Predict \( \Delta H>\Delta U \) or \( \Delta H<\Delta U \)
a. \( C(\text { graphite })+O_{2}(g) \longrightarrow C O_{2}(g) \)
b. \( \boldsymbol{P C l}_{5}(\boldsymbol{g}) \longrightarrow \boldsymbol{P C l}_{3}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) \)
A. a. \( \Delta H=\Delta U ; \) b. \( \Delta H>\Delta U \)
В. а. \( \Delta H>\Delta U ; \) b. \( \Delta H=\Delta U \)
c. a. \( \Delta H>\Delta U ; \) b. \( \Delta H<\Delta U \)
D. None of these


The IUPAC name of the given compound
is :
A. 3-ethylcyclobut-1-en-2-ol
B. 4-ethylcyclobut-2-en-1-ol
c. 2-ethylcyclobuten-3-1-ol
D. 4-ethylcyclobut-1-en-3-ol


A husband and wife have normal vision
but fathers of both of them were colour
blind. Probability of their first daughter to be colour blind is
A . 25\%
B. 50\%
c. 75\%
D. 0\%


A vessel contains 1.6 g of dioxygen at STP \( (273.15 K, 1 \text { atm pressure }) . \) The gas is now transferred to another vessel at
constant temperature, where pressure becomes half of the original pressure. The volume of the new vessel is:
A . 2.24
B. 22.4 L
c. \( 11.2 \mathrm{L} \)
D. 1.12 L


Factorise the expression: \( 7 p^{2}+21 q^{2} \)
\( \mathbf{A} \cdot 7\left(p^{2}+q^{2}\right) \)
B. \( \left(p^{2}-3 q^{2}\right) \)
C \( .7\left(p^{2}+3 q^{2}\right) \)
D. \( \left(p q^{2}+3 q^{2}\right) \)


Which pair of elements can form multiple bond with itself and oxygen?
A. \( F, N \)
B. \( N, C l \)
c. \( N, P \)
D. \( N, C \)


Which of the following waves is progressing in the \( y \) direction?
A \( . x=x_{0} \cos (\omega t-k y) \)
в. \( y=y_{0} \cos (\omega t-k y) \)
c. \( y=y_{0} \cos k x \sin \omega t \)
D. \( y=y_{0} \sin k x \cos \omega t \)


The equilibrium constant \( \boldsymbol{K}_{\boldsymbol{p}} \) for the reaction \( N_{2} O_{4}(g) \rightleftharpoons 2 N O_{2}(g) \) is 4.5
What would be the average molar mass (in g/mol) of an equilibrium
mixture of \( N_{2} O_{4} \) and \( N O_{2} \) formed by
the dissociation of pure \( N_{2} O_{4} \) at a total
pressure of 2 atm?
\( \mathbf{A} \cdot 69 \)
в. 57.5
\( c .80 .5 \)
D. 85.5


Identify the correct statement:
A. Electrostatic forces are much weaker than the gravitational forces.
B. Electrostatic forces are much stronger than the gravitational forces.
C . Electrostatic forces are comparable to the gravitational forces
D. All of the above


Ten millilitres of a gaseous hydrocarbon was exploded with oxygen. After the explosion, there was a contraction of 20 \( \mathrm{ml} \) in volume. On shaking the residual gaseous mixture with \( \mathrm{KOH} \), there was a
further concentration of \( 20 \mathrm{ml} \) in
volume. Molecular formula is \( \boldsymbol{C}_{\boldsymbol{x}} \boldsymbol{H}_{\boldsymbol{y}} \cdot \) All
the volumes were recorded at the same
temperature and pressure. Here \( \mathbf{x}+\mathbf{y} \) is:


For \( 0<a<x, \) then the minimum value
of the function \( \log _{a} x+\log _{x} a \) is
A .
B. 2
\( c \cdot 4 \)
D.


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


In aqueous solution \( \boldsymbol{E} \boldsymbol{u}^{2+} \) acts as
A. an oxidsing agent
B. reducing agent
c. can act as either of these
D. can act as redox agent


Renal rickets are bending of weight bearing long bones in
A. Infants
B. Young children
c. Adolescents
D. Elderly persons


Vital capacity of human lung for air
\( A \cdot 4000 m \)
B. 1500 \( \mathrm{m} \) ।
\( c \cdot 1000 m \)
D. 500 m1


If the line \( x-1=0 \) is the directrix of
the parabola \( y^{2}-k x+8=0, \) then one
of the values of \( k \) is
A \( .1 / 8 \)
B. 8
\( c \cdot 4 \)
D. \( 1 / 4 \)


The value of \( a \) if the series \( 4, a, 16 \) are in
\( \mathrm{GP} \)
\( A \cdot 8 \)
B. 12
c. 10
D. none of these


Two mirrors are arranged as shown in the figure. Light is incident on the first
mirror at an angle of \( 35^{\circ} . \) The light
reflects towards a second mirror.
Determine the angle \( \boldsymbol{\theta} \)


The value of Planck's constant
is
\( \mathbf{A} \cdot 6.627 \times 10^{-34} \)joulesec.
B. \( 6.083 \times 10^{-34} \) joulesec.
c. \( 6.627 \times 10^{-27} \) joulesec.
D. \( 6.627 \times 10^{-30} \) joulesec.


A rectangle has sides of lengths \( 6 \mathrm{cm} \)
and \( 8 c m . \) Two magnetic poles each of
pole strength ' \( m \) ' are placed at the ends of one side of smaller length and magnetic force acting between them is
\( F^{\prime} . \) If they are moved to new positions of same rectangle so that they are diagonally opposite. Find the final force acting on each pole.


Which is more ionic?
\( N a F, N a C l, N a B r, N a I \)


When the object is at distance \( u_{1} \) and
\( u_{2} \) from a lens, a real image and virtual
image are formed respectively having the same magnification. The focal length of the lens is :
A \( . u_{1}-u_{2} \)
в. \( \frac{u_{1}-u_{2}}{2} \)
c. \( \frac{u_{1}+u_{2}}{2} \)
D. \( u_{1}+u_{2} \)


Statement: \( 0_{3} \) is acidic in solution.
State whether the given statement is true or false
A . True
B. False


\( \boldsymbol{i}^{3}=\frac{\mathbf{1}}{\boldsymbol{i}}=\frac{\mathbf{1}}{\boldsymbol{i}} \times \frac{\boldsymbol{i}}{\boldsymbol{i}}=\frac{\boldsymbol{u}}{\boldsymbol{1}}=-\boldsymbol{i} \)


Three schools situated at \( P, Q \) and \( R \) in the figure are equidistant from each other as shown in the figure. Find
\( \angle Q O R \)


Match the lists and find the correct
option.
(a) Viroid infecting
(i) 6,500 nucleotides tomato plant
(b) \( T M V \)
(ii) \( 300-400 \) nucleotides
(iii) Two identical
(c) Polio virus \( \quad \) molecules of \( R N A \)
(d) Lentivirus
(iv) Many sided
(v) Prion
\( A \cdot(a)-(i i),(b)-(i),(c)-(i v),(d)-(i i i) \)
B. (a) - (iii), (b) - (i), (c) - (iv), (d) - (ii)
C. \( (a)-(i i),(b)-(i v),(c)-(v),(d)-(i) \)
D. \( (a)-(i),(b)-(i v),(c)-(v),(d)-(i) \)


When a battery connected across a
resistor of \( 16 \Omega, \) voltage across the resistor is \( 12 \mathrm{V} \). When the same battery
is connected across a resistor of \( 10 \Omega \)
voltage across it is 11 V. The internal resistance of the battery (in ohm) is :
A \( \cdot \frac{10}{7} \)
B. \( \frac{20}{7} \)
c. \( \frac{25}{7} \)
D. \( \frac{30}{7} \)


Radioactive disintegration differs from a chemical change in being:
A. an exothermic change
B. a spontaneous process
c. a nuclear process
D. a unimolecular first-order reaction


A survey regarding the height (in cm) of
51 girls of class \( X \) of a school was
conducted and the following data was
obtained:
\( \begin{array}{ll}\text { Height in } \mathrm{cm} & \text { Number of Girls } \\ \text { Less than } 140 & 4 \\ \text { Less than } 145 & 11 \\ \text { Less than } 150 & 29 \\ \text { Less than } 155 & 40 \\ \text { Less than } 155 & 46 \\ \text { Less than } 165 & 51\end{array} \) Find the median height.


What would happen if forest disappears?
A. Flood
B. Global warming
c. Extinction of animal
D. All of the above


The gall bladder temporarily stores bile.
A. True
B. False


Schiff's and Piria method is used for the
estimation of:
A. nitrogen
B. sulphur
c. halogens
D. oxygen


Define magnetic lines of force and state its two properties.


If \( A \) is square matrix of order \( 3, \) then
\( \left|A d j\left(A d j A^{2}\right)\right|= \)
A \( \cdot|A|^{2} \)
B \( \cdot|A|^{4} \)
c. \( |A|^{8} \)
D・ \( |A|^{16} \)


According to the Bohr Theory, which of the following transitions in the hydrogen atom will give rise to the least energetic photon?
A \( n=5 \) to \( n=3 \)
3
в. \( n=6 \) to \( n=1 \)
c. \( n=5 \) to \( n=4 \)
D. \( n=6 \) to \( n=5 \)


If \( |\boldsymbol{A}|=2, \) where \( \boldsymbol{A} \) is a \( \mathbf{3} \times \mathbf{3} \) matrix.
Then find \( |\boldsymbol{3} \boldsymbol{A}| \)


Find the area of a parallelogram \( \boldsymbol{A B C D} \)
if three of its vertices are
\( \boldsymbol{A}(\mathbf{2}, \mathbf{4}), \boldsymbol{B}(\mathbf{2}+\sqrt{\mathbf{3}}, \mathbf{5}) \) and \( \boldsymbol{C}(\mathbf{2}, \mathbf{6}) \)


A solid cylinder of mass, \( m \), and radius,
\( r, \) is rotating at an angular velocity, \( \omega \)
when a non-rotating hoop of equal mass and radius drops onto the cylinder. In terms of its initial angular velocity, \( \omega \)
what is its new angular velocity, \( \omega^{\prime} ? \)
A \( \cdot \omega^{\prime}=\frac{\omega}{3} \)
B. \( \omega^{\prime}=\frac{3 \omega}{4} \)
\( \mathbf{C} \cdot \omega^{\prime}=\omega \)
\( \mathbf{D} \cdot \omega^{\prime}=3 \omega \)
E \( \cdot \omega^{\prime}=\frac{2 \omega}{3} \)


Artificial rain based on the principle of :
A. coagulation
B. electro phroetic effect
C. emulsification
D. a Tyndall effect


When 5.0 gram of \( B a C l_{2} \) is dissolved in
water to have \( 10^{6} \) gram of solution. The concentration of a solution is:
A . 2.5 ppm
в. 5 ррт
\( c .5 M \)
D. \( 5 g L^{-1} \)


Chymotrypsin is produced by
A . Liver
B. Pancreas
c. stomach
D. Duodenum


The element with the electronic
configuration \( [X e] 4 f^{14} 5 d^{1} 6 s^{2} \) is a:
A. representative element
B. transition element
C . actinide element
D. Lanthanide element


\( 25 \mathrm{mL} \) of a solution containing ferrous sulphate and ferric sulphate, acidified
with \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) is reduced by metallic zinc.
The solution requires \( 34.25 \mathrm{mL} \) of \( 0.1 \mathrm{N} \)
solution of \( \boldsymbol{K}_{2} \boldsymbol{C r}_{2} \boldsymbol{O}_{7} \) for oxidation
However, before reduction with zinc, 25
mL of same solution requires \( 22.45 \mathrm{mL} \)
of same \( K_{2} C r_{2} O_{7} . \) Calculate the weight
of \( F e_{2}\left(S O_{4}\right)_{3} \) present in gram per litre of the solution (in nearest integer)


Assertion
The \( d_{c-o} \) in bridging carbonyl group is Ionger than that of terminal carbonyl group.
Reason
With an increase in the extent of
synergic bonding, the \( C-O \) bond
length increases.
Read the above assertion and reason
and choose the correct option regarding
¡t.
A. Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-
B. Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation fo statement-
c. statement-1 is true, statement-2 is false
D. statement-1 is false, statement-2 is true


Synaptonemal complex is site of
A. Spindle attachment
B. Replication
c. Chromatid separation
D. Chromosome alignment and recombination


What causes lightning?
A. Excessive electric charge in the atmosphere
B. Increased chemical energy in the atmosphere
C. Attraction between two oppositely charged clouds
D. All of the above


A scientist proposes a new temperature scale in which the ice point is \( 25 x \) (X is the new unit of temperature) and the steam point is 305 X. The specific heat capacity of water in this new scale is \( \left(\text { in } J k g^{-1} X^{-1}\right) \)
A \( .4 .2 \times 10^{3} \)
B. \( 3.0 \times 10^{3} \)
c. \( 1.2 \times 10^{3} \)
D. \( 1.5 \times 10^{3} \)


In which of the following compounds, \( \boldsymbol{S} \) atom has +6 oxidation state?
This question has multiple correct options
A. \( H_{2} S O_{5} \)
в. \( H_{2} S_{2} O_{8} \)
c. \( N a_{2} S_{4} O_{6} \)
D. \( H_{2} S O_{4} \)


The refractive index of an equilateral prism is \( \sqrt{3} . \) What is the angle of minimum deviation.?
A \( \cdot 45^{\circ} \)
B. \( 60^{\circ} \)
c. \( 37^{\circ} \)
D. \( 72^{\circ} \)


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


Anish spends \( 20 \% \) of his income for
paying bills and \( 15 \% \) for buying groceries. If his income is \( R s .9000 \)
what is the amount spent by him on bills and groceries?


Which of the following is the correct order of boiling point?
A. chloroethane < ethane < ethanol
B. ethane < chloroethane < ethanol
c. ethanol \( < \) ethane \( < \) chloroethane
D. ethane > chloroethane > ethanol


Oxidation states shown by lanthanoids is/are
This question has multiple correct options
\( A \cdot+2 \)
B. +3
\( c \cdot+4 \)
D. None of these


Define the term polymerisation.


f \( ^{n} C_{8}=^{n} C_{5} \), then the value of \( n \) is
\( A \cdot 2 \)
B. 3
c. 1
D. 13


The focal length of a concave lens is \( 2 m \)
Calculate the power of the lens.


