and \( B \) inside a sphere of radius \( R . A \)
small ball slips along wire. The time
taken by the ball to slip from \( \boldsymbol{A} \) to \( \boldsymbol{B} \) will
be:
A \( \frac{2 \sqrt{g r}}{g \cos \theta} \)
\( \frac{2 \sqrt{g R \cos \theta}}{g} \)
\( \mathbf{c} \cdot 2 \sqrt{R / g} \)
D. \( \frac{g R}{\sqrt{g \cos \theta}} \)


Which may be attached with adenine base in RNA?
A. Guanine
B. Cytosine
c. Uracil
D. Thymine


A plane wavefront of wavelength \( \lambda \) is incident on a single slit of width a. The
angular width of principal maximum
is?
\( A \cdot \frac{\lambda}{a} \)
в. \( \frac{2 \lambda}{a} \)
\( c \cdot \frac{a}{\lambda} \)
D. \( \frac{a}{2 \lambda} \)


Solve: \( \frac{x^{2}-(y-z)^{2}}{(x+z)^{2}-y^{2}}+\frac{y^{2}-(x-z)^{2}}{(x+y)^{2}-z^{2}}+ \)
\( \frac{z^{2}-(x-y)^{2}}{(y+z)^{2}-x^{2}}= \)
\( A \)
B.
\( c \cdot 1 \)
\( D \)


As the temperature of a conductor
increases, its resistivity and
conductivity change. The ratio of resistivity to conductivity
A. increases
B. decreases
c. remains constant
D. may increase or decrease depending on the actual temperature


Mathematical relation for conversion of
Temperature from Celsius scale to
Fahrenheit scale is:
A \( \cdot F=\frac{5}{9} C+32 \)
B . \( C=\frac{9}{5} F+32 \)
c. \( F=\frac{9}{5} C+32 \)
D. \( F=\frac{9}{5} C-32 \)


What of the following is true of the
virus?
A. They are obligate intracellular parasites.
B. They are bigger than bacteria.
C. They contain both DNA and RNA.
D. They are non-specific for their hosts.
E. They can reproduce in non-living medium.


When we make tea, coffee or lemonade,
particles of one type of matter get into the spaces between particles of the other. Why?
A. Particles are too large
B. Particles do not have space among them
c. There are enough space between particles of matter
D. None of above.


Optical fibres transmit light along its axis, by the process of :
A. total internal reflection
B. refraction
c. interference
D. diffraction


Aluminium is diagonally related to
A \( . L i \)
B. \( S \) i
\( c . B e \)
D. \( B \)


Select the correct statement(s)
pertaining to Chipko movement.
A. It was led by sunderlal Bahuguna.
B. It was a tree hugging movement.
c. It commenced in the Tehri-Garhwal district
D. All of the above


If \( y=\left[\log \log \sin x^{\circ}\right]^{7}, \) find \( \frac{d y}{d x} \)
A \( \cdot \frac{6 \pi}{180^{\circ}}\left[\log \left(\log \sin x^{\circ}\right)\right]^{7} \cdot \frac{\tan x^{\circ}}{\log \sin x^{\circ}} \)
в. \( \frac{7 \pi}{180^{\circ}}\left[\log \left(\log \sin x^{\circ}\right)\right]^{6} \cdot \frac{\cot x^{\circ}}{\log \sin x^{\circ}} \)
c. \( \frac{\pi}{30^{\circ}}\left[\log \left(\log \sin x^{\circ}\right)\right]^{7} \frac{\cot x^{\circ}}{\log \sin x^{\circ}} \)
D. none of these


Write any two uses of isotopes.


Find the derivative of the following functions from first principle \( \frac{1}{x^{2}} \)


Common salt consists of which non-
metal?
A. lodine
B. Carbon
c. oxygen
D. Sulphur


Blasting of TNT is done by mixing it with:
A . \( \mathrm{NH}_{4} \mathrm{Cl} \)
в. \( \mathrm{NH}_{4} \mathrm{NO}_{3} \)
c. \( \mathrm{NH}_{4} \mathrm{NO}_{2} \)
D. \( \left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4} \)


While studying the saponification reaction, what do you observe when you mix an equal amount of colourless vegetable oil and \( 20 \% \) aqueous solution of \( N a O H \) in a beaker?
A. The colour of the mixture has become dark brown
B. A brisk effervescence is taking place in the beaker
c. The outer surface of the beaker has become hot
D. The outer surface of the beaker has become cold


Five identical capacitor plates, each of
area \( A, \) are arranged such that the
adjacent plates are at a distance \( \boldsymbol{d} \)
a part. The plates are connected to a
source of emf \( V \) as shown in figure.
Match the following?


Assertion: Cimetidine is an antacid.
Reason: Antacid increases secretion of
HCl from gastric cells.
A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true but reason is not the correct explanation of assertion.
c. If assertion is true but reason is false.
D. If both assertion and reason are false


\( \mathbf{f} \boldsymbol{A}=\left[\begin{array}{lll}\mathbf{1} & \mathbf{4} & \mathbf{0} \\ \mathbf{2} & \mathbf{5} & \mathbf{0} \\ \mathbf{3} & \mathbf{6} & \mathbf{0}\end{array}\right] \) and \( \boldsymbol{B}=\left[\begin{array}{lll}\mathbf{3} & \mathbf{2} & \mathbf{1} \\ \mathbf{1} & \mathbf{2} & \mathbf{3} \\ \mathbf{4} & \mathbf{5} & \mathbf{6}\end{array}\right] \)
and \( C=\left[\begin{array}{lll}3 & 2 & 1 \\ 1 & 2 & 3 \\ 7 & 8 & 9\end{array}\right], \) Then evaluate
\( \operatorname{matrix} \boldsymbol{A B}-\boldsymbol{B C} \)


Assertion
Helium shows only positive deviations
from ideal behaviour.
Reason

Helium is an inert gas.
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


Solve \( \sin x+\cos x=1+\sin x \cdot \cos x \)
then \( 2 n \pi \pm \frac{\pi}{4} \)
If true then enter 1 and if false then
enter 0


If \( \mathbf{A} \) and \( \mathbf{B} \) are two events such that
\( \mathbf{P}(\mathbf{A})=\frac{\mathbf{3}}{\mathbf{4}} \) and \( \mathbf{P}(\mathbf{B})=\frac{\mathbf{5}}{8}, \) then
This question has multiple correct options
A \( \cdot 1 \geq P(A \cup B) \geq \frac{3}{4} \)
в. \( P\left(A^{\prime} \cup B\right) \leq \frac{1}{4} \)
c. \( \frac{3}{8} \leq P(\mathrm{A} \cap B) \leq \frac{5}{8} \)
D. \( \frac{1}{8} \leq P\left(A \cap B^{\prime}\right) \leq \frac{3}{8} \)


Choose the correct structure for
propane.
\( \mathbf{A} \cdot C H_{3}-C H_{2}-C H_{3} \)
в. \( C H_{3}-\underset{O}{\|}-O H \)
c. \( C H_{3}-O-C_{3} H_{7} \)
D. \( C H_{3}-C-C H_{3} \)
॥
监
\( o \)
E \( \cdot C H_{3}-C H_{2}-N H_{2} \)


Write the quadratic polynomial with zeros -2 and \( \frac{1}{3} \)


The door of a working refrigerator inside
a closed room was left open. Then
A. The room will be cooled slightly
B. The temperature of the room will be lowered
C. The temperature of the room will not be affected
D. The room will be warmed up gradually


All covalent compounds possess coordinate covalent bonds.
A. True
B. False


A condenser of capacity \( 2 \mu F \) is charged
to a potential of \( 200 \mathrm{V} \). It is now connected to an uncharged condenser of capacity \( 3 \mu F \). The common potential is :
A . 200
B. \( 100 \mathrm{V} \)
c. \( 80 v \)
D. 40


Which derivative of coal is more viscous
in nature?
A. coke
B. Coal tar
c. coal gas
D. Graphite


Find the sum of the total number of
\( P-\hat{P}-P \) angle and \( P-P \) sides in \( P_{4} \)
molecule.


Find the first term of a G.P. in which
\( S_{8}=510 \) and \( r=2 \)


A system of identical cylinder and plates is shown in figure. All the cylinders are identical and there is no slipping at any contact. The velocity of lower and the upper plates are \( v \) and \( 2 v \) respectively, as shown. Then the ratio of angular speeds of the upper cylinders to lower cylinder is:
A \( \cdot \frac{1}{3} \)
в.
\( c \)
D. None of these


A work is done by 10 workers in 6 hours? How many workers will be required to do the same work in 4 hrs?
A . 10
B . 15
c. 20
D. None of these


Which of the following units is not a
base unit?
A. metre
B. candela
c. ampere
D. pascal


Select correct statements about the
given reaction?
A. In the conversion of (C) to (D) attacking reagent is electron deficient.
B. If \( C C l_{4} \) is used in the reaction instead of \( C H C l_{3} \), the
product is soluble in \( N a H C O_{3} \) solution.
\( c \)
\[
\text { Product }(\mathrm{D}) \frac{\mathrm{AC}_{2} \mathrm{O}}{\mathrm{ACONa}} \rightarrow \stackrel{\mathrm{H}+}{\longrightarrow} \square
\]
D. Conversion of (B) to (C) is electrophilic aromatic substitution reaction


Assertion
Sulphide ores are concentrated by froth flotation process.
Reason
Pine oil forms emulsions in water.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


What is the relationship between the groups in the following molecule?
A. They are cis to one another.
B. They are trans to one another.
C. They are axial to one another
D. They are equatorial to one another.


In the Bohr model of a hydrogen atom, the centripetal force is furnished by the coulomb attraction between the proton
and the electron. If \( a_{0} \) is the radius of
the ground state orbit, \( m \) is the mass
and \( e \) is the charge on the election and
\( \varepsilon_{0} \) is the vacuum permittivity, the speed
of the electron is?
A. 0
B. \( \frac{e}{\sqrt{\varepsilon_{0} a_{0} m}} \)
c. \( \frac{e}{\sqrt{4 \pi \varepsilon_{0} a_{0} m}} \)
D. \( \sqrt{\frac{4 \pi \varepsilon_{0} a_{0} m}{e}} \)


Evaluate the following:
\( \int_{0}^{5}(x+1) d x \)


A beam of protons enters a uniform
magnetic field of \( 0.3 T \) with a velocity of
\( 4 \times 10^{5} \mathrm{m} / \mathrm{s} \) in a direction making an
angle of \( 60^{\circ} \) with the direction of
magnetic field. The path of motion of the particle will be :
A . circular
B. straight line
c. parabolic
D. helical


Examples of Surfactants among the following are:
This question has multiple correct options
A. sulfonates
B. fatty acids
c. alkaline oxides
D. aryl chlorides


In pteridophytes, xylem contains
A. vessels
B. Tracheids
c. xylem parenchyma
D. xylem sclrerenchyma


\( \frac{5}{x+y}-\frac{2}{x-y}=-1 \)
\( \frac{15}{x+y}+\frac{7}{x-y}=10 \)


A police car with a siren of frequency \( 8 k H z \) is moving with uniform velocity \( 36 k m / h r \) towards a tall building which reflects the sound waves. The speed of sound in air is \( 320 m / s . \) The frequency
of the siren heard by the car driver is:
A. \( 8.50 k H z \)
B. \( 8.25 k H z \)
c. \( 7.75 k H z \)
D. \( 7.50 k H z \)


State true or false.
Is it possible to have a regular polygon
whose each exterior angle is \( 32^{\circ} \)
A. True
B. False


Find number of all such functions \( \boldsymbol{y}= \)
\( f(x) \) which are one-one?
A . 0
B . \( 3^{5} \)
\( \mathrm{c} \cdot^{5} P_{3} \)
D. \( 5^{3} \)


Why is convection not significant in
solids?
A. Due to crystalline structure of solids, their density does not change
B. Impurities in solids gain the energy from convection.
C. Molecules of solids vibrate while moving from one part to other
D. Molecules of solids are tightly bound and not free to move.


A parents has two children. If one of
them is boy, then the probability that other is, also a boy, is
A \( \cdot \frac{1}{2} \)
B. \( \frac{1}{4} \)
\( c \cdot \frac{1}{3} \)
D. None of these


If \( A \) is the area of a triangle whose vertices are
\( (1,2,3),(-2,1,-4),(3,4,-2), \) then
the value of \( 4 A^{2} \) is
A . 1098
B. 1056
c. 1218
D. 1326


A coil of inductance \( 5 \mathrm{H} \) is joined to a
cell of emf \( 6 \mathrm{V} \) through a resistance \( 10 \Omega \) at time \( t=0 . \) The EMF across the coil at
time \( t=\ln \sqrt{2} s \) is:
\( A \cdot 3 v \)
B. 1.5
c. \( 0.75 v \)
D. 4.5


The value of of \( K_{P} \) for dissociation
\( 2 H I \rightleftharpoons H_{2}+I_{2} \) is \( 1.84 \times 10^{-2} . \) If the
equilibrium concentration of \( \boldsymbol{H}_{2} \) is
0.4789 mole \( L^{-1}, \) calculate the
concentration of \( \boldsymbol{H} \boldsymbol{I} \) at equilibrium.
A \( . a=0.25 \)
В. \( a=3.53 \)
c. \( a=88 \)
D. \( a=2.22 \)


The spin magnetic moment of cobalt in
the compound \( K_{2}\left[C o(S C N)_{4}\right] \) is :
A \( \cdot \sqrt{3} \) ВМ
B. \( \sqrt{8} \) Вм
c. \( \sqrt{15} \) ВМ
D. \( \sqrt{24} \) BM


The rate of flow of an electric charge is known as:
A. Electric potential
B. Electric conductance
c. Electric current
D. None of these


A zygote which has an \( X \) chromosome inherited from the father will develop
into a
\( A \cdot B O y \)
B. Girl
c. \( x \) chromosome does not determine the sex of a child
D. Either boy or girl


If the \( K_{b} \) value in the hydrolysis
reaction, \( \boldsymbol{B}^{+}+\boldsymbol{H}_{2} \boldsymbol{O} \rightleftharpoons \boldsymbol{B O H}+\boldsymbol{H}^{+} \) is
\( 1.0 \times 10^{-6}, \) then the hydrolysis constant
of the salt would be:
A \( .1 .0 \times 10^{-6} \)
В. \( 1.0 \times 10^{-7} \)
c. \( 1.0 \times 10^{-8} \)
D . \( 1.0 \times 10^{-9} \)


If \( f(x)=\frac{e^{x^{2}}-\cos x}{x^{2}}, \) for \( x \neq 0 \) is
continuous at \( \boldsymbol{x}=\mathbf{0}, \) then value of \( \boldsymbol{f}(\mathbf{0}) \)
is
A \( \cdot \frac{2}{3} \)
в. \( \frac{5}{2} \)
\( c \cdot 1 \)
D.


