In a photoelectric experiment, the collector plate is at \( 2.0 \mathrm{V} \) with respect to the emitter plate made of copper \( (\phi= \) 4.5 \( e V \) ). the emitter is illuminated by a
source of monochromatic light of
wavelength \( 200 \mathrm{nm} \)
A. The minimum kinetic energy of the photo electrons reaching the collector is 0
B. The maximum kinetic energy of the photo electrons reaching collector is 3.7 ev.
c. If the polarity of the battery is reversed then answer to part A will be o
D. If the polarity of the battery is reversed then answer to part B will be 1.7 eV


Which of the following is a fossil fuel?
I Tar
II Coal
III Petroleum
A. I only
B. I and II only
c. Il and III only
D. I, II and III


Which of the following is an indication of adolescence growth spurt??
A. Growth in height and weight
B. Adulthood
c. change in skin
D. None of the above


What is the largest angle of the
triangle?
\( A \cdot x \)
B.
\( c \cdot z \)
\( D \)


Consider the line \( x=\sqrt{3} y \) and the
circle \( x^{2}+y^{2}=4 \)
What is the area of the region in the first quadrant enclosed by the \( x \) -axis, the line \( x=\sqrt{3} y \) and the circle?
A \( \cdot \frac{\pi}{3} \)
в.
\( ^{C} \cdot \frac{\pi}{3}-\frac{\sqrt{3}}{2} \)
D. None of the above


Let \( u_{1} \) and \( u_{2} \) be two urns such that \( u_{1} \)
contains 3 white, 2 red balls and \( u_{2} \)
contains only 1 white ball. A fair coin is tossed. If head appears, then 1 ball is
drawn at random from urn \( u_{1} \) and put
into \( u_{2} . \) However, if tail appears, then 2
balls are drawn at random from \( u_{1} \) and
put into \( u_{2} . \) Now, 1 ball is drawn at
random from \( u_{2} \). Then, probability of the
drawn ball from \( u_{2} \) being white is
A \( \cdot \frac{13}{30} \)
в. \( \frac{23}{30} \)
c. \( \frac{19}{30} \)
D. \( \frac{11}{30} \)


A ring a radius \( r \) is rotating about a
vertical axis along its diameter with
constant angular velocity \( \omega . \) A read of
mass \( m \) remains at rest w.r.t. ring at the
position shown in figure. Then \( w^{2} \) is
A \( \cdot \frac{g}{\sqrt{3 r}} \)
B. \( \frac{2 g}{\sqrt{3}} \)
\( c \cdot \frac{\sqrt{3} g}{n} \)
\( D \)


If \( A \) and \( B \) are two events such that
\( \boldsymbol{P}(\boldsymbol{A})=\mathbf{0 . 4}, \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B})=\mathbf{0 . 7} \) and
\( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})=\mathbf{0 . 2} \) then \( \boldsymbol{P}(\boldsymbol{B}) \) is equal to
A . 0.1
B. 0.3
\( c .0 .5 \)
\( D \)


Count total number of Significant Figures in 3.0800
A. 3
B. 5
\( c \)
\( D \)


In an electric generator,split rings are
used for
A. Converting DC to AC
B. Converting AC to DC
c. Reducing power consumption
D. To split the current


Rhizoids of hepaticopsida and anthocerotopsida are
A. Multicellular and branched
B. Unicellular and unbranched
c. Unicellular and branched
D. Multicellular and unbranched


In a dicot root vascular cambium is
A. Partially primary and partially secondary in origin
B. completely primary in origin
C. completely second in origin
D. not found


The highest energy in Balmer series, in the emission spectra of hydrogen is represented by:
\( \left(R_{H}=109737 \mathrm{cm}^{-1}\right) \)
\( \mathbf{A} \cdot 4389.48 \mathrm{cm}^{-1} \)
в. \( 2194.74 \mathrm{cm}^{-1} \)
c. \( 5486.85 \mathrm{cm}^{-1} \)
D. 27434.25cm"


Plexiglass is a polymer of
A . acrylic acid
B. methylacrylate
c. methyl methacrylate
D. methyl propacrylate


Evaluate:
\( \mathbf{2}+\mathbf{2}^{\mathbf{2}}+\mathbf{2}^{\mathbf{3}}+\ldots .+\mathbf{2}^{\mathbf{9}}= \)
A. 1396
в. 1022
c. 1587
D. 1478


Acceleration of block A varies with time
as shown in figure the value of coefficient of kinetic friction between
the block \( A \) and \( B \) is
A . 0.5
B. 0.6
\( c \cdot 0.4 \)
D. None of these


The nucleus \( _{92} \mathrm{X}^{234} \) emits \( 3 \alpha \) -particles and then one \( \beta \) -particle. The end
product will be
A \( \cdot 84 \mathrm{Y}^{222} \)
В. \( 87 \mathrm{Y}^{228} \)
\( \mathbf{c} \cdot_{84} \mathbf{Y}^{228} \)
D・ \( _{87} \mathrm{Y}^{222} \)


Find the value of \( \csc 10^{\circ}-\sqrt{3} \sec 10^{\circ} \)


Assertion
An electric bulb becomes dim, when the
electric heater in parallel circuit is switched on.
Reason
Dimness decreases after sometime.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


What do you do in the following
situations :
(a) Exposed to exhaust fumes in traffic.
(b) Exposed to a series of fire crackers with high sound level.
(c) Get turbid drinking water during
monsoon.


(A) If water is heated to \( 350 \mathrm{K} \), then pOH
will increase to 8
(R) \( K_{w} \) increases with increase in
temperature.
\( A \). Both (R) and (A) are true and reason is the. correct explanation of assertion
B. Both (R) and (A) are true but reason is not correct explanation of assertion
C. Assertion (A) is true but reason (R) is false
D. Assertion (A) and reason (R) both are false
E. Assertion (A) is false but reason (R) is true


Select the correct match of the
following pair with respect to type of
coelom exhibited by them.
A. A- Platyhelminthes, B- Nematodes, C- Annelids
B. A- Nematodes, B- Annelids, C- Platyhelminthes
C. A- Platyhelminthes, B- Annelids, C- Nematodes
D. A- Annelids, B- Platyhelminthes, C- Nematodes


Evaluate: \( \int \frac{x^{2}+1}{x^{4}+1} d x \) equals
A. \( \frac{1}{\sqrt{2}} \tan ^{-1}\left(\frac{x^{2}-1}{\sqrt{2} x}\right)+C \)
B. \( \frac{1}{\sqrt{2}} \tan ^{-1}\left(\frac{1-x^{2}}{\sqrt{2} x}\right)+C \)
c. \( \frac{1}{2} \tan ^{-1}\left(\frac{x^{2}-1}{\sqrt{2} x}\right)+C \)
D. \( \frac{1}{2} \tan ^{-1}\left(\frac{1-x^{2}}{\sqrt{2} x}\right)+C \)


Correct statement for the given
compound.
A. Both P and Q can show geometrical isomerism
B. Only P can show geometriclal siomerism
C. Only Q can show geometrical isomerism
D. Neither P nor Q can show geometrical isomerism


Explain the term with example:Monomer


Find Voltage in the circuit?


A bus can be stopped by applying a retarding force \( F \) when it is moving with speed \( v \) on a level road. The distance covered by it before coming to rest is \( s \) If the load of the bus increases by \( 50 \% \) because of passengers, for the same speed and same retarding force, the distance covered by the bus to come to rest shall be:
A . \( 1.5 s \)
в. \( 2 s \)
\( c \cdot 1 s \)
D. 2.5


Pressure exerted by a sharp needle on a
surface is
A. more than the pressure exerted by a blunt needle
B. less than the pressure exerted by a blunt needle
C . equal to the pressure exerted by a blunt needle.
D. None of these


Find the real and imaginary parts of the complex number \( z=\frac{3 i^{20}-i^{19}}{2 i-1} \)


If 1 is zero of the polynomial \( p(x)= \)
\( a x^{2}-3(a-1) x-1 \) then the value of
'a' is
A .
B. -
\( c \cdot-2 \)
D.


A moving bullet hits a solid target
resting on a frictionless surface and gets embedded in it. What is conserved
in this process?
A. Both momentum and kinetic energy
B. Kinetic energy alone
c. Momentum alone
D. Neither momentum nor kinetic energy


Identify the combination of compounds that undergo aldol condensation followed by dehydration to produce but \( -2- \) enal
A. methanal and ethanal
B. two moles of ethanal
c. methanal and propanone
D. Ethanal and propanone
E. two moles of ethanol


\( f_{n}(x)=e^{f_{n-1}(x)} \) for all \( n \epsilon N \) and
\( f_{0}(x)=x, \) then \( \frac{d}{d x}\left\{f_{n}(x)\right\} \) is
This question has multiple correct options
A \( \cdot f_{n}(x) \frac{d}{d x}\left\{f_{n-1}(x)\right\} \)
В \( \cdot f_{n}(x) f_{n-1}(x) \)
\( \mathbf{c} \cdot f_{n}(x) f_{n-1}(x) \cdots f_{2}(x) \cdot f_{1}(x) \)
D. none of these


The relative strength of two weak bases at same concentration may be given as:
This question has multiple correct options
\( ^{\mathbf{A}} \cdot \frac{K_{b_{1}}}{K_{b_{2}}} \)
\( ^{\mathrm{B}} \cdot\left[\frac{\left[O H^{-}\right]_{1}}{\left[O H^{-}\right]_{2}}\right. \)
c. \( \frac{\alpha_{1}}{\alpha_{2}} \)
D. \( \frac{\sqrt{K_{b_{1}}}}{\sqrt{K_{b_{2}}}} \)


Which of the following is present in sillk
fibre?
A. carbohydrate
B. Lipids
c. Proteins
D. Fats


Flux through the rectangular piece of area \( 10 \mathrm{cm} \) by \( 20 \mathrm{cm} \) when placed \( (\mathrm{as} \) shown in an uniform electric field of
\( 200 \mathrm{N} / \mathrm{C}, \) ) is
A \( \cdot \) 4.0 \( N m^{2} / C \)
B . 3.5 \( N m^{2} / C \)
c. \( 2.5 \mathrm{Nm}^{2} / \mathrm{C} \)
D. zer


Let \( \boldsymbol{E}=\boldsymbol{x}^{3}\left(\boldsymbol{x}^{3}+\mathbf{1}\right)\left(\boldsymbol{x}^{\mathbf{3}}+\mathbf{2}\right)\left(\boldsymbol{x}^{\mathbf{3}}+\right. \)
\( \mathbf{3}) ; \boldsymbol{x} \epsilon \boldsymbol{R} \). Then minimum value of \( \boldsymbol{E} \) be
\( A \)
B. - -
\( c \cdot-1 \)
D. Minimum value is not attained


Two balloons \( A \) and \( B \) containing, 0.2 mole and 0.1 mole of helium at room
temperature and 2.0 atm. respectively are connected. When equilibrium is
established, the final pressure of \( \boldsymbol{H} e \) in the system
A. \( 01 . \) at
B. 1.5 atm
c. 0.5 atm
D. 2.0 atm


Which of the following is gemdihalide?
A \( \cdot C H_{3}-C H(B r)-C H_{2} B r \)
В. \( C H_{3}-C H B r_{2} \)
C. \( C H_{3}-C H(B r)-C H_{2}-C H_{2} B r \)
D. \( B r C H_{2} C H_{2} B r \)


What is redox reaction? In the reaction
\( Z n O+C \rightarrow Z n+C O \) which
substance gets oxidised and which gets reduced?


Water is boiled under a pressure of 1.0atm. When an electric current of
\( 0.50 A \) from a \( 12 V \) supply is passed for 300 second through a resistance in thermal contact with it, it is found that
\( 0.789 g \) of water is vapourized. The molar internal energy change at boiling point (373.15K) is
A. \( =37.9 k J m o l^{-1} \)
В. \( =27.5 k J \) mol \( ^{-1} \)
\( \mathbf{c} .=47.5 k J m o l^{-1} \)
\( \mathbf{D} \cdot=17.5 k J m o l^{-1} \)


The oxoacid of sulphur which contains
two sulphur atoms in different
oxidation states is:
A. pyrosulphurous acid
B. hyposulphurous acid
c. pyrosulphuric acid
D. persulphuric acid


Solve \( : a^{2}-(b+5) a+5 b=0 \)


The following table shows the age distribution of cases of a certain disease admitted during a year in a particular hospital
\( \begin{array}{ll}\text { Age } & \text { 5 } \\ \text { (in } & \text { - } \\ \text { Years) } & \text { 14 }\end{array} \) 15
25
34 24 44
No. of 6 11
\( \begin{array}{ll}21 & 23\end{array} \)
case
Find the nearest integer to the modal
age.


