A charge \( (5 \sqrt{2}+2 \sqrt{5}) \) coulomb is placed on the axis of an infinite disc at a distance a from the centre of disc. The
flux of this charge on the part of the disc having inner and outer radius of a and 2a will be :
A \( \cdot \frac{3}{2 \varepsilon_{0}} \)
в. \( \frac{1}{2 \varepsilon_{0}} \)
c. \( \frac{2[\sqrt{5}+\sqrt{2}]}{\varepsilon_{0}} \)
D. \( \frac{2 \sqrt{5}+5 \sqrt{2}}{2 \varepsilon_{0}} \)


For the circuit shown in Figure, the
equivalent resistance between \( \boldsymbol{A} \) and \( \boldsymbol{C} \)
is
\( A \cdot \frac{12}{11} \)
B. \( \frac{13}{11} \)
\( c \cdot \frac{14}{11} r \)
\( D \cdot \frac{15}{11} \)


Solve: \( \int \cos ^{2} x \sin ^{2} x d x \)


A light paddle wheel placed in the path of \( \quad \) will rotate
A. cathode rays
B. \( \alpha \) -rays
c. \( \beta \) -rays
D. all the above


A uniform metre rule which has a mass
of \( 75 g \) is suspended by a thread at the
\( 75 \mathrm{cm} \) mark and is balanced by a mass
of weight Whanging from the \( 90 \mathrm{cm} \)
mark. Calculate the value of W.
A . 75 g
B. 125 g
\( c \cdot 150 g \)
D. 250 g


The effectiveness of a catalyst is minimum at its optimum temperature.
A. True
B. False


Figure \( P \) represents the reproductive
organs of Chara plant and figure \( Q \)
represents the reproductive organs of
earthworm. Select the option which
correctly identifies male reproductive organs of the two organisms.
\( \mathbf{A} \cdot A \) and \( D \)
\( B . B \) and \( C \)
\( \mathbf{c} . A \) and \( C \)
\( D . B \) and \( D \)


An inverted vessel (bell) lying at the bottom of a lake, \( 50.6 \mathrm{m} \) deep has \( 50 \mathrm{cc} \) of air trapped in it. The bell is brought to
the surface of lake. The volume of the
trapped air will now be
A . 200 ç
B. 250 cc
c. 300 cc
D. 350 cc


The point X-axis which is equidistant from the point (3,5) and (4,2) is
A. (-6,0)
B . (-7, 0)
c. (7, 0)
D. (-5, 0)


What role does the molecular
interaction play in a solution of alcohol and water?


Match the EM waves from list I with
corresponding Inventors in list II:


\( 40 \% \) of all high school students hate
roller coasters; the rest love them. \( 20 \% \)
of those students who love roller
coasters own chinchillas. What
percentage of students love roller
coasters but do not own a chinchilla?
A . 45
B . 30
c. 50
D. 48


\( \int e^{x}\left(\frac{1+\sqrt{1-x^{2}} \sin ^{-1} x}{\sqrt{1-x^{2}}}\right) d x= \)
A \( \cdot \frac{e^{x}}{\sqrt{1-x^{2}}}+c \)
B . \( e^{x} \sin ^{-1} x+c \)
c. \( e^{x}\left(e^{\sin ^{-1} x}+\frac{1}{\sqrt{1-x^{2}}}\right)+c \)
D. \( e^{\sin ^{-1} x}+\frac{1}{\sqrt{1-x^{2}}}+c \)


A worker is paid Rs 200 for 8 days work. If he works for 20 days, how much will
he get?


The sum of the squares of sine of the
angles made by the line \( A B \) with
\( \boldsymbol{O} \boldsymbol{X}, \boldsymbol{O} \boldsymbol{Y}, \boldsymbol{O} \boldsymbol{Z} \) where \( \boldsymbol{O} \) is the origin is
A . 1
B . 2
\( c \cdot-1 \)
D. 3


Show that \( \sqrt{2}+\sqrt{3} \) is an irrational
number.


A body of mass 5 kg has momentum of
\( 10 \mathrm{kg} \mathrm{m} / \mathrm{sec} . \) When a force of \( 0.2 \mathrm{N} \) is
applied on it for 10 sec, the change in its kinetic energy is:
A . 4.4
в. 3.3
c. 5.5
D . 1.1 J


The strongest acid among the following is:
A. o-methoxyphenol
B. m-methoxyphenol
c. p-methoxyphenol
D. phenol


The refractive indices of substances
P,Q, Rand \( \$ \) are 1.38,1.46,1.56 and 1.24 respectively. When light travelling in air is incident on these substances at
equal angles, the angle of refraction will be maximum in
\( A \cdot P \)
B.
\( c . R \)
D. s


If \( y=\sqrt{\frac{1-x}{1+x} \text { then find }\left(1-x^{2}\right) \frac{d y}{d x}+} \)
\( y= \)
A . 1
B. -
\( c \cdot 2 \)
D.


If \( \left(\frac{x}{3}+1, y-\frac{2}{3}\right)=\left(\frac{5}{3}, \frac{1}{3}\right) \) find the
values of \( x \) and \( y \)


In an ac circuit, \( \mathrm{V} \) and I are given by \( \boldsymbol{V}=\mathbf{1 5 0} \sin (\mathbf{1 5 0} \boldsymbol{t}) \boldsymbol{V} \boldsymbol{a n d} \boldsymbol{I}= \)
\( 150 \sin \left(150 t+\frac{\pi}{3}\right) A \)
The power dissipated in the circuit is
A . \( 106 \mathrm{w} \)
B. 150 \( \mathrm{w} \)
c. \( 5625 \mathrm{w} \)
D. zero


Cells of Deiters occur in
A. Utriculus
B. Retina of eyes
c. Organ of Corti
D. Sebaceous glands


Maximum ferromagnetism is found in?
A . \( F e \)
в. \( N i \)
c. \( C o \)
D. None


A compound containing two \( -O H \) groups attached to one carbon atom is
unstable but which one of the following is stable?
\( A \)
в.
\( c \)
D. Al


The compound statement, "If you want to top the school, then you do not study hard" is equivalent to
A. "If you want to top the school, then you need to study hard"
B. "If you will not top in the school, then you study hard""
c. "If you study hard, then you will not top the school".
D. "If you do not study hard, then you will top in the school"


\( \frac{\sigma_{00}}{000}= \)
\( \frac{000}{200} \)
\( \infty \)


Some properties of sulphuric acid are listed below. Choose the role played by sulphuric acid as \( A, B, C \) or \( D \) which is
responsible for the reaction (i) to (v) Some role/s may be repeated:
\( Z n+2 H_{2} S O_{4}(\text {conc.}) \rightarrow Z n S O_{4}+ \)
\( \boldsymbol{S O}_{2}+\boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{O} \)
A . Dilute acid
B. Dehydrating agent
c. Non-volatile acid
D. Oxidising agent


Name a physical quantity that remains constant in a uniform circular motion.
A. Velocity
B. Acceleration
c. Momentum
D. Angular speed


A horizontal force of 10 newton is
necessary to just hold a block stationary against a wall, The coefficient of friction between the lock
and the wall is 0.2. The weight of block
is
A. 50
B. 100 N
\( c \cdot 2 N \)
D. 20 N


If \( \boldsymbol{y}=\mathbf{2}^{2^{x}}, \) then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}= \)
A \( \cdot y(\log 2)^{2} \times 2^{x} \)
В . \( y \times 2(\log 2) 2^{x} \)
C \( \cdot y \times 2(\log 2)^{2} \times 2^{x} \)
D. \( -y(\log 2) \times 2^{x} \)


\( \boldsymbol{S b F}_{5} \) reacts with \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{4} \) and \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{6} \) to
form ionic compounds \( \left[\boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{3}^{+}\right]\left[\boldsymbol{S b} \boldsymbol{F}_{6}\right]^{-} \boldsymbol{a n d}\left[\boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{5}^{+}\right]\left[\boldsymbol{S b} \boldsymbol{F}_{6}^{-}\right] \)
The geometry of \( X e F_{3}^{+} \) ion and \( X e F_{5}^{+} \) ion, respectively, is :
A. sqare pyramidal, T-shaped
B. bent T-shaped, square pyramidal
c. see-saw, square pyramidal
D. square pyramidal, see-saw


A resistance of \( R \Omega \) draws a current from
a potentiometer. The potentiometer has a
total resistance \( R_{0} \Omega . \) A voltage V is
supplied to the potentiometer. The
voltage across \( \mathrm{R} \) when the sliding contact
is in the middle of the potentiometer is:
A \( \cdot \frac{2 V R}{4 R_{0}+R} \)
В. \( \frac{4 V R}{R_{0}+R} \)
\( \mathbf{c} \cdot \frac{V R}{R_{0}+4 R} \)
D. \( \frac{2 V R}{R_{0}+4 R} \)


\( N_{2} O \) (laughing gas) finds use in the
following except:
A. as a propellant for whipped ice-cream.
B. as an anaesthetic
C. for the preparation of \( N_{3} H \)
D. as fuel for rockets


Evaluate: \( \int_{\alpha}^{\beta} \sqrt{\frac{\boldsymbol{x}-\boldsymbol{\alpha}}{\boldsymbol{\beta}-\boldsymbol{x}}} \boldsymbol{d} \boldsymbol{x} \)
A \( \cdot \frac{\pi}{2}(\beta-\alpha) \)
В \( \cdot \frac{\pi}{2}(\alpha-\beta) \)
c. \( \pi(\beta-\alpha) \)
D. \( \pi(\alpha-\beta) \)


Which electronic shell is at a higher
energy level \( \boldsymbol{K} \) or \( \boldsymbol{L} \) ?


Let \( x_{1}, x_{2}, \ldots, x_{n} \) be \( n \) observations such
that \( \sum x_{i}^{2}=400 \) and \( \sum x_{i}=80 . \) Then a
possible value of \( n \) among the following is :
A. 15
B. 18
\( c \cdot 12 \)
D.


Eight small drops, each of radius \( r \) and
having same charge \( q \) are combined to form a big drop. The ratio between the potentials of the bigger drop and the smaller drop is
A . 8: 1
B . 4: 1
c. 2: 1
D. 1: 8


The pulley in arrangements in Fig. (a) and Fig. (b) are identical. The mass of
the rope is negligible. In Fig (a), the mass \( m \) is lifted up by attaching a mass \( 2 \mathrm{m} \) to the other end of the rope. In
(b), \( m \) is lifted up by pulling the other end of the rope with a constant
downwards force \( F=2 m g \). The acceleration of \( \mathrm{m} \) is the same in both
cases.
\( (\mathbf{a}) \)
(b)
A. True
B. False


The IUPAC name of the following compound is \( 3-(\text { trichloromethyl }) \) benzoic acid.
A. True
B. False


\( \sim[(\boldsymbol{p} \wedge \boldsymbol{q}) \rightarrow(\sim \boldsymbol{p} \vee \boldsymbol{q})] \) is
A. Tautology
B. Contradiction
c. Neither (A) nor (B)
D. Either (A) or (B)


Which of the following chemical reaction(s) is (are) involved in the
developing of photographic plate?
This question has multiple correct options
\( \mathbf{A} \cdot C_{6} H_{4}(O H)_{2}+2 A g B r \rightarrow 2 A g+C_{6} H_{4} O_{2}+2 H B r \)
B. \( \left.A g B r+2 N a_{2} S_{2} O_{3} \rightarrow N a_{3}\left[A g S_{2} O_{3}\right)_{2}\right]+N a B r \)
\( \mathbf{c} \cdot A g B r+2 N H_{3}(a q) \rightarrow\left[A g\left(N H_{3}\right)_{2}\right] B r \)
D. \( 2 A g B r+N a_{2} S_{2} O_{3} \rightarrow A g_{2} S_{2} O_{3}+2 N a B r \)


\( 1.5 \mathrm{g} \) of a monobasic acid, when dissolved in 150 g of water, lowers the freezing point by \( 0.165^{\circ} \mathrm{C} .0 .5 \mathrm{g} \) of the same acid when titrated, after
dissolution in water, requires \( 37.5 \mathrm{ml} \) of N/10 alkali. Calculate the degree of
dissociation of the acid \( ?\left(K_{f} \text { for water }=\right. \) \( \left.1.86^{\circ} \mathrm{C} \mathrm{mol}^{-1}\right) \)
A . \( 11.34 \% \)
в. \( 34.64 \% \)
c. \( 65.36 \% \)
D. \( 89.64 \% \)


The magnetic induction in vacuum at a plane surface of a uniform isotropic magnetic is equal to \( B \), the vector \( \vec{B} \)
forming an angle \( \alpha \) with the normal of the surface. The permeability of the
magnetic is equal to \( \mu \). Find the
magnitude of the magnetic induction
\( B^{\prime} \) in the magnetic in the vicinity of its surface.


A monochromatic beam of
electromagnetic radiation has an
intensity of \( 1 W / m^{2} . \) Then the average
number of photons per \( m^{3} \) for a \( 10 \mathrm{MeV} \)
\( \gamma \) ray is \( ? \)
A . 4166
B. 3000
c. 5000
D. 2083


Number of solutions satisfying \( |\boldsymbol{x}|+ \) \( |x-2| \leq 2 \) for \( x \in R \) is


The catalytic activity of the transition
metals and their compounds is
described to:
A. their chemical reactivity
B. their ability to adopt multiple oxidation states and their non complexing ability
C. their unfilled d-orbital
D. their ability to adopt multiple oxidation states and their complexing ability


Consider the following nuclear reactions:
\( 1 . \frac{14}{7} N+_{2}^{4} H e \longrightarrow_{8}^{17} O+_{1}^{1} H \)
2. \( _{4}^{9} B e+_{1}^{1} H \longrightarrow_{3}^{9} L i+_{2}^{4} H e \)
3. \( _{\mathbf{1 2}}^{24} \boldsymbol{M} \boldsymbol{g}+_{\mathbf{2}}^{\mathbf{4}} \boldsymbol{H} \boldsymbol{e} \longrightarrow_{\mathbf{1 4}}^{\mathbf{2 7}} \boldsymbol{S} \boldsymbol{i}+_{\mathbf{0}}^{\mathbf{1}} \boldsymbol{n} \)
4. \( \frac{10}{5} \boldsymbol{B}+_{2}^{4} \boldsymbol{H} e \longrightarrow \frac{13}{7} \boldsymbol{N}+_{0}^{1} \boldsymbol{n} \)
Examples of induced radioactivity would include the reactions:
A. 3 and 4
B. 1 and 2
c. 1,3 and 4
D. 1,2,3 and 4


Find the domain of the following
function:
\( \boldsymbol{f}(\boldsymbol{x})=\operatorname{cosec}^{-1}\left[\mathbf{1}+\sin ^{2} \boldsymbol{x}\right], \) where
denotes the greatest integer function


In a diagram \( \boldsymbol{O} \) is the centre of circle.
Calculate the value \( a \)
A . 43
B. 53
\( c \cdot 63 \)
D. 33


During which phase of growth, cell increases in volume
A. Exponential
B. Cell division
c. Differentiation
D. Enlargement


The following is an example of a single displacement reaction:
\( \boldsymbol{M} \boldsymbol{g}_{(s)}+\boldsymbol{Z} \boldsymbol{n}\left(\boldsymbol{N} \boldsymbol{O}_{3}\right)_{2(a q)} \rightarrow \boldsymbol{Z} \boldsymbol{n}_{(s)}+ \)
\( M g\left(N O_{3}\right)_{2(a q)} \)
How else can this reaction be
classified?
A. A precipitate reaction
B. An acid-base reaction
c. A neutralization reaction
D. A redox reaction


If the matrix is a square matrix and it contains 36 elements, then the order of the matrix is:
\( \mathbf{A} \cdot 4 \times 4 \)
B. \( 8 \times 8 \)
\( \mathbf{c} \cdot 6 \times 6 \)
D. \( 3 \times 3 \)


What were the limitations of Newlands'
classification?
A. It was applicable only for lighter elements
B. He adjusted two elements on the same place
C. The pattern was only observed up to calcium
D. All of the above


Identity the true statement regarding nitrates of all metals.
A \( \cdot \) All nitrates decompose to give \( N O_{2} \)
B. All nitrates are soluble in water.
C. All nitrates are insoluble in water
D. All nitrates are stable to heatt


Which particle among the following will have the smallest de-Broglie wavelength, assuming that they have the same velocity?
A. A positron
B. A photon
c. An \( \alpha \) particle
D. A neutron


Find the frequency of 1 MeV photon. Given wavelength of a \( 1 \mathrm{keV} \) photon is \( 1.24 \times 10^{-9} m \)
Hint: \( \boldsymbol{E}=\boldsymbol{h} \boldsymbol{\nu} \)


From a lot of 6 items containing 2
defective items, a sample of 4 items are
drawn at random. Let the random
variable X denote the number of
defective items in the sample. If the
sample is drawn without replacement, find Mean of X.


