In which addition to alkene, syn
addition takes place?
A \( \cdot H_{2}(P d) \)
в. \( M n O_{4}^{-} / O H^{-} \)
\( \mathrm{c} \cdot O s O_{4}, \mathrm{NaH} \mathrm{SO}_{3} \)
D. All


A string is clamped at both the ends and it is vibrating in its 4 th harmonic. The equation of the stationary wave is \( \boldsymbol{Y}=\mathbf{0 . 3} \sin (\mathbf{0 . 1 5 7} \boldsymbol{x}) \cos (\mathbf{2 0 0} \boldsymbol{\pi} \boldsymbol{t}) . \) The
length of the string is: (All quantities are in SI units)
A \( .20 m \)
в. \( 80 m \)
c. \( 60 m \)
D. \( 40 m \)


The value of the sum \( \sum_{n=1}^{13}\left(i^{n}+i^{n+1}\right) \) where \( i=\sqrt{-1}, \) equals
\( \mathbf{A} \cdot i \)
B . \( i-1 \)
\( c \cdot-i \)
D.


A parallel plate capacitor of plate area \( A \) and plate separation \( d \) is charged to
potential difference \( V \) and then the battery is disconnected. A slab of
dielectric constant \( k \) is then inserted
between the plates of the capacitor so as to fill the space between the plates. If
\( Q, E \) and \( W \) denote respectively, the magnitude of charge on each plate, the electric field between the plates (after
the slab is inserted) and the work done
on the system, in question, in the process of inserting the slab, then:
This question has multiple correct options
A \( \cdot Q=\frac{\epsilon_{0} A V}{d} \)
в. \( Q=\frac{\epsilon_{0} k A V}{d} \)
c. \( \quad E=\frac{V}{k d} \)
D. \( W=-\frac{\epsilon_{0} A V^{2}}{2 d}\left(1-\frac{1}{k}\right) \)


If \( I=\int_{0}^{\frac{\pi}{2}} \log (\cos x \cos 2 n x) d x \) then 1
is same as
\( \int_{0}^{\frac{\pi}{2}} \cot x \cos (2 n x) d x \)
B. \( \int_{0}^{\frac{\pi}{2}} \cot x \sin (2 n x) d x \)
c. \( \int_{0}^{\frac{\pi}{2}} \tan x \cos (2 n x) d x \)
D \( \frac{1}{2 n} \int_{0}^{\frac{\pi}{2}} \tan x \sin (2 n x) d x \)


State True or False.
Tricalcium phosphate is used as a nutritional supplement and occurs naturally in cow milk.
A. True
B. False


The ratio of acceleration due to gravity at a depth \( h \) below the surface of earth
and at a height \( h \) above the surface for \( \boldsymbol{h}<<\boldsymbol{R} \)
A. constants only when \( h<<R \)
B. increases linearly with \( h \)
C. increases parabolically with \( h \)
D. decreases


List-I \( \quad \) List-II
A)Rayon 1) \( C H_{2} O+C_{6} H_{5} O H \)
B)Silicone polymers
2) \( \boldsymbol{F}_{2} \boldsymbol{C}=\boldsymbol{C} \boldsymbol{F}_{2} \)
\( \mathbf{R} \)
C) Bakelite
3) HO-Si-OH
1
\( \mathbf{R} \)
D) Teflon
4) Cellulose
A. \( A-4 B-3 C-1 D-2 \)
B. A-1 B-3 C-2 D-4
c. \( A-4 B-2 C-3 D-1 \)
D. A-2 B-4 C-3 D-1


Three amplifier stages each with a gain of 10 are cascaded. The overall gain is
A . 10
B. 30
\( c .1000 \)
D. 100


Which one of the following is correctly
paired?
A. Trygon - Monitor
B. Ichthyophis - Crow
c. Varanus - stingray
D. carvus - Limbless amphibian
E. Pristis - Sawfish


Prove that:
\( \sin ^{6} \theta+\cos ^{6} \theta+3 \sin ^{2} \theta \cos ^{2} \theta=1 \)


How does the creation of variations in
the species promote survival?


\( \mathrm{CO}_{2} \) is gas, while \( \mathrm{SiO}_{2} \) is solid
because:
\( \mathbf{A} \cdot C O_{2} \) is a linear molecule, while \( S i O_{2} \) is angular.
B. van der Waals' forces are very strong in \( S i O_{2} \)
\( \mathrm{C} \cdot \mathrm{CO}_{2} \) is covalent, while \( \mathrm{SiO}_{2} \) is ionic.
D. \( S i \) cannot form stable bonds with \( O \), hence \( S i \) has to form a \( 3 D \) lattice


A soluction contains \( 7 g \) of solute (molar \( \operatorname{mass} 210 g \operatorname{mol}^{-1} \) ) in \( 350 g \) of acetone
raised the boiling point of acetone from
\( 56^{\circ} C \) to \( 56.3^{\circ} C \)
The value of ebullioscopic constant of acetone in \( K . K g m o l^{-1} \) is:
A . 2.66
в. 3.15
c. 4.12
D. 2.86


2.2 \( g \) of an alcohol (A) when treated with
\( \boldsymbol{C H}_{3}- \) Mgl liberates \( 560 \mathrm{mL} \) of \( \boldsymbol{C H}_{4} \) at
STP. Alcohol (A) on dehydration followed by ozonolysis gives ketone (B) along with (C). Oxime of ketone (B) contains
\( 19.17 \% \) N. (A) on oxidation gives ketone
(D) having the same number of the carbon atom.
The molecular mass of (A) is?
A . 74
B. 88
\( c \cdot 60 \)
D. 102


Read the following statements and select the option having both incorrect statements.
(i) Condoms decrease sperm motility.
(ii) Diaphragms, cervical caps and vaults are for both males and females.
(iii) IUDs are inserted by-expert nurses.
(iv) Sterilisation is a terminal method
to prevent further pregnancy.
A. (i) and (iii)
B. (i) and (ii)
c. (iii) and (iv)
D. (ii) and (iv)


Which of the following statement is incorrect regarding physisorption?
A. It occurs because of Van der Waals' forces
B. More easily liauiefiable gases are adsorbed readily.
c. Under high pressure, it results into multi molecular layer on adsorbent surface
D. Enthalpy of adsorption \( \left(\Delta \mathrm{H}_{\text {adsorption }}\right) \) is low and positive


Match the List-I with List-II.


Cyclone collector is used for minimizing
A. Radioactive pollution
B. Air pollution
c. Noise pollution
D. water pollution


Which inorganic compound is also
known as azane?
A. Ammonium chloride
B. Sulphur Dioxide
c. Ammonia
D. None of above


Assertion
The flow of heat energy from one body to the other depends upon the amount of heat energy in them
Reason
Heat flows from lower temperature of the body to higher temperature of the body
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


Which of the following uses the most
water?
A. Industrial use
B. Agricultural use
c. Domestic use
D. Electronics


How can the production of dihydrogen obtained from coal gasification, be increased?


Five compounds with formula \( C_{4} H_{8} B r_{2} \) How many structure of (X) are possible?
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
\( D .5 \)


Surface tension of Iyophilic sols is:
A . lower than that of \( H_{2} O \)
B. equal to that of \( H_{2} O \)
c. more than that of \( H_{2} O \)
D. none of these


If \( g(x) \) is the inverse of \( f(x) \) and \( f^{\prime}(x)=\frac{1}{1+x^{3}}, \) then \( g^{\prime}(x) \) is equal to
A \( . g(x) \)
в. \( 1+g(x) \)
c. \( _{1+\{g(x)\}^{3}} \)
D. \( \frac{1}{1+\{g(x)\}^{3}} \)
\( E \)


Function \( x-\sin x \) has
A. a maxima
B. a minima
c. a maxima and a minima
D. no maxima and no minima


If \( \bar{a}, \bar{b}, \bar{c} \) are non-coplanar vectors and if \( \bar{d} \) is such that \( \bar{d}=\frac{1}{x}(\bar{a}+\bar{b}+\bar{c}) \) and
\( \overline{\boldsymbol{d}}=\frac{\mathbf{1}}{\boldsymbol{y}}(\overline{\boldsymbol{b}}+\overline{\boldsymbol{c}}+\overline{\boldsymbol{d}}) \) where \( \mathbf{x} \) and \( \mathbf{y} \) are non
zero real numbers, then \( \frac{1}{x y}(\bar{a}+\bar{b}+ \) \( \overline{\boldsymbol{c}}+\overline{\boldsymbol{d}})= \)
B. \( -\bar{a} \)
\( c . \overline{0} \)
D . \( 2 \bar{a} \bar{a} \bar{a} \)


The element present in traces in insulin is:
A. Iron
B. cobalt
c. zinc
D. Magnesium


toppr OG
Q Type your question
these alphabets have been correctly
matched with the parts which they
indicate
A. A- Root hair, B- Epiblema, C- Cortex, D- Endodermis, EPassage cell, F- Pericycle, G- Pith, H- Phloem, IMetaxylem, J- Protoxylem
B. A- Root hair, B- Epiblema, C- Cortex, D- Endodermis, EPassage cell, F- Pith, G- Pericycle, H- Metaxylem, IPhloem, J- Protoxylem
C. A- Root hair, B- Epiblema, C- Cortex, D- Endodormis, EPericycle, F- Passage cell, G- Phloem, H- Pith, IProtoxylem, J- Metaxylem
D. A- Root hair, B- Cortex, C- Epiblema, D- Pericycle, EEndodermis, F- Pith, G- Passage cell, H- Phloem, Protoxylem, J- Metaxylem


The friction coefficient between a road
and the tyre of a vehicle is \( 4 / 3 . \) Find the maximum incline the road may have so
that once hard brakes are applied and the wheel starts skidding, the vehicle going down at a speed of \( 36 k m / h r \) is stopped within \( 5 m \)


A spherical convex surface of radius of
curvature \( R \) separates \( \operatorname{air}\left(\mu_{a}=1\right) \) from
\( \operatorname{glass}\left(a \mu_{g}=1.5\right) . \) The centre of
curvature is in the glass. A point object P placed in air is found to have a real image \( Q \) in the glass. The line PQ cuts the surface at a point 0 and \( P 0=0 Q \) The distance PO is equal to
A. 5R
B. 3R
\( c \cdot 2 R \)
D. 1.5 R


The reaction which proceeds with
evolution of heat is called:
A. exothermic
B. endothermic
C. may be exothermic or endothermic
D. neither endothermic nor exothermic


The surface of a conductor is an
equipotential surface:


The effective length of a simple pendulum is the sum of the following three: length of string, radius of bob, and length of hook. In a simple pendulum experiment, the length of the string, as measured by a meter scale, is \( 92.0 \mathrm{cm} . \) The radius of
the bob combined with the length of the hook, as measured by a vernier
callipers, is \( 2.15 \mathrm{cm} . \) The effective length of the pendulum is
\( \mathbf{A} \cdot 94.1 \mathrm{cm} \)
B. \( 94.2 \mathrm{cm} \)
c. \( 94.15 \mathrm{cm} \)
D. \( 94 \mathrm{cm} \)


The vapour pressure of ethanol and methanol are \( 44.5 \mathrm{mm} \) and \( 88.7 \mathrm{mm} \mathrm{Hg} \) respectively. An ideal solution is
prepared at the same temperature by mixing 60 g of ethanol with 40 gof methanol. The total vapour pressure of the solution is:
A. \( 67.13 \mathrm{mm} \) Hg
B. 66.13 \( \mathrm{mm} \) Нв
c. \( 76.13 \mathrm{mm} \) нв
D. None of the above


An object comprises of a uniform ring of
radius \( R \) and a uniform chord \( A B \) (not
necessarily made of the same material) as shown. Which of the following cannot
be the centre of mass of the object?
\( \mathbf{A} \cdot(\mathrm{R} / 3, \mathrm{R} / 3) \)
в. \( (R / 2, R / 2) \)
c. \( (\mathrm{R} / 4, \mathrm{R} / 4) \)
D. none of the above


Among the following, the element which show inert-pair effect are :
This question has multiple correct options
\( A \cdot B i \)
B. sn
\( c \cdot P b \)
D.


Name the phylum in which notochord is
present


Assertion
Interhalogen compounds are more reactive than halogens (except fluorine).
Reason
They all undergo hydrolysis giving halide ion derived from the smaller
halogen and anion derived from larger
halogen.
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


Assign oxidation number to the
underlined element in \( N a H_{2} P O_{4} \)


If \( A M \) and \( G M \) of two positive numbers a and b are 10 and 8 respectively,find the numbers


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


Define metal. Arrange the major
metallic elements present in the earth
crust in decreasing order of their percentage of occurrence?


Calculate the vertical height of a mercury column (in \( \mathrm{m} \) ) which exerts a
pressure of \( 81600 P a . \) (Density of mercury is \( 13.6 g c m^{-3} \) and \( g=10 m \)
\( s^{-2} \)


If one line of the pair of lines \( a x+ \)
\( 2 b x y+b y^{2}=0 \) bisects the angle bet.
Co-ordinates axes in the quadrant
\( A \cdot a-b=12 b \)
B. \( a+b=-2 b \)
\( c \cdot a+b=2 b \)
D. \( (a-b)^{2}=4 b^{2} \)


Calamine is used to reduce the
irritating effect of ant bite/sting because it reacts with (X) released due
to the bit /sting of ants with (Y) present in calamine. \( (\mathrm{X}) \) and \( (\mathrm{Y}) \) respectively
are:
A. sodium hydrogen carbonate and formic acid
B. formic acid and zinc carbonate
c. acetic acid and common salt
D. hydrochloric acid and zinc oxide


Composition of the nuclei of two atomic
species \( X \) and \( Y \) are given as under
\[
\begin{array}{r}
\boldsymbol{X} \boldsymbol{Y} \\
\text { Protons }=\boldsymbol{6}
\end{array}
\]
Neutrons \( =\mathbf{6} \)
Given the mass numbers of \( X \) and \( Y \).
What is the relation between the two
species?


