Identify the analgesic.
\( \mathbf{A} \cdot \) Heroine
B. Morphine
C. Codeine
D. None of these


A line passes through the points whose position vectors \( \hat{\mathbf{i}}+\hat{\mathbf{j}}-\mathbf{2} \hat{\boldsymbol{k}} \) and \( \hat{\mathbf{i}}- \)
\( 3 \hat{j}+\hat{k} . \) Then the position vector of a
point on it at a unit distance from the first point is
A \( \cdot \frac{1}{5}(5 \hat{i}+\hat{j}-7 \hat{k}) \)
B \( \cdot \frac{1}{5}(5 \hat{i}+9 \hat{j}-13 \hat{k}) \)
c. \( (\hat{i}-4 \hat{j}+3 \hat{k}) \)
D. \( (\hat{i}+4 \hat{j}+3 \hat{k}) \)


In series \( L-R \) circuit, \( X_{L}=R \). Now a
capacitor with \( X_{C}=R \) added in series.
New power factor:
A. Same as initial
B. \( \frac{1}{\sqrt{2}} \) times the initial
c. \( \frac{1}{2} \) times the initial
D. \( \sqrt{2} \) times the initial


A projectile is given an initial velocity of \( \hat{\mathbf{i}}+2 \hat{j} . \) The cartesian equation of its
path is \( \left(\boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} \boldsymbol{s}^{-2}\right) \)
A \( \cdot y=2 x-5 x^{2} \)
В . \( y=x-5 x^{2} \)
C \( .4 y=2 x-5 x^{2} \)
D. \( y=2 x-25 x^{2} \)


State whether the statement is True or
False. The square of \( \left(5-x+\frac{2}{x}\right) \) is equal to \( 21+x^{2}+\frac{4}{x^{2}}-10 x+\frac{10}{x} \)
A. True
B. False


\( \boldsymbol{F} \boldsymbol{e}_{2}\left(\boldsymbol{S} \boldsymbol{O}_{4}\right)_{3} \) solution:
A. Turns blue litmus red
B. Turns red litmus blue
C. Turns phenolphthalein solution pink
D. Both (b) and c)


Solve \( \cot \theta+\tan \theta=2 \csc \theta \)


A \( 1 \mu F \) capacitor is charged to 200 V and then connected in parallel (+ve to +ve) with a \( 4 \mu F \) capacitor charged to \( 100 \mathrm{V} \) The resultant potential difference is :
A. \( 120 \mathrm{V} \)
B. 60
c. \( 180 v \)
D. \( 150 \mathrm{v} \)


Dinoflagellates have a mesokaryotic cell organisation. Which of the following features is not related to such cellular
organisation?
A. single nuclear membrane
B. No spindle formation
c. Presence of histones
D. Permanently condensed chromosomes


Which tissue gives rise to secondary growth?
A. Apical meristem
B. Adventitious root
c. Axillary bud
D. vascular cambium


How does the branching of hydrocarbon chain of synthetic detergents affect their biodegradability?
A. More branching leads to biodegradability
B. More branching leads to non-biodegradability
C. No effect
D. None of these


If \( \bar{a} \) and \( \bar{b} \) are non-collinear unit vectors
and \( |\bar{a}+\bar{b}|=\sqrt{3} \) then \( (2 \bar{a}+5 \bar{b}) \)
\( (3 \bar{a}-\bar{b})=? \)
A \( \cdot \frac{15}{4} \)
в. \( \frac{15}{2} \)
c. 15
D. 16


A \( 1 \mathrm{kg} \) ball drops vertically onto the floor with a speed of \( 25 \mathrm{m} / \mathrm{s} \) and rebounds with a speed of \( 10 \mathrm{m} / \mathrm{s} \) What is the
impulse acting on the ball?


Gram positive bacteria differ from gram negative bacteria in the structure of
their
A. Nucleoid
B. Cytoplasm
c. Cell wall
D. Ribosomes


Write the first five fterms of the
following square or find obtain the
corresponding series: \( \boldsymbol{C} \boldsymbol{I}_{1}=-\mathbf{1}, \boldsymbol{a} \boldsymbol{n}= \)
\( \frac{a n-1}{n}, n \geq 2 \)


If \( z=x+i y \) and \( x^{2}+y^{2}=16, \) then the
range of \( \|\boldsymbol{x}|-| \boldsymbol{y}\| \) is
A . [0,4]
B. [0,2]
c. [2, \( 4] \)
D. none of these


The potential energy \( U \) for a force field \( \vec{F} \) is such that \( U=-K x y, \) where \( K \) is
a constant. Then
\( \mathbf{A} \cdot \vec{F}=K y \hat{i}+K x \hat{j} \)
В . \( \vec{F}=K x \hat{i}+K y \hat{j} \)
c. \( \bar{F} \) is a conservative force
D. \( \vec{F} \) is a non-conservation force


The condition for destructive
interference is phase difference should
be equal to
A. odd integral multiple of \( \pi \)
B. Integral multiple of \( \pi \)
c. odd integral multiple of half \( \pi \)
D. Integral multiple of half \( \pi \)


If \( \boldsymbol{A}=\left[\begin{array}{ccc}5 & 5 x & x \\ 0 & x & 5 x \\ 0 & 0 & 5\end{array}\right] \) and \( \left|A^{2}\right|=25 \)
then \( |x| \) is equal to?
A \( \cdot \frac{1}{5} \)
B. 5
\( c \cdot 5^{2} \)
D.


The drug cimetidine was designed to:
This question has multiple correct options
A. prevent the interaction of histamine with receptors
B. stimulates the secretion of pepsin
C. reduce gaestro intestinal juices
D. all of the above


A uniform wire of length I and mass \( \mathrm{M} \) bented in the shape of semicircle of
radius \( r \) as shown in figure.Calculate moment of inertia about \( X X^{\prime} \)
A \( \cdot \frac{M l^{2}}{2 \pi^{2}} \)
в. \( \frac{4 M l^{2}}{\pi^{2}} \)
c. \( \frac{4 M l^{2}}{4 \pi^{2}} \)
D. None of the above


What will be the uncertainty in velocity
of a bullet with a mass of \( 10 g \) whose
position is known with \( \pm 0.01 \mathrm{mm} \) ?


The minimum charge on an object is:
A. 1 coulomb
B. 1 stat coulomb
C \( .1 .6 \times 10^{-20} \) coulomb
D. \( 1.6 \times 10^{-19} \) coulomb


When a running horse suddenly stops, the rider falls forwards.
A. True
B. False


A sample of hydrogen atoms gas contains 100 atoms \( A \| \) the atoms are
excited to the seventh state. The total
energy released by all the atoms is \( \frac{4800}{49} \) Ry( Where Ry \( =13 \) eV) then discuss the following things
a) Maximum energy of the emitted
photon will be less then \( \frac{4800}{49} R y \)
b)Maximum energy of the emitted
photon may be grater than \( \frac{48}{49} R y \)
c)The value of \( n=6 \)
d)total number of photon that can be emitted this sample may be less than 600


A man walks on a rough surface, the angle between the force of friction and
the instantaneous velocity of the person is :
A . \( \pi \)
в. \( \frac{\pi}{2} \)
c. \( 2 \pi \)
D. zero


On the treatment of the following
compound with a strong acid, the most
susceptible site for bond cleavage is:
A. \( O_{2}-C_{3} \)
В \( \cdot O_{5}-C_{6} \)
c. \( C_{4}-O_{5} \)
\( \mathrm{D} \cdot C_{1}-O_{2} \)


A number of two-digit numbers having the property that they are perfectly divided by the sum of their digits with quotient equal to \( 7, \) is:
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
\( D \)


What would be the efficiency of a Carnot engine operating with boiling water as one reservoir and a freezing mixture of ice and water as the other reservoir?
A . \( 27 \% \)
B. 77 \%
c. \( 20 \% \)
D. 67 \%


Given that \( \boldsymbol{P}(\boldsymbol{3}, \boldsymbol{2},-\boldsymbol{4}), \boldsymbol{Q}(\boldsymbol{5}, \boldsymbol{4},-\boldsymbol{6}) \) and
\( R(9,8,-10) \) are collinear. Find the ratio in which \( Q \) divides \( P R \)


If a new noble gas is discovered then, what will be its atomic number?
A . 87
в. 104
c. 118
D. 132


Assertion
The equation \( 4 x^{3}-9 x^{2}+2 x+1=0 \)
has atleast one real root in (0,1)
Reason
If 'f' is a continuous function such that
\( \int_{a}^{b} f(x)=0, \) the the equation \( f(x)=0 \) has atleast one real root in \( (a, b) \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which one of the following reactions is
incorrect?
A \( . \) Maltose \( +H_{2} O \stackrel{\text { Maltase }}{\rightarrow} \) Glucose \( + \) Fructose
B . Sucrose \( +H_{2} O \stackrel{\text { Invertase }}{\rightarrow} \) Glucose \( + \) Fructose
c. Glucose \( +H_{2} O \stackrel{Z y m a s e}{\rightarrow} \) Ethyl alcohol \( +C O_{2} \)
D. \( S t a r c h+H_{2} O \stackrel{\text { Diastase }}{\rightarrow} \) Glucose only


toppr
Q Type your question
salvaluilicio " 2
and a variable voltage source V. The
correct circuit to carry out the
experiment is
\( A \)
B.
\( c \)
\( D \)


Calculate the electric current in the
circuit shown.
A \( .1 .5 A \)
в. \( 0.5 A \)
\( c .2 .5 A \)
0.2


The mixture of colourless gases is:
A \( \cdot C O_{2} \)
в. \( C O \)
\( c \cdot c o_{2}+c O \)
D. \( C O_{2}+C O+H_{2} O \)


What happen when rain falls on soil without vegetational cover?
A. Rain water percolates into soil efficiently.
B. Rain water cause loss of surface soil.
c. Rain water leads to fertility of the soil.
D. Does not cause any changes in the soil


An electromagnetic wave radiates outwards from a dipole antenna, with
\( E_{0} \) as the amplitude of its electric field
vector. The electric field \( B_{0} \) which
transports significant energy from the source falls off as
A \( \cdot \frac{1}{r^{3}} \)
B. \( \frac{1}{r^{2}} \)
\( c \cdot \frac{1}{r} \)
D. remains constant


If \( f(x)=a x^{2}+b x+c \) is divided by
\( (b x+c), \) then the remainder is:
This question has multiple correct options
A \( \cdot \frac{a c^{2}}{b^{2}} \)
B. \( \frac{a c^{2}}{b^{2}}+2 c \)
c. \( f\left(-\frac{c}{b}\right) \)
D. \( \frac{a c^{2}+2 b^{2} c}{b^{2}} \)


In column-I some equilibrium or nonequilibrium states are given. In columnII the charges \( +Q \) and \( -Q \) are fixed
while charges \( q \) or \( -q \) are moveable
point charges as shown in figure. Match the correct options


The sum of the first tern and the fifth
term of an ascending A.P. is 26 and the product. of the second term by the fourth term is \( 160 . \) And the sum of the
first seven terms of this AP.
A . 110
B. 114
c. 112
D. 116


Simplify \( \left(5 p^{2}-3\right)+\left(2 p^{2}-3 p^{3}\right) \)


The length and breadth of a field are measured as: \( l=(120 \pm 2) m \) and \( ^{x} \) \( (100 \pm 5) m, \) respeatiprely. What is the area of the fi Happy Father's Day


An electric dipole of diploe moment \( \overrightarrow{\boldsymbol{p}} \) placed in uniform electric field \( \overrightarrow{\boldsymbol{E}} \) has
minimum potential energy when angle between \( \vec{p} \) and \( \overrightarrow{\boldsymbol{E}} \)
\( ^{A} \cdot \frac{\pi}{2} \)
B. zero
c. \( \pi \)
D. \( \frac{3 \pi}{2} \)


Mammalian lungs are
A. Hollow
B. Soft and spongy
C. Both A and B
D. None of the above


In the interval \( \boldsymbol{x} \epsilon\left(\boldsymbol{e}^{2 r \boldsymbol{\pi}+\boldsymbol{\pi} / 4}, \boldsymbol{e}^{2 \boldsymbol{r} \boldsymbol{\pi}+\boldsymbol{5} \boldsymbol{\pi} / \boldsymbol{4}}\right) \)
in which the function \( f(x)= \)
\( \sin \left(\log _{e} x\right)+\cos \left(\log _{e} x\right) \) is
A. decreasing
B. increasing
c. const.
D. no monotonicity


The gases are at absolute temperature
\( 300^{\circ} \mathrm{K} \) and \( 350^{\circ} \mathrm{K} \) respectively. The
ratio of average kinetic energy of their molecules is
A .6: 7
B. 36: 49
\( c \cdot 7: 6 \)
D. 343: 216


The value of:
\( \lim _{n \rightarrow 0} \cos \left(\frac{x}{2}\right) \cos \left(\frac{x}{4}\right) \cos \left(\frac{x}{8}\right) \dots \dots \cos \left(\frac{x}{2^{n}}\right) \)
is


Units of electric flux are :
A \( \cdot \frac{N-m^{2}}{C^{2}} \)
в. \( \frac{N}{C^{2}-m^{2}} \)
c. volt \( -m \)
D. volt \( -m^{3} \)


Inverse circular functions,Principal values of \( \sin ^{-1} x, \cos ^{-1} x, \tan ^{-1} x \)
\[
\begin{array}{c}
\tan ^{-1} x+\tan ^{-1} y=\tan ^{-1} \frac{x+y}{1-x y} \\
x y<1 \\
\pi+\tan ^{-1} \frac{x+y}{1-x y}, \quad x y>1
\end{array}
\]
(a) \( \tan ^{-1} \frac{1}{4}+2 \tan ^{-1} \frac{1}{5}+\tan ^{-1} \frac{1}{6}+ \)
\[
\tan ^{-1} \frac{1}{x}=\frac{\pi}{4}
\]
(b) \( \tan ^{-1}(x-1)+\tan ^{-1} x+ \)
\[
\tan ^{-1}(x+1)=\tan ^{-1} 3 x
\]


When n small drops of a conducting
liquid, each of surface charge density \( \sigma \)
and radius \( r \) are made to combine to
form a big drop of radius \( R \), then:
A \( . \) potential becomes \( n^{1 / 3} \) times original potential and charge density decreases to \( n^{1 / 3} \) times original charge density
B. potential becomes \( n^{2 / 3} \) times and charge density increases to \( n^{1 / 3} \) times original charge density
C . potential and charge density decrease to \( n^{4 / 3} \) times original values
D. potential and charge density increase to n times original values


The location of villi is:
A. Large intestine
B. Small intestine
c. Stomach
D. None of the above


If \( \operatorname{Re}\left(\frac{z+2 i}{z+4}\right)=0 \) then \( z \) lies on a circle with center:
A \( \cdot(-2,-1) \)
B. (-2,1)
c. (2,-1)
D. (2,1)


The displacement of the medium in a sound wave is given by the equation
\( \boldsymbol{y}_{1}=\boldsymbol{A} \cos (\boldsymbol{a} \boldsymbol{x}+\boldsymbol{b} \boldsymbol{t}) \) where \( \boldsymbol{A}, \boldsymbol{a} \& \boldsymbol{b} \) are
positive constants. The wave is reflected by an obstacle situated at
\( \boldsymbol{x}=\mathbf{0} . \) The intensity of the reflected
wave is 0.64 times that if the incident
wave
(a) What are the wavelength and frequency of the incident wave?
(b) Write the equation for the reflected
wave.
(c) In the resultant wave formed after
reflection, find the minimum value of
the particle speed in the medium?


