volume of carbon dioxide produced.


A hydride of nitrogen which is acidic is :
A . \( N H_{3} \)
в. \( N_{2} H_{2} \)
c. \( N_{2} H_{4} \)
D. \( N_{3} H \)


Steriod hormones work as
A. They enter into target cells and binds with specific receptor and activates specific genes to form protein
B. They binds to cell membrane
C. They catalyse information of cAMP
D. None of the above


o-Hydroxy benzaldehyde is a liquid at room temperature while p-hydroxy benzaldehyde is a_- - melting solid.
A. low
B. equal
c. high
D. none


Ambidentate ligands can show linkage isomerism.
A . True
B. False


An alkaline earth metal:
A . potassium
B. calcium
c. lead
D. copper


The Electromagnetic wave travelling in a medium has relative permeability 1.3 and relative premittivity 2.14. The speed
of EM wave in that medium will be.
\( \mathbf{A} \cdot 13.6 \times 10^{6} \mathrm{m} / \mathrm{s} \)
B . \( 1.8 \times 10^{6} \mathrm{m} / \mathrm{s} \)
c. \( 3.6 \times 10^{8} \mathrm{m} / \mathrm{s} \)
D. \( 1.8 \times 10^{8} \mathrm{m} / \mathrm{s} \)


Which of the following stage is affected by colchicine?
A. Metaphase
B. Prophase
c. Interphase
D. Anaphase


Nucleic acid (DNA) is not found in
A. Nucleus and nucleolus
B. Peroxysome and ribosome
c. Mitochondria and plastid
D. chloroplast and nucleosome


If the annual increase in the population be \( 20 \% \) and the present population be
\( 10,000 . \) What will be the population
after 3 years?
A . 16,000
B. 17,280
\( c \cdot 14,400 \)
D. 1,728


Consider a rigid square \( A B C D \) as in
the figure with \( A \) and \( B \) on the \( x \) and \( y \)
axis respectively. When \( A \) and \( B \) slide
along their respective axes, the locus of
\( C \) forms a part of
A. A circle
B. A parabola
C. A hyperbola
D. An ellipse which is not a circle


Evaluate \( \int \frac{\tan ^{7} \sqrt{x} \sec ^{2} \sqrt{x}}{\sqrt{x}} d x \)


The type of pollution caused by spraying DDT is:
A. air and soil
B. air and water
c. air
D. air, water and soil


A lending library has a fixed charge for first 3 days and an additional charges for each day there after. Sarika paid Rs.
27 for a book kept for 7 days while Sonali paid Rs.21 for the book she kept for 5 days. find the fixed charge and the additional charge per day.


Choose the correct answer from
alternatives given. If \( \vec{E} \) and \( \vec{B} \) represent electric and magnetic field vectors of an electromagnetic wave, the direction of propagation of the wave is along
\( \mathbf{A} \cdot \vec{B} \times \vec{E} \)
в. \( \vec{B} \)
\( c \cdot \vec{E} \)
D. \( \vec{E} \times \vec{B} \)


Which of the following statement is/are
correct?
We can construct a quadrilateral:
A. when its opposite sides are given
B. when its four angles and a side are given
c. when its diagonals are given
D. when its three angles and any two adjacent sides are given


If \( f(x) \) is continuous and \( f\left(\frac{9}{2}\right)=\frac{2}{9} \) then \( \lim _{x \rightarrow 0} f\left(\frac{1-\cos 3 x}{x^{2}}\right) \) is equal to:
A \( \cdot \frac{9}{2} \)
в. \( \frac{2}{9} \)
\( c \cdot 0 \)
D. \( \frac{8}{9} \)


In how many ways can 13 question
papers be arranged so that the best and the worst are never come together?
A . \( 12 ! \times 11 \)
В. \( 11 \times 12 ! \)
c. \( 12 !^{2} \)
D. none of these


Write as percentage \( 4 \frac{4}{20} \)
A. \( 84 \% \)
B. \( 420 \% \)
c. \( 8.4 \% \)
D. \( 42 \% \)


The equation \( \frac{x^{2}}{2-a}+\frac{y^{2}}{a-5}+1=0 \)
represents an ellipse if \( \boldsymbol{a} \in \)
\( ^{\mathbf{A}} \cdot\left(2, \frac{3}{2}\right) \cup\left(\frac{3}{2}, 5\right) \)
в. \( \left(2, \frac{3}{2}\right) \)
c. \( \left(1, \frac{3}{2}\right) \)
D. \( \left(\frac{3}{2}, 5\right) \)


The value of Kc for the reaction
\( 3 O_{2}(g) \rightleftharpoons 2 O_{3}(g) \) is \( 1.7 \times 10^{-56} \mathrm{at} \)
\( 25^{\circ} \mathrm{C} . \) Do you expect pure air at \( 25^{\circ} \mathrm{C} \) to
contain much \( O_{3} \) (ozone) when \( O_{2} \) and
\( O_{3} \) are in equilibrium ? If the
equilibrium concentration of \( \boldsymbol{O}_{2} \) in air
\( \operatorname{at} 25^{\circ} C \) is \( 8 \times 10^{3} M, \) what is the
equilibrium concentration of \( \boldsymbol{O}_{3} ? \)
\( \mathbf{A} \cdot \) Yes, \( \sim 3 \times 10^{-32} \) mol \( / L \)
B. Yes, \( 6 \times 10^{-32} \) mol \( / L \)
C. Yes, \( \sim 9 \times 10^{-32} \) mol \( / L \)
D. None of these


Work done in moving an electric charge
\( q \) in an electric field does not depend
upon:
A. Magnitude of the charge
B. Potential difference between two points
c. Mass of the particle
D. All of these


An experiment showed that a lead chloride solution is formed when \( 6.21 \mathrm{g} \)
of lead combines with \( 4.26 \mathrm{g} \) of chlorine. What is the empirical formula of this chloride?
\( [P b=207 ; C l=35.5] \)
A. \( P b C l_{3} \)
в. \( P b C l_{2} \)
\( \mathbf{c} \cdot P b C l_{4} \)
D. \( P b C l \)


Steam distillation is used for the
extraction of
A. essential oil
B. higher alkynes
c. mineral oils
D. fatty acids


Herbaceous plant that dies back to
ground each year but sprouts again from under ground parts is?
A. Perennial
B. Biennial
c. Annual
D. Winter annual


A man has 80 pens. He sells some of these at \( 15 \% \) profit and the rest at
10\% loss. Overall he gets a profit of 10\% Find how many pens were sold at \( 15 \% \) profit ?


Select the correct I.U.P.A.C. name for
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right]\left[\boldsymbol{C o}(\boldsymbol{O} \boldsymbol{N} \boldsymbol{O})_{6}\right] \)
A. Hexaamminecobalt(II) hexanitrito-0 cobalt(II)
B. Hexaamminecobalt(III) hexanitrito-N cobaltate(III)
c. Hexaamminecobaltate(III) hexanitrito-0 cobaltate(II)
D. Hexaamminecobalt(III) hexanitrito-0 cobaltate(III)


Butyraldehyde are produced commercially by:
A. hydroformylation
B. hydroacetylation
c. formylation
D. acetylation


What temperature reading on the fahrenheit scale is five times the
reading on the celsius scale?


A body of mass \( 2 k g \) is thrown upward with initial velocity \( 20 m / s . \) After \( 2 s \) find its kinetic energy will be: \( (\boldsymbol{g}= \) \( \left.10 m / s^{2}\right) \)
A. \( 400 J \)
B. 200 J
c. \( 100 J \)
D. zero


The following table shows the number of students and the time they utilized daily for their studies. Find the mean
time spent by students for their studies by direct method.
\( \begin{array}{lllll}\text { Time } & \mathbf{0}- & \mathbf{2}- & \mathbf{4}- & \mathbf{6}- \\ \text { (hrs.) } & \mathbf{2} & \mathbf{4} & \mathbf{6} & \mathbf{8}\end{array} \)
No. of
12
students
A. 4 hrs
B. 5 hrs
c. 4.36 hrs
D. 5.36 hrs


The mass defect per nucleon is called
A. binding energy
B. packing fraction
c. ionisation energy
D. excitation energy


Exophthalmic goitre (Grave's disease) is caused due to
A. Hypofunction of the thyroid
B. Hyperfunction of the thyroid
c. Hypofunction of the parathyroid
D. Hyperfunction of the parathyroid


The work done in stretching a spring of force constant \( \mathrm{k} \) from \( \boldsymbol{y}_{1} \) and \( \boldsymbol{y}_{2} \) from
mean position will be
A \( \cdot \frac{k}{2}\left(y_{2}^{2}-y_{1}^{2}\right) \)
B. \( \frac{k}{2}\left(y_{1}^{2}-y_{2}^{2}\right) \)
\( \mathbf{c} \cdot k\left(y_{2}-y_{1}\right) \)
D. zero


Soil fertilizer contains
key element.
A. carbon
B. nitrogen
c. oxygen
D. neon
E. argon


Force between two identical bar
magnets whose centres are \( r \) metre
apart is \( 4.8 N \), when their axes are in
the same line. If separation is increased
to \( 2 r, \) the force between them is
reduced to.

This question has multiple correct options
A . \( 0.3 N \)
B. \( 0.6 N \)
c. \( 2.4 N \)
D. \( 1.2 N \)


State whether the given statement is True or False :

The value of G depends upon the mass of the two objects.
A. True
B. False


Two solid cylinders \( P \) and \( Q \) of same mass and same radius start rolling down a fixed inclined plane from the same height at the same time. Cylinder
\( P \) has most of its mass concentrated
near its surface, while \( Q \) has most of its
mass concentrated near the axis. Which
statement(s) is (are) correct?
A. Both cylinders \( P \) and \( Q \) reach the ground at the same time
B. Cylinder \( P \) has larger linear acceleration than cylinder
\( Q \)
C. Both cylinders reach the ground with same translational kinetic energy.
D. Cylinder \( Q \) reaches the ground with larger angular speed


What is ecological succession. Mention
its different steps. Explain Hydrach and Xerarch succession with diagramatic representation.


Hydrogen resembles halogens as:
A. hydrogen forms diatomic molecule
B. it combines with metal and non-metals to form
compounds
C. both \( A \) and \( B \)
D. none of the above


An electricity generating machine consists of a turbine and a
A. Dynamo
B. core
c. Heat
D. sun


Name the device used to measure the
following:
(a) Size of your shoulder.
(b) Size of your wrist.
(c) Your height.
(d) Your weight.
(e) Cloth for curtain.
(f) Circumference of round table,


Offspring formed by sexual reproduction exhibit more variation than those formed by asexual reproduction because
A. Sexual reproduction is a lengthy process
B. Gametes of parents have qualitatively different genetic composition
c. Genetic material comes from parents of two different species
D. Greater amount of DNA is involved in sexual reproduction


Find the supplementary angle of \( 40^{\circ} \)


If two SHMs of different amplitudes are added together, the resultant SHM will be a maximum if the phase difference between them is
\( \mathbf{A} \cdot \pi / 2 \)
в. \( \pi / 4 \)
\( c \)
D. \( 2 \pi \)


Solve the system of inequalities graphically \( \mathbf{3} \boldsymbol{x}+\mathbf{2} \boldsymbol{y} \leq \mathbf{1 5 0}, \boldsymbol{x}+\mathbf{4} \boldsymbol{y} \leq \mathbf{8 0}, \boldsymbol{x} \leq \mathbf{1 5}, \boldsymbol{y} \)


Write the additive inverse of each of the
following rational numbers:
\( \frac{-11}{-25} \)


The number of molecules in 4.25 g of
\( N H_{3} \) is :
A \( \cdot 1.505 \times 10^{23} \)
B. \( 3.01 \times 10^{23} \)
c. \( 6.02 \times 10^{23} \)
D. none of these


Which of the following chemical bond is present between \( \mathrm{H} \) and \( \mathrm{Cl} \) in \( \boldsymbol{H} \boldsymbol{C l} \) ?
A. Ionic bond
B. co-ordinate covalent bond
c. Non-Covalent bond
D. Polar covalent bond


What should be added to \( 6 x^{2}-3 x y+ \)
\( 4 y^{2} \) to get \( 2 y^{2}+x y-4 x^{2} ? \)
A. \( -x^{2}-y^{2}+4 y \)
B . \( -10 x^{2}-y^{2}+4 x y \)
c. \( x^{2}-2 y^{2}+4 x \)
D. \( -10 x^{2}-2 y^{2}+4 x y \)


The value of \( \frac{4}{\tan ^{2} 60^{0}}+\frac{1}{\cos ^{2} 30^{0}}- \)
\( \sin ^{2} 90^{0} \) is equal to


A smaller subunit of ribosome has a
binding site for \( _{-}--_{-}- \) and the larger subunit has two binding sites for tRNA
molecules.
A \( \cdot \mathrm{Mg}^{+} \)
B. Peptidyl transferase
c. mRNA
D. None of the above


Which overlapping is involved in \( \boldsymbol{H} \boldsymbol{C l} \)
molecule?
A . \( s-s \) overlap
B. \( p-p \) overlap
c. \( s-d \) overlap
D. \( s-p \) overlap


A \( 5 c m \) long needle lies along the principal axis axis of a concave mirror
of focal length \( 20 \mathrm{cm} \) in such a way that
the end closer to the pole is \( 40 \mathrm{cm} \) from
it. Find the length of the image of the needle formed by the mirror.


