Which of the following is an intensive
property?
A. Enthalpy
B. Entropy
c. Density
D. Mass


Which one is not correct for e.m.f. of a
galvanic cell?
This question has multiple correct options
\( \mathbf{A} \cdot E_{c e l l}=E_{O P_{a n o d e}}+E_{R P_{c a t h a d e}} \)
B. \( E_{\text {cell}}=E_{O P_{L H S}}+E_{R P_{\text {RHS}}} \)
C \( . E_{\text {cell}}= \) higher oxidation potential - lower oxidation potential
D. \( E_{\text {cell}}= \) lower oxidation potential - higher oxidation potential


Write the equation of 25 cycle current
sine wave having rms value of \( 30 A \)


Solve : \( \int \frac{x d x}{\left(x^{2}+a^{2}\right)\left(x^{2}+b^{2}\right)} \)


The perimeter of a parallelogram,whose one side measures 12 inches, is 72 inches. Find the length of its other three sides.
A. 12,12,36
B. 12, 18, 18
c. 12,24,24
D. 12,30,30


Four charges are arranged on y-axis as shown in figure. then the electric field at
point \( \boldsymbol{P} \) is proportional to:
\( A \cdot \frac{1}{d} \)
B. \( \frac{1}{d^{2}} \)
c. \( \frac{1}{d^{4}} \)
D.


A block is given a initial push along rough horizontal fixed table surface and
after some time it stops due to friction.
For the system of block and table
A. temperature increase
B. heat supplied is positive
c. heat supplied is negative
D. total energy decreases


One molecule of glucose in Calvin cycle
is formed from
A \( \cdot 6 C O_{2}+12 A T P \)
в. \( 6 C O_{2}+30 A T P+12 N A D P H \)
c. \( 6 C O_{2}+18 A T P+12 N A D P H \)
D. \( 6 C O_{2}+18 A T P+30 N A D P H \)


Lanthanoids are characterized by the filling of the:
A. penulimate 4f energy level
B. antepenultimate 4f energy level
c. penultimate 3f energy level
D. antepenultimate 3f energy level


Which of the following hydride have lowest boiling point?
A \( \cdot H_{2} O \)
в. \( H_{2} S \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{Se} \)
D. \( H_{2} T e \)


Charge is a
A. scalar
B. vector
c. tensor
D. non-existent


\( \mathrm{BP}=2 \mathrm{AC} \)
f the above statement is true then
mention answer as 1 , else mention 0 if
false


Differentiate between
Mitral valve and semilunar valve


Which set of molecules is polar?
A. \( \operatorname{XeF}_{4}, I F_{7}, S O_{3} \)
в. \( P C l_{5}, C_{6} H_{6} \)
c. \( \operatorname{sn} C l_{2}, s O_{2}, N O_{2} \)
D. \( C O_{2}, C S_{2}, C_{2} H_{6} \)


The solubility of \( \boldsymbol{P b}(\boldsymbol{O H})_{2} \) in water is
\( 6.7 \times 10^{-6} M . \) Calculate the solubility of
\( \boldsymbol{P b}(\boldsymbol{O H})_{2} \) in a buffer solution of \( \mathrm{pH}=\mathbf{8} \)
A \( .3 .2 \times 10^{-3} \)
B. \( 12 \times 10^{-3} \)
c. \( 1.2 \times 10^{-3} \)
D. \( 6 \times 10^{-4} \)


The mean of the following natural
numbers \( 1,2,3, \dots 10 \) is
A . 6.5
в. 4.5
\( c .5 .5 \)
D. 5.4


The arithmetic mean of 5,6,8,9,12,13
17 is
A . 20
B. 15
c. 10
D. 25


Two mark Questions:
Differentiate between the two cells
enclosed in a mature male
gametophyte of an angiosperm.


At room temperature, the reaction
between \( N O \) and \( O_{2} \) to give \( N O_{2} \) is
fast, while that between \( C O \) and \( O_{2} \) is
slow. It is due to:
A. \( \mathrm{CO} \) is smaller in size than that of \( \mathrm{NO} \)
B. \( \mathrm{CO} \) is poisonous
C. the activation energy for the reaction, \( 2 N O+O_{2} \rightarrow \)
\( 2 N O_{2} \) is less than \( 2 C O+O_{2} \rightarrow 2 C O_{2} \)
D. none of the above


Rays of light from Sun falls on a
biconvex lens of focal length \( f \) and the
circular image of Sun of radius \( r \) is formed on the focal plane of the lens. Then
A. Area of image is \( \pi r^{2} \) and area is directly proportional of \( f \)
B. Area of image is \( \pi r^{2} \) and area is directly proportional to \( t^{2} \)
c. Intensity of image increases if \( f \) is increased
D. If lower half of the lens is covered with black paper, area will become half


If nucleons in an excited state fall to a
lower energy level, energy is emitted as
A. \( \alpha- \)rays
B. \( \beta- \)rays
c. \( \gamma- \) rays
D. \( X- \) rays


One of the statements of Dalton's
atomic theory is given below "compounds are formed when atoms of different elements combine in a fixed
ratio. "Which law of chemical
combination is not related to this
statement?

This question has multiple correct options
A. Law of conservation of mass
B. Law of multiple proportion
c. Avogadro's law
D. Law of definite proportion


The domain of \( \frac{10^{x}+10^{-x}}{10^{x}-10^{-x}} \) is
A. \( R \)
в. \( R-\{0\} \)
c. \( R-\{1\} \)
D. \( R^{+} \)


Draw a rough sketch of a quadrilateral KLMN. State two pairs of opposite
angles.


A ray of light undergoes deviation of \( 30^{\circ} \) when incident on an equilateral prism of refractive index \( \sqrt{2} \). The angle made
by the ray inside the prism with the base of the prism is then
A \( \cdot 30^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 60^{\circ} \)
D. zero


Critical temperature can be defined as
the
A. Temperature at which there is no motion between the molecules
B. Temperature at which a gas is converted into its liquid state
C. Temperature at which volume of a gas becomes zero
D. Temperature above which a gas cannot be liquefied no matter however high the pressure may be


Match the column I and II and select the
correct option from the codes given below:
(P)
\( (Q) \)
\begin{tabular}{lll}
Column I & \multicolumn{2}{l} { Column II } \\
Liquid & (i) & Highly compressible \\
Gas & (ii) & Definite volume \\
Plasma & (iii) & Super low density \\
BoseEinstein condensate & (iv) & Super energetic \\
\hline
\end{tabular}
(R)
\( (s) \)
A. \( (P)-(i),(Q)-(i i),(R)-(i i i),(S)-(i v) \)
B. (P)-(ii), (Q)-(i),(R)-(iii),(S)-(iv)
C. (P)-(ii), (Q)-(i),(R)-(iv),(S)-(iii)
D. (P)-(iii), (Q)-(i),(R)-(ii),(S)-(iv)


The element which was observed in
solar spectrum is
A. Helium
B. Xenon
c. Neon
D. Argon


Evaluate \( \int r^{4}\left(7-\frac{r^{5}}{10}\right) d r \)


If two waves are represented by \( y_{1}= \)
\( 2 \sin (4 x-300 t) \) and \( y_{2}=\sin (4 x- \)
\( 300 t-0.2) \) then, their superposed wave
will have angular frequency
A. \( 150 / \pi \)
в. \( 150 \pi \)
\( c .300 \)
D. \( 600 \pi \)


The secondary battery is such a battery:
A. which cannot be recharged
B. which can be recharged
C. which can be reused after replacing its chemical
D. which is charged by primary cells


Match the chemicals in column I with
their uses on column II:
Column I
(A) Sodium perborate
(I) Disinfectant
(B) Chlorine
(II) Antiseptic
(C) Bithional
(III) Milk bleaching agent
(D) Potassium sterate
(IV) Soap
B. A=II, B=|II, C=IV, D=1
C \( . A=\| I, B=I, C=11, D=I V \)
D. A=IV, B=I, C=II, D=III


Assertion
The reaction \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{O}_{3}+\boldsymbol{6} \boldsymbol{H}^{+}+\boldsymbol{6} \boldsymbol{e}^{-} \rightleftharpoons \)
\( X e+3 H_{2} O, E^{\circ}=2.1 V \) is not feasible
thermodynamically to oxidise \( H_{2} O \)
Reason
There is a high activation energy barrier between oxidation state +6 and 0 of \( X e \)
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 true but Reason is false
D. Assertion is false but Reason is true


If the product of two numbers is 10 and
their sum is \( 7, \) which is the greatest of the two numbers?
A . -2
B. 2
\( c .5 \)
D. 4


In the sequence of the given reactions, the starting compound \( \boldsymbol{P} \) is:
\( \mathrm{P} \frac{(1) \mathrm{Br}_{2}}{(2) \mathrm{S}_{\mathrm{n}} \mathrm{HCl}}>2 \frac{(1) \mathrm{NaNO}_{2 \mathrm{HCl}}}{273-278 \mathrm{K}} \times \frac{\mathrm{KMnO}_{4}}{(2) \mathrm{H}_{2} \mathrm{O} / \mathrm{H}_{3} \mathrm{PO}_{2}} \)
A . o-nitro toluene
B. m-nitro toluene
c. o-bromo toluene
D. p-nitro toluene


The sum of squares of deviations for 10
observations taken from mean 50 is
250. Then Co-efficient of variation is
A . \( 10 \% \)
B. \( 40 \% \)
\( c .50 \% \)
D. None


Low density polythene is prepared by:
A. Free radical polymerizaiton
B. Cationic polymerization
c. Anionic polymerization
D. Ziegler - Natta polymerization


If \( A \) is \( 2 \times 3 \) matrix and \( A B \) is a \( 2 \times 5 \)
matrix, then \( B \) must be a
A. \( 3 \times 5 \) matrix
B. \( 5 \times 3 \) matrix
c. \( 3 \times 2 \) matrix
D. \( 5 \times 2 \) matrix


Consider the reaction,
\( \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{3}+}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{S} \boldsymbol{C} \boldsymbol{N}^{-}(\boldsymbol{a} \boldsymbol{q}) \rightleftharpoons \)
\( \boldsymbol{F} \boldsymbol{e} \boldsymbol{S} \boldsymbol{C} \boldsymbol{N}^{2-}(\boldsymbol{a} \boldsymbol{q}) \)
How will the equilibrium position shift
if \( A g N O_{3}(a q) \) is added? \( (A g S C N \) is insoluble)


The correct order of equivalent
conductance at infinite dilution of
\( L i C l, N a C l \) and \( K C l \) is :
A. \( L i C l>N a C l>K C l \)
в. \( K C l>N a C l>L i C l \)
c. \( N a C l>K C l>L i C l \)
D. \( L i C l>K C l>N a C l \)


Very short answer type.
Name the principal excretory organs of
cockroach.


Complete the following:
Hand Spindle : \( \ldots \). Spinning of yarn on large scale : spinning machine.
A. Charaleha
B. Takla
c. Handloom
D. None of the above


In series LCR circuit \( R=18 \Omega \) and
impedance is \( 33 \Omega \). An r.m.s. voltage
\( 220 V \) is applied across the circuit. The true power consumed in a.c. circuit is
A . \( 200 W \)
в. \( 400 \mathrm{W} \)
c. \( 600 W \)
D. \( 800 W \)


The DNA model proposed by Watson and
Crick
A. combined many of the findings of other researches also studying DNA such as Rosalind Franklin and Chargaff.
B. showed the double helix nature of the molecule
C. presented a molecule with sugar-phosphate backbones on the outside and paired bases on the inside
D. all of the above


In the adsorption of oxalic acid on
activated charcoal, the activated
charcoal is called:
A. adsorbent
B. adsorbate
c. adsorber
D. absorber


Which of the following can be oxidised
by acidified \( \boldsymbol{K}_{2} \boldsymbol{C r}_{2} \boldsymbol{O}_{7} ? \)
A. Nitrate ions
B. Sulphite ions
c. Ferric ions
D. Borate ions


For a reaction that has \( [\boldsymbol{A}] \) and \( [\boldsymbol{B}] \) both doubled, the rate goes up by a factor of
8. The rate law is: rate\( =\boldsymbol{k}[\boldsymbol{A}]^{m}[\boldsymbol{B}]^{2} \)
What is the rate order with respect to
\( [\boldsymbol{A}] ? \)
A. Third order
B. Second order
c. First order
D. Can not be determined with the given information


An electron after being accelerated through a potential difference \( 100 \boldsymbol{V} \)
enters a uniform magnetic field of \( 0.004 T \) perpendicular to its direction of motion. Calculate the radius of the path described by the electrons.


Identify the action involved when a north pole of magnet brought near another north pole of magnet it repels?
A. Pushing
B. Throwing
c. Pulling
D. Lifting


What should be the state of compounds which decompose on passing electric current?
A. Plasma
B. Solid
c. Gas
D. Molten or aqueous


A flat circular coil of \( n \) turns, area \( A \) and resistance \( \boldsymbol{R} \) is placed in a uniform
magnetic field \( B \). The plane of coil is
initially perpendicular to \( B \). When the
coil is rotated through an angle of \( 180^{\circ} \)
about one of its diameter, a charge \( Q_{1} \)
flows through the coil. When the same
coil after being brought to its initial position, is rotated through an angle of
\( 360^{\circ} \) about the same axis a charge \( Q_{2} \)
flows through it. Then \( Q_{2} / Q_{1} \)
A . 1
B . 2
c. \( 1 / 2 \)
D.


