Choose the correct answer from the
alternatives given. The cells constituting walls of blood capillaries are known as:
A. endothelial cells
B. cords
c. oxyntic cells
D. plasma cells


A two-step mechanism has been suggested for the reaction of nitric oxide and bromine. \( N O(g)+B r_{2}(g) \stackrel{K_{1}}{\longrightarrow} N O B r_{2}(g) \)
\( N O B r_{2}(g)+N O(g) \stackrel{K_{2}}{\longrightarrow} 2 N O B r(g) \)
The observed rate law is, rate \( = \)
\( \boldsymbol{k}[\boldsymbol{N} \boldsymbol{O}]^{2}\left[\boldsymbol{B} \boldsymbol{r}_{2}\right] . \) Hence, the rate
determining step is :
A \( \cdot N O(g)+B r_{2}(g) \rightarrow N O B r_{2}(g) \)
в. \( N O B r_{2}(g)+N O(g) \rightarrow 2 N O B r(g) \)
c. \( 2 N O(g)+B r_{2}(g) \rightarrow 2 N O B r(g) \)
D. none of these


A two-digit number is thrice as large as the sum of its digits, and the square of that sum is equal to the trippled required number. Find the number


Four elements \( A, B, C \) and \( D \) have atomic
numbers 12,13,14 and 15 respectively
Which of these elements will form the
most basic oxide?


The unit vector in the direction of \( \vec{A}= \)
\( \mathbf{3} \hat{\mathbf{i}}+\mathbf{4} \hat{\mathbf{j}} \) is :
A \( \cdot \hat{A}=\frac{\hat{i}+\hat{j}}{7} \)
B. \( \hat{A}=\frac{3 \hat{i}+4 \hat{j}}{5} \)
c. \( \hat{A}=\hat{i}+\hat{j} \)
D. \( _{\hat{A}}=\frac{4 \hat{i}-3 \hat{j}}{5} \)


A drop of each of the following, is placed separately on four slides. Which one of them will not coagulate?
A. Blood serum
C. Whole blood from pulmonary vein
D. Blood plasma


Number of roots of \( |\sin | x||=x+|x| \) in
\( [-2 \pi, 2 \pi] \) is
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 6


The acceleration due to gravity \( g \) and
density of the earth \( \rho \) are related by
which of the following relations.? (where \( G \) is the gravitational constant
and \( R_{E} \) is the radius of the earth)
\( ^{\mathbf{A}} \cdot_{\rho}=\frac{4 \pi G R_{E}}{3 g} \)
в. \( \rho=\frac{3 g}{4 \pi G R_{E}} \)
c. \( _{\rho}=\frac{3 G}{4 \pi g R_{E}} \)
D. \( \rho=\frac{4 \pi g R_{E}}{3 G} \)


A projectile shot at an angle of \( 45^{\circ} \) above the horizontal strikes the wall of a
building \( 30 m \) away at a point \( 15 m \)
above the point of projection. Initial velocity of the projectile is
\( \left(\operatorname{take} g=9.8 m / s^{2}\right) \)
\( \mathbf{A} \cdot 14 m / s \)
B. \( 14 \sqrt{2} \mathrm{m} / \mathrm{s} \)
c. \( 14 \sqrt{3} \mathrm{m} / \mathrm{s} \)
D. \( 14 \sqrt{5} \mathrm{m} / \mathrm{s} \)


\( \int(\tan x-\cot x)^{2} d x= \)
A \( \cdot \tan x+x+c \)
B. \( \tan x-x+c \)
c. \( \tan x-\cot x+c \)
D. \( \tan x-\cot x-4 x+c \)


If the equilibrium constant for \( N_{2}(g)+ \)
\( O_{2}(g) \rightleftharpoons 2 N O(g) \) is \( K, \) the equilibrium
constant for \( \frac{1}{2} N_{2}(g)+\frac{1}{2} O_{2}(g) \rightleftharpoons \)
\( N O(g) \) will be:
A. \( K \)
B. \( K^{2} \)
c. \( K^{\frac{1}{2}} \)
D・\( \frac{1}{2} K \)


Which of the following part/s of the human digestive system involves both chemical and mechanical ways of
digestion?
A. Oesophagus
B. Stomach
c. Mouth
D. Both B and C


Assertion: Amphoteric species acts as either an acid or a base.

Reason: It contains both hydrophobic and hydrophilic regions.
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false


Select the correct statement.
A. Secretion is the ejection of waste material from the body
B. Excretion is the release of material within the body.
C. Secretion and excretion both are the movement of unwanted material in the blood.
D. Excretion is the release of unwanted material from the
body


Which of the following is not in the form
of G.P.?
A. \( 2+6+18+54+\dots \)
B. \( 3+12+48+192+\ldots \)
c. \( 1+4+7+10+\dots \)
D. \( 1+3+9+27+\ldots \)


Identify which of the following
statement is correct for acceleration
due to gravity on earth:
A. It is abbreviated with the letter \( R \)
B. It has a magnitude of \( 9.8 \mathrm{cm} / \mathrm{sec}^{2} \) away from the center of earth
C. It has a magnitude of \( 9.8 \mathrm{m} / \mathrm{sec}^{2} \) toward the center of earth
D. Acceleration tends to increase with a greater mass
E. Acceleration tends to decrease with force


\( \mathbf{f} \mathbf{A}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{0} & -\mathbf{2} \\ \mathbf{2} & \mathbf{- 3} & \mathbf{4}\end{array}\right], \) then the matrix
\( X \) for which \( 2 X+3 A=0 \) holds true is
\( \mathbf{A} \cdot\left[\begin{array}{ccc}-\frac{3}{2} & 0 & -3 \\ -3 & -\frac{9}{2} & -6\end{array}\right] \)
\( \mathbf{B} \cdot\left[\begin{array}{ccc}\frac{3}{2} & 0 & -3 \\ 3 & -\frac{9}{2} & -6\end{array}\right] \)
\( \mathbf{C} \cdot\left[\begin{array}{lll}\frac{3}{2} & 0 & 3 \\ 3 & \frac{9}{2} & 6\end{array}\right] \)
\( ^{\mathrm{D}} \cdot\left[\begin{array}{ccc}-\frac{3}{2} & 0 & 3 \\ -3 & \frac{9}{2} & -6\end{array}\right] \)


The prime cause of altitude sickness in men due to ascent on high mountains
is
A. Excess of \( \mathrm{CO}_{2} \) in blood
B. Decreased efficiency of haemoglobin
c. Decreased partial pressue of oxygen
D. Decreased proportion of oxygen in air


The impulse of a body is equal to:
A. Rate of change of its momentum.
B. Change in its momentum.
C. The product of force applied on it and the time of application of the force.
D. Both (B) and (C)


Identify which of the following light rays has the highest energy?
A . Violet
B. Green
c. Yellow
D. orange
E. Red


Find \( a, b \) such that \( 18, a, b,-3 \) are in
\( \boldsymbol{A P} \)


Let \( A \) and \( B \) be two events such that
\( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B}) \geq \mathbf{3} / \mathbf{4} \) and \( \mathbf{1} / \mathbf{8} \leq \boldsymbol{P}(\boldsymbol{A} \cap \)
\( \boldsymbol{B}) \leq \mathbf{3} / \mathbf{8} \)
Statement
1: \( \boldsymbol{P}(\boldsymbol{A})+\boldsymbol{P}(\boldsymbol{B}) \geq \mathbf{7} / \mathbf{8} \)
statement
2: \( \boldsymbol{P}(\boldsymbol{A})+\boldsymbol{P}(\boldsymbol{B}) \leq 11 / 8 \)
A. Both the statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT1
B. Both the statements are TRUE and STATEMENT 2 is not the correct explanation of STATEMENT
c. STATEMENT1 is TRUE and STATEMENT 2 is FALSE
D. STATEMENT1 is FALSE and STATEMENT 2 is TRUE


If \( \boldsymbol{y}=(\boldsymbol{x}+\sqrt{\boldsymbol{x}^{2}+\boldsymbol{a}^{2}})^{n} \) then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}= \)
\( A \cdot y \)
в. \( n y \)
c. \( \frac{n y}{\sqrt{x^{2}+a^{2}}} \)
D. \( \frac{y}{\sqrt{x^{2}+a^{2}}} \)


Choose the correct answer among the
alternatives given :
The end product of (Q) in the following
sequence of reaction is:
\( A \)
в.
\( c \)
\( D \)


The sum of the first n terms of an A.P. is
\( 3 n^{2}+6 n . \) Find the nth term of this A.P.


The resultant of two vectors \( \vec{P} \) and \( \vec{Q} \) is
\( \vec{R} \) If \( \vec{Q} \) is doubled then the new resultant vector is perpendicular to \( \vec{P} \) Then magnitude of \( \overrightarrow{\boldsymbol{R}} \) is:
\( ^{\mathbf{A}} \cdot \frac{P^{2}-Q^{2}}{2 P Q} \)
в. \( Q \)
c. \( \frac{P}{Q} \)
D. \( \frac{P+Q}{P-Q} \)


A very pure form of carbon monoxide
can be obtained from:
A. sodium hexacyanoferrate
B. sodium oxalate
c. formic acid
D. nickel tetracarbony!


"If two angles and a side of one triangle are equal to two angles and a side of another triangle, then the two triangles must be congruent". Is the statementt true? Why?


The figure obtained by joining the midpoints of the adjacent sides of a rectangle of sides \( 8 \mathrm{cm} \) and \( 6 \mathrm{cm} \) is
A . a rectangle of area \( 24 \mathrm{cm}^{2} \)
B. a square of area \( 25 \mathrm{cm}^{2} \)
c. a rhombus of area \( 24 \mathrm{cm}^{2} \)
D. a trapezium of area \( 12 \mathrm{cm}^{2} \)


Wolframite ore is separated from
tinstone ore by the process of:
A. roasting
B. electromagnetic separation
c. smelting
D. calcination


The density of a metal at normal
pressure is \( \rho . \) It's density when it is
subjected to an excess pressure p is \( \rho \) '.
If \( \mathrm{B} \) is the bulk modulus of the metal,
the ratio \( \rho^{\prime} / \rho \) is :
A. \( \frac{1}{1-p / B} \)
в. \( 1+\frac{P}{B} \)
c. \( \frac{1}{1-B / p} \)
D. \( 1+B / p \)


The empirical formula of a compound is
\( C H_{2} . \) The mass of 1 liter of this gas is exactly equal to that of 1 liter of nitrogen under similar conditions. The molecular
formula of the gas is:
A. \( C_{2} H_{4} \)
в. \( O_{3} H_{6} \)
c. \( C_{6} H_{12} \)
D. \( C_{4} H_{8} \)


How many elements in group 14 are
used as semiconductor?


The standard Gibbs free energy change,
\( \Delta G^{0} \) is related to equilibrium constant,
\( K_{p} \) as:
A \( . K_{p}=-R T \ln \Delta G^{0} \)
B. \( \quad K_{p}=\left[\frac{e}{R T}\right]^{\Delta G^{0}} \)
\( c \cdot_{K_{p}}=-\frac{\Delta G}{R T} \)
D. \( K_{p}=e^{-\Delta G^{0} / R T} \)


Air is a mixture. Prove this statement.


A body is dropped form the top of a tower. It falls through 40 m during the last two seconds of its fall.The height of
tower in \( \mathrm{m} \) is \( \left(\boldsymbol{g}=\mathbf{1 0 m} \boldsymbol{s}^{-2}\right) \)
\( A \cdot 45 \mathrm{m} \)
B. 50 \( m \)
c. \( 60 \mathrm{m} \)
D. 80 \( m \)


\( f(m)=2, \) find the value of \( m^{2}-m+1 \)


A train of length \( 200 \mathrm{m} \) traveling at a speed of \( 30 m s^{-1} \) overtakes another
train of length \( 300 \mathrm{m} \) traveling at a speed of \( 20 m s^{-1} \) in the same direction.
The time taken by the first train to pass the second train is:
A. 50 s
B. 10 s
c. \( 20 \mathrm{s} \)
D. 40


Diabetes insipidus is due to
A. Hyposecretion of vasopressin(ADH)
B. Hypersecretion of insulin
C. Hyposecretion of insulin
D. Hypersecretion of vasopressin (ADH).


\( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{l}\frac{\sin (a+1) x+\sin x}{x} \text { if } x<0 \\ \frac{\left(x+b x^{2}\right)^{\frac{1}{2}-x^{\frac{1}{2}}}}{b x^{3 / 2}} \text { if } x>0\end{array}\right. \)
\( f(0)=c \) is continuous at \( x=0 \) then
A \( \cdot a=\frac{-3}{2}, c=\frac{1}{2}, b \neq 0 \)
B \cdot \( a=b=\frac{1}{2}, c=0 \)
C \( \cdot a=b=\frac{1}{2}, c=0 \)
D \( \cdot a=\frac{1}{2} b \neq 0 c=1 \)


Temperature on the internal energy?


A gaseous hydrocarbon contains \( 85.7 \% \)
carbon and \( 14.3 \% \) hydrogen. 1 liter of the hydrocarbon weighs \( 1.26 \mathrm{g} \) at NTP? Determine the molecular formula of the
hydrocarbon.


Solve the given inequalities graphically:
\( \mathbf{3} \boldsymbol{x}+\mathbf{2} \boldsymbol{y} \leq \mathbf{1 2}, \boldsymbol{x} \geq \mathbf{1}, \boldsymbol{y} \geq \mathbf{2} \)


The major product of the reaction is:
\( A \)
B.
\( c \)
\( D \)


Name the cavity in the pelvic girdle, into which the head of the femur fits.


When zinc react with dilute sulphuric acid hydrogen is produced in:
A. molecular form
B. combined form
c. nascent form
D. hydrogen will not form


Explain why lactose is not absorbed by the small intestine


Amino acids usually exist in the form of zwitter ions. This means that they
consist of:

This question has multiple correct options
A. the basic \( N H_{2} \) group and acidic \( C O O H \) group
B. the basic group and the acidic \( C O O^{-} \) group
c. basic group and acidic group
D. no acidic or basic group as such


The enzyme which converts glucose to
glucose- 6 -phosphate is
A. Phosphorylase
B. Glucose phosphorylase
c. Hexokinase
D. Phosphoglucomutase


If \( ^{n} C_{10}=^{n} C_{15}, \) find \( ^{27} C_{n} \)


I a \( \triangle A B C, \angle A=90^{\circ}, C A=A B \) and \( D \) is a
point on AB produced prove that \( \boldsymbol{D} \boldsymbol{C}^{2}=\boldsymbol{B} \boldsymbol{D}^{2}=\boldsymbol{2} \boldsymbol{A} \boldsymbol{B} \times \boldsymbol{A} \boldsymbol{D} \)


In an A.P. the sum of terms equidistant from the beginning and end is equal to?


Under certain circumstances, a nucleus can decay by emitting a particle more massive than an \( \alpha \) -particle. Consider
the following decay processes:
\( 223 R a \rightarrow \frac{209}{82} P b+\frac{14}{6} C \)
88
\( 223 R a \rightarrow 219 R n+4 H e \)
88
Calculate the \( Q \) -values for these decays and determine that both are
energetically allowed.


Match the column.


An alternating current generator has an
internal resistance \( \boldsymbol{R}_{\boldsymbol{g}} \) and an internal
reactance \( X_{g} . \) It is used to supply power to a passive load consisting of a
resistance \( \boldsymbol{R}_{g} \) and a reactance \( \boldsymbol{X}_{\boldsymbol{L}} . \) For maximum power to be delivered from the generator to the load, the value of
\( X_{L} \) is equal to
A . zero
в. \( X_{g} \)
c. \( -x_{g} \)
D. \( R_{g} \)


Fluorocarbons are effective scavengers
for ozone due to:
A. photolytic reaction of \( O_{2} \) producing \( C l \) radicals
B. photolytic decomposition of \( O_{3} \) producing \( O \) radicals
C. photolytic decomposition of \( O_{3} \) by \( C l \) radicals into \( O_{2} \)
D. photolytic production of oxides of nitrogen


What is a solenoid? Draw the pattern of magnetic field lines of
(i) A current carrying solenoid and
(ii)A bar magnet. List two distinguishing features between the
two fields.


A solenoid \( 60 \mathrm{cm} \) long and of radius 4.0 cm has 3 layers of windings of 300 turns each. A \( 2.0 \mathrm{cm} \) long wire of mass \( 2.5 \mathrm{g} \) lies inside the solenoid (near its centre) normal to its axis; both the wire and the axis of the solenoid are in the
horizontal plane. The wire is connected through two leads parallel to
the axis of the solenoid to an
external battery which supplies a current of \( 6.0 \mathrm{A} \) in the wire. What value
of current (with appropriate sense of circulation) in the windings of the solenoid can support the weight of the wire? \( g=9.8 m s^{-2} \)


What is the relation between the above
given compounds?
A. Chain isomers
B. Positional isomers
c. Homologs
D. Metamers


Which of the following compounds have highest melting point?
A. Only I
B. Only II
c. I and ॥
D. II and III


In a transformer, in which the losses
may be neglected, the ratio of the primary voltage to secondary voltage is found to be \( 4: 1 . \) The ratio of the
primary to secondary turns and the ratio of the primary current to secondary current are respectively in
the ratio of :
\( A \cdot 4: 1 \& 1: 4 \)
B. \( 1: 4 \& 4: 1 \)
c. \( 4: 1 \& 4: 1 \)
D. \( 1: 4 \& 1: 4 \)


Assume the dipole model for earth's magnetic field B which is given by thevertical component of magnetic field, \( B_{V}=\frac{\mu_{o}}{4 \pi} \frac{2 m \cos \theta}{r^{3}} \) and the
horizontal component of magnetic field \( B_{H}=\frac{\mu_{o}}{4 \pi} \frac{m \sin \theta}{r^{3}}, \) where \( \theta=90^{\circ}- \)
latitude as measured from magnetic
equator, then the loci of point for which
dip angle is \( \pm \mathbf{4 5}^{\circ} \)
\( \mathbf{A} \cdot \tan ^{-1}(3) \)
\( \mathbf{B} \cdot \tan ^{-1}(2) \)
\( \mathbf{c} \cdot \tan ^{-1}(0.5) \)
\( \mathbf{D} \cdot \tan ^{-1}(1) \)


The magnifications produced by a convex lens for two different positions of
an object are \( m_{1} \) and \( m_{2} \) respectively
\( \left(m_{1}>m_{2}\right) . \) If \( d \) is the distance of
separation between the two positions of the object then the focal length of the lens is
A. \( \sqrt{m_{1} m_{2}} \)
в. \( \frac{d}{\sqrt{m_{1}-m_{2}}} \)
c. \( \frac{d m_{1} m_{2}}{m_{1}-m_{2}} \)
D. \( \frac{d}{m_{1}-m_{2}} \)


Which aortic arch is absent in a frog?
A \( \cdot 1^{s t}, 2 \) and 5 th
B. 3rd and 4 th
c. 3 rd, 4 th and 5 th
D. 5th and 6th


If the temperature is increased, what
will be the effect on the resistance of a
conductor?
A. Does not change
B. Decrease
c. Increase
D. cannot say


The plane \( x=0 \) divides the joinning of (-2,3,4) and (1,-2,3) in the ratio
A .2: 1
B. 1: 2
c. 3: 2
D. -4: 3


The asymptotes of a hyperbola \( 4 x^{2}- \)
\( 9 y^{2}=36 \) are
A. \( 2 x \pm 3 y=1 \)
в. \( 2 x \pm 3 y=0 \)
c. \( 3 x \pm 2 y=1 \)
D. None


The average of 15 numbers is 18 The average of first 8 is 19 and that last 8 is
17 then the 8 th number is
A . 15
B . 16
c. 18
D. 20


The state of rest or state of motion of a
body can be changed by using
A. Pressure
B. Force
c. Heat
D. None of these


Write IUPAC names of the given
compounds:
\( C H_{3} \)
\( C H_{3}-C H_{2}-C_{C H_{3}}^{\prime} C-C H_{2} C l \)


What helps the snakes to slither?
A. It's streamlined body shape
B. Long backbone and many interconnected muscles
c. Presence of setae
D. None of the above


State the working principle of a potentiometer with the help of the circuit diagram, explain how a potentiometer is used to compare the emf's of the two primary cell obtain the required expression used for comparing
the emf's.


Which of the following statements is/are correct for the Lanthanoids?
A. The 4f electrons do not take part in bonding
B. The 4f electrons can neither be removed to produce ions nor be made to take part in crystal field stabilization of complexes
c. The 4 felectrons in the antepenultimate shell are very effectively shielded by the 5 s and 5 p electrons
D. All of the above


Subtract the second expression from the first expression
\( \boldsymbol{x}+\mathbf{2} \boldsymbol{y}+\boldsymbol{z},-\boldsymbol{x}-\boldsymbol{y}-\mathbf{3} \boldsymbol{z} \)


The family Fabaceae is alternatively known as
A. Leguminosae
B. Solanaceae
c. compositae
D. Malvaceae


The permanganate ion is an excellent oxidizing agent in aqueous solutions.
When the half reaction, \( M n O_{4}^{-}+ \)
\( \boldsymbol{H}^{+}+\boldsymbol{e}^{-} \rightarrow \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{2}+\boldsymbol{H}_{2} \boldsymbol{O} \) is
balanced, the correct coefficients for the species involved are:
A. 1,4,4,1,2
B. 1,4,2,1,2
c. 1,4,3,1,2
D. 1,4,1,1,2


Iron sheets are covered with a layer of Zinc i.e., galvanized mainly to
A. harden the surface
B. increase the surface
c. prevent action of water only
D. prevent action of oxygen and water


Match process (in List I) with
electrolytes (in List II).


Flow of blood in the ventral vessel of
earthworm is
A. Forward
B. Backward
c. Backward in half of it and forward in another half
D. All of these


A particle of charge \( 16 \times 10^{-18} C \)
moving with velocity \( 10 m / s \) along the
X-axis enters a region where a
magnetic field of induction \( B \) is along the \( Y \) -axis, and an electric field of
magnitude \( 10 V m^{-1} \) is along the negative Z-axis. If the charged particle continues moving along the X-axis, the
magnitude of \( B \) is :
A \( \cdot 1 W b / m^{2} \)
B . \( 10^{5} \mathrm{Wb} / \mathrm{m}^{2} \)
\( \mathbf{c} \cdot 10^{6} W b / m^{2} \)
D. \( 10^{-3} W b / m^{2} \)


Define Henry's law.


Prove
If \( A \) and \( B \) are \( n \) squared skew
symmetrics matrices then \( \boldsymbol{A B} \) is
symmetric if and only if \( \boldsymbol{A} \) and \( \boldsymbol{B} \)
commute.


