Parachute mechanism of fruit and seed
dispersal is common in compositae due to the structure called
A. Bracts
B. Thorns
c. corolla
D. Pappus


Give the names and atomic numbers of
the first and last members of the
lanthanide series.


What energy conversion does take place
in a generator when it is in use?
A. The electrical energy changes into the electrical energy.
B. The mechanical energy changes into the mechanical
energy.
C. The electrical energy changes into the mechanical energy.
D. The mechanical energy changes into the electrical
energy.


The plasma membrane of animal cells
is elastic due to the presence of
A. Lipids
B. Carbohydrates
c. Proteins
D. water


A uniform cylinder of radius \( R \) is
spinned about its axis to the angular
velocity \( \omega_{0} \) and then placed into a corner. The coefficient of friction
between the corner walls and the
cylinder is \( \mu_{2} . \) How many turns will the cylinder accomplish before it stops?


Area of the region bounded by \( y= \)
\( e^{x}, y=e^{-x}, x=0 \) and \( x=1 \) in sq. units
is:
\( ^{A} \cdot\left(e+\frac{1}{e}\right)^{2} \)
\( ^{\text {B }}\left(e-\frac{1}{e}\right)^{2} \)
\( ^{c} \cdot\left(\sqrt{e}+\frac{1}{\sqrt{e}}\right)^{2} \)
D \( \left(\sqrt{e}-\frac{1}{\sqrt{e}}\right)^{2} \)


\( S: A \) reaction \( 2 S O_{2}+O_{2} \rightleftharpoons 2 S O_{3} ; \) has
\( \boldsymbol{K}_{\boldsymbol{p}} \) at \( \boldsymbol{2} \boldsymbol{9} \boldsymbol{8} \boldsymbol{K} \) and \( \boldsymbol{5 0 0} \boldsymbol{K} \) as \( \boldsymbol{4} \boldsymbol{. 0} \times \boldsymbol{1 0}^{24} \)
and \( 8.5 \times 10^{10} \) respectively.
\( \mathrm{E}: \) The \( \boldsymbol{E}_{a} \) for the forward reaction is
lesser than \( E_{b} \) for the backward
reaction.
A. s is correct but E is wrong
B. s is wrong but E is correct
c. Both \( \mathrm{S} \) and \( \mathrm{E} \) are correct and \( \mathrm{E} \) is correct explanation 0 \( S \)
D. Both S and E are correct but E is not correct explanation of


Which of the following statements concerning protium, deuterium and
tritium is not true?
A. They are isotopes of each other
B. They have similar electronic configurations
c. They exist in the nature in the ratio of 1: 2: 3
D. Their mass numbers are in the ratio of 1: 2: 3


There are three events \( A, B, C \) one
which must and only one can happen; the odds are 8 to 3 against \( A, 5 \) to 2
against \( B . \) The odds against \( C \) is 43:
17k. Find the value of \( k \) ?


The rate of change of the volume of a cone with respect to the radius of its
base is-
\( \mathbf{A} \cdot \pi^{2} h \)
в. \( \frac{4}{3} \pi r h \)
c. \( \frac{4}{3} \pi r^{2} h \)
D. \( \frac{2}{3} \pi r h \)


When is \( H_{\alpha} \) line in the emission
spectrum of hydrogen atom obtained? Calculate the frequency of the photon emitted during this transition.


In fig two circular flower bds have been
shown on two sides of a lawn \( A B C D \) of
side \( 56 \mathrm{m} \). If the centre of each circular
flower bed is the point of intersection \( \boldsymbol{O} \)
of the diagonals of the square lawn, find
the sum of the areas of the lawn and
flower beds
\( \mathbf{A} \cdot 4032 m^{2} \)
B . \( 4428 \mathrm{m}^{2} \)
\( \mathbf{c} \cdot 4628 m^{2} \)
D. None of these


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


Salivary duct of cockroach opens at
A. Hypopharynx
B. Epipharynx
c. Left mandible
D. Right mandible


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


Show that \( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left(\cos \boldsymbol{h}^{-1} \boldsymbol{x}\right)=\frac{\mathbf{1}}{\sqrt{\boldsymbol{x}^{2}-\mathbf{1}}} \)


Which of the following binomial expressions has a least term
independent of \( x ? \)
\( ^{\mathrm{A}} \cdot\left(\sqrt{x}-\frac{3}{x^{2}}\right)^{1} \)
B. \( \left(x+\frac{1}{x}\right)^{6} \)
c. \( (1+x)^{32} \)
\( ^{\mathrm{D}}\left(\frac{3}{2} x^{2}-\frac{1}{3 x}\right)^{9} \)


Chlorophyll contains \( 2.68 \% \) of \( M g \) by
weight. Then the number of \( M g \) atom in
\( 2.00 \mathrm{g} \) of chlorophyll is:
(Atomic mass of \( M g=24) \)


Which of the following is/are correct
regarding homogeneous differential
equation?
This question has multiple correct options
A. Represented in the form: \( M(x, y) d x-N(x, y) d y=0 \)
B. Represented in the form: \( M(x, y) d x+N(x, y) d y=0 \)
C. Both \( M(x, y), N(x, y) \) are homogeneous functions of the same degree
D. \( M(x, y), N(x, y) \) are homogeneous functions with different degrees


Which of the following methods is suitable for preventing an iron frying pan from rusting?
A. Applying grease
B. Applying paint
C. Applying a coating of zinc
D. All of the above


Write the main reason for the stability of colloidal sols.


Solve the following system of linear equations using matrix method: \( 3 x+ \)
\( \boldsymbol{y}+\boldsymbol{z}=\mathbf{1}, \mathbf{2} \boldsymbol{x}+\mathbf{2} \boldsymbol{z}=\mathbf{0}, \mathbf{5} \boldsymbol{x}+\mathbf{5} \boldsymbol{y}+ \)
\( \mathbf{2} z=\mathbf{2} \)


How is the critical angle related to the refractive index of the medium?


The fraction of collisions that posses
the energy \( \boldsymbol{E}_{\boldsymbol{a}} \) is given by:
A \( \cdot f=e^{\frac{-E q}{R T}} \)
B . \( f=e^{\frac{E}{m}} \)
C . \( f=e^{-E a . R T} \)
D. \( f=e^{\text {Ea. } R T} \)


f \( \Delta A B C \) and \( \Delta X Y Z \) are congruent
then \( \Delta A B C \ldots \ldots . \Delta X Y Z \)
\( A \cdot \cong \)
B. \( = \)
\( c \cdot \approx \)
D.


Assertion
Smaller the orbit of the planet around
the sun, shorter is the time it takes to
complete one revolution
Reason
According to Kepler's third law of
planetary motion, square of time period is proportional to cube of mean distance from sun
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


Form the differential equation corresponding to \( y^{2}-2 a y+x^{2}=a^{2} b y \)
eliminating a.


Differentiate wirh respect to
\( \sqrt{x+\frac{1}{x}} \)


Which one is false about kranz
anatomy?
A. Bundle sheath have large chloroplast and less developed grana.
B. Mesophyll cells have large chloroplasts.
C. It is found in atriplex, sugarcane, maize.
D. Plant having it have better photosynthesizing power than \( c_{3} \) plants.


The work function of a metal is \( 4.2 \mathrm{eV} \). If
radiation of \( 2000 A^{\circ} \) falls on the metal,
the kinetic energy of the fastest photoelectron is:
A . \( 1.6 \times 10^{-19} \mathrm{J} \)
В. \( 16 \times 10^{-10} J \)
c. \( 3.2 \times 10^{-19} \mathrm{J} \)
D. \( 6.4 \times 10^{-10} \mathrm{J} \)


If A's income is \( 20 \% \) more than \( \mathrm{B} \), then
B's income is
A. same as A's
B. 20\% less than A's
C \( \cdot 16 \frac{2}{3} \% \) less than A's
D. 15\% less than A's


A convex lens of focal length \( 20 \mathrm{cm} \) is placed coaxially with a concave mirror of focal length \( 10 \mathrm{cm} \) at a distance of
\( 50 c m \) apart from each other. A beam of
light coming parallel to the principal axis is incident on the convex lens. Find
the position of the final image formed by this combination. Draw the ray diagram showing the formation of the image.


Give plausible explanation for each of the following:
(i) Why are amines less acidic than alcohols of comparable molecular
masses?
(ii) Why do primary amines have higher boiling point than tertiary amines?
(iii) Why are aliphatic amines stronger bases than aromatic amines?


The number of words that can be formed
out of the letters of the word "ARTICLE"
so that the vowels occupy even places is
A .574
B. 36
\( c .754 \)
D. 144


Infrared radiation are detected by
A. spectrometer
B. pyrometer
c. nanometer
D. photometre


A body of mass \( 5 k g \) moving on a horizontal surface with a velocity of
\( 10 m s^{-1} \) comes to rest in \( 2 s . \) The force
required to make this body move with a
velocity of \( 10 \mathrm{ms}^{-1} \) on the same surface
is:
A. zero
в. \( 10 N \)
c. \( 25 N \)
D. \( 50 N \)


In a semi-conducting material the
mobilities of electrons and holes are \( \mu_{e} \)
and \( \mu_{h} \) respectively. Which of the following is true?
A \( \cdot \mu_{e}>\mu_{h} \)
в. \( \mu_{e}<\mu_{h} \)
c. \( \mu_{e}=\mu_{h} \)
\( \mathbf{D} \cdot \mu_{e}=0 ; \mu_{h}>0 \)


What is a secondary cell?


Roasting is carried out to
This question has multiple correct options
A. convert sulphide ore to oxide
B. remove water of hydration
C. melt the ore
D. remove carbon and sulphur impurities


The unit of concentration may be given
by :
A. gram per millilitre (g/mı)
B. kilogram per litre (kg/I)
c. gram per litre (g/I)
D. all of the above


The elements belonging to which group are called representative elements? This question has multiple correct options
A. 1 and 2
B. 3 to 12
\( c .13 \) to 18
D. Element lying at the bottom of periodic table


A block of mass \( 5 k g \) is on a rough horizontal surface and is at rest. Now a
force of \( 24 N \) is imparted to it with negligible impluse. If the coefficient of
kinetic friction is 0.4 and \( g=9.8 m / s^{2} \)
then the acceleration of the block is
A \( \cdot 0.26 m / s^{2} \)
B. \( 0.39 \mathrm{m} / \mathrm{s}^{2} \)
c. \( 0.69 m / s^{2} \)
D. \( 0.88 m / s^{2} \)


\( \mid=H e \)
\( \|=N e \quad\| I=A r \quad I V=K r \)
Decreasing order of melting point of compound I-IV follows:
B. |> || > || > > IV
c. ॥> ||| > |V>1
D. II>IV>III>1


Which of the following statements is not correct about the given reaction? \( \boldsymbol{K}_{4}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{6} \frac{\text {Oxidation}}{\boldsymbol{\leftrightarrow}} \boldsymbol{F} \boldsymbol{e}^{3+}+\boldsymbol{C O}_{2}+\right. \)
\( \mathbf{N} \boldsymbol{O}_{\mathbf{3}}^{-} \)
A. Fe is oxidised from \( F e^{2+} \) to \( F e^{3 \text { - }} \)
B. Carbon is oxidised from \( C^{2+} \) to \( C^{4+} \).
c. \( \mathrm{N} \) is oxidised from \( N^{3} \) - to \( N^{5+} \)
D. Carbon is not oxidised


In which of the following processes is nitrogen oxidized?
A \( \cdot N H_{4}^{\oplus} \rightarrow N_{2} \)
B \( . N O_{3}^{\ominus} \longrightarrow N O \)
\( \mathrm{c} \cdot \mathrm{NO}_{2} \longrightarrow \mathrm{NO}_{2}^{\circ} \)
D. \( N O_{3}^{\ominus} \longrightarrow N H_{4}^{\oplus} \)


Phenol reacts with \( P C l_{5} \), the main
product is:
\( A \)
\[
\mathrm{Ph}-\mathrm{O}-\underbrace{\mathrm{O}}_{\mathrm{Cl}}^{\mathrm{l}}-\mathrm{Cl}
\]
B.
\[
\mathrm{Ph}-\mathrm{O}-\underset{\mathrm{C}}{\mathrm{P}}^{\mathrm{O}}-\mathrm{O}-\mathrm{Ph}
\]
\( c \)
\[
\mathrm{Ph}--\mathrm{O}-\begin{array}{c}
\mathrm{O} \\
\mathrm{P} \\
\mathrm{OPh}
\end{array}-\mathrm{O}-\mathrm{Ph}_{\mathrm{h}}
\]
D. none of thes


Heat of combustion \( \Delta H^{o} \) for
\( \boldsymbol{C}(\boldsymbol{s}), \boldsymbol{H}_{2}(\boldsymbol{g}) \) and \( \boldsymbol{C H}_{4}(\boldsymbol{g}) \) are \( -\mathbf{9 4},-\mathbf{6 8} \)
and \( -213 k c a l / \) mol respectively. Then
\( \Delta H^{o} \) for \( C(s)+2 H_{2}(g) \rightarrow C H_{4} \) is:
A \( .-17 k c a l / m o l \)
B. -111 kcal / mol
c. \( -170 \mathrm{kcal} / \mathrm{mol} \)
D. \( -85 k c a l / m o l \)


If \( 1.0 \mathrm{k} \) cal of heat is added to \( 1.2 \mathrm{L} \) of \( \mathrm{O}_{2} \)
in a cylinder of constant pressure of 1 atm, the volume increases to 1.5 L.
Calculate \( \Delta H \) and \( \Delta U \) of the process.


8
8
8
8


The work function of a metal is \( 6 e V \). If
two photons each having energy \( 4 e V \)
strike with the metal surface
(i) Will the emission be possible?
(ii) Why?


Two refracting media are separated by
a spherical interface as shown in figure.
PP' is the principle axis. \( \mu_{1} \) and \( \mu_{2} \) are
the refractive indices of medium of
incidence and medium of refraction
respectively. Then,
This question has multiple correct options
\( \mathbf{A} \cdot \) if \( \mu_{2}>\mu_{1} \) then there cannot be a real image of real object
\( \mathbf{B} \cdot \) if \( \mu_{2}>\mu_{1} \) then there cannot be a real image of virtual object.
\( \mathrm{C} \cdot \) if \( \mu_{1}>\mu_{2} \) then there cannot be a virtual image of virtual object
D. if \( \mu_{1}>\mu_{2} \) then there cannot be a real image of real
object


There are 30 tickets numbered from 1 to
30 in a box and a ticket is drawn at
random. If \( A \) is the event that the
number on the ticket is a perfect
square, then write the sample \( S, n(S) \) the event \( \boldsymbol{A} \) and \( \boldsymbol{n}(\boldsymbol{A}) \)


Which of the following statements is incorrect?
A. Adsorption always leads to a decrease in enthalpy and entropy of the system
B. Adsorption arises due to unsaturation of valence forces of atoms or molecules on the surface
C. Adsorption increases with rise in temperature.
D. Adsorption decreases the surface energy


Which of the following reagent is used in the conversion of benzene diazonium
chloride to chlorobenzene?
A \( \cdot C u_{2} C l_{2} \)
в. \( C u C l_{2} \)
c. \( F e C l_{2} \)
D. \( F e C l_{3} \)


A force vector applied on a mass is represented by \( \overrightarrow{\boldsymbol{F}}=\mathbf{6} \hat{\mathbf{i}}-\mathbf{8} \hat{\mathbf{8}}+\mathbf{1 0} \hat{\mathbf{k}} \) and
accelerates with \( 1 m / s^{2} \). what is the
mass of the body?
A. \( 10 \mathrm{kg} \)
B . \( 10 \sqrt{2} \mathrm{kg} \)
c. \( 2 \sqrt{10} \mathrm{kg} \)
D. 20 kg


Why do we not get crushed under the
atmospheric pressure?
A. Internal pressure equals atmospheric pressure
B. Internal pressure is less than the atmospheric pressure
C. Internal pressure is more than the atmospheric
pressure
D. None of the above


All of these secretes digestive enzyme,
except
A. Salivary glands.
B. Liver
c. Pancreas.
D. Small intestine
E. Stomach.