At \( t=0, \) the displacement of a particle
in S.H.M. is half its amplitude. Its initial phase is:
A \( \cdot \frac{\pi}{6} \) rad
B \( \cdot \frac{\pi}{3} \) rad
c. \( \frac{2 \pi}{3} \) rad
D. \( \frac{\pi}{2} \) rad


Bromine atom is available in two
isotopes, 79
35 Br \( (49.7 \%) \) and 81
35
\( (50.3 \%), \) the average atomic mass of bromine atom is :
A . 79.016
B. 80.076
c. 80.006
D. 81.016


The image of an object formed by a concave lens is:
A. Virtual, inverted and diminished
B. Virtual, upright and diminished
c. Virtual, inverted and enlarged
D. Virtual, upright and enlarged


Which of the following statements is incorrect when \( \Delta P Q R \cong \Delta L M N ? \)
\( \mathbf{A} \cdot \angle P=\angle L \)
в. \( \angle Q=\angle M \)
c. \( \angle R=\angle N \)
D. none of these


Convert chlorobenzene to \( \mathrm{p} \)
chloranitrobenzene.


Which of the following is correct?
A. Spinal cord is a part of central nervous system.
B. Nerves are continuous fibres.
C. Reflexes are not controlled by nerves.
D. None of the above.


In an isosceles triangle the sine of the
base angle is three times as large as
the cosine of the vertex angle. Find the sine of the base angle.


\( A B \) and \( C D \) are two chords of a circle
which intersect each other internally at
\( \boldsymbol{P} . \) If \( \boldsymbol{C P}=\boldsymbol{4} \mathrm{cm}, \boldsymbol{A P}=\mathbf{8} \mathrm{cm}, \boldsymbol{P B}=\mathbf{2} \)
\( \mathrm{cm}, \) then find \( P D \)


Which is used in alcoholic beverages?
A. Methanol
B. Ethanol
c. Phenol
D. Glycerol


Which of the following orbital
overlapping is not possible according to
VBT?
\( A \)
B.
\( c \)
D. All of these


Two gases A\&B having same pressure \( P \)
volume \( V \) and absolute temperature T are
mixed. If the mixture has volume and
temperature as \( \vee \& \) T respectively then
the pressure of mixture is
\( A \cdot 2 P \)
B.
\( c \cdot P / 2 \)
D. \( 4 P \)


The hydrolysis constant of the salts NaA and NaB [of two weak acids HA and HB]
\( \operatorname{are} 10^{-8} \) and \( 10^{-10} \) respectively. If the
dissociation constant \( K_{a} \) of weak acid
\( \mathrm{HC} \) is \( 10^{-5}, \) then decreasing order of the acid strength would be -
\( \mathbf{A} \cdot \) НВ>НС>НА
В. НА>НВ>нс
c. нВ>НА>нс
D. None of these


An electric field is uniform, and in the
positive \( x \) direction for positive \( x, \) and uniform with the same magnitude but
in the negative \( x \) direction for negative
\( x . \) It is given that \( \boldsymbol{E}=\mathbf{2 0 0} \hat{\boldsymbol{i}} \boldsymbol{N} / \boldsymbol{C} \) for
\( \boldsymbol{x}>\mathbf{0} \) and \( \boldsymbol{E}=-\mathbf{2 0 0} \hat{\boldsymbol{i}} \boldsymbol{N} / \boldsymbol{C} \) for \( \boldsymbol{x}<\mathbf{0 . A} \)
right circular cylinder of length \( 20 \mathrm{cm} \)
and radius \( 5 \mathrm{cm} \) has its centre at the
origin and its axis along the \( x \) -xis so that one face is at \( x=+10 \mathrm{cm} \) and the
other is at \( x=-10 \mathrm{cm} \)
(a) What is the net outward flux through
each flat face?
(b) What is the flux through the side of the cylinder?
(c) What is the net outward flux through the side of the cylinder?


Insulators have very high:
A. boiling point
B. melting point
C. specific heat capacity
D. freezing point


A uniform chain has a mass \( m \) and
length \( l \). It is held on a frictionless table
with two third of its length hanging over the edge. Find the work done injust
pulling the hanging part back on the
table.


Which of the following statements is
incorrect?
A. Number of electron for \( n+l=5 \) in \( C o^{+3} \) ion is six
B. In electronic configuration of Mn, electrons having value of \( m+l=0 \) are 13
C. Three radial nodes are present in the spherically symmetrical orbital of the fourth main shell
D. None of the above


\( \lim _{x \rightarrow 2} \frac{2 x+5}{8-x^{3}} \)


Which of the following is not a process
of preparation of hydrogen peroxide?
A. Auto-oxidation of 2-ethylanthraquinol.
B. By passing oxygen through boiling water
C. By oxidation of isopropyl alcohol
D. By reaction of barium peroxide with dil. \( H_{2} S O_{4} \)


Two metals \( M \) and \( N \) have the following values of ionization energies. Find
energy required for formation of \( \boldsymbol{M}^{+} \)
from \( M, M^{+2} \) from \( M^{+}, \) and total
energy required to form \( M^{+2} \) from \( M \)
Do similar calculations for metal \( N \)
\( I E_{1} \quad I E_{2} \)
\[
496 \quad 4560
\]
738 1450


toppr
Q Type your question
shown in Fig. (a)
In figure (b) the second lens is an
equiconcave lens of focal length \( 10 \mathrm{cm} \)
and made of a material of refractive
index \( 1.5 . \) In both cases, the second lens
has an aperture equal to 1 cm.
Now, a liquid of refractive index \( \mu \) is
filled to the right of the second lens in
case \( B \) such that the area illuminated
in both the cases is the same.

Determine the refractive index of liquid.
\( \mathbf{a} \)
\( (\mathbf{b}) \)
A .
B . 2.5
\( c .3 \)
D. 1.5


The rough estimation of visible matter
in the universe is:
A . \( 70 \% \)
B. \( 80 \% \)
\( \mathrm{c} .90 \% \)
D. \( 10 \% \)


'X' speaks truth in \( 60 \% \) of the cases and
'Y' in \( 50 \% \) of the cases. The probability that they contradict each other while narrating the some incident, is
A \( \cdot \frac{1}{2} \)
B. \( \frac{3}{4} \)
\( c \cdot \frac{3}{5} \)
D. None of these


Dissociation of an indicator can be
considered as, \( \boldsymbol{H} \boldsymbol{I} \boldsymbol{n} \rightleftharpoons \boldsymbol{H}^{+}+\boldsymbol{I} \boldsymbol{n}^{-} \)
colours of \( \boldsymbol{H} \boldsymbol{I} \boldsymbol{N} \) and \( \boldsymbol{I} \boldsymbol{n}^{-} \) are different.
Which statement is correct?
This question has multiple correct options
A. Solution assumes colours of \( H \) In when \( p H=p K-1 \)
B. Solution assumes colours of \( I n^{-} \) when \( p H=p K+1 \)
C. Solution assumes colours of \( H I n^{-} \) when \( p H=p K+1 \)
D. Solution assumes colours of \( I n^{-} \) when \( p H=p K-1 \)


Which of the following non-metal is hard yet brittle?
A. Graphite
B. Selenium
c. sulphur
D. Diamond


If \( \boldsymbol{x} \boldsymbol{\epsilon}[-1,0), \operatorname{then} \boldsymbol{\pi}-\left(\cos ^{-1}\left(2 \boldsymbol{x}^{2}-\right.\right. \)
1) \( \left.-2 \sin ^{-1} x\right) \) is equal to
A \( \cdot-\frac{\pi}{2} \)
в.
c. \( \frac{3 \pi}{2} \)
D. - 2 \( \pi \)


If the value of the determinant
\( \left|\begin{array}{lll}\boldsymbol{a} & \boldsymbol{h} & \boldsymbol{g} \\ \boldsymbol{h} & \boldsymbol{b} & \boldsymbol{f} \\ \boldsymbol{g} & \boldsymbol{f} & \boldsymbol{c}\end{array}\right| \) is \( \left(\boldsymbol{a} \boldsymbol{b} \boldsymbol{c}+\boldsymbol{2} \boldsymbol{x}-\boldsymbol{a} \boldsymbol{f}^{2}-\boldsymbol{b} \boldsymbol{g}^{2}-\right. \)
\( \left.c h^{2}\right), \) then what is the value of \( ^{\prime} x^{\prime} ? \)


Two A.P's have the same common
difference. The difference between their
\( 100^{t h} \) terms is \( 111222333 . \) What is
the difference between their millionth
terms?
A . 111222333
B. 222 111 333
c. 333 111222
D. 111333222


The median of 230 observations is 46
Find \( a \) and \( b \)
\( \begin{array}{lllll}\text { Class } & \begin{array}{l}10- \\ 20\end{array} & \begin{array}{l}20- \\ 30\end{array} & \begin{array}{l}\text { 30- } \\ 40\end{array} & \begin{array}{l}\text { 40- } \\ 50\end{array}\end{array} \)
Frequency 12 30 \( a \)


Copper forms two chlorides \( C u C l \) and
\( \boldsymbol{C u} \boldsymbol{C l}_{2} \)
(a) Identify the copper ions in these compounds?
(b) What is the valency of copper in each of these compounds?
(c) By writing the sub-shell electronic configuration of copper, find out a subshells from which the electrons are lost
to form these ions.
(d) Write the period and group to which
copper belongs.
(Hint: Atomic number of copper \( =\mathbf{2 9} \) )


For the pressure-volume work
expression, the term pressure in the
expression refers to
gas pressure.
\( \mathbf{A} \cdot W=-P_{e x} \cdot \Delta P \)
\( \mathbf{B} \cdot W=-P_{e x} \cdot \Delta V \)
\( \mathbf{C} \cdot W=-P_{e x} \cdot \Delta C \)
\( \mathbf{D} \cdot W=-P_{e x} \cdot \Delta D \)


If the following transformation is done with an alkene as an intermediate
product, an aldehyde with \( x \) number of carbons is produced alongside with benzaldehyde. What is \( x \) ?


A purse contains only 25 paise and 10 paise coins. The total amount in the
purse is \( R s .8 .25 . \) If the number of 25
paise coins is one-third the number of 10 paise coins, then the total number of
coins in the purse is:


What are the advantages of Integrated Circuits (IC)


Evaluate :
\( \int\left(1+2 x+3 x^{2}+4 x^{3}+\dots\right) d x \)
\( |\boldsymbol{x}|<\mathbf{1}) \)


The friction between moving surfaces in contact can be increased by polishing them.
A. True
B. False


Q Type your question
\( \left(\sigma_{1}>\sigma_{2}\right) \) are placed near each other
separated by distance 'd. A small
change ' \( q \) ' is placed in between two
plates such that there is no effect on charge distribution on plates. Now this
charge is moved at an angle of \( 45^{\circ} \) with the horizontal towards plate having
charge density \( \sigma_{2} \) by distance ' \( a^{\prime}(a< \) \( <\boldsymbol{d}) . \) Find the work done by electric
field in the process.
A \( \cdot \frac{q a\left(\sigma_{1}-\sigma_{2}\right)}{5 \sqrt{2} \epsilon_{0}} \)
B. \( \frac{q a\left(\sigma_{1}-\sigma_{2}\right)}{2 \sqrt{2} \epsilon_{0}} \)
c. \( \frac{q a\left(\sigma_{1}-\sigma_{2}\right)}{3 \sqrt{2} \epsilon_{0}} \)
D. \( \frac{q a\left(\sigma_{1}-\sigma_{2}\right)}{4 \sqrt{2} \epsilon_{0}} \)


Ethanoic acid is obtained by the \( \ldots . . \) of ethanol
A. Combustion
B. Oxidation
c. Reduction
D. Subsitution


Charge(Q) on capacitor( of capacitance
C) and potential difference(V) across it are related as:
A. \( Q=C \times V \)
в. \( Q=C / V \)
c. \( Q=V / C \)
D. Cannot be related


Simple interest on a certain sum of
money for 4 years at \( 4 \% \) per annum exceeds the compound interest on the
same sum for 3 years at 5 per cent per annum by Rs. 228. Find the sum.


The arithmetic mean of 12 and 20 is :
A . 12
B. 14
c. 16
D. 18


Consider the cell:
\( \boldsymbol{P t}\left|\boldsymbol{H}_{2}\left(\boldsymbol{p}_{1} \boldsymbol{a t m}\right)\right| \boldsymbol{H}^{\oplus}\left(\boldsymbol{x}_{1} \boldsymbol{M}\right) \| \boldsymbol{H}^{\oplus}\left(\boldsymbol{x}_{2} \boldsymbol{N}\right. \)
The cell reaction be spontaneous if This question has multiple correct options
\( \mathbf{A} \cdot p_{1}=p_{2} \) and \( x_{1}>x_{2} \)
B . \( p_{1}=p_{2} \) and \( x_{1}<x_{2} \)
C \( . x_{1}=x_{2} \) and \( p_{1}>p_{2} \)
D. \( x_{1}=x_{2} \) and \( p_{1}<p_{2} \)


The circumference of a circle is
measured as \( 28 c m \) with an error of
\( 0.01 \mathrm{cm} . \) The percentage error in the
area is
A \( \cdot \frac{1}{14} \)
в. 0.01
\( c \cdot \frac{1}{7} \)
D. none of these


The gas that is responsible for global warming is


The correct IUPAC name of the following
compound is:


Protein required for coagulation of blood is
A. Haemoglobin
B. Globulin
c. Fibrinogen
D. Albumin


The coordinates of a point \( \mathrm{P} \) are (3,12,4) w.r.t origin \( 0, \) then the direction cosines of \( O P \) are
\( \mathbf{A} \cdot 3,12,4 \)
B. \( \frac{1}{4}, \frac{1}{3}, \frac{1}{2} \)
c. \( \frac{3}{\sqrt{13}}, \frac{1}{\sqrt{13}}, \frac{2}{\sqrt{13}} \)
D. \( \frac{3}{13}, \frac{12}{13}, \frac{4}{13} \)


A long straight conductor carrying \( \boldsymbol{I}_{1} \) is placed in the plane of ribbon at a
distance a from the near edge of a
ribbon of width b, which carries \( \boldsymbol{I}_{2} \)
parallel to the wire. Find the force of attraction per unit length between the
two.


