In the picture shown below, the man is:
A. applying force on the stool
B. applying pressure on the stool
c. not applying any force on the stool
D. adding to the gravitational pull of earth on the stool


State true or false:
With reference to the figure,
\( \mathbf{2} \boldsymbol{P} \boldsymbol{R}=\boldsymbol{A} \boldsymbol{B}+\boldsymbol{A} \boldsymbol{C} \)
A. True
B. False


Coal is formed from:
A. dead animals
B. dead vegetation
C. both of the above
D. none of the above


n the circuit shown, what is the
potential difference \( V_{P Q} ? \)
\( A \cdot+3 V \)
B. \( +2 v \)
c. \( -2 v \)
D. None of thes


Arrange the following according to proper sequence or hierarchical level Pisces, Chordata, Animalia
A. Pisces - chordata - Animalia
B. Chordata - Animalia - Pisces
c. Animalia - chordata - Pisces
D. None of the above


Differentiate (three) between DNA and
RNA.


In the process \( I_{2}+I^{-} \rightleftharpoons I_{3}^{-}( \) in aq
medium) intially there are 2 mole \( I_{2} \) and 2 mole I.But at equilibrium, due to
addition of \( A g N O_{3(a q)}, 1.75 \) mole of yellow ppt is obtained. \( K_{c} \) for the
process is \( \left(V_{\text {flask}}=1 d m^{3}\right) \) nearly
A. 0.08
B. 0.02
c. 0.16
D. 0.12


Assertion
The magnetic field at the ends of a very long current carrying solenoid is half of that at the center.
Reason
If the solenoid is sufficiently long, the field within it is uniform.
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


Write the structure of
Potassiumhexacyanochromate(III).
\( \mathbf{A} \cdot K_{4}\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right] \)
\( \mathbf{B} \cdot K_{3}\left[C r(C N)_{6}\right] \)
\( \mathbf{c} \cdot K_{3}\left[F e(C N)_{6}\right] \)
D \( \cdot K_{2}\left[N i(C N)_{4}\right] \)


Give an example of each of
homopolymer and copolymer.


In one of the industrial processes used for the manufacture of
sodium hydroxide, a gas \( X \) is formed as
a by-product. The gas \( X \) reacts
with lime water to give a compound \( Y \) which is used as a bleaching agent in the chemical industry. Identify \( \boldsymbol{X} \) and \( \boldsymbol{Y} \)
A. \( X \) is chlorine; \( Y \) is baking soda
B. \( X \) is chlorine; \( Y \) is bleaching powder
c. \( X \) is hydrogen; \( Y \) is potash
D. \( X \) is hydroge; \( Y \) is plaster of paris


Define element.
A. Can be broken down by chemical reactions into simpler substances
B. Cannot be broken down by chemical reactions into simpler substances
C. Maybe be broken down by chemical reactions into simpler substances
D. Both b and c


The way in which carbon is reused
through the ecosystem is known as
A. Energy recycling
B. The energy pyramid
c. The biotic/abiotic cycle
D. The carbon cycle


A mass of \( 0.5 \mathrm{kg} \) is suspended from wire, then length of wire increases by 3 mm then work done [RPMT 2000]
A \( \cdot 4.5 \times 10^{-3} \) Joule
B. \( 7.5 \times 10^{-3} \) Joule
c. \( 9.3 \times 10^{-3} \) Joule
D. \( 2.5 \times \) Joule


Chlorine is used to prepare:
A. phosgene
B. mustard gas
c. tear gas
D. All


Standard deviation of a distribution is
called
A. point estimation
B. sample error
c. standard error
D. interval estimation


A charged parallel plate capacitor of
distance
(d) has \( U_{0} \) energy. A slab of
dielectric constant (K) and thickness
(d) is then introduced between the
plates of the capacitor. The new energy of the system is given by:
A \( . \) к \( U_{0} \)
B. \( K^{2} U_{0} \)
\( c \cdot \frac{U_{0}}{K_{0}} \)
D. \( \frac{U_{0}}{K^{2}} \)


\( \Delta A B C \) is an isosceles right triangle
with area \( P . \) The radius of the circle that
passes through the point \( A, B \) and \( C \) is:
\( A \cdot \sqrt{P} \)
B. \( \sqrt{\frac{P}{2}} \)
c. \( \frac{\sqrt{P}}{2} \)
D. \( \sqrt{2 P} \)


Which element has the highest electronegativity?
A. \( K \)
в. \( C a \)
c. \( B r \)
D. \( K r \)
E. \( Z n \)


\( \forall \boldsymbol{n} \in \boldsymbol{N}, \boldsymbol{2} \cdot \boldsymbol{4}^{2 n+1}+\boldsymbol{3}^{3 n+1} \) is divisible by
\( A \cdot 7 \)
B. 5
c. 11
D. 209


Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}: \)
\( \sin \boldsymbol{x}-\boldsymbol{3} \boldsymbol{x}=\mathbf{5} \boldsymbol{y} \)


If \( \boldsymbol{A}=\left[\begin{array}{cc}\boldsymbol{a} & \boldsymbol{p} \\ \boldsymbol{b} & \boldsymbol{q} \\ \boldsymbol{c} & \boldsymbol{r}\end{array}\right]_{\mathbf{3} \times \mathbf{2}} \) then determinant
\( \left(A A^{T}\right) \) is equal to
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( a^{2}+b^{2}+c^{2} \)
c. \( p^{2}+q^{2}+r^{2} \)
D. \( p^{2}+q^{2} \)


Observe the table and state whether the
income tax is to be paid or not with
reason for the following persons having
taxable income of \( F . Y .2012-13 \) as
given below:
The
tax
is to
be
paidd
or
not \( \begin{array}{ll}\text { Person } & \begin{array}{l}\text { Age } \\ \text { (in } \\ \text { year) }\end{array} & \begin{array}{l}\text { Taxable } \\ \text { income }\end{array} \\ & \text { income }\end{array} \)
\begin{tabular}{lcc}
Sau. & \multirow{2}{*} {25} & Rs. \\
Shalini & & 1,30,000
\end{tabular}
Shri. Dhiraj \( \quad 32 \quad \begin{array}{l}\text { Rs. } \\ 2,85,000\end{array} \)
Shri
Shashibhai \( \quad 80 \quad \begin{array}{l}\text { Rs. } \\ 2,70,000 \\ \text { stret }\end{array} \) \( \begin{array}{lcc}\mathrm{smt} & & \mathrm{Rs} \\ \text { Minakshi } & & 2,40,000\end{array} \)


Determine the pH value of \( 0.001 M \)
acetic acid solution if it is \( 2 \% \) ionised at
this concentration. How can the degree
of dissociation of this acetic acid
solution be increased?


Which of the following reactions will get affected by increase in pressure? Also mention whether the change will cause the reaction to go to the right or left direction
\( \boldsymbol{C H}_{4}(\boldsymbol{g})+\mathbf{2 S}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{C S}_{2}(\boldsymbol{g})+ \)
\( 2 H_{2} S(g) \)
\( C O_{2}(g)+C(s) \rightleftharpoons 2 C O(g) \)
\( \mathbf{4} N \boldsymbol{H}_{3}(\boldsymbol{g})+\mathbf{5} \boldsymbol{O}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{4} \boldsymbol{N} \boldsymbol{O}(\boldsymbol{g})+ \)
\( 6 H_{2} O(g) \)
\( C_{2} H_{4}(g)+H_{2}(g) \rightleftharpoons C_{2} H_{6}(g) \)
\( \operatorname{COCl}_{2}(g) \rightleftharpoons C O(g)+C l_{2}(g) \)
\( \boldsymbol{C a} \boldsymbol{C O}_{3}(\boldsymbol{s}) \rightleftharpoons \boldsymbol{C a O}(\boldsymbol{s})+\boldsymbol{C O}_{2}(\boldsymbol{g}) \)


Assertion
Fruit formation process shows increase
in rate with passage of time.
Reason
Hydrolysis of ester is a homogeneous autocatalytic reaction.
A. Both Assertion and Reason are correct and the Reason
is the correct explanation of the Assertion
B. Both Assertion and Reason are correct but the Reason is not the correct explanation of the Assertion
C. The Assertion is correct but the Reason is incorrect
D. Both Assertion and Reason are incorrect


Minority carriers in a p-type
semiconductor are
\( \mathbf{A} \cdot \) free electrons
B. holes
C. neither holes nor free electron
D. both holes and free electrons


What is Rosenmund's reaction? What is
the purpose of adding \( B a S O_{4} \) in this
reaction?


What is the significance of atrio-
ventricular node and atrio-ventricular
bundle in the functioning of heart?


An ionic bond is formed when:
A. the combining atoms gain electrons
B. the combining atoms lose electrons
C. a metallic element reacts with a nonmetallic element
D. two metallic elements react


The real number \( x \) when added to its
inverse gives the minimum value of the
\( \operatorname{sum} \operatorname{at} x= \)
\( (\boldsymbol{x} \in+\boldsymbol{R}) \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. 3
\( c \cdot 2 \)
D.


The flowers are composed of
A. Petals, sepals, filament and carpel
B. Sepals, petals, stamen and pistil
C. Sepals, petals, anther and pistil
D. Petals, sepals, ovary and anther


A long cylindrical wire carries a linear charge density of \( 3 \times 10^{-8} \mathrm{Cm}^{-1} . \) An
electron revolve around it in a circular
path under the influence of the
attractive force. \( K E \) of the electron is :
A . \( 1.44 \times 10^{-7} J \)
В . \( 2.88 \times 10^{-17} J \)
D. \( 8.64 \times 10^{-17} J \)


A body is weighed by a spring balance
to be \( 1000 \mathrm{N} \) at the north pole. How much will it weigh(in \( \mathrm{N} \) ) at the equator? Account for the earth's rotation only.


The binding energy per nucleon of \( C^{12} \) is
\( E_{1} \) and that of \( C^{13} \) is \( E_{2} . \) The energy
required to remove one neutron from
\( C^{13} \) is
A \( \cdot 12 E_{1}+12 E_{2} \)
в. \( 13 E_{2}-12 E_{1} \)
c. \( 12 E_{2}-13 E_{1} \)
D. \( 13 E_{2}+12 E_{1} \)


The van't Hoff factor indicates the
number of solute particles produced per formula unit that dissolves.
If true enter 1 , if false enter 0 .


Why does the Sun appear reddish early in the morning?


Find the area of the given figure.


Convert \( 20^{\circ} \mathrm{C} \) into Kelvin and
Fahrenheit scale.


\( A B \) and \( C D \) are smooth, parallel, horizontal rails on which a conductor \( T \)
can slide. A cell, E, drives current
through the rails and \( T \)

This question has multiple correct options
A. The current in the rails will set up a magnetic field ove
B. T will experience a force to the right
C. \( T \) will experience a force to the left
D. Twill not experience any force


An LC circuit has \( L=5 \mathrm{mH} \) and \( C=20 \mu \mathrm{F} \)
\( \boldsymbol{v}=\mathbf{5} \times \mathbf{1 0}^{-\mathbf{3}} \) coswt is supplied.
is twice the resonant frequency. Find
the maximum charge stored in the
capacitor:
A. 66.6 nc
B. 11.3 nc
c. 23.2 nc
D. 33.3 nç


The most accepted line of descent in
human evolution is
A. Australopithecus\( \rightarrow \) Ramapithecus\( \rightarrow \)
Homo sapiens \( \rightarrow \) Homo habilis
B. Homo erectus \( \rightarrow \) Homo habilis \( \rightarrow \) Homo sapiens
C . Ramapithecus \( \rightarrow \) Homo habilis \( \rightarrow \) Homo erectus \( \rightarrow \)
Homo sapiens
D. \( \$ \$ \) Australopithecus lrightarrow Ramapithecus |rightarrow Homol erectus Irightarrow Homol habilis Irightarrow Homo sapiens


Alcoholic fermentation uses
A. Ribosomes
B. Golgi bodies
c. Mitochondrial enzymes
D. Cytoplasmic enzymes


Larynx is also called as
A. Voice box
B. Sound box
\( c . \) Black box
D. All of the above


A \( 120 m \) long train is going from East to
West with velocity \( 10 m s^{-1} \) A bird,
flying due East with velocity \( 5 m s^{-1} \)
crosses the train. Calculate the time
taken by the bird to cross the train.


Find the cube of 108


Find the bond order of peroxide ion.


Roots do not occur in
A. Wolffia
c. Utricularia
D. All the above


\( H_{2} O_{2} \) can be obtained when following
react with \( H_{2} S O_{4} \) except with:
A \( \cdot P b O_{2} \)
в. \( B a O_{2} \)
c. \( N a_{2} O_{2} \)
D. \( K O_{2} \)


Which of the following compounds is
not colored?
A. \( N a_{2} C u C l_{4} \)
в. \( N a_{2} C d C l_{4} \)
\( \mathbf{c} \cdot N a_{3}\left[F e(C N)_{6}\right] \)
D. \( K_{3}\left[F e(C N)_{6}\right] \)


Half life of a radio active element is 5
min 10 sec. Time taken for \( 90 \% \) of it to
disintegrate is nearly This question has multiple correct options
A. 100 min
B. 1000 sec
\( \mathrm{c} \cdot 10^{4} \mathrm{sec} \)
D. \( 10^{4} \) min


If a charged particle projected in a gravity-free room deflects, then
A. there must be an electric field
B. there must be a magnetic field
c. both fields cannot be zero
D. none of these


Hydrogen bonding is present in which of the following species? This question has multiple correct options
A. \( C H_{3} N H_{2} \)
в. \( C H_{3} \)
с. \( C H_{3} \) СООН
D. \( C C l_{3} C H(O H)_{2} \)


An exothermic reaction which proceeds with decrease in volume will give
maximum yield at high \( P \) and low \( T \)
If true enter 1 , if false enter 0 .