Light from a discharge tube containing hydrogen atoms falls on the surface of a piece of sodium. The kinetic energy of the fastest photoelectrons emitted from sodium is \( 0.73 e V \). The work function
for sodium is \( 1.82 e V . \) The rocoil speed
of emitting atom assuming it to be at rest before ionisation is (lonisation potential of hydrogen is \( 13.6 e V \) ).
B . \( 1.80 \mathrm{ms}^{-1} \)
c. \( 8.10 m s^{-1} \)
D. \( 0.81 \mathrm{ms}^{-1} \)


The coefficient of restitution (e) for a
perfectly elastic collision is
A . -1
B.
\( c \cdot \alpha \)
\( D \)


The major product of the following
reaction is:-
\( \boldsymbol{C H}_{3} \)
\( \boldsymbol{C H}_{3}-\underset{\boldsymbol{H}}{\boldsymbol{C}}-\boldsymbol{C} \boldsymbol{H} \boldsymbol{C H}_{3} \frac{\boldsymbol{C H}_{3} \boldsymbol{O H}}{\boldsymbol{B} \boldsymbol{r}} \)
A. \( \quad C H_{3}-C_{I}^{I H_{3}}-C_{\mid}^{I} H C H_{3} \)
B. \( \quad C H_{3} \)
\[
C H_{3}-C_{I}^{\perp}-C H=C H_{2}
\]
c. \( \quad C H_{3} \)
\[
C H_{3}-C_{1}^{\prime}-C H_{2} C H_{3}
\]
\[
\begin{array}{l}O C H_{3}\end{array}
\]
D.
\[
C H_{3}-C=C H C H_{3}
\]


dentify the type of force in diagram
A. Push
B. Pull
c. No force is acting
D. Both A and B


Name any one instrument which works
on the principle of tangent law in magnetism


A closely wound solenoid \( 80 \mathrm{cm} \) long has 5 layers of windings of 400 turns each. The diameter of the solenoid is 1.8
\( \mathrm{cm} . \) If the current carried is \( 8.0 \mathrm{A} \)
estimate the magnitude of B inside the solenoid near its centre :
A \( .1 .5 \times 10^{-2} T \), opposite to the axis of solenoid
B . \( 2 \times 10^{-2} T \), along the axis of solenoid
C . \( 3.5 \times 10^{-2} T \), along the axis of solenoid
D. \( 1.5 \times 10^{-2} T \) along the axis of solenoid


A rectangular field is half as wide as it
is long and is completely enclosed by \( x \) yards of fencing. The area in terms of \( x \)
is
A \( \cdot \frac{x^{2}}{2} \)
в. \( 2 x^{2} \)
c. \( \frac{2 x^{2}}{9} \)
D. \( \frac{x^{2}}{18} \)
E. none of these


The frequency of a source is \( 20 \mathrm{kHz} \). The frequencies of sound wave produced by it in water and air will be :
A. Same as that of source \( \simeq 20 \mathrm{kHz} \)
B . > 20 kHz
\( \mathrm{c} .<20 \mathrm{kHz} \)
D. Depends upon velocity


The reflection of the point \( \boldsymbol{P}(1,0,0) \) in the line \( \frac{\boldsymbol{x}-\mathbf{1}}{\mathbf{2}}=\frac{\boldsymbol{y}+\mathbf{1}}{\mathbf{- 3}}=\frac{\boldsymbol{z}+\mathbf{1 0}}{\mathbf{8}} \) is
A \( \cdot(3,-4,-2) \)
B \( \cdot(5,-8,-4) \)
c. (1,-1,-10)
D. (2,-3,8)


Schrodinger wave equation
2. Heisenberg uncertainty principle
3. Millikan oil drop experiment
4. Chadwick's discovery of neutron Of the scientific milesiones listed
above, which is the most ancient and most modern respectively?
A \( \cdot 1,4 \)
в. 3, 4
\( c \cdot 2, \)
D. 3,


If the line \( a x+b y+c=0 \) is a normal
to the rectangular hyperbola \( \boldsymbol{x} \boldsymbol{y}=\mathbf{1} \)
then
This question has multiple correct options
A \( . a>0, b>0 \)
в. \( a>0, b<0 \)
c. \( a<0, b>0 \)
D. \( a<0, b<0 \)


At critical temperature, the surface tension of a liquid is
A . zero
B. infinity
c. the same as that at any other temperature
D. can not be determined


Name of the drug whose structure is
given below is:
A. chloramphenicol
B. vancomycin
C. penicillin
D. ofloxacin


The conductivity of N/50 solution of KC
in a cell at \( 25^{\circ} \mathrm{C} \) is \( 0.002765 \mathrm{Scm}^{-1} . \) If
the resistance of a cell containing this
solution is 400 ohm, cell constant will
be:
A \( .1 .106 \mathrm{cm}^{-1} \)
В. \( 3.101 \mathrm{cm}^{-1} \)
D. None of these


Determine the true formula of the
compound whose molecular mass is 90.0 grams and contains \( 40.0 \% \) carbon \( 6.67 \% \) hydrogen, and \( 53.33 \% \) oxygen
A \( \cdot C_{2} H_{2} O_{4} \)
в. \( C H_{2} O_{4} \)
\( \mathbf{c} \cdot C_{3} H_{6} \)
D. \( C_{3} H O_{3} \)
E \( \cdot C_{3} H_{6} O_{3} \)


What is the final speed of the sphere's
centre of mass in ground frame when eventually pure rolling sets in
\( A \cdot \frac{5}{-11} \)
7
\( v \)
B. 2 \( 7^{v} \)
\( c \cdot 7 \)
\( v \)
\( v \)
\( D \cdot 7 \)
\( 2^{v} \)


I. If \( \boldsymbol{x}-\boldsymbol{y}=\boldsymbol{x} \boldsymbol{y}=\mathbf{1}-\boldsymbol{x}-\boldsymbol{y}, \) then \( \boldsymbol{x}+\boldsymbol{y} \)
is \( \frac{5}{6} \)
II. The system of equations \( 3 x+2 y=a \)
and \( 5 x+b y=4 \) has infinitely many
solutions for \( x \) and \( y, \) then \( a=4, b=3 \)
III. If \( \frac{x}{a}+\frac{y}{b}=2 \) and \( a x-b y=a^{2}-b^{2} \)
then \( \boldsymbol{x}=\boldsymbol{a}, \boldsymbol{y}=\boldsymbol{b} \)
Which is true?
This question has multiple correct options
A . I only
B. ॥ only
c. ॥ Il only
D. None of these


Fresh milk has a pH of
6. How do you
think the pH will change as it turns into curd? Explain your answer.


\( \int_{0}^{\infty} \frac{\log x}{1+x^{2}} d x \)


Keystone species is of
A. Always dominant
B. Useful in maintaining structure and function of biotic community
c. with maximum biomass
D. All the above


Which sector is the single-largest
consumer of fresh water in India?
A. Agriculture
B. Industry
c. Domestic
D. Power


After a storm, a man walks out onto his
porch. Looking to the east, he sees a rainbow that has formed above his
neighbor's house. What time of day it is?
A. Evening
B. Morning
c. Night
D. Dawn


Convert \( \left[\begin{array}{cc}1 & -1 \\ 2 & 3\end{array}\right] \) into on identity matrix by suitable raw transformation.


The number of triangles with any three of the length 1,4,6 and \( 8 \mathrm{cms}, \) as sides is
\( A \cdot 4 \)
B. 2
\( c \cdot 1 \)
D.


The above diagram shows a number line.

The above number line represents the
solution for:
A. \( -3 \leq x \) and \( x>4 \)
B. \( -3<x<4 \)
c. \( -3 \leq x<4 \)
D. \( -3<x \) and \( x \leq 4 \)


2.84 gms of methyl iodide was completely converted into \( C H_{3} M g I \) and the product was decomposed by the excess of ethanol. The volume of the
gaseous hydrocarbon produced at NTP will be
A . 22.4 lit
B. 2240 lit.
c. 0.448 lit.
D. 224 lit


Define
1) entropy
2) enthalpy and write the sign of \( \Delta \boldsymbol{H} \)
and \( \Delta S \) for the reaction:
\( \mathbf{2} C l(\boldsymbol{g}) \rightarrow \boldsymbol{C l}_{2}(\boldsymbol{g}) \)


A radially symmetrical and diploblastic animal is
A. Roundworm
B. Earthworm
c. Hydra
D. Liver Fluke


During a New moon phase, what is the configuration of Moon, Earth, and Sun?
A. Moon is between Earth and Sun
B. Sun is between Moon and Earth
c. Earth is between Moon and Earth.
D. They are not in a straight line.


Which one of the following can be used as monomer in polymerisation
reaction?
A. \( C H_{3} C H_{2} C l \)
в. \( C H_{3} C H_{2} \) ОН
\( \mathbf{c} \cdot C_{6} H_{6} \)
D. \( C_{3} H_{6} \)


Poisson's ratio of a material is 0.5
applied to wire of this material, these in
the cross-section area increase in the
length is.


\( V_{m} \) is the maximum voltage between trends of the secondary terminal of a
transformer used in a half wave
rectifier. When the PN junction diode is reverse biased, what will be the
potential difference between two ends
of the diode?
A. zero
в. \( \frac{V_{m}}{2} \)
c. \( V_{m} \)
D. \( 2 V_{m} \)


Construct \( \Delta A B C \) in which \( A B=4.5 \mathrm{cm} \)
\( A C=4.5 \mathrm{cm} \) and \( \angle B=50^{\circ} . \) Check
whether you get two triangles.


Which is the best nucleophile in polar
solvent?
\( A \cdot F^{-} \)
B . \( C l^{-} \)
c. \( B r \)
D. \( I^{-} \)


A fish-eating bird species was found to
have a specific, heavy metal
concentration of 700,000 ppt (parts per
trillion). The conclusion based on the
data is
A. Air pollution may have caused this bird species to inhale dangerous amounts of heavy metals while migrating.
B. The entire population of the bird species, from which this sample was taken, died
C. The population of this bird species exploded, causing an ecosystem imbalance.
D. Pollutants tend to collect in areas of land where this
bird species nests.
E. This bird species is at a high trophic level on the food chain.


The physical properties of elements changes according
to
A. classification of elements in groups and periods
B. classification of elements in groups
c. classification of elements in periods
D. None of these


Anjana buys a purse for \( R s .523 .80 \)
including \( 8 \% \) VAT. Find the new selling price of the purse if VAT increase to \( 10 \% \)


Match the columns


Which of the following has 0-0 linkage:
A \( \cdot \mathrm{H}_{2} \mathrm{S}_{2} \mathrm{O}_{6} \)
в. \( \mathrm{H}_{2} \mathrm{S}_{2} \mathrm{O}_{8} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{S}_{2} \mathrm{O}_{3} \)
D. \( \mathrm{H}_{2} \mathrm{S}_{4} \mathrm{O}_{6} \)


A ray of light passes from glass, having
a refractive index of \( 1.6, \) to air. The angle of incidence for which the angle of refraction is twice the angle of incidence is
A \( \cdot \sin ^{-1}\left(\frac{4}{5}\right) \)
в. \( \sin ^{-1}\left(\frac{3}{5}\right) \)
\( ^{\mathbf{c}} \cdot \sin ^{-1}\left(\frac{5}{8}\right) \)
D. \( \sin ^{-1}\left(\frac{2}{5}\right) \)


For which value of \( p \) does the equation
\( 4 x+p y+8=0 \) and \( 2 x+2 y+2=0 \)
have unique solution?


In Fleming's left hand rule, thumb shows direction of
A. current
B. Field
c. Motion
D. charge


The wire having a green plastic covering is a:
A. Live wire
B. Neutral wire
c. Earth wire
D. None of these


Assertion
The order of densities of the various
allotropes of phosphorus is as follows:
black phosphorus, red phosphorus, white phosphorus.
Reason
As tendency of polymerisation increases, the compactness of substance also increases.
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


Which of the following is not true regarding the normal distribution?
A. the point of inflecting are at \( X=\mu \pm \sigma \)
B. skewness is zero
c. maximum heigth of the curve is \( \frac{1}{\sqrt{2 \pi}} \)
D. mean = media = mode


In charging by conduction, the charged
object
A. ends up oppositely charged to the object used to charge it.
B. ends up similarly charged to the object used to charge it.
C. discharges the object used to charge it, completely.
D. discharges the object used to charge it, to some extent


The calculated bond order in \( \boldsymbol{H}_{2}^{-} \) ion is :
A . 12
в. \( 1 / 2 \)
c. \( -1 / 2 \)
D.


Which of the following is used in artificial respiration?
A. \( O_{2}+C O_{2} \)
B. \( O_{2}+C O \)
c. \( O_{2}+H_{2} \)
D. all of these


A uniform solid cylindrical roller of mass 'm' is being pulled on a horizontal surface with force F parallel to the surface and applied at its centre. If the acceleration of the cylinder is 'a' and it
is rolling without slipping then the
value of 'F' is:
\( A \cdot 2 \mathrm{ma} \)
B \cdot \( \frac{3}{2} \mathrm{ma} \)
\( c . \) ma
D・言ma


If Hunds rule is not obeyed by some elements given below then which atom has maximum magnetic moment This question has multiple correct options
A . \( F e \)
в. \( C u \)
\( c \cdot C r \)
D. \( M n \)


Evaluate:
\( \left(153^{2}\right)-\left(147^{2}\right) ? \)


Chemical \( A \) is used for water softening
to remove temporary hardness. \( A \) reacts
with \( N a_{2} C O_{3} \) to generate caustic soda.
When \( C O_{2} \) is bubbled through \( A \), it
turns cloudly. What is the chemical
formula of \( \boldsymbol{A} \) ?
A \( \cdot C a C O_{3} \)
в. \( C a O \)
\( \mathbf{c} \cdot \operatorname{Ca}(O H)_{2} \)
D. \( \operatorname{Ca}\left(H C O_{3}\right)_{2} \)


The number of \( \boldsymbol{A} \) in \( \boldsymbol{T}_{\boldsymbol{p}} \) such that \( \boldsymbol{A} \) is either symmetric or skew-symmetric or both, and det \( (A) \) divisible by \( p, \) is
A \( \cdot(p-1)^{2} \)
в. \( 2(p-1) \)
c. \( (p-1)^{2}+1 \)
D. \( 2 p-1 \)


An generator works on the principle of


Simplify:
\( \frac{m^{2}-n^{2}}{(m+n)^{2}} \times \frac{m^{2}+m n+n^{2}}{m^{3}-n^{3}} \)


A: The corpuscular theory fails in explaining the velocities of light in air and water.
B: According to corpuscular theory, the light should travel faster in a 'denser medium than in a rarer medium.
A. If both A and B are true but the B is the correct explanation of A
B. If both A and B are true but the B is not the correct explanation of A
c. If A is true but B is false
D. If both the A and B are false
E. If B is true but A is false


For any two real number, an operation defined by \( a * b=1+a b \) is.
A. Commutative but not associative
B. Associative but not commutative
c. Neither Commutative nor associative
D. Both commutative and associative


Solve the differential equation:
\( (x-\sqrt{x y}) d y=y d x \)


Describe this topic:
Effect of sewage discharge on some important characteristics of a river


Which of the following is the fastest?
A. Cheetah
B. wind
c. sound
D. Light


What would be the effect on burning if
the proportions of nitrogen and oxygen in air were reversed?
A. The atmosphere would be explosive
B. Oxygen reacting with the nitrogen to form poisonous nitrous oxides
c. The digestion of protein would be affected
D. All of the above


Assertion
When a vessel is heated,the heat is transferred from base to another
part,bringing the vessel to uniform temperature.This process is cannot be reversed.
Reason
If the process is reversed it will violate the second law of thermodynamics as the part of the vessel will not get cooler spontaneously and warm up at the
base.
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


