If \( \boldsymbol{a} \cdot \boldsymbol{i}=\boldsymbol{a} \cdot(\boldsymbol{j}+\boldsymbol{i})=\boldsymbol{a} \cdot(\boldsymbol{i}+\boldsymbol{j}+\boldsymbol{k}) \)
then \( a \) is equal to
\( \mathbf{A} \cdot i \)
B. \( k \)
\( c \cdot j \)
D \( \cdot(i+j+k) \)


Two identical blocks \( A \) and \( B \) connected
by a massless string are placed on a frictionless horizontal plane. A bullet having same mass moving with
a speed u strikes block \( \mathrm{B} \) from behind as shown. If the bullet gets embedded into the block \( \mathrm{B} \), then find the impulse on A due to tension in the string.
A \( \cdot \frac{m}{3} \)
в. \( \frac{2 m u}{3} \)
\( c \cdot \frac{m u^{2}}{3} \)


\( 4 \frac{1}{2}+2 \frac{5}{7} \times \frac{7}{19}-\frac{7}{19} \div 2 \)


Assertion
The coil in the resistance boxes are
made by doubling the wire.
Reason
Thick wire is required in resistance box.
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


The essential chemical components of
many coenzymes are
A. Proteins.
B. Nucleic acid
c. carbohydrates.
D. Vitamins.


Find the radius and centre of the circle
\( x^{2}+y^{2}-24 y+128=0 \)


Antiseptics are a class of
drugs.
A. analgesic
B. antipyretic
c. tranquilizer
D. antibiotic


\( \int \frac{x^{4}}{x^{2}+1} d x \)


The energy wastage occurs during
A. Dark respiration
B. Photosynthesis
C . Glycolysis
D. Photorespiration


The unit of specific heat is
\( \mathbf{A} \cdot \operatorname{cal}^{o} \mathrm{C} \)
B . \( \operatorname{cal} /\left(\mathrm{g}^{\circ} \mathrm{C}\right) \)
c. cal/g
D. none of these


Solve:
\( \lim _{x \rightarrow 3} \frac{\left(x^{\frac{1}{3}}+3 \sqrt{3}\right)\left(x^{\frac{1}{3}}-3 \sqrt{3}\right)}{x-3} \)


If \( \boldsymbol{A}=\left[\begin{array}{rr}\mathbf{2} & -\mathbf{3} \\ -\mathbf{4} & \mathbf{1}\end{array}\right], \) then ad
\( \left(3 A^{2}+12 A\right) \) is equal to:
A. \( \left[\begin{array}{ll}51 & 63 \\ 84 & 72\end{array}\right] \)
B. \( \left[\begin{array}{ll}51 & 84 \\ 63 & 72\end{array}\right] \)
c. \( \left[\begin{array}{cc}72 & -63 \\ -84 & 51\end{array}\right] \)
D. \( \left[\begin{array}{cc}72 & -84 \\ -63 & 51\end{array}\right] \)


In hierarchical classification, class is
interpolated between
A. Family and genus
B. Phylum and order
c. order and family
D. Kingdom and phylum


If the function \( \mathbf{f}(\boldsymbol{x})= \) \( \frac{\log (1+\boldsymbol{a} \boldsymbol{x})-\log (1-\boldsymbol{b} \boldsymbol{x})}{\boldsymbol{x}} \) for \( \boldsymbol{x} \neq \mathbf{0} \) is
continuous at \( x=0 \) then \( f(0)= \)
A \( . a-b \)
B. \( a+b \)
\( \mathbf{c} \cdot \log a+\log b \)
D. \( \log a-\log b \)


For the \( V \) -t graph shown displacement
during 15 seconds is
\( A \cdot 25 m \)
B. \( 50 \mathrm{m} \)
\( c \). zero
D. \( 75 \mathrm{m} \)


A charge \( Q \) is uniformly distributed over the surface of two concentric
conducting spheres of radii \( R \) and \( r \)
\( (R>r) \) such that surface charge
densities are same for both spheres.
Then potential at the common center of
these spheres is
A \( \cdot \frac{k Q(R+r)}{R r} \)
B. \( \frac{k Q(R+r)}{\left(R^{2}+r^{2}\right)} \)
c. \( \frac{k Q}{\sqrt{R^{2}+r^{2}}} \)
D \( \quad k Q\left(\frac{1}{R}-\frac{1}{r}\right) \)


1. True OR
2. False:
\( \mathrm{m} \) - chlorobromobenzene is an isomer of
\( \mathrm{m} \) - bromochlorobenzene.


Figure. shows the \( P-V \) plot of an ideal
gas taken through a cycle \( A B C D A \). The
part \( A B C \) is a semi-circle and \( C D A \) is
half of an ellipse. Then
This question has multiple correct options
A. the process during the path \( A \rightarrow B \) is isothermal
B. heat flows out of the gas during the path \( B \rightarrow C \rightarrow \)
c. work done during the path \( A \rightarrow B \rightarrow C \) is zero
D. positive work is done by the gas in the cycle \( A B C D A \)


Atmosphere of big cities is polluted most by :
A. Automobile exhausts
B. Radioactive fall out
c. Household waste
D. Pesticide residue


I.F of \( x \frac{d y}{d x}=\left(2 y+2 x^{4}+x^{2}\right) \) is:
A . \( x^{-2} \)
B . \( x^{-1} \)
c. \( x \)
D. \( x^{2} \)


\( A \) bag \( X \) contains 4 white balls and 2
black balls, while another bag \( \boldsymbol{Y} \)
contains 3 white balls and 3 black balls
Two balls are drawn (without
replacement) at random from one of the bags and were found to be one white
and one black. Find the probability that the balls were drawn from bag \( Y \)


The use of aspartame is limited to cold
foods and drinks because:
A. it is unstable to heat and decomposes at cooking temperature
B. it is 500 times sweeter than cane sugar
C. it becomes bitter at cooking temperature
D. it reacts with the food at cooking temperature


One angle of a six-sided polygon is \( 140^{\circ} \)
and the other angles are equal. Find the measure of each equal angle.
\( \mathbf{A} \cdot 116 \)
B . \( 126^{\circ} \)
\( c \cdot 112^{\circ} \)
D. 118


Prove that the sum of the distances
from the focus of the points in which a conic is intersected by any circle, whose centre is at a fixed point on the transverse axis, is constant.


When light is refracted from a surface, which of its following physical parameters does not change?
A. Velocity
B. Amplitude
c. Frequency
D. wavelength


When the current and voltage of an
electric circuit is given. Then power can
be calculated by:
A. multiplying the current by the difference between the voltage going into and going out of the device
B. multiplying the resistance by the resistance and the current
C. multiplying the voltage by the difference between the current going into and going out of the device
D. multiplying the current by the voltage
E. multiplying the current by the resistance


Which of the following was carried out
by Rutherford in his experiment?
A. Fast moving alpha-particles were made to fall on a thin silver foil.
B. Fast moving beta-particles were made to fall on a thin gold foil
C. Fast moving alpha-particles were made to fall on a thin gold foil
D. Fast moving gamma-particles were made to fall on a thin gold foil


A wheel moves in the xy plane such that
the location of its center is given by
equations
\( \mathbf{x}_{\mathbf{0}}=\mathbf{1 2 t}^{3}, \mathbf{y}_{\mathbf{0}}=\mathbf{R}=\mathbf{2}, \) where \( \mathbf{x}_{o} \) and \( \mathbf{y}_{o} \)
are measured in metre and \( t \) in
seconds.
The angular displacement of a radial
line measured from a vertical reference
line is \( \Theta=8 t^{4}, \) where \( \Theta \) is in radians
(given \( v_{o} \) is the velocity of center of
wheel


Let the vector \( \vec{a}, \vec{b}, \vec{c} \) and \( \vec{d} \) be such \( \operatorname{that}(\overrightarrow{\boldsymbol{a}} \times \overrightarrow{\boldsymbol{b}}) \times(\overrightarrow{\boldsymbol{c}} \times \overrightarrow{\boldsymbol{d}})=\mathbf{0} \cdot \operatorname{Let} \boldsymbol{P}_{1} \)
and \( P_{2} \) be planes determined by the pairs of vectors \( \vec{a}, \vec{b} \) and \( \vec{c}, \vec{d} \)
respectively then the angle between \( P_{1} \)
and \( P_{2} \) is
A. 0
в. \( \frac{\pi}{4} \)
c. \( \frac{\pi}{3} \)
D. \( \frac{\pi}{2} \)


With the help of suitable examples describe the various types of vascular bundles in plants.


A ray of light is ancident at angle of \( 35^{\circ} \)
on a plane mirror. What is angle \( \theta \) ?
A . \( 35^{\circ} \)
B. \( 45^{\circ} \)
\( c \cdot 55 \)
D. none of these


A helicopter rises vertically with a speed of \( 100 \mathrm{m} / \mathrm{s} \). If helicopter has length \( 10 \mathrm{m} \) and horizontal component
of earth's magnetic field is \( 5 \times \)
\( 10^{-3} W b / m^{2}, \) then the induced emf
between the tip of nose and tail of helicopter is:
A. \( 50 v \)
B. 0.5 \( v \)
\( c \cdot 5 v \)
D. 25 V


Energy produced in nuclear power plants is example of:
A. controlled nuclear fission
B. uncontrolled nuclear fission
c. controlled nuclear fusion
D. uncontrolled nuclear fusion


If a piece of copper having internal cavity weighs 264 gms.in air and 221 gms. in water, then volume of the cavity is \( \ldots . . . . . . . . . . . . . . . . . \) Density of copper \( =8.8 \) \( \left.g / c m^{3}\right) \)
\( \mathbf{A} \cdot 10 \mathrm{cm}^{3} \)
В. \( 11 \mathrm{cm}^{3} \)
\( \mathbf{c} \cdot 13 c m^{3} \)
D. \( 15 \mathrm{cm}^{3} \)


topp
\( Q \) Type your question
xture of (A) and (B


Which primitive man lived on earth at t he end of pleistocene era?
A. Australopithecus
B. Zinzanthropus
c. Neanderthal man
D. Atlantic man


Assertion
The conversion of a fresh precipitate
into colloidal state by the action of solute or solvent is called peptisation.
Reason

Peptisation is a property of colloidal
state
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


Thermoreceptor sensillae of cockroach are located on
A. Tarsus of leg
B. Anal cerci and anal styles
c. Labrum, maxillae and labium
D. Antenna, maxillary and labial palps


Define degree measure of an angle.


Which one of the following statement is
incorrect?
A \( \cdot \) Greater the formation constant \( \left(K_{f}\right) \) of a complex ion,
greater is its stability.
B. Greater the positive charge on the central metal ion, greater is the stability of the complex.
C. Greater is the basic character of the ligand, lesser is the stability of the complex.
D. Chelate complexes have high stability constants.


What happens when? Sodium acilate react with soda lime?


Suld
and mass \( 1 \mathrm{kg} \) are placed (fixed)
symmetrically about a movable
central charge of magnitude \( 5 \times \)
\( 10^{-5} C \) and mass 0.5 kg as shown. The
charge at \( P_{1} \) is removed. The
acceleration of the central charge is:
\( \left[\text { Given } \boldsymbol{O} \boldsymbol{P}_{1}=\boldsymbol{O} \boldsymbol{P}_{2}=\boldsymbol{O} \boldsymbol{P}_{3}=\boldsymbol{O} \boldsymbol{P}_{4}=\right. \)
\( \left.O P_{5} 1 m ; \frac{1}{4 \pi \varepsilon_{0}}=9 \times 10^{9} \text { in SI units }\right] \)
A \( .9 m s^{-2} \) upwards
B. \( 9 m s^{-2} \) downwards
C \( .4 .5 \mathrm{m} \mathrm{s}^{-2} \) upwards
D. \( 4.5 m s^{-2} \) downwards


The minimum number of unequal
forces in a plane that can keep a particle in equilibrium is
\( A \cdot 4 \)
B. 2
\( c \cdot 3 \)
D.


(a) Define a spherical mirror.
(b) Distinguish between a cancave
mirror and a convex mirror.
(c) What is the difference between a
real image and a virtual image?


Total number of valency (or bonding)
electrons required to form a molecule, where \( n= \) no. of atoms in a molecule:
A \( .2 n-2 \)
B . \( n-2 \)
\( \mathbf{c} \cdot n+2 \)
D. \( 2 n \)


The number of equivalents of \( N a_{2} S_{2} O_{3} \) required for the volumetric estimation
of one equivalent of \( C u^{2+} \) is:
\( A \)
B.
\( c \cdot 3 / 2 \)
D. 3


A sinusoidal wave of frequency \( 500 H z \)
has a speed of \( 350 m / s \). The phase difference between two displacements at a certain point at times 1 ms apart is
A \( \cdot \frac{\Pi}{4} \)
в. \( \frac{\text { П }}{2} \)
\( c . \Pi \)
D. \( \frac{3 \Pi}{2} \)


If z satisfies \( |z-1|<|z+3| \) then \( \omega= \)
\( 2 z+3-i \) satisfies
This question has multiple correct options
A \( .|\omega-5-i|<|\omega+3+1| \)
B. \( |\omega-5|<|\omega+3| \)
C \( . I_{m}(i \omega)>1 \)
D \cdot \( |a r g(\omega-1)|<\frac{\pi}{2} \)


Among the following, the species that is both paramagnetic and coloured is :
B. \( \left[T i C l_{6}\right]^{2-} \)
\( \mathbf{c} \cdot\left[V O_{4}\right]^{3} \)
D. \( \operatorname{Cr} \mathrm{O}_{2} \mathrm{Cl}_{2} \)


Pressure of \( 1 \mathrm{g} \) of an ideal \( \operatorname{gas} \mathrm{A} \) at \( 27^{\circ} \mathrm{C} \) is found to be 2 bar. When 2 g of another ideal gas \( \mathrm{B} \) is introduced in the same
flask at same temperature the pressure becomes 3 bar. What is the relationship between their molecular masses?
A \( \cdot 2 M_{B}=M_{A} \)
В . \( M_{B}=M_{A} \)
C \( . M_{B}=4 M_{A} \)
D. \( M_{B}=2 M_{A} \)


If \( |\vec{A}|=|\vec{B}|, \) then what is the angle between \( \vec{A}+\vec{B} \) and \( \vec{A}-\vec{B} \)
A \( \cdot 90^{\circ} \)
B. 60
\( c .30 \)
D. 0