On the basis of following features identify the correct option.
I. This element exist in gaseous state at room temperature.
Il. This element has germicidal properties.
III. This element has 7 electrons in
valence shell.
A. lodine
B. Chlorine
C. Both (A) and (B)
D. Neither (A) nor (B)


The perimeter of an isosceles triangle is \( 42 \mathrm{cm} \) and its base is \( 1 \frac{1}{2} \) times its congruent sides. the area of the triangle


State the effect on the divergence of the leaves of a gold leaf electroscope on bringing a negatively charged rod near it if the electroscope is negatively
charged:
A. Divergence decreases
B. Divergence increases
c. Divergence remains same
D. can't say


(i) Write down the IUPAC name of the following complex:
\[
\left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{5}\left(\boldsymbol{N} \boldsymbol{O}_{2}\right)\right]\left(\boldsymbol{N} \boldsymbol{O}_{3}\right)_{2}
\]
(ii) Write the formula for the following
complex:

Potassium tetracyanidonickelate(II)


The radius of a planet is \( R_{1} \) and \( a \)
satellite revolves around it in a radius \( \mathrm{R} \)
2
Time period of revolution is \( T . \) Find the
acceleration due to gravity.
\( ^{\mathbf{A}} \cdot \frac{4 \pi^{2} R_{2}^{3}}{R_{1}^{2} T^{2}} \)
B. \( \frac{4 \pi^{2} R_{2}^{2}}{R_{1} T^{2}} \)
\( ^{\mathrm{c}} \cdot \frac{2 \pi^{2} R_{2}^{3}}{R_{1} T^{2}} \)
D. \( \frac{4 \pi^{2} R_{2}}{T^{2}} \)


Calculate the value of \( \log \boldsymbol{K}_{\boldsymbol{p}} \) (nearest integer) for the reaction, \( N_{2}(g)+ \)
\( \mathbf{3} \boldsymbol{H}_{\mathbf{2}}(\boldsymbol{g}) \rightleftharpoons \mathbf{2} \boldsymbol{N} \boldsymbol{H}_{\mathbf{3}}(\boldsymbol{g}) \) at \( \mathbf{2 5}^{\circ} \boldsymbol{C} . \) The
standard enthalpy of formation of
\( N H_{3}(g) \) is \( -46 \mathrm{kJ} \) and standard
entropies of \( N_{2}(g), H_{2}(g), N H_{3}(g) \) are
\( \mathbf{1 9 1}, \mathbf{1 3 0}, \mathbf{a n d} \mathbf{1 9 2} \mathbf{J K}^{-\mathbf{1}} \mathbf{m o l}^{-\mathbf{1}} \)
respectively. \( \left(\boldsymbol{R}=\mathbf{8 . 3} \boldsymbol{J} \boldsymbol{K}^{-1} \boldsymbol{m o l}^{-1}\right) \)


Fill in the blank:
Stars appear to move from
A. West to East
B. East to west
c. North to South
D. Northeast to Southwest


Assertion
Each molecule of NADPH and two ATP
are required for the fixation of one
molecule of \( \boldsymbol{C O}_{2} \)
Reason
Three molecule of NADPH and two ATP
are required the for fixation of one
molecule of \( \boldsymbol{C O}_{2} \)
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


For each of the differential equations
given in exercises 1 to 12 .find the general solution. \( \frac{d y}{d x}+2 y=\sin x \)


If \( a^{2}-a b=0, \) which of the following is
the correct conclusion?
\( \mathbf{A} \cdot a=0 \)
B . \( a=b \)
\( \mathbf{c} \cdot a^{2}=b \)
D. either \( a=0 \) or \( a=b \)


\( \boldsymbol{F}(\boldsymbol{x}, \boldsymbol{y})=\boldsymbol{x}^{3}+\boldsymbol{y}^{3}+\boldsymbol{3} \boldsymbol{x}^{2} \boldsymbol{y}+\boldsymbol{3} \boldsymbol{x} \boldsymbol{y}^{2} \cdot \mathrm{I} \)
this homogeneous function


Which of the following Lanthanoid is radioactive?
A. Cerium
B. Promethium
c. Thulium
D. Lutetium


For the given reaction the equilibrium expression
\( \mathbf{2} \boldsymbol{A}_{(\boldsymbol{g})}+\boldsymbol{B}_{(\boldsymbol{g})} \Leftrightarrow \mathbf{3} \boldsymbol{C}_{(\boldsymbol{g})}+\boldsymbol{D}_{(\boldsymbol{g})} \)
\( \mathbf{A} \cdot[A]^{2}[B][D] \)
В. \( \frac{[C]^{3}[D]}{\left.[A]^{2}[] B\right]} \)
c. \( \frac{[2 C][D]}{[2 A][B]} \)
D. \( \frac{[D]}{[A]^{2}[B]} \)
E \( \cdot \frac{[A]^{2}[B]}{[C]^{3}[D]} \)


Which of the following is true about vitamins?
A. Vitamins in the humanbody are needed in large amounts.
B. Vitamins are secreted by ductless glands.
C. Vitamins are synthesized by an organisms.
D. Vitamins A,D,E and K are fat soluble whereas vitamins
of the B group and vitamin C are water soluble


In the circuit shown in figure, all wires
have equal resistance \( r . \) The equivalent
resistance between \( A \) and \( B \) is \( - \) Find 5
\( \boldsymbol{x} \)


Mangifera is a..
A. Variety
B. Genus
c. Species
D. Class


If (-4,3) and (4,3) are two vertices of an
equilateral triangle, find the coordinates that the origin lies in the
interior,
(ii) exterior of the triangle.


Which is characteristic of unstable
nucleus?
This question has multiple correct options
\( \mathbf{A} \cdot n / p \) ratio is high
B. Low binding energy
C. High packing fraction
D. None of these


\( f\left(\sin ^{-1} x\right)^{2}+\left(\cos ^{-1} x\right)^{2}=\frac{17 \pi^{2}}{36}, \) find
\( \boldsymbol{x} \)


Taj mahal is threatened by which atmospheric pollutant released by Mathura refinery?
\( A \cdot S O_{2} \)
в. \( C O_{2} \)
c. \( C O \)
D. \( C l_{2} \)


The density of \( O_{2} \) at \( \mathrm{NTP} \) is \( 1.429 \mathrm{g} / \mathrm{L} \) the standard molar volume:
\( \mathbf{A} \cdot 22.4 L \)
B. \( 11.2 L \)
c. \( 33.6 L \)
D. \( 5.6 L \)


Maximum greenhouse gas is released by which country?
A. India
B. France
c. usa
D. Britain


Two particles having mass \( \mathrm{M} \) and \( \mathrm{m} \) are moving in circular paths having radii R and r. If their time periods are same then the ratio of their angular velocities will be:
A. MR : mrr
B. \( M: m \)
c. \( R: r \)
D. 1:


The food we take in our body travels through a long and complex path. Which starts from mouth to anus. Which is the
correct sequence of process on food in the digestive system?
A. Digestion \( \rightarrow \) Absorption \( \rightarrow \) Egestion \( \rightarrow \) Ingestion
B. Ingestion \( \rightarrow \) Egestion \( \rightarrow \) Digestion \( \rightarrow \) Absorption
c. Digestion \( \rightarrow \) Ingestion \( \rightarrow \) Absorption \( \rightarrow \) Egestion
D. Ingestion \( \rightarrow \) Digestion \( \rightarrow \) Absorption \( \rightarrow \) Egestion


Fossils are the
A. Dead remains of living organism
B. Coal mines
c. Kind of natural resource
D. Living beings


What is the correct representation of
solubility product of \( A g_{2} C r O_{4} ? \)
A \( \cdot\left[A g^{+}\right]^{2}\left[C r O_{4}^{-2}\right] \)
B \( \cdot\left[A g^{+}\right]\left[C r O_{4}^{-2}\right] \)
c. \( \left[2 A g^{+}\right]\left[C r O_{4}^{-2}\right] \)
D. \( \left[2 A g^{+}\right]^{2}\left[C r O_{4}^{-2}\right] \)


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):
os as \( 1+\sin \)


Prove that \( (1+\cot A+\tan A)(\sin A- \)
\( \cos A)=\sin A \tan A-\cot A \cos A \)


Which of the following cells give rise to the blastema in Hydra?
A . Interstitial cells
B. Mesenchymal cells
c. Neoblasts
D. All of the above


Which cell division is found during cleavage?
A. Amitosis
B. Mitosiss
c. closed mitosis
D. Meiosis


In which of the following is the radius of the first orbit minimum?
A. A Hydrogen atom
B. A tritium atom
C. Triply ionized beryllium
D. Double ionized helium


While preparing oxygen from potassium permanganate, the hard glass test tube must be held steady
A. True
B. False


Identify the information learned from
the curve of an acceleration time
graph?
A. The position of the object
B. The displacement of the object
c. The velocity of the object
D. The acceleration of the object
E. None of the above


Different states of matter
are
A . Gas
B. Liquid
c. Solid
D. all of above


The three thermodynamic states \( P, Q \)
and \( R \) of a system are connected by the paths shown in the figure given on the right. The entropy change in the processes \( \boldsymbol{P} \rightarrow \boldsymbol{Q}, \boldsymbol{Q} \rightarrow \boldsymbol{R} \) and \( \boldsymbol{P} \rightarrow \boldsymbol{R} \)
along the paths indicated are
\( \triangle S_{P Q}, \triangle S_{Q R} \) and \( \triangle S_{P R} \) respectively. If the process \( P \rightarrow Q \) is adiabatic and
irreversible, while \( P \rightarrow R \) is adiabatic
and reversible, the correct statement is:
A. \( \triangle S_{Q R}>0 \)
В. \( \Delta S_{P R}>0 \)
c. \( \triangle S_{Q R}<0 \)
D. \( \triangle S_{P Q}>0 \)


Assertion (A) : Due to annihilation of
electron positron pair, at least \( 2 \gamma \) -ray
photons are produced.
Reason
(R) : This is in accordance with
conservation of linear momentum.
A. Both A \& R are true and R is the correct explanation of \( A \)
B. Both A \& R are true and R is not correct explanation of
C. A is true but R is false
D. A is false but R is true


The distance moved by a freely falling body (starting from rest) during the \( 1^{s t}, 2^{n d} \) and \( 3^{r d} \ldots n^{t h} \) second of its
motion, are proportional to
A \( \cdot(n-1) \)
в. \( (2 n-1) \)
c. \( \left(n^{2}-1\right) \)
D. \( (2 n-1) / n^{2} \)


Which of the following quantum numbers are correct for the outermost
electron of sodium atom?
A. \( n=4, l=0, m=0, s=\pm 1 / 2 \)
В. \( n=3, l=0, m=0, s=-1 / 2 \)
c. \( n=3, l=1, m=\pm 1, s=+1 / 2 \)


The monoenergetic beams of electronics moving along \( + \) y direction enters a region of uniform electric and magnetic fields. If the beam goes straight through, then in which direction these simultaneously field \( \vec{B} \) and \( \vec{E} \) are directed?


Calculate the pH of \( 1.0 \times 10^{-3} \mathrm{M} \)
sodium phenolate, \( N a O C_{6} H_{5} \cdot K_{a} \) for
\( \boldsymbol{H} \boldsymbol{O} \boldsymbol{C}_{6} \boldsymbol{H}_{5} \) is \( \boldsymbol{0 . 6} \times \mathbf{1 0}^{-10} \)


If in the expansion of \( (1-x)^{2 n-1}, \) the
coefficient of \( x^{r} \) denoted by \( a_{r}, \) then :
\( \mathbf{A} \cdot a_{r-1}+a_{2 n-r}=0 \)
В \( \cdot a_{r-1}-a_{2 n-r}=0 \)
c. \( a_{r-1}+2 a_{a n-r}=0 \)
D. None of these


Why does the amplitude of a vibrating body continuously decrease during damped vibrations?


Which structure represents a
compound that dissolves in water to
form an acidic solution?
\( A \)
B. \( H-C-C=C \)
\( _{H} \)
\( c \)
\( D \)


A ball falling-in a lake of depth \( 400 \mathrm{m} \) has a decrease of \( 0.2 \% \) in its volume at
the bottom. The bulk modulus of the
material of the ball is \( \left(\text { in } N m^{-} 2\right) \)
A \( \cdot 9.8 \times 10^{9} \)
B . \( 9.8 \times 10^{10} \)
c. \( 1.96 \times 10^{10} \)
D. \( 9.8 \times 10^{11} \)
E \( .1 .96 \times 10^{9} \)


The domain of the function \( f(x)= \) \( \sqrt{\cos ^{-1}\left(\frac{1-|x|}{2}\right)} \)
A \( \cdot(-3,3) \)
в. [-3,3]
C \( \cdot(-\infty,-3) \cup(-3, \infty) \)
D. \( (-\infty,-3) \cup(3, \infty) \)


Non-metals which are present in fertilizers and enhance the growth of
plants is:
A. nitrogen
B. phosphorus
c. potassium
D. both \( A \) and \( B \)


If \( y=x^{2} \sin x, \) then \( \frac{d y}{d x} \) will be
A. \( x^{2} \cos x+2 x \sin x \)
B. \( 2 x \sin x \)
C \( \cdot x^{2} \cos x \)
D. \( 2 x \cos x \)


The angle subtended by the vector \( \overline{\boldsymbol{A}}= \) \( 4 \hat{i}+3 \hat{j}+12 \hat{k} \) with the \( x \) -axis is
A \( \cdot \sin ^{-1}\left(\frac{3}{13}\right) \)
B \( \cdot \sin ^{-1}\left(\frac{4}{13}\right) \)
c. \( \cos ^{-1}\left(\frac{4}{13}\right) \)
D \( \cdot \cos ^{-1}\left(\frac{3}{13}\right) \)


If \( \sin \theta=\cos \left(2 \theta-45^{\circ}\right), \quad 0<(2 \theta- \)
\( \left.45^{\circ}\right)<90^{\circ}, \) then \( \tan \theta \)
A . -1
B.
c.
D. \( \frac{1}{\sqrt{3}} \)


In acids, methyl orange turns:
A . red
B. blue
c. green
D. yellow


A long straight conductor, carrying a
current \( i, \) is bent to form an almost
complete circular loop of radius \( r \) as
shown. The magnetic field at the centre
of the loop:
A \( \cdot \) has magnitude \( \frac{\mu_{0} i}{r}\left(1-\frac{1}{\pi}\right) \)
B. has magnitude \( \frac{\mu_{0} i}{r}\left(1+\frac{1}{\pi}\right) \)
c. has magnitude \( \frac{\mu_{0} i}{2 r}\left(1-\frac{1}{\pi}\right) \)
D. has magnitude \( \frac{\mu_{0} i}{2 r}\left(1+\frac{1}{\pi}\right) \)


A car is traveling at a high speed when it banks into a sharp left turn. Which of the following statements best describes the reason a passenger in the vehicle is pressed outwards against the
right side of the vehicle?
A. The centrifugal force of the circular turn pushes them outwards
B. The centripetal force of the circular turn pushes them outwards
C. The passenger's inertia maintains their velocity through the circular path since objects in motion tend to stay in motion
D. The force of friction between the seat and the passenger does not generates sufficient force
E. The force exerted by the door on the passenger does not exert sufficient force


The structure of the compound with
molecular formula \( C_{8} H_{14} \) that has 12
secondary and 2 tertiary H atoms is:
A. Bicyclo [2.2.2] octane
B. 1,2-Dimethyl cyclohexane
c. Bicyclo [3.2.1] octane
D. Tricyclo [2.2.2.0] octane


The heat measured for a reaction in
bomb calorimeter is :
A \( . \Delta G \)
в. \( \Delta H \)
c. \( \Delta U \)
D. \( P \Delta V \)


A cyclotron is used to:
A. accelerate neutrons
B. accelerate electrons
c. accelerate protons
D. accelerate \( \alpha \) -particles


The vector \( \overrightarrow{A B}=3 \hat{i}+4 \hat{k} \) and \( \overrightarrow{A C}= \) \( \mathbf{5} \hat{\mathbf{i}}-\mathbf{2} \hat{\mathbf{j}}+\mathbf{4} \hat{\boldsymbol{k}} \) are the sides of a \( \boldsymbol{\Delta} \boldsymbol{A} \boldsymbol{B} \boldsymbol{C} \)
where \( A \) is the origin. The length of
median through \( \boldsymbol{A} \) is
A. \( \sqrt{72} \)
B. \( \sqrt{33} \)
c. \( \sqrt{288} \)
D. \( \sqrt{18} \)


Mixotrophic nutrition is exhibited by the kingdom
A. Monera
B. Protista
c. Animalia
D. None of the above


The solubility of a sparingly soluble salt
\( A . B_{y} \) in water at \( 25^{\circ} \mathrm{C} 1.4 \times 10^{4} \) M. The
solubility product is \( 1.1 \times 10^{11} . \) The
possibilities are:
A. \( x=1, y=2 \)
в. \( x=2, y=1 \)
c. \( x=1, y=3 \)
D. \( x=3, y=1 \)


The angular momentum of an electron in the hydrogen atom is \( \frac{3 h}{2 \pi} \). Here h is Planck's constant. The kinetic energy of
this electron is:
A . 4.53 ev
B. 1.51 eV
c. 3.4 ev
D. 6.8 ev


A potential difference of \( 5 V \) is applied
across a conductor of length \( 10 \mathrm{cm} . \) If
drift velocity of electrons is \( 2.5 \times \)
\( 10^{-4} m / s, \) then electron mobility will be
A \( .5 \times 10^{-4} \mathrm{m}^{2} \mathrm{V}^{-1} \mathrm{s}^{1} \)
B. \( 5 \times 10^{-6} \mathrm{m}^{2} \mathrm{V}^{-1} \mathrm{s}^{1} \)
c. \( 5 \times 10^{-2} \mathrm{m}^{2} \mathrm{V}^{-1} \mathrm{s}^{1} \)
D. zero


What is the minimum and maximum
unit of measurement of mass?


