The \( \boldsymbol{K}_{s p} \) for \( \boldsymbol{C r}(\boldsymbol{O H})_{3} \) is \( 1.6 \times 10^{-30} \)
The solubility of this compound in water
is:
\( \mathbf{A} \cdot 4 \sqrt{1.6 \times 10^{-30}} \)
в. \( 4 \sqrt{1.6 \times 10^{-30} / 27} \)
c. \( 1.6 \times 10^{-9} \)
D. \( 2 \sqrt{1.6 \times 10^{-30}} \)


Select the anion which is the
strongest bronsted base.
A \( \cdot C l O_{4}^{-} \)
B. \( C l O_{3}^{-} \)
\( \mathrm{c} \cdot \mathrm{ClO}_{2}^{-} \)
D. \( C l O^{-} \)


Establish Lens maker's formula \( \frac{1}{f}=(\mu-1)\left(\frac{1}{R_{1}}-\frac{1}{R_{2}}\right) \)


Assertion(A): \( A, B, C \) are positive angles such that \( A+B+C=7 \pi \), then
maximum value of \( \cot A \cot B \cot C= \)
\( \frac{1}{3 \sqrt{3}} \)
Reason(R): \( A . M . \geq G . M \)
A. A is true, R is false
B. Both A and R are false
c. A is false, R is true
D. Both A and R are true


Explain why dilute nitric acid is generally considered a typical acid but not so in its reaction with metals?


Locate the centre of mass of three
particles of mass \( \boldsymbol{m}_{1}=\mathbf{1} \boldsymbol{k} \boldsymbol{g}, \boldsymbol{m}_{2}= \)
\( 2 k g \) and \( m_{3}=3 k g \) at the corners of an
equilateral triangle of each side of \( 1 \boldsymbol{m} \)


A lichen having much branched system of cylindrical or ribbon-like branches but a small thallus, is called as
A. Foliose lichen
B. Fruticose lichen
c. crsutaceous lichen
D. Thallose lichen


Assertion
The vectors \( \overrightarrow{\boldsymbol{A}}=\mathbf{2} \hat{\mathbf{i}}-\mathbf{3} \hat{\mathbf{j}}+\hat{\boldsymbol{k}} \) and \( \overrightarrow{\boldsymbol{B}}= \)
\( \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\boldsymbol{k}} \) are mutually perpendicular.
Reason
\( \overrightarrow{\boldsymbol{A}} \bullet \overrightarrow{\boldsymbol{B}}=0 \)
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


An organic compound with molecular
formula \( C_{9} H_{10} O \) forms 2,4 -DNP
derivative, reduces Tollen's reagent and undergoes Cannizaro reaction. On vigorous oxidation it gives a dicarboxylic acid which is used in the preparation of terylene. Identify the organic compound.


The synthesis of RNA and protein takes place in which phase of the cell cycle?
A. S phase
B. M phase
c. \( G_{1} \) and \( G_{2} \) phase
D. None of the above


State whether True or False
The square of \( \sqrt{5}-2 \) is \( 9-4 \sqrt{5} \)


is any material that can be made to react so that it releases
chemical or nuclear energy as heat.
A . Fossil fuel
B. Fuel
\( c . \) oil
D. All of the above


Which of the following are
diastereomers?
i. Me H
ì.
\( (\mathbf{I}) \)
iii. \( \underset{\mathbf{H}}{\mathbf{H}}+\underbrace{\mathbf{C O O} \mathbf{H}}_{\mathbf{M e}} \mathbf{B r} \)
iv.
A. (I) and (III)
B. (II) and (IV)
c. (I) and (II)
D. None of the above


Which of the following is correct for dimensionless quantity?
A. It does not exist
B. It always has a unitt
c. It never has a unit
D. It may have a unitt


A particle of mass \( m \) moving in the \( x \) direction with speed \( 2 y \) is hit by another particvle of mass \( 2 m \) moving in \( \boldsymbol{y} \) direction with speed \( \boldsymbol{v} . \) If the collision is perfectly inelastic, the percentage
loss in the energy during the collision is close to:
A . 44\%
B. 50\%
c. 56\%
D. 62\%


Correct balanced equation from the
following reactions is:
\( \mathbf{A} \cdot S+3 H N O_{3} \rightarrow H_{2} S O_{4}+N O_{2}+3 H_{2} O \)
B \( \cdot S+H N O_{3} \rightarrow H_{2} S O_{4}+2 N O_{2}+H_{2} O \)
\( \mathbf{c} \cdot S+3 H N O_{3} \rightarrow H_{2} S O_{4}+6 N O_{2}+2 H_{2} O \)
\( \mathbf{D} \cdot S+6 H N O_{3} \rightarrow H_{2} S O_{4}+6 N O_{2}+2 H_{2} O \)


An ecosystem does not normally alter because it is in a state of
A. Homeostasis
B. Imbalance
c. Deficient light
D. Deficient components


Optical fibre works on the principle of
A. Scattering
B. Refraction
c. Total internal reflection
D. Interference


Which of the following is a correct statement about veins?
A. Valves are absent
B. They carry blood towards heart
c. They always carry oxygenated blood
D. They carry blood away from heart


Assertion (A) : Isotopes of an element
can be separated by using a mass
spectrometer Reason (R): Separation of isotopes is possible due to difference in electron number of isotopes.
A. Both A and R are true and R is correct explanation of A
B. Both A and R are true and R is not correct explanation of A
C. A is true but R is false
D. A is false but R is true


Fat is digested in the
A. Large intestine
B. spleen
c. Mouth
D. Small intestine


A dome of a building is in the form of a hemisphere. From inside, it ws white-
washed at the cost of RS. \( 498.96 . \) If the
\( \operatorname{cost} \) of white-washing is Rs. 2.00 per
square metre, find the
(i) inside surface area of the dome,
(ii) volume of the air inside the dome.


Calcium imide on hydrolysis will give gas (B) which on oxidation by bleaching powder gives gas \( (\mathrm{C}) . \) Gas \( (\mathrm{C}) \) on reaction with magnesium gives compound (D). (D) on hydrolysis gives again gas \( (\mathrm{B}) .(\mathrm{B}),(\mathrm{C}) \) and \( (\mathrm{D}) \)
respectively are:
A. \( N H_{3}, N_{2}, M g_{3} N_{2} \)
B. \( N_{2}, N H_{3}, M g_{3} N_{2} \)
c. \( N_{2}, N_{2} O_{5}, M g\left(N O_{3}\right)_{2} \)
D. \( N H_{3}, N O_{2}, M g\left(N O_{2}\right)_{2} \)


State the appropriate scientific reasons
for the following statements.
An ion is a charged particle.


The area of the region bounded by the parabola \( (\boldsymbol{y}-\mathbf{2})^{2}=(\boldsymbol{x}-\mathbf{1}), \) the
tangent to the parabola at the point (2,3) and the X-axis is?
\( A \cdot 3 \)
B. 6
\( c .9 \)
D. 12


Which of the following are caused due to the unplanned clearing of land?
(i) The destruction of habitats
(ii) Soil erosion
(iii) Land slides
(iv) Global warming
A. only (i), (ii) and (iii)
B. Only (i), (ii) and (iv)
C. Only (i), (iii) and (iv)
D. (i), (ii), (iii) and (iv)


Which of the following statements is
correct?
A. The maximum number of unpaired electrons in a subshell is equal to \( 2 l+1 \)
B. The maximum value of magnetic moment for an atom with \( l=2 \) subshell is 3.9
C. The total spin of \( 3 d^{6} \) configuration is 3
D. Both A and B


A boy has the blood group 0. What is true of the inheritance of this blood
group in his case?
A. His mother should be with AB blood group
B. Both his parents could be heterozygous A group
c. His father could be homozygous B group
D. His mother could be homozygous A group


You are provided with a negatively charged gold leaf electroscope. State and explain what happens when an ebonite rod rubbed with fur is brought near the disc of electroscope.
A. divergence increases
B. divergence decreases
c. divergence remains same
D. can't say


The gravitational force of each planet in our solar system is different.The diagram below shows four planets listed in order from least amount of relative gravity to greatest amount of relative gravity. A person would weigh the most standing on which planet?
Mercury

Least Relative Gravity
Venus
Earth
Jupiter Greatest Relative Gravity
A. Mercury
B. Venus
c. Earth
D. Juipter


\( 92 U^{238} \) absorbs a neutron. The product emits an electron. This product further emits an electron. The result is
\( A \cdot_{94} P u^{239} \)
В \( \cdot_{90} P u^{23} \)
\( \mathrm{c} \cdot_{93} \mathrm{Pu}^{237} \)
D \( \cdot \) \( _{94} P u^{23} \)


Represent the following mixed infinite decimal periodic fractions as common fractions:
\( \frac{b-x}{\sqrt{b}-\sqrt{x}}-\frac{b^{3 / 2}-x^{3 / 2}}{b-x} \)


Which of the following lanthanide ion is paramagnetic?
A \( \cdot C e^{4} \)
в. \( Y b^{2} \)
\( c \cdot L u^{3} \)
D. \( E u^{2} \)


Figure shows a conducting loop placed near a long straight wire carrying a current \( i \) as shown. If the current
increases continuously, then the direction of the induced current in the
loop is clockwise.
True or false?


Show that the lines whose d.c's are
given by \( 2 l+2 m-n=0, m n+n l+ \)
\( l m=0 \) are perpendicular to each other


The approximate size of the nucleus of \( 64 N i \) is:
\( : 88^{\text {. }} \) :
\( A \cdot 3 \) fm
B. 4 fm
c. 5 fm
\( D \cdot 2 \mathrm{fm} \)


Which of the following gases has maximum solubility in water?
A. \( N_{2} \)
в. \( H_{2} \)
\( c \cdot O_{2} \)
D. \( N H_{3} \)


If alpha particle, proton and electron
move with the same momentum, then
their respective de-Broglie wavelengths
\( \lambda_{\alpha}, \lambda_{p}, \lambda_{e} \) are related as
A \( \cdot \lambda_{\alpha}=\lambda_{p}=\lambda_{e} \)
B . \( \lambda_{\alpha}<\lambda_{p}<\lambda_{e} \)
c. \( \lambda_{\alpha}>\lambda_{p}>\lambda_{e} \)
D. \( \lambda_{p}>\lambda_{e}>\lambda_{\alpha} \)
E \( \cdot \lambda_{p}<\lambda_{e}<\lambda_{\alpha} \)


Sodium [Na] and Sulphur [S] both are present in third period of modern periodic table. Which is more metallic
and why?


A positively charged sphere suspended with a silk thread is slowly pushed in a
metal bucket. After its insertion the lid
is closed. What will be the electric field
intensity inside when the sphere has touched the bucket?
\( (\sigma \) is the surface charge density of sphere)
A. zero
в. \( \frac{\sigma}{2 \varepsilon_{0}} \)
c. \( \frac{\sigma}{\varepsilon_{0}} \)
D. None of these


(a) Following reactions occur at cathode during the electrolysis of aqueous sodium chloride solution:
\( N a^{+}(a q)+e^{-} \longrightarrow N a(s) E^{0}= \)
\( -2.71 V \)
\( \boldsymbol{H}^{+}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{e}^{-} \longrightarrow \frac{\mathbf{1}}{\mathbf{2}} \boldsymbol{H}_{2}(\boldsymbol{g}) \boldsymbol{E}^{0}= \)
\( 0.00 V \)
On the basis of their standard reduction
electrode potential \( \left(\boldsymbol{E}^{0}\right) \) values
which reaction is feasible at the
cathode and why?
(b) Why does the cell potential of mercury cell remain constant throughout its life?


Among the following, the species that is both tetrahedral and diamagnetic is:
A \( \cdot\left[N i C l_{4}\right]^{2+} \)
B. \( N i(C O)_{4} \)
c. \( \left[N i(C N)_{4}\right]^{2+} \)
D. \( \left[N i\left(H_{2} O\right)_{6}\right]^{2+} \)


A plane mirror makes an angle of \( 30^{\circ} \) with horizontal. If a vertical ray strikes
the mirror, find the angle between mirror and reflected ray
A . \( 30^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 90^{\circ} \)


A chemical bond between two atoms is:
A. The tunnel in an atom through which the other one can pass
B. The energy of the individual atoms
c. The link between them
D. A third, connecting atom


For the equilibrium, the equilibrium concentration of \( S O_{3} \) will be affected by:
\( \mathbf{2} \boldsymbol{S} \boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{O}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{2} \boldsymbol{S} \boldsymbol{O}_{3}(\boldsymbol{g}), \boldsymbol{\Delta} \boldsymbol{H}= \)
\( -198 k J \)
This question has multiple correct options
A. doubling the volume of the reaction vessel
B. increasing the temperature at constant volume
c. adding more oxygen to the reaction vessel
D. adding helium to the reaction vessel at constant volume


At a particular temperature and
atmospheric pressure, the solid and liquid phases of a pure substance can
exist in equilibrium. Which of the following term defines this temperature? This question has multiple correct options
A. Normal melting point
B. Equilibrium temperature
c. boiling point
D. Freezing point


A uniform rod of length L lies on a smooth horizontal table A particle
moving on the table strikes the rod perpendicularly at an end stops.


For the reaction, \( \boldsymbol{A}(\boldsymbol{g})+\boldsymbol{B}(\boldsymbol{g}) \rightarrow \)
\( C(g)+D(g) \)
\( \Delta H^{0} \) and \( \Delta S^{0} \) are,respectively \( -29.8 k J m o l^{-1} \) and \( -0.100 k J K^{-1} \)
\( \operatorname{mol}-1 \) at \( 298 \mathrm{K} \)
The equilibrium constant for the
reaction at \( 298 K \) is :


There are \( _{--} \) gravitational lines of force inside a spherically symmetric shell
A. Infinitely many
B. Zero
c. varying number depending upon surface area
D. Varying number depending upon volume


Why is the series arrangement not used for domestic circuits?


The order of \( 2 y\left(\frac{d y}{d x}\right)^{2}+5 x\left(\frac{d^{2} y}{d x^{2}}\right)=0 \)
is
\( A \cdot 3 \)
B.
\( c \cdot 2 \)
D.