A solid right circular wax cone of height \( 12 \mathrm{cm} \) and radius \( 4 \mathrm{cm} \) is melted and
smaller wax cones of height \( 4 \mathrm{cm} \) and
radius \( 2 \mathrm{cm} \) are made The number of
smaller cones will be
\( A \cdot 48 \)
B. 18
\( c \cdot 24 \)
D. 36


The additive identity element in the set
of integers is:
A .
B. - -
c. 0
D. None of these


According to Aufbau principle, the correct order of energy of \( 3 d, 4 s \) and \( 4 p \) orbitals is :
A. \( 4 p<3 d<4 s \)
в. \( 4 s<4 p<3 d \)
c. \( 4 s<3 d<4 p \)
D. \( 3 d<4 s<4 p \)


A train takes 3 hrs to travel between
Mumbai and Pune with a average speed
of \( 65 k m p h . \) Find the distance between
the two cities.
A . \( 195 k m \)
B . \( 21.66 k m \)
c. \( 130 k m \)
D. None of these


Choose the 0 DD one out of the following terms given and name the CATEGORY to
which the others belong:
Bile, Urea, Uric acid, Ammonia.


Which of the following compounds is found abundantly in nature?
A. Fructose
B. Starch
c. Glucose
D. Cellulose


What is the wavelength (in \( n m \) ) of gamma-rays whose energy is 1.50 eV?
A. \( 827.5 \mathrm{nm} \)
В. 627.5 nm
c. \( 927.5 \mathrm{nm} \)
D. None of these


Assertion
For an ideal gas in a cyclic process and in an isothermal process change in
internal energy is zero.
Reason
In both processes there is no change in temperature.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


If \( a, b, c \) are the percentage errors in the measurement of \( A, B \) and \( C, \) then the
percentage error in ABC would be
approximately
A \( . a b c \)
B . \( a+b+c \)
c. \( a b+b c+a c \)
D. \( \frac{a}{b}+\frac{b}{c}+\frac{c}{a} \)


The length of side of a square loop is
4m. This loop is placed in a uniform magnetic field of 2.5 t. Outside the loop, the magnetic field is zero and it is coming out side from magnetic field perpendicularly with velocity \( 2 \mathrm{m} / \mathrm{s} \). Find the value of induced emf in loop after
one second.


At sun rise or at sun set the sun
appears to be reddish while at mid day it looks white. This is because
A. Scattering due to dust particles and air molecules causes this phenomenon
B. The sun is cooler at sun rise or at sunset
c. Refraction causes this phenomenon
D. Diffraction sends red rays to the earth at these times


In the refining of silver by electrolytic method what will be the weight of 100 g Ag anode if 5 ampere current is passed for 2 hours? Purity of silver is \( 95 \% \) by weight. in gram is:
A . 57
B. 32
c. 60
D. 13


Two triangles are ....... if two sides and included angle of one triangle are equal to two sides and included angle of the other triangle.
A. congruent
B. unequal
c. equilateral
D. none of these


The value of an estate in January 1905 started gradually declining in such a way that at the end of each year it was worth only \( x \) times its value at the beginning of the year. What was its worth in end December \( 1910 ? \)
(1) It was worth Rs. 10109 in the end of
December 1906
(2) It was worth Rs. 12345 in the
beginning of January 1905


Which of the following is not a major option for managing hazardous waste?
A. Reducing the production of waste while increasing the amount generated
B. Reducing the volume and/or hazard of the wastee
c. Long-term storage or disposal
D. Dumping at sea


A circular platform is mounted on a
vertical frictionless axle. Its radius is
\( r=2 m \) and its moment inertia is \( I= \)
\( 200 k g m^{2} . \) It is initially at rest. A \( 70 k g \)
man stands on the edge of the platform
and begins to walk along the edge at
speed \( v_{0}=10 m s^{-1} \) relative to the
ground. The angular velocity of the
platform is
A \( .1 .2 \mathrm{rad} \mathrm{s}^{-1} \)
B. 0.4 rad \( s^{-1} \)
c. 2.0 rad \( s^{-1} \)
D. 7.0 rad \( s^{-1} \)


If \( \tan x+\tan \left(x+\frac{\pi}{3}\right)+ \)
\( \tan \left(x+\frac{2 \pi}{3}\right)=3, \) then
A \( \cdot \tan x=1 \)
B. \( \tan 2 x=1 \)
\( \mathbf{c} \cdot \tan 3 x=1 \)
D. None of these


Choose the correct answer from the
alternative given
Amongst \( T i F_{6}^{2-}, C o F, C u_{2} C l_{2} \) and
NiCl, which are the colourless
species? (atomic number of \( \mathrm{Ti}=22, \mathrm{Co}= \) \( 27, C u=29, N i=28) \)
A \( \cdot C o F_{6}^{3-} \) and \( N i C l_{4}^{2} \)
B . \( T i F_{6}^{2-} \) and \( C u_{2} C l_{2} \)
c. \( C u_{2} C l_{2} \) and \( N i C l_{4}^{2} \)
D. \( T i F_{6}^{2-} \) and \( C o F_{6}^{3-} \)


\( \boldsymbol{C}_{\mathbf{1}}-\boldsymbol{H}, \boldsymbol{C}_{2}-\boldsymbol{H}, \boldsymbol{C}_{3}-\boldsymbol{H} \) and \( \boldsymbol{C}_{4}-\boldsymbol{H} \)
homolytic bond dissociation energy is in order:
A \( \cdot C_{2}-H>C_{3}-H>C_{4}-H>C_{1}-H \)
B. \( C_{1}-H>C_{4}-H>C_{2}-H>C_{3}-H \)
\( \mathbf{c} \cdot C_{2}-H>C_{3}-H>C_{1}-H>C_{4}-H \)
D. \( C_{1}-H>C_{4}-H>C_{3}-H>C_{2}-H \)


Lungs in the thoracic cavity is seperated form the abdominal cavity by means of
A. Peritonium
B. Pleura
c. Trechea
D. Diaphragummumumnnmmm


Which of following is used to absorb carbon dioxide evolved during the estimation of carbon present in an
organic compound?
A. Sodium hydroxide
B. Potassium hydroxide
c. Potassium carbonate
D. Calcium carbonate


Find the oxidation number of \( P \) in
\( \boldsymbol{M} \boldsymbol{g}_{2} \boldsymbol{P}_{2} \boldsymbol{O}_{7} \)


Give the IUPAC name of the given compounds
\[
\mathrm{CH}_{3}-\mathrm{NH}-\mathrm{CHO}
\]


Pick the odd one out from the following based on the nature of energy possessed by them. (moving car, water stored in a tank, a book on a table,
ceiling fan in OFF position)


Find the simple interest and the
amount when
Principal= \( \boldsymbol{R s} . \boldsymbol{6 4 0 0}, \boldsymbol{r a t e}=\boldsymbol{6} \% \boldsymbol{p} \boldsymbol{a} \)
and \( \operatorname{tim} e=2 \) years


Family Planning has made minimum impact in rural areas because of
A. non availability of birth control measure
B. social orthodoxy and psychological factors
c. lack of adequate fund
D. defective planning


Given the following:
\( \boldsymbol{C}(s)+\boldsymbol{O}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g}) ; \boldsymbol{\Delta} \boldsymbol{H}= \)
\( -394 k J / m o l \)
\( 2 H_{2}(g)+O_{2}(g) \rightarrow 2 H_{2} O(l) ; \Delta H= \)
\( -\mathbf{5 6 8} k J / \operatorname{mol} C_{2} H_{5} O H(l)+ \)
\( \mathbf{3} O_{2}(\boldsymbol{g}) \rightarrow \mathbf{2} \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g})+ \)
\( \mathbf{3} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) ; \boldsymbol{\Delta} \boldsymbol{H}=-\mathbf{1 0 5 8} \boldsymbol{k} \boldsymbol{J} / \boldsymbol{m o l} \)
Using the given data, the heat of formation of ethanol is:
A. \( -582 k J / m o l \)
в. \( 71.8 k J / \) тод
c. \( -244 k J / \) mol
D. +782 kJ / mol


How does ionization enthalpy vary in a group and a period?


Phenolphthalein is a synthetic indicator and its color in acidic and basic
solutions, respectively are:
A. red and blue
B. blue and red
c. pink and colorless
D. colorless and pink


The gas with lower critical temperature is easily adsorbed on platinum
If true then enter 1 else enter 0 .


\( \boldsymbol{C H}_{3} \)
\( \boldsymbol{C H}_{3}-\dot{\boldsymbol{N}}-\boldsymbol{C H}_{3} \) the IUPAC name is:
A. Trimethyl amine
B. 2-methyl ethanamine
c. N,N-Dimethylmethanamine
D. Trimethyl ammonia


Which of the following cannot be used as an antacid?
A. Rantidine
B. Cimetidine
c. Metal hydroxides
D. None of the above


A certain charge \( Q \) is divide at first into
two parts \( (q) \) and \( (Q-q) . \) Later on the
charges are placed at a certain
distance. If the force of interaction
between the two charges is maximum
then:
A \( \cdot(Q / q)=(4 / 1) \)
B \cdot \( (Q / q)=(2 / 1) \)
c. \( (Q / q)=(3 / 1) \)
D・ \( (Q / q)=(5 / 1) \)


Let the function \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be defined
by \( \boldsymbol{f}(\boldsymbol{x})=\mathbf{2} \boldsymbol{x}+\cos \boldsymbol{x} \) then \( \boldsymbol{f} \)
A. Has maximum at \( x=0 \)
B. Has minimum at \( x=\pi \)
c. Is an increasing function
D. Is a decreasing


A digestive enzyme, salivary amylase, in the saliva being digestion of
A. Protein
B. Nucleic acids
c. Fats
D. Carbohydrates


What could arrow 1 possibly represent in
the above diagram?
A. Carbon dioxide
B. Oxygen
c. water
D. Energy


Write the names of the monomers of
PHBV polymer


Differentiate the following
\( (x+2)^{3} \)


If \( \vec{a}, \vec{b}, \vec{c}, \vec{d}, \vec{e}, \vec{f} \) are position vectors of 6 points \( A, B, C, D, E \& F \) respectively such that \( \mathbf{3} \overrightarrow{\boldsymbol{a}}+\mathbf{4} \overrightarrow{\boldsymbol{b}}=\mathbf{6} \overrightarrow{\boldsymbol{c}}+\overrightarrow{\boldsymbol{d}}=\mathbf{4} \overrightarrow{\boldsymbol{e}}+\mathbf{3} \overrightarrow{\boldsymbol{f}}=\overrightarrow{\boldsymbol{x}} \)
then
This question has multiple correct options
\( \mathbf{A} \cdot \overline{A B} \) is parallel to \( \overline{C D} \)
B. line AB, CD and EF are concurrent
c. \( \vec{x} \) \( \overline{7}^{\text {is position vector of the point dividing CD in ratio } 1} \)
6
D. A, B, C, D, E \& F are coplanar


Find the shortest distance between
lines: \( \frac{x-1}{1}=\frac{y-2}{3}=\frac{z-3}{2} \) and
\( \frac{x-4}{2}=\frac{y-5}{3}=\frac{z-6}{1} \)
A . \( \sqrt{6} \)
B. \( \sqrt{5} \)
\( c \cdot \sqrt{3} \)
D. 6


Which of the following pairs give \( C l_{2} \) at
room temperature?
A. \( \operatorname{conc.HCl}+ \) KMnO\( _{4} \)
в. \( N a C l+ \) conc. \( H_{2} S O_{4} \)
c. \( N a C l+M n O_{2} \)
D. \( N a C l+ \) conc. \( H N O_{3} \)


Suppose, \( A=\frac{d y}{d x} \) of \( x^{2}+y^{2}=4 \) at \( (\sqrt{2}, \sqrt{2}), B=\frac{d y}{d x} \) of \( \sin y+\sin x= \)
\( \sin x \cdot \sin y \operatorname{at}(\pi, \pi) \) and \( C=\frac{d y}{d x} \) of
\( 2 e^{x y}+e^{x} e^{y}-e^{x}=e^{x y+1} \) at \( (1,1), \) then
\( (A-B-C) \) has the value equal to
A. \( \frac{1}{2} \)
в. \( \frac{1}{3} \)
c. 1
D. 2


Accumulation of charges causes in the clouds.
A . rain
B. earthquake
c. lightning
D. storm


Consider the reaction: \( C l_{2}+2 K I \rightarrow \)
\( \boldsymbol{I}_{2}+2 \boldsymbol{K} \boldsymbol{C l} \)
Which species will be reduced at the cathode?
A \( \cdot C l_{2} \)
В. \( I_{2} \)
c. \( I^{-} \)
D. \( C l \)


State whether True or False:
A series resonant circuit is commonly called a tank circuit.
A. True
B. False


Compare the reproduction in Hydra and
Amoeba.


Measure the length of \( A B \) with a ruler.
Then \( A B=? \)
A \( .7 .5 \mathrm{cm} \)
B. \( 9.6 \mathrm{cm} \)
\( c .10 \mathrm{cm} \)
D. \( 8.4 \mathrm{cm} \)


A double slit interference experiment is set up in a chamber that can be
completely evacuated with monochromatic light, an interference pattern is observed when the container
is open to the air. As the container is
evacuated, a careful observer will not that the interference fringes
A. don't change at all
B. move slightly farther apart
C. move slightly closer together
D. disappear completely


Deduce the relation for the magnetic induction at a point along the axis of a
circular coil carrying current.


A man is \( 45 \mathrm{m} \) behind the bus when the
bus start accelerating from rest with acceleration 2.5. With what minimum velocity should the man start running to catch the bus
A . 12
B . 14
c. 15
D. 16


Choose the correct answer from the
alternatives given
Which of the following is not a macronutrient?
A . ca
B. P
\( c . \) мn
D.


