Look at the Venn diagram below. Which
of the following can be placed in 'Z'?
A. Water
B. Dry ice
\( c . \) Salt
D. Jelly


A tree increases annually by one-fourth of its height. By how much will it increase after 2 years, if it stands today \( 64 \mathrm{cm} \) high?
A. \( 76 \mathrm{cm} \)
B. 80 cm
\( c .100 \mathrm{cm} \)
D. \( 105 \mathrm{cm} \)


Three times the complement of an angle
is \( 20^{\circ} \) more than its supplement. Find
the angle.


A single 6 -sided die is rolled. What is the probability of rolling a 4 on the die?
A \( \cdot \frac{1}{12} \)
B. \( \frac{2}{3} \)
\( c \cdot \frac{3}{2} \)
D.


What is the effect of temperature on
solubility of a gas?
A. Solubility of a gas increase with rise in temperature
B. Solubility of a gas decreases with rise in temperature
c. No effect
D. Sometimes increases with increase in temperature sometimes decreases


If two of the zeros of equation \( 2 x^{4}- \) \( 3 x^{3}-3 x^{2}+6 x-2, \) are \( \sqrt{2} \) and \( -\sqrt{2} \)
and other two are \( ^{\prime} a^{\prime} \) and \( ^{\prime} b^{\prime}, \) then \( a b= \)
0. \( P \), then the value of \( p= \)


Write the values of far point and near point of the human eye with normal vision.


H.C.F. of 26 and 91 is:
A . 13
в. 2366
\( c .91 \)
D. 182


Which group of hydrocarbon is most
toxic?
A. Saturated hydrocarbon
B. Long chain hydrocarbon
C . Polycyclic aromatic hydrocarbon
D. Unsaturated hydrocarbon


Which of the following is the density of
nitrogen at STP?
в. \( 0.65 g / L \)
D. \( 1.25 g / L \)
E \( .1 .60 g / L \)


If the vectors \( \vec{a}, \vec{b} \) and \( \vec{c} \) are represented by the sides \( B C, C A \) and \( A B, \) of a triangle respectively, then
\( \mathbf{A} \cdot \vec{a} \cdot \vec{b}+\vec{b} \cdot \vec{c}+\vec{c} \cdot \vec{a}=0 \)
В . \( \vec{a} \times \vec{b}=\vec{b} \times \vec{c}=\vec{c} \times \vec{a} \)
c. \( \vec{a} \cdot \vec{b}=\vec{b} \cdot \vec{c}=\vec{c} \cdot \vec{a} \)
D. \( \vec{a} \times \vec{b}+\vec{b} \times \vec{c}+\vec{c} \times \vec{a}=0 \)


Assertion \( (\mathrm{A}): N H_{4} N O_{3} \) on gently
heating gives \( N_{2} O \) Reason(R): \( N_{2} O \) is acidic in nature
The correct answer is :
A. Both (A) and (R) are true and
(R) is the correct explanation of (A)
B. Both (A) and (R) are true and
(R) is not the correct explanation of (A)
c. (A) is true and
(R) is false
D. (A) is false but (R) is true


In water-gas shift reaction, hydrogen gas is produced from the reaction of
steam with:
A. methane
B. coke
c. carbon monoxide
D. carbon dioxide


The functional group which is found in amino acid is
A. СООН
в. \( N H_{3} \)
c. \( C H_{3} \)
\( D \cdot \operatorname{both} A \& B \)


In phenol carbon atom attached to -OH group undergoes:
A \( \cdot s p^{3} \) hybridisation
B. sp hybridisation
c. \( s p^{2} \) hybridisation
D. No hybridisation


\( \left|\begin{array}{ccc}\mathbf{1} & \mathbf{1} & \mathbf{1} \\ \boldsymbol{p} & \boldsymbol{q} & \boldsymbol{r} \\ \boldsymbol{p} & \boldsymbol{q} & \boldsymbol{r}+\mathbf{1}\end{array}\right| \) is equal to
A \( \cdot q-p \)
B. \( q+p \)
\( c \cdot q \)
\( D \)


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


In n-type semiconductor, majority charge carriers are
A. electrons
B. neutrons
c. holes
D. protons


The area bounded by the curve \( x^{2}=4 y \)
and straight line \( x=4 y-2 \) is
\( A \cdot \frac{3}{8} \)
B.
\( c \cdot \frac{7}{8} \)
D.


Ozone layer of stratosphere requires protection from indiscriminate use of:
A. fungicides, insecticides, bactericides and medicines
B. aerosols and high flying jets
C. atomic explosions and industrial wastes
D. weather balloons


Which of the following have identical value of e/m?
A. A proton \& a neutron
B. A proton \& a deuterium
c. Deutorium \& an \( \alpha \) -particle
D. An electron and \( \gamma \) -rays


A human T lymphocyte in the mitotic metaphase stage will contain how many DNA molecules (exclude the DNA
of mitochondria)?
A . 23
B. 46
\( c \cdot 184 \)
D. 92


In the reaction \( 2 N a_{2} S_{2} O_{3}+I_{2} \rightarrow \)
\( N a_{2} S_{4} O_{6}+2 N a I, \) the oxidation state
of sulphur is :
A. decreased
B. increased
c. unchanged
D. none of these


An ideal monoatomic gas undergoes
expansion according to \( \boldsymbol{P}=\boldsymbol{b} \boldsymbol{V}, \) Where
b' is a constant.Molar heat capacity of
gas in the process is
A \( \cdot \frac{3 R}{2} \)
в. \( 2 R \)
c. \( \frac{5 R}{2} \)
D. 3R


What is the number of neck canal cells
in the archegonium of Gnetales?
A. 0
B. 4
\( c \cdot 8 \)
\( D \cdot 16 \)


Determine the value of \( x \) so that equal
stresses are produced in each wire.
A \( .1 .33 m \)
3. \( 2.5 \mathrm{m} \)
\( c .3 .6 m \)
D. \( 2.1 m \)


A type of electromagnetic wave has
wavelength \( 50 A \)

State one use of this type of wave.


What will be \( p H \) of aqueous salt
solution of \( A B \) if \( p K_{a} \) of weak acid \( H A \)
is 4 and \( p K_{b} \) of weak base \( \mathrm{BOH} \) is \( 5 ? \)
\( \mathbf{A} \cdot \mathbf{5} \)
B. 7.5
\( c .6 .5 \)
D. 11.5


Which of the following pair of triangles
are congruent by RHS criterion?
(i)
(ii)
(iii)
(iv)
\( A \cdot \) (i) and (ii)
B. (iii) and (iv)
c. (i) and (iii)
D. (ii) and (iv)


Refer to the given table illustrating the characteristics of the body plan of some invertebrate embryos.
Select the correct sequence which
corresponds to the phyla represented with \( P, Q, R, S, \) and \( T \)
\begin{tabular}{|c|c|c|c|c|}
\hline \( \mathrm{P} \) & \( \mathrm{Q} \) & \( \mathrm{R} \) & \( \mathrm{s} \) & \( \mathrm{T} \) \\
\hline Acoelomate & Acoelomate & Pseudocoelomate & Schizocoelom & Enterocoelom \\
\hline Diploblastic & \multicolumn{3}{|c|} { Triploblastic } \\
\hline Incomplete or blind gut & \multicolumn{2}{|c|} { Complete gut } \\
\cline { 2 - 3 } & \multicolumn{2}{|c|} { (Tube-withint-a-tube) } \\
\hline \multicolumn{2}{|c|} { Without true segmentation } & With segmentation \\
\hline
\end{tabular}
A. Cnidaria - Platyhelminthes - Nematoda Echinodermata - Annelida
B. Cnidaria - Nematoda - Platyhelminthes Echinodermata - Annelida
c. Platyhelminthes - Nematoda - Annelida Echinodermata - chordata
D. Cnidaria - Platyhelminthes - Nematoda - Annelida Echinodermata


What is an atomic mass?


The correct order of decreasing acid strength of trichloroacetic acid (A), trifluoro acetic acid (B), acetic acid (C)
and formic acid (D) is
A. \( A>B>C>D \)
в. \( A>C>B>D \)
с. \( B>A>D>C \)
D. \( B>D>C>A \)


The initial number of atoms of a
radioactive element with half life 100
days, is \( 9.6 \times 10^{26} . \) The number of
atoms remaining undecayed after 500 days, will be
A \( \cdot 9.6 \times 10^{25} \)
B . \( 3.84 \times 10^{25} \)
\( \mathrm{c} \cdot 3 \times 10^{25} \)
D. \( 19.2 \times 10^{25} \)


Distinguish between the following.
Energy and Power


The radius of the first orbit of the \( e^{-} \) of a
hydrogen atom is \( 5.3 \times 10^{11} m \), what is
the radius of its second orbit.?
A. \( 3.12 \times 10^{-10} \mathrm{m} \)
В. \( 2.12 \times 10^{-10} \mathrm{m} \)
c. \( 4.12 \times 10^{-10} \mathrm{m} \)
D. \( 5.12 \times 10^{-10} \mathrm{m} \)


How many 3 letter code can be formed
by using the five vowels without repetitions?


Give an example of a motion in which the displacement is zero, but the distance travelled is not zero.


The total \( K E \) of an ideal monoatomic
\( \operatorname{gas} \operatorname{at} 27^{\circ} \mathrm{C} \) is :
A. 900 call \( l \)
B. 1800 cal
c. 300 call \( l \)
D. None


Which is not correct?
A. Embryology - Aristotle
B. Taxonomy - Carlous Linnaeus
C. Paleontology - Leonardo de Vinci
D. None of the above


Assertion
Under free expansion, \( \left(\frac{d U}{d V}\right)_{T} \) is \( +v e \) when
attractive forces are dominant between
gas molecules [U, V, T represent internal
energy, volume and temperature of gas respectively].
Reason
Internal energy is a state 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. Assertion is incorrect but Reason is correct


What is the name of \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3} ? \)


Find the temperature at which volume and pressure of 28 gm nitrogen gas becomes \( 10 d m^{3} \& 2.46 \) atm
respectively. (Molar mass of nitrogen
\( \operatorname{gas}=28 g / m o 1^{-1} \)


An electron of charge e and mass \( \mathrm{m} \) is moving in circular path of radius r with a uniform angular speed. Then which of the following statements are correct? This question has multiple correct options
A. The equivalent current flowing in the circular path is proportional to \( r^{2} \)
B. The magnetic moment due to circular current loop is independent of
C. The magnetic moment due to circular current loop is equal to \( 2 \mathrm{e} / \mathrm{m} \) time the angular momentum of the electron
D. The angular momentum of the particle is proportional to the areal velocoty of electron.


Ortho-and-para-hydrogens have
A. Identical chemical properties but different physical properties
B. Identical physical and chemical properties
C. Identical physical properties but different chemical properties
D. Different physical and chemical properties


Write the following statement in five different ways conveying the same meaning
\( \mathbf{p}: \) If triangle is equiangular then it is an obtuse angled triangle


Evaluate the following:
\( \lim _{n \rightarrow \infty} \frac{\cos n+\sin n}{n^{2}} \)


Chlorination of toluene in presence of
light and heat followed by treatment with aqueous NaOH gives:
A . o-cresol
B. p-cresol
c. Mixture of o-cresol and p-cresol
D. Benzoic acid


Ahmed, Batuk and Chand share \( \$ 1000 \)
in the ratio 8: 7: 5

Calculate the amount each receives.


Fill in the blank:
Ursa major appears to revolve around
the
A. sirius
B. Alpha Persei
c. Pole star
D. Alpha Centauri


Find the terms \( a_{2}, a_{3}, a_{4} \) and \( a_{5} \) of a
geometric sequence if \( a_{1}=10 \) and the
common ratio \( r=-1 \)


An object is thrown vertically upwards and rises to a height of \( 10 \mathrm{m} \). Calculate the time taken by the object to reach the highest point:
A . 3.88 s
B. 2.87 s
c. 1.43 s
D. 1.01 s


In the adjoining figure \( A B= \)
\( 12 \mathrm{cm}, C D=8 \mathrm{cm}, \angle A B D= \)
\( \angle A E C \angle E D C=90^{\circ} . \) If \( B E=x, \) then
A. \( x \) has two possible values whose difference is 4
B. \( x \) has two possible values whose sum is 2
c. \( x \) has only one value and \( x \geq 12 \)
D. \( x \) cannot be determined with the given information


Non-osmotic theory' for active absorption of water was proposed by
A. Thimann and Kramer
B. O. Hertig
c. Atkins and Priestly
D. J. C. Bose


The table below- shows the daily
expenditure on food of 25 households in a locality.
\( \begin{array}{llll}\text { Daily } & \text { 100- } & \text { 150- } & \text { 200- } \\ \text { nenses } & \text { 150 } & \text { 200 } & \text { 250 } \\ \text { (in Rs.) } & \text { 150 } & \text { (i) }\end{array} \) expenses 250 (in Rs.)
No. of households
12
Find the mean daily expenses on food by a suitable method


Assertion
UV radiation causes photo-dissociation of ozone into \( O_{2} \) and \( 0, \) thus causing damage to the stratospheric ozone layer.
Reason
Ozone hole is resulting in global warming and climate change.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A value of \( x \) satisfying the equation \( x^{2}+b^{2}=(a-x)^{2} \) is:
A \( \cdot \frac{b^{2}+a^{2}}{2 a} \)
в. \( \frac{b^{2}-a^{2}}{2 a} \)
c. \( \frac{a^{2}-b^{2}}{2 a} \)
D. \( \frac{a-b}{2} \)


Give two examples for oxidation reduction reaction


\( P(x, y) \) is a point on a straight line which makes intercepts a and b on the
\( x, y \) axes respectively, then the minimum value of \( x^{2}+y^{2}= \)
A \( \cdot \frac{a^{2}+b^{2}}{a^{2} b^{2}} \)
B. \( \frac{a^{2}-b^{2}}{a^{2}+b^{2}} \)
c. \( \frac{a^{2}-b^{2}}{2\left(a^{2}+b^{2}\right)} \)
D. \( \frac{\mathrm{a}^{2} b^{2}}{\left(\mathrm{a}^{2}+b^{2}\right)} \)


Ethylene dibromide \( \left(C_{2} H_{4} B r_{2}\right) \) and
1, 2 - dibromopropane \( \left(C_{3} H_{6} B r_{2}\right) \)
forms a series of ideal solution over the
whole range of composition. At \( 85^{\circ} C \)
the vapour pressure of these pure liquids are are \( 183 \mathrm{mmHg} \) and 127 mm \( H g \) respectively. 10gm of ethylene dibromide is
dissolved in \( 80 g m \) of \( 1,2- \) dibromo - propane. Calculate the
partial pressures of each components and the total pressure of the solution at
\( 85^{\circ} C \)
Calculate the composition of vapour in equilibrium with the above and express as mole fraction of ethylene dibromide.