Electron acceptors in ETS are arrange according to
A. Decreasing positive potential
B. Increasing positive potential
c. Increasing negative potential
D. None of the above


Which thickening agent widely used in food, textile and pharmaceutical industry is extracted from kelps?
A. Cellulose
B. Mucilage
c. Fucic acid
D. Alginic acid


In the polar aprotic solvent, the increasing order of nucleophilicity is:
\( \boldsymbol{C F}_{3} \boldsymbol{C H}_{2} \boldsymbol{O}^{-}, \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{O}^{-}, \boldsymbol{C F}_{3} \boldsymbol{C H}_{2} \)
A \( \cdot C F_{3} C H_{2} O^{-}=C H_{3} C H_{2} O^{-}<C F_{3} C H_{2} S^{-}< \)
\( C H_{3} C H_{2} S^{-} \)
B. \( C F_{3} C H_{2} O^{-}<C H_{3} C H_{2} O^{-}<C F_{3} C H_{2} S^{-}< \)
\( C H_{3} C H_{2} S^{-} \)
c. \( C F_{3} C H_{2} O^{-}<C H_{3} C H_{2} O^{-}>C F_{3} C H_{2} S^{-}< \)
\( C H_{3} C H_{2} S^{-} \)
D. \( C F_{3} C H_{2} O^{-}>C H_{3} C H_{2} O^{-}>C F_{3} C H_{2} S^{-}> \)
\( C H_{3} C H_{2} S^{-} \)


Assertion
If an object is projected from the earth's surface with escape velocity, path of the
object will be parabola.
Reason
When object is projected with a velocity less than escape velocity from horizontal surface and greater than orbital velocity, path of the object will be ellipse.
A. STATEMENT-1 is True, STATEMENT-2 is True:
STATEMENT-2 is a correct explanation for STATEMENT-
B. STATEMENT-1 is True, STATEMENT-2 is True:
STATEMENT-2 is NOT a correct explanation for STATEMENT-1
c. STATEMENT-1 is True, STATEMENT-2 is False
D. STATEMENT-1 is False, STATEMENT-2 is True


A man saved RS. 200 in each of the first three months of his service. In each of
the subsequent months his saving
increases by Rs. 40 more than the saving of immediately previous month. His total saving from the start of service
will be Rs. 11040 after.
A. 18 months
B. 19 months
c. 20 months
D. 21 months


During the manufacture of Chlorine by the electrolysis of brine, the by-products
are :
This question has multiple correct options
\( \mathbf{A} \cdot \mathbf{H}_{2} \)
B. NaOH
c. \( N a C l+\mathrm{H}_{2} \)
D. NaCl


In a laminar flow the velocity of the liquid in contact with the walls of the tube is
A. zero
B. Maximum
c. In between zero and maximum
D. Equal to critical velocity


During protein synthesis the anticodon on tRNA pairs with
A. Codon on tRNA
B. Codon on mRNA
c. Ribosome unit
D. Codon on rRNA


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


Select the correct order of acidic nature
of non-metal oxide:
This question has multiple correct options
A. \( S O_{2}>S O_{3} \)
в. \( S O_{3}>S O_{2} \)
c. \( N O<N O_{2} \)
D. \( N O>N O_{2} \)


Which of the following statements are
incorrect ?
\( A \cdot S O_{3} \) is a stronger oxidising agent and more, acidic
\( \operatorname{than} S O_{2} \)
B. Selenium forms only two oxoacids i. e., selenous acid \( H_{2} S e O_{3} \) ) and selenic acid \( \left(H_{2} S e O_{4}\right) \)
C. The acidic strength and oxidizing power of oxo-acids are greater in +6 oxidation state than in +4 oxidation state.
D. The thermal stability of oxides of group 16 elements decreases in the order.
\( S O_{2}>S e O_{2}>T e O_{2}>P o O_{2} \)


If \( M_{2}= \) magnetization of a
paramagnetic sample, \( \mathrm{B}= \) external magnetic field, \( T= \) absolute temperature, \( C= \) curie constant then according to Curie's law in magnetism, the correct relation is
A \( \cdot M_{z}=\frac{T}{C B} \)
В. \( \quad M_{z}=\frac{C B}{T} \)
\( ^{\mathrm{c}} \cdot_{C}=\frac{M_{z}}{T} \)
D. \( _{C}=\frac{T^{2}}{M_{z} B} \)


Which of the following is not a
thermodynamic state function?
A. Internal energy
B. Work done
c. Enthalpy
D. Entropy


Which of the following oxidation state is not shown by Manganese?
\( A \cdot+1 \)
B. +2
\( c \cdot+4 \)
D. +7


A doctor has prescribed a corrective lens of power +1.5 D. Find the focal length of the lens. Is the prescribed lens diverging or converging?


A saturn year is 29.5 times the earth
year. How far is the saturn from the sun
if the earth is \( 1.50 \times 10^{8} k m \) away from
the sun?


When the angle of reflection is \( 40^{\circ}, \) the
angle between normal and the mirror
will be :
A \( \cdot 40^{\circ} \)
В. \( 90^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 60^{\circ} \)


A line passing through the origin and making an angle \( \frac{\pi}{4} \) with the line \( y- \) \( \mathbf{3} \boldsymbol{x}=\mathbf{5} \) has the equation
This question has multiple correct options
A. \( x+2 y=0 \)
в. \( 2 x=y \)
c. \( x=2 y \)
\( \mathbf{D} \cdot y+2 x=0 \)


Which of the following can show coordination isomerism?
(i) \( \left[\boldsymbol{C u}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\right]\left[\boldsymbol{P t C l}_{4}\right] ; \) (ii)
\( \left[\boldsymbol{F e}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right]_{2}\left[\boldsymbol{P t}(\boldsymbol{C N})_{6}\right]_{3} \quad ; \) (iii)
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right]\left[\boldsymbol{C r}\left(\boldsymbol{C}_{2} \boldsymbol{O}_{4}\right)_{3}\right] ; \) (iv)
\( \left[\boldsymbol{P t}(\boldsymbol{e n})_{3}\right]\left(\boldsymbol{S O}_{4}\right)_{2} \)


A stone projected vertically up from the ground reaches a height \( y \) in its path at
\( t_{1} \) seconds and after further \( t_{2} \) seconds
reaches the ground. The height \( y \) is
equal to
A \( \cdot \frac{1}{2} g\left(t_{1}+t_{2}\right) \)
B \( \cdot \frac{1}{2} g\left(t_{1}+t_{2}\right)^{2} \)
\( \mathbf{c} \cdot \frac{1}{2} g t_{1} t_{2} \)
D. \( g t_{1} t_{2} \)


Find the values of \( x \) and \( y, \) if \( \frac{\mathbf{2}}{\boldsymbol{x}}+\frac{\mathbf{6}}{\boldsymbol{y}}=\mathbf{1 3} ; \quad \frac{\mathbf{3}}{\boldsymbol{x}}+\frac{\boldsymbol{4}}{\boldsymbol{y}}=\mathbf{1 2} \)
A \( \cdot x=\frac{1}{6}, y=\frac{2}{3} \)
B. \( x=\frac{1}{3}, y=\frac{2}{3} \)
c. \( x=\frac{1}{7}, y=\frac{2}{3} \)
D. \( x=\frac{1}{2}, y=\frac{2}{3} \)


Gram negative monerans lacking cell wall show reproduction by
A. Elementary bodies
B. Binary fission
c. conidia formation
D. Endospore formation


The volume of a rectangular block of stone is \( 10368 d m^{3} \) Its dimensions re in
the ratio 3: 2: 1 If its entre surface is
polished at 2 paise per \( d m^{2} \) then the
total cost will be
\( A \cdot R s 31.50 \)
B. Rs 31.68
c. Rs 63
D. Rs 63.36


\( \lim _{x \rightarrow-5} \frac{2 x^{2}+9 x-5}{x+5} \)


Q Type your question
Why may be members of the same family, it does mean that they will behave in similar ways.

The same things can be said about elements in a group ("family") on the periodic table. For example, fluorine and iodine are members of the halogen family, but their physical properties are different, as shown in the table below.
Melting Point \( \quad \) Boiling Point Element \( \quad\left(^{\circ} C\right) \)
\( \left(^{\circ} C\right) \)
Fluorine
\[
220
\]
\( \begin{array}{ll}\text { lodine } & +118 \\ & +184\end{array} \)
What of the following is the BEST explanation for these differences in melting and boiling point?
This question has multiple correct options
A. Fluorine has a higher value for electronegativity than iodine
B. The covalent bond in the fluorine molecule is stronger than the covalent bond in the iodine molecule
C. lodine molecules are larger and more polarizable than fluorine molecules
D. Fluorine is a nonpolar molecule, but iodine is a polar molecule


At \( 80^{\circ} \mathrm{C}, \) the vapour pressure of pure
liquid \( \mathbf{A}^{\prime} \) is \( \mathbf{5} \mathbf{2 0} \mathbf{m m} \mathbf{H} \boldsymbol{g} \) and that of
pure liquid B' is 1000 mm \( H g \). If a
mixture solution of \( \mathbf{A}^{\prime} \) and \( \mathbf{B}^{\prime} \) boils at
\( 80^{\circ} \mathrm{C} \) and 1 atm pressure, the amount of A' in the mixture is:
\( [1 a t m=760 m m H g] \)
A. 48 mol\%
B . 50 mol\%
c. 52 mol\%
D. 34 mol\%


A ball is projected from the ground at angle \( \theta \) with the horizontal. After \( 1 s, \) it
is moving at angle \( 45^{\circ} \) with the horizontal and after \( 2 s \) it is moving
horizontally. What is the velocity of projection of the ball?
A \( \cdot 10 \sqrt{3} m s^{-1} \)
B \( \cdot 20 \sqrt{3} m s^{-1} \)
D. \( 20 \sqrt{2} \mathrm{ms}^{-1} \)


Jogen's taxable income for \( 2010-11 \) is
Rupees \( 5,00,000 . \) The tax rates are (i) nil for first \( 1,50,000, \) (ii) \( 10 \% \) for \( 1,50,001-3,00,000 \) and (iii) \( 20 \% \) for
the remaining. His Tax liability is:
A. Rs 45000
B. Rs 50000
c. Rs 55000
D. Rs 60000


\( \frac{x^{4}}{(x-1)(x-2)}=x^{2}+3 x+k+ \)
\( \frac{16}{x-2}-\frac{1}{x-1} \Rightarrow k= \)
\( A \)
B.
\( c .9 \)
D.


Which of the following will replace hydrogen from acids to form salts? \( \boldsymbol{S}, \boldsymbol{P}, \boldsymbol{N} \boldsymbol{a}, \boldsymbol{S} \boldsymbol{i} \)


Write the formula of curved \& total
surface areas of a hemisphere. Also find the ratio between then


You are given three bulbs \( 25 \mathrm{W}, 40 \mathrm{W} \) and \( 60 \mathrm{W} \). Which of them has the
lowest resistance?
A. 25 watt bulb
B. 40 watt bulb
c. 60 watt bulb
D. Insufficient data


In hydrogen spectrum, the wavelength of the line is \( 656 \mathrm{nm} \), where as in the
spectrum of a distant galaxy, the line wavelength is \( 706 \mathrm{nm} \). Estimated speed of galaxy with respect to the earth is :
A \( \cdot 2 \times 10^{8} m / s \)
В. \( 2 \times 10^{7} m / s \)
c. \( 2 \times 10^{6} \mathrm{m} / \mathrm{s} \)
D. \( 2 \times 10^{5} \mathrm{m} / \mathrm{s} \)


Using section formula prove that the point \( (0.7 .-7),(1,4,-5) \) and
(-1,10,-9) are collinear.


A binomial scientific name contains
A. Names of genera and family
B. Names of genera and species
C. Names of species and class
D. Names of class and kingdom


Solve the inequality and show the graph
of the solution on number line:
\( 3(1-x)<2(x+4) \)


If \( h(x)=2 x, g(x)=x^{2}, f(x)=2 \), then
find \( (f \circ g \circ h)(x) \)


Find the local maxima and local
minima for the given function and also find the local maximum and local
minimum values \( f(x)=\sin x- \)
\( \cos x, 0<x<2 \pi \)


Assertion
There is no difference in the graphs of momentum an velocity of a body performing SHM.
Reason
Momentum is proportional to velocity of
a body.
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 are incorrect


Arrange the following in increasing lattice energy.
\( B e C O_{3}, M g C O_{3}, C a C O_{3}, S r C O_{3}, B c \)


Why is Tyndall effect shown by colloidal particles? State four instances of observing the Tyndall effect?


Polyps and medusae are similar in
which one of the following context?
A. Both can be motile
B. Both are diploblastic.
c. Both are herbivorous.
D. Both have mature gonads.


Fill in the blank:
The planet farthest from the Sun is
A. Jupiter
B. Saturn
c. Uranus
D. Neptune


A proton and an alpha particle having the same kinetic energy are allowed to pass through a uniform magnetic field perpendicular to the direction of their motion. Compare the radii of the paths of proton and alpha particle.


List 1 and List 2 contains four entries
each. Entries of List 1 are to be matched
with some entries of List 2. One or more
than one entries of List 1 may have the matching with the same entries of List
2


The equatorial magnetic field of earth is
0.4G. Then its dipole moment on equator is
A \( \cdot 1.05 \times 10^{23} \mathrm{Am}^{2} \)
В. \( 2.05 \times 10^{23} \mathrm{Am}^{2} \)
c. \( 1.05 \times 10^{21} A m^{2} \)
D. \( 2.05 \times 10^{21} \mathrm{Am}^{2} \)


The given diagram shows respiratory
system of man.Which of the following
correctly shows the functions of the parts labelled \( \mathrm{W}, \mathrm{X}, \) Y and \( \mathrm{Z} \) ?
A. W-Facilitates movement of air by expansion and contraction, \( \mathrm{X} \) - Traps dust and helps to filter inhaled air, Y - Prevents the wind pipe from collapsing, Z - Help in exchange of gases.
B. W-Helps in gaseous exchange, \( x \) - Traps dust and helps to filter inhaled air, Y - Serves as a common passage for air and food, \( z \) - Protect the lungs from damage.
C. W-Prevents the wind pipe from collapsing, \( x \) - Serves as a common passage for air and food, Y - Helps in upward and downward movement of ribcage, Z - Trap dust and help to filter inhaled air
D. W- Facilitates movement of air by expansion and contraction, X - Helps in gaseous exchange, Y - Serves as a common passage for food and air, Z- Protect the lungs from damage.


Compare the physical properties of metals and non-metals in general with reference to malleability.
A. Both are malleable
B. None are malleable
c. only metals are malleable
D. only non-metals are malleable


If \( |\boldsymbol{x}|<1, \) then \( \lim _{n \rightarrow \infty}\{(1+x)(1+ \)
\( \left.\left.\boldsymbol{x}^{2}\right)\left(1+\boldsymbol{x}^{4}\right) \ldots . .\left(1+\boldsymbol{x}^{2 n}\right)\right\} \) is equal to
A \( \cdot \frac{1}{x-1} \)
в. \( \frac{1}{1-x} \)
c. \( 1-x \)
D. \( x-1 \)


\( \boldsymbol{S} \boldsymbol{O}_{2} \) turns limewater milky, \( \boldsymbol{3} .2 \boldsymbol{g} \) of \( \boldsymbol{S} \boldsymbol{O}_{2} \)
gives milkyness is:


What is the age of puberty in boys and girls?


