A rigid bar of mass \( 15 k g \) is supported
symmetrically by three wires each \( 2 m \) long. Those at each end are of copper and the middle one is of iron. Determine
the ratio of their diameters if each is to
have the tension? (Given E for copper =
\( 110 \times 10^{9} N / m^{2} \) and \( E \) for iron \( =190 \times \)
\( \mathbf{1 0}^{\mathbf{9}} \mathbf{N} / \boldsymbol{m}^{\mathbf{2}} \)
A . 12.6: 2
в. 1.31: 1
c. 4.65: 3
D. 2.69 : 4


In an AC circuit
A. The average value of current is zero
B. The average value of square of current is zero
C . The average power dissipation is zero
D. The rms current is \( \sqrt{2} \) time of peak current


If the resultant of all external forces is
zero, then velocity of centre of mass will
be
A. zero
B. constant
\( \mathbf{c} \cdot \) either \( (a) \) or \( (b) \)
D. neither \( (a) \) nor \( (b) \)


Ammonia is filled in weather balloons
that work at very high altitudes because it is:
A . a neutral gas
B. a compound of nitrogen
c. lighter than air
D. liquefied at low temperature


The general formula for alcohol is:
A. \( C_{n} H_{2 n}+1 O H \)
в. \( C_{n} H_{2 n}+2 O H \)
c. \( C_{n} H_{2 n}-2 O H \)
D. \( C_{n} H_{2 n} \)


If \( \sin A=x, \cos B=y \) and \( A+B+ \)
\( C=0, \) then \( x^{2}+2 x y \sin C+y^{2} \) is
equal to
\( \mathbf{A} \cdot \sin ^{2} C \)
B. \( \cos ^{2} C \)
c. \( 1+\sin ^{2} C \)
D. \( 1+\cos ^{2} C \)


Which surfaces are said to be smooth?
A. As long as the irregularities of surfaces are small as compared to the wavelength of the incident light.
B. As long as surface irregularities are large compared to the wavelength of the incident light
C. As long as surface smoothness are small as compared to wavelength of reflected light
D. As long as the surface irregularities are large as compared to the wavelength of reflected light.


An object is placed on the surface of a
smooth inclined plane of inclination \( \boldsymbol{\theta} \). It
takes time \( t \) to reach the bottom. If the
same object is allowed to slide down a rough inclined plane of same
inclination \( \theta \), it takes times nth to reach
the bottom where \( n \) number greater
than \( 1 . \) The coefficient of friction \( \mu \) is
given by:
A \( \cdot \mu=\tan \theta\left(1-1 / n^{2}\right) \)
B \cdot \( \mu=\cot \theta\left(1-1 / n^{2}\right) \)
c. \( \mu=\tan \theta\left(1-1 / n^{2}\right)^{1 / 2} \)
D. \( \mu=\cot \theta\left(1-1 / n^{2}\right)^{1 / 2} \)


bacteria are microbes that
work in the absence of oxygen.


Ozone hole is
A. Hole of ozone layers
B. Decrease in concentration of ozone
C. Thining of ozone in stratosphere
D. Increase of ozone in antartic region


Find the \( 10^{t h} \) term of a \( G P \) whose \( 8^{t h} \)
term is 192 and the common ratio is 2


Describe the purification of colloidal solutions by Dialysis method with a neat diagram.


Which of the following is an excellent fuel?
A. Solid fuel
B. Liquid fuel
c. Gaseous fuel
D. None of the above


The IUPAC name of the following
compound is ethenylbenzene
A. True
B. False


The molecular formula of the organic
acid is:
A \( \cdot C_{2} H_{6} \)
B. \( C_{2} H_{5} O_{2} \)
c. \( C_{2} H_{6} O_{2} \)
D. \( C_{2} H_{4} O \)


Assertion
Virtual image can be photographed.
Reason

Only a real image can be formed on a
SCreen
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Which of the following organelles work as cellular garbage disposal systems?
A. Endoplasmic reticulum
B. Golgi complex
c. Lysosomes
D. Mitochondria


The coefficient of \( x^{3} \) in \( \left(\sqrt{x^{5}}+\frac{3}{\sqrt{x^{3}}}\right)^{6} \)
is
\( \mathbf{A} \cdot \mathbf{0} \)
в. 120
\( c \cdot 420 \)
D. 540


In the electrolysis of aqueous \( N a C l \) solution, side reactions taking place
are :
(I) \( 2 O H^{-}+C l_{2} \rightarrow 2 O C l^{-}+H_{2} O \)
(II) \( 2 N a+2 H_{2} O \rightarrow 2 N a O H+H_{2} \)
(III) \( 4 O H^{-} \rightarrow O_{2}+2 H_{2}+4 e^{-} \)
Select the correct alternate :
A \( . \) (I) and (III)
B. (II) and (III)
c. (I) and (II)
D. (I), (II), and (III)


The actual value of the acceleration of
gravity is \( 9.8 \mathrm{m} / \mathrm{s} \). Physics students in a laboratory experiment use a pendulum to determine the acceleration of gravity. Their experimental value is \( 9.2 m / s \)
What is their percent error?
A . \( 0.60 \% \)
B. \( 60 \% \)
\( c .6 .5 \% \)
D. \( 61 \% \)
E . \( 6.1 \% \)


The hydrogen sulphate of a certain
metal has the formula \( M H S O_{4} \). The formula of the metal oxide is:
A. \( M O \)
в. \( M O_{2} \)
c. \( M_{2} O \)
D. \( M_{2} O_{2} \)


\( \left[\begin{array}{lll}\boldsymbol{x} & \boldsymbol{4} & \boldsymbol{1}\end{array}\right]\left[\begin{array}{ccc}\boldsymbol{2} & \boldsymbol{1} & \boldsymbol{2} \\ \boldsymbol{1} & \boldsymbol{0} & \boldsymbol{2} \\ \boldsymbol{0} & \boldsymbol{2} & \boldsymbol{-} \boldsymbol{4}\end{array}\right]\left[\begin{array}{c}\boldsymbol{x} \\ \boldsymbol{4} \\ -\boldsymbol{1}\end{array}\right]=\mathbf{0} \)
then find \( x \)


Write whether the following statements are true or false with proper justification for your answer.
The secretion of the sting of silk worm forms the silk fibre.
A. True
B. False


Match the atomic numbers 4,14,8,15
and 19 with a non-metal of valency 4
A . 4
B. 8
\( c \cdot 14 \)
D. 15


Explain the following term with a suitable example:
Food preservatives


Assertion
According to crystal field theory, during
complex formation, the d- orbitals split
and form two sets of orbitals \( t_{2 g} \) and \( e_{g} \)
Reason

Splitting of \( \mathrm{d} \) - orbitals occurs only in case of strong field ligand
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


\( \boldsymbol{B} \boldsymbol{r}_{2}+\boldsymbol{O} \boldsymbol{H}^{-}(\boldsymbol{H} \boldsymbol{o} \boldsymbol{t}) \rightarrow(\boldsymbol{P})+ \)
\( (Q) ;(P)+(Q)+H^{+} \rightarrow B r_{2} \)
\( (P) \) gives yellow precipitate with
\( A g N O_{3},(P) \) and \( (Q) \) are:
A. \( B r^{-}, B r O^{-} \)
B. \( B r^{-}, B r O_{3} \)
c. \( B r O^{-}, B r O_{3}^{-} \)
D. \( B r O^{-}, B r O 4 \)


The ion that is isoelectronic with \( C O \)
and has same bond order is:
A \( . C N^{-} \)
B. \( O_{2}^{\text {t }} \)
\( c \cdot O_{2} \)
D. \( N_{2}^{\text {th }} \)


Which of the following groups would enhance the reactivity of electrophilic aromatic substitution -
\( A .-C N \)
в. \( -C H O \)
\( \mathrm{c} \cdot-C H_{3} \)
D. \( -N O_{2} \)


Which of the following is/are true
regarding rancidity?

This question has multiple correct options
A. On keeping for long time, the oxidation of oils and fats, changes the taste and odour of food.
B. To prevent rancidity, food is stored in air tight containers.
C. Rancidity can also be prevented by addition of antioxidants.
D. To prevent rancidity, packed food items are flushed with an inert gas like nitrogen.


A swimmer can swim in still water with
speed \( v \) and the river is flowing with speed \( v / 2 . \) What is the ratio of the time
taken to swimming across the river in the shortest time to that of
swimming across the river over the shortest distance?
\( A \cdot \frac{\sqrt{3}}{2} \)
B.
\( c \cdot 2 \)
D. \( \sqrt{3} v \)


Four metallic plate each with a surface
area of \( A \) are placed at a distance \( d \)
from each other. The plates are
connected as shown in the circuit
diagram. Then the capacitance of the
system between a and b is-
\( \mathbf{A} \cdot \frac{3 \epsilon_{0} A}{d} \)
В. \( \frac{2 \epsilon_{0} A}{d} \)
\( \mathbf{c} \cdot \frac{2 \epsilon_{0} A}{3 d} \)
D. \( \frac{3 \epsilon_{0} A}{2 d} \)


Two numbers are selected at random
from the number \( 1,2, \ldots, n . \) Let \( p \) denote the probability that the difference
between the first and second is not less
than \( m \) (where \( 0<m<n \) ). If \( n=25 \)
and \( \boldsymbol{m}=\mathbf{1 0}, \) find \( \mathbf{5} \boldsymbol{p} \)


Match the nucleic acid and its model
from the given columns.
Nucleic acid
(A) DNA
(p) Double helical
(B) tRNA (two dimensional)
(q) Clover leaf
(C) tRNA (three dimensional
(r) Hair pin
(D) rRNA
(s) L Shape
A. A-p, B-q, C-s, D-r
B. A-p, B-r, C-q, D-s
c. A-p, B-s, C-q, D-r
D. A-p, B-s, C-r, D-q


Which of these is an example for zygomorphic flower with imbricate aestivation?
A. Calotropis
B. Mustard
c. canna
D. cassia
E. Cucumber


Abbreviation BMR in biology stands for
A. Birth mortality rate
B. Basal metabolic rate
C. Bone marrow regeneration
D. All of the above


Define electronegativity. Why standard entropy of an elementary substanceis not zero whereas standard
enthalpy of formation is taken as zero?


Solve \( \int \sqrt{\frac{\boldsymbol{a}-\boldsymbol{x}}{\boldsymbol{a}+\boldsymbol{x}}} \boldsymbol{d} \boldsymbol{x} \)


When molten \( A l C l_{3} \) is electrolysed with
a current of 0.5 ampere to produce 27 g
\( \mathbf{A I} \)
litres of \( \mathrm{Cl}_{2} \) at \( \mathrm{STP} \) are formed
A . 22.4
B. 33.6
c. 24.47
D. 36.7


If \( X \) and \( Y \) are two sets, then \( X \cap \)
\( (\boldsymbol{Y} \cup \boldsymbol{X})^{\prime} \) equals
\( \mathbf{A} \cdot X \)
в. \( Y \)
\( c \cdot \phi \)
D. None of these


\( \boldsymbol{p} \boldsymbol{t}(\boldsymbol{5},-\boldsymbol{2}) \) is the mid pt of line segment
joining the \( p t s\left(\frac{x}{2}, \frac{y+1}{2}\right) \) and \( (x+ \) \( \mathbf{1}, \boldsymbol{y}-\mathbf{3}) \) then find the value of \( \boldsymbol{x} \) \& \( \boldsymbol{y} \)


Calculate the cell EMF in mV for:
\( \boldsymbol{P t}\left|\boldsymbol{H}_{2}(\boldsymbol{1} \boldsymbol{a} \boldsymbol{t m})\right| \boldsymbol{H} \boldsymbol{C l}(\boldsymbol{0} . \boldsymbol{0} \boldsymbol{1} \boldsymbol{M})|\boldsymbol{A} \boldsymbol{g} C l(s)| \boldsymbol{A} \)
if \( \Delta G_{t}^{o} \) values are at \( 25^{\circ} \mathrm{C} \) \( -109.56 \frac{k J}{m o l} \) for \( A g C l(s) \) and
\( -130.79 \frac{k J}{m o l} \) for \( \left(H^{+}+C l^{-}\right)(a q) \)
A \( .456 m V \)
в. \( 654 m V \)
c. \( 546 m V \)
D. None of these


The function of bile is to
A. Activate pancreatic lipases
B. Emulsify fat droplets
C . Congeal fat droplets
D. Digest fats
E. Is produced in the pancreas


The standard reduction potential of two reactions are given. \( \boldsymbol{A} \boldsymbol{g} \boldsymbol{C l}_{(s)}+\boldsymbol{e}^{-} \rightarrow \boldsymbol{A} \boldsymbol{g}_{(s)}+\boldsymbol{C l}_{(a q)}^{-} ; \boldsymbol{E}^{\ominus}= \)
\( \mathbf{0 . 2 2 V} \)
(i)
\( \boldsymbol{A} \boldsymbol{g}_{(a q)}^{+}+\boldsymbol{e}^{-} \rightarrow \boldsymbol{A} \boldsymbol{g}_{(s)} ; \boldsymbol{E}^{\ominus}=\mathbf{0 . 8 0 V} \)
The solubility product of \( A g C l \) under standard conditions of temperature is:
A \( .1 .6 \times 10^{-5} \)
В. \( 1.5 \times 10^{-8} \)
c. \( 3.2 \times 10^{-10} \)
D. \( 1.5 \times 10^{-10} \)


Assertion
Respiratory pathway is considered as an amphibolic pathway.
Reason
It involves both anabolism and
catabolism.
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


Cinnamic acid \( (\boldsymbol{P h}-\boldsymbol{C H}=\boldsymbol{C H}- \)
COOH) is nitrated preferably at
and it is
nitration of benzene.
A. m-position, faster
B. o and p-positions, faster
c. m-position, slower
D. o and p-positions, slower


The isomers which can be inter
converted through rotation around a single bond are:
A. conformers
B. diastereomers
c. enantiomers
D. positional isomers


A ball of mass m collides head on with
another ball at rest. The KE of the
system left is \( 50 \% \). Find the coefficient of restitution.
A \( \cdot \frac{1}{\sqrt{2}} \)
B. \( \frac{\sqrt{2}}{3} \)
\( c \cdot \frac{1}{2} \)
D. zero


If \( \boldsymbol{P}(\boldsymbol{A})=\mathbf{0 . 8} \) and \( \boldsymbol{P}(\boldsymbol{B} \mid \boldsymbol{A})=\mathbf{0 . 4}, \) Find
\( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B}) \)


Find the standard deviation of
\( \mathbf{9}, \mathbf{1 6}, \mathbf{2 3}, \mathbf{3 0}, \mathbf{3 7}, \mathbf{4 4}, \mathbf{5 1} \)


An overhead tank having some water
possesses energy.
A. Kinetic
B. Potential
c. Thermal
D. Electrical


Factors which govern the force experienced by a current carrying conductor placed in a uniform magnetic field depends on
A. strength of the magnetic field in which conductor is placedd
B. strength of current flowing through the conductor.
c. length of conductor.
D. all


If the relative permeability of a medium
is \( \mu_{r} \) and its dielectric constant is \( \varepsilon_{r} \)
then the velocity of light in that medium will be
A \( \cdot \sqrt{\frac{\mu_{r}}{\varepsilon_{r}}} \)
в. \( \frac{1}{\sqrt{\mu_{r} \varepsilon_{r}}} \)
C \( \cdot \sqrt{\mu_{r} \varepsilon_{r} / \mu_{\varepsilon_{0}}} \)
D. \( \sqrt{\mu_{e} \varepsilon_{0} / \mu_{x} \varepsilon_{r}} \)


When \( S O_{2} \) is passed in a solution of
potassium iodate, the oxidation state of iodine changes from:
A . +5 to 0
B. +5 to -1
c. -5 to 0
D. -7 to -1


Charged particle (charge= \( q ; \) mass \( = \)
\( \boldsymbol{m} \) ) is rotating in a circle of radius \( \boldsymbol{R} \)
with uniform speed \( V \), Ratio of its magnetic moment \( (\mu) \) to the angular
momentum \( (L) \) is
\( ^{\mathrm{A}} \cdot \frac{q}{2 m} \)
в. \( \frac{q}{m} \)
c. \( \frac{q}{4 m} \)
D. \( \frac{2 q}{m} \)


Two charges \( q \) and \( -q \) are kept apart.
Then at any point on the perpendicular bisector of line joining the two charges:
A. the electric field strength is zero
B. the electric potential is zero
c. both electric potential and electric field strength are zero
D. both electric potential and electric field strength are non-zero


Calculate the angular velocity and linear velocity of a minute hand of
length \( 10 c m \)


Which of the following is FALSE ?
A. some of the energy produced by the light bulb takes the form of heat
B. the battery is the source of the electrons flowing around the circuit
C. the current entering the light bulb equals the current leaving the light bulb
D. the potential in the wire to the left of the light bulb differs from the potential in the wire to the right of the bulb


An object is acted on by a retarding force of \( 10 N \) and at a particular instant
its kinetic energy is \( 6 J . \) The object will
come to rest after it has travelled a
distance of:
\( A \cdot 3 \)
\( \frac{5}{5} \mathrm{m} \)
в. \( \frac{5}{3} \) m
c. \( 4 \mathrm{m} \)
D. 16


Why is Iymph called as filtered blood?