Which of the following treatment will
convert starch directly into glucose?
A. Heating with dilute \( H_{2} S O_{4} \)
B. Fermentation by diastase
C. Fermentation by zymase
D. Heating with dilute \( N a O H \)


Asprin is an:
A. analgesic
B. antipyretic
c. antimalarial
D. both analgesic and antipyreticc


An aqueous solution of a metal bromide
\( M B r_{2}(0.05 M) \) is saturated with \( H_{2} S \)
The minimum \( p H \) at which \( M S \) will
precipitate is \( \boldsymbol{X} ? \boldsymbol{K}_{s p} \) for \( \boldsymbol{M} \boldsymbol{S}=\mathbf{6 . 0} \times \)
\( 10^{-21} \)
[Concentration of saturated \( \boldsymbol{H}_{2} \boldsymbol{S}= \)
\( \mathbf{0 . 1} M ; K_{1}=10^{-7} \) and \( K_{2}=1.3 \times \)
\( \left.10^{-13} \text {for } H_{2} S\right] \)
\( A \)
B. 3
\( c \cdot 5 \)
D. None of these


What is the role of phosphate ion in a detergent?
A. It reduces pH of the water
B. It increases pH of the water
C. It removes \( C a^{2+} \) and \( M g^{2+} \) ions from water that causes hardness
D. It increases its solubility in water


The elements with atomic numbers
\( \mathbf{9}, \mathbf{1 7}, \mathbf{3 5}, \mathbf{5 3}, \mathbf{8 5} \) are all :
A . noble gases
B. halogens
c. heavy metals
D. light metals


If square matrices \( A \) and \( B \) are such
that \( \boldsymbol{A} \boldsymbol{A}^{\prime}=\boldsymbol{A}^{\prime} \boldsymbol{A}, \boldsymbol{B} \boldsymbol{B}^{\prime}=\boldsymbol{B}^{\prime} \boldsymbol{B}, \boldsymbol{A} \boldsymbol{B}^{\prime}= \)
\( \boldsymbol{B}^{\prime} \boldsymbol{A} \)
then is the statement \( A B(A B)^{\prime}= \)
\( (A B)^{\prime} A B \) is
where \( A^{\prime} \) is transpose of \( A \)
If true enter 1 else enter 0


External fertilization occurs in the
majority of
A. Algae
B. Fungi
c. Liverworts
D. Mosses


Using the factor theorem it is found
that \( b+c, c+a \) and \( a+b \) are three
factors of the determinant \( \left|\begin{array}{ccc}-2 a & a+b & a+c \\ b+a & -2 b & b+c \\ c+a & c+b & -2 c\end{array}\right| . \) The other factor
in the value of the determinant is
A . 4
B. 2
\( \mathbf{c} \cdot a+b+c \)
D. none of these


In North west corner rule if the demand
in the column is satisfied one must
move to the
A. left cell in the next column
B. right cell in the next row
c. right cell in the next column
D. left cell in the next row


The principal value of \( \arg (z) \) lies in the interval:
\( ^{\mathrm{A}} \cdot\left[0, \frac{\pi}{2}\right] \)
в. \( (-\pi, \pi] \)
\( \mathbf{c} \cdot[0, \pi] \)
D. \( (-\pi, 0] \)


A strip of copper and another germanium are cooled from room
temperature to \( 80 \mathrm{K} \). Theresistance of
A. each of these decreases
B. copper strip increases and that of germanium decreases
c. copper strip decreases and that of germanium increases
D. each of these increases.


Which of the following statement is true
about RNA?
A. It contains adenine paired to thymine
B. One of the bases from DNA is replaced by uracil
C. It contains the sugar deoxyribose
D. Its nucleotides contain twice as many phosphate groups as DNAs nucleotides


Water content of skeletal muscles is
\( \% \)
A . 25
B. 50
c. 75
D. 90


Which of the following reagent would you choose for the conversion shown below:
\( \boldsymbol{A} \boldsymbol{r} \boldsymbol{N}_{2}^{+} \boldsymbol{C l}^{-} \longrightarrow \boldsymbol{A} \boldsymbol{r} \boldsymbol{F} \)
A. only \( H B F_{4} \)
в. \( H F \)
\( c \cdot F_{2} \)
D. \( H B F_{4} / \)Heat


Select the correct statement(s) out of
the following:
i) A sigma
(s) bond is formed when
two s-orbitals overlap.
ii) \( A \) pi \( (p) \) bond is formed when two \( p \) orbitals overlap sideways.
iii) An sigma bond is weaker than pi
bond.
B. ii and iii
c. i only
D. ii only


Decide whether \( m^{2}+m+2=4 m \) is a
quadratic equation


Why was the method of classification,
suggested by Dobereiner, discarded?
A. The weights were wrongly calculated
B. Many elements were unknown at that time
c. only three triads were formed from the elements known at that time
D. None of the above


Let \( m \) be a positive integer. Then al pairs of integers \( (x, y) \) such that \( x^{2}\left(x^{2}+y^{2}\right)=y^{m+1} \) is \( x=t^{5}+t^{3}, y= \)
\( t^{4}+t^{2} \)
If true then enter 1 and if false then
enter 0
A. True
B. False


Boron occurs in nature in the form of
two isotopes having atomic mass 10 and \( 11 . \) Calculate the percentage abundances of two isotopes respectively in a sample having atomic mass 10.80
A . 10,90
B. 30, 70
c. 20,80
D. 25,75


Which of the following is a
homogeneous differential equation?
\( \mathbf{A} \cdot(4 x+6 y+5) d y+(3 y+2 x+4) d x=0 \)
B. \( (x y) d x+\left(x^{3}+y^{3}\right) d y=0 \)
C \( \cdot\left(x^{3}+2 y^{2}\right) d x+2 x y d y=0 \)
D \( \cdot y^{2} d x+\left(x^{2}+x y+y^{2}\right) d y=0 \)


A permanent magnet has the shape of a sufficiently thin disc magnetized along
its axis. The radius of the disc is \( \boldsymbol{R}= \)
1.0 \( c m . \) Evaluate the magnitude of a
molecular current \( I^{\prime} \) flowing along
the rim of the disc if the magnetic induction at the point on the axis of the disc, lying at a distance \( \boldsymbol{x}=\mathbf{1 0} \boldsymbol{c m} \)
from its centre, is equal to \( B=30 \mu T \)


A bud in Hydra develops an outgrowth through repeated division at a
A. Secure site
B. Abstract site
c. specific site
D. Wrong site


De-Broglie relation describes the relationship of wavelength of an electron with:
A . mass
B. energy
c. momentum
D. charge


Bakelite is an example of:
A. elastomer
B. fibre
c. thermoplastic
D. thermosetting polymer


When carbonates are reacted with \( \boldsymbol{H} \boldsymbol{C l} \)
the gas evolved is:
A \( \cdot C l_{2} \)
в. \( C O_{2} \)
\( c \cdot O_{2} \)
D. \( H_{2} \)


No. of chromosomes present in human
cell is:
A . 46
B. 23
\( c \cdot 2.3 \)
D. 4.6


Assertion
A wire bent into an irregular shape with
the points \( P \) and \( Q \) fixed. If a current \( I \)
passed through the wire, then the area
enclosed by the irregular portion of the
wire increases.
Reason
Opposite currents carrying wires repel
each other
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


You are thrown ahead when your car
suddenly comes to a halt and you are thrown backwards when your car
rapidly accelerates. Which law of Newton is involved in this?
A. Third law
B. Second law
c. First law
D. Law of gravitation


Volume of a cube whose edge measures
\( \mathbf{5 . 8} \mathrm{cm} \) is :
A. 195.12 cu cm
B. 195.118 cu cm
c. 195.112 cu cm
D. 195.21 cu cm


One feature of image formed by plane mirrors is lateral inversion which
means:
A. the top part of the image appears downward and vice versa
B. left and right sides of the image are interchanged
c. image appears inverted both sideways and upside down
D. all the above


If \( \boldsymbol{A}=\left[\begin{array}{ll}\boldsymbol{a} & \boldsymbol{b}\end{array}\right], \boldsymbol{B}=\left[\begin{array}{ll}-\boldsymbol{b} & -\boldsymbol{a}\end{array}\right] \) and \( \boldsymbol{C}= \)
\( \left[\begin{array}{c}\boldsymbol{a} \\ -\boldsymbol{a}\end{array}\right], \) then the correct statement is
A. \( A=-B \)
В. \( A+B=A-B \)
c. \( A C=B C \)
D. \( C A=C B \)


Two parallel rail tracks run north-south. Train A moves north with a speed of 54 \( k m h^{-1} \) and train \( B \) moves south with a
speed of \( 90 \mathrm{kmh}^{-1}, \) What is the
a. the relative velocity of B with respect
to A?
b. the relative velocity of the ground with respect to B?
c. a velocity of a monkey running on the roof of the train A against its motion (with its velocity of \( 18 \mathrm{kmh}-1 \) with respect to the train \( A \) ) as observed by a
man standing on the


Mendel selected Pea as material for his
experiments because
A. It is an annual plant with comparatively short life cycle
B. The flowers are self-pollinated
c. The number of seeds produced is quite large
D. All the above


Sound can be produced by
A. striking a tuning fork
B. plucking a stretched rubber string
C . flicking a thin ruler
D. all the actions above


Copper deficiency resulting a disease which is known as
A. skin disease
B. Menkes disease
c. Anaemia
D. Night blindness


In a general form of G.P. \( a, a r, a r^{2}, a r^{3} \ldots \)
what is 'r'?
A. terms
B. common difference
c. common ratio
D. constant


Aquatic ecosystem help in
A. Reduce pollution
B. Absorption of nutrients
C . Recycle of nutrients
D. Both A and B


Which one of the following sets contribute to the global warming?
\( A \cdot S O_{2}, S O_{3}, O_{2} \)
B. \( N_{2}, C_{2} H_{6}, S O_{3} \)
c. \( C O_{2}, C H_{4}, C F C s \)
\( \mathrm{D} \cdot \mathrm{H}_{2}, \mathrm{NO}_{2}, \mathrm{SO}_{2} \)


Diffraction gratings provide much brighter interference pattern since more light passes through them compared with double slits.
A . True
B. False


The space between proton and electron in hydrogen atom is :
A. absolutely empty
B. full of electromagnetic radiation
C. full of air
D. full of ether


During electrolysis of a salt solution
\( 0.05 \mathrm{F} \) of electricity deposits \( 1.6 \mathrm{g} \) of divalent metal. Theatomic wt. of the
metal is :
A . 32
B. 16
\( c \cdot 64 \)
D. 1.6


The distance of the point (1,3) from the
line \( 2 x+3 y=6, \) measured parallel to
the line \( 4 x+y=4, \) is
A \( \cdot \frac{5}{\sqrt{13}} \) units
B. \( \frac{3}{\sqrt{17}} \) units
c. \( \sqrt{17} \) units
D. \( \frac{\sqrt{17}}{2} \) units


The curve represents the \( \boldsymbol{I}-\boldsymbol{V} \)
characteristics of which optoelectronic
device?
A. Solar Cell
B. Photo-diode
c. Light Emitting Diode (LED)
D. None of these


Find the order of magnitude of 38500 \( \mathbf{k g} \)


Which of the following enzymes has/have heme as a prosthetic group?
(i) Catalase
(ii) Carboxypeptidase
(iii) Succinic dehydrogenase
(iv) Peroxidase
\( A \cdot( \) i) only
B. (i) and (ii)
c. (ii) and (iii)
D. (iii) and (iv)
E. (i) and (iv)


The prosthetic group present in nucleoproteins is
A. nucleic acids
B. lipids
c. carbohydrates
D. phosphoric acid


Find the torque of a force \( \overrightarrow{\boldsymbol{F}}=-\mathbf{3} \hat{\mathbf{i}}+ \)
\( \hat{\boldsymbol{j}}+\boldsymbol{5} \widehat{\boldsymbol{k}} \) acting at the point \( \overrightarrow{\boldsymbol{r}}=\boldsymbol{7} \hat{\boldsymbol{i}}+ \)
\( \mathbf{3} \widehat{\boldsymbol{j}}+\widehat{\boldsymbol{k}} \)
\( \mathbf{A} \cdot 14 \hat{i}-38 \hat{j}+16 \hat{k} \)
B . \( 4 \hat{i}-4 \widehat{j}+6 \hat{k} \)
c. \( \$ \$-13-16 \) lhat \( \{k\}-38 \) lhat \( \{j\}-16 \mid \) hat \( \{i\} \$ \$ \)
D. none of these


\( \mathbf{1} \boldsymbol{g} \boldsymbol{f}= \)
A. \( 250 N \)
B. 980 dynes
c. 56 dynes
D. All


Explain the utility of systematic.


Find the equation of the plane passing through (2,0,1) and (3,-3,4) and perpendicular to \( \boldsymbol{x}-\mathbf{2} \boldsymbol{y}+\boldsymbol{z}=\mathbf{6} \)


Write down IUPAC name of \( C H_{3}-N H \)


The number of hydrogen bonds between Guanine and Cytosine; and between
Adenine and Thymine in DNA are:
A \( \cdot 1,2 \)
B. 3, 2
\( c \cdot 3, \)
D. 2,


Evaluate \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{n} \) in \( [-\mathbf{1}, \mathbf{1}], \boldsymbol{n} \boldsymbol{\epsilon} \boldsymbol{Z}^{+} \)


The differential coefficient of \( \boldsymbol{f}\left(\log _{e} \boldsymbol{x}\right) \)
with respect to \( x, \) where \( f(x)=\log _{e} x \)
is
A \( \cdot \frac{x}{\log _{e} x} \)
в. \( \frac{1}{x} \log _{e} x \)
c. \( \frac{1}{x \log _{e} x} \)
D. none of these


The electrical resistance of a conductor
depends upon.
A. Size of conductor
B. Temperature of conductor
c. Geometry of conductor
D. All of these


Which substance does NOT dissolve
well in water?
A \( \cdot N H_{3} \)
B. \( C_{4} H_{10} \)
c. \( C_{12} H_{22} O_{11} \)
D. \( H_{2} S O_{4} \)


The substraction of 3 from \( 2 x \) is
represent as
A. \( 2 x-3 \)
B. 3-2xx
\( c \cdot 2 x+3 \)
\( D \cdot \frac{2 x}{3} \)


If Sum of two numbers \( =-21 \) and
Product \( =-100 \)
Then find the two numbers


An object is kept \( 60 \mathrm{cm} \) from a lens
gives a virtual image \( 20 \mathrm{cm} \) in front of lens. What is the focal length of the lens? Is it converging lens or diverging lens?