Write the chemical equation for its reaction with ethanol to form compound
\( B \)


Abiotic component in an ecosystem is
A. water
B. Daphnia
C. Bacteria
D. chlorella


Assertion
Reversible systems are difficult to find
in real world.
Reason
Most processes are dissipative in
nature.
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 structure of \( I B r_{2}^{-} \) involves hybridisation of the type:
\( A \cdot s p^{3} \)
B . \( s p^{3} d \)
c. \( s p^{3} d^{2} \)
D. none of these


Multiply \( \frac{6}{13} \) by the reciprocal of \( \frac{-7}{16} \) is \( \frac{-96}{q}, \) then \( q \) is equal to


Formula for the following compound
Thallium (I) sulphate is \( T l_{2} S O_{4} \)
A. True
B. False


If \( A=\{1,2\} \) and \( B=\{3,4\} \) then find
\( A \times B \)
\( \mathbf{A} \cdot A \times B=\{(1,3),(1,2),(2,3),(2,4)\} \)
B \( . A \times B=\{(1,3),(1,4),(2,3),(2,4)\} \)
\( \mathbf{c} \cdot A \times B=\{(1,3),(1,4),(2,1),(2,4)\} \)
D . \( A \times B=\{(1,3),(1,4),(2,3),(2,1)\} \)


\( f(G=\{7,8\} \text { and } H=\{5,4,2\}, \) find
\( G \times H \) and \( H \times G \)


If the time period of a planet is decreased by \( 10 \% \), and the initial radius of orbit is R. What is the change
in radius of its orbit after the change in
the time period?
A \( 3 \sqrt{32} R \)
n \( \sqrt{32} \sqrt{32} \)
в. \( \sqrt{34} R \)
\( \mathbf{c} \cdot 3 \sqrt{9} R \)
D. \( 3 \sqrt{81} R \)


Ferrous sulphate decomposes with the
evolution of a gas having a characteristic odour of burning sulphur Identify the type of reaction.
A. Redox reaction
B. Precipitation reaction
c. Double displacement reaction
D. Thermal decomposition reaction


\( A \) and \( B \) are two points on the axis and the perpendicular bisector respectively of an electric dipole. A and B are far away from the dipole and at equal distances from it. The potentials at \( A \)
and \( \mathrm{B} \) are \( V_{A} \) and \( V_{B} \) respectively. Then
A. \( V_{A}=V_{B}=0 \)
в. \( V_{A}=2 V_{B} \)
\( \mathbf{c} \cdot V_{A} \neq 0, V_{B}=0 \)
D. \( V_{A} \neq 0, V_{B} \neq 0 \)


List five things you have done over the last one week to-
(a) Conserve our natural resources.
(b) Increase the pressure on our natural
resources.


A solid cylinder is rolling down on an inclined plane without slipping. The length of the plane is \( 30 m \) and its angle
of inclination is \( 30^{\circ} . \) If the cylinder starts from rest then its velocity at the bottom of the inclined plane is:
A \( \cdot 14 m s^{-1} \)
B. \( 28 m s^{-1} \)
\( \mathbf{c} \cdot 7 m s^{-1} \)
D. \( 35 m s^{-1} \)


The equation of the tangent to the
curves \( x=t \cos t \) and \( y=t \sin t \) at the
origin is?
\( \mathbf{A} \cdot x=0 \)
в. \( y=0 \)
c. \( x+y=0 \)
D. \( x-y=0 \)


Coconut water is rich in
A. Auxins
B. Gibberellin
c. Abscisic acid
D. Cytokinin


The damping force on a oscillator is directly proportional to the velocity. The Unit of the constant of proportionality
are:
A. \( \mathrm{kgs}^{-1} \)
B. kgs
c. \( \operatorname{kgms}^{-2} \)
D. kgms


A sigma bond is formed by the overlapping of
A. \( s-s \) orbital alone
B. \( s \) and \( p \) orbital alone
c. \( s-s, s-p \) or \( p-p \) orbital along internuclear axis
D. \( p-p \) orbital along the sides


Deltoid ridge is found in which one of the following bones?
A. Radius
B. Ulna
c. Humerus
D. Femur


The number of electrons involved in
electrode reaction by 1 coulomb charge is:
A \( \cdot 6.85 \times 10^{14} \)
B. \( 19.85 \times 10^{18} \)
c. \( 6.85 \times 10^{18} \)
D. \( 16.85 \times 10^{15} \)


The threshold wavelength for emission of photoelectrons from a metal surface is \( 6 \times 10^{-7} \mathrm{m} . \) The work function of the
material of the metal surface is :
A \( \cdot 3.33 \times 10^{-19} \mathrm{J} \)
J. \( 3.33 \times 10^{-19} \)
В \( \cdot 6.67 \times 10^{-19} \mathrm{J} \)
С. \( 1.23 \times 10^{-19} \mathrm{J} \)
J \( 5 \times 10^{-1.2} \)
D. \( 2.37 \times 10^{-19} \mathrm{J} \)


These ions differ in their number of
electrons by eight :
A. \( M g^{+} \) and \( F^{+} \)
B. \( L i^{+} \) and \( N e \)
\( c \cdot O^{2-} \) and \( O^{-} \)
D. \( N \) and \( P^{3-} \)
E \( \cdot C a^{2+} \) and \( C l \)


Evaluate \( \frac{n !}{(r !) \times(n-r) !}, \) when \( n=15 \)
and \( r=12 \)


if \( \hat{i}, \hat{r}, \hat{n} \) are unit vectors along incident ray in air, refracted ray in a medium, normal respectively and \( \mu \) is refractive
index of medium, then the correct choice is:
A \( \cdot(\hat{i} \times \hat{n})=\mu(\hat{n} \times \hat{r}) \)
B . \( \mu(\hat{i} \times \hat{n})=\hat{n} \times \hat{r} \)
c. \( \hat{i} . \hat{n}=\mu(\hat{n} . \hat{r}) \)
D. \( \mu(\hat{i} . \hat{n})=\hat{n} . \hat{r} \)


Cement is manufactured from:
A . clay
B. limestone
c. sodium chloride
D. both A and B


Iron fillings and water are placed in a 5 litre vessel and sealed. The tank was
heated to \( 1000^{\circ} \mathrm{C} \). Upon analysis the
tank was found to contain \( 1.1 g \) of
hydrogen and \( 42.5 g \) of water vapour. If the reaction in the tank is represented by
\( 3 F e(s)+4 H_{2} O(g) \rightleftharpoons F e_{3} O_{4}(s)+ \)
\( 4 H_{2}(g) \)
the value of equilibrium constant, \( \boldsymbol{K}_{c} \) is
A . 30
B. 0.03
\( c .3 \)
D. 0.003


An object of height \( 6 \mathrm{cm} \) is placed perpendicular to the principal axis of a concave lens of focal length \( 5 \mathrm{cm} . \) Use lens formula to determine the position, size and nature of the image if the distance of the object from the lens is 10
\( \mathrm{cm} \)


\( \lim _{x \rightarrow 0} \frac{1-\cos (1-\cos 2 x)}{x^{4}} \)


The standard cell potential for \( Z n\left|Z n^{2+}\right|\left|C u^{2+}\right| C u \) is \( 1.10 V . \) When the
cell is completely discharged, \( \log \left[Z n^{2+}\right] /\left[C u^{2+}\right] \) is closest to:
A. 37.3
B. 0.026
c. 18.7
D. 0.052


Match the Column-I with Column-II.


The necessary condition in making of a junction transistor (E-emitter, B-base
and C-collector)
A. \( E \) is heavily doped, \( B \) is thin and lightly doped and \( C \) is moderately doped
B. E and C are lightly doped and B is thick and heavily doped
C. \( \mathrm{E} \) and \( \mathrm{B} \) are heavily doped and \( \mathrm{C} \) is lightly doped
D. \( \mathrm{E} \) and \( \mathrm{B} \) are lightly doped an \( \mathrm{C} \) is heavily doped


pistons \( A \) and \( B \) of area of cross section
\( 8 c m^{2} \) and \( 320 c m^{2} \) respectively, are joined at their bottom by a tube and
they are completely filled with water. Find \( :(\mathrm{i}) \) the pressure on piston \( \mathrm{A} \), (ii) the pressure on piston \( \mathrm{B} \), and (iii) the thrust on piston B.(consider effort on
piston \( \mathbf{A} \boldsymbol{E}=\mathbf{4} \boldsymbol{k} \boldsymbol{g} \boldsymbol{f}) \)
\( \mathbf{A} \cdot(\mathrm{i}) 5 \mathrm{kg} f \mathrm{cm}^{-2} \)
(ii) \( 5 \mathrm{kg} f \mathrm{cm}^{-2} \)
(iii) \( 160 \mathrm{kgf} \)
B. (i) 5 kgf \( c m^{-2} \)
(ii) \( 5 \mathrm{kg} \mathrm{fcm}^{-2} \)
(iii) \( 16 \mathrm{kg} f \)
C \( \cdot\left(\text { i) } 10 \text { kgf } c m^{-2}\right. \)
(ii) \( 10 \mathrm{kg} \mathrm{fcm}^{-2} \)
(iii) \( 160 \mathrm{kg} f \)
D. (i) \( 0.5 \mathrm{kg} \mathrm{fcm}^{-2} \)
(ii) \( 0.5 \mathrm{kg} \mathrm{fcm}^{-2} \)
(iii) \( 160 \mathrm{kg} f \)


Magnetic lines do not intersect one-
another because:
A. they are at a distance
B. they are in the same direction
C. they are parallel to one another
D. in the point of intersection there will be two direction of the magnetic field, which is impossible


The specific heat capacities of two
bodies \( A \) and \( B \) is 1: 2 and masses in
the ratio 3: 4 respectively. The ratio of
their heat capacities is:
A .3: 2
B. 2: 3
c. 6: 16
D. 3: 8


What is the ratio of electric field
intensity at distance \( 5 \mathrm{cm} \) to that at 10
\( \mathrm{cm} \) from a point charge \( Q \) in air?
A . 2: 1
B. 1: 2
c. 4: 1
D. 1: 4


At \( 100^{\circ} \mathrm{C} \) and 1 atm, if the density of
liquid water is \( 1.0 g \mathrm{cm}^{-3} \) and that of
water vapour is \( 0.0006 g \mathrm{cm}^{-3}, \) then the volume occupied by water molecules in
1 litre of steam at that temperature is:
\( A \cdot 6 c m^{3} \)
B. \( 60 \mathrm{cm}^{3} \)
c. \( 0.6 \mathrm{cm}^{3} \)
D. \( 0.06 \mathrm{cm}^{3} \)


If \( 4 \sin ^{-1} x+\cos ^{-1} x=\pi, \) then find the
value of \( \boldsymbol{x} \)


Which one of the gas dissolves in
\( H_{2} S O_{4} \) to give oleum?
\( A \cdot S O_{2} \)
в. \( H_{2} S \)
\( c \cdot S_{2} O \)
\( \mathrm{D} \cdot \mathrm{SO}_{3} \)


Which gas contributes most of green house effect?
A. сFC
B. Freon
\( c \cdot C O_{2} \)
D. \( C H_{4} \)


One element has atomic weight \( 39 . \) Its electronic configuration is
\( 1 s^{2}, 2 s^{2} 2 p^{6}, 3 s^{2}, 3 p^{6} 4 s^{1} . \) The true
statement for that element is:
A. more I.E
B. transition element
C. isotone with \( _{18} A r^{36} \)
D. stable oxide \( M_{2} O \)


If \( e \) and \( e^{\prime} \) be the eccentricities of two
conics \( S \) and \( S^{\prime} \) such that \( e^{2}+\left(e^{\prime}\right)^{2}= \)
\( 3, \) then both \( S \) and \( S^{\prime} \) are
A. Ellipses
B. Parabolas
c. Hyperbolas
D. None of these


The set of values of \( ^{\prime} x^{\prime} \) which
satisfies the inequation \( \sqrt{x^{2}-18 x+72}<(x-1) \) is
\( A \cdot \phi \)
B \( \cdot[1,2) \)
\( \mathrm{c} \cdot[12, \infty) \)
D・(1,2)


\( \frac{\phi}{\phi} \)


\( \boldsymbol{C}_{\boldsymbol{6}} \boldsymbol{H}_{\boldsymbol{5}} \boldsymbol{N}_{2} \boldsymbol{C l} \frac{\boldsymbol{C u} C l}{\boldsymbol{H C l}} \boldsymbol{C}_{\boldsymbol{6}} \boldsymbol{H}_{\boldsymbol{5}} \boldsymbol{C l} \)
Above reaction is :
A. Gattermann's reaction
B. Sandmeyer's reaction
c. Wurtz's reaction
D. Frankland's reaction


Calculate the energy released in MeV
during the reaction \( _{3}^{7} L i+_{1}^{1} H \rightarrow \)
\( 2\left[\begin{array}{l}4 \\ 2\end{array} \boldsymbol{H} e\right] \) if the masses of \( _{3}^{7} L i_{11}^{1} \boldsymbol{H} \) and
\( _{2}^{4} H e \) are 7.018,1.008 and \( 4.004 a m u \)
respectively.


What mass of \( C O_{2} \) will be formed when
\( 6 \mathrm{g} \) of carbon is burnt in \( 32 \mathrm{g} \) of oxygen?
\( A \cdot 38 g \)
B. 12 g
\( c \cdot 26 g \)
D. 22


Lenz's law is in accordance with the law
of conservation of
A. electric current
B. energy
c. electro motive force
D. electric charge


If circular coil with \( N_{1} \) turns is changed
in to a coil of \( N_{2} \) turns. What will be the
ratio of self inductances in both cases.
A \( \cdot \frac{N_{1}}{N_{2}} \)
B. \( \frac{N_{2}}{N_{1}} \)
c. \( \frac{N_{1}^{2}}{N_{2}^{2}} \)
D. \( \sqrt{\frac{N_{1}}{N_{2}}} \)


A uniform wire of length \( 4 m \) and area of
\( \operatorname{cross} \operatorname{section} 2 m m^{2} \) is subjected to
longitudinal force produced an
elongation of 1 mm.lf \( Y=0.2 \times 10^{11} \mathrm{NM}^{-2} \)
elastic potential energy stored in the body is
A. \( 0.5 J \)
\( J \)
в. \( 0.05 J \)
c. \( 0.005 J \)
D. \( 5.0 J \)


Evaluate the following definite integral:
\( \int_{-1}^{1} \frac{1}{x^{2}+2 x+5} d x \)


Which of the following is not a property of magnetic lines of force?
A. They neither have origin nor end.
B. These lines do not intersect
c. outside the magnet their direction is from north pole to south pole and inside the magnet these are from south to north pole.
D. None


An element \( X \) has an atomic number
32 has some properties similar to metal
and some to non-metal. The \( X \) is among
the:
A . metal.
B. non-metal.
c. metalloid.
D. none of these


Which of the following statement is NOT
true?
A. Flame can be seen over burning solids and liquids
B. Type of flame depends upon the amount of oxygen available
C. Invisible zone of a flame is the least hot zone
D. Blue-zone indicates complete combustion of fuel


Which of the chemicals used to soften
hard water?


