Fig. shows a point charge of \( 0.5 \times 10^{-6} \)
\( \mathrm{C} \) at the center of the spherical cavity of
radius \( 3 c m \) of a piece of metal. The
electric field at :
This question has multiple correct options
A. A (2cm from the charge) is 0
B. A (2 cm from the charge) is \( 1.125 \times 10^{7} \mathrm{NC}^{-1} \)
C. B ( \( 5 \mathrm{cm} \) from the charge ) is 0
D. B (5cm from the charge) is \( 1.8 \times 10^{6} \mathrm{NC}^{-1} \)


Define fuel cell and write its two
advantages.


\( \mathrm{ft} \mathrm{A}=\left[\begin{array}{ccc}1 & 0 & 1 \\ 0 & 1 & 2 \\ 0 & 0 & 4\end{array}\right] \) then show that
\( |3 A|=27|A| \)


The error in measurement caused by
positioning the eye incorrectly is called
A. parallel error
B. standard error
c. eye error
D. parallax error


A specimen of iron of permeability \( 8 \times \)
\( 10^{-3} \) Weber/A m is placed in a
magnetic field of strength \( 160 \mathrm{A} / \mathrm{m} \) Magnetic induction in this iron is:
\( \mathbf{A} \cdot 0.8 W b / m^{2} \)
B. \( 5 \times 10^{5} \mathrm{Wb} / \mathrm{m}^{2} \)
c. \( 1.28 W b / m^{2} \)
D . \( 20 \times W b / m^{2} \)


Put the following in the form \( A+i B: \) \( \frac{(1+i)^{2}}{3-i} \)


Find the value of \( \sin ^{-1}\left(\frac{3}{5}\right)+ \)
\( \tan ^{-1}\left(\frac{1}{7}\right) \)


If \( A \) and \( B \) be two finite sets such that
the total number of subsets of A is 960
more than the total number of subsets
of \( \mathrm{B}, \) then \( n(A)-n(B) \) (where \( n(x) \)
denotes the number of elements in set
\( x \) ) is equal to?


A ring \( (R), \) a disc \( (D), \) a solid sphere \( (S) \) and a hollow sphere with thin walls (H), all having the same mass and radii, start together from rest at the top of an inclined plane and roll down without slipping. This question has multiple correct options
A. All of them will reach the bottom of the incline together.
B. The body with the maximum radius will reach the bottom first.
c. They will reach the bottom in order \( \mathrm{S}, \mathrm{D}, \mathrm{H}, \mathrm{R} \)
D. All of them will have the same kinetic energy at the bottom of the incline


The potentials of two wires coming from electric poles to our houses are:
A. 440 volt and \( 220 \mathrm{v} \)
B. OV and 110v
c. ov and \( 220 v \)
D. 300V and 500v


(a) If the roots of the equation, \( (b- \)
\( c) x^{2}+(c-a) x+(a-b)=0 \) be equal
then prove thar \( a, b, c \) are in arithmetical
progression.
(b) If \( a(b-c) x^{2}+b(c-a) x+c(a- \)
b) \( =0 \) has equal roots, prove that \( a, b, c \)
are in harmonical progression.


The distribution of electrons in various
shells of an atom is given by
A. Dalton
B. Rutherford
c. Bohr-Bury scheme
D. None of the above


If \( y=\cos \left(m \cos ^{-1} x\right), \) show that
\( \left(1-x^{2}\right) \frac{d^{2} y}{d x^{2}}-x \frac{d y}{d x}+m^{2} y=0 \)


A pole of 6 metres in height casts a shadow of 3.6 metres at a certain time
of the day. Find the length of the shadow
cast by a 4.5 metres tower at the same time.


The electrode connected to the negative terminal of a battery in a discharge tube is called
A. Anode
B. cathode
c. electrolyte
D. none of these


The maximum value of \( \mathbf{f}(\mathbf{x})= \) \( \frac{1}{2 e^{x}+e^{-x}} \) is:
A \( \cdot \frac{1}{2 \sqrt{2}} \)
B. \( 2 \sqrt{2} \)
\( c \cdot \frac{1}{2} \)
D. \( \frac{\mathrm{e}}{2 \mathrm{e}^{2}+1} \)


A spherical mirror produces an image of magnification -1 on a screen placed at a distance of \( 50 \mathrm{cm} \) from the mirror.
(a) Write the type of mirror.
(b) Find the distance of the image from
the object.
(c) What is the focal length of the mirror
\( ? \)
(d) Draw the ray diagram to show the image formation in this case.


Marcello Malpighi after whom malpighian corpuscles are named was born in
A. Germany
B. Italy y
C. Australia
D. Austria


Light of wavelength \( 6328 A \) is incident normally on a slit having a width of
\( 0.2 m m . \) The angular width of the central maximum measured from
minimum to minimum of diffraction
pattern on a screen 9.0 meters away will
be about
A. 0.36 degree
B. 0.18 degree
c. 0.72 degree
D. 0.09 degree


In the pulley system shown, if radii of the bigger and smaller pulley are \( 2 \mathrm{m} \) and \( 1 \mathrm{m} \), respectively and the
acceleration of block \( A \) is \( 5 m / s^{-2} \) in the downward direction, the
acceleration of block B will be :
A \( \cdot 0 \mathrm{ms}^{-2} \)
B. \( 5 \mathrm{ms}^{-2} \)
\( \mathrm{c} \cdot 10 \mathrm{ms}^{-2} \)
D. \( \frac{5}{2} m s^{-3} \)


Differentiate the following functions
with respect to \( x \) :
\( \tan ^{-1}\left\{\frac{x^{1 / 3}+a^{1 / 3}}{1-(a x)^{1 / 3}}\right\} \)


Which of the following compounds do
not exist?
\( N_{4}, P_{4}, P C I_{5}, N C I_{5}, P_{2} O_{5}, N O_{2}, P O_{2} \)
A. \( N_{4}, N C I_{5}, N O_{2} \)
B. \( N_{4}, N C I_{5}, P O_{2} \)
c. \( P C I_{5}, N C I_{5}, P O_{2} \)
D. All of these


A very small circular loop of radius \( a \) is
initially \( (a t t=0) \) coplanar and
concentric with a much larger fixed
circular loop of radius \( b \). A constant
current \( I \) flows in the larger loop. The smaller loop is rotated with a constant
angular speed \( \omega \) about the common diameter. The emf induced in the
smaller loop as a function of time \( t \) is:
\( ^{\mathbf{A}} \cdot \frac{\pi a^{2} \mu_{0} I}{2 b} \omega \cos (\omega t) \)
в. \( \frac{\pi a^{2} \mu_{0} I}{2 b} \omega \sin \left(\omega^{2} t^{2}\right) \)
\( ^{\text {c. }} \frac{\pi a^{2} \mu_{0} I}{2 b} \omega \sin (\omega t) \)
D \( \cdot \frac{\pi a^{2} \mu_{0} I}{2 b} \omega \sin ^{2}(\omega t) \)


In a new set of units, unit of mass is 10
kg, unit of length is \( 1 \mathrm{km} \) and unit of time is 1 minute. The value of 1 joule in this new hypothetical system is
A \( \cdot 3.6 \times 10^{-4} \) new units
B. \( 6 \times 10^{7} \) new units
c. \( 10^{11} \) new units
D. \( 1.67 \times 104 \) new units


Parallax method is useful
A. for measuring speed of the light.
B. for measuring distances of star.
C. for finding the intensity of the light.
D. None of the above.


If \( A(-1,3), B(1,-1) \) and \( C(5,1) \) are the vertices of a triangle \( A B C \) find the length of the median passing through
the vertex \( A \).
A. 5 units
B. 6 units
c. 15 units
D. None of these


Among the following, the molecule with the highest dipole moment is :
A \( . C H_{3} C l \)
B . \( C H_{2} C l_{2} \)
c. \( C H C l_{3} \)
D. \( C C l_{4} \)


Solve
\( 6 m^{2}-11 m+6=0 \)


The recovery of silver from the solutions used in developing and fixing photographic film and prints present just such a problem. Silver is an expensive metal, and the recovery is profitable. Moreover, if not recovered, the silver ions would constitute and
undesirable pollutant in water supplies The equation in which silver recovered from such solution is \( : A g_{2} C O_{3} \stackrel{\Delta}{\rightarrow} \)
\( 2 A g+C O_{2}+\frac{1}{2} O_{2} \)


The change in the shape of the lens
while seeing distant and nearby objects


A uniform rod of mass \( m \) and length \( l \) is kept vertical with the lower end
clamped. It is slightly pushed to let it fall down under gravity. Find its angular speed when the rod is passing through its lowest position. Neglect any friction at the clamp. What will be the linear speed of the free end at this instant?


Boyle's law may be expressed as \( (\boldsymbol{d} \boldsymbol{P} / \boldsymbol{d} \boldsymbol{V})_{\boldsymbol{T}}=-\boldsymbol{K} / \boldsymbol{V}^{2} \)
If true enter 1 else 0
A.


If \( \frac{3 x-1}{5}-\frac{1+x}{2}=3-\frac{x-1}{2}, \) then \( x= \)
\( A \cdot 2 \)
B. 3
\( c \cdot 7 \)
D. 12/7


In the following figure, ABCD is a parallelogram.
Then find the value of \( x \)


Which of the following statement(s)
is/are correct?
This question has multiple correct options
A. Conductors are materials that allow the flow of electric current, whereas dielectric (insulators) do not
B. The main difference between conductor and dielectric
behavior is the amount of available free electrons
C. Not all conductors have the same level of conductivity, just as not all insulators are resistant to electric
current.
D. Both A and B only


An infinitely long cylinder of radius
\( \mathrm{R}=2 \mathrm{cm} \) carries a uniform charge density
\( =18 \mu \mathrm{C} / \mathrm{m} 3 \)
Calculate the electric field at distance
\( r=1 \mathrm{cm} \)
from the axis of the cylinder.
A. The magnitude of electric field intensity at the \( x x \) axis of charged body is \( \left(\frac{p r^{2}}{2 \epsilon_{0} d}\right) \)
B. The magnitude of electric field intensity at the \( x x \) axis of charged body is zero.
C. The magnitude of electric field intensity at the yy axis of charged body is \( \left(\frac{p d^{2}}{2 \epsilon_{0}}\right) \)
D. The magnitude of electric field intensity at the \( x x \) any point in the cavity is \( \frac{p^{2}}{2 \epsilon_{0}} d \)


A chain of mass \( M \) is placed on a
smooth table with \( 1 / n \) of its length \( L \) hanging over the edge. The work done in
pulling the hanging portion of the chain back to the surface of the table is:
A. \( M g L / n \)
в. \( M g L / 2 n \)
c. \( M g L / n^{2} \)
D. \( M g L / 2 n^{2} \)


Classify the following curve as open or
closed:


The angle of incidence in a plane mirror
is \( -\ldots----- \) angle of reflection
A. equal to
B. greater than
c. less than
D. none of these


If \( R \) is the radius of the earth and \( g \) the
acceleration due to gravity on the earth's surface, then mean density of the earth is:
A \( \cdot \frac{4 \pi G}{3 g R} \)
в. \( \frac{3 \pi R}{4 g G} \)
c. \( \frac{3 g}{4 \pi R G} \)
D. \( \frac{r g}{12 R G} \)


Which of the following complex has
least oxidation state of Fe?
\( \mathbf{A} \cdot K_{3}\left[F e(O H)_{6}\right] \)
B. \( K_{2}\left[F e O_{4}\right] \)
\( \mathbf{c} \cdot F e S O_{4}\left(N H_{4}\right)_{2} S O_{4} \cdot 6 H_{2} O \)
D. \( \left[F e(C N)_{6}\right]^{-3} \)


A compound microscope has an objective of focal length \( 4 \mathrm{mm} \) and an eyepiece of focal length \( 25 \mathrm{mm} \). The objective produces a real image at a distance of \( 180 \mathrm{mm} \). If the eye-piece is in normal adjustment, then the magnification is
A . 45
B. 90
\( c \cdot 225 \)
D. 440


The state of hybridization for the transition state of hydolysis
mechanism of \( B C l_{3} \) and \( S F_{4} \) are
respectively:
A \( \cdot s p^{2}, s p^{3} d \)
в. \( s p^{3}, s p 3 \)
\( \mathbf{c} \cdot s p^{3}, s p^{3} d^{2} \)
\( \mathbf{D} \cdot s p^{3}, s p^{3} d \)


An inductor \( 200 m H, \) capacitor \( 500 \mu F \)
resistor \( 10 \Omega \) are connected in series
with a \( 100 V \), variable frequency ac
source.
Calculate:
(i) frequency at which power factor of circuit its unity
(ii) current amplitude at this frequency
(iii) Q-factor.


Ecosystem has two components. They
are
A. Trees and fungi
B. Living and non living
c. Plants and animals
D. None of these


Name the red pigment which carries
oxygen in blood.


Which of the following shows the bending of light from denser (D) medium into a rarer (R) medium?
A.
в.
c.
D.


\( M e C H O \stackrel{N a O H, \Delta}{\longrightarrow} A \stackrel{K O H, \Delta}{\longrightarrow} B \)
B is:
A \( \cdot \operatorname{Me}(C H=C H)_{3} C H O \)
в. \( M e C H=C H C H O \)
c. \( \operatorname{Me}(C H=C H)_{2}-C H O \)
\( D \)
(4) \( \mathrm{Me}+\mathrm{CH}=\mathrm{CH}=_{4} \mathrm{CHO} \)


The perimeter of a triangle \( A B C \) is \( 27 \mathrm{cm} \) and the ratio between the
lengths of its sides is 2: 3: 4 find the
sides.
A .6,9,12
в. 3,6,9
c. 3,4,5
D. None


Name the type of polymerisation (addition or condensation) and name
the monomers in polyethylene.


1 parsec = metres


The production of dihydrogen obtained from coal gasification can be increased by reacting carbon monoxide of syngas mixture with steam in presence of a
catalyst iron-chromium. What is this
process called?
A. Hydrogen reaction
B. Water-gas shift reaction
c. coal-gas shift reaction
D. syn gasification


Name the parts \( a, b \) and \( c \)


A moving body makes a perfectly inelastic collision with a second body of
equal mass at rest K.E lost during collision is of initial
K.E.
A \( \cdot 1 / 4 \)
B. 1/2
\( c \)
D.