When magnesium ribbon burns in air, it forms white ash. The chemical name of
white ash is:
A. Magnesium dioxide
B. Milk of magnesium
c. Milk of magnesia
D. Magnesium oxide


The various types of hydrides and
examples of each type are given below. Hydride types Compounds
\( (A) \) Electron deficient
\( (i) L i H \)
\( (B) \) Saline
\( (i i) C H_{4} \)
\( (C) \) Electron precise
\( (i i i) N H_{3} \)
\( (D) \) Interstitial
\( (i v) B_{2} H_{6} \)
\( (\boldsymbol{E}) \) Electron rich
\( (\boldsymbol{v}) \boldsymbol{C r} \boldsymbol{H} \)
Choose the correct matching from the codes given below.
A \( \cdot(A)-(i i),(B)-(i v),(C)-(v),(D)-(i i i),(E)-(i) \)
B. \( (A)-(i v),(B)-(i),(C)-(i i),(D)-(v),(E)-(i i i) \)
C. \( (A)-(i v),(B)-(i i i),(C)-(v),(D)-(i i),(E)-(i) \)
D. \( (A)-(v),(B)-(i i i),(C)-(i v),(D)-(i i),(E)-(i) \)
E \( .(A)-(i v),(B)-(v),(C)-(i),(D)-(i i),(E)-(i i i) \)


During inspiration, the diaphragm
A. Relaxes to become dome-shaped
B. Contracts and flattens
c. Expands
D. shows no change


Least reactive isotope of hydrogen among the following is:
\( \mathbf{A} \cdot_{1} H^{1} \)
B \( \cdot_{1} D^{2} \)
\( \mathbf{c} \cdot_{1} T^{3} \)
D. all are equally reactive


One plate of parallel plate capacitor is smaller than the other. The charge on
the smaller plate:
A. will be less than other
B. will be more than other
c. will be equal to other
D. will depend upon the medium between the plates


The load versus strain graph for four
wires of the same material is shown in
the figure. The thickest wire is
represented by the line
\( A \cdot O B \)
в. \( O A \)
\( c \cdot O D \)
D. \( O C \)


If \( \overrightarrow{\mathrm{A}}, \overrightarrow{\mathrm{B}} \) and \( \overrightarrow{\mathrm{C}} \) are non-zero vectors, and if \( \overrightarrow{\mathbf{A}} \times \overrightarrow{\mathbf{B}}=\mathbf{0} \) and \( \overrightarrow{\mathbf{B}} \times \overrightarrow{\mathbf{C}}=\mathbf{0}, \) then the
value of \( \overrightarrow{\mathbf{A}} \times \overrightarrow{\mathbf{C}} \) is:
A .
B.
c. \( \mathrm{B}^{2} \)
D. \( A C \cos \theta \)


The frequency of resulting spectral line, in cycle per seconds is:
A. \( 1.93 \times 10^{-11} \)
В. \( 2.9 \times 10^{16} \)
c. \( 1.93 \times 10^{11} \)
D. \( 2.9 \times 10^{-11} \)


Two coils have a mutual inductance of
\( 0.005 H . \) The current changes in the first coil according to equation \( \boldsymbol{I}= \)
\( I_{0} \)sin\( \omega t, \) where \( I_{0}=10 A \) and \( \omega= \)
100 \( \pi \) rad / s. The maximum value of emf
(in volt) in the second coil is.
A . \( 2 \pi \)
в. \( 5 \pi \)
c. \( \pi \)
D. \( 4 \pi \)


A wave travelling along the x-axis is described by the equation \( \boldsymbol{y}(\boldsymbol{x}, \boldsymbol{t})= \)
\( 0.005 \cos (\alpha x-\beta t) \) if the wavelength
and the time period of the wave are \( 0.08 m \) and \( 2.0 s \) respectively, then \( \alpha \)
and \( \beta \) in appropriate units are
A. \( \alpha=25.00 \pi, \beta=\pi \)
B. \( \alpha=\frac{0.08}{\pi}, \beta=\frac{2.0}{\pi} \)
c. \( \alpha=\frac{0.04}{\pi}, \beta=\frac{1.0}{\pi} \)
D. \( \alpha=12.50 \pi, \beta=\frac{\pi}{2.0} \)


Estradiol is known as the
A. Primary female sex hormone
B. Primary male sex hormone
c. secondary female sex hormone
D. Secondary sex hormone


A ray of monochromatic green light
enters a liquid from air, as shown in
figure. The angle 1 is \( 45^{\circ} \) and angle 2 is
\( 30^{\circ} \) Find the refractive index of light.
\( A \)
B. \( \sqrt{0.5} \)
\( c \cdot \sqrt{2} \)
D.


A particle is thrown vertically up with speed u so that distance covered in last
second of flight is \( 35 m . \) If then initial
speed of throw is
A. \( 20 \mathrm{m} / \mathrm{s} \)
в. \( 26.45 \mathrm{m} / \mathrm{s} \)
c. \( 40 m / s \)
D. \( 50 \mathrm{m} / \mathrm{s} \)


\( H e^{+} \) is in \( n^{t h} \) state.lt emits two
successive photons of wavelength \( 103.7 n m \) and \( 30.7 n m, \) to come to
ground state the value of \( n \) is:
A . 4
B. 5
\( c \cdot 6 \)
D.


In the graph \( (1), A, B \) and \( C \) respectively
are:
\( A \cdot S O_{3}, S O_{2} \) and \( O_{2} \)
B. \( S O_{3}, O_{2} \) and \( S O_{2} \)
\( c \cdot S O_{2}, O_{2} \) and \( S O_{3} \)
D. \( O_{2}, S O_{2} \) and \( S O_{3} \)


Structure containing an amine group is
\( \mathbf{A} \cdot C H_{3}-C H_{2}-C H_{3} \)
в. \( C H_{3}-\underset{O}{\|}-O H \)
c. \( C H_{3}-O-C_{3} H_{7} \)
E . \( C H_{3}-C H_{2}-N H_{2} \)


For a given exothermic reaction \( \boldsymbol{K}_{\boldsymbol{p}} \) and \( K_{p}^{\prime} \) are the equilibrium constants at
temperature \( T_{1} \) and \( T_{2} \) respectively. Assuming that heat of reaction is constant in temperature range between
183. \( T_{1} \) and \( T_{2} \) it is readily observed
that:
\( \mathbf{A} \cdot K_{p}=K_{p}^{\prime} \)
B . \( K_{p}=1 / K_{p}^{\prime} \)
\( \mathbf{c} \cdot K_{p}>K_{p}^{\prime} \)
D. \( K_{p}<K_{p}^{\prime} \)


For a cell the graph between the potential difference (V) across the
terminals of the cells and the current (I)
drawn from the cell is shown in the
figure. The emf and the internal
resistance of the cell are:


S.I. unit of Magnetic flux is:
A. ampere-meter
B. ampere \( m^{2} \)
C. weber
D. weber \( / \mathrm{m}^{2} \)


A horizontal platform with an object placed on it is executing simple harmonic motion in the vertical
direction. The amplitude of oscillation is \( 3.92 \times 10^{-3} \) m. What should be the
least period of these oscillations, so that the object is not detached from the
platform?
A. 0.145 sec
B. 0.1556 sec
c. \( 0.1256 \mathrm{sec} \)
D. \( 0.1356 \mathrm{sec} \)


\( C_{6} H_{12} \) and \( C_{6} H_{6} \) are the examples of
aromatic and aliphatic hydrocarbons respectively.
A. True
B. False


If \( K_{1} \) and \( K_{2} \) are the respective
equilibrium constants for the two reactions
\( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{6}(\boldsymbol{g})+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{X} \boldsymbol{e} \boldsymbol{O} \boldsymbol{F}_{4}(\boldsymbol{g})+ \)
\( 2 H F(g) \)
\( \boldsymbol{X} \boldsymbol{e} \boldsymbol{O}_{4}(\boldsymbol{g})+\boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{6}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{X} \boldsymbol{e} \boldsymbol{O} \boldsymbol{F}_{4}(\boldsymbol{g})+ \)
\( \boldsymbol{X} \boldsymbol{e} \boldsymbol{O}_{3} \boldsymbol{F}_{2}(\boldsymbol{g}) \)
the equilibrium constant of the
following reaction is:
\( \boldsymbol{X} \boldsymbol{e} \boldsymbol{O}_{4}(\boldsymbol{g})+\boldsymbol{2} \boldsymbol{H} \boldsymbol{F}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{X} \boldsymbol{e} \boldsymbol{O}_{3} \boldsymbol{F}_{2}(\boldsymbol{g})+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \) will be:
A \( . K_{1} / K_{2}^{2} \)
В. \( K_{1} \times K_{2} \)
c. \( K_{1} / K_{2} \)


\( = \)
\( + \)
\( +\infty \)


A standard hydrogen electrode has a zero potential because:
A. Hydrogen can be most easily oxidised
B. Hydrogen has only one electron
C. The electrode potential is assumed to be zero
D. Hydrogen is the lightest element


Which of the following is a Lanthanoid?
A. Ta
B. Rh
\( c . \) Th
D. Lu


(a) Write down formula for the
magnification obtained by a spherical mirror.
(b) Name a mirror that can give an erect and enlarged image of an object.
(c) Define the principle focus of a
convex mirror.


Find the locus of a complex number,
\( z=x+i y, \) satisfying the relation \( \left|\frac{z-3 i}{z+3 i}\right| \leq \sqrt{2} \)
Illustrate the locus of \( z \) in the Argand
plane.


\( \boldsymbol{C H}_{3} \boldsymbol{C O C l}+\boldsymbol{H}_{2} \frac{\boldsymbol{P d} / \boldsymbol{B a S O}_{4}}{\boldsymbol{\}} \)
\( \boldsymbol{C H}_{3} \boldsymbol{C H O}+\boldsymbol{H C l} \)
Which of the following option is correct about the given reaction?
A. Aldol condensation
B. Clemmensen reduction
c. Rosenmund reduction
D. carbylamine reaction


\( A B \) and \( C D \) are two parallel chords of a circle such that \( A B=10 \mathrm{cm}, C D=24 \mathrm{cm} \)
If the chords are on opposite sides of the centre and distance between them is 17
\( \mathrm{cm}, \) the radius of the circle is
\( A \cdot 10 \mathrm{cm} \)
B. \( 11 \mathrm{cm} \)
c. \( 12 \mathrm{cm} \)
D. \( 13 \mathrm{cm} \)


CO is toxic because it forms complex
with \( \quad \) in the blood
A. carbohydrate
B. protein
c. haemoglobin
D. none of these


Suppose a planet exists whose mass
and radius both are half that of the
earth The acceleration due to gravity on
the surface of this planet will be double
\( ? \)


Two uncharged bodies on rubbing, get charged due to:
A. conduction
B. friction
c. induction
D. none of these


The magnetic effect of electric current is used in a/an:
A. electric motor
B. geyser
c. electromagnet
D. electric bulb


Two particles \( X \) and \( Y \) having equal
charges after being accelerated thorough the same potential difference enter a region of uniform magnetic field and describe circular paths of radius
\( \boldsymbol{R}_{1} \) and \( \boldsymbol{R}_{2} \) respectively. the ratio of
mass of \( X \) to that of \( Y \) is
\( \mathbf{A} \cdot \sqrt{R_{1} / R_{2}} \)
в. \( R_{2} / R_{1} \)
c. \( \left(R_{1} / R_{2}\right)^{2} \)
D. \( R_{1} / R_{2} \)


Assertion
\( F \) -atom has less electron affinity than
\( C l^{-} \) atom.
Reason
Additional electrons are repelled more
effectively by \( 3 p \) electrons in \( C l \) atom than by \( 2 p \) electrons in \( F \) -atom.
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


\( \mathbf{f}\left[\begin{array}{ccc}\boldsymbol{x}-\boldsymbol{y} & \mathbf{1} & \boldsymbol{z} \\ \mathbf{2} \boldsymbol{x}-\boldsymbol{y} & \boldsymbol{0} & \boldsymbol{w}\end{array}\right]=\left[\begin{array}{ccc}-\mathbf{1} & \mathbf{1} & \mathbf{4} \\ \mathbf{0} & \mathbf{0} & \mathbf{5}\end{array}\right] \) find
\( \boldsymbol{x}, \boldsymbol{y}, \boldsymbol{z}, \boldsymbol{w} \)


Assertion
Combustion of \( N_{2} \) to give NO is
endothermic.
Reason
Bond energy of \( N_{2} \) is very high.
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


f \( x, y, z \) are all different and if \( \left|\begin{array}{lll}\boldsymbol{x} & \boldsymbol{x}^{2} & \boldsymbol{1}+\boldsymbol{x}^{3} \\ \boldsymbol{y} & \boldsymbol{y}^{2} & \boldsymbol{1}+\boldsymbol{y}^{3} \\ \boldsymbol{z} & \boldsymbol{z}^{2} & \boldsymbol{1}+\boldsymbol{z}^{3}\end{array}\right|=\boldsymbol{0} \operatorname{then} 1+\boldsymbol{x} \boldsymbol{y} \boldsymbol{z}= \)
A . -1
B.
\( c \cdot 1 \)
D. 2


Very short answer type.
What is serum?