A chain couples and rotates two wheels in a bicycle. The radii of bigger and smaller wheels are \( 0.5 m \) and \( 0.1 m \)
respectively. The bigger wheel rotates at
the rate of 200 rotations per minute, then the rate of rotation of smaller
wheel will be:
A. 1000 rpm
в. \( \frac{50}{3} \) грт
c. 200 rpm
D. 40 rp


At polarising angle, the angle between the reflected ray and refracted ray from a surface


If \( y=\frac{(1-x)^{2}}{x^{2}} \) where \( x \neq \)
\( 0, \) then \( \frac{d y}{d x} i s \)
A \( \cdot \frac{2}{x^{2}}+\frac{2}{x^{3}} \)
B. \( -\frac{2}{x^{3}}+\frac{2}{x^{2}} \)
\( c \cdot-\frac{2}{x^{2}}+\frac{2}{x^{3}} \)
D. \( -\frac{2}{x^{2}}-\frac{2}{x^{3}} \)


The order of basic strength of
\( \boldsymbol{C}_{\boldsymbol{6}} \boldsymbol{H}_{\boldsymbol{5}} \boldsymbol{N} \boldsymbol{H}_{\mathbf{2}}(\mathbf{1}), \boldsymbol{C}_{2} \boldsymbol{H}_{\boldsymbol{5}} \boldsymbol{N} \boldsymbol{H}_{2}(\boldsymbol{2}) \)
\( \left(C_{2} H_{5}\right)_{2} N H(3), \) and \( N H_{3}(4) \) is:
A. \( 1<4<2<3 \)
в. \( 1<2<3<4 \)
c. \( 4<3<2<1 \)
D. \( 3<2<4<1 \)


Differentiate between
Spike and catkin


The capacity of cell is measured in:
A. amperes
B. ampere-hour
c. watts
D. watt-hours


The height of an equilateral triangle of side 'a' is given by
A \( \cdot \frac{a \sqrt{2}}{2} \)
B. \( \frac{a \sqrt{3}}{2} \)
c. \( \frac{a \sqrt{3}}{4} \)
D. \( \frac{a \sqrt{2}}{3} \)


Write the number of lines of symmetry
in each letter 'SYMMETRY'.


What is the structural difference
between high density polythene (HDP) and low density polythene (LDP)?


When heating \( P C l_{5}, \) it decompose
\( P C l_{3} \) and \( C l_{2} \) in form of gas. The vapour density of gas mixture is 70.2 and 57.9
at \( 200^{\circ} \mathrm{C} \) and \( 250^{\circ} \mathrm{C} \). The degree of
dissociation of \( P C l_{5} \) at \( 200^{\circ} C \) at \( 250^{\circ} C \)
is:
A . \( 48.50 \% \) and \( 80 \% \)
B. 60\% and 70\%
c. \( 70 \% \) and \( 80 \% \)
D. 80\% and 90\%


Explain the applications of coordination compounds in the field of metal purification giving an example :


Find \( g \circ f \) and \( f \circ g \) when \( f: R \rightarrow R \) and \( g: R \rightarrow R \) are defined by \( f(x)= \)
\( 2 x+3 \) and \( g(x)=x^{2}+5 \)


Calcium hydroxide (slaked lime) is used in :
A. plastics and dyes
B. fertilizers
c. antacids
D. white washing


The partial pressure(atm) of HI in the equilibrium mixture is
A . 6.385
в. 12.77
c. 40.768
D. 646.58


Which phenomenon occurs during the following change? Solid wax left out in the sun.
A. Sublimation
B. Melting
c. condensation
D. Evaporation


Which of the following combinations of \( 0.20 M \) aqueous solutions will form a precipitate on mixing?
I. \( A g N O_{2} \) and \( H C l \)
Il. \( B a C_{2} H_{2} O_{2} \) and \( M g S O_{4} \)
III. \( \boldsymbol{K} \boldsymbol{I} \) and \( \boldsymbol{P b}\left(\boldsymbol{N} \boldsymbol{O}_{3}\right)_{2} \)
A. I only
B. I and II only
c. I and III only
D. II and III only
E . ।, II, and III


What word describes the relationship between the plant and the nitrogen fixing bacteria?
A. Parasitic
B. Carnivorous
c. Infection
D. Mutualistic, saprophytes


If velocity of an electromagnetic wave in
a medium is \( 3 \times 10^{8} m / s \) then find
refractive index of medium.
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c .0 .5 \)
D. 0.25


Calculate the ratio of the times taken by a uniform solid sphere and a disc of the same mass and the same diameter to
roll down through the same distance from rest on a smooth inclined plane.
A .15: 14
B. \( \sqrt{15}: \sqrt{14} \)
C. \( 15^{2}: 14^{2} \)
a \( .14^{2}: 14^{2} \)
D. \( \sqrt{14}: \sqrt{15} \)


An object starts from rest and attains a
uniform acceleration of \( 4 m s^{-2} \). what
will be its velocity at the end of half a
meter?


The angle between the axes of two polaroids so as to reduce the intensity of the incident unpolarised light to \( 1 / 3 \)
and \( 1 / 10 \) are \( \left(\operatorname{given}, \cos 35^{\circ}=0.8192\right. \)
and \( \left.\cos 63^{\circ}=0.4540\right) \)
A \( .35^{\circ}, 63^{\circ} \)
в. \( 55^{\circ}, 27^{\circ} \)
\( c \cdot 63^{\circ}, 35 \)
D. \( 27^{\circ}, 55^{\circ} \)


is naturally occurring
growth inhibitor.
A. Ethylene
B. Abscissic acid
c. cytokinin
D. Gibberellins


If \( K_{a} \) for an acid, \( H A \) is \( 1 \times 10^{-6} \), then
\( K_{b} \) for \( A^{-} \) would be:
A \( \cdot 10^{-9} \)
B . \( 10^{-5} \)
\( c \cdot 10^{-8} \)
D. \( 10^{-3} \)


The wavefront of a light beam is given by the equation \( \boldsymbol{x}+\mathbf{2} \boldsymbol{y}+\mathbf{3} \boldsymbol{z}=\boldsymbol{c} \)
(where \( c \) is arbitrary constant) then what is the angle made by the direction of light with the y-axis?
A \( \cdot \cos ^{-2} \frac{2}{\sqrt{14}} \)
B. \( \cos ^{-1} \frac{2}{\sqrt{14}} \)
\( \mathrm{c} \cdot \cos ^{-3} \frac{2}{\sqrt{14}} \)
D. \( \cos ^{-4} \frac{2}{\sqrt{14}} \)


Observe the pictures given below and tell the life process shown in each of these
\( (a) \)
\( (b) \)
\( (c) \)


A \( p \) -type semiconductor has acceptor levels 57 me \( V \) above the valance band.
The maximum wavelength of light required to create a hole is (Planck's
constant \( \left.h=6.6 \times 10^{-34} J-s\right) \)
A \( .57 \AA \)
В. \( 57 \times 10^{-3} \dot{A} \)
c. 217100 月
D . \( 11.61 \times 10^{-33} \dot{A} \)


The main source of lead is PbS. It is
converted to Pb by:-
(i) \( P b S \frac{a i r}{\Delta} P b O+S O_{2} \frac{C}{\Delta} P b+C O_{2} \)
(ii) \( P b S \frac{a i r}{\Delta} P b O+P b S \stackrel{\Delta}{\longrightarrow} P b+S O_{2} \)
Self reduction process is:
\( A \)
B. i
c. both
D. none


There are two thin wire rings, each of radius R, whose axes coincide. The charges on the rings are \( \mathrm{q} \) and q.Evaluate the potential difference between the centers of the rings separates by a distance a.
A \( \cdot \frac{q}{\pi \varepsilon_{0}}\left[\frac{1}{R}+\frac{1}{\sqrt{R^{2}+a^{2}}}\right] \)
B \( \cdot \frac{q}{2 \pi \varepsilon}\left[\frac{1}{R}+\frac{1}{\sqrt{R^{2}+a^{2}}}\right] \)
c. \( \frac{q}{2 \pi \varepsilon_{0}}\left[\frac{1}{R}-\frac{1}{\sqrt{R^{2}+a^{2}}}\right] \)
D. \( \frac{2 q}{\pi \varepsilon_{0}}\left[\frac{1}{R}-\frac{1}{\sqrt{R^{2}+a^{2}}}\right] \)


The non-metal with valency 1 in period 3
is :
A. \( N a \)
в. \( M g \)
c. \( A l \)
D. \( C l \)


The displacement of a particle executing SHM at any instant \( t \) is \( x= \) \( 0.01 \sin 100(t+0.05) \) then its time
period will be
A . \( 0.06 \mathrm{s} \)
B. 0.2
c. \( 0.1 \mathrm{s} \)
D. 0.02


The \( p H \) of an acid buffer can be raised
by 2 units by
A. Increaseing the concentration of both weak acid and salt by two moles
B. Increasing the concentration of both the acid and salt by 10 times
c. Diluting the solution by 10 times
D. Increasing the concentration of the salt by 10times and decreasing concentration of the acid by 10 times


Let \( A \) be a non-empty set such that \( A \times \) \( A \) has 9 elements among which are
found (-1,0) and \( (0,1), \) then
\( \mathbf{A} \cdot A=\{-1,0\} \)
В \( \cdot A=\{0,1\} \)
C \( \cdot A=\{-1,0,1\} \)
D \( \cdot A=\{-1,1\} \)


The force between two parallel wires
carrying currents has been used to
define
A. ampere
B. coulomb
c. volt
D. watt


Which is common in respiration and photosynthesis?
A. Oxidation
B. Phytochrome
c. cytochrome
D. Photosystem


The use of Helmholtz coils is to produce
A. uniform magnetic field
B. non-uniform magnetic field
c. varying magnetic field
D. zero magnetic field


Solve \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\boldsymbol{x} \cos \boldsymbol{x} \)


calculate the mass for
(1) 0.5 moles of oxygen \( \left(O_{2}\right) \)
(2) 0.5 moles of ozone \( \left(O_{3}\right) \)


Li Is soluble in water but \( L i F \) is not,
why?


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


The smallest number by which 392 must be multiplied so that the product is a perfect cube, is
A . 3
B. 5
\( c \cdot 7 \)
D. 9


In what ratio is the line segment joining
(-3,-1) and (-8,-9) is divided at the point \( \left(-5, \frac{-21}{5}\right) ? \)


State true or false:
100 is a perfect cube
A. True
B. False


Identify \( A \) and \( B \) in the following reaction
sequence:
\( C_{2} H_{6} \stackrel{A}{\longrightarrow} C_{2} H_{5} C l \frac{Z n / T H F}{\longrightarrow} B \)
A \( \cdot C l_{2} / u v \) light and \( C_{4} H_{1} \)
B. \( P C l_{3} \) and \( C_{2} H_{4} \)
c. \( H C l \) and \( C_{2} H_{6} \)
D. \( C l_{2} \) and \( C_{2} H_{2} \)


Which of the following properly explains why the atomic radius decreases going cross a period from left to right?
A. As you cross the period from left to right, the number of electron orbital shells decreases as the number of protons remains constant
B. As you cross the period from left to right, the number of protons decreases as the number of electron orbitals remains constant.
C. As you cross the period from left to right, the number of electron orbital shells increases as the number of protons remains constant
D. As you cross the period from left to right, the number of protons increases as the number of electron orbitals remains constant


A retailer gets a discount of \( 40 \% \) on the printed price of an article. The retailer sells it at the printed price. What is the gain or loss percent?
A. \( 12 \% \) gain
B. \( 12 \% \) loss
c. \( _{66} \frac{2}{3} \% \) gain
D. \( 66 \frac{2}{3} \% \) loss


You mix two colorless solutions and the
resulting mixture becomes cloudy What type of reaction was observed?
A . A physical reaction
B. A redox reaction
C . A precipitation reaction
D. An acid base reactions


Above diagram represents an atom \( X \)
Atom 'X' is a reducing agent.
A . True
B. False


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


Simplify and give reasons:
\( (-2)^{7} \)
\( \mathbf{A} \cdot-128 \)
в. 128
\( c \cdot-28 \)
D. None of these


\( 100 \mathrm{ml} \) of liquid \( \mathrm{A} \) and \( 25 \mathrm{ml} \) of liquid \( \mathrm{B} \) is mixed to give a solution which does not obey Raoult's law. The volume of the
solution:
A. will be 125 \( \mathrm{m} \) ।
B. can be > or < than 125 \( \mathrm{m} \)
c. can be greater than, equal to or less than \( 125 \mathrm{m} \)
D. will be less than 125 \( \mathrm{m} \) ।


\( \frac{\sqrt{0}}{\frac{6}{x}} \) \( \frac{\sqrt{2}}{2} \)


In the expansion of \( \left(3^{-x / 4}+3^{5 x / 4}\right)^{n} \)
the sum of binomial coefficient is 64
and term with the greatest bionomial coefficient term exceeds the third term
by \( (n-1) \) the value of \( x \) must be
\( A \cdot 0 \)
B.
\( c \cdot 2 \)
D. 3


A cubic vessel (with faces horizontal \( + \)
vertical) contains an ideal gas at NTP. The vessel is being carried by a rocket which is moving at a speed of \( 500 \mathrm{m} / \mathrm{s} \) in vertical direction. The pressure of the
gas inside the vessel as observed by us on the ground.
A. Remains the same because \( 500 \mathrm{m} / \mathrm{s} \) is very much smaller than \( v_{r m s} \) of the gas
B. Remains the same because motion of the vessel as a whole does not affect the relative motion of the gas molecules and the walls
C. will increase by a factor equal to \( \left[v_{r m s}^{2}+(500)^{2}\right] / v_{r m s}^{2} \)
where \( v_{r m s} \) was the original means square velocity of the gas
D. Will be different on the top wall and bottom wall of the vessel


A \( 1.0 k g \) bar of copper is heated at atmospheric pressure \( (1.01 \times \) \( \left.10^{5} N / m^{2}\right) . \) If its temperature
increases from \( 20^{\circ} \mathrm{C} \) to \( 50^{\circ} \mathrm{C} \), the
change in its internal energy is \( 2322 p \) in \( J \) ). What is the value of p? \( \alpha= \) \( \mathbf{7 . 0} \times \mathbf{1 0}^{-\mathbf{6}} /^{o} \boldsymbol{C}, \boldsymbol{\rho}=\mathbf{8 . 9 2} \times \)
\( 10^{3} k g / m^{3} \) and \( , c=387 J / k g^{o} C \)


Prove the following by mathematical
induction \( 1+2+3+\cdots+n< \)
\( \frac{1}{8}(2 n+1)^{2} \)


Write all pairs of vertically opposite
angles.