Negation of " \( 2+3=5 \) and \( 8<10 " \) is
A \( .2+3 \neq 5 \) and \( <10 \)
B. \( 2+3=5 \) and \( 8 \Varangle 10 \)
\( c \cdot 2+3 \neq 5 \) or \( 8 \Varangle 10 \)
D. None of the above


Which of the following is a quadratic
equation?
A \( \cdot x^{\frac{1}{2}}+2 x+3=0 \)
B \( \cdot(x-1)(x+4)=x^{2}+1 \)
\( \mathbf{c} \cdot x^{4}-x+5=0 \)
D. \( (2 x+1)(3 x-4)=2 x^{2}+3 \)


5
00
10


Acetaldehyde can be used for making synthetic:
A. protein
B. perfumes
c. rubbers
D. sugar


Evaluate \( : \int \frac{\cos x-\sin x}{\sqrt{8-\sin 2 x}} d x \)
A \( \cdot \sin ^{-1}\left(\frac{1}{3}(\sin x+\cos x)\right) \)
B \( \cdot \sin ^{-1}\left(\frac{1}{2}(\sin x+\cos x)\right) \)
c. \( \sin ^{-1}\left(\frac{1}{3}(\sin x-\cos x)\right) \)
D. \( \cos ^{-1}\left(\frac{1}{3}(\sin x+\cos x)\right) \)


Draw the structure of \( B F_{3} \)


Assertion
If the hydrogen atoms of benzene are replaced by deuterium atoms then the reactivity of benzene ring is decreased
for ESR.
Reason
The bond strength of \( C \) -D is more than \( C \) -
H, so reaction depends on the bond strength of \( C-D \) and \( C-H \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which of the following is true about Mendeleev's Periodic Table?
A. Systematic study of elements
B. Prediction of new elements
c. correction of doubtful atomic weights
D. All of the above


Let \( * \) be a binary operation on \( Z \) defined by \( a * b=a+b-4 \) for all \( a, b \in Z \)
Find the identity element in \( Z \)


Ethers have lower boiling points than their corresponding isomeric alcohols
because of?
A. hydrogen bonding in alcohols that is absent in ethers due to low polarity
B. hydrogen bonding in ethers due to high polarity
c. insolubility of ethers in water due to less polarity
D. inertness of ethers as compared to alcohols.


Which is not true for anaphase?
A. Golgi body and endoplasmic reticulum are reformed
B. Chromosomes move to opposite poles
C . Spindle poles move farther apart
D. Centromeres split and chromatids separate


Which of the following reactions is used
to make a fuel cell?
\( \mathbf{A} \cdot C d(s)+2 N i(O H)_{3}(s) \rightarrow C d O(s)+2 N i(O H)_{2}(s)+ \)
\( H_{2} O(l) \)
\( \mathbf{B} \cdot P b(s)+P b O_{2}(s)+2 H_{2} S O_{4}(a q) \rightarrow 2 P b S O_{4}(s)+ \)
\( 2 H_{2} O(l) \)
\( \mathbf{c} \cdot 2 H_{2}(g)+O_{2}(g) \rightarrow 2 H_{2} O(l) \)
D. \( 2 F e(s)+O_{2}(g)+4 H^{+}(a q) \rightarrow 2 F e^{2+}(a q)+2 H_{2} O(l) \)


Which of the following organic compounds polymerizes to form the polyester Dacron?
A. Propylene and para \( H O-\left(C_{6} H_{4}\right)-O H \)
B. Benzolic acid and ethanol
c. Terepthalic acid and ethylene glycol
D. Benzoic acid and para \( H O-\left(C_{6} H_{4}\right)-O H \)


\( \boldsymbol{C H} \equiv \boldsymbol{C}-\boldsymbol{C H}_{3} \frac{40 \% \boldsymbol{H}_{2} \boldsymbol{S O}_{4}}{1 \% \boldsymbol{H g S O}_{4}} \boldsymbol{B} \)
Then, \( B \) is :
A. acetone
B. trichloroacetone
c. acetaldehyde
D. chloral


One mole of \( H_{2} O \) and one mole of \( C O \)
are taken in \( 10 \mathrm{L} \) vessel and heated to
725 K. At equilibrium \( 40 \% \) of water (by mass) reacts with \( \mathrm{CO} \) according to the
equation, \( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g})+\boldsymbol{C O}(\boldsymbol{g}) \rightleftharpoons \)
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g}) \)
What is the value of equilibrium constant \( \left(K_{c}\right) \) for the reaction.
A .44
B. 4.
\( c \cdot 0.44 \)
D. 2.22


The element which has the highest first
ionization energy is:
A. hydrogen
B. xenon
c. fluorine
D. helium


The solubility of \( C a C O_{3} \) is \( 7 \mathrm{mg} / \mathrm{L} \)
Calculate the \( K_{s p} \) of \( B a C O_{3} \) when
\( N a_{2} C O_{3} \) is added slowly a solution
containing equimolar concentration of
\( C a^{2+} \) and \( B a^{2+} \) and no precipitate is
formed until \( 90 \% \) of \( B a^{2+} \) has been
precipitated as \( B a C O_{3} \)
A \( \cdot 1.1 \times 10^{-10} \)
B . \( 5 \times 10^{-10} \)
c. \( 1.1 \times 10^{-8} \)
D . \( 5 \times 10^{-6} \)


Three girls Reshma, Salma and Mandip are playing a game by standing on a circle of radius \( 5 \mathrm{m} \) drawn in a park.
Reshma throws a ball to Salma. Salma
to Mandip, Mandip to Reshma. If the distance between Reshma and Salma
and between Salma and Mandip is \( 6 \mathrm{m} \) each, what is the distance
between Reshma and Mandip?
\( \mathbf{A} \cdot 4.8 \mathrm{m} \)
B. \( 9.6 \mathrm{m} \)
\( c \cdot 2.4 m \)
D. \( 7.2 \mathrm{m} \)


The difference between a two digit number and the number obtained by
the interchanging the digits is \( 27 . \) What is the difference between the two digits of the number?
\( A \cdot 9 \)
B. 6
c. 12
D. 3


\( \mathbf{3} C l_{2}+\boldsymbol{x} \boldsymbol{N} \boldsymbol{a} \boldsymbol{O} \boldsymbol{H} \longrightarrow \boldsymbol{N} \boldsymbol{a} \boldsymbol{C l}+ \)
\( \boldsymbol{N a C l O _ { 3 }}+\boldsymbol{H}_{2} \boldsymbol{O}, \) then \( \mathbf{x} \) is


The enthalpy of formation of \( N H_{3}(g) \) is
\( -46.2 \mathrm{kJ} \mathrm{mol}^{-1} . \) The heat of the following
reaction is:
\( 2 N H_{3}(g) \rightarrow N_{2}(g)+3 H_{2}(g) \)
B . \( +46.2 \mathrm{kJ} \)
c. \( -92.4 \mathrm{kJ} \)
D. \( +92.4 \mathrm{kJ} \)


A magnet of moment \( 1.2 A m^{2} \) is kept
suspended in a magnetic field of
induction \( 2 \times 10^{-6} \). The work done in
rotating it through \( 120^{\circ} \) is:
A \( \cdot 2.4 \times 10^{-6} J \)
B . \( 4.8 \times 10^{-6} J \)
c. \( 1.2 \times 10^{-6} J \)
D. \( 3.6 \times 10^{-6} J \)


In figure, square \( J K L M \) is inscribed in
circle \( O . \) If the radius is \( 6, \) calculate the
area of the shaded region, to the nearest
tenth.
A . 10.3
B. 18.2
c. 22.8
D. 28.3
E . 38.6


Number of ways in which 9 different
prizes be given to 5 students if one particular boy receives 4 prizes \( \& \) the rest of the students can get any
numbers of prizes, is:
A \( \cdot^{9} \mathrm{C}_{4} \cdot 2^{10} \)
B. \( ^{9} \mathrm{C}_{5} \cdot 5^{4} \)
c. \( 4.4^{5} \)
D. none


A has 3 shares in a lottery in which
there are 3 prizes and 6 blanks; \( B \) has 1 share in a lottery in which there is 1
prize and 2 blanks: show that \( A^{\prime} s \)
chance of success is to B's as 16 to 7


Match the enzyme in column I with its
function in column II.


The position of oldest secondary phloem
is :
A. Just outside the vascular cambium
B. Just inside the primary phloem
c. Just inside the vascular cambium
D. Just outside the primary xylem


If two similarly charged particles are brought near one another, the potential energy of the system will:
\( A \). increase
B. decrease
c. remains the same
D. equal to the K.E.


The \( p H \) of \( 0.1 ~ M \) solution of the following salts increases in the order
A. \( N a C l<N H_{4} C l<N a C N<H C l \)
в. \( \operatorname{NaCN}<N H_{4} C l<N a C l<H C l \)
c. \( H C l<N a C l<N a C N<N H_{4} C l \)
D. \( H C l<N H_{4} C l<N a C l<N a C N \)


A gaseous mixture contains \( C O_{2}(g) \)
and \( N_{2} O(g) \) in 2: 5 ratio by mass. The
ratio of the number of molecules is:
A .5: 2
B . 2: 5
c. 1: 2
D. 5: 4


A coin is tossed 150 times and the
outcomes are recorded. The frequency distribution of the outcomes \( H \) (i.e, head)
and \( T \) (i.e, tail) is given below :
Outcome
\[
\begin{array}{ll}
\boldsymbol{H} & \boldsymbol{T} \\
& \\
85 & 65
\end{array}
\]
Frequency
Find the value of \( P(H) \), i.e, probability of
getting a head in a single trial.
A \( . P(H)=0.75 \) (approx)
B . \( P(H)=0.9 \) (approx)
C. \( P(H)=0.15 \) (approx)
D. None of these


The solution of \( \frac{d y}{d x}=\frac{y^{2}}{x y-x^{2}} \)
A. \( y=c e^{x y} \)
B. \( y=\frac{e^{\frac{y}{x}}}{c} \)
c. \( \log y=x y+c \)
D. \( \log x=x y+c \)


a) Define Kohlrausch's law of
independent migration of ions. Give its
applications.
b) Describe the salient features of the
Collision theory of reaction rates of bimolecular reactions.


In the figure,A and B are the centres of
the two intersecting circles.Which
Euclid's axiom will prove that the \( \triangle A B C \) is an equilateral triangles?
A. If equals are added to equals,the wholes are equal.
B. Things which are double of the same things are equal to one another
c. Things which are equal to the same thing are equal to one another.
D. If equals are subtracted from equals,the remainders are equal.


The value of \( c \) in Rolle's theorem for the
function \( \boldsymbol{f}(\boldsymbol{x})=\cos \frac{\boldsymbol{x}}{2} \) on \( [\boldsymbol{\pi}, \boldsymbol{3} \boldsymbol{\pi}] \) is
\( A \cdot 0 \)
B. \( 2 \pi \)
c. \( \frac{\pi}{2} \)
D. \( \frac{3 \pi}{2} \)


The velocity of a body varies with time
as \( V=3 t^{2}+2 . \) Find the instantaneous
acceleration \( t=3 \) sec
A \( \cdot 31 m / s^{2} \)
B . \( 18 \mathrm{m} / \mathrm{s}^{2} \)
c. \( 3 m / s^{2} \)
D . \( -2 / 3 \mathrm{m} / \mathrm{s}^{2} \)


Which of the following has the longest covalent bond distance?
A \( . C=C \)
в. \( C=H \)
c. \( C=N \)
D. \( C=O \)


Define mobility. Give its unit.


Which of the vitamins given below is
water soluble?
A. Vitamin \( C \)
B. Vitamin \( D \)
c. Vitamin \( E \)
D. Vitamin \( K \)


A vehicle moving with a constant acceleration from \( A \) to \( B \) in a straight
line \( A B, \) has velocities \( u \) and \( v \) at \( A \) and
B respectively. C is the mid point of AB. If time taken to travel from A to C is
twice the time to travel from \( C \) to \( B \) then
the velocity of the vehicle \( v \) at \( B \) is:
A . \( 5 u \)
B. \( 6 u \)
c. \( 7 u \)
D. \( 8 u \)


Select the correct option:
Lipids are arranged within the
membrane with
A. Polar heads toward inner side and the hydrophobic tails toward outerside
B. Both heads and tails toward outerside
C. Heads toward outerside and tail towards inside
D. Both heads and tails toward innerside


If the value charge density of a dielectric sphere with a cavity (a shown
in the figure) is \( \rho . \) Find the electrostatic
self energy.


Choose the correct option(s)
A. When we see a virtual image in plane mirror, a real image is formed on the retina of our eye
B. A plane mirror always forms a real image of virtual object
C. A bi-concave lens may form a real image
D. A bi-convex lens may form a virtual image
E. Answer required


Three identical resistors each of
resistance \( R \) are connected to an ideal
cell of voltage \( V \) as shown. Total power
dissipated in all three resistors is:
\( A \cdot \frac{3 V^{2}}{2 R} \)
\( B \cdot \frac{3 V^{2}}{B} \)
c. \( \frac{V^{2}}{3 R} \)
D. \( \frac{2 V^{2}}{3 R} \)


\( 1 \times 10^{-3} \mathrm{kg} \) of urea is present in 400
cubic centimetre solution at \( 310 \mathrm{K} \)
Calculate the approximate osmotic pressure of the solution. \( \left(\boldsymbol{R}=\mathbf{8 . 3 1 4} \boldsymbol{J} \boldsymbol{m o l}^{-1} \boldsymbol{K}^{-1}, \) molecular \right.
weight of urea \( =60 \) )
\( A \cdot 1 \) atm
B. 2 atm
\( c \cdot 4 a t m \)
\( D \cdot 5 \) atm


The most common fullerene is \( C_{60} .60 \)
C-atoms are arranged in
pentagons and hexagons.
\( \mathbf{A} \cdot 12,20 \)
B. 16,26
c. 12,40
D. 16,40


If \( f(x) \) is a differentiable function,
\( \boldsymbol{f}^{\prime}(\boldsymbol{x}) \geq \mathbf{2}, \) for all \( \boldsymbol{x} \in \boldsymbol{R}, \boldsymbol{f}(\mathbf{1})=\mathbf{2} \)
then possible value of \( f(3) \) are This question has multiple correct options
A. 5
B. 6
\( c \cdot 7 \)
D.


The mode for the following frequency
distribution:
\begin{tabular}{lllll}
Size of & \multicolumn{1}{l} { Size } \\
items & Frequency & of items & Frequency \\
\( 0-4 \) & 5 & \( 20-24 \) & 10 \\
\( 4-8 \) & 7 & \( 24-28 \) & 6 \\
\( 8-12 \) & 9 & \( 28-32 \) & 3 \\
\( 12-16 \) & 17 & \( 32-36 \) & 1 \\
\( 16-20 \) & 12 & \( 36-40 \) & 0 \\
\hline
\end{tabular}
\( \mathbf{S}: \)
\( \mathbf{A} \cdot 32.66 \)
B . 14.61
\( \mathbf{c} \cdot 14 \)
D. none of these


What weight of zinc would be required to produce enough hydrogen to reduce \( 8.5 \mathrm{g} \) of copper oxide completely into copper?