An electron in an excited state of \( L i^{2+} \)
ion has angular momentum 3 h/2 \( \pi \). The
de Broglie wavelength of the electron in
this state in \( p \pi \alpha_{0} \) (where \( \alpha_{0} \) is the Bohr
radius). The value of \( p \) is :


The probability of student \( A \) passing an examination is \( \frac{2}{9} \) and of students, \( B \) passing is \( \frac{5}{9} . \) Assuming the two events:
\( A \) passes'. \( B \) passes' as independent, find the probability of only \( A \) passing the examination


A bullet of mass \( m \) moving horizontally with a velocity \( v \) strikes a block of wood
of mass \( M \) and gets embedded in the block. The block is suspended from the ceiling by a massless string. The height to which block rises is:
\( A \)
\[
\frac{v^{2}}{2 g}\left(\frac{m}{M+m}\right)^{2}
\]
в.
\[
\frac{v^{2}}{2 g}\left(\frac{M+m}{m}\right)^{2}
\]
\( ^{\mathrm{c} \cdot} \frac{v^{2}}{2 g}\left(\frac{m}{M}\right)^{2} \)
\( D \)
\[
\frac{v^{2}}{2 g}\left(\frac{M}{m}\right)^{2}
\]


A radioactive material decays by simultaneous emission of two particles with half-lives 1620 yr and 810 yr respectively. The time in years after which one-fourth of material remains, is
A . 1080 yr
B. 2340 yr
c. 4860 yr
D. 3240 yr


A common character of monocot and
dicot roots is
A. Exarch protoxylem
B. Endarch xylem
c. Number of xylem strands
D. Occurrence of secondary growth


Consider a hypothetical hydrogen like
atom. The wavelength in \( A \) for the
spectral lines for transition from \( \boldsymbol{n}=\boldsymbol{p} \)
\( \operatorname{ton}=1 \) are given by- \( \lambda=\frac{1500}{p^{2}-1} \)
Where \( \boldsymbol{p}=\mathbf{2}, \mathbf{3}, \mathbf{4}, \) (given \( \boldsymbol{h} \boldsymbol{c}= \)
\( 12400 e V / A) \)
This question has multiple correct options
A. The wavelength of the least energetic and the most energetic photons in this series is 2000 A, 1500 A
B. Difference between energies of fourth and this orbit is \( 0.40 \mathrm{eV} \)
C. Energy of second orbit is 6.2 eV
D. The ionization potential of this element is \( 8.27 V \)


Work done by centripetal force in revolving a satellite around the earth is
A . zero
B. unity
c. infinity
D. nothing can be decided


Given \( A \) -B-C the co-ordinate of point \( A \) is the smallest.lf \( \mathrm{d}(\mathrm{A}, \mathrm{B})=7.5, \mathrm{d}(\mathrm{B}, \mathrm{C}):=13,8 \)
and the coordinate of point \( \mathrm{B} \) is \( 8.5, \) then find the coordinates of points \( A \) and \( C \)
\( A \cdot A \leftrightarrow 0, C \leftrightarrow 63.2 \)
B. \( A \leftrightarrow 5, C \leftrightarrow 40 \)
\( \mathrm{c} \cdot \mathrm{A} \leftrightarrow 1, \mathrm{C} \leftrightarrow 22.3 \)
D. \( A \leftrightarrow 3, C \leftrightarrow 18 \)


The maximum intensity produced by
two coherent waves of intensity \( \boldsymbol{I}_{1} \) and
\( \boldsymbol{I}_{2} \) will be
A \( \cdot I_{1}+I_{2} \)
В \( \cdot I_{1}^{2}+I_{2}^{2} \)
\( \mathbf{c} \cdot I_{1}+I_{2}+2 \sqrt{I_{1} I_{2}} \)
D. zero


Identify whether the following sequence is a geometric sequence or not -3,9,-27,81


Find the value of the following.
\( 55 \% \) of \( R s 1 \) in paise


During the formation of \( N a C l \), which processes are endothermic?
A. Sublimation
B. Ionization
c. Bond dissociation
D. All of these


If \( \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{0} & \mathbf{1} \\ -\mathbf{1} & \mathbf{0}\end{array}\right] \) then determinant of \( [\boldsymbol{A}] \)
is
\( \mathbf{A} \cdot \mathbf{1} \)
B. -
c. 0
D.


The general electronic configuration of d-block element is \( (n-1) d^{1-10} n s^{1-2} \)
where \( n \) is the outer most shell.

However, palladium does not follow this general electronic configuration. It has an electron configuration \( [\boldsymbol{K} \boldsymbol{r}]^{36} \boldsymbol{4} \boldsymbol{d}^{10} \boldsymbol{5} \boldsymbol{s}^{0} \)
in order to have stability. Give a reason behind it.


Migration of sol particles under influence of electrical field is known as
1. electrophoresis
2. field effect
3. electrolysis
4. none of the above
Choose the correct option


Assertion
Electrons revolve round the nucleus at
high speeds.
Reason
The motion of electrons
counterbalances the nuclear forces of
attraction.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which of the following will not sublime?
A. Ammonium chloride
B. Camphor
c. lodine
D. Bromine


If the two members of a Dobereiner's
triad are chlorine and iodine, then
the third member of this triad is :
A. fluorine
B. bromine
c. sodium
D. calcium


Find the cube of 133:


In the circuit above, \( \boldsymbol{R}_{1}=\mathbf{2} \boldsymbol{R}_{3} \) and
\( R_{3}=2 R_{2} . \) If the source voltage is \( V_{1} \)
find the power dissipated in \( \boldsymbol{R}_{\mathbf{1}} \)
\( \mathbf{A} \cdot \frac{\left(V_{1}\right)^{2}}{7 R_{2}} \)
B. \( \frac{\left(V_{1}\right)^{2}}{14 R_{2}} \)
c. \( \frac{\left(3 V_{1}\right)^{2}}{7 R_{2}} \)
D. \( \frac{\left(V_{1}\right)^{2}}{49 R_{2}} \)
E \( \cdot \frac{\left(3 V_{1}\right)^{2}}{49 R_{2}} \)


Q Type your question
user. Given below are some of the
applications of science. Formulate your views on whether the particular application is good, bad or something that cannot be so clearly categorised:
(a) Mass vaccination against small pox
to curb and finally eradicate this disease from the population. (This has already been successfully done in
India).
(b) Television for eradication of
illiteracy and for mass communication of news and ideas.
(c) Prenatal sex determination
(d) Computers for increase in work efficiency
(e) Putting artificial satellites into
orbits around the Earth
(f) Development of nuclear weapons
(g) Development of new and powerful techniques of chemical and biological
warfare).
(h) Purification of water for drinking
(i) Plastic surgery
(j) Cloning


Keratin, a structural protein is present
in?
A. hair
B. wool
c. silk
D. all of these


A wave travelling on a string as shown
in figure gets reflected at an open boundary. Then
A. Phase reversal takes place at the boundary
B. Wavelength changes at the boundary
c. Phase reversal dosent take place
D. speed of the reflected ray takes place


The characteristic equation of a matrix \( A \) is \( \lambda^{3}-5 \lambda^{2}-3 \lambda+2 I=0 \) then
\( |\boldsymbol{a} \boldsymbol{d} \boldsymbol{j} \boldsymbol{A}|= \)
\( \mathbf{A} \cdot \mathbf{4} \)
B . 25
c. 9
D. 30


Intercalary meristem is derivative of
A. Promeristem
B. Primary meristem
c. Lateral meristem
D. Secondary meristem


If \( \alpha, \beta \) are two different values of \( \theta \) lying
between 0 and \( 2 \pi \) which satisfy the
equation \( 6 \cos \theta+8 \sin \theta=9 . \) Find
\( \sin (\alpha+\beta) \)


In which of the following compounds
the C-H bond is strongest and acidic in nature ?
A. Methane
B. Ethane
c. Ethylene
D. Acetylene


The difference between the wave
number of \( 1^{s t} \) line of Balmer series of
paschen series for \( L i^{2+} \) ion is:
\( A \cdot \frac{R}{36} \)
в. \( \frac{5 R}{36} \)
\( c .4 R \)
D. \( \frac{R}{4} \)


Construct a quadrilateral \( \boldsymbol{A B N V} \) where \( \boldsymbol{A} \boldsymbol{V}=\mathbf{7} \boldsymbol{c m}, \boldsymbol{B} \boldsymbol{A}=\mathbf{8} \boldsymbol{c m}, \boldsymbol{B} \boldsymbol{N}= \)
\( \mathbf{1 0} c \boldsymbol{m}, \boldsymbol{N} \boldsymbol{V}=\mathbf{5} \boldsymbol{c m} \) and \( \boldsymbol{B} \boldsymbol{V}=\mathbf{1 1} \boldsymbol{c m} \)
The relation between diag. \( A N \) and
diag. \( \boldsymbol{B} \boldsymbol{V} \) is
A. \( A N>B V \)
B. \( A N<B V \)
c. \( A N=B V \)
D. None of the above


Using the identity \( (x+a)(x+b)= \)
\( x^{2}+(a+b) x+a b, \) find the values of
the following:
\( \mathbf{9 5} \times \mathbf{1 0 3} \)


A non-biodegradable waste is:
A. Metallic tins
B. Plastic
c. Polythene
D. All the above


The drift velocity of an electron is
doubled if the applied electric field across the conductor is
A. three times
B. doubled
c. half
D. four times


A point charge \( +Q \) is placed at point 0 as shown in the figure. Is the potential difference \( V_{A}-V_{B} \) positive, negative
or zero?


Among \( \boldsymbol{V}(\boldsymbol{Z}=\mathbf{2 3}), \boldsymbol{C r}(\boldsymbol{Z}=\mathbf{2 4}) \)
\( M n(Z=25) \) and \( F e(Z=26), \) which
will have the highest magnetic
moment?
A. \( V \)
в. \( C r \)
\( c . M n \)
D. \( F e \)


Two ships \( A \) and \( B \) are \( 10 k m \) apart on a line running south to north. Ship \( \boldsymbol{A} \) farther north is streaming west at \( 20 k m / h r \) and ship \( B \) is streaming north at \( 20 k m / h r . \) What is their
distance of closest approach and how long do they take to reach it?
A. \( 4 \sqrt{2} \mathrm{km}, 15 \mathrm{min} \)
В. \( 5 \sqrt{5} \) km, 15 min
c. \( 5 \sqrt{2} \mathrm{km}, 20 \mathrm{min} \)
D. \( 2 \sqrt{2} \mathrm{km}, 15 \mathrm{min} \)


Two particles \( A \) and \( B \), initially at rest, moves towards each other under a
mutual force of attraction. At the
instant when the speed of \( A \) is \( v \) and the
speed \( B \) is \( 2 v, \) the speed of centre of
mass is :
A . zero
в.
c. \( 1.5 v \)
D. \( 3 v \)


Among the electrolytes,
\( N a_{2} S O_{4}, C a C l_{2}, A l_{2}\left(S O_{4}\right)_{3} \) and
\( N H_{4} C l, \) the most effective coagulating
agent for \( S b_{2} S_{3} \) solution is:
A \( \cdot N a_{2} S O_{4} \)
в. \( C a C l_{2} \)
\( \mathbf{c} \cdot A l_{2}\left(S O_{4}\right) \)
D. \( N H_{4} C l \)


Slope of the line that is perpendicular to
the line whose equation \( 4 x+5 y=14 \)
is
A \( -\frac{4}{5} \)
в.
\( c \cdot \frac{4}{5} \)
D. \( -\frac{5}{4} \)


Solve \( \frac{\mathbf{7}}{\mathbf{4}}-\boldsymbol{p}=\mathbf{1 1} \)


Two liquids at temperatures \( 60^{\circ} \mathrm{C} \) and
\( 20^{\circ} \mathrm{C} \) respectively have masses in the ratio 3: 4 and their specific heats in the
ratio \( 4: 5 . \) If the two liquids are mixed, the resultant temperature is
\( \mathbf{A} \cdot 70^{\circ} C \)
B. \( 50^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 40^{\circ} C \)
D. \( 35^{\circ} \mathrm{C} \)


Systematic error occurred due to poor
calibration of instrument that can be
corrected by
A. taking several readings
B. replacing instruments
c. taking mean of values
D. taking median of values


Figure shows human urinary system
with structures labelled \( A \) to \( D \). Select
options which correctly identifies and gives their characteristics and
functions.
A. B - Pelvis-Broad funnel shaped space inner to hillum directly connected to loops of Henle
B. c- -Medulla - -Inner zone of kidney and contains complete nephrons
c. D - cortex - Outer part of kidney and do not contain any part of nephrons
D. A-Adrenal gland-Located at the anterior part of kidney, secrete catecholamines, which stimulate glycogen breakdown


Solve the following pair of linear (simultaneous) equations by the method of elimination:
\( \boldsymbol{y}=\boldsymbol{4} \boldsymbol{x}-\mathbf{7} \)
\( 16 x-5 y=25 \)
A \( \cdot x=\frac{3}{2}, y=6 \)
B・ \( x=\frac{5}{2}, y=3 \)
c. \( _{x}=\frac{7}{4}, y=2 \)
D. \( x=\frac{9}{2}, y=0 \)


Choose the wrong statement in the
process of protein synthesis.
A. After uncoiling of DNA molecule, one strand acts as a template for the formation of mRNA.
B. In the presence of DNA polymerase enzyme, the mRNA is formed based on the triplet codes.
C. The mRNA that leaves nucleus reaches cytoplasm and gets attached with 30 S ribosomal subunit
D. The amino acids are transferred from the intracellular amino acid pool to the active ribosomes by the tRNA.


If \( a \) and \( b \) are two variables and \( (a, b)= \)
\( (b, a), \) then
\( \mathbf{A} \cdot a=0 \)
В. \( b=0 \)
\( \mathbf{c} \cdot a=b \)
\( \mathbf{D} \cdot a \pm b \)


Increasing order of stability of
I. \( \boldsymbol{K}_{\mathbf{2}} \boldsymbol{C} \boldsymbol{O}_{\boldsymbol{3}} \)
Il. \( \boldsymbol{M} \boldsymbol{g} \boldsymbol{C} \boldsymbol{O}_{3} \)
\( \| N a_{2} C O_{3} \)
\( A \)
B. II
c. ॥
D.


