n given figure the value of \( x \) is :
\( \mathbf{A} \cdot 120^{\circ} \)
B. \( 110^{\circ} \)
\( c \cdot 80^{c} \)
D. \( 100^{\circ} \)


The migration of colloidal particles
under the influence of an electric field
is known as?
A. electro-osmosis
B. brownian movement
c. cataphoresis
D. dialysis


Can a solution be heterogeneous?


Why \( N C l_{3} \) and \( P C l_{3} \) are hydrolysed
differently?


Curie's law states that magnetic
susceptibility is
A. inversely proportional to the absolute temperature
B. exponentially related to temperature
C. directly proportional to the absolute temperature
D. does not depend on temperature


Decreasing order of p-orbital character in the following is:
A) \( S i O_{2} \)
B) \( C O_{2} \)
C) Graphite
A . A>B>C
B. B>A>C
c. В>С>А
D. A>C>B


Derive an expression for the magnetic induction at a point due to an infinitely long straight conductor carrying current. Write the expression for the magnetic induction when the conductor is placed in a medium of permeability
\( \mu^{\prime} \)


Write first four terms of the AP, when
the first term \( a \) and the common
difference \( d \) are given as follows \( a= \)
\( -1.25, d=-0.25 \)
A. First four terms of the given AP are -1.25,-1.70,-1.95,-2.00
B. First four terms of the given AP are -1.25,-1.50,-1.75,-2.00
c. Not an AP
D. None of these


Mark the correct statement.
a) Metals lose their lustre on keeping in
air.
b) Gold is lustrous
c) Metals are lustrous and can be
polished.
\( A \cdot a, b \)
B. b,
\( c \cdot \) а,
D. All of the above


toppr
Q Type your question
\( A \)
3
\( c \)
\( D \)


The sum of the series \( 1+2(1+1 / n)+3 \)
\( (1+1 / n)^{2}+\ldots . \infty \quad \) is given \( b y \)
A \( \cdot n^{2}+1 \)
the 1
B \( \cdot n(n+1) \)
c. \( n(1+1 / n)^{2} \)
\( \mathbf{D} \cdot n^{2} \)


The utilization of nitrogen as nitrogen
\( \operatorname{gas}\left(N_{2}\right) \) can be done by
A. Producers
B. Primary consumers
c. Secondary consumers
D. Tertiary consumers
E. Decomposers


Calculate the number of electrons
constitute one coulomb of charge.


Match the column I with column II
Types of processes Features
(A)Isothermal
\( (p) \quad \Delta Q=0 \)
(B)Isobaric
(q) Volume
constant
(C)Isochoric
Pressure constant
(D)Adiabatic
Temperature constant
\( A \cdot(A)-(s),(B)-(r),(C)(q),(D)(p) \)
B. (A) - (p), (B) - (s), (C) (r), (D) (q)
\( c \cdot(A)-(q),(B)-(r),(C)(p),(D)(s) \)
\( D \cdot(A)-(r),(B)-(p),(C)(q),(D)(s) \)


Quicklime is not used to dry \( H C l \) gas because \( _{---}-_{-}(C a O \) is alkaline \( \mathrm{CaO} \) is acidic, \( \mathrm{CaO} \) is neutral


Evaluate the following:
\( \left|\begin{array}{ccc}\boldsymbol{x}+\boldsymbol{\lambda} & \boldsymbol{x} & \boldsymbol{x} \\ \boldsymbol{x} & \boldsymbol{x}+\boldsymbol{\lambda} & \boldsymbol{x} \\ \boldsymbol{x} & \boldsymbol{x} & \boldsymbol{x}+\boldsymbol{\lambda}\end{array}\right| \)


Auxin inhibits the growth
of
A. Apical buds
B. Parthenocarpic development of fruits
c. Lateral axillary buds
D. Roots of cuttings


Which of the following is Lewis acid?
A. \( C_{2} H_{5} O H \)
в. \( B F_{3} \)
c. \( C l^{-} \)
D. \( N H_{3} \)


8 times a 2 digit number is equal to 3 times the number obtained by reversing
the order of the digit. If the difference
between digit is 5 then find the number.


Which of the following statements are false?
(i) Outer cortex and inner medulla are the two zones in kidney.
(ii) Medulla is divided into few renal pyramids.
(iii) Pyramid projects into calyx.
(iv) Inward extension of cortex between
the pyramids is called renal column of Bertini.
A. (i) and (iv)
B. (ii) and (iv)
c. (ii) and (iii)
D. None of these


Which of the following element(s) is not essential for life to originate and
flourish on a planet?
A. carbon
B. hydrogen
c. oxygen
D. uranium


Construct a \( \triangle A B C \) in which \( A B= \)
\( 4 \mathrm{cm}, \angle B=60^{\circ} \) and altitude \( C L= \)
\( 3 \mathrm{cm} . \) Construct a \( \triangle A D E \) similar to
\( \triangle A B C \) such that each side of \( \triangle A D E \)
is \( \frac{3}{2} \) times that of the corresponding
side of \( \triangle A B C \)


The mass of the particle is 2 kg. It is projected as shown in four different ways with same speed of \( 10 \mathrm{m} / \mathrm{s} / \). Find
out the work done by gravity by the
time the stone fails on ground.
A. 2000
B. 4000 J
c. 6000 J
D. 8000 J


Highlousuelto thaligic ul olut \( u \) lias
charges \( \boldsymbol{q},+2 \boldsymbol{q} \) and \( -\boldsymbol{q} \) arranged on its
vertices, as shown.What does the sign
of \( U \) signify?
A. The negative sign means that work was done on the agent who assembled these charges in moving them in from infinity.
B. The positive sign means that work was done on the agent who assembled these charges in moving them in from infinity
C. The negative sign means that work was done by the agent who assembled these charges in moving them in from infinity
D. The positive sign means that work was done by the agent who assembled these charges in moving them in from infinity


Given line \( A B \) is parallel to line \( C D \)
\( \angle C H G \) and \( \angle E G B \) are:
A. Non-congruent
B. Congruent
c. Complementary
D. None of these


Find the value of a for which the
function \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{a} \boldsymbol{x}^{3}-\boldsymbol{3}(\boldsymbol{a}+\boldsymbol{2}) \boldsymbol{x}^{2}+ \)
\( 9(a+2) x-1 \) is decreasing for all \( x \in \)
\( \boldsymbol{R} \)


If \( \left(\tan ^{-1} x\right)^{2}+\left(\cot ^{-1} x\right)^{2}=\frac{5 \pi^{2}}{8}, \) then \( x \)
A . -1
B.
c. 1
D. 2


The number of binary operation on \( \{1,2, \) \( 3 \ldots n\} \) is..
\( \mathbf{A} \cdot 2^{n} \)
B \( \cdot n^{2} \)
c. \( n^{3} \)
D. \( n^{2} \)


1 nano metre \( (1 \mathrm{nm}) \) is equal to
\( \mathbf{A} \cdot 10^{-7} \mathrm{m} \)
В. \( 10^{-9} \mathrm{m} \)
\( \mathbf{c} \cdot 10^{9} \mathrm{m} \)
D. None of these


How many of the given carbonyl
compounds are less reactive than formaldehyde with respect to nucleophilic addition?


A block of mass \( m \) and surface area \( A \)
just begins to slide down an inclined plane when the angle of inclination is \( \pi / 5 . \) Keeping the mass of the block
same, if the surface area is doubled, the inclination of the plane at which
the block starts sliding will be:
A \( . \pi / 5 \)
в. \( \pi / 10 \)
c. \( 2 \pi / 5 \)
D. \( \pi / 5 \sqrt{2} \)


Literacy rate of male population is population.
A. higher than female
B. lower than female
c. same as female
D. none of the above


The value of the integral \( \int_{1}^{2} \sqrt{(2 x+3)\left(3 x^{2}+4\right)} d x \) cannot
exceed
\( A \cdot \sqrt{48} \)
B. \( \sqrt{66} \)
c. \( \sqrt{73} \)
D. none of these


Which of the following reactions will yield 2,2-dibromopropane?
A. \( C H_{3}-C H=C H_{2}+H B r \)
в. \( C H_{3}-C \equiv C H+2 H B r \)
c. \( C H_{3}-C H=C H B r+H B r \)
D. \( C H \equiv C H+2 H B r \)


A street car moves rectilinear from
station \( \boldsymbol{A} \) to the next station \( \boldsymbol{B}( \) from rest to rest \( ) \) with an acceleration
varying according to the law \( \boldsymbol{f}=\boldsymbol{a}- \)
\( b x ; \) where \( a \) and \( b \) are constants and \( x \) is
the distance from station \( \boldsymbol{A} \). The
distance between the two stations and
the maximum velocity are
A \( \cdot x=\frac{2 a}{b}, v_{m a x}=\frac{a}{\sqrt{b}} \)
B. \( x=\frac{b}{2 a}, v_{m a x}=\frac{a}{\sqrt{b}} \)
c. \( _{x}=\frac{a}{2 b}, v_{\max }=\frac{b}{\sqrt{a}} \)
D. \( x=\frac{a}{b}, v_{\max }=\frac{\sqrt{a}}{b} \)


A tissue paper soaked with polluted
water showed \( K_{\alpha} \) peaks at \( 78.9 \mathrm{pm}, 146 \) \( \mathrm{pm}, 158 \mathrm{pm} \) and \( 198 \mathrm{pm} . \) Find the
elements it contained.


Purine base with methyl substituents occurring in plants are
A. Caffeine
B. Theophylline
c. Theobromine
D. All of the above


Let \( A \) and \( B \) are two matrices of same
order \( 3 \times 3 \) given by \( A= \) \( \left[\begin{array}{ccc}1 & 3 & \lambda+2 \\ 2 & 4 & 6 \\ 3 & 5 & 8\end{array}\right] B=\left[\begin{array}{lll}3 & 2 & 4 \\ 3 & 2 & 5 \\ 2 & 1 & 4\end{array}\right] \) If
\( t r(A B)^{t}+t r(B A)^{t}=t r(A B) \) then the
value of \( 2 \lambda \) equals
A . 103
в. 206
\( c .-103 \)
D. -206


The potential energy between electron and proton is given by \( U=\frac{K e^{2}}{3 r^{3}} \)

According to Bohr's theory, the energy in
the \( n^{t h} \) orbit of such a
hypothetical atom will be proportional to
\( \mathbf{A} \cdot n^{6} \)
B . \( n^{4} \)
c. \( n^{2} \)
D. \( n \)


If \( \boldsymbol{y}=\sec \left(\tan ^{-1} x\right), \) then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \) at \( \boldsymbol{x}=\mathbf{1} \) is
equal to.
A \( \cdot \frac{1}{\sqrt{2}} \)
B. \( \frac{1}{2} \)
\( c \cdot 1 \)
D. \( \sqrt{2} \)


Vectors \( \vec{a} \) and \( \vec{b} \) make an angle \( \theta=\frac{2 \pi}{3} \) If \( |\vec{a}|=1,|\vec{b}|=2 \) then
\( \{(\vec{a}+3 \vec{b}) \times(3 \vec{a}-\vec{b})\}^{2}= \)
A . 225
B. 250
c. 275
D. 300


Which of the following test is performed by carbohydrates?
A. Biuret test
B. Nitroprusside test
c. Ninhydrin test
D. Molisch's test


The Van der Waal's equation of state for some gases can be expressed as:
\( \left(\boldsymbol{P}+\frac{\boldsymbol{a}}{\boldsymbol{V}^{2}}\right)(\boldsymbol{V}-\boldsymbol{b})=\boldsymbol{R} \boldsymbol{T} \)
where \( P \) is the pressure, \( V \) is the molar volume, and \( T \) is the absolute
temperature of the given sample of gas and \( a, b \) and \( R \) are constants.

In the above problem, the dimensional formula for \( \mathrm{RT} \) is same as that of
A. Energy
B. Force
c. specific heat
D. Latent heat


State True or False.
\( 24 t h \) electron in \( C r \) enters in \( 3 d \) -orbital.
A. True
B. False


Calculate the molarity of \( 9.8 \% \) solution
of \( \mathbf{H}_{2} \mathbf{S O}_{4} \) if the density of the solution is
\( 1.02 \mathrm{gmL}^{-1} \)


The inner transition elements are the
elements in which the added electrons
go to:
\( A \cdot(n-1) d- \) orbitals
B. (n-2) f-orbitals
c. (n-1) d-orbitals and (n-1) f-orbitals
D. (n-1) d-orbitals and ns orbitals


A species is taxonomically
A. A group of evolutionary related populations
B. A population with common characteristics as evolutionary base of variation
C. A fundamental unit in the phylogenetic history of organisms
D. A group of individuals capable of reproducing and producing fertile offsprings


topp
Q type your question
rom the center plate. A source of
onstant EMF is connected to the
system such that the center plate is connected to the positive terminal and the left and right plates are connected
to the negative terminal Which of the following diagrams correctly depicts the electric field lines (shown as arrows) in the region between the plates?


\( K_{a} \) for the reaction; \( F e^{3+}(a q .)+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) \rightleftharpoons \boldsymbol{F} \boldsymbol{e}(\boldsymbol{O} \boldsymbol{H})^{2+}(\boldsymbol{a} \boldsymbol{q} \cdot)+ \)
\( H_{3} O^{+}(a q .) \) is \( 6.5 \times 10^{-3} . \) What is the
maximum \( p H \) value which could be
used do that at least \( 80 \% \) of the total
ion \( (I I I) \) in a dilute solution exists as
\( \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{3}+} \boldsymbol{?} \)
A . 2
B. 2.41
c. 2.79
D. 0.59


What is Reverberation?


Simplify \( \frac{\sin 35^{\circ}}{\cos 55^{\circ}}+\frac{\cos 55^{\circ}}{\sin 35^{\circ}}-2 \cos ^{2} 60^{\circ} \)


The temperature at which the volume of
ideal gas is zero is:
A \( .+274 K \)
В. \( -273^{\circ} \mathrm{C} \)
\( c \cdot 273^{\circ} C \)
D. \( -273 K \)


The point \( (p, p+1) \) lies on the locus of the point which moves such that its distance from the point (1,0) is twice the distance from \( (0,1) . \) The value of \( \frac{1}{2 p^{2}}+\frac{1}{2 p^{4}} \) is equal to


show that \( \sqrt{2+\sqrt{2+\sqrt{2+2 \cos 8 \theta}}}= \)
\( 2 \cos \theta, 0<\theta<\frac{\pi}{8} \)


A nucleus of element \( X \) is represented \( \operatorname{as}_{26}^{56} X \)
Which is an isotope of element \( X ? \)
\( A \cdot \frac{26}{56} X \)
B \( \cdot \frac{54}{26} X \)
\( \mathbf{c} \cdot \underset{24}{56} X \)
\( \mathrm{D} \cdot_{28}^{54} \mathrm{X} \)


Which plants has a trap, which looks and shows like a flower to insects?
A. Drosera
B. Balsam
c. Lotus
D. Venus Fly trap


Catenation property is maximum in group sixteen for:
A. oxygen
B. selenium
c. sulphur
D. telurium


Leptotene chromosomes have
A. two chromatids
B. one chromatids
c. four chromatids
D. no chromatids


Which of the following is not correctly
matched with respect to the processes involved in the extractive metallurgy of
the respective metal?
\( \mathbf{A} \cdot A l_{2} O_{3} \cdot 2 H_{2} O \rightarrow A l: \) Leaching, precipitation
calcination and electrolytic reduction (molten state)
B. \( A g_{2} S \rightarrow A g \) : Leaching and displacement method
C \( . P b S \rightarrow P b \) : Froth flotation process, roasting and self
reduction
D. \( K C l . M g C l_{2} .6 H_{2} O \rightarrow M g \) : Dehydration by simple heating and electrolytic reduction in aqueous phase


Assertion
Allosteric enzymes show feed back inhibition.
Reason
The inhibitor is competitive.
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


What sum of money will yield Rs. 170.10
as simple interest in 2 years 3 months
at \( 6 \% \) per annum?


