The work function of a metal in \( 4 e V . \) For
the emission of photoelectrons of zero velocity from the metal surface, the wavelength of the incident radiation should be
\( \mathbf{A} \cdot 1700 \hat{A} \)
в. 2700 А
\( c \cdot 3100 \hat{A} \)
D \( \cdot 5900 \),


Write the future products of Green
chemistry.


Read the following about pollution and
identify the correct matching combinations.
\( \begin{array}{lll}\text { List I } & \text { List II } & \text { List III } \\ \text { (A) Chernobyl } & \begin{array}{l}\text { Accidental } \\ \text { leakage }\end{array} & \begin{array}{l}\text { Radioactive } \\ \text { wastes }\end{array} \\ \begin{array}{l}\text { (B) Elnino } \\ \text { effect }\end{array} & \begin{array}{l}\text { Global } \\ \text { warming }\end{array} & \begin{array}{l}\text { Causing } \\ \text { climatic } \\ \text { change }\end{array} \\ \begin{array}{l}\text { (C) } \\ \text { Chlorofloro } \\ \text { carbons }\end{array} & \begin{array}{l}\text { Ozone } \\ \text { degradation }\end{array} & \begin{array}{l}\text { Fluorine } \\ \text { atoms } \\ \text { released }\end{array} \\ \begin{array}{l}\text { (D)Snow } \\ \text { blindness }\end{array} & \begin{array}{l}\text { UV-B } \\ \text { Radiation }\end{array} & \begin{array}{l}\text { Inflammation } \\ \text { of cornea }\end{array}\end{array} \)
\( A \cdot A, C \)
B. A, D
\( c \cdot A, B, D \)
D. B.


The weight of a body on the surface of the moon is \( \frac{1}{6} t h \) of that on the earth's surface. It is because acceleration due
to gravity on the surface of the moon is
six times that on the surface of the
earth.
A . True
B. False


The mass of \( _{2} H e^{4} \) nnucleus is 0.03
amu less than the sum of the masses of
2 protons and 2 neutrons. What is the
binding energy per nucleon?


When \( K C l O_{3} \) is heated, it decomposes
into \( K C l \) and \( O_{2} . \) If some \( M n O_{2} \) is
added, the reaction goes much faster
because :
A. \( M n O_{2} \) decomposes to give \( O_{2} \)
B. \( M n O_{2} \) provides heat by reacting
C. Better contact is provided by \( M n O_{2} \)
D. \( M n O_{2} \) acts as a catalyst


The dielectric strength of air is \( 3.0 \times \)
\( 10^{6} N C^{-1} . \) The largest charge that a
\( 0.30 \mathrm{cm} \) radius metal sphere can hold without sparking is:
A. 9 nc
B. 8.2 nc
\( c \cdot 6 n c \)
D. 3 nc


Vitamin \( B_{2}, \) a water soluble vitamin is
also known as:
A. ascorbic acid
B. riboflavin
c. thiamine
D. pyridoxine


Solve \( \int x \sin ^{2} x d x \)
A \( \cdot \frac{(x-1)}{2}\left(x-\frac{\cos 2 x}{2}\right)+C \)
в. \( \frac{(x-1)}{2}\left(x-\frac{\sin 2 x}{2}\right)+C \)
c. \( \frac{(x+1)}{2}\left(x-\frac{\sin 2 x}{2}\right)+C \)
D. None of these


In a school \( 10 \% \) of the boys are same in
number as one -fourth of the girls. What is the ratio of boys to girls in that school?
A .3: 2
B. 5: 2
\( c \cdot 2: 1 \)
D. 4: 3


A convex lens magnifying glass is of
A. Long focal length
B. Short focal length
c. very long focal length
D. All the above


Holmes signals can be given by using:
A. \( C a C_{2}+C a C N_{2} \)
В. \( C a C_{2}+C a_{3} P_{2} \)
\( \mathbf{c} \cdot C a C_{2}+C a C O_{3} \)
D. \( C a_{3} P_{2}+C a C N_{2} \)


The mole fraction of water in \( 20 \% \)
aqueous hydrogen peroxide solution is:
A . 0.2
B. 0.8
\( \mathbf{c} .0 .883 \)
D. 0.117


The two kidneys lie
A. At the level of ovaries
B. At the same level
C. Left kidney at a higher level than the right one
D. Right kidney at a higher level than the left one


If the equation for the line shown in the following graph is \( y=\frac{1}{3} x+3, \) what is
the value of \( k \cdot n ? \)
A . 9
B. 12
c. 15
D. 18
E . 24


An ice cube of edge length \( 20 \mathrm{cm} \) is
floating in a tank of base area \( 2500 \mathrm{cm}^{2} \)
filled with water to \( 22 c m \) height. The displacement of centre of mass of whole system (in \( \mathrm{cm} \) ), when ice cube melts completely will be
\( \left(\rho_{i c e}=900 k g / m^{3}, \rho_{\omega}=\right. \)
\( \left.\mathbf{1 0 0 0 k g} / \boldsymbol{m}^{3}, \boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{\mathbf{2}}\right) \)
A . 1
в. 1.5
\( c \cdot 1.32 \)
D. 1.44


The effect of an impulse force on the body is measured only in terms of its
A. Force
B. Moment of momentum
c. Impulse
D. None of these


Assertion
The balancing of chemical equations is based on the law of conservation of
mass.
Reason
Total mass of reactants is equal to total
mass of products.
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 instrument is used to view
astronomical bodies.


Set of values of \( x \) in [0,7] for which \( g(x) \)
is negative is
\( A \cdot(2,7) \)
B. (3,7)
\( c \cdot(4,6) \)
D. (5,7)


According to Cartesian Sign Convention
A. Object distance is always -ve
B. Object distance is always +ve
C. Image distance is always -ve
D. Image distance is always +ve


Which of the metal ores can be obtained
in hydrometallurgical reduction?


A mass of ideal gas at pressure \( \boldsymbol{P} \) is expanded isothermally to four times the
original volume and then slowly compressed adiabatically to its original
volume. Assuming \( \gamma \) to be \( 1.5, \) the new
pressure of gas is
A \( .2 P \)
в. \( P \)
c. \( 4 P \)
D. \( \frac{P}{2} \)


Consider the following \( E^{0} \) values:
\( E_{F e^{3+} / F e^{2+}}^{0}=+0.77 V ; E_{S n^{2+} / S n}^{0}=-0.14 V \)
Under standard conditions the EMF for
the reaction
\( S n_{(s)}+2 F e_{(a q)}^{3+} \rightarrow 2 F e^{2+}_{(a q)}+S n_{(a q)}^{2+} \) is :
A . \( 1.68 \mathrm{v} \)
B . \( 1.40 \mathrm{V} \)
c. \( 0.91 v \)
D. \( 0.63 \mathrm{v} \)


The graph above shows the magnitude of the force applied to an initially stationary \( 20 k g \) curling rock over time.
Find out the velocity of the rock after the force has been applied to it?
A \( .1 .25 \mathrm{m} / \mathrm{s} \)
в. \( 5 m / s \)
\( \mathrm{c} \cdot 10 \mathrm{m} / \mathrm{s} \)
D. \( 25 m / s \)
E. \( 50 m / s \)


Describe the connecting link reaction between glycolysis and Kreb's cycle.


The interval of time that elapses between two consecutive passages of a fixed star (other than the sun) across the meridian is called
A. mean solar day
B. mean sidereal day
C. mean solar year
D. mean sidereal year


Real image can be obtained on a screen
A. True
B. False


In which of the following positions \( A, B \)
and \( C \) of a cuboid will it exert maximum
pressure?
\( A \cdot A \)
B. B
\( c \cdot c \)
D. In all positions it will exert equal pressure


Select incorrect statement
A. If salt-bridge is removed, potential falls to zero
B. Liquid-junction potential developed across the boundary of the two solutions of different concentration cells are used
c. calomel electrode contains calcium chloride solution in contact with \( P t \) electrode
D. Quinhydrone electrode is reversible to \( H^{+} \)


Which algal members reproduce exclusively by non-motile spores and non-motile sexual gametes?
A. Phaeophyceae
B. Rhoddophyceae
c. cyanophyceae
D. chrysophyceae


In the Contact process, sulphur trioxide is not converted to sulphuric acid by
reacting it with water. Instead a twostep procedure is used. The equations for the two steps involved are:
\( \boldsymbol{S} \boldsymbol{O}_{\boldsymbol{x}}+\boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \rightarrow \boldsymbol{H}_{2} \boldsymbol{S}_{2} \boldsymbol{O}_{\boldsymbol{y}} \)
\( \boldsymbol{H}_{2} \boldsymbol{S}_{2} \boldsymbol{O}_{7}+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
Find the value of \( x \) and \( y: \)
A. \( x=2, y=5 \)
в. \( x=3, y=5 \)
c. \( x=2, y=7 \)
D. \( x=3, y=7 \)


In the given pair of compounds, in which
pair second compound has higher boiling point than first compound?
4
and
в. НО\( - \)СН\( _{2}- \)СН\( _{2}- \)ОН апа \( C \)Нз\( _{3}- \)СН\( _{2}- \)ОН
\( c \)
and
\( D \)
and


Solve
\( \int \frac{d y}{y}=\int \frac{d x}{x} \)


Let \( \boldsymbol{O} \) be the origin and \( \boldsymbol{A} \) be the point \( (64,0) . \) If \( P \) and \( Q \) divide \( O A \) in the ratio
\( \mathbf{1}: \mathbf{2}: \mathbf{3}, \) then the point \( \boldsymbol{P} \) is
\( ^{\mathbf{A}} \cdot\left(\frac{32}{3}, 0\right) \)
в. (32,0)
\( ^{\mathbf{c}} \cdot\left(\frac{64}{3}, 0\right) \)
D. (16,0)
E \( \cdot\left(\frac{16}{3}, 0\right) \)


If \( \vec{x} \) and \( \vec{y} \) are two non-collinear vectors
and \( a, b \) and \( c \) represent the sides of a
\( \Delta A B C \) satisfying \( (a-b) \vec{x}+(b- \)
\( c) \overrightarrow{\boldsymbol{y}}+(\boldsymbol{c}-\boldsymbol{a})(\overrightarrow{\boldsymbol{x}} \times \overrightarrow{\boldsymbol{y}})=0, \) then \( \Delta \boldsymbol{A} \boldsymbol{B C} \)
is ( where \( \vec{x} \times \vec{y} \) is perpendicular to the
plane of \( \vec{x} \text { and } \vec{y}) \)
A. An acute-angle triangle
B. An obtuse-angled triangle
c. Right-angled triangle
D. A scalene triangle


An object is placed at a distance u from a simple microscope of focal length \( f \) the angular magnification obtained depends
A. on f but not on u
B. on u but not on f
c. on f as well as u
D. neither on f nor of u


Draw electron dot structure of ethyne


In a cylindrical water tank here are two small holes \( Q \) and \( P \) on the wall at a
depth of \( h_{1} \) from the upper level of water
and at a height of \( h_{2} \) from the lower end of the tank, respectively, as shown in
the figure. Water coming out from both the holes strike the ground at the same
point. The ratio of \( h_{1} \) and \( h_{2} \) is
\( A \)
B.
\( c \cdot>1 \)
D.


The angle between any two faces is
\( A \cdot \cos ^{-1}(1 / 3) \)
B. \( \cos ^{-1}(1 / 4) \)
c. \( \pi / 3 \)
\( \mathbf{D} \cdot \cos ^{-1}(1 / 2) \)


Q Type your question
reaction as shown below. Write the
structures of \( A, B, C, D \) and \( E \) in the
following reactions:
OR
(a) Write the structures of main
products when benzene diazonium chloride reacts with the following regents:
(i) \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{2}+\boldsymbol{H}_{2} \boldsymbol{O} \)
\( (\text { ii }) C u C N / K C N \)
\( (\text { iii }) \boldsymbol{H}_{2} \boldsymbol{O} \)
(b) Arrange the following in the increasing order of their basic character in an aqueous solutions:
\( \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{N} \boldsymbol{H}_{2},\left(\boldsymbol{C}_{2} \boldsymbol{H}_{5}\right)_{2} \boldsymbol{N} \boldsymbol{H},\left(\boldsymbol{C}_{2} \boldsymbol{H}_{5}\right)_{3} \boldsymbol{N} \)
(c) Give a simple chemical test to distinguish between the following pair
of compounds:
\( \boldsymbol{C}_{2} \boldsymbol{H}_{5}-\boldsymbol{N} \boldsymbol{H}_{2} \boldsymbol{a n d} \boldsymbol{C}_{6} \boldsymbol{H}_{5}-\boldsymbol{N} \boldsymbol{H}- \)
\( \boldsymbol{C H}_{3} \)


What is Knot?
A. Unit of measuring wind velocity
B. Unit of measuring air pressure
C. Unit of measuring temperature
D. Condition of sky


Solve: \( \lim _{x \rightarrow 2} \frac{a^{\tan x}-a^{\sin x}}{\tan x-\sin x}, a>0 \)


Photons of energy \( 1 e V \) and \( 2.5 e V \) successively illuminated a metal whose
work function is \( 0.5 e V . \) The ratio of
maximum speeds of emitted electron is
A .1: 3
B. 1: 2
c. 3: 1
D. 2: 1


Prove that: \( \frac{\sin A-2 \sin ^{3} A}{2 \cos ^{3} A-\cos A}=\tan A \)


The nature of \( \pi \) -bonds in perchlorate
ion is :
A \( . O(d \pi)-C l(p \pi) \)
в. \( O(p \pi)-C l(d \pi) \)
c. \( O(d \pi)-C l(d \pi) \)
D. \( O(p \pi)-C l(p \pi) \)


Prove that \( \sin ^{-1}(2 x \sqrt{1-x^{2}})= \)
\( 2 \cos ^{-1} x, \frac{1}{\sqrt{2}} \leq x \leq 1 \)


A particle moves on a line according to
the law \( s=a t^{2}+b t+c . \) If the
displacement after 1 sec is \( 16 \mathrm{cm}, \) the velocity after 2 sec is \( 24 \mathrm{cm} / \mathrm{sec} \) and acceleration is \( 8 \mathrm{cm} / \mathrm{sec}^{2}, \) then
A. \( a=4, b=8, c=4 \)
В. \( a=4, b=4, c=8 \)
c. \( a=8, b=4, c=4 \)
D. none of these


Which of the following represents an incorrect match?
A. Marsupials-Kangaroos, opossums, Koalas
B. Ungulates - Pigs, Giraffes, Camels
c. Rodentia - Hamster, Beaver, Rat
D. None of these


If \( \frac{\sin A}{\sin B}=\frac{\sqrt{3}}{2} \) and \( \frac{\cos A}{\cos B}=\frac{\sqrt{5}}{2}, 0< \)
\( A, B<\frac{\pi}{2}, \) then find the value of
\( \tan A+\tan B \)
A \( \cdot \frac{\sqrt{5}-\sqrt{3}}{\sqrt{3}} \)
B. \( \frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}} \)
c. \( \frac{\sqrt{3}+\sqrt{5}}{\sqrt{5}} \)
D. \( \frac{\sqrt{3}+\sqrt{5}}{\sqrt{3}} \)


(i) What is the role of \( t \) -butyl peroxide in the polymerization of ethene?
(ii) Identify the monomers in the following polymer:
\( \left[-N H-\left(C H_{2}\right)_{6}-N H-C O-(C H\right. \)
(iii) Arrange the following polymers in the increasing order of their intermolecular forces:
Polystyrene, Terylene, Buna \( -S \)
Write the mechanism of free radical
polymerization of ethene.