Which of the following is true regarding an Ne atom with a mass number of 20
and an \( O^{2-} \) ion with a mass number of
\( 16 ? \)
A. The contain the same number of protons
B. The contain the same number of neutrons
C. The contain the same number of protons plus neutrons
D. They are isoelectronic.
E. They are isomers


The value of \( \lim _{x \rightarrow \infty} \frac{\sqrt{1+x^{4}}-\left(1+x^{2}\right)}{x^{2}} \) is
A \( .-1 \)
B.
\( c \cdot 2 \)
D. none of these


The condition where only anthers are
fused throughout the entire lengths and filaments are free is
A. Synandrous
B. Gynandrous
c. Protandrous
D. syngenesius


At the top of a mountain a thermo meter read \( 7^{0} \mathrm{C} \) and barometer reads \( 70 \mathrm{cm} \) of
Hg. At the bottom of the mountain the barometer reads \( 76 \mathrm{cm} \) of Hg and thermometer reads \( 27^{0} \) C. The density of
air at the top of mountains is times the density at the bottom.
A . 0.99
B. 0.9
c. 0.89
D. 0.95


\( \left[\begin{array}{cc}\boldsymbol{a}+\boldsymbol{b} & \boldsymbol{2} \\ \mathbf{5} & \boldsymbol{b}\end{array}\right]=\left[\begin{array}{ll}\mathbf{6} & \mathbf{5} \\ \mathbf{2} & \mathbf{2}\end{array}\right], \) then find \( \boldsymbol{a} \)


Which of the following noble gases has the highest positive electron gain enthalpy value?
A. Helium
B. Krypton
c. Argon
D. Neon
E. Xenon


The temperature at which \( R M S \)
velocity of \( \boldsymbol{O}_{2} \) is equal to the \( \boldsymbol{R} \boldsymbol{M} \boldsymbol{S} \)
velocity of \( S O_{2} \) at \( 327^{\circ} C \) is:
A. \( 273 K \)
в. \( 300 K \)
\( \mathbf{c} \cdot 100^{0} C \)
D. \( 1200 K \)


Evaluate \( \int_{0}^{1}\left(2 x^{2}+x+1\right) d x \)


What are the factors that determine the
angle of deviation in a prism?
A. angle of incidence
B. wave length
c. angle of the prism
D. all the above


Find the area of bounded by \( y=\sin x \) from \( \boldsymbol{x}=\frac{\boldsymbol{\pi}}{\boldsymbol{4}} \) to \( \boldsymbol{x}=\frac{\boldsymbol{\pi}}{\boldsymbol{2}} \)
A \( \cdot \frac{\sqrt{2}-1}{\sqrt{2}} \)
B. \( \frac{1}{2} \)
\( c \cdot \frac{1}{4} \)
D. None of these


Which of the following solutions of Na \( C l \) will have the highest specific
conductance?
B. \( 0.1 N \)
c. \( 0.01 N \)
D. \( 1.0 N \)


A nucleus at rest split into two nuclear
parts having radii in the ratio 1:2. Their
velocities are in the ratio
\( A \cdot 8: \)
B. 6:
\( c \cdot 4: \)
D. 2:


Which of the following ion is pulled in a poplast by the auxin during growth?
A . \( N a^{\text {t }} \)
в. \( K^{+} \)
c. \( M g^{2+} \)
D. \( H^{+} \)


If \( y=\left(x^{2}+1\right) \sin x \) then \( \left(\frac{\pi}{2}\right)^{2}- \)
\( y_{20}\left(\frac{\pi}{2}\right) \) is equal to


A square \( A B C D \) and a circle are drawn
a graph sheet such that the vertices of the square \( A B C D \) are
\( \boldsymbol{A}(-\mathbf{2}, \mathbf{2}), \boldsymbol{B}(\mathbf{2}, \mathbf{2}), \boldsymbol{C}(\mathbf{2},-\mathbf{2}), \boldsymbol{D}(-\mathbf{2},- \)
and the circle with centre (0,0) and
radius \( 2 \mathrm{cm} \) is cut off from the above
square \( A B C D . \) Find the area of the
remaining region in the square \( A B C D \).


If two structures of same cross-
sectional area, but different numerical
apertures \( \mathrm{NA}_{1} \) and \( \boldsymbol{N} \boldsymbol{A}_{2}\left(\boldsymbol{N} \boldsymbol{A}_{2}<\boldsymbol{N} \boldsymbol{A}_{1}\right) \)
are joined longitudinally, the numerical a perture of the combined structure is
A \( \cdot \frac{N A_{1} N A_{2}}{N A_{1}+N_{2}} \)
B. \( N A_{1}+N A_{2} \)
c. \( N A_{1} \)
D. \( N A_{2} \)


The particular solution of \( \frac{d y}{d x}+ \) \( \frac{\boldsymbol{y}+\boldsymbol{2}}{\boldsymbol{x}+\boldsymbol{2}}=\boldsymbol{0} \) at (1,2) is given by
A \( . x y+2(x+y)=8 \)
B. \( x y+8(x+y)=2 \)
c. \( (x+2)+2(y+2)=8 \)
D. \( 8(x+2)+(y+2)=2 \)


An amount of money fetches a simple Interest of Rs.4,320 at the rate of 4
percent per annum at the end of 6 years. What is the principal amount?
A . \( R s .24,000 \)
B. Rs.12,000
c. \( R s .18,000 \)
D. \( R s .20,000 \)


A state of matter is characterized by
A. temprature
B. pressure
c. phase transition
D. none of above


Three-point charges \( 1 \mathrm{C}, 2 \mathrm{C} \), and \( 3 \mathrm{C} \) are
placed at the corners of an equilateral
triangle Of side \( 1 \mathrm{m} \). The work required to
move these charges to the corners of a
smaller equilateral triangle Of side \( 0.5 \mathrm{m} \)
in two different ways as in fig.(A) and
(B)Calculate the work done
A \( \cdot 9 \times 10^{9} \)
B \( .99 \times 10^{9} \)
\( \mathbf{c} \cdot 89 \times 10^{9} \)
D \( .29 \times 10^{9} \)


In gymnosperms, the pollination is
A. Anemophilous - micropylar
B. Anemophilous - stigmatic
C. Entomophilous - micropylar
D. Entomophilous - stigmatic


A ball of mass \( \mathrm{m} \) is dropped from a high building and strikes the ground 4 seconds later. Calculate the height of the building.
A \( .20 m \)
в. \( 40 m \)
c. \( 60 m \)
D. 80m
E . \( 100 m \)


A battery of \( 100 \mathrm{V} \) is connected to series combination of two identical parallel-
plate condensers. If dielectric of constant 4 is slipped between the plates of second condenser, then the potential difference on the condensers will respectively become:
\( A \cdot 80 \vee, 20 v \)
B. \( 75 \vee, 25 \mathrm{V} \)
c. \( 50 v \), \( 80 v \)
D. 20 V, 80 V


A quarter cylinder of radius \( R \) and
refractive index 1.5 is placed on a table.
A point object \( P \) is kept at a distance of
\( m R \) from it as shown in figure. For what
value of \( \boldsymbol{m} \) for which a ray from \( \boldsymbol{P} \) will
emerge parallel to the table?
\( A \cdot 2 \)
\( \overline{3} \)
B. 3 \( \overline{2} \)
\( c \cdot \frac{4}{3} \)
D. 3 4


What is straight chain polymer? How is it formed?


Decide whether sets \( A \) and \( B \) are equal
sets or not. \( \boldsymbol{A}=\mathbf{2}, \mathbf{4}, \mathbf{6}, \mathbf{8}, \boldsymbol{B}=\{\mathbf{x} \mid \mathbf{x} \) is a
positive even natural number less than
9


The carbon atoms in diamond are
bonded to each other by:
A. ionic bond
B. coordinate bond
c. hydrogen bonds
D. covalent bonds


Which of the following contains a covalent bond?
A. copper
в. \( N a C l \)
c. germanium
D. helium


\( \boldsymbol{E}_{c e l l}^{o}=\boldsymbol{E}_{O \boldsymbol{P}}^{o}+\boldsymbol{E}_{R P}^{o} \) if two electrodes are
connected.
If true enter 1 , else enter 0 .


Which of the following is not used as an antacid?
A. Magnesium hydroxide
B. Sodium carbonate
c. Sodium bicarbonate
D. Aluminium phosphate


The decreasing order of electron affinity is:
A. \( I>B r>C l>F \)
B. \( B r>C l>F>l \)
c. \( F>C l>B r>l \)
\( \mathrm{D} \cdot C l>F>B r>l \)


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


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


Which of the following is not a use of baking soda?
A. In medicines as antacid
B. As a component of baking powder
c. In removing permanent hardness of water
D. In fire extinguishers


The re-activity of \( \mathrm{Ca}, \mathrm{Sr}, \mathrm{Mg} \) and Ba with water follow the order:
A. \( S r>B a>M g>C a \)
в. \( B a>S r>C a>M g \)
c. \( C a>M g>B a>S r \)
\( \mathbf{D} \cdot S r>C a>M g>B a \)


\( \mathbf{A}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{2} & \mathbf{- 3} \\ \mathbf{5} & \mathbf{0} & \mathbf{2} \\ \mathbf{1} & \mathbf{- 1} & \mathbf{1}\end{array}\right] \) and \( \mathbf{B}= \)
\( \left[\begin{array}{ccc}3 & -1 & 2 \\ 4 & 2 & 5 \\ 2 & 0 & 3\end{array}\right] \)
Find the matrix \( C \) satisfying the relation
\( A+2 C=B \)


The cross-over frequency \( f_{c} \) is
A \( \cdot \frac{1}{2 \pi \sqrt{L C}} \)
B. \( \frac{1}{2 \pi R C} \)
c. \( \frac{R}{2 \pi I} \)
D. none


The first term of an AP is 148 and the
common difference is \( -2 . \) If the AM of
first \( n \) terms of the \( A P \) is \( 125, \) then the
value of \( n \) is
A . 18
B . 24
c. 30
D. 36
E . 48


What is pressure on swimmer \( 10 \mathrm{m} \)
below the surface of a lake?
Atmospheric pressure is


The element of an electric heater is
made of :
A. Tin
B. Copper
c. Nichrome
D. Tungsten


Larger the slope of a displacement-time
graph
A. lesser the velocity
B. higher the velocity
c. lesser the acceleration
D. higher the acceleration


Solve the following system of inequalities graphically \( 2 x+y \geq \)
\( 8, x+2 y \geq 10 \)


Which transition will occur when a
hydrogen atom is irradiated with
radiation of wavelength 103 nm?
\( A \)
B. \( I I \)
\( c . I V \)
\( D \)


In which vertebrate oxygenated and deoxygenated blood gets mixed?
A . Fish
B. Amphibian
c. Bird
D. Mammal


At \( 1000 K, K_{w} \) value can be:
\( \mathbf{A} \cdot 1 \times 10^{-6.98} \)
В . \( 1 \times 10^{-7} \)
c. \( 1 \times 10^{-71} \)
D. \( 1 \times 10^{-14} \)


A ball falls from a height of \( 5 m \) and strikes the roof of a lift. If at time of
collision, lift is moving in the upward
direction with a velocity of \( 1 \mathrm{ms}^{-1} \). Then the velocity with which the ball rebounds after collision will be :
A \( \cdot 13 \mathrm{ms}^{-1} \) upwards
B. \( 12 \mathrm{ms}^{-1} \) downwards
C. \( 12 \mathrm{ms}^{-1} \) upwards
D. \( 11 \mathrm{ms}^{-1} \) downwards


Briefly explain the following terms:
Sericulture


If the circumference of the base of a
cylinder is \( 44 c m \) and height \( 20 c m \), then its lateral surface area is
A. 440 sq.cm
B. 880 sq.cm
c. \( 88 s q . c m \)
D. 44 sq.cm


\( \sqrt[3]{-13824}=? \)
A . -24
B. -28
\( c .-26 \)
D. -34


Number of nodal planes in \( \pi^{*} 2 p_{x} \) are:
A . zero
B. one
c. two
D. three


In Young's double slit experiment, if monochromatic light used is replaced by white light then :
A. no fringes are observed
B. only central fringe is white, all other fringes are coloured
c. all bright fringes become white.
D. all bright fringes have colour between violet and red


Write the electronic configuration of \( \boldsymbol{K} \)
and \( N e ? \)


The Figure shows a parallel \( L-C-R \)
circuit connected to a variable
frequency 200V source. L \( =5 \mathrm{H}, \mathrm{C}=80 \mu \mathrm{F} \)
and \( R=40 \Omega \). What is the ems
current in the circuit at resonance?
\( A \cdot 5 A \)
B. 10 A
c. \( \frac{5}{\sqrt{2}} \)
D. \( 5 \sqrt{2} A \)


It is given that the image formed by an optical device is virtual, erect and diminished. Image is formed between
the focus and optical centre on the same side as that of the object. Object is placed between infinity and device. Identify the device used.
A. Concave lens
B. Convex lens
c. Plane mirror
D. Spherical mirror


A bulb is connected to a cell. How is the
resistance of circuit affected if another
identical bulb is connected in series?
A. Resistance is doubled
B. Resistance is same
c. Resistance is tripled
D. Resistance is one half


In nodal plane probability of finding an electron is:
A . zero
B. one
c. maximum
D. none of the these


\( A l O_{2}^{-} \) ion in aqueous solution exists as
\( \mathbf{A} \cdot\left[A l(O H)_{4}\right]^{-} \)
в. \( \left[A l(O H)_{4}\left(H_{2} O\right)\right]^{-} \)
c. \( \left[A l(O H)_{4}\left(H_{2} O\right)_{2}\right] \)
D \( \cdot\left[A l(O H)_{6}\right]^{-} \)


Pick up the saprophyte angiosperm.
A . Urticularia
B. Dionaea
c. Monotropa
D. Nepenthes


How many coins are to be tossed at
once to get 64 outcomes in total?


What is the voltage of the electricity that is generally supplied to a house?
\( \mathbf{A} \cdot 400 V \)
B. \( 200 \mathrm{V} \)
\( \mathbf{c} \cdot 220 V \)
D. \( 260 V \)


Three of the six vertices of regular hexagon are chosen at random. The
probability that the triangle with these vertices is equilateral, equals
A. \( 1 / 2 \)
в. \( 1 / 5 \)
c. \( 1 / 10 \)
D. \( 1 / 20 \)


With the help of a chart, explain the
method of sex determination in
honeybees.


Vant Hoff factor for a dilute solution
of glucose is:
A . 0
B.
c. 1.5
\( D \)


the following cumulative frequency
distribution:
\( \begin{array}{ll}\text { Marks } & \text { Number of students } \\ \text { o and above } & 80 \\ \text { 10 and above } & \text { 77 } \\ \text { 20 and above } & \text { 72 } \\ \text { 30 and above } & 65 \\ \text { 40 and above } & \text { 55 } \\ \text { 50 and above } & \text { 43 } \\ \text { 60 and above } & 28 \\ \text { 70 and above } & 16 \\ \text { 80 and above } & 10 \\ \text { 90 and above } & 8 \\ \text { 100 and above } & \text { 0 }\end{array} \)


If the nuclear radius of \( ^{27} A l \) is 3.6 Fermi,
the approximate nuclear radius of \( ^{64} \mathrm{Cu} \) in Fermi is
A . 4.8
в. 3.6
\( c .2 .4 \)
D. 1.


If a matrix has 13 elements, then the
possible dimensions (orders) of the matrix are
\( \mathbf{A} \cdot 1 \times 13 \) or \( 13 \times 1 \)
B. \( 1 \times 26 \) or \( 26 \times 1 \)
c. \( 2 \times 13 \) or \( 13 \times 2 \)
D. \( 13 \times 13 \)


Camphor is seperated from NaCl by the method:
A. Sublimation
B. Distillation
c. Sedimentation
D. Evaporation


Which of the following is a not plant disease caused by mycoplasma
A. Bunchy top of papaya
B. Aster yellow disease of sunflower
c. Little leaf disease of brinjal
D. Green ear disease of bajra


The magnitude of charge on an electron
in coulombs is :
A \( \cdot 1.76 \times 10^{11} \)
B. \( 1.6 \times 10^{-19} \)
c. \( 9.1 \times 10^{-3} \)
D. None of these


A teacher of a class wants to set one
question from each of two exercises in a
book. If there are 15 and 12 questions in the two exercises respectively, then in
how many ways can the two questions be selected?


