Buildings are more susceptible to a lightning strike because
A. they are higher than their surroundings.
B. roofs of buildings are wet in rainy season and hence become good conductors of electricity.
c. the top of the building is wet and acquires an opposite charge to a cloud passing over the top by induction
D. All of the above


Arrange the following in order of decreasing acidic strength. nitrophenol
(1), p-cresol (II), m-cresol phenol (IV) :
A \( . I>I V>I I>I I I \)
\( I \)
B. \( I V>I I I>I I>I \)
c. \( I>I I>I I I>I V \)
\( . I I I>I I>I>I V \)
\( V \)


Inductive reactance of a coil is
expressed in
A. Amphere
B. onm
c. volt
D. weber


In a Std. \( X \) class, out of 40 students, 10
students use spectacles, 2 students
have positive power and 8 students
have negative power of lenses in their spectacles. Answer the following questions:
(i) What does the negative power
indicate?
(ii) What does the positive power indicate?
(iii) Generally which type of spectacles
do most of the students use?
(iv) What defect of eyesight do most of the students suffer from?
(v) Give two possible reasons for the above defect.


Draw a Venn-diagram to show the
relationship between two overlapping sets \( A \) and \( B \). Now shade the region
representing \( \boldsymbol{A} \cap \boldsymbol{B} \)


Q Type your question
\( \left(\frac{a x}{d t}\right) \) is plotted against \( \log [A], \) then the
graph is of the type:
\( A \)
B.
\( c \)
\( D \)


The U shaped vessel used in Nelson cell
is lined inside with asbestos which:
A. helps in the separation of cathode and anode compartments
B. acts as an insulator.
C. helps \( H^{+} \) ions to reduced to \( H_{2} \) gas
D. allows the dissociation of steam.


Q Type your question
now-famous oil-drop experiment. In that experiment, tiny oil drops were sprayed into a uniform electric field between a
horizontal pair of oppositely charged plates.The drops were observed with a magnifying eyepiece, and the electric field was adjusted so that the upward force on some negatively charged oil drops was just sufficient to balance the
downward force of gravity. That is, when suspended, upward force qE just equaled mg. Millikan accurately measured the charges on many oil drops and found the values to be whole number multiples of \( 1.6 \times 10^{-19} C \) the
charge of the electron. For this, he won the Nobel prize. If a drop of mass \( 1.08 \times \)
\( 10^{-14} k g \) remains stationary in an
electric field of \( 1.68 \times 10^{5} N C^{-1} \), then
the charge of this drop is :
A. \( 6.40 \times 10^{-19} \mathrm{C} \)
B . \( 3.2 \times 10^{-19} C \)
c. \( 1.6 \times 10^{-19} C \)
D. \( 4.8 \times 10^{-19} \mathrm{C} \)


Four equal charges q each are placed at four corners of a square of side a each. Work done in carrying a charge q from its centre to infinity is:
A. zero
В. \( \frac{2 q^{2}}{\pi \varepsilon_{0} a} \)
c. \( \frac{\sqrt{2} q^{2}}{\pi \varepsilon_{0} a} \)
D. \( \frac{q^{2}}{2 \pi \varepsilon_{0} a} \)


To balance the bridge in the circuit, the values of \( \mathrm{R} \) is
\( A \cdot 8 \Omega \)
B. \( 4 \Omega \)
\( c \cdot 20 \Omega \)
D. \( 12 \Omega \)


Assertion
The morphology of mycoplasma is not
specific
Reason
They lack a rigid cell wall
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


There is continuous multiplication in
cell nuclei and all nuclei have same
genetic information. The cell is undergoing
A. Multiple rounds of karyokinesis, but no cytokinesis
B. Multiple rounds of the M phase, but no rounds of the phase
c. Multiple rounds of cytokinesis, but no rounds of karyokinesis
D. Multiple rounds of the cell cycle, but no rounds of mitosis
E. multiple rounds of the S phase, but no other phases of the cell cycle


In the above problem, the angular acceleration
of the particle at \( t=2 \sec \) is
rads\( ^{-2} \)
A \( \cdot 14 \)
B. 16
\( c \cdot 18 \)
D. 24


The rate of certain hypothetical reaction \( A+B+C \rightarrow \) products is given by \( \boldsymbol{r}=-\frac{\mathbf{d}[\boldsymbol{A}]}{\mathbf{d} \boldsymbol{t}}=\boldsymbol{K}[\boldsymbol{A}]^{1 / 2} \boldsymbol{K}[\boldsymbol{B}]^{1 / 3} \boldsymbol{K}[\boldsymbol{C}]^{1 / 4} \)
The order of the reaction:
\( A \)
в. \( \frac{1}{2} \)
\( c \cdot 2 \)
D. \( \frac{13}{12} \)


Find \( a, b \) in \( \int \frac{x+2}{\left(x^{2}+3 x+3\right) \sqrt{x+1}} d x= \)
\( \frac{\boldsymbol{a}}{\sqrt{\boldsymbol{b}}} \tan ^{-1}\left\{\frac{\boldsymbol{x}}{\sqrt{\mathbf{3}(\boldsymbol{x}+\mathbf{1})}}\right\}+\boldsymbol{C} \)
This question has multiple correct options
\( \mathbf{A} \cdot a=2 \)
B. \( b=3 \)
\( \mathbf{c} \cdot a=3 \)
\( \mathbf{D} \cdot b=2 \)


In the reaction,
\( \mathbf{2} \boldsymbol{N} \boldsymbol{H}_{3}(\boldsymbol{g})+\mathbf{5} \boldsymbol{F}_{2} \rightarrow \boldsymbol{N}_{2} \boldsymbol{F}_{4}+\boldsymbol{6} \boldsymbol{H} \boldsymbol{F} \)
\( 3.56 g N_{2} F_{4} \) is obtained by mixing \( 2 g \)
\( N H_{3} \) and \( 8 \mathrm{g} F_{2} . \) The percentage yield of the production is:
A . 81.28\%
B . 71.2\%
c. \( 68 \% \)
D. 79\%


Using the \( \in-\delta \) definition prove that
\( \lim _{x \rightarrow-2}(3 x+8)=2 \)


The life span of a Daniel cell may
increased by:
A. large Cu electrode
B. lowering of CuSO \( _{4} \) concentration
C. lowering of ZnSO \( _{4} \) concentration
D. large zinc electrode


On the basis of following reactions, identify the correct matchings. \( \boldsymbol{A}_{(a q)}+\boldsymbol{A l} \stackrel{\text {heat}}{\longrightarrow} \boldsymbol{B}_{(\boldsymbol{g a s})} \) (colorless
combustible gas which is lightest) \( \boldsymbol{A}_{(\boldsymbol{a q})}+\boldsymbol{C} \stackrel{\text {heat}}{\longrightarrow} \boldsymbol{P} \boldsymbol{H}_{3(\boldsymbol{g a s})} \)
\( \boldsymbol{A}_{(a q)}+\boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{C l} \stackrel{\text {heat}}{\longrightarrow} \boldsymbol{D}_{(\boldsymbol{g} a s)}( \) turns red
litmus blue)
A. \( A=N a O H \) and \( C=P_{4} \)
в. \( A=C H_{3} C O O H \) and \( B=C H_{4} \)
C. \( A=K O H, D=N H_{3} \) and \( C=H_{3} P O_{4} \)
D. \( A=H C l, B=H_{2} \) and \( C=H_{3} P O_{4} \)


Find the region on Y-axis in which reflected rays are present. Object is at \( A \)
(2,0) and \( \mathrm{MN} \) is a plane mirror, as shown in Fig.


Generally, good conductors have low specific heat capacity. True/False? Justify your answer.


Mass of beaker=10g Mass of mixture+beaker=25g Mixture contains \( 30 \% \) sand. Find the
weight of sand.
\( A \cdot 58 \)
B. \( 4.5 \mathrm{g} \)
\( c \cdot 3 g \)
D. 3.5 g


Construct a triangle \( A B C \) in which
\( A B+A C=5.6 c m, B C=4.5 c m \) and
\( \angle B=45^{\circ} \)


The \( 9^{t h} \) term of an A.P. is 449 and \( 449^{t h} \)
term is 9 The term which is equal to
zero is
A \( \cdot 501^{t h} \)
B . \( 502^{\text {th }} \)
\( \mathbf{c} \cdot 508^{t h} \)
D. None of these


The energy equivalent of 1 amu is
A. 931 eV th
В. \( 93.1 V \)
\( \mathbf{c} .931 \mathrm{MeV} \)
D. \( 9.31 \mathrm{MeV} \)


The functional groups present in the following compound is:
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{C O O H} \)
A. carboxylic acid
B. carbonate
c. alcohol
D. carboxylate


Which of the following statement(s) is/are correct when a mixture of \( N a C l \)
and \( K_{2} C r_{2} O_{7} \) is gently warmed with
conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} ? \)
This question has multiple correct options
A. A deep red vapor is evolved.
B. The vapor when passed into NaOH solution gives yellow solution of \( N a_{2} C r O_{4} \)
c. chlorine gas is evolved.
D. chromyl chloride is formed.


On adding \( N a O H \) to ammonium
sulphate, a colourless gas with pungent odour is evolved which forms a blue
coloured complex with \( C u^{2+} \) ion.
Identify the gas.


(i) Why does a bottle of soft drink cool faster when surrounded by ice cubes
than by ice cold water, both at \( 0^{\circ} \mathrm{C} \) ?
(ii) A certain amount of heat \( Q \) will
warm \( 1 g \) of material \( X \) by \( 3^{\circ} C \) and \( 1 g \) of
material \( Y \) by \( 4^{o} C . \) Which material has a higher specific heat capacity?


If \( \int \frac{1}{\left(x^{2}+4\right)\left(x^{2}+9\right)} d x=A \tan ^{-1} \frac{x}{2}+ \)
\( B \tan ^{-1}\left(\frac{x}{3}\right)+C \) then \( A-B= \)
A \( \cdot \frac{1}{6} \)
B. \( \frac{1}{30} \)
\( c \cdot-\frac{1}{3} \)
D. \( -\frac{1}{6} \)


The electricity developed on objects, when they are rubbed with each other is
called:
A. Frictional potential
B. Frictional electricity
c. Static electricity
D. Static potential


Series can be defined as:
A. a number of things or events that are arranged or happen one after the other.
B. a set of regularly presented television shows involving the same group of characters or the same subject.
C. set of books, articles, etc., that involve the same group of characters or the same subject
D. All of the above


Describe oxygen-haemoglobin dissociation curve


A canon after firing recoils due to newton's third law of motion.
A . True
B. False


Chloragogen cells are present in
A. Body wall of Leucosolenia
B. Blood of earthworm
C. Coelomic fluid of earthworm
D. Blood of cockroach


State whether true or false:
A concave lens is used as a magnifying glass
A. True
B. False


Integrate: \( \int \tan ^{3} x d x \)


In which types of frames Newtons laws can be applied?


5 is a rational number. It can be written
as
A \( \cdot \frac{5}{1} \)
B. \( \frac{1}{5} \)
\( c \cdot \frac{5}{5} \)
D. \( \frac{5}{25} \)


\( \int \frac{(x+3) e^{x}}{(x+4)^{2}} d x \) is equal to
A. \( \frac{1}{(x+4)^{2}}+C \)
в. \( \frac{e^{x}}{(x+3)}+C \)
c. \( \frac{e^{x}}{(x+4)^{2}}+C \)
D. \( \frac{e^{x}}{(x+4)} \)


Find out the number of bivalents in
zygotene stage, if there are 60
chromosomes in \( G_{1} \) phase.
A . 60
B. 30
c. 15
D. 45


Find the vector equation of the plane passing through the points (2,5,-3),(-2,-3,5) and (5,3,-3)


The ammonia evolved from the
treatment of \( 1.50 \mathrm{g} \) of an organic compound for the estimation
of nitrogen was passed in \( 100 \mathrm{ml} \) of 0.5 M sodium hydroxide solution for complete neutralization.
The organic compound is:
A. thiourea
B. benzamide
c. urea
D. acetamide


If an electric current is passed through a nerve, the man
A. begins to laugh
B. begins to weep
\( \mathbf{c} . \) is excited
D. becomes insensitive to pain


Two cars \( A \) and \( B \) are travelling in the
same direction with velocities \( \boldsymbol{v}_{A} \) and
\( \boldsymbol{v}_{B}\left(\boldsymbol{v}_{A}>\boldsymbol{v}_{B}\right) . \) When the car \( \boldsymbol{A} \) is at a
distance \( d \) behind the car \( B \) the driver
of the car \( A \) applies brakes producing a
uniform retardation \( a \). There will be no
collision when
A \( \cdot \quad d<\frac{\left(v_{A}-v_{B}\right)^{2}}{2 a} \)
B. \( d<\frac{v_{A}^{2}-v_{B}^{2}}{2 a} \)
c. \( _{d}>\frac{\left(v_{A}-v_{B}\right)^{2}}{2 a} \)
D. \( d>\frac{v_{A}^{2}-v_{B}^{2}}{2 a} \)


Find the oxidation numbers to the
underlined species in the following compounds or ions.
A) \( N a \underline{B} H_{4} \)
B) \( \boldsymbol{H}_{2} \boldsymbol{P} \boldsymbol{t} \boldsymbol{C l}_{\boldsymbol{6}} \)


Rhombic sulphur remains stable below
\( 95.6^{\circ} \mathrm{C} \)
A. True
B. False


What is hybrid vehicle technology? Expalin is advantages with a suitable example?