Identify the group of plants possessing leaf tendrils.
A. Pea, Glory lily
B. Cucumber, Pumpkin
c. watermelon, Grapevine
D. All of these


A bird is flying towards north with a
velocity \( 40 \mathrm{kmh}^{-1} \) and a train is
moving with velocity \( 40 \mathrm{kmh}^{-1} \) towards east. What is the velocity of the bird noted by a man in the train?
A \( \cdot 40 \sqrt{2} k m h^{-1} N-E \)
в. \( 40 \sqrt{2} k m h^{-1} S-E \)
c. \( 40 \sqrt{2} k m h^{-1} N-W \)
D. \( 40 \sqrt{2} k m h^{-1} S-W \)


An e.m.f. of 5 volt is produced by a self inductance, when the current changes at a steady rate from 3 A to 2 A in 1 millisecond. The value of self
inductance is
A . zero
в. 5 н
c. 5000 н
D. 5 mH


Agent Orange was named so because of
A. orange colour
B. orange stripe on packet
C. production of orange cloud
D. killing all greenery


A parallel plate condenser has plates of
area \( 200 \mathrm{cm}^{2} \) and separation \( 0.05 \mathrm{cm} \)
The space between plates have been
filled with a dielectric having \( \mathbf{k}=\mathbf{8} \) and
then charged to 300 volts. The stored energy:
A . \( 121.5 \times 10^{-6} \mathrm{J} \)
В. \( 28 \times 10^{-6} \mathrm{J} \)
D. \( 1.6 \times 64 \times 10^{-5} \mathrm{J} \)


A double convex thin lens made of glass
(refractive index, \( =1.5 \) ) has both radii of
curvature of magnitude \( 20 \mathrm{cm} \) Incident light rays parallel to the axis of the lens will converge at a distance \( d \) in
\( \mathrm{cm}, \) such that :
\( \mathbf{A} \cdot d=10 \)
В. \( d=20 / 3 \)
c. \( d=40 \)
D. \( d=20 \)


When we press the bulb of a
dropper,with its nozzle kept under water
,air in the dropper is seen to escape in the form of bubbles.lf we then,release
the pressure on the bulb,water gets
filled in the dropper.The rise in water in the dropper is due to
A. Liquid pressure
B. Weight of the bulb
c. Gravity of the earth
D. Atmospheric pressure


Discuss the countinuity of the following
function at \( \boldsymbol{x}=\mathbf{0} \)
\( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{ll}\frac{1-\cos x}{x^{2}}, & x \neq 0 \\ \frac{1}{2}, & x=0\end{array}\right. \)


Solve \( : \frac{2}{x}+\frac{2}{3 y}=\frac{1}{6} \) and \( \frac{3}{x}+\frac{2}{y}=0 \)
Hence, find ' \( m^{\prime} \) for which \( y=m x-4 \)
A \( . x=3 ; y=-5 \) and \( m=2 \)
B. \( x=6 ; y=-4 \) and \( m=0 \)
c. \( x=2 ; y=-3 \) and \( m=0 \)
D. \( x=4 ; y=-4 \) and \( m=2 \)


Earthquakes can be predicted in advance
A . True
B. False
c. Ambiguous
D. Data insufficient


If \( f(x) \) is given by \( f(x)=(\cos x+ \)
\( i \sin x)(\cos 3 x+i \sin 3 x) \dots .(\cos (2 n- \)
1) \( x+i \sin (2 n-1) x \) ), then \( f^{\prime \prime}(x) \) is
equal to
\( \mathbf{A} \cdot n^{3} f(x) \)
B . \( -n^{4} f(x) \)
\( \mathbf{c} \cdot-n^{2} f(x) \)
D \( \cdot n^{4} f(x) \)


If \( x^{3}-y^{3}+3 x y^{2}-3 x^{2} y+1=0, \) then
\( \operatorname{at}(0,1) \frac{d y}{d x} \) equals
\( \mathbf{A} \cdot \mathbf{1} \)
B. -
\( c \cdot 2 \)
D.


Current commercial method for
producing ibuprofen is a stunning
application of Green chemistry because
A. ibuprofen is an anti-inflammatory drug and has various applications
B. the previous method required large amounts of solvents and generated large wastes compared to the current method
C. it has very important medicinal value
D. this compound has very less side effects after usage


The process of converting hydrated alumina into anhydrous alumina is called:
A. roasting
B. calcination
c. smelting
D. dressing


\( \left|\begin{array}{ccc}1 & a & a^{2}-b c \\ 1 & b & b^{2}-c a \\ 1 & c & c^{2}-a b\end{array}\right| \) is equal to
\( A \)
B . \( \sum a^{2}(b-c) \)
c. \( 2 \sum a^{2}(b-c) \)
D. \( -2 \sum a b(a-b) \)


Acid turn blue litmus :
A. green
B. red
c. yellow
D. orange


If the eccentricity of an ellipse is \( \frac{5}{8} \) and
the distance between its foci is \( 10, \) then
find latus-rectum of the ellipse.


Find the ratio of the distances traveled
by a body falling freely from rest in the first, second and third seconds
respectively.
A. 1: 4: 9
B. 1: 2: 3
\( \mathbf{c} \cdot 1: 9: 25 \)
D. 1: 3: 5


Carbon dioxide entering erythrocytes reacts with water to form carbonic acid.
The enzyme catalyzing this
A. Carbonic anhydrase
B. Carboxypeptidase
c. Hydrolase
D. oxidoreductase


Which of the following is the buffer solution of strong acidic nature?
A. \( H C O O H+H C O O^{-} \)
в. \( C H_{3} C O O H+C H_{3} C O O \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}+\mathrm{C}_{2} \mathrm{O}_{4}^{2} \)
D. \( H_{3} B O_{3}+B O_{3}^{3-} \)


Draw the circuit arrangement for
studying the \( V_{I} \) characteristics of a p-n
junction diode in reserve bias. Plot the
\( V-I \) characteristics in this case.


ASSERTION: In froth floatation process,
sodium ethyl xanthate is used as a collector.

REASON: Sulphide ores are water soluble.
A. If both assertion and reason are CORRECT, and the reason is the CORRECT explanation of the assertion
B. If both assertion and reason are CORRECT, but the reason is NOT the CORRECT explanation of the assertion
C. If assertion is CORRECT but reason is INCORRECT.
D. If assertion is INCORRECT but reason is CORRECT.


A brick with dimensions of \( 20 \mathrm{cm} \times \)
\( 10 c m \times 5 c m \) has a weight 500 gwt.
Calculate the pressure exerted by it when it rests on different faces.
A \( \cdot \) case (i) \( P_{1}=1.25 g w t c m^{-2}, \) Case (ii) \( P_{2}=5 g w t c m^{-2} \) Case (iii) \( P_{3}=5 g w t c m^{-2} \)
B. case (i) \( P_{1}=2.5 g w t c m^{-2} \), Case (ii) \( P_{2}=5 g w t c m^{-2} \)
Case (iii) \( P_{3}=10 \) gwtem \( ^{-2} \)
C. case (i) \( P_{1}=5 g w t c m^{-2} \), Case (ii) \( P_{2}=25 g w t c m^{-2} \) Case (iii) \( P_{3}=15 \) gwtcm \( ^{-2} \)
D. case (i) \( P_{1}=2.5 g w t c m^{-2} \), Case
(ii) \( P_{2}=2.5 g w t c m^{-2} \)
Case (iii) \( P_{3}=10 g w t c m^{-2} \)


f \( \boldsymbol{A}=\left(\begin{array}{ll}1 & -1 \\ 2 & -2\end{array}\right) \) Find \( 5 \boldsymbol{I}-8 \boldsymbol{A} \)


Choose the correct statement from the
following
This question has multiple correct options
A. When same charges are separated by different distances in the same medium, \( F d^{2}= \) constant
B. On doubling the distance of separation between two charges, the electric force between two charges becomes one fourth
C. Repulsion is the sure test of electrification
D. Sl unit of electric field is farad


Match the components of lac operon of
E. coli with their functions. Choose the
answer with the correct combination of
alphabets of the two columns.


When \( P C l_{3} \) reacts with sulphuric acid, sulphuryl chloride is formed as the final product. This shows that sulphuric acid
A. has two hydroxyl groups in its structure.
B. is a derivative of sulphur dioxide
c. is a dibasic acid
D. has greater affinity for water


Consider the following statements about acceleration due to gravity on earth and mark the correct
statement(s):
A. The value of \( g \) is constant throughout
в. \( g^{\prime}=g\left(1-\frac{d}{r}\right) \)
\( \mathrm{c} . g \) is slightly less (by about \( 1 \% \) ) when distance \( <200 \mathrm{m} \)
D. \( g \) is slightly greater when distance \( <200 m \)


Show that the four triangles as shown in the adjoining fig. formed by diagonals and sides of rhombus are congruent.


\( \mathbf{f} \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{0} \\ \mathbf{0} & \mathbf{1}\end{array}\right] ; \boldsymbol{B}=\left[\begin{array}{ll}\boldsymbol{a} & \boldsymbol{c} \\ \boldsymbol{b} & \boldsymbol{d}\end{array}\right], \) then show
that \( (A . B)^{-1}=B^{-1} . A^{-1} \)


Cotton fibers are separated from seeds
by:
A. combing
B. knitting
c. weaving
D. rubbing


Correlated characters are similar traits
found in
A. All members of a population
B. All races of a species
c. All species of a genus
D. All the above


Let \( a, b, c \) be three distinct positive real numbers in G.P., then \( a^{2}+2 b c-3 a c \) is
\( A \cdot>0 \)
\( B .<0 \)
\( c_{c}=0 \)
D. can't be found out


A hemispherical bowl of internal radius \( 9 \mathrm{cm} \) is full of liquid. This liquid is to be filled into conical shaped small
containers each of diameter \( 3 \mathrm{cm} \) and
height \( 4 \mathrm{cm} . \) How many containers are
necessary to empty the bowl?


Prove the following statements:
\( \cos ^{4} \boldsymbol{A}-\sin ^{4} \boldsymbol{A}+\mathbf{1}=\boldsymbol{2} \cos ^{2} \boldsymbol{A} \)


The algebraic form of an arithmetic
sequence is \( 5 n+3 \)
a. What is the first form of the
sequence?
b. What will be the remainder if the term
of the sequences are divide by \( 5 ? \)


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


For a solution of a non-electrolyte in water, the Van't Hoff factor is :
A. Always equal to 0
в. \( \leq 1 \)
c. Always equal to
D. \( >1 \) but \( <2 \)


The equilibrium constant \( \boldsymbol{K}_{\boldsymbol{p}} \) for the
reaction \( 2 H_{2}(g)+O_{2}(g) \rightleftharpoons 2 H_{2} O(g) \)
at \( 2000 \mathrm{K} \) is \( 1.6 \times 10^{7} . \) The equilibrium
constant of the reaction \( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \rightleftharpoons \)
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\frac{1}{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \) is
A. \( 6.25 \times 10^{-8} \)
B . \( 2.5 \times 10^{-4} \)
c. \( 7.5 \times 10^{-12} \)
D. \( 4 \times 10^{-6} \)


Why mercury do not evaporate at room
temperature?
A. Because melting point of mercury is higher
B. Because boiling point of mercury is higher
C. Because boiling point of mercury is lower
D. Because boiling point of mercury is equal to room temperature


The slope of the line whose inclination is \( 30^{\circ} \) is \( \frac{1}{\sqrt{m}} . \) Find the value of \( m \)


Is the colour of 620 nm light and 780
nm light same? Is the colour of \( 620 \mathrm{nm} \)
light and 621 nm light same? How many colours are there in white light?


Very short answer type:
Why are pollen grains produced in enormous quantity in maize?


Find the product \( (3+\sqrt{2})(3-\sqrt{2}) \)


If \( S \) is stress and \( Y \) is Young's modulus
of material of wire, then energy stored in the wire per unit volume is:
\( \mathbf{A} \cdot 2 S^{2} Y \)
в. \( \frac{s}{Y x} \)
c. \( \frac{2 Y}{S^{2}} \)
D. \( \frac{s^{2}}{2 Y} \)


Explain why is ortho nitrophenol more acidic than ortho methoxyphenol?


Which one of the following sequences was proposed by Darwin and Wallace for organic evolution:
A. overproduction, variations, constancy of population size, natural selection
B. Variations, constancy of population size, overproduction, natural selection
c. overproduction, constancy of population size, variations, natural selection
D. Variations, natural selection, overproduction constancy of population size


Which of the following illustrate the
anomalous properties of Lithium?
This question has multiple correct options
A. Lithium is softer than the other group I metals
B. Lithium forms nitride, \( L i_{3} N \) unlike other group
metals
C. The melting and boiling point of Lithium are comparatively high
D. none of these


A student measures the thickness of a
copper wire using standard instruments and reports it as \( 0.1 \mathrm{cm} \)
\( 0.15 \mathrm{cm} \) and \( 0.157 \mathrm{cm} . \) The instruments
used to find these measurements are
and
respectively.
A. vernier calipers, ordinary scale, screw gauge
B. ordinary scale,vernier calipers, screw gauge
C. screw gauge, vernier calipers, ordinary scale,
D. ordinary scale, screw gauge, vernier calipers


Animals like scorpions, cockroaches lizards, mice sharing our abodes (homes) and food live in our homes, are
called
A. Cultigens
B. Inquilines
c. Living fossil
D. Domesticated


What are primary valencies and
secondary valencies give an example?


