A coordination complex of type \( M X_{2} Y_{2} \)
(M-metal ion; \( X, Y \) -monodentate ligands), can have either a tetrahedral
or a square planar geometry. The maximum number of possible isomers in these two cases are respectively:
A \( \cdot 1 \) and 2
B. 2 and1
c. 1 and 3
D. 3 and 2


The complex number \( z \) satisfying the
equations \( |z|-\mathbf{4}=|z-i|-|z+\mathbf{5} i|= \)
\( \mathbf{0}, \) is
This question has multiple correct options
A. \( \sqrt{3}-i \)
В. \( 2 \sqrt{3}-2 i \)
c. \( -2 \sqrt{3}-2 i \)
D. 0


Write mechanism of cleaning action of detergents.


The primary and secondary valency of Co in the octahedral complex
\( \boldsymbol{C o C l}_{3} \cdot \boldsymbol{5} \boldsymbol{N} \boldsymbol{H}_{3} \) are
A. 6 and 3
B. 3 and 6
\( c \cdot 4 \) and 3
D. 3 and


Find the domain and range of the following function:
\( \frac{\boldsymbol{x}+\boldsymbol{4}}{|\boldsymbol{x}+\mathbf{4}|} \)


In Liebig's method for the estimation of \( \mathrm{C} \) and \( \mathrm{H}, \) if the compound also contains both halogens and sulphur then which of the following is kept near the exit of the combustion tube?
A . Silver wire
в. \( P b C r O_{4} \)
c. Both (a) and (b)
D. Cu gauge


Identify the antifertility drug.
A. Ethynylestradiol
B. Novestrol
c. Norethindrone
D. None of these


A compound has the following composition by weight: \( N a= \) \( \mathbf{1 8 . 6 0 \%}, \boldsymbol{S}=\mathbf{2 5 . 8 0 \%}, \boldsymbol{H}=\mathbf{4 . 0 2 \%} \) and
\( O=51.58 \% . \) Assuming that all the
hydrogen atoms in the compound are part of water of crystallization, the correct molecular formula of the
compound is:
A. \( N a_{2} S_{2} O_{3} \cdot 3 H_{2} O \)
в. \( N a_{2} S O_{4} \cdot 5 H_{2} O \)
c. \( N a_{2} S O_{4} \cdot 10 H_{2} O \)
D. \( N a_{2} S_{2} O_{3} \cdot 5 H_{2} O \)


If \( \vec{r}=3 \hat{i}+2 \hat{j}-5 \hat{k}, \vec{a}=2 \hat{i}-\hat{j}+\hat{k} \)
\( \overrightarrow{\boldsymbol{b}}=\hat{\boldsymbol{i}}+\boldsymbol{3} \hat{\boldsymbol{j}}-\boldsymbol{2} \hat{\boldsymbol{k}}, \overrightarrow{\boldsymbol{c}}=-\boldsymbol{2} \hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}-\boldsymbol{3} \hat{\boldsymbol{k}} \)
such that \( \vec{r}=\lambda \vec{a}+\mu \vec{b}+v \vec{c}, \) then \( \mu, \frac{\lambda}{2} \)
\( \boldsymbol{v} \) are in
A. \( H . P \)
в. \( G . P \)
c. \( A . G . P \)
D. A.P


Growth of pollen tube through the style towards the embryo sac is an example of
A. Geotropism
B. Hydrotropism
c. Thigmotropism
D. chemotropism


During the kinetic study of the reaction,
\( \mathbf{2} \boldsymbol{A}+\boldsymbol{B} \rightarrow \boldsymbol{C}+\boldsymbol{D} \) following results
were obtained.
\( \begin{array}{lll} & {[\mathrm{A}]} & {[\mathrm{B}]} \\ & \text { Run } & \text { in } & \text { in } \\ & \text { M } & \text { M }\end{array} \) Iniitial rate of
formation of D in
\( \boldsymbol{m} \boldsymbol{s}^{-1} \)
0.1
\( 0 . \)
\( 6.0 \times 10^{-3} \)
\( \begin{array}{ll}0.2 & 7.2 \times 10^{-2}\end{array} \)
0.3
\( 2.88 \times 10^{-1} \) 0.3
0.4
0.4
\( \begin{array}{ll}0.1 & 2.40 \times 10^{-2}\end{array} \)
On the basis of above data which one is
correct?
A \( \cdot r=k[A]^{2}[B] \)
B. \( r=k \) (A)[B]
C \( \cdot r=k[A]^{2}[B]^{2} \)
D . \( r=k[A][B]^{2} \)


Find a quadratic equation whose roots
\( \operatorname{are} \alpha, \beta \) such that \( \alpha+\beta=3 \) and \( \alpha^{3}+ \)
\( \boldsymbol{\beta}^{\mathbf{3}}=\mathbf{9} \)


Which of the following is NOT used in making photographic plates using colloidal sols?
A. Silver bromide
B. Gelatin
c. Glass plate
D. Argyrol


Solve the following simultaneous equations:
\( \frac{7}{2 x+1}+\frac{13}{y+2}=27, \frac{13}{2 x+1}+ \)
\( \frac{7}{y+2}=33 \)


Drugs that bind to the receptor sites and inhibit its natural function are
called analgesics.
A. True
B. False


The D.E. obtained from \( y=c x^{2}+c^{3} \) is
\( ^{\mathbf{A}} \cdot\left(\frac{d y}{d x}\right)^{3}+4 x^{4} \frac{d y}{d x}=8 x^{3} y \)
\( ^{\mathbf{B}}\left(\frac{d y}{d x}\right)^{3}-4 x^{4} \frac{d y}{d x}=8 x^{3} y \)
\( ^{\mathrm{c}}-\left(\frac{d y}{d x}\right)^{3}-4 x^{4} \frac{d y}{d x}=8 x^{3} y \)
\( \left(\frac{d y}{d x}\right)^{3}-4 x^{4} \frac{d y}{d x}=-8 x^{3} y \)


A block of mass \( 15 k g \) is placed on a long trolley. The coefficient of friction between the block and trolley is 0.18 The trolley accelerates from rest with
\( 0.5 m / s^{2} \) for 20 sec, then what is the friction force?
A . \( 3.5 N \)
в. \( 133.3 N \)
\( c .7 .5 N \)
D. None of these


Heart of cockroach is
A. Four chambered
B. Ventral to gut
C. Longitudinal and beaded
D. Three chambered


Peptization is a :
A. process of converting a colloidal solution into precipitate
B. process of converting precipitate into colloidal solution
C . process of converting soluble particles to form colloidal solution
D. process of bringing colloidal molecule into solution


A 50 gram bead slides on a frictionless
wire as shown above. At what point on
the wire will the bead come to a
complete stop? The initial speed at \( C \) is \( \sqrt{2 g h} \)
A. Point \( A \)
B. Point B
c. Point \( c \)
D. Point D
E. Point E


In which of the following, the chemical formula and the name are incorrectly
matched?
A \( \cdot_{K}\left[P t\left(N H_{3}\right) C l_{5}\right] \) - potassium
amminepentachloroplatinate(IV)
в. \( \left[A g(C N)_{2}\right]^{-}- \) dicyanoargentate (1) ion
\( c \)
\( K_{3}\left[C r\left(C_{2} O_{4}\right)_{3}\right] \) - potassium trioxalatochromate(II)
D. \( _{N a_{2}}[N i(E D T A)] \) - sodium
ethylenediaminetetraacetonickelate(IV)


Examine the continuity of:
\[
\begin{aligned}
\boldsymbol{f}(\boldsymbol{x}) &=\boldsymbol{x}^{2}-\boldsymbol{x}+\boldsymbol{9} \text { for } \boldsymbol{x} \leq \mathbf{3} \\
&=\boldsymbol{4} \boldsymbol{x}+\mathbf{3} \quad \text { for } \boldsymbol{x}>\mathbf{3}, \boldsymbol{a} \boldsymbol{t} \boldsymbol{x}=\boldsymbol{3}
\end{aligned}
\]


A one litre sphere and a two litre sphere are connected with a capillary tube of negligible volume. They contain an ideal \( \operatorname{gas} \) at \( 27^{\circ} \mathrm{C} \) at a pressure of \( 100 \mathrm{cm} \) of \( \mathrm{Hg} \)
Keeping the temperature of one litre sphere constant at \( 27^{\circ} \mathrm{C} \), if
temperature of two litre sphere is
increased to \( 127^{0} \mathrm{C} \), then the final pressure
is
A. \( 110 \mathrm{cm} \) of \( \mathrm{Hg} \)
B. 120 cm of Hg
c. \( 150 \mathrm{cm} \) of \( \mathrm{Hg} \)
D. 200 cm of Hg


Find the general solution of \( \sec \theta+1= \) \( (2+\sqrt{3}) \tan \theta \)


Polyphosphates like sodium hexametaphosphate (calgon) are used as water softening agents because they:
A. form soluble complexes with anionic species
B. precipitate anionic species
c. form soluble complexes with cationic species
D. precipitate catatonic species


Explore and answer:
Does pure water conduct electricity? If not, what can we do to make it conduct?


A straight line through origin 0 meets the lines \( 3 y=10-4 x \) and \( 8 x+6 y+ \)
\( 5=0 \) at points \( A \) and \( B \) respectively
Then 0 divides the segment \( A B \) in the
ratio:
A .2: 3
B. 1: 2
c. 4: 1
D. 3: 4


The electrons are more likely to be
found:
\( A \). in the region a and \( b \)
B. in the region a and \( c \)
c. Only in the region
D. Only in the region a


Which of the following is incorrect?
A \( . \) lonic product of \( D_{2} O>H_{2} O \)
B. Solubility of inorganic substances of \( H_{2} O>D_{2} O \)
C . Mass of \( D_{2} O>H_{2} O \)
D. Heat of fusion of \( D_{2} O>H_{2} O \)


Find the electric field at a distance " \( z " \)
from the plane. This question has multiple correct options
A \( \cdot \vec{E}=\frac{\sigma}{2 \epsilon_{0}} \hat{k} \) for \( z>0 \)
B・ \( \vec{E}=-\frac{\sigma}{2 \epsilon_{0}} \hat{k} \) for \( z>0 \)
c. \( \vec{E}=\frac{\sigma}{2 \epsilon_{0}} \hat{k} \) for \( z<0 \)
D・ \( \vec{E}=-\frac{\sigma}{2 \epsilon_{0}} \hat{k} \) for \( z<0 \)


A sphere of mass \( m \) and radius \( r \) is
pushed onto the fixed horizontal surface such that it rolls without
slipping from the beginning. The
minimum speed v of its mass centre at
the bottom so that it rolls completely around the loop of radius \( (\boldsymbol{R}+\boldsymbol{r}) \)
without leaving the track in between is \( \operatorname{given} \operatorname{as} v=\sqrt{\frac{x}{7} g R} \) Find \( x \)


Assertion
Substances which at room temperature retain their ferromagnetic property for a long period of time are called
permanent magnets.
Reason
Permanent magnet can be made by placing a ferromagnetic rod in a solenoid and passing current through it.
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


Select the correct option regarding the
given figure.
A. \( \mathrm{D} \) is eosinophil which is found more in asthma patients
B. B is lymphocyte which helps in blood clotting.
C. \( C \) is neutrophil which is phagocytic in nature
D. A is monocyte which releases histamine, serotonin and heparin.


How many \( S-S \) linkage(s) is/are
present in sodium tetrathionate?
\( A \cdot 4 \)
B. 3
\( c \cdot 2 \)
D.


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


For the reaction, \( N_{2} O_{4}(g) \underset{K_{2}}{\rightleftharpoons} K_{1} \)
\( 2 N O_{2}(g), \) the rate of disappearance of
\( N O_{2} \) will be :
A \( \cdot K_{1}\left[N_{2} O_{4}\right]-K_{2}\left[N O_{2}\right]^{2} \)
B . \( 2 K_{1}\left[N_{2} O_{4}\right]-2 K_{2}\left[N O_{2}\right]^{2} \)
c. \( K_{2}\left[N O_{2}\right]^{2}-K_{1}\left[N_{2} O_{4}\right] \)
D \( \cdot 2 K_{2}\left[N O_{2}\right]^{2}-2 K_{1}\left[N_{2} O_{4}\right] \)


Mr. Ambani purchased a car of 3,00,000 and a bike for his son for
1, 00, 000. He sold the car at a profit of
\( 10 \% \) and bike at a loss of \( 20 \% . \) What is
the net gain or loss?
A . 2\% gain
B. 1.5\% gain
c. \( 2.5 \% \) loss
D. 2.5\% gain


Lactic acid is called so because it is
obtained from sour milk.
A. True
B. False


Buckminster fullerene is the allotropic
form of:
A. nitrogen
B. carbon
c. sulphur
D. iodine


An electric current is passed through
silver voltameter connected to a water
voltameter. The cathode of the silver
voltameter weighed \( 0.108 g \) more at the end of the electrolysis. The volume of oxygen evolved at STP is:
\( \mathbf{A} \cdot 56 \mathrm{cm}^{3} \)
В. \( 550 \mathrm{cm}^{3} \)
\( c \cdot 5.6 \mathrm{cm}^{3} \)
D. \( 11.2 \mathrm{cm}^{3} \)
E . \( 22.4 \mathrm{cm}^{3} \)


Which of the following statement is not
correct?
A. vitamins are synthesized within the body
B. hormones are synthesized within the body
C. hormones are also known as chemical messengers
D. hormones are highly potent and so are produced in small quantities


Prove that the straight line joining the mid-points of the opposite sides of a parallelogram divides it in to two parallelograms of equal area.


Water waves in a shallow dish are \( 6 \mathrm{cm} \)
long. At one point, the water moves up and down at a rate of 4.8 oscillations/s.
What is the speed of the water waves?
A. \( 0.288 \mathrm{m} / \mathrm{s} \)
в. \( 0.3 \mathrm{m} / \mathrm{s} \)
c. \( 1.25 \mathrm{m} / \mathrm{s} \)
D. \( 1.2 \mathrm{m} / \mathrm{s} \)


If the threshold energy for ejection of electron from metal is 1.4 eV and light of 3eV falls on the metal, then the kinetic
energy of photoelectron emitted will be:
A \( .2 .6 \times 10^{-19} \mathrm{J} \)
В. \( 1.6 \times 10^{-18} \mathrm{J} \)
c. \( 2.2 \times 10^{-19} \mathrm{J} \)
D. \( 3.2 \times 10^{-20} \mathrm{J} \)


The force between two identical charges
placed at a distance of \( r \) in vacuum is
\( F . \) Now, a slab of dielectric of constant 4 is inserted between these two charges.
If the thickness of the slab is \( \frac{r}{2}, \) then the force between the charges will become:
A. \( F \)
в. 3
\( \overline{5}^{F} \)
c. \( _{\overline{9}}_{F} \)
D. \( \frac{F}{2} \)


Give an account of factors which affect
photosynthesis.