Which of the following is a weak electrolyte?
A. \( N a_{2} C O_{3} \)
в. \( K H C O_{3} \)
c. \( \left(C H_{3} C O O\right)_{2} P b \)
D. All of the above


Find the area of \( \square A B C D \)
\( \mathbf{A} \cdot 4(24+25 \sqrt{3}) c m^{2} \)
B \( \cdot 4(25+24 \sqrt{3}) c m^{2} \)
\( \mathbf{c} \cdot 2(24+25 \sqrt{3}) c m^{2} \)
D. None of these


Acid rain is caused by:
A. deforestation
B. \( C O_{2} \)
\( \mathrm{c} \cdot \mathrm{CO} \)
D. oxides of sulphur and nitrogen


The exchange of gases in the alveoli of the lungs takes place by
A. Osmosis
B. Simple diffusion
c. Passive transport
D. Active transport


A metal which does not react with cold
water but reacts with steam to liberate
\( H_{2} \) gas is :
A. \( N a \)
в. \( M g \)
c. \( A u \)
D. \( F e \)


What is the action of acidified
potassium dichromate on the following:
1. \( \boldsymbol{H}_{2} \boldsymbol{S} \)


Solve: \( \frac{\sin ^{3} \frac{x}{2}-\cos ^{3} \frac{x}{2}}{2+\sin x}=\frac{\cos x}{3} \)
A. \( x=(2 n+1) \frac{\pi}{2}, n \epsilon z \)
B \( \cdot x=(4 n+1) \frac{\pi}{2}, n \epsilon z \)
C \( \cdot x=(4 n+1) \frac{\pi}{4}, n \epsilon z \)
D \( \cdot x=(2 n+1) \frac{\pi}{4}, n \epsilon z \)


An electron is projected in the same
direction of uniform magnetic field.
Then
A. the electron turns to right
B. the electron turns to left
C. the electron velocity remains constant
D. the electron velocity decreases in magnitude


Subtract \( 4 p^{2} q-3 p q+5 p q^{2}-8 p- \)
\( 7 q-10 \) from \( 18-3 p+11 q+5 p q \)
\( 2 p q^{2}+5 p^{2} q \)
A \( \cdot p q^{2}-7 p^{2} q+8 p q+18 q+5 p+28 \)
B . \( p^{2} q-7 p q^{2}+8 p q+18 p+5 q+28 \)
C \( \cdot p q^{2}-7 p^{2} q+8 p q+18 p+5 q+28 \)
D. \( p^{2} q-7 p q^{2}+8 p q+18 q+5 p+28 \)


In a salt solution, the flow of current is:
A. same as the direction of positive ions
B. opposite to the direction of negative ions
c. both a and b
D. opposite to the direction of positive ions


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


The degree of dissociation of
\[
\boldsymbol{P C l}_{5}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{P C l}_{3}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g})
\]
with increase in
pressure at equilibrium.
A . increases
B. decreases
c. first increases and then decreases
D. first decreases and then increases


Explain Curie's law for a paramagnetic
substance.


\( \lim _{x \rightarrow 3} \frac{\sqrt{4-x}-\sqrt{x-2}}{15-5 x} \)


A parallel beam of monochromatic unpolarised light is incident on a transparent dielectric plate of refractive index \( \frac{1}{\sqrt{3}} . \) The reflected beam is completely polarised. Then the angle of incidence is
\( A \cdot 30^{\circ} \)
B. \( 60^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 75^{\circ} \)


Heat of neutralization of \( \boldsymbol{H} \boldsymbol{C l} \) and
\( N a O H \) is \( x \) kJ and that of \( C H_{3} C O O H \)
and \( N a O H \) is \( y \) kJ. What is heat of
ionization of \( \boldsymbol{C H}_{3} \) COOH.
В. \( (y-x) \) к)
D. \( -(x+y) \) k)


If the half life period for a first order
reaction is 69.3 seconds, what is the
value of its rate constant?


If the mass defect of \( _{5} B^{11} \) is \( 0.081 u, \) its
average binding energy (in \( M e V \) ) is:
A . 8.60
B. 6.85
\( c .5 .60 \)
D. 5.86


Seeds of gymnosperms have three
generations, that is
A. Two sporophytic and one gametophytic generation
B. Two gametophytic and one sporophytic
C. All three sporophytic generations
D. All three gametophytic generations


Assertion
During change of state, specific heat of a substance is zero.
Reason
Specific heat of a substance is directly proportional to change of heat and inversely proportional to change in temperature
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Choose the correct answer:
Sound can travel through
A. Gases only
B. Solids only
c. Liquids only
D. solids, liquids and gases


Which of the following has least polar
\( C-X \) bond?
A. \( H_{3} C-C H=C H_{2}-C l \)
в. \( H O-C H=C H_{2}-C l \)
c. \( O_{2} N-C H=C H_{2}-C l \)
D. \( H S-C H=C H_{2}-C l \)


Among cellulose, polyvinyl chloride, nylon and natural rubber, in which of the polymer intermolecular force of attraction is weakest?
A. Nylon
B. Polyvinyl chloride
c. cellulose
D. Natural rubber


\( \mathbf{A}= \) the domain of \( \mathbf{f} \) where \( \mathbf{f}(\mathbf{x})=\log \mathbf{x}^{2} \)
and \( \mathbf{B}= \) the domain of \( \mathbf{g} \) where \( \mathbf{g}(\mathbf{x})= \) \( 2 \log x, \) then \( \mathbf{A}-\mathbf{B}= \)
\( A \cdot \phi \)
В \( \cdot(-\infty, 0) \)
c. \( (0, \infty) \)
D. (0,1)


\( f(x)=\left\{\begin{array}{l}x-5 ; x \leq 1 \\ 4 x^{2}-9 ; 1<x \leq 2 \\ 3 x^{2}+4 ; x>2\end{array}\right. \)
Then \( \boldsymbol{f}\left(\boldsymbol{2}^{+}\right)-\boldsymbol{f}\left(\boldsymbol{2}^{-}\right)= \)
\( A \)
B. 2
\( c \)
\( D \)


In the ladder network shown, current
through the resistor \( 3 \Omega \) is \( 0.25 A . \) The
input voltage ' \( V^{\prime} \) is equal to
A . \( 10 V \)
B . \( 20 V \)
\( c .5 V \)
D. \( \frac{15}{2} v \)


One card is drawn from a pack of 52 cards. What is the probability that the card drawn is either a red card or a
king?
A \( \cdot \frac{1}{2} \)
в. \( \frac{6}{13} \)
c. \( \frac{7}{13} \)
D. \( \frac{27}{52} \)


Find the maximum value of \( f(x)=1 \)
\( x^{2} \) if \( -2 \leq x \leq 2 \)
A . 2
B.
c. 0
D. -
E . -2


Cube of all odd natural numbers are odd
A. True
B. False
c. Ambiguous
D. Data insufficient


For constructing a triangle whose perimeter and both base angles are given, the first step is to:
A. Draw a base of any length
B. Draw the base of length = perimeter
c. Draw the base angles from a random line.
D. Draw a base of length \( =\frac{1}{3} \times \) perimeter.


Which of the following represents the given sequence of hybridisation of carbon atoms from left to right :
\( \boldsymbol{s} \boldsymbol{p}^{2}, \boldsymbol{s} \boldsymbol{p}^{2}, \boldsymbol{s} \boldsymbol{p}, \boldsymbol{s} \boldsymbol{p} ? \)
A. \( H_{2} C=C H-C \equiv C H \)
В \( \cdot_{H C} \equiv C-C H=C H_{2} \)
c. \( H_{3} C-C H=C H-C H_{3} \)
D. \( H_{2} C=C H-C H=C H_{2} \)


In a certain population \( 10 \% \) of the people are rich, \( 5 \% \) are famous and \( 3 \% \) are rich and famous. The probability that a person picked at random from the population is either famous or rich but not both, is equal to
A . 0.07
B. 0.08
c. 0.09
D. 0.12


Prove that square of any positive integer is always of the form \( 4 m, 4 m+ \) \( 1,4 m+4 \) or \( 4 m+9 \)


On the voyage of the Beagle, Darwin \( (1809-1882) \) found that flora and fauna
of temperate South America are most
similar to that of
A. Tropical South America
B. Australia
c. Asia
D. Europe


A large number of particles are placed around the origin, each at a distance \( \mathrm{R} \) from the origin. The distance of the center of mass of the system from the origin is.
\( \mathbf{A} \cdot+R \)
в. \( \leq R \)
\( c \cdot>R \)
\( D . \geq R \)


Find the equation of the ellipse whose
vertices are \( (\pm \mathbf{9}, \mathbf{0}) \) and foci are
\( (\pm \mathbf{5}, \mathbf{0}) \)


What is CFL?
A. Compact Fluorescent Lamp
B. Compact Fluorescent Lamina
C. Complete Fluorescent Light
D. Controlled Fluorescent Light


A body, under the action of a force \( \overrightarrow{\boldsymbol{F}}= \) \( 6 \hat{i}-8 \hat{j}+10 \hat{k}, \) acquires an acceleration
of \( 1 m / s^{2} . \) The mass of this body must
be:
A \( \cdot 10 \sqrt{2} k g \)
в. \( 2 \sqrt{10} k g \)
c. \( 10 \mathrm{kg} \)
D. 20 kg


Two identical balls each of mass in are
moving in opposite direction with a speed v. if they collide elastically maximum potentail energy stored in the ball is :
A. 0
в. \( \frac{1}{2} m v^{2} \)
\( \mathrm{c} \cdot m v^{2} \)
\( \mathbf{D} \cdot 2 m v^{2} \)


Knowing that the Chemistry of lanthanoids (Ln) is dominated by its +3 oxidation state, which of the
following statements is incorrect?
A. Because of the large size of the \( \operatorname{Ln}( \) (II) ions the bonding in its compounds is predominantly ionic in character.
B. The ionic sizes of Ln
(III) decrease in general with increasing atomic number
c. \( \mathrm{Ln} \) (III) compounds are generally colourless
D. Ln (III) hydroxides are mainly basic in character


The excitation energy of first excited
state of a hydrogen like atom is \( 40.8 e V \)
Find the energy needed to remove the electron to form the ion.


The probability that \( A \) hits a target is \( \frac{1}{3} \) and the probability that \( B \) hits it, is \( \frac{2}{5} \) What is the probability that the target
will be hit, if each one of \( A \) and \( B \) shoots
at the target?


\( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\frac{\boldsymbol{x}+\boldsymbol{y}+\mathbf{1}}{\mathbf{2} \boldsymbol{x}+\mathbf{2} \boldsymbol{y}+\mathbf{3}} \)


Assertion
Suspended particulate matter (SPM) is an important pollutant released by diesel vehicles.
Reason
Catalytic converters greatly reduce pollution caused by automobiles.
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 coeffecients of the middle term in
the binomial expansion in powers of \( x \) of \( (1+\alpha x)^{4} \) and \( (1+\alpha x)^{6} \) is the same
if \( \boldsymbol{\alpha} \) equals
A \( \cdot-\frac{5}{3} \)
в. \( \frac{10}{3} \)
\( c \cdot \frac{3}{10} \)
D.


If \( a,(a-2) \) and \( 3 a \) are in \( A P, \) then the
value of \( a \) is
A . -3
B. -
\( c .3 \)
D. 2


Reaction \( \boldsymbol{A}+\boldsymbol{B} \longrightarrow \boldsymbol{C}+\boldsymbol{D} \) follows rate
\( \operatorname{law}, \boldsymbol{r}=\boldsymbol{k}[\boldsymbol{A}]^{1 / 2}[\boldsymbol{B}]^{1 / 2} \) starting with \( \mathbf{1} \boldsymbol{M} \)
of \( A \) and \( B \) each. What is the time taken
for concentration of \( \boldsymbol{A} \) become \( \mathbf{0 . 1} \boldsymbol{M} \) ?
\( \left[\text { Given } 2.303 \times 10^{-2} s e c^{-1}\right] \)
\( \mathbf{A} \cdot 10 \sec \)
B. 100sec
c. 1000 sec
D. 434 sec


The values of current(l) flowing through a given resistor of resistance (R), for the corresponding values of potential difference (V) across the resistor are as
given
\( \begin{array}{lll}\mathbf{0 . 5} & \mathbf{1 . 0} & \mathbf{1 . 5}\end{array} \) V(volts) 2.0
0.1 0.3 I(amperes) 0.2
Plot a graph between current(l) and
potential difference (V) and determine the resistance (R) of the resistor.


Action of paint-gun is based on:
A. Bernoulli's principle
B. Boyle's law
C. Faraday's law
D. Archimedes's principle


Which of the following is considered Drosophila of a plant kingdom?
A. Neurospora
B. Synchytrium
c. Peziza
D. Amanita


Select the correct statements about
SHE:
This question has multiple correct options
\( \mathbf{A} \cdot \) The \( E_{O P}^{o} / R_{R P}^{o} \) for SHE has been arbitrarily assigned to be zero at all temperatures.
B. SHE refers for \( P t, H_{2}(g) \mid H^{+}(a q) \)
C. SHE is very susceptible to electrode poisoning.
D. SHE is very susceptible to dissolved oxygen, \( \mathrm{H}_{2} \mathrm{S} \) and all other reducing species.


Vant Hoff's equation is
A \( \cdot \log \frac{K_{2}}{K_{1}}=\frac{-\Delta H^{0}}{2.303 R}\left[\frac{T_{2}-T_{1}}{T_{2} T_{1}}\right] \)
B. \( \log \frac{K_{2}}{K_{1}}=\frac{\Delta H^{0}}{2.303 R}\left[\frac{T_{2}-T_{1}}{T_{2}+T_{1}}\right] \)
C. \( \log \frac{K_{2}}{K_{1}}=\frac{\Delta H^{0}}{2.303 R}\left[\frac{T_{2}-T_{1}}{T_{2} T_{1}}\right] \)
D. \( \log _{\frac{K_{1}}{L}=\frac{\Delta H^{0}}{2.203 R}}\left[\frac{T_{3}+T_{1}}{T_{1} 2_{1}}\right] \)


\( \operatorname{Let} g(x)=2 f\left(\frac{x}{2}\right)+f(x-2) \) and
\( \boldsymbol{f}^{\prime \prime}(\boldsymbol{x})<\mathbf{0} \forall \boldsymbol{x} \in(\mathbf{0}, \mathbf{2}), \) then \( \boldsymbol{g}(\boldsymbol{x}) \)
increases in
A \( \cdot\left(\frac{1}{2}, 2\right) \)
в. \( \left(\frac{4}{3}, 2\right) \)
c. (0,2)
(年. \( 0,2,2) \)
D. \( \left(0, \frac{4}{3}\right) \)


An object \( 10 \mathrm{cm} \) from lens, has a virtual image at \( 10 \mathrm{cm} \) from the object. The power of the lens is
A. 10 diopters
B. -10 diopters
c. 5 diopters
D. - diopters


The water forecasting department uses as the unit of pressure
A. bar
в. \( N m^{-2} \)
\( c . P a \)
D. mm of \( H g \)


Theoretical efficiency of fuel cell is:
A. nearly \( 60 \% \)
B. 50\%
c. \( 33 \% \)
D. nearly 100\%


A can do a piece of work in 10 days, and
B can do the same work in 20 days. With the help of \( C \), they finished the work in 4 days. \( C \) can do the work in how many days, working alone?


The \( p H \) of the solution 5 mL of \( \frac{M}{5} H C l+10 m L \) of \( \frac{M}{10} N a O H \) is:
A. 5
B. 3
\( c \cdot 7 \)
D.