The length of an elastic string is \( \boldsymbol{X} \boldsymbol{m} \)
when the tension is \( 8 N, \) and \( Y m \) when
the tension is \( 10 N . \) The length in
metres when the tension is \( 18 N \) in
terms of \( X \) and \( Y \)


Suppose values taken by a variable are such that \( a \leq x, \leq b \) where \( x, \) denote
the value of \( x \) in the \( i^{t h} \) class for \( i= \)
\( l, 2, \cdots n, \) then
A \( \cdot a^{2} \leq \operatorname{Var}(x) \leq b \)
B \cdot \( a^{2} \leq a^{2}(x) \leq b^{2} \)
\( ^{\mathrm{c}} \cdot \frac{a^{2}}{4} \leq \operatorname{Var}(x) \)
D. \( \operatorname{Var} x \leq(b-a)^{2} \)


Observe the given figure and answer
Label A and B.
4. A- sperm, B- ovum
B. A- ovum, B- sperm
C. A- ovary, B- spern
D- ovary, B- testis


A liquid of density \( \rho_{1} \) is flowing through
a tube of varying cross-section. A manometer containing a liquid of
density \( \rho_{2} \) is connected to the tube as shown. The area of cross section of the
tube at points \( A \) and \( B \) are \( a_{1} \) and \( a_{2} \)
respectively. The rate of flow of the liquid through the tube is
A \( \cdot a_{1} a_{2} \sqrt{\frac{2 \rho_{2} g h}{\rho_{1}\left(a_{2}^{2}-a_{1}^{2}\right)}} \)
в. \( \quad a_{1} a_{2} \sqrt{\frac{2 g h}{\rho_{1}\left(a_{2}^{2}-a_{1}^{2}\right)}} \)
c. \( \frac{a_{1}}{a_{2}} \sqrt{\frac{2 \rho_{2} g h}{\rho_{1}\left(a_{2}^{2}-a_{1}^{2}\right)}} \)
D. \( a_{1} a_{2} \sqrt{\frac{2 \rho_{1} g h}{\rho_{2}\left(a_{2}^{2}-a_{1}^{2}\right)}} \)


The particular solution of the differential equation
\( \left[\boldsymbol{x} \sin ^{2}\left(\frac{y}{x}\right)-\boldsymbol{y}\right] \boldsymbol{d} \boldsymbol{x}+\boldsymbol{x} \boldsymbol{d} \boldsymbol{y}=\mathbf{0} \)
satisfying the condition \( y=\frac{\pi}{4}, \) when
\( \boldsymbol{x}=\mathbf{1}, \) is
\( \mathbf{A} \cdot \tan \left(\frac{y}{x}\right)=\log (e x) \)
B \( \cdot \tan \left(\frac{x}{y}\right)=\log (e x) \)
C \( \cdot \cot \left(\frac{y}{x}\right)=\log \left(\frac{e}{x}\right) \)
D \( \cdot \cot \left(\frac{y}{x}\right)=\log (e x) \)


Which of the following orders is correct regarding basicity of indicated molecules?
A. N, N - Dimethyltoluidine > p - toluidine >aniline > p nitroaniline
B. Aniline > N, N - dimethyl- p - toluidine > p - toluidine > aniline
c. p - Toluidine > N, N - dimethyl - p - toluidine > aniline
- nitroaniline
D. N, N-Dimethyltoluidine > aniline > p -toluidine > p nitroaniline


Obtain the differential equation by
eliminating the arbitrary constants from the following equation:
\( \boldsymbol{y}=\boldsymbol{c}_{1} \boldsymbol{e}^{2 \boldsymbol{x}}+\boldsymbol{c}_{2} \boldsymbol{e}^{-\boldsymbol{2} \boldsymbol{x}} \)


Explain the mechanism of the following
reaction. \( \mathbf{2} \boldsymbol{C} \boldsymbol{H}_{3}-\boldsymbol{C} \boldsymbol{H}_{2}-\boldsymbol{O} \boldsymbol{H} \frac{\boldsymbol{H}^{+}}{4 \mathbf{1} \mathbf{3} \boldsymbol{K}} \boldsymbol{C} \boldsymbol{H}_{3}- \)
\( \boldsymbol{C H}_{2}-\boldsymbol{O}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{3}+\boldsymbol{H}_{2} \boldsymbol{O} \)


If \( A \) and \( B \) are arbitrary events, then
\( \mathbf{A} \cdot P(A \cap B) \geq P(A)+P(B) \)
B \( \cdot P(A \cap B) \leq P(A)+P(B) \)
C \( \cdot P(A \cap B)=P(A)+P(B) \)
D. none of these


Noble gas are adsorbed by:
A. anhydrous calcium chloride
B. ferric hydroxide
C . concentrated \( H_{2} S O_{4} \)
D. activated coconut charcoal


Identify the diagrams, based on which
the given pair of triangle can be said
SSS congruent?
A. figure A
B. figure C
c. figure D
D. figure B


What cross-sections do you get when you cut a brick horizontally?
A . Circle
B. Trianglel
c. rectangle
D. None of these


The area bounded by the curves \( y= \)
\( \log x, y=\log |x|, y=|\log x| \) and \( y= \)
\( |\log | x|| \)
A. 4 sq. units
B. 6 sq. units
c. 10 sq. units
D. None of these


Mass \( m_{1} \) strikes \( m_{2} \) which is at rest.
The ratio of masses for which they will
collide again is : (Collisions between
ball and wall are elastic. Coefficient of
restitution between \( m_{1} \) and \( m_{2} \) is \( e \)
and all the surfaces are smooth
A \( \cdot \frac{e}{2+e} \)
B. \( \frac{2 e}{2+e} \)
\( c \)
\( D \)


The half-life of a radio active nuclide is
0.693 minutes. The time (in minutes)
required for the disintegration of this nuclide from 10 grams to one gram is
\( \mathbf{A} \cdot 0.693 \)
B.
c. 6.93
D. 2.303


positions 'A' and 'B' starting at the same
time and reach the point 'C' (along
straight line) simultaneously when
wind was not blowing. On a windy day
they head towards 'C' but both reach the point 'D' simultaneously in the same
time which they took to reach 'C'. Then
the wind is blowing in
A. North-West direction
B. North-East direction
C. Direction making an angle \( 0<\theta<90^{\circ} \) (but not \( 45^{\circ} \)
with North towards West
D. North direction


Crown ethers are:
A. cyclic ethers
B. mixed ethers
C. ethers with other several functional groups
D. not ethers


Which valence shell electrons
arrangement is that of a metallic element?
\( A \cdot 2, \)
B. 2,4
c. 2,5
D. 2,7


Assertion
Two bodies at different temperatures, if brought in thermal contact do not necessary settle to the mean temperature.
Reason
The two bodies may have different thermal capacities.
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


The distance of closest approach of an
\( \alpha \) - particle fired towards a nucleus with
momentum \( p \),is \( r . \) The distance of
closest approach when the
momentum of \( \alpha \) -particle is \( 2 p \) is
A \( \cdot 2 r \)
B. \( 4 r \)
\( c \cdot r / 2 \)
D. \( r / 4 \)


Evaluate \( \int \frac{2 x}{1+x^{2}} d x \)


The defective condition of
accommodation of the eye in which distant objects are clearly seen but near objects are indistinct is
A. Astigmatism
B. Presbyopia
c. Myopia
D. Hypermetropia


The modern periodic table explains the periodicity of the properties of the elements and relates them to their:
A. Charge
B. Electron number
c. Electronic configuration
D. Atomic mass


Bonding between deoxyribose and base in pyrimidine nucleoside molecule is :-
A \( \cdot 1^{\prime}-1^{\prime} \) glycosidic linkage
B . \( 1^{\prime}-6^{\prime} \) glycosidic linkage
C \( \cdot 1^{\prime}-9^{\prime} \) glycosidic linkage
D. \( 1^{\prime}-4^{\prime} \) glycosidic linkage


State whether the shapes in the given pair are similar. If they are similar enter
else if not similar then enter 0


A magnetic field lines due to a straight wire carrying a current are
A. Straight
B. Circular
c. Parabolic
D. Elliptical


Correct IUPAC nomenclature of given
compound is :
A. 1 -Bromo-3-chlorocyclohex-4-ene.
B. 3-Bromo-5-chlorocyclohex-1-ene.
c. 4 -Bromo-6-chlorocyclohex-1-ene.
D. 5-Bromo-3-chlorocyclohex-1-ene.


An ester can be prepared by the reaction
of:
A. two alcohols
B. an alcohol and an aldehyde
C \( . \) an alcohol and an organic acid
D. an organic acid and an aldehyde
\( E \). an acid and a ketone


Soil has five components. The
proportions of different components are
A. Mineral Matter- \( 40 \% \), Organic Matter- \( 10 \% \), Soil Moisture \( -25 \% \), Soil Atmosphere \( -25 \% \), Soil OrganismVariable
B. Mineral Matter- \( 40 \% \), Organic Matter- \( 10 \% \), Soil Moisture \( -25 \% \), Soil Atmosphere \( -25 \% \), Soil Organism\( 10 \% \)
C. Mineral Matter- \( 40 \% \), Organic Matter- \( 10 \% \), Soil Moisture \( -35 \% \), Soil Atmosphere \( -25 \% \), Soil Organism\( 10 \% \)
D. Mineral Matter-30\%, Organic Matter-20\%, Soil Moisture \( -25 \% \), Soil Atmosphere \( -25 \% \), Soil Organism\( 10 \% \)


Which of the following explode on heating?
A . Azides
B. Sulphates
c. chlorides
D. Phosphides


Let a relation \( \boldsymbol{R} \) be defined by \( \boldsymbol{R}= \)
\( \{(4,5),(1,4),(4,6),(7,6),(3,7)\} . \) The
relation \( R^{-1} \circ R \) is given by
A \( \cdot\{(1,1),(4,4),(7,4),(4,7),(7,7)\} \)
B - \{(1,1),(4,4),(4,7),(7,4),(7,7),(3,3)\}
c. \{(1,5),(1,6),(3,6)\}
D. None of these


How is gold extracted from its ore?


If a monovalent metal ion carries \( 1.6 \times \)
\( 10^{-19} \) coulomb of electricity, what is the
amount of electricity carried by one gram molecular mass of the metal
ions?
\( \mathbf{A} \cdot 9.6336 \times 10^{4} \)coulomb
B. \( 10.6336 \times 10^{4} \) coulomb
c. \( 95.336 \times 10^{4} \) coulomb
D. \( 96.336 \times 10^{4} \) coulomb


If the earth has no rotational motion, the
weight of a person on the equator is \( W \)
Determine the speed with which the earth would have to rotate about its
axis so that the person at the equator will weight \( \frac{3}{4} W . \) Radius of the earth is \( 6400 k m \) and \( g=10 m / s^{2} \)


If a current circular loop is placed in a
\( x-y \) plane as shown in adjoining
figure and a magnetic field is applied along z-axis, then the loop will
A. Contract
B. Expand
c. Move towards \( -x- \) axis
D. Move towards \( +x- \) axis


Acetylsaliylic acid is a pain killer and is commonly known as:
A. Paracetamol
B. Ibuprofen
c. Aspirin
D. Penicillin


"Determination of biological oxygen demand (BOD) can help in suggesting the quality of a water body". Explain.


Assertion
The presence of nitro group facilitates nucleophilic substitution reaction in aryl halide
Reason
The intermediate carboniun is
stablised due to the presence of the nitro group.
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 are correct


Following reaction describes the rusting
of iron.
\( 4 F e+3 O_{2} \rightarrow 4 F e^{3+}+6 O^{2-} \)
Which one of the following statement is (are) correct?
This question has multiple correct options
A. This is an example of a oxidation reaction
B. Metallic iron is oxidised to \( F e^{3} \)
c. \( F e^{3+} \) is an oxidizing agent
D. Metallic iron is a strong reducing agent


Least distance of distinct vision for a
normal person is about :
A . \( 1 \mathrm{m} \)
B. 0.5 \( m \)
c. \( 0.25 \mathrm{m} \)
D. None of these


During the process of electrorefining of \( C u, \) some metals present as impurity settle as anode mud. These are:
\( \mathbf{A} \cdot \operatorname{Sn} \) and \( A g \)
B. \( P b \) and \( Z n \)
c. \( A g \) and \( A u \)
D. Fe and \( N i \)


The general solution of the differential equation \( \frac{\boldsymbol{y} \boldsymbol{d} \boldsymbol{x}-\boldsymbol{x} \boldsymbol{d} \boldsymbol{y}}{\boldsymbol{y}}=\mathbf{0} \) is
A \( . x y=C \)
В. \( x=C y^{2} \)
c. \( y=C x \)
D. \( y=C x^{2} \)


What is the major product of the
reaction: methyl cyclopentene
\( +\boldsymbol{K} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4} / \boldsymbol{H}^{+} / \boldsymbol{C o l d} \rightarrow ? \)
\( A \)
B.
\( c \)
\( D \)


Equation of a plane making X-intercept
4, Y-intercept \( (-6), \mathrm{Z} \) -intercept 3 is
A. \( 3 x-4 y+6 z=12 \)
B. \( 3 x-2 y+4 z=12 \)
c. \( 4 x-6 y+3 z=1 \)
D. \( 4 x-3 y+2 z=12 \)


If \( \boldsymbol{k}>\mathbf{0},|\boldsymbol{z}|=|\boldsymbol{w}|=\boldsymbol{k} \) and \( \boldsymbol{\alpha}=\frac{\boldsymbol{z}-\overline{\boldsymbol{w}}}{\boldsymbol{k}^{2}+\boldsymbol{z} \overline{\boldsymbol{w}}} \)
then \( \operatorname{Re}(\alpha) \) equal
A .
B.
\( c . k \)
D. none of these


If \( \boldsymbol{A} \subset \boldsymbol{B}, \) then \( \boldsymbol{A} \cap \boldsymbol{B} \) is
A. \( B \)
в. \( A \backslash B \)
\( c . A \)
D. \( B \backslash A \)


Find the sum of money that amounts to
Rs.5050 in six years at 5\% per annum.


Write Ampere circuital law in
mathematical form. Derive an
expression of magnetic field at the axis of a current carrying long solenoid. Draw necessary diagram.


Peroxydisulphuric acid has the
following bond:
A \( . O \leftarrow O=O \)
в. \( \leftarrow O=O \rightarrow \)
\( c \cdot>0 \rightarrow O< \)
D. \( -O-O- \)


Simplify and express with positive exponents \( \frac{169 \times x^{-5}}{13^{-3} \times 26 \times x^{-5}} \)


Acetic acid is a dimer in benzene due
to:
A. condensation reaction
B. hydrogen bonding
c. presence of carboxylic group
D. presence of hydrogen atom at \( \alpha \) -carbon


Maltose is made of:
A. \( \alpha \) -D-glucose
B. \( \alpha, \beta \) -D-glucose
C . glucose and fructose
D. fructose only


Observe the diagram given below. What
happens after the above stage?
A. The ovary splits open.
B. Ovary develops into a fruit and ovules into seeds.
c. The ovules are dispersed
D. Germination of seeds takes place


Find the co-ordinates of a point, which is at a distance of 21 units from the
point \( \boldsymbol{A}=(\mathbf{1},-\mathbf{3}, \mathbf{4}) \) in the direction of vectors \( 2 \hat{i}-3 \hat{j}-6 \hat{k} \)


Write the IUPAC names of the following coordination compounds:
(i) \( \left[\boldsymbol{C r}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{3} \boldsymbol{C l}_{3}\right] \)
(ii) \( \boldsymbol{K}_{\mathbf{3}}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{\boldsymbol{6}}\right] \)
(iii) \( \left[\operatorname{CoBr}_{2}(e n)_{2}\right]^{+} \)


\( \int 5^{m x} 7^{n x} d x, m, n \in N \) is equal to
This question has multiple correct options
\( \mathbf{A} \cdot \frac{5^{m x}+7^{n x}}{m \log 5+n \log 7}+K \)
B. \( \frac{e^{(m \log 5+n \log 7) x}}{\log 5^{m}+\log 7^{n}}+K \)
C \( \cdot \frac{(m \cdot n) 5^{m x}+7^{n x}}{m \log 5+n \log 7}+K \)
D. None of these


One litre of water at \( 30^{\circ} C \) is mixed with
one litre of water at \( 50^{\circ} C . \) The
temperature of the mixture will be
A . \( 80 \mathrm{c} \)
B. more than 50c but less than 80C
\( c \cdot 20 c \)
D. between \( 30 c \) and 500


The decrease in \% in \( \left[\boldsymbol{H}^{+}\right] \) when \( \boldsymbol{p} \boldsymbol{H} \)
increases by 0.1 will be:
A . 10
B. 30
c. 50
D. 20


Out of benzene and phenol, phenol is
more easily nitrated
because
A. presene of -OH group in phenol increases the electron density at ortho and para - position
B. presene of -OH group in phenol decreases the electron density at ortho and para - position
c. nitration being electrophilic substitution requires less density at ortho and para- position
D. phenol is more reactive than benzene due to -R effect


According to collision theory, write
name of two factors which increases
the rate of reaction as temperature increase.