Zygotic meiosis occurs in
A. Gymnosperms
B. Ferns
c. Moss
D. Algae


A potential barrier V volts exists across a P-N junction. The thickness of the depletion region is 'd'. An electron with velocity 'v' approaches P-Njunction from N-side. The velocity of the electron crossing the junction is:
A \( \cdot \sqrt{v^{2}+\frac{2 V e}{m}} \)
B. \( \sqrt{v^{2}-\frac{2 V e}{m}} \)
\( c \)
D. \( \sqrt{\frac{2 V e}{m}} \)


A ball of mass 'm' drops from a height 'h which sticks to mass-less hanger after
striking. Neglect overturning, find out the maximum extension in the rod.
Assuming rod is massless


A fair coin is tossed five times. If the out
comes are 2 heads and 3 tails (in some
order), then what is the probability that the fourth toss is a head?
A \( \cdot \frac{1}{4} \)
B. \( \frac{2}{5} \)
\( c \cdot \frac{1}{2} \)
D. \( \frac{3}{5} \)


An element X has 7 electrons in its shell. What is true about the element \( x \)
\( ? \)
I. It belongs to period 9 of modern periodic table.
II. Its atom contains 9 protons.
III. It has a valency of 1
IV. Its atoms can accept an electron to acquire noble gas configuration.
\( A \cdot(1) \) and (11)
B. (II), (III), (IV)
c. (III) and (IV)
D. (II) and (IV)


A dispersion of liquid in water is an example of a colloidal
A. Aerosol
B. Emulsion
c. Foam
D. Gel


The IUPAC name of \( \boldsymbol{H}_{3} \boldsymbol{C}-\underset{\boldsymbol{O} \boldsymbol{C}_{3} \boldsymbol{H}_{7}}{\boldsymbol{H}}- \)
\( \boldsymbol{C}_{3} \boldsymbol{H}_{7} \) is:


The mass of an oxygen atom is 1600 u. Find its order of magnitude in \( \mathrm{kg} \)


\( _{6}^{14} \boldsymbol{C} \rightarrow_{7}^{14} \boldsymbol{N}+\boldsymbol{X} \)
The above nuclear reaction is an
example of :
A. \( \alpha \) decay
B \( \cdot \beta^{-} \) decay
\( \mathbf{c} \cdot \beta^{+} \) decay
D. Fusion
E . \( \gamma \) decay


An iron ball of mass \( \boldsymbol{m}=\mathbf{5 0} \boldsymbol{g} \) falls from
a height of \( h_{1}=5 m \) and rises upto
\( h_{2}=2 m \) after colliding with the
horizontal surface. If the time of the
glass half is \( \Delta t=0.02 s, \) find the
average contact force exerted on the ball by the horizontal surface.


A raised hammer possesses:
A. K.E. only
B. gravitational P.E.
c. electrical energy
D. sound energy


Name the enudeate component of the blood cells.


Which of the following options, which describe the dependence of drift
velocity \( v_{d} \) on electric field \( E, \) obeys
Ohm's law?
A \( \cdot v_{d} \propto E \)
В \( \cdot v_{d} \propto E^{2} \)
\( \mathbf{c} \cdot v_{d} \propto \sqrt{E} \)
D. \( v_{d}= \) constant


Assertion
Energy of electron in 1st orbit of \( \boldsymbol{H} \boldsymbol{e}^{+} \) is
more than that in Hydrogen atom.
Reason
Nuclear charge is more in \( H e^{+} \) than in
Hydrogen.
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


'Nodes of Ranvier' are found in
\( A \). Brain
B. Heart
\( c \cdot \) Axon
D. Eye


The coefficient B in the virial equation
of state has unit:
\( \boldsymbol{P} \boldsymbol{V}_{\boldsymbol{m}}=\boldsymbol{R} \boldsymbol{T}\left(\boldsymbol{1}+\frac{\boldsymbol{B}}{\boldsymbol{V}_{m}}+\frac{\boldsymbol{C}}{\boldsymbol{V}_{\boldsymbol{m}}^{2}}+\ldots . .\right) \)
A. mole
B. L/mole
c. L-mole
\( D \)


If the bond dissociation energies of \( \boldsymbol{X} \boldsymbol{Y} \)
\( X_{2} \) and \( Y_{2} \) (all diatomic molecules) are
in the ratio of 1: 1: 0.5 and \( \Delta_{1} H \) for the
formation of \( X Y \) is \( -200 k J \) mol\( ^{-1} . \) The
bond dissociates energy of \( X_{2} \) will be:
A \( .100 \mathrm{kJ} \mathrm{mol}^{-1} \)
в. 200 kJ mol-
c. \( 800 k J \) mol \( ^{-1} \)
D. \( 400 \mathrm{kJ} \mathrm{mol}^{-1} \)


Which of the following relation is
correct?
\( \mathbf{A} \cdot I^{s t} \) IE of \( C>I^{s t} \) IE of \( B \)
B \( \cdot I^{s t} \) IE of \( C<I^{s t} \) IE of \( B \)
C \( \cdot I I^{n d} \) IE of \( C>I I^{n d} \) IE of \( B \)
D. Both (B) and (C)


Fungi share all of the characteristics listed below with plants except
A. Heterotrophy
B. Sexual reproduction
c. composed of eukaryotic cells
D. Engage in mutualistic relationships with other organisms
E. Multicellularity


A fair die is rolled 180 times. The
expected number of 6 is
A . 50
B. 30
c. 10
D.


A particle falling with constant acceleration covers \( 3 m \) distance in
third second of its motion. The distance
covered in first 5 second shall be: (Take
\( \boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} \boldsymbol{s}^{-2} \mathbf{)} \)
A . \( 5 m \)
B. \( 15 m \)
\( c .30 m \)
D. \( 45 \mathrm{m} \)


If \( \boldsymbol{f}(\boldsymbol{x}+\boldsymbol{y})=\boldsymbol{f}(\boldsymbol{x}) \boldsymbol{f}(\boldsymbol{y}) \forall \boldsymbol{x}, \boldsymbol{y} \) and
\( \boldsymbol{f}(\mathbf{5})=\mathbf{2}, \boldsymbol{f}^{\prime}(\mathbf{0})=\mathbf{3} ; \) then \( \boldsymbol{f}^{\prime}(\mathbf{5}) \) is equal
to-
A .2
B. 4
\( c \cdot 6 \)
D. 8


The e/m ratio is maximum for:
A . \( D^{+} \)
в. \( H e^{+} \)
\( \mathrm{c} \cdot H^{+} \)
D. \( H e^{2+} \)


The two complex numbers satisfying
the equation \( z \bar{z}-(1+i) z- \)
\( (3+2 i) \bar{z}+(1+5 i)=0 \) are
A \( .1+i, 3+2 i \)
B. \( 1+i, 3-2 i \)
c. \( 1-i, 3+2 i \)
D. \( 1-i, 3-2 i \)


The increasing order of the rate of
oxidation with \( H I O_{4} \) of the following is:
\( (\Pi) \)
(III)
\( (\mathrm{IV}) \)
A. \( |V<\|\mid<\|<1 \)
B. \( |<||<|||<\mid V \)
C. \( |V<\|\mid=\|<1 \)
D. \( \mid<\|=\|<I V \)


Needles \( N_{1}, N_{2} \) and \( N_{3} \) are made of a ferromagnetic, a paramagnetic and a diamagnetic substance respectively. A
magnet when brought close to them will
A. attract all three of them.
B. attract \( \mathrm{N}_{1} \) and \( \mathrm{N}_{2} \) strongly but repel \( \mathrm{N}_{3} \)
C. attract \( \mathrm{N}_{1} \) strongly, \( \mathrm{N}_{2} \) weakly and repel \( \mathrm{N}_{3} \) weakly
D. attract \( \mathrm{N}_{1} \) strongly, but repel \( \mathrm{N}_{2} \) and \( \mathrm{N}_{3} \) weakly


The working of magnetic braking of trains is based on
A. Steady current
B. Eddy current
c. Alternating current
D. Pulsating current


All the particles of a body are situated at a distance \( R \) from the origin. The
distance of centre of mass of the body from the origin is
\( A .=R \)
в. \( \leq R \)
\( c \cdot>R \)
\( D . \geq R \)


Which of the following has an ester linkage?
A. Nylon - 6,6
B. Dacron
c. PVC
D. Bakelite


Find the number of chloride(s) which do not impart color to the flame from the
following:
\( \boldsymbol{B} \boldsymbol{e} \boldsymbol{C l}_{2}, \boldsymbol{S r} \boldsymbol{C l}_{2}, \boldsymbol{M} \boldsymbol{g} \boldsymbol{C l}_{2}, \boldsymbol{C a C l}_{2}, \boldsymbol{B a C l}_{2} \)


Which one of the following species is stable in aqueous solution
A \( \cdot M n O_{4}^{2} \)
в. \( M n O_{4}^{3} \)
\( c \cdot C r^{2} \)
D. \( C u^{+} \)


toppr
Q Type your question
Kelvin along the Y-axis, which of the
curves in Fig. 4.1 most correctly represents this behavour?
\( A \)
B.
\( c \)
\( D \)


If vectors \( a \) and \( b \) be respectively equal \( \operatorname{to} 3 \hat{i}-4 \hat{j}+5 \hat{k} \) and \( 2 \hat{i}+3 \hat{j}-4 \hat{k} . \) Find
the unit vector parallel to \( \overrightarrow{\boldsymbol{a}}+\overrightarrow{\boldsymbol{b}} \)


A particle \( P \) is fixed at certain point in
horizontal plane and another particle \( Q \)
is moving around \( \mathrm{P} \) in circular path (with centre 0 ) of radius 'r' with
constant speed 'u'.' 'P' observes the
motion of 'Q'. Pick out correct statement
A. Velocity of approach between \( \mathrm{P} \) and \( \mathrm{Q} \) will be variable.
B. Velocity of approach between \( P \) and \( Q \) will be always negative.
C. Velocity of approach between \( \mathrm{P} \) and \( \mathrm{Q} \) will be always constant.
D. None of these


Electric door bell employs
A. Permanent Magnet
B. Electromagnet
c. Thermistor
D. Electric bulb


A trihybrid cross is made between two plants with genotypes \( \mathrm{A} / \mathrm{a} \) B/b \( \mathrm{C} / \mathrm{c} \), how many offsprings of such cross will have a genotype a/a b/b c/c?
A . \( 1 / 64 \)
B. \( 1 / 4 \)
\( c \cdot 1 / 16 \)
D. 1/32


Whose precise observations and records of the positions of the planets were very important to Johannes Kepler, in enabling him to formulate his laws of
planetary motion?
A. Galieo Galilei
B. Tycho Brahe
c. Nicolaus Copernicus
D. Isaac Newton
E. Edmond Halley


Shoe flower belongs to
A. Solanaceae
B. Malvaceae
c. Papillonaceae
D. Liliaceae


The mass \( 100 g \) and \( 300 g \) at a given time have velocities \( 10 \hat{i}-7 \hat{j}-3 \hat{k} \) and \( \mathbf{7} \hat{\mathbf{i}}-\mathbf{9} \hat{\mathbf{j}}+\mathbf{6} \hat{\boldsymbol{k}} \) respectively. Determine
velocity of \( \boldsymbol{C O} \boldsymbol{M} \)


The monomer \( (G=M e \text { or } C l) \) when
treated with Zieglar - Natta catalyst undergo polymerisation as shown in the figure. Which of the following statement is not true considering the process
given above?
\[
\begin{aligned}
\mathrm{n} / \sqrt{\backslash} \frac{\text { Zieglar-Natta }}{\text { Catalyst }} &=[\sqrt{1}]_{\mathrm{n}}=\\
& \text { cis-poly-1,3-butadiene }
\end{aligned}
\]
A. The general class of polymer formed is known as homopolymer
B. The polymer obtained is stereoregular
C. Buna-N can be prepared using above process
D. Synthetic rubber can be formed by above process using 1,3 - butadiene


Which of the following example is correctly matched?
A. Butter - gel
B. Smoke - emulsion
c. Paint- foam
D. Milk - aerosol


If \( \vec{n} \) is a vector of magnitude \( \sqrt{3} \) and is equally inclined with an acute angle with the coordinate axes. Find the
vector and cartesian forms of equation
of a plane which passes through (2,1,-1) and is normal to \( \vec{n} \)


Find the value of \( x \) for which the
derivative of the function \( f(x)= \) \( 20 \cos 3 x+12 \cos 5 x-15 \cos 4 x \)
is equal to zero?


Q Type your question-
and of fixed emf, the resistor \( \boldsymbol{R}_{1} \) has
fixed resistance and the resistance of
resistor \( \boldsymbol{R}_{2} \) can be varied (but \( \boldsymbol{R}_{2} \) is
always nonzero). Then the electric power
delivered to the resistor of resistance
\( R_{1} \) is independent of the value of
resistance \( \boldsymbol{R}_{2} \)
Reason
f potential difference across a fixed
resistance is unchanged, the power delivered to the resistor remains
constant.
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


At \( 1200^{\circ} C, \) the following equilibrium is established between chlorine atoms \&
molecule.
\( \boldsymbol{C l}_{2}(\boldsymbol{g}) \rightleftharpoons \mathbf{2} \boldsymbol{C l}(\boldsymbol{g}) \)
The composition of the equilibrium mixture may be determined by measuring the rate of effusion of the mixture through a pinhole. It is found
that at \( 1200^{\circ} \) Cand 1 atm pressure the
mixture effuses 1.16 times as fast as
krypton effuses under the same condition.
Calculate the equilibrium constant \( \boldsymbol{K}_{c} \)
A \( .3 .1 \times 10^{5} \)
В . \( 6.3 \times 10^{4} \)
c. \( 12.6 \times 10^{5} \)
D. None of these


The boiling point of \( 95 \% \) ethanol is higher than that of absolute ethanol.
A. True
B. False


The value of \( b \) for which the function
\( f(x)=\sin x-b x+c \) is a strictly
decreasing function \( \forall x \in R \)
A. \( b \in(-1,1) \)
в. \( b \in(-\infty, 1) \)
C. \( b \in(1, \infty) \)
D. \( b \in[1, \infty) \)


Show that \( \int_{0}^{\pi / 2} f(\sin 2 x) \sin x d x= \)
\( \sqrt{2} \int_{0}^{\pi / 4} f(\cos 2 x) \cos x d x \)


A relation \( R \) is defined on the set \( z \) of
integers as follows. \( (x, y) \in R \Leftrightarrow x^{2}+ \)
\( \boldsymbol{y}^{2}=25 . \) Express \( \boldsymbol{R} \) and \( \boldsymbol{R}^{-1} \) as the set
of ordered pairs and hence find their respective domains.


