\( A B C \) is a triangle, the point \( P \) is on side \( B C \) such that \( 3 \overrightarrow{B P}=2 \overrightarrow{P C} \), the
point \( Q \) is on the line \( \overrightarrow{C A} \) such that \( 4 \overrightarrow{C Q}=\overrightarrow{Q A} . \) If \( R \) is the common point of \( \overrightarrow{A P} \& \overrightarrow{B Q}, \) then the ratio in which the line joining \( \boldsymbol{C} \boldsymbol{R} \) divides \( \overrightarrow{\boldsymbol{A}} \boldsymbol{B} \) is
A .2: 5
B. 3: 8
c. 4: 1
D. 6: 1


A string of length 0.4 m and mass \( 10^{-2} k g \) is tightly clamped at its ends.
The tension in the string is \( 1.6 N \) Identical wave pulses are produced at one end at equal intervals of time \( \Delta t \)
The value of \( \Delta t \) which allows
constructive interference between
successive pulses is
A . \( 0.05 s \)
B. \( 0.10 s \)
c. \( 0.20 s \)
D. \( 0.40 s \)


f \( z_{1}=6+i z_{2}=3-4 i \) then find \( z_{1} z_{2} \)


On treatment with dilute \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
ethene forms ethanol
A. True
B. False


The negative slope of a velocity-time graph implies
A. accelerated motion
B. retarded motion
c. uniform motion
D. no motion


In a region of uniform magnetic
induction \( B=10^{-2} \) tesla, a circular coil
of radius \( 30 \mathrm{cm} \) and resistance \( \pi^{2} \) ohm is rotated about an axis, which is perpendicular to the direction of B and which forms a diameter of coil. If the
coil rotates at 200 r.p.m., the amplitude of alternating current induced in the coil is :-
A \( \cdot 4 \pi^{2} \mathrm{m} \)
B. 30 mA
\( c \cdot 6 m \)
D. 200 mA


Let \( \vec{u}, \vec{v}, \vec{w} \) be such that \( |\vec{u}|=1,|\vec{v}|= \)
\( \mathbf{2},|\overrightarrow{\boldsymbol{w}}|=\mathbf{3} . \) If the projection of \( \overrightarrow{\boldsymbol{v}} \) along \( \overrightarrow{\boldsymbol{u}} \)
is equal to that of \( \vec{w} \) along \( \vec{u} \) and \( \vec{v}, \vec{w} \) are perpendicular to each other then \( |\vec{u}-\vec{v}+\vec{w}| \) equals
A. \( \sqrt{14} \)
B. \( \sqrt{7} \)
\( c \cdot 2 \)
D. 14


Consider the following steps. \( \boldsymbol{A}(\boldsymbol{g}) \overrightarrow{\boldsymbol{E}_{1}} \)
\( \boldsymbol{A}^{+}(\boldsymbol{g}) \underset{\boldsymbol{E}_{2}}{\longrightarrow} \boldsymbol{A}^{2+}(\boldsymbol{g}) \underset{\boldsymbol{E}_{3}}{\longrightarrow} \boldsymbol{A}^{3+}(\boldsymbol{g}) \) Third
ionization energy of \( \boldsymbol{A}(\boldsymbol{g}) \) is \( ? \)
A. \( E_{1}+E_{2} \)
B . \( E_{1}+E_{2}+E_{3} \)
\( \mathbf{c} \cdot\left(E_{1}+E_{2}+E_{3}\right)^{/ 3} \)
D. \( E_{3} \)


The value of \( \int_{0} \overline{\mathbf{2}} \log \left(\frac{\mathbf{4}+\mathbf{3} \sin \boldsymbol{x}}{\mathbf{4}+\mathbf{3} \cos \boldsymbol{x}}\right) \boldsymbol{d} \boldsymbol{x} \) is
A . 2
B. \( \frac{3}{4} \)
\( c \cdot 0 \)
D. - 2


f \( \tan ^{-1} \frac{x-3}{x-4}+\tan ^{-1} \frac{x+3}{x+4}=\frac{3}{4}, \) then
find the value of \( x \)


Which of the following is a condensation homopolymer?
A. Nylon - 6,6
B. Nylon - 6
c. Bakelite
D. Dacron


Which of the following is the most significant law of motion given by
Newton?
A. First law of motion
B. Second law of motion
c. Third law of motion
D. Zeroth law of motion


Answer in one word.
Name the law behind the dissolution of
\( C O_{2} \) gas in soft drinks under high
pressure.


In ecological succession,
A. Pioneer species move into new communities first
B. Climax communities have lower total biomass than preceding communities
C. Species diversity is greatest in the early stages of succession
D. Climax communities shift constantly
E. All of the above


One molecule of an enzyme is able to catalyse conversion of two molecules of substrate into products in 5 minutes.
Ten molecules of enzyme and 25 molecules of substrate are mixed in a
test tube. At the end of 10 minutes the
test tube will have
A. Products only
B. Products and enzymes molecules
c. Products and 5 unreacted substrate molecules
D. Products, enzyme molecules and 5 molecules of substrate


Write the approximate weight of a body
of mass \( 5 k g ? \)
B. \( 5 N \)
c. \( 0.5 N \)
D. \( 50000 N \)


Find the sum: \( (-7)+(-9)+4+16 \)


From the given reactions, which is a
redox reaction?
A \( \cdot C u(s)+H_{2} O(g) \rightarrow C u(s)+H_{2} O(l) \)
в. \( 2 C u(s)+O_{2}(g) \rightarrow 2 C u O(s) \)
c. \( C(s)+2 H_{2} \rightarrow C H_{4}(g) \)
D. \( 4 A l(s)+3 O_{2}(g) \rightarrow 2 A l_{2} O_{3}(s) \)


Which of the following enzyme is not of protein origin?
A. Hexokinase
B. Synthetase
c. Endonuclease
D. Ribozyme


State whether given statement is True or Falsel
n p-njunction diode, the current in the reverse biased junction is generally very small
A. True
B. False


Find the principal and general solution
of the equation \( \sec x=2 \)


Tracheary elements are involved in
A. Mechanical strength
B. Food trasnlocation
c. conduction of minerals
D. Both A and C


The foreign exchange reserves in 1997
98 was how many times that in 1994
\( 95 ? \)
A. 0.7
B. 1.
\( c \cdot 1.4 \)
D. 1.5


When the plane surface of a planoconvex lens of refractive index 1.5 is
silvered, it behaves like a concave mirror with \( \boldsymbol{f}=\mathbf{3 0} \) cm.When its convex
surface is silvered, it will behave like a
concave mirror of focal length:
\( \mathbf{A} \cdot 10 \mathrm{cm} \)
B. \( 20 \mathrm{cm} \)
c. \( 30 \mathrm{cm} \)
D. \( 45 \mathrm{cm} \)


Metals have .............. electrons in valence
shell.
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 3 \)
D. All of the above


Sulphur is used in:
A. welding
B. electroplating
C . vulcanising rubber
D. the manufacture of paints


A planet is moving in an elliptical path around the sun as shown in
figure.Speed of planet in position \( P \) and
\( \mathrm{Q} \) are \( \boldsymbol{v}_{1} \) and \( \boldsymbol{v}_{2} \) respectively with \( \boldsymbol{S} \boldsymbol{P}= \)
\( r_{1} \) and \( S Q=r_{2} \) then \( v_{1} / v_{2} \) is equal to
then
A \( \cdot \frac{r_{1}}{r_{2}} \)
в. \( \frac{r_{2}}{r_{1}} \)
c. consonant
D.


Read the following statements and answer whether the given statement is
true or false.

Energy stored in an inductor \( =\frac{1}{2} L V^{2} \)
A. True
B. False


Predict whether van't HOff factor
\( (i) \) is
less than one or greater than one in the
following:
(i) \( C H_{3} C O O H \) dissolved in water
(ii) \( C H_{3} C O O H \) dissolved in benzene


What are pesticides and herbicides? Explain with examples.


Give an example of
¡) Globular proteins.
ii) Naturally occurring optically inactive
amino acid.


Solve: \( \lim _{h \rightarrow 0} \frac{\sqrt{\boldsymbol{x}+\boldsymbol{h}}-\sqrt{\boldsymbol{x}}}{\boldsymbol{h}}, \boldsymbol{x} \neq \mathbf{0} \)


Number \( \frac{3}{625} \) is a terminating decimal or a non-terminating repeating decimal? Write it in decimal form


Write an example for a metal which can
be refined by liquation?


The image of a candle flame formed by a lens is obtained on a screen placed on the other side of the lens. If the image is
three times the size of the flame and
the distance between lens and image is
\( 80 \mathrm{cm}, \) at what distance has the candle
been placed from the lens? What is the nature of the image and the lens?


Among the other elements present in the earth's crust, hydrogen stands in which position in abundance by mass?
A. Fourth
B. Sixth
c. Eighth
D. Ninth


The first term of the geometric
progression \( b_{1}, b_{2}, b_{3}, \ldots \) is unity. For
what value of the common ratio of the
progression is \( 4 b_{2}+5 b_{3} \) at a
minimum?


State True or False.
In the purification of bauxite ore as a preliminary step in the production of \( A l \)
\( \left.[\boldsymbol{A l}](\boldsymbol{O H})_{4}\right]^{-} \) can be converted to
\( A l(O H)_{3} \) by passing \( C O_{2} \) through it.


Pyruvic acid is obtained by:
A. oxidation of acetaldehyde cyanohydrin
B. oxidation of formaldehyde cyanohydrin
c. oxidation of acetone cyanohydrin
D. None of the above


\( \boldsymbol{n} \stackrel{\boldsymbol{L} t}{\rightarrow} \infty\left[\frac{\boldsymbol{1}^{3}}{\boldsymbol{n}^{4}+\boldsymbol{1}^{4}}+\frac{\boldsymbol{2}^{\boldsymbol{3}}}{\boldsymbol{n}^{4}+\mathbf{2}^{4}}+\ldots+\right. \)
\( \left.\frac{\mathbf{1}}{\boldsymbol{2} \boldsymbol{n}}\right]= \)
A. \( \frac{1}{4} \log 4 \)
B. \( \frac{1}{2} \log 2 \)
c. \( \frac{1}{4} \log 3 \)
D. \( \frac{1}{4} \log 2 \)


Which of the following compounds will not undergo Friedel-Craft reaction easily?
A . cumene
B. xylene
c. nitrobenzene
D. toluene


A reflecting surface is represented by the equation \( Y=\frac{2 L}{\pi} \sin \left(\frac{\pi x}{L}\right), 0 \leq \)
\( x \leq L . \) A ray travelling horizontally
becomes vertical after reflection. The
coordinates of the point(s) where this ray is incident is
A . True
B. False


In a cuboid,of 3 sides are \( 4 a^{2} b^{2}, 6 a^{2} b^{2} \) and \( 6 a \), then the volume of the cuboid
is
A \( \cdot 144 a^{5} b^{4} \)
B. \( 144 a^{3} b^{2} \)
c. \( 144 a^{2} b^{3} \)
D. \( 12 a^{2} b^{2} \)


Tollen's reagent is:
A. ammoniacal cuprous chloride
B. ammoniacal cuprous oxide
C. ammoniacal silver nitrate
D. ammoniacal silver chloride


Which of the following is true in respect of adsorption?
A. \( \Delta G<0 ; \Delta S>0 ; \Delta H<0 \)
B. \( \Delta G<0 ; \Delta S<0 ; \Delta H<0 \)
\( \mathrm{c} \cdot \Delta G>0 ; \Delta S<0 ; \Delta H<0 \)
D. \( \Delta G>0 ; \Delta S>0 ; \Delta H>0 \)


An inverted image can be seen in a
convex mirror,
A. under no circumstances
B. when the object is very far from the mirror
C. when the object is at a distance equal to the radius of curvature of the mirror
D. when the distance of the object from the mirror is equal to the focal length of the mirror


Which of the following hormones is responsible for hoarseness in voice, beard, moustaches etc. in males?
A. Gonadotropic hormone
B. Adrenaline
c. Thyroid
D. All of the above


State and prove the law of conservation
of momentum.


The expression in the vector form for the
point \( \vec{r}_{1} \) of intersection of the plane \( \vec{r}_{1} \cdot \vec{n}=d \) and the perpendicular line
\( \vec{r}=\vec{r}_{0}+t \vec{n} \) where \( t \) is a parameter
given by
A \( \cdot \overrightarrow{r_{1}}=\overrightarrow{r_{0}}+\left(\frac{d-\overrightarrow{r_{0}} \cdot \vec{n}}{\vec{n}^{2}}\right) \vec{n} \)
B \( \cdot \overrightarrow{r_{1}}=\overrightarrow{r_{0}}+\left(\frac{\overrightarrow{r_{0}} \cdot \vec{n}}{\vec{n}^{2}}\right) \vec{n} \)
C・ \( _{\overrightarrow{r_{1}}}=\overrightarrow{r_{0}}+\left(\frac{\overrightarrow{r_{0}} \cdot \vec{n}-d}{|\vec{n}|}\right) \vec{n} \)
D \( \overrightarrow{r_{1}}=\overrightarrow{r_{0}}+\left(\frac{\overrightarrow{r_{0}} \cdot \vec{n}}{|\vec{n}|}\right) \vec{n} \)


(a) What is fermentation? Give one
example.
(b) Write the balanced chemical
equations of the reactions taking place in the manufacture of ethyl alcohol from
sugar.


Relation between magnetic moment and angular velocity is
\( A . M \propto \omega \)
B. \( M \propto \omega^{2} \)
c. \( M \propto \sqrt{\omega} \)
D. None of these


\( \mathrm{f} \mathrm{A}=\left[\begin{array}{cc}1 & 3 \\ 3 & 2 \\ 2 & 5\end{array}\right], \mathrm{B}=\left[\begin{array}{cc}-1 & -2 \\ 0 & 5 \\ 3 & 1\end{array}\right] \).Find the
matrices D such that \( \boldsymbol{A}+\boldsymbol{B}-\boldsymbol{D}=\boldsymbol{O} \)
e. zero matrices


When an aqueous solution of sodium fluoride is electrolysed, the gas
liberated at anode is \( O_{2} \)
If true enter 1 , else enter 0 .