Three rods of the same mass are placed as shown in the figure. What will be the
coordinate of centre of mass of the
system?
A \( \cdot\left(\frac{a}{2}, \frac{a}{2}\right) \)
в. \( \left(\frac{a}{\sqrt{2}}, \frac{a}{\sqrt{2}}\right) \)
c. \( \frac{2 a}{3}, \frac{2 a}{3} \)
D. \( \left(\frac{a}{3}, \frac{a}{3}\right) \)


The number of significant figures in the
numbers \( 4.8000 \times 10^{4} \) and 48000.50
are respectively
A . 5 and 6
B. 5 and 7
\( c \cdot 2 \) and 7
D. 2 and 6


Calculate \( Q \) value of the following nuclear reaction.
\[
_{13} A l^{27}+_{2} H e^{4} \longrightarrow_{14} S i^{30}+_{1} H^{1}+Q
\]
The exact mass of \( _{13} A l^{27} \) is \( \mathbf{2 6 . 9 8 1 5} \mathbf{a m u},_{\mathbf{1 4}} \mathbf{S i}^{\mathbf{3 0}} \mathbf{i s} \mathbf{2 9 . 9 7 3 8} \boldsymbol{a m u} \)
\( _{2} H e^{4} \) is \( 4.0026 a m u \) and \( _{1} H^{1} \) is
1.0078 amu.


The rate of formation of \( S O_{3} \) in the
following reaction \( 2 S O_{2}+O_{2} \rightarrow 2 S O_{3} \)
is \( 10 g \) sec \( ^{-1} \). The rate of disappearance
of \( \boldsymbol{O}_{2} \) will be:
A. \( 5 g \) sec \( ^{-1} \)
B. \( 100 g \) sec \( ^{-1} \)
\( \mathrm{c} .20 \mathrm{g} \) sec
D. \( 2 g \) sec \( ^{-1} \)


In the following circuit, the \( 1 \Omega \) resistor dissipates power P. If the resistor is
replaced by \( 9 \Omega \), the power dissipated in
it is
\( A \cdot P \)
B. \( 3 P \)
\( c .9 P \)
D. \( P / 3 \)


A rectangular tank of base area \( 100 m^{2} \)
has a height of 2 m. Calculate the
thrust at the bottom of the tank, if it is
filled upto the brim with water of
density \( 10^{3} k g m^{-3} \)


A loop of area \( 1 m^{2} \) is placed in a
magnetic field \( B=2 T \), such that plane
of the loop is parallel to the magnetic
field. If the loop is rotated by \( 180^{\circ}, \) the
amount of net charge passing through any point of loop, if its resistance is
\( 10 \Omega \) is :
A. \( 0.4 C \)
B. \( 0.2 C \)
\( c .0 .8 C \)
D. \( 0 C \)


A plano-convex lens (focal length \( f_{2} \)
refractive index \( \mu_{2} \), radius of curvature
\( R \) ) fits exactly into a plano-concave lens
(focal length \( f_{1} \), refractive index \( \mu_{1} \) radius of curvature \( \boldsymbol{R} \) ). Their plane
surfaces are parallel to each other. Then, the focal length of the combination will be :
A \( . f_{1}-f_{2} \)
в. \( f_{1}+f_{2} \)
c. \( \frac{R}{\mu_{2}-\mu_{1}} \)
D. \( \frac{2 f_{1} f_{2}}{f_{1}+f_{2}} \)


At noon the sun appears white because:
A. light is least scattered.
B. all the colours of the white light are scattered away.
c. blue colour is scattered the most.
D. red colour is scattered the most.


A sulphate of a metal (A) on heating evolves two gases \( (\mathrm{B}) \) and \( (\mathrm{C}) \) and an
oxide (D). Gas
(B) turns \( K_{2} C r_{2} O_{7} \) paper green while gas (C) forms a trimer in which there is no S-S bond.
Compound (D) with conc. HCl forms a Lewis acid
(E) which exists in a dimer. Compounds \( (A),(B),(C),(D) \) and \( (E) \) are respectively:
A. \( F e S O_{4}, S O_{2}, S O_{3}, F e_{2} O_{3}, F e C l_{3} \)
в. \( A l_{2}\left(S O_{4}\right)_{3}, S O_{2}, S O_{3}, A l_{2} O_{3}, F e C l_{3} \)
c. FeS\( , S O_{2}, S O_{3}, F e S O_{4}, F e C l_{3} \)
D. FeS, \( S O_{2}, S O_{3}, F e_{2}\left(P O_{4}\right)_{3}, F e C l_{2} \)


Biomolecules are
A. inorganic materials
B. organic materials
C . all the carbon compounds obtained from living tissues
D. only DNA and RNA


The unit of time period and frequency are, respectively
\( \mathbf{A} \cdot s, H z \)
B. \( H z, s \)
c. \( H z, C \)
D. \( C, N \)


In specific heat of a substance is infinite, it means
A. Heat is given out
B. Heat is taken out
C. No change in temperature takes place whether heat is taken in or given out
D. All of the above


Two particles \( A \) and \( B \) are projected with same speed so that ratio of their
maximum heights reached is \( 3: 1 . \) If
the speed of \( A \) is doubled without
altering other parameters, the ratio of horizontal ranges attained by A and B is?


What is rectification? Explain the working of a fullwave rectifier. Draw necessary circuit diagram.


n figure, \( A B, C D \) and \( E F \) are three
parallel lines. If \( 4 y=5 x \) and \( z=y-30 \)
find \( \angle q \)
\( A \cdot 120 \)
В. \( 110^{\circ} \)
\( c \cdot 100 \)
D. 90


What is \( \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}|\sin x| d x \) equal to \( ? \)
\( A \cdot 2 \)
B. 1
\( c . \pi \)
D.


A rubber cord catapult has crosssection area \( 25 m m^{2} \) and initial length of rubber cord is \( 10 \mathrm{cm} \). It is stretched to
\( 5 c m \) and then released to project a
missile of mass 5gm. Taking, \( \boldsymbol{Y}_{\text {rubber}}= \)
\( 5 \times 10^{8} N / m^{2}, \) velocity of projected
missile is
A \( \cdot 20 m s^{-1} \)
B. \( 100 \mathrm{ms}^{-1} \)
\( \mathbf{c} \cdot 250 m s^{-1} \)
D. \( 200 m s^{-1} \)


Bulliform cells differ from other cells in
being
A. Large, thin-walled, vacuolate containing water
B. Large, thick-walled, contain abundant chloroplasts
c. small, thick-walled, contain starch
D. Small, thin-walled, contain calcium oxalate


Transport of \( C O 2 \) is in the form of
A. Sulphates
B. Phosphates
c. carbonates
D. chloride


If \( \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{1} & -\mathbf{2} \\ \mathbf{3} & \mathbf{0}\end{array}\right], \boldsymbol{B}=\left[\begin{array}{cc}\mathbf{- 1} & \mathbf{4} \\ \mathbf{2} & \mathbf{3}\end{array}\right], \boldsymbol{C}= \)
\( \left[\begin{array}{cc}\mathbf{0} & \mathbf{1} \\ \mathbf{- 1} & \mathbf{0}\end{array}\right], \) then \( \mathbf{5} \boldsymbol{A}-\mathbf{3} \boldsymbol{B}+\mathbf{2} \boldsymbol{C}= \)
\( \mathbf{A} \cdot\left[\begin{array}{cc}8 & 20 \\ 7 & 9\end{array}\right] \)
\( \mathbf{B} \cdot\left[\begin{array}{cc}8 & -20 \\ 7 & -9\end{array}\right] \)
\( \mathbf{c} \cdot\left[\begin{array}{cc}-8 & 20 \\ -7 & 9\end{array}\right] \)
\( \mathbf{D} \cdot\left[\begin{array}{cc}8 & 7 \\ -20 & -9\end{array}\right] \)


Absolute zero is
\( \mathbf{A} \cdot-273^{\circ} C \)
в. \( -273^{\circ} \) F
\( \mathbf{c} \cdot-273^{\circ} K \)
D. None of these


During one dimensional collision or
head on collision:
a) The bodies move along the line
joining their centre of mass before and after collision.
b) The bodies should move in opposite direction.
c) The bodies change their direction after collision.
d) The bodies move along the line joining their centre of mass before and after collision either in same direction
or in opposite direction.
A. Only a is correct
B. Only a \& b are correct
\( c . \) a, b \( \& \mathrm{c} \) are correct
D. Only a and d are correct


Using properties of determinant, prove
the following:
\[
\mid \begin{array}{ccc}
1+a^{2}-b^{2} & 2 a b & -2 b \\
2 a b & 1-a^{2}+b^{2} & 2 a \\
2 b & -2 a & 1-a^{2}-b^{2}
\end{array}
\]
\( \left(1+a^{2}+b^{2}\right)^{3} \)


Equation of one of the sides of an isosceles right angled triangle whose hypotenuse is \( 3 x+4 y=4 \) and the
opposite vertex of the hypotenuse is \( (2,2), \) will be \( ? \)
A. \( x-7 y+12=0 \)
в. \( 7 x+y-12=0 \)
c. \( x-7 y+16=0 \)
D. \( 7 x+y+16=0 \)


Slow oxidation of chloroform in air leads
to the formation of:
A. formyl chloride
B. formic acid
c. \( \operatorname{cocl}_{2} \)
D. trichloro acetic acid


Explain the term :Electroplating.


The second law of refraction is also
named after its discoverer as:
A. Newton's law
B. Faraday's law
c. Snell's law
D. Charles'law


Which of the following is imbibiant?
A. Proteins
B. Pectin
c. starch
D. All of the above


What is the direction of magnetic field at the centre of a coil carrying clockwise current?
A. No direction
B. normal to the axis of coil inwards
c. Along the axis of coil inwards.
D. Along the axis of coil outwards


Which of the following is not a sink for
co?
A. Haemoglobin
B. Microorganims present in the soil
c. oceans
D. None of the above


Which among the following represent chelating ligands?
A \( . S C N^{-} \)
в. \( C N \)
c. 2,2 - dipyridyl
D. \( O H^{-} \)


Four numbers are inserted between the
numbers 4 and 39 such that an \( A P \)
results. Find"the biggest of these four numbers.
A . 33
B. 31
\( c \cdot 32 \)
D. 30


Nitric acid is a:
A. diprotic acid
B. strong acid
C . organic acid
D. both \( A \) and \( C \)


\( C l_{2} \) reacts with excess of ammonia
gives:
A \( . N H_{4} C l \)
в. \( N C l_{3} \)
c. \( N_{2} C l \)
D. none of these


Choose the correct answer from the
alternatives given :
Directions for questions 71 to 75: Study
the following graph carefully to answer
these questions. Production (in lakh tonnes) of six units
of a company in 2006 and 2007

What is the average production of all
units (in lakh tonnes) for the year \( 2007 ? \)
ロ 2006
A . 95
B. 92
\( c .87 \)
D. 93


Differentiate between regular and
diffused reflection. Does diffused
reflection mean the failure of the laws of
reflection?


Select the wrong relation(s).
This question has multiple correct options
\( \Delta S=\left(\frac{\partial E}{\partial T}\right)_{p} \times n F \)
\( \mathbf{B} \cdot-\Delta S=(\partial E \partial T)_{p} \times n F \)
\( \left(\frac{\partial E}{\partial T}\right)_{p}=\left(\frac{\partial \Delta S}{\partial T}\right) \)
\( ^{\mathbf{D}} \cdot\left(\frac{\partial E}{\partial T}\right)_{p}=\frac{\Delta H+n E F}{T} \)


The differential equation whose
solution is \( A x^{2}+B y^{2}=1, \) where \( A \) and
B are arbitrary constants is of
A. second order and second degree
B. first order and second degree
c. first order and first degree
D. second order and first degree


Is zero a rational number? Justify


The Poisson's ratio of a material is \( 0.4 . \) If
a force is applied to a wire of this material, there is a decrease of cross-
sectional area by \( 2 \% . \) The percentage increase in its length is :
A . \( 3 \% \)
в. 2.5\%
c. \( 1 \% \)
D. 0.5\%


A vector is represented by \( 3 \hat{i}+\hat{j}+2 \hat{k} \)
has length in \( X Y \) plane
\( A \cdot 2 \)
B. \( \sqrt{14} \)
c. \( \sqrt{10} \)
D. \( \sqrt{5} \)


Which growth hormone is responsible for apical dominance?
A . Auxin
B. Cytokinin
c. Gibberellin
D. Ethylene


Which one of them is more ionic \( L i C l \) or
\( N a C l ? \)
\( \mathbf{A} \cdot N a C l \)
в. Licl
c. Both are equally ionic
D. Can't say


The value of acceleration due to gravity
is \( 980 \mathrm{cm} s^{-2} \). What will be its value if
the unit of length is kilometer and that
of time is minute?