Metals of high purity (to be used in semiconductors) are obtained by
zone-refining. If true enter 1 , else enter 0 .


The stage up to which glycolysis and fermentation have a common pathway is
A. Dihydroxyacetone.
B. 3-phosphoglyceradehyde
c. Pyruvate.
D. Glucose-6-phosphate.


A disc of radius \( 0.1 ~ m \) rolls without
sliding on a horizontal surface with a velocity of \( 6 m / s^{-1} \). Then, it ascends a
smooth continuous track as shown in
the figure. Given, \( g=10 m s^{-1}, \) the
height up to which it will ascend is
\( \left(\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2}\right) \)
A \( .2 .4 n \)
в. 0.9 т
\( c .2 .7 m \)
D. \( 1.8 \mathrm{m} \)


Which one of the following is not a property of a gas?
A. Can be compressed
B. No definite shape
c. Definite volume
D. Definite mass


State True or False
\( 13 m^{2}-2 m^{2}=11 m^{2} \)
A. True
B. False


Correct the underline part of the
following statements appropriately if it
is wrong.

The ampearage of the fuse wire must be reduced as the power of the equipment included in the circuit is increased.


In the absence of greenhouse gases, the temperature of earth's surface will fall
to
A \( \cdot 0^{\circ} \mathrm{C} \)
B . \( -5^{\circ} \mathrm{C} \)
c. \( -10^{\circ} \mathrm{C} \)
D. \( -20^{\circ} \mathrm{C} \)


Which one of the following pairs of compounds illustrates the law of multiple proportions?
A. \( H_{2} O, N a_{2} O \)
в. \( M g O, N a_{2} O \)
c. \( N a_{2} O, B a O \)
D. \( S n C l_{2}, S n C l \)


Combustion of glucose takes place according to the equation.
\( \boldsymbol{C}_{6} \boldsymbol{H}_{12} \boldsymbol{O}_{6}+\boldsymbol{6} \boldsymbol{O}_{2} \rightarrow \boldsymbol{6} \boldsymbol{C} \boldsymbol{O}_{2}+ \)
\( 6 H_{2} O \triangle H=0=-72 k-c a l \)
The energy required for combustion of \( 1.6 g \) of glucose is:
A \( .0 .064 k- \) cal \( l \)
B. \( 0.64 k- \) cal
c. \( 6.4 k-c a l \)
D. \( 64 k- \) cal


Find the values of \( x \) for which \( y= \)
\( [x(x-2)]^{2} \) is an increasing function.


The area (in square units) bounded by
the curves \( x=-2 y^{2} \) and \( x=1-3 y^{2} \)
is
A \( \cdot \frac{2}{3} \)
B.
\( c \cdot \frac{4}{3} \)
D.


A bullet of mass \( 10 \times 10^{-3} \mathrm{kg} \) moving
with a speed of \( 20 m s^{-1} \) hits an ice
block \( \left(0^{\circ} c\right) \) of \( 990 g \) kept at rest on a frictionless floor and gets embedded in
it. If ice takes \( 50 \% \) of \( K . E, \) for melting,
then the mass of the ice block that has
melted is \( (J=4.2 J / C a l) \) (Latent heat
of ice \( =\mathbf{8 0} \) cal \( / \mathbf{g} \) )
A. 6
B. 3
c. \( 6 \times 10^{-3} \)
D. \( 3 \times 10^{-3} \)


At \( 300 K, 36 g \) of glucose present per
litre in its solution has an osmotic
pressure of 4.98 bar. If the osmotic
pressure of solution is 1.52 bar at the
same temperature, what would be its concentration?
A \( \cdot 11 g L^{-1} \)
в. \( 22 g L^{-1} \)
c. \( 36 g L^{-1} \)
D. \( 42 g L^{-1} \)


A cyclotron is used to accelerate
A. Neutron
B. Only positively charged particles
C . Only negatively charged particles
D. Both positively and negatively charged particles


Find the matrix \( A \), such that \( \left[\begin{array}{l}4 \\ 1 \\ 3\end{array}\right] A= \) \( \left[\begin{array}{ccc}-4 & 8 & 4 \\ -1 & 2 & 1 \\ -3 & 6 & 3\end{array}\right] \)


Assertion
Atomic sizes of \( C s \) and \( F r \) are almost
similar.
Reason
Cs and Fr belong to same group.
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 phenomenon of bending of light at the surface of separation of two media
is called:
A. Refraction of light
B. Reflection of light
c. Deflection of light
D. Absorption of light


Check if given series is \( A P \) or not? If
they form an \( A P \), find the common
difference \( d \) and write three more terms.
\( 0.2,0.22,0.222,0.2222, \ldots . \)


\( A \) and \( B \) are two sets having 3 and 4
elements respectively and having 2 elements in common. The number of
relations which can be defined from \( \boldsymbol{A} \)
to \( B \) is
A \( \cdot 2^{5} \)
B. \( 2^{10}-1 \)
\( \mathbf{c} \cdot 2^{12}-1 \)
D. None of these


Ebonite handles are used to handle hot
utensil because they are bad conductors of heat.
A. True
B. False


Let \( x^{k}+y^{k}=a^{k},(a, k>0) \) and
\( \frac{d y}{d x}+\left(\frac{y}{x}\right)^{1 / 3}=0, \) then \( k \) is :
A \( \cdot \frac{1}{3} \)
B. \( \frac{2}{3} \)
\( c \cdot \frac{4}{3} \)
\( D \cdot 3 \)
\( \overline{2} \)


In \( V \) -1 characteristic of a p-n junction, reverse biasing results in
A. leakage current
B. the current barrier across junction increases
c. no flow of current
D. large current


The number of optical isomers of
\( \boldsymbol{C H}_{3} \boldsymbol{C H}(\boldsymbol{O H}) \boldsymbol{C H O} \) is:
\( \mathbf{A} \cdot \mathbf{0} \)
B . 2
\( c .3 \)
D.


light year = -


The squamous epithelium is mainly involved in
A. Protection
B. Absorption
c. Secretion
D. None of these


A nut is opened by a wrench of length \( 10 \mathrm{cm} . \) If the least force required is
\( 5.0 N, \) find the moment of force needed
to turn the nut.
\( A .50 N m \)
в. \( 0.5 N \mathrm{cm} \)
c. \( 5 N m \)
D. \( 0.5 N \) m


Miriam notices when she goes to the beach that sometimes the water rises
as high as the pier. At other times of the day, the water barely covers the pillars under the pier. These differences in
water level are primarily due to the gravitational influence of which of the following?
A. The sun
B. The Moon
c. Asteroids
D. comets


Give chemical equations for Etard reaction.


Explain the process of external
respiration


If the integers \( m \) and \( n \) are chosen at
random from 1 to 100 , then the
probability that a number of the form
\( 7^{m}+7^{n} \) is divisible by 5 is
A \( \cdot \frac{1}{5} \)
B. \( \frac{1}{7} \)
\( c \cdot \frac{1}{4} \)
D. \( \frac{1}{49} \)


The metal present in vitamin \( B_{12} \) is:
A. magnesium
B. cobalt
c. copper
D. zinç


The moment of the force, \( \overrightarrow{\boldsymbol{F}}=\mathbf{4} \hat{\mathbf{i}}+ \)
\( 5 \hat{j}-6 \hat{k} \) at (2,0,-3) about the point
\( (2,-2,-2), \) is given by
\( \mathbf{A} \cdot-8 \hat{i}-4 \hat{j}-7 \hat{k} \)
B . \( -4 \hat{i}-\hat{j}-8 \hat{k} \)
\( \mathbf{c} .-7 \hat{i}-8 \hat{j}-4 \hat{k} \)
D. \( -7 \hat{i}-4 \hat{j}-8 \hat{k} \)


A charge \( q \) is placed at the centre of the
line joining two equal charges \( Q \). The
system of the three charges will be in equilibrium if \( q \) is equal to?


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


\( \angle A \) and \( \angle B \) are supplementary angles.
\( \angle A=x+10^{\circ} \) and \( \angle B=x-10^{\circ}, \) find
\( \angle A \) and \( \angle B \)


The temperature at which two bodies appear equally hot or cold when touched by a person is:
A \( \cdot 0^{0} C \)
B . \( 37^{0} C \)
\( \mathbf{c} \cdot 25^{0} C \)
D. \( 4^{0} C \)


A manufacturer uses a concave lens
instead of a convex lens in a magnifying glass by mistake. What will be the effect on the working of the lens?
A. Images will be blurred
B. Images will be clearer.
c. Images will be diminished.
D. Images will be further magnified.


Pressure at a bottom in pond is 6 atm.
The greatest integer less than or equal to the depth of the pond (in meters) is \( (60+x) . \) Find \( x \)


The sum of the coefficients in the
balanced equation of \( \boldsymbol{C o}+\boldsymbol{N} \boldsymbol{i}^{2+} \rightarrow \)
\( \boldsymbol{C o}^{\boldsymbol{3}+}+\boldsymbol{N} \boldsymbol{i}, \) is:
A . 5
B. 2
\( c \cdot 3 \)
D. 10
E . 13


Which of the following is not a correct
statement for the neuroglial cells?
A. Neuroglial makes up more than one half of the volume of the neural tissue in our body
B. It protects and supports the neurons
C. When this cell is suitably stimulated an electrical disturbance is generated which swiftly travels along its Plasma membrane
D. All the given options are correct


The size of Mo is very similar to:
A . \( L a \)
в. \( H f \)
\( c . T a \)
D. \( W \)


The piston in the cylinder head of a locomotive has a stroke (twice the
amplitude) of \( 1.0 \mathrm{m} . \) If the piston moves with simple harmonic motion with an angular frequency of 200 rad/min, what it its maximum speed?


Statement 1: For an element with an
atomic number of \( 17, \) the most probable
oxidation number is +1
Statement 2: The outer energy level of the halogen family has a tendency to add one electron to itself
A. Both Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement 1
B. Both Statement 1 and Statement 2 are correct and Statement 2 is not the correct explanation of Statement 1.
c. statement 1 is correct but Statement 2 is not correct
D. Statement 1 is not correct but Statement 2 is correct
E. Both the Statement 1 and Statement 2 are not correct.


Find the sum to \( n \) terms of the A.P
\( \mathbf{5}, \mathbf{2},-\mathbf{1},-\mathbf{4},-\mathbf{7}, \dots . \)


Write two properties of magnetic lines
of force.


An organic compund contains \( \boldsymbol{C}= \) \( \mathbf{4 0 \%}, \boldsymbol{H}=\mathbf{1 3 . 3 3 \%} \) and \( \boldsymbol{N}=\mathbf{4 6 . 6 7 \%} . \) Its
emperical formula is:
A. \( C_{2} H_{2} N \)
в. \( C_{3} H_{7} N \)
c. \( C H_{4} N \)
D. \( C H N \)


In the figure shown find the equivalent capacitance between terminals 'A' and
B'. The letters have their usual meaning capacitance is \( \frac{\boldsymbol{x} \varepsilon_{0} \boldsymbol{A}}{\mathbf{1 0 d}} \) then \( \mathbf{x} \) is?


Construct a triangle \( A B C \) in which
base \( A B=5 c m, \angle A=30^{\circ} \) and \( A C- \)
\( B C=2.5 \mathrm{cm} \)


\( \begin{array}{cc}\boldsymbol{C H}_{\mathbf{3}}-\underset{\mathbf{O}}{\mathbf{C}} \boldsymbol{H}- & \boldsymbol{C} \boldsymbol{H}-\boldsymbol{C} \boldsymbol{H}_{3} \\ & \boldsymbol{O} \boldsymbol{H}\end{array} \)
IUPAC name of the given compound is :
A. Butane-2,3-diol
B. 1-Methy|-propane-1,2-diol
c. Both (A) and (B)
D. None of these


The probability that a man will be alive in 40 years is \( \frac{3}{5}, \) and the probability
that his wife will also survive 40 years is \( \frac{2}{3} . \) Find the probability that both will be alive
A
B. \( \frac{4}{5} \)
\( c \cdot \frac{2}{15} \)
D. \( \frac{6}{15} \)


The ratio in which the line joining (3,4,-7) and (4,2,1) is dividing the \( x y \) plane
A .3: 4
B . 2: 1
\( c \cdot 7: 1 \)
D. 4: 3


In a surface tension experiment with a
capillary tube water rises up to 0.1 m. If the same experiment is repeated on an artificial satellite which is revolving around the earth. The rise of water in a
capillary tube will be
A. \( 0.1 m \)
в. \( 9.8 m \)
\( \mathrm{c} \cdot 0.98 \mathrm{m} \)
D. Full length of capillary tube


For two vectors \( \overrightarrow{\boldsymbol{A}} \) and \( \overrightarrow{\boldsymbol{B}}, \overrightarrow{\boldsymbol{A}}+\overrightarrow{\boldsymbol{B}}=\overrightarrow{\boldsymbol{C}} \)
and \( |\vec{A}|+|\vec{B}|=|\vec{C}| . \) The angle between
two vectors is:
A .
в. \( \pi / 3 \)
c. \( \pi / 2 \)
D.


Which of the given elements \( A, B, C, D \) and E with atomic number 2,3,7,10
and 30 respectively belong to the same period?
\( A \cdot A, B, C \)
B. В, С, D
c. А, D, ह
D. B, D, E


The mud houses are cooler in summer
and warmer in winter. It happen due to
the reason that.
A. Mud is a good conductor of heat
B. Mud is a bad conductor of heat
C. Mud work as an isothermal layer between ground and air
D. Mud is a superconductor of heat


Find the cube root of: 175616
A . 56
B. 46
\( c .66 \)
D. 76


The equation of the circle which
touches \( x \) -axis and whose center is (1,2)
is
\( \mathbf{A} \cdot x^{2}+y^{2}-2 x+4 y+1=0 \)
B . \( x^{2}+y^{2}-2 x-4 y+1=0 \)
\( \mathbf{c} \cdot x^{2}+y^{2}+2 x+4 y+1=0 \)
D. \( x^{2}+y^{2}-4 x+2 y+4=0 \)


A gas bubble, from an explosion under water, oscillates with a period \( \boldsymbol{T} \) proportional to \( P^{a} d^{b} E^{c}, \) where \( P \) is the
static pressure, \( d \) is the density of water
and \( E \) is the total energy of the
explosion. The values of \( a \ldots \ldots . b \ldots . . . . . . \) and
\( \mathcal{C} \)


Mark the incorrect relation.
A \( \cdot N_{0}=N E^{\lambda t} \)
B . \( \tau=1.44 t_{0.5} \)
\( ^{\mathrm{c}} N=N_{0}\left(\frac{1}{2}\right)^{n} \)
D. \( t_{1 / 2}=2.303 \lambda \log 2 \)


C.O.D. stands for
A. Chemical oxygen demand
B. Control of diese
c. csiumoxide deposition
D. Cemistry of depositions


Identify the given figures \( A, B, C, D \) and
E.
\( E \)
A. A: Marginal, B: Axile, C: Free central, D: Parietal, E:
Basal
B. A: Marginal, B: Parietal, C: Free central, D: Axile, E: Basal
C . A: Marginal, B: Axile, C: Parietal, D: Free central, E:
Basal
D. A: Marginal, B: Axile, C: Parietal, D: Basal, E: Free central


What is meant by the statement that
"the atomic number of sodium is
eleven"?