At \( 50 \mathrm{C} \), liquid \( N H_{3} \) has ionic product is
\( 10^{-30} . \) How many amide \( \left(N H_{2^{-}}\right) \) ions
are present per \( m m^{3} \) in pure liquid \( N H_{3} ?\left(\operatorname{take} N_{A}=6 \times 10^{23}\right) \)


In the figure, an equilateral triangle of side \( 6 \mathrm{cm} \) and its circumcircle is shown
Find the area of shaded portion. Take \( (\boldsymbol{\pi}=\mathbf{3 . 1 4}, \sqrt{\mathbf{3}}=\mathbf{1 . 7 3}) \)
A. \( 22.11 \mathrm{cm}^{2} \)
B. \( 22 \mathrm{cm}^{2} \)
c. \( 21.11 \mathrm{cm}^{2} \)
D. \( 23.11 \mathrm{cm}^{2} \)


If \( 2 f(\sin x)+f(\cos x)=x, \) then
\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}} \boldsymbol{f}(\boldsymbol{x}) \) is
\( \mathbf{A} \cdot \sin x+\cos x \)
B. 2
c. \( \frac{1}{\sqrt{1-x^{2}}} \)
D. none of these


A conductor consists of a circular loop
of radius \( R=10 \mathrm{cm} \) and two straight,
long sections as shown in figure.The
wire lies in the plane of the paper and
carries a current of \( i=7.00 A \)
Determine the magnitude and direction
of the magnetic field at the centre of the
loop.


The general solution of the differential
equation \( y d x-x d y+x^{2} \cdot \sin y d y+ \)
\( \left(1+x^{2}\right) d x=0, \) is equal to:
A \( \cdot x^{2}=(c+1) x+x \cdot \cos y-y \)
B . \( x^{2}=(c+1) x+x . \cos y+y \)
c. \( x^{2}=c x+x . \cos y+y-1 \)
D. \( x^{2}=c x+x . \cos y+y+1 \)


Assertion \( (A): \) The eccentricity of an ellipse is \( \frac{\mathbf{3}}{\mathbf{5}} \)
Reason \( (\boldsymbol{R}): \) The equation of the ellipse is \( x=5 \cos \theta, y=4 \sin \theta \)
A. Assertion and reason both are correct and reason is an explanation.
B. Assertion and reason both are correct and reason is not an explanation
c. Assertion is incorrect and reason is correct
D. Assertion is correct and reason is incorrect


Water and chlorobenzene are
immiscible liquids. Their mixture boils
at \( 89^{\circ} \mathrm{C} \) under a reduced pressure of
\( 7.7 \times 10^{4} \) Pa. The vapour pressure of
pure water at \( 89^{\circ} \mathrm{C} \) is \( 7 \times 10^{4} \mathrm{Pa} \)
Weight percent of chlorobenzene in the distillate is:
A . 50
B. 60
c. 79
D. 38.46


A nucleus (mass no. 238) initially at rest decay into another nucleus (mass
no. 234 ) emitting an \( \alpha \) particle (mass
no. 4 ) with the speed of \( 1.17 \times \) \( 10^{7} m / \)sec Find the recoil speed of the
remaining nucleus.


Two spherical conductors \( A \) and \( B \) of
radii \( 1 \mathrm{mm} \) and \( 2 \mathrm{mm} \) separated by a distance of \( 5 \mathrm{cm} \) and are uniformly charged. If the spheres are connected by a conducting wire then in equilibrium condition, the ratio of the magnitude of
the electric fields at the surfaces of
spheres \( A \) and \( B \) is:
A . 4: 1
B. 1: 2
c. 2: 1
D. 1: 4


Which of the following layers of atmosphere absorb UV light radiations?
A. lonosphere
B. Ozonosphere
c. Troposphere
D. None of these


For a transistor, the current ratio \( \boldsymbol{\alpha}_{d c}= \) \( \frac{69}{70} . \) The current gain \( \beta_{d c} \) is
\( \mathbf{A} \cdot 66 \)
B. 67
\( c \cdot 69 \)
D. 71


The complex studied by Werner had a composition corresponding to the
formula \( P t C l_{4} .2 K C l . \) From electrical
conductance measurements, he
determined that each formula unit
contained three ions. He also found that
silver nitrate did not give a precipitate of \( A g C l \) with this complex. Write a
formula for this complex that agrees with this information.


The value of \( ^{95} C_{4}+\sum_{j=1}^{5} 100-j C_{3} \) is
\( \mathbf{A} .^{95} C_{5} \)
В. \( ^{100} C_{4} \)
\( \mathrm{c} .^{99} \mathrm{C}_{4} \)
D. \( ^{10} C_{5} \)


A good soil is that which
A. Holds whole of the water entering into it
B. Allows limited amount of water into it
C. Allows the water to percolate slowly into it
D. Allows the water to pass very quickly from it


A reflex arc does not involve
A. A receptor
B. A sensory pathway
C. A motor pathway
D. The brain


Which are position isomers?
\( A \)
and
B.
and
\( c \)
and
\( D \)
and


The rate law for a single step reaction
\( \mathbf{2} \boldsymbol{A}+\boldsymbol{B} \rightarrow \boldsymbol{P} \) is \( \boldsymbol{k}[\boldsymbol{A}][\boldsymbol{B}] \)
A. True
B. False


Two point charges \( 10^{-5} \mathrm{C} \) and \( -10^{-5} \mathrm{C} \) are released from large separation. Their masses are 100 gm and 200 gm. If velocity of approach (in \( \mathrm{m} / \mathrm{s} \) ) of them when they are separated by distance \( 3 m \) is \( \frac{x}{4} m / s . \) Then \( x \) is :
A . 12
B. 1
\( c \cdot 4 \)
D. 8


Q Type your question.
according to the balanced equation:
\( \boldsymbol{C}_{6} \boldsymbol{H}_{12} \boldsymbol{O}_{6}+\boldsymbol{6} \boldsymbol{O}_{2}+\boldsymbol{3} \boldsymbol{0} \boldsymbol{A} \boldsymbol{D} \boldsymbol{P}+\boldsymbol{3} \boldsymbol{0} \boldsymbol{P}_{i} \rightarrow \)
\( 6 H_{2} O+6 C O_{2}+30 A T P \)
ATP is then hydrolyzed by cells for a variety of biochemical processes. Changes in free energy between glucose oxidation and ATP hydrolysis were compared. The table below illustrates the data collected:
Reaction Change in Free Energy \( (\triangle G \)
Glucose \( \quad-686 \mathrm{kcal} / \mathrm{mol} \)
Oxidation
ATP Hydrolysis
-13 kcal/mol
Which statement best explains the
data?
A. Both glucose oxidation and ATP hydrolysis, are exergonic because they have negative \( \triangle G \) values
B. Both glucose oxidation and ATP hydrolysis, are exergonic because their products have more free energy than their reactants
c. Both glucose oxidation and ATP hydrolysis, are endergonic because they have negative \( \triangle G \) values
D. Both glucose oxidation and ATP hydrolysis, are endergonic because their products have less free energy than their reactants


In a transformer the transformation
ratio is \( 0.3 . \) If \( 220 \mathrm{V} \) ac is fed to the
primary, then the voltage across the secondary will be
A . \( 44 \mathrm{V} \)
B. 55
\( c \cdot 60 v \)
D. 66 V


Given two independent events \( A, B \)
such that \( \boldsymbol{P}(\boldsymbol{A})=\mathbf{0 . 3}, \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 6} \)
Determine
\( \boldsymbol{P}(\boldsymbol{A} \boldsymbol{a} \boldsymbol{n} \boldsymbol{d} \boldsymbol{B}) \)


Assertion
In comparison to ethyl chloride it is difficult to carry out nucleophilic substitution on vinyl chloride.
Reason

Vinyl group is electron donating.
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


Initially spring is relaxed. A person starts pulling the spring by applying a variable force \( F \). Where has the work
gone?
A. It is stored in the form of thermal energy in spring
B. It is stored in the form of potential energy in spring
C. It is stored in the form of kinetic energy in spring
D. Cannot be determined


Bells are made of metal and not of wood
because:
This question has multiple correct options
A. Metals are elastic than wood
B. The density of the metal is greater than that of wood
C. The sound is not conducted by metals but is radiated
D. Wood dampens vibrations faster


An ordered triplet corresponds to in three dimensional
space.
A. three points
B. a unique point
c. a point in each octant
D. infinite number of points


Oxidation states of the metal in the
minerals haematite and magnetite, respectively are:
A. II, Ill in haematite and III in magnetite
B. II, III in haematite and II in magnetite
c. Il in haematite and II, lII in magnetite
D. III in haematite and II, III in magnetite


Decreasing order of stability of \( \boldsymbol{O}_{2}, \boldsymbol{O}_{2}^{-} \)
\( O_{2}^{+}, \) and \( O_{2}^{2-} \) is:
A \( \cdot O_{2}>O_{2}^{+}>O_{2}^{2-}>O_{2}^{-} \)
B. \( O_{2}^{-}>O_{2}^{2-}>O_{2}^{+}>O_{2} \)
\( \mathrm{c} \cdot O_{2}^{+}>O_{2}>O_{2}^{-}>O_{2}^{2} \)
D. \( O_{2}^{2-}>O_{2}^{-}>O_{2}>O_{2}^{+} \)


Newton assumes that sound
propagation in gas takes under
A. isothermal condition
B. adiabatic condition
c. isobaric condition
D. isentropic condition


According to above histogram, Which group has the maximum number of
workers?
4.810
B. 820
\( c \cdot 830 \)
\( D \cdot 840 \)


The elements of the group 16 are also called:
A. helogens
B. noble gases
c. chalcogens
D. alkaline earth metals


Select the correct order of \( C-0 \) bond
order in mixed phosphine carbonyl
complex:
\( \mathbf{A} \cdot\left[\left(P h_{3} P\right)_{3} M o(C O)_{3}\right]>\left[\left(P h_{2} P C l\right)_{3} M o(C O)_{3}\right]> \)
\( \left(P h P C l_{2}\right)_{3} M o(C O)_{3} \)
\( \mathbf{B} \cdot\left[\left(P h_{3} P\right)_{3} M o(C O)_{3}\right]>\left[\left(P h_{2} P C l\right)_{3} M o(C O)_{3}\right]< \)
\( \left(P h P C l_{2}\right)_{3} M o(C O)_{3} \)
\( \mathbf{C} \cdot\left[\left(P h_{3} P\right)_{3} M o(C O)_{3}\right]=\left[\left(P h_{2} P C l\right)_{3} M o(C O)_{3}\right]> \)
\( \left(P h P C l_{2}\right)_{3} M o(C O)_{3} \)
\( \mathbf{D} \cdot\left[\left(P h_{3} P\right)_{3} M o(C O)_{3}\right]<\left[\left(P h_{2} P C l\right)_{3} M o(C O)_{3}\right]> \)
\( \left(P h P C l_{2}\right)_{3} M o(C O)_{3} \)


In fig. ABCD is a parallelogram. What
are the values of \( p \) and \( q ? \)
If \( \angle C B E=100^{\circ} \)
\( \mathbf{A} \cdot \angle p=100^{\circ}, \angle q=80^{\circ} \)
B . \( \angle p=80^{\circ}, \angle q=100^{\circ} \)
c. \( \angle p=\angle q \)
D. None


Three identical wires are bent into
semi-circular arcs each of radius \( \boldsymbol{R} \)
These arcs are connected with each
other to form a closed mesh such that
one of them lies in x-y plane, one in \( y-z \) plane and the other in z-x plane as
shown in figure. In the region of space, a uniform \( \vec{B}=B_{0}(\hat{i}+\hat{j}) \) exists, whose magnitude increases at a constant rate
\( \boldsymbol{d} \boldsymbol{B} / \boldsymbol{d} \boldsymbol{t}=\boldsymbol{\alpha} . \) Calculate the magnitude of
emf induced in the mesh and mark
direction of flow of induced current in
the mesh.


\( \sqrt{1-x^{2}}+\sqrt{1-y^{2}}=a(x-y) \)
Then prove that \( \frac{d y}{d x}=\frac{\sqrt{1-y^{2}}}{\sqrt{1-x^{2}}} \)


The area of the parallelogram ABCD is
\( 90 c m^{2}(\text { see Fig.9.13 ) EC }=F D . \) Find
\( \boldsymbol{A}(\boldsymbol{A} \boldsymbol{B} \boldsymbol{E} \boldsymbol{F}) \)
\( \mathbf{A} \cdot 45 c m^{2} \)
B. \( 60 \mathrm{cm}^{2} \)
\( \mathrm{c} \cdot 90 \mathrm{cm}^{2} \)
D. \( 180 \mathrm{cm}^{2} \)


The radius of a circle with centre 0 is 7
\( \mathrm{cm} . \) Two radii OA and \( \mathrm{OB} \) are drwan at right angles to each other. Find the areas of minor and major segments.


Pesticides \( \& \) insecticides are available
in the form of :
A. powders
B. sprays
c. emulsions
D. all of these


Botanical garden of the forest research
institute was established in
A. Darjeeling
B. Dehradun
c. Bangalore
D. Lucknow


What is maximum in a pond-
ecosystem?
A. Primary consumers
B. Secondary consumers
c. Producers
D. Decomposers


For the reaction \( N_{2}+3 X_{2} \rightarrow 2 N X_{3} \)
where \( \boldsymbol{X}=\boldsymbol{F}, \boldsymbol{C l} \) (the average bond
energies are \( \boldsymbol{F}-\boldsymbol{F}=\mathbf{1 5 5} \boldsymbol{k} \boldsymbol{J} \boldsymbol{m o l}^{-1} \)
\( N-F=272 k J m o l^{-1}, C l-C l= \)
\( 242 k J m o l^{-1}, N-C l= \)
\( 200 k J m o l^{-1} \) and \( N \equiv N= \)
\( 941 k J \) mol \( ^{-1} \) ). The heats of formation
of \( N F_{3} \) and \( N C l_{3} \) in \( k J m o l^{-1} \)
respectively, are closest to:
A. -226 and +467
B. +226 and -467
c. -151 and +311
D. +151 and -311


is an organic compound, was manufactured from ammonium
cyanate, which is an inorganic compound.