In an electric field of a point charge \( \boldsymbol{q}, \) a
certain charge is carried from point \( \boldsymbol{A} \)
to \( B, C, D, E . \) Then, the work done
\( A \). is least along path \( A B \)
C. is zero along all paths
D. is least along path \( A E \)


In the figure given, there are two convex
lens \( L_{1} \) and \( L_{2} \) having focal length of \( f_{1} \)
and \( f_{2} \) respectively. The distance
between \( L_{1} \) and \( L_{2} \) will be:
\( A \cdot f_{1} \)
\( \mathbf{B} \cdot f_{2} \)
\( c \cdot f_{1}+f_{2} \)
D. \( f_{1}-f_{2} \)


What is distillation.


The puffed-up appearance of dough is due to fermentation by yeast. Identify the gas liberated during the process
A. Methane
B. Carbon dioxide
c. Hydrogen sulphide
D. Ammonia


Protons and neutrons inside the
nucleus are called


Consider the following equilibrium:
\( \boldsymbol{x}_{2(g)}+\mathbf{2} \boldsymbol{H}_{2(\boldsymbol{g})} \rightarrow \mathbf{2} \boldsymbol{H}_{2} \boldsymbol{X}_{(\boldsymbol{g})}+\boldsymbol{e n e r g y} \)
Addition of \( X_{2} \) to a system described by the above equilibrium will:
A. Increase the equilibrium concentration of \( \left[H_{2}\right] \)
B. Increase the equilibrium concentration of \( \left[H_{2} X\right] \)
C. Decrease the equilibrium concentration of \( \left[H_{2} X\right] \)
D. Have no effect on the equilibrium concentrations
E. Decrease the amount of heat energy given off by the


Polymer formation from monomers
starts by:
A. Condensation reaction between monomers
B. Coordination reaction between monomers
C. Conversion of one monomer into other monomer
D. Hydrolysis of monomers


The blood calcium level is lowered by
the deficiency of
A. Both calcitonin and parathormone
B. Calcitonin
c. Parathormone
D. Thyroxine


The uncharged metallic sphere \( \mathbf{A} \)
suspended as shown in the given figure
is given a push so that it moves towards the +ve plate. Which of the following statements is correct?
A. A touches the positive plate and remains in contact with it
B. A touches positive plate and then moves towards negative plate and remains in contact with it.
C. A moves to and fro between the two plates with a constant time period
D. A moves to and fro between the two plates with an increasing time period.


A horizontal circular loop carries a
current that looks clockwise when
viewed from above. It is placed by an equivalent magnetic dipole consisting
of a south pole \( S \) and a north pole \( N \)
This question has multiple correct options
A. The line \( S N \) should be along a diameter of the loop.
B. The line \( S N \) should be perpendicular to the plane of the loop.
C. The south pole should be below the loop.
D. The north pole should be below the loop.


A molecule of a substance has a
permanent electric dipole moment of magnitude \( 10^{-30} \mathrm{cm} . \) A mole of this substance is polarised by applying a strong electrostatic field of magnitude \( 10^{7} \mathrm{V} m^{-1} \). the direction of the field is
changed by an angle \( 60 . \) The heat released by the substance In aligning its dipole along the new direction of the
field is:
A . - 6 J
B. -3 J
c. 3
\( D .6 \)


Find the value of \( p \) if following function \( \boldsymbol{f}(\boldsymbol{x})= \)
\[
\left\{\begin{array}{ll}
\frac{\sqrt{1+p x}-\sqrt{1-p x}}{x}, & \text { if }-1 \leq x< \\
\frac{2 x+2}{x-2}, & \text { if } 0 \leq x<1
\end{array}\right.
\]
is continuous at \( x=0 \)


Two drops of the same radius are falling through air with a steady velocity of \( 5 \mathrm{cm} \) per sec. If the two drops coalesce, the terminal velocity would be
A. \( 10 \mathrm{cm} \) per sec
B. 2.5 \( \mathrm{cm} \) per sec
c. \( 5 \times(4)^{1 / 3} \) cm per sec
D. \( 5 \sqrt{3} \mathrm{cm} \) per sec


Shown in the figure here is a convergent
lens placed inside a cell filled with a liquid. The lens has focal length +20
\( \mathrm{cm} \) when in air and its material has
refractive index \( 1.50 . \) If the liquid has
refractive index \( 1.60, \) the focal length of
the system is
\( A \cdot+80 \mathrm{cm} \)
B. - 80 cm
C. \( -24 \mathrm{cm} \)
\( D .-100 \mathrm{cm} \)


Tangent to parabola \( \boldsymbol{y}^{2}=\mathbf{4} \boldsymbol{x}+\mathbf{5} \) which
is parallel to \( \boldsymbol{y}=2 \boldsymbol{x}+\mathbf{7} \)
A. \( y-2 x-3=0 \)
В. \( y=x+3 \)
c. \( y-2 x+1=0 \)
D. \( y=x+1 \)


Evaluate the following definite integral:
\( \int_{e}^{e^{2}}\left\{\frac{1}{\log x}-\frac{1}{(\log x)^{2}}\right\} d x \)


If \( E_{e}, E_{\alpha} \) and \( E_{p} \) represents the kinetic energies of an electron, alpha particle and a proton respectively, each moving with same de Broglie wavelength, then:
A \( \cdot E_{e}=E_{\alpha}=E_{p} \)
В . \( E_{e}>E_{p}>E_{\alpha} \)
c. \( E_{\alpha}>E_{p}>E_{e} \)
D. \( E_{e}=E_{p}=E_{\alpha} \)


If \( 13.6 e V \) energy is required to ionize
the hydrogen atom, then the energy required to remove an electron from
\( \boldsymbol{n}=\mathbf{2} \) is
A. \( 10.2 \mathrm{eV} \)
B. 0 eV
c. 3.4 eV
D. 6.8 eV


A bar magnet has coercivity \( 4 \times \) \( 10^{3} A m^{-1} . \) It is placed in a solenoid
having 40 turns per \( \mathrm{cm} \) and is \( 1.2 \mathrm{m} \) long. The current carried by the solenoid to demagnetize the bar magnet is :
\( A \cdot 6 A \)
в. \( 8 A \)
c. \( 5.78 A \)
D. none of these


The halogen which forms maximum number of interhalogen compounds is:
\( \mathbf{A} \cdot F_{2} \)
в. \( C l_{2} \)
c. \( B r_{2} \)
D. \( I_{2} \)


toppr LoGin non
Q Type your question_
bonding.
Sample \( \quad \) Appearance \( \quad \) Melting
\[
\begin{array}{l}\text { Point } \\ \left(^{\circ} C\right)\end{array}
\] and
condu
onduc
aqueo \begin{tabular}{llll}
\( \mathrm{A} \) & Shiny & 962 & \( \mathrm{co} \) \\
\( \mathrm{B} \) & Crystalline & 801 & \( \mathrm{a} \) \\
& & & \( \mathrm{sol} \) \\
\( \mathrm{C} \) & Powdery & 186 & \( \mathrm{not} \) \( \mathrm{co} \) \\
\hline
\end{tabular} onduc
Based on this data, identify the type of bonds present in each sample.
A. Sample A is a metal.
Sample B is a salt.
Sample \( C \) is a molecule
B. Sample A is a molecule
Sample B is a metal.
Sample \( c \) is a salt.
c. Sample A is a salt.
Sample B is a metal.
Sample \( C \) is a molecule.
D. Sample A is a molecule.
\( B \) is a salt
Sample C is a metal.


Sensitivity of potentiometer can be increased by
A. increasing the e.m.f. of the cell.
B. increasing the length of the potentiometer.
c. decreasing the length of the potentiometer wire.
D. none of these.


The amount of energy released in burning \( 1 \mathrm{kg} \) of coal is
\( A .3 M J \)
в. 30 М
c. \( 300 M J \)
D. \( 3000 M J \)


The value of \( G \) for two bodies in vacuum
is \( 6.67 \times 10^{-11} N / m^{2} / K g^{2} . \) Its value in
a dense medium of density
\( 10^{10} g m / c m^{3} \) will be:
A \( .6 .67 \times 10^{-11} N / m^{2} / K g \)
B. \( 6.67 \times 10^{-31} N / m^{2} / K g \)
c. \( 6.67 \times 10^{-21} N / m^{2} / K g \)
D. \( 6.67 \times 10^{-10} N / m^{2} / K g \)


For a reaction \( \boldsymbol{R} \rightarrow \boldsymbol{P} \), the concentration
of a reactant changes from \( 0.05 M \) to
\( 0.04 M \) in 30 minutes. What will be the
average rate of reaction in minutes?
A \( \cdot 4 \times 10^{-4} \mathrm{M} \min ^{-1} \)
В. \( 8 \times 10^{-4} \mathrm{M} \min ^{-1} \)
\( \mathrm{c} \cdot 3.3 \times 10^{-4} \mathrm{M} \min ^{-1} \)
D. 2.2 \( \times 10^{-4} \mathrm{M} \) min\( ^{-1} \)


From below what is used to generate electricity in thermal power plants?
A. Fossil Fuels
B. water
c. solar energy
D. Nuclear energy


By using the properties of definite integrals, evaluate the integral \( \int_{0}^{\frac{\pi}{2}} \cos ^{2} x d x \)


During the phase change, when water
freezes, its converted to ice in which
molecules is in more structured order.
Why doesn't this contradict the Second
Law of Thermodynamics?
A. Because the density of the water is decreasing
B. Because the water is gaining entropy as it goes from liquid to solid state
C. Because the water's internal energy is decreasing
D. Because the surroundings are losing entropy
E. Because the surroundings are gaining entropy


A magnetic needle free to rotate in a vertical plane parallel to the magnetic meridian has its North tip pointing down at \( 22^{0} \) with the horizontal. the
horizontal component of the earth's magnetic field at the place is known to be 0.35 G.The magnitude of the earth's magnetic field at the place will be:-
A . 0.68 G
B. 0.36 G
\( c \cdot 0.83 G \)
D. 0.86 G


If a circuit made up of a resistance \( 1 \Omega \) and inductance \( 0.01 \mathrm{H}, \) and alternating emf \( 200 \mathrm{V} \) at \( 50 \mathrm{H} \) is connected, then
the phase difference between the
current and the emf in the circuit is :


The nucleus of a diploid organism
contains 3 ng of DNA in \( G_{1} \) phase. Which
one of the following statements describes the state of the cell at the end
of S phase?
A. The nucleus divides into two, and each nucleus contains 3 ng of DNA.
B. The nucleus does not divide, and it contains 3 ng of DNA.
c. The nucleus divides into two, and each nucleus contains \( 1.5 \mathrm{ng} \) of DNA
D. The nucleus does not divide, and it contains 6 ng of DNA.


Identify the correct order of reactivity of metals among the following.
A. \( C u<F e<Z n<A l<N a \)
B. \( F e<Z n<C u<N a<A l \)
c. \( Z n<C u<F e<A l<N a \)
D. \( C u<Z n<A l<N a<F e \)
\( e \)


A boy is standing in front of a plane mirror at a distance of \( 3 \mathrm{m} \) from it, if the
boy moves \( 1 \mathrm{m} \) backward, the distance between the image and the boy is
\( A \cdot 2 m \)
B. \( 4 \mathrm{m} \)
\( c \cdot 8 m \)
D. none of these


When hydrogen sulphide is reacted with sulphuric acid, which products are formed?
This question has multiple correct options
A . \( S \)
в. \( S O_{2} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{S}_{2} \mathrm{O} \)
\( \mathrm{D} \cdot \mathrm{SO}_{3} \)


The 5 th term in the expansion of
\( \left(2 x^{2}+\frac{3}{x}\right)^{5} \) is
B. \( 810 . x^{-4} \)
\( c \cdot 810 \)
D. \( 810 . x^{-5} \)


Which is/are the correct statement(s)
regarding the polymer kevlar? This question has multiple correct options
A. It is a polyamide.
B. It is a copolymer.
c. It has elastic property
D. It is an addition polymer.


Figure shows a three arm tube in which
a liquid is filled upto levels of height \( l \). It
is now rotated at an angular frequency
\( \omega \) about an axis passing through arm \( B \)
The angular frequency \( \omega \) at which level
of liquid in arm \( B \) becomes zero.
A \( \cdot \sqrt{\frac{2 g}{5 l}} \)
B. \( \sqrt{\frac{2 g}{l}} \)
\( c \cdot \sqrt{\frac{3 g}{l}} \)
D. None of the above


In the diagram a rat is passing through
a broken prism,find angular deviation
for the ray:
A \( \cdot 105^{\circ} \)
B \( .30^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 15^{\circ} \)


In a smooth stationary cart of length \( d \)
a small block is projected along it's length with velocity v towards front.
Coefficient of restitution for each
collision is e. The cart rests on a smooth
ground and can move freely. The time taken by block to come to rest w,r.t cart
is
\( A \)
B. \( \frac{e d}{(l+e) v} \)
\( c \cdot d \)
D. infinite


The probability of selecting a green marble at random from a jar that
contains only green, white and yellow marbles is \( 0.25 . \) The probability of selecting a white marble at random from the same jar is \( \frac{1}{3} . \) If this jar contains 10 yellow marbles. What is the total number of marbles in the jar?


\( \frac{\sin \theta+\sin 2 \theta}{1+\cos \theta+\cos 2 \theta}=\tan \theta \)


When soap or detergent dissolves in
water, which of the following is true?
A. The polar water soluble ( hydrophilic) head is on the surface of the micelle whereas non polar oil soluble (hydrophobic) tail is in the center of the micelle.
B. The polar water soluble ( hydrophilic) head is in the center of the micelle whereas non polar oil soluble (hydrophobic) tail is on the surface of the micelle
C. The polar water soluble ( hydrophilic) head is in the center of the micelle.
D. Non polar oil soluble (hydrophobic) tail is on the surface of the micelle.


After examining the blood groups of husband and wife, the doctor advised them not to have more than one child.
The blood groups of the couple are likely
to be
A. Male Rh" and female Rh
B. Male Rht and female Rht
C. Female \( \mathrm{Rh}^{-} \) and male \( \mathrm{Rh}^{+} \)
D. Male Rh - and female Rh


For the principal value:
\( \cos ^{-1}\left(\frac{1}{2}\right)-2 \sin ^{-1}\left(-\frac{1}{2}\right) \)


Two metallic oxides contain \( 27.6 \% \) and
\( 30 \% \) oxygen respectively. If the formula
of the first oxide is \( X_{3} O_{4}, \) that of the
second will be ?
A. \( X O \)
B. \( X O_{2} \)
\( \mathrm{c} \cdot \mathrm{X}_{2} \mathrm{O}_{5} \)
D. \( X_{2} O_{3} \)


Hominids evolved during
A. Oligocene
B. Pliocene
c. Pleistocene
D. Miocene


There are two identical small holes on
the opposite sides of a tank containing liquid. The tank is open at the top. The
difference in height between the two
holes is \( h \). As the liquid comes out of the two holes, the tank will experience a net horizontal force proportional to:
A \( \cdot h^{1 / 2} \)
B.
\( c \cdot h^{3 / 2} \)
\( D \cdot h^{2} \)


Rh factor was discovered by
A. Landsteiner and Weiner
B. William Harvey
c. Malpighi
D. None of these


Very short answer type.
Unlike of conventional breeding programme, it is possible to evolve a cytoplasmic hybrid from two different genera using tissue culture.