The value of \( \sqrt{\mathbf{9 0 0}}+\sqrt{\mathbf{0 . 0 9}}- \)
\( \sqrt{0.000009} \) is
A . 30.297
в. 30.197
c. 30.097
D. 30.397


The sides of an equilateral triangle are increasing at the rate of \( 2 \mathrm{cm} / \mathrm{s} \). The rate at which the area increases when
the side is \( 10 \mathrm{cm} \), is
\( \mathbf{A} \cdot \sqrt{3} c m^{2} / s \)
B. \( 10 \mathrm{cm}^{2} / \mathrm{s} \)
c. \( 10 \sqrt{3} \mathrm{cm}^{2} / \mathrm{s} \)
D. \( \frac{10}{\sqrt{3}} c m^{2} / s \)


The cyclic process from \( X \) to \( Y \) is an isothermal process.
If the pressure of the gas at \( X \) is \( 4.0 \mathrm{kPa} \) and the volume is 6.0 cubic meters, and
if the pressure at \( Y \) is \( 8.0 \mathrm{kPa} \), what is the volume of the gas at \( Y ? \)
A . 12.0 cubic meters
B. 16.0 cubic meters
c. 3.0 cubic meters
D. 4.0 cubic meters
E . 2.0 cubic meters


What is the correct definition of
reflectance?
A. Difference between amount of light absorbed by the surface and amount of light reflected.
B. The amount of light reflected by a surface is known as reflectance.
C. The ratio of the amount of the light reflected from a surface to the amount of light falling on the surface is called reflectance.
D. The ratio of amount of light falling on a surface to the amount of light reflected on the surface is called reflectance.


Which of the following will have two stereoisomeric forms?
(I) \( \left[\boldsymbol{C r}\left(\boldsymbol{N O}_{3}\right)_{3}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{3}\right] \)
(II) \( \boldsymbol{K}_{\mathbf{3}}\left[\boldsymbol{F} \boldsymbol{e}\left(\boldsymbol{C}_{2} \boldsymbol{O}_{4}\right)_{3}\right] \)
(III) \( \left[\boldsymbol{C o C l}_{2}(\boldsymbol{e n})_{2}\right]^{+} \)
\( (\operatorname{lv})\left[\operatorname{CoBr} C l(O x)_{2}\right]^{3-} \)
A . I only
B. I and II
c. Ill and IV
D. All of these


The polymer polyurethanes are formed by treating di-isocyanate with:
A. butadiene
B. isoprene
c. glycol
D. acrylonurile


The gas produced from thermal
decomposition of \( \left(N H_{4}\right)_{2} C r_{2} O_{7} \) is:
A. Oxygen
B. Nitric oxide
c. Ammonia
D. Nitrogen


lonic compounds do not exist as
A. molecules
B. ions
c. compounds
D. all of the above


Reabsorption of \( N a^{+} \) is controlled by which one of the following hormones?
A. Aldosterone
B. Estrogen
c. Glucocorticoids
D. Testosterone


A motion can be periodic and not
oscillatory.
A. True
B. False


Find the square of the following number without multiplication.
46
A . 2116
B. 2002
c. 2424
D. 1988


An unbiassed coins are tossed. Find the
probability of getting at most one head.


A body of mass \( \mathrm{M} \) and charge q is
suspended from a string. When slightly displaced, it oscillates with period T. If a uniform electric field acts vertically downwards, then the new time period
will be:
A \( \cdot T^{\prime}=T \)
в. \( T^{\prime}<T \)
c. \( T^{\prime}>T \)
D. cannot be predicted


Soil erosion by wind brings about the serious damage in soil by changing
the
A. Soil permeability
B. Soil structure
c. Soil texture
D. Soil plasticity


Assertion
Diode lasers are used as optical sources in optical communication.
Reason

Diode lasers consume less energy.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A \( 20 g \) ball hits a wall at \( 45^{\circ} \) angle with
a speed of \( 15 \mathrm{ms}^{-1} \) and rebounds
perpendicular to the direction of
incidence with same speed. Find the
impulse receive by the ball.


Identify the correct statement.
A. Non-conventional sources of energy cause more pollution.
B. Ozone is a harmless gas present in atmosphere.
C. Chlorofluorocarbons break down to chlorine atoms by ultraviolet radiation
D. Trees do not help in decreasing sound pollution.


State Kirchoff's current law and also
give the sign convention for current.


If \( p \) 's truth value is \( T \) and \( q^{\prime} \) s truth value
is \( F, \) then which of the following have
the truth value \( T \) ?
(i) \( p \vee q \)
(ii) \( \sim \boldsymbol{p} \vee \boldsymbol{q} \)
\( (\text { iii) } p \vee(\sim q) \)
\( (\text { iv }) p \wedge(\sim q) \)
A \( \cdot(i),(\text { ii) }, \) (iii)
B. (i), (iii), (iv)
c. (i), (ii), (iv)
D. (ii), (iii), (iv)


The charge carriers in a p-type
semiconductor are:
A. electrons only
B. holes only
C. holes in larger numbers and electrons in smaller numbers
D. holes and electrons in equal numbers


Spores are
A. Tiny cells protected by thick walls to survive unfavorable conditions
B. Buds formed in long chains
C. Outgrowths from parent organism
D. New organisms growing from tuberous roots


The number of nodal planes in \( ^{\sigma} 2 P_{x} \) molecular orbital is
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c .3 \)
D. 2


Calculate \( \boldsymbol{E}^{\circ} \) of the following half-cell
reaction at \( 298 K \)
\( \boldsymbol{A} \boldsymbol{g}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{2}^{+}+\boldsymbol{e}^{-} \rightarrow \boldsymbol{A} \boldsymbol{g}+\boldsymbol{2} \boldsymbol{N} \boldsymbol{H}_{3} \)
\( \boldsymbol{A} \boldsymbol{g}^{+}+\boldsymbol{e}^{-} \rightarrow \boldsymbol{A} \boldsymbol{g} ; \boldsymbol{E}_{A \boldsymbol{g}^{+} / A \boldsymbol{g}}^{\circ}=\mathbf{0 . 8 0} \boldsymbol{V} \)
\( \boldsymbol{A} \boldsymbol{g}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{2}^{+} \rightleftharpoons \boldsymbol{A} \boldsymbol{g}^{+}+\boldsymbol{2} \boldsymbol{N} \boldsymbol{H}_{3} ; \boldsymbol{K}=\boldsymbol{6} \times \)
\( 10^{-8} \)


A thin equiconvex glass lens \( \left(\mu_{g}=1.5\right) \) is being placed on the top of a vessel of
height \( h=20 \mathrm{cm} \) as shown in fig. \( A \)
luminous point source is being placed
at the bottom of vessel on the principal axis of the lens. When the air is on both
the side of the lens the image of
luminous source is formed at a
distance of \( 20 \mathrm{cm} \) from the lens out side
the vessel. When the air inside the
vessel is being replaced by a liquid of
refractive index \( \mu_{1} \), the image of the
same source is being formed at a distance \( 30 \mathrm{cm} \) from the lens outside
the vessel. If \( \mu_{1} \) is approximately \( \frac{x}{100} \) Find \( \boldsymbol{x} \)


In a steady state the temperature of the ends \( A \) and \( B \) of a \( 20 \mathrm{cm} \) long rod \( A B \) is
\( 100^{\circ} \mathrm{C} \) and \( 0^{\circ} \mathrm{C} . \) The temperature at the point c distant \( 9 \mathrm{cm} \) from a is :
A \( \cdot 45^{\circ} \mathrm{C} \)
В. \( 55^{\circ} \) С
\( c \cdot 60^{\circ} \mathrm{C} \)
D. \( 65^{\circ} \mathrm{C} \)


Why is electric power transmitted over
long distances at high voltage?
A. To minimize power loses due to Joule's heating
B. To maximize power loses due to Joule's heating
C. To balance power loses due to Joule's heating
D. None


Which of the following is a heterocyclic amine?
A. Aniline
B. Piperidine
c. Benzylamine
D. None of these


Assertion
The photoelectrons produced by a
monochromatic light beam incident on
a metal surface, have a spread in their
kinetic energies.
Reason
The work function of the metal varies as
a function of depth from the surface.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


A ball is dropped from a height h. If the coefficient of restitution be e, then to
what height will it rise after jumping
twice from the ground?
\( A \cdot e h / 2 \)
B. 2 en
\( c \cdot e h \)
D. \( e^{4} h \)


In a maths paper there are 3 sections
\( A, B \) and \( C . \) Section \( A \) is compulsory.
Out of sections \( B \) and \( C \) a student has
to attempt any one. Passing in the paper means passing in \( A \) and passing in \( B \) or \( C . \) The probability of the student
passing in \( A, B \) and \( C \) are \( p, q \) and \( 1 / 2 \) respectively. If the probability that the student is successful is \( 1 / 2 \) then
A. \( p=q=1 \)
в. \( p=q=1 / 2 \)
c. \( p=1, q=0 \)
D. \( p=1, q=1 / 2 \)


Give reasons Dioxygen is a gas while Sulphur is a solid at room temperature


Value of g is:
A. maximum at poles
B. maximum at equator
C . same everywhere
D. minimum at poles


Zone refining is a method to obtain:
This question has multiple correct options
A. ultra pure boron
B. ultra pure lead
c. ultra pure silicon
D. all


A 10 pF parallel plate capacitor is charged with a \( 4.0 \mathrm{V} \) battery. While the capacitor is still connected to the battery, a dielectric slab ( \( k=5.0 \) ) is inserted between the plates to
completely fill the gap. How much electric potential energy is stored in the capacitor after inserting the dielectric?
\begin{tabular}{l}
A \( .5 .3 \times 10^{-10} J \) \\
\hline
\end{tabular}
В . \( 4.0 \times 10^{-10} \mathrm{J} \)
c. \( 4.6 \times 10^{-10} J \)
D. \( 5.6 \times 10^{-10} \mathrm{J} \)


\( \sqrt{2 x-3}+\sqrt{7-3 x} \)


Time taken for an electron to complete one revolution in the Bohr orbit of
hydrogen atom is:
A \( \cdot \frac{4 \pi^{2} m r^{2}}{n h} \)
в. \( \frac{n h}{4 \pi^{2} m r} \)
c. \( \frac{2 \pi m r}{n^{2} h^{2}} \)
D. \( \frac{h}{2 \pi m r} \)


A double star is a system of two stars of
masses \( \mathrm{m} \) and \( 2 \mathrm{m}, \) rotating about their centre of mass only under their mutual
gravitational attraction. If \( r \) is the
separation between these two stars
then their time period of rotation about their centre of mass will be proportional
to.
This question has multiple correct options
A \( \cdot \frac{3}{2} \)
B.
c. \( \quad_{m} \frac{1}{2} \)
D. \( _{m^{-}} \frac{1}{2} \)


Which of the following reagent is used to identify carbonyl group from other functional groups?
A. Schiff reagent
B. Fehling solution
c. 2,4-dinitrophenylhydrazine
D. Tollen's reagent


Why do certain algae like Laminaria,
Sargassum, etc. have brown colour?


Assertion: A negative catalyst retards
the rate of chemical reaction.

Reason: Presence of negative catalyst boosted up the energy of activation.
A. Assertion is correct but Reason is wrong
B. Assertion is wrong but Reason is correct
c. Both Assertion and explanation are correct and Reason is correct explanation of Assertion
D. Both Assertion and explanation are correct but Reasor is not correct explanation of Assertion


Dvide the following redox equations into oxidation half equation and reduction half equation.
\( \boldsymbol{a}) \boldsymbol{P}_{(s)}+\boldsymbol{P} \boldsymbol{O}_{4(a q)}^{3} \boldsymbol{H} \boldsymbol{P} \boldsymbol{O}_{3(a q)}^{2} \)
\( \boldsymbol{b}) \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{2(a q)} \longrightarrow \boldsymbol{N} \boldsymbol{O}_{3(a q)}^{-}+\boldsymbol{N} \boldsymbol{O}_{(g)} \)
\( \boldsymbol{c}) \boldsymbol{I} \boldsymbol{O}_{\boldsymbol{3}(\boldsymbol{a q})}^{-}+\boldsymbol{R e}_{(s)} \longrightarrow \boldsymbol{R e} \boldsymbol{O}_{4(\boldsymbol{a q})}+\boldsymbol{I}_{(a q)} \)


Stability of an atom was successfully explained by Rutherford's atomic model
A. True
B. False


An object is placed upright on the axis of a thin convex lens at a distance of
four focal lengths \( (4 f) \) from the center of the lens. An inverted image appears at a distance of \( \frac{4}{3} f \) on the other side of the lens. What is the ratio of the height of the image of the height of the object?
A . \( 1 / 3 \)
B. \( 3 / 4 \)
c. \( 4 / 3 \)
D. 3/1


\( M g \) forms \( M g(I I), \) because of:
A. The oxidation state of \( M g \) is +2
B. Difference between \( I . P_{1} \) and \( I . P_{2} \) is greater than 16.0 \( e v \)
c. There are only two electrons in the outermost energy level of \( M g \)
D. Difference between \( I . P_{1} \) and \( I . P_{2} \) is less than 11 ev


Cell would normally proceed to mitosis
without interruption
A. Once it has entered the S phase
B. Once it has entered the \( G_{2} \) phase
C. At any time during cell division activity
D. None of these


Which of the following are the common consequences of atmospheric pressure in our daily life.
A. Sucking a drink with a straw
B. Filling a syringe with a liquid
c. Filling ink in a fountain pen
D. All of the above


Odd electron bond is present in:
A. \( N O \)
в. \( N O_{2} \)
c. \( C l O_{2} \)
D. all of the above


If the perimeter of rectangle is \( 24 \mathrm{m} \) represent this in the form of equation.