Water holding capacity of the soil depends upon
A. Chemical composition of soil
B. Particle size of soil
c. Aggregation of soil particle
D. All of these


Find the common area (in sq. units) enclosed by the parabolas \( 4 y^{2}=9 x \) and
\( 3 x^{2}=16 y \)


The harnessing of water resources by building dams has social, economic
and \( \ldots \)


Null point with \( 1 V \) cell comes out to be \( 55 \mathrm{cm} \) and with \( R=10 \Omega \) it is \( 50 \mathrm{cm} \)
What is the internal resistance of the
cell?
A . \( 0.5 \Omega \)
В. \( 0.4 \Omega \)
\( c .1 \Omega \)
D. \( 0.2 \Omega \)


Prove that at any time, the total number of persons on the earth who shake hands an odd number of times is even


Name various parts of stamen


A point moves in xy-plane according to
equation \( \boldsymbol{x}=\boldsymbol{a} \boldsymbol{t}, \boldsymbol{y}=\boldsymbol{a t}(\boldsymbol{1}-\boldsymbol{b} \boldsymbol{t}) \) where \( \boldsymbol{a} \)
and \( b \) are positive constants and \( t \) is time. The instant at which velocity
vector is at \( \pi / 4 \) with acceleration
vector is given by:
A \( \cdot \frac{1}{a} \)
B. \( \frac{1}{b} \)
\( c \cdot \frac{1}{a}+\frac{1}{b} \)
D \( \cdot(a+b)\left(a^{2}+b^{2}\right) \)


The solubility of \( P b F_{2} \) in water at \( 25^{\circ} C \)
is \( \sim 10^{-3} M . \) What is its solubility in
\( \mathbf{0 . 0 5} \boldsymbol{M} \boldsymbol{N} \boldsymbol{a} \boldsymbol{F} \) solution?
Assume the latter to be fully ionised.
A . \( 1.6 \times 10^{-6} M \)
В. \( 1.2 \times 10^{-6} M \)
c. \( 1.2 \times 10^{-5} M \)
D. \( 1.6 \times 10^{-4} M \)


The pair of gases responsible for acid rain are:
A. \( H_{2}, O_{3} \)
в. \( C H_{4}, O_{3} \)
c. \( N O_{2}, S O_{2} \)
D. \( C O, C H_{4} \)


\( \boldsymbol{C}_{5} \boldsymbol{H}_{12}+\boldsymbol{C l}_{2} \stackrel{\text {light}}{\rightarrow} \boldsymbol{C}_{5} \boldsymbol{H}_{11} \boldsymbol{C l}^{N \boldsymbol{a} / \text {ether}} \)
Only one structure of B is possible. (A),
(B) and (C) are?
\( A \)
B.
c. both are correct
D. none is correct


What are Antiseptics? Give example


What is the name of the compound
shown in the structure?
A . 1,3,5 -trinitrobenzene
B. 2,4,6- trinitrobenzene
c. 3,5 -trinitro-niro-benzene
D. 1,3,5 -benzenetrinitro


Which primitive man used stones to pro
duce fire?
A. Java man
B. Neanderthal man
c. Cro-Magnon man
D. All of the above


If \( x+y=\sin (x-y) \) then \( \frac{d y}{d x} \) is equal
to
A \( \cdot \frac{1}{2} \)
B. 0
c. -1
D.


Which of the following is conserved when light waves interfere?
A. momentum
B. amplitude
c. energy
D. intensity


A potentiometer wire is \( 10 \mathrm{m} \) long and a potential difference of \( 6 V \) is maintained between its ends.The emf of a cell which
balances against a length of \( 180 \mathrm{cm} \) of the potentiometer wire is:
A . 1.8 \( v \)
B. 1.1 \( v \)
c. \( 1.08 \mathrm{v} \)
D. 1.2


Which is not the electron geometry of covalent molecules?
A. Pentagonal bipyramidal
B. Octahedral
c. Hexagonal
D. Tetrahedral


The main factor responsible for the depletion of ozone layer is addition of in the atmosphere.
\( \mathbf{A} \cdot M n \)
в. \( C l \)
c. \( N a \)
D. \( C o \)


Identify \( X \) and \( Y \) in the following
reaction sequence \( \boldsymbol{X} \stackrel{\boldsymbol{Z} \boldsymbol{n}}{\boldsymbol{Y}} \boldsymbol{Y} \underset{\boldsymbol{Z} \boldsymbol{n}-\boldsymbol{H}_{2}}{\frac{\boldsymbol{O}_{\boldsymbol{2}}}{\boldsymbol{O}}}\left(\boldsymbol{C H}_{\boldsymbol{3}}\right)_{2} \boldsymbol{C O}+\boldsymbol{C H}_{2} \boldsymbol{O} \)
A. \( X=\left(C H_{3}\right)_{2} C_{\text {In }}^{C H} C H_{3}, Y=C H_{3} C H=C H C H_{3} \)
в. \( X=\left(C H_{3}\right)_{2} C H C H_{2} B r, Y=C H_{3} C H=C H C H_{3} \)
c. \( X=\left(C H_{3}\right)_{2} C B r C H_{2} B r, Y=\left(C H_{3}\right)_{2} C=C H_{2} \)
D. \( X=\left(C H_{3}\right)_{2} C(B r)-C H_{2} B r, Y=\left(C H_{3}\right)_{2} C=C H_{2} \)


Match the items in List 1 with those in
List 2


is/are used in the
manufacture of bakelite polymer.
A. Propyl alcohol
B. Phenol
c. Formaldehyde
D. both B and C


According to Werner's coordination theory, there are kinds of
valency, and
primary valency of a central metal ion is
satisfied with
A. three, negative, positive, cations
B. different, negative, positive, anions
C. two, primary, secondary, anions
D. two, saturated, unsaturated, cations


Fructose gives negative silver mirror test with ammoniacal silver nitrate
A. True
B. False


List out the following actions on the basis of contact force and non contact
force.
a) Lifting a chair
b) The falling of a coconut from the tree
c) Friction between the road and the
tyre of a car
d) A comb attracts bits of paper
e) Attraction between two magnets


topp
rype vourquestion
above. If a student plots graphs of the
square of maximum charge \( \left(Q_{\operatorname{Max}}^{2}\right) \) on the capacitor with time (t) for two
different values \( L_{1} \) and \( L_{2}\left(L_{1}>L_{2}\right) \) of
then which of the following represents
this graph correctly? (plots schematic and not drawn to scale


What does the path of an object look
like when it is in uniform motion?


When acetone and chloroform are
mixed, hydrogen bonding takes place between them. Such a liquid pair will
cause:
A. Positive deviation from Raoult's law
B. Negative deviation from Raoult's law
c. No deviation from Raoult's law
D. cannot be predicted


A metal box with a square base and
vertical height is to contain \( 1024 \mathrm{cm}^{2} \)
The material for the top and the bottom
\( \operatorname{costs} \mathrm{Rs} .5 / \mathrm{cm}^{2} \) and the material for the
sides costs Rs. \( 2.50 / c m^{2} \). Find the least
\( \operatorname{cost} \) of the box.


The complex number \( \frac{1+2 i}{1-i} \) lies in
which quadrant of the complex plane.
A. First
B. second
c. Third
D. Fourth


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


The ratio between the sum of \( n \) terms of
two A.P.'s is \( 3 n+8: 7 n+15 . \) Find the
ratio between their 12 th terms.
A \( \cdot \frac{7}{10} \)
B. \( \frac{7}{18} \)
c. \( \frac{7}{12} \)
D. \( \frac{7}{16} \)


All antihistamines inhibit the action of
the compound histamine which causes inflammation in the body. This drug is classified
A. on the basis of pharmacological effect
B. on the basis of drug action
c. on the basis of chemical structure
D. on the basis of molecular targets


Wilkinson catalyst is:
\( \mathbf{A} \cdot\left[\left(P h_{3} P\right)_{3} R h C l\right]\left(E t=C_{2} H_{5}\right) \)
\( \mathbf{B} \cdot\left[E t_{3} P\right)_{3} I r C l \)
\( \mathbf{c} \cdot\left[E t_{3} P\right)_{3} R h C l \)
\( \mathbf{D} \cdot\left[P h_{3} P\right)_{3} I e C l \)


List any three human activities which
would lead to an increase in the carbon
dioxide content of air.


Using Rolle's theorem, find points on the
curve \( \boldsymbol{y}=\mathbf{1 6}-\boldsymbol{x}^{2}, \boldsymbol{x} \in[-\mathbf{1}, \mathbf{1}], \) where
tangent is parallel to \( x- \) axis.


A spaceship is released in a circular orbit near the Earth's surface. How
much additional velocity will have to be
given to the spaceship in order to escape out of this orbit?
\( \begin{array}{ll}\text { A. } 3.28 & \text { m/s }\end{array} \)
В. \( 3.28 \times 10^{3} \mathrm{m} / \mathrm{s} \)
C \( .3 .28 \times 10^{7} \mathrm{m} / \mathrm{s} \)
D. \( 3.28 \times 10^{-3} \mathrm{m} / \mathrm{s} \)


Which of the following aryl amine undergoes diazotization most readily?
\( A \)
B.
\( c \)
\( D \)


Give two equivalent versions of Euclid's fifth postulate.


The thermal decomposition of
HCOOH is a first-order reaction with
a rate constant of \( 2.4 \times 10^{-3} s^{-1} \) at
certain temperature. How long will it take for three-fourths of the initial
quantity of \( H C O O H \) to decompose?
A. 578 sec
B. 225 sec
\( c .436 \mathrm{sec} \)
D. 57.8 sec


Write any two characteristics of first
order reaction.


Which of the following values are possible?

This question has multiple correct options
\( \mathbf{A} \cdot \sin \theta=0 \)
в. \( \sec \theta=\frac{1}{2} \)
\( \mathbf{c} \cdot \tan \theta=1 \)
D. \( \operatorname{cosec} \theta=\sqrt{3} \)


The following are some statements about diagonal relationship.
i) It is due to nearly same size, electronegativity and same polarising power
ii) \( L i \) has similar properties with \( H_{2} \)
iii) \( B e O, A l_{2} O \) are amphoteric in
nature
iv) All \( d \) -block elements are stable
A. Only (i) correct
B. Only (ii) correct
c. only (iii) correct
D. Only (iv) is correct


The stability of dihalides of \( \mathrm{Si}, \mathrm{Ge}, \mathrm{Sn} \) and Pb increases steadily in the
sequence:
\( A \cdot \operatorname{Gex}_{2} \ll \operatorname{six}_{2} \ll \sin x_{2} \ll \operatorname{Pb} x_{2} \)
B. \( \operatorname{six}_{2} \ll \operatorname{Gex}_{2} \ll \operatorname{Pb} x_{2} \ll \sin x_{2} \)
c. \( \operatorname{six}_{2} \ll \cos x_{2} \ll \operatorname{sn} x_{2} \ll \operatorname{pbx}_{2} \)
D. \( P b x_{2} \ll \operatorname{sn} x_{2} \ll G e x_{2} \ll \operatorname{six}_{2} \)


Integrate \( \int e^{\log (\sec x+\tan x)} \sqrt{1+\tan ^{2} x} d x \)


Rain drops are falling with a constant speed by the time they reach the ground
because.
A. Rain drops originate in outer space where the gravitational forces are negligible
B. The force due to air resistance increases with the speed of the rain drops until it balances the gravitational force
C. Rain drops are two light and hence not affected by acceleration due to gravity
D. The force due to air resistance is constant and
balances the gravitational force


toppr 5
Q Type your question-
gate and from the door of the house.
Select the correct possible circuit(s)
required.
\( A \)
в.
\( c \)
\( D \)


Which element among the following will not have an oxidation number of \( -1 ? \)
A. \( F \) in \( H F \)
B. \( C l \) in \( N a C l \)
\( c \cdot O \operatorname{in} H_{2} O_{2} \)
D. \( F \) in \( N a F \)
E \( . H \) in \( N a_{2} H P O_{4} \)


Ozone layer acts as
A. Natural sun block
B. Artificial block
c. Semi natural
D. None of these


A coil carrying current \( l \) has radius and number of units \( n \). It is rewound so that radius of new coil is \( \frac{r}{4} \) and it
carries current \( l . \) The ratio of magnetic moment of new coil to that of original
coil is
A .
B. \( \frac{1}{2} \)
\( c \cdot \frac{1}{4} \)
D. 8


Reproduction is a
A. Biological process
B. Chemical process
C . Physical process
D. None of the above


If \( \boldsymbol{x}-\frac{\mathbf{1}}{\boldsymbol{x}}=\mathbf{9}, \) the value of \( \boldsymbol{x}^{2}+\frac{\mathbf{1}}{\boldsymbol{x}^{2}} \) is
A. 83
B. 79
c. 11
D.


Find union of \( A \) and \( B \), and represent it
using Venn diagram:
\( \boldsymbol{A}=\{\mathbf{1}, \mathbf{2}, \mathbf{3}\}, \boldsymbol{B}=\{\mathbf{4}, \mathbf{5}, \mathbf{6}\} \)


When light is refracted into a denser
medium,
A. its wavelength and frequency both increase
B. its wavelength increases but frequency remains unchanged
C. its wavelength decreases but frequency remains unchanged
D. its wavelength and frequency both decrease


Show that the function \( x^{x} \) is minimum
at \( \boldsymbol{x}=\frac{\mathbf{1}}{\boldsymbol{e}} \)


Liquid metals used for making
thermometer is:
A. zirconium
B. mercury
c. lead
D. none of the above


Which is the most acidic site?


Oxygen is
A. yellow in colour
B. colourless gas
c. brown in colour
D. colourless solid


Prove that the function \( f(x)=x+|x| \)
\( x \in R \) is not one-one.


Find the co-ordinates of the points of trisection of the line joining the points (-3,0) and (6,6)


For each graph given below, four linear equations are given. Out of these find the equation that represents the given
graph.Equations are
A) \( y=x \)
B) \( \boldsymbol{x}+\boldsymbol{y}=\mathbf{0} \)
C) \( y=2 x \)
D) \( 2+3 y=7 x \)


If universal gravitational constant \( (G) \) speed of light \( (c), \) and time (t) are base units then the dimensional formula of
mass can be represented as?
A \( \cdot\left[G^{1} c^{3} t^{1}\right] \)
\( \mathbf{B} \cdot\left[G^{-1} c^{3} t^{1}\right] \)
C. \( \left[G^{-1} c^{-2} t^{-1}\right] \)
\( \mathbf{D} \cdot\left[G^{1} c^{-3} t^{-1}\right] \)


Consider an \( \alpha \) -particle just in contact with a \( _{92}^{238} \mathrm{U} \) nucleus. The Coulombic repulsion energy (i.e, the height of the Coulombic barrier between \( ^{238} \mathrm{U} \) and
alpha particle) assuming that the distance between them is equal to the
sum of their radii is
\( \mathbf{A} \cdot 16.35 M e V \)
в. \( 46.66 \mathrm{MeV} \)
c. 22.24 MeV
D. 26.14 \( M e V \)


Let \( C \) be the capacitance of a capacitor discharging through a resistor
R.Suppose \( t \) is the time taken for the energy stored in the capacitor to be reduced to half its initial value and t2 is
the time taken for the charge to reduce to one fourth its initial value.Then the
ratio t1/t2 will be


f \( \alpha, \beta \) and \( \gamma \) are the angles which a half ray makes with the positive direction of the axes, then \( \sin ^{2} \alpha+\sin ^{2} \beta+\sin ^{2} \gamma \) is
equal to
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c \cdot 0 \)
D. -


1.0 molal aqueous solution of an
electrolyte \( A_{2} B_{3} \) is \( 60 \% \) ionized. The
boiling point of the solution at 1 atm is:
\( \left[\boldsymbol{K}_{\boldsymbol{b}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)}=\mathbf{0 . 5 2} \boldsymbol{K} \boldsymbol{k g} \boldsymbol{m o l}^{-1}\right] \)
A. \( 274.76 \mathrm{K} \)
B. 377 К
c. 376.4 к
D. \( 374.72 \mathrm{K} \)


If the volume of a sphere is numerically equal to the surface area of the sphere, then find its radius.