Which of the following contain disulphide linkages?

This question has multiple correct options
A. Oxytocin
B. Vasopressin
c. Insulin
D. Haemoglobin


Tissue is defined as a structural
organization of a group of similar or dissimilar cells to carry out a specific function.
A. True
B. False


When a particle executing SHM
oscillates with a frequency \( \nu, \) then the
kinetic energy of the particle:
A. changes periodically with a frequency of \( \nu \)
B. changes periodically with a frequency of \( 2 \nu \)
C . changes periodically with a frequency of \( \frac{\nu}{2} \)
D. remains constant


Which law is involved in the act of
cleaning a carpet by beating it with a stick ?
A. First law of motion
B. Second law of motion
c. Law of conservation of energy
D. Law of conservation of mass


Define geometric growth.


Balance the following equation.
\( \boldsymbol{P b S}+\boldsymbol{O}_{2} \longrightarrow \boldsymbol{P b O}+\boldsymbol{S O}_{2} \)


If \( \left|\frac{z_{1}+z_{2}}{z_{1}-z_{2}}\right|=1 \) then \( \frac{z_{1}}{z_{2}} \) is
A . positive real
B. negative real
c. purely imaginary
D.


A cylinder of radius \( 6 \mathrm{cm} \) and height
\( h c m \) is filled with ice cream. The ice
cream is then distributed among 10 children in identical cones having hemispherical tops. The radius of the
base of the cone is \( 3 \mathrm{cm} \) and its height
is \( 12 \mathrm{cm} . \) Then the height \( h \) of the
cylinder must be
A. \( 100 / 7 \mathrm{cm} \)
B. \( 18 \mathrm{cm} \)
c. \( 15 \mathrm{cm} \)
D. \( 200 / 11 \mathrm{cm} \)


The standard reduction potentials of \( C u^{2+} \mid C u \) and \( C u^{2+} \mid C u^{\oplus} \) are 0.337 V
and \( 0.153 \mathrm{V} \), respectively. The standard electrode potential of \( C u \oplus \mid C u \) half cell
is:
A . \( 0.184 \mathrm{v} \)
в. 0.827
c. \( 0.521 \mathrm{v} \)
D. 0.490


A metallic shpere of radius \( 1.0 \times \) \( 10^{-3} m \) and density \( 1.0 \times 10^{4} k g / m^{3} \)
enters a tank of water after a free fall,
falling through a distance of h in the earth's gravitational field. If its velocity remains unchanged after entering water, determine the value of \( h \)
[Given : coefficient of viscosity of water
\( =1.0 \times 10^{-3} N-s / m^{2}, g=10 m / s^{2} \)
and density of water \( \left.=1.0 \times 10^{3} k g / m^{3}\right] \)
A. 20 \( m \)
B. 40 \( m \)
\( c \cdot 80 m \)
D. \( 10 \mathrm{m} \)


Using the given hints, identify the option with correct coal product and its
use.
(1) Almost pure form of carbon
A. Coke, manufacture of steel
B. coal tar, manufacture of paints
c. coke, manufacture of plastics
D. Coal tar, extraction of metals


The present population of a city is
15000. If it increases at the rate of \( 4 \% \)
per annum. Find its population after 2
years
\( \mathbf{A} \cdot 16224 \)
B . 26224
c. 36224
D. 46224


A person is know to speak the truth 4
times out of \( 5 . \) He throws a die and
reports that it is a ace. The probability that it is actually a ace is
A. \( 1 / 3 \)
в. 2 \( / 9 \)
c. \( 4 / 9 \)
D. \( 5 / 9 \)


\( \mathrm{DE}=2.4 \mathrm{cm}, \) find the length of BC


Let \( \boldsymbol{x} \in \boldsymbol{R} \) and let
\( \boldsymbol{P}=\left[\begin{array}{lll}1 & 1 & 1 \\ 0 & 2 & 2 \\ 0 & 0 & 3\end{array}\right], Q=\left[\begin{array}{lll}2 & x & x \\ 0 & 4 & 0 \\ x & x & 6\end{array}\right] \) and
\( \boldsymbol{R}=\boldsymbol{P Q P}^{-1} \)
Then which of the following is are
correct

This question has multiple correct options
A. there exists a real number x such that \( P Q=Q P \)
B.
det \( R=\operatorname{det}\left[\begin{array}{lll}2 & x & x \\ 0 & 4 & 0 \\ x & x & 5\end{array}\right]+8 \) for all \( x \in R \)
C. For \( x=1 \) there exists a unit vector \( \alpha \hat{i}+\beta \hat{j}+\gamma \hat{k} \) for
which are \( R\left[\begin{array}{l}\alpha \\ \beta \\ \gamma\end{array}\right]=\left[\begin{array}{l}0 \\ 0 \\ 0\end{array}\right] \)
D. \( \quad \) For \( x=0 \) if \( R\left[\begin{array}{l}1 \\ a \\ b\end{array}\right]=6\left[\begin{array}{l}1 \\ a \\ b\end{array}\right] \) then \( a+b= \)


\( \int \frac{x}{\left(x^{2}+4\right) \sqrt{x^{2}+1}} d x= \)
\( \frac{1}{\sqrt{k}} \tan ^{-1} \sqrt{\frac{x^{2}+1}{3}}+c . \) what is \( k ? \)


Cathode rays are deflected
towards
A. positive electrode
B. negative electrode
c. both electrode
D. none of these


Protein synthesis in an animal cell
occurs
A. On ribosomes present in cytoplasm, ER as well as in mitochondria
B. On ribosomes present in the nucleolus as well as in cytoplasm.
c. only on ribosomes attached to the nuclear envelope and endoplasmic reticulum.
D. only on the ribosomes present in cytosol


Show that the lines \( \widehat{P Q} \) are \( \overrightarrow{R Q} \) paralle
where \( P, Q, R, S \) are the points
(2,3,4),(4,7,8),(-1,-2,1) and
(1,2,5) respectively.


\( \operatorname{Let} \vec{a}=4 \vec{i}+3 \vec{j} \) and \( \vec{b}=3 \vec{i}+4 \vec{j} . \) Find
the magnitude of \( \overrightarrow{\boldsymbol{a}}+\overrightarrow{\boldsymbol{b}} \)


A couple can never be replaced by a single force.
A . True
B. False


What is organic chemistry?


Which of the following bonds link the
base of one chain and the base of other
chain of DNA?
A. Hydrogen bonds
B. Covalent bonds
c. lonic bonds
D. None of the above


is an imaginary line perpendicular to the surface where the reflection
occurs.


Gravitational force on the surface of the moon is only \( \frac{1}{6} \) as strong as gravitational force on the earth. What is
the weight in newtons of a \( 10 k g \) object
on the moon and on the earth?


A man buys two cycles for a total cost of Rs. \( 900 . \) By selling one cycle at a loss of \( 20 \% \) and the other at a profit of \( 25 \%, \) he makes a profit of Rs. 90 on the whole transaction. Find the cost price of each
cycle.
A . Rs. 200; Rs. 500
B. Rs. 300; Rs. 600
c. Rs. 400; Rs. 700
D. Rs. 500; Rs. 800


\( \mathbf{A}=\left[\begin{array}{ccc}-\boldsymbol{q} \boldsymbol{r} & \boldsymbol{p}(\boldsymbol{q}+\boldsymbol{r}) & \boldsymbol{p} \boldsymbol{r}+\boldsymbol{p} \boldsymbol{q} \\ \boldsymbol{p} \boldsymbol{q}+\boldsymbol{q} \boldsymbol{r} & -\boldsymbol{p} \boldsymbol{r} & \boldsymbol{p} \boldsymbol{q}+\boldsymbol{q} \boldsymbol{r} \\ \boldsymbol{q} \boldsymbol{r}+\boldsymbol{p} \boldsymbol{r} & \boldsymbol{q} \boldsymbol{r}+\boldsymbol{p} \boldsymbol{r} & \boldsymbol{-} \boldsymbol{p} \boldsymbol{q}\end{array}\right] \)
then \( |\boldsymbol{A}| \) equals:
\( ^{A} \cdot\left(\sum p q\right)^{2} \)
\( ^{\mathrm{B}}\left(\sum p^{2} q^{2}\right)^{2} \)
\( c \cdot\left[\sum(q r)^{3}\right. \)
\( ^{\mathrm{D}} \cdot\left(\sum p q\right)^{\frac{3}{2}} \)


If \( n=67 \) then find the unit digit of
\( \left[3^{n}+2^{n}\right] \)
\( A \)
B. 10
\( c \cdot 5 \)
D. None


Let \( g(x)= \) \( \int_{0}^{x} f(t) d t, \quad f \quad \) is such that \( \quad \frac{1}{2} \leq \)
\( \boldsymbol{f}(\boldsymbol{t}) \leq \mathbf{1} \)
for \( \boldsymbol{t} \boldsymbol{\epsilon}[\mathbf{0}, \mathbf{1}] \) and \( \mathbf{0} \leq \boldsymbol{f}(t) \leq \)
\( \frac{1}{2} \) for \( t \epsilon[1,2] . \) Then
\( \boldsymbol{g}(\boldsymbol{2}) \) satisfies the inequality
A \( \cdot-\frac{3}{2} \leq g(2) \leq \frac{1}{2} \)
в. \( 0 \leq g(2) \leq 2 \)
c. \( \frac{3}{2} \leq g(2) \leq \frac{5}{2} \)
D. \( 2 \leq g(2) \leq 4 \)


Which of the following varies from species to species?
\( A \cdot A=T \)
\( B \cdot C=G \)
c. \( A+G=C+T \)
D. AT/GC ratio


Some properties of sulphuric acid are listed below. Choose the role played by
sulphuric acid as \( A, B, C \) or \( D \) which is
responsible for the reaction
(i) to (v).
Some role/s may be repeated:
\( \boldsymbol{S}+\boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4}(\text {conc.}) \rightarrow \boldsymbol{3} \boldsymbol{S} \boldsymbol{O}_{2}+\boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{O} \)
A . Dilute acid
B. Dehydrating agent
c. Non-volatile acid
D. oxidising agent


Al reacts with conc. \( H_{2} S O_{4} \) and forms:
A. \( S O_{3} \)
в. \( S O_{2} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \)
D. s(vap)


If \( \boldsymbol{P}=\{\text { factors of } 36\} \) and \( \boldsymbol{Q}=\{ \) factors of \( 48\}, \) find \( Q-P \)


\( \vec{a}=4 \hat{i}-\hat{j}+\hat{k} \quad \) and \( \quad \vec{b}=p \hat{i}+2 \hat{j}+ \)
\( 3 \hat{k} \) are mutually perpendicular, then
find the value of \( \mathrm{p} \)


What does the shaded region represent in the figure given below?
A \( \cdot(P \cup Q)-(P \cap Q) \)
В . \( P \cap(Q \cup R) \)
\( \mathbf{c} \cdot(P \cap Q) \cap(P \cap R) \)
D \( \cdot(P \cap Q) \cup(P \cap R) \)


You have a spinning wheel with 3 green
sectors, 1 blue sector and 1 red sector, if
the probability of getting a non-blue
sector is \( \frac{4}{m} . \) Then, the value of \( m \) is
\( A, 5 \)
B. 4
\( c . \)
\( D \)


Which is not true for a detergent molecule?
A. It has a non-polar organic part and polar group
B. It is not easily biodegraded.
c. It is a sodium salt of fatty acid
D. It is a surface active reagent


Why are low spin tetrahedral complexes rarely observed?


If \( \vec{A} \times \vec{B}=\overrightarrow{0} \) and \( \vec{B} \times \vec{C}=\overrightarrow{0}, \) then the
angle between \( \vec{A} \) and \( \vec{C} \) may be :
A . 0
в.
\( c \cdot \frac{\pi}{2} \)
D. none of these


\( H_{3} B O_{3} \) is a:
A. monobasic acid and weak Lewis acid
B. monobasic acid and weak Bronsted acid
C. monobasic acid and strong Lewis acid
D. tribasic acid and weak Bronsted acid


Write the inverse of the statement-
If you do not drink your milk, you will not be strong.
A. If you are strong, then you drink your milk
B. If you do not drink your milk, then you are strong
C. If you drink your milk, then you are strong
D. None of the above


The Rolle's theorem is applicable in the interval \( -1 \leq x \leq 1 \) for the function
\( \mathbf{A} \cdot f(x)=x \)
\( \mathbf{B} \cdot f(x)=x^{2} \)
\( \mathbf{c} \cdot f(x)=2 x^{3}+3 \)
\( \mathbf{D} \cdot f(x)=|x| \)


The time taken for an electron to
complete one revolution in Bohr orbit of hydrogen atom is :
A \( \cdot \frac{4 m^{2} \pi r^{2}}{n^{2} h^{2}} \)
в. \( \frac{n^{2} h^{2}}{4 m r^{2}} \)
c. \( \frac{4 \pi^{2} m r^{2}}{n h} \)
D. \( \frac{n h}{4 \pi^{2} m r^{2}} \)


Select the wrong statement.
A. Diatoms are chief producers in the oceans.
B. Diatoms are microscopic and float passively in water.
C. The walls of diatoms are easily destructible.
D. 'Diatomaceous earth' is formed by the cell walls of diatoms.


Why rubber band is considered as a
solid?
A. It takes the shape of the container
B. It has fixed volume
c. It has negligible compressibility
D. It changes shape under force and regains the shape when the force is removed


In the figure shown below, the
maximum possible unknown resistance \( (X), \) that can be measured by
the post office box are \( X_{\max } \) is fiven by
\( R \times 10^{5} \Omega, \) then \( R \) is (given that in this
experiment, we can take out only one plug from arm \( A B \) and only one plug from arm BC, but from arm AD we can
take out many plugs):
\( A \)
B.
\( c \)
E. none of thes


What are protozoa?