The electronic configuration is \( 1 s^{1} \) for
A. protium atom
B. deuterium atom
c. tritium atom
D. all of the above


If \( f: R \rightarrow R \) defined by \( f(x)=\frac{x-1}{2} \)
find \( (f o f)(x) \)


When 1 g of ice melts at \( 0^{\circ} \boldsymbol{C} \)
A. 80 cal of heat is liberated
B. 80 cal of heat is absorbed
c. no heat is required
D. none of these


The urinary opening is known as
A. Urinary bladder
B. Ureter
C. Urethera
D. None of the above


Chlorine was first discovered by:
A. Haber
B. Moissan
c. scheele
D. Solvay


What will happen, if Rhizobium is
inoculated in wheat field?
A. No increase in production (nitrogen content of soil remains same
B. A lot of increase in production (nitrogen content of soil increase)
c. Fertility of soil decreases
D. Fertility of soil increases


Which equation represents the line that
passes through the point (2,3) and is parallel to the \( y \) -axis?
\( \mathbf{A} \cdot x=2 \)
B. \( y=3 \)
c. \( x=3 \)
D. \( y=2 \)


Define glycolysis and Krebs cycle


Which reaction is more spontaneous theoretically?
A . \( I \)
B. II
c. Both equally
D. Can't be predicted


Solve graphically the following pairs of
equations
\( \boldsymbol{y}=\mathbf{2} \boldsymbol{x}+\mathbf{1} ; \boldsymbol{y}+\mathbf{3} \boldsymbol{x}-\mathbf{6}=\mathbf{0} \)
\( \mathbf{A} \cdot(1,3) \)
B \( \cdot(2,3) \)
\( \mathbf{c} \cdot(4,3) \)
D. None of these


A body of \( 2 g \) carrying a charge of \( 0.1 \times \) \( 10^{-6} C \) starts from rest from the positive
plate and moves to the negative plate of a parallel plate condenser connected to a voltage supply of \( 30 k V \). The final velocity
is:
A \( \cdot \sqrt{3} m s^{-1} \)
B. \( \frac{\sqrt{3}}{12} m s^{-1} \)
c. \( \frac{1}{\sqrt{2}} m s^{-1} \)
D. zero


Do the points \( \boldsymbol{A}(\boldsymbol{3}, \boldsymbol{2}), \boldsymbol{B}(-\boldsymbol{2},-\boldsymbol{3}) \) and
\( C(2,3) \) form a triangle? If \( s o, \) name the type of triangle formed.


If the surface normal vector \( \hat{n} \) makes an
angle \( \theta \) with the electric field \( \vec{E} \), then
the electric flux through a surface of
\( \operatorname{area} d S \) is given by
A. \( \phi=E d S \sin \theta \)
\( \mathbf{B} \cdot \phi=E d S \cos \theta \)
c. \( \phi=d S \cos \theta \)
D. \( \phi=E \cos \theta \)


Area of the region bounded by the
curves, \( \boldsymbol{y}=\boldsymbol{e}^{\boldsymbol{x}}, \boldsymbol{y}=\boldsymbol{e}^{-\boldsymbol{x}} \) and the straight
line \( x=1 \) is given by
A \( \cdot\left(e-e^{-1}+2\right) \) sq.unit
B \( \cdot\left(e-e^{-1}-2\right) \) sq.unit
c. \( \left(e+e^{-1}-2\right) \) sq.unit
D. None of the above


Give a brief account of lightning
conductors.


toppr
\( Q \)
electrostatic field is maintained in
a direction normal to the common axis
of the coils. A narrow beam of (single
species) charged particles al
accelerated through \( 15 k V \) enters this region in a direction perpendicular to both the axis of the coils and the
electrostatic field. If the beam remains
undeflected when the electrostatic field
is \( 9.0 \times 10^{-5} V m^{-1}, \) make a simple
guess as to what the beam contains. Why is the answer not unique?

Consider two parallel co-axial circular coils of equal radius \( R \), and number of turns \( N, \) carrying equal currents in the same direction, and separated by a distance \( R \) Show that the field on the
axis around the mid-point between the coils is uniform over a distance that is
small as compared to \( R \), and is given by, \( \boldsymbol{B}=\mathbf{0 . 7 2} \frac{\boldsymbol{\mu}_{0} \boldsymbol{N I}}{\boldsymbol{R}} \)
[Such an arrangement to produce a nearly uniform magnetic field over a small region is known as Helmholtz coils \( ] \)


\( 5 g \) of unknown gas has pressure \( P \) at a
temperature \( \boldsymbol{T} \boldsymbol{K} \) in a vessel. On
increasing the temperature by \( 50^{\circ} \mathrm{C}, 1 \mathrm{g} \) of the gas was given out to maintain the pressure \( \boldsymbol{P} \). The original temperature
was:
A . \( 73 K \)
в. \( 100 K \)
c . \( 200 K \)
D. none of these


The total flux passing through the cube
is:
\( \mathbf{A} \cdot(B+C+D) L^{2} \)
B . \( 2(B+C+D) L^{2} \)
\( \mathbf{c} \cdot 6(B+C+D) L^{2} \)
D. zero


The correct order of basic strength of
the following are:
\( \mathbf{1} \)
2
3
4.
A \( .1>2> \)
в. \( 4>2>3>1 \)
c. \( 3>4>2>1 \)
D. \( 3>2>4>1 \)


Write definition of Curie temperature for ferromagnetic substance.


IUPAC name of \( \boldsymbol{H}_{2}\left[\boldsymbol{P t} C l_{6}\right] \) is:
A. hydrogen hexachloroplatinate (IV)
B. dihydrogen hexachloroplatinate (IV)
c. hydrogen hexachloroplatinic (IV) acid
D. hexachloroplatinic (IV) acid


What is the density of wet air with \( 75 \% \) relative humidity at 1 atm and \( 300 \mathrm{K} \) ?
Given : vapour pressure of \( H_{2} O \) is 30 torr
and average molar mass of air is
\( 29 g / m o l \)
A. \( 1.614 g / L \)
в. \( 0.96 g / L \)
c. \( 1.06 g / L \)
D. \( 1.164 g / L \)


The cavities of brain are lined by
A. Cuboidal cells
B. Polygonal cells
C. Ependymal cells
D. simple squamous cells


Which of the following atom doesn't have its valency as one?
A. Lithium
B. Hydrogen
c. Magnesium
D. Sodium


When the self-inductance of the
primary and secondary coil is doubled, then the mutual inductance of the two
coils is :
A. Halved
B. Doubled
c. Quadrupled
D. Reduced to one-fourth


The name of complex ion, \( \left[\boldsymbol{F e}(\boldsymbol{C N})_{\boldsymbol{6}}\right]^{\boldsymbol{3}-} \)
is:
A. Hexacyanoiron (III) ion
B. Hexacyanitoferrate (III) ion
c. Tricyanoferrate (III) ion
D. Hexacyanidoferrate (III) ion


Lenz's law is based on conservation of
A. charge
B. mass
c. energy
D. momentum


If the binary operation \( * \) is on set of
integers \( Z \) is defined as
\( a * b=a+2 b^{2}, \) then the value of \( (8 * \)
\( \mathbf{3}) * \mathbf{2} \)
A . 26
B. 22
\( c .32 \)
D. 34


If \( \boldsymbol{y}=\sin ^{-1}\left[\operatorname{atan}^{-1} \sqrt{\frac{1-x}{1+x}}\right] \) then find
\( \frac{d \boldsymbol{y}}{d x} \)


The condition under which
transpiration would be most rapid
A. High humidity
B. Excess of water in soil
C. Low humidity, high temperature, guard cells are turgid (open) and moist soil
D. Low velocity of wind


Anthers with only two microsporangia
are found in
A. Cucurbitaceae
B. Leguminosa
c. cruciferae
D. Malvaceae


Which of the following statements is true, if \( \Delta P Q R \cong \Delta L M N ? \)
\( \mathbf{A} \cdot P Q=M N \)
в. \( Q R=L N \)
c. \( P R=L M \)
D. \( Q P=M L \)


\( \mathbf{f} \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{2} \\ \mathbf{3} & \mathbf{4}\end{array}\right], \) find \( |\mathbf{2} \boldsymbol{A}| \)


The value of \( c \) in Lagrange's theorem for
the function \( |x| \) in the interval [-1,1] is
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( 1 / 2 \)
c. \( -1 / 2 \)
D. non existent in the interval


If the area enclosed between the curves
\( \boldsymbol{y}=\boldsymbol{k} \boldsymbol{x}^{2} \) and \( \boldsymbol{x}=\boldsymbol{k} \boldsymbol{y}^{2},(\boldsymbol{k}>\mathbf{0}), \) is \( \mathbf{1} \)
square unit. Then \( k \) is?
A \( \cdot \frac{1}{\sqrt{3}} \)
в. \( \frac{2}{\sqrt{3}} \)
c. \( \frac{\sqrt{3}}{2} \)
D. \( \sqrt{3} \)


A renewable exhaustible natural
resource is:
A . coal
B. petroleum
c. minerals
D. forest


The median of the following observations \( 11,12,14,(x-2),(x+ \)
4) \( ,(x+9), 32,38,47 \) arranged in
ascending order is \( 24 . \) Find the value of
\( x \) and hence find the mean.


Based on the type of dispersed phase,what type of colloids are micelles?


A circular park of radius \( 20 m \) is
situated in a colony. Three boys Ankur, Syed and David are sitting at equal distance on its boundary each having a toy telephone in his hands to talk to each other. Find the length of the string of each phone.


The fluid present in the anterior part of the eye in front of the eye lens is


Thomson's model of atom is also known
as:
This question has multiple correct options
A. water-melon model
B. raisin pudding model
c. plum pudding model
D. Rutherford's model


In triangle \( A B C \), the altitude from \( A \) to
\( B C \) meets \( B C \) at \( D \) and the altitude
from \( B \) to \( C A \) meets \( A D \) at \( H . \) If \( A D= \)
\( 4 \mathrm{cm}, B D=3 \mathrm{cm} \) and \( C D=2 \mathrm{cm} \) and
if \( \frac{A B}{B D}=\frac{A H}{H D}, \) then the length of \( H D \)
is
\( ^{\text {A } \cdot \frac{\sqrt{5}}{2} \mathrm{cm}} \)
в. \( \frac{3}{2} \mathrm{cm} \)
c. \( \sqrt{5} \mathrm{cm} \)
D. cn


Figure shows two conducting
thin concentric shells of radii \( r \) and \( 3 r \)
The outer shell carries charge \( q \) and the
inner shell is neutral. The amount of
charge that flows from the inner shell to
the earth after the key K is closed is
equal to \( (1 / n)^{t h} \) of the charge on the
outer shell. What is the value of n?


Two bodies \( \mathrm{M} \) and \( \mathrm{N} \) of equal mass are suspended from two separate massless
spring of force constant \( k_{1} \) and \( k_{2} \)
respectively. If the two bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitude of vibration of \( \mathrm{M} \) to that of \( \mathrm{N} \) is?
\( \mathbf{A} \cdot \frac{k_{1}}{k_{2}} \)
В. \( \sqrt{\frac{k_{1}}{k_{2}}} \)
\( \mathbf{c} \cdot \frac{k_{2}}{k_{1}} \)
D. \( \sqrt{\frac{k_{2}}{k_{1}}} \)


Pure water boils at \( 99.725^{\circ} C \) at shimla.
If \( K_{b} \) for water is \( 0.51 K m o l^{-1} k g, \) the
boiling point of 0.69 molal urea solution will be:
A . 100.35
B. 100.08
c .99 .37
D. None of these


When potassium magnate is treated with ozone, the compound obtained as product is:
\( \mathbf{A} \cdot K M n O_{4} \)
в. \( M n O_{2} \)
c. \( M n O_{4} \)
D. all of these


In SHM the net force towards mean
position is related to its displacement
(x) from mean position by the relation
\( \mathbf{A} \cdot F \propto x \)
B . \( F \propto \frac{1}{x} \)
c. \( F \propto x^{2} \)
D. \( F \propto \frac{1}{x^{2}} \)


A molecule with a dipole moment p is placed in electric field of strength E. Initially the dipole is aligned parallel to the field. If the dipole is to be rotated to be anti parallel to the field, the work required to be done by an external agency is
A . - 2pE
B . -pE
c. pE
D. 2pE


Which of the following is not the outcome while Spinning a wheel
\( A \)
B. B
\( c \cdot c \)
\( D \)


A boy of height \( 1.5 m \) with his eye leve
at \( 1.4 m \) stands before a plane mirror of
length \( 0.75 m \) fixed on the wall. The
height of the lower edge of the mirror above the floor is \( 0.8 m . \) Then
A. the boy will see his full image
B. the boy cannot see his hair
c. the boy cannot see his feet
D. the boy can neither see his hair nor his feet


The stability of dihalides of \( \boldsymbol{S} \boldsymbol{i}, \boldsymbol{G} \boldsymbol{e} . \boldsymbol{S} \boldsymbol{n} \)
and \( P b \) increases steadily in the
sequence:
A. \( P b X_{2}<\operatorname{SnX}_{2}<\operatorname{GeX}_{2}<\operatorname{SiX}_{2} \)
в. \( G e X_{2}<\operatorname{Si} X_{2}<\operatorname{SnX}_{2}<P b X_{2} \)
c. \( \operatorname{si} X_{2}<\operatorname{Ge} X_{2}<\operatorname{Pb} X_{2}<\operatorname{SnX}_{2} \)
D. \( \operatorname{SiX}_{2}<\operatorname{GeX}_{2}<\operatorname{SnX}_{2}<P b X_{2} \)


What is the hybridisation of \( \left[N i(C N)_{4}\right]^{2-} ? \)
A \( \cdot d s p^{2} \)
B . \( s p d^{2} \)
\( c \cdot s p^{3} \)
D. None of these


Fuse has \( \dots . \) and \( \dots . ? \)
A. high resistance, high melting point
B. high resistance, low melting point
C . low resistance, high melting point
D. low resistance, low melting point


n figure \( D \) and \( E \) are the mid points of
sides \( A B \) and \( A C \) respectively of \( \triangle A B C \)
Find \( \angle E D B \)
\( A \cdot 110 \)
\( 3 \cdot 120 \)
\( c \cdot 70^{\circ} \)
\( D \cdot 80 \)


Which of the following statements are
true regarding oxides of nitrogen?
This question has multiple correct options
\( \mathbf{A} \cdot N O_{2} \) is a mixed anhydride of \( H N O_{2} \) and \( H N O_{3} \)
B. \( N_{2} O_{3} \) is not soluble in water.
C \( \cdot N_{2} O \) and \( N O \) are anhydrides of \( H N O_{2} \)
D. \( N_{2} O_{5} \) is anhydride of \( H N O_{3} \)


A person sold an article for Rs. 230 and
incurred a loss of \( 8 \% . \) What should be
the selling price in order to earn a profit
of \( 8 \% ? \)
A . Rs. 430
B. Rs. 320
c. Rs. 270
D. Rs. 180


What is the difference between the
centre of gravity and the centre of
mass?