The primary winding of transformer has 500 turns whereas its secondary has \( \mathbf{5 0 0 0} \) turns. The primary is connected to an A.C supply of \( 20 V, 50 H z \). The secondary will have an output of
A. \( 2 V, 5 H z \)
в. \( 200 V, 500 H z \)
\( \mathbf{c} \cdot 2 V, 50 H z \)
D. \( 200 V, 50 H z \)


What type of materials gives flame?
A. All materials
B. Materials which vaporise on heating
C. Materials which melt on heating
D. None of the above


Centre point of a lens is called
A. Centre of curvature
B. Pole
c. Origin
D. optical centre


What is the order of rotational
symmetry of the above pattern?
\( A \cdot 3 \)
\( B \)
\( c \cdot 6 \)
D. 12


In the reaction : \( N O_{2}+C O \leftrightharpoons N O+ \)
\( C O_{2}, \) the equilibrium state may be
recognized by the constancy of color.
A. True
B. False


A compound whose molecules are
superimposable on their mirror images even though they contain asymmetric carbon atoms is called:
A. a threo compound
B. an erythro compound
c. a meso compound
D. none of these


If \( R \) be a relation defined from \( A= \)
\{1,2,3,4\} to \( B=\{1,3,5\}, \) i.e. \( (a, b) \in \)
\( R \) iff \( a<b \) then \( R o R^{-1} \) is
A \( \cdot\{(1,3),(1,5),(2,3),(2,5),(3,5),(4,5)\} \)
B・ \( \{(3,1),(5,1)(3,2),(5,2),(5,3),(5,4)\} \)
c. \{(3,3),(3,5),(5,3),(5,5)\}
D \( \cdot\{(3,3),(3,4),(4,5)\} \)


A smooth massless wedge is pushed by
a horizontal force \( \boldsymbol{P} \)
\( \mathbf{A} \cdot \) If \( P=0, \) than \( N<m g \cos \theta, ; \mathrm{N}=\mathrm{Normal} \) reaction
received by the block
B. If \( P>0, \) than \( N=m g \cos \theta \)
C. If \( a=0, \) than \( N=m g \cos \theta,= \) acceleration of the wedge.
D. none of these


A plane wave of sound traveling in air is incident upon a plane water surface. The angle of incidence is \( 60^{\circ} . \) Assuming
Snell's law to be valid for sound, it follows that the sound wave will be
refracted into the water away from the normal.
A. True
B. False


Aminoglycosides are usually used as:
\( A \). antibiotic
B. analgesic
c. hypnotic
D. antifertility


By selling a saree for \( R s 3000 \) the
shopkeeper made a profit of \( 20 \% . \) what was the cost price of the saree?


\( \boldsymbol{S} \boldsymbol{F}_{4} \stackrel{\text {hydrolysis}}{\boldsymbol{X}}+\boldsymbol{Y} \)
\( \boldsymbol{X}+\boldsymbol{H}_{2} \boldsymbol{S} \rightarrow \boldsymbol{Z} \)
Here, \( Z \) is :
\( A \cdot S O_{3} \)
B. colloidal sulphur
c. gaseous sulphur
D. solid sulphur


Carbohydrates are commonly found as
starch in plant storage organs.Which of the following five properties of starch makes it useful as a storage material?
(A) Easily translocated
(B) Chemically non-reactive
(C) Easily digested by animals
(D) Osmotically inactive
(E) Synthesized during photosynthesis
The useful proeprties are
\( A \cdot(A),(C) \) and (E)
B. (A) and (E)
c. (B) and (C)
D. (B) and (D)


Trimolecular reactions are
uncommon because:
A. the probability of three molecules colliding at an instant is very low
B. the probability of three molecules colliding at an instant is high
C. the probability of three molecules colliding at an instant is zero
D. the probability of many molecules colliding at an instant is high


Which of the following is used to reduce friction :
Streamlines
2. Use of ball bearings
3. Lubrication
\( A \cdot 1 \& 2 \) only
B. 1 \& 3 only
c. \( 2 \& 3 \) only
D. 1,2 \& 3


\( \frac{k}{i} \)


Fluorobenzene \( \left(C_{6} H_{5} F\right) \) can be
synthesised in the lab:
A. by heating phenol with HF and KF
B. from aniline by diazotization followed by heating the diazonium salt with \( H B F_{4} \)
C. by direct fluorination of benzene with \( F_{2} \) gas
D. by reacting bromo benzene with NaF solution


Benzoic acid undergoes dimerisation
in benzene solution.The vant Hoff factor
is related to the degree of association
\( \alpha^{\prime} \) of the acid as :
A \( . i=1-\alpha \)
B . \( i=1+\alpha \)
C \( i=1-\frac{\alpha}{2} \)
D. \( i=1+\frac{\alpha}{2} \)


Let \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}, \boldsymbol{g}(\boldsymbol{x})=\tan \boldsymbol{x} \) and \( \boldsymbol{h}(\boldsymbol{x})= \)
\( \ln x \)
What is \( [f o(f o f)](2) \) equal to?
A .2
B. 8
c. 16
D. 256


1 kgf \( = \)
\( \mathbf{A} \cdot 9.8 N \)
В. \( 98 N \)
c. \( 980 N \)
D. none of these


PQRS is a parallelogram. QM is the
height from \( Q \) to \( S R \) and \( Q N \) is the height
from \( Q \) to PS. If \( S R=12 c m \) and \( Q M=7.6 \)
\( \mathrm{cm} . \) Find \( \mathrm{QN}, \) if \( \mathrm{PS}=8 \mathrm{cm} \)


The most basic amine among the following is:
A . \( p \) - toluidine
B. \( o \) - nitroaniline
c. \( p \) - nitroaniline
D. \( 2,4- \) dinitroaniline


Find the value of \( x ? \)


What is the function of copper-T?
A. Stops zygote formation
B. Checks mutation
c. stops obliteration of blastocoels
D. stops fertilization


Axile placentation, trimerous flower and superior ovary are characteristic feature of family
A. Cucurbitaceae
B. compositae
c. Solanaceae
D. Liliaceae


The surface tension of soap solution is
\( 0.05 N m^{-1} . \) If the diameter of the soap
bubble is \( 4 \mathrm{cm} . \) The excess pressure
inside the soap bubble over that of outside is .................. Pascal:
A . 10
в. 1.0
c. \( 0 . \)
D. 0.25


Find \( k, \) if \( f \) is continuous at \( x=0 \) wher
\( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{l}\frac{16^{x}-2^{x}}{k^{x}-1} \text { when } x \neq 0 \\ 3 \text { when } x=0\end{array}\right. \)


Displacement of a particle executing simple harmonic motion is represented by \( \boldsymbol{Y}=\mathbf{0 . 0 8} \sin \left(3 \pi t+\frac{\pi}{4}\right) \) metre.
Then calculate:-
(a) Time period.
(b) Initial phase
(c) Displacement from mean position at \( t=\frac{7}{36} \) sec.


An account earning \( 4.4 \% \) interest
compounded quarterly for 5 years would have a balance of how much if the
principal was Rs. 1500?


What is the structure of \( \$ \$ P H_{-} 3 C I_{-} 2 \$ \)
\( \$ ? \)
A. Trigonal bipyramidal with apical H atoms.
B. Square pyramidal with apical H atom
C. Trigonal bipyramidal with apical Cl atoms.
D. Square pyramidal with apical Cl atom


In the sequence
\( \mathbf{1}, \mathbf{2}, \mathbf{2}, \mathbf{3}, \mathbf{3}, \mathbf{3}, \mathbf{4}, \mathbf{4}, \mathbf{4}, \mathbf{4}, \dots, \) where \( \boldsymbol{n} \)
consecutive terms have the value \( n \), the
\( 150^{t h} \) term is
A . 17
B . 16
c. 18
D. none of these


Find \( \frac{d y}{d x}, \) when
\( \boldsymbol{x}=\boldsymbol{a}(\mathbf{1}-\cos \boldsymbol{\theta}) \) and \( \boldsymbol{y}=\boldsymbol{a}(\boldsymbol{\theta}+\sin \boldsymbol{\theta}) \)
\( \operatorname{at} \theta=\frac{\pi}{2} \)


When \( C H_{3} C H_{2} C H C l_{2} \) is treated with
\( N a N H_{2}, \) the product formed is:
A. \( C H_{3}-C H=C H_{2} \)
в. \( C H_{3}-C \equiv C H \)
\( c \)
\( D \)


Which of the following are synthetic
fibres?
This question has multiple correct options
\( A \). Wool
B. cotton
c. Acrylic
D. Polystyrene


Rain drops, each of radius \( r, \) are falling through air with steady velocity v. If eight drops coalesce to form a big drop, then the big drop so formed will fall with velocity?


\( f(x)=x^{3}-3 x^{2}+2 x \) then find the
value of \( p(x) \) at \( x=2 \)


The circuit shown in figure was set up
to determine the emf of a thermocell. As
Pis moved away from \( X \) to \( Y \), the
galvanometer deflection is always in
the same direction but decrease
continuously until Y is reached. In order
to obtain a balance point between \( X \)
and \( Y, \) it is necessary to
A. decreases R
B. increases R
c. reverse the terminals of E
D. interchange the hot and cold iunctions


The annual maintenance cost of a
machine in a factory over a seven years
period is represented in the histogram.
In which year the maintenance cost is
\( 2500 ? \)
A . \( 1998-1999 \)
в. \( 2000-2001 \)
c. \( 2001-2002 \)
D. \( 1995-1996 \)


The energy band gap of a superconductor formed near the critical
temperature is due to
A. the exponential decrease in heat capacity
B. the exponential increase in heat capacity
c. the gradually decrease in heat capacity
D. the gradually increase in heat capacity


\( H_{2} O_{2} \) involves in the reaction as an
oxidising agent, when it is added to:
A \( . \) CaOCl
в. \( O_{3} \)
c. \( A g_{2} O \)
D. KI


The specific conductivity of a saturated
solution of silver chloride is \( 2.30 \times \)
\( 10^{-6} \) mho \( c m^{-1} \) at \( 25^{\circ} C . \) Calculate the
solubility of silver chloride at \( 25^{\circ} \mathrm{C} \) if
\( \lambda_{A g^{+}}=61.9 m h o c m^{2} m o l^{-1} \) and
\( \boldsymbol{\lambda}_{C l^{-}}=\mathbf{7 6 . 3} \boldsymbol{m h o c m}^{2} \boldsymbol{m o l}^{-1} \)


Find a vector perpendicular to each of the vectors \( \vec{a}+\vec{b} \) and \( \vec{a}-\vec{b}, \) where \( \vec{a}= \) \( \hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}}, \overrightarrow{\boldsymbol{b}}=\hat{\boldsymbol{i}}+\boldsymbol{2} \hat{\boldsymbol{j}}+\boldsymbol{3} \hat{\boldsymbol{k}} \)
A \( \cdot \frac{\hat{i}}{i}-\hat{2} \hat{j}+\hat{2} k \)
B.
c. \( -\hat{i}-\hat{3} j+\hat{2 k} \)
D. None of these


The range of the data 25.7,16.3,2.8,21.7 24.3,22.7,24.9 is
A . 22
в. 22.9
c. 21.7
D. 20.5


\( 0.61 \mathrm{g} \) of an organic substance was heated in carius tube and the sulphuric acid formed was precipitated as
\( B a S O_{4} \) with \( B a C l_{2} . \) The weight of the
\( \operatorname{dry} B a S O_{4} \) was 0.53 g. Find the percentage of Sulphur.
A . \( 11.90 \% \)
B . 43\%
c. \( 23.04 \% \)
D. 51.2\%


A person of height h standing at the centre of room looking towards a plane mirror hanging on a wall, can see the bottom edge of the wall behind him if
minimum length of the mirror is:
\( A \cdot h \)
B. \( h / 2 \)
\( c \cdot h / 3 \)
D. \( h / 4 \)


If \( \boldsymbol{A}=\left[\begin{array}{cc}\cos \boldsymbol{\theta} & -\sin \boldsymbol{\theta} \\ \sin \boldsymbol{\theta} & \cos \boldsymbol{\theta}\end{array}\right], \) then \( \boldsymbol{A} \boldsymbol{A}^{\boldsymbol{T}} \)
equals
\( A \cdot\left[\begin{array}{cc}\cos 2 \theta & -\sin 2 \theta \\ \sin 2 \theta & \cos 2 \theta\end{array}\right] \)
B. \( \left[\begin{array}{cc}\cos ^{2} \theta & \sin ^{2} \theta \\ \sin ^{2} \theta & \cos ^{2} \theta\end{array}\right] \)
c. \( \left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right] \)
D. \( \left[\begin{array}{ll}0 & 0 \\ 0 & 0\end{array}\right] \)


Thermal water pollution is caused due
to:
A. use of water as a coolant by power plants
B. use of water for sewage treatment
C. use of water as a disinfectant
D. use of water as washing source


Use the mirror equation to show that an
object placed between \( f \) and \( 2 f \) of \( a \) concave mirror produces a real image
beyond \( 2 f \)


Which among the following is not found in mammals?
A. Hepatic portal system
B. Hypophyseal portal system
C. Renal portal system
D. Hepatic and hypophyseal portal system


Select the correct orders of bond angles.
This question has multiple correct options
\( \mathbf{A} \cdot H-\hat{P}-H\left(P H_{3}\right)<F-\hat{P}-F\left(P F_{3}\right) \)
B \( \cdot F-\hat{N}-F\left(N F_{3}\right)<H-\hat{N}-F\left(N H_{3}\right) \)
\( \mathbf{c} \cdot F-\hat{O}-F\left(O F_{3}\right)<H-\hat{O}-H\left(H_{2} O\right)<C l-\hat{O}- \)
\( \mathrm{Cl}\left(\mathrm{O} \mathrm{Cl}_{2}\right) \)
D. \( H-\hat{P}-H\left(P H_{3}\right)>F-\hat{P}-F\left(P F_{3}\right) \)


Find the value of cube root of the
number \( 6860 . \) (Round off your number to the nearest hundredth)
A . 19.003
B. 19.00
c. 19.32
D. 19.008


Which of the following examples is/are oil-in-water-type emulsion?
\( A \cdot \ln k \)
B. Detergent
c. Soap
D. Milk


Velocity of a particle moving in \( x- \) axis is given as \( v=\alpha \sqrt{x} \) where \( \alpha \) is positive
constant. If initially particle was at
origin, the position of particle at time \( t \)
is
A \( \cdot \frac{\alpha^{2} t^{2}}{4} \)
в. \( 3 \alpha^{2} \frac{t^{2}}{4} \)
c. \( \quad \alpha^{2} \frac{t^{2}}{2} \)
D. \( 3 \alpha^{2} \frac{t^{2}}{2} \)


Three rods of equal lengths are joined to form an equilateral triangle \( A B C \). D is the of AB. The coefficient of linear
expansion is \( \alpha_{1} \) for material of \( \operatorname{rod} A B \)
and \( \alpha_{2} \) for \( n \) rods \( A C \) and \( B C \). It the
distance DC remains constant for small
changes in temperature.


Find the derivative of the following functions from first principle:
\( \sin (x+1) \)


Which of the following method involves the movement of molecules from
the region of higher concentration to the lower concentration?
A. Diffusion
B. Osmosis
c. Chemiosmosis
D. Plasmolysis


Choose the most reactive among the
following compound:
\( \mathbf{A} \)
B.
\( c \)
\( D \)


The heat change for the following reaction:
\( C(s)+2 S(s) \rightarrow C S_{2} \) is known as:
A. Heat of vaporization
B. Heat of solution
c. Heat of fusion
D. Heat of formation


Establish the relation amongst \( u, v \) and
\( f \) for concave lens.