Which of the following are isobars?
A \( . \) Ce, \( \mathrm{Se} \)
B. Fe, Se
\( \mathrm{c} \cdot \mathrm{Fe}, \mathrm{Ce} \)
D. Ce, Ni


\( \operatorname{Let} f(x)=\left\{\begin{array}{ll}g(x) \cdot \cos \frac{1}{x} & \text { if } x \neq 0 \\ 0 & \text { if } x=0\end{array}\right. \)
where \( g(x) \) is an even function
differentiable at \( x=0, \) passing through
the origin. Then \( \boldsymbol{f}^{\prime}(\mathbf{0}) \)
A. is equal to 1
B. is equal to 0
c. is equal to 2
D. does not exist


The length of a strip measured with a
meter rod is \( 10.0 \mathrm{cm} \) its width measured
with a vernier caliper is \( 1.00 \mathrm{cm} . \) The least count of the meter rod is \( 0.1 \mathrm{cm} \) and that of vernier caliper caliper 0.01 \( \mathrm{cm} \) water will be error in its area?
\( \mathbf{A} \cdot \pm 13 \% \)
B. \( \pm 7 \% \)
\( c . \pm 4 \% \)
D. \( \pm 2 \% \)


A wound watch spring has
energy.
A. mechanical
B. kinetic
C . potential
D. kinetic and potential


\( R s .2000 \) is lent out at \( 10 \% \) pa SI for 5 years. Find amount after 5 years
A . 2000
в. 3000
\( c .1000 \)
D. None


Simplify \( \tan ^{-1} \sqrt{2}-\cot ^{-1}(1 / \sqrt{2}) \)


What is the common difference of an AP
whose nth term is \( \boldsymbol{x} \boldsymbol{n}+\boldsymbol{y} ? \)
\( \mathbf{A} \cdot x+y \)
B. \( y \)
\( c \)
D. - \( x \)


Which of the following is not an essential chordate character?
A. Notochord
B. Vertebral column
c. Pharyngeal gill slilits
D. Dorsal hollow nerve cord


At the rate of \( 10 \% \) per annum
compounded quarterly, how long would
it take for a sum of Rs. 10000 to
compound to Rs. 20736
A. 1 year
B. 2 years
c. 3 years
D. 4 years


Pentavalence in phosphorus is more stable when compared to that of nitrogen even though they belong to same group is due to:
A. reactivity of phosphorus
B. inert nature of nitrogen
c. hydrogen and sulphurous acid
D. large size of phosphorus atom


For each \( k \epsilon N, \) let \( C_{k} \) denote the circle
whose equation is \( x^{2}+y^{2}=k^{2} . \) On the
circle \( C_{k}, \) a particle moves k units in the
anticlockwise direction. After
completing its motion on \( C_{k}, \) the
particle moves to \( C_{k+1} \) in the radial direction. The motion of the particle continues in this manner. The particle starts at \( (1,0) . \) If the particle crossed the positive direction of the \( x \) -axis for
the first time of the circle \( C_{n} \) then \( n \) is
A . 7
B. 6
\( c \cdot 2 \)
D. none of these


The current gain of transistor in a
common emitter circuit is \( 40 . \) The ratio
of emitter current to base current is
\( \mathbf{A} \cdot 40 \)
B. 41
c. 42
D. 43


In earthworm, the septal nephridia begin from behind \( \ldots \ldots . . . . \) segment.
\( \mathbf{A} \cdot 18 \)
B . 17
\( c \cdot 15 \)
\( D \cdot 13 \)


Change in length per unit length per unit change in temperature is defines as coefficient of linear expansion. Type 1
for true and 0 for false


Potentiometer measures potential more
accurately because
A. it measures potential in the open circuit
B. it uses sensitive galvanometer for null deflection
C. it uses high resistance potentiometer wire
D. it measures potential in the closed circuit


The angular momentum of the \( \alpha- \)
particles which are scattered through large angles by the heavier nuclei, is conserved because
A. of the nature of repulsive forces
B. the kinetic energy is conserved
c. the potential energy is conserved
D. there is no external torque


Write Nernst equation for Daniel cell at
equilibrium condition and derive
relationship between \( E_{(\text {cell})}^{o} \) and
equilibrium constant \( \left(\boldsymbol{K}_{c}\right) \)


Integrate \( \int_{0}^{2} \log x d x \)


If the value of \( 1 \frac{2}{3}+2 \frac{4}{5}=\frac{x}{y} \) then find
\( \boldsymbol{x}+\boldsymbol{y} \)


Evaluate
i) \( \int \frac{x^{2}+1}{x^{4}+1} d x \)
\( i i) \int \frac{d x}{x^{2}+1} \)


Photoreceptors of Earthworm occur on
A. Clitellum
B. Anal segment
c. Dorsal surface
D. Lateral sides


The reaction \( \boldsymbol{C r}_{2} \boldsymbol{O}_{3}+\boldsymbol{2} \boldsymbol{A} \boldsymbol{l} \rightarrow \boldsymbol{A l}_{2} \boldsymbol{O}_{3}+ \)
\( 2 C r\left(\triangle G^{0}=-421 k J\right) \) is
thermodynamically feasible due to -ve
value of \( \triangle G . \) Why does this reaction not take place at room temperature?
A. Certain amount of activation energy is essential for thermodynamically feasible reactions also.
B. Due to high melting point of chromium oxide the reaction does not take place
c. overall value of \( \triangle G \) for the net reaction becomes positive
D. Molecules of \( C r_{2} O_{3} \) and \( A \) l are not oriented properly


Find \( y \)
\( \mathbf{A} \cdot 45^{\circ} \)
B \( .60^{\circ} \)
\( c \cdot 15^{c} \)
D . 20


Two trains are moving with velocities \( \boldsymbol{v}_{1}=\mathbf{1 0} \boldsymbol{m} \boldsymbol{s}^{-1} \) and \( \boldsymbol{v}_{2}=\mathbf{2 0} \boldsymbol{m} \boldsymbol{s}^{-1} \) on the
same track in opposite directions. After
the application of brakes if their
retarding rates are \( a_{1}=2 m s^{-2} \) and
\( a_{1}=1 m s^{-2} \) respectively, then the
minimum distance of separation between the trains to avoid collision is
\( \mathbf{A} \cdot 150 m \)
В. \( 225 \mathrm{m} \)
c. \( 450 m \)
D. \( 300 m \)


Nitrogenous base present in DNA are
(a) Thymine
(b) Cytosine
(c) Adenine
(d) Guanine
\( A \cdot a, b, c \)
B. a, c, d
\( c \cdot b, c, d \)
D. all


Which of the following functions (is) are injective map(s)?
A \( \cdot f(x)=x^{2}+2, x \in(-\infty, \infty) \)
B. \( f(x)=|x+2|, x \in[-2, \infty) \)
C. \( f(x)=(x-4)(x-5), x \in(-\infty, \infty) \)
D. \( f(x)=\frac{4 x^{2}+3 x-5}{4+3 x-5 x^{2}}, x \in(-\infty, \infty) \)


Define Lateral Section?


\( \frac{\cos ^{2} 30^{\circ}+\cos 30^{\circ} \sin 30^{\circ}+\sin ^{2} 30^{\circ}}{\cos ^{3} 30^{\circ}-\sin ^{3} 30^{\circ}} \)


In the sequence of reactions (A) is:
\( (A) \stackrel{N a}{\rightarrow}(B)^{C_{2} H_{5} I / h e a t} \)
\( (\boldsymbol{C}) \stackrel{\boldsymbol{H I} / \text {heat}}{\rightarrow} \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{I} \)
A . acetic acid
B. methyl alcohol
c. ethyl alcohol
D. propionic acid


At a certain location in Africa, a
compass points \( 12^{\circ} \) west of the
geographic north. The north tip of the magnetic needle of a dip circle placed in the plane of magnetic meridian
points \( 60^{\circ} \) above the horizontal. The
horizontal component of the Earth's
field is measured to be \( 0.16 G . \) Specify the direction and magnitude of the Earth's field at the location.
A \( \cdot 32^{\circ} \) west of geographic meridian and \( 3.2 \times 10^{-4} T \)
B . \( 12^{\circ} \) west of geographic meridian and \( 0.32 \times 10^{-4} \mathrm{T} \)
C. \( 12^{\circ} \) east of geographic meridian and \( 0.32 \times 10^{-4} \mathrm{T} \)
D. \( 32^{\circ} \) east of geographic meridian and \( 3.2 \times 10^{-4} T \)


A prism having an apex angle of \( 4^{\circ} \) and
refractive index of 1.50 is located in
front of a vertical plane mirror as shown
in the figure. A horizontal ray of light is incident on the prism. The total angle
through which the ray is deviated is?
\( \mathbf{A} \cdot 4^{\circ} \) clockwise
B. \( 178^{\circ} \) clockwise
c. \( 2^{\circ} \) clockwise
D. \( 8^{\circ} \) clockwise


The order and degree of the differential
equation
\( \left[\left\{x-\left(\frac{d y}{d x}\right)^{2}\right\}^{\frac{3}{2}}\right]^{2}=\left(a^{2} \frac{d^{2} y}{d x^{2}}\right) \)
\( A \)
B. 1,2
\( c .2,2 \)
D. \( 1, \)


The single-bonded metallic radius of sodium is 157 pm. Assume that the increment between radii of different
magnitudes is 60 pm.The van der Waals' radius \( N a \) in \( \mathrm{pm} \) is \( (209+x) \)
Find value of \( \boldsymbol{x} \)


Do liquids exert pressure on the sides of the container they are kept in? Justify.


Calculate the orbital angular
momentum of the following orbitals:
(a) \( 3 p \)
(b) \( 3 d \)
(c) \( 3 s \)


Alkene \( (\mathrm{X})\left(C_{5} H_{1} 0\right) \) on ozonolysis gives a mixture of two compounds \( (Y) \) and \( (Z) \) Compound (Y) gives positive Fehling's test and iodoform test. Compound \( (z) \) does not give Fehling's test but give iodoform test. Compounds \( (X),(Y) \) and
(z) are?
A \( \cdot X=C_{6} H_{5} C O C H_{3}, Y=C H_{3} C H O, Z= \)
\( C H_{3} C O C H_{3} \)
B. \( X=C H_{3}-C H=\underset{C H_{3}}{C}-C H_{3}, Y= \)
\( C H_{3} C H O, Z=C H_{3} C O C H_{3} \)
c. \( X=C H_{3} C H_{2} C H=C H_{2}, Y= \)
\( C H_{3} C H_{2} C H O, Z=H C H O \)
D. \( X=C H_{3}-C H=C H-C H_{3}, Y= \)
\( C H_{3} C H O, Z=C H_{3} C H O \)


Which of these are examples of evolution by anthropogenic action?
(i) Adaptive radiation of marsupials of
Australia.
(ii) Appearance of antibiotic resistant
microbes.
(iii) Evolution of finches in Galapagos islands.
(iv) Appearance of dark winged moth in England during post industrialisation period.
(v) Convergent evolution of placental mammals in Australia.
A. (i) and (ii)
B. (v) only
c. (ii) only
D. (ii) and (iv) only
E. (iii) and (v) only


Allium cepa is a member of
A. Poaceae
B. Brassicaceae
c. Solanaceae
D. Liliaceae


If a copper wire is stretched to make its
radius decrease by \( 0.1 \% \), then the percentage increase in its resistance is approximately:
A . 0.1\%
B. 0.2\%
c. \( 0.4 \% \)
D. 0.8\%


Which method is used to get very pure germanium used in semiconductor?
A. Vapour-phase refining
B. Electrolysis
c. Liquation
D. zone-refining


Which statement about light waves and
sound waves is correct?
A. Both light waves and sound waves show the Doppler effect
B. Light waves can be diffracted but sound waves cannot be diffracted
c. Sound waves are transverse waves and light waves are longitudinal waves
D. Sound waves can travel in a vacuum but light waves control travel in a vacuum.


Draw a triangle with sides \( 5 \mathrm{cm}, 6 \mathrm{cm} \) and \( 6 \mathrm{cm} . \) Draw a square having the same area as the triangle.


A ball of mass \( m \) moving with velocity \( v \) collides elastically with another ball of identical mass coming from opposite direction with velocity \( 2 v \). Their velocities after collision will be :
A. \( -v, 2 v \)
В. \( -2 v, v \)
c. \( v,-2 v \)
D. \( 2 v,-v \)


Nerve fibre is
A. A thin nerve
B. Fibre formed by many axons
C. Fibre formed by ensheathing of axon in myelinated fibre
D. Fibre formed by ensheathing of a dendrite


Mutual inductance of two coils can be
increased by
A. decreasing the number of turns in the coils
B. increasing the number of turns in the coils
c. winding the coils on wooden cores
D. none of these.


In a ripple tank,15 full ripples are produced in one second. if the distance between a trough and the next crest is 20 c.Calculate frequency
A . 2 н \( z \)
B. 12 Hz
\( c \cdot 15 \mathrm{Hz} \)
D. 22 Hz


A function \( f(X) \) which satisfies the relation \( \boldsymbol{f}(\boldsymbol{X})=\boldsymbol{e}^{\boldsymbol{x}}+\int_{0}^{1} \boldsymbol{e}^{\boldsymbol{x}} \boldsymbol{f}(\boldsymbol{t}) \boldsymbol{d} \boldsymbol{t}, \) then
\( \boldsymbol{f}(\boldsymbol{X}) \) is
A \( \cdot \frac{e^{x}}{2-e} \)
B \( \cdot(e-2) e^{x} \)
\( c \cdot 2 e^{x} \)
D. \( \frac{e^{x}}{2} \)


Prove the following identities:
\( 1+\cos ^{2} 2 x=2\left(\cos ^{4} x+\sin ^{4} x\right) \)


The numerical value of the atmospheric
pressure on the surface of earth in
pascal is
A \( \cdot 1.013 \times 10^{5} \) pascal
B. 10 bar
c. 1.10325 bar
D. None


The sum of first 10 terms of the A.P.
\( -2,1,4,7, \) is:
A . 115
в. 230
\( c .1000 \)
D. 620


A planet of radius \( \boldsymbol{R}=\frac{\mathbf{1}}{\mathbf{1 0}} \times \)
(radiusof Earth) has the same mass
density as Earth. Scientists dig a well of depth \( \frac{R}{5} \) on it and lower a wire of the same length and of linear mass density \( 10^{-3} k g m^{-1} \) into it. If the wire is not touching anywhere, the force applied at the top of the wire by a person holding it in place is (take the radius of Earth \( = \)
\( 6 \times 10^{6} m \) and the acceleration due to
gravity of Earth is \( 10^{-2} \) )
\( \mathbf{A} \cdot 96 N \)
в. \( 108 N \)
c. \( 120 N \)
D. \( 150 N \)


Select the correct pattern of
arrangement of reproductive structures
for gymnosperms.
A. Spores \( \rightarrow \) Sporophylls \( \rightarrow \) Sporangia \( \rightarrow \) Strobill
B. Spores \( \rightarrow \) Sporangia \( \rightarrow \) Sporophylls \( \rightarrow \) Strobili
c. sporangia \( \rightarrow \) Sporophylls \( \rightarrow \) Spores \( \rightarrow \) Strobili
D. Spores \( \rightarrow \) Sporangia \( \rightarrow \) Strobili \( \rightarrow \) Sporophylls


What are tetrasaccharides? Give its
general formula and an example.


A number of \( X-X \) bond exists in
which of the following compounds
having the general form of \( \boldsymbol{X}_{2} \boldsymbol{H}_{6} ? \) This question has multiple correct options
\( \mathbf{A} \cdot B_{2} H_{6} \)
в. \( C_{2} H_{6} \)
c. \( A l_{2} H_{6} \)
D. \( \operatorname{si}_{2} H_{6} \)


\( 2 H_{2} \) is needed to make one molecule of
water, here \( ^{\prime} 2 H_{2}^{\prime} \) means:


The number of significant figures in \( 6.023 \times 10^{23} \) is
\( \mathbf{A} \cdot \mathbf{4} \)
B. 3
\( c \cdot 2 \)
D . 23


The number of terms that are integers in the binomial expansion of \( (\sqrt{7}+ \) \( \sqrt[3]{5})^{35} \) is
A . 4
B. 5
\( c \cdot 6 \)
D.