An atrioventricular valve prevents the
back flow or leakage of blood from-
A. The right ventricle into the right atrium
B. The left atrium into the left ventricle
c. The aorta into the left ventricle
D. The pulmonary vein into the right atrium


\( H C l \) is present in which of the following things?
A. Gastric juices of mammals
B. Volcanic emissions
c. Both \( A \) and \( B \)
D. None of the above


Which of the following is correct for a
step up transformer?
\( \mathbf{A} \cdot N_{s}=N_{p} \)
В. \( N_{s}<N_{p} \)
\( \mathbf{c} \cdot N_{s}>N_{p} \)
D. Nothing can be said


Non-cellular layer that connects epithelium to connective tissue is?
A. Dermis
B. Epidermis
c. Basement membrane
D. None of the above


If \( a, b, c \) are in A.P., then \( \frac{1}{\sqrt{b}+\sqrt{c}} \) \( \frac{1}{\sqrt{\boldsymbol{c}}+\sqrt{\boldsymbol{a}}}, \frac{1}{\sqrt{\boldsymbol{a}}+\sqrt{\boldsymbol{b}}} \) are in
A . G.P.
B. H.P.
c. A.P.
D. None of these


Express in terms of bases to the power of exponenets
\( 8.9^{2} \)


Assertion
Wrought iron is more malleable and
ductile than steel.
Reason
It contains slightly less percentage of
carbon.
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 and Reason is correct


Which among the following is the most reactive?
A \( \cdot C l_{2} \)
в. \( B r_{2} \)
\( \mathbf{c} \cdot I_{2} \)
D. ICl


An astronomical refracting telescope will have large angular magnification and high resolution, when it has an
objective lens of :
A. Large focal length and large diameter
B. Small focal length and large diameter
c. Small focal length and small diameter
D. Large focal length and small diameter


If \( \boldsymbol{A}=\left[\begin{array}{lll}\boldsymbol{a} & \boldsymbol{0} & \boldsymbol{0} \\ \boldsymbol{0} & \boldsymbol{a} & \boldsymbol{0} \\ \boldsymbol{0} & \boldsymbol{0} & \boldsymbol{a}\end{array}\right], \) then the value of
\( |\boldsymbol{A}||\mathbf{A} \mathbf{d} \mathbf{j} \boldsymbol{A}| \)
A \( \cdot a^{3} \)
в. \( a^{6} \)
\( c \cdot a^{9} \)
\( D \cdot a^{2} \)


If the dicot stem is stained for starch,
the most intense colouration would
develop in
A. epiblema
B. phloem
c. endodermis
D. pith


Which forces are involved in holding the drugs to the active site of enzymes?


Out of the two magnetic materials, 'A' has relative permeability slightly greater than unity while 'B' has less than unity. Identify the nature of the materials 'A' and 'B'. Will their
susceptibilities be positive or negative?


When \( I \) is equal to one half of its maximum value, what is the value of
\( |Q| ? \)


A conducting disc of radius r rotates with a small constant angular velocity \( \omega \) about its axis. A uniform magnetic
field B exists parallel to the axis of rotations. Find the motional emf
between the center and the periphery of
the disc.


The angle between the lines \( y-x+ \)
\( \mathbf{5}=\mathbf{0} \) and \( \sqrt{\mathbf{3}} x-\boldsymbol{y}+\mathbf{7}=\mathbf{0} \) is/are:
A \( \cdot 15^{\circ} \)
В. \( 60^{\circ} \)
\( \mathbf{c} \cdot 165^{\circ} \)
D. \( 75^{\circ} \)


Express each of the following as a fraction in simplest form:
\( 9.2 \% \)


The maximum number of valence
electrons possible for atoms in the second period of the periodic table is :
A .2
B. 8
c. 18
D. 32


The mass of a metallic beam of uniform
thickness and of length \( 6 m \) is \( 60 k g \) The beam lies horizontally and symmetrically on two vertical pillars
which are separated by a distance \( 3 m \)
A person of mass \( 75 \mathrm{kg} \) is walking on
this beam. The closest distance to
which the person can approach one end of the beam so that the beam does not
tilt down is (neglect thickness of pillars):
\( \mathbf{A} \cdot 30 \mathrm{cm} \)
B. 20 \( c m \)
c. \( 15 \mathrm{cm} \)
D. \( 10 \mathrm{cm} \)


Early transition metals occur in nature as oxides but the late transition metals
occur as sulphides. If it is true enter 1 , else enter 0


A vehicle moving at a speed of \( 15 \mathrm{m} / \mathrm{s} \) is stopped by applying brakes which produce a uniform acceleration of -0.5
\( m / s^{2} . \) The distance covered by the vehicle before it stops is:
A . \( 100 \mathrm{m} \)
B. 200 \( \mathrm{m} \)
c. 250 \( \mathrm{m} \)
D. 225 m


The average power dissipation in pure inductance in AC circuit, is
A \( \cdot 1 / 2 L i^{2} \)
B . \( 2 L i^{2} \)
c. \( L i^{2} / 4 \)
D. zero


A box contains two white balls, three
black balls and four red balls. No. of
ways can three balls be drawn from the
box if at least one black ball is to be
included in the draw is
A . 129
B. 84
c. 64
D. None


Two perfectly elastic particles \( A \) and \( B \) of equal masses travelling along the
line joining them with velocity \( 15 \mathrm{ms}^{-1} \)
and \( 10 \mathrm{ms}^{-1} \) respectively collide. Their velocities after the elastic collision will
be \( \left(\text { in } m s^{-1}\right) \) respectively
A. 20 and 5
B. 10 and 15
\( c \cdot 25 \) and 20
D. 0 and 25


If \( |\vec{a}|=|\vec{b}|=|\vec{c}|=1, \vec{a} \cdot \vec{b}=\vec{b} \cdot \vec{c}= \)
\( \vec{c} \cdot \vec{a}=\frac{1}{2} \operatorname{then}[\vec{a}, \vec{b}, \vec{c}]= \)
A . 1
B. \( \frac{1}{2} \)
c. \( \frac{1}{\sqrt{2}} \)
D. \( \frac{\sqrt{3}}{2} \)


SQUID helps in studying
A. lung cancer
B. heart beats
C. weaker magnetic waves from brain
D. electrical impulses from heart


Name the two types of microscopes.


The total number of isomers including stereoisomers for 1,3-dimethyl cyclohexane is
A. \( 2, \) cis and trans both optically inactive
B. 3, one cis and two optically active trans forms
c. 3 , one trans and two optically active cis forms
D. \( 4, \) two cis (optically active) and two trans (optically active


A body of mass \( \frac{1}{4} \) kg moving with velocity \( 12 \mathrm{m} / \mathrm{s} \) is stopped by applying a force of \( 0.6 \mathrm{N} \). Calculate the time taken
to stop the body. Also calculate the impulse of this force.


A hemispherical body is placed in a
uniform electric field E. What is the flux
linked with curved surface, if field is
perpendicular to base in figure.
\( \mathbf{A} \cdot 2 \pi R^{2} E \)
\( \mathbf{B} \cdot \pi R^{2} E / 2 \)
\( \mathbf{C} \cdot \pi R^{2} E \)
D. Zero


Find out the correct order of succession
levels in xerarch.
A. Lichen, moss stage, annual herb stage, perennial herb stage, shrub stage, forest
B. Annual herb stage, perennial herb stage, lichen moss stage, shrub stage, forest
C. Perennial herb stage, annual herb stage, lichen moss stage, shrub stage, forest
D. Shrub stage, forest, annual herb stage, perennial herb stage, lichen moss stage
E. Forest, shrub stage, annual stage, perennial herb stage, lichen moss stage


Complete the following, so as to make a
true statement:
A quadrilateral has sides


For the same angle of incidence, the
angles of refraction in media \( \mathrm{P}, \mathrm{Q}, \mathrm{R} \) and
\( \mathrm{S} \) are \( 50^{\circ}, 40^{\circ}, 30^{\circ}, 20^{\circ}, \) respectively. The
speed of light is minimum in medium:
\( A \cdot P \)
B.
\( c \cdot R \)
\( D \cdot s \)


Point charges each of magnitude \( Q \) are
placed at three corners of a square as shown in the diagram.

What is the direction of the resultant
electric field at the fourth corner?
A. \( O C \)
в. \( O E \)
\( c . O D \)
\( D, O B \)


Ethanol on reaction with acetic
anhydride gives:
A . acetic ester
B. formic ester
c. ethanoic acid
D. ethyl acetate and ethanoic acid


Arrange Li, Na, K, Rb, Cs in order of increasing electronegativity:
A. \( C s<R b=K<N a<L i \)
B. \( R b<C s=L i<N a<L \)
c. \( C s<R b=N a<L i<K \)
D. None of these


A man sets his watch by a whistle that is \( 2 k m \) away. How much will his watch
be in error. (speed of sound in air
\( \mathbf{3 3 0} \boldsymbol{m} / \boldsymbol{s}) \)
A. 3 second fast
B. 3 second slow
\( c .6 \) second fast
D. 6 second slow


Magnesium ribbon is burnt in an
atmosphere of nitrogen gas to form solid magnesium nitride. This is a :
A. synthesis reaction
B. combination reaction
c. displacement reaction
D. none of the above


Statement I : An exothermic reaction
has a positive \( \Delta \boldsymbol{H} \) value
Because
Statement II : Heat must be added to
the reaction for the reaction to occur
A. Statement 1 and Statement 2 are correct and
Statement 2 is the correct explanation of Statement 1.
B. Both the Statement 1 and Statement 2 are correct and Statement 2 is not the correct explanation of Statement 1.
c. Statement 1 is correct but Statement 2 is not correct.
D. Statement 1 is not correct but Statement 2 is correct.
E. Both the Statement 1 and Statement 2 are not correct.


The printed price of \( V C D \) player is
Rs \( 7,500 . \) If a sales tax of \( 8 \% \) is charged
from the buyers, Find the price at which it is sold


In the quantitative analysis of the
second group in a laboratory, \( \boldsymbol{H}_{2} \boldsymbol{S} \) gas is passed in an acidic medium for
precipitation. When \( C u^{2+} \) and \( C d^{2+} \)
react with \( K C N, \) then for a product, the
true statement is:
A \( \cdot K_{2}\left[C u(C N)_{4}\right] \) more soluble
В - \( K_{2}\left[C d(C N)_{4}\right] \) less stable
c. \( K_{3}\left[C u(C N)_{2}\right] \) less stable
D. \( K_{2}\left[C d(C N)_{3}\right] \) more stable


Which is the descriptive term that indicates there is a large quantity of solute, compared with the amount of solvent, in a solution?
A . Dilute
B. concentrated
c. Unsaturated
D. Saturated
E. Supersaturated


A silver wire has a resistance of \( 2.1 \Omega \) at
\( 27.5^{\circ} \mathrm{C}, \) and a resistance of \( 2.7 \Omega \) at
\( 100^{\circ} \mathrm{C} . \) Determine the temperature coefficient of resistivity of silver.