A coil has self inductance of 0.01 H. The
current through it is allowed to change
at the rate of \( 1 A \) in \( 10^{-2} \) s. The induced
emf is
A . \( 1 V \)
B. 2
\( c .3 V \)
D. \( 4 V \)


The equilibrium concentration of \( [\boldsymbol{B}]_{e q} \) for the reversible reaction \( \boldsymbol{A} \rightleftharpoons \boldsymbol{B} \) can
be evaluated by the expression:
A \( \cdot K_{c}[A]_{e}^{-1} \)
B. \( \frac{K_{f}}{K_{b}}[A]_{e}^{-1} \)
\( \mathbf{c} \cdot K_{f} K_{b}^{-1}[A]_{e} \)
D. \( K_{f} K_{b}[A]^{-1} \)


For two events, \( A \) and \( B \), it is given that \( \boldsymbol{P}(\boldsymbol{A})=\frac{\mathbf{3}}{\mathbf{5}}, \boldsymbol{P}(\boldsymbol{B})=\frac{\mathbf{3}}{\mathbf{1 0}} \) and \( \boldsymbol{P}(\boldsymbol{A} \mid \boldsymbol{B})= \)
\( \mathbf{2} \)
\( \frac{2}{3} . \) If \( \bar{A} \) and \( \bar{B} \) are the complementary
events of \( A \) and \( B \), then what is \( P(\bar{A} \mid \bar{B}) \)
equal to?
\( A \cdot \frac{3}{7} \)
B. \( \frac{3}{4} \)
\( c \cdot \frac{1}{3} \)
D.


Find the general solution of the
differential equation:
\( (1+x)\left(1+y^{2}\right) d x+ \)
\( (1+y)\left(1+x^{2}\right) d y=0 \)


Let \( \boldsymbol{P}(\boldsymbol{x}) \) be a polynomial, which when divided by \( (x-3) \) and \( (x-5) \) leaves
remainders 10 and \( 6, \) respectively. If the polynomial is divided by \( (x-3)(x-5) \)
then the remainder is
A \( .-2 x+16 \)
B . 16
\( c \cdot 2 x-16 \)
D. 60


The radius of a sphere is measured to be \( (2.1 \pm 0.5) c m . \) Calculate its surface
area with error limits.


Passage cells are found in
A. Epidermis
B. Endodermis
C. Pericycle
D. Lenticels


What is the nature of the graph:
\( \boldsymbol{y}=\boldsymbol{6} e^{-4 \boldsymbol{x}} \)
A. monotonically increasing
B. monotonically decreasing
c. Increasing then decreasing
D. decreasing then increasing


State whether the given reaction is true
or false:

Heavy water is used to control nuclear
reactions.
A. True
B. False


Name the law or principle to which the following observations confirm:
(1) When water is added to a \( 1.0 M \)
aqueous solution of acetic acid, the
number of hydrogen ion \( \left(\boldsymbol{H}^{+}\right) \)
increases.
(2) When 9650 coulombs of electricity is passed through a solution of copper sulphate, \( 3.175 g \) of copper is deposited on the cathode (atomic weight of \( \boldsymbol{C u}= \)
63.5)
(3) When ammonium chloride is added
to a solution of ammonium hydroxide, the concentration of hydroxyl ions
decreases.


The standard quantity used for comparison is called Unit.
A. True
B. False


A fuse wire of radius \( 0.1 \mathrm{mm} \) melts when
a current(in A) of \( 10 \mathrm{A} \) is passed through
it. Find the current at which a fuse wire
of \( 0.12 \mathrm{mm} \) will melt.


The equilibrium constant for a reaction is \( 1 \times 10^{20} \) at \( 300 K . \) The standard

Gibbs energy change for this reaction is
A . -115 kJ
B. +115 k
\( c .+166 k J \)
D. -166 k


Consider the situation shown. The wire
AB is sliding on fixed rails with a constant velocity. If the wire \( A B \) is replaced by semi-circular wire, the magnitude of induced e.m.f will
A. increase
B. decrease
c. remain the same
D. increase or decrease depending on whether the semicircle buldges towards the resistance or away from it


The velocity of an \( e^{-} \) in excited state of
H-atom is \( 1.093 \times 10^{6} \) m/s. What is the
circumference of this orbit?
A \( \cdot 3.32 \times 10^{-10} \mathrm{m} \)
В. \( 6.64 \times 10^{-10} \mathrm{m} \)
c. \( 13.30 \times 10^{-10} \mathrm{m} \)
D. \( 13.28 \times 10^{-8} \mathrm{m} \)


If \( n(P \times Q)=0 \) then \( n(P) \) can possibly
be
A .
B. 10
c. 20
D. Any value


Red phosphorus is less reactive than yellow phosphorus because
A. its colour is red
B. it is tetratomic
c. it is hard
D. it is highly polymerized


Which of the following properties of halogens increases with the increasing atomic number?
(I) lonization energy,
(II) Ionic radius,
(III) The bond energy of the \( \boldsymbol{X}_{2} \)
molecule,
(IV) Enthalpy of vaporisation.
A. IV
B. ।,॥
c. ॥।,V
D. I,II, III


Consider the ten numbers
\( \boldsymbol{a r}, \boldsymbol{a r}^{2}, \boldsymbol{a r} \boldsymbol{3}, \ldots \ldots \ldots \boldsymbol{a} \boldsymbol{r}^{10} \)
If their sum is 18 and the sum of their
reciprocal is 6 then the product of these ten numbers, is
A \( \cdot 3^{5} \)
B . \( 3^{8} \)
\( c \cdot 3^{1} 0 \)
D. \( 3^{1} 5 \)


If \( \frac{1}{\sqrt{2}}<x<1, \) then \( \cos ^{-1} x+ \)
\( \cos ^{-1}\left(\frac{x+\sqrt{1-x^{2}}}{\sqrt{2}}\right) \) is equal to
A \( \cdot 2 \cos x^{-1} \)
B. \( 2 \cos ^{-1} x \)
\( c \cdot \frac{\pi}{4} \)
\( D \)


Calculate the image distance for an object of height 12 mm at a distance of
\( 0.20 m \) from a concave lens of focal
length \( 0.30 m, \) and state the nature and
size of the image.


Insulators are materials having an electrical conductivity equal to:
A. Between \( 10^{-8} \mathrm{S} / \mathrm{cm} \) to \( 10^{3} \mathrm{S} / \mathrm{cm} \)
B. \( <10^{-8} \) S/cm
C. Equal to \( 10^{3} \mathrm{S} / \mathrm{cm} \)
\( \mathbf{D} \cdot>10^{3} \mathrm{S} / \mathrm{cm} \)


Gypsum on heating gives:
This question has multiple correct options
\( ^{\mathbf{A}} \cdot \operatorname{CaSO}_{4} \cdot \frac{1}{2} H_{2} O \)
B \( \cdot C a S O_{4} \)
\( \mathbf{c} \cdot C a O \)
\( \mathbf{D} \cdot C a S+O_{2} \)


Hydrogen atom in the basic medium is balanced by which of the following species?
A \( \cdot O H^{-} \)
в. \( H^{+} \)
c. \( H_{3} O^{+} \)
D. \( H_{2} \)


The number of stomatal and epidermal
in 1 m area of leaves of \( A, B, C, D \)
plants are given below.
Is \begin{tabular}{lll}
Plant & Number of Stomatal & Number of epidermal cells \\
\hline \( \mathrm{A} \) & 40 & 730 \\
\( \mathrm{B} \) & 60 & 510 \\
\( \mathrm{C} \) & 70 & 450 \\
\( \mathrm{D} \) & 30 & 620
\end{tabular}
Identify the two plants having least stomatal index.
\( A \cdot A, D \)
B. A, C
\( c \cdot A, B \)
D. B, C


In a sample of radioactive material, what percentage of the initial number of active nuclei will decay during one
mean life?
A . \( 37 \% \)
B. \( 50 \% \)
\( c \cdot 63 \% \)
D. \( 69 \% \)


Which of the following polymers has the empirical formula identical with its
monomer?
A. Teflon
B. Nylon - 6, 6
c. Dacron
D. Bakelite


All of the following are true about ion
EXCEPT:
A. lons can be formed by adding electrons to a neutral atom
B. lons can be formed by removing electrons from a neutral atom
c. lons can be formed by removing neutrons from a neutral atom.
D. lons can be positive and negative in charge


The Fahrenheit and Kelvin scales of
temperature will give the same reading
at
A . -40
в. 313
c. 574.25
D. 732.75


If the vectors \( \vec{A}=a \hat{i}+\hat{j}-2 \hat{k} \) and \( \hat{B}= \)
\( \boldsymbol{a} \hat{\boldsymbol{i}}-\boldsymbol{a} \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \) are perpendicular to each
other then the positive value then the positive value of 'a' is
A. zero
в.
\( c \cdot-1 \)
D. 3


Cell is the basic unit of life'. Explain the
statement.


Taxol is obtained from
A. Taxus
B. Acetabularia
c. cycas
D. Pinus


Which of the following statement(s)
is/are correct for Halogens.
This question has multiple correct options
A. A halogen which is liquid at room temperature is bromine
B. The most electro-negative element is fluorine
C. The most reactive halogen is fluorine
D. The strongest oxidizing agent iodine


A shelf contains 15 books, of which 4
are single volume and the others are 8
and 3 volumes respectively. In how
many ways can these books be arranged on the shelf so that order of
the volumes of same work is
maintained ?
A . \( 4 ! \)
в. \( 8 ! \)
\( c .3 ! \)
D. 4!:8:3!3!


If \( \lambda_{v}, \lambda_{x}, \lambda_{m} \) represents the wavelengths of vision, X-ray and microwaves
respectively then
A \( \cdot \lambda_{m}>\lambda_{x}>\lambda_{v} \)
в. \( \lambda_{m}>\lambda_{v}>\lambda_{x} \)
c. \( \lambda_{v}>\lambda_{x}>\lambda_{m} \)
D \( \cdot \lambda_{v}>\lambda_{m}>\lambda_{x} \)


If \( a, b, c \) are distinct and the roots of \( (b- \)
c) \( x^{2}+(c-a) x+(a-b)=0 \) are equal ,then
\( a, b, c \) are in
A. Arithmetic progression
B. Geometric progression
c. Harmonic progression
D. Arithmetico-Geometric progression


Predict whether the following equation
will take place or not. \( \boldsymbol{C u}_{(s)}+\mathbf{2 H}_{(a q)}^{+} \rightarrow \boldsymbol{C u}_{a q}^{2+}+\boldsymbol{H}_{2(g)} \)
Given that \( \boldsymbol{E}_{\boldsymbol{C u}^{2+} \mid \boldsymbol{C u}}^{0}=\boldsymbol{0 . 4 4} \boldsymbol{V} ; \boldsymbol{E}_{\boldsymbol{H}^{+} \mid \boldsymbol{H}_{2}}^{0}= \)
0


The area bounded by \( y=\cos x, y= \)
\( \boldsymbol{x}+\mathbf{1}, \boldsymbol{y}=\mathbf{0} \) is
A \( \cdot \frac{3}{2} \)
B. \( \frac{2}{3} \)
\( c \cdot \frac{1}{2} \)
D. \( \frac{5}{2} \)


Assertion
The order of the differential equation of
all conics whose centre lies at (0,0) is 3
Reason
The order of differential equation.is
same as the number of arbitrary unknowns (constants) in the given
curve.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A diatomic molecule is made of two
masses \( m_{1} \) and \( m_{2} \) which are
separated by a distance \( r . \) If we
calculate its rotational energy by applying Bohr's rule of angular momentum,its energy will be given by
\( n \) is an integer)
A \( \cdot \frac{\left(m_{1}+m_{2}\right)^{2} n^{2} h^{2}}{2 m_{1}^{2} m_{2}^{2} r^{2}} \)
В \( \cdot \frac{n^{2} h^{2}}{2\left(m_{1}+m_{2}\right) r^{2}} \)
c. \( \frac{2 n^{2} h^{2}}{\left(m_{1}+m_{2}\right) r^{2}} \)
D. \( \frac{\left(m_{1}+m_{2}\right) n^{2} h^{2}}{2 m_{1} m_{2} r^{2}} \)


The algae which decomposes human urine is
A. Spirullina
B. Chlorella
c. volvox
D. chlamydomonas


\( S_{1}, S_{2} \) are foci of an ellipse of major axis
of length 10 units and \( P \) is any point on the ellipse such that perimeter of
triangle \( P S_{1} S_{2} \) is \( 15 . \) Then eccentricity
of the ellipse is:
A . 0.5
B. 0.25
c. 0.28
D. 0.75


If we divide the unknown two-digit number by the number consisting of the same digits written in the reverse order,
we get 4 as a quotient and 3 as a remainder. Now if we divide the
required number by the sum of its
digits, we get 8 as a quotient and 7 as a remainder. Find the number.


\( \operatorname{any} \Delta A B C, \Pi\left(\frac{\sin ^{2} A+\sin A+1}{\sin A}\right) \)
is always greater than This question has multiple correct options
\( A \cdot 9 \)
B. 3
c. 27
D. 81


The line spectra of two elements are
different because:
A. the elements do not have the same number of
neutrons
B. they have different mass numbers
C. their outermost electrons are at different energy levels
D. all of the above


Which of the following will form hydrogen bond between the molecules
of the substances?
A \( \cdot C H_{4} \)
в. \( H B r \)
c. \( H C l \)
D. \( H_{2} O \)
E. \( H_{2} \)


ff \( (x)=x+\sin x ; g(x)=e^{-x} ; u= \)
\( \sqrt{\boldsymbol{c}+\mathbf{1}}-\sqrt{\boldsymbol{c}} ; \boldsymbol{v}=\sqrt{\boldsymbol{c}}-\sqrt{\boldsymbol{c}-\mathbf{1}} ;(\boldsymbol{c}>\mathbf{1}) \)
A \( . f o g(u) \geq f o g(v) \)
B. \( f o g(u) \leq f o g(v) \)
\( \mathbf{c} . f o g(u)>f o g(v) \)
D. \( f o g(u)<f o g(v) \)


A heat engine takes in \( 700 J \) of heat
from high-temperaturere reservoir and rejects \( 500 J \) of heat to a lower
temperature reservoir. How much work does the engine do in each cycle?
\( \mathbf{A} \cdot 100 J \)
в. 20 \( J \)
c. \( 200 J \)
D. \( 10 J \)


At resonance, the angle \( \phi \) is
A.
B. \( \frac{\pi}{2} \)
c. \( \frac{\pi}{6} \)
D. zero


The vertical component of the earth's magnetic field is:
A. zero at the magnetic pole
B. Zero at the geographic pole
c. Same everywhere
D. zero at the magnetic equator


Draw parallelogram ABCD with the following data:
\( A B=6 \mathrm{cm}, A D=5 \mathrm{cm} \) and \( \angle D A B= \)
\( 45^{\circ} \)
Let \( A C \) and \( D B \) meet in 0 and let \( E \) be the
mid-point of Bc. Join OE. then,

OE II AB. ( Enter 1 if true or 0 otherwise)