The charge flowing through a resistance \( R \) varies with time \( t \) as \( Q=a t-b t^{2} \)
where \( a \) and \( b \) are positive constants.
Calculate the total heat produced in \( R \)


An electron is projected so that it crosses three different regions of space
as shown. if \( B_{1}, B_{2} \) and \( B_{3} \) are the
magnetic field in the region,then:
\( A \cdot B_{1} \) is inward
B. \( B_{2} \) is outward
\( c \cdot B_{3} \) is inward
D. All of these


What is the nature of the graphs of a system of linear equations with exactly
one solution?
A. Parallel lines
B. Perpendicular lines
c. coincident lines
D. Intersecting lines


What type of mirrors do we use in our
houses to see ourselves?
A. Convex mirror
B. Plane mirror
c. Concave mirror
D. Any of the above


The eccentricity of the conic \( x^{2}+ \)
\( 2 y^{2}-2 x+3 y+2=0 \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( \frac{1}{\sqrt{2}} \)
\( c \cdot \frac{1}{2} \)
D. \( \sqrt{2} \)
\( E \)


Velocity-time graph of a particle moving
in a straight line is shown in the figure. Find the total displacement of the
particle
\( 4.40 \mathrm{m} \)
\( B .60 \mathrm{m} \)
\( c \cdot 80 m \)
D. \( 100 \mathrm{m} \)


State whether true or false:
Rain water is a non-conductor of
electricity.
A. True
B. False


Given there are 3 isotopes of hydrogen \( \left(^{1} \boldsymbol{H},^{2} \boldsymbol{H} \text { and }^{3} \boldsymbol{H}\right) \) and \( \boldsymbol{2} \) isotopes of
oxygen \( \left(^{15} \boldsymbol{O} \text { and }^{16} \boldsymbol{O}\right), \) how many peaks
would be expected on a mass spectrum
for the hydronium ion, \( \boldsymbol{H}_{3} \boldsymbol{O}^{+} \) ?
\( \mathbf{A} \cdot \mathbf{6} \)
B. 7
c. 8
D.


If a copper wire is stretched to make it \( 0.1 \% \) longer, the \( \% \) change in the resistance is
A . 0.3\%
B. 0.2\%
c. 0.1\%
D . 0.02\%


Two balls \( A \) and \( B \) of masses \( m \) and \( 2 m \)
are in motion with velocities \( 2 v \) and \( v \)
respectively. What is the ratio of their
momentum?
A . 1: 2
B. 2:
\( c \cdot 1: \)
D. 4:


\( \int_{\frac{1}{\sqrt{3}}}^{0} \frac{\boldsymbol{d} \boldsymbol{x}}{\left(\mathbf{2} \boldsymbol{x}^{2}+\mathbf{1}\right) \sqrt{\boldsymbol{x}^{2}+\mathbf{1}}} \)
A \( \cdot-\tan ^{-1} \frac{1}{2} \)
B. \( \tan ^{-1} 1 \)
c. \( -\tan ^{-1} \frac{1}{3} \)
D. \( \tan ^{-1} \frac{1}{\sqrt{2}} \)


The resistance \( \boldsymbol{R}=\frac{\boldsymbol{V}}{\boldsymbol{I}} \) where \( \boldsymbol{V}= \)
\( (100 \pm 5) V \) and \( I=(10 \pm 0.2) A . \) The
percentage error in \( \mathrm{R} \) is?
A \( .5 .2 \% \)
в. \( 4.8 \% \)
c. \( 7 \% \)
D. \( 3 \% \)


Find the radius and energy of a \( H e^{+} \) ion
in the state \( n=4 \)


Tubular heart of cockroach has how
many chambers?
A . 10
B. 13
c. 12
\( D \)


Fill in the blank:
charges collect or
accumulates near the lower edges of
clouds.
A. Positive
B. Neutral
c. Negative
D. None of the above


Light travels at the speed of \( 2.25 \times 10^{8} \)
\( \mathrm{m} / \mathrm{s} \) in medium \( \mathrm{A} \) and \( 2 \times 10^{8} \mathrm{m} / \mathrm{s} \) in
the medium B.Which medium is
optically denser? Is optical density related to the density of the medium?


Two wires of Aluminium have same
weight and have lengths of \( 10 \mathrm{m} \) and 20m. Their resistances are in the ratio.
A .1: 2
B . 2: 1
c. 4: 1
D. 1: 4


Use Euclids division algorithm to find the HCF of 441,567,693


Find minimum value of \( F \) required to slide this block.
\( A \cdot(1) 20 N \)
B. (2) 40
\( c \cdot(3) 60 \)
D. (4) 120 \( \mathrm{N} \)


If \( \vec{p}_{2} \) is free to rotate about an axis,
perpendicular to the plane and passing
through \( A, \) the angle between \( \vec{p}_{2} \) and \( \vec{p}_{1} \)
will be :
A \( \cdot \sin ^{-1}\left(\frac{1}{3}\right) \)
\( B \cdot \tan ^{-1}(3) \)
\( \mathbf{c} \cdot \cos ^{-1}\left(\frac{1}{3}\right) \)
\( D \cdot \cot ^{-1}(3) \)


Milk is an emulsion in which:
A. a gas is dispersed in water
B. lactose is dispersed in water
C. milk fat is dispersed in water
D. a solid is dispersed in water


Two vibrating strings of the same
material but length \( L \) and \( 2 L \) have radii
\( 2 r \) and \( r \) respectively. They are
stretched under the same tension. Both
the string vibrate in their fundamental
modes, the one of length \( L \) with
frequency \( v_{1} \) and other with frequency
\( \boldsymbol{v}_{2} . \) The ratio \( \boldsymbol{v}_{1} / \boldsymbol{v}_{2} \) is given by
A . 2
B. 4
c. 8
D.


f \( \sqrt{18225}=135, \) then the value of \( \sqrt{18225}+\sqrt{182.25}+\sqrt{1.8225} \)
\( +\sqrt{0.018225} \) is


If uncertainty in position of the electron is \( _{--}-_{-}, \) then the uncertainty in its momentum would be infinity.


The rays produced in the above experiment consist of
A. protons
B. neutrons
C. positrons
D. neutrinos


Read the following statements \( (A-E) \)
and answer the question which follows them.
(A) In liverworts, mosses, and ferns
gametophytes are free-living.
(B) Gymnosperms and some ferns are heterosporous.
(C) Sexual reproduction in Fucus, Volvox and Albugo is oogamous.
(D) The sporophyte in liverworts is more
elaborate than that is mosses.
(E) Both, Pinus and Marchantia are
dioecious.
How many of the above statements are
correct?
A. One
B. Two
c. Three
D. Four


For the following statements. write T for True and F for False
(a) J.J. Thomson proposed that the nucleus of an atom contains only
nucleons.
(b) A neutron is formed by an electron and a proton combining together. Therefore, it is neutral.
(c) The mass of an electron is about
\( \mathbf{1} \)
\( \mathbf{2 0 0 0} \)
times that of proton.


What amount is \( 15 \% \) less than \( 80 ? \)


Which one of the following has \( 0-0 \)
bond?
A \( \cdot \mathrm{H}_{2} \mathrm{S}_{2} \mathrm{O}_{6} \)
в. \( \mathrm{H}_{2} \mathrm{S}_{2} \mathrm{O}_{7} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{S}_{2} \mathrm{O}_{5} \)
D. \( \mathrm{H}_{2} \mathrm{S}_{2} \mathrm{O}_{8} \)


Which of the given mentioned positions in the given compound is more reactive towards electrophilic substitutions?
\( A \)
B.
\( c .5 \)
D.


The formula for coefficient of variation
(C.V.) is given by


The following table gives the route length (in thousand kilometres) of the Indian Railways in some of the years:
Year
\( \begin{array}{lll}1960- & 1970- & 1980-\end{array} \)
is and 61
Route length (in \( \quad \) 56 \( \quad \) 60 thousand kilometres)
Represent the above data with the help of a bar graph.


Which of the following statements are
correct?
A.Tapeworms are hermaphrodites and undergo self-fertilization.
B. Earthworms are hermaphrodites and undergo self-fertilization.
C. Tapeworms are hermaphrodites but undergo cross-fertilization.
D. Earth worms are hermaphrodites but undergo cross-fertilization.
A . A and B
B. B andc
\( c \cdot c \) and \( D \)
D. D and A


Ammonia gas is collected by (an upward displacement of air, a downward displacement of water, a downward displacement of air)


Sun maintains its shining because of
A. the fission of helium
B. chemical reactoin
c. fusion of hydrogen nuclei
D. burning of carbon


The bond angle around the central atom
is maximum for:
A \( . H_{2} O \)
в. \( H_{2} S e \)
\( \mathrm{c} \cdot H_{2} \)
D. \( H_{2} T e \)


Let mean value of \( \boldsymbol{f}(\boldsymbol{x})=\frac{1}{\boldsymbol{x}+\boldsymbol{c}} \) over
interval (0,2) is \( \frac{1}{2} \ell n 3 \) then positive
values of \( c \) is
A . 12
в. 1
\( c \cdot 2 \)
\( D \cdot \frac{3}{3} \)


Arrangement of sepals and petals in the bud condition is called as
A. Ptyxis
B. Placentation
c. Aestivation
D. Phyllotaxy


Redox reaction involves reaction
between:
A. The electrolytic cell when fused \( M g C l_{2} \) is subjected to
electrolysis
B. When fused \( M g C l_{2} \) is heated
C. When fused \( M g C O_{3} \) is strongly heated
D. None of the above


Redox reactions are reactions during which electron transfer takes place.
Here magnesium atom transfers two
electrons one each to the two chlorine
atoms
i) What are the products of this
reaction?
ii) Write the balanced equation for the
complete reaction.
iii) Which element is being oxidized?
iv) Which element is being reduced?
v) Write the reduction part of the
reaction?


The maximum number of covalent
bonds are present in:
A. ethane
B. methane
c. ethyne
D. ethene


If \( a x^{n-1}+b x^{n-2}+c x^{n-3} \) is a cubic
polynomial where \( n \in N, \) then find the
value of \( \boldsymbol{n} \)


Assertion
A sphere is performing pure rolling on a rough horizontal surface with constant angular velocity,frictional force acting
on the sphere is zero
Reason
Velocity of conduct point is zero.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The bicarbonate of alkali metal which
does not exist in solid state is:
A. \( L i H C O_{3} \)
в. \( \operatorname{NaH} \mathrm{CO}_{3} \)
c. \( K H C O_{3} \)
D. \( R b H C O_{3} \)


Cellular totipotency is demonstrated by
A. Only gymnosperm cells
B. All plant cells
c. All eukaryotic cells
D. only bacterial cells


Two isomers of a compound
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{3} \boldsymbol{C l}_{3}\right]\left(\boldsymbol{M} \boldsymbol{A}_{3} \boldsymbol{B}_{3} \text { type }\right) \) are
shown in the figures. The isomers can
be classified as:
\( (\mathbf{i}) \)
A. (i) fac-isomers
(ii) mer-isomer
B. (i) optical-isomer
(ii) trans-isomer
C. (i) mer-isomer
(ii) fac-isomer
D. (i) trans-isomer
(ii) cis-isomer.


The equivalent resistance across \( A \) and
B is
A . \( 2 \Omega \)
B. 3\Omega
\( c .4 \Omega \)
D. \( 5 \Omega \)


There is a stream of neutrons with a
kinetic energy of 0.0327 eV. If the halflife of neutrons is 700 s, what fraction of neutrons will decay before they travel a distance of \( 10 \mathrm{m} ? \) Given mass of
neutron \( =1.676 \times 10^{-27} k g \)


Vertical sections of a wing of a fan are shown in the following figures. The maximum up thrust will be in figure.
\( A \)
в.
\( c \)
\( D \)


Small fish get stuck near the bottom of a shark and derives its nutrition from it.
This kind of association is called as
A. Symbiosis
B. Commensalism
c. Predation
D. Parasitism


The sources of dissolved oxygen in
water is
A. photosynthesis
B. natural aeration
c. mechanical aeration
D. all of the above


Which of the following measures can be
taken up to control air pollution?
A. Planting trees
B. Travelling to school on a bicycle or on public transport or carpooling
C. Restricting cigarette smoking
D. All of the above


Reflect shape \( A \) in \( x-a x \) is. Label the
image shape B


When zinc is treated with conc. \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \)
an oxide of nitrogen is formed. The change in oxidation state of nitrogen during this reaction is:
A . +5 to 0
B. +5 to +2
\( \mathbf{c} \cdot+5 \) to +4
D. +5 to +1


Give the condensed formula
of Hexanedial:
A \( \cdot O H C\left(C H_{2}\right)_{4} C H O \)
в. \( O H C\left(C H_{2}\right)_{3} C H O \)
с. \( O H C\left(C H_{2}\right)_{4} \) СООН
D. \( \operatorname{COOH}\left(C H_{2}\right)_{3} \)COOH


A container shaped like a right circular
cylinder having diameter \( 12 \mathrm{cm} \) and height \( 15 \mathrm{cm} \) is full of ice cream. The ice cream is to be filled into cones of height \( 12 \mathrm{cm} \) and diameter \( 6 \mathrm{cm}, \) having a hemispherical shape on the top. Find
the number of such cones which can be
filled with ice cream.


Find \( S_{n} \) for each of the geometirc series described below.
(i) \( a=3, t_{8}=384, n=8 \)
(ii) \( a=5, r=3, n=12 \)


The most metallic element among the following is :
A. \( P \)
в. \( A s \)
\( c . B i \)
D. \( S b \)


A charge is kept at the centre of a shell. Shell has charge Quniformally distibuted over its surface and radius \( \mathrm{R} \)
The force on the central charge due to the shell is :
A. towards left
B. towards right
c. upward
D. zero


The primary and secondary coil of a transformer have 50 and 1500 turns
respectively. If the magnetic flux \( \phi \) linked with primary coil is given by
\( \phi=\phi_{0}+4 t, \) where is in webers, \( t \) is
time in seconds and \( \phi \) is a constant, the
output voltage across the secondary coil is:
\( A \cdot 150 V \)
B. 90
c. \( 120 v \)
D. \( 180 \mathrm{V} \)


The number of points at which the function \( \boldsymbol{f}(\boldsymbol{x})=|\boldsymbol{x}-\mathbf{0 . 5}|+|\boldsymbol{x}-\mathbf{1}|+ \)
\( \tan x \) does not have a derivative in the
interval (0,2) is/are?
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D.


\( \boldsymbol{C}_{\boldsymbol{g} \text {raphite}}+\boldsymbol{O}_{\mathbf{2}(\boldsymbol{g})} \rightarrow \boldsymbol{C} \boldsymbol{O}_{2(\boldsymbol{g})} ; \boldsymbol{\Delta} \boldsymbol{H}= \)
\( -393.5 k J, \Delta H \) of the reaction cannot
be:
A. Heat of formation of \( C O_{2} \)
B. Heat of combustion of \( C O_{2} \)
c. Heat of reaction
D. Heat of transition


The first amino acid formed during
translation
A. Occupies the aminyl site first, then the peptidyl site
B. Occupies the aminyl site before the attachment of the large portion of the ribosome
C. Of the polypeptide chain is methionine
D. All of the above
E. None of the above


Which of the following is/are examples
of artificial sweetener?
This question has multiple correct options
A. Sucralose
B. Saccharin
c. Neotame
D. Aspartame


Is this optically active?