The electronic configuration of the
starting and ending elements of fourth
period are:
\( \mathbf{A} \cdot 4 s^{1} \) and \( 3 d^{10} 4 s^{2} 4 p^{6} \)
B \( \cdot 4 s^{1} \) and \( 4 s^{2} 3 d^{10} \)
C \( .4 s^{2} 3 d^{1} \) and \( 4 s^{2} 4 p^{6} \)
D. \( 4 s^{2} 3 d^{1} \) and \( 4 s^{2} 3 d^{10} \)


Cellular micromolecules are
A. Amino acids, Water, Minerals and Sugars
B. Glycogen, Amino acids, Minerals and Nucleotides
C. Water, Minerals, Nucleic acids, Amino acids and Nucleotides
D. Sugars, Water, Minerals, Proteins and Nucleotides


The ratio of nuclear magneton and Bohr
magneton is
\( \mathbf{A} \cdot m_{e} / m_{p} \)
в. \( m_{p} / m_{e} \)
\( \mathbf{c} \cdot m_{e} m_{p} \)
\( \mathbf{D} \cdot 2 m_{p} / m_{e z} \)


If \( \boldsymbol{A}=\left[\begin{array}{ccc}\boldsymbol{4} & \mathbf{1} & \boldsymbol{0} \\ \mathbf{1} & -\mathbf{2} & \mathbf{2}\end{array}\right], \boldsymbol{B}= \)
\( \left[\begin{array}{ccc}\mathbf{2} & \mathbf{0} & -\mathbf{1} \\ \mathbf{3} & \mathbf{1} & \mathbf{4}\end{array}\right], \boldsymbol{C}=\left[\begin{array}{c}\mathbf{1} \\ \mathbf{2} \\ -\mathbf{1}\end{array}\right] \) and
\( (\mathbf{3} \boldsymbol{B}-\mathbf{2} \boldsymbol{A}) \boldsymbol{C}+\mathbf{2} \boldsymbol{X}=\mathbf{0} \) then \( \boldsymbol{X}= \)
A \( \cdot \frac{1}{2}\left[\begin{array}{c}3 \\ 13\end{array}\right] \)
в. \( \frac{1}{2}\left[\begin{array}{c}3 \\ -13\end{array}\right] \)
c. \( \frac{1}{2}\left[\begin{array}{c}-3 \\ 13\end{array}\right] \)
D. \( \left[\begin{array}{c}3 \\ -13\end{array}\right] \)


An open knife edge of mass M is dropped from a height h on a wooden
floor. If the blade penetrates \( S \) into the wood, the average resistance offered by the wood to the blade is?


What evidence does fetal science
provides in the case of the phylum
chordata?


Find the area of each of the following
figures.


Cathode rays have velocities
A. Equal to that of light
B. Greater than that of light
C. Less than that of light
D. Greater than that of matter waves


Cambium is most active in
A. Summer
B. Winter
c. All seasons
D. Snow areas


At \( 90^{\circ} \mathrm{C} \), the vapour pressure of toluene is 400 torr and that of \( \sigma-x y \) lene is
150 torr. What is the composition of the
liquid mixture the boils at \( 90^{\circ} \mathrm{C}, \) when
the pressure is 0.50 atm? What is the composition of vapour produced?
A. Toluene 8 mol\%, Toluene=3.2 mol\%
B. Toluene 15mol\%, Toluene=36 mol\%
c. Toluene 85 mol\%, Toluene=64 mol\%
D. Toluene 92 mol\%, Toluene \( =96.8 \mathrm{mol\%} \)


If \( G . M .=18 \) and \( A . M .=27, \) then \( H . M . \) is
A \( \cdot \frac{1}{18} \)
B. \( \frac{1}{12} \)
\( c \cdot 12 \)
D. \( 9 \sqrt{6} \)


The molar conductivity of \( 0.05 M B a C l_{2} \)
solution at \( 25^{\circ} \mathrm{C} \) is \( 223 \Omega^{-1} \mathrm{cm}^{2} \) mol \( ^{-1} \)
What is its conductivity?


If \( f(x)=x^{11}+x^{9}-x^{7}+x^{3}+ \)
1 and \( f\left(\sin ^{-1}(\sin 8)\right)=\alpha, \alpha \) is a
constant, the \( \left.f \tan ^{-1}(\tan 8)\right) \) is equal
to
Note : consider 8 in radians.
\( A \)
B. \( \alpha-2 \)
c. \( \alpha+2 \)
D. \( 2-\alpha \)


Torques of equal magnitude are applied to a hollow cylinder and a solid sphere, both having the same mass and radius. The cylinder is free to rotate about its standard axis of symmetry, and the sphere is free to rotate about an axis passing through its centre. Which of the two will acquire a greater angular speed after a given time.


In Young's double-slit experiment, the
separation between the slits is \( \boldsymbol{d} \) distance between the slit and screen is
\( D(D>>d) . \) In the interference pattern,
there is a maxima exactly in front of
each slit. Then the possible wavelength(s) used in the experiment
are
A \( \cdot d^{2} / D, d^{2} / 2 D, d^{2} / 3 D \)
B . \( d^{2} / D, d^{2} / 3 D, d^{2} / 5 D \)
C . \( d^{2} / 2 D, d^{2} / 4 D, d^{2} / 6 D \)
D. none of these


Find the number of lines of symmetry in the figure.
\( A \)
B. 2
\( c \cdot 3 \)
\( D \)


Construct a triangle \( A B C \) in which
\( B C=5.6 \mathrm{cm}, \angle B=45^{\circ} \) and \( A B+ \)
\( \boldsymbol{A C}=\boldsymbol{8} \boldsymbol{c m} \)


If the value of a third order determinant
is \( 11, \) then the value of the determinant
of \( A^{-1}= \)
A . 1
B. 121
\( c \cdot 1 / 11 \)
D. \( 1 / 121 \)


Zinc dust in alcoholic solution is a
specific reagent in the preparation of alkenes. That act as:
A. dehydrohalogenating agent
B. dehydrating agent
c. dehydrogenating agent
D. dehalogenating agent


Figure shows a fixed square frame of
wire having a total resistance r placed
coplartarly with a long, straight wire
The wire carries a current i given by \( i= \)
\( i_{2} \cos (2 \pi t / T), \) Find \( (a) \) the flux of the
magnetic field through the square frame
(b) the emf induced in
the frame and
(c) the heat developed in the frame in the time interval 0 to 10 T.


Very short answer type. Name the hormone whose deficiency causes diabetes insipidus.


Gas assumes the shape and volume of its container
A . True
B. False


Which of the following electrolyte will be most effective in coagulation of gold sol
\( ? \)
A. \( N a N O_{3} \)
B . \( K_{4}\left[\operatorname{Fe}(C N)_{6}\right] \)
c. \( N a_{3} P O_{4} \)
D. \( M g C l_{2} \)


If \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{cl}\frac{\sin (a+2) x+\sin x}{x} ; & x<0 \\ b ; & x=0 \\ \frac{\left(x+3 x^{2}\right)^{1 / 3}-x^{1 / 3}}{x^{4 / 3}} ; & x>0\end{array}\right. \)
is continuous at \( x=0, \) then \( a+2 b \) is
equal to?
\( A \)
B. -2
\( c \cdot 1 \)
D.


The monomers of Buna-S polymers are:
A. vinyl chloride and vinylidene
B. styrene and butadiene
C . acrylonitrile and butadiene
D. isobutylene and isoprene


The electric charges are distributed in a small volume. The flux of the electric
field through a spherical surface of
radius \( 10 \mathrm{cm} \) surrounding the total charge is \( 20 V \) m. The flux over a
concentric sphere of radius \( 20 \mathrm{cm} \) will
be
A \( .20 \mathrm{V} . \mathrm{m} \)
B. \( 25 V . m \)
c. \( 40 V . m \)
D. 200V.m


Let \( \boldsymbol{f}(\boldsymbol{x})=\frac{(\boldsymbol{x}-\boldsymbol{a})(\boldsymbol{x}-\boldsymbol{b})}{(\boldsymbol{x}-\boldsymbol{c})} \) Which of the
following are TRUE?
This question has multiple correct options
A. Range of \( f(x) \) is \( R, b \leq c \leq a \)
B. Range of \( f(x) \) is \( R, a \leq c \leq b \)
C. Range of \( f(x) \) is proper subset of \( R \),for \( a \leq b \leq c \)
D. Range of \( f(x) \) is proper subset of \( R \),for \( c \leq b \leq a \)


Three coins are tossed together Find,
The probability of getting no tail


A positron and an electron come close together to give a neutral one called
A. Electronium
B. Positronium
c. \( \gamma \) -photon
D. \( \beta \) -particle


Attraction or repulsion between two objects can also be seen us another
form of
A. pull or push
B. pull only
c. push only
D. none of the above


How is it that ice-cream appears cooler
to the mouth than water at \( 0^{\circ} C ? \)


The exhausted permutit used for removing permanent hardness is regenerated by treating \( 10 \% \) NaCl solution.

If this is true enter 1 , if false enter 0 .


A particle of mass \( m \) is subjected to an attractive central force of magnitude
\( k / r^{2}, k \) being a constant. If at the instant when the particle is at an extreme position in its closed orbit, at a
distance \( a \) from the centre of force, its
speed is \( (k / 2 m a), \) if the distance of other extreme position is \( b \). Find \( a / b \)
\( A \cdot 4 \)
B. 3
\( c \cdot 5 \)
D. 6


A particle is kept at rest at a distance \( \boldsymbol{R} \) (earth's radius) above the earth's surface. The minimum speed with which it should be projected so that it does not return is
A \( \cdot \sqrt{\frac{G M}{4 R}} \)
в. \( \sqrt{\frac{G M}{2 R}} \)
c. \( \sqrt{\frac{G M}{R}} \)
D. \( \sqrt{\frac{2 G M}{4 R}} \)


A cnidarian receives nutrients and
oxygen by diffusion from its
A. blood vesse
B. Iymph vessel
c. gastro-vascular cavity
D. book lungs and vill


A particle is moving eastward with a velocity \( 5 m s^{-1} . \) In \( 10 s \) the velocity
changes to \( 5 m s^{-1} \) northwards. The
average acceleration in this time is:
A \( \cdot \frac{1}{\sqrt{2}} m s^{-2} \) towards North - west
B. \( \frac{1}{2} m s^{-2} \) towards North - west
c. \( \frac{1}{\sqrt{2}} m s^{-2} \) towards North - East
D \( \cdot \frac{1}{2} m s^{-2} \) towards North - East


A solid cylinder starts rolling down on an inclined plane from its top and \( V \) is
the velocity of its centre of mass on reaching the bottom of inclined plane. If a block starts sliding down on an
identical inclined plane but smooth,
from its top, then the velocity of block on reaching the bottom of inclined plane is :
A \( \cdot \frac{V}{\sqrt{2}} \)
B. \( \sqrt{2} V \)
c. \( \sqrt{\frac{3}{2}} V \)
D. \( \sqrt{\frac{2}{3}} V \)


Study of digestion of starch by salivary
amylase and effect of \( p H \) and temperature on it.


What will be the area of the field
\( A B G F E A ? \)
\( \mathbf{A} \cdot 7225 m^{2} \)
B. \( 8225 \mathrm{m}^{2} \)
\( c \cdot 6225 m^{2} \)
D. \( 6725 m^{2} \)


Using section formula show that the
points \( \boldsymbol{A}(\mathbf{2},-\mathbf{3}, \mathbf{4}), \boldsymbol{B}(-\mathbf{1}, \mathbf{2}, \mathbf{1}) \) and
\( C\left(0, \frac{1}{3}, 2\right) \) are collinear.


If sodium chloride is added to silver
nitrate solution:
a. Which precipitate is formed?
b. Name the type of reaction.
c. Write the chemical equation.


In the preparation of ary1 halides by sandmeyer's reaction, name the:
1) Catalyst used
2) Gas liberated


The charge flowing through a resistance \( R \) varies with time \( t \) as \( Q=a t-b t^{2} \)
where a and b are positive constants.
The total heat produced in \( \boldsymbol{R} \) is:
A \( \cdot \frac{a^{3} R}{6 b b} \)
B. \( \frac{a^{3} R}{3 b} \)
c. \( \frac{a^{3} R}{2 b} \)
D. \( \frac{a^{3} R}{b} \)


What is the meaning of ductility?


Form an equation \( a x^{2}+b x y+c y^{2} \) by
subtracting the sum of \( x^{2}-5 x y+2 y^{2} \)
and \( y^{2}-2 x y-3 x^{2} \) from the sum of
\( 6 x^{2}-8 x y-y^{2} \) and \( 2 x y-2 y^{2}-x^{2} \)
Find \( \boldsymbol{a}+\boldsymbol{b}+\boldsymbol{c} \)


The area of the region bounded by the
curves \( \boldsymbol{y}=|\boldsymbol{x}-\mathbf{1}| \) and \( \boldsymbol{y}=\mathbf{3}-|\boldsymbol{x}| \) in
square units is


Molarity is defined as:
A. the number of moles of solute dissolved in one \( d m^{3} \) of
the solution.
B. the number of moles of solute dissolved in \( 1 \mathrm{kg} \) of
solvent
C. the number of moles of solute dissolved in \( 1 d m^{3} \) of the
solvent.
D. the number of moles of solute dissolved in 100 ml of
the solvent.