Name the quadrilaterals which have
both line and rotational symmetry of
order more than 1


\( \boldsymbol{A}=\left[\begin{array}{cc}\boldsymbol{x} & -\mathbf{7} \\ \mathbf{7} & \boldsymbol{y}\end{array}\right] \) is a skew-symmetric
matrix,
then \( (x, y)= \)
A \( .(1,-1) \)
B. (7,-7)
\( c \cdot(0,0) \)
D. (14,-14)


What is the weight of oxygen required for the complete combustion of 2.8 kg of ethylene?
A. 2.8kg
B. 10.5kg
c. \( 9.6 \mathrm{Kg} \)
D. 96Kg


The specific heat capacity of water is:
A \( \cdot 1 \) cal \( g^{-1} \)
в. 10 cal \( g^{-1} \)
c. 2 cal \( g^{-1} \)
D. 30 cal \( g^{-1} \)


A ball of mass m moves towards a
moving wall of infinite mass with a speed 'v' along the normal to the wall. The speed of the wall is 'u' toward the ball. The speed of the ball after elastic
collision with wall is
A. \( u+v \) away from the wall
B. \( 2 u+v \) away from the wall
c. \( |u-v| \) away from the wall
D. \( |v-2 u| \) away from the wall


A travelling wave has an equation of the form \( \boldsymbol{A}(\boldsymbol{x}, \boldsymbol{t})=\boldsymbol{f}(\boldsymbol{x}+\boldsymbol{v} \boldsymbol{t}) . \) The relation
connecting positional derivative with
time derivative of the function is:
A \( \cdot \frac{d A}{d t}=\pm v^{2} \frac{d A}{d x} \)
в. \( \frac{d A}{d t}=\pm v \frac{d A}{d x} \)
c. \( \left.\frac{d A}{d t}=\pm \sqrt{(} v\right) \frac{d A}{d x} \)
D. \( \frac{d A}{d t}=(2 \pi v / \lambda) \frac{d A}{d x} \)


Three bags contain 2 silver, 5 copper coins, and 3 silver, 4 copper coins and 5 silver, 2 copper coins respectively. A bag
is chosen at random and a coin is
drawn from it which happens to be silver. What is the probability that it has come from third bag?


During adolescence, an adult gains in height and \( \ldots \ldots . . . \) in weight.
A . \( 10 \%, 20 \% \)
B. 30\%, 60\%
c. 25\%, 50\%
D. 40\%, 80\%


Find the middle terms in the expansion
of \( (5 x-7 y)^{7} \)


Chlorine. If atomic mass of Chlorine is
\( 35.5, \) then the mass ratio of these
isotopes is \( x: 1, \) where \( x \) is :


A particle in SHM is described by the displacement function: \( \boldsymbol{x}(\boldsymbol{t})= \) \( \boldsymbol{A} \cos (\boldsymbol{\omega} \boldsymbol{t}+\boldsymbol{\phi}) \cdot \) If the initial \( (\mathbf{t}=\mathbf{0}) \)
position of the particle is \( 1 \mathrm{cm} \) and its initial velocity is \( \pi \mathrm{cm} / \mathrm{sec}, \) what is the amplitude?
A. \( \sqrt{2} \mathrm{cm} \)
B. \( 2 c m \)
c. \( \sqrt{7} c m \)
D. \( 12 \mathrm{cm} \)


A parallel plate capacitor is charged to \( 60 \mu C . \) Due to a radioactive source, the
plate loses charge at the rate of \( 1.8 \times \) \( 10^{-8} C / s . \) The magnitude of
displacement current is:
A . \( 1.8 \times 10^{-8} \mathrm{C} / \mathrm{s} \)
B. \( 3.6 \times 10^{-8} \mathrm{C} / \mathrm{s} \)
c. \( 4.1 \times 10^{-11} \mathrm{C} / \mathrm{s} \)
D. \( 5.7 \times 10^{-12} \mathrm{C} / \mathrm{s} \)


Calculate the least amount of work that
must be done to freeze one gram of
water at \( 0^{0} C \) by means of the refrigerator.The temperature of the surrounding is \( 27^{0} C . \) How much heat is
passed on the surrounding in this process? Latent heat of fusion \( \boldsymbol{L}= \)
\( 80 \mathrm{cal} / \mathrm{g} \)
\( \mathbf{A} \cdot 87.91 \mathrm{cal} \)
B. 97.91 cal
c. 88.95 cal
D. 89.95 cal


kg of iron at \( 100^{\circ} \mathrm{C} \) can melt more ice
than \( 1 \mathrm{Kg} \) of copper at same temperature. Explain \( .(\text {Iron}= \)
\( 0.117 \mathrm{cal} g^{-1 o} C^{-1} ; s_{c o p p e r}= \)
\( \left.0.093 \operatorname{cal} g^{-1}^{o} C^{-1}\right) \)


Condensation of steam is not a
chemical change.
A. True
B. False


Two identical balls \( A \) and \( B \) are kept on a smooth table as shown. B collides with
A with speed v. For different conditions mentioned in List I, match with speed of A after collision given in List II.


Calculate force on an electron in a
uniform electric field of \( 5 \times 10^{4} \mathrm{N} / \mathrm{C} \) due
north.


A person travels \( 6 \mathrm{m} \) towards the east
and \( 8 \mathrm{m} \) towards north from there again
he traveled \( 16 \mathrm{m} \) towards the south. What is the displacement covered by the person?
A . \( 10 \mathrm{m} \)
в. 20 m
c. \( 30 \mathrm{m} \)
D. \( 40 \mathrm{m} \)


Define bond length in a molecule.


Covalent compounds are generally
A. good conductors of electricity
B. bad conductors of electricity
c. semiconductors of electricity
D. none of these


Two coherent monochromatic light beams of intensities \( I \) and \( 4 I \) are
superposed. The maximum and minimum possible resulting intensities
are :
A \( .5 I \) and 0
B. \( 5 I \) and \( 3 I \)
c. \( 9 I \) and \( I \)
D. \( 9 I \) and \( 3 I \)


Which of the following is a sulphur containing amino acid
A. Alanine
B. Glycine
c. Methionine
D. valine


In the nucleic acids, the phosphate ions are bonded with sugar at:
A. 5,3 locations
B. 5, 2 locations
c. 3,1 locations
D. 5, 1 locations


Which of the following has the highest molar conductivity?
\( \mathbf{A} \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{6}\right] C l_{3} \)
B . \( \left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5} \mathrm{Cl}\right] \mathrm{Cl}_{2} \)
c. \( \left[C o\left(N H_{3}\right)_{4} C l_{2}\right] C l \)
D. \( \left[C o\left(N H_{3}\right)_{3} C l_{3}\right] \)


Assuming the particle was located at the origin initialy, find the equation of trajectory \( \boldsymbol{y}(\boldsymbol{x}), \) where \( \boldsymbol{y} \) and \( \boldsymbol{x} \)
are displacements of the body along the vertical and the horizontal respectively
A \( \cdot y(x)=x \tan \alpha-\left(\frac{g}{v_{0}^{2} \cos ^{2} \alpha}\right) x^{2} \)
B \( \cdot y(x)=x \tan \alpha+\left(\frac{g}{2 v_{0}^{2} \cos ^{2} \alpha}\right) x^{2} \)
c. \( y(x)=x \tan \alpha+\left(\frac{g}{v_{0}^{2} \cos ^{2} \alpha}\right) x^{2} \)
D. \( y(x)=x \tan \alpha-\left(\frac{g}{2 v_{0}^{2} \cos ^{2} \alpha}\right) x^{2} \)


\( C H_{3} C H_{2} C O O H \frac{B r / R e d p}{\Delta} \)
\( (A) \stackrel{a l c . N H_{3}}{ } B \)
The final product (B) in the above reaction is
A. Alanine
B. Pyruvic acid
c. citric acid
D. Lactic acid


The orbital with maximum number of
possible orientations is:
\( A \cdot s \)
B. \( p \)
\( c \cdot d \)
D. \( f \)


Solve the following systems of
equations. \( x(\sqrt{(x+y)^{2}}=3 x, x \sqrt{(x-y)^{2}} \)
1) \( ^{2}=\mathbf{0} \)


State whether True or False
Factorization of \( x^{2}-y^{2}-2 y z-z^{2} \) is
\( (x+y+z)(x-y-z) \)
A. True
B. False


Distribution law was given by:
A. Henry
B. Van't Hoff
C. Nernst's
D. Ostwald


How many water molecule(s) is/are
present in dead burnt plaster?


Which is the correct match?
A. Dendrite - Accepts signal / stimulus
B. Dendrite - Sends signal / stimulus
C. Axon-Smallest part of neuron
D. Synaptic knob - Present at the end of dendron


Write the degree of the differential
equation \( \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}+\boldsymbol{x}\left(\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}\right)^{2}= \)
\( 2 x^{2} \log \left(\frac{d^{2} y}{d x^{2}}\right) \)


A steady P.D. of \( 10 V \) produces heat at a
rate of \( ^{\prime} x^{\prime} \) in a resistor. The peak value of A.C. voltage which will produce heat at the rate of \( x / 2 \) in the same resistor
is:
A . \( 5 V \)
B. \( 5 \sqrt{2} v \)
\( c .10 V \)
D. \( 10 \sqrt{2} \mathrm{v} \)


Consider this reaction. \( 2 N O_{2(g)}+ \)
\[
\boldsymbol{O}_{\boldsymbol{3}(\boldsymbol{g})} \rightarrow \boldsymbol{N}_{2} \boldsymbol{O}_{\boldsymbol{5}(\boldsymbol{g})}+\boldsymbol{O}_{\boldsymbol{2}(\boldsymbol{g})}
\]
The reaction of nitrogen dioxide and ozone represented in first order in
\( N O_{2(g)} \) and \( O_{3(g)} . \) Which of these possible reaction mechanisms is consistent with the rate law?
\[
\text { Mechanism I. } \quad N O_{2}+O_{3} \rightarrow N O_{3}+
\]
\( \boldsymbol{O}_{2} \) slow
\[
N O_{3}+N O_{2} \rightarrow N_{2} O_{5}
\]
fast
\[
\text { Mechanism II. } \boldsymbol{O}_{3} \rightleftharpoons \boldsymbol{O}_{2}+\boldsymbol{O}
\]
fast
\[
N O_{2}+O \rightarrow N O_{3}
\]
slow
\[
N O_{3}+N O_{2} \rightarrow N_{2} O_{5}
\]
fast
A. I only
B. II only
c. both I and


A pond/lake is
A. A biome
B. A natural ecosystem
C. An artificial ecosystem
D. A community of plants and animals only


What do you mean by the
"concentration" of a substance?
A. It is the measure of undissolved substances
B. It refers to the impurities
C. Concentration refers to the amount of substance per defined space
D. It means total mass of the un dissolved gases


A man running round a racecourse notes that the sum of the distances of
two flag-posts from him is always \( 10 m \) and the distance between the flag-posts
is \( 8 m . \) The area of the path he encloses
is
A. \( 18 \pi \) square metres
B. \( 15 \pi \) square metress
c. \( 12 \pi \) square metress
D. \( 8 \pi \) square metres


A battery of internal resistance \( 4 \Omega \) is
connected tot he network of resistance
as shown. In order to give the maximum power to the network, the value of \( \operatorname{Rin} \Omega \)
should be:
\( A \cdot \frac{4}{9} \)
\( B \cdot \frac{8}{9} \)
\( c \cdot 2 \)
\( D \cdot 18 \)


A body falls from a height \( h=200 m \)
The ratio of distance travelled in each
\( 2 \sec \) during \( t=0 \) to \( t=6 \) sec of the
journey is
A. 1: 4: 9
B. 1: 2: 4
\( \mathrm{c} \cdot 1: 3: 5 \)
D. 1: 2: 3


Which of the following is a non contact force?
A. muscular
B. electrostatic attraction
c. elastic spring force
D. friction force


(a) Draw the structures of the following molecules:
(i) \( N_{2} O_{5} \)
(ii) \( \boldsymbol{H} \boldsymbol{C l O}_{4} \)
(b) Explain the following observations:
(i) \( H_{2} S \) is more acidic than \( H_{2} O \)
(ii) Fluorine does not exhibit any
positive oxidation state.
(iii) Helium forms no real chemical
compound.


0
From the following figure, \( \tan C \) is \( \frac{1}{m} \)
The value of \( \boldsymbol{m} \) is:


The molecular weight of chlorophyll \( \alpha \) is
A . 907
B. 893
c. 91
D. 712


Which is More acidic in
Cyclopentadiene and cyclopropane and why?


State whether true or false:
Rainbow is produced by the dispersion of sunlight by tiny raindrops in the air.
A. True
B. False


Consider a finite insulated, uncharged conductor placed near a finite positively charged conductor. The uncharged body must have a potential:
A. less than the charged conductor and more than at infinity.
B. more than the charged conductor and less than at infinity.
c. more than the charged conductor and more than at infinity.
D. less than the charged conductor and less than at infinity.


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


Antidepresent drug among the following is:
A. phenelzine
B. promethazine
c. naproxen
D. cimetidine


What is shape selective catalysis?


The Mond process is used for the:
A. extraction of \( M o \)
B. purification of \( N i \)
c. purification of \( Z r \) and \( T i \)
D. extraction of \( Z n \)


The population of a city increases at the rate of \( 4 \% \) per year. If in time \( t, \) the
population becomes \( p \), then equation of
\( p \) in terms of \( t \) is
A.
\[
p=e^{\frac{t}{25}}
\]
В. \( \quad p=4 . e^{\frac{t}{25}} \)
c. \( \quad_{p=c . e} \frac{t}{25} \)
D.
\[
p=\frac{1}{25} e^{4 t}
\]


How much current is drawn by the motor of 1 H.P. from 220 volt supply.
A. 3.4A
B. 2A
\( c \cdot 6 A \)
D. 22A


Solve the systems of equations:
\( \frac{\boldsymbol{x}-\mathbf{2}}{\mathbf{4}}+\frac{\boldsymbol{y}+\mathbf{1}}{\mathbf{3}}=\mathbf{2} ; \frac{\boldsymbol{x}+\mathbf{1}}{\mathbf{7}}+\frac{\boldsymbol{y}-\mathbf{3}}{\mathbf{2}}= \)
\( \frac{1}{2} \)
A \( \cdot(6,2) \)
в. (2,2)
c. (2,3)
(年. (2,3,3)
D. (3,4)


Nitrates of all metals are
A. unstable
B. colored
c. insoluble in water
D. soluble in water


\( \mathbf{5 0 m} \boldsymbol{L} \) of \( \mathbf{0 . 1 0} \boldsymbol{M} \boldsymbol{N} \boldsymbol{a}_{3} \boldsymbol{P} \boldsymbol{O}_{4}+\mathbf{5 0 m} \boldsymbol{L} \) of
\( \mathbf{0 . 1 0} \boldsymbol{M} \boldsymbol{N a H}_{2} \boldsymbol{O}_{4} \)


The change in potential of the half-cell \( C u^{2+} / C u, \) when aqueous \( C u^{2+} \)
solution is diluted 100 times at \( 298 K ? \)
\( \left[\frac{2.303 R T}{F}=0.06\right] \)
A. Increases by \( 120 \mathrm{mV} \)
B. Decreases by \( 120 \mathrm{mV} \)
c. Increases by \( 60 \mathrm{mV} \)
D. Decreases by \( 60 \mathrm{mV} \)
E. No change


What is thermodynamic equilibrium?


