There are four resistors of 12 ohm each.
Which of the following values is/are possible by their combinations (series and / or parallel)? This question has multiple correct options
\( \mathbf{A} \cdot 9 \) ohm
B. 16 ohm
c. 12 ohm
D. 30 ohm


In the given figure, if \( P Q R S \) is a
rectangle which one is true?
\( \mathbf{A} \cdot A r \Delta(A P S)=A r \Delta(Q R B) \)
B. \( P A=R B \)
\( \mathbf{c} \cdot A r(P Q S)=A r(Q R S) \)
D. All of the above


Which one of the following relations on
\( R \) is equivalence relation
A. \( x R_{1} y \Leftrightarrow|x|=\mid y \)
В. \( x R_{2} y \Leftrightarrow x \geq y \)
c. \( x R_{3} y \Leftrightarrow x \mid y \)
D. \( x R_{4} y \Leftrightarrow x<y \)


Which of the following soap/detergent has least biodegradability?
A. \( C H_{3}-\left(C H_{2}\right)_{11}-O S O_{2} N a \)
в. \( C_{17} H_{35}- \) СОО Na
\( c \)
\( D \)


Which one of the following is correct?
A. A mineral cannot be an ore
B. An ore cannot be a mineral
C. All minerals are ores
D. All ores are minerals


A few normal seedling of tomato were kept in a dark room. After few days they were found to have become white-
coloured like albions. Which of the
following terms will you use to describe
them?
A. Mutated
B. Embolised
c. Etiolated
D. Defoliated


The white solid compound \( A \) decomposes quite rapidly on heating in the presence of a black substance \( X \) to form a solid compound B and a gas C. When an aqueous solution of compound B is reacted with silver nitrate solution, then a white precipitate of silver chloride is obtained along with potassium nitrate solution. Gas C does not burn itself but helps to burn other things.

What do you think that black substance \( \mathbf{X} \) and \( \mathrm{What} \) is its function?


toppr
Q Type your question
generated across the coil during one
cycle is
\( A \)
B.
\( c \)
\( D \)


Erythropoietin stimulates
A. Osmoregulation
B. Formation of RBC
c. Reduces blood pressure
D. Formation of WBC


Which of the following statement is not
true for meiosis?
A. It is a process in which the chromosomes duplicate only once
B. It is a process in which the cell divides twice
C. The karyokinesis skips one of the phases compared to mitosis
D. It results in the formation of four haploid cells


A charges of \( 8.7 \times 10^{-18} C \)
A. Does exist
B. Does not exist
c. Exists for a short time
D. Exists only if placed in higher orbits


A man donated \( 5 \% \) of his income to a
charitable organization and deposited \( 20 \% \) of the remainder in bank. Now if he
has \( R s 1919 \) left, what is his income?


Which of the following is not a mineral
acid?
A. \( H C l \)
в. \( H_{2} S O_{4} \)
c. \( H N O_{3} \)
D. \( H_{2} C O_{3} \)


What will happen during roasting?
A. The sulphide ores are converted into oxides
B. The oxide ores are converted into sulphides
C. The sulphide ores are converted into carbonates
D. The oxide ores are converted into carbonates.


A calorie is a unit of heat energy and its
value is \( 4.18 \mathrm{J} \) where \( 1 J=1 k g m^{2} s^{-2} \)
Suppose we use a new system of units in which unit of mass equals \( \boldsymbol{\alpha} \) kg, the
unit of length equals \( \beta \mathrm{m} \) and the unit
of the time is \( \gamma \) sec. Then the value of a
calorie in the new system of units is
then
A \( \cdot \) 4.18 \( \frac{\gamma^{2}}{\alpha \beta^{2}} \)
B. \( 4.18 \frac{\alpha \beta^{2}}{\gamma^{2}} \)
c. \( 4.18 \frac{\gamma^{2}}{\alpha} \)
D. \( 4.18 \frac{\beta^{2}}{\alpha \gamma^{2}} \)


If \( |z|=1 \) and \( w=\frac{z-1}{z+1}(z \neq-1) \) then
\( \operatorname{Re}(w) \) is
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( \frac{-1}{|z+1|^{2}} \)
c. \( \frac{1}{|z+1|^{2}} \)
D. \( \frac{\sqrt{2}}{|z+1|^{2}} \)


Green house effect is caused by
A \( . N O_{2} \)
в. \( C O \)
\( c \cdot C O_{2} \)
D. \( O_{2} \)


In an organization of pollution control board, engineers are represented by a
circle, legal experts by a square and
environmentalist by a triangle. Who is
most represented in the board as shown
in the figure?
A. Environmentalists
B. Engineers with legal background
c. Legal Experts
D. Environmentalists with Engineering background


nanometer is \( _{-1-} \) centimeter
A \( \cdot 10^{-8} \)
B. \( 10^{-7} \)
\( \mathrm{c} \cdot 10^{-9} \)
D. \( 10^{-6} \)


The cell in which the following reaction
occurs:
\( 2 F e^{3+}(a q)+2 I^{-}(a q) \rightarrow 2 F e^{2+}(a q)+ \)
\( \boldsymbol{I}_{2}(\boldsymbol{s}) \)
has \( E_{c e l l}^{\circ}=0.236 V \) at \( 298 K . \) Calculate
the standard Gibbs energy of the cell
reaction. (Given : \( 1 \boldsymbol{F}= \)
\( \left.\mathbf{9 6}, \mathbf{5 0 0} \boldsymbol{C} \boldsymbol{m o l}^{-\mathbf{1}}\right) \)


Which of the following is a statement?
A. I like lions
B. Logic is an interesting subject
C. A triangle is a circle and 10 is a prime number
D. None of these.


Mark the example which in not correctly
matched?
A. Air pollutants - Oxides of sulphur, nitrogen and carbon
B. Particulate pollutants - Dust, mist fumes
C. Global warming - Methane, ozone, CFCs
D. Water soluble chemical pollutants - Oxides of nitrogen, carbon and sodium


A car moving on a straight road
accelerates from a speed of \( 4.1 \mathrm{m} / \mathrm{s} \) to
a speed of \( 6.9 m / s \) in \( 5 s . \) Its average
acceleration is
A. \( 0.5 \mathrm{m} / \mathrm{s}^{2} \)
B . \( 0.6 \mathrm{m} / \mathrm{s}^{2} \)
c. \( 0.56 \mathrm{m} / \mathrm{s}^{2} \)
D. \( 0.65 \mathrm{m} / \mathrm{s}^{2} \)


Aniline when treated with \( N a N O_{2} \) and
\( H C l \) at \( 0-5^{0} C \) gives
as a product.
A. chloroaniline
B. benzene diazonium chloride
c. chlorobenzene
D. dichlorobenzene


Evaluate the following definite integral:
\( \int_{0}^{2} \frac{1}{4+x-x^{2}} d x \)


\( \boldsymbol{S} \boldsymbol{O}_{2} \) turns acidified \( \boldsymbol{K}_{2} \boldsymbol{C r}_{2} \boldsymbol{O}_{7} \)
A. green
B. blue
\( c \cdot \) red
D. orange


Write the value of the determinant
\[
\left[\begin{array}{cc}
\boldsymbol{p} & \boldsymbol{p}+\mathbf{1} \\
\boldsymbol{p}-\mathbf{1} & \boldsymbol{p}
\end{array}\right]
\]
when \( p=1342 \)


Root pressure theory was supported by
A. Dixon
B. Stephen Hales
c. Levitt
D. sachs


Assertion
A photocell is called an electric eye.
Reason
When light is incident on some
semiconductor its electrical resistance
is reduced
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


In the year 2000 , rice formed \( 20 \% \) of the total food gain production in a country. In the next year, the total food grain production increased by \( 20 \% \) and the rice production was \( 25 \% \) of the total food grain production. What is the increase in the production of rice from
\( \mathbf{2 0 0 0} \) to \( \mathbf{2 0 0 1} \) ?


Which light is most effective in seed
germination?
A. Green
B. Far red
c. Red
D. Blue


In the reaction, \( 4 C r O_{5}+6 H_{2} S O_{4} \rightarrow \)
\( 2 C r_{2}\left(S O_{4}\right)_{3}+6 H_{2} O+7 O_{2}, \) which
statement is wrong?
A. It is a disproportionation reaction.
B. It is an intramolecular redox reaction
c. \( C r O_{5} \) acts as oxidant and reductant both.
D. cracts as oxidant and 0 acts as reductant


A susceptibility of a certain magnetic material is \( 400 . \) What is the class of the
magnetic material?
A. Diamagnetic
B. Paramagnetic
c. Ferromagnetic
D. Ferroelectric


Assertion
For a particle performing SHM, its speed decreases as it goes away from the mean position.
Reason
In SHM, the acceleration is always
opposite to the velocity of the particle.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which of the following is not a function of neuron?
A. Receive information
B. Conduct a signal
c. Form the myelin sheath
D. Co-ordinate metabolic activities


Taking the mass of a proton to be \( 1.67 \times 10^{-27} \mathrm{kg}, \) the order of magnitude
of the number of protons in 1 g is \( 5.88 \times \) \( \mathbf{1 0}^{(\mathbf{2 0}+\boldsymbol{x})} \). What is \( \boldsymbol{x} \)


A ball with a weight of 20 N is thrown vertically upward. What is the acceleration of the ball just as it
reaches the top of its path?
A. \( 10 m / s^{2} \) downward
B. \( 10 \mathrm{m} / \mathrm{s}^{2} \) upward
c. \( 20 m / s^{2} \) downward
D. \( 20 m / s^{2} \) upward
E. zero


A positive charge q is placed in a spherical cavity made in a positively charged sphere. The centres of sphere and cavity are displaced by a small distance \( \vec{l} \). Force on charge q is :
A . in the direction parallel to vector \( \vec{l} \)
B. in radial direction
c. in a direction which depends on the magnitude of charge density in sphere
D. direction can not be determined


State True or False.
Caphosol a supersaturated calcium phosphate solution is used in the prevention and treatment of oral mucositis caused by chemotherapy or radiotherapy.
A. True
B. False


Which of the ions will give colorless aqueous solution?
A \( \cdot N i^{2} \)
B. \( F e^{2} \)
c. \( C u^{2+} \)
D. \( C u^{+} \)


During the estimation of phosphorous present in an organic compound, weighed amount of the organic compound is heated with:
A. conc. nitric acid
B. conc. sulphuric acid
c. conc. hydrochloric acid
D. Mixture of conc. nitric acid and conc. sulphuric acid


Given is a diagram showing a defect of
human eye
Study it and answer the following
question:

Give two possible reasons for this
defect of eye in human being.


For which of these redox pairs, the reduction potential vary with pH This question has multiple correct options
\( \mathbf{A} \cdot A m O_{2}^{2+} / A m O_{2}^{+} \)
B. \( A m O_{2}^{2+} / A m^{4} \)
c. \( M n O_{4}^{-} / M n^{2+} \)
D. \( Z n^{2+} / Z n \)


Calorimeters are generally made of
A. copper
B. brass
c. aluminium
D. zinc


The electronic configuration of few elements is given below. Mark the statement which is not correct about
these elements.
(i) \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{1} \)
(ii) \( 1 s^{2} 2 s^{2} 2 p^{5} \)
(iii) \( 1 s^{2} 2 s^{2} 2 p^{6} \)
\( (\text { iv }) 1 s^{2} 2 s^{2} 2 p^{3} \)
A . (i) is an alkali metal.
B. (iii) is a noble metal.
c. (i) and (ii) form ionic compounds.
D. (iv) has high ionisation enthalpy


With the help of the given clues, unscramble the letters to make a
meaningful word. HCEO (A reflected sound wave)


Each electrical appliance is provided
with a
Fill in the blank.
\( A \cdot 3 \)
B. 2
\( c \)
D. 4


Chlorine gas reacts with red hot
calcium oxide to give:
A. bleaching powder and dichlorine monoxide
B. bleaching powder and water
C . calcium chloride and chlorine dioxide
D. calcium chloride and oxygen


\( \int \frac{3 x+1}{\left(x^{3}-x^{2}-x+1\right)} d x \)


The dielectric to be used in a parallelplate capacitor has a dielectric constant of 3.60 and a dielectric
strength of \( 1.60 \times 10^{7} V / \) m. The
capacilnr is to have a capacitance of \( 1.25 \times 10^{-9} F \) and must be able to \( u \)
withstand a maximum potential difference of 5500 V. The minimum area
the plates of the capacitor may have is
equal to \( 135 \times 10^{-x} m^{2} . \) The value of \( x \)
is:


Anemone fish can live safely within the tentacles of sea anemones because
they have specialised scales that are immune to the stings. Which organ helps in the stinging mechanism?
A. Nematocysts
B. Pinacocytes
c. choanocyte
D. Nectophore


Give reason
Spore formation not a method of
reproduction in bacteria


Nuclear fusion occur in
A. Atom bomb
B. Hydrogen bomb
C. Neutron bomb
D. None of these


A bag contains 5 red balls, 3 black balls and 4 white balls. Three balls are drawn
at random. The probability that they are not of same colour is
\( ^{\mathrm{A}} \cdot \frac{37}{44} \)
в. \( \frac{31}{44} \)
c. \( \frac{21}{44} \)
D. \( \frac{41}{44} \)


The solubility of solutions which are neither exothermic nor endothermic
increases with increase in temperature
A. True
B. False


Guanine is an example of:
A. a nitrogenous base
B. a nucleoside
c. a nucleotide
D. phosphate


Give balanced chemical equations for the following reactions:
Hydrogen sulphide treated with concentrated sulphuric acid.


If \( a, b, c \) are in A.P. \( b-a, c-b \) and \( a \) in
G.P., then \( \boldsymbol{a}: \boldsymbol{b}: \boldsymbol{c} \) is
A . 1: 2: 3
B. 1: 3: 5
\( c \cdot 2: 3: 4 \)
D. None of these


Find the H.C.F. of the following numbers using prime factorization method.
81,117


Rational numbers are closed under
A. addition
B. subtraction
c. multiplication
D. all of the above


Vermi-processing toilet is
A. Alternative sources of energy.
B. Alternative arrangement of sewage disposal.
C. Alternative arrangement of sewage treatment.
D. None of the above.


The work function of aluminium is 4.2
eV. If two photons, each of energy 3.5 eV strike an electrons of aluminium, then
emission of electrons
A. Will be possible
B. Will not be possible
c. Data is incomplete
D. Depends upon the density of the surface


The length of a wire is increased by
1 \( m m \) on the application of a given load In a wire of the same material, but of length and radius twice that of the first, on application of the same load, extension is
A. \( 0.25 \mathrm{mm} \)
в. \( 0.5 \mathrm{mm} \)
\( \mathrm{c} .2 \mathrm{mm} \)
D. \( 4 \mathrm{mm} \)


Find the squares of 99 using the identity
\( (a-b)^{2}=a^{2}-2 a b+b^{2} \)


Which will exert more pressure. 150kg mass on \( 10 m^{2} \) or \( 50 \mathrm{kg} \) mass on \( 10 m^{2} ? \)
Give reason.