Differentiate \( (x)^{\tan x}+(\tan x)^{x} \) w.r.t \( x \)


Four pipes can fill a tank in 70 min. How Iong will it take to fill the tank by 7 pipes?
A . 20 min
B. 35 min
\( c .40 \) min
D. None of these


Find the square of the following
numbers using the identity \( (a-b)^{2}= \)
\( a^{2}-2 a b+b^{2}: \)
495


Formation of \( N a C l \) is best shown by:
A. born-haber cycle
B. wilkinson's synthesis
c. haber process
D. none of these


Primary amine \( \left(\boldsymbol{R} \boldsymbol{N} \boldsymbol{H}_{2}\right) \) reacts with nitrous acid to give :
A \( \cdot R N H_{3}^{+} N O_{2} \)
в. RОН
c. ROR
D. None of these


In the ellipse distance between the foci
is equal to the distance between a focus
and one end of minor axis then its
eccentricity is
A \( \cdot \frac{1}{2} \)
B.
\( c \cdot \frac{1}{3} \)
D.


The degree and order of the differential equation of the family of all parabolas whose axis is \( x \) -axis are respectively:
A . 2,1
в. 1,2
\( c .3,2 \)
D. 2,3


Supposing the ionisation energy of hydrogen like species is 960 eV. Find out the value of principal quantum number having the energy equal to - 60
\( \mathrm{eV} \)
\( A \cdot n=2 \)
B. \( n=3 \)
\( c \cdot n=4 \)
\( D \cdot n=5 \)


The equation \( \frac{x^{2}}{8-t}+\frac{y^{2}}{t-4}=1 \) will
represent an ellipse if
A. \( t \in(1,5) \)
B. \( t \in(2,8) \)
c. \( t \in(4,8)-\{6\} \)
D. \( t \in(4,10)-\{6\} \)


The sum of first \( ^{\prime} n^{\prime} \) terms of an
Arithmetic Progression is " \( 5 n^{2}-2 n " \)
Find the \( 20^{t h} \) term?
A . 1960
в. 183
c. 203
D. 193


Asthma is characterised by
A. Spasm in bronchial muscle
B. Alveolar wall degradation
c. Pain in lungs
D. Damage in diaphragm


The flame of candle has three zones. The
outer zone is yellow, the middle zone is blue and the inner zone is black. Which
is correct regarding this?
A. The outer zone is least hot
B. The middle zone is hottest
c. The inner zone is least hot
D. All the zones have same temperature


The female gametophytes are retained on the parent sporophyte in
A. Homosporous species of pteridophytes
B. Heterosporous species of pteridophytes
c. Both are correct
D. Both are incorrect


In what two ways is mitotic division in
an animal cell different from the mitotic
division in a plant cell?


State whether given statement is True or False

The process of convection can takes
place only in liquid and gases.
A. True
B. False


There are 8 buses running from Kota to Jaipur and 10 buses running from Jaipur to Delhi. In how many ways a person can travel from Kota to Delhi via
Jaipur by bus?


In hydrogen atom, an electron is revolving in the orbit of radius \( 0.53 \dot{A} \)
with \( 6.6 \times 10^{15} \) radiation/s. Magnetic
field produced at the centre of the orbit is
A. \( 0.125 W b / m^{2} \)
B. \( 1.25 W b / m^{2} \)
c. \( 12.5 W b / m^{2} \)
D. \( 125 W b / m^{2} \)


The emf of a galvanic cell, with electrode potentials of \( Z n=+0.76 V \)
is:
A \( .-1.1 V \)
B. \( +1.1 V \)
\( \mathbf{c} .+0.34 V \)
D. \( +0.76 V \)


toppr
Q Type your questiò
(i) \( \frac{-}{2 x}+\frac{-}{3 y}=2 ; \frac{-}{3 x}+\frac{-}{2 y}=\frac{-}{6} \)
(ii) \( \frac{\mathbf{2}}{\sqrt{\boldsymbol{x}}}+\frac{\mathbf{3}}{\sqrt{\boldsymbol{y}}}=\mathbf{2} ; \frac{\mathbf{4}}{\sqrt{\boldsymbol{x}}}-\frac{\mathbf{9}}{\sqrt{\boldsymbol{y}}}=-\mathbf{1} \)
(iii) \( \frac{4}{x}+3 y=14 ; \frac{3}{x}-4 y=23 \)
(iv) \( \frac{\mathbf{5}}{\boldsymbol{x}-\mathbf{1}}+\frac{\mathbf{1}}{\boldsymbol{y}-\mathbf{2}}=\mathbf{2} ; \frac{\mathbf{6}}{\boldsymbol{x}-\mathbf{1}}- \)
\( \frac{3}{y-2}=1 \)
\( (v) \frac{7 x-2 y}{x y}=5 ; \frac{8 x+7 y}{x y}=15 \)
(vi) \( 6 x+3 y=6 x y ; 2 x+4 y=5 x y \)
(vii) \( \frac{\mathbf{1 0}}{\boldsymbol{x}+\boldsymbol{y}}+\frac{\mathbf{2}}{\boldsymbol{x}-\boldsymbol{y}}=\mathbf{4} ; \frac{\mathbf{1 5}}{\boldsymbol{x}+\boldsymbol{y}}- \)
\( \frac{5}{x-y}=-2 \)
(viii) \( \frac{1}{3 x+y}+\frac{1}{3 x-y}= \)
\( \frac{3}{4} ; \frac{1}{2(3 x+y)}-\frac{1}{2(3 x-y)}=\frac{-1}{8} \)


In the experimental set up of metre
bridge shown in the figure, the null
point is obtained at a distance of \( 40 \mathrm{cm} \)
from A. If a \( 10 \Omega \) resistor is connected in
series with \( R_{1}, \) the null point shifts by
10cm. The resistance that should be
connected in parallel with \( \left(\boldsymbol{R}_{1}+\mathbf{1 0}\right) \boldsymbol{\Omega} \)
such that the null point shifts back to its initial position is?
A. \( 40 \Omega \)
в. \( 60 \Omega \)
\( c .20 \Omega \)
D. \( 30 \Omega \)


A uniform electric field and a uniform
magnetic field are produced, and are pointed in the same direction. An
electron is projected with its velocity pointed in the same direction
A. The electron will turn to its left
B. The electron velocity will decrease in magnitude
c. The electron will turn to its right
D. The electron velocity will increase in magnitude


The geometric mean of 4.9 and 0.4 is
A . 1.4
B. 2.4
c. \( 4 . \)
D. 5.2


Write the chemical name of bleaching
powder and write its properties.


Two particles \( A_{1} \) and \( A_{2} \) of masses
\( \boldsymbol{m}_{1}, \boldsymbol{m}_{2}\left(\boldsymbol{m}_{1}>\boldsymbol{m}_{2}\right) \) have the same de
Broglie wavelength. Then
A. their momenta are the same
B. their energies are the same.
c. momentum of \( A_{1} \) is less than momentum of \( A_{2} \)
D. energy of \( A_{1} \) is more than the energy of \( A_{2} \)


Distinguish between polar molecules and non polar molecules


Which of the following are measures of central tendency
A. Percentile, Quartile, Median
B. Median,Mode, Percentile
c. Percentile, Quartile, Mode
D. Mean,Mode, Median


Solve: \( \boldsymbol{x}(\boldsymbol{3} \boldsymbol{x}+\mathbf{1 4})+\boldsymbol{8} \)
A \( \cdot(x+4)(3 x+2) \)
в. \( (x+2)(x+4) \)
c. \( (x-4)(x+6) \)
D. \( (x-2)(4 x+5) \)


Let \( (a-b \cos y)(a+b \cos x)=a^{2}-b^{2} \)
and \( \frac{d y}{d x}=\frac{\sin x f(y))}{(a+b \cos x)^{2}} \cdot \) If \( a^{2}-b^{2}= \)
\( 192, \) then \( f(\pi / 2) \)


calculate the current through a \( 60 \mathrm{W} \) lamp rated for \( 250 \mathrm{V} \). if the line voltage falls to \( 200 \mathrm{V} \), how is the power consumed by the bulbs affected?


Plastic deformation results from the
following
A. Slip
B. Twinning
c. Both slip and twinning
D. creep


0.2 mol sample of hydrocarbon, \( C_{X} H_{Y} \) yields after complete combustion with
excess \( \boldsymbol{O}_{2} \) gas, 0.8 mol of \( \boldsymbol{C} \boldsymbol{O}_{2} \) and \( \mathbf{1 . 0} \)
mol of \( \boldsymbol{H}_{2} \boldsymbol{O} . \) Hence, the hydrocarbon is :
A. \( C_{4} H_{10} \)
в. \( C_{4} H_{8} \)
c. \( C_{4} H_{6} \)
D. \( C_{8} H_{16} \)


Which among the following are necessary and sufficient conditions for
spontaneous reactions.
\( A \cdot \Delta H=- \) ve only
B. \( \Delta \mathrm{S}= \) -ve only
c. Both \( \Delta \mathrm{H}=- \) -ve and \( \Delta \mathrm{S}=+\mathrm{ve} \)
D. \( \Delta G=+v e \)


Assume that the earth moves around
the sun in a circular orbit of radius \( \mathrm{R} \)
and there exists a planet which also
moves around the sun in circular orbit
with an angular speed twice as large as
that of the earth. The radius of the orbit
of the planet is
A \( \cdot \frac{-2}{3} R \)
B. \( \frac{2}{3} R \)
c. \( \frac{-1}{3} R \)
D. \( \frac{R}{\sqrt{2}} \)


What is the link between domestic
waste and acid rain?


A bag contains six red four green and eight white balls If a ball is picked at random the probability that it is not white is
\( A \cdot 1 / 3 \)
B. 4/9
\( c \cdot 5 / 9 \)
D. 2/3


A car of mass \( 500 \mathrm{kg} \), moving with the velocity of \( 4 \mathrm{m} / \mathrm{s} \) accelerates uniformly and attains the velocity of \( 8 \mathrm{m} / \mathrm{s} \) in 10
seconds. Calculate the initial and final
momentum of the object. find the magnitude of the force exerted on the car to provide this acceleration.


The metal generally mixed with gold while making ornaments is:
A . zinc
B. iron
c. silver
D. copper


Assertion \( (A): f(x)=\sin (\pi[x]) \) is
differentiable every where [] is greatest
integer function
Reason \( (\mathrm{R}): \) If \( \mathbf{x}=\mathbf{n} \boldsymbol{\pi} \Rightarrow \sin \boldsymbol{x}=\mathbf{0} \forall \mathbf{n} \in \)
\( \mathbf{Z} \) then
A. Both (A) and (R) are true and R is correct explanation for A
B. Both (A) and (R) are true and R is not correct explanation for
c. (A) is true (R) is false
D. (A) is false (R) is true


Explain with a neat diagram, how a p-n junction diode is used as a half wave rectifier.


Evaluate:
\( \int \frac{2^{x+1}-5^{x-1}}{10^{x}} d x \)


If two mirrors are kept at \( 60^{0} \) to each
other, then the number of images formed by them is


Find the energy of photon in each of the following:
A. Microwaves of wavelength \( 1.5 \mathrm{cm} \)
B. Red light of wavelength 660 nm
C. Radiowaves of frequency \( 96 M H z \)
D. \( X- \) rays of wavelength 0.17 nm


the following reaction?
\( A \)
\( B \)
\( c \)
\( D \)


Identify on which of the following, specular reflection would most likely to
occur.
A. mirror
B. wall
c. sheet of paper
D. ceiling
E . cat's fur


State in which of the following examples the force of attraction between particles of matter is almost negligible.
A. Piece of stone
B. Water droplets
c. A light gas
D. All of the above


A system is said to be isolated if it can
neither exchange matter nor energy with surroundings.
If true enter 1 , else enter 0 .


Phase difference at the central point changes by \( \pi / 3 \) when a thick film having refractive index 1.5 and
thickness \( 0.4 \mu m \) is placed in front of
upper slit of a YDSE setup. If the wavelength (in \( n m \) ) of the light used is \( 600 \mathrm{k}, \) find \( \mathrm{k} \)


Find the root of \( 2 x+\frac{x}{2}=20 \)


An air-gap parallel plate capacitor is
fully charged by a battery.
What combination of two
measurements will allow someone to
calculate the magnitude of the electric
field in between the capacitor plates?
A. The potential difference of the battery and the area of the plates.
B. The charge on the plates and the distance between the plates.
C. The charge on the plates and the area of the plates.
D. The area of the plates and the distance between the plates
E. More than two measurements are needed to calculate the electric field in between the capacitor plates.


Start of synthesis of chlorophyll in a plant seedling is stimulated by
A . Gibberellins
B. Indole acetic acid
c. kinin
D. Light


State or True or False.
HCl is a gas while HF is a liquid at room temperature.
A. True
B. False


Compute the area of the figure which lies in the first quadrant inside the
curve \( x^{2}+y^{2}=3 a^{2} \& \) is bounded by
the parabola \( x^{2}=2 a y \& y^{2}= \)
\( 2 a x(a>0) \)


n Fig., \( D E F G \) is a square in a triangle
\( A B C \) right angled at \( A \)
Prove that
\( \Delta A G F \sim \Delta D B G \)
ii) \( \Delta A G F \sim \Delta E F C \)


Deep black soils are considered highly productive because of their high proportion of
A. Clay and Humus
B. Sand and Zinc
c. Gravel and Calcium
D. silt and Earthworm


has living cells.
A. Xylem
B. Phloem
c. Sclerenchyma
D. All of the above


Differentiate with respective to \( x \) \( \log (\sec x+\tan x) \)


Which choice shows the answer to the
following mathematical operation with the correct number of significant figures? \( \frac{12.55}{3.0}=4.18333 \)
A . 4.18333
в. 4.2
c. 4.18
D. 4.183
E . 37.45


Three unbaised coins are tossed find
the probability distribution of the
number of heads occurring on the
topmost faces.