What is the amount of urea dissolved
per litre, if aqueous solution is isotonic with \( 10 \% \) cane sugar solution: (mol. wt of urea \( =\mathbf{6 0} \) )?
A \( .200 g / L \)
в. \( 19.2 g / L \)
c. \( 17.54 g / L \)
D. \( 16.7 g / L \)


(i) Which allotrope of phosphorus is more reactive and why?
(ii) How the supersonic jet aeroplanes are responsible for the depletion of ozone layers?
(iii) \( F_{2} \) has lower bond dissociation
enthalpy than \( C l_{2} \). Why?
(iv) Which noble gas is used in filling balloons for meteorological observations?
(v) Complete the equation: \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{2}+ \)
\( \boldsymbol{P} \boldsymbol{F}_{5} \longrightarrow \)


Teeth and bones are made of mainly:
A . Calcium silicate
B. Calcium phosphate
c. Calcium silicon phosphate
D. Calcium hydrogen phosphate


Before arranging the experiment "Carbon dioxide evolved during the process of respiration"; the seeds must be
A. Completely dried
B. Boiled to soften them
c. Soaked in vinegar
D. Kept moist till germination


Stem tendrils are found in
A. Cucurbita and Pisum
B. Pisum and Lathyrus
c. vitis and Passiflora
D. Smilax and Geranium


Three bodies \( A, B \) and \( C \) are in thermal
equilibrium. The temperature of \( B \) is
\( 45^{\circ} \mathrm{C}, \) then the temperature of \( C \) is
A \( \cdot 45^{\circ} \mathrm{C} \)
в. \( 50^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 40^{\circ} C \)
D. Any temperature


An air chamber of volume \( V \) has a neck
of cross-sectional area a into which a
light ball of mass \( \mathrm{m} \) just fits and can move up and down without friction. The
diameter of the ball is equal to that of
the neck of the chamber. The ball is
pressed down a little and released. If the bulk modulus of air is \( \mathrm{B} \), the time period
of the oscillation of the ball is
A \( \cdot T=2 \pi \sqrt{\frac{B a^{2}}{m V}} \)
B \( \cdot T=2 \pi \sqrt{\frac{B V}{m a^{2}}} \)
\( \mathbf{c} \cdot T=2 \pi \sqrt{\frac{m B}{V a^{2}}} \)
\( \mathbf{D} \cdot T=2 \pi \sqrt{\frac{m V}{B a^{2}}} \)


Mark the correct alternative of the
following. For the function \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}+\frac{\mathbf{1}}{\boldsymbol{x}} \)
A. \( x=1 \) is a point of maximum
B. \( x=-1 \) is a point of minimum
c. Maximum value> minimum value
D. Maximum value < minimum value


Seven homogeneous bricks, each of length L, are arranged as shown in figure. Each brick is displaced with respect to the one in contact by \( \boldsymbol{L} / \mathbf{1 0} \)
Find the \( x \) coordinate of the center of
mass relative to the origin 0


Explain the action of phenolphthalein indicator in the titration of acetic acid
versus sodium hydroxide


Which of the following are isotone of \( 76 G e ? \)
32
This question has multiple correct options
A \( \cdot \frac{77}{32} \mathrm{Ge} \)
e
\( \mathrm{c} \cdot \frac{77}{34} \mathrm{Se} \)


When an acetyl chloride is heated with
Na salt of a carboxylic acid, the
product is an:
A. ester
B. anhydride
c. alkene
D. aldehyde


Which site of an enzyme is called allosteric site?
A. which binds to the cell wall
B. where drugs bind to an enzyme
C. which is not the active site, where some drugs bind to an enzyme
D. none of these


The hardest material out of the
following is :
A. diamond
B. steel
c. aluminium
D. glass


Which among the following is a rootless plant?
A. Nymphaea
B. Sagittaria
c. ceratophyllum
D. Vallisneria


Calculate the temperature of a hydrogen-oxygen flame assuming that
the gases at \( 25^{\circ} \mathrm{C} \) are mixed in stoichiometric proportion and react
completely to give \( H_{2} O(g) . \Delta H_{298}^{\circ} \) of combustion of \( \boldsymbol{H}_{2} \) is \( -\mathbf{5 8} \) kcal \( \boldsymbol{m o l}^{-1} \)
The reaction is at constant pressure
and the \( C_{p} \) values are \( (7 / 2) R \) for each
gas. \( (\boldsymbol{R}=\mathbf{2} \boldsymbol{c} \boldsymbol{a} \boldsymbol{l}) \)
A. \( 8583.71 K \)
B . \( 9583.71 K \)
c. \( 4283.71 \mathrm{K} \)
D. None of the above


Refer to the given paragraph and
answer the following question. Plant P is
the only source of food for the caterpillars of a butterfly species, \( Q \) Plant P depends on the adults of the butterfly species \( Q \) for pollination. Infact, animal \( Q \) is the only pollinator of plant \( P \) in nature. Animal \( R \) feeds
exclusively on the caterpillars of the butterfly species, Q. Animal R In turn is the prey of animal S.Which of the
following is likely to happen if animal
is hunted to extinction?
A. Animal R wit continuously feed on animal Q which may lead to coex-tinction of both \( \mathrm{P} \) and \( \mathrm{Q} \) with time.
B. The populations of both animals \( Q \) and \( R \) will increase, however the population of plant P will decrease with time
C. Population of animal R will Increase while population of animal Q will decrease with time.
D. Both (A) and (C)


Find all two-digit numbers such that the sum of the digits constituting the number is not less than \( 7 ; \) the sum of
the squares of the digits is not greater than \( 30 ; \) the number consisting of the same digits written in the reverse order is not larger than half the given number


A balloon is ascending at the rate of 14
\( m s^{-1} \) at a height of \( 98 \mathrm{m} \) above the ground when the food packet is dropped from the balloon. After how much time
and with what velocity does it reach the ground ? Take \( g=9.8 m s^{-2} \)


Evaluate \( \lim _{x \rightarrow 0} \log \frac{\sin x}{x} \)


Which are the intensive properties?
This question has multiple correct options
A. Temperature
B. Pressure
C. Density
D. Heat


State the differences between:
Decay and putrefaction


Pressure due to the weight of ice will be
maximum at
\( A \)
\( B \)
C. both 1 and 2
D. neither 1 nor 2


Ribulose diphosphate carboxylase enzyme catalyzes the carboxylation
reaction between
A. Oxaloacetic acid and acetyl CoA
B. \( C O_{2} \) and ribulose 1,5 diphosphate
c. Ribulose diphosphate and phosphoglyceraldehyde
D. PGA and dihydroxy acetone phosphate


Value of 'g' on moon is of
the value of 'g' on earth. Fill in the blank.
A. One third
B. One sixth
c. one fourth
D. one tenth


Determine the differential equation of
parabolas with foci at origin and axes
along X-axis.
Hint: \( y^{2}=4 a(x-a) \)
\( \mathbf{A} \cdot y^{3}\left(\frac{d y}{d x}\right)^{2}=2 x y \frac{d y}{d x}-1 \)
B \( y^{4}\left(\frac{d y}{d x}\right)^{2}=2 x y \frac{d y}{d x}-1 \)
\( ^{\mathbf{C}} y^{3}\left(\frac{d y}{d x}\right)^{2}=2 x y \frac{d y}{d x}-2 \)
D \( y^{4}\left(\frac{d y}{d x}\right)^{3}=2 x y \frac{d y}{d x}-1 \)


Which of the following gives evidence to kinetic theory of gases?
A. assumption of kinetic theory
B. Boyle's law
c. idea of mean free path
D. diffusion and evaporation


Power dissipated in pure inductance will be
\( ^{A} \cdot \frac{L I^{2}}{2} \)
В \( \cdot 2 L I^{2} \)
c. \( \frac{L I^{2}}{4} \)
D. zero


At a place on the surface of earth vertical component of earth's field is two times that of horizontal component.
Then the latitude angle at that place is
\( \mathbf{A} \cdot \tan ^{-1}(2) \)
B \cdot \( \tan ^{-1}(1 / 2) \)
\( c \cdot 45^{\circ} \)
D. \( 0^{\circ} \)


If \( \overrightarrow{e_{1}}=(1,1,1) \) and \( \overrightarrow{e_{2}}=(1,1,-1) \) and
\( \vec{a} \) and \( \vec{b} \) are two vectors such that \( \overrightarrow{e_{1}}=2 \vec{a}+\vec{b} \) and \( \overrightarrow{e_{2}}=\vec{a}+2 \vec{b}, \) then
the angle between \( \vec{a} \) and \( \vec{b} \) is
A \( \cdot \cos ^{-1}\left(\frac{7}{9}\right) \)
B. \( \cos ^{-1}\left(\frac{7}{11}\right) \)
\( ^{\mathrm{c}} \cdot \cos ^{-1}\left(-\frac{7}{11}\right) \)
D. \( \cos ^{-1}\left(\frac{6 \sqrt{2}}{11}\right) \)


The total number of terms in the
expansion of \( (x+y)^{50}+(x-y)^{50} \) is
A . 51
B . 26
\( c .102 \)
D. 25


A boy held a book of \( 1 \mathrm{kg} \) at a height of 1 metre for 60 seconds. Calculate the
work done :
A . 60 J
B. 30 J
c. 15 J
D.


The correct formula of diammine
dichlorodicyano chromate (III) is :
\( \mathbf{A} \cdot\left[\operatorname{Cr} C l_{2}(C N)_{2}\left(N H_{3}\right)_{2}\right]^{3+} \)
B . \( \left[C r C l_{2}(C N)_{2}\left(N H_{3}\right)_{2}\right]^{3} \)
\( \mathbf{c} \cdot\left[C r C l_{2}(C N)_{2}\left(N H_{3}\right)_{2}\right. \)
D. \( \left[C r C l_{2}(C N)_{2}\left(N H_{3}\right)_{2}\right] \)


\( 98 \mathrm{g} H_{2} S O_{4} \) is added in water no. of moles of ions produced will be?
\( \mathbf{A} \cdot 0.3 N_{a} \)
B. \( 0.3 \times 6.023 \times 10^{23} \)
\( \mathrm{c} .0 .3 \times 98 \)
D. 0.3


Find the value of \( x \) if
\( \left|\begin{array}{ccc}\boldsymbol{x}-\mathbf{2} & \mathbf{2} \boldsymbol{x}-\mathbf{3} & \mathbf{3} \boldsymbol{x}-\mathbf{4} \\ \boldsymbol{x}-\mathbf{4} & \mathbf{2} \boldsymbol{x}-\mathbf{9} & \mathbf{3} \boldsymbol{x}-\mathbf{1 6} \\ \boldsymbol{x}-\mathbf{8} & \mathbf{2} \boldsymbol{x}-\mathbf{2 7} & \mathbf{3} \boldsymbol{x}-\mathbf{6 4}\end{array}\right|=\mathbf{0} ? \)


The following equation represents a method of purification of nickel by:
\( N i(\text {impure})+4 C O \stackrel{320 K}{\longrightarrow} \)
\( N i(C O)_{4} \stackrel{420 K}{\longrightarrow} N i(\text {pure})+4 C O \)
A. Cupellation
B. Mond's process
c. van Arkel method
D. zone refining


Among the following which is not the \( \pi \) -
bonded organomettalic compound?
\( \mathbf{A} \cdot K\left[P t C l_{3}\left(\eta^{2}-C_{2} H_{4}\right)\right] \)
\( \mathbf{B} \cdot F e\left(\eta^{5}-C_{5} H_{5}\right)_{2} \)
\( \mathbf{c} \cdot C r\left(\eta^{6}-C_{6} H_{6}\right)_{2} \)
\( \mathbf{D} \cdot\left(C H_{3}\right)_{4} S n \)


Write the decimals shown in the
following place value table:
\( \begin{array}{llll}\text { Thousands } & \text { Hundreds } & \text { Tens } \\ \text { (i) } & & & \\ \text { (ii) } & 9 & 5 & 4 \\ \text { (iii) } & & & \\ & & & \end{array} \)


\( \ln a \Delta A B C \) if sides a and b remain
constant such that \( \alpha \) is the error in \( C \)
then relative error in its area is
A. \( \alpha \cot C \)
B. \( \alpha \sin C \)
\( c \cdot \alpha \tan C \)
D. \( \alpha \cos C \)


Write IUPAC name:


The cause of guttation is mainly due to
A. Root pressure
B. Osmosis
c. Transpiration pull
D. cohesive force


Write the units of rate constants for
zero order and first order reactions.


An ellipsoidal cavity is carved within a perfect conductor. A positive charge q is
placed at the centre of the cavity. The points \( A \) and \( B \) are on the cavity surfaces as shown in the figure. Then
This question has multiple correct options
A. Electric field near A in the cavity = Electric field near B in the cavity
B. Charge density at A = charge density at B
c. Potential at \( A= \) potential at \( B \)
D. Total electric flux through the surface of the cavity is \( q / \epsilon_{0} \)


The following circut represents
A. OR gate
B. XOR gate
C. AND gate
D. NAND gate


Root pressure is due to
A. Passive transport
B. Gravitation
c. Active transport
D. None of the above


Two convex lenses of focal lengths \( f_{1} \)
and \( f_{2} \) form images with magnification
\( \boldsymbol{m}_{1} \) and \( \boldsymbol{m}_{2}, \) when used individually for an object kept at the same distance
from the lenses. Then \( f_{1} / f_{2} \) is:
A \( \cdot \frac{m_{1}\left(1+m_{2}\right)}{m_{2}\left(1+m_{2}\right)} \)
в. \( \frac{m_{1}\left(1+m_{2}\right)}{m_{2}\left(1+m_{1}\right)} \)
c. \( \frac{m_{2}\left(1+m_{1}\right)}{m_{1}\left(1+m_{2}\right)} \)
D. \( \frac{m_{2}\left(1+m_{2}\right)}{m_{1}\left(1+m_{1}\right)} \)


Which of the following law(s) is/are included in Boolean algebra?
A. Commutative Law
B. Associative Law
c. Distributive Law
D. All of the above


The reaction, \( \boldsymbol{R} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{C O O H} \frac{\boldsymbol{R} e d \boldsymbol{P}}{\boldsymbol{B r}_{2}} \)
\( \boldsymbol{R}-\boldsymbol{C} \boldsymbol{H}_{2}-\underset{\boldsymbol{B} \boldsymbol{r}}{\boldsymbol{C}} \boldsymbol{H}-\boldsymbol{C O O H} \) is called:
A. Reimer-Tiemann reaction
B. Hell-volhard-zelinsky reaction
c. Cannizzaro reaction
D. Sandmeyer reaction


In the process of burning of magnesium in air, magnesium undergoes:
A. reduction
B. sublimation
c. oxidation
D. all of these


A boy throws a ball upwards with a velocity of \( 9.8 m s^{-1} . \) How high does
t go?


A uniform meter scale of mass \( 1 k g \) is placed on table such that a part of the scale is beyond the edge. If a body of
mass \( 0.25 k g \) is hung at the end of the scale then the minimum length of
scale that should lie on the table so that
it does not tilt is :
\( \mathbf{A} \cdot 90 \mathrm{cm} \)
B. \( 80 \mathrm{cm} \)
\( \mathbf{c} .70 \mathrm{cm} \)
D. \( 60 \mathrm{cm} \)


Name the pairs of adjacent angles in
the figures.


The first sign of puberty in female is
A. Breast development.
B. Menstruation.
c. High pitch of voice
D. sprouting of pubic hairs.


The length of a metal wire is \( L_{1} \) when
the tension is \( T_{1} \) and \( L_{2} \) when the
tension is \( T_{2} . \) The unstretched length of
wire is :
A \( \cdot \frac{L_{1}+L_{2}}{2} \)
в. \( \sqrt{L_{1} L_{2}} \)
c. \( \frac{T_{2} L_{1}-T_{1} L_{2}}{T_{2}-T_{1}} \)
D. \( \frac{T_{2} L_{1}+T_{1} L_{2}}{T_{2}+T_{1}} \)


Four particles, each of mass \( 1 \mathrm{kg} \) are placed at the corners of a square OABC of side \( 1 \mathrm{m} .0 \) is at the origin of the coordinate system. OA and OC are aligned along positive X-axis and positive Y-axis respectively. the position the vector of the center of mass is (in
\( \mathrm{m}) \)


Choose the correct options -
This question has multiple correct options
A. The metal added to gold to harden it is iron
B. The molten metal that catches fire in chlorine gas and gives off white fumes is sodium.
C. The metal that forms two types of its oxide and rust in moisture is iron. The formulas of its oxides are :
\( \mathrm{FeO} ; \mathrm{Fe}_{2} \mathrm{O}_{3} \)
D. The metal used in hot water systems is copper, because it is a good conductor of heat and electricity


Hydro metallurgy is used in the extraction of:
A. \( C u \)
в. \( A l \)
\( \mathrm{c} \cdot M g \)
D. Na


The properties of a compound are:
A. Similar to the properties of its constituents
B. Similar to the properties of one of the constituents
C. Different from the properties of its constituents
D. None of these


Find \( c \)
\( \lim _{x \rightarrow 0} \frac{\log \tan \left(\frac{\pi}{4}+a x\right)}{\sin b x}=c \frac{a}{b} \)


What should be the change in velocity of a body, if its mass is increased by four times for the same K.E of the body?