A chord is a
A. segment
B. sector
C . circle
D. arc


Consider the Earth to be a homogenous sphere. Scientist A goes deep down in a mine and scientist B goes high up in a balloon. The gravitation field measured by
A. A goes on decreasing and that by B goes on increasing
B. B goes a decreasing and that by A goes on increasing
c. each remains unchanged
D. each goes on decreasing


Negatively geotrophic roots are found in
A. Colocasia
B. Cycas
c. cactus
D. coleus


Which one of the following oxyacids of chlorine is the least oxidizing in nature?
A . HOCl
в. \( \mathrm{HClO}_{2} \)
c. \( \mathrm{HClO}_{4} \)
D. HClO


State whether the following statement is true or false.
Enter 1 for true and 0 for false
\( f(x) \) is differentiable at a point \( P, \) if
there exists a unique tangent at point \( \boldsymbol{P} \)


\( \boldsymbol{C H}_{4}+\boldsymbol{O}_{2} \rightarrow \boldsymbol{C O}_{2}+\boldsymbol{H}_{2} \boldsymbol{O} \) is:
A. combustion reaction
B. redox Reaction
c. both \( A \) and \( B \)
D. none of the above


The specific heat of water is \( 1 c a l^{-1} g^{-1} C^{-1} . \) Its value in S.I units is
approximately
A .
B. 4.2
c. 420
D. 4200


The correct name for the complex
\( \left[\boldsymbol{C r}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right]\left[\boldsymbol{C o}\left(\boldsymbol{C}_{2} \boldsymbol{O}_{4}\right)_{3}\right] \) is:
A. hexaaminechromium(III) trioxalatocobalt (III)
B. hexaamminechromate
(III) trioxalatocobalate (III)
c. hexaamminechromium
(III) trioxalatocobaltate (III)
D. hexaamminechromate
(III) trioxalatocobalt (III)


Find the principal value of:
\( \sin ^{-1}\left(\frac{\sqrt{\mathbf{3}}-1}{2 \sqrt{2}}\right) \)


Einstein was awarded the Nobel Prize
for his work on
A. Photoelectric effect
B. Special theory of relativity
c. Brownian motion
D. General theory of relativity
E. Quantum theory


In given figures sides \( A B \) and \( A C \) and
median \( A D \) of a triangle \( A B C \) are
respectively proportional to sides \( \boldsymbol{P Q} \)
and \( P R \) and median \( P M \) of another
triangle \( P Q R . \) Show that \( \triangle A B C \sim \)
\( \triangle \boldsymbol{P} \boldsymbol{Q} \boldsymbol{R} \)


There are 5 percent defective items in a large bulk of items. The probability that a sample of 10 items will include not more than one defective item is \( \left(\frac{19^{9} \times 29}{20^{x}}\right), \) then what is the value of
\( \boldsymbol{x} \)


The difference between I and II energy levels is
A \( \cdot 1.5 \times 10^{-18} \mathrm{J} \)
B \( .3 \times 10^{-18} J \)
c \( \cdot 6 \times 10^{-18} J \)
D. \( 12 \times 10^{-18} \mathrm{J} \)


Of the following groups, which secrete and deposit calcium carbonate and appear like corals?
A. Red algae
B. Brown algae
c. Blue green algae
D. All of the above
E. None of the above


Two balls of same mass are dropped from the same height \( h, \) on to the floor. the first ball bounces to a height h/4,
after the collection \( \& \) the second ball to
a height h/16. the impulse applied by
the first \( \& \) second ball on the floor are \( \boldsymbol{I}_{1} \)
and \( I_{2} \) respectively. then
A \( \cdot 5 I_{1}=6 I_{2} \)
B \( .6 I_{1}=5 I_{2} \)
\( \mathbf{c} \cdot 3 I_{1}=2 I_{2} \)
D. \( 2 I_{1}=I_{2} \)


The resistance can be increased by :
A. decreasing the area
B. decreasing the length
c. either (A) or (B)
D. none of these


Two concentric shells of radii \( d \) and \( 2 d \)
respectively are placed far away from a parallel plate capacitor. Each plate of the capacitor is a square of side \( d \) and
separation between the plates is \( d / 4 \pi \)
The charge on the plates are \( q \) and \( -q \)
Then the keys \( k_{1} \) and \( k_{2} \) are closed, find
the charges on the shells and electric
potential energy left in the parallel plate capacitor in equilibrium.


Which among the following is an example of a semiconductor?
A. cuprous oxide
B. iron
c. copper
D. aluminium


If the distance travelled by a freely falling body in the last second of its journey is equal to the distance travelled in the first 2 s, the time of descent of the body is
\( \mathbf{A} \cdot 5 s \)
в. \( 1.5 s \)
c. \( 2.5 s \)
D. \( 3 s \)


LPG has a lower energy density than either petrol or fuel-oil, so the equivalent \( _{\text {一一一一一一 }} \) is higher.
A. fuel-consumption
B. fuel-absorption
c. fuel density
D. fuel capacity


The following pair of compounds is best described as:
A . identical
B. diastereomers
c. enantiomers
D. none of the above


Find the circumference and area of a
circle of radius \( 8.4 \mathrm{cm} \)


Co-efficient of restitution is defined as
the ratio of
A. Velocity of separation and approach
B. Velocity of approach and separation
c. Ratio of velocity of objects
D. None


If the sum of the first p terms of an AP is
\( a p^{2}+b p, \) find its common difference.


Statement 1: Ethane is considered to be
a saturated hydrocarban. Statement 2: Ethene has a triple bond.
A. Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement 1
B. Both the Statement 1 and Statement 2 are correct and Statement 2 is not the correct explanation of Statement 1.
c. Statement 1 is correct but Statement 2 is not correct.
D. Statement 1 is not correct but Statement 2 is correct
E. Both the Statement 1 and Statement 2 are not correct


The converse of converse of the
statement \( \boldsymbol{p} \Longrightarrow \sim \boldsymbol{q} \) is
\( \mathbf{A} \cdot \sim q \Longrightarrow p \)
в. \( p \Longrightarrow q \)
\( \mathbf{c} \cdot p \Longrightarrow \sim q \)
D. \( q \Longrightarrow \sim p \)


Carbon hydrides of the type, \( C_{n} H_{2 n+2} \) do not act as Lewis acid or Lewis base.They behave as normal carbon hydrides because:
A. carbon hydrides are electron-rich hydrides
B. carbon hydrides are electron-deficient hydrides
c. carbon hydrides are electron-precise hydrides
D. carbon hydrides are non-stoichiometric hydrides


\( \ln \Delta L M N, \angle L=60^{\circ}, \angle M=50^{\circ} . \) If
\( \Delta L M N \sim \Delta P Q R, \) then the value of
\( \angle R \) is
A \( \cdot 40^{\circ} \)
B. 30
\( c \cdot 70 \)
D. \( 110^{\circ} \)


A negative point charge \( 2 q \) and \( a \)
positive charge \( q \) are fixed at a distance
\( l \) apart. Where should a positive test
charge \( Q \) be placed on the line connecting the charge for it to be in equilibrium? What is the nature of the equilibrium with respect to longitudinal
motions?


At high altitudes,
A. Blood pressure exceeds much more than atmospheric pressure
B. Blood pressure is less than atmospheric pressure
C. Blood pressure equals the atmospheric pressure
D. None


Find the area of a parallelogram, whose
one side is \( 6.8 \mathrm{cm} \) and the
perpendicular distance of their from the
opposite vertex is \( 7.5 \mathrm{cm} \)


Wet catalysis processes of sulphuric acid differ from other contact sulfuric
acid processes in that
the
A. feed gas contains excess moisture when it comes into contact with the catalyst
B. feed gas contains less moisture when it comes into contact with the catalyst
c. feed gas contains no moisture when it comes into contact with the catalyst
D. none of the above


A small source of sound moves on a
circle as shown in fig. and an observer is
sitting at \( O . \) Let at \( v_{1}, v_{2}, v_{3} \) be the
frequencies heard when the source is at \( A, B \) and \( C \) respectively.
A \( \cdot v_{1}>v_{2}>v_{3} \)
в. \( v_{1}=v_{2}>v_{3} \)
с. \( v_{2}>v_{3}>v_{1} \)
D. \( v_{1}>v_{3}>v_{2} \)


If in Bohr's atomic model, it is assumed that force between electron the proton
varies inversely as \( r^{4}, \) b energy of the system will be proportional to:
\( \mathbf{A} \cdot n^{2} \)
B . \( n^{4} \)
\( c \cdot n^{6} \)
D. \( n^{8} \)


The lower percolation rate refers that the soil
A. Can hold water for less time
B. Can hold water for more time
c. cannot hold water
D. None of the above


Which of the following statements are
correct?
This question has multiple correct options
\( \mathbf{A} \cdot \sin 1>\sin 1^{\circ} \)
B. \( \tan 2<0 \)
\( \mathbf{c} \cdot \tan 1>\tan 2 \)
D. \( \tan 2<\tan 1<0 \)


There are no forces of attraction
between the molecules of inert gases.
A. True
B. False


\( \frac{2 x+1}{(x-1)\left(x^{2}+1\right)}=\frac{A}{x-1}+ \)
\( \frac{B x+C}{x^{2}+1} \Rightarrow C= \)
A .
B. 1/2
\( c \cdot-1 / 2 \)
D. 5/2


\( \mathbf{f} \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{1}^{2} & \mathbf{2}^{\mathbf{2}} & \mathbf{3}^{2} \\ \mathbf{2}^{\mathbf{2}} & \mathbf{3}^{\mathbf{2}} & \mathbf{4}^{2} \\ \mathbf{3}^{\mathbf{2}} & \mathbf{4}^{\mathbf{2}} & \mathbf{5}^{\mathbf{2}}\end{array}\right] \) then \( |\boldsymbol{A} \boldsymbol{d} \boldsymbol{j} \boldsymbol{A}|= \)
\( A \)
B . 16
\( c \cdot 64 \)
D. 128


Shown in the figure are the position time graph for two children going home from the school. Which of the
following statements about the
relative motion is true after both of
them started moving? Considering 1
Dimensional motion, their
relative velocity
A. first increases and then decreases
B. first decreases and then increases
\( c . \) is zero
D. is non zero constant


If fourth therm of an \( A . P \) is thrice its
first term and seventh term
\( -2(\text {thirdterm})=1 \) then its common difference is ?
A . 1
B . 2
\( c .-2 \)
D.


A ball rises to the surface of a liquid with constant velocity. The density of the liquid is four time the density of the material of the ball. the frictional force
of the liquid on the rising ball is greater than the weight of the ball by a factor of
A .2
B. 3
\( c \cdot 4 \)
\( D \)


Find the value of \( x \) in the number line.
\[
\begin{array}{ccc}
1 & 1 & 1 & 1 \\
0 & \sqrt{x} & 6
\end{array}
\]


One litre of helium under a pressure of 2 atm and at \( 27^{\circ} \mathrm{cis} \) heated until its
pressure and volume are doubled. The
final temperature attained by the gas is
\( A \cdot 927 K \)
B . \( 927^{\circ} \mathrm{C} \)
\( c \cdot 1200^{0} c \)
D. None


Friction should always be avoided.
A. True
B. False


(a) Draw the structures of the following molecules:
(i) \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{2} \)
(ii) \( \boldsymbol{C l} \boldsymbol{F}_{3} \)
(b) Explain the following observations:
(i) Nitrogen is much less reactive than phosphorus.
(ii) Despite having greater polarity, hydrogen fluoride boils at a lower temperature than water
(iii) Sulphur has a greater tendency for catenation than oxygen in the same
group.


The suitable reagent(s) will be:
A \( \cdot C r O / H_{2} O / \) acetone
\( \mathbf{B} \cdot\left[A g\left(N H_{3}\right)_{2}\right)^{\oplus}(\text {aqueous}), H^{+} \)
c. \( C r O / H C l / \) pyridine
\( D \)
соома


The number of structural isomers for
\( \mathbf{C}_{6} \mathbf{H}_{14} \) is:
\( A \cdot 3 \)
B. 4
\( c \cdot 5 \)
D. 6


\( 63 \div \sqrt{0.0049} \) equals
A . 1.285
B. 900
\( c \cdot 90 \)
D. 12.85


If \( K_{1} \) and \( K_{2} \) are the respective
equilibrium constants for the two
reactions:
\( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{6}(\boldsymbol{g})+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \Leftrightarrow \boldsymbol{X} \boldsymbol{e} \boldsymbol{O} \boldsymbol{F}_{4}(\boldsymbol{g})+ \)
\( 2 H F(g) \)
\( \boldsymbol{X} \boldsymbol{e} \boldsymbol{O}_{4}(\boldsymbol{g})+\boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{6}(\boldsymbol{g}) \Leftrightarrow \boldsymbol{X} \boldsymbol{e} \boldsymbol{O} \boldsymbol{F}_{4}(\boldsymbol{g})+ \)
\( \boldsymbol{X} \boldsymbol{e} \boldsymbol{O}_{3} \boldsymbol{F}_{2}(\boldsymbol{g}) \)
The equilibrium constant of the reaction \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{O}_{4}(\boldsymbol{g})+\boldsymbol{2} \boldsymbol{H} \boldsymbol{F}(\boldsymbol{g}) \Leftrightarrow \)
\( X e O_{3} F_{2}(g)+H_{2} O(g) \) will be:
A \( . K_{1} \times K_{2} \)
в. \( \frac{K_{2}}{K_{1}} \)
c. \( \frac{K_{1}}{\left(K_{2}\right)^{2}} \)
D. \( \frac{K_{1}}{K_{2}} \)


NaH is an example of :
A. Electron-rich hydride
B. Molecular hydride
C . Saline hydride
D. Metallic hydride


What is the electronic configuration of phosphorus?
A .2,8,5
B. 2, 8,4
c. 2,8,6
D. 2, 8, 3


Water proofing agent changes the angle
of contact:
A. from an obtuse to acute value
B. from an acute to obtuse value
C - from obtuse to \( \frac{\pi}{2} \)
D. from acute to \( \frac{\pi}{2} \)


Find the equations of the lines for which \( \tan \theta=-1, \) where \( \theta \) is the angle of
inclination of the line and \( x- \) intercept
is 4


A \( 1.2 c m \) long pin is placed perpendicular to the principal axis of a
convex mirror of focal length \( 12 \mathrm{cm}, \) at a
distance of \( 8 \mathrm{cm} \) from it. Find the
location of the image. Find the height of the image.


In an election between two candidates,
one got \( 55 \% \) of the total valid votes,
\( 20 \% \) of the votes were invalid. If the total
number of votes was 7500 , the number of valid votes that the other candidate
got, was:
A . 3260
в. 2700
\( c .1290 \)
D. 1600


If the time period of a pendulum is \( 25 s \)
What is the frequency of the pendulum?
A \( \cdot 4 \times 10^{-2} \mathrm{Hz} \)
в. \( 4 \times 10^{-1} \mathrm{Hz} \)
c. \( 25 \times 10^{-2} \mathrm{Hz} \)
D. \( 2 \times 10^{-2} \mathrm{Hz} \)


The power in series \( R L C \) -circuit with
\( A C \) source is given by :
A. zero
B. \( V I \sin \phi \)
c. \( V I \)
D. \( V I \cos \phi \)


Find the area of a parallelogram with
base \( 32 \mathrm{cm} \) and height \( 16.5 \mathrm{cm} \)


Mosses and ferns are found in moist
and shady places because both
A. Depend for their nutrition on microorganisms which can survive only at low temperature
B. Do not need sunlight for photosynthesis
c. Require presence of water for fertilisation
D. Cannot compete with sun-loving plants


Evaluate the following integral:
\( \int \frac{x}{\sqrt{4-x^{4}}} d x \)


A straight segment \( O C \) (of length \( L \) ) of
a circuit carrying a current \( I \) is placed along the \( x \) -axis. Two infinitely long straight wires \( A \) and \( B \), each extending
from \( z=-\infty \) to \( +\infty, \) are fixed at \( y= \)
\( -a \) and \( y=+a \) respectively, as shown
in the figure. If the wires \( A \) and \( B \) each
carry a current \( I \) into the plane of the
paper, obtain the expression for the force acting ont he segment \( O C . \) What
will be the force on \( O C \) if the current in
the wire \( B \) is reversed?