If \( v_{e} \) is escape velocity and \( v_{o} \) is orbital
velocity of a satellite for orbit close to the earth's surface, then these are
related by :
A \( \cdot v_{o}=v_{e} \)
B. \( v_{e}=\sqrt{2 v_{o}} \)
c. \( v_{e}=\sqrt{2} v_{o} \)
D. \( v_{o}=\sqrt{2} v_{e} \)


Drinking mineral water drink with low
levels \( (\sim 0.02 \) ppm ) of pesticide for long period would
A. Cause cancer of intestine
B. Lead to accumulation of pesticides in the body
c. Cause leukaemia in most of the people
D. Produce immunity against mosquito


In the HCl molecule, the separation between the nuclei of the two atoms is
about \( 1.27 \dot{A}\left(1 \dot{A}=10^{-10} m\right) . \) Find the
approximate location of the CM of the molecule, given that a chlorine atom is about 35.5 times as massive as a
hydrogen atom and nearly all the mass
of an atom is concentrated in its
nucleus.


\( \mathbf{A t} t=0, \) the function \( f(t)=\frac{\sin t}{t} \) has
This question has multiple correct options
A. A minimum
B. A discontinuity
c. A point of inflexion
D. A maximum


1.0 \( g \) of a weak monobasic acid \( (H A) \) when dissolved in \( 150 \mathrm{mL} \) water, lowers
the freezing point by \( 0.186^{\circ} \mathrm{C} \). Also \( 1.0 \mathrm{g} \) of the same acid required 125 mL of a 0.10N Nate solution for complete neutralisation. Determine dissociation
constant \( \left(k_{a}\right) \) of the weak acid. \( k_{f} \) of
water is \( 1.86 \mathrm{K} \mathrm{kg} \) mol \( ^{-1} \)
A \( \cdot 4.16 \times 10^{-3} \)
B . \( 2.38 \times 10^{-6} \)
c. \( 6.43 \times 10^{-3} \)
D. \( 3.78 \times 10^{-6} \)


Fill in the blank with appropriate word
to complete the sentence.
The Amavasya night occurs about days after the Poonima night


Protein which is both structural and
enzymatic is
A. Troponin
B. Myosin
c. Trypsin
D. Actin


The value of \( \int_{-1}^{1} x|x| d x \) is
\( A \cdot 2 \)
B. 1
c. 0
D. None of these


\( 5 g \) each of \( C a C O_{3} \) and \( S r C O_{3} \) was
shaken well in a litre of water.
Concentration of \( \boldsymbol{C} \boldsymbol{a}^{2+}, \boldsymbol{S} \boldsymbol{r}^{2+} \) and \( \boldsymbol{C} \boldsymbol{O}_{3}^{2-} \)
will be:
\( \boldsymbol{K}_{s p_{C a C o_{3}}}=4.8 \times 10^{-9} \) and \( K_{s p_{s r C O_{3}}}= \)
\( 1.1 \times 10^{-10} \)
\( \mathbf{A} \cdot\left[C a^{2+}\right]=7.0 \times 10^{-5} M,\left[S r^{2+}\right]=1.50 \times 10^{-6} M \)
\( \left[C O_{3}^{2-}\right]=6.85 \times 10^{-5} M \)
В. \( \left[C a^{2+}\right]=1.50 \times 10^{-6} M,\left[S r^{2+}\right]=7.0 \times 10^{-5} M \)
\( \left[C O_{3}^{2-}\right]=6.85 \times 10^{-5} M \)
C \( \cdot\left[C a^{2+}\right]=6.85 \times 10^{-5} M,\left[S r^{2+}\right]=1.50 \times 10^{-6} M \)
\( \left[C O_{3}^{2-}\right]=7.0 \times 10^{-5} M \)
D. None of these


\( \int \frac{e^{x}(x-1)}{x^{2}} d x= \)
A \( \cdot \frac{1}{x} e^{x}+c \)
B. \( x e^{-x}+c \)
c. \( \frac{1}{x^{2}} e^{x}+c \)
D. \( \left(x-\frac{1}{x}\right) e^{x}+c \)


If \( z_{1} \) and \( z_{2} \) are two complex numbers,
then \( R e\left(z_{1} z_{2}\right) \) is:
\( \mathbf{A} \cdot \operatorname{Re}\left(z_{1}\right) \operatorname{Re}\left(z_{2}\right) \)
B \( \cdot \operatorname{Re}\left(z_{1}\right) \cdot \operatorname{Re}\left(z_{2}\right)-\operatorname{Im}\left(z_{1}\right) \cdot \operatorname{Im}\left(z_{2}\right) \)
\( \mathbf{c} \cdot \operatorname{Im}\left(z_{1}\right) \cdot \operatorname{Re}\left(z_{2}\right) \)
D. \( \operatorname{Re}\left(z_{1}\right) . \operatorname{Im}\left(z_{2}\right) \)


A uniform rod of length \( 4 L \) and mass \( M \)
is suspended form a horizontal roof by
two light strings of length \( L \) and \( 2 L \) as
shown. Then the tension in the left
string of length \( L \) is:
\( A \cdot \frac{M g}{2} \)
в. \( \frac{M g}{3} \)
c. \( \frac{3}{5} M g \)
D. \( \frac{M g}{_{1}} \)


Zinc reacts with dil. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) to give \( \boldsymbol{H}_{2} \)
It also reacts with conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) to give
\( \boldsymbol{S} \boldsymbol{O}_{2} \)
If true enter 1 , else enter 0


The maximum number of
stereoisomers possible for the ion \( [\stackrel{I V}{\left.P d\left(N H_{3}\right)_{2}\left(H_{2} O\right)_{2} B r_{2}\right]^{2+}} \) is


What is the velocity of electron present in first Bohr orbit of hydrogen atom?
A \( \cdot 2.18 \times 10^{5} m / s \)
B \( \cdot 2.18 \times 10^{6} m / s \)
C \( .2 .18 \times 10^{-18} \mathrm{m} / \mathrm{s} \)
D. \( 2.18 \times 10^{-9} \mathrm{m} / \mathrm{s} \)


Concentrated \( N H O_{3} \) forms \( N O_{2}^{+} \) in the
presence of:
A. Conc.H\( _{2} \)SO\( _{4} \)
в. \( F e \)
c. \( F e B r_{3} \)
D. \( A l C l_{3} \)


What is the empirical formula of vanadium oxide, if 2.74 g of metal oxide contains 1.53 g of metal? (Atomic mass: \( \boldsymbol{V}=\mathbf{5 2}, \boldsymbol{O}=16) \)
\( A \cdot V_{2} O_{3} \)
B. VO
\( c \cdot V_{2} O_{5} \)
D. \( V_{2} O_{7} \)


Evaluate :
\( \int_{0}^{\pi} \frac{x \tan x}{\sec x+\tan x} \)


Name any two seeds of plant which are used as a source of biodiesel.


The correct statement(s) about \( C r^{2+} \)
and \( M n^{3+} \) is(are):
[Atomic numbers of \( \mathbf{C r}=\mathbf{2 4} \) and \( \mathbf{M n}= \)
This question has multiple correct options
A. \( C r^{2+} \) is a reducing agent
B. \( M n^{3+} \) is an oxidizing agent
c. Both \( C r^{2+} \) and \( M n^{3+} \) exhibit \( d^{4} \) electronic configuration
D. When \( C r^{2+} \) is used as a reducing agent, the chromium ion attains \( d^{5} \) electronic configuration


What is nutrition? What type of
nutrition is seen in green plants and the majority of animals?


If \( p q=3, \) then \( p^{3} q^{4}+p^{4} q^{5}= \)
A \( \cdot 12 q \)
в. \( 7 p+9 q \)
c. \( 12 p+20 q \)
D. \( 96 p \)
E. \( 108 q \)


Three wires \( A, B, C \) made of the same
material and radius have different
lengths. The graphs in the figure shows
the elongation-load variation. The
longest wire is:
\( A \)
B. B
\( c \cdot c \)
D. Al


The number of two-digit numbers which
are of the form \( x y \) with \( y<x \) are given
by
A . 60
B. 55
c. 50
D. 45


The Venn diagram shows sets \( \xi, P \) and
\( Q \)
The shaded region in the Venn diagram
represents set
\( A \cdot P \cap Q \)
в. \( P^{\prime} \cap Q \)
c. \( P \cap Q^{\prime} \)
D. \( P^{\prime} \cap Q^{\prime} \)


A college teacher has the following
absentee record of 50 students of a
class for the whole year. Find the
median.
\( \begin{array}{lllll}\text { Number } & \mathbf{0}- & \mathbf{4}- & \mathbf{8}- & \mathbf{1 2}- \\ \text { of days } & \mathbf{4} & \mathbf{8} & \mathbf{1 2} & \mathbf{1 6}\end{array} \)
Number
of students
A. 11.66
B. 12.66
c. 13.66
D. 10.66


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


Describe the process of respiration in the following part of a plant.
Root.


Identify the product \( A \) in the following
reaction.
\( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{6}+\boldsymbol{3} \boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \boldsymbol{A}+\boldsymbol{6} \boldsymbol{H} \boldsymbol{F} \)


Estimate the value of cube root of the
number 1333
A . 10.99
B. 20.10
c. 12.45
D. 10.56


A sample of pure water, irrespective of source, contains \( 88.89 \% \) oxygen and \( 11.11 \% \) hydrogen by mass. The data supports the:
A. law of conservation of mass
B. law of constant composition
c. law of multiple proportion
D. law of reciprocal proportion


There is some change in length when a 33000N tensile force is applied on a steel rod of the area of cross section
\( \mathbf{1 0}^{-3} \mathbf{m}^{2} . \) The change in temperature required to produce the same elongation if the steel rod is heated is:
(The modulus of elasticity is \( 3 x \) \( 10^{11} N m^{-2} \) and coefficient of linear
expansion of steel is \( 1.1 \times 10^{-5} 0 C^{-1} \) )
A \( \cdot 20^{\circ} \)
В. \( 15^{\circ} \mathrm{C} \)
\( \mathrm{c} \cdot_{10^{0}} \mathrm{C} \)
D. \( 0^{0} C \)


A prism splits white light into constituent colours(VIBGYOR). Choose
the correct option.
A. White light is composed of seven colours
B. We cannot see other colours in wavelengths 380nm to 700nm
c. We cannot see other colours outside wavelengths \( 380 n m \) to \( 700 n m \)
D. None of the above


Name the type of motion when a girl is skipping a rope and moving forward


Which one of the following compounds give only one mono brominated product
\( ? \)
A. 2-Methylbutane
B. 2,2,2-Diethylpentane
c. 2,2,3,3 -tetramethylbutane
D. 2-Methylpropane


Evaluate the following question. \( \lim _{x \rightarrow a} \frac{(x)^{3 / 2}-(a)^{3 / 2}}{x-a} \)


The flow of sap from endodermis toward xylem parts of the plants is due to:
A. Symplast pathway
B. Passage pathway
c. Apoplast pathway
D. HSK pathway


Naphthalene balls used to repel moths and other insects are obtained from \( X \)
These days \( Y \), a petroleum product, is used in place of \( X \) for metalling the roads. What are \( X \) and \( Y \) respectably?
A. Coke, coal
B. Coal, coke
c. Bitumen, coal tar
D. Coal tar, bitumen


Which of the following is a to criteria to classify drugs?
A. Chemical structure
B. Molecular targets
c. Drug action
D. All of these


A compound \( A \) of boron reacts with
\( N M e_{3} \) to give an adduct \( B \) which on hydrolysis gives a compound \( C \) and a
gas \( D . \) Compound \( C \) is an acid.
Compound \( \boldsymbol{C} \) is :
\( A \). diborane
B. boric acid
c. borate salt
D. none of these


Number of cell organelles involved in photorespiration are
A. one
B. Two
c. Three
D. Four


Write the angle between the curves \( y= \)
\( e^{-x} \) and \( y=e^{x} \) at their point of
intersection.


Two persons \( A \) and \( B \) wear glasses of
optical powers (in air) \( P_{1}=+2 D \) and
\( P_{2}=+1 D \) respectively. The glasses
have refractive index \( 1.5 . \) Now they jump into a swimming pool and look at each other. B appears to be present at distance \( 2 m(f r o m A) \) to \( A . A \) appears to
be present at distance \( 1 \mathrm{m} \) (from B) to B,
then
This question has multiple correct options
A. Refractive index of water is 1.2
B. Actual distance between A and B is \( \frac{200}{3} \mathrm{cm} \)
c. Actual distance between A and B is 50 cm
D. Combined power of two glass (when placed in contact in air) is \( +3 D \)


For \( Z n^{2+}, N i^{2+}, C u, \) and \( C r^{2+} \) which of
the following statements is correct?
A. only \( Z n^{2+} \) is colourless and \( N i^{2+}, C u^{2+} \) and \( C r \) are coloured
B. All the ions are coloured
c. All the ions are colourless
D. \( Z n^{2+} \) and \( C u^{2+} \) are colourless while \( N i^{2+} \) and \( C r^{2+} \) are coloured


Four divers of the same weight dive from four different heights \( 10 \mathrm{m}, 9 \mathrm{m}, 12 \) \( m \) and \( 8 m \) as shown here. The diver
from which height will have the highest
kinetic energy on hitting the water below?
A . 10 meters
B. 9 meters
c. 12 meters
D. 8 meters


Which of the following material is
known as lunar caustic?
\( \mathbf{A} \cdot A g C l \)
в. \( A g N O_{3} \)
c. \( N a O H \)
D. \( N a N O_{3} \)


If two angles are complementary of each other, then each angle is:
A. an obtuse angle
B. a right angle
c. an acute angle
D. a supplementary angle


At infinite dilution stage, the solution of
\( C H_{3} C O O H \) in water does not contain :
A. \( H^{+} \) ion
в. \( C H_{3} C O O^{-} \) ion
c. \( C H_{3} C O O H \) molecule
D. all of these


The photoelectric effect represent that
A . Light has a particle nature
B. Electron has a wave nature
c. Proton has a wave nature
D. None of the above


Let \( L \) be the set of all lines in a plane
and \( R \) be the relation in \( L \) defined as
\( \boldsymbol{R}=\left\{\left(\boldsymbol{L}_{1}, \boldsymbol{L}_{2}\right): \boldsymbol{L}_{1} \perp \boldsymbol{L}_{2}\right\} . \) Show that \( \boldsymbol{R} \) is
symmetric but neither reflexive nor transitive.