The number of students spent more
than 5 hours in watching \( \mathrm{TV}, \) is
A . 32
B.
\( c \)
D. 14


Distinguish between anaphase of mitosis and anaphase I of meiosis.


The energy required to break a mercury drop of \( 1 c m \) radius into 1000 small
drops of equal size is \( \ldots \ldots J \) (given the
surface tension of mercury is
\( 0.4 N . m^{-1} \)
A. \( 144 \pi \times 10^{-2} \)
B. \( 1.44 \pi \)
c. \( 14.4 \pi \times 10^{-4} \)
D. 144


Two bodies \( X \) and \( Y \) carry charges \( -6.6 \mu C \) and \( -5 \mu C \).How many electrons should be transferred from \( X \) and Yso that they
acquire equal charges?
A \( .2 \times 10^{12} \)
B . \( 5 \times 10^{14} \)
\( c \cdot 5 \times 10^{12} \)
D. \( 5 \times 10^{13} \)


Find \( \frac{d y}{d x} \) when \( x^{2}+y^{2}=c^{2} \)


All cells of sex organs can form gametes in
A. Algae
B. Bryophyta
c. Pteridophyta
D. Gymnosperm


Match List - I (Event) with List - II (Order
of the time interval for happening of the
event) and select the correct option from the options given below the lists.
List - 1
(a) Rotation period of
(i) earth
Revolution period of
(ii)
(b) earth
\( (c) \)
Period of a light
(iii) wave
\( (d) \)
Period of a sound
iv wave
A \( \cdot(a)-(i),(b)-(i i),(c)-(i i i),(d)-(i v) \)
B. (a)-(ii), (b)-(i), (c)-(iv), (d)-(iii)
\( c \cdot(a)-(i),(b)-(i i),(c)-(i v),(d)-(i i i) \)
D. (a)-(ii), (b)-(i), (c)-(iii), (d)-(iv)


\( \left[\begin{array}{ccc}10 & 20 & 30 \\ 20 & 45 & 80 \\ 30 & 80 & 171\end{array}\right]= \)
\( \left[\begin{array}{lll}1 & 0 & 0 \\ 2 & 1 & 0 \\ 3 & 4 & 1\end{array}\right]\left[\begin{array}{lll}x & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 1\end{array}\right]\left[\begin{array}{lll}1 & 2 & 3 \\ 0 & 1 & 4 \\ 0 & 0 & 1\end{array}\right] \) then
\( \boldsymbol{x}= \)
\( A \cdot 10 \)
B. 20
\( c \cdot 30 \)
D. 40


Which of the following compounds possesses Lewis acid character? This question has multiple correct options
A \( . A l F_{3} \)
в. \( \operatorname{siF}_{4} \)
c. \( P F_{5} \)
D. \( B F_{3} \)


The escape velocity for the earth is \( v_{e} \)
The escape velocity for a planet whose radius is four times and density is nine times that of the earth, is :
A. \( 36 v_{e} \)
B. \( 12 v_{e} \)
\( c \cdot 6 v_{e} \)
D. \( 20 v_{c} \)


The value of Planck's constant is
\( 6.63 \times 10^{34} \mathrm{Js} . \) The speed of light is \( 3 \times \)
\( 10^{17} \mathrm{nm} s^{1} . \) Which value is closest to the
wavelength in nanometer of a quantum
of light with a frequency of \( 6 \times 10^{15} s^{1} ? \)
A . 10
B. 25
\( c .50 \)
D. 75


One sound wave strikes a person's ear every \( 1 / 100 \) of a second. The speed of sound where the person is located is
\( 345 m / s \)
What is the frequency of the sound?
A. \( 3.45 \mathrm{Hz} \)
в. \( 34,500 \mathrm{Hz} \)
c. \( 0.01 \mathrm{Hz} \)
D. \( 100 \mathrm{Hz} \)
E . \( 2.9 \mathrm{Hz} \)


Draw the v-t graph of uniform motion \&
The area under the v-t graph gives the displacement of the particle in a given time.
A. True
B. False


The formula to find variance is
This question has multiple correct options
\( \mathbf{A} \cdot \frac{\sum x^{2}}{n}-\left(\frac{\sum x}{n}\right) \)
\( ^{\mathrm{B}} \cdot \frac{\sum x^{2}}{n}-\left(\frac{\sum x}{n}\right)^{2} \)
C. \( \frac{\sum x^{2}}{n}-(\bar{x})^{2} \)
\( ^{\mathrm{D}} \cdot \frac{\sum x}{n}-\left(\frac{\sum x}{n}\right)^{2} \)


A coil of resistance \( 10 \Omega \) and 1000 turns
have the magnetic flux line of \( 5.5 \times \)
\( 10^{-4} W b . \) If the magnetic flux changed
to \( 5 \times 10^{-4} W \) b. in 0.1 sec, then the
induced charge in coil is
A. \( 50 \mu C \)
B. \( 5 \mu C C \)
\( c \cdot 2 \mu C \)
D. \( 20 \mu C \)


Find the length of \( B D \) in the given
figure
\( \mathbf{A} \)
B.
\( c \cdot 12 \)
0.15


A current of \( 0.01 \mathrm{mA} \) passes through the potentiometer wire of a resistivity of
\( 10^{9} \Omega \mathrm{cm} \) and area of cross-section
\( 10^{-2} \mathrm{cm}^{2} . \) The potential gradient is
A \( \cdot 10^{9} V / m \)
В. \( 10^{11} V / m \)
\( \mathbf{c} \cdot 10^{10} V / m \)
D. \( 10^{8} V / m \)


Energy band gap size for semiconductors is in the range
\( e V \)
\( \mathbf{A} \cdot 1-2 \)
B. \( 2-3 \)
\( \mathbf{c} \cdot 3-4 \)
\( \mathrm{D} \cdot>4 \)


evaluate:
\( \mathbf{3} \boldsymbol{x}-\mathbf{5} \boldsymbol{y}=\mathbf{1 6} ; \boldsymbol{x}-\mathbf{3} \boldsymbol{y}=\mathbf{8} \)


If \( P(A)=\frac{1}{4}, P(\bar{B})=\frac{1}{2} \) and \( P(A \cup \)
B) \( =\frac{5}{9}, \) then \( P(A / B) \) is
\( ^{A} \cdot \frac{7}{36} \)
в.
c. \( \frac{7}{18} \)
D. \( \frac{7}{72} \)


Below is a chart describing the
parameters of 5 metal wires:
\begin{tabular}{lll}
Wire & Length \( (\boldsymbol{m}) \) & Diameter \( (\boldsymbol{m m}) \) \\
1 & 1 & 0.5 \\
2 & 1 & 1 \\
4 & 2 & 0.5 \\
5 & 2 & 1 \\
\hline 6 & 2 & 2 \\
\hline
\end{tabular} Assuming all of the wires are made
from the same material, rank these
wires from highest to lowest resistance.
A. 4,5,6,1,3,2
B. 3,2,1,6,5,4
C. 4,1,5,2,6,3
D. 1,4,2,5,3,6
E. 4,5,6,1,2,3


From the periodic table select three possible non-metals which can show disproportionation reaction.


In the diagrams we conventionally show veins in blue.What is the actual colour
of the blood following through the following?
(i) In arteries
(ii) In veins (iii) In
capillaries


When \( F e C r_{2} O_{4} \) (chromite) is reduced with Carbon in an electric-arc furnace:
A \( \cdot \) crand \( F e_{2} O_{3} \) are formed
B. Fe and \( C r_{2} O_{3} \) are formed
c. Fe and Cr (ferrochrome) are formed
D. \( F e C r O_{4} \) is formed


A large glass slab \( (\mu=5 / 3) \) thickness \( 8 \mathrm{cm} \) is placed over a point source of light on a plane surface. It is seen that
light emerges out of the top surface of
the slab from a circular area of radius \( \mathbf{R} \)
cm. What is the value of R?


Butter is an example of which type of colloid?
A. solid in liquid
B. Liquid in solid
c. Liquid in liquid
D. Gas in liauid


The center of reflex arc is
\( A \). Brain
B. Spinal cord
c. Neuron
D. Stimulus


A voltmeter having a resistance of \( 998 \Omega \) is connected to a cell of emf \( 2 \mathrm{V} \) and
internal resistance \( 2 \Omega . \) The error in the
measurement of emf will be.
A \( \cdot 4 \times 10^{-1} \mathrm{V} \)
B . \( 2 \times 10^{-3} \mathrm{V} \)
c. \( 4 \times 10^{-3} v \)
D. \( 2 \times 10^{-1} \mathrm{V} \)


Assertion
Catalytic converters in automobiles help in reducing pollution.
Reason
Hydrocarbons are oxidised into \( C O_{2} \)
and \( H_{2} O \) in the presence of an Oxidation catalyst (Pt or Pd) and NO is
reduced to \( N_{2} \) by reduction catalyst. Catalytic converter has dual catalyst system.
\[
\begin{array}{r}
\boldsymbol{C}_{\boldsymbol{x}} \boldsymbol{H}_{\boldsymbol{y}}+\left(\boldsymbol{x}+\frac{\boldsymbol{y}}{4}\right) \boldsymbol{O}_{2} \longrightarrow \boldsymbol{x} \boldsymbol{C} \boldsymbol{O}_{2}+ \\
\frac{y}{2} \boldsymbol{H}_{2} \boldsymbol{O} \quad \boldsymbol{2} \boldsymbol{N} \boldsymbol{O}+\boldsymbol{2} \boldsymbol{C O} \longrightarrow \boldsymbol{N}_{2}+
\end{array}
\]
\( 2 C O_{2} \)
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


Calcium oxide is usually made by the thermal decomposition of materials, such as limestone or seashell, that contain calcium carbonate in a lime
kiln.
A. True
B. False


ldentify the wrong description of the
given figures
A . 1 represents far sightedness
B. 2 is correction for short sightedness
c. 3 represent far sightedness
D. 4 represents correction for far sightedness


The probability of guessing the correct answer to a certain questions is \( \frac{x}{2} . \)
the probability of not guessing the correct answer is \( \frac{3 x}{2}, \) then find the value
of \( x \)


Give one word for the following. An acid prepared from sulphur.


In the melting of ice at \( 0^{\circ} \mathrm{C} \), which are
favorable conditions?
A. High T \& High P
B. Low T \& High P
c. Low T \& Low P
D. High T \& Low P


J.J. Thomson found that:
A. Electron have negligible mass
B. It have one unit of negative charge
c. Option A and B both
D. None of the above


Which of the following compounds can act as a Lewis base?
A. \( H C l O_{2} \)
в. \( N H_{2} N H_{2} \)
c. \( N H_{4}^{+} \)
D. \( B F_{3} \)


As shown in the figure, a charge \( +2 C \) is situated at the origin 0 and another charge \( +5 C \) is on the \( x \) -axis at the point
A. The later charge from the point \( A \) is then brought to a point \( \mathrm{B} \) on the \( \mathrm{y} \) -axis. The work done is :
\( \left(\operatorname{given} \frac{1}{4 \pi \epsilon_{0}}=9 \times 10^{9} N m^{2} C^{-2}\right) \)
A \( \cdot 45 \times 10^{9} J \)
В \( \cdot 90 \times 10^{9} J \)
c. zero
D. \( -45 \times 10^{9} J \)


A capacitor of capacitance \( C_{0} \) is
charged to a potential \( V_{0} \) and then
isolated. A small capacitor \( C \) is then
charged from \( C_{0}, \) discharged and charged again. This process is being
repeated \( n \) times. Due to this, the
potential of the larger capacitor is
decreased to \( V \). The value of \( C \) is :
\( ^{\mathbf{A}} \cdot_{C_{0}}\left(\frac{V_{0}}{V}\right)^{1 / n} \)
\( ^{\mathrm{B}} C_{0}\left[\left(\frac{V_{0}}{V}\right)^{1 / n}-1\right] \)
\( ^{\mathbf{c}} \cdot_{C_{0}}\left[\left(\frac{V}{V_{0}}\right)-1\right]^{n} \)
\( ^{\mathrm{D}} C_{0}\left[\left(\frac{V_{0}}{V}\right)^{n}+1\right] \)


If \( f(x)=\frac{x^{3}}{3}-\frac{5 x^{2}}{2}+6 x+7 \) increas
in the interval \( T \) and decreases in the
interval \( S \), then which one of the
following is correct?
A \( . T=(-\infty, 2) \cup(3 \infty) \) and \( S=(2,3) \)
в. \( T=\Phi \) and \( S=(-\infty, \infty) \)
c. \( T=(-\infty, \infty) \) and \( S=\Phi \)
D. \( T=(2,3) \) and \( S=(-\infty, 2) \cup(3, \infty) \)


Which of the following is the first step of glycolysis?
A. Breakdown of glucose
B. Phosphorylation of glucose
c. conversion of glucose into fructose
D. Dehydrogenation of glucose


In the adjoining figure \( A, B, \) and \( C \) represents three progressive waves.
Which of the following statement about the waves is correct?
A \( \cdot \) wave \( \mathrm{C} \) lags behind in phase by \( \frac{\pi}{2} \) from \( \mathrm{A} \) and \( \mathrm{B} \) leads
by \( \frac{\pi}{2} \)
B. Wave C leads in phase by \( \pi \) from \( A \) and \( B \) lags behind by \( \pi \)
C. wave C leads in phase by \( \frac{\pi}{2} \) from A and lags behind by
\( \frac{\pi}{2} \)
D. Wave C lags behind in phase by \( \pi \) from \( \mathrm{A} \) and \( \mathrm{B} \) leads by \( \pi \)


Imagine that you are sitting in a chamber with your back to one wall. An electron beam, moving horizontally from back wall towards the front wall, is
deflected by strong magnetic field to your right side. What is the direction of
magnetic field?


The probability of a man hitting a target in one trial is \( \frac{1}{4} . \) The chances of hitting the target at least once in \( n \) trials exceeds \( \frac{2}{3}, \) then the value of \( n \) equals
\( A \cdot 2 \)
B. 4
\( c \cdot 6 \)
D. 8


If \( a+b+c \neq 0 \) and \( \left|\begin{array}{lll}a & b & c \\ b & c & a \\ c & a & b\end{array}\right|=0 \)
then using properties of determinants, prove that \( \boldsymbol{a}=\boldsymbol{b}=\boldsymbol{c} \)


The shape of water molecule which
should be tetrahedral has a bent or
distorted tetrahedral shape with a bond
angle \( 104.5^{\circ} . \) What could be the reason
for this?
A. \( l p \) - \( l p \) repulsion is more than \( l p \) - \( b p \) repulsion
c. \( l p \) -lp repulsion is equal to \( l \)p-\( - \)bp repulsion
D. Presence of lone pair does not affect the bond angle


\( \operatorname{Let} \boldsymbol{I}_{n}=\int_{0}^{\pi} \frac{\sin ^{2}(\boldsymbol{n} \boldsymbol{x})}{\sin ^{2} \boldsymbol{x}} \boldsymbol{d} \boldsymbol{x}, \boldsymbol{n} \in \boldsymbol{N}, \) then
A \( \cdot I_{n+2}+I_{n}=21_{n+1} \)
В. \( I_{n}=I_{n+1} \)
\( \mathbf{c} \cdot I_{n}=n \pi \)
D. \( I_{1}, I_{I}, I_{3}, \ldots \ldots I_{n} \) are in harmonic progression


Methyl orange is a \( _{-}-_{-}-_{-}-_{-}-_{-} \) type of indicator.