The electrical conductivity of a semiconductor increases when
electromagnetic radiation of
wavelength shorter than 600 nm is incident on it. The energy band gap (in
eV) for the semiconductor is
A . 1.50
в. .075
c. 2.06
D. 1.35
E . 0.90


f \( \boldsymbol{I}=\int \frac{\boldsymbol{d} \boldsymbol{x}}{\left(\boldsymbol{e}^{\boldsymbol{x}}+\mathbf{2}\right)^{3}}, \) then I equals
A \( \cdot \frac{1}{8} x-\frac{1}{8} \log \left(e^{x}+2\right)+\frac{e^{x}+3}{4\left(e^{x}+2\right)^{2}}+C \)
B. \( \frac{1}{8} x+\frac{1}{8} \log \left(e^{x}+2\right)+\frac{e^{x}}{4\left(e^{x}+2\right)^{2}}+C \)
c. \( \frac{1}{8} x+\frac{1}{8} \log \left(e^{x}+2\right)+\frac{e^{x}}{\left(e^{x}+2\right)^{2}}+C \)
D. none of these


If the origin is the centroid of the triangle whose vertices are \( \boldsymbol{A}(\mathbf{2}, \boldsymbol{p},-\mathbf{3}), \boldsymbol{B}(\boldsymbol{q},-\mathbf{2}, \mathbf{5}) \) and \( \boldsymbol{R}(-\mathbf{5}, \mathbf{1}, \boldsymbol{r}) \)
then find the values of \( \boldsymbol{p}, \boldsymbol{q}, \boldsymbol{r} \)


Number of 4 digit numbers of the form
\( N=a b c d \) which satisfy following three
conditions
(i) \( 4000 \leq N<6000 \) (ii) \( N \)
is multiple of 5 (iii) \( 3 \leq b<c \leq 6 \) is
equal to
A . 12
B . 18
\( c \cdot 24 \)
D. 48


Using properties of determinant, prove
\[
\text { that }\left|\begin{array}{lll}
\boldsymbol{b}+\boldsymbol{c} & \boldsymbol{a}-\boldsymbol{b} & \boldsymbol{a} \\
\boldsymbol{c}+\boldsymbol{a} & \boldsymbol{b}-\boldsymbol{c} & \boldsymbol{b} \\
\boldsymbol{a}+\boldsymbol{b} & \boldsymbol{c}-\boldsymbol{a} & \boldsymbol{c}
\end{array}\right|=\mathbf{3} \boldsymbol{a} \boldsymbol{b} \boldsymbol{c}-\boldsymbol{a}^{3}-
\]
\( b^{3}-c^{3} \)


\( 50^{\circ} \mathrm{C} \) is \( \ldots \ldots . . . . . . . .^{\circ} \mathrm{F} \)
A . 132
B. 122
\( c \cdot 140 \)
D. 150


The circuit below shows three different
resistors connected in series to a
battery. The ammeter reading is 120 A. How much current flows through each resistor?
\( A \cdot 40 A \)
B. 120 A
c. 360 A
D. We cannot determine the current values without knowing the resistor values
E. We cannot determine the current values with knowing the battery voltage


The species that undergo(es) disproportionation in alkaline medium is/are:
This question has multiple correct options
A \( \cdot C l_{2} \)
B . \( M n O_{4}^{2} \)
\( c \cdot N O_{2} \)
D. \( C l O_{4}^{-} \)


Which of the following fibres are made of polyamides?
A. Dacron
B. Orlon
c. Nylon
D. Rayon


Which of the following statements is not correct regarding preparation of
NaOH?
A. NaOH is prepaid by electrolysis of sodium chloride in castner-Kellner cell.
B. Sodium metal discharged at cathode combines with mercury to form sodium amalgam
c. chlorine is evolved at anode
D. Amalgam is heated to separate Na and Hg


Metals are ............., i.e., they make sound when hit with an object.
A. sonorous
B. lusturous
c. reactive
D. brittle


Which of the following is not a
characteristic feature of all chordates?
A. Dorsal Nerve Cord
B. Presence of Coelom
C. Pharyngeal gill clefts in the early embryonic stage
D. Diaphragm that separates thorax and abdomen


A cylinder of mass 5 kg is held in vertical position. If the height of the cylinder is \( 6 \mathrm{cm} \) and radius of cross section is \( 4 \mathrm{cm} \) then find the pressure
acting on its bottom surface.


A: In interference pattern, intensity of
successive fringes due to achromatic light is not same.
R: In interference, only redistribution of
energy takes place.
A. Both A and R are true, and R is correct explanation of
B. Both A and R are true, and R is not correct explanation of A
c. A is true but R is false
D. A is false but R is true


The primary and secondary valency of a central metal ion in \( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4} \boldsymbol{C O}_{3}\right] \boldsymbol{C l} \)
complex is and
respectively.
A .2,6
B. 4,6
c. 4,5
D. 3,6


Assertion
Water dropped at the rate of \( 2 m^{3} / \) sec in
to a cone of semi-vertical angle of \( 45^{0} \) The rate at which periphery of the water surface changes with height of water in the cone of \( 2 m \) is \( 2 m / s e c \)
Reason
The rate of change of periphery of water surface is \( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{t}}(\boldsymbol{2} \boldsymbol{\pi} \boldsymbol{r}) \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is false but Reason is correct


Which of the following element belongs
to the group \( 18 ? \)
\( \mathbf{A} \cdot H \)
в. \( N e \)
c. \( C l \)
D. \( F \)


In which one of the following, the BOD (Biochemical Oxygen Demand) of sewage (S), distillery effluent (DE), paper mill effluent (PE) and sugar mill effluent (SE) have been arranged in ascending order
\( A \cdot S E<S<P E<D E \)
B. SE <PE <S <DEE
c. \( P E<S<S E<D E \)
D. \( S<D E<P E<S E \)


In the given circuit what is the potentia
drop across resistance?
A. \( 40 v \)
B. 80
\( c \cdot 120 v \)
D. zer


Greenhouse effect is due to the
presence of
A. Ozone layer in the atmosphere
B. Infrared light reaching the earth
C. Moisture layer in the atmosphere
D. \( \mathrm{CO}_{2} \) layer in the atmosphere


Curie temperature is the temperature
above which
A. Paramagnetic material becomes ferromagnetic material
B. Ferromagnetic material becomes diamgnetic material
C. Ferromagnetic material becomes paramagnetic material
D. Paramagnetic material becomes diamagnetic material


Xenon reacts with fluorine at \( 873 \mathrm{K} \) and
7 bar to form \( X e F_{4} . \) In this reaction the
ratio of Xenon and fluorine required is :
A . 1: 5
B. 10:
c. 1: 3
D. 5:


The bacteria culture grows at a rate
proportional to its size. After 2 hours
there are 600 bacteria and after 8
hours the count is 75000 . Find the
initial population and when the
population reach \( 200000 ? \)


Calculate total moment of the two
forces about \( \boldsymbol{O} \)
A. \( 2 N m \) (clockwise)
B. \( 2 N \) m(anti clockwise)
c. \( 4 N m \) (clockwise)
D. \( 4 N m \) (anti clockwise)


If \( C_{1}=\{x: 1<x<2\} \) and \( C_{2}=\{x: \)
\( 4<x<5\}, \) find \( P\left(C_{1} \cup C_{2}\right) \)


If \( A=\{2,4\} \) and \( B=\{3,4,5\}, \) then
\( (\boldsymbol{A} \cap \boldsymbol{B}) \times(\boldsymbol{A} \cup \boldsymbol{B}) \) is
A \( \cdot\{(2,2),(3,4),(4,2),(5,4)\} \)
B - \{(2,3),(4,3),(4,5)\}
c. \{(2,4),(3,4),(4,4),(4,5)\}
D \( \cdot\{(4,2),(4,3),(4,4),(4,5)\} \)


In a hydrogen like atom, when an electron jumps from the M-shell to the L-shell, the wavelength of emitted radiation is \( \lambda \). If an electron jumps from
N-shell to the L-shell, the wavelength of emitted radiation will be?
A \( \cdot \frac{27}{20} \lambda \)
в. \( \frac{16}{25} \lambda \)
c. \( \frac{20}{27} \lambda \)
D. \( \frac{25}{16} \lambda \)


You spin a globe at 2.5 rads/sec and
then give it a push to speed it up to 3 rads/ sec. If it takes 0.2 secs to change the speed of the globe, what is the
angular acceleration in \( r a d / s e c^{2} ? \)
A . 2.5
B. 3
\( c \cdot 5 \)
D. 10


Mohan has two daughters. He blames his wife for bearing only daughters and no son. How will you convince Mohan
that his wife has no role in giving birth to daughters only so that she should not be blamed for it. Further, females are
rather more important component of society, What values are involved in this advice?


On a cold day when a room temperature
is \( 15^{\circ} \mathrm{C}, \) the metallic cap of a pen
becomes much colder than its plastic body, though both are at the same
temperature of \( 15^{\circ} \mathrm{C} \), because
A. metals have higher thermal capacity than plastics
B. plastics have a lower density than metals
C. metals are good conductor of heat
D. plastics have a higher thermal conductivity than metals


Estimate the average drift speed of
conduction electrons in a copper wire of
cross-sectional area \( 1.0 \times 10^{-7} m^{2} \)
carrying a current of 1.5 A. Assume the
density of conduction electrons to be
\( 9 \times 10^{28} m^{-3} \)


An equilibrium mixture for the reaction
\( \mathbf{2} \boldsymbol{H}_{2} \boldsymbol{S}(\boldsymbol{g}) \rightleftharpoons \mathbf{2} \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{S}_{2}(\boldsymbol{g}) \) has
1 mole of \( H_{2} S, 0.2 \) mole of \( H_{2} \) and
0.8 mole of \( S_{2} \) in a 2 litre flask. The
value of \( \boldsymbol{K}_{c} \) in mol \( \boldsymbol{L}^{-1} \) is
\( \mathbf{A} \cdot 0.004 \)
B. 0.08
c. 0.016
D. 0.160


A bullet of mass \( A \) and velocity \( B \) is fired into a block of wood of mass \( C . \) If loss of
any mass and friction be neglected, then velocity of the system must be
\( ^{\text {A }} \cdot \frac{A B}{A+C} \)
в. \( \frac{A+C}{B+C} \)
c. \( \frac{A C}{B+C} \)
D. \( \frac{A+B}{A C} \)


Energy band gap size for insulators is in the range \( e V \)
\( \mathbf{A} \cdot 1-2 \)
B. \( 0-4 \)
c. \( 0-5 \)
\( D \cdot>5 \)


ABCD is a parallelogram as shown in figure. If \( A B=2 A D \) and \( P \) is mid-point of
\( A B, \) then \( \angle C P D \) is equal to
\( A \cdot 90^{\circ} \)
B. \( 60^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 135^{\circ} \)


The oxidation potential of
\( Z n, C u, A g, H_{2} \) and \( N i \) are 0.76,-0.34
-0.80,0,0.55 volt respectively. Which of the following reaction will provide maximum voltage?
A. \( Z n+C u^{2+} \rightarrow C u+Z n^{2+} \)
B. \( Z n+2 A g^{+} \longrightarrow 2 A g+Z n^{2+} \)
c. \( H_{2}+C u^{2+} \rightarrow 2 H^{+}+C u \)
D. \( H_{2}+N i^{2+} \rightarrow 2 H^{+}+N i \)


Which of the following labilisers found on membrane of lysosome?
A. Cortisone and cortisol
B. Cholesterol and heparin
c. Testosterone and progesterone
D. cholesterol and progesterone


If \( A=\left[\begin{array}{lll}0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & 1 & 1\end{array}\right] \) then \( \operatorname{Adj}(A)= \)
A \( \cdot\left[\begin{array}{ccc}-1 & +8 & -5 \\ 1 & -6 & 3 \\ -1 & 2 & -1\end{array}\right] \)
B. \( \left[\begin{array}{ccc}-1 & +1 & -1 \\ 8 & -6 & 2 \\ -5 & 3 & -1\end{array}\right] \)
C. \( \left[\begin{array}{ccc}1 & -1 & 1 \\ 8 & -6 & 2 \\ -5 & 3 & -1\end{array}\right] \)
D. \( \left[\begin{array}{ccc}-1 & -8 & 5 \\ -1 & 6 & -3 \\ 1 & -2 & 1\end{array}\right] \)


If \( f(x)=\frac{x^{2}-x}{x^{2}+2 x}, \) find the domain of \( f(x) \) Show that \( f \) is one-one.


Five waveforms moving with equal
speeds on the x-axis
\( \boldsymbol{y}_{1}=\boldsymbol{8} \sin (\boldsymbol{\omega} \boldsymbol{t}+\boldsymbol{k} \boldsymbol{x}) ; \boldsymbol{y}_{2}= \)
\( 6 \sin \left(\omega t+\frac{\pi}{2}+k x\right) ; y_{3}= \)
\( \mathbf{4} \sin (\omega t+\pi+k x) \)
\( \boldsymbol{y}_{4}=2 \sin \left(\omega t+\frac{3 \pi}{2}+k x\right) \)
\( \boldsymbol{y}_{5}=4 \sqrt{2} \sin \left(\omega t-k x+\frac{\pi}{4}\right) \) are
superimposed on each other. The resulting wave is:
\( ^{\mathrm{A}} \cdot_{8 \sqrt{2} \cos k x \sin \left(\omega t+\frac{\pi}{4}\right)} \)
B. \( 8 \sqrt{2} \sin \left(\omega t-k x+\frac{\pi}{4}\right) \)
c. \( \quad 8 \sqrt{2} \sin k x \cos \left(\omega t+\frac{\pi}{4}\right) \)
\( \mathbf{D} \cdot 8 \sin (\omega t+k x) \)


What is silk reeling?
A. The process of taking out threads from the cocoon is called reeling.
B. When the eggs hatch into larvae, they are fed on mulberry leaves.
C. The cocoons are dipped in hot water and the silk fibres a re separated.
D. The cocoons are dipped in iodine solution and the silk fibers are separated.