Fuse should be connected to \( \ldots . . \) wire of
the circuit
A. Earth
B. Neutral
c. Phase
D. Any of the above


Bleaching powder reacts with carbon
dioxide gas to form \( C a C O_{3} \) and \( C l_{2} \)
If true enter 1 , else enter 0 .


A heater at \( 220 V \) boils a volume of
water in 5 minutes time. If the heater is
operated at \( 110 V \), the same volume of
water will boil in \( 10 n \) minutes. Find the
value of \( n ? \)


(a) Define molar conductivity of a solution and explain how molar
conductivity changes which change in concentration of solution for a weak and
a strong electrolyte?
(b) The resistance of a conductivity cell
containing \( 0.001 M \) KCl solution at 298
Kis \( 1500 \Omega \). What is the cell constant if
the conductivity of \( 0.001 \mathrm{M} \) KCl solution
at \( 298 \mathrm{K} \) is \( 0.146 \times 10^{-3} \mathrm{S} \mathrm{cm}^{-1} \) ?


A nucleus, with mass number \( m \) and
atomic number \( n, \) emits one \( \alpha \) particle
and one \( \beta \) particle. The mass number and atomic number of the resulting nucleus will be respectively
(Assume \( \beta \) is positron)
A. \( (m-2), n \)
B. \( (m-4),(n-1) \)
c. \( (m-4),(n-2) \)
D. \( (m+4),(n-1) \)


If \( M \) is a \( 3 \times 3 \) matrix, where \( M^{T} M= \)
\( \boldsymbol{I} \) and \( \operatorname{det}(\boldsymbol{M})=\mathbf{1} \) then prove that
\( \operatorname{det}(M-I)=0 \)


Heavily doped p-n junction diode which emits light when it is forward biased is/are:
A. zener diode
B. photo-diode
c. light emitting diode
D. all of the above


Find \( \sin ^{-1}\left(\frac{\sqrt{\mathbf{3}}+1}{2 \sqrt{2}}\right)= \)


Conventional flow of current will always be from -
A. p type \( \rightarrow \) n type
B. n type \( \rightarrow \) p type
c. \( n \) Type \( \rightarrow \) n type
D. None of these


The number of significant figures in \( 5.23 \times 10^{5} \) is :
\( \mathbf{A} \cdot \mathbf{8} \)
B. 3
\( c \cdot 4 \)
D. infinite


Five hundred kids are going to Goa. The first bus to Goa will start when \( 40 \% \) of
the kids report at the bus station. If 180
kids have arrived, the first bus will to
wait for how many kids to arrive?


The equation of an altitude of an equilateral triangle is \( \sqrt{\mathbf{3}} x+y=2 \sqrt{3} \)
and one of the vertices is \( (3, \sqrt{3}), \) then the possible number of triangles are,
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c \cdot 3 \)
D. 4


Which of the following is the most important use of electroplating:
A. increase corrosion
B. makes material shining
c. provides resistance to corrosion
D. none of these


A bar magnet placed in non-uniform magnetic field experiences.
A. Only torque
B. Only force
c. Both torque and force
D. Neither force not torque


If \( 0<x<\pi, \) then
\( \frac{\sin 8 x+7 \sin 6 x+18 \sin 4 x+12 \sin 2 x}{\sin 7 x+6 \sin 5 x+12 \sin 3 x} \)
is equal to
\( \mathbf{A} \cdot \mathbf{6} \)
B. 4
\( c \cdot 3 \)
D. 2
E . 8


For the gaseous reaction \( N_{2} O_{4} \Leftrightarrow 2 N O_{2} \)
\( \mathbf{A} \cdot \Delta H>\Delta E \)
B. \( \Delta H<\Delta E \)
c. \( \Delta H=\Delta E \)
D. \( \Delta H \geq \Delta E \)


The function \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{l}\frac{e^{1 / x}-1}{e^{1 / x}+1}, \quad x \neq 0 \\ 0, \quad x=0\end{array}\right. \)
A. is continuous at \( x=0 \)
B. is not continuous at \( x=0 \)
c. is not continuous at \( x=0, \) but can be made continuous at \( x=0 \)
D. None of these


Setting of cement is:
A. exothermic reaction
B. endothermic reaction
C. neither endothermic nor exothermic
D. None of the above


With increase of temperature, the frictional force acting between two
surfaces increases.
A. True
B. False
c. Ambiguous
D. Data Insufficient


If two square matrices \( A \) and \( B \) are of same order and, \( \operatorname{Tr}(\boldsymbol{A})=\mathbf{3}, \boldsymbol{T} \boldsymbol{r}(\boldsymbol{B})=\mathbf{5} \)
\( \operatorname{then} \operatorname{Tr}(\boldsymbol{A}+\boldsymbol{B})= \)
A . 15
B. 8
\( c \cdot 3 / 5 \)
D. cannot be determined


The magnetic field in a certain region is given by \( \vec{B}=(4.0 \hat{i}-1.8 \hat{k}) \times 10^{-3} T \)
How much flux passes through a \( 5.0 \mathrm{cm}^{2} \) area loop in this region if the
loop lies flat on the \( x-y \) plane?
A \( \cdot 8 \times 10^{-5} \mathrm{Wb} \)
B . \( 3 \times 10^{-5} \mathrm{Wb} \)
c. \( 9 \times 10^{-7} W b \)
D. \( 3 \times 10^{-7} \mathrm{Wb} \)


If A.M of two numbers be twice their G.M
then the numbers are in the ratio
A \( .2: \sqrt{3} \)
B. \( 2+\sqrt{3}: 2-\sqrt{3} \)
c. \( 2+\sqrt{5}: 2-\sqrt{5} \)
D. 2:


If \( \overline{O A}=i+j+k, \overline{A B}=3 i-2 j+ \)
\( k, \overline{B C}=i+2 j-2 k \) and \( \overline{C D}=2 i+ \)
\( j+3 k \) then find the vector \( \overline{O D} \)
A. \( 7 i-2 j-6 k \)
B. \( 7 i+2 j+3 k \)
c. \( 7 i+2 j+5 k \)
D. None of these


If \( n^{2}=(n+6), \) then find the value of \( n \)
A. \( n=-2,-3 \)
в. \( n=3,2 \)
c. \( n=-3,2 \)
D. \( n=-2,3 \)


The resistance of wire of mass \( \mathrm{m} \) and
constant length is proportional to
A . \( m \)
в. \( \frac{1}{m} \)
\( \mathrm{c} \cdot m^{2} \)
D. \( m^{3} \)


The coordinates of a point in 3 -D space is \( (3,1,2) . \) Then the position vector of the point is:
A \( .3 \hat{i}+3 \hat{j}+3 \hat{k} \)
B. \( 3 \hat{i}+2 \hat{j}+\hat{k} \)
c. \( 3 \hat{i}+\hat{j}+2 \hat{k} \)
D. \( \hat{i}+2 \hat{j}+3 \hat{k} \)


Assertion
If infinity is taken as reference, the
gravitational potential is negative everywhere on the surface of earth.
Reason

Every body on its surface is bound to
gravitational attraction of earth.
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


If the standard deviation for the marks
obtained by a student in monthly tests is 36 then the variance is
\( A \cdot 6 \)
B. 36
\( c \cdot 1296 \)
D. None of these


The angles of some triangles are given below. Classify each triangle acuteangled,obtuse-angled or right-angled on the basis of its angles. \( \boldsymbol{a} \cdot \boldsymbol{9} \boldsymbol{0}^{o}, \boldsymbol{4} \boldsymbol{5}^{o}, \boldsymbol{4} \boldsymbol{5}^{\boldsymbol{o}} \)
\( b .60^{\circ}, 60^{\circ}, 60^{\circ} \)
\( c .80^{\circ}, 60^{\circ}, 40^{\circ} \)
\( \boldsymbol{d} . \boldsymbol{9} \boldsymbol{2}^{o}, \mathbf{5} \boldsymbol{0}^{o}, \boldsymbol{3} \boldsymbol{8}^{\boldsymbol{o}} \)
\( e .120^{\circ}, 50^{\circ}, 10^{\circ} \)
\( \boldsymbol{f} \cdot \boldsymbol{9} \boldsymbol{0}^{o}, \boldsymbol{3} \boldsymbol{5}^{o}, \boldsymbol{5} \boldsymbol{5}^{\boldsymbol{o}} \)


When hydrogen burns in oxygen, water is formed and when water is
electrolysed then hydrogen and oxygen are produced. What type of a
reaction takes place
(i) in the first case,
(ii) in the second case?
A. In both the cases, i.e. (i) and (ii), a combination reaction takes place
B. In the first case, a combination reaction takes place and in the second case, a decomposition reaction takes place.
c. In the first case, a combination reaction rakes place and in the second case, a displacement reaction takes place.
D. In the first case, a displacement reaction takes place and in the second case, a decomposition reaction takes place.


The equilibrium constant for the
isomerisation of butane at \( 25^{\circ} C \) is
\( \boldsymbol{K}_{c}=\mathbf{8} \)
Butane \( \rightarrow \) Isobutane
If \( 5.8 \mathrm{g} \) butane is introduced into a \( 12.5 \mathrm{L} \) vessel at \( 25^{\circ} C . \) What mass of isobutane
will be present at equilibrium?
A. \( 5.15 \mathrm{g} \)
B. 2.56
c. 7.49 g
D. 5.80 g


Evaluate \( \int_{0}^{2}\left(x^{2}+4\right) d x \)


Let
\( \boldsymbol{f}(\boldsymbol{x})=\left|\begin{array}{ccc}2 \cot \boldsymbol{x} & -\mathbf{1} & \mathbf{0} \\ \mathbf{1} & \cot \boldsymbol{x} & -\mathbf{1} \\ \mathbf{0} & \mathbf{1} & \mathbf{2} \cot \boldsymbol{x}\end{array}\right| \)
then


Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be a function defined by
\( \boldsymbol{f}(\boldsymbol{x})=(\mathbf{1}-\boldsymbol{x})^{\frac{1}{3}} \) is :
A. one-one and onto
B. many one and onto
c. one-one and into
D. many one and into


How many faradays are required to reduce one mole of \( M n O_{4}^{\ominus} \) to \( M n^{2+} ? \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c .3 \)
D.


The shortest distance between z-axis
and the line
\( \boldsymbol{x}+\boldsymbol{y}+\mathbf{2} \boldsymbol{z}-\mathbf{3}=\mathbf{0}=\mathbf{2} \boldsymbol{x}+\mathbf{3} \boldsymbol{y}+\mathbf{4} \boldsymbol{z} \)
\( 4, \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c \cdot 4 \)
D. 3


A stone is dropped freely from the top of a tower and it reaches the ground in \( 4 s \)
taking \( g=10 m s^{-2} \), calculate the height of the tower.
\( A \cdot 80 m \)
B. \( 40 \mathrm{m} \)
\( c \cdot 4 m \)
D. 20 \( m \)


What is the product B?


An object of size \( 7 \mathrm{cm} \) is placed at \( 27 \mathrm{cm} \)
in front of a concave mirror of focal
length \( 18 \mathrm{cm} . \) At what distance from the mirror should a screen be placed, so that a sharp focused image can be obtained ? Find the size and the nature
of the image.


Suggest the aspects of reproductive
health which need to be given specia
attention in the present scenario.


The mechanism of the reaction:
\( 2 N O+O_{2} \longrightarrow 2 N O_{2} \) is,
\( N O+N O \overbrace{K_{-1}}^{k_{1}} N_{2} O_{2}(f a s t) \)
\( N_{2} O_{2}+O_{2} \stackrel{k_{2}}{\longrightarrow} 2 N O_{2}(s l o w) \)
The rate constant of the reaction is :
A \( \cdot k_{2} \)
B. \( k_{2} k_{1}\left(k_{-1}\right) \)
\( c \cdot k_{2} k \)
D. \( k_{2}\left(\frac{k_{1}}{k_{1}}\right) \)


The middle term in the expansion of
\( \left(\frac{x}{y}+\frac{y}{x}\right)^{8} \) is
\( A \cdot^{8} C_{5} \)
в. \( ^{8} \mathrm{C}_{6} \)
\( \mathrm{c} \cdot^{8} \mathrm{C}_{4} \)
D. \( ^{8} \mathrm{C}_{2} \)


Man is ............ in nutrition.
A. Chemotrophic
B. Phototropic
c. Heterotrophic
D. All of the above


A block of weight 100 N lying in a
horizontal surface just to move when a
horizontal force of 25N acts on it.
Determine the coefficient of static
friction


Q Type your question
Model 18 el \( x \quad 20 \)
Model 5 el
Model \( z \) 19 11
The table above shows the number of TV
sets that were sold during a three-day
sale. The prices of models \( X, Y \) and \( Z \)
\( \operatorname{are} \$ 99, \$ 199, \) and \( \$ 299, \) respectively.
Which of the following matrix
representations gives the total income,
in dollars, received from the sale of the
TV sets for each of the three days?
\( \mathbf{A} \)
\( \begin{array}{ll}199 & 299\end{array} \) \( \left[\begin{array}{ccc}20 & 18 & 3 \\ 16 & 5 & 8 \\ 19 & 11 & 10\end{array}\right][99 \)
B. \( \left[\begin{array}{ccc}20 & 18 & 3 \\ 16 & 5 & 8 \\ 19 & 11 & 10\end{array}\right]\left[\begin{array}{c}99 \\ 199 \\ 299\end{array}\right] \)
\( c \)
\( 199 \quad 2 \)
99
299]\( \left[\begin{array}{ccc}20 & 18 & 3 \\ 16 & 5 & 8 \\ 19 & 11 & 10\end{array}\right] \)
D. \( \left[\begin{array}{c}99 \\ 199 \\ 299\end{array}\right] \quad\left[\begin{array}{ccc}20 & 18 & 3 \\ 16 & 5 & 8 \\ 19 & 11 & 10\end{array}\right] \)
E . \( \bullet \cdot 199\left[\begin{array}{ccc}20 & 18 & 3 \\ 16 & 5 & 8 \\ 19 & 11 & 10\end{array}\right]+299\left[\begin{array}{ccc}20 & 18 & 3 \\ 16 & 5 & 8 \\ 19 & 11 & 10\end{array}\right] \)


A student says that he had applied a force \( F=k \sqrt{x} \) on a particle moved in simple harmonic motion. He refuses to
tell whether \( k \) is a constant or not.
Assume that he has worked only with
positive \( x \) and no other force acted on
the particle.
A . As \( x \) increases \( k \) increases
B. AS \( x \) increases \( k \) decreases
C. As \( x \) increases \( k \) remains constant
D. The motion cannot be simple harmonic.