An emf will not be inducted in the coil, if ?


lodoform belongs to which of the following alkyl halide?
A. Primary alkyl halide
B. Secondary alkyl halide
c. Tertiary alkyl halide
D. None of these


Read the following bar graph (Fig. 23.12)
and answer the following questions:
State each of the following whether true
or false

The number of government companies
have decreased over the year 1957 to
1983
A. True
3 Fals


The cyclic polymerization of methyl acetylene produces :
A. benzene
B. o-xylene
C. 1,3,5 -trimethyl benzene
D. 1,3,5-trimethyl cyclohexane


\( \operatorname{Let} \mathbf{f}(\mathbf{x})=\frac{\sin \mathbf{4} \boldsymbol{\pi}[\mathbf{x}]}{\mathbf{1}+[\mathbf{x}]^{2}}, \mathbf{w h e r e}[x] \) is the
greatest integer less than or equal to \( x \) then
A \( \cdot f(x) \) is not differentiable at some points
B. \( f(x) \) exists but is different from zero
\( c \cdot f(x)=0 \) for all \( x \)
D. \( f^{\prime}(x)=0 \) but \( f \) is not a constant function


Represent the following complex number in trigonometric form:
\( \sqrt{3} i \)


The type of joint between the human skull bones is called:
A. cartilaginous joint
B. hinge joint
c. fibrous joint
D. synovial joint


Evaluate the integral \( \int_{0}^{1} \sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right) d x \) using
substitution.


Heating sodium chloride with conc.
\( H_{2} S O_{4} \) gives:
A. sodium sulphate
B. sodium bisulphate and \( H_{2} S O_{4} \)
c. sodium bisulphate and HCI
D. reaction does not occur


Identify the organic compound \( A \) which is widely used as a preservative in pickles and has a molecular formula
\( C_{2} H_{4} O_{2} . \) This compound reacts with ethanol to form a sweet-smelling
compound \( \boldsymbol{B} \)


Which of the following spectrochemical series is true?
A \( \cdot S C N^{-}<N H_{3}<F^{-}<e n<C O \)
B . \( S C N^{-}<F^{-}<N H_{3}<e n<C O \)
c. \( S C N^{-}<F^{-}<e n^{-}<N H_{3}<C O \)
D. \( S C N^{-}<F^{-}<e n^{-}<C O^{-}<N H_{3} \)


Which of the following react with \( C l_{2} \)
and \( B r_{2} \) at room temperature and in
the absence of diffused sunlight to produce dihalogen derivatives?
A. Cyclobutane
B. cyclopentane
c. cyclohexane
D. All of these


Which of the following is/are \( \alpha \) -amino
acid?
\( A \)
B.
c. Both (A) and (B)
D. None of these


Which of the following is one of the gases responsible for green house effect?
A \( \cdot C O_{2} \)
в. \( H_{2} S \)
c. \( N_{2} \)
D. None of the above


A regular hexagon of side \( 10 \mathrm{cm} \) has a charge \( 5 \mu C \) at each of its vertices.
Calculate the potential at the centre of the hexagon.
\( \mathbf{A} \cdot 5.8 \times 10^{6} V \)
В. \( 3.2 \times 10^{6} V \)
c. \( 9.3 \times 10^{6} V \)
D. \( 2.7 \times 10^{6} V \)


(a) How do primary, secondary and teritary amines react with nitrous acid?
(b) Elucidate the structure of glucose.


Other names of cork, cork cambium and
secondary cortex are
A. Phellem, phellogen and phelloderm
B. Phellogen, phellem and phelloderm
c. Pelloderm, phellem and phellogen
D. Phelloderm, phellogen and phellem


State whether true or false:
Mean free path order for some gases at
\( 273 \mathrm{K} \) and 1 atm \( \mathrm{P} \) is
\( \boldsymbol{H} \boldsymbol{e}>\boldsymbol{H}_{2}>\boldsymbol{O}_{2}>\boldsymbol{N}_{2}>\boldsymbol{C} \boldsymbol{O}_{2} \)
A. True
B. False


Which of the following is(are) true
statement(s)?
Consider the following reaction
\[
\mathrm{CH}_{2}=\stackrel{\mathrm{CH}_{3}}{\mathrm{C}-\mathrm{CH}_{2}} \stackrel{\mathrm{CH}_{3}}{\mathrm{CH}-\mathrm{CH}_{2} \mathrm{OH}} \frac{\mathrm{H}_{2} \mathrm{SO}_{4}}{\longrightarrow} \underbrace{\mathrm{CH}_{3}}_{\mathrm{CH}_{3}}
\]
This question has multiple correct options
A. Reaction is initiated by protonation of \( -O H \) followed by formation of carbocation intermediate
B. Reaction is initiated at \( C=C \) bond forming a tertiary carbocation
C. Here intramolecular reaction is favoured by entropy of reaction
D. The same reaction can also be done using \( N a O H \) catalyst


The covering of lungs in human is
A. Peritoneum
B. Pericardium
c. Pleural membrane
D. Glission capsuls


The strength of H-bonding order is:
\( \mathbf{A} \cdot H_{2} O>H_{2} O_{2}>H-F \)
\( \mathbf{B} \cdot H_{2} O_{2}>H_{2} O>H F \)
\( \mathbf{c} \cdot H F>H_{2} O>H_{2} O_{2} \)
\( \mathbf{D} \cdot H F=H_{2} O=H_{2} O_{2} \)


The sequence of DNA base is GCACCTAT.
Then, the sequence of m-RNA is
A . CGUGGAUA
в. СGTGGATA
c. сGUGGATA
D. СGтGGтАТ


Consider the situation shown in the
figure. The tension in the string attached to \( 0.50 \mathrm{kg} \)


Differentiate between disinfectants and
antiseptics.


Do you hear the sound when bell jar is completely evacuated?


Which of the following would show the LARGEST increase in solubility with increasing pressure based on intermolecular force knowledge?
\( A \). Ammonia
B. Calcium oxide
c. Potassium bromide
D. Sodium hydroxide


Identify the lettered compounds \( D \) to \( G \)
in the following reaction schemes.


In which of the following molecules/ion, all the bonds are not equal?
A. \( X e F_{4} \)
в. \( B F_{4}^{-} \)
c. \( S F_{4} \)
D. \( \operatorname{siF}_{4} \)


A 0.2595 g of an organic compound by Carius method gave 0.350 g of barium sulphate. Calculate the percentage of sulphur in the compound.
A . \( 19 \% \)
B. 18.52\%
c. \( 17.42 \% \)
D. 11\%


Which of the following hydride is 'electron
-precise' type?
\( \mathbf{A} \cdot H F \)
в. \( H_{2} \) 0
\( \mathrm{c} \cdot \operatorname{si} H_{4} \)
D. \( P H_{3} \)


Differentiate the following functions
with respect to \( \boldsymbol{x} \) \( \log \left(\frac{x^{2}+x+1}{x^{2}-x+1}\right) \)


Drugs which act as competitive inhibitors, preferentially attach to the active sites prior to substrate molecules.
If this is true enter \( 1, \) if false enter 0 .


Bernoulli's equation is important in the
field of :
A . electrical circuits
B. magnetism
c. flow of liquids
D. photoelectric effect


If \( I=\int_{1 / \pi}^{\pi} \frac{1}{x} \cdot \sin \left(x-\frac{1}{x}\right) d x, \) then \( I \) is
equal to
A . 0
в. \( \pi \)
c. \( _{\pi-\frac{1}{\pi}} \)
D. \( \pi+\frac{1}{\pi} \)


If LPG cylinder contains a mixture of butane and isobutane, then the amount
of oxygen that would be required for combustion of 1 kg of it will be:
A. \( 1.8 \mathrm{kg} \)
в. \( 2.7 \mathrm{kg} \)
c. \( 4.5 \mathrm{kg} \)
D. \( 3.58 \mathrm{kg} \)


Which is the best synthesis of the ether
(A) shown in the figure?


\( A D \) is a diameter of a circle and \( A B \) is
a chord. If \( \boldsymbol{A} \boldsymbol{D}=\mathbf{3 4} \boldsymbol{c m}, \boldsymbol{A B}=\mathbf{3 0} \boldsymbol{c m} \)
the distance of \( A B \) from the centre of
the circle is
\( A \cdot 17 \mathrm{cm} \)
\( 3.15 \mathrm{cm} \)
\( c .4 \mathrm{cm} \)
\( 8.8 m \)


Let \( \boldsymbol{y}=\boldsymbol{y}(\boldsymbol{x}) \) be the solution of the
differential equation, \( \left(x^{2}+1\right)^{2} \frac{d y}{d x}+ \)
\( 2 x\left(x^{2}+1\right) y=1 \) such that \( y(0)=0 \)
\( \sqrt{\boldsymbol{a} \boldsymbol{y}}(1)=\frac{\boldsymbol{\pi}}{\mathbf{3 2}}, \) then the value of 'a' is:
A \( \cdot \frac{1}{2} \)
B. \( \frac{1}{16} \)
\( c \cdot \frac{1}{4} \)
D.


IUPAC name of compound is:
A. 3,3 -dimethylpropanoic acid
B. 2-methylbutanoic acid
c. 3-Methylbutanoic acid
D. none of these


A paramagnetic substance when placed in an externally applied non-uniform magnetic field tends
to
A. increase the applied field
B. decrease the applied field
c. vary the applied field
D. change the applied field


The term Bryophyta was given by
A. Darwin
B. Braun
C. Aristotle
D. Galen


If we join any two points on a circle
through centre, we get a
A. Radius
B. Diameter
c. chord
D. None of these


Which of the following will increase the voltage of the cell?
\( \boldsymbol{S} \boldsymbol{n}(\boldsymbol{s})+\boldsymbol{2} \mathbf{A} \mathbf{g}^{+}(\boldsymbol{a} \boldsymbol{q}) \rightarrow \boldsymbol{2} \boldsymbol{A} \boldsymbol{g}(\boldsymbol{s})+\boldsymbol{S} \boldsymbol{n}^{2+} \)
A. Increase in the concentration of \( \operatorname{Sn}^{2+} \) ions
B. Increase in the concentration of \( A g^{+} \) ions
c. Increase in the size of silver rod
D. Removal of salt bridge


The percentage errors in the measurement of mass and speed are
\( 2 \% \) and \( 3 \% \), respectively. How much will be the maximum error in the
estimation of KE obtained by
measuring mass and speed?
A . \( 5 \% \)
B. 1\%
\( c .8 \% \)
D. \( 11 \% \)


For a point charge of +3.50 uC what is the radius of the equipotential surface which is at a potential of \( 2.50 \mathrm{kV} ? \)


Photorespiration requires this activity by an enzyme
A. Hydrolase
B. Oxygenase
c. carboxylase
D. ATPase


Write Kohlrausch law and give one
application of it


'Quick Silver' is called:
A \( . A g \)
в. \( A l \)
c. \( H g \)
D. \( A u \)


Continuous addition of sugars in fed batch fermentation is done to
A. Degrade sewage
B. Produce methane
c. obtain antibiotics
D. Purify enzymes


Alkynes exhibit types of isomerism:
A. chain
B. position
C. functional
D. all of the above


Given line \( A B \) is parallel to line \( C D \)
\( \angle A G E \) and \( \angle B G H \) are:
A. Non-congruent
B. congruent
c. Supplementary
D. None of these


Consider the process on a system
shown in fig. During the process, the
work done by the system
A. Continuously increases
B. Continuously decreases
C. First increases then decreases
D. First decreases then increases


Bag \( I \) contains 2 blacks and 8 red balls, bag IIcontains 7 black and 3 red balls
and bag \( I I I \) contains 5 black and \( 5 v \)
red balls. One bage is chosen at random and a ball is drawn from it which is
found to bered. Find the probability that the ball is drawn from bag \( I I \)


Which of the following is responsible for the growth in circumference or girth of stem and root in plants (in crucifers)?
A. Xylem
B. Phloem
c. cortex
D. Cambium (meristematic tissue)


If Akhil takes 10 hours and Santosh
takes 12 hours to travel to chennai from
hyderabad then the average velocity of Akhil is more than that of Santosh.
A . True
B. False


\( \frac{x^{2}}{\left(x^{2}+1\right)\left(x^{2}+4\right)}=\frac{A}{x^{2}+1}+ \)
\( \frac{B}{x^{2}+4} \Rightarrow A+B= \)
A.
B.
\( c \cdot 2 \)
D. 3


The principal argument of \( z=-3+3 i \)
is:
A \( \cdot \frac{\pi}{4} \)
B. \( -\frac{\pi}{4} \)
c. \( \frac{3 \pi}{4} \)
D. \( -\frac{3 \pi}{4} \)


The resistance of a hot tungsten filament is about 10 times the cold
resistance. What will be the resistance
of \( 100 W, 200 V \) lamp when not in use?
A . \( 20 \Omega \)
B. \( 40 \Omega \)
c. \( 200 \Omega \)
D. \( 400 \Omega \)


Match the compounds/reactions in List with their formula in List II. Matching
can be one or more than one.


In the circuit shown in figure. Current
through \( R_{2} \) is zero if \( R_{4}=2 \Omega \) and
\( \boldsymbol{R}_{3}=\mathbf{4} \boldsymbol{\Omega} \)
In this case:
A . current through \( R_{3} \) is \( 2 A \)
B. current through \( R_{4} \) is 3 A
\( c . \) both (1) and (2) are correct
D. both (1) and (2) are wrong


Statement a. Photorespiration
decreases photosynthetic output.
Statement b. In photorespiratory pathway, neither ATP nor NADPH is
produced
A. Both the statements a and b are correct.
B. Both the statements a and b are wrong
C. Statement a is correct and statement b is wrong.
D. Statement b is correct and statement a is wrong.