A Gardner waters the plants by a pipe of
diameter 1 mm. The water comes out at
the rate or \( 10 \mathrm{cm}^{3} / \) sec. The reaction force exerted on the hand of the Gardner
is:
A. 0 N
В. \( 1.27 \times 10^{-2} N \)
c. \( 1.27 \times 10^{-4} N \)
D. 0.127


Increase in body temperature makes oxygen haemoglobin curve to shift?
A. Right
B. Left
c. central
D. None of these


How many of the following species have the trigonal planar shape,
\( N I_{3}, I_{3}^{-}, S O_{3}^{2-}, N O_{3}^{-} ? \)


Assertion
The rate of reaction can also increase
w.r.t its product if one of the product act as catalyst.
Reason
A catalyst lowers the activation energy
of reactions.

Read the above assertion and reason
and choose the correct option regarding
¡t.
A. Both Assertion and Reason are true Reason is the correct explanation to Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation to Assertion
c. Assertion is true but Reason is false
D. Both Assertion and Reason are false


State whether the following statements
are true or false.

Removal of the tip of coleoptile deprives it of a growth promoting substance.
A. True
B. False


Find Ampere force acting on the frame.
A. \( F=4.0 \mu N \)
в. \( F=0.80 \mu N \)
c. \( F=0.40 \mu N \)
D. \( F=8.0 \mu N \)


Which of the following figures
represents the magnetic lines of force
due to an isolated north pole?
\( A \)
B.
\( c \)
D.


Let \( A B C D \) be a quadrilateral with area
18, with side \( A B \) parallel to the side
\( C D \) and \( A B=2 C D . \) Let \( A D \) be
perpendicular to \( A B \) and \( C D . \) If a circle is drawn inside the quadrilateral \( A B C D \) touching all the sides, then its
radius is:
A . 3
B . 2
\( c \cdot \frac{3}{2} \)
\( D \)


The least electropositive metal among the following is :
A . Au
в. Мв
\( c \cdot A \)
D. zn


The sum of squares of deviation of
variates from their A. M. is always:
A. zero
B. Minimum
c. Maximum
D. Nothing can be said


Wool fibre cannot be obtained from
which of the following?
A. Goat
B. Llama
c. Alpaca
D. Moth


Waldsterben is
A. Decline in forests
B. Development of fog
C. Harm to sculptures, statues and buildings
D. All of the above


The compound \( N a_{2} I r C l_{6} \) reacts with triphenylphosphine in diethyleneglycol
in an atmosphere of \( C O \) to give
\( \left[\operatorname{Ir} C l(C O)\left(P P h_{3}\right)_{2}\right], \) known as 'Vaska's
compound'. The number of unpaired electrons and oxidation state of iridium
in the complex respectively is:
[Atomic number of \( \boldsymbol{I r}=\mathbf{7 7}] \)
\( A \cdot 0,0 \)
B. \( 0, \)
\( c \cdot 1, \)
D. 1,2


Identify the balanced chemical reaction of sodium chloride and sulphuric acid:
A \( \cdot 2 N a C l+H_{2} S O_{4} \rightarrow N a_{2} S O_{4}+2 H C l \)
в. \( 2 N a C l+H_{2} S O_{4} \rightarrow 2 N a_{2} S O_{4}+2 H C l \)
c. \( 2 N a C l+2 H_{2} S O_{4} \rightarrow N a_{2} S O_{4}+2 H C l \)
D. \( 2 \mathrm{NaCl}+\mathrm{H}_{2} \mathrm{SO}_{4} \rightarrow 2 \mathrm{Na}_{2} \mathrm{SO}_{4}+3 \mathrm{HCl} \)


Evaluate: \( (l+m)-4 m \)


\( 50 \mathrm{g} \) of \( \mathrm{CaCO}_{3} \) is allowed to react with 70 g of \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4} \). Calculate :
(i) amount of \( \boldsymbol{C} \boldsymbol{a}_{\boldsymbol{3}}\left(\boldsymbol{P} \boldsymbol{O}_{4}\right)_{2} \) formed
(ii) amount of unreacted reagent


The equation of a wave propagating along a stretched string is given by \( \boldsymbol{Y}=\mathbf{4} \sin 2 \boldsymbol{\pi}[(\boldsymbol{t} / \mathbf{0 . 0 2})-(\boldsymbol{x} / \mathbf{1 0 0})] \)
where \( Y \) and \( x \) are in \( \mathrm{cm} \) and \( t \) in
second. Determine direction in which
wave is propagating.


If \( \boldsymbol{A}=\left[\begin{array}{cc}-\boldsymbol{i} & \mathbf{0} \\ \mathbf{0} & \boldsymbol{i}\end{array}\right], \) then \( \boldsymbol{A}^{\prime} \boldsymbol{A} \) is equal to
A . \( I \)
B. \( -i A \)
\( c .-I \)
D. \( i A \)


A company with 10,000 shares of Rs.100 each, declares an annual
dividend of \( 5 \% \)
What should be the annual income of a ma who has 72 shares in the company?


The error in the measurement of the
radius of a sphere is \( 1 \% . \) Find the error in the measurement of volume?


When acetaldehyde is reacted with LiAIH4 what is the product formed?
A. \( C H_{3} \) СООН
в. \( C H_{3} C H_{2} \) ОН
\( \mathbf{c} \cdot C H_{3} O H \)
D. нсоон


Arteries are best defined as the vessels
which
A. Supply oxygenated blood to the different organs
B. Carry blood away from the heart to different organs
c. Break up into capillaries which reunite to form a vein
D. Carry blood from one visceral organ to another visceral organ


A coil of wire is placed in a changing magnetic field. If the number of turns in the coil is decreased, the voltage induced across the coil will
A. increase
B. decrease
c. remain constant
D. be excessive


If \( \left.f(x)=\left(a-x^{n}\right)^{1 / n} \text { where } a>0 \text { and }\right\} \)
\( n \) is a positive integer then \( (\text { fof })(x) \) is
A. \( f(x) \)
B.
\( c \cdot 0 \)
\( D \)


Among the following which one has more acidic character?
A. \( B_{2} O_{3} \)
a
в. \( C O_{2} \)
c. \( N_{2} O_{3} \)
D. None of these


Which of the following is quadratic polynomial
\( \mathbf{A} \cdot x+2 \)
B. \( x^{2}+2 \)
c. \( x^{3}+2 \)
D. \( 2 x+2 \)


Solve the inequality and show the graph
of the solution on number line:
\( 5 x-3 \geq 3 x-5 \)


Find the magnitude and direction of the force vector applied to the loop if the
vector \( \vec{p}_{m} \) is parallel to the straight conductor.
A \( \cdot \vec{F}=20 \)
В . \( \vec{F}=10 \)
c. \( \vec{F}=0 \)
D. \( \vec{F}=50 \)


\( \operatorname{Let} f(x)=\left(\frac{\tan \left(\frac{\pi}{4}-x\right)}{\cot 2 x}\right)\left(x \neq \frac{\pi}{4}\right) \)
The value which should be assigned to at \( \frac{\pi}{4} \) so that it is continuous
everywhere, is
A \( \cdot \frac{1}{2} \)
B.
\( c \cdot 2 \)
D. None of these


In triangle \( A B C, P \) is the mid-point of side BC.A line through P and parallel to CA meets \( A B \) at point \( Q ; \) and a line through \( Q \) meets at \( S . Q S \) parallel to BC
meets median AP at point R. prove that:
(i) \( A P=2 A R \)
(ii) \( \mathrm{BC}=4 \mathrm{QR} \)


The rate of reaction is doubled for every
\( 10^{0} C \) rise in temperature. the increase
in reaction rate as a result of rise in
temperature from \( 10^{0} C \) to \( 100^{0} C \) is:
A . 112
в. 512
c. 400
D. 614


A bullet of mass \( 0.01 \mathrm{kg} \) is fired from a gun of mass \( 5 \mathrm{kg} \) with velocity of \( 250 \mathrm{m} / \mathrm{s} \) calculate the speed with which the gun
recoils.
A. \( 0.50 \mathrm{m} / \mathrm{s} \)
B. \( 0.25 \mathrm{m} / \mathrm{s} \)
c. \( 0.05 \mathrm{m} / \mathrm{s} \)
D. \( 0.025 \mathrm{m} / \mathrm{s} \)


\( \boldsymbol{A}=(\mathbf{2}+\mathbf{1})\left(\mathbf{2}^{2}+\mathbf{1}\right)\left(\mathbf{2}^{4}+\right. \)
1) \( \dots . .\left(2^{2016}+1\right) . \) The value of
\( (\boldsymbol{A}+\mathbf{1})^{\frac{1}{2016}} \) is
\( \mathbf{A} \cdot \mathbf{4} \)
в. 2016
c. \( 2^{403} \)
D.


Simplify : \( \frac{2^{2009}-2^{2007}}{2^{2006}-2^{2008}} \)
A . -4
B . - -
\( c \cdot-1 \)
D.


Which buffer solution comprising of the
following has its \( p H \) value greater than
\( 7 ? \)
A \( \cdot C H_{3} C O O H+C H_{3} C O O N a \)
в. \( H C O O H+H C O O K \)
c. \( C H_{3} C O O N H_{4} \)
D. \( N H_{4} O H+N H_{4} C l \)


A block of mass \( 5 k g \) is (i) pushed in
case \( (A) \) and (ii) pulled in case \( (B), \) by
force \( \boldsymbol{F}=\mathbf{2 0} \boldsymbol{N}, \) making an angle of \( \boldsymbol{3 0}^{\boldsymbol{o}} \)
with the horizontal, as shown in the
figures. The coefficient of friction
between the block and floor is \( \mu=0.2 \)
The difference between the
accelerations of the block, in case (B)
and case (A) will be:
\( \left(g=10 m s^{-2}\right) \)
\( (\mathrm{B}) \)
\( \mathbf{A} \cdot 0 m s^{-2} \)
B. \( 0.8 m s^{-2} \)
c. \( 0.4 m s^{-2} \)
D. \( 3.2 \mathrm{ms}^{-2} \)


Which of the following cell of intestine
secretes GIP?
A. I cell
B. K cell
c. Beta cell
D. None of the above


The correct order of \( E_{M^{2+} / M}^{0} \) values with a negative sign for the four successive elements \( \mathrm{Cr}, \mathrm{Mn}, \mathrm{Fe} \) and \( \mathrm{Co} \) is:
\( A \cdot F e>M n>C r>C 0 \)
B. \( \mathrm{Cr}>\mathrm{Mn}>\mathrm{Fe}>\mathrm{Co} \)
\( \mathrm{c} \cdot \mathrm{Mn}>\mathrm{Cr}>\mathrm{Fe}>\mathrm{Co} \)
D. \( \mathrm{Cr}>\mathrm{Fe}>\mathrm{Mn}>\mathrm{Co} \)


Rutherford's experiment for the first time proved that atom has:
A. Protons
B. Nucleus
c. Neutrons
D. Electrons


What is not something that a phase
equilibrium line shows?
A. The equilibrium point between solid and liquid
B. The equilibrium point between liquid and gas
C. The equilibrium point between liquid and solid
D. The equilibrium point between solid and gas
E. The equilibrium point between gas and vapor


From the given triangle \( A B C, \) find the
measure of an \( \angle A C B \)


Find the value of \( k \) for which the
equation \( 2 x^{2}-k x+3=0 \) will have
two real and equal roots.


Two beads of masses \( m_{1} \) and \( m_{2} \) are
threaded on a smooth circular wire of
radius' \( a^{\prime} \) fixed in a vertical plane. \( B \) is
stationary at the lowest point when \( \boldsymbol{A} \) is
gently dislodged from rest at the
highest point. \( A \) collides with \( B \) at the
lowest point. The impulse given to \( \boldsymbol{B} \)
due to collision is just great enough to
carry it to the level of the centre of the
circle while \( A \) is immediately brought
to rest by the impact. Find \( \boldsymbol{m}_{1}: \boldsymbol{m}_{2} \)


An object of \( 10 \mathrm{cm} \) is placed in front of a plane mirror. The height of image will be
A. \( 5 \mathrm{cm} \)
B. \( 15 \mathrm{cm} \)
c. \( 20 \mathrm{cm} \)
D. \( 10 \mathrm{cm} \)


topp \( E \)
Q туре your question
velocity (v) and acceleration (a) of the rock when it is at its highest position?
\( c \)
in
\[
a
\]
\( D \)
0
\[
v=0 \quad a=0
\]


With \( V=0 \) at infinity, what is the
electric potential at corner A?
A \( \cdot 6 \times 10^{4} V \)
В. \( -7.8 \times 10^{5} V \)
c. \( 8.4 \times 10^{5} V \)
D. None of these


The common ratio is calculated in
A . A.P.
в. G.P.
c. н.P.
D. I.P.


The weak zones around the boundaries
of plates underneath Earth, which are prone to slide and cause earthquake are commonly known as:
A. fault zone
B. eruption zone
c. explosive zone
D. sliding zone


A boy buys 9 apples for \( R s .9 .60 \) and
sells them at 11 for \( R s .12 \). Find his
gain or loss percent.


The cytoplasm and nucleus are enclosed within the


A train is moving at a constant speed \( \mathrm{V} \) when its driver observes another train
in front of him on the same track and
moving in the same direction with constant speed v. If the distance
between the trains is \( x, \) then what
should be the minimum retardation of
the train so as to avoid collision?
A \( \cdot \frac{(V+v)^{2}}{x} \)
B. \( \frac{(V-v)^{2}}{x} \)
C \( \frac{(V+v)^{2}}{2 x} \)
D. \( \frac{(V-v)^{2}}{2 x} \)


0.1 mole of \( H_{2} \) and 0.2 mole of \( I_{2} \) are
made to react in order to attain
equilibrium \( \boldsymbol{H}_{2}+\boldsymbol{I}_{2} \rightleftharpoons \mathbf{2} \boldsymbol{H} \boldsymbol{I} . \mathrm{At} \)
equilirbrium \( 20 \% H_{2} \) is converted into
\( H I, \) calculate amount of \( H I \) formed


If \( f(x)=\sin x, \) find \( \frac{d y}{d x} \)
A \( \cdot \cos x \)
B. \( -\cos x \)
c. \( \cot x \)
D. \( -c o t^{2} x \)


A wire loop is rotated in a uniform
magnetic field about an axis perpendicular to the field. The direction
of the current induced in the loop
reverse once each
A . quarter revolution
B. half revolution
c. full revolution
D. two revolution


A balloon is pumped at the rate of a cm \( ^{3} \) /minute. The rate of increase of its
surface area when the radius is \( b \mathrm{cm} \), is
A \( \cdot \frac{2 a^{2}}{b^{4}} \mathrm{cm}^{2} / \mathrm{min} \)
B. \( \frac{a}{2 b} \mathrm{cm}^{2} / \mathrm{min} \)
c. \( \frac{2 a}{b} \mathrm{cm}^{2} / \mathrm{min} \)
D. none of these


Only two isomeric monochloro
derivatives are possible for (excluding stereo \( ): \)
\( A \cdot n- \) butane
B. 2, 2 - dimethylpentane
c. benzene
D. neopentane


When one glucose molecule is
completely oxidised, it changes
A. 36 ADP molecules into 36 ATP molecules
B. 38 ADP molecules into 38 ATP molecules
C. 30 ADP molecules into 30 ATP molecules
D. 32 ADP molecules into 32 ATP molecules


Identify a possible graph for function \( \boldsymbol{f} \)
given by
\( \boldsymbol{f}(\boldsymbol{x})=-\boldsymbol{2}|\boldsymbol{x}| \)
A. graph a
B. graph b
c. graph c
D. graph d


Calculate the moment of inertia of a
thin ring of mass \( m \) and radius \( R \) about
an axis passing through its centre and perpendicular to the plane of the ring.