A bullet of mass \( \mathrm{m} \) is fired from a gun of mass M. The recoiling gun compresses a spring of force constant k by a distance d. Then the velocity of the bullet is :
A. \( k d \sqrt{M / m} \)
в. \( \frac{d}{M} \sqrt{k m} \)
c. \( \frac{d}{m} \sqrt{k M} \)
D. \( \frac{k M}{m} \sqrt{d} \)


The criterion for a spontaneous process is :
A. \( \triangle G>0 \)
в. \( \triangle G<0 \)
c. \( \Delta G=0 \)
D. \( \triangle S_{f o t a l}<0 \)


A square of side L meters lies in the \( x-y \)
plane in a region where the magnetic field is given by \( \overline{\boldsymbol{B}}=\boldsymbol{B}_{0}(\mathbf{2} \hat{\boldsymbol{i}}+\boldsymbol{3} \hat{\boldsymbol{j}}+ \)
\( 4 \hat{k}) T \) Where \( B_{0} \) is constant. The
magnitude of flux passing through the
square is:
\( \mathbf{A} \cdot 2 B_{0} L^{2} \mathbf{W} \mathbf{b} \)
B. 3 \( B_{0} L^{2} \) wh
\( \mathbf{c} \cdot 4 B_{0} L^{2} \mathbf{w} \mathbf{b} \)
D. \( \sqrt{2} 9 B_{0} L^{2} \) wh


Two walls of thickness \( d_{1} \) and \( d_{2} \)
thermal conductivities \( K_{1} \) and \( K_{2} \) are
in contact. In the steady state if the temperatures at the outer surfaces are
\( T_{1} \) and \( T_{2}, \) the temperature at
the common wall will be
A. \( \frac{K_{1} T_{1}+K_{2} T_{2}}{d_{1}+d_{2}} \)
в. \( \frac{K_{1} T_{1} d_{2}+K_{2} T_{2} d_{1}}{K_{1} d_{2}+K_{2} d_{1}} \)
c. \( \frac{\left(K_{1} d_{1}+K_{d} d_{2}\right) T_{1} T_{2}}{T_{1}+T_{2}} \)
D. \( \frac{K_{1} d_{1} T_{1}+K_{2} d_{2} T_{2}}{K_{1} d_{1}+K_{2} d_{2}} \)


Which of the following element has metallic lustre?
A. \( F \)
в. \( C l \)
\( c \cdot B r \)
D. \( I \)


Forest floor is known as the floor for the
animal habitat. Which of the following animals are present on the forest floor?
A. Parrot
B. Snakes
c. Pigeon
D. None of the above


A man invests Rs. 5,600 at \( 14 \% \) per
annum compound interest for 2 years. Calculate the amount at the end of the
first year


Select the correct option given below:
When \( 1.5 k g \) of ice at \( 0^{\circ} C \) mixed with
\( 2 k g \) of water at \( 70^{\circ} C \) in a container, the
resulting temperature is \( 5^{\circ} \mathrm{C} \) the heat
of fusion of ice is \( \left(s_{w a t e r}=\right. \) \( \left.4186 J K g^{-1} K^{-1}\right) \)
A \( \cdot 1.42 \times 10^{5} \mathrm{J} \mathrm{kg}^{-1} \)
В. \( 2.42 \times 10^{5} \mathrm{J} \mathrm{kg}^{-1} \)
c. \( 3.42 \times 10^{5} \mathrm{J} \mathrm{kg}^{-1} \)
D. \( 4.42 \times 10^{5} \mathrm{J} \mathrm{kg}^{-1} \)


Sclerenchymatous cells in their cell walls have large percentage of
A. Cellulose
B. Pectin
c. Lignin
D. Silica


The number of significant figures in
0.0045 is:
A . two
B. three
c. four
D. five


The angular speed of rotation of earth about its axis at which the weight of man standing on the equator becomes half of its weight at the poles is given by:
A. 0.034 rads\( ^{-1} \)
B. \( 8.75 \times 10^{-4} \)rads\( ^{-1} \)
c. \( 1.23 \times 10^{-2} \mathrm{rads}^{-1} \)
D. \( 7.65 \times 10^{-7} \)rads\( ^{-1} \)


Assertion
The area bounded by the curve \( y= \) \( \sin ^{-1} x \& \) the line \( x=0 \&|y|=\frac{\pi}{2} \) is \( \sqrt{2} \)
square units.
Reason
The domain \& principal value branch of \( y=\sin ^{-1} x \operatorname{are}[-1,1] \&\left[\frac{-\pi}{2}, \frac{\pi}{2}\right] \)
respectively
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


Tasar silkworm feeds on leaves of
A. Mulberry
B. castor
\( c . \) Ber
D. Rubber


Hailstones falling from atmosphere relates to:
A. static friction
B. rolling friction
c. sliding friction
D. fluid friction


The \( L=12 \mathrm{cm}, b=10 \mathrm{cm}, h=8 \mathrm{cm} \)
of a room. Find the total area of 4 walls.


If the probabilities of the events \( \boldsymbol{A} \cap \)
\( B, A, B \) and \( A \cup B \) are in A.P.with
second term of A.P. is equal to common difference then \( A \) and \( B \) are
A. independent
B. equally likely
c. mutually exclusive
D. can't be determined


For a ideal gas.
This question has multiple correct options
A. The change in internal energy in a constant pressure process from temperature \( T_{1} \) to \( T_{2} \) is equal to \( N C_{V}\left(T_{2}-T_{1}\right), \) where \( C_{V} \) is the molar specific heat at
constant volume and \( n \) is the number of moles of the
gas
B. The change in internal energy of the gas and the work done by the gas are equal in magnitude in an adiabatic process
C. The internal energy does not change in an isothermal process
D. No heat is added or removed in an adiabatic process


The resistance of a bulb filament is 100
\( \Omega \) at a temperature of \( 100^{0} \mathrm{C} \). If its temperature coefficient of resistance be 0.005 per \( ^{0} \mathrm{C} \), its resistance will become \( 200 \Omega \) at a temperature of :
A \( \cdot 300^{0} \mathrm{C} \)
B. \( 400^{\circ} \mathrm{C} \)
\( c \cdot 500^{0} c \)
D. 200^


The positions of a particle moving along a straight line are \( x_{1}=50 \mathrm{m} \) at 10.30
a.m. and \( x_{2}=55 \mathrm{m} \) at 10.35 a.m.
respectively. What is the displacement of the particle between 10.30 a.m. and
10.35 a.m.?
\( A \cdot 2 m \)
B. \( 5 \mathrm{m} \)
\( c \cdot 7 m \)
D. \( 9 \mathrm{m} \)


Consider the following two statements A and B and identify the correct choice:
A) The rotational kinetic energy of a rolling body is always greater than its translational kinetic energy.
B) The maximum value of radius of
gyration of a rolling body cannot be greater than the radius of that body.
A. A is true but B is false
B. A is false but B is true
c. Both A and B are true
D. Both A and B are false


One micron is equal to
\( \mathbf{A} \cdot 10^{6} m \)
В \( \cdot 10^{3} m \)
\( \mathbf{c} \cdot 10^{-6} m \)
D. \( 10^{-3} m \)


The point(s) on the curve \( y^{3}+3 x^{2}= \)
\( 12 y \) where the tangent is vertical, is
\( (\operatorname{are}) \)
A \( \cdot\left(\pm \frac{4}{\sqrt{3}},-2\right) \)
B \( \cdot\left(\pm \frac{\sqrt{11}}{3}, 1\right) \)
\( \mathbf{c} \cdot(0,0) \)
D. \( \left(\pm \frac{4}{\sqrt{3}}, 2\right) \)


Find the square root of 256


When we can observe sparks on an
electric post?
A. When there is huge rain
B. When there is thunderstorm
C. When wind blows and shakes the wire
D. All of the above


Plaque is
A. Hard, protective covering on the tooth
B. Soft covering of the tooth which is present below the visible part
C. The cavity which contains nerves and blood vessels in a tooth
D. Sticky film of food, saliva and bacteria near the gums


\( \mathbf{f} \boldsymbol{I}=\int \cot ^{-1}\left(\frac{\boldsymbol{a}^{2}-\boldsymbol{a} \boldsymbol{x}+\boldsymbol{x}^{2}}{\boldsymbol{a}^{2}}\right) \boldsymbol{d} \boldsymbol{x}, \) then
equals
\( \mathbf{A} \cdot_{x \tan ^{-1}}\left(\frac{x}{a}\right)-(x-a) \tan ^{-1}\left(\frac{x-a}{a}\right)+C \)
B \( \cdot \frac{a}{2} \log \left(2 a^{2}-2 a x+x^{2}\right)-\frac{a}{2} \log \left(x^{2}+a^{2}\right)+C \)
C \( \cdot x \tan ^{-1}\left(\frac{x}{a}\right)+(x-a) \tan ^{-1}\left(\frac{x-a}{a}\right)+\frac{a}{2} \log \left(2 a^{2}-\right. \)
\( \left.2 a x+x^{2}\right)+C \)
D. none of these


What is the mechanical equivalent of spring constant \( \mathrm{k} \) in \( \mathrm{LC} \) oscillating circuit?
A \( \cdot \frac{1}{L} \)
в. \( \frac{1}{C} \)
c. \( \frac{L}{C} \)
D. \( \frac{1}{L C} \)


A rectangular water-tank measuring
\( 80 \mathrm{cm} \times 60 \mathrm{cm} \times 60 \mathrm{cm} \) is filled from a
pipe of cross-sectional area \( 1.5 \mathrm{cm}^{2}, \) the water emerging at \( 3.2 \mathrm{m} / \mathrm{s} \). How long does it take to fill the tank?
A. 10 minutes
B. 15 minutes
c. 13 minutes
D. 12 minutes


Find the coordinates of the foci, the
vertices the eccentricity and the length of the latus rectum of the hyperbola \( 5 y^{2}-9 x^{2}=36 \)


Which element has the highest first ionization potential?
A .
B. Ne
c. не
D.
E. \( L \)


\( \sqrt{x} e^{\sqrt{x}} d x \) is equal to:
A \( \cdot 2 \sqrt{x}-e^{\sqrt{x}}-4 \sqrt{x e^{\sqrt{x}}}+c \)
B \( \cdot(2 x-4 \sqrt{x}+4) e^{\sqrt{x}}+c \)
c. \( (2 x+4 \sqrt{x}+4) e^{\sqrt{x}}+c \)
D. \( (1-4 \sqrt{x}) e^{\sqrt{x}}+c \)


Identify the correct match(es) in the
following table:
\( \begin{array}{ll}\text { Element } & \text { Column A } \\ \text { Sodium } & \text { Non-metal } \\ \text { Sulphur } & \text { Lanthanide } \\ \text { Manganese } & \text { Metal } \\ \text { Cerium } & \text { Transition metal }\end{array} \)
A. Sodium- Metal
B. Sulphur- Non metal
c. Manganese- Transition metal
D. all of these


Referring to the \( v^{2} \) -s diagram of a
particle, find the displacement of the particle during the last two seconds.


A solution of acetone is ethanol:
A. shows a negative deviation from Raoult's law
B. shows a positive deviation from Raoult's law
C. behaves like a near ideal solution
D. obeys Raoult's law


Prove that
\( \sin ^{-1} \frac{3}{5}+\sin ^{-1} \frac{8}{17}=\cos ^{-1} \frac{36}{85} \)


A certain metal has high concentration in the Earth's crust and its oxides
cannot be reduced by carbon. Which is
the most suitable method for the
extraction of such a metal?
A. Alumino thermite process
B. Electrolysis process
c. van-Arkel's process
D. cupellation


Two blocks each of the mass \( m \) are
attached to the ends of massless rod
which pivots as shown in fig. Initially the rod is held in the horizontal position
and then released. Calculate the net
torque on this system above pivot.
\( \mathbf{A} \cdot\left(m l_{2} g-m l_{1} g\right) \hat{k} \)
B. \( \left(m l_{1} g+m l_{2} g\right) \hat{k} \)
\( \mathbf{c} \cdot\left(m l_{1} g-m l_{2} g\right) \hat{k} \)
D. \( -\left(m l 1 g+m l_{2} g\right) \hat{k} \)


Find the area of a quadrant of a circle
whose radius is \( 7 \mathrm{cm} \)


If in triangles \( \boldsymbol{X} \boldsymbol{Y} \boldsymbol{Z}, \boldsymbol{X} \boldsymbol{Y}=\boldsymbol{X} \boldsymbol{Z} \) and
\( M, N \) are the midpoints of \( X Y, Y Z \) and which one of the following is
correct?
\( \mathbf{A} \cdot M N=Y Z \)
в. \( N Y=N Z=M N \)
c. \( M X=M Y=N Y \)
D. \( M N=M X=M Y \)


The above mentioned formal formula is
that of
\[
\oplus \bigoplus_{(5)} \widehat{C_{(5)}} A_{5} G(2)
\]
A. Tobacco
B. Tulip
c. soybean
D. Sunhemp


\( f^{n} C_{3}=^{n} C_{2}, \) then \( n \) is equal to
\( A \cdot 2 \)
B. 3
\( c .5 \)
D. None of these


In aqueous solutions, amino acids mostly exist as:
A \( . N H_{2}-C H R-C O O H \)
в. \( N H_{2}-C H R-C O O^{-} \)
c. \( _{N H_{3} C H R C O O H}^{+} \).
D. \( H_{3} \stackrel{+}{N C H R C O O} \)


Two balls of equal masses are thrown upwards along the same vertical line at
an interval of 2 seconds with the same
initial velocity of \( 39.2 m s^{-1} . \) The total
time of flight of each ball, if they collide at a certain height, and the collision is perfectly inelastic, will be
A. \( 5 s \) and \( 3 s \)
B. \( 10 s \) and \( 6 s \)
c. \( 5 \sqrt{15 s} \) and \( 3 \sqrt{15 s} \)
D. \( (5+\sqrt{15}) s \) and \( (3+\sqrt{15}) s \)


The abbreviation PDI refers
to
A. name of the polymer
B. polydispersity index of the polymer
C . application of the polymer
D. polydiagonal index


Suppose you want to negotiate a curve
with a radius of 50 meters and a bank
angle of 15 degrees. If the coefficient of friction between your tires and the
pavement is \( 0.50, \) what is the
maximum speed that you can safely use?
A. \( 30 \mathrm{m} / \mathrm{s} \)
B. \( 5 \mathrm{m} / \mathrm{s} \)
c. \( 21 \mathrm{m} / \mathrm{s} \)
D. \( 10 \mathrm{m} / \mathrm{s} \)


Veins are strands on the
lamina.
A. conducting
B. Transpirational
c. Exceptional
D. Flattened


A ray of light incident on the interface of
the medium \( A \) and \( B \) and it passes
through medium \( B \) as shown in above
figure. Choose the correct option.
A. Medium 1 is more dense than medium 2
B. Medium 1 less dense than medium 2
C. The speed of the light in medium 1 is greater than the speed of the light in medium 2
D. The frequency of the light in medium 1 is greater than the frequency of the light in medium 2
E. The wavelength is the same in medium 1 and medium 2


Which of these terms is used in the
classification of species?
A. Division
B. Phylumm
c. class
D. All of the above


A metalo xide has the formula \( X_{2} O_{3} . \) It
can be reduced by hydrogen to give free metal and water.0.1596 g of metal oxide requires \( 6 \mathrm{mg} \) of hydrogen for complete reduction. Calculate the atomic weight of the metal(in amu).