In the reaction:
\( \mathbf{2} C O(\boldsymbol{g})+\boldsymbol{O}_{2}(\boldsymbol{g}) \rightleftharpoons \mathbf{2} \boldsymbol{C} \boldsymbol{O}(\boldsymbol{g}) \)
entropy_ -
A. decreases
B. increases
c. constant
D. none


When 0.1 mol \( \operatorname{CoCl}_{3}\left(N H_{3}\right)_{5} \) is treated
with excess of \( A g N O_{3}, 0.2 \) mole of
\( A g C l \) are obtained. The conductivity of solution will correspond to
A. 1: 3 electrolyte
B. 1: 2 electrolyte
c. 1: 1 electrolyte
D. 3: 1 electrolyte


State whether true or false:
The position of centre of gravity of a body remains unchanged even when the body is deformed.
A. True
B. False
c. Ambiguous
D. Data insufficient


Which property of white phosphorus is common to red phosphorus:
A. It burns when heated in air
B. It racts with hot caustic soda solution to give
phosphine
C. It shown chemiluminescence
D. it is soluble in carbon disulphide


Dalton suggested that atoms were indestructible and unchangeable to
explain:
A. why mass is conserved in chemical reactions.
B. why elements combine in fixed weight ratios to form compounds.
c. why elements are characterized by the mass of their atoms
D. why compounds combine in fixed weight ratios in chemical reactions


If \( a, b \in A, a * b \in A \) then
\( A . * \) is a unary operation in \( A \)
В. \( a * b=b * a \)
c. \( * \) is a binary operation in \( A \)
D. \( a * b \neq b * a \)


Add an express the sum as a mixed
fraction:
\( \frac{-31}{6} \) and \( \frac{-27}{8} \)


True statements for the chemical
reaction of the formation of lithium
oxide is:
\( 4 L i(s)+O_{2}(g) \rightarrow 2 L i_{2} O(s) \)
A. lithium metal is the oxidizing agent
B. oxygen gas is the reducing agent
c. lithium is oxidized
D. oxygen is oxidized
E. oxygen loses two electrons to become \( O^{-2} \) ion


The coefficient of cubical expansion of
copper is \( 5.1 \times 10^{-5} \) per \( C . \) Coefficient
of linear expansion is \( \boldsymbol{K} \times \mathbf{1 0}^{-\mathbf{5}} \) per \( \boldsymbol{C} \)
Find value of \( \mathrm{K} \)


A square wire of side \( 3.0 \mathrm{cm} \) is placed \( 25 c m \) in front of a concave mirror of
focal length \( 10 c m, \) with its centre on the axis of the mirror and its plane normal to the axis. The area enclosed by the
image of the wire is :
A \( .7 .5 \mathrm{cm}^{2} \)
в. \( 6.0 \mathrm{cm}^{2} \)
\( c \cdot 4.0 \mathrm{cm}^{2} \)
D. 3.0 \( \mathrm{cm}^{2} \)


Peroxisomes are found in
A. Bundle sheath
B. Endospem
C . Mesophyll cell
D. Vascular bundle


Which has zero dipole moment?
A . \( C l F \)
в. \( P C l_{3} \)
\( \mathrm{c} \cdot \operatorname{SiF}_{4} \)
D. \( C F C l_{3} \)


Derive an expression for the capacitance of a parallel plate capacitor. Why does the capacitance
increase by using dielectric in
capacitor?


Write four steps to control water
pollution.


If \( \sum_{r=0}^{25}\left\{^{50} C_{r} .^{50-r} C_{25-r}\right\}=K\left(^{50} C_{25}\right) \)
then \( K \) is equal to:
A \( \cdot 2^{25}-1 \)
B . \( (25)^{2} \)
\( c \cdot 2^{25} \)
\( D \cdot 2^{2} \)


The excretory system of human beings includes a pair of ............, a pair of \( \ldots . . . . . . . \) a and a ............ which helps in the filtration of blood.
A. Kidneys, ureters, urinary bladder, urethra
B. Urethra, ureters, urinary bladder, kidneys
C. Kidneys, urethra, ureters, urinary bladder
D. Kidneys, urinary bladder, ureters, urethra


Find the value of \( x \) for which \( f(x)= \)
\( \sqrt{\sin x-\cos x} \) is defined, \( x \epsilon[0,2 \pi] \)
\( ^{\mathbf{A}} \cdot_{x \epsilon}\left[\frac{\pi}{8}, \frac{5 \pi}{8}\right] \)
В \( \cdot x \in\left[\frac{\pi}{4}, \frac{3 \pi}{4}\right] \)
\( ^{\mathbf{C}} \cdot_{x \epsilon}\left[\frac{\pi}{6}, \frac{5 \pi}{6}\right] \)
D. \( x \in\left[\frac{\pi}{4}, \frac{5 \pi}{4}\right] \)


In aqueous solution \( \mathrm{Eu}^{2+} \) acts as :
A . an oxidsing agent
B. reducing agent
C. can act as either of these
D. can not act as either of these


Which of the following is associated with the closure of stomata?
A. Turgidity
B. Flaccidity
c. stoma
D. Transpiration


Identify the redox reaction taking place
in a beaker.
\( \left.\mathbf{A} \cdot Z n_{(} s\right)+C u_{(a q)}^{2+} \rightarrow Z n_{(a q)}^{2++}+C u(s) \)
B. \( \left.C u(s)+2 A g_{(a q)}^{+} \rightarrow C u_{(a q)}^{2+}+2 A g_{(} s\right) \)
C \( \left.\cdot C u_{(} s\right)+Z n_{(a q)}^{2+} \rightarrow Z n(s)+C u_{(a q)}^{2+} \)
\( \left.\text { D. }\left.2 A g_{(} s\right)+C u_{(a q)}^{2+} \rightarrow 2 A g_{(a q)}^{+}+C u_{(} s\right) \)


Prove that for two complex numbers \( z_{1}, z_{2},\left(z_{1}-z_{2}\right)^{2}=z_{1}^{2}-2 z_{1} z_{2}+z_{2}^{2} \)


Discuss the mechanism of alkaline
hydrolysis of bromomethane.


Show that angles between any two \( \operatorname{diagonals} \boldsymbol{\theta}=\cos ^{-1}\left(\frac{1}{3}\right) \)


Which oxide is insoluble in aqueous
sodium hydroxide?
A . Mgo
в. \( A l_{2} O_{3} \)
\( \mathrm{c} \cdot P_{4} O_{10} \)
\( \mathrm{D} \cdot \mathrm{SO}_{2} \)


If a ship of mass \( 4 \times 10^{7} \) kg initially at
rest is pulled by a force of \( 5 \times 10^{4} \mathrm{N} \)
through a distance of 4 m, then the
speed of the ship will be (resistance due to water is negligible)
\( \mathbf{A} \cdot 5 m s^{-1} \)
B . \( 1.5 \mathrm{ms}^{-1} \)
\( \mathrm{c} \cdot 60 \mathrm{ms}^{-1} \)
D. \( 0.1 \mathrm{ms}^{-1} \)


List the effects of force with example


In which of the following systems, doubling the volume of the container causes a shift to right?
A \( \cdot H_{2}(g)+I_{2}(g) \leftrightharpoons 2 H I(g) \)
B . \( 2 C O(g)+O_{2}(g) \leftrightharpoons 2 C O_{2}(g) \)
C \( . N_{2}(g)+3 H_{2}(g) \leftrightharpoons 2 N H_{3}(g) \)
D. \( P C l_{5}(g) \leftrightharpoons P C l_{3}(g)+C l_{2}(g) \)


What is the \( 7^{t h} \) term in an infinite G.P.
\( 3+42+588+\dots ? \)
A . 12588608
B . 22588608
c. 32588608
D. 42588608


What are apoplast and symplast?


\( \int_{0}^{\pi / 4} \tan ^{2} x d x= \)
A \( \cdot 1-\frac{\pi}{4} \)
B \( \cdot 1+\frac{\pi}{4} \)
c. \( \frac{-\pi}{4}-1 \)
D. \( \frac{\pi}{4}-1 \)


A step supplies water at \( 22^{\circ} \mathrm{C} \). A man
take 1 liter per minute at \( 37^{\circ} \mathrm{C} \) from the
geyser. the power of geyser is
A. 2100 \( w \)
B. 1050 \( w \)
c. 1575 w
D. 525 w


Rainbows are caused due to:
A. scattering of white light
B. dispersion of white light
C. reflection of white light
D. none of these


Which is haploid in Gymnosperm?
A. Root, shoot, endosperm
B. Endosperm, pollen grain, megaspore
C. Root, leaf, bud
D. Bulbil, buds, microspore


Categories the given equations under
respective phases and select the
correct option.
\[
\begin{array}{r}
\text { "I. } C_{6} \mathrm{H}_{12} \mathrm{O}_{6}+2 \mathrm{NAD}^{+}+2 \mathrm{ADP}+2 \mathrm{Pi} \rightarrow \\
\qquad 2 \mathrm{C}_{3} \mathrm{H}_{4} \mathrm{O}_{3}+2 \mathrm{ATP}+2 \mathrm{NADH}+2 \mathrm{H}^{+}
\end{array}
\]
Il. Pyruvic acid + \( 4 \mathrm{NAD}^{+}+\mathrm{FAD}^{+}+2 \mathrm{H}_{2} \mathrm{O}+\mathrm{ADP}+\mathrm{Pi} \rightarrow \)
\[
3 \mathrm{CO}_{2}+4 \mathrm{NADH}+4 \mathrm{H}^{+}+\mathrm{ATP}+\mathrm{FADH}_{2}
\]
A. I-Glycolysis ; II-Fermentation ; III-Krebs' cycle
B. I-Krebs' cycle ; II - Fermentation ; III -Glycolysis
C. I-Krebs' cycle ;II- Glycolysis ; III- Fermentation
D. I- Glycolysis ; II- Krebs' cycle ; III-Fermentation


The intensity of sound after passing through a slab decreases by \( 20 \% . \) On passing through two such slabs, the intensity will decrease by
A . \( 30 \% \)
B. \( 36 \% \)
c. \( 40 \% \)
D. \( 50 \% \)


Two triangles are congruent if they have
the same and
A. Not sure
B. Shape
c. Both B and D
D. size


Bombax leaf is
A. Tripinnate
B. Unipinnate
C . Multifoliate
D. Quadrifoliate


If \( \operatorname{Sin}^{2} A+\operatorname{Cos}^{2} B+\operatorname{Sin}^{2} C=1, \) then
the triangle \( A B C \) is
A. isosceles
B. equilateral
c. right angled
D. scalene


A radioactive element \( X \) has an atomic
number of \( 100 . \) It decays directly into an element \( Y \) which decays directly into an element \( Z . \) In both processes a charged particle is emitted. Which of the following statement would be true?
A. \( Y \) has an atomic number of 102
B. \( Z \) has an atomic number of 10
c. \( Z \) has an atomic number of 97
D. \( Z \) has an atomic number of 99


Let, coordinates of the two points \( A \& B \) be (1,2) and \( (7,5), \) respectively. The line
\( A B \) is rotated through \( 45^{\circ} \) in anticlockwise direction about the point of
trisection of \( \mathrm{AB} \) which is nearer to B. The
equation of the line in the new position is
A. \( 2 x-y-6=0 \)
в. \( x-y-1=0 \)
c. \( 3 x-y-11=0 \)
D. none of these


A mixture of \( S O_{2} \) and \( O_{2} \) at 1
atmosphere in the ratio of 2: 1 is
passed through a catalyst at \( 1170^{\circ} \mathrm{C} \) for attainment of equilibrium. The exit
gas is found to contain \( 87 \% S O_{3} \) by
volume. Calculate \( \boldsymbol{K}_{\boldsymbol{p}} \) for the reaction, \( \boldsymbol{S O}_{2}(\boldsymbol{g})+\frac{1}{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{S} \boldsymbol{O}_{3}(\boldsymbol{g}) \)


The volume of water required to make \( 0.20 \mathrm{M} \) solution from \( 16 \mathrm{ml} \) of \( 0.5 \mathrm{M} \) solution is:
A . \( 40 \mathrm{ml} \)
B. 16 \( \mathrm{ml} \)
c. \( 50 \mathrm{ml} \)
D. 24 m


A man is known to speak the truths 3 out of 4 times. He throw a die and report
that it is six. The probability that it is actually a six, is
A \( \cdot \frac{3}{8} \)
B. \( \frac{1}{5} \)
\( c \cdot \frac{3}{4} \)
D. None of these


In order to increase the resistance of a
given wire of uniform cross-section to four times its value, a fraction of its
length is stretched uniformly till the full length of the wire becomes \( \frac{3}{2} \) times the original length.What is the value of this
fraction?
\( A \cdot \frac{1}{4} \)
B. \( \frac{1}{8} \)
\( c \cdot \frac{1}{16} \)
D. \( \frac{1}{6} \)


What must be added to \( x^{3}+3 x-8 \) to
\( \operatorname{get} 3 x^{3}+x^{2}+6 ? \)
A \( \cdot 2 x^{3}+x^{2}-3 x+14 \)
B \( \cdot 2 x^{2}+x^{2}+14 \)
c. \( 2 x^{3}+x^{2}-6 x-14 \)
D. None of these


Derivative of \( \tan ^{3} \theta \) with respect to \( \sec ^{3} \theta \) at \( \theta=\frac{\pi}{3} \) is
A \( \cdot \frac{3}{2} \)
B. \( \frac{\sqrt{3}}{2} \)
\( c \cdot \frac{1}{2} \)
D. \( -\frac{\sqrt{3}}{2} \)


When an unpolarised light is polarized, then the intensity of light of the polarized wave :
A. remains the same
B. gets doubled
c. gets halved
D. depends on the colour of the light.


Volume is inversely proportional to pressure is:
A. Boyle's law
B. Charles's law
c. Avogadro's principle
D. ideal gas law


Area enclosed by the graph of the function \( y=\ln ^{2} x-1 \) lying in the \( 4 t h \)
quadrant is
\( A \cdot \frac{2}{e} \)
B. \( \frac{4}{e} \)
c. \( _{2}\left(e+\frac{1}{e}\right) \)
D. \( 4\left(e-\frac{1}{e}\right) \)


Explain why objects moving in fluids must have special shapes.


The equilibrium constant for the
reaction \( \boldsymbol{C O}(\boldsymbol{g})+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \rightleftharpoons \)
\( \boldsymbol{C O}_{2}(\boldsymbol{g})+\boldsymbol{H}_{2}(\boldsymbol{g}) \) is \( \mathbf{7 . 3} \) at \( \mathbf{4 5 0}^{\circ} \boldsymbol{C} \) \&1
atm pressure. The initially
concentration of water \( \operatorname{gas} C O \& H_{2} \) in
equimolar ratio \( \& \) steam are 2 moles \( \& \) 5 moles respectively. The number of moles of \( C O, H_{2}, C O_{2} \& H_{2} O \) (vapour) at equilibrium are
\( \boldsymbol{n}_{C O_{2}}=\mathbf{0 . 9 2 8}, \boldsymbol{n}_{\boldsymbol{H}_{2}}=\mathbf{1 . 9 2 8}, \boldsymbol{n}_{C O}= \)
\( \mathbf{0 . 0 7 2}, \boldsymbol{n}_{\boldsymbol{H}_{2}} \boldsymbol{o}=\mathbf{4 . 0 7 2} \)
If true enter 1 , else enter 0 .
A.


\( \mathbf{f}^{n} \boldsymbol{C}_{\boldsymbol{r}-\mathbf{1}}=\mathbf{3 6},^{\boldsymbol{n}} \boldsymbol{C}_{\boldsymbol{r}}=\mathbf{8 4} \) and \( ^{\boldsymbol{n}} \boldsymbol{C}_{\boldsymbol{r}+\mathbf{1}}= \)
\( 126, \) then \( r \) is
\( A \cdot 1 \)
B . 2
\( c .3 \)
D.