Calculate percentage degree of hydrolysis in a \( 0.1 ~ M \) solution of
\( \boldsymbol{C H}_{3} \boldsymbol{C O O N a} \)
Given that \( :\left[\boldsymbol{K}_{\boldsymbol{a}} \boldsymbol{o} \boldsymbol{f} \boldsymbol{C H}_{3} \boldsymbol{C O O H}=\right. \)
\( \left.\mathbf{1 0}^{-\mathbf{5}}\right] \)
A . 1.0
B. 0.01
\( c \cdot 10^{-4} \)
D. None of these


In a resting muscle fibre, tropomyosin
partially covers
A. ca-binding sites on actin
B. Ca-binding sites on troponin
c. Actin binding sites on myosin
D. Myosin binding sites on actin


If \( 3 \tan ^{-1} x+\cot ^{-1} x=\pi, \) then \( x \)
equals:
\( \mathbf{A} \cdot \mathbf{0} \)
B.
c. -1
D.


Assertion
\( (A): \overline{G A}+\overline{G B}+\overline{G C}=\overline{0} \) where \( G \) is
the centroid of triangle \( A B C \).
Reason
\( (R): \overline{A B}= \) P.V of \( B- \) P.V of \( A \)
A. Both Assertion \& Reason are individually true \& Reason is correct explanation of Assertion
B. Both Assertion \& Reason are individually true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true


Mark the correct alternative of the
following.
Let \( f(x)=2 x^{3}-3 x^{2}-12 x+5 \) on
\( [-2,4] . \) The relative maximum occurs at
\( \boldsymbol{x}=? \)
A . -2
B. - -
\( c \cdot 2 \)
D. 4


Solids, liquids and gases can diffuse
into
A. solids
B. liquids
c. gases
D. plasma


The highest value of \( \Psi \)
is
\( \mathbf{A} \cdot \mathbf{1} \)
B.
c. 10
D. 100


If radius of earth is increased, without
change in its mass, will the length of
day increase, decrease or remain same?


Which of the following is a tetrabasic acid?
A. orthophosphoric acid
B. Orthophosphorous acid
c. Metaphosphoric acid
D. Pyrophosphoric acid


8
8
8
8
8


The self inductance of a choke coil is 10
mH. When it is connected with a 10 V
D.C. source, then the loss of power is 20
watt. When it is connected with 10 volt
A.C. source loss of power is 10 watt. The frequency of A.C. source will be.
A . 50 нz
в. 60 на
c. 80 Нz
D. 100 Н \( z \)


A current carrying conductor
experiences a force when placed in a
magnetic field. Type 1 for true and 0 for false


If \( a+\frac{1}{a}=4 \) and \( a \neq 0, \) find \( a^{2}+\frac{1}{a^{2}} \)
A . 14
B. 12
c. 17
D. 19


Match the statements in Column A, with
those in Column B.


Which of the following is not a
drawback of Rutherford's model?
A. Rutherford did not mention any direct link between the charge of the nucleus and the atomic mass
B. He did not mention the relation between the charge of the nucleus and atomic number
C. Both A and B
D. None of these


The froth floatation process is used for the concentration of:
A. ore having low density
B. ore having magnetic nature
c. ore having high density
D. ore having water soluble gangue


A uniform rod of length \( L \) rests on a
frictionless horizontal surface. The rodd
is pivoted about a fixed frictionless axis at one end. The rod is initially at rest. A bullet travelling parallel to the horizontal surface and perpendicular to the rod with speed \( v \) strikes the rod at its centre and becomes embedded in it.
The mass of the bullet is one-sixth the
mass of the rod. What is the final
angular velocity of the rod?
A \( \cdot \omega=\frac{v}{9 L} \)
B. \( \omega=\frac{2 v}{9 L} \)
\( c \cdot \omega=\frac{3 v}{9 L} \)
D. \( \omega=\frac{5 v}{9 L} \)


are:
and
A. enatiomers
B. optical inactive diastereomers
c. optical active diastereomers
D. identical


Zeise's salt is :
A \( \cdot \operatorname{Fe}\left(\eta^{5}-C_{5} H_{5}\right)_{2} \)
B \( \cdot \operatorname{Cr}\left(\eta^{6}-C_{6} H_{6}\right)_{2} \)
c. \( _{K}\left[P t\left(\eta^{2}-C_{2} H_{4}\right) C l_{3}\right] \)
D. \( K\left[P t\left(\eta^{2}-C_{2} H_{4}\right)_{2} C l_{2}\right] \)


In a constant volume calorimeter, 5 g of gas with molecular weight 40 was burnt in excess of oxygen at 298 K. The temperature of the calorimeter was found to increase from \( 298 \mathrm{K} \) to 298.75
K due to the combustion process. Given that the heat capacity of the calorimeter is \( 2.5 \mathrm{kJK}^{-1} \), the numerical
value for the \( \triangle \boldsymbol{U} \) of combustion of the
\( \operatorname{gas} \operatorname{in} \mathrm{kJ} \operatorname{mol}^{-1} \mathrm{is} \)
A . 15
в. 12
\( c \cdot \) э०
D.


Five eighteenths is equals to
A \( \cdot \frac{15}{18} \)
в. \( \frac{18}{5} \)
c. 5.18
D. \( \frac{5}{18} \)


\( (\operatorname{cosec} A-\sin A)(\sec A-\cos A)= \)
\( \frac{1}{\tan A+\cot A} \)
[Hint: Simplify LHS and RHS separately]


Find the minimum wavelength of \( X \) -ray produced if \( 10 \mathrm{kV} \) potential difference is applied across the anode and cathode of the tube.
A \( \cdot 12.4 \mathrm{A}^{\circ} \)
B. 12.4 nm
\( c \cdot 1.24 \mathrm{nm} \)
D. \( 1.24 \mathrm{A}^{\circ} \)


One of the angles forming a linear pair is a right angle. What can you say about its other angle?


Hormone with no effect on heart beat is
A. Oxytocin
B. Adrenaline
c. Noradrenaline
D. Thyroxine


A ball is projected vertically upwards. Its speed at half of maximum height is \( 20 m / s . \) The maximum height attained by it is [Take \( \left.\boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} / \boldsymbol{s}^{2}\right] \)
A . 35 m
в. 15 т
\( c .25 m \)
D. \( 40 m \)


Find the area of the triangle with
vertices at the points:
(0,0),(6,0) and (4,3)


Points \( X \) and \( Y \) are taken on the sides
QR and RS, respectively of a parallelogram PQRS, so that \( Q X=4 X R \) sand \( \mathrm{RY}=4 \mathrm{YS} \). The line \( \mathrm{XY} \) cuts the line
PR at Z. Find the ratio PZ:ZR.
\( \mathbf{A} \cdot 4: 21 \)
в. 3: 4
c. 21: 4
D. 4: 3


One side of a right-angles triangular scarf is \( 80 \mathrm{cm} \) and its longest side is 1
\( \mathrm{m} . \) Find its cost at the rate of Rs 250 per
\( \boldsymbol{m}^{2} \)


The protostele in which xylem core is Smooth and rounded is
A. Haplostele
B. Actinostlele
c. Plectostele
D. siphonostele


Phosphorus mostly exists in free state.
A. True
B. False


A positively charged rod is brought near the disc of a positively charged gold leaf electroscope. State your observation
A. Divergence increases.
B. Divergence decreases.
c. Divergence remains same
D. cant say


Which of the following colors of light has the lowest frequency?
A. Yellow
B. Violet
c. orange
D. Blue
E. Green


Heterogamesis is
A. Formation of two types of gametes
B. Morphological distinction of male and female
gametes
C. Formation of two types of gametes by one sex and one type by other \( \operatorname{sex} \)
D. Formation of two types of gametes by both the sexes


A ray of light passing through an equilateral triangular prism gets deviated at least by \( 30 . \) Then, the refractive index of the material of the
prism must be :
\( \mathbf{A} \cdot \leq \sqrt{2} \)
в. \( \geq \sqrt{2} \)
\( c \cdot \leq \sqrt{3} \)
\( D \cdot \geq \sqrt{3} \)


The electronic configuration of calcium
is \( 2,8,8,2 . \) Find the valency of the element?
A . 1
B . 2
\( c .3 \)
D.


The electrical resistivity of a conducting wire is \( \mathrm{K} \). If its length and area of crosssection are doubled then the new
resistivity of the wire will be :
\( A \cdot K \)
в. 2 к
c. \( K / 2 \)
D. \( K / 4 \)


The force on a particle of mass \( 10 g \) is \( (10 \hat{i}+5 \hat{j}) N . \) If it starts from rest, what
would be its position at time \( t=5 s ? \)
A . \( (12500 \hat{i}+6250 \hat{j}) m \)
B. \( (6250 \hat{\imath}+12500 \hat{j}) m \)
c. \( (12500 \hat{i}+12500 \hat{j}) m \)
D. \( (6250 \hat{i}+6250 \hat{j}) m \)


The correct statement(s) pertaining to
the adsorption of a gas on a solid surface is(are):
(i) adsorption is always exothermic.
(ii) physisorption may transform into chemisorption at high temperature.
(iii) physisorption increases with increasing temperature but chemisorption decreases with increasing temperature
(iv) chemisorption is more exothermic than physisorption, however, it is very slow due to the higher energy of
activation.
A. (i) and (iv) only
B. (ii) and (iii) only
c. (i), (ii) and (iv) only
D. All of these


\( y=[x(x-3)]^{2} \) is increasing when
A \( \cdot 0<x<\frac{3}{2} \)
B. \( 0<x<\infty \)
c. \( -\infty<x<0 \)
D. \( 1<x<3 \)


It is hotter for the same distance over
the top of the fire than it is by the side is mainly because
A. air conducts heat upwards.
B. heat is radiated upwards
c. convection takes more heat upwards
D. convection, conduction and radiation all contribute significantly in transferring heat upwards.


Identify the correct reason for zero
dipole moment.
This question has multiple correct options
A. The molecule may be homoatomic
B. There may be a dative bond in the molecule
C. The molecule may be heteroatomic and symmetric
D. There may be lone pairs in the molecule


\( f \sum_{i=1}^{10}\left(x_{i}-15\right)= \)
12 and \( \sum_{i=1}^{10}\left(x_{i}-15\right)^{2}=18 \) then the
S.D. of observations \( \boldsymbol{x}_{1}, \boldsymbol{x}_{2} \ldots \ldots . . \boldsymbol{x}_{10} \) is
A \( \cdot \frac{2}{5} \)
B. \( \frac{3}{5} \)
\( c \cdot \frac{4}{5} \)
D. None of these


Optic thalami are
A. Optic lobes
B. Optocoels
C. Lateral walls of diencephalon
D. None of the above


Assertion
Heat and work are "definite quantities"
Reason
Heat and work are not properties of a
system their values depend on the path
of the process and vary accordingly.
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 \( A \) and \( B \) be two invertible matrices of
order \( 3 \times 3 . \) If det \( \left(A B A^{T}\right)=8 \) and det
\( \left(A B^{-1}\right)=8, \) then det \( \left(B A^{-1} B^{T}\right) \) is
equal to:
A \( \cdot \frac{1}{4} \)
B. 16
\( c \)
D. \( \frac{1}{16} \)


In the reaction \( \boldsymbol{P b O}+\boldsymbol{C} \rightarrow \boldsymbol{P b}+\boldsymbol{C O} \)
A. \( P b O \) is oxidised
B. c acts as oxidising agentt
\( c \cdot c \) acts as a reducing agent
D. This reaction does not represent a redox reaction


Mixed/Compound/Composite event


\( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\boldsymbol{x}^{2}+\boldsymbol{2} \boldsymbol{x}+\boldsymbol{4} \) find \( \boldsymbol{y} \) in terms of \( \boldsymbol{x} \)


The acid that can be used as a hypnotic
is :
A. tartaric acid
B. benzoic acid
c. barbituric acid
D. butanoic acid


Phenol with \( C C l_{4} \) and \( K O H \) gives salicylic acid. The reaction is known as:
A. Friedel-Craft reaction
B. Reimer - Tiemann reaction
c. Rosenmund's reaction
D. siemlet reaction


After attaining puberty boys develop voice.
A . Low
B. High pitchedd
c. Deep
D. Low pitched


In an atom an electron excites to the
fourth orbit.When it jumps back to the energy level one a spectrum is formed. Total number of spectral lines in this spectrum would be
\( A \cdot 3 \)
B. 4
\( c \cdot 5 \)
D. 6


Number of molecules having non-zero
dipole moment
\( \boldsymbol{B} e C l_{2}, \boldsymbol{X} e \boldsymbol{F}_{2}, \boldsymbol{N} \boldsymbol{H}_{3}, \boldsymbol{P} C l_{3} \boldsymbol{F}_{2}, \boldsymbol{P} \boldsymbol{C l}_{2} \boldsymbol{F}_{3}, \boldsymbol{B} \)


An example of G.P. is
A \( \cdot-1, \frac{1}{2}, \frac{1}{4}, \frac{1}{8} \dots \)
в. \( -1, \frac{3}{2}, \frac{1}{2},-\frac{1}{2} \)
c. \( _{1, \frac{1}{2}, \frac{1}{4}, \frac{1}{6} \ldots} \)
D. \( 1, \frac{1}{2}, \frac{1}{4}, \frac{1}{8} \ldots \)


Sublimation process is used:
A. to separate mixtures that contain a sublimate with a non-volatile component from a non-sublimate impurity
B. to separate mixtures that contain a sublimate with a volatile component from a non-sublimate volatile impurity
C. to separate mixtures that contain a sublimate with a volatile component from a non-sublimate impurity
D. none of above


A suitable unit for expressing the strength of electric field is :
A. v/C
B. \( \mathrm{c} / \mathrm{m} \)
c. N/C
D. c/N


A line touches a circle of radius \( 4 \mathrm{cm} \)
Another line is drawn which is tangent
to the circle. If the two lines are parallel then distance between them is
A \( .4 \mathrm{cm} \)
в. 6 ст
\( c .7 c m \)
D. \( 8 \mathrm{cm} \)