In a cylinder, 2.0 moles of an ideal
monatomic gas initially at \( 1.0 \times \)
\( 10^{6} P a \) and \( 300 K \) expands until its
volume doubles. Compute the work done if the expansion is isothermal, adiabatic and isobaric.


The figure shows a mixture of blue,
green and red colour ray incident on the right angled prism. The critical angles
of the material of prism for red, green
and blue colours are \( 46^{\circ}, 44^{\circ} \) and \( 43^{\circ} \)
respectively. The arrangement will
separate:
A. red colour from green and blue
B. blue colour from green and red
c. green colour from red and blue
D. all the three colours


By using identity.
\( (\mathbf{7} 99)^{2}=? \)


For a mass on a spring, which is
maximized when the displacement of the mass from its equilibrium position is zero?
A. Frequency
B. Amplitude
c. Period
D. wavelength
E. Kinetic Energy


Which protein present in muscle is
insoluble in water?
A. Carotene
B. Insulin
c. Albumin
D. Myosin


How many moles of electrons are involved in the conversion of 1 mole
\( C r_{2} O_{7}^{2-} \) into \( C r^{3+} \) ion?


Given positive integers \( i>1, n>2 \) and that the coefficients of \( (3 r)^{t h} \) and \( (r+ \)
2) \( ^{t h} \) terms in the bionomial expansion
of \( (1+x)^{2 n} \) are equal, then
A \( . n=2 r \)
B. n=3r
c. \( n=2 r+1 \)
D. None of these.


its y-coordinate.


Which of the following is/are disproportionation reactions?
This question has multiple correct options
\( ^{\mathbf{A}} \cdot_{H_{2}} O_{2} \rightarrow H_{2} O+\frac{1}{2} O_{2} \)
B . \( H N O_{3}+H C l \rightarrow N O+C l_{2}+H_{2} O \)
c. \( 3 C l O^{-} \rightarrow C l O_{3}^{-}+2 C l^{-} \)
D. \( C l_{2}+H_{2} O \rightarrow H C l+H C l O \)


A test tube containing molasses solution and yeast is kept in a warm
place overnight. The gas collected from this mixture
A. Extinguishes the flame
B. Bursts into flame when ignited
c. Turns lime water milky
D. Both (a) and (c)


The length and breadth of a rectangle
are in the ratio \( 2: 1 . \) If the area of the
field is 72 sq.m, find the cost of fencing
the field with barbed wire at the ratio of
Rs 15 per metre.


Coloured attractive structures of flower
Bougainvillea are the
A. Calyx
B. Petaloid bracts
c. Foliage leaves
D. Epicalyx


A flash light cell reaction is :
\( \mathbf{2} M n O_{2}+Z n^{2+}+2 e^{-} \longrightarrow Z n+ \)
\( M n_{2} O_{4} . \) The current rating of the
flashlight is \( 4.6 \mathrm{mA} \). The time for which we can use this light, if we start
with 3.5 g of \( M n O_{2} \) is:
A \( .8 .44 \times 10^{5} s \)
B. \( 8.76 \times 10^{5} s \)
c. \( 8.96 \times 10^{5} s \)
D. None of these


Reflex action immediately involves
A. Spinal cord
B. Cerebellum
c. Medulla oblongata
D. optical lobe


IUPAC name of the compound is:
\( \boldsymbol{C H}_{3}-\underbrace{C}_{C H_{3}}^{C H_{3}}-B r \)


HCl gas occurs in free state in :
A. volcanic gases
B. gastric juices of mammals
c. both \( A \) and \( B \)
D. soil


A block \( A \), whose weight is \( 200 N \), is
pulled up a slope of length \( 5 m \) by
means of a constant force \( \boldsymbol{F}(=\mathbf{1 5 0} \boldsymbol{N}) \)
as illuminated in figure. By how much has the potential energy of the block \( \boldsymbol{A} \)
increased?
\( A \cdot 0 J \)
В. \( 750 J \)
\( c .600 J \)
D. \( 450 J \)


semıcırcle block trom alr is shown
below. Consider the given figure and select the correct option which correctly
identifies the true (T) and false (F)?
(i) There is no change in the direction of
ray at \( P \) because light ray incident on
semicircular block at \( 90^{\circ} \)
(ii) As light rays enters the semicircular block, its frequency remains the same.
(iii) Wavelength of light rays as it enters the block decreases.
(iv) Speed of light as it enters the block
increases.
A . T F FT
B. FTTF
c. न T T \( F \)
\( D \cdot F F F \)


As the temperature of a metallic
resistor is increased, the product of resistivity and conductivity:
A . increases
B. decreases
c. may increase or decrease
D. remains constant


Value based questions. When an animal is wounded, its overall blood pressure rises, but the area in
the vicinity of the wound swells as a result of local vasodilation. Why?


A point initially at rest moves along \( x- \) axis. Its acceleration varies with time
as \( a=(6 t+5) m / s^{2} . \) If it starts from
origin, the distance covered in \( 2 s \) is.
A. \( 20 m \)
в. 18 т
\( \mathrm{c} \cdot 16 \mathrm{m} \)
D. 25


Structural isomerism and
stereoisomerism should be considered
in answering this question. Compound is reacted with KOH dissolved in
ethanol. Three isomeric alkenes with
molecular formula \( C_{4} H_{8} \) are formed.
What is J?
\( \mathbf{A} \cdot C H_{3}-C H_{2}-C H_{2}-C H_{2}-B r \)
B. \( C H_{3}-_{I}^{C H}-C H_{2}-C H_{3} \)
\( \mathbf{c} . C H_{3}-C H-C H_{2}-B r \)
\( _{C H_{3}} \)
D. \( C H_{3} \)
\( C H_{3}-C-B r \)
\( _{C H_{3}} \)


The sum of the fractions \( \frac{1}{2}+\frac{1}{6}+\frac{1}{12}+ \) \( \frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}+ \)
\( \frac{1}{110}+\frac{1}{132} \) is
\( A \cdot \frac{7}{8} \)
в. \( \frac{11}{12} \)
\( c \cdot \frac{15}{16} \)
D. \( \frac{17}{18} \)


The number and type of bonds between two carbon atoms in \( C a C_{2} \) are:
A. one sigma ( \( \sigma \) ) and one pi ( \( \pi \) )-bond
B. one sigma ( \( \sigma \) ) and two pi ( \( \pi \) )-bonds
c. one sigma ( \( \sigma \) ) and one and a half pi ( \( \pi \) )-bonds
D. one sigma ( \( \sigma \) )-bond


\( \bar{a} \) and \( \bar{b} \) are non-zero vectors such that
\( \bar{a} \times \bar{b}=\bar{b} \times \bar{a} \) then \( \bar{b}, \bar{a} \) are
A. this result is always true
B. this result is impossible
c. parallel to each other
D. perpendicular to each other


The pressure of a monoatomic gas increases linearly from \( 4 \times \) \( 10^{5} N m^{-2} t o 8 \times 10^{-5} N m^{-2} \) when its
volume increases from \( 0.2 m^{3} \) to \( 0.5 m^{3} \)
calculate (a) work done by the gas, (b) increase in internal energy (c) mass of heat supplied and (d) molar heat
capacity of the gas.


Which among the following plots are liner (a-x) is the concentration of the
reactant remaining after time, t?
(1):- (a-x) vs t, for a first order reaction
(2)\( :-(a-x) \) vs \( t, \) for a zero order reaction
(3):- (a-x) vs t, for a second order
reaction
(4):-1/ (a-x) vs t, for a second order
reaction
A. 1 and 2
B. 1 and 3
\( c \cdot 2 \) and 3
D. 2 and 4


If numbers \( a, b \) and \( c \) are in \( A P, \) then
A. \( b-a=c-b \)
B. \( b+a=c+b \)
c. \( a-c=b-d \)
D. None of these


Divide: \( \left(-16 x^{6}-24 x^{4}\right) \) by \( \left(-8 x^{3}\right) \)
A \( \cdot 2 x^{3}+3 x \)
B \( .2 x^{2}+3 \)
c. \( -2 x^{3}-3 x \)
D. \( -2 x^{2}-3 \)


00
00
00
00
000


An election was contested by two
candidates \( A \) and \( B . \) In all, there were
25000 voters. \( 80 \% \) of the votes were
polled. If A got \( 60 \% \) of the total votes polled, how many votes did B get?


A body of mass 100 g is moving with a velocity of \( 15 \mathrm{m} / \mathrm{s} \). The momentum associated with the ball will be:
A. \( 0.5 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
B. \( 1.5 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
c. \( 2.5 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
D. 3.2 Ns


In which of the following pair of complexes, the experimental magnetic moment and the geometric shapes
same?
A \( \cdot K\left[M n O_{4}\right] \) and \( K_{2}\left[N i C l_{4}\right] \)
B. \( _{K_{2}\left[N i(C N)_{4}\right] \text { and } K_{4}\left[N i(C N)_{4}\right]} \)
c. \( _{K_{2}\left[N i(C N)_{4}\right] \text { and } K_{2}\left[N i\left(N H_{3}\right)_{2} C l_{2}\right]} \)
D. \( _{K_{3}\left[F e(C N)_{6}\right] \text { and } K_{4}\left[F e(C N)_{6}\right.} \)


For which of the following parameters
the structural isomers \( \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH} \) and
\( \mathbf{C H}_{3} \mathbf{O C H}_{3} \) would be expected to have
the same values?
A. Heat of vaporisation
B. Vapour pressure at the same temperature
c. Boiling points
D. Gaseous densities at the same temperature and pressure


Differentiate the following function with
respect to \( x \)
\( x^{2} e^{x} \) log \( x \)
A \( \cdot x e^{x}(x \log x+2 \log x) \)
B. \( x e^{x}(1+2 \log x) \)
C \( \cdot x e^{x}(1+x \log x) \)
D. \( x e^{x}(1+x \log x+2 \log x) \)


\( C H_{2}=C=C H_{2} \)
Which of the following structure is most appropriate for this molecules?
\( A \)
B.
\( c \)
\( D \)


10
80
8


Given above is the bar graph indicating
the marks obtained out of 50 in
mathematics paper by 100 students.
Read the bar and answer the following
questions:
What is the number of students getting
less than 20 marks?


When a body is in translatory
equilibrium
A. the body is definitely at rest
B. the body is definitely in the state of uniform motion
C. the body will be either at rest or in the state of uniform motion
D. none of these


A sample of ammonia has a mass of
51.1 \( g \). How many molecules are in this
sample?
A. \( 1.8 \times 10^{23} \) molecules
B. \( 3.6 \times 10^{23} \) molecules
c. \( 9.1 \times 10^{23} \) molecules
D. \( 1.8 \times 10^{24} \) molecules


Identify the incorrect statement.
A. \( M g \) burns in air releasing dazzling light rich in UV rays.
B. \( C a C l_{2} .6 H_{2} O \) when mixed with ice gives freeing
mixture.
C . \( M g \) cannot form complexes.
D. \( B e \) can form complexes due to its very small size.


Fill the blanks with the correct option:
position potential mechanical chemical light kinetic.
1.An electric fan converts electrical
energy into \( _{\text {一一一一一一一吃 }} \) ergy.
2.Coking gas converts_- - energy
into heat energy.
3.The energy possessed by a spring is \( _{\text {therg. }} \)
4.The energy possessed by a body due to its \( _{\text {the called potential energy }} \)
5.The energy possessed by a body due to its motion is called_- - - energy


Part of ozone is destroyed over poles during
A. Polar spring
B. Winter
c. Summer
D. Period of snow fall


To obtain an isotope of a given radioactive atom, the atom must emit
A. one alpha and one beta particle
B. one alpha and two beta particle
c. two alpha and two beta particle
D. three alpha and four beta particle


The sum of two rational numbers is \( \frac{-2}{3} \) If one of them is \( \frac{-8}{15}, \) find the other.


Which is largest endocrine gland?
A. Thyroid
B. Liver
c. Pituitary
D. Thymus


Assertion \( (\mathrm{A}): N O_{2} \) is paramagnetic
molecule, whereas \( N_{2} O_{4} \) is
diamagnetic Reason (R): Molecules with unpaired electrons are Diamagnetic.
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)
\( c \cdot(A) \) is true and
(R) is false
D. (A) is false but (R) is true


Find the square of the following
numbers using the identity \( (a+b)^{2}= \)
\( a^{2}+2 a b+b^{2}: \)
\( \mathbf{2 0 9} \)


Find the coordinates of the vertices of
an equilateral triangle of side 2 a as
shown in the figure.


In the given figure, what is the magnetic field induction at point 0
A \( \cdot \frac{\mu_{0} l}{4 \pi r} \)
в. \( \frac{\mu_{0} l}{4 r}+\frac{\mu_{0} l}{2 \pi r} \)
c. \( \frac{\mu_{o} l}{4 r}+\frac{\mu_{0} l}{4 \pi r} \)
D. \( \frac{\mu_{0} l}{4 r}-\frac{\mu_{0} l}{4 \pi r} \)


A brass tray in the shape of a parallelogram was polished at a total \( \operatorname{cost} \) of \( \operatorname{Rs} 2,250 \) at the rate of Rs 20 per
\( 10 \mathrm{cm}^{2} . \) If the altitude of the
parallelogram is \( 45 \mathrm{cm}, \) find the length of its base.


K shell of \( _{7}^{14} N \) has 2 electrons. How
many electrons are present in the
shell ?


Total vapour pressure of mixture of
mol of \( A\left(P_{A}^{0}=150 \text { tor } r\right) \) and 2 mol of \( B \)
\( \left(P_{B}^{0}=240 \text { tor } r\right) \) is 200 torr. In this case
A. there is positive deviation from Raoult's law
B. there is negative deviation from Raoult's law
c. there is no deviation from Raoult's law
D. molecular masses of A and B are also required for calculating the deviation


A keystone species is the one which has
A. A small proportion of total biomass but has a huge impact on the community's organisation and survival.
B. A plenty of biomass but low impact on community's organisation.
C. A rare species with little impact on biomass and other species in the community.
D. A dominant species which has a large proportion of biomass and which affects many other species.