When you touch a vessel on a stove your
body feels hot. Why?
A. Heat energy is transferred from vessel to the body
B. Heat energy is transferred from body to the vessel
C. Kinetic energy is transferred from vessel to the body
D. Kinetic energy is transferred from body to the vessel


Write formulas for the following compounds. Tin (IV) oxide


Assertion
An elements nuclear charge is equal to
the number of protons in the nucleus
Reason
The only charged particles in the
nucleus are neutrons
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The block of mass \( M \) moving on the
frictionless horizontal surface collides
with the spring of spring constant \( \boldsymbol{K} \)
and compresses it by length \( L \). The maximum moment of the block after
collision is
A \( \cdot \sqrt{M K} L \)
в. \( \frac{K L^{2}}{2 M} \)
c. zero
D. \( \frac{M L^{2}}{K} \)


Which is the drug used by health workers in the management of acute respiratory illness?
A. Co - trimoxazole
B. Chloramphenicol
c. Benzyl penicillin
D. Gentamycin


Conversion of milk into curd is :
A. a physical property of milk
B. a chemical property of milk
C . a physical change
D. a chemical change


An object of mass \( 2 \mathrm{kg} \) is sliding with a
constant velocity of \( 4 m s^{-1} \) on a frictionless horizontal table. The force
required to keep the object moving with the same velocity is:
A. 32 N
B. on
\( c \cdot 2 n \)
\( D \cdot 8 N \)


The product of two rational numbers is
\( -7 . \) If one of the numbers is \( -5, \) find the
other.


The base of an isosceles triangle is \( \frac{4}{3} \) \( \mathrm{cm} . \) The perimeter of the triangle is
62
\( \frac{a}{15} \mathrm{cm} . \) What is the length of either of remaining equal sides?


Find the value of a if \( 34,45,56, a \) if they
are in AP
A . 67
B. 66
\( c \cdot 65 \)
D. 69


When sulphur is boiled with \( N a_{2} S O_{4} \)
solution, the compound formed is:
A. Sodium sulphide
B. Sodium sulphate
c. Sodium persulphate
D. Sodium thiosulphate


3.65 grams of HCl is dissolved in 16.2 grams of water. The mole fraction of HCI
in the resulting solution is:
A . 0.4
B. 0.3
\( c .0 .2 \)
D. \( 0 . \)


The unit of magnification is :
\( \mathbf{A} \cdot m \)
B. \( m^{2} \)
\( \mathrm{c} \cdot m^{-1} \)
D. it has no units


Cloud seeding is a technique used, to
induce rain that was first used by the
USA in \( 1946 . \) It has also been done in
Karnataka and other places in India.
What is it?
A. An agricultural practice that depends on clouds
B. Introduction of particles in clouds to increase condensation
C. Making clouds and placing them in the sky.
D. Trimming the clouds into seed like structures


A structural steel rod has a radius of
\( 10 m m \) and a length of \( 1.0 m . A 100 k N \)
force stretches it along its length. Calculate (a) stress,
(b) elongation, and
(c) strain on the rod. Young's modulus,
of structural steel is \( 2.0 \times 10^{11} N m^{2} \)


toppr
Q Type your question
battery has essentially no internal resistance, and all the wires are
essentially resistanceless, too. When a
light bulb is unscrewed, no current flows through that branch of the circuit.
For instance, if light bulb 2 is unscrewed, current flows only around
the lower loop of the circuit, which consist of the battery and light bulb 1. The more current flows through a light bulb, their equivalent resistance is
\( \boldsymbol{R}_{e q}=\boldsymbol{R}_{1}+\boldsymbol{R}_{2} . \) By contrast, when two
reisistors are wired in parallel, their net resisance is given by \( \frac{1}{R_{e q}}=\frac{1}{R_{1}}+\frac{1}{R_{2}} \)
Bulb 2 is now screwed in as a result,
bulb 1:
A. turns off
B. becomes dimmer
C. stays about the same brightness
D. becomes brighter


Which of the following statements is
correct?
\( \mathbf{A} \cdot p K_{w} \) increases with increase of temperature
B. \( p K_{w} \) decreases with increase of temperature
\( \mathbf{c} \cdot p K_{w}=14 \) at all temperatures
D. \( p K_{w}=p H \) at all temperatures


For an ideal solution, \( \Delta_{m i x} H \) is


A gas absorbs \( 250 J \) of heat and
expands from 1 litre to 10 litre at constant temperature against external
pressure of 0.5 atm. The values of \( q, w \) and \( \triangle \boldsymbol{U} \) will be respectively:
A. \( -250 J, 455 J, 710 J \)
\( J \)
В. \( 250 J,-455 J,-205 J \)
c. \( -250 J,-455 J,-205 J \)
D. \( -250 J, 455 J, 205 J \)


Which of the following is used to distinguish ethylene and acetylene?
A. Alkaline \( K M n O_{4} \)
B. Bromine water
c. Amm.cuprous chloride
D. \( \operatorname{concH}_{2} \mathrm{SO}_{4} \)


A chord of a circle radius \( 14 \mathrm{cm} \) makes
a right angle at the centre. Find the areas of the minor and major segments of the circle


Ref. image Half-life is independent of concentration of reactant. After minutes
volume of \( N_{2} \) gas is \( 10 L \) and after
complete reaction it is \( 50 L \). Hence rate
constant is :
A \( \cdot(2.303 / 10) \log 5 \min ^{-1} \)
B . \( (2.303 / 10) \log 1.25 \mathrm{min}^{-1} \)
c. \( (2.303 / 10) \log 2 \) min \( ^{-1} \)
D. \( (2.303 / 10) \log 4 \min ^{-1} \)


Assertion
Finely divided iron does not form ferric chloride with hydorchloric acid.
Reason
Hydrochloric acid produces hydrogen gas with iron.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


In which one of the following, the two names refer to one and the same thing?
A. Tricarboxylic acid cycle and urea cycle
B. Krebs cycle and Calvin cycle
c. Tricarboxylic acid cycle and citric acid cycle
D. Citric acid cycle and Calvin cycle


If \( \int f(x) d x=2\{f(x)\}^{3}+c, \) and
\( f(x) \neq 0 \) then \( f(x) \) is
A \( \cdot \frac{x}{2} \)
B . \( x^{3} \)
c. \( \frac{1}{\sqrt{x}} \)
D. \( \sqrt{\frac{x}{3}} \)


Find the quantifier which best describes the variable of the open
sentence \( x^{2}+2 \geq 0 \)
A. Universal.
B. Existential.
c. Neither (a) nor (b)
D. Does not exist.


The value of \( c \) in Lagrange's theorm for
the function \( f(x)=\log \sin x \) in the
interval \( [\boldsymbol{\pi} / \mathbf{6}, \mathbf{5} \boldsymbol{\pi} / \mathbf{6}] \) is
\( \mathbf{A} \cdot \pi / 4 \)
в. \( \pi / 2 \)
\( \mathrm{c} \cdot 2 \pi / 3 \)
D. none of these


Anything that influences the valence electrons will affect the chemistry of the element. Which one of the following
factors does not affect the valence
shell?
A. Valence principal quantum number (n)
B. Nuclear charge
c. Nuclear mass
D. Number of core electrons


State the postulate of Bohr's theory regarding emission off a photon


Rain is falling vertically with a speed of \( 20 m / s . \) After sometime wind starts blowing with a speed of \( 12 m / s \) in east to west direction in which direction
should a boy waiting at a bus stop hold his umbrella.


The values of k for which the roots are
real and equal of the following equation \( 3 x^{2}-5 x+2 k=0 \) is
\( k=\frac{25}{24} \)
A. True
B. False


Select the correct statement
A. Histone protein is present in all prokaryotes but absent in animal cell
B. ER is absent in eukaryotes but presents in prokaryotes
C. Nuclear membrane is absent in prokaryotes but nuclear membrane is present in eukaryotes
D. Ribosome is present in eukaryotic cells but absent in prokaryotic cells


Harish borrowed a certain sum of
money from Girish at \( 6 \frac{2}{3} \% \) simple
interest. If he paid an interest of \( \boldsymbol{R} \boldsymbol{s} . \boldsymbol{7} \boldsymbol{0} \boldsymbol{0} \)
for 100 days, how much money did Hari borrow from Girish?


A monoatomic ideal gas \( \left(C_{V}=\frac{3}{2} R\right) \) is
allowed to expand adiabatically and reversibly from initial volume of \( 8 \mathrm{L} \) at
\( 300 \mathrm{K} \) to a volume of \( V_{2} \) at \( 250 \mathrm{K} . V_{2} \) is:
(Given \( \left.(4.8)^{1 / 2}=2.2\right) \)
A . \( 10.5 \mathrm{L} \)
B. 23 L
\( c .8 .5 \)
D. 50.5


Two medians drawn from acute angles
of a right angled triangle intersect at an angle \( \frac{\pi}{6} . \) If the length of the hypotenuse
of the triangle is 3 units, then area of the triangle (in sq. units) is
A. \( \sqrt{3} \)
B. 3
\( c \cdot \sqrt{2} \)
D. 9


A pure inductor of self inductance \( 1 \mathrm{H} \) is connected across an alternating voltage of \( 115 \mathrm{V} \) and frequency \( 60 \mathrm{Hz} \). The
reactance \( X_{L} \) and peak current
respectively are
в. 337.12, 0.43 А
c. 377.1\Omega, 0.43 A
D. 3.7\Omega, 0.42 A


Number of identical terms in the
sequence \( 2,5,8,11 \ldots \) upto 100 terms
are
A . 17
B. 33
c. 50
D. 147


Which of the following option is correct
for colloids?
A. Blue color of the sky is due to the scattering of light by colloidal dust particles in air
B. Sea water looks blue due to scattering of light by the colloidal impurities present in sea water
C. Blood is a colloidal solution
D. All of the above


If \( I \) is the center of a circle inscribed in
a triangle \( A B C, \) then \( |B C| I A+ \) \( |\boldsymbol{C A}| \boldsymbol{I B}+|\boldsymbol{A B}| \boldsymbol{I C} \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( I A+I B+I C \)
c. \( \frac{I A+I B+I C}{3} \)
D. \( \frac{I A+I B+I C}{2} \)


In the figure, find the measure of
\( \angle M P N \)


The work done in moving a charge of 5 coulombs from a point at 230 volts to another point at 240 volts is.
A. 50
B . 15
c. 100
D. 500


Which of the following is a true
statement?
A. Among the carbonyl compounds, ketones have slightly higher boiling points than the isomeric aldehydes. This is due to the presence of two electron releasing groups around the carbonyl carbon which makes them more polar.
B. Among the carbonyl compounds, ketones have slightly lower boiling points than the isomeric aldehydes. This is due to the presence of two electron releasing groups around the carbonyl carbon which makes them more polar.
C. Among the carbonyl compounds, ketones have slightly lower boiling points than the isomeric aldehydes. This is due to the presence of two electron releasing groups around the carbonyl carbon which makes them less polar.
D. Among the carbonyl compounds, ketones have slightly higher boiling points than the isomeric aldehydes. This is due to the presence of two electron releasing groups around the carbonyl carbon which makes them less polar.


The resonant frequency of the given RLC
circuit.


The value of D.I. \( \int_{-2010}^{2010} x^{2010} \cot ^{-1}(2010 x) d x \) is equal to
A \( \cdot \frac{\pi}{2011}(2011)^{2010} \)
B. \( \frac{\pi}{2010}(2010)^{2011} \)
C. \( \frac{\pi}{2011}(2010)^{2011} \)
D. \( \frac{\pi}{2010}(2011)^{2010} \)


Starch is saccharide.


Two angles of a triangle are \( \cot ^{-1} 2 \) and
\( \cot ^{-1} 3 . \) Then the third angle
A.
в. \( \frac{3 \pi}{4} \)
c.
D.


State whether the given statement is True or False.
\( C u O \) can't be reduced by carbon but it
can be reduced by \( H_{2} \)
\( \operatorname{given}: \Delta G_{f}^{\circ} \) for \( C u O=-129.7 \mathrm{kJ} \mathrm{mol}^{-1} \)
\( C O=-137.2 \mathrm{kJ} \mathrm{mol}^{-1} \mathrm{H}_{2} \mathrm{O}=-237.2 \mathrm{kJ} \)
\( m o l^{1} \)


There are n married coupled at a party. Each person shakes hand with every person other than her or his spouse. Find the total number of hand shakes.


Who was the Indian scientist who was
primarily responsible for setting of nuclear reactors in India?
A. H. J. Bhabha
B. V. A. Sarabhai
c. Dr. A. P. J. Abdul Kalam
D. G. Madhavan Nair


The correct order of acidity of the three groups (marked X,Y,Z)in the given species is:
A \( . x>y>z \)
В \( . x>z>y \)
\( \mathbf{c} \cdot y>z>x \)
D. \( z>y>x \)


All the mass of the atom resides in the
A. nucleus
B. molecules
\( c . \) ions
D. orbit


A survey show that \( 63 \% \) of the american
likes cheese whereas \( 76 \% \) of the
american like apples if \( x \% \) of the
american like both cheese and apples find the value of \( x \)


Differentiate between \( n, 2 n \) and \( n+n \) conditions.


No contact force acts on a bucket when
it is being pulled out of a well using a
rope
A. True
B. False


A body cools in 7 minutes from \( 60^{\circ} \mathrm{C} \) to
\( 40^{\circ} \mathrm{C} \). If the temperature of surrounding
is \( 10^{\circ} \mathrm{C}, \) the temperature after next 7
minutes will be :
\( \mathbf{A} \cdot 32^{\circ} C \)
B . \( 38^{\circ} \mathrm{C} \)
c. \( 22^{\circ} \mathrm{C} \)
D. None of these


Chlorine gas removes hydrogen from \( \boldsymbol{H}_{2} \boldsymbol{S} \) solution, forming \( \mathrm{HCl} \) and leaving behind sulphur.
A. True
B. False


Choose the correct answers from the
following given. The mammalian excretory system involves all of the following except
A. reabsorption of high molecular weight proteins from the glomerular filtrate
B. active transport of chloride ions from the filtrate into the peritubular tissues
c. release of nitrogenous wastes into the intestines
D. hormonal control of permeability of walls in various excretory tubules


Twenty pillows can be bought for \( R s 5120 \) How many pillows can be bought for \( R s \mathbf{7 9 3 6} ? \)


A metre stick is balanced on a knife
edge at its centre. When two coins, each of mass 5 g are put one on top of the other at the \( 12.0 \mathrm{cm} \) mark, the stick is
found to be balanced at \( 45.0 \mathrm{cm} . \) What
is the mass of the metre stick?