The current in the primary circuit of a
potentiometer is \( 0.2 \mathrm{A} \). The specific resistance and cross section of the
potentiometer wire are \( 4 \times 10^{-7} \) ohm
metre and \( 8 \times 10^{-7} m^{2} \) respectively. The
potential gradient will be equal to:
A. \( 0.1 \mathrm{V} / \mathrm{m} \)
B. \( 0.2 \vee / \mathrm{m} \)
c. \( 1 \mathrm{v} / \mathrm{m} \)
D. \( 0.5 \vee / \) m


\( C_{6} H_{5} N_{2} C l^{C u_{2} C l_{2} / H C l} \) this reaction is
named as:
A. Sandmeyer
B. Swarts
c. wurtz-Fittig
D. Finkelstein


n an automobile factory, certain parts are to be fixed into the chassis in a
section before it moves into another
section. On a given day, one of the three persons \( A, B \) and \( C \) carries out this task. \( A \) has \( 45 \% \) chance, \( B \) has \( 35 \% \)
chance and \( C \) has \( 20 \% \) chance of doing
the task. The probability that \( A, B \) and
\( C \) will take more than the allotted time is \( \frac{1}{6}, \frac{1}{10} \) and \( \frac{1}{20} \) respectively. If it is found that the time taken is more than
the allotted time, what is the probability that \( A \) has done the task?


Evaluate the following determinant:
\[
\left|\begin{array}{ccc}
102 & 18 & 36 \\
1 & 3 & 4 \\
17 & 3 & 6
\end{array}\right|
\]


The bromination involves so called
bromonium ions.Among the given statements identify the one which does
not appply:
A. bromonium ions are 3-membered rings
B. bromonium ions are intermediates in the formation of halohydrins
c. bromonium ions are intermediate in the formation of vicinal dibromides by addition of bromides to alkenes
D. bromonium ions of asymmetrical alkenes are attacked by nucleophiles at the least subtituted alkene c-atom


It cost Rs 4020 to paint the inner curved surface area of hemisphere of radius
8 \( m \). If it is painted at rate of Rs.
10 per \( m^{2} \). Find inner curved surface.
A. \( 402 m^{2} \)
в. \( 400 \mathrm{m}^{2} \)
c. \( 200 m^{2} \)
D. \( 201 m^{2} \)


Which of the following statements is
not correct about sucrose?
A. It does not posses a free aldehydic (or) ketonic group
B. On hydrolysis, it produce invert sugar
C. It is a D-glucoside
D. It undergoes mutarotation


Select the correct order of polarizing
power of cation.
\( \mathbf{A} \cdot N a^{+}<M g^{2+}<S i^{4+}<A l^{3+} \)
B. \( M g^{2+}>S i^{4+}>A l^{3+}>N a^{+} \)
\( \mathbf{C} \cdot N a^{+}<M g^{2+}<A l^{3+}<S i^{4+} \)
\( \mathbf{D} \cdot A l^{3+}<S i^{4+}<M g^{2+}<N a^{+} \)


Which of the following is mostly used as a drinking water source by us?
A. Sea water
B. Glaciers
c. Ground water
D. None of these


Displacement x of a particle moving in one dimension is related to time \( t \) by the equation \( t=\sqrt{x}+2 . \) The displaclcement of the particle when its velocity is zero, is (Here \( x \) is in metre
and \( t \) is in second
\( A \cdot 4 \)
B. 2
\( c \)
\( D \)


An organic compound A containing
\( C, H \) and \( O \) has a pleasant odour with
boiling point of \( 78^{\circ} \mathrm{C} . \) On boiling A with
concentrated \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4}, \) a colourless gas
is produced which decolourises
bromine water and alkaline \( K M n O_{4} \)
The organic liquid \( A \) is:
A \( \cdot C_{2} H_{5} C l \)
в. \( C_{2} H_{5} \)СООСН\( _{3} \)
\( \mathbf{c} \cdot C_{2} H_{5} O H \)
D. \( C_{2} H_{6} \)


A block of mass \( 20 \mathrm{kg} \) is slowly slid up on a smooth incline of inclination53 \( ^{o} \) by
a person. Calculate the work done by the person in moving the block through a distance \( 4 \mathrm{m}, \) if the driving force is \( (\mathrm{a}) \) parallel to the incline and (b) in the
horizontal direction. \( \left[\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2}\right] \)


Which of the following is used for the fabrication of Integrated circuits?
A. Semiconductors
B. Metalss
c. Insulators
D. Alloys.


Find the area of a quadrilateral whose sides are \( A B=3 c m, B C=4 c m \)
\( C D=6 c m \) and \( D A=5 \mathrm{cm} \) and
diagonal \( \boldsymbol{A C}=\mathbf{5} \boldsymbol{c m} \)
\( \mathbf{A} \cdot 16 \mathrm{cm}^{2} \)
B. \( 18 \mathrm{cm}^{2} \)
\( c \cdot 20 c m^{2} \)
D. \( 22 \mathrm{cm}^{2} \)


A group of atoms can function as a ligand only when :
A. it is a small molecule
B. it has an unshared electron pair
c. it is a negatively charged ion
D. it is a positively charged ion


What is a long-sighted eye ? State one cause of long-sightedness. Name the lens used for correcting longsightedness.


Explain the structure of fructose.


For the \( 1^{s t} \) order reaction, \( A(g) \rightarrow \)
\( \mathbf{2} \boldsymbol{B}(\boldsymbol{g})+\boldsymbol{C}(\boldsymbol{s}), \boldsymbol{t}_{\mathbf{1} / \mathbf{2}}=\mathbf{2 4} \) min. The
reaction is carried out taking a certain mass of 'A' enclosed in a vessel
in which it exerts a pressure of \( 400 \mathrm{mm} \) Hg. The pressure of the reaction mixture after the expiry of 48 min will be:
\( A \cdot 700 \mathrm{mm} \)
B. 600 mm
c. \( 500 \mathrm{mm} \)
D. \( 1000 \mathrm{mm} \)


Lightning is also known as:
A. Mechanical energy
B. Electric discharge.
c. Potential current
D. Kinetic current


A particle hanging from a spring
stretches it by \( 1 \mathrm{cm} \) at earth's surface.
Radius of earth is \( 6400 k m . \) At a place
\( 800 k m \) above the earths surface, the same particle will stretch the spring by
A \( .0 .79 \mathrm{cm} \)
B. \( 1.2 \mathrm{cm} \)
\( c .4 c m \)
D. \( 17 \mathrm{cm} \)


Which of the following statement is
incorrrect:
A. Phenol gives positive bromine water test
B. Aniline gives foul smelling compound on reaction with \( C H C l_{3}+K O H \)
C. Formic acid gives positive Tollen's test
D. Nitrobenzene gives poitive Tollen's test


A thermodynamic property is that
physical quantity
A. which is used in thermochemistry.
B. which obeys all the laws of thermodynamics.
C. which is used to define a state of the system.
D. which is used in measuring thermal change.


If \( \overrightarrow{\boldsymbol{F}} \) is the force acting on a particle
having position vector \( \vec{r} \) and \( \vec{\tau} \) be the torque of this force about the origin, then :
A \( \cdot \vec{r} . \vec{\tau}=0 \) and \( \vec{F} \cdot \vec{\tau} \neq 0 \)
В . \( \vec{r} . \vec{\tau} \neq 0 \) and \( \vec{F} . \vec{\tau}=0 \)
c. \( \vec{r} . \vec{r}>0 \) and \( \vec{F} . \vec{\tau}<0 \)
D . \( \vec{r} . \vec{r}=0 \) and \( \vec{F} . \vec{\tau}=0 \)


Evaluate \( \int e^{x}\left(x^{2}+2 x\right) d x \)


The angle between the lines \( y-x+ \)
\( \mathbf{5}=\mathbf{0} \) and \( \sqrt{\mathbf{3}} \boldsymbol{x}-\boldsymbol{y}+\mathbf{7}=\mathbf{0} \) is/are
This question has multiple correct options
A \( \cdot 15^{\circ} \)
B. \( 60^{\circ} \)
\( \mathbf{c} \cdot 165^{\circ} \)
D. \( 75^{\circ} \)


The probability that, on the examination
day, the student \( S_{1} \) gets the previously
allotted seat \( R_{1} \) and NONE of the
remaining students gets the seat previously allotted to him/her is?
\( A \cdot \frac{3}{40} \)
B. \( \frac{1}{8} \)
c. \( \frac{7}{40} \)
D. \( \frac{1}{5} \)


On a squared paper, sketch the following: A triangle with a horizontal line of symmetry but no vertical line of
symmetry.


The primary of a transformer has 100 turns and operates at \( 100 \mathrm{V} \)
The number of turns in the secondary, if the output voltage is \( 2000 V \) is
A . 2000
в. 200
c. 100
D. 500


ff \( \boldsymbol{x}=\mathbf{3}+\mathbf{3}^{\mathbf{1} / \mathbf{3}}+\mathbf{3}^{\mathbf{2} / 3} \) then \( \boldsymbol{x}^{\mathbf{3}}-\mathbf{9} \boldsymbol{x}^{\mathbf{2}}+ \)
\( 18 x-12= \)
A . 2
B. 3
c. 0
D. 5


\( \frac{\frac{2}{2}}{\frac{1}{2}} \)


The structures \( A \) and \( B \) represent:
(A)
(B)
A. Enantiomers
B. Diastermers
c. Homomers
D. Racemic mixture


When a polythene piece is rubbed with wool, it acquires negative charge.
A. True
B. False


\( f(\Omega A=5 \mathrm{cm}, A B=8 \mathrm{cm} \text { and } O D \) is
perpendicular to \( A B, \) then \( C D \) is equal
to:
\( A \cdot 2 \mathrm{cm} \)
B. \( 3 \mathrm{cm} \)
\( c .4 \mathrm{cm} \)
\( 0.5 \mathrm{cm} \)


For a reaction taking place in a container in equilibrium with its surroundings, the effect of temperature
on its equilibrium constant \( \boldsymbol{K} \) in terms of change in entropy is described by This question has multiple correct options
A. With increase in temperature, the value of \( K \) for exothermic reaction decreases because the entropy change of the system is positive
B. With increase in temperature, the value of \( K \) for endothermic reaction increases because unfavourable change in entropy of the surroundings decreases
c. with increase in temperature, the value of \( K \) for endothermic reaction increases because the entropy change of the system is negative
D. With increase in temperature, the value of \( K \) for exothermic reaction decrease because favourable change in entropy of the surroundings decreases


A line \( L \) has intercepts \( a \) and \( b \) on the coordinate axes. When the axes are rotated
through an angle, keeping the origin fixed,
the same line \( L \) has intercepts \( p \) and \( q \)
Which of the following options is correct?
A \( \cdot a^{2}+b^{2}=p^{2}+q^{2} \)
B. \( \frac{1}{a^{2}}+\frac{1}{b^{2}}=\frac{1}{p^{2}}+\frac{1}{q^{2}} \)
C. \( a^{2}+p^{2}=b^{2}+q^{2} \)
D. \( \frac{1}{a^{2}}+\frac{1}{p^{2}}=\frac{1}{b^{2}}+\frac{1}{q^{2}} \)


Two supplementary angles are in the ratio \( 5: 7 . \) Find the smallest angle.
\[
\begin{array}{l}
1^{s t} \text { angle }=\frac{5}{12} \times 180^{\circ} \text { and } \\
2^{n d} \text { angles }=\frac{7}{12} \times 180^{\circ}
\end{array}
\]
\( \mathbf{A} \cdot 80 \)
B. 75
c. 65
D. 90


Match the columns and find the correct
answer
\( \begin{array}{lllll} & \text { Column I } & & \text { Column II } \\ \text { (a) } & \text { Streptomyces } & \text { (p) } & \begin{array}{l}\text { Food } \\ \text { poisoning }\end{array} \\ \text { (b) } & \text { Rhizobium } & \text { (q) } & \begin{array}{l}\text { Source of } \\ \text { antibiotic }\end{array} \\ \text { (c) } & \text { Nitrosomonas } & \text { (r) } & \begin{array}{l}\text { Nitrogen } \\ \text { fixation }\end{array} \\ \text { (d) } & \text { Acetobacter } & \text { (s) } & \text { Nitrification } \\ & \text { (t) } & \begin{array}{l}\text { Vinegar } \\ \text { synthesis }\end{array}\end{array} \)
\( \mathbf{A} \)
\( a-s, b-t, c-p, d-r \)
B. a-t, b-p, c-r, d-s
\( c \cdot a-q, b-r, c-p, d-t \)
D. \( a-q, b-r, c-s, d-t \)


If \( P_{n} \) denotes the product of all the coefficients in the expansion of
\( (1+x)^{n} \) and \( 9 ! P_{(n+1)}=10^{9} P_{n} . \) Then
\( \boldsymbol{n}= \)
A . 10
B. 9
c. 19
D. 11


圈


If \( \frac{a^{n}+b^{n}}{a^{n-1}+b^{n-1}} \) is the A.M. between \( a \) and
\( b, \) then find the value of \( n \)


Two small balls having equal positive charge \( Q \) (coulomb) on each are
suspended by two insulating strings of equal length \( L \), from a hook
fixed to a stand. If the whole set up is
taken in a satellite
then the angle \( \theta \) between the two strings is : (in equillibrium)
A \( \cdot O^{\circ} \)
В. \( 90^{\circ} \)
\( c \cdot 180^{\circ} \)


Assertion
Hydrolysis of ester is an example of
auto-catalytic reaction.
Reason
A catalyst speeds up the process
without participating in the
mechanism.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


What is the apparent oxidation state of
\( \boldsymbol{K} \) element in the compound \( \boldsymbol{K} \boldsymbol{H} \boldsymbol{C} \boldsymbol{O}_{3} ? \)
A \( .+1 \)
B. +2
\( c \cdot+3 \)
D. +4
\( \mathrm{E} \cdot+5 \)


The de Broglie wavelength of an electron
moving with a velocity of \( 1.5 \times \) \( 10^{8} m s^{-1} \) is equal to that of a photon.
Find the ratio of the kinetic energy of
the photon to that of the electron.