A ball is thrown from rear end of the
compartment of train to the front end which is moving at a constant horizontal velocity. An observer \( \boldsymbol{A} \) sitting in compartment and another
observer \( B \) standing on the ground draw
the trajectory. They will have
A. equal horizontal and equal vertical ranges.
B. equal vertical ranges but different horizontal ranges
c. different vertical ranges but equal horizontal ranges
D. different vertical ranges and different horizontal ranges


The elements \( A \) and \( B \) combine
together to give two compounds \( A_{2} B_{3} \)
and \( A B_{2} . \) The weight of 0.2 mole of
\( A_{2} B_{3} \) is \( 26 g \mathrm{m} \). The weight of 0.3 mole of
\( A B_{2} \) is \( 24 \mathrm{gm} . \) Then the atomic weights of \( A \) and \( B \) respectively.
A. 15,20
B. 20,25
c. 20,30
D. 25,30


Which metal can exist in a form that
gives sparks on scratching?
A. Antimony
B. Leadd
c. Tin
D. Thallium


Assertion
Total current entering a circuit is equal
to leaving the circuit by Kirchhoff's law.
Reason
It is based on conservation of energy.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion.
C. Assertion is correct but Reason is incorrect.
D. Both Assertion and Reason are incorrect.


A water tank of height \( 10 m, \) completely filled with water is placed on a level
ground. It has two holes one at \( 3 m \) and
the other at \( 7 m \) from its base. The water
ejecting from:
A. both the holes will fall at the same spot
B. upper hole will fall farther than that from the lower hole
c. upper hole will fall closer than that from the lower hole
D. more information is required


On introducing a transparent \( \operatorname{slab}(\mu) \) the central fringe shifts to the point originally occupied by the fifth bright fringe. The thickness of the slab is
\( ^{\mathbf{A}} \cdot \frac{5 \lambda}{\mu-1} \)
в. \( \frac{4 \lambda}{\mu-1} \)
c. \( \frac{\mu-1}{4 \lambda} \)
D. \( \frac{\mu-1}{5 \lambda} \)


A particle moves along a circle of a fixed
radius with a variable centripetal
acceleration \( a_{n}=k t^{n}, \) where \( k \) is a
constant and \( t \) is time. If slope of \( \boldsymbol{P}-\boldsymbol{t} \)
graph on log-log scale is \( 2, \) then value of
\( n \) is
(Here, \( P \) is instantaneous power)
A . 1
B. 2
\( c .-1 \)
D. 3


Oil refineries, paper factories, textile
and sugar mills, chemical factories are responsible for water pollution.These industries discharge harmful chemicals into revers and streams, and pollute water. The chemicals released include
A. arsenic
B. Ieadd
c. fluorides
D. all of the above


Which waves are used as signal
through fog and why?


The air in the path of lightning goes up to a temperature of about
\( \mathbf{A} \cdot 300^{\circ} C \)
в. \( 3000^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 300000^{\circ} \mathrm{C} \)
D. \( 30000^{\circ} \mathrm{C} \)


A block of mass \( 10 \mathrm{kg} \) is moving horizontally with a speed of \( 1.5 m s^{-1} \) on a smooth plane. If a constant vertical force \( 10 N \) acts on it, the displacement of the block from the point of application of the force at the end of 4
seconds is
A. \( 5 m \)
B. \( 20 m \)
c. \( 18 m \)
D. \( 10 m \)


If collision between the balls is
completely inelastic, then :
A. there is no loss of kinetic energy of the system
B. entire kinetic energy of the system is lost
C. kinetic energy loss in the system is less than 50\%
D. kinetic energy loss in the system is more than 50\%


Nitrogen molecule is chemically less active because of its:
A. small atomic energy.
B. high dissociation energy
c. high electronegativity.
D. stable electronic configuration


Which of the following statement(s) is
(are) true?
This question has multiple correct options
A \( \cdot \) Ionisation energy \( \alpha \frac{1}{\text { Screening effect }} \)
B. The first ionization energies of Be and Mg are more than ionization energies of \( B \) and \( A I \) respectively.
C. Atomic and ionic radii of Niobium and Tantalum are
almost same.
D. Metallic and covalent radii of potassium are \( 2.3 A^{\circ} \)
and \( 2.03 A^{\circ} \) respectively.


Find out what the slope of the grah
gives us.


What is the key element in soil
fertilizer?
A. carbon
B. Nitrogen
c. oxygen
D. Neon
E. Argon


A wooden toy is in the form of a cone
surmounted on a hemisphere. The diameter of the base of the cone is 16
\( \mathrm{cm} \) and its height is \( 15 \mathrm{cm} . \) Find the cost
of painting the toy at Rs.7 per \( 100 \mathrm{cm}^{2} \)


Three charges are placed at the vertices
of an equilateral triangle of side a as shown in the figure. The force
experienced by the charge plced at the vertex \( A \) in a direction normal to \( B C \) is :
\( A \)
\( \mathbf{B} \cdot-Q^{2}\left(4 \pi \varepsilon_{0} a^{2}\right) \)
c. zero
\( ^{\mathrm{D}} \cdot \frac{Q^{2}}{\left(2 \pi \varepsilon_{0} a^{2}\right)} \)


Two trains \( A \) and \( B, 100 m \) and \( 60 m \)
long,are moving in opposite directions on parallel tracks.The velocity of the shorter trains is 3 times that of the
longer one.If the trains take 4 s to cross
each other, the velocities of the trains
are


The molecule having permanent dipole
moment is:
A. \( S F_{4} \)
в. \( X e F_{4} \)
\( \mathrm{c} \cdot \operatorname{siF}_{4} \)
D. \( B F_{3} \)


Factorize:
\( \boldsymbol{x}^{\mathbf{1}}+\boldsymbol{x}^{\mathbf{2}} \times \mathbf{2} \mathbf{5} \)


Carbon particles and smoke from
factories:
A. increase the rate of respiration in plants
B. decrease the rate of photosynthesis in plants
C. increase the absorption of carbon dioxide by plants
D. decrease the rate of transpiration in plants


The maximum value of \( \frac{\log x}{x} \) in \( (2, \infty) \)
is
A. 5
B. \( \frac{5}{e} \)
\( \mathbf{c} \cdot e^{e} \)
D.


A \( 5 \mathrm{m} \) long aluminium wire \( (\boldsymbol{Y}=\mathbf{7} \times \)
\( \left.10^{10} N m^{-2}\right) \) of diameter \( 3 \mathrm{mm} \) supports
a \( 40 \mathrm{kg} \) mass. In order to have the same
elongation in the copper wire \( (\boldsymbol{Y}= \)
\( \left.12 \times 10^{10} N m^{-2}\right) \) of the same length
under the same weight, the diameter should now be (in \( \mathrm{mm} \) ).
A . 1.75
в. 1.5
c. 2.5
D. 5.0


The AC voltage across a resistance can be measured using a
A. moving magnet galvanometer
B. moving coil galvanometer
c. hot wire voltmeter
D. potentiometer


If \( \tan \theta+\tan \phi=a, \cot \theta+\cot \phi= \)
\( \boldsymbol{b}, \boldsymbol{\theta}-\boldsymbol{\phi}=\boldsymbol{\alpha} \neq \mathbf{0}, \) then
This question has multiple correct options
\( \mathbf{A} \cdot a b>4 \)
в. \( a b<4 \)
\( ^{\mathbf{c}} \tan ^{2} \alpha=\frac{a b(a b-4)}{(a+b)^{2}} \)
D \( \sec ^{2} \alpha=\frac{(a-b)^{2}+a^{2} b^{2}}{(a+b)^{2}} \)


Alpha-particles that come closer to nuclei in Rutherford's alpha particle scattering experiment:
A. are deflected more
B. are deflected less
c. make more collisions
D. None of the above


The potential difference in open circuit for a cell is \( 2.2 \mathrm{V} \). When a \( 4 \Omega \) resistor is
connected between its two electrodes
the potential difference becomes \( 2 \mathrm{V} \) The internal resistance of the cell will be
A . \( 1 \Omega \)
B. \( 0.2 \Omega \)
\( c .2 .5 \Omega \)
D. \( 0.4 \Omega \)


A ballet dancer, dancing on a smooth floor is spinning about a vertical axis with her arms folded with angular
velocity of 20 rad/s. When the stretches
her arms fully, the spinning speed decreases in 10 rad/s/. If \( I \) is the
initial moment of inertia of the dancer
the new moment of inertia is
\( \mathbf{A} \cdot 21 \)
B. 31
c. \( I / 2 \)
D. \( I / 3 \)


The domain of the function \( \sin ^{-1} 2 x \) is:
\( \mathbf{A} \cdot[0,1] \)
B . [-1,1]
c. [-2,2]
D. \( \left[\frac{-1}{2}, \frac{1}{2}\right] \)


Introduction of which rod in a nuclear
reactor controls chain reaction?
A. Iron rods
B. Silicon rods
c. Cadmium rods
D. Platinum rods


The electric permittivity nad magnetic
permeability of free space are \( \varepsilon_{0} \) and \( \mu_{0} \) respectively. The index of refraction of
the medium, if \( \varepsilon \) and \( \mu \) are the electric
permittivity and magnetic permeability in a medium is :
A \( \cdot \frac{\varepsilon \mu}{\varepsilon_{0} \mu_{0}} \)
\( ^{\text {В }}\left(\frac{\varepsilon \mu}{\varepsilon_{0 \mu_{0}}}\right)^{1 / 2} \)
c. \( \frac{\varepsilon_{0} \mu_{0}}{\varepsilon_{\mu}} \)
\( ^{\mathrm{D}}\left(\frac{\varepsilon_{0} \mu_{0}}{\varepsilon \mu}\right)^{1 / 2} \)


A man 2 metres tall walks away from a lamp post 5 metres height at the rate of \( 4.8 \mathrm{km} / \mathrm{hr} . \) The rate of increase of the length of his shadow is
A. \( 1.6 \mathrm{km} / \mathrm{hr} \)
B. \( 6.3 \mathrm{km} / \mathrm{hr} \)
c. \( 5 \mathrm{km} / \mathrm{hr} \)
D. 3.2 km/hr


Which of the following statements is
not correct?
A. Physical adsorption is monolayer
B. Physical adsorption is reversible in nature
C. Physical adsorption is involves low activation energy
D. The extent of physical adsorption decreases with increases in temperature


Given \( : \boldsymbol{u}=\mathbf{1}+\boldsymbol{i} \sqrt{\mathbf{3}} \) and \( \boldsymbol{v}=\sqrt{\mathbf{3}}+\boldsymbol{i} \)
Calculate \( \frac{u^{3}}{v^{4}} \)
A \( \cdot(1 / 4)-i \sqrt{1 / 4} \)
B. \( (3 / 4)-i \sqrt{3} / 4 \)
c. \( (1 / 4)-i \sqrt{3} / 4 \)
D. none of these


In a collection of \( \mathrm{H} \) atom, electrons make a transition from 5th excited
state to 2 nd excited state, then the
maximum number of different types of photons observed are:
\( A \cdot 3 \)
B. 4
\( c \cdot 6 \)
D. 15


The coefficient of \( x \) in \( \left(x^{2}+\frac{c}{x}\right)^{5} \) is
A . 20
B. 10
\( c \cdot 10 c^{3} \)
D. 20 \( c^{3} \)


The equation of motion for an oscillating particle is given by
\( \boldsymbol{x}=\boldsymbol{3} \sin (\boldsymbol{4} \boldsymbol{\pi} \boldsymbol{t})+\boldsymbol{4} \cos (\boldsymbol{4} \boldsymbol{\pi} \boldsymbol{t}), \) where \( \boldsymbol{x} \) is
in mm and t is in second
This question has multiple correct options
A. The motion is simple harmonic
B. The period of oscillation is 0.5 s
c. The amplitude of oscillation is \( 5 \mathrm{mm} \)
D. The particle starts its motion from the equilibrium


A wooden rod is dipped in a cup of ice cream. The other end of wooden rod
A. Becomes cold by process of conduction
B. Becomes cold by process of radiation
c. Becomes cold by process of convection
D. Does not become cold


The correct increasing covalent nature
is:
A. \( N a C l<L i C l<B e C l_{2} \)
в. \( B e C l_{2}<N a C l< \)LiСl
c. \( B e C l_{2}<L i C l<N a C l \)
D. \( L i C l<N a C l<B e C l_{2} \)


If the point (0,2) is equidistant from the points \( (3, k) \) and \( (k, 5) \) then the
value of \( k \) is
\( A \cdot 0 \)
B . 2
c. -2
D. None of these


Determine which of the following match
is correct:
\( \begin{array}{lllll} & \text { List I } & & \text { List II } & \\ & & & & \\ 1 & \text { Phosphorus } & \mathrm{a} & \text { fuel } & \\ 2 & \text { Nitrogen } & \mathrm{b} & \text { lights } & \\ 3 & \text { Carbon } & \mathrm{c} & \text { crackers } \\ 4 & \text { Oxygen } & \mathrm{d} & \text { plant fertilizers } \\ 5 & \text { Neon } & \mathrm{e} & \text { respiration }\end{array} \)
\( A \)
1-e, 2-a, 3-d, 4-c, 5-b
, 4-e, 5-b
B. \( 1-c, 2-d, 3-a, \)
\( c \cdot 1-b, 2-d, 3-e \)
4-a, 5-c
D. \( 1-c, 2-d, 3-b, 4-e, 5-c \)


Match Column I and Column II


In figure points \( A, B, C \) and \( D \) are the
centre of four circles that each have a
radius of length one unit. If a point is
selected at random from the interior of
square ABCD.What is the probability
that the point will be chosen from the
shaded region?
A \( \cdot\left(1-\frac{\pi}{4}\right) \)
в. \( \left(1-\frac{\pi}{2}\right) \)
\( c \cdot\left(1-\frac{\pi}{6}\right) \)
D. \( \left(2-\frac{\pi}{4}\right) \)


Which of the following is an acid?
A \( \cdot C a(O H)_{2} \)
в. \( P(O H)_{3} \)
c. \( N H_{4} O H \)
D. \( N a O H \)


Which of the following statements is correct about reflex arc?
(i). Reflex arcs are efficient quick
responses.
(ii). Reflex arcs are evolved for functioning in the absence of true thought processes.
(iii). A reflex arc is a neural pathway that controls reflex action.
A \( . \) (i), (ii) and (iii)
B. Only (i)
c. only (ii)
D. Only (i) and (ii)


Indicate the incorrect statement:
A. Number of hybrid orbitals formed is equal to no. of atomic involved
B. \( 2 p_{x} \) and \( 2 p_{y} \) - orbitals of carbon can be hybridized to yield two new more stable orbitals
C. Effective hybridisation is not possible with orbitals of widely different energies
D. The concept of hybridisation has a greater significance in the VB theory of localised orbitals than \( M O \) theory.