Fill in the Blanks
Angular displacement is a vector quantity for (very small/even large)


The gate whose output is low if and only if all inputs are high, is
A. NAND
B. AND
\( c . \) ов
D. None of these


The pH of 0.001M HCN is:
\( A \cdot 3 \)
в. 1
c. between 3 \& 7
D. 7


Nitya and Satya have some marbles with them. Nitya says to Satya, "If you give one marble to me, we will have equal number of marbles. Satya says to Nitya, "If you give me one marble, I will have twice the number of marbles you
have". How many marbles do Nitya and Satya have respectively?
A \( \cdot 4,6 \)
в. 5,7
\( c \cdot 6,4 \)
D. 7,5


The chemical reaction, \( 2 O_{3} \rightarrow 3 O_{2} \)
proceeds as follows;
\( O_{3} \rightleftharpoons O_{2}+O \dots(\text { Fast }) \)
\( \boldsymbol{O}+\boldsymbol{O}_{3} \rightarrow \boldsymbol{2} \boldsymbol{O}_{2} \ldots(\text { Slow }) \)
The rate law expression should be:
A \( \cdot r=K\left[O_{3}\right]^{2} \)
B . \( r=K\left[O_{3}\right]^{2}\left[O_{2}\right]^{-1} \)
\( \mathbf{c} \cdot r=K\left[O_{3}\right]\left[O_{2}\right] \)
D. unpredictable


State true or false:
\( \sqrt{2} \) is not a rational number.
A. True
B. False


State True or False.
Molten Potassium burns in air forming potassium superoxide
A. True
B. False


Find the value of the unknown interior
angle \( x \) in the following figure.


Which of the following has \( X-0-X \)
linkage?
(1) \( \boldsymbol{H}_{2} \boldsymbol{S}_{4} \boldsymbol{O}_{6} \)
(2) \( \boldsymbol{H}_{\mathbf{6}} \boldsymbol{P}_{\mathbf{6}} \boldsymbol{O}_{\mathbf{1} \mathbf{8}} \)
\( \boldsymbol{P}_{4} \boldsymbol{O}_{10} \)
(4)
\( N a_{2} B_{4} O_{5}(O H)_{4} .8 H_{2} O \)
(5)\( N a_{2} S_{2} O_{8} \)
(6) \( K_{2} S_{2} O_{7} \)
(7) \( K_{2} C r_{2} O_{7} \)
(8) \( N a_{4} P_{2} O_{8} \)
(9) Hypophosphoric acid
A. 5
B. 9
\( c \cdot 7 \)
D.


de Broglie relation is true for
A. All particles
B. Charged particles only
c. Negatively charged particles only
D. Massless particles like photons only


Consider the following parallelograms. ind the values of the unknowns \( x, y, z \)
A \( . X=60^{\circ}, Y=100^{\circ}, Z=20^{\circ} \)
B . \( X=28^{\circ}, Y=112^{\circ}, Z=28^{\circ} \)
c. \( X=65^{\circ}, Y=105^{\circ}, Z=20^{\circ} \)


Succession showing changes in communities at a place is called
A. Geographical succession
B. Biotic succession
C. Physiographic succession
D. climatic succession


What is the atomic number of the
element with symbol Uus?
A . 117
B. 116
c. 115
D. 114


Two springs \( P \) and \( Q \) of force constant \( k_{p} \) and \( k_{Q}\left(k_{Q}=\frac{k_{p}}{2}\right) \) are stretched by applying forces of equal magnitude. If the energy stored in \( Q \) is \( E \), then the energy stored in P is?
A . E/2
B. 2E
c.
D. E/4


State whether the statement is true or
false:
Na is more stable than \( N a^{+} \)


The dimensional formula for electric
flux is
A \( \cdot\left[M L^{3} I^{-1} T^{-3}\right. \)
B \( \cdot\left[M^{2} L^{2} I^{-1} T^{-2}\right] \)
C . \( \left[M L^{3} I^{1} T^{-3}\right] \)
\( \mathbf{D} \cdot\left[M L^{-3} I^{-1} T^{-3}\right] \)


A 10 m long potentiometer wire is
connected to a battery having a steady voltage. A Leclanche cell is balanced at
\( 4 m \) length of the wire. If the length is kept the same, but its cross-section is doubled, the null point will be obtained
at:
\( \mathbf{A} \cdot 8 m \)
в. \( 4 m \)
c. \( 2 m \)
D. None of these


The number of \( \mathbf{P}-\mathbf{O}-\mathbf{P} \) bonds in
cyclic metaphosphoric acid is :
\( A \cdot O \)
B. 2
\( c \cdot 3 \)
D. 4


Two parallel conductors \( P \) and \( Q \) of equal lengths carry currents I and \( 5 I \) respectively in the same direction, then.
A. They will repel each other with the same force
B. They will attract each other with the same force
c. A will attract but B will repel
D. B will attract but A will repel


If \( \boldsymbol{A}\left(\boldsymbol{a}^{2}, \boldsymbol{2} \boldsymbol{a}\right) \boldsymbol{B}=\left(\frac{\mathbf{1}}{\boldsymbol{a}^{2}}, \frac{\boldsymbol{-} \boldsymbol{2}}{\boldsymbol{a}}\right), \boldsymbol{P}=(\boldsymbol{1}, \boldsymbol{0}) \)
then \( \frac{\boldsymbol{1}}{\boldsymbol{P} \boldsymbol{A}}+\frac{\boldsymbol{1}}{\boldsymbol{P} \boldsymbol{B}}= \)


Atomic number 56 belongs to which
block ?
\( A \)
B. \( p \)
\( c \cdot d \)
D. \( f \)


Which of the following is the stable enol form of \( 1,3- \) cyclohexanedione?
\( A \cdot i \)
B. i i
c. iii
D. iv
\( E \)


For \( \boldsymbol{y}^{2}-\mathbf{2 0 0} \boldsymbol{x}=\mathbf{0}, \) focal distance of a
point \( (2,20), \) is
A . 48
B. 50
c. 52
D. 20


Which of the following characteristics can be related to cartilaginous joints?
A. Permit slight movements
B. Are found between the bodies of vertebrae
c. Are found in symphysis
D. All of the above


The resistance of one ohm is very
approximately equal to that of a column of mercury \( 1.06 m \) long and of
uniform cross-section of one hundredth
of \( 1 \mathrm{cm}^{2} \). Find the resistivity of mercury.
A \( \cdot 6.4 \times 10^{-7} \Omega m \)
В . \( 7.4 \times 10^{-7} \Omega m \)
c. \( 9.4 \times 10^{-7} \Omega m \)
D. \( 2.4 \times 10^{-7} \Omega m \)


\( \operatorname{Let} \boldsymbol{A}(\mathbf{2} \hat{\boldsymbol{i}}+\boldsymbol{3} \hat{\boldsymbol{j}}+\mathbf{5} \hat{\boldsymbol{k}}) \boldsymbol{B}(-\hat{\boldsymbol{i}}+\boldsymbol{3} \hat{\boldsymbol{j}}+2 \hat{\boldsymbol{k}}) \)
and \( C(\lambda \hat{i}+5 \hat{j}+\mu \hat{k}) \) are vertices of \( a \) triangle and its median through \( A \) is equally inclined to the positive directions of the axes. The value of \( \lambda+ \)
\( \mu \) is equal to
A . -7
B . 2
c. 7
D. 17


toppr OG
Q Type your question_
sphere has the same amount of charge.
Assume each pair is isolated.

For which pair is there a point between
them on the dotted line where the
electric field magnitude is zero and a
point between them on the dotted line
where the electric potential is zero?
A . 1
B. 2
\( c \cdot 3 \)
\( \mathbf{D} \cdot 4 \)
E. None of the pairs has points that meet these conditions


At a particular temp, a solution that has dissolved as much solute as it is
capable of dissolving is said to be a :
A. saturated solution
B. unsaturated solution
c. both \( A \) and \( B \)
D. none of the above


The electrolytic reduction process is used for the extraction of:
A. highly electropositive metals
B. metalloids
c. less active metals
D. transition metals


Find the equation to the ellipse, whose focus is the point \( (-1,1), \) whose directrix is the straight line \( \boldsymbol{x}-\boldsymbol{y}+ \) \( \mathbf{3}=\mathbf{0}, \) and whose eccentricity is \( \frac{\mathbf{1}}{\mathbf{2}} \)


If you study the effect of substrate concentration on an enzymatic reaction, what kind of curve would you
obtain?


If a particle moving along a line following the law \( t=a s^{2}+b s+c \) then
the retardation of the particle is
proportional to
A. Square of displacement
B. Square of velocity
c. cube of displacement
D. Cube of velocity


A satellite is revolving round the earth
with orbital speed \( v_{0} \). If it is imagined to stop suddenly, the speed with which it will strike the surface of the earth would
be \( \left(v_{e}- \) escape speed of a body from \right. earth's surface)
A \( \cdot \frac{v_{e}^{2}}{v_{0}} \)
в. \( v_{0} \)
c. \( \sqrt{v_{e}^{2}-v_{0}^{2}} \)
D. \( \sqrt{v_{e}^{2}-2 v_{0}^{2}} \)


Match the reagents in list II for forming the products in list I from propene as the starting reactant.


The standard deviation of15 terms is 6
and each item is decreased by 1. Then
the standard deviation of new data is?
A . 5
B. 7
c. \( \frac{91}{15} \)
D. 6


if \( a, b, c \) as well as \( d, e, f \) are in G.P.with same common ratio then set of points
\( (a, d),(b, e),(c, f) \) are
A. collinear
B. concurrent
c. lies on a circle
D. lie on an ellipse


An element \( ^{\prime} X^{\prime} \) on emitting an \( \alpha \)
particle, do not change its group number in the periodic table. The element is:
A. lanthanum
B. cerium
c. lawrencium
D. radium


What will be the missing number in the following equation \( (-8) \times-----= \) (+32)\( ? \)


The expansion of \( \left[\boldsymbol{x}+\left(\boldsymbol{x}^{\mathbf{3}}-\mathbf{1}\right)^{\mathbf{1} / 2}\right]^{\mathbf{5}}+ \)
\( \left[x-\left(x^{3}-1\right)^{1 / 2}\right]^{5} \) is a polynomial of
degree
\( \mathbf{A} \cdot \mathbf{8} \)
B. 7
\( c \cdot 6 \)
D. 5


Write IUPAC names of the following compounds and classify them into primary, secondary and tertiary amines.
(i) \( \left(\boldsymbol{C} \boldsymbol{H}_{3}\right)_{2} \boldsymbol{C} \boldsymbol{H} \boldsymbol{N} \boldsymbol{H}_{2} \)
\( \boldsymbol{C H}_{3}\left(\boldsymbol{C H}_{2}\right)_{2} \boldsymbol{N} \boldsymbol{H}_{2} \)
\( \left(\text { iii) } C H_{3} N H C H\left(C H_{3}\right)_{2}\right. \)
\( \left(\boldsymbol{C} \boldsymbol{H}_{3}\right)_{3} \boldsymbol{C} \boldsymbol{N} \boldsymbol{H}_{2} \)
\( (v) C_{6} H_{5} N H C H_{3} \)
\( \left(\boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C} \boldsymbol{H}_{2}\right)_{2} \boldsymbol{N} \boldsymbol{C} \boldsymbol{H}_{3} \)
\( (v i i) m-B r C_{6} H_{4} N H_{2} \)


The vibrations or the pressure
variations inside the inner ear are
converted into electrical signals by the
A. cochlea
B. tympanic Membrane
c. pinna
D. anvil


The device used to generate large amount of electricity is
A . electric cell
B. storage battery
c. solar cell
D. electric generator


What is the catalyst used in the
preparation of oxygen from hydrogen peroxide?
A. Manganese dioxide
B. Magnesium oxide
c. Nickel, Platinum, Palladium
D. No catalyst is used


Mass of a body is \( 210 \mathrm{gm} \) and its density is \( 7.981 g m / c m^{3} . \) What will be its volume with regard to significant digits?
A \( \cdot 26.312 \mathrm{cm}^{3} \)
В. \( 26 \mathrm{cm}^{3} \)
\( \mathbf{c} \cdot 27 c m^{3} \)
D. \( 26.3 c m^{3} \)


The order of the differential equation of the parabola whose axis is parallel to \( y- \) axis is:
\( A \)
B. 2
\( c \cdot 3 \)
D. 4


Assertion
The point \( \boldsymbol{A}(\mathbf{1}, \mathbf{0}, \mathbf{7}) \) is the mirror image of the point \( B(1,6,3) \) in the line \( : \frac{x}{1}= \) \( \frac{\boldsymbol{y}-\mathbf{1}}{\mathbf{2}}=\frac{\boldsymbol{z}-\mathbf{2}}{\mathbf{3}} \)
Reason
The line \( \frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3} \) bisects
the line segment joining \( \boldsymbol{A}(\mathbf{1}, \mathbf{0}, \mathbf{7}) \) and \( \boldsymbol{B}(\mathbf{1}, \mathbf{6}, \mathbf{3}) \)
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


Statement \( 1: A \) 0.2 \( M \) solution of
carbonic Acid is a weaker conductor of
electricity than a \( 0.2 \mathrm{M} \) solution of \( \boldsymbol{H} \boldsymbol{B} \boldsymbol{r} \)
Statement 2: In solutions with the
same concentration of solute
molecules, \( \boldsymbol{H}_{2} \boldsymbol{C O}_{3} \) is less dissociated
than \( H B r \)
A. Both Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement 1
B. Both Statement 1 and Statement 2 are correct and Statement 2 is not the correct explanation of Statement 1.
c. Statement 1 is correct but Statement 2 is not correct
D. Statement 1 is not correct but Statement 2 is correct.
E. Both the Statement 1 and Statement 2 are not correct


Assertion: When two coils are wound on
each other, the mutual induction
between the coils is maximum.
Reason: Mutual induction does not
depend on the orientation of the coils.
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion.
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true


If a block moving up at \( \boldsymbol{\theta}=\mathbf{3 0}^{\mathbf{0}} \) with a
velocity \( 5 \mathrm{m} / \mathrm{s}, \) stops after \( 0.5 \mathrm{sec}, \) then
\( \mu \) is:
A . 0.58
B. 0.42
\( c . \) о.
D. 023


The pH of a solution of \( B(O H)_{2} \) is 10.6
Calculate the solubility and solubility product of hydroxide.