Which of the following is useful in explaining the polarity of water?
I. The solution process.
II. The ionization process.
III. The high conductivity of distilled
water
A. I only
B. II only
c. I and II only
D. Il and III only
E. I, II and III


Evaluate: \( \int \frac{x^{4}+1}{1+x^{6}} d x \)
A \( \cdot \tan ^{-1}(x)-\tan ^{-1}\left(x^{3}\right)+c \)
B \cdot \( \tan ^{-1}(x)-\frac{1}{3} \tan ^{-1}\left(x^{3}\right)+c \)
c. \( \tan ^{-1}(x)+\tan ^{-1}\left(x^{3}\right)+c \)
D. \( \tan ^{-1}(x)+\frac{1}{3} \tan ^{-1}\left(x^{3}\right)+c \)


If the points \( \boldsymbol{A}(1,2), B(2,3) C(a, 2) \) and \( D(4,3) \) form a parallelogram, find the
value of \( a \) and height of the
parallelogram taking \( A B \) as base.
A. \( a=1, h=2 \)
В. \( a=1, h=1 \)
c. \( a=3, h=1 \)
D. \( a=2, h=3 \)


The position vector of a particle at time \( t^{\prime} \) is given by \( \vec{r}=t^{2} \hat{t}+t^{3} \hat{j} \). The velocity
makes an angle \( \theta \) with positive \( x \) -axis. Find the of \( \frac{\boldsymbol{d} \boldsymbol{\theta}}{\boldsymbol{d} \boldsymbol{t}} \) at \( \boldsymbol{t}=\frac{\sqrt{\mathbf{2}}}{\mathbf{3}} \)


The expression for the determination of Poisson's ratio for rubber is
A \( \cdot \sigma=\frac{1}{2}\left[1-\frac{d V}{A d L}\right] \)
в. \( \sigma=\frac{1}{2}\left[1+\frac{d V}{A d L}\right] \)
c. \( _{\sigma}=\frac{1}{2} \frac{d V}{A d L} \)
D. \( \sigma=\frac{d V}{A d L} \)


Two simple Harmonic Motions of
angular frequency 100 and 1000 rad \( S^{-1} \)
have the same displacement amplitude. The ratio of their maximum accelerations is :
A \( \cdot 1: 10^{3} \)
B \( \cdot 1: 10^{4} \)
c. 1: 10
D. \( 1: 10^{2} \)


\( \frac{a^{n}+b^{n}}{a^{n-1}+b^{n-1}} \) is the AM between \( a \) and \( b \)
if \( n \) is
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( \frac{1}{2} \)
\( c \cdot 1 \)
D. -


Which of the following conditions cannot be corrected by using a correcting lens? This question has multiple correct options
A. astigmatism
B. night blindness
c. cataract
D. colourblindness


Find the area of the segment AYB shown
in figure, if radius of the circle is \( 21 \mathrm{cm} \) and \( <A O B=120^{\circ} .\left(U s e \pi=\frac{22}{7}\right) \)


Which of the following represents the
correct IUPAC name for the
compounds concerned?
a) But-3-yn-1-ol
b) But-4-ol-1-yne


Find the complementary of the angle
\( \mathbf{3 0}^{\circ} \)


Let \( k \) be a positive real number and let \( \boldsymbol{A}=\left[\begin{array}{ccc}2 \boldsymbol{k}-\mathbf{1} & \boldsymbol{2} \sqrt{\boldsymbol{k}} & \boldsymbol{2} \sqrt{\boldsymbol{k}} \\ \boldsymbol{2} \sqrt{\boldsymbol{k}} & \boldsymbol{1} & -\boldsymbol{2} \boldsymbol{k} \\ -\boldsymbol{2} \sqrt{\boldsymbol{k}} & \boldsymbol{2} \boldsymbol{k} & -\boldsymbol{1}\end{array}\right] \) and \( \boldsymbol{B}= \)
\( \left[\begin{array}{ccc}0 & 2 k-1 & \sqrt{k} \\ 1-2 k & 0 & 2 \sqrt{k} \\ -\sqrt{k} & -2 \sqrt{k} & 0\end{array}\right] \)
f \( \operatorname{det}(a d j A)+\operatorname{det}(a d j B)= \)
\( \mathbf{1 0}^{\mathbf{6}}, \) then \( [\boldsymbol{k}] \) is equal to
[Note: adj M denotes the adjoint of a square matrix M and [k] denotes the largest integer less than or equal to \( \mathrm{k} \) ].
\( A \)
в.
\( c . \)
\( D \)


A force of \( 16 \mathrm{N} \) is applied on a block of
mass \( 4 \mathrm{kg} \) with \( \mu=0.6 \) Then the force
of friction acting on the block is \( 4 K \) newton Find the value of \( K \)
\[
\mu=.6-\sqrt{4 k g} \mid \rightarrow F=16 \mathrm{N}
\]
\( A \cdot 4 \)
B. 3
\( c \cdot 6 \)
\( D \)


Which are good conductors?
This question has multiple correct options
A. silicon
B. Silver
c. copper
D. glass


Relation \( R \) in the set \( A \) of human beings
in a town at a particular time given by
\[
\boldsymbol{R}=\{(\boldsymbol{x}, \boldsymbol{y}): \boldsymbol{x} \text { is } \boldsymbol{w} \boldsymbol{i} f e \boldsymbol{o} \boldsymbol{f} \boldsymbol{y}\}
\]
enter 1 -reflexive and transitive but not
symmetric 2-reflexive only 3-Transitive only 4-Equivalence 5-Neither reflexive, nor symmetric, nor transitive


The order in which the following oxides are arranged to decreasing basic nature is \( A l_{2} O_{3}<M g O<C u O<N a_{2} O \)
A. True
B. False


The acceleration of a charged particle in a uniform electric field is : (where specific
charge of a particle \( \left.=\frac{q}{m}\right) \)
A. proportional to its charge only
B. inversely proportional to its mass only
C. proportional to its specific charge
D. inversely proportional to specific charge


topp 5
Q Type your question
\( \mathbf{B} \)
\( r \)
D


If a starfish is cut into pieces, each piece grow into a complete animal. The process is called-
A. Regeneration
B. Reproduction
c. Healing of wounds
D. Growth


For two events \( \boldsymbol{A} \) and \( \boldsymbol{B} \) if \( \boldsymbol{P}(\boldsymbol{A})= \)
\( P\left(\frac{A}{B}\right)=\frac{1}{4} \) and \( P\left(\frac{B}{A}\right)=\frac{1}{2}, \) then
A. \( A \) is subevent of \( B \)
B. \( A \) and \( B \) are mutually exclusive
\( ^{\mathrm{c}},_{A} \) and \( B \) independent and \( P\left(\frac{A^{\prime}}{B}\right)=\frac{3}{4} \)
D. None of these


Find: \( \int x^{2} \cdot \log x d x \)


State true or false
A probability experiment was conducted. Following number is considered as a probability of an outcome?
\( \mathbf{1 . 4 5} \)
A. True
B. False


Suppose that \( f \) is differentiable
function with the property \( \boldsymbol{f}(\boldsymbol{x}+\boldsymbol{y})= \)
\( f(x)+f(y)+x^{2} y^{2} \) and
\( \lim _{x \rightarrow 0} \frac{f(x)}{x}=10 \) then \( f^{\prime}(0) \) is equal
to


\( \mathbf{A} \)
D.C. generator is based on the
principle of
A. magnetic effect ofcurrent
B. lighting effect ofcurrent
c. electrochemical induction
D. electromagnetic induction


Why is it advised to tie any luggage kept on the roof of a bus with a rope?


Define the following term of the circle. Chord


A body of mass \( 4 \mathrm{kg} \) is acted on by a
force which varies as shown in the
graph below. Find the change in
momentum that this body undergoes.
A. 280 Ns
B. 140 Ns
c. \( 70 \mathrm{Ns} \)
D. 210 Ns


\( K_{2} C r_{2} O_{7} \) turns starch iodide paper to
blue colour.
If this is true enter 1 , if false enter 0 .


Establish the formula for intensity of magnetic field at the centre of a current carrying circular coil.


Two different coils have self inductance
\( \boldsymbol{L}_{1}=\mathbf{8} \boldsymbol{m} \boldsymbol{H} \) and \( \boldsymbol{L}_{2}=\boldsymbol{2 m} \boldsymbol{H} . \) The
currents in both are increasing at the
same constant rate. At a certain instant
of time, the power given to the two coils
is the same. At this moment the
current, the induced voltage and energy
stored in the first coil are \( i_{1}, V_{1} \) and \( U_{1} \)
respectively. The corresponding values
in the second coil are \( i_{2}, V_{2} \) and \( U_{2} \) respectively. Then the values of \( \frac{i_{1}}{i_{2}}, \frac{V_{1}}{V_{2}} \) and \( \frac{\boldsymbol{U}_{1}}{\boldsymbol{U}_{2}} \) are respectively:
A \( \cdot \frac{1}{4}, 4, \frac{1}{4} \)
в. \( 4, \frac{1}{4}, \frac{1}{4} \)
c. \( \frac{1}{4}, \frac{1}{4}, 4 \)
D. \( _{4,4, \frac{1}{4}} \)


Which of the following statement is not
correct?
A. All metal are solids at room temperature.
B. All metal are good conductors of heat and electricity.
C. All metal form basic oxides.
D. All metal possess lustre when freshly prepared.


Which of the following aqueous solutions should have the highest boiling point?
A. \( 1.0 M \) NaOH
в. \( 1.0 M \) Na\( _{2} \) SO \( _{4} \).
с. \( 1.0 M \) NH\( _{4} N O_{3} \)


Gems and rubies, coloured glass are solid in solid type colloids.
Enter 1 if true else enter 0 .


The figure shows the velocity (v) of a
particle plotted against time (t)
This question has multiple correct options
A. the particle changes its direction of motion at some point
B. the acceleration of the particle remains constant
c. the displacement of the particle is zerc
D. the initial and final speeds of the particle are the


The adjacent graph shows the extension
(1) of a wire of length \( 1 \mathrm{m} \) suspended from the top of a roof at one end and
with load 'W' connected to the other end.
If the cross-sectional area of the wire is
\( 10^{-6} m^{-2}, \) calculate the Young modulus
of the material of the wire:
A \( \cdot 2 \times 10^{-11} \)
В. \( 2 \times 10^{10} \)
\( c \cdot 2 \times 10^{11} \)
D. \( 2 \times 10^{-10} \)


A boat is sailing at a velocity \( 3 \hat{i}+4 \hat{j} \) with respect to ground and water in river is flowing with a velocity \( -3 \hat{i}-4 \hat{j} \)
Relative velocity of the boat with respect to water is :-
\( A \cdot 8 \hat{3} \)
B . \( 5 \sqrt{2} \hat{j} \)
c. \( 6 \hat{i}+8 \hat{j} \)
D. \( -6 \hat{i}-8 \hat{j} \)


Radius of nucleus may be given as \( \boldsymbol{R}_{N}=\boldsymbol{R}_{0} \cdot \boldsymbol{A}^{1 / 3}, \) where \( \boldsymbol{A}= \)
massnumber and \( R_{0}= \) Constant
Calculate the density of nucleus of an
atom if \( \boldsymbol{R}_{0}=\mathbf{1 . 2} \times \mathbf{1 0}^{-\mathbf{1 5}} \)
\( \left[N_{A}=6 \operatorname{times} 10^{23} \times 8 \pi \times(1.2)^{3}=\right. \)
\( \mathbf{1 0 0 0} \)


\( \boldsymbol{C C l}_{4} \rightleftharpoons \boldsymbol{C}+\mathbf{2 C l}_{2} \)
The equilibrium constant \( p K \) for the given reaction at \( 700^{0} C \) is 0.76 atm.
The initial pressure of carbon tetrachloride that will produce a total equilibrium pressure of 1.20 atm at
\( \mathbf{7} \mathbf{0 0}^{\mathbf{o}} \mathbf{C} \) is:
A. 0.22 atm
B. 0.44 atm
c. 0.84 atm
D. 0.11 atm


Points \( A, B, C \) and \( D \) are midpoints of
the sides of square \( J \) ETS. If the area of
JETS is 36 sq.cm, then the area of
\( A B C D \) is
A. 3 sq. cm
B. 7.5 sq. \( \mathrm{cm} \)
c. 9 sq. cm
D. 18 sq. cm


Solution set of \( \left|\begin{array}{ccc}\boldsymbol{x} & \boldsymbol{3} & \boldsymbol{5} \\ \boldsymbol{2} & \boldsymbol{6} & \boldsymbol{1 0} \\ \boldsymbol{7} & \boldsymbol{2 1} & \boldsymbol{3 5}\end{array}\right|=0 \)
\( A \cdot \phi \)
B. (1)
\( c . R \)
D. (0)


Give reasons for the \( H_{2} O \) is less acidic
\( \operatorname{than} \boldsymbol{H}_{2} \boldsymbol{S} \)


Number of chiral centers in maltose are


Find the domain and range of each of the following real value functions:
\( \boldsymbol{f}(\boldsymbol{x})=-|\boldsymbol{x}| \)


According to Bernoulli's equation the
expression which remains constant is:
\( ^{\mathbf{A}} \cdot p+\frac{\rho v^{2}}{2} \)
\( ^{\mathbf{B}} P+\frac{\rho v^{2}}{2}-\rho g h \)
\( \mathbf{c} \cdot P+\rho g h \)
\( P+\rho g h+\frac{\rho v^{2}}{2} \)


Which of the following statements are
correct?
A \( . \Delta H \) is a state function
B. Value of \( \Delta H \) is independent of path taken
c. \( \Delta H \) can be determined under standard condition
D. All of the above


For the formation of \( M g C l_{2}, \) which of
the followings are correct? This question has multiple correct options
A. \( M g \) loses two electrons
B. each \( C l \) atom gains 2 electrons
c. each \( C l \) atom gains one electron
D. \( M g \) and \( C l \) shares electron to gain stable octet configuration


The number of ways in which the letters
of the word \( A R R A N G E \) can be
permuted such that the \( R \) 's occur together is
A. \( \frac{7 !}{2 ! 2 ! ! !} \)
в. \( \frac{7 !}{2 !} \)
c. \( \frac{6 !}{2 !} \)
D. \( 5 ! \times 2 ! \)


Find the equation of the set of points which are equidistant from the points (1,2,3) and (3,2,-1)


If the products of ozonolysis are acetone
and formaldehyde, what is the initial compound?
\( A \)
в.
c.
D.