An achromatic combination of concave
and convex lens has power 5 D. If the power of convex lens is 4 D, then the
magnitude of focal length of concave lens is?


In an inductance coil the current
increases from zero to \( 6 A \) in 0.3 second
by which an induced e.m.f. of \( 60 \mathrm{V} \) is produced in it. The value of coefficient of self-induction of coil is :
A. \( 1 H \)
в. \( 0.5 H \)
\( c .2 H \)
D. \( 3 H \)


Choose the correct answer from the
alternatives given. The gland that prepares the body to react to stress by releasing epinephrine is the:
A. anterior pituitary
B. posterior pituitary
c. adrenal cortex
D. adrenal medulla


A curved section of a rod is banked for a
speed \( v \). If there is no friction between
road and tyres of the car, then:
A. car is more likely to slip at speeds higher than \( v \) than speeds lower than \( v \)
B. car cannot remain in static equilibrium on the curved section
c. car will not slip when moving with speed \( v \)
D. None of the above


If \( A \) and \( B \) are two mutually exclusive
events such that \( P(A)=0.55 \) and
\( P(B)=0.35 \) then \( P(\bar{A} \cup \bar{B})= \)
A \( \cdot \frac{1}{4} \)
B.
\( c \)
D.


SONAR works on the principle of:
A. Reflection of sound waves
B. Momentum of sound waves
C. Energy of sound waves
D. Refraction of sound waves


A sphere pure rolls on a rough inclined plane with initial velocity \( 2.8 \mathrm{m} / \mathrm{s} \). Find
the maximum distance on the inclined
plane.
velocity
A. 2.74 m
В. 5.48 m
c. 1.38 m
D. \( 3.2 \mathrm{m} \)


The conductivity measurement of a coordination compound of Cobalt (III) shows that it dissociates into 3 ions in
solution. The compound is:
A. Hexaamminecobalt (III) chloride
B. Pentaamminesulphatocobalt (III) chloride
c. Pentaamminechloridocobalt
(III) sulphate
D. Pentaamminechloridocobalt (III) chloride


Assertion
Scum is formed when hard water is
treated with soap.
Reason
Hard water contains calcium and magnesium ions. When soap comes in contact with hard water, these ions
form calcium and magnesium salts of
fatty acids which are insoluble in water. These calcium or magnesium salts precipitate out in the form of scum.
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


In \( N O_{3}^{-} \) ion, the number of bond pair and lone pair of electrons on nitrogen atom is/are:
A .2,2
B. 3,
\( c \cdot 1,3 \)
D. 4,0


The number of beats produced per second by two tuning fork when sounded together is \( 4 . \) One of them has a frequency of \( 250 \mathrm{Hz} \) and if waxed, number of beats become 6. The
frequency of the other tuning fork is
A . 254 \( \mathrm{H} \)
B. 252 нz
c. 248 н на
D. 246 нz


Assertion
IF a resistor is connected to a battery,
the current increases when the
temperature increases.
Reason
For resistors, resistance increases with
increase in temperature.
A . Assertion is incorrect and Reason is correct
B. Both Assertion and Reason are correct but Reason is the correct explanation for Assertion
c. Both Assertion and Reason are correct but Reason is not the correct explanation for assertion
D. Assertion is correct and Reason is incorrect


The cell wall of fungi and bacteria contain
A. N-acetyl glucosamine
B. Glucosamine
c. Mannose
D. Cellulose


Figure shows \( (x, t),(y, t) \) diagram of a
particle moving in 2-dimensions. If the particle has a mass of \( 500 \mathrm{g} \), the force acting on the particle is
A. \( 1 \mathrm{N} \) along \( \mathrm{y} \) -axis
B. 1 N along x-axis
c. \( 0.5 \mathrm{N} \) along \( \mathrm{x} \) -axis
D. 0.5 N along y-axis


A metal sphere of radius \( r_{1} \) charged to a
potential \( V_{1} \) is then placed in a thin
walled uncharged conducting spherical
shell of radius \( r_{2} . \) Determine the
potential acquired by the spherical
shell after it has been connected for
short time to a sphere by a conductor.


The correct order of strength of H-bond
in the following compound:
\( \mathbf{A} \cdot H_{2} O>H_{2} O_{2}>H F>H_{2} S \)
B \( \cdot H F>H_{2} O_{2}>H_{2} O>H_{2} S \)
\( \mathbf{c} \cdot H F>H_{2} O>H_{2} S>H_{2} O_{2} \)
\( \mathbf{D} \cdot H F>H_{2} O>H_{2} O_{2}>H_{2} S \)


If incident ray lies in \( x \) -y plane, reflected ray lies in \( x \) -y plane, then the normal ray will lie in:
A. x-y plane
B. y-z plane
c. x-z plane
D. It does not depend on planes


If \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) and \( \boldsymbol{g}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) are defined
by \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}-[\boldsymbol{x}] \) and \( \boldsymbol{g}(\boldsymbol{x})=[\boldsymbol{x}] \) for
\( \boldsymbol{x} \in \boldsymbol{R}, \) where \( [\boldsymbol{x}] \) is the greatest integer
not exceeding \( x, \) then for every \( x \in \) \( \boldsymbol{R}, \boldsymbol{f}(\boldsymbol{g}(\boldsymbol{x}))= \)
A . \( x \)
в. 0
c. \( f(x) \)
D. \( g(x) \)


Which of the following is not an example of heterogeneous catalytic
reaction?
A. ostwald's process
B. Haber's process
c. combustion of coal
D. Hydrogenation of vegetable oils


Statement - l: He -II has high viscosity
and flows downward.

Statement - II: Liquid helium is used as
cryogenic liquid.
A. Both I and II are true. II is correct
explanation of I.
B. Both I and II are true. II is not correct
explanation of I
C. I is true but II is false
D. I is false but II is true


Arrange the level of difficulty of walking on the following surfaces in increasing order.
a) On wooden floor
b) On concrete
floor
c) On wet marble
d) On dry marble
\( A \cdot c<b<a<d \)
B. \( d<c<b<a \)
\( c \cdot b<a<d<c \)
\( D \cdot a<d<c<b \)


A survey regarding the heights (in cm) of 51 girls of Class \( X \) of a school
was conducted and data was obtained
as shown in table. Find their median.
\( \begin{array}{ll}\text { Height (in cm) } & \text { Number of girls } \\ \text { Less than } 140 & 4 \\ \text { Less than } 145 & 11 \\ \text { Less than } 150 & 29 \\ \text { Less than } 155 & 40 \\ \text { Less than } 160 & 46 \\ \text { Less than } 165 & 51\end{array} \)


Greater is the coagulation power, lesser in coagulating value.
A. True
B. False


Assertion
Thick layers of muscles are present in the wall of alimentary canal.
Reason
These muscles help in the mixing of food materials with the enzymes
coming from different glands in the alimentary canal.
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


Three substances given below are kept in the open for a few days and some
changes were observed.

Which of the substances will show
chemical changes?
A. Eggs
B. Plastic bottle
c. Both eggs and moth balls
D. All eggs, plastic bottle and the moth balls


\( \boldsymbol{C}_{3} / \boldsymbol{4}+\boldsymbol{C}_{5} / \boldsymbol{6}+\boldsymbol{C}_{7} / \boldsymbol{8}+\ldots \ldots= \)
\( ^{\mathbf{A} \cdot \frac{2^{n+1}-n^{2}-n-2}{2(n+1)}} \)
\( ^{\text {В } \cdot \frac{\left.2^{n+2}+n^{2}+n-2\right)}{n+1}} \)
c. \( \frac{\left(3^{n+2}-n^{2}-n-2\right)}{n+1} \)
D. None of these


A sharp image of a distant object is obtained on a screen by using a convex lens. In order to determine the focal
length of the lens. you need to measure the distance between the
A. lens and the object
B. lens and the screen
c. object and the screen
D. lens and the screen and also object and the screen


A dipole of moment \( \vec{p} \) is placed in a uniform electric field \( \vec{E} \). If the force on the dipole is \( \vec{F} \) and the torque is \( \vec{\tau} \). Then
This question has multiple correct options
\( \mathbf{A} \cdot \vec{F}=0 \)
B . \( \vec{F}=|\vec{p}| \vec{E} \)
\( \mathbf{c} \cdot|\vec{\tau}|=\vec{p} . \vec{E} \)
D . \( \vec{\tau}=\vec{p} \times \vec{E} \)


Do all the stars in the sky move? Explain


\( 4.4 \mathrm{g} \) of an oxide of nitrogen gives \( 2.24 \mathrm{L} \) of nitrogen. 60 g of another oxide of nitrogen gives 22.4 L of nitrogen at STP. This data illustrates the law of:
A. conservation of mass
B. multiple proportions
c. constant proportions
D. gaseous volume


Which is not a product of root?
A. Sugarbeet
B. Carrot
c. Radish
D. Potato


The slope of the tangent to the locus \( y=\cos ^{-1}(\cos x) \) at \( x=\frac{\pi}{4} \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B.
\( c \cdot 2 \)
D. -


What are covalent compounds? Write
any three features and give two
examples.


A plane sound wave traveling with velocity 'v' in a medium A reaches a point on the interface of medium \( A \) and
medium B. If velocity of sound in
medium B is \( 2 v \), the angle of incidence
for total internal reflection of the wave
will be greater than \( \left(\sin 30^{\circ}=0.5 \) and \right.
\( \left.\sin 90^{\circ}=1\right) \)
A \( \cdot 15^{\circ} \)
B . 30
\( c \cdot 45^{\circ} \)
D. \( 90^{\circ} \)


Lymph does not contain
A. Leucocytes
B. Plasma
c. Erythrocytes
D. None of the above


At \( 800 \mathrm{K} \) a reaction mixture contained
0.5 mole of \( S O_{2} .0 .12 \) mole of \( O_{2} \) and 5
mole of \( S O_{3} \) at equilibrium. \( K_{c} \) for the
equilibrium \( 2 S O_{2}+O_{2} \rightleftharpoons 2 S O_{3} \) is 833
lit/ mole. If the voiume of the container
is 1 litre, calculate how much \( O_{2} \) is to be added at this equilibrium in order to get
5.2 moles of \( S O_{3} \) at the same temperature.
A. 2.34 mole
B. 0.34 mole
c. 1.43 mole
D. 3.23 mole


Idea of inertia came from:
A. Newton's third law of motion
B. Newton's second law of motion
C. Newton's first law of motion
D. Law of gravitation


An ice cream truck travels around many circular curves at constant speeds.
Each table represents the speed of the truck and radii for some of these curves
During which curve is the magnitude of the truck's acceleration the greatest??
A. Radius of curve - Speed of Truck, \( 30 \mathrm{m}-5 \mathrm{m} / \mathrm{s} \)
B. Radius of curve - Speed of Truck, \( 60 \mathrm{m}-10 \mathrm{m} / \mathrm{s} \)
c. Radius of curve - Speed of Truck, \( 90 \mathrm{m}-15 \mathrm{m} / \mathrm{s} \)
D. Radius of curve - speed of Truck, \( 120 \mathrm{m}-20 \mathrm{m} / \mathrm{s} \)
E. The magnitude of the acceleration for the ice cream truck on all these curves is the same


For a first order gas phase reaction:
\( \boldsymbol{A}_{(\boldsymbol{g})} \rightarrow \boldsymbol{2} \boldsymbol{B}_{(\boldsymbol{g})}+\boldsymbol{C}_{(\boldsymbol{g})} \)
\( P_{0} \) be initial pressure of \( A \) and \( P, \) the
total pressure at time ' \( t^{\prime} . \) Integrated rate
equation is:
A \( \cdot \frac{2.303}{t} \log \left(\frac{P_{0}}{P_{0}-P_{t}}\right) \)
B. \( \frac{2.303}{t} \log \left(\frac{2 P_{0}}{3 P_{0}-P_{t}}\right) \)
c. \( \frac{2.303}{t} \log \left(\frac{P_{0}}{2 P_{0}-P_{t}}\right) \)
D \( \cdot \frac{2.303}{t} \log \left(\frac{2 P_{0}}{2 P_{0}-P_{t}}\right) \)


A living cell is characterized by the presence of several cellular structures
and molecular processes. The correct statement regarding living cells is
A. The nucleus is a characteristic feature of all living cells
B. An mRNA sequence is never completely represented in its translated product
c. Anticodons are located on the rRNA
D. splicing of introns in prokaryotes occurs in the cytoplasm


If \( A \) and \( B \) are independent event such \( \operatorname{that} \boldsymbol{P}\left(\boldsymbol{A} \cap \boldsymbol{B}^{\prime}\right)=\frac{\boldsymbol{3}}{25} \) and \( \boldsymbol{P}\left(\boldsymbol{A}^{\prime} \cap \boldsymbol{B}\right)= \)
\( \frac{8}{25}, \) then \( P(A)= \)
A . \( 1 / 5 \)
в. \( 3 / 8 \)
c. \( 2 / 5 \)
D. \( 4 / 5 \)


How many 10 digits number can be written by using digits (9 and 2) ?
\( \mathbf{A} \cdot^{10} C_{1}+^{9} C_{2} \)
B . \( 2^{10} \)
\( c \cdot^{10} C_{2} \)
D. 10


In oxidation test of sulphur, sulphur gets oxidised to:
A. sodium sulphate
B. sodium sulphite
c. sulphur dioxide
D. sulphuric acid


If the line \( 2 x+3 y+12=0 \) cuts the
axes at \( A \) and \( B \), then the equation of
the perpendicular bisector of \( A B \) is
A. \( 3 x-2 y+5=0 \)
B. \( 3 x-2 y+7=0 \)
c. \( 3 x-2 y+9=0 \)
D. \( 3 x-2 y+8=0 \)


f \( M=\{b, h, i\} ; N=\{b, c, d, e\} \) and
\( s=\{e, f, g\}, \) determine \( M \cap N \cap S \)
and represent it in a venn diagram.