The solubility of anhydrous \( A l C l_{3} \) and
hydrous \( A l C l_{3} \) in diethyl ether are \( S_{1} \)
and \( S_{2} \) respectively, Then :
в. \( S_{1}>S_{2} \)
c. \( s_{1}<S_{2} \)
D. \( S_{1}<S_{1} \) but not \( S_{1}=S_{2} \)


A unit vector perpendicular to \( \hat{\mathbf{i}}-\mathbf{2} \hat{\mathbf{j}}+ \) \( \hat{k} \) and \( \hat{3} i-\hat{j}+2 \hat{k} \) is
\( \frac{A \hat{i}+3 \hat{j}+7 \hat{k}}{\sqrt{83}} \)
B. \( \frac{-3 \hat{i}+\hat{j}+5 \hat{k}}{\sqrt{35}} \)
c. \( \frac{5 \hat{i}+3 \hat{j}-7 \hat{k}}{\sqrt{83}} \)
D. \( \frac{3 \hat{i}-5 \hat{j}+7 \hat{k}}{\sqrt{83}} \)


Identify the following substances which are underlined:

An alkaline gas which produces dense white fumes when reacted with hydrogen chloride gas.


Which of the following is not a property
of charge?
A. Additivity
B. Quantization
c. continuity
D. conservation


The figure shows the various positions (labelled by subscripts) of small
magnetised needles \( P \) and \( Q \). The arrows
show the direction of their magnetic
movement.configuration corresponds to
the lowest potential energy among all
the configurations shown
A . \( P Q_{3} \)
в. \( P Q_{4} \)
\( c \cdot P Q_{5} \)
D. \( P Q_{6} \)


If the electric field to the right of the two
sheets is \( K \sigma / \varepsilon_{0} . \) Find \( \mathrm{K} ? \)


What are the various constituents of
domestic sewage? Discuss the effect of sewage discharge in a river.


The value of \( f(0), \) so that the function
\( \boldsymbol{f}(\boldsymbol{x})= \)
\( \frac{\sqrt{a^{2}-a x+x^{2}}-\sqrt{a^{2}+a x+x^{2}}}{\sqrt{a+x}-\sqrt{a-x}} \)
becomes continuous for all \( x, \) is given
by
\( \mathbf{A} \cdot a^{3 / 2} \)
B. \( a^{1 / 2} \)
c. \( -a^{1 / 2} \)
D. \( -a^{3 / 2} \)


If \( A \) and \( B \) are two non-empty sets
having n elements in common, then what is the number of common
elements in the sets \( A \times B \) and \( B \times A ? \)
\( A \cdot n \)
B \( \cdot n^{2} \)
\( c \cdot 2 n \)
D. zero


The ratio of masses of two metal
spheres \( A \) and \( B \) is \( 8: 1 . \) If the
temperatures are \( 2000 K \) and \( 1000 K \)
respectively, then the ratio of the rates of their energy emission will be
A . 4:
B. 16:
c. 64:
D. 128:


A block of mass \( m \) slides down the
plane inclined at an angle 60 with an acceleration \( \frac{g}{2} . \) Find the coefficient of kinetic friction?


Choose the correct answer from the
alternatives given. Which among the following does not represent Maxwell's equation?
A \( \cdot \phi \bar{E} \cdot d A=\frac{q}{\varepsilon_{0}} \)
B \( \cdot \phi \bar{B} \cdot \overline{d A}=0 \)
c. \( \phi \bar{E} .-\overline{d l}=\frac{-d B}{d t} \)
D. \( \phi \bar{E} \cdot \overline{d l}=\mu_{0} I_{C}+\mu_{0} \varepsilon_{0} \frac{d \phi E}{d t} \)


The S.D. of scores 1,2,3,4,5 is
A \( \cdot \sqrt{2} \)
B. \( \sqrt{3} \)
\( c \cdot \frac{2}{5} \)
D.


Who wrote the book origin of species?


Which of the following can be used as
dielectric?
This question has multiple correct options
A. Mineral oil
B. Electrets
C. Sulfur hexafluoride
D. None of the above


Which acid is used as table vinegar?
A. Formic acid
B. Acetic acid
c. Picric acid
D. None of these


Cut a transverse section of young stem of a plant from your school garden and observe it under the microscope. How would you ascertain whether it is monocot stem or dicot stem. Give
reasons.


Epoxides are:
A. unsaturated ethers
B. mixed ethers
C . cyclic ethers
D. none of these


The response of human ear to sound in
terms of its shrillness is known as:
A. frequency
B. pitch
c. loudness
D. amplitude


Solve \( \left(-\frac{3}{5}\right)^{-3} \)


Which of the following is expected to have a linear structure?
\( A \cdot S O_{2} \)
в. \( C O_{2} \)
\( \mathrm{c} \cdot \mathrm{CO}_{3}^{2} \)
D. \( S O_{4}^{2-} \)


A parenchymatous cell has 20 units of DNA. It starts to divide mitotically
How many units of DNA would it have during anaphase, and


For the acidification of sodium extract
for testing sulphur by lead acetate test, acetic acid was used in test tube \( A \) and
sulphuric acid was used in test tube B. Which one of them will give the correct
result?
A. Test tube A
B. Test tube B
c. Both of them
D. Neither of them


A particle A having a charge of \( 5.0 \times \)
\( 10^{-} 7 C \) is fixed in a vertical wall. \( A \)
second particle \( B \) of mass 100 g and having equal charge is suspended by a
silk thread of length \( 30 \mathrm{cm} \) above the
particle A. Find the angle of thread with
the vertical when it stays in
equilibrium.


A \( H e^{+} \) ion is in its first excited state.
Its ionization energy is?
A .6 .04 ev
B. 13.60 ev
c. 54.40 ev
D. 48.36 ev


Bioassay of IAA is
A. Avena curvature test
B. Callus test
c. Leaf disc test
D. \( \alpha \) -amylase test


If one root of the equation \( x^{2}+p x+ \)
\( \boldsymbol{q}=\mathbf{0} \) is 3 times the other prove that
\( 3 p^{2}=16 q \)


Assertion
In a triangle \( A B C \) if \( \tan A: \tan B: \)
\( \tan C=1: 2: 3 \) then \( A=45^{\circ} \)
Reason
If \( p: q: r=1: 2: 3 \) then \( p=1 \)
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


If \( 2 \tan \beta+\cot \beta=\tan \alpha, \) prove that
\( \cot \beta=2 \tan (\alpha-\beta) \)


100 g of water at \( 70^{\circ} \mathrm{C} \) is added to 120 g
of water at \( 30^{\circ} C \) contained in a vessel.
The final temperature of mixture is
\( 40^{\circ} \mathrm{C} . \) Calculate the thermal capacity of
the vessel.


Which of the following gas is obtained, when ethylene chloride reacts with alcoholic potash?
A. \( C_{2} H_{4} \)
в. \( C_{2} H_{6} \)
\( \mathbf{c} \cdot C_{2} H_{2} \)
D. \( C_{2} H_{5} C l \)


toppr
Q Type your question
List I
The value of the determinant
A. \( \quad\left|\begin{array}{lll}x+2 & x+3 & x+5 \\ x+4 & x+6 & x+9 \\ x+8 & x+11 & x+15\end{array}\right| \) is
If one of the roots of the
equation
B. \( \left|\begin{array}{ccc}7 & 6 & x^{2}-13 \\ 2 & x^{2}-13 & 2 \\ x^{2}-13 & 3 & 7\end{array}\right|=0 \)
is \( x+2 \), then the sum of all other
five roots is
The value of
C. \( \quad\left|\begin{array}{ccc}\sqrt{6} & 2 i & 3+\sqrt{6} \\ \sqrt{12} & \sqrt{3}+\sqrt{8} i & 3 \sqrt{2}+\sqrt{6} i \\ \sqrt{18} & \sqrt{2}+\sqrt{12} i & \sqrt{27}+2 i\end{array}\right| \)
If \( f(\theta)= \)
D. \( \quad\left|\begin{array}{ccc}\cos ^{2} \theta & \cos \theta \sin \theta & -\sin \theta \\ \cos \theta \sin \theta & \sin ^{2} \theta & \cos \theta \\ \sin \theta & -\cos \theta & 0\end{array}\right| \)
then \( f(\pi / 3) \)
\( \mathbf{A} \cdot A-i v, B-i i i, C-i i, D-i \)
B . \( A-i, B-i i i, C-i i, D-i v \)
c. \( A-i i, B-i i i, C-i v, D-i \)
D. \( A-i i i, B-i v, C-i i, D-i \)


In order to form branching, a saturated organic compound must have a minimum of:
A. four carbon atoms
B. three carbon atoms
c. five carbon atoms
D. any number of carbon atoms


If he has maintained a uniform velocity
for the last \( 50 m \) and he covered that
distance in \( 1 s \) determine the velocity at
the end of \( 350 m \)


\( A B C D \) is a parallelogram whose
diagonals intersects each other at right
angles if the length of the diagonals are
16 centimetre and 12 centimetre find
the length of all sides and its perimeter


If each entry of a data is decreased by 8 what is the change in the arithmetic mean?
A. Remains the same
B. Decreases by 8
C. Increases by 8
D. Can't be determined


Which of the following sets divide by budding?
A. Hydra, Sponges, Paramecium
B. Hydra, Amoeba, Plasmodium
c. Hydra, Cnidarians, Paramecium
D. Cnidarians and Sponges


If in a man, normal glucose conc. increases to \( 190 \mathrm{mg} / 100 \mathrm{ml} \). Which of the following will occur?
A. Extra glucose will get deposited in form of ketone bodies
B. Extra glucose is changed to glycogen and get stored in liver
c. Extra glucose will be excreted by kidney.
D. All of the above


M g of ice at \( 0^{\circ} \mathrm{C} \) is to be converted to
water at \( 0^{\circ} \mathrm{C} \). If \( \mathrm{L} \) is the latent heat of
fusion of ice, the quantity of heat required for the above operation would
be:
A . \( M L \) cal
в. \( \frac{M^{2}}{L} \)
\( ^{\mathrm{c}} \cdot \frac{M}{L} \mathrm{cal} \)
D. none of these


At maturity, the sieve plates become impregnated with
A . Cellulose
B. Pectin
c. suberin
D. Lignin
E. callose


Among the electrolyte
\( N a_{2} S O_{4}, C a C l_{2}, A l_{2}\left(S O_{4}\right)_{3} \) and
\( N H_{4} C l, \) the most effective coagulating
agent for \( \boldsymbol{S b}_{2} \boldsymbol{S}_{3} \) sol 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. \( N H_{4} C l \)


If \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{ll}\frac{\sqrt{1+p x}-\sqrt{1-p x}}{x} & -1 \leq x<0 \\ \frac{2 x+1}{x-2} & 0 \leq x \leq 1\end{array}\right. \)
continuous in the interval \( [-1,1], \) then
\( \boldsymbol{p}= \)
A . -
B. \( \frac{-1}{2} \)
\( c \cdot \frac{1}{2} \)
\( D \)


Why is electrical wiring usually covered with a layer of plastic?
A. To make it strong
B. To help electricity flow in it
c. To make it safe
D. To make it beautiful


What is the molar mass of ammonium
carbonate \( \left(N H_{4}\right)_{2} C O_{3} ? \)
A. \( 48.06 g / \) mol
B. \( 96.11 g / \) mol
c. \( 82.09 g / \) mol
D. \( 78.05 g / \) mol
E . \( 192.2 g / \) mol


A die is thrown once. If \( A \) is the event
"the number appearing is a multiple of
\( 3 " \) and \( B \) is the event "the number
appearing is even" Are the event A and B independent?


Is it possible to have an accelerated motion with a constant speed? Name such type of motion
A. Yes, Uniform Circular Motion
B. Yes, Non-Uniform Circular Motion
c. Yes, Uniform Linear Motion
D. No


The weakest acid among the following
is :
\( \mathbf{A} \cdot \mathbf{H}_{2} \mathbf{S} \mathbf{O}_{4} \)
в. \( \mathrm{H}_{2} \mathrm{SO}_{3} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{SeO}_{4} \)
D. \( \mathrm{H}_{2} \mathrm{SeO}_{3} \)


State true or false:
If angles forming a linear pair are of equal measure, then each of these
angles is of measure \( 90^{\circ} \)
A. True
B. False


Aniline is soluble in which of the
following organic reagents?
A. Benzene
B. Ether
c. Alcohol
D. All of above


The number of turns in th coil of an \( a c \)
generator is 5000 and the area of the
coil is \( 0.25 m^{2} . \) The coil is rotated at the
rate of 100 cycles/s in a magnetic field
of \( 0.2 T . \) The peak value of emf
generated is nearly:
A. \( 786 k V \)
\( V \)
в. \( 440 \mathrm{kV} \)
c. \( 220 k V \)
D. \( 157.1 k V \)


Predict the structure of the following and indicate whether the bond angles are likely to be dissorted from the
theoretical values:
\( \boldsymbol{B} \boldsymbol{C l}_{3} \)


Write down a pair of integers whose
sum is -7
A . -5,-2
в. 5,2
\( c \cdot-1,-6 \)
D. both A and C


State whether given statement is True or False

In order to transmit sound waves, the
medium should possess elasticity and inertia.
A. True
B. False


toppr \( E \)
Q Type your question.
0
\( A \)
\( \begin{array}{lll}A & B & Y \\ 0 & 0 & 1\end{array} \)
010
101
в. \( A B \cdot Y \)
\( 0 \quad 0 \quad 1 \)
0.11
101
c.
\( A B Y \)
00
011
101
110
D. \( A B Y \)
00.1
011


The correct order of bond angles is:
\( \mathbf{A} \cdot H_{2} S<N H_{3}<B F_{3}<S i H_{4} \)
B. \( N H_{3}<H_{2} S<S i H_{4}<B F_{3} \)
\( \mathbf{c} \cdot H_{2} S<N H_{3}<S i H_{4}<B F_{3} \)
\( \mathbf{D} \cdot H_{2} S<S i H_{4}<N H_{3}<B F_{3} \)


f \( \operatorname{cosec} A=2, \) find the value of
\( \frac{1}{\tan A}+\frac{\sin A}{1+\cos A} \)


If \( \vec{a}=x \vec{i}-y \vec{j}, \vec{b}=y \vec{i}+x \vec{j} \) and \( \mid \vec{a} \times \)
\( \vec{b} \mid=5, \) then locus of \( (x, y) \) is
A. Hyperbola
B. Parabola
c. Ellipse
D. Circle


Osmotic pressure of a solution is
A. Greater than pure solvent
B. Less than pure solvent
C . Equal to pure solvent
D. Less than or greater than pure solvent


Consider the diagram given above.
Parts labelled as 'A','B','C', 'D' and 'E'
respectively indicate
A. Illium, femur, tibia, pubis and sacrum
B. Pubis, tibia, femur, ilium and sacrum
C. llium, tibia, femur, pubis and sacrum
D. Pubis, tibia, femur, ilium and ulna
E. Pubis, femur, tibia, ilium and sacrum


The principal value of \( \sin ^{-1}\left\{\sin \frac{5 \pi}{6}\right\} \) is
A \( \cdot \frac{\pi}{6} \)
в. \( \frac{5 \pi}{6} \)
c. \( \frac{7 \pi}{6} \)
D. none of these


A student has obtained a magnified image of a flame on a screen using a
convex lens. To draw the corresponding ray diagram, to show the image formation, which of the following two
rays whose paths after refraction are shown she should select?
A . I and II
B. Il and III
c. III and IV
D. I and III


The positive value of \( \Delta \) S indicates that:
A. the system becomes less disordered
B. the system becomes more disordered
C. the system is in equilibrium position
D. the system tends to reach at equilibrium position.