Which postulate of Dalton's atomic theory is the result of the law of conservation of mass?
A. All matter is made of very tiny particles called atoms
B. Atoms of a given element are identical in mass and chemical properties
c. Atoms of different elements have different masses and chemical properties
D. Atoms are indivisible particles and cannot be created nor destroyed


For the chemical reaction \( 5 B r^{\ominus}+ \)
\( B r O_{3}^{\ominus}+6 H^{\oplus} \rightarrow 3 B r_{2}+3 H_{2} O \)
Rate \( =k\left[B r^{\ominus}\right]\left[B r O_{3}^{\ominus}\right]\left[H^{\oplus}\right]^{2} \) The
molecularity and order of reaction with
respect to \( \left[B r^{\ominus}\right] \) is:
A .5,1
в. 1,5
\( c .1,1 \)
D. 6,2


If \( f(x)=x^{2}+\frac{1}{x^{2}}, \) then find the
minimum value of the function \( g(x)= \) \( \boldsymbol{f}(\boldsymbol{x})+\boldsymbol{f}\left(\frac{1}{\boldsymbol{x}}\right) \)


Define electric flux. Write its Sl unit.


A lady gives a dinner party for six guests. The number of ways in which they may be selected from ten friends,
if two of the friends will not attend the
party together, is?
A .112
в. 140
\( c \cdot 164 \)
D. None of these


Marsilea belongs
A . Lycopsida
B. Pteropsida
c. Psilopsida
D. sphenopsida


Write the electronic configuration of
Lithium \( \left(\boldsymbol{L} \boldsymbol{i}_{2}\right) \) molecule. What is its
bond order?


An ionization chamber with parallel conducting plates as anode and
cathode, has \( 5 \times 10^{7} \) electrons and the
same number of singly charged positive ions per \( c m^{3} . \) The electrons are moving
towards the anode with velocity \( 0.4 \mathrm{m} / \mathrm{s} \) The current density from anode to
cathode is \( 4 \mu A / m^{2} . \) The velocity of positive ions moving towards cathode is
A. \( 0.4 m s^{-1} \)
B. zero
c. \( 1.6 m s^{-1} \)
D. \( 0.1 m s^{-1} \)


Prove the following identities. \( \sin h(-x)=-\sin h x \)


use Euclid's division algorithm to find
the H.C.F. of 135 and 714


Nuclear fusion produces:
\( A \cdot \) argon
B. deuterium
c. helium
D. krypton


The number of roots of the equation \( x+2 \tan x=\frac{\pi}{2} \) in the interval \( [0,2 \pi] \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c \cdot 3 \)
D. Infinite


A paste of substance \( A \) is used to
decorate the ceiling of your home.
Write the reaction of substance \( A \) with
\( \boldsymbol{H}_{2} \boldsymbol{O} \)


Given below are some characteristics of
vessels and tracheids.
(i) Multicellular with wide lumen
(ii) Dead cells
(iii) Cell walls are lignified
(iv) Discontinues lumen due to
presence of end walls
(v) Long, cylindrical tube-like structure
(vi) Elongated cells with tapering ends Categorize the above characteristics
with vessels \( (x) \) and tracheids \( (y) \) and select the correct option.
A. \( x-(i),(\text { (i), (iii) }),(v), Y-(i \text { i) }, \) (iii), (iv), (vi)
B. X-(i), (iii), (vi), Y- (ii), (iii), (iv), (v)
c. \( x-(i),(\text { iv }),(v), Y-(\text { ii), (iv) },(v),(v i) \)
D. \( x-(i),(\text { ii) },(v),(v i), Y-(i), \) (iii), (iv), (vi)


A metal M of atomic weight 54.94 g has a density of 7.42 g/cc. The apparent volume occupied by one atom of the
metal will be:
A. \( 8.13 \times 10^{-23} c c \)
B . \( 1.83 \times 10^{23} c c \)
c. \( 1.23 \times 10^{-23} c c \)
D. \( 7.404 c c \)


The ratio of the specific charge (e/m) of a proton to that of an \( \alpha \) particle is
A . 1: 2
B . \( 1: 1 / 4 \)
\( c \cdot 1: 4 \)
D. 1:1/2


Which of the following is correct about
fermentation?
A. Bread gets fermented due to formation of lactic acid.
B. Pulled up appearance of dough is due to production of \( C O_{2} \)
C. Fermentation in muscles produces alcohol
D. Both A and B


In \( 1899, \) Ernest Rutherford studied the absorption of radioactivity by thin sheets of metal foil and found two
components:
A. alpha radiation and beta radiation
B. gamma radiation and beta radiation
c. alpha radiation and gamma radiation
D. none of the above


Leaching is commercially carried out for in the concentration of:
A . galena
B. argentite
c. copper pyrites
D. tin stone


What is the angle between the lines
\( \frac{\boldsymbol{x}-\mathbf{2}}{\mathbf{1}}=\frac{\boldsymbol{y}+\mathbf{1}}{-\mathbf{2}}=\frac{\boldsymbol{z}+\mathbf{2}}{\mathbf{1}} \) and \( \frac{\boldsymbol{x}-\mathbf{1}}{\mathbf{1}}= \)
\( \frac{2 y+3}{3}=\frac{z+5}{2}=? \)
\( ^{A} \cdot \frac{\pi}{2} \)
в.
c. \( \frac{\pi}{6} \)
D. None of the above


Which of the following algebraic operations with scalar and vector physical quantities are meaningful.
(i) adding any two vectors
(ii) adding a scalar to a vector of the same dimensions
(iii) multiplying any vector by any scalar
(iv) multiplying any two scalars
(v) adding any two scalars
(vi) adding a component of a vector to the same vector.
A. Only (iii) \& (iv) are permissible
B. Only (ii) \& (iv) are permissible
c. only (iii) \& (v) are permissible
D. Only (i) (iii) (iv) (v)\& (vi) are permissible


If \( x \) and \( y \) are arbitrary extensive variables; then:

This question has multiple correct options
A. \( (x+y) \) is an extensive variable
B. \( x / y \) is an intensive variable
c. \( d x / d y \) is an intensive variable
D. Both (b) and (c)


Short / Long answer type questions. Explain why there, is greater emphasis on a molecular approach to understand life today than before


Two identical fuses are rated at 10 A. If
they are joined
(A) in parallel, the combination acts as
a fuse of rating 20 A
(B) in parallel, the combination acts as a fuse of rating 5 A
(C) in series, the combination acts as a
fuse of rating 10 A
(D) in series, the combination acts as a
fuse of rating \( 20 \mathrm{A} \) Select the correct options
\( A \cdot A, B \)
B. A, C
c. В, D
D. B, C, D


When the angle between incident ray
and mirror is increased. What will be
the effect on angle of reflection?
A . It will decrease
B. It will increase
c. It will remain constant
D. Can't be predicted


Sl unit of momentum is
A. dyne \( \cdot \)sec
в. \( g \cdot \mathrm{cms}^{-1} \)
c. \( N s \)
\( \mathbf{D} \cdot g m \cdot s \)


If an object is thrown vertically up, with the initial speed \( u \) from the ground, then the time taken by the object to return back to the ground is
\( ^{\mathrm{A}} \cdot \frac{u^{2}}{2 g} \)
в. \( \frac{u^{2}}{g} \)
c. \( \frac{u}{2 g g} \)
D. \( \frac{2 u}{g} \)


The highest evolutionary fitness is shown by
A. A Cheetah that catches the most prey
B. A Fox that successfully avoids predators
c. A Tortoise that has lived for over 100 years
D. A Wolf that recovers quickly from a wound
E. A Gorilla that reproduces several times


The value of \( A \) in the following reaction
is
\( _{4} \mathrm{Be}^{9}+_{2} \mathrm{He}^{4}=_{6} \mathrm{C}^{A}+_{0} \mathrm{n}^{1} \)
A . 14
B. 10
c. 12
D. 16


Out of 0.1 molal aqueous solution of
glucose and 0.1 molal aqueous solution of \( K C l, \) which one will have higher boiling point and why?


Lymph can be defined as
A. Blood minus corpuscles
B. Blood minus plasma
C. Blood minus WBC
D. Blood minus RBC and platelets


The dimensional formula of coefficient
of viscosity is
\( \mathbf{A} \cdot\left[M L T^{-1}\right] \)
B . \( \left[M^{-1} L^{2} T^{-2}\right] \)
\( \mathbf{c} \cdot\left[M L^{-1} T^{-1}\right] \)
D. none


Assume that each born child is equally likely to be a boy or a girl. If a family has two children, what is the conditional
probability that both are girls given that
(i) the youngest is a girl, (ii) at least one is a girl?
A. 0.33,0.34
В. 0.88,0.98
c. 0.78,0.67
D. 0.5,0.33


Which is a better method to find out if a
body possesses charge?
A. Attraction test
B. Repulsion test
c. Either A or B
D. None of the above


The degree of the differential equation \( \frac{d y}{d x}-x=\left(y-x \frac{d y}{d x}\right)^{-4} \)
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
\( D \)


is the electrical charges generated by rubbing.
A. electricity
B. static charge
\( c . \) both a and \( b \)
D. none of the above


Radio isotope useful in treating blood
cancer is
A. Cobalt 40
B. Carbon 60
c. cobalt 60
D. Carbon 14


A die is tossed twice. Find the
probability of getting 4,5 or 6 on the
toss and 1,2,3 or 4 on the second toss.


The shortest distance between the lines
\( \frac{x-3}{3}=\frac{y-8}{-1}=\frac{z-3}{1} \) and
\( \frac{\boldsymbol{x}+\mathbf{3}}{\mathbf{- 3}}=\frac{\boldsymbol{y}+\mathbf{7}}{\mathbf{2}}=\frac{\boldsymbol{z}-\mathbf{6}}{\mathbf{4}} \) is:
A \( \cdot 2 \sqrt{30} \)
B. \( \frac{7}{2} \sqrt{30} \)
\( c .3 \)
D. \( 3 \sqrt{30} \)


If \( A M \) between \( p^{t h} \) and \( q^{t h} \) terms of an \( A P \)
be equal to the AM between \( r^{t h} \) and \( s^{t h} \)
term of the \( A P, \) then \( p+q \) is equal to
A \( \cdot r+s \)
в. \( \frac{r-s}{r+s} \)
c. \( \frac{r+s}{r-s} \)
D. \( r+s+1 \)


The wavelength of the first number of Balmer series of hydrogen spectrum is:
\( \left[\mathrm{R} \text { for hydrogen }=1.09678 \times 10^{7} \mathrm{m}^{-1}\right] \)
A \( .6564 \AA \)
в. 5743 А
c. 3782 ,
D. 7532 月


A parallel plate capacitor with plates separated by air acquires \( 1 \mu \mathrm{C} \) of charge
when connected to a battery of \( 500 \mathrm{V} \). The
plates still connected to the battery are then immersed in benzene \( (k=2.25) \)
Then a charge flows from the battery is :
A. \( 1.25 \mu \) С
B. \( 2.28 \mu \) С
c. \( 1 / 4 \mu \) с
D. \( 4.56 \mu \) С


When \( K M n O_{4} \) act as an oxidising agent and ultimately form \( M n O_{4}^{2-}, M n O_{2}, M n_{2} O_{3} \) and \( M n^{2+} \)
then the numbers of electrons
transferred in each case, respectively,
are :
A .4,3,1,5
B. 1, 5, 3, 7
\( c \cdot 1,3,4,5 \)
D. 3, 5, 7,


If a beam of electrons travels in a
straight line in a certain region.Can we say there is no magnetic field?


When chlorine reacts with a gas \( X, \) an explosive inorganic compound Y is formed. Then X and Y will be:
A. \( X=O_{2} \) and \( Y=N C l_{3} \)
B. \( X=N H_{3} \) and \( Y=N C l_{3} \)
c. \( X=O_{2} \) and \( Y=N H_{4} C l \)
D. \( X=N H_{3} \) and \( Y=N H_{4} C l \)


Which of the following pairs
is/are functional isomers?
This question has multiple correct options
A. butan-2-ol and ethoxy ethane
B. ethanal and vinyl alcohol
C . acetaldehyde and acetone
D. ethanoic acid and methyl formate


The mass of nitrogen per gram in hydrazine is exactly one and half the
mass of nitrogen in the compound ammonia.
The fact illustrates the:
A. law of conservation of mass
B. multiple valency of nitrogen
C. law of multiple proportion
D. law of definite proportion


If the sum and difference of two
numbers are 20 and 8 respectively then the difference of their squares is :
A \( \cdot 12 \)
B. 28
\( c \cdot 160 \)
D. 180


Fill in the blank
is pattern of electrical
charges in Earth's atmosphere.
A. Electricity
B. Space electricity
c. Ground electricity
D. Atmospheric electricity


Explain why sliding friction is less than static friction.


Sodium benzoate gives benzene in presence of following:
\( \mathbf{A} \cdot N a O H+C a O \)
B. \( K_{2} C r_{2} O_{7}+H_{2} S O_{4} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{SO}_{4} \)
D. \( C r_{2} O_{3} \)


If \( \boldsymbol{x}=\frac{\boldsymbol{a}+\boldsymbol{b}}{\boldsymbol{a}-\boldsymbol{b}} \) and \( \boldsymbol{y}=\frac{\boldsymbol{a}-\boldsymbol{b}}{\boldsymbol{a}+\boldsymbol{b}}, \) find \( \boldsymbol{x}-\boldsymbol{y} \)


The weight of a person on Earth is 600
N. His weight on Moon will appear as:
A . zero
B. 100 N
c. 600 N
D. 6300 N


Quartz is a crystalline variety of :
A . Silicon carbide
B. Sodium silicate
c. silica
D. silicon


The sun subtends an angle of \( (1 / 2)^{\circ} \) at earth.The image of the sun is obtained on a screen using a converging lens of focal length \( 1.5 \mathrm{cm} . \) The diameter of the image will be :
A. \( 0.13 \mathrm{mm} \)
B. \( 0.9 \mathrm{mm} \)
\( c .1 .8 \mathrm{mm} \)
D. 0.6 mm


If the two observations are 10 and 0
their arithmetic mean is
A . 10
B. 0
c. 5
D. none of the above


Two types of boxes \( A, B \) are to be
placed in a truck having capacity of 10
tons. When 150 boxes of type \( A \) and 100 boxes of type \( B \) are loaded in the truck, it weighs 10 tons. But when 260 boxes
of type \( A \) are loaded in the truck, it can
still accommodate 40 boxes of type \( B \)
so that it is fully loaded. Find the weight of each type of box.