The radius of a sphere of lead is \( 8 \mathrm{cm} \)
The number of spheres of radius \( 5 \mathrm{mm} \) made by melting it will be
A. 6000 approx
B. Greater than 4000 and less than 5000
c. Greater than 3000 and less than 4000
D. Less than 3000


\( \begin{array}{ll}\text { Indicator } & \text { pH range } \\ \text { Methyl violet } & 0.3-1.8 \\ \text { Methyl orange } & 2.8-3.8 \\ \text { Congo red } & 2.8-4.8 \\ \text { Methyl red } & 3.8-6.1 \\ \text { Bromothylmol blue } & 6.0-7.9 \\ \text { Phenol Red } & 6.8-8.6\end{array} \) The table above shows the pH ranges of some common indicators. Given that
\( K_{a} \) is \( 7.3 \times 10^{-10} \) for boric acid
\( \left(H_{3} B O_{3}\right), \) Choose an indicator that can
be used for the titration of
\( \mathbf{0 . 1 0} \boldsymbol{M} \boldsymbol{K} \boldsymbol{H}_{2} \boldsymbol{B} \boldsymbol{O}_{3} \) with \( \mathbf{0 . 1 0} \mathbf{M} \mathbf{~ H C l} \)
A. Methyl orange
B. Congo Red
C. Methyl Red
D. Phenol Red


The electric dipole is placed along the \( x \)
axis at the origin \( O . A \) point \( P \) is at a
distance of \( 20 \mathrm{cm} \) from this origin such
that \( O P \) makes an angle \( 60^{\circ} \) with the \( x \)
axis. If the electric field at \( P \) makes an
angle \( \theta \) with the \( x \) -axis, the value of \( \theta \)
would be
A \( \cdot \frac{\pi}{3} \)
B. \( \tan ^{-1} \frac{\sqrt{3}}{2} \)
c. \( \frac{2 \pi}{3} \)
D. \( \frac{\pi}{3}+\tan ^{-1} \frac{\sqrt{3}}{2} \)


What is correct IUPAC name of
compound?
A. 4-cyclopropyl-4-propyl-1-hexene
B. 4-ethyl-4-cycloproyl-1-heptene
C. 4 -cyclopropyl-4-ethyl-1-heptene
D. Both \( A \) and \( C \)


Given: \( \frac{20 !}{18 !}=380 \)
A. True
B. False
c. Either
D. Neither


s-t graph of a particle in motion in shown
in fig . calculate
A . I) Total distance covered
B. II) Displacement
C. III) Average speed
D. IV) Average velocity


\[
\begin{array}{c}
\boldsymbol{M} \boldsymbol{X}(\mathbf{s o l i d})+\boldsymbol{E}_{1} \rightarrow \boldsymbol{M}^{+}+\boldsymbol{X}^{-} ; \\
\boldsymbol{M}^{+}+\boldsymbol{n} \boldsymbol{H}_{2} \boldsymbol{O} \rightarrow\left[\boldsymbol{M}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{n}\right]^{+}+\boldsymbol{E}_{2} \\
\boldsymbol{X}^{-}+\boldsymbol{m} \boldsymbol{H}_{2} \boldsymbol{O} \rightarrow\left[\boldsymbol{X}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{m}\right]^{-}+\boldsymbol{E}_{3}
\end{array}
\]
\( E_{1}, E_{2} \) and \( E_{3} \) are energies, then correct
statement is :
A. Compound \( (M X) \) soluble in water if \( E_{3}-E_{2}>E_{1} \)
B. compound soluble in water \( E_{3}+E_{2}<E_{1} \)
C. compound soluble in water if \( E_{1}+E_{2}>E_{3} \)
D. compound soluble in water if \( E_{2}+E_{3}>E_{1} \)


The radius of a sphere is \( 9 \mathrm{cm} \) lt is melted and drawn into a wire of
diameter 2 mm Find the lenght of the
wire in meters
A . 972
B. 792
\( c \cdot 292 \)
D. 97.2


A vector \( \vec{A} \) when added to the vector \( \vec{B}=3 \hat{i}+4 \hat{j} \) yields a resultant vector that is in the positive y-direction and has a magnitude equal to that of \( \vec{B} \). Find the magnitude of \( \vec{A} \).
A. \( \sqrt{10} \)
B . 10
\( c .5 \)
D. \( \sqrt{15} \)


Evaluate the integral \( \int_{-2 \pi}^{2 \pi} \sin ^{5} x d x \)
A \( \cdot \frac{\pi^{2}}{2} \)
в. \( \frac{\pi}{15} \)
c. \( \frac{\pi}{17} \)
D. 0


Anthracene is
A. Aromatic
B. non aromatic
c. anti aromatic
D. Cannot be predicted


Write four solutions for the
following equation.
\( x=4 y \)
\( A \ldots(0,1),(4,1) ;(8,2) \) and (12,3)
\( B \ldots(0,0),(4,2) ;(8,2) \) and (12,3)
\( (-\infty, 0),(4,1) ;(8,3) \) and (12,3)
\( D \ldots(0,0),(4,1) ;(8,2) \) and (12,3)


The work function of a substance is
4.0eV. The longest wavelength of light that can cause photoelectron emission from this substance is approximately
A . \( 5400 A^{\circ} \)
в. \( 4000 A^{\circ} \)
c. \( 3100 A^{\circ} \)
D. 2200A \( ^{\text {0 }} \)


Figure shows the trajectory of a projections fired at an angle \( \theta \) with the horizontal. The elevation angle of the
highest point as seen from the point of
launching is \( \varphi . \) The relation between \( \varphi \)
\( \operatorname{ans} \theta \) is
A \( \cdot \tan \phi=\frac{1}{2} \tan \theta \)
B. \( \tan ^{2} \phi=\frac{1}{2} \tan ^{2} \)
\( \mathbf{c} \cdot \sin \phi=\frac{1}{2} \sin \theta \)
D. \( \cos ^{2} \phi=\frac{1}{2} \cos ^{2} \theta \)


Find the total number of distinct vehicle
numbers that can be formed using two letters followed by two numbers. Letters
need to be distinct.
A . 60000
B. 65000
c. 70000
D. 75000


Fossil fuels are:
This question has multiple correct options
A. Coal
B. Biogas
C. Natural gas
D. Petroleum


Assertion
Statement-1: The order of \( \pi \) bond
formation tendency is \( \boldsymbol{S} \boldsymbol{i}-\boldsymbol{O}<\boldsymbol{P}- \)
\( \boldsymbol{O}<\boldsymbol{S}-\boldsymbol{O}<\boldsymbol{C l}-\boldsymbol{O} \)
Reason
On moving from left to right along a period, the effective nuclear charge generally increases and consequently
the energy of the \( 3 d \) -orbital decreases from \( \boldsymbol{S} \boldsymbol{i}, \rightarrow \boldsymbol{P} \rightarrow \boldsymbol{S} \rightarrow \boldsymbol{C l} \)
A. Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-
B. Statement-1 is true, statement-2 is true and statement-2 is not the correct explanation for statement-1
c. statement- lis true, statement-2 is false
D. Statement-1 is false, statement-2 is true


In basidiocarp of Agaricus campestris,
each gill has
A. Two zones of monokaryotic hyphae
B. Three zones of monokaryotic and diploid hyphae
C. Three zones of dikaryotic hyphae
D. Two zones of dikaryotic and diploid huphae


The distance of a galaxy from the earth is of the order of \( 10^{25} \) m. The time taken
by light to reach the earth from the galaxy is
A. \( 3 \times 10^{14} \) s
B . \( 3 \times 10^{16} \) s
c. \( 3 \times 10^{18} \mathrm{s} \)
D. \( 3 \times 10^{20} \mathrm{s} \)


Convert into mixed fractions.
(a) \( \frac{3}{2} \)
\( (b) \frac{24}{5} \)


Which of the following bases are strong electrolytes?
\( \mathbf{A} \cdot K O H \)
в. \( N a O H \)
c. \( L i O H \)
D. All of the above


40
20
0.20
0.8


\( 20 \% \) of a radioactive element
disintegrates in 1 hr.The percentage of the radioactive element disintegrated
in \( 2 h r s \) will be
A . \( 36 \% \)
B. 64\%
c. \( 60 \% \)
D. 40\%


Which one is incorrect name?
A. Propyne
B. But-2-yne
c. Pent-3-yne
D. But-1 -yne


\( F_{2} C=C F_{2} \) is a monomer of:
A. Teflon
B. Glyptal
c. Buna-s
D. Nylon


If two straight lines intersect the measures of the vertically opposite angles are
A. equal
B. not equal
c. cannot be determined
D. none of these


Which of the following statement is/are
true?
A. Sudden action in response to something in the environment is called reflex action.
B. The path through which the signals are transmitted from a receptor to a muscle or a gland is called reflex
\( \operatorname{arc} \)
C. Motor neurons carry signals from receptors to spinal cord.
D. Both A and B.


Which of the following substance in the gaseous state will form purple vapour?
A. Oxygen
B. Sulphur dioxide
c. lodine
D. Ammonia


If point (3,0) lies on the graph of the
equation \( 2 x+b y=k, \) then the value of
\( \boldsymbol{k} \) is :
\( \mathbf{A} \cdot \mathbf{6} \)
B. 3
\( c \cdot 2 \)
D.


The first genes may have developed
when
A. Protobionts grew and divided
B. Short RNA strands self-replicated
c. DNA molecules produced RNA molecules
D. Polypeptides became catalyticc


In a reaction, \( \boldsymbol{A} \rightarrow \boldsymbol{B}+\boldsymbol{C}, \) the following
data were obtained:
t in seconds
\( \mathbf{0} \quad \mathbf{9 0 0} \)
Concentration of \( \boldsymbol{A} \quad \mathbf{5 0 . 8} \quad \mathbf{1 9 . 7} \quad \mathbf{7 . 6} \)
Prove that it is a first order reaction.


An inorganic salt is lemon yellow in colour. It becomes orange in colour like methyl orange when it is acidic and again becomes yellow when it is alkaline. The inorganic salt will be :
A. copper nitrate
B. ferric chloride
c. potassium chromate
D. potassium ferricyanide


Photochemical smog does not contain
A. PAN
B. Ozone
c. Nitrogen dioxide
D. \( S O_{2} \)


Two identical balls \( P \) and \( Q \) are
projected with same speeds in vertical
plane from same point \( \boldsymbol{O} \) with making
projection angles with horizontal \( 30^{\circ} \)
and \( 60^{\circ}, \) respectively and they fall
directly on plane \( A B \) at points \( P^{\prime} \) and
\( Q^{\prime} \) respectively. Which of the following
statement is true about distance as
given in options?
A \( \cdot A P^{\prime}>A Q^{\prime} \)
B. \( A P^{\prime}<A Q^{\prime} \)
c. \( A P^{\prime} \leq A Q^{\prime} \)
D. As there are complimentary projection angles


Which of the following is weakest lewis acid?
A \( \cdot B C l_{3} \)
в. \( A l C l_{3} \)
\( \mathbf{c} \cdot G a C l_{3} \)
D. \( \operatorname{InCl}_{3} \)


When the magnetic flux associated with a coil changes an emf is induced in the circuit. State Faraday's law of electromagnetic induction.


Which one of the following is correct
match?
A . A- Interfascicular cambium, B- Intrafasicular
cambium, C- Pericycle, D- Pith
B. A- - Intrafascicular cambium, B- -Interfascicular cambium, C- Pith, D- Pericycle
C. A- Pericycle, B- Interfascicular cambium, C- Pith, D Primary phloem
D. A- Pericycle, B- Pith, C- - Interfascicular cambium Dntrafascicular cambium


Simplify: \( \frac{\left(3^{3}\right)^{-2} \times\left(2^{2}\right)^{-3}}{\left(2^{4}\right)^{-2} \times 3^{-4} \times 4^{-2}} \)


For every,one \( ^{37} C l \) isotope there are three \( ^{35} C l \) isotopes, in a sample of
chlorine. What will be the average
atomic mass of chlorine?
A . 35
B. 37
c. 35.5
D. 35.6


\( \underbrace{\frac{\pi}{m}}_{n} \)


Secondary sewage treatment is mainly
\( \mathbf{a} \)
A. Biological process
B. Physical process
c. Mechanical process
D. Chemical process


16g of sulphur completely reacts with
38 g of \( F_{2} \) to form \( S F_{x} . \) The value of \( x \) is:
(Atomic mass of \( \boldsymbol{F}=\mathbf{1 9} \) )
A .
B. 2
\( c \cdot 4 \)
D. 6


A hole is made at the bottom of a tank
filled with water (density \( \left.=10^{3} k g / m^{3}\right) \)
If the total pressure at the bottom of the \( \operatorname{tank} \) is \( 3 \operatorname{atm}\left(1 a t m=10^{5} N / m^{2}\right) \)
then the velocity of efflux is
\( \mathbf{A} \cdot \sqrt{400} \mathrm{m} / \mathrm{s} \)
B. \( \sqrt{200} \mathrm{m} / \mathrm{s} \)
c. \( \sqrt{600} \mathrm{m} / \mathrm{s} \)
D. \( \sqrt{500} \mathrm{m} / \mathrm{s} \)


A charge 'q' moves in a region where electric field and magnetic field both exist, then force on it is : -
\( \mathbf{A} \cdot q(\vec{V} \times \vec{B}) \)
B \( \cdot q \vec{E}+q(\vec{V} \times \vec{B}) \)
\( \mathbf{c} \cdot q \vec{E}+q(\vec{B} \times \vec{V}) \)
\( \mathbf{D} \cdot q \vec{B}+q(\vec{E} \times \vec{V}) \)


List- -
List- II
A) \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \)
-3,+5 oxidation state
B) \( N H_{4} N O_{3} \)
\( \frac{-1}{3} \) oxidation state
C) \( N_{3} H \)
+5 oxidation state
D) \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3} \)
+3 oxidation state
5)
oxidation state
The correct match is :
A. A-3, B-1, C-2, D-4
B. A-5, B-2, C-3, D-4
c. A-1, B-2, C-3, D-4
D. A-4, B-3, C-2, D-5


Given that \( A B C D \) is a quadrilateral. Is \( \boldsymbol{A B}+\boldsymbol{B C}+\boldsymbol{C D}+\boldsymbol{D A}<\mathbf{2}(\boldsymbol{A C}+ \)
\( B D) ? \)


Read the assertion and reason carefully
to mark the correct option out of the
options given below:
Assertion: At height \( h \) from ground and
at depth \( h \) below ground, where \( h \)
is approximately equal to \( 0.62 R \)
the value of \( g \) acceleration due to
gravity is same.