What is especially observed when a
beam of light is passed through a colloidal solution?


How did Whittaker classify the
organisms? What was the basis for classification?


Coelenterates are animals.
A. Amphibian
B. Terrestrial
c. Aquatic
D. Aerial


An induced e.m.f. is produced when a
magnet is plunged into a coil. The strength of the induced e.m.f. is independent of
A. the strength of the magnet
B. number of turns of coil
c. the resistivity of the wire of the coil
D. speed with which the magnet is moved


Count total number of significant figures in 0.00418
A. 5
B. 4
\( c \cdot 3 \)
\( D \)


"If we control population growth, then we prosper". Negative of this proposition is:
A. If we do not control population growth, we prosper
B. If we control population, we do not prosper
c. we control population and we do not prosper
D. If we don't control population, we do not prosper


A convex spherical refracting surface
with radius \( R \) separates a medium
having refractive index \( 5 / 2 \) from air. As an object is moved towards the surface from far away from the surface along
the principle axis, its image
A. Changes from real to virtual when it is at a distance \( R \) from the surface
B. Changes from virtual to real when it is at a distance \( R \) from the surface
c. changes from real to virtual when it is at a distance \( 2 R / 3 \) from the surface
D. Changes from virtual to real when it is at a distance \( 2 R / 3 \) from the surface


\( \frac{a}{a-c}+\frac{b}{b-c} \)


Answer the following questions:
On the basis Hardy-Schulze rule explain
why the coagulating power of phosphate is higher than chloride?


A particle of mass \( 1 \mathrm{gm} \) and charge \( 1 \mu C \) is held at rest on a frictionless horizontal surface at distance \( 1 \mathrm{m} \) from the fixed charge 2 mC. If the particle is released, it will be repelled. The speed of the particle when it is at a distance of
\( 10 \mathrm{m} \) from the fixed charge
A \( \cdot 60 m s^{-1} \)
B. \( 100 \mathrm{ms}^{-1} \)
c. \( 90 m s^{-1} \)
D. \( 180 \mathrm{ms}^{-1} \)


If \( A=\{1,3,5,6\} \) and \( B=\{2,4\} . \) Find
\( A \times B \) and \( B \times A \)


One picogram (pg) is equal to how many base pairs (bp)?
A \( \cdot 1 \times 10^{9} \)
B . \( 0.965 \times 10^{9} \)
c. \( 0.965 \times 10^{10} \)
D. \( 0.963 \times 10^{8} \)


How does anisole react with \( H N O_{3} \) in
presence of Suphuric acid?


\( \sqrt[n]{[-1]} \)
\( i \)
\( \underbrace{\frac{\pi}{n} \underbrace{n}_{n}+\underbrace{ }_{\rightarrow n}} \)


A person climbs up a stalled escalator in \( 60 s . \) If standing on the same but escalator running with constant velocity he takes 40 s. How much time
is takne by the person to walk up the
moving escalator?
\( \mathbf{A} \cdot 37 s \)
в. \( 27 s \)
c. \( 24 s \)
D. \( 45 s \)


f \( \boldsymbol{A}=\{\mathbf{5}, \boldsymbol{6}, \boldsymbol{7}, \boldsymbol{8}\} \) and \( \boldsymbol{B}=\{\boldsymbol{6}, \boldsymbol{8}, \boldsymbol{1} \boldsymbol{0}\} \)
find total elements in \( (\boldsymbol{A} \cup \boldsymbol{B}) \times(\boldsymbol{A} \cap \)
\( B) \)


limit of BOD prescribed by Central
Pollution Control Board for discharge of industrial and municipal waste waters into natural surface waters is
A. \( <3.0 \) ppm
в. \( <10 \) ррт
c. \( <30 \) ppm
D. < 100 ppm


The first term of an arithmetic
progression \( a_{1}, a_{2}, a_{3}, \dots \) is equal to unity. At what value of the difference of
the progression is \( a_{1} a_{3}+a_{2} a_{3} \) at a
minimum?


Which of the following does not form magnetic element?
\( A \cdot B H \)
в. \( B v \)
\( c . \) dip
D. declination


If \( A, B, C \) are in A.P., then \( \frac{\sin A-\sin C}{\cos C-\cos A}=? \)


The monthly profits earned by shops of a shopping complex are shown as the following frequency distribution. Draw ogive curve for the below data.
Profit
(in
05- 25- 45 thousano \( \begin{array}{lll}\text { 25 } & \text { 45 } & \text { 65 }\end{array} \)
Rs)
No. of shops


Part of pectoral girdle is
A. Ileum
B. Glenoid cavity
c. Acetabulum
D. Sternum


A pendulum clock consists of an iron rod connected to a small, heavy bob. If it is designed to keep correct time at
\( 20^{\circ} \mathrm{C}, \) how fast or slow will it go in
24 hours at \( 40^{\circ} \mathrm{C} \) ? Coefficient of linear
expansion of iron \( =1.2 \times 10^{-6} /^{\circ} \mathrm{C} \)
A . 10.4 sec.
B . 1.04 sec.
c. 0.52 sec.
D. 5.02 sec.


Two plates (area \( =5 \) ) charged to \( +q_{1} \)
and \( +q_{2}\left(q_{2}<q_{1}\right) \) are brought closer to
form a capacitor of capacitance \( C \). The potential difference across the plates is
A \( \cdot \frac{q_{1}-q_{2}}{2 C} \)
в. \( \frac{q_{1}-q_{2}}{C} \)
c. \( \frac{q_{1}-q_{2}}{4 C} \)
D. \( \frac{2\left(q_{1}-q_{2}\right)}{C} \)


When we go from solid to gaseous state, the speed of sound
A. increases
B. increases or decreases
c. decreases
D. constant


The temperature as measured by the
thermometer shown here will be:
A \( \cdot 84^{\circ} \mathrm{C} \)
в. \( 86^{\circ} \mathrm{C} \)
\( \mathrm{c} \cdot 88^{\circ} \mathrm{C} \)
D. \( 90^{\circ} C \)


Give IUPAC name of the following compound:
\( \boldsymbol{C H} \equiv \boldsymbol{C}-\boldsymbol{C}\left(\boldsymbol{C H}_{3}\right) \)
A. 3,3 - dimethylpropyne
B. 3,3-dimethylbutyne
c. 2,2-dimethylbut-3-yne
D. None of these


Maximum frequency of emission is obtained for the transition:
A \( . n=2 \) to \( n=1 \)
B. \( n=6 \) to \( n=2 \)
c. \( n=1 \) to \( n=2 \)
D. \( n=2 \) to \( n=6 \)


A wave or a pulse is reflected normally from the surface of a denser medium
back into the rarer medium. The phase change caused by the reflection-
A .
B . \( \pi / 2 \)
\( c \)
D. \( 3 \pi / 2 \)


Which one of the following is a correct
statement?
A. Bleaching powder is a compound
B. Bleaching powder is mixture of calcium chloride and calcium hypochloride
C. Bleaching powder is a mixture of calcium chloride,calcium hypochlorite and slaked lime
D. Bleaching powder is a mixture of sodium chloride and sodium hypochloride


With reference to semiconductor
devices, define a p-type semiconductor
and a Zener diode. What is the use of a
Zener diode?


Pure \( N_{2} \) gas is obtained from:
A. \( N H_{3}+N a N O_{2} \)
в. \( N H_{4} C l+ \) NaNO \( _{2} \)
\( \mathbf{c} \cdot N_{2} O+C a \)
D. \( \left(N H_{4}\right)_{2} C r_{2} O_{7} \)


An infinite nonconducting sheet has a
surface charge density \( \boldsymbol{\sigma}= \)
\( 0.10 \mu C / m^{2} \) on one side. How far apart
are equipotential surfaces whose potentials differ by \( 50 V ? \)
A. \( 8.8 \mathrm{mm} \)
B. \( 8.8 \mathrm{cm} \)
\( c .8 .8 m \)
D. \( 8.8 \mu m \)


On increase of temperature, a saturated solution converts into
solution.


According to the reaction above, what mass of oxygen gas is required to produce \( 88 g \) of carbon dioxide? \( \boldsymbol{C}+\boldsymbol{O}_{2}=\boldsymbol{C} \mathbf{0}_{2} \)
A . \( 12 g \)
в. \( 16 g \)
c. \( 24 g \)
D. \( 64 g \)


Are covalent bonds always non polar?
A. True
B. False


Why \( L i I \) is more soluble than \( K I \) in
ethanol?


The focal length of a symmetric biconvex lens is \( 20 \mathrm{cm} \). If the refractive
index of the material of the prism is 1.5
the radius of curvature of one of two
surfaces is
\( A \cdot 10 \mathrm{cm} \)
B. 20 cm
c. \( 40 \mathrm{cm} \)
D. 80 cm


f \( \boldsymbol{y}=\sin \boldsymbol{p} \boldsymbol{x} \) prove that
\( \boldsymbol{\Delta}=\left|\begin{array}{lll}\boldsymbol{y} & \boldsymbol{y}_{1} & \boldsymbol{y}_{2} \\ \boldsymbol{y}_{3} & \boldsymbol{y}_{4} & \boldsymbol{y}_{5} \\ \boldsymbol{y}_{6} & \boldsymbol{y}_{7} & \boldsymbol{y}_{8}\end{array}\right|=0 \)
where \( y_{r}, \) means \( r-t h \) differential
coefficient of \( \boldsymbol{y} \)


Two lamps one rated \( 60 \mathrm{W}, 220 \mathrm{V} \) and the other \( 40 \mathrm{W}, 220 \mathrm{V} \) are connected in
parallel to a \( 220 \mathrm{V} \) electric supply mains. What is the total current drawn from the
electric mains if the voltage of electric supply is \( 220 \mathrm{V} ? \)


The value of \( 60^{\circ} \) in centesimal system is
A \( \cdot \frac{100^{9}}{3} \)
в. \( \frac{200^{9}}{3} \)
c. \( \frac{140^{9}}{3} \)
D. \( \frac{160^{9}}{3} \)


Which of the following does not contain
covalent bond?
A. \( C o C l_{2} \)
в. \( M n O_{4}^{-} \)
\( \mathrm{c} \cdot \mathrm{Cr} \mathrm{O}_{4}^{2} \)
D. \( C r_{2} O_{7}^{2-} \)


Select an incorrect option regarding the
given figure.
A. \( P \) is a compound gland with exocrine and endocrine
B. \( R \) is formed from duct of gall bladder along with the hepatic duct.
C. \( R \) is guarded by a sphincter of Oddi
D. Q stores bile which is actually produced in liver


The magnification of the image when an object is placed at a distance \( x \) from the
principle focus of a mirror of focal length \( f \) is?
A \( \cdot \frac{x}{f} \)
B. \( 1+f / x \)
c. \( \frac{f}{x} \)
D. \( _{1-\frac{f}{x}} \)


f \( \boldsymbol{O} \boldsymbol{x}_{\mathbf{1}}+\boldsymbol{a} \boldsymbol{e}^{-} \rightleftharpoons \boldsymbol{R} e \boldsymbol{d}_{1}, \quad \boldsymbol{E}_{1}^{\boldsymbol{o}} \)
\( \boldsymbol{O} \boldsymbol{x}_{2}+\boldsymbol{b} \boldsymbol{e}^{-} \rightleftharpoons \boldsymbol{R} e d_{2}, \quad \boldsymbol{E}_{2}^{o} \)
The potential at the equivalence point is :
A. \( _{E}=\frac{a E_{1}^{o}+b E_{2}^{o}}{(a+b)} \)
B. \( \quad E=\frac{a E_{1}^{o}-b E_{2}^{o}}{(a+b)} \)
c. \( _{E=\frac{b E_{1}^{o}-a E_{2}^{\circ}}{(a+b)}} \)
D. \( \quad E=\frac{a E_{1}^{o}-b E_{2}^{o}}{(a-b)} \)


Assertion
Photosynthesis takes place in all green
plants.
Reason
Chlorophyll is essential for
photosynthesis.
A. Both A and R are true but R is the correct explanation of
B. Both A and R are true but R is not a correct explanation of
c. \( A \) is true but \( R \) is false
D. A is false but R is true


The force-extension graph of a metal
wire is shown.

At which point on the graph does the metal wire stop obeying Hooke's law?


The star which lies immediately above the Earth's North Pole is called the
A. pole star
B. alpha Centauri
c. sun
D. none of these


Which of the following statements is
not true about brain?
A. The main thinking part of brain is hind brain.
B. Centres of hearing, smell, memory, sight etc. are located in fore brain
C. Involuntary actions like salivation, vomiting, blood pressure are controlled by the medulla in the hind brain.
D. None of the above.


Chloride shift occurs in response to
A . \( H^{+} \)
в. \( K^{+} \)
\( \mathrm{c} \cdot \mathrm{H} \mathrm{CO}_{3} \)
D. \( N a^{+} \)


The hybridization of sulphur in peroxodisulphuric acid is:
\( A \cdot s p^{2} \)
В \( \cdot s p^{3} \)
c. \( s p \)
D. \( s p^{3} d \)


The important considerations in deciding if a reaction will be
spontaneous are :
A. stability \& state of reactants
B. energy gained \& heat evolved
c. exothermic energy \& randomness of the products
D. endothermic energy \& randomness of the products
E. endothermic energy \& structure of the products


Write the negative (additive inverse) of
each of the following:
-1


If \( \overline{\boldsymbol{F}}=\mathbf{2} \overline{\boldsymbol{i}}-\mathbf{3} \overline{\boldsymbol{j}} \boldsymbol{N} \) and \( \overline{\boldsymbol{r}}=\mathbf{3} \overline{\boldsymbol{i}}+\mathbf{2} \overline{\boldsymbol{j}} \boldsymbol{m} \)
The torque \( \boldsymbol{\tau} \) is:
\( \mathbf{A} \cdot 12 \hat{k} \)
в. \( 13 \hat{k} \)
c. \( -12 \hat{k} \)
D. \( -13 \hat{k} \)


Two lead spheres of \( 20 \mathrm{cm} \) and \( 2 \mathrm{cm} \) diameter are placed with their centres 1.0 \( m \) apart. Calculate the force of
attraction between the two spheres. The
radius of the earth is \( 6.37 \times 10^{6} m \), its
density is \( 5.51 \times 10^{3} k g / m^{2} \) and
relative density of lead is 11.5


Intramolecular hydrogen bond is
present in:
A. water
B. o-nitrophenol
c. p-nitrophenol
D. methylamine


Find out the average angular speed and
angular speed of the second hand of
clock.