One word answer
Write the IUPAC name of


Which of the option is a linear equation?
A \( \cdot y-3=\frac{1}{4}(x-2) \)
В. \( y+2=x^{3} \)
c. \( 3 \sqrt{x}-y=6 \)
D. \( x+y^{4}=0 \)


Image of an object is seen in a plane
mirror, the distance from the mirror to
the image depends on
A. The wavelength of light
B. The distance of the object from the mirror
c. The distance of both the observer and the object to the mirror
D. The thickness of the mirror


If the normal to the curve \( y=f(x) \) at
(3,4) makes angle \( \frac{3 \pi}{4} \) with \( O \bar{X} \) then
\( \boldsymbol{f}^{1}(\mathbf{3})= \)
A . -1
B.
c. \( (-3 / 4) \)
D. \( (4 / 3) \)


The domain of the functions \( f(x)= \) \( \sqrt{\log \left(2 x-x^{2}\right)} \) is
A \( .(0,2) \)
B. [0,2]
\( c \cdot\{1\} \)
D. none


Which one contains up to ten electrons
from the following?
A . \( 1 s \)
B . \( 2 s \)
\( c \cdot 3 s \)
D. \( 3 p \)
E . \( 3 d \)


The avalanche breakdown in \( p-n \)
junction is due to
A. shift of Fermi level.
B. cumulative effect of conduction band electron
c. widening of forbidden gap.
D. high impurity concentration.


The capacitor offers zero resistance to
A. D.C. only
B. A.C. \& D.C.
c. A.C. only
D. neither A.C. nor D.C.


Number of real solution of the given equation for \( x, \int x^{2} e^{x} d x=0 \)


Let \( \omega \) be the angular velocity of the earth's rotation about its axis. Assume
that the acceleration due to gravity on the earth's surface has the same value
at the equator and the poles. An object weighed at the equator gives the same reading as a reading taken at a depth a below earth's surface at a pole \( (d<< \)
\( \boldsymbol{R} \) ) The value of \( \boldsymbol{d} \) is
\( ^{\mathrm{A}} \cdot \frac{\omega^{2} R^{2}}{g} \)
B. \( \frac{\omega^{2} R^{2}}{2 g} \)
\( ^{\mathrm{c}} \cdot \frac{2 \omega^{2} R^{2}}{g} \)
D. \( \frac{\sqrt{R g}}{g} \)


Choose the correct answer from the
alternatives given
A plane electromagnetic wave of frequency \( 25 M H z \) travels in free space
along \( X \) -direction. At a particular point in space and time, electric field \( \overrightarrow{\boldsymbol{E}}= \) \( 6.3 \hat{j} V / m . \) What is \( B \) at this point
A \( .1 .2 \times 10^{-6} T \)
B . \( 1.2 \times 10^{-8} T \)
c. \( 2.1 \times 10^{-6} T \)
D. \( 2.1 \times 10^{-8} T \)


If either \( \vec{a}=\overrightarrow{0} \) or \( \vec{b}=\overrightarrow{0}, \) then \( \vec{a} \times \vec{b}=\overrightarrow{0} \)
Is the converse true? Justify your
answer with an example.


the potential energy of interaction between two particles with the distance
separating them \( r \)
1. \( \mathrm{B} \) and \( \mathrm{D} \) are equilibrium points.
2. \( C \) is a point of stable equilibrium.
3. The force of interaction between the
two particles is attractive between points \( C \) and \( D \) and repulsive between \( D \)
and E.
4. The force of interaction between
particles is repulsive between points \( \mathrm{E} \)
and F.
Which of the above statements are
correct?
A. 1 and 2
B. 1 and 4
c. 2,3 and 4
D. 2 and 4


The self disintegration, spontaneous emission of \( \alpha, \beta \) and \( \gamma \) rays by nuclei of certain elements is


If \( 4 \cos ^{2} \theta+15 \cos \theta-4=0, \) find the
value of \( \left(\log _{2} \cos \theta\right)^{-5}: \)
A . -1
в. \( -\frac{1}{32} \)
\( c . \)
D. none of these


Three mass points each of mass \( m \) are
placed at the vertices of an equilateral
triangle of side \( 1 . \) What is the
gravitational potential at the centroid of
the triangle.


Find the derivative of the following fuctions (it is to be understood that
\( a, b, c, d, p, q, r \) and \( s \) are fixed non-zero
constants and \( \boldsymbol{m} \text { and } \boldsymbol{n} \text { are integers }) \) \( \frac{x}{\sin ^{2} x} \)


State True or False.
A balanced equation contains equal number of atoms of each element on
both sides of the equation.
A. True
B. False


Is \( M g O+C l \rightarrow M g C l+O_{2} \)
reduction reaction?


Which figure below shows two quadrilaterals related by both rotational symmetry and line symmetry?
A. Figure
B. Figure i
C. Figure iii
D. None of these


The energy released in nuclear
disintegrations in the interior of earth
is
A. the geothermal energy
B. the hydro electric energy
c. the heat energy
D. the chemical energy


Which one of the following is bad conductor of electricity?
A. Acid
B. coal
c. Distilled water
D. Human body


What are the differences between a
pinnately compound leaf and a branch bearing simple leaves?


Two concentric spheres of radius \( R \) and
\( 2 R \) have charges \( Q \) and \( 2 Q . \) The potential at a point \( \mathrm{P} \) situated at a point 3R/2 distance from common centre is
\( V, \) Now if outer sphere is earthed, the
potential at point \( P \) is :
A. \( V / 5 \)
в. \( V / 10 \)
c. \( V / 3 \)
D. \( V \)


The multiplication of 10.610 with 0.210 upto correct number of significant figure is
A . 2.2281
B . 2.228
\( c \cdot 2.23 \)
D. 2.3


Write a rational number between \( \sqrt{2} \)
and \( \sqrt{\mathbf{3}} \)
A \( \cdot \frac{3}{2} \)
B. \( \frac{4}{2} \)
\( c \cdot \frac{5}{2} \)
D. 5


Consider the reactions:
\( \boldsymbol{C}(s)+\mathbf{2} \boldsymbol{H}_{2}(\boldsymbol{g}) \longrightarrow \boldsymbol{C} \boldsymbol{H}_{4}(\boldsymbol{g}) ; \boldsymbol{\Delta} \boldsymbol{H}= \)
\( -\boldsymbol{X} \boldsymbol{k} c a l \)
\( \boldsymbol{C}(\boldsymbol{g})+\boldsymbol{4} \boldsymbol{H}(\boldsymbol{g}) \longrightarrow \boldsymbol{C} \boldsymbol{H}_{4}(\boldsymbol{g}) ; \boldsymbol{\Delta} \boldsymbol{H}= \)
\( -\boldsymbol{X}_{1} \boldsymbol{k} c a l \)
\( \boldsymbol{C H}_{4}(\boldsymbol{g}) \longrightarrow \boldsymbol{C H}_{3}(\boldsymbol{g})+\boldsymbol{H}(\boldsymbol{g}) ; \boldsymbol{\Delta} \boldsymbol{H}= \)
\( +\boldsymbol{Y} \boldsymbol{k} c a l \)
The average bond energy of \( C-H \) bond
is
A \( \cdot \frac{X}{4} k c a l m o l^{-1} \)
B. \( Y \) kcal mol-
c. \( \frac{X_{1}}{4} k c a l m o l^{-} \)
D. \( X_{1} \) kcal mol\( ^{-1} \)


If \( a=3 x-5 y, b=6 x+3 y \) and \( c= \)
\( 2 y-4 x, \) then \( a+b-c= \)


A step up transformer operates on a
\( 230 V \) line and supplies to a load \( 2 A \)
The ratio of primary to secondary
windings is \( 1: 25 . \) Determine the
primary current.
A . \( 8.8 A \)
B . \( 12.5 A \)
c. \( 25 A \)
D. \( 50 A \)


The salary of Ramesh is \( 25 \% \) more than
that of Anil's salary By what percentage
is Anil's salary less than that of Ramesh's?


Assertion
The moon appears purely white during the day but after sunset its colour is
yellowish hue.
Reason
The scattered blue component of white light is mixed with yellow, the colour becomes white.
A. Assertion is True. Reason is also True and is the correct explanation of the Assertion
B. Assertion is True. Reason is also True but is not the correct explanation of Assertion.
c. Assertion is True and Reason is False
D. Assertion is False and Reason is True


Find the value of \( ^{\prime} x^{\prime} \) and \( ^{\prime} y^{\prime} \) for the equations \( \frac{a^{2}}{x}-\frac{b^{2}}{y}=0 ; \frac{a^{2} b}{x}+\frac{b^{2} a}{y}= \)
\( \boldsymbol{a}+\boldsymbol{b} \) where \( \boldsymbol{x}, \boldsymbol{y} \neq \mathbf{0} \)
A . \( x=a^{2}, y=b^{2} \)
B . \( x=b^{2}, y=a^{2} \)
c. \( x=\frac{b}{a}, y=\frac{a}{b} \)
D. \( x=\frac{1}{b}, y=\frac{1}{a} \)


Find the value of the unknown interior
angle \( x \) in the following figure.


Use identities to evaluate \( (\mathbf{9 7})^{2} \)
A. 9,109
B. 9,409
c. 9,909
D. 9,209


Show that if a straight line is perpendicular to one of the two or more parallel lines, then it is also perpendicular to the remaining lines.


Give a brief account on reproduction in animals


Calculate the vapour pressure of an
aqueous solution of 1.0 molal glucose solution at \( 100^{\circ} \mathrm{C} \)


The gravitational pull or force exerted by the earth on a body is called its on the surface of the earth.
A. true weight
B. mass
c. gravitational mass
D. inertial mass


The distance of the object from the lens is \( 1 / x \). Find out the value of \( x ? \)


Assertion
\( \int_{-1}^{1} \frac{\sin x-x^{4}}{4-|x|} d x \) is same as
\( \int_{0}^{1} \frac{-2 x^{4}}{4-|x|} d x \)
Reason \( \int_{-1}^{1}(f(x)+g(x)) d x=2 \int_{0}^{1} f(x) d x \) if \( g(x) \)
is an odd function and \( f(x) \) is an even
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


Find \( \int \frac{\sin ^{6} x}{\cos ^{8} x} d x \)


Identify the type of force involved when loaded cart is moved.
A. Lifting
B. Pulling
c. Running
D. Reading


A heavy rod of length \( L \) and weight \( W \) is
suspended horizontally by two vertical ropes as shown. The first rope is
attached to the left end of the rod while
the second rope is attached a distance \( \boldsymbol{L} \)
\( \overline{4} \) from right end. The tension in the
second rope is :
A \( \cdot \frac{W}{2} \)
в. \( \frac{W}{4} \)
c. \( \frac{W}{3} \)
D. \( \frac{2 W}{3} \)
E. \( W \)


Given 3 identical boxes \( 1,2, \& 3 . \) Each containing 2 coins. \( \ln \) box 1 , both are gold coins \( \& \) in box 2 both are silver
coins and in box 3 there is 1 silver and 1
gold coin. A person chooses a box at random and takes out the coin. If the
coin is gold then what is the probability that it is coming from the first box?


Represent the complex number \( 2+3 i \)
in argand plane


Give examples of two one-one functions
\( f_{1} \) and \( f_{2} \) from \( R \) to \( R \) such that \( f_{1}+ \)
\( \boldsymbol{f}_{2}: \boldsymbol{R} \rightarrow \boldsymbol{R}, \) defined by \( \left(\boldsymbol{f}_{1}+\boldsymbol{f}_{2}\right)(\boldsymbol{x})= \)
\( f_{1}(x)+f_{2}(x) \) is not one-one.


Cooking pans have plastic handles.
A. True
B. False


The possible relationship between
magnitudes of \( " \boldsymbol{V}_{1} \) " and \( " \boldsymbol{V}_{2} \) " is :
\( \mathbf{A} \cdot V_{1}>V_{2} \)
\( \mathbf{B} \cdot V_{1}<V_{2} \)
\( \mathbf{c} \cdot V_{1}=V_{2} \)
D. Both A and C


A calorimeter contains \( 400 g \) of water at
a temperature of \( 5^{\circ} \mathrm{C} \). Then, \( 200 g \) of
water at a temperature of \( +10^{\circ} \mathrm{C} \) and
\( 400 g \) of ice at a temperature of \( -60^{\circ} \mathrm{C} \) are added. What is the final
temperature(in \( ^{o} C \) ) of the contents of the calorimeter? Specific heat capacity of water \( =\mathbf{1 0 0 0} \) cal / kg/K. Specific
latent heat of fusion of ice \( =\mathbf{8 0} \times \)
1000 cal / kg. Relative specific heat of
ice \( =\mathbf{0 . 5} \)


Determine the contrapositve of each of the following statements:
If \( x \) is less than zero, then \( x \) is not
positive.


Explain why to ionize \( M g \) to \( M g^{+2} \) it
needs three times as much energy as to
form \( M g^{2+} \)


Below critical micelle concentration
(CMC)
A. salt behaves like normal electrolyte.
B. substance like grease, fat dissolve by emulsification.
C. the viscosity of solution is very high.
D. surfactant molecules undergo association to form cluster.


The value of \( f(0) \) so that the function
\( f(x) \frac{\log \left(1+\frac{x}{a}\right)-\log \left(1-\frac{x}{b}\right)}{x},(x \neq 0) \)
is continuous at \( x=0 \) is
A \( \cdot \frac{a+b}{a b b b b b} \)
B . \( \frac{a-b}{a b b b b} \)
c. \( \frac{a b}{a+b b} \)
D. \( \frac{a b}{a-b} \)


The susceptibility and permeability of a perfectly diamagnetic substance is
A . 1 and 0
B. 0 and 1
c. -1 and 0
D. -1 and 1


Identify the correct arrangement of
tissues in an old dicot stem
A. Cork, Cork cambium, Oldest phloem, Bast, Vascular cambium, Sec. xylem
B. Secondary xylem, Vascular cambium, Bast, Oldest phloem, Cork cambium, Cork
C. Cork, Cork cambium, Oldest pholem, Bast, Vascular cambium, Heart wood
D. Heart wood, Vascular cambium, Youngest phloem, Oldest phloem, Sec.cotex, Cork cambium, Cork


Which one of these is a monomer of
Bakelite?
A. Vinyl acetate
B. Tetrafluoroethylene
c. Formaldehyde
D. Propylene


Which of the following elements will
form an acidic oxide?
A. An element with atomic number 7
B. An element with atomic number 3
C. An element with atomic number 12
D. An element with atomic number 19


Assertion: Faraday's laws are consequences of conservation of energy Reason: In a purely resistive A.C. circuit
the current lags behind the e.m.f. in
phase
A. If both assertion and reason are true but the reason is the correct explanation of assertion.
B. If both assertion and reason are true but the reason is not the correct explanation of assertion
c. If assertion is true but reason is false
D. If both the assertion and reason are false.
E. If reason is true but assertion is false


Carbon forms four covalent bonds by sharing its four valence electrons with univalent atoms, e.g., hydrogen. After the formation of four bonds, carbon attains the electronic configuration of :
A. helium
B. neon
c. argon
D. krypton


Consider the equilibrium \( 2 N O(g)+ \)
\( \boldsymbol{C l}_{2} \rightleftharpoons 2 \boldsymbol{N} \boldsymbol{O} \boldsymbol{C l}(\boldsymbol{g}) \) for which \( \boldsymbol{\Delta} \boldsymbol{H}^{\boldsymbol{o}}= \)
\( -77.07 k J m o l^{-1} . \) How will the amount
of \( C l_{2} \) at equilibrium be affected?
A. Removal of NO (g)
B. Addition of NOCI \( (g) \)
c. Raising the temperature
D. All the above


Coal and petroleum are formed from the
dead remains of organisms and are
known as:
A . fuels
B. fossil fuels
c. diesel
D. None of these


Write the name of deficiency diseases
of Vitamin A, Vitamin \( B_{1}, \) Vitamin C
and Vitamin D.