The value of \( (27 \times 2744)^{\frac{1}{3}} \) is
A . 40
B. 42
c. 22
D. 32


Prove the following \( \left[\begin{array}{llll}1 & 3 & 2 & 0 \\ 4 & 1 & 5 & 9 \\ 3 & 2 & 1 & 3\end{array}\right] \pm \)
\( \left[\begin{array}{cccc}1 & 0 & 5 & 8 \\ 2 & 3 & 5 & 8 \\ 1 & -5 & 2 & 3\end{array}\right] \)
\( =\left[\begin{array}{cccc}2 & 3 & 7 & 8 \\ 6 & 4 & 9 & 14 \\ 4 & -3 & 3 & 6\end{array}\right] \) for plus
\( =\left[\begin{array}{cccc}0 & 3 & -3 & -8 \\ 4 & 2 & 1 & 4 \\ 0 & 7 & -1 & 0\end{array}\right] \) for minus


The input to the digital circuit are as
shown below. The output Y is:
\( \mathbf{A} \cdot A+B+\bar{C} \)
B . \( (A+B) \bar{C} \)
c. \( \bar{A}+\bar{B}+\bar{C} \)
\( \mathbf{D} \cdot \bar{A}+\bar{B}+C \)


Which of the following metal produces
nitrous oxide with dil. \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \)
A . \( F e \)
в. \( Z \) и
c. \( C u \)
D. \( A g \)


Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be defined by \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \frac{\boldsymbol{x}+\mathbf{1}}{\boldsymbol{x}^{2}+\mathbf{2}}, \boldsymbol{x} \in \boldsymbol{R} \).Find \( \boldsymbol{f}(\mathbf{0}) \)


\( \frac{3+2 i \sin \theta}{1-2 i \sin \theta} \) will be purely imaginary, if
\( \boldsymbol{\theta}= \)
A \( \cdot 2 n \pi-\frac{\pi}{3} \)
в. \( n \pi+\frac{\pi}{3} \)
c. \( n \pi-\frac{\pi}{3} \)
D. None of these


Which of the given enzyme is not concerned with the irreversible reaction
of glycolytic pathway?
A. Phosphofructo kinase
B. Hexokinase
c. Triose phosphate mutase
D. Pyruvate kinase


When the muscles of the heart relax
A. Blood flows from lungs into the left auricle
B. Blood is pumped into the right auricle from all over the body
C. Both a and b
D. Blood flows from the left ventricle to the rest of the
body


Which one of the following is true about the p-type and n-type semi-conductor?
A. n-type semi-conductor have holes in majority
B. the concentration of electrons and holes are equal in both n-type and p-type semiconductors.
C. n-type semi-conductors have free electrons in majority
D. p-type semi-conductor has excess negative charge


Two marks on a glass rod \( 10 \mathrm{cm} \) apart are found to increase their distance by
\( 0.08 \mathrm{mm} \) when the rod is heated from \( 0^{\circ} \)
\( \mathrm{C} \) to \( 100^{\circ} \mathrm{C} \). A flask made of the same
glass as that of rod measures a volume
of \( 1000 \mathrm{cc} \) at \( 0^{\circ} \mathrm{C} \). The volume it
measures at \( 100^{\circ} \mathrm{C} \) in cc is
A . 1002.4
B. 1004.2
c. 1006.4
D. 1008.2


From \( 8-y+2 y^{2} \) take away
\( \left(y^{2}-7-2 y\right) \)
A \( \cdot y^{2}+y+15 \)
B. \( 5 y^{2}-1 \)
c. \( 3 y-7 y^{2}+11 \)
D. None of these


The ground state energy of hydrogen
atom is \( -13.6 \mathrm{eV} . \) The energy of second
excited state \( H e^{+} \) ion in eV is:
A . -6.04
B . -27.2
c. -54.4
D. - 3.


f \( 2 x-Y=\left[\begin{array}{ccc}3 & -3 & 0 \\ 3 & 3 & 2\end{array}\right] \) and \( 2 Y+X= \)
\( \left[\begin{array}{ccc}\mathbf{4} & \mathbf{1} & \mathbf{5} \\ -\mathbf{1} & \mathbf{4} & -\mathbf{4}\end{array}\right] \)
then find \( X \) and \( Y \)


The frequency of vibration of the string is given by \( \boldsymbol{v}=\frac{\boldsymbol{p}}{\mathbf{2 l}}\left[\frac{\boldsymbol{F}}{\boldsymbol{m}}\right]^{1 / 2} \)
Here, p is the number of segments in the string and I is the length. The dimensional formula for m will be
\( \mathbf{A} \cdot\left[M^{0} L T^{-1}\right] \)
B \( \cdot\left[M L^{0} T^{-1}\right] \)
\( \mathbf{c} \cdot\left[M L^{-1} T^{0}\right] \)
\( \mathbf{D} \cdot\left[M^{0} L^{0} T^{0}\right] \)


Xenon is a noble gas but it forms
compounds, Why? Draw the structure of any two compounds:


A metal block is experiencing an atmospheric pressure of \( 1 \times 10^{5} N / m^{2} \)
when the same block is placed in a vaccum chamber the fractional change in its volume is (the bulk modulus of
metal is \( \left.1.25 \times 10^{11} N / m^{2}\right) \)
A \( \cdot 4 \times 10^{-7} \)
В. \( 2 \times 10^{-7} \)
c. \( 8 \times 10^{-7} \)
D. \( 1 \times 10^{-7} \)


From a standard deck of cards, one card is drawn. Find the probability that the card is red and a queen
A \( \cdot \frac{1}{2} \)
в. \( \frac{4}{13} \)
c. \( \frac{1}{26} \)
D. \( \frac{12}{13} \)


When a body is undergoing undamped vibration, the physical quantity that remains constant is
A. amplitude
B. velocity
c. acceleration
D. phase


ff \( f(x)\left|\begin{array}{cccc}x & & \cos x & e^{x^{2}} \\ \sin & x & x^{2} & \sec x \\ \tan x & x^{4} & 2 x^{2}\end{array}\right| \) then
\( \int_{-\pi / 2}^{\pi / 2} \boldsymbol{f}(\boldsymbol{x}) \boldsymbol{d} \boldsymbol{x}= \)
A .
B.
\( c \cdot 2 \)
\( D \)


How many spherical lead shots each
\( 4.2 \mathrm{cm} \) in diameter can be obtained
from a rectangular solid (cuboid) of lead with dimensions
\( \left.66 c m, 42 c m, 21 c m . \text { (Take } \pi=\frac{22}{7}\right) \)
A. 1500
B. 1200
c. 1300
D. 1600


In a three-dimensional coordinate
system, P, Q and R are images of a point \( \mathbf{A}(\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}) \) in the \( \boldsymbol{x}-\boldsymbol{y}, \boldsymbol{y}-\boldsymbol{z} \) and \( \boldsymbol{z}-\boldsymbol{x} \)
planes, respectively. If G is the centroid of triangle PQR, then area of triangle AOG is (O is the origin)-
A .
B . \( a^{2}+b^{2}+c^{2} \)
C \( \cdot \frac{2}{3}\left(a^{2}+b^{2}+c^{2}\right) \)
D. None of these.


Which of the following is not a feature of mechanical model of atom?
A. Electrons can have same quantum numbers
B. Orbital quantum numbers tell us what energy level the electron is in
c. Higher orbits have more energy
D. All of the above


Electricity produced by flowing water is called:
A. wind energy farm
B. Nuclear power
c. water power
D. None of these


Probability density functions are always
A. decreasing
B. increasing
c. positive
D. negative


\( ^5 C_{4}=_{-} \)
\( A \cdot 4 \)
B. 5
c. 20
D . 24


Form the differential equation
representing the family of curves \( \boldsymbol{y}= \)
\( \boldsymbol{m} \boldsymbol{x}, \) where \( m \) is arbitrary constant.


Explain why \( H_{2} \) and \( O_{2} \) do not react at
room temperature


Which of the following is widely accepted to respire in absence of oxygen?
A . Yeast
B. Potato
c. chlorella
D. Grass


Which of the following compound contains both ionic and covalent bonds?
\( \mathbf{A} \cdot K C N \)
в. \( N a C l \)
c. \( H C l \)
D. \( A l C l_{3} \)


Two plane mirrors are inclined at angle
\( \boldsymbol{\theta} \boldsymbol{\theta} \) is equal to
A \( \cdot 90^{\circ} \)
B. 60
\( c .45 \)
D. \( 30^{\circ} \)


In the following reaction:
\( \mathbf{3} \boldsymbol{B} \boldsymbol{r}_{2}+\boldsymbol{6} \boldsymbol{C} \boldsymbol{O}_{3}^{2-}+\boldsymbol{3} \boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \mathbf{5} \boldsymbol{B} \boldsymbol{r}^{-}+ \)
\( \boldsymbol{B} \boldsymbol{r} \boldsymbol{O}_{3}^{-}+\boldsymbol{6} \boldsymbol{H} \boldsymbol{C} \boldsymbol{O}_{3}^{-} \)
This question has multiple correct options
A. bromine is oxidised and carbonate is reduced
B. bromine is oxidised
c. bromine is neither oxidised nor reduced
D. bromine is reduced


Which side of the heart (left or right) contains oxygenated blood?


If \( Z_{1}=-1 \) and \( Z_{2}=i, \) then find \( \boldsymbol{A} \boldsymbol{r} \boldsymbol{g}\left(\frac{\boldsymbol{Z}_{1}}{\boldsymbol{Z}_{2}}\right) \)


Treatment with lime remove hardness of
water caused by:
A. \( C a C l_{2} \)
в. \( \mathrm{CaSO}_{4} \)
c. \( \operatorname{Ca}\left(H C O_{3}\right)_{2} \)
D. \( C a C O_{3} \)


State whether the following statement
is true or not:
\( 7-\sqrt{2} \) is irrational.
A. True
B. False


S.I. unit of electrical conductivity is
A. siemen
B. Siemen/metre
c. siemen metre
D. Ohm metre


Match the column.


The shoulder and fore limb are
connected to the heart by
A. Dorsal aorta
B. Subclavian artery
c. oesophageal
D. Occipito-vertebral


If \( P(A)=\frac{7}{13}, P(B)=\frac{9}{13} \) and \( P(A \cap \)
\( B)=\frac{4}{13}, \) find \( P(A / B) \)


The focal length of a lens depends on:
A. color of light
B. radius of curvature of the lens
c. material of the lens
D. all of the above


A ball moving with a speed \( v \) hits a
massive wall and returns with speed \( v \)
The impact lasts for time \( \Delta t, \) then
which of the following are correct:
This question has multiple correct options
A . average force acting on the ball is \( \frac{2 m v}{\Delta t} \)
B. average force acting on the ball is \( \frac{m v}{\Delta t} \)
c. kinetic energy of the ball becomes twice
D. kinetic energy of the ball remains the same


How much positive and negative charge
is there in a cup of water? Take mass of 1 cup of water as 250 g. Mass of \( 6.02 \times 10^{23} \) molecules of water
is 18 g.


On electrolysis of water, oxygen is collected at:
A. cathode
B. anode
c. oxygen is not formed
D. abode


n the circuit shown below emf of each
batter y is 5V; and has an internal
resistance of \( 1.0 \Omega . \) The current in the
circuit \( \left(I_{0}\right) \) and the reading in an ideal
voltmeter (V) are
A \( \cdot I_{0}=1 A, V=0 \)
В . \( I_{0}=5 A, V=0 \)
c. \( I_{0}=1 A, V=1 \)
D . \( I_{0}=5 A . V=1 \)


Photosynthesis is held in the leaf of a plant. In which synthesis organic material called ................ This food
materials are transported by ........... tissue to all parts of the plant.


Find the angular displacement (in rad) of a particle moving on a circle with angular velocity \( (2 \pi) \) rad/s in \( 15 s \)
\( \mathbf{A} \cdot 2 \pi \)
B. \( 30 \pi \)
\( c . \pi \)
D. \( 9 \pi \)


Correct pair of compounds which gives blue colouration/precipitate and white
precipitate, respectively, when their Lassaigne's test is separately done is:
A. \( N H_{2} N H_{2} . H C l \) and \( C l C H_{2} C O O H \)
B. \( N H_{2} C S N H_{2} \) and \( P H C H_{2} C l \)
c. \( N H_{2} N H_{2} C O O H \) and \( N H_{2} C O N H_{2} \)
D.
and


A compound of sodium does not give
\( C O_{2} \) when heated but it gives \( C O_{2} \)
when treated with dilute acids. A
crystalline compound is found to have
37.1\% Na and 14.52\% \( \boldsymbol{H}_{\mathbf{2}} \boldsymbol{O} \). Hence, the
compound is :
A. \( N a H C O_{3} .10 H_{2} O \)
B. \( N a H C O_{3} .5 H_{2} O \)
c. \( N a_{2} C O_{3} .10 H_{2} O \)
D. \( N a_{2} C O_{3} . H_{2} O \)


Why is reflecting type telescope preferred over astronomical?


Four particles of masses \( \mathrm{m}, 2 \mathrm{m}, 3 \mathrm{m} \) and
\( 4 m \) are at the vertices of a
parallelogram in \( x \) y plane with one of the adjacent angle 60 and smaller side
a and larger side 2a. The mass m is at
the origin and mass \( 4 \mathrm{m} \) on the \( \mathrm{x} \) -axis. The centre of mass of the system is
A \( \cdot\left(\frac{33 \mathrm{a}}{20} ; \frac{5 \sqrt{3} \mathrm{a}}{2}\right) \)
B \( \cdot\left(\frac{a}{2} ; \frac{3 a}{2}\right) \)
\( ^{\mathrm{C}}\left(0.95 \mathrm{a} ; \frac{\sqrt{3 \mathrm{a}}}{4}\right) \)
D. \( \left(\frac{\sqrt{3 \mathrm{a}}}{2} ; 0.82 \mathrm{a}\right) \)


What is the product formed when
hydrated \( C a S O_{4} \) is heated to \( 125^{\circ} C \)
instead of \( 200^{\circ} \mathrm{C} ? \)
\( \mathbf{A} \cdot\left(C a S O_{4}\right) \frac{1}{2} H_{2} O \)
в. \( \operatorname{CaSO}_{4} \frac{3}{4} \mathrm{H}_{2} \mathrm{O} \)
\( \mathrm{c} \cdot \mathrm{CaSO}_{4} \)
D. \( C a O+S O_{3} \)


Calculate the entropy change in surrounding when 1.00 mol of \( H_{2} O(l) \) is formed under standard condition
\( \triangle_{f} \boldsymbol{H}^{\ominus}=-\mathbf{2} \mathbf{8 6} \boldsymbol{K} \boldsymbol{J} \boldsymbol{m o l}^{-1} \)


Select a lustrous material out of the
following substances.
Gold, Sand, Silver, Rubber


Glycogen, on hydrolysis, gives:
A . lactose and glucose
B. only glucose
c. glucose and fructose
D. glucose and maltose


find the 7 th term in the expansion of \( \left(4 x-\frac{1}{2 \sqrt{x}}\right)^{13} \)
A \( .439296 x^{7} \)
В. \( 439296 x^{4} \)
c. \( 439396 x^{7} \)
D. \( 43396 x^{4} \)


\( Q \) Type your question
of the following graphs given below
correctly describes the possible motion of the object?
\( A \)
B.
\( c \)
D.