Which of the following is used as an antipyretic medicine?
A. Quinine
B. Paracetamol
c. Luminal
D. Morphine


Electroplating is a very useful process widely used in industry for coating metal objects with a thin layer of :
A. metals
B. non-metals
c. alloy
D. salts


Which of the following is correct for \( X \) rays?
A. It has a beam of electrons
B. It is electromagnetic waves
c. It is positively charged particle
D. It is negatively charged particles


The additive inverse of \( \frac{-a}{b} \) is
A \( \cdot \frac{a}{b} \)
B. \( \frac{b}{a} \)
c. \( \frac{-b}{a} \)
D. None of these


A body starts from rest with an
acceleration \( a_{1} . \) After two seconds
another body \( B \) starts from rest with an
acceleration \( a_{2} \). If they travel equal
distances in fifth second after the
starts of \( A, \) the ratio \( a_{1}: a_{2} \) will be
equal to:
A .9: 5
B. 5: 7
\( \mathrm{c} .5: 9 \)
D. 7: 9


Inductive resistance \( 25 \Omega \) and
capacitive resistance \( 75 \Omega \) are
connected across \( 250 V \) mains in
series. Find the rms potential difference across inductor and capacitor.


Assertion (A): Noble gases have
highest ionization energies in their respective periods. Reason (R): The outermost shell of noble
gases is completely filled.
A. Both \( A \) and \( R \) are correct and \( R \) is the correct explanation of \( A \)
B. Both \( A \) and \( R \) are correct and \( R \) is not the correct explanation of \( A \)
c. \( A \) is true but \( R \) is false
D. \( A \) is false but \( R \) is true


\( N a+K^{+} \) pump represents
A. Active transport
B. Passive transport
c. osmosis
D. simple diffusion


A very dilute saturated solution of a
sparingly soluble salt \( A_{3} B_{4} \) has a
vapour pressure of 20 mm of \( H g \)
at temperature \( T, \) while pure water
exerts a pressure of 20.126 mm \( H g \) at
the same temperature

The solubility product constant of \( \boldsymbol{A}_{3} \boldsymbol{B}_{4} \)
at the same temperature is \( 5.4 \times 10^{-x} \)
value of \( x \) is


causes pimples in both boys and girls at puberty.
A. Increased activity of sweat and sebaceous gland
B. Decreased activity of sweat and sebaceous gland
C. Inactivity of sweat and sebaceous glan
D. Viral infection


Differentiate between.
Sporangiospores and conidiospores


The effective equivalent resistance
between A and B in the figure, is?
A \( \cdot \frac{3}{2} \)
B. \( \frac{2}{3} \) R
c. \( \frac{2}{5} \) R
D. 2 R


Two cars 1 and 2 move with velocities \( v_{1} \)
and \( v_{2} \) respectively, on a straight road in same direction. When the cars are
separated by a distance d, the driver of car 1 applies brakes and the car moves
with uniform retardation \( a_{1} \)
Simultaneously, car 2 starts
accelerating with \( a_{2} \). If \( v_{1}>v_{2} \). Find the minimum initial separation between the cars to avoid collision between
them.


Solve
\( 1.2+2.2^{2}+3.2^{3}+\ldots+n .2^{n}=(n- \)
1) \( 2^{n+1}+2 \)


The function
\( \boldsymbol{f}(\boldsymbol{x})\left\{\begin{array}{l}\frac{\sin \sqrt[3]{\boldsymbol{x}} \log (1+\boldsymbol{3} \boldsymbol{x})}{\left(\tan ^{-1} \sqrt{\boldsymbol{x}}\right)^{2}\left(\boldsymbol{e}^{\boldsymbol{5}} \sqrt[3]{\boldsymbol{x}}-\mathbf{1}\right)} \quad, \boldsymbol{x} \neq \mathbf{0} \\ \boldsymbol{a}, \quad \boldsymbol{x}=\mathbf{0}\end{array}\right. \)
is continuous at \( \boldsymbol{x}=\mathbf{0}, \) if
\( \mathbf{A} \cdot a=0 \)
B. \( a=\frac{5}{3} \)
\( \mathbf{c} \cdot a=2 \)
D. \( a=\frac{3}{5} \)


Mention any two types of electron emission


Write the real and imaginary part of \( (i-\sqrt{3})^{3} \)


One gram of \( ^{226} \) Ra has an activity of nearly \( 1 C \) i. The half life of \( ^{226} R a \) is
A. 1582 yrs
B. 12.5 hrs
c. 140 days
D. \( 4.5 \times 10^{9} \) yrs


What is the distance of the point
\( (p, q, r) \) from the \( x- \) axis.


Show that the vectors \( 2 \vec{i}-\vec{j}+\vec{k}, \vec{i}- \) \( 3 \vec{j}-5 \vec{k} \) and \( -3 \vec{i}+4 \vec{j}+4 \vec{k} \) are the
sides of a right angled triangle.


The half life of \( C-14 \) is 5600 years. \( A \)
sample of freshly cut wood from a tree contains \( 10 \mathrm{mg} \) of \( \mathrm{C}-14 . \) The amount left in the sample after 50000 years is \( (a- \)
\( x) \times 100 . \) The value of \( (a-x) \times 100 \) is :
A . \( 1 \mathrm{mg} \)
B. 2 mg
c. \( 3 \mathrm{mg} \)
D. \( 4 \mathrm{mg} \)


Consider the satellites revolving round the earth at different heights.The ratio of their orbital speed is 3: 2 . If one of them is at a height of \( 200 \mathrm{Km} \), the height of the other satellite is (Radius of the earth is \( R=6400 \mathrm{Km} \)
A. \( 8450 K m \)
в. 845 Кт
c. \( 84.5 K m \)
D. \( 84500 K m \)


In a Young's double slit experiment set
up, source \( S \) of wavelength \( 500 n m \)
illuminates two slits \( S_{1} \) and \( S_{2} \) which
act as two coherent sources. The source
\( S \) oscillates about its own position
according to the equation \( y=0.5 \sin \pi t \)
where \( y \) is in \( \mathrm{mm} \) and \( t \) in seconds. The
minimum value of time \( t \) for which the
intensity at point \( P \) on the screen
exactly infront of the upper slit becomes minimum is :
\( A \cdot 1 s \)
B. \( 2 s \)
\( c .3 s \)
D. \( 1.5 s \)


If a planet consists of a satellite whose
mass and radius were both half that of
the earth, then the acceleration due to
gravity at the surface of the planet would be
A. \( 5.0 \mathrm{ms}^{-2} \)
B. \( 6.5 \mathrm{ms}^{-2} \)
c. \( 7.9 \mathrm{ms}^{-2} \)
D. \( 19.6 \mathrm{ms}^{-2} \)


Uncertainty in position of a 0.25 g particle is \( 10^{-5} \mathrm{m} . \) The uncertainty in its
velocity will be:-
\( \left(h=6.6 \times 10^{-34} J s\right) \)
A. \( 1.2 \times 10^{34} \)
B . \( 2.1 \times 10^{-29} \)
c. \( 1.6 \times 10^{-20} \)
D. \( 1.7 \times 10^{-9} \)


In which animal, blood is red but blood
corpuscles are absent?
A. Cockroach
B. Earthworm
c. Birds
D. Bedbug


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


Which of the following is considered the first thermoplastic?
A. PVC
B. Polystyrene
c. Melamine
D. Celluloid


Explain how Charles' law helps us in finding out the absolute zero value.


Explain why the standard reduction
potentials for \( C u^{2+} \longrightarrow C u^{+} \) and
\( C u^{+} \longrightarrow C u \) are +0.15 and +0.50 volt
respectively, yet that for \( \boldsymbol{C u}^{2} \longrightarrow \boldsymbol{C u} \) is
+0.34 volt.


A student determined to test the law of
gravity for himself walks off a sky scraper \( 320 \mathrm{m} \) high with a stopwatch in hand and starts his free fall (zero initial
velocity). 5 second later, superman
arrives at the scene and dives off the
roof to save the student. What must be
superman's initial velocity in order that he can save the student. [Assume that
the superman's acceleration is that of any freely falling body.] \( \left(g=10 m / s^{2}\right) \)
\( A .98 \mathrm{m} / \mathrm{s} \)
в. \( \frac{275}{3} \mathrm{m} / \mathrm{s} \)
c. \( \frac{187}{2} \mathrm{m} / \mathrm{s} \)
D. It is not possible.


Esterification of the acid \( (P) \) with the
alcohol (Q) gives:
A. only one enantiomer
B. a mixture of diastereomer
c. a mixture of enantiomer
D. only one fraction on fractional distillation


Royal jelly is secreted from
A. Hypopharyngeal gland
B. Salivary gland
C . Milk gland
D. Integumentary gland


When two moles of Hydrogen atoms join together to form a mole of hydrogen molecules in closed rigid vessel with
diathermic walls:
\( \boldsymbol{H}(\boldsymbol{g})+\boldsymbol{H}(\boldsymbol{g}) \longrightarrow \boldsymbol{H}_{2}(\boldsymbol{g}) \)
A \( . w<0 \)
B. \( \Delta U= \) negative
C \( \cdot q_{\text {system}}= \)positive
D. \( q_{\text {surrounding}}= \)negative


Find the integral value of \( x, \) if \( \left|\begin{array}{ccc}\boldsymbol{x}^{2} & \boldsymbol{x} & \mathbf{1} \\ \mathbf{0} & \boldsymbol{2} & \mathbf{1} \\ \boldsymbol{3} & \boldsymbol{1} & \boldsymbol{4}\end{array}\right|=\mathbf{2} \mathbf{8} \)


State whether given statement is True or False
The resistance of intrinsic
semiconductors increase with increase
in temperature
A. True
B. False


The magnetic lines of forces due to the horizontal component of Earth's magnetic field will be
A . circular
B. elliptical
c. curved
D. horizontal and parallel


Prove that \( \sqrt{3} \) is irrational.


Which of the following is oncogenic
virus
A. Human immunodeficiency virus type 2
B. Vesicular stomatitis indiana virus
c. Human herpes virus
D. Epstein-Barr Virus


In an election, candidate \( A \) got \( 75 \% \) of
the total valid votes. If \( 15 \% \) of the total
votes were declared invalid and the
total numbers of votes is 560000 , find
the number of valid vote polled in favour of candidate.
A . 357000
B. 365796
c. 375000
D. 500000


Find the derivative of the following functions (it is to be understood that
\( a, b, c, d, p, q, r \) and \( s \) are fixed non-zero
constants and \( m \) and \( n \) are integers)
\( (a x+b)^{n}(c x+d)^{m} \)


\[
\begin{array}{rlr}
\text { If } \boldsymbol{f}(\boldsymbol{x}) & =\frac{\sin 4 \boldsymbol{x}}{\mathbf{5} \boldsymbol{x}}+\boldsymbol{a} & \text { for } \boldsymbol{x}>\mathbf{0} \\
& =\boldsymbol{x}+\mathbf{4}-\boldsymbol{b} & \text { for } \boldsymbol{x}<\mathbf{0} \\
& =\mathbf{1} & \text { for } \boldsymbol{x}=\mathbf{0}
\end{array}
\]
is continuous at \( x=0 . \) Find \( a \& b \)


The force that must be applied to a steel wire \( 6 m \) long and diameter \( 1.6 m m \) to produce an extension of \( 1 \mathrm{mm}[\boldsymbol{y}= \) \( \left.2.0 \times 10^{11} N . m^{-2}\right] \) is approximate.
A. \( 100 N \)
в. \( 50 N \)
\( c .67 N \)
D. 33.5N


The freezing point on a thermometer is
marked as \( 20^{\circ} \) and the boiling point as
\( 150^{\circ} . \) A temperature of \( 60^{\circ} \mathrm{C} \) on this thermometer will be read as
A \( \cdot 40^{\circ} \)
B . \( 65^{\circ} \)
\( \mathrm{c} \cdot 98^{\circ} \)
D. \( 110^{\circ} \)


A charge \( +q \) is fixed to each of three
corners of a square. On the empty corner a charge \( Q \) is placed such that there is no
net electrostatic force acting on the
diagonally opposite charge. Then:
A. \( Q=-2 q \)
в. \( Q=-2 \sqrt{2} q \)
c. \( Q=-\sqrt{2} q \)
D. \( Q=-4 q \)


We should wash our eyes with clean water between what intervals?
A. Daily
B. Frequently
c. monthly
D. weekly


The number of solutions of the equation
\( \mathbf{2}\left(\boldsymbol{\operatorname { S i n }}^{-1} \boldsymbol{x}\right)^{2}-\mathbf{5} \operatorname{Sin}^{-1} \boldsymbol{x}+\mathbf{2}=\mathbf{0} \) is
A .
в.
\( c \cdot 2 \)
\( D \)


In a common base circuit, if the
collector base voltage is changed by \( \mathbf{0 . 6} \boldsymbol{V}, \) collector current changes by \( 0.02 m A . \) The output resistance will be
A \( \cdot 10^{4} \Omega \)
B \( \cdot 2 \times 10^{4} \Omega \)
c. \( 3 \times 10^{4} \Omega \)
D. \( 4 \times 10^{4} \Omega \)


Match column-I with column-II


\( \boldsymbol{H} \boldsymbol{C l}(\boldsymbol{g}) \) and \( \boldsymbol{H} \boldsymbol{C l}(\boldsymbol{a} \boldsymbol{q}) \) have different
behaviour towards litmus.
A. True
B. False


A ball of mass m moving with velocity collides elastically with another ball of identical mass coming from the opposite direction with velocity \( 2 v \) Their velocities after collision are :
A . \( -v, 2 v \)
в. \( -2 v, v \)
c. \( v,-2 v \)
D. \( 2 v,-v \)


Identify the elements in the Periodic Table:
A: Which shows diagonal relationship to \( B e \)
B: Which shows diagonal relationship to
\( L i \)
A. \( A: A l, B: M g \)
в. \( A: S i, B: M g \)
c. \( A: M g, B: A l \)
D. \( A: A l, B: S i \)


Upward and downward movement of diaphragm occur consecutively. Why?


Velocity of a particle of mass \( 2 \mathrm{kg} \) varies with time \( t \) according to the equation \( \overrightarrow{\boldsymbol{v}}=(2 \boldsymbol{t} \hat{\boldsymbol{i}}+\boldsymbol{4} \hat{\boldsymbol{j}}) \boldsymbol{m} / \boldsymbol{s} . \) Here \( \boldsymbol{t} \) is in seconds.
Find the impulse imparted to the particle in the time interval from \( t=0 \)
to \( t=2 s \)
A \( \cdot 8 \hat{i} N-s \)
В. \( 10 \hat{i} N-s \)
c. \( 12 \hat{i} N-s \)
D. \( 16 \hat{i} N-s \)


How many terms of the series
\( 12,16,20, \dots . . \) must be taken to make
the sum equal to \( 208 ? \)


When 19 is subtracted from the product of \( p \) and \( 4, \) the result is 17
Then, the value of \( p \) is
A \( \cdot \frac{-1}{9} \)
B. \( \frac{1}{9} \)
\( c .-9 \)
D.