In case of aldehydes and ketones there is the addition of nucleophile but in case of acyl compound, there is a nucleophilic substitution.
A. True
B. False


Briefly, answer the following questions given below.
(i) State two reasons for the increase of population in India.
(ii) What is the significance of amniotic fluid?
(iiii) What is the function of ear
ossicles?
(iv) Mention any two activities of the
WHO
(v) State Mendel's law of dominance.


The length of latus rectum of the parabola \( (x-2 a)^{2}+y^{2}=x^{2} \) is
A \( .2 a \)
B. \( 3 a \)
\( c \cdot 6 a \)
D. \( 4 a \)


Which part of plant is modified into (i)
Pitcher in Pitcher Plant (ii) Tendril in Pumpkin (iii) Haustoria in Cuscuta (iv) Tendril in Pea.


The stickiness of honey which mainly consists of water and sugar is due to:
A. presence of sugar
B. strong bonding in sugar
c. hydrogen bonding
D. presence of some organic compound


Gases which increase the temperature
of the atmosphere such as carbon dioxide, methane, chlorofluorocarbon, etc are known as \( _{--} \) -gases.
A. Green house
B. Blue house
c. white house
D. Red house


Which organism was the nuclear donor for Dolly?
A. Finn Dorset
B. Scottish black face
c. sally
D. Rosette


Consider the following statements:
1. Coefficient of variation depends on
the unit of measurement of the variable.
2. Range is a measure of dispersion
3. Mean deviation is least when
measured about median.
Which of the above statements are
correct?
A. 1 and 2 only
B. 2 and 3 only
c. 1 and 3 only
D. 1,2 and 3


Classify the following function as injection, surjection or bijection:
\( \boldsymbol{f}: \boldsymbol{Z} \rightarrow \boldsymbol{Z} \) given by \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{\boldsymbol{3}} \)


The most commonest component of kidney stones is
A. Calcium oxalate
B. Uric acid
c. cysteine
D. Magnesium phosphate


In the Lewis dot structure \( X \) : the
predictable oxidation number is :
A \( .+1 \)
в. - -
\( c \cdot+2 \)
D. -2
\( \mathrm{E} \cdot+3 \)


Three similar cells, each of emf \( 2 V \) and
internal resistance \( r \) send the same
current through an external resistance of \( 2 \Omega, \) when connected in series or in
parallel. Then the magnitude of current flowing through the external resistance is :
\( \mathbf{A} \cdot 0.75 A \)
в. \( 1 A \)
\( c .1 .5 A \)
D. zero


Specific heat capacity is for
conductors of heat and for
insulators of heat.
A. low, low
B. low, high
c. high, high
D. high, low


Explain the importance of fossils in
deciding evolutionary relationships.


Sketch the region bounded by the curves \( \boldsymbol{y}=\sqrt{\mathbf{5}-\boldsymbol{x}^{2}} \) and \( \boldsymbol{y}=|\boldsymbol{x}-\mathbf{1}| \)
and find its area using intergration.


The wavefront of a lightbeam is given by the equation \( x+2 y+3 z=c, \) (where \( c \)
is arbitary constant) the angle made by the direction of light with the y-axis is:
A \( \cdot \cos ^{-1} \frac{1}{\sqrt{14}} \)
B. \( \cos ^{-1} \frac{2}{\sqrt{14}} \)
c. \( \sin ^{-1} \frac{1}{\sqrt{14}} \)
D. \( \sin ^{-1} \frac{2}{\sqrt{14}} \)


\( \int \frac{x^{2}-1}{x^{3} \sqrt{2 x^{4}-2 x^{2}+1}} d x \) is equal to
A \( \cdot \frac{\sqrt{2 \mathrm{x}^{4}-2 \mathrm{x}^{2}+1}}{\mathrm{x}^{2}}+\mathrm{c} \)
в. \( \frac{\sqrt{2 \mathrm{x}^{4}-2 \mathrm{x}^{2}+1}}{\mathrm{x}^{3}}+\mathrm{c} \)
c. \( \frac{\sqrt{2 x^{4}-2 x^{2}+1}}{x}+c \)
D. \( \frac{\sqrt{2 \mathrm{x}^{4}-2 \mathrm{x}^{2}+1}}{2 \mathrm{x}^{2}}+\mathrm{c} \)


If \( \boldsymbol{f}(\boldsymbol{y})=\boldsymbol{e}^{\boldsymbol{y}}, \boldsymbol{g}(\boldsymbol{y})=\boldsymbol{y} ; \boldsymbol{y}>\mathbf{0} \) and
\( \boldsymbol{F}(\boldsymbol{t})=\int_{0}^{t} \boldsymbol{f}(\boldsymbol{t}-\boldsymbol{y}) \boldsymbol{g}(\boldsymbol{y}) \boldsymbol{d} \boldsymbol{y}, \) then which
of the following is true?
A \( \cdot F(t)=e^{t}-(1+t) \)
B \( \cdot F(t)=t e^{t} \)
c. \( F(t)=t e^{-t} \)
D. \( F(t)=1-e^{-t}(1+t) \)


Two particles of masses \( m_{1} \) and \( m_{2} \) are
dropped from height \( h_{1} \) and \( h_{2} \). They
reach the earth after times \( t_{1} \) and \( t_{2} \)
respectively, Then:
A \( \cdot \frac{t_{1}}{t_{2}}=\sqrt{\frac{h_{1}}{h_{2}}} \)
B. \( \frac{t_{1}}{t_{2}}=\sqrt{\frac{h_{2}}{h_{1}}} \)
c. \( \frac{t_{2}}{t_{1}}=\frac{h_{2}}{h_{1}} \)
D. none of these


Find the value of determinant, \( \left|\begin{array}{ccc}1 & a & a^{2}-b c \\ 1 & b & b^{2}-c a \\ 1 & c & c^{2}-a b\end{array}\right| \)


Equanil is a/an
A. artificial sweetener
B. tranquilizer
c. antihistamine
D. antifertility drug


If \( C \) and \( D \) are two events such that
\( \mathbf{C} \subset \mathbf{D} \) and \( \mathbf{P}(\mathbf{D}) \neq \mathbf{0}, \) then the correct
statement among the following is
\( ^{\mathbf{A}} \cdot p\left(\frac{C}{D}\right)=\mathrm{P}(\mathrm{C}) \)
\( ^{\mathbf{B}} \cdot p\left(\frac{C}{D}\right) \geq \mathrm{P}(\mathrm{C}) \)
\( ^{c} \cdot p\left(\frac{C}{D}\right)<\mathrm{P}(\mathrm{C}) \)
\( P\left(\frac{C}{D}\right)=\frac{P(D)}{P(C)} \)


Choose the wrong statement among the following
This question has multiple correct options
A. The pressure at a point in a fluid is directly proportional to the depth of the point from the surface
B. The pressure at a point is independent of acceleration due to gravity
C. The pressure at a point is directly proportional to the area of cross section
D. The pressure at a point is proportional to the density of the fluid


What are the maximum speeds of a
particle executing SHM of amplitude A and time period \( T \)
\( \mathbf{A} \cdot\left(V_{\max }=4 \pi A / T, V_{\min }=0\right) \)
B . \( \left(V_{\max }=\pi A / T, V_{\min }=0\right) \)
C \( \cdot\left(V_{\max }=\pi A / 2 T, V_{\min }=2 \pi A / T\right) \)
D. \( \left(V_{\max }=2 \pi A / T, V_{\min }=0\right) \)


In the metallurgy of copper, the impure metal got after Bessemerization is called:
A. Blister copper
B. Wrought copper
c. Brass copper
D. Pig copper


Which of the following which has the
highest molar conductivity?
\( \mathbf{A} \cdot\left[C o\left(N H_{3}\right)_{5} C l\right] B r \)
в. \( \left[C o\left(N H_{3}\right)_{5} C l\right] S O_{4} \)
\( \mathbf{c} \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{5} C l\right] N O_{2} \)
D. \( \left[\operatorname{Co}\left(N H_{3}\right)_{4} C l\right] \cdot 2 H_{2} O \)


Find odd one w.r.t meiotic cell cycle
A. DNA replication occurs once only i.e., before Gap- 2
B. Karyokinesis occurs twice
C. Reduction of ploidy at metaphase-
D. Crossing over in tetrad stage


\( A B C D \) is a quadrilateral such that \( A B=5 c m, B C=4 c m ; C D= \)
\( 7 c m, A D=6 c m \) and diagonal \( B D= \)
\( 5 c m, \) then the \( A(\square A B C D) \) is \( 4(3+ \)
\( \sqrt{6}) c m^{2} \)
A. True
B. False


State whether given statement is True or False

In p-njunction diode, the forward bias current is very small as compared to the reverse bias current.
A. True
B. False


A liquid is kept in a cylindrical vessel, which is rotated along its axis. The liquid rises at the side. If the radius of the vessel is \( 5 \mathrm{cm} \) and the frequency of rotation is 4 rev/s, then the difference in the height of the liquid at the centre of
the vessel and its sides is:
A. \( 8 \mathrm{cm} \)
B. 2 \( \mathrm{cm} \)
c. \( 40 \mathrm{cm} \)
\( D \cdot 4 \mathrm{cm} \)


Which one of the following is the differential equation that represents the family of curves \( y=\frac{1}{2 x^{2}-c} \) where
\( c \) is an arbitrary constant?
A \( \cdot \frac{d y}{d x}=4 x y^{2} \)
B. \( \frac{d y}{d x}=\frac{1}{y} \)
c. \( \frac{d y}{d x}=x^{2} y \)
D. \( \frac{d y}{d x}=-4 x y^{2} \)


Fill in the blanks.
The perimeters of two similar triangles are \( 25 \mathrm{cm} \) and \( 15 \mathrm{cm} \) respectively. If one side of the first triangle is \( 9 \mathrm{cm}, \) then corresponding side of second triangle is


The value of \( \Delta H \) for the combustion of
\( \mathrm{C}(\mathrm{s}) \) is \( -94.4 \mathrm{Kcal} . \) The heat of
formation of \( \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g}) \) is:
A. -49.5 Kcal
B. - -94.4 Kcal
c. -188.0 Kcal
D. More data required


\( K M n O_{4} \) reacts with oxalic acid
according to the equation \( 2 M n O_{4}^{-}+5 C_{2} O_{4}^{2-}+16 H^{+} \rightarrow \)
\( \mathbf{2} M n^{2+}+\mathbf{1 0} C O_{2}+\mathbf{8} H_{2} O \)

Here \( , 20 m L \) of \( 0.1 \mathrm{M} K M n O_{4} \) is
equivalent to:

This question has multiple correct options
A \( \cdot 120 m L \) of 0.25 M \( H_{2} C_{2} O_{4} \)
B. \( 50 m L \) of 0.10 M \( H_{2} C_{2} O_{4} \)
c. \( 25 m L \) of 0.20 M \( H_{2} C_{2} O_{4} \)
D. \( 50 m L \) of \( 0.20 \mathrm{M} \mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4} \)


The magnetic field at a point due to a current carrying conductor is directly proportional to:
This question has multiple correct options
A. Resistance of the conductor
B. Thickness of the conductor
C. Current flowing through the conductor
D. Distance from the conductor


Find the area tabletop, which is in the
shape parallelogram with base \( 4 m \) and
height \( 5 m \) Find its area.


Which of the following statement(s)
is/are correct regarding the amplitude
vs frequency curve for a driven system? This question has multiple correct options
A. Smaller the damping, taller and narrower the resonance peak
B. The amplitude tends to infinity when it equals to natural frequency results in zero damping
C. The resonant amplitude decreases with increasing damping
D. Small damping results in driving frequency almost equal to natural frequency


If \( x^{2}+\frac{1}{x^{2}}=102, \) then \( x-\frac{1}{x} \) is equal to
\( \mathbf{A} \cdot \mathbf{8} \)
B. 10
c. 12
\( D \)


Surahi and Matki are made from
A. Sandy soil
B. Loamy soil
c. Black soil
D. silt


If \( a^{3}-3 a^{2} b+3 a b^{2}-b^{3} \) is divided by
\( (a-b), \) then the remainder is
A \( \cdot a^{2}-a b+b^{2} \)
B \( \cdot a^{2}+a b+b^{2} \)
\( c \)
D.


At \( 700 K, C O_{2} \) and \( H_{2} \) react to form
\( C O \) and \( H_{2} O . \) For this process \( K_{c} \) is
0.11. If a mixture of 0.45 mole of \( C O_{2} \)
and 0.45 mole of \( H_{2} \) is heated at \( 700 K \)
(i) Find out the amount of each gas at equilibrium state.
(ii) After equilibrium is reached another
0.34 mole of \( C O_{2} \) and 0.34 mole of \( H_{2} \) are added to the reaction mixture. Find
the composition of the mixture at the
new equilibrium state.


The enthalpy changes for two reactions are given by the equations:
\( 2 C r(s)+1 \frac{1}{2} O_{2}(g) \longrightarrow \)
\( \boldsymbol{C r}_{2} \boldsymbol{O}_{3}(\boldsymbol{s}) ; \boldsymbol{\Delta} \boldsymbol{H}=-\mathbf{1 1 3 0} \boldsymbol{k} \boldsymbol{J} \)
\( C(s)+\frac{1}{2} O_{2}(g) \longrightarrow C O(g) ; \Delta H= \)
\( -110 k J \)
What is the enthalpy change, in \( k J, \) for
the reaction?
\( \mathbf{3} C(s)+C r_{2} O_{3}(s) \longrightarrow 2 C r(s)+ \)
\( \mathbf{3} \boldsymbol{C O}(\boldsymbol{g}) \)
A. \( -1460 k J \)
в. \( -800 k J \)
\( c .+800 k J \)
D. \( +1020 k J \)
\( \mathrm{E} \cdot+1460 k J \)


Which of the following is a most explosive compound?
A \( \cdot \mathrm{xeF}_{6} \)
в. \( \mathrm{xe} \mathrm{e}_{4} \)
c. \( \mathrm{xeF}_{2} \)
D. XeF \( _{4} \)


A transistor is a/an
A . chip
B. insulator
c. semiconductor
D. metal


Polyurethanes
A. have structural features of both an ester and an amide
B. have the formula \( H_{2} N-C_{\|}-O-C H_{2}-C H_{3} \)
C. are obtained from p-phenylene disocyanate and ethylene glycol
D. are used as foam rubber in upholstery


"All gases have the same number of moles in the same volume at constant
temperature and pressure:. This statments belongs to :
A. Boyle's law
B. Charles's law
c. Avogadro's principle
D. ideal gas law
E. Dalton's law


The quantity of charge (in Faraday) required to reduce 96 g Mg from molten solution of \( \mathrm{MgCl}_{2} \) is :


The driver of a train moving with a constant speed \( v_{1} \) along a straight track sights another train at a distance
d ahead of him on the same track
moving in the same direction with a
constant speed \( v_{2} . \) He at once applies
the brakes and gives his train a
constant retardation \( \mathrm{f} \). There will be a
collision of the trains if:
A \( \cdot v_{1}>v_{2} \) and \( \frac{\left(v_{1}-v_{2}\right)^{2}}{2 f}<d \)
в. \( _{v_{1}}<v_{2} \) and \( \frac{\left(v_{1}+v_{2}\right)^{2}}{2 f}>d \)
c. \( _{v_{1}>v_{2} \text { and }} \frac{\left(v_{1}-v_{2}\right)^{2}}{2 f}>d \)
D \( v_{1}>v_{2} \) and \( \frac{\left(v_{1}^{2}-v_{2}^{2}\right)}{2 f}>d \)


The fourth term of a G.P. is 27 and the
7th term is \( 729, \) find the 5 th term of G.P.