\( \int_{2}^{3}(1+2 x) d x \)


Find the square root of the following number by the prime factorisation method.
4356


a) Draw an ideal pyramid of energy and mention the units.
b) What is an ecological succession?


Out of following which are random
variables
This question has multiple correct options
A. \( x= \) "Number of heads when two coins are tossed
B. \( x= \) "Sum of digits on uppermost face of two dice
c. solution of " \( X-4=0 " \)
D. \( x= \) "Raining


Find the current passing through battery immediately after key ( \( K \) ) is
closed. It is given that initially all the capacitors are uncharged (Given that \( R=6 \Omega \text { and } C=4 \mu F) \)
\( A \cdot 1 A \)
\( c .3 A \)
0.24


In an experiment, the resistance of a
material is plotted as a function of temperature (in some range). As shown in the figure, it is a straight line. One may conclude that:
A \( \cdot R(T)=\frac{T_{0}}{T^{2}} \)
B . \( R(T)=R_{0} e^{-T^{2} / T_{0}^{2}} \)
C \( \cdot R(T)=R_{0} e^{-T_{0}^{2} / T^{2}} \)
D. \( R(T)=R_{0} e^{T^{2} / T_{0}^{2}} \)


A closed curve encircles several conductors.The line integral \( \int \overrightarrow{\boldsymbol{B}} \cdot \boldsymbol{d} \overrightarrow{\boldsymbol{l}} \)
around this curve is \( 3.83 \times 10^{-7} T-m \)
If you were to integrate around the curve in the opposite direction, what
could be the value of the line integral?


The value of gravitation constant is \( \boldsymbol{G}=\mathbf{6 . 6 7} \times \mathbf{1 0}^{-\mathbf{1 1}} \boldsymbol{N}-\boldsymbol{m}^{2} / \boldsymbol{k g}^{2} \) in SI
units. Convert it into CGS system of
units.
A. Thus, value of G in CGS system of units is 6.67 x \( 10^{-8} \) dyne \( c m^{2} / g^{2} \)
B. Thus, value of G in CGS system of units is \( 6.67 \times \) \( 10^{-9} \) dyne \( c m^{2} / g^{2} \)
c. Thus, value of G in CGS system of units is 6.67 x \( 10^{-7} \) dyne \( c m^{2} / g^{2} \)
D. Thus, value of G in CGS system of units is 6.67 x \( 10^{-10} \) dyne \( c m^{2} / g^{2} \)


Choose the incorrect statement.
A. Size of \( 4 d \) and \( 5 d \) series elements is almost same
B. Generally, negative value of standard reduction potential \( \left(M^{2+} / M\right) \) of \( 3 \mathrm{d} \) -series element decreases across the period
\( \mathrm{C} \cdot \mathrm{Cr}_{2} \mathrm{O}_{7}^{2-} \) has one type of \( \mathrm{Cr}-\mathrm{O} \) bond length
D. Generally, actinide and lanthanide shows +3 oxidation
state


f \( \left|z_{1}\right|=2,\left|z_{2}\right|=3,\left|z_{3}\right|=4 \) and
\( \left|2 z_{1}+3 z_{2}+4 z_{3}\right|=4 \) then the absolute
value of \( 8 z_{3} z_{2}+27 z_{3} z_{1}+64 z_{1} z_{2} \)
equals
A .24
B . 48
\( c \cdot 72 \)
D. 96


Assertion
The differential equation of all circles in
a plane is of order 3
Reason
Only one circle can be drawn through any three points in a plane
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


Some equipotential surfaces of the
magnetic scalar potential are shown in figure.Magnetic field at a point in the region is
A \( \cdot 10^{-4} \) न
B . \( 0.5 \times 10^{-4} \) T
c. \( 2 \times 10^{-4} \) न
D. None of these


Which has maximum internal energy at
298 K?
A. Helium gas
B. Oxygen gas
c. Ozone gas
D. All are equal


The difference between simple interest and compound interest on a certain sum of money for 3 years at \( 5 \% \) per annum is Rs. 122. Find the sum
\( A \cdot \) Rs. 12,200
B. Rs. 15,000
c. Rs. 16,500
D. Rs. 16,000


Express \( \boldsymbol{A}= \)
\( \{(a, b): 2 a+b=5, a, b \in W\} \) as the
set of ordered pairs.


The equation of a straight line passing through the point (1,2) and inclined at
\( 45^{\circ} \) to the line \( y=2 x+1 \) is
A. \( 5 x+y=7 \)
в. \( 3 x+y=5 \)
c. \( x+y=3 \)
D. \( x-y+1=0 \)


Sushant has a vessel, of the form of an inverted cone, open at the top, of height \( 11 c m \) and radius of top as \( 2.5 \mathrm{cm} \) and is
full of water. Metallic spherical balls each of diameter \( 0.5 \mathrm{cm} \) are put in the
vessel due to which \( \left(\frac{2}{5}\right) \) th of the water in the vessel flows out. Find how many
balls were put in the vessel. Sushant
made the arrangement so that the water that flows out irrigates the flower beds. What value has been shown by
Sushant?


The definitive experiments with cathode-ray tubes were done by
in 1879
A. Michael Faraday
B. William Crookes
c. william whewell
D. Johannes Hittorf


Find the geometric mean between 16
and 81
A . 4
B. 9
\( c .36 \)
D. 18


The gravitational force of attraction between two bodies at a certain
distance is \( 10 \mathrm{N} \). If the distance
between them is doubled, the force of
attraction:
A. decreases by \( 50 \% \)
B. decreases by \( 75 \% \)
C. increases by \( 50 \% \)
D. increases by \( 75 \% \)


Correct IUPAC naming of the given
compound is :
A . 2-methyl-2-bromopropane
B. 2-methyl-3-bromopropane
c. 2-bromo-2-methylpropane
D. 2,2,2 -trimethylbromomethane


Which of the following is not a saturated hydrocarbon?
A. Cyclohexane
B. Benzene
c. Butane
D. Isobutane


Which of the following is not an isotope of hydrogen atom?
A. Protium
B. Deuterium
c. Tritium
D. Platinum


\( K_{P} \) for the reaction \( N_{2}+3 H_{2} \rightleftharpoons \)
\( 2 N H_{3} \) at \( 400 C \) is \( 1.64 \times 10^{-4} . \) Find \( K_{C} \)
Also find \( \triangle G^{\oplus} \) using \( K_{P} \) and \( K_{C} \)
values and interpret the differences.
A. \( K_{C}=0.025 \) \( \triangle G^{\oplus}=+11.733 k c a l \)
в. \( K_{C}=2.001 \) \( \triangle G^{\oplus}=+19.249 k c a l \)
c. \( K_{C}=0.5006 \) \( \triangle G^{\oplus}=+11.733 k c a l \)
D. \( K_{C}=1.5 \) \( \triangle G^{\oplus}=+15.22 k c a l \)


Ozone depleting substances are:
A. photochemical oxidants
B. polynuclear aromatic hydrocarbons
C. chlorofluorocarbons
D. cadmium and lead


If Ram takes 4 seconds by path 1 and Shyam takes 5 seconds by the path 2 to
go from \( P \) to \( Q \), find the average velocity
of Shyam?
\( A \cdot 25 \mathrm{m} / \mathrm{s} \)
B. 20 \( \mathrm{m} / \mathrm{s} \)
\( c \cdot 10 m / s \)
D. \( 40 \mathrm{m} / \mathrm{s} \)


Mention the role of Methanobacterium in
rumen of cattle.


For the cell Pt \( \mid \mathbf{H}_{2}(0.4 \text { at } m) \mid \mathbf{H}^{+}(p H=1) \) \( \left.\|(p H=2) \mid H_{2} 90.1 \text { atm }\right) \mid P t . \) The
measured potential at \( 25^{\circ} \mathrm{C} \) is:
A . \( -0.1 V \)
B. \( -0.5 V \)
c. \( -0.041 V \)
D. \( -0.030 V \)


The band gaps of a conductor, semiconductor and insulator are
respectively \( \boldsymbol{E} \boldsymbol{g}_{1}, \boldsymbol{E} \boldsymbol{g}_{2} \) and \( \boldsymbol{E} \boldsymbol{g}_{3} . \) The
relationship between them can be given
as.
A \( . E g_{1}=E g_{2}=E g_{3} \)
в. \( E g_{1}<E g_{2}<E g_{3} \)
c. \( E g_{1}>E g_{2}>E g_{3} \)
D. \( E g_{1}<E g_{2}>E g_{3} \)


Study this figure and answer the
question. What would B and C
represent?
A. Zonly
B. Wonly
\( c . z \) and \( w \)
\( D . \) ww


\( \operatorname{Given} M=(0,1,2) \) and \( N=(1,2,3) \)
Find \( (M \cup N) \times(M-N) \)


Maxwell's four equations are written as
(i) \( \oint \overrightarrow{\boldsymbol{E}} \cdot \overrightarrow{\boldsymbol{d}} \boldsymbol{s}=\frac{\boldsymbol{q}_{0}}{\varepsilon_{0}} \)
(ii) \( \oint \vec{B} \cdot \vec{d} s=0 \)
(iii) \( \oint \vec{E} . \overrightarrow{d l}=\frac{d}{d t} \oint \vec{B} \cdot \vec{d} s \)
\( (\text { iv }) \oint \vec{B} \cdot \vec{d} s=\mu_{0} \varepsilon_{0} \frac{d}{d t} \oint \vec{E} \cdot \vec{d} s \)
Out of the four Maxwell's equation above, which one shows the non-
existence of monopoles?
\( A \cdot \) (i) and (iv)
B. (ii) only
c. (iii) only
D. none of these


A uniform electric field and a uniform
magnetic field acting along the same direction in a certain region. If an electron is projected along the direction of the fields with a certain velocity, then
A. It will turn towards left of direction of motion
B. It will turn towards right to direction of motion
c. Its velocity will increase
D. Its velocity will decrease


Which of the following is correct about
Phase \( A \rightarrow \) Phase \( C ? \)
A. Sublimation
B. Deposition
c. Vaporization
D. condensation
E. Melting


A converging lens of focal length \( f_{1} \) is placed in front of and coaxially with a
convex mirror of focal length \( f_{2} \). Their
separation is \( d \). A parallel beam of light
incident on the lens returns as a
parallel beam from the arrangement. This question has multiple correct options
A. The beam diameter of the incident and reflected beams must be the same
в. \( d=f_{1}-2 \mid f_{2} \)
c. \( d=f_{1}-\left|f_{2}\right| \)
D. If the entire arrangement is immersed in water, the conditions will remain unaltered


Antifoaming agents prevent the generation of free radicals which damage the food. If this is true enter 1 , if false enter 0 .


Which of the following is a correct comparison between mitosis and
meiosis?
A. Meiosis II resembles mitosis when sister chromatids
split
B. Both prophase of mitosis and meiosis include pairing up of homologous chromosomes
C. In mitosis, aligning of maternal and paternal chromosomes can be random whereas, in meiosis, the alignment is fixed
D. Replication of chromosomes occurs at the start of mitosis and meiosis during prophase


The large bright stars with a cool
surface of \( 2000^{\circ} \mathrm{C} \) to \( 3000^{\circ} \mathrm{C} \), formed
during the later stages of the evolution
of a star like the sun as it runs out of
\( H_{2} \) fuel at its center
are
\( \mathbf{A} \cdot \) red dwarf
c. red giants


The area bounded by \( \boldsymbol{y}=\boldsymbol{x}^{2}, \boldsymbol{y}=[\boldsymbol{x}+ \)
1], \( x \leq 1 \) and the \( y \) -axis is
A \( \cdot \frac{1}{3} \)
B. \( \frac{2}{3} \)
\( c \cdot 1 \)
D.


The total number of isomers for a
square planar complex \( \left[\boldsymbol{M}(\boldsymbol{F})(\boldsymbol{C l})(\boldsymbol{S C N})\left(\boldsymbol{N O}_{2}\right)\right] \)
A . 12
B. 8
c. 16
\( D \)


The plot given below is of the average power delivered to an LRCLRC circuit
versus frequency. The quality factor of
the circuit is:
A . 5.0
B. 2.0
\( c .2 .5 \)
D. 0.4


Find the volume of a hemisphere of
radius \( 6.3 \mathrm{cm}(\pi=22 / 7) \)
A \( .523 .9 \mathrm{cm}^{3} \)
B . \( 520.91 \mathrm{cm}^{3} \)
D. \( 510.91 \mathrm{cm}^{3} \)


If \( y=\sqrt{x}+\frac{1}{\sqrt{x}}, \) show that \( 2 x \frac{d y}{d x}+ \)
\( \boldsymbol{y}=\mathbf{2} \sqrt{\boldsymbol{x}} \)


Which is the best description of the
behaviour of bromine in the reaction
given below?
\( \boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{B} \boldsymbol{r}_{2} \rightarrow \boldsymbol{H} \boldsymbol{O} \boldsymbol{B} \boldsymbol{r}+\boldsymbol{H} \boldsymbol{B} \boldsymbol{r} \)
A. Proton acceptor only
B. Both oxidised and reduced
c. oxidised only
D. Reduced only


A cellular organization between a single cell and a complete organism is controlled by
A. organs
B. Tissues
c. Enzymes
D. Proteins


What is internal energy change of
combustion for methanol?
Reaction
\( \mathbf{A} \cdot-680 k J / \)mole
B . \( -6.8 k J / \) mole
c. \( -567 k J / \) mole
D. \( -5.67 k J / \) mole


Average value of current or voltage over
a half cycle can be zero also. This depends on the time interval (of course
T/2) over which average value is to be found.Why?


is a self adjusting force.


The value of 0.423 is
A \( \cdot \frac{419}{990} \)
в. \( \frac{423}{1000} \)
c. \( \frac{419}{999} \)
D. \( \frac{419}{1000} \)


Which one of the following oxides is reduced by water gas to obtain the metal during its extraction?
A. \( N i O \)
в. \( Z n O \)
c. \( W O_{3} \)
D. \( F e_{2} O_{3} \)


If the surface of a liquid is plane, then
the angle of contact of the liquid with the walls of container is
A . Acute angle
B. obtuse angle
\( c .90^{\circ} \)
D. \( 0^{\circ} \)


Give the functional group of the following.
\( -\mathrm{COOH} \)
A. Aldehydic group
B. Alcoholic group
c. Ketonic group
D. Carboxylic group


Two point mass \( m_{1} \) and \( m_{2} \) are placed
at point \( A \) and \( B \) respectively as shown in figure.Point A is the centre of hollow sphere of uniformly distributed total
mass \( m_{3} . \) Consider only gravitational
interaction between all masses and
neglect other gravitational forces.
Select the incorrect alternative.
A . Hollow sphere and point mass \( m_{1} \) moves with same acceleration
B. \( m_{1} \) and \( m_{2} \) moves with same acceleration
C. Net force on \( m_{1} \) is non-zero
D. Net force on hollow sphere and point mass \( m_{1} \) as a system is equal to force experienced by point mass \( m_{2} \) in magnitude


\( \mathrm{IF} \sin \Theta=\frac{8}{17} \) where \( 0^{\circ}<\Theta<90^{\circ} \)
then \( \tan \Theta+\sec \Theta \) is
\( A \cdot \frac{1}{3} \)
B. \( \frac{2}{3} \)
\( c \cdot \frac{4}{3} \)
D.