The figure given below show three
velocity substrate concentration curves
for an enzyme reaction. What do the
curves a, b and c depict respectively?
A. a- Normal enzyme reaction
b- Competitive inhibition
c- Non-competitive inhibition
B. a- Enzyme with an allosteric modulator added
b- Normal enzyme activity
c- Competitive inhibition
C. a- Enyzme with an allosteric stimulator
b- Competitive inhibitor added
c- Normal enzyme reaction
D. a- Normal enzyme reaction
b- Non-competitive inhibitor added
c- Allosteric inhibitor added


In a triangle \( A B C, \angle A-\angle B=15^{\circ} \) and
\( \angle B-\angle C=30^{\circ}, \) find \( \angle A, \angle B \) and \( \angle C \)


\( B r_{2} \rightarrow B r O_{3}^{-}+B r^{-}(\text {acidic }) \) is a
balanced equation.
If true enter 1 , else enter 0 .
\( A \)


A radioactive nucleus decays by \( \boldsymbol{\beta} \)
emission. Both \( \beta \) and neutrino move
mutually at right angle with momentum \( 6 \times 10^{-21} k g m s^{-1} \) and \( 3 \times \)
\( 10^{-21} k g m s^{-1} . \) The direction of recoil of
nucleus with respect to electron is :
A \( \cdot \tan ^{-1}\left(\frac{1}{2}\right) \)
B. \( \tan ^{-1}(2) \)
c. \( _{180-\tan ^{-1}}\left(\frac{1}{2}\right) \)
D. \( 180-\tan ^{-1}(2) \)


Heating the ore is in the presence of air is ?
A. roasting
B. melting
c. calcination
D. none of these


Immediately below the current carrying wire a stream of electrons are projected parallel to the wire as shown. They will
be
A. accelerated to the right
B. retarded
D. deflected downwardd


Given the correct order of initials T or \( F \)
for the following statements. Use T if the statement is true and \( F \) it is false.
Statement-1: \( \pi \) bond is formed by
sidewise overlapping of \( \boldsymbol{d}_{\boldsymbol{x}^{2}-\boldsymbol{y}^{2}} \) and \( \boldsymbol{p}_{\boldsymbol{y}} \)
orbital along x-axis. Statement-2: Zig-zag geometry would be suggested for the \( \left[\boldsymbol{I}(\boldsymbol{C} \boldsymbol{N})_{2}\right]^{-} \)
A. T,
в. F,
c. न, न
D. F,


A binary operation \( ^{*} \) on the set \{0,1,2,3,4,5\} is defined as \( \boldsymbol{a} * \boldsymbol{b}=\left\{\begin{array}{c}\boldsymbol{a}+\boldsymbol{b}, \text { if } \mathbf{a}+\mathbf{b}<\mathbf{6} \\ \mathbf{a}+\mathbf{b}-\mathbf{6} \text { if } \mathbf{a}+\mathbf{b} \geq \mathbf{6}\end{array}\right\} \) show
that zero is the identity element of this
operational each element 'a' of the set is invertible with 6 -a being the inverse of
\( \mathbf{a}^{\prime} \)


State whether given statement is True or False
The circuit phase angle is the angle between the total current and the
applied (source) voltage.
A. True
B. False


Given that \( N_{2}(g)+3 H_{2}(g) \rightarrow \)
\( \mathbf{2} N \boldsymbol{H}_{3}(\boldsymbol{g}) ; \boldsymbol{\Delta}_{r} \boldsymbol{H}=-\mathbf{9} 2 \boldsymbol{K} \boldsymbol{J}, \) the
standard molar enthalpy of formation in
\( \boldsymbol{K} \boldsymbol{J} \boldsymbol{m o l}^{-1} \) of \( \boldsymbol{N} \boldsymbol{H}_{3}(\boldsymbol{g}) \) is :
A . -92
B. +46
\( c \cdot+92 \)
D. -46


Which of the following elements are
called representative elements?
\( \mathbf{A} \cdot p \) block elements only
B. \( s \) and \( p \) block elements only
C. \( d \) block elements only
D. \( s \) block elements only


Two students ordered tea in a
restaurant and wanted for a friend who
was to join them shortly. One of them poured hot tea in his cup and mixed cold milk in it and the other poured hot tea but mixed the cold milk only after
the friend came after five minutes. Now
the temperature of the cup of tea of the
A. Second student is higher
B. Both student is same
c. First student is higher
D. First student is less by \( 20 \mathrm{c} \) that of the second student


Drugs, which on interaction with macromolecular targets produce a biological response which is therapeutic and useful, are called:
A. medicines
B. super drugs
c. enzymes
D. proteins


A pair of number cubes is rolled up.What is the probability that the sum is odd given that the sum is greater than or equal to 9
A \( \cdot \frac{1}{6} \)
в. \( \frac{3}{28} \)
\( c \cdot \frac{2}{6} \)
D.


Give the IUPAC name for the following alcohols. Classify as primary or secondary or teritiary alcohol \( \left(\boldsymbol{C H}_{3}\right)_{3} \boldsymbol{C}-\underset{\boldsymbol{o} \boldsymbol{H}}{\boldsymbol{C}} \boldsymbol{H}-\boldsymbol{C}_{2} \boldsymbol{H}_{5} \)


If there are no heat losses, the quantity of heat gained by the cold body is equal
to the quantity of by the hot body.


Which compound is formed when calcium carbide reacts with heavy
water?
\( \mathbf{A} \cdot C_{2} D_{2} \)
в. \( C a D_{2} \)
c. \( C D_{2} \)
D. \( C a_{2} d_{2} \)


A cell divides in order to?
A. Maintain size of nucleus
B. Maintain bulk of cytoplasm
C. Maintain balance between bulk of cytoplasm and nucleus
D. Maintain size of chromosomes


Let \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{l}\frac{1-\sin ^{3} x}{3 \cos ^{2} x}, \quad \text { if } \quad x<\frac{\pi}{2} \\ \begin{array}{ll}a, \quad i f \quad x=\frac{\pi}{2} & \quad \text { . If } f(x) \\ \frac{b(1-\sin x)}{(\pi-2 x)^{2}}, & \text { if } \quad x>\frac{\pi}{2}\end{array}\end{array}\right. \)
continuous at \( x=\frac{\pi}{2}, \) find \( a \) and \( b \)


n the figure \( \Delta A B C, D E \| \) \( B C, A(\Delta A D E)=48 \) sq.cm., \( \frac{A D}{D B}=\frac{4}{5} \)
Find the area of \( \Delta B E C \)
A . 60 sq.cm
B. 95 sq.cm
c. 108 sq.cm
D. 135 sa.cm


If \( \sin ^{-1} x+\sin ^{-1} y+\sin ^{-1} z=\frac{3 \pi}{2} \) and
\( \boldsymbol{f}(\mathbf{2})=\mathbf{2}, \boldsymbol{f}(\boldsymbol{a}+\boldsymbol{b})= \)
\( \boldsymbol{f}(\boldsymbol{a}) \boldsymbol{f}(\boldsymbol{b}), \forall \boldsymbol{a}, \boldsymbol{b} \boldsymbol{\epsilon} \boldsymbol{R}, \) then
\( \boldsymbol{x}^{f(\mathbf{2})}, \boldsymbol{y}^{f(4)}, \boldsymbol{z}^{f(\boldsymbol{6})} \) are in
This question has multiple correct options
A. A.P
в. G.
c. н.
D. None


Evaluate: \( \lim _{x \rightarrow a} \frac{x^{14}-a^{14}}{x^{-7}-a^{-7}} \)


A parallelogram \( A B C D \) has sides \( A B=24 \mathrm{cm}, A D=16 \mathrm{cm} . \) The
distance between the sides \( A B \) and
DC is \( 10 \mathrm{cm} . \) Find the distance
between the sides \( A D \) and \( B C= \)
\( \mathbf{A} \cdot 16 \mathrm{cm} \)
B. \( 18 \mathrm{cm} \)
c. \( 15 \mathrm{cm} \)
D. \( 26 \mathrm{cm} \)


\( \operatorname{Let} A=\{a, b, c, d\} \) and \( B=\{x, y, z\} \)
What is the number of elements in \( \boldsymbol{A} \times \)
\( B ? \)
\( \mathbf{A} \cdot \mathbf{6} \)
B. 7
c. 12
D. 64


\( (\Delta l) \) of a wire of length \( 1 \mathrm{m} \) suspended
from the top of a . roof at one end and
with a load W connected to the other
end. If the cross-sectional area of the
wire is \( 10^{-6} m^{2}, \) calculate the Young's
modulus of the material of the wire.
A \( \cdot 2 \times 10^{11} N / m^{2} \)
B . \( 2 \times 10^{-11} N / m^{2} \)
\( \mathbf{C} \cdot 3 \times 10^{-12} N / m^{2} \)
D \( \cdot 2 \times 10^{-13} N / m^{2} \)


The most widely accepted theory for
ascent of sap in trees is
A . Capillarity
B. Role of atmospheric pressure
C. Pulsating action of living cell
D. Transpiration pull and cohesion theory of Dixon and Joly


Trachea, tracheids, wood fibres, and
parenchymatous tissues are found in
A. Xylem
B. Cambium
c. cortex
D. Phloem


The angular momentum of a particle relative to a certain point \( O \) varies with time as \( \vec{M}=a+\vec{b} t^{2}, \) where \( \vec{a} \) and \( \vec{b} \) are
constant vectors, with \( \vec{a} \perp \vec{b} \). If the force moment \( \vec{N} \) relative to the point \( O \)
acting on the particle when the angle between the vectors \( \vec{N} \) and \( \vec{M} \) equals \( 45^{\circ} \) is given as \( \vec{N}=x \sqrt{\frac{a}{b}} \vec{b} . \) Find \( x \)


The reagent that gives an acid chloride on treatment with a carboxylic acid is?
This question has multiple correct options
A \( \cdot P C l_{5} \)
в. \( P C l_{3} \)
c. \( \operatorname{socl}_{2} \)
D. \( (C O C l)_{2} \)


Give one example of antibiotic.


If the pressure of \( N_{2} / H_{2} \) mixture in a
closed apparatus is 100 atm and \( 20 \% \) of the mixture reacts then the pressure
at the same temperature would be:
A. 100
B. 90
c. 85
D. 80


Empirical formula of glucose is :
A. \( C_{6} H_{12} O_{6} \)
в. \( C_{3} H_{6} O_{3} \)
c. \( C_{2} H_{4} O_{2} \)
D. \( C H_{2} O \)


Simplify the following expression.
\( 6 x y+13 x-2 y x-5 x \)


6-amino purine is:
A. adenine
B. adenosine
c. cytidine
D. thymidine


State the main function of thylakoids.


Second law of refraction is also called:
A. Shell's Law
B. Snell's Law
c. Hooke's Law
D. none of the above


what is the velocity of a monkey running on the roof of the train \( A( \) moving with velocity \( 54 k h / h r) \) against its motion
with a velocity of \( 18 \mathrm{km} h^{-1} \) with respect
to the train \( A \) as observed by a man standing on the ground?
A \( \cdot 5 \mathrm{m} s^{-1} \)
B. \( 10 \mathrm{m} s^{-1} \)
c. \( 15 \mathrm{m} \mathrm{s}^{-1} \)
D. 20 \( \mathrm{m} \mathrm{s}^{-1} \)


The period of oscillation of a simple pendulum in the experiment is recorded as \( 2.63 s, 2.56 s, 2.42 s, 2.71 s \) and \( 2.80 s \)
respectively. The average absolute error is:
A . \( 0.1 \mathrm{s} \)
B. 0.11s
\( c \cdot 0.01 \)
D. 1.0s


Let \( X \) represent the difference between
the number of heads and the number of
tails obtained when a coin is tossed 6
times. What are possible values of \( X ? \)
в. 0,2,4,6
c. 6,7,7,2
D. 6,4,2,0


It is a gyre of marine debris particles found by Charles Moore in the Central North Pacific Ocean. It is characterised
by exceptionally high relative concentrations of pelagic plastics, chemical sludge and other debris. What is it called?
A. Pacific trash vortex
B. The grand junk of Pacific
c. Great Pacific garbage patch
D. Both (A) and (C)


Find the points on the \( x \) -axis such that their perpendicular distance from the \( \operatorname{line} \frac{x}{a}+\frac{y}{b}=1 \) is \( a b>0 \)
A \( \cdot\left(\frac{a}{b}(b \pm \sqrt{a^{2}+b^{2}}), 0\right) \)
в. \( \left(\frac{a}{b}(-b \pm \sqrt{a^{2}+b^{2}}), 0\right) \)
c. \( \left(\frac{b}{a}(a \pm \sqrt{a^{2}+b^{2}}), 0\right) \)
D \( \cdot\left(\frac{b}{a}(-a \pm \sqrt{a^{2}+b^{2}}), 0\right) \)


Assertion
Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be a function such that
\( f(x)=x^{3}+x^{2}+3 x+\sin x . \) Then, \( f \) is
one-one.
Reason
\( f(x) \) is decreasing function
A. Assertion and Reason are correct and the reason is the correct explanation for the assertion
B. Assertion and Reason are correct and the reason is Not the correct explanation for the assertion.
c. Assertion is correct while the Reason is incorrect
D. Assertion is incorrect while the Reason is correct


An npn transistor receives
voltage to the collector terminal and \( _{-}-_{-}-_{-}-_{-}- \) voltage to the base terminal for proper operation
A. positive, positive
B. positive, negative
c. negative, positive
D. negative, negative


\( \boldsymbol{K}_{s p} \) of \( Z e_{3}\left(P O_{4}\right)_{4} \) in terms of solubility
\( (S) \) is:
\( \mathbf{A} \cdot 108 S^{7} \)
B . \( 4 S^{3} \)
\( \mathrm{c} \cdot 6912 S^{7} \)
D. none of these


Figure shows ray diagram of a
A. simple microscope
B. compound microscope
c. Binoculars
D. Telescope


Transformation of uranium-238 into
thorium-234 is done by the process:
A. gamma decay
B. nuclear fusion
c. alpha decay
D. positron emission
E. nuclear fission


In a full wave rectifier in which input
voltage is represented by \( V=V_{M} \sin \omega t \)
then peak inversion voltage of non conducting diode will be?
A. \( -V_{M} \)
B. \( V_{M} / 2 \)
с. \( 2 V_{M} \)
D. 0


When current \( i \) is flowing through a conductor, the drift velocity is \( v \). If the value of current through the conductor and its area of cross-section is doubled,
then new drift velocity will be
A . \( 4 v \)
в. \( \frac{v}{2} \)
c. \( \frac{v}{4} \)
D. \( v \)


Statement related to center of gravity
that is incorrect is
A. The center of gravity of an object is defined as the point through which its whole weight appears to act.
B. The center of gravity is sometimes confused with the center of mass.
C. The center of gravity always lies inside the object.
D. For an object placed in a uniform gravitational field, the center of gravity coincides with the center of mass.