The area of the region
\( \left\{(x, y): x y \leq 8,1 \leq y \leq x^{2}\right\} \) is
\( \mathbf{A} \cdot 16 \log _{6} 2-6 \)
в. \( 8 \log _{6} 2-\frac{7}{3} \)
\( \mathrm{c} \cdot_{16 \log _{6} 2-\frac{14}{3}} \)
D. \( 8 \log _{6} 2-\frac{14}{3} \)


Brain is the main \( \ldots \). centre of the body
A. Peripheral
B. Nervous
c. Chemical
D. Physical


Fill in the blanks.
(i) Zero has
(ii) The numbers
and are their own
reciprocals.
(iii) The reciprocal of -5
is
(iv) Reciprocal of \( \frac{1}{x}, \) where \( x \neq 0 \)
is
(v) The product of two rational numbers is always a
(vi) The reciprocal of a positive rational number is


Assertion
The equation \( 2\left(\sin ^{-1} x\right)^{2}- \)
\( 5\left(\sin ^{-1} x+2\right)=0 \)
Reason
\( \sin ^{-1}(\sin x)=x \) if \( x \epsilon[-1.57,1.57] \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion false but Reason is true


The point \( \left(x_{1}, y_{1}\right),\left(x_{2}, y_{2}\right),\left(x_{1}, y_{2}\right) \) and
\( \left(x_{2}, y_{1}\right) \) are always \( ? \)
A. Collinear
B. concyclic
c. vertices of square
D. vertices of a rhombus


Water is flowing in a streamline motion
through a tube with its axis horizontal.
Consider two points \( A \) and \( B \) in the tube
at the same horizontal level.
This question has multiple correct options
A. The pressures at \( A \) and \( B \) are equal for any shape of the tube
B. The pressures are never equal
C. The pressures are equal if tube has a uniform crosssection.
D. The pressures may be equal even if the tube has a nonuniform cross-section.


What is flash point of a material?


Write any two distinguishing features between conductors, semiconductors and insulators on the basis of energy
band diagrams.


A certain color of light towards the purple end of the visible spectrum has a
wavelength of 420 nm in a vacuum.
What is the frequency of this light? The speed of light in a vacuum is
\( 3.00 \times 10^{8} m / s \)
\( \mathbf{A} \cdot 126 H z \)
В . \( 1.26 \times 10^{11} \mathrm{Hz} \)
c. \( 7.1 \times 10^{14} \mathrm{Hz} \)
D. \( 1.4 \times 10^{-15} \mathrm{Hz} \)
E \( \cdot 1.4 \times 10^{-6} \mathrm{Hz} \)


During the melting of a slab of ice at
\( 273 K \) at atmospheric pressure:
This question has multiple correct options
A. Positive work is done by the ice-water on the atmosphere
B. Positive work is done on the ice-water by the atmosphere
C. The internal energy of the ice-water increases
D. The internal energy of the ice-water system decreases


A school has 11 Maths teachers and 7
Science teachers. In how many ways can they be seated in a round table so
that all the Science teachers do not sit
together?
\( \mathbf{A} \cdot 18 !-(12 ! \times 7 !) \)
B . \( 17 !-(12 ! \times 7 !) \)
c. \( 17 !-(11 ! \times 7 !) \)
D. \( 18 !-(11 ! \times 7 !) \)


The RNA which takes part in the
synthesis of proteins is:
A. m-RNA
B. r-RNA
c. t-RNA
D. All of the above


Which is wrong IUPAC name?
This question has multiple correct options
\( \mathbf{A} \cdot C H_{3} C H_{2} C H_{2} C O O C H_{2} C H_{3}(\text { Ethylbutanoate }) \)
B. \( C H_{3} C H C H_{2} C H O \) (3-Methyl butanol)
\[
\begin{array}{l}_{C H_{3}}\end{array}
\]
\( \mathbf{c} \cdot C H_{3}-C H-C H-C H_{3} \quad \) (2-Methyl-3-butanol)
\[
\begin{array}{l}\mid \\ O H \quad C H_{3}\end{array}
\]
D. \( C H_{3} C H C O C H_{2} C H_{3} \) (2-methyl-3-pentanone)
\[
\begin{array}{l}C H_{3}\end{array}
\]


At \( 298 \mathrm{K} \) temperature, \( A \) hydrogen gas electrode is made by dipping platinum wire in a solution of HCl of \( \mathrm{pH}=10 \) and
by passing hydrogen gas around the platinum were at one atm pressure. The potential of electrode would be?
\( \mathbf{A} \cdot 0.59 \mathrm{V} \)
B. \( 0.118 v \)
c. \( 1.18 v \)
D. \( 0.059 \mathrm{V} \)


An electron in an atom absorbs
radiation of wavelength \( 392 . n . m \) and later on it emits energy in the from of photons of two different wavelengths. If one of the wavelength is 712 n.m.
Calculate the other


Universal gas constant R has the value?
A . 0.08206 L. atm.mol \( ^{-1} K^{-1} \)
B. \( 8.206 L . a t m . m o l^{-1} K^{-1} \)
c. 8.314 L.atm.mol\( ^{-1} K^{-1} \)
D. 2L.atm.mol-1 \( K^{-1} \)


Statement-1: \( C a H_{2} \) is used as main
source to transport gas as 1 pound of it
gives 16.5 cubic feet \( \boldsymbol{H}_{2} \)

Statement-2: It is difficult to transport
\( \boldsymbol{H}_{2} \) gas.
A. Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-
B. Statement-1 is True, Statement-2 is True; Statement- is not a correct explanation for Statement- -
c. Statement- 1 is true, Statement- 2 is false.
D. Statement-1 is false, Statement-2 is true


The value of \( ^{47} C_{4}+\sum_{j=1}^{5}(52-j) C_{3} \) is
A. \( 47_{5} \)
B. \( ^{52} C_{5} \)
c. \( ^{52} C_{4} \)
D. \( ^{52} C_{3} \)


Heavy water \( \left(D_{2} O\right) \) is
A. A product of oxygen and hydrogen.
B. Ordinary water containing dissolved salts of heavy metals.
C. Water of mineral springs.
D. Water produced by repeated distillation and condensation.


A radioactive substance of half life 69.3
days is kept in a container. The time in which \( 80 \% \) of the substance will
disintegrate will be
A. 1.61 days
B. 16.1days
c. 161 days
D. 1610 days


Two parallel chords in a circle are \( 10 \mathrm{cm} 10 \mathrm{cm} \) and \( 24 \mathrm{cm} 24 \mathrm{cm} \) long. If
the radius of the circle is \( 13 \mathrm{cm} 13 \mathrm{cm} \) find the distance between the chords if
thay lie on the same side of the centre.


Which of the following is not optically active?
A. Glycine
B. Lysine
c. Aspartic acid
D. Isoleucine


A particle executes SHM between \( \boldsymbol{x}= \)
\( -A \) to \( x=+A . \) The time taken for it to
go from 0 to \( \frac{A}{2} \) is \( T_{1} \) and to go from \( \frac{A}{2} \) to \( A \) is \( T_{2} \) then \( \frac{T_{1}}{T_{2}} \) is?
\( A \cdot 2 \)
B. \( \frac{1}{2} \)
\( c \cdot 4 \)
D.


Two parallel rails of a railway track
insulated from each other and with the
ground are connected to a millivoltmeter. The distance between
the rails is one metre. A train is
traveling with a velocity of \( 72 k m / h \)
along the track. The reading of the millivoltmeter \( (\text { in } \boldsymbol{m} \boldsymbol{V}) \) is :
(Vertical component of the earths
magnetic induction is \( \left.2 \times 10^{-5} T\right) \)
A. 144
в. 0.72
c. 0.4
D. 0.2


The mean free path of conduction
electrons in copper is about \( 4 \times \)
\( 10^{-8} \) m. Find the electric field which
can give, on an average, \( 2 e V \) energy to a conduction electron in a block of
copper.
A \( \cdot 6 \times 10^{7} V / m \)
B . \( 7 \times 10^{7} V / m \)
c. \( 5 \times 10^{7} V / m \)
D. \( 5 \times 10^{9} V / m \)


Assertion
A steady current is flowing in a conductor hence there is an electric
field within the conductor and
Reason
In case of steady current, there can be
no accumulation of charges, so no
electric field can be established.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


What is the name given to a cylindrical
coil whose diameter is less in
comparison to its length?


Harry goes to a shop to buy a watch costing Rs. 1404 including sales tax of \( 8 \% \). He asks the shopkeeper to reduce the price of the watch so that he can save an amount equal to the sales tax. The reduction in the price of the watch
is
A . Rs. 108
B. Rs. 104
c. Rs. 112.32
D. None of these


The ratio of the dimension of Planck's
constant and that of the moment of
inertia is the dimension of :
A. Velocity
B. Angular momentum
c. Time
D. Frequency


Assertion
In humans, the gamete contributed by the male determines whether the child
produced will be male or female.
Reason

Sex in humans is a polygenic trait
depending upon a cumulative effect of
some genes on X-chromosome and
some on \( Y \) - chromosome.
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


Solve :
\( \int 2^{x} \cdot e^{x} d x \)


The magnetic field energy in an inductor changes from maximum value to minimum value in \( 5.0 m s, \) when
connected to an \( A C \) source. The
frequency of the source is
\( A \cdot 20 H z \)
B. 50 Н
c. 200 н \( z \)
D. 500 нz


\( \mathrm{R} \) is a relation in \( \mathrm{A} \) and \( (\mathrm{a}, \mathrm{b}) \notin \mathrm{r}, \) implies
(b, a) \( \notin \mathrm{R} \) then \( \mathrm{R} \) is said to be relation
A. symmetric
B. contradictory
c. skew symmetric
D. none of these


Which of the following does not yield wool?
A . Camel
B. Sheep
c. Deer
D. Goat


If \( \boldsymbol{P}=\boldsymbol{x}^{3}-\frac{\mathbf{1}}{\boldsymbol{x}^{3}} \) and \( \boldsymbol{Q}=\boldsymbol{x}-\frac{\mathbf{1}}{\boldsymbol{x}}, \boldsymbol{x} \in \)
\( (1, \infty) \) then minimum value of \( \frac{P}{Q^{2}} \) is:
\( A \cdot \) is \( 2 \sqrt{3} \)
B. is \( 4 \sqrt{3} \)
c. does not exist
D. None of these


Is force needed to keep a moving body in motion? Which one of the Newton's laws
follow this ?
A. No, first law
B. Yes, third law
c. No, second law
D. Yes, first law.


What is the mass of a mole of water
containing \( 50 \% \) of heavy water \( \left(D_{2} O\right) ? \)
A . \( 19 g \)
в. \( 18 g \)
c. \( 20 g \)
D. 21 \( g \)


the point \( P, \) the flux of the electric field
through the closed surface:
A. will remain zero
B. will becomes positive
c. will become negative
D. will become undefined


If \( \boldsymbol{x}=\boldsymbol{c} \boldsymbol{y}+\boldsymbol{b} \boldsymbol{z}, \boldsymbol{y}=\boldsymbol{a} \boldsymbol{z}+\boldsymbol{c} \boldsymbol{x}, \boldsymbol{z}=\boldsymbol{b} \boldsymbol{x}+ \)
\( a y, \) where \( x, y, z \) are not all zero, then
the value of \( a^{2}+b^{2}+c^{2}+2 a b c \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
c. -1
D. None of these


Given: \( \angle C A B=75^{\circ} \) and \( \angle C B A=50^{\circ} \)
Find the value of \( \angle D A B+\angle A B D \)


A host cell has intracellular bacterial
symbionts. If growth rate of the bacterial symbiont is \( 10 \% \) higher than the host cell, after ten generations of the host cell, the density of bacteria is host cell will increase:
A . By 10\%
B. Two fold
c. Ten fold
D. Hundred fold


Find the slope of the line which make the following angle with the positive direction of \( x- \) axis
\( -\frac{\pi}{4} \)


Assertion
Addition of \( H C l(a q .) \) to \( H C O O H(a q .) \) decrease the ionization of
HCOOH(aq.).
Reason
Due to common ion effect of \( \boldsymbol{H}^{+} \)
ionization of \( H C O O H \) decrease.
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 is not applicable for graphite?
A. The carbon atoms are linked with three carbon atom in planes stacked one over the other
B. It is solid crystalline allotrope of carbon.
c. It can be used for making electrodes
D. It is hard and cannot be used as lubricant


Expressing \( \vec{a} \) and \( \vec{b} \) as linear combinations of \( \vec{c} \) and \( \overrightarrow{\boldsymbol{d}} \) we \( \operatorname{get} \overrightarrow{\boldsymbol{a}}= \)
\( k \vec{c}+m \vec{d} \) and \( \vec{b}=h \vec{c}+r \vec{d} \)
Find integer part of \( \boldsymbol{k}+\boldsymbol{m}+\boldsymbol{h}+\boldsymbol{r} \) ?
\( -\boldsymbol{a}+\boldsymbol{b}=-\boldsymbol{c} ; \mathbf{2} \boldsymbol{a}-\boldsymbol{b}=\boldsymbol{c}+\boldsymbol{d} \)
A \( \cdot \frac{21}{4} \)
в. \( \frac{27}{8} \)
c. \( \frac{25}{8} \)
D. \( \frac{33}{8} \)
E \( \frac{31}{8} \)
F. \( \frac{29}{8} \)
G. \( \frac{23}{8} \)


The undigested, semisolid food is called
A. Anus
B. Faeces
c. Rectum
D. vill


The oxidation number of \( C \) in
\( \boldsymbol{C H}_{4}, \boldsymbol{C H}_{3} \boldsymbol{C l}, \boldsymbol{C H}_{2} \boldsymbol{C l}_{2}, \boldsymbol{C H} \boldsymbol{C l}_{3} \) and
\( C C l_{4} \) are respectively :
в. +2,+4,0,-4,-2
c. -4,-2,0,+2,+4
D. -2,-4,0,+4,+2


If the point \( P(k-1,2) \) is equidistant
from the points \( \boldsymbol{A}(\boldsymbol{3}, \boldsymbol{k}) \) and \( \boldsymbol{B}(\boldsymbol{k}, \boldsymbol{5}) \)
then how many values of \( k \) are
obtained?

Write \( 0, \) if the value cannot be
determined


In angiosperms various stages of
reductional division can best be
studied in
A. Young anthers
B. Mature anthers
c. Mature ovules
D. Endosperm cells


The magnetic induction at the centre 0
is?