What is a Land Breeze, and how is it
produced?


If \( \boldsymbol{y}=\left(\tan ^{-1} \boldsymbol{x}\right)^{2} \)
S.T \( \left(\boldsymbol{x}^{2}+\mathbf{1}\right)^{2} \boldsymbol{y}_{2}+\boldsymbol{2} \boldsymbol{x}\left(\boldsymbol{x}^{2}+\mathbf{1}\right) \boldsymbol{y}_{1}=\mathbf{2} \)


Last stable community is succession which depends on climate is
A. Seral community
B. Climax community
c. Poineer community
D. None of the above


The half period of a first order reaction is 10 minutes. Then its rate constant is:
A \( \cdot 6.93 \times 10^{2} \min ^{-1} \)
B . \( 0.693 \times 10^{-2} \mathrm{min}^{-1} \)
c. \( 6.93 \times 10^{-2} \min ^{-1} \)
D. \( 69.3 \times 10^{-1} \mathrm{min}^{-1} \)


Which of the following polymers is not
correctly matched?
A. Formation of dacron - Step-growth polymerisation
B. Formation of polytetrafluoroethene - Step-growth polymerization
C. Formation of polythene - Chain-growth polymerization in presence of benzoyl peroxide
D. Formation of polyacrylonitrile - Chain-growth polymerization in presence of peroxide


Two particle of equal masses have velocities \( \vec{V}_{1}=2 i m / s \) and the second particle has velocity \( 2 \hat{j} \) m/s. The first particle has an acceleration \( \overrightarrow{a_{1}}=(3 \hat{i}+ \)
\( \mathbf{3} \hat{\boldsymbol{j}}) \frac{m}{s^{2}} \) while the acceleration of the other particle is zero. The center of mass of the particle moves in a :
A . circle
B. parabola
c. straight line
D. ellipse


At which stage of meiosis the chromosome number reduces to half?
A. Anaphase!
B. Anaphase II
c. Telophase I
D. Telophase II


In the figure, \( \angle P Q R=\angle P R Q, \) then
prove that \( \angle P Q S=\angle P R T \)


An isolated hollow metal sphere is electrically neutral (no excess charge)
and supported on an insulating stand. A small amount of negative charge is suddenly placed at one point \( P \) on this
metal sphere. If we check on this excess negative charge a few seconds later we will find one of the following
possibilities:
A. All of the excess charge remains right around P.
B. The excess charge has distributed it self evenly over the outside surface of the sphere.
C. The excess charge is evenly distributed over the inside and outside surface
D. Most of the charge is still at point \( P \), but some will have spread over the sphere.


A particle with charge \( e \) and mass \( m \) moving along the X-axis with a uniform speed \( u \), enters a region where a
uniform electric field \( E \) is acting along
the Y-axis. The particle starts to move in a parabola. Its focal length (neglecting any effect of gravity) is :
\( ^{A} \cdot \frac{2 m u^{2}}{e E} \)
в. \( \frac{e E}{2 m u^{2}} \)
c. \( \frac{m u}{2 E} \)
D. \( \frac{m u^{2}}{2 e E} \)


An electric heater supplies heat to a
system at a rate of \( 100 \mathrm{W} \). If system
performs work at a rate of 75 joules per second. At what rate is the internal
energy increasing?


What are the major products of the given reactions?


Find the volume of cylinder, if the radius
of its base is \( 1.5 \mathrm{cm} \) and its height is
\( \mathbf{5} c m \)


The drug given during hypertension is?
A. Streptomycin
B. Chloroxylenol
c. Equanil
D. Aspirin


Factorise: \( 12 a x-4 a b+18 b x-6 b^{2}= \)
0


I ne taple pelow laentıries triree energy
terms that must be considered in
discussing the energy involved in forming aqueous solutions of solid ionic electrolytes.
Term \( \quad \) Symbol
Lattice Energy of Solute
\[
\triangle H_{l a t t i c e}
\]
Enthalpy of Solution
\[
\triangle H_{\text {solution}}
\]
Enthalpy of Hydration
\[
\triangle H_{h y d r a t i o n}
\]
Which of the following equations
CORRECTLY expresses the relationship between the lattice energy of the solid
solute, the enthalpy of solution, and the
enthalpy of hydration of a solution of an electrolyte in water?
A \( . \triangle H_{\text {solution}}=\triangle H_{\text {lattice}}+\triangle H_{\text {hydration}} \)
B. \( \triangle H_{\text {hydration}}=\triangle H_{\text {solution}}+\triangle H_{\text {latice}} \)
C \( . \triangle H_{\text {lattice}}=\Delta H_{\text {solution}}+\triangle H_{\text {hydration}} \)
D. \( \triangle H_{\text {solution}}=\triangle H_{\text {hydration}}-\triangle H_{\text {lattice}} \)


The brass scale of a barometer gives
correct reading at \( 0^{\circ} \mathrm{C} \). The barometer
reads \( 75 \mathrm{cm} \) at \( 27^{\circ} \mathrm{C} \). what is the correct
atmospheric pressure at \( 27^{\circ} \mathrm{C} \). The
coefficient of linear expansion \( \boldsymbol{\alpha} \) of
brass is \( 2.0 \times 10^{-5} \) degree/celcius


Monuments of marble can be destroyed
by:
A. sulphur dioxide pollution
B. carbon monoxide pollution
c. pesticide pollution
D. dust particles


In a junction transistor the emitter, base and collector are made of
A. extrinsic semiconductors
B. intrinsic semiconductors
c. both A and B
D. metal.


The value of \( 7 x-42 \) is
A. \( 7(x-6) \)
B. \( 7(x+6) \)
\( c \cdot-7(x-6) \)
D. \( -7(x+6) \)


State whether the given statement is True or False.

Derivative of \( y=2 x^{5} \) with respect to \( x \)
is \( 10 x^{4} \)
A. True
B. False


Ovules convert into in the
mature fruit.
A. Seeds
B. Fruits
c. stamens
D. All of the above


\( \mathbf{5} \boldsymbol{x}^{\mathbf{3}}+\mathbf{5} \boldsymbol{x}^{\mathbf{2}}+\mathbf{4} \boldsymbol{x}+\mathbf{3}+\mathbf{4} \boldsymbol{x}^{\mathbf{2}}+\mathbf{5} \boldsymbol{x}= \)
A \( \cdot 9 x^{3}+4 x^{2}+4 x+5 \)
B . \( 5 x^{3}+5 x^{2}+9 x+4 \)
\( \mathbf{c} \cdot 5 x^{3}+9 x^{2}+9 x+3 \)
D. None of the above


What would you use to obtain a real and inverted image for any position of an object ?
A. a concave mirror or a concave lens
B. a convex mirror or a convex lens
c. a concave mirror or a convex lens
D. a convex mirror or a concave lens


Construct a histogram for the marks
obtained by 600 students in the VII class annual examinations.
\( \mathbf{3 6 0} \quad \mathbf{4 0 0} \quad \mathbf{4 4 0} \) Marks
No. of
students 125 140


The moment of inertia of a circular disc
of radius \( 2 m \) and mass \( 1 k g \) about an
axis passing through its centre of mass
and perpendicular to plane is \( 2 k g-m^{2} \)
Its moment of inertia about an axis
parallel to this axis and passing through its edge in \( k g-m^{2} \) is
A . 10
B. 8
\( c \cdot 6 \)
D. 4


Find the correct combination
(A) DCMU- \( \ldots \). Herbicide... non-cyclic electron transport
(B) PMAtranspiration
(C) Colchicine.
male sterility
(D) Solnite-Sodium
alginate..........Encapsulation of somatic embryos.
A \( \cdot a, b \)
в. \( a, c \)
\( c \cdot b, c \)
D. b.d


Amount of \( \mathrm{CO}_{2} \) fixed annually is about
A \( \cdot 70 \times 10^{11} \) kg
B . \( 70 \times 10^{11} \mathrm{kg} \)
c. \( 70 \times 10^{13} \mathrm{kg} \)
D. \( 70 \times 10^{13} \mathrm{g} \)


If velocity of \( \alpha- \) particle is made \( 1 / 3 \)
times, then \( \% \) variation in distance of
closest approach will be: (with respect to initial)
A. 300\%
B. 600\%
c. \( 800 \% \)
D. 80\%


Thermal decomposition of \( K C l O_{3}(s) \) in
presence of \( M n O_{2}(s) \) is homogeneous
catalysis.
A . True
B. False


Which of the following will show a negative deviation from Raoult's law?
A. Acetone-benzene
B. Acetone-ethanol
c. Benzene-methanol
D. Acetone-chloroform


Lanthanoid contraction is due to
increase in:
A. atomic number
B. effective nuclear charge
c. atomic radius
D. valence electrons


Which of the following is not due to air pollution?
A. Thinning of the ozone layer
B. Increase in the number of diabetic patients
c. Destruction of habitats
D. Global warming


Which of the following compounds has
a melting point of \( 606^{\circ} \mathrm{C} \) ?
A. cupric iodide
B. cuprous iodide
c. ferric iodide
D. ferrous iodide


The specific heat of water is
1 cal \( g^{-1} \) o \( C^{-1} \). Its value in S.I. units is approximately
\( A \)
B. 4.
c. 420
D. 4200


toppr
Q Type your question
of densities \( \sigma_{1} \) and \( \sigma_{2} \) and viscosities
\( \eta_{1} \) and \( \eta_{2}, \) respectively. They float in
equilibrium with the sphere \( P \) in \( L_{1} \) and
sphere \( Q \) in \( L_{2} \) and the string being taut
f sphere \( P \) along in \( L_{2} \) has terminal
velocity \( \vec{V}_{P} \) and \( Q \) along in \( L_{1} \) has
terminal velocity \( \vec{V}_{Q}, \) then

This question has multiple correct options
\( ^{\mathbf{A} \cdot} \frac{\left|\vec{V}_{P}\right|}{\left|\vec{V}_{Q}\right|}=\frac{\eta_{1}}{\eta_{2}} \)
\( ^{\mathbf{B}} \cdot \frac{\left|\vec{V}_{P}\right|}{\left|\vec{V}_{Q}\right|}=\frac{\eta_{2}}{\eta_{1}} \)
\( \mathbf{c} \cdot \vec{V}_{P} \cdot \vec{V}_{Q}>0 \)
D. \( \vec{V}_{P} \cdot \vec{V}_{Q}<0 \)


Electro magnetic waves are transverse in nature as is evident by
A. polarization
B. interference
c. reflection
D. deffraction


Which of the following order of acidic strength is correct?
A. \( H C l O>H C l O_{2}>H C l O_{3}>H C l O_{4} \)
в. \( H C l O_{4}>H C l O_{2}>H C l O_{3}>H C l O \)
с. \( H C l O_{2}>H C l O>H C l O_{4}>H C l O_{3} \)
D. \( H C l O_{4}>H C l O_{3}>H C l O_{2}>H C l O \)


Symbol for steradian is
A. st
B. sa
\( c \cdot s r \)
D. sn


It is said that Taj is getting destroyed
due to
A. Flood in Yamuna river
B. Decomposition of marble as a result of high temperature
c. Air pollutant released from oil refinery of Mathura
D. All of the above


The number of employees in companies
\( A, B \) and \( C \) are in the ratio 3: 2: 4
respectively. If the number of employees in the three companies is increased by \( 20 \%, 30 \% \) and \( 15 \% \) respectively, what will be the new ratio of employees working in companies \( A, B \) and \( C \)
respectively?
\( \mathbf{A} \cdot 18: 13: 24 \)
B. 13: 18: 23
\( \mathbf{c} \cdot 17: 13: 23 \)
D. 18: 13: 23


A man of mass \( 50 \mathrm{kg} \) falls freely from a height of \( 40 \mathrm{m} \) into a swimming pool and just come to rest at the bottom of the pool. Assume that the average upward force on the man due to water is \( 1000 \mathrm{N} . \) If depth of water in the pool is \( d \)
then \( \boldsymbol{d} \) is \( \left(\boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} / \boldsymbol{s}^{2}\right) \)
A. 20
B. \( 40 \mathrm{m} \)
\( c \cdot 10 m \)
\( D .5 \mathrm{m} \)


If \( p \) is \( T \) and \( q \) is \( F, \) then which of the
following have the truth value \( T \) ?
\( (i) p \vee q \)
\( (i i) \sim p \vee q \)
\( (i i i) p \vee(\sim q) \)
\( (i v) p \wedge(\sim q) \)
A \( \cdot(i),(i i),(i i i) \)
B. \( (i),(i i),(i v) \)
c. \( (i),(i i i),(i v) \)
D. \( (i i),(i i i),(i v) \)


If the empirical formula of potash alum
is \( K A l\left(S O_{4}\right)_{x}, 12 H_{2} O, \) then the value
of 'x' in \( \boldsymbol{K} \boldsymbol{A l}\left(\boldsymbol{S} \boldsymbol{O}_{4}\right)_{x}, \boldsymbol{1} \boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{O} \) is:
\( A \)
B. 2
\( c \cdot 3 \)
D. 4


Which of the following type of waves is used in the SONAR device?
A. radio waves
B. audible sound waves
c. infrasonic waves
D. ultrasonic waves


If a copper wire is bend to make a
square whose area is \( 324 \mathrm{cm} 2 \). If the
same wire is bent to form a semicircle, then find the radius of semicircle.