The mobility of the \( N H_{4}^{+} \) ions is
\( \mathbf{7 . 6 2 3} \times \mathbf{1 0}^{-8} \mathbf{m}^{2} / \boldsymbol{V} \boldsymbol{s} . \) Calculate:
(a) the molar conductivity of \( \boldsymbol{N} \boldsymbol{H}_{\mathbf{4}}^{+} \) ion;
(b) Velocity of the ion of 15 volt are applied across the electrodes \( 25 \mathrm{cm} \)
apart


The standard heat of combustion of
graphite carbon is \( -393.5 \mathrm{KJ} \mathrm{mol}^{-1} \). The
standard enthalpy
of \( \mathrm{CO}_{2} \) is
A \( \cdot+393.5 \) KJ \( \mathrm{mol}^{-1} \)
B . - -393. 5 KJ mol-1
C . +196.75 КJ \( \mathrm{mol}^{-1} \)
D . -196.75 KJ mol-


Angular and spherical nodes in \( 3 s \) is:
A . \( 1, \)
в. 1,0
\( c \cdot 2,0 \)
D. 0,2


Which of the following metals generally occur in liquid state at room
temperature?
A. Mercury
B. Bromine
c. Gallium
D. A and c both


The graph drawn between pressure and
volume in Boyle's law experiment is
shown in figure for two different gases. If the same amount of both the gases has
been taken, then the relationship between their molecular weights will be
A \( . M_{2}<M_{1} \)
\( \mathbf{B} \cdot M_{1}<M_{2} \)
\( \mathbf{c} \cdot M_{1}=M_{2} \)
\( \mathbf{D} \cdot M_{1}^{3}=M_{2} \)


Coelenterata are
A. Ureotelic
B. Uricotelic
C. Ammonotelic
D. None of the above


The position in the periodic table to
which the lanthanides and
actinides metals belong:
A. alkali metals
B. alkaline earth metals
c. transition elements
D. inner transition elements


Which of the following is not suitable for use in dasiccator to dry substance?
A . conc. \( H_{2} S O_{4} \)
в. \( N a_{2} S O_{4} \)
c. \( C a C l_{2} \)
D. \( P_{4} O_{10} \)


In a construction job, following are some probabilities given:
Probability that there will be strike is \( 0.65, \) probability that the job will be completed on time if there is no strike is \( 0.80, \) probability that the job will be completed on time if there is strike is
0.32. Determine probability that the construction job will get complete on
time
A .0 .438
в. 0.538
\( c \cdot 0.488 \)
D. None of these


Find the coordinates of point which
divides the line joining the points (3,4) and (6,1) in the ratio of 1: 2


Determine the width of the region where the fringes will be visible
\( A \cdot 4 c m \)
B. \( 6 \mathrm{cm} \)
\( c .2 c m \)
D. 3 cm


In electromagnetic spectrum, the
frequencies of \( \gamma \) -rays and ultraviolet
rays are denoted by \( n_{1}, n_{2} \) and \( n_{3} \) respectively then.
A \( \cdot n_{1}>n_{2}>n_{3} \)
в. \( n_{1}<n_{2}<n_{3} \)
c. \( n_{1}>n_{2}<n_{3} \)
D. \( n_{1}<n_{2}>n_{3} \)


Approximately what percent of the universe is believed to consist of
hydrogen?
A . 25\%
B. 50\%
c. 75\%
D. 90\%


Classification of life forms is closely
related to their evolution.' Do you agree
with this statement? Comment with an
example.


A balloon contains 14.0 L of air at 760
torr. What will be the volume of the
balloon when it is taken to a depth of 10 ft. in a swimming pool? Assume that the temperature of the air and water are equal. (Density: \( \boldsymbol{H} \boldsymbol{g}=\mathbf{1 3 . 6} \mathrm{g} / \mathrm{mL} . \)
A . 47.5
B . 42.5
c. 44.5
D. 50


Two particles are executing \( S . H . M \) of same amplitude and frequency along the same straight line path. They pass each other when going in opposite directions, each time their displacement is half of their amplitude. What is the phase difference between
them?
A \( .5 \pi / 6 \)
в. \( 2 \pi / 3 \)
c. \( \pi / 3 \)
D. \( \pi / 6 \)


If \( \boldsymbol{y}^{2}=\boldsymbol{x}^{2}-\boldsymbol{x}+\mathbf{1} \) and \( \quad \boldsymbol{I}_{\boldsymbol{n}}=\int \frac{\boldsymbol{x}^{\boldsymbol{n}}}{\boldsymbol{y}} \boldsymbol{d} \boldsymbol{x} \)
and \( \boldsymbol{A I}_{3}+\boldsymbol{B I}_{2}+\boldsymbol{C I}_{1}=\boldsymbol{x}^{2} \boldsymbol{y} \) then
ordered triplet \( A, B, C \) is
\( ^{A} \cdot\left(\frac{1}{2},-\frac{1}{2}, 1\right) \)
В . (3,1,0)
\( \mathbf{c} \cdot(1,-1,2) \)
D. \( \left(3,-\frac{5}{2}, 2\right) \)


Energy required to break one bond in DNA is approximately:
\( \mathbf{A} \cdot \sim 1 \mathrm{eV} \)
в. 0.1 ev
c. \( \sim 0.01 \) ev
D. \( \sim 2.1 \mathrm{eV} \)


The two electrons have the following sets of quantum numbers. \( x: 3,2,-2,+1 / 2 \)
\( Y: 3,0,0,+1 / 2 \)
What is true of the following?
A. \( x \) and \( Y \) have same energy
B. \( x \) and \( Y \) have unequal energy
c. \( x \) and \( Y \) represent same electron
D. None of the statement is correct


In a mammalian cell the longest and the most active phase of the cell cycle is
A. Sphase
B. \( G_{1} \) Phase
c. \( G_{2} \) Phase
D. None of these


What is the use of a Zener diode?


Write a note on plumbosolvency?


Multiplicative inverse of \( 2 \frac{2}{7} \) is 2.2
A. True
B. False
c. cannot say
D. None


Removal of the unwanted materials like
sand, clays, etc. from the ore is known
as or
A. concentration, dressing, benefaction
B. separation, refining, gangue
c. magnetic separation, Purification, gangue
D. washing, refining, amalgamation


The volume vs. temperature graph of
mole of an ideal gas is given below.
The pressure of the gas (in atm) at
\( X, Y \) and \( Z, \) respectively, are:
A. 0.328,0.820,0.820
0
B. 3.28,8.20,3.28
c. 0.238,0.280,0.280
D. 32.8,0.280,82.0


Give the name of the complex
compound \( \boldsymbol{K}_{3}\left[\boldsymbol{F} e\left(\boldsymbol{C}_{2} \boldsymbol{O}_{4}\right)_{3}\right] \) according
to IUPAC system:
A. Potassium Ferric oxalate
B. Potassium trioxalatoiron(II)
c. Potassium trioxalatoferrate(III)
D. Tripotassium trioxalatoferrate(III)


If the rms current through a \( 6.8 k \Omega \)
resistor is \( 8 m A \), the rms voltage drop
across the resistor is
\( \mathbf{A} \cdot 5.44 V \)
в. \( 54.4 \mathrm{V} \)
c. \( 7.07 V \)
D. 8V


If \( f^{\prime \prime}(x)=-f(x) \) and \( g(x)=f^{\prime}(x) \) and
\( \boldsymbol{F}(\boldsymbol{x})=\left(\boldsymbol{f}\left(\frac{x}{2}\right)\right)^{2}+\left(\boldsymbol{g}\left(\frac{x}{2}\right)\right)^{2} \) and given
that \( F(5)=5, \) then \( F(10) \) is equal to
A . 5
B. 10
c. 0
D. 15


Find \( a, b \) and \( n \) in the expression of \( (a+b)^{n} \) if the first three terms of the
expansion are 729,7290 and 30375
respectively.


For the given circuit of P-Njunction
diode which is correct:
A. In F.B. the voltage across R is
B. In R.B. the voltage across R is
C. In F.B. the voltage across \( \mathrm{R} \) is \( 2 \mathrm{V} \)
D. In R.B. the voltage across \( R \) is \( 2 v \)


Potential due to an electric dipole is represented by:
(where \( p \) is the dipole moment, \( r(>> \)
2a) is the distance at which the
potential \( V \) of the dipole is calculated
and \( \theta \) is the angle between the distance
vector and the dipole.)
A \( \cdot V=\frac{p \cos \theta}{4 \pi \epsilon_{c} r^{4}} \)
B. \( V=\frac{p \sin \theta}{4 \pi \epsilon_{o} r^{2}} \)
c. \( V=\frac{p \sin \theta}{4 \pi \epsilon_{o} r^{4}} \)
D. \( V=\frac{p \cos \theta}{4 \pi \epsilon_{o} r^{2}} \)


\( \boldsymbol{C o}^{2+}(\boldsymbol{a q} \cdot)+\boldsymbol{S C N}^{-}(\boldsymbol{a q} \cdot) \rightarrow \)
Complex \( (\boldsymbol{X}) \)
\( N i^{2+}(a q .)+ \)
dimethylglyoxime \( \frac{N H_{4} O H}{\longrightarrow} \)
Complex \( (\boldsymbol{Y}) \)
The coordination number of cobalt and
nickel in both the complexes \( (X) \) and \( (Y) \) is four. The geometry of complexes \( (x) \) and (Y) are respectively:
A. tetrahedral and square planar
B. both tetrahedral
c. square planar and tetrahedral
D. both square planar


The colourless KBr or KI solutions turn
red and deep brown respectively on passing chlorine through it. Give reason


The botanical name of "Indian rai" is
A. Brassica campestris
B. Brassica juncea
c. Brassica nigraa
D. Brassica alba


Under the action of a central force, there
is a conservation of
A. Angular momentum only
B. Mechanical energy only
C. Angular momentum and mechanical energy
D. Neither angular momentum nor mechanical energy


\( " L i_{2} C O_{3} \) decomposes into \( C O_{2} \) and
\( L i_{2} O \) but other alkali carbonates are
thermally stable." Answer whether the above statement is
true or false.
If true enter 1 , else enter 0 .


Find the sum of the coefficients when
given equation is balanced.
\( \boldsymbol{A l}_{2}\left(\boldsymbol{S O}_{4}\right)_{3}+\boldsymbol{C a}(\boldsymbol{O H})_{2} \rightarrow \boldsymbol{A l}(\boldsymbol{O H})_{3}+ \)
\( \boldsymbol{C} \boldsymbol{a} \boldsymbol{S} \boldsymbol{O}_{4} \)
A . 5
B. 6
\( c \cdot 7 \)
D. 8
E . 9


Which of the following is most stable :
\( \mathbf{A} \cdot \mathbf{N I}_{3} \)
B. NF
c. \( \mathrm{NBr}_{3} \)
D. NCl_


topp \( E \)
Q туре your question
\( C u(s) \)
\( \boldsymbol{E}_{\text {cll }}^{o}=\mathbf{1 . 1 0} \boldsymbol{V} \)
\( \boldsymbol{X}-\boldsymbol{a} \boldsymbol{x} \boldsymbol{i} \boldsymbol{s}: \log _{10} \frac{\left[\boldsymbol{Z} \boldsymbol{n}^{2+}\right]}{\left[\boldsymbol{C u}^{2+}\right]}, \quad Y- \) axis \( : \boldsymbol{E}_{c e l l} \)
\( A \)
B.
\( c \)
\( D \)


State the following pair of sets
are equal or not
If they are equal then write 1 , else 0
\( \mathrm{E}=\left\{x: x^{2}+8 x-9=0\right\} \) and \( \mathrm{F}=\{1,-9\} \)


Using properties of determinants prove
that :
\( \left|\begin{array}{lll}\boldsymbol{x} & \boldsymbol{a} & \boldsymbol{a} \\ \boldsymbol{a} & \boldsymbol{x} & \boldsymbol{a} \\ \boldsymbol{a} & \boldsymbol{a} & \boldsymbol{x}\end{array}\right|=(\boldsymbol{x}+\mathbf{2} \boldsymbol{a})(\boldsymbol{x}-\boldsymbol{a})^{2} \)


The numbers of \( \boldsymbol{F} \hat{\boldsymbol{I}} \boldsymbol{F} \) angle equal to \( \boldsymbol{9 0}^{\boldsymbol{o}} \)
and less than \( 90^{\circ} \) in \( I F_{7} \) are and
respectively.

If the answer is 15 and 9 then represent as 159


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


If \( I \) is the unit matrix of order \( n, \) where
\( k \neq 0 \) is a constant then \( \operatorname{adj}(k I)= \)
A \( \cdot k^{n}(\operatorname{adj} I) \)
B. \( k(\operatorname{adj} I) \)
c. \( k^{2}(\operatorname{adj} I) \)
D. \( k^{n-1}(\text { adj } I) \)


What are the products obtained from the reaction given below? MeOEt \( \stackrel{H I}{\longrightarrow} ? \)
A . \( M e I \) and \( E t O H \)
B. \( M e O H \) and \( E t I \)
c. \( M e I, M e O H, E t I \) and \( E t O H \)
D. None of the above


Which of the following is not a property of hydrogen?
A. It is a colourless, odorless gas
B. It is highly combustible
c. It is highly poisonous gas
D. It is lighter than air


The inverse of a symmetric matrix is
A. symmetric
B. skew-symmetric
c. diagonal matrix
D. singular matrix


When heat is added to a system at constant temperature, which of the following is possible :
A. internal energy of system increases
B. work is done by system
c. neither internal energy increases nor work done by
D. internal energy increases and also work done by


Humans and animals are dependent on
plants.
A. Directly
B. Indirectly
c. Both A and B
D. None of the above


For the following arithmetic
progressions write the first term \( a \) and the common difference \( d: \)
\( \frac{1}{5}, \frac{3}{5}, \frac{5}{5}, \frac{7}{5}, \dots . . \)


\( \ln \Delta A B C \) and \( \Delta D E F, A B=D F \) and
\( \angle A=\angle D . \) The two triangles will be
congruent by SAS axiom if :
A \( . \) BC \( = \) EF
B. AC = DE
\( c \cdot B C=D E \)
D. AC = EF


f \( x, y \in\{1,2,3,4\} \) then check whether
\( \boldsymbol{f}=\{(\boldsymbol{x}, \boldsymbol{y}): \boldsymbol{y}=\boldsymbol{x}+1\} \) is a function?


Which one of the following statements
is correct?
A. The standard deviation for a given distribution is the square ofthe variance
B. The standard deviation for a given distribution is the square root of the variance
C. The standard deviation for a given distribution is equal to the variance
D. The standard deviation for a given distribution is halfofthe variance


A person standing near a train, which is moving with high speed, is pulled towards the train due
A. Pressure difference
B. Temperature difference
c. Gravitational force of the train
D. speed of the train


Find the lateral surface area and total
surface area of a cuboid which is \( 8 \mathrm{m} \)
long, \( 5 \mathrm{m} \) broad and \( 3.5 \mathrm{m} \) high.