Which one of the following is a food preservative? Equanil, Morphine, Sodium Benzoate


The ion exchange resin which remove metal ions from hard water consist of
giant organic molecule containing:
A. - Cl group
в. \( - \) COOH group
c. \( -O H \) group
D. \( -N H_{2} \) group


The centre of gravity of an object is whether it is placed near the
surface of the Earth or near the surface
of the Moon.
A. same
B. different
c. depend on the situation
D. none


What happens to molar conductivity
when one mole of \( K C l \) dissolved in one
litre is diluted to five liters?


p and q are straight lines. If \( \angle a= \)
\( \angle \boldsymbol{b}=\angle \boldsymbol{c}=\angle \boldsymbol{d}, \) find \( \angle \boldsymbol{a} \)
\( \mathbf{A} \cdot 97^{\circ} \)
B \( .49 .5^{\circ} \)
\( \mathbf{c} \cdot 19.4^{\circ} \)
D \( .24 .25^{\circ} \)


Somites/metameres/segments present in the body of earthworm are
A . \( 60-80 \)
B. 80-100
\( c \cdot 100-120 \)
D. 120-160


Find a vector \( \vec{x} \) which is perpendicular to both \( \vec{A} \) and \( \vec{B} \) but has magnitude equal to that of \( \vec{B} \). Vector \( \vec{A}=3 \hat{i}- \) \( \mathbf{2} \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \) and \( \overrightarrow{\boldsymbol{B}}=\mathbf{4} \hat{\mathbf{i}}+\mathbf{3} \hat{\mathbf{j}}-\mathbf{2} \hat{\boldsymbol{k}} \)
A \( \cdot \frac{1}{\sqrt{10}}(\hat{i}+10 \hat{j}+17 \hat{k}) \)
B \( \cdot \frac{1}{\sqrt{10}}(\hat{i}-10 \hat{j}+17 \hat{k}) \)
c. \( \sqrt{\frac{29}{390}}(\hat{i}-10 \hat{j}+17 \hat{k}) \)
D. \( \sqrt{\frac{29}{390}}(\hat{i}+10 \hat{j}+17 \hat{k}) \)


Which is more stable in the below
given pair?
\( M n O_{4}^{-} \) and \( R e O_{4}^{-} \)
\( \mathbf{A} \cdot M n O_{4}^{-}=R e O_{4}^{-} \)
B. \( M n O_{4}^{-}<R e O_{4}^{-} \)
\( \mathbf{c} \cdot M n O_{4}^{-}>R e O_{4} \)
D. None of these


A loop of area \( 0.5 m^{2} \) is placed in a
magnetic field of strength \( 2 T \) in
direction making an angle of \( 30^{\circ} \) with the field. The magnetic flux linked with the loop will be
A \( \cdot \frac{1}{2} W b \)
в. \( \sqrt{\frac{3}{2}} W b \)
c. \( 2 \mathrm{Wb} \)
D. \( \frac{\sqrt{3}}{2} W b \)


By selling an article for Rs 600 more, Karthik would have made \( 5 \% \) profit on
his sale invested of a \( 11 \% \) loss. What was
his cost price?
A. 3750
B. 3650
c. 3350
D. 3950


\( \mathrm{n} \) the Fig., if \( \boldsymbol{O} \boldsymbol{X}=\frac{1}{2} \boldsymbol{X} \boldsymbol{Y}, \boldsymbol{P} \boldsymbol{X}=\frac{1}{2} \boldsymbol{X} \boldsymbol{Z} \)
and \( O X=P X \), then
A. \( X Y=Y Z \)
В. \( X Y=X Z \)
c. \( X Z=Y Z \)
D. None of these


Charging by friction is accompanied by loss or gain of electrons. State which
body loses electrons when a glass rod is rubbed with silk.
A. glass rod
B. silk
c. hand
D. both glass rod and silk


Lassaigne's test for the detection of nitrogen will fail in the case of:
A. \( N H_{2} C O N H_{2} \)
B. \( N H_{2} C O N H_{2} . H C l \)
c. \( N H_{2} N H_{2} \)
D. \( C_{6} H_{5} N H N H_{2} .2 H C l \)


Hydrogen burns with:
A. smoky flame
B. yellow flame
C. blue flame
D. pale yellow flame


The areas of the pistons in a hydraulic
machine are \( 5 c m^{2} \) and \( 625 c m^{2} . \) What
force on the smaller piston will support
a load of \( 1250 N \) on the larger piston?


The oxidation state of chromium in the
final product formed by the reaction between KI and acidified potassium
solution is:
\( A \cdot+4 \)
B. +6
\( c \cdot+2 \)
\( D \cdot+3 \)


Is the following statement True or False?
\( (\boldsymbol{A}-\boldsymbol{B}) \cup(\boldsymbol{B}-\boldsymbol{A})=(\boldsymbol{A} \cup \boldsymbol{B}) \cap \)
\( \left(A^{\prime} \cup B^{\prime}\right) \)
If True then write answer as 1
If False then write answer as 0


Evaluate \( \int \sqrt{1+y^{2}} \cdot 2 y d y \)
A \( \cdot I=\frac{2}{3}\left(1+y^{2}\right)^{3 / 2}+C \)
B. \( _{I=} \frac{2}{5}\left(1-y^{2}\right)^{3 / 2}+C \)
c. \( _{I=} \frac{2}{3}\left(1-y^{2}\right)^{3 / 2}+C \)
D. None of these.


In a closed circuit the e.m.f. and internal
resistance of the generator are \( \boldsymbol{E} \) and \( \boldsymbol{r} \)
respectively. If the external resistance
in the circuit is \( R \), then the Ohm's law
has the form:
\( ^{\mathrm{A}} \cdot_{I}=\frac{E}{(R+r)} \)
в. \( I=\frac{E}{R} \)
c. \( _{I=\frac{E}{r}} \)
D. \( _{I}=\frac{E}{R-r} \)


If the r.m.s. value of A.C. is \( l_{r m s} \) then peak
value is -
A \( \cdot \sqrt{2} l_{r m s} \)
B \( \cdot l_{r m s} / \sqrt{2} \)
\( \mathrm{c} \cdot 2 \sqrt{2} l_{m s} \)
D \( \cdot 2 l_{m s} \)


\( \frac{1}{(x-1)(x-2)}+\frac{1}{(x-2)(x-3)}= \)
\( \frac{2}{3}, x \neq 1,2,3 . \) Find sum of values of \( x \)


The p.d. at the ends of a cathode ray tube is increased to 9 times its original potential difference Then
I. The velocity of cathode rays increases
to .... times
II. The energy of cathode rays increases
to.... times
A . 9,3
в. 9.9
\( c .3 .9 \)
D. 3,3


Heater of an electric kettle is made of a
wire of length L and diameter d. It takes
4 minutes to raise the temperature of \( 0.5 \mathrm{kg} \) water by \( 40 \mathrm{K} . \) This heater is replaced by a new heater having two wires of the same material, each of
length L and diameter 2d. The way these wires are connected is given in the options. How much time in minutes will it take to raise the temperature of the
same amount of water by \( 40 \mathrm{K} ? \) This question has multiple correct options
A. 4 if wires are in parallel
B. 2 if wires are in series
c. 1 if wires are in series
D. 0.5 if wires are in parallel


Two free positive charges \( 4 q \) and \( q \) are
at a distance \( l \) apart. What charge \( Q \) is needed to achieve equilibrium for the entire system and where should it be
placed from charge \( q ? \)
\( \left.^{\mathbf{A}} \cdot Q=\frac{4}{9} q \quad \text { (negative at } \frac{l}{3}\right) \)
\( \left.^{\mathrm{B}} Q=\frac{4}{9} q \quad \text { (positive at } \frac{l}{3}\right) \)
\( \left.^{\mathrm{c}} Q=q \quad \text { (positive at } \frac{l}{3}\right) \)
\( \left.^{\mathrm{D}} Q=q \quad \text { (negative at } \frac{l}{3}\right) \)


What is soil erosion?


An electron enters with a velocity \( v \) to
the right in a magnetic field \( B \), also to the right. What direction is the force \( \boldsymbol{F} \)
on the electron?
A. An upward force
B. A downward force
c. A force to the left
D. No force if felt


The process of removing dissolved
substances from a colloidal solution by means of diffusion through a suitable
membrane is termed as dialysis.
A. True
B. False
c. Ambiguous
D. none of these


Fill up the blank with suitable words
Expression for latent heat of fusion is


The vacuum above the surface of
mercury in a barometer is called
A. Newton's vacuum
B. Torricelli's vacuum
c. Einstein's vacuum
D. Rutherford's vacuum


Smoke or dust dispersed in air is called
\( A \cdot F O g \)
B. \( \operatorname{smog} \)
c. наzе
D. Mist


1.19 g mixture of Cu, Zn and Al contain \( 50 \% \) copper by weight and \( 3 \times 10^{21} \)
atoms of zinc, find gram atoms of
aluminium in given mixture? (Atomic mass of \( \boldsymbol{A l}=\mathbf{2 7} ; \boldsymbol{C u}=\mathbf{6 3 . 5 5}, \boldsymbol{Z n}= \)
\( \mathbf{6 5 . 0} \) ) \( \left[\boldsymbol{N}_{\boldsymbol{A}}=\boldsymbol{6} \times \mathbf{1 0}^{\mathbf{2 3}}\right] \)
A. 0.001
B. 0.27
c. 0.01
D. 0.027


A mapping function \( \boldsymbol{f}: \boldsymbol{X} \rightarrow \boldsymbol{Y} \) is one-
one, if
A. \( f\left(x_{1}\right) \neq f\left(x_{2}\right) \) for all \( x_{1}, x_{2} \in X \)
B. \( f\left(x_{1}\right)=f\left(x_{2}\right) \Rightarrow x_{1}=x_{2} \) for all \( x_{1}, x_{2} \in X \)
C. \( x_{1}=x_{2} \Rightarrow f\left(x_{1}\right)=f\left(x_{2}\right) \) for all \( x_{1}, x_{2} \in X \)
D. none of these


For determination of resistance of a coil
which of two methods is better Ohm's
Law method or metre bridge method?


Assertion
In Hoffmann bromide reaction, the
amine formed has one carbon atom less
than the parent \( 1^{\circ} \) amide. Because
Reason
\( N- \) methyl acetamide undergoes Hoffmann bromamide reaction
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


Carbonyl group is converted into
methylene group by?
A. Acidic reduction
B. Raney Ni
c. Basic hydrolysis
D. Normal Hydrogenation


Alkali metals dissolve in liquid
ammonia and produces
A. deep blue solution
B. a solution which are conducting in nature
c. red coloured solution
D. Both 1 and 2


Two cars are moving in the same direction with the same speed
\( 30 k m / h r . \) They are separated by a
distance of \( 5 k m \) the speed of a car
moving in the opposite direction if it
meets these two cars at interval of 4
minutes, will be:
A. \( 40 k m / h r \)
в. \( 45 k m / h r \)
c. \( 30 k m / h r \)
D. \( 15 k m / h r \)


If \( E_{1} \) and \( E_{2} \) are two events such that \( \boldsymbol{P}\left(\boldsymbol{E}_{1}\right)=\frac{\mathbf{1}}{\mathbf{4}}, \boldsymbol{P}\left(\boldsymbol{E}_{2}\right)=\frac{\mathbf{1}}{\mathbf{2}} ; \boldsymbol{P}\left(\frac{\boldsymbol{E}_{1}}{\boldsymbol{E}_{2}}\right)=\frac{\mathbf{1}}{\mathbf{4}} \)
then choose the correct options.
A. \( E_{1} \) and \( E_{2} \) are mutually exclusive
B. \( E_{1} \& E_{2} \) are dependent
c. \( E_{1} \) and \( E_{2} \) are independent
D. \( E_{1} \) and \( E_{2} \) are exhaustive


All metals on reaction with \( H C l \)
liberate \( \boldsymbol{H}_{2} \) gas.
A. True
B. False


The weight (in-grams) of \( A g N O_{3} \) present in \( 100 \mathrm{ml} \) of \( 0.25 \mathrm{M} \) solution:
A . 4.25
B. 2
c. 17
D. 1.


Find the limit:\( \lim _{x \rightarrow 3}\left[\frac{\sqrt{x^{2}+1}-\sqrt{10}}{x-3}\right] \)


An ac voltage is applied to a resistance \( \mathrm{R} \) and an inductor \( \mathrm{L} \) in series. If \( \mathrm{R} \) and
the inductive reactance are both equal
to \( 3 \Omega, \) the phase difference between the
applied voltage and the current in the circuit is:
A. zero
в.
\( c \cdot \frac{\pi}{4} \)
D. \( \frac{\pi}{2} \)


Assertion
In dicot stem, the endodermis is also referred to as the starch sheath.
Reason
The cells of the endodermis are rich in
starch grains.
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 nucleus of the hydrogen atom is called as:
A. neutron
B. electron
c. proton
D. nucleons


\( \boldsymbol{K}^{+}, \boldsymbol{A} \boldsymbol{r}, \boldsymbol{C l}^{-} \) are iso electronic species
A. True
B. False


The number of photo electrons emitted
per second depend on the
of incident radiatic.