The enzyme which converts glucose to glucose- 6 -phosphate is
A. Phosphorylase
B. Glucose-6-phosphate
c. Hexokinase
D. Glucose synthetase


\( f \arg (z)<0 \) then find \( \arg (-z)-\arg (z) \)


\( \mathbf{1 0 \mu A s}= \)
coulombs.
A \( \cdot 10^{-4} \)
-4
B. \( 10^{-5} \)
\( \mathrm{c} \cdot 10^{-3} \)
D. \( 10^{-6} \)


A man wearing glasses of focal length \( +1 \mathrm{m} \) cannot clearly see beyond \( 1 \mathrm{m} \)
A. if he is farsighted
B. if he is nearsighted
c. if his vision is normal
D. in each of these case


If both the mass and radius of the earth
decrease by \( 1 \% \) the value of This question has multiple correct options
A. acceleration due to gravity would decrease by nearly \( \% \)
B. acceleration due to gravity would increase by 1\%
c. escape velocity from the earth's surface would decrease by \( 1 \% \)
D. the gravitational potential energy of a body on earth's's surface will remain unchanged


The circumference of a circle is \( 100 \mathrm{cm} \)
Then the side of a square inscribed in the circle is:
A \( \cdot \frac{100 \sqrt{2}}{\pi} \mathrm{cm} \)
B. \( \frac{50 \sqrt{2}}{\pi} \mathrm{cm} \)
c. \( \frac{100}{\pi} \mathrm{cm} \)
D. \( 50 \sqrt{2} \mathrm{cm} \)


The electronic configuration of the first artificial element:
A \( \cdot 4 f^{4} 5 d^{1} 6 s^{2} \)
B . \( 4 f^{1} 5 d^{4} 6 s^{2} \)
c. \( 5 f^{4} 6 d^{1} 7 s^{2} \)
D. \( 5 f^{3} 6 d^{1} 7 s^{2} \)


Titan is the largest satellite of the planet
A. Mars
B. Venus
c. Saturn
D. Jupiter


Find the absolute maximum and
minimum values of the function f given by \( f(x)=\cos ^{2} x+\sin x, x \in[0, \pi] \)


Which of the following is a physical change?
A. Magnetisation of iron
B. Curdling of milk
c. Burning of a candle
D. cooking of food


i) From differential equation of linear
S.H.M., obtain an expression fro acceleration, velocity and displacement of a particle performing S.H.M.
ii) A sonometer wire 1 metre long
weighing \( 2 g \) in is resonance with a
turning fork of frequency \( 300 H z . \) Find tension in the sonometer wire.


A square matrix \( \mathbf{B} \) of order \( \mathbf{3}, \) has \( |\boldsymbol{B}|= \)
\( \mathbf{7}, \) find \( \mid \boldsymbol{B} \) adj \( \mathbf{B} \mid \)


Give reasons why a paper written in
ordinary ink is bleached by chlorine whereas it cannot bleach printed ink.


Water released from dams is measured
in?
A. Feet per second or CFS
B. Liters
c. cusesc
D. Feet


Solve \( 8 t+5=2 t-31 \) for the value of \( t \)


The series \( 1^{2}-2^{2}+3^{2}-4^{2}+\ldots .+ \)
\( 99^{2}-100^{2}= \)
A . -5050
B. 5050
c. 11000
D. -11000


Choose the correct answers from the
alternatives given :
Each codon calls for a specific
A. carbohydrate
B. polypeptide
c. amino acid
D. protein


\( \ln \Delta O A B, \) if \( O A=\vec{a}, \overrightarrow{O B}=\vec{b} . L \) is mid
point of \( \boldsymbol{O A} \) and \( \boldsymbol{M} \) is point on \( \boldsymbol{O B} \) such that \( \boldsymbol{O} \boldsymbol{M}: \overrightarrow{\boldsymbol{M}} \boldsymbol{B}=\boldsymbol{2}: 1 . \) If \( \boldsymbol{P} \) is mid
point of \( L M \) then \( \overrightarrow{A P}= \)
A \( \cdot \frac{1}{3} \vec{b}-\frac{3}{4} \vec{a} \)
B \( \cdot \frac{1}{3} \vec{b}+\frac{3}{4} \vec{a} \)
c. \( \frac{1}{3} \vec{a}-\frac{3}{4} \vec{b} \)
D. \( \frac{1}{3} \vec{a}+\frac{3}{4} \vec{b} \)


Find the slope of the line joining the points (0,0) and \( (\sqrt{3}, 3) \)


Among the following, the correct statement about cathode ray discharge tube is:
A. the electrical discharge can only be observed at highh pressure and at low voltages
B. in the absence of external electrical or magnetic field, cathod rays travel in straight lines
c. the chatacteristics of cathode rays depend upon the material of electrodes
D. the chatacteristics of cathode rays depend upon the gas present in the cathod rays tube


The value of \( \tan \left\{2 \tan ^{-1} \frac{1}{5}-\frac{\pi}{4}\right\} \) is
A .
B.
\( c \cdot \frac{7}{17} \)
D. none of these


... of Roads is done by raising the outer edges of the road slightly above the leve of inner edge, to avoid accidents.
A. Finishing
B. Banking
c. Inclination
D. None of these


The phenomenon of light bending on change of medium is called:
A. reflection
B. refraction
c. dispersion
D. total internal reflection


Dissolution of \( C a H_{2} \) in water is an
auto-redox process.
If true enter 1 , else enter 0
\( A \)


Expand
(i) \( (\sqrt{3}+\sqrt{2})^{4} \)


Which cannonball reaches a higher
elevation?
\( A \cdot A \)
B. B
c. Both reaches same height
D. Cannot be judged


Write short note on chrome plating?


In which of the following is the energy loss maximum?
A. sonometer
B. tuning fork
c. thin tube
D. broader pipe


Assertion
For four half-cell reactions involving different number of electrons,
\( \boldsymbol{E}_{4}=\boldsymbol{E}_{1}+\boldsymbol{E}_{2}+\boldsymbol{E}_{3} \)
Reason
\( \boldsymbol{\Delta} \boldsymbol{G}_{4}=\boldsymbol{\Delta} \boldsymbol{G}_{1}+\boldsymbol{\Delta} \boldsymbol{G}_{2}+\boldsymbol{\Delta} \boldsymbol{G}_{3} \)
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. Assertion is incorrect but Reason is correct


In the above network, current flows from
\( M \) to \( N, \) when
A. \( q \) closed, ropened and p closed
B. q opened, p opened and r closed.
C. q opened, p closed and r closed.
D. q closed, p closed and r opened


A boy sitting on the top most berth in the compartment of a train which is
just going to stop on a railway station, drops an apple aiming at the open hand of his brother situated vertically below his hands at a distance of about \( 2 \mathrm{m} \)
The apple will fall
A. In the hand of his brother
B. Slightly away from the hands of his brother in the direction of motion of the train
c. Slightly away from the hands of his brother in the direction opposite to the direction of motion of the train
D. None of these


The frequency of a wave is 5 Hz. It refers to (type of wave)
A . ultrasonics
B. microwaves
c. infrasonics
D. radio waves


A dice is thrown \( 2 n+1 \) times, \( n \epsilon N \)
The probability that faces with even numbers show odd number of times is
A \( \cdot \frac{2 n+1}{4 n+3} \)
B. less than \( \frac{1}{2} \)
c. greater than \( \frac{1}{2} \)
D. none of these


The product of two consecutive integers is \( 600 . \) Find the second integer.
A .24
B . 23
c. 25
D. 26


If \( n \) is a positive integer, then the value
of the determinant \( \left|\begin{array}{ccc}\boldsymbol{a}^{n}-\boldsymbol{x} & \boldsymbol{a}^{\boldsymbol{n}+1}-\boldsymbol{x} & \boldsymbol{a}^{\boldsymbol{n}+\mathbf{2}}-\boldsymbol{x} \\ \boldsymbol{a}^{\boldsymbol{n}+\mathbf{3}}-\boldsymbol{x} & \boldsymbol{a}^{\boldsymbol{n}+\mathbf{4}}-\boldsymbol{x} & \boldsymbol{a}^{\boldsymbol{n}+\mathbf{5}}-\boldsymbol{x} \\ \boldsymbol{a}^{\boldsymbol{n}+\mathbf{6}}-\boldsymbol{x} & \boldsymbol{a}^{\boldsymbol{n}+\mathbf{7}}-\boldsymbol{x} & \boldsymbol{a}^{\boldsymbol{n}+\boldsymbol{8}}-\boldsymbol{x}\end{array}\right|= \)
\( \mathbf{A} \cdot \mathbf{1} \)
B.
\( c .-1 \)
D. None of these


Which of the following reactions is not a part of Solvay's process for preparation of sodium carbonate?
\( \mathbf{A} \cdot 2 N H_{3}+H_{2} O+C O_{2} \rightarrow\left(N H_{4}\right)_{2} C O_{3} \)
B. \( \left(N H_{4}\right)_{2} C O_{3}+H_{2} O+C O_{2} \rightarrow 2 N H_{4} H C O_{3} \)
c. \( 2 N H_{4} H C O_{3} \rightarrow\left(N H_{4}\right)_{2} C O_{3}+H_{2} O+C O_{2} \)
D. \( N H_{4} H C O_{3}+N a C l \rightarrow N H_{4} C l+N a H C O_{3} \)


Considering mode of asexual reproduction, match the Column I with I and select the correct option.
\( \begin{array}{ll}\text { Column I } & \text { Column II } \\ \text { a. Yeast } & \text { i. Fragmentation } \\ \text { b. Penicillium } & \text { ii. Zoospores } \\ \text { c. Filamentous algae } & \text { iii. Budding } \\ \text { d. Chlamydomonas } & \text { iv.Conidia }\end{array} \)
\( A \)
\( a-i i i, b-i v, c-i, d-i i \)
в. \( a-i i, b-i i i, c-i, d-i v \)
c. \( a-i v, b-i i i, c-i i, d-i \)
D. \( a-i i i, b-i i, c-i, d-i v \)


A \( 300 \Omega \) resistor, a \( 0.250 H \) inductor
and a \( 8.00 \mu F \) capacitor are in series
with an ac source with voltage amplitude \( 120 V \) and angular frequency \( 400 r a d / s . \) Which of the following is/are
correct?
This question has multiple correct options
A. Voltage amplitude across the resistor is \( 97.9 V \)
B. Voltage amplitude across the inductor is \( 32.6 \mathrm{V} \)
c. voltage amplitude across the capacitor is \( 102 V \)
D. Voltage amplitude across the resistor is \( 32.6 V \)


State true or false:
If \( a+2 b=5 ; \) then
\( a^{3}+8 b^{3}+30 a b=125 \)
A. True
B. False


A constant electric current flows for 4
hours through two electrolytic cells connected in series. One contains
\( A g N O_{3} \) solution and second contains
\( C u C l_{2} \) solution. During this time, 4 grams of \( A g \) is deposited in the first cell. How many grams of Cu is deposited in the second cell?
A . 2.176 g
в. \( 0.176 \mathrm{g} \)
c. \( 1.176 \mathrm{g} \)
D. None of the above


Which one of the alkaline earth metals
shows some anomalous behaviour and
has same electronegativity as aluminium?
A. sr
в. са
c. Ва
D. Be


A body is executing simple harmonic motion of amplitude \( a \) and period \( T \)
about the equilibrium position \( \boldsymbol{x}=\mathbf{0} \)
Large numbers of snapshots are taken
at random of this body in motion. The probability of the body being found in a
very small interval \( \boldsymbol{x} \) to \( \boldsymbol{x}+|\boldsymbol{d} \boldsymbol{x}| \) is
highest at
A. \( x=\pm a \)
В. \( x=\pm a / 2 \)
c. \( x=0 \)
D. \( x=\pm a / \sqrt{2} \)


The top in figure has a moment of
inertia of \( 4.00 \times 10^{-4} k g-m^{2} \) and is
initially at rest. It is free to rotate about
the stationary axis \( \boldsymbol{A} \boldsymbol{A}^{\prime} \) A string
wrapped around a peg along the axis of the top, is pulled in such a manner as to
maintain a constant tension of \( 2.5 M . \) If
the string does not slip while it is unwound from the peg, what is the
angular speed of the top after \( 80.0 \mathrm{cm} \)
string has been pulled off the peg?
A \( .75 \mathrm{rad} / \mathrm{s} \)
B. 50 rad \( / s \)
c. \( 125 r a d / s \)
D. 100 rad \( / s \)


A body of mass \( m \) was slowly hauled up
the hill by a force \( F \) as shown in the figure, which at each point was directed
along a tangent to the trajectory. Find
the work performed by this force, if the
height of the hill is \( h, \) the length of its
base is \( l \) and the coefficient of friction
is \( \mu . \) (Given acceleration due to gravity
\( =g) \)
A \( . W_{F}=m g h+\mu m g l \)
В. \( W_{F}=m g h-\mu m g l \)
c. \( W_{F}=\mu m g l-m g h \)
2.


Two roads \( O A \) and \( O B \) intersect at an
angle fo \( 60^{\circ} . \) A car driver approaches 0
from \( A, \) where \( A O=800 \) metres, at a
uniform speed of 20 metres per second.
Simultaneously a runner starts running
from \( \boldsymbol{O} \) towards \( \boldsymbol{B} \) at uniform speed of \( \mathbf{5} \)
metres per second. Find the time when the car and the runner are closest.
A \( \cdot \frac{240}{7} \) sec
B. \( \frac{260}{7} \) sec
c. \( \frac{250}{7} \mathrm{sec} \)
D. \( \frac{210}{7} \mathrm{sec} \)


Say Yes or No:
Can an object reverse the direction of
its motion even though it has constant acceleration?