In which energy level is the outer electron in rubidium located?
A . 85
B. 2
c. 37
\( D \)
\( E .5 \)


\( 80 \% \) of a first order reaction was
completed in 70 min. How much it will take for \( 90 \% \) completion of a reaction?
A. 114 min
B. 140 min
c. \( 100 \mathrm{min} \)
D. 200 min


Which of the following is not a reflex action?
A. Salivation
B. Sweating
c. Withdrawal of hand when pinched by needle
D. None of these


A transistor is essentially
A. a current operated device
B. power driven device
C . a voltage operated device
D. resistance operated device


A drug called colchicine interferes in
mitosis during the spindle microtubule formation; it does so by
A. Arresting chromosome movement
B. Breaking microtubules
c. Thickening microtubles
D. Arresting centriole movement


Which of the following is used to
prepare \( C l_{2} \) gas at room temperature
from concentrated \( \boldsymbol{H} \boldsymbol{C l} \) ?
A. \( M n O_{2} \)
в. \( H_{2} \).
c. \( K M n O_{4} \)
D. \( C r_{2} O_{3} \)


Which of the following factors is responsible for the formation of
concentrated urine?
A. Low levels of antidiuretic hormone
B. Maintaining hyperosmolarity towards inner medullaryyy interstitium in the kidneys
c. secretion of erythropoietin by Juxtaglomerular complex
D. Hydrostatic pressure during glomerular filtration


The specific conductivity of \( N / 10 K C l \)
solution at \( 20^{\circ} \mathrm{C} \) is 0.0212 oh \( m^{-1} \mathrm{cm}^{-1} \)
and the resistance of the cell containing
this solution at \( 20^{\circ} C \) is 55 ohm. The
cell constant is:
A \( \cdot 4616 \mathrm{cm}^{-1} \)
B. \( 1.166 \mathrm{cm}^{-1} \)
c. \( 2.173 \mathrm{cm}^{-1} \)
D. \( 3.324 \mathrm{cm}^{-1} \)


A sphere is rolled on a rough horizontal
surface. It gradually slows down and stops. The force of friction tends to:
This question has multiple correct options
A. decrease linear velocity
B. increase linear momentum
c. decrease angular velocity
D. increase angular velocity


Which of the following is not a controlled process?
A. Transpiration
B. Guttation
c. Both A and B
D. None of the above


Two parallel chords \( A B \) and \( C D \) are 3.9
cm apart and lie on opposite sides of the centre of a circle. If \( A B=1.4 \mathrm{cm} \)
and \( C D=4 \mathrm{cm}, \) find the radius of the
circle.
A. \( 3 \mathrm{cm} \)
B. \( 3.2 \mathrm{cm} \)
\( c .2 .3 \mathrm{cm} \)
D. \( 2 \mathrm{cm} \)


In the reaction, \( \boldsymbol{H}_{2} \boldsymbol{P} \boldsymbol{O}_{4}^{-}+\boldsymbol{H}_{2} \boldsymbol{O}(l)= \)
\( \boldsymbol{H}_{3} \boldsymbol{O}^{+}(\boldsymbol{l})+\boldsymbol{H} \boldsymbol{P} \boldsymbol{O}_{4}^{2-}(l) \) the
hydrogen phosphate ion is the:
A. bronsted acid
B. bronsted base
c. conjugate acid
D. conjugate base


Compute mode of the following
distribution by inspection method.
\( \begin{array}{ccccccc}\chi & 1 & 2 & 3 & 4 & 5 & 6 \\ f & 4 & 6 & 8 & 12 & 17 & 11\end{array} \)
\( \mathbf{A} \cdot 15.09 \)
B. 5
c. 14.42
D. 15


A uniform rod of length \( L \) rests against
a smooth wall as shown in figure. Find
the friction coefficient between the
ground and the lower end if the
minimum angle that the rod can make
with the horizontal is \( \theta \)
A \( \cdot \frac{L \cos ^{2} \theta \sin \theta}{2 h-l \cos \theta \sin ^{2} \theta} \)
B. \( \frac{L \cos \theta \sin ^{2} \theta}{2 h-l \operatorname{cs} \theta \sin ^{2} \theta} \)
c. \( \frac{L \cos ^{2} \theta \sin \theta}{2 h-l \cos ^{2} \theta \sin \theta} \)
D. \( \frac{L \cos \theta \sin ^{2} \theta}{2 h-l \cos ^{2} \theta \sin \theta} \)


When resistor are connected in series
what remains same.?
A. current
B. Voltage
c. Resistance
D. power


(i) \( B a C_{2}+N_{2} \stackrel{\Delta}{\rightarrow}(B) \)
(ii) \( \boldsymbol{C a C}_{2}+\boldsymbol{N}_{2} \stackrel{\boldsymbol{\Delta}}{\rightarrow}(\boldsymbol{A}) \)
Identify \( (\boldsymbol{A}) \) and \( (\boldsymbol{B}) \)
A \( \cdot A: C a(N=C=N) ; \) В \( : B a(C \equiv N) \)
B. \( A: C a(N=C=N) ; \) В \( : B a_{2}(C \equiv N)_{4} \)
c. \( A: C a(N=C=N)_{2} ; \) в: \( B a(C \equiv N)_{2} \)
D. \( A: C a(N=C=N)_{2} ; \) B: \( B a_{2}(C \equiv N)_{4} \)


During translation, if the codon on \( m \) RNA is AUG, then
(i) What is the sequence of anticodon
present on corresponding t-RNA?
(ii) Name the amine acid carried by this
t-RNA.


State whether the statement is True or
False.

The square of \( (x+3 y) \) is equal to \( x^{2}+ \)
\( 6 x y+9 y^{2} \)
A. True
B. False


The shape of \( C H C l_{3} \) molecule is
A. linear
B. pyramidal
c. tetrahedral
D. trigonal bipyramidal


Simplify:
\( (2 x+y)^{3}+(2 x-y)^{3} \)


The total number of \( \angle \boldsymbol{F} \boldsymbol{I} \boldsymbol{F} \) angles in
\( I F_{7} \) having the bond angle value of \( 90^{\circ} \)
is


Each resistance shown in figure is \( 2 \Omega \) The equivalent resistance between \( \boldsymbol{A} \) and \( B \) is
\( A .2 \Omega \)
в. \( 1 \Omega \)
\( c \cdot 4 \Omega \)
\( D .5 \Omega \)


\( \int \frac{x^{2}+x-1}{x^{2}+x-6} d x= \)
\( \mathbf{A} \cdot x+\log p+5|+\log | x-2 \mid+c \)
B . \( x-\log |x+3|+\log |x-2|+c \)
c. \( x-\log |x+3|-\log |x-2|+c \)
D. None of these


In a buffer solution consisting
\( N a H_{2} P O_{4} \) and \( N a_{2} H P O_{4} \)
(1) \( N a H_{2} P O_{4} \) is acid and \( N a_{2} H P O_{4} \)
is salt
(2) The pH of solution can be calculated using the relation:
\( \boldsymbol{p} \boldsymbol{H}=\boldsymbol{p} \boldsymbol{K}_{2}+\log _{10} \frac{\left[\boldsymbol{H} \boldsymbol{P} \boldsymbol{O}_{4}^{2-}\right]}{\left[\boldsymbol{H}_{2} \boldsymbol{P} \boldsymbol{O}_{4}^{-}\right]} \)
(3) The \( N a_{2} H P O_{4} \) is acid and
\( N a H_{2} P O_{4} \) is salt
(4) The pH cannot be calculated.
A. 1,2 and 3 are correct
B. 1 and 2 are correct
\( c \cdot 2 \) and 4 are correct
D. 1 and 3 are correct


Find the distance covered by the bolt during the free fall.
\( \mathbf{A} \cdot 1.3 m \)
B. \( 1.6 m \)
\( \mathrm{c} \cdot 13 \mathrm{m} \)
D. 16 \( m \)


The value of \( \int_{-4}^{-5} e^{(x+5)^{2}} d x+ \)
\( \mathbf{3} \int_{1 / 3}^{2 / 3} e^{9(x-2 / 3)^{2}} d x \)
A . \( 2 / 5 \)
в. \( 1 / 5 \)
\( c \cdot 1 / 2 \)
D. none of these


What do you mean by: The specific heat capacity of copper is \( 0.4 J g^{-1} K^{-1} \)
A . \( 0.4 J \)
B. 2
\( c .3 \)
D.


The molar enthalpy of vaporization benzene at its boiling point(350K) is \( 30.84 \mathrm{kJ} / \mathrm{mol} . \) What is the molar internal
energy change?For how long would a 12 volt source need to supply a \( 0.5 \mathrm{A} \) current in order to vaporize \( 7.8 g \) of sample at its boiling point?


Derive the equation of the locus of a point twice as far from (-2,3,4) as from
(3,-1,-2)


On the basis of the following observations made with aqueous
solutions. assign secondary valences to metals in the following compounds:
Formula
of AgCl precipitated per mole of the compounds with excess AgNO,
\( (i) P d C l_{2} .4 N H_{3} \)
\( (i i) N i C l_{2} .6 H_{2} O \)
\( (\text {iiii}) P t C l_{4} .2 H C l \)
\( (i v) C o C l_{3} .4 N H_{3} \)
\( (v) P t C l_{2} \cdot 2 N H_{3} \)


Which of the following diagrams does not represent a streamline flow?
\( A \)
в.
\( c \)
D.


Decimal representation of a rational
number cannot be:
A. Terminating
B. Non-Terminating
c. Non-Terminating, Repeating
D. Non-Terminating, Non-Repeating


Which of the following is not a classification of drugs?
A. on the basis of pharmacological effect
B. On the basis of drug action
c. on the basis of chemical structure
D. None


When \( 4 g^{3}-3 g^{2}+g+k \) is divided by
\( g-2, \) the remainder is \( 27 . \) Find the
value of \( k \)
\( \mathbf{A} \cdot \mathbf{3} \)
B. 5
c. 8
D. 12
E . 10


Construct a triangle \( A B C \) in which \( B C= \)
\( 8 c m, \angle B=45^{0} \) and \( A B-A C=3.5 \mathrm{cm} \)


Integrate the following function with
respect to \( x \) \( \frac{\sec ^{3} x}{\csc x} \)


Tangents drawn from the point \( \boldsymbol{P}(\mathbf{1}, \boldsymbol{8}) \)
to the circle \( x^{2}+y^{2}-6 x-4 y-11= \)
0 touch the circle at the point \( A \) and \( B \)
The equation of the circumcentre of the
\( \triangle \boldsymbol{P} \boldsymbol{A} \boldsymbol{B} \) is
A \( \cdot x^{2}+y^{2}+4 x-6 y+19=0 \)
B . \( x^{2}+y^{2}-4 x-10 y+19=0 \)
c. \( x^{2}+y^{2}-2 x+6 y-29=0 \)
D. \( x^{2}+y^{2}+6 x-4 y+19=0 \)


The direction of force on a current
carrying conductor placed in a magnetic field is given by :
A. Fleming's Left Hand Rule
B. Fleming's Right Hand Rule
c. End Rule
D. Right Hand Palm Rule


How many different words can be formed using all the letters of the word 'ALLAHABAD' when both \( L^{\prime} s \) are not
together
A. 4200
B. 5812
\( c .6000 \)
D. 5250


In instantaneous current in a metallic
wire is \( \mathrm{i}=(5+10 \mathrm{t}) \mathrm{A} \) then find amount of
charge flown through it from \( t=2 s \) to \( t=3 s \) is
A . 100
B. 24C
c. \( 30 c \)
D. 40C


The horizontal rows in Mendleev's table
were called :
A. groups
B. rows
c. periods
D. none of the above


For a given reaction, \( \boldsymbol{H}_{2} \boldsymbol{O}(l) \rightleftharpoons \)
\( H_{2} O(s) a t 0^{\circ} C \) and 1 bar, which of the
following is true?
A. \( \Delta G=0 \)
в. \( \Delta S=0 \)
c. \( \Delta H=0 \)
D. \( \Delta U=0 \)


A line \( y=x \) is rotated through \( 45^{\circ} \)
Find the new angle made by line with \( x \) axis.
A \( \cdot 90^{\circ} \)
B. \( 80^{\circ} \)
\( c .75^{\circ} \)
D. None of these


Which of the following energy change involves frictional force?
A. Chemical energy to heat energy
B. Kinetic energy to heat energy
C. Potential energy to sound energy
D. chemical energy to kinetic energy