Which of the given two routes to allyl isopropyl ether is more efficient? Explain


Divide: \( \left(6 a^{5}+8 a^{4}+8 a^{3}+2 a^{2}+\right. \)
\( 26 a+35) \) by \( \left(2 a^{2}+3 a+5\right) \)
Answer: \( 3 a^{3}-3 a^{2}+a+7 \)
A . True
B. False


The general solution of \( 4 \tan ^{2} \theta= \) \( \mathbf{3} \sec ^{2} \boldsymbol{\theta} \) is \( \boldsymbol{\theta}=\boldsymbol{n} \boldsymbol{\pi} \pm \frac{\boldsymbol{\pi}}{\boldsymbol{m}} . \) Then, find the
value of \( \boldsymbol{m} \)


A good surfactant will have a:
A. hydrophilic tail
B. hydrophilic head and a long hydrophobic tail
C. hydrophobic head and tail
D. hydrophilic head and a short hydrophobic tail


Pick the odd one out.
The parts of the alimentary canal are (Pharynx. Mouth, Buccal Cavity, Pancreas)


Assertion
Humans are considered advanced from
all its primates relatives, because of the large cranial capacity and high intelligence
Reason
A lumbar curve is present in man, which is also present in apes.
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


Assertion
In a decay process of a nucleus, the
mass of products is less than that of
the parent.
Reason
The rest mass energy of the products must be less than that of the parent
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


What is the difference between
polarised light and unpolarished light based on the direction of electric vector
\( (\vec{E}) ? \)


The artery which supplies blood to the diaphragm is known as
A. Cardiac artery
B. Phrenic artery
c. Lingual artery
D. Lumbar artery


The volume of a gas is reduced to \( \frac{1}{4} \) of
its initial volume adiabatically at \( 27^{\circ} \)
The final temperature of the gas (if \( \gamma= \)
1.4) will be
A. \( 27 \times(4)^{0.4} K \)
B . \( 300 \times(1 / 4)^{0.4} K \)
c. \( 100 \times(4)^{\text {) } \cdot 4} K \)
D. \( 300 \times(4)^{0.4} \mathrm{K} \)


The product of \( \frac{x^{2}-4}{x+1} \) and \( \frac{2 x+2}{x-2} \) is
A \( .2 x-4 \)
B. 0
c. \( 2 x+4 \)
D.


If \( \frac{1}{2}<|x|<1, \) then which of the following are real? This question has multiple correct options
\( A \cdot \sin ^{-1} x \)
B. \( \tan ^{-1} x \)
\( \mathrm{c} \cdot \sec ^{-1} x \)
D. \( \cos ^{-1} x \)


Simplify:
\( \left[3 a^{2}-2 a^{2}+9 a^{2}-\left\{6 a^{2}-\right.\right. \)
\( \left.\left(-2 a^{2}+3 a^{2}\right)\right\} \)


Copper, which is extracted from cuprite, is a/an:
A. sulphide ore
B. carbonate ore
c. oxide ore
D. halide ore


Which of the following problems is associated with the burning of coal?
A. Acid rain
B. Carbon dioxide emissions
c. Ash with toxic metal impurities
D. All of these


How many hydrate isomers of
\( \left[\boldsymbol{C u}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{4}\right] \boldsymbol{C l}_{2} \) are possible?


A body moves from point \( A \) and \( B \) under the action of a force, varying in
magnitude as shown in figure below.
Obtain the work done. Force is
expressed in newton and displacement
is in metre


Which of the following reactions does not occur in stratosphere?
A. \( O_{2}+U V \rightarrow O+O \)
в. \( O_{2}+O \rightarrow O_{3} \)
c. \( C l+O_{3} \rightarrow O_{2}+C l O \)
D. \( S O_{3}+H_{2} O \rightarrow H_{2} S O_{4} \)


Find the number of ordered pairs in
\( \boldsymbol{R}^{-1} \boldsymbol{o} \boldsymbol{R} \)


is a sum of numbers.
A. sequence
B. series
\( c . \) term
D. constant


If \( f(x)=\cos \left[\frac{1}{2} \pi^{2}\right] x+\sin \left[\frac{1}{2} \pi^{2}\right] x \)
\( [x] \) denoting the greatest integer
function, then
A. \( f(0)=0 \)
в. \( f\left(\frac{\pi}{3}\right)=\frac{1}{4} \)
c. \( f\left(\frac{\pi}{2}\right)=1 \)


\( 520 \mathrm{gm} \) mixture of \( F e_{2} O_{3} \) and \( \mathrm{Fe} 0 \)
reacts completely with 158 gm \( K M n O_{4} \) in acidic medium. Calculate the mole \( \% \)
of \( F e_{2} O_{3} \) in mixture


Balance the following reaction.
\( \boldsymbol{C r}_{2} \boldsymbol{O}_{7}^{2-}+\boldsymbol{C}_{2} \boldsymbol{H}_{4} \boldsymbol{O}+\boldsymbol{H}^{+} \rightarrow \)
\( \boldsymbol{C}_{2} \boldsymbol{H}_{4} \boldsymbol{O}_{2}+\boldsymbol{C} \boldsymbol{r}^{3+} \)
A \( \cdot C r_{2} O_{7}^{2-}+3 C_{2} H_{4} O+8 H^{+} \rightarrow 3 C_{2} H_{4} O_{2}+2 C r^{3+}+ \)
\( 4 H_{2} O \)
B . \( C r_{2} O_{7}^{2-}+C_{2} H_{4} O+8 H^{+} \rightarrow 3 C_{2} H_{4} O_{2}+5 C r^{3+}+H_{2} O \)
C. \( C r_{2} O_{7}^{2-}+4 C_{2} H_{4} O+4 H^{+} \rightarrow C_{2} H_{4} O_{2}+2 C r^{3+}+ \)
\( 4 H_{2} O \)
D. None of these


Which statements are correct about
lactose?
This question has multiple correct options
\( \mathbf{A} \cdot\left(C_{1}-\beta\right)(O H) \) of glucose is linked with \( \left(C_{4}-O H\right) \) of galactose
B \( \cdot\left(C_{1}-\beta\right)(O H) \) of galactose is linked with \( \left(C_{4}-O H\right) \) of \( \beta \) -glucose
C. It is hydrolysed both by lase and lactase
D. It exhibits mutarotation


In Thomson mass spectrograph \( \mathrm{E} \perp \overrightarrow{\mathrm{B}} \)
then the
velocity of undeflected electron beam
will be :-
A \( \cdot \frac{|\vec{E}|}{|\vec{B}|} \)
B. \( \overrightarrow{\mathrm{E}} \times \overrightarrow{\mathrm{B}} \)
\( ^{\mathbf{C}} \cdot \frac{|\vec{B}|}{|\vec{E}|} \)
D. \( \frac{E^{2}}{B^{2}} \)


Calculate the \( K_{h} \) and pH of 0.05 N
\( N H_{4} C l \) solution where \( K_{b}=1.8 \times \)
\( 10^{-5} \)


\( 4 \mathrm{kg} \) of hot water at \( 343 \mathrm{k} \) is added to 6kg of water at 293 k.The resultant temp. is 313 k. calculate the heat lost by the hot water and heat gained by the cold water assuming that there is no
heat loss to the surroundings.


Which of the following statement are
true?
A. Charge \( q_{3} \) applies a large force on charge \( q_{2} \) than on
charge \( q_{1} \)
B. Charge \( q_{3} \) applies a smaller force on charge \( q_{2} \) than on
charge \( q_{1} \)
C. Charge \( q_{3} \) applies equal force on bothy the charges.
D. Charge \( q_{3} \) applies no force on any of the charges.


If the ratio of circumference of two
circles is \( 4: 9, \) then what is the ratio of
their areas is?
A .9: 4
B. 16: 81
c. 4: 9
D. 2: 3


Vascular bundle having cambium is
A. Open
B. closed
c. collateral
D. conjoint


If an incident light ray is reflected back along its original path by a plane mirror, then its angle of incidence is:
A \( \cdot 0^{\circ} \)
B. \( 90^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 30^{\circ} \)


Surface gravity of different planets in correct decreasing order is
A. Neptune, Jupiter, Saturn, Earth
B. Jupiter, Neptune, Earth, Saturn
c. Jupiter, Neptune, Saturn, Earth
D. Jupiter, Uranus, Neptune, Saturn


Juxta-glomerular apparatus is made up
of
A. Juxta-glomerular cell, macula densa and lacis cell
B. Juxta-glomerular cell, Purkinjee cell and chief cell
C. Juxta-glomerular cell, lacis cell and myoepithelial cell
D. Juxta-glomerular cell, macula densa and argentaffin cell


Atmospheric pressure at sea level is approximately equal to
A \( \cdot 10^{5} N / m^{2} \)
В. \( 10^{7} N / m^{2} \)
\( \mathbf{c} \cdot 10^{3} N / m^{2} \)
D. \( 10^{1} N / m^{2} \)


The digestion of food in amoeba is
A. Intracellular
B. Intercellular
c. Intravenous
D. None of the above


Three particles of identical masses \( \boldsymbol{m} \)
are kept at the vertices of an equilateral triangle of each side length 'a'. Find the gravitational force of attraction on any one of the particles.


A sum is divided among four persons in the ratio \( 3: 4: 5: 8 . \) If the second
largest share is \( \operatorname{Rs} 2500, \) what is the total sum?
A . Rs 10000
B. Rs 15000
c. Rs 1000
D. Rs 1500


Consider the integral \( \boldsymbol{I}= \) \( \int_{0}^{\pi} \ln (\sin x) d x . \) What is \( \int_{0}^{\frac{\pi}{2}} \ln \)
\( (\sin x) d x \) equal to?
A . \( 4 I \)
B. 2I \( I \)
c. \( I \)
D. \( \frac{I}{2} \)


Which of the following reactions is used to prepare aryl fluorides from diazonium salts and fluoroboric acid?
A. Sandmeyer reaction
B. Balz-Schiemann reaction
c. Gattermann reaction
D. Swarts reaction


A solid metallic sphere of radius \( r \) is
allowed to fall freely through air. If the frictional resistance due to air is
proportional to the cross-sectional area and to the square of the velocity, then the terminal velocity of the sphere is proportional to which of the following?
A \( \cdot r^{2} \)
B.
\( c \cdot r^{3 / 2} \)
D. \( r^{1 / 2} \)


(a) Draw the labelled diagram of Daniell cell.
(b) Write the half-reactions of oxidation
and reduction taking place on electrodes.


What is the range of gravitational force.
\( ? \)
\( A \cdot 10^{-2} m \)
B . \( 10^{-15} \mathrm{m} \)
c. infinite
D. \( 10^{-10} \mathrm{m} \)


Radiation pressure on any surface:
A. is dependent on wavelength of the light used
B. is dependent on nature of surface and intensity of light used
C. is dependent on frequency and nature of surface
D. depends on the nature of source from which light is coming and on nature of surface on which it is falling.


Who had proposed theory of cohesion and adhesion forces?
A. Dixon and Jolly (1894)
B. Dixon and Benson (1885)
C. Dixon and Jolly (1950)
D. sir Jagdish Chandra Bose (1850)


Write the set of values of \( a \) for which the
function \( f(x)=a x+b \) is decreasing
for all \( \boldsymbol{x} \in \boldsymbol{R} \)


The point \( P \) on the parabola \( y^{2}=4 a x \)
for which IPR PQI is maximum, where R \( (-a, 0), Q(0, a), \) is
A \( \cdot(a, 2 a) \)
в. \( (a,-2 a) \)
c. \( (4 a, 4 a) \)
D. \( (4 a,-4 a) \)


Evaluate: \( \int x^{-9} d x \)


If the median of the distribution
(arranged in ascending order) \( 1,3,5,7,9, x, 15,17, \) is \( 8, \) what is the
value of \( x ? \)
A . 11
B. 13
c. \( 9<x<15 \)
D. \( 9 \leq x \leq 15 \)
5


Calcium hydroxide is found in:
A. window cleaner
B. soap
c. lime water
D. milk of magnesia


The number of possible products for \( x \)
and \( y \) is :
\( \bigwedge_{\mathrm{OH}} \frac{\mathrm{n}_{\mathrm{A}}^{+}}{\Delta} \) Possible products \( \frac{\mathrm{Br}_{\mathrm{r}} / \mathrm{ccl}_{4}}{(x)}(y) \) products
\( A \cdot 2,4 \)
B. 3, 5
\( c \cdot 3,6 \)
D. 3,4


The breathing rate of an adult at exercise and rest respectively will be
A. 25 and 18 times per minute
B. 18 and 25 times per minute
c. 35 and 28 times per minute
D. 28 and 35 times per minute


A particle of mass M moves along the \( x \)
axis with speed \( V_{0} \) and collides and
sticks to a particle of mass \( m \) moving
with a speed \( V_{0} \) along y-axis. The velocity of the combined particle after the collision:
\( ^{\mathbf{A}} \cdot \frac{M \hat{i}+m \hat{j}}{(M+m)} V_{0} \)
B. \( \frac{m \hat{i}+M \hat{j}}{(M+m)} V_{0} \)
c. \( (m \hat{i}+M \hat{j}) V_{0} \)
D. Zero


A coin is tossed with a velocity of \( 3 \mathrm{m} / \mathrm{s} \)
at
A.
a) What happens to the velocity along
AB, along DE and at C?
b) What happens to the acceleration of the coin along \( A C \) and \( C E ? \)
c) What is the distance and vertical
displacement covered by the coin between A and E.