The moment of inertia of a straight thin
rod of mass \( M, \) length \( L \) about an axis
perpendicular to its length and passing through its one end is :


A straight road has two sections \( A B \) (highly rough) and \( B C( \) slightly rough),a body of mass m rolling without friction in \( A B \) at \( t=0 . \) After some time it enters
the section \( B C \) then in this section,
A . friction start acting
B. pure rolling in BC
C. forward slipping takes place
D. none of the above


A solution of the differential equation \( \left(\frac{d y}{d x}\right)-x \frac{d y}{d x}+y=0 \) is


The absolute refractive index of glass
and water are \( 3 / 2 \) and \( 4 / 3, \) respectively. If the speed of light in glass is \( 2 \times 10^{8} \)
\( \mathrm{m} / \mathrm{s}, \) calculate the speed of light in :
(a) vacuum
(b) water


In reactions involving gaseous reactants and gaseous products, the
units of rate are:
A. Atm
B. Atm-sec
C. Atm.sec-
D. \( A t m^{2} s e c^{2} \)


Identify the compound having hydrogen bonding.
A. water
B. Chlorine gas
c. oxygen gas
D. Neon


\( B e^{3+} \) and a proton are accelerated by
the same potential, their de-Broglie wavelenghts have the ratio (assume
mass of proton \( = \) mass of neutron):
A .1: 2
B. 1: 4
c. 1: 1
D. \( 1: 3 \sqrt{3} \)


Ammeter is used to
measure
A. current
B. voltage
c. charge
D. resistance


since there are 10 water molecules in
washing soda, hence it is known as:
A. sodium bicarbonate decahydrate
B. sodium carbonate decahydrate
c. sodium bicarbonate nanohydrate
D. sodium decahydrate


\( \left(\frac{m}{m}\right) \)
mand
nth
ith
ution
\( ^{M(s)+\frac{1}{2} x_{1} \rightarrow M^{+} X-(s)} \)
ใermsseseous met geeous cati
def
tortereonmere
nswer
'spositien why


The displacement of a charge \( Q \) in the
electric field \( \boldsymbol{E}=\boldsymbol{e}_{1} \boldsymbol{l}+\boldsymbol{e}_{2} \boldsymbol{j}+\boldsymbol{e}_{3} \boldsymbol{k} \) is
\( \boldsymbol{r}=\boldsymbol{a} \boldsymbol{i}+\boldsymbol{b} \boldsymbol{j} . \) The work done is
A \( Q\left(a e_{1}+b e_{2}\right) \)
() \( a\left(a_{1}+b_{2}\right)+b_{2}+b_{2} \)
в. \( Q \overline{a e_{1}^{2}+b e_{2}^{2}} \)
c. \( Q\left(e_{1}+e_{2}\right) \overline{a^{2}+b^{2}} \)
D. \( Q \overline{e_{1}^{2}+e_{1}^{2}} a+b \)


When equivalent of \( \boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{O} \boldsymbol{H} \& \boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{C l} \)
are same then salt formula to be
applied or buffer?


With the propagation of a longitudinal wave through a material medium, the quantities transmitted in the direction of propagation are
A. Energy, momentum and mass
B. Mass and momentum
c. Energy and mass
D. Energy and momentum


Find the area of shaded region?


If market price \( =\boldsymbol{R} \boldsymbol{s} . \boldsymbol{9} \boldsymbol{9} \boldsymbol{0} \) and
percentage of discount is 10 , then find the selling price.


If \( \boldsymbol{f}: \boldsymbol{A} \rightarrow \boldsymbol{B} \) is a constant function
which is onto then \( B \) is
A. a singleton set
B. a null set
c. an infinite set
D. a finite set


The gravitational force of attraction between two masses depend on the distance between them is \( G= \)
gravitaional constant \( =\boldsymbol{k} \times \)
\( 10^{-11} N m^{2} k g^{-2} . \) what is the value of \( k ? \)


Solve: \( 4 x+\frac{6}{y}=15 \) and \( 6 x-\frac{8}{y}= \)
\( \mathbf{1 4} \)
A. \( x=2 ; y=3 \)
В. \( x=3 ; y=2 \)
c. \( x=1 ; y=5 \)
D. \( x=4 ; y=1 \)


Mrs. Goyal has to pay \( 4 \% \) sales tax in addition to the price if a certain article. Find the price of her article, if she pays
\( \boldsymbol{R} \boldsymbol{s} . \mathbf{2 6 0} \) in all?


Which of the following element is represented by electronic configuration \( \mathbf{1} \boldsymbol{s}^{2} \mathbf{2} \boldsymbol{s}^{2} \mathbf{2} \boldsymbol{p}_{\boldsymbol{x}}^{1} \mathbf{2} \boldsymbol{p}_{\boldsymbol{y}}^{\mathbf{1}} \boldsymbol{2} \boldsymbol{p}_{z}^{1} \)
A. Nitrogen
B. Oxygen
c. Fluorine
D. sulphur


The elongation produced in a copper wire of length \( 2 \mathrm{m} \) and diameter \( 3 \mathrm{mm} \) when a force of \( 30 \mathrm{N} \) is applied is \( [\mathrm{Y}= \) \( \left.1 \times 10^{11} \mathrm{N} \cdot \mathrm{m}^{-2}\right] \)
A. \( 8.5 m m \)
B. \( 0.85 \mathrm{mm} \)
c. \( 0.085 m m \)
D. \( 85 m m \)


Satellites \( A \) and \( B \) are orbiting around
the earth in orbits of ratio \( R \) and \( 4 R \)
respectively. The ratio of their areal
velocities is
A . 1: 2
B. 1: 4
\( c \cdot 1: 8 \)
D. 1: 16


Presence of electrons is shown by three
dimensional shape of orbit with:
A. high probability
B. low probability
c. no probability
D. slow ratio


Which of the following is an example of
exothermic reaction?
\( \mathbf{A} \cdot H_{2}(g)+C l_{2}(g) \rightarrow 2 H C l(g) ; \Delta H=-184.6 k J \)
B. \( N_{2}(g)+O_{2}(g) \rightarrow 2 N O(g) ; \Delta H=+180.8 k J \)
\( \mathbf{c} \cdot C(\text {graphite})+H_{2} O(g) \rightarrow C O(g)+H_{2}(g) ; \Delta H= \)
\( +1314 k J \)
D. \( C(\text { graphite })+2 S(s) \rightarrow C S_{2}(l) ; \Delta H=+91.9 k J \)


Determine the loss in kinetic energy of the system as whole as a result of the
collision.
\( ^{\mathbf{A}} \cdot \frac{1}{6} m v^{2} \)
в. \( \frac{1}{7}^{m v^{2}} \)
\( \mathrm{c} \cdot m v^{2} \)
D. \( \frac{m v^{2}}{5} \)


Let \( a, b, c \in R \) be such that \( a+b+ \)
\( \boldsymbol{c}>\mathbf{0} \) and \( \boldsymbol{a b c}=\mathbf{2 .} \) Let \( \boldsymbol{A}=\left[\begin{array}{lll}\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} \\ \boldsymbol{b} & \boldsymbol{c} & \boldsymbol{a} \\ \boldsymbol{c} & \boldsymbol{a} & \boldsymbol{b}\end{array}\right] \)
If \( A^{2}=I, \) then value of \( a^{3}+b^{3}+c^{3} \) is
\( A \cdot 7 \)
B.
\( c \cdot 0 \)
\( D \)


A ray of light is incident on a prism A \( B C \) of refractive index \( \sqrt{3} \) as shown in
figure.
(a) Find the angle of incidence for which
the deviation of light ray by the prism
A \( B C \) is minimum.
(b) By what angle the second prism must be rotated, so that the final ray
suffer net minimum deviation.
A \( \cdot 30^{\circ}, 60^{\circ} \)
B . \( 60^{\circ}, 30^{\circ} \)
\( \mathbf{c} \cdot 60^{\circ}, 60^{\circ} \)
D. None of these


toppr
Q Type your question
rhis question has multiple correct options
\( A \)
B.
\( c \)
\( D \)


The construction of \( \Delta E F G \) when
\( F G=3 c m \) and \( m \angle G=60^{\circ} \) is possible
when difference of \( E F \) and \( E G \) is equal
to:
A . \( 3.2 \mathrm{cm} \)
B. \( 3.1 \mathrm{cm} \)
\( \mathrm{c} .3 \mathrm{cm} \)
D. 2.8 \( c m \)


The acid which contains a peroxo
linkage is :
A. Sulphurous acid.
B. Pyrosulphuric acid
c. Dithionic acid.
D. Caro's acid


Considering their electrons affinities, it is possible for alkali metals to form an
anion like \( \mathrm{M}^{-} \) where M represents an
alkali metal. If true enter 1 , else enter 0 .


Differentiate the following w.r.t. \( x: \) \( e^{\sin ^{-1} x} \)


Determination of the chlorine is
possible without preparing sodium extract in
\( A \)
\( B \)
с. \( C H_{2}=C H C H_{2} C \)
\( C \)
D. All of thes


Which scientist established the
elementary character of hydrogen?
A. Robert Boyle
B. Henry Cavendish
c. Lavoiser
D. scheele


A complex whose IUPAC name is not
correctly written is :
\( \mathbf{A} \cdot F e\left(\sigma-C_{5} H_{5}\right)_{2}, \) Bis \( \left(\eta^{5} \text { -cyclopentadienyl liron }(0)\right. \)
B. \( C r\left(C_{6} H_{6}\right)_{2}, \) Bis \( \left(\eta^{5} \) -benzene)chromium(o) \right.
\( \mathbf{c} \cdot\left[C o C l_{2}\left(H_{2} O\right)_{4}\right] C l .2 H_{2} O \)
Tetraaquadichlorocobalt(III)chloride-2-water
D. \( \left[Z n(N C S)_{4}\right]^{2-} \), Tetrathiocyanato-N-zincate(II)ion


Uniform Circular Motion refers to a
motion of an object in a circle at a
constant
A. Velocity
B. Speed
c. Both
D. None


How many obligate categories or ranks
are found in a hierarchical level
of classification?


For any four points \( P, Q, R, S \) \( |\overrightarrow{P Q} \times \overrightarrow{\boldsymbol{R}} \boldsymbol{S}-\overrightarrow{\boldsymbol{Q} \boldsymbol{R}} \times \overrightarrow{\boldsymbol{P}} \boldsymbol{S}+\overrightarrow{\boldsymbol{R}} \boldsymbol{P} \times \overrightarrow{\boldsymbol{Q}} \boldsymbol{S}| \) is
equal to 4 times the area of the triangle.
A. PQR
B. QRS
c. PRS
D. PQS


Find the value of the unknown exterior \( x \)
in the following diagrams.


Give one disadvantage of using a solar cell.


The correct increasing order of 10 Dq. value for the given chromium complexes is :
(1) \( \left[\boldsymbol{C r}(\boldsymbol{e n})_{3}\right]^{3+} \)
(2)\( \left[\boldsymbol{C r}(\boldsymbol{o x})_{3}\right]^{3-} \)
(3) \( \left[\boldsymbol{C r} \boldsymbol{F}_{\mathbf{6}}\right]^{3-} \)
(4) \( \left[\boldsymbol{C r}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right]^{3+} \)
A. \( 4<3<1<2 \)
в. \( 3<2<4<1 \)
c. \( 4<3<2<1 \)
D. \( 3<4<1<2 \)


Modulus of rigidity of ideal liquids is
A . infinity
B. zero
c. unity
D. some finite small non-zero constant value


Height of a person depends on their
A. Genes
B. Blood
c. Habits
D. None of the above


The planet which shows retrograde motion is
A. Venus
B. Mercury
c. Jupiter
D. Mars


To prevent soil erosion, a farmer plants a hedge across a field. This method
works because
A. The hedge prevents the soil from direct impact of rainwater.
B. The roots of plants prevent the soil erosion.
c. The hedge absorbs minerals from the soil, which makes it most compact.
D. None of the above


Evaluate:
\( (a-3 b)^{2}-4(a-3 b)-21 \)


The battery connections required to forward bias a pnjunction are
A. tve terminal to p and -ve terminal to \( n \)
B. -ve terminal to p and +ve terminal to n
c. - -ve terminal to p and-ve terminal to
D. None of these


\( \beta \) sulphur is stable between:
A \( \cdot 114^{\circ} \mathrm{C} \) to \( 160^{\circ} \mathrm{C} \)
B . \( 95.6^{\circ} \mathrm{C} \) to \( 119^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 160^{\circ} C \) to \( 230^{\circ} C \)
D. \( 112.8^{\circ} \mathrm{C} \) to \( 140^{\circ} \mathrm{C} \)


The nucleus of tritium consist of
A. 1 proton + 1 neutron
B. 1 proton + 3 neutron
c. 1 proton \( + \) zero neutrons
D. 1 proton +2 neutrons


The circuit is equivalent to
A. NOR gate
B. AND gate
c. NAND gate
D. or gate


The name of largest endocrine gland of
our body is


If \( y=\frac{x+c}{1+x^{2}}, \) then the value of \( x y \)
where \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\mathbf{0} \) is
A \( \cdot \frac{1}{2} \)
B. \( \frac{3}{4} \)
\( c \cdot \frac{5}{4} \)
D. None of these


The points (7,2) and (-1,0) lie on a line
A. \( 7 y=3 x-7 \)
B. \( 4 y=x+1 \)
c. \( y=7 x+7 \)
D. \( x=4 y+1 \)


An object is held \( 20 c m \) away from a
converging lens of focal length \( 10 \mathrm{cm} \) Find the position of the image formed.