Boron and nitrogen form bonds analogous to carbon-carbon bonds. For example, compound ammonia borane,
\( N H_{3}-B H_{3}, \) contains \( B-N \) bond
analogous to the \( C-C \) bond in ethane.
Borazine \( \left(B_{3} N_{3} H_{6}\right) \) is analogous to benzene and is prepared by reacting
\( N H_{4} C l \) with \( B C l_{4} \) followed by
reduction using \( L i B H_{4} . \) The correct statement(s) is/are:
This question has multiple correct options
A. boron nitride \( (B N) \) has a structure similar to graphite and is a good conductor of electricity
B. the \( B \) -center in borazine is susceptible to nucleophilic attack
c. ethane is a gas at room temperature, while ammonia borane is not so
D. the reaction of \( H C l \) with borazine gives hexachloro derivative of borazine


\( \boldsymbol{H}_{2} \boldsymbol{O}_{2}+\boldsymbol{H}_{2} \boldsymbol{O}_{2} \rightarrow \boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{O}_{2}, \) is an
example of disproportionation because:
A. oxidation number of oxygen only decreases
B. oxidation number of oxygen only increases
c. oxidation number of oxygen decreases as well as increase
D. oxidation number of oxygen neither decreases nor increases


Are the following set of ordered pairs functions? If so, examine whether the
mapping is injective or surjective:
(i)
\( \{(x, y): x \text { is a person, } y \text { is the mother } o \)
(ii)
\( \{(a, b): a \) is a person, b is the ancestor o


If a and b are real numbers and \( (a+ \)
\( i b)^{11}=1+3 i, \) then \( (b+i a)^{11} \) is equal
to
A . \( i+3 \)
B. \( 1+3 i \)
\( c \cdot 1-3 i \)
D. 0
E \( .-i-3 \)


The force between two magnetic poles is \( F \) when they are separated by certain distance. If the distance between the two
poles is doubled and strength of each pole is tripled. The percentage change in the force between the two poles is :
A. \( 125 \% \)
B. \( 100 \% \)
c. \( 50 \% \)
D. \( 25 \% \)


State whether the following statements
are true or false.
In pteridophytes, the gametophyte is dominant, while sporophyte is a dependent generation
A. True
B. False


The Born Haber cycle below represents the energy changes occurring at \( 298 \mathrm{K} \) when \( \mathrm{KH} \) is formed from its elements
\( \mathbf{v}: \Delta \boldsymbol{H}_{\text {atomisation}} \mathrm{K}=\mathbf{9 0} \mathrm{kJ} / \mathrm{mol} \)
\( \mathbf{w}: \Delta \boldsymbol{H}_{\text {ionisation}} \mathbf{K}=\mathbf{4 1 8} \mathbf{k J} / \mathrm{mol} \)
\( \mathbf{x}: \boldsymbol{\Delta} \boldsymbol{H}_{\text {dissociation}} \mathrm{H}=436 \mathrm{kJ} / \mathrm{mol} \)
\( \mathbf{y}: \boldsymbol{\Delta} \boldsymbol{H}_{\text {electronaffinity}} \mathbf{H}=\mathbf{7 8} \mathbf{k} \mathbf{J} / \mathrm{mol} \)
\( \mathbf{z}: \boldsymbol{\Delta} \boldsymbol{H}_{\text {lattice}} \mathrm{KH}=710 \mathrm{kJ} / \mathrm{mol} \)
In terms of the letters \( v \) to \( z \)
the expression for \( \Delta \boldsymbol{H}_{i} \) of \( \mathrm{K} \) is \( \boldsymbol{\Delta} \boldsymbol{H}_{i}=\boldsymbol{w} / 2 \)
If true enter 1 , else enter 0
A. 0
B. 1
\( c \cdot 2 \)
D. 3


Which statements describe the
condition(s) required for a successful
formation of a product in a reaction?
A. The collision must involve a sufficient amount of energy, provided from the motion of the particles, to overcome the activation energy
B. The relative orientation of the particles has little or no effect on the formation of the product
C. The relative orientation of the particles has an effect only if the kinetic energy of the particles is below some minimum value
D. The relative orientation of the particles must allow for formation of the new bonds in the product
E. The energy of the incoming particles must be above a certain minimum value and the relative orientation of
the particles must allow for formation of new bonds in the product


Cups are not made of metals. The
reason is:
A. Metals are good conductors
B. Metals are bad conductors
c. Metals are expensive
D. None of the above


What is Binomial Nomenclature?Who
proposed it?


Assertion
The foreign substances such as soaps, polymers, metal oxides can be used to stabilize an emulsion.
Reason
Sometimes, demulsifiers are used to
destabilize the emulsions when their
presence is undesired.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


If \( \cos ^{-1}\left(\frac{x^{2}-y^{2}}{x^{2}+y^{2}}\right)=\tan ^{-1} a, \) prove
that \( \frac{d y}{d x}=\frac{y}{x} \)


The mirror used in periscope is:
A. convex mirror
B. concave mirror
c. plane mirror
D. any of the above can be used


Draw the structures of Harworth
projection formula of fructose.


The given graph shows variation (with
distance r from center) of :
A. Electric field of a uniformly charged sphere
B. potential of a uniformly charged spherical shell
C. potential of a uniformly charged sphere
D. Electric field of a uniformly charged spherical shell


If both the dipoles are free to rotate
about the axes, perpendicular to the plane xoy and passing through 0 and \( A \) respectively, then they will orient themselves such that
A \( \cdot \vec{p}_{1} \) is at right angles to \( \vec{p}_{2} \)
B. both \( \vec{p}_{1} \) and \( \vec{p}_{2} \) are along \( \overrightarrow{O A} \)
c. \( \overrightarrow{p_{1}} \) is parallel to \( \vec{p}_{2} \)
D. \( \overrightarrow{p_{1}} \) is antiparallel to \( \overrightarrow{p_{2}} \)


Explain how painting of an iron gate prevents it from rusting?


Bucket handle movements is seen in
\( \mathbf{A} \cdot 1^{s t} \) rib
B. \( 3^{r d} \) rib to \( 5^{t h} \) rib
c. \( 6^{t h} \) rib to \( 10^{t h} \) rib
D. \( 11^{t h} \) and \( 12^{t h} \) rib


Which of the following polymers is used to manufacture clothes for firefighters?
A. Thiokol
B. Kevlar
c. Nomex
D. Dynel


In cockroaches, during the digestion of food, the enzyme cellulase is synthesized by
A. Saliva
B. Lining cells of midgut
c. Bacteria in the midgut
D. Cellulase is never synthesizedd


Select correct statement(s) regarding
given complexes:
\( \mathbf{A} \cdot\left[F e(C O)_{5}\right], \) the orbitals used for hybridization in \( \mathrm{Fe} \) atom are \( s, p_{x}, p_{y}, p_{z}, d_{z 2} \) and its is high spin complex
\( \mathbf{B} \cdot\left[P t\left(N H_{3}\right)_{2} C l_{2}\right], \) the orbitals used for hybridization on
Pt atom are \( s, p_{x}, p_{y}, d_{x^{2}-y^{2}} \) and it is low spin complex
C \( \cdot\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+} \), the orbitals used for hybridization in \( \mathrm{Cr} \)
atom are \( s, p_{x}, p_{y}, p_{z}, p_{x^{2}}, d_{x^{2}-y^{2}} \) and it is high spin complex
D. \( N i(C O)_{4} \), the orbitals used for hybridization in \( \mathrm{Ni} \) atom are, \( s, p_{x}, p_{y}, p_{z}, \) and it is low spin complex


Given below is a diagram representing a stage during mitotic cell division.
Study it carefully and answer the questions that below:
How will you differentiate between
mitosis and meiosis on the basis of the
chromosome number in the daughter
cells?


Find force on semicircular ring due to
point charge \( \boldsymbol{q} \)


If \( \boldsymbol{x}=\boldsymbol{a}(\boldsymbol{\theta}-\sin \theta) \) and \( \boldsymbol{y}=\boldsymbol{a}(\boldsymbol{1}+\cos \boldsymbol{\theta}) \)
then \( \frac{d y}{d x} \) is
A . \( \cot \theta \)
B. \( \cot \frac{\theta}{2} \)
\( c \cdot-\cot \frac{\theta}{2} \)
D. none of these


The following acts both as an acid and
as a base:
A . HCl
в. \( S O_{4}^{2} \)
\( \mathrm{c} \cdot P O_{4}^{3} \)
D. \( H S O_{4} \)


The absolute configuration of the chiral centers in the following Fischer
projection are:
A \( \cdot 2(S), 3(R) \)
B. \( 2(R), 3(S) \)
c. \( 2(R), 3(R) \)
D. \( 2(S), 3(S) \)


:he rate constant of reaction \( 2 A+ \)
\( B \longrightarrow C \) is \( 2.57 \times 10^{-5} \) it \( m o l e^{-1} s e c^{-1} \)
after 10 sec. \( 2.65 \times 10^{-5} \) it
mole \( ^{-1} \) sec \( ^{-1} \) after 20 sec. and \( 2.55 \times \)
\( 10^{-5} \) it mole\( ^{-1} \)sec\( ^{-1} \) after 30 sec. The
order of the reaction is:
A.
B. 1
\( c \cdot 2 \)
D. 3


Explain allotropes of Sulphur?


When a bus starts suddenly, the person falls backwards because of
A. Inertia of rest of the passenger
B. Inertia of motion of the passenger
c. Inertia of rest of the bus
D. None of the above


A human heart on an average beat 72 times a minute. Calculate its frequency
\( \mathbf{A} \cdot 72 s^{-1} \)
B \( \cdot 1.2 s^{-1} \)
\( \mathrm{c} \cdot 4320 s^{-1} \)
D. None


A vertical pencil of rays comes from bottom of a tank filled with a liquid. When it is accelerated with an
acceleration of \( 7.5 \mathrm{m} / \mathrm{s}^{2}, \) the ray is seen
to be totally reflected by liquid surface. What is minimum possible refractive index of liquid?
A. slightly greater than \( 4 / 3 \)
B. slightly greater than \( 5 / 3 \)
c. slightly greater than 1.5
D. slightly greater than 1.75


There are how many kinds of charges?
A. one
B. Two
c. Three
D. Four


is derivable and has a continuous
derivative at \( \boldsymbol{x}=\mathbf{0} \)
A \( . m \in(1, \infty) \)
B. \( m \in[2, \infty) \)
c. \( m \in(2, \infty) \)
D. \( m \in(-\infty, 2) \)


Multiple Correct Answers Type The Sl unit of inductance, henry, can be
written as
This question has multiple correct options
A. Weber/ampere
B. Volt-second / ampere
c. Joule/(ampere) \( ^{2} \)
D. Ohm-second


If \( \int \frac{x^{5} d x}{\sqrt{1+x^{3}}}=\frac{2}{9} \sqrt{a+x^{3}}\left(x^{3}-b\right)+C \)
then the value of \( 2 a+3 b \) is equal to


When incomplete combustion loss is high, the fuel gas analysis shows a large amount of :
A \( \cdot C O_{2} \)
B. co
\( c \cdot O_{2} \)
D.


What is Alcohol?


A tracheid is
A. With multinucleate condition
B. Unicellular
C . Multicellular
D. None of these


I nree laentıcal square metal plates
\( M_{1}, M_{2} \) and \( M_{3} \) of side \( 10 \mathrm{cm} \& 5 \mathrm{mm} \)
thick are arranged as shown in figure.
The plates are separated by sheets of
paper \( 0.5 \mathrm{mm} \) thick \( \& \) of dielectric
constant \( 5 . \) The outer plates are
connected together \( \& \) connected to
lower potential while inner plate to higher potential terminal of a battery. Capacitance between the terminals of
the battery is : \( \left(\epsilon_{0}=8.910^{-12} C^{2} / N-\right. \)
\( \left.\boldsymbol{m}^{2}\right) \)
A. \( 1780 p F \)
В. \( 890 p F \)
\( \mathbf{c} .445 p F \)
D. \( 222.5 p F \)


Two capacitors of capacitance \( C_{1} \) and
\( C_{2} \) are connected in parallel across a
battery. If \( Q_{1} \) and \( Q_{2} \) respectively be the charges on the capacitors, then \( \frac{Q_{1}}{Q_{2}} \) will be equal to :
A. \( \frac{C_{2}}{C_{1}} \)
в. \( \frac{C_{1}}{C_{2}} \)
c. \( \frac{C_{1}^{2}}{C_{2}^{2}} \)
D. \( \frac{C_{2}^{2}}{C_{1}^{2}} \)


What percent to the average sales of
branches \( B_{1} B_{2} \) and \( B_{3} \) in 2007 is the
average sales of branches
\( B_{1}, B_{2}, \) and \( B_{6} \) in \( 2006 ? \)
\( A .75 \% \)
В. \( 77 \% \)
\( c .87 .5 \% \)
D. \( 70 \% \)


Composition of Ziegler-Natta catalyst
is:
A \( \cdot\left(E t_{3}\right)_{3} \) Al.TiCla
В \( \cdot(M e)_{3} \) Аl.TiCl
\( \mathbf{c} \cdot(E t)_{3} A l \cdot T i C l_{4} \)
D・ \( (E t)_{3} \) Al.Pt \( C l_{4} \)


The sum of all six exterior angles of triangle is
A . 180
в. 360
c. 720
D. 90


The distance between the lines \( 3 x+ \)
\( \mathbf{4} \boldsymbol{y}=\mathbf{9} \) and \( \mathbf{6} \boldsymbol{x}+\mathbf{8} \boldsymbol{y}+\mathbf{1 5}=\mathbf{0} \) is
\( A \cdot \frac{3}{10} \)
в. \( \frac{33}{10} \)
\( c \cdot \frac{33}{5} \)
D. none of these


Three horses \( H_{1}, H_{2}, H_{3} \) entered a field which has seven portions marked
\( \boldsymbol{P}_{1}, \boldsymbol{P}_{2}, \boldsymbol{P}_{3}, \boldsymbol{P}_{4}, \boldsymbol{P}_{5}, \boldsymbol{P}_{6} \) and \( \boldsymbol{P}_{7} . \) If no two
horses are allowed to enter the
same portion of the field, in-how many
ways can the horses graze the grass of the field?