What do you understand by symbiotic nitrogen fixation? Describe the role of leghaemoglobin in nitrogen fixation. Outline the process of nitrogen fixation as it takes place in the
bacteroid inhabiting a legume nodule.


Assertion
Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be any function. Define
\( \boldsymbol{g}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) by \( \boldsymbol{g}(\boldsymbol{x})=|\boldsymbol{f}(\boldsymbol{x})| \) for all \( \boldsymbol{x} \)
Then, \( g \) is continuous is \( \boldsymbol{f} \) is
continuous.
Reason
Composition of two continuous functions is a continuous function
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The number of sigma and pi bonds in
a molecule of cyanogen are:
A .4,3
в. 3,4
\( c .5,2 \)
D. 3,5


toppr 5
Q Type your question
\( A \)
B.
\( c \)
\( D \)
\( E \)


Explain the role of allosteric site in enzyme inhibition.


Then, length (in \( c m \) ) of each of the sides
of the triangle is
\( \mathbf{A} \cdot 3,4,4 \)
в. 2.7,3.7,3.4
c. 2.3,4.2,3.6
D. 4,1.8,4


Identify \( A, B, C, D \) and \( E ? \)


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
\( |\boldsymbol{A}||\boldsymbol{a} \boldsymbol{d} \boldsymbol{j}(\boldsymbol{A})| \) is
A \( \cdot a^{3} \)
в. \( a^{6} \)
\( c \cdot a^{9} \)
D. \( a^{2} \)


ff \( (x)=\left\{\begin{array}{l}x^{2} x \geq 0 \\ x x<0\end{array}\right. \)
then \( (f o f)(x) \) is given by
A \( \cdot x^{2} \) for \( x \geq 0 \) and \( x \) for \( x<0 \)
B. \( x^{4} \) for \( x \geq 0 \) and \( x^{2} \) for \( x<0 \)
c. \( x^{4} \) for \( x \geq 0 \) and \( -x^{2} \) for \( x<0 \)
D. \( x^{4} \) for \( x \geq 0 \) and \( x \) for \( x<0 \)


Q Type your question
shooting competition. Use a graph
sheet and draw an ogive for the distribution.
\( \begin{array}{ll}\text { Scores } & \text { No. of shooters } \\ 0-10 & 9 \\ 10-20 & 13 \\ 20-30 & 20 \\ 30-40 & 26 \\ 40-50 & 30 \\ 50-60 & 22 \\ 60-70 & 15 \\ 70-80 & 10 \\ 80-90 & 8 \\ 90-100 & 7\end{array} \) Use your graph to estimate the median.


A bus of mass 1000 kg has an engine which produces a constant power of 50 kW. If the resistance to motion,
assumed constant is \( 1000 \mathrm{N} \). The
maximum speed at which the bus can travel on level road and the acceleration
when it is travelling at \( 25 \mathrm{m} / \mathrm{s}, \) will respectively be?
A \( .50 \mathrm{m} / \mathrm{s}, 1.0 \mathrm{m} / \mathrm{s}^{2} \)
B. \( 1.0 \mathrm{m} / \mathrm{s}, 50 \mathrm{m} / \mathrm{s}^{2} \)
\( \mathbf{c} \cdot 5.0 \mathrm{m} / \mathrm{s}, 10 \mathrm{m} / \mathrm{s}^{2} \)
D. \( 10 \mathrm{m} / \mathrm{s}, 5 \mathrm{m} / \mathrm{s}^{2} \)


In triangle \( A B C \) is right-angled at \( B \)
and \( B D \) is perpendicular to \( A C, \) then
find:
\( \cot \angle D B A \) is \( \frac{m}{12} . \) value of \( \mathrm{m} \) is,


A ray of light travelling in air strikes a
glass slab of \( 30^{\circ} . \) Calculate the angle of
refraction if refractive index of glass is
\( \mathbf{1 . 5} \)


Square root of 375 is -


1 \( m L \) of methyl acetate was added to a
flask containing \( 20 m L \) of \( N / 20 H C l \)
maintained at \( 25^{\circ} \mathrm{C} .2 \mathrm{m} L \) of the
reaction mixture were withdrawn at
different intervals and titrated with a
standard alkali solution. The following
results were obtained:
Time
\( \mathbf{7 5} \)
\( \mathbf{1 1 9} \)
\[
(\min )
\]
\( \mathbf{0} \)
Alkali
\[
\begin{array}{l}
\text { used }( \\
m L)
\end{array} \quad \begin{array}{l}
19.24 \\
\qquad 24.20
\end{array} \quad 26.60
\]
Show that the reaction follows first
order kinetics.


What is the name of the compound
shown in the figure?
\[
\begin{array}{rl}
\mathbf{H} & \mathbf{H} \\
\mathbf{H}-\mathbf{C}-\mathbf{C}- & \mathbf{H} \\
\mathbf{I} & \mathbf{I} \\
\mathbf{H} & \mathbf{H}
\end{array}
\]
A. 1-methyl propane
B. 3-methyl propane
c. Butane
D. 2-methyl butane


Evaluate: \( \int\left(\frac{1}{(\ln x)}-\frac{1}{(\ln x)^{2}}\right) d x \)
equals


Define Brownian movement. What is the
cause of Brownian movement in
colloidal particles? How is it
responsible for the stability of Colloidal
Sol?


Atoms with same atomic number and
different mass numbers are called:
A. Isobars
B. Isomers
c. Isotones
D. Isotopes


Displacement between max. P.E. position and max. \( K . E . \) position for a particle executing simple harmonic motion is:
A \( \cdot \pm \frac{a}{2} \frac{a}{2} \)
B. \( +a \)
\( c \cdot \pm a \)
D. -


A beam of protons with a velocity \( 4 \times \) \( 10^{5} m s^{-1} \) enters a uniform magnetic
field of \( 0.3 \mathrm{T} \) at an angle of \( 60^{\circ} \) to the
magnetic field. Find the pitch of the helix (which is the distance travelled by a proton in the beam parallel to the magnetic field during one period of the rotation). Mass of the proton \( =1.67 \times \)
\( \mathbf{1 0}^{-2 \mathbf{7}} \mathbf{k g} \)
\( A \cdot 2.3 \mathrm{cm} \)
B. 5.35 \( \mathrm{cm} \)
\( c \cdot 4.35 \mathrm{cm} \)
D. 6.35 \( \mathrm{cm} \)


The vessel leading blood into the Bowman's capsule is known as
A. Afferent arteriole
B. Efferent arteriole
c. Renal vein
D. Renal artery


The variation of \( A_{m} \) acetic acid with
concentration is correctly represented
by:
\( A \)
B.
\( \mathbf{c} \)
D.


An excited \( H e^{+} \) ion emits two photons in succession, with wavelengths
\( 108.5 n m \) and \( 30.4 n m, \) in making a
transition to ground state. The quantum number \( n, \) corresponding to its initial excited state is (for photon of wavelength \( \lambda \), energy \( E=\frac{1240 e V}{\lambda(\operatorname{in} n m)} \) )
\( \mathbf{A} \cdot n=5 \)
B . \( n=4 \)
\( \mathbf{c} \cdot n=6 \)
D. \( n=7 \)


A saturated hydrocarbon is shown by
\( C_{n} H_{20} . \) The value of \( n \) in this
compound is:
A . 18
B. 10
\( c \cdot 9 \)
D. 8


Write the molecular and structural
formulae of:
Thiosulphuric acid.


The product of five consecutive numbers is always divisible by?
\( \mathbf{A} \cdot 60 \)
B. 12
\( c \cdot 120 \)
D. 72


STATEMENT-1: Formation of water gas
is endothermic reaction.

STATEMENT-2: To prevent unwanted
reaction, hot air \( \& \) steam are
introduced into the
generator alternatively.
A. STATEMENT-1 is True, STATEMENT-2 is True:
STATEMENT-2 is a correct explanation for STATEMENT-
1
B. STATEMENT-1 is True, STATEMENT-2 is True:
STATEMENT-2 is NOT a correct explanation for STATEMENT-1
c. STATEMENT-1 is True, STATEMENT-2 is False
D. STATEMENT-1 is False, STATEMENT-2 is True


Cork Cambium of dicot stem originates
from
A. Dedifferentiated parenchyma cells of cortex
B. Dedifferentiated collenchyma cells of cortex
C. Parenchyma cells of medullary ray
D. Parenchyma cells of pericycle


In a mixture of gases. the average number of degrees of freedom per molecule is \( 6 . \) The rms speed of the molecules of the gas is c. The velocity of sound in the gas is xc/3. Find \( x \)


A plane which passes through the point (3,2,0) and the line \( \frac{x-3}{1}=\frac{y-7}{5}= \)
\( \frac{z-4}{4} \) is?
A. \( x-y+z=1 \)
в. \( x+y+z=5 \)
c. \( x+2 y-z=1 \)
D. \( 2 x-y+z=5 \)


Arif took a loan of Rs. 80,000 from a bank. If the rate of interest in \( 10 \% \) per
amount find the difference in amounts he would be paying after \( 1 \frac{1}{2} \) years if the interest is compounded half yearly.


When metals and their sulphides are simply mixed with dispersion medium?
A. Forms lyophillic colloids
B. Forms lyophobic colloids
c. Do not form colloids
D. Forms GEL


If the ratio of the corresponding sides of two similar triangles is \( 2: 3, \) then the
ratio of their corresponding altitude is :
A. 3: 2
B. 16: 81
\( c \cdot 4: 9 \)
D. 2:3


Which of the following is an electropositive element?
A. Nitrogen
B. Oxygen
c. Sodium
D. Argon


How does number of (i) valence
electrons (ii) valency; vary on moving from to right:
(a) in the second period of a periodic table ?
(b) in the third period of a periodic table
\( ? \)


Construct a triangle \( A B C, \) whose
perimeter is \( 12 \mathrm{cm} \) and whose sides are
in the ratio 2: 3: 4


Electric charge given to the hollow conductors resides
A. On the outer surface
B. At the centre
c. on the inner surface
D. Uniformly on the outer as well as on the inner surface


If a plane passes through a fixed point
(2,3,4) and meets the axes of reference
in \( A, B \) and \( C, \) the point of intersection
of the planes through \( A, B, C \) parallel to the coordinate planes can be
This question has multiple correct options
A \( \cdot(6,9,12) \)
B \( \cdot(4,12,16) \)
\( \mathbf{c} \cdot(1,1,-1) \)
D. (2,3,-4)


The silk fibres are held together in cocoon by a substance known as
A. Sericin
B. Cement
c. Glue
D. None of the above


Integrate the function \( \frac{\cos x}{\sqrt{1+\sin x}} \)


Which of the following limits vanish?


An \( \alpha- \) particle and a proton have their
masses in the ratio 4: 1 and charges
in the ratio \( 2: 1 . \) Find ratio of their de-
Broglie wavelengths when both move with equal velocities.
\( \mathbf{A} \cdot 1: 4 \)
B. 4: 1
c. 1: 2
\( D \cdot 2: 1 \)


A sacred lake is
A. Dal Lake of Kashmir
B. Khecheopalri Lake of Sikkim
C. Suraj Khand Lake of Haryana
D. Chilka Lake of Odisha


Estimate the mean free path of a
cosmic ray proton in the atmosphere at sea level. Given \( \sigma=10^{-26} \mathrm{cm}^{2} \)
\( \mathbf{A} \cdot 10^{4} c m \)
B. \( 10^{-4} \mathrm{cm} \)
\( \mathbf{c} \cdot 10^{6} c m \)
D. \( 10^{-6} \mathrm{cm} \)


A ray of light travelling in the direction \( \frac{1}{2}(\hat{i}+\sqrt{3} \hat{j}) \) is incident on a plane mirror. After reflection, it travels along the direction \( \frac{1}{2}(\hat{i}-\sqrt{3} \hat{j}) . \) The angle of
incidence is \( 30^{\circ} \)
A. True
B. False


\( G(1,1,-2) \) is the centroid of the
triangle \( A B C \) and \( D \) is the mid point of
\( \boldsymbol{B C} \cdot \) If \( \boldsymbol{A}=(-1,1,-4), \) then \( \boldsymbol{D}= \)
\( ^{\mathbf{A}} \cdot\left(\frac{1}{2}, 1, \frac{-5}{2}\right) \)
в. (5,1,2)
c. (-5,-1,-2)
D. (2,1,-1)


State Bohr's postulate of hydrogen atom which successfully explains the emission lines in the spectrum of
hydrogen atom. Use Rydberg formula to determine the
wavelength of \( \boldsymbol{H}_{\boldsymbol{\alpha}} \) line.
[Given: Rydberg constant \( \boldsymbol{R}= \)
\( 1.0310^{7} m^{-1} \)


In the figure, diagonals \( A C \) and \( B D \) of
quadrilateral \( A B C D \) intersect at \( O \)
such that \( O B=O D \), show that
\( a r(\Delta D O C)=a r(\Delta A O B) \)


Average cardiac output is
A. 4 litres per minute
B. 6.3 litres per minute
C. 5.0 litres per minute
D. 7.3 litres per minute


What is SHE? Explain its construction and application.


As the height of the liquid column increases, the pressure exerted by a liquid at the lowest point
A . decreases
B. depends on the nature of liquid
c. increases
D. none of the aove


What are sex hormones? Describe any
one male and one female sex hormones.


The position vectors of three points are \( \mathbf{2} \overrightarrow{\boldsymbol{a}}-\overrightarrow{\boldsymbol{b}}+\mathbf{3} \overrightarrow{\boldsymbol{c}}, \overrightarrow{\boldsymbol{a}}-\mathbf{2} \overrightarrow{\boldsymbol{b}}+\boldsymbol{\lambda} \overrightarrow{\boldsymbol{c}} \) and \( \boldsymbol{\mu} \overrightarrow{\boldsymbol{a}}-\mathbf{5} \overrightarrow{\mathbf{b}} \)
where \( \vec{a}, \vec{b}, \vec{c} \) are non coplanar vectors then the points are collinear when
A \( \cdot \lambda=-2, \mu=\frac{9}{4} \)
B. \( \lambda=-\frac{9}{4}, \mu=2 \)
c. \( \lambda=\frac{9}{4}, \mu=-2 \)
D. None of these


The vapour pressure of water at \( 23^{\circ} C \) is \( 19.8 \mathrm{mm} .0 .1 \mathrm{mole} \) glucose is dissolved in \( 178.2 \mathrm{g} \) water. What is the vapour pressure (in \( \mathrm{mm} \) ) of the resultant solution?
\( A \cdot 19 \)
B. 19.602
c. 19.402
D. 19.202


If \( y=\log [\tan x], \) find \( \frac{d y}{d x} \)


Sodium forms \( N a^{+} \) ion but it doesnot
form \( N a^{2+} \) because of
A. very low value of first and second 1.
B. very high value of first and second 1.
c. high value of first l.E and low value of second l.E
D. low value of first l.E and high value of second l.