A ball of \( 0.5 k g \) collided with wall at \( 30^{\circ} \) and bounced back elastically. The speed of ball was \( 12 m / s . \) The contract
remained for 1 sec. What is the force
applied by wall on ball:
A \( \cdot 12 \sqrt{3} N \)
N \( \sqrt{3} \sqrt{3} \)
в. \( 6 \sqrt{3} N \)
c. \( 3 \sqrt{3} N \)
D. \( \sqrt{3} N \)


A square, non-singular matrix \( \boldsymbol{A} \)
satifies \( \boldsymbol{A}^{2}-\boldsymbol{A}+\mathbf{2} \boldsymbol{I}=\mathbf{0}, \) then \( \boldsymbol{A}^{-1}= \)
\( \mathbf{A} \cdot I-A \)
в. \( \frac{(I-A)}{2} \)
c. \( I+A \)
D. \( \frac{(I+A)}{2} \)


The velocity of a particle moving in the positive direction of the \( x \) axis varies as
\( V=\alpha \sqrt{x} \) where \( \alpha \) is a
positive constant. Assuming that at the moment \( t=0 \) the particle was
located at the point \( x=0, \) find
acceleration at \( t=51 s \)
\( A \cdot \alpha^{2} \)
B . \( \alpha^{2} / 2 \)
\( c \cdot a \)
D. \( \alpha^{3} \)


(1) The reflected pulse will be in same orientation of incident pulse due to a
phase change of \( \pi \) radians.
(2) During reflection the wall exerts a force on string in upward direction. For the above given two statements choose the correct option given below.
A. Only (1) is true
B. Only (2) is true
c. Both are true
D. Both are wrong


How can be rule be brought in
equilibrium by using an additional
weight of \( 40 g f ? \)
A. By placing the additional weight of \( 80 g f \) at the 30 cm mark
mark
c. By placing the additional weight of \( 40 g f \) at the 30 cm mark
D. By placing the additional weight of \( 40 g f \) at the 70 cm mark


The de-Broglie wavelength \( \left(\boldsymbol{\lambda}_{B}\right) \) associated with the electron orbiting in the second excited state of hydrogen atom is related to that in the ground
state \( \left(\lambda_{G}\right) \) by :
A \( \cdot \lambda_{B}=\lambda_{G} / 3 \)
B . \( \lambda_{B}=\lambda_{G} / 2 \)
\( \mathbf{c} \cdot \lambda_{B}=2 \lambda_{G} \)
D. \( \lambda_{B}=3 \lambda_{G} \)


Which of the following is/are derived by Hisenberg in his uncertainty principle?
A \( \cdot \Delta p \times \Delta x=\frac{h}{4 \pi} \)
B . \( \triangle v \times \triangle x=\frac{h}{4 \pi m} \)
C \( \cdot \triangle E \times \Delta t=\frac{h}{4 \pi} \)
D. \( \Delta p \times \Delta E=\frac{h}{4 \pi} \)


When HCl reacts with silver nitrate, it
forms a white precipitate of :
A . silver nitrite
B. silver hydroxide
c. silver chloride
D. Both (B) and (C)


A copper rod of diameter \( 1 \mathrm{cm} \) and
length \( 8 \mathrm{cm} \) is drawn into a wire of
length \( 18 \mathrm{cm} \) of uniform thickness. Find
the thickness of the wire.


Consider the cell;
\( \boldsymbol{V}^{2+}+\boldsymbol{V} \boldsymbol{O}^{2+}+\boldsymbol{2} \boldsymbol{H}^{+} \rightarrow \boldsymbol{2} \boldsymbol{V}^{3+}+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O} ; \boldsymbol{E}^{o}=\mathbf{0 . 6 1 6} \boldsymbol{V} \)
\( \boldsymbol{V}^{3+}+\boldsymbol{A} \boldsymbol{g}^{+}+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \boldsymbol{V} \boldsymbol{O}^{2+}+ \)
\( \mathbf{2} \boldsymbol{H}^{+}+\boldsymbol{A} \boldsymbol{g} ; \boldsymbol{E}^{o}=\mathbf{0 . 4 3 9} \boldsymbol{V} \)
Potential of \( \boldsymbol{E}_{\boldsymbol{V}^{3+} / \boldsymbol{V}^{2+}}^{\boldsymbol{o}} \) is :
(Given that \( \left.\boldsymbol{E}_{A g^{+} / A g}^{o}=\mathbf{0 . 7 9 9} \boldsymbol{V}\right) \)
A. \( -0.256 V \)
\( v \)
B. \( 0.256 \mathrm{V} \)
c. \( 1.055 V \)
D. \( 0.177 V \)


The formation of oxanium salt of
ether is due to:
A. protonation of 0 atom in ether
B. donation of an e pair by 0 atom in ether
c. the attachment of a proton to 0 atom in ether by coordination
D. all the above


Temperature of 2 moles of a
monoatomic gas is increased from T to
2T. Match the following two columns.


For a given alkyl group, the boiling point is in the order:
\( \mathbf{A} \cdot R I<R B r<R C l \)
B . \( R I<R C l<R B r \)
c. \( R B r<R I<R C l \)
D . \( R C l<R B r<R I \)


Two wires carrying equal current \( I \) are a
distance \( a \) apart.
If the current through wire one is doubled while the current through the wire two is tripled, what is the ratio of the force that wire two exerts on wire 1
\( F_{1} \) ) to the force that wire one exerts on
wire \( 2\left(F_{2}\right) ? \)
A . 4: 09
B. 2:03
\( c \cdot 1: 0 \)
D. 3:02
E. 9: 04


A steel ring of radius \( r \) and cross
sectional area \( A \) is fitted on to a wooden
disc of radius \( \boldsymbol{R}(\boldsymbol{R}>\boldsymbol{r}) . \) If Young;s
modulus be \( Y \), then the force with
which the steel ring is expanded, is
\( ^{\mathbf{A}} \cdot_{A Y} \frac{R}{r} \)
в. \( \quad A Y\left(\frac{R-r}{r}\right) \)
c. \( \frac{Y(R-r)}{A} \frac{r}{r} \)
D. \( \frac{Y r}{A R} \)


Assertion: The fluorine has lower
reactivity.

Reason: \( \boldsymbol{F}-\boldsymbol{F} \) bond has low bond
dissociation energy
A. Both assertion and reason are true and the reason is a correct explanation of the assertion
B. Both assertion and reason are true but reason is not a correct explanation of the assertion
c. Assertion is true but reason is false
D. Both the assertion and reason are false
E. Assertion is false but the reason is true


A hydrogen electrode placed in a buffer
solution of \( C H_{3} C O O N a \) and \( C H_{3} C O O H \)
in the ratios \( x: y \) and \( y: x \) has electrode
potential values \( E_{1} \) volts and \( E_{2} \) volts
respectively at \( 25^{0} \mathrm{C} \). The \( p K_{a} \) value of
acetic acid is :
\( \left[E_{1} \text { and } E_{2} \text { are oxidation potentials }\right] \)
A \( \cdot \frac{E_{1}+E_{2}}{0.118} \)
В. \( \frac{E_{2}-E_{1}}{0.118} \)
\( c \cdot-\frac{E_{1}+E_{2}}{0.118} \)
D. \( \frac{E_{1}-E_{2}}{0.118} \)


A die is thrown. If \( A \) is the event that the
number on upper face is an even, then
write sample space and event \( \boldsymbol{A} \) in set
notation.


A parallel beam of particles of mass \( m \)
moving with velocities \( v \) impinges on
a wall at an angle \( \theta \) to its normal. The number of particles per unit volume in the beam is \( n \). if the collision of
particles with the wall is elastic, then find the pressure exerted by this beam
on the wall.


On conducting U tube can slide inside
the other as shown in figure 25.28
maintaining electrical contacts
between the tubes. The magnetic field
\( B \) is perpendicular to the plane of the
figure. If each tube moves towards the
other at a constant speed \( v \) then the
induced emf in terms of \( B, l \) and \( v \)
where \( l \) is the width of each tube, will be
\( \mathbf{A} \cdot B l v \)
B. \( -B l v \)
\( c .2 B l v \)
D. zero


Find the mass of silver deposited when
a current of 1.5 ampere is passed through silver nitrate solution for 5 min. (Atomic mass of \( A g \) is 108 g)


115410
monochromatic point source emitting
light of wavelength \( \lambda=500 \) nm. A thin
lens of circular shape of focal length \( 0.10 m \) is cut into two identical halves
\( L_{1} \) and \( L_{2} \) by a plane passing through a
diameter. The two halves are placed
symmetrically about the central axis
SO with a gap of 0.5 mm. The distance
along the axis from \( S \) to \( L_{1} \) and \( L_{2} \) is
\( 0.15 m, \) while that from \( L_{1} \) and \( L_{2} \) to \( O \)
is 1.30 m. The screen at \( O \) is normal to
\( \boldsymbol{S O} \)
If the third intensity maximum occurs
at point \( A \) on the screen, find distance
OA in mm.


Sewage water is purified by
A. microorganisms
B . light
\( c . \) fish
D. aquatic plant


Natural rubber and gutta-percha
respectively, are
A. cis-polyisoprene and trans-polyisoprene
B. both are cis-polyisoprene
C. both are trans-polyisoprene
D. trans-polychloroprene and cis-polychloroprene


\( \int \cos x \sqrt{4-\sin ^{2} x} d x \)
A. \( \frac{t}{2} \sqrt{4-t^{2}}-\frac{1}{2} \cdot 4 \sin ^{-1} \frac{t}{2} \)
B \( \cdot \sqrt{4-t^{2}}+4 \sin ^{-1} \frac{t}{2} \)
C \( \cdot \frac{t}{2} \sqrt{4-t^{2}}+\frac{1}{2} \cdot 4 \sin ^{-1} \frac{t}{2} \)
D \( \cdot \frac{t}{2} \sqrt{4+t^{2}}+\frac{1}{2} \cdot 4 \sin ^{-1} \frac{t}{2} \)


Which one of the following is a strong electrolyte?
A. \( P b B r_{2} \)
в. \( C u C l_{2} \)
c. \( A g N O_{3} \)
D. All of the above


f \( \boldsymbol{P}=(\boldsymbol{x}, \boldsymbol{y}), \boldsymbol{F}_{1}=(\boldsymbol{3}, \boldsymbol{0}) \) and \( 16 \boldsymbol{x}^{2}+ \)
\( \mathbf{2 5} \boldsymbol{y}^{2}=\mathbf{4 0 0}, \) then \( \boldsymbol{P} \boldsymbol{F}_{1}+\boldsymbol{P} \boldsymbol{F}_{2} \) equals
\( \mathbf{A} \cdot \mathbf{8} \)
B. 6
c. 10
D. 12


Assertion
The preparation of lyophobic sol is more complex than the lyophilic sols.
Reason
Stabilizers are required to add extra stability to Iyophilic sols.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


In which of the following cases more friction is desirable?
A. Movement of piston in a cylinder
B. Braking of a vehicle
c. Running on a track
D. All of the above


A particle is dropped from rest from a
large height. Assume \( g \) to be constant
throughout, the motion. The time taken
by it to fall through successive
distances of \( 1 \mathrm{m} \) each will be
\( \mathbf{A} \cdot \) All equal, being equal to \( \sqrt{2 / g} \) second
B. In the ratio of the square roots of the integers 1,2,3
C. In the ratio of the difference in the square roots of the integers, i.e., \( \sqrt{1},(\sqrt{2}-\sqrt{1}),(\sqrt{3}-\sqrt{2}),(\sqrt{4}-\sqrt{3}), \ldots \)
D. In the ratio of the reciprocals of the square roots of the integers, i.e., \( \frac{1}{\sqrt{1}}, \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{3}}, \ldots \)


Vulcanization of rubber helps to make
rubber hard and resistant to hot and
cold conditions.
A. True
B. False


When a ray of light travels from an optically more denser medium to an optically less denser medium, the angle of incidence is always ........... than the angle of refraction.
A . less
B. more
c. same as
D. data insufficient


if \( a \neq 6, b, c \) satisfy \( \left|\begin{array}{ccc}a & 2 b & 2 c \\ 3 & b & c \\ 4 & a & b\end{array}\right|=0 \)
then \( a b c= \)
\( \mathbf{A} \cdot a+b+c \)
B.
\( c \cdot b^{3} \)
\( \mathbf{D} \cdot a b+b-c \)


Assertion
Carbon has ability to form long carbon
chains.
Reason
Carbon has a unique property of ability to form long straight and branched
chains called catenation.
Read the assertion and reason carefully
and answer the question on the basis of following options. You have to select the
one that best describes the two
statements.
A. If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
B. If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion
c. If Assertion is correct but Reason is incorrect
D. If Assertion is incorrect but Reason is correct.


In the reaction sequence.
\( A, B \) and \( C \) are given by the set are:
\( \mathbf{A} \cdot C H_{3} C H_{2} C H O, C H_{3} C H_{2} C H_{2} C l, C H I_{3} \)
B. \( C H_{3} C O C H_{3}, C C l_{3}-C_{V}-C H_{3}, C H I_{3} \)
\( \mathrm{c} \cdot \mathrm{CH}_{3} \mathrm{COCH}_{3}, \mathrm{CCl}_{3}-\underset{\mathrm{OH}}{C}\left(\mathrm{CH}_{3}\right)_{2}, \mathrm{CHI}_{3} \)
\( \mathrm{D} \cdot \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CHO}, \mathrm{CCl}_{3}-\underset{\mathrm{OH}}{\mathrm{CH}}-\mathrm{CH}_{2}-\mathrm{CH}_{3}, \mathrm{CHI}_{3} \)


A element \( C \) dissolves both in acid and
alkali. It is an example of :
A. allotropic nature of \( C \)
B. dimorphic nature of \( C \)
c. amorphous nature of \( C \)
D. amphoteric nature of \( C \)


A wire is bent in the form of a semicircle
of radius \( r \) and carries a current of \( i \)
The magnetic induction at the centre of the semicircle is
A \( \cdot \frac{\mu_{o} i}{2 r} \)
в. \( \frac{\mu_{o} i}{8 r} \)
c. \( \frac{\mu_{o} i}{4 r} \)
D. \( \frac{\mu_{o} i}{r} \)


Two force \( 5 k g-w t . \) And \( 10 k g-w t \) are
acting with an inclination of \( 120^{\circ} \)
between them. Find the angle when the
resultant marks with \( 10 k g-w t \)


Compare rates of loss heat by the body
at temperatures \( 527^{\circ} C \) and \( 127^{\circ} C \)
Temperature of surrounding is \( 27^{\circ} C \)


The fluid that reaches those parts of the body where blood does not reach


Eutrophication of water bodies leading to killing of fishes is mainly due to nonavailability of
A. Food
B. Light
c. Essential minerals
D. oxygen


Find the equation of a line passing through the points \( A(3,-5) \) and (4,-8)
A. \( 3 x+y=4 \)
B. \( 3 x+2 y=5 \)
\( c \cdot x+3 y=4 \)
\( D \cdot 4 x=3 y \)


If we multiply or divide both sides of a linear equation with a non-zero number, then the solution of the linear equation:
A. changes
B. remains the same
c. changes in case of multiplication only
D. changes in case of division only


Max scored 6 marks more than what he
did in the previous examination in
which he scored \( 30 . \) Maria scored 30
marks more than she did in the previous examination in which she
scored \( 60 . \) Who showed less
improvement?