The areas of two similar triangles ABC
and PQR are \( 64 \mathrm{cm}^{2} \) and \( 121 \mathrm{cm}^{2} \)
respectively. If \( Q R=15.4 \mathrm{cm}, \) find \( B C \)


Maximum life span of a dog in years is
A. 5
B. 10
c. 15
D. 20


BOD is
A. The-amount of \( O_{2} \) utilised by organisms in water
B. The amount of \( O_{2} \) utilised by micro organisms for decomposition
C. The total amount of \( O_{2} \) present in water
D. All of the above


The volatility of \( H F \) is low as compare to other Hydra acid of Halogen because
of:
A. its low polarizability
B. the weak dispersion interaction between the molecules
c. its small molecular mass
D. its strong hydrogen bonding


Due to which phenomena the combination of red, green and blue forms the same white colour
A. Due to persistence of vision
B. Due to reflection
c. Due to refraction
D. Due to deviation


\( \mathbf{1}^{2}+\mathbf{2}^{2}+\ldots+\boldsymbol{n}^{2}>\frac{n^{3}}{3}, \boldsymbol{n} \in \mathbf{N} \)


A closely wound solenoid \( 80 \mathrm{cm} \) long
has 5 layers of winding of 400 turns each. The diameter of the solenoid is
1.8 \( c m . \) If the current \( 8.0 A \) flows in it
the magnitude of magnetic field inside the solenoid near its centre will be
\( \mathbf{A} \cdot 8 \pi \times 10^{-3} T \)
В . \( 6 \pi \times 10^{-3} T \)
c. \( 4 \pi \times 10^{-3} T \)
D. \( 3 \pi \times 10^{-3} T \)


Assertion
A charge, whether stationary or in motion produces a magnetic field around it.
Reason
Moving charges produce only electric field in the surrounding space.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which of the following substances cause permanent hardness of water?
A. \( C a C l_{2} \)
в. \( \mathrm{Ca}\left(\mathrm{HCO}_{3}\right)_{2} \)
c. \( C a C O_{3} \)
D. All of the above


Find the heat lost by a copper cube of
mass 400 g when it cool from \( 100^{\circ} \mathrm{C} \) to
\( 30^{\circ} \mathrm{C} . \) (Specific of heat of copper \( = \) \( \left.\mathbf{3} 9 \mathbf{0} J \mathbf{k} g^{-1}^{o} \mathbf{C}^{-1}\right) \)
A. 50000
B. 10000
c. 10920 J
D. 10900 J


Which one of the following statements in regard to the excretion by the human kidneys is correct?
A. Ascending limb of loop of Henle is impermeable to electrolytes.
B. Descending limb of Loop of Henle is impermeable to water
c. Distal convoluted tubule is incapable of reabsorbing \( H C O_{3}^{-} \)
D. Nearly 99 per cent of the glomerular filtrate is reabsorbed by the renal tubules


The shortest and longest wave number in \( \mathrm{H} \) spectrum of Lyman series is \( (\mathrm{R}= \) Rydberg constant):
A \( \cdot \frac{3}{4} \) R, R
в. \( \frac{1}{R}, \frac{4}{3}, \) R
c. \( _{R, \frac{4}{3} R} \)
D. \( _{R,} \frac{3}{4} R \)


Find the principal argument of the complex number \( \sin \frac{6 \pi}{5}+ \)
\( i\left(1+\cos \frac{6 \pi}{5}\right) \)
A \( \cdot \arg (z)=\frac{9 \pi}{10},|z|=-2 \cos \frac{3 \pi}{5} \)
B. \( \arg (z)=\frac{\pi}{10},|z|=-2 \cos \frac{3 \pi}{5} \)
c. \( \arg (z)=\frac{9 \pi}{10},|z|=2 \cos \frac{3 \pi}{5} \)
D. \( \arg (z)=\frac{9 \pi}{10},|z|=-2 \cos \frac{2 \pi}{5} \)


ff \( \left[\begin{array}{cc}2 & -1 \\ 2 & 0\end{array}\right]+2 A=\left[\begin{array}{cc}-3 & 5 \\ 4 & 3\end{array}\right], \) then the
matrix A equals
A. \( \left[\begin{array}{ll}-5 & 6 \\ 2 & 3\end{array}\right] \)
B. \( \left[\begin{array}{cc}-\frac{5}{2} & 3 \\ 1 & \frac{3}{2}\end{array}\right] \)
\( \mathbf{c} \cdot\left[\begin{array}{cc}-\frac{5}{2} & 6 \\ 2 & 3\end{array}\right] \)
D. \( \left[\begin{array}{cc}-5 & 8 \\ 1 & 3\end{array}\right] \)


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


Moseley's equation is represented as
\( \sqrt{\boldsymbol{v}}=\boldsymbol{a}(\boldsymbol{Z}-\boldsymbol{b}) \) where a and b are
constants If \( \boldsymbol{O} \boldsymbol{A}=\mathbf{1}, \) then atomic
number of the elements showing
frequency of \( 400 H z \) is?
A . 2
\( B \)
\( c .40 \)
0.19


\( \mathbf{2} C u_{2} S+\mathbf{3} O_{2}(g) \stackrel{h e a t}{\longrightarrow} \underline{a}+\underline{b} \)
A \( \cdot a=2 C u_{2} O, b=2 S O_{2} \)
В . \( a=4 C u O_{2}, b=2 S O_{3} \)
C \( . a=2 C u O, b=4 S O_{2} \)
D. \( a=3 C u S, b=2 S O_{2} \)


Solve
\( \int \frac{x^{6}-1}{1+x^{2}} d x \)


Ethyl chloride to Ethene conversions can be carried out by \( C_{2} H_{5} C l+K O H(\text {alcoholic soln.}) \rightarrow \)
\( \boldsymbol{C H}_{2}=\boldsymbol{C H}_{2}+\boldsymbol{H C l} \)
A. True
B. False


Glucose, synthesized in leaves are
transported in the form of
A. Starch
B. Sucrose
c. Fructose
D. carbon dioxide


A ball is projected from level ground with a velocity of \( 40 \mathrm{m} / \mathrm{s} \) at an angle of
\( 30^{\circ} \) from the ground. Calculate the vertical component of the projectile's velocityjust before it strikes the ground?
(Take \( \left.\sin 30^{\circ}=0.5, \cos 30^{\circ}=0.87\right) \)
\( A \cdot 10 \mathrm{m} / \mathrm{s} \)
B. 20 \( \mathrm{m} / \mathrm{s} \)
\( c .30 \mathrm{m} / \mathrm{s} \)
D. 35 m/s
E. \( 40 \mathrm{m} / \mathrm{s} \)


Which of the following structure will not be common to mitotic cell of a higher
plant?
A. Cell plate
B. Centromere
c. Centriole
D. spindle fibre


n trapezium \( A B C D \), side \( A B \| C D \)
and diagonals \( A C \) and \( B D \) intersect
each other at \( \boldsymbol{O} \)
Prove that: \( \frac{\boldsymbol{O A}}{\boldsymbol{O C}}=\frac{\boldsymbol{O D}}{\boldsymbol{O B}} \)


Common name of bicyclopentadienyl
iron (II) is ferrocene. If true enter 1 , else
enter 0


Find \( n \) If the middle term in the
expansion of \( \left(x^{2}+\frac{1}{x}\right)^{n} \) is \( 924 x^{6} \)
\( A \cdot 4 \)
B. 12
\( c \cdot 14 \)
D. None of these


A particle executes a simple harmonic motion of amplitude \( 1.0 \mathrm{cm} \) along the
principal axis of convex lens of focal
length \( 12 c m . \) The mean position of
oscillation is at \( 20 \mathrm{cm} \) from the lens.
Find the amplitude of oscillation of the
image of the particle.


White light is a mixture of
A. seven colors
B. nine colors
c. fifteen colors
D. seventeen colors


Which of the following fibre can be drawn into very fine fibres that can be woven like any other yarn?
A. Terylene
B. Rayon
c. Acrylic
D. Nylon


In the figure above, three lines intersect
at a point.
If \( \boldsymbol{f}=\mathbf{8 5}^{\boldsymbol{o}} \) and \( \boldsymbol{c}=\mathbf{2 5}^{\boldsymbol{o}}, \) what is the
value of \( a ? \)
Note : Figure not drawn to scale
A \( \cdot 60^{\circ} \)
B. \( 65^{\circ} \)
\( c \cdot 70^{\circ} \)
D. \( 75^{\circ} \)


The lines \( 3 x-4 y=4 \) and \( 6 x-8 y- \)
\( \mathbf{7}=\mathbf{0} \) are tangents to the same circle. Then is radius is ?
A \( \cdot \frac{1}{4} \)
B. \( \frac{1}{2} \)
\( c \cdot \frac{3}{4} \)
D. \( \frac{3}{2} \)


Which of the following statements is
not true about polymers?
A. Polymers have high viscosity
B. Polymers do not carry any charge
C . Polymers scatter light
D. Polymers have low molecular weight


Dimensional formula of universal
gravitational constant \( G \) is-
A \( \cdot M^{-1} L^{3} T^{-2} \)
B . \( M^{-1} L^{2} T^{-2} \)
c. \( M^{-2} L^{3} T^{-2} \)
D. \( M^{-2} L^{2} T^{-2} \)


Select an appropriate scale and draw a ray diagram for the observation at
S.No.2. Also find the approximate value of magnification.


The arithmetic mean (average) of a set
of 50 numbers is \( 38 . \) If two numbers,
namely, 45 and \( 55, \) are discarded, the mean of the remaining set of numbers is :
A . 36.5
B. 37
c. 37.2
D. 37.5
E . 37.52


if the distance between the foci is equal
to the length of the latus-rectum. Find
the eccentricity of the ellipse.
A. \( \frac{\sqrt{5}-1}{2} \)
B. \( \frac{\sqrt{5}+1}{2} \)
c. \( \frac{\sqrt{5}-1}{4} \)
D. None of these


Jet aeroplanes work on the principle of conservation of, which of the
following:
A . Mass
B. Momentum
c. Energy
D. Force


A mass of \( 3 \mathrm{kg} \) is dropped from alower of \( 125 \mathrm{m} \) high. After 3 s its \( \mathrm{K} \). E. will be :
A . 1300 J
B. 1050 J
c. 750
D. 550


For what value of \( \boldsymbol{m}, \) the points \( (\boldsymbol{3}, \mathbf{5}) \) \( (m, 6) \) and \( \left(\frac{1}{2}, \frac{15}{2}\right) \) are collinear?
\( A \cdot 9 \)
B. 5
\( c .3 \)
D.


Name the cation and anion in given reaction:
\( 2 S O_{2} \rightleftharpoons S O^{2+}+S O_{3}^{2-} \)
A \( \cdot S O^{2+}: \) Sulphide \( S O_{3}^{2-}: \) Sulpharyl
B . \( S O^{2+}: \) Sulpharyl \( S O_{3}^{2-}: \) Sulphite
c. \( S O^{2+}: \) Sulphite \( S O_{3}^{2-}: \) Sulphide
D. None of these


The differential equation of the family of curves \( v=\frac{A}{r}+B, \) where \( A \) and \( B \) are
arbitrary constants is
A \( \cdot \frac{d^{2} v}{d r^{2}}+\frac{1}{r} \frac{d v}{d r}=0 \)
B. \( \frac{d^{2} v}{d r^{2}}-\frac{2}{v} \frac{d v}{d r}=0 \)
c. \( \frac{d^{2} v}{d r^{2}}+\frac{2 d v}{r d r}=0 \)
D. \( \frac{d^{2} v}{d r^{2}}+\frac{2}{v} \frac{d v}{d r}=0 \)


The
\( \boldsymbol{E}^{\ominus} \) for \( \boldsymbol{C u}^{2+} / \boldsymbol{C u}^{\oplus}, \boldsymbol{C u}^{\oplus} / \boldsymbol{C u}, \boldsymbol{C u}^{2+} / \boldsymbol{C} \)
are \( 0.15 \vee, 0.50 \mathrm{V}, \) and \( 0.325 \mathrm{V} \)
respectively. The redox cell showing redox reaction \( 2 C u^{+}, \rightarrow C u^{2+}+C u \)
is made. \( E^{\ominus} \) of this cell reaction and
\( \Delta G^{\ominus} \) may be :
A \( \cdot E^{\ominus}=0.175 V \) or \( E^{\ominus}=0.350 V \)
B. \( n=1 \) or 2
c. \( \Delta G^{\ominus}=-33.775 k J \)
D. All of these


The term cytoskeleton was given by
A. Koltzoff
B. Rhodin
c. menke
D. Park


Two charges \( q_{1}=12 \times 10^{-9} \mathrm{C} \) and \( q_{2}= \)
\( -12 \times 10^{-9} C \) are placed \( 10 c m \) apart. The
potential at a point \( 6 \mathrm{cm} \) from \( q_{1} \) on the
line joining the two charges is :
A. 3500 Volt
B. 900 Volt
c. \( 1800 V \) olt
D. -900 Volt


Find number of \( p \pi-d \pi \) bonds in:
a) Disulphate
b) Triphosphate
c) Trimetaphosphate
d) Trimer of \( \boldsymbol{S O}_{3} \)
e) \( P_{4} O_{10} \)
f) \( P_{4} O_{6} \)


State the following statement is True or False:

The total path length is always equal to the magnitude of the displacement vector of a particle.
A. True
B. False


Two circular conducting loops of radii
\( R_{1} \) and \( R_{2} \) are laying concentrically in
the same plane. If \( \boldsymbol{R}_{1}>\boldsymbol{R}_{2} \) then the
mutual inductance (M) between them
will be proportional to:
A \( \cdot \frac{R_{1}}{R_{2}} \)
в. \( \frac{R_{2}}{R_{1}} \)
c. \( \frac{R_{1}}{R_{2}^{2}} \)
D. \( \frac{R_{2}^{2}}{R_{1}} \)


Calculate the maximum kinetic energy
(in eV) of the emitted photoelectrons.
A . 1.5
B. 2.36
c. 3.85
D. 4.27


A vessel is filled with water and
kerosene oil. The vessel has a small hole
in the bottom. Neglecting viscosity if
the thickness of water layer is \( h_{1} \)
and kerosene layer is \( h_{2} \) then the
velocity \( v \) of flow of water will be (Given:
density of water is \( \rho_{1} \) g/ \( c c \) and that of
kerosene is \( \rho_{2} \) g/cc, neglecting viscosity):
A \( . v=\sqrt{2 g\left(h_{1}+h_{2}\right)} \)
B. \( v=\sqrt{2 g\left[h_{1}+h_{2}\left(\frac{\rho_{2}}{\rho_{1}}\right)\right]} \)
C. \( v=\sqrt{2 g\left(h_{1} \rho_{1}+h_{2} \rho_{2}\right)} \)
D \( v=\sqrt{2 g\left[h_{1}\left(\frac{\rho_{1}}{\rho_{2}}\right)+h_{2}\right]} \)


Space between two concentric conducting spheres of radii a and \( b(b>a) \) is filled with a medium of
resistivity \( \rho . \) The resistance between the
two spheres will be :
A \( \cdot \frac{\rho}{4 \pi}\left(\frac{1}{a}-\frac{1}{b}\right) \)
в. \( \frac{\rho}{2 \pi}\left(\frac{1}{a}-\frac{1}{b}\right) \)
c. \( \frac{\rho}{2 \pi}\left(\frac{1}{a}+\frac{1}{b}\right) \)
D. \( \frac{\rho}{4 \pi}\left(\frac{1}{a}+\frac{1}{b}\right) \)


Area bounded by \( x^{2}=4 a y \) and \( y= \)
\( \frac{8 a^{3}}{x^{2}+4 a^{2}} \) is:
A \( \cdot \frac{a^{2}}{3}(6 \pi-4) \)
в. \( \frac{\pi a^{2}}{3} \)
c. \( \frac{a^{2}}{3}(6 \pi+4) \)
D.


Biological equilibrium is equilibrium amongst
A. Producers and decomposers
B. Producers and consumers
c. Producers, consumers and decomposers
D. consumers and decomposers


Solve the inequality and represent the solution graphically on number line. \( 5(2 x-7)-3(2 x+3) \leq 0,2 x+19 \leq \)
\( \mathbf{6} \boldsymbol{x}+\mathbf{4 7} \)