The displacement of a body executing SHM is given by \( x=A \sin \left(2 \pi t+\frac{\pi}{3}\right) . \) The first time from \( t=0 \) when the velocity is maximum is:
A. 0.33 sec
B. 0.16 sec
c. \( 0.25 \mathrm{sec} \)
D. \( 0.5 \mathrm{sec} \)


Which of the following is a monomer of teflon?
A. Difluoroethane
B. Trifluoroethane
c. Tetrafluoroethane
D. None of these


A conductive base is provided to the
gold-leaf electroscope so that
A. the leaves discharge before tearing if an excess charge is applied.
B. the leaves discharge before tearing if negative charge is applied.
c. the leaves discharge before tearing if positive charge is applied.
D. All of the above


Find \( \boldsymbol{x} \) and \( \boldsymbol{y}, \) when \( \boldsymbol{x}+\boldsymbol{y}=\left[\begin{array}{cc}\mathbf{7} & \mathbf{0} \\ \mathbf{2} & \mathbf{5}\end{array}\right] \)
and \( \boldsymbol{x}-\boldsymbol{y}=\left[\begin{array}{cc}\mathbf{3} & \mathbf{0} \\ \mathbf{0} & \mathbf{3}\end{array}\right] \)


Assertion
Subaerial stem modifications
participate in vegetative reproduction.
Reason
They store water and food.
A. Assertion and reason are true, reason is correct explanation of assertion.
B. Assertion and reason are true,reason is not the correct explanation of assertion.
c. Assertion is true reason is false
D. Assertion is false reason is true


How safe would you consider an
umbrella made of bamboo frames
during lightning? Give reasons.


A drop of water of radius \( 0.0015 \mathrm{mm} \) is falling in air. If the coefficient of
viscosity of air is \( 1.8 \times 10^{-5} k g / m s \)
what will be the terminal velocity of the drop? (density of water \( =1.0 \times \) \( 10^{3} k g / m^{2} \) and \( g=9.8 \mathrm{N} / \mathrm{kg} \) ). The
density of air can be neglected
A \( .2 .72 \times 10^{-4} \mathrm{m} / \mathrm{s} \)
B . \( 3.72 \times 10^{-4} \mathrm{m} / \mathrm{s} \)
c. \( 0.72 \times 10^{-4} \mathrm{m} / \mathrm{s} \)
D. \( 12.72 \times 10^{-4} \mathrm{m} / \mathrm{s} \)


Reactio
Appearance

Dull gray solid \( \quad \) Dissolved Unknown metal #1 \( \quad \) with white \( \quad \) of clearga oxide coating
Solid; lustrous, Unkr smooth silvergray surface
The addition of dilute \( H N O_{3} \) to
unknown metal # 2 produced an orange
gas.What is the likely identity of this
gas?
\( \mathbf{A} \cdot C l_{2} \)
в. \( H_{2} \)
\( c \cdot O_{2} \)
D. \( N O_{2} \)


The cube root of 4.096 is
A . 1.6
B. 1.7
\( c \cdot 1.8 \)
D. 2.6


The number of electric lines of force that
radiate outwards from \( 8.85 \mu \mathrm{C} \) of charges
in a vacuum is:
A \( \cdot 10^{-6} \)
- \( ^{-6}-10 \)
B. \( 10^{-12} \)
\( c \cdot 10^{12} \)
D. \( 10^{\circ} \)


Which of the alkyl halide has minimum boiling point?
A. \( C H_{3} F \)
в. \( C H_{3} C l \)
\( \mathrm{c} \cdot C H_{3} B r \)
D. \( C H_{3} I \)


The potentiometer wire 10 m long and
20 ohm resistance is connected to a
3 volt emf battery and a 10 ohm
resistance. The value of potential
gradient in volt\( / \boldsymbol{m} \) of the wire will be
A . 1.0
B. 0.2
c. \( 0 . \)
D. 0.02


Which organic chemical bond between two carbon atoms can be easily disrupted?
A. A triple bond
B. A double bond
c. A single bond
D. An aromatic ring


\( A B C D \) is a trapezium in which \( A B \| \) \( C D ; B C \) and \( A D \) are non-parallel sides. It
is given that \( A B=75 c m, B C= \)
\( 42 c m, C D=30 c m \) and \( A D=39 c m \)
Find the area of the trapezium.


Although phenoxide ion has more number of resonating structures than carboxylate ion, carboxylic acid is a stronger acid than phenol. Why?


The half-period T for the decomposition
of ammonia on tungsten wire was measured for different initial pressures
\( P \) of ammonia at \( 25^{\circ} \mathrm{C} \). Then:
\( P(m m \)
\( \begin{array}{llll}11 & 21 & 48 & 73\end{array} \)
Hg)
\( \mathrm{T}(\mathrm{sec}) \)
48 92
\[
\text { 210 } \quad 320
\]
This question has multiple correct options
A. Zero order reaction
B. First order reaction
C. Rate constant for reaction is 0.114 mol lit \( ^{-1} \) sec \( ^{-1} \)
D. Rate constant for reaction is 1.14 seconds


\( \mathbf{A} \triangle \boldsymbol{A} \boldsymbol{B} \boldsymbol{C} \) in which \( \boldsymbol{A} \boldsymbol{B}= \)
\( \mathbf{5 . 4} \mathbf{c m}, \angle \boldsymbol{C} \boldsymbol{A} \boldsymbol{B}=\mathbf{4 5}^{\circ} \) and \( \boldsymbol{A} \boldsymbol{C}+\boldsymbol{B} \boldsymbol{C}= \)
\( \mathbf{9} \mathrm{cm} . \) Then, perimeter of \( \Delta \boldsymbol{A B C} \) is
A. \( 14.4 \mathrm{cm} \)
B. \( 11.4 \mathrm{cm} \)
\( c .12 .4 \mathrm{cm} \)
D. \( 15.4 \mathrm{cm} \)


Which of the following represents calgon?
A \( . N a_{2} A l_{2} S i_{2} O_{8} \)
в. \( M g_{3}\left(P O_{4}\right)_{2} \)
c. \( N a_{2}\left[N a_{4}\left(P O_{3}\right)_{6}\right] \)
D. \( N a_{2}\left[M g_{2}\left(P O_{3}\right)_{6}\right] \)


A beam of light consisting of red, green and blue is incident on a right angled prism. The refractive index of the material of the prism for the above red, green and blue wavelengths are 1.39 1.44 and 1.47 respectively. The prism will
A. separate part of the red color from the green and blue colors
B. separate part of the blue color from the red and green colors
c. Separate all the three colors from the other two colors
D. not separate even partially any color from the other two colors


An Unsaturated solution can be
converted into saturated solution
A. by adding more solute to the solvent
B. by removing solute from the solvent
c. by increasing temperature
D. Both b and c


For \( \boldsymbol{r}=\mathbf{0}, \mathbf{1}, \ldots ., \mathbf{1 0}, \) let \( \boldsymbol{A}_{r}, \boldsymbol{B}_{r} \) and \( \boldsymbol{C}_{\boldsymbol{r}} \)
denote, respectively, the coefficient of
\( x^{r} \) in the expansions of \( (1+x)^{10},(1+x)^{20} \) and \( (1+x)^{30} . \) Then
\( \sum_{r=1}^{10} A_{r}\left(B_{10} B_{r}-C_{10} A_{r}\right) \) is equal to
A. \( B_{10}-C_{10} \)
B . \( A_{10}\left(B_{10}^{2}-C_{10} A_{10}\right) \)
c. 0
D. \( C_{10}-B_{10} \)


Choose the correct statement for the
following
A. Magnetic lines give direction of magnetic field while electric field lines do not
B. Electric lines give direction of electric field while magnetic field lines do not
C. Electric lines of force are closed curves but not magnetic lines of force
D. Magnetic field lines are closed curved but electric field lines are not


If each observation of the raw data,
whose variance is \( \sigma^{2}, \) is multiplied by \( k \)
then new variance
A. raised by \( k \) times
B. raised by \( k^{2} \) times
c. reduced by \( k \) times
D. reduced by \( k^{2} \) times


\( f(x)=\log \frac{(1+x)}{1-x} \) then \( f(\log (x))=? \)
A \( \cdot \log (1+\log x)-\log (1-\log x) \)
B. \( \log (1+\log x)+\log (1-\log x) \)
c. \( \log (1-\log x)-\log (1-\log x) \)
D. None of these


Q Type your question
si und changes taking place against external atmospheric pressure:
1. \( \quad \boldsymbol{N}_{2}(\boldsymbol{g})+\boldsymbol{3} \boldsymbol{H}_{2}(\boldsymbol{g}) \longrightarrow \boldsymbol{2} \boldsymbol{N} \boldsymbol{H}_{3}(\boldsymbol{g}) \)
Il. \( \quad \boldsymbol{N} \boldsymbol{H}_{\mathbf{4}} \boldsymbol{H} \boldsymbol{S}(\boldsymbol{s}) \longrightarrow \boldsymbol{N} \boldsymbol{H}_{3}(\boldsymbol{g})+ \)
\( \boldsymbol{H}_{2} \boldsymbol{S}(\boldsymbol{g}) \)
III. \( C(s)+C O_{2}(g) \longrightarrow 2 C O(g) \)
IV. \( C_{2} H_{6}(g)+3.5 O_{2}(g) \longrightarrow \)
\[
\mathbf{2} \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{3} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l})
\]
\( \|\quad\| I \)
\( a+-\quad+ \)
b. - \( +0+ \)
\( \mathbf{C}_{\cdot}-\quad-\quad+\quad+ \)
\[
\mathbf{d}+++-
\]
\( A \cdot a \)
B.
\( c \cdot c \)
\( D \)


In aqueous solution, \( \boldsymbol{H}_{2} \) will not reduce:
A \( \cdot F e^{3} \)
B. \( C u^{2+} \)
c. \( A g^{+} \)
D. \( Z n^{2+} \)


The kinetic energy of an electron accelerated from rest through a potential difference of 5V will be:
A . \( 5 ~ J \)
B. 5 erg
\( c .5 e V \)
D. \( 8 \times 10^{-10} \) eV


Placentation is axile in the ovary of
A. China Rose
B. Sunflower
c. Pea
D. Ranunculus


The maximum value of \( \sin \left(x+\frac{\pi}{5}\right)+\cos \left(x+\frac{\pi}{5}\right), \) where
\( \boldsymbol{x} \in\left(0, \frac{\pi}{2}\right) \) is attained at
\( ^{A} \cdot \frac{\pi}{20} \)
в. \( \frac{\pi}{15} \)
c. \( \frac{\pi}{10} \)
D.


\( \int_{0}^{\pi / 2} \frac{1}{1+\sqrt[4]{\tan x}} d x= \)
A . \( \pi / 4 \)
в. \( \pi / 3 \)
\( c \cdot 0 \)
D. None of these


Consider the values of \( \Delta H^{o} \) (in
\( \left.k J m o l^{-1}\right) \) and for \( \Delta S^{o}\left(\operatorname{in} J m o l^{-1} K^{-1}\right) \)
given for four different reactions. For
which reaction will \( \Delta G^{o} \) increase the
most positive) when temperature is
increased from \( 0^{\circ} C \) to \( 25^{\circ} \mathrm{C} \) ?
A \( . \Delta H^{o}=50, \Delta S^{o}=50 \)
B . \( \Delta H^{o}=90, \Delta S^{o}=20 \)
c. \( \Delta H^{o}=-20, \Delta S^{o}=-50 \)
D. \( \Delta H^{o}=-90, \Delta S^{o}=-20 \)


If \( n \) is an integer between 0 and 21 then
the minimum value of \( n !(21-n) ! \) is
A . \( 9 ! 2 ! \)
B . \( 10 ! 11 ! \)
c. \( 20 ! \)
D. 21!


If \( A \) is the area and \( 2 s \) the sum of three
sides of a triangle, then
\( ^{\mathrm{A}} \cdot_{A} \leq \frac{s^{1.5}}{3 \sqrt{3}} \)
в. \( _{A} \leq \frac{s^{1.5}}{2} \)
\( ^{\mathrm{c}} \cdot_{A}>\frac{s^{1.5}}{\sqrt{3}} \)
D. None of these


Which series of reactions will achieve
the following transformation?
A \( \cdot 1:\left[l l_{2} / C C l_{4} \text { 2: } B r_{2}\right. \)
в. \( 1: H B r \) \( 2: C l_{2} / C C l \)
c. \( 1: C l_{2} / C C l_{4} \) २: \( N B S / h v \)
D. \( 1: N B S / h v \) 2: \( C l_{2} / C C l_{4} \)


Most abundant metal in the earth's
crust is


The number of moles of \( K M n O_{4} \) that will be needed to react completely with one mole of sulphite ion in acidic
solution is:
A . \( 3 / 5 \)
B. 2/5
c. \( 4 / 5 \)
\( D \)


Write two structure differences between
DNA and RNA.


Consider the following pairs.
Intake and utilization of
A. Nutrition
- nutrients for energy requirements
Derives nutrition from
B. Saprophytes - dead organic
matters
Animals and
c. Heterotrophs
D. Chemotrophic \( \mathrm{N}_{2} \) fixing bacteria
The correctly paired groups are given in
\( A \cdot A, B \) and \( C \)
B. B, C and D
C. \( A, B, C \) and \( D \)
D. \( A, C \) and \( D \)


An inductor is connected to a battery through a switch. The emf induced in the inductor is much larger when the switch is opened as compared to the emf induced when the switch is closed.
Is this statement true or false?


The electric charge for electrode deposition of one gram equivalent of a substance is:
A \( \cdot 1 \) ampere \( s^{-1} \)
B. 96500 coulomb \( s^{-1} \)
c. 1 ampere hour \( ^{-1} \)
D. 1 coulomb \( s^{-1} \)


Acetylene can be obtained by the reaction:
A \( \cdot H C O O K \frac{\text { Electrolysis }}{\rightarrow} \)
B. \( C H I_{3}+A g \stackrel{\Delta}{\longrightarrow} \)
c. \( C H_{3} C H_{2} O H \frac{\operatorname{conc} . H_{2} S O_{4}}{443 K} \)
D. \( B e_{2} C+H_{2} O \rightarrow \)


10grams of a radioactive element is
disintegrated to 1gram in 2.303 minutes The half-life (in minutes) of that
radioactive element is:
A \( \cdot \frac{1}{0.693} \)
B. 6.93
c. 1
D. 0.693


A machine has three parts, \( A, B \) and \( C \)
whose chances of being defective are 0.02,0.10 and 0.05 respectively. The machine stops working if any one of the arts becomes defective. What is the
probability that the machine will not stop working?
A . 0.06
B. 0.16
c. 0.84
D. 0.94


State whether given statement is True or False :

There is no possibility of having mixed hearing loss with both conductive and
sensori-neural element.
A. True
B. False


Which among the following will be the softest metal?
A. Sodium
B. Aluminium
\( c . \) Iron
D. All of the above


If half part of a convex lens is covered, the focal length \( _{\text {一一一一一 }} \) change, but the intensity of the image
A. does, increases
B. does not, increases
c. does, decreases
D. does not, decreases


The unit of specific conductivity is:
\( \mathbf{A} \cdot \operatorname{oh} m^{-1} c m^{-1} \)
В. ohm \( \mathrm{cm}^{-2} \)
\( \mathbf{c} \cdot \) ohm \( ^{-1} c m \)
D. ohm \( \mathrm{cm} \)


Why does ice float on water?