Which of the following shown \( C-C \)
bonds is the strongest?
\( A \)
B \( .>C=C< \)
c. \( -C-C= \)
D. \( -C \equiv C- \)


Primitive Man who built up dwelling huts and buried its dead was
A. Java Ape Man
B. Cro-Magnon Man
c. Peking Man
D. Neanderthal Man


Find the middle term(s) in the
expansion of :
\( \left(\frac{p}{x}+\frac{x}{p}\right)^{9} \)
A \( \cdot \frac{126 x}{p}, \frac{126 p}{x} \)
В \( \cdot \frac{126}{p}, 126 x \)
\( ^{\mathrm{C}} \cdot \frac{160 x^{2}}{p}, \frac{162 x}{p^{2}} \)
D. None of these


Saturated solution of NaCl on heating:
A. becomes supersaturated
B. becomes unsaturated
c. remains saturated
D. vaporises


Find the particular solution of the differential equation:
\( \boldsymbol{y}(\mathbf{1}+\log \boldsymbol{x}) \frac{\boldsymbol{d} \boldsymbol{x}}{\boldsymbol{d} \boldsymbol{y}}-\boldsymbol{x} \log \boldsymbol{x}=\mathbf{0} \)
when \( y=e^{2} \) and \( x=e \)


Palaeontologists unearthed a human skull during excavation. A small fragment of the scalp tissue was still attached to it. Only little DNA could be extracted from it. If the genes of the ancient man need to be analysed, the
best way of getting sufficient amount of DNA from this extract is
A. Hybridising the DNA with a DNA probe
B. Subjecting the DNA to polymerase chain reaction
c. Subjecting the DNA to gel electrophoresis
D. Treating the DNA with restriction endonucleases


Air contains \( O_{2} \) and \( N_{2} \) in the ratio of
1:4. Calculate the ratio of solubilities in
terms of mole fraction of \( \boldsymbol{O}_{2} \) and \( \boldsymbol{N}_{2} \)
dissolved in water at atmospheric pressure and room temperature at
which Henry's constant for \( \boldsymbol{O}_{2} \) and \( \boldsymbol{N}_{2} \) are \( 3.30 \times 10^{7} \) torr and \( 6.60 \times 10^{7} \) tor
respectively.


Find the range if \( [2 \sin x]+[\cos x]= \)
\( -3, \) then the range of the function
\( f(x)=\sin x+\sqrt{3} \cos x \) in \( [0,2 \pi] \)
(where [.] denotes the greatest integer function)
A \( \cdot(2,-1) \)
B \( \cdot\left(-1,-\frac{1}{2}\right) \)
\( \mathbf{c} \cdot(-2,-1) \)
D. None of these


If \( a_{n} \) is a sequence such that \( a_{1}=1 \)
\( \boldsymbol{a}_{2}=\mathbf{1}+\boldsymbol{a}_{1}, \boldsymbol{a}_{3}=\mathbf{1}+\boldsymbol{a}_{1} \boldsymbol{a}_{2}, \boldsymbol{a}_{n+1}= \)
\( 1+a_{1} a_{2} a_{3} \dots \dots a_{n} \) then find the value of \( \frac{1}{a_{1}}+\frac{1}{a_{2}}+\frac{1}{a_{3}}+\frac{1}{a_{4}} \dots \dots \)


Assertion
Fr burns in air forming \( \boldsymbol{F} \boldsymbol{r} \boldsymbol{O}_{2} \)
Reason
The larger alkali metal ions stabilities
\( O_{2}(\text { superoxide }) \)
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Assertion
Low level of noradrenaline causes
depression.
Reason
Equanil is used in controlling
depression.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
C. Assertion is correct but Reason is incorrect.
D. Both Assertion and Reason are incorrect.


Which of the following is Loschmidt
number?
A \( \cdot 6 \times 10^{23} \)
3 \( ^{3} 100-10^{0} \)
B . \( 2.69 \times 10^{25} \)
\( \mathrm{c} \cdot 3 \times 10^{23} \)
D. None of these


IUPAC name of aniline is:
A. phenylamine
B. aminobenzene
c. benzylamine
D. benzenamine


Which one represents pulmonary
circulation?
A. Left auricle (oxygenated blood) \( \rightarrow \) lungs (deoxygenated blood) \( \rightarrow \) Right auricle
B. Left auricle (deoxygenated blood) \( \rightarrow \) lungs (oxygenated blood) \( \rightarrow \) Right auricle
C. Left auricle (oxygenated blood) \( \rightarrow \) lungs (deoxygenated blood) \( \rightarrow \) Left auricle
D. Right auricle (deoxygenated blood) \( \rightarrow \) lungs (oxygenated blood) \( \rightarrow \) Left auricle


Why \( I C l_{3} \) is more reactive than \( I_{2} ? \)


The feasibility of a chemical reaction can be explained based on \( \Delta \boldsymbol{H}, \boldsymbol{\Delta} \boldsymbol{S} \)
and \( \Delta G \)
For \( 2 O_{3}(g) \rightarrow 3 O_{2}(g), \) if the reaction is
feasible, then:
This question has multiple correct options
\( \mathbf{A} \cdot \Delta S=+v e \)
в. \( \Delta G=+v e \)
c. \( \Delta H=-v e \)
\( \mathbf{D} \cdot \Delta G=-v e \)


The domain of the function \( f(x)= \) \( \frac{\sin ^{-1}(x-3)}{\sqrt{9-x^{2}}} \) is
A \( \cdot[1,2] \)
в. [2,3]
c. [2,3]
D. [1,2)


Construct a \( \Delta A B C \) in which \( A B=5 c m . \)
\( \mathrm{B}=60^{\circ} \) altitude \( \mathrm{CD}=3 \mathrm{cm} . \) Construct
\( \Delta \mathrm{AQR} \) similar to \( \Delta \mathrm{ABC} \) such that side
of \( \Delta A Q R \) is 1.5 times that of the corresponding sides of \( \Delta A C B \)


Inner and outer radii of a spool are \( r \) and
\( R \) respectively. A thread is wound over
its inner surface and placed over a
rough horizontal surface. Thread is
pulled by a force \( F \) as shown in fig. then
in case of pure rolling:
A. Thread unwinds, spool rotates anticlockwise and friction act leftwards.
B. Thread winds, spool rotates clockwise and friction acts leftwards
C. Thread winds, spool moves to the right and friction act rightwards.
D. Thread winds, spool moves to the right and friction does not come into existence


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


Calculate the \( p H \) of a \( 2.0 M \) solution of
\( N H_{4} C l .\left[K_{b}\left(N H_{3}\right)=1.8 \times 10^{-5}\right] \)
A. \( p H=4.477 \)
в. \( p H=7.455 \)
D. \( p H=11.46 \)


B.O.D. is connected with
A . Organic matter
B. Microbes
C. Microbes and organic matter
D. None of the above


Find the sum of the series whose nth
term is:
\( 2 n^{3}+3 n^{2}-1 \)


Foolish seedling disease of rice led to the discovery of
\( A \cdot \) IAA
в. GA
c. АВА
D. 2, 4-D


A batsman deflects a ball by an angle of
\( 45^{\circ} \) without changing its initial speed
which is equal to \( 54 \mathrm{km} / \mathrm{hr} \). Mass of the
ball is \( 0.15 \mathrm{kg} \). What is the impulse imparted to the ball?
A. \( 4.2 \mathrm{kg} \mathrm{m} / \mathrm{s} \) in the direction of the final velocity
B. \( 4.2 \mathrm{kg} \mathrm{m} / \mathrm{s} \) in the direction of the initial velocity
c. \( 4.2 \mathrm{kg} \mathrm{m} / \mathrm{s} \) in the direction opposite to the initial velocity
D. \( 4.2 \mathrm{kg} \mathrm{m} / \mathrm{s} \) directed along the bisector of the initial and the final directions of the velocity


What is Lanthanoid contraction?
Mention one of its consequences.


Observe the following chemical reaction
\( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{4}+\boldsymbol{O}_{2} \boldsymbol{F}_{2} \rightarrow \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{\mathbf{6}}+\boldsymbol{O}_{2} \)
Enter 1 if true else 0


The heterosporous species, the female gametophyte remains on the parent sporophytes for variable periods.


\( 25 \mathrm{cm}^{3} \) of oxalic acid completely neutralise 0.064 g of sodium hydroxide. Molarity of the oxalic acid solution is
A .0 .064
B. 0.045
\begin{tabular}{l}
c. 0.015 \\
\hline
\end{tabular}
D. 0.032


In the following reaction:
\( \boldsymbol{S} \boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{S}(\boldsymbol{g}) \rightarrow \boldsymbol{3} \boldsymbol{S}(\boldsymbol{s})+ \)
\( 2 H_{2} O(l), \) the number of moles sulphur
formed by 2 moles each of \( S O_{2} \) and
\( \boldsymbol{H}_{2} \boldsymbol{S} \) is :


How many \( \boldsymbol{O}_{2} \) molecules are present in
\( 2.0 \mathrm{L} \) of oxygen gas at \( 27^{\circ} \mathrm{C} \)
temperature and 3.0 atm pressure?
A \( \cdot 1.0 \times 10^{23} \)
В. \( 1.5 \times 10^{23} \)
c. \( 1.5 \times 10^{24} \)
D. \( 2.5 \times 10^{24} \)


Universal Gravitational Constant is
measured by
A. Newton's Experiment
B. Cavendish's Experiment
c. Max's Experiment
D. de Broglie's Experiment


When the bob of a simple pendulum is displaced to one extreme position \( \mathrm{P} \) and then released, it swings towards the centre position \( Q \) and then to the other extreme position R. At which position does the bob have maximum
kinetic energy?
A. Between P and Q
B.
\( c \cdot R \)
D. Between Q and R


Let \( \boldsymbol{O A B C} \) be a parallelogram and \( \boldsymbol{D} \) the midpoint of \( \boldsymbol{O} \boldsymbol{A} \). The ratio in which
\( O B \) divides \( C D \) in the ratio
A .1: 2
B. 1: 3
\( c \cdot 1: 4 \)
D. 2: 1


Carbonic anhydrase is mostly active in
A. RBC
B. WBC
c. Blood Plasma
D. Blood Platelets


If the sphere of radius \( 6 \mathrm{cm} \) is melted
and drawn into a wire of radius \( 0.02 \mathrm{cm} \)
then the length of the wire is:


A certain freezing process requires that room temperature be lowered from \( 40 \mathrm{C} \) at the rate of \( 5 C \) every hour. What will be the room temperature 10 hours after the process begins?


A sum of Rs. 15500 was lent partly at \( 5 \% \)
and partly at \( 8 \% \) p.a. simple interest. The total interest received after 3 years was
Rs. \( 3000 . \) The ratio of the money lent at \( 5 \% \) at that lent at \( 8 \% \) is
\( A \cdot 8: 5 \)
B. 5: 8
\( c \cdot 31: 6 \)
D. 16 :15


Assertion
Pb \( C l_{2} \) is more stable than \( P b C l_{4} \)
Reason

PbCl \( _{4} \) is powerful oxidising agent.
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


Sameer took suphur powder on a spatula and heated it. He collected the gas evolved by inverting a test tube over
it. What will be the action of gas on moist litmus paper?


The major step involved in extraction of a metal after its ore is :
A. concentration
B. reduction
c. purification
D. all of these


Degree of hydrolysis \( (\alpha) \) for a salt of strong acid and weak base This question has multiple correct options
A. is independent of dilution
B. increases with dilution
c. increases with decrease in \( K_{b} \)
D. increases with increase in temperature


What is a bisexual flower?