If the gravitational constant is expressed in terms of dynesm\( ^{-2} \boldsymbol{k g}^{2} \)
how will the value of G change:
A \( .6 .67 \times 10^{-11} \) dynes \( k g^{2} m^{-2} \)
B . \( 6.67 \times 10^{-8} \) dynes \( k g^{2} m^{-2} \)
c. \( 6.67 \times 10^{-6} \) dynes \( k g^{2} m^{-2} \)
D. \( 6.67 \times 10^{-3} \) dynes \( \operatorname{kg}^{2} m^{-2} \)


Due to diagonal relationship between
Be and \( A l \) :
A. both are metals
B. both are metalloids
c. both form polymeric covalent hydrides
D. none of these


The ratio of the magnetic field at the centre of a current carrying circular wire and the magnetic field at the centre of a square coil made from the same length of wire is
A \( \cdot \frac{\pi}{2 \sqrt{2}} \)
в. \( \frac{\pi}{4 \sqrt{2}} \)
c. \( \frac{\pi^{2}}{4 \sqrt{2}} \)
D. \( \frac{\pi^{2}}{8 \sqrt{2}} \)


Figure show the lines of equipotentials
in the region. The potentials are shown with the equipotentials. If electric
intensities are \( E_{P} \) and \( E_{S}, \) then
\( \mathbf{A} \cdot E_{P}=E_{S} \)
В. \( E_{P}>E_{S} \)
\( \mathbf{c} \cdot E_{S}>E_{P} \)
D. \( E_{P}-E_{S}=0 \)


Instrument used to accelerate nuclear
projectiles is called
This question has multiple correct options
A. particle accelerator
B. cyclotron
c. nuclear fission reactor
D. none of these


A hall has dimensions \( 24 m \times 8 m \times \)
6 \( m \). The length of the longest pole which
can be accommodated in the hall is
A. 26
B. 28 m
\( c \cdot 30 m \)
D. 36 m


Which of the following is included in laws of refraction?
This question has multiple correct options
A \( \cdot \frac{\sin i}{\sin r}=\mu \)
B. The incident ray, the refracted ray and normal at the point of incidence all lie in the same plane
c. \( \angle i=\angle r, \) where \( r \) is angle of refraction
D. \( \angle i<\angle r \), where \( r \) is angle of refraction


A force \( F=x^{2}+2 x+1 \) acts on a
particle in the x direction, where \( \boldsymbol{F} \) is in
newton and \( x \) in metre. Find the work
done by this force during a displacement from \( \boldsymbol{x}=-\mathbf{1} \boldsymbol{m} \) to \( \boldsymbol{x}= \)
\( \mathbf{2 . 0 m} \)


A 50 kg crate is being pushed across a horizontal floor by a horizontal force of \( 575 \mathrm{N} \). If the coefficient of sliding friction is \( 0.25, \) what is the acceleration
of the crate?


The preparation of benzene from acetylene can also be said as:
A. oxidation
B. polymerization
c. dehydration
D. condensation


The internal resistance of a cell of emf 2
V is \( 0.1 \pi \). If it is connected to a
resistance of \( 3.9 \pi, \) then the voltage across the cell will be (in volts)
A \( .2 v \)
B. \( 0.5 v \)
c. \( 1.95 v \)
D. 2.5v


Shekar is one member of a group of 5
persons. If 3 out of these 5 persons is to be chosen for a committee, find the probability of Shekar being in the committee


Find the value of \( \mu \) for which one root of
the quadratic equation \( \mu x^{2}-14 x+ \)
\( 8=0 \) in 6 times the other.


Which of the following is not a unit of time?
This question has multiple correct options
A. Parsec
B. Light year
c. Micron
D. second


Richard got a discount of \( 10 \% \) on the suit he bought. The marked price was
\( \mathbf{5}, \mathbf{0 0 0} \) for the suit. If he had to pay sales tax of \( 10 \% \) on the price at which he bought, how much did he pay?


Maria invested 8000 Rs in a business
She would be paid interest at \( 5 \% \) per
annum compounded annually. Find :
(i) The amount credited against her
name at the end of the second year.
(ii) The interest for the 3 rd year.


\( 25 x^{2}-\left(x^{2}-36\right)^{2}= \)
A \( \cdot(x-4)(x+4)(x+9)(x-9) \)
B \( \cdot(x-4)(4+x)(x+9)(9-x) \)
\( \mathbf{c} \cdot(x+4)(x+4)(x-9)(x-9) \)
D \( \cdot(x-4)(4-x)(x+9)(9+x) \)


\( \operatorname{Let} \mathbf{P}=(\mathbf{1}, \mathbf{0},-\mathbf{1}) \boldsymbol{Q}=(-\mathbf{1}, \mathbf{2}, \mathbf{0}) \mathbf{R}= \)
\( (2,0,-3) S=(3,-2,-1), \) then the
length of the component of \( R S \) on \( P Q \) is
A . \( 1 / 3 \)
B . \( 2 / 3 \)
c. \( 4 / 3 \)
D. \( 5 / 3 \)


Mendeleev used a Sanskrit numeral
before the names of the predicted elements. What was the term used for
it?
A. sasi
B. Eka
c. Astan
D. Pancan


Find the area of the triangle formed by the midpoints of the sides of \( \Delta A B C \) where \( \boldsymbol{A}=(\mathbf{3}, \mathbf{2}), \boldsymbol{B}=(-\mathbf{5}, \mathbf{6}) \) and \( \boldsymbol{C}= \)
(8,3)


\( \operatorname{Let} p(x)=a x^{2}+b x+c \) be a quadratic
polynomial. It can have at most
A. One zero
B. Two zeros
c. Three zeros
D. None of these


How much amount of \( \boldsymbol{C u} \boldsymbol{S O}_{4} \cdot \boldsymbol{5} \boldsymbol{H}_{2} \boldsymbol{O} \)
required for liberation of \( 2.54 g I_{2} \) when titrated with \( K \) I?
A . \( 2.5 \mathrm{gm} \)
в. \( 4.99 \mathrm{gm} \)
c. \( 2.4 \mathrm{gm} \)
D. \( 1.2 \mathrm{gm} \)


The niche of a species is meant for
A. The specific place where an organism lives
B. The specific function of species and its competitive power
c. The habitat and specific functions of a species
D. None of these


What stimulates the auditory nerve?
A. the movement of the three ear ossicles
B. the movement of stirrup
C. the movement of fluid in the cochlea
D. all


The diagram shows two magnets and
two iron rods placed in a line.

Which magnetic poles are induced at the ends \( J \) and \( K \) of the iron rods?
A. Pole induced at end \( J-N \), pole induced at end \( K-N \)
B. Pole induced at end \( J-N \), pole induced at end \( K-S \)
C. Pole induced at end \( J-S \), pole induced at end \( K-N \)
D. Pole induced at end \( J-S \), pole induced at end \( K-S \)


The input resistance of a common emitter transistor amplifier, if the
output resistance is \( 500 \mathrm{k} \Omega \), the
current gain \( \alpha=0.98 \) and the power
\( \operatorname{gain} \) is \( 6.0625 \times 10^{6}, \) is
\( \mathbf{A} \cdot 198 \Omega \)
в. 300\Omega
c. \( 100 \Omega \)
D. \( 400 \Omega \)


The elevation in boiling point of a
solution of 13.44 g of \( C u C l_{2} \) (Molar mass 134.4 ) in \( 1 \mathrm{kg} \) water is:
\( \left[\boldsymbol{K}_{\boldsymbol{b}}=\mathbf{0 . 5 2} \mathrm{K} \text { molality }^{-1}\right] \)
A . 0.16
B. 0.05
c. \( 0 . \)
D. 0.2


Which of the following reagents is used
to test the presence of \( S O_{2} \) gas?
A. Acidified potassium manganate
B. Alkaline potassium manganate
c. Alkaline potassium dichromate
D. Acidified potassium dichromate


\( \operatorname{Sum} 3,-4, \frac{16}{3}, \dots \) to \( 2 n \) terms.


The correct option with respect to the Pauling electronegativity values of the elements is:
This question has multiple correct options
A. Ga <Ge
B. \( S i<A l \)
\( c \cdot p>s \)
D. B <C


Earthworm is
A. Ureotelic
B. Ammoneotelic
c. Uricotelic
D. Both (1) and (2)


Statement -1: NAND and NOR gates are called digital building blocks. Statement-2: The repeated use of NAND (or NOR) gates can produce all the basis or complicated gates.
A. Statement-1 is false, Statement-2 is true
B. Statement 1-is true, Statement - 2 is true and Statement- -2 is correct explanation of Statement-1
c. Statement 1 -is true, Statement - 2 is true and statement- - 2 is not correct explanation of statement- -
D. Statement 1-is true, Statement-2 is false


A potential difference of \( 100 \mathrm{V} \) is applied
across a resistor of resistance \( 50 \Omega \) for 6
minutes and 58 seconds. Find the heat
produced in 1) joule 2) calorie


\( \operatorname{Let} g(x)=1+x-[x] \quad \) and \( f(x)= \)
\( \left\{\begin{array}{lll}-1 & \text { if } & \boldsymbol{x}<\mathbf{0} \\ \mathbf{0} & \text { if } & \boldsymbol{x}=\mathbf{0}, \text { then } \forall \boldsymbol{x}, \boldsymbol{f} \boldsymbol{o} \boldsymbol{g}(\boldsymbol{x}) \\ \mathbf{1} & \boldsymbol{i f} & \boldsymbol{x}>\mathbf{0}\end{array}\right. \)
equals
\( A \)
B.
c. \( f(x) \)
D. \( g(x) \)


The ionizable valency of \( \mathrm{Ni} \) in \( \mathrm{Ni}(\mathrm{CO})_{4} \) is
\( A \cdot 2 \)
B. 4
\( c \cdot 0 \)
D.


Amongst \( N H_{3}, B e C l_{2}, C O_{2} \) and \( H_{2} O \)
the non-linear molecules are:
A. \( B e C l_{2} \) and \( H_{2} O \)
в. \( B e C l_{2} \) and \( C O_{2} \)
c. \( N H_{3} \) and \( H_{2} O \)
D. \( N H_{3} \) and \( C O_{2} \)


Let \( \boldsymbol{f}:[\mathbf{2}, \mathbf{7}] \rightarrow[\mathbf{0}, \infty] \) be a continuous
and differentiable function. Then, the
value of \( (\boldsymbol{f}(\mathbf{7})- \)
\( f(2)) \frac{(f(7))^{2}+(f(2))^{2}+f(2) \cdot f(7)}{3}, \) is
(where \( c \epsilon(2,7)) \)
\( \mathbf{A} \cdot 3 f^{2}(c) f^{\prime}(c) \)
B. \( 5 f^{2}(c) . f(c) \)
c. \( 5 f^{2}(c) \cdot f^{\prime}(c) \)
D. none of these


Solve and verify the result:
\( \frac{2 x}{3}=18 \)


If \( D \) be subset of the set of all rational
numbers which can be expressed as terminating decimals, then \( D \) is closed under the binary operations of:
A. addition, subtraction and division
B. addition, multiplication and division
C. addition, subtraction and multiplication
D. subtraction, multiplication and division


If each edge of a cube is doubled, how
many times will its volume increase?


Which of the following is a
characteristic of analog ICs?
A. They can be used for analog input and output signals only.
B. They cannot be used for analog input and output signals
C. Input signal is analog but output signal is digital.
D. Output signal is analog but input signal is digital.


the linear acceleration of the ball down
the plane is \( x g \sin \theta-\mu g \cos \theta . \) Find \( x \)


The dispersion of white light occurs
because the angle of of
different colours is different when
passing through the glass prism.
A . reflection
B. refraction
c. incidence
D. none of these


Calculate the number of moles in
(i) \( 8 g \) of oxygen atoms
(ii) \( 4.088 \times 10^{21} \) number of oxygen
atoms (Atomic mass of \( \boldsymbol{O}=\mathbf{1 6} \boldsymbol{u}) \)


A \( 100 N \) force makes an angle of \( \theta \) with
the \( x \) -axis and has a y-component of
\( 30 N . \) Then the \( x \) -component of the force
is:-
В. \( 95.39 N \)
c. \( 104.4 N \)
D. \( 0 N \)


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


Which of the following is an amphoteric oxide?
\( \mathbf{A} \cdot M g O \)
в. \( A l_{2} O_{3} \)
\( \mathrm{c} \cdot \operatorname{si} 0_{2} \)
D. \( P_{2} O_{5} \)


\( \mathbf{2} \cdot \boldsymbol{C}_{\mathbf{0}}+\mathbf{2}^{2} \cdot \frac{\boldsymbol{C}_{1}}{\mathbf{2}}+\mathbf{2}^{\mathbf{3}} \cdot \frac{C_{2}}{\mathbf{3}}+\ldots+ \)
\( \mathbf{2}^{n+1} \cdot \frac{C_{n}}{n+1}= \)
A \( \cdot \frac{3^{n+1}-1}{2(n+1)} \)
B . \( \frac{3^{n+1}-1}{n+1} \)
\( \mathrm{c} \cdot \frac{3^{n}-1}{n+1} \)
D. \( \frac{3^{n+1}}{n+1} \)


More than \( 70 \% \) of world's fresh water
is contained in
A. Antarctica
B. Polar ice
c. Glaciers and Mountains
D. Greenland


Find the mode for the following data:
\( \begin{array}{llll}\text { Farm } & 12 & 13 & 14 \\ \text { size } & & \end{array} \)
\( \mathbf{1 5} \)
Number
of
animals 4
A . 13
B. 14
c. 19
D. All the above


The movement of water from higher water potential to lower water potential through a semi-permeable membrane is called as
A. Diffusion
B. Osmosis
c. Plasmolysis
D. Imbibition


Two radioactive materials \( \boldsymbol{X}_{1} \) and \( \boldsymbol{X}_{2} \)
have decay constants \( 6 \lambda \) and \( 3 \lambda \) respectively. If initially they have the same number of nuclei, then the ratio of
the number of nuclei of \( X_{1} \) to that of \( X_{2} \) will be \( \frac{1}{e} \) after a time.
A \( \cdot \frac{1}{6 \lambda} \)
B. \( \frac{1}{3 \lambda} \)
c. \( \frac{3}{6 \lambda} \)
D. \( \frac{6}{9 \lambda} \)