Two men of equal masses stand at
opposite ends of the diameter of a
turntable disc of a certain mass,
moving with constant angular velocity.
The two men make their way to the
middle of the turntable at equal rates. In
doing so will
A. kinetic energy of rotation has increased while angular momentum remains same.
B. kinetic energy of rotation has decreased while angular momentum remains same.
C. kinetic energy of rotation has decreased but angular momentum has increased.
D. both, kinetic energy of rotation and angular momentum have decreased.


Heat capacity of a substance is infinite.
It means:
A. heat is given out
B. heat is taken in
c. no change in temperature whether heat is taken in or given out
D. all of the above


When does a fuse cut off current? How
does it do it?


According to Bohr theory, the angular momentum of electron in 5 th orbit is:
A \( \cdot_{25} \frac{h}{\pi} \)
в. \( _{1} \frac{h}{\pi} \)
\( \mathrm{c} \cdot_{10} \frac{h}{\pi} \)
D. \( _{2.5} \frac{h}{\pi} \)


Given that tidal volume is \( 600 \mathrm{ml} \) inspiratory reserve volume is \( 2500 \mathrm{ml} \) and expiratory reserve volume is \( 800 \mathrm{ml} \)
what is the value of vital capacity of lung?
A . \( 3900 \mathrm{ml} \)
B. 3300ml
\( c .3100 \mathrm{ml} \)
D. \( 1400 \mathrm{ml} \)


For a particle performing linear S.H.M. Its average speed over one oscillation is \( (a=a m p l i t u d e \text { of } S . H . M, n= \) frequency of oscillation)
A . \( 2 a n \)
B. 4an
c. \( 6 a n \)
D. \( 8 a n \)


A rational number can be expressed
as a terminating decimal if the denominator has factors:
\( A \cdot 2 \) or 5
в. 2,3 от 5
c. 3 or 5
D. None of these


Work done in moving an object through an equipotential surface is
A. Positive
B. Negative
c. zero
D. Depends on the field direction


Water obtained from which of the
following sources is a good conductor of electricity?
A . Tap
B. Ponds
c. wells
D. All of the above


\( \Delta G^{o}(298 K) \) for the reaction \( \frac{1}{2} N_{2}+ \)
\( \frac{3}{2} H_{2} \stackrel{K_{1}}{\rightleftharpoons} N H_{3} \) is \( -16.5 \mathrm{kJ} \) mol\( ^{-1} . \) The
equilibrium constant \( \left(K_{1}\right) \) at \( 25^{\circ} C \)
\& the equilibrium constant \( K_{2} \) and \( K_{3} \)
for the following reactions are \( N_{2}+3 H_{2} \stackrel{K_{2}}{\rightleftharpoons} 2 N H_{3} \)
\( N H_{3} \stackrel{K_{3}}{\rightleftharpoons} \frac{1}{2} N_{2}+\frac{3}{2} H_{2} \)
A \( \cdot K_{1}=779.4, K_{2}=6.074 \times 10^{5} ; K_{3}=1.283 \times 10^{-3} \)
B . \( K_{1}=779.4, K_{2}=2.183 \times 10^{5} ; K_{3}=3.576 \times 10^{3} \)
C . \( K_{1}=124.4, K_{2}=6.074 \times 10^{5} ; K_{3}=2.34 \times 10^{3} \)
D. None of these


g mixture of glucose and urea present in \( 250 \mathrm{mL} \) aqueous solution shows the
osmotic pressure of 0.74 atm at \( 27^{\circ} C \)
Assuming solution to be diluted, which
are correct?
1. Percentage of urea in the mixture is
17.6
2. Relative lowering of the vapour
pressure of this solution is \( 5.41 \times 10^{-4} \)
3. The solution will boil at \( 100.015^{\circ} C \), if
\( K_{b} \) of water is \( 0.5 \mathrm{K} \) molality \( ^{-1} \)
4. If glucose is replaced by the same amount of sucrose, the solution will
show higher osmotic pressure at \( 27^{\circ} C \)
5. If glucose is replaced by the same amount of \( N a C l \), the solution will show
lower osmotic pressure at \( 27^{\circ} \mathrm{C} \)
A. 1,2,3
в. 1,2,3,5
c. 2,4,5
D. 1,4,5


The nucleophilicities of \( \boldsymbol{R}_{3} \boldsymbol{C}^{-}, \boldsymbol{R}_{2} \boldsymbol{N}^{-} \)
\( R O^{-} \) and \( F^{-} \) decrease in the order:
\( \mathbf{A} \cdot R_{3} C^{-}>R_{2} N^{-}>R O^{-}>F^{-} \)
В \( \cdot F^{-}>R O^{-}>R_{2} N^{-}>R_{3} C^{-} \)
c. \( R O^{-}>F^{-}>R_{2} N^{-}>R_{3} C^{-} \)
D. \( R_{3} C^{-}>R O^{-}>F^{-}>R_{2} N^{-} \)


Which of the following properties
correctly explain the compound \( S i O_{2} ? \)
A. Linear, basic
B. Tetrahedral, acidic
c. Tetrahedral, basic
D. Linear, acidic


Statement \( 1: A \) piece of zinc placed in a
blue copper nitrate solution will
displace the copper from the solution,
producing copper metal and a colorless
\( Z n^{2+} \) solution.
Statement 2: Copper is a much more active metal than zinc.
A. Both Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement 1.
B. Both Statement 1 and Statement 2 are correct and Statement 2 is not the correct explanation of Statement 1.
c. Statement 1 is correct but Statement 2 is not correct.
D. Statement 1 is not correct but Statement 2 is correct.
E. Both the Statement 1 and Statement 2 are not correct.


Complex formation method is used for the extraction of:
\( A \cdot z n \)
B. Agg
c. ну
D. cu


If the squares of the lengths of the tangents from a point \( P \) to the circles \( \boldsymbol{x}^{2}+\boldsymbol{y}^{2}=\boldsymbol{a}^{2}, \boldsymbol{x}^{2}+\boldsymbol{y}^{2}=\boldsymbol{b}^{2} \) and \( \boldsymbol{x}^{2}+ \)
\( y^{2}=c^{2} \operatorname{are} \) in A.P., then
This question has multiple correct options
A \( \cdot a^{2}, b^{2}, c^{2} \) are in A.P
B. \( \frac{1}{a^{2}}, \frac{1}{b^{2}}, \frac{1}{c^{2}} \) are in \( \mathrm{H.P} \)
c. \( a^{2}, b^{2}, c^{2} \) are in G.P
D. \( \frac{1}{a^{2}}, \frac{1}{b^{2}}, \frac{1}{c^{2}} \) are in A.F.


Disease caused due to poor sanitation
is
A. cancer
B. Typhoid.
c. Polio
D. Both B and C


The velocity \( v \) of a particle is given by the equation \( v=6 t^{2}-6 t^{3}, \) where \( v \) is in
the \( m s^{-1}, t \) is the instant of time in
seconds while 6 and 6 are suitable
dimensional constants. At what values
of \( t \) will the velocity be maximum and minimum? Determine these maximum
and minimum values of the velocity.


ff \( \mathbf{A}=\left[\begin{array}{cccc}\cos & \boldsymbol{\theta} & \sin & \boldsymbol{\theta} \\ \boldsymbol{s i n} & \boldsymbol{\theta} & -\boldsymbol{\operatorname { c o s }} & \boldsymbol{\theta}\end{array}\right], \mathbf{B}=\left[\begin{array}{cc}\mathbf{1} & \mathbf{0} \\ -\mathbf{1} & \mathbf{1}\end{array}\right] \)
\( \mathbf{C}=\boldsymbol{A} \boldsymbol{B} \boldsymbol{A}^{\boldsymbol{T}} \)
then \( A^{T} C A \) equals to \( (n \quad \in \quad N) \)
A. \( \left[\begin{array}{cc}-n & 1 \\ 1 & 0\end{array}\right] \)
B. \( \left[\begin{array}{cc}1 & -n \\ 0 & 1\end{array}\right] \)
C. \( \left[\begin{array}{cc}0 & 1 \\ 1 & -n\end{array}\right] \)
D. \( \left[\begin{array}{cc}1 & 0 \\ -n & 1\end{array}\right] \)


A radiation is incident on a metal
surface of work function \( 2.3 e V \). The
wavelength of incident radiation is
600 nm. If the total energy of incident
radiation is \( 23 J \), then the number of
photoelectrons is
A. zero
B \( \cdot>10^{4} \)
\( \mathbf{c} \cdot=10^{4} \)
D. None of these


Calculate the weight of \( C a O \) required to
remove the hardness of 1000000 litre of
water containing 1.62 g of \( C a C O_{3} \) per litre.


Which of the following is a biodegradable polymer?
A.
\[
f H N-\left(C H_{2}\right)_{6} N H C O-\left(C H_{2}\right)_{4}-C_{7}^{\prime}
\]
B. \( \quad_{t H N-\left(C H_{2}\right)_{5}-C \dagger_{n}}^{o} \)
\( c \)
\( \left.\left[\begin{array}{l}\mathbf{0} \\ \mathbf{c}\end{array}\right]\left[\begin{array}{l}- \\ \end{array}\right]-\mathbf{C O O}-\left(\mathbf{C H}_{2}\right)_{2}-\mathbf{O}\right] \)
D. \( +H N-\left(C H_{2}\right)_{5} C O N H-C H_{2}-\stackrel{\|}{C}+_{n} \)


Find what the following equations become when the origin is shifted to the
point (1,1)\( ? \)
(i) \( x^{2}+x y-3 x-y+2=0 \)
\( \boldsymbol{x}^{2}-\boldsymbol{y}^{2}-\boldsymbol{2} \boldsymbol{x}+\boldsymbol{2} \boldsymbol{y}=\mathbf{0} \)
(iii) \( \boldsymbol{x y}-\boldsymbol{x}-\boldsymbol{y}+\mathbf{1}=\mathbf{0} \)
\( \boldsymbol{x} \boldsymbol{y}-\boldsymbol{y}^{2}-\boldsymbol{x}+\boldsymbol{y}=\mathbf{0} \)


Assertion
If two half reaction with electrode
potential \( E_{1}^{o} \) and \( E_{2}^{o} \) gives a third half
reaction, then \( \Delta G_{3}^{o}=\Delta G_{1}^{o}+\Delta G_{2}^{o} \)
Reason
\( \boldsymbol{E}_{\mathbf{3}}^{\boldsymbol{o}}=\boldsymbol{E}_{\mathbf{1}}^{\boldsymbol{o}}+\boldsymbol{E}_{\mathbf{2}}^{\boldsymbol{o}} \)
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


A cylindrical bar magnet is kept along the axis of a circular coil. On rotating the magnet about its axis, the coil will
have induced in it
A . a current
B. no current
c. only an e.m.f.
D. both an e.m.f. and a current


Animals breathe, oxygen and give
out
A. Carbon dioxide
B. Oxygen
c. Nitrogen
D. Hydrogen


A rod of length \( L \) is pivoted at one end and is rotated with a uniform angular
velocity in a horizontal plane. Let \( T_{1} \) and
\( T_{2} \) be tension at the points \( L / 4 \) and
\( 3 L / 4 \) always from the pivoted end. Then
A \( \cdot T_{1}>T_{2} \)
B \( \cdot T_{1}=T_{2} \)
\( \mathbf{c} \cdot T_{1}<T_{2} \)
D. The relation between \( T_{1} \) and \( T_{2} \) depends on whether the rod rotates clockwise or anticlockwise


The substance capable of being drawn
into a wire is called:
A . pliable
B. ductile
c. malleable
D. flexible


If the coefficient of friction is \( \sqrt{3}, \) the
angle of friction:
A \( .30^{\circ} \)
B. \( 60^{\circ} \)
\( c \cdot 45^{\circ} \)
D. 37


If \( 1+\sin ^{2} \theta=3 \sin \theta \cos \theta \) then the
solution set in \( \left[0, \frac{\pi}{2}\right] \) is
A \( \cdot\left\{\frac{\pi}{4}, \cos ^{-1}(1 / 3)\right\} \)
B \( \cdot\left\{\frac{\pi}{4}, \tan ^{-1}(1 / 2)\right\} \)
c. \( \left\{\frac{\pi}{3}, \tan ^{-1}(1 / 3)\right\} \)
D \( \cdot\left\{\frac{\pi}{6}, \sin ^{-1}(1 / 3)\right\} \)


The domain of \( \boldsymbol{f}(\boldsymbol{x})=\sqrt{\log \left(\frac{\boldsymbol{7} \boldsymbol{x}-\boldsymbol{x}^{2}}{\mathbf{1 2}}\right.}) \)
is
в. \( (-\infty, 4] \)
c. \( [3, \infty) \)
()
D. [3,4]


Four elements \( A, B, C \) and \( D \) have atomic
numbers 12,13,14 and 15 respectively
Which of them will have largest atomic
radii?


The price of sugar is increased by \( 20 \% \) By what percent must the consumption of sugar be decreased so that the expenditure on sugar may remain the same (upto the nearest integer)?


The acceleration due to gravity
with an increase in height
and depth.