For path \( \boldsymbol{A} \rightarrow \boldsymbol{B} \) optical path is
A \( \cdot 2(a+b) \)
В. \( 2(a-b) \)
\( c \cdot a+b \)
D. \( a-b \)


For finding the greatest common divisor
of two given integers. A method based
on the division algorithm is used called
A. Euclid's division algorithm
B. Euclid's addition algorithm
C. Euclid's subtraction algorithm
D. Euclid's multiplication algorithm


Among the following, the incorrect
statement is:
A. at low pressure, real gases show ideal behaviour
B. at very low temperature, real gases show ideal behaviour
C. at Boyle's temperature, real gases show ideal behaviour
D. at very large volume, real gases show ideal behaviour


If \( y=\sqrt{\frac{1-\sin ^{-1} x}{1+\sin ^{-1} x}} \) then \( y^{\prime}(0) \) is equal
to
\( \mathbf{A} \cdot \mathbf{1} \)
B. \( 1 / 2 \)
\( c \cdot-1 \)
D. \( \sqrt{2} / 3 \)


Statement 1
The wavelenght equivalent of \( 1 \mathrm{eV} \) is \( 1.24 \times 10^{-6} \) metre
and
Statement 2:
Electron volt is the energy imparted to an electron accelerated by a potential
difference of 1 volt.
A. Statement 1 is True, Statement 2 is True; statement 2 is correct explanation for statement 1
B. Statement 1 is True, Statement 2 is True; statement 2 is not a correct explanation for statement 1
c. Statement 1 is True, Statement 2 is False
D. Statement 1 is False, Statement 2 is True


A solution is prepared by dissolving \( 5.64 \mathrm{g} \) of glucose in \( 60 \mathrm{g} \) of water. Calculate the molality of the solution.
A. \( 0.2611 \mathrm{m} \)
B. 1.21 \( \mathrm{m} \)
\( c \cdot 1.044 \mathrm{m} \)
D. 0.522 \( \mathrm{m} \)


In Young's double slit experiment, the interference pattern obtained with white light will be
A. the central fringe bright and alternate bright and dark fringes
B. the central fringe achromatic and coloured fringes for small path difference
c. the central fringe dark
D. the central fringe coloured


Calculate the pH of \( 0.1 M H C l \)


Which of the following layer of the soil contains more humus?
A. Top soil
B. Subsoil
c. Bedrock
D. None of the above


Find the mode of the data given below:
\begin{tabular}{|l|c|c|c|c|c|}
\hline Class & \( 20-29 \) & \( 30-39 \) & \( 40-49 \) & \( 50-59 \) & \( 60-69 \) \\
\hline Frequency & 15 & 20 & 50 & 30 & 10 \\
\hline
\end{tabular}


Oxygen required for terminal oxidation enters mitochondria as
A. Glucose
B. Activated acetic group
c. oxygen gas
D. Pyruvic acid


If \( b \) is zero of the polynomial \( p(x)= \)
\( a x^{2}-3(a-1) x-1, \) then find the
value of \( \boldsymbol{a} \)


Select the correct I.U.P.A.C name for
\( \boldsymbol{F} \boldsymbol{e}_{4}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{6}\right]_{3}: \)
A. Iron
(III) hexacyanidoferrate (II)
B. Iron
(III) hexacyanidoferrate (III)
\( c . \) Iron
(III) hexacyanidoiron (III)
D. Iron
(II) hexacyanidoiron (II)


Which among the following states is highly densely populated?
A. Delhi
B. Pondicherry
c. west Bengal
D. chandigarh


5f series elements are known
as
A. Lanthanides
B. Representative elements
c. Transition elements
D. Actinides


\( \mathbf{f}\left|\begin{array}{ccc}\boldsymbol{a}+\boldsymbol{b} & \boldsymbol{b}+\boldsymbol{c} & \boldsymbol{c}+\boldsymbol{a} \\ \boldsymbol{c}+\boldsymbol{a} & \boldsymbol{a}+\boldsymbol{b} & \boldsymbol{b}+\boldsymbol{c} \\ \boldsymbol{b}+\boldsymbol{c} & \boldsymbol{c}+\boldsymbol{a} & \boldsymbol{a}+\boldsymbol{b}\end{array}\right|=\boldsymbol{t} \times \operatorname{det} \) of
circulant matrix whose elements of first
column are \( a, b, c \)
then 't' equals
A . 5
B. 6
\( c \cdot-2 \)
\( D \)


Identify the correct order of reactivity in electrophilic substitution reaction of
the following compounds
1. Benzene, 2. Toluene, 3.
Chlorobenzene, 4. Nitrobenzene
\( A \cdot(1)>(2)>(3)>(4) \)
B. \( (4)>(3)>(2)>(1) \)
\( c \cdot(2)>(1)>(3)>(4) \)
\( D \cdot(2)>(3)>(1)>(4) \)


\( z_{1} \) and \( z_{2} \) are two non-zero complex
numbers such that \( \left|z_{1}\right|=\left|z_{2}\right| \) and
\( \arg z_{1}+\arg z_{2}=\pi, \) then \( z_{2} \) equals
\( A \cdot z_{1} \)
B. \( -\overline{z_{1}} \)
\( \mathbf{c} \cdot z_{1} \)
D. \( -z_{1} \)


If \( a, b, c \) are in A.P., then show that the
following are also in A.P. \( \boldsymbol{b}+\boldsymbol{c}, \boldsymbol{c}+\boldsymbol{a}, \boldsymbol{a}+\boldsymbol{b} \)


Height of Stratosphere above earth's surface in \( (\mathrm{Km}) \) is:
A . \( 0-10 \)
B. 10-50
c. \( 50-85 \)
D. 85-100


Casparian strips are characteristic feature of endodermis, made up of
A. Cutin
B. Pectin
c. suberin
D. Cellulose


The moment of inertial about the center
of mass of the unified body after the
collision is
A \( \cdot \frac{48}{5} m r^{2} \)
B. \( \frac{48}{3} m r^{2} \)
c. \( \frac{24}{5} m r^{2} \)
D \( \cdot \frac{24}{3} m r^{2} \)


When plastics are burnt toxic
substances are released into the air
causing water pollution.
A. True
B. False


(Magnesium/Chlorine) oxide is
used for the lining of steel making
furnace.


Two circular plates of radius \( R \) are kept
at distance \( h \) to make a parallel plate capacitor as shown in the figure. Then the capacitance of this capacitor is:
A \( \cdot \frac{\varepsilon_{0} \pi R^{2}}{h} \)
B. \( \frac{\varepsilon_{0} 2 \pi R}{h} \)
c. \( \frac{2 \varepsilon_{0} 2 \pi R^{2}}{h} \)
D. none of these


Find the G.P whose \( 5^{t h} \) term is 48 and
\( 8^{t h} \) term is 384


Study the following diagrams in which the path of a ray of light
passing through a glass prism as traced by four students \( P, Q, R \) and \( S \) is
shown. The student who has traced the
path correctly is :
\( A \)
B. \( Q \)
\( c . R \)
\( D \)


Assertion
For practical purposes, the earth is used as a reference at zero potential electrical circuits. and
Reason
The electrical potential of a sphere of radius \( R \) with charge \( Q \) uniformly distributed on the surface is given by
\( \frac{Q}{4 \pi \varepsilon_{0} R} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Which conserved motif occur in
Escherichia coli genes?
A. TATA box
B. CAAT box
c. Pribnow box
D. None of the above


The prokaryotic cells are represented by all except
A. Red algae
B. Blue green algae
c. Mycoplasma
D. Ray fungi


Q Type your question
connected to a resistance \( R \) and two
ideal inductors \( L_{1} \) and \( L_{2} \) through a
switch \( S \) as shown. There is no mutual
inductance between the two inductors.
The switch \( S \) is initially open. At \( t=0 \)
the switch is closed and current begins
to flow. Which of the following options is/are correct?
This question has multiple correct options
A \( \cdot \) At \( t=0, \) the current through the resistance \( R \) is \( \frac{V}{R} \)
B. After a long time, the current through \( L_{2} \) will be \( \frac{V}{R} \frac{L_{1}}{L_{1}+L_{2}} \)
C. After a long time, the current through \( L_{1} \) will be \( \frac{V}{R} \frac{L_{2}}{L_{1}+L_{2}} \)
D. The ratio of the currents through \( L_{1} \) and \( L_{2} \) is fixed at all times \( (t>0) \)


A line of charge extends along a X-axis whose linear charge density varies
directly as x. Imagine a spherical
volume with its centre located on X-axis
and is moving gradually along it. Which
of the graphs shown in figure
correspond to the flux with the \( x \)
coordinate of the centre of the volume
\( A \)
B.
\( c \)
\( D . d \)


Which of the following is not true about
antifertility drugs?
A. Birth control pills contain a mixture of synthetic estrogen and progesterone derivatives.
B. Both compounds i.e.estrogen and progesterone are vitamins.
C. Progesterone is supposed to suppress ovulation.
D. Norethindrone is an example of synthetic progesterone derivative.


In which of the following reactions does
\( O_{2} \) acts as an oxidant?
This question has multiple correct options
\( \mathbf{A} \cdot 3 O_{2} \rightarrow 2 O_{3} \)
B. \( 2 F_{2}+O_{2} \rightarrow 2 F_{2} \) O
c. \( N_{2}+O_{2} \rightarrow 2 N O \)
D. \( C+O_{2} \rightarrow C O_{2} \)


If \( \Delta M N O \cong \Delta Q P R, \) write the six
corresponding parts.


Cell constant has unit:
A \( \cdot s m^{-1} \)
B . \( m s^{-1} \)
\( \mathrm{c} \cdot m^{-1} \)
D. \( m^{-2} \)


Show that the equation of normal at any point on the curve \( x=3 \cos t-\cos ^{3} t \)
\( \boldsymbol{y}=\mathbf{3} \sin t-\sin ^{3} \boldsymbol{t} \) is
\( 4\left(y \cos ^{3} t-x \sin ^{3} t\right)=3 \sin 4 t \)


Reflection of light from the surface of separation back into the denser
medium is called
A. Critical reflection
B. Total internal reflection
c. Reversibility
D. All


Prove that \( 5-\sqrt{3} \) is an irrational
number.


Length of one loop of B DNA is
\( A .3 .4 \mathrm{nm} \)
B. 0.34 nm
\( c \cdot 20 \mathrm{nm} \)
D. \( 10 \mathrm{nm} \)


If the planes \( \boldsymbol{x}-\boldsymbol{c} \boldsymbol{y}-\boldsymbol{b} \boldsymbol{z}=\boldsymbol{0}, \boldsymbol{c} \boldsymbol{x}-\boldsymbol{y}+ \)
\( \boldsymbol{a} \boldsymbol{z}=\mathbf{0} \) and \( \boldsymbol{b} \boldsymbol{x}+\boldsymbol{a} \boldsymbol{y}-\boldsymbol{z}=\mathbf{0} \) pass
through a stright line,then the value of \( a^{2}+b^{2}+c^{2}+2 a b c \) is:
A . 1
B. 2
\( c .3 \)
D. none of these


Diffraction of light was discovered by :
A. Young
B. Hertz
c. Grimaldi
D. Malus


Line through the points (-2,6) and (4,8) is perpendicular to the line through the points (8,12) and \( (x, 24) . \) Find the value
of \( x \)


A fly wheel rotating at 600 rev/min is
brought under uniform deceleration and
stopped after 2 minutes, then what is
angular deceleration in \( r a d / s e c^{2} ? \)
A \( \cdot \frac{\pi}{6} \)
в. \( 10 \pi \)
\( c \cdot \frac{1}{12} \)
D. 300


Phallic organs in cockroach are related
to
A. Male excretory system
B. Male reproductive system
D. Female reproductive system


A solution of sodium metal in liquid ammonia acts as a strong reducing agent due to the presence of:
\( A \). sodium amide
B. sodium ions
c. sodium hydride
D. solvated electrons


Find the remainder when \( 10 x-4 x^{2}-3 \)
is divided by \( x+2 \) using remainder
theorem.
A . -60
B. 39
\( c .-39 \)
D. None of these


Assertion
Lead storage battery is galvanic cell
without salt bridge.
Reason
A secondary cell is rechargeable cell.
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


Two identical balls \( A \) and \( B \) are
released from the position shown in Fig.
1.205. They collide elastically with each other on the horizontal portion. The ratio
of heights attained by \( A \) and \( B \) after collision is (neglect friction)
\( A \cdot 1: 4 \)
в. 2: 1
\( c .4: 13 \)
D. 2: 5


The value of \( \int \frac{d x}{\left(1-x^{2}\right)^{3 / 2}} \) equals
\( \mathbf{A} \cdot x \sqrt{1-x^{2}}+c \)
B \( \cdot \frac{x}{2 \sqrt{1-x^{2}}}+c \)
\( \mathbf{C} \cdot \frac{x}{\sqrt{1-x^{2}}}+c \)
D. \( \frac{2 x}{\sqrt{1-x^{2}}}+c \)


\( \int_{0}^{\pi / 2} \sin x \cos x d x \) is equal to:


Which of the following statements
is/are correct about the following
reactions?