Simplify:
\( \left(1+\frac{x^{2}-y^{2}-z^{2}}{2 y z}\right)\left(\frac{1}{x+y-z}+\frac{1}{z+}\right. \)


The four tyres of an automobile are inflated to a pressure of \( 2.0 \times 10^{5} \mathrm{Pa} \)
Each Tyre has an area of \( 0.024 m^{2} \) in
contact with the ground. Determine the weight of the automobile.
A \( \cdot 1.92 \times 10^{4} \mathrm{N} \)
B . \( 1.92 \times 10^{5} \mathrm{N} \)
c. \( 1.92 \times 10^{6} \mathrm{N} \)
D. \( 2.92 \times 10^{4} \mathrm{N} \)


toppr
Q Type your question_
this region of space. The correct
arrangement for it to escape
undeviated is :
\( \mathbf{A} \)
\( B \)
\( c \)
D.


The terminal voltage of a cell in open circuit condition is \( _{-}-_{-}-_{-} \) its emf.
A. more than
B. less than
c. equal to
D. square of


The vapour pressure of a moist gas at
\( 100^{\circ} \mathrm{C} \) is \( 750 \mathrm{mm} \) and the aqueous
tension at the same temperature is
10 mm. The vapour pressure of the dry
gas is :
\( A \cdot 750 \mathrm{mm} \)
B. 760 mm
c. \( 740 \mathrm{mm} \)
D. 720 mm


Oxygen carrying capacity of human blood is reduced due to the pollution of air by
A \( \cdot C O_{2} \)
B. co
\( c \cdot S O_{2} \)
D. \( O_{3} \)


Which of the following is not formed as intermediate in the polymerisation of alkenes and their derivatives?
A. Carbonium ion
B. Carbanion
c. Free radical
D. Carbene


Additive inverse of 10 is
A. 0
в. -10
\( c .8 \)
D. none


An element with variable (more than
one) valency and stored under water, is :
A. phosphorous
B. arsenic
c. sulphur
D. sodium


Which of the following is a
constant polynomial?
\( \mathbf{A} \cdot p(x)=7+3 x \)
B \( . p(x)=7 \)
C \( . p(x)=7 x+7 \)
D. \( p(x)=4 x+3 \)


Take any point 0 in the interior of \( a \) triangle PQR. is
\( \boldsymbol{O Q}+\boldsymbol{O R}>\boldsymbol{Q} \boldsymbol{R} ? \)


General formula for mono halogen
derivatives of alkane is:
A. \( C_{n} H_{n+1} X \)
B. \( C_{n} H_{2 n} X_{2} \)
c. \( C_{n} H_{2 n-1} X \)
D. \( C_{n} H_{2 n+1} X \)


The flux linked with a coil of any instant
\( t \) is given by \( \phi=t^{2}-5 t+25 . \) The
induced emf \( \operatorname{at} t=4 s \) is?
A \( .2 v \)
B. \( -3 v \)
c. \( 4 v \)
D. - \( 4 v \)


The negation of the compound
proposition \( \boldsymbol{p} \vee(\sim \boldsymbol{p} \vee \boldsymbol{q}) \) is
A \( . p \wedge q \)
B.
\( c \cdot f \)
D. \( (p \wedge q) \wedge \sim p \)


Find the measure of the supplementary
angle pair of \( 60^{\circ} . \) (in degrees)


\( \operatorname{Let} f(x)=\frac{a x+b}{x+1}, l i m_{x \rightarrow 0} f(x)=2 \)
and \( \lim _{x \rightarrow \infty} f(x)=1 \) then \( f(-2)= \)
A . 1
B . 2
c. -1
D.


How many consecutive odd numbers will be needed to obtain the sum of \( 4^{3} ? \)
A .2
B. 3
\( c \cdot 4 \)
D.


The principal value of
\( \cos ^{-1}\left[\frac{1}{\sqrt{2}}\left(\cos \left(\frac{9 \pi}{10}\right)-\sin \left(\frac{9 \pi}{10}\right)\right)\right] \) is
\( \mathbf{A} \cdot \frac{3 \pi}{20} \)
B. \( \frac{7 \pi}{200} \)
\( \mathbf{C} \cdot \frac{7 \pi}{10} \)
D. none of these


Two persons each of mass m are
standing at the two extremes of a
railroad ear of mass \( M \) resting on a smooth track. The person on left jumps to the left with a horizontal speed \( u \) with
respect to the state of the car before the jump. Thereafter, the other person jumps to the right, again with the same horizontal speed \( u \) with respect to the
state of the car before his jump. Find the velocity of the car after both the
persons have jumped off


In the given figure, we have \( \angle 1=\angle 3 \)
and \( \angle 2=\angle 4 \), then:
4. \( \angle A=\angle C \)
3. \( \angle A=\angle D \)
\( c \cdot \angle A=\angle B \)
\begin{tabular}{l}
\( . \angle B=\angle L \) \\
\hline
\end{tabular}


In the lower parts of the stratosphere, there is no change in temperature with altitude. This zone is called
A. Thermosphere
B. Isothermal Zone
c. Ozone layer
D. Ionosphere


State the laws of Reflection along with a
suitable diagram.


Which of the following is the correct order of the rate of reaction of
\( C_{6} H_{6}, C_{6} D_{6} \) and \( C_{6} T_{6} \) towards
sulphonation?
A. same rates of reactions of \( C_{6} D_{6}, C_{6} D_{6} \) and \( C_{6} T_{6} \)
в. \( C_{6} T_{6}>C_{6} D_{6}>C_{6} H_{6} \)
c. \( C_{6} H_{6}>C_{6} D_{6}>C_{6} T_{6} \)
D. \( C_{6} T_{6}>C_{6} D_{6}=C_{6} T_{6} \)


The soil profile is an arrangement in a
soil of its:
A. horizontal layout
B. vertical layout
c. diagonal layout
D. the depth of soil


Observe the following statements regarding purification of bauxite:
I. During Hall's process, silica is removed as Si (vapour).
II. Bauxite ore contaminated with
\( F e_{2} O_{3} \) is purified in Baeyer's process.
III. During Serpeck's process, \( A l N \) is formed.
A. I, II and III are correct
B. Only I and II are correct
c. only land III are correct
D. Only II and III are correct


The best method for preparing primary amines from alkyl halides without
changing the number of carbon atoms in the chain is:
A. Hofmann bromamide reaction
B. Gabriel phthalimide synthesis
c. sandmeyer reaction
D. Reaction with \( N H_{3} \)


Assuming that concentration of \( C a^{2+} \)
ions in solution is in equal equivalence ratio to chloride ions, the hardness of water is :
A \( .9 .180 \times 10^{3} \) ppm
B . \( 6.180 \times 10^{3} \) ppm
c. \( 12.180 \times 10^{3} \) ppm
D. \( 4.180 \times 10^{3} \) ppm


Find \( \int_{0}^{5}(x+1) d x \) as limit of a sum


IUPAC name of \( \boldsymbol{C} \boldsymbol{H}_{3}-\boldsymbol{O}-\underset{\boldsymbol{I}}{\boldsymbol{C} \boldsymbol{H}_{3}} \boldsymbol{H}-\boldsymbol{C} \boldsymbol{H}_{3} \)
is
A. 3-Methoxy propane
B. 2-Methyl methoxy ethane
c. 1-Methoxy-1-methyl ethane
D. Methoxy isopropane


What are \( X \) and \( Y ? \)
\( \|+N B S \quad \longrightarrow \quad X \frac{(i) M g / \text { ether }}{(i i) C_{2}_{2}:} Y Y \)
A. \( x: 1 \) -bromo cyclohex- 1 -ene \( Y \) : Cyclohex- 1 -enoic acid
B. \( x: 1- \) bromo cyclohex-2-ene Y: Cyclohex-2-enal
c. \( x: 3 \) -bromo cyclohexene \( Y \) : Cyclohex-2-enoic acid
D. None of these


In our society the women are often
blamed for giving birth to daughters. Can you explain why this is not correct?


When the velocity of a relativistic charged particle increases, it's specific charge
A . Decreases
B. increases
c. Remains same
D. First decreases then increases


Given an angle \( \theta, \) which of the following angles cannot be obtained by using the method of construction of angle bisectors?
\( A \cdot \frac{\theta}{2} \)
в. \( \frac{\theta}{4} \)
\( c \cdot \frac{\theta}{6} \)
\( D \cdot \frac{\theta}{8} \)


Solve:
\( \lim _{x \rightarrow 0} \frac{\sin ^{3} x^{2}}{x^{6}} \)
\( \mathbf{A} \cdot \mathbf{1} \)
B.
\( c \cdot-1 \)
D. \( \infty \)


Many persons like to use asthma as an excuse for not being able to do well in
sports. Try telling them about Down Fraser, who was the first women to break 60 sec in 100 m freestyle swimming. The first women to win four Olympic gold medals and the first swimmer to win the same event in three
consecutive Olympics was asthmatic. On the basis of the above passage,
answer the following question.
¡) Mention the qualities, which might have helped her to win medals at three Olympics consecutively.


What is the value of \( \sqrt{7.84}+ \) \( \sqrt{0.0784}+\sqrt{0.000784}+\sqrt{0.00000784} \)
\( ? \)
A . 3.08
B. 3.108
c. 3.1008
D. 3.1108


\( \lim _{x \rightarrow 1} \frac{(\log (1+x)-\log 2)\left(3.4^{x-1}-3 x\right)}{1} \)
\( \left.\left.\left\{(7+x)_{3}^{1}\right)-(1+3 x)^{\frac{1}{2}}\right)\right\} \sin \pi x \)


Which compound is a secondary alcohol?
A. Butan-1-ol
B. Butan-2-ol
c. Isobutyl alcohol
D. 2-Methylpropan-2-ol


The following techniques are used to estimate quantitatively other elements (nitrogen, sulphur \( \& \) halogens) in organic compounds. Identify the name of the method and the element which is
estimated by the following methods:
A known mass of an organic compound is heated with fuming nitric acid in presence of silver nitrate.
A known mass of an organic compound
is heated with copper oxide in the
atmosphere of carbon oxide.


If the two lines represented by \( x^{2}\left(\tan ^{2} \theta+\cos ^{2} \theta\right)-2 x y \tan \theta+ \)
\( \boldsymbol{y}^{2} \sin ^{2} \boldsymbol{\theta}=\mathbf{0} \) make angles \( \boldsymbol{\alpha}, \boldsymbol{\beta} \) with the
\( x \) -axis, then
This question has multiple correct options
\( A \cdot \tan \alpha+\tan \beta=4 \operatorname{cosec} 2 \theta \)
\( \mathbf{B} \cdot \tan \alpha \tan \beta=\sec ^{2} \theta+\tan ^{2} \theta \)
c. \( \tan \alpha-\tan \beta=2 \)
D. \( \frac{\tan \alpha}{\tan \beta}=\frac{2+\sin 2 \theta}{2-\sin 2 \theta} \)


Factors responsible for the rapid spread
of bread mould on slices of bread are
This question has multiple correct options
A. Large number of spores
B. Availability of moisture and nutrients in bread.
C. Presence of tubular branched hyphae.
D. Formation of round shaped sporangia.


(a) Explain adaptive radiation with the help of suitable example.
(b) Cite an example where more than one adaptive radiations have occurred in an isolated geographical area. Name the type of evolution your example depicts and state why it is so named.


Find the measure of the supplementary
angle of \( 54^{\circ} \)
A \( \cdot 26^{\circ} \)
B . \( 126^{\circ} \)
\( c \cdot 34^{\circ} \)
D. \( 134^{\circ} \)


The density of \( 3 M \) solution of \( N a C l \) is
\( 1.25 g m l^{-1} . \) The molality of the solution
is:
A \( .2 .79 \mathrm{m} \)
В. 1.79 m
c. \( 3.5 \mathrm{m} \)
D. 5.58 m


A sphere 'P' of mass 'm' moving with velocity 'u' collides head-on with another sphere 'Q' of mass 'm' which is at rest. The ratio of final velocity of 'Q' to initial velocity of 'P' is \( . \cdot(e= \)
coefficient of restitution)
A \( \cdot \frac{e-1}{2} \)
\( ^{\mathrm{B}}\left[\frac{e+1}{2}\right]^{1 / 2} \)
c. \( \frac{e+1}{2} \)
\( ^{\mathrm{D} \cdot}\left[\frac{e+1}{2}\right]^{2} \)


Which of the following properties of plastic make it most convenient to use?
A. It is non-reactive
B. Light, strong and durable
c. Easily remouldable
D. All of the above


When \( n \) is a even natural number then
the value of \( x \) is
This question has multiple correct options
A. 0
в. \( \pi / 2 \)
\( \mathrm{c} \cdot 2 \pi / 3 \)
D. \( \pi \)


Evaluate \( \int_{1}^{4}(x-1) d x \)


\( \boldsymbol{C a C O}_{3}+\boldsymbol{2 H C l} \rightarrow \boldsymbol{C a C l}_{2}+\boldsymbol{H}_{2} \boldsymbol{O}+ \)
\( \boldsymbol{C O}_{2} \)
The mass of calcium chloride formed
when 2.5 g of calcium carbonate is dissolved in excess of hydrochloric acid
is:
A . 1.39 g
в. 2.78 g
c. \( 5.18 \mathrm{g} \)
D. 17.8 g


The electric field at a point due to an electric dipole, or an axis inclined at an
angle \( \theta\left(<90^{\circ}\right) \) to the dipole axis, is perpendicular to the dipole axis, if the angle \( \boldsymbol{\theta} \) is
A \( \cdot \tan ^{-1} \)
B. \( \tan ^{-1}\left(\frac{1}{2}\right) \)
\( \mathbf{c} \cdot \tan ^{-1}(\sqrt{2}) \)
D \( \cdot \tan ^{-1}\left(\frac{1}{\sqrt{2}}\right) \)


If \( m \) be the slope of a tangent to the
curve \( e^{2 y}=1+4 x^{2}, \) then
\( \mathbf{A} \cdot m<1 \)
B . \( |m| \leq 1 \)
\( \mathrm{c} \cdot|m|>1 \)
D. None of these


Suppose \( n(\geq 3) \) persons are sitting in row. Two of them are selected at
random. The probability that they are not together is
A \( \cdot 1-\frac{2}{n} \)
в. \( \frac{2}{n-1} \)
c. \( _{1-\frac{1}{n}} \)
D. None of these


Bond energies can be obtained by using the following relation:
\( \Delta H(\text {reaction})=\sum \) Bond energy of
bonds, broken in the reactants \( -\Sigma \) Bond energy of bonds, formed in the products.