The molecular action of ultra violet light is mainly reflected through
A. Photodynamic action
B. Destruction of hydrogen bonds between DNA strands
c. Formation of pyridine
D. Destruction of ester bonds


Find, if possible, \( (\boldsymbol{f} \circ \boldsymbol{g})(\boldsymbol{0}) \)
\( f(x)=\frac{1}{(x+1)}, g(x)=\frac{1}{(x-1)} \)


Larger the slope of a velocity-time graph
A. lower is the acceleration
B. higher is the acceleration
C . lower the displacement
D. higher the displacement


Which of the following shows highest oxidation number in combined state?
A. \( O s \)
в. \( R u \)
c. Both (1) \& (2)
D. None


A solution of sucrose (molar mass \( =342 \)
\( \left.g m o l^{-1}\right) \) has been prepared by dissolving 68.5 g of sucrose in 1000 g of water. The freezing point of the solution obtained will be:
\( \left[\mathrm{K}_{f} \text { for water }=1.86 \mathrm{K} \mathrm{kg} \mathrm{mol}^{-1}\right] \)
A . - \( 0.372 \mathrm{c} \)
B. 0.520C
c. \( +0.372 c \)
D. 0.570C


Which of the following is used in the vulcanization
of rubber?
A. SF \( _{6} \)
B. \( \mathrm{SF}_{4} \)
c. \( \mathrm{SF}_{2} \)
D. \( \mathrm{S}_{2} \mathrm{Cl}_{2} \)


Lovish has 6 hours to spend in Ha Ha Tonka State Park. He plans to drive
around the park at an average speed of 20 miles per hour, looking for a good trail to hike. Once he finds a trial he
likes, he will spend the remainder of his time hiking it. He hopes to travel more than 60 miles total while in the park. If
he hikes at an average speed of 1.5 miles per hour, which of the following systems of inequalities can be solved for the number of hours Lovish sends
driving d, and the number of hours he spends hiking, h while he is at the park?
A. \( 1.5 h+20 d>60, h+d \leq 6 \)
B. \( 1.5 h+20 d>60, h+d \geq 6 \)
\( c \cdot 1.5 h+20 d<0, h+d \geq 360 \)
0
D. \( 20 h+1.5 d>6, h+d \leq 60 \)


Chloroethane is reacted with alcoholic
potassium hydroxide. The product formed is :
\( A \cdot C_{2} H_{6} O \)
в. \( C_{2} H_{6} \)
\( \mathbf{c} \cdot C_{2} H_{4} \)
D. \( C_{2} H_{4} O \)


Bleaching powder dissolves in water to
form:
A \( \cdot C a(O H)_{2}, C l_{2} \)
B. \( \mathrm{Ca}^{+2}, \mathrm{Cl}^{-}, \mathrm{ClO}_{2}^{-} \)
c. \( \mathrm{Ca}^{2+}, \mathrm{Cl}^{-}, \mathrm{ClO}_{3} \)
D. \( \mathrm{Ca}^{2+}, \mathrm{C} 1^{-}, \mathrm{ClO}_{4}^{-} \)


Let \( f \) be differentiable for all \( x \). If
\( \boldsymbol{f}(1)=-2 \) and \( \boldsymbol{f}^{\prime}(\boldsymbol{x}) \geq 2 \) for \( \boldsymbol{x} \in[\mathbf{1}, \boldsymbol{6}] \)
This question has multiple correct options
A. \( f(6)<8 \)
B. \( f(6) \geq 8 \)
D. \( f(6) \leq 5 \)


A ball of mass M thrown upward if the air resistance is considered constant
(R) What will be times of Ascent and
decent. Give Mathematical proof.


How much force should be applied on an
area of \( 10^{-4} m^{2} \) to get a pressure of
\( \mathbf{1 5} \boldsymbol{P} \boldsymbol{a} ? \)


In the given arrangement the maximum
value of \( F \) for which there is no relative
motion between the blocks
A \( \cdot \mu m_{1} \S \)
В. \( \mu\left(m_{1}+m_{2}\right) \) в
\( c \)
\[
\mu m_{1} g\left(\frac{m_{1}}{m_{2}}+1\right)
\]
D. zero


Show that \( 2 \tan ^{-1} x+\sin ^{-1} \frac{2 x}{1+x^{2}} \) is
constant for \( x \geq 1 . \) Also find that
constant.


Assertion(A): In the dissociation of
\( P C l_{5} \) at constant pressure and
temperature addition of helium at equilibrum increases the dissociation
of \( \boldsymbol{P} \boldsymbol{C l}_{5} \)
Reason(R): Helium removes \( C l_{2} \) from
the field of action.
A. Both Assertion and Reason are true and Reason is correct explanation of Assertion.
B. Both Assertion and Reason are true but Reason is not correct explanation of Assertion
c. Assertion is true but Reason is false.
D. Both Assertion and Reason are false


Assertion
Drift velocity of electrons is
independent of time.
Reason
Electrons are accelerated in the
presence of electric field.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


\( \boldsymbol{y}(\boldsymbol{x}, \boldsymbol{t})=\mathbf{0 . 8} /\left[(\boldsymbol{4} \boldsymbol{x}+\boldsymbol{5} \boldsymbol{t})^{2}+\mathbf{5}\right] \)
represents a moving pulse, where \( x \) and
\( y \) are in meter and \( t \) in second. Then
This question has multiple correct options
A. pulse is moving in \( +x \) direction
B. in \( 2 s \) it will travel a distance of 2.5 m
c. its maximum displacement is 0.16 m
D. it is symmetric pulse


Which of the following statements are
correct for the \( \boldsymbol{S O}_{\boldsymbol{4}}^{\boldsymbol{2}-} \) ion?
This question has multiple correct options
A. It is tetrahedral.
B. All the \( S-O \) bond length are equal, and shorter than
expected.
C. It contains four \( \sigma \) -bonds between the \( S \) and the \( O \) atoms, two \( \pi \) -bonds delocalized over the \( S \) and the four \( O \) atoms, and all the \( S-O \) bonds have a bond
order of 1.5
D. Oxidation state of sulphur is +6 and all oxygen in 2


The physical quantity which has the
dimensional formula \( \left[M T^{-3}\right] \) is:
A. Surface tension
c. Solar constant
D. compressibility


Determine the current in \( 2 \Omega \) resistor
\( A \cdot 1 A \)
B. 1.5
\( c \cdot 0.9 A \)
D. 0.6


A vector is represented by \( 3 \bar{i}+\bar{j}+2 \bar{k} \)
It's length in \( x y \) plane is:
\( A \cdot 2 \)
B. \( \sqrt{14} \)
c. \( \sqrt{10} \)
D. \( \sqrt{5} \)


Which of the following will not enhance nutritional value of food?
A. Minerals
B. Artificial sweeteners
c. Vitamins
D. Amino acids


Glucose, gatactose and fructose all
have the same molecular size and
composition and their absorption through the mucosal cells takes place
A. At the same rate
B. Glucose is absorbed most rapidly
c. Fructose is absorbed most rapidly
D. Galactose is absorbed most rapidly


Which among the following is nonlinear in shape?
\( \mathbf{A} \cdot H C N \)
в. \( B e C l_{2} \)
\( c \cdot I_{3}^{+} \)
D. \( I_{3} \)


When \( K M n O_{4} \) reacts with \( H_{2} O_{2} \) in acidic medium then which of the
following is formed?
\( \mathbf{A} \cdot M n^{+2} \)
B. \( M n^{+7} \)
c. \( M n O_{2} \)
D. \( M n_{2} O_{3} \)


Find \( \int\left(x^{2}+1\right) d x \)


Sita and Geta are friends, what is the
probability that both will have different birthdays (ignoring a leap year)
A \( \cdot \frac{1}{365} \)
в. \( \frac{1}{364} \)
c. \( \frac{364}{365} \)
D. None of these


A scientist performs an experiment and takes 100 readings. He repeats the same experiment and now takes 400 readings. By doing so :
A. the probable error remains the same
B. the probable error is halvedd
c. the probable error is doubled
D. the probable error reduces by a factor of \( 1 / 4 \)


'Red tides' are produced by
A. Red algae
B. Dinoflagellates
c. Diatoms
D. Brown algae


Find and correct errors of the following mathematical expressions:
\( \frac{3 x}{3 x+2}=\frac{1}{2} \)


Which of the following will not slow deflection from the path on passing through an electric field? Proton, cathode rays, electron, neutron


A transformer has 500 turns in its
primary and 1000 turns in its secondary winding.The primary voltage is \( 200 \mathrm{V} \) and the load in the secondary is 100
ohm.Calculate the current in the
primary,assuming it to be a ideal transformer.
A . 25 A
B. 45 A
\( c \cdot 8 A \)
D. 22 A


How is a speed skater able to glide across the ice? How can the skater
increase friction between the ice and
the skates? What effect does
an increase in friction have on the
skater's speed?


The electric field in a region is radially outward with magnitude \( \mathrm{E}=2 \mathrm{r} . \) The charge contained in a sphere of radius a
\( =2 \mathrm{m} \) centred at the origin is \( 4 x \pi \epsilon_{0} . \) Find
the value of \( x \)


Choose the correct answers from the
alternatives given During electron transport each molecule of NADH produces how many molecules of ATP?
\( A \)
B. 2
\( c \cdot 3 \)
D. 4


People can spin a ball on their finger
This is due to
A. the centre of gravity of the ball is on his finger.
B. the resultant force is passing through the centre of gravity of the ball.
c. the resultant force is passing through the centre of the ball
D. both A and B


Friction reduces efficiency of machines
due to:
A. Production of heat
B. Wearing out of moving parts
C. Increase in energy consumption
D. All of the above


For the hydrides of nitrogen family going down the group:
A. stability decreases.
B. reducing activity increases.
c. bond angle HMH decreases.
D. All the above variations followed


Reaction of acids with alcohols is also
known as:
A. esterification
B. saponification
c. alkalisation
D. none of these


The gas emitted by supersonic jet planes that slowly depletes the concentration of ozone layer is
A. \( C O \)
B. \( N O \)
\( c \cdot s O_{2} \)
D. \( O_{2} \)
E . \( H F \)


High BOD indicates
A. Highly polluted water
B. Less pollution in water
c. Less sewage
D. Less microorganisms


A hydrated colorless solid (A) is water
soluble and finds use in medicine as a
purgative. When a solution of (A) is treated with ammonium phosphate, a white precipitate is formed. (A) gives a pink mass in cobalt nitrate cavity test What is \( (A) ? \)
A \( . F e S O_{4} .7 H_{2} \)
в. \( N a_{2} S O_{4} .10 H_{2} \)
c. \( M g S O_{4} .7 H_{2} O \)
D. \( \operatorname{CaSO}_{4} .2 \mathrm{H}_{2} \)


Find the area enclosed between the
curves \( \boldsymbol{y}=\boldsymbol{x} \) and \( \boldsymbol{y}=\boldsymbol{x}^{2} \) from \( \boldsymbol{x}=\mathbf{0} \)
and \( \boldsymbol{x}=\mathbf{1} \)


From thee top of a building \( 60 \mathrm{m} \) high the angle of depression of the top and the bottom of a tower are observed to be
\( 30^{\circ} \) and \( 60^{\circ} . \) Find the height of the
tower
A. \( 60 \mathrm{m} \)
B. \( 40 \mathrm{m} \)
c. \( 80 \mathrm{m} \)
D. \( 70 \mathrm{m} \)


Which of the following components is a part of the pectoral girdle?
A. Acetabulum
B. Glenoid cavity
c. llium
D. Sternum


When \( 1.20 g \) of sulphur is melted with \( 15.00 g \) of naphthalene, the solution
freezes at \( 77.2^{\circ} \mathrm{C} \).. What is the molar
mass of this form of sulphur?
Data for Naphthalene:
Melting point, \( \mathrm{M} . \mathrm{P}=80^{\circ} \mathrm{C} \)
Freezing point depression constant, \( k_{f}=6.80^{\circ} \mathrm{C} \boldsymbol{m}^{-1} \)
A . \( 180 g \) mol \( ^{-1} \)
B. \( 194 g \) mol \( ^{-1} \)
c. \( 260 g \) mol \( ^{-1} \)
D. \( 450 \mathrm{g} \) mol \( ^{-1} \)


In Balanoglossus
A. Sexes are united and fertilization is external
B. Sexes are separate and fertilization is external
C. Sexes are separate and fertilization is internal
D. Sexes are united and fertilization is internal


Two batteries of different emf and
internal resistances connected in series
with each other and with an external
load resistor. The current is 3.0 A. When
the polarity of one battery is reversed, the current becomes 1.0 A. The ratio of
the emf of the two batteries is :
A .2 .5: 1 \)
в. 2: 1
c. 3: 2
D. 1: 1


If \( \boldsymbol{A}=\left|\begin{array}{ll}\mathbf{0} & \mathbf{0} \\ \mathbf{1} & \mathbf{1}\end{array}\right| \) then the value of \( \boldsymbol{A}+ \)
\( \boldsymbol{A}^{2}+\boldsymbol{A}^{3}+\ldots+\boldsymbol{A}^{n}=? \)
\( A \cdot A \)
B. nA
c. \( (n+1) A \)
\( D \)


Two second wave travel out from a
common point have frequencies \( 30 \mathrm{Hz} \)
and \( 40 \mathrm{Hz} \) respectively where phase difference between the after 0.8 second.
\( ? \)
A . zero
B. \( \frac{\pi}{4} \)
c. \( \frac{5 \pi}{2} \)
D. \( 5 \pi \)


If a mark of size \( 0.2 \mathrm{cm} \) on the surface
of a glass sphere of diameter \( 10 \mathrm{cm} \) and
\( \mu=1.5 \) is viewed through the
diametrically opposite point, where will the image be seen and of what size?


Reduce the equation \( 2 x+3 y-4=0 \)
to slope-intercept form and find its slope and \( y- \) intercept


Which of the following properties of light can be observed in the working of a periscope? This question has multiple correct options
A. Light does not travel in a straight line
B. Light reflects from a mirror
c. Light travels in a straight line
D. Light refracts through a mirror


Which one is mismatched?
A. Hydra vulgaris \( \rightarrow \) Sea water
B. Hydra gangetic \( \rightarrow \) Fresh water
c. obelia \( \rightarrow \) Sea water
D. Physalia \( \rightarrow \) Sea water


Arrangement of the following areas between the curves is descending order:
\( \mathbf{A}: \boldsymbol{y}^{2}=\mathbf{4} \boldsymbol{x}, \boldsymbol{x}^{2}=\mathbf{4} \boldsymbol{y} \)
\( \mathbf{B} \cdot \boldsymbol{y}=\boldsymbol{x}, \boldsymbol{y}=\boldsymbol{x}^{3} \)
\( \mathbf{C} \cdot \boldsymbol{y}^{2}=\mathbf{8} \boldsymbol{x}, \boldsymbol{y}=\mathbf{2} \boldsymbol{x} \)
\( \mathbf{D} \cdot \boldsymbol{y}=\sqrt{\boldsymbol{x}}, \boldsymbol{y}=\boldsymbol{x}^{2} \)
\( A \cdot A, B, C, D \)
B. A,C,B,D
c. \( \mathrm{D}, \mathrm{B}, \mathrm{C}, \mathrm{A} \)
D. D,C,B,A


Portion AB of the wedge shown in figure is rough and BC is smooth, A solid cylinder rolls without slipping from \( A \) to
B. The ratio of transnational kinetic
energy to rotational kinetic energy. when the cylinder reaches point \( C \) is
\( A \cdot 3 / 4 \)
B.
\( c \cdot 7 / 5 \)
\( 0.8 / 3 \)


Resolving limit of a healthy eye is


The correct statement from the
following is:
A. Light exhibits particle nature in propagation and wave nature in mutual interaction with matter.
B. Light exhibits both wave nature and particle nature in mutual interaction with matter.
C. Light exhibits both wave and particle nature in propagation.
D. Light exhibits wave nature in propagation and particle nature in mutual interaction with matter


Calculate area enclosed by a circle of
diameter \( 1.06 ~ m \) to correct number of
significant figures.
A. \( 0.883 m^{2} \)
В. \( 0.0883 m^{2} \)
с. \( 0.88333 m^{2} \)
D. \( 0.8830 m^{2} \)


Plasmodesmata take part in
A. Synchronous mitotic divisions
B. Cytoplasmic streaming
C. Movement of substances between cells
D. Locomotion in unicellular organisms