A helicopter is to reach a point \( 200000 m \) east of his existing place. Its velocity relative to wind blowing at \( 30 k m h^{-1} \) from northwest taking
scheduled arrival time duration as
40minute is
B. \( 279 \hat{i}+21 \hat{j} \)
c. \( 729 \hat{i}+12 \hat{j} \)
D. \( 12 \hat{i}+729 \hat{j} \)


Assertion
Specific heat of a body is always greater than its thermal capacity.
Reason
Thermal capacity is the heat required for raising temperature of unit mass of the body through unit degree.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct, but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both assertion and reason are incorrect


A \( 200 F \) capacitor is initially charged to \( 20 V \) and then shorted across a \( 5 m H \)
inductor. The angular frequency of oscillation is
A. 1000 rad\( / \)s
B. 100 rad\( / \)s
c. 10000 rad\( / \)s
D. \( 1 r a d / s \)


Calculate the e.m.f of the following cell reaction at \( 298 K: \)
\( \boldsymbol{M} \boldsymbol{g}_{(s)}+\boldsymbol{C u}^{2+}(\mathbf{0 . 0 0 0 1 M}) \rightarrow \)
\( M g^{2+}(0.001 M)+C u_{(s)} \)
The standard potential \( \left(\boldsymbol{E}^{o}\right) \) of teh cell
is \( 2.71 V \)


A conductor is moved in a varying magnetic field. Name the law which determines the direction of current
induced in the conductor:
A. Fleming's right hand rule
B. Mohr's right hand rule
c. Fleming's left hand rule
D. Mohr's left hand rule


In L-C-R circuit power of 3 mH
inductance and \( 4 \Omega \) resistance, EMF
\( \boldsymbol{E}=\mathbf{4} \cos \mathbf{1 0 0 0} \boldsymbol{t} \) volt is applied. The
amplitude of current is
A \( .0 .8 \AA \)
в. \( \frac{4}{7} \)
c. \( 1.0 \dot{A} \)
D. \( \frac{4}{\sqrt{7}} \dot{A} \)


The EMF (in Volts) for the following electrodes are
\( \boldsymbol{P t}, \boldsymbol{H}_{2} \mid \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4}(\boldsymbol{p} \boldsymbol{H}=\mathbf{2 . 0}) \)


Which of the following statements is
not true?
A. The ratio of the mean speed to the \( R M S \) speed is independent of the temperature
B. The square of the mean speed of the molecules is equal to the mean squared speed at certain temperature
C. Mean kinetic energy of the gas molecules at any given temperature is independent of the mean speed
D. The difference between rms speed and mean speed at any temperature for different gases diminishes as larger and larger molar masses are considered


What is the effect of release of \( C O_{2} \) gas
on atmosphere?
A . Global warming
B. Photochemical smog
c. Ozone layer depletion
D. Tsunami


Assertion
(A) : Noble gases have very low boiling
points.
Reason
(R) : All noble gases have general
electronic configuration of \( \boldsymbol{n} \boldsymbol{s}^{2} \boldsymbol{n} \boldsymbol{p}^{6} \)
\( (\operatorname{except} H e) \)
A. Both (A) and (R) are true but (R) is correct explanation of (A)
B. (A) is false but (R) is true
c. (A) is true but (R) is false
D. Both (A) and (R) are true but (R) is not the correct explanation of (A)


A particle experiences constant acceleration for 20 s after starting from
rest. If it travels a distance of \( X_{1} \) in the
first 10 s and a distance of \( X_{2} \), in the
remaining 10 s, then which of the following is true?
A. \( X_{1}=2 X_{2} \)
В. \( X_{1}=X_{2} \)
\( \mathbf{c} \cdot X_{1}=3 X_{2} \)
D. \( 3 X_{1}=X_{2} \)


In the figure, \( m \angle P O Q=30^{\circ} \) and radius
OP \( =12 \mathrm{cm} . \) Find the given area of sector O-PRQ (Given \( \pi=3.14) \)
A. \( 37.68 \mathrm{cm}^{2} \)
\( \mathbf{B} \cdot 57.68 \mathrm{cm}^{2} \)
\( \mathbf{c} \cdot 47.68 \mathrm{cm}^{2} \)
D. none of these


Two wave are represented by equation
\( \boldsymbol{y}_{1}=\boldsymbol{a} \sin \omega t \) and \( \boldsymbol{y}_{2}=\boldsymbol{a} \cos \omega \boldsymbol{t} . \) Then
the first wave:
A. leads the second by \( \pi \)
B. lags the second by \( \pi \)
c. leads the second by \( \frac{\pi}{2} \)
D. lags the second by \( \frac{\pi}{2} \)


Which of the following pentahalides does not exist?
A. PF \( _{5} \)
B. \( \mathrm{PCl}_{5} \)
c. \( \mathrm{PBr}_{5} \)
D. PI


Let \( f \) be a polynomial function such
that \( \boldsymbol{f}(\mathbf{3} \boldsymbol{x})=\boldsymbol{f}^{\prime}(\boldsymbol{x}) \cdot \boldsymbol{f}^{\prime \prime}(\boldsymbol{x}), \) for all \( \boldsymbol{x} \in \)
\( \boldsymbol{R} \). Then:
A \( \cdot f(2)+f^{\prime}(2)=28 \)
B . \( f^{\prime \prime}(2)-f^{\prime}(2)=0 \)
\( \mathbf{c} \cdot f^{\prime \prime}(2)-f(2)=4 \)
D \( \cdot f(2)-f^{\prime}(2)+f^{\prime \prime}(2)=10 \)


A liquid takes 5 min. to cool from \( 80^{\circ} \mathrm{C} \)
to \( 50^{\circ} \mathrm{C} \). How much time does it take to
cool from \( 60^{\circ} \mathrm{C} \) to \( 30^{\circ} \mathrm{C} \) ? Temperature of
surroundings is \( 20^{\circ} \mathrm{C} \)
A. 2 mins
B. 3 mins
c. 5.5 mins
D. None of these


Select the correct statement:
A. Nitric Oxide is isoelectronic with \( C O_{2} \)
B. Nitric Oxide is diamagnetic
C. Nitric Oxide is an endothermic compound
D. Nitric Oxide gas is used to induce general anesthesia


Number of moles of \( S_{2} O_{3}^{2-} \) present in
the sample is:
A . 0.0005
B. 0.01
c. 0.0025
D. 0.02


\( \int_{0}^{1} \tanh x d x= \)
\( A \cdot \log (e+1 / e) \)
B. \( \log (e-1 / e) \)
\( \mathbf{c} \cdot \log (\mathrm{e} / 2+1 / 2 \mathrm{e}) \)
D. \( \log \left(\frac{e}{2}-\frac{1}{e}\right) \)


In a compound microscope the intermediate image is :
A. real, inverted \& magnified
B. real, erect \& magnifiedd
c. virtual, erect \& magnified
D. virtual, erect \& reduced


If \( \cot A \cdot \cot B=2, \) then what is the value
of \( \cos (A+B) \cdot \sec (A-B) ? \)
\( A \cdot 1 / 3 \)
B. 2/3
\( c \)
\( D \)


A proton moves in the positive \( z- \)
direction after being accelerated from
rest through a potential difference \( V \)
The proton then passes through a region with a uniform electric field \( E \) in
the positive x-direction and a uniform
magnetic field \( B \) in the positive \( y- \) direction, but the proton's trajectory is not affected. If the experiment were
repeated using a potential difference of
\( 2 V, \) the proton would then be
A. deflected in positive \( x \) -direction
B. deflected in negative \( x \) -direction
c. deflected in positive \( y \) -direction
D. deflected in negative \( y \) -direction


Predict which of the following compounds will have a lower boiling point than 1-butanal
A. 1-butanol
B. 2-butanol
c. butanoic acid
D. 1-butene


Assertion
A vector cannot be divided by other
Vector.
Reason
A vector can be dived by a scalar.
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 of the following base is used for cleaning and commonly known as lye?
\( \mathbf{A} \cdot C a(O H)_{2} \)
в. \( N a O H \)
c. КОН
D. All of the above


The value of \( \sum_{n=0}^{100} i^{n !} \) equals \( (\text { where } i= \) \( \sqrt{-1}) \)
A . -1
B.
\( c \cdot 2 i+95 \)
D. \( 96+i \)


The equilibrium constant for the reaction:
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{I}_{2}(\boldsymbol{g}) \Leftrightarrow 2 \boldsymbol{H} \boldsymbol{I}(\boldsymbol{g}) \) is \( 64, \) at
certain temperature.The equilibrium
concentrations of \( H_{2} \) and \( H I \) are 2 and
16 mollit\( ^{-1} \) respectively. The
equilibrium concentration (in molLit \( ^{-1} \)
of \( I_{2} \) is ?
A . 16
B. 4
\( c \cdot 8 \)
D. 2


In Young's double slit experiment, distance between two slits is \( 0.28 \mathrm{mm} \)
and distance between slits and screen
is \( 1.4 \mathrm{m} \). Distance between central bright hinge and third bright fringe is \( 0.9 \mathrm{cm}, \) what is the wavelength of light used?
A \( .4000 A^{\circ} \)
в. \( 6000 A^{\circ} \)
c. \( 3000 A^{\circ} \)
D. \( 5000 A^{\circ} \)


Find the area of the shaded region in
figure ,if \( \mathrm{PQ}=24 \mathrm{cm}, \mathrm{PR}=7 \mathrm{cm} \) and \( \mathrm{O} \) is
the centre of the circle.
A \( \cdot 100.98 \mathrm{cm}^{2} \)
B \( \cdot 161.54 \mathrm{cm}^{2} \)
c. \( 101.54 \mathrm{cm}^{2} \)
D. None of these


Period between initiation of two
successive leaves or nodes is
A. Plastochron
B. Diurnal cyclicity
c. Internode
D. Allelopathy


An element \( A \) combines with oxygen to
form an oxide \( A O . \) This oxide is
electrically conducting. Find
(A) the number of valence electrons in \( A \)
(B) the group to which the element \( \boldsymbol{A} \)
belongs
(C) the formula of the compound when
\( A \) reacts with chlorine


The modal class is
A \( .60-65 \)
В. \( 55-60 \)
\( c .50-55 \)
D. none of these


Name the compound of chlorine 1 which is an anesthetic 2 . which is used
as a refrigerant 3. which is a disinfectant 4. which is used to make
pipes and tubes
5. which liberates
chlorine on exposure to air.


Mean free path in kinetic theory can be
written as: ( every symbol has standard
meaning
A \( \cdot l=\frac{\mu}{2 p} \sqrt{\frac{\pi K_{B} T}{m}} \)
B. \( l=\frac{\mu}{2 p} \sqrt{\frac{3 \pi K_{B} T}{2 m}} \)
\( \mathbf{c} \cdot l=\frac{\mu}{p} \sqrt{\frac{\pi K_{B} T}{2 m}} \)
D \( \cdot l=\frac{3 \mu}{2 p} \sqrt{\frac{\pi K_{B} T}{2 m}} \)


It was found that electrons have
negligible mass but have one unit of negative charge. Which of the following
model satisfies this statement??
A. Thomson's atomic model
B. Goldstein's atomic model
c. chadwick's atomic model
D. None of the above


The value of Faraday number in Sl unit
is:
A. 9.65 coulomb \( / \mathrm{kg} \) - equivalent
B . \( 9.65 \times 10^{7} \) coulomb \( / \mathrm{kg} \) - equivalent
c. \( 9.65 \times 10^{-7} \) coulomb / \( k g \) - equivalent
D. 9.65 coulomb \( / g \) - equivalent


In fig, sides \( Q P \) and \( R Q \) of triangle
\( P Q R \) are produced to point \( S \) and \( T \)
respectively. If angle \( S P R=135^{\circ} \) and
angle \( P Q T=110^{\circ}, \) find \( \angle P R Q \)


Every body continues to be in its state of rest or of non-uniform motion in a straight line unless compelled by some external force to act otherwise. This is
stated by:
A. Newton's 1st law
B. Newton's 2nd law
c. Newton's 3rd law
D. None of the above


Compartments \( A \) and \( B \) have the
following combinations solution.
Indicate the number of solutions which
is/are isotonic.
A. I only
B. III only
c. IV only
D. II only


In the arrangement shown below a block
of mass \( 2700 \mathrm{kg} \) is in equilibrium on
applying a force F. The value of force F is \( d_{l i q u i d}=0.75 g c m^{-3} \) is
A . \( 147 N \)
B . \( 300 N \)
c. \( 153 N \)
D. \( 1755 N \)


The product of \( r \) consecutive integers is divisible by This question has multiple correct options
A.
\( ^{\text {В }} \sum_{k=1}^{r-1} k \)
\( c \cdot r \)
D. none of these


The Taj Mahal has become a matter of
concern:
A. because it is located in Agra city
B. because of its bustling manufacturing centre in the populous city
c. because pollutants in air are discolouring its white marble
D. none of these


Different words being formed by
arranging the letters of the word "INTERMEDIATE".All the words obtained
are written in the form of a dictionary, If vowels \( \& \) consonants occupy their original places, then the number of permutations is
A \( \cdot \frac{6 !}{2 !} \times \frac{6 !}{2 !} \)
в. \( \frac{6 !}{3 !} \times \frac{6 !}{2 !} \)
c. \( \frac{6 ! \times 6 !}{3 ! 2 ! 2 !} \)
D. None of these


The electric field in a region is radially
outward with magnitude \( \boldsymbol{E}=\boldsymbol{\alpha} \boldsymbol{r} \)
Calculate the charge contained in a sphere of radius \( R \) centered at the
origin. Calculate the value of the charge
if \( \alpha=100 V m^{-2} \) and \( R=0.30 \mathrm{m} \)
A \( \cdot 3 \times 10^{-7} C \)
В. \( 12 \times 10^{-10} \mathrm{C} \)
c. \( 3 \times 10^{-10} C \)
D. \( 7 \times 10^{-10} C \)


Which of the following are incorrectly
matched?
\begin{tabular}{|c|l|c|c|}
\hline & \multicolumn{1}{|c|} { Material } & Natural Source & \multirow{2}{*} { Artificial Source } \\
\cline { 3 - 5 } & & & \\
\hline (i) & Themoplastic & \( \sqrt{ } \) & \( \times \) \\
(ii) & Jute & \( \curlyvee \) & \( \times \) \\
(iii) & Cellulose & \( \times \) & \( \vee \) \\
(iv) & Polythene & \( \sqrt{ } \) & \( \times \) \\
\hline
\end{tabular}
A . (i) and (ii)
B. (i), (ii) and (iii)
\( \mathbf{C} \cdot(\mathbf{i}),(\text { iii }) \) and (iv)
D. All of these


Which element has a dicey position in the modern periodic table?
A. Hydrogen
B. Helium
c. Argon
D. Neon


Journey in a train is adventurous
particularly when you have a seat. The girl sitting near window ate a banana and dropped the peel from the window. Her co-passenger looking through the window found that it dropped vertically
down and touched the ground in \( 0.2 s \)
After sometime she requested her sister sitting on the upper berth to drop a chocolate bar.The sister dropped the bar, but it fell in front of the girl instead of reaching her hand. She was angry but the co-passenger calmed her by saying that she dropped exactly in line of your hand but as the train is accelerating it did not reach you and fell in front of you. If a projectile has velocity greater than escape velocity which trajectory it
will follow
A. elliptic
B. hyperbola
c. vertical straight
D. parabolic


\( \int_{0}^{\infty} e^{-a x} d x(a>0)= \)
\( A \cdot a \)
B. 0
\( c \cdot \frac{1}{a} \)
D. \( \frac{-1}{a} \)


\( H_{2} O_{2} \) is considered as dibasic acid, as
it can form:
A. peroxide and super oxides
B. hydroperoxides and peroxides
c. peroxides and dioxides
D. dioxides only


Find the nucleotide sequence of the
MRNA which codes for the sequence of amino acids - 'Met - Leu - Val - Arg - Ala' and choose the correct option from
below:
A. AUG - GAU - GAA - UAU - UGU
B. AUG - GAU - GAA - CGU - GCC
c. AUG - CUA - GUG - UAU - UGU
D. AUG - CUA - GUG - CGU - GCC


What is the monomer unit for teflon?
\( \mathbf{A} \)
B.
\( c \)
D.