Haematuria is
\( A \). RBCs in urine
B. WBCs in urine
C. Both A and B
D. None of the above


In Rutherford's \( \alpha \) -rays scattering experiment, gold foils are used because of
A. high malleability
B. ductility
c. high melting point
D. high ionisation energy


Phosphine is prepared by the reaction
of :
A \( \cdot \) P and \( H_{2} S O_{4} \)
B. P and NaOH
c. \( \mathrm{P} \) and \( \mathrm{H}_{2} \mathrm{S} \)
D. P and \( H N O_{3} \)


Secondary growth occurs through
A. Formation and division of meristematic cells
B. Vascular region
C . Cortical region
D. Both B and C


The energy of an electron in the first Bohr orbit is -13.6 ev then find the energy
of \( H e^{+} \) in the same Bohr orbit.
A. 27.2 ev
B. -27.2 ev
c. 54.4 ev
D. - 54.4 ev


A \( 1 ~ M e V \) positron encounters a 1 Me \( V \)
electron travelling in opposite direction The total energy released is (in MeV)
A .2
в. 3.02
c. 1.02
D. 2.04


For the reaction \( 2 A+B \leftrightharpoons C \)
1 moles of \( A, 2 \) moles of \( B \) and 4 moles
of \( C \) were taken initially in \( 1 L \) vessel. At
equilibrium moles of \( C \) was 0.5 what is
the equilibrium constant?
A \( \cdot 1.4 \times 10^{-3} \)
B . \( 1.1 \times 10^{-2} \)
c. \( 3.5 \times 10^{-4} \)
D. \( 2.8 \times 10^{-2} \)


A transformer is used to light a 140 watt, 24 volt lamp from \( 240 V \) AC mains.
The current in the main cable is 0.7
amp. The efficiency of the transformer
is
A . \( 48 \% \)
B . \( 63.8 \% \)
c. \( 83.3 \% \)
D. 90\%


Which of these are respiratory poisons or inhibitors of ETC?
A. Cyanides
B. Antimycin A
c. Carbon monoxide
D. All of these


The first inorganic pesticide to be used commercially was
A. Bordeaux mixture
B. Burgandy mixture
c. D.D.T.
D. 2-4 D


A light ray is incident on air-liquid
interface at \( 45^{\circ} \) and is refracted at \( 30^{\circ} \)
What is the refractive index of the
liquid? For what angle of incidence will the angle between reflected ray and
refracted ray be \( 90^{\circ} ? \)


The explosive compound of \( N_{2} \) is:
A. \( N_{2} O_{5} \)
в. \( N H_{3} \)
c. \( N F_{3} \)
D. \( N C l_{3} \)


A vessel of volume \( V \) contains \( n_{1} \) moles
of oxygen and \( n_{2} \) moles of carbon dioxide
at absolute temperature T. The pressure of the mixture is
A. \( \frac{\left(n_{1}+n_{2}\right) R T}{V} \)
В. \( \frac{\left(n_{1}-n_{2}\right) R T}{V} \)
c. \( \frac{n_{1} n_{2} R T}{V} \)
D. \( \frac{n_{1} R T}{n_{2} V} \)


What does a body produce when it vibrates?
A. Heat
B. Sound
c. Light
D. Electricity


Ozonolysis of which molecule give this
product?
A. 1,2 dimethyl cyclohexyne
B. Dodecene
c. 1,2 dimethyl cyclohexene
D. None of these


A double star system consists of two stars \( A \) and \( B \) which have time periods
\( T_{A} \) and \( T_{B} . \) Radius \( R_{A} \) and \( R_{B} \) and
\( \operatorname{mass} M_{A} \) and \( M_{B}, \) choose the correct
answer,
A \( \cdot\left(T_{A} / T_{B}\right)^{2}=\left(R_{A} / R_{B}\right)^{3} \)
B. If \( T_{A}>T_{B} \) then \( R_{A}>R_{B} \)
\( \mathbf{c} \cdot T_{A}=T_{B} \)
D. \( T_{A}>T_{B} \) then \( M_{A}>M_{B} \)


\( \operatorname{Let} \vec{A}=(\hat{i}+\hat{j}) \) and, \( \vec{B}=(2 \hat{i}-\hat{j}) . \) The
magnitude of a coplanar vector \( \overrightarrow{\boldsymbol{C}} \) such that \( \vec{A} \cdot \vec{C}=\vec{B} \cdot \vec{C}=\vec{A} \cdot \vec{B}, \) is given by:
A \( \cdot \sqrt{\frac{10}{9}} \)
B. \( \sqrt{\frac{5}{9}} \)
c. \( \sqrt{\frac{-09}{2}^{9}} \)
D. \( \sqrt{\frac{9}{12}} \)


Highest concentration of auxins exist
A. At the base of various plant organs
B. At growing tip of plants
c. In leaves
D. In xylem and phloem cell only


Noble gases are stable because their valence shell contains:
A . 2 electrons
B. 8 electrons
c. both \( A \) and \( B \)
D. none of the above


Which of the following is not present in Crude oil?
A. Vanadium
B. Nickel
c. chromium
D. copper


Why carbohydrates are important in our diet?


When a corroded metal object is rubbed
by a sand paper then:
A. outer metal surface is removed
B. metal becomes thin
c. outer corroded layer will be removed
D. all of the above


Perform the division: \( x^{3}-5 x^{2}+8 x-4 \)
by \( \boldsymbol{x}-\mathbf{2} \)


Intrinsic heterophylly is found in all
except
A. cotton
B. Buttercup
c. coriander
D. Larkspur


Less amount of energy is required to
remove 's' electron than 'p' electron.
A. True
B. False


A particle projected from 0 and moving
freely under gravity strikes
the horizontal plane passing through 0 at a distance \( R \) from the starting
point 0 as shown in the figure. Then
This question has multiple correct options
A. there will be two angles of projection if \( R g<u^{2} \)
B. the two possible angles of projection are complementary
c. the product of the possible times of flight from 0 to \( A \) is \( \frac{2 R}{g} \)
D. there will be more than two angles of projection if \( R g=u^{2} \)


Fuse wire is made up of an alloy of which has high resistance and


Carbohydrates are present in the
plasmalemma in the form of
A. Lignin
B. Cellulose
c. Hemicellulose
D. Phospholipids (glycolipids) and phosphoproteins (glycoproteins)


A conducting ring of radius \( r \) is rolling without slipping with a constant angular velocity \( \omega \) (figure). If the
magnetic field strength is \( B \) and is directed into the page then the emf induced across \( P Q \) is
A. \( B \omega r^{2} \)
в. \( \frac{B \omega}{2} \)
c. \( 4 B \omega r^{2} \)
D. \( \frac{B \omega}{4} \)


What is the IUPAC name of \( \boldsymbol{C H}_{3} \boldsymbol{C H}= \)
\( \boldsymbol{C H}-\boldsymbol{C O O H} ? \)
A. 2-Butenoic acid
B. Crotonic acid
c. 2-Butanoic acid
D. 3-Butenoic acid


Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} ; \) if \( \boldsymbol{y}=\tan ^{-1}\left(\frac{\sin \boldsymbol{x}}{\mathbf{1}+\cos \boldsymbol{x}}\right) \)


Which of the following is an organ of mastication in the cockroach?
A. Labrum
B. Labium
c. Mandibles
D. Maxilla


Suppose \( x, y, z \) are positive integers \( (\neq \)
1) if \( \Delta=\operatorname{det} \) of \( \left[\begin{array}{ccc}1 & \log _{x} y & \log _{x} z \\ \log _{y} x & 1 & \log _{y} z \\ \sin (x+y) & -\cos (x+y) & \sin ^{2} z\end{array}\right] \)
then \( \Delta \) is 1 ) Independent of \( x \) II) Independent of \( y \) IIII Independent of \( z \) The which of the above statement is
are correct
A. only land II
D. all the three I,II,III


The specific conductance at \( 298 \mathrm{K} \) of AgCl solution In water was determined
to be \( 1.826 \times 10^{-6} \) ohm \( ^{-1} \mathrm{cm}^{-1} . \) The ionic
conductances \( A g^{+} \) and \( C l^{-} \) are 61.92 and 76.34 respectively. What is the solubility of AgCl in water?
A \( \cdot 2.1 \times 10^{-4} \mathrm{gL}^{-1} \)
B . \( 1.32 \times 10^{-5} \mathrm{gL}^{-1} \)
c. \( 1.9 \times 10^{-3} \mathrm{gL}^{-1} \)
D. 2.1 \( \times 10^{-6} \mathrm{gL}^{-1} \)


The following truth table corresponds to the logic gate
\( \begin{array}{ccc}\mathbf{A} & \mathbf{B} & \mathbf{X} \\ 0 & 0 & 0 \\ 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 1\end{array} \)
A. NAND
B. OR
C . AND
D. xor


A point is on the \( x \) -axis. What are its \( y \)
coordinate and \( z \) -coordinates?


Why self induction is called inertia of
electricity?


A pulse on a string is shown in the figure. P is particle of the string. Then state which of the following is incorrect
A. If P is stationary point, then pulse consists of two waves travelling in opposite direction
B. If P is moving upwards, then pulse is travelling in positive direction
C. If P is moving downwards, then pulse is travelling in negative direction
D. none of these is incorrect


A large ship can float but a steel needle
sinks because of
A. Viscosity
B. Surface tension
c. Density
D. None of these


Histogram are a great way to show results of
A . categories
B. continuous data
c. both \( A \) and \( B \)
D. None of these


The study of the spatial arrangements of atoms in molecules and their effects
on the chemical and physical properties of substances is called:
A. Stereo chemistry
B. Analytical chemistry
c. Nuclear chemistry
D. spectroscopy


State whether true or false:
A simple barometer is compact and portable.
A. True
B. False


A card sheet divided into squares each of size \( 1 \mathrm{mm}^{2} \) is being viewed at a
distance of \( 9 \mathrm{cm} \) through a magnifying glass (a converging lens of focal length \( 9 \mathrm{cm} \) ) held close to the eye.

In order to view the squares distinctly with the maximum possible magnifying
power.
(a) What is the magnification produced by the lens? How much is the area of each square in the virtual image?
(b) What is the angular magnification (magnifying power) of the lens?
(c) Is the magnification in
(a) equal to the magnifying power in (b)? Explain:


What are metals?


Select the incorrect statement(s).
This question has multiple correct options
A. Monosaccharides are insoluble in organic solvents like diethyl ether.
B. Anomers of cyclic monosaccharides differ in the position of the \( -O H \) group at the hemiacetal carbon.
C. In D-Ribose, the \( -O H \) group used to form the fivemembered furanose ring is located on \( C_{4} \) carbon.
D. Aldopentoses and ketohexoses form pyranose rings in solution


\( A 2 \mathrm{m} \) long metallic rod rotates with an
angular frequency of 200 rads\( ^{-1} \) about an axis normal to the rod passing through its one end. The other end of the
rod is in contact with a circular metallic
ring. A constant magnetic field of \( 0.5 \mathrm{T} \) parallel to the axis exists everywhere. The emf developed between the centre and the ring is then
A . 100 v
B. 200 V
c. 300 \( v \)
D. \( 400 \mathrm{v} \)


What does Le Chatelier's Principle
state?
A. That any change in a substance on one side of the equation, either in concentration, temperature, pressure or volume, results in an equilibrium shift to oppose the change until a new equilibrium is reached.
B. That the forward rate of a reaction equals the reverse rate of a reaction.
C. That equilibrium is always achieved in any reaction.
D. That any change in a substance on one side of the equation results in an equilibrium shift to increase the change until a new equilibrium is reached.
E. That equilibrium is never achieved in a reaction.


Equilibrium constant for the reaction,
\( A_{2}+B_{2} \rightleftharpoons 2 A B, \) at a given
temperature is 2 while is the degree of
dissociation for \( \boldsymbol{A}_{2} \) is:
A . 0.2
B. 0.5
c. \( \frac{1}{1+\sqrt{2}} \)
D. \( \frac{\sqrt{2}}{1+\sqrt{2}} \)


Which word also means 'growing'?
A. waxing
B. Waning
C. Gibbous
D. crescent


Which of the following is a functional
groups?
A. Hydroxyl group
B. Aldehyde group
c. carboxylic group
D. All of the above


What is meant by dentition?


Six resistances of each 12 ohm are
connected as shown in the fig. The
effective resistance between the
terminals \( A \) and \( B \) is:
\( A \cdot 8 \Omega \)
B. \( 6 \Omega \)
c. \( 4 \Omega \)
D. \( 12 \Omega \)


Vascular bundles are bicollateral while
corolla is plicate in bud in family
A . Asteraceae
B. Solanaceae
c. Liliaceae
D. Fabaceae


In astronomical observations, signals observed from the distant stars are
generally weak. If the photon detector receives a total of \( 3.15 \times 10^{-18} J \) from
the radiations of \( 600 \mathrm{nm}, \) calculate the number of photons received by the detector.


In a \( \Delta A B C, \angle A B C=\angle A C B \) and the
bisectors of \( \angle A B C \) and \( \angle A C B \)
intersect at 0 such that \( \angle B O C=120^{\circ} \)
Show that \( \angle A=\angle B=\angle C=60^{\circ} \)


Heavy hydrogen is used:
A. in filling balloons
B. in studying reaction mechanism
C. in calculating heat of formation
D. as oxidizing agent


The decreasing order of \( A r S_{N} \) reaction
with \( C_{2} H_{5} O^{\ominus} / E t O H \) is:
A \( \cdot(I)>(I I)>(I I I)>(I V) \)
B. \( (I V)>(I I I)>(I I)>(I) \)
C. \( (I I I)>(I V)>(I I)>(I) \)
D. \( (I V)>(I I I)>(I)>(I I) \)


Choose the correct answers from the
alternatives given. The phosphate bonds of ATP are referred
to as high-energy bonds because their
A. Hydrolysis has a relatively high free energy of activation
B. Formation releases a relatively large amount of energy
c. Hydrolysis is exergonio
D. Bond energy is relatively highh


A dikaryotic cell has
A. Two haploid nuclei
B. Diploid zygote
C. Two similar nuclei
D. Two dissimilar haploid nuclei


In the electrochemical series, metals
are arranged in order of their tendency
to
A. release halogens from their salts
B. become reduced
c. react with water
D. lose electrons


Which among the following compounds
is used as selective weed killer?
A . Picric acid
B. 2, 4-dichlorophenoxy acetic acid
c. 2,4,6 -trichlorophenoxy acetic acid
D. Salol


Q Type your question
(i.e, acoelomate, pseudocoelomate and
coelomate)
Spongilla, Sea anemone, Planaria,
Liverfluke Wuchereria, Ascaris, Nereis,
Earthworm, Scorpion, Birds, Fishes,
Horse.
A. (i)Acoelomate: Spongilla, Sea anemone, Planaria, Liver fluke.
(ii) Pseudocoelomate: Wuchereria, Ascaris.
(iii) Coelomate: Nereis, Earthworm, Scorpion, Birds, Fishes, Horse.
B. (i)Acoelomate: Wuchereria, Ascaris.
(ii) Pseudocoelomate: Spongilla, Sea anemone, Planaria, Liver fluke.
(iii) Coelomate: Nereis, Earthworm, Scorpion, Birds, Fishes, Horse.
C. (i)Acoelomate: Nereis, Earthworm, Scorpion, Birds, Fishes, Horse.
(ii) Pseudocoelomate: Spongilla, Sea anemone, Planaria, Liver fluke.
(iii) Coelomate: Wuchereria, Ascaris.
D. (i)Acoelomate: Nereis, Earthworm, Sea anemone, Planaria, Liver fluke.
(ii) Pseudocoelomate: Spongilla, Scorpion, Birds, Fishes, Horse.
oelomate: Wuchereria, Ascaris.