The heat developed in a system is proportional to the current through it.
Then
A. it cannot be Thomson heat.
B. it cannot be Peltier heat
c. it cannot be Joule heat.
D. it can be any of the three heats mentioned above


A parallelogram with a pair of the consecutive sides equal, is a
A . square
B. rectangle
c. rhombus
D. circle


The following ratio is generally constant for a given species :-
\( A \cdot T+C / G+A \)
B. \( G+C / A+T \)
c. \( A+C / T+G \)
D. A + G / C +T


When Boron nucleus \( \left(_{5}^{10} B\right) \) is
bombarded by neutrons, \( \boldsymbol{\alpha}- \) particles
are emitted. The resulting nucleus is of the element and has the
mass number
A. \( L i, 7 . \)
B. \( L i, 8 . \)
c. \( N a, 7 \)
D. \( L i, 9 . \)


The position of a particle along along \( x \) axis is given by \( x=a+b t^{2}, \) where \( a= \)
\( 8.5 \mathrm{m}, \mathrm{b}=2.5 \mathrm{m} \) and \( t \) is in seconds.
What is its average velocity at \( t=2.0 \) s? What will be its average velocity between \( t=2 s \& t=4 s ? \)


The second ionization energies among Li. Be. \( B \) and \( C \) s lowest for
\( \mathbf{A} \cdot L i \)
в. \( B e \)
\( c . B \)
D. \( C \)


Explain sewage treatment


In a first-order reaction \( \boldsymbol{A} \rightarrow \boldsymbol{B} \), if k is
rate constant and initial concentration
of the reactant \( A \) is 0.5 M then the half-
life is:
A \( \cdot \frac{\ln 2}{k} \)
в. \( \frac{0.693}{0.5 k} \)
c. \( \frac{\log 2}{k} \)
D. \( \frac{\log 2}{k \sqrt{0.5}} \)


The energy possessed by coal, petroleum and natural gas is called
A. kinetic energy
B. potential energy
c. chemical energy
D. hydro energy


The law of electromagnetic induction has been used in the construction of
A. Generator
B. Electric motor
c. Galvanometer
D. None of these


After the period of how many days half moon can be seen?
A. 7 or 22 days
B. 1 or 30 days
c. 15 days
D. 10 or 17 days


For a journey the cost of a child ticket is
\( \frac{1}{3} \) rd of the cost of an adult ticket. If the
\( \operatorname{cost} \) of tickets for 4 adults and 5
children is Rs. 85 , the cost of a child
ticket is
A. Rs.
B. Rs. 6
c. Rs. 10
D. Rs. 15


Mention any two differences between
soap and synthetic detergent.


Out of the total number of student who
opted for the given three subject, in the
year \( 2009,38 \% \) were girls. How many
boys opted for mathematics in the
same year?
\( \mathbf{7} \)
\( \mathbf{M}_{\mathbf{a}} \)
\( \mathbf{A} \cdot 1322 \)
B. 1332
\( \mathbf{c} \cdot 1312 \)
D. Cannot be determined
E. None of these


For the discontinuous function given
below, find the value of \( \boldsymbol{f}(-\mathbf{3}) \) \( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{ll}\boldsymbol{x}^{2}+\mathbf{1}, & \boldsymbol{i f} \quad \boldsymbol{x}<\mathbf{0} \\ \frac{\boldsymbol{2} \boldsymbol{x}}{\mathbf{3}}-\mathbf{1}, & \boldsymbol{i f} \quad \boldsymbol{0}<\boldsymbol{x}<\mathbf{3} \\ \boldsymbol{4}-\boldsymbol{x}, & \boldsymbol{i f} \quad \boldsymbol{x}>3\end{array}\right. \)
\( A \cdot-3 \)
B.
\( c \cdot 10 \)
D. - 3, 7, and 10


Monds process is used for the
purification of


What is the importance of plasma
proteins?


Two waves of intensities \( I \) and \( 4 I \)
superimpose. The minimum and maximum intensities will respectively
be
A. \( I, 9 I \)
B. \( 3 I, 5 I \)
c. \( I, 5 I \)
D. None of these


A can is taken out from a refrigerator at
\( 0^{\circ} \mathrm{C} . \) The atmospheric temperature is
\( 25^{\circ} \mathrm{C} . \) If \( t_{1} \) is the time taken to heat from
\( 0^{\circ} \mathrm{C} \) to \( 5^{\circ} \) and \( t_{2} \) is the time taken from
\( 10^{\circ} \mathrm{C} \) to \( 15^{\circ} \mathrm{C}, \) then
A \( \cdot t_{1}>t_{2} \)
в. \( t_{1}<t_{2} \)
c \( \cdot t_{1}=t_{2} \)
D. There is no relation


Significantly higher level of urea in the blood is the indication of
A. Liver damage
B. Kidney damage
c. Heart attack
D. spleen damage


In how many different ways can the
letters of the word \( ^{\prime} L E A D I N G^{\prime} \) be
arranged such that all the consonants are together?
\( \mathbf{A} \cdot 576 \)
в. 625
\( c \cdot 676 \)
D. 720


\( 1.3+3.5+5.7+\ldots+(2 n-1)(2 n+1)= \)
\( \frac{n\left(4 n^{2}+6 n-1\right)}{3} \)


State which of the following are equations (with a variable ). Give reason
for your answer. Identify the variable from the equations with a variable. \( \frac{4}{2}=2 \)


Write main differences between the
properties of white phosphorus and red phosphorus.


The single-celled organisms are called


The lines of symmetry of a \( -\ldots---- \) are the lines joining the mid-points of the opposite sides.
A. square
B. triangle
c. rectangle
D. isosceles


Evaluate: \( \int e^{x}(\tan x+\log (\sec x)) d x \)


Which features are characteristic of
insect-pollinated flowers?
A. Bright petals, large feathery stigmas
B. Bright petals, rough sticky pollen
c. Large feathery stigmas, nectaries
D. Small light pollen, nectarines


State True or False.
Magnetic lines of force do not intersect
A. True
B. False


The number of terms whose values
depends on \( x \) in the expansion of \( \left(x^{2}-2+\frac{1}{x^{2}}\right)^{n} \) is
\( \mathbf{A} \cdot 2 n+1 \)
B. \( 2 n \)
\( c \)
D. none of these


An element with a mass number of 81
contains \( 31.7 \% \) more neutrons as compared to protons. Identify the element.
A. Sç
B. Ва
\( c \cdot B r \)
\( D \)


The simplified value of \( \frac{1+i}{1-i} \) is
\( \mathbf{A} \cdot \mathbf{1} \)
в.
\( c \cdot-i \)
D. \( 2 i \)


Let \( n_{1}, n_{2}, n_{3} \dots \) are the frequencies of
segments of a stretched string, then the frequency \( n \) of the string can be given
by
A \( \cdot n=n_{1}+n_{2}+n_{3}+\dots \)
B. \( n=\sqrt{n_{1} \times n_{2} \times n_{3} \times \ldots} \)
c. \( \frac{1}{n}=\frac{1}{n_{1}}+\frac{1}{n_{2}}+\frac{1}{n_{3}}+\dots \)
D. None of the above


Are the following name correct according to IUPAC system of nomenclature? If not, give the correct
names.
Tert. butanol


Which of the following combinations give finally an isotope of the parent element?
A. \( \alpha, \alpha, \beta \)
в. \( \alpha, \gamma, \alpha \)
c. \( \alpha, \beta, \beta \)
\( \mathbf{D} \cdot \beta, \gamma, \alpha \)


What will be the effect of intermittent
light on photosynthesis?
A. It will increase
B. It will decrease
c. will not be effected
D. Process will stop


In human zygote male sex is determined by
A. Strength of father
B. Nutrition of mother
c. composition of required chromosome pair
D. None of the above


If two soap bubbles of different radii are
connected by a tube, then:
A. air flows from bigger bubble to the smaller bubble till sizes become equal
B. air flows from bigger bubble to the smaller bubble till sizes are interchanged
c. air flows from smaller bubble to bigger
D. there is no flow of air


In context with the industrial
preparation of hydrogen from water gas
\( \left(C O+H_{2}\right), \) which of the following is the
correct statement?
\( \mathbf{A} \cdot \mathrm{CO} \) and \( \mathrm{H}_{2} \) are fractionally separated using differences in their densities
B. \( \mathrm{CO} \) is removed by absorption in aqueous \( \mathrm{Cu}_{2} \mathrm{Cl}_{2} \) solution
C \( . H_{2} \) is removed through occulsion with Pd
D. \( C O \) is oxidised to \( C O_{2} \) with steam in the presence of a
catalyst followed by absorption of \( C O_{2} \) in alkali


A vertical line \( l \) passes through the point \( (2,3) . \) A horizontal line \( m \) passes
through the point \( (-1,6) . \) Where do lines \( l \) and \( m \) intersect?
\( \mathbf{A} \cdot(0,5) \)
в. (2,6)
c. (6,2)
D. (-1,3)
E \( .(3,-1) \)


Termination of chain growth in protein synthesis is brought about by
A. UUG, UGC, UCA
B. UCG, GCG, ACC
c. UAA, UAG, UGA
D. UUG, UAG, UCG


When \( M n O_{2} \) is fused with \( K O H, \) a
coloured compound is formed. The product and its colour is:
A \( \cdot K_{2} M n O_{4}, \) green
B. \( K M n O_{4} \), purple
c. \( M n_{2} O_{3} \), brown
D. \( M n_{3} O_{4} \), black


Electronic configuration of element T is 2, 8, 7. Under which category this element belongs to?
A . Alkali metal
B. Alkaline metal
c. Noble gases
D. Non-metal


The formula of students t-distribution
is
A \( \cdot t=\frac{s}{\sqrt{n}} \)
в. \( t=\frac{|\bar{X}-\mu|}{s} \)
c. \( \quad t=\frac{|\bar{X}-\mu|}{\frac{s}{\sqrt{n}}} \)
D. \( \quad t=\frac{\sqrt{n}}{s} \)


Find the smallest number that must be
subtracted from 6868 to make it a
perfect cube.


Why is the cooling unit of a refrigerator made at the top?


A triangle \( A B C \) in which \( A B=A C, M \) is a point on \( A B \) and \( N \) is a point on \( A C \) such that if BM=CN then AM=AN
A. True
B. False


The following reaction is known as:
\( \boldsymbol{C}_{6} \boldsymbol{H}_{6}+\boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C l} \frac{A l C l_{3}}{(\boldsymbol{a n h y} .)} \boldsymbol{C}_{6} \boldsymbol{H}_{5} \boldsymbol{C H}_{3}+ \)
\( \boldsymbol{H} \boldsymbol{C l} \)
A. Wurtz-Fittig reaction
B. Friedel-Crafts reaction
c. Rosenmund reaction
D. Sandmeyer reaction


Secondary growth generally occurs in
A. Monocots
B. Dicots
c. Gymnosperms
D. Both (b) and (c)


Far point of a healthy eye is:
\( \mathbf{A} \cdot 50 \mathrm{cm} \)
B. \( 25 \mathrm{cm} \)
c. 1 metre
D. infinity


Which among the following is not an electronic component used in constructing a toroid?
A. copper wires
B. laminated iron
c. ferrite core
D. aluminium powder


True or False.
Cars are made from steel which is an
alloy of carbon and aluminium.


Match the names with the tissues
shown. Choose the answer, which gives
the correct combination of the
alphabets.
\( \begin{array}{ll}\text { Cells } & \text { Tissues } \\ \text { A. Erythocytes } & \text { p. Bone } \\ \text { B. Chondrocytes } & \text { q. Neuron } \\ \text { c. osteocytes } & \text { r. Cartilage } \\ \text { D. Schwann cells } & \text { s. Blood } \\ & \text { t. Adipose tissue }\end{array} \)
A. \( A-s, B-r, C-t, D-p \)
B. A-s, B-r, C- p, D- q
\( c \cdot A-s, B-q, C-p, D-t \)
D. \( A-s, B-p, C-r, D-q \)


Starch is composed of two polysaccharides namely:
A. amylopectin and glycogen
B. amylose and glycogen
c. amylose and amylopectin
D. amylose and amylopectin and glycogen


Soap mixed with water below critical
micelle concentration behaves as:
A. associated colloid
B. macromolecular colloid
c. normal electrolytic solution
D. multimolecular colloid


A block of mass 2 kg falls from the wall at height of \( 2.3 \mathrm{m} \). Calculate the velocity just before it hits the ground. \( (g= \)
\( -9.8 \frac{m}{s^{2}} \)
A \( \cdot-6.76 \frac{n}{s} \)
В. \( -26.86 \frac{m}{s^{2}} \)
\( \mathbf{c} \cdot 45.08 \frac{m}{s} \)
D. \( 13.43 \frac{m}{s} \)
E \( \cdot 3.36 \frac{m}{s} \)


Which of the following gives purest form of nitrogen?
A. Thermal decomposition of ammonium nitrate
B. Treating aqueous solution of ammonium chloride with sodium nitrite
C. Thermal decomposition of sodium or barium azide
D. Liquefaction and fractional distillation of air


An organic compound contains \( C, H \) and \( O . \) If \( C(\%): H(\%)=6: 1, \) what is the
simplest formula of the compound given that one mole of the compound contains half as much oxygen as would
be required to burn all the \( C \) and \( H \)
atoms in it to \( C O_{2} \) and \( H_{2} O ? \)
\( \mathbf{A} \cdot C H_{2} O \)
в. \( C_{2} H_{4} O_{3} \)
\( \mathbf{c} \cdot C_{3} H_{6} \)
D. \( C_{3} H_{6} O_{2} \)


Complete the given reaction. \( 2 M n^{2+}+5_{--}(i)_{--}+8 H_{2} O \rightarrow 2_{--} \)
\( (i i)_{--}+16 H^{+} \)
\( (i i)_{--}+10_{--} \)
A \( \cdot(i)-S O_{4}^{2-},(i i)-M n O_{4}^{-},(i i i)-S_{2} O_{8}^{2-} \)
B . \( (i)-S_{2} O_{8}^{2-},(i i)-M n O_{4}^{-},(i i i)-S_{2} O_{4}^{2} \)
C \( \cdot(i)-M n O_{4}^{-},(i i)-S_{2} O_{8}^{2-},(i i)-S O_{4}^{2} \)
D \( \cdot(i)-S_{2} O_{8}^{2-},(i i)-S O_{4}^{2-},(i i i)-M n O_{4} \)


Define matter.