Match List-I with List-II.
List - 1
a) Red lead
p) Lead monoxide
b) Litharge
q) An ore of lead
c) Galena
r) An ore of tin
d) Cassiterite
s) Minium
A \( \cdot a-r ; b-s ; c-p ; d-q \)
B. \( a-r ; b-q ; c-r ; d-p, q \)
c. \( a-s ; b-p ; c-q ; d-r \)
D. a-r; b-s; c-q; ;d-p


Number of words which begins with a vowel and ends with a consonant by permuting the letters of the word
HARSHITA"
A . 2340
в. 2700
\( c .1800 \)
D. 1980


The sex hormone, which controls the
development and maintenance of
pregnancy, is:
A . cortisone
B. thyroxine
c. progesterone
D. estrone


Describe with chemical equation the Laboratory method for the preparation of ammonia.Write its reaction with the
following:
(i) Oxygen in presence of platinum at
\( 800^{\circ} \mathrm{C} \)
(ii) Red hot copper oxide.


"Law of priority" says that the valid name of an organism is
A. Most popular name
B. Name given in Latin
c. oldest used name
D. oldest name modified by new workers


Name of the process.
\( A \cdot \) Solvay
B. Ammonia-soda
C. Both (A) \& (B) correct
D. None of the above


The theory of demographic transition deals with transition from
A. low to high death rates and birth rates
B. high to low birth rates and death rates
c. high to low birth rates only
D. low to high death rates only


A thin bar of mass \( M \) and length \( L \) is
free to rotate about a fixed horizontal
axis through a point at its end. The bar
is brought to a horizontal position and then released. The axis is perpendicular
to the rod. The angular velocity when it
reaches the lowest point is This question has multiple correct options
A. directly proportional to its length and inversely proportional to its mass
B. independent of mass and inversely proportional to the square root of its length
C. dependent only upon the acceleration due to gravity and the length of the bar
D. directly proportional to its length and inversely proportional to the acceleration due to gravity


When a body is in SHM, match the
statements in Column A with that in
Column B
Column A
Column B
a) Velocity is maximum
e) At half of the amplitude
b) Kinetic energy is At the mean position \( 3 / 4 \) th of total energy
c) Potential energy is
g) At extreme position \( 3 / 4 \) th of total energy
d) Acceleration is
h) \( \mathrm{At} \sqrt{3} / 2 \) times amplitude maximum
A. a-f, b-e, c-h, d-g
B. a-e, b-f, c-g, d-h
c. a-g, b-h, c-e, d-f
D. a-h, b-e, c-f, d-e


To develop proton gradient in respiration the required energy come from the oxidation of
A. NADH
B. NADH and \( H_{2} O \)
\( c \cdot O_{2} \) and \( \mathrm{NADH} \)
D. \( O_{2} \)


If \( f(x)=x^{2}-3 x+4 \), then find the
value of \( x \) satisfying \( f(x)=f(2 x+1) \)


Assertion
Work done by the electrostatic field on a charge moving around a closed circular
or elliptical path will be zero.
Reason
Electrostatic field is a conservative
field.
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


Read the following graph and answer
the question given below

What is the ratio of the highest marks to the lowest marks obtained by the
student ?
\( \mathbf{A} \cdot 2: 11 \)
B. 9: 2
\( c \cdot 2: 9 \)
D. 11: 2


The energy gap in glass at room temperature is:
A. greater than that in a semiconductor
B. less than that in a good conductor
C . greater than that in a good conductor
D. both (A) and (C) are true


Consider the dehydrohalogenation of 2 bromo-2-methylhexane with methoxide and tert-butoxide.Which of the following statements is true?
A. Methoxide gives more and t-butoxide gives less Hofmann product
B. Methoxide gives more and t-butoxide gives less Saytzeff product
c. Saytzeff product is the major product in both cases
D. Hofmann product is major in both cases


Acetabulum is associated with
A. Pelvic girdle
B. Pectoral girdle
c. olfactory lobe
D. Rib cage


The process by which heat is transferred without the help of any
material medium is called


Hydrogen chloride was first detained in
pure form by :
A. Newton
B. Pascal
c. Priestley
D. Blackmann


First time heart structure is evolved in
phylum.


A \( 20 k g \) load is suspended by a wire of
\( \operatorname{cross} \operatorname{section} 0.4 m m^{2} . \) The stress
produced in \( \mathrm{N} / \mathrm{m}^{2} \) is :
\( A \cdot 4.9 \times 10^{-6} \)
B. \( 4.9 \times 10^{8} \)
\( c \cdot 49 \times 10^{8} \)
D. 2.45 \times 10 \( ^{-6} \)


Minimum and maximum \( z=5 x+2 y \)
subject to the following constraints:
\( x-2 y \leq 2 \)
\( 3 x+2 y \leq 12 \)
\( -3 x+2 y \leq 3 \)
\( \boldsymbol{x} \geq \mathbf{0}, \boldsymbol{y} \geq \mathbf{0} \)


\( \lim _{x \rightarrow a} \frac{x^{2}-a^{2}}{x-a} \)


\( M n O_{4}^{2-}(1 \text { mole }) \) in neutral aqueous medium disproportionate to
A \( \cdot 2 / 3 \) mole \( M n O_{4}^{-} \) and \( 1 / 3 \) mole \( M n O_{2} \)
B . 1/3 mole \( M n O_{4}^{-} \) and \( 2 / 3 \) mole \( M n O_{2} \)
\( \mathrm{c} \cdot 1 / 3 \) mole of \( M n_{2} O_{7} \) and \( 1 / 3 \) mole of \( M n O_{2} \)
D. \( 2 / 3 \) mole of \( M n_{2} O_{7} \) and \( 1 / 3 \) mole of \( M n O_{2} \)


A wire bent as shown in Figure carries a current \( I \). Find the magnetic field at \( P: \)
A \( \frac{\mu_{0}}{4} \)
в. \( \frac{3 \mu_{0}}{2 R} \)
c. \( \frac{7 \mu_{0} I}{8 R} \)
D. \( \frac{\mu_{0}}{8_{D}} \)


Given \( \overline{\boldsymbol{a}}+\overline{\boldsymbol{b}}+\overrightarrow{\boldsymbol{c}}+\overline{\boldsymbol{d}}=\mathbf{0}, \) which of the
following statements is/are not a
correct statement?
A \( \cdot \vec{a}, \vec{b}, \vec{c} \) and \( \vec{d} \) must be a null vector.
B. The magnitude of ( \( \vec{a}+\vec{c} \) ) equals the magnitude of \( a(\vec{b}+\vec{d}) \)
C. The magnitude of \( \vec{a} \) can never be greater than the summ of the magnitudes of \( \vec{b}, \vec{c} \) and \( \vec{d} \)
D. \( b+\vec{c} \) must He in the plane of \( \vec{a} \) and \( \vec{d} \) if \( \vec{a} \) and \( \vec{d} \) are not collinear and in the line of \( \vec{a} \) and \( \bar{d} \), if they are collinear.


The no-of order of rotational symmetry
of B, E, D?.


Heavy water is used in atomic reactor
as:
A. coolant
B. moderator
c. both coolant and moderator
D. neither coolant nor moderator


What are the products of the above
reaction?
\( \mathbf{A} \cdot\left(C H_{3}\right)_{2} C H-N H\left(C H_{3}\right) \) and \( C O \)
B. \( \left(C H_{3}\right)_{2} C H-N\left(C H_{3}\right)_{2} \) and \( C O \)
\( \mathbf{c} \cdot\left(C H_{3}\right)_{2} C H-N H\left(C H_{3}\right) \) and \( C O_{2} \)
\( \mathrm{D} \cdot\left(C H_{3}\right)_{2} C H-N\left(C H_{3}\right)_{2} \) and \( C O_{2} \)


What is the function of P-protein?
A. To carry out photosynthesis in leaves
B. To carry out transport of organic solutes through phloem
c. Passive protein present in phaseolus seeds
D. The protein of pollen grains


A solid sphere, a solid cylinder, a hollow sphere and a hollow cylinder (all of the same mass ) simultaneously start rolling down from top of an inclined plane, then the time to reach bottom of inclined plane is :
A. minimum for solid cylinder, maximum for hollow sphere
B. minimum for hollow sphere, maximum for solid cylinder
c. minimum for solid sphere, maximum for hollow cylinder
D. minimum for hollow cylinder, maximum for solid sphere


How would you demonstrate that a
momentary current can be obtained by the suitable use of a magnet, a coil of
wire and galvanometer?


\( 20 a^{2}-45= \)
\( \mathbf{A} \cdot 5(3-2 a)(3+2 a) \)
B. \( 5(2 a-3)(2 a-3) \)
\( \mathbf{c} \cdot 3(5+2 a)(5-2 a) \)
D. \( 3(2 a+5)(2 a-5) \)


The oxidation number of the nitrogen atom in the ammonium ion is :
\( A \cdot+3 \)
\( B .+2 \)
\( c \cdot+1 \)
\( D \cdot-2 \)
E. - -


A plot of displacement of a particle with
time is as shown in the figure. The
equation of SHM is
A \( . x= \) Asinwt
B. \( x= \) Acoswt
c. \( x=- \) Acoswt
D. \( x=- \) Asinwt


Two balls shown in figure are identical Ball \( A \) is moving towards right with a
speed \( v \) and the second ball is at rest. Assume all collisions to be elastic.

Show that the speed of the balls remain unchanged after all the collisions have takes place (Assume frictionless surface)


A path \( 1 \mathrm{m} \) wide is built along the border and inside a square garden of side \( 30 \mathrm{m} \) Find :
i) The area of the path


Describe the role played by protein pumps during active transport in plants.


IUPAC name of the compound:
\( \boldsymbol{C}_{2} \boldsymbol{H}_{5}-\boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right)-\boldsymbol{C H}_{2}- \)
\( \boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right)_{2} \)
A. 2,4 dimethylhexane.
B. 1, 3 dimethylhexane.
c. 2,2 dimethylhexane
D. 3, 5 dimethylhexane


Specialised cells in the stomach
release \( H C l \) to aid digestion. If they
release too much \( H C l \), the excess can
be neutralized by antacid tablets.
Which of the following should be more effective ingredient of antacid tablets?
\( \mathbf{A} \cdot M g(O H)_{2} \)
в. \( A l(O H) \)
\( \mathbf{c} \cdot \operatorname{Ca}(O H)_{2} \)
D. \( H_{2} S O_{4} \)


Assertion
Every collision of reactant molecule is
not successful.
Reason
Every collision of reactant molecule
with proper orientation is successful
one.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Which of the following orbitals is closer to nucleus?
\( A \cdot 5 f \)
B. 6d
\( c \cdot 7 s \)
D. \( 7 p \)


\( A B C \) is an isosceles triangle in which \( A B \)
\( =A C A \) circle through \( B \) touches side \( A C \)
at its mid point \( \mathrm{D} \) and intersects \( \mathrm{AB} \) at
\( P, \) then \( A P \) will be-
\( A \cdot 2 A D \)
B \( \cdot \frac{1}{2} A B \)
c. \( \frac{1}{4} A B \)
D. \( \frac{1}{2} A C \)


The velocity-time graph of a particle
moving along X-axis is shown in figure. Match the entries of Column I with
entries of Column II.


If a converging beam of light is incident on a concave mirror, the reflected light:
This question has multiple correct options
A. may form a real image
B. must form a real image
c. may be a parallel beam
D. may form a virtual image


Calculate the electronegativity of chlorine from bond energy of \( \boldsymbol{C l}-\boldsymbol{F} \)
bond \( \left(61 k c a l m o l^{-1}\right) F- \)
\( F\left(38 k c a l m o l^{-1}\right) \) and \( C l-C l \) bond
\( \left(58 k c a l m o l^{-1}\right) \) and electronegativity
of fluorine \( 4.0 e V \)
A. 1.42 eV
в. 1.89 eV
c. 2.67 eV
D. 3.22 eV


Why are xylem and phloem called as complex tissues?