This question has multiple correct options
\( A \). path I is feasible.
B. path II is feasible.
C. PhCl cannot be trinitrated because Cl and two \( N O_{2} \) atoms deactivate the ring towards further SE reaction.
D. 2,4 -Dinitrophenol can be nitrated beacuse the two deactivating \( N O_{2} \) groups prevent ring oxidation


A roller of diameter \( 70 \mathrm{cm} \) and length
\( 2 \mathrm{m} \) is rolling on the ground What is the area covered by the roller in 50 revolutions?
A. \( 180 m^{2} \)
в. \( 200 m^{2} \)
c. \( 220 m^{2} \)
D. \( 240 m^{2} \)


Find the particular solution of the difference equation
\( \left(1-y^{2}\right)(1+\log x) d x+2 x y d y=0 \)
given that \( y=0 \) when \( x=1 \)


A transformer lowers emf from \( 220 V \) to
\( 12 V \) If the number of turns in primary
coil is 8800 , how many turns are there in the secondary coil?
A . 200
B. 300
\( c \cdot 480 \)
D. 500


Prove \( \tan ^{-1} \frac{3}{4}+\tan ^{-1} \frac{3}{5}-\tan ^{-1} \frac{8}{19}= \)
\( \frac{\pi}{4} \)


Two equal charges of magnitude \( Q \) each
are placed at a distance d apart. Their electrostatic energy is E. A third charge
\( -Q / 2 \) is brought midway betway these two charges. The electrostatic energy of the system is now.
A . \( -2 E \)
B . \( -E \)
\( c .0 \)
D. E


Assertion
In aqueous solution, \( S O_{2} \) reacts with
\( H_{2} S \) forming sulphur.
Reason
SO is an effective reducing agent.
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.


toppr
Q Type your question
with same speed. P is a point on a line
joining the beams, at a distance \( x \) from
any one beam. The magnetic field at P is
B. If \( \mathrm{B} \) is plotted against \( \mathrm{x} \), which of the
following best represents the resulting
curve ?
\( A \)
B.
\( c \)
\( D \)


\( = \)
\( d x^{\prime}-1 \)
\( d x \)
\( d \)
\( d \)


A biconvex lens of focal length \( f \) and
radii of culvature of both the surfaces \( \boldsymbol{R} \)
is made of a material of refractive index
\( \boldsymbol{n}_{1} . \) This lens is placed in a liquid of
refractive index \( n_{2} \). Now this lens will
behave like This question has multiple correct options
A. Either as a convex or as a concave lens depending solely on R
B. A convex lens depending on \( n_{1} \) and \( n_{2} \)
C. A concave lens depending on \( n_{1} \) and \( n_{2} \)
D. A convex lens of same focal length irrespective of R, \( n_{1} \) and \( n_{2} \)


In the given figure, \( a=15 \mathrm{m} / \mathrm{s}^{2} \)
represents the total acceleration of a particle moving in the clockwise direction in a circle of radius \( \boldsymbol{R}=\mathbf{2 . 5 m} \)
at a given instant of time. The speed of
the particle is:
\( \mathbf{A} \cdot 6.2 m / s \)
B. \( 4.5 m / s \)
\( c .5 .0 m / s \)
D. \( 5.7 m / s \)


If \( \boldsymbol{P}=\left(\boldsymbol{x}_{1}, \boldsymbol{y}_{1}\right), \boldsymbol{Q}=\left(\boldsymbol{x}_{2}, \boldsymbol{y}_{2}\right) \) and \( \boldsymbol{R}= \)
\( \left(x_{3}, y_{3}\right) \) are three points of a triangle in
\( \mathbb{R}^{2} . \) Then, area of a \( \triangle P Q R \) in terms of determinant of matrix \( M= \) \( \left[\begin{array}{ccc}\mathbf{1} & \mathbf{1} & \mathbf{1} \\ \boldsymbol{x}_{\mathbf{1}} & \boldsymbol{x}_{\mathbf{2}} & \boldsymbol{x}_{\boldsymbol{3}} \\ \boldsymbol{y}_{\boldsymbol{1}} & \boldsymbol{y}_{\boldsymbol{2}} & \boldsymbol{y}_{\boldsymbol{3}}\end{array}\right] \) is
A. \( -\mid \operatorname{det}(M) \)
B. |det(M)||
\( ^{\mathbf{c} \cdot \frac{1}{2} \mid \operatorname{det}(M)} \)
D. \( 2|\operatorname{det}(M)| \)


2 NADH \( \left(\boldsymbol{H}^{+}\right) \) produced during anaerobic glycolysis yield
A. 6 ATP molecules
B. 4 ATP molecules
c. 8 ATP molecules
D. None of the above


IUPAC Name of is:
A. 3-methylcyclohexene
B. 1- methylcyclohex-2-ene
c. 6 -methylcyclohexene
D. 1-methylcyclohex -5-ene


Water is added to the solution M such
that the mole fraction of water in the
solution becomes 0.9. The boiling point of this solution is :
A . \( 380.4 \mathrm{k} \)
B . 376.35 К
c. 375.5 к
D. 354.7 к


The catalytic power of enzyme is
represented by
\( \mathbf{A} \cdot V_{m a x} \)
B. \( K_{m} \) constant
C. Turn over number
D. Both (2) and (3)


Hydrogen combines with chlorine to form HCl. It also combines with sodium to form NaH. If sodium and chlorine also
combine with each other, they will do so in the ratio of their masses as:
A. 23: 35.5
в. 35.5 :23
\( c \cdot 1: 1 \)
D. 23:


The structures of \( \left[N i(C O)_{4}\right] \) and
\( \left[N i\left(\left(P h_{3}\right)_{3} P\right)_{2} C l_{2}\right] \) are:
A. square planar in both cases
B. tetrahedral and square planar respectively
c. tetrahedral in both cases
D. square planar and tetrahedral respectively


Which property of sodium is being used
in street lights?
A. It shows photoelectric effect
B. It has low melting point
C. Sodium atom emits photons in the yellow region of visible spectrum, due to electrically stimulated transitions
D. Sodium vapours show golden colour


We have a basket full of apples, oranges
and mangoes. If \( 50 \% \) are apples, \( 30 \% \) are oranges, then what percent are mangoes?


Sketch the graph \( y=|x-5| . \) Evaluate \( \int_{0}^{1}|x-5| d x . \) What does this value of the integral represent on the graph?


A particle is executing SHM along a straight line. Its velocities at distances
\( x_{1} \) and \( x_{2} \) from the mean position are \( V_{1} \)
and \( V_{2} \) respectively. Its time period is:
A \( \cdot 2 \pi \sqrt{\frac{V_{1}^{2}-V_{2}^{2}}{x_{1}^{2}-x_{2}^{2}}} \)
B \( \cdot 2 \pi \sqrt{\frac{x^{2}+x_{2}^{2}}{\sqrt{1}+V_{2}^{2}}} \)
C \( \cdot 2 \pi \sqrt{\frac{x^{2}-x^{2}}{V_{2}^{2}-V_{1}^{2}}} \)
D. \( 2 \pi \sqrt{\frac{v^{2}+V_{2}^{2}}{x^{2}+x_{2}^{2}}} \)


Which of the following order of acidic
strength is correct:
\( \mathbf{A} \cdot R C O O H>R O H>H O H>H C \equiv C H \)
B . \( R C O O H>H O H>R O H>H C \equiv C H \)
c. \( R C O O H>H O H>H C \equiv C H>R O H \)
D . \( R C O O H>H C \equiv C H>H O H>R O H \)


Lightning is nothing but
A . electric discharge
B. electricity
c. electro - magnetic discharge
D. magnetic effect


The process of making colloidal solution from a precipitate is called
A. coagulation
B. vulcanization
c. peptization
D. flocculation


\( 10 \mathrm{kg} \) of a metals melted and recast into a cylinder of diameter \( 6 \mathrm{mm} \) and \( 25 \mathrm{cm} \)
long. Find the density of the cylinder. If this cylinder is again melted and recast into 7 equal sized cubes find the density
of each cube. Whet do you infer about densities found?


In the light emerging from calcite
crystal:
A. Both 0 -ray and E-ray are partially polarised
B. Both O-ray and E-ray are completely polarised
C. O-ray is partially polarised and E-ray is completely polarised.
D. O-ray is completely polarised and E-ray is partially polarised.


A conducting gas is in the form of a long cylinder. Current flows through the gas along the length of the cylinder. The current is distributed uniformly across
the cross-section of the gas. Disregard thermal and electrostatic forces among
the gas molecules. Due to the magnetic fields set up inside the gas and the
forces which they exert on the moving ions, the gas will tend to
A. expand
B. contract
c. expand and contract alternately
D. none of the above


A solid is in the form of a cylinder with hemispherical ends. Total height of the
solid is \( 19 \mathrm{cm} \) and the diameter of the
cylinder is \( 7 \mathrm{cm} \). Find the volume and total surface area of the solid.


\( \boldsymbol{C H}_{3}-\underset{\boldsymbol{O} \boldsymbol{H}}{\boldsymbol{C}}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}- \)
\( B \)
\( \dot{C}-C H_{3} \)
\( I \)
\( B r \)
The IUPAC name of the above given
compound is:
A. 6,6 -Dibromoheptan- - -ol
B. 2,2-dibromoheptan-6-ol
c. 6,6 -dibromo- - hydroxyheptane
D. 2,2-dibromo-6-hydroxyheptane


Adding an alpha particle to nucleus of sodium atom, product will be
A . \( N a^{\text {t }} \)
в. \( M g^{2+} \)
c. \( A l^{2} \)
D. \( A l \)


An aqueous solution at room temperature is \( 0.1 M \) with respect to
ammonium chloride and \( 0.1 M \) with
respect to \( N H_{4} O H\left(p K_{b}=5\right), \) the \( p H \)
of the solution is:
A . 7.5
B. 6.8
c. 6.5
D. 9.


A point moves along \( x \) axis. Its position
at time \( t \) is given by \( x^{2}=t^{2}+1 . \) Its
acceleration at time \( t \) is:
A \( \cdot 1 / x^{3} \)
B . \( 1 / x^{4} \)
c. \( -1 / x^{3} \)
D. \( 1 / x \)


Which product can not be formed in
given reaction?
\( A \)
B.
\( c \)
\( D \)


How many moles of \( H C \) OONa must
be added to \( 1 L \) of \( 0.1 M \) HCOOH to
prepare a buffer solution with a \( p H \) of
\( \mathbf{3 . 4 ?} \)
(Given: \( \boldsymbol{K}_{\boldsymbol{a}} \) for \( \boldsymbol{H} \boldsymbol{C O O H}=\boldsymbol{2} \times \mathbf{1 0}^{-4} \mathbf{)} \)
A . 0.01
B. 0.05
\( c .0 . \)
D. 0.2


Which of the following methods are used for the conversion of carboxylic acids into acid chlorides
\( (R C O O H \longrightarrow R C O C l) ? \)
This question has multiple correct options
A \( \cdot R C O O H+S O C l_{2} \longrightarrow \)
в. \( R C O O H+P C l_{5} \rightarrow \)
c. \( R C O O H+C l_{2} \rightarrow \)
D. \( R C O O H+P+C l_{2} \rightarrow \)


Assertion
\( A l_{2} O_{3} \) is converted into \( A l \) by reduction
with carbon at high temp
Reason
Carbon has greater affinity for oxygen than aluminium
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect and Reason is correct


f \( \boldsymbol{y}=\cos ^{2}\left(45^{\circ}+x\right)(\sin x-\cos x)^{2} \)
then the maximum value of y is:


The total energy of a simple harmonic oscillator is proportional to
A. amplitude
B. square of amplitude
c. frequency
D. velocity


If value of \( \mathbf{x} \) which satisfy equation
\( \left(\cot ^{-1} x\right)^{2}-3\left(\cot ^{-1} x\right)+2>0 \) is \( x< \)
\( \cot a \) or \( x>\cot b \)
Find the value of \( a+b \)
A . 1
B. 2
\( c .3 \)
D. 4


How is the phenomenon of reflection used in making a kaleidoscope? What are the applications of a kaleidoscope?


A solid sphere of radius \( R \) has a charge
\( Q \) distributed in its volume with a
charge density \( \rho=\kappa r^{a}, \) where \( \kappa \) and \( a \)
are constants and \( r \) is the distance
from its centre.
If the electric field at \( r=\frac{R}{8} \) is \( \frac{1}{8} \) times
that at \( r=R, \) find the value of \( a \)
A . 2.0
B. 3.2
c. 2.5
D. 0.2


The two strands of DNA in the double
helix is connected by
A. Covalent bonding
B. Ionic bonding
c. Hydrogen bonding
D. Hydrophobic interactions
E. Teritary structure


Shunt wire should be
\( A \). Thick and long
B. Thick and short
c. Thin and long
D. Thin and short


If electromagnetic rays are incident on
a semiconductors its conductivity.
A. Increases
B. Increases with increases frequency
C. Increases when frequency increases above certain frequency
D. Increases when wavelength is increases above a certain wavelength


Given that \( i-j, i+2 j \) are two vectors. Find a unit vector coplanar with these vectors and perpendicular to the first vector i - j. Find also the unit vector which is perpendicular to the plane of the two given vectors. Do you thus obtain an orthonormal triad?
This question has multiple correct options
A. \( k \)
B. \( \frac{1}{\sqrt{2}}(i+j) \)
\( c \cdot-k \)
D. \( \frac{1}{\sqrt{2}}(i-j) \)


If \( a+i b=\frac{(x+i)^{2}}{2 x^{2}+1}, \) prove that \( a^{2}+ \)
\( b^{2}=\frac{\left(x^{2}+1\right)^{2}}{\left(2 x^{2}+1\right)^{2}} \)


Strength of magnetic field is defined as
A. Number of field lines passing normally through a unit surface
B. Electric field lines passing the loop
C. Current through surface
D. Number of electrons passing a specific point per unit time


George Bentham and J.D. Hooker divided
dicots into
A. 3 divisions
B. 3 sub-divisions
c. 2 sub-kingdoms
D. 3 sub classes


\( 40 \mathrm{ml} \) of \( \frac{M}{4} \) solution of a weak monobasic acid \( \left(\mathrm{K}_{a}=2 \times 10^{-12} \mathrm{at} 25^{0} \mathrm{C}\right) \)
is treated with M/12 sodium hydroxide
solution. The concentration of \( \mathrm{H}^{+} \) ions
at the equivalence point is :
A \( \cdot 1.41 \times 10^{-12} \) М
B. \( \sqrt{5} \times 10^{-13} \) М
c. \( 4 \sqrt{2} \times 10^{-13} \) М
D. \( 2 \sqrt{5} \times 10^{-13} \) М


Which of the following motion of law is (are) involved in the motion of the
rocket?