The reactance at a circuit Is zero. it Is
possible mat me circuit contains
This question has multiple correct options
\( A . \) an inductor and a capacitor
B. an inductor but no capacitor
C. so a capacitor but no inductor
D. neitherr an inductor nor a capacitor


A two litre vessel contains 0.48 mole of
\( C O_{2}, 0.48 \) mole of \( H_{2}, 0.96 \) mole of \( C O \) at equilibrium
\[
\boldsymbol{C O}_{2}(\boldsymbol{g})+\boldsymbol{H}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g})+
\]
\( \boldsymbol{C O}(\boldsymbol{g}) \)
How many \( g m \) (only integer part) of \( \boldsymbol{H}_{2} \) must be added to bring the concentration of \( C O \) to \( 0.6 M ? \)


Assertion
10 decades make a century.
Reason
century makes 100 years and 1 decade
make 10 years.
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


Five identical spaceships take off from Planet \( X \), and each passes by Planet \( Y \)
at a constant speed on its way to Planet
\( Z \). A science station on Planet \( Y \)
observes them passing by. At which of the following speeds spaceship would be observed to have the greatest length?
A \( \cdot 6 \times 10^{7} m / S \)
В. \( 9 \times 10^{7} m / S \)
c. \( 1 \times 10^{8} m / S \)
D. \( 1.5 \times 10^{8} \mathrm{m} / \mathrm{S} \)
E . \( 2 \times 10^{8} m / S \)


The displacement \( y \) of a particle, if \( \operatorname{given} \operatorname{by} y=4 \cos ^{2}\left(\frac{t}{2}\right) \sin (1000 t) \)
This expression may be considered to be a result of the superposition of how many simple harmonic motions?
\( \mathbf{A} \cdot \mathbf{4} \)
B. 3
\( c \cdot 2 \)
D. 5
E. 6


If matrix \( A \) is an circulant matrix whose
elements of first row are \( \mathbf{a}, \mathbf{b}, \mathbf{c} \) all \( >\mathbf{0} \)
such that abc \( =\mathbf{1} \)
and \( A^{T} A=I \) then \( a^{3}+b^{3}+c^{3} \) equals
\( A \cdot 0 \)
B. 3
\( c .1 \)
D. 4


Find the mode when median is 12 and
mean is 16 of a data.


The cleaning action of a soap is due to soap lather, which reduced the interfacial tension and solubilises the
oily dirt into the water by emulsification.
A. True
B. False


Two stones are thrown up
simultaneously from the edge of a cliff \( 200 \mathrm{m} \) high with initial speeds of
\( 15 m s^{-1} \) and \( 30 m s^{-1} . \) Verify that the
graph shown in Fig.correctly represents the time variation of the relative
position of the second stone with
respect to the first. Neglect air
resistance and assume that the stones
do not rebound after hitting the ground.
Take \( \boldsymbol{g}=10 m s^{-2} . \) Give the equations
for the linear and curved parts of the
plot


A galvanometer is an instrument
capable to measure
A. small voltage
B. small current
\( c \). both (a) and (b)
D. none of these


The solution of
\( \frac{3 \sin \theta-\sin 3 \theta}{1+\cos \theta}+\frac{3 \cos \theta+\cos 3 \theta}{1-\sin \theta}= \)
\( 4 \sqrt{2} \cos \left(\theta+\frac{\pi}{4}\right) \)
\( \mathbf{A} \cdot n \pi \)
В . \( n \pi+\frac{\pi}{12} \)
c. \( n \pi \pm \frac{\pi}{2} \)
D. \( 2 n \pi \)


The distance between the wires of
electric mains is \( 12 \mathrm{cm} . \) These wires
exprience 4 mgwt per unit length. The value of current flowing in each wire will be if they carry current in same direction
A . \( 4.85 \mathrm{A} \)
B. zero
\( \mathbf{c} \cdot 4.85 \times 10^{-2} A \)
D. \( 85 \times 10^{-4} A \)


The diameter of a wire as measured by
a screw gauge was found to be \( 1.002 \mathrm{cm}, 1.004 \mathrm{cm} \) and \( 1.006 \mathrm{cm} . \) The
absolute error in the third reading is:
A \( .0 .002 \mathrm{cm} \)
B. \( 0.004 \mathrm{cm} \)
c. zero
D. \( 1.002 \mathrm{cm} \)


The condition that the chord \( x \cos \alpha+ \)
\( \boldsymbol{y} \sin \boldsymbol{\alpha}-\boldsymbol{p}=\mathbf{0} \) of \( \boldsymbol{x}^{2}+\boldsymbol{y}^{2}-\boldsymbol{a}^{2}=\mathbf{0} \) may
subtend a right angle at the centre of the circle is
A \( \cdot a^{2}=2 p^{2} \)
B \( \cdot p^{2}=2 a^{2} \)
c. \( a=2 p \)
D. \( p=2 a \)


A piece of ice of mass \( 40 g \) is dropped
into \( 200 g \) of water at \( 50^{\circ} \mathrm{C} \). Calculate the final temperature of the water after all the ice has melted. Specific heat
capacity of water \( =4200 J k g^{-1} K^{-1} \)
Specific latent heat of fusion of ice \( = \)
\( 336 \times 10^{3} J k g^{-1} \)


A body is dropped from a height of \( 80 \mathrm{m} \) on to a horizontal floor and impings
repeatedly. If it stops in 6 seconds, the
total distance travelled by it before stops is (nearly). \( \left(\boldsymbol{g}=\mathbf{1 0 m} \boldsymbol{s}^{-2}\right) \)
\( \mathbf{A} \cdot 86.6 \mathrm{m} \)
B. \( 95 \mathrm{m} \)
c. \( 100 \mathrm{m} \)
D. \( 110 \mathrm{m} \)


Amit buys few grams of gold at the poles as per the instruction of one of his friends. He hands over the same when
he meets him at the equator. Will the friend agree with the weight of gold bought? If not, why? [Hint: The value of g
is greater at the poles than at the equator.


How many molecules of water would be consumed to support one Calvin cycle?
A. one
B. Two
c. Four
D. six


The major product formed when \( 2- \)
butene is reacted with \( O_{3} \) followed by
treatment with \( Z n / H_{2} O \) is
A. \( C H_{3} \) СООН
в. \( C H_{3} C H O \)
c. \( C H_{3} C H_{2} O H \)
D. \( C H_{2}=C H_{2} \)


0.01 mole of \( N a_{2} C_{2} O_{4} \) dissolve in
alkaline solution. This solution is
titrated with \( \mathrm{V} \mathrm{ml} \) 0.1 \( \boldsymbol{M} \boldsymbol{K} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4} \)
solution. Find out \( V \)
A .200
в. \( \frac{200}{3} \)
c. 40
D. \( \frac{100}{3} \)


What happens to the water table of a place having droughts for a long period
of time?
A. It gets higher because of continuous evaporation and flow
B. It gets lower because of continuous evaporation and flow
c. It gets replenished continuously
D. can't say anything


Prove if \( 21\left(a^{2}+b^{2}+c^{2}\right)=(a+2 a b+ \)
\( 4 c)^{2} \) then \( a, b, c \) are in G.P.


By which factor the magnetic field produced by a wire at distance \( 2 \mathrm{cm} \) from the wire than at \( 4 \mathrm{cm} \) from the wire
is stronger if wire length is \( 2 \mathrm{m} \) and carries a 10 -amp current :
A .2
B. \( 2 \sqrt{2} \)
\( c \cdot 4 \)
D. \( 4 \sqrt{2} \)
\( E \)


The value of \( c \) in Lagrange's theorem for
the function in the interval [-1,1] is
\[
f(x)=\left\{\begin{array}{cl}
x \cos \left(\frac{1}{x}\right), & x \neq 0 \\
0, & x=0
\end{array}\right.
\]
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( \frac{1}{2} \)
\( c \)
\[
-\frac{1}{2}
\]
D. Non existent in the interva


Add the following \( \mathbf{2} p^{2} \boldsymbol{q}^{2}-\mathbf{3} \boldsymbol{p} \boldsymbol{q}+\boldsymbol{4}=\mathbf{0}, \mathbf{5}+\mathbf{7} \boldsymbol{p} \boldsymbol{q} \)
\( 3 p^{2} q^{2}=0 \)


If \( \frac{\boldsymbol{S}-\boldsymbol{8}}{\boldsymbol{3}}=\frac{\boldsymbol{S}-\boldsymbol{3}}{\boldsymbol{2}}, \) then the value of \( \boldsymbol{S} \) is
\( \mathbf{A} \cdot \mathbf{5} \)
B. -7
\( c \cdot 7 \)
D. None of these


The \( K_{a} \) of a weak monobasic is \( 1 \times \)
\( 10^{-5} . \) The percentage of ionsation in a
decimolar acid solution is :
A . \( 0 . \)
B. 10
c. 0.01
D.


The aqueous solution of sodium
cyanide is basic in nature. This is due to the hydrolysis of:
A. sodium ions
B. cyanide ions
c. cyanide ions and sodium ions
D. isocyanide ions


Describe the structure of the heart of a
man. Draw a neat labelled diagram of it.


A particle is revolving in a circular path
of radius \( 200 m \) at a speed of \( 20 m / s . \) lts speed is increasing at the rate of \( \sqrt{5} m / s^{2} . \) Its acceleration is
\( \mathbf{A} \cdot 2 m / s^{2} \)
В. \( \sqrt{7} m / s^{2} \)
c. \( 3 m / s^{2} \)
D. \( \sqrt{5} m / s^{2} \)


\( \boldsymbol{Z} \boldsymbol{n}(\boldsymbol{s})\left|\boldsymbol{Z} \boldsymbol{n} \boldsymbol{C l}_{2}(\boldsymbol{a} \boldsymbol{q}) \| \boldsymbol{C l}^{-}(\boldsymbol{a} \boldsymbol{q})\right| \boldsymbol{C l}_{2}(\boldsymbol{g}) \mid \boldsymbol{C} \)
In the electrochemical cell described by the cell diagram above, what reaction occurs at the anode?
A. \( Z n \rightarrow Z n^{2+}+2 e \)
B. \( Z n^{2+}+2 e \rightarrow Z n \)
c. \( C l_{2}+2 e \rightarrow 2 C l \)
D. \( 2 C^{-} \rightarrow C l_{2}+2 e \)
E \( . Z n+C l_{2} \rightarrow Z n C l_{2} \)


In a gold leaf electroscope, its stem is
made up of:
A. wood
B. brass
c. glass
D. ebonite


Divide \( \left(9 x^{2}-24 x+16\right) \) by \( (3 x-4) \)
A \( .3 x-4 \)
B. \( 4 x-3 \)
c. \( (3 x-4)(3 x-4) \)
D. \( 9 x^{2}-16 \)


Expand \( \left[\boldsymbol{x}-\frac{\boldsymbol{2}}{\boldsymbol{3}} \boldsymbol{y}\right]^{\boldsymbol{3}} \)


Solve
\( \lim _{x \rightarrow 3} \frac{x^{3}-7 x^{2}+15 x-9}{x^{4}-5 x^{3}+27 x-27} \)


Separation of impurities from the extracted metals is generally done by
A. distillation
B. sedimentation
c. electrolysis
D. none of the above


Given ABCD is a parallelogram, find the
measure of \( x-2 y+z \) in degrees form
the following figure


(a) In a typical nuclear reaction e.g
\( _{1}^{2} \boldsymbol{H}+_{1}^{2} \boldsymbol{H} \rightarrow_{2}^{3} \boldsymbol{H}+_{0}^{1} \boldsymbol{n}+\mathbf{3} .2 \mathbf{7} M e \boldsymbol{V} \)
although number of nucleons is conserved, yet energy is released, How? Explain.
(b) Show that nuclear density in a given nucleus is independent of mass number A.


A proton is identical to:
A. the nucleus of helium
B. the nucleus of a hydrogen atom
C . a molecule of a hydrogen
D. an atom of hydrogen


Theorem: For any \( \boldsymbol{x} \in \boldsymbol{R} \quad \sinh ^{-1} \boldsymbol{x}= \)
\( \log _{e}(x+\sqrt{x^{2}+1}) \)


NaOH is formed according to the following reaction:
\( 2 N a+\frac{1}{2} O_{2} \longrightarrow N a O_{2} \)
\( N a_{2} O+H_{2} O \longrightarrow 2 N a O H \)
To make 4 g \( N a O H, N a \) required is :
A . 4.6 g
в. 4.0 g
c. 2.3 g
D. 0.23 g


Given the hypothetical reaction \( 2 A+ \) \( \boldsymbol{B} \rightleftharpoons \boldsymbol{C}+\mathbf{3} \boldsymbol{D}, \) the equilibrium constant
for this reaction is:
I. Directly proportional to the
concentration of \( D^{3} \)
II. Inversely proportional to the concentration of \( \boldsymbol{A} \)
III. inversely proportional to the concentration of \( C \)
A. I, II, and III
B. I and II only
c. ॥ and III only
D. I only


\( \mathbf{P} \) is the midpoint of the part of the line \( 3 x+y-2=0 \) intercepted between the
axes. Then the image of \( \mathbf{P} \) in origin is
\( \mathbf{A} \cdot\left(-1,-\frac{1}{3}\right) \)
B \( \cdot\left(-\frac{1}{3},-4\right) \)
\( ^{c} \cdot\left(-\frac{1}{3},-1\right) \)
D. (-2,-3)


Name the two organic compounds which have the same molecular formula
\( C_{2} H_{6} O . \) Will they react with \( P C l_{5} ? \) If
they react, what are the products formed?


What is the electric potential at the
center of the triangle in figure


Find the static friction force acting on
the cone \( A, \) if \( \omega=1.0 \) rad/s.
\( \mathbf{A} \cdot F_{f r}=12 N \)
\( \mathbf{B} \cdot F_{f r}=6 N \)
\( \mathbf{C} \cdot F_{f r}=18 N \)
\( \mathbf{D} \cdot F_{f r}=3 N \)


(a) Why are the connections between
the resistors in a meter bridge made of
thick copper strips?
(b) Why is it generally preferred to
obtain the balance point in the middle
of the meter bridge wire?
(c) Which material is used for the meter
bridge wire and why?
OR
A resistance of \( \mathrm{R} \Omega \) draws current from
a potentiometer as shown in the figure.
The potentiometer has a total
resistance \( R_{0} \Omega . \) A voltage \( V \) is supplied
to the potentiometer. Derive an
expression for the voltage across \( \mathrm{R} \) when the sliding contact is in the
middle of the potentiometer.