Work out the following divisions:
\( (10 x-25) \div(2 x-5) \)


The process of photoelectric emission depends on
A. Temperature of incident light
B. Nature of surface
c. speed of emitted photo electrons
D. Speed of the incident light


Assertion: A series combination of cells
is used when their internal resistance
is much smaller than the external
resistance
Reason: It follows from the relation \( \boldsymbol{I}= \) \( \frac{n E}{R+n r}, \) where the symbols have their standard meaning.
A. Both (A) and (R) are true and (R) is the correct explanation of A
B. Both (A) and (R) are true but (R) is not the correct explanation of A
c. (A) is true but (R) is false
D. (A) is false but (R) is true


How many ATP molecules produced by anaerobic oxidation of one molecule of
glucose?
\( A \cdot 2 \)
B. 4
\( c \cdot 38 \)
D. 34


\( \int_{0}^{2} x \sqrt{x+2}\left(\text { Put } x+2=t^{2}\right) \)


metal generally occurs in free
state.
A. Sodium
B. Platinum
c. Magnesium
D. Potassium


The graph of an Identity function is?
A. A straight line parallel to X axis
B. A straight line parallel to Y axis
c. A straight line passing through the origin
D. None


Which of the following steps should be
followed to convert a given word problem into a Quadratic Equation?
A. Represent the unknown quantity/ies with variables \( (x \) y etc.
B. Express the information of the problem mathematically in the form of an equation.
c. check if the equation formed is in one variable and the degree of the equation is 2
D. All of the above


A long straight wire is carrying current
in \( +z \) direction. The \( x \) -y pkane contains a closed circular loop carrying current
\( I_{2} \) and not encircling the straight wire. The force on the loop will be.
B . \( \mu_{0} I_{1} I_{2} / 4 \pi \)
c. zero
D. Depends on the distance of the circle of the loop from the wire


Check whether the following are perfect cubes?
(i) 400
(ii) 216
(iii) 729
(iv) 250
(v) 1000
(vi) 900


Why is there a gradual increase in the
ionisation energy from \( L i \) to \( N e ? \)
A. Increase in atomic size
B. Decrease in nuclear charge
c. Atomic size remains same
D. Increase in nuclear charge


The sum n terms of two A Ps are in ratio \( \frac{7 n+1}{4 n+27} \) Find the ratio of their 11 th terms
A \( \cdot \frac{148}{111} \)
в. \( \frac{213}{311} \)
c. \( \frac{221}{343} \)
D. \( \frac{114}{157} \)


Find the acute angle between the two lines:
\( A B \) and \( C D \) passing through the points \( \boldsymbol{A} \equiv(\mathbf{3}, \mathbf{1},-\mathbf{2}), \boldsymbol{B} \equiv(\mathbf{4}, \mathbf{0},-\mathbf{4}) \) and \( \boldsymbol{C} \equiv \)
\( (4,-3,3), D \equiv(6,-2,2) \)


The rate of change of concentration of any one of the reactants or products at a particular moment of time is known
as the ?
A. Average rate
B. Instantaneous rate
c. Rate of disintegration
D. None of these


The magnetic field perpendicular to the plane of a conducting ring of radius \( r \) changes at the rate \( \frac{d B}{d t} \) This question has multiple correct options
A \( \cdot \) The emf induced in the ring is \( \pi r^{2} \frac{d B}{d t} \)
B. The emf induced in the ring is \( 2 \pi r \frac{d B}{d t} \)
C. The potential difference between diametrically opposite points on the ring is half of the induced emf.
D. All points on the ring are at the same potential.


Hydrolysis of one mole of peroxodisulphuric produces:
A. two moles of sulphuric acid.
B. two moles of peroxomonosulphuric acid
c. one mole of sulphuric acid and one mole of peroxomonosulphuric acid.
D. one mole each of sulphuric acid peroxomonosulphuric acid and hydrogen peroxide.


Assume you are sitting in sun for 2.5 hours. The area of your body exposed normally to sun rays \( 1.3 m^{2} . \) The
intensity of sun rays is 1.1 Kilowatt \( / m^{2} \)
If your body completely absorbs the sun rays then the momentum transferred to your body will be (in \( \mathrm{Kg}-\mathrm{m} / \mathrm{s} \) ):
\( \mathbf{A} \cdot 0.043 \)
B. 0.037
c. 0.61
D. -0.91


What is the sum of all prime numbers between 100 and \( 120 ? \)
\( \mathbf{A} \cdot 652 \)
в. 650
\( c \cdot 644 \)
D. 533


The change in magnetic field lines in a coil is the cause of induced electric
current in it. Name the underlying phenomenon.


Q Type your question
4
\( B \)
\( c \)
\( D \)


A particle executing simple harmonic motion along y-axis has its motion described by the equation \( y= \) \( \boldsymbol{A} \sin (\boldsymbol{\omega} \boldsymbol{t})+\boldsymbol{B} . \) The amplitude of the
simple harmonic motion is:
\( A \cdot A \)
в. \( B \)
c. \( A+B \)
D. \( \sqrt{A+B} \)


The consumption of electrical energy in the house is measured in terms of:
A. Kilowatt hour
B. Watt hour
c. Joules
D. Kilo joules


Write the approximate wavelengths for red light.
A \( \cdot 1000 A^{\circ} \)
\( ^{\circ} \)
B. 2000A"
c. \( 4000 A^{\circ} \)
D. \( 8000 A^{\circ} \)


\( \cos ^{-1}\left(\cos \left(\frac{7 \pi}{5}\right)\right) \) is equal to
\( A \cdot \frac{3 \pi}{5} \)
B. \( \frac{2 \pi}{5} \)
\( c \cdot \frac{-7 \pi}{5} \)
D. \( \frac{7 \pi}{5} \)
E \( \cdot \frac{-2 \pi}{5} \)


What is root pressure?


Find the minimum distance of any point on the curve \( x^{2}+y^{2}+2 x y=8 \) from
the origin.


Which of the following types of hydrogen requires maximum energy for its formation?
A. Nascent hydrogen
B. Atomic hydrogen
c. ortho hydrogen
D. Parahydrogen


\( Z n C O_{3} \) is thermally more stable than
\( M g C O_{3}, \) because
A \( \cdot M g(O H)_{2} \) exhibits only properties while \( Z n(O H)_{2} \) is amphoteric
B. polarising action of \( Z n^{2+} \) with 18 -electron configuration on the anion is larger than that of \( M g^{2} \) with a noble-gas electron configuration and of same size and charge
c. both (a) and (b) are correct
D. none of the above is correct


Carbon is less reactive than \( O_{2}, C l_{2} \) etc.
because:
A. it is a non-metal having low valency
B. the covalent bonds between various carbon atoms are very strong
c. it is black
D. none of the above


The function \( \boldsymbol{f} \) defined by \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{3}- \)
\( 3 x^{2}+5 x+7, \) is:
A. increasing in \( R \)
B. decreasing in \( R \)
C . decreasing in \( (0, \infty) \) and increasing in \( (-\infty, 0) \)
D. increasing in \( (0, \infty) \) and decreasing in \( (-\infty, 0) \)


A number subtracted by 30 gives 14 subtracted by 3 times the number. Find
the number


Which three dimensional
representation is used mainly for determining conformational relationship?
A. Newman Projection
B. Wedge-Dash Notation
c. Fischer Projection
D. All of the above


A rubber cord of density d, Youngs modulus Y and length L is suspended vertically. If the cord extends by a length \( 0.5 \mathrm{L} \) under its own weight, then Lis
A \( \cdot \frac{Y}{2 d g} \)
в. \( \frac{Y}{d g} \)
c. \( \frac{2 Y}{d g} \)
D. \( \frac{d g}{2 Y} \)
E \( \cdot \frac{d g}{Y} \)


Which characteristic the weak
intermolecular forces of attraction in a
liquid?
A. High boiling point
B. High vapour pressure
c. High critical temperature
D. High heat of vaporization


Sulphur trioxide is dissolved in heavy
water to form a compound X. The hybridisation state of sulphur in \( X \) is :
\( A \cdot s p^{2} \)
B \( \cdot s p^{3} \)
\( c \cdot s p \)
D. \( d s p^{2} \)


The unit of thermal capacity is
A . cal/ \( ^{\circ} \mathrm{C} \)
B. cal/g
c. \( \operatorname{cal} / \mathrm{g} /^{\circ} \mathrm{C} \)
D. none of these


What is 'SONAR' ? State the principle on which it is based.


Find \( \mathbf{k} \) if \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{l}\frac{2^{x+2}-16}{4^{x}-16}, \quad \text { if } \quad x \neq 2 \\ k, \quad \text { if } \quad x=2\end{array}\right. \)
continuous at \( \quad x=2 \)


In a meter bridge experiment \( S \) is a
standard resistance. \( \boldsymbol{R} \) is a resistance
wire. It is found that balancing length is \( l=25 \mathrm{cm} . \) If \( R \) is replaced by a wire of
half length and half diameter that of \( \boldsymbol{R} \)
of same material, then the balancing
distance \( \left.l^{\prime} \text { (in } c m\right) \) will now be


\( A \) and \( B \) are events with \( P(A)= \)
\( \mathbf{0 . 5}, \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 4} \) and \( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})=\mathbf{0 . 3} \)
Find the probability that
i) A does not occur
ii) neither A nor B occurs


A clinic lines on magnetic map
represent the lines of
A. zero declination
B. equal declination
c. zero dip
D. equal dip


Find the degree of the differential equation: \( \sqrt{1+\left(\frac{d y}{d x}\right)^{2}}=4 x \)
\( A \cdot 1 \)
B. 2
\( c \cdot 4 \)
D. None of these


Draw the magnetic field lines for a
current carrying solenoid when a rod made of
(i) copper, (ii) aluminium and
(iii) iron are inserted within the
solenoid as shown.


Statement A: With an increase in the
frequency of AC supply inductive reactance increases.
Statement B: With an increase in the
frequency of AC supply capacitive reactance increase.
A. A is true but B is false
B. Both A and B are true
c. A is false but B is true
D. Both A and B are false


Atoms of the transition element are
smaller than those of the s-block
elements. This is because of
A. usual contraction in size across a horizontal period
B. orbital electrons are added to the penultimate d-shell rather than to the outermost shell of the atom
c. both A and B
D. none of the above


Combustion is the process of burning a
fuel, is
(A) an oxidation and an exothermic
reaction.
(B) a reduction and an endothermic
reaction.
A. Only A is true
B. Only B is true
c. Both A and B are true
D. Both A and B are false


Magnitude of e.m.f. produced in a coil when a magnet is inserted into it does
not depend upon:
A. Number of turns in the coil
B. Speed of the magnet
c. Magnetic strength of magnet
D. Temperature of coil


The correct electronic configuration of element having mass number 24 and
number of neutrons 12 is
A .2,8,1
B. 2,8,2
\( c \cdot 2,8 \)
D. 2,8,3


\( \int e^{x}[\log (x+\sqrt{x^{2}-1})+ \)
\( \left.\frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left(\cos \boldsymbol{h}^{-1} \boldsymbol{x}\right)\right] \boldsymbol{d} \boldsymbol{x}= \)
\( \mathbf{A} \cdot e^{x} \sin h^{-1} x+c \)
B . \( e^{x} \log (x+\sqrt{x^{2}+1})+c \)
\( \mathbf{c} \cdot e^{x} \cosh ^{-1} x+c \)
D. \( -e^{x} \sinh ^{-1} x+c \)


A symmetric double convex lens is cut in two equal parts by a plane perpendicular to the principle axis. If
the power of the original lens is \( 4 D \), the
power of a cut lens will be
A . \( 2 D \)
в. \( 3 D \)
\( c .4 D \)
D. \( 5 D \)


When a dielectric slab is introduced
between the two plates of condenser then its capacity
A. remains constant
B. increases
c. decreases
D. may increase or decrease depending on the material of dielectric slab


\( 7 g \) of nitrogen occupies a volume of 5 litres under certain conditions. Under
the same conditions one mole of a gas,
having molecular weight \( 56, \) occupies a volume of ?
A \( .40 L \)
B. \( 20 L \)
c. \( 10 L \)
D. \( 80 L \)


\( \frac{\pi}{r_{p}} \)


Differentiate w.r.t. \( x \)
\( \boldsymbol{y}=(\cos \boldsymbol{x})\left(1-\sin ^{2} \boldsymbol{x}\right) \)


A businessman, by means of a false balance defrauds to an extent of \( 10 \% \) in
buying goods and \( 10 \% \) in selling goods. Then, by how much percent does he gain?
A . 21\%
B. 20\%
c. \( 19 \% \)
D. 18\%


Applications of Bernoulli's theorem can
be seen in the
A. dynamic lift of Aeroplane
B. hydraulic press
c. helicopter
D. none of these


\( \boldsymbol{H}_{\alpha} \) line of Balmer series is \( \mathbf{6 5 0 0} \boldsymbol{A} \). The
wave length of \( \boldsymbol{H} \gamma \) is?
A. \( 4815 \AA \)
в. 4298 А
c. \( 7800 \hat{h} \)
D. 3800 月


An open can of oil is accidentally dropped into a lake; assume the oil
spreads over the surface as a circular disc of uniform thickness whose radius
increases steadily at the rate of \( 10 \mathrm{cm} / \) sec. At the moment when the radius is 1
meter, the thickness of the oil slick is
decreasing at the rate of \( 4 \mathrm{mm} / \mathrm{sec}, \) how fast it is decreasing when the radius is
2 meters.


Which of the following taxonomic group contains the greatest number of organisms?
A. Class
B. Order
c. Phylum
D. Family


n identical capacitors are connected in parallel to a potential difference \( V \) These capacitors are then reconnected
in series, their charges being left undisturbed. The potential difference obtained is:
A . zero
B. (n-1)V
\( c \cdot n v \)
D. \( n^{2} V \)


Prove that work done by an ideal gas in
an adiabatic process is \( W= \) \( \frac{\boldsymbol{P}_{i} \boldsymbol{V}_{i}-\boldsymbol{P}_{f} \boldsymbol{V}_{f}}{\gamma-\mathbf{1}}, \) using the intergration
\( \int \boldsymbol{P} \boldsymbol{d} \boldsymbol{V} \)


Will it be possible to judge the sex of the child by them?


Let \( * \) be the binary operation on \( N \) given by \( a * b=L . C . M \) of \( a \) and \( b . \) Find
(i) \( 5 * 7,20 * 16 \) (ii) Is \( * \) commutative?
iii) Is \( * \) associative?


An indicator which changes its colour
from blue to red in acids is litmus
solution.
A. True
B. False


Use Euclid's division lemma to show
that the square of any positive integer is either of the form \( 3 m \) or \( 3 m+1 \) for
some integer \( \boldsymbol{m} \)


Give reasons:
o-nitrophenol is more volatile than \( \mathrm{p} \) nitrophenol


The soft, sticky layer formed on the tooth which is harmful is
A. Enamel
B. Plaque
c. Dentine
D. Pulp


For geometric isomers of 3hexene:
A. M.P. is high and dipole moment high for trans
B. M.P. is low and dipole moment low for trans
c. M.P. is high and dipole moment low for trans
D. M.P. is low and dipole moment high for trans


Which of the following statement is not correct regarding the motion of a particle in a straight line?
A. x-tgraph is a parabola, if motion is uniformly accelerated.
B. v-tus a straight line inclined to the time axis, if motion is uniformly accelerated.
c. x-tus a straight line inclined to the time axis, if motion is uniform and acceleratioin is zero
D. v-tgraph is a parabola, if motion is uniform and acceleratioin is zero


The difference between volume and
pressure coefficients of an ideal gas is:
A \( \cdot \frac{1}{273} \)
B. 273
c. \( \frac{2}{273} \)
D. Zero


Nitrogen reacts with a metal \( M \) to
produce a compound \( X . \) This compound
\( X, \) when dissolved in water forms
pungent gas \( Y \) which can be identified easily by the formation of white fumes in the presence of \( \boldsymbol{H} \boldsymbol{C l} \)
Identify the compound \( \boldsymbol{X} \)
A. Iron nitride
B. Calcium nitride
c. Nitrolim
D. Sodium nitride


A function \( f(x)=\sqrt{1-2 x}+x \) is
defined from \( D_{1} \rightarrow D_{2} \) and is onto. If
the set \( D_{1} \) is its complete domain then
the set \( D_{2} \) is
A \( \cdot\left(-\infty, \frac{1}{2}\right] \)
в. \( (-\infty, 2) \)
\( \mathbf{c} \cdot(-\infty, 1) \)
D \( \cdot(-\infty, 1] \)


Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}: \)
\( \boldsymbol{y}=\boldsymbol{e}^{\left(1+\log _{e} \boldsymbol{x}\right)} \)


Two projectiles are thrown at angles \( \Theta \)
and \( \left(90^{\circ} \Theta\right) \) with same speed. The ratio
of their horizontal ranges are
\( A \cdot 1: 1 \)
B. \( 1: \tan \theta \)
\( c \cdot \tan \theta: 1 \)
\( \mathbf{D} \cdot \tan ^{2} \Theta: 1 \)


If due to some injury, the chordae tendinae of the tricuspid valve of the human heart partially becomes nonfunctional, what will be the immediate
effect?
A. The flow of blood into the pulmonary artery will be reduced
B. The flow of blood into the aorta will be slowed down
c. The pacemaker will stop working.
D. The blood will tend to flow back into the left atrium.