Absolute alcohol can be prepared from
rectified spirit by:
This question has multiple correct options
A. Azeotropic distillation with benzene
B. Fractional distillation
C. Keeping over fresh CaO for few hours and then distilling
D. Distillation under reduced pressure


If for \( \boldsymbol{x} \in\left(\mathbf{0}, \frac{\mathbf{1}}{\mathbf{4}}\right), \) the derivative
\( \tan ^{-1}\left(\frac{6 x \sqrt{x}}{1-9 x^{3}}\right) \) is \( \sqrt{x} . g(x), \) then \( g(x) \)
equals:
A \( \cdot \frac{3}{1+9 x^{3}} \)
в. \( \frac{9}{1+9 x^{3}} \)
c. \( \frac{3 x \sqrt{x}}{1-9 x^{3}} \)
D. \( \frac{3 x}{1-9 x^{3}} \)


State whether the following statements
are true or false.

Carrier proteins are necessary for active transport to occur.
A. True
B. False


An oxide of iodine \( (I=127) \) contains
\( 25.4 \mathrm{g} \) of iodine for \( 8 \mathrm{g} \) of oxygen. Its formula will be :
A \( \cdot I_{2} O_{3} \)
B. \( I_{2} O \)
\( \mathrm{c} \cdot I_{2} O_{5} \)
D. \( I_{2} O_{7} \)


Which types of molecules form micelle?
A. non polar molecules
B. polar molecules
c. sufactant molecules
D. Any of the above


Find the derivate of \( e^{\sqrt{2 x+1}} \) with respect
to \( x \) at \( x=12 \)


In a transformer the output current and
voltage are \( 4 \mathrm{A} \) and \( 20 \mathrm{V} \) respectively. If the ratio of number of turns in the
primary and secondary coil is 2: 1 respectively, what is the input current and voltage ?
\( A \cdot 2 A \) and 40
B. 1 A and 20
c. 4 A and \( 10 v \)
D. 8 A and 40 v


The power (P) of a wave, whose amplitude (A) and area of cross section
of the medium is \( \mathrm{S} \), is related to its time period (T) by:
A \( \cdot P / T^{2}= \) constant
B. \( P T^{2}= \) constant
c. \( P T= \) constant
D. \( P / T= \) constant


Proteinaceous nature of enzyme was
suggested by
A. T. cech
B. Kuhne
c. E. Buchner
D. Northrop


The atomic weight of zinc is \( 65.4 . \) The volume of dry hydrogen at NTP liberated by treating \( 6.54 g \) of zinc with dilute sulphuric acid would be:
A . 22.4 litres
B. 11.2 litres
c. 2.24 litres
D. 1.12 litres


Simplify: \( \frac{\boldsymbol{f}^{2}}{\boldsymbol{g}}-\boldsymbol{f} \)
A. \( \frac{f}{g}(f+g) \)
в. \( f\left(\frac{f}{g}+f\right) \)
c. \( \quad f^{2}\left(\frac{1}{g}-\frac{1}{f}\right) \)
D. \( f^{2}\left(\frac{1}{g}+1\right) \)


Differentiate the following functions
with respect to \( \boldsymbol{x} \) \( \tan ^{-1}\left\{\frac{\cos x+\sin x}{\cos x-\sin x}\right\},-\frac{\pi}{4}<x<\frac{\pi}{4} \)


toppr
Q Type your question
would be:-
\begin{tabular}{|l|l|}
\hline & \\
\hline & \\
\hline
\end{tabular}
\( A \)
\begin{tabular}{|l|l|}
\hline\( \uparrow \) & \\
\hline \\
\hline
\end{tabular}
\( B \)
\begin{tabular}{|c|c|}
\hline & \\
\hline & \\
\hline
\end{tabular}
\( c \)
\begin{tabular}{|c|c|}
\hline 0 & \\
\hline & \( \downarrow \) \\
\hline
\end{tabular}
\( D \)
\begin{tabular}{|c|c|}
\hline & \\
\hline & \\
\hline
\end{tabular}


Write constant term
\( x^{2} y+x y^{2}+5 x y-4 \)


Ammonia is used as refrigerating agent. Why?


If \( f(x) \) is a differentiable function in the
interval \( (0, \infty) \) such that \( f(1)= \) 1 \( \operatorname{and} \lim _{t \rightarrow x} \frac{t^{2} f(x)-x^{2} f(t)}{t-x}=1, \) for eacch
\( \boldsymbol{x}>0, \) then \( \boldsymbol{f}(\mathbf{3} / 2) \) is equal to:
\( \mathbf{A} \cdot \frac{13}{6} \)
B . \( \frac{23}{18} \)
c. \( \frac{25}{9} \)
D. \( \frac{31}{18} \)


\( \begin{array}{cccc}\boldsymbol{H} & \boldsymbol{H} & & \boldsymbol{H} & \boldsymbol{H} \\ \boldsymbol{C} & = & \boldsymbol{C} & +\boldsymbol{H}-\boldsymbol{H} \rightarrow \boldsymbol{H}- & \boldsymbol{C} & -\boldsymbol{C}-\boldsymbol{H} \\ \boldsymbol{H} & \boldsymbol{H} & & \boldsymbol{H} & \boldsymbol{H}\end{array} \)
From the following bond energies:
\( \boldsymbol{H}-\boldsymbol{H} \) bond energy: \( \mathbf{4 3 1 . 3 7 k J} \quad \boldsymbol{m o l}^{-1} \)
\( C=C \) bond energy:
606.10 \( k J \quad \) mol \( ^{-1} \)
\( \boldsymbol{C}-\boldsymbol{C} \) bond energy: \( \mathbf{3 3 6 . 4 9 k J} \quad \boldsymbol{m o l}^{-1} \)
\( C-H \) bond energy: \( 410.50 k J \quad m o l^{-1} \)
Enthalpy for the reaction will be:
\( \begin{array}{ll}\text { A } . & 553.0 k J\end{array} \quad \) mol \( ^{-1} \)
B. 1523.6kJ mol"
C . \( -243.6 k J \quad \) mol \( ^{-1} \)
D. \( -120.0 k J \quad \) mol \( ^{-1} \)


Write any four differences between
step-up and step-down transformer


An equation for the line that passes
through (10,-1) and is perpendicular to \( y=\frac{x^{2}}{4}-2 \) is
A. \( 4 x+y=39 \)
в. \( 2 x+y=19 \)
c. \( x+y=9 \)
D. \( x+2 y=8 \)


Isotopes of an element differ in the.
A. atomic number
B. Number of nucleons
C. Number of neutrons
D. Mass number


Motion of artificial earth satellites
around the earth is powered by
A . Liquid fuel
B. Solar batteries
C. Atomic energy
D. None of the above


Decline in the activity of the enzyme hexokinase by Glucose-6-phosphate is caused by
A. Non-competitive
B. competitive modulators
c. Allosteric modulators
D. Denaturation of enzymes
E. Increased by substrate concentration


Which one is not a free-living Protozoa?
A. Amoeba
B. Euglena
c. Giardia
D. Noctiluca


A vessel of volume 4 litres contains a
mixture of \( 8 ~ g \) of \( 0_{2}, 14 \) g of \( \mathrm{N}_{2} \) and \( 22 \mathrm{g} \)
of \( \mathrm{CO}_{2} \) at \( 27^{\circ} \mathrm{C} \). The pressure exerted by the mixture is
A \( \cdot 5 \times 10^{6} N / m^{2} \)
B . \( 6 \times 10^{3} N / m^{2} \)
c. 10 atmosphere
D. \( 7.79 \times 10^{5} N / m^{2} \)


Androgens are secreted from
A. Ovary and placenta
B. Testis and adrenal
C. Ovary and testes
D. Thymus and parathyroid


Which of the following group organisms show the presence of pharyngeal slits at some point of their development?
A. Arthropoda
B. Bryozoa
c. chordata
D. Cnidaria
E. Mollusca


Which of the following statements is correct regarding actinides?
A. All are synthetic elements
B. Include element 104
c. Have only short lived isotopes
D. Have variable valency


In electrolysis of sodium hydroxide solution:
A. hydrogen is discharged at cathode.
B. hydrogen is discharged at anode
c. sodium is liberated at anode
D. no hydrogen is liberated


Find \( A B \)
\( \mathbf{A} \)
3
\( c \)
\( D \)


The anodic half-cell of lead-acid battery
is recharged unsing electricity of 0.05
Faraday. The amount of \( P b S O_{4} \)
electrolyzed in g during the process is :
(Molar mass of \( \boldsymbol{P b S O}_{4}=\mathbf{3 0 3 g m o l}^{-1} \) )
A . 22.8
B. 15.2
\( c .7 .6 \)
D. 11.4


The splash of sound was heard 6 s after
dropping a stone into a well \( 125 \mathrm{m} \) deep. The velocity of sound is:
A. \( 350 \mathrm{cm} / \mathrm{s} \)
B. \( 125 \mathrm{m} / \mathrm{s} \)
\( \mathbf{c} \cdot 392 \mathrm{cm} / \mathrm{s} \)
D. \( 0 \mathrm{cm} / \mathrm{s} \)


Find the angle between the vectors \( \hat{i}- \) \( 2 \widehat{j}+3 \widehat{k} \) and \( 3 \hat{i}-2 \widehat{j}+\widehat{k} \)


The ratio of magnetic moments of Fe(III) and Co(III) is:
A. \( \sqrt{5}: \sqrt{7} \)
B. \( \sqrt{35}: \sqrt{24} \)
c. 7: 3
D. \( \sqrt{24}: \sqrt{15} \)


The thermo-chemical equation for solid and liquid rocket fuel are given below:
\( \mathbf{2} A l(s)+\mathbf{1} \frac{1}{2} O_{2}(g) \longrightarrow \)
\( \boldsymbol{A l}_{2} \boldsymbol{O}_{3}(\boldsymbol{s}), \boldsymbol{\Delta} \boldsymbol{H}=-\mathbf{1 6 6 7} . \boldsymbol{8 k} \boldsymbol{J} \)
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\frac{1}{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \longrightarrow \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}), \boldsymbol{\Delta} \boldsymbol{H}= \)
\( -285.9 k J \)
Then, \( \Delta H \) for the reaction:
\( A l_{2} O_{3}(s) \longrightarrow 2 A l(s)+1 \frac{1}{2} O_{2}(g) \) is :
A. \( 1667.8 \mathrm{kJmol}^{-1} \)
B. \( 1222.3 \mathrm{kJmol}^{-1} \)
c. \( 1458.2 \mathrm{kJmol}^{-1} \)
D. \( 1785.3 \mathrm{kJmol}^{-1} \)


divided into three parts \( A, B \) and \( C \) Piston I and II are connected by a rigid rod and can move without friction
inside the cylinder. Piston I is perfectly conducting while piston II is perfectly insulating. The initial state of \( \operatorname{gas}(\gamma= \)
1.5) present in each compartment \( \mathbf{A}, \mathbf{B} \)
and \( C \) is as shown. Now, compartment \( A \)
is slowly given heat through a heater \( H \) such that the final volume of \( C \) becomes \( \frac{4 V_{0}}{9} . \) Assume the gas to be ideal and find the heat supplied by the heater.
A \( .18 P_{o} V_{o} \)
B. \( 12 P_{o} V_{o} \)
\( \mathrm{c} \cdot 9 P_{o} V_{o} \)
D. \( 25 P_{o} V_{o} \)


The value of
\( \mathbf{1 0 1} \lim _{n \rightarrow \infty}\left(\frac{\mathbf{1}+\mathbf{2}^{100}+\ldots+\boldsymbol{n}^{100}}{\mathbf{n}^{101}}\right) \)
\( A \cdot 2 \)
B.
\( c \cdot 6 \)
\( D \)


Which of the following statement is not
correct about two parallel conductors
carrying equal currents in the same
direction?
A. each of the conductors will experience a force
B. the two conductors will repel each other
C. there are concentric lines of force around each
conductor
D. each of the conductors will move if not prevented from doing so


Draw the graph for the variation of
resistivity of a conductor with
temperature.


The \( G . M . \) of the numbers
\( \mathbf{3}, \mathbf{3}^{2}, \mathbf{3}^{3}, \dots, \mathbf{3}^{n} \) is
A \( \cdot \frac{2}{n} \)
в. \( \frac{n-1}{2} \)
c. \( \frac{n}{3} \)
D. \( \frac{n+1}{2} \)


A man cannot see distinctly less than \( 15 c m \) and more than \( 100 c m . \) He uses a
concave lens of focal length \( -100 \mathrm{cm} \) to see the distant objects clearly. What will be his new near point?
\( \mathbf{A} \cdot 25 \mathrm{cm} \)
в. \( 17.64 m \)
c. 21.64
D. \( 25.74 \mathrm{cm} \)


If \( p \rightarrow(q \vee r) \) is false, then the truth
values of \( p, q, r \) are respectively
\( \mathbf{A} \cdot \mathbf{T}, \mathbf{F}, \mathbf{F} \)
B. F, F, F
c. F, T, T
D. Т, т, \( F \)


ff \( \boldsymbol{f}:[\mathbf{0}, \boldsymbol{\Pi}] \rightarrow[-\mathbf{1}, \mathbf{1}], \mathbf{f}(\mathbf{x})=\cos \mathbf{x}, \) then
is.
\( A \cdot \) one-one
B. onto
c. one-one onto
D. none of these


Write the \( n^{t h} \) term \( a_{n} \) of the \( A P \) with
first term \( a \) and common difference \( d \)


The world's first fully synthetic plastic
was:
A. Polystyrene
B. Nylon
c. Bakelite
D. Teflon


Write the inclination of a line which is
parallel to x-axis.