Isomerisms exhibited by
\( \left[\boldsymbol{C r}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{2}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{2} \boldsymbol{C l}_{2}\right]^{+} \) are:
A. ionisation, optical
B. hydrate, optical
c. geometrical, optical
D. coordinate, geometrical


The rate constant of a reaction is 110
seconds and 210 seconds at \( 27 \mathrm{C} \) and
\( 37 \mathrm{C} \) respectively. Calculate activation energy of the reaction \( (R=8.314 \mathrm{JK} \)
\( \left.m o l^{-1}\right) \)


The number of alkenes (consider
stereochemistry of the alkene too) that can be hydrogenated to form methyl cyclohexane is :


Five forces are separately applied to the flat object lying on a horizontal table of negligible friction as shown in the
figure above. The line of action of each force is shown by a dashed line. Identify
which of the five forces will cause the
object to rotate about point \( O ? \)
\( A \)
B.
\( c \)
\( D \)
E


If \( x^{4}+\frac{1}{x^{4}}=194, \) then \( x^{3}+\frac{1}{x^{3}} \) is equal
to
A . 76
B. 52
c. 64
D. None of these


An astronaut can't hear his companion at the surface of the moon because:
A. Produced frequencies are above the audio frequency
B. There is no medium for sound propagation
C. Temperature is too low during night and too highh during day
D. There are too many craters on the surface of the moon


A liquid mixture of benzene \( (B) \) and
toluene \( (T) \) contains 1 mole each of \( B \)
and \( T \)
\( \boldsymbol{P}_{\boldsymbol{T}}^{\boldsymbol{o}}=\mathbf{4 . 2 7 4} \boldsymbol{k} \boldsymbol{N} \boldsymbol{m}^{-2} \) and \( \boldsymbol{P}_{\boldsymbol{B}}^{\boldsymbol{o}}= \)
\( \mathbf{1 3 . 7 3 4} \mathbf{k} \mathbf{N m}^{-\mathbf{2}} \)
If the pressure is reduced further, pressure \( \left(\text { in } k N m^{-2}\right) \) (write only integer part) at which the last trace of liquid does disappear
is


In \( I C l_{4}^{\ominus}, \) the shape is square planer. The number of bond pair-lone pair repulsion
at \( 90^{\circ} \) are:
A. 6
B. 8
c. 12
D. 4


\( \boldsymbol{x}= \)
\( \operatorname{cosec}\left(\tan ^{-1}\left(\cos \left(\cot ^{-1}\left(\sec \left(\sin ^{-1} a\right)\right)\right)\right.\right. \)
\( \sec \left(\cot ^{-1}\left(\sin \left(\tan ^{-1}\left(\operatorname{cosec}\left(\cos ^{-1} a\right)\right)\right)\right.\right. \)
where \( a \in[0,1] . \) Then which of the
following options is correct?
A \( \cdot x^{2}+a^{2}=3 \)
В. \( x=y \)
c. \( y^{2}+a^{2}=3 \)
D. All of these


Which of the following metal oxides are reduced by self reduction method? This question has multiple correct options
\( \mathbf{A} \cdot C u_{2} O \)
в. \( P b O \)
c. \( H g O \)
D. \( \mathrm{CaO} \)


A card is drawn from a well-shuffled
deck of playing cards. Find the probability of drawing a face card.
\( A \cdot \frac{8}{13} \)
в. \( \frac{3}{13} \)
c. \( \frac{4}{13} \)
D. \( \frac{1}{4} \)


The difference in the oxidation numbers
of the two types of sulphur atoms in
\( N a_{2} S_{4} O_{6} \) is:
A. 5
B. 4
\( c \cdot 6 \)
D. 8


Plants store waste materials in
A. Old leaves
B. Vacuoles
c. Both A and B
D. None of the above


fin a \( \triangle D E F, G H \| E F \) and \( D G \)
\( \boldsymbol{E G}=\boldsymbol{2}: \boldsymbol{3} \) then the value of
\( \frac{\operatorname{ar}(\triangle D G H)}{\operatorname{ar}(\triangle D E F)} \)
A \( \cdot \frac{2}{15} \)
B. \( \frac{4}{15} \)
c. \( \frac{4}{25} \)
D. \( \frac{2}{25} \)


Which of the following are uses of
sulphur?
This question has multiple correct options
A. Sulphur is used in preparation of conducting wires
B. A mixture of zinc and sulphur on heating with sulphur produces a greyish residue of zinc sulphide
C. Sulphur is an element belonging to VI A group
D. Sulphur is a nonmetallic element.


The function \( f(x)=\sin ^{-1}(\cos x) \) is
A. Discontinuous at \( x=0 \)
B. continuous at \( x=0 \)
C. differentiable at \( x=0 \)
D. None of these


A biased coin is tossed twice.The
probability of head is twice the tail.The PDF of number of heads is
\( \begin{array}{llll}\mathbf{x} & \mathbf{0} & \mathbf{2} & \mathbf{2}\end{array} \)
\( p(x) \quad \frac{a}{d} \quad \frac{b}{d} \quad \frac{c}{d} \)
then values of \( a, b, c, d \) are
A. \( a=1, b=2, c=3, d=4 \)
В. \( a=1, b=4, c=4, d=9 \)
c. \( a=1, b=4, c=4, d=10 \)
D. \( a=1, b=2, c=1, d=4 \)


A gas mixture 3.67 L in volume contain
\( C_{2} H_{4} \) and \( C H_{4} \) is proportion of 2: 1 by
moles and is at \( 25^{\circ} \mathrm{C} \) and 1 atm. If the
\( \boldsymbol{\Delta} \boldsymbol{H}_{C}^{\circ}\left(\boldsymbol{C}_{2} \boldsymbol{H}_{4}\right) \) and \( \boldsymbol{\Delta} \boldsymbol{H}_{C}^{\circ}\left(\boldsymbol{C} \boldsymbol{H}_{4}\right) \) are
-1400 and \( -900 \mathrm{kJ} / \mathrm{mol} \) find heat evolved
on burning this mixture
A. \( 20.91 \mathrm{kJ} \)
J.
B. 50.88 kJ
c. 185 k
D. 160 k


What will be the number of heart beats
per minute if the stroke volume of heart increases with the total volume of blood
remains same?
A. Remains constant
B. Decreases
c. Increases
D. Becomes erratic


Which one of the following statements
is correct with respect to salt water balance inside the body of living organisms?
A. When water is not available camels do not produce urine but store urea in tissues
B. Salmon fish excretes lot of stored salt through gill membrane in fresh water.
c. Paramecium discharges concentrated salt solution by contractile vacuoles.
D. The body fluids of fresh water animals are generally hypotonic to surrounding water.


Electronegativity of inert gases is :
A . low
B. highh
c. zero
D. abnormally high


A gas undergoes a thermodynamical process but the volume of the gas does not change. What is the nature of this
process?
A. Isothermal
B. Adiabatic
c. Isobaric
D. Isochoric


If true enter 1 , else enter 0 .
The oppositely charged ion pair is more stable than the separated ions.


Let \( A B \) and \( C D \) be two parallel lines and \( \stackrel{\leftrightarrow}{P Q} \) be a transversal. Let \( \stackrel{\leftrightarrow}{P Q} \)
intersect \( A^{\leftrightarrow} B \) in \( L . \) Suppose the bisector
of \( \angle A L P \) intersect \( C D \) in \( R \) and the bisector of \( \angle P L B \) intersect \( \stackrel{\leftrightarrow}{C D} \) in \( \mathrm{S} \)
Prove that
\( \angle \boldsymbol{L} \boldsymbol{R} \boldsymbol{S}+\angle \boldsymbol{R} \boldsymbol{S} \boldsymbol{L}=\boldsymbol{9} \boldsymbol{0}^{\boldsymbol{o}} \)


Light incident on a rotating mirror \( \mathrm{M} \) is returned to a fixed mirror N placed
\( 22.5 k m \) away from M. The fixed mirror reflects it back to M (along the same path) which in turn reflects the light again along a direction that makes an
angle of \( 27^{\circ} \) with the incident direction.
The speed of rotation of the mirror is:
A .250 rps
в. 500 rps
c. 1000 rps
D. 125 rps


In the Down's process of obtaining
sodium, \( C a C l_{2} \) is added:
A. To get high yield of sodium
B. To improve the quality of sodium obtained
C. To lower the operating temperature
D. To act as a reducing agent


What is the formal charge on the
chlorine atom in the oxyacid \( H O C l O_{2} \) if it contains single bonds?
A . -2
B. - 1
\( c \cdot+1 \)
D. +2


2 mole each of \( S O_{3}, C O, S O_{2} \) and \( C O_{2} \)
is taken in a one lit. vessel. If \( \boldsymbol{K}_{c} \) for
\( \boldsymbol{S} \boldsymbol{O}_{3}(\boldsymbol{g})+\boldsymbol{C O}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{S} \boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g}) \)
is \( 1 / 9 \) then:
A. Total no. of moles at equilibrium are less than 8
B . \( n\left(S O_{3}\right)+n\left(C O_{2}\right)=4 \)
\( \mathbf{c} \cdot\left[n\left(S O_{2}\right) / n(C O)\right]<1 \)
D. Both \( (B) \) and \( (C) \)


If the distance between a point \( P \) and
the point (1,1,1) on the line \( \frac{x-1}{3}= \)
\( \frac{y-1}{4}=\frac{z-1}{12} \) is \( 13, \) then the coordinates
of \( P \) are
A. (3,4,12)
В. \( \left(\frac{3}{13}, \frac{4}{13}, \frac{12}{13}\right) \)
c. (4,5,12)
D. (40, 53, 157)


Which of the following pair gives
effervescence with \( N a H C O_{3} ? \)
\( \boldsymbol{C H}_{3} \boldsymbol{C O C l} \)
\( (I) \)
\( \boldsymbol{C H}_{3} \boldsymbol{C O C H}_{3} \)
\( (I I) \)
\( \boldsymbol{C H}_{3} \boldsymbol{C O O C H}_{3} \)
\( (I I I) \)
\( \boldsymbol{C H}_{3} \boldsymbol{C O O C O C H} \)
\( (I V) \)
A. I and II
B. I and IV
c. ॥ and III
D. I and III


A nuclear reaction is given as
\( \boldsymbol{p}+^{15} \boldsymbol{N} \rightarrow_{Z}^{A} \boldsymbol{X}+\boldsymbol{n} \)
Find, \( A, Z \) and identify the nucleus \( X \)


When an object undergoes acceleration
A. Its speed always increases
B. Magnitude of velocity may remain constant
C. It always falls towards the earth
D. A force always acts on it


Linear momentum of an electron in Bohr orbit of H-atom (principal quantum
number \( n \) ) is proportional to:
A \( \cdot \frac{1}{n^{2}} \)
B. \( \frac{1}{n} \)
\( c \)
\( \mathbf{D} \cdot n^{2} \)


A car A moves with the velocity of
\( 20 m s^{-1} \) and car \( B \) with velocity \( 15 m s^{-1} \)
as shown in the figure. Find the relative Velocity of B w.r.t. A and A w.r.t. B.


Assertion
Isotopes of an element have same
chemical properties
Reason
Chemical properties do not depend on
the number of neutrons
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The relation between internal energy U, pressure \( P \) and volume \( V \) of a gas in an adiabatic process is \( U=a+b P V, \) where a and b are positive constants. What is the value of \( \gamma \) ?
A. \( \frac{a}{b} \)
B. \( \frac{b+1}{b} \)
c. \( \frac{a+1}{a} \)
D.


The thermal capacity of 10 g of a substance is \( 8 \mathrm{cal}^{0} C^{-1} \) then its specific
heat is 1.25 cal \( g^{-1} o C^{-1} \)
State whether given statement is True/False
A. True
B. False


A projectile ofmass \( m \) is thrown with a
velocity v making an angle \( 60^{\circ} \) with the horizontal, neglecting air resistance, the change in momentum from the departure A to its arrival at B, along the vertical directions:
\( A \cdot 2 m \)
B. \( \sqrt{3} \mathrm{mv} \)
\( c .3 m v \)
D. \( \frac{m v}{\sqrt{3}} \)


Which of the following relations is not
correct?
A \( \cdot \frac{Y}{\eta}=2(1+\sigma) \)
в. \( \frac{Y}{3 K}=1-2 \sigma \)
c. \( _{Y}=\frac{9 K \eta}{3 K+\eta} \)
D. \( \frac{Y}{\eta}+\frac{Y}{3 K}=3 \)


Red on first draw and white on second
draw


Differentiate between
Open bundle and closed bundle


Radii of two conducting circular loops are \( b \) and \( a \) respectively, where \( b>>a \)
Centres of both loops coincide but planes of both loops are perpendicular to each other. The value of mutual
inductance for these loops.
A \( \cdot \frac{\mu_{0} \pi b^{2}}{2 a} \)
B. zero
c. \( \frac{\mu_{0} \pi a b}{2(a+b)} \)
D. \( \frac{\mu_{0} \pi a^{2}}{2 b} \)


The below reaction is the gold-plating process reaction.
\[
\boldsymbol{A} \boldsymbol{u}^{3+}(\boldsymbol{a q})+\boldsymbol{3} \boldsymbol{e}^{-} \rightarrow \boldsymbol{A} \boldsymbol{u}(\boldsymbol{s})
\]
If \( 0.600 g \) of \( A u \) is plated onto a metal how many coulombs are used?
\( \mathbf{A} \cdot 299 C \)
B. \( 868 C \)
\( c .2,990 C \)
D. \( 8,680 C \)


The decreasing order of dipole moment of the following is :
\( \boldsymbol{I} \cdot \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C l} \)
II. \( \boldsymbol{C H}_{3} \boldsymbol{B r} \)
III \( \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{F} \)
A \( \cdot(I)>(I I)>(I I I) \)
в. \( (I)>(I I I)>(I I) \)
c. \( (I I)>(I)>(I I I) \)
D. \( (I I)>(I I I)>(I) \)


Find the derivative of \( \boldsymbol{y}= \) \( \tan ^{-1}\left(\frac{\boldsymbol{a} \boldsymbol{x}-\boldsymbol{b}}{\boldsymbol{b} \boldsymbol{x}+\boldsymbol{a}}\right) \)


Two wires, each of radius \( r, \) but of
different materials are connected
together end to end. If the densities of
charge carriers in the two wires are in the ratio \( 1: 4, \) the ratio of the drift velocity of electrons in the two wires will be \( . . \)
A . 1: 2
B. 2:
\( c \cdot 1: 4 \)
D. 4:


To \( 500 c m^{3} \) of water \( 3.0 \times 10^{-3} k g \) of
acetic acid is added. If \( 23 \% \) of acetic
acid is dissociated, what will be the depression of freezing point? \( \left[K_{f} \) and density of water are \right. \( 1.86 K k g m o l^{-1} \) and \( 0.997 g c m^{-3} \)
respectively
в. \( 0.33 K \)
c. \( 0.98 K \)
D. \( 0.68 K \)


Which has the highest entropy per mol of the substance?
A \( . H_{2} \) at \( 25^{\circ} \mathrm{C} \) and 1 atm
B. \( H_{2} \) at STP
C. \( H_{2} \) at \( 100 \mathrm{K} \) and \( 1 \mathrm{atm} \)
\( D \cdot H_{2} \) at \( 0 \mathrm{K} \) and 1 atm


Breathing:
A. ventilates lungs
B. draws air into airways
C. expels air from airways
D. all of these


How many pi bonds are present in phosgene?
A.
B. 2
\( c \cdot 3 \)
\( D \)


The instantaneous potential difference
between points \( A \) and \( B \) is :
A \( \cdot 8 \sin \left(50 \pi t+37 \frac{\pi}{180}\right) \)
B \( \cdot 8 \sin \left(50 \pi t-37 \frac{\pi}{180}\right) \)
c. \( 10 \sin (50 \pi t) \)
D. \( 10 \cos (50 \pi t) \)


Which of the following factors affect the oxygen dissociation curve?
A. Partial pressure of carbon dioxide
B. \( p H\left(H^{+} \) ion concentration) \right.
c. Temperature
D. Partial pressure of oxygen
E. All of the above


A body is sliding down an inclined plane having coefficient of friction \( 0.5 . \) If the normal reaction is twice that of the
resultant downward force along the
incline, the angle between the inclined plane and horizontal is
A \( \cdot 15^{\circ} \)
B . \( 30^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 60^{\circ} \)


ABCD is quadrilateral, \( A C=19 \mathrm{cm} \). the length of perpendicular from B and D on AC are \( 5 \mathrm{cm} 7 \mathrm{cm} \) respectively. Then, the area of ABCD in sq. cm is:


Chitin occurs in the wall of
A. Bacteria
B. Algae
c. Fungi
D. Yeast


An example of cladode is
A. Phyllanthus symbolic
B. Jatropha cursus
C. Euphorbia tirucalli
D. None of the above


The G.M. of n positive terms \( \boldsymbol{x}_{1}, \boldsymbol{x}_{2}, \ldots . . \boldsymbol{x}_{n} \)
is
A \( \cdot\left(x_{1} \times x_{2} \times \ldots \ldots \times x_{n}\right)^{n} \)
B \( \cdot \frac{1}{n}\left(x_{1} \times x_{2} \times \ldots \times x_{n}\right) \)
c. \( \left(x_{1} \times x_{2} \times \ldots \times x_{n}\right)^{1 / n} \)
D. None of these


Eighty-nine students of class VIII appeared for a combined test in Maths
and Physics. If 62 students passed in
both \( ; 4 \) failed in Maths and Physics and
7 failed only in Maths. Use a Venndiagram to find: how many passed in Maths.