Baking powder contains:
\( \mathbf{A} \cdot N a H C O_{3}, C a\left(H_{2} P O_{2}\right)_{2} \) and starch
B. \( N a H C O_{3}, C a\left(H_{2} P O_{2}\right)_{2} \)
\( \mathbf{c} \cdot N a H C O_{3}, \) starch
\( \mathbf{D} \cdot N a H C O_{3} \)


Relation between amino acids and
proteins is similar to the one between:
A. nucleotides and nucleic acids
B. RNA and DNA
c. Glucose and fructose
D. Glucose and Mannose


In a thermodynamic process, helium gas obeys the law, \( \boldsymbol{T} \boldsymbol{P}^{-2 / 5}= \) constant.
The heat is given to \( n \) moles of \( H e \) in
order to raise the temperature from \( \boldsymbol{T} \) to
\( \mathbf{2} T \) is :
\( A \cdot 8 R T \)
в. \( 4 R T \)
c. \( 16 R T \)
D. Zero


Ammonia is the end product of
A. Glucose breakdown
B. Fatty acid metabolism
C. Protein metabolism
D. Breakdown of biogenic amines


A point P moves in xy-plane In such a way that \( [|x|]+[|y|]=1 \) were [.] denotes the greatest integer function. Area of the region representing all possible positions of the point 'P' is equal to
A. 4 sq. units
B. 16 sq. units
c. \( 2 \sqrt{2} \) sq. units
D. 8 sq. units


Write denaturing factors for proteins?


Assertion
The minimum value of the expression
\( \sin \alpha+\sin \beta+\sin \gamma \) where \( \alpha, \beta, \gamma \) are
real number such that \( \boldsymbol{\alpha}+\boldsymbol{\beta}+\boldsymbol{\gamma}=\boldsymbol{\pi} \)
is negative because-
Reason
\( \alpha, \beta, \gamma \) are angles of a triangle.
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


Name the compound in this figure?
\[
\left(\mathbf{C H}_{3}\right)_{2} \mathbf{C H}-\mathbf{C H}=\mathbf{C H}-\mathbf{C H}_{2}-\mathbf{C H}
\]


Classify Vitamins \( A, B, C \) and \( D \)
depending upon their solubility in water
and fat and compare them.


A good fuel has these qualities:
This question has multiple correct options
A. Should have high calorific value
B. Should be costly
c. should cause pollution
D. Should be easy to transport


The horizontal distance between two
bodies, when their velocity are
perpendicular to each other, is
A. \( 1 m \)
B. \( 0.5 \mathrm{m} \)
\( c .2 m \)
D. \( 4 m \)


In a class of 50 student, there one 20
girls. The percentage of girls is


A cylinder of gas assumed to contain 11.2 \( k g \) of butane \( C_{4} H_{10} \). If a normal
family needs \( 20000 k J \) of energy per day. The cylinder will last: (Given that \( \Delta H \) for combustion of butane is -2658
kJ)
A . 20 days
B. 25 days
c. 26 days
D. 24 days


Figure shows a closed surface which intersects a conducting sphere. If a positive charge is placed at point \( P \), find the sign of flux passing through the curved surface S.


A source of frequency \( 500 H z \) emits
waves of wavelength 0.2 m. The time
the wave takes to travel a distance of
\( 300 m \) is :
A. 75 seconds
B. 60 seconds
c. 12 seconds
D. 3 seconds


If \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{3} & \mathbf{4} \\ \mathbf{5} & \mathbf{6} \\ \mathbf{7} & \mathbf{8}\end{array}\right] \) and \( \boldsymbol{B}=\left[\begin{array}{lll}\mathbf{3} & \mathbf{5} & \mathbf{7} \\ \mathbf{4} & \mathbf{6} & \mathbf{8}\end{array}\right] \)
then which one of the following is
correct?
\( A \cdot B \) is the inverse of \( A \)
B. \( B \) is the adjoint of \( A \)
c. \( B \) is the transpose of \( A \)
D. None of the above


A truck of mass \( M \) is at rest on a
frictionless road. When a monkey of
mass \( m \) starts moving on the truck in
forward direction, the truck recoils with
a speed \( v \) backward on the road, with what velocity is the monkey moving
with respect to truck?


\( (a . b)+(b . c) \div(c . a) \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot \frac{1}{3} \)
D.


Filling the blanks. A mixture of sulphur and charcoal can be separated by method.


Relative permittivity and permeability of
a material are \( \varepsilon_{r} \) and \( \mu_{r} \) respectively. The
values of these quantities allowed for a diamagnetic material are
\( \mathbf{A} \cdot \varepsilon_{r}=0.5, \mu_{r}=1.5 \)
\( \mathbf{B} \cdot \varepsilon_{r}=1.5, \mu_{r}=0.5 \)
\( \mathbf{c} \cdot \varepsilon_{r}=0.5, \mu_{r}=0.5 \)
\( \mathbf{D} \cdot \varepsilon_{r}=1.5, \mu_{r}=1.5 \)


Two strings with mass per unit length of \( 25 g / c m \) and \( 9 g / c m \) are joined together in series. The reflection coefficient for the vibration waves are
A \( \cdot \frac{9}{25} \)
в. \( \frac{3}{5} \)
c. \( \frac{1}{16} \)
D. \( \frac{9}{16} \)


\( \pi \) bond is formed by:
A. overlapping of hybridised orbitals
B. overlapping of s-s orbitals
C. head on overlapping of \( p \) -p orbitals
D. \( p-p \) collateral overlapping


\( \mathbf{A} \)
\( 12 \Omega \) resistance is cut into three equal parts and then connected in triangular form. Determine the equivalent resistance between two ends of any side
of the triangle.


Find the distance of the point \( P(3,4,4) \) from the point, where the line joining the point \( A(3,-4,-5) \) and \( B(2,-3,1) \) intersects the plane \( 2 x+y+z=7 \)


\( M \) is a metal above hydrogen in the
activity series and its oxide has the
formula \( M_{2} O . \) This oxide when
dissolved in water forms the
corresponding hydroxide which is a good conductor of electricity. In the above context answer the following:
State the reaction taking place at the cathode.


In a typical differentiated cell, which functional category of genes would most likely be continuously expressed?
A. Genes that code for production of ribosomes
B. Genes that promote cell division
c. Genes that produce telomerase
D. Genes that produce growth factor


An astronaut in a spaceship the sky
appears black due to:
A. Absence of atmosphere in his neighbourhood
B. Light from the sky is absorbed by the medium surrounding him
c. The fact at the height, sky radiations are only in the infra-red and the ultraviolet region
D. None of these


What do you understand by rate of a reaction? Explain why the rate of a reaction cannot be measured by dividing the total amount of reactant consumed by the time taken.


Which of the following examples does not represent disproportionation?
A \( \cdot M n O_{2}+4 H C l \rightarrow M n C l_{2}+C l_{2}+2 H_{2} O \)
в. \( 2 H_{2} O_{2} \rightarrow 2 H_{2} O+O_{2} \)
c. \( 4 K C l O_{3} \rightarrow 3 K C l O_{4}+K C l \)
D. \( 3 C l_{2}+6 N a O H \longrightarrow 5 N a C l+N a C l O_{3}+3 H_{2} O \)


Two square metal plates \( A \) and \( B \) are of
the same thickness and material. The
side of \( B \) is twice that of \( A \). If the
resistances of \( A \) and \( B \) are denoted by \( \boldsymbol{R}_{A} \) and \( \boldsymbol{R}_{B}, \) Then \( \left(\frac{\boldsymbol{R}_{\boldsymbol{A}}}{\boldsymbol{R}_{\boldsymbol{B}}}\right) \) is
\( A \cdot \frac{1}{2} \)
B. 2
\( c .1 \)
\( D \)


Using differentials the approximate value of \( \sqrt{401} \) is
A . 20.100
B. 20.025
c. 20.030
D. 20.125


Explain zone refining.


Which of the following statements are
true for the function \( f(x) \) defined for
\( -1 \leq x \leq 3 \) in the figure shown?
This question has multiple correct options
A. \( \lim _{x \rightarrow-1^{+}} f(X)=1 \)
B. \( \lim _{x \rightarrow 2} f(X) \) does not exist
\( \mathbf{c} \cdot \lim _{x \rightarrow 1^{-}} f(X)=2 \)
D. \( \lim _{x \rightarrow 0^{+}} f(X)=\lim _{x \rightarrow 0^{-}} f(X) \)


The angle between electric dipole moment \( P \) and the electric field \( E \) when
the dipole is in stable equilibrium is
A . 0
B. \( \frac{\pi}{4} \)
\( c \cdot \frac{\pi}{2} \)
D. \( \pi \)


Two straight lines \( u=0 \) and \( v=0 \) pass through the origin and angle between them is \( \tan ^{-1}\left(\frac{7}{9}\right) . \) If the ratio of the slope of \( v=0 \) and \( u=0 \) is \( \frac{9}{2} \) then their equations are
This question has multiple correct options
A. \( y+3 x=0 \) and \( 3 y+2 x=0 \)
B. \( 2 y+3 x=0 \) and \( 3 y+x=0 \)
c. \( 2 y=3 x \) and \( 3 y=x \)
D. \( y=3 x \) and \( 3 y=2 x \)


Find the fourth vertex of the
parallelogram whose consecutive
vertices are (8,4),(5,7),(-1,1)


\( \delta \)
\( d \)
\( d \)
\( \sigma \)


A simple pendulum is oscillating with
amplitude \( A \) and angular frequency \( \omega \)
At displacement \( x \) from mean position,
the ratio of kinetic energy to potential energy is
A \( \cdot \frac{x^{2}}{A^{2}-x^{2}} \)
B. \( \frac{x^{2}-A^{2}}{x^{2}} \)
c. \( \frac{A^{2}-x^{2}}{x^{2}} \)
D. \( \frac{A-x}{x} \)


How many distinct positive integers are
possible with the digits 1,3,5,7 without repitition?


Find the ratio in which the line joining
\( A(1,-5) \) and \( B(-4,5) \) is divided by
the \( x-a x \) is. Also find the co-ordinates
of the point of division.


The order and degree of the differential
equation of all parabola whose axis is \( x \) axis
\( A \cdot 2, \)
B. 2,
\( c \cdot 1,2 \)
D. 1,1


Why does the development of endosperm preceeds that of embryo?


At what point on the line joining the two charge is the electric potential zero.


A ball falls from a height of \( 5 m \) and strikes the roof of a lift. If at the time of
collision, lift is moving in the upward direction with a velocity of \( 1 m / s, \) then the velocity with which the ball rebounds after collision will be :
A. \( 11 \mathrm{m} / \mathrm{s} \) downwards
B. 12 \( m / s \) upwards
c. \( 13 \mathrm{m} / \mathrm{s} \) upwards
D. 12 \( m / s \) downwards


The valence electronic configuration of
magnesium is:
A \( \cdot 4 s^{1} \)
B. \( 4 s^{2} \)
\( c \cdot 3 s^{1} \)
\( D \cdot 3 s^{2} \)


A rod \( 1.5 m \) longis placed along the
principal axis of a convex mirror of focal length \( 60 \mathrm{cm} \). The near and of the rod is
1 \( m \) from the pole of the convex mirror.
The length of the image of the rod is
\( \mathbf{A} \cdot 15 \mathrm{cm} \)
B . \( 14.44 \mathrm{cm} \)
\( c \cdot 6.62 c m \)
D. \( 10.88 \mathrm{cm} \)


If \( A \) and \( B \) are two events such that
\( \boldsymbol{A} \subset \boldsymbol{B} \) and \( \boldsymbol{P}(\boldsymbol{B}) \neq 0, \) then which of the
following is correct? This question has multiple correct options
\( ^{\mathbf{A}} \cdot p(A \mid B)=\frac{P(B)}{P(A)} \)
B \cdot \( P(A \mid B)<P(A) \)
C \( \cdot P(A \mid B) \geq P(A) \)
D. None of these


\( N_{2} O \) is heavier than \( O_{2} \)
A. True
B. False


The perimeter of a triangle is \( 8+ \) \( 13 a+7 a^{2} \) and two of its sides are
\( 2 a^{2}+3 a+2 \) and \( 3 a^{2}-4 a-1 . \) Find
the third side of the triangle.


Elevation in boiling point was \( 0.52^{\circ} \mathrm{C} \) when 6 g of a compound \( X \) was dissolved in 100 g of water. Molecular mass of the compound M in \( g \) mol \( ^{-1} \) is:
\( K_{b} \) for water is \( 0.52 \mathrm{Km}^{-1} \).)
A . 120
B. 60
\( c \cdot 600 \)
D. 180


Assertion
Radial vascular bundle is the
characteristic of majority of the roots including dicots and monocots.
Reason
Monocot stem is characterized by collatral open vascular bundle.
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


(i) Distinguish between a conductor
and a semi conductor on the basis of
energy band diagram
(ii) The following figure shows the input waveforms \( (A, B) \) and the output waveform (Y) of a gate. Identify the gate, write its truth table and draw its logic symbol.


ord sto ob ort


Unit of current is denoted by:
A.
B. A
\( c . k \)
D.


\( \mathbf{A} \)
\( 5 V \) battery of negligible internal
resistance is connected across a \( 200 V \)
battery and a resistance of \( 39 \Omega \) as
shown in the figure. Find the value of the
current


The sum of four consecutive terms which are in an arithmetic progression is 32 and the ratio of the product of the first and the last term to the product of
two middle terms is 7: 15 . Find the
number.