Two rods having thermal conductivities in the ratio of 5: 3 and having equal length length and equal cross-section are joined by face to face. If the temperature of free end of first rod is
\( 100^{\circ} \mathrm{C} \) and temperature of free end of
second rod is \( 20^{\circ} c, \) then temperature of the junction, is-
A \( \cdot 90^{\circ} \mathrm{C} \)
B . \( 85^{\circ} \mathrm{C} \)
\( \mathrm{c} \cdot 70^{\circ} \mathrm{C} \)
D. \( 50^{\circ} \mathrm{C} \)


The element having highest ionisation potential is :
\( \mathbf{A} \cdot H \)
B. \( N \)
\( c \cdot O \)
D. \( H e \)


Match List I with List II
List-I
a) \( 0.00366 /^{0} \mathrm{C} \)
e) Avagadros
Number
b) \( 6.023 \times 10^{23} \) molecules \( f \) ) Universal gas
constant
c) \( -273^{0} \mathrm{C} \)
g) Pressure
coefficient of gas
d) \( 8.31 \mathrm{J} / \mathrm{K} \) -mole
h) Intercept of \( \mathrm{V}-\mathrm{T} \)
graph at constnat
pressure
A. a-g, b-e, c-h, d-f.
B. a-f, b-g c-e,d-h.
c. a-g,b-e,c-f, d-h.
D. a-g,b-f, c-e, d-h


Part of earth covered by water is about :
A . 71\%
B. 50\%
c. 92\%
D. 87\%


Find the value of \( \lim _{x \rightarrow 1} e(1+\sin \pi x)^{\cot \pi x} \)


Zone refining is a method to obtain:
A. very high temperature
B. ultra pure \( A l \)
c. ultra pure metals
D. ultra pure oxides


Which of the following plant had developed an obligate symbiotic relationship with a moth called
Tagetecula, in relation to pollination
A. Amorphophallus
B. Ficus
c. Salvia
D. Yucca


The solubility of \( A g_{2} S \) is:
\( \left[\boldsymbol{K}_{s p}=\mathbf{2 5 6} \times \mathbf{1 0}^{-\mathbf{6}}\right] \)
A \( \cdot 4 \times 10^{-2} \)
В. \( 4 \times 10^{-3} \)
c. \( 0.4 \times 10^{-2} \)
D. \( 0.4 \times 10^{-3} \)


Two forces acting in opposite directions
have a resultant of \( 10 \mathrm{N} 10 \mathrm{N} \). What are the
magnitudes of the two forces?
\( \mathbf{A} \cdot F_{1}=40 N, F_{2}=30 N \)
B. \( F_{1}=30 N, F_{2}=40 N \)
C . \( F_{1}=50 N, F_{2}=40 N \)
D. \( F_{1}=100 N, F_{2}=60 N \)


The resultant of two forces \( P \) and \( q \) is
right angle to \( P \), the resultant of \( P \) and
\( Q \) acting at the same angle is at right
angle to \( Q \). Prove that \( P \) is the
geometric mean of \( Q \) and \( Q \) (i.e. \( P= \)
\( \sqrt{\boldsymbol{Q} \boldsymbol{q}} ? \)


What is the force on a body of mass \( \boldsymbol{m} \)
when it is moving with a constant velocity?
A \( . m g \)
B. 0
c. \( \frac{m}{g} \)
D.


One atmosphere is numerically equal to approximately:
\( \begin{array}{lll}\text { A } \cdot 10^{6} & \text { dyne } & c m^{-2}\end{array} \)
B. \( 10^{2} \) dyne \( c m^{-2} \)
D. \( 10^{8} \) dyne \( c m^{-2} \)


A ball of mass 'm' moving horizontally
which velocity 'u' hits a wedge of mass
\( M^{\prime} . \) The wedge is situated on a smooth
horizontal source. If after striking with wedge the ball starts moving in vertica
direction and the wedge starts moving
in horizontal plane. Calculated
a) The velocity of wedge \( V \)
b) The velocity (v) at which the ball
moves in vertical direction.
c) The impulse imparted by the ball on
the wedge.
d) The coefficient of restitution \( e=? \)


The resistance between \( A \) and \( B \) is
\( A \cdot 8 \Omega \)
В. \( 4 \Omega \)
\( c .3 .75 \Omega \)
D. \( 2 \Omega \)


The point which is equidistant from the points \( (\boldsymbol{a}, \boldsymbol{0}, \boldsymbol{0}),(\boldsymbol{0}, \boldsymbol{b}, \boldsymbol{0}),(\boldsymbol{0}, \boldsymbol{0}, \boldsymbol{c}) \) and
(0,0,0) is:
\( \mathbf{A} \cdot(a, b, c) \)
B . \( (\sqrt{a}, \sqrt{b}, \sqrt{c}) \)
c. \( (2 a, 2 b, 2 c) \)
D. \( \left(\frac{a}{2}, \frac{b}{2}, \frac{c}{2}\right) \)


If \( x=t^{3}+t+5 \& y=\sin t \) then
\( \frac{d^{2} y}{d x^{2}}= \)
A. \( \frac{\left(3 t^{2}+1\right) \sin t+6 t \cos t}{\left(3 t^{2}+1\right)^{3}} \)
B. \( \frac{\left(3 t^{2}+1\right) \sin t+6 t \cos t}{\left(3 t^{2}+1\right)^{2}} \)
c. \( \frac{\left(3 t^{2}+1\right) \sin t+6 t \cos t}{\left(3 t^{2}+1\right)^{2}} \)
D. \( \frac{c o s t}{3 t^{2}+1} \)


Why does sun appear to be bigger and brighter as compared to other stars?


Suppose that the letter cards for the word \( M \) ATHEMATICS were putt
face down and mixed up and a card is
picked up at random. What is the probability of picking up a vowel?


Prove that the product of \( n \) geometric
mean between any two numbers is \( n \) th power of their \( G . M \)


The heat required to completely
evaporate 18 grams of water at \( 98^{\circ} \mathrm{C} \)
\( \left(H_{v}=2259 J / g \text { and } c=4.18 J / g K\right) \)
A. 40,812 joules
B. 40,512 joules
c. 40,666 joules
D. 150 joules
E . \( 6.12 \times 10^{6} \) joules


If the coefficient of the middle term in
the expansion of \( (1+x)^{2 n+2} \) is \( p \) and
the coefficients of middle terms in the
expansion of \( (1+x)^{2 n+1} \) are \( q \) and \( r \)
then
A \( . p+q=r \)
В. \( p+r=q \)
\( \mathbf{c} \cdot p=q+r \)
D. \( p+q+r=0 \)


Differentiate \( y=\sin b x^{2} \) w.r.t \( x \)


All the values/s of \( (1+i)^{\frac{1}{2}} \) are


Spherical balls of radius R are falling in
a viscous fluid of velocity v. The
retarding viscous force acting on the spherical ball is
A. directly proportional to R but inversely proportional to
\( v \)
B. directly proportional to both radius R and velocity v.
c. inversely proportional to both radius R and velocity v
D. inversely proportional to R but directly proportional to velocity v


The energy of hydrogen atom in \( n^{t h} \) orbit
is \( E_{n} \) then the energy in \( n^{t h} \) orbit of singly ionised helium atom will be:
\( A \cdot 4 E_{n} \)
в. \( 2 E_{n} \)
c. \( E_{n} / 4 \)
D. \( E_{n} / 2 \)


Mark out the correct statement(s)
This question has multiple correct options
\( A . \) in both fission and fusion processes, the mass of reactant nuclide is greater than the mass of product nuclide
B. in fission process, BE per nucleon of reactant nuclide is less than the binding energy per nucleon of product nuclide
C. in fusion process, BE per nucleon of reactant nuclide is less than the binding energy per nucleon of product nuclide
D. in fusion process, BE per nucleon of reactant nuclide is greater than the binding energy per nucloen of product nuclide


Adam's apple is prominent in
A. Boys of any age
B. Adolescent girls
c. Girls of any age
D. Adolescent boys


n figure, circle \( O \) has diameter \( \overline{A B} \) of
the length \( 8 . \) If smaller circle \( P \) is
\( \operatorname{tangent} \) to diameter \( \overline{A B} \) at point \( O \) and
is also tangent to circle \( O \), calculate the
approximate area of the shaded region.
A . 3.14
B. 6.28
\( c .9 .42 \)
D. 12.57
E . 25.13


The work done on an object does not depends upon the:
A. displacement
B. force applied
c. angle between force and displacement
D. initial velocity of the object


Assertion
Heteronomous segmentation, i.e., the division of labor resulting in
dissimilarity of the metamers of the
different regions of the body, is found in the phyla Annelida, Arthropoda and
Chordata.
Reason
None of these have true coelom.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect.
D. Assertion is incorrect but Reason is correct.


A compound \( \boldsymbol{X} \) with molecular formula
\( C_{3} H_{8} O \) can be oxidized to a compound
\( Y \) with the molecular formula \( C_{3} H_{6} O_{2} \)
The number of double bonds in \( Y \) is:


Define the cis-trans isomerism? Show
the cis-trans isomers of
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4} \boldsymbol{C l}_{2}\right]^{+} \)


Observe the graph given. Identify the
state the population growth rate
marked by \( X \) in the given graph
of Por
A . Goa
B. Kerala
C. Sikkim
D. Nagalano


When 1 mol gas is heated at constant volume temp. is raised from 298 to 308
K. Heat supplied to the gas is 500 J. Then which statement is correct?
\( A \cdot q=w=500 \mathrm{J}, \mathrm{U}=0 \)
B. \( q=U=500 \), \( w=0 \)
\( c \cdot q=w=600,1, U=0 \)
D. \( U=0, q=w=400 \)


Write the principal value of :
\( \left[\cos ^{-1} \frac{\sqrt{3}}{2}+\cos ^{-1}\left(-\frac{1}{2}\right)\right] \)


What is the solubility of \( \boldsymbol{A I}(\boldsymbol{O} \boldsymbol{H})_{3}\left(\boldsymbol{K}_{s p}=1 \times 10^{-33}\right) \) in a
buffer solution \( \boldsymbol{p} \boldsymbol{H}=\mathbf{4} ? \)
В \( \cdot 10^{-6} M \)
c. \( 1 \times 10^{-4} M \)
D. \( 0.25 \times 0^{-8} M \)


Assertion
A polarised atom can be approximated as a dipole.
Reason
Electric field induces the charge separation in the atom.
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 radio can tune over the frequency range of a portion of MW broadcast
band: \( (800 \mathrm{kHz} \text { to } 1200 \mathrm{kHz} \) ). If its LC
circuit has an effective inductance of
\( 200 \mu \mathrm{H}, \) what must be the range of its variable capacitor? [Hint: For tuning, the natural frequency
i.e., the frequency of free oscillations of
the LC circuit should be equal to the frequency of the radiowave.]


A pump is used to lift \( 500 k g \) of water
from a depth of \( 80 m \) in \( 10 s \) (Take \( g=10 m s^{-2} \) ). Calculate the work
done by the pump.
A \( \cdot 16 \times 10^{5} J \)
В. \( 4 \times 10^{5} J \)
c. \( 4 \times 10^{8} J \)
D. \( 2 \times 10^{5} J \)


The number of water molecule(s) not
coordinated to copper ion directly in \( \boldsymbol{C u} \boldsymbol{S O}_{4} \cdot \boldsymbol{5} \boldsymbol{H}_{2} \boldsymbol{O} \) is:
A .4
B. 3
\( c .1 \)
D.


\( \boldsymbol{n} \) -propyl alcohol and isopropyl alcohol can be chemically distinguished by which reagent?
A \( \cdot P C l_{5} \)
B. Reduction
c. Oxidation with potassium dichromate
D. Ozonolysis


A rope, under a tension of \( 200 N \) and
fixed at both ends, oscillates in a second-harmonic standing wave pattern. The displacement of the rope is given by \( : \boldsymbol{y}=\mathbf{0 . 1} \sin \left(\frac{\boldsymbol{\pi} \boldsymbol{x}}{\mathbf{2}}\right) \sin 12 \boldsymbol{\pi} \boldsymbol{t} \)
Where \( x=0 \) at one end of the rope, \( x \) is
in meters and \( t \) is in seconds. The speed of the progressive waves \( (\operatorname{in} m / s) \) on the rope is


Java Man is
A. Pithecanthropus erectus
B. Pithecanthropus pekinensis
C. Komo rhodesiensis
D. Homo heidelbergensis


Which of the following compounds have higher enolic content than keto
content?
\( A \)
B.
\( c \)
\( D \)


\( 1^{s t} \) excitation potential for the \( \mathrm{H}- \) like(hypothetical)sample is 24V. Choose the correct statement.
This question has multiple correct options
A \( \cdot 1^{s t} \) excitation potential for the \( \mathrm{H} \) like(hypothetical)sample is 24v
B. Ionisation energy of the sample is 32 ev
C. Binding energy of \( 3^{r d} \) excited state is 2 ev
D. \( 2^{\text {nd }} \) excitation potential of the sample is \( \frac{32 \times 8}{9} V \)


The value of earth's magnetic field can
be
A . \( 0.5 G \)
в. \( 5 G \)
\( c \cdot 10 G \)
D. \( 50 G \)


The mass number of \( X \) is 23 which
contains 15 electrons. What is the
atomic mass of \( \boldsymbol{X} \) ?
A . 38 amu
B. 23 amu
c. 18 amu
D. None of above


Pratyush took sulphur powder on a
spatula and heated it. He collected the
gas evolved by inverting a test tube over it, as shown in the figure above.
(a) What will be the action of gas on
(i) dry litmus paper?
(ii) moist litmus paper?
(b) Write a balanced chemical equation
for the reaction taking place.


Explain how the eye adjusts itself when a person enters a dark cinema hall from bright sunshine.


The equilibrium constant of a reaction is 300 , if the volume of the reaction
flask is tripled, the equilibrium constant will be:
A . 100
B. 300
\( c .250 \)
D. 150


Which of the following can be obtained by subjecting ethyl alcohol to oxidation?