This question has multiple correct options
A. Newton's first law of motion
B. Newton's second law of motion
c. Newton's third law of motion
D. All of the above


The specific conductance of saturated
solution of \( C a F_{2} \) is \( 3.86 \times 10^{-5} \) ohm
\( c m^{-1} \) and that of water used for
solution is \( 0.15 \times 10^{-5} \). The specific
conductance of \( C a F_{2} \) alone is:
A. \( 3.71 \times 10^{-5} \)
В. \( 4.01 \times 10^{-5} \)
c. \( 3.7 \times 10^{-4} \)
D . \( 3.86 \times 10^{-4} \)


If \( \boldsymbol{y}= \)
\( (1+x)\left(1+x^{2}\right)\left(1+x^{4}\right) \dots\left(1+x^{2^{n}}\right) \)
then \( \frac{d y}{d x} \) at \( x=0 \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B. - -
c. 0
D. none of these


If \( \boldsymbol{A}\left(\mathbf{1}, \boldsymbol{p}^{2}\right) ; \boldsymbol{B}(\mathbf{0}, \mathbf{1}) \) and \( \boldsymbol{C}(\boldsymbol{p}, \boldsymbol{0}) \) are the
co ordinates of three points then the value of \( p \) for which the area of triangle
ABC is minimum, is
A \( \cdot \frac{1}{\sqrt{3}} \)
B. \( -\frac{1}{\sqrt{3}} \)
c. \( \frac{1}{\sqrt{3}} \) or \( -\frac{1}{\sqrt{3}} \)
D. None


If
\( x, v \) and \( a \) denote the displacement the velocity and the acceleration of a particle executing simple harmonic
motion of time period \( T, \) then, which of
the following does not change with time?
в. \( \frac{\mathrm{aT}}{\mathrm{x}} \)
c. \( a T+2 \pi v \)
D. \( \frac{\mathrm{aT}}{\mathrm{v}} \)


An electric filament bulb can be worked
from
A. DC supply only
B. AC supply only
c. Battery supply only
D. All above


Electrons are ejected from the metal when a light of certain frequency strikes the surface of a metal, This phenomenon is known as photoelectric effect and the ejected electrons are called photoelectrons.

If true then type \( 1, \) if false then type 0


A particle moves from the point \( (2.0 \hat{i}+ \) \( 40 \hat{j}) m, \) at \( t=0, \) with an initial velocity \( (5.0 \hat{i}+4.0 \hat{j}) m s^{-1} . \) It is acted upon by a
constant force which produces a constant acceleration \( (4.0 \hat{i}+ \) \( 4.0 \hat{j}) m s^{-2} . \) What is the distance of the
particle from the origin at time \( 2 s ? \)
A \( .20 \sqrt{2} \mathrm{m} \)
B. \( 10 \sqrt{2} \mathrm{m} \)
\( c .5 \mathrm{m} \)
D. \( 15 \mathrm{m} \)


The plates of parallel-plate condenser are being moved away with velocity v. If the plate separation at any instant of time is \( d \) then the rate of change of capacitance with time is proportional to
A \( \cdot d^{2} \)
B. \( d \)
\( c \cdot d^{-2} \)
D. \( d^{-1} \)


Wheel-arid-axle and rope move in:
A. same direction
B. opposite direction
C. perpendicular direction
D. there is no relation between the two


Give any two differences between alkene and alkane.


As shown in above figure which of the
following angles are equal
A \( . \angle 1 \) and \( \angle 2 \)
B. \( \angle 1 \) and \( \angle 3 \)
\( c \cdot \angle 1 \) and \( \angle 4 \)
D. None of the above


The differential equation of a body projected from the earth is given by \( \frac{d v}{d t}=-g-k v . \) The distance travelled by the body at any time \( t \) is given by \( x= \) \( \left(\frac{\boldsymbol{g}}{\boldsymbol{k}^{2}}+\frac{\boldsymbol{u}}{\boldsymbol{k}}\right)\left(\mathbf{1}+\boldsymbol{e}^{-\boldsymbol{k} \boldsymbol{t}}\right)-\frac{\boldsymbol{g}}{\boldsymbol{k}} \boldsymbol{t} \)
A. True
B. False


Which of the following azeotropes is not
correctly matched?
\( \mathbf{A} \cdot H N O_{3}(68 \%)+H_{2} O(32 \backslash \%): \) Maximum boiling
azerotrope, boiling point \( =393.5 K \)
B \( \cdot H_{2} O(43 \%)+H I(57 \%): \) Minimum boiling azeotrope, boiling point \( =290 K \)
C \( \cdot C_{2} H_{5}(95.5 \%)+H_{2} O(4.5 \%): \) Minimum boiling azerotrope, boiling point \( =351.15 K \)
D. Chloroform (93.2\%) \( +C_{2} H_{5} O H \) (6.8\%): Minimum boiling azeotrope, boiling point \( =332.3 K \) )


Which one of the following statements
about starch is correct?
A. It occurs in the cell walls of plants
B. It is a disaccharide
C. It is present in roots and seeds of plants
D. It gives a red orange precipitate on boiling with Fehlings solution


A solid uniform disk of mass m rolls
without slipping down a fixed inclined plane with an acceleration a. The
frictional force on the disk due to
surface of the plane is?
A . 2 ma
B. \( 3 / 2 \) ma
c. \( m a / 2 \)
D. \( 1 / 2 \) ma


Among \( V_{2} O_{5} \) and \( P t, \) which is a better
catalyst for formation of \( S O_{3} \) from \( S O_{2} \)
by contact process? Why?


The one which does not represent a
force in any context is:
A. friction
B. impulse
c. tension
D. weight
E. viscous drag


Coal and petroleum are called fossil fuels.
A. True
B. False
c. Ambiguous
D. Data insufficient


lens of an eye is a transparent spherical structure which :
A . reflects light
B. scatters light
c. refracts light
D. diffracts light


\( \int_{1}^{e} e^{\frac{x^{2}-2}{2}}\left(\frac{1}{x}+x \log x\right) d x \)
\( \int_{1}^{e} e^{x^{2}}-2\left(\frac{1}{x}+x \log x\right) d x \)


Integrate \( \int_{4}^{7} \frac{(11-x)^{2}}{x^{2}+(11-x)^{2}} d x \)


Find out the correct stereoisomeric
product for the following reaction
A. \( d- \) form
B. \( l \) -form
c. Meso-form
D. Racemic mixture


Which of the following conditions is
incorrect for \( \psi: \)
A. \( \psi \) must be single valued at any particular point
B. \( \psi \) must be finite
c. \( \psi \) must be positive
D. \( \psi \) must be a continuous function of its coordinates


A temperature difference of \( 27^{\circ} \mathrm{C} \) on the
Kelvin scale is
A . 27
B. 300 K
c. \( -246 K \)
D. zero


If \( A \) and \( B \) are two non singular matrices of the same order such that
\( B^{r}=I, \) for some positive integer \( r>1 \)
\( \operatorname{then} \boldsymbol{A}^{-1} \boldsymbol{B}^{r-1} \boldsymbol{A}-\boldsymbol{A}^{-1} \boldsymbol{B}^{-1} \boldsymbol{A}= \)
A . \( I \)
B. \( 2 I \)
\( c \cdot O \)
D. \( -I \)


From the list of compounds given below, identify the compounds which can give only two position isomers:
(a) Hexane
(b) Pentene
(c) Heptyne
(d) Propanol
(e) Pentanone
\( \mathbf{A} \cdot a, d \) and \( b \)
B. \( b, d \) and \( e \)
\( \mathbf{c} \cdot e, a \) and \( c \)
D. \( b, c \) and \( d \)


Find the equation of directrix and
length of latus rectum of the parabola \( x^{2}=16 y \)
A. \( y-4=0 \) and 16
B. \( y+4=0 \) and 16
c. \( y-4=0 \) and 4
D. \( y+4=0 \) and 4


Hertz stands for number of oscillations
per:
A. second
B. Minute
c. Hour
D. Milli second


If the mass of a body is M on the surfrace of the earth, then its mass on
the surface of the moon will be:
A \( \cdot \frac{M}{6} \)
в. \( M \)
\( c \cdot M+6 \)
D. zero


One of the two slits in YDSE is painted over, so that it transmits only light
waves having intensity half of the intensity of the light waves having half of the intensity of the light waves through the other slit. As a result of this
A. fringe pattern disappears
B. bright fringes become brighten and dark ones become darker
c. dark and bright fringes get fainter
D. dark fringes get brighter and bright fringes get darker


Assertion: P-V graph (at constant
temperature) for ideal gas is rectangular
parabola
Reason: Ideal gas obeys Charle's law
A. Both assertion (A) and reason (R) are correct and R gives the correct explanation
B. Both assertion (A) and reason (R) are correct but R doesnt give the correct explanation
C. A is true but R is false
D. A is false but R is true


The acceleration of a body projected upwards with a certain velocity is
A. \( 9.8 \mathrm{m} / \mathrm{s}^{2} \)
B. -9.8 \( m / s^{2} \)
c. zero
D. insufficient data


Combustion is an
A. exothermic reaction
B. endothermic reaction
C. displacement reaction
D. reduction reaction


What is the mass of \( 6.022 \times 10^{23} \)
formula units of \( \left(N H_{4}\right)_{2} S O_{4} ? \)
A. \( 234.11 g \)
в. \( 132.11 g \)
c. \( 210.29 g \)
D. \( 342.14 g \)


Which shape is associated with the orbital designated by \( n=2, l=1 ? \)
A. Spherical
B. Tetrahedral
c. Dumb-bell
D. Pyramidal


Calculate the deviation suffered by a ray which is incident on a plane
horizontal mirror at an angle of \( 60^{\circ} \) to
the normal
A \( \cdot 120^{\circ} \)
B. \( 90^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 60^{\circ} \)


Add the following expressions: \( 3 x+ \) \( y-8 \) and \( y+4-7 x \)
A. \( 4 x+2 y-4 \)
в. \( -4 x+2 y-4 \)
c. \( -4 x+3 y-4 \)
D. \( 4 x+3 y+4 \)


Correct the following statements:
(a) Surgical methods of contraception prevent gamete formation.
(b) All sexually transmitted diseases are completely curable.
(c) Oral pills are very popular
contraceptives among the rural women.
(d) In E. T. techniques, embryos are always transferred into the uterus.


\( 50 g \) of oil of specific heat capacity \( 2.2 J / g^{o} C \) is cooled from \( 350^{\circ} C \) to
\( 25^{\circ} \mathrm{C} . \) Calculate the heat energy given
out by the oil
A . \( 35.75 J \)
B. \( 35,75000 J \)
c. \( 35,75 J \)
D. \( 35,750 J \)


In an a.c. circuit \( \mathrm{V} \) and I are given by \( V=50 \sin 50 t \) volt and \( I= \)
\( 100 \sin (50 t+\pi / 3) \mathrm{mA} . \) The power
dissipated in the circuit
A. 2.5 kw
B. 1.25 kw
c. \( 5.0 \mathrm{kw} \)
D. 500 watt


The median of the following distribution
is
\( \begin{array}{lllll}\text { Class } & 35- & 45- & 55- & 65- \\ \text { interval } & 45 & 55 & 65 & 70\end{array} \) Frequency \( \quad 8 \quad 12 \quad \) 20 10
A . 56.
B. 57.5
c. 58.7
D. 59


An American plant that had become a troublesome waterweed in India is
A. Trapa bispinosa
B. Cyperus rotundus
c. Eichhornia crassipes
D. Typha latifolia


In which of the given pairs the two compounds are allotropes of the same
element?
\( \mathbf{A} \cdot B r_{2} \) and \( H g \)
B. \( C l_{2} \) and \( F_{2} \)
C. \( N H_{4}^{+} \) and \( H_{3} O^{+} \)
D. Fe and \( C O \)
E. Diamond and graphite


If \( A M \) and \( C N \) are perpendiculars on
the disgonal \( B D \) of a parallelogram
\( A B C D, \) Is \( \triangle A M D \cong \triangle C N B ? \) Give
reason


Which of the following pairs illustrates the law of multiple proportions?
A. \( P H_{3}, H C l \)
в. \( P b O, P b O_{2} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{S}, \mathrm{SO}_{2} \)
D. \( C u C l_{2}, C u S O_{4} \)


For a polynomial, dividend is \( x^{4}+4 x- \)
\( 2 x^{2}+x^{3}-10, \) quotient is \( x^{2}+3 x- \)
\( 3 x^{2}+4 x+12 \) and remainder is 14
then divisor is equal to
A. \( x^{2}+2 \)
B . \( x^{2}-2 \)
c. \( x+2 \)
D. None of these


If \( A=\left|\begin{array}{cc}0 & 1 \\ 2 & 4\end{array}\right|, B=\left|\begin{array}{cc}-1 & 1 \\ 2 & 2\end{array}\right| \)
\( c=\left|\begin{array}{cc}1 & 0 \\ 1 & 0\end{array}\right|, \) then \( 2 A+3 B-C= \)
A \( \cdot\left|\begin{array}{cc}-4 & 5 \\ 9 & 14\end{array}\right| \)
в. \( \left|\begin{array}{cc}4 & 3 \\ 9 & 10\end{array}\right| \)
с. \( \left|\begin{array}{cc}4 & -5 \\ 9 & 14\end{array}\right| \)
О \( \cdot\left|\begin{array}{cc}-4 & 5 \\ 14 & 9\end{array}\right| \)


How are the states of rest and motion
relative?


The charge/size ratio of a cation determines its polarising power. Which one of the following sequences represents the increasing order of the polarising power of cationic species?
\( \left[\boldsymbol{K}^{+}, \boldsymbol{C} \boldsymbol{a}^{2+}, \boldsymbol{M} \boldsymbol{g}^{2+}, \boldsymbol{B} \boldsymbol{e}^{2+}\right] \)
A \( \cdot M g^{2+}<B e^{2+}<K^{+}<C a^{2+} \)
B . \( B e^{2+}<K^{+}<C a^{2+}<M g^{2+} \)
C \( \cdot K^{+}<C a^{2+}<M g^{2+}<B e^{2+} \)
D. \( C a^{2+}<M g^{2+}<B e^{2+}<K^{+} \)


the self inductance of the primary coil.


What is the source of micro-organisms as water pollutant?
A. Chemicals used for killing insects, fungi and weeds
B. Domestic sewage
c. Mining of uranium containing minerals
D. chemical fertilizers


If a vector \( 2 \hat{i}+3 \hat{j}+8 \hat{k} \) is perpendicular to the vector \( 4 \hat{i}-4 \hat{j}+\alpha \hat{k}, \) then the
value of \( \alpha \) is


State four uses of plane mirrors.