In Young's double slit experiment, the
two slits act as coherent sources of
equal amplitude \( A \) and wavelength \( \lambda \). In
another experiment with the same set up the two slits are same of equal amplitude of wavelength \( \lambda \) but are
incoherent. The ratio of intensity of light at the mid point of the screen in the first to the second case is?
A . 4: 1
B . 2: 1
\( c \cdot 1: 1 \)
D. 1: 2


A weight ' \( W \) ' can be just supported on a
rough horizontal plane by a force ' \( \boldsymbol{F} \) '
either acting along the plane or
horizontally. If \( \theta \) is the angle of friction, then \( \frac{\boldsymbol{F}}{W} \) is
A \( \cdot \tan \theta \)
B. \( \sec \theta \)
\( c \cdot \sin \theta \)
\( D \cdot \cos \theta \)


Equilibrium constant has a definite value of every reaction at a given temperature. It is independent of concentration and
A. temperature
B. pressure
c. activation energy
D. catalyst involved


\( \boldsymbol{S}_{N^{1}} \) reactivity of the following halides,
(i) \( \left(\boldsymbol{C} \boldsymbol{H}_{3}\right)_{3} \boldsymbol{C} \boldsymbol{B r} \)
(ii) \( \left(C_{6} H_{5}\right)_{2} C H B r \)
(iii) \( \left(C_{6} H_{5}\right)_{2} C\left(C H_{3}\right) B r \)
(iv) \( \left(C H_{3}\right)_{2} C H B r \) will be in the order:
\( \mathbf{A} \cdot i v>i>i i>i i i \)
в. \( i i>i> \) iii \( > \) iv
\( \mathbf{c} \cdot i>i i i>i i>i v \)
D. \( i i i>i i>i>i v \)


What is the breath rate in human
beings?


The rest energy of electron or positron is
\( \mathbf{A} \cdot 0.51 \mathrm{MeV} \)
B. 1 MeV
c. \( 1.02 \mathrm{MeV} \)
D. 1.5 Mev


Determine the contrapositive of the following statements:
If it snows, then they do not drive the
car.


\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left(\sqrt{\boldsymbol{3}} \sin \left(\boldsymbol{2} \boldsymbol{x}+\frac{\boldsymbol{\pi}}{\boldsymbol{3}}\right)+\cos \left(\boldsymbol{2} \boldsymbol{x}+\frac{\boldsymbol{\pi}}{\boldsymbol{3}}\right)\right) \)
A. \( 4 \cos 2 x \)
B . \( -4 \sin 2 x \)
\( c .4 \sin 2 x \)
D. \( -4 \cos 2 x \)


Oxygen is divalent whereas sulphur exhibits a valency of 2,4 or \( 6 . \) This is
due to :
A. high electro negativity of oxygen than sulphur
B. large size of sulphur atom
c. high ionisation potential of oxygen
D. availability of vacant d-orbitals in the valenc shell of sulphur


The number of terms of an \( A . P . \) is even;
the sum of the odd terms is \( 24, \) and of
the even terms is 30 and the last term
exceeds the first by \( 10.5, \) then the number of terms in the series is
A . 8
B. 4
\( c .6 \)
D. 10


Examples of opto-electronic devices are This question has multiple correct options
A. Light Emitting Diodes (LED)
B. Zener diode
c. Solar cells
D. Photodiodes


A ray of light is incident on a plane
mirror AB. The angle of incidence is \( 60^{\circ} \)
The ray is reflected from \( A B \) and strikes another plane mirror BC placed at right angles to mirror AB. The angle of reflection at BC is:
A . \( 135^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 30^{\circ} \)


The magnetic flux density \( B \) is changing in magnitude at a constant
rate \( d B / d t . \) A given mass \( m \) of copper
drawn into a wire of radius \( a \) and
formed into a circular loop of radius \( r \) is
placed perpendicular to the field \( B \). The induced current in the loop is \( i . \) The resistivity of copper is \( \rho \) and density is
d. The value of the induced current \( i \) is
\( ^{\mathbf{A}} \cdot \frac{m}{2 \pi \rho d} \frac{d B}{d t} \)
В. \( \frac{m}{2 \pi a^{2} d} \frac{d B}{d t} \)
c. \( \frac{m}{4 \pi a d} \frac{d B}{d t} \)
D. \( \frac{m}{4 \pi \rho d} \frac{d B}{d t} \)


What questions will you ask a doctor to
know about endocrine glands?


A cooking pot should have
A. high specific heat and low conductivity
B. high specific heat and high conductivity
C. low specific heat and low conductivity
D. low specific heat and high conductivity


Which one of the above oxidation curve
is wrongly presented in the given Gibbs
free energy vs temperature graph?
A. \( C \rightarrow C O_{2} \)
B. \( T i \rightarrow T i O_{2} \)
\( c, P b \rightarrow P b O \)
D. \( M g \rightarrow M g O \)


A bullet of mass 60 g moving with a velocity of \( 500 m s^{-1} \) is brought to rest in 0.01 s. Find the impulse and the average force of the blow.


The inverse proposition of \( (\boldsymbol{p} \wedge \sim \boldsymbol{q}) \Rightarrow \boldsymbol{r} \)
is
\( A \cdot \sim r \Rightarrow \sim p \vee q \)
в. \( p \vee q \Rightarrow \sim r \)
\( \mathbf{c} \cdot r \Rightarrow p \wedge \sim q \)
D. none of these.


If \( \vec{b}=3 \hat{i}+4 \hat{j} \) and \( \vec{a}=\hat{i}-\hat{j} \) the vector
having the same magnitude as that of \( \vec{b} \) and parallel to \( \vec{a} \) is
A \( \cdot \frac{5}{\sqrt{2}}(\hat{i}-\hat{j}) \)
B. \( \frac{5}{\sqrt{2}}(\hat{i}+\hat{j}) \)
\( \mathbf{c} \cdot 5(\hat{i}+\hat{j}) \)
D. \( 5(\hat{i}-\hat{j}) \)


A body is displaced from (0,0) to \( (1 m, 1 m) \) along the path \( x=y \) by a force \( \boldsymbol{F}=\left(\boldsymbol{x}^{2} \hat{\boldsymbol{j}}+\boldsymbol{y} \hat{\boldsymbol{i}}\right) \boldsymbol{N} . \) The work done
by this force will be :
A \( \cdot \frac{4}{3} J \)
в. \( \frac{5}{6} J \)
\( c \cdot \frac{3}{2} J \)
D. \( \frac{7}{5} J \)


If \( I=\int \sec ^{2} x \operatorname{cosec}^{4} x d x=A \cot ^{3} x+ \)
\( B \tan x+C \cot x+D \) then
This question has multiple correct options
A \( \cdot A=-\frac{1}{3} \)
в. \( B=2 \)
c. \( C=-2 \)
D. none of these


If a piece of soft iron is placed inside the
coil \( n \) number of turns and current is
passed in the coil from a battery, what name is then given to the device so obtained?
A. spectrometer
B. gravitometer
c. barometer
D. electromagnet


Which of the following statement is
incorrect?
A. Sodium and potassium are soft and silvery white metals.
B. Sodium and potassium in air get tarnished due to the formation of a layer of oxide or carbonates.
C. Sodium and potassium burn in dry oxygen (excess) gives peroxides.
D. Sodium and potassium are kept under kerosene to avoid contact with air and moisture.


Haemoglobin contains \( 4.6 \% \) of iron by mass. If the compound contains a
single atom of iron then what is its molar mass in \( g \) mol\( ^{-1} \) ?
A . 1217.4
в. 1324.7
c. 1232.4
D. 1317.5


The acidic hydrolysis of ether (X) shown
above is fastest when:
A. one phenyl group is replaced by a methyl group
B. one phenyl group is replaced by a para-methoxyphenyl group
c. two phenyl groups is replaced by two para methoxyphenyl groups
D. no structural change is made to X.


State two advantages and disadvantages of friction.


A step down transformer reduces \( 220 \mathrm{V} \)
to \( 11 \mathrm{V} \).The primary coil draws \( 5 \mathrm{A} \) current and secondary coil supplies 90A.Efficiency of the transformer will be
A . 4.4\%
B. 20\%
c. 33\%
D. 90\%


According to the equation,
\( \boldsymbol{n} \boldsymbol{C} \boldsymbol{H}_{2}=\boldsymbol{C} \boldsymbol{H}_{2} \rightarrow\left(-\boldsymbol{C} \boldsymbol{H}_{2}-\boldsymbol{C} \boldsymbol{H}_{2}-\right)_{n} \)
When \( 100 g \) of ethylene polymerises to polyethylene, then the weight of polyethylene produced will be:
A \( \cdot \frac{n}{2} \) g
в. \( 100 \mathrm{g} \)
c. \( \frac{100}{n} \mathrm{g} \)
D. \( 100 n \) g


Construct a triangle \( A B C, \) whose base
\( B C=6 c m, \angle B=60^{\circ} \) and altitude
\( A D=4 \mathrm{cm} \)


The difference between the maximum
and the minimum observation in the
data is
A. class interval
B. frequency
c. cumulative frequency
D. range


In a given electric field, \( \beta- \) particles are
deflected more than \( \alpha- \) particles, inspite of \( \alpha- \) particles having larger charge.
A. True
B. False


\( \frac{k}{c} \)


If matrix \( \mathbf{A}=[\boldsymbol{a} \boldsymbol{i} \boldsymbol{j}]_{3 \times 2}, \) and \( \boldsymbol{a} \boldsymbol{i} \boldsymbol{j}=(\boldsymbol{3} \boldsymbol{i}- \)
\( 2 j)^{2}, \) then find the matrix \( A \)


Solve \( : \boldsymbol{y} \log \boldsymbol{y} \frac{d \boldsymbol{x}}{d \boldsymbol{y}}+\boldsymbol{x}-\log \boldsymbol{y}=\mathbf{0} \)


Which of the following is the most common auxin?
A . GA
B. ABA
c. Kinetin
D. IAA


Find the area of the region bounded by
the parabola \( y^{2}=2 x \) and the line \( x- \)
\( \boldsymbol{y}=\mathbf{4} . \) And \( \mathbf{1 8} \boldsymbol{s} \boldsymbol{q} \) unit.


What is the angle between two vector forces of equal magnitude such that their resultant is one-third of either of
the original forces?
\( ^{\mathbf{A}} \cdot \cos ^{-1}\left(-\frac{17}{18}\right) \)
B. \( \cos ^{-1}\left(-\frac{1}{3}\right) \)
\( c \cdot 45^{\circ} \)
D. \( 120^{\circ} \)


Find the amount of zinc in gram
necessary to produce \( 224 m l \) of \( H_{2} \) by the reaction with sulphuric acid.


\( \frac{[0]}{\infty} \)


Explain two ways by which food industries prevent rancidity. Discuss the importance of decomposition reaction in metal industry with three points.


For an ideal binary liquid system:
This question has multiple correct options
A. the change in temperature \( (\Delta H) \) is zero
B. Raoult's law is obeyed
c. change in volume \( (\Delta V) \) is zero
D. none of the above


During interference phenomenon of two
wave it is observed that maximum
amplitude to minimum amplitude ratio is \( 9: 7 . \) Find the intensity ratio of waves.


\( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \rightarrow \boldsymbol{2} \boldsymbol{H}^{+}+\boldsymbol{O}_{2}+\boldsymbol{2} \boldsymbol{e}^{-} \)
The above equation represent which of
the following behaviour of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} ? \)
A. Reducing
B. Oxidising
c. Basic
D. Catalytic


toppr
Q Type your question
City \( \mathbf{A} \)
\begin{tabular}{ll}
Temperature \( \left.^{(o} \boldsymbol{F}\right) \) & Frequency \\
80 & 3 \\
79 & 14 \\
78 & 2 \\
77 & 1 \\
76 & 1 \\
\hline
\end{tabular} City B
\( \begin{array}{ll}\text { Temperature }\left(^{o} \boldsymbol{F}\right) & \text { Frequency } \\ 80 & 6 \\ 79 & 3 \\ 78 & 2 \\ 77 & 4 \\ 76 & 6\end{array} \) Which of the following is true about the
data shown for these 21 days?
A. The standard deviation of temperatures in City A is larger.
B. The standard deviation of temperatures in City B is arger
c. The standard deviation of temperatures in City A is the same as that of City B
D. The standard deviation of temperatures in these cities cannot be calculated with the data provided.


The pH of a solution of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) is 6.0
Some chloride gas is bubbled into this solution. Which of the following is correct?
A. The pH of the resultant solution is less than 6.0 and \( 0 x \)
B. The pH of the resultant solution is less than 8.0
c. \( C l O_{2} \) will be formed in the resultant solution
D. None of these


A cell can be balanced against \( 110 \mathrm{cm} \) and 100
\( \mathrm{cm} \) of potentiometer wire, respectively with and
without being short circuited through a resistance of 10 . Its internal resistance
is -
A. 2.0 ohm
B. zero
c. 1.0 ohm
D. 0.5 ohm


The reaction \( 2 N O+B r_{2} \rightarrow 2 N O B r \)
is supposed to follow the following mechanism
(i) \( N O+B r_{2} \rightleftharpoons N O B r_{2} \)
(ii) \( N O B r_{2}+N O \stackrel{s l o w}{\rightarrow} 2 N O B r \)
The rate law expression is:
A \( \cdot r=K^{\prime}[N O]^{2}\left[B r_{2}\right] \)
B . \( r=K^{\prime}[N O]^{2}\left[B r_{2}\right]^{2} \)
c. \( r=K^{\prime}[N O]\left[B r_{2}\right. \)
D . \( r=K^{\prime}[N O]^{1}\left[B r_{2}\right] \)


If \( f(x)=\frac{x}{x^{2}+1} \) is increasing function
then the value of \( x \) lies in
A. \( R \)
В \( \cdot(-\infty,-1) \)
\( c \cdot(1, \infty) \)
D. (-1,1)


If \( \cos ^{-1} x+\cos ^{-1} y=\frac{\pi}{2} \) then prove that
\( \cos ^{-1} x=\sin ^{-1} y \)


In the given word 'Felidae', it is the of the tiger having the generic name Felis.
A. Order
B. Class
c. Family
D. Genus


The order of the differential equation whose general solution is given by \( \boldsymbol{y}=\left(\boldsymbol{C}_{1}+\boldsymbol{C}_{2}\right) \cos \left(\boldsymbol{x}+\boldsymbol{C}_{3}\right)-\boldsymbol{C}_{4} \boldsymbol{e}^{\boldsymbol{x}+\boldsymbol{C}_{5}} \)
where, \( C_{1}, C_{2}, C_{3}, C_{4}, C_{5} \) are arbitrary constants, is
\( \mathbf{A} \cdot \mathbf{5} \)
B. 4
\( c .3 \)
D.


Equipotential lines are shown, what is
the approximate voltage at point \( P \) in the diagram?
A . 12 \( v \)
B. \( 8.0 \mathrm{v} \)
\( c \cdot 8.5 v \)
D. \( 6.0 \mathrm{v} \)


The resistance of a galvanometer is \( 50 \Omega \) and the current required to give full-scale deflection is \( 100 \mu A \). In order
to convert it into an ammeter, reading upto \( 10 A, \) it is necessary to put
resistance of:
\( \mathbf{A} \cdot 5 \times 10^{-3} \Omega \) in parallel
B. \( 5 \times 10^{-4} \Omega \) in parallel
\( \mathrm{c} \cdot 10^{5} \Omega \) in series
D. \( 99950 \Omega \) in series


The figure shows the electric field lines
a round a conductor.
(a) At which of the four points is the
field strongest?
(b) At which point is there a negative
charge?