This question has multiple correct options
A. Ethyl acetate
B. Acetic acid
c. Diethyl ether
D. Acetaldehyde


Which one of the following mixture is non-ideal solution?
A. Chloroform and acetone
B. Benzene and toulene
c. Chlorobenzene and bromobenzene
D. Bromoethane and chloroethane


A dipole is placed in a uniform electric field with its axis parallel to the field. It experiences:
A. both a net force and torque
B. only a net force
c. neither a net force nor a torque
D. only a torque


How will you identify with the help of an experiment whether a given beam of light is of polarized light or of unplolarised light?


group elements are known
as chalcogens.
A. VIA
B. VA
c. zero
D. None of these


* Explain the construction and working of an electric generator (AC). Draw a neat diagram and label it.


Which one of the following metals can not be extracted by using Al as a reducing agent
A. \( N a \) from \( N a_{2} O \)
B. \( C r \) from \( C r_{2} O_{3} \)
c. \( M n \) from \( M n O_{2} \)
D. Fe from \( F e_{2} O_{3} \)


Among of alkali metals, the metal with highest ionization potential is :
A. \( L \)
B. Na a
\( c \cdot k \)
D. Rb


In the following reaction \( X \) and \( Y \) are respectively, \( C_{2} H_{2} \stackrel{X}{\rightarrow} C_{6} H_{6} \stackrel{Y}{\longrightarrow} \)
\( \boldsymbol{C}_{\boldsymbol{6}} \boldsymbol{H}_{\boldsymbol{5}} \boldsymbol{S} \boldsymbol{O}_{\boldsymbol{3}} \boldsymbol{H} \)
A. iron tube, heating \( N a_{2} S O_{4} \)
B. zn, conc. \( H_{2} S O_{4} \)
c. red hot iron tube, fusing \( H_{2} S O_{4} \)
D. \( H_{2} / P d, B a S O_{4} d i l . H_{2} S O_{4} \)


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


The cell junctions called as tight, adhering and gap junctions are found in
A. Epithelial tissue
B. Neural tissue
c. Muscular tissue
D. connective tissue


The figure illustrates correction of vision for a certain defect of human eye.
Identify the defect which is corrected
here.
A. Myopia
B. Hypermetropia
c. Astigmatism
D. Nigh Blindness


With the help of an example justify the following statement: "A trait may be inherited, but may not be expressed".


On moving down the group, the
tendency to gain electrons:
A. decreases
B. increases
C. increases and then decreases
D. decreases and then increases


In the figure \( P Q, P R \) and \( B C \) are the
tangents to the circle. BC touches the
circle at \( X . \) If \( P Q=7 \mathrm{cm}, \) find the
perimeter of \( \triangle \boldsymbol{P B C} \)


What will be the number of heartbeats
per minute, if the stroke volume of heart increases with the total volume of blood
remains same?
A. Remains constant
B. Decreases
c. Increases
D. Becomes erratic


The number of Ip-bp repulsion present
in \( C l F_{3} \) at nearly 90 degree angle
are


Various theories were put forth to study the nature of atom. The main postulates of Dalton's atomic theory are :
This question has multiple correct options
A. all matter are composed of atoms
B. all matters are composed of molecules
c. all atoms of an element are identical.
D. the atoms of different elements vary in size and mass


Which of the following materials is responsible for the cause of animal death?
A. Paper
B. Plastic
c. Chemicals
D. None of the above


A particle of charge \( q \) and mass \( m \) is moving through a region of space where crossed magnetic and electric fields produce a zero net force on the charge. At a later time, the Electric field is
reduced by a factor of two. What effect will this have on the motion
of the particle? Select all that apply.
A. The particle will continue to move in a circle of the same radius.
B. The particle will eventually move in a circle of twice the radius
C. The particle will eventually move in a circle of half the radius
D. The particle will eventually follow a curved-noncircular path
E. The particle will follow a straight line path.


Which of the following statement is
not correct?
A. Double bond is shorter than a single bond.
B. Sigma bond is weaker than \( \pi \) -bond.
C. Double bond is stronger than hydrogen bond.
D. Covalent bond is stronger than hydrogen bond.


Draw the Lewis dot formula for \( \boldsymbol{N} \boldsymbol{H}_{3} \)
How many unshared pairs of electrons
are in the outer shell of the central
nitrogen atom?
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. 4
E. 6


The rate of chemical reaction is directly proportional to the equilibrium constant.

In which of the following process reaction will be completed first?
A. \( K=10 \)
B . \( K=1 \)
\( \mathbf{c} \cdot K=10^{3} \)
D. \( K=10^{-2} \)


Which of the following statements correctly completes the statement? Except for glycine, which is achiral, all the amino acids present in proteins
A. are chiral but racemic
B. have the \( L \) configuration at their \( \alpha \) carbon
c. have the \( R \) configuration at their \( \alpha \) carbon
D. have the \( S \) configuration at their \( \alpha \) carbon


How would you name the following
compound?


A radioactive nuclide emits \( \gamma \) -rays due
to:
A \( . K \) -electron capture
B. nuclear transition from higher to lower energy state
C. presence of greater number of neutrons than protons
D. presence of greater number of protons than neutrons


is the collective name for layers of
soil.
A. A-horizon
B. B-horizon
c. c-horizon
D. Soil profile


A flag-staff 20 metres long standing on a wall 10 metres high subtends an
angle whose tangent is 0.5 at a point on
the ground. If \( \theta \) is the angle subtended
by wall at that point then \( \tan \theta= \)
A . 1
B. \( \frac{1}{3} \)
c. \( _{1 \text { or }} \frac{1}{3} \)
D.


The D.E of the family of rectangular hyperbolas which have the coordinate
axes as asymptotes is:
A. \( x y_{1}+y=0 \)
в. \( x y_{2}+y_{1}=0 \)
\( \mathbf{c} \cdot x y_{2}=y \)
D. \( x y_{2}+y=0 \)


\( A t 817, K_{p} \) for the reaction between
\( C O_{2}(g) \) and excess hot graphite \( (s) \) is
10 atm.
(a) The sum of equilibrium
concentration of the gases at \( 817^{\circ} \mathrm{C} \) is
\( X M \) and a total pressure of 5 atm.
(b) At \( Y \) atm total pressure, the gas
contains \( 5 \% C O_{2} \) by volume.
The value of \( 1000(X+Y) \) is


Two capillary tubes of diameters 3.0 \( \mathrm{mm} \) and \( 6.0 \mathrm{mm} \) are joined together to form a U-tube open at both ends. If the U-tube is filled with water, what is the
difference in its levels in the two limbs
of the tube? Surface tension of water at
the temperature of the experiment is \( \mathbf{7 . 3} \times \mathbf{1 0}^{-\mathbf{2}} \mathbf{N} / \mathbf{m} . \) Take the angle of
contact to be zero and density of water to be \( 10^{3} k g / m^{3}\left(g=9.8 m / s^{2}\right) \)
\( A \cdot 5 \mathrm{mm} \)
B. 10 \( \mathrm{mm} \)
c. \( 15 \mathrm{mm} \)
D. 20 mm


An electron of mass \( m_{e}, \) initially at rest,
move through a certain distance in a
uniform electric field in time \( t_{1} . A \)
proton of mass \( m_{p}, \) also, initially at rest
takes time \( t_{2} \) to move through an equal distance in this uniform electric field.
Neglecting the effect of gravity, the ratio \( t_{2} / t_{1} \) is nearly equal to
A. 1
в. \( _{\left(m_{p} / m_{e}\right)^{1 / 2}} \)
\( ^{\mathbf{c}} \cdot\left(m_{e} / m_{p}\right)^{1 / 2} \)
D. 1836


The mass of a gas molecules is \( 4 \times 10^{-30} \mathrm{kg} \)
If \( 10^{23} \) molecules strike per second at \( 4 \mathrm{m}^{2} \)
area with a velocity \( 10^{7} \mathrm{m} / \mathrm{s} \), then the
pressure exerted on the surface will be
A. 1 Pascal
B. 3 Pascal
c. 2 Pascal
D. 4 Pascal


Which reagent is used for bromination of methyl phenyl ether?
A. \( B r_{2} / C H_{3} C O O H \)
в. \( B r_{2} / \)Red\( P \)
c. \( B r_{2} / F e B r_{3} \)
D. \( H B r / \Delta \)


A man can read the number of a distant
bus clearly but is not able to read a book clearly. Which defect of the eye is he suffering from?
A. Myopia
B. Hypermetropia
c. cataract
D. Astigmatism


The increasing order of the acidity of the following acids is:
।) \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{3} \)
॥ᅵ \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3} \)
III) \( \mathrm{HClO}_{3} \)
A . |>॥|>||
B. \( \mid>\|>\| \)
c. |||>| >|
D. ||>|||>|


\( \ln S_{N} 1, \) the first step involves the formation of:
A. free radical
B. carbanion
c. carbocation
D. final product


The value of current in the above
diagram is (diode assumed to be ideal
one)
A . 0
в. \( 1 A \)
c. \( 1.66 A \)
D. 15A


Which of the following is based on mechanical effect of electric current?
A. AC Dynamo
B. DC Dynamo
c. AC or DC motor
D. Electric Geyser


It is easier to cut with a sharp knife
than with a blunt one.


Give a reason for the following. Inert gases do not form ions.


Let \( \boldsymbol{A}=\{-1,1\}, \) Then discuss whether
the given functions from \( A \) to itself are one-one onto or bijective:
(i) \( f(x)=\frac{x}{2} \)
(ii) \( g(x)=|x| \)
(iii) \( h(x)=X^{2} \)


Grouping of algae is based on
A. Food reserve
B. Colony formation
c. shape
D. Pigments.


Evaluate:
\( \int \frac{e^{x}}{\sqrt{5-4 e^{x}-e^{2 x}}} d x \)


Find 4 rational numbers between
\( \frac{1}{6} \) and \( \frac{3}{8} \)


A refrigerator is
A. head engine
B. an electric motor
C. heat engine working in backward direction
D. air cooler


Find the coefficient of \( x^{-7} \) in the
expansion of \( \left(\boldsymbol{a} \boldsymbol{x}-\frac{\mathbf{1}}{\boldsymbol{b} \boldsymbol{x}^{2}}\right)^{11} \)
\( \begin{array}{ll}\text { A. } & ^{11} C_{5}\end{array} \)
В. \( ^{10} C_{4} \)
c. \( ^{11} C_{4} \)
D. \( ^{10} C_{5} \)


A giant spadix is formed in a species of
A. Colocasia
B. Caladium
c. Amorphophallous
D. Pathos


State whether the statement is True or
False. The cube of \( \left(x-\frac{1}{2}\right) \) is equal to \( x^{3}- \)
\( \frac{3 x^{2}}{2}+\frac{3 x}{4}-\frac{1}{8} \)
A . True
B. False


The reason of psuedopodium formation
is
A. Difference in the viscosity
B. change in the temprature
c. chemical changes
D. Difference in pressure


Why does the thickness of depletion layer of pn-junction increases in reverse biasing ?Draw the circuit diagram of reverse biasing.


What is myopia? Explain two possible
reasons of myopia. How can it be
corrected? Explain with suitable
diagram.


Write the differences between asexual
and sexual reproduction.


If \( (n+1)^{3}-(n)^{3}=n+1, \) then which
of the following can be the value of \( n ? \)
\( \mathbf{A} \cdot \mathbf{0} \)
B . 2
c. -2
D. Cannot be determined


Find
\( \int \tan ^{-1} \frac{x}{\sqrt{a^{2}-x^{2}}} d x ;|x|\langle a \)


Organic compound which we daily use as a food is :
A. Proteins
B. Fats
c. vitamins
D. All of these


\( \lim _{x \rightarrow 0} \frac{x\left(e^{x}-1\right)}{1-\cos x} \) is equal to
\( A \cdot 0 \)
B. \( \infty \)
\( c \cdot-2 \)
D.


Very short answer type.
What are the function performed by nephrons?


An electron enters a uniform magnetic
field with a path perpendicular to the field lines and moves in a circular path
of radius \( \boldsymbol{R} \)

A positron (same mass of an electron
but opposite charge) enters the same magnetic field in a path perpendicular to the field with four times the kinetic
energy. Compared to the electrons path, the
radius of the protons circular path is:
A. The same radius
B. Twice as large
c. \( 1 / 2 \) as large
D. 4 times larger


A small conducting sphere of radius \( a \)
carrying a charge \( +Q, \) is placed inside
an equal and oppositely charged conducting shell of radius \( b \)
such that their centers coincide.
Determine the potential at a point
which is at a distance \( c \) from center
such that \( a<c<b \)
A. \( k(Q / c+Q / b) \)
в. \( k(Q / a+Q / b) \)
c. \( k(Q / a-Q / b) \)
D. \( k(Q / c-Q / b) \)


The set of points \( (x, y) \) whose distance from the line \( y=2 x+2 \) is the same as
the distance from (2,0) is a parabola. This parabola is congruent to the
parabola in standard form \( y=K x^{2} \) for
some \( K \) which is equal to
A \( \frac{\sqrt{5}}{12} \)
в. \( \frac{\sqrt{5}}{4} \)
c. \( \frac{4}{\sqrt{5}} \)
D. \( \frac{12}{\sqrt{5}} \)


What is the value of acceleration due to
gravity at height equal to half the
radius of earth from surface of earth.
[take \( \left.g=10 m / s^{2} \text { at earth surface }\right] \)


The first sex attractant pheromone
identified was that of
A . cat
B. Dog
c. Gypsy moth
D. Human


Phosgene can obtained when:
A. white phosphorus reacts with alkali
B. calcium phosphide reacts with water.
C. chloroform reacts with air.
D. bone comes in contact with water.