Paracetamol is a/an:
A. both antipyretic and analgesic
B. analgesic
C . antipyretic
D. antimalarial


An object \( 2.5 \mathrm{cm} \) high is placed at a
distance of \( 10 \mathrm{cm} \) from a concave
mirror of radius of curvature \( 30 \mathrm{cm} . \) The
size of the image is:
\( \mathbf{A} \cdot 9.2 \mathrm{cm} \)
в. \( 10.5 \mathrm{cm} \)
c. \( 5.6 \mathrm{cm} \)
D. \( 7.5 \mathrm{cm} \)


Two bodies of masses \( 2 k g \& 1.8 k g \) are
separated by \( 20 m \)
The force between them becomes 4
times at a distance of :
A . \( 5 m \)
B. \( 10 m \)
\( c .20 m \)
D. None of them


Laughing gas is obtained by heating:
A \( . N H_{4} C l \)
в. \( \left(N H_{4}\right)_{2} S O_{4} \)
c. \( N H_{4} C l+N a N O_{2} \)
D. \( N H_{4} N O_{3} \)


The cost price of a computer is Rs.19,500. An additional Rs.450 was
spent on installing a software. If it is
sold at \( 12 \% \) profit, find the selling price
of the computer


Which of the following is true about the
reaction quotient?
A. It relates the ratio of the concentrations of products to reactants once the reaction has reached chemical equilibrium.
B. It is always equal to the equilibrium constant.
C. It can never be equal to the equilibrium constant.
D. It relates the concentrations of products to reactants at any point in time.
E. None of these answers are correct


Solubility product of a sulphide \( M S \) is
\( 3 \times 10^{-25} \) and that of another sulphide
\( N S \) is \( 4 \times 10^{-40} . \) In ammoniacal
solution:
A. only NS gets precipitated
B. only MS gets precipitated
c. no sulphide precipitates
D. both sulphides precipitate


Evaluate the given integral. \( \int \frac{5 x+3}{\sqrt{x^{2}+4 x+10}} d x \)


Apoenzyme is a
A. Protein
B. Carbohydrate
c. vitamin
D. Amino acid


A system is taken from state \( A \) to state
B along two different paths 1 and 2 . The work done on the system along these
two paths are \( W_{1} \) and \( W_{2} \) respectively. The heat absorbed by the system along
these two paths are \( Q_{1} \) and \( Q_{2} \) respectively. The internal energies at \( A \)
and \( \mathrm{B} \) are \( U_{A} \) and \( U_{B} \) respectively. Then,
\( \mathbf{A} \cdot W_{1}=W_{2}=U_{B}-U_{A} \)
в. \( Q_{1}=Q_{2}=U_{A}-U_{B} \)
c. \( Q_{1}+W_{1}=Q_{2}+W_{2}=U_{A}+U_{B} \)
D. \( Q_{1}+\left(-W_{1}\right)=Q_{2}+\left(W_{2}\right)=U_{B}-U_{A} \)


The acid used in lead storage cell is:
A. Phosphoric acid
B. Nitric acid
c. Sulphuric acid
D. Hydrochloric acid


The type of muscle fibre present in the wall of alimentary canal is
A. Smooth muscle fibre
B. Striped muscle fibre
c. Cardiac muscle fibre
D. Both A and B


Which type of mirror is used by a dentist?
A . Plane
B. convex
c. concave
D. Both (b) and (c)


The process used for the seperation of those solids which sublime on heating from non volatile solids is :
A. Evaporation
B. Distillation
C. Filteration
D. Sublimation


The order of pH of \( 0.200 \mathrm{M} \) solutions of
\( N H_{4} N O_{3}, N a N O_{3} \) and \( N a_{2} C O_{3} \) is :
A. \( N H_{4} N O_{3}<N a_{2} C O_{3}<N a N O_{3} \)
в. \( N H_{4} N O_{3}<N a N O_{3}<N a_{2} C O_{3} \)
c. \( N a_{2} C O_{3}<N a N O_{3}<N H_{4} N O_{3} \)
D. \( N a_{2} N O_{3}<N H_{4} N O_{3}<N a_{2} C O_{3} \)


The particle used by Rutherford in \( \alpha \) -ray scattering experiment
was
A. neutron
B. electron
c. helium nuclei
D. x rays


Two trains are approaching each other on parallel tracks with same velocity.
The whistle sound produced by one train is heard by a passenger in another train. If actual frequency of whistle is
\( 620 \mathrm{Hz} \) and apparent increase in its frequency is \( 100 \mathrm{Hz} \), the velocity of one of the two trains is (Velocity of sound in air \( \left.=335 m s^{-1}\right) \)
A. 90kmph
B. 72 kmph
c. \( 54 \mathrm{kmph} \)
D. 36 kmph


\( \sec h^{-1}\left(\frac{1}{5}\right)= \)
\( \mathbf{A} \cdot \log (\sqrt{24}+5) \)
\( \mathbf{B} \cdot \log 5+\sqrt{27} \)
\( \mathbf{C} \cdot \log 26+\sqrt{5} \)
D. \( \log 27+\sqrt{5} \)


In a triangle the measured of the angles are \( x, x+20, \) and \( 2 x . \) What is the value of
x?


A river flows \( 3 \mathrm{km} / \mathrm{h} \) and a man is capable of swimming at the rate of
\( 2 k m / h . \) He wishes to cross it such that the displacement parallel to river is minimum. In which direction should he
swim?
\( ^{A} \cdot \sin ^{-1}\left(\frac{2}{3}\right) \)
B. \( \cos ^{-1}\left(\frac{2}{3}\right) \)
\( ^{\mathbf{c}} \cdot \tan ^{-1}\left(\frac{2}{3}\right) \)
D. \( \cot ^{-1}\left(\frac{2}{3}\right) \)


The mean of 2,7,6 and \( x \) is 15 and the
mean of \( 18,1,6, x \) and \( y \) is \( 10 . \) What is the value of y?
A . -5
B. -10
\( c .-20 \)
D. -30


In \( \Delta A B C, 4 \sin A \cos B=1 \) and
\( \tan B=3 \tan A . \) Then \( \sin C= \)
A \( \cdot \frac{1}{4} \)
в. \( \frac{1}{2} \)
\( c \cdot \frac{3}{4} \)
D.


The natural frequency of an LC - circuit
is 1,25,000 cycles per second. Then the capacitor \( C \) is replaced by another capacitor with a dielectric medium of dielectric constant k. In this case, the
frequency decreases by \( 25 k H z . \) The
value of k is:
A . 3.0
B. 2.
c. 1.56
D. 1.7


The storage form of food in plants and animals are
A. Starch and glycogen
B. Starch and cellulose
c. Glycogen and cellulose
D. Starch in both


The value of \( \left(\int_{0}^{\pi / 6} \sec ^{2} x d x\right)^{2} \) is:


n right triangle \( A B C, \overline{D E} \)
\( B C, C D=1.5, \) and \( B E=2.0 \)
The sine of angle \( \theta \) is equal to
\( \mathbf{A} \cdot \mathbf{1} \)
2
B. 3 4
\( c \cdot \frac{\sqrt{2}}{2} \)
\( \frac{\sqrt{3}}{2} \)
E . 3
\( F \)


Two identical blocks \( A \) and \( B \) are
connected by a spring as shown in figure. Block \( A \) is not connected to the wall parallel to y-axis. B is compressed from the natural length of spring and
then left. Neglect friction. Match the following two columns.


The differential equation of all circles passing through the origin and having their centres on the \( x \) -axis is
A \( \cdot y^{2}=x^{2}+2 x y \frac{d y}{d x} \)
B. \( y^{2}=x^{2}-2 x y \frac{d y}{d x} \)
c. \( x^{2}=y^{2}+x y \frac{d y}{d x} \)
D. \( x^{2}=y^{2}+3 x y \frac{d y}{d x} \)


For an ideal binary solution \( (A) \) and \( (B) \)
\( \boldsymbol{y}_{A} \) is the mole fraction of \( \boldsymbol{A} \) in vapor
phase. Which of the following plot should be linear?
A \( \cdot P_{\text {total }} \) vs \( y_{A} \)
B. \( P_{\text {total }} \) vs \( y_{B} \)
\( ^{c} \frac{1}{P_{\text {total}}} \) vs \( y_{A} \)
D. \( \frac{1}{P_{\text {total }}} \) vs \( y_{B}+y_{A} \)


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


Explain why an induced current must flow in such a direction so as to oppose
the change producing it


Which of the following has its application in theatrical make-up?
A. Flexible collodion
B. Non-flexible collodion
c. mixture of A and B
D. None


What must be added to \( x^{3}-3 x^{2}- \)
\( 12 x+19, \) so that the result is exactly
divisible by \( x^{2}+x-6 ? \)
A \( .2 x+5 \)
в. \( 4 x-4 \)
c. \( 2 x+3 \)
D. \( -2 x-5 \)


A 10 meter long thick rubber pipe is suspended from one of its ends. The extension produced in the pipe under its own weight will be \( :(Y=5 \times \)
\( 10^{6} N / m^{2} \) and density of rubber \( = \)
\( \left.1500 k g / m^{3}\right) \)
\( \mathbf{A} \cdot 1.5 m \)
B. \( 0.15 \mathrm{m} \)
\( \mathrm{c} .0 .015 \mathrm{m} \)
D. \( 0.0015 \mathrm{m} \)


Identify the type of reaction when ethanol is burnt in air to form carbon
dioxide, water and releases heat:
This question has multiple correct options
A. Redox reaction
B. Combustion reaction
c. Esterificaton reaction
D. synthesis reaction


Figure shows a wedge \( A \) of mass \( 6 \mathrm{m} \)
smooth semicircular groove of radius a
\( =8.4 \mathrm{m} \) placed on a smooth horizontal
surface. A small block B of mass m is
released from a position in groove where its radius is horizontal. Find the
speed (in \( \mathrm{ms}^{-1} \) ) of bigger block when
smaller block reaches its bottommost
position
A. \( 3 m / s \)
B. \( 2 m / s \)
\( c .7 m / s \)
\( \mathbf{D} \cdot 4 m / s \)


Let \( \boldsymbol{A}=\{\boldsymbol{x}, \boldsymbol{y}, \boldsymbol{z}\}, \boldsymbol{B}=\{\boldsymbol{u}, \boldsymbol{v}, \boldsymbol{w}\} \) and
\( \boldsymbol{f}: \boldsymbol{A} \rightarrow \boldsymbol{B} \) be defined by \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \boldsymbol{u}, \boldsymbol{f}(\boldsymbol{y})=\boldsymbol{v}, \boldsymbol{f}(\boldsymbol{z})=\boldsymbol{w} . \) Then \( \boldsymbol{f} \) is
A. surjective but not injective
B. injective but not surjective
c. bijective
D. none of these


The maximum vertical distance
through which a fully dressed astronaut canjump on the earth is \( 0.5 m . \) If mean
density of the Moon is two-third that of the earth and radius is one quarter that of the earth, the maximum vertical
distance which he can jump on the
Moon and the ratio of the time of
duration of the jump on the Moon to hold on the earth are
в. \( 6 m, 3: \) ?
\( c .3 m, 1: 6 \)
D. \( 6 m, 1: 6 \)


The parabola \( y^{2}=4 x \) and \( x^{2}=4 y \)
divide the square region bounded by the \( \operatorname{lines} x=4, y=4 \) and the coordinate
axes. If \( S_{1}, S_{2} \) and \( S_{3} \) are respectively
the areas of these parts numbered from
top-to-bottom, then \( S_{1}: S_{2}: S_{3} \) is
A. 1: 1: 1
B. 2: 1: 2
c. 1: 2: 3
D. 1: 2: 1


Ozone in stratosphere is depleted by
A \( \cdot C F_{2} C l_{2} \)
в. \( C_{7} H_{16} \)
c. \( C_{6} H_{6} C l_{6} \)
D. \( C_{6} F_{6} \)


Fill in the blanks:
A spherical mirror whose reflecting surface is curved inwards is called a
mirror.


Which of the following can be expected to influence the rate of a chemical
reactions?
(I) The temperature at which it is carried out.
(II) The amount of each specific reactant present.
(III) The presence of a catalyst.
A . I only
B. III only
c. I and II only
D. Il and III only
E . I,II and III


Use the Ellingham diagram for oxides to
find:
1. If \( A I \) will reduce chromium oxide
2. At what temperature C will reduce magnesium oxide, and
3. At what temperature mercuric oxide will decompose into its elements.


Which of the following group have - \( \boldsymbol{I} \) effect ?
This question has multiple correct options
A \( \cdot-\vec{N}\left(C H_{3}\right)_{3} \)
B. \( -N H_{3} \)
\( c .-\bar{o} \)
D. \( -C O O^{-} \)


Eccentricity of the hyperbola whose
asymptotes are given by \( 3 x+2 y+ \)
\( \mathbf{5}=\mathbf{0} \) and \( \mathbf{2} \boldsymbol{x}+\mathbf{3} \boldsymbol{y}+\mathbf{5}=\mathbf{0} \) is
A \( \cdot \sqrt{2} \)
B. \( \frac{3}{2} \)
\( c \cdot 2 \)
D. None of these


A radioactive nucleus can decay by two different processes. The mean value
period for the first process is \( Z_{1} \) and
that for the second process is \( Z_{2} \). The effective mean value period for the two
processes is:
A \( \cdot \frac{Z_{1}+Z_{2}}{2} \)
в. \( Z_{1}+Z_{2} \)
c. \( \sqrt{Z_{1} Z_{2}} \)
D. \( \frac{Z_{1} Z_{2}}{Z_{1}+Z_{2}} \)


Amitosis is shown by
A. Bacteria
B. Hydra
c. Euglena
D. None of the above


In \( \Delta A B C, A B=A C \) and \( A D \) is
perpendicular bisector of \( \boldsymbol{B C} \). The
property by which \( \Delta A D B \) is not
congruent to \( \Delta A D C \) is
A. SAS property
B. SSS property
c. RHS property
D. AAA property


The points (-2,5) and (3,-5) are plotted in xy planes. Find the slope and \( y \) intercept of the line joining the points.