A conducting loop carrying a current \( \boldsymbol{I} \) is placed in a uniform magnetic field pointing into the plane of the paper as
shown. The loop will have a tendency to:
A. contract
B. expand
c. move towards +ve x-axis
D. move towards ve x axis


is a good conductor of electricity.
A. lodine
B. Graphite
c. sulphur
D. Bromine


Simplify \( \sum_{n=1}^{3} \frac{n}{n^{4}+4} \)
A . 0.2773
B. 0.3753
c. 0.3353
D. 0.2573


An object weights \( 72 N \) on earth. Its weight at a height of \( \boldsymbol{R} / 2 \) from earth is:
A . \( 32 N \)
в. \( 56 N \)
c. \( 72 N \)
D. Zero


10 mangoes are to be distributed
among 5 persons. The probability that at least one of them will receive none is :
A \( \cdot \frac{35}{143} \)
в. \( \frac{108}{143} \)
c. \( \frac{18}{143} \)
D. \( \frac{125}{143} \)


The domain of \( \mathbf{f}(\mathbf{x})=\frac{\mathbf{3}}{\mathbf{4}-\mathbf{x}^{2}}+ \)
\( \log _{10}\left(x^{3}-x\right) \) is
A \( .(1,2) \)
B. (-1,0)\( \cup(1,2) \)
c. (1,2)\( \cup(2, \infty) \)
D. (-1,0)\( \cup(1,2) \cup(2, \infty) \)


If \( \vec{A}=-4 \hat{i}+3 \hat{j} \) and \( \vec{B}=2 \hat{i}+5 \hat{j} \) and
\( \vec{C}=\vec{A} \times \vec{B} \) then \( \vec{C} \) makes an angle of :
A \( \cdot 45^{0} \) with \( \mathrm{x} \) -axis
B. \( 180^{\circ} \) with \( Y \) -axis
\( c \cdot 0^{0} \) with \( \mathrm{z} \) -axis
D. \( 180^{\circ} \) with \( z \) -axis


Improper fraction of \( 12 \frac{1}{6} \) is
\( A \cdot \frac{72}{6} \)
в. \( \frac{73}{6} \)
c. \( \frac{108}{6} \)
D. \( \frac{85}{6} \)


Select \( X \) and \( Y \) out of:
\( M n O_{4}^{-} / O H^{-} \)
I: \( \boldsymbol{H} \boldsymbol{C O}_{3} \boldsymbol{H} \)
B. X-II,Y- -
c. \( x-1, y- \)


Find \( \boldsymbol{K} \)
If \( \boldsymbol{K}^{2}+\boldsymbol{4} \boldsymbol{K}+\mathbf{8}, \boldsymbol{2} \boldsymbol{K}^{2}+\mathbf{3} \boldsymbol{K}+\boldsymbol{6} \) and
\( 3 K^{2}+4 K+4 \) are any 3 consecutive
terms of \( \boldsymbol{A} \cdot \boldsymbol{P} \)


If \( f(x)=\frac{x+1}{x-1} ; \) then \( f\left(\frac{1}{2}\right)= \)
A \( \cdot \frac{1}{2} \)
B. \( -\frac{1}{2} \)
\( c \cdot \frac{3}{2} \)
D. -


Why can no two elements have a same
atomic number?


State and prove Brewster's law.


If \( A \) is a square matrix such that \( A^{2}= \)
\( I, \) then \( A^{-1} \) is equal to
A . \( I \)
в. 0
\( c . A \)
\( \mathbf{D} \cdot I+A \)


Draw, wherever possible, a rough sketch
of:

A triangle with only line symmetry and
no rotational symmetry of order more
than 1


Which of the following can convert
acidified \( C r_{2} O_{7}^{2-} \) to green product?
\( \mathbf{A} \cdot S O_{2}, H_{2} S O_{3} \) and \( H_{2} S O_{4} \)
B. \( S O_{2}, H_{2} S \) and \( H_{2} S O_{3} \)
\( \mathbf{c} \cdot S O_{3}, H_{2} S \) and \( F e^{3+} \)
D. \( S O_{3}^{-}, H_{2} S \) and \( F e^{+2} \)


is an additional amount of
money you pay based on a percentage of the selling price of goods and services that are purchased.
A. income tax
B. sales tax
c. property tax
D. VAT


Which one of the following isomers of
\( P B r C l_{3} \) have no dipole moment?
A. Only I
B. I and II
c. II and III


A compound of phosphorous and sulphur contains 1.24 g of phosphorous in 2.2 g of the compound. The formula of the compound is:
A \( \cdot P_{4} S_{3} \)
в. \( P_{3} S_{4} \)
\( \mathrm{c} \cdot P_{3} S_{2} \)
D. \( P_{2} S_{3} \)


The diameter of a circle is \( 10 \mathrm{cm} . \) Find
the length of the arc, in cm, (nearest integral value), when the
corresponding central angle is \( 45^{\circ} \)


If \( z=\frac{\lambda D}{4 d} \)
A \( \cdot[3-2 \sqrt{2}]^{2} \)
B \( \cdot[3+\sqrt{2}]^{2} \)
c. \( [3-\sqrt{2}]^{2} \)
D \( \cdot[3+2 \sqrt{2}]^{2} \)


Suppose the vitreous humour of the eye
dries off. Then what will be its effect on
our eyes?
A. The eye ball will swell up
B. The eyeball will collapse
c. A brighter image will be formed on retina
D. Cornea will become dry


Match the answers given in list 1 with the questions in list 2


In our body, carbon monoxide interferes with the transport of
A. Carbon dioxide
B. Ammonium sulphate
c. oxygen.
D. Hydrogen peroxide


Calvin cycle occurs in
A. Chloroplast
B. Cytoplasm
C . Mitochondria
D. Glyoxysomes


Find the magnitude and the direction of
acceleration of the body \( m_{2} \) when the
formerly stationary system of masses
starts moving.
A \( .5 g \)
B. \( 0.05 g \)
c. \( 0.005 g \)
D. \( 0.5 g \)


A ball is released from the top of height 'h' metres. It takes 't' seconds to reach
the ground. Where is the ball at the time t/2 \( s ? \)
A \( \cdot \operatorname{At}\left(\frac{h}{4}\right) \) from the ground
B. \( \operatorname{At}\left(\frac{h}{2}\right) \) from the ground
c. \( \operatorname{At}\left(\frac{3 h}{4}\right) \) from the ground
D. Depends upon mass and volume of the bal


The one that is not a carbonate is:
A. bauxite
B. siderite
c. calamine
D. malachite


The sound heard after reflection from a
rigid surface is called echo.
A. True
B. False


In a plane transmission grating, the width of a ruling is \( 12000 A \) and the width of a slit is \( 8000 A \), the grating element is:
A. \( 20 \mu m \)
В. \( 2 \mu m \)
c. \( 200 \mu m \)
D. \( 10 \mu m \)


Cathode ray tube is operating at \( 5 \mathrm{kV} \) Then,what is the K.E. acquired by the electrons?
A. 5 ev
B. 5 MeV
c. \( 5 \mathrm{keV} \)
\( D .5 v \)


Calculate the temperature values at
which the molecules of the first two
members of the homologous series,
\( C_{n} H_{2 n+2} \) will have the same rms speed
\( \operatorname{as} C O_{2} \) gas at \( 770 \mathrm{K} . \) The normal b.p. of
\( n- \) butane is 273 K. Assuming ideal gas behavior of \( n- \) butane up to this
temperature, calculate the mean velocity and the most probable velocity of its molecules at this temperature.


C-C and \( C=C \) bond lengths are unequal
in :
A. benzene
B. 1,3 buta-di-ene
c. 1,3 cyclohexa-di-ene
D. none of the above


Let \( U=R( \) the set of all real numbers ) If
\( A=\{x: x \in R, 0<x<2\}, B= \)
\( \{x: x \in R, 1<x \leq 3\} \), then
A. \( A \cup B=\{x: x \in R \text { and } 0<x \leq 3\} \)
B. \( A \cap B=\{x: x \in R \text { and } 1<x<2\} \)
c. \( A-B=\{x: x \in R \text { and } 0<x \leq 1\} \)
D. all of these


The early stage human embryo distinctly possesses
A. Gills
B. Gill slits
c. External ear (pinna)
D. Eye brows


What is the order of rotational
symmetry about the marked point?


Visible expression of the genetic phenomenon of crossing over is called
A. Recombination
B. Condensation
c. chiasmata
D. Spiralization


Two electric charges of \( 9 \mu C \) and \( -3 \mu C \) are placed \( 0.16 m \) apart in air. There will be
a point \( \mathrm{P} \) at which electric potential is
\( z \) ero on the line joining the two charges
and in between them. The distance of \( \mathrm{P} \)
from \( 9 \mu C \) charge is:
A \( .0 .14 m \)
B. \( 0.12 m \)
c. \( 0.08 m \)
D. \( 0.06 m \)


Charge density on the surface of a conducting solid depends upon:
A. The density of the conductor
B. The shape of the conductor
c. The size of the conductor
D. The age of the conductor
E. The substance of the conductor


If \( 1 \mathrm{g} \mathrm{cm}^{-3}=10^{3} \mathrm{kg} \mathrm{m}^{-3} \) then
\( 10^{6} k g m^{-3}= \)
A \( \cdot 10^{-3} g c m^{-3} \)
В \( \cdot 10^{6} g c m^{-3} \)
\( \mathbf{c} \cdot 10^{3} g c m^{-3} \)
D. \( 10^{-6} g c m^{-3} \)


Find and correct errors of the following mathematical expressions:
\( x+2 x+3 x=6 x \)


Solve the given differential equation:
\( \boldsymbol{y}^{2} \boldsymbol{d} \boldsymbol{x}+\left(\boldsymbol{x}^{2}-\boldsymbol{x} \boldsymbol{y}+\boldsymbol{y}^{2}\right) \boldsymbol{d} \boldsymbol{y}=\mathbf{0} \)


When copper reacts with conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
the oxidation state of sulphur is not changed.
If true enter 1 , else enter 0 .


Assertion
If \( \vec{u} \) and \( \vec{v} \) are unit vectors inclined at
an angle \( \alpha \) and \( \vec{x} \) is a unit vector
bisecting then angle between them, then \( \vec{x}=\frac{\vec{u}+\vec{v}}{\sqrt{2}} \)
Reason
If \( A B C \) be an isosceles triangle with
\( A B=A C, \) then vector representing
bisector of angle \( \boldsymbol{A} \) is given by \( \overrightarrow{\boldsymbol{A D}}= \) \( \frac{\overrightarrow{\boldsymbol{A B}}+\overrightarrow{\boldsymbol{A C}}}{2} \)
A. Both Assertion \& Reason are individually true \& Reason is correct explanation of Assertion
B. Both Assertion \& Reason are individually true but Reason is not the ,correct (proper) explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true


A force \( F=3 \hat{i}+2 \hat{j}+c \hat{j} N \) causes a displacement \( \vec{r}=c \hat{i}+4 \hat{j}+c \hat{k} m . \) The
work done is \( 36 J . \) Find the value(s) of \( c \)
A \( . c=3,7 \)
В. \( c=4,-7 \)
c. \( c=5,-7 \)
D. \( c=6,7 \)


Smooth surface produces - - - - friction than a rough surface.
A . Less
B. More
c. constant
D. None of these above


Find the mode for the following frequency table.
Wages(Rs.) \( \quad 250 \quad 300 \quad 350 \)
Number of
workers 15 16


Define the terms
(a) Plastic
(b) Adhesive


Find the sum of:
-127 and 300


The medium through which the sound travels fastest is empty space.
A. True
B. False
c. Ambiguous
D. Data insufficient


Radioactivity can be effected by :
A. temperature
B. pressure
c. radiation
D. all of these


Which of the following statements is
not true about \( K M n O_{4} ? \)
A. Its solution is unstable in acidic medium.
B. A green coloured solution containing \( M n O_{3}^{+} \) ions is
formed when a small quantity of \( K M n O_{4} \) is added to
concentrated \( H_{2} S O_{4} \)
C. \( M n O_{4}^{-} \) changes to \( M n^{2+} \) in basic solution
D. It acts as a self-indicator in the titration with \( F e^{2+} \) or
\( C_{2} O_{4}^{2-} \)


Find work done in the isobaric process.
A. \( W=1245 \mathrm{J} \)
B. \( W=1255 \) J
c. \( W=1254 J \)
D. \( W=1240 \mathrm{J} \)


If the Earth shrinks such that its
density becomes 8 times its present value then the new duration of the day in hours will be : (assume that there is
no change in axis of rotation of the earth)
A .24
B. 12
\( c \cdot 6 \)
\( D \)


A student has to answer 10 questions,
choosing at least 4 questions from each
of parts \( A \) and \( B . \) If there are 6
questions in part \( A \) and 7 questions in
part \( B \), in how many ways can the student choose 10 questions?


The length of a wire required to
manufacture a solenoid of length \( l \) and
self-induction \( L \) is (cross-sectional
area is negligible)
A \( \cdot \sqrt{\frac{2 \pi L l}{\mu_{0}}} \)
в. \( \sqrt{\frac{\mu_{0} L l}{4 \pi}} \)
c. \( \sqrt{\frac{4 \pi L l}{\mu_{0}}} \)
D. \( \sqrt{\frac{\mu_{0} L l}{2 \pi}} \)


What is the S.I. unit of electrical power?
A. watts
B. joules
c. volts
D. ampere


Calculate \( p H \) of \( 0.00424 M \)
aqueous solution of \( K O H \)


Solve the following inequation and write
the solution set :
\[
\begin{array}{r}
13 x-5<15 x+4<7 x+ \\
12, x \in R
\end{array}
\]
Represent the solution on a real number
line.


\( \int_{-\pi / 2}^{\pi / 2} \frac{d x}{\theta^{\sin x}+1} \) is equal to
\( A \cdot-\frac{\pi}{2} \)
в. \( \frac{\pi}{2} \)
\( c \cdot 0 \)
D.


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 (1) and (3) are true.


State whether true or false:
Natural fibres are obtained from plants and animals.
A. True
B. False


Uniform circular motion can also be
represented by a simple harmonic oscillator.

State whether given statement is True/False?
A. True
B. False


When the atomic magnetic moments
are randomly oriented in a solid its magnetic behavior is termed as
A. semi-magnetic.
B. anti-ferromagnetic
C. paramagnetic.
D. poly crystalline.