Integral proteins are embedded in the phospholipid bilayer, and also called transmembrane proteins. Often times these integral proteins serve as channels through which molecules move across the cell membrane.
Proteins embedded in the interior of the
bilayer of the membrane are \( \ldots \). and
are made up of non-polar
A. Nonpolar, Nucleic acids
B. Polar, Amino acids
c. Hydrophilic, Nucleic acids
D. Hydrophobic, Amino acids


Carboxylic acids have higher boiling points than aldehydes, ketones and
even alcohols of comparable molecular mass. It is due to their
A. more extensive association of carboxylic acid via van der Waals force of attraction
B. formation of intramolecular H-bonding
c. formation of intermolecular H-bonding
D. formation of carboxylate ion


If \( 4 .^{n} C_{6}=33 .^{n-3} C_{3} \) then \( n \) is equal to
\( \mathbf{A} \cdot \mathbf{9} \)
B. 10
c. 11
D. none of these


Sewage water can be purified by
A . Aquatic plant
B. Microorganism
c. Penicillin
D. Fishes


How many sigma bonds are in a molecule of diethyl ether, \( \left(C_{2} H_{5}\right)_{2} O ? \)
\( A \cdot 14 \)
B. 12
\( c \cdot 8 \)
D. 16


8 gram of NaOH is mixed with 9.8 gram
of \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4}, \) the pH of the solution is:
A. more than 7
B. 7
c. less than 7
D. cant be said


Find the \( \Delta H \) of the following reaction.
\( \boldsymbol{O} \boldsymbol{F}_{2}(\boldsymbol{g})+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \longrightarrow \boldsymbol{O}_{2}(\boldsymbol{g})+ \)
\( 2 H F(g) . \) Average bond energies of \( O- \)
\( \boldsymbol{F}, \boldsymbol{O}-\boldsymbol{H}, \boldsymbol{O}=\boldsymbol{O} \) and \( \boldsymbol{H}-\boldsymbol{F} \) are \( \boldsymbol{4 4} \)
111,118 and 135 kcal mol \( ^{-1} \)
respectively.
A. \( \Delta H=-78 \) k cal
в. \( \Delta H=+78 \) k cal
c. \( \Delta H=-498 \) k cal


A source of sound producing wavelength \( 50 \mathrm{cm} \) is moving away from a stationary observer with \( \frac{1}{5}^{t h} \) speed of sound. Then what is the wavelength of sound heard by the observer?
\( \mathbf{A} \cdot 55 \mathrm{cm} \)
B. \( 40 \mathrm{cm} \)
\( c .60 \mathrm{cm} \)
D. \( 70 \mathrm{cm} \)


The domain of \( f(x)=\sqrt{\frac{\log _{3}|x-2|}{|x|}} \) is
\( A \cdot(-\infty,-1] \cup[3, \infty) \)
в. [2,3]
c. [1,2)\( \cup(2,3] \)
D. [0,3]


It is advised to tie any luggage kept on the roof of the bus with a rope.Why?


yual diape
\( P Q R S^{\prime} \) of dimensions, \( l \times l \) is placed
inside a constant and uniform Magnetic Field \( \vec{B}=B_{0}\left(\frac{1}{\sqrt{2}} \hat{i}+\frac{1}{\sqrt{2}} \hat{j}\right) \) as shown
in the figure such that it's sides are
initially parallel to the \( X \) and \( Y \) axes. Which of the following is the value for the "magnetic flux" associated with the
square loop initially (as in the figure above)?
A \( \cdot \theta_{S}=\frac{B_{0}}{\sqrt{2}} l^{\prime} \)
В . \( \theta_{s}=B_{0} l \)
c. \( \theta_{\mathrm{s}}=0 \)
D. \( \theta_{S}=\sqrt{2} B_{0} l^{2} \)


Flouride in drinking water causes
harmful effect on bones and teeth when
its concentration becomes:
A. greater than 10 ppm
B. less than 1 ppm
c. greater than 15 ppm
D. greater than 2 ppm


Which of the following reactions will not resulting the formation of carbon-
carbon bonds?
A. Reimer-Tieman reaction
B. Cannizaro reaction
c. Wurtz reaction
D. Friedel-Crafts acylation


Carolus Linnaeus classified plant kingdom on the basis of
A. Floral morphology
B. Overall morphology of plants
c. Type of sexual reproduction
D. Anatomical character


2000 cal of heat is supplied to 200 g of water. Find the rise in temperature. (Specific heat of water \( =1 \) cal \( g^{-1^{\circ}} \boldsymbol{C}^{-1} \) )
\( \mathbf{A} \cdot 10^{\circ} \mathrm{C} \)
B . \( 20^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 30^{\circ} C \)
D. \( 40^{\circ} \mathrm{C} \)


A line makes angle \( \theta_{1}, \theta_{2}, \theta_{3}, \theta_{4} \) with the
diagonals of the cube. Show that \( \cos ^{2} \theta_{1}+\cos ^{2} \theta_{2}+\cos ^{2} \theta_{3}+\cos ^{2} \theta_{4}= \)
\( \frac{4}{3} ? \)


\( b \)
\( d \)


In the diagram shown, a positively charged rod is brought near the knob of an uncharged electroscope. The leaves will :
A. diverge and will be negatively chargedd
B. diverge and will be positively charged
C. converge and will be negatively chargedd
D. converge and will be positive chargedd
E. converge and will remain neutral


Find the derivative \( : \cot x \)


The group of the element with electronic configurations: \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{2} \) is
2. If true enter 1 , else enter 0 .


Why is it desirable to use unleaded
petrol in vehicles fitted with catalytic
converters?


Gold has a very low specific heat
compared to water.
Based on this fact alone, which of the
following do we know is true?
A. Gold melts at a much higher temperature than water.
B. If I add heat to a chunk of gold, its temperature will go up more than a pot of water to which I add the same amount of heat.
C. If 1 add heat to a chunk of gold, its temperature will go up less than a pot of water to which I add the same amount of heat.
D. If I add heat to a chunk of gold, its temperature will go up more than a pot of the same mass of water to which I add the same amount of heat.
E. If I add heat to a chunk of gold, its temperature will go up less than a pot of the same mass of water to which add the same amount of heat.


For the electrostatic charge system as
shown in Fig. 3.121 , find
a. The net force on electric dipole, and
b. Electrostatic energy of the system


A \( 5.25 \% \) solution of a substance is isotonic with a \( 1.5 \% \) solution of urea
(molar mass \( =60 g m o l^{-1} \) ) in the same
solvent. If the densities of both the
solutions are assumed to be equal to \( 1.0 g c m^{-3}, \) molar mass of the substance will be:
A . \( 105.0 g \) mol \( ^{-1} \)
B. \( 210.0 g \) mol \( ^{-1} \)
c. \( 90.0 g \) mol \( ^{-1} \)
D. \( 15.0 g m o l^{-1} \)


A gulab jamun, contains sugar syrup up to about \( 30 \% \) of its volume. Find
approximately how much syrup would be found in 45 gulab jamuns, each shaped like a cylinder with two, hemispherical ends with length \( 5 \mathrm{cm} \)
and diameter \( 2.8 \mathrm{cm} \)


A heater is designed to operate with a
power of \( 1000 W \) in a \( 100 V \) line. It is
connected in combination with a
resistance of \( 10 \Omega \) and a resistance \( R \)
to a \( 100 \mathrm{V} \) mains as shown in the
figure. What will be the value of \( R \) so
that the heater operates with a power of
\( \mathbf{6 2 . 5} \boldsymbol{W} ? \)
A . \( 15 \Omega \)
B. \( 10 \Omega \)
\( c .5 \Omega \)
D. \( 25 \Omega \)


What is the speed in rpm if the apparent weight of the person at the highest point is zero?
A. 1.87 rpm
B. 2.87 rpm
c. 3.32 rpm
D. 2.08 rpm


Write the inclination of a line which is
Perpendicular to y-axis


Assertion: For the flow to be
streamlined, value of critical velocity should be as low as possible Reason: Once the actual velocity of flow of liquid becomes greater than the critical velocity, the flow becomes turbulent.
A. Both assertion and reason are true and reason is correct explanation of assertion
B. Both assertion and reason are true but reason is not the correct explanation of assertion.
c. Assertion is true but reason is false.
D. Both assertion and reason are false.


The relation between \( t \) and distance \( x \) is
\( \boldsymbol{t}=\boldsymbol{a} \boldsymbol{x}^{2}+\boldsymbol{b} \boldsymbol{x} \) where \( \boldsymbol{a} \) and \( \boldsymbol{b} \) are
constants. Express the instantaneous acceleration in terms of instantaneous
velocity.


An object is thrown vertically upward with a non zero velocity. If gravity is turned off at the instant the object
reaches the maximum height, what will happen?
A. The object continues to move in a straight line
B. The object will be at rest
C. The object falls back with uniform velocity
D. The object falls back with uniform acceleration


A particle moves from \( A \) to \( B \) such that
\( \boldsymbol{x}=\boldsymbol{t}^{2}+\boldsymbol{t}-\mathbf{3} . \) Its average velocity from
\( t=2 s \) to \( t=5 s \) is
\( A \cdot 6 m s^{-1} \)
3. \( 8 m s^{-1} \)
\( c \cdot 8.5 m s^{-1} \)
D. \( 7 \mathrm{ms}^{-1} \)


Which one of the following enzyme is absent in invertebrates?
A. Pepsin
B. Trypsin
c. Lipase
D. Amyalase


How many faradays of electricity will be
required by \( 3 \times 10^{12} \) electrons?


Two protons are kept at a separation of
\( 40 A^{o} . F_{n} \) is the nuclear force and \( F_{e} \) is
the electrostatic force between them.
Then
A. \( F_{n} \gg F_{e} \)
в. \( F_{n}=F_{e} \)
\( \mathrm{c} \cdot F_{n} \ll F_{e} \)
D. \( F_{n} \approx F_{e} \)


When heat is absorbed by the system, the sign of the value of \( q \) is taken to be
A. positive.
B. Negative
c. zero
D. None of these


Solve:
\( 5(4 x+1)-2-(5 x+3)=15 \)


What is the composition of water? In
what volume are its two constituent
combined?


Which one of the following scientist's name is correctly matched with the theory put forth by him?
A. De Vries - Theory of natural selection
B. Darwin - Theory of pangenesis
c. Weismann - Theory of continuity of germplasm
D. Pasteur - Theory of inheritance of acquired characters


(a) Write the principle of working of a metre bridge.
(b) In a metre bridge, the balance point
is found at a distance \( l_{1} \) with
resistances \( \mathrm{R} \) and \( \mathrm{S} \) as shown in the
figure. An unknown resistance X is now
connected in parallel to the resistance
and the balance point is found at a
distance \( l_{2} . \) Obtain a formula for \( X \) is
terms of \( l_{1}, l_{2} \) and \( s \)


The reaction of \( \mathrm{P}_{4} \) with aqueous NaOH
gives:
A \( \cdot P(O H)_{3} \)
в. \( P_{2} O_{5} \)
c. \( P(O H)_{5} \)
D. \( P H_{3} \)


The process due to which an uncharged body acquires electric charges when held near a charged body is called:
A. conduction
B. induction
c. convection
D. none of these


Which of the following contributes the least toward the atomic mass of an
element?
A. Protons
B. Neutrons
c. Electrons
D. Isotopes
E. Ions


A bag contains 6 white, 5 black and 4
red balls. Find the probability of getting either a white or a black ball in a single
draw. If the answer is \( a / b, \) where HCF of
\( a \) and \( b \) is \( 1, \) then find \( b-a ? \)


Evaluate
\( \left|\begin{array}{ccc}265 & 240 & 219 \\ 240 & 225 & 198 \\ 219 & 198 & 181\end{array}\right| \)


The purest zinc is made by
A. Electrolytic refining
B. zone refining
c. The van-Arkel method
D. Mond process


Eutrophication is often seen in
A. Mountains
B. Deserts
c. Fresh water lakes
D. Ocean


The electrolyte used in electrolytic
refining of impure aluminium is
\( \mathbf{A} \cdot A I_{2} O_{3}+C a F_{2} \)
B. \( N a_{3} A l F_{6}+C a F_{2} \)
\( \mathbf{c} \cdot A l_{2} O_{3}, N a_{3} A l F_{6} a n d C a F_{2} \)
D. Any aluminium salt is molten state


Predict product in the given reaction


Fill in the blanks
(a) Most liquids that conduct electricity are solutions of
and
(b) The passage of an electric current through a solution causes
effects.
(c) If you pass current through copper sulphate solution, copper gets
deposited on the plate connected to the terminal of the battery.
(d) The process of depositing a layer of any desired metal on another material
by means of electricity is called


Sulphur forms the chlorides \( S_{2} C l_{2} \) and
\( \boldsymbol{S C l}_{2} . \) The equivalent mass of sulphur in
\( \boldsymbol{S C l}_{2} \) is \( 16 \mathrm{g} / \) mol. Therefore, the
equivalent mass of sulphur in \( S_{2} C l_{2} \) is:
B . \( 16 \mathrm{g} / \mathrm{mol} \)
\( \mathbf{c} \cdot 64 \mathrm{g} / \mathrm{mol} \)
D. \( 8 \mathrm{g} / \mathrm{mol} \)


In some old texts it is mentioned that
\( 4 \pi \) lines of force originate from each unit positive charge. Comment on the
statement in view of the fact that \( 4 \pi \) is
not an integer.