Which element was not known when
Mendeleev gave his classification?
A. Germanium
B. Gallium
c. Scandium
D. All of the above


The phenomenon of interference is
shown by
A. longitudinal mechanical waves only
B. transverse mechanical waves only
C. non mechanical transverse waves only
D. all the above types of waves


The value of 'c' in Rolle's theorem for the
function \( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{c}\boldsymbol{x}^{2} \cos \left(\frac{1}{\boldsymbol{x}}\right), \boldsymbol{x} \neq \mathbf{0} \\ \mathbf{0}, \boldsymbol{x}=\mathbf{0}\end{array}\right. \)
the interval [-1,1] is?
A \( \cdot \frac{-1}{2} \)
B. \( \frac{1}{4} \)
\( c \cdot 0 \)
D. Non-existent in the interval


Assertion
At \( 25^{\circ} C \), the pH of \( 10^{-8} M \) HClis 8
Reason
pH of acidic solution is always below 7
\( \operatorname{at} 25^{\circ} C \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but the Reason is correct


How many employees get to work in less
than 20 minutes?
\( A \cdot 4 \)
B. 6
c. 10
D. 15


Arrange the following in increasing
order of solubility in \( \boldsymbol{H}_{2} \boldsymbol{O} \)
\( \boldsymbol{A} \boldsymbol{g} \boldsymbol{C l}, \boldsymbol{A} \boldsymbol{g} \boldsymbol{B r}, \boldsymbol{A} \boldsymbol{g} \boldsymbol{I}, \boldsymbol{A} \boldsymbol{g} \boldsymbol{F} \)
A. \( A g I<A g B r<A g C l<A g F \)
B. \( A g I<A g B r<A g F<A g C l \)
c. \( A g I<A C l<A g B r<A g F \)
D. None of these


In the plots of radial distribution
function for the hydrogen 3 s orbital versus 'r', the no. of peaks are:
\( A \cdot 3 \)
B. 2
\( c \)
D.


A clinical thermometer can not be used
to measure
A. Room temperature
B. Human body temperature
c. Temperature of a boiling water
D. Temperature of a lake water


Receptors of hormones are generally:
A. carbohydrates
B. vitamins
c. lipids
D. protiens


Which of the following is a semiconductor?

This question has multiple correct options
A. Constantan
B. Porcelain
c. Germanium
D. silicon


A ball moving with velocity \( 2 m / s \) collides head on with another stationary
ball of double the mass. If the
coefficient of restitution is \( 0 \cdot 5, \) then
their velocities \( (\operatorname{in} m / s) \) after collision
will be
A . 0,1
в. 1,1
c. \( 1,0 \cdot 5 \)
D. 0,2


If \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}(\boldsymbol{x}-\boldsymbol{2})(\boldsymbol{x}-\boldsymbol{4}), \mathbf{1} \leq \boldsymbol{x} \leq \mathbf{4} \)
then a number satisfying the conditions of the mean value theorem is
\( \mathbf{A} \cdot \mathbf{1} \)
B. \( \frac{5}{2} \)
\( c .3 \)
D. \( \frac{7}{2} \)


A point object is placed at the center of
a glass sphere of radius \( 6 \mathrm{cm} \) and refractive index \( 1.5 . \) The distance of virtual image from the surface is :
A. \( 6 \mathrm{cm} \)
B. \( 4 \mathrm{cm} \)
c. \( 12 \mathrm{cm} \)
D. \( 9 \mathrm{cm} \)


If the probability of an event is \( 1, \) then it
is an:
A. impossible event
B. absolutely certain event
c. exhaustive event
D. sure event


solve \( : \boldsymbol{y}-\frac{\boldsymbol{y}}{\mathbf{2}}=\frac{\mathbf{7}}{\mathbf{4}}-\frac{\boldsymbol{y}}{\boldsymbol{4}}-\frac{\boldsymbol{y}}{\boldsymbol{4}} \)


A \( 2 k W \) electric heater is placed in 2.5
kg of water at \( 25^{\circ} \mathrm{C} \). calculate the time
taken to increase the temperature by
\( 50^{\circ} \mathrm{C} \)
A. 4 min 38 sec
B. 5 min 03 sec
c. 2 min
D. 159 sec


Study the statements given below.
X: In humans, the gamete contributed by the male determines whether the
child produced will be male or female.
Y: Sex in humans is a polygenic trait depending upon a cumulative effect of
some genes on X chromosome and
some on Y chromosome.
A. If both \( x \) and \( Y \) are true and the \( Y \) is the correct explanation of the X.
B. If both \( x \) and \( Y \) are true but \( Y \) is not the correct explanation of the X.
c. If \( x \) is true but \( Y \) is false
D. If both \( x \) and \( Y \) are false


If half life of a first order reaction is
\( 2.31 \times 10^{3} \) min, the time it takes for
one-fifth of the reaction to be left behind
in min. is \( _{-}-_{-}-_{-}-_{-}-_{-} . \) (give the
answer in \( 1000 \times \) form


Let \( \cos ^{-1}\left(4 x^{3}-3 x\right)=a+b \cos ^{-1} x \)
\( x \in\left(\frac{1}{2}, 1\right], \) then the value of \( \lim _{y \rightarrow a} b \cos (y) \)
is
A. \( -\frac{1}{3} \)
в. -3
\( c \cdot \frac{1}{3} \)
D. 3


A sphere of mass \( m \) moving with a
constant velocity \( \boldsymbol{v} \) hits another
stationary sphere of the same mass. If \( e \)
is the coefficient of restitution, then the
ratio of the velocities of the first sphere
to the second spheres after the collision
will be :
A \( \cdot\left(\frac{1+e}{1-e}\right) \)
B \( \cdot\left(\frac{e-1}{e+1}\right) \)
c. \( \left(\frac{1-e}{e+1}\right) \)
D. \( \left(\frac{1+e}{e-1}\right) \)


Calculate the minimum and maximum
number of electrons which may have
magnetic quantum number, \( \boldsymbol{m}=+\mathbf{1} \) and spin quantum number, \( s=-\frac{1}{2} \) in Chromium \( (\mathrm{Cr}) \)
A . 0,1
в. 1,2
c. 4,6
D. 2,


State Yes or No. \( \lim _{x \rightarrow 3^{+}} \frac{x}{[x]} \) is equal to \( \lim _{x \rightarrow 3^{-}} \frac{x}{[x]} \)


A nucleus, kept at rest in free space, break up into two smaller nuclei of
masses \( m \) and \( 2 m . \) Total energy
generated in this fission is E. The bigger part is radioactive, emits five gamma ray photons in the direction opposite to its velocity, and finally comes to rest. Now, answer the following questions:
\( \left(\operatorname{given} ; h=6.6 \times 10^{-34} ; m=1.00 \times\right. \)
\( \mathbf{1 0}^{-\mathbf{2 6}} \mathbf{k g}, \boldsymbol{E}=\mathbf{3 . 6 3} \times \mathbf{1 0}^{-\mathbf{8}} \mathbf{m s}^{-\mathbf{1}} \)
The wavelength of the gamma ray is?
\( \begin{array}{l}\text { A } \cdot 0.02 A^{0} \\ ^{0}\end{array}^{0} \cdot 0.0 A A^{0} \)
B. \( 0.03 A^{\circ} \)
c. \( 0.04 A^{\circ} \)
D. \( 0.05 A^{\circ} \)


Which of the following are true or false?
a) T-distribution varies from+infinity to infinity
b)The variance of \( t \) distribution and the
variance of normal distribution become
closer and closer as the size of the
sample increases.
A. both (a) and (b) are true
B. both (a) and (b) are false
c. (a) is true but (b) is false
D. (a) is false but (b) is true


Which of the following compounds will given racemic mixture on nucleophilic
substitution by \( O H^{\ominus} \) ion?
(a) \( \boldsymbol{C H}_{3}-\boldsymbol{C H}-\boldsymbol{B r} \)
\( \boldsymbol{C}_{2} \boldsymbol{H}_{5} \)
\( \boldsymbol{1} \)
\( \boldsymbol{B} \)
(b) \( \boldsymbol{C H}_{3}-\underset{C_{2} \boldsymbol{H}_{5}}{\boldsymbol{C}}-\boldsymbol{C H}_{3} \)
(c) \( \boldsymbol{C H}_{3}-\underset{\boldsymbol{C}_{2} \boldsymbol{H}_{5}}{\boldsymbol{C} \boldsymbol{H}}-\boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{B} \boldsymbol{r} \)
в. \( (a),(b),(c) \)
c. \( (b),(c) \)
(n)
D. \( (a),(c) \)


Complete the following statements:
(i) Probability of an event \( \mathrm{E}+ \) Probability
of the event not \( \mathrm{E}= \)
(ii) The probability of an event that cannot happen is

Such an
event is called
(iii) The probability of an event that is
certain to happen is

Such an
event is called
(iv) The sum of the probabilities of all
the elementary events of an experiment
is
(v) The probability of an event is greater than or equal to and less than
or equal to


Electric switches and
appliances should be tested only with
A. Right hand
B. Left hand
c. Both hands
D. Electric tester


Two rings have their \( M . I \) in the ratio 2
1, If their diameters are in ratio of 2: 1
then the ratio of their masses will be:
\( \mathbf{A} \cdot 2: 1 \)
B. 1: 1
c. 1: 2
\( \mathbf{D} \cdot 1: 4 \)


Which among the following is the smallest prefix?
A. mill
B. nano
c. fermi
D. deci


If \( x+\frac{1}{x}=7 \) the value of \( x^{4}+\frac{1}{x^{4}} \) is
A .2401
в. 2023
c. 2209
D. 2207


Locate the points representing the complex number z for which
\( \frac{\pi}{3}<\arg z \leq \frac{\pi}{2} \) represents portion of
the first quadrant located between rays emerging from origin at angles of \( \frac{\pi}{3} \) and \( \frac{\pi}{2} . \) If this is true enter 1 , else enter 0


\( f^{n-1} C_{r}=\left(k^{2}-3\right)^{n} C_{r+1}, \) then \( k \)
B. \( [2, \infty) \)
c. \( [-\sqrt{3}, \sqrt{3}] \)
D. \( (\sqrt{3}, 2] \)


Among the following outermost configuration of metals, which shows the highest oxidation state:
A \( \cdot 3 d^{3} 3 s^{2} \)
B . \( 3 d^{5} 4 s^{1} \)
\( \mathbf{c} \cdot 3 d^{5} \mathbf{f} s^{2} \)
D. \( 3 d^{6} 4 s^{2} \)


\( \mathrm{f} \int_{0}^{\pi / 2} \log (\sin \mathrm{x}) \mathrm{d} \mathrm{x}=\mathrm{k} \) then
\( \int_{0}^{\pi / 2} \log (\cos x) d x \)
A \( \cdot \frac{k}{2} \)
B . \( 2 k \)
\( c .-3 k \)
D.


In the chemical reaction \( \boldsymbol{P}+\boldsymbol{Q} \rightarrow \boldsymbol{P} \boldsymbol{Q} \)
if the concentration of \( P \) and \( Q \) are
increased by two fold, the reaction rate:
A. decreases to half
B. increased by two fold
c. increased by eight fold
D. increased by four fold


In IUPAC system, alkynes are named as derivatives of corresponding alkanes by replacing 'ane' by the suffix 'yne'.
A. True
B. False


\( \int_{0}^{5} x^{3}\left(25-x^{2}\right)^{7 / 2} d x \)


Fill in the blank:
is the second nearest
star from the Earth.
A. Pole star
B. Sun
c. Alpha Centauri
D. Alpha Persei


State whether true or false. \( \frac{5}{11} \) is an irrational number.
A. True
B. False


The method to prepare PMA polymer
from methyl acrylate can be given as:
\( A \)
\[
\mathrm{R}-\mathrm{C} \equiv \mathrm{CH} \quad \stackrel{\mathrm{CO}+\mathrm{ROH}}{\longrightarrow}
\]
в.
\[
\mathrm{HC} \equiv \mathrm{CH} \frac{\mathrm{CO}+\mathrm{CH}_{3} \mathrm{OH}}{\mathrm{Ni}(\mathrm{CO})_{4}}
\]
c.
\[
\mathrm{HC} \equiv \mathrm{CH}-\frac{\mathrm{CO}+\mathrm{H}_{2} \mathrm{O}}{\mathrm{Ni}(\mathrm{CO})_{4}}
\]
D. none of these


\( \boldsymbol{C u O}(\boldsymbol{s})+\boldsymbol{H}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{C u}(\boldsymbol{s})+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) \)
In this reaction, is reduced.
A. copper oxide
B. copper
c. hydrogen
D. water


Consider the cell :
\( A g_{(s)} \mid A g C l \) (saturated solution) \( \mid A g N O_{3(a q)} \)
EMF of the above cell is given by:
Given: \( \left(\boldsymbol{K}_{s p} \text { of } \boldsymbol{A} \boldsymbol{g} \boldsymbol{C l}=\mathbf{1 . 0} \times \mathbf{1 0}^{-\mathbf{1 0}} \boldsymbol{M}^{\mathbf{2}}\right) \)
This question has multiple correct options
A \( \cdot E_{c e l l}=0.059 \log \left[K_{s p}(A g C l)\right]^{1 / 2} \)
B. \( E_{c l l}=0.059 \log \frac{1}{\left[K_{s p}(A g C l)\right]^{1 / 2}} \)
c. \( E_{\text {cll}}=0.059 \times 5 V \)
D. \( E_{\text {cll}}=296 \mathrm{mV} \)


Show that the points \( (3,3),(h, 0) \) and
\( (0, k) \) are collinear, if \( \frac{1}{n}+\frac{1}{k}=\frac{1}{3} \)


Carbon monoxide is produced by:
A. incomplete combustion of fuels
B. complete combustion of fuels
C. neutralization of fuels
D. none of these


A light ray is incident on a transparent sphere of index \( =\sqrt{2}, \) at an angle of
incidence \( =45 . \) What is the deviation of
a tiny fraction of the ray, which enters the sphere, undergoes two internal reflections and then refracts out into air
\( ? \)
A . 270
B. 240
\( c . \) 30
D. 180


If the polynomial \( (x+1)^{2015}-x^{2015}-1 \)
is divided by \( \left(x+x^{2}+x^{3}\right) \), then the
remainder is
A. \( x^{2}-x \)
B. \( x^{2}+x \)
c. 1
D.