Find the correct statement from the
given one:
A. deuterium can replace the normal hydrogen in water molecules to form heavy water
B. deuterium can not replace the normal hydrogen in water molecules to form heavy water
C. hydrogen can replace deuterium in water molecules to form water
D. none of these


The acceleration of aparticle is \( a= \) \( \mathbf{3} \boldsymbol{t}^{2} \hat{\boldsymbol{i}}+\mathbf{5} \boldsymbol{t} \hat{\boldsymbol{j}}-\left(\boldsymbol{8} \boldsymbol{t}^{3}+\mathbf{4 0 0}\right) \hat{\boldsymbol{k}} \boldsymbol{m} \boldsymbol{s}^{-2} . \) The
change in velocity form \( t=0 \) to \( 10 s \) is
\( \boldsymbol{n}_{1} \hat{\boldsymbol{i}}+\boldsymbol{n}_{2} \hat{\boldsymbol{j}}-\boldsymbol{n}_{3} \hat{\boldsymbol{k}} \)
A \( \cdot n_{1}=1000 \mathrm{ms}^{-1} \)
в. \( n_{2}=250 \mathrm{ms}^{-1} \)
c. \( n_{3}=2400 \mathrm{ms}^{-1} \)
D. All of these


State whether the following statement
is True or False.

Sum of two prime numbers is always
even


When we stand on loose sand, our feet
go deep into the sand. But when we lie down on the sand our body does not go that deep into the sand. But when we lie down on the sand our body does not go
that deep in the sand. Why?


The perimeters of two similar triangles is in the ratio \( 3: 4 . \) The sum of their
areas is 75 sq. cm. Find the area of each triangle in sq. cm.
A . 30,45
B. 27,48
c. 25,50
D. None of these


The earth's radius is \( \mathrm{R} \) and acceleration
due to gravity at its surface is g. If a
body of mass \( m \) is sent to a height \( h= \) \( \boldsymbol{R} \)
\( \frac{i}{5} \) from the earth's surface, the
potential energy increases by
A . mgh
в. \( \frac{4}{5} m g h \)
c. \( \frac{5}{6} \) mgh
D. \( \frac{6}{7} \) mgh


If to an intrinsic semiconductor, a pentavalent element is added as impurity, one get extrinsic semi conductor of \( _{--}-_{-}- \) type
A. n-type
B. p-type
C. intrinsic
D. Both A and B


For case III what is the direction of the
electric force exerted by the field on the
\( +1 \mu C \) charged object when at \( A \) and
when at \( B ? \)
A. left at \( A \) and left at \( B \)
B. right at \( A \) and right at \( B \)
C. left at A and right at B
D. right at A and left at B
E. no electric force at either positions


When \( C u O \) reacts with hydrogen, \( \dots \)....... is
reduced.
A. \( C u O \)
в. \( H_{2} \)
c. \( C u \)
D. \( H_{2} O \)


The water equivalent of a copper
calorimeter is 4.5 g. If specific heat of
copper is \( 0.09 c a l / g /^{0} C, \) then \( \left(L_{f}=\right. \)
\( 80 c a l / g m \)
This question has multiple correct options
A. Mass of the calorimeter is \( 0.5 \mathrm{kg} \)
B. Thermal capacity of the calorimeter is \( 4.5 \mathrm{cal}^{0} / \mathrm{C} \)
C. The heat required to raise the temperature of the calorimeter by \( 8^{0} C \) will be 36 cal.
D. Heat required to melt \( 15 \mathrm{gm} \) of ice at \( 0^{\circ} \mathrm{C} \) Placed in the calorimeter will be 1200 cal


The condition in which the eye lens
becomes milky and cloudy is called
A. Myopia
B. Cataract
c. Hypermetropia
D. Presbyopia


\( \mathrm{PQ} \)


The increase in length of a wire on stretching is \( 0.025 \% \). If its Poisson's
ratio is \( 0.4, \) then the percentage decrease in the diameter is :
A . 0.01
B. 0.02
c. 0.03
D. 0.04


\( A \) has 3 tickets of a lottery containing 3 prizes and 9 blanks. \( B \) has two tickets
of another lottery containing 2 prizes and 6 blanks. The ratio of their chances
of success is
A \( \cdot \frac{32}{55}: \frac{15}{28} \)
в. \( \frac{32}{55}: \frac{13}{28} \)
c. \( \frac{34}{55}: \frac{13}{28} \)
D. \( \frac{34}{55}: \frac{15}{28} \)


The metal oxide rectifier used for
electrolytic process is placed along with the transformer:
A. Inside the oil
B. Outside the transformer but near to it
c. outside the transformer but far from it
D. Half immersed in the oi


Identify \( X \) and \( Y \) in the given
polymerization reactions:
A. \( x= \) Bakelite, \( Y= \) Novolac
B. \( x= \) Novolac, \( Y= \) Melamine
\( \mathrm{c} \cdot \mathrm{X}= \) Bakelite, \( \mathrm{Y}= \) Malamine
D. \( x= \) Novolac, \( Y= \) Bakelite


The equation \( \sin ^{-1} x-\cos ^{-1} x= \)
\( \cos ^{-1}\left(\frac{\sqrt{3}}{2}\right) \) has
A. No solution
B. Unique solution
c. Infinite solution
D. None of these


What is the ratio of the speed of light in a vacuum to the speed of light in a particular material is called?
A. The coefficient of diffraction of the materia
B. The index of refraction of the material
c. The coefficient of refraction of the material
D. The index of diffraction of the material
E. The modulus of diffraction of the material


When an organic compound is heated
with dry cupric oxide and the gases evolved are passed through lime water which turns milky, the gas may be
or


Ekectron microscope is based on the principle
A. Photoelectric effect
B. Wave nature of electron
c. superconductivity
D. Laws of electromagnetic induction


The greatest algal count in response to phosphorus addition was observed at
location
Control
Nitrogen
Phosphorus
\( A \)
B. 2
\( c \cdot 3 \)
\( D \cdot 4 \)
\( E . \)


Assertion
Electron affinity of \( \boldsymbol{F} \) is less than \( \boldsymbol{C l} \)
Reason

Additional electrons are repelled more
effectively by \( 3 p \) -electrons in \( C l \) -atom
than by \( 2 p \) -electrons in \( F \) -atom.

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. Assertion is incorrect but Reason is correct


The shape of \( X e F_{6} \) is :
A. square planar
B. distorted octahedral
c. square pyramidal
D. pyramidal


\( \boldsymbol{H}_{2}+\boldsymbol{I}_{2} \rightarrow 2 \boldsymbol{H} \boldsymbol{I} \)
What is the \( K_{e q} \) for the reaction shown
above if \( \boldsymbol{H}_{2}=\mathbf{1} \) atm, \( \boldsymbol{I}_{2}=\mathbf{2} \) atm and
\( \boldsymbol{H} \boldsymbol{I}=\boldsymbol{3} \) atm?
A . 0.33
в. 3
\( c \cdot 0.22 \)
D. 0.67
E . 4.5


The halo compound of methane used as fire extinguisher under the name Pyrene is:
A. \( C H C l_{3} \)
в. \( C H_{2} C l_{2} \)
c. \( C C l_{2} F_{2} \)
D. \( C C l_{4} \)


Simplify the following using laws of
exponents.
\( \left(3^{2}\right) \times\left(3^{2}\right)^{4} \)


\( \mathbf{2} \times \mathbf{2} \times \mathbf{2} \times \mathbf{3} \times \mathbf{3} \times \mathbf{1 3}=\mathbf{2}^{\mathbf{3}} \times \mathbf{3}^{\mathbf{2}} \times \mathbf{1 3} \)
is equal to
A. 1004
в. 828
c. 724
D. 936


The lines \( \frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4} \) and
\( \frac{\boldsymbol{x}-\mathbf{3}}{\mathbf{1}}=\frac{\boldsymbol{y}-\boldsymbol{k}}{\mathbf{2}}=\frac{\boldsymbol{z}}{\mathbf{1}} \) intersect if \( \boldsymbol{K} \)
equals
\( A \cdot \frac{3}{2} \)
в. \( \frac{9}{2} \)
c. \( \frac{-2}{9} \)
D. \( \frac{-3}{2} \)


In Thomson's model,
embedded in a positively charged pudding.
A . electrons
B. neutrons
c. protons
D. ions


Which of the following is intensive
property?
(I) Internal energy
(III) pH
(III) Boiling point
\( (\mid V) \) EMF
(V) Molar entropy
A . ।.॥.III,IV,V
B. ॥,॥ᅵ,IV
c. ॥ा,॥
D. \( \|,\|, \) IV \( , v \)


Evaluate the Given limit: \( \lim _{x \rightarrow 3}(x+3) \)


How many moles of electrons weighs
one kilogram? [Mass of electron \( =\mathbf{9 . 1 0 8} \times \mathbf{1 0}^{-\mathbf{3 1}} \mathbf{k g} \)
Avogadro's number \( =6.023 \times 10^{23} \)
A. \( 6.023 \times 10^{23} \)
в. \( \frac{1}{9.108} \times 10^{31} \)
c. \( \frac{6.023}{9.108} \times 10^{54} \)
D. \( \frac{1}{9.108 \times 6.023} \times 10^{8} \)


An object is placed on the surface of a smooth inclined plane of inclination \( \boldsymbol{\theta} \). It
takes timer to reach the bottom. If the
same object h allowed to slide down a
rough inclined plane of inclination \( \boldsymbol{\theta} \), it takes time \( n t \) to reach the bottom, where \( n \) is a number greater than 1 . The coefficient of friction \( \mu \) is given by
A \( \cdot \mu=\tan \theta\left(1-\frac{1}{n^{2}}\right) \)
B \cdot \( \mu=\cos \theta\left(1-\frac{1}{n^{2}}\right) \)
c. \( _{\mu}=\tan \theta \sqrt{1-\frac{1}{n^{2}}} \)
D. \( \mu=\cos \theta \sqrt{1-\frac{1}{n^{2}}} \)


Balance the following redox reactions in basc medium:
\[
M n O_{4}^{-}+I^{-} \longrightarrow M n O_{2}+I O_{3}^{-}
\]
A \( \cdot 2 M n O_{4}^{-}+I^{-}+H_{2} O \longrightarrow 2 M n O_{2}+I O_{3}^{-}+2 O H^{-} \)
B. \( 3 M n O_{4}^{-}+I^{-}+H_{2} O \longrightarrow 4 M n O_{2}+I O_{3}^{-}+2 O H^{-} \)
\( \mathrm{c} \cdot 3 \mathrm{Mn} \mathrm{O}_{4}^{-}+I^{-}+\mathrm{H}_{2} \mathrm{O} \longrightarrow 5 \mathrm{MnO}_{2}+\mathrm{IO}_{3}^{-}+2 \mathrm{OH}^{-} \)
D. None of these


Which pair of statements about
diamond and graphite is correct?
A. Diamond and graphite are both pure carbon. They are both macromolecules
B. Diamond and graphite can both be used as electrodes Graphite is also used as a lubricant
c. Diamond has covalent bonds. Graphite has ionic bonds
D. Diamond is hard with a high melting point. Graphite is soft with a low melting point.


Assertion
Deforestation sequesters \( C O_{2} \) from atmosphere.
Reason
Global warming is beneficial for plants and human health.
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 distance between the point \( P(x, y, z) \) and plane \( x z \) is :
A . \( x \)
B. \( y \)
\( c \)
D. \( x y \)


Botanical snakes are
A . Algae
B. Fungi
c. Bryophytes
D. Pteridophytes


If \( 6 t h \) term of a G.P is \( -1 / 32, \) and 9 th
term is \( 1 / 256, \) then the 11 th term is
A . 1024
B. 1/1024
c. \( 1 / 256 \)
D. \( 1 / 512 \)


If \( * \) is a binary operation in \( \boldsymbol{A} \) then
A. \( A \) is closed under
B. \( A \) is not closed under
c. \( A \) is not closed under \( + \)
D. \( A \) is closed under -


Bernoulli's theorem is a consequence of the law of conservation of :
A. Angular momentum
B. Mass
c. Energy
D. Momentum


Indicate whether each of the following
pairs are :
A. I- enantiomers, II- diastereomers, III- enantiomers
B. I- identical, II- enantiomers, III- enantiomers
c. I- enantiomers, II- diastereomers, III- identical
D. I- enantiomers, II- identical, III- identical


Changes in growth of children can be determined through
A. Height
B. Weight
c. Both A and B
D. Length


Abag contains 6 white and an unknown
number of black balls \( (\leq 3) \) Balls are
drawn one by one with replacement from this bag twice and is found to be white on both occasion. Find the
probability that the bag had exactly' \( 3^{\prime} \)
Black balls.


Place the decimal point at the correct position in the following products.
\( \mathbf{6 . 3} \times \mathbf{5}=\mathbf{3 1 5} \)


Which of the following quantities is the
same for all ideal gases at the same temperature? This question has multiple correct options
A. The kinetic energy of 1 molecule
B. The kinetic energy of \( 1 \mathrm{g} \)
c. The number of the molecules in 1 mole
D. The number of molecules in 1 \( g \)


Given \( \boldsymbol{f}: \boldsymbol{x} \rightarrow \mathbf{2} \boldsymbol{x}+\boldsymbol{p} \) and \( \boldsymbol{f}^{-1}: \boldsymbol{x} \rightarrow \)
\( \boldsymbol{m}(\boldsymbol{4} \boldsymbol{x}+\boldsymbol{3}), \) where \( \boldsymbol{p} \) and \( \boldsymbol{m} \) are
constants. Find the value of \( p \) and value
of \( \boldsymbol{m} \)


Write the chemical formula of baking
soda.


Referring to the molecular sketch and table above, choose the option that best describes the percentage of carbon in the molecule, in terms of both atomic
composition and mass-percent composition.
A. Carbon makes up approximately \( 25 \% \) of the atoms and \( 25 \% \) of the mass
B. Carbon makes up approximately 40\% of the atoms, and \( 40 \% \) of the mass
c. carbon makes up approximately 25\% of the atoms, and \( 40 \% \) of the mass
D. carbon makes up approximately \( 40 \% \) of the atoms. and \( 25 \% \) of the mass


ICBN was adopted in
A . 1951
B. 1971
c. 196
D. 1981


Family Compositae can be distinguished from Solanaceae in
A. Capitulum inflorescence
B. Gamopetalous corolla
c. Epipetalous stamens
D. Bicarpellary gynoecium


Determine the area of the
region enclosed by the curve \( \boldsymbol{y}= \) \( \sqrt{x+1} \) in [0,4] and the \( x \) -axis and the
lines \( \boldsymbol{x}=\mathbf{0}, \boldsymbol{x}=\mathbf{4} \)


List the uses of neon and argon gases.