Bond energy depends on three factors:
a. greater is the bond length, lesser is the bond energy
b. bond energy increases with the bond
multiplicity
c. bond energy increases with the electronegativity difference between the bonding atoms. Which among the following sequences is correct about the bond energy of \( C-C, C=C, \) and
\( C \equiv C \) bonds?
A. \( C=C>C \equiv C>C-C \)
\( C \)
в. \( C \equiv C<C=C<C-C \)
c. \( C \equiv C>C=C>C-C \)


Write the type of reaction. Ethene is burnt in the presence of oxygen to form carbon dioxide, water
and releases heat and light.
A. Endothermic reaction
B. Combustion reaction
c. Redox reaction
D. Esterificaton reaction


Identify the quantifier in the following
statements and write the negation of
the statements
(i) There exists a number which is equal
to its square
(ii) For every real number \( x, x \) is less
\( \operatorname{than} x+1 \)
(iii) There exists a capital for every state in India


Draw sketches to show the relative
positions of prominent stars in
(a) Ursa Major and
(b) Orion


First natural cytokinin was discovered by
A . Miller
B. Letham
c. Calvin
D. Haberlandt


A light source is placed \( 100 \mathrm{cm} \) away from a screen. A converging lens placed at a certain position between the source and the screen focuses the image of the source on the screen. The lens is moved
a distance of \( 40 \mathrm{cm} \) and it is found that
it again focuses the image of the source on the screen. The focal length of the lens is
\( A \cdot 21 \mathrm{cm} \)
B. 30 cm
c. \( 40 \mathrm{cm} \)
D. \( 67 \mathrm{cm} \)


A line segment whose end points lie on the circle is called \( \ldots \ldots . . . . . . . \) to the circle.
A. Chord
B. tangent
c. Radius
D. Diameter


A triangular loop is placed in a dot \( \Theta \) magnetic field as shown in figure. The
direction of induced current is
clockwise in the loop if magnetic field is


Aeciospores of Puccinia are produced on
A. Berberis leaves
B. Wheat leaves
c. Mustard leaves
D. Raphanus leaves


The structure of \( F_{2} S e O \) is analogous to:
A. \( S O_{3} \)
в. \( C l O_{3}^{-} \)
\( \mathrm{c} \cdot \mathrm{XeO}_{3} \)
D. \( (B) \) and \( (C) \) both


What happens to the reading of
\( A_{1}, A_{2}, A_{3} \) and \( A \) when the bulb \( B_{2} \) gets
fused?
A \( . A_{1}=1 A, A_{2}=0 A, A_{3}=0 A \) and \( A=2 A \)
B. \( A_{1}=1 A, A_{2}=0 A, A_{3}=1 A \) and \( A=2 A \)
C. \( A_{1}=2 A, A_{2}=0 A, A_{3}=1 A \) and \( A=2 A \)
D. \( A_{1}=1 A, A_{2}=0 A, A_{3}=1 A \) and \( A=1 A \)


If the sum of first \( p \) terms of an \( A . P . \) is equal to the sum of first \( (p+q) \) terms
is zero. Where \( \boldsymbol{p} \neq \boldsymbol{q} \)


Write true(T) or false(F) for the
following.

Tubectomy is the placing of a diaphragm on the cervix.
A. True
B. False


What is hydathode?


If \( (x+i y)^{3}=u+i v, \) then prove that \( \frac{u}{x}+\frac{v}{y}=4\left(x^{2}-y^{2}\right) \)


An organic compound of molecular
formula \( C_{3} H_{6} O \) did not give a silver
mirror with Tollen's reagent, but gave an oxime with hydroxylamine, it may be:
A \( \cdot C H_{3} C O C H_{3} \)
в. \( C_{2} H_{5} C H O \)
c. \( C H_{2}=C H-C H_{2}-O H \)
D. \( C H_{3}-O-C H=C H_{2} \)


\( A \) and \( B \) are two objects with mass 6 kg and 34 kg respectively. Then
A. A has more inertia than \( B \)
B. B has more inertia than A
c. A and B both have same inertia
D. none of the above is true


Which of the following is a merit of Dalton's atomic theory?
A. Laws of chemical combination
B. Distinction between the fundamental particle of an element (atom) and that of a compound (molecule)
C. Both A and B
D. None of the above


Which of the following ion is not
isoelectronic with \( O^{-2} \) ?
A \( \cdot N^{-3} \)
В. \( N a^{+} \)
\( c \cdot F^{-} \)
D. \( T i^{+3} \)


Clotting of blood is brought about by
\( A \cdot \) RBCs
B. WBCs
c. Platelets
D. Plasma


\( H_{2} \) is not widely used as the reducing agent in metallurgic process because:
This question has multiple correct options
A. many metals react with \( H_{2} \) at elevated temperature forming hydrides
B. there is a risk of explosion from \( H_{2} \) and \( O_{2} \) present in the air
C . reducing power of \( H_{2} \) does not increase with temperature
D. reducing power of \( H_{2} \), increases with temperature


Which of the following observations of \( \alpha \)
-ray scattering experiment lead to the presence of small positively charged
nucleus in the centre?
This question has multiple correct options
A. Most of the \( \alpha \) -particles passed straight
B. Most of the \( \alpha \) -particles rebounded after hitting the atoms
c. only a few \( \alpha \) -particles deflected away from their path
D. Very few \( \alpha \) -particles rebounded


A wire of length \( l \) carries a current \( i \) along x-axis. A magnetic field exits given by \( \boldsymbol{B}=\boldsymbol{B}_{0}(\hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}}) \boldsymbol{T} \). The
magnitude of the magnetic force acting on the wire is
A \( . i l B_{0} \)
в. \( \sqrt{3} B_{0} \) il
c. \( 2 i l B_{0} \)
D. \( \sqrt{2} B_{0} \) il


The classification of elements in
the modern periodic table is based on
their:
A. increasing order of their atomic number
B. atomic weight
c. atomic volume
D. equivalent weight


Which of the following carbohydrates is the essential constituent of all cell
walls?
A . starch
B. maltose
c. cellulose
D. sucrose


Froth flotation method cannot be
employed for the concentration of:
A. zinc blende
B. Pyrolusite
c. copper pyrites
D. cinnabar


A hydrogen gas. electron is made by dipping platinum wire in a solution of \( H C I \) of \( p H=10 \) and by passing hydrogen gas around the platinum wire at one atm pressure.The oxidation potential of electrode would be?
A . \( 1.18 V \)
в. \( 0.059 V \)
c. \( -0.59 V \)
D. \( 0.118 \mathrm{V} \)


A keto ester (X) with molecular formula
\( C_{6} H_{10} O_{3} \) on treatment with \( \mathrm{NaOH} \) and
\( I_{2} \) does not give iodoform but on boiling with dilute KOH gives a compound (Y)
with molecular formula \( C_{4} H_{5} O_{3} K \) which upon acidification followed by heating undergoes decarboxylation to give acetone. The keto ester (X) is?
A. \( C H_{3} C O C H_{2} C H_{2} C O O C H_{3} \)
в. \( C H_{3} C O C H_{2} C O O C_{2} H_{5} \)
c. \( C H_{3} C H_{2} O C H_{2} \) СООСН\( _{3} \)
D. \( C H_{3} C O C H\left(C H_{3}\right) C O O C H_{3} \)


A heterotroph obtains its carbon supply
from
A. organic chemicals
в. \( C O_{2} \)
c. Methane
D. Cyanide.


A glass prism of refractive index 1.5 is
placed in water of refractive index 1.33 The minimum value of the angle of the prism so that it will not be possible to
have any emergent ray is :
A \( .150^{\circ} \)
B . \( 125^{\circ} \)
\( c \cdot 165 \)
D. \( 180^{\circ} \)


Find the value of 'p' for which the
quadratic equatio has equal roots, \( (p+1) n^{2}+2(p+3) n+(p+8)=0 \)


Area of square is 10,000 sq m Then its side measures(in \( \mathrm{m}) \)


Find the sum of the following vectors:
\( \overrightarrow{\boldsymbol{a}}=\hat{\boldsymbol{i}}-\boldsymbol{3} \hat{\boldsymbol{k}}, \overrightarrow{\boldsymbol{b}}=2 \hat{\hat{\boldsymbol{j}}}-\hat{\boldsymbol{k}}, \overrightarrow{\boldsymbol{c}}=\boldsymbol{2} \hat{\boldsymbol{i}}-\boldsymbol{3} \hat{\boldsymbol{j}}+ \)
\( \mathbf{2} \hat{\boldsymbol{k}} \)


Two children are at the opposite end of an iron pipe. One struks the end of the pipe with a stone. Calculate the ratio of the time taken by sound waves in air and in iron to reach the other child. Use
speed of sound in (i) air \( =344 m s^{-1} \)
and
(ii) iron \( =\mathbf{5 1 3 0 m s}^{-1} \)


The minimum value of \( |Z-1+2 i|+ \)
\( |4 i-3-Z| \) is
A \( \cdot \sqrt{5} \)
B. 5
c. \( 2 \sqrt{13} \)
D. \( \sqrt{15} \)


Stability of coordination compounds increases with increase in charge
density of the metal ions.
A. True
B. False


What is the shape of the \( I B r_{2}^{-} \) ion?
A. Linear
B. Bent shape with bond angle of about \( 90^{\circ} \)
C. Bent shape with bond angle of about \( 109^{\circ} \)
D. Bent shape with bond angle of about \( 120^{\circ} \)


Placentation is swollen and axile in
family
A . Asteraceae
B. Liliaceae
c. Fabaceae
D. Solanaceae


The solution of the two simultaneous
equations \( 2 x+y=8 \) and \( 3 y=4+4 x \)
is
A. \( x=4, y=1 \)
в. \( x=1, y=4 \)
c. \( x=2, y=4 \)
D. \( x=3, y=-4 \)


Very Short Answer Types:
In which phase, there is an active
synthesis of RNA and proteins and no change in DNA contents of the cell?


A wire \( A B \) is carrying a steady current 12 A and is lying on the table. Another wire CD carrying 5 A is held directly above \( A B \) at a height of \( 1 \mathrm{mm} \). Find the mass per unit length of the wire CD so that it remains suspended at its position when left free. Give the directions of the
current flowing in \( \mathrm{CD} \) with respect to that in \( A B[\text { Take the value of } g= \)
\( \left.10 m s^{-2}\right] \)


(i) Name the sweetening agents used in the preparation of sweets for a diabetic patient?
(ii) What are antibiotics? Give an
example?
(iii) Give two example of macromolecules that are chosen as
drug targets?


\( \int \frac{1}{\sqrt{1-4 x^{2}}} d x= \)
\( A \cdot \sin ^{-1} 2 x+c \)
B. \( \frac{1}{2} \sin ^{-1} 2 x+c \)
c. \( \left(\sin ^{-1} 2 x\right)^{2}+c \)
D. \( \frac{1}{2}\left(\sin ^{-1} 2 x\right)^{2}+c \)


In a series LCR circuit connected to an
a.c. source of voltage \( \boldsymbol{v}=\boldsymbol{v}_{m} \sin \omega \boldsymbol{t} \)
use phasor diagram to derive an expression for the current in the circuit. Hence, obtain the expression for the power dissipated in the circuit. Show that power dissipated at resonance is maximum.


An accumulator of emf 2 Volt and
negligible internal resistance is connected across a uniform wire of
length \( 10 \mathrm{m} \) and resistance \( 30 \Omega \). The
appropriate terminals of a cell of emf
\( 1.5 V o l t \) and internal resistance \( 1 \Omega \) is
connected to one end of the wire, and
the other terminal of the cell is
connected through a sensitive galvanometer to a slider on the wire. If the balancing change when the cell of
1.5 volt is shunted with a resistance of \( 5 \Omega \) is \( \frac{x}{4} m . \) Find \( x \)


Transcription means synthesis of
A. DNA
B. Protein
c. mRNA
D. Enzyme


Which metal is leached from its ore by the use of \( K C N \)
A. copper
B. zinç
c. Gold
D. Iron


Two spheres of mass \( M \) and \( 4 M \) are connected by a rod whose mass is negligible, and the distance between the centers of each sphere is \( d \)
The \( 4 M \) sphere is moved a distance \( d / 3 \) towards the smaller sphere. How far has the Center of Mass for the
entire object moved?
A. The Center of Mass has not moved, because both spheres still have their original masses
в. \( d / 15 \)
\( c \cdot d / 5 \)
D. \( 4 d / 15 \)
E . \( 8 d / 15 \)


The following histogram shows the
frequency distribution of the ages of 22
teachers in a school:
What is the number of eldest and
youngest teachers in the school?


Give a reason for the following observations:
(a) Naphthalene balls disappear with time without leaving any solid.
(b) We can get the smell of perfumes
sitting several metres away.