Int he given figure \( l\|\boldsymbol{m}\| \boldsymbol{n} \). If \( \boldsymbol{x}=\boldsymbol{y} \)
and \( a=b, \) then
\( \mathbf{A} \cdot l \| n \)
B. \( l<n \)
c. \( l>n \)
D. \( D \| n \)


The inequality, \( P(n)=n !>2^{n} \) is true
for
\( \mathbf{A} \cdot n \geq 4 \)
в. \( n>1 \)
c \( . n>2 \)
D. \( \forall n \in N \)


When the bulb of a constant volume
hydrogen thermometer is placed in melting ice, the pressure recorded is \( 80 \mathrm{cm} \mathrm{Hg} \) and when immersed is boiling water, it is \( 113 \mathrm{cm} \) Hg. When the bulb is placed in another boiling liquid, the pressure recorded is
\( 143 \mathrm{cm} \) Hg.What is the boiling point of the liquid?


Aroids store food in
A. Inflorescence
B. Enlarged root
c. Leaf bases
D. Swollen stem


If \( \boldsymbol{y}=\boldsymbol{f}(\boldsymbol{x}) \) satisfies the property \( (\boldsymbol{x}- \)
\( \boldsymbol{y}) \boldsymbol{f}(\boldsymbol{x}+\boldsymbol{y})-(\boldsymbol{x}+\boldsymbol{y}) \boldsymbol{f}(\boldsymbol{x}-\boldsymbol{y})= \)
\( 4 x y\left(x^{2}-y^{2}\right), f(1)=1, \) then the
number of real roots of \( \boldsymbol{f}(\boldsymbol{x})=\mathbf{4} \) will be
A . 1
B . 2
\( c \cdot 3 \)
D.


The sequence of bases on \( \mathrm{m} \) -RNA
molecule synthesized on the
GCATATGGA strand of DNA is
A. cGuAUACCU
в. СGтАТАСст
c. тАсяссятс
D. Атсясятт


Magnification produced by a convex mirror is \( \frac{1}{3}, \) then distance of the object from mirror is
A \( \cdot \frac{f}{3} \)
в. \( \frac{2 f}{3} \)
c. \( 1 f \)
D. \( 2 f \)


Normallly the body temperature of healthy person is

Degree celcius?
A . 25
B. 37
\( c . \) 30
D. 32


State which of the following are equation (with a variable) given reason and tell your answer. identify the variable from the equation with a variable.
\( \mathbf{7}=(\mathbf{1 1} \times \mathbf{2}) \div \boldsymbol{p} \)


If the wavelength of a sound source is
reduced by a factor of \( 2, \) what happens to the waves frequency? What happens to its speed?


Construct a \( 2 \times 3 \) matrix \( A=\left[a_{i j}\right] \)
whose elements are given by \( \boldsymbol{a}_{\boldsymbol{i} j}= \)
\( \mathbf{2}(\boldsymbol{i}-\boldsymbol{j}) \)
В. \( \left[\begin{array}{ccc}0 & -2 & 4 \\ 2 & 0 & -2\end{array}\right] \)
\( \begin{array}{lll}\text { c. } & {\left[\begin{array}{ccc}0 & -2 & -4 \\ 2 & 0 & 2\end{array}\right]} \\ & \text { I }\end{array} \)
D. \( \left[\begin{array}{ccc}0 & -2 & 4 \\ 2 & 0 & 2\end{array}\right] \)


Short / Long answer type questions. Despite the great heterogeneity of representative protistans, are there features that all members share?


\( \operatorname{Let} \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{1} & \frac{\mathbf{3}}{2} \\ \mathbf{1} & \mathbf{2}\end{array}\right], \boldsymbol{B}= \)
\( \left[\begin{array}{cc}\mathbf{4} & -\mathbf{3} \\ -\mathbf{2} & \mathbf{2}\end{array}\right] \) and \( \boldsymbol{C}_{\boldsymbol{r}}= \)
\( \left[\begin{array}{cc}r .3^{r} & 2^{r} \\ 0 & (r-1) 3^{r}\end{array}\right] \) be 3 given matrices.
Compute the value of
\( \sum_{r=1}^{50} t r \cdot\left((A B)^{r} C_{r}\right) .(\text { where } t r .(A) \)
denotes trace of matrix \( \mathbf{A} \) )
\( \mathbf{A} \cdot 3\left(49.3^{50}+1\right) \)
B \( \cdot 3\left(49.3^{49}+1\right) \)
C \( .3\left(49.3^{48}+1\right) \)
D. None of these


Which one of the following can produce maximum induced emf?
A. 50 ampere DC
B. 50 ampere, \( 50 H z \) AC
c. 50 ampere, \( 500 \mathrm{Hz} \) АС
D. 100 ampere DC


The polynomial \( 3 x-2 \) is a.
A. Linear polynomial
B. Quadratic polynomial
c. Cubic polynomial
D. constant polynomial


Which of the following is correct
regarding the chemical symbol \( \boldsymbol{A} \boldsymbol{r} \)
A. One mole of argon
B. One atom of argon
c. Both a mole or an atom of argon
D. Neither a mole or an atom of argon
E. One molecule of argon


During evaporation, the entropy of
system:
A. increases
B. decreases
c. remains constant
D. none of these


The Balmer series of hydrogen spectra
lies in:
A. visible region spectra
B. ultra violet spectra
c. infrared region spectra
D. \( \gamma \) -rays spectra


IF \( P(A)=\frac{1}{3}, P(B)=\frac{1}{12} \) and \( P(A r \)
\( B)=\frac{1}{36}, \) are the events \( A \) and \( B \) independent?


Two identical sound waves each of
loudness \( \beta \) interfere constructively at a
point to produce a sound level of
\( \mathbf{A} \cdot 6 \beta \)
B. \( 3 \beta \)
\( \mathbf{c} \cdot \beta+3 \)
\( \mathbf{D} \cdot \beta+6 \)


If the \( p^{t h}, q^{t h} \) and \( r^{t h} \) terms of an A.P. are
\( P, Q, R \) respectively, then \( P(q-r)+ \)
\( Q(r-p)+R(p-q) \) equals
A.
B.
c. par
D. p \( + \) ar


When an object is heated it..............and
when it cools it.


Find the centre of mass of the letter \( F \)
which cut from a uniform metal sheet
from point \( \mathbf{A} \)
A . \( 15 / 7,33 / 7 \)
B. 15/7, 23/7
c. 22/7, 33/7
D. 33/7, 22/7


The correct relation between elevation
of boiling point and molar mass of
solute is:
A \( \ldots_{M_{2}}=\frac{K_{b} \times W_{2}}{\Delta T_{b} \times W_{1}} \)
В. \( M_{2}=\frac{K_{b} \times W_{1}}{\Delta T_{b} \times W_{2}} \)
\( ^{\mathrm{C}} \cdot_{M_{2}}=\frac{\Delta T_{b} \times K_{b}}{W_{1} \times W_{2}} \)
D. \( M_{2}=\frac{\Delta T_{b} \times W_{1}}{K_{b} \times W_{2}} \)


If \( \alpha \) and \( \beta \) are angles in the first quadrant \( \tan \alpha=\frac{1}{7}, \sin \beta=\frac{1}{\sqrt{10}} \) then
using the formula \( \sin (A+B)= \)
\( \sin A \cos B+\cos A \sin B \) one can find
the value of \( (\boldsymbol{\alpha}+\mathbf{2} \boldsymbol{\beta}) \) to be
A \( \cdot 0^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 60 \)
D. \( 90^{\circ} \)


The suffix- 'oideae' is used for
A. Tribe
B. Family
c. class
D. Subfamily


\( 45^{0} \) in radians is \( \left(\frac{\pi}{2}\right)^{c} \)
If true then enter 1 and if false then
write 0


Due to a force of \( (6 \hat{i}+2 \hat{j}) \mathrm{N} \) the displacement of a body is \( (3 \hat{i}-\hat{j}) m \)
then the work done is?
A . 16
в. 12
\( c .8 \)
D. zero


The most abundant protein is
A. Rubisco
B. Haemoglobin
C. Ferredoxin
D. cytochrome


Common origin of man and chimpanzee is best shown by
A. Dental formula
B. Cranial capacity
c. Binocular vision
D. chromosome number


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


A neutral atom of an element with nuclear charge 11 times and mass 23 times that of hydrogen. Find the ratio of
electrons to protons present in its stable ion.
A . 1:
B. 5: 6
c. 10: 1
D. 12:11


The van't Hoff's factor for \( 0.1 \mathrm{M} \)
\( B a\left(N O_{3}\right)_{2} \) solution is \( 2.74 . \) The degree of dissociation is:
A . \( 91.3 \% \)
B. 87\%
c. \( 100 \% \)
D. 74\%


Fusion reaction takes place at about:
A \( \cdot 3 \times 10^{2} K \)
В. \( 3 \times 10^{3} K \)
c. \( 3 \times 10^{4} K \)
D. \( 3 \times 10^{6} K \)


The equation of a progressive wave is given by \( \boldsymbol{y}=\mathbf{1 0} \sin (\mathbf{5} \boldsymbol{t}-\boldsymbol{x}) . \) The wave
gets reflected from a open boundary The equation of the reflected wave is
A \( . y=10 \sin (5 t-x) \)
B. \( y=-10 \sin (5 t-x) \)
c. \( y=10 \sin (5 t+x) \)
D. \( y=10 \sin (5 t+x+\pi) \)


Solve: \( 8 x-3 \leq 2 x+6 \)


Find the distance between
\( (x+3, x-3) \) from the origin.


Fluid friction depends on
A. speed of the object
B. shape of the object
c. nature of fluid
D. all of the above


What are the conditions for an ideal
solution which obeys Raoult's law over
the entire range of concentration?
A \( \cdot \Delta_{m i x} H=0, \Delta_{m i x} V=0, P_{\text {Total}}=p_{A}^{o} x_{A}+p_{B}^{o} x_{B} \)
B. \( \Delta_{\operatorname{mix}} H=+v e, \Delta_{\operatorname{mix}} V=0, P_{\text {Total}}=p_{A}^{o} x_{A}+p_{B}^{o} x_{B} \)
C. \( \Delta_{\operatorname{mix}} H=0, \Delta_{\operatorname{mix}} V=+v e, P_{\text {Total}}=p_{A}^{\circ} x_{A}+p_{B}^{o} x_{B} \)
D. \( \Delta_{\text {mix}} H=0, \Delta_{\text {mix}} V=0, P_{\text {Total}}=p_{B}^{o} x_{B} \)


The meniscus of a liquid contained in one of the limbs of a narrow U-tube is
held electromagnet with the meniscus in line with the field. The liquid is seen to rise. This indicates that the liquid is
A. anti-ferromagneticç
B. paramagnetic
c. diamagnetic
D. non-magnetic


The velocity of a body at time \( t=0 \) is in the north-east direction and it is
moving with and acceleration of \( 2 m / s \)
directed towards the south, The
magnitude and direction of the velocity of the body after 5 sec will be.


A ray of light is incident on the hypotenuse of a right-angled prism after travelling parallel to the base
inside the prism. If \( \mu \) is the refractive
index of the material of the prism, the maximum value of the base angle for which light is totally reflected from the hypotenuse is:
A \( \cdot \sin ^{-1}\left(\frac{1}{\mu}\right) \)
B. \( \tan ^{-1}\left(\frac{1}{\mu}\right) \)
c. \( \sin ^{-1}\left(\frac{\mu-1}{\mu}\right) \)
D \( \cdot \cos ^{-1}\left(\frac{1}{\mu}\right) \)


Name the carbonate which is not
decomposed by heating? This question has multiple correct options
A. Sodium carbonate
B. Potassium carbonate
c. Magnesium carbonate
D. None of these


A potential difference \( V \) is applied to a
copper wire of length \( l \) and thickness \( d \)
If \( V \) is doubled, the drift velocity:
A. Is doubled
B. Is halved
c. Remain same
D. Becomes zero


Name the octants in which the following
points lie:
\( (1,2,3),(4,-2,3)(4,-2,-5),(4,2,-5) \)


When propyne is treated with aqueous sulphuric acid in presence of mercuric sulphate, the major product is
A. propanal
B. propyl hydrogen sulphate
c. propanol
D. propanone


Which is not the green house gas among the following?
A. Chlorofluorocarbons
B. Argon
c. water vapour
D. Carbon-dioxide


The commercial production of water gas utilize the reaction under standard conditions:
\[
\begin{array}{r}
\boldsymbol{C}+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \longrightarrow \\
\boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{C O}
\end{array}
\]
The heat required for this endothermic reaction may be supplied by adding a limited amount of air and burning some
carbon to \( C O_{2} . \) How many g of carbon
must be burnt to \( C O_{2} \) to provide enough heat for the water-gas conversion of 100 g carbon?
Neglect all heat losses to the
environment.Also \( \Delta_{f} H^{\circ} \) of \( \mathrm{CO}, H_{2} O(g) \)
and \( C O_{2} \) are -110.53,241.81 and -393.51
kJ/mol respectively.
A . \( 33.4 g \)
в. \( 66.72 g \)
c. \( 15.18 g \)
D. None of these


The correct order of increasing bond length of \( \mathrm{C}-\mathrm{H}, \mathrm{C}-\mathrm{O}, \mathrm{C}-\mathrm{C} \) and \( \mathrm{C}=\mathrm{C} \) is :
A. C-H<C-O<C-C<C=C
B. C-H<C=C<C-O<C-C
c. \( c-c<c=c<c-0<c-H \)
D. C-O<C-H<C-C<C=C


Consider the following statements in respect of the function \( f(x)=x^{3}- \)
\( \mathbf{1}, \quad \boldsymbol{x} \boldsymbol{\epsilon}[-\mathbf{1}, \mathbf{1}] \)
\( f(x) \) is increasing in [-1,1]
\( f^{\prime}(x) \) has no root in (-1,1) Which of the statements given above is/ are correct?
A. Onlyı
B. Only II
c. Both I and II
D. Neither I nor II


What are Damped vibrations?