Which substance present in cotton
Cloth forms hydrogen bond with water?
A. Nucleic acid
B. Cellulose
c. Phenol
D. RNA


The equation of a simple harmonic
wave is given by \( \boldsymbol{y}= \)
\( 6 \sin 2 \pi(2 t-0.1 x), \) where \( x \) and \( y \) are
in \( m m \) and \( t \) is in seconds. The phase
difference between two particles \( 2 m m \)
apart at any instant is
A \( \cdot 18^{\circ} \)
В. \( 36^{\circ} \)
\( c \cdot 54^{\circ} \)
D. \( 72^{\circ} \)


Estrous cycle is characteristic of
A. Human females
B. Mammalian females
C. Mammalian females other than primates
D. Mammals


Consider the statements \( \$ 1 \) and \( s 2: \)
S1: Conductivity always increases with decrease in the concentration of
electrolyte.
S2: Molar conductivity always increases with decrease in the concentration of
electrolyte.

The correct option among the following is:
A. Both S1 and S2 are correct
B. s1 is wrong and s2 is correct
\( c . \) s1 is correct and s2 is wrong
D. Both S1 and S2 are wrong


Explain the following:
(a) A chimney smokes when a fresh fire is started under it.
(b) Small holes are provided at the bottom of the chimney in an oil lamp.
(c) Land becomes warmer than water
during the day.


\( \boldsymbol{K}_{1} \) and \( \boldsymbol{K}_{2} \) are equilibrium constants for reaction (i) and (ii)
\( N_{2}(g)+O_{2}(g) \rightleftharpoons 2 N O(g) \dots(i) \)
\( N O(g) \rightleftharpoons \frac{1}{2} N_{2}(g)+\frac{1}{2} O_{2}(g) \dots(\text { ii }) \)
Then:
A \( \cdot K_{1}=\left(1 / K_{2}\right)^{2} \)
B \( \cdot K_{1}=K_{2}^{2} \)
C \( . K_{1}=1 / K_{2} \)
D. \( K_{1}=\left(K_{2}\right)^{\circ} \)


The diagram below shows a hydraulic lift. A force is applied at side 1 and an output force is generated at side 2
Which of the following is true.?
A. the force at the side lis greater than the force at side 2
B. The force at the side lis less than the force at side 2 .
C. The pressure at side 1 is greater than the force at side
2
D. The pressure at side 1 is less than the pressure at side
2


Molecular formula of Retinol is:
A \( \cdot C_{20} H_{29} O H \)
в. \( C_{17} H_{35} O H \)
\( \mathbf{c} \cdot C_{12} H_{25} O H \)
D. \( C_{17} H_{33} O H \)


The ether when treated with \( H \)
produces
\( \bigcirc\rangle-_{0}-\mathrm{cH}_{2}-\langle\bigcirc\rangle \)
\( \bigcirc\rangle-\mathrm{c} \mathrm{H}_{2} \)
\( \bigcirc\rangle-\mathrm{cH}_{2} \mathrm{o} \)
\( \bigcirc\rangle \)
\( \sqrt{0}-0 \)


Suppose \( 5 \% \) of men and \( 0.25 \% \) of women have grey hair. A grey haired person is selected at random. What is the probability of this person being male? Assume that there are equal
number of males and females.


When light suffers reflection at the
interface between water and glass, the change of phase in the reflected wave is
A. zero
в. \( \pi \)
\( c \cdot \pi / 2 \)
D. 2 \( \pi \)


How many bond pair and lone pair are there in \( C O_{3}^{2-} ? \)


Sketch shown is of an electrolytic cell used in the extraction of aluminium:
What is the substance of which the
electrode A is made?
A. Graphite
B. Diamond
\( c . \) Iron
D. Aluminium


Water is a kind of \( _{-1-} \) oxide.
A. acidic
B. basic
c. neutral
D. metal


Origin is the centre of circle passing through the vertices of an equilateral triangle whose median is of length \( 3 a \)
then equation of the circle is?
A \( \cdot x^{2}+y^{2}=a^{2} \)
B . \( x^{2}+y^{2}=2 a^{2} \)
c. \( x^{2}+y^{2}=3 a^{2} \)
D. \( x^{2}+y^{2}+4 a^{2} \)


Which of the liquids in each of the following pairs has a higher vapour pressure?
A. Alcohol, glycerine
B. Mercury, water
c. petrol, kerosene
D. None of these


An f-shell containing 6 unpaired electrons can exchange:
A. 6 electrons
B. 9 electrons
c. 12 electrons
D. 15 electrons


State true or false:
Difference of any two sides of a triangle is equal to the third side.
A. True
B. False


A freshly obtained precipitate of \( S n O_{2} \)
is peptized by little of \( K O H \) to give a
sol. The sol particles may be represented as:
\( \mathbf{A} \cdot\left[S n O_{2}\right] K^{+} \)
B . \( \left[S n P_{2}\right] O H^{-} \)
\( \mathbf{c} \cdot\left[\operatorname{Sn} O_{2}\right] S n^{4+} \)
D. \( \left[S n O_{2}\right] S n O_{3}^{2} \)


\( \boldsymbol{H}_{2} \boldsymbol{S} \) precipitates aqueous \( \boldsymbol{Z} \boldsymbol{n} \boldsymbol{C l}_{2} \)
solution in :
A. Acidic medium.
B. Neutral medium
c. Both (a) and (b).
D. None of these.


Sound travels fast in \( _{\text {一一一一一一一 }} \) than
liquids


If \( \boldsymbol{x}=\boldsymbol{a} \boldsymbol{t}^{2}, \quad \boldsymbol{y}= \)
2at then \( \boldsymbol{d}^{2} \boldsymbol{y} / \boldsymbol{d} \boldsymbol{x}^{2}= \)
A \( \cdot \frac{-1}{t^{2}} \)
в. \( \frac{1}{t^{2}} \)
c. 0
D. \( \frac{1}{2 a^{3}} \)


What is the product of the following
reaction?
3-methyl-2-pentene+Br \( _{2} / H_{2} O \rightarrow \)
\( A \)
B.
\( c \)
\( D \)


The element having the least size from the following is :
A. boron
B. carbon
c. sluminium
D. silicon


Figure shows a uniformly charged
hemisphere of radius R. It has a volume
charge density p. If the electric field at
point \( 2 R, \) above its center is \( E, \) then
what is the electric field at the point \( 2 R \)
below its center?
\( \mathbf{A} \cdot \rho R / 6 \varepsilon_{0}+E \)
\( \mathbf{B} \cdot \rho R / 12 \varepsilon_{0}-E \)
\( \mathbf{c} \cdot-\rho R / 6 \varepsilon_{0}+E \)
\( \mathbf{D} \cdot \rho R / 12 \varepsilon_{0}+E \)


What type of spectroscopy would be the best tool to analyze a clear and colorless solution for the presence of a functional group like an alcohol group \( (-O H) ? \)
A. uv spectroscopy.
B. IR spectroscopy
c. Mass spectroscopy.
D. Photoelectron spectroscopy


A photon of frequency n causes photoelectric emission from a surface
with threshold frequency \( v_{o} \). the de
Broglie wavelength \( \lambda \) of the photoelectron emitted is given as:
A \( \cdot \Delta n=\frac{h}{2 m \lambda} \)
B. \( \Delta n=\frac{h}{\lambda} \)
\( ^{\mathrm{C}}\left[\frac{1}{v_{o}}-\frac{1}{v}\right]=\frac{m c^{2}}{h} \)
D. \( \lambda=\sqrt{\frac{h}{2 m \Delta n}} \)


The valency, that is the combining capacity of oxygen is :
A . 1
B. 2
\( c \cdot 3 \)
D. None of these


The average of the total deficit of the middle five deficit is closest to the
deficit of which country?
A . Korea
B. South Africa
\( c \cdot \) UAE
D. None of these


In the circuit shown in figure, if
ammeter and voltmeter are ideal, then
the consumed in \( 9 \Omega \) resistor will be
A . 3.33 W
в. 4 И
c. \( 1.44 W \)
D. \( 500 W \)


Which of the following compounds can exist as an meso compounds?
A. 1,2 -dichlorobutane
B. 2, 3-dichloropentane
c. 2,3 -dichlorobutane
D. 1,2 -dichloropentane


In Dumas method percentage of nitrogen in an organic compound is estimated in the form of
A. \( N_{2} \) gas
в. \( N O \)
c. \( N H_{3} \)
D. \( N_{2} O_{5} \)


Magnetic moment of \( \boldsymbol{C r}(\boldsymbol{Z}= \) \( \mathbf{2 4}), \boldsymbol{M n}^{+}(\boldsymbol{Z}=\mathbf{2 5}) \) and \( \boldsymbol{F} \boldsymbol{e}^{\mathbf{2}+}(\boldsymbol{Z}=\mathbf{2 6}) \)
are \( x, y, z . \) They are in order:
A. \( x<y<z \)
в. \( x=y<z \)
c. \( z<x=y \)
D. \( x=y=z \)


Which of the following is false?
A. Bracket spectral series for which \( n_{1}=4 \) and \( n_{2}=5,6 \) 7,....lies in the infrared region of the electromagnetic radiation
B. The orbital 3d \( _{z}^{2} \) is symmetrical about z-axis
C. The orbital 3d \( _{x y} \) ha no probability of finding electron along \( x \) - and \( y \) -axis
D. The orbital 3d \( _{x^{2}-y^{2}} \) has no probability of finding electron along \( x \) -axis and \( y \) -axis


Given that \( \cos 50^{\circ} 18^{\prime}= \)
0.6388 and \( \cos 50^{\circ} 42^{\prime}=0.6334, \) then
the possible value of \( \cos 50^{\circ} 20^{\prime} \) is
A . 0.6293
B. 0.6307
c. 0.636
D. 0.6414


What are the reaction sequences of
glucosazone formation?


Which fat soluble vitamin is present in liver cell?
A. \( A \)
в. \( D \)
\( c . E \)
D. Both Vitamin A and D


State True or False.
The atomic number of Uus is 117


Assertion
The focal length of the concave mirror is \( f \) and distance of the object from the
focus is \( u . \) The magnification of the
image will be \( \boldsymbol{f} / \boldsymbol{u} \)
Reason
Magnification= \( \frac{\text {size of object}}{\text {size of image}} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which equation represents charge
balanced equation for a solution of \( \boldsymbol{H}_{2} \boldsymbol{S} \)
in water?
\( \mathbf{A} \cdot\left[H^{+}\right]=2\left[S^{2-}\right]+\left[H S^{-}\right]+\left[O H^{-}\right] \)
B \( \cdot\left[H^{+}\right]=\left[O H^{-}\right] \)
C \( \cdot\left[H^{+}\right]=\left[S^{2-}\right]+\left[H S^{-}\right]+\left[H^{+}\right] \)
D. \( \left[H^{+}\right]=\left[S^{2-}\right]+\left[H S^{-}\right]+\left[O H^{-}\right] \)


Leptoids and hydroids are the vascular
supply of
A. Pteridophytes
B. Irish mosses
c. Liverworts
D. All of the above


When \( 16.8 g \) of white solid \( X \) was
heated \( 4.4 g \) of acid gas : \( (A) \) that
turned lime water milky was driven of
together with \( 1.8 g \) of a gas \( (B) \) which condensed to a colourless liquid the
solid that remained \( (Y) \) dissolved in
water to give an alkaline solution, which
with excess of \( B a C l_{2} \) solution gave a
white precipitate \( (Z) . \) The precipitate
effervescence with acid giving of \( \boldsymbol{C O}_{2} \)
gas. Identify the compound \( A, B \) and
write the chemical equations for the
thermal decomposition of \( X \)
\( \mathbf{A} \cdot(A)-C O_{2} \)
\( (B)-H_{2} O \quad X \rightarrow N a_{2} C O_{3} \)
B. \( (A)-C O_{2} \)
\( (B)-H_{2} O_{2} \quad X \rightarrow N a C O_{3} \)
\( \mathbf{c} \cdot(A)-C O_{2} \)
\( (B)-H_{2} O_{2} \quad X \rightarrow N a_{2} C O_{3} \)
D. \( (A)-C O_{2} \)
\( (B)-H_{2} O \quad X \rightarrow N a C O_{3} \)


Assertion
A charged metallic sphere when brought nearer to an uncharged metallic sphere, it may exert an attractive force, but once they touch
each other, they exert repulsive force.
Reason
The net electric field Inside a conductor
is zero.
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


Angular momentum of a system a particles changes, when
A. Force acts on a body
B. Torque acts on a body
C. Direction of velocity changes
D. None of these


What is photorespiration? Explain the mechanism and its significance.


Find the mean deviations about the mean for the following data:
Marks \( i \) \( \begin{array}{ll}10- & 2 \\ 20 & 3\end{array} \) \( \begin{array}{ll}20- & 3 \\ 30 & 4\end{array} \)
30
obtained 40
Number of 2 student


The number of \( \sigma \) and \( \pi \) bonds in \( C_{2} H_{2} \)
is:
A. 0 and 4
B. 2 and 2
\( c .3 \) and 2
D. 4 and 2


What moves the food in the digestive
organs?