Find the coordinates of the point of trisection of the line segment joining (1,-2) and (-3,4)


The standard fixed point for temperature measurement is used
these days is :
A. melting point of ice at S.T.P.
B. that temperature at which ice, water and water vapour coexist
c. that temperature at which pure ice and pure water coexist
D. none of the above


There are two wires of same material
and same length while the diameter of second wire is two times the diameter
of first wire, then the ratio of extension
produced in the wires by applying same load will be
A . 1: 1
B . 2: 1
c. 1: 2
D. 4: 1


Choose the correct answer from the
alternatives given
When carbon dioxide binds to
haemoglobin, which of the following compounds is formed?
A. Carbonic acid
B. Hydrogencarbonate ions
c. Oxyhaemoglobin
D. Carbaminohaemoglobin


A boat travels from south bank to north
bank of a with a maximum speed of 8
km/h. To arrive at a opposite to the point of start, the boat should start angle :
\( \mathbf{A} \cdot \tan ^{-1}(1 / 2) W \) of \( \mathrm{N} \)
B. \( \tan ^{-1}(1 / 2) N \) of \( w \)
c. \( 30^{\circ} \mathrm{WofN} \)
D. \( 30^{\circ} \) Nof \( W \)


If \( \boldsymbol{A}=\left(\begin{array}{ll}\mathbf{3} & \mathbf{5} \\ \mathbf{7} & \mathbf{9}\end{array}\right) \) is written as \( \boldsymbol{A}=\boldsymbol{P}+\boldsymbol{Q} \)
where \( \boldsymbol{P} \) is a symmetric matrix and \( \boldsymbol{Q} \) is skew-symmetric matrix, then write the \( \operatorname{matrix} \boldsymbol{P} \)


Evaluate the following limits. \( \lim _{x \rightarrow 1} \frac{1-x^{-1 / 3}}{1-x^{-2 / 3}} \)


If Aufbau rule is not followed, \( \boldsymbol{K}-\mathbf{1 9} \)
will be placed in block.
A . \( s \)
B . \( p \)
\( c \cdot d \)
D. \( f \)


Which of the following statement
regarding \( C_{4} \) plants is false?
A. The primary \( C O_{2} \) acceptor is a 5 carbon molecule.
B. The initial carboxylation reaction occurs in mesophyll.
C . The leaves that fix \( C O_{2} \) have two cell types.
D. The chloroplasts are dimorphic.
E. The Calvin pathway does not take place in the mesophyll cells but does so only in the bundle sheath cells.


If the points \( (a, 0),(0, b), \) and (1,1) are
collinear then
A \( \cdot \frac{1}{a}+\frac{1}{b}=1 \)
B. \( a+b=1 \)
\( c \cdot a+b=2 \)
D. \( \frac{1}{a}-\frac{1}{b}=1 \)


Assertion
Use of aspartame is limited to cold foods and soft drinks
Reason
Aspartame is roughly 100 times as
sweet as cane sugar.
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


For an ideal binary liquid solution with \( \boldsymbol{p}_{\boldsymbol{x}}^{0}>\boldsymbol{p}_{\boldsymbol{y}}^{0} \) in which relation between \( \boldsymbol{X}_{\boldsymbol{x}} \)
(mole fraction of \( x \) in liquid phase) and
\( Y_{x} \) (mole of fraction of \( x \) in vapour
phase) is correct where \( \boldsymbol{X}_{\boldsymbol{y}} \) and \( \boldsymbol{Y}_{\boldsymbol{y}} \) are mole fraction of \( y \) in liquid and vapour phase respectively.
A \( \cdot X_{x}>Y_{x} \)
в. \( X_{x}=Y_{x} \)
с. \( \frac{X_{x}}{X_{y}}<\frac{Y_{x}}{Y_{y}} \)
D. \( X_{x}, Y_{x}, X_{y} \) and \( Y_{y} \) cannot be correlated


The soil which is transported by force of gravity is known as
A . Colluvial
B. Eolian
c. Alluvial
D. Glacial soil


The correct order of decreasing \( \boldsymbol{H}- \)
\( C-H \) angle in the following molecule
is
A. \( |>||>||| \)
B. \( \|>|>||| \)
C. \( \|\mid>\|>1 \)
D. \( |>|||>|| \)


The unified atomic mass unit is the
standard unit that is used for
indicating mass on an atomic or molecular scale. If true enter 1 , else
enter 0


The cells used in a wrist watch undergo:
A. physical change
B. periodic change
c. chemical change
D. none of the above


Which of the following is the
enantiomer of the following substance?
A. It does not have a non-superposable enantiomer
B.
\( c \cdot \| \)
D. III


Find the order and degree of \( [1+ \) \( \left.\boldsymbol{y}^{\prime}^{2}\right]^{1 / 2}=\boldsymbol{x}^{2}+\boldsymbol{y} \)
A . 1,2
в. 2,1
c. 1,1
D. 2,2


If the letters of the word "VARUN" are
written in all possible ways and then are arranged as in a dictionary, then the rank of the word VARUN is?
A . 98
B. 99
\( c \cdot 100 \)
D. 101


Find \( \int \frac{x+1}{(x+2)(x+3)} d x \)


f \( \vec{a}=\vec{b}+\vec{c}, \) then is true that \( |\vec{a}|=|\vec{b}|+ \)
\( |\vec{c}| \) ? Justify your answer.


\( 10 \mathrm{ml} \) of \( \mathrm{KMnO}_{4} \) Solution is required it completely oxidise acidic solution of 30
\( \mathrm{ml} \) of 1.5 Volume strength \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \)
Calculate normality of \( K M n O_{4} \) Solution:
A. 0.4
B. 0.65
\( c \cdot 0.8 \)
D. 0.19


Solve for \( \boldsymbol{a}: \boldsymbol{4} \boldsymbol{a}-\boldsymbol{9}>\boldsymbol{9} \boldsymbol{a}-\boldsymbol{2} \boldsymbol{4} \)
\( \mathbf{A} \cdot a>3 \)
B. \( a<3 \)
c. \( a<-3 \)
D. \( a<9 \)


Chemical composition of a cell's
components approx. \% dry weight
A. Carbohydrate, protein, fat, and nucleic acid
B. Protein, fats, nucleic acid and carbohydrate
C. Protein, fats, carbohydrates and nucleic acid.
D. Carbohydrate, fats, proteins and nucleic acid


Assertion
Sound waves do not travel through
vacuum
Reason
Sound waves are mechanical waves,
which require a medium for their
propagation
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


Exactly \( 100 \mathrm{m} L \) of oxygen is collected
over the water of \( 23^{\circ} \mathrm{C} \) and \( 800 \mathrm{mm} \)
pressure. Calculate the approximate value of the volume of dry oxygen at NTP. (as nearest integer)
[Vapour pressure of water at \( 23^{\circ} \mathrm{C} \) is 21
\( m m \)


Find the volume of a sphere whose
radius is
\( \mathbf{0 . 6 3} \boldsymbol{m} \)


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


A certain alkaloid has \( 70.8 \% \) carbon, 6.2
\( \% \) hydrogen, \( 4.1 \% \) nitrogen and the rest oxygen.What is its empirical formula?
в. \( C_{20} \) Ноо \( \mathrm{NO}_{4} \)
c. \( C_{21} H_{20} N O_{3} \)
D. \( C_{20} \mathrm{H}_{19} \mathrm{NO}_{3} \)


What is the current in branch \( A B \) of the
circuit shown?
A . \( 1.5 A \)
в. \( 2 A \)
c. \( 1.33 A \)
D


The standard reduction potential of
\( E_{B i^{3+} / B i}^{o} \) and \( E_{C u^{2+} / C u}^{o} \) are \( 0.226 \mathrm{V} \) and
\( 0.344 \mathrm{V} \) respectively. A mixture of salts of Bi and Cu at unit concentration each
is electrolysed at \( 25^{\circ} \mathrm{C} \). To what value
\( \operatorname{can}\left[C u^{2+}\right] \) be brought down before
bismuth starts to deposit during electrolysis?
В. \( 10^{-3} M \)
\( \mathbf{c} \cdot 10^{-5} M \)
D. \( 10^{-6} M \)


The value of equilibrium constant \( \left(\boldsymbol{K}_{\boldsymbol{f}}\right) \)
for the reaction: \( Z n^{2+}(a q)+ \)
\[
4 O H^{-}(a q) \rightleftharpoons Z n(O H)_{4}^{2-}(a q) \text { is }
\]
represented in scientific notation as
\( \boldsymbol{p} \times \mathbf{1 0}^{\boldsymbol{q}}, \) then q is:
Given \( : Z n^{2+}(a q)+2 e^{-} \rightarrow \)
\[
\begin{array}{c}
\operatorname{Zn}(s) ; \boldsymbol{E}^{0}=-\mathbf{0 . 7 6} \boldsymbol{V} \\
\boldsymbol{Z n}(\boldsymbol{O H})_{4}^{2-}(\boldsymbol{a q})+\boldsymbol{2 e}^{-} \rightarrow \\
\boldsymbol{Z n}(\boldsymbol{s})+\boldsymbol{4 O H}^{-}(\boldsymbol{a q}) ; \boldsymbol{E}^{0}=-\mathbf{1 . 3 6} \boldsymbol{V} \\
\boldsymbol{2 . 3 0 3} \frac{\boldsymbol{R T}}{\boldsymbol{F}}=\mathbf{0 . 0 6}
\end{array}
\]
A . 20
B. 10
c. 15
D. 21


A bar magnet moves toward two
identical parallel circular loops with a
constant velocity \( v \) as shown in figure
This question has multiple correct options
A. Both the loops will attract each other
B. Both the loops will repel each other
C. The induced current in \( A \) is more than that in \( B \)
D. The induced current is same in both the loops
E. answer required


The difference of the squares of two
consecutive odd integers is divisible by which of the following integers?
\( A \cdot 3 \)
B. 6
\( c \cdot 7 \)
D. 8


nitrobenzene is most reactive towards
nucleophilic aromatic substitution?
\( A \)
B.
\( c \)
D.


On the basis of Werner's theory explain,
why cobalt amine complex,
\( \mathrm{CoCl}_{3} 4 \mathrm{NH}_{3} \) when treated with
\( A g N O_{3} \) solution precipitates only one
\( C l^{-} \) ion even though there are three
\( C l^{-} \) ions?


An example of vat dye is:
This question has multiple correct options
A. indigo
B. alizarin
C. malachite green
D. martius yellow


The relation between \( U, p \) and \( V \) for an ideal gas in an adiabatic process is given by relation \( U=a+b p V \). Find the value of adiabatic exponent \( \gamma \) of this
gas.
A \( \frac{b+1}{b} \)
в. \( \frac{b+1}{a} \)
c. \( \frac{a+1}{b} \)
D. \( \frac{a}{a+b} \)


Systema Naturae' was written by
A. Lamarck
B. Cuvier
C. Aristotle
D. Linnaeus


After what time will he be able to
overtake the bus?
A. 4 sec
B. 8 sec
c. 12 sec
D. 16 sec


Find the cube root of each of the
following numbers by prime Factorization method:
(i) 729
(ii) 343
(iii) \( 512(\text { iv ) } 0.064 \)
\( \mathbf{0 . 2 1 6} \)
\( (v i) 5 \frac{23}{64}(v i i)-1.331(v i i i) \)
-27000


If \( z=(\sqrt{3}+i) \) then find \( \operatorname{Re}(z) \) and
\( \operatorname{lm}(z) \)


Five point charges, each of value \( +q \) are placed on five vertices of a regular hexagon of side L. What is the magnitude of the force on a point charge of value -q placed at the centre of the hexagon?


An atom with atomic number 21
belongs to the category of:
A. \( s \) -block elements
B. \( p \) -block elements
c. \( d \) -block elements
D. \( f \) -block elements


Compute the total energy in the circuit
at \( t=2.00 m s \)
A \( .2 .5625 \mu J \)
B . \( 4.5625 \mu J \)
\( \mathbf{c} .6 .5625 \mu J \)
D. \( 8.5625 \mu J \)


In a compound microscope, the focal lengths of two lenses are \( 1.5 \mathrm{cm} \) and 6.25 \( \mathrm{cm} . \) If an object placed at \( 2 \mathrm{cm} \) from objective and the final image is formed at 25 from eye lens, the distance
between the two lenses is
A \( .6 .00 \mathrm{cm} \)
B. \( 7.75 \mathrm{cm} \)
\( \mathrm{c} .9 .25 \mathrm{cm} \)
D. \( 11.0 \mathrm{cm} \)


If 'N' is the number of turns in a circular
coil then the value of self inductance
varies as
A . \( N^{0} \)
B.
c. \( N^{2} \)
D. \( N^{-2} \)


Correct sequence of layers of bacterial
cell envelope from outward to inward is
A. Cell wall \( \rightarrow \) Glycocalyx \( \rightarrow \) Cell membrane
B. Cell membrane \( \rightarrow \) Glycocalyx \( \rightarrow \) Cell wall
c. Glycocalyx \( \rightarrow \) Cellwall \( \rightarrow \) Cell membrane
D. Glycocalyx \( \rightarrow \) Cell membrane \( \rightarrow \) Cell wall


ff \( y=y(x) \) satisfies the differential
equation
\[
\begin{array}{c}
\mathbf{8} \sqrt{\boldsymbol{x}}(\sqrt{\mathbf{9}+\sqrt{\boldsymbol{x}}}) \boldsymbol{d} \boldsymbol{y}= \\
(\sqrt{4+\sqrt{\mathbf{9}+\sqrt{\boldsymbol{x}}}})^{-1} \boldsymbol{d} \boldsymbol{x}, \boldsymbol{x}>\mathbf{0} \text { and } \\
\boldsymbol{y}(\mathbf{0})=\sqrt{\mathbf{7}}, \text { then } \boldsymbol{y}(\mathbf{2 5 6})_{---}
\end{array}
\]
A . 16
B. 80
\( c .3 \)
\( D \)


Which one of the following helps in
transportation of \( \boldsymbol{C O}_{2} \) ?
A. Acetylcholinesterase
B. Transferase
c. Transacetylase
D. Carbonic anhydrase


\( f(\vec{a}, \vec{b}, \vec{c} \) are unit vectors such that \( \vec{a}+\vec{b}+\vec{c}=0, \) find the value of \( \vec{a} \cdot \vec{b}+\vec{b} \cdot \vec{c}+\vec{c} \cdot \vec{a} \)


Verify whether the function \( \boldsymbol{f}: \mathrm{AB} \) where \( \boldsymbol{A}=\boldsymbol{R}-\{\mathbf{3}\} \) and \( \boldsymbol{B}= \)
\( \boldsymbol{R}-\{1\}, \) defined by \( \boldsymbol{f}(\boldsymbol{x})=\frac{\boldsymbol{x}-\boldsymbol{2}}{\boldsymbol{x}-\boldsymbol{3}} \) is
one-one and on-to or not. Give reason.