In electrophilic aromatic substitution
reactions of chlorobenzene, the
ortho/para-directing ability of chlorine is due to its
A. positive inductive effect \( (+I) \)
B. negative inductive effect \( (-I) \)
c. positive resonance effect \( (+R) \)
D. negative resonance effect \( (-R) \)


If \( P(n) \) is statement such that \( P(3) \) is true. Assuming \( \mathrm{P}(\mathrm{k}) \) is true \( \Rightarrow P(k+1) \)
is true for all \( k \geq 2, \) then \( P(n) \) is true.
A. For all \( n \)
B. For \( n \geq 3 \)
c. For \( n \geq 4 \)
D. None of these


The time period of a seconds' pendulum
A. 1 second
B. 2 seconds
c. 3 seconds
D. 4 seconds


\( \int(\log x)^{2} d x \)


A \( 20 k g \) load is suspended from the
lower end of a wire \( 10 \mathrm{cm} \) long and \( 1 \mathrm{mm} \)
\( ^{2} \) in cross sectional area. The upper half of the wire is made of iron and the lower
half with aluminium. The total
elongation in the wire is
\( \left(Y_{i r o n}=20 \times 10^{10} \mathrm{N} / \mathrm{m}^{2}, Y_{A l}=7 \times 10^{10}\right. \)
\( \left.\mathrm{N} / \mathrm{m}^{2}\right) \)
A \( \cdot 1.92 \times 10^{-4} \mathrm{m} \)
B. 17.8 \( \times 10^{-3} \mathrm{m} \)
c. \( 1.78 \times 10^{-3} \mathrm{m} \)
D. \( 1.92 \times 10^{-3} \mathrm{m} \)


Benzene diazonium chloride on reaction
with aniline in the presence of dilute hydrochloric acid gives:
\( A \)
B.
\( c \)
\( D \)


If \( x=a(\cos 2 t+2 t \sin 2 t) \) and \( y= \)
\( a(\sin 2 t-2 t \cos 2 t) \) then find \( \frac{d^{2} y}{d x^{2}} \)


A long spring when stretched by \( x c m \)
has a potential energy \( v . \) On increasing the stretching to \( n x c m, \) the potential energy stored in the spring will be
A \( . n v \)
B . \( n^{2} v \)
\( c \cdot n v^{3} \)
D. \( n v^{-2} \)


Hard water when passed through ion
exchange resin containing \( R C O O H \) group, becomes free from :
A \( \cdot C l \)
B. \( S O_{4}^{-2} \)
\( \mathrm{c} \cdot \mathrm{H}_{3} \mathrm{O}^{+} \)
D. \( C a^{+2} \)


Which physical quantity determines the direction of flow of heat energy?
A. Temperature
B. Amplitude
c. Frequency
D. wavelength


An object of mass \( 5 k g \) falls from rest
through a vertical distance of \( 20 m \) and
attains a velocity of \( 10 \mathrm{m} / \mathrm{s} \). How much work is done by the resistance of air on
the object? \( \left(\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2}\right) \)
A . \( 250 J \)
В. \( -650 J \)
c. \( -750 J \)
D. \( 950 J \)


The equation of projectile is \( y=16 x- \)
\( \frac{5 x^{2}}{4} \) Find the horizontal range.
\( \mathbf{A} \cdot R=13.8 m \)
В. \( R=8 m \)
c. \( R=12.8 \mathrm{m} \)
D. \( R=9 m \)


A force \( \overrightarrow{\boldsymbol{F}}=(2 \hat{\boldsymbol{i}}+\boldsymbol{3} \hat{\boldsymbol{j}}) \boldsymbol{N} \) acts ona
particle and displaces it form initial position \( \overrightarrow{x_{1}}=(3 \hat{i}+4 \hat{j}) m \) to final position \( \overrightarrow{x_{2}}=(2 \hat{i}+3 \hat{j}) m, \) then work
done by force, is
\( \mathbf{A} \cdot-19 J \)
в. \( -5 . J \)
c. \( 12 J \)
D. \( 19 J \)


A sphere of diameter \( 12.6 \mathrm{cm} \) is melted
and cast into a right circular cone of height \( 25.2 \mathrm{cm} . \) The diameter of the base of the cone is?
A \( .158 .76 \mathrm{cm} \)
B . \( 79.38 \mathrm{cm} \)
c. \( 12.6 \mathrm{cm} \)
D. \( 69.39 \mathrm{cm} \)


Find an equation of the line
perpendicular to the line \( 3 x+6 y=5 \)
and passing through the point (1,3) Write the equation in the standard form.


An aeroplane flies at constant speed in a horizontal straight path. Two horizontal forces act on the plane. One
is the thrust of the propellers that pushes it forward, and the other is the
force of air resistance that acts in the
opposite direction. Then:
A. thrust force is more
B. air resistance is more
c. both thrust by propellers and air resistance are equal
D. data insufficient


How much percentage of atmosphere is made of nitrogen?
A. 78percent
B. 90percent
c. 88 percent
D. 82 percent


The complex ion \( \left[\boldsymbol{F e}(\boldsymbol{C N})_{\boldsymbol{6}}\right]^{\boldsymbol{4}-} \) contains:
\( \mathbf{A} \cdot s p^{3} d^{2} \) hybrid orbitals with octahedral structure
B. total 104 electrons on \( F e^{+2} \)
C. six sigma Bonds
D. total of 36 electrons on \( F e^{2+} \) ions.


What change occurs, if the monochromatic light used in Young's double slit experiment is replaced by white light?
A. only the central fringe is white and all other fringes are observed coloured
B. No fringes are observedd
c. All the bright fringes become white.
D. All the bright fringes are coloured between
violet and red


If \( f(x)=\frac{x+1}{x-1}, \) what is the value of
\( \boldsymbol{f}\left(\boldsymbol{f}\left(\boldsymbol{f}\left(\boldsymbol{f}\left(\left(\frac{3}{5}\right)\right)\right)\right)\right) ? \)
A . -
B.
\( c .0 .6 \)
D. 1.3
E. 7


Write two differences each in the
following:
(i) DNA and RNA,
(ii) \( \alpha \) -Amino acid and
Protein.


Which of the following is true in the case of an adiabatic process, where
\( \gamma=C_{p} / C_{v} ? \)
A \( \cdot p^{1-\gamma} T^{\gamma}= \) constant
B . \( p^{\gamma} T^{1-\gamma}= \) constant
C \( \cdot p T^{y}= \) constant
D. \( p^{\gamma} T= \) constant


Which of the following is an example of oxidation?
A \( \cdot S n^{+2}-2 e^{-} \rightarrow S n^{+} \)
B. \( F e^{+3}+e^{-} \rightarrow F e^{+} \)
c. \( C l_{2}+2 e^{-} \rightarrow 2 C l \)
D. None of the above


The chord joining the points where \( x=p \) and \( x=q \) on the curve \( y=a x^{2}+b x+c \)
is parallel to the tangent at the point on the curve whose abscissa is
A. \( \frac{p+q}{2} \)
В. \( \frac{p-q}{2} \)
c. \( \frac{p q}{2} \)
D. \( \frac{p}{q} \)


Assertion
A number 2.746 rounded off to three
significant figures is \( 2.75, \) while the number 2.743 would be 2.74
Reason
In rounding off the uncertain digits, the preceding digit is raised by 1 if the insignificant digit to be dropped is more than 5 and is left unchanged if the latter is less than 5
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The volume of \( 2.8 ~ g \) of \( C O \) at \( 27^{0} C \) and
0.821 atm pressure is:
A . 1.5 litre
B. 3 litre
c. 30 litre
D. 0.3 litre


For which value of the given system of equations have infinitely many solution \( (k-3) x+3 y=k \) and \( k x+k y=12 \)
A . -6
B. 6
\( c \cdot 0 \)
D. 3


Which of the following statements is/are correct?
This question has multiple correct options
A. Methane was named as fire damp as it forms explosive mixture with air
B. Primary suffixes are added to the root word to show saturation or unsaturation in a C atom
C. The IUPAC name of valerie acid is pentanoic acid
D. The common name of hexanoic acid is caproic acid


If the ionization energy for hydrogen atom is \( 13.6 e V \), then the ionization energy for \( \boldsymbol{H} \boldsymbol{e}^{+} \) ion should be:
A . \( 13.6 e V \)
B. \( 6.8 e V \)
c. \( 54.4 e V \)
D. \( 72.2 e V \)


The tissue covering the external surface of animal and internal surface of
visceral organs is
A. Adipose tissue
B. Connective tissue
c. cartilaginous tissue
D. Epithelial tissue


The metal that is good conductor of
heat is :
\( A \cdot A B \)
B. Pb
c. ну
D. both A and B


A cylindrical diving bell, whose length is \( 150 \mathrm{cm} \) is lowered to the bottom of tank.
The is found to raise \( 50 \mathrm{cm}, \) into
bell.Assuming the atmospheric pressure at the sunrise equivalent to
1000 \( c m \) of the water and the
temperature as constant the depth of the tank


Only tenth-, eleventh-, and twelfth-
grade students attend Washington High School. The ratio of tenth graders to the
school's total student population is 86:
\( 255, \) and the ratio of eleventh graders to
the school's total student population is
\( 18: 51 . \) If a student is selected at
random from the entire school, the
grade in which the student is most likely to be is:
A. Tenth
B. Eleventh
c. Twelfth
D. All grades are equally likely
E. Cannot be determined from the given information


In a two child family, one child is a boy. What is the probability that the other child is a girl?


Removal of parathyroids in human
beings result in
A. Tetany
B. Simmond's disease
c. Myxoedema
D. Addison's disease


Form the differential equation of all concentric circle at the origin.
A \( \cdot x-y \frac{d y}{d x}=0 \)
в. \( x+y \frac{d y}{d x}=0 \)
c. \( _{x-y} \frac{d y}{d x}=1 \)
D. None of these


Correct statement about carbonyl group
¡s:
A. Bond between carbon and oxygen is non-polar
B. Its non-planar
C. Oxygen have octet in valence shell
D. Carbon atom is \( s p^{3} \) hybridised


Calculate the ratio of the angular
momentum of the earth about its axis
due to its spinning motion to that about the sun due to its orbital motion.

Radius of the earth=6400km and radius
of the orbit of the earth about the sun is
equal to \( 1.5 \times 10^{8} \mathrm{km} \)


Which of the following statements is correct about the equilibrium constant?
A. Its value increases by increase in temperature
B. Its value decreases by decrease in temperature
C. Its value may increase or decrease with increase in temperature
D. Its value is constant at all temperature


Find the sum of the following APs:
(i) \( 2,7,12, \dots, \) to 10 terms.
(ii) \( 37,33,29, \dots, \) to 12 terms.
(iii) \( 0.6,1.7,2.8, \dots, \) to 100 terms.
(iv) \( \frac{1}{15}, \frac{1}{12}, \frac{1}{10}, \dots, \) to 11 terms.


Find the total volume of these three
identical toy blocks


Which of the following material is likely to have least friction?
A. wood
c. glass
D. paper


\( \vec{A} \) is a vector which when added to the resultant of vectors \( (2 \hat{i}-3 \hat{j}+4 \widehat{k}) \) and \( (\widehat{\boldsymbol{i}}+\boldsymbol{5} \widehat{\boldsymbol{j}}+\boldsymbol{2} \widehat{\boldsymbol{k}}) \) yields a unit vector along
the y-axis. Then vector \( \vec{A} \) is:
A . \( -3 \hat{i}-\widehat{j}-6 \widehat{k} \)
B. \( 3 \hat{i}+\widehat{j}-6 \widehat{k} \)
c. \( 3 \hat{i}-\widehat{j}+6 \widehat{k} \)
D. \( 3 \hat{i}+\widehat{j}+6 \widehat{k} \)


In an experiment, the following observations were recorded:
\( \boldsymbol{L}=\mathbf{2 . 8 2 0 m}, \boldsymbol{M}=\mathbf{3 . 0 0 k g}, \boldsymbol{l}= \)
\( 0.087 c m, \) diameter \( D=0.041 c m \)
Taking \( g=9.81 m s^{-2} \) and using the
formula, \( Y=\frac{4 M g}{\pi D^{2} l}, \) find the maximum permissible error in \( Y \)


Order of \( \left(\frac{d y}{d x}+3 x\right)^{3 / 2}=x+\frac{3 d y}{d x} \) is:
\( A \cdot 3 \)
B. 2
\( c \)
\( D \)


\( \boldsymbol{I}=\int \frac{\mathbf{1}}{\boldsymbol{x} \log \boldsymbol{x}} \boldsymbol{d} \boldsymbol{x} \)


Which one form negative ions in an
ionic bond?
A. Alkali metalss
B. Alkaline earth metals
c. Noble gases
D. Halogens
E. Transition metals


Adjacent sides of a parallelogram are \( 5 c m \) and \( 3.5 \mathrm{cm} . \) One of its diagonals is
\( 6.5 \mathrm{cm} . \) Then what is the area of
parallelogram?
A. \( 8 \sqrt{3} \mathrm{cm}^{2} \)
В. \( 9 \sqrt{3} \mathrm{cm}^{2} \)
\( \mathbf{c} \cdot 10 \sqrt{3} \mathrm{cm}^{2} \)
D. \( 12 \sqrt{3} \mathrm{cm}^{2} \)


If \( A \) is a matrix of order \( 3 \times 4 \), then both
\( A B^{T} \) and \( B^{T} A \) are defined if order of \( B \)
is
\( A \cdot 3 \times 3 \)
B. \( 4 \times 4 \)
c. \( 4 \times 3 \)
D. \( 3 \times 4 \)


A person invested Rs 1,600 for 3 years
and Rs 1,100 for 4 years at the same rate of simple interest. The total interest
from these investments was Rs 506
Find the rate percent per annum
A. 5\%
B \( \cdot 5 \frac{1}{2} \% \)
c. \( 6 \% \)
D. \( 6 \frac{1}{2} \% \)


A body of mass \( 36 g m \), moves with
S.H. \( M \) of amplitude \( A=13 \mathrm{cm} \) and
period \( \boldsymbol{T}=\mathbf{1 2} \) sec. At a time \( \boldsymbol{t}=\mathbf{0}, \) the
displacement is \( \boldsymbol{x}=+\mathbf{1 3} \) cm. The
shortest time of passage from \( \boldsymbol{x}= \)
\( +6.5 \mathrm{cm} \) to \( x=-6.5 \) is ?
\( \mathbf{A} \cdot 4 \sec \)
B. 2 sec
\( \mathrm{c} \cdot 6 \mathrm{sec} \)
D. 3 sec


The middle term in the expansion of
\( \left(\frac{2 x}{3}-\frac{3}{2 x^{2}}\right)^{2 n} \) is
A \( \cdot 2^{n} \mathrm{C}_{n} \)
B \cdot \( (-1)^{n}\left[(2 n !) /(n !)^{2}\right] \cdot x^{-n} \)
\( \mathrm{c} \cdot_{2 n} \mathrm{C}_{n} \cdot \frac{1}{x^{n}} \)
D. none of these