The high melting point of \( S i O_{2} \) is due
to:
A. sp hybridised silicon atom
B. tetrahedral polymer structure
c. its solid state
D. \( S p^{2} \) hybridised silicon atom


Which of the following is logically equivalent to \( \sim(\sim p \Rightarrow q) ? \)
A \( \cdot p \wedge q \)
В . \( p \wedge \sim q \)
\( \mathrm{c} \cdot \sim p \wedge q \)
D \( . \sim p \wedge \sim q \)


A \( 20 k g \) load is suspended from the
lower end of a wire \( 10 \mathrm{cm} \) long and \( 1 \mathrm{mm} \)
\( ^{2} \) in cross sectional area. The upper half of the wire is made of iron and the lower
half with aluminium. The total
elongation in the wire is
\( \left(Y_{i r o n}=20 \times 10^{10} \mathrm{N} / \mathrm{m}^{2}, Y_{A l}=7 \times 10^{10}\right. \)
\( \left.\mathrm{N} / \mathrm{m}^{2}\right) \)
A \( \cdot 1.92 \times 10^{-4} \mathrm{m} \)
B. 17.8 \( \times 10^{-3} \mathrm{m} \)
c. \( 1.78 \times 10^{-3} \mathrm{m} \)
D. \( 1.92 \times 10^{-3} \mathrm{m} \)


n the figure \( \angle \boldsymbol{P}+\angle \boldsymbol{Q}+\angle \boldsymbol{R}+\angle \boldsymbol{S}+ \)
\( \angle \boldsymbol{T}=\boldsymbol{2} \) right angles
\( 4 . \) True
3. Falss


Which statements are correct about the
reaction?
\[
\mathbf{R}-\|^{*}_{\mathbf{M e}}^{\mathbf{O}} \underbrace{\mathbf{D}}_{\mathbf{O}} \ddot{\mathbf{N}} \mathbf{H}_{2} \frac{\mathbf{B r}_{2}+\stackrel{\Theta}{\mathbf{O H}}}{\Delta} \begin{array}{c}
\text { Mixture of } \\
\mathbf{1}^{\circ} \text { amines }
\end{array}
\]
This question has multiple correct options
A. A mixture of two amines is formed, which suggests that rearrangement is intramolecular
B. If \( R \) is chiral, it migrates with retention of configuration.
\( c \)
\[
\left[\begin{array}{c}
0 \\
R-C \\
\| \\
\dot{N}
\end{array}\right]
\]
A mixture of four different amines is formed, which suggests that a free acyl nitrene (diag) intermediate is formed.
D. A mixture of two different amines and a free acyl nitrene intermediate is formed.


has a radius \( \boldsymbol{R} \) and height \( \boldsymbol{L}_{\mathbf{0}} \). The
cylinder is open at its bottom and has a
small hole at its top. A piston of mass
\( M \) is held at a distance \( L \) from the top
surface as shown in Fig. The
atmospheric pressure is \( \boldsymbol{p}_{0} \)
The piston is now pulled out slowly and
held at a distance \( 2 L \) from the top. The
pressure in the cylinder between its top
and the piston will then be:
\( \mathbf{A} \cdot P_{0} \)
в. \( \frac{P_{0}}{2} \)
c. \( \frac{P_{0}}{2}-\frac{M g}{\pi R^{2}} \)
D. \( P_{0}-\frac{M g}{\pi R^{2}} \)


A photoelectric cell emits electrons when illuminated by a \( 60 ~ W \) bulb. If the same cell is illuminated by replacing it with a \( 40 W \) bulb, the observation that can be made is
A. No photoelectric effect takes place
B. Number of photoelectrons increases
c. The kinetic energy of photoelectrons decreases
D. Number of photoelectrons decreases


Identify the correct option(s) related
with the physical properties of the unknown compounds [X] and [Y] formed as major and minor product
respectively in the given reaction.
This question has multiple correct options
A. Water solubility of [Y] is greater than [X]
B. Boiling point of [Y] is greater than [X]
C. Melting point of [Y] is greater than [X]
D. \( [x] \) is more volatile than \( [Y] \)


The volume of glass vessel is \( 1000 \mathrm{cc} \) at
\( 20^{\circ} \mathrm{C} . \) What volume of mercury should
be poured into it at this temperature so that the volume of the remaining space does not change with temperature? Coefficient of cubical expansion of
mercury and glass are \( 1.8 \times \) \( \mathbf{1 0}^{-4} /^{\circ} \mathbf{C} \) and \( \mathbf{9 . 0} \times \mathbf{1 0}^{-\mathbf{5}} /^{\circ} \mathbf{C} \)
respectively.
A . 100 c.
в. \( 10 \mathrm{cc} \)
c. \( 500 c c \)
D. 5 с.


Find the area (sq.units) bounded by \( \boldsymbol{y}=\sin ^{-1} \boldsymbol{x} \) and \( \boldsymbol{y}=\cos ^{-1} \boldsymbol{x} \) and \( \mathbf{x} \) -axis.


What do you mean by electrical
resonance? An LC circuit is in a
condition of resonance. If \( C=1.0 \times 10^{-6} \)
\( F \) and \( L=0.25 H, \) then find the frequency
of oscillation of the circuit.


How many alkene on catalytic hydrogenation given isopentane as a product?
\( A \cdot 2 \)
B. 4
\( c \cdot 3 \)
D.


\( \mathrm{f} f_{0}^{\pi / 3} \frac{\cos }{3+4 \sin x} d x= \)
\( K \log \frac{(3+2 \sqrt{3})}{3} \) then \( K \) is
A \( \cdot \frac{1}{2} \)
B.
\( c \cdot \frac{1}{4} \)
D.


\( A 750 H z, 20 V \) source is connected to a resistance of \( 100 \Omega, \) an inductance of \( 0.1803 H \) and a capacitance of \( 10 \mu F \) all
in series. Calculate the time in which
the resistance (thermal capacity
\( \left.2 J /^{o} C\right) \) will get heated by \( 10^{\circ} \mathrm{C} \). (lgnore radiation)
A . 6.8 min
B. 5.8 min
c. 7.8 min
D. 9.8 min


Explain why
(a) The blood pressure in humans is
greater at the feet than at the brain
(b) Atmospheric pressure at a height of about \( 6 \mathrm{km} \) decreases to nearly half of its value at the sea level, though the
height of the atmosphere is more than \( 100 \mathrm{km} \)
(c) Hydrostatic pressure is a scalar quantity even though pressure is force divided by area


Solve the following differential equation \( \left(x^{2}+1\right) \frac{d y}{d x}=1 \)


Write an essay on clotting of blood.


Rockets are lunched in Eastward
direction to take advantage of:
A. The clear sky on Eastersn side
B. The thinner atmosphere on this side
c. both A and B
D. non of the above


The displacement of \( m^{\prime} \) on \( M \) is
A \( .0 .3 m \)
в. \( 0.2 m \)
c. \( 0.98 m \)
D. \( 0.1 m \)


If a quadrilateral \( A B C D \) is such that
\( A B=b, A D=d \) and \( A C=m b+p d \)
\( (m+p \geq 1), \) then the area of the
quadrilateral is \( k(p+m)|b \times d|, \) where
\( k \) is equal to
A \( \cdot \frac{1}{4} \)
B. \( \frac{1}{8} \)
\( c \cdot \frac{1}{2} \)
D. None of these


The linear relation between the vectors
\( \boldsymbol{a}+\boldsymbol{3} \overline{\boldsymbol{b}}+\boldsymbol{4} \boldsymbol{c}, \overline{\boldsymbol{a}}-\boldsymbol{2} \overline{\boldsymbol{b}}+\boldsymbol{3} \overline{\boldsymbol{c}}, \overline{\boldsymbol{a}}+\mathbf{5} \overline{\boldsymbol{b}}-\boldsymbol{2} \overline{\boldsymbol{c}} \)
\( 6 \bar{a}+14 \bar{b}+4 \bar{c} \) is
\( \mathbf{A} \cdot(\bar{a}+3 \bar{b}+4 \bar{c})+2(\bar{a}-2 \bar{b}+3 \bar{c})+ \)
\[
\text { 2 }(\bar{a}+5 \bar{b}-2 \bar{c})-1(6 \bar{a}+14 \bar{b}+4 \bar{c})=\overline{0}
\]
B . \( 1(\bar{a}+3 \bar{b}+4 \bar{c})+2(\bar{a}-2 \bar{b}-3 \bar{c})+ \)
\[
\text { 3 }(\bar{a}+5 \bar{b}-2 \bar{c})-2(7 \bar{a}+14 \bar{b}+4 \bar{c})=\overline{0}
\]
C \( .1(\bar{a}+3 \bar{b}+4 \bar{c})+2(\bar{a}-2 \bar{b}+3 \bar{c})+ \)
\[
\text { 3 }(\bar{a}+5 \bar{b}-2 \bar{c})-1(6 \bar{a}+14 \bar{b}+4 \bar{c})=\overline{0}
\]
D. \( (\bar{a}+3 \bar{b}+4 \bar{c})+(\bar{a}-2 \bar{b}+3 \bar{c})+ \)
\[
(\bar{a}+5 \bar{b}-2 \bar{c})-(6 \bar{a}+14 \bar{b}+4 \bar{c})=\overline{0}
\]


Assertion
Zinc is used in the galvanization of iron.
Reason
Its coating on iron articles increases their life by protecting them from
rusting.
A. If both Assertion and Reason are correct and Reason is the correct explanation of Assertion
B. If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion
C. If Assertion is correct but Reason is incorrect
D. If Assertion is incorrect but Reason is correct


The elevator shown in figure is descending, with an acceleration of 2
\( m / s^{2} . \) The mass of the block \( A \) is 0.5 kg.
The force exerted by the block A on the block B is -
\( A \cdot 2 N \)
в. 4 ।
\( c \cdot 6 N \)
\( D \cdot 8 n \)


Which of the following part of the bird is modified as wings?
A. Breast bones
B. Forelimbs
c. Hindlimbs
D. All of the above


The solution of the differential equation \( \left(\frac{d y}{d x}\right)^{2}-3 x\left(\frac{d y}{d x}\right)-2 y=8 \)
A \( \cdot y=2 x^{2}+4 \)
B . \( y=2 x^{2}-4 \)
\( \mathbf{c} \cdot y=2 x+4 \)
D. \( y=2 x-4 \)


Match the definition to the apt term in
the list given below:
The principle that transmission of an impulse is either at full strength or not
at all-
all-or-none law, colour vision, afferent nerves, efferent nerves, fovea centralis
impulse, macula lutea, myopia,
neuron reflex, statoreceptor, visual acuity meninges, blind spot


What is the nature of the graph: \( y= \)
\( 2 x^{2} \)
A. parabola passing through origin
B. Hyperbola passing through origin
c. ellipse passing through origin
D. Hyperbola but not passing through origin


Ethylene chloro hydrin is the product of following reaction:
A. \( C H_{2}=C H_{2}+H O C l \)
в. \( C H_{2}=C H_{2}+H_{2} \)
\( \mathbf{c} \cdot C H_{2}=C H_{2}+C l_{2} \)
D. \( C H_{2}=C H_{2}+H O B r \)


When we press the bulb of dropper with
its nozzle kept in water, air in the
dropper is seen to escape in the form of bubbles. Once we release the pressure
on the bulb, water gets filled in the
dropper. The rise of water in the dropper
is due to:
A. Pressure of water
B. Gravity of the earth
c. shape of rubber bulb
D. Atmospheric pressure


When a liquid is heated retaining its liquid state, then its molecules gain
A. Kinetic energy
B. potential energy
c. heat energy
D. both kinetic and potential energy


The current in the coil is reversed, and
the coil is rotated about its vertical axis
by an angle of \( 90^{\circ} \) in the anticlockwise
sense looking from above. Predict the direction of the needle. Take
the magnetic declination at the places to be zero.


\( \left|\begin{array}{ccc}2 & -3 & 3 \\ 2 & 2 & 3 \\ 3 & -2 & 2\end{array}\right| \)


Properties of magnetic lines of force
are:
A. The imaginary lines which represent the direction of magnetic field, are known as magnetic lines of force.
B. Magnetic lines of force are closed curves.
C. Outside the magnet their direction is from north pole to south pole and inside the magnet these are from south to north pole.
D. All


A thin uniform rod of mass \( M \) and
length \( L \) is hinged at its upper end released from rest in horizontal
position. The tension at a point located
at a point located at a point, when the
rod becomes vertical, will be:
A \( \cdot \frac{22 M g}{27} \)
в. \( \frac{11 M g}{13} \)
c. \( \frac{6 M g}{11} \)
\( \mathbf{D} \cdot 2 M q \)


The formula of potassium superoxide is
A \( \cdot K O_{2} \)
в. \( K_{2} \) о
c. \( K_{2} O_{2} \)
D. None of these


Describe anomalous behaviour of
fluorine with the other elements of
group 17 with reference to:
Polyhalide ions.