\( \boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{S}+\boldsymbol{N} \boldsymbol{a} \boldsymbol{C} \boldsymbol{N}+\boldsymbol{Z} \boldsymbol{n} \longrightarrow \boldsymbol{A} \boldsymbol{g} \)
This method of extraction of Ag by
complex formation and then its displacement is called
A. Parke's method
B. Mac Arthur- Forrest method
c. Serpeck method
D. Hall's method


Purines possess nitrogen at which
position?
A. 1,2,4 and 6 position
B. 1, 3, 5 and 7 position
c. 1,3,7 and 9 position
D. 1,2,6 and 8 position


The complete range of values of \( ^{\prime} a^{\prime} \) such that \( \left(\frac{1}{2}\right)^{|x|}=x^{2}-a \) is satisfied for maximum number of values of \( \boldsymbol{x} \) is
B \( \cdot(-\infty, \infty) \)
c. (-1,1)
D. \( (-1, \infty) \)


The substance used to reduce iron ore
to iron in the lower part of the blast furnace is:
A. coke
B. charcoal
c. carbon monoxide
D. carbon black


If \( \mu_{s}, \mu_{k} \) and \( \mu_{r} \) are coefficient of static
friction, sliding friction and rolling friction, then
A \( \cdot \mu_{s}<\mu_{k}<\mu_{r} \)
B . \( \mu_{k}<\mu_{r}<\mu_{s} \)
c. \( \mu_{r}<\mu_{k}<\mu_{s} \)
D. \( \mu_{r}=\mu_{k}=\mu_{s} \)


The image of a square hole in a screen illuminated by light is obtained on another screen with the help of a converging lens. The distance of the
hole from the lens is \( 40 \mathrm{cm} \). If the area
of the image is nine times that of the
hole, the focal length of the lens is :
\( \mathbf{A} \cdot 30 \mathrm{cm} \)
B. \( 50 \mathrm{cm} \)
c. \( 60 \mathrm{cm} \)
D. \( 75 \mathrm{cm} \)


Name the parts labelled \( A, B, C \) and \( D \)
A. A: Kidney, B: Urinary Bladder, C: Urethra, D: Ureter
C. A: Kidney, B: Urethra, C: Collecting duct, D: Anus
D. A: Kidney, B: Seminiferous tubules, C: Uterus, D: Ureter


Ureotelic organisms like mammals
excrete urea in their urine, that is
formed in
A . spleen
B. kidney
c. liver
D. gall bladder


How many cubic metres of earth must
be dug to make a well 14 metres deep and 4 metres in diameter?


Evaluate:
\( \int_{0}^{1} \frac{d x}{1+x^{2}} \)


The function \( f(x)=x^{9}+3 x^{7}+64 \) is
increasing on
A. \( R \)
в. \( (-\infty, 0) \)
\( c \cdot(0, \infty) \)
D. \( R_{0} \)


The following distribution gives the
state-wise teacher-student ratio in
higher secondary schools of India. Find
the mode and mean of this data.
Interpret, the two measures.
\( \begin{array}{llll}\text { Number } & & \text { Number } & \\ \text { of } & \text { Number } & \text { of } & \text { Numb } \\ \text { students } & \text { of } & \text { students } & \text { of } \\ \text { per } & \text { States/U.T } & \text { per } & \text { states } \\ \text { teacher } & & \text { Teacher } & \\ \text { 15-20 } & 3 & \text { 35-40 } & 3 \\ \text { 20-25 } & 8 & 40-45 & 0 \\ \text { 25-30 } & 9 & \text { 45-50 } & 0 \\ \text { 30-35 } & 10 & \text { 50-55 } & 2\end{array} \)


We chew the food with the
A . Teeth
B. Tongue
c. Mouth
D. None of the above


Assertion: Alkyl halides are polar in
nature, but they are almost insoluble in
water

Reason: They can neither form Hydrogen bond nor they can break hydrogen bond between water molecules.
A. Both Assertion and Reason are true and Reason is the correct explanation to Assertion
B. Both Assertion and Reason are true and Reason is not the correct explanation to Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true


An organic compound contains \( \boldsymbol{C}, \boldsymbol{H} \) and 0.0 .3 g of this compound on combustion yielded 0.44 g of \( C O_{2} \) and 0.18 g of \( H_{2} O . \) If the weight of 1 mole of compound is \( 60, \) then the molecular formula is :
A. \( C_{2} H_{4} O_{2} \)
в. \( C_{4} H_{6} O_{2} \)
c. \( C_{2} H_{6} \) 0
D. \( C_{2} H_{4} O \)


The cyton of reflex in central nervous
system and autonomal nervous system
is
A. Sensory
B. Mixed
c. Motor
D. All of the above


The density of liquid mercury is \( 13.6 g c m^{-3} . \) How many moles of
mercury are there in 1 litre of the metal?
(Atomic mass of \( \boldsymbol{H} \boldsymbol{g}=\mathbf{2 0 0} \) )


Ecosystem has
A. Plant and animal
B. Air and \( H_{2} O \)
C. Soil and light
D. Biotic and abiotic component


In which ratio does the \( Y Z \) plane divide
the line joining the points (-2,4,7) and (3,-5,8)


The kinetic energies of a planet in an elliptical orbit about the Sun, at
positions \( A, B \) and \( C \) are \( K_{A}, K_{B} \) and
\( K_{C} \) respectively. \( A C \) is the major axis and \( S B \) is perpendicular to \( A C \) at the position of the Sun \( S \) as shown in the
figure. Then.
A \( \cdot K_{B}<K_{A}<K_{C} \)
B. \( K_{A}<K_{B}<K_{C} \)
с. \( K_{B}>K_{A}>K_{C} \)
D. \( K_{A}>K_{B}>K_{C} \)


Which of the following does not contain
silicon?
A. Kaoline
B. Agate
c. Ruby
D. Quartz


dipole moment?
\( \mathbf{A} \)
B.
\( c \)
D.


White phosphorus reacts with caustic
soda. The products are \( P H_{3} \) and
\( N a H_{2} P O_{2} . \) This reaction is an example
of
A. oxidation
B. reduction
c. neutralization
D. disproportionation


Out of \( N H_{3}, P H_{3} \) and \( A s H_{3} \) boiling
point of \( N H_{3} \) is maximum and that of
\( P H_{3} \) is minimum.
If true enter 1 , else enter 0
\( A \)


The ratio of speed of electron in ground state of hydrogen atom to that of light is
A \( \cdot \frac{1}{137} \)
в. \( \frac{1}{207} \)
c. \( \frac{2}{237} \)
D. \( \frac{1}{237} \)


Three capacitors of capacitances \( 2 \mathrm{pF}, 3 \) pF and 4 pF are connected in parallel.
(a) What is the total capacitance of the
combination?
(b) Determine the charge on each
capacitor if the combination
is connected to a \( 100 \mathrm{V} \) supply.


A person presses the earth least where
he is :
A. Sitting
B. Standing
c. Running
D. Lying on the ground


The potential gradients on the
potentiometer wire are \( V_{1} \) and \( V_{2} \) with
an ideal cell and a real cell of same emf
in the primary circuit then
A. \( V_{1}=V_{2} \)
в. \( V_{1}>V_{2} \)
c. \( V_{1}<V_{2} \)
D. \( V_{1} \leq V_{2} \)


If \( f(x)=\lim _{n \rightarrow \infty}\left[2 x+4 x^{3}+\dots \dots+\right. \)
\( \left.2 n x^{2 n-1}\right](0<x<1) \) then \( \int f(x) d x \) is
equal to
A. \( -\sqrt{1-x^{2}}+ \) constant
в. \( \frac{1}{\sqrt{1-x^{2}}}+ \) constant
c. \( \frac{1}{x^{2}-1}+ \) constant
D. \( \frac{1}{1-x^{2}}+ \) constant


\( Z n+H_{2} S O_{4} \rightarrow A \)
If we bring a burning splinter near the gas produced in the given reaction,it burns with a pop sound. The gas \( A \) is:
\( A \cdot O_{2} \)
в. \( N_{2} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \)
D. \( C O_{2} \)


Which is the final main product of the following reaction of trans-1,2-
dibromocyclohexane?
\( A \)
B.
\( c \)
D.


Resultant of two vectors \( \vec{P} \) and \( \vec{Q} \) is
inclined at \( 45^{\circ} \) to either of them. What
is the magnitude of the resultant?
\( \mathbf{A} \cdot \sqrt{P^{2}+Q^{2}} \)
B . \( \sqrt{P^{2}-Q^{2}} \)
\( c \cdot P+Q \)
D. \( P-Q \)


\( \frac{\cos 15^{\circ}-\sin 15^{\circ}}{\cos 15^{\circ}+\sin 15^{\circ}}=\frac{1}{\sqrt{3}} \)


Ozone layer of upper atmosphere is being destroyed by
A. chlorofluorocarbon
в. \( S O_{2} \)
c. Photochemical oxidants/O \( _{2} \) and \( C O_{2} \)
D. Smog


Cow milk, an example of neutral emulsion is stabilized by:
A . fat
B. water
c. casein
D. \( M g^{2+} \) ions


Rutherford's model was not able to
explain:
A. Rebounding of alpha particles
B. Deflection of aplha particles
c. concentration of positive charge at centre
D. Line spectra of Atom


Electricity can be obtained by oxidation-reduction reaction in voltaic
cell.
A. True
B. False


Find \( \frac{d y}{d x} \) while:
\( \boldsymbol{x}^{\boldsymbol{y}}+\boldsymbol{y}^{\boldsymbol{x}}=\boldsymbol{a}^{\boldsymbol{b}} \)


Ethylamine dissolves in water due to intermolecular H-bonding. If this is true enter 1 , if false enter 0 .


\( 150 g \) of ice is mixed with \( 100 g \) of water
at temperature \( 80^{\circ} \mathrm{C} \). The latent heal of
ice is 80 cal \( / g \) and the specific heat of
water is 1 cal \( / g^{\circ} \) C. Assuming no heat loss to the environment, the amount of
ice which does not melt is :
A. \( 100 g \)
в. \( 0 g \)
c. \( 150 g \)
D. \( 50 g \)


Integrate the function \( \frac{x+2}{\sqrt{x^{2}-1}} \)


A shotput is a metallic sphere of radius \( 4.9 \mathrm{cm} . \) If the density of the metal is 7.8
g. per \( \mathrm{cm}^{3} \), find the mass of the shotput.


The electronic configuration of an element is \( 1 s^{2}, 2 s^{2}, 2 p^{6}, 3 s^{2} 3 p^{3} . \) what is
the atomic number (X) of the element
which is just below the above given element in the periodic table. find the
value of \( \boldsymbol{X} \)


Two particle \( A \) and \( B \) move anticlockwise with the same speed v in a circle of radius \( \mathrm{R} \) and are
diamertrically opposite to each other at \( t=0, A t \) this instant


Describe the process of respiration in the following parts of a plant.
Leaves.


topp
\( Q \)
more steeply for positive \( V \) than at higher temperatures, and at successively higher temperatures the asymmetry in the curve becomes less and less pronounced. The current - - voltage relation for a source may also be represented graphically. For a source represented by \( \boldsymbol{V}_{a b}=\boldsymbol{E}-\boldsymbol{I} \boldsymbol{r}, \) that is, \( \boldsymbol{V}=\boldsymbol{E}-\boldsymbol{I} r, \) The
graph appears in Figure (b). The ntercept on the \( V \) -axis, corresponding to the open circuit condition \( (\boldsymbol{I}=\mathbf{0}) \), is
at \( V=E \), and the intercept on the \( I \) -
axis, corresponding to a short-circuit situation \( (V=0), \) is at \( I=\frac{E}{r} \)
This relation may be used to find the current in a circuit containing a non linear device, as in fig (c). Its current voltage relation is shown in fig \( (d) \) and terminal voltage \( V=E-I r \) is also
plotted on this graph, each curve represents a current-voltage relation that must be satisfied, so the
ntersection represents the only possible values of \( V \) and \( I \). This amounts to a graphical solution of two simultaneous equation of \( V \) and \( I \), one of which is nonlinear.

When a device has a nonlinear voltage\( V \)
current relation, the quantity \( \frac{-}{I} \) is not constant. This ratio may still be called resistance, but now it varies with current; it is constant only for a device obeying Ohm's law. Often a more useful quantity is \( \frac{d V}{d I}, \) which expresses the relation between a small change in current and the resulting voltage change. This is called dynamic or incremental resistance. Which of the following vacuum tube devices shows negative resistance?
4. Diod


The curve \( 5 x^{2}+12 x y-22 x-12 y- \)
\( \mathbf{1 9}=\mathbf{0} \) is.
A . Ellipse
B. Parabola
c. Hyperbola
D. Parallel straight lines


Show that the four points \( A, B, C, D \) with position vectors \( \vec{a}, \vec{b}, \vec{c}, \vec{d} \) respectively such that \( 3 \vec{a}-2 \vec{b}+5 \vec{c}-6 \vec{d}=\overrightarrow{0}, \) are
coplanar. Also find the position vector of the point of intersection of the line
segments \( A C \) and \( B D \)


When white light enters a prism, its gets splits into its constituent colours. This is because of
A. high density of prism material
B. \( \mu, \) which is different for different wavelengths
c. diffraction of light
D. interference of light


Fill in the blanks:
¡. \( \quad \) taste is a
characteristic property of all acids in
aqueous solution.
ii. Acids react with some metals to
produce
iii. Because aqueous acid solutions conduct electricity, they are identified
as
iv. Acids react with bases to produce a
and water.
v. Acids turn
different colours.


Which of the following has the highest
electronegativity?
A. \( C \)
в. \( M g \)
\( c \cdot O \)
D. \( S \)


Choose the correct alternatives.
This question has multiple correct options
A. For a general rotational motion, angular momentum \( L \) and angular velocity \( \omega \) need not be parallel
B. For a rotational motion about a fixed axis, angular momentum \( L \) and angular velocity \( \omega \) are always parallel
C. For a general translational motion, momentum \( p \) and velocity \( v \) are always parallel
D. For a general translational motion, acceleration \( a \) and velocity \( v \) are always parallel


Match the corresponding entries of
column-I with column-II


Class sporozoa of phylum protozoa is characterised by
A. Flagella
B. cilia
c. Parasitism
D. None of the above


If \( 10^{2 y}=25, \) then \( 10^{-y} \) equals to
A. \( -\frac{1}{5} \)
в. \( \frac{1}{50} \)
c. \( \frac{1}{625} \)
D. \( \frac{1}{5} \)


\( \frac{1}{2}-\frac{1}{2.2^{2}}+\frac{1}{3.2^{3}}+\ldots \ldots= \)
A \( \cdot \)
\[
\begin{array}{l}\text { B } \cdot \frac{1}{2} \log _{2}\left(\frac{3}{2}\right) \\ \text { c. } \log _{e}\left(\frac{2}{3}\right) \\ \text { D } \cdot \frac{1}{2} \log _{e}\left(\frac{2}{3}\right)\end{array}
\]


Let \( T_{r} \) be the rth term of an A.P.
whose first term is \( a \), and common
difference is \( d \). If for some positive integers \( \boldsymbol{m}, \boldsymbol{n}, \boldsymbol{T}_{\boldsymbol{m}}=\frac{\mathbf{1}}{\boldsymbol{n}} \) and \( \boldsymbol{T}_{\boldsymbol{n}}=\frac{\mathbf{1}}{\boldsymbol{m}} \)
then \( \boldsymbol{a}-\boldsymbol{d}= \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( \frac{1}{m}+\frac{1}{n} \)
c. \( \frac{1}{m n} \)
D.