An earth's satellite moves in a circular
orbit with an orbital speed \( 6280 \mathrm{ms}^{-1} \)
Find the time of revolution.
A. 130 min
B. 145 min
c. 155 min
D. 175 min


\( \triangle A B C \sim \triangle D E F . \) Explain whether the
two similar triangles may be congruent
as well.


what is the measure of complementary
angle of \( 20^{\circ} \)


What happens when white phosphorus
is heated with concentrated \( N a O H \)
solution in an inert atmosphere of \( C O_{2} \) ?


Which of the following elements can be involved in \( \mathrm{p} \pi-d \pi \) bonding?
A. carbon
B. Nitrogen
c. Phosphorus
D. Boron


Match the column.
\( \begin{array}{ll}\text { Substrate } & \text { Enzyme } \\ \text { (A) Ribonucleotide } & \text { (i) Chitinase } \\ \text { (B) Chitin } & \text { (ii) Cellulase } \\ \text { (C) Cellulose } & \text { (iii) Ribonuclease }\end{array} \)
A . A-i, B-ii, C-iii
B. A-iii, B-i, C-ii
C . A-iii, B-ii, C-i
D. A-ii, B-ii, C-iii


Extraction of zinc from zinc blende is
achieved by:
A. electrolytic reduction
B. roasting followed by reduction with carbon
C. roasting followed by reduction with another metal
D. roasting followed by self reduction


Evaluate \( : \int \frac{1+\log x}{x(2+\log x)(3+\log x)} d x \)


set of irrational numbers is \( \{\sqrt{\mathbf{8}}, \boldsymbol{\pi}\} \)
A . True
B. False


Study the graph which shows results of
three different experiments \( P, Q \) and \( R \)
Now compare curves \( Q \) and \( R \) and
answer the following question:
Which factor has been altered to
produce the differences you can see
between two curves?
\( A \cdot C O_{2} \) concentration
B. Temperature
\( c . \) Both \( A \) and \( B \)
D. None of the above


\( \frac{\cos ^{-1}(41 / 49)}{\sin ^{-1}(2 / 7)}= \)
\( A \cdot 4 \)
B. 3
\( c \cdot 2 \)
\( D \)


If \( A \) and \( B \) are square matrices such
that \( B=-A^{-1} B A, \) then \( (A+B)^{2} \) is
equal to
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( A^{2}+B^{2} \)
c. \( A^{2}+2 A B+B^{2} \)
D. \( A+B \)


Prove that the points (4,5),(7,6),(6,3),(3,2) are the
vertices of a parallelogram. Is it a rectangle?


The terminal voltage of a cell in open circuit condition is
A. Less than its emf
B. More than its emf
c. Equal to its emf.
D. Depends on its internal resistance.


Two particles executing SHM of same frequency, meet at \( x=+A / 2, \) while
moving in opposite directions. Phase difference between the particles is


Potassium chlorate on decomposition gives:
This question has multiple correct options
A. potassium chloride
B. oxygen gas
c. chlorine gas
D. potassium oxide


Identify the correct statement about
work energy theorem
This question has multiple correct options
A. work done by all the conservative forces is equal to the decrease in potential energy.
B. work done by all the forces except the conservative forces is equal to the change in mechanical energy.
C. work done by all the forces is equal to the change in kinetic energy.
D. work done by all the forces is equal to the change in potential energy.


Complex formation in solution results in:
This question has multiple correct options
A. change in solubility of sparingly soluble salt
B. change in pH of solution
C . change in freezing point
D. change in chemical nature


A galvanometer (coil resistance \( 99 \Omega) \) is converted into a ammeter using a
shunt of \( 1 \Omega \) and connected as shown in
the figure ( \( i \) ). The ammeter reads \( 3 A \)
The same galvanometer is converted
into a voltmeter by connecting a resistance of \( 101 \Omega \) in series. This
voltmeter is connected as shown in
figure (ii). Its reading is found to be \( 4 / 5 \)
of the full scale reading. Find the range of the ammeter and voltmeter


The oxidation state of an element in a
particular compound can be defined as:
A. the charge acquired by its atom on the basis of electronegative consideration from other atoms in the molecule
B. the residual charge acquired by it s atom after removing all electronegative atoms from the molecule
C. the valency of the most electronegative atom present in the molecule
D. total number of electrons accepted by an atom to form a molecule


Write S.I. unit of charge
A .
B. A
C. \( \mathrm{N} \mathrm{m}^{2} \)
D. None of the above


A tuning fork of frequency \( 340 H z \) is vibrated just above the tube of \( 120 \mathrm{cm} \) height. Water is poured slowly in the tube. What is the minimum height of water necessary for the resonance?
speed of sound in air \( =340 m / s \)
\( \mathbf{A} \cdot 45 \mathrm{cm} \)
B. \( 30 \mathrm{cm} \)
c. \( 40 \mathrm{cm} \)
D. \( 25 \mathrm{cm} \)


State whether the given statement is true or false.

Statement: There are four categories among which various surfactants are
divided. They are
1. Non-ionic Surfactant
2. Anionic Surfactant
3. Cationic Surfactant
4. Zwitterionic surfactants
A. True
B. False


When a rectangular coil is rotated in a uniform magnetic field about an axis passing through its centre and perpendicular to the field, the emf induced in the coil varies:
A. Linearly
B. Exponentially
c. sinusoidally
D. None of these


If the number of electric lines of force
emerging out of a closed surface is \( 1000, \) then the charge enclosed by the surface is
A \( \cdot 8.854 \times 10^{-9} C \)
В. \( 8.854 \times 10^{-4} C \)
c. \( 8.854 \times 10^{-1} C \)
D. \( 8.854 C \)


The barrier potential of a p-njunction depends on:
(a) type of semi conductor material
(b) amount of doping
(c) temperature
Which one of the following is correct?
A. (a) and (b) only
B. (b) only
c. (b) and (c) only
D. (a), (b) and (c)


Very short answer type:
For tissue culture or micropropagation an explant is selected from the tip of the shoot.


With the help a labelled diagram explain, construction and working of an electric generator (Dynamo).


General electron configuration of d-block
elements is:
\( \mathbf{A} \cdot n s^{2} n p^{6} n d^{1-10} \)
B \( \cdot(n-1) d^{1-10} n s^{0-2} n p^{0-6} \)
\( \mathbf{c} \cdot(n-1) d^{1-10} n s^{1-2} \)
\( \mathbf{D} \cdot n d^{1-9} n s^{0-2} \)


A boy running, children fighting in the ground, baby chewing food are movements caused by growth.
A. True
B. False


Assertion
\( H N O_{3} \) oxidises sulphur to \( H_{2} S O_{4} \) acid (S+VI) but only oxidises selenium to
\( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{e} \boldsymbol{O}_{3}(\boldsymbol{S} \mathbf{e}+1 \mathbf{V}) \)
Reason
In selenium atoms, the electrons are more tightly held by the nucleus on account of increased nuclear charge.
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


Simplify:
\( \boldsymbol{p}^{2} \boldsymbol{q}-\boldsymbol{p} \boldsymbol{q}^{2}-\boldsymbol{p} \boldsymbol{q}+\boldsymbol{r}^{2} \)


Find the centre and radius of the circle
\( \boldsymbol{x}^{2}+\boldsymbol{y}^{2}+2 \boldsymbol{a} \boldsymbol{x}-\boldsymbol{2} \boldsymbol{b} \boldsymbol{y}+\boldsymbol{b}^{2}=\mathbf{0} \)


If the stamens can swing freely on the filaments, the condition is called
A. Basifixed
B. Dorsifixed
c. versatile
D. Adnate


In the presence of \( S O_{3}^{2-} \) and \( S^{2-} \) in a
mixture, on adding dil. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4}, \) one
notices:
A. \( S O_{2} \) and \( H_{2} S \) are not formed
B. \( S O_{2} \) and \( H_{2} S \) formed during change undergoes a redox change forming colloidal sulphur and thus, no smell
c. a smell of burning sulphur
D. a smell of rotten egg


The spray of PMA causes
A. Decrease in transpiration
B. Increase in transpiration
C. Increase in absorption
D. Increase in guttation


Prove by using venn diagram
\( \boldsymbol{A}-(\boldsymbol{B} \cup \boldsymbol{C})=(\boldsymbol{A}-\boldsymbol{B}) \cap(\boldsymbol{A}-\boldsymbol{C}) \)


On an xy-graph, what is the length of a line segment drawn from (3,7) to (6,5)
\( ? \)
A \( \cdot \sqrt{13} \)
B . 16
c. 17
D. 18
E . 20


In a new system, unit of mass is \( 10 \mathrm{kg} \) unit of length is \( 5 \mathrm{m} \) and unit of time is
10s. Then in the new system 5N is equal
to :
A. 5 new units
B. 10 new units
c. 15 new units
D. 20 new units


Consider this equilibrium, for which \( \Delta H<0 \)
\( \boldsymbol{H} \boldsymbol{g} \boldsymbol{O}(\boldsymbol{s})+\boldsymbol{4} \boldsymbol{I}^{-}(\boldsymbol{a} \boldsymbol{q} \cdot)+\boldsymbol{H}_{2} \boldsymbol{O}(l) \rightleftharpoons \)
\( \boldsymbol{H} \boldsymbol{g} \boldsymbol{I}_{4}^{2-}+\boldsymbol{2} \boldsymbol{O} \boldsymbol{H}^{-} \)
Which changes will increase the
equilibrium concentration \( \boldsymbol{H} \boldsymbol{g} \boldsymbol{I}_{4}^{2-} \) ?
I. Increasing the mass of \( \boldsymbol{H} \boldsymbol{g} \boldsymbol{O}(\boldsymbol{s}) \)
present
II. Increasing \( \left[\boldsymbol{I}^{-}\right] \)
III. Adding \( 1 M H C l \)
A. \( I \) only
B. II only
c. \( I I \) and \( I I I \) only
D. \( I, I I \) and \( I I I \)


Energy band gap between valence band and conduction band for conductor is:
A. more than semiconductors
B. Zero
c. more than insulators
D. None of these


The \( p K_{a} \) of acetylsalicylic acid (aspirin) is 3.5 The pH of gastric juice in human stomach is about \( 2-3 \) and the pH in
the same intestine is about \( 8 . \) Aspirin will be
A. Unionised in the small intestine and in the stomach
B. Completely ionised in the small intestine and in the stomach
c. lonised in the stomach and almost unionised in the samılı intestine
D. lonised in small intestine and almost unionised in the stomach


A charge \( q \) is placed at corner of a closed cube the flux related with any
face of cube.
A \( \cdot \) Must be \( \frac{q}{8 \epsilon_{0}} \)
в. мау be \( \frac{q}{\epsilon_{0}} \)
c. Must be zero
D. May be zero


A solid has hemispherical base with diameter \( 8.5 \mathrm{cm} \) and it is surmounted
by a cylinder height \( 8 \mathrm{cm} \) and diameter
of cylinder is \( 2 \mathrm{cm} \). Find the volume of this solid. \( (\pi=3.14) \)


Q Type your question
status when the applied force is
removed. They are termed as elastic. Those of which not regaining are called
plastic. There may be delay in the regaining in some materials. They are said to have got elastic aftereffect,
since they have gone beyond the elastic limit. Repeated application and removal of force break at any point time and so are avoided.
The stress strain graph for two materials \( A \) and \( B \) is shown in the
following figure:
If the intensity of \( A \) and \( B \) is \( E_{A} \) and \( E_{B} \) respectively, then
В. \( E_{A}>E_{B} \)
c. \( E_{A}<E_{B} \)
D. \( E_{A}<<E_{B} \)


Consider \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{ll}\boldsymbol{x}[\boldsymbol{x}]^{2} \log _{(1+x)} \boldsymbol{2} & \text { for }-1<\boldsymbol{x}<0 \\ \frac{\ln e^{x^{2}}+2 \sqrt{\{x\}}}{\tan \sqrt{x}} & \text { for } \mathbf{0}<\boldsymbol{x}<1\end{array}\right. \)
where \( \left[^{\star}\right] \&\left\{^{\star}\right\} \) are the greatest integer function \& fractional part function respectively, then -
A. \( f(0)=\ln 2 \Rightarrow f \) is continuous at \( x=0 \)
B. \( f(0)=2 \Rightarrow f \) is continuous at \( x=0 \)
C. \( f(0)=e^{2} \Rightarrow f \) is continuous at \( x=0 \)
D. f has an irremovable discontinuity at \( x=0 \)


For a matrix \( \boldsymbol{A}\left(\begin{array}{ccc}\mathbf{1} & \mathbf{0} & \mathbf{0} \\ \mathbf{2} & \mathbf{1} & \mathbf{0} \\ \mathbf{3} & \mathbf{2} & \mathbf{1}\end{array}\right), \) if \( \boldsymbol{U}_{1}, \boldsymbol{U}_{2} \)
and \( U_{3} \) are \( 3 \times 1 \) column matrices
satisfying \( \boldsymbol{A} \boldsymbol{U}_{\mathbf{1}}= \)
\( \left(\begin{array}{l}1 \\ 0 \\ 0\end{array}\right), A U_{2}\left(\begin{array}{l}2 \\ 3 \\ 0\end{array}\right), A U_{3}=\left(\begin{array}{l}2 \\ 3 \\ 1\end{array}\right) \) and \( U \) is
\( 3 \times 3 \) matrix whose columns are \( U_{1}, U_{2} \)
and \( U_{3} \)
Then sum of the elements of \( U^{-1} \) is
A . 6
B. \( 0(z e r o) \)
\( c . \)
D. \( 2 / 3 \)


The cofactors of elements in second row
of the determinant \( \left|\begin{array}{ccc}\mathbf{2} & \mathbf{- 1} & \mathbf{4} \\ \mathbf{4} & \mathbf{2} & \mathbf{- 3} \\ \mathbf{1} & \mathbf{1} & \mathbf{2}\end{array}\right| \) are
\( \mathbf{A} \cdot 5,6,4 \)
В. 6,0,-3
c. 5,1,8
\( \mathbf{D} \cdot 6,0,3 \)


\( \Delta B A C \cong \Delta D E C, A B \| D E, \) if \( \angle B \) is
\( 90^{\circ} \) and \( \angle C \) is \( 50^{\circ} \)
Find \( \angle A \) and \( \angle D=\dots \)
A . \( 35^{\circ} \)
В \( \cdot 50^{\circ} \)
\( \mathbf{c} \cdot 40^{\circ} \)
D. \( 55^{\circ} \)


Drift velocity \( v_{a} \) varies with the intensity
of elastic filed as per the relation:
A \( \cdot v_{a} \) is directly proportionate to
B. \( v_{a} \) is inversely proportionate to E
\( \mathbf{c} \cdot v_{a} \) is constant
D. \( v_{a} \) is directly proportional to \( E^{2} \)


A DNA molecule that recognizes specific transcription factors that can stimulate transcription of nearby genes is depicted by
A. Promoter
B. Enhancer
c. operator
D. Euchromatin
E. Heterochromatin


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


toppr
Q Type your question
The space between the conductors is
filled with air. The inner and outer
conductors are carrying currents of
equal magnitudes and in opposite directions

Then the variation of magnetic field
with distance from the axis is best
plotted as:
4
3
\( c \)
2


A ball of mass \( 5 ~ K g \) strikes against wall
at an angle of \( 45^{\circ} \) and is reflected at the
same angle. Find the change in
momentum


Two circular loops lie side by side in the same plane. One is connected to a
source that supplies an increasing current, the other is a simple closed ring. Is the induced current in the ring is in the same direction as that in the loop connected to the source or opposite? What if the current in the first loop is
decreasing?