In the process of nuclear fusion
A. only heavy nucleus break into light nuclei
B. fusion of light nuclei at normal temperature takes place
C. fusion of light nuclei at high pressure and low temperature takes place
D. fusion of light nuclei at high pressure and high temperature takes place


A spring of spring constant \( \boldsymbol{K} \) is fixed at
one end has a small block of mass \( m \)
and charge \( q \) is attached at the other
end. The block rests over a smooth
horizontal surface. A uniform and
constant magnetic field \( B \) exists
normal to the plane of the paper as
shown in the figure. An electric field \( \overrightarrow{\boldsymbol{E}}=\boldsymbol{E}_{0} \hat{\boldsymbol{i}}\left(\boldsymbol{E}_{0} \text { is a positive constant }\right) \) is
switched on at \( t=0 \) sec. The block
moves on the horizontal surface without
ever lifting off the surface. Where is the normal reaction acting on the block
maximum?


0.1 mol each of ethyl alcohol and acetic
acid are allowed to react and at
equilibrium, the acid was exactly neutralised by \( 100 \mathrm{mL} \) of \( 0.85 \mathrm{N} \) NaOH. If no hydrolysis of ester is supposed to
have undergo, find \( \boldsymbol{K}_{\boldsymbol{C}} \)
A. \( K_{C}=0.006 \)
в. \( K_{C}=0.031 \)
C . \( K_{C}=1.34 \)
D. \( K_{C}=3.1 \)


Find unit vector perpendicular to the plane passing through the points (1,2,3),(2,-1,1) and (1,2,-4)


Bleaching powder is prepared from:
A. caustic potash
B. caustic soda
c. slaked lime
D. magnesium chloride


Which of the follwing does not belong to
the group formed by the others?
A. Iron
B. Tin
c. Glass
D. stee


How many of the following are strong electrolytes?
a. \( \boldsymbol{N} \boldsymbol{H}_{\mathbf{3}} \)
b. \( \boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{C l} \)
c. \( \boldsymbol{C H}_{3} \boldsymbol{C O O H} \)
d. \( C H_{3} C O O N a \)
e. \( \boldsymbol{H} \boldsymbol{C l} \)
f. \( \boldsymbol{N} \boldsymbol{a} \boldsymbol{C l} \)


The breaking stress of aluminium is
\( \mathbf{7} . \mathbf{5} \times \mathbf{1 0}^{7} \mathbf{N m}^{-2} . \) The greatest length of
aluminium wire that can hang vertically without breaking is
(Density of aluminium is \( 2.7 \times \) \( \left.10^{3} k g m^{-3}\right) \)
A \( \cdot 283 \times 10^{3} m \)
В. \( 28.3 \times 10^{3} m \)
c. \( 2.72 \times 10^{3} m \)
D. \( 0.283 \times 10^{3} m \)


How many nodal plane is/are present in
\( \sigma_{p-p} \) bonding molecular orbital?


\( \frac{a-x}{a} \)
\( a \)


In the Bohr's model of hydrogenlike atom the force between the nucleus
and the electron is modified as
\[
\boldsymbol{F}=\frac{\boldsymbol{e}^{2}}{\boldsymbol{4} \boldsymbol{\pi} \varepsilon_{0}}\left(\frac{1}{\boldsymbol{r}^{2}}+\frac{\boldsymbol{\beta}}{\boldsymbol{r}^{3}}\right), \text { where } \boldsymbol{\beta} \text { is a }
\]
constant. For this atom, the radius of
the \( n \) th orbit in terms of the Bohr radius
\[
\left(a_{0}=\frac{\varepsilon_{0} h^{2}}{m \pi e^{2}}\right) i s
\]
A \( \cdot r_{n}=a_{0} n-\beta \)
\( \mathbf{B} \cdot r_{n}=a_{0} n^{2}+\beta \)
\( \mathbf{c} \cdot r_{n}=a_{0} n^{2}-\beta \)
\( \mathbf{D} \cdot r_{n}=a_{0} n+\beta \)


The complex number \( \frac{2^{n}}{(1+i)^{2 n}}+ \) \( \frac{(1+i)^{2 n}}{2^{n}}, \quad n \in \)
\( \boldsymbol{Z}, \quad \boldsymbol{i s} \quad \boldsymbol{e q u a l} \quad \boldsymbol{t o} \)


\( n \) small drops of same size are charged
to \( V \) volts each. If they coalesce to form a signal large drop, then its potential will be :
A. \( V / n \)
в. \( V n \)
\( \mathbf{c} \cdot V n^{1 / 3} \)
\( \mathbf{D} \cdot V n^{2 / 3} \)


At \( 0^{\circ} \mathrm{C} \) temperature and 1 atmospheric
pressure a given mass of gas occupies a volume of \( 273 c c \). Its volume at the same
pressure and at \( 50^{0} \mathrm{C} \) is
\( \mathbf{A} \cdot 323 c c \)
B. \( 273 c c \)
c. \( 546 c c \)
D. \( 112 c c \)


f \( a, b, c \) are in A.P then \( a\left(\frac{1}{b}+\frac{1}{c}\right), b\left(\frac{1}{c}+\frac{1}{a}\right), c\left(\frac{1}{a}+\frac{1}{b}\right) \)
are in
A. \( A . P . \)
в. G.P.
c . \( H . P \)
D. A.G.P


If \( \boldsymbol{A}=\{\mathbf{1}, \mathbf{2}\}, \boldsymbol{B}= \)
\( \left\{x: x \in N \text { and } x^{2}-9=0\right\}, \) Find \( A \times \)
\( \boldsymbol{B} \)


A wire of length L metre carrying current ampere is bent in the form of a circle.
What is the magnitude of magnetic
dipole moment?
A \( \cdot I L^{2} / 4 \pi \)
B . \( I^{2} L^{2} / 4 \pi \)
c. \( I^{2} L / 8 \pi \)
D. \( I L^{2} / 8 \pi \)


Assertion
Voltmeter is much better than a
potentiometer for measuring emf of cell
Reason

A potentiometer draws no current while measuring emf of a 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. Assertion is incorrect but Reason is correct


Let \( f(x)=x^{3}-16 x \) and let \( c \) be the
number that satisfies the Mean value
theorem for \( f \) on the interval [-4,2]
What is \( c \) ?
A . -1
B . 2
\( c \cdot 0 \)
D. -


Fill the blank spaces: \( \frac{4}{-9} \times \ldots . .=\frac{7}{6} \times \)
A \( \cdot \frac{-4}{9}, \frac{7}{6} \)
в. \( \frac{4}{-9}, \frac{7}{6} \)
c. \( \frac{7}{6}, \frac{4}{-9} \)
D. \( \frac{7}{6}, \frac{7}{6} \)


Both temporary and permanent
hardness in water is removed
by
A. boiling
B. filtration
c. distillation
D. decantation


The area of a trapezium is \( 540 \mathrm{cm}^{2} . \) If
the ratio of parallel sides is 7: 5 and the
distance between them is \( 18 \mathrm{cm} \), find the lengths of parallel sides.


A body executing SHM has its velocity \( 10 c m / s \) and \( 7 c m / s \) when its
displacements from mean position are
\( 3 c m \) and \( 4 c m \) respectively. The length of path is
\( \mathbf{A} \cdot 10 \mathrm{cm} \)
B. \( 9.5 \mathrm{cm} \)
c. \( 4 c m \)
D. \( 11.36 \mathrm{cm} \)


Universal gravitational constant is given by \( 6.67 \times 10^{-11} N m^{2} k g^{-2} . \) Then
the no. of significant figures in it is:
A . 14
B. 2
\( c \cdot 3 \)
D. 11


Mention any two activities of animals
which get cues from diurnal and seasonal variations in light intensity.


The number of carbon atoms present in
a molecule of simple ether is:
A. always even
B. always odd
c. either even or odd
D. unpredictable


How will you use two identical prisms so that a ray of white light incident on one prism emerges out of the second prism as white light? Draw the diagram.


The cost of electricity required to deposit \( 1 g m \) of \( M g \) is \( R s .5 . . \) How much would it cost to deposit 10 gm. of
\( A l ?(A t w t . A l=27, M g=24) \)
A. \( R s .10 .00 \)
B. Rs. 27.00
c. \( R s .44 .44 \)
D. Rs. 66.67


Six capacitors each of capacitance of
\( 2 \mu F \) are connected as shown in the
figure. The effective capacitance
between \( A \) and \( B \) is
\( \mathbf{A} \cdot 12 \mu F \)
B. \( -\mu F \)
\( F F \)
\( c .3 \mu F \)
D. \( 6 \mu F \)


It takes 16 min to boil some water in
an electric kettle. Due to some defect it
becomes necessary to remove \( 10 \% \) turns of the heating coil of the kettle. After repairs, how much time will it take
to boil the same mass of water?
A. 17.7 min
B. 14.4 min
c. 20.9 min
D. 13.7 min


The output \( (X) \) of the logic circuit shown
in the figure will be
\( \mathbf{A} \cdot X=\bar{A} . \bar{B} \)
В . \( X=\overline{A . B} \)
\( \mathbf{c} . X=A . B \)
D. \( X=\overline{A+B} \)


The most suitable material to be used
as the core of an electromagnet is (soft, hard) iron.


Which of the following is not formed during glycolysis?
A. Pyruvate
B. NADH
c. АтР
D. FADH


4 charges are placed each at a distance
a' from origin. The dipole moment of
configuration is :
A \( \cdot 2 q a \hat{j} \)
в. \( 3 q a \hat{j} \)
\( \mathbf{c} \cdot 2 a q[\hat{i}+\hat{j}] \)
\( 0 . \) none


A coil made of insulated copper wire is
connected to a galvanometer. What will
happen if a bar magnet is pushed into the coil ?
outside
opposite


Effective capacitance of parallel
combination of two capacitors \( C_{1} \) and
\( C_{2} \) is \( 10 \mu F \). when these capacitors are individually connected to a voltage
source of \( 1 V \), the energy stored in the capacitor \( C_{2} \) is 4 times that of \( C_{1} \). If
these capacitors are connected in series, their effective capacitance will be:
\( \mathbf{A} \cdot 8.4 \mu F \)
в. \( 3.2 \mu F \)
c \( .1 .6 \mu F \)
D. \( 4.2 \mu F \)


Tincal mainly contains:
A. \( N a N O_{3} \)
в. \( N a_{2} B_{4} O_{7} .10 H_{2} O \)
\( \mathbf{c} \cdot N a_{2} C O_{3} \)
D. \( N a_{2} S O_{4} \)


Which of the following \( P \) most stable?
A . Red
B. White
c. Black
D. All of these


During anaerobic respiration in yeast
A. Water and \( C O_{2} \) are end products
в. \( C O_{2}, C_{2} H_{5} O H \) and energy are end products
C. \( H_{2} S, C_{6} H_{12} O_{6} \) and energy are the end products
D. \( H_{2} O, C O_{2} \) and energy are the only end products


The wavelength of light is 589 nm. What is its order of magnitude in metre?


One mole of an ideal gas is compressed from 0.5 lit to 0.25 lit. During the
compression, \( 23.04 \times 10^{2} J \) of work is
done on the gas and heat is removed to keep the temperature of the gas constant at all times. Find the
temperature of the gas. (Take universal gas constant \( \boldsymbol{R}=\mathbf{8 . 3 1} \boldsymbol{J} \boldsymbol{m o l}^{-1} \boldsymbol{K}^{-1} \mathbf{)} \)


The kinetic energy acquired by a mass \( \mathrm{m} \) after travelling a fixed distance from rest under the action of constant force
is
A. directly proportional to \( \sqrt{m} \)
B. directly proportional to
c. independent of \( m \)
D. directly proportional to \( \frac{1}{\sqrt{m}} \)


Lead accumulator is:
A. acid storage cell
B. alkali storage cell
\( c \cdot \) both
D. cant be predicted


The mass of hydrogen molecule us \( 3.32 x \) \( 10^{-27} \) kg.If \( 10^{23} \) hydrogen molecules
strike per second at \( 2 \mathrm{cm}^{2} \) area of a rigid
wall at an angle \( 45^{0} \) from the normal and
rebound back with speed of \( 1000 \mathrm{m} / \mathrm{s} \)
then the pressure exerted on the wall is
A. 2 Pascal
B. 2.34 \times 10 \( ^{3} \) Pascal
c. \( 0.23 \times 10^{3} \) Pascal
D. 23.4 x 10 \( ^{3} \) Pascal


Monerans bearing conidia for reproduction belong to
A. Eubacteria
B. Archaebacteria
c. Actinomycetes
D. Mycoplasma


Pure methane can be produced by:
A. Wurtz reaction
c. soda lime decarboxylation
D. reduction with \( H_{2} \)


In the arrangement shown in figure the
mass \( M \) is very heavy compared to \( \boldsymbol{m}(\boldsymbol{M}>+>\boldsymbol{m}) . \) The tension \( \boldsymbol{T} \) in the
string suspended from the ceiling is
A. \( 4 m g \)
в. \( 2 m g \)
c. zero
D. None of the above


Select the pairs(s) in which bond angle of first member is higher than second
one.
A. \( B r O_{3}^{-}, C l O_{3} \)
B. \( A s I_{3}, S b I_{3} \)
c. \( S b B r_{3}, S b I_{3} \)
D. \( N F_{3}, N H_{3} \)


A gun fires a bullet of mass 50 g with a velocity of \( 30 \mathrm{m} \mathrm{s}^{-1} \). Because of this
gun is pushed back with a velocity of 1
\( \mathrm{m} \mathrm{s}^{-1} . \) Mass of the gun is :
\( A \cdot 3.5 \mathrm{kg} \)
c. \( 1.5 \mathrm{kg} \)
D. 2 kg


A gas is undergoing an adiabatic process. At a certain stage \( A \), the values
of volume and temperature \( \equiv\left(V_{0}, T_{0}\right) \) and the magnitude of the slope of \( \mathrm{V}-\mathrm{T} \)
curve is \( \mathrm{m} \). Find the value of \( C_{P} \) and \( C_{V} \)


In presence of small amount of water,
\( P C l_{5} \) hydrolyzes to form:
A \( \cdot P C l_{3} \)
в. Рос
c. \( P O C l_{3} \)
D. \( H_{3} P O_{3} \)


The nature of \( \boldsymbol{F e}_{2} \boldsymbol{O}_{3} \) is:
A . acidic
B. basic
c. amphoteric
D. none of these


Obtain a mirror equation for a spherical mirror.