Assertion
Alcohols are dehydrated to hydrocarbons in the presence of acidic
zeolites.
Reason
Zeolites are microporous catalysts.
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 ball of mass \( 100 g \) is thrown with a
speed of \( 15 \mathrm{m} / \mathrm{s} \). Calculate its kinetic
energy.


ff \( \left[\begin{array}{cc}\boldsymbol{x} & \mathbf{2} \\ \mathbf{1 8} & \boldsymbol{x}\end{array}\right]=\left[\begin{array}{cc}\mathbf{6} & \mathbf{2} \\ \mathbf{1 8} & \mathbf{6}\end{array}\right] \) then \( \mathbf{x}= \)
\( A \cdot \pm 6 \)
B. 6
\( c .-5 \)
D.


An LCR series circuit with \( 100 \Omega \)
resistance is connected to an ac source
of \( 200 \mathrm{V} \) and of frequency of \( 300 \mathrm{rad} / \mathrm{s} \) When only the capacitance is removed, the current lags behind the voltage by
\( 60^{0} . \) When only the inductance is
removed, the current leads the voltage
by \( 60^{0} \) the current through the circuit is:
\( A \cdot 1 A \)
B. 2 A
\( c \cdot 3 A \)
D. \( 4 \mathrm{A} \)


The relation between frequency \( (n) \) and
wavelength \( (\lambda) \) of a sound wave is given
by
\( (v \text { is velocity, } n \text { is frequency and } T \) is time-period)
A \( . v=n \lambda \)
В. \( n=-v \lambda \)
c. \( v=\frac{n}{2 \lambda} \)
D. \( n=\frac{T}{\lambda} \)


When an unpolarized light of intensity
\( I_{0} \) is incident on a polarizing sheet, the intensity of the light which does not get transmitted, is :
A . zero
В. \( I_{0} \)
c. \( \frac{I_{0}}{2} \)
D. \( \frac{I_{0}}{4} \)


If there are no heat losses to the
surroundings, the quantity of heat gained by the cold body is equal to the quantity of heat lost by the hot body.
A. True
B. False


If a selected student has been found to
pass the examination then find out the
probability that he is the only student to have passed the examination.
\( ^{\mathbf{A}} \cdot_{P\left(E_{1} / A\right)}=\frac{4}{[n(2 n+1)]^{2}} \)
в. \( \quad P\left(E_{1} / A\right)=\frac{2}{[n(2 n+1)]^{2}} \)
\( ^{\mathrm{c}} P\left(E_{1} / A\right)=\frac{4}{[n(n+1)]^{2}} \)
D. \( \quad P\left(E_{1} / A\right)=\frac{2}{[n(n+1)]^{2}} \)


Explain why phenolphthalein is used as an indicator in acid-base titration


Which equation represents the line that
passes through the point (2,1) and is parallel to the \( x \) -axis?
A. \( y=2 \)
B. \( y=1 \)
\( \mathbf{c} \cdot x=1 \)
D. \( x=2 \)


If \( \boldsymbol{A}=\mathbf{1} \hat{\mathbf{1}}+\mathbf{2} \hat{\boldsymbol{j}}-\boldsymbol{R} \) and \( \hat{\boldsymbol{B}}=\mathbf{3} \hat{\mathbf{1}}+\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \)
then
Find unit vector along \( \overrightarrow{\boldsymbol{A}} \)
A. \( \vec{A}+\vec{B} \)
В \( \cdot|\vec{A}+\vec{B}| \)
C . Unit vector along the direction of \( |\hat{A}+\hat{B}| \)
D. None of the above


Write the suitable quantifier for all
values of \( x \) there is no real number such
that \( x^{2}+2 x+2=0 \)
A. Universal quantifier (\forall)
B. Existential quantifier
c. Both
D. None


Let \( \boldsymbol{y}=\boldsymbol{f}(\boldsymbol{x}) \) be a differentiable curve
satisfying \( \int_{2}^{x} f(t) d t+2=\frac{x^{2}}{2}+\int_{x}^{2} t^{2} f(t) d t, \) then
\( \int_{-\pi / 4}^{\pi / 4} \frac{\boldsymbol{f}(\boldsymbol{x})+\boldsymbol{x}^{9}-\boldsymbol{x}^{3}+\boldsymbol{x}+\mathbf{1}}{\cos ^{2} \boldsymbol{x}} \boldsymbol{d} \boldsymbol{x} \)
equals-
A . 0
B.
\( c \cdot 2 \)
\( D \)


A coin is tossed 150 times and the
outcomes are recorded. The frequency distribution of the outcomes \( H \) (i.e.,
head) and \( T \) (i.e., tail) is given below :
Outcome
\[
\begin{array}{ll}
\boldsymbol{H} & \boldsymbol{T} \\
& \\
85 & 65
\end{array}
\]
Frequency
Find the value of \( P(H) \), i.e., probability of
getting a head in a single trial.
\( \mathbf{A} \cdot P(H)=0.769(\text { approx }) \)
B . \( P(H)=0.663 \) (approx)
\( \mathbf{c} \cdot P(H)=0.567(\text { approx }) \)
D. None of these


How far from the midpoint of the stick
is the center of mass of the stick-puck
combination after the collision?
A. \( l \) \( \overline{2} \)
B. \( \frac{l}{3} \)
c. \( \frac{l}{4} \)
D. None of these


Write the equations for the reactions taking place at anode and cathode in lead storage cell.


The atomic number of elements of first
transition series lie in the range of:
A. 19 to 28
B. 20 to 29
\( c .21 \) to 30
D. 22 to 31


Choose the correct statement or
statements:

This question has multiple correct options
A. every scalar matrix is an identity matrix
B. every identity matrix is a scalar matrix
C. transpose of transpose of a matrix gives the matrix ¡tself
D. for every square matrix A there exists another matrix B such that \( A B=I=B A \)


The bending of light as it passes from one medium into another is commonly known as
A . Reflection
B. Refraction
c. scattering
D. Dispersion


Climate of the world is threatened by
A . Increasing amount of atmospheric \( \mathrm{CO}_{2} \)
B. Decreasing amount of atmospheric \( C O_{2} \)
c. Increasing concentration of atmospheric \( O_{2} \)
D. Decreasing amount of atmospheric \( O_{2} \)


A bus is moving on a straight road towards North with a uniform speed of
\( \mathbf{5 0} \mathrm{km} / \mathrm{h} . \) If the speed remains
unchanged after turning through \( 90^{\circ} \)
the increase in the velocity of the bus in the turning process is?


Which of the following is chloroprene?
\( \mathbf{A} \cdot C H_{2}=C H-C H=C H_{2} \)
B.
\[
\begin{array}{c}
C H_{2}=C-C H=C H_{2} \\
C_{1}
\end{array}
\]
\( c \)
\[
C H_{3}-C=C=C H_{2}
\]
\[
C l
\]
D.
\[
C H_{3}-C=C H_{2}-C H_{3}
\]
\( C \)


If the ratio of base radius and height of a cone is 1: 2 and percentage error in radius is \( \lambda \%, \) then the error in its volume is
A . \( \lambda \% \)
B . 2\lambda\%
c. \( 3 \lambda \% \)
D. none of these


Find the equation of the set of points \( \boldsymbol{P} \)
the sum of whose distances from
\( A(4,0,0) \) and \( B(-4,0,0) \) is equal to 10


What will be the unit digit of \( 98765^{3} \)
\( \mathbf{A} \cdot \mathbf{5} \)
B. 0
\( c \cdot 2 \)
D. 3


An ebonite rod rubbed with fur and a
glass rod rubbed with silk cloth are brought nearer to each other. Then:
A. they will attract each other
B. they will repel each other
C. nothing will happen to them,
D. they will get heated up


Find the value of \( x \) and \( y \)
A \( \cdot x=10^{\circ}, y=7 \)
B . \( x=18^{\circ}, y=5 \)
\( \mathbf{C} \cdot x=9^{o}, y=6 \)
D. \( x=7^{\circ}, y=6 \)


Many persons like to use asthma as an excuse for not being able to do well in sports. Try telling them about Down
Fraser, who was the first women to
break 60 sec in 100 m freestyle swimming. The first women to win four Olympic gold medals and the first swimmer to win the same event in three
consecutive Olympics was asthmatic. On the basis of the above passage,
answer the following question.
i) Describe her achievements in the
field of swimming.


What are acetals and hemiacetals?


A system undergoes a cyclic process in
which it absorbs \( Q_{1} \) heat and gives out
\( Q_{2} \) heat. The efficiency of the process is
\( \eta \) and the work done is \( W \)
This question has multiple correct options
A \( . W=Q_{1}-Q_{2} \)
в. \( \eta=\frac{W}{Q_{1}} \)
c. \( \eta=\frac{Q_{2}}{Q_{1}} \)
D. \( \eta=1-\frac{Q_{2}}{Q_{1}} \)


If \( A \) and \( B \) are events of the same
experiments with \( \boldsymbol{P}(\boldsymbol{A})=\mathbf{0 . 2}, \boldsymbol{P}(\boldsymbol{B})= \)
0.5, then find the maximum value of
\( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B}) \)


\( 2 g m \) of radio active element undergoes
\( 3.7 \times 10^{8} \) disintegrations per second.
Its curie value is
A \( .2 g \)
в. \( 0.02 g \)
\( c .200 g \)
D. 3700g


Integrate the function \( \frac{1}{\sqrt{(2-x)^{2}+1}} \)


A contract on construction job specifies a penalty for delay of completion beyond a certain date as follows \( R s 200 \) for the
first day, \( \boldsymbol{R} \boldsymbol{s} \) 250 for the second day
Rs 300 for the third day, etc. the penalty
for each succeeding day being \( R s 50 \)
more than for the preceding day. How much money the contractor has to pay as penalty, if he has delayed the work by
30 days?


Balance the following equations by ion electron method.
\( \boldsymbol{H}_{2} \boldsymbol{S}+\boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \rightarrow \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4}+\boldsymbol{N} \boldsymbol{O}_{2}+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O} \)


Write an expression for the displacement current


A ring takes time \( t_{1} \) and \( t_{2} \) for sliding down and rolling down an inclined plane
of length \( L \) respectively for reaching the
bottom. The ratio of \( t_{1} \) and \( t_{2} \) is
A \( \cdot \sqrt{2}: 1 \)
B. \( 1: \sqrt{2} \)
c. 1: 2
D. 2: 1


\( \mathrm{KE}= \)
\( \mathbf{A} \cdot \operatorname{mgh} \)
\( \mathbf{B} \cdot m v^{2} \)
\( \mathbf{c} \cdot \frac{1}{2} m g h \)
D \( \cdot \frac{1}{2} m v^{2} \)


With the advancement of age, hair of males start thinning due to
A. Falling of hair
B. Low ATP formation
c. Reduced rate of protein synthesis
D. None of the above


Evaluate: \( \boldsymbol{y}=\lim _{\boldsymbol{x} \rightarrow \mathbf{0}}(\sin \boldsymbol{x})^{\tan \boldsymbol{x}} \)


Consider the points \( \boldsymbol{A}(\boldsymbol{a}, \boldsymbol{b}+\boldsymbol{c}) \)
\( B(b, c+a), \) and \( C(c, a+b) \) be the
vertices of \( \triangle \mathrm{ABC} \). The area of \( \triangle \mathrm{ABC} \) is:
A \( \cdot 2\left(a^{2}+b^{2}+c^{2}\right) \)
B . \( a^{2}+b^{2}+c^{2} \)
c. \( 2(a b+b c+c a) \)
D. None of these


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


Two similar holotypes are called
A. Mesotypes
B. Meotypes
c. syntypes
D. Isotypes


The negative Zn pole of Daniel cell,
sending a constant current through a circuit, decreases in mass by 0.13 g in 30 minutes. If the chemical equivalent of Zn and Cu and 32.5 and 31.5 respectively, the increase in the mass of the positive Cu pole in this time is :
A. 0.180 g
B. 0.141g
c. \( 0.126 \mathrm{g} \)
D. 0.242


In Thomsons method, a beam of
electrons accelerated through a p.d. of \( 285 V, \) passes undeflected through
perpendicular electric and magnetic
fields of intensities \( 10^{5} V / m \) and
\( 10^{-2} W b / m^{2} \) respectively. Then the value of e/m of electron is:
A \( \cdot 1.75 \times 10^{11} C / k g \)
В. \( 1.66 \times 10^{11} C / k g \)
c. \( 1.84 \times 10^{11} C / k g \)
D. \( 1.89 \times 10^{11} C / k g \)


Assertion
Current in wire-1 is in the direction as
shown in figure.The bottom wire is fixed.To keep the upper wire stationary current in it should be in opposite direction.
Reason
Under the above condition,equilibrium
of upper wire is stable.
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 sinusoidal voltage \( V=200 \sin 314 t \) is
applied to a \( 10 \Omega \) resistor. Find the peak
voltage
\( \mathbf{A} \cdot 200 V \)
B. \( 400 \mathrm{V} \)
\( \mathbf{c} .600 V \)
D. \( 800 \mathrm{V} \)


Explain \( N a^{+} \) has completely filled \( K \) and \( \boldsymbol{L} \) shells.


Find the value of
\( \tan ^{-1}\left[2 \cos \left(2 \sin ^{-1} \frac{1}{2}\right)\right] \)


If \( D=\left|\begin{array}{cc}3 \sqrt{5} & 6 \\ 5 & m\end{array}\right|=0 \)
Find the value of \( \boldsymbol{m} \)
A . \( \sqrt{5} \)
B. \( 4 \sqrt{5} \)
\( c \cdot \sqrt{3} \)
D. \( 2 \sqrt{5} \)


Three masses are placed on the x-axis:
\( 300 \mathrm{g} \) at origin, \( 500 \mathrm{g} \) at \( \mathrm{x}=40 \mathrm{cm} \) and \( 400 \mathrm{g} \) at \( x=70 \mathrm{cm} . \) The distance of the center of mass from the origin is:
A. \( 45 \mathrm{cm} \)
B. 50cm
c. зост
D. \( 40 \mathrm{cm} \)


Two polarizers have their axes inclined
at \( 45^{\circ} \) to each other. If unpolarized light
of intensity \( I \) is incident on the first
poilarizer, then the intensity of transmitted light through second
polarizer is:
A \( \cdot \frac{I}{4} \)
B. \( \frac{1}{2} \)
c. \( I \)
D.