Which of the following is not an allotropic form of carbon?
A. Fluorine
B. Fullerene
c. Diamond
D. Graphite


Who first suggested presence of growth regulatory chemicals in plants?
A. went
B. sachs
c. Darwin
D. Paal


Sutural joints are present between
A. Thumb and metatarsal
B. Humerus and radio-ulna
C. Parietals of skull
D. Glenoid cavity and pectoral girdle


Which of the following is the property of
a system
A. pressure and temperature
B. internal energy
c. volume and density
D. all of the above


Saran is a copolymer of
A. vinyl chloride and vinyl acetate
B. vinylidene chloride and vinyl chloride
C . ethylene chloride and vinyl chloride
D. vinyl acctate and methyl acetate


Band gap in a semiconductor is of the
order
A. 6 eV
B. 0.60 eV
c. 60 eV
D. 0 eV


A battery of e.m.f. \( 3.0 \mathrm{V} \) supplies current through a circuit in which the
resistance can be changed. A high resistance voltmeter is connected
across the battery. When the current is
\( 1.5 \mathrm{A}, \) the voltmeter reads \( 2.7 \mathrm{V} \). The
internal resistance of the battery is
A . \( 4 \Omega \)
в. \( 1.2 \Omega \)
c. \( 0.2 \Omega \)
D. 2\Omega


According to postulated of Bohr's atomic model, the electron has a
definite amount of energy and the electron does not lose or gain energy
while moving:
A. in the orbit
B. in the nucleus
c. in the atom
D. in the molecul


What is respiration? Explain the process of respiration in human beings. (Figure not required)


It is desired to construct a cylindrical
vessel of capacity 500 cubic metres open at the top.What should be the dimensions of the vessel so that the
material need is minimum, given that the thickness of the material used is 2
\( \mathrm{cm} \)
\( ^{\mathbf{A}} \cdot \quad r=\left(\frac{100}{\pi}\right)^{1 / 3}, h=5\left(\frac{100}{\pi}\right)^{1 / 3} \)
B. \( _{r}=\left(\frac{500}{\pi}\right)^{1 / 3}=h \)
\( r=\left(\frac{1000}{\pi}\right)^{1 / 3}, h=\left(\frac{125}{\pi}\right)^{1 / 3} \)
\( r=\left(\frac{20}{\pi}\right)^{1 / 3}, h=\left(\frac{100}{\pi}\right)^{1 / 3} \)


An ecosystem consists of components comprising living organisms


State Gauss law in electrostatics. Using the law derive an expression for electric field due to a uniformly charged thin spherical shell at a point outside the shell.


If \( a^{x}=b^{y}=c^{z} \) and \( b^{2}=a c, \) then show
that \( \boldsymbol{y}=\frac{\boldsymbol{2} \boldsymbol{z} \boldsymbol{x}}{\boldsymbol{z}+\boldsymbol{x}} \)


A bullet of mass \( m \) is fired with a
velocity \( v \) into a fixed log of wood and penetrates a distance s before coming to rest. Assuming that the path of the bullet in the log of wood is horizontal, the average resistance offered by the log of wood is
A \( \cdot \frac{m v}{2 s^{2}} \)
в. \( \frac{m v^{2}}{2 s} \)
c. \( \frac{2 s}{m v^{2}} \)
D. \( \frac{m s^{2}}{2 v} \)


The IUPAC name of \( \left(C H_{3}\right)_{2} C H C H_{2} B r \)
is :
A. 1-Bromo-2-methyl propane
B. 2-bromo-2-methyl propane
c. 1-bromo-1-methyl propane
D. 2-bromo-1-methyl propane


Which of the following compound on heating gives oxygen as the only gas product?
A. Phosphate
B. Sulphate
c. Nitrate
D. Carbonate


Given a sample of one mole of the indicated gas at the following
conditions
Which of the following has the highest molecular speed?
A \( . H e \) at \( 100^{\circ} \mathrm{C} \) and 1 atm
B. \( H e \) at \( 25^{\circ} C \) and 1 atm
c. \( A r \) at \( 25^{\circ} C \) and 1 atm
D. \( A r \) at \( 25^{\circ} C \) and 2 atm
E. \( A r \) at \( 0^{\circ} C \) and 1 atm


Which of the following is true for a
telescope?
A. Final image is real and inverted.
B. It increases the size of the object.
C. It increases the angle subtended by image at the eye of the observer.
D. Smaller telescopes are more powerful


Assertion
If \( \boldsymbol{B} \subset \boldsymbol{A}, \) then \( \boldsymbol{P}(\boldsymbol{A} \cap \overline{\boldsymbol{B}})=\boldsymbol{P}(\boldsymbol{A})- \)
\( \boldsymbol{P}(\boldsymbol{B}) \)
Reason
\( (\boldsymbol{A} \cap \overline{\boldsymbol{B}}) \cup \boldsymbol{B}=\boldsymbol{A} \)
A. Both Assertion \& Reason are individually true \& Reason is correct explanation of Assertion
B. Both Assertion \& Reason are individually true but Reason is not the , correct (proper) explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true


An electric current through a metallic conductor produces around it.
A. Magnetic field
B. Mechanical force
c. Induced current
D. None


A parallelogram whose sides are \( 10 \mathrm{cm} \) and \( 5 \mathrm{cm} \) has one diagonal of \( 8 \mathrm{cm}, \) then the length of the other diagonal is
\( \mathbf{A} \cdot 12 \mathrm{cm} \)
B. \( 11 \mathrm{cm} \)
\( \mathrm{c} \cdot 14 \mathrm{cm} \)
D. None of these


A stationary point of \( \mathrm{f}(\mathrm{x})=\sqrt{16-\mathrm{x}^{2}} \)
is
\( A \cdot(4,0) \)
B. (-4, 0)
D. (-4,4)


In man, expired air contains oxygen
about
A . \( 4 \% \)
B . 10\%
c. \( 16 \% \)
D. 20\%


An aqueous solution of \( C H_{3} C O O H \)
has a \( \mathrm{pH}=3 \) and acid dissociation
constant of \( C H_{3} C O O H \) is \( 10^{-5} . \) What
will be the concentration of acid taken
initially?
A. \( 0.1 \mathrm{M} \)
B. 0.11 М
c. 0.09 М
D. 0.101 М


Which is paramagnetic and coloured?
A. \( K_{2} C r_{2} O_{7} \)
B \( \cdot\left(N H_{4}\right)_{2}\left[T i C l_{6}\right] \)
\( c \cdot v O S O_{4} \)
D. \( K_{3}\left[C u(C N)_{4}\right] \)


Find the \( 7^{t h} \) term of \( \left(3 x^{2}-\frac{1}{3}\right)^{10} \)
A \( \cdot \frac{66}{3} x^{7} \)
в. \( \frac{70}{3} x^{7} \)
c. \( \frac{66}{3} x^{8} \)
D. \( \frac{70}{3} x^{8} \)


In a galvanic cell, the electrons flow
from:
A. anode to cathode through the solution
B. cathode to anode through the solution
C. anode to cathode through the external circuit
D. cathode to anode through the external circuit


When a stone is thrown upwards:
A. Kinetic energy increases and Potential energy decreases
B. both Kinetic energy and Potential energy increase
C. Kinetic energy decreases and Potential energy increases
D. both remain constant


A vertical narrow smooth tube is bent
from it's diameter such that one
semicircular part of the tube is
horizontal and the other part is vertical
A smooth ball is released from the
highest point of the tube. If the
maximum speed of ball is \( \boldsymbol{x} \boldsymbol{m} / \boldsymbol{s}, \) then
the value of \( x \) is :
(neglect collision at bending) (take
\( \boldsymbol{R}=\mathbf{2 . 5 m} \) and \( \boldsymbol{g}=\mathbf{9 . 8 m} / \boldsymbol{s}^{2} \)


How does one explain the emission of electrons from a photosensitive surface with the help of Einstein's photoelectric equation?


The product of three consecutive even numbers when divided by 8 is \( 720 . \) The product of their square root is :
A. \( 12 \sqrt{10} \)
(1) 10111
B. 24\sqrt10
\( c \cdot 120 \)
D. None of these


Solve :
\[
\boldsymbol{x}^{2}+4 \boldsymbol{x}-\mathbf{6 0}=\mathbf{0}
\]


\( \operatorname{Let} f(x)=\left\{\begin{array}{ll}x^{n} \sin \frac{1}{x}, & x \neq 0 \\ 0, & x=0\end{array}, \) then \right.
\( f(x) \) is continuous but not differentiable
at \( x=0 \) if
A \( . n \in(0,1] \)
B. \( \mathrm{n} \in[1, \infty) \)
c. \( n \in(-\infty, 0) \)
\( \mathbf{D} \cdot \mathbf{n}=0 \)


A mono energetic electron beam with the speed of \( 5.2 \times 10^{6} m s^{-1} \) enters into
the magnetic field of induction \( 3 x \)
\( 10^{-4} T, \) directed normal to the
beam. Then the radius of the circle
traced by the beam:
\( \left(\operatorname{given} e / m=1.76 \times 10^{11} C K g^{-1}\right) \)
B. \( 0.98 m \)
\( c .0 .089 m \)
D. \( 9.8 m \)


Reticulate venation is a characteristic
of dicots. An exception to this generalisation?
A. Calophyllum
B. Ficus
c. Hibiscus
D. Zizyphus


There is a circular hole in a metal plate,
when the plate is heated, the radius of hole
A. Increases
B. Decreases
c. Unchanged
D. Depends upon metal


Hydraulic brakes are based on
A. Pascal's law
B. Torricelli's law
c. Newton's law
D. Boyle's law


Evaluate :
\( \lim _{x \rightarrow \infty} \frac{3 x^{2}+4 x+5}{4 x^{2}+7} \)


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


Metals are said to be shiny. Why do metals generally appear to be dull? How can their brightness be restored?


The instanteous speed of an object at the midpoint of a trip is defined to be
the
A. Distance it travels divided by the time the trip takes
B. Distance it travels multiplied by the time the trip takes
c. the speed precisely at the midpoint of the trip
D. the distance travelled during a very small time interva near the mid point of the trip
E. the initial speedplus the acceleration times half the time of the train


Which of the following product are correct?
uestion has multiple corrrect option


Which is the correct expression in the
formation of \( \mathrm{NaCl} \) ?
\( \mathbf{A} \cdot \Delta H_{f}=\Delta H_{s u b}+E_{i}+0.5 E_{b o n d} \) dissociation \( +E_{e a}+ \)
\( U_{\text {lattice enthalpy}} \)
\( \mathbf{B} \cdot \Delta H_{f}=\Delta H_{s u b}-E_{i}+0.5 E_{b o n d} d i s s o c i a t i o n+E_{E A}+ \)
\( U_{\text {lattice enthalpy}} \)
\( \mathbf{C} \cdot \Delta H_{f}=\Delta H_{s u b}+E_{i}-0.5 E_{b o n d} d i s s o c i a t i o n+E_{E A}+ \)
\( U_{\text {lattice enthalpy}} \)
\( \mathbf{D} \cdot \Delta H_{f}=\Delta H_{s u b}+E_{i}+0.5 E_{b o n d} d i s s o c i a t i o n+E_{E A}- \)
\( U_{\text {lattice enthalpy}} \)


Explain why rate of evaporation of an aqueous solution decreases with increase in humidity?


An observer is approaching with
velocity \( v \) towards a light source. If the
velocity of light is \( c, \) then velocity of light with respect to observer will be
A . \( c-v \)
B.
\( \mathrm{c} \cdot c+v \)
D. \( \sqrt{1-v^{2} / c^{2}} \)


If a body acquires electric charge temporarily under the influence of
charged body, then the process is called:
A. conduction
B. induction
c. radiation
D. dispersion


Blood platelets are present in the blood
of
A. Fishes
B. Amphibians
c. Reptiles
D. Mammals


Point, Plane: \( (0,0,0), 3 x-4 y+12 z= \)
3


If \( \tan \beta=\frac{n \sin \alpha \cos \alpha}{1-n \sin ^{2} \alpha}, \) show that
\( \tan (\alpha-\beta)=(1-n) \tan \alpha \)


A source of sound moves towards a
listener with a velocity equal to that of
sound. If the source emits n waves per
second, then the listener moving away from the source with the same velocity receives
A. n waves per sec
B. 2n waves per sec
c. zero waves per sec
D.


Why is a ventilator provided in a room?


The frequency of sound waves can be
expressed in
A . \( \mathrm{Hz} \)
B . cycle/second
\( c \cdot s^{-1} \)
D. all the above


The principle behind the working of an atom bomb is:
A. Nuclear fussion
B. Nuclear fission
c. Radioactivity
D. None of these


In the diagram on a lunar eilpse, if the positions od sun,Earth and moon are shown by \( (-4,6),(k,-2) \) and (5,-6)
respectively, then find the value of \( \mathrm{k} \)


Two particles are executing simple harmonic motion of the same
amplitude \( A \) and frequency \( \omega \) along the \( \boldsymbol{x}-\boldsymbol{a} \boldsymbol{x} \boldsymbol{i} \boldsymbol{s} . \) Their mean position is
separated by distance \( \boldsymbol{X}_{\mathbf{0}}\left(\boldsymbol{X}_{\mathbf{0}}>\boldsymbol{A}\right) . \) If
the maximum separation
between them is \( \left(X_{0}+A\right), \) the phase
difference between their motion is :-
A \( \cdot \frac{\pi}{4} \)
в. \( \frac{\pi}{6} \)
c. \( \frac{\pi}{2} \)
D. \( \frac{\pi}{3} \)


The conduction band and valency band of a good conductor are
A. well separated.
B. just touch.
c. very close.
D. overlapped.


If \( \hat{\boldsymbol{i}}-\boldsymbol{3} \hat{\boldsymbol{j}}+\boldsymbol{5} \hat{\boldsymbol{k}} \) bisects the angle between
\( \hat{a} \) and \( -\hat{i}+2 \hat{j}+2 \hat{k}, \) where \( \hat{a} \) is a unit
vector, then
A \( \cdot \hat{a}=\frac{1}{105}(41 \hat{i}+88 \hat{j}-40 \hat{k}) \)
B・ \( \hat{a}=\frac{1}{105}(41 \hat{i}+88 \hat{j}+40 \hat{k}) \)
C \( \quad \hat{a}=\frac{1}{105}(-41 \hat{i}+88 \hat{j}-40 \hat{k}) \)
D・ \( \hat{a}=\frac{1}{105}(41 \hat{i}-88 \hat{j}-40 \hat{k}) \)


Main factor which limits the rate of
photosynthesis on a clear day is
A. Chlorophyll
B. Light
\( c \cdot C O_{2} \)
D. water


The lattice energy of the carbonates of
Mg, Ca, Sr and Ba follow the order:
A. \( M g C O_{3}>C a C O_{3}>S r C O_{3}>B a C O_{3} \)
в. \( C a C O_{3}>S r C O_{3}>B a C O_{3}>M g C O_{3} \)
c. \( B a C O_{3}>S r C O_{3}>C a C O_{3}>M g C O_{3} \)
D. \( \operatorname{Sr} \mathrm{rCO}_{3}>\mathrm{MgCO}_{3}>\mathrm{CaCO}_{3}>\mathrm{BaCO}_{3} \)


The common refrigerant chlorofluoro-
methane (freon) and \( \mathrm{NO}_{2} \) is a serious
pollutant because
A. It lowers atmospheric temperature.
B. It prevents cloud condensation
c. It destroys haemoglobin
D. It disrupts \( O_{3} \) layer.