Using elementary tansormations, find
the inverse of each of the matrices, if it
exists in \( \left[\begin{array}{ll}2 & 1 \\ 1 & 1\end{array}\right] \)


The structure of hydrocarbon
is
\( \mathbf{A} \cdot M e C \equiv C-H \)
\( \mathbf{B} \cdot H_{2} C=C=C H_{2} \)
\( \mathbf{c} \cdot H_{2} C \equiv C H_{2} \)
D. All of the above


Dipole moment of chlorobenzene is
lower than that of cyclohexyl chloride.
Give reason:


A uniform magnetic field of \( 1.5 T \) exists
in a cylindrical region of radius \( 10.0 \mathrm{cm} \)
it's direction being parallel to the axis along east to west. A current carrying wire in north-south direction passes through this region. The wire intersects the axis and experiences a force of \( 1.2 N \) downwards. If the wire is turned
from north-south to northeast-
southwest direction, then the magnitude and the direction of the
force is
A. \( 1.2 N \), upwards
B. \( 1.2 \sqrt{2} N \), downward
c. \( 1.2 N \), downwards
D. \( \frac{1.2}{\sqrt{2}} N, \) downwards


Reduce the equation \( 4 x+6 y-7=0 \)
to intercept form.Hence find the length of the segment intercepted between the
axes.


The major product(s) of the following reaction is(are):
\( A \cdot P \)
в. \( Q \)
\( c . R \)
D.


A step down transformer has 50 turns
on secondary and 1000 turns on primary winding. If a transformer is connected
to \( 220 V, 1 A \) A.C. source, what is output
current of the transformer?
A \( \cdot \frac{1}{20} A \)
B. 20 A
\( c \cdot 100 A \)
D. 2 A


What is the minimum frequency of
sound waves needed to prepare
emulsion from two immiscible liquids?


Explain the types of waste based on its nature and degradation


Which of the following pairs of substances illustrate the law of multiple proportions?
A. \( C O \) and \( C O_{2} \)
B. \( H_{2} O \) and \( D_{2} O \)
c. \( N a C l \) and \( N a B r \)
D. \( M g O \) and \( M g(O H)_{2} \)


If \( \boldsymbol{x}^{\boldsymbol{a}} \boldsymbol{y}^{\boldsymbol{b}}=\boldsymbol{e}^{\boldsymbol{m}}, \boldsymbol{x}^{\boldsymbol{c}} \boldsymbol{y}^{\boldsymbol{d}}=\boldsymbol{e}^{\boldsymbol{n}}, \Delta_{\mathbf{1}}= \)
\( \left|\begin{array}{ll}\boldsymbol{m} & \boldsymbol{b} \\ \boldsymbol{n} & \boldsymbol{d}\end{array}\right|, \triangle_{2}=\left|\begin{array}{ll}\boldsymbol{a} & \boldsymbol{m} \\ \boldsymbol{c} & \boldsymbol{n}\end{array}\right| \) and \( \Delta_{\boldsymbol{3}}=\left|\begin{array}{ll}\boldsymbol{a} & \boldsymbol{b} \\ \boldsymbol{c} & \boldsymbol{d}\end{array}\right| \)
the value of \( x \) and \( y \) are respectively
A \( \cdot \frac{\Delta_{1}}{\Delta_{3}} \) and \( \frac{\Delta_{2}}{\Delta_{3}} \)
B. \( \frac{\Delta_{2}}{\Delta_{1}} \) and \( \frac{\Delta_{3}}{\Delta_{1}} \)
\( ^{\mathbf{c}} \cdot \log \left(\frac{\Delta_{1}}{\Delta_{3}}\right) a n d \log \left(\frac{\Delta_{2}}{\Delta_{3}}\right) \)
\( \mathbf{D} \cdot e^{\Delta_{1} / \Delta_{3}} \) and \( e^{\Delta_{2} / \Delta_{3}} \)


An automobile is started from rest with
one of its doors initially at right angles. If the hinges of the door are toward the front of the car, the door will shut as the
automobile picks up speed. The acceleration a is constant and the
centre of mass is at a distance d from
the hinges. The time \( T \) needed for the doors to close is given by:
\( \left[\text {Given}: \int_{0}^{\frac{\pi}{2}} \frac{\boldsymbol{d} \boldsymbol{\theta}}{\sqrt{\sin \theta}}=\boldsymbol{N}\right] \) (Consider
the door as a square plate)
A \( \cdot \mathrm{T}=(\sqrt{\frac{3 \mathrm{d}}{2 \mathrm{a}}}) \mathrm{N} \)
B. \( \mathrm{T}=(\sqrt{\frac{\mathrm{d}}{3 \mathrm{a}}}) \mathrm{N} \)
c. \( \mathrm{T}=(\sqrt{\frac{2 \mathrm{d}}{\mathrm{a}}}) \mathrm{N} \)
D. \( \mathrm{T}=(\sqrt{\frac{2 \mathrm{d}}{3 \mathrm{a}}}) \mathrm{N} \)


The quotient and remainder when
\( 3 x^{4}+6 x^{3}-6 x^{2}+2 x-7 \) is divided by
\( x-3 \) are
A. Quotient: \( 3 x^{3}+15 x^{2}+39 x+119 \) and Remainder: 350
B. Quotient: \( 3 x^{3}+10 x^{2}+39 x+119 \) and Remainder: 35
C . Quotient: \( 3 x^{3}+15 x^{2}+39 x+119 \) and Remainder: 50
D. Quotient: \( 3 x^{3}+15 x^{2}+119 \) and Remainder: 350


In aqueous solution of soap, head is towards the surface of water and tail is
pointing away from the water. if true, enter 1 , else enter 0 .


Find the domain and range of the
following real functions:
¡) \( \boldsymbol{f}(\boldsymbol{x})=-|\boldsymbol{x}| \)
ii) \( \boldsymbol{f}(\boldsymbol{x})=\sqrt{\mathbf{9}-\boldsymbol{x}^{2}} \)


Which of the following compounds are not soluble in water?
A. Formaldehyde
B. Acetaldehyde
c. Acetone
D. None of the above


An electrically heating coil is placed in a calorimeter containing 360 g of \( \mathrm{H}_{2} \mathrm{O} \) at \( 10^{\circ} \mathrm{C} . \) The coil consumes energy at the
rate of \( 90 \mathrm{W} \). The water equivalent of calorimeter and the coil is 40 g. The temperature of water after 10 minutes
will be
A \( \cdot 42.15^{0} \mathrm{C} \)
в. \( 32.14^{\circ} \mathrm{C} \)
c. \( 22.14^{\circ} \mathrm{C} \)
D. \( 52.14^{\circ} \mathrm{C} \)


Copy the diagram given below and
complete the path of light ray till it
emerges out of the prism. The critical
angle of glass is \( 42^{\circ} . \) In your diagram
mark the angles wherever necessary.


Show that vector area of a quadrilateral \( A B C D \) is \( \frac{1}{2}(A C \times B D), \) where \( A C \)
and \( B D \) are its diagonals.


\( \cos ^{4} \theta-\sin ^{4} \theta+1 \) is equal to:
A \( \cdot 2 \cos e c^{2} \theta \)
B. \( -2 \cos e c^{2} \theta \)
c. \( \frac{2}{\tan ^{2} \theta} \)
D. \( \frac{2 \cot ^{2} \theta}{\cos e c^{2} \theta} \)


The plates of a parallel plate capacitor are given charges \( +4 Q \) and \( -2 Q \). The capacitor is then connected across an uncharged capacitor of same capacitance as first one \( (=C) \). Find the
final potential difference between the plates of the first capacitor.


A compound with molar mass 180 is
acylated with \( C H_{3} C O C l \) to get a
compound with molar mass
390. The number of amino groups present per molecules of the former
compounds is:


Consider the equilibrium
\( N H_{4} C l(s) \rightleftharpoons N H_{3}(g)+H C l(g) . A n \)
inert gas is added to the system at constant volume and temperature. The correct statement(s) is/ are:
This question has multiple correct options
A. the partial pressures of \( N H_{3} \) and \( H C l \) in the system will increase
B. the partial pressures of \( N H_{3} \) and \( H C l \) in the system will remain the same
c. the partial pressures of \( N H_{3} \) and \( H C l \) in the system will decrease
D. the entropy of the system will increase


The highest concentration of was found in Hartley coal ash.
A. Leadd
B. Germanium
c. Antimony
D. carbon


If the 20 th and 21 st terms in the
expansion of \( (1+x)^{40} \) are equal, then
the value of \( x \) is
A \( \cdot \frac{20}{21} \)
в. \( \frac{21}{20} \)
c. 25
D. \( \frac{1}{25} \)


An object of height \( 10 \mathrm{cm} \) is placed at a distance \( 100 \mathrm{cm} \) before the convex
mirror perpendicular below the principal axis. If the focal length of the mirror is \( 10 \mathrm{cm}, \) on applying the Cartesian sign convention. Find the signs of object distance, focal length and height of the object.
A. \( u=100 \mathrm{cm}, f=-10 \mathrm{cm}, h=-10 \mathrm{cm} \)
в. \( u=100 \mathrm{cm}, f=10 \mathrm{cm}, h=20 \mathrm{cm} \)
c. \( u=100 \mathrm{cm}, f=-10 \mathrm{cm}, h=10 \mathrm{cm} \)
D. \( u=-100 \mathrm{cm}, f=10 \mathrm{cm}, h=10 \mathrm{cm} \)


Capacity of a parallel plate condenser is \( 10 \mu F \) when the distance between the plates is \( 8 \mathrm{cm} . \) If the distance between the plates is reduced to \( 4 \mathrm{cm}, \) its capacity will be:
A. \( 10 \mu F \)
B. \( 15 \mu F \)
c. \( 20 \mu F \)
D. \( 40 \mu F \)


\( \mathrm{CaO} \) and \( \mathrm{NaCl} \) have the same crystal
structure and approximately the same
ionic radii. If \( U \) is the lattice energy of
Na \( C l \), the approximate lattice energy
of \( C a O \) is:
A. \( U / 2 \)
B. \( U \)
\( c .2 U \)
D. \( 4 U \)


Wood of Gymnosperms is composed of
A. Only tracheids in the xylem
B. Only vessels and xylem parenchyma
C. Only fibres and xylem parenchyma
D. Only fibres and vessels


There are 27 drops of a conducting fluid. Each drop has radius \( r, \) and each of
them is charged to the same potential \( V_{1} \).They are then combined to form a bigger drop.The potential of the bigger drop is \( V_{2} \).Find the ratio \( V_{2} / V_{1} \). Ignore
the change in density of the fluid on combining the drops.


State whether true or false:
Ropes made by rayon are used in cranes and elevators.
A. True
B. False


If there is rise of melting point then latent heat required would be

Complete the sentence
A. More
B. Less
c. No change
D. Same


For \( \Delta A B C \) and \( \Delta D E F, A B= \)
\( \boldsymbol{F} \boldsymbol{E}, \boldsymbol{B} \boldsymbol{C}=\boldsymbol{E} \boldsymbol{D} \) and \( \angle \boldsymbol{B}=\angle \boldsymbol{E} \)
Therefore
A. \( \Delta A B C \cong \Delta D E F \)
B. \( \Delta A B C \cong \Delta E D F \)
c. \( \Delta B C A \cong \Delta D E F \)
D. \( \Delta B C A \cong \Delta E D F \)


Let \( S \) be the set of all functions \( f: \)
\( [0,1] \rightarrow R, \) which are continuous on
[0,1] and differentiable on \( (0,1) . \) Then
for every \( f \) in \( S, \) there exists \( a c \in(0,1) \)
depending on \( f, \) such that
\( ^{\text {A } \cdot \frac{f(1)-f(c)}{1-c}=f^{\prime}(c)} \)
B \cdot \( |f(c)-f(1)|<(1-c)\left|f^{\prime}(c)\right| \)
c. \( |f(c)+f(1)|<(1+c)\left|f^{\prime}(c)\right| \)
D \( \cdot|f(c)-f(1)|<\mid f^{\prime}(c) \)


Write the spherical mirror's formula and explain the meaning of each symbol used in it.


A ray of light passes from water to air. Will the speed of light increase or
decrease?