Simplify \( (7 a-5 b)\left(49 a^{2}+35 a b+\right. \)
\( \left.25 b^{2}\right) \)


Which of the following mixture is called
aqua regia?
A. Three parts of \( d i l . H C I \) and 1 part of conc.\( H N O_{3} \)
B. Two parts of cone. \( H C I \) and two parts of conc.H\( N O_{3} \)
C. Three parts of cone. \( H C I \) and 1 part of \( d i l . H N O_{3} \)
D. Three parts of conc.\( H C I \) and 1 part of conc.H\( N O_{3} \)


How many images are formed for a point object kept in between two plane
mirrors \( M_{1} \) and \( M_{2}, \) at right angles to
each other?
A . 1
B. 2
\( c .3 \)
\( D \cdot 4 \)


If \( \omega \neq 1 \) is cube root of unity, and \( A= \) \( \left[\begin{array}{ccc}\mathbf{1} & \boldsymbol{\omega} & \boldsymbol{\omega}^{2} \\ \boldsymbol{\omega} & \boldsymbol{\omega}^{2} & \mathbf{1} \\ \boldsymbol{\omega}^{2} & \mathbf{1} & \boldsymbol{\omega}\end{array}\right] \) is
This question has multiple correct options
A. symmetric
B. skew symmetric
c. singular
D. orthogonal


The temperature of the centre of the Earth is about
A \( \cdot 4000^{\circ} \mathrm{C} \)
в. \( 6000^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 10^{4^{\circ}} C \)
D. \( 10^{6^{\circ}} \mathrm{C} \)


The product(s) is / are:
\( (\mathbf{B}) \)
A. (A) is an alcohol; (B) is an aldehyde
B. (A) is an aldehyde; (B) is an alcohol
C. (A) and (B) both are alcohols
D. (A) and
(B) both are aldehydes


Platelets are a source of
A. Fibrinogen
B. Calcium
c. Thromoboplastin
D. Heamoglobin


In Escherichia coli there is no alternation
of generations, because
A. Chromosomes do not fuse
B. It does not have chromosomes
C. There is neither syngamy not reduction division
D. Its cells do not exchange genetic material with each other


Eleven forces each equal to \( 5 N \) act on a particle simultaneously. If each force makes an angle \( 30^{\circ} \) with the next one,
the resultant of all forces is
В. 55 N
\( c .5 N \)
D. zero


Which among the following elements
has largest atomic size?
\( A \cdot B \)
в. А।
\( c \cdot \) Ga
D. In


Alternating current is flowing in inductance \( L \) and resistance \( R \). The
frequency of source is \( \frac{\omega}{2 \pi} . \) Which of the
following statement is correct.
A. For low frequency the limiting value of impedance is \( L \)
B. For high frequency the limiting value of impedance is \( L \omega \)
C. For high frequency the limiting value of impedance is \( R \)
D. For low frequency the limiting value of impedance is \( L \omega \)


Aluminium has a density of \( 2.7 g / c c \)
The mass of \( 15 c c \) of aluminium is
\( \mathbf{A} \cdot 45 g \)
в. \( 40.5 g \)
c. \( 80 g \)
D. \( 100 g \)


If the ratio of HM and GM of two
quantities is \( 12: 13, \) then the ratio of
the number is ?
A . 1: 2
B . 2: 3
c. 3: 4
D. None of these


With the help of equations briefly explain the bleaching action of chlorine.


The relative contribution of various
green house gases to global warming is given in the following diagram:
Identify the green house gases.
A \( \cdot A=C O_{2} ; B=C H_{4} ; C=N_{2} O ; D=C F C s \)
B. \( A=C O_{2} ; B=C F C s ; C=C H_{4} ; D=N_{2} O \)
C. \( A=C F C s ; B=C O_{2} ; C=C H_{4} ; D=N_{2} O \)
D. \( A=C F C s ; B=C H_{4} ; C=C O_{2} ; D=N_{2} O \)


When copper is placed in the atmosphere for sufficient time a green crust is formed ion its surface the
composition of green crust is
\( \mathbf{A} \cdot C u(O H)_{2} \)
в. \( C u O \)
c. \( C u C O_{3} \)
D. \( C u C O_{3} . C u(O H)_{2} \)


In human sperm, besides autosomes
the chromosome complement contains
A. \( x \) and \( y \)
B. Either X or Y
c. Y only
D. x only


The sum of three consecutive terms of
an \( A P \) is 21 and the sum of the squares
of these terms is 165: Find these terms


If \( y^{2}=4 a x, \) then \( \frac{\left(1+y_{1}^{2}\right)^{3 / 2}}{y_{2}} \) at \( x=a \)
is
A. \( -4 \sqrt{2} a \)
an \( a \sqrt{2} \) an \( \sqrt{2} \)
B. \( 4 \sqrt{2} a \)
\( c \cdot \frac{4 \sqrt{2}}{a} \)
D. \( -4 a \)


Explain how sexual reproduction gives
rise to more viable variations than
asexual reproduction. How does this affect the evolution of those organisms that reproduce sexually?


In a box containing only purple and green marshmallows, 6 marshmallows
are purple. If the probability of choosing
a purple marshmallow from the box is \( \frac{1}{3}, \) calculate the number of green marshmallows in the box.
\( A \cdot 2 \)
B. 6
c. 9
D. 12
E . 18


Froth flotation process used for the
concentration of sulfide ore
\( \mathbf{A} \cdot \) is based on the difference in wettability of different minerals
B. uses sodium ethly xanthate, \( C_{2} H_{5} O C S_{2} N a \) as collector
C. uses \( N a C N \) as depressant in the mixture of ZnS and PbS when ZnS forms soluble complex and Pbs forms froth
D. all of the above statements are correct


\( A^{\prime} \) s salary is same as 4 times \( B^{\prime} s \)
salary. If together they earn Rs. 3,750 a month, find the salary of each.
A. \( A \) 's = Rs. \( 3000 ; B \) 's = Rs. 750
B. \( A^{\prime} \) 's \( = \) Rs. \( 2000 ; B \) 's = Rs. 800
c. \( A \) 's \( = \) Rs. \( 2500 ; B \) 's \( = \) Rs. 900
D. \( A \) 's = Rs. \( 4500 ; B \) 's = Rs. 1000


A body moves along curved path of a quarter circle. The ratio of magntude of displacement to distance is
A \( \cdot \frac{\pi}{2 \sqrt{2}} \)
B.
\( c \cdot \frac{2 \sqrt{2}}{\pi} \)
D. \( \frac{3 \pi}{2 \sqrt{2}} \)


A circular blackish ring on the glass plate kept over the candle flame
indicates
A. Complete combustion
B. Dark zone of the flame
c. Non-luminous zone
D. Luminous zone


In which of the following tympanum is absent?
A. Bird
B. Frog
c. Lizard
D. snake


Which one among the following reactants produces hydrogen?
\( \mathbf{A} \cdot Z n+H C I \)
в. \( B a O_{2}+H C I \)
c. \( K_{2} S_{2} O_{8}+H_{2} O \)
D. \( N a_{2} O_{2}+H C I \)


Which of the following is a chemical change:
A. melting of ice
B. boiling of water
c. rusting of iron
D. tearing a paper


Write the name of four respiratory disorders with symptoms.


An isolated system can exchange:
A. matter with the surroundings
B. energy with the surroundings
C. both \( A \) and \( B \)
D. none of the above


A barometer is faulty. When the true barometer reading are 73 and \( 75 \mathrm{cm} \) of Hg, the faulty barometer reads \( 69 \mathrm{cm} \)
and \( 70 \mathrm{cm} \) respectively. What is the total length of the barometer tube?


What are conductors and insulators?
Give examples.


State whether given statement is True or False

The sum of all the voltage drops around a single closed loop in a circuit is zero.
A. True
B. False


Premolar are absent in
A. Adult teeth in man
B. Mammalian teeth in general
C. Permanent teeth of man
D. Deciduous teeth of man


\( x=t \cos t, y=t+\sin t . \) Then \( \frac{d^{2} x}{d y^{2}} \) at
\( t=\frac{\pi}{2} \) is
A \( \cdot \frac{\pi+4}{2} \)
в. \( -\frac{\pi+4}{2} \)
c. -2
D. none of these


A mirror and a source of light are situated at the origin \( \mathrm{O} \) and at a point on \( \mathrm{O} X, \) respectively. A ray of light from the source strikes the mirror and is
reflected. If the direction ratios of the
normal to the plane are \( 1,-1,1, \) then find the DCs of the reflected ray.
A \( \cdot \frac{1}{3}, \frac{2}{3}, \frac{2}{3} \)
в. \( -\frac{1}{3}, \frac{2}{3}, \frac{2}{3} \)
\( c \cdot-\frac{1}{3},-\frac{2}{3},-\frac{2}{3} \)
D. \( -\frac{1}{3},-\frac{2}{3}, \frac{2}{3} \)


Explain the preparation of Buna-N with equation.


According to Mendeleev's periodic table, one element whose atomic mass is
greater than that of nickel is placed
before Nickel. Name the element:
A. copper
B. Iron
c. zinc
D. cobal


Identical metal plates are located in air at equal distance \( d \) from one another
The area of each plate is equal to \( A \). If
the capacitance of the system between \( P \) and \( Q \) if the plates are interconnected
as shown in the figure is given as \( \frac{x}{3} \varepsilon_{0} \frac{A}{d} \) Find \( x: \)


Prokaryotes are characterized by
A. A true nucleus with double layered nuclear membrane is absent.
B. Well developed nucleus with double layered nuclear membrane present.
C. Presence of cell wall made of mucopolysaccharides and absence of cell organelles like mitochondria and chloroplasts.
D. Autotrophic in nature and only DNA is present.


Which of the following is correct regarding jaundice?
A. Skin turns yellow
B. Eyes turn yellow
c. Liver gets affected
D. All of these


Two moles of \( P C l_{5} \) are heated in a
closed vessel of 2 litre capacity. When
the equilibrium is attained \( 40 \% \) of it has been found to be dissociated. What
is the value of \( K_{c} \) in \( m o l / d m^{3} ? \)
A. 0.532
B. 0.266
c. 0.133
D. 0.174
E . 0.25


Is Rolle's theorem valid for the function
\( \boldsymbol{y}=\boldsymbol{x}^{3}+\boldsymbol{4} \boldsymbol{x}^{2}-\boldsymbol{7} \boldsymbol{x}-\mathbf{1 0} \) in the
interval [-1,2]


A charge of \( 4 \times 10^{-8} C \) is uniformly
distributed over the surface of sphere of
radius \( 1 \mathrm{cm} . \) Another hollow sphere of
radius \( 5 \mathrm{cm} \) is concentric with the
smaller sphere. Find the intensity of the
electric field \( \left(\text { in } N C^{-1}\right) \) at a distance
\( 2 c m \) from the centre. \( k=9 \times 10^{-9} S I \)


Which of the following describes an object that allows no light to pass through it?
A. Transparent
в. ०раяче
c. Translucent
D. Diffuse


Which of the following leaf fibres are considered hard because of high lignin content in their cell walls
A . Agave
B. Yucca
c. Musa textilis
D. All of the above


A bag contains 3 red and 2 black balls. One ball is drawn from it at random.
Find the probability of drawing a red
ball.


Mid latitude lakes undergo mixing
more than equatorial lakes, select the
correct reason.
A. The midlatitude lakes turn over twice a year
B. Midlatitude lakes develop a thermocline
C. Water is densest at 4
D. All of the above
E. They don't - equatorial lakes have more mixing


A long cylindrical vessel of volume
and linear coefficient of expansion \( \alpha \)
contains a liquid. The level of liquid has not changed on heating.The volume coefficient of real expansion of liquid is
A. \( \frac{V-a}{V} \)
B. \( \frac{V+a}{V} \)
c. \( \frac{v}{V-a} \)
D. 3a


Ethylbenzene with bromine in presence
of \( F e B r_{3} \) predominantly gives
\( A \)
B.
\( c \)
\( D \)


Smoke particles from a chimney exhibit
A. Random or irregular motion
B. Circular motion only
c. Linear motion only
D. Rotational motion only


Prove that the line joining the mid-
points of two equal chords of a circle subsent equal angles with the chord.


Antiseptic are the chemical which either \( _{-}-_{-}-_{-} \) or \( _{-}-_{-}- \) the growth of microorganisms and are applied to the
A. kill, prevent, living tissues
B. kill, prevent, non-living objects
c. increase, decrease, living tissues
D. kill, increase, non-living tissues


If the coordinates of vertices of
a triangle is always rational then the triangle cannot be
A. Scalene
B. Isosceles
c. Rightangle
D. Equilateral


Assertion
Fine particles in atmosphere scatter the
light of shorter wavelength more.
Reason
Sky appears blue.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


If \( \vec{b} \) and \( \vec{c} \) are the position vectors of the points \( \mathrm{B} \) and \( \mathrm{C} \) respectively, then the position vector of the point D such that \( \overrightarrow{B D}=4 \overrightarrow{B C} \) is
A \( \cdot 4(\vec{c}-\vec{b}) \)
в. \( -4(\vec{c}-\vec{b}) \)
c. \( 4 \vec{c}-3 \vec{b} \)
D \( \cdot 4 \vec{c}+3 \vec{b} \)


What difference is seen in the intensity (brightness) of the image of the flame
on the screen?


In the figures, sides \( X Y \) and \( Y Z \) and
median XA of a triangle XYZ are
propotional to sidesDE,EF and median
DB of \( \triangle D E F \). Show that \( \Delta X Y Z \sim \)
\( \Delta D E F \)


If the following statement is true, enter
1 or else 0.

The set of even natural numbers less
than 21 and the set of odd natural
numbers less than 21 have equal
number of elements and are termed as
equivalent sets.


Prove that \( \sin ^{-1} \frac{3}{5}-\sin ^{-1} \frac{8}{17}= \)
\( \cos ^{-1}\left(\frac{84}{85}\right) \)


Give reason: An iron chair feels colder
than a wooden chair in winter


In solar water heater, a coper pipe with
its outer surface painted in black is fixed in the form of a coil in a box.
A. The only purpose of bending copper pipe is to increase the capacity of water storage.
B. Bending copper pipe as a coil helps to increase the surface area for heating.
C. Both (1) and
(2) are true
D. Both (1) and
(2) are false


Why does a molecule of water shows
\( 104^{\circ} 30^{\prime} \) bond angle and \( C H_{4} \) has
\( 109^{\circ} 28^{\prime}, \) although both of them show
\( s p^{3} \) hybridization?


In which part of the atmosphere, \( \boldsymbol{O}_{3} \) is
present?
A. Mesosphere
B. Stratosphere
c. Troposphere
D. Lithosphere