Hypodermis (panniculus adiposus) of the skin is formed of
A. Adipose connective tissue
B. Epithelial tissue
c. Muscular tissue
D. Areolar connective tissue


If the three points with position vectors \( \bar{a}-2 \bar{b}+3 \bar{c}, 2 \bar{a}+\lambda \bar{b}-4 \bar{c},-7 \bar{b}+10 \bar{c} \)
are collinear, then \( \lambda= \)
\( A \)
B. 2
\( c .3 \)
D. none of these


Solve each of the following equations and also verify your solution:
\( \frac{7}{x}+35=\frac{1}{10} \)


What is the stereochemistry of the
product(s) for an \( S_{N} 2 \) Reaction?
A. \( R \)
B. \( S \)
c. Racemic mixture
D. No chiral center in product


A hydrocarbon with formula \( C_{8} H_{18} \) gives one monochloro derivative. The
hydrocarbon is:
A. n-octane
B. 2 methyl heptane
c. 2,2,4 - trimethylpentane
D. 2,2,3,3 , tetramethylbutane


The electric field \( E \) is uniform in the
shaded area and makes an angle \( \theta \)
with the normal. The conductivity of the
material in which the area \( \$ \) lies is \( \sigma \)
The electric current flowing out of the shaded area is
A. \( \sigma E S \cos \theta \)
B . \( \sigma E S \cos ^{2} \theta \)
c. \( \sigma E S \sin \theta \)
D. \( \sigma E S \sin ^{2} \theta \)


Figure (a) and figure (b) both are
showing the variation of resistivity \( (\rho) \)
with temperature (T) for some
materials. Identify the type of these
materials.
A. Conductor and semiconductor
B. Conductor and Insulator
c. Insulator and semiconductor
D. Both are conductors


Eichler divided plant kingdom in
A. Two divisions
B. Four divisions
c. Ten divisions
D. Five divisions


A slide projector gives a magnification
10. If a slide of dimensions \( 3 \mathrm{cm} \times 2 \mathrm{cm} \)
is projected on the screen the area of image screen is
A \( .6000 \mathrm{cm}^{2} \)
в. \( 600 \mathrm{cm}^{2} \)
\( c \cdot 60^{2} \mathrm{cm}^{2} \)
D. \( 6 \mathrm{cm}^{2} \)


Which of the following is laboratory preparation of dihydrogen?
A \( \cdot 3 F e+4 H_{2} O(\text {steam}) \rightarrow F e_{3} O_{4}+4 H_{2} \)
в. \( 2 N a+2 H_{2} O \rightarrow 2 N a O H+H_{2} \)
c. \( C a H_{2}+2 H_{2} O \rightarrow C a(O H)_{2}+2 H_{2} \)
D. \( Z n+H_{2} S O_{4}(d i l .) \rightarrow Z n S O_{4}+H_{2} \)


Which power supply can be used in electric bell
A. \( A C \)
в. \( D C \)
c. can't be predicted
D. Both A and B


\( f f(x)=\left|\begin{array}{ccc}x & \cos x & e^{|x|} \\ \sin x & x^{2} & \sec x \\ \tan x & 1 & 2\end{array}\right| \) then the
value of \( \int_{-\pi / 2}^{\pi / 2} f(x) d x \) is equal to


\( B e H_{2} \) and \( M g H_{2} \) are prepared using the reagent:
This question has multiple correct options
A . \( L i H \)
в. \( A l H_{3} \)
c. LiAlH\( _{4} \)
D. \( H_{2} \)


Calgon is an industrial name given
to
A. normal sodium phosphate
B. sodium meta-aluminate
c. sodium hexametaphosphate
D. hydrated sodium aluminium silicate


In onion root tip during metaphase stage of mitiosis the number of kinetochores will be -
\( A \cdot 4 \)
B. 8
\( c \cdot 16 \)
D. 32


A group of closely related, structurally and functionally similar organism which interbreed with one another in
nature, but not with organisms of other groups is known as
A. Order
B. Genus
c. species
D. Family


\( N_{2} O_{4} \) dissociates as \( N_{2} O_{4} \rightleftharpoons 2 N O_{2} \)
At \( 55^{\circ} \mathrm{C} \) and one atmosphere, \( \% \)
decomposition of \( N_{2} O_{4} \) is \( 50.3 \% . \) At
what \( \boldsymbol{P} \) and same temperature, the equilibrium mixture will have the ratio
of \( N_{2} O_{4}: N O_{2} \) as \( 1: 8 ? \)


ABCD is a parallelogram, \( A E \perp D C \) and \( \boldsymbol{C F} \perp \boldsymbol{A D} . \) If \( \boldsymbol{A B}=\mathbf{1 6} \mathrm{cm}, \boldsymbol{A} \boldsymbol{E}=\mathbf{8} c \boldsymbol{m} \)
and \( \boldsymbol{C F}=\mathbf{1 0} \mathrm{cm}, \) find \( \boldsymbol{A} \boldsymbol{D} \)


The area of the triangle formed by the
\( \operatorname{lines} x+y=3, x-3 y+9=0 \) and
\( 3 x-2 y+1=0 \) is
A \( -\frac{16}{7} \) sq. units
B \( \cdot \frac{10}{7} \) sq. units
c. 4 sq. units
D. 9 sq. units


An example of water soluble vitamin is:
A. vitamin D
B. vitamin E
c. vitamin A
D. vitamin C


\( \boldsymbol{A l}^{3+}(\boldsymbol{a q})+\boldsymbol{3} \boldsymbol{e}^{-} \rightarrow \boldsymbol{A l}(\boldsymbol{s}) ; \boldsymbol{E}^{\circ}= \)
\( -1.66 V \)
\( \boldsymbol{C u}^{2+}(\boldsymbol{a q})+\boldsymbol{2} \boldsymbol{e}^{-} \rightarrow \boldsymbol{C u}(\boldsymbol{s}) ; \boldsymbol{E}^{\circ}= \)
\( +0.34 V \)
What voltage is produced under standard conditions to give a
spontaneous reactions by combination of these two-half cells?
A \( .1 .32 \mathrm{V} \)
W
в. \( -1.32 v \)
c. \( 2.00 V \)
D. \( -2.00 V \)


The shaded region in the diagram is:
\( A \cdot A \cup B \)
B . \( A \)
\( c \cdot B^{\prime} \)
D. \( A \cap B \)


If in \( \triangle P Q R \) and \( \triangle L M N, \angle P=\angle M= \)
\( \mathbf{6 0}^{\circ}, \boldsymbol{P Q}: \boldsymbol{M} \boldsymbol{L}=\boldsymbol{P} \boldsymbol{R}: \boldsymbol{M} \boldsymbol{N} \) and \( \angle \boldsymbol{N}= \)
\( 55^{\circ}, \) then \( \angle Q \) is:
A .50
B. 55
\( c \cdot 65 \)
D. 75


Find the value of \( k, \) so that the function
\( f(x) \) is continuous at the indicated
point \( \left.\boldsymbol{f}(\boldsymbol{x}) \begin{array}{l}=\frac{8^{x}-2^{x}}{k^{x}-1} \text { for } \boldsymbol{x} \neq \boldsymbol{o} \\ =\boldsymbol{2} \quad \boldsymbol{x}=\mathbf{0}\end{array}\right\} \boldsymbol{a} \boldsymbol{t} \boldsymbol{x}=0 \)


A conductivity cell filled with
\( 0.01 M A g N O_{3} \) solution gives at \( 25^{\circ} C \)
a resistance of \( 1442 \Omega \). If the molar
conductivity of \( 0.01 M A g N O_{3} \) solution is \( 124.8 \Omega^{-1} c m^{2} m o l^{-1}, \) what
is the cell constant?


A sings with a frequency \( (n) \) and \( B \) sings with a frequency \( 1 / 8 \) that of \( A \). If
the energy remains the same
and the amplitude of \( A \) is \( a \), then
amplitude of \( \boldsymbol{B} \) will be
A . \( 2 a \)
B. \( 8 a \)
c. \( 4 a \)
D.


The fossils of Cro-Magnon were found in
A. Algeria - In ternifine deposits
B. Germany - In ravines
C. France - Rock shelters
D. Africa - Olduvi


The frequency of \( e^{-} \) in the first Bohr orbit in a H-atom is:
A. \( 6530 \times 10^{12} \mathrm{Hz} \)
В. \( 6840 \times 10^{12} \mathrm{Hz} \)
c. \( 6430 \times 10^{12} \mathrm{Hz} \)
D. \( 6734 \times 10^{12} \mathrm{Hz} \)


The kinetic energy of an \( \alpha- \) particle
which flies out of the nucleus of a \( R a^{226} \)
atom in radioactive disintegration is 4.78 \( M \) ev. Find the total energy evolved
during the escape of the \( \alpha- \) particle.


The numerator of a fraction is 5 less
than its denominator. If 3 is added to
the numerator and denominator both, the fraction becomes \( \frac{4}{5} . \) Find the original fraction.
A \( \cdot \frac{1}{22} \)
в. \( \frac{17}{22} \)
c. \( \frac{17}{2} \)
D. \( \frac{7}{22} \)


Which of the following functions is every where continuous-
A . \( x+|x| \)
B . \( x-|x| \)
c. \( x|x| \)
D. All of the above


An alloy weighing 1.05 g of \( P b-A g \) was dissolved in desired amount of
\( H N O_{3} \) and the volume was made 350
\( \mathrm{mL} . \) An \( \mathrm{Ag} \) electrode was dipped in
solution and \( E_{\text {cell}} \) of the cell
K. The percentage of lead in alloy is (divide answer by 25 ) :
Given: \( \boldsymbol{E}_{A \boldsymbol{g}^{+} / \boldsymbol{A} \boldsymbol{g}}^{o}=\mathbf{0 . 8 0} \boldsymbol{V} \)


If a charge is moving along the direction of coulomb's force of an electric field,
A. work is done by the electric field
B. energy is used from some outside source
c. strength of field decreases
D. energy of the system is decreased


A thin brass sheet at \( 10^{\circ} C \) and a thin
steel sheet at \( 20^{\circ} C \) have the same
surface area. The common temperature at which both would have the same area
is: (Coefficients of linear expansion for brass and steel are \( 19 \times 10^{-6} /^{\circ} \mathrm{C} \) and
\( 11 \times 10^{-6} /^{\circ} C \quad \) respectively
A. \( -3.75^{\circ} \mathrm{C} \)
B . \( -2.75^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 2.75^{\circ} \mathrm{C} \)
D. \( 3.75^{\circ} \mathrm{C} \)


Which conformation of ethane has the
lowest potential energy?
A. Eclipsed
B. Skew
c. staggered
D. All will have equal potential energy


An object having a velocity \( 4.0 m / s \) is
accelerated at the rate of \( 1.2 m / s^{2} \) for 5.0s. Find the distance travelled during
the period of acceleration
A . \( 35 m \)
B. \( 55 m \)
\( c .60 m \)
D. 20m


The approximate radius of polonium nucleus of mass number 210 is:
\( \mathbf{A} \cdot 8 \times 10^{-6} m \)
B. \( 8 \times 10^{-5} m \)
\( \mathbf{c} \cdot 4 \times 10^{-6} m \)
D. none of these


A particle performing SHM has a period of \( 6 s \) and amplitude of \( 8 \mathrm{cm} . \) The particle starts from the mean position
and moves towards the positive extremity. At what time will it have the maximum amplitude
A . \( 6 s \)
B. 4.5s
\( c \cdot 1.5 s \)
D. 3 s


Show that \( \boldsymbol{A}(\mathbf{2}, \mathbf{3}), \boldsymbol{B}(\mathbf{4}, \mathbf{5}) \) and \( \boldsymbol{C}(\mathbf{3}, \mathbf{2}) \)
can be the vertices of a rectangle. Find the coordinates of the fourth vertex


State the amount of charge on each
particle in a cathode ray tube
A. \( -3.2 \times 10^{-19} \mathrm{C} \)
В. \( -1.6 \times 10^{-19} \mathrm{C} \)
c. \( +1.6 \times 10^{-19} C \)
D. \( +3.2 \times 10^{-19} \mathrm{C} \)


A reciever has a pressure of \( 144 \mathrm{cm} \) of \( \mathrm{Hg} \) After two strokes with an exhaust pump,
the pressure is \( 36 \mathrm{cm} \) of Hg. After another
two strokes the pressure will be.
\( \mathbf{A} \cdot \) 9cm of \( \mathrm{Hg} \)
B. \( 2.4 \mathrm{cm} \) of \( \mathrm{Hg} \)
\( \mathbf{C} . \) 6cm of \( \mathrm{Hg} \)
D. \( 3 \mathrm{cm} \) of \( \mathrm{Hg} \)


If trans-2-butene is treated with \( \boldsymbol{B} \boldsymbol{r}_{2}- \)
\( H_{2} O \) containing some \( N a C l \) and \( A l C l_{3} \)
how many different dihalides (including stereoisomers)would result?


In the figure shown, the plank is being
pulled to the right with a constant
speed \( v . \) If the cylinder does not slip
then
A. The speed of the centre of mass of the cylinder is 22
B. The speed of the centre of mass of the cylinder is zero
C. The angular velocity of the cylinder is \( v / R \)
D. The angular velocity of the cylinder is zero


Two charges of \( +1 \mu C \&+5 \mu C \) are
placed \( 4 c m \) apart, the ratio of the force
exerted by both charges on each other will be -
A . 1: 1
B. 1: 5
c. 5: 1
D. 25: 1


A primary amine \( \{\mathrm{B} \) ), on treatment with
a solution of \( A u C l_{3} \) in conc. \( H C l \) yields
a compound whose formula would be?
\( \mathbf{A} \cdot(B H)^{+} \cdot A u C l_{4}^{-} \)
B \( \cdot\left(B H_{2}\right)^{+} \cdot A u C l_{4}^{-2} \)
\( \mathbf{c} \cdot(B H)^{+} \cdot H A u C l_{4} \)
D. \( B . A u C l_{4} \)


Door hinge is about \( 1.5 \mathrm{m} \) away from handle, and a boy applies a force of \( 4 \mathrm{N} \) moment of force will be
A. \( 5.5 \mathrm{N} \) m
B. 2.66 N m
\( c \cdot 6 N m \)
D. 2.5 N m


A mixture of the sulphides of
\( A s_{2} S_{3}, S b_{2} S_{3} \) and \( B i_{2} S_{3} \) was treated
with a \( N a_{2} S \) solution. \( A s_{2} S_{3} \) remained undissolved.
A. True
B. False


A water tank has the shape of a right circular cone with its vertex down. Its
altitude is \( 10 \mathrm{cm} \) and the radius of the
base is \( 15 \mathrm{cm} \). Water leaks out of the
bottom at a constant rate of
1 \( c u \) cm / sec. Water is poured into the
\( \operatorname{tank} \) at a constant rate of \( C \) cu.cm / sec.
Compute \( C \) so that the water level will
be rising at the rate of \( 4 \mathrm{cm} / \) sec at the
instant when the water is \( 2 \mathrm{cm} \) deep.