A bullet of mass \( m \) is being fired from a
stationary gun of mass \( M . \) If the
velocity of the bullet is \( v, \) the velocity of
the gun is
A \( \cdot \frac{M v}{m+M} \)
B. \( \frac{m v}{M} \)
c. \( \frac{(M+m) v}{M} \)
D. \( \frac{M+m}{M v} \)


Two lenses of power +12 D and -2 D are put in contact. What is their equivalent focal length?
\( A \cdot 10 \mathrm{cm} \)
B. 12.5 \( \mathrm{cm} \)
\( c \cdot 16.6 \mathrm{cm} \)
D. \( 8.33 \mathrm{cm} \)


Light travels in a straight line because:
A. it is not absorbed by atmosphere
B. its velocity is very high
c. diffraction effect is negligible
D. due to interference


Identify the correct and incorrect statements.
A. The four nucleotide bases are not
necessarily present in DNA in exact equal proportions.
B. The total amount of purines are equal to the total amount of pyrimidines.
C. DNA ligase enzyme act to hydrolyse or breakdown a polynucleotide chain into its component nucleotides.
D. Nuclease enzymes are capable of restoring an intact DNA duplex.
A. B is correct but A, C and D are wrong
B. A and B are wrong but C and D are correct
c. \( A, B \) and \( C \) are correct but D is wrong
D. A and B are correct but C and D are wrong
E. B, C and D are correct but A is wrong


In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios. \( \tan \theta=11 \)


Which of the following is not known?
A. \( X e F_{6} \)
в. \( X e F_{4} \)
c. \( K r F_{6} \)
D. \( C s_{2} X e F_{6} \)


The area between the curves \( y=\sqrt{x} \)
and \( \boldsymbol{y}=\boldsymbol{x}^{3} \) is
A \( \cdot \frac{1}{12} \) sq. units
в. \( \frac{5}{12} \) sq. units
c. \( \frac{3}{5} \) sq. units
D. \( \frac{4}{5} \) sq. units


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


\( \left|\begin{array}{ccc}a^{2} & b^{2} & c^{2} \\ (a+1)^{2} & (b+1)^{2} & (c+1)^{2} \\ (a-1)^{2} & (b-1)^{2} & (c-1)^{2}\end{array}\right|= \)
\( k(a-b)(b-c)(c-a), \) then find the
value of \( -\boldsymbol{k} \)


A sum of Rs. 1000 is lent to be returned
in 11 monthly installments of Rs. 100 each, interest being simple. The rate of interest
A \( \cdot g \frac{1}{11} \% \)
B. \( 10 \% \)
c. \( 11 \% \)
D. \( 21 \frac{9}{11} \% \)


Which of the following pair has same properties?
\( \mathbf{A} \cdot \) Na, \( \mathbf{K} \)
в. Na, Mg
\( c \cdot 0, F \)
D. \( H_{2}, C I_{2} \)


A body of mass \( 6 \mathrm{kg} \) is under a force of 6 N which causes displacement in it given by \( S=\frac{t^{2}}{4} \) at where 't' is time. The
work done by the force in 2 s is:
A . 12
B. 9 J
c. 6 J
D. 3 J


The distance between two magnetic
poles is doubled and their pole-strength is also doubled. The force between them
A. Increases to four times
B. Decreases by half
c. Remains unchanged
D. Increases to two times


Unit for pressure used in weather maps is millibar. 1 millibar is equal to
A. 1000 bar
B. 100kPa
c. \( 100 \mathrm{Pa} \)
D. tatm


The vertebral column is connected to
the pelvic girdle in the:
A. coccygeal region
B. sacral region
c. cervical region
D. lumbar region


Which of the following represents Ohm's Law?
A. \( 1=Q . \)
B. I = V.R
\( c \cdot 1=\frac{R}{V} \)
\( D \cdot 1=\frac{V}{R} \)


At present a firm manufacturing 2000 items it is estimated that the rate of
change of production (P) with respect to additional number of workers \( (x) \) is
given by \( \frac{d P}{d x}=100-12 \sqrt{x} . \) If the firm employes
25 more workers then the new
production is?
A . 2500
в. 3000
c. 3500
D. 4500


Element \( X \) is a metal with a valency \( 2, Y \) is a non-metal with a valency 3.Write an
equation, to show how Y forms an ion.


Differentiate the following function from first principle:
\( \sin ^{-1}(2 x+3) \)


In a Fresnel's bi-prism experiment, the fringe of width 0.05 mm is observed on
a screen at a distance of \( 1.5 m \) from the
source. When a convex lens is placed between the source and the screen, for
two positions of the lens image of interfering sources are produced on the screen. The separation between the two
images being 0.04 and \( 0.01 m m \) respectively. The wavelength of light used is
\( \mathbf{A} \cdot 6.67 n m \)
B. \( 0.667 n m \)
\( c .667 n m \)
D. \( 667 A^{\circ} \)


The points \( P, Q, R, S, T, U, A \) and \( B \) on
the number line are such that \( \boldsymbol{T} \boldsymbol{R}= \)
\( \boldsymbol{R S}=\boldsymbol{S U} \) and \( \boldsymbol{A P}=\boldsymbol{P Q}=\boldsymbol{Q B} . \) Name
the rational numbers represented by
\( \boldsymbol{P}, \boldsymbol{Q}, \boldsymbol{R}, \boldsymbol{S} \)


IUPAC name of given compound is :
A. cyclohexa-3,4-dienylethanone
B. 1-(cyclohexa-2, 3-dienyl)ethanone
c. 2 -(cyclohexa- 2,4 -dienylethanone
D. 1 -(cyclohexa-2, 4 -dienyl)ethanone


Fermentation of lactic acid does not
form
A. ATP
в. \( C O_{2} \)
c. NADH
D. NADH and \( C O_{2} \)


Some organisms and their type of reproductions are given below. Find the correct alternative showing the correct
pair-
(a) Paramecium
(1) Spore formation
(b) Hydra
(2) Budding
(c) Mucor
(3) Fission
(d) Spirogyra
(4) Fragmentation
A. \( a-1, b-2, c-3, d-4 \)
4
B. a- 3, b- 4, c- 2, d-1
c. a- \( 2, b-3, c-4, d-1 \)
D. a- 3, b- 2, c-1, d-4


Which of the following overlap is/are
correct?
This question has multiple correct options
\( A \)
\( 00+00 \)
0
в.
\( 00+00 \)
0
c. \( \infty+\infty \)
\( 00+\infty \)
D. None of the above


The order of reactivity of carboxylic acid
derivatives is:
A. Acid Chloride \( > \) Ester \( > \) Amide \( > \) Acid Anhydride
B. Acid Chloride \( > \) Acid Anhydride \( > \) Ester \( > \) Amide
C. Acid Chloride \( > \) Amide \( > \) Acid Anhydride \( > \) Ester
D. Acid Anhydride > Ester > Amide > Acid Chloride


Integrate the rational function
\( \frac{1}{x\left(x^{n}+1\right)} \)


Hydrogen bomb is based on the
principle of
A. uncontrolled fusion reaction
B. controlled fusion reaction
c. uncontrolled fission reaction
D. controlled fission reaction


The main constituent of coal is:
A. carbon
B. oxygen
\( c . \) air
D. water


The noble gases do not usually form
chemical compounds because:
A. they have very stable nuclei
B. they are not polar
C. the bonds between their atom are very strong
D. they already have completely filled valance electron shell


Water samples with \( B O D \) values of
\( 4 p p m \) and \( 18 p p m, \) respectively, are:
A. highly polluted and clean
B. highly polluted and highly polluted
c. clean and highly polluted
D. clean and clean


Let \( \boldsymbol{f}(\boldsymbol{x} \boldsymbol{y})=\boldsymbol{f}(\boldsymbol{x}) \cdot \boldsymbol{f}(\boldsymbol{y}) \) for all \( \boldsymbol{x}, \boldsymbol{y} \in \boldsymbol{R} \)
f \( f^{\prime}(1)=2 \) and \( f(4)=4, \) then \( f^{\prime}(4) \)
equal to
\( \mathbf{A} \cdot \mathbf{4} \)
B.
c. \( \frac{1}{2} \)
D. 8


Assertion
The pressure of a fixed amount of an ideal gas is proportional to its temperature
Reason
Frequency of collisions and their impact both increase in proportion to the
square root of temperature
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


\( \int \frac{\boldsymbol{x}}{\boldsymbol{x}^{4}+\boldsymbol{x}^{2}+1} \boldsymbol{d} \boldsymbol{x} \)
( \( ^{\mathbf{B}} \cdot=\frac{1}{\sqrt{3}} \tan ^{-1}\left(\frac{2 x^{2}+1}{\sqrt{3}}\right)+C \)
\( =\frac{1}{\sqrt{3}} \sin ^{-1}\left(\frac{2 x^{2}+1}{\sqrt{3}}\right)+C \)
C \( =\frac{1}{\sqrt{2}} \tan ^{-1}\left(\frac{x^{2}+1}{\sqrt{2}}\right)+C \)
\( =\frac{1}{\sqrt{2}} \sin ^{-1}\left(\frac{x^{2}+1}{\sqrt{2}}\right)+C \)


Carbon resistors are of two types:
A. composition type resistor and film type resistor
B. rheostat and film type resistor
C. rheostat and variable resistor
D. composition type resistor and rheostat


From the diagram, what is the angle of
reflection?
A \( \cdot 10^{\circ} \)
B \( \cdot 20^{\circ} \)
\( c \cdot 30^{\circ} \)
D \( .40^{\circ} \)


ous' acid of a non-metal 'X' has 2 'O'
atoms. Per acid of the same non metal
has the formula
A. \( H X O_{2} \)
в. \( H_{2} X O_{4} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{XO}_{2} \)
D. \( H X O_{4} \)


Construct a triangle \( A B C \) whose
perimeter \( 12 \mathrm{cm} \) and whose base angles
are \( 65^{\circ} \) and \( 85^{\circ} \)


In terms of Bohr radius \( a_{0}, \) the radius of the second Bohr orbit of a hydrogen
atom is given by:
\( A \cdot 8 a_{0} \)
в. \( 4 a_{0} \)
\( c \cdot 2 a_{0} \)
D. \( \sqrt{2} a_{0} \)


Which one of the following is not charachterised of displacement?
A. As it is a vector it has magnitude direction and a unitt
B. It may be positive,negative or zero
c. The magnitude of displacement is equal to the shortest distance between the initial and final positions of the particle
D. A number of displacement are added of subtracted alebraically.


Male gametophyte with least number of cells is present in
A. Pteris
B. Funaria
c. Lilium
D. Pinus


The remainder when \( 4 a^{3}-12 a^{2}+ \)
\( 14 a-3 \) is divided by \( 2 a-1, \) is
A \( \cdot \frac{2}{3} \)
в. \( \frac{5}{3} \)
\( c \cdot \frac{6}{7} \)
D. \( \frac{3}{2} \)


Two concentric circular coils one of
small radius \( r_{1} \) and the other of large
radius \( r_{2} \) such that \( r_{1}<<r_{2} \) are placed
co-axially with centres coinciding. Obtain the mutual inductance of the
arrangement.


A right circular cone and a right circular cylinder have equal base and equal height. If radius of the base and the height, are in the ratio \( 5: 12, \) then ratio of the total surface area of the cylinder to that of the cone is
A . 3:
B. 13:
c. 17: 9
D. 34:


If half-life of a substance is 5 yrs, then
the total amount of substance left after
15 years, when initial amount is 64
grams is:
A. 16 grams
B. 2 grams
c. 32 grams
D. 8 grams


In an electrical circuit two resistors of 2
\( \Omega \) and \( 4 \Omega \) respectively are connected in series to a \( 6 \mathrm{V} \) battery. The heat dissipated by the \( 4 \Omega \) resistor in 5 s will be
A . 5 J
B. 10
c. 20
D. 30


Calculate the charge on a body if \( 10^{5} \) electrons have been added to it
\( \mathbf{A} \cdot-1.6 \times 10^{-14} C \)
В. \( 1.6 \times 10^{-14} C \)
c. \( 1.6 \times 10^{14} C \)
D. \( -1.6 \times 10^{14} C \)


Define electric potential and write down its dimension.


Give the IUPAC names of the given
compounds:


Two vertical rods of equal lengths, one of steel and the other of copper, are
suspended from the ceiling, at a distance I apart and are connected
rigidly to a rigid horizontal bar at their
lower ends. If \( A_{S} \) and \( A_{C} \) be their
respective cross-sectional areas, and
\( \boldsymbol{Y}_{\boldsymbol{S}} \) and \( \boldsymbol{Y}_{C}, \) their respective Young's
moduli of elasticities, where should a
vertical force \( F \) be applied to the horizontal bar in order that the bar
remains horizontal?


75.2 \( g \) of \( C_{6} H_{5} O H \) (phenol) is dissolved
in a solvent of \( K_{f}=14 . \) If the depression in freezing point is \( 7 \mathrm{K} \) then find the \( \% \) of phenol that dimerises.


f \( n(A)=7, n(B)=8 \) then find the
maximum and minimum number of
elements of \( A U B \)


Assertion
In the motion of projectile the horizontal component of velocity remains constant
Reason
The force on the projectile is gravitational force which acts only in vertically downward direction
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


Two particles of masses \( m_{1} \) and \( m_{2} \) are moving velocities \( \vec{V}_{1} \) and \( \vec{V}_{2} \) Momentum
of the particle of mass \( m_{1} \) with respect to center of mass is
A. zero
B. \( \frac{m_{1} m_{2}}{m_{1}+m_{2}}\left(\vec{V}_{1}-\vec{V}_{2}\right) \)
c. \( \frac{m_{2}}{m_{1}+m_{2}}\left(\vec{V}_{1}-\vec{V}_{2}\right) \)
D. None of these


When resonance is produced in a series
\( L C R \) circuit, then which of the following
is not correct?
A. Current in the circuit is in phase with the applied voltage
B. Inductive and capacitive reactance are equal
C. If \( R \) is reduced, the voltage across capacitor wil increase
D. Impedance of the circuit is maximum.