If \( \boldsymbol{I}=\int_{0}^{\pi} x^{3} \log \sin x d x \) and \( I= \)
\( \int_{0}^{\pi} x^{2} \log (\sqrt{2} \sin x), \) then the value of
\( \frac{4}{3 \pi} I \) is equal to


Which of the following are needed for
blood clotting?
A \( \cdot \mathrm{Ca}^{++} \) and vitamin E
B. \( \mathrm{Ca}^{++} \) and vitamin \( \mathrm{K} \)
c. \( K^{+} \) and vitamin A
D. \( K^{+} \) and vitamin \( K \)


Assertion
Fahrenheit is the smallest unit
measuring temperature.
Reason
Fahrenheit was the first temperature
scale used for measuring temperature.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Reason is correct but Assertion is incorrect
D. Both Assertion and Reason are incorrect


Sodium benzene sulphonate after
reaction with \( N a O H \) undergoes acidic hydrolysis, the compound formed would be:
A. phenol
B. benzoic acid
c. benzene
D. disodium benzaldehyde


The chemical name of baking soda is:
A. sodium hydrogen carbonate
B. sodium carbonate
c. sodium bisulphite
D. none of the above


The amount of \( \left(N H_{4}\right)_{2} S O_{4} \) to be added
to \( 500 \mathrm{mL} \) of \( 0.01 \mathrm{m} N H_{4} O H \) solution
\( \boldsymbol{p} \boldsymbol{K}_{\boldsymbol{a}} \) for \( \boldsymbol{N} \boldsymbol{H}_{4}^{+} \) is \( \boldsymbol{9} .2 \boldsymbol{6} \) ) prepare a buffer
of \( p H=8.26 \) is?
A. 0.05 mole
B. 0.025 mole
c. 0.10 mole
D. 0.005 mole


The mass of the moon is about \( 1.2 \% \) of
the mass of the earth. Compared to the gravitational force that earth exerts on the moon, the gravitational force of the moon exerted on earth:
A. Is the same
B. Is smaller
c. Is greater.
D. Varies with its phase


Which one of the following represents
forward bias diode?
\( A \)
в.
\( c \)
D.


Assertion
In woody stems, the amount of
heartwood continues to increase year
after year.
Reason
The cambial activity continues
uninterrupted.
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


Casparian strips are in nature.
A. Impermeable
B. Semipermeable
c. Differentialy permeable
D. All of the above


How many molecules of water are
present in a 0.25 mole of \( H_{2} O ? \)
A. \( 6.0 \times 10^{22} \)
В. \( 4.5 \times 10^{23} \)
c. \( 1.5 \times 10^{23} \)
D . \( 18 \times 10^{23} \)


Efforts to repeat the cloning of Dolly the sheep have been unsuccessful. The scientists who claim to have cloned
Dolly have been challenged to produce additional evidence that Dolly is really derived from an adult cell (as originally claimed), rather than fetal cells which might have contaminated the experiment (as the skeptics suggest) Which of the following could provide evidence that Dolly was created from an
adult cell, rather than a fetal cell
A. Dolly's DNA finger prints
B. The heterozygosity of random pieces of Dolly's DNA
c. The melting point of Dolly's DNA
D. The length of Dolly's telomeres
E. Dolly's biological clock


The magnitude of the force between a pair of conductors, each of length
\( 110 \mathrm{cm}, \) carrying a current of \( 10 \mathrm{A} \) each
and separated by a distance of \( 10 \mathrm{cm} \) is \( \left(\mu_{0}=4 \pi \times 10^{-7} H / m\right) \)
\( \mathbf{A} \cdot 55 \times 10^{-5} N \)
В. \( 44 \times 10^{-5} N \)
\( \mathbf{c} \cdot 33 \times 10^{-5} N \)
D. \( 22 \times 10^{-5} N \)


What will be the magnitude of e.m.f.
induced in a 200 turns coil with cross
section area \( 0.16 m^{2} ? \) The magnetic
field through the coil changes from \( 0.10 W b m^{-2} \) to \( 0.30 W b m^{-2}, \) at a
uniform rate over a period of 0.05 s
\( \mathbf{A} \cdot 128 V \)
B. \( 130 V \)
c. \( 118 V \)
D. \( 132 V \)


When a current flows through a conductor, its temperature
A. increases
B. decreases
c. remains same
D. may increase or decrease


In the following reaction,
\[
\begin{array}{c}
\boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{2}+\boldsymbol{B} \boldsymbol{r} \boldsymbol{O}_{3}^{-}+\boldsymbol{H}_{2} \boldsymbol{O} \longrightarrow \boldsymbol{B} \boldsymbol{r} \boldsymbol{O}_{4}^{-}+ \\
\boldsymbol{X} \boldsymbol{e}+\boldsymbol{2} \boldsymbol{H} \boldsymbol{F}:
\end{array}
\]
This question has multiple correct options
A \( . X e F_{2} \) is an oxidising agent
B. \( X e F_{2} \) is an reducing agent
\( \mathrm{C} \cdot B r O_{3}^{-} \) is oxidised to \( B r O_{4}^{-} \)
D. \( X e F_{2} \) is reduced to HF


The essential difference between an AC
generator and a DC generator is that:
A. AC generator has an electromagnet while a DC generator has permanent magnet.
B. DC generator will generate a higher voltage.
C. AC generator will generate a higher voltage.
D. AC generator has slip rings while DC generator has a commutator.


Find the power of concave lens of focal
length \( 10 m \)
A \( .0 .1 D \)
в. \( -0.1 D \)
\( c .10 D \)
D. \( -10 D \)


The molecular structure of a compound
is as below:
\( \mathrm{H}-\mathrm{S}-\mathrm{H} \)
What is the name of the compound?
A. Sulphuric acid
B. Sulphur dioxide
c. Hydrogen sulphide
D. Sodium hydroxide


If \( (1+i)^{2 n}+(1-i)^{2 n}=-2^{n+1} \) where
\( i=\sqrt{-1} \) for all those \( n, \) which are
A. even
B. odd
c. multiple of 3
D. None of these


tood
voo
corresponding P-V diagram fo
ess is (all figure are schemati nd not drawn to scale)


A body having kinetic energy \( k \) moving on a rough horizontal surface is stopped at a distance \( x \) by constant frictional
force. The force of friction exerted on the
body is
A \( \cdot \frac{k}{x} \)
B. \( \frac{\sqrt{k}}{x} \)
c. \( \frac{k}{\sqrt{x}} \)
D. \( k x \)


If the volume of a cube is \( 3 \sqrt{3} a^{3} \) then
total surface area of the cube is
A \( \cdot 6 a^{2} \)
B . \( \sqrt{3} a^{2} \)
\( c \cdot 18 a^{2} \)
D. \( 6 \sqrt{3} a^{2} \)


Compute the following sum:
\( \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{3} & \mathbf{- 2} \\ \mathbf{1} & \mathbf{4}\end{array}\right] \) and \( \boldsymbol{B}=\left[\begin{array}{cc}-\mathbf{2} & \mathbf{4} \\ \mathbf{1} & \mathbf{3}\end{array}\right] \)


Assertion - Sound wave is an example of longitudinal wave. Reason - In longitudinal waves, the
constituents of the medium oscillate
perpendicular to the direction of wave propagation.
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


Considering a system having two
masses \( m_{1} \) and \( m_{2} \) in which first mass
is pushed towards centre of mass by a
distance \( a \). The distance the second
mass must be moved to keep centre of mass at same position is :
A \( \cdot \frac{m_{1}}{m_{2}} a \)
в. \( \frac{m_{1} m_{2}}{a} \)
c. \( \frac{m_{2}}{m_{1}} \)
D. \( \left(\frac{m_{2} m_{1}}{m_{1}+m_{2}}\right) a \)


Saccharin \( \left(\boldsymbol{K}_{\boldsymbol{a}}=\mathbf{2} \times \mathbf{1 0}^{-\mathbf{1 2}}\right) \) is a weak
acid represented by formula \( \boldsymbol{H} \boldsymbol{S} \boldsymbol{a} \boldsymbol{C} . \boldsymbol{A} \)
\( 4 \times 10^{-4} \) mole of saccharin is dissolved
is \( 200 \mathrm{mL} \) of water of \( P h=3 \), Assuming
no change in volume, calculate \( \left[\boldsymbol{S a C}^{\ominus}\right] \) in the solution at equilibrium.
A \( \cdot 4 \times 10^{-12} \mathrm{M} \)
В . \( 4 \times 10^{-8} M \)
c. \( 4 \times 10^{-10} M \)
D. \( 4 \times 10^{-6} M \)


Among \( \boldsymbol{C a} \boldsymbol{H}_{2}, \boldsymbol{B} \boldsymbol{e} \boldsymbol{H}_{2}, \boldsymbol{B} \boldsymbol{a} \boldsymbol{H}_{2}, \) the order
of ionic character is
A. \( B e H_{2}<B a H_{2}<C a H_{2} \)
в. \( B e H_{2}<C a H_{2}<B a H_{2} \)
c. \( B a H_{2}<B e H_{2}<C a H_{2} \)
D. \( C a H_{2}<B e H_{2}<B a H_{2} \)


General value of \( \theta \) satisfying the
eqation \( \tan ^{2} \theta+\sec 2 \theta=1 \) is
\( \mathbf{A} \cdot m \pi, n \pi \pm \frac{\pi}{3}, m, n \in I \)
В \( \cdot m \pi, n \pi \pm \frac{\pi}{4}, m, n \in I \)
c. \( m \pi, n \pi \pm \frac{\pi}{6}, m, n \in I \)
D. \( m \pi, n \pi \pm \frac{\pi}{8}, m, n \in I \)


How do you expect the metallic hydrides to be useful for hydrogen storage? Explain.


Heterogametic sex determination
based on the number of sex
chromosomes among the following are
A. \( X X-X O \) and \( X X-X Y \) methods
B. \( Z O-Z Z \) and \( Z W-Z Z \) methods
c. \( X X-X Y \) and \( Z W-Z Z \) methods
D. \( X X-X O \) and \( Z O-Z Z \) methods


A person in an elevator accelerating upwards with an acceleration of \( 2 m s^{-2} \)
tosses a coin vertically upwards with a speed of \( 20 m s^{-1} \). After how much time
will the coin fall back into his hand?
(Take \( g=10 m s^{-2} \)
A \( \cdot \frac{5}{3} s \)
в. \( \frac{3}{10} s \)
c. \( \frac{10}{3} s \)
D. \( \frac{3}{5} s \)


Which of the following is a synthetic polymer?
A. Poyethylene
B. Nylon - 6
c. Terylene
D. All


If one \( G . M .^{\prime} G^{\prime} \) and two arithmetic
means \( p \) and \( q \) be inserted between any
two given number then \( G^{2} \) is:
\( \mathbf{A} \cdot(2 p+q)(2 q-p) \)
в. \( (2 p-q)(q+p) \)
c. \( (2 p-q)(2 q-p) \)
D. \( (p+q)(q+p) \)


A weight lifter jerks \( 220 k g \) vertically
through 1.5meters and holds still at
that height for two minutes. The work done by him in lifting and in holding it still are respectively (Take \( \boldsymbol{g}=\mathbf{9 . 8} \boldsymbol{m} / \boldsymbol{s} \)
):
A. \( 220 J, 330 J \)
в. \( 3234 J, 0 \)
c. \( 2334 J, 10 J \)
D. \( 0,3234 J \)


A current of \( 5 A \) passes through a copper conductor (resistivity \( =1.7 \times \)
\( 10^{-8} \Omega m \) ) of radius of cross-section
5 \( m \) m. Find the mobility of the charges if
their drift velocity is \( 1.1 \times 10^{-3} m / s \)
A \( \cdot 1.3 m^{2} / V s \)
B. \( 1.5 \mathrm{m}^{2} / \mathrm{Vs} \)
\( \mathbf{c} \cdot 1.8 m^{2} / V s \)
D. \( 1.0 m^{2} / V s \)


On the basis of the following features identify correct option:
I. They require no material medium.
II. They are always transverse.
I. They are produced by accelerating charged particles
A. Mechanical waves
B. Electro-magnetic waves
c. Both (1) and (2)
D. Neither (1) and (2)


A ray incident at an angle of incidence
\( 60^{0} \) enters a glass sphere of refra
A . \( 30^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 65^{\circ} \)
D. \( 90^{\circ} \)


A man turns on rotating table with an
angular speed \( \omega . \) He is holding two equal masses at arms length. Without moving his arms, he just drops the two masses. How will his angular speed change?
A. less than \( \omega \)
B. more than \( \omega \)
c. it will be equal to
D. it will be more than \( \omega \) if the dropped mass is more than \( 9.8 \mathrm{Kg} \) and it will be less than \( \omega \) if the mass dropped is less than \( 9.8 \mathrm{Kg} \)


If the radius of a circle is diminished by
\( 10 \%, \) then its area is diminished by:
A . \( 10 \% \)
B. \( 19 \% \)
\( c \cdot 20 \% \)
D. \( 36 \% \)


A deuterium reaction that occurs in a
hypothetical experimental fusion reactor occurs in two stages
(i) two deuterium \( \left(_{1} D^{2}\right) \) nuclei fuse
together to form a tritium nucleus, with
a proton as a by-product: \( D(D, p) T \)
(ii) a tritium nucleus fuses with
another deuterium nucleus to form a
\( \left(_{2} H e^{4}\right) \) nucleus with neutron as a by-
product \( \boldsymbol{T}(\boldsymbol{D}, \boldsymbol{n})_{2} \boldsymbol{H} \boldsymbol{e}^{4} \)
Compute
(a) the energy released in
each of two the stages and the energy released in the combined reaction.
(b) the energy released per deuterium nucleus.
Given \( \left(_{1} D^{2}\right)=2.014102 \) a.m.u
\( _{1} T^{3}=3.016049 a . m . u \)
\( _{2} H e^{4}=4.002603 a . m . . \)
\( \mathbf{1} \boldsymbol{H}^{\mathbf{1}}=\mathbf{1} . \mathbf{0 0 7 8 2} \mathbf{5} \boldsymbol{a} . \boldsymbol{m} . \boldsymbol{u} \)
\( \mathbf{o} \boldsymbol{n}^{\mathbf{1}}=\mathbf{1 . 0 0 8 6 6 5 a} . \boldsymbol{m} . \boldsymbol{u} \)


\( \triangle A B C, D E \| B C, \) find the value of \( x \)


If \( \sum_{i=1}^{18}\left(x_{i}-8\right)=9 \) and
\( \sum_{i=1}^{18}\left(x_{i}-8\right)^{2}=45, \) then standard
deviation of \( x_{1}, x_{2}, \dots, x_{18} \) is
A \( \cdot \frac{4}{9} \)
B. \( \frac{9}{4} \)
\( c \cdot \frac{3}{2} \)
D. \( \frac{3}{4} \)


What happens when
(i) chlorobenzene is treated with
\( \boldsymbol{C l}_{2} / \boldsymbol{F} \boldsymbol{e} \boldsymbol{C l}_{3} \)
(ii) ethyl chloride is treated with
\( A g N O_{2}, \) and
(iii) 2-bromopentane is treated with alcoholic KOH?
Write the chemical equation in support
of your answer.


What is meant by diffraction of light?


What are weak and strong bases?


Write the chemical equation for the preparation of ethene from below,
a) alkyl halides
b) vicinal dihalide


The figure shows Ghanshyam's squareshaped field. Find the perimeters of the
cabbage and cauliflower patches. Are
they equal?