The Bryophytes are usually found in
A. Damp and Shaded areas
B. Marine habitat
c. sandy soils
D. xeric habitat


Find the distance of the point (-6,0,0)
from the plane \( 2 x-3 y+6 z=2 \)


The compound shown above exibits cis-
trans isomerism. Identify the correct statement(s).
This question has multiple correct options
A. \( C \) is isomer has neither plane of symmetry and nor centre of symmetry
B. \( C \) is isomer has planar symmetry and is optically inactive
C. Trans isomer has centre of symmetry and is optically inactive
D. Trans isomer has no plane of symmetry and is optically inactive


Thermal conductivity of a metal rod depends on:
A. area of cross section
B. temperature gradient
c. time of flow of heat
D. none of these


After black and white photographic film has been developed, unreacted silver bromide is removed by reaction with
sodium thiosulfate.
\( A g B r+2 N a_{2} S_{2} O_{3} \rightarrow 4 N a^{+}+ \)
\( \boldsymbol{B} \boldsymbol{r}^{-}+\left[\boldsymbol{A} \boldsymbol{g}\left(\boldsymbol{S}_{2} \boldsymbol{O}_{3}\right)_{2}\right]^{3-} \)
What is the function of the thiosulfate
ion?
A. To make the silver ions soluble
B. To oxidise the silver ions
c. To reduce the bromine
D. To reduce the silver ions


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


IUPAC name of above compound is:
A. 1,2 - dichlorobenzene
B. m-dichloro benzene
C. 1,6 - dichloro benzene
D. o- dichloro benzene


If \( C_{1}: x^{2}+y^{2}-20 x+64=0 \) and
\( C_{2}: x^{2}+y^{2}+30 x+144=0 . \) Then the
length of the shortest line segment \( \boldsymbol{P Q} \)
which touches \( C_{1} \) at \( P \) and to \( C_{2} \) at \( Q \)
is
A . 10
B. 15
\( c \cdot 22 \)
D. 27


The vestige of the tail is made up of four fused bones. They are known as
A. Sacrum.
в. \( \operatorname{coccy} x \)
c. Sternum.
D. Root.


By simply looking at the pair of angles
given in figure. State which of the angle in the pairs is greater.


Differentiate between the scalar and
vector quantities, giving two examples
of each.


Two magnetic poles each of magnetic pole strength \( 16 A m \) are placed at a distance of \( 2 m \) apart. Find magnetic force acting on each pole.
A \( \cdot 4 \times 10^{-7} N \)
В. \( 16 \times 10^{-7} N \)
c. \( 32 \times 10^{-7} N \)
D. \( 64 \times 10^{-7} N \)


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


The pancreas located just \( \ldots \ldots . . \) the
stomach.
A. Below
B. Upon
c. Right side
D. Left side


Draw the graph of function \( \boldsymbol{f}(\boldsymbol{x})= \)
\( |x| / x . \) Is \( f(x) \) defined at \( x=0 ? \) Does the
limit of \( f(x) \) exist when \( x \rightarrow 0 ? \)


When one litre of a saturated solution of
\( P b C l_{2} \) (molecular weight \( =278 \) g/mol) is evaporated, the residue is found to
weigh 2.78 g. If \( K_{s p} \) of \( P b C l_{2} \) is
represented as \( y \times 10^{-6}, \) then find the
value of \( \boldsymbol{y} \)


In conversion of sucrose to glucose, the
enzyme is:
A. zymase
B. lipase
c. invertase
D. diastase


Electric field intensity is the strength of an electric field at any point which is the electric force per unit
charge experienced by a test charge placed at that point.
A. Greater than
B. Lesser than
c. Equal to
D. None


Expand each of the following, using suitable identities:
\( (x+2 y+4 z)^{2} \)


The A.P. in which \( 8^{t h} \) term is -15 and
\( 9^{t h} \) term is \( -30 . \) Find the sum of the
first 10 numbers.


A man weighing \( 50 k g f \) is standing on a
wooden plank of \( 1 m \times 0.5 m . \) What will
be the pressure exerted by it on the ground.


Find the equations to the straight lines
which pass through the point \( (h, k) \) and
are inclined at an angle \( \tan ^{-1} m \) to the
straight line \( \boldsymbol{y}=\boldsymbol{m} \boldsymbol{x}+\boldsymbol{c} \)


For a cell reaction involving a two-electron change, the standard emf of the cell is found to be \( 0.295 \mathrm{V} \) at \( 25^{\circ} \mathrm{C} \). The
equilibrium constant of the reaction at
\( 25^{\circ} \mathrm{C} \) will be :
A \( \cdot 1 \times 10^{-10} \)
B . \( 29.5 \times 10^{-2} \)
c. 10
D. \( 1 \times 10^{10} \)


Two soap bubbles of radii r and 2r are
connected by a capillary tube-valve
arrangement as shown in the diagram.
The valve is now opened. Then which one
of the following will be the result:
A. The radii of the bubbles will remain unchanged
B. The bubbles will have equal radii
c. The radius of the smaller bubble will increase and that
bigger bubble will decrease
D. Ine radius of the smaller bubble will decrease and that of the bigger bubble will increase


A body of mass \( 15 \mathrm{kg} \) is raised from certain depth. If the work done in
raising it by \( 10 \mathrm{m} \) is \( 1620 \mathrm{J} \), its velocity at this position is
\( \mathbf{A} \cdot 2 m s^{-1} \)
B. \( 4 m s^{-1} \)
\( \mathrm{c} \cdot 1 \mathrm{ms}^{-1} \)
D. \( 8 m s^{-1} \)


Equal weight of \( \boldsymbol{X} \) (At. wt. \( =36 \) ) and \( \boldsymbol{Y} \) (At. wt. \( =24) \) are reacted to form the
compound \( \boldsymbol{X}_{2} \boldsymbol{Y}_{3} . \) Then:
A. \( X \) is the limiting reagent
B. \( Y \) is the limiting reagent
c. no reactant is left over and mass of \( X_{2} Y_{3} \) formed is double the mass of \( X \) taken
D. none of these


What is calcination?


Which of the following can be used as dielectric?
A. Plastics
в. Mica
c. Porcelain
D. All of the above


An n-type and p-type silicon can be obtained by doping pure silicon with:
A. arsenic and phosphorous
B. indium and aluminium
c. phosphorous and indiumm
D. aluminium and boron


A product obtained by mixing caustic soda with vegetable oils is:
A . acid
B. base
c. soap
D. vinegar


The product formed in the reaction is
\( B C l_{3}+H_{2} O \longrightarrow \) Product :
\( \mathbf{A} \cdot H_{3} B O_{3}+H C l \)
в. \( B_{2} O_{3}+ \) НОС\( l \)
c. \( B_{2} H_{6}+H C l \)
D. no reaction


If \( \boldsymbol{x}+\frac{\mathbf{1}}{\boldsymbol{x}}=\boldsymbol{a}+\boldsymbol{b} \) and \( \boldsymbol{x}-\frac{\mathbf{1}}{\boldsymbol{x}}=\boldsymbol{a}-\boldsymbol{b} \)
then, which of the following is correct?
\( \mathbf{A} \cdot a b=1 \)
B. \( a b=2 \)
\( \mathbf{c} \cdot a+b=0 \)
\( \mathbf{D} \cdot a=b \)


Find the 12 rational number between
-1 and \( 2 ? \)


A sonar echo takes \( 4.4 s \) to return from a
submarine. If the speed of sound in
water is \( 1500 m s^{-1}, \) then the distance of submarine from the sonar is:
A \( .1500 m \)
в. \( 3000 m \)
c. \( 3300 m \)
D. 3600m


In the extraction of aluminium by electrolytic process, cryolite is added to
A. lower the melting point of alumina
B. increase the electrical conductivity
c. minimise the anode effect
D. remove impurities from alumina


The atomic number of an element is 21
and the number of neutrons in its atom
is \( 18 . \) Find the mass number of the
element?
A . 40
B. 35
\( c .39 \)
D. 41


Two bodies of masses 50 g and 100 g are taken with water equivalents 10 g and 20 g respectively. Then the values of their specific heat capacities are
\[
\begin{array}{l}
\text { cal } g^{-1} C^{-1} \text {and } \\
\text { cal } g^{-10} C^{-1}
\end{array}
\]
A \( \cdot \frac{1}{5} \) and \( \frac{1}{5} \)
B \cdot \( \frac{1}{3} \) and \( \frac{1}{3} \)
C \( \cdot \frac{11}{5} \) and \( \frac{11}{5} \)
D. \( \frac{1}{2} \) and \( \frac{1}{2} \)


In an experiment a sphere of aluminium
of mass \( 0.20 k g \) is heated upto \( 150^{\circ} C \)
Immediately, it is put into water of
volume \( 150 c c \) at \( 27^{\circ} C \) kept in a
calorimeter of water equivalent of
\( 0.025 k g . \) Final temperature of the
system is \( 40^{\circ} \mathrm{C} \). The specific heat of
aluminium is :
(take 4.2 Joule \( =1 \) calorie)
\( \mathbf{A} \cdot 434 J / k g-^{o} C \)
B . \( 378 J / k g-^{o} C \)
\( \mathbf{c} \cdot 476 J / k g-^{o} C \)
D . \( 315 \mathrm{J} / \mathrm{kg}-^{\circ} \mathrm{C} \)


Value based questions. Give a one-word scientific term for the
following:
Body cavity developed by splitting of mesoderm.


If \( S_{1}, S_{2} \) and \( S_{3} \). are the sums of first \( n \) natural numbers, their squares and
their cubes respectively, then
\( \boldsymbol{S}_{3}\left(\mathbf{1}+\mathbf{8} \boldsymbol{S}_{1}\right)= \)
\( A \cdot S_{2}^{2} \)
в. \( 9 S_{2} \)
\( \mathrm{c} \cdot 9 S_{2}^{2} \)
D. None


At what angle should a body be projected with a velocity \( 24 \frac{m}{s} \) just to
pass over the obstacle \( 14 \mathrm{m} \) high of a distance of \( \left.24 m . \text { (Take } g=10 m / s^{2}\right) \)
\( \mathbf{A} \cdot \tan \theta=3.8 \)
B. \( \tan \theta=1 \)
\( \mathbf{c} \cdot \tan \theta=3.2 \)
D. \( \tan \theta=2 \)


Find the relation between critical angle "C" of a glass prism and its Angle of Prism "A", such that all the rays will reflect back while hitting second surface of prism
A. \( A<2 C \)
в. \( 2 A<C \)
c. \( A>2 C \)
D. \( 2 A>C \)


Copper contains \( 8.4 \times 10^{28} \) free
electrons \( / m^{3} . \) A copper wire of crosssectional area \( 7.4 \times 10^{-7} m^{2} \) carries a
current of 1 A. The electron drift speed is approximately.
A \( \cdot 10^{-8} \mathrm{m} / \mathrm{s} \)
B. \( 10^{3} \mathrm{m} / \mathrm{s} \)
\( c \cdot 1 m / s \)
D. \( 10^{-3} \mathrm{m} / \mathrm{s} \)


One of the satellites of Jupiter has an orbital period of 1.769 days and the radius of the orbit is \( 4.22 \times 10^{8} m \)
Show that the mass of Jupiter is about
one-thousandth that of the sun.


Which of the following alkenes is
least reactive towards anionic
polymerization?
A. \( H_{2} C=C H C H_{3} \)
в. \( H_{2} C=C F_{2} \)
c. \( H_{2} C=C H C N \)
D. \( H_{2} C=C H C_{6} H_{5} \)


Among the following ions which has the highest paramagnetism?
\( \mathbf{A} \cdot\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+} \)
B・ \( \left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+} \)
\( \mathbf{c} \cdot\left[\mathrm{Cu}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+} \)
\( D \cdot\left[z n\left(H_{2} O\right)_{6}\right]^{2+} \)


An alloy which does not contain copper
is:
A. Bronze
B. Magnalium
c. Brass
D. Bell metal


Acid anhydrides on reaction with primary amines gives:
A . amide
B. imide
c. secondary amine
D. imine


If \( \boldsymbol{a} \boldsymbol{x}^{2}+\boldsymbol{2} \boldsymbol{h} \boldsymbol{x} \boldsymbol{y}+\boldsymbol{b} \boldsymbol{y}^{2}+\boldsymbol{2} \boldsymbol{g} \boldsymbol{x}+\boldsymbol{2} \boldsymbol{f} \boldsymbol{y}+ \)
\( c=0 \) represents a pair of parallel lines, then \( \sqrt{\frac{g^{2}-a c}{f^{2}-b c}}= \)
A.
B. \( \sqrt{\frac{a}{b}} \)
\( c \cdot \sqrt{\frac{b}{a}} \)
\( D \cdot \frac{b}{a} \)


The \( C-O-C \) bond angle in dimethyl
ether is:
A \( .111 .7^{\circ} \)
B . \( 108.5^{\circ} \)
\( c \cdot 109^{\circ} \)
D. \( 120^{\circ} \)


Diethyl ether dissociates when it reacts
with:
A . \( N a O H \)
в. \( H_{2} O \)
c. \( H I \)
D. \( K M n O_{4} \)


A capillary tube is immersed vertically
in water and the height of the water
column is \( x \). When this arrangement is
taken into a mine of depth \( d \), the height
of the water column is \( y . \) If \( R \) is the radius of the earth, the ratio \( \frac{x}{y} \) is :
A \( \cdot\left(1-\frac{d}{R}\right) \)
B \( \cdot\left(1-\frac{2 d}{R}\right) \)
c. \( \left(\frac{R-d}{R+d}\right) \)
D. \( \left(\frac{R+d}{R-d}\right) \)


What is the percentage of free carbon in anthracite?
A . 30
B. 60
\( c \cdot 90 \)
D. 95


Show that \( \frac{\log x}{x} \) has a maximum value
at \( \boldsymbol{x}=\boldsymbol{e} \)


Given information is shown marked on
the diagrams as shown,

To prove that \( A C B \) and DFE are congruent by SAS, what additional information is
needed?
\( \mathbf{A} \cdot E F \cong B C \)
B. \( \angle D F E \cong \angle A B C \)
\( \mathbf{c} \cdot D E \cong A B \)
D. \( \angle D F E \cong \angle A C B \)


The average atomic mass of a mixture containing 79 mole percent of \( ^{24} \mathrm{Mg} \) and
remaining 21 mole percent of \( ^{25} \mathrm{Mg} \) and \( ^{26} \mathrm{Mg}, \) is \( 24.31 . \) Mole percent of \( ^{26} \mathrm{Mg} \) is :
A. 5
B. 20
\( c \cdot 10 \)
D. 15


A sewage treatment process in which a portion of the decomposer bacteria present in the waste is recycled in the beginning of the process is called
A. Cyclic treatment
B. Primary treatment
c. Activated sludge treatment
D. Tertiary treatment


Are the triangle shown in Fig
congruent?why?