Nascent hydrogen is most powerful reducing agent than ordinary hydrogen
because:
A. nascent hydrogen is in atomic state and atoms are more active than molecules
B. nascent hydrogen is evolved in small bubbles containing the gas under great pressure
C. nascent hydrogen is activated by the energy liberated in the reaction in which it is formed, so the nascent hydrogen becomes more energized and active
D. all of them


A thin lens has a focal length of \( -50 c m \) What kind of lens is it?
A. concave lens
B. Convex lens
c. Concano convex lens
D. None


Following table compares properties of
red phosphorus and white phosphorus.
Which is incorrect comparison?
A. Red- Nontoxic and has polymeric structure; White -
Toxic, waxy discrete tetrahedral \( P_{4} \) molecule
B. Red - Discrete tetrahedral \( P_{4} \) molecule; White -
Polymeric structure
C. Red - High m.p., less reactive; White - Low m.p., more reactive
D. Red - Shows no phosphorescence in air; White - Shows phosphorescence in air


A small amount of \( M n O_{2} \) is added to
\( H_{2} O \) taken in a test tube
(a) Suggest an experiment to identify the gas liberated.
(b) Write the chemical equation of the reaction taking place.
(c) What is the role of \( M n O_{2} \) in this
chemical reaction?


Interpreting a balanced chemical
equation.


If \( \boldsymbol{y}=\boldsymbol{x}^{3} \log \left(\frac{1}{x}\right) . \) Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \)


The radius of circle is \( 9 \mathrm{cm} \). Find the
length of an arc of this circle which cuts
off a chord of length equal to the radius.


Describe the excretory system of human beings.


Determine \( V \) for \( r<R \)
A \( \cdot \frac{\rho}{6 \epsilon_{0}}\left(3 R^{2}\right) \)
В. \( \frac{\rho}{6 \epsilon_{0}}\left(r^{2}\right) \)
c. \( \frac{\rho}{6 \epsilon_{0}}\left(3 R^{2}-r^{2}\right. \)
D. \( \frac{\rho}{6 \epsilon_{0}}\left(3 R^{2}+r^{2}\right) \)


f \( \cos (\alpha+\beta) \sin (\gamma+\theta)=\cos (\alpha- \)
\( \beta) \sin (\gamma-\theta) . \) show that \( \tan \theta= \)
\( \tan \alpha \tan \beta \tan \gamma \)


A particle is executing a two dimensional motion. What is
the minimum number of velocity-time graphs required to study the motion of the particle using graphs?
\( A \)
B. 2
\( c \cdot 3 \)
D. 4


In figure \( 26, \overline{R T} \) is a diameter of the
semicircle. If \( \mathrm{RS}=2 \) and \( \mathrm{ST}=3, \) then the
area of the semicircle is
\( A \cdot \frac{13 \pi}{2} \)
B. \( \frac{13 \pi \pi}{4 \pi} \)
\( \mathbf{c} \cdot \frac{13 \pi}{6} \)
\( \mathbf{D} \cdot \frac{13 \pi}{8} \)
E. cannot be determined from the information given


Which of the following are disadvantages of hydro power plant?
A. Dams can be constructed only in a limited number of places
B. Large areas of agricultural land and human habitation are sacrificed
C. Methane is released contributing to green house effect
D. All of above


A point charge \( +10 \mu C \) is at a distance
5 \( c m \) directly above the centre of a
square of side \( 10 \mathrm{cm} \), as shown in the
figure. What is the magnitude of the electric flux through the square?
A \( \cdot 1.2 \times 10^{5} \mathrm{Nm}^{2} / \mathrm{C} \)
B . \( 1.9 \times 10^{5} \mathrm{Nm}^{2} / \mathrm{C} \)
c. \( 3.2 \times 10^{5} \mathrm{Nm}^{2} / \mathrm{C} \)
D. \( 4.2 \times 10^{5} \mathrm{Nm}^{2} / \mathrm{C} \)


Which of the following is asexual method of reproduction?
A. Division
B. Budding
c. spore formation
D. All of the above


The bond order is not three for:
A \( \cdot N_{2}^{+} \)
B. \( O_{2}^{2+} \)
c. \( N_{2} \)
D. \( N O^{+} \)


The standard deviation of 25 numbers
is \( 40 . \) if each of the numbers is
increased by \( 5, \) then the new standard deviation will be
A . 40
B. 45
c. \( _{40}+\frac{21}{25} \)
D. None of these


A particle starts from a point \( \mathrm{P} \) at \( \mathrm{a} \) distance of A/2 from the mean position
0 and travels towards left as shown in
the figure. If the time period of \( \mathrm{SHM} \) executed about 0 is \( \mathrm{T} \) and amplitude \( \mathrm{A} \)
then the equation of the motion of
particle is:
This question has multiple correct options
A \( \cdot x=A \sin \left(\frac{2 \pi}{T} t+\frac{\pi}{6}\right) \)
B. \( x=A \sin \left(\frac{2 \pi}{T} t+\frac{5 \pi}{6}\right) \)
c. \( x=A \cos \left(\frac{2 \pi}{T} t+\frac{\pi}{6}\right) \)
D. \( x=A \cos \left(\frac{2 \pi}{T} t+\frac{\pi}{3}\right) \)


Compute the heat generating while transferring 96000 coulomb of charge in one hour through a potential difference of 50 V.


Principle of similitude forms the basis
for:
A. comparing two identical equipments
B. designing models so that the result can be converted to prototypes
C. hydraulic designs
D. performing acceptance tests


A non-ecofriendly source of energy is
A. Tidal energy
B. Wind energy
c. Solar energy
D. Nuclear energy


In which of the following cells, use of salt bridge to eliminate liquid junction potential is not necessary?
A \( \cdot P t H_{2}(g)|H C l| A g C l(s) \mid A g \)
B . \( H g\left|H g_{2} C l_{2}(s)\right| K C l \)saturated\( |H C l(a q)| H_{2}(g) P t \)
c. \( Z n\left|Z n S O_{4} \| C u S O_{4}\right| C u \)
D. \( Z n\left|Z n S O_{4}\right| F e^{3+}(a q), F e^{2+}(a q) \mid P t \)


Which of the following ion involved in the above process will show paramagnetism?
A \( \cdot V^{5} \)
B . \( V^{4} \)
\( c \cdot O^{2} \)
D. \( V O_{3}^{-} \)


Which property of colloidal solution is
used to determine then nature of
charge on the particles?
A. Sedimentaion
B. Electrophoresis
c. Dialysis
D. Ultrafiltration


The potential energy of a rocket of mass \( 100 k g \) at height \( 10^{7} m \) from earth surface is \( 4 \times 10^{9} \) Joule. The weight of
the rocket at height \( 10^{9} \) will be
\( \mathbf{A} \cdot 4 \times 10^{-2} N \)
В . \( 4 \times 10^{-3} N \)
c. \( 8 \times 10^{-2} N \)
D. \( 8 \times 10^{-3} N \)


The correct statement about the
following disaccharide is:

This question has multiple correct options
A. ring
(a) is pyranonse with \( \alpha \) - glycosidic link
B. ring
(a) is furanonse with \( \alpha \) - glycosidic link
C . ring
(b) is furanonse with \( \alpha \) - glycosidic link
D. ring
(b) is pyranonse with \( \beta \) - glycosidic link


A mass of \( 5 \mathrm{kg} \) is suspended from a spring of stiffness \( 46 \mathrm{kN} / \mathrm{m} . \) A dashpot is fitted between the mass and the
support with a damping ratio of 0.3 Calculate the damped frequency.
A. \( 14.56 \mathrm{Hz} \)
B. 14.28 Hz
c. \( 14.42 \mathrm{Hz} \)
D. 14.14 нz


Which of the following statements are
correct?
(i) Hydra has a number of cilia around its mouth.
(ii) Frog uses its long, sticky tongue to catch insects
(iii) Mosquito sucks up the blood of animals with its tentacle.
A. (i) and (iii) only
B. (i) only
c. (ii) only
D. (ii) and (iii) only


Figure shows a container having liquid
of variable density.The density of liquid \( \operatorname{varies} \operatorname{as} \rho=\rho_{0}\left(4-\frac{3 h}{h_{0}}\right) \) Here \( h_{0} \) and
\( \rho_{0} \) are constants and h is measured
from bottom of the container. A solid
block of small dimensions whose
density is \( \frac{5}{2} \rho_{0} \) and mass \( m \) is released from bottom of the tank. Prove that the
block will execute simple harmonic
motion. Find the frequency of oscillation
\( ? \)


A radioactive nucleus undergoes a series of decays according to the scheme \( \boldsymbol{A} \stackrel{\boldsymbol{\alpha}}{\longrightarrow} \boldsymbol{A}_{1} \stackrel{\boldsymbol{\beta}}{\longrightarrow} \boldsymbol{A}_{2} \stackrel{\boldsymbol{\alpha}}{\longrightarrow} \boldsymbol{A}_{3} \stackrel{\gamma}{\longrightarrow} \boldsymbol{A}_{4} \)
If the mass number and atomic number
of \( A \) are 180 and \( 72, \) respectively, then
what are these number for \( \boldsymbol{A}_{4} \) ?
A. 172 and 69
B. 174 and 70
c. 176 and 69
D. 176 and 70


Hydrolysis of \( \boldsymbol{P C l}_{3} \) produces:
A. \( H_{3} P O_{3}+H C l \)
в. \( H_{3} P O_{3}+H_{2} O \)
\( \mathbf{c} \cdot H_{3} P O_{4}+H C l \)
D. \( P H_{3}+H C l O \)


Maximum expiration after full inspiration is called as
A. Vital capacity
B. Lung capacity
c. Tidal volume
D. Residual volume


The development of different juvenile and adult foliage is called as
A. Heterophylly
B. Hydrophily
c. Plasticity
D. Dedifferentiation


The line \( x+y=a \) meets the axis of \( x \)
and \( y \) at \( A \) and \( B \) respectively. \( A \)
triangle \( \triangle A M N \) is inscribed in the \( \triangle O A B, O \) being the origin, with right
angle at \( N . M \) and \( N \) lie respectively on
\( O B \) and \( A B . \) If the area of the triangle \( \triangle A M N \) is \( \frac{3}{8} \) of the area of the \( \triangle O A B \) then \( \frac{A N}{B N} \) is equal to
A.
B. 2
\( c .3 \)
\( D \)


If an electron enters with a velocity \( \bar{v}= \) \( v_{0} \hat{j} \) into a cubical region in a uniform electromagnetic field and the orbit of the electron is found to spiral down
inside the cube in plane parallel to \( x-y \) plane then the configuration of electric field and magnetic field is then
A \( \cdot \bar{E}=E_{0} \hat{j}, \bar{B}=B_{0} \hat{k} \)
B . \( \bar{E}=E_{0} \hat{i}, \bar{B}=B_{0} \hat{k} \)
c. \( \bar{E}=E_{0} \hat{i}, \bar{B}=B_{0} \hat{j} \)
D. \( \bar{E}=E_{0} \hat{j}, \bar{B}=B_{0} \hat{\jmath} \)


A point object \( \boldsymbol{O} \) is placed at a distance
of \( 0.3 m \) from a convex lens (focal
length \( 0.2 m \) ) cut into two halves each
of which is displaced by \( 0.0005 m \) as
shown in the figure.
f this arrangement will generate more
than one image, then what will be the
total number of images?
4
B.
\( c \)
D


topp
Tropovur
precipitation. Which of the following netric titration
vs NaO
axis \( \Rightarrow \) Volume of alkali adde
y-axis \( \Rightarrow \) conductivity


Which of the following elements has a
zero valency?
A .
в. не
\( c \cdot 0 \)
\( D \)


What is the rutherford's atomic model?


PX bisects angle P. If True enter 1 else if
False enter 0


Solve:
\( \boldsymbol{f}(\boldsymbol{x})=\sqrt{\mathbf{9}-\boldsymbol{x}^{2}}=\mathbf{0} \)


The plant tissues commonly found in fruit walls of nuts and pulp of some fruits like guava are termed as
A. Fibres
B. Tracheids
c. Sclereids
D. vesselss


\( s_{1} \) and \( s_{2} \) are the correct sources of
light. P is a point on the screen such
that \( s_{2} p-s_{1} p=0.01029 \mathrm{cm} \) wavelength
of the light used is \( 6000 A^{\circ} . \) The order
of the fringe form at \( P \) is.


Amongst the following the lowest degree of paramagnetism per mol of the compound at \( 298 \mathrm{K} \) will be shown by:
A \( \cdot \) FeSO\( _{4} \cdot 6 H_{2} \) O
в. \( N i S O_{4} .6 H_{2} O \)
\( \mathrm{c} \cdot \mathrm{MnSO}_{4} \cdot 4 \mathrm{H}_{2} \mathrm{O} \)
D. \( C u S O_{4} .5 H_{2} O \)


Which one is odd process?
A. Translation
B. Transformation
c. Transduction
D. conjugation


Which of the following is called as dynamic living entity?
A. Oceans
B. Villages
c. cities
D. Forests


Tidal energy is harnessed by:
A. transporting sea water to a close dam.
B. constructing a submerged dam.
C. constructing a dam across a narrow opening to the sea.
D. constructing an overhead dam.


Which of the following species are formed by Lewis acid-base interaction? This question has multiple correct options
A \( \cdot C H_{4} \)
в. \( N a B F_{4} \)
\( \mathbf{c} \cdot P C l_{4}^{+} \)
\( \mathbf{D} \cdot A l(O H)_{4}^{-} \)


The spontaneous decomposition of radio nuclei is a first order rate
process.U-238 disintegrates with the emission of \( \alpha \) -particles and has a half-
life of \( 4.5 \times 10^{9} \) years. If at time \( t=0,1 \)
mole of U-238 is present, what will be the number of nuclei left after 1 billion
years?
A \( \cdot 5.16 \times 10^{23} \)
3
B . \( 5.16 \times 10^{20} \)
\( \mathbf{c} \cdot 5.16 \times 10^{19} \)
D. None of these


If \( P(x, y, z) \) is a point on the line segment joining \( Q(2,2,4) \) and \( R(3,5,6) \) such that the projection of \( \overrightarrow{O P} \) on the axes are \( \frac{13}{5}, \frac{19}{5}, \frac{26}{5} \)
respectively, then \( P \) divides \( Q R \) in ratio
A .1: 3
B. 2: 3
c. 3: 2
D. 3: 1


Find the volume of largest sphere
covered out of a cube of side \( 7 \mathrm{cm} \)


Which enzymes has more affinity towards substrate?


In addition to the rock particles, the soil contains
A. Air and water
B. Water and plants
c. Minerals, organic matter, air and water
D. Water, air and plants


Construct a triangle XYZ in which \( \angle Y= \)
\( 30^{0}, \angle Z=90^{0} \) and \( X Y+Y Z+Z X=11 \mathrm{cm} \)


\( N_{2} O_{5} \) decomposes to \( N_{2} O_{4} \) and \( O_{2} \) as :
\( N_{2} O_{5} \rightarrow N_{2} O_{4}+\frac{1}{2} O_{2} \)
The pressure \( P_{1} \) at any stage is related
to \( p_{0} \) and \( x, \) the fraction of dissociation,
as:
\( \mathbf{A} \cdot p_{0} \)
B. \( \left(1+\frac{1}{2} x\right) p_{0} \)
c. \( _{1-\frac{3}{2} p_{0}} \)
D. \( \frac{3}{2} x p_{0} \)


Lanthanide and actinides resemble in:
A. electronic configuration
B. oxidation state
c. ionisation energy
D. formation of complexes


Obtain differential equation from the
relation \( \boldsymbol{A} \boldsymbol{x}^{2}+\boldsymbol{B} \boldsymbol{y}^{2}=1, \) where \( \boldsymbol{A} \) and \( \mathbf{B} \)
are constants


Define absorptive and holozoic nutrition.