Absorption of digested food chiefly
occurs in
A. Stomach
B. Colon
c. Small intestine
D. Large intestine


Find the point where the line of
intersection of the planes \( x-2 y+z= \)
1 and \( x+2 y-2 z=5 \) intersects the
plane \( 3 x+2 y+z+6=0 \)
A \( \cdot P(1,-2,-4) \)
B . \( P(1,2,-4) \)
c. \( P(1,-2,4) \)
D. None of these


If \( a^{2}+b^{2}+c^{2}=35 \) and \( a b+b c+ \)
\( c a=23 ; \) find \( a+b+c \)
\( A \cdot \pm 7 \)
B. ±2
\( c .\pm 9 \)
\( \mathrm{D} \cdot \pm 14 \)


A certain buffer solution contains equal
concentrations of \( B^{+} \& B O H . \) If the \( K_{b} \)
of \( B O H \) is \( 10^{-10} . \) The \( p H \) of buffer is:
A . 14
B. 4
c. 10
D.


Which of the following prevents soil erosion?
A. Animals
B. Rocks
c. Plants
D. Mountains


A man walks 12 steps in Northern direction and turns left to walk 5 steps, then returns to the initial point by the
shortest path. Find the distance
travelled given each step is \( 0.3 \mathrm{m} \)
A . \( 5.1 \mathrm{m} \)
B. \( 9 \mathrm{m} \)
\( c \cdot o m \)
D. 3.6 m


Statement 1: The angular nodes in a \( 2 p \) shell is one.
Statement 2: p-shell is dumb-bell shaped.
A. Statement 1 is true, statement 2 is true; statement 2 is correct explanation for statement
B. Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1
c. Statement 1 is True, statement 2 is False
D. Statement 1 is False, statement 2 is True.


If we introduce a large thin metal plate
between two points charges, what will
happen to the force between the charges?


Magnetic field intensity of a shot magnet at a distance \( 1 \mathrm{m} \). on axial line
is 1 Oersted. At a distance \( 2 \mathrm{m} \). on the
same line the intensity in Oersted is
then :-
A . 0.75
B. 0.125
\( c .0 .25 \)
D. 0.5


The direction cosines of a line equally
inclined to three mutually perpendicular lines having D.C.'s as
\( \ell_{1} m_{1} n_{1}: \ell_{2} m_{2} n_{2}: \ell_{3} m_{3} n_{3} \) are
A. \( l_{1}+l_{2}+l_{3}, m_{1}+m_{2}+m_{3}, n_{1}+n_{2}+n_{3} \)
B \( \cdot\left(\pm \frac{1}{\sqrt{3}}, \pm \frac{1}{\sqrt{3}}, \pm \frac{1}{\sqrt{3}}\right) \)
\( ^{\mathbf{c}} \cdot\left(\pm \frac{1}{\sqrt{2}}, \pm \frac{1}{\sqrt{3}}, \pm \frac{1}{\sqrt{4}}\right) \)
D. none of these


\( \cos ^{-1} x=\log (y)^{1 / m} \)
Evaluate \( \frac{d y}{d x} \)


A moving coil galvanometer is based on
the
A. heating effect of current
B. magnetic effect of current
c. chemical effect of current
D. peltier effect of current


The \( K_{s p} \) value for some sulphides are
\( \boldsymbol{K}_{s p}\left(\boldsymbol{B} \boldsymbol{i}_{2} \boldsymbol{S}_{3}\right)=\mathbf{1} \cdot \boldsymbol{2} \times \mathbf{1 0}^{-98} \)
\( \boldsymbol{K}_{s p}\left(\boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{S}\right)=\boldsymbol{4} \times \mathbf{1 0}^{-48} ; \boldsymbol{K}_{s p}(\boldsymbol{N} \boldsymbol{i} \boldsymbol{S})= \)
\( 1.6 \times 10^{-25} . \) An unknown cation \( X^{+} \)
was added to a solution of \( N a_{2} S \). The
precipitation of sulphide of the cation
was found to occur before \( N i S \) but after
\( A g_{2} S . \) The \( K_{s p} \) value for the sulphide of
cation \( X^{+} \) is closest to:
A \( \cdot 1 \times 10^{-26} \)
B. \( 1 \times 10^{-44} \)
C. \( 1 \times 10^{-65} \)
D. \( 1 \times 10^{-95} \)


The \( \Delta H_{t}^{\circ} \) for \( C O_{2(g)}, C O_{(g)} \) and \( H_{2} O_{(g)} \)
are -393.5,-110.5 and \( -241.8 k J \) mol \( ^{-1} \) respectively the
standard enthalpy change (in \( \boldsymbol{K} \boldsymbol{J} \) ) for
the reaction \( C O_{2(g)}+H_{2(g)} \rightarrow C O_{(g)}+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O}_{(g)} \) is:
\( \mathbf{A} \cdot 524 \cdot 1 \)
B. 41.2
c. 262.5
D. -41.2


An element has number of proton \( =7 \) Then what will be its atomic number?
A . 9
B. 7
\( c \cdot 16 \)
\( D \)


Aluminium is obtained by the
electrolysis of pure \( A l_{2} O_{3}, \) dissolved in:
A. alumina
B. bauxite
c. cryolite and flourspar
D. feldspar


A body is released from the top of the tower of height \( \boldsymbol{H} \). It takes \( \boldsymbol{t} \) time to reach the ground. The position of body \( \frac{t}{2} \)
time after release will be
A. at \( \frac{H}{2} \) metres from ground
B. at \( \frac{H}{4} \) metres from ground
c. at \( \frac{3 H}{4} \) metres from the ground
D. \( a t \frac{H}{6} \) metres from the ground


How to identify periodic and non periodic motion.


Coefficient of \( \boldsymbol{x}^{k},(\mathbf{0} \leq \boldsymbol{k} \leq \boldsymbol{n}) \) in
expansion of \( \boldsymbol{P}=\mathbf{1}+(\mathbf{1}+\boldsymbol{x})+(\mathbf{1}+ \)
\( \boldsymbol{x})^{2} \ldots \ldots+(1+\boldsymbol{x})^{n} \)
A. \( ^{n} C_{k} \)
B. \( ^{n+1} C_{n-k-1} \)
c. \( ^{n} C_{n-k} \)
D. \( ^{n+1} C_{k+1} \)


If between any two quantities there be
inserted two arithmetic means \( \boldsymbol{A}_{1}, \boldsymbol{A}_{2} \)
two geometric means \( G_{1}, G_{2}: H_{1} H_{2}= \)
\( \boldsymbol{A}_{\mathbf{1}}+\boldsymbol{A}_{\mathbf{2}}: \boldsymbol{H}_{\mathbf{1}}+\boldsymbol{H}_{\mathbf{2}} \)


The correct statement for \( \alpha \) elimination
is?
A. It forms cyclic compounds
B. It forms carbine or substituted carbine
C. Two atoms are removed from \( \alpha \) and \( \beta \) positions
D. \( \ln C H C l_{3} ; \alpha \) elimination is not possible


If
[] denotes the greatest integer less than or equal to the real number under
consideration, and \( -1 \leq x<0, \quad 0 \leq \)
\( y<1,1 \leq z<2, \) the value of the determinant \( \left|\begin{array}{ccc}{[\boldsymbol{x}]+\mathbf{1}} & {[\boldsymbol{y}]} & {[\boldsymbol{z}]} \\ {[\boldsymbol{x}]} & {[\boldsymbol{y}]+\mathbf{1}} & {[\boldsymbol{z}]} \\ {[\boldsymbol{x}]} & {[\boldsymbol{y}]} & {[\boldsymbol{z}]+\mathbf{1}}\end{array}\right| \)
is
\( A \cdot[x] \)
в. \( [y] \)
\( c \cdot[z \)
D. none of these


Solve the differential equation: \( y d x- \)
\( \boldsymbol{x} \boldsymbol{d} \boldsymbol{y}+\boldsymbol{3} \boldsymbol{x}^{2} \boldsymbol{y}^{2} \boldsymbol{e}^{\boldsymbol{x}^{3}} \boldsymbol{d} \boldsymbol{x} \)
A \( \cdot \frac{x}{y}=e^{x^{3}}+c \)
В. \( -\frac{x}{y}=e^{x^{-3}}+c \)
c. \( -\frac{x}{y}=e^{x^{3}}+c \)
D. \( \frac{x}{y}=e^{x^{-3}}+c \)


\( 4 g H_{2} \) and \( 127 g I_{2} \) are mixed and heated lit closed vessels until
equilibrium is reached. If the equilibrium concentration of \( \boldsymbol{H} \boldsymbol{I} \) is \( 0.05 M \) total number of moles present
at equilibrium is:
A . 3.25
в. 1.75
c. 2.25
D. 2.5


A gun is mounted on a railroad car. The
mass of the car, the gun, the shells and
the operator is \( 50 \mathrm{m} \) where \( \mathrm{m} \) is the mass of the one shell. If the muzzle
velocity of shell is \( 200 \mathrm{m} / \mathrm{s} \), what is recoil speed of car after second shot?
A \( \cdot \frac{200}{49} \mathrm{m} / \mathrm{s} \)
в. \( 200\left(\frac{1}{48}+\frac{1}{48}\right) \mathrm{m} / \mathrm{s} \)
\( ^{\mathrm{c}} \cdot_{200}\left(\frac{1}{48}+\frac{1}{49}\right) \mathrm{m} / \mathrm{s} \)
D. \( 200\left(\frac{1}{48}+\frac{1}{48 \times 49}\right) \mathrm{m} / \mathrm{s} \)


Let \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}, \boldsymbol{g}(\boldsymbol{x})=\tan \boldsymbol{x} \) and \( \boldsymbol{h}(\boldsymbol{x})= \)
\( \ln x \)
For \( \boldsymbol{x}=\frac{\sqrt{\boldsymbol{\pi}}}{\mathbf{2}}, \) what is the value of
\( [\boldsymbol{h o}(\boldsymbol{g} \boldsymbol{o} \boldsymbol{f})(\boldsymbol{x})] ? \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot \frac{\pi}{4} \)
D.


A 0.15 molal solution of \( K_{4}\left[F e(C N)_{6}\right. \)
in water freezes at \( -0.65^{\circ} \mathrm{C} \). What is
the apparent percentage of dissociation of this compound in this solution? \( \left[\boldsymbol{K}_{f} \text { for water }=\mathbf{1 . 8 6}^{\circ} \boldsymbol{C} \boldsymbol{m o l}^{-1}\right] \)
A . 0.33
B. 0.52
\( c .0 .63 \)
D. 0.79


What will be the value of \( \Delta G^{o}, \) if the
equilibrium constant of the reaction is 10 at \( 27^{0} C ? \)
A. \( -50.44 \mathrm{kJ} \mathrm{mol}^{-1} \)
B. - 5.744 k \( J \) mol \( ^{-1} \)
c. \( -25.44 \mathrm{kJ} \mathrm{mol}^{-1} \)
D. \( -10 ~ k J \) mol\( ^{-1} \)


A uniformly tapering conical wire is made from a material of Young's
modulus \( Y \) and has a normal,
unextended length \( L \). The radii, at the upper and lower ends of this conical
wire, have values \( R \) and \( 3 R \)
respectively. The upper end of the wire is fixed to a rigid support and a mass \( M \) is suspended from its lower end. The equilibrium extended length,of this wire, would equal to:
A \( \cdot L\left(1+\frac{1}{3} \frac{M g}{\pi \Upsilon R^{2}}\right) \)
в. \( L\left(1+\frac{2}{9} \frac{M g}{\pi \Upsilon R^{2}}\right) \)
c. \( _{L}\left(1+\frac{1}{9} \frac{M g}{\pi \Upsilon R^{2}}\right) \)
D. \( L\left(1+\frac{2}{3} \frac{M g}{\pi \Upsilon R^{2}}\right) \)


Increased with the addition of a catalyst
A. Standard voltaic potential
B. Entropy
c. Enthalpy
D. Reaction rate
E. Gibbs free energy


The state \( S_{1} \) is:
A . \( 1 s \)
в. \( 2 s \)
c. \( 2 p \)
D. \( 3 s \)


\( \ldots B r O_{3}^{-}(a q)+\ldots B r^{-}(a q)+ \)
\( \ldots \boldsymbol{H}^{+}(\boldsymbol{a} \boldsymbol{q}) \rightarrow \ldots \boldsymbol{B} \boldsymbol{r}_{2}(\boldsymbol{l})+\ldots \boldsymbol{H}_{2} \boldsymbol{O} \)
After balancing the above equation.
What is the ratio of coefficient \( B r O_{3}^{-} \) to
\( B r^{-} ? \)
A .1: 5
B. 1: 3
\( c \cdot 1: 2 \)
D. 1:
E. 2: 3


Eye is more sensitive to yellow color
Why are then danger signals red?


Three planets of same density and with
radii \( \mathbf{R}_{1}, \mathbf{R}_{2} \) and \( \mathbf{R}_{3}, \) such that \( \mathbf{R}_{1}= \)
\( 2 \mathrm{R}_{2}=3 \mathrm{R}_{3}, \) have gravitation fields on
the surfaces \( \mathrm{E}_{1}, \mathrm{E}_{2}, \mathrm{E}_{3} \) and escape velocities \( \mathbf{v}_{\mathbf{1}}, \mathbf{v}_{\mathbf{2}}, \mathbf{v}_{\mathbf{3}} \) respectively, Then
This question has multiple correct options
A \( \cdot \frac{\mathrm{E}_{1}}{\mathrm{E}_{2}}=\frac{1}{2} \)
в. \( \frac{\mathrm{E}_{1}}{\mathrm{E}_{3}}=3 \)
c. \( \frac{v_{1}}{v_{2}}=2 \)
D. \( \frac{v_{1}}{v_{3}}=\frac{1}{3} \)


State True or False.
Plastic sulphur has an octahedral
shape.
A. True
B. False


If the transition of electron takes place
from \( n=4 \) state, then the maximum
number of spectral lines obtained for transition to ground state will be
A. 6
B. 12
c. 18
D. 24


In pure HCOOH liquid, concentration of \( H C O O^{-}=10^{-3} M \) at \( 27^{0} C . \) What is
the self ionisation constant at \( 27^{0} C ? \)
\( \left(k=\left[\boldsymbol{H} \boldsymbol{C O O H}_{2}^{+}\right]\left[\boldsymbol{H} \boldsymbol{C O O}^{-}\right]\right) ? \)
A \( \cdot 10^{-3} \)
B . \( 10^{3} \)
\( c \cdot 10^{6} \)
D. \( 10^{-6} \)


State any one difference between
interference of light and diffraction of
light.