Which of the following cannot form oxo ion?
\( \mathbf{A} \cdot P u O_{2}^{+} \)
B. \( \mathrm{CeO}_{2}^{+} \)
\( \mathbf{c} \cdot U O_{2}^{2+} \)
D. \( N p O_{2}^{\text {th }} \)


The image formed by a plane mirror is always
A. Real and erect
B. Virtual and erect
c. Real and inverted
D. Virtual and inverted


What is tubular secretion? Name the
substances secreted through the renal tubules.


The heat energy is required to raise the
temperature of \( 18 \mathrm{m} \) of water by \( 1^{\circ} \mathrm{C} \) is:
A . \( 1 J \)
B . 2.1
c. \( 4.2 J \)
D. 8.4J


Select the correct option.
(a) Energy of ground state of \( \boldsymbol{H} e^{+} \)
\[
(i)+6.04 e v
\]
(b) Potential energy of I orbit of \( \boldsymbol{H}- \)
atom
(ii) -27.2 eV
(c) Kinetic energy of II excited state of
\( \boldsymbol{H} e^{+} \)
(iii) +54.4 ev
(d) Ionisation potential of \( \boldsymbol{H} \boldsymbol{e}^{+} \)
(iv) \( -54.4 \mathrm{eV} \)
\( A \cdot a(i), b \) (ii) \( , c \) (iii), d (iv)
B. a (iv), b (iii), c (ii), d(i)
\( c \cdot a(i v), b(i i), c(i), d \) (iii)
D. a (ii), b (iii), c (i), d (iv)


What is an electromagnet ? List any two
uses


The oxidation of toluene to
benzaldehyde by chromyl chloride is called:
A. Etard reaction
B. Riemer - Tiemann reaction
c. Wurtz reaction
D. Cannizzaro's


A car travels first \( 30 \mathrm{km} \) with a uniform
speed of \( 60 \mathrm{kmh}^{-1} \) and then next 30
\( \mathrm{km} \) with a uniform speed of \( 40 \mathrm{kmh}^{-1} \)
Calculate the total time of journey,
A. 50 min
B. 75 min
\( c .60 \mathrm{min} \)
D. \( 100 \mathrm{min} \)


\( \triangle \boldsymbol{R} \boldsymbol{S} \boldsymbol{T} \sim \triangle \boldsymbol{U} \boldsymbol{A} \boldsymbol{Y} . \ln \triangle \boldsymbol{R} \boldsymbol{S} \boldsymbol{T}, \boldsymbol{R} \boldsymbol{S}= \)
\( 6 c m, \angle S=50^{\circ}, S T=7.5 \mathrm{cm} . \) The
corresponding sides of \( \triangle R S T \) and
\( \triangle U A Y \) are in the ratio \( 5: 4 . \) Construct
\( \triangle \boldsymbol{U} \boldsymbol{A} \boldsymbol{Y} \)


If \( \tan \theta=\frac{1}{\sqrt{5}} \) and \( \theta \) lies in the first
quadrant, the value of \( \cos \theta \) is
A \( \cdot \frac{1}{\sqrt{6}} \)
B. \( \frac{\sqrt{5}}{\sqrt{6}} \)
c. \( \frac{-1}{\sqrt{6}} \)
D. \( \frac{-\sqrt{5}}{\sqrt{6}} \)


Fill in the blanks:
A convex lens of \( _{\text {一一一一一一 }} \) focal length gives a greater magnification than lenses of \( _{\text {一一一一一一一 }} \) focal length.
A. short, short
B. short, long
c. long, short
D. Iong, long


A piece of metal weighs 45 g in air and \( 25 \mathrm{g} \) in a liquid of density \( 1.5 \times \) \( 10^{3} k g-m^{-3} \) kept at \( 30 C . \) When the
temperature of the liquid is raised to \( 40 C, \) the metal piece weighs 27 g. The density of liquid at \( 40 \mathrm{C} \) is \( 1.25 \times \) \( 10^{3} k g-m^{-3} . \) The coefficient of linear
expansion of metal is
A. \( 1.3 \times 10^{-3} / C \)
в. \( 5.2 \times 10^{-3} / C \)
c. \( 2.6 \times 10^{-3} / C \)
D. \( 0.26 \times 10^{-3} / C \)


By which way you can dispose the
useless chemicals?
A. The rule is to add concentrated acid to water slowly
B. Dispose of chemicals in the proper places following posted procedures. Do not return them to their original containers
C. Carefully replace unused or excess chemicals into their properly labeled containers from which they
came
D. Flush eyes with water at the eyewash fountain for at least 15 minutes, and then report the accident for further help
E. The rule is to add water to the concentrated acid slowly


ff \( \boldsymbol{f}: \boldsymbol{R}-\{\mathbf{0}\} \rightarrow \boldsymbol{R} \) is defined by
\( f(x)=x^{3}-\frac{1}{x^{3}} \) then show that \( f(x)+ \)
\( \boldsymbol{f}\left(\frac{1}{x}\right)=\mathbf{0} \)


Consider the barometer shown in figure.
Density of mercury is \( \rho . \) A small hole is
made at point \( S \) as shown. The
mercury comes out from this hole with
speed \( \boldsymbol{v} \) equal to :
A \( \cdot \sqrt{2 g h} \)
B. \( \sqrt{2 g H} \)
c. \( \sqrt{2 g(H-h)} \)
D. None of these


If the middle term of \( (1+x)^{2 n} \) is the
greatest term then \( x \) lies between
A. \( n-1<x<n \)
в. \( \frac{n}{n+1}<x<\frac{n+1}{n} \)
c. \( n<x<n+1 \)
D. \( \frac{n+1}{n}<x<\frac{n}{n+1} \)


State whether true or false:
The unit of voltage is \( J C^{-1} \)


The amyloplasts look like
A. Proplastids
B. Elaioplast
c. Aleuroplast
D. chloroplast


Probability that \( A \) speaks truth is \( \frac{4}{5} . A \) coin is tossed. A reports that a head appears. The probability that actually there was head is
A \( \cdot \frac{4}{5} \)
B. \( \frac{1}{2} \)
c. \( \frac{1}{5} \)
D. \( \frac{2}{5} \)


Sulphur is used in the of
rubber.
A. condensation
B. vulcanization
c. addition
D. substitution


A body is sliding down an inclined plane (angle of inclination \( 45^{\circ} \) ). If the coefficient of friction is 0.5 and \( g= \)
\( 9.8 m / s^{2}, \) then the downward
acceleration of the body in \( m / s^{2} \) is:
A \( \cdot \frac{4.9}{\sqrt{2}} \)
B. \( 4.9 \sqrt{2} \)
C. \( 19.2 \sqrt{2} \)
D. 4.9


Which of the following is not a disproportionation reaction?
\( N H_{4} N O_{3} \stackrel{\Delta}{\longrightarrow} N_{2} O+H_{2} O \)
II. \( \boldsymbol{P}_{4} \stackrel{\Delta}{\longrightarrow} \boldsymbol{P} \boldsymbol{H}_{3}+\boldsymbol{H} \boldsymbol{P} \boldsymbol{O}_{2}^{\ominus} \)
III. \( \boldsymbol{P C l}_{5} \stackrel{\boldsymbol{\Delta}}{\longrightarrow} \boldsymbol{P C l}_{3}+\boldsymbol{C l}_{2} \)
IV. \( \boldsymbol{I} \boldsymbol{O}_{3}^{\ominus}+\boldsymbol{I}^{\ominus} \longrightarrow \boldsymbol{I}_{2} \)
A . ।, ॥
B. I, III, IV
c. ॥, IV
D. ।, II


\( t \)


\( f * \) is a binary operation on set \( N \),of
natural no defined as \( a * b=H C F \) of
\( (a, b) . \) Evaluate \( 3 *(2 * 5) \)


Arrange the following values of \( n \) in ascending order.
\( \boldsymbol{A}:^{n} \boldsymbol{P}_{5}=^{n} \boldsymbol{P}_{6} \Rightarrow \boldsymbol{n}= \)
\( \boldsymbol{B}:^{\boldsymbol{n}} \boldsymbol{P}_{12}=^{\boldsymbol{n}} \boldsymbol{P}_{\boldsymbol{8}} \Rightarrow \boldsymbol{n}= \)
\( \boldsymbol{C}:^{n} \boldsymbol{C}_{(\boldsymbol{n}-\mathbf{3})}=\mathbf{1 0} \Rightarrow \boldsymbol{n}= \)
\( \boldsymbol{D}:^{(\boldsymbol{n}+1)} \boldsymbol{P}_{5}:^{\boldsymbol{n}} \boldsymbol{P}_{6}=\mathbf{1}: \boldsymbol{2} \Rightarrow \boldsymbol{n}= \)
\( A \). САВ D
в. САDВ
c. АСВD
D. DBAC


An example of chelating ligand is:
A \( \cdot N O_{2} \)
B. Chloro
c. Bromo
D. en


topp
grapillation Which one of the following
\( T= \) time peric
:


Expand: \( \left(a^{2}+4 b^{2}\right)(a+2 b)(a-2 b) \)


The table given below shows a list of
organisms and their methods of
reproduction
What do \( P, Q \) and \( R \) repersent?
\begin{tabular}{|l|c|}
\hline Organism & Method of reproduction \\
\hline Sponge & \( \mathrm{P} \) \\
Planaria & \( \mathrm{Q} \) \\
Hydra & \( \mathrm{R} \) \\
\hline
\end{tabular}
A. P- Fission, Q - Budding,
R - Regeneration
B. P- Sporulation, Q - Regeneration,
\( \mathrm{R} \) - Budding
C. P- Binary fission,
Q- Sporulation,
R - Regeneration
D. P - Gemmules, Q - Regeneration,
R - Budding


What does mean by mass defect? Establish relation between mass defect
and nuclear binding energy. And hence write the expression for binding energy per nucleon.


Find the sum of all 2 - digit numbers divisible by 3
A. 1335
в. 1445
\( c .1665 \)
D. 1555 55


Balance the following redox reaction \( \left(\boldsymbol{C r}_{2} \boldsymbol{O}_{7}\right)_{(a q)}^{2-}+\boldsymbol{F} \boldsymbol{e}_{(a q)}^{2+} \rightarrow \boldsymbol{C r}_{(a q)}^{3+}+\boldsymbol{F} \boldsymbol{e}_{(a q)}^{3+} \)
(acidic medium)


Fossils are present in metamorphic rocks. State true or false.
A. True
B. False


Which is correct in common Cockroach
A. Nitrogenous excretory product is urea.
B. Food is ground by mandibles and gizzard.
C. Malpighian tubules are excretory organs that project out from coelom.
D. Oxygen is transported by haemoglobin in blood.


Calculate the shortest and longest wavelengths in hydrogen spectrum of
Lyman series.


\( \int_{0}^{\pi / 2} \frac{1}{a^{2} \sin ^{2} x+b^{2} \cos ^{2} x} d x \)


Which of the following shows that the earth behaves as a magnet?
A. Repulsion between like poles
B. Attraction between unlike poles
C. Existence of null points in the magnetic field of a bar magnet
D. Non existence of monopoles


Explain why:
(a) An antacid tablet is taken when you suffer from acidity.
(b) Calamine solution is applied on the skin when an ant bites.
(c) Factory waste is neutralised before disposing it into the water bodies.


Two straight lines drawn on the same
displacement - time graph make an \( 30^{\circ} \)
and \( 60^{\circ} \) with time axis respectively as
shown in fig-1. What is the ratio of the
two velocities?
Figure -1


The sum \( \mathbf{V}_{\mathbf{1}}+\mathbf{V}_{\mathbf{2}}+\ldots+\mathbf{V}_{\mathbf{n}} \) is
A \( \cdot \frac{1}{12} \mathrm{n}(\mathrm{n}+1)\left(3 \mathrm{n}^{2}-\mathrm{n}+1\right) \)
B. \( \frac{1}{12} \mathrm{n}(\mathrm{n}+1)\left(3 \mathrm{n}^{2}+\mathrm{n}+2\right) \)
C \( \cdot \frac{1}{2} \mathrm{n}\left(2 \mathrm{n}^{2}-\mathrm{n}+1\right) \)
D \( \cdot \frac{1}{3}\left(2 \mathrm{n}^{3}-2 \mathrm{n}+3\right) \)


Name the largest kelp?