The value of \( \cos ^{-1}\left(\cos \frac{5 \pi}{4}\right) \) is?
A \( \cdot \frac{-3 \pi}{4} \)
в. \( \frac{3 \pi}{4} \)
c. \( \frac{-5 \pi}{4} \)
D. \( \frac{5 \pi}{4} \)


Radius of 1st orbit of \( \boldsymbol{H} \) \& some orbit of
\( B e^{3+} \) is same. Energy of their orbit of
\( B e^{3+} \) is :
\( \mathbf{A} \cdot-54.4 e V \)
B. \( -13.6 e V \)
c. \( -108.8 e V \)
D. \( -27.2 e V \)


Calculate the standard deviation of the
following data:
18 \( \quad \) 23 \( \begin{array}{lllll}x & 3 & 8 & 13 & 18\end{array} \) A a \( f \quad \) 7 \( \quad 10 \quad \) 15 \( \quad 10 \quad 8 \)


is a device which is
based on multiple reflection and isused for sending amplified sound in a particular direction
\( A \). Bulb horn
B. Megaphone
c. Ear trumpet
D. al


If the tangent \( P Q \) and \( P R \) are drawn to
the circle \( x^{2}+y^{2}=a^{2} \) from the point
\( P\left(x_{1}, y_{1}\right), \) then the equation of the
circumcircle of \( \triangle \boldsymbol{P Q R} \) is
A \( \cdot x^{2}+y^{2}-x x_{1}-y y_{1}=0 \)
B . \( x^{2}+y^{2}+x x_{1}+y y_{1}=0 \)
c. \( x^{2}+y^{2}-2 x x_{1}-2 y y_{1}=0 \)
D. None of these


Find the cube of \( :\left(2 a+\frac{1}{2 a}\right) ; a \neq 0 \)
A \( \cdot 8 a^{3}+6 a+\frac{3}{2 a}+\frac{1}{8 a^{3}} \)
в. \( 8 a^{3}+3 a+\frac{3}{a}+\frac{1}{8 a^{3}} \)
c. \( 8 a^{3}+3 a+\frac{6}{a}+\frac{1}{8 a^{3}} \)
D. \( 8 a^{3}+6 a+\frac{6}{a}+\frac{1}{8 a^{3}} \)


Autonomic nervous system controls
A. Voluntary activities
B. Involuntary activites
C. Both A and B
D. None of the above


A 50 V d.c power supply is used to charge a battery of eight lead
accumulators, each of emf \( 2 \mathrm{V} \) and
internal resistance \( 1 / 8 \Omega \). The charging current also runs a motor connected in
series with the battery. The resistance of the motor is \( 5 \Omega \) and the steady current supply is 4 A. The mechanical power stored in the motor is
A. \( 80 \mathrm{w} \)
B. 40 \( w \)
\( c \cdot 64 w \)
D. 30 w


Nonmetals contain number
of electrons in their outmost shell
A .1,2 or 3
B. 8,9 or 10
c. 10,20 or 30
D. 5,6 or.7


Fill in the blanks.
A mixture of calcium cyanamide and carbon is known as


How many electrons, protons and
neutrons are there in \( 16 g \) of \( _{8} O^{16} ? \)


Ram moves in east direction at a speed
of \( 6 m / s \) and Shyam moves \( 30^{\circ} \) east of
north at a speed of \( 6 m / s \). The magnitude of their relative velocity is
A. \( 3 m / s \)
в. \( 6 m / s \)
c. \( 6 \sqrt{3} \mathrm{m} / \mathrm{s} \)
D. \( 6 \sqrt{2} \mathrm{m} / \mathrm{s} \)


Given that \( m^{2}=27^{2 / 3} \times 16^{-3 / 2}, \) find
the value of \( m \)
A \( \cdot \frac{9}{34} \)
в. \( \frac{3}{16} \)
\( c \cdot \frac{3}{8} \)
D. \( \frac{3}{4} \)


The center of gravity of an object is
A. the sum of its moments divided by the weight of the specific object.
B. the sum of its moments divided by the overall weight of the object.
C. the sum of its moments of product of the overall weight of the object.
D. none of the above


If \( a, b, c \) and \( d \) are in harmonic progression, then \( \frac{1}{a}, \frac{1}{b}, \frac{1}{c} \) and \( \frac{1}{d}, \) are in progression.
\( A \cdot A P \)
в. GP
c. нр
D. AGP


If \( A \) and \( B \) are acute angles such that
\( \sin A=\sin ^{2} B, 2 \cos ^{2} A=3 \cos ^{2} B \)
then
This question has multiple correct options
\( A \cdot A=\frac{\pi}{6} \)
B. \( A=\frac{\pi}{2} \)
c. \( B=\frac{\pi}{4} \)
D. \( B=\frac{\pi}{3} \)


Which of the following statement is
false?
A. Smooth muscles are found in urinary bladder,alimentary canal and genital tract
B. A striated muscle is syncytium (multinucleate)
C. The cytoplasm of striated muscle is called endoplasm
D. The plasma membrane and ER of striated muscles are called sarcolemma and sarcoplasmic reticulum respectively


The scientific name of oak silkworm is
A. Bombyx mori
B. Antheraea pernyi
C. Antheraea assamensis
D. Attacus ricinin


Double vagina is found in
A. Monotremata
B. Eutheria
c. Marsupials
D. All of the above


The value of "c" if the line \( \boldsymbol{x}+\mathbf{4} \boldsymbol{y}=\mathbf{9} \)
pases through \( (\mathbf{5}, \boldsymbol{c}) \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. - 1
c. 0
D. None of these


The mass of planet Jupiter is \( 1.9 \times 10^{27} \)
kg and that of the Sun is \( 1.99 \times 10^{30} \mathrm{kg} \)
The mean distance of Jupiter from the
Sun is \( 7.8 \times 10^{11} \) m. Calculate the
gravitational force which Sun exerts on Jupiter. Assuming that Jupiter moves in circular orbit around the Sun, also
calculate the speed of Jupiter. \( \boldsymbol{G}= \)
\( \mathbf{6 . 6 7} \times \mathbf{1 0}^{-\mathbf{1 1}} \mathbf{N m}^{\mathbf{2}} \mathbf{k g}^{-\mathbf{2}} \)
\( \mathbf{A} \cdot=5 \times 10^{23} \mathrm{N} \)
B. \( =4.15 \times 10^{23} \mathrm{N} \)
\( \mathbf{C} .=15 \times 10^{23} \mathbf{N} \)
D. \( =1 \times 10^{23} \mathrm{N} \)


Find \( \bar{x} \) using shortcut method.
A . 37
B . 38
c. 39
D. 40


Oxygen and sulphur are identical in
respect of :
A. chemical properties
B. distribution of electrons in outer shell
c. atomicity
D. electronic configuration


Two equal drops are falling through air
with a steady velocity of \( 5 \mathrm{cm} s^{-1} . \) If the drop coalesces, the new terminal velocity will become:
A. \( 5 \times 2 c m s^{-1} \)
B . \( 5 \times \sqrt{2} \mathrm{cms}^{-1} \)
C \( .5 \times(4)^{\frac{1}{3}} \mathrm{cm} s^{-1} \)
D. \( \frac{5}{\sqrt{2}} c m s^{-1} \)


Assertion
A raindrop after falling through some height attains a constant velocity
Reason
At constant velocity, the viscous drag is
just equal to its weight.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


A string of mass \( \mathrm{m} \) is fixed at both ends. The fundamental tone oscillations are excited in the strong with angular frequency \( \omega \) and maximum
displacement amplitude A. Find the total energy curtained in the string.
\( \mathbf{A} \cdot \frac{1}{2} m \omega^{2} A^{2} \)
B \( \cdot \frac{1}{4} m \omega^{2} A^{2} \)
\( \mathbf{C} \cdot \frac{1}{6} m \omega^{2} A^{2} \)
D. \( \frac{1}{8} m \omega^{2} A^{2} \)


Which one of the following ore is not concentrated by froth floatation
process?
A. Copper pyrites
B. Galena
c. Pyrolusite
D. zinc blende


Shape of eye ball is:
A. flat
B. spherical
c. oval
D. fish shaped


A metallic conductor at \( 10^{\circ} \mathrm{C} \) connected
in the left gap of Meter Bridge gives balancing length \( 40 \mathrm{cm} . \) When the
conductor is at \( 60^{\circ} \mathrm{C} \), the balance point
shifts by \( 5 \mathrm{cm} . \) The temperature coefficient of resistance of the material
of the wire
A . (1 / 210) / \( ^{\circ} \mathrm{C} \)
B. (1 / 220) / \( ^{\circ} \mathrm{C} \)
\( c \cdot(1 / 200) /^{\prime} c \)
D. (1 / 201) / \( ^{\circ} \mathrm{C} \)


Assertion
Homo habilis was the first tool maker.
Reason : He was cave-dweller.
A. If both the assertion and the reason are true and the
reason is a correct explanation of the assertion
B. If both the assertion and reason are true but the reason is not a correct explanation of the assertion
C. If the assertion is true but the reason is false
D. If both the assertion and reason are false
E. If the assertion is false but reason is true


\( \boldsymbol{C H}_{3}-\boldsymbol{C H}=\boldsymbol{C H}-\boldsymbol{C} \equiv \boldsymbol{C H} \)
What is the IUPAC name of the given compound?


If \( \frac{4 z_{1}}{9 z_{2}}+\frac{4 \overline{z_{1}}}{9 \overline{z_{2}}}=0, \) then the value of
\( \left|\frac{z_{1}-z_{2}}{z_{1}+z_{2}}\right| \) is
A \( \cdot \frac{4}{9} \)
в. \( \frac{9}{4} \)
\( c \cdot 1 \)
\( D \)


One atomic mass unit is equal to \( 1.67 \times 10^{-27} k g \)
A. True
B. False


At \( 298 \mathrm{K}, \Delta_{f} S^{\ominus} \) element \( =0 \)
A. True
B. False


The relation \( R \) on the set \( Z \) of all integer
numbers defined by \( (x, y) \epsilon R \Leftrightarrow x-y \)
is divisible by \( n \) is
A. Equivalence
B. Symmetric only
c. Reflexive only
D. Transitive only


Construct a quadrilateral \( \boldsymbol{V} \boldsymbol{A} \boldsymbol{B} \boldsymbol{N} \)
where \( \boldsymbol{V} \boldsymbol{A}=\mathbf{7} \boldsymbol{c m}, \boldsymbol{A B}=\boldsymbol{8} \boldsymbol{c m}, \boldsymbol{B} \boldsymbol{N}= \)
\( \mathbf{1 0} c \boldsymbol{m}, \boldsymbol{A} \boldsymbol{N}=\mathbf{1 2} \boldsymbol{c m} \) and \( \boldsymbol{V} \boldsymbol{B}=\mathbf{1 1} \boldsymbol{c m} \)
The measure of side \( V N \) is :
A. \( 6 \mathrm{cm} \)
B. \( 6.5 \mathrm{cm} \)
\( c \cdot 5 \mathrm{cm} \)
D. \( 5.2 \mathrm{cm} \)


Find the correct answers about
glomerular filtrate
1. Formed continuouslythrough ultrafiltration of blood
2. Lipid free fluid collects in the lumen
of Bowmans capsule
3. Protein free fluid collects in the
lumen of Bowmans capsule
4. Formed by process of selective reabsorption.
A .1,2,3 correct
B. 1,2 correct
c. \( 2,4, \) correct
D. 1,3 correct


Which of the following does not yield wool?
A. Yak
B. Camel
c. Goat
D. woolly dog


A photon of energy \( 4 e V \) is incident on a
metal surface whose work function is
\( 2 e V . \) The minimum reverse potential to be applied for stopping the emission of electrons is:
\( \mathbf{A} \cdot 2 V \)
B. \( 4 V \)
c. \( 6 V \)
D. \( 8 V \)


In Lac operon if a mutation occurs in
the middle gene of the structural genes
then
A. \( \beta \) - galactosidase will not be synthesised
B. Permease will not be synthesised
c. Transacetylase will not be synthesized
D. Lactose digestion will be rapid


Explain the structure of the plasma membrane as proposed by singer and Nicolson \( (1972), \) with a diagram


How the dot patterns in Braille system easily recognized?
A. They are depressed slightly to make the dots easier to touch
B. Two dots are made together so that the dots become more easier to touch
c. The dots are raised slightly to make them easier to touch
D. None of these


All are true about bacterial endospores
except
A. Sporulation in bacteria is a method of reproduction.
B. The spores of all the medically important bacteria are killed by autoclaving at \( 121^{\circ} \mathrm{C} \) for 15 minutes.
C. Spores can be stained by modified Ziehl-Neelsen technique.
D. Bacterial spores helps them to survive under unfavourable conditions.


A human body excretes certain material by a law similar to radioactivity. The body excretes half the amount injected in \( 24 h . \) Find the time in which activity
falls to \( 3 \mu C i . \) If a person is injected
technitium \( \left(t_{1 / 2}=6 h\right) \) and its activity just after the injection is \( 6 \mu C i \)
A. \( 4.8 h \)
в. \( 6 h \)
\( c \cdot 6.3 h \)
D. none of these


What is the range between \( f_{1} \) and \( f_{2} \) of
an RLC circuit that resonates at
\( 150 k H z \) and has a \( Q \) of \( 30 ? \)
A . \( 100.0 k H z \) to \( 155.0 k H z \)
B. \( 147.5 k H z \) to \( 152.5 k H z \)
c. \( 4500 k H z \) to \( 295.5 k H z \)
D. \( 149970 H z \) to \( 150030 H z \)


Simplify:
\( \mathbf{2 0}(\boldsymbol{y}+\mathbf{4})\left(\boldsymbol{y}^{2}+\mathbf{5} \boldsymbol{y}+\mathbf{3}\right) \div \mathbf{5}(\boldsymbol{y}+\mathbf{4}) \)
A \( \cdot 5\left(y^{2}+5 y+3\right) \)
B \( \cdot 4\left(y^{2}-5 y+3\right) \)
\( \mathbf{c} \cdot 4\left(y^{2}+5 y-3\right) \)
D. \( 4\left(y^{2}+5 y+3\right) \)


When we jump out of a boat standing
in water it moves
A. to our sides
B. opposite to our direction
c. in our direction
D. does't move at all


The probability that there would be 1,2
or 3 persons riding a bicycle are 0.85,0.12 and 0.03 respectively. The expected number of persons per bicycle is
A . 2
B.
c. 1.18
D. 3


Which of the following could be named
as \( 2- \) pentanone?
A. \( R-C O O H \)
в. \( R-C H O \)
c. \( R-C O-R \)
D. \( R-C O O-R \)
E \( . R-C O-N H_{2} \)


\( C u \) exhibits two types of valencies \( C u^{+} \) and \( C u^{++} . \) When chlorine reacts with
copper why only \( C u C l_{2}\left(C u^{++}\right) \) is formed?


Find the area of the quadrilateral whose vertices \( \operatorname{are}(\mathbf{6}, \mathbf{9}),(\mathbf{7}, \mathbf{4}),(\mathbf{4}, \mathbf{2}) \) and \( (\mathbf{3}, \mathbf{7}) \)


Evaluate \( \int \frac{d x}{x^{2}-4 x+13} \)


Derive the formula for equivalent capacitance when the capacitors are connected in series.


which of the following sterilizes water?
A \( \cdot C O_{2} \)
в. \( O_{3} \)
c. \( N_{2} \)
D. \( S O_{3} \)


Strongest electrolyte among the following is :
A. water
B. chlorous acid
c. acetic acid
D. hydrofluoric acid
E. hypochlorous acid


IF \( A \) be a square matrix, then \( \boldsymbol{A}+\boldsymbol{A}^{\boldsymbol{T}} \)
is a symmetric matrix?
A. True
B. False


If \( a, b, c \) are the sides of a triangle and \( s \) \( =\frac{a+b+c}{2}, \) then prove that \( 8(s-a)(s- \)
b) \( (s-c) \leq a b c \)


The acceleration of a particle as a
function of time \( t \) is given as \( a=k . t^{5 / 2} \)
If initial speed of the particle \( (a t t=0) \)
is \( u \) then its velocity \( v \) as a function of
time \( t \) is given as :
A \( \cdot v=u+\frac{2}{5} k t^{5 / 2} \)
B. \( v=u+\frac{2}{7} k t^{7 / 2} \)
c. \( v=u+k t^{5 / 2} \)
D. \( v=u+k t^{7 / 2} \)


Write an account of position, structure and functions of pituitary gland.