Assertion: The boiling point of \( \boldsymbol{H}_{2} \boldsymbol{O} \) is higher than the boiling point of \( \boldsymbol{H}_{2} \boldsymbol{S} \).
Reason: \( \boldsymbol{H}_{2} \boldsymbol{S} \) has a greater molecular
mass than \( \boldsymbol{H}_{2} \boldsymbol{O} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are correct and Reason is not the correct explanation of Assertion
c. Assertion is correct but Reason is not correct
D. Assertion is not correct but Reason is correct
E. Both the Assertion and Reason are not correct


Which is used as a rocket fuel?
B. Polybutadiene
c. Both (A) and (B)
D. None of these


Identify the substance that is not a
water softener.
A . \( N a O H \)
в. \( N a_{2} C O_{3} \)
c. \( N a_{2} A l_{2} S i_{2} O_{8} \)
D. \( M g C l_{2} \)


Every diagonal in a parallelogram divides it in to congruent triangles.If
true enter 1 else 0


A weight of \( 120 k N \) is placed on top of a metal column. The length of the column is compressed by 0.25 mm. The column obeys Hooke's law when compressed. How much energy is stored in the compressed column?
\( \mathbf{A} \cdot 15 J \)
в. \( 30 J \)
\( c .15 k J \)
D. 30kJ


State whether the given statement is
true or false:
The presence of harmful or objectionable material in sufficient quantity in water to measurably degrade its quality is called as water pollution.
A. True
B. False


Differentiate the following function with
respect to \( x \)
\( \left(2 x^{2}-3\right) \sin x \)
A \( \cdot 4 x \sin x+\left(2 x^{2}+3\right) \cos x \)
B. \( 4 x \sin x+\left(2 x^{2}-3\right) \sin x \)
c. \( 4 x \sin x+\left(2 x^{2}-3\right) \cos x \)
D. \( 4 x \cos x+\left(2 x^{2}-3\right) \cos x \)


An organic compound 'A' produces a gas with brisk effervescence when
sodium bicarbonate is added to it. The
compound 'A' contains same number of carbons as in ethane. The compound 'A' reacts with ethanol to form a sweet
smelling compound 'C' in presence
of conc. \( H_{2} S O_{4} . A \) and \( C \) respectively are
A. ethanoic acid and ethyl ethanoate
B. methanoic acid and ethyl methanoate
c. ethanoic acid and sodium ethanoate
D. methanoic acid and sodium methanoate


A ladder \( 10 \mathrm{m} \) long rests against a vertical wall with the lower end on the
horizontal ground. The lower end of the ladder is pulled along the ground away
from the wall at the rate of \( 3 c m / s \) The
height of the upper end while it is descending at the rate of \( 4 \mathrm{cm} / \mathrm{s} \), is
A. \( 4 \sqrt{3} m \)
В. \( 5 \sqrt{3} m \)
c. \( 5 \sqrt{2} m \)
D. \( 6 m \)


A boy weighing \( 25 k g f \) climbs up from
the first floor at height \( 3 m \) above the
ground to the third floor at height \( 9 m \)
above the ground. What will be the increase in the gravitational potential energy? Consider \( \boldsymbol{g}=10 m s^{-2} \)
\( \mathbf{A} \cdot 1 k J \)
B. \( 1.3 k J \)
c. \( 1.5 k J \)
D. None of these


In the structureof \( \boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{S} \boldsymbol{F}_{4}, \) to decide
the plane in which \( C=S \) is present the
following bond angle values are given:
Axial \( \boldsymbol{F}-\boldsymbol{S}-\boldsymbol{F} \text { angle (idealised }=180) \)
\( \Rightarrow 170 \)

Equatorial \( \boldsymbol{F}-\boldsymbol{S}-\boldsymbol{F} \) angle (idealised \( = \)
120)\( \Rightarrow 97 \)
After deciding the plane of double bond, which of the
following statement is/are correct?
A. Two \( C-H \) bonds are in the same plane of axial \( S-F \)
bonds
B. Two \( C-H \) bonds are in the same plane of equatorial \( S-F \) bonds
C. Total five atoms are in the same plane
D. Equatorial \( S-F \) bonds are perpendicular to plane of \( \pi \) - bond


Two,weights of \( 5 \mathrm{kg} \) and \( 10 \mathrm{kg} \) are placed on a horizontal table of height \( 1.5 \mathrm{m} \) Which weight will have more potential energy?
\( A \cdot 5 \mathrm{kg} \)
в. \( 10 \mathrm{kg} \)
c. Both will have equal energy
D. None of the above


Which of the following will yield a mixture of 2-chlorobutene and 3
chlorobutene on treatment with \( \boldsymbol{H} \boldsymbol{C l} \) ?
A. \( C H_{2}=C=C H=C H_{3} \)
в. \( H_{2} C=\begin{array}{c}C-C H=C H_{2} \\ C H_{3}\end{array}-C H=C \)
c. \( C H_{2}=C H-C H=C H_{2} \)
D. \( H C \equiv C-C H=C H_{2} \)


The three flat blocks as shown in the
figure are positioned on the \( 37^{\circ} \) incline
and a force \( P \) parallel to the inclined
plane is applied to the middle block. The
upper block is prevented from moving by a wire which attaches it to the fixed
support. The masses of three blocks in
kg and coefficient of static function for
each of the three pairs of contact surfaces are shown in the figure.
Determine the maximum value which
force \( P \) may have before slipping take place anywhere. \( \left(\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2}\right) \)


Leucoplasts are present in
A. Green cells
B. Pigmented cells other than green
C. Non pigmented cells
D. Both A and B


An electric heater operating at \( 220 \mathrm{V} \) boils \( 5 l \) of water in 5 minutes. If it is
used on a \( 110 \mathrm{V} \) line, it will boil the
same amount of water in:
A . 10 minutes
B. 20 minutes
c. 5 minutes
D. 1 minute


All members of group 14 when heated n in oxygen form oxides. Which of the following is the correct trend of oxides?
A. Dioxides \( C O_{2}, \operatorname{Si} O_{2} \) and \( G e O_{2} \) are acidic while \( S n O_{2} \) and \( P b O_{2} \) are amphoteric.
B. \( \mathrm{c} 0, \) Ge0, SnO and PbO are amphoteric.
c. Monoxides react with haemoglobin to form toxic compounds.
D. All oxides burn with blue flame


The term independent of \( x \) in \( \left(\frac{1}{2} x^{\frac{1}{3}}+\right. \)
\( \left.\boldsymbol{x}^{\frac{-1}{5}}\right)^{8} \) is
A. \( \frac{35}{8} \)
B. 7
c. \( \frac{7}{2} \)
D . 28


The electric field \( \vec{E} \) in the overlapped
region is
A. non-uniform
c. \( \frac{p}{3 \varepsilon_{0}} \)
D. \( \frac{-p}{3 \varepsilon_{0}} \)


Which one of the following pairs of cells and their secretion is correctly
matched?
A. Oxyntic cells - a secretion with pH between 2.0 and 3.0
B. Alpha cells of islets of Langerhans - secretion that decreases blood sugar leve
c. Kupffer cells - a digestive enzyme that hydrolyses nucleic acids
D. None of these


Alveoli ane the tiny sacks of air in lungs
whose average diameter is \( 5 \times 10^{-5} \mathrm{m} \)
Consider a oxygen molecule \( (5.3 \times \)
\( \mathbf{1 0}^{-\mathbf{2 6}} \mathbf{k g} \) ) trapped within a sec
Calculate uncertainty in velocity of oxygen molecule.
A \( \cdot 1.98 \times 10^{-5} m s^{-1} \)
В . \( 2 \times 10^{-8} \mathrm{ms}^{-1} \)
\( \mathbf{c} \cdot 5 \times 10^{-5} m s^{-} \)
D. \( 3 \times 10^{-8} \mathrm{ms}^{-1} \)


Evaluate the following integral:
\( \int \sec ^{2} x d x \)
\( A \cdot 2 \tan x+C \)
B. \( \tan 2 x+C \)
\( \mathbf{c} \cdot \tan x+C \)
D. None of these


Formula of Halothane is:
A. \( C F_{2} C l_{2} \)
в. \( C F_{2} C l \)
c. \( C F_{3}-C H C l B r \)
D. \( \left(C_{2} F_{4}\right) \)


Find the value of \( x \) :
\( \frac{\boldsymbol{x}-\mathbf{5}}{\mathbf{2}}-\frac{\boldsymbol{x}-\mathbf{3}}{\mathbf{5}}=\frac{\mathbf{1}}{\mathbf{2}} \)


Find the value of \( 99 \times 101 \) using
standard identity
A . 9999
B. 9989
\( \mathrm{c} .9979 \)
D. 1009


When one mole of an ideal gas is compressed to half its initial volume and simultaneously heated to twice its initial temperature, the change in
entropy \( (\triangle S) \) is :
A \( . C_{V} \) ln2
B. \( C_{P} \) ln2
c. \( R l n 2 \)
D \( \cdot\left(C_{V}-R\right) \ln 2 \)


The non-metal which cannot be oxidised
to its corresponding acid by nitric acid is :
A. carbon
B. sulphur
c. phosphorus
D. chlorine


A bullet of mass \( 50 g m \) is fired from below into a bob of mass \( 450 \mathrm{gm} \) of a pendulum. The bullet remains into the bob and the bob rises upto a height 1.8 \( m . \) Find \( \vec{V} \) of bullet.


What do you think would have
happened if humans also give birth to a large number of babies at the same
time?


The sum of the reciprocals of object distance and image distance is equal to the of a mirror.
A. focal length
B. reciprocal of the focal length
c. radius of curvature
D. reciprocal of the radius of curvature


The electronic configuration of
halogens in their valence shell is:
\( A \cdot n s^{2} \)
B. \( \mathrm{ns}^{2} \mathrm{np}^{6} \)
\( c \cdot n s^{0} \)
D. \( \mathrm{ns}^{2} \mathrm{np}^{5} \)


\( \sim(p \Leftrightarrow q) \) is equivalent to
\( \mathbf{A} \cdot \sim p \wedge \sim q \)
B \( . \sim p \vee \sim q \)
\( \mathbf{C} \cdot(p \wedge \sim q) \vee(\sim p \wedge q) \)
D. none of these


Why are vitamin A and vitamin C
essential to us? Give their important
sources.


Age of a tree can be estimated by
A. Its height and girth
B. Biomass.
c. Number of annual rings
D. Diameter of its heartwood.


Which of the following statement
regarding \( D_{2} O \) is correct?

This question has multiple correct options
A. It is an isotope of hydrogen
B. It is used as a bleaching agent
c. It is used as a moderatorin atomic reactors
D. It is used as a coolant in atomic reactors


Match the following.
If
A matches with a and with number 2
What number does F match with?


Sunil gave his clothes to his younger brother Hari when he outgrew. What is this practice known as?
A. Recycling
B. Reusing
c. Reducing
D. Reinventing


What is the power produced by an appliance marked "240 V, 2 A"?
A. \( 8.3 \mathrm{mw} \)
B. 60 \( w \)
c. \( 120 \mathrm{w} \)
D. \( 480 \mathrm{w} \)


The speed of light is about \( 2 \times 10^{5} \)
miles per second. On an average, it takes light about 500 seconds to travel
from the sun to Earth. What is the
average distance from Earth to the sun?
Write your answer in scientific notation.


In the given circuit the cells have zero
internal resistance. The currents (in
Amperes) passing through resistance
\( R_{1}, \) and \( R_{2} \) respectively, are \( _{-}--1 \)
A .2,2
B. 0,1
c. 1,2
D. 0.5,0


What happens when you strike a metal plate with a metal stick?
A. The plate vibrates and produces sound.
B. The plate vibrates and does not produce sound
c. The plate does not vibrate but produces sound.
D. The plate neither vibrates nor produces sound


Two trains are each 50 m long moving
parallel towards each other at speeds \( 10 m / s \) and \( 15 m / s \) respectively, at what time will they pass each other?


Find the derivative of \( \boldsymbol{y}=\frac{\boldsymbol{x}}{\sqrt{\boldsymbol{a}^{2}-\boldsymbol{x}^{2}}} \)


The brownish yellow colour of nitric acid is removed by:
A. bubbling air through warm acid
B. bubbling acid
c. passing ammonia through acid
D. adding little Mg powder


The ratio of the radii of gyration of the disc about its axis and about a tangent perpendicular to its plane will be:
A \( \cdot \frac{1}{\sqrt{3}} \)
в. \( \sqrt{\frac{3}{2}} \)
c. \( \frac{1}{\sqrt{2}} \)
D. \( \sqrt{\frac{5}{3}} \)


Why is the maximum concentration of
pesticides found in human beings?


Prove that the sequence, whose general
\( \operatorname{term} \) is \( a_{n}=2.3^{n}, \) is a geometric
progression and find the stint of the first eight terms.


Conjugate base of \( \boldsymbol{H} \boldsymbol{P} \boldsymbol{O}_{4}^{2-} \) is:
\( \mathbf{A} \cdot P O_{4}^{3-} \)
в. \( H_{2} P O_{4}^{-} \)
c. \( H_{3} P O_{4} \)
D. \( H_{4} P O_{3} \)


Frictional force in a ceiling fan is reduced by using
A. Reduced air resistance
B. Ball bearings
c. Both (A) and (B)
D. None of the above


Q Type your question-
axis. What would be the direction of
force on a positive test charge located
at the origin?
\( \mathbf{A} \)
B.
\( c \)
\( D \)


Two satellites \( A \) and \( B \) of masses \( m_{1} \)
and \( m_{2}\left(m_{1}=2 m_{2}\right) \) are moving in
circular orbits of radii \( r_{1} \) and
\( r_{2}\left(r_{1}=4 r_{2}\right), \) respectively, around the
earth. If their periods are \( T_{A} \) and \( T_{B} \)
then the ratio \( T_{A} / T_{B} \) is
A .4
B . 16
\( c \cdot 2 \)
D. 8


The sensitiveness of a moving coil galvanometer can be increased by decreasing
A. the number of turns in the coil
B. the area of coil
c. the magnetic field
D. the couple per unit twist of the suspension


The ratio of thermal capacities of two copper spheres of radii \( 5 \mathrm{cm} \) and \( 10 \mathrm{cm} \)
is
\( A \cdot 1: 4 \)
B. 4:
c. 1: 8
D. 8: 1


Which of the following is a restatement of first law of thermodynamics:
A. Guy-Lassac's Law
B. The principle of entropy
C. The principle of enthalpy
D. conservation of energy
E. Avogadro's hypothesis


In an election involving two candidates, 68 votes were found invalid. The
winning candidate scores \( 52 \% \) and wins by 98 votes. The total number of votes
casted is
A. 2450
B. 2382
\( c . \) 2158
D. 2518


Consider the equation \( 2+\mid x^{2}+4 x+ \)
\( \mathbf{2} \mid=\boldsymbol{m}, \boldsymbol{m} \in \boldsymbol{R} \) Set of all real values of
\( m \) so that given equation has four distinct solutions, is
в. (1,2)
\( c \cdot(1,3) \)
D. (2,4)