What concentration of nitrogen should
be present in a glass of water at room
temperature? Assume a temperature of
\( 25^{\circ} \mathrm{C}, \) a total pressure of 1 atmosphere
and mole fraction of nitrogen in air of \( 0.78 .\left(K_{H} \text { for nitrogen }=8.42 \times 10^{-7}\right. \)
\( \mathrm{M} / \mathrm{mm} \mathrm{Hg} \)


In plastic deformation, deformation is
A . reversible
B. permanent
\( c \). both
D. none


The orthocentre of the triangle \( A B C \) is \( B \) and the circumstances is \( S(a, b) . \) If \( A \) is the origin, then the coordinates of \( C \)
are:
A. \( (2 a, 2 b) \)
в. \( \quad\left(\frac{a}{2}, \frac{b}{2}\right) \)
c. \( \sqrt{\left(a^{2}+b^{2}, 0\right)} \)
D. None


Which symbol is used for the element
carbon?
A. \( C \)
в. \( C a \)
\( c \cdot c n \)
D. \( C o \)
ह. \( C u \)


An insectivorous// carnivorous plant is
A. Viscum
B. Parkinsonia
c. santalum
D. Utricularia


A particle executes simple harmonic
motion with an amplitude of \( 4 \mathrm{cm} . \) At the mean position the velocity of the particle is \( 10 \mathrm{cm} / \mathrm{s} \). The distance of the particle from the mean position when its speed becomes \( 5 \mathrm{cm} / \mathrm{s} \) is
A \( \cdot \sqrt{3} \mathrm{cm} \)
B. \( \sqrt{5} \mathrm{cm} \)
c. \( \pm 2(\sqrt{3}) \) cm
D. \( 2(\sqrt{5}) \mathrm{cm} \)


\( \lim _{x \rightarrow 0} \frac{2 x^{2}+3 x+4}{2}= \)
A .2
B.
\( c \cdot 3 \sqrt{5} \)
D. \( 2 \sqrt{5} \)


Which is fully fluorinated polymer?
A. Neoprene
B. Teflon
c. Thiokol
D. PVC


Write down ten positive rational
numbers such that numerator -
denominator for each of them is -2
Write them in increasing order


The following amine is:
A. strongly acidic
B. weakly acidic
c. strongly basic
D. weakly basiç


Conservation of momentum in a
collision between particles can be understood from
A. Conservation of energy
B. Newton's first law only
c. Newton's second law only.
D. Both Newton's second and third law.


A real image is
A. always erect
B. either erect or inverted
C . always inverted
D. neither erect nor inverted


Which one of the following is a property of a monochromatic, plane
electromagnetic wave in free space?
A. Electric and magnetic fields have a phase difference of \( \pi / 2 \)
B. The energy contribution of both electric and magnetic fields are equal
c. The direction of propagation is in the direction of \( \bar{B} \) x \( \bar{E} \)
D. The pressure exerted by the wave is the product of its speed and energy density


If radius of long solenoid is reduced to half of original without changing other physical factor,then its self inductance
will change-
A. \( 1 / 3 \) times
B. \( 1 / 2 \) times
c. \( 1 / 5 \) times
D. \( 1 / 4 \) times


Pinacolone is:
A. 2,3 -dimethyl- 2,3 -butanediol
B. 3, 3-dimethyl-2-butanone
C. 1 -phenyl-2-propanone
D. 1,1 -diphenyl-1, 2-ethandiol


The hardest substance in human body
is
A. Dentine
B. Collagen
c. Melanin
D. Enamel


Consider the following groups \( A \) and \( B \) \( A: 3,4,5, \ldots . . \) upto n terms \( \mathrm{B}: 15,19,23, \ldots \ldots \) upto n terms
If the mean deviations of groups \( A \) and \( B \) about their means are \( \boldsymbol{\alpha} \) and \( \boldsymbol{\beta} \)
respectively then
A \( . \beta=5 \alpha \)
в. \( \beta=4 \alpha+3 \)
c. \( \beta=4 \alpha \)
D. None


Write two methods of preparation of
methyl alcohol. Describe giving diagram. Give such a test of methyl alcohol which is not given by ethyl alcohol which is not given by ethyl alcohol. Give the chemical reactions.


Which one of the mirror below (in the
absence of the other mirrors) would
cause light from a distant source on the left side of the paper to be focussed to a
point that is closest to the mirror?
\( A \)
B. B
\( c \cdot c \)
\( D \)


The buildings which do not have a
sewage system can
A. construct drainage tanks
B. Construct septic tanks
c. construct sewage water bodies
D. construct septic canals


The coach of a cricket team buys 3 bats
and 6 balls for \( c 3900 \). Later, she buys
another bat and 3 more balls of the
same kind for \( c 1300 . \) Represent this situation algebraically and geometrically


If \( (3-2 x) \) and \( (5 x+8) \) are factors of
\( \left(-10 x^{2}+h x-k\right), \) then the values of \( h \)
and \( k \) are respectively
A. -1 and 24
B. 1 and 24
c. -1 and -24
D. 1 and -24


Which of the following metal do no
evolve \( \boldsymbol{H}_{2} \) gas from dil. acid?
A \( \cdot A\left(E_{A^{+} / A}^{o}=0.25 V\right) \)
B \( \cdot B\left(E_{B / B^{+}}^{0}=+0.22 V\right) \)
c. \( C\left(E_{C^{+} / C}^{0}=0.30 V\right) \)
D・ \( D\left(E_{D / D^{+}}^{0}=+0.44 V\right) \)


Assertion
Deoxyribose \( C_{5} H_{10} O_{4} \) is not a
carbohydrate.
Reason
Carbohydrates are hydrates of carbon
so, compounds which follow \( C_{x}\left(H_{2} O\right)_{y} \) formula are carbohydrates.
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


n fig. I I I and p I Find values of \( x, y \)
\( z, t \)


Which among the following is the lowest grade vertebrate?
A. Agnatha
B. Cyclostomata
c. Echinodermates
D. Both A and B


The frequency of optical waves is of the
order of


Waves are used to rotate
to generate electricity. Fill in the gap.
A. Rotor of Dynamo
B. Turbine of dam
c. Wheel of wind mill
D. Armature of motor


Energy produced in a chemical reaction is a specific type of :
A. kinetic energy
B. elastic energy
c. potential energy
D. entropy
E. thermal energy


Following reaction,
\( \left(\boldsymbol{C H}_{3}\right)_{3} \boldsymbol{C B r}+\boldsymbol{H}_{2} \boldsymbol{O} \longrightarrow \)
\( \left(C H_{3}\right)_{3} C O H+H B r \) is an example of
A. elimination rection
B. free radical substitution
c. nucleophilic substitution
D. electrophilic substitution


Which of the following is responsible for the \( 80 \% \) depreciation in the ozone layer?
A. Chloroflurocarbon
B. Chloride ion
c. sulphur ion
D. Magnesium ion


Evaluate the definite integral \( \int_{0}^{\frac{\pi}{4}} \frac{\sin x \cos x}{\cos ^{4} x+\sin ^{4} x} d x \)


A physical quantity P is given by \( \boldsymbol{P}= \) \( \frac{A^{3} B^{1 / 2}}{C^{-4} D^{3 / 2}} . \) Which quantity among \( A, B, C \)
and D brings in the maximum percentage error in P?


DNA synthesis takes place in which of the following phase?
A. S phase
B. \( G_{1} \) phase
c. \( \mathrm{G}_{2} \) phase
D. None of the above


Which one of the following statements is correct?
A \( \cdot e^{x} \) is a increasing function
B. \( e^{x} \) is a decreasing function.
\( \mathrm{c} \cdot e^{x} \) is neither increasing nor decreasing function
D. \( e^{x} \) is a constant function


\( f(x)=\frac{k^{x}}{k^{x}+\sqrt{k}}(k>0) \) then
\( \sum_{r=1}^{2 n-1} 2 f\left(\frac{r}{2 n}\right)=a n+b \) where \( a-b \)
is equal to


Describe the principle and working of a meterbridge


During adsorption which of the following is positive?
A \( . \Delta G \)
в. \( T \Delta S \)
c. \( \Delta G+T \Delta S \)
D. none of these


Turnbull's blue is:
\( \mathbf{A} \cdot F e_{3}\left[F e(C N)_{6}\right]_{2} \)
\( \mathbf{B} \cdot K_{4} F e(C N)_{6} \)
\( \mathbf{C} \cdot K_{3} F e(C N)_{6} \)
D. \( N a_{4} F e(C N)_{6} \)


The sodium salt of methyl orange has \( 7 \% \) sodium. What is the minimum
molecular weight of the compound?
A. 420
в. 375
c. 329
D. 295


In meiosis,
A. A single nucleus gives rise to two identical daughter nuclei
B. The daughter nuclei are genetically identical to the parent nucleus
C. The centromeres separate at the onset of anaphase I
D. Homologous chromosomes synapse in prophase I


Electrolyte \( \quad K C l \quad K N O_{3} \) \( \boldsymbol{H} C l \)
\[
\begin{array}{ll}
\Lambda_{\left(S c m^{2}\right.}^{\Lambda \infty}_{\left.m o l^{-1}\right)}^{\infty} & 149.9
\end{array}
\]
\( 426 . \)
Calculate \( \Lambda^{\infty}_{H O A c} \) using appropriate molar conductances of the electrolytes
listed above at infinite dilution in \( \boldsymbol{H}_{2} \boldsymbol{O} \)
\( \operatorname{at} 25^{\circ} C \)
\( \mathbf{A} \cdot 517.2 \)
B. 552.7
c. 390.7
D. 217.5


Assertion: The aqueous solution of
\( C F_{3} C O O^{-} N a^{+} \) is more basic than the
aqueous solution of \( \boldsymbol{C H}_{3} \boldsymbol{C O O}^{-} \boldsymbol{N a}^{+} \)
for the same concentration of salt.
Reason: The salt derived from a weak
acid and strong base hydrolyses to
generate a basic solution.
A. Both Assertion and Reason are correct and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation of Assertion
C. Assertion is correct but Reason is not correct
D. Assertion is not correct but Reason is correct
E. Both Assertion and Reason are not correct


Identify the harmful radiations emitted by the sun.
A . Ultra violet
B. Infra red
c. Visible
D. Radio waves


Solve:
\( \frac{65}{12}-x=\frac{33}{-4} \)


Assertion
Stomata are "turgor operated valves"
Reason
Stomata show reversible turgor
changes
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


As you go down in a group, the alkali metals become:
A. brighter
B. hotter
c. more reactive
D. less reactive


If \( y=A \sin 5 x, \) then \( \frac{d^{2} y}{d x^{2}}= \)
\begin{tabular}{l}
A. \( -25 y \) \\
\hline
\end{tabular}
в. \( 25 y \)
c. \( 5 y \)
D. \( -5 y \)


\( 100 \mathrm{ml} \) of liquid \( \mathrm{A} \) and \( 50 \mathrm{ml} \) of liquid \( \mathrm{B} \) are mixed to form \( 138 \mathrm{ml} \) of solution. It
is :
A. Ideal solution
B. High boiling azeotrope
c. Low boiling azeotrope
D. None of these


Person who cannot see distant objects is suffering from
A. Cataract
B. Hypermetropia
c. Long sightedness
D. Myopia


The diameters of two plantes are in the ration 4: 1 and their density in the ration 1: 2 The acceleration due to gravity on
the planets will be in ratio,
A \( \cdot 1: 2 \)
B. 2:3
\( c \cdot 2: \)
\( D \cdot 4: \)


When precipitation comes down to the earth in the liquid form, it is called
A . cloud
B. rain
c. snow
D. ice


The no. of hydroxyl group in pyrophosphoric acid is:
A . 3
B. 4
\( c .5 \)
\( D \)


The coefficient of dispersion for the given distribution is
A . 3.06
в. . 306
c. 30.6
D. None of these


A bag contains 3 red and 3 green balls
and a person draws out 3 at random. He then drops 3 blue balls into the bag and again draws out 3 at random. The chance that the 3 later balls being all of different colors is
A . \( 15 \% \)
B . 20\%
c. \( 60 \% \)
D. 40\%


Find the value of \( k, \) if the points
\( A(7,-2), B(5,1) \) and \( C(3,2 k) \) are
collinear.