Biogas is produced due to the fermentation of the slurry of animals dung.
A . Pesticides
B. Anaerobic
c. coal
D. Methane


Molar mass of \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) is :


f \( a+b+c=0 \), show that
\( \mathbf{6}\left(\boldsymbol{a}^{\mathbf{5}}+\boldsymbol{b}^{\mathbf{5}}+\boldsymbol{c}^{\mathbf{5}}\right)= \)
\( \mathbf{5}\left(\boldsymbol{a}^{3}+\boldsymbol{b}^{3}+\boldsymbol{c}^{3}\right)\left(\boldsymbol{a}^{2}+\boldsymbol{b}^{2}+\boldsymbol{c}^{2}\right) \)


The distribution of sale of shirts sold in
a month in a departmental store is as under. Calculate the model size of shirts
sold.
\( \begin{array}{llll}\text { 80- } & \text { 85- } & \text { 90- } & \text { 95- }\end{array} \)
\[
\begin{array}{lll}
\text { Size } & \text { 80- } & \text { 85- } \\
\text { (in } & \text { 85 } & \text { 90 }
\end{array}
\]
\( 95 \quad 100 \)
\( \mathrm{cm} \)
No
of 3
85
155
shirts sold


Solve: \( \int \tan (x) d x=? \)


Pollution from animal excreta and
organic waste from kitchen can be most profitably minimised by
A. Storing them in underground storage tanks
B. Using them for producing biogas
c. vermiculture
D. using them directly as biofertilizers


A capacitor of capacitance \( 2 \mu F \) is connected in the tank circuit of an
oscillator oscillating with a frequency of 1 kHz. If the current flowing in the circuit is \( 2 \mathrm{mA} \), the voltage across the capacitor will be :
A . \( 0.16 \mathrm{v} \)
B. 0.32
c. 79.5 \( v \)
D. \( 159 \mathrm{V} \)


Prove that the sum of all interior angles
of a \( \Delta \) is \( 180^{\circ} \)


If in a circular coil A of radius R, current
is flowing and in another coil B of radius \( 2 \mathrm{R} \) a current 2 I is flowing, then
the ratio of the magnetic fields \( B_{A} \) and
\( \mathrm{B}_{B}, \) produced by them will be
A
B. 2
\( c \cdot 1 / 2 \)
D. 4


\( \frac{\pi}{\frac{\pi}{6}} \)


When the tension in a metal wire is \( T_{1} \)
its length is \( l_{t} \). When the tension is \( T_{2} \)
its length is \( l_{2} \). The natural length of
wire is
\( ^{\mathbf{A}} \cdot \frac{T_{2}}{T_{1}}\left(l_{1}+l_{2}\right) \)
в. \( T_{1} l_{1}+i_{2} l_{2} \)
c. \( \frac{l_{1} T_{2}-l_{2} T_{1}}{T_{2}-T_{1}} \)
D. \( \frac{l_{T_{2}-l_{2} T_{1}}}{T_{2}+T_{1}} \)


According to IUPAC nomenclature,
sodium nitroprusside is named is:
A. Sodium pentacyanonitrosyl ferrate(III)
B. Sodium nitroferricyanide
C. Sodium nitroferrocyanide
D. Sodium pentacyanonitrosyl ferrate(II)


The shaded region in the Venn diagram
represents


Show that \( A(3,-2) \) is a point trisection of the line segment joining the points
(2,1) and (5,-8)
Also find the co-ordinates of the other
points of trisections.


There are two uncharged identical metallic spheres 1 and 2 of radius \( r \)
separated by a distance \( d(d>>r) . A \) charged metallic sphere of same radius having charge \( q \) is touched with one of the sphere. After sometime it is moved
away from the system. Now the uncharged sphere is earthed. Charge on earthed sphere is :
\( A \cdot+\frac{q}{2} \frac{q}{2} \)
B. \( -\frac{q}{2} \)
c. \( -\frac{q r}{2 d} \)
D. \( -\frac{q d}{2 r} \)


If 4 men earn Rs 360 in one day, then how much does a man earn in one day?
A . 90
B. 30
\( c \cdot 120 \)
D. 60


Two astronauts on the surface of the
moon cannot talk to each other. Why
A. There is no atmosphere on the surface of the moon
B. There is no medium in between the two astronauts
C. The sounds cant propagate
D. All


Minimum percentage increase in the kinetic energy of a satellite orbiting close to the surface of the earth so that
it will escape the earth's gravitational pull is
A . 50\%
B. 150\%
c. \( 100 \% \)
D. 200\%


Explain why the given names in the following are wrong. Give the correct name in each case:
3-propyl-4-methylbutan-1-oic acid


A body of mass travels in a straight line with a velocity \( v=k x^{3 / 2} \) where \( k \) is a
constant. The work done in displacing the body from \( x=0 \) to \( x \) is proportional
to:
\( \mathbf{A} \cdot x^{1 / 2} \)
B. \( x^{2} \)
c. \( x^{3} \)
D. \( x^{5 / 2} \)


The angles of a triangle are in the ratio 2: 1: 3. Is the triangle right-angled triangle,
A. True
B. False


Let \( \bar{a}, \bar{b}, \bar{c} \) and \( \bar{d} \) be position vectors of four points \( A, B, C \) and \( D \) lying in a
plane. If \( (\bar{a}-\bar{d}) \cdot(\bar{b}-\bar{c})=0= \)
\( (\bar{b}-\bar{d}) \cdot(\bar{c}-\bar{a}), \) then \( \Delta A B C \) has \( D \) as
A . in-centre
B. circum-centre
c. ortho-centre
D. centroid


To what effect potential a proton beam be subjected to give its protons a wavelength of \( 1 \times 10^{-10} \mathrm{m} ? \)
A. 0.0826 volts
B. 0.0346 volts
c. 0.0567 volts
D. 0.0234 volts


Conduction of heat is possible:
A. when the bodies are apart from each other
B. when the bodies have same temperature and in thermal contact
C. when they have different temperatures maintaining distance between them
D. bodies should be in contact and should have different
temperatures


\( C_{7} H_{16} \) has 9 isomers How many of these isomers have quaternary
carbons?
A . 1
B . 2
\( c .3 \)
D. 4


Find \( g o f(x), \) if \( f(x)=8 x^{3} \) and \( g(x)= \)
\( \boldsymbol{x}^{\mathbf{1} / \mathbf{3}} \)


A particle of mass \( m \) describes a circle
of radius \( r . \) The centripetal acceleration of the particle is \( \frac{4}{r^{2}} . \) Then the momentum of the particle is
A \( \cdot_{2} \frac{m}{r} \)
в. \( 2 \frac{m}{\sqrt{r}} \)
c. \( 4 \frac{m}{\sqrt{r}} \)
D. None of these


Force of cohesion develops due to
A . Attraction between similar molecules
B. Attraction between different molecules
c. surface tension at the interface
D. All the above.


Cotyledon of maize grain is called as
A. Plumule
B. Coleorhiza
c. coleoptile
D. Scutellum


What is the characteristic of haustorial
roots of cuscuta?
A. Presence of both xylem and phloem
B. Presence of only xylem
c. Presence of phloem
D. Absence of both xylem and phloem


The area of a field is in the shape of a
trapezium measures \( 1440 m^{2} \). The
perpendicular distance between its parallel sides is \( 24 m . \) If the ratio of the
parallel sides is \( 5: 3 . \) What is the length
of the longer parallel side?
A . \( 75 \mathrm{m} \)
B. \( 70 m \)
c. \( 80 m \)
D. \( 85 m \)


The equation \( a x^{2}+b y^{2}+c x+c y=0 \)
represents a pair of straight lines, when This question has multiple correct options
\( \mathbf{A} \cdot a+b=0 \)
B . \( c=0 \)
c. \( a+c=0 \)
D. \( c(a+b)=0 \)


A nonzero external force acts on a
system of particles, The velocity and the acceleration of the centre of mass are
found to be \( v_{0} \) and \( a_{0} \) at an instant \( t . \) It
is possible that :
This question has multiple correct options
A \( \cdot v_{0}=0, a_{0}=0 \)
0
в. \( v_{0}=0, a_{0} \neq 0 \)
c. \( v_{0} \neq 0, a_{0}=0 \)
D. \( v_{0} \neq 0, a_{0} \neq 0 \)


Construct a right angle \( \triangle A B C, \) right
angled at \( B, \) when hypotenuse \( C A= \) \( 7.0 \mathrm{cm} \) and \( A B=4.3 \mathrm{cm} . \) Measure the
length of \( B C \)


Name an alkali used in the
manufacture of soap.


Rohit bought 12 registers for Rs 156, find the cost of 7 such registers. (in Rs.)


A charge q is distributed over two spheres of radii \( R \) and \( r \) such that their surface densities are equal. What is the
ratio of the charges on the spheres?
A \( \cdot \frac{r}{R} \)
в. \( \frac{r^{2}}{R^{2}} \)
c. \( \frac{r^{3}}{R^{3}} \)
D. \( \frac{r^{4}}{R^{4}} \)


The sum of three numbers which are
consecutive terms of an A.P is \( 21 . \) If the
second number is reduced by \( 1 \& \) the
third is increased by \( 1, \) we obtain three
consecutive terms of a G.P., find the
numbers.


In Utricularia, the leaves are modified to
form
A. Bladders
B. Tendrilss
c. Hooks
D. Pitchers


Which of the following is solid at room temperature?
A. \( C O \)
в. \( C O_{2} \)
\( \mathrm{c} \cdot \operatorname{si} 0_{2} \)
D. \( O F_{2} \)


Which of the following is a silent killer gas, which combines with haemoglobin in the blood?
A \( \cdot C O_{2} \)
в. \( C O \)
c. \( N O \)
D. \( N O_{2} \)


If the systolic pressure is \( 120 \mathrm{mm} \mathrm{Hg} \) and diastolic pressure is \( 80 \mathrm{mm} \) Hg, the pulse pressure is
B. \( 120+80=200 \mathrm{mm} \mathrm{Hg} \)
c. \( 120-80=40 \mathrm{mm} \) Hg
\( \mathbf{D} \cdot \frac{120}{80}=1.5 \mathrm{mm} \mathrm{Hg} \)


The time taken by a particle performing
SHM to pass from point \( A \) to \( B \) where
its velocities are same is 2 s. After
another \( 2 s \) it returns to \( B \). The ratio of
distance \( O B \) to its amplitude (where \( O \)
is the mean position) is :
A. \( 1: \sqrt{2} \)
B . \( (\sqrt{2}-1): 1 \)
c. 1: 2
D. \( 1: 2 \sqrt{2} \)


What is the atomic mass (u) of
chlorine?
A . 34
B. 35.5
\( c \cdot 33 \)
D. 35


In the reaction :-
\[
\begin{array}{r}
\boldsymbol{C u} \boldsymbol{S O}_{4} \cdot \boldsymbol{3} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{s}) \rightleftharpoons \mathbf{2} \boldsymbol{C u} \boldsymbol{S} \boldsymbol{O}_{4} \\
\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{s})+\mathbf{2} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{v})
\end{array}
\]
Dissociation pressure is \( 7 \times 10^{-3} \) atm
at 25 and \( \Delta H=2700 \) cal. If the
dissociation pressure at 127 is \( X \times \)
\[
10^{-3} \text {atm, then } 100 X
\]
is


A small mass slides down an inclined
plane of inclination \( \boldsymbol{\theta} \) with the horizontal. The co-efficient of friction is
\( \mu=\mu x \) where \( x \) is the distance
through which the mass slides down
and \( \mu \) a constant. Then the speed is
maximum after the masscovers a
distance of:
A \( \cdot \frac{\cos \theta}{\mu_{0}} \)
B. \( \frac{\sin \theta}{\mu_{0}} \)
\( c \cdot \frac{\tan \theta}{\mu_{0}} \)
D. \( \frac{2 \tan \theta}{\mu_{0}} \)


The principal protein of cilia and flagella is
A. Tubulin
B. Albumin
c. Globulin
D. Gliadin


Which prism surface will behave as
mirror?


The atomic number of elements \( A, B \) and \( C \) are \( (Z-1), Z \) and \( (Z+1) \) respectively. B is an inert gas (not helium). Which element among \( A, B \) and
C has the highest ionization energy? Why?


How many seconds are there in a week?
A . 60480
B. 604800
c. 6048000
D. 6048


A metal rope of density \( 6000 \mathrm{kg} / \mathrm{m}^{3} \) has
breaking stress \( 9.8 \times 10^{8} N m^{-2} . \) This
rope is used to measure the depth of the sea. Then the depth of the sea that can be measured with out breaking is
A \( \cdot 10 \times 10^{3} \)
B . \( 20 \times 10^{3} \)
c. \( 30 \times 10^{3} \)
D. \( 40 \times 10^{3} \mathrm{m} \)


Find the species/elemental atom that has a minimum number of unpaired electrons.
\( A \cdot K r^{+} \)
B. \( M n^{2+} \)
\( \mathrm{c} \cdot \mathrm{Fe}^{3} \)
D. \( O^{+} \)


Given the standard potential of the
following at \( 25^{\circ} \mathrm{C} . M n O_{2} \rightarrow M n^{3+} \)
\( \boldsymbol{E}^{\ominus}=\mathbf{0 . 9 5} \boldsymbol{V} \)
\( M n^{3+} \rightarrow M n^{2+} ; E^{\ominus}=1.51 V \)
The standard potential of \( M n O_{2} \rightarrow \)
\( M n^{2+} \) is :
A . \( 1.23 \mathrm{v} \)
B. 0.2 \( v \)
c. \( 0.02 \mathrm{v} \)
D. None of these


Which of the following oxo-acids of sulphur has maximum number of \( \mathrm{p} \pi-\mathrm{d} \)
\( \pi \) bonds in it?
A \( \cdot H_{2} S_{2} O_{2} \)
в. \( H_{2} S_{2} O_{3} \)
c. \( H_{2} S_{2} O_{5} \)
D. \( H_{2} S_{2} O_{8} \)


Solution of \( \boldsymbol{y}^{2} \boldsymbol{d} \boldsymbol{x}+\left(\boldsymbol{x}^{2}-\boldsymbol{x} \boldsymbol{y}+\boldsymbol{y}^{2}\right) \boldsymbol{d} \boldsymbol{y}= \)
\( \mathbf{0} \)
A \( \cdot \tan ^{-1}\left(\frac{x}{y}\right)+\log y+c=0 \)
B \( \cdot 2 \tan ^{-1}\left(\frac{x}{y}\right)+\log y+c=0 \)
\( \mathbf{c} \cdot \log y(y+\sqrt{x^{2}+y^{2}})+\log y+c=0 \)
D \cdot \( \log y(y-\sqrt{x^{2}+y^{2}})+\log y+c=0 \)


Selection of temperature to carry out a reduction process depends so as to make:
A. \( \Delta G \) negative
B. \( \Delta G \) positive
c. \( \Delta H \) negative
D. \( \Delta H \) positive


Which of the following statements
about Rutherford's model of an atom
are correct?
This question has multiple correct options
A. It considered the nucleus is positively charged.
B. It established that the \( \alpha \) -particles are four times as heavy as a hydrogen atom.
C. It can be compared to the solar system
D. It was in agreement with Thomson's model.