A rod \( A B \) of mass \( m \) and length \( l \) is positively charged with linear charge density \( \lambda \mathrm{C} / \mathrm{m} \). It is pivoted at end \( \mathrm{A} \) and is hanging freely. If a horizontal electric field \( \boldsymbol{E} \) is switched on in the region, find the angular acceleration of the rod with
which it starts
A \( \cdot \frac{E \lambda}{2 m} \)
в. \( \frac{3 E \lambda}{2 m} \)
c. \( \frac{3 E \lambda}{m} \)
D. zero


From mean value theorem, \( \boldsymbol{f}(\boldsymbol{b})- \) \( \boldsymbol{f}(\boldsymbol{a})=(\boldsymbol{b}-\boldsymbol{a}) \boldsymbol{f}^{1}\left(\boldsymbol{x}_{1}\right) ; \boldsymbol{a}<\boldsymbol{x}_{1}< \)
bif \( f(x)=\frac{1}{x} \) then \( x_{1}= \)
\( A \cdot \sqrt{a b} \)
B. \( \frac{a+b}{2} \)
c. \( \frac{a b}{a+b} \)
D・ \( \frac{a-b}{b-a-a-b} \)


A spectrometer gives the following reading when used to measure the angle of a prism. Main scale reading:
58.5 degree, Vernier scale reading : 9 divisions. Given that 1 division on main
scale corresponds to 0.5 degree. Total divisions on the vernier scale is 30 and
match with 29 divisions of the main
scale. The angle of the prism from the above data:
A . 58.59 degree
B. 58.77 degree
c. 58.65 degree
D. 59 degree


" \( K_{2} O \) is paramagnetic while
\( K O_{2} a n d K_{2} O_{2} \) are diamagnetic."
Answer whether the above statement is
true or false. If true enter 1 , else 0


Given two independence events \( A \) and \( B \) such that \( P(A)=0.3 \) and \( P(B)= \)
0.6. Find \( P(B / A) \)


Co-ordination number of central metal
\( \operatorname{atom} \operatorname{in} N a_{3}\left[A l\left(C_{2} O_{4}\right)_{3}\right] \) and
\( \left[\boldsymbol{C o}(\boldsymbol{e n})_{2} \boldsymbol{C l}\right] \boldsymbol{C l} \) are:
A. 6 and 6
B. 6 and 5
c. 5 and 5
D. 6 and 4


A conducting rod \( \mathrm{AB} \) moves parallel to
X-axis in a uniform magnetic field,
pointing in the positive X-direction. The
end \( A \) of the rod gets
A. positively charged
B. negatively charged
c. neutral
D. first positively charged and then negatively charged


Calculate the \( \Delta \boldsymbol{H}_{f}^{o} \) of \( \boldsymbol{C}_{\boldsymbol{6}} \boldsymbol{H}_{12} \boldsymbol{O}_{6}(\boldsymbol{s}) \) from
the following data:
\( \Delta \boldsymbol{H}_{c o m b}\left[\boldsymbol{C}_{6} \boldsymbol{H}_{12} \boldsymbol{O}_{6}(\boldsymbol{s})\right]= \)
\( -2816 k J / m o l \)
\( \boldsymbol{\Delta} \boldsymbol{H}_{f}^{o} \quad \) of \( \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g})=-\boldsymbol{3} \boldsymbol{9} \boldsymbol{3} . \boldsymbol{5} \boldsymbol{k} \boldsymbol{J} / \boldsymbol{m} \boldsymbol{l} \)
\( \Delta H_{f}^{o} \quad \) of \( H_{2} O(l)=-285.9 k J / m o l \)
A. \( -126.0 k J / m o l \)
В. \( -1260 k J / m o l \)
c. \( -1220 k J / m o l \)
D. \( -160 k J / \) mol


The area of region bounded by curve \( y=\cos 2 x, \) line \( x=0 \) and \( x=\frac{\pi}{3} \) is
A \( \cdot \frac{2-\sqrt{3}}{4} \)
B. \( \frac{\sqrt{3}}{4} \)
c. \( \frac{4-\sqrt{3}}{4} \)
D. \( \frac{\sqrt{3}-4}{4} \)


Mitochondria are sites of
A. Oxidative phosphorylation
B. Photolysis
C. Phosphorylation
D. Starch synthesis.


\( \mathbf{A} \)
\( \mathbf{5 0 0} \Omega \) resistor and a capacitor \( C \) are
connected in series across \( 50 H z . A C \)
supply mains. The r.m.s potential
difference recorded on voltmeter \( V_{1} \) and
\( V_{2} \) are \( V_{1}=120 V \) and \( V_{2}=160 \mathrm{V} . \) The
power taken from the mains is:
4. \( 480 \mathrm{W} \)
В. 240 И
c. \( 28.8 W \)
D. \( 14.4 \mathrm{W} \)


Write the value of \( \tan \left(2 \tan ^{-1} \frac{1}{5}\right) \)


A positively charged particle having some mass is resting in equilibrium at a height H above the center of a fixed, uniformly and positively charged ring of radius R. The force of gravity (mg) acts downwards. The equilibrium of the particle at the given position (H) for small vertical displacement will be:
(Assume \( g \) is uniform)
\( ^{\mathbf{A}} \cdot \) stable if \( H<\frac{R}{2} \)
B. stable if \( H=\frac{R}{\sqrt{2}} \)
c. unstable if \( H<\frac{R}{\sqrt{2}} \)
D. stable if \( H=\frac{R}{2} \)


When the object is at focus of a concave mirror, the image is formed at
A. the focus
B. the centre of curvature
c. within focus
D. infinity


Camphor kept in an open vessel disappears by the process of:
A. diffusion
B. sublimation
c. evaporation
D. condensation


A plane intersects the co ordinate axes
at \( A, B, C . \) If \( O=(0,0,0) \) and (1,1,1) is
the centroid of the tetrahedron \( O A B C \)
then the sum of the reciprocals of the
intercepts of the plane
\( \mathbf{A} \cdot 12 \)
B. \( \frac{4}{3} \)
c. 1
\( D \cdot \frac{3}{4} \)


Pugazh has been given four choices for his pocket money by his father. Which of the choices should he taken in order to
get the maximum money?
\( A \)
\( \frac{2}{3} \) of \( R s 150 \)
B. \( \frac{3}{5} \) of \( R s 150 \)
c. \( \frac{1}{6} \) of \( R s 150 \)
D. \( \frac{1}{5} \) of \( R s 15 \)


Read the following five statements (A to
E) and select the option with all correct
statements:
This question has multiple correct options
A. Mosses and Lichens are the first organisms to colonise a bare rock
B. Selaginella is a homosporous pteridophyte
c. Coralloid roots in cycas have VAM
D. Main plant body in bryophytes to gametophytes, male present within sporangia located on sporophyte


Effective capacitance between \( A \) and \( B \)
in the figure shown is (all capacitances
\( \operatorname{are} \operatorname{in} \mu \boldsymbol{F}) \)
\( ^{A} \cdot \frac{3}{14} \mu F \)
в. \( \frac{14}{3} \mu F \)
\( c \cdot 21 \mu F \)
D. \( 23 \mu F \)


Nitrogen reacts with \( O_{2} \) to form reddish
brown fumes of \( N O_{2} \)
A. True
B. False


In a series \( \mathrm{L}, \mathrm{R}, \mathrm{C}, \) circuit which is
connected to a.c. source. When resonance is obtained then net
impedance Z will be
A. \( z=R \)
B. \( z=L-1 / C \)
\( c \cdot z=L \)
D. z = 1/C


A plane mirror makes an angle of \( 30^{\circ} \)
with the horizontal. If a vertical ray strikes the mirror. Find the angle
between the mirror and the reflected
ray?


\( (5 i)\left(-\frac{3}{5} i\right) \)


Food in plants is translocated in the form of
A. Glucose
B. Starch
c. sucrose
D. Fructose


Calculate the uncertainty in the velocity of a wagon of mass 3000 kg. whose
position is known to an accuracy of 土10pm.


In an electrochemical cell, anode and
cathode are
A. Positively and negatively charges ions
B. Positively and negatively charges electrodes
C. Negatively and positively charged electrodes
D. Negatively and positively charged ions


Forest is a purifier of
A. Air
B. Water
c. Soil
D. All of the above


Column - II and choose the correct
option from the following.
\( A \cdot A-3, B-4, C-1, D-5, E-2 \)
B. \( A-2,8-3, C-1, D-5, E-4 \)
\( C \cdot A-3, B-4, C-5, D-1, E-2 \)
\( D \cdot A-4, B-5, C-1, D-2, E-3 \)
\( E \cdot A-3, B-1, C-2, D-4, E-5 \)


Reflection from a smooth surface is
called reflection.
A. Regular
B. Irregular
c. Multiple
D. Total internal


Method used for the concentration of
sulphide ore is :
A. hand picking
B. froth floatation
c. magnetic separation
D. leaching


A steel ball strikes a fixed smooth steel
plate placed on a horizontal surface at an angle \( \theta \) with the vertical. If the
coefficient of restitution is \( e \), the angle
at which the rebound will take place is
\( A \cdot \theta \)
B. \( \tan ^{-1}\left[\frac{\tan \theta}{e}\right] \)
\( c \cdot e \tan \theta \)
D. \( \tan ^{-1}\left[\frac{e}{\tan \theta}\right] \)


If \( \tan \theta+\frac{1}{\tan \theta}=2, \) find the value of
\( \cot ^{2} \theta+\frac{1}{\cot ^{2} \theta} \)


A current of \( 10 \mathrm{A} \) is flowing in a wire of
length \( 1.5 \mathrm{m} . \) A force of \( 15 \mathrm{N} \) acts on it when it is placed in a uniform magnetic field of 2 T. The angle between the magnetic field and the direction of the
current is:
A \( .30^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 90^{\circ} \)


Glycogen stored in liver and muscles of
a man is a:
A. monosaccharide
B. polysaccharide
c. protein
D. fat


Coulomb's Law agrees with
A. Newtons 3rd Law of Motion
B. Newtons 1st Law of Motion
C. Newtons 2 nd Law of Motion
D. All of the above


Magnetic field at the center (at nucleus) of the hydrogen-like atoms (atomic number \( =Z \) ) due to the motion
of electron in \( n^{t h} \) orbit is proportional to
A \( \cdot \frac{n^{3}}{z^{5}} \)
B. \( \frac{n^{4}}{z} \)
c. \( \frac{z^{2}}{n^{3}} \)
D. \( \frac{z^{3}}{n^{5}} \)


The streaks of bright light seen during lightning is essentially the path followed by:
A. UV rays from sun
B. Gamma rays
c. Accumulated electric charges
D. None of the above


A parallel plate capacitor has area
\( 20 c m^{2} \) and separation between the plates is 0.1 m \( m . \) The dielectric break
down strength is \( 3 \times 10^{6} v / m \)

The maximum r.m.s voltage which can be safely applied is :
\( \mathbf{A} \cdot 210 V \)
в. \( 300 V \)
c. \( 100 V \)
D. 200


What is chemical kinetics and
chemical thermodynamics?


The velocity-time graph given shows the
motion of a cyclist. Find the distance
covered by the cyclist in 15 seconds.
A . \( 200 m \)
в. 500 m
\( c .400 m \)
D. \( 300 m \)


For what (finite) value of \( x \operatorname{does} F(x)= \)
\( \mathbf{0 ?} \)


Cruciform corolla is found in
A. Pisum
B. Radish
c. China Rose
D. Sunflower


ff \( \overrightarrow{\boldsymbol{p}}=\mathbf{3} \overrightarrow{\boldsymbol{a}}-\mathbf{5} \overrightarrow{\boldsymbol{b}} ; \overrightarrow{\boldsymbol{q}}=\mathbf{2} \overrightarrow{\boldsymbol{a}}+\overrightarrow{\boldsymbol{b}} ; \overrightarrow{\boldsymbol{r}}=\overrightarrow{\boldsymbol{a}}+ \)
\( 4 \vec{b} ; \vec{s}=-\vec{a}+\vec{b} \) are four
vectors such that \( \sin (\vec{p} \wedge \vec{q})=1 \) and \( \sin (\vec{r} \wedge \vec{s})=1 \) then \( \cos (\vec{a} \wedge \vec{b}) \) is
A \( \cdot-\frac{19}{5 \sqrt{43}} \)
B.
\( c \cdot 1 \)
D. \( \frac{19}{5 \sqrt{43}} \)


If \( \sin \theta=\frac{1}{2}, \cos \phi=1, \) where \( 0<\theta<\frac{\pi}{2} \)
and \( 0<\phi \leq \frac{\pi}{2}, \) then \( (\cot (\theta+2 \phi))^{2} \) is
equal to:


If \( (1+a x)^{n}=1+8 x+24 x^{2}+\dots ; \) then
\( \frac{a-n}{a+n} \) is equal to
\( \mathbf{A} \cdot \mathbf{3} \)
B. \( \frac{-1}{3} \)
c. -3
D.