Solve :
\( \int x \sqrt{1+2 x^{2}} d x \)


In which of the following isolations is no reducing agent required?
A. Iron from haematire
B. Tin from tin oxide
c. Mercury from cinnabar
D. zine from zinc blende


If a body starts from rest and travels
\( 120 \mathrm{cm} \) in the \( 6^{t h} \) second then what is
the acceleration?
\( \mathbf{A} \cdot 0.20 m / s^{2} \)
В. \( 0.027 m / s^{2} \)
C. \( 0.218 \mathrm{m} / \mathrm{s}^{2} \)
D. \( 0.003 m / s^{2} \)


When was the first test tube baby born?
A. 2 January 1981
B. 25 July 1978
c. 3 August 1975
D. 4 February 1982


Solve the following linear equations. If
\( x+7-\frac{8 x}{3}=\frac{17}{6}-\frac{5 x}{2}, \) then \( x \) is equal
to
A . -5
B. - 1
\( c \cdot 2 \)
\( D \)


The number of ways, in which 12
identical coins can be put into 5 different purses, if none of the purses
remain empty, is
A. 660
B. 110
\( c \cdot 165 \)
D. 330


pH of some solution is given by \( \boldsymbol{p} \boldsymbol{H}= \) \( \frac{\boldsymbol{p} \boldsymbol{K}_{\boldsymbol{a}_{1}}+\boldsymbol{p} \boldsymbol{K}_{\boldsymbol{a}_{2}}}{\mathbf{2}} . \) This formula is valid for
the compound \( N a H_{2} B O_{3} \)
A . True
B. False


The area of cross section of the wider
tube shown in figure is \( 900 \mathrm{cm}^{2} \). If the
boy standing on the piston weighs 45
kg, the difference in the levels of water
in the two tubes.
A. \( 50 \mathrm{cm} \)
B. 25cm
c. \( 75 \mathrm{cm} \)
D. 100 \( \mathrm{cm} \)


The process of walking involves:
A. Newton's first law of motion
B. Newton's second law of motion
C. Newton's third law of motion
D. Conservation of momentum


A car travels 1000 meters north and the
1000 meters south. The entire trip takes
200 seconds. What is the car's average velocity for the trip?
A. \( 10 \mathrm{m} / \mathrm{s} \)
в. \( 20 \mathrm{m} / \mathrm{s} \)
c. \( 100 m / s \)
D. \( 200,000 \mathrm{m} / \mathrm{s} \)
E . \( 0 m / s \)


Tyndall effect is not observed in:
A. smoke
B. emulsions
c. sugar solution
D. gold sol


In a potentiometer the balancing length
of the string is found to be \( 2.5 \mathrm{m} \) for \( \mathrm{a} \)
cell of e.m.f. 1.5 volt. Find the balancing length of the string for another cell of
e.m.f. 1.2 volt on the same
potentiometer.


In deodorant soaps, the additive added
is:
A. glycerol
B. stearic acid
c. potassium bicarbonate
D. 3,4,5-tribromo salicylaldehyde


Hormones are secreted by ductless
glands of human body. lodine containing hormone is:
A. testosterone
B. adrenaline
c. thyroxine
D. insulin


The above given figure is a structure of:
This question has multiple correct options
A. diethyl ether
B. dimethyl ether
\( c . \) ethoxy ethane
D. methoxy methane


The given graphs (a) and (b) represent the variation of the opposition offered by the circuit element to the flow of
alternating current, with frequency of the applied emf. Identify the circuit element corresponding to each graph.


In the Avogadro's number \( 6.023 \times 10^{23} \)
the number of significant figures will
be:


Determine the domain and range of the
relation R defined by \( \boldsymbol{R}=\left\{\left(\boldsymbol{x}, \boldsymbol{x}^{3}\right): \boldsymbol{x} \) is \right.
a prime number less than \( 10\} \)


The elements which partially conduct electricity are called as
A. Conductors
B. Insulators
c. Semiconductors
D. None of these


Occurrence of mirage effect in deserts
in summer is example of
A. reflection
B. refraction
c. photoelectric effect
D. bending of heat


If the probability distribution of a random variable x is
\( \boldsymbol{X}=\boldsymbol{x}_{1}: \quad-2 \quad-1 \quad \mathbf{0} \quad \mathbf{1} \quad \mathbf{2} \quad \mathbf{3} \)
\( \boldsymbol{p}\left(\boldsymbol{X}=\boldsymbol{x}_{1}\right): \mathbf{0 . 1} \quad \boldsymbol{k} \quad \mathbf{0 . 2} \quad \mathbf{2 k} \mathbf{0 . 3} \boldsymbol{k} \)
then the mean of \( x \) is
A . 0.6
B. 0.8
\( c .1 .0 \)
D. 0.3


Which of the following is a rational function?
A \( \cdot \frac{1}{3} \sqrt{4 x^{3}+4 x+7} \)
в. \( \frac{3 x^{3}-7 x+1}{x-2}, x \neq 2 \)
c. \( \frac{3 x^{5}+5 x^{3}+2 x+7}{x^{3 / 2}}, x>0 \)
D. \( \frac{\sqrt{1+x}}{2+5 x}, x \neq-2 / 5 \)


Hydrogen is similar to alkali metals in terms of:
A. electronic configuration
B. reducing agent
c. valency
D. all of the above


\( \int_{0}^{\pi} x \cdot \log (\sin x) d x= \)
A \( \cdot \pi^{2} \log (2) \)
В. \( \frac{\pi^{2}}{2} \log (2) \)
c. \( \frac{\pi^{2}}{4} \)
D. \( -\frac{\pi^{2}}{2} \log (2) \)


The solution of the differential equation \( \frac{d^{2} y}{d x^{2}}+3 y=-2 x \) is
A \( \cdot c_{1} \cos \sqrt{3} x+c_{2} \sin \sqrt{3} x-\frac{2}{3} x \)
B. \( c_{1} \cos \sqrt{3} x+c_{2} \sin \sqrt{3} x-\frac{4}{5} \)
\( \mathbf{c} \cdot_{c_{1} \cos \sqrt{3} x+c_{2} \sin \sqrt{3} x-2 x^{2}+\frac{4}{9}} \)
D. \( c_{1} \cos \sqrt{3} x+c_{2} \sin \sqrt{3} x-\frac{2}{3} x^{2}+\frac{4}{9} \)


A proton exerts a force on a proton which is
This question has multiple correct options
A. gravitational
B. electromagnetic
c. nuclear
D. weak


If \( \boldsymbol{A}=(\mathbf{2},-\mathbf{3}, \mathbf{1}), \boldsymbol{B}=(\mathbf{3},-\mathbf{4}, \mathbf{6}) \) and \( \boldsymbol{C} \)
is a point of trisection of \( A B, \) then \( C_{y}= \)
A \( \cdot \frac{11}{3} \)
B. -11
c. \( \frac{10}{3} \)
D. \( \frac{-11}{3} \)


State Tangent Law in magnetism.


Chemical reactions require energy for
A. Oxidation
B. Entropy
c. Activation
D. Enthalpy


Give the reagent that would best
accomplish the following
transformation:
\( \mathbf{A} \cdot M C P B A \)
в. \( C H_{3} \) СООН
\( \mathbf{c} \cdot\left(C H_{3}\right)_{3} \operatorname{COOC}\left(C H_{3}\right) \)
D. \( B r_{2} / N a O H \)


Reactions with Appearance dilute \( \boldsymbol{H C l} \)
Dull grey Dissolved Unknown solid with \( \quad \) with metal white oxide \( \quad \) bubbles of coating \( \quad \) clear gas
Solid
Unknow lustrous, No smooth \( \quad \) reaction metal 2 \( \quad \) silver-grey rface
Identify the gas(transparent) produced with the addition of dilute \( H C l \) to
unknown metal 1.
\( \mathbf{A} \cdot C l_{2} \)
\( \mathbf{B} \cdot H_{2} \)
\( c \cdot O_{2} \)
D. \( C O_{2} \)
E \( . N O_{2} \)


If the \( 5^{t h} \) term of an \( A P \) is three times
the first term then prove that the \( 7^{t h} \)
term is twice the third term.


Which of the following Statement is
false?
A. Range is rigidly defined.
B. Range can be calculated for open-ended intervals.
C. Range is not based on all the terms of a given data.
D. Range does not give a clear picture of variation in Data


A compound consisting of two elements, \( X \) and \( Y \) has equal mass of
them. If their atomic weights are 30 and
20 respectively, the molecular formula of that compound (Mol. wt. \( =120 \) ) could
be:
B. \( X_{3} Y_{3} \)
c. \( X_{2} Y_{3} \)
D. \( X_{3} Y_{2} \)


A light ray is moving from denser (refractive index \( =\mu \) ) to air. If the angle of
incidence is half the angle of refraction,
find out the angle of refraction.


The temperature of a body decreased
from \( 200^{\circ} \) to \( 100^{\circ} \) in 1 hour. Determine
how many degrees the body cooled in one hour more if the environment
temperature is \( 0^{\circ} ? \)
A \( .30^{\circ} \)
B . \( 40^{\circ} \)
\( c \cdot 50^{\circ} \)
D. \( 60^{\circ} \)


State briefly the difference between
white blood cells and the red blood cells.


State the reason for the relation \( \boldsymbol{R} \) on
the set \{1,2,3\} given by \( R= \)
\{(1,2),(2,1)\} not to be transitive


The number of simple covalent bonds
(B-H) present in diborane:
A .2
B. 4
\( c \cdot 6 \)
\( D \)


In which of the following molecule/ion all the bonds are not equal?
A. \( X e F_{4} \)
B. \( B F_{4}^{-} \)
\( \mathbf{c} \cdot C_{2} H_{4} \)
D. \( \operatorname{siF}_{4} \)


Charges \( Q_{1} \) and \( Q_{2} \) are placed inside
and outside respectively of an
uncharged conducting shell. Their seperation is \( r \) This question has multiple correct options
A. The force on \( Q_{1} \) is zero
B. The force on \( Q_{1} \) is \( k \frac{Q_{1} Q_{2}}{r^{2}} \)
c. The force on \( Q_{2} \) is \( k \frac{Q_{1} Q_{2}}{r^{2}} \)
D. The force on \( Q_{2} \) is zero.


Find the areas of the triangles the
whose coordinates of the points are
respectively. \( (a, b+c),(a, b-c) \) and \( (-a, c) \)


Simplify.
\( \frac{25 \times t^{-4}}{5^{-3} \times 10 \times t^{-8}}(t \neq 0) \) is \( \frac{m t^{4}}{2} \)
The value of \( m \) is


A steel cable with a radius of \( 1.5 \mathrm{cm} \) supports a chairlift at a ski area. If the
maximum stress is not to exceed
\( 10^{8} N m^{-2}, \) what is the maximum load
the cable can support?


Classify the following pair of line as coincident, parallel or intersecting
\( \boldsymbol{x}-\mathbf{2} \boldsymbol{y}+\mathbf{3}=\mathbf{0} \) \& \( \mathbf{3} \boldsymbol{x}-\mathbf{6} \boldsymbol{y}+\mathbf{9}=\mathbf{0} \)
A. Parallel
B. Intersecting
c. coincident
D. None of these


If \( \sqrt{1-x^{6}}+\sqrt{1-y^{6}}=a\left(x^{3}-y^{3}\right) \)
and \( \frac{d y}{d x}=f(x, y) \sqrt{\frac{1-y^{6}}{1-x^{6}}} \) then
\( \begin{array}{ll}\text { A } \cdot f(x, y)=\frac{y}{x} & \text { B. } f(x, y)=\frac{x^{2}}{y^{2}} \\ \text { c. } f(x, y)=2 \frac{y^{2}}{x^{2}} & \\ \text { D. } f(x, y)=\frac{y^{2}}{x^{2}} & \end{array} \)


\( 0.1 m^{3} \) of water at \( 80^{\circ} C \) is mixed with
\( 0.3 m^{3} \) of water at \( 60^{\circ} \mathrm{C} \). The final
temperature of the mixture is
\( A \cdot 65^{\circ} C \)
B . \( 70^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 60^{\circ} \mathrm{C} \)
D. \( 75^{\circ} \mathrm{C} \)


Determine the oxidation state of the
underlined element in \( \underline{I} C l \)
A \( .+1 \)
B. +4
\( c \cdot+2 \)
D. +3


The plane \( 2 x+3 y+k z-7=0 \) is
parallel to the line whose direction
ratios are (2,-3,1) then \( k= \)
\( \mathbf{A} \cdot \mathbf{5} \)
B. 8
c. 1
\( D \)


The 4 th term of a G.P. is square of its second term, and the first term, and the
first term is \( -3 . \) Find its \( \mathbf{7}^{t h} \) term.


A polygon has 44 diagonals. Find the number of its sides.


An anti-forest measure is
A. Afforestation
B. Selective grazing
C . Clearing forest
D. Selective felling


A starts from rest and moves with
acceleration \( a_{1} . \) Two seconds later, \( \mathrm{B} \)
starts from rest and moves with an
acceleration \( a_{2} . \) If the displacement of \( A \)
in the \( 5^{t h} \) second is the same as that of
\( \mathrm{B} \) in the same interval, the ratio of \( a_{1} \) to
\( a_{2} \) is
A 9: 5
5
B. 5: 9
c. 1: 1
D. 1: 3


Let \( \boldsymbol{f}= \)
\{(1,1),(2,3),(0,-1),(-1,-3)\} be a
function described by the formula \( f(x)=a x+b \) for some integers \( a, b \)
Determine \( a, b \)
A \( . a=2, b=-1 \)
В. \( a=1, b=0 \)
c. \( a=0, b=-1 \)
D. None of these


In a geometrical progression first term and common ratio are both \( \frac{1}{2}(\sqrt{3}+i) \) Then the absolute value of the nth term
of the progression is
\( \mathbf{A} \cdot 2^{n} \)
B . \( 4^{n} \)
\( c \)
D. none of these


Hardness of water is mainly due to the
B. calcium and sodium
c. sodium and magnesium
D. calcium and potassium


Outermost shell cannot have more than
electrons.
A .2
B. 4
\( c \cdot 6 \)
\( D \)


A particle of mass \( m \) and charge \( q \)
moving with velocity \( V \) enters Region
\( I I \) normal to the boundary as shown in
the figure. Region II has a uniform
magnetic field \( B \) perpendicular to the
plane of the paper. The length of the
Region \( \boldsymbol{I} \boldsymbol{I} \) is \( \ell \) Choose the correct
choice(s).