If the displacement of an object is proportional to square of time, then the object moves with
A. uniform velocity
B. uniform acceleration
c. increasing acceleration
D. decreasing acceleration


A wire of a length 2 m carrying a
current of \( 1 \mathrm{A} \) is bend to form a circle.
The magnetic moment of the coil is
\( \left(i n A-m^{2}\right): \)
(a) \( 1 / \pi \)
(b) \( \pi / 2 \)


Which of the following are the two key concepts of Darwinian theory of evolution?
A. Genetic drift and mutation
B. Adaptive radiation and homology
c. Mutation and natural selection
D. Branching descent and natural selection


What is the half life of a radioactive
substance if \( 75 \% \) of its given amount
disintegrate in 60 min?
A . 30 min
B. 45 min
\( c .75 \) min
D. 90 min


When two immiscible liquids are shaken together vigorously, it may form
\( A \). a solution
B. a tincture
c. a sediment
D. a hydrated solution
E. a colloidal dispersion


If \( \frac{x^{2}}{f(4 a)}=\frac{y^{2}}{f\left(a^{2}-5\right)} \) respresents and
ellipse with major axis as y-axis and \( \boldsymbol{f} \) is a decreasing function, then
A \( . a \in(-\infty, 1) \)
B . \( a \in(5, \infty) \)
c. \( a \in(1,4) \)
D. \( a \in(-1,5) \)


Assertion
The function \( y=f(x), \) defined
parametrically as \( \boldsymbol{y}=\boldsymbol{t}^{2}+\boldsymbol{t}|\boldsymbol{t}|, \boldsymbol{x}= \)
\( \mathbf{2} t-|\boldsymbol{t}|, \boldsymbol{t} \in \boldsymbol{R}, \) is continuous for all rea
\( \boldsymbol{x} \)
Reason
\( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{ll}2 \boldsymbol{x}^{2}, & \boldsymbol{x} \geq \mathbf{0} \\ \mathbf{0}, & \boldsymbol{x}<\mathbf{0}\end{array}\right. \)
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


Solve the following pair of linear (simultaneous) equations by the method of elimination:
\( \boldsymbol{x}+\mathbf{8} \boldsymbol{y}=\mathbf{1 9}, \mathbf{2} \boldsymbol{x}+\mathbf{1 1} \boldsymbol{y}=\mathbf{2 8} \)
A. \( x=3 \) and \( y=2 \)
B. \( x=12 \) and \( y=5 \)
c. \( x=1 \) and \( y=6 \)
D. \( x=9 \) and \( y=-6 \)


The property of ultrasonic waves used in manufacturing emulsion for photographic films is its,
A. High speed
B. High frequency
c. Higher wavelength
D. High amplitude


For complete phosphorylation of a glucose molecule, how many ATP molecules are required?
\( A \cdot 4 \)
B. 2
\( c \cdot 6 \)
D. 8


According to law of conservation of
energy, the energy can neither be
nor
A . created, destroyed
B. destroyed, suppliedd
c. absorbed, emitted
D. emitted, absorbed


A string vibrates in 4 segments to a frequency of 400 Hz. What frequency will cause it to vibrate into 7 segments?
A. \( 700 H z \)
в. \( 500 H z \)
c. \( 400 \mathrm{Hz} \)
D. \( 100 H z \)


When the reaction is at equilibrium,the value of \( \Delta G \) is
\( A \)
B.
\( c \cdot 3 \)
D. \( 1 / 2 \)


Match the following
\begin{tabular}{llll}
State of matter & A & B \\
\hline 1 & Gas & Soil & Milk \\
2 & Solid & Kerosene & Oxygen \\
3 & Liquid & Carbon Monoxide & Peas
\end{tabular}


Select the species having zero oxidation state at the underlined elements.
This question has multiple correct options
\( \mathbf{A} \cdot\left(C H_{3}\right)_{2} S O \)
B. \( \underline{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11} \)
c. \( H_{2} S O_{3} \)
D. \( \underline{N}_{2} H_{4} \)


Find the value of \( \tan ^{-1}\left(\tan \frac{2 \pi}{3}\right) \)


If in two triangles \( A B C \) and \( P Q R \) \( \frac{A B}{Q R}=\frac{B C}{P R}=\frac{C A}{P Q} . \) Write a relation
between the two triangles.


12 g of impure cyanogen undergoes hydrolysis by two different paths.
\( (\boldsymbol{C N})_{2}+\mathbf{4} \boldsymbol{H}_{2} \boldsymbol{O} \rightarrow\left(\boldsymbol{N} \boldsymbol{H}_{4}\right)_{2} \boldsymbol{C}_{2} \boldsymbol{O}_{4} \)
ii. \( (\boldsymbol{C N})_{2}+\mathbf{2 H}_{\mathbf{2}} \boldsymbol{O} \rightarrow \boldsymbol{N} \boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{N} \boldsymbol{H}_{2} \)
When 11.52 g of pure ammonium
carbonate \( \left[\left(N H_{4}\right)_{2} C O_{3}\right] \) was heated
the exact amount of urea was obtained.
\( 20 \mathrm{mL} \) of \( 1.6 \mathrm{M} \) acidic \( K M n O_{4} \) is
required to completely oxidise. The percentage progress of the reaction in path (ii) is:
A . \( 40 \% \)
B. \( 60 \% \)
c. \( 30 \% \)
D. \( 70 \% \)


If the radius of the earth were to shrink
by \( 1 \% \), its mass remaining the same, the acceleration due to gravity on the
earth's surface would:
A. Decrease by \( 1 \% \)
B. Remain unchanged
C. Increase by \( 1 \% \)
D. Increase by 2\%


Verify Rolle's theorem the function \( f(x)=x^{3}-4 x \) on \( [-2,2] . \) If you think
it is applicable in the given interval then find the stationary point?
A. Yes Rolle's theorem is applicable and stationary point is \( x=\pm \frac{2}{\sqrt{3}} \)
B. No Rolle's theorem is not applicable
c. yes Rolle's theorem is applicable and \( x=2 \) or -2
D. none of these


Assertion
Soap solutions appears cloudy
Reason
Soap micelles are large enough to scatter light
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


\( \left|\begin{array}{lll}a^{2}+2 a & 2 a+1 & 1 \\ 2 a+1 & a+2 & 1 \\ 3 & 3 & 1\end{array}\right|= \)
\( A \cdot(1-a)^{3} \)
В - \( (a-1)^{2} \)
c. \( (a-1)^{3} \)
D・ \( (a+1)^{2} \)


What is the average sale of all the
branches (in thousand numbers) for the
year \( 2006 ? \)
\( A \cdot 73 \)
\( B .80 \)
\( c \cdot 83 \)
0.88


Only a part heat energy absorbed can be converted to work by heat engine because:
This question has multiple correct options
A. Heat engine dumps some heat as a waste into it's environment.
B. As heat flows in, it brings along some entropy that increases with heat transfer
c. Statement given is false, heat can be converted into work completely
D. None of the above


When concentrated nitric acid is heated
with \( P_{2} O_{5}, \) it forms:
A \( . H_{3} P O_{4} \)
в. \( N O_{2} \)
c. \( N_{2} O_{5} \)
D. \( N O \)


Recently discovered elements (August 2003 ) with atomic number 113 and 115
have valence electrons in:
A . \( s \) -orbital
B. \( p \) -orbital
c. \( d \) -orbital
D. \( f \) -orbital


Find total number of subsets of \( A=\{5,7\} \)


Draw the graph of each of the following
equations:
iv) \( \boldsymbol{x}+\mathbf{7}=\mathbf{0} \)


In a meter bridge the length of the wire is \( 100 \mathrm{cm} . \) The point at which will the balance be obtained if the two
resistances are in the ratio 2: 3 is
A \( \cdot 1) \) 20cm
B. 2) 40cm
c. 3 ) \( 28.6 \mathrm{cm} \)
D. 4) 44.1cm


A smooth tube of certain mass is
rotated in a gravity-free space and realeased. The two balls shown in the
figure move towards the ends of the tube. For the whole system, which of the following quantities is not conserved
A. Angular momentum
B. Linear momentum
c. Kinetic energy
D. Angular speed


A long fibre like process coming out of the cyton of a nerve cell is
\( A \cdot A \times O n \)
B. Dendron
c. Neurolemma
D. Neurofibrils


Construct \( \Delta P Q R \) such that, \( m \angle P= \)
\( \mathbf{8 0}^{o}, \boldsymbol{m} \angle \boldsymbol{Q}=\mathbf{7} 0^{o}, l(\boldsymbol{Q} \boldsymbol{R})=\mathbf{5 . 7} \boldsymbol{c m} \)


Which of the following cations is not hydrolyzed in aqueous solution?
(i) \( M g^{2+} \)
\( (\text { ii }) C a^{2+} \)
\( (\text { iii }) N a^{+} \)
\( (\text { iv }) \boldsymbol{K}^{+} \)
A. (i), (ii)
B. (iii), (iv)
c. (i), (ii), (iii), (iv)
D. (i), (ii), (iii)


Unit of plane angle is
A. Radian
B. Steradian
c. Degree
D. Celcius


Impure \( \boldsymbol{N} \boldsymbol{i}+\boldsymbol{4} \boldsymbol{C} \boldsymbol{O} \stackrel{\boldsymbol{6} \boldsymbol{0}-\boldsymbol{8} \boldsymbol{0}^{o} \boldsymbol{C}}{\longrightarrow} \)
\( N i(C O)_{4} \stackrel{180^{0} C}{\longrightarrow} N i+4 C O \)
The above process of purification of the metal is known as:
A. van arkel process
B. pyrometallurgy
c. mond process
D. zone refining


Why do soaps not work in hard water?


\( \int_{0}^{\pi / 4} \sec ^{7} \theta \sin ^{3} \theta d \theta \)
A \( .1 / 12 \)
в. \( 3 / 12 \)
c. \( 5 / 12 \)
D. none of these


(a) An em wave is travelling in a medium with a velocity \( \vec{v}=v \hat{i} \). Draw a
sketch showing the propagation of the em wave, indicating the direction of the oscillating electric and magnetic fields.
(b) How are the magnitudes of the electric and magnetic fields related to
the velocity of the em wave?


A telephone cable at a place has four long straight horizontal wires carrying a current of \( 1.0 \mathrm{A} \) in the same direction
east to west. The earth's magnetic field at the place is \( 0.39 \mathrm{G}, \) and the angle of
dip is \( 35^{\circ} . \) The magnetic declination is
nearly zero. What are the resultant magnetic fields at points 4.0 \( \mathrm{cm} \) below the cable?


The dimension of the universal constant
of gravitation \( G \) is
\( \mathbf{A} \cdot\left[M L^{2} T^{-1}\right] \)
B. \( \left[M^{-1} L^{3} T^{-2}\right] \)
\( \mathbf{c} \cdot\left[M^{-1} L^{2} T^{-2}\right] \)
D・ \( \left[M L^{3} T^{-2}\right] \)


If line \( \frac{\boldsymbol{x}-\mathbf{2}}{\mathbf{3}}=\frac{\boldsymbol{y}-\mathbf{4}}{\mathbf{4}}=\frac{\boldsymbol{z}+\mathbf{2}}{\mathbf{1}} \) is
parallel to planes \( \mu x+3 y-2 z+d= \)
0 and \( x-2 \lambda y+z=0, \) then value of \( \lambda \)
and \( \mu \) are
A \( \cdot\left(\mu=4, \lambda=-\frac{2}{3}\right. \)
B. \( \mu=-6, \lambda=-2 \)
c. \( _{\mu}=\frac{-10}{3}, \lambda=\frac{-1}{2} \)
D. \( \mu=\frac{-10}{3}, \lambda=\frac{1}{2} \)


What are the major causes of water pollution? Explain.


\( (-1)^{11} \) value is
\( A \cdot+1 \)
B.
\( c \cdot-1 \)
D. none of these


Using elementary row transformation, find the inverse of \( \left[\begin{array}{ccc}2 & 0 & -1 \\ 5 & 1 & 0 \\ 0 & 1 & 3\end{array}\right] \)


LASER belongs to the range of
A. Infrared rays
B. Visible light
c. uv rays
D. X-rays


The first term of an \( A . P \) is \( p \) and its
common difference is \( q \). Find its 10 th
term


In a measurement of quantum
efficiency of photosynthesis in green plants, it was found that 10 quanta of red light of wavelength \( 6850 A \) were needed to release one molecule of \( \boldsymbol{O}_{2} \)
The average energy storage in this
process is 112 kcal per mol of \( O_{2} \) evolved. What is the energy conversion efficiency in this experiment?
Given: 1 cal \( =4.18 J ; N_{A}=6 \times \)
\( \mathbf{1 0}^{\mathbf{2 3}} ; \boldsymbol{h}=\mathbf{6 . 6 3} \times \mathbf{1 0}^{-\mathbf{3 4}} \boldsymbol{J} . \boldsymbol{s} \)
A . 23.5
B . 26.9
c. 66.34
D. \( 73 . \)


The plane \( a x+b y+c z+(-3)=0 \)
meet the co-ordinate axes in \( A, B, C . \) Then
centroid
of the triangle is
A. \( (3 a, 3 b, 3 c) \)
в. \( \left(\frac{3}{a} \frac{3}{b}, \frac{3}{c}\right) \)
\( ^{\mathbf{C}} \cdot\left(\frac{a}{3}, \frac{b}{3}, \frac{c}{3}\right) \)
D. \( \left(\frac{1}{a}, \frac{1}{b}, \frac{1}{c}\right) \)


The ratio of the relative rise in pressure for adiabatic compression to that for isothermal compression is :
\( A \cdot \gamma \)
B. \( \frac{1}{\gamma} \)
c. \( 1-\gamma \)
D. \( \frac{1}{1-\gamma} \)


What is the correct relationship
between the \( p H^{\prime} s \) of isomolar solutions
of sodium oxide \( \left(p H_{1}\right), \) sodium
sulphide \( \left(p H_{2}\right), \) sodium selenide \( \left(p H_{3}\right. \)
)and sodium telluride \( \left(p H_{4}\right) ? \)
A \( . p H_{1}<p H_{2}<p H_{3}<p H_{4} \)
в. \( p H_{1}>p H_{2}>p H_{3}>p H_{4} \)
c. \( p H_{1}<p H_{2}<p H_{3} \approx p H_{4} \)
D. \( p H_{1}>p H_{2} \approx p H_{3}>p H_{4} \)


In the dehydration of an alcohol with concentrated sulphuric acid, which reaction step is the rate-limiting step?
A. Protonation of alcohol
B. Elimination of water from protonated alcohol
c. Elimination of proton
D. Unimolecular elimination of hydroxide from alcohol


Assertion
Woolen clothes keep the body warm in
winter
Reason
Air is a bad conductor of heat.
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


Kaliedoscope is made by using:
A. convex mirror
B. concave mirror
c. plane mirror
D. spherical mirror


Show that the square of any positive integer is of the form \( 4 \mathrm{m} \) or \( 4 \mathrm{m}+1 \) for any integer \( m \)


For \( \boldsymbol{x} \in \boldsymbol{R}-\{\boldsymbol{n} \boldsymbol{\pi}\}, \) the graph is: \( \boldsymbol{y}= \)
\( x+\sin x \)
A. Monotonically Increasing
B. Monotonically Decreasing
c. Either \( A \) or \( B \)
D. None of these


Which of the following forms cationic micelles above certain concentration?
A. Sodium dodecyl sulphate
B. Sodium acetate
c. urea
D. cetyltrimethyl ammonium bromide


A siren placed at a railway platform is emitting sound of frequency 5 KHz. \( A \)
passenger sitting in a moving train \( \mathbf{A} \) records a frequency of \( 5.5 \mathrm{KHz} \) while the train approaches the siren. During
his return journey in a different tran B he records a frequency of 6.0 KHz while approaching the same siren. The ratio of velocity of train \( \mathrm{B} \) to that of train \( \mathrm{A} \) is
A \( \cdot \frac{242}{252} \)
B. 2
c. \( \frac{5}{6} \)
D. \( \frac{11}{6} \)


Simplify \( \frac{x}{\sqrt{x+4}}, x>0 \)


Explain:
The molecules during collisions attain threshold energy and only then they result in chemical reaction. Certain
collisions inspite of possessing thr es hold energy do not result in chemical reactions. This is because the
orientation of collisions is not suitable
for a chemical reaction. Thus, the collisions which are associated with
threshold energy and proper orientation only result in chemical reaction.