Turnbull's blue is \( \boldsymbol{F e}_{3}\left[\boldsymbol{F e}(\boldsymbol{C N})_{6}\right]_{2} \)
A. True
B. False


Self inductance of long solenoid is directly proportional to- \( (A \) is area of cross section)
A. \( A \)
B . \( A^{2} \)
c. \( A^{3} \)
D. \( A^{4} \)


A person is painting his house walls. He stands on a ladder with a bucket
containing paint in one hand and a brush in other. Suddenly the bucket slips from his hand and falls down on
the floor. If the bucket with the paint
had a mass of \( 0.6 k g \) and was at a
height of \( 2.0 m \) at the time it slipped,
how much gravitational potential energy is lost together with the paint?


Electrolytic reduction of alumina to aluminium by Hall-Heroult's process is carried out
A. in the presence of sodium chloride
B. in the presence of flourite
C. in the presence of cryolite which forms a melt with lower melting temperature
D. in the presence of cryolite which forms a melt with higher melting temperature


Choose the correct answer from the
alternatives given The heart sound dup is produced when:
A. mitral valve is opened
B. mitral valve is closed
c. tricuspid valve is opened
D. semilunar valve at the base of aorta gets closed


When waves of same intensity from two coherent sources reach a point with
zero path different the resulting intensity is \( \mathrm{K} \). When the above path difference is \( \lambda / 4 \) the intensity becomes
\( A \cdot K \)
B. K/2
\( c \cdot k / 4 \)
D. K/8


Identify \( A \) and \( B \)


\( \boldsymbol{g}(\boldsymbol{x}+\boldsymbol{y})=\boldsymbol{g}(\boldsymbol{x})+\boldsymbol{g}(\boldsymbol{y})+\mathbf{3} \boldsymbol{x} \boldsymbol{y}(\boldsymbol{x}+ \)
\( \boldsymbol{y}) \forall \boldsymbol{x}, \boldsymbol{y} \boldsymbol{\epsilon} \boldsymbol{R} \) and \( \boldsymbol{g}^{\prime}(\mathbf{0})=-4 . \) The value of
\( \boldsymbol{g}^{\prime}(1) \) is
A . 0
B.
c. -1
D. none of these


Let \( \mathbf{f}=\left\{\begin{array}{ll}\mathbf{a x}^{2}+\mathbf{1} & \text { for } \mathbf{x}>\mathbf{1} \\ \mathbf{x}+\mathbf{a} & \text { for } \mathbf{x} \leq \mathbf{1}\end{array} \text { then } \mathbf{f}\right. \)
is derivable at \( x=1 \) if
\( \mathbf{A} \cdot \mathbf{a}=0 \)
B. \( a=\frac{1}{2} \)
\( \mathbf{c} \cdot \mathbf{a}=1 \)
\( \mathbf{D} \cdot \mathbf{a}=\mathbf{2} \)


What is the sum of the squares of direction cosines of the line joining the points (1,2,-3) and (-2,3,1)\( ? \)
\( A \cdot O \)
B.
\( c \cdot 3 \)
D. \( \frac{2}{\sqrt{26}} \)


\( \ln \operatorname{an} A . P . \) if \( \frac{S_{m}}{S_{n}}=\frac{m^{4}}{n^{4}} \) then prove that
\( \frac{T_{m+1}}{T_{n+1}}=\frac{(2 m+1)^{3}}{(2 n+1)^{3}} \)


What is menstruation? Why does it
occur?


The area bounded by curves \( 3 x^{2}+ \)
\( \mathbf{5} \boldsymbol{y}=\mathbf{3} 2 \) and \( \boldsymbol{y}=|\boldsymbol{x}-\mathbf{2}| \) is
A . 25
B. 17/2
c. \( 33 / 2 \)
D. 33


The electric field in the region \( b>r>a \)
is \( \boldsymbol{E}=\frac{\boldsymbol{Y}}{\boldsymbol{4} \boldsymbol{\pi} \varepsilon_{0}} \frac{\boldsymbol{Q}}{\boldsymbol{r}^{2}} . \) Find \( \boldsymbol{Y} ? \)


Write the following into simple test form;
(1) \( \sin \left\{2 \tan ^{-1} \sqrt{\frac{1-n}{1+n}}\right\} \)


ff \( x, y, z \) are positive, then prove that \( (x+y+z)\left(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\right) \geq 9 \)


IF \( A, B, C \) are non-singular \( n \times n \)
matrices, then \( (A B C)^{-1}= \)
\( \mathbf{A} \cdot A^{-1} C^{-1} B^{-1} \)
B. \( C^{-1} B^{-1} A^{-1} \)
c. \( C^{-1} A^{-1} B^{-1} \)
D. \( B^{-1} C^{-1} A^{-1} \)


Differentiate between.
Planogametic copulation and gametangial copulation


A geo-stationary satellite is orbiting the earth at a height of 6 R above the
surface of earth, R being the radius of earth. The time period of another satellite at a height of \( 2.5 \mathrm{R} \) from the surface of earth is
A. 10 hr
B \( \cdot(-6 / \sqrt{2}) h r \)
\( c \cdot 6 h r \)
D. \( 6 \sqrt{2} h r \)


Assertion
Basic difference between an electric
line of force and magnetic lines of force is that former is discontinuous and the
latter is continuous or endless.
Reason
No electric lines of force exist inside a
charged body but magnetic lines do
exist inside a magnet.
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


Factorize :
\( a^{4}+4 b^{4}+3 a^{2} b^{2} \)
\( \mathbf{A} \cdot\left(a^{2}+a+2 b^{2}\right)\left(a^{3}-a b+2 b^{3}\right) \)
B \( \cdot\left(a^{2}-a b-2 b^{2}\right)\left(a^{2}-a b+2 b^{2}\right) \)
\( \mathbf{C} \cdot\left(a^{3}+b+2 b^{3}\right)\left(a^{2}-a b+2 b^{2}\right) \)
D \( \cdot\left(a^{2}+a b+2 b^{2}\right)\left(a^{2}-a b+2 b^{2}\right) \)


The mass of a box measured by a grocer's balance is 2.3 kg. Two gold pieces of masses 20.15 g and 20.17 g are added to the box. The total mass of the
box is:
A. 2.3 kg
B. 2.34 kg
c. \( 2.340 \mathrm{kg} \)
D. 2.3403 kg


Find it is a perfect cubes or not?
\( \mathbf{3 3 7 5} \)


The splitting of white light into its colored components is called
A. spectrum
B. Dispersion
c. Deviation
D. Refraction


A copper rod and a steel rod maintain a difference in their lengths constant=10
\( \mathrm{cm} \) at all temperatures. If their
coefficients of expansion are \( 1.6 \times \) \( 10^{-5} K^{-1} \) and \( 1.2 \times 10^{-5} K^{-1}, \) then the
length of the Cu rod is
A. \( 40 \mathrm{cm} \)
B. 30 cm
c. \( 32 \mathrm{cm} \)
D. 24 cm


Assertion
If two objects of different masses have the same momentum, then the lighter body possess greater velocity.
Reason
For all bodies, momentum always
remains the same.
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 compound whose aqueous solution has the highest \( p H \) is :
A . \( N a C l \)
в. \( N a H C O_{3} \)
c. \( N a_{2} C O_{3} \)
D. \( N H_{4} C l \)


The area under velocity-time graph gives:
A. acceleration
B. distance
c. displacement
D. velocity


In hydra the type of reproduction is
A. Binary fission
B. Budding
c. Multiple fission
D. None of these


The complex ion transdichlorobis(ethylenediamine) rhodium
(III) is optically active.
A. True
B. False


Among the following which can form ions with a \( 2+ \) charge?
A . Alkali metal
B. Alkaline earth metal
c. Transition metal
D. Halogen
E. Noble gas


Bakane disease is connected with
discovery of
A . GA
B. IAA
c. АВА
D. 2, 4-D


A snap bubble is being blown on a tube
of radius \( 1 \mathrm{cm} \). the surface tension of the
soap solution is \( 0.05 \mathrm{N} / \mathrm{m} \) and the
bubble makes an angle of \( 60^{\circ} \) with the
tube as shown. The excess of pressure
over the atmospheric pressure in the
tube is:
\( A \cdot 5 P a \)
B. 1 Pa
c. \( 10 \mathrm{Pa} \)
D. 20 Pa


In the circuit shown here, \( \boldsymbol{E}_{\mathbf{1}}=\boldsymbol{E}_{2}= \)
\( \boldsymbol{E}_{3}=2 \boldsymbol{V} \) and \( \boldsymbol{R}_{1}=\boldsymbol{R}_{2}=\boldsymbol{4} \) ohms. The
current flowing between points \( A \) and \( B \)
through battery \( \boldsymbol{E}_{2} \) is :-
A . zero
B. 2 amp from A to B
c. 2 amp from \( B \) to \( A \)
D. none of the above


Barrier potential of a p-njunction diode does not depend on:
A. Diode design
B. Doping density
c. Temperature
D. Forward bias


Polar covalent compounds are
in gaseous state, but ionizes in aqueous solution state.
A. electrolytes
B. non-electrolytes
c. soluble
D. none of the above


Find the value of \( \left|\begin{array}{cc}2+i & 2-i \\ 1+i & 1-i\end{array}\right| \) if \( i^{2}= \)
-1
A. A complex quantityyy
B. real quantity
c. 0
D. cannot be determined


Match the following
Column - I Column - II
a) A nearly ideal solution
p) \( H_{2} O+ \)
\[
C_{2} H_{5} O H
\]
b) A solution
q) \( C_{6} H_{6}+ \) showing positive deviation \( \quad C_{6} H_{5} C H_{3} \)
c) A solution
r) \( C_{6} H_{6}+C H C l_{3} \)
showing negative deviation
s) \( C H_{3} C O C H_{3}+ \)
d) An azeotropic mixture
\[
C_{2} H_{5} O H
\]
\( t \)
\( \Delta H \) and \( \Delta V \) are
positive
and \( \Delta V \)
\( \Delta H \)
u) are negative
\( \mathbf{A} \cdot \mathrm{A}-\mathrm{q} ; \mathrm{B}-\mathrm{s}, \mathrm{t} ; \mathrm{C}-\mathrm{r}, \mathrm{u} ; \mathrm{D}-\mathrm{p} \)
B. \( A-s ; B-s, t ; C-r ; D-q, p \)
\( \mathbf{C} \cdot A-q ; B-s ; C-r ; D-p, t \)
D. \( A-r ; B-p ; C-s, t ; D-q \)


According to the laws of reflection,
angle of incidence is equal to angle of reflection
A. True
B. False


Find the values of \( x, \) if \( \left|\begin{array}{ll}\mathbf{2} & \mathbf{3} \\ \mathbf{4} & \mathbf{5}\end{array}\right|=\left|\begin{array}{ll}\boldsymbol{x} & \mathbf{3} \\ \mathbf{2} \boldsymbol{x} & \mathbf{5}\end{array}\right| \)


Which one of the following mammalian cells is not capable of metabolizing glucose to carbon-dioxide aerobically
A. White blood cells
B. Unstriated muscle cells
c. Liver cells
D. Red blood cells


What smallest number should 7803 be
multiplied with so that the product becomes a perfect cube


toppr \( E \)
Q Type your question
The graph between \( \frac{\mathrm{i}}{\boldsymbol{d t}} \) and time will
be of the type:
B.
\( c \)
\( D \)


Let \( \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{2} & \mathbf{4} \\ \mathbf{3} & \mathbf{2}\end{array}\right], \boldsymbol{B}=\left[\begin{array}{cc}\mathbf{1} & \mathbf{3} \\ -\mathbf{2} & \mathbf{5}\end{array}\right] \) and
\( \boldsymbol{C}=\left[\begin{array}{cc}\mathbf{- 2} & \mathbf{5} \\ \mathbf{3} & \mathbf{4}\end{array}\right] . \) Find:
\( \boldsymbol{A}-\mathbf{2} \boldsymbol{B}+\mathbf{3} \boldsymbol{C} \)


The displacement of a particle varies with time as \( \boldsymbol{x}=\boldsymbol{a} e^{-\boldsymbol{\alpha} \boldsymbol{t}}+\boldsymbol{b} \boldsymbol{e}^{\boldsymbol{\beta} \boldsymbol{t}} \) where
\( a, \alpha, b, \beta \) are positive constants. The
velocity of the particle will
A. be independent of \( \alpha \) and \( \beta \)
B. drop to zero when \( \alpha=\beta \)
c. go on decreasing with time
D. go on increasing with time


In the reaction: \( 3 C l_{2}+6 N a O H \longrightarrow \)
\( \mathbf{5} N a C l+N a C l O_{3}+3 H_{2} O, C l_{2} \) acts
purely as an oxidizing agent.
If true enter 1 , else enter 0 .
A.


Two glass bulbs of volumes \( 500 \mathrm{cm}^{3} \)
and \( 200 \mathrm{cm}^{3} \) are connected with a narrow
tube. Both of them are filled with air at
70mm of \( \mathrm{Hg} \) and at \( 17^{\circ} \mathrm{C} \) and sealed. The
bulb of small volume is kept in ice and the other with larger volume is kept in steam. Then find the pressure of the gas in the bulb.
A. \( 51 \mathrm{mm} \) of \( \mathrm{Hg} \)
B. 200cm of Hg
c. 873mm of Hg
D. 200m of Hg