This question has multiple correct options
A. The particle enters Region III only if its velocity \( \mathrm{V}> \)
\( \frac{q \ell}{m} \)
B. The particle enters Region III only if its velocity \( \mathrm{V}< \)
\( \frac{q \ell}{m} \)
C. Path length of the particle in Region II is maximum when velocity \( \mathrm{V}=\frac{\mathrm{q} \ell \mathrm{B}}{\mathrm{m}} \)
D. Time spent in Region II is same for any velocity V as long as the particle returns to Region 1


JJ Thomson discovered which
subatomic particle?
A. protron
B. electron
c. neutron
D. nucleus


If 0.80 mol of \( M n O_{2} \) and 146 g of \( H C l \) react, then number of moles of \( C l_{2} \)
formed is (as nearest integer):
\( M n O_{2}+4 H C l \longrightarrow M n C l_{2}+C l_{2}+ \)
\( 2 H_{2} O \)


If \( 3 \Theta \) is an acute angle, solve the
following equation \( \Theta \) :
\( (\operatorname{cosec} 3 \Theta-2)(\cot 2 \Theta-1)=0 \)


What is the magnitude of linear velocity
of the stick plus puck after the collision?
\( \mathbf{A} \cdot v_{i} \)
B. \( \frac{v_{i}}{3} \)
\( c \cdot \frac{v_{i}}{2} \)
D. \( \frac{v_{i}}{\sqrt{2}} \)


The radius of \( H e^{+} \) ion is \( x \dot{A} \) in its
ground state. The radius of \( L i^{2+} \) ion in the ground state \( (\boldsymbol{A}) \) is:
A \( \cdot \frac{2 x}{3} \)
в. \( \frac{3 x}{2} \)
c. \( \frac{2}{3 x} \)
D. \( \frac{3}{2 x} \)


The electric current is produced by the stored water in dams,which possess:
A. Wind Energy
B. Potential Energy
C. Kinetic Energy
D. Solar Energy


What is the disadvantage of
photorespiration? Explain how the photorespiratory losses are overcome in plants like sugarcane.


A closely wound flat circular coil of 25
turns of wire has diameter of \( 5 \mathrm{cm} \)
which carries current of 4 amperes, the flux density at the centre of a coil will be
A \( \cdot 1.256 \times 10^{-3} \) tesla
В. \( 1.679 \times 10^{-5} \) tesla
c. \( 1.512 \times 10^{-5} \) telsa
D. \( 2.28 \times 10^{-4} \) telsa


Ethyl bromide and isopropyl chloride can be distinguished by:
A. alcoholic \( A g N O_{3} \)
B. comparing their colours
c. burning the compounds on spatula
D. aqueous KOH solution


Let \( a_{n} \) denote the number of all \( n \) -digit
positive integers formed by the digits
0,1 or both such that no consecutive
digits in them are \( 0 . \) Let \( b_{n}= \) the
number of such \( n \) -digit integers ending
with digit 1 and \( c_{n}= \) the number of such \( n \) -digit integers ending with digit
0. The value of \( b_{6} \) is
\( A \cdot 7 \)
B. 8
\( c .9 \)
D. 11


If \( z_{1} \) and \( z_{2} \) both satisfy the relation \( z+ \) \( \bar{z}=2|z-1| \) and \( \arg \left(z_{1}-z_{2}\right)=\frac{\pi}{4} \)
then the imaginary part of \( \left(z_{1}+z_{2}\right) \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. None of these


In angiosperms, triple fusion produces
A. Polar nucleus
B. Secondary nucleus
c. Primary endospermic nucleus
D. Zygotic nucleus


A material of \( 0.25 \mathrm{cm}^{2} \) cross sectional
area is placed in a magnetic field of strength \( (H) 1000 A m^{-1} . \) Then the
magnetic flux produced is:
[Susceptibility of material is 314 and
Permeability of free space, \( \mu_{0}=4 \pi \times \)
\( 10^{-7} H m^{-1} \)
A . \( 8.33 \times 10^{-8} \mathrm{Wb} \)
В. \( 1.84 \times 10^{-6} \mathrm{Wb} \)
\( \mathbf{c} \cdot 9.87 \times 10^{-6} \mathrm{Wb} \)
D. \( 3.16 \times 10^{-8} \mathrm{Wb} \)


Write down the general features of
fungi


Consider the figure given. Each
capacitor has capacitance \( C . \) The
capacitance between 1 and 3 is :
\( A \cdot \frac{3 C}{4} \)
B. \( \frac{3 C}{2} \)
\( c \cdot \frac{5 C}{2} \)
D. \( \frac{50}{1} \)


Isogonic lines of a magnetic map represent lines joining places with
same
A. \( B \) н
B. dip
c. zero dip
D. declination


The function \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) defined by
\( f(x)=(x-1)(x-2)(x-3) \) is.
A. One-one but not onto
B. Onto but not one-one
c. Both one-one and onto
D. Neither one nor onto


During origin of life, nucleoprotein gave most probably the first sign of
A . Life
B. Amino Acids
c. Soil
D. Sugar


Assertion
Carbohydrates are most suitable for the
production of energy in the body than protein and fats.
Reason
Carbohydrates can be stored in the tissues as glycogen and can be used for production of energy whenever
necessary.
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 production of an electromotive force across an electrical conductor in a
changing magnetic field is known as an Electromagnetic induction. Enter 1 for True and 2 for False.


1, 2 - dichloro ethane is which type of
halide?
A. Geminal halide
B. Vicinal halide
c. Alkylidene halide
D. Allylic halide


To get a driver's license, an applicant must pass a written test and a driving
test. Past records show that \( 80 \% \) of the
applicants pass the written test and 60 \( \% \) of those who have passed the written
test pass the driving test. Based on these figures, how many applicants in a random group of 1,000 applicants
would you expect to get driver's licenses?
A . 200
B . 480
c. 600
D. 750
E . 800


A body in uniform motion moves with:
A. constant velocity
B. constant speed
c. constant acceleration
D. none of these


In crystalline \( \boldsymbol{H}_{2} \boldsymbol{O}_{2}, \) the dihedral angle is increased to 100
A. True
B. False


The percentage increase in magnetic
field B when the space within a current carrying toroid is filled with aluminium
\( \left(X=2.1 \times 10^{-5}\right) \) is
A \( .0 .2 \% \)
B. \( 2 \times 10^{-3} \% \)
c. \( 2 \times 10^{-2} \% \)
D. \( 2 \times 10^{-4} \% \)


A body dropped freely has covered half of the total distance in the last second.
The total journey time is
A. \( (2+\sqrt{2}) s \)
B. \( (2-\sqrt{2}) s \)
c. \( 2 s \)
D. \( (2+\sqrt{3}) s \)


The graph gives the magnitude \( B(t) \) of \( a \)
uniform magnetic field that exist throughtout a conducting loop.
perpendicular to the plane of the graph
according to the magnitude of the emf induced in the loop greatest first
A. \( b>(d=\epsilon)<(a=c) \)
В. \( b>(d=\epsilon)>(a=c) \)
c. \( b<d<\epsilon<\epsilon<c \)
D. \( b>(a=c)>(d=\epsilon) \)


\( D_{2} O \) differ in the following except:
A. freezing point
B. density
c. ionic product of water
D. its reaction with sodium


When resonance of two sound waves
occurs, resultant wave have:
A. a loud sound
B. absorption of light waves
c. a dark color
D. transmission of light waves
E. a light color


Which pair of molecules will have a permanent dipole moment for both
members?
A. \( N O_{2} \) and \( O_{3} \)
B. \( \operatorname{SiF}_{4} \) and \( C O_{2} \)
c. \( \operatorname{SiF}_{4} \) and \( N O_{2} \)
D. \( N O_{2} \) and \( C O_{2} \)


The oxidation number of \( X e \) in \( X e O F_{2} \)
is:
\( A \cdot O \)
B. 2
\( c \cdot 4 \)
D.


Assertion
Bohr had to postulate that the electrons in stationary orbits around the nucleus
do not radiate.
Reason
According to classical physics all moving electrons radiate.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


A heavy box is to be dragged along a rough horizontal floor. To do so, person A
pushes it at an angle \( 30^{\circ} \) from the horizontal and requires a minimum force \( \boldsymbol{F}_{A}, \) while person \( \mathrm{B} \) pulls the box at
an angle \( 60^{\circ} \) from the horizontal and
needs minimum force \( \boldsymbol{F}_{B} \). If the
coefficient of friction between the box
and the floor is \( \frac{\sqrt{3}}{5}, \) find the ratio \( \frac{F_{A}}{F_{B}} \)
A. \( \sqrt{3} \)
в. \( \frac{5}{\sqrt{3}} \)
c. \( \sqrt{\frac{3}{2}} \)
D. \( \frac{2}{\sqrt{3}} \)


Which is an acidic indicator?
A. Phenolphthalein
B. Methylorange
c. Both \( (A) \) and \( (B) \)
D. None of these


What is the degeneracy of the level of \( \boldsymbol{H} \)
-atom that has energy \( \left(-\frac{R_{H}}{9}\right) ? \)
A . 16
B. 9
\( c \cdot 4 \)
\( D \)


A particle of mass \( m \) moving with a velocity \( (3 \hat{i}+2 \hat{j}) m s^{-1} \) collides with
another body of
mass \( M \) and finally moves with velocity
\( (-2 \hat{i}+\hat{j}) m s^{-1} . \) Then during the
collision:

This question has multiple correct options
A. Impulse received by \( m \) is \( m(5 \hat{i}+\hat{j}) \)
B. Impulse received by \( m \) is \( m(-5 \hat{i}-\hat{j}) \)
C. Impulse received \( M \) is \( m(-5 \hat{i}-\hat{j}) \)
D. Impulse received by \( M \) is \( m(5 \hat{i}+\hat{j}) \)


Which one of the following conditions need not be present for photosynthesis to proceed?
A. water
B. Oxygen
c. Light
D. chlorophyll


When a metal sphere is heated
maximum percentage increase occurs in its :
A. Density
B. Surface area
c. Radius
D. volume


To a solution of acetic acid, solid
sodium acetate is added gradually. When \( x \) mole of salt is added, the pH has
a certain value. If y mole of salt is
added, the pH change by 0.6 units to the previous pH. What is the ratio of \( x \) and
y?


Binding energy per nucleon of three nuclei \( A, B \) and \( C \) are 5.5,8.5 and 7.5
respectively. Which one of the following nuclei is most stable?
A. \( A \)
в. \( C \)
\( c . B \)
D. cannot be predicted


Find the following limit:
\( \lim _{x \rightarrow 1} \frac{\sqrt[3]{x}-1}{\sqrt{x}-1} \)


Choose the correct answers from the
alternatives given
Exudation
A. Takes place during positive root pressure
B. Takes place during negative root pressure
c. Is unrelated with root pressure
D. Is related with photosynthesis


toppr
Q Type your question
acid such as conc. \( H_{2} S O_{4} \) as a catalyst.
The reaction is reversible and generally
the equilibrium constant for
the esterification is close to \( 1 . \) As it is a
reversible reaction, different methods
are used to increase the yield of ester. It is established that the mechanism of
esterification under such conditions
involves initial protonation of the acid
followed by the attack of the alcohol as
a nucleophile.
The correct statement(s)
is/are
This question has multiple correct options
A. When esterification is carried out using molar ratio of acid and alcohol as 1: 10 , the yield of the ester with respect to the acid should be close to \( 90 \% \)
B. The function of conc.\( H_{2} S O_{4} \) is also to increase the free energy change of the reaction and thereby increasing the equilibrium constant
C. When an ester is heated with acidified water the protonation will be more favourable at the acyl oxygen atom than at the alkoxy oxygen atom
D. When butyl hexanoate is heated with a large excess of methanol in the presence of a small quantity of conc. \( H_{2} S O_{4} \), methyl hexanoate is the major product


Which vitamin rich food items should
we eat to keep our eyes healthy?
A. Vitamin D
B. Vitamin A
c. Vitamin E
D. Vitamin c


Cisplatin used for the treatment
of
A. Cancer
в. Нा
c. Anemia
D. cholera


Is Fe, Co, Ni are Dobereiner triad?


Select the correct order of \( \mathrm{C} \) - \( \mathrm{O} \) bond
Iength:
\( \mathbf{A} \cdot\left[M(C O)_{3}\left(P F_{3}\right)\right]<\left[M(C O)_{3}\left(P C l_{3}\right)\right]< \)
\( \left[M(C O)_{3}\left(P M e_{3}\right)\right] \)
\( \mathbf{B} \cdot\left[M(C O)_{3}\left(P F_{3}\right)\right]>\left[M(C O)_{3}\left(P C l_{3}\right)\right]> \)
\( \left[M(C O)_{3}\left(P M e_{3}\right)\right] \)
\( \mathbf{c} \cdot\left[M(C O)_{3}\left(P F_{3}\right)\right]=\left[M(C O)_{3}\left(P C l_{3}\right)\right]= \)
\( \left[M(C O)_{3}\left(P M e_{3}\right)\right. \)
\( \mathbf{D} \cdot\left[M(C O)_{3}\left(P F_{3}\right)\right]=\left[M(C O)_{3}\left(P C l_{3}\right)\right]> \)
\( \left[M(C O)_{3}\left(P M e_{3}\right)\right] \)


The overall goal of glycolysis, Krebs cycle and the electron transport system is the formation of
A. ATP in small stepwise reactions
B. ATP in one large oxidation reaction
c. sugars
D. Nucleic acid


In which of the following cases can the average velocity of a particle in a timeinterval can be found by using geometry only given the velocity-time graphs?
A. Velocity-time graph is a set of straight line with different slopes
B. Velocity-time graph is a straight line with constant slope and no discontinuities
c. velocity-time graph is a set of straight lines with same slopes but with discontinuities
D. Average velocity can always be found by using geometry only


The moon is about \( 384000 \mathrm{km} \) from the
earth and its path around the earth is
nearly circular. Find circumference of
the path travelled by the moon every
month.


Haemoglobin present in human blood binds to oxygen in which oxidation
state?
A \( \cdot F e^{2} \)
B. \( F e^{3} \)
\( \mathrm{c} \cdot F e^{4} \)
D. \( F e^{+} \)


Sum of nine terms of the series \( \log a+ \)
\( \log \frac{a^{2}}{b}+\log \frac{a^{3}}{b^{2}}+\log \frac{a^{4}}{b^{3}}+\ldots . . i s- \)
A . \( 36 \log a-28 \log b \)
B. \( 45 \log a-36 \log b \)
c. \( 55 \log a-45 \log b \)
D. \( 66 \log a-55 \log b \)


Factorize:
\( 2 m^{2}+39 m+19 \)


For a chemical reaction, \( \boldsymbol{m} \boldsymbol{A} \longrightarrow \boldsymbol{x} \boldsymbol{B} \)
the rate law is \( r=k[A]^{2} . \) If the
concentration of \( A \) is doubled, the
reaction rate will be :
A. doubled
B. quadrupled
c. increases by 8 times
D. unchanged


The cartesian product \( \boldsymbol{A} \times \boldsymbol{A} \) has \( \mathbf{9} \)
elements among which are found
(-1,0) and \( (0,1) . \) Find the set \( A \) and the
remaining elements of \( \boldsymbol{A} \times \boldsymbol{A} \)


A liquid drop having surface energy ' \( E \) " is spread into 512 droplets of same size. The final surface energy of the droplets
is
A \( .2 E \)
в. \( 4 E \)
\( c .8 E \)
D. \( 12 E \)