The rate of the chemical reaction
doubles for an increase of \( 10 \mathrm{K} \) in
absolute temperature from \( 298 \mathrm{K} \)
Calculate \( \boldsymbol{E}_{\boldsymbol{a}} \)


The lanthanide ion that would show
colour is:
\( \mathbf{A} \cdot S m^{3+} \)
B. \( L a^{3} \)
c. \( L u^{3} \)
D. \( G d^{3} \)


Which term is caused by the random movement of electrons in molecules?
A. lonic Bonding
B. Metallic Bonding
c. Hydrogen Bonding
D. London Dispersion Forces


Ultra - violet rays are detected by:
A. Fluoroscence
B. Thermopile
C. Thermo - couple
D. Thermometer


The no .. of white balls in a bag is 4 if the total no of balls in bag are 12. Find the probability of picking white ball.
A \( \cdot 1 / 3 \)
B. 2/3
\( c \cdot 3 / 2 \)
D. 3


Suppose we know that \( f(x) \) is continuous and differentiable on the
interval \( [-7,0], \) that \( f(-7)=-3 \) and
that \( f^{\prime}(x) \leq 2 . \) What is the largest possible value for \( \boldsymbol{f}(\mathbf{0}) ? \)
A . 12
B. 22
c. 11
D . 24


Arrange the following in decreasing order of enol content.
i. Diethyl malonate
ii. Acetoacetic ester(AAE or EAA)
iii. Acetyl acetone
¡v. PhCOCH \( _{2} \mathrm{COCH}_{3} \)
\( A \cdot(\text { iv })>(\text { iii })>(\text { ii })>(i) \)
B. (iv) > (iii) > (i) > (ii)
c. (iii) \( >(\text { iv })>(\text { ii })>( \) i)
\( D \cdot(\text { iii) }>(i v)>(i)>(i i) \)


The compound used as smoke screen:
A. \( P C l_{3} \)
в. \( P C l_{5} \)
\( \mathrm{c} \cdot P H_{3} \)
D. \( H_{3} P O_{3} \)


The given graphs (a) and (b) represent the variation of the opposition offered by the circuit element to the flow of
alternating current, with frequency of the applied emf.ldentify the circuit
element corresponding to each graph


An infinite long plate has surface
charge density
sigma As shown in the figure, a point
charge \( q \) is moved from \( A \) to \( B \) Net work
done by electric field is:


Two long thin wires \( A B C \) and \( D E F \) are
arranged as shown in figure. They carry
equal current \( I \) as shown. The
magnitude of the magnetic field at \( O \) is
A. zero
в. \( \mu_{0} I / 4 \pi a \)
c. \( \mu_{0} I / 2 \pi a \)
D. \( \mu_{0} I / 2 \sqrt{2} \pi a \)


An article passing through two hands is sold at a profit of \( 38 \% \) at the original cost price. If the dealer makes a profit of \( 20 \%, \) then the profit per cent made by the second is:
A . 15
B. 12
c. 10
D. 5


Which of the following sets is not a
finite set?
\( \mathbf{A} \cdot\left\{(x, y): x^{2}+y^{2} \leq 1 \leq x+y, \quad x, y \in R\right\} \)
B \( \cdot\left\{(x, y): x^{2}+y^{2} \leq 1 \leq x+y, \quad x, y \in Z\right\} \)
\( \mathbf{c} \cdot\left\{(x, y): x^{2} \leq y \leq|x|, \quad x, y \in Z\right\} \)
D. \( \left\{(x, y): x^{2}+y^{2}=1, x, y \in Z\right\} \)


The work done in bringing a unit positive charge from infinite distance to a point at distance \( x \) from a positive charge \( Q \) is \( W \). Then the potential \( \phi \) at that point is:
A. \( \frac{W Q}{x} \)
B. \( W \)
c. \( \frac{W}{x} \)
D. \( W Q \)


Dolly, the famous animal was a
A. Donkey
B. Girl
c. cloned sheep
D. Normal sheep


Let \( A=\{1,2,3\} . \) The total number of
distinct relations that can be defined
over \( A \) is:
A \( \cdot 2^{9} \)
B. 6
\( c .8 \)
D. None of the above


The value of \( \int_{\frac{7 \pi}{4}}^{\frac{7 \pi}{3}} \sqrt{\tan ^{2} x} d x \) is equal to
A. \( 2 \log 2 \)
B. \( \log 2 \sqrt{2} \)
\( c \cdot \log 2 \)
D. \( \log \sqrt{2} \)


The arithmetic mean of first ten natural
numbers is
A . 5.5
B. 6
\( c .7 .5 \)
D. 10


Generally atmospheric \( C O_{2} \) is not limiting for hydrophytes since
A. These plants fix \( H_{2} S \) in their photosynthesis.
B. These plants obtain \( C O_{2} \) from water in the form of \( H C O_{3}^{-} \)
c. Glucose is not required for their respiration.
D. All of the above


A steel cylinder of 8 litres capacity contains hydrogen gas at 12 atm pressure. At the same temperature, how
many cycle tubes of 4 litres capacity at
2 atm can be filled up with this gas?
A \( \cdot 12 \)
B. 48
\( c \cdot 5 \)
D. 10


The product of the time period of a wave and its frequency is
A . Infinite
B. Zero
c. More than unity but less than infinity
D. Unity


The interior angle of a regular polygon is
\( \mathbf{1 5 6}^{\circ} \). Find the number of sides of the
polygon.


Methanogens, growing anaerobically on cellulosic material produce.
A. Methane
B. Methane and carbon dioxide
c. Methane and hydragen
D. Methane, carbon dioxide and hydrogen


Which of the following is diamagnetic in nature?
\( \mathbf{A} \cdot\left[F e(C N)_{6}\right]^{3-} \)
B. \( N i C l_{4}^{2} \)
\( \mathbf{c} \cdot\left[N i(C O)_{4}\right] \)
D. \( \left[M n C l_{4}\right]^{2-} \)


Five equal resistances each of
resistance \( R \) are connected as shown in
the Figure. A battery of V volts
is connected between \( A \) and \( B \). The
current flowing in AFCEB will be :
A \( \cdot \frac{V}{R} \)
в. \( \frac{V}{2 R} \)
c. \( \frac{2 V}{R} \)
D. \( \frac{3 V}{R} \)


If the shortest distance between the
\( \operatorname{lines} 2 x+y+z-5=0=3 x+2 y+ \)
\( 4 z+\lambda \) and \( x \) -axis is \( \frac{3}{\sqrt{26}}, \) then the
value of \( \lambda \) is
A . -4
B. -
c. -6
D. -


A balloon of weight \( \boldsymbol{w} \) is falling vertically downward with a constant
acceleration \( (\boldsymbol{a}<\boldsymbol{g}) . \) The magnitude of
the air resistance is:
A . \( w \)
в. \( _{w\left(1+\frac{a}{g}\right)} \)
c. \( w\left(1-\frac{a}{g}\right) \)
D. \( w \frac{a}{g} \)


A device used to measure volume of
liquids is
This question has multiple correct options
A. Burette
B. Density bottle
c. Pipette
D. common balance


Bundle of His' is a part of which one of the following organs in humans?
A. Pancreas
B. Brain
c. Heart
D. Kidney


A water proof protective tissue with suberized walls is
A. Bark
B. Bast
c. Intraxyllary fibres
D. Tylose


A man travels 1 mile due east, 5 mile
due south, 2 mile due east and finally
9 miles due north. How far is the
starting point?
A. 3 miles
B. 5 miles
c. 4 miles
D. between 5 miles and 9 miles


Find the sum of \( 2 n \) terms of the series
\( \mathbf{5}^{\mathbf{3}}+\mathbf{4 . 6}^{\mathbf{3}}+\mathbf{7}^{\mathbf{3}}+\mathbf{7}^{\mathbf{3}}+\mathbf{4 . 8}^{\mathbf{3}}+\mathbf{9}^{\mathbf{3}}+ \)
\( 4.10^{3}+\ldots \)


\( \frac{a \cos x+b x \sin x-5}{x^{4}} \) is finite, then
\( \boldsymbol{a}= \)
A \( \cdot \frac{5}{2} \)
B. 5
\( c \cdot \frac{2}{5} \)
D.


If the total number of \( \boldsymbol{H}_{2} \) molecules is
double of the \( O_{2} \) molecules then the
ratio of total kinetic energies pf \( \boldsymbol{H}_{2} \) to
that of \( O_{2} \) at \( 300 \mathrm{K} \) is :
A .1: 1
B. 1: 2
\( c \cdot 2: \)
\( D \cdot 1: 3 \)


Find, if possible, the slope of the line through the points (2,5) and (-4,5)


Which of the following element is most electropositive?
\( \mathbf{A} \cdot H \)
в. \( M g \)
\( c . C a \)
D. \( S \) i


Assertion
STATEMENT-1: \( 1.3 .5 \ldots . .(2 n-1)> \)
\( \boldsymbol{n}^{\boldsymbol{n}}, \boldsymbol{n} \boldsymbol{\epsilon} \boldsymbol{N} \)
Reason
STATEMENT-2: The sum of the first \( n \)
odd natural numbers is equal to \( n^{2} \)
A. Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-
B. Statement-1 is True, Statement-2 is True; Statementis Not a correct explanation for Statement-
c. statement- - is True, Statement-2 is False
D. Statement- 1 is False, Statement- 2 is True


Identify the geometric progression.
A \( .1,3,5,7,9, \dots \)
в. 2,4,6,8,10
\( \mathbf{c} \cdot 5,10,15,25,35 \)
D. \( 1,3,9,27,81 \dots \)


\( \sec ^{-1} 2 \)


A survey shows that \( 63 \% \) of the Americans like cheese where as \( 76 \% \)
like apples. If \( x \% \) of the Americans like
both cheese and apples, then
A \( . x=39 \)
B. \( x=63 \)
c. \( 39 \leq x \leq 63 \)
D. None of these


Solve the following pair of equations by reducing them to a pair of linear equations
\( \frac{5}{x-1}+\frac{1}{y-2}=2 \) and \( \frac{6}{x-1}- \)
\( \frac{3}{y-2}=1 \)


Identify the pair of electrolytes in which, one contains only ions and the other contains unionized molecules in
addition to ions respectively.
A. Potassium hydroxide, nitric acid
B. Carbonic acid, potassium chloride
c. Sodium hydroxide, carbonic acid
D. Barium sulphate, acetic acid


Compare carbon tertrachloride and sodium chloride with regards to
solubility in water and electrical conductivity.


A large cylindrical tank has a hole of area \( A \) at its bottom and water is
poured into the tank through a tube of cross-section area \( \boldsymbol{A} \) ejecting water at
the speed \( v \). Which of the following is
true?
A. Water level in tank keeps on rising
B. No water can be stored in the tank
c. water level will rise to height \( v^{2} / 2 g \) and then stop
D. The water level will be oscillating


Which of the following statement is
are correct?
This question has multiple correct options
A. White phosphorus is unstable while red phosphorus is stable
B. White phosphorus glows in the dark while red phosphorus does not glow
C. White phosphorus and red phosphorus are odourless
D. White phosphorus is brittle while red phosphorus is softy waxy


The \( p H \) mouth should always be:
A. more than 7
B. less than 5
\( c \cdot 7 \)
D. more than 5.5


Which integer is the additive inverse of
itself?
A . -1
B.
c. 0
\( D \)


According to Bohr's theory of hydrogen atom it can be concluded that the
radius of stable orbits is proportional to
\( \mathbf{A} \cdot n^{2} \)
B. \( \frac{1}{n} \)
\( c \)
D. \( \frac{1}{n^{2}} \)


Establish the relation \( S_{n} t h=u+ \)
\( \frac{a}{2}(2 n-1), \) where the letters have their
usual meaning.


Write a balanced chemical equation for the following:

Flowers of sulphur boiled with calcium
hydroxide.


The process of carrying out the
reduction of metal oxides by heating with coke is termed as:
A. Roasting
B. Smelting
c. zone refining
D. ore dressing


The nucleosomes are attached by
\( \mathbf{A} \cdot \) SAT DNA
B. Linker DNA
c. Viral DNA
D. None of the above


Linear combination of two hybridised orbitals belonging to two atoms and each having one electron leads to the
formation of:
A. sigma bond
B. double bond
c. co-ordinate covalent bond
D. pi bond


Huygens principle of secondary waves
A. allow us to find the focal length of a thick convex lens.
B. give us the magnifying power of the microscope.
C. is a geometrical method to find, the position of a wave front
D. is used to determine the velocity of light.


Bacteria that can grow in the absence of
oxygen are called as
A. Anaerobes
B. Molds
c. Aerobes
D. Yeasts


A circular coil ABCD carrying a current is placed in a unifrom magnetic field if the magnetic force on the segment AB the force on the remaining segment BCDA is:


The hybrid orbitals used by Phosphorus
n the formation of \( \mathbf{P C l}_{5} \) are :
\( A \cdot s p^{3} \)
B \( \cdot \operatorname{sp}^{2} \)
c. \( d s p^{2} \)
\( D \cdot s p^{3} d \)


Mr.Subbarao started work in 2014 at an
annual salary of \( R s .10,000 \) and receive
an increment of \( \boldsymbol{R s} . \mathbf{7 5 0} \) each year. In
which year did his income reach
Rs. 17,500


Long term usage of insecticides results
in
A. Sensitivity in insects
B. Kills insects
c. Resistance in insect
D. Decrease in insect population


Prove that:
\[
\sin 38^{\circ}+\sin 22^{\circ}=\sin 82^{\circ}
\]


Which of the following is not a solid
fuel?
A. Paraffin
B. coal
c. Tallow
D. Benzene


Write the name of monomers used for
getting the following polymers:
(i) Bakelite
(ii) Neoprene


State the following statement is True or False

The length of a rectangle \( (x) \) exceeds its
breadth by \( 3 \mathrm{cm} . \) The area of a rectangle is 70 sq.cm, then the equation is
\( x(x-3)=70 \)
A. True
B. False


Classify the following as primary,
secondary and tertiary alcohol. Also,
write the IUPAC name of the given
compound.


A circular plate of diameter \( ^{\prime} \boldsymbol{d}^{\prime} \) is kept
in contact with a square plate of edge
\( d^{\prime} \) as shown in figure. The density of material and thickness are same
everywhere. The center of mass of the
composite system will be
A. inside the circular plate
B. inside the square plate
c. at the point of contact
D. outside the syestem


\( \mathbf{A} \)
\( 1 k W \) heater is meant to operate at
\( 200 V . \) How many units of electrical
energy will it consume in a month (of 30
days) if it operates 10 h daily at the specified voltage \( (200 \vee) ? \)


An electron revolving in an orbit of
radius \( 0.5 \mathrm{A} \) in a hydrogen atom executes 10 revolutions per second. The
magnetic moment of electron due to its orbital motion will be
A \( \cdot 1256 \times 10^{-37} \) amp.m \( ^{2} \)
B. \( 653 \times 10^{-26} \) amp.m \( ^{\text {2 }} \)
c. zero
D. \( 256 \times 10^{-26} \) amp.m \( ^{2} \)


Friction is minimised by using
A. Wheels and ball bearings
B. More number of tyres in a car
c. Rough surfaces
D. None of these


A particle of mass \( m \) is located in a unidimensional potential field, where
the potential energy of the particle
depends on the coordinates as \( U(x)= \)
\( U_{0}(1-\sin b x) ; \) where \( U_{0} \) and \( b \) are
constant. find the period of small
oscillations that the particle performs about the equilibrium position.
A \( \cdot \frac{2 \pi}{b^{2}} \sqrt{\frac{m}{U_{0}}} \)
В. \( \frac{\pi}{b} \sqrt{\frac{m}{U_{0}}} \)
c. \( \frac{\pi^{2}}{2 b} \sqrt{\frac{m}{U_{0}}} \)
D. \( \frac{2 \pi}{b} \sqrt{\frac{m}{U_{0}}} \)


Assertion
All \( C-C-C \) bonds angles in
Isobutene \( \left(\boldsymbol{C H}_{3}-\underset{\mid}{\boldsymbol{C}}=\boldsymbol{C H}_{2}\right) \) are
\( \boldsymbol{C H}_{3} \)
different.
Reason
\( C H_{3}( \) Methyl group) show steric crowding.
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 average kinetic energy of \( O_{2} \) at a
particular temperatures is \( 0.768 \mathrm{eV} \)
The average kinetic energy of \( N_{2} \) molecules in eV at the same
temperature is?
A . 0.0015
B. 0.0030
c. 0.048
D. 0.768


A body of mass \( m \) rests on a horizontal
plane with a friction coefficient \( \mu \). At
\( t=0, \) a horizontal force is applied \( (F= \)
\( a t) \) where \( a \) is a constant vector. Find
the distance traversed in first \( t \) sec.
\( ^{\mathbf{A}} \cdot \frac{a}{6 m}\left(t-\frac{\mu m g}{a}\right)^{3} \)
в. \( \frac{a}{6 m} t^{3} \)
c. \( \frac{a}{6 m} t^{3}-\frac{\mu g t^{2}}{2} \)
D. \( \frac{a}{6 m} t^{3}-\frac{\mu g t^{2}}{3} \)


What are the components of a
nucleotide?