The dissociation of \( C a C O_{3} \) takes place
as per the equation,
\( \boldsymbol{C a} \boldsymbol{C O}_{3}(\boldsymbol{s}) \Leftrightarrow \boldsymbol{C a O}(\boldsymbol{s})+ \)
\( \boldsymbol{C O}_{2}(\boldsymbol{g}) ; \quad \boldsymbol{\Delta} \boldsymbol{H}=\mathbf{1 1 0} \boldsymbol{k} \boldsymbol{J} \)
If the reaction is carried out in a closed
vessel, the pressure of \( C O_{2} \) is increased
and reaches a constant value when:
A. Temperature is increased
B. Temperature is decreased
c. volume of vessel is increased
D. Amount of \( C a C O_{3} \) is decreased


Two sample of Hydrogen and Oxygen of
same mass possess same pressure and volume. The ratio of their temperature is
A . 1: 8
B. 1: 16
c. 8: 1
D. 16: 1


Which of the following path is assumed for the electron in the theory of
Rutherford?
A. Elliptical
B. Circular
c. spiral
D. All of the above


Martha picked out a pair of shoes she
wanted and brought them to the front of
the store to pay. The cashier told her
that the shoes were on sale for \( 30 \% \) off
the original price. She rang up the sale
price plus \( 5 \% \) sales tax, so Martha
ended up paying \( \$ 58.80 \) for the shoes.
What was the original price for the
shoes?
\( \mathbf{A} \cdot \$ 70 \)
B. \( \$ 75 \)
\( c . \$ 80 \)
D. \( \$ 85 \)
E . \( \$ 90 \)


According to Schrodinger model, nature of electron in an atom is as:
A. particles only
B. wave only
c. both simultaneously
D. sometimes wave and sometimes particle


toppr
Q Type your question
can emit a \( \beta \) particle \( \left(\beta_{1}\right) \) and come to
ground state by either emitting one \( \gamma \)
ray \( \left(\gamma_{1}\right) \) or emitting two \( \gamma \) rays \( \left(\gamma_{3} \& \gamma_{4}\right) \)
(ii) it can emit one \( \beta \) particle \( \left(\beta_{2}\right) \) and
come to ground state by emitting \( \gamma_{2} \)
ray.
Atomic masses : \( ^{198} A u=197.9682 \) a.m.u.
\( ^{198} \boldsymbol{H} \boldsymbol{g}=\mathbf{1 9 7 . 9 6 6 2} \) amu \( , 1 \) amu \( = \)
\( 930 M e V / c^{2} \)
The energy levels of the nucleus are shown in figure. What is the maximum kinetic energy of
emitted \( \beta_{2} \) particles?
A. \( 1.44 \mathrm{MeV} \)
в. \( 0.59 \mathrm{MeV} \)
c. \( 1.86 \mathrm{MeV} \)
D. \( 1.46 M \)


A proton and an electron initially at rest are accelerated by the same potential difference. Assuming that a proton is 2000 times heavier than an electron, what will be the relation between the de
Broglie wavelength of the proton \( \left(\boldsymbol{\lambda}_{\boldsymbol{p}}\right) \)
and that of electron \( \left(\boldsymbol{\lambda}_{e}\right) \) ?
A \( \cdot \lambda_{p}=2000 \lambda_{e} \)
B. \( \lambda_{p}=\frac{\lambda_{e}}{2000} \)
c. \( \lambda_{p}=20 \sqrt{5 \lambda_{e}} \)
D. \( \lambda_{p}=\frac{\lambda_{e}}{20 \sqrt{5}} \)


The value of \( \left|\begin{array}{ccc}1+x & 2 & 3 \\ 1 & 2+x & 3 \\ 1 & 2 & 3+x\end{array}\right| \) is
A \( \cdot(x-6) x^{2} \)
в. \( (x-6) \)
c. \( x^{2}(x+6) \)
D. \( (x-6) \)


Find the distance of the point (6,8) and the origin.


Which of the following anticodon sequence will bind to the transcribed codon \( 5^{\prime}-A C T-3^{\prime} ? \)
A . 3'-ACU-5'
B. 3'-TGA-5'
c. 3'-UGA-5'
D. 5'-UGA-3'
E. None of the above


If the plane a \( 2 x-3 y+5 z-2=0 \)
divides the line segment joining (1,2,3) and \( (2,1, k) \) in the ratio 9: 11
then \( k \) is
A .
в. -2
c. -10
D. \( -\frac{1}{2} \)


A car travels the first half of the
distance between two places with a speed of \( 60 k m p . \) The speed of the car for
the rest of the distance so that its
average speed becomes \( 90 k m p h \)
A. \( 60 \mathrm{kmph} \)
в. \( 90 \mathrm{kmph} \)
c. \( 120 \mathrm{kmph} \)
D. \( 180 \mathrm{kmph} \)


Which of the correct statement for the
given acids?
A. Phosphinic acid is a diprotic acid while phosphonic acid is a monoprotic acid.
B. Phosphinic acid is a monoprotic acid while phosphonic acid is a diprotic acid
c. Both are triprotic acids.
D. Both are diprotic acids


The position vector of \( \boldsymbol{P} \) relative to \( \boldsymbol{Q} \) as
a function of time is \( (\text { in } \boldsymbol{k} \boldsymbol{m}) \)
A \( \cdot \frac{128 t}{10^{3}} \hat{\imath}+\left(\frac{252 t}{10^{3}}-60 t\right) \)
3 \( \frac{252 t}{10^{3}} \hat{\imath}-\left(\frac{128 t}{10^{3}}\right) \)
c. \( \frac{128 t}{10^{3}} \hat{\imath}-\left(\frac{252 t}{10^{3}}\right) \)
D \( \cdot \frac{252 t}{10^{3}} \hat{\imath}+60 t \)


If \( x^{y}-y^{x}=1, \) then the value of \( \frac{d y}{d x} \) is :


A fly wheel rotating at 600 rev/min is brought under uniform deceleration and
stopped after 2 minutes, then what is
angular deceleration in rad/sec \( ^{2} \) ?


If \( A+B+C=\pi \) then which of the
following are true?
i. \( \tan 3 A+\tan 3 B+\tan 3 C= \)
\( \tan 3 A \tan 3 B \tan 3 C \)
ii. \( \cot \frac{A}{2}+\cot \frac{B}{2}+\cot \frac{C}{2}= \)
\( \cot \frac{A}{2} \cot \frac{B}{2} \cot \frac{C}{2} \)
A. only 1st statement is true
B. only 2nd statement is true
c. both statements are true
D. both statements are false


In Figure a spherical part of radius \( \frac{R}{2} \) is
removed from a bigger solid sphere of
radius \( R . \) Assuming uniform mass
distribution, a shift in the centre of
mass will be:
\( A \cdot \frac{-R}{6} \)
B. \( -\frac{R}{14} \)
\( \mathbf{c} \cdot \frac{R}{9} \)
D. \( \frac{R}{3} \)


Octane contains carbon
and \( ------- \) hydrogen atoms.
A . 8,16
в. 8,18
\( c \cdot 8,14 \)
D. 8, 20


Find external force required to move the conductor with the given acceleration.


A triangle can have:
A. Two right angles
B. Two obtuse angles
C. All angles more than \( 60^{\circ} \)
D. Two acute angles


Solve the absolute value of inequation \( \left|\frac{2 x-1}{3}\right| \leq 5 \)


n Figure, \( P Q \) is a chord of length \( 8 \mathrm{cm} \)
of a circle of radius \( 5 \mathrm{cm} . \) The tangents
at \( P \) and \( Q \) intersect at a point \( T . \) The
ength of \( T P \) is equal to \( \frac{w}{3}, \) then the
value of \( a \) is


The image of the point (3,-1,11) w.r.t
the line \( \frac{\boldsymbol{x}}{\mathbf{2}}=\frac{\boldsymbol{y}-\boldsymbol{2}}{\boldsymbol{3}}=\frac{\boldsymbol{z}-\boldsymbol{3}}{\boldsymbol{4}} \) is


The one has maximum radioactive
activity
A. Uranium
B. Plutonium
c. Radium
D. Thorium


what is the value of
\( \left|\begin{array}{ccc}\boldsymbol{a} & \boldsymbol{a}^{2} & \boldsymbol{a}^{\boldsymbol{3}}-\mathbf{1} \\ \boldsymbol{b} & \boldsymbol{b}^{2} & \boldsymbol{b}^{3}-\mathbf{1} \\ \boldsymbol{c} & \boldsymbol{c}^{2} & \boldsymbol{c}^{\boldsymbol{3}}-\mathbf{1}\end{array}\right|=? \)


The given setup is the heating of
ammonium chloride. While heating
solid ammonium chloride, it converts
into:
A. solid
B. liquid
\( c \cdot \) gas
D. none of these


Consider the situation shown in figure.
The wire \( A B \) slides on the fixed rails with
a constant velocity. If the wire \( A B \) is replaced by a semicircular wire, the
magnitude of the induced current will
A. Increase
B. Remain the same
c. Decrease
D. Increase or decrease depending on whether the semicircle bulges towards the resistance or away from it.


Solve. \( \frac{4 x+8}{5 x+8}=\frac{5}{6} \)


Assertion
TIBA \( (2,3,5 \) -triiodobenzoic acid) functions as antiauxin.
Reason
It blocks transport of auxin.
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


Let \( \hat{a} \) and \( \hat{b} \) be two unit vectors. If the vectors \( \vec{c}=\hat{a}+2 \hat{b} \) and \( \vec{d}=5 \hat{a}-4 \hat{b} \) are
perpendicular to each other, then the angle between \( \hat{a} \) and \( \hat{b} \) is
A. \( \frac{\pi}{6} \)
в.
\( c \cdot \frac{\pi}{3} \)
D. \( \frac{\pi}{4} \)


Horse shoe magnet is
A. v shaped
B. P shaped
c. u shaped
D. All


Write a balanced chemical equation for each of the following:
(i) Burning of ethane in plentiful supply of air.
(ii) Action of water on Calcium carbide.
(iii) Heating of Ethanol at \( 170^{\circ} \mathrm{C} \) in the
presence of conc. Sulphuric acid.


A cylinder of mass \( 10 k g \) and radius
\( 15 \mathrm{cm} \) is rolling perfectly on a plane of
inclinato of \( 30^{\circ} . \) The coefficient of
static friction \( \mu_{k}=0.25 . \) If the
inclination \( \theta \) of the plane is increased,
at what value of \( \theta \) does the cylinder begin to skid, and not roll perfectly?
A \( .37^{\circ} \)
В. \( 53^{\text {? }} \)
\( c \cdot 90^{\circ} \)
D. \( 0^{\circ} \)


Technique of growing plants without soil in nutrient solution is called
A. Parthenogenesis
B. Hydroponics
c. Aquaculture
D. Tissue culture


State whether the given statement is
true or false:

Bleaching powder contains about 50 \% available chlorine.
A. True
B. False


An ideal inductor takes a current of \( 10 A \)
when connected to a \( 125 V, 50 H z A C \)
supply. A pure resistor across the same
source takes 12.5 A. If the two are
connected in series across a \( 100 \sqrt{2} V \)
\( 40 H z \) supply, the current through the circuit will be
\( \mathbf{A} \cdot 10 A \)
B. \( 12.5 A \)
\( c .20 A \)
D. \( 25 A \)


A die is thrown:
\( \boldsymbol{P} \) is the event of getting an odd number
\( Q \) is the event of getting an even number.
\( R \) is the event of getting a prime
number.
Which of the following pairs is mutually exclusive?
A. \( P, Q \)
в. \( Q, R \)
\( c . P, R \)
D. None of these


What is the minimum energy required to launch a satellite of mass \( m \) from the
surface of a planet of mass \( M \) and radius \( R \) in a circular orbit at an
altitude of \( 2 R ? \)
A \( \cdot \frac{2 G m M}{3 R} \)
в. \( \frac{G m M}{2 R} \)
c. \( \frac{G m M}{3 R} \)
D. \( \frac{5 G m M}{6 R} \)


The expression \( 32 x^{3}+108 y^{3} \) can be
expressed in factor as
A \( \cdot(4 x+3 y)\left(4 x^{2}-6 x y+9 y^{2}\right) \)
B . \( (4 x-3 y)\left(4 x^{2}+6 x y+9 y^{2}\right) \)
C \( \cdot(4 x+3 y)\left(4 x^{2}+6 x y+9 y^{2}\right) \)
D. None of these


For two parallel lines and a transversal
\( \angle 1=74^{\circ} . \) For which pair of angle
measures is the sum the least?
A. \( \angle 1 \) and a corresponding angle
B. \( \angle 1 \) and the corresponding co-interior angle
C. \( \angle 1 \) and its supplement
D. \( \angle 1 \) and its complement


Callose carbohydrates can be traced in
A. vessels
B. Tracheids
c. sieve cells
D. sieve tubes


Identify the incorrect statement(s) with
respect to \( \mathbf{C O} \) :
This question has multiple correct options
A. it combines with water to give carbonic acid.
B. it combines with haemoglobin of the blood.
C. it is a powerful oxidising agent.
D. \( \mathrm{CO} \) is weak field ligand.


The azeotropic mixture of water and HCl
boils at \( 108.5^{\circ} \mathrm{C} \). When this mixture is
distilled, it is possible to obtain
A. pure \( H C l \)
B. pure water
c. neither pure HCI nor pure water
D. both pure HCl and pure water


A gas at a temperature of \( 27^{0} \mathrm{C} \) is heated
at a constant pressure to triple its volume. The final temperature of the gas
will be:
A \( \cdot 27^{0} \)
B . \( 627^{\circ} \mathrm{C} \)
c. \( 627 \mathrm{k} \)
D. \( 900^{\circ} \mathrm{C} \)


\( H_{2} O_{2} \) cannot oxidise :
A . \( P b S \)
В. \( N a_{2} S O_{3} \)
\( c \cdot O_{3} \)
D. KI


The direction cosine of a line which is
perpendicular to both the lines whose direction ratios are 1,2,2 and 0,2,1 are
A \( \cdot \frac{-2}{3}, \frac{1}{3}, \frac{2}{3} \)
B. \( \frac{2}{3}, \frac{-1}{3}, \frac{2}{3} \)
c. \( \frac{2}{3}, \frac{1}{3}, \frac{-2}{3} \)
D. \( \frac{2}{3}, \frac{-1}{3}, \frac{-2}{3} \)


Amines are classified as primary, secondary and tertiary amine.
(a) Represent the structure of secondary and tertiary amine.
(b) How will you convert nitrobenzene to
aniline?
(c) Aniline does not undergo Friedel-
Crafts reaction. Why?