When a solid melts, the temperature:
A. increases
B. decreases
c. remains same
D. can't say


Find the value of the solid obtained by
the complete revolution of the ellipse \( \frac{x^{2}}{36}+\frac{y^{2}}{25}=1 \) about \( x- \) axis.


Draw a labeled sketch of the human eye.


A body of mass \( m=1 k g \) is moving in a
medium and experiences a fractions
force \( F=-k v, \) where \( v \) is the speed of
the body. The initial speed is \( v_{0}= \)
\( 10 m s^{-1} \) and after \( , 10 s \) its energy
becomes half of initial energy. Then, the value of \( k \) is
A. \( 10 \ln \sqrt{2} \)
2 \( \ln \log 2 \)
B. \( \ln \sqrt{2} \)
\( c \cdot \frac{\ln 2}{20} \)
D. \( 10 \ln 2 \)
E . \( \ln 2 \)


The line passing through the points \( (5,1, a) \) and \( (3, b, 1) \) crosses the \( y z \) plane at the point \( \left(0, \frac{17}{2}, \frac{-13}{2}\right) . \) Then
A \( \cdot a=2, b=8 \)
В. \( a=4, b=6 \)
c. \( a=6, b=4 \)
D. \( a=8, b=2 \)
2


A microscope has an objective of focal
length \( 1.5 \mathrm{cm} \) and eye piece of focal
length \( 2.5 \mathrm{cm} . \) If the distance between
objective and eye-piece is \( 25 \mathrm{cm} \). What is the approximate value of magnification produced for relaxed
eye?
[Disclaimer: Option A is changed from
\( \mathbf{7 5} \) to \( \mathbf{1 8 3 . 3 3} \) as the correct answer is
183.33 which is not present in the given options.]
A . 183.33
B. 110
c. 140
D. 25


When 2 g of gas \( A \) is introduced into an evacuated flask kept at \( 25^{\circ} C \), the
pressure was found to be 1 atmosphere If 3 g of another gas \( B \) is then added to the same flask, the pressure becomes 1.5 atm. Assuming ideal behaviour, the ratio of molecular weights \( \left(M_{B}: M_{A}\right) \)
is :
A . 1: 3
B. 3:
c. 2: 3
D. 3:


For the reaction, \( S O_{2}(g)+\frac{1}{2} O_{2}(g) \rightleftharpoons \)
\( \boldsymbol{S} \boldsymbol{O}_{3}(\boldsymbol{g}), \) the value of \( \boldsymbol{K}_{c} \) is \( 1.7 \times 10^{12} \) at
\( 300 K . \) Calculate the equilibrium
constants for the following reactions at
\( \mathbf{3 0 0 K}: \)
(।) \( 2 S O_{2}(g)+O_{2}(g) \rightleftharpoons 2 S O_{3}(g) \)
\( (\mathrm{II}) \boldsymbol{S} \boldsymbol{O}_{3}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{S} \boldsymbol{O}_{2}(\boldsymbol{g})+\frac{1}{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \)


Cytokinin is not found in
\( A . \) Root apex
B. Shoot apex
c. Young fruits
D. Mature fruits


\( X e F_{6} \) dissolves in anhydrous HF to give a good conducting solution which contains:
A \( \cdot H^{+} \) and \( X e F_{7}^{-} \) ions
B. \( H F_{2}^{-} \) and \( X e F_{5}^{+} \) ions
C. \( H X e F_{6}^{+} \) and \( F^{-} \) ions
D. none of these


Fill in the Blanks
The surface above the water will look
ike a \( _{-1}-_{-}-_{-} \) to a fish.


Discuss the theory involved in the manufacture of sulphuric acid by
contact process.


(5,-2),(6,4) and (7,-2) are the vertices
of a - m.... triangle.
A. equilateral
B. right angle
c. scalene
D. isosceles


The distance between two parallel lines \( 3 x+4 y+10=0 \) and \( 3 x+4 y-10= \)
\( \mathbf{0} \) is
A .
в. \( -4 \sqrt{5} \)
\( c \cdot 2 \sqrt{5} \)
D. 4


The existence of a negative charge on a body implies that it has:
A. lost some of its electrons
B. lost some of its atoms
c. acquired some electrons from outside
D. acquired some protons from outside


The chemical formula of \( X, Y \) and \( Z \)
are:
\[
\begin{array}{l}
\mathrm{X}+\mathrm{Na}_{2} \mathrm{CO}_{3} \longrightarrow \mathrm{Y}+\mathrm{Z} \\
\mathrm{CO}_{2}
\end{array}
\]
\( Z(\text { milky cloud }) \)
\( \mathbf{A} \cdot C a O, C a(O H)_{2}, N a O H \)
B. \( N a O H, C a O, C a C O_{3} \)
\( \mathbf{c} \cdot N a O H, C a(O H)_{2}, C a C O_{3} \)
D. \( C a(O H)_{2}, N a O H, C a C O_{3} \)


Mass per unit of a semicircular disc of
total mass m radius R varies linearly
with radial distance from the point 0 (base centre). Find the height of centre of mass from 0
A \( \cdot \frac{2 R}{\pi} \)
в. \( \frac{3 R}{2 \pi} \)
c. \( \frac{4 R}{3 \pi} \)
D. \( \frac{3 R}{8} \)


The potential energy of a particle
varies with distance \( x \) as shown in the
graph. The force acting on the particle is
zero at:
\( A \).
B
\( c . \) В and \( c \)
D. A and


A particle of mass \( m \) is made to move with uniform speed u along the perimeter of a regular polygon of \( n \) sides. What is the magnitude of impulse applied by the particle at each corner of the polygon?


The set of all values of \( ^{\prime} x^{\prime} \) satisfying the inequation \( \left(\frac{1}{|x|-3}\right) \leq \frac{1}{2} \) is
A \( (-\infty,-5) \cup(-3,3) \cup[5, \infty) \)
B . \( (-\infty,-5] \cup[-3,3] \cup[5, \infty) \)
c. \( (-\infty,-5) \cup(-3,3) \cup(5, \infty) \)
D. None of the above


For the combination of gates shown
here, which of the following truth table
part is not true?
\( \mathbf{A} \cdot A=0, B=1, C=1 \)
B . \( A=0, B=0, C=0 \)
C \( . A=1, B=1, C=1 \)
D. \( A=1, B=0, C=1 \)


Assertion
Angiosperms lack flagellate male
gametes.
Reason
Sperms are not dependent on water for
fertilization.
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.


Evaluate \( :(1+i)^{6}+(1-i)^{3} \)


Iron have much lower specific heat
than:
A. steel
B. Copper
c. water
D. none of the above


Which of the following opening occurs
in pair?
A. obturator foramen
B. Foramen magnum
c. Foramen ovalis
D. Fenestra rotundus


Sum the series:
\( 1-\frac{1}{3}+\frac{1}{3^{2}}-\frac{1}{3^{3}}+\frac{1}{3^{4}} \dots \dots \infty \)
\( A \cdot \frac{3}{4} \)
B. \( \frac{4}{3} \)
\( c \cdot \frac{2}{3} \)
D. 3


Maximum oxidation state is shown by
which pair of elements?
A \( . N p, P u \)
в. \( C f, B k \)
c. \( N p, \) Pr
D. \( A c, T h \)


Find \( \int \frac{x+3}{\sqrt{5-4 x+x^{2}}} d x \)


Select correct statement(s):
This question has multiple correct options
A. \( C e, P r \) and \( N d \) are \( f \) -block elements
B. \( C u, P d \) and \( N i \) are d-block elements
\( \mathbf{c} \cdot C u\left([A r] 3 d^{10} 4 s^{1}\right) \) and \( K\left([A r] 4 s^{1}\right) \) have been placed in sblock.
D. \( S i, G e \) and \( A s \) are metalloids


According to the electromagnetic wave theory, light consists of electric and
magnetic fields which are
A. parallel to each other
B. perpendicular to each other
C . inclined at an angle of \( 45^{\circ} \) to each other
D. none of these


Which of the following is not correctly matched?
A. Gelatin - Lyophilic colloid
B. Gold sol - Lyophilic colloid
C. Arsenious sulphide - Lyophobic colloid
D. Ferric hydroxide - Lyophobic colloid


Let
\( \boldsymbol{\Delta}_{1}=\left|\begin{array}{ccc}\mathbf{1} & \cos \boldsymbol{\alpha} & \cos \beta \\ \cos \boldsymbol{\alpha} & \boldsymbol{1} & \cos \gamma \\ \cos \beta & \cos \gamma & 1\end{array}\right| \)
and \( \Delta_{2}=\left|\begin{array}{ccc}0 & \cos \alpha & \cos \beta \\ \cos \alpha & 0 & \cos \gamma \\ \cos \beta & \cos \gamma & 0\end{array}\right| \)
If \( \Delta_{1}=\Delta_{2}, \) find \( \sin ^{2} \alpha+\sin ^{2} \beta+\sin ^{2} \gamma \)


The equation of a straight line which
passes through the point (1,-2) and cuts off equal intercept from axes will be:
A. \( x+y=1 \)
B. \( x-y=1 \)
c. \( x+y+1=0 \)
D. \( x-y-2=0 \)


Which of the following will give addition reaction and why?
\( \boldsymbol{C}_{4} \boldsymbol{H}_{10}, \boldsymbol{C}_{2} \boldsymbol{H}_{6}, \boldsymbol{C}_{2} \boldsymbol{H}_{4}, \boldsymbol{C} \boldsymbol{H}_{4}, \boldsymbol{C}_{3} \boldsymbol{H}_{8}, \boldsymbol{C}_{3} \boldsymbol{H}_{4} \)


The ratio of the moment of inertia of
circular ring \& circular disc having the same mass \( \& \) radii about an axis
passing the \( c . m \& \) perpendicular to plane is
A . 1: 1
B . 2: 1
c. 1: 2
D. 4: 1


(1)
Convert I to II.


A \( 7.2 V \) zener diode \( \left(7.2 V \text { at } 20^{\circ} C\right) \) has a positive temperature coefficient of
\( 0.0007 /^{o} C . \) What is the zener voltage at
\( 45^{\circ} \mathrm{C} ? \)
A \( .7 .20 V \)
B. \( 7.33 V \)
c. \( 7.13 V \)
D. \( 6.36 V \)


Solve the following systems of equations:
\( \frac{1}{5 x}+\frac{1}{6 y}=12 \)
\( \frac{1}{3 x}-\frac{3}{7 y}=8, x \neq 0, y \neq 0 \)


Which of the following reaction represent the decrease in entropy?
I. \( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \rightarrow \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) \)
Il. \( \boldsymbol{F e}^{2+}(\boldsymbol{a q})+\boldsymbol{S}^{2-}(\boldsymbol{a q}) \rightarrow \boldsymbol{F} \boldsymbol{e} \boldsymbol{S}(\boldsymbol{s}) \)
III. \( 2 S O_{3}(g) \leftrightharpoons 2 S O_{2}(g)+O_{2}(g) \)
A. I only
B. I and II only
c. ॥ and III only
D. III only
E . I, II, and III


Graph between electric potential and the x-coordinate is given and the electric field is along the x-axis.Then
find total charge in various cubes
placed with one edge along positive \( x \) axis


a) Write partial structure of:
¡) Neoprene
ii) Terylene (Dacron)
iii) Nylon - 6
b) Explain the preparation of Buna-N with equation


The length of a minute hand of a wall
clock is \( 8.4 \mathrm{cm} . \) Find the area swept by it in half an hour.
A \( \cdot 100 \mathrm{cm}^{2} \)
В. \( 110.88 \mathrm{cm}^{2} \)
\( \mathrm{c} \cdot 120 \mathrm{cm}^{2} \)
D. \( 130 \mathrm{cm}^{2} \)


If \( K_{p} \) for a reaction is \( \frac{1}{9} \times 10^{-2} a t m^{-2} \) at
500K. Magnitude of \( K_{c} \) will be [Take \( R= \) 0.08]
A. \( 3 \times 10^{-1} \)
В . \( \frac{1}{9} \times 10^{-2} \)
\( c \cdot \frac{16}{9} \)
D. Data insufficient


rotating in the horizontal plane with
constant angular speed \( \omega, \) as shown in
the figure. At time \( t=0, \) a small insect
starts from \( O \) and moves with constant
speed \( v \) with respect to the rod towards
the other end. It reaches the end of the
rod at \( t=T \) and stops. The angular
speed of the system remains \( \omega \)
throughout. The magnitude of the torque \( |\vec{\tau}| \) on the system about \( \boldsymbol{O}, \) as a function of time is best represented by
which plot?
\( A \cdot A \)
B. B
\( c \cdot c \)
D.


How does the progeny termed from asexual reproduction differs from those formed by sexual reproduction?