Hydrogen loses its electron to form \( \boldsymbol{H}^{+} \)
in this respect, it resembles:
A. halogens
B. alkali metalss
c. transition element
D. alkaline earth metals


1 TORR is equal to
A. \( 1 \mathrm{mm} \) of \( \mathrm{Hg} \)
B. \( 10 \mathrm{mm} \) of \( \mathrm{Hg} \)
\( \mathrm{c} .0 .5 \mathrm{mm} \) of \( \mathrm{Hg} \)
D. \( 5 \mathrm{mm} \) of \( \mathrm{Hg} \)


are used to absorb the
neutrons in a nuclear reactor.


The Sl unit of coefficient of mutual
inductance of a coil is
A. henry
B. volt
c. farad
D. weber


For any sets \( A \) and \( B \) Show that \( P(A \cap \) \( \boldsymbol{B})=\boldsymbol{P}(\boldsymbol{A}) \cap \boldsymbol{P}(\boldsymbol{B}) \)


Place the decimal point at the correct position in the following products. \( 16 \times 2.47=3952 \)


Five dice are thrown simultaneously. If
the occurrence of an odd number in a
single dice is considered a success, find the probability of maximum three
successes.


Aluminium hydroxide, \( A l(O H)_{3} \) is
insoluble in water, but dissolves readily
in both acidic and basic solutions. Such
behaviour is characteristic of
A. amphoteric behaviour
B. a buffer
c. hydrophilic behaviour
\( D \cdot \) none


The sensor is exposed for \( 0.1 s \) to a
\( 200 W \) lamp \( 10 m \) away. The sensor has opening that is 20 mm in a diameter
How many photons enter the sensor if the wavelength of light is 600 mm? (assume that all the energy of the lamp is given off as light).
A . \( 1.53 \times 10^{11} \)
B. \( 1.53 \times 10^{2} \)
c. \( 1.53 \times 10^{4} \)
D. \( 1.53 \times 10^{13} \)


Air stream horizontally across an
aeroplane wing of area \( 3 \mathrm{m}^{2} \) weighing 250 kg. The air speed is \( 60 \mathrm{m} / \mathrm{s} \) and 45 \( \mathrm{m} / \mathrm{s} \) over respectively. What is the lift on the wing? (Density of air 1.293 g/1)


0
0
0
00


A circular coil of 200 turns and of radius
\( 20 c m \) carries a current of \( 5 A . \) Calculate
the magnetic induction at a point along
its axis, at a distance three times the
radius of the coil from its centre.


Assertion
All food chains will come to stand still if
bacteria disappear from earth.
Reason
Bacteria are only associated with the soil fertility and hardly have any role in food chains.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


In the figure shown below, the
maximum and the minimum possible
unknown resistance \( (X), \) that \( \operatorname{can} b e \)
measured by the post office box are \( X_{\max } \) is given by \( R \times 10^{5} \Omega, \) then R is :
(In this experiment, we take out only
one plug in arm \( A B \) and only one plug in
\( \operatorname{arm} \mathrm{BC}, \) but in arm \( \mathrm{AD} \) we can take out
many plugs):


\( \boldsymbol{R}=\sqrt{\boldsymbol{P}^{2} \boldsymbol{Q}^{2}-\boldsymbol{2} \boldsymbol{P} \boldsymbol{Q} \sin (\boldsymbol{\theta}-\boldsymbol{9} \boldsymbol{0})} \)
Here \( \boldsymbol{P}=\mathbf{1 0 1} \boldsymbol{g}, \boldsymbol{Q}=\mathbf{1 0 6} \boldsymbol{g}, \) and \( \boldsymbol{\theta}= \)
\( \mathbf{1 0 9}^{\boldsymbol{O}} \)


For a very dilute solution of \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3} \)
Van't Hoff factor is:
\( \mathbf{A} \cdot i=7 \)
B. \( i=3 \)
\( c \cdot i=4 \)
\( \mathbf{D} \cdot i=5 \)


For the decomposition of 1 mole of
sodium chlorate, determine \( \Delta \boldsymbol{H}_{\text {reaction}} \)
\( \left(\Delta H_{f}^{0} \text { values: } N a C l O_{3}(s)=-85.7\right. \)
kcal/ mol, \( N a C l(s)=-98.2 \mathrm{kcal} / \mathrm{mol} \)
\( \left.\boldsymbol{O}_{2}(\boldsymbol{g})=\mathbf{0} \text { kcal } / \text { mol }\right) \)
A . -183.9 kcal
B. -91.9 kcal
c. +45.3 kcal
\( \mathbf{D} \ldots+22.5 \mathrm{kcal} \)
E . -12.5 kcal


The ratio of density of the nucleus of \( _{47}^{108} \mathrm{Ag} \) assuming \( r_{n u c l e u s} \) is \( 1.3 A^{1 / 3} \times \)
\( 10^{-13} \mathrm{cm}, \) where \( A \) is mass number of
nucleus, with density of metallic silver \( 10.5 g c m^{3}, \) expressed in terms of \( \times 10^{13} \)
is:


Gaussian surface measures the electric
field
A. parallel to the surface area
B. tangent to the surface area
c. perpendicular to the surface area
D. anti-parallel to the surface area


In Thomson's model of the atom, which
of the following statements are correct?
(i) The mass of the atom is assumed to
be uniformly distributed over the atom.
(ii) The positive charge is assumed to be uniformly distributed over the atom.
(iii) The electrons are uniformly distributed in the positively charged
sphere
(iv) The electrons attract each other to
stabilize the atom.
A. (i), (ii) and (iii)
B. (i) and (iii)
c. (i) and (iv)
D. (i), (iii) and (iv)


Choose the correct answer from the
alternatives given Hydroponics is a technique of growing:
A. submerged Plants
B. free-floating aquatic plants
c. terrestrial plants in sand
D. plants in aqueous balanced nutrient medium


In the microphone, used in the public address system.
A. Electric signals are first converted into sound waves
B. Sound waves are directly transmitted
c. Sound waves are converted into electric signals which are amplified and transmitted
D. Amplification is not required


Match column I with column II and
select the correct answer using the
codes given below.
Column I
Column II
A Father of genetics
Palaeontology
B Dihybrid cross
Gregor Mendel
C Study of fossils
\( (r) \)
3: 1
D Nictitating membrane,
Analogous organs ear muscles and
vermiform appendix E Wings of insects, bat and bird
Vestigial organs
\( A \cdot A-(q) ; B-(r) ; C-(p) ; D-(t) ; E-(s) \)
B. \( A-(r) ; B-(q) ; C-(p) ; D-(t) ; E-(s) \)
c. \( A-(r) ; B-(q) ; C-(p) ; D-(s) ; E-(t) \)
D. \( A-(r) ; B-(p) ; C-(q) ; D-(s) ; E-(t) \)


Which of the following is a sign of adolescence?
A. Increase in the volume of head hair
B. Decrease in body weight
c. sudden growth of height
D. Increase in energy


A circular loop of area \( 1 \mathrm{cm}^{2}, \) carrying a current of \( 10 \mathrm{A}, \) is placed in a magnetic field of \( 0.1 \mathrm{T} \) perpendicular to the plane of the loop. The torque on the loop due to the magnetic field is?
A. zero
B. \( 10^{-4} \mathrm{N}-\mathrm{m} \)
\( c \cdot 10^{-2} N-m \)
D. 1N-m


If the sum of 5 terms of an \( A . P . \) is same
as the sum of its 11 terms then sum of
\( \mathbf{1 6} \) is
A. 0
B . 16
\( c .-16 \)
D. 32


\( -1 / 3 \) oxidation state of nitrogen will be obtained in case of
A. hydroxylamine
B. oxime
c. hydrazoic acid
D. none of these


toppr
Q Type your question
\( N H_{4} O H \) molecules. \( N H_{4} O H \) again
dissociates into \( N H_{4}^{+} \) and \( O H^{-} \) ions.
In solution therefore, we have \( N H_{3} \)
molecules, \( N H_{4} O H \) molecules and
\( N H_{4}^{+} \) ions and the following equilibrium exist:
\( N H_{3}(g) \) (pressure \( P \) and concentration
\( \boldsymbol{c} \) ) Initially \( \rightleftharpoons \boldsymbol{N} \boldsymbol{H}_{3}(l)+\boldsymbol{H}_{2} \boldsymbol{O} \rightleftharpoons \)
\( N H_{4} O H \rightleftharpoons N H_{4}^{+}+O H^{-} \)
Let \( c_{1} \) mol \( / L \) of \( N H_{3} \) pass in liquid
state which on dissolution in water
froms \( c_{2} \) mol \( / L \) of \( N H_{4} O H \). The solution contains \( c_{3} \) mol \( / L \) of \( N H_{4}^{+} \) ions

If \( P \) is the partial pressure of ammonia at equilibrium, then which of the following is constant?
\( ^{A} \cdot \frac{P}{c_{1}} \)
в. \( \frac{p}{c_{0}} \)
\( c \cdot \frac{p}{c_{2}} \)
D. \( \frac{p}{c_{3}} \)


If a T.S. is done through \( 20^{t h} \) segment of Pheretima, it will contain
A . Intestinal cacea
B. Prostate gland
c. Intestine
D. Both B and C


If \( \cos ^{2} x+\cos ^{2} 2 x+\cos ^{2} 3 x=1, \) then
A \( x=(2 n+1) \frac{\pi}{4}, n \in I \)
в. \( _{x}=(2 n+1) \frac{\pi}{2}, n \in I \)
c. \( _{x=n \pi \pm} \frac{\pi}{6}, n \in I \)
D. None of these


\( 1^{\circ} \) alcohols preferably undergo
dehydration in presence of \( A l_{2} O_{3} \)
A. \( E_{1} \)
в. \( E_{2} \)
c. \( S_{N} 1 \)
D. \( S_{N} 2 \)


The diatomaceous earth is used to
insulate boilers and steam pipes
because
A. The wall of diatoms is deposited with calcium.
B. The diatomaceous earth is cheap.
c. It is a good conductor of heat.
D. The wall of diatoms is made of silica


Solvay process is used for the manufacture of :
A . \( N a O H \)
в. \( N a_{2} C O_{3} .10 H_{2} O \)
\( \mathrm{c} \cdot K_{2} \mathrm{CO}_{3} \)
D. \( N a_{2} O_{2} \)


Let \( X \) be a variate taking values
\( x_{1}, x_{2}, \ldots . . x_{n} \) and \( Y \) be a variate taking
values \( y_{1}, y_{2}, \dots . y_{n} \) such that \( y_{i}= \)
\( \mathbf{6} \boldsymbol{x}_{\boldsymbol{i}}+\mathbf{3} ; \quad \boldsymbol{i}=\mathbf{1}, \boldsymbol{2}, \ldots \boldsymbol{n} . \) If \( \boldsymbol{V} \boldsymbol{a} \boldsymbol{r}(\boldsymbol{Y})=\boldsymbol{3 0} \)
then \( \sigma_{X} \) is equal to
A \( \cdot \frac{5}{\sqrt{6}} \)
в. \( \sqrt{\frac{5}{6}} \)
c. 30
D. \( \sqrt{30} \)


Oxidation of
manganese dioxide \( \left(M n O_{2}\right) \) gives
chlorine.
A. \( H C l \)
в. \( H_{2} S O_{4} \)
c. \( H N O_{3} \)
D. \( H C O O H \)


Express in centimetres.
\( \mathbf{0 . 6 9 m} \)


How many histogen are present in a
monocot root apex?
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 3 \)
\( D \cdot 4 \)


A tissue is a
A. A group of separate organs that coordinated in their activities
B. Group of similar cells that function together in a specialised activity
C. Layer of cells surrounding an organ
D. Sheet of cells, one layer thick


Why do the lines of the magnetic field not cross each other?


In presence of a catalyst, what happens
to the chemical equilibrium?
This question has multiple correct options
A. Energy of activation of the forward and backwards reactions are lowered by same amount.
B. Equilibrium amount is not disturbed.
C. Rates of forward and reverse reaction increase by the same factor
D. More product is formed.


Soil carried by gravity is
A. Alluvial
B. Colluvial
c. Elluvial
D. Glacial


The maximum value of the function
\( f(x)=x^{3}+2 x^{2}-4 x+6 \) exists at
A. \( x=-2 \)
B. \( x=1 \)
c. \( x=2 \)
D. \( x=-1 \)


Explain why mitosis is called equational and meiosis is called reductional division?


Mark the INCORRECT statement:
A. Light travels along a straight line
B. A mirror does not change the medium of light falling on it
C. Things are only visible when light from our eyes reaches the object
D. All visible things either reflect or emit light


If the perimeter of one of the faces of a
cube is \( 40 \mathrm{cm} \), then what is its volume?


In how many ways can 3 people be seated in a row containing 7 seats?


A uniform steel wire of length \( 3 m \) and
are of cross section \( 2 m m^{2} \) is extended
through \( 3 m m \) Calculate the energy
stored in the wire, if the elastic limit is
not exceeded


'Z' is not.
A. Atomic number
B. Impedance
C. Zeta potential
D. Partition function


What is a curve?
A. A line which is not straight and does not any sharp edges
B. It is a polygon
C . It is a quadrilateral
D. A line with sharp edges.