What provides surface for the vapors to cool and condense in a fractionating column?
A. Glass beads
B. water
c. sand
D. salt


For the given experimental setup, the oscillation frequency of the mass is
\( \boldsymbol{f} \cdot \boldsymbol{S}_{1} \) and \( \boldsymbol{S}_{2} \) are identical springs. One
spring is now removed, then frequency
will become.
A . \( 2 f \)
B. \( \frac{f}{\sqrt{2}} \)
c. \( \frac{f}{\sqrt{3}} \)
D. \( \sqrt{2} f \)


If \( A \) is a matrix of order \( 2 \times 3, B \) is a
matrix of order \( 3 \times 5 \), then what in the
order of matrix \( (A B) \) or \( (A B)^{t} \)


Assertion
The \( V \rightarrow t \) graph perpendicular to time
axis is not possible in practice.
Reason
Infinite acceleration can not be realized
in practice.
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


An electric kettle has two coils when
one of these is switched on the water in
the kettle boils in 6 min. When the
other coil is switched on, the water boils
in 3 min. If the two coils are connected
in series, the time taken to boil the
water in the kettle is
\( \mathbf{A} \cdot 3 \min \)
B. 6 min
c. 2 min
D. 9 min


All halogens are:
A. s-block elements
B. d-block elements
C . representative elements
D. transition elements


Amphoteric oxides of Mn and Cr are:
\( \mathbf{A} \cdot M n O \) and \( C r O \)
B. \( M n_{2} O_{3} \) and \( C r_{2} O_{3} \)
c. \( M n O_{2} \) and \( C r_{2} O_{3} \)
D. \( M n_{2} O_{7} \) and \( C r O_{3} \)


Construct \( \triangle X Y Z \) in which \( X Y= \)
\( 4.5 \mathrm{cm}, Y Z=5 \mathrm{cm} \) and \( Z X=6 \mathrm{cm} \)


Scattering of light by colloidal particles is known as:
A. Tyndall effect
B. Brownian motion
c. Reflection
D. Rectilinear propagation


\( 2.66 \mathrm{g} \) chloride of a metal when treated with silver nitrate solution give 2.87 g of silver chloride. 3.37 g of another chloride of the same metal give 5.74 g of silver chloride when treated with silver nitrate
solution. Show that the results are in
agreement with a law of chemica combination.


Assertion
The value \( \int_{-4}^{-5} \sin \left(x^{2}-3\right) d x+ \)
\( \int_{-2}^{-1} \sin \left(x^{2}+12 x+33\right) \) is zero
Reason
\( \int_{-a}^{a} f(x) d x=0 \) if \( f(x) \) is an odd function.
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


If the standard deviation of a population is \( 9, \) the population variance is:
\( \mathbf{A} \cdot \mathbf{9} \)
B. 3
c. 21
D. 81


\( \lim _{x \rightarrow 0} \frac{(1-\cos 2 x)^{2}}{2 x \tan x-x \tan 2 x} \) is :-
A . -2
B. \( -\frac{1}{2} \)
\( c \cdot \frac{1}{2} \)
D. 2


A conductor ABOCD moves along its
bisector with a velocity of \( 1 \mathrm{ms}^{-1} \) through a perpendicular magnetic field
of \( 1 \mathrm{Wbm}^{-2} \), as shown in the figure. If all
the four sides are of \( 1 \mathrm{m} \) length each,
then the induced emf between point \( A \)
and D is :
A. zero
в. 1.41
\( c \cdot 0.71 v \)
D. none of the above


Discuss the nature of bonding in the following coordination entities on the basis of valence bond theory:
(i) \( \left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{\mathbf{6}}\right]^{4-}\left(\text { ii) }\left[\boldsymbol{F} \boldsymbol{e} \boldsymbol{F}_{6}\right]^{3-}(\text { iii })\right. \)
\( \left[\boldsymbol{C o}\left(\boldsymbol{C}_{2} \boldsymbol{O}_{4}\right)_{3}\right]^{3-}(\text { iv })\left[\boldsymbol{C o} \boldsymbol{F}_{6}\right]^{3-} \)


What is the standard reduction
potential \( \left(\boldsymbol{E}^{o}\right) \) for \( \boldsymbol{F} \boldsymbol{e}^{\mathbf{3}+} \rightarrow \boldsymbol{F} \boldsymbol{e} \)
Given that:
\( \boldsymbol{F} \boldsymbol{e}^{2+}+\boldsymbol{2} \boldsymbol{e} \boldsymbol{6}-\rightarrow \boldsymbol{F} \boldsymbol{e} ; \boldsymbol{E}_{\boldsymbol{F}}^{o} \boldsymbol{e}_{\boldsymbol{F} e^{2+} / \boldsymbol{F} e}= \)
\( -0.47 V \)
\( \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{3}+}+\boldsymbol{e}^{-} \rightarrow \boldsymbol{F} \boldsymbol{e}^{2+} ; \boldsymbol{E}_{\boldsymbol{F} e^{3+} / \boldsymbol{F} e^{2+}}^{o}= \)
\( +0.77 V \)
A \( .+0.057 V \)
в. \( +0.30 V \)
c. \( -0.30 V \)
D. \( -0.057 V \)


Which of the following quantities:(1) magnetic declination (II) dip is used to determine the strength of earths magnetic field at a point on the earths
surface
\( A \). Both \( 1 \& \| \)
B. Neither I nor II
c. I only
D. II Only


Oxygen is prepared by:
A. potassium chlorate
B. potassium perchlorate
c. hydrogen peroxide
D. both \( A \) and \( c \)


Which of the following transitions will involve maximum amount of energy?
A \( . M \rightarrow M^{+}+e^{-} \)
B. \( M^{-} \rightarrow M^{+}+2 e^{-} \)
\( \mathbf{c} \cdot M^{2+} \rightarrow M^{3+}+e^{-} \)
D. \( M^{+} \rightarrow M^{2+}+e^{-} \)


The following reaction is probably:
\( \mathbf{2} \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{O} \boldsymbol{H} \frac{\boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4}}{\boldsymbol{H} e a t} \)
\( \left(\boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2}\right)_{2} \boldsymbol{O}+\boldsymbol{H}_{2} \boldsymbol{O} \)
A . an \( E 2 \) -type reaction involving the protonated alcohol as the substrate
B. an \( S_{N} 1 \) type reaction involving the protonated alcohol as the substrate
c. an \( E 1 \) type reaction involving the protonated alcohol as the substrate
D. an \( S_{N} 2 \) type reaction involving the protonated alcohol as the substrate


The length of a conductor is halved. Its conductance will be?
A. Halvedd
B. Unchanged
c. Doubled
D. Quadrupled


Universe comprises of :
A. Only System
B. Only Surroundings
C. Both System and Surroundings
D. None of the above


Bulb is a modified
A . Leaf
B. Shoot
\( c . \) Root
D. Flower


Assertion
The rotation of earth on its axis is an
example of gyroscopic precession
Reason

The axis of the earth is tilted and its
mass is huge.
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 important conclusions on the
formation of trihalomethanes are which
of the following?
A. Chlorination of natural waters causes the formation of chloroform and other trihalomethanes because of the
reaction of \( O C l^{-} \) on DOC present in the water
B. Use of both ammonia and chlorine in water treatment
has reduced the level of the trihalomethanes due to
the formation of the chloroamines, which react more slowly than free chlorine
C. Finally, the concentration of the trihalomethanes above \( 100 \mu \) g/l are considered unsafe for drinking water
D. All of the above


A long coaxial cable consists of two thin-walled conducting cylinders with
inner radius \( 2 c m \) and outer radius \( 8 c m \)
The inner cylinder carries a steady current \( 0.1 A \), and the outer cylinder
provides the return path for that current. The current produces a magnetic field between the two cylinders. Find the energy stored in the
magnetic field for length \( 5 m \) of the
cable. Express answer in \( n J \) (use
\( \ln 2=0.7) \)


The atomic weight of Ne is 20.2. Ne is mixture of \( N e^{20} \) and \( N e^{22} . \) The relative
abundance of the heavier isotope is:
A . \( 90 \% \)
B. 20\%
c. \( 40 \% \)
D. \( 10 \% \)


Write \( I U P A C \) names of the following compound:


Which triad belongs to the same group and same period?
A. \( C u, A g, A u \)
в. \( F e, C o, N i \)
c. \( Z n, C d, H g \)
D. None of these


If \( \Delta G \) standard is zero, this means:
A. the reaction is spontaneous at standard conditions
B. the reaction is non spontaneous at standard conditions
C. the system is at equilibrium at standard conditions
D. the reaction is both non spontaneous and at equilibrium
E. the reaction is both spontaneous and at equilibrium


The IUPAC name of \( \boldsymbol{C H}_{\mathbf{3}}-\boldsymbol{O}- \)
\( \boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right)-\boldsymbol{C H}_{3} \) is:


State work energy theorem.


Eight chairs are numbered 1 to
8. Two
women and three men wish to occupy one chair each. First, the women choose
the chairs amongst the chairs marked 1
to 4 then the men select the chairs
amongst the remaining. The number of
possible arrangements are:


If the angle of incidence is \( 80^{\circ}, \) what will be the angle of reflection with respect to the normal drawn perpendicular at the point of reflection?
A . \( 80^{\circ} \)
B. \( 100^{\circ} \)
\( c \cdot 160^{\circ} \)
D. \( 20^{\circ} \)


Among the following compounds, the most acidic is:
A. p-nitrophenol
B. p-hydroxybenzoic acid
c. o-hydroxybenzoic acid
D. none


Formula of feldspar is:
A. \( K_{2} O . A l_{2} O_{3} .6 S i O_{2} \)
B. \( K_{2} O_{3} . A l_{2} O_{3} .6 s i_{2} O_{2} .2 H_{2} O \)
c. \( A l_{2} O_{3} .2 S i O_{2} .2 H_{2} O \)
D. \( 3 M g O .4 S i O_{2} . H_{2} O \)


A ball of mass \( 20 g \) hits a wall at an
angle \( 45^{\circ} \) with a velocity of \( 15 m s^{-1} . \) If
the ball rebounds at \( 90^{\circ} \) to the direction
of incidence, calculate the impulse
received by ball.


A bag contain 8 red, 3 white and 9 blue
balls. If three balls are drawn at random,
determine the probability that all the three balls are blue balls
A \( \cdot \frac{7}{93} \)
в. \( \frac{6}{92} \)
c. \( \frac{7}{95} \)
D. \( \frac{8}{95} \)


On the set \( Q \) of all rational numbers, if a
binary operation \( * \) is defined by \( a * b= \) \( \frac{a b}{5} . \) Prove that \( * \) is associative on \( Q \)


There is an electric field \( \overrightarrow{\mathrm{E}}=\frac{a x^{3} \hat{i}+b y^{4} \widehat{j}+c z^{2} \widehat{k}}{a x^{4}+b y^{5}+c z^{3}} \)
at any \( (x, y, z) \) coordinates in the space
except origin, Where a,b \& c are constant.
Find the electrostatic flux passing
through a sphere of radius R whose
center is at the origin.
\( \mathbf{A} \cdot \pi R \)
\( \mathbf{B} \cdot 2 \pi R \)
\( \mathbf{c} .4 \pi R \)
D. Zero


Two candles of the same height are lighted at the same time. The first is
consumed in 4 hours and the second in
3 hours. Assuming that each candle burns at a constant rate, in how many
hours after being lighted was the first candle twice the height of the second?
A \( \cdot \frac{3}{4} \) hr.
B. \( \frac{11}{2} \) hr.
c. \( 2 h r \)
D. \( \frac{12}{5} \) h.
E \( \cdot \frac{21}{2} \) hr.


Construct a triangle \( \boldsymbol{A B C} \), where \( A B=4 c m, B C=5 c m \) and \( \angle A B C= \)
\( 45^{\circ} . \) Also, find the maximum length of
side \( \boldsymbol{A C} \)


The diagram shows part of the curve \( y=\frac{1}{16}(3 x-1)^{2}, \) which touches the \( x \)
axis at the point P. The point \( Q(3,4) \) lies
on the curve and the tangent to the
curve at \( Q \) crosses the \( x \) -axis at \( R \)
State the \( x \) -coordinate of \( P \)


The co-ordination number of a metal in
co-ordination compound is:
A. same as primary valency
B. sum of primary and secondary valences
c. same as secondary valency
D. none of the above


Match the column.


A 5 digit number divisible by 3 is to be formed using the numerals 0,1,2,3,4
\& 5 without repetition. The total number of ways this can be done is
A . 3125
в. 600
c. 240
D. 216


For a \( \Delta A B C, A B=4 \mathrm{mm}, B C=5 \)
\( \mathrm{mm} \) and \( \boldsymbol{A C}=\mathbf{6} \) mm. If \( \boldsymbol{\Delta} \boldsymbol{A} \boldsymbol{B} \boldsymbol{C} \cong \)
\( \Delta D E F, \) then \( E F=_{-}- \)
\( \mathbf{A} \cdot 4 \mathrm{mm} \)
B. \( 6 \mathrm{mm} \)
\( c .5 \mathrm{mm} \)
D. cannot be determined


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


dentify the type of reaction indicated by
line \( A \) in the diagram.
A. Uncatalyzed exothermic
B. Catalyzed exothermic
c. Catalyzed endothermic
E. Reversible


Evaluate the integral \( \int_{0}^{\pi} \frac{d x}{a+b \cos x} \) where \( a>b \)
A \( \cdot \pi \sqrt{a^{2}-b^{2}} \)
an \( \pi \sqrt{a^{2}-b^{a^{2}}} \)
в. \( \pi a b \)
c. \( \frac{\pi}{\sqrt{a^{2}+b^{2}}} \)
D. \( \frac{\pi}{\sqrt{a^{2}-b^{2}}} \)


f \( \boldsymbol{A}=\left[\begin{array}{ll}\boldsymbol{4} & \boldsymbol{7} \\ \boldsymbol{6} & \boldsymbol{5}\end{array}\right], \) find \( |\boldsymbol{3} \boldsymbol{A}| \)


Divide a line segment of length \( 10 \mathrm{cm} \)
internally in the ratio 3: 2


Image formed by a plane mirror is:
A. erect, virtual and of same size of the object
B. inverted, real and of smaller size than the object
C. erect, real and of same size as the object
D. inverted, virtual and of smaller size of the object


An iron ball and a wooden ball are
released from a height in vacuum. The speed of the iron ball would be:
A. Same to the speed of the wooden ball
B. More than the speed of the wooden ball
c. Lesser than the speed of the wooden ball
D. None


Which of the follwoing is not used as food preservative?
A. sodium benzoate
B. sodium sulphate
c. salts of sorbic acid
D. acetyl salicylic acid


Temporary hardness can be removed by mixing water with slaked lime, this process is known as softening of water
A. True
B. False


Which of the following is ferromagnetic.
A. Cu, Ag, Au
B. Fe, Co, Ni
c. \( z n, \) Сd, \( \mathrm{Hg} \)
D. \( \mathrm{Ca}, \mathrm{Sr}, \mathrm{Ba} \)


Aluminum (Al) atom has ground-state
electron configuration as:
\( \mathbf{A} \cdot 1 s^{2} 2 s^{2} 2 p^{1} \)
B \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{1} \)
\( \mathbf{C} \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{1} \)
D. \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{1} 3 p^{12} \)
E \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{1} 3 p^{12} 4 p^{6} \)


Which of the followoing oxoanions contain \( S-S \) bond?