Global warming can be controlled by
A. Reducing deforestation, cutting down use of fossil fuel
B. Reducing reforestation, increasing the use of fossil fuel
C. Increasing deforestation, slowing down the growth of human population
D. Increasing deforestation, reducing efficiency of energy usage


The unit of thermal capacity is :
A \( \cdot c a l /^{\circ} C \)
в. \( c a l / g \)
c. \( \operatorname{cal} / g^{\circ} C \)
D. cal


Name the property indicated in the following:
\( \frac{22}{23} \cdot \frac{23}{22}=1 \)


Glycolysis process completes in what
part of the cell?


Which of the following enzyme is produced in the kidneys?
A. Rennin
B. Renin
c. Uricase
D. Arginase


If doubling the voltage across a resistor doubles the current through the resistor
then
A. the resistor value decreased.
B. the resistor value increased
c. the resistor value did not change.
D. it is impossible to determine the change in the resisto value


Three concentric spherical metallic shells \( A, B \) and \( C \) of radii \( a, b \) and \( c(a<b<c) \) have charge densities
\( \sigma,-\sigma \) and \( \sigma \) respectively. If the shells \( A \)
and \( C \) are at same potential, then the
relation between \( a, b \) and \( c \) is
A \( . a+b+c=0 \)
B . \( a+c=b \)
c. \( a+b=c \)
D. \( a=b+c \)


The cosine of the obtuse angle formed by medians drawn from the vertices of
the acute angles of an isosceles rightangled triangle is \( -\frac{k}{5}, \) where \( k= \)


Brady's reagent is:
\( A \)
\( \left[C u\left(N H_{3}\right)_{4}\right] S O_{4} \)
B. \( K M n O_{4} / N a I O_{4} \)
\( c \)
D.


Two weight \( w_{1} \) and \( w_{2} \) are connected by a light thread which passes over a light smooth pulley. If the pulley is raised upward with an acceleration equal to \( g \) then tension in the thread will be
A \( \cdot \frac{2 w_{1} w_{2}}{w_{1}+w_{2}} \)
в. \( \frac{w_{1} w_{2}}{w_{1}+w_{2}} \)
c. \( \frac{4 w_{1} w_{2}}{w_{1}+w_{2}} \)
D. \( \frac{4 w_{1} w_{2}}{w_{1}-w_{2}} \)


What do you mean by closed vascular bundle ?
A. Presence of cambium
B. Absence of cambium
c. Presence of periderm
D. None of these


An object moves with constant acceleration a. Which of the following expressions are also constant?
A \( \cdot \frac{d v \mid}{d t} \)
в. \( \mid \frac{d v}{d t} \)
c. \( \frac{d\left(v^{2}\right)}{d t} \)
D. \( \frac{d\left(\frac{v}{|v|}\right)}{d t} \)


A ring disc and solid sphere are having
same speed of their COM at the bottom
of incline as shown in the figure. If
surface of incline is sufficiently rough.
The ratio of height by ring, disc and
sphere is
A . 15: 14: 20
B . 20: 15: 14
c. 14: 20: 15
D. 7: 5: 15


Differentiate: \( \mathbf{5}^{\mathbf{5}^{5 x}}=\boldsymbol{t} \)


At an airport, a bored child starts to walk backwards on a moving platform. The child accelerates relative to the
platform with \( a=-0.5 m / s^{2} \) relative to
the platform. The platform moves with a constant speed \( v=+1.0 m / s \) relative to the
stationary floor In 4.0 seconds, how much will the child have been displaced relative to the floor?
\( A \cdot 8 m \)
в. \( 4 m \)
\( c .3 m \)
D. \( 0 m \)
E. \( -4 m \)


The oxidation state of the underlined
element in the given compound is:
\( C_{12} H_{22} O_{11} \)
A \( .+5 \)
\( B \cdot+4 \)
\( c \cdot 0 \)
D. none of these


Chemisorption is irreversible.
A. True
B. False


Prove \( 3 \sin ^{-1} x=\sin ^{-1}\left(3 x-4 x^{3}\right), x \in \)
\( \left[-\frac{1}{2}, \frac{1}{2}\right] \)


A short bar magnet allowed to fall along the axis of horizontal metallic ring.
Starting from rest, the distance falls by the magnet in one second may be:
A . \( 4.0 \mathrm{m} \)
B. \( 5.0 \mathrm{m} \)
c. \( 6.0 m \)
D. \( 7.0 m \)


In the above cell cathodic cell reaction
and number of electrons involved are:
A \( \cdot 2 A g^{+}+2 e^{-} \rightarrow 2 A g, 2 e^{-} \)
B. \( A g^{+}+e^{-} \rightarrow A g, 1 e^{-} \)
\( \mathbf{c} \cdot 2 H^{+}+2 e^{-} \rightarrow H_{2}, 2 e^{-} \)
D. \( H^{+}+e^{-} \rightarrow \frac{1}{2} H_{2}, e^{-} \)


A solution in which, still more number of solute can be dissolved, is known as:
A. unsaturated
B. super saturated
c. saturated
D. dilute
E. concentrated


What type of bond formation takes place in liquor ammonia? Explain.


Pyrolysis of wood yields
A. Alcohol
B. Charcoal
C. Charcoal and wood gas
D. Charcoal, wood gas, tar and oil


Ramesh deposited \( R s .7800 \) in a bank which pays him \( 12 \% \) p.a.What is amount which he receives after 3
months.


The number \( 0.211211121111211111 \ldots \)
is a.
A. Terminating decimal
B. Non-terminating repeating decimal
c. Non-terminating and non-repeating decimal
D. None of these


The ratio ofthe radius of the orbit for the
electron orbiting the hydrogen nucleus to that of an electron orbiting a deuterium nucleus is
A . 1:
B. 1:
c. 2:
D. 1:3


The three solutions of the equation \( \boldsymbol{f}(\boldsymbol{x})=\mathbf{0} \) are \( -\mathbf{2}, \mathbf{0}, \) and \( \mathbf{3} . \) Therefore, the
three solutions of the equation \( f(x- \)
2) \( =\mathbf{0} \) are


The term in dependent of \( x \) in \( \left(1+x+2 x^{3}\right)\left(\frac{3 x^{2}}{2}-\frac{1}{3 x}\right)^{9} \)
A \( \cdot \frac{25}{54} \)
в. \( \frac{17}{54} \)
\( c \cdot \frac{1}{6} \)
D. \( -\frac{17}{51} \)


A particle moves along a straight line
according to the law \( s=16-2 t+3 t^{3} \)
where \( s \) metres is the distance of the
particle from a fixed point at the end of \( t \) second. The acceleration of the particle
at the end of 2 s is
A \( \cdot 3.6 m / s^{2} \)
B. \( 36 m / s^{2} \)
c. \( 36 k m / s^{2} \)
D. \( 360 m / s^{2} \)


Volume of a hemisphere is 19404 cubic \( \mathrm{cm} . \) The total surface area is
A. 2772 sq.cm
B. 4158 sq.cm
c. 5544 sq.cm
D. 1386 sq.cm


f the electric potential of the inner shell
is \( 10 V \) and that of the outer shell is \( 5 V \)
then the potential at the centre will be
\( 4.10 V \)
\( 3.5 V \)
\( c .15 V \)
D


Which of the following statements best explains the law of conservation of
mass?
A. \( 100 \mathrm{g} \) of water is heated to give steam
B. A sample of \( N_{2} \) gas is heated at constant pressure without any change in mass
c. \( 36 g \) of carbon combines with 32 g of oxygen to form \( 68 \mathrm{g} \) of \( \mathrm{CO}_{2} \)
D. 10 g of carbon is heated in vacuum without any change in mass


The size of the nucleus is
approximately:
A \( \cdot 10^{-18} \mathrm{m} \)
B . \( 10^{-10} \mathrm{m} \)
\( c \cdot 10^{-8} \mathrm{m} \)
D. none of these


Of the following outer electronic configurations of atoms, the highest oxidation state is achieved by which one of them?
A \( \cdot(n-1) d^{8} n s^{2} \)
B . \( (n-1) d^{5} n s^{1} \)
c. \( (n-1) d^{3} n s^{2} \)
D. \( (n-1) d^{5} n s^{2} \)


Which of the following is a rapid type of water absorption in plants?
A. Active absorption
B. Passive absorption
c. continuous absorption
D. Pulsating absorption


Two planets revolves around the sun
with frequencies \( N_{1} \) and \( N_{2} \) revolutions
per year. If their average radii (orbital)
be \( R_{1} \) and \( R_{2} \) respectively, then \( R_{1} / R_{2} \)
is equal to:
A \( \cdot\left(N_{1} / N_{2}\right)^{2 / 3} \)
a
B . \( \left(N_{1} / N_{2}\right)^{3 / 2} \)
C \( \cdot\left(N_{2} / N_{1}\right)^{2 / 3} \)
D. \( \left(N_{2} / N_{1}\right)^{3 / 2} \)


Molar mass of ethanol \( \left(C_{2} H_{5} O H\right) \) is :
A . 34.2
B. 38.9
c. 46.1
D. 45.1
E . 62.1


The potential difference across a \( 6 \Omega \)
resistor is \( 12 V . \) The current flowing in
the resistor will be
A \( .4 A \)
B. 2A
\( c \cdot 0.5 A \)
D. 1A


The value of 'g' at the depth from the ground goes on
A. increasing
B. fluctuating
c. decreasing
D. varying


Suppose for 40 observations, the variance is \( 50 . \) If all the observations are
increased by \( 20, \) the variance of these increased observation will be
A . 20
B. 50
c. 30
D. None of these


What happens when wilted vegetable are dipped in water
A. They regain their size
B. Remain to be same
c. colour will change
D. Decrease in size because of lose of water


A biconvex lens made of
glass(refractive index 1.5 ) has two
spherical surfaces having radii 20cm and \( 30 \mathrm{cm} . \) Calculate its focal length.


Express the trigonometric ratios
\( \sin A, \sec A \) and \( \tan A \) in terms of \( \cot A \)
\( ^{\mathbf{A}} \cdot \sin A=\frac{1}{\sqrt{\cot A+1}} \)
\( \sec A=\frac{\sqrt{\cot ^{2} A-1}}{\cot A} \)
\( \tan A=\frac{1}{\cot A} \)
B. \( \sin A=\frac{1}{\sqrt{\cot ^{2} A+1}} \)
\( \sec A=\frac{\sqrt{\cot ^{2} A+1}}{\cot A} \)
\( \tan A=\frac{1}{\cot A} \)
\( ^{\mathrm{C}} \cdot \sin A=\frac{1}{\sqrt{\cot A-1}} \)
\( \sec A=\frac{\sqrt{\cot ^{2} A+\sin A}}{\cot A} \)
\( \tan A=\frac{1}{\cot A} \)
D. None of these


Nitrogen can form only one chloride with
chlorine which is \( N C l_{3} \) whereas \( P \) can
form \( P C l_{3} \) and \( P C l_{5} . \) This is:
A. due to absence of \( d \) -orbitals in nitrogen
B. due to difference in size of \( N \) and \( P \)
c. due to higher reactivity of \( P \) towards \( C l \) than \( N \)
D. due to presence of multiple bonding in nitrogen


What was the aim of launching of Aryabhatta satellite?
A. To study the Moon
B. To study the Atmosphere
c. To study the Mars planet
D. To study the space


The force 'F' acting on a particle of mass \( \mathrm{m}^{\prime} \) is indicated by the force-time graph shown below. The change in momentum
of the particle over the time interval
from zero to 8 s is
A. 24 Ns
B. 20 Ns
\( c \cdot 12 \mathrm{Ns} \)
\( D \cdot 6 \mathrm{Ns} \)


If the mean of \( x+4,5,3,6,7 \) is 5 then
find \( x \)


Very short answer type.
Name the hormone that regulates each of the following: urinary elimination of
water


A chord of a circle of radius \( 15 \mathrm{cm} \)
subtends an angle of \( 60^{\circ} \) at the centre. Find the areas of the corresponding minor and major segments of the circle. (Use \( \pi=3.14 \text { and } \sqrt{3}=1.73) \)


For a particle executing SHM, which kinetic parameter will be equal to zero At equilibrium position,
A. velocity
B. acceleration
c. kinetic energy
D. none of the above


Find the sum of :
-52 and 52


Current \( I \) is flowing in a coil of area \( A \)
and number of turns is \( N \), then
magnetic moment of the coil is \( M \)
equal to
A. \( N I A \)
в. \( N I / A \)
\( \mathbf{c} \cdot N I / \sqrt{A} \)
D. \( N^{2} A I \)


Progressive diminishing size of
diatoms is prevented by the production of
A. Auxospores
B. Arthrospores
c. zoospores
D. Basidiospores


A metal rod \( 40 \mathrm{cm} \) long is dropped on to a wooden floor and rebounds into air.
Compressional waves of many frequencies are thereby set up in the rod. If the speed of compressional waves in the rod in \( 5500 \mathrm{m} / \mathrm{s} \), what is the lowest frequency of compressional waves to which the rod resonated as it
rebounds?
A . 675 \( \mathrm{H} \)
в. 6875 Н
c. \( 16875 \mathrm{Hz} \)
D. о нz


Fe is made passive by:
A \( \cdot \) dil. \( H_{2} S O_{4} \)
B. dil. НСl
c. conc. \( H N O_{3} \)
D. conc. \( H_{2} \) SO \( _{4} \)


In photorespiration, what is the role of peroxisome?
A. Help in oxidation of glycolate
B. Help in oxygenation of glycolate
c. Help in synthesis of PGA
D. Help in reduction of glyoxylate


Solve:
\( \mathbf{1 0} \leq-\mathbf{5}(\boldsymbol{x}-\mathbf{2})<\mathbf{2 0} \)


What would happen if a recombinant DNA is inserted within the coding
sequence of an enzyme, \( \beta \) galactosidase?
A. This will result in the inactivation of the enzyme
B. The presence of chromogenic substrate will give blue coloured colonies
c. The recombinant colonies do not produce any colour
D. Both (1) and (3) are correct