\( y=e^{x}+e^{-x} \) prove that \( \frac{d y}{d x}=\sqrt{y^{2}-4} \)


Which of the following polymer is biodegradable?
A. \( f C H_{2}-C=C H-C H_{2} \) t \( _{n} \)
\[
\begin{array}{l}_{C l} \\ \text { (i) }\end{array}
\]
B. \( \quad\left(C H_{2}-C H=C H-C H_{2}-C H_{2}-C H\right) \)
\( \begin{array}{ccc}\mathrm{c} \cdot\left(O-C_{\mathrm{I}}^{H}-C H_{2}-C-O-C H\right. & -C H_{2}-C t_{n} \\ C_{H_{3}} & _{O}^{\mid J} & _{C H_{2} C H_{3}}\end{array} \)


An iron pillar has some part in the form of a right circular cylinder and remaining in the form of a right circular cone. The radius of base of each of cone
and cylinder is \( 8 \mathrm{cm} . \) The cylindrical
part is \( 240 \mathrm{cm} \) high and the conical part is \( 36 \mathrm{cm} \) high. Find the weight of pillar,
if \( 1 \mathrm{cm}^{3} \) of iron weight \( 10 \mathrm{g} \)
A. \( 826.65 \mathrm{kg} \)
B. 705.23 kg
c. \( 506.88 \mathrm{kg} \)
D. none of these


Determine the relationship between the
two molecules shown
A. identical molecules
B. diastereomers
c. enantiomers
D. constitutional iso


Which among the following is not a prokaryote?
A. Nostoc
B. Saccharomyces
c. oscillatoria
D. Mycobacterium


Which is the least electronegative element?
A. Lithium
B. Carbon
c. Boron
D. Fluorine


Choose the incorrect statement.
\( \mathbf{A} \cdot B e C O_{3} \) is kept in the atmosphere of \( C O_{2}, \) since it is least thermally stable.
B. \( B e \) dissolves in alkali forming \( \left[B e(O H)_{4}\right]^{2-} \)
C \( . B e F_{2} \) forms complex ion with \( N a F \) in which \( B e \) goes with cation.
D. \( B e F_{2} \) forms complex ion with \( N a F \) in which \( B e \) goes
with anion.


The species that contain peroxide ions is/are:
This question has multiple correct options
A. \( K O_{2} \)
в. \( \operatorname{Sr} O_{2} \)
\( \mathbf{c} \cdot B a O_{2} \)
D. \( N a_{2} O_{2} \)


In dimethyl ether, oxygen is tetrahedrally hybridized the bond angle
is \( _{--}^{o}(110 / 119) \)


\( \boldsymbol{A}(\boldsymbol{3}, \boldsymbol{2}, \boldsymbol{0}), \boldsymbol{B}(\boldsymbol{5}, \boldsymbol{3}, \boldsymbol{2}), \boldsymbol{C}(-\boldsymbol{9}, \boldsymbol{6},-\boldsymbol{3}) \) are
three points forming a triangle and \( A D \) is the bisectors of the \( \angle B A C \) meet BC
at \( D, \) then co-ordinates of \( D \) are:
\( ^{\mathbf{A}} \cdot\left(\frac{17}{16}, \frac{57}{16}, \frac{28}{16}\right) \)
в. \( \left(\frac{38}{16}, \frac{57}{16}, \frac{17}{16}\right) \)
\( ^{\mathbf{C}} \cdot\left(\frac{38}{16}, \frac{17}{16}, \frac{57}{166}\right) \)
D. \( \left(\frac{57}{16}, \frac{38}{16}, \frac{17}{16}\right) \)


A loop of flexible conducting wire of
length \( l \) lies in magnetic field B which is normal to the plane of loop. A current lis
passed through the loop. The tension developed in the wire to open up is:
A \( \cdot \frac{\pi}{2} B I l \)
в. \( \frac{B I l}{2} \)
c. \( \frac{B I l}{2 \pi} \)
D. \( B I l \)


A body is thrown up with velocity \( u \) to
reach a height \( h \). When the velocity is half the initial velocity, its height from the point of projection is:
A \( \cdot \frac{h}{2} \)
B. \( \frac{h}{4} \)
\( c \cdot \frac{3 h}{4} \)
\( D \)


A boy carrying a box on his head is walking on a level road from one place to another on a straight road is doing no work against gravity.
A. True
B. False


The angle of dip at a place horizontal and vertical components of earth's magnetic field are equal, is :
A \( \cdot 90^{\circ} \)
B . \( 30^{\circ} \)
\( c \cdot 45 \)
D. \( 0^{\circ} \)


\( I=\int_{0}^{\pi / 2} \frac{x \sin x \cos x}{\cos ^{4} x+\sin ^{4} x} d x \)
\( \therefore \boldsymbol{I}=\boldsymbol{\pi}^{2} / \boldsymbol{k} \)
what is k?


\( 100 c m^{3} \) of \( N H_{3} \) diffuses through a pin
hole in 32.5 second. How much time(in
seconds) will \( 60 c c \) of \( N_{2} \) take to diffuse
under same condition?


has 6 valence electrons.
A. Nitrogen
B. Oxygen
c. Chlorine
D. Neon
E. Beryllium


The total surface area of a solid cylinder
is \( 462 \mathrm{cm}^{2} \). Its curved surface area is
one third of total surface area. Find the
volume of the cylinder.
A \( \cdot 229 ~ c m^{3} \)
В. \( 509 \mathrm{cm}^{3} \)
\( \mathbf{c} \cdot 439 \mathrm{cm}^{3} \)
D. \( 539 ~ c m^{3} \)


The adiabatic and isothermal volume
elasticities \( E_{\phi} \) and \( E_{\theta} \) of a gas, are
related as
\( ^{\mathbf{A}} \cdot \frac{E_{\phi}}{E_{\theta}}=\gamma \)
в. \( \frac{E_{\theta}}{E_{\phi}}=\gamma \)
c. \( E_{\phi}-E_{\theta}=\gamma \)
D. \( E_{\theta}-E_{\phi}=\gamma \)


Solve \( \frac{\mathbf{6 x}+\mathbf{1}}{\mathbf{3}}+\mathbf{1}=\frac{\boldsymbol{x}-\mathbf{3}}{\mathbf{6}} \)


Member of Dipnoi are native of
A. India.
B. Africa and Australia.
c. New Zealand
D. None of the above


If the dr's the line are \( (1+\lambda, 1-\lambda, 2) \)
and it makes an angle \( 60^{\circ} \) with the \( Y \) -
axis then \( \lambda \) is
A \( .1 \pm \sqrt{3} \)
B. \( 4 \pm \sqrt{5} \)
c. \( 2 \pm 2 \sqrt{3} \)
D. \( 2 \pm \sqrt{5} \)


(i) Find the real values of \( x \) and \( y \) for
which \( z_{1}=9 y^{2}-4-10 i x \) is complex
conjugate of each other.
(ii) Find the value of \( x^{4}-x^{3}+x^{2}+ \)
\( 3 x-5 \) if \( x=2+3 i \)


Assertion
Osmotic pressure of \( 0.1 N \) urea solution
is less than that of \( 0.1 M \) NaCl
solution.
Reason
Osmotic pressure is not colligative property.
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


If \( 10,000 V \) are applied across an \( X \) -ray tube, find the ratio of wavelength of the incident electrons and the shortest
wavelength of \( X \) -ray coming out of the X-ray tube, given \( e / m \) of electron \( = \) \( 1.8 \times 10^{11} C k g^{-1} \)
\( \mathbf{A} \cdot 1: 10 \)
B. 10: 1
c. 5: 1
D. 1: 5


Which of the following elements shows allotropy?
\( A \cdot \) Mg
B. cs
\( c \cdot s n \)
D. zn


Histiocyte of brain is a
A. Reticular cell
B. Microglial cell
c. Hessel's granule
D. Monocyte


Three concentric conducting spherical
shells of radii \( \boldsymbol{R}, 2 \boldsymbol{R} \) and \( \boldsymbol{3} \boldsymbol{R} \) carry
charges \( Q,-2 Q \) and \( 3 Q, \) respectively
Compute the potential at \( r=R \), and
the charges on the spheres of radii \( \boldsymbol{R} \)
and \( 3 R \)
A \( \cdot \frac{Q+2 Q_{1}}{12 \pi \varepsilon_{0} R}, Q_{1}=\frac{Q}{4}, Q_{2}=\frac{7 Q}{2} \)
в. \( \frac{Q+2 Q_{1}}{12 \pi \varepsilon_{0} R}, Q_{1}=\frac{Q}{2}, Q_{2}=\frac{7 Q}{2} \)
c. \( \frac{Q+2 Q_{1}}{12 \pi \varepsilon_{0} R}, Q_{1}=\frac{Q}{2}, Q_{2}=\frac{7 Q}{4} \)
D. \( \frac{Q+2 Q_{1}}{12 \pi \varepsilon_{0} R}, Q_{1}=\frac{Q}{4}, Q_{2}=\frac{7 Q}{4} \)


A charge \( q \) is in a circular motion
perpendicular to the magnetic field B. The angular velocity of charge in radian per second will be
\( \mathbf{A} \cdot \frac{q B}{m} \)
В. \( \frac{q B}{\mu m} \)
c. \( \frac{q}{m B} \)
D. \( \frac{q m B}{2 \pi} \)


Sodium extract of thioruea will be
colour in Lassaigne's test.
A. Blue
B. Redd
c. Yellow
D. Green


What is electrolysis?
A. Decomposition of substance by passing electricity
B. Decomposition of substance by heating
C. Decomposition of substance by redox reaction
D. Addition of hydrogen


A group of similar cells performing the similar functions are known as
A . Cell
B. Organ
c. Tissue
D. None of the above


Inertia of a body has direct dependence
on:
A. Velocity
B. Volume
c. Mass
D. Density


Let \( M \) and \( N \) be two \( 3 \times 3 \) be two non-
singular skew symmetric matrices
such that \( M N=N M \) further, if \( M \neq \)
\( n^{2} \). If \( P T \) denotes the transpose of \( P \) then
\( M^{2} N^{2}\left(M^{T} N\right)^{-1}(M N)^{-1} T \) is equal to


Identify the decimal and whole number
from the following.
\( \mathbf{0 . 6 5 1} \)


A virtual image is
A. always erect
B. either erect or inverted
C . always inverted
D. neither erect nor inverted


is a mixture of sand and clay.
A . clay
в. Humus
c. silt
D. Loam


When a source emits light of particular wavelength and the source is moving away from us, the wavelength appears
A . Longer
B. First longer and then shorter
c. Unaltered
D. shorter


Which one is more stable in the
following pairs of complexes? Give
reasons.
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{O}_{2}\right)_{6}\right]^{4-} \) and \( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{O}_{2}\right)_{\boldsymbol{6}}\right]^{3-} \)
ii) \( \boldsymbol{K}_{4}\left[\boldsymbol{F} e(\boldsymbol{C} \boldsymbol{N})_{6}\right] \) and \( \boldsymbol{K}_{3}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{6}\right] \)
\( \left(\text { iii) }\left[\boldsymbol{C O}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right]^{2+} \) and \right.
\( \left[\boldsymbol{C O}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right]^{2+} \)


A body of mass 2 kg starts with an initial velocity \( 5 \mathrm{m} / \mathrm{s} \). If the body
is acted upon by a time dependent force
(F) as shown in the figure, then work
done on the body in 20 s is


and that of an ideal Voltmeter is
infinite. A Voltmeter and an Ammeter
are connected in the circuit as shown.
Resistance of ammeter is say \( \boldsymbol{R} / \mathbf{1} \mathbf{0} \) and
that of Voltmeter is \( 10 R \). Then:
A. Percentage error in the reading of Ammeter (compared to that measured, if both Ammeter and voltmeter were ideal) is \( 1.0 \% \)
B. Percentage error in the reading of voltmeter is \( 10.0 \% \)
c. Both (a) and
(b) are correct
D. Both
(a) and
(b) are wrong


The differential equation of the family of circles with fixed radius 5 units and
centre on the line \( y=2 \) is
A \( \cdot(x-2)\left(y^{1}\right)^{2}=25-(y-2)^{2} \)
B . \( (y-2)\left(y^{1}\right)^{2}=25+(y-2)^{2} \)
C \( \cdot(y-2)^{2}\left(y^{1}\right)^{2}=25-(y-2)^{2} \)
D. \( (x-2)^{2}\left(y^{1}\right)^{2}=25-(y-2)^{2} \)


A magnetic needle is kept in a
nonuniform magnetic field. It
A. may experience a force but certainly not a torque
B. may experience a torque but certainly not a force
C. may experience both a torque as well as force
D. will certainly experience neither a force not a torque


Which of the following samples will have the same number of atoms as 40 g calcium?
A. 24 g magnesium
B. 64 g silphur
c. 14 g nitrogen
D. 8 g oxygen


Which among the following has the largest dipole moment
A \( . N H_{3} \)
в. \( H_{2} \) 0
c. \( H I \)
\( \mathrm{D} \cdot \mathrm{SO}_{3} \)


Two identical balls each of mass \( 4 \mathrm{kg} \) are moving towards each other with speeds \( 2 \mathrm{m} / \mathrm{s} \) and \( 3 \mathrm{m} / \mathrm{s} \) respectively they undergo head on perfectly elastic collision. the impulse imparted by one ball on other is:
A . \( 12 \mathrm{Ns} \)
B. 8 Ns
c. \( 20 \mathrm{Ns} \)
D. \( 40 \mathrm{Ns} \)


A sample of a hydrate of barium chloride weighing \( 61 \mathrm{g} \) was heated until all the water of hydration is removed. The dried sample weighed 52 g. The formula of the hydrated salt is : (atomic mass, \( \mathrm{Ba}=137 \mathrm{amu}, \mathrm{Cl}=35.5 \text { amu }) \)
A. BaCl \( _{2} .4 \mathrm{H}_{2} \mathrm{O} \)
B. BaCl_.2H_O
c. ваСг_на 0
D. BaCl \( _{2} .3 \mathrm{H}_{2} \mathrm{O} \)


The complement of \( \left(90^{\circ}-a\right) \) is :
A . -
B. \( \left(90^{\circ}+a\right) \)
C. \( \left(90^{\circ}-a\right) \)
D.