This question has multiple correct options
\( A \cdot S_{2} O_{3}^{2-} \)
B. \( S_{2} O_{4}^{2-} \)
\( \mathrm{c} \cdot S_{2} \mathrm{O}_{6}^{2-} \)
D. \( S_{2} O_{7}^{2} \)


Which of the following is true about
Mendeleev's periodic table?
A. The accommodation of the noble gases in the periodic table did not disturb the position of other elements
B. Noble gases were known at the time when Mendeleev gave the periodic table
C. When noble gases were discovered, they got a place in Mendeleev's periodic table as a separate row
D. All of the above


The rate constant of a zero order
reaction is 0.2 mol \( d m^{-3} h^{-1} . \) If the
concentration of the reactant after 30
minutes is 0.5 mol \( d m^{-3} . \) Then its initial concentration would be :-
A. \( 0.60 \mathrm{mol} \) d \( m^{-3} \)
B. 0.15 moldm \( ^{-3} \)
c. 0.25 mol \( d m^{-3} \)
D. 4.00 mol \( d m^{-3} \)


Find the distance of point (1,-2,3)
from the plane \( \boldsymbol{x}-\boldsymbol{y}+\boldsymbol{z}=\mathbf{5} \)
measured parallel to the line whose direction cosines are
proportional to 2,3,-6


If \( X, F \) and \( U \) respectively denotes displacement, force acting on a particle and potential energy of a particle, then:
A \( . U=F \)
B. \( F=+\frac{d U}{d x} \)
c. \( F=-\frac{d U}{d x} \)
D. \( F=\frac{1}{x}\left(\frac{d U}{d x}\right) \)


Draw a lake showing different zones.
Why are they called so?


5000
\( \frac{\frac{m}{m}}{\frac{m}{m}} \)


Mark the correct alternative of the
following. If the measures of the angles of a
triangle are \( (2 x)^{o},(3 x-5)^{o} \) and \( (4 x- \)
13) \( ^{\circ} . \) Then the value of \( x \) is?
A . 22
B . 18
c. 20
D. 30


Which of the following is the parent element of the element \( \frac{102}{20} \Omega \) if it is
formed as a result of \( 3 \alpha \) and \( 2 \beta^{-} \)
decays?
A \( \cdot \frac{90}{16} \Gamma \)
B . \( \frac{114}{24} \Phi \)
\( \mathrm{c} \cdot_{28}^{114} \mathrm{\Theta} \)
D. \( _{8}^{12} \Delta+_{12}^{90} \Xi \)


When mercury is reacted with hot and
conc. sulphuric acid, the gas evolved is:
A \( . H_{2} \)
в. \( S O_{2} \)
\( c \cdot S O_{3} \)
D. \( O_{2} \)


In Funaria
A. Male and female reproductive organs are on different plants
B. Male and female reproductive organs are on the same plane but on different branches
C. Male and female reproductive organs are on the same plant and on the same branch
D. None of the above


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


Lanthanides are also known as:
A. Transition elements
B. Rare gases
c. coinage metals
D. Rare earths


Two simple harmonic motions are
represented by the equations. \( \boldsymbol{y}_{1}=\mathbf{1 0} \sin \frac{\boldsymbol{\pi}}{\boldsymbol{4}}(1 \mathbf{2} \boldsymbol{t}+\mathbf{1}), \boldsymbol{y}_{2}= \)
\( \mathbf{5}(((\sin 3 p t+\sqrt{3} \cos 3 p t) \)
The ratio of their amplitudes is
A . 1: 1
B. 1: 2
c. 3: 2
D. 2: 3


If \( f(x)=\left|\begin{array}{ccc}a & -1 & 0 \\ a x & a & -1 \\ a x^{2} & a x & a\end{array}\right|, \) by using
properties of determinants, find the
value \( \boldsymbol{f}(\mathbf{2 x})-\boldsymbol{f}(\boldsymbol{x}) \)


A force \( F=-6 x^{3} \) is acting on a block
moving along x-axis. Work done by this
force is:
This question has multiple correct options
A. Positive in displacing the block from \( x=3 \) to \( x=1 \)
B. Positive in displacing the block from \( x=-3 \) to \( x=-1 \)
c. Negative in displacing the block from \( x=0 \) to \( x=4 \)
D. zero in displacing the block from \( x=-2 \) to \( x=+2 \)


Is the following equation a quadratic equation? \( (x+2)^{3}=x^{3}-4 \)
A. Yes
B. No
c. Ambiguous
D. Data insufficient


If a conductor has a potential \( V \neq 0 \)
and there are no charges anywhere else outside, then
A. there must be charges on the surface or inside itself
B. there cannot be any charge in the body of the conductor
c. there must be charges only on the surface
D. there must be charges inside the surface


Two bodies of unequal masses possess
the same momentum. Which of the
following can be concluded?
A. Heavier mass possesses lesser K.
B. The masses of the two bodies are in the direct ratio of their velocities
c. Lighter mass possesses less K.E.
D. Both (A) and (B)


Primary battery is a battery:
A. which can be recharged.
B. which cannot be reconditioned by replacing chemical.
c. which cannot be reused.
D. which cannot be recharged.


State brewsters law.
The value of brewster's angle for a transparent medium is different for
light of different colours. give reason?


The Henry's law constant for the
solubility of \( \mathrm{N}_{2} \) gas in water at \( 298 \mathrm{K} \) is
\( 1.0 \times 10^{5} \) atm. The mole fraction of \( \mathrm{N}_{2} \)
in air is \( 0.8 . \) The number of moles of \( \mathrm{N}_{2} \)
from air dissolved in 10 moles of water
at \( 298 \mathrm{K} \) and 5 atm pressure is?
A \( \cdot 4.0 \times 10^{-4} \)
B . \( 4.0 \times 10^{-5} \)
c. \( 5.0 \times 10^{-4} \)
D. \( 4.0 \times 10^{-6} \)


Let \( a_{n} \) be the nth term of the G.P. of positive numbers. Let \( \sum_{n=1}^{100} a_{2 n}=\alpha \) and \( \sum_{n=1}^{100} a_{2 n-1}=\beta, \) such that \( \alpha \neq \beta . \) Prove
that the common ratio of the G.P. is \( \frac{\boldsymbol{\alpha}}{\boldsymbol{\beta}} \)


The critical points of the function \( f(x)=(x-2)^{2 / 3}(2 x+1) \) are
A. 1 and 2
B. 1 and \( -\frac{1}{2} \)
c. -1 and 2
\( D \)


Which one of the following methods is used to measure distance of a planet or
a star from the earth?
A. Echo method
B. Parallax method
c. Triangulation method
D. None of these


The average binding energy per nucleon is maximum for the nucleus:
\( \mathbf{A} \cdot_{2} H e^{4} \)
B \( \cdot_{8} O^{16} \)
\( \mathbf{c} \cdot_{26} F e^{56} \)
D・ \( _{92} U^{238} \)


In the equation \( x+y=4, \) what is the
value of \( x \) if \( y=2 ? \)
\( A \cdot 2 \)
B. 4
\( c \cdot 6 \)
D.


What is Zeise's Salt and Ferrocene?
Explain with structure?


A ball is dropped into coaltar. Its
velocity-time curve will be
\( A \)
\( B \)
\( \mathbf{c} \)
D.


Which of the following statement(s)
is/are correct?
\( \mathbf{A} \cdot \operatorname{In}\left[\operatorname{CoBr} C l(e n)_{2}\right]^{+} \) geometrical isomerism exists,
while optical isomerism does not exist
B. Potassium aquadicyanosuperoxoperoxochromate(III) is IUPAC name of \( K_{2}\left[\mathrm{Cr}(\mathrm{CN})_{2} \mathrm{O}_{2}\left(\mathrm{O}_{2}\right)\left(\mathrm{H}_{2} \mathrm{O}\right)\right] \)
C. There are 3 geometrical and 15 stereisomers possible for \( \left[P t\left(N O_{2}\right)\left(N H_{3}\right)\left(N H_{2} O H\right)(p y)\right]^{+} \) and
\( \left[P t B r C l I\left(N O_{2}\right)\left(N H_{3}\right)(p y)\right] \) respectively
D. \( A \) cis and trans forms are not diastereomers to each
other


The temperature of a one mole of diatomic gas changes from \( 4 \mathrm{T} \) to \( \mathrm{T} \) in adiabatic process. If \( R \) is universal gas constant. Then work done
A \( \cdot \frac{15 R T}{3} \)
в. \( \frac{15 R T}{2} \)
c. \( \frac{3 R T}{15} \)
D. \( \frac{12 R T}{5} \)


Select the correct statement(s) about
above reaction:
This question has multiple correct options
A. The product is a racemic mixture.
B. Racemisation occurs due to enolisation
C. The reaction passes through a cyclic transition state
D. The intermediate of the reaction is a carbanion.


Assertion
In a woman after hysterectomy, the
ovarian cycle is stopped
Reason
Because \( F S H \) is not secreted.
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 sum of first \( p \) terms of an A.P. is
equal to the sum of the first \( q \) terms,
then find the sum of the first \( (p+q) \)
terms.


\( N F_{3} \) is stable. But, \( N C l_{3} \) is explosive.
Identify the reason:
A. \( N C l_{3} \) undergoes hydrolysis whereas \( N F_{3} \) does not.
B . \( N C l_{3} \) decomposes on heating and \( N F_{3} \) does not
c. \( N C l_{3} \) is a gaseous substance and \( N F_{3} \) is liquid
D. \( N C l_{3} \) undergoes sublimation while \( N F_{3} \) does not


Fe is made passive by:
A \( \cdot d i l . H_{2} S O_{4} \)
в. dil. \( H C l \)
c. \( a q u a-r e \)eja \( a \)
D. conc.H\( _{2} \) SO \( _{4} \),


Explain the steps involved in the formation of root module.


The unit of rate constant for zero order
reaction is:
A \( \cdot s^{-1} \)
B \( \cdot \operatorname{mol} L^{-1} s^{-1} \)
c. \( L m o l^{-1} s^{-1} \)
D. \( L^{2} m o l^{-2} s^{-1} \)


Sulphide ores of metals are usually concentrated by froth floatation process. Which one of the following sulphide ores offers an exception and is concentrated by chemical leaching?
A. Galena
B. Copper pyritee
c. sphalerite
D. Argentite


A body of mass \( 1.5 \mathrm{kg} \) is allowed to slide down along a quadrant of a circle from the horizontal position. In reaching to the bottom, Its velocity is \( 8 \mathrm{m} / \mathrm{s} \). The
work done in overcoming the friction is
12J. The radius of circle is


Find the value of
\( \frac{\boldsymbol{i}^{592}+\boldsymbol{i}^{590}+\boldsymbol{i}^{588}+\boldsymbol{i}^{586}+\boldsymbol{i}^{584}}{\boldsymbol{i}^{582}+\boldsymbol{i}^{580}+\boldsymbol{i}^{578}+\boldsymbol{i}^{576}+\boldsymbol{i}^{574}}-\mathbf{1} \)


The ratio of magnetic field at the centre
of a current carrying coil to its
magnetic moment is \( x \). If the current
and radius both are doubled, the new
ratio will become:
A \( .2 x \)
B. \( 4 x \)
c. \( x / 4 \)
D. \( x / 8 \)


If in a wire of Young's modulus \( Y \)
longitudinal strain \( X \) is produced then
the potential energy stored in its unit volume will be :
A. \( 0.5 Y X^{2} \)
2
В. \( 0.5 Y^{2} X \)
c \( .2 Y X^{2} \)
D. \( Y X^{2} \)


A secondary growth proceeds, in a dicot stem, the thickness of
A. sapwood increases
B. heartwood increases
c. both sapwood and heartwood increases
D. both sapwood and heartwood remains the same


The graph of the curve \( x^{2}=3 x-y-2 \)
is
A \( \cdot \) between the lines \( x=1 \) and \( x=\frac{3}{2} \)
B. between the lines \( x=1 \) and \( x=2 \)
C. strictly below the line \( 4 y=1 \)
D. none of these


The name given by Newlands to the arrangement created by him was:
A. law of octane
B. law of octaves
c. law of octagon
D. law of eight elements


Consider the following statements:
1. If 18 men can earn Rs. 1,440 in 5 days, then 10 men can earn Rs. 1,280 in 6 days.
2. If 16 men can earn Rs. 1,120 in 7
days, then 21 men can earn Rs. 800 in 4
days. Which of the above statements is/are
correct?
A. 1 only
B. 2 only
c. Both 1 and 2
D. Neither 1 nor 2


What amount of heat must be supplied to \( 2.0 \times 10^{-2} k g \) of nitrogen (at room
temperature) to raise its temperature
by \( 45^{\circ} \mathrm{C} \) at constant pressure?
(Molecular mass of \( \boldsymbol{N}_{2}=\mathbf{2 8}: \boldsymbol{R}= \)
\( 8.3 m o l^{-1} K^{-1} . \)


Fluorine differs from the other halogens
due to:
A. Small size
B. Very high electronegativity
c. Non-availability of d-orbitals
D. All of these


Parallel venation is a characteristic
feature of
A. Monocotyledon
B. Dicotyledon
c. Pteridophytes
D. Bryophytes


\( \int\left(\frac{x^{6}-1}{x^{2}+1}\right) d x \)


If the radius and the height of a right circular cylinder are doubled, its volume becomes
A. 2 times
B. 3 times
c. 4 times
D. 8 times


State whether the given statement is true
or false.
Statement: Metal has the tendency to lose electron so they are reducing in nature while non-metals have the
tendency to gain electrons so they are oxidizing in nature
A. True
B. False


Write down the number of significant figures in the following value.
\( \mathbf{0 . 0 6 2 8 c m} \)
A . four
B. three
c. \( t w o \)
D. one


Assertion
Development is the sum of growth and
differentiation.
Reason
Development in plants is under the control of extrinstic factors only.
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


Balance reaction when dil. HCl is added
to lead nitrate solution.
A \( \cdot \operatorname{Pb}\left(N O_{2}\right)_{2}+2 H C l \rightarrow P b C l_{2}+2 H N O_{3} \)
В \( \cdot_{2 P b}\left(N O_{3}\right)_{2}+2 H C l \rightarrow 2 P b C l_{2}+H N O_{3} \)
c. \( \operatorname{Pb}\left(N O_{3}\right)_{2}+2 H C l \rightarrow P b C l_{2}+2 H N O_{3} \)
D. \( \operatorname{Pb}\left(N O_{3}\right)_{2}+H C l \rightarrow P b C l_{2}+H N O_{3} \)


A step-down transformer increases the input current \( 4 A \) to 24 A at the secondary. If the, number of turns in the
primary coil is \( 330, \) the number of turns in the secondary coil is
A . 60
B. 50
\( c \cdot 65 \)
D. 45
E. 55


A chord \( A B \) of a circle, of radius \( 14 \mathrm{cm} \)
makes an angle of \( 60^{\circ} \) at the centre of
the circle. Find the area of the minor
segments of the circle.