A charge q exists at a distance or \( \mathrm{R} \)
from a spherical concave mirror of
mass of radius of curvature R, Let
mirror subtends a half angle \( \theta=30^{\circ} \) at
the angle.
Flux passing through the mirror is
\( A \)
B. \( \frac{q \sin ^{2} 30^{\circ}}{\varepsilon_{0}} \)
c. \( \frac{q \sin ^{2} 30}{2 \varepsilon_{0}} \)
D. \( \frac{q \sin ^{2} 15^{\circ}}{2 \varepsilon_{0}} \)


Find the coordinates of the foci, the
vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse \( 4 x^{2}+9 y^{2}=36 \)


Subtract \( 4 p^{2} q-3 p q+5 p q^{2}-8 p+ \)
\( 7 q-10 \) from \( 18-3 p-11 q+5 p q \)
\( 2 q^{2}+5 p^{2} q \)
A \( \cdot 28+5 p-18 q+8 p q-2 q^{2}+p^{2} q-5 p q^{2} \)
B . \( 8+11 p-18 q+8 p q-2 q^{2}+p^{2} q-5 p q^{2} \)
C. \( 28-5 p+18 q-8 p q+2 q^{2}-p^{2} q+5 p q^{2} \)
D. none


In cyclotron, for a given magnet, radius of the semicircle traced by positive ion is directly proportional
to (v=velocity of positron ion)
A \( \cdot v^{-2} \)
B . \( v^{-1} \)
\( c \)
\( D \cdot v^{2} \)


Bond order of nitric oxide is:
\( A \cdot 1 \)
B. 2.5
\( c \cdot 2 \)
D. 1.5


The given conversion can be carried out
by which process?
\( (\mathrm{A}) \)
\( \mathbf{A} \cdot i . H B r+ \) peroxide \( i i . M e_{3} C^{\ominus}, \Delta i i i . O_{3} / H_{2} O \)
B. i.H Br in. \( C_{2} H_{5} O^{\ominus}, \Delta \) iii. \( O_{3} / H_{2} O \)
C \( . \) i.H I i i. \( M e O^{\ominus}, \Delta \) ii \( . O_{3} / Z n- \) acid
D. \( H C l+ \) peroxide


Fahrenheit scale divides the two fixed
points into:
A. 180 parts
B. 212 parts
c. 100 parts
D. 32 parts


Two bodies of equal weight are kept at heights of h and 1.5 h respectively. The ratio of their P.E. will be:
A . 3: 2
B. 2: 3
c. 1:
D. none of these


\( \boldsymbol{C H}_{3} \boldsymbol{C H O}+\boldsymbol{H C H O} \frac{\boldsymbol{H e a t}}{\text {Dil. } \boldsymbol{N a O H}} \)
\( \boldsymbol{A} \frac{\boldsymbol{H}_{3} \boldsymbol{O}^{+}}{\boldsymbol{H} C N} \boldsymbol{B} \)
The structure of compound \( B \) is :
\( \mathbf{A} \cdot C H_{3}-C H-C O O H \)
\( _{O H} \)
в. \( C H_{2}=C H-\underset{I N}{_{I}} \begin{array}{c}C H-O H \\ \end{array} \)
с. \( C H_{3} C H_{2}-C H-C O O H \)
он
D. \( C H_{2}=C H-C H-C O O H \)
o \( _{H} \)


Mass spectrograph helps in the detection of isotopes because they:
A. have different atomic masses
B. have same number of electrons
c. have same atomic number
D. have same atomic masses


The point on the curve \( y=\sqrt{x-1} \)
where the tangent is perpendicular to the line \( 2 x+y-5=0 \) is
A. (2,-1)
в. (10,3)
c. (2,1)
()
D. (5,-2)


Which of the following is the solution
set of the equation \( 2 \cos ^{-1} x= \) \( \cot ^{-1}\left(\frac{2 x^{2}-1}{2 x \sqrt{1-x^{2}}}\right) \)
A \( .(0,1) \)
B . \( (-1,1)-\{0\} \)
c. (-1,0)
D. [-1,1]


Multiply \( \left(3 p-q^{2}\right)\left(7 q+4 p^{4}\right) \)


Two coins are tossed once, where
(i) \( E: \) tail appears on one coin, \( \boldsymbol{F}: \) one
coin shows head
(ii) \( E: \) no tail appears, \( \boldsymbol{F}: \) no head
appears
Determine \( \boldsymbol{P}(\boldsymbol{E} \mid \boldsymbol{F}) \)
A .1,0
в. 1,0.2
c. 0,2
D. 1,3


The equilibrium constant for the reaction \( 3 A+2 B \rightleftharpoons C \) will be:
A \( \cdot \frac{[3 A][2 B]}{[C]} \)
\( ^{\mathbf{B}} \cdot \frac{[A]^{3}[B]}{[C]} \)
c. \( \frac{[C]}{[A]^{3}[B]^{2}} \)
D. \( \frac{[C]}{[3 A][2 B]} \)


Which of the following part protects the eye and gives it shape?
A. Choroid
B. Sclera
c. Yellow spot
D. Ciliary muscles


The age of adolescence is
A. \( 9-12 \) years.
B. 13-19 years.
c. 15 -20 years.
D. None of the above.


What type of sorus is present in Nephrolepis?
A. coenosorus
B. simple
c. Mixed
D. None of the above


The population in India has almost tripled since
per Census 2011
A . 1921
B. 1941
c. 195
D. 2001


Addition of 0.1 mole of which of the
following to a buffer solution consisting
of 1 mole each of \( C H_{3} C O O H \& \)
\( \boldsymbol{C H}_{3} \) COONa causes greater increase
in \( p H ? \)
A. \( H C l \)
в. \( C H_{3} \) СООН
c. \( C H_{3} \) COONa
D. \( N a O H \)


State whether the given statement is true or false.
If \( \boldsymbol{p}^{1-2 x} \times \sqrt{\boldsymbol{p}}=\boldsymbol{q}^{1-2 x} \times \sqrt{\boldsymbol{q}} ; \boldsymbol{p} \neq \boldsymbol{q} \) then
value of \( \boldsymbol{x} \) is \( \frac{\mathbf{3}}{\mathbf{4}} \)
A. True
B. False


The radius of nucleus is:
A. proportional to its mass number
B. inversely proportional to its mass number
C. proportional to the cube root of its mass number
D. not related to its mass number


The angle of contact between a glass capillary tube of length \( 10 \mathrm{cm} \) and a
liquid is \( 90^{\circ} . \) If the capillary tube is
dipped vertically in the liquid, then the liquid
A. Will rise in the tube
B. Will get depressed in the tube
c. Will rise up to \( 10 \mathrm{cm} \) in the tube and will over flow
D. Will neither rise nor fall in the tube


Show that the function \( f(x)=\frac{x-2}{x+1} \)
for \( \boldsymbol{x} \neq \mathbf{0} \) is increasing.


Ozone loss was first detected into the
stratosphere over the
A . Arctic
B. Antarctic
c. Africa
D. Australia


\( \ln \) a closed system \( : \boldsymbol{A}(s) \rightleftharpoons 2 \boldsymbol{B}(\boldsymbol{g})+ \)
\( 3 C(g) \) if the partial pressure \( C \) is of
doubled then partial pressure B wil be:
A. Twice the original pressure
B. Half of its original pressure
c. \( \frac{1}{2 \sqrt{2}} \) times, the original pressure
D. \( 2 \sqrt{2} \) times its original pressure


Half life of radioactive element depends
upon
A. amount of element present
B. temperature
c. pressure
D. nature of element


Assertion
An astronaut in an orbiting space
station above the Earth experiences
weightlessness.
Reason
An object moving around the Earth
under the influence of Earths
gravitational force is in a state of free-
fall.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The graph above shows the variation in
concentration of reactants and
products as \( H_{2} \) and \( I_{2} \) react to form \( \mathrm{H} \) at a temperature. Equilibrium is
reached when the concentration of HI is
\( A \cdot A \)
B. B
\( c . c \)
D.
\( E \)


Assertion
For a reaction at equilibrium,the Gibb's free energy of reaction is minimum at constant temperature and pressure.
Reason
The Gibb's free energy of both reactants and products increases and become
equal at equilibrium.

Read the above assertion and reason
and choose the correct option regarding
¡t.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The ratio of the mango trees and orange
trees is \( 7: 9 . \) If 5 mango trees and 5
orange trees were planted in addition
the ratio would be \( 27: 34 . \) Find the
number of mango trees.


The magnification produced by a mirror is \( +\frac{1}{3} . \) Then the mirror is a
A. Concave mirror
B. Convex mirror
c. Plane mirror
D. plano convex mirror


\( \operatorname{Let} f(x)=\frac{x^{2}-9 x+20}{x-[x]} \) where \( [x] \) is
the greatest integer not greater than \( x \) then
This question has multiple correct options
A \( \cdot \lim _{x \rightarrow 5^{-}} f(x)=0 \)
B . \( \lim _{x \rightarrow 5^{+}} f(x)=1 \)
c. \( \lim _{x \rightarrow 5} f(x) \) does not exists
D. none of these


In our society, women are blamed for
producing female children. Choose the correct option for sex determination in
humans.
A. Due to some defect like aspermia in man
B. Due to genetic makeup of some particular sperm which fertilizes the eggg
c. Due to genetic makeup of the eggs
D. Due to some defect in women


Unit of power of a lens is :
A . Metre
B. Dyne
c. Dioptre
D. None of these


Select pair of compounds in which both have different hybridization but have
same molecular geometry.
A. \( B F_{3}, B r F_{3} \)
в. \( I C l_{2}^{-}, B e C l_{2} \)
c. \( B C l_{3}, P C l_{3} \)
D. \( P C l_{3}, N C l_{3} \)


Assertion
The electrolysis of potassium iodide, \( \mathrm{K} \) I produces electrical energy.
Reason
Electrolytic cells convert chemical energy into electrical energy
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Multi-directional flow of a variety of
organic and inorganic solutes occurs
through.
A. Xylem
B. Vascular tissue
c. Phloem
D. Root


Antinocking agent added to petrol is commonly
A. Tetramethyl or tetraethyl lead
B. Dibromoethane
c. Both A and B
D. octane


A particle of mass \( m \) and carrying a charge \( e \) is fired perpendicular to a uniform magnetic induction \( B \) with a
velocity \( v . \) The time period of revolution for the subsequent motion is given by
A \( \cdot \frac{2 \pi B}{m e} \)
в. \( \frac{2 \pi e}{B} \)
с. \( \frac{2 \pi m}{B e} \)
D. \( \frac{\pi B e}{m} \)


The total energy of an electron in the ground state of the hydrogen atom is
-13.6 eV. The kinetic energy of an
electron in the first excited state is:
\( \mathbf{A} \cdot 1.7 \mathrm{eV} \)
B. 3.4 ev
c. 6.8 ev
D. 13.6 ev


Father says to son "I am 9 times as old
as you were when i was as old as you are". If the sum of their present ages is
50 years. What is the age of father?


Lead storage battery has anode and cathode respectively made up of:
A \( . P b \) and \( P b O_{2} \)
в. \( P b O_{2} \) and \( P b \)
\( c . \) both \( P b \)
D. both \( P b O_{2} \)


Match the following A
\( \mathbf{A} \)
1-b, 2-c, 3-a, 4-d
B. \( 1-c, 2-d, 3-b, 4-a \)
c. \( 1-a, 2-c, 3-b, 4-d \)
D. \( 1-c, 2-a, 3-d, 4-b \)


The rosette habit of cabbage can be changed by application of
\( A \cdot \) IAA
в. яА
c. ABA
D. Ethaphon


Round off following number upto four significant figures
45.689
A . 45.689
B. 45.69
c. 45.68
D. 45.7


The radius of gyration of a disc about its axis passing through its centre and perpendicular to its plane is
A. \( R / \sqrt{2} \)
в. \( R / 2 \)
c. \( \sqrt{2 R} \)
D. 2 \( R \)


If \( \left|\begin{array}{lll}\boldsymbol{a} & \boldsymbol{a}^{2} & \mathbf{1}+\boldsymbol{a}^{3} \\ \boldsymbol{b} & \boldsymbol{b}^{2} & \mathbf{1}+\boldsymbol{b}^{3} \\ \boldsymbol{c} & \boldsymbol{c}^{2} & \boldsymbol{1}+\boldsymbol{c}^{3}\end{array}\right|=\mathbf{0} \) and vectors
\( \left(1, a, a^{2}\right),\left(1, b, b^{2}\right) \) and \( \left(1, c, c^{2}\right) \) are non
coplanar then \( a b c \) equals
A . -1
B. 1
\( c \cdot 0 \)
D.


Which of the following are isotones?
This question has multiple correct options
A. \( A r_{18}^{40} \)
B. \( C a_{a_{0}^{2}}^{2} \)
c. \( S c_{c 13}^{43} \)
D. \( S c_{21}^{41} \)


Plastic is bad for environment because:
A. they are non-biodegradable
B. they harm aquatic life
C. they are toxin carrier
D. all of these


Other name of alkyl halide is :
A. Monohalo-alkanes
B. Dihalo-alkanes
C. Trihalo-alkanes
D. None of these


Calculate the number of electrons lost
or gained the changes:
\( \mathbf{3} \boldsymbol{I}_{2}+\boldsymbol{6} \boldsymbol{N} \boldsymbol{a} \boldsymbol{O} \boldsymbol{H} \rightarrow \boldsymbol{N} \boldsymbol{a} \boldsymbol{I} \boldsymbol{O}_{3}+\mathbf{5} \boldsymbol{N} \boldsymbol{a} \boldsymbol{I}+ \)
\( \mathbf{3} \boldsymbol{H}_{\mathbf{2}} \boldsymbol{O} \)


Complete the analogy:
Glass : Insulator : : Copper:


A distinct endodermis is a constant
feature of
A. Dicot leaves
B. Monocot stems
c. Monocot leaves
D. Dicot stema


If an object is placed at a distance \( \mathrm{R} \)
from the pole of first surface, then the real image is formed at a distance \( \mathrm{R} \)
from the pole of the second surface. The refractive index \( \mu \) of the sphere is given
by
A . 1.5
B. 2
\( c \cdot \sqrt{2} \)
D. none of these


\( \ln S O_{3} \) how many \( p \pi-d \pi \) bonds are
present?
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D.


Alkaline earth metals are :
A. reducing agent
B. dehydrating agent
c. amphoteric
D. oxidising agent


Find out the value of I in the circuit
shown in figure.
\( A \cdot 5 A \)
в. 2.5
\( c \cdot 10 A \)
\( D \cdot 4 A \)


Discuss the continuity of the following functions:
(a) \( f(x)=\sin x+\cos x \)
(b) \( f(x)=\sin x-\cos x \)


Mention the function of pneumatophore


\( A B C \) and BDF are two equilateral triangles such that \( \mathrm{D} \) is the mid-point of BC The ratio of the areas of triangles \( A B C \) and BDF is
A . 2: 1
B. 1: 2
c. 4: 1
D. 1: 4


In a circuit, the frequency is \( \boldsymbol{f}=\frac{\mathbf{1 0 0 0}}{\mathbf{2} \pi} \)
\( \mathrm{Hz} \) and the inductance is 2 henry, then
the reactance will be
\( A \cdot 200 \Omega \)
в. 200 \( \mu \) \Omega
c. \( 2000 \Omega \)
D. 2000 \( \mu \Omega \)


Find the angles of a triangle that are in
ratio 2: 2: 5


Three charged particles are collinear and are in equilibrium, then
A. all the charged particle have the same poarity
B. the equilibrium is unstable
C. all the charged particles cannot have the same polarity
D. both (b) and (c) are correct.


If \( \boldsymbol{A}+\boldsymbol{B}+\boldsymbol{C}=\boldsymbol{\pi}, \) then
\( \left|\begin{array}{ccc}\sin (\boldsymbol{A}+\boldsymbol{B}+\boldsymbol{C}) & \sin \boldsymbol{B} & \cos \boldsymbol{C} \\ \sin \boldsymbol{\theta} & \tan \boldsymbol{A} \\ \cos (\boldsymbol{A}+\boldsymbol{B}) & -\tan \boldsymbol{A} & \boldsymbol{0}\end{array}\right|= \)


State the two Kirchhoff's rules used in
electric networks. How are there rules
justified?


Draw a circle and mark a radius.


Which one of the following can be considered as an example of secondary consumer?
A. A fish that feeds on algae
B. A hawk that feeds on a mouse that feeds on an insect
C. A plant that is parasitic to another plant
D. A lion that eats a gazelle that feeds on grass
E. A beetle that feeds on nectar


Which phenomenon is/are observed during washing of clothes by detergents? This question has multiple correct options
A. Micelle formation
B. Adsorption
c. Emulsification
D. Foaming


The equation for a wave travelling in \( x \) direction on a string is : \( y=3(\sin 3.14 x- \)
\( 314 t), \) then

Find the maximum velocity of particle
of the string.