Difference between \( \Delta H \) and \( \Delta E \) for the
combustion of liquid benzene at \( 27^{\circ} \mathrm{C} \)
is:
A \( .7 .48 k J \)
в. \( 3.47 k J \)
c. \( 14.86 k J \)
D. \( 5.73 k J \)


Which of the meristem is responsible for secondary growth?
A. Apical
B. Lateral
c. Intercalary
D. Basal


A soft metal stored under kerosene is:
A. sodium (Na)
B. calcium(Ca)
c. lithium (Li)
D. magnesium (Mg)


State whether the given statement is true or false:
\( A g C l \) is less soluble in aqueous
sodium chloride solution than in pure
water
A. True
B. False


A body is said to be under balanced
forces when the resultant force acting
on the body is
A. Unity
B. zero
c. Infinite
D. None of these


Area bounded by the curves satisfying the conditions \( \frac{x^{2}}{25}+\frac{y^{2}}{36} \leq 1 \leq \frac{x}{5}+\frac{y}{6} \)
is given by
A \( \cdot 15\left(\frac{\pi}{2}+1\right) \) sq.units
B. \( \frac{15}{4}\left(\frac{\pi}{2}-1\right) \) sq.units
c. \( 30(\pi-1) \) sq.unit
D. \( \frac{15}{2}(\pi-2) \) sq.unit


Gravitational potential energy is
negative. This implies
A. Energy is rising along negative \( x \) axis
B. A particle is trapped in this potential
C. The particle is moving in the opposite direction
D. Energy is decreasing in the direction of motion of the particle


The experiment is to repeatedly toss a coin until first tail shows up. Identify the type of the sample space.
A. Finite sample space
B. Continuous sample space
c. Infinite discrete sample space
D. None of these


If \( \vec{a}=\hat{i}+\hat{j}+\hat{k}, \vec{b}=\hat{i}+\hat{j}-\hat{k}, \vec{c}=\hat{i}- \)
\( \hat{j}+\hat{k} \) and \( \overrightarrow{\boldsymbol{d}}=\hat{\mathbf{i}}-\hat{\mathbf{j}}-\hat{\boldsymbol{k}}, \) then \( (\overrightarrow{\boldsymbol{a}} \times \overrightarrow{\boldsymbol{b}}) \times \)
\( (\vec{c} \times \vec{d})= \)
A . 0
B . \( 3 \hat{i}-5 \hat{j}+7 \hat{k} \)
c. \( 5 \hat{j}-8 \hat{k} \)
D. - \( -8 \hat{k} \)


Which one of the following does not undergo sublimation?
A. iodine
B. sodium chloride
c. ammonium chloride
D. None of these


at opposite sides of an infinitely long straight conducting wire as shown in the figure. If current in the wire is slowly
decreased, then the direction of the
nduced current will be :
A. clockwise in \( A \) and anticlockwise in \( B \)
3. anticlockwise in \( A \) and clockwise in \( B \)
c. clockwise in both \( A \) and \( B \)
D. anticlockwise in both \( A \) and \( B \)


What concentration of \( \boldsymbol{F}- \)
\( \boldsymbol{C H}_{2} \boldsymbol{C O O H},\left(\boldsymbol{K}_{\boldsymbol{a}}=\boldsymbol{2} \boldsymbol{6} \times \mathbf{1 0}^{-\boldsymbol{3}}\right) \) is
needed so that \( \left[\boldsymbol{H}^{+}\right]=\mathbf{2} \times \mathbf{1 0}^{-\mathbf{3}} \) ?
A \( \cdot 1.53 \times 10^{-3} M \)
В. \( 2.6 \times 10^{-3} M \)
c. \( 5.2 \times 10^{-3} M \)
D. \( 3.53 \times 10^{-3} \) М


Solve \( \sqrt{\frac{x^{2}-a^{2}}{x}} d x \)


The order of basic character of given
oxides is :
A. \( N a_{2} O>M g O>A l_{2} O_{3}>C u O \)
в. \( M g O>A l_{2} O_{3}>C u O>N a_{2} O \)
c. \( A l_{2} O_{3}>M g O>C u O>N a_{2} O \)
D. \( C u O>N a_{2} O>M g O>A l_{2} O_{3} \)


Biosystematics aims at
A. The classification of organisms based on the morphological characters
B. Identification and arrangement of organisms on the basis of their cytological characteristics
C. Delimiting various taxa of organisms and establishing their relationship
D. The classification of organisms based on their evolutionary history and establishing their phylogeny on the totality of various parameters from all fields of studies


How does the force of gravitation, between two bodies change when the distance between them is reduced to
half?
A. It is halved
B. It is doubled
c. It is quadrupled
D. It remains unaffected


If \( h \) is Plancks constant, the
momentum of a photon of wavelength
\( 0.01 A^{\circ} \) is
\( \mathbf{A} \cdot 10^{-2} h \)
B. \( h \)
\( c \cdot 10^{2} \)
D. \( 10^{12} h \)


Out of 25 children in a class, 15 are girls What is the percentage of girls?


Q Type your question
columns each of length \( l \), cross
sectional radius \( r \) and young's
modulus \( Y \). What should be the
minimum cross - section radius \( r, \) so
that the beam bearing more load, can
escape from buckling?
\( \left(\frac{m g l^{2}}{\pi^{3} Y}\right)^{1 / 4} \)
\( ^{\mathrm{B}}\left(\frac{2 m g l^{2}}{3 \pi^{3} Y}\right)^{1 / 4} \)
\( \left(\frac{m g l^{2}}{3 \pi^{3} Y}\right)^{1 / 4} \)
\( \left(\frac{3 m g l^{2}}{2 \pi^{3} Y}\right)^{1 / 4} \)


Find the mean for the following distribution
\( \begin{array}{lllll}\text { Marks } & \begin{array}{l}10- \\ 20\end{array} & \begin{array}{l}20- \\ 30\end{array} & \begin{array}{l}\text { 30- } \\ 40\end{array} & \begin{array}{l}\text { 40- } \\ 50\end{array}\end{array} \)
Frequency 6 8 13


The wavelength of de broglie waves associated with a beam of protons of
kinetic energy \( 5 \times 10^{2} \mathrm{eV} \)
(Mass of each photon \( =\mathbf{1 . 6 7} \times \mathbf{1 0}^{-\mathbf{2 7}} \mathbf{K g} \)
\( \boldsymbol{h}=\mathbf{6 . 6 2} \times \mathbf{1 0}^{-\mathbf{3 4}} \mathbf{J s} \)
A. \( 2.42 \times 10^{-12} \mathrm{m} \)
B . \( 4.24 \times 10^{-12} \mathrm{m} \)
c. \( 1.82 \times 10^{-12} \mathrm{m} \)
D. \( 1.28 \times 10^{-12} \mathrm{m} \)


For the equilibrium, \( \boldsymbol{P C l}_{5} \leftrightharpoons \boldsymbol{P C l}_{3}+ \)
\( C l_{2} ; K_{c}=\frac{\alpha^{2}}{1-\alpha} V, \) temperature
remaining constant. Then:
A . \( K_{c} \) will decrease with increase in volume
B. \( K_{c} \) will increase with increase in volume
C. \( K_{c} \) will not change with the change in volume
D. \( K_{c} \) may increase or decrease with the change in volume depending upon its numerical value


Assertion
The mobility of sodium ion is lower than that of potassium ion.
Reason
The ionic mobilities depend on the effective radius of the ion.
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 difference in molecular weight
between two successive compounds in alkane homologous series is


Latent heat of fusion of ice is:
A \( .336 k J k g^{-1} \)
в. \( 663 k J k g^{-1} \)
c. \( 363 k J k g^{-1} \)
D. \( 636 k J k g^{-1} \)


Find the product of \( (\boldsymbol{m}-\mathbf{1})(\boldsymbol{m}- \)
2)\( (m-3) \)


Anagrams are made by using the letters
of the word \( ^{\prime} \boldsymbol{H} \boldsymbol{I} \boldsymbol{N} \boldsymbol{D} \boldsymbol{U} \boldsymbol{S} \boldsymbol{T} \boldsymbol{A} \boldsymbol{N}^{\prime} \) In how
many of these anagrams do the vowels
and consonants occupy the same relative positions as in
IHINDUST \( \boldsymbol{A} \boldsymbol{N}^{\prime} \)


\( \lim _{x \rightarrow 1}\left(\frac{1}{x-1}-\frac{2}{x^{2}-1}\right)= \)
A . 1 3
B. \( \frac{-1}{2} \)
\( c \cdot \frac{1}{2} \)
D. \( \frac{-1}{3} \)


Steam at \( 100^{\circ} \mathrm{C} \) is added slowly to
\( 1400 g m \) of water at \( 16^{\circ} C \) until the
temperature of water is raised to \( 80^{\circ} \mathrm{C} \)
The mass of steam required to do this is
\( \left(\boldsymbol{L}_{\boldsymbol{v}}=\mathbf{5 4 0} \boldsymbol{c a l} / \boldsymbol{g m}\right) \)
A \( .160 g m \)
В. \( 125 \mathrm{gm} \)
\( \mathrm{c} .250 \mathrm{gm} \)
D. \( 320 g m \)


Choose the correct order of excretory organs in cockroach, earthworm and
rabbit respectively.
A. skin, Malpighian tubules and kidney
B. Malpighian tubules, nephridia and kidney
c. Nephridia, Malpighian tubules and kidney
D. Nephridia, kidney and green gland


If the lines \( \frac{x-1}{2}=\frac{y+1}{3}=\frac{z}{5 t-1} \)
and \( \frac{\boldsymbol{x}+\mathbf{1}}{\mathbf{2} \boldsymbol{s}+\mathbf{1}}=\frac{\boldsymbol{y}}{\mathbf{2}}=\frac{\boldsymbol{z}}{\mathbf{4}} \) are parallel to
each other, then value of s,t will be
A \( \cdot_{6,} \frac{5}{7} \)
B. \( \frac{1}{2}, 1 \)
c. \( _{3,} \frac{5}{7} \)
D. \( 4, \frac{7}{10} \)


Calculate the degree of ionization of
\( 0.05 \mathrm{M} \) acetic acid if its \( \boldsymbol{P} \boldsymbol{K}_{\boldsymbol{a}} \) value is
4.74. How is the degree of dissociation
affected when its solution also contains
(a) \( 0.01 \mathrm{M} \)
(b) \( 0.1 \mathrm{M} \) in \( H C l ? \)


If \( \boldsymbol{A}=\left[\begin{array}{ll}\boldsymbol{\alpha} & \mathbf{0} \\ \mathbf{1} & \mathbf{1}\end{array}\right] \) and \( \boldsymbol{B}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{0} \\ \mathbf{5} & \mathbf{1}\end{array}\right], \) then
value of \( \alpha \) for which \( A^{2}=B \), is
A .
B. -
\( c \cdot 4 \)
D. No real value


\( \frac{\boldsymbol{x} \boldsymbol{y}}{\boldsymbol{x}+\boldsymbol{y}}=\frac{\boldsymbol{6}}{\mathbf{5}} \)
\( \frac{x y}{y-x}=6 \)
A. \( x=-2, y=3 \)
в. \( x=3, y=2 \)
c. \( x=2, y=3 \)
D. \( x=-3, y=-2 \)


\( \sin ^{-1}\left(3 x-2-x^{2}\right)+\cos ^{-1}\left(x^{2}-4 x+\right. \)
3) \( =\frac{\pi}{4} \) can have a solution for \( x \epsilon \)
A . [1,2]
B \( \cdot\left(\frac{3+\sqrt{5}}{2}, 2+\sqrt{2}\right) \)
\( \left(\frac{3-\sqrt{5}}{2}, 2-\sqrt{2}\right) \)
D \( \cdot\left(2-\sqrt{2}, \frac{3-\sqrt{5}}{2}\right) \cup\left(\frac{3-\sqrt{5}}{2}, 2+\sqrt{2}\right) \cup\{2\} \)


Find the \( 20^{t h} \) term of an A.P. whose \( 5^{t h} \)
term is 15 and the sum of its \( 3^{r d} \) and \( 8^{t h} \)
terms is 34


Derive an expression for the magnetic induction at a point on the axis of a current carrying circular coil using Biot-Savart law.