Undigested food or thyme does not pass through
A. pancreas
B. duodenum
c. large intestine
D. stomach


is called as animal
starch.
A. Starch
B. Glycogen
c. cellulose
D. None of the above


Find \( \angle D O C \)
\( \mathbf{A} \cdot 45^{\circ} \)
B \( .50^{\circ} \)
\( c \cdot 30^{\circ} \)
\( \mathbf{D} \cdot 65^{\circ} \)


State whether the following statement
is true/false.
\( \frac{2375}{375} \) is not a terminating decimal
A. True
B. False


An element with atomic number 82
belongs to the group:
A . 16
B. 12
\( c \cdot 14 \)
\( D \cdot 2 \)


\( \left[B a^{2+}\right] \) when \( C a S O_{4} \) starts just precipitation will be:
\( \mathbf{A} \cdot\left[B a^{2+}\right]=4.58 \times 10^{-7} M \)
B . \( \left[B a^{2+}\right]=5.58 \times 10^{-7} M \)
C \( \cdot\left[B a^{2+}\right]=4.85 \times 10^{-7} M \)
D. None of these


Domain formation is the necessary
feature of
A. ferro magnetism
B. paramagnetism
c. diamagnetism
D. electro magnetism


A car, starting from rest, accelerates at
the rate \( \boldsymbol{f} \) through a distance \( \boldsymbol{S}, \) then
continues at constant speed for time \( t \)
and then decelerates at the rate \( \frac{f}{2} \) to come to rest. If the total distance
traversed is \( 15 S, \) then
A \( \cdot S=\frac{1}{2} f t^{2} \)
B . \( S=\frac{1}{4} f t^{2} \)
\( \mathbf{c} \cdot S=\frac{1}{72} f t^{2} \)
D. \( S=\frac{1}{6} f t^{2} \)


If \( O_{3} \) is dissociating into \( O_{2} \) then
molecular weight of \( O_{3} \) may be:
A . 48
B. 64
c. 40
D. 50


Out of \( \mathrm{HPO}_{3} \) and \( \mathrm{H}_{3} \mathrm{PO}_{2} \) the more
powerful oxidant is :
\( A \cdot \mathrm{HPO}_{3} \)
в. \( \mathrm{H}_{3} \mathrm{PO}_{2} \)
c. equal
D. None


\( \boldsymbol{y}_{1}=\mathbf{8} \boldsymbol{8} \sin (\boldsymbol{\omega} \boldsymbol{t}-\boldsymbol{k} \boldsymbol{x}) \) and \( \boldsymbol{y}_{2}= \)
\( 6 \sin (\omega t+k x) \) are two waves travelling
in a string of area of cross-section \( s \) and
density \( \rho . \) These two waves are
superimposed to produce a standing
wave. Find the total amount of energy
crossing through a node per second.
A \( \cdot \frac{2 \rho \omega^{3} s}{k} \)
B. \( \frac{3 \rho \omega^{3} s}{k} \)
c. \( \frac{5 \rho \omega^{3} s}{k} \)
D. \( \frac{6 \rho \omega^{3} s}{k} \)


Determine the. oxidation state of
chromium in the finfll product formed by the reaction between KI and acidified potassium dichromate solution.
\( A \cdot+3 \)
\( B .+2 \)
\( c \cdot+1 \)
\( D \ldots-3 \)


For what phase difference between two
SHMs will the amplitude of the
resultant SHM be zero
A . \( \pi / 2 \)
в. \( 2 \pi \)
\( c . \pi \)
D. 0


After stem cutting, induction of rooting by auxin treatment would be beneficial in which of the following?
A. Marchantia
B. Wheat
c. cuscuta
D. Bougainvillea


Which of them can be used as a
catalyst?
A. Neodymium phosphide
B. Cerium phosphate
c. Praseodymium oxide
D. Neodymium(III) nitrate


Layer test is associated with :
A. chloroform
B. pyrene
C. bromine
D. wood alcoho


Active and passive transports across
cell membrane differ in
A. Passive transport is non-selective
B. Passive transport is along the concentration gradient while active transport is due to metabolic energy
c. Active transport is more rapid
D. Passive transport is confined to anions while active transport in confined to cations


The angles of triangle are \( x, 5 x, 9 x \) then
find the angles of triangle.


How much ammonia 1 M solution of
ammonium hydroxide contains? (in g)
\( A \cdot 35 g \)
B. 17 g
\( c \cdot 348 \)
D. None of these


The sensitivity of a galvanometer will increase if
A. radius of coil is increased
B. number of turns in coil is decreased
c. radius of coil is decreased
D. a strong field is used


The surface of a metal is illuminated
with the light of 400 nm. The kinetic energy of the ejected photoelectrons
was found to be \( 1.68 \mathrm{eV} \). The work
function of the metal is :
\( (h c=1240 \mathrm{eV} . n m) \)
A . \( 3.09 \mathrm{eV} \)
в. \( 1.41 \mathrm{eV} \)
c. \( 1.51 \mathrm{eV} \)
D. \( 1.68 \mathrm{eV} \)


If the temperature scale is changed
from \( ^{0} \mathrm{C} \) to \( ^{0} \mathrm{F} \). the numerical value of
specific heat will
\( A \). increase
B. decrease
c. remain unchanged
D. nothing can be said


Secretin stimulates secretion of
bicarbonate from
A. Liver
B. Kidneys
c. Pancreas
D. Stomach


In an AC series circuit, the
instantaneous current is maximum
when the instantaneous voltage is
maximum. The circuit element
connected to the source will be
A. Pure indicator
B. Pure capacitor
C. Pure resistor
D. Combination of a capacitor and an indicator


Which of the following is an example of an aldopentose?
A. D-Ribose
B. Glyceraldehyde
c. Fructose
D. Erythrose


Let the perpendicular from any point on
the line \( 2 x+11 y=5 \) upon the lines
\( 24 x+7 y=20 \) and \( 4 x-3 y=2 \) have
the lengths \( p \) and \( p^{\prime} \) respectively. Then
A \( \cdot 2 p=p^{\prime} \)
В . \( p=p^{\prime} \)
c. \( p=2 p^{\prime} \)
D. none of these


Fill in the blank.
In longitudinal waves, the particles vibrate in direction of
propagation.
A. parallel
B. perpendicular
c. \( 45^{\circ} \) inclined
D. \( 60^{0} \) inclined


If \( A \) and \( B \) mutually exclusive events associated with a random experiment such that \( \boldsymbol{P}(\boldsymbol{A})=\mathbf{0 . 4} \) and \( \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 5} \)
then find \( \boldsymbol{P}(\boldsymbol{A} \cap \overline{\boldsymbol{B}}) \)


Find the Variance and Standard
Deviation of the values 4,4,4,4,4,4
using short-cut method.
A .4
B. 0
c. 12
D. None of these


Gibberellins could be extracted from
A. Rice
B. Fungus
c. Diseased plant
D. None of the above


A proton is accelerated to one-tenth of the velocity of light. If its velocity can be measured with a precision \( \pm 1 \% \), then its uncertainty in position is:
A \( \cdot 1.05 \times 10^{-13} m \)
В. \( 1.13 \times 10^{-13} \mathrm{m} \)
c. \( 1.15 \times 10^{-13} \mathrm{m} \)
D. \( 1.25 \times 10^{-13} \mathrm{m} \)


The order and degree of
\( \left[\frac{d^{2} y}{d x^{2}}+\left(\frac{d y}{d x}\right)^{2}\right]^{1 / 2}=\frac{d^{3} y}{d x^{3}} \) is:
\( A \cdot 1,2 \)
B. 3,
c. 3,2
D. 2,


Which solution has the greatest percent
ionization?
\( \mathbf{A} \cdot 0.10 \mathrm{M} N H_{3}\left(K_{b}=1.8 \times 10^{-5}\right) \)
B. 0.25 M \( H N O_{2}\left(K_{1}=4.5 \times 10^{-4}\right) \)
C . 1.000 M HCOOH \( \left(K_{a}=1.7 \times 10^{-4}\right) \)
D . \( 2.000 \mathrm{M} C H_{3} N H_{2}\left(K_{b}=4.4 \times 10^{-4}\right) \)


Which is a common standard for
calibrating a bomb calorimeter in teaching laboratories?
A . Acetic acid
B. Benzoic acid
c. Picric acid
D. Pheno


Show that the function \( f \) given by
\( f(x)=10^{x} \) is increasing for all \( x \)


Astronauts communicate with one
another on moon with the help of
A. radio waves
B. sound waves
c. ultrasound waves
D. infrasound waves


Red phosphorous is less soluble and less volatile than white phosphorous
because of :
A. Polymerized structure
B. Discrete P
4
molecules
c. Its red colour
D. It is less reactive


Draw a labelled diagram showing the vertical section of the human brain.
State two functions each of the
cerebrum, cerebellum and medulla oblongata


The time taken by a particle in reaching from a trough to its next crest in a transverse wave is
A . \( T / 4 \)
B. T/2
c.
D. 3T/4


Differentiate the following functions
with respect to \( \boldsymbol{x} \) \( \cos ^{-1}\left\{\frac{\cos x+\sin x}{\sqrt{2}}\right\},-\frac{\pi}{4}<x<\frac{\pi}{4} \)


The probability distribution of a random variable \( X \) is given below:
\[
\begin{array}{lllll}
\mathrm{x}: & 0 & 1 & 2 & 3 \\
\mathrm{P}(\mathrm{x}): & \mathrm{k} & \frac{k}{2} & \frac{k}{4} & \frac{k}{8}
\end{array}
\]
Determine the value of \( X, \) if \( k=\frac{8}{X} \)


What is meant by vinegar and gasohol?
What are their uses?


What is Solar Panel? Write its main
three uses.


An element \( X \) forms two oxides \( X O \)
and \( X O_{2} . \) The oxide \( X O \) is neutral but
\( X O_{2} \) is acidic in nature. The element \( X \)
is most likely to be:
A. sulphur
B. carbon
c. calcium
D. hydrogen


Artificial (man-made) wool is known by
the name:
A. rayon
B. acrylicc
c. polycot
D. none of these


Which of the following process does not occur through convection
A. boiling of water
B. land breeze and sea breeze
c. circulation of air around furnace
D. heating of glass bulb through filament


A plank of mass \( 5 k g \) placed on a
frictionless horizontal plane. Further a
block of mass \( 1 k g \) is placed over the
plank. A massless spring of natural
length \( 2 m \) is fixed to the plank by its
one end. The other end of spring is
compressed by the block by half of
spring's natural length. They system is now released from the rest. What is the
velocity of the plank when block leaves the plank? (The stiffness constant of
spring is \( 100 N / m \) ).


Which of the followings is/are correct?
This question has multiple correct options
A. In the structure of \( I F_{2}^{+} \) bond angle is smaller than the tetrahedral angle because of lone pair-lone pair repulsion
B. In the structure of \( I F_{4}^{+} \), there is \( s p^{3} \) hybridisation with bond angle of \( 109^{\circ} 28^{\prime} \)
C. In the structure of \( I F_{6}^{+} \), there are six bonding electrons and no lone pairs
D. In the structure of \( I F_{4}^{+} \), two F-atoms one at equatorial positions and two are inclined at an angle less than \( 120^{\circ} \) due to lone pair-bond pair repulsion


What is the percentage of persons who read only two papers?
A \( .19 \% \)
(年 \( 1.1 \% \)
B. \( 31 \% \)
c. \( 44 \% \)
D. None of the above


Draw a labelled diagram of an electric
generator


A closed vessesl contains 8 gms of
oxygen and \( 7 \mathrm{gm} \) of Nitrogen. Total pressure at a certain temperature is 10
atm. When all the oxygen is removed from the system without chage
in temperature then the pressure will be
A. \( 10 \times 7 / 15 \) atm
B. 10 x 8/15atm
c. \( 10 \times 8 / 16 \) atm
D. \( 10 \times 8 / 32 \) atm


The oxyacids of phosphorous which show powerful reducing properties but no oxidizing
properties are :
A. \( H_{3} P O_{2}, H_{3} P O_{3} \)
в. \( H_{3} P O_{2}, H_{3} P O_{4} \)
\( \mathrm{c} \cdot H_{3} P O_{3}, H_{3} P O_{4} \)
D. \( H P O_{3}, H_{3} P O_{3} \)


Solve the following differential equation \( \cos x \frac{d y}{d x}-\cos 2 x=\cos 3 x \)


Red rot of sugarcane and white rust of radish respectively are caused by
A. Albugo candida and Cercospora
B. Colletotrichum and Fusarium
c. Pythium and Phytophthora
D. Albugo candida and Puccinia graminis
E. Colletotrichum and Albugo candida


Maximum number of enzymes are
found in
A . Herbivores
B. Carnivores
c. Omnivores
D. None of these


The position of xylem position in secondary xylem is
A. Exarch
B. Endarch
c. Mesarch
D. None of the above


Which hormone controls secretion of
oestrogen?
A. Progesterone
B. Follicle stimulating hormone
c. Aldosterone
D. Adrenaline


Two conducting spheres of radii \( r_{1} \) and
\( r_{2} \) are equally charged. The ratio of their
potentials is :
A \( \cdot r_{1} / r_{2} \)
в. \( r_{2} / r_{1} \)
\( \mathbf{c} \cdot r_{1}^{2} / r_{2}^{2} \)
\( \mathbf{D} \cdot r_{2}^{2} / r_{1}^{2} \)


A given charge situated at certain distance from an electric dipole in the end on position, experiences a force F. If the distance of charge is doubled, the force acting on the charge will be
A \( .2 F \)
в. \( F / 2 \)
c. \( F / 4 \)
D. \( F / 8 \)


Archinephros occurs in
A. Adult hagfish
B. Larva of hagfish
c. Molluscs
D. Anamniotes


A solution contains 2.80 moles of
acetone \( \left(C H_{3} C O C H_{3}\right) \) and 8.20 moles
of \( C H C l_{3} \). Calculate the mole fraction
of acetone.(give answer in \( 110 X) \)


Which among the following is most reactive to give nucleophilic addition?
A. \( F C H_{2} C H O \)
в. \( C l C H_{2} C H O \)
\( \mathrm{c} \cdot B r C H_{2} C H O \)
D. \( I C H_{2} C H O \)