The first scientific study leading to the formulation pf laws of inheritance was carried out by
A. Drawin
B. Huge De Vries
c. Lemderek
D. Mendel


For a reaction if \( \boldsymbol{K}_{\boldsymbol{p}}>\boldsymbol{K}_{c}, \) the forward
reaction is favoured by:
A . low pressure
B. high pressure
c. high temperature
D. low temperature


A closed coil having 100 turns is rotated
in a uniform magnetic field \( B=4.0 \times \)
\( 10^{-4} T \) about a diameter which is
perpendicular to the field. The angular velocity of rotation is 300 revolution per minute. The area of the coil is \( 25 \mathrm{cm}^{2} \)
and its resistance is \( 4.0 \Omega . \) Find (a) the average emf developed in half a turn from a position where the coil is perpendicular to the magnetic field,
(b)the average emf in full turn and the net charge displaced in part (a).


Suppose \( f \) is differentiable at \( x=1 \) and \( \lim _{h \rightarrow 0} \frac{1}{h} f(1+h)=5, \) then
\( \mathbf{A} \cdot f^{\prime}(1)=4 \)
B \( \cdot f^{\prime}(1)=3 \)
\( \mathbf{c} \cdot f^{\prime}(1)=6 \)
D. None of these


What is the equivalent mass \( I O_{4}^{-} \) when
it is converted into \( I_{2} \) in acid medium?
A. M/6
в. м/7
c. м/5
D. M/4


Find the value of the expression \( \sec ^{-1}\left(\frac{x+1}{x-1}\right)+\sin ^{-1}\left(\frac{x-1}{x+1}\right) \)


Name the germ layers from which the following tissues or organs are produced.
I. Kidneys
II. Internal ear
III. Trachea
A. I- Endoderm; II- Ectoderm; III- Mesoderm
B. I- Endoderm; II- Mesoderm; III-Ectoderm
c. I- Ectoderm; II- Endoderm; III- Mesoderm
D. I- Mesoderm; II-Endoderm; III-Ectoderm
E. I- Mesoderm; II- Ectoderm; II- Endoderm


Find \( \vec{a} . \vec{b}, \) when \( \vec{a}=\hat{j}+2 \hat{k} \) and \( \vec{b}=2 \hat{i}+ \)
\( \hat{\boldsymbol{k}} \)


In our eyes, too much exposure to ultraviolet rays causes:
A. cataracts
B. muscular degeneration
c. both A and B
D. neither A nor B


A battery of 20 cells (each having e.m.f. 1.8 volt and internal resistance 0.1 ohm
is charged by 220 volts and the charging current is 15 A. The resistance to be put in the circuit is
A . 10.27 ohms
B. 12.27 ohms
c. 8.62 ohms
D. 16.24 ohms


Calculate the formal charge on the all
atoms present in the molecules \( N O_{3}^{-} \)


If the force per unit length on wire \( \boldsymbol{B} \) is
given by \( 2.88 \times 10^{-x} N m^{-1} . \) Find \( x \)


The infinite sum \( 1+ \) \( \frac{4}{7}+\frac{9}{7^{2}}+\frac{16}{7^{3}}+\frac{25}{7^{4}}+\dots \dots \) equals
A \( \cdot \frac{27}{14} \)
в. \( \frac{21}{13} \)
c. \( \frac{49}{27} \)
D. \( \frac{256}{147} \)


A potential barrier of \( 0.5 \mathrm{V} \) exists across a p-njunction
(i) If the depletion region
is \( 5 \times 10^{-7} \) m wide. What is the average
intensity of the eectric field in this
region?
(ii) An electron with speed \( 5 \times \)
\( 10^{5} \mathrm{m} / \mathrm{s} \) approaches the \( \mathrm{p} \) -n junction
from the n-side with what speed will it enter the p-side?


The coefficient of variations of two
series are 58 and \( 69 . \) Their standard
deviations are 21.2 and \( 51.6 . \) What are
their arithmetic means?


Solve:
\( \frac{3 a-2}{7}-\frac{a-2}{4}=2 \)


\( X T Q \cong \Delta X S Q \)


In the circuits shown below the
ammeter \( A \) reads \( 4 a m p \) and the
voltmeter \( V \) reads 20 volts. The value of
the resistance \( \boldsymbol{R} \) is
A. Slightly more than 5 ohms
B. Slightly less than 5 ohms
c. Exactly 5 ohms
D. None of the above


If \( \boldsymbol{y}=\log _{e}\left(\boldsymbol{x}+\log _{e}(\boldsymbol{x}+\ldots .)\right), \) then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \)
at \( \left(x=e^{2}-2, y=\sqrt{2}\right) \) is
A \( \cdot \frac{1}{e^{\sqrt{2}}-1} \)
B. \( \frac{\log 2}{2 \sqrt{2}\left(e^{2}-1\right)} \)
\( ^{\mathbf{c}} \cdot \frac{\sqrt{2} \log \frac{e}{2}}{\left(e^{2}-1\right)} \)
D. None of these


Some statements about heavy water are given below.
(i) Heavy water is used as moderator in nuclear reactors
(ii) Heavy water is more associated then ordinary water
(iii) Heavy water is more effective solvent than ordinary water Which of the above statements are
correct?
A \( \cdot \) (i) and (ii)
B. (i), (ii) and (iii)
c. (ii) and (iii)
D. (i) and (iii)


According to Bohr hypothesis, discrete quantity is
A. Momentum
B. Angular velocity
c. Potential energy
D. Angular momentum


The formation of water from \( \boldsymbol{H}_{2}(\boldsymbol{g}) \) and
\( O_{2}(g) \) is an exothermic process because:
A. the chemical energy of \( H_{2}(g) \) and \( O_{2}(g) \) is more than that of water
B. the chemical energy of \( H_{2}(g) \) and \( O_{2}(g) \) is less than that of water
C. the temperature of \( H_{2}(g) \) and \( O_{2}(g) \) is higher than that of water
D. the temperature of \( H_{2}(g) \) and \( O_{2}(g) \) is lower than that of water


Which of the following Lanthanoid is radioactive?
A. Cerium
B. Promethium
c. Thulium
D. Lutetium


Assertion
Distance covered by a moving body is always greater than zero.
Reason
Displacement of a particle can be
greater than or less than or equal to
zero.
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 will exhibit maximum ionic conductivity?
A \( \cdot K_{4}\left[\operatorname{Fe}(C N)_{6}\right] \)
B. \( \left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right] \mathrm{Cl}_{3} \)
\( \mathbf{c} \cdot\left[C u\left(N H_{3}\right)_{4}\right] C l_{2} \)
D. \( \left[N i(C O)_{4}\right] \)


The value of
\( \sin ^{-1}\left[\cot \left[\sin ^{-1}(\sqrt{\frac{2-\sqrt{3}}{4}})+\cos ^{-1}\right.\right. \)
is


A regular hexagon of side \( 10 \mathrm{cm} \) has a charge \( 5 \mu C \) at each of its vertices.
Calculate the potential at the centre of the hexagon.


Convert \( 40^{\circ} 20^{\prime} \) into radian measure.
A \( \cdot \frac{121}{540} \pi \) radians
в. \( \frac{121}{570} \pi \) radians
c. \( \frac{120}{513} \pi \) radians
D. None


Explain how \( Z n+2 A g N O_{3} \rightarrow 2 A g+ \)
\( Z n\left(N O_{3}\right)_{2} \) is a redox reaction.


Which of the following is not a function of transpiration?
A. Excretion of minerals
B. Cooling of leaves
c. Uptake of water
D. Uptake of minerals


The following data gives the amount of loans (in crores of rupees) disbursed by
a bank during some years:
Year \( \begin{array}{lll}1992 & 1993 & 1994 \\ 4 & 19999\end{array} \)
Loan
in
crores 28
55
of rupees
Represent the above data with the help of a bar graph.


How is the heat energy supplied to a liquid used during boiling at a fixed temperature?


Solve the following system of equations by using Matrix inversion method.
\( \mathbf{2} \boldsymbol{x}-\boldsymbol{y}+\mathbf{3} \boldsymbol{z}=\mathbf{9}, \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}=\mathbf{6}, \boldsymbol{x}- \)
\( \boldsymbol{y}+\boldsymbol{z}=\mathbf{2} \)


Select the incorrect statements about
the wave function?
A. \( \psi \) may be zero
B. \( \psi \) must be single value, continuous
C . \( \psi \) has no physical significance
D. \( \psi \) gives the probability density of finding electrons.


DHOKALA is a \( --------- \) type of solution.
A. solid-in-solid
B. solid-in-gas
c. solid-in-liquid
D. gas-in-solid


The graph relates \( \ln K_{e q} . v s . \frac{1}{T} \) for a
reaction. The reaction must be :
A. exothermic
B. endothermic
c. \( \Delta H \) is negligible
D. spontaneous


If corresponding angles of two triangles are equal, then they are known as
A . Equiangular triangles
B. Adjacent angles
c. supplementary angles
D. complementary angles


Write one difference in each of the
following:
(a) Multimolecular colloid and
Associated colloid
(b) Coagulation and Peptization
(c) Homogeneous catalysis and Heterogeneous catalysis


Let \( x \) be a number which exceeds its
square by the greatest possible quantity, then \( x= \)
A. \( 1 / 2 \)
B . \( 1 / 4 \)
c. \( 3 / 4 \)
D. \( 1 / 3 \)


Swimming is based on Newton's:
A. First law of motion
B. second law of motion
c. third law of motion
D. law of gravitation


Let \( P(n) \) denote the statement that
\( \boldsymbol{n}^{2}+\boldsymbol{n} \) is odd. It is seen that \( \boldsymbol{P}(\boldsymbol{n}) \Rightarrow \)
\( P(n+1), P(n) \) is true for all
\( \mathbf{A} \cdot n>1 \)
B.
c \( . n>2 \)
D. None of these


Name the pores in a leaf through which respiratory exchange of gases takes place.


The work done in dragging a stone of mass 100 kg up an inclined plane 1 in 100 through a distance of \( 10 \mathrm{m} \) is:
A . 100 J
B. 980 J
c. 9800
D. 98 J


The volume of gases evolved at \( S T P \) by
passing \( 0.1 A \) of current for \( 965 g \) through an aqueous solution of
potassium acetate:
A . \( 22.4 m L \)
в. \( 11.2 m L \)
\( c .89 .6 m L \)
D. \( 44.8 \mathrm{mL} \)


A thin rod placed long \( x \) -axis from \( x=-a \) to \( x=+a, \) the rod carries a change uniformly distributed along its length with linear charge density \( \lambda \). The
potential at the point \( P(2 a, 0,0) \) will be
A \( \cdot \frac{\lambda}{\pi \epsilon_{0}} \operatorname{In} 3 \)
в. \( \frac{\lambda}{4 \pi \epsilon_{0}} \) In 2
c. \( \frac{\lambda}{4 \pi \epsilon_{0}} \) In 3
D. \( \frac{\lambda}{\pi \epsilon_{0}} \) In 2


The prehistoric man who lived on earth, during late pleistocene period is
A. Neanderthal man
B. Australopithecus
c. Java man
D. Cromagnon man


Two blocks of mass \( m_{1} \) and \( m_{2} \) are
connected by a non deformed light spring on a horizontal table. The coefficient of friction between the
blocks and table is \( \mu \). The minimum
force applied on block 1 which will move the block 2 also is given as \( \mu g\left(m_{1}+\frac{m_{2}}{x}\right) . \) Find \( x \)


Lightest isotope in the periodic table is:
A. tritium
B. deuterium
c. protium
D. none of these


To achieve DC from \( A C, A C \) be applied
across
\( A \cdot B D \)
B. AC
\( c \). ВС
\( D \cdot c D \)
E. Al


Which mode of expressing
concentration is independent of
temperature?
A. Molality
B. Percent by mass
c. Mole fraction
D. All of these


A uniform chain of mass \( M \) and length
\( \boldsymbol{L} \) is held vertically in such a way that its lower end just touches the horizontal floor. The chain is released from rest in
this position. Any portion that strike the floor comes to rest. Assuming that the chain does not form a heap on the floor,
calculate the force exerted by it on the
floor when a length \( x \) has reached the
floor


The area of the smaller part bounded by the semicircle \( \boldsymbol{y}=\sqrt{\mathbf{4}-\boldsymbol{x}^{2}}, \boldsymbol{y}=\boldsymbol{x} \sqrt{\mathbf{3}} \)
and x-axis is
A \( \cdot \frac{\pi}{3} \)
в. \( \frac{2 \pi}{3} \)
c. \( \frac{4 \pi}{3} \)
D.


Assertion
For liquid dishwashing, non-ionic type
of detergent are used.
Reason
Remove grease and oil by micelle formation.
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 particles revolves along a circle with a
uniform speed. The motion of the
particle is
A. one dimensional
B. two dimensional.
c. translatory
D. oscillatory