If the mean of following frequency distribution. is \( 2.6, \) then the values of
is
\( \begin{array}{llllll}x_{i} & 1 & 2 & 3 & 4 & 5\end{array} \)
\( f_{i} \quad 5 \quad 4 \quad \) f \( \quad 2 \quad 3 \)
\( A \cdot 3 \)
B.
c. 8
D. None of these


Identify the correct statement:
\( A \). \( A \) and \( B \) will have the same mass afterwards.
B. A will have more mass than B afterwards.
C. A will have lesser mass than B afterwards.
D. None of these


The internal energy of a compressed
real gas, as compared to that of the normal gas at the same temperature, is
A . less
B. more
c. sometimes less, sometimes more
D. none of these


A block of mass \( 0.1 \mathrm{kg} \) is held against a wall by applying a horizontal force of 5 N on the block. If the coefficient of friction
the block and the wall is \( 0.5, \) the
magnitude of the frictional force acting on the block is:
A. \( 2.5 \mathrm{N} \)
B. 0.98 N
c. \( 4.9 \mathrm{N} \)
D. 10 N


What is the true weight of an object in a geostationary satellite that weighed exactly \( 10.0 \mathrm{N} \) at the north pole?


Radon is a :
A. Trade name of a nylon
B. Explosive
c. Drug
D. Radioactive noble gas


For a \( 3 \times 3 \) matrix \( A, \) if det \( A=4, \) then det
(Adj. A) equals
A . -4
B. 4
c. 16
D. 64


If \( \boldsymbol{A}=\{1,2,3\}, \) show that a one-one
function \( \boldsymbol{f}: \boldsymbol{A} \rightarrow \boldsymbol{A} \) must be onto.


Two point charges \( Q \) and \( -Q / 4 \) placed
along the \( x \) -axis are separated by a
distance \( r . \) Take \( -Q / 4 \) as origin and it
is placed at the right of \( Q . \) Then
the potential is zero.
\( \mathbf{A} \cdot \) at \( x=r / 3 \) only
B. at \( x=-r / 5 \) only
C. both at \( x=r / 3 \) and at \( x=-r / 5 \)
D. there exist two points on the axis where the electric field is zero


Which among the following is a synthetic plant hormone?
\( A \cdot \) IAA
B. GAA
c. \( 2,4- \) D
D. ABA


In the following figure, the radius of the
circle is \( 7 \mathrm{cm} \) and \( m(a r c R Y S)=30^{\circ} \)
find find:
\( \boldsymbol{A}(\boldsymbol{P} \boldsymbol{R} \boldsymbol{X} \boldsymbol{S}) \)


Hydrogen sulphide \( \left(\boldsymbol{H}_{2} \boldsymbol{S}\right) \) is a strong reducing agent. Which of the following reactions shows its reducing action?
A \( \cdot C d\left(N O_{3}\right)_{2}+H_{2} S \rightarrow C d S+2 H N O_{3} \)
B. \( C u S O_{4}+H_{2} S \rightarrow C u S+H_{2} S O_{4} \)
c. \( 2 \mathrm{FeCl}_{3}+\mathrm{H}_{2} \mathrm{S} \rightarrow 2 \mathrm{Fe} \mathrm{Cl}_{2}+2 \mathrm{HCI}+\mathrm{S} \)
D. \( P b\left(N O_{3}\right)_{2}+H_{2} S \rightarrow P b S+2 C H_{3} C O O H \)


For a first order reaction rate constant
is \( 1 \times 10^{-5} \sec ^{-1} \) having \( E_{a}= \)
\( 1800 k J / \) mol. Then the value of \( \ell n A \) at
\( \boldsymbol{T}=\mathbf{6 0 0} \boldsymbol{K} \) is:
A . 151.7
в. 349.3
c. 24.7
D. 11.34


If the mass of two bodies become
double \( \& \) also the distance between
them becomes twice the gravitational force will be :
A . Double
B. half
\( c \cdot 4 \)
D. Remain same


What is the tension of each wire?
A . \( 25 N \)
в. \( 50 N \)
\( c .75 N \)
D. \( 100 N \)


A thin uniform sheet of metal of uniform
thickness is cut into the shape bounded
by the line \( x=a \) and \( y=\pm k x^{2}, \) as
shown. Find the coordinates of the
centre of mass


Which of the following electronic configurations in the outermost shell is
characteristic of alkali metals?
A \( \cdot(n-1) s^{2} p^{6} n s^{2} p^{1} \)
B . \( (n-1) s^{2} p^{6} d^{10} n s^{1} \)
C \( \cdot(n-1) s^{2} p^{6} n s^{1} \)
D \( \cdot n s^{2} n p^{6}(n-1) d^{1} \)


Heavy water is used as ir
nuclear reactor


There are two concentric spherical
shells of radii r and 2r. Initially a charge
\( \mathrm{Q} \) is given to the inner shell.Now, switch
\( S_{1} \) is closed and opened then \( S_{2} \) is
closed and opened and the process is
repeated \( n \) times for both the keys
alternatively. Find the final potential
difference between the shells


The correct increasing order of basic
strength for the following compounds is:
\( (\mathbf{I}) \)
(II)
\( (\mathbf{I I I}) \)
\( \mathbf{A} \cdot\|<\| 1<1 \)
B. \( \|I|<|<\| \)
C. \( \|I<\|<1 \)
D. \( \|<I<\| 1 \)


What is Chemical Equilibrium? Write any four main characteristics of
chemical equilibrium?


Find the equation of the hyperbola whose foci are \( (0, \pm \sqrt{10}) \) and passing through the point (2,3)


Identify the statement which best
define the uncertainty principle?
A. We cannot know for certain when any given radioactive particle will undergo decay
B. We cannot know both the momentum and the position of a particle at the same time
c. The laws of physics are the same in all intertial reference frames
D. Light exhibits both wave and particle properties
E. An unobserved particle can be in two places at the same time


A certain current liberated 0.504 g of
hydrogen in 2 hours. How many grams of copper can be liberated by the same current flowing for the same time in copper sulphate solution?
A. \( 31.8 \mathrm{g} \)
B. \( 16.0 \mathrm{g} \)
c. \( 12.7 \mathrm{g} \)
D. \( 63.5 \mathrm{g} \)


The domestic sewage in large cities
A. Has a high BOD level, as site containes both aerobic and anaerobic bacteria.
B. Is processed by aerobic and then anaerobic bacteria in the secondary treatment in the Sewage Treatment Plants (STPs).
C. When treated in STPs does not really require the aeration step as the sewage contains adequate oxygen.
D. Has very high amounts of suspended solids and dissolved salts.


What will be the weight of a body of
mass \( m \) kg at the centre of the earth?
A. \( m g \) newton
B. \( m / g \) newton
c. \( m \) newton
D. 0 newton


From the following chemical reactions determine the relative Bronsted-Lowery acid strengths (strongest to weakest). \( \boldsymbol{H} \boldsymbol{C l O}_{4}(\boldsymbol{s o l})+\boldsymbol{C H}_{3} \boldsymbol{C O O H}(l) \longrightarrow \)
\( \boldsymbol{C H}_{3} \boldsymbol{C}(\boldsymbol{O H})_{2}^{+}(\boldsymbol{s o l})+\boldsymbol{C l O}_{\boldsymbol{4}}^{-}(\boldsymbol{a q}) \)
\( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4}(\boldsymbol{s} \boldsymbol{o l})+\boldsymbol{C H}_{3} \boldsymbol{C O O H}(l) \rightleftharpoons \)
\( \boldsymbol{C H}_{3} \boldsymbol{C}(\boldsymbol{O H})_{2}^{+}(\boldsymbol{s o l})+\boldsymbol{C l O}_{4}^{-}(\boldsymbol{s o l}) \)
A \( \cdot H C l O_{4}>C H_{3} C(O H)_{2}^{+}>H_{2} S O_{4} \)
в. \( H C l O_{4}>C H_{3} C O O H>H_{2} S O_{4} \)
c. \( H C l O_{4}>H_{2} S O_{4}>C H_{3} C(O H)_{2}^{+} \)
D. \( H C l O_{4}>H_{2} S O_{4}>C H_{3} C O O H \)


The radius of the orbit of a hydrogen atom is 0.85 nm. The velocity of an electron in this orbit is:
A \( .5 .44 \times 10^{5} \mathrm{m} / \mathrm{s} \)
В. \( 5.62 \times 10^{5} \mathrm{m} / \mathrm{s} \)
c. \( 5.48 \times 10^{5} \mathrm{m} / \mathrm{s} \)
D. \( 5.67 \times 10^{5} \mathrm{m} / \mathrm{s} \)


If order of matrix \( A \) is \( 4 \times 3 \) and order of
matrix \( B \) is \( 3 \times 5 \) then order of matrix
\( \boldsymbol{B}^{\prime} \boldsymbol{A}^{\prime} \) is:
\( \mathbf{A} \cdot 5 \times 2 \)
B. \( 4 \times 5 \)
\( \mathbf{c} \cdot 5 \times 4 \)
D. \( 3 \times 2 \)


Which method of purification is represented by the following equation? \( \boldsymbol{T} \boldsymbol{i}(\boldsymbol{s})+\boldsymbol{2} \boldsymbol{I}_{2}(\boldsymbol{g}) \stackrel{\boldsymbol{5} \mathbf{2} 3 \boldsymbol{k}}{\longrightarrow} \boldsymbol{T} \boldsymbol{i} \boldsymbol{l}_{4}(\boldsymbol{g}) \frac{\mathbf{1 7 0 0} \boldsymbol{k}}{\boldsymbol{\}} \)
\( \boldsymbol{T} \boldsymbol{i}(\boldsymbol{s})+\boldsymbol{2} \boldsymbol{I}_{2}(\boldsymbol{g}) \)
A. zone refining
B. Cupellation
c. Poling
D. Van Arkel


State whether the following statements
are true or false.
Motile reproductive bodies are completely absent in Rhodophyta.
A. True
B. False


A non uniform sphere can be kept on a
rough inclined plane so that it is in equilibrium. In the figure below the dots represents location of centre of mass. In
which one of the positions can sphere
be in equilibrium?
\( A \)
B.
\( c \cdot c \)
\( D \)


Karim sold a shirt at a loss of \( 10 \% . \) Had
he sold it for Rs. 60 more he would have
gained \( 5 \% \) on it. Find the cost price of the shirt.


\( \operatorname{Let} \boldsymbol{R}= \)
\{(1,3),(4,2),(2,4),(2,3),(3,1)\} be a
relation on the set \( A=\{1,2,3,4\} . \) The
relation \( \boldsymbol{R} \) is
A. A function
B. Transitive
C. Not symmetric
D. Reflexive


Match the terms of Column A correctly
with the phrases given in Column B.


State whether the following statement
is true or false:
\( P b(I I) \) salts are easily oxidized to
\( P b(I V) \) salts
A. True
B. False


Consider the given reaction and identify INCORRECT statement(s)
This question has multiple correct options
A. Reaction involves formation of carbocation
B. Reaction proceeds by formation of transition state
c. Reaction follows 2 nd order kinetics
D. Reaction proceeds with retention as well as inversion of configuration


Assertion
Glucose does not gives \( 2,4-D N P \)
test.
Reason
Glucose exists in cyclic hemiacetal form
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 longest cell in human body
is
A. Neuron
B. Muscle fibre
c. Epithelial cell
D. Bone cell


What do carbon credits signify?
A. Credits given in the course of carbon products sales
B. Entitlements to emit certain quantity of green house gases
C. Permissible amount of Carbon dioxide in the atmosphere
D. The extent of carbon required to ensure sustainable development


Assertion
CuFeS is concentrated by froth
flotation method.
Reason
CuFeS \( _{2} \) is main ore of copper.
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 and Reason is correct


Eight spheres of same radius from a
metallic sphere of \( 10 \mathrm{cm} \) radius, are
formed. Find the surface area of each
sphere so obtained.


In the electrolytic refining of copper, \( A g \) and \( A u \) are found:
A. on Cathode
B. on anode
c. in the anodic mud
D. in the cathodic mudd


Sound is produced in a bamboo flute because:
A. air starts vibrating
B. bamboo starts vibrating
c. airhits the bamboo
D. direction of air is changed


\( C_{2} D_{2} \frac{L i / a q \cdot N H_{3}}{ } C_{2} D_{2} H_{2}(\text {trans}) \)
This reaction mechanism proceeds
through:
A. electrophilic addition
B. nucleophilic addition
c. free radical addition
D. None of these


The tube length of microscope is \( 10 \mathrm{cm} \) and the focal length of its objective is 5 \( \mathrm{cm} . \) If the eye lens has focal length 0.5 \( \mathrm{cm} . \) then the magnification of microscope for relaxed eye is :
A . 45
в. 100
c. 25
D. 10


EMF of Ni-Cd battery is dependent on the concentration of:
A. \( C d(O H)_{2} \)
B. \( N i(O H)_{2} \)
\( c \cdot O H^{-} \)
D. None of these


A sphere A impinges directly on an identical sphere \( \mathrm{B} \) at rest. If e is the coefficient of restitution then the ratio
of the velocities of \( A \) and \( B \) after impact
is
A \( \cdot \frac{1+e}{1-e} \)
в. \( \frac{1-e}{1+e} \)
c. \( \frac{e}{1-e} \)
D. \( \frac{e}{1+e} \)


Molecular weights of macromolecules are determined by :
A. elevation of boiling point
B. depression in freezing point
c. osmotic pressure
D. None of these


A helicopter is flying at a height of 500 \( m \). If all of sudden its engines stops working, the helicopter will fall on the earth in \( _{--} \) seconds?
A . 10
B. 12
c. 15
D. 20


Endodermis acts as biological check post and prevents wall to wall flow of materials because it has.
A. Casparian strips
B. Barrel-shaped cells
c. Passage cells
D. specialised thickenings


Find out the wavelength of the next line in the series having lines of spectrum of \( \boldsymbol{H} \) -atom of wavelengths \( \mathbf{6 5 6 5} \boldsymbol{\boldsymbol { A }}, \mathbf{4 8 6 3} \boldsymbol{\boldsymbol { A }} \)
\( 4342 A \) and \( 4103 \dot{A} \)


How many of the following will show tautomerism?
(iii) Me, \( c_{\text {Ch }}^{\text {? }} \)
(vil)


\( \sin \left(2 \tan ^{-1} \sqrt{\frac{1-x}{1+x}}\right) \)


Which one of the following statement is
correct for \( \boldsymbol{d}^{4} \) ions \( [\mathrm{P}=\text { pairing energy }] ? \)
A. When \( \Delta_{0}>P \), low-spin complex form
B. When \( \Delta_{0}<P \), low-spin complex form
c. When \( \Delta_{0}>P \), high-spin complex form
D. When \( \Delta_{0}<P \), both high-spin and low-spin complexes form


The character of monocot is
A. Net-veined leaves
B. Annual rings
c. Seed with two masses of stored food
D. Conducting strands scattered in ground tissue