Which of the following statements
is/are true about nitrogen?
This question has multiple correct options
A. Its atomic number is 7
B. It is very difficult to identify
C. It is a typical non metal
D. Ease of formation of triple bond


Consider the following hydrides and arrange them in increasing order of bond angles:
(।) \( N H_{3} \)
(II) \( \boldsymbol{P H}_{\mathbf{3}} \)
(III) \( \boldsymbol{A} \boldsymbol{s} \boldsymbol{H}_{3} \)
\( (\mid V) S b H_{3} \)
A. \( I<I I<I I I<I V \)
в. \( I V<I I I<I I<I \)
c. \( I<I I I<I I<I V \)
D. \( I V<I I<I I I<I \)


A boy of mass \( 30 \mathrm{kg} \) sitting at a
distance of \( 2 \mathrm{m} \) from the middle of see-
saw. Where should a boy of mass \( 40 \mathrm{kg} \) sit so as to balance the see -saw?


(a) What is linearly polarized light. Describe briefly using a diagram how sunlight is polarised.
(b) Unpolarised light is incident on a Polaroid. How would the intensity of transmitted light change when the Polaroid is rotated?


In rusting of iron, iron is oxidised and \( \mathrm{O}_{2} \)
is reduced. The no. of electrons used
during reduction \( \mathrm{O}_{2} \) are :


Why does all weather phenomena take place in the troposphere?


Write any four salient features of the Double helix structure of DNA.


The rate for the reaction between ionic
compounds cannot be determined
because they are generally:
A. immeasurably slow reactions
B. moderately slow reactions
c. instantaneous reactions
D. not precipitation reaction


If the diameter of a circle decreases to
its \( \frac{1}{4} \) then its radius decreases to
A \( \cdot \frac{1}{2} \)
B. 4
\( c \cdot \frac{1}{4} \)
D.


If \( \vec{a} \) and \( \vec{b} \) are two non-zero and non collinear vectors, then \( \vec{a}+\vec{b} \) and \( \vec{a}-\vec{b} \)
are
A. linearly dependent vectors
B. linearly independent vectors
c. linearly dependent and independent vectors
D. none of the above


The condition of no-slip in rotation of a
pulley attached to a mass using a
string refers to
\( \mathbf{A} \cdot v=R \omega ; v \) is the linear velocity, \( \omega \) is the angular
velocity and \( \mathrm{R} \) is the radius
B. \( a=R \alpha ; a \) is the linear acceleration, \( \alpha \) is the angular acceleration and \( \mathrm{R} \) is the radius
C \( . v=R \omega \) and \( a=R \alpha ; v \) is the linear velocity, \( \omega \) is the
angular velocity, \( \alpha \) is the angular acceleration and \( \mathrm{R} \) is
the radius
\( ^{\mathrm{D}} T=M \frac{v^{2}}{R} ; T \) is the tension in the string, \( v \) is the linear
velocity, and \( R \) is the radius


State the name of a regular polygon of 4 sides.
A. Square
B. Trapezium
c. Rectangle
D. Parallelogram


A tissue present in guava pulp and tea leaves is
A. Sclereid
B. Chlorenchyma
c. collenchyma
D. Aerenchyma


In human, the prothrombin required for blood clotting is produced in
A. Liver
B. Stomach
c. Pancreas
D. spleen


What is bad ozone and good ozone?


If the coefficients of \( x^{2} \) and \( x^{3} \) are both
zero, in the expansion of the expression \( \left(1+a x+b x^{2}\right)(1-3 x)^{15} \) in powers of \( x \)
then the ordered pair \( (a, b) \) is equal to:
A. (28,315)
B. (-54,315)
c. (-21,714)
D. (24,861)


A photoelectric cell is illuminated by a
point source of light \( 1 \mathrm{m} \) away. When the source is shifted to 2 m then
A. each emitted electron carries one quarter of the initial
energy
B. number of electrons emitted is half the initial number
C. each emitted electron carries half the initial energy
D. number of electrons emitted is a quarter of the initial number


Rectilinear propagation is:
A. Mode of travelling in curved lines
B. Mode of travelling in straight lines
C. Ability to bend around obstacles
D. Displaying the phenomenon of diffraction


Find the value of \( x \) for which the matrix
product
\[
\left[\begin{array}{ccc}
2 & 0 & 7 \\
0 & 1 & 0 \\
1 & -2 & 1
\end{array}\right]\left[\begin{array}{ccc}
-x & 14 x & 7 x \\
0 & 1 & 0 \\
x & -4 x & -2 x
\end{array}\right] \text { equa }
\]
to an identity matrix.


Represent \( \frac{1}{1-\cos \theta+2 i \sin \theta} \) in the
form \( \boldsymbol{A}+\boldsymbol{i} \boldsymbol{B} \)


According to the Boltzmann's law of equipartition of energy, the energy per degree of freedom and at a temperature
T K is :
A. (3/2) KT
B. (2/3) KT
c. кт
D. 1/2 KT


\( \frac{24}{8} \) can be expressed in percentage as \( \% \)


For a reaction, \( 2 H I \rightleftharpoons H_{2}+I_{2} \) at
equilibrium, \( 7.8 \mathrm{g}, 203.2 \mathrm{g} \) and \( 1638.4 \mathrm{g} \)
of \( \boldsymbol{H}_{2}, \boldsymbol{I}_{2} \) and \( \boldsymbol{H} \boldsymbol{I} \) respectively
were found. Calculate \( \boldsymbol{K}_{\boldsymbol{C}} \)
A. \( K_{C}=2.1 \)
В. \( K_{C}=0.019 \)
c. \( K_{C}=0.005 \)
D. \( K_{C}=0.27 \)


Solve: \( \tan ^{-1} 2 x+\tan ^{-1} 3 x=\frac{\pi}{4} \)


What is meant by natural frequency of vibration of a body?


What is E in the outer region of the first
plate?
A \( \cdot \frac{1}{2} \times 10^{-10} N / C \)
B . \( 2 \times 10^{-10} N / C \)
c. \( 0 N / C \)
D . \( 5 \times 10^{-10} \mathrm{N} / \mathrm{C} \)


A candle is placed in front of an optical instrument, and an image is obtained as inverted, real, and on the same side
of the device. Identify the device that would produce the types of images described above.
A. Concave mirror
B. Convex mirror
c. concave lens
D. Convex lens
E. Flat mirror


In the circuit shown the cells \( A \) and \( B \)
have negligible resistances.For \( \boldsymbol{V}_{\boldsymbol{A}}= \)
\( 12 V, R_{1}=500 \Omega \) and \( R=100 \Omega \) the
galvanometer \( (G) \) shows no deflection.
The value of \( V_{B} \) is :-
A . \( 12 V \)
B. \( 6 V \)
\( c .4 V \)
D. \( 2 V \)


Untreated domestic sewage has a low:
A. BOD value
B. \% of dissolved \( 0_{2} \)
c. amount of dissolved salts
D. value of suspended organic matter


The following data shows the average age of men in various countries in a
certain year:

Country India Nepal China
Average age \( \operatorname{lin} \) 52 \( \quad \) 60 years)
Represent the above information by a
bar graph.


Assertion
An ideal fluid is flowing through a pipe. Speed of fluid particles is more at places where pressure is low.
Reason
Bernoulli's theorem can be derived from
work-energy theorem.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which of the following pairs represent the same rational number?
This question has multiple correct options
A \( \cdot \frac{-7}{21} \) and \( \frac{3}{9} \)
B. \( \frac{-16}{20} \) and \( \frac{20}{-25} \)
c. \( \frac{-2}{-3} \) and \( \frac{2}{3} \)
D. \( \frac{-3}{5} \) and \( \frac{-12}{20} \)
E \( \frac{8}{-5} \) and \( \frac{-24}{15} \)
F. \( \frac{1}{3} \) and \( \frac{-1}{9} \)


An \( \alpha \) -particle is bombarded on \( ^{14} \mathrm{N} \). As a
result, a \( ^{17} \) O nucleus is formed and a
particle is emitted. This particle is a
A. neutron
B. proton
c. electron
D. positron


A \( 50 H z \) alternating current of crest value \( 2.0 . A \) flows through the primary of a transformer. If the mutual inductance
between the primary and secondary is \( 0.25 H . \) The crest voltage induced in the
secondary is
A . \( 50 V \)
B. \( 100 V \)
c. \( 200 V \)
D. 300V


Fill in the blanks:
The most tremor-threatened areas in
India are Kashmir, and
A. Western, Eastern Himalayas
B. Northern, Western Himalayas
C. Eastern, Central Himalayas
D. Western, Central Himalayas


The nucleus for cloning of dolly was taken from
A. Finn dorset sheep
B. Scottish black face ewe
c. Both A and B
D. None of these


The equation of a wave is given by \( \boldsymbol{y}= \) \( 10 \sin \left[\frac{2 \pi t}{30}+\alpha\right] . \) If the displacement is
\( 5 c m \) at \( t=0, \) then the total phase at
\( t=7.5 s \) will be
A \( \cdot\left(\frac{2 \pi}{3}\right) r a d \)
В. \( \left(\frac{2 \pi}{5}\right) \) rad
c. \( \left(\frac{\pi}{3}\right) \) rad
D. \( \left(\frac{\pi}{2}\right) \) rad


\( \boldsymbol{R} \boldsymbol{C O C l}+\boldsymbol{H}_{2} \stackrel{\boldsymbol{P d}+\boldsymbol{B a S O}_{4}}{\longrightarrow} \boldsymbol{A} \stackrel{\boldsymbol{H C N}}{\longrightarrow} \boldsymbol{B} \stackrel{\boldsymbol{H}_{3} \boldsymbol{O}}{\longrightarrow} \)
\( C \)
In the reaction sequence \( A, B \) and \( C \) are given by the set:-
\( \begin{array}{llll}\text { A. } R C H O, & R C H(O H) C N, & R C H(O H) C H_{2} N H_{2}\end{array} \)
в. \( R C H O, \quad R C H(O H) C N, \quad R C H(O H) C O O H \)
\( c \)
\( \mathrm{RCHO} \)
D. \( R C H O, \quad R-C H_{2}-C N, \quad R-C H_{2}-C O O H \)


Which of the following is/are reduction reaction ?
A. Hydrogenation of alkene and alkyne
B. Ozonolysis with \( O_{3} / Z n \)
c. Halogenation of alkene
D. All of these


An \( L-C \) circuit consists of an
inductor of \( L=0.0900 H \) and a
capacitor of \( C=4 \times 10^{-4} F . \) The initial
charge on the capacitor is \( 5.00 \mu C \) and the initial current in the inductor is
zero. When the current in the inductor
has half its maximum value, what is
the energy stored in the inductor?
A \( .7 .8 \times 10^{-9} J \)
B . \( 9.8 \times 10^{7} J \)
c. \( 7.8 \times 10^{7} J \)
D. \( 9.8 \times 10^{-7} J \)


Angle of minimum deviation for a prism of refractive index 1.5 is equal to the angle of prism of given prism. Then, the
angle of prism is \( \left(\sin 48^{\circ} 36^{\prime}=\right. \)
0.75)
A . \( 80^{\circ} \)
B . \( 41^{\circ} 24^{\prime} \)
\( c \cdot 60 \)
D . \( 82^{\circ} 48^{\prime} \)


Calculate the capacitance (in farads) of
a charged, parallel-plate capacitor. Given the potential difference between
the plates is equal to \( X \) volts and the
amount of charge on the POSITIVE plate
is equal to \( Y \) coulombs.
A \( \cdot \frac{X}{2 Y} \)
в. \( \frac{Y}{2 X} \)
\( c \cdot \frac{Y}{X} \)
D. \( \frac{2 Y}{X} \)
E \( \cdot \frac{2 X}{Y} \)


State Kepler's third law.


Consider the following reactions in equilibrium with initial concentration of \( 0.01 \mathrm{M} \) of every species (assuming the same equilibrium constant same)
\( (\mid) P C l_{5}(g) \rightleftharpoons P C l_{3}(g)+C l_{2}(g) \)
\( (\|) 2 \boldsymbol{H} \boldsymbol{I}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{I}_{2}(\boldsymbol{g}) \)
\( (\| I) N_{2}(g)+3 H_{2}(g) \rightleftharpoons 2 N H_{3}(g) \)
Arrange these reactions in the order of the extent to which it takes place.
A \( . \) ।>॥>
c. ॥<॥ा《


The equation of altitude through \( B \) to
side \( A C \) is
A. \( r=k+t(7 i-10+2 k) \)
в. \( r=k+t(-9 i+6 j-2 k) \)
c. \( r=k+t(7 i-10 j-2 k) \)
D. \( r=k+t(7 i+10 j+2 k) \)


\( K^{+} \) and \( F^{-} \) have identical radius about
1. 34 A. What should be the atomic
radius of \( K \) and \( F \) atoms?


Find the number of terms in an
arithmetic progression with the first term 2 and the last term being \( 62, \) given that common difference is 2
A . 31
B. 40
\( c \cdot 22 \)
D. 27


If a system left over a period of time, What happens to the amount of its
usable energy?
A . increases
B. decreases
c. remains constant
D. increases until the heat of friction equal the original potential energy in the system
E. decreases until no heat is left in the system


\( \underbrace{\begin{array}{l}a \\ 0\end{array}} \)
\( = \)


A person working with phosphorus suffer from a disease in which bones
decay. It is known as:
A. arthrities.
B. phossy jaw.
c. rickets
D. cancer


Black Jack is a sulphide ore.
A. True
B. False


A body is projected horizontally from a point above the ground and motion of the body is described by the equation
\( \boldsymbol{x}=\mathbf{2} \boldsymbol{t}, \boldsymbol{y}=\mathbf{5} \boldsymbol{t}^{2} \) where \( \boldsymbol{x}, \) and \( \boldsymbol{y} \) are
horizontal and vertical coordinates in
meter after time \( t . \) The initial velocity of the body will be
A. \( \sqrt{29} \mathrm{m} / \mathrm{s} \) horizontal
B . \( 5 \mathrm{m} / \mathrm{s} \) horizontal
c. \( 2 m / s \) vertical
D. \( 2 m / s \) horizontal


Two moles of an ideal gas at \( 300 K \) were cooled at constant volume so that
the pressure is reduced to half the
initial value. Then as a result of heating at constant pressure, the gas expands till it attains the original temperature
Find the total heat absorbed by the gas, if \( R \) is the gas constant.
A. \( 150 R \) \( J \)
в. \( 300 R \) Л
c. \( 75 R J \)
D. \( 100 R J \)


Write the equations for
i) The action of \( S O_{2} \) with chlorine in the
presence of charcoal
ii) The action of \( S O_{3} \) with concentrated
sulphuric acid
iii) The action of ozone with lead
sulphide.


Find the simple interest if \( P=R s .500, R \) \( =2 \% \) per six months \( \& \mathrm{T}=2 \frac{1}{2} \) years.
A. Rs. 20
B. Rs. 25
c. Rs. 40
D. Rs. 50