A circular track of radius \( 300 \mathrm{m} \) is banked at an angle \( \frac{\pi}{12} \) radian. If the coefficient of friction between wheel of a
vehicle and road is \( 0.2, \) the maximum safe speed of vehicle is :
A \( \cdot 28 m s^{-1} \)
B . 38 \( m s^{-1} \)
\( \mathrm{c} \cdot 18 \mathrm{ms}^{-1} \)
D. \( 48 \mathrm{ms}^{-1} \)


Succession in a 6 metre deep pond exhibits a sequence of
A. Submerged Plants - Reeds \( \rightarrow \) Herbs \( \rightarrow \) Floating Plants
\( \rightarrow \) Shrubs \( \rightarrow \) Trees
B. Floating Plants - Submerged Plants \( \rightarrow \) Reeds \( \rightarrow \) Herbs
\( \rightarrow \) Shrubs \( \rightarrow \) Trees
c. Shrubs\rightarrow Trees \( \rightarrow \) submerged Plants \( \rightarrow \) Floating Plants
\( \rightarrow \) Reeds \( \rightarrow \) Herbs
D. Submerged Plants \( \rightarrow \) Floating Plants \( \rightarrow \) Reeds \( \rightarrow \) Herbs \( \rightarrow \) Shrubs \( \rightarrow \) Trees


A stone falls freely under gravity. It
covers distances \( h_{1}, h_{2} \) and \( h_{3} \) in the
first 5 second, the next \( 5 s \) and next
5 second respectively. The relation
between \( h_{1}, h_{2} \) and \( h_{3} \) is :
A \( \cdot h_{1}=2 h_{2}=3 h_{3} \)
B. \( h_{1}=\frac{h_{2}}{3}=\frac{h_{3}}{5} \)
c. \( h_{2}=3 h_{1} \) and \( h_{3}=3 h_{2} \)
D. \( h_{1}=h_{2}=h_{3} \)


Which hormone causes dilation of blood
vessels, increased oxygen consumption, and glycogenolysis?
A . ACTH
B. Insulin
c. Adrenaline
D. Glucagon


The correct order of boiling point is:
A \( . I>I I>I I I \)
B. \( I I I>I I>I \)
c. \( I I>I>I I I \)
I I \( I>I I I>I I \)
1


Which of the following is a natural satellite of our planet?
A. Moon
B. Sun
c. Jupiter
D. Saturn


Which of the following are intensive
properties?
This question has multiple correct options
A. heat capacity
B. refractive index
c. specific volume
D. entropy


When ammonia is passed over heated
Cu0, it is oxidized to:
A. \( N H O_{2} \)
в. \( N_{2} \),
c. \( N_{2} \)
D. \( N O_{2} \)


Coal tar belongs to a class of drugs known as:
A. aldehydes
B. alcohols
c. keratoplastics
D. none of above


Is it possible to have a polygon whose
sum of interior angles is \( 320^{\circ} ? \)
A. Yes
B. No
c. Ambiguous
D. Data not sufficient


The electrolytic process by which an oxide of metal is coated over metal
surface is called:
A. electrolysis
B. electroplating
c. anodising
D. electrorefining


Which of the following does not truly represent the property indicated against it?
A. \( B r_{2}<C l_{2}<F_{2} \) : Oxidising power
B. \( B r<C l<F \) : Electronegativity
c. \( B r<F<C l \) : Electron affinity
D. \( B r_{2}<C l_{2}<F_{2}: \) Bond energy


Calculate the enthalpy of formation of
\( \Delta H_{f} \) for \( C_{2} H_{5} O H \) from tabulated data and its heat of combustion as
represented by the following equations:
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\mathbf{1} / \mathbf{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \longrightarrow \)
\( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) ; \boldsymbol{\Delta} \boldsymbol{H}^{o}=-\boldsymbol{2} \mathbf{4} 1.8 \boldsymbol{k} \boldsymbol{J} \boldsymbol{m o l}^{-1} \ldots(\boldsymbol{i}) \)
\( \boldsymbol{C}(\boldsymbol{s})+\boldsymbol{O}_{2}(\boldsymbol{g}) \longrightarrow \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g}) ; \boldsymbol{\Delta} \boldsymbol{H}^{o}= \)
\( -393.5 k J m o l^{-1} \ldots(i i) \)
\( \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{O} \boldsymbol{H}(\boldsymbol{l})+\boldsymbol{3} \boldsymbol{O}_{2}(\boldsymbol{g}) \longrightarrow \)
\( \mathbf{3} \boldsymbol{H}_{\mathbf{2}} \boldsymbol{O}(\boldsymbol{g})+\mathbf{2} \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g}) ; \boldsymbol{\Delta} \boldsymbol{H}^{o}= \)
\( -1234.7 k J \ldots(i i i) \)
A. \( -2747.1 k J \mathrm{mol}^{-1} \)
в. \( -277.7 k \) J \( m o l^{-1} \)
c. \( -277.7 . k J m o l^{-1} \)
D. \( 2747.1 k J \) mol \( ^{-1} \)


Which of the following is not a chemical cell
A. Simple voltaic cell
B. Leclanche cell
c. Daniel cell
D. Solar cell


\( \frac{2}{2} \)


Assertion
Carbonate and hydroxide ores are concectrated by forth floatation
process.
Reason
In forth floatation process, mineral oil is used due to it preferentitally wets the gangue particles.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A particle in SHM is described by the displacement function: \( \boldsymbol{x}(\boldsymbol{t})= \) \( \boldsymbol{A} \cos (\boldsymbol{\omega} \boldsymbol{t}+\boldsymbol{\phi}) . \) If the initial \( (\boldsymbol{t}=\mathbf{0}) \)
position of the particle is \( 1 \mathrm{cm} \) and its initial velocity is \( \omega \mathrm{cm} / \mathrm{sec}, \) what is the
initial phase angle? This question has multiple correct options
A \( \cdot \frac{3 \pi}{4} \)
в. \( \frac{7 \pi}{4} \)
c. \( \frac{7 \pi}{2} \)
D. \( \frac{\pi}{4} \)


If \( f: R \rightarrow R \) and \( g: R \rightarrow R \) are defined
by \( f(x)=2 x+3, g(x)=x^{2}+7, \) then
the values of \( x \) for which \( f[g(x)]=25 \)
\( A \cdot \pm 1 \)
B. ±2
\( c .\pm 3 \)
D. ±4


The boiling points of haloalkane compounds are higher than haloarene compounds. Why?
A. Dipole-dipole intraction
B. Vanderwaal forces
c. Large surface area
D. Intramolecular forces


\( \lim _{x \rightarrow 0} \frac{\sqrt{16+x}-4}{x} \) is
\( A \cdot 4 \)
B. 8
\( c \cdot \frac{1}{4} \)
D.


If the range of a gun which fires a shell with muzzle speed \( v \), is \( R \), then the angle of elevation of the gun is
\( ^{\mathbf{A}} \cdot \cos ^{-1} \frac{v^{2}}{R g} \)
B. \( \cos ^{-1} \frac{R g}{v^{2}} \)
c. \( \frac{1}{2} \sin ^{-1} \frac{v^{2}}{R g} \)
D. \( \frac{1}{2} \sin ^{-1} \frac{R g}{v^{2}} \)


\( f(x)=\frac{x}{5}+\frac{5}{x} \) is increaing in
A. (-5,0)
в. (0,5)
c. \( (-\infty,-5) \cup(5, \infty) \)
D. (-5,5)


One mole of an ideal monoatomic gas is
heated at a constant pressure from \( 0^{\circ} \mathrm{C} \)
to \( 100^{\circ} \mathrm{C} . \) Then the change in the internal energy of the gas is (Given \( \boldsymbol{R}=\mathbf{8 . 3 2} \boldsymbol{J} \boldsymbol{m o l}^{-1} \boldsymbol{K}^{-1} \mathbf{)} \)
A \( .0 .83 \times 10^{3} J \)
в. \( 4.6 \times 10^{3} J \)
c \( .2 .08 \times 10^{3} J \)
D. \( 1.25 \times 10^{3} J \)


Arrange the following compounds in increasing order of their reactivity in nucleophilic addition reactions. Ethanal, Propanal, Propanone, Butanone
A. Butanone < Propanone <Propanal < Ethanal
B. Propanone <Butanone < Ethanal>>Propanal
c. Propanal < Ethanal < Propanone < Butanone
D. Ethanal <Propanal<Propanone <Butanone


G.J. Mendel died in
\( \mathbf{A} \cdot 1984 \)
B. 1894
\( c \cdot 1884 \)
D. 1926


For the hypothetical reactions, the
equilibrium constant \( \boldsymbol{K}_{\boldsymbol{p}} \) values are
given:
\( \boldsymbol{A} \rightleftharpoons \boldsymbol{B} ; \boldsymbol{K}_{\mathbf{1}}=\mathbf{2} ; \boldsymbol{B} \rightleftharpoons \boldsymbol{C} ; \boldsymbol{K}_{2}=\mathbf{4} ; \boldsymbol{C} \rightleftharpoons \)
\( \boldsymbol{D} ; \boldsymbol{K}_{3}=\boldsymbol{3} \)
The equilibrium constant \( (K) \) for the
reaction \( \boldsymbol{A} \rightleftharpoons \boldsymbol{D} \) is:
A .48
B. 6
\( c \cdot 24 \)
D. 12


Henry Cavendish discovered hydrogen.
A. True
B. False


Which of the following is a red liquid?
A. \( S F_{4} \)
в. \( S F_{6} \)
c. \( S C l_{2} \)
D. \( S_{2} C l_{2} \)


The equation of wave is given by \( Y= \)
\( A \sin \omega\left(\frac{x}{v}-k\right) \) where \( \omega \) is the angular
velocity and v is the linear velocity. The dimensions of k is:
A . \( [L T] \)
в. \( [T] \)
\( \mathbf{c} \cdot\left[T^{-1}\right] \)
\( \mathbf{D} \cdot\left[T^{-2}\right] \)


Which of the following is/are not
correctly matched?

This question has multiple correct options
A. Basic strength of oxides: \( C s_{2} O<R b_{2} O<K_{2} O<N a_{2} O< \)
\( L i_{2} O \)
B. Stability of peroxides: \( N a_{2} O_{2}<K_{2} O_{2}<R b_{2} O_{2}<C s_{2} O_{2} \)
C . Stability of bicarbonates: \( L i H C O_{3}<N a H C O_{3}< \)
\( K H C O_{3}<R b H C O_{3}<C s H C O_{3} \)
D. Melting point: \( N a F<N a C l<N a B r<N a I \)


The stratospheric ozone depletion leads
to
A. Global warming
B. Increase in the incidence of skin cancers
c. Forest fires
D. All of the above


A negatively charged ebonite rod is made to touch an insulated brass
sphere. The brass sphere gets electrically charged by the process of
A. conduction
B. induction
c. radiation
D. all the above


Find the centre and radius of each of the
following circle. \( (x-5)^{2}+(y-3)^{2}=20 \)


Let \( A \) and \( B \) are two matrices of same
order \( 3 \times 3 \) given by \( A= \) \( \left[\begin{array}{ccc}1 & 3 & \lambda+2 \\ 2 & 4 & 6 \\ 3 & 5 & 8\end{array}\right] B=\left[\begin{array}{ccc}3 & 2 & 4 \\ 3 & 2 & 5 \\ 2 & 1 & 4\end{array}\right] \) If \( \lambda=4 \)
\( \operatorname{then} \frac{1}{6}\{\operatorname{tr}(A B)+\operatorname{tr}(B A)\} \) is equal to
\( A \cdot 42 \)
B. 37
\( c .35 \)
D. None of thes


Gases \( X \) and \( Y \) are respectively:
A. \( C l_{2}, I_{2} \)
в. \( H C l, I_{2} \)
c. \( H C l, H I \)
D. \( H C l O, I_{2} \)


If \( \beta \neq 1 \) be any nth root of unity then
prove that \( 1+3 \beta+5 \beta^{2}+\ldots .+ \)
\( n \) terms \( =-\frac{2 n}{1-\beta} \)


Study the following statement:
"Two intersecting lines cannot be perpendicular to the same line".
Check whether it is an equivalent version to the Euclid's fifth postulate.
A. True
B. False


When a lens is inserted between an
object and a screen which are at a fixed distance apart, the size of the image in either \( 6 \mathrm{cm} \) and \( 2 / 3 \mathrm{cm} \). The size of the
object in cm is then
\( A \cdot 9 \)
B. 4
\( c \cdot 3 \)
D.


A particle tied to a string of negligible
weight and length \( L \) is rotated in a horizontal circular path with constant angular velocity having time period \( T . \) If
the string length is shortened by \( L / 2 \)
while the particle is in motion, the time
period is:
A . 47
в. 27
c. \( T / 2 \)
D. \( T / 4 \)


Which hormone has the anti-insulin
effect?
A. Calcitonin
B. cortisol
c. oxytocin
D. Aldosterone


Darwin said that all the organisms
reproduce
A. With mutations
B. Uprightly
c. Prolifically
D. Independently


In acid medium, which of the following
colour is obtained when
phenolphthalein is added?
A. Pink
B. Yellow
c. Green
D. Colourless


What is the effective resistance
between points \( \mathrm{P} \) and \( \mathrm{Q} \) ?
\( A \cdot 5 \Omega \)
B. \( 10 \Omega \)
\( c .15 \Omega \)
D. 20 \( \Omega \)


Write the polynomial \( 3 x^{2}-5 x-2 \) as a
product of two first degree polynomials.


Find the derivative of \( f(x) \) \( \frac{d}{d x}\left(e^{2 x}\right) \)


In a circle with center \( 0, \) central angle \( A O B \) has a measure of \( \frac{5 \pi}{4} \) radians. The area of the sector formed by central
angle \( A O B \) is what fraction of the area
of the circle?
A \( \cdot \frac{5}{8} \)
B. \( \frac{8}{5} \)
c. \( \frac{16}{5} \)
D. \( \frac{4}{5} \)


Draw ray diagrams each showing (i) myopic eye and
(ii) hypermetropic eye.