Reason: Value of \( g \) decreases both
sides, in going up and down.
A. If both assertion and reason are true and the reason is the correct explanation of the assertion
B. If both assertion and reason are true but reason is not the correct explanation of the assertion
c. If assertion is true but reason is false
D. If assertion is false but reason is true


AB ia a potentiate wire of length \( 100 \mathrm{cm} \)
and is resistance is \( 10 \Omega \). It is connected
in series with a resistance \( \boldsymbol{R}=\mathbf{4 0 \Omega} \)
and a battery of emf \( 2 \mathrm{V} \) and negligible
internal resistance. If a source of
unknown potentiate wire, the value of \( \mathrm{E} \)
is:
\( A \cdot 0.8 V \)
B. \( 1.6 v \)
c. \( 0.06 \mathrm{v} \)
D. \( 0.16 \mathrm{v} \)


If \( _{-}- \) sides of a triangle are respectively equal to the sides of
the other triangle, then the triangles are congruent.
A. Three
B. Two
c. one
D. None


Pteridophyta do not have
A. Roots
B. Stem
c. Flowers
D. Leaves


What are normal elements?


Which of the following reactions will not
produce any hydrogen gas?
A. Reaction between \( F e \) and dil. \( H C l \)
B. Reaction between \( Z n \) and conc. \( H_{2} S O_{4} \)
C. Reaction between \( Z n \) and \( N a O H \)
D. Electrolysis of \( N a C l \) in Nelson's cell.


\( R \) is a relation on set \( A \) then \( \left[\left(R^{-1}\right)^{-1}\right]^{-1} \)
is
\( A \cdot R \)
B . \( R^{-1} \)
c. \( A \times A \)
D. None of these


The function \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) defined by
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{4}^{\boldsymbol{x}}+\boldsymbol{4}^{|\boldsymbol{x}|} \) is
A. One-one and into
B. Many-one and into
c. one-one and onto
D. Many-one and onto


All are examples of cranial reflexes but
not
A. Salivation
B. Scratching
c. Blushing
D. Sneezing


\( \boldsymbol{B} \stackrel{\text {Liadlar}}{\longleftrightarrow} \boldsymbol{R}-\boldsymbol{C} \equiv \boldsymbol{C}-\boldsymbol{R} \stackrel{N a / N \boldsymbol{H}_{3}}{\longrightarrow} \boldsymbol{A} \)
What is \( A \) and \( B \) in the given raction repectivley?


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


How much energy is required to change
\( 2 K g \) of ice at \( 0^{0} C \) into water at \( 20^{0} C ? \)
(specific latent of heat of fusion of
water \( =3,34,000 J / K g, \) specific heat capacity of water \( =4200 J K g^{-1} K^{-1} \) ).


The spaces between molecules is least
in :
A. Solid
B. Liquid
c. Gases
D. Vapour


Which of the following alkyl halides
undergoes \( S_{N} 1 \) reaction the fastest?
A. methyl chloride
B. ethyl chloride
c. isobutyl chloride
D. tert-butyl chloride


The fifth and fifteenth term of an \( A . P . \)
are 13 and \( -17 . \) find sum of first 21
terms of an \( \boldsymbol{A} \boldsymbol{. P .} \)


Gibberellins cause
or
Gibberellins stimulate
A. Elongation of internodes
B. Curvature of coleoptile
c. cell division
D. Initiation of lateral roots


A uniform wire of Youngs modulus Y is stretched by a force within the elastic limit. If \( S \) is the stress produced in the
wire and \( \varepsilon \) is the strain in it, the
potential energy stored per unit volume is given by
This question has multiple correct options
A \( \cdot \frac{1}{2} \varepsilon S \)
в. \( \frac{1}{2} Y \varepsilon^{2} \)
c. \( \frac{s^{2}}{2 Y} \)
D. \( \frac{1}{2} Y \varepsilon S \)


In Riccia, apical growth occurs by
A. One apical cell
B. single pyramid like cells
C. A row of 3-5 apical cells
D. A row of 10 apical cells


State true or false.
In the figure, \( l \| \boldsymbol{m} \) and \( \mathrm{M} \) is the midpoint
of line segment \( A B . \) Then \( M \) is also the
midpoint of any line segment having its
endpoints \( C \) and \( D \) on \( l \) and \( m \)
respectively.
A. True
B. False


Solve \( \lim _{x \rightarrow 0} \frac{\sqrt{2+x}-\sqrt{2}}{x} \)


A body of mass m moves in a circular
path with uniform angular velocity. The motion of the body has constant
A. Acceleration
B. Velocity
c. Momentum
D. Kinetic energy


Which pair of numbers are rationalising
factors to one another
This question has multiple correct options
\( A \cdot 2 \sqrt{3} \) and \( \sqrt{3} \)
B \( \cdot 3^{1 / 3}-3^{-1 / 3} \) and \( 3^{2 / 3}+1+3^{-2 / 3} \)
\( x^{1 / x}-x^{-1 / n} \) and \( \left(\frac{n-1}{n}-x \frac{n-2}{n}+\ldots \ldots . . x^{-}\left(\frac{n-1}{n}\right)\right) \)
\( \sqrt[3]{5}+\frac{1}{\sqrt[3]{5}} \) and \( \sqrt[3]{5^{2}}+1-\frac{1}{\sqrt[3]{5^{2}}} \)


The most important method of making steel is:
A. BOP process
B. BOD process
c. Pudding process
D. Smelting


Figure shows a rectangular conductor PQRS in which the Conductor PQ is free
to move in a uniform magnetic field
perpendicular to the plane of the paper. The filed extends from \( x=0 \) to \( x=b \) and is
zero for \( x>b \). Assume that only the arm
PQ possesses resistance r. when the
\( \operatorname{arm} \) PQ is pulled outward from \( x=0 \) to
\( x=2 b \) and is then moved back to \( x=0 \)
with constant speed \( v, \) Determine the expression for the flux and induced emf
Sketch the variations of these
quantities with distance \( 0 \leq x \leq 2 b \)


\( \boldsymbol{S}_{1} \rightarrow \) Conductivity increases on decreasing concentration of electroyte
\( \boldsymbol{S}_{1} \rightarrow \) Molar Conductivity increases on
decreasing concentration of electroyte
\( A \cdot S_{1} \) is true, \( S_{2} \) is False
B. Both \( S_{1} \& S_{2} \) are true
c. Both \( S_{1} \& S_{2} \) are false
D. \( S_{1} \) is false, \( S_{2} \) is true


Distinguish between Mitosis \& Meiosis


\( H C l O_{4}, H N O_{3} \) and \( H C l \) are all very
strong acids in aqueous solutions. In glacial acetic acid medium, their acid strength is such that:
A \( \cdot H C l O_{4}>H N O_{3}>H C l \)
в. \( H N O_{3}>H C l O_{4}>H C l \)
c. \( H C l>H C l O_{4}>H N O_{3} \)
D. \( H C l>H C l O_{4} \sim H N O_{3} \)


Convert \( 2 \mathrm{m} \) into nanometer:


2.82 \( \mathrm{g} \) of glucose is dissolved in 30 g of water. The mole fraction of glucose in the solution is:
A . 0.01
B. 0.99
c. 0.52
D. 1.66


Find the potential gradient along AB
A \( \cdot 0.1 \mathrm{Vcm}^{-1} \)
B. \( 0.03 \mathrm{Vcm}^{-1} \)
c. \( 0.04 \mathrm{Vcm}^{-1} \)
D. \( 0.02 \mathrm{vcm}^{-1} \)


Is \( \frac{\mathbf{6 3}}{\mathbf{9 0}} \) a terminating rational number?
Justify.


Q Type your question
brand \( Q \).The amounts (in \( \mathrm{kg} \) ) of nitrogen, phosphoric acid, potash, and
chlorine in a bag of each brand are
given in the table. Tests indicate that
the garden needs at least \( 240 k g \) of
phosphoric acid, at least 270 kg of
potash and at most \( 310 k g \) of chlorine.
If the grower wants to minimise the amount of nitrogen added to the garden, how many bags of each brand should be used? What is the minimum
amount of nitrogen added in the
garden?
\( \begin{array}{llll}\text { Kg per bag } & & & \\ & & \text { Brand } P & \text { Brand } Q \\ & & & \\ \text { Nitrogen } & 3 & 3.5 & \\ \text { Phosphoric acid } & 1 & 2 & \\ \text { Potash } & 3 & 1.5 & \\ \text { Chlorine } & 1.5 & 2 & \end{array} \)


A body is fired vertically upward. At half the maximum height, the velocity of the body is \( 10 \mathrm{m} / \mathrm{s} \). The maximum height raised by the body is
\( \mathbf{A} \cdot 0 m \)
в. 10 т
\( \mathrm{c} .15 \mathrm{m} \)
D. 20 \( m \)


Solve the following system of equations by the method of substitution:
\( \mathbf{3} \boldsymbol{x}-\mathbf{4} \boldsymbol{y}=\mathbf{1 0}, \mathbf{4} \boldsymbol{x}+\mathbf{3} \boldsymbol{y}=\mathbf{5} \)


\( \boldsymbol{C H}_{3} \boldsymbol{C O O H} \) is a:
A. reducing agent
B. dehydrating agent
c. drying agent
D. pickling agent


\( \sum_{k=1}^{10} k . k != \)
A . 10
B. 111
\( c \cdot 10 !+1 \)
D. 11!-1


The production of offsprings by sexual or asexual process is called as
A. Division
B. Growth
c. Reproduction
D. All of the above


Identify the favourable conditions for the formation of ionic bond.
A. Low IP value of metal, low EA value of non-metal.
B. High IP value of metal, high EA value of non-metal.
c. Low IP value of metal, high EA value of non-metal
D. HighIP value of metal, low IP value of non-metal.


An electron having a charge e moves with a velocity v in X-direction. A magnetic field acts on it in Y-direction. The force on the electron acts in
A. positive direction of Y-axis
B. negative direction of Y-axis
c. positive direction of Z-axis
D. negative direction of Z-axis


The probability that at least one of the events \( A \) and \( B \) occurs is \( \frac{3}{5} . \) If \( A \) and \( B \) occur simultaneously with probability \( \frac{1}{5} \operatorname{then} P\left(A^{\prime}\right)+P\left(B^{\prime}\right) \) is
A \( \cdot \frac{2}{5} \)
B. \( \frac{4}{5} \)
\( c \cdot \frac{6}{5} \)
D.


Select the one which describe the best
among all the given options. To determine whether a water solution of
\( N a_{2} S_{2} O_{3} \) at room temperature is
supersaturated, one can:
A. heat the solution to its boiling point
B. add water to the solution
c. add a crystal of \( N a_{2} S_{2} O_{3} \) to the solution
D. acidify the solution
E. cool the solution to its freezing point


The figure shows a planet in elliptical orbit around the sun S. The kinetic
energy of the planet will be maximum
when the planet is at:
\( A \cdot P_{1} \)
в. \( P_{2} \)
\( c \cdot P_{3} \)
\( \mathbf{D} \cdot P_{4} \)


What is/are the advantage of MCB over
fuses?
This question has multiple correct options
A. Its wire melts unlike fuses wire
B. It automatically turn off to save from excess electricity
c. It takes less time to break the circuit as compare to fuse while overloading
D. None of these


Which statements is/are correct?
This question has multiple correct options
A. Physical adsorption is multi-layer, non-directional and non-specific.
B. Chemical adsorption attains equilibrium some late.
C . Physical adsorption is due to valence of atoms.
D. Chemical adsorption is more stronger than physical adsorption.


\( C a^{2+} \) and \( M g^{2+} \) ions
A. Reduce excitability of nerves and muscles.
B. Increase excitability of nerves and muscles.
C. Conduct nerve impulses.
D. Both B and C.


During inhalation and exhalation which
of the following is seen
This question has multiple correct options
A. Ribs move up and outward, diaphragm moves down
B. Ribs move down and inwards, diaphragm moves up
C. Ribs move down and outwards, diaphragm moves down
D. Ribs move up and inwards, diaphragm moves down


Choose the correct options regarding
the nature of oxides formed by \( L i \) and
\( \boldsymbol{B e}: \)
This question has multiple correct options
A \( \cdot L i_{2} O \) is acidic while \( B e O \) is basic
B. \( B e O \) is amphoteric.
\( \mathrm{c} \cdot \mathrm{Li}_{2} \mathrm{O} \) is basic
D. \( L i_{2} O \) and \( B e O \) both are amphoteric


Select the correct statement(s) about
the given polymer:
(i) Monomer is \( \boldsymbol{C H}_{2}=\boldsymbol{C H}-\boldsymbol{C H}= \)
\( \boldsymbol{C H}_{2} \) and \( \boldsymbol{C H}_{2}=\boldsymbol{C H}-\boldsymbol{C N} \)
(ii) It is a copolymer.
(iii) It is an addition polymer.
\[
\left[\begin{array}{cc}
\mathrm{CH}_{2}-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\mathrm{CH} \\
& \mid \\
& \mathrm{CN}
\end{array}\right]_{\mathrm{n}}
\]
\( A \cdot(i) \) and (ii) only
B. (iii) only
c. (ii) only
D. (i), (ii) and (iii)


The maximum oxidation state shown by
\( M n \) in its compound is :
\( A \cdot+4 \)
B. +5
\( c \cdot+6 \)
D. +7


Eutrophication refers to
A. High production in an aquatic ecosystem
B. Low production in an aquatic ecosystem
C. Low production in a terrestrial ecosystem
D. Stable production in a terrestrial ecosystem


The equilibrium constants of a reaction is \( 73 . \) Calculate standard free energy
change.
В. 0.632 k \( J \) mol \( ^{-1} \)
c. 60.32 kJ \( m o l^{-1} \)
D. \( -10.632 k J \) mol\( ^{-1} \)


The number of \( A \) in \( T_{p} \) such that \( \operatorname{det}(A) \) is not divisible by p is?
\( A \cdot 2 p^{2} \)
B . \( p^{3}-5 p \)
c. \( p^{3}-3 p \)
D. \( p^{3}-p^{2} \)


A body is executing simple harmonic motion. At a displacement \( x \), its
potential energy is \( E_{1} \) and at
displacement \( y, \) its potential energy is
\( \boldsymbol{E}_{2} \) The potential energy \( \mathrm{E} \) at a displacement \( (x+y) \) is
A \( \cdot E_{1}+E_{2} \)
B. \( \sqrt{E_{1}^{2}+E_{2}^{2}} \)
c. \( E_{1}+E_{2}+2 \sqrt{E_{1} E_{2}} \)
D. \( \sqrt{E_{1} E_{2}} \)


The temperature co-efficient of
resistance of a wire is \( 0.0012 /^{\circ} \mathrm{C} \). Its
resistance is \( 1 \Omega \) at \( 300 K . \) At what
temperature, its resistance will be \( 2 \Omega ? \)
A . \( 1133 K \)
B. \( 854 K \)
c. \( 1217 K \)
D. \( 1154 K \)


What type of reaction occurs between ethene and hydrogen?
A. Addition
B. Dehydration
c. substitution
D. Oxidation


f \( x+y+z=0 \) then what is the value
of
\( \frac{1}{x^{2}+y^{2}-z^{2}}+\frac{1}{y^{2}+z^{2}-x^{2}}+ \)
\( \frac{1}{z^{2}+x^{2}-y^{2}} \)
A \( \cdot \frac{1}{x^{2}+y^{2}+z^{2}} \)
в.
c. -1
D.