Non - disjunction in meiosis results in:
A. Trisomy
B. Normal diploid
c. Gene mutation
D. None


Complete and balance the given
reaction:
\( \boldsymbol{P b}\left(\boldsymbol{N} \boldsymbol{O}_{3}\right)_{2} \stackrel{\boldsymbol{h e a t}}{\longrightarrow} \)
Which among the following are form a part of the product:
This question has multiple correct options
A. \( P b O \)
в. \( N O_{2} \)
\( c \cdot O_{2} \)
D. \( P b N O_{2} \)


In electro-refining, thick sheets of pure copper are obtained at:
A. cathode
B. anode
c. electrode
D. none of the above


SONAR set up consists of :
A. a transmitter
B. a detector
c. channe
D. all of the above


A particle travels \( 10 \mathrm{m} \) in first 5 seconds
\( 10 \mathrm{cm} \) in next 3 seconds. Assuming constant acceleration what is the
distance travelled in next 2 second?
\( \mathbf{A} \cdot 8.3 \mathrm{m} \)
B. \( 9.3 \mathrm{m} \)
c. \( 10.3 \mathrm{m} \)
D. None of these


In how much time would Rs 5000
amount to Rs 6655 at \( 10 \% \) p.a compound interest?


Let \( A=\{4,6,8,10\} \) and \( B= \)
\{3,4,5,6,7\} and \( f: A \rightarrow B \) be defined
by \( f(x)=\frac{1}{2} x+1, \) then represent \( f \) by:
(i) An arrow diagram
(ii) A set of
ordered pairs (iii) \( A \) table


Differentiate the following w.r.t \( x: \frac{e^{x}}{\sin x} \)


The electric volt is a measure of
electrical potential. Identify which of the following can be defined as a volt.
A. Opposition to electrical motion
B. Number of particles in motion
c. work per unit charge
D. Field strength per unit of force
E. Electrostatic discharge


What is the standard deviation of the
\( 5,5,10,10,10 ? \)
A .2 .44
B. 1.44
\( c \cdot 5 \)
\( D \)


Identical metal plates are located in air at equal distance \( d \) from one another.
The area of each plate is equal to \( A \). If
the capacitance of the system between \( P \) and \( Q \) if the plates are interconnected
as shown in the figure \( \boldsymbol{x} \varepsilon_{0} \frac{\boldsymbol{A}}{\boldsymbol{d}} \). Find \( \boldsymbol{x} \)


Identify a unicellular organism often considered as a connecting link between plants and animals.
A. Monocystis
B. Paramecium
c. Euglena
D. Entamoeba


A particle with restoring force proportional to displacement and resisting force proportional to velocity
is subjected to a force \( \boldsymbol{F} \) sinw. If the
amplitude of the particle is maximum
for \( \omega=\omega_{1} \) and the energy of the particle
is maximum for \( \omega=\omega_{2} \) then (where \( \omega_{0} \)
natural frequency of oscillation of particle)
\( \mathbf{A} \cdot \omega_{1}=\omega_{0} \) and \( \omega_{2} \neq \omega_{0} \)
B . \( \omega_{1}=\omega_{0} \) and \( \omega_{2}=\omega_{0} \)
C \( \cdot \omega_{1} \neq \omega_{0} \) and \( \omega_{2}=\omega_{0} \)
D. \( \omega_{1} \neq \omega_{0} \) and \( \omega_{2} \neq \omega_{0} \)


An oil-soluble dye is mixed with
emulsion and the emulsion remains
colourless. Then, it is :
A . oil in water emulsion
B. water in oil emiulsion
c. oil in oil emulsion
D. water in water emulsion


Find the value of the following
determinant:
\( \left|\begin{array}{cc}1.2 & 0.03 \\ 0.57 & -0.23\end{array}\right| \)
A. -0.266
B. -0.2471
c. -0.2381
D. -0.2931


State True or False:
A light entering normal to one of the
surfaces of \( 30^{\circ}, 90^{\circ}, 60^{\circ} \) prism suffers total internal reflection on one of the
surfaces.
A. True
B. False


The angle between the two refracting
surfaces of a total reflecting prism is :
\( \mathbf{A} \cdot 90 \)
B. 60
\( c \cdot 45 \)
D. 30


What is the main product obtained by the cross-aldol condensation of benzene
carbaldehyde and 1-Phenyl-Ethane-1
one?
\( A \)
\[
\sqrt{\square}>\mathrm{cH}_{2}-\mathrm{cH}=\mathrm{cH}-\mathrm{co} \sqrt{\bigcirc}
\]
B.
\( \langle\square\rangle-\mathrm{cH}_{2}-\mathrm{cH}=\mathrm{cH} \sqrt{\Delta} \)
\( D \)


Holdfast, stipe and frond constitute the plant body in case of
A. Rhodophyceae
B. Chlorophyceae
c. Phaeophyceae
D. all of these


Write the degree of each of the following polynomials:
(i) \( 5 x^{3}+4 x^{2}+7 x \)
(ii) \( 4-y^{2} \)
(iii) \( 5 t-\sqrt{7} \)
(iv) 3


The increase of pressure on ice \( \rightleftharpoons \) water system at constant temperature will lead to :
A. a decrease in the entropy of the system
B. an increase in the Gibbs energy of the system
c. no effect on the equilibrium
D. a shift of the equilibrium in the forward direction


Write IUPAC names of the products obtained by the ozonolysis of 2 Ethylbut-1-ene.


The value of
\( \lim _{n \rightarrow \infty}\left[\frac{\sqrt{\boldsymbol{n}+\mathbf{1}}+\sqrt{\boldsymbol{n}+\mathbf{2}}+\ldots+\sqrt{\boldsymbol{n}+\boldsymbol{r}}}{\boldsymbol{n} \sqrt{\boldsymbol{n}}}\right. \)
is
A \( \cdot \frac{2(2 \sqrt{2}-1)}{3} \)
B. \( \frac{(2 \sqrt{2}-1)}{3} \)
c. \( \frac{(2 \sqrt{2}+1)}{3} \)
D. \( \frac{(\sqrt{2}+1)}{3} \)


STATEMENT - 1: The volume of largest
sphere that can be carved out from cube of side a cm is \( \frac{1}{6} \pi a^{3} \)

STATEMENT - 2: Volume of sphere is \( \frac{4}{3} \pi r^{3} \) and for largest sphere to carved from cube radius of sphere \( = \) side of
cube
A. Statement - 1 is True, Statement - 2 is True, Statement 2 is a correct explanation for Statement - 1
B. Statement - 1 is True, Statement - 2 is True : Statement 2 is NOT a correct explanation for Statement - 1
c. statement - 1 is True, Statement - 2 is False
D. Statement - 1 is False, Statement - 2 is True


Select the correct order with respect to
boiling point of the given compounds.
A. \( H_{2} O>H_{2} S>H_{2} S e>H_{2} T e \)
в. \( H_{2} O>H_{2} T e>H_{2} S e>H_{2} S \)
c. \( H_{2} T e>H_{2} S e>H_{2} S>H_{2} O \)
D. \( H_{2} S>H_{2} O>H_{2} T e>H_{2} S e \)


Does the following pairs represent the same rational number:
\( \frac{-7}{21} \) and \( \frac{3}{9} \)


Consider an ideal gas contained in a vessel. If the intermolecular interaction
suddenly begins to act, which of the following will happen:
A. the observed pressure decreases
B. the observed pressure increases
c. the observed pressure remains same
D. none of these


In which of the following complex ion, the central metal ion is in a state of
\( s p^{3} d^{2} \) hybridisation?
\( \mathbf{A} \cdot\left[C o F_{6}\right]^{3-} \)
B \cdot \( \left[\operatorname{Co}\left(N H_{3}\right)_{6}\right]^{3+} \)
c. \( \left[F e(C N)_{6}\right]^{3} \)
D \cdot \( \left[\operatorname{Cr}\left(N H_{3}\right)_{6}\right]^{3+} \)


In order to apply a force on the body:
A. there has to be an interaction
B. there must be no interaction
c. sometimes there may be an interaction.
D. None of these


DE \( \boldsymbol{C H}_{3}-\boldsymbol{C H}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{3} \frac{A l_{2} \boldsymbol{O}_{3}}{573 \boldsymbol{K}} \)
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}=\boldsymbol{C H}-\boldsymbol{C H}_{3} \)
Butane-2-ol
2-ene


If \( P(n) \) is the statement \( ^{\prime \prime} n^{2} \) is even"
then what is \( \boldsymbol{P}(\mathbf{9}) \) ?


Name the smooth muscle of urinary
bladder
A . Cardiac muscle
B. Detrusor muscle
c. Dartos muscle
D. Gubernaculum


In the bessemerisation of sulphide ore of copper, there is self-reduction giving
copper metal.
If true enter 1 , else enter 0 .


Which of the following is a step-growth polymer?
A. Polyacrylonitrile
B. Polyisoprene
c. Nylon
D. Polythene


For what positive values of ' \( m \) ' roots of given equation
is equal, distinct, imaginary \( \boldsymbol{x}^{2}- \)
\( \boldsymbol{m} \boldsymbol{x}+\boldsymbol{9}=\mathbf{0} \)


If the weight of a body on the surface of the moon is \( 100 \mathrm{N} \), what is its mass?
\( \left.=1.6 \mathrm{ms}^{-2}\right) \)
\( A \cdot 160 \mathrm{kg} \)
B. 62.5 kg
\( c \cdot 6.25 \mathrm{kg} \)
D. 625 kg


A stream line body with relative density
\( d_{1} \) falls into air from a height \( h_{1} \) on the
surface of a liquid of relative density \( \boldsymbol{d}_{2} \)
where \( d_{2} \) is greater than \( d_{1} \). The time of immersion of the body into the liquid will be
\( A \)
\[
\sqrt{\left(\frac{2 h_{1}}{g}\right)} \times \frac{d_{1}}{d_{2}-d_{1}}
\]
в.
\[
\sqrt{\left(\frac{2 h_{1}}{g}\right)}
\]
\( c \)
\[
\sqrt{\left(\frac{2 h_{1}}{g}\right)} \times \frac{d_{1}}{d_{2}}
\]
D.
\[
\sqrt{\left(\frac{2 h_{1}}{g}\right)} \times \frac{d_{2}}{d_{1}}
\]


Stomata is grass leaf are
A. Rectangular
B. Dumb-bell shapedd
C. Barrel shaped
D. Kidney shaped


This problem is caused only when a
mother has a child with the
phenotype.
A. Unsensitized \( R h^{+}, R h^{-} \)
B. Sensitized \( R h^{-}, R h^{-} \)
C. Unsensitized \( R h^{-}, R h^{+} \)
D. Unsensitized \( R h^{-}, R h^{-} \)
E . Sensitized \( R h^{-}, R h^{+} \)


The domain of \( \boldsymbol{f}(\boldsymbol{x})=\frac{\sin ^{-1} \boldsymbol{x}}{\boldsymbol{x}} \) is
\( \mathbf{A} \cdot[-1,1] \)
B. \{0\}
\( c \cdot[-1,0) \)
D. None of these


One of the steps involved in the depletion of ozone in the stratosphere by nitric acid ( \( N O \) ) may be represented
as:
\[
\begin{array}{c}
\boldsymbol{N O}(\boldsymbol{g})+\boldsymbol{O}_{3}(\boldsymbol{g}) \longrightarrow \boldsymbol{N} \boldsymbol{O}_{2}(\boldsymbol{g})+ \\
\boldsymbol{O}_{2}(\boldsymbol{g})
\end{array}
\]
The oxidation number of \( N \) changes
from +2 to +4
If true enter 1 , else enter 0


Find the values of \( k, \) if the points \( \boldsymbol{A}(\boldsymbol{k}+ \) 1, \( 2 k \) ), \( B(3 k, 2 k+3) \) and \( C(5 k+1,5 k) \)
are collinear.
This question has multiple correct options
A .
B. \( \frac{1}{2} \)
\( c \cdot 2 \)
D. 2.


Biochemical Oxygen Demand \( (B O D) \) is the amount of oxygen required (in ppm)
A. for the photochemical breakdown of waste present in \( 1 m^{3} \) volume of a water body
B. by bacteria to break-down organic waste in a certain volume of a water sample
c. for sustaining life in a water body.
D. by anaerobic bacteria to break down inorganic waste present in a water body


Represent the solution of the following inequality on the real number line:
\( \frac{2 x+5}{3}>3 x-3 \)


If 5 times the \( 5^{t h} \) term of an A.P is the
same as 7 time the \( 7^{t h} \) term, then find
its \( 12^{t h} \) terms.
A . 0
B. 11
c. 14
D. 18


In diborane:
A. four bridged hydrogen atoms and two terminal hydrogen atoms are present
B. two bridged hydrogen atoms and four terminal hydrogen atoms are present
C. three bridged hydrogen atoms and three terminal hydrogen atoms are present
D. there are no bridged hydrogen atoms in diborane, only hyrogen bonds are present.


Name two plants which have fibrous
root.


Animal that lives only in water is
\( A \cdot F \operatorname{rog} \)
B. Fish
c. crocodile
D. Duck


An electric bulb is rated \( 220 V \) and
\( 100 W, \) when it is operated on \( 110 V \)
the power consumed will be
A . \( 100 \mathrm{W} \)
в. \( 75 \mathrm{W} \)
\( \mathbf{c} .50 W \)
D. \( 25 W \)


Find \( \frac{d y}{d x}, \) if \( y=\log \left(\sqrt{x}-\frac{1}{\sqrt{x}}\right) \)


Milk is an emulsion of water in oil type.
A. True
B. False


When iodine is reacted ozone in
water,thee product formed is:
A. \( H I \)
в. НЛ
\( \mathrm{c} \cdot \mathrm{HIO}_{2} \)
D. \( H I O_{3} \)


A child inserted a needle in a man's ear.
The man became deaf. Why
A. the needle damaged the oval window
B. the needle damaged the stirrup
c. the needle damaged the ear drum
D. all


Two resistors of 60 ohms and 40 ohms
are arranged in series across a 220 volt supply. How much heat is produced by this combination in half a minute?
A . 12860
B . 152698J
\( c . \) 650
D. 145200