An ideal gas is taken around the cycle
ABCDA as shown in figure. The net work done during the cycle is equal to:
A. zero
B. positive
c. negative
D. we cannot predict


Stem elongation caused by
A. Gibberellin and florigen
B. Auxin and gibberellin
C. Florigen and kinin
D. Kinin and auxin


A zero vector has
A. any direction
B. no direction
C . many direction
D. None of these


Carbonyl compounds react with phenyl hydrazine to form:
A . oxime
B. phenyl hydrazone
c. hydrazone
D. semicarbazone


What is the atomic number (Z) of the
noble gas that reacts with fluorine?
A . 54
B. 10
c. 18
D. 2


Some materials have electrons that are
tightly bound to the nucleus and are not free to travel within the substance.
These materials are called
A. conductors
B. insulators
c. semiconductors
D. none of these


Find the value of \( x \) in each of the
following figure, if \( \boldsymbol{I} \| \boldsymbol{m} \)


As shown in the experimental setup,
two cells with the same \( e m f E \) and
different internal. resistance \( r_{1} \) and \( r_{2} \)
are connected in series to an external
resistance \( \boldsymbol{R} \). Value of \( \boldsymbol{R} \) so that the
potential difference across the cell be
zero, is :
\( \mathbf{A} \cdot r_{1}+r_{2} \)
в. \( \frac{r_{1}}{r_{2}} \)
\( c \cdot r_{1}-r_{2} \)
\( D \cdot r_{1} r_{2} \)


Bottle of \( \mathbf{P} \mathrm{Cl}_{3} \) is kept stoppered
because it :
A. explodes
B. gets oxidized
\( c . \) is volatalised
D. reacts with moisture


The solution of the differential equation, \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=(\boldsymbol{x}-\boldsymbol{y})^{2}, \) when \( \boldsymbol{y}(\mathbf{1})=\mathbf{1}, \) is
\( ^{\mathrm{A}} \cdot \log _{e}\left|\frac{2-y}{2-x}\right|=2(y-1) \)
\( ^{\mathbf{B}} \cdot \log _{e}\left|\frac{2-x}{2-y}\right|=x-y \)
c. \( -\log _{e}\left|\frac{1+x-y}{1-x+y}\right|=x+y-2 \)
D. \( -\log _{e}\left|\frac{1-x+y}{1+x-y}\right|=2(x-1) \)


In ecotone which species become abundant?
A. Sibling species
B. Endemic species
c. Rare species
D. Edge species


Which of the following is/are unit of time
A. Solar day
B. Hour
c. Mean solar day
D. All


Write the correct option by observing
the figures.
A. Magnetic field in \( A \) stronger.
B. Magnetic field in \( B \) stronger.
C. Magnetic field in \( A \) and \( B \) are same
D. Magnetic field in \( A \) and \( B \) are weaker.


In chordates, which of the following
helps in locomotion?
A. Jointed chitinous appendages attached to muscles
B. Muscles attached to an exoskeleton
C. Paired muscles attached to an endoskeleton
D. All of the above
E. None of the above


The pulley and string are shown in Fig. smooth and of negligible mass. For the
system to remain in equilibrium, the
angle \( \theta \) should be
\( A \cdot 0^{0} \)
B. \( 30^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 60^{\circ} \)


Given J-tube has \( 2.4 ~ m L \) of air at a
pressure of 1 atm. On adding mercury,
volume of air is reduced to \( 1.9 m L \) as
shown. Difference in the level of mercury
in two columns is?
\( A .700 m m \)
В. \( 200 \mathrm{mm} \)
\( c .900 m m \)
D. \( 760 \mathrm{mm} \)


The graph below shows potential energy and kinetic energy plotted against time of a ball thrown straight up from the 10
storey building.
At what point on the graph does the
potential energy of the object equal the
kinetic energy of the object?
\( A \cdot A \)
в. \( B \)
\( c . c \)
D. \( D \)
E. \( E \)


Which of following heavy metals does not belong to a category of chemical pollutants?
A. \( C d \)
в. \( H g \)
c. \( N i \)
D. \( F e \)


Two identical copper spheres carrying chatges \( +Q \) and \( -9 Q \) separated by a certain distance has attractive force \( F \)
If the spheres are allowed to touch eacxh other and moved to distance of
separation 'x'. So that the force between
them becomes \( \frac{4 F}{9} . \) Then \( x \) is equal to
\( A \cdot d \)
B. 2d
\( c \cdot d / 2 \)
D. 4d


If the speed of body moving in circle is doubled and the radius is halved, its
centripetal acceleration becomes
A. Eight times
B. Four times
c. Two times
D. Sixteen times


Consider fusion of \( H e \) plasma. At what
temperature fusion at a distance 2 fm
is possible
A \( .2 .23 \times 10^{9} K \)
В. \( 22.3 \times 10^{9} K \)
\( \mathbf{c} \cdot 2.23 \times 10^{8} K \)
D. none of these


n given figure \( C \) is centre of circle. \( A O \)
and \( B O \) are tangents to circle. \( C M \perp \)
\( A B \)
\( \mathbf{f} \boldsymbol{A} \boldsymbol{C}=\boldsymbol{A} \boldsymbol{B}=\mathbf{6} \boldsymbol{c m}, \) then find \( \boldsymbol{A} \boldsymbol{M} \)
\( A \cdot 3 c m \)
8. 4 ст
\( c .5 \mathrm{cm} \)
D. \( 6 \mathrm{cm} \)


Assertion: The Gibbs free-energy equation can be used to predict the solubility of a solute. Reason: The solubility of most salts increases as temperature increases.
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false


Let \( \boldsymbol{A}=\{\mathbf{1}, \mathbf{2}, \mathbf{3}, \mathbf{4}, \mathbf{5}, \mathbf{6}\} \) and let \( \boldsymbol{R}= \)
\( \{(a, b): a, b \in A \text { and } b=a+1\} . \) Show
that \( R \) is not transitive.


Bleaching powder has the molecular
formula:
A \( \cdot C a C l O_{3} \)
B. Caclo
c. \( C a O C l_{2} \)
\( \mathbf{D} \cdot \operatorname{Ca}(O C l)_{2} \)


f \( y=\left(\tan ^{-1} x\right)^{2}, \) show that \( (1+ \)
\( \left.x^{2}\right)^{2} \frac{d^{2} y}{d x^{2}}+2 x\left(1+x^{2}\right) \frac{d y}{d x}-2=0 \)


A uniform cylindrical wire is subjected to a longitudinal tensile stress of \( 5 \times \) \( 10^{7} N / m^{2} . \) Young's modulus of the
material of the wire is \( 2 \times 10^{11} N / m^{2} \)
The volume change in the wire is \( 0.02 \% \)
The fractional change in the radius is
A. \( 0.25 \times 10^{-4} \)
B. \( 0.5 \times 10^{-4} \)
c. \( 0.1 \times 10^{-4} \)
D. \( 1.5 \times 10^{-4} \)


A box contains 6 green balls, 4 blue balls and 5 yellow balls. A ball is drawn at random. Find the probability of
(a) Getting a yellow ball.
(b) Not getting a green ball.
A \( \cdot \frac{1}{5}, \frac{1}{3} \)
в. \( \frac{4}{15}, \frac{3}{15} \)
c. \( \frac{1}{3}, \frac{3}{5} \)
D. \( \frac{2}{3}, \frac{1}{15} \)


The equivalent inductance between \( \mathbf{A} \)
and B is
\( A \)
B. 1
\( c \cdot 3 H \)
\( D \)


Imagine a light planet revolving around a very massive star in a circular orbit or
radius \( R \) with a speed of revolution \( T . \) If the gravitational force of attraction between the planet and the star is proportional to \( \boldsymbol{R}^{-\mathbf{5} / 2}, \) then
A \( \cdot T^{2} \) is proportional to \( R^{2} \)
B . \( T^{2} \) is proportional to \( R^{7 / 2} \)
c. \( T^{2} \) is proportional to \( R^{3 / 2} / 2 \) proportional
D. \( T^{2} \) is proportional to \( R^{3.75} \)


Which of the following substances are not absorbed into the lymphatic
system?
A. Fatty acids
B. Glycerol
c. Fat soluble vitamins
D. water soluble vitamins


The speed-time graph for a body is
shown in the given figure. The
displacement between \( t=1 \) second
and \( t=7 \) second is nearest to:
\( \mathbf{A} \cdot 1.5 m \)
В. 2 т
\( c .3 n \)
D. \( 4 m \)


What is an intrinsic semi conductor?
Give two examples.


If \( A=\left[\begin{array}{cc}2 & -1 \\ -1 & 2\end{array}\right], \) then the general
solution of \( \sin \theta=\left|A^{2}-4 A+3 I\right| \) is
A \( . n \pi \)
B \( \cdot 2 n+1 \frac{\pi}{2} \)
c. \( n \pi+(-1)^{n} \frac{\pi}{2} \)
D. \( 2 n \pi, n \epsilon z \)


Refraction occurs due to:
A. Change in direction of light
B. Change in speed of light
C . Change in quality of light
D. All


Plutons are the members of solar
system with highly titled orbits. This statement is
A. True
B. False


The area of an equilateral triangle is
\( 49 \sqrt{3} c m^{2} . \) Taking each angular point as
centre, a circle is described with radius
equal to half the length of the side of the triangle as shown in figure. Find the
area of the triangle not included in the circle. [Take \( \sqrt{\mathbf{3}}=\mathbf{1 . 7 3}] \)
\( \mathbf{A} \cdot 5.67 \mathrm{cm}^{2} \)
B. \( 6.12 \mathrm{cm}^{2} \)
c. \( 7.77 \mathrm{cm}^{2} \)
D. \( 7.98 \mathrm{cm}^{2} \)


An aircraft executes a horizontal loop at
a speed of \( 720 \mathrm{km} / \mathrm{h} \) with its wings
banked at \( 15^{0} . \) What is the radius of the
loop?


The phenomenon of echo of sound waves is due to:
A. Reflection
B. Interference
c. Diffraction
D. All of the above


Anaerobic bacteria digest animal waste and produce biogas(Change-A). The biogas is then burnt as fuel(Change-B). The following statements pertain to these changes. Choose the correct one.
A. Process-A is a chemical change
B. Process-B is a chemical change
C. Both processes A and B are chemical changes
D. None of these processes is a chemical change


The relation \( R \) is defined in \( A= \)
\{1,2,3\} by \( a R b \) if \( \left|a^{2}-b^{2}\right| \leq 5 . \) Which
of the following is false?
A \( \cdot R=\{(1,1),(2,2),(3,3),(2,1),(1,2),(2,3),(3,2)\} \)
В. \( R^{-1}=R \)
C. Domain of \( R=\{1,2,3\} \)
D. Range of \( R=\{5\} \)


Which of the following metal gives hydrogen with all of these reactants:
water, acids, alkalis?
A. \( F e \)
в. \( Z n \)
c. \( M g \)
D. Na


Two wires of same length are shaped into square and a circle. if they carry same current ratio of magnetic moment is
A . \( 2: \pi \)
в. \( \pi: 3 \)
\( c \cdot \pi: 4 \)
D. \( 1: \pi \)


Assertion
As temperature increases, heat of
reaction also increases for exothermic
as well as for endothermic reactions.
Because
Reason
\( \Delta \mathrm{H} \) varies with temperature as given by
\( \Delta H_{2}\left(a t T_{2}\right)=\Delta H_{1}\left(a t T_{1}\right)+ \)
\( \Delta C_{P}\left(T_{2}-T_{1}\right) \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


An electric dipole is placed at the centre of a sphere, choose the correct options:
A. electric field is zero at every point on the surface
B. flux is zero across the surface
C. no circle is present in the sphere which is equipotentia
D. none of the above


The equilibrium constant for the reaction \( N_{2}(g)+O_{2}(g) \leftrightharpoons 2 N O(g) \) is
\( 4 \times 10^{-4} \) at \( 2000 \mathrm{K} . \) In the presence of a
catalyst, the equilibrium is attained three times faster. The
equilibrium constant in the presence of the catalyst at \( 2000 \mathrm{K} \) is:
A. \( 40 \times 10^{-4} \)
B. \( 4 \times 10^{-4} \)
c. \( 4 \times 10^{-3} \)
D. \( 4 \times 10^{-8} \)


A silver wire has temperature
coefficient of resistivity \( 4 \times 10^{-3} /^{\circ} C \)
and its resistance at \( 20^{\circ} \mathrm{C} \) is \( 10 \Omega \)
Neglecting any change in dimensions due to the change in temperature, its
resistance at \( 40^{\circ} \mathrm{C} \) is?
A . \( 0.8 \Omega \)
в. \( 1.8 \Omega \)
\( c .9 .2 \Omega \)
D. \( 10.8 \Omega \)
E . \( 11.6 \Omega \)


A gas at a pressure of 325 torr exerts a
force of

Non an area of \( 5.5 m^{2} \)
A \( \cdot 2 \times 10^{3} \)
B. 10
\( c \cdot 1.0 \)
D. \( 2.4 \times 10^{5} \)


Find the area cut off from the parabola
\( 4 y=3 x^{2} \) by the straight line \( 2 y= \)
\( 3 x+12 \)
A. 25 sq.units
B. 27sq.units
c. \( 36 s q \).units
D. 16 sq.units


Let \( A \) be the area bounded by the curve
\( \boldsymbol{y}=(\tan x)^{n} \) for \( n>2 \) and the lines
\( x=0 \) and \( y=0 \) and \( x=\frac{\pi}{4} \) then the
range of \( \boldsymbol{A}_{\mathbf{1 0}} \) is
\( ^{\mathrm{A}} \cdot\left(\frac{1}{20}, \frac{1}{16}\right) \)
B. \( \left(\frac{1}{18}, \frac{1}{16}\right) \)
\( ^{c \cdot}\left(\frac{1}{14}, \frac{1}{10}\right) \)
D. \( \left(\frac{1}{22}, \frac{1}{18}\right) \)


The probability of event is 1
A. Sure
B. Impossible
c. exclusive
D. mutually exclusive


Which tax is paid to government for the sales of certain goods and services?
A. VAT
B. sales tax
c. income tax
D. business tax


If \( \boldsymbol{y}=\frac{1}{\mathbf{3 - 4 x}} \) then \( \boldsymbol{y}_{n}(1) \) equals
A .
B \( \cdot(-1)^{n+1} n ! \)
c. \( n ! 4^{n}(-1)^{n+1} \)
D. None of these


Check whether the given equation is a quadratic equation
\( x+\frac{3}{x}=x^{2} \)


At a constant pressure of 200,000 Pa a gas expands from a volume of 1.0 cubic
meter to 2.0 cubic meters.

If the gas absorbs \( 100,000 J \) of energy during this expansion, what is the change in internal energy of the gas during the expansion?
\( \mathbf{A} \cdot 500,000 J \)
в. \( 300,000 J \)
c. \( -500,000 J \)
D. \( -300,000 J \)
E . \( -100,000 J \)


When the gases; sulphur dioxide and hydrogen sulphide mix in the presence
of water, the reaction \( S O_{2}+2 H_{2} S \rightarrow \)
\( 2 H_{2} O+3 S \) occurs
Here hydrogen sulphide is acting as:
A. an oxidizing agent
B. a reducing agent
c. a dehydrating agent
D. a catalyst