Which of the following is not true for atomic number?
A. It indicates the number of protons in the nucleus
B. It is represented usually by z
c. It is identical with the mass number
D. It is constant for a given element


Arrange the following in correct order based on increasing toxicity.
(a) Urea
(b) Uric acid
(c) Ammonia
A. a-b-c
B. b-a-c
c. \( c-a-b \)
D. c-b-a


If \( e^{x}=y+\sqrt{1+y^{2}}, \) then the value of \( y \)
is
A \( \cdot \frac{1}{2}\left(e^{x}+e^{-x}\right) \)
в. \( \frac{1}{2}\left(e^{x}-e^{-x}\right) \)
c. \( \quad \frac{-x}{2} \)
D. \( _{e^{x}}+e^{\frac{-x}{2}} \)


A nuclear transformation is denoted by
\( X(n, \alpha)_{3}^{7} L i . \) Which of the following is
the nucleus of element \( X ? \)
\( \mathbf{A} \cdot \frac{12}{6} C \)
B . \( \frac{10}{5} B \)
\( c \cdot_{5}^{9} B \)
\( \mathrm{D} \cdot_{4}^{11} \mathrm{Be} \)


How will you prepare iodoform in the laboratory with the help of ethyl alcohol?


Find the interest for the principal Rs. 4110 at the rate of \( 3 \% \) for 4 years.
A . 343.50
B. 493.20
c. 460.19
D. 531.12


If the radian measures of two angles of a triangle are as given below. Find the radian measure and the degree measure of the third angle.
(i) \( \frac{5 \pi}{9}, \frac{5 \pi}{18} \)
(ii) \( \frac{3 \pi}{5}, \frac{4 \pi}{15} \)


Earth is a planet. Choose the option that is a negation of this statement.
A. Earth is round
B. Earth is not round
c. Earth revolves round the sun
D. Earth is not a planet


solve :
\( \frac{p}{3}+\frac{p}{4}=55-\frac{p+40}{5} \)


The negative of the statement "If a
number is divisible by 15 then it is
divisible by 5 or \( 3^{\prime \prime} \)
A. If a number is not divisible by \( 15, \) then it is not divisible by 5 and 3
B. A number is divisible by 15 and it is not divisible by 5 or 3
C. A number is not divisible by 15 or it is not divisible by 5 and 3
D. A number is divisible by 15 and it is not divisible by 5 and 3


Complete the following reaction Propene \( \frac{\boldsymbol{H}_{2} \boldsymbol{S O}_{4}}{\boldsymbol{H}_{2} \boldsymbol{O}, \boldsymbol{\Delta}} \boldsymbol{A} \)


Acceleration-displacement graph of a
particle executing SHM is as shown in
the figure. The time period of oscillation is (in sec)
A \( \cdot \frac{\pi}{2} \)
B. \( 2 \pi \)
\( c \)
D. \( \frac{\pi}{4} \)


In a medium in which, a transverse
progressive wave travelling, the phase difference between the points with a separation of \( 1.25 \mathrm{cm} \) is \( \pi / 4 . \) If the frequency of wave \( 1000 H z \), the velocity
in the medium is :
A \( \cdot 10^{4} m s^{-1} \)
В. \( 125 \mathrm{ms}^{-1} \)
c. \( 100 m s^{-1} \)
D. \( 10 \mathrm{ms}^{-1} \)


The work done in increasing the size of
a soap film from \( 10 \mathrm{cm} \times 6 \mathrm{m} \) to
\( 10 c m \times 11 c m \) is \( 3 \times 10^{-4} J . \) The
surface tension of the film is:
A \( \cdot 1.0 \times 10^{-2} N / m \)
B . \( 6.0 \times 10^{-2} \mathrm{N} / \mathrm{m} \)
c. \( 3.0 \times 10^{-2} N / m \)
D. \( 1.5 \times 10^{-2} N / m \)


Parabolas \( \boldsymbol{y}^{2}=\mathbf{4} \boldsymbol{a}\left(\boldsymbol{x}-\boldsymbol{c}_{1}\right) \) and \( \boldsymbol{x}^{2}= \)
\( 4 a\left(y-c_{2}\right), \) where \( c_{1} \) and \( c_{2} \) are variable
are such that they touch each other. Locus of their point of contact is
A \( . x y=2 a^{2} \)
В . \( x y=4 a^{2} \)
c. \( x y=a^{2} \)
D. none of these


Choose the correct statement among
the following.
This question has multiple correct options
A. Radial distribution function
\( \mathbf{B} \cdot\left(\Psi^{24 \pi^{2}} d r\right) \)
C \( . \Psi(r) \Psi(\theta) \Psi(\Phi))=\Psi(x / y / z) \) is independent of \( \theta \) and \( \phi \)
D. '2p'orbital with quantum numbers.n=2,|=1,m=0,also shows angular dependence


The magnetic field at center \( O \) of the
\( \operatorname{arcin} \) figure is
A \( \cdot \frac{\mu_{0} I}{4 \pi \times r}[\sqrt{2}+\pi] \)
\( ^{\mathbf{B}} \cdot \frac{\mu I}{2 \pi r}\left[\frac{\pi}{4}+(\sqrt{2}-1)\right] \)
C \( \frac{\mu_{0}}{4 \pi} \times \frac{I}{r}[(\sqrt{2}-\pi)] \)
\( ^{\mathrm{D}} \cdot \frac{\mu_{0}}{4 \pi} \times \frac{I}{r}\left[\left(\sqrt{2}+\frac{\pi}{4}\right)\right] \)


The function \( \boldsymbol{f}(\boldsymbol{x})=\frac{\boldsymbol{x}}{1+\boldsymbol{x} \tan \boldsymbol{x}} \) has
A. one point of minimum in the interval \( (0, \pi / 2) \)
B. one point of maximum in the interval \( (0, \pi / 2) \)
C. no point of maximum,no point of minumum in the interval \( (0, \pi / 2) \)
D. two points of maximum in the interval \( (0, \pi / 2) \)


On long standing, bleaching powder undergoes auto oxidation.
A. True
B. False


Which one of the four trapezoids is not
similar to the other three?
\( A \cdot A \)
B. B
\( c \cdot c \)
\( D \)


An artificial satellite moving in a circular orbit around the earth has a
total energy \( \boldsymbol{E}_{0} . \) Its potential energy is
A. \( -E_{0} \)
в. \( E_{0} \)
c. \( 2 E_{0} \)
D. \( -2 E_{0} \)


If \( \boldsymbol{y}=\sqrt{(\boldsymbol{a}-\boldsymbol{x})(\boldsymbol{x}-\boldsymbol{b})}-(\boldsymbol{a}- \)
\( b) \tan ^{-1} \sqrt{\frac{a-x}{x-b}}(a>b) \) then \( \frac{d y}{d x}= \)
A. \( \sqrt{\frac{a-x}{x-b}} \)
B . \( \sqrt{(a-x)(x-b)} \)
c. 0
D.


Name the functional group present in HCOOH.


IUDs are ideal contraceptives for
females who want to delay pregnancy and/or space children. Explain?


Assertion
Gauss's law show diversion when
inverse square law is not obeyed.
Reason

Gauss's law is a consequence of
conservation of charges.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
C. Assertion is correct but Reason is incorrect.
D. Both Assertion and Reason are incorrect.


Which disaccharide is present in milk?
A. Maltose
B. Galactose
c. sucrose
D. Lactose


Which of the following compounds of elements in group IV is expected to be most ionic?
A. \( P b C l_{2} \)
в. \( P b C l_{4} \)
c. \( C C l_{4} \)
D. \( \operatorname{sicl}_{4} \)


What fraction lies exactly halfway between \( \frac{2}{3} \) and \( \frac{3}{4} ? \)
A \( \cdot \frac{3}{5} \)
в. \( \frac{5}{6} \)
c. \( \frac{7}{12} \)
D. \( \frac{9}{16} \)
E \( \frac{17}{24} \)


Which of the following statements can
help you to determine the direction of
induced current in Electromagnetic
Induction?
A. Induced current flows such that it increase the total
value of current
B. Induced current flows such that it reduces the total value of current
C. Induced current flows such that direction of magnetic field produced from induced current opposes change in external magnetic field
D. Induced current flows such that direction of magnetic field produced from induced current opposes external magnetic field


Which of the following sequences is correct regarding regulation of kidney
function?
A. An excess loss of water from body \( \rightarrow \) Hypothalamus \( \rightarrow \) Ormoreceptors \( \rightarrow \) Neurohypophysis \( \rightarrow \) ADH \( \rightarrow \) Increases water permeability of DCT and CT \( \rightarrow \) Prevention of diuresis
B. An excess loss of fluid from body \( \rightarrow \) Ormoreceptors \( \rightarrow \) Hypothalamus \( \rightarrow \) Neurohypophysis \( \rightarrow A D H \rightarrow \) Increases wter permeability of DCT and \( \mathrm{CT} \rightarrow \) PRevention of diuresis
C. An excess loss of fluid from body \( \rightarrow \) Ormoreceptors \( \rightarrow \) Hypothalamus \( \rightarrow \) Neurohypophysis \( \rightarrow \) Aldosterone \( \rightarrow \) Water permeability of DCT and CT increases \( \rightarrow \) Prevention of diuresis
D. An excess loss of fluid from body \( \rightarrow \) Ormoreceptor \( \rightarrow \) Hypothalamus \( \rightarrow \) Adenohypophysis \( \rightarrow \) ADH \( \rightarrow \) Increases water permeability of DCT and CT \( \rightarrow \) Prevention of diuresis


The muscles of alimentary canal is a
type of
A. Cardiac muscle
B. Straited muscle
c. Unstriated muscles
D. None of the above


A. \( A-4, B-3, C-2, D- \)
B. A-3, B-2, C-4, D-1
c. \( A-4, B-5, C-2, D-3 \)
D. A-1, B-2, C-3, \( D-4 \)


If \( D_{30} \) is the set of all divisors of
\( \mathbf{3 0}, \boldsymbol{x}, \boldsymbol{y} \boldsymbol{\epsilon} \boldsymbol{D}_{30}, \) we define \( \boldsymbol{x}+\boldsymbol{y}= \)
\( \boldsymbol{L} \boldsymbol{C} \boldsymbol{M}(\boldsymbol{x}, \boldsymbol{y}), \boldsymbol{x} \cdot \boldsymbol{y}=\boldsymbol{G} \boldsymbol{C} \boldsymbol{D}(\boldsymbol{x}, \boldsymbol{y}), \boldsymbol{x}^{\prime}= \)
\( \frac{30}{x} \) and \( f(x, y, z)=(x+y) \cdot\left(y^{\prime}+z\right) \)
then \( f(2,5,15) \) is equal to
A .2
B. 5
c. 10
D. 15


A brass rod of length \( 30 \mathrm{cm} \) is joined to
a copper rod of length \( 60 \mathrm{cm} \). The two rods are of the same thickness and at
initial temperature of \( 20^{\circ} \mathrm{C} \). What is the change in length of the combined rod,
when the same is heated to \( 160^{\circ} \mathrm{C} \)

Coefficients of linear expansion of brass
and copper are \( 1.9 \times 10^{-5}^{\circ} C^{-1} \) and
\( 1.7 \times 10^{-5}^{\circ} C^{-1} \) respectively


When an air bubble of radius r rises from
the bottom to the surface of a lake, its radius becomes \( 5 r / 4( \) the pressure of
the atmosphere is equal to the \( 10 \mathrm{m} \) height of water column).ff the temperature is constant and the surface tension is neglected, the depth of the lake is
A . 3.53m
B. 6.53m
c. \( 9.53 \mathrm{m} \)
D. 12.53m


Two identical cylindrical vessels with
their bases at the same level, each
contains a liquid of density \( \rho \)
The height of the liquid in one vessel is
\( h_{1} \) and that in the other is \( h_{2} . \) The area
of either base is A. The work done by
gravity in equalizing the levels when the vessels are interconnected, is:
A \( \cdot \operatorname{Agg}\left(\frac{h_{1}-h_{2}}{2}\right) \)
B. \( \operatorname{Apg}\left(\frac{h_{1}-h_{2}}{2}\right)^{2} \)
\( ^{\mathbf{c}} \cdot \operatorname{A\rhog}\left(\frac{h_{1}-h_{2}}{4}\right) \)
D \( \operatorname{Apg}\left(\frac{h_{1}-h_{2}}{4}\right)^{2} \)


Ceratium is
A. Dinoflagellate
B. Diatom
C. Slime Mould
D. Sporozoan


A positive integer \( n \leq 5 \), such that \( \int_{0}^{1} e^{2 x-1}(x-1)^{n} d x=\frac{1}{4}\left(\frac{7}{e}-e\right) \)


If \( |\vec{a}+\vec{b}|<|\vec{b}-\vec{a}| \) then angle between \( \vec{a} \) and \( \vec{b} \) is
A \( \cdot \frac{\pi}{2} \)
в.
c. acute
D. obtuse


The least value of \( e^{\sin ^{-1} x}+e^{\cos ^{-1} x} \) is
A \( \cdot 1+e^{\pi / 2} \)
B . \( 2 e^{\pi / 2} \)
\( \mathbf{c} \cdot e^{\pi / 4} \)
D \( \cdot 2 e^{\pi / 4} \)


Calculate the displacement for a body, if the workdone is \( 130 \mathrm{J} \) and force
applied is \( 19.5 \mathrm{N} \)
A. 6.66 m
B. 130 \( m \)
\( c .2535 \mathrm{m} \)
D. 20 \( m \)


A block slides down on an incline of angle \( 30^{\circ} \) with an acceleration \( \frac{g}{4} . \) Find the coefficient of kinetic friction.
A \( \cdot \frac{1}{2 \sqrt{2}} \)
B. 0.6
c. \( \frac{1}{2 \sqrt{3}} \)
D. \( \frac{1}{\sqrt{2}} \)


Which process of purification is represented by the following scheme?
\( \underset{\text { impure }}{\boldsymbol{T i}}+\mathbf{2 I}_{\mathbf{2}} \stackrel{\mathbf{2 5 0}^{\circ} \boldsymbol{C}}{\boldsymbol{\pi} \boldsymbol{i} \boldsymbol{I}_{4}} \frac{\mathbf{1 4 0 0}^{\boldsymbol{o}} \boldsymbol{C}}{\boldsymbol{p} \boldsymbol{p} \boldsymbol{i}}+ \)
\( 2 I_{2} \)
A. Cupellation
B. Electrolytic refining
c. zone refining
D. Van-Arkel process


The point 0 lies inside a triangle \( P Q R \) such that \( \Delta O P Q, \Delta O Q R \) and \( \Delta O R P \) are equal in area. Then,the point 0 is
called as
A. incentre
B. centroid
c. circumcentre
D. orthnocentric