Velamen tissue in orchids is found in
A. Shoot
B. Root
c. Leaves
D. Flowers


The slope of a line is double of the slope of another line. If tangent of the angle between them is \( \frac{1}{3}, \) find the slopes of the lines.


Which of the following will react fastest
with \( \boldsymbol{A} \boldsymbol{g}^{*} \)
\( A \)
в.
\( c \)
\( D \)


State Kirchhoff's laws of electrical
circuits with the help of suitable circuit diagram. Write formula of zero deflection of Wheatstone bridge.


Assertion
Environment signals such as light and gravity also affect phase or stage of growth
Reason
Gravity and light leads to differential auxin concentration which is
responsible for differential growth.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Select the correct order of magnetic
moment (in B.M.) from the following
options:
\( \mathbf{A} \cdot\left[M n C l_{4}\right]^{2-}>\left[C o C l_{4}\right]^{2-}>\left[F e(C N)_{6}\right]^{4-} \)
B . \( \left[F e(C N)_{6}\right]^{4-}>\left[M n C l_{4}\right]^{2-}>\left[C o C l_{4}\right]^{2} \)
C \( \cdot\left[F e(C N)_{6}\right]^{4-}>\left[\operatorname{CoCl}_{4}\right]^{2-}>\left[M n C l_{4}\right]^{2} \)
D. \( \left[M n C l_{4}\right]^{2-}>\left[F e(C N)_{6}\right]^{4-}>\left[C o C l_{4}\right]^{2-} \)


toppr
Q Type your question
by
\( A \)
B.
\( \mathbf{c} \)
\( D \)


There are five resistors in a given series
circuit and each resistor has \( 6 V \)
dropped across it. The source voltage
A . is \( 6 V \)
B. depends on the current flow
c. depends on the resistor values
D. is \( 30 V \)


What is methane? Draw its electron dot
structure. Name the type of bonds formed in this compound. Why are such compounds
(i) Are Poor conductors of electricity and
(ii) Have low melting and boiling points? What happens when this compound burns in oxygen?


Evaluate \( : \int \frac{\log x}{x} d x \)


\( \operatorname{Resolve} \frac{x^{4}-x^{2}+1}{x^{2}\left(x^{2}+1\right)^{2}} \) into partial
fractions.
A \( \cdot-\frac{2}{x^{2}}+\frac{1}{\left(x^{2}+1\right)^{2}} \)
B. \( -\frac{1}{x^{2}}+\frac{3}{\left(x^{2}+1\right)^{2}} \)
c. \( \frac{1}{x^{2}}-\frac{5}{\left(x^{2}+1\right)^{2}} \)
D. \( \frac{1}{x^{2}}-\frac{3}{\left(x^{2}+1\right)^{2}} \)


Draw the diagram that explains the formation of an image by a plane mirror.


A solution containing \( 62 g \) ethyl glycol
in \( 250 g \) water is cooled to \( -10^{\circ} \mathrm{C} \). If \( K_{f} \)
for water is \( 1.86 K k g m o l^{-1}, \) the
amount of water \( (\text { in } g \) ) separated as ice is:
A . 32
B. 48
\( c \cdot 16 \)
D. 64


of intensity \( I \) is incidents on a glass plate as shown, in the figure. Another identical glass plate is kept close to the
first-one and parallel to it. Each glass plate reflects \( 25 \% \) of the light incident on it and transmits the remaining. Then
the ratio of the maximum and
minimum intensities in the
interference pattern formed by the two
beams obtained after one reflection at
each plate is
A . 7: 1
B. 49: 1
c. 4: 1
D. 16: 9


A body is executing S.H.M. When its displacement from the mean position is \( 4 \mathrm{cm} \) and \( 5 \mathrm{cm}, \) the corresponding
velocity of the body is \( 10 \mathrm{cm} / \mathrm{sec} \) and 8 \( \mathrm{cm} / \mathrm{sec} . \) Then the time period of the body is:
A \( .2 \pi \sec \)
B . \( \pi / 2 \) sec
\( c . \pi \mathrm{sec} \)
D. 3\pi/2 sec


The existence of isotopes is due to the presence of different number of
A. electrons
B. protons
c. neutrons
D. atoms


Purkinje fibre is found in
A. Conduction system of heart
B. Brain
c. Nephrons of kidneys
D. Sensation of skin


A thin spherical conducting shell of radius \( \mathrm{R} \) has a charge \( \mathrm{q} \). Another charge
Q is placed at the centre of the shell. The electrostatic potential at a point \( \mathbf{P} \) which is at a distance \( \frac{\boldsymbol{R}}{\mathbf{2}} \) from the centre of the shell is:
\( ^{\mathbf{A}} \cdot \frac{2 Q}{4 \pi \epsilon_{0} R}-\frac{2 q}{4 \pi \epsilon_{0} R} \)
В. \( \frac{2 Q}{4 \pi \epsilon_{0} R}+\frac{2 q}{4 \pi \epsilon_{0} R} \)
c. \( \frac{(q+Q)}{4 \pi \epsilon_{0} R}+\frac{2}{R} \)
D. \( \frac{2 Q}{4 \pi \epsilon_{0} R} \)


In young's experiment, the source of red light of wavelength \( 7 \times 10^{-7} \) m. When a
thin glass plate of refractive index 1.5 at this wavelength is put in the path of one of the interfering beams, the central fringe shifts by \( 10^{-3} m \) to the position previously occupied by the 5 th bright fringe. If the thickness of the plate is \( \boldsymbol{X} \boldsymbol{\mu} \boldsymbol{m} \)
Find \( X ? \)


following graphs correctly represents
the variation of extension in the length
of a wire with the external load?
\( A \)
B.
\( c \)
D.


Derive the relation between the
resistances of the arms of a

Wheatstone bridge in its balance condition. Write its two applications.


a \( \mathrm{R} \) b if "a and b are animals in different
zoological parks" then R is
A. only reflexive
B. only symmetric
c. only transitive
D. equivalence


The velocity of a reaction is doubled for
every \( 10^{\circ} \mathrm{C} \) rise in temperature. If the
temperature is raised to \( 50^{\circ} \mathrm{C} \), the
reaction velocity increases by about:
A. 12 times
B. 16 times
c. 32 times
D. 50 times


Which of the following equations has two distinct real roots ?
A \( \cdot 2 x^{2}-3 \sqrt{2} x+\frac{9}{4}=0 \)
В. \( x^{2}+x-5=0 \)
c. \( x^{2}+3 x+2 \sqrt{2}=0 \)
D. \( 5 x^{2}-3 x+1=0 \)


Mark the option which correctly
differentiates between solar and lunar
eclipse:
A. When the moon comes in between the earth and the
sun and if all the three are in same straight line, solar eclipse occurs. And when the earth comes in between the sun and the moon and if all the three are in same straight line, lunar eclipse occurs.
B. When the earth comes in between the sun and the
moon and if all the three are in same straight line, solar eclipse occurs. And, when the earth comes in between the sun and the moon and if all the three are
in same straight line, lunar eclipse occurs.
C. Both A and B are wrong.
D. Sun's shadow causes solar eclipse and moon's shadow causes lunar eclipse.


A hollow double concave lens is made of
very thin transparent material. It can be
filled with air or either of two liquid \( L_{1} \)
or \( L_{2} \) having refractive indices \( \mu_{1} \) and
\( \mu_{2} \) respectively \( \left(\mu_{2}>\mu_{1}>1\right) . \) The lens
will diverge a parallel beam of light if it is filled
This question has multiple correct options
A. \( L_{1} \) and immersed in \( L_{2} \)
B. \( L_{2} \) and immersed in water
c. water and immersed in \( L_{2} \)
D. Air and immersed in either water or \( L_{1} \) or \( L_{2} \)


In scenario \( 1, \) a person pulls with a force \( F \) on a string of length \( 2 d \) that is connected to a spring scale. The other end of the spring scale is connected to a post by a string of length d. In scenario
2, the person pulls on the string of length \( 2 d \) with a force of \( F, \) and \( a \) second person stands where the post was in scenario \( 1, \) and also pulls with a force of \( F \). If the spring scale reads 50 N in scenario \( 1, \) what does the spring scale read in scenario \( 2 ? \)
A. \( 50 \mathrm{N} \)
B. 67
c. \( 100 \mathrm{N} \)
D. 133 N
E. \( 150 \mathrm{N} \)


The bleaching action of chlorine is an oxidation reaction. Why?


The relative number of atoms of
elements, \( X \) and \( Y \) in a compound is 0.25 and \( 0.5 . \) The empirical formula of compound is:
A . \( X Y \)
в. \( X_{2} Y \)
c. \( X Y_{2} \)
D. \( X_{2} Y_{2} \)


What is the reference angle, \( \rho ? \)
\( \mathbf{A} \cdot \rho=30^{\circ} \)
\( \mathbf{B} \cdot \rho=45^{\circ} \)
\( \mathbf{C} \cdot \rho=56^{\circ} \)
D \( \cdot \rho=270^{\circ} \)


Consider six wires into or out of the
page, all with the same current. Rank the line integral of the magnetic field(from most positive to most
negative) taken counterclock wise around each loop shown as positive in accordance with right hand screw rule.
\( \mathbf{A} \cdot B>C>D>A \)
В . \( B>C=D>A \)
c. \( B>A>C=D \)
D. \( C>B=D>A \)


At equilibrium, if \( \boldsymbol{K}_{\boldsymbol{p}}=\mathbf{1}, \) then:


In the given arrangement, mass of the block is \( \mathrm{M} \) and the surface on which the
block is placed is smooth. Assume all pulleys to be massless and frictionless,
strings to be inelastic and light, \( \boldsymbol{R}_{1}, \boldsymbol{R}_{2} \)
and \( R_{3} \) to be light supporting rods. The
acceleration of point \( \mathrm{P} \) will be (A is fixed) :
\( A \cdot O \)
B. \( \infty \)
c. \( \frac{4 F}{M} \)
D. \( \frac{2 F}{M} \)


If \( \mathrm{E}, \mathrm{m}, \mathrm{I} \) and \( \mathrm{G} \) denote energy, mass,
angular momentum and gravitational constant respectively, then the quantity \( \left(\frac{E l^{2}}{m^{5} G^{2}}\right) \) has the dimensions of then
A. mass
B. length
\( c . \) time
D. angle.


Standard electrode potentials of
\( \boldsymbol{F} \boldsymbol{e}^{2+}+\boldsymbol{2} \boldsymbol{e}^{-} \rightarrow \boldsymbol{F} \boldsymbol{e} \) and \( \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{3}+}+\boldsymbol{3} \boldsymbol{e}^{-} \rightarrow \)
\( F e \) are \( -0.440 V \) and \( -0.036 V \)
respectively. The standard electrode potential \( \left(\boldsymbol{E}^{o}\right) \) for \( \boldsymbol{F} \boldsymbol{e}^{\mathbf{3}+}+\boldsymbol{e}^{-} \rightarrow \boldsymbol{F} \boldsymbol{e}^{2+} \)
is:
\( \mathbf{A} \cdot-0.476 V \)
В. \( -0.404 V \)
c. \( +0.404 V \)
D. \( +0.772 V \)


is easy to administer and
transparent.
A. profit
B. vat
c. sales tax
D. discount


Choose the correct answer from the
alternatives given. Which of the following is not true for
electromagnetic waves?
A. They transport energy.
B. They have momentum.
C. They travel at different speeds in air depending on their frequency.
D. They travel at different speeds in medium depending on their frequency.


The escape velocity from the earth is
\( 11 k m s^{-1} . \) The escape velocity from a
planet having twice the radius and same mean density as that of earth is
\( \mathbf{A} \cdot 5.4 \mathrm{kms}^{-1} \)
B . \( 11 k m s^{-1} \)
\( \mathbf{c} \cdot 22 k m s^{-1} \)
D. None of the above


The \( Q \) factor of a series LCR circuit with
\( \mathrm{L}=2 \mathrm{H}, \mathrm{C}=32 \mu \mathrm{F} \) and \( \mathrm{R}=10 \Omega \mathrm{is} \)
A . 15
B. 20
\( c \cdot 25 \)
D. 30


Assertion
In tropical rainforest 0 horizon and \( A \) horizon of soil profile are shallow and
nutrient poor
Reason
Excessive growth of micro organism in soil depletes its organic content
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which one of the following statements
is correct with respect to kidney
function regulation?
A. When someone drinks lot of water, ADH release is
suppressed
B. Exposure to cold temperature stimulates ADH release
C. An increase in glomerular blood flow stimulates formation of angiotensin II
D. During summer when body loses lot of water by evaporation the release of ADH is suppressed


For the equilibrium in a closed vessel
\( \boldsymbol{P C l}_{5}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{P} \boldsymbol{C l}_{3}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) \)
\( K_{p} \) is found to be double of \( K_{c \cdot} \) This is
attained when:
A. \( T=2 K \)
в. \( T=12.18 K \)
c. \( T=24.36 K \)
D. \( T=27.3 K \)


Which figure is an example of top view?
A. figure 1
B. figure 2
c. figure 4
D. figure 3


If \( C O_{2} \) is passed into waste water
containing \( C r O_{7}^{2-} \) (yellow) then:
A. Solution turns green due to formation of \( C r^{3} \)
B. Solution turns blue due to formation of \( C r O_{5} \)
C. Solution turns orange due to formation of \( C r_{2} O_{7}^{2} \)
D. No effect takes place


The degree of the polynomial \( x^{2}- \) \( 5 x^{4}+\frac{3}{4} x^{7}-73 x+5 \) is
A. 7
B. \( \frac{3}{4} \)
\( c \cdot 4 \)
D. -73


STATEMENT-1: The oxidation state of Tl
is +1
STATEMENT-2: Moving from top to
bottom in \( I I I A \) group, the stability of
+1 oxidation state increases.
A. STATEMENT-1 is True, STATEMENT-2 is True:
STATEMENT-2 is a correct explanation for STATEMENT-
B. STATEMENT-1 is True, STATEMENT-2 is True:
STATEMENT-2 is NOT a correct explanation for STATEMENT-1
c. STATEMENT-1 is True, STATEMENT-2 is False
D. STATEMENT-1 is False, STATEMENT-2 is True