The correct structural formula of
butanoic acid is


A limbless lizard is
A. Amblyrhynchus
B. ophisaurus
c. Draco
D. Moloch


Two faraday of electricity is passed
through a solution of \( C u S O_{4} \). The mass
of copper deposited at the cathode is :
(at mass of \( \boldsymbol{C u}=\mathbf{6 3 . 5} \boldsymbol{u} \) ).
A. \( 127 g \)
в. \( 0 g \)
c. \( 63.5 g \)
D. \( 2 g \)


Study the food web given and answer the question
Which of the following organisms in the
given food web act both as a predator
and a prey?
A. I, II and IV
B. II, III and IV
c. ॥, ॥ा, v, vı and vı
D. II, III and vı


Hailstone at \( 0^{\circ} \mathrm{C} \) falls from a height of
1 km on an insulating surface
converting whole of its kinetic energy into heat. What part of it will melt?
\( \left(\boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} / \boldsymbol{s}^{2}\right) \)
A \( \cdot \frac{1}{33} \)
B. \( \frac{1}{8} \)
c. \( \frac{1}{33} \times 10^{-4} \)
D. All of it will melt


The first anti-microbial to be discovered
is:
A. Soframicin
B. Pencillin
c. oflaxacin
D. Terpineol


What are the possible number of outcomes if a card is drawn from a pack
of 52 cards?
A . 20
B . 30
\( c \cdot 42 \)
D. 52


The bundle of axon is known as
A. Nerve
B. Cyton
\( c \cdot \) Axon
D. None of these


The torque exerted by the wheel on the student is
A. having horizontal component only
B. having vertical component only
c. having horizontal as well as vertical component
D. there is no torque at any time on the student


In the figure (not drawn to scale), BCF is
an isosceles triangle with \( \mathrm{FC}=\mathrm{FB}, \mathrm{EBF} \)
and \( A B C \) are straight lines, EB is paralle
to GC. Find \( x \).
A \( .264^{\circ} \)
B. \( 84^{\circ} \)
\( c \cdot 118^{\circ} \)
D. 200


The IUPAC name of the compound
\( \boldsymbol{C H}_{3} \boldsymbol{C H}=\boldsymbol{C H C} \equiv \boldsymbol{C H} \) is :
A. pent-4-yn-2-ene
B. pent-3-en-1-yne
c. pent-2-en-4-yne
D. pent-1-yn-3-ene


8
8
8


If the sum of the coefficients of \( x^{2} \) and
coefficients of \( x \) in the expansion of
\( (1+x)^{m}(1-x)^{n} \) is equal to \( -m, \) then
the value of \( 3(n-m) \) is
(Note \( : \boldsymbol{m}, \boldsymbol{n} \text { are distinct }) \)


Write the common name and IUPACC
name for the following:
a) \( C H_{3} C H_{2} C H O \)
\( \boldsymbol{C H}_{3} \boldsymbol{C O C H}_{3} \)
c) \( \boldsymbol{C H}_{3}-\boldsymbol{C} \boldsymbol{H}-\boldsymbol{C H}_{3} \)
\[
_{\boldsymbol{O H}}
\]
\( \boldsymbol{C H}_{3} \boldsymbol{C O O H} \)
e) \( H C H O \)


The graph between \( \log \frac{X}{m} \) v/s log P is straight-line inclined at an angle \( 45^{\circ} \) with intercept 0.30. What will be the rate of adsorption at pressure of 0.4
atm?
A. 0.4
в. 0.6
\( c \cdot 0.8 \)
D. 0.9


The length of the perpendicular from the origin to the plane passing through the point \( a \) and containing the line \( r=\bar{b}+ \)
\( \lambda \bar{c} \) is
A \( \cdot \frac{[a b c]}{|a \times b+b \times c+c \times a|} \)
В. \( \frac{[a b c]}{|a \times b+b \times c|} \)
c. \( \frac{[a b c]}{|b \times c+c \times a|} \)
D. \( \frac{[a b c]}{|a \times b+c \times a|} \)


If \( \boldsymbol{x}=-1, \) then find \( \frac{\boldsymbol{x}^{4}-\boldsymbol{x}^{3}+\boldsymbol{x}^{2}}{\boldsymbol{x}-\mathbf{1}} \)
A. \( -\frac{3}{2} \)
в. \( -\frac{1}{2} \)
c. 0
D. \( \frac{1}{2} \)
E \( \cdot \frac{3}{2} \)


Find an expression for the magnetic dipole moment and magnetic field induction at the centre of a Bohr's
hypothetical hydrogen atom in the \( n^{t h} \)
orbit of the electron in terms of
universal constants.


Two tiny spheres, each of mass \( M, \) and
charges \( +\boldsymbol{q} \) and \( -\boldsymbol{q} \) respectively, are connected by a massless rod of length,
L. They are placed in a uniform electric field an an angle \( \theta \) with the \( \vec{E}\left(\theta=0^{\circ}\right) \)
Calculate the minimum time in which
the dipole axis becomes parallel to the field line.


The length, breadth and height of a room are \( 850 \mathrm{cm}, 625 \mathrm{cm} \) and \( 475 \mathrm{cm} \)
Find the length of the longest rod that
cam measure the dimensions of the
room exactly.


In the reaction given below, at constant pressure, the work done by system on surrounding is?
\( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \rightarrow \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) \)
A. positive
B. negative
c. no work is done
D. positive at temperatures above critical temperature


X0 type of sex determination is seen in
A. Man
B. Grasshopper
c. Drosophila
D. Birds
E. Horses


The correct sequence of different layers
of the atmosphere from the surface of
the Earth upwards is
A. Troposphere, Stratosphere, lonosphere, Mesosphere
B. Stratosphere, Troposphere, lonosphere, Mesosphere
C. Troposphere, Stratosphere, Mesosphere, lonosphere
D. Stratosphere, Troposphere, Mesosphere, lonosphere


Magnetic moment of bar magnet is \( M \) The work done in turning the magnet by
\( 90^{\circ} \) in direction of magnetic field \( B \) will
be
A. zero
в. \( \frac{1}{2} M B \)
c. \( 3 M B \)
D. \( M B \)


In a \( H- \) like atom for an electron
revolving in nth orbit, the variation of
\( \log _{10} K E \) versus \( \log _{10} z \) is plotted as
following Where \( z \) is an atomic number
and kinetic energy of the electron (in
\( \mathrm{eV} \) ). If \( \boldsymbol{O} \boldsymbol{A}=\log _{10} \mathbf{3} . \boldsymbol{4} \) then find the
value of principal quantum number of the electron.


Carbohydrates are used by body mainly:
A. for obtaining vitamins
B. as a source of energy
c. for building muscles
D. for all its development needs


What is the percentage weight of metallic elements in the constitution of
calcium carbonate?


As wave travels, intensity
A. increases
B. remains same
c. decreases
D. becomes negative


How can you verify that a current carrying wire produces a magnetic field with the help of an experiment?


If vectors \( \bar{b}, \bar{c}, \bar{d} \) are not coplanar then
prove that \( (\overline{\boldsymbol{a}} \times \overline{\boldsymbol{b}}) \times(\overline{\boldsymbol{c}} \times \overline{\boldsymbol{d}})+(\overline{\boldsymbol{a}} \times \overline{\boldsymbol{c}}) \times(\overline{\boldsymbol{d}} \times \)
\( \vec{b})+(\bar{a} \times \bar{d}) \times(\bar{b} \times \bar{c}) \) is parallel to \( \bar{a} \)


\( \boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{H} \boldsymbol{S}(s) \rightleftharpoons \boldsymbol{N} \boldsymbol{H}_{3}(\boldsymbol{G})+\boldsymbol{H}_{2} \boldsymbol{S}(\boldsymbol{g}) \)
The equilibrium pressure at \( 25^{\circ} C \) is
0.660 atm. What is \( K_{p} \) for the reaction?
\( \mathbf{A} \cdot 0.109 \)
B. 0.218
c. 1.89
D. 2.18


Describe the principal, construction and working of a single-phase \( A C \) generator


The eccentricity of the conic represented by \( \sqrt{(x+2)^{2}+y^{2}}+ \)
\( \sqrt{(x-2)^{2}+y^{2}}=8 \) is
A \( \cdot \frac{1}{3} \)
в. \( \frac{1}{2} \)
\( c \cdot \frac{1}{4} \)
D.


Which of the following is a weak bleaching agent?
A. concentrated sulphuric acid
B. Dihydrogen gas
c. sulphur
D. Sulphur dioxide


Find the vertices of the triangle whose mid point of sides are (3,1),(5,6) and (-3,2)
A \( \cdot(-1,7)(-5,-3)(6,5) \)
B . (7,1)(2,3)(4,1)
c. (-1,7)(-5,-3)(11,5)
D. (1,7)(5,3)(-11,5)


Choose the correct statements. The
coefficient of static friction depends on
This question has multiple correct options
\( A \). the material of the bodies in contact
B. quality of machining of the surfaces in contact
C. presence of foreign matter between the surfaces
D. area of the surfaces in contact


Hydrogentaion of vegetable ghee at
\( 25^{\circ} C \) reduces the pressure of \( H_{2} \) from 2 atm to 1.2 atm in 50 minute. The rate of
reaction in terms of change of molarity per second is:
A \( \cdot 1.09 \times 10^{-5} \) mollitre \( ^{-1} \sec ^{-1} \)
B. \( 2.90 \times 10^{-5} \) mollitre \( ^{-1} \) sec \( ^{-1} \)
c. \( 3.29 \times 10^{-5} \) mollitre \( ^{-1} \) sec \( ^{-1} \)
D. None of these


How kidney functions are regulated? Add a note on kidney transplantation?


A train travels from Agra to Delhi with a
constant speed of \( 50 k m h^{-1} \) and returns from Delhi to Agra with a
constant speed of \( 40 \mathrm{km} \mathrm{h}^{-1} \). Find the
average speed of the train.


In photocell cesium, coated oxidized silver cathode emits electrons for
A. visible light.
B. ultraviolet
c. infrared light
D. x-rays


Assertion
Most of the premature babies suffer
from Respiratory distress syndrome
Reason
Lecithin (surfactant) is secreted on the
inner side of the alveoli and prevent
collapsing of aveolar wall
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


\( \boldsymbol{I} \boldsymbol{f} \sin 5 \boldsymbol{\theta}=\boldsymbol{a} \sin ^{5} \boldsymbol{\theta}+\boldsymbol{b} \sin ^{3} \boldsymbol{\theta}+ \)
\( \operatorname{csin} \theta \) then
\( (A) a-2 c=5 \)
(B) \( a-2 c=6 \)
(C) \( b+3 c=5 \)
(D) \( b+3 c=-5 \)
The general solution of \( \tan 3 \theta \tan \theta= \)
1 is given \( (n \in \boldsymbol{I}) \)
\( \mathbf{A} \cdot a=20, b=-10, c=5 \)
B . \( a=1, b=-20, c=5 \)
\( \mathbf{c} . a=16, b=-2, c=5 \)
D. \( a=16, b=-20, c=5 \)


Two spheres of radii \( 3 \mathrm{cm} \) and \( 5 \mathrm{cm} \) are charged to potentials 3000 V and 4500 V respectively. They are then connected by
a thin metallic wires. The loss of electric
energy in this process is?
\( \mathbf{A} \cdot 2 \times 10^{-8} \mathbf{J} \)
B \( \cdot 4 \times 10^{-8} \mathrm{J} \)
D . \( 2.36 \times 10^{-7} \) J


Which of the following steps of respiration is amphibolic?
A. Glycolysis
B. Oxidative decarboxylation of pyruvate
c. TCA cycle
D. Oxidative phosphorylation


The magnifying power of a simple microscope can be increased if we use
eye piece of :
A. higher focal length
B. smaller focal length
c. higher diameter
D. smaller diameter


List four causes and consequences of deforestation.


If \( \vec{A} \cdot \vec{B}=\vec{A} \times \vec{B}, \) then angle between \( \vec{A} \) and \( \vec{B} \) is
A . 45
B. 30
\( c \cdot 60^{\circ} \)
D. \( 90^{\circ} \)


Determine the contrapositive of the following statement:
If \( x \) is an integer and \( x^{2} \) is odd, then \( x \) is
odd.


Which of the following is paramagnetic :
A. NO
в. \( N O_{2} \)
c. \( C l O_{2} \)
D. All


Sulphuric acid is produced by lead chamber process with following exothermic reaction
\[
2 S O_{2}+O_{2} \stackrel{N O}{\rightleftharpoons} 2 S O_{3} \stackrel{H_{2} O}{\longrightarrow} H_{2} S O_{4}
\]
What is the role of NO in the given
exothermic reaction?
A. Oxidizing agent
B. Reducing agent
c. catalyst
D. None of these


A wave is travelling on a string with the frequency 4 cycles per second, and its speed is 0.08 meters per second. Calculate the wavelength of the wave?
A . \( 0.25 \mathrm{m} \)
B. \( 0.55 m \)
c. \( 3.125 \mathrm{m} \)
D. \( 0.02 \mathrm{m} \)
E. 12.55 m


A student is observing the diagram showing the path of a ray of light passing through a glass prism. He would find that for all angles of incidence the ray of light bends:
A. Towards the normal while entering into the prism and away from the normal while emerging out of the prism,
B. Away from the normal while entering into the prism and towards the normal while emerging out of the prism,
C. Away from the normal while entering as well as while emerging out of the prism,
D. Towards the normal while entering as well as while emerging out of the prism.


Which complex has \( d s p^{2} \) hybridization
and square planar shape?
A \( \cdot\left[N i(C N)_{4}\right]^{2-} \)
B \( \cdot\left[C u\left(N H_{3}\right)_{4}\right]^{2+} \)
c. \( \left[P t(C l)_{4}\right]^{2-} \)
D. All


A particle executes simple harmonic oscillation
with an amplitude a. The period of oscillation is
T. The minimum time taken by the
particle to travel half of the amplitude from the equilibrium position is:
A. \( T / 2 \)
в. \( T / 4 \)
\( c \cdot T / 8 \)
D. T/12


2 mole ideal He gas and 3 mole ideal \( H_{2} \)
gas at constant volume find out \( C_{v} \) of
mixture
A \( \cdot \frac{21 R}{10} \)
в. \( \frac{11 R}{10} \)
c. \( \frac{21 R}{5} \)
D. \( \frac{11 R}{5} \)


\( \triangle \boldsymbol{A B C}, \boldsymbol{X} \boldsymbol{Y} \| \boldsymbol{B C}, \frac{\boldsymbol{A} \boldsymbol{Y}}{\boldsymbol{C Y}}=\frac{1}{2} \) and
\( A X=4 . \) Find \( B X \)


We know that any odd positive integer
is of the form \( 4 q+1 \) or \( 4 q+3 \) for some
integer \( \boldsymbol{q} \) Thus, we have the following two cases.
A \( \cdot n^{2}-1 \) is divisible by 8
B . \( n^{2}+1 \) is divisible by 8
c. \( n-1 \) is divisible by 8
D. \( n+1 \) is divisible by 8


Given below is a redox reaction. Which
of the following types the reaction belong to? \( \boldsymbol{C u}^{+\mathbf{2 + 6 - 2}} \boldsymbol{O}_{4(a q)}+\boldsymbol{Z} \boldsymbol{n}_{(s)} \rightarrow \boldsymbol{C u}_{(s)}+ \)
\( \underset{Z n S O_{4(a q)}}{+2+6+-2} \)
A. Combination reaction
B. Decomposition reaction
c. Metal displacement reaction
D. Non-metal displacement reaction