In a circle of diameter \( 40 \mathrm{cm} \), the length
of a chord is \( 20 \mathrm{cm} . \) Find the length of minor arc of the chord.


Calculate the value of the acceleration
due to gravity at a place \( 3,200 k m \)
above the surface of the earth.


Which of the following elements in an
organic
compound cannot be detected by Lassaigne's
test?
\( A \cdot N \)
B. \( s \)
c. \( c \) ।
D.


Assertion
BOD(Biological oxygen demand) is a
device that is used to measure quality
of water.
Reason
High BOD is observed in highly polluted
water
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


Flattened sacs of Golgi are separated from each other by a space which is
\( A \cdot 13 \hat{A} \)
B. 130 \( \dot{A} \)
c. 125 ,
D. 300 \( \vec{A} \)


Consider the following statement regarding human.
a. Duodenum is the longest part of small intestine
b. Hepatic and cystic ducts release their
secretions into common bile duct
whose opening is controlled by
sphincter of Oddi
c. Ileocaecal valve is present at the
junction of small intestine and large intestine
d. Mechanical digestion and chemical digestion of food occurs in buccal cavity, stomach and small intestine Which of the following choices is
correct?
A. A and B only
B. B and C only
C. \( \mathrm{C} \) and \( \mathrm{D} \) only
D. \( A, B, C \) and \( D \)


If for all \( x, y \) the function \( f \) is defined by
\( \boldsymbol{f}(\boldsymbol{x})+\boldsymbol{f}(\boldsymbol{y})+\boldsymbol{f}(\boldsymbol{x}) \cdot \boldsymbol{f}(\boldsymbol{y})=1 \) and
\( \boldsymbol{f}(\boldsymbol{x})>0 . \) When \( \boldsymbol{f}(\boldsymbol{x}) \) is differentiable
\( \boldsymbol{f}^{\prime}(\boldsymbol{x})= \)
A . -1
B. 1
\( c .0 \)
D. cannot be determined


The atomic number \( (z) \) of an element is
25. In its ground state, how many electrons are present in the N shell:
A . 13
B. 2
c. 15
D. 3


The distance of the eye-lens from the retina is \( x \). For a normal eye, the maximum focal length of the eye-lens
\( \mathbf{A} \cdot=x \)
в. \( <x \)
\( c \cdot>x \)
\( D \cdot=2 x \)


Conductivity of a saturated solution of a sparingly soluble salt \( A B \) at \( 298 K \) is
\( 1.85 \times 10^{-5} S m^{-1} . \) Solubility product of
the salt \( A B \) at \( 298 K \) is :
\( \left[\text { Given } \boldsymbol{\Lambda}_{\boldsymbol{m}}^{o}(\boldsymbol{A B})=\mathbf{1 4 0} \times\right. \)
\( \left.10^{-4} S m^{2} m o l^{-1}\right] \)
A. \( 1.32 \times 10^{-12} \)
В. \( 1.74 \times 10^{-12} \)
C \( .5 .7 \times 10^{-12} \)
D. \( 7.5 \times 10^{-12} \)


Assertion
Both o-hydroxy benzaldehyde and phydroxy benzaldehyde have same molecular weight and show H-bonding.
Reason

Melting point of p-hydroxy benzaldehyde is more than o-hydroxy benzaldehyde.
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


Copper-T is a device that prevents
A. Fertilisation
B. Implantation of blastocyst
c. Egg maturation
D. Ovulation


Quantities remaining constant in a collision are
A. Momentum, kinetic energy and temperature
B. Momentum but not kinetic energy and temperature
C. Kinetic energy and temperature but not momentum
D. None


The three vertices of a parallelogram \( A B C D, \) taken in order are \( A(1,-2) \)
\( B(3,6) \) and \( C(5,10) . \) Find
the coordinates of the fourth vertex D.
A. \( D(3,2) \)
в. \( D(-3,2) \)
c. \( D(3,-2) \)
D. \( D(3,3) \)


Sum \( 2 a-b, 4 a-3 b, 6 a-5 b, \dots \) to \( n \)
terms.


A light beam travelling in the \( x \) direction is described by the electric field \( \boldsymbol{E}_{\boldsymbol{y}}=\left(\mathbf{3 0 0} \boldsymbol{V} \boldsymbol{m}^{-1}\right) \sin \quad \boldsymbol{\omega}(\boldsymbol{t}-\boldsymbol{x} / \boldsymbol{c}) \)
An electron is constrained to move
along the y-direction with a speed of \( 2.0 \times 10^{7} m^{-1} \) Find the maximum
electric force and the maximum
magnetic force on the electron
A \( \cdot 4.8 \times 10^{-17} \mathrm{N}, \) zero
В. \( 4.2 \times 10^{-18} N, 1.8 \times 10^{-8} N \)
c. \( 4.8 \times 10^{-17} N, 3.2 \times 10^{-18} N \)
D. zero, zero


The number of \( \boldsymbol{A} \) in \( \boldsymbol{T}_{\boldsymbol{p}} \) such that \( \boldsymbol{A} \) is either symmetric or skew-symmetric or both, and det(A) divisible by \( p \) is:
A \( \cdot(p-1)^{2} \)
в. \( 2(p-1) \)
c. \( (p-1)^{2}+1 \)
D. \( 2 p-1 \)


Solve for \( x: \)
\( \frac{x+7}{3}=1+\frac{3 x-2}{5} \)


A girl is pushing a box towards east
direction. In which direction should her
friend push the box so that it moves faster in the same direction?
A. North
B. South
c. East
D. west


If \( \frac{1}{k}=\frac{1}{3}+\frac{1}{4} \) then the value of \( K \) is
A \( \cdot 1 \frac{5}{7} \)
в. \( 2 \frac{5}{7} \)
\( \mathrm{c} \cdot_{3} \frac{5}{7} \)
D. \( _{4} \frac{5}{12} \)


Four resistors are connected as shown
in figure. A \( 6 V \) battery of negligible
resistance is connected across
terminal \( \boldsymbol{A C} \). The potential difference
\( \operatorname{across} \) terminals \( B \) and \( D \) will be :
A . \( 0 V \)
в. \( 1.5 V \)
\( c .2 V \)
D. \( 3 V \)


shows compound inflorescence.
A. Sunflower
B. zinnia
c. Marigold
D. Neem


Granular \( V_{2} O_{5} \) is used as catalyst for
conversion of \( S \) into \( S O_{2} \) in the
manufacture of \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
A. True
B. False


There is a cuboid of dimensions \( 1 \times \)
\( b \times h \) and thermal capacity 'K' units. On
doubling the dimensions of the cuboid. Find the thermal capacity.


Many persons like to use asthma as an excuse for not being able to do well in sports. Try telling them about Down Fraser, who was the first women to
break 60 sec in 100 m freestyle swimming. The first women to win four
Olympic gold medals and the first swimmer to win the same event in three
consecutive Olympics was asthmatic. On the basis of the above passage, answer the following question.
i) What do you mean by asthma?


Correct sequence of stages of
succession on a bare rock is?
A. Lichens \( \rightarrow \) Mosses \( \rightarrow \) Grasses \( \rightarrow \) Shrubs \( \rightarrow \) Trees
B. Trees \( \rightarrow \) Shrubs \( \rightarrow \) Lichens \( \rightarrow \) Mosses \( \rightarrow \) Grasses
C. Mosses \( \rightarrow \) Shrubs \( \rightarrow \) Trees \( \rightarrow \) Lichens \( \rightarrow \) Grasses
D. Mosses \( \rightarrow \) Lichens \( \rightarrow \) Grasses \( \rightarrow \) Shrubs \( \rightarrow \) Trees


\( \mathbf{2} \boldsymbol{x}+\mathbf{3} \boldsymbol{y}=\left[\begin{array}{ll}\mathbf{2} & \mathbf{3} \\ \mathbf{4} & \mathbf{0}\end{array}\right] \) and \( \mathbf{3} \boldsymbol{x}+\mathbf{2} \boldsymbol{y}= \)
\( \left[\begin{array}{cc}2 & -2 \\ -1 & 5\end{array}\right] . \) Find the value of \( x \& y \)


Which of the following structures
represents terylene?
B.
\[
\left[-\mathrm{ocH}_{2}-\mathrm{cH}_{2}-\mathrm{o}-\mathrm{c}-\mathrm{c}_{\mathrm{b}} \mathrm{H}_{4}-\mathrm{C}-\right]_{\mathrm{n}}
\]
\( c \)
\[
\left[-\mathrm{CH}_{2}-\mathrm{CH}=\mathrm{CH}=\mathrm{CH}_{2}-\mathrm{C}_{\mathrm{n}}-\mathrm{CH}_{2}-\right]_{\mathrm{n}}
\]
\( D \)
\( \left(-\mathrm{CH}_{2}-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}_{2}-\right)_{\mathrm{n}} \)


Electron and proton are accelerated through one volt of potential difference, the ratio of their wavelengths is equal
to:
A. \( \frac{m_{p}}{m_{e}} \)
В \( \cdot \frac{m_{p} V_{e}}{m_{e} V_{p}} \)
c. \( \frac{m_{p}^{2}}{m_{e}^{2}} \)
D. \( \sqrt{\frac{m_{p}}{m_{e}}} \)


The synthetic steroid ethynylestardiol
(1) is a compuond used in the birth control pill. How many asymmetric (stereogenic) centres are present in compound (1) ?
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
\( D \)


\( \mathbf{5 0} \boldsymbol{m} \boldsymbol{L} \) of \( \mathbf{0 . 0 5} \boldsymbol{M} \boldsymbol{N} \boldsymbol{a}_{2} \boldsymbol{C O}_{3} \) is titrated
against \( 0.1 M H C l . \) On adding \( 40 m L \) of \( H C l, p H \) of the solution will be
[Given for \( \boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{O}_{3}, \boldsymbol{p} \boldsymbol{K}_{\boldsymbol{a}_{1}}= \)
\( \mathbf{6 . 3 5} ; \boldsymbol{p} \boldsymbol{K}_{\boldsymbol{a}_{2}}=\mathbf{1 0 . 3 3} ; \log \mathbf{3}= \)
\( \mathbf{0 . 4 7 7}, \log \mathbf{2}=\mathbf{0 . 3 0}] \)
A . 6.35
B. 6.526
c. 8.34
D. 6.173


Which amino acid is present only in bacteria and cyanobacteria?
A. Glycine
B. Tyrosine
c. Glutamic acid
D. Diaminopimellic acid


If the work done in blowing a soap
bubble of volume \( ^{\prime} V^{\prime} \) is \( W \), then the
work done in blowing is soap bubble of
volume \( ^{\prime} 2 V^{\prime} \) is
A \( .4 W \)
B. \( 8 W \)
\( \mathbf{c} \cdot 2^{1 / 3} W \)
\( \mathbf{D} \cdot 4^{1 / 3} W \)


If the quadratic equation \( x^{2}+b x+ \)
\( \mathbf{7 2}=\mathbf{0} \) has two distinct integer roots,
then the number of all possible values of bis
A . 12
B. 9
c. 15
D. 18


Chlorine atom in \( C H_{3} C H_{2} C l \) is
attached to:
\( A \cdot s p^{3} \) carbon
B. \( s p^{2} \) carbon
c. \( s p \) carbon
D. none of the above


An electron is in an excited state in a
hydrogen like atom. It has a total energy
-3.4eV. The kinetic energy of the electron is E and its de Broglie wavelength is \( \lambda \)
A. \( E=6.8 e V, \lambda=6.6 \times 10^{-10} m \)
B . \( E=3.4 e V, \lambda=6.6 \times 10^{-10} m \)
C . \( E=3.4 e V, \lambda=6.6 \times 10^{-11} \mathrm{m} \)
D. \( E=6.8 e V, \lambda=6.6 \times 10^{-11} m \)


DNA strands are anti-parallel because
of
A. H bonds
B. Phosphate diester bonds
c. Disulphide bonds
D. Phosphate bonds


What is biogeography? How do Darwin's finches provide the biogeographical evidence in favour of evolution?


is said to be done only when the force applied on a body makes the body
to move.
A. work
B. Momentum
c. Retardation
D. None of these


At constant pressure and at a temperature of \( 27^{0} \mathrm{C}, \) if the volume of a
given amount of gas is to be raised three times, the temperature to which the gas should be heated is
A \( \cdot 27^{0} \mathrm{c} \)
B. \( 625^{\circ} \) С
c. \( 627^{\circ} \) С
D. \( 273^{0} \mathrm{C} \)


The particle \( X \) in the following nuclear
reaction is \( _{5}^{B} 10+_{2}^{H e} 4 \longrightarrow_{7}^{N} 13+X \)
A. \( P \)
в.
\( c \cdot e \)
D.


A magnesium ribbon is burnt in oxygen
to give a white compound \( \boldsymbol{X} \) accompanied by the emission of light. If the burning ribbon is now placed in an atmosphere of nitrogen, it continues to
burn and forms a compound \( Y . \) Write
the chemical formula of \( X \) and \( Y: \)
A. \( x \rightarrow M g O ; y \rightarrow M g N \)
В. \( x \rightarrow 2 M g O ; y \rightarrow M g_{2} N_{3} \)
C \( . x \rightarrow M g O ; y \rightarrow M g_{3} N_{2} \)
D. None of these


The function \( f(x)=\sin x-k x-c \)
where \( k \) and \( c \) are constants, decreases
always when
\( \mathbf{A} \cdot k>1 \)
в. \( k \geq 1 \)
c. \( k<1 \)
D. \( k \leq 1 \)
E . \( k<-1 \)


If the projections of the line segment \( A B \) on the coordinate axes are \( 12,3, k \)
and \( A B=13, \) then \( k^{2}-2 k+3 \) is equal
to:
This question has multiple correct options
A . 0
B.
c. 11
D. 27


Prove that:
\( \left|\begin{array}{ccc}-a^{2} & a b & a c \\ a b & -b^{2} & b c \\ a c & b c & -c^{2}\end{array}\right|=4 a^{2} b^{2} c^{2} \)


Circumference of the edge of
hemispherical bowl is \( 132 \mathrm{cm} \). Find the capacity of the bowl


Evaluate \( \left|\begin{array}{cc}\sqrt{\mathbf{6}} & \sqrt{\mathbf{5}} \\ \sqrt{\mathbf{2 0}} & \sqrt{\mathbf{2 4}}\end{array}\right| \)


Select the state functions among the following:
This question has multiple correct options
A. temperature
B. entropy
c. work
D. enthalpy


The tautomeric form which is less
stable is called?
A. enol form
B. keto form
c. labile form
D. all of these


\( 58.5 g m \) of \( N a C l \) and \( 180 g m \) of
glucose were separately dissolved in
1000 \( m l \) of water. Identify the correct
statement regarding the elevation of boiling point (b.p.) of the resulting solutions.
A. \( N a C l \) solution will show higher elevation of b.p.
B. Glucose solution will show higher elevation of b.p.
C. Both the solutions will show equal elevation of b.p.
D. The b.p. elevation will be shown by neither of the solutions