Which of the following is not obtained by direct reaction of constituent elements?
A. \( \mathrm{XeO}_{3} \)
в. \( \mathrm{xeF}_{2} \)
c. \( \mathrm{xeF}_{6} \)
D. \( \mathrm{xeF}_{4} \)


A stone dropped from the top of a tower
is found to travel \( \frac{5}{9} \) th of height of the tower during the last second of its fall. The time of fall is
A . \( 2 s \)
B. \( 3 s \)
c. \( 4 s \)
D. \( 5 s \)


Chloroplast have stacked portions called
A. Grana
B. Stroma
c. Lamellae
D. None of these


Vitamin K cannot be produced by humans. What is true about the
presence of vitamin \( \mathrm{K} \) in bloodstream even though a person's diet is lacking in vitamin K?
A. Vitamin K is synthesized in the liver using hormones absorbed from ingested plant cells
B. Vitamin K is a byproduct of protein degradation during digestion.
c. Vitamin K is synthesized by bacteria that inhabit the colon
D. Vitamin K can be produced by exposure to sunlight.
E. None of the above


The real part of \( (i-\sqrt{3})^{13} \) is
A \( \cdot 2^{-10} \sqrt{3} \)
B. \( -2^{12} \sqrt{3} \)
\( \mathrm{c} \cdot 2^{-12} \sqrt{3} \)
D. \( -2^{-12} \sqrt{3} \)
E \( .-2^{10} \sqrt{3} \)


A uniform elastic plank moves over a smooth horizontal plane due to a
constant force \( \boldsymbol{F}_{0} \) distributed uniformly over the end face. The surface of the end
face is equal to \( S \) and Young's
modulus of the material is \( E . \) If the
compressive strain of the plank in
the direction of the acting force is \( \sigma= \) \( \frac{\boldsymbol{F}_{0}}{\boldsymbol{x} \boldsymbol{S} \boldsymbol{E}}, \) find the value of \( ^{\prime} \boldsymbol{x}^{\prime} \)


The ratio of the time taken by a body moving with uniform acceleration in
reaching two points \( P \) and \( Q \) along a straight line path is \( 1: 2 . \) If the body starts from rest and moves linearly, the ratio of the distance between \( P \) and \( Q \)
from the starting point is:
\( A \cdot 4: \)
B. 1: 4
c. 2: 3
D. 3:


Which of the following forms an ideal
solution?
This question has multiple correct options
A. Acetone and phenol
B. Bromoethane and chloroethane
c. \( C C l_{4} \) and \( S i C l_{4} \)
D. Bromobenzene and Chlorobenzene


The internal length, breadth and height of a box are \( 30 \mathrm{cm}, 24 \mathrm{cm} \) and \( 15 \mathrm{cm} \)
Find the largest number of cubes which can be placed inside this box if the edge of each cube is \( 4 \mathrm{cm} \)


Which one of the following is not a
Lewis Acid?
\( \mathbf{A} \cdot B F_{3} \)
в. \( A l C l_{3} \)
c. \( B e C l_{2} \)
D. \( \operatorname{SnCl}_{2} \)


An open tank with a square base and vertical sides is to be constructed from a metal sheet so as to hold a given
quantity of water. Show that the cost of the material will be least when depth of the tank is half of its width.


The complex having the highest
magnetic moment is :
\( \mathbf{A} \cdot\left[\operatorname{Zn}\left(H_{2} O\right)_{6}\right]^{2} \)
B . \( \left[\operatorname{Cr}\left(\text { Ha}_{2} \text { O }\right)_{6}\right]^{2} \) '
\( \mathbf{c} \cdot\left[M n\left(H_{2} O\right)_{6}\right]^{2+} \)
D \( \cdot\left[C u\left(H_{2} O\right)_{6}\right]^{2} \)


The uniform disc shown in the figure
has a moment of inertia of \( 0.6 k g m^{2} \)
around the axis that passes through 0
and is perpendicular to the plane of the
page. If a segment is cut out from
the disc as shown, the moment of inertia of the remaining disc is \( \frac{1}{x} k g m^{2} \)
Find \( x \)


A steel wire of original length \( 1 \mathrm{m} \) and
cross-sectional area \( 4.00 \mathrm{mm}^{2} \) is
clamped at the two ends so that it lies horizontally and without tension. If a load of \( 2.16 \mathrm{kg} \) is suspended from the middle point of the wire, what would be
its vertical depression?Y of the steel \( = \) \( \mathbf{2 . 0} \times \mathbf{1 0}^{1 \mathbf{1}} \mathbf{N m}^{-\mathbf{2}} \)
take \( \mathfrak{g}=10 m s^{-2} \)


A square loop is placed near a long straight current carrying wire as shown Match the following two columns


The above experiment is done at \( N T P \) The stop cock is opened for certain time and then closed. After effusion, the bulb
\( A \) contains \( 0.1 g m \) of \( D_{2} \). Find out the number of mole of \( H_{2} \) in bulb \( B \).


If the electric field at all points on a
closed Gaussian surface is zero, does
this mean that the net charge enclosed
by the surface is zero?
A. Yes; zero field everywhere means zero flux everywhere.
B. Yes; zero electric field means that there are no charges of any kind in the region.
C. No; there may be some positive and some negative charges enclosed within the surface.
D. No; zero field could be caused by charges outside of the surface as well as inside the surface.
E. No; it is impossible for charges to exist and yet electric field to be zero everywhere.


Choose the correct statements (s) from
the following?
This question has multiple correct options
A. Mechanical waves need medium for their propogation
B. Sound cannot travel through vaccum
C. Mechanical waves transport energy from one place to another
D. Sound waves are non mechanical waves


Van Arkel method of purification of metals involves converting the metal to
\( \mathbf{a}: \)
A. volatile compound
B. volatile unstable compound
c. non-volatile stable compound
D. none of these


Which one of the following compounds involve in disproportionation reaction with water?
A. \( X e F_{2} \)
в. \( X e F_{4} \)
c. \( X e F_{6} \)
D. \( X e O_{2} F_{2} \)


For the equilibrium \( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) \rightleftharpoons \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \)
at 1 atm and \( 298 K \)
A. standard free energy change is equal to zero \( \left(\triangle G^{\circ}=\right. \)
0)
B. free energy change is less than zero ( \( \triangle G<0 \) )
c. standard free energy change is less than zero \( \left(\triangle G^{\circ}<\right. \)
0
D. standard free energy change is greater then zero \( \left(\triangle G^{\circ}>0\right) \)


The dependence of acceleration due to gravity g on the distance r from the centers of the earth assumed to be a
sphere of radius \( R \) of uniform density is as shown figure below.
The correct figure is
\( (i) \)
(ii)
(iii)
(iv)
\( A \cdot(i) \)
B. (ii)
\( c \)
D. Güvüù


A solid cylinder of mass \( \mathrm{M} \) and radius \( \mathrm{R} \) rolls down an inclined plane without slipping. The speed of its centre of mass when it reaches the bottom is (h is the height of inclined plane) :
A. \( \sqrt{2 g h} \)
в. \( \sqrt{\frac{4}{3} g h} \)
c. \( \sqrt{\frac{3}{4} g h} \)
D. \( \sqrt{\frac{4 g}{h}} \)


If three elements \( X, Y, \) and \( Z \) form a Dobereiner's triad and atomic weights of \( X \) and \( Z \) are 9 and 40 respectively
then the atomic weight of the element \( Y \) is approximately:
A . 24.
B. 49
c. 34.5
D. 29


Which of the following is a true Chalcogen:
A. Nitrogen
B. Oxygen
c. Polonium
D. Chlorine


If the difference between the standard
deviation and
variance of a data is 12 then find the
sum of the variance and standard
deviation of that data
A . 20
B . 15
c. 18
D. 22


Which one of these does not pertain to B-cells?
A. Have passed through the thymus
B. Synthesize and liberate antibodies
c. Have antibody-mediated immunity
D. Have specific receptors


A man had to walk a certain distance.
He covered two thirds of it at 4 kmph
and the remaining at 5 kmph. If the total time taken is 42 minutes, find the
total distance.


The compound with no dipole moment
is:
A. methyl chloride
B. carbon tetrachloride
c. methylene chloride
D. chloroform


If two or more vectors are parallel to the same line, irrespective of their magnitudes and directions, then they
are
A. Co-initial vectors
B. Collinear vectors
c. equal vectors
D. unit vectors


In
\( \Delta P Q R, \) an exterior angle at \( R \) is
represented by \( 5 x+10 . \) If the two non-
adjacent interior angles are represented by \( 3 x+15 \) and \( 3 x-20 \)
find the value of the exterior angle, \( \angle R \)
A \( .90^{\circ} \)
B. \( 80^{\circ} \)
\( c \cdot 84^{\circ} \)
D. \( 85^{\circ} \)


The moon's radius is \( 1 / 4 \) that of the
earth and its mass \( 1 / 80 \) times that of
the earth. If \( g \) represents the acceleration due to gravity on the surface of the earth, then on the surface of the moon its value is:
\( A \cdot g / 4 \)
B. \( g / 5 \)
\( c \cdot g / 6 \)
D. g/8


Convert the following temperatures to
the Celsius scale.
\( (a) 293 K \)
(b) \( 470 K \)


\( 4, \frac{8}{3}, \frac{16}{9}, \frac{32}{27} \dots \) is a
A. arithmetic sequence
B. geometric sequence
C . geometric series
D. harmonic sequence


In the adjoining figure, \( A B C D \) is an
isosceles trapezium. If \( \angle A= \)
\( \mathbf{6 0}^{\circ}, \boldsymbol{D C}=\mathbf{2 0} \boldsymbol{c m} \) and \( \boldsymbol{A} \boldsymbol{D}=\mathbf{1 5} \boldsymbol{c m} \)
find the length of \( \boldsymbol{A B} \)


The position of a body moving along \( x- \)
axis at time \( t \) is given by \( \boldsymbol{x}=\left(\boldsymbol{t}^{2}-\boldsymbol{4} \boldsymbol{t}+\right. \)
6) \( m . \) The distance travelled by body in
time interval \( t=0 \) to \( t=3 \) s is
\( \mathbf{A} \cdot 5 m \)
B. \( 7 m \)
c. \( 4 m \)
D. \( 3 m \)


The approximate tilt of the moons orbit
is:
A. 15 degrees
B. 10 degrees
c. 5 degrees
D. 1 degree


Which of the following points lie on the negative side of \( x- \) axis ? This question has multiple correct options
A. (-4,0)
в. (-3,2)
c. (0,-4)
D. (5,-7)


Assertion
The value of 1 Micron is equal to \( 10^{-5} m \)
Reason
Micron is the unit for measuring
microscopic distance.
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


For inert gases, \( \frac{C_{p}}{C_{v}}=-\dots- \)
A . 1.33
B. 1.40
c. 1.66
D. can't be predicted


When stationary waves are set up, pick
out the correct statement from the
following:
A. all the particles in the medium are in the same phase of vibration at all times and distances
B. the particles with an interval between two consecutive nodes are in phase, but the particles in two such consecutive intervals, are of opposite phase
C. the phase lag along the path of the wave increases as the distance from the source increases
D. only antinodes are in same phase


\( C_{6} H_{6}+B r_{2} \stackrel{F e}{\rightarrow} C_{6} H_{5} B r+H B r \) is an
example for:
A. free radical substitution reaction
B. electrophilic substitution reaction
c. nucleophilic addition reaction
D. nucleophilic substitution reaction


The number of six-digit numbers that can be formed from the digits
1,2,3,4,5,6 and 7 so that digits do not
repeat and the terminal digits are even is
A .144
B. 72
c. 288
D. 720


In the figure below, \( \angle Q>\angle R \) and \( M \) is
a point on \( Q R \) such that \( P M \) is the
bisector of \( \angle Q P R \) If the perpendicular
from \( P \) on \( Q R \) meets \( Q R \) at \( N \) then prove that \( \angle M P N=\frac{1}{2}(\angle Q-\angle R) \)


Among \( \boldsymbol{B F}_{3}, \boldsymbol{N}\left(\boldsymbol{S} \boldsymbol{i} \boldsymbol{H}_{3}\right)_{3}, \boldsymbol{N}\left(\boldsymbol{C} \boldsymbol{H}_{3}\right)_{3}, \boldsymbol{O}\left(\boldsymbol{S} \boldsymbol{i} \boldsymbol{H}_{3}\right)_{2} \)
the number of molecules or molecular
ions which have back bonding is:
A . 1
B. 3
\( c \cdot 4 \)
D. all \( l \)


Newton's first law of motion is also
called Galileo's law of:
A. Conservation of momentum
B. Inertia
c. Friction
D. conservation of mass


f we write equation as \( a x+b y+c=0 \)
then \( b=? \)
4
B.
\( c \)
\( D \)


Choose the correct answer from the
alternatives given.
In which of the following forms \( C O_{2} \) is mostly carried in blood?
A. Hydrogencarbonate ions
B. Carbonic acid
c. Carbonate ions
D. Carbaminohaemoglobin


Which principle is the basis for the transmission of light through fiber optic cables even if the cable is bent?
A. Photoelectric effect
B. Uncertainty principle
c. Light diffraction
D. Light polarization
E. Total internal reflection


According to Engler and Prantl, the angiosperms were directly derived from
A. Gymnosperms
B. Bryophytes
c. Pteridophytes
D. Proto-angiosperms (hypothetical)


During which phase, the pulling apart of the chromosomes to the opposite poles of the cell take place?
A. Interphase
B. Prophase
c. Metaphase
D. Anaphase
E. Telophase


Phosphine cannot be prepared by which
of the following rreaction?
A. White P is heated with NaOH
B. Red P is heated with NaOH
c. \( C a_{3} P_{2} \) is heated with water
D. Phosphorus trioxide is boiled with water


Explain the relation between the area of contact and pressure exerted on a body.


A body weighs \( 72 N \) on the surface of
earth. What is the gravitational force on it due to earth at a height equal to half the radius of the earth from the
surface?
B. \( 28 N \)
\( c .16 N \)
D. 32 N


Reduction occurs at cathode in:
A. galvanic cell
B. electrolytic cell
C. both galvanic and electrolytic cell
D. neither galvanic nor electrolytic cell