Red phosphorous is used in making:
A . red plastics
B. red dyes for plastics
c. safety match-striking surfaces
D. air fresheners


The process by which a solid changes directly into gas is called:
A. decantation
B. sublimation
c. condensation
D. sedimentation


Velamen present in orchids help in
A. Support
B. Respiration
c. Absorption of moisture from air
D. synthesizing food


DL and BM are the height on sides AB and AD respectively of parallelogram ABCD. If the area of the parallelogram is
\( 1470 \mathrm{cm}^{2}, \mathrm{AB}=35 \) and \( \mathrm{AD}=49 \mathrm{cm} \)
find the length of BM and DL.


State whether true or false:
An electromagnet requires a continuous supply of current to maintain the magnetic field.
A. True
B. False


The resistance across \( A \) and \( B \) in the
given figure will be:
\( \mathbf{A} \cdot 3 R \)
в. \( R \)
\( c \cdot \frac{R}{3} \)
D. None of the above


A spherical volume contains a
uniformly distributed charge density of
\( 2 \times 10^{-4} \mathrm{Cm}^{-3} . \) The electric field at a
distance of \( 4 \mathrm{cm} \) from the centre is :
A . \( 3 \times 10^{5} \)
B . \( 3 \times 10^{4} \)
\( c \cdot 2 \times 10^{5} \)
D. \( 3 \times 10^{6} \)


Synthetic auxins are employed for
A. Ripening of fruits
B. Increasing size of fruits
c. Killing weeds
D. Preventing elongation of internodes


Liquid kerosene fills a conical vessel of
base radius \( 2 \mathrm{cm} \). and height \( 3 \mathrm{cm} . \) This liquid leaks through a hole in the bottom and collects in a cylindrical jar of radius \( 2 \mathrm{cm} . \) The total height of kerosene after all of it is collected in the
cylindrical jar is -
\( \mathbf{A} \cdot \pi \mathrm{cm} \)
B. \( 2 \pi \mathrm{cm} \)
\( c \cdot 1 \mathrm{cm} \)
\( D \cdot 2 \mathrm{cm} \)


An observer finds the magnitudes of the acceleration of two bodies to be the
same. This necessary implies that the
two bodies.
A. are at rest with respect to each other
B. are at rest or move with constant velocities with respect to each other
C. are accelerated with respect to each other
D. may be at rest, moving with constant velocities or accelerated with respect to each other


Mark the incorrect option:
A. A force always make an object to move
B. A force has both magnitude and direction
C. A force can be represented by an arrow
D. Force is a vector quantity


Cheese is a
A. Glubular protein
B. Conjugated protein
C. Denatured protein
D. Derived protein


Anaerobic respiration of
animals/humans produces
A. Glucose and \( \mathrm{O}_{2} \)
B. \( \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH} \) and \( \mathrm{CO}_{2} \)
C. Lactic acid and water
D. \( \mathrm{CO}_{2} \) and \( \mathrm{H}_{2} \mathrm{O} \)


A Child's learning and socialization are most influenced by their


The current I and voltage V graphs for a given metallic wire of two different
temperatures \( T_{1} \) and \( T_{2} \) are shown in the following figure. It is concluded that:
A \( \cdot T_{1}>T_{2} \)
в. \( T_{1}<T_{2} \)
c. \( T_{1}=T_{2} \)
D. \( T-1=2 T_{2} \)


Rutherford's atomic model told that the
whole concentration of an atom is
located at the:
A. centre of atom
B. outside of atom
c. distributed throughout the atom
D. middle layer of atom


If at the same temperature and pressure, the densities of two diatomic
gases are \( d_{1} \) and \( d_{2} \) respectively, the
ratio of mean kinetic energy per
molecule of gases will be :
A . 1: 1
B . \( d_{1}: d_{2} \)
D. \( \sqrt{d_{2}}: \sqrt{d_{1}} \)


A verandah of width \( 2.25 \mathrm{m} \) is
constructed all along outside a room which is \( 5.5 m \) long and 4 m wide. Find
The cost of cementing the floor of the verandah at the rate of \( R s .200 \) per \( m \)


What happens when white phosphorus is heated with caustic soda?
Which of the following are possible
products?
This question has multiple correct options
\( \mathbf{A} \cdot \mathbf{P H}_{3} \)
В. РН \( _{5} \)
\( \mathrm{c} \cdot \mathrm{NaH}_{2} \mathrm{PO}_{2} \)
D. \( \mathrm{NaH}_{4} \mathrm{PO}_{2} \)


A function of time given by
\( (\sin \omega t-\cos \omega t) \) represents
A. simple harmonic motion
B. non-periodic motion
c. periodic but not simple harmonic motion
D. oscillatory but not simple harmonic motion


Calculate Mean Deviation about
Median
\( \begin{array}{lllll}\text { Class } & 0- & 10- & 20- & 30 \\ & 10 & 20 & 30 & 40\end{array} \)
Frequency \( \quad 5 \quad 10 \quad 20 \)
\( A \cdot 7 \)
B. 8
c. 19
D.


For the equilibrium, \( \boldsymbol{L i C l} \cdot \mathbf{3 N H}_{3}(s) \rightleftharpoons \boldsymbol{L i C l} \cdot \boldsymbol{N} \boldsymbol{H}_{3}(s)+ \)
\( 2 N H_{3}(g) \quad K_{p}=9 a t m^{2} \) at \( 37^{\circ} C \)
A 5 litre vessel contains 0.1 mole of
\( L i C l \cdot 3 N H_{3} . \) How many moles of \( N H_{3} \)
should be added to the flask at this
temperature to derive the backward reaction for completion? \( \boldsymbol{R}=\mathbf{0 . 0 8 2} \boldsymbol{a t m . L / m o l K} \)
A . 0.2
в. 0.59
\( c \cdot 0.69 \)
D. 0.79


Specific heat of aluminium is
\( 0.25 c a l / g^{o} C . \) The water equivalent of an aluminium vessel of mass one
kilogram is
\( \mathbf{A} \cdot 40 g m \)
в. \( 250 g m \)
\( \mathbf{c} \cdot 25 g m \)
D. \( 2.5 g m \)


Solubility of \( A g C l \) in \( 0.1 \mathrm{M} A g N O_{3} \) is
\( 10^{-9} M . \) Its solubility in \( 0.1 \mathrm{M} H C l \) is
A \( \cdot 10^{-9} M \)
В. \( 10^{-10} \) И
\( \mathbf{c} \cdot 10^{-5} M \)
D. none of these


The incomplete graph shows Dinesh's
savings from January to April. Dinesh
saved a total of Rs. 730 during the four
months. The amount of money saved in
February was as much as that saved in
March. How much did he save in March?
A . Rs.245
B. Rs.275
c. Rs.250
D. Rs.295


The ion that has \( s p^{3} d^{2} \) hybridization for the central atom, is:
A \( \cdot\left[I C l_{2}\right]^{-} \)
B . \( \left[I F_{6}\right]^{-} \)
c. \( \left[I C l_{4}\right]^{-} \)
\( \mathbf{D} \cdot\left[B r F_{2}\right] \)


Acetic acid is a
volatile acid than \( \boldsymbol{H}_{2} \boldsymbol{C O}_{3} \)
A. less
B. more
c. equally
D. can't say


The system of giving one name to the
individual is called as
A. Quasibinomial system
B. Semibinomial system
c. Mononoial system
D. Uninomial system


Give a relation \( \mathrm{R}=\{(1,2),(2,3)\} \) on the set
of natural numbers, add a minimum number of ordered pairs.
This question has multiple correct options
A. enlarged relation is symmetric
B. enlarged relation is transitive
c. enlarged relation is reflexive.
D. enlarged relation is equivalence relation


\( \int_{0}^{\pi} \frac{d x}{1+2^{\tan x}}= \)
\( A \cdot O \)
B . \( \pi / 4 \)
c. \( \pi / 2 \)
D.


Four particles are in \( x-y \) plane at :
(1) \( 1 k g \) at (0,0)\( \quad(2) 2 k g \) at
(1,0)\( \quad(3) 3 k g \) at (1,2)
(4) \( 4 k g \) at (2,0)
The centre of mass is located at:
A. (0.3,1.2)
В. (1.3,0.6)
c. (0.5,1.4)
D. (1.2,0.3)


Evaluate; \( \int_{0}^{\frac{2}{3}} \frac{d x}{4+9 x^{2}} \)


Which of the following correctly defines a species?
A. species is the lowest category of taxonomic hierarchy
B. It is the basic unit of classification.
c. It is the largest unit of classification.
D. Both A and B


For an LCR circuit, the power transferred
from the driving source to the driven
oscillator is \( \boldsymbol{P}=\boldsymbol{I}^{2} \boldsymbol{Z} \) cos \( \boldsymbol{p} \) Then
A. the power factor \( \cos \phi>0, P>0 \)
B. the driving force can give no energy to the oscillator (P \( =0 \) ) in some cases.
C. the driving force cannot syphon Out (P \( <0 \) ) the energy out of oscillator.
D. all of these.


Which of the following will form \( \sigma \) -bond (generally)?
A. s-s overlapping
B. Hybrid orbital overlapping
c. s-p overlapping
D. All of these


Impure chloroform gives precipitate
with \( A g N O_{3} \) due to the presence of:
A \( \cdot C O C l_{2} \)
в. НС l
c. \( C H_{2} C l_{2}+H C l \)
D. \( C C l_{4} \)


Gymnosperms do not have
A. Trees
B. Shrubs
c. Lianas
D. Herbs


What is earthing?
A. Passage of large electric current resulting from a lightning into the earth
B. Burying electric charge into the earth
C. Preventing electric charge from entering the earth
D. None of the above


If a body starts from rest and moves with uniform acceleration, then the displacement of the body is directly proportional to the cube of the time.
A . True
B. False


Assertion : Phenylketonuria is a recessive hereditary disease caused by
the body's failure to oxidize an amino acid phenylalanine to tyrosine, because of a defective enzyme

Reason : It results in the presence of phenylalanine in the urine
A. If both the assertion and the reason are true and the reason is a correct explanation of the assertion
B. If both the assertion and reason are true but the reason is not a correct explanation of the assertion
c. If the assertion is true but the reason is false
D. If both the assertion and reason are false
E. If the assertion is false but reason is true


An iron ball at \( 40^{\circ} \mathrm{C} \) is dropped in a mug
containing water at \( 40^{\circ} \mathrm{C} \)
The heat will
A. flow from iron ball to water
B. not flow from iron ball to water or from water to iron ball
c. flow from water to iron ball.
D. increase the temperature of both


If the lines \( \frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4} \) and
\( \frac{\boldsymbol{x}-\mathbf{3}}{\mathbf{1}}=\frac{\boldsymbol{y}-\boldsymbol{k}}{\mathbf{2}}=\frac{\boldsymbol{z}}{\mathbf{1}} \) intersect, then the
value of \( k \) is
A \( \cdot \frac{3}{2} \)
B. \( \frac{9}{2} \)
\( c \cdot-\frac{2}{9} \)
D. \( -\frac{3}{2} \)


In a closed insulated container, a liquid
is stirred, with a paddle to increase the temperature. Which of the following is
true?
A. \( \triangle E=W \neq 0, q=0 \)
В. \( \triangle E=W=q \neq 0 \)
c. \( \triangle E=0, W=q \neq 0 \)
D. \( W=0, \Delta E=q \neq 0 \)


Statement I: In the kinetic theory of gases, collisions between gas particles and the walls of the container are
considered elastic.

Statement II: Gas molecules are
considered pointlike, volumeless
particles with no intermolecular forces
and in constant, random motion.
A. Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement 1
B. Both the Statement 1 and Statement 2 are correct and Statement 2 is not the correct explanation of Statement 1
c. Statement 1 is correct but Statement 2 is not correct
D. Statement 1 is not correct but Statement 2 is correct
E. Both the Statement 1 and Statement 2 are not correct


Write down all possible subsets of the following set.
\( \{a\} \)


Assertion
Sound is considered a longitudinal
wave
Reason
Longitudinal waves cause the medium to vibrate parallel to the direction of the
wave
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


Two sets \( A \) and \( B \), of the three bulbs,
each, are glowing in two separate
rooms. When one of the bulbs in set \( A \) is
fused, the other two bulbs also cease to
glow. But in set \( B \), when one bulb fuses,
the other two bulbs continue to glow.
Explain why this phenomenon occurs


The function of enzymes in the non-
living system is to:
A. transport oxygen
B. provide immunity
c. catalyse biochemical reaction
D. none of the above


The half-life of a radioactive element is
8 hours. A given number of nuclei of that element is reduced to \( 1 / 4 \) of that number after two hours.
A . True
B. False


\( H_{2} O \) vapours on passing through anhydrous
\( C u S O_{4} \) turns it to:
A. green
B. blue
c. violet
D. white


Experimental analysis shows that a compound contains 0.015 moles of iron
and 0.0225 moles of sulfur. What is
the empirical formula of this compound?
A. \( F e_{2} S_{3} \)
в. \( F e_{3} S \)
c. \( F e S \)
D . \( F e_{7} S_{8} \)


A short bar magnet has a magnetic moment of \( 0.39 J T^{-1} . \) The magnitude
and direction of the magnetic field produced by the magnet at a distance of \( 20 \mathrm{cm} \) from the centre of the magnet
on the equatorial line of the magnet is
A. 0.049 G, N-S direction
B. 4.9 G, S-N direction
c. 0.0195 G, S-N direction
D. \( 19.5 \mathrm{G} \), N-S direction


The relation between time \( t \) and
displacement \( \boldsymbol{x} \) is \( \boldsymbol{t}=\boldsymbol{\alpha} \boldsymbol{x}^{2}+\boldsymbol{\beta} \boldsymbol{x} \) where
\( \alpha \) and \( \beta \) are constants then acceleration
of particle is proportional to-
\( \mathbf{A} \cdot v^{3} \)
B \( \cdot v^{2} \)
c. \( v^{3 / 2} \)
D. \( v^{2 / 3} \)


State the law of conservation of mass.
State the main points of Landolt's
experiment for experimental evidence of the law.


Select the correct reason for given statement 'Fluoride of \( A l \) is ionic while
chloride is covalent'.
A . IE of \( A l \) in \( A l F_{3}>A l C l_{3} \)
B. EA of fluorine > chloride
C . Lattice energy of \( A l F_{3}>A l C l_{3} \)
D. EA of fluorine < chlorine


Derive Newton's formula for thin lens.


Electric field at a distance \( x \) from the
origin its given as \( \boldsymbol{E}=\frac{\mathbf{1 0 0 N}-\boldsymbol{m}^{2} / \boldsymbol{C}}{\boldsymbol{x}^{2}} \)
Then potential difference between the
points situated at \( x=10 m \) and \( x= \)
\( 20 m \) is:
\( A \cdot 5 V \)
B. \( 10 V \)
\( c .15 V \)
D. \( 4 V \)


Which major product is formed in the free-radical bromination of methane by
limited supply of bromine?
A. Bromomethane
B. Dibromomethane
c. Tribromomethane
D. Tetra bromomethane