Which of the following cannot react with NaOH?
\( A . B e \)
в. \( F e \)
c. \( A l \)
D. Zn


What is the nature of the graph: \( y=\frac{4}{x} \)
A. Rectangular hyperbola in first and third quadrant
B. Rectangular hyperbola in first and second quadrant
C. Hyperbola but not rectangular hyperbola
D. Rectangular hyperbola in second and fourth quadrant


What is the nature of force between the
colliding bodies?
A. External
B. conservative
\( c . \) Internal
D. Non conservative


A beaker of height '3h' has a radius 'h'. A thin rod of height 'h' is placed to the wall
of the beaker. A person can see the top
end of the rod from the opposite edge of the beaker through a pin hole. When the beaker is filled with a liquid up to a height '2h', the person can see the bottom end of the rod. The refractive
index of the liquid is :
\( A \cdot \frac{3}{2} \)
B. \( \frac{\sqrt{3}}{2} \)
\( c \cdot \frac{5}{2} \)
D. \( \sqrt{\frac{5}{2}} \)


What does J J Thomson model failed to
explain-
A. scattering of Alpha particles
B. neutality of atom
\( c . \) both of above
D. none of these


Salts of alkylbenzene sulphonates are called:
A. soaps
B. detergents
c. both \( (A) \) and \( (B) \)
D. None of the above


The equation of the straight line which is perpendicular to \( 7 x-8 y=6 \) and
passing through (-4,5) is
A. \( 8 x+7 y=3 \)
в. \( 7 x+8 y=3 \)
c. \( 8 x-7 y=3 \)
D. \( 7 x-8 y=3 \)


Solve
\( \int\left(\frac{x-1}{x+1}\right)^{4} d x= \)


During photosynthesis, for the synthesis of one mole of glucose, the
number of ATP and NADPH \( _{2} \) required are
... and \dots.... respectively.
A. 12,18
B. 18,12
\( c \cdot 6,12 \)
D. 18,18


If \( M_{0} \) is the mass of an oxygen isotope
\( \mathrm{s} \mathrm{O}^{17}, M_{p} \) and \( M_{n} \) are the masses of a proton and a neutron respectively, the nuclear binding energy of the isotope is
\( \mathbf{A} \cdot\left(M_{O}-8 M_{p}\right) c^{2} \)
В \( \cdot\left(M_{O}-8 M_{p}-9 M_{n}\right) c^{2} \)
c. \( M_{O} c^{2} \)
D. \( \left(M_{O}-17 M_{n}\right) c^{2} \)


The value of \( k, \) of the roots of the
equation \( 2 k x^{2}+2 k x+2=0 \) are
equal is
\( A \cdot \frac{4}{5} \)
B. 4
c. 1
D.


It is often said that the world is
witnessing now a second industrial revolution, which will transform the
society as radically as did the first. List some key contemporary areas of science and technology, which are responsible for this revolution.


A hemisphere of radius \( R \), made of
glass of refractive index \( (3 / 2) \) is placed on the table. A point source of light is placed at a distance \( 2 R \) from the centre of hemisphere. If source is viewed diametrically opposite side of hemisphere. Find the position of image of source.
\( A \cdot 5 R \)
в. 6 R
c. 7ह
D. 8R


Arsine produces hydrogen gas on heating. The pressure of produced hydrogen was measured, at consant
volume and temperature, as follows:
Time \( \quad \) o \( \quad 5.5 \quad 6.5 \) (hours)

Pressure \( \quad \) 0.965 \( \quad \) 1.060 \( \quad 1.076 \) \( (a+m) \)
Calculate the specific rate and half-life
peroid of reaction assuming the reaction to be of first-order.


If \( \Delta \mathrm{E} \) is the heat of reaction for
\( C_{2} H_{5} O H_{(l)}+3 O_{2(g)} \rightarrow 2 C O_{2(g)}+3 H_{2} O_{(l)} \) at
constant volume, the \( \Delta \mathrm{H} \) (Heat of
reaction at constant pressure) at constant temperature is:
A. \( \Delta \mathrm{H}=\Delta \mathrm{E}+2 \mathrm{RT} \)
B. \( \Delta \mathrm{H}=\Delta \mathrm{E} \) -2RT
c. \( \Delta \mathrm{H}=\Delta \mathrm{E}+\mathrm{RT} \)
D. \( \Delta \mathrm{H}=\Delta \mathrm{E}-\mathrm{RT} \)


The length,breadth and thickness of a rectangular copper sheet are \( 4 c m, 2.5 c m \) and \( 1.56 c m \) respectively.
Find the area of the sheet to corrected
significant figures.
A \( \cdot 40.3 \mathrm{cm}^{2} \)
B . \( 40.28 \mathrm{cm}^{2} \)
c. \( 40 \times 10^{2} \mathrm{cm}^{2} \)
D. \( 0.4 \times 10^{2} \mathrm{cm}^{2} \)


Solve \( \int \frac{1}{x^{5}}\left(1+x^{4}\right) d x \)


Which of the following is an ionic compound?
A. \( C a C_{2} \)
в. \( N a H \)
c. \( B e C l_{2} \)
D. \( B F_{3} \)


The molecules of nitrogen monoxide and nitrogen dioxide differ by a multiple
of the mass of one oxygen. The statement can be understood by the concept of :
A. Law of multiple proportion
B. Nuclear fusion
c. van dar Waals forces
D. Graham's Law of Diffusion(Effusion)
E. Triple point


Number of points of focal minima of the functions \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}+\frac{\mathbf{1}}{\boldsymbol{x}^{2}}-\mathbf{8} \boldsymbol{x}-\frac{\boldsymbol{8}}{\boldsymbol{x}}+ \)
7 are
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D.


How will you pure potassium
permanganate crystals from its ore, pyrolusite? Give the reaction involve


Parikshit makes a cuboid of plasticine of sides \( 5 \mathrm{cm}, 2 \mathrm{cm}, 5 \mathrm{cm} . \) How many
such cuboids will he need to form a
cube?


One molecule of haemoglobin will combine with four molecules of oxygen.
If \( 1.0 g \) of haemoglobin combines with
\( 1.642 m l \) of oxygen at body temperature
\( \left(27^{\circ} C\right) \) and a pressure of 760 tor \( r \) what is the molar mass of haemoglobin?
A. 6,00,000
в. 1,50,000
c. 15,000
D. 60,000


Isotopes of iodine is used in
the treatment of goiter.
A. \( I-132 \)
в. \( I-133 \)
c. \( I-13 \)
D. \( I-130 \)


The distance from the origin to the centroid of the tetrahedron formed by
the points \( (0,0,0),(a, 0,0),(0, b, 0),(0,0, c) \) is:
A \( \cdot \frac{\sqrt{a+b+c}}{4} \)
B. \( \frac{\sqrt{a+b+c}}{3} \)
c. \( \frac{\sqrt{a^{2}+b^{2}+c^{2}}}{16} \)
D. \( \frac{\sqrt{a^{2}+b^{2}+c^{2}}}{4} \)


Assertion
The linear portion of the stress-strain
curve is the elastic region and the slope
is the modulus of elasticity or Young's
Modulus.
Reason Young's Modulus is the ratio of the
compressive stress to the longitudinal
strain.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


If the planes \( 2 x-y-3 z-7=0 \) and
\( 4 x-2 y+5 k z+9=0 \) are parallel
then \( 5 k^{2}+6= \)
A \( \frac{-6}{5} \)
в. \( \frac{-5}{6} \)
c. \( \frac{36}{5} \)
D. \( \frac{66}{5} \)


A throws a coin 3 times. If he get a head all three times, he is to get a reward of Rs.200, on the other hand if he does not
get 3 heads he is to loose Rs.40. He is
expected to win Rs.
A . Rs. 50
B. Rs. (-10)
c. Rs. 35
D. Rs. 10


In the given figures, which of the
following satisfies A.S.A. condition for
congruence?
A . Figure I
B. Figure I and II
C . Figure
D. None of these


The reagent \( \boldsymbol{X} \) used for the following reaction is:
\[
\mathbf{R}-\mathbf{C}=\mathbf{C R}^{\prime}+\mathbf{H}_{2} \stackrel{\mathbf{X}}{\longrightarrow} \underset{\mathbf{H}^{\prime}}{\mathbf{C}} \mathbf{C}=\mathbf{C}_{\mathbf{H}}^{\prime \mathbf{R}^{\prime}}
\]
A . \( N i \)
в. \( P d / C \)
c. LiAlH\( _{4} \)
D. \( N a / \)Liquid \( N H_{3} \)


The matrix of bone and cartilage can be distinguished by the presence of
A . Haversian canal
B. Lacuna
c. chromatophores
D. Adipose cells


Which of the following differs in nature from others?
A. Vasopressin
B. Thyroid
c. oxytocin
D. Insulin


When bismuth chloride is poured into a large volume of water, the white precipitate formed is:
\( \mathbf{A} \cdot B i_{2} O_{3} \)
в. \( B i_{2} O_{4} \)
c. В гОС
D. none of the above


Pneumatophore is present in
A. Rhizophora
B. Nerium
c. Hibiscus
D. Acaccia


A square \( A B C D \) of side 1 mm is kept
at distance \( 15 \mathrm{cm} \) in front of the
concave mirror as shown in fig. The
focal length of the mirror is \( 10 \mathrm{cm} \). The
length of the perimeter of its image will
be :
\( A \cdot 8 m m \)
B. \( 2 m m \)
\( \mathrm{c} .12 \mathrm{mm} \)
D. \( 6 m m \)


Which isotope of hydrogen is/are radioactive in nature?
A. Protium and deuterium
B. Tritium only
c. Tritium and deuterium
D. Only deuterium


The high amount of E. coli in water is the indicator of
A. Hardness of water
B. Industrial pollution
c. Sewage pollution
D. Presence of chlorine in water


Which of the following is/are contact forces
A. Normal force
B. Tension force
c. Friction force
D. All


Find the equation of the line joining \( A(1,3) \) and \( B(0,0) \) using determinants.


Number of points having position vector \( \boldsymbol{a} \hat{\boldsymbol{i}}+\boldsymbol{b} \hat{\boldsymbol{j}}+\boldsymbol{c} \hat{\boldsymbol{k}}, \) where \( \boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c} \)
\{1,2,3,4,5\} such that \( 2^{a}+3^{b}+5^{c} \) is
divisible by 4 is
A. 140
B. 70
\( c .100 \)
D. none of these


Gibberellin was first extracted from
A. Fusarium
B. Gellidium
c. Gracillaria
D. Aspergillus


Unpolarised light is passed through a
polaroid \( P_{1} . \) When this polarised beam
passes through another polaroid \( P_{2} \) and
if the pass axis of \( \boldsymbol{P}_{2} \) makes angle \( \boldsymbol{\theta} \)
with the pass axis of \( P_{1} \), then write the expression of intensity for the polarised
beam passing through \( P_{2} . \) Draw a plot showing the variation of intensity when \( \theta \) varies from 0 to \( 2 \pi \)


A plane electromagnetic wave travelling in a non magnetic medium is given by
\( \boldsymbol{E}=\left(\boldsymbol{9} \times \mathbf{1 0}^{8} \boldsymbol{N} \boldsymbol{C}^{-1}\right) \boldsymbol{s i n}[(\boldsymbol{9} \times \)
\( \left.10^{8} \text { rads}^{-1}\right) t-\left(6 m^{-1}\right) x \)
Where \( x \) is in metre and \( t \) is in second.
The dielectric constant of the medium
is:
A. 5
B. 4
\( c \cdot 3 \)
D.


Explain the density of rational numbers with examples.


Liquids flow from a higher to a lower level. Which liquid can climb up the walls of the glass vessel in which it is kept?
A. Liquid helium
B. Alcohol
c. water
D. Liquid nitrogen


A spring of force constant \( k \) is cut into
two pieces such that one piece is twice as long as the other. Then the longer piece will have a force constant of:
\( \mathbf{A} \cdot 3 k \)
в. \( \frac{2 k}{3} \)
\( c \cdot \frac{3 k}{2} \)
D. \( 6 k \)


A worker is paid Rs 210 for 6 days work. If his total income of the month is Rs
\( 875, \) for how many days did he work?


In what year did Nathan Thomson plant
the seeds?
A. \( 1719 \pm 2 \)
B. \( 1819 \pm 2 \)
c. \( 1519 \pm 2 \)
D. \( 1919 \pm 2 \)


A straight wire lying in a horizontal plane carries a current from north to
south. What will be the direction of
magnetic field at a point just underneath it?
A. Towards north.
B. Towards east
c. Towards west
D. Towards south.


On to a sphere of radius \( \boldsymbol{R} / 2 \) and
density \( \rho_{2} \) with centre at \( C_{2} \) a second
solid sphere is moulded with density \( \rho_{1} \)
radius \( R \) and centre \( C_{1} \). Find the force
experienced by a point mass \( m \) at point
\( P \) at a distance \( y \) from the combination
as shown.


Evaluate the following definite integral:
\( \int_{0}^{1}\left(3 x^{2}+2 x\right) d x \)


The following questions are based on the preparation of ammonia gas in the laboratory:
Name the compound normally used as a drying agent during the process.


Can we represent every decimal number
in the form of \( \frac{p}{q} \) or not? Explain it.


If \( f(x)=\frac{4-7 x}{7 x+4}, \lim _{x \rightarrow 0} f(x)=l \) and
\( \lim _{x \rightarrow \infty} f(x)=m \) the quadratic equation
having roots as \( \frac{1}{l} \) and \( \frac{1}{m} \) is
A \( \cdot x^{2}-1=0 \)
B. \( x^{2}-x+1=0 \)
c. \( x^{2}-\frac{1}{2}=0 \)
D. \( x^{3}-1=0 \)


Find three consecutive terms in A.P.
such that their sum is 21 and their
products is 315


Solve \( \frac{\mathbf{7}}{\mathbf{8}}+\frac{\mathbf{5}}{\mathbf{1 2}} \times \frac{\mathbf{9}}{\mathbf{1 0}}-\frac{\mathbf{1}}{\mathbf{4}} \)


A spring balance whose maximum extension of its spring is \( 20 \mathrm{cm} \) can
sustain a maximum load of \( 20 k g_{w t} \)
within its elastic limit on the surface of
the earth. Now the same balance
is taken to the moon. Given that
gearth \( =6 g_{\text {moon }}, \) what is the maximum
mass of the load that can be attached to
the balance to have half its maximum
extension?
A . 76
B. 65
c. 60
D. 55


Which of the following has a very high
\( \boldsymbol{K}_{\boldsymbol{a}} ? \)
A. Bronsted acid
B. Bronsted base
c. Strong acid
D. weak base


In a test tube, there is \( 18 g \) of glucose \( \left(C_{6} H_{12} O_{6}\right) 0.08 \) mole of glucose is taken out. Glucose left in the test tube
is:
A. \( 0.10 g \)
в. \( 0.02 g \)
c. 0.10 mole
D. 3.60 \( g \)


An azeotropic solution of two liquids has boiling point lower than either of them when it:
A. shows a negative deviation from Raoult's law
B. shows no deviation from Raoult's law
c. shows positive deviation from Raoult's law
D. is saturated


A stone is projected from the ground
with a velocity of \( 14 \mathrm{ms}^{-1} . \) One second
later it clears a wall \( 2 m \) high. The angle
of projection is \( \left(\boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} \boldsymbol{s}^{-2}\right) \)
A \( \cdot 45^{\circ} \)
B. \( 30^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 15^{\circ} \)