Which of the following species have undistorted octahedral structures?
1. \( \boldsymbol{S F}_{\mathbf{6}} \)
2. \( \boldsymbol{P F}_{\mathbf{6}}^{-} \)
3. \( \boldsymbol{S} \boldsymbol{i} \boldsymbol{F}_{\boldsymbol{6}}^{2-} \)
4. \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{\boldsymbol{6}} \)
A. 2,3 and 4
B. 1,3 and 4
\( c .2 \) and 3
D. 1,2 and 3


How does respiration occur in the stem of the plant?


Say true or false.
The volume of a sphere is equal to twothird of the volume of a cylinder whose height and diameter are equal to the
diameter of the sphere.
A. True
B. False


Give the target gland for
gonadotrophins (LH and FSH).


\( \cos x+\cos y=\frac{4}{5}, \cos x-\cos y=\frac{2}{7} \)
The value of \( 14 \tan \left(\frac{x-y}{2}\right)+ \)
\( \mathbf{5} \cot \left(\frac{\boldsymbol{x}+\boldsymbol{y}}{\mathbf{2}}\right) \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot \frac{5}{4} \)
D.


\( A B \| D E \). Find the measure of \( \angle A O D \)


A projectile aimed at a mark which is in
the horizontal plane through the point of projection falls a cm short of it when the
elevation is \( \alpha \) and goes \( b c m \) too far
when the elevation is \( \beta . \) Show that if the
velocity of projection is same in all the case, the proper elevation is \( \frac{1}{2} \sin ^{-1}\left[\frac{b \sin 2 \alpha+a \sin 2 \beta}{a+b}\right] \)


If \( \boldsymbol{P}(\boldsymbol{A})=\mathbf{0 . 7}, \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 5 5}, \boldsymbol{P}(\boldsymbol{C})= \)
\( \mathbf{0 . 5}, \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})=\boldsymbol{x}, \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{C})= \)
\( \mathbf{0 . 4 5}, \boldsymbol{P}(\boldsymbol{B} \cap \boldsymbol{C})=\mathbf{0 . 3} \) and \( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B} \cap \)
\( C)=0.2, \) then
A. \( 0.2 \leq x \leq 0.45 \)
в. \( 0.2 \leq x \leq 0.5 \)
c. \( 0.2 \leq x \leq 0.65 \)
D. \( 0.2 \leq x \leq 1 \)


An infinitely long time charge having a uniform charge per unit length \( \lambda \) lies at a distance d from a point 0 as shown in Fig. Determine the total electric flux
through the surface of sphere of radius
R centered at 0 resulting from this line charge. Consider both cases where Rd.
\( A \)
B. \( \frac{7 \lambda \sqrt{R^{2}-d^{3}}}{\varepsilon_{0}} \)
c. \( \frac{7 \lambda \sqrt{R^{2}-d^{2}}}{2 \varepsilon_{0}} \)
\( D \)


What is the function of
sclerenchymatous tissue?
A. Flexibilty
B. Tenderness
c. strength
D. All of the above


The bond order of a molecule is given by:
A. the difference between the number of electrons in
bonding and antibonding orbitals
B. total number of electrons in bonding and antibonding orbitals
C. twice the difference between the number of electrons in bonding and antibonding orbitals
D. half the difference number of electrons in bonding and antibonding orbitals


If angle of repose is \( 30^{\circ}, \) then coefficient of friction will be
\( \mathbf{A} \cdot \mathbf{1} \)
B . 15
c. \( \frac{1}{\sqrt{3}} \)
D. \( \frac{\sqrt{3}}{2} \)


Bundle of His is a network of
A. Nerve fibres found throughout the heart
B. Muscle fibres distributed throughout the heart walls
C. Muscle fibres found only in the ventricle wall
D. Nerve fibres distributed in ventricles


A battery of emf \( E_{0}=12 \mathrm{V} \) is connected across a \( 4 \mathrm{m} \) long uniform wire having
resistance \( \frac{4 \Omega}{m} . \) The cells of small emfs \( \varepsilon_{1} \)
\( =2 V \) and \( \varepsilon_{2}=4 V \) having internal
resistance \( 2 \Omega \) and \( 6 \Omega \) respectively, are connected as shown in the figure. If
galvanometer shows no deflection at the point \( \mathrm{N} \), find the distance of point \( \mathrm{N} \)
from the point \( \mathbf{A} \)


The oxidation number of carboxylic
carbon atom in \( C H_{3} C O O H \) is


Correct wrong statements if found any from those given below:
(a) When difference in electronegativity increases, the possibility of covalent bonding increases.
(b) Electronegativity increases while moving from left to right along a period.
(c) lonic bond is present in \( \boldsymbol{H} \boldsymbol{C l} \) molecule.
(d) Partial ionic bond is also there in
polar molecule


Shrutii secured \( 60 \% \) marks in
Mathematics \( 55 \% \) in english and \( 60 \% \) in Hindi. If the maximum marks in the
subject were 75,60 and 65 respectively, find her aggregate percentage of mark.


Which of the following is general electron configuration of \( 4 d \) series?
\( \mathbf{A} \cdot 4 s^{1+o 2} 3 d^{1+t 01} \)
B. \( 4 s^{1 t o 2} 4 d^{1+t 01} \)
\( \mathbf{c} \cdot 5 s^{1 t o 2} 5 d^{1 t o 10} \)
D. \( 5 s^{1 \operatorname{to} 2} 4 d^{1 \text { lto } 10} \)


Match the following:
Biodegradable \( \mathbf{F} \)
(i) \( \quad(p) \quad \) Hydroxybuta B
p polymer poing
(ii) Phenol
2-chlorobuta-1
(ii) Bakelite
(ig) Phenol
Neoprene
(iv) Glyptal
(r) 2-chlore
diene
(iii) 2-chlo
diene
\( \mathbf{A} \cdot i-p, i i-q, i i i-r, i v-s \)
B \( . i-q, i i-p, i i i-r, i v-s \)
\( \mathbf{c} \cdot i-p, i i-q, i i i-s, i v-r \)
D. \( i-s, i i-r, \) ii \( i-p, i v-q \)


A solution prepared by dissolving a \( 2.50 g \) sample of an unknown compound dissolved in \( 34.0 g \) of benzene,
\( C_{6} H_{6} \) boils at \( 1.38^{\circ} C \) higher than pure benzene. Which expression gives the molar mass of the unknown compound
\( ? \)
Compound \( K_{b} \)
\( \boldsymbol{C}_{6} \boldsymbol{H}_{6} \quad \boldsymbol{2 . 5 3}^{\circ} \boldsymbol{C} \cdot \boldsymbol{m}^{-1} \)
A \( \cdot 2.53 \times \frac{2.50}{1.38} \)
в. \( _{1.38} \times \frac{34.0}{2.53} \times 2.50 \)
c. \( 2.50 \times 10^{3} \times \frac{2.53}{34.0} \times \frac{1}{1.38} \)
D. \( 2.50 \times 10^{3} \times \frac{1.38}{34.0} \times 2.53 \)


Find the total cost of wooden fencing around a circular garden of diameter \( 28 m . \) If \( 1 m \) of fencing costs 2300


A sinusoidal voltage \( V=200 \sin 314 t \)
is applied to a \( 10 \Omega \) resistor. Find rms
voltage.
A . \( 141.4 V \)
B. \( 314.2 V \)
c. \( 519.6 V \)
D. 278.9V


Divide as directed.
\( \mathbf{5} 2 p q r(p+q)(q+r)(r+p) \div \)
\( \mathbf{1 0 4 p q}(\boldsymbol{q}+\boldsymbol{r})(\boldsymbol{r}+\boldsymbol{p}) \)


The straight lines \( \mathbf{x}+\mathbf{2 y}-\mathbf{9}=\mathbf{0}, \mathbf{3 x}+ \)
\( 5 y-5=0 \) and \( a x+b y-1=0 \) are
concurrent if the straight line \( 22 x- \)
\( 35 y-1=0 \) passes through the point
\( A \cdot(a, b) \)
в. \( (b, a) \)
c. \( (-a, b) \)
D. (-a,-b)


What is the correct way of writing a
scientific name ? Illustrate with
example.


Wavelength of a laser beam can be used as a standard of:
A. time
B. temperature
c. angle
D. length


Vitamin A is essential for good
eyesight.
A. True
B. False


The air which is taken in or given out during a single breath is known as
A. Residual air
B. Vital air
c. Tidal air
D. All of the above


A natural growth regulator is
A. \( 2,4- \) D
B. Benzaldehyde
c. NAA
D. Ethylene


Which one of the following statements
can best explain the term critical
concentration of an essential element?
A. Essential element concentration below which plant growth is retarded
B. Essential element concentration below which plant growth becomes enhanced
C. Essential element concentration below which plant remains in the vegetative phase
D. None of the above


The function \( \mathbf{f}(\mathbf{x})=\mathbf{2} \log (\mathbf{x}-\mathbf{3})- \)
\( x^{2}+6 x+3 \) increases in the interval
A . (3,4)
в. \( (-\infty, 2) \)
\( c \cdot(3, \infty) \)
D. None ot these


The IUPAC name of
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{\mathbf{3}}\right)_{\boldsymbol{6}}\right]\left[\boldsymbol{C r}\left(\boldsymbol{C}_{\boldsymbol{2}} \boldsymbol{O}_{\boldsymbol{4}}\right)_{\boldsymbol{3}}\right] \)
is
A. Hexaamminecobalt (III) tris (Oxalato) chromate (III)
B. Hexaamminecobalt (III) tris (Oxalato) chromium (III)
C. Hexaamminecobalt (II) tris (Oxalato) chromium (III)
D. Hexaamminecobalt (III) trisoxalatochromate (III)


Find differential equation of all circles in the first quadrant which touch the co-ordinate axis.


is a degradation phenomenon in which the electrons in a plastic are so strongly attracted to
oxygen atoms.
A. Oxidation
B. Reduction
c. Hydrolysis
D. Polymerization


Name the top view of the diagram.
A. pentagon
B. square
C . rectangle
D. triangle


A charge \( Q \) is distributed over two
concentric hollow spheres of radii \( a \) and \( b(a>b), \) so that the surface charge
densities are equal. The potential at the common centre is \( \frac{1}{4 \pi \epsilon_{0}} \) times
A \( \cdot k Q\left(\frac{a+b}{a^{2}+b^{2}}\right) \)
в. \( 2 Q\left(\frac{a+b}{a^{2}+b^{2}}\right) \)
\( c \cdot Q \)
D. \( \frac{Q}{2}\left(\frac{a+b}{a^{2}+b^{2}}\right) \)
E \( \cdot \frac{Q}{4}\left(\frac{a+b}{a^{2}+b^{2}}\right) \)


If the major axis of an ellipse is three times the minor axis, then its
eccentricity is equal to
A \( \cdot \frac{1}{3} \)
B. \( \frac{1}{\sqrt{3}} \)
c. \( \frac{1}{\sqrt{2}} \)
D. \( \frac{2 \sqrt{2}}{3} \)
E \( \frac{2}{3 \sqrt{2}} \)


If \( f(z)=\frac{1-z^{3}}{1-z}, \) where \( z=x+i y \) with \( z \neq 1, \) then \( R e \overline{\{f(z)\}}=0 \) reduces to
A \( \cdot x^{2}+y^{2}+x+1=0 \)
B . \( x^{2}-y^{2}+x-1=0 \)
c. \( x^{2}-y^{2}-x+1=0 \)
D. \( x^{2}-y^{2}+x+1=0 \)
E \( \cdot x^{2}-y^{2}+x+2=0 \)


Give a brief account of the counter
current mechanism.


A copper rod of length \( l \) is rotated about one end, perpendicular to the uniform
magnetic field \( B \) with constant angular velocity \( \omega . \) The induced emf between
two ends of the rod is:
A \( \cdot \frac{1}{2} B \omega l^{2} \)
в. \( B \omega l^{2} \)
c. \( \frac{3}{2} B \omega l^{2} \)
D . \( 2 B \omega l^{2} \)


Describe a method to determine the
specific heat capacity of a solid, like a piece of copper.
\( A \)


With the help of the given clues, unscramble the letters to make a
meaningful word. RAYXLN (produces sound in humans)


The angles of dip at the poles and the equator respectively are.
A . \( 30^{\circ}, 60^{\circ} \)
B . \( 0^{\circ}, 90^{\circ} \)
c. \( 45^{\circ}, 90^{\circ} \)
D. \( 90^{\circ}, 0^{\circ} \)


Sulphate of an alkaline earth metal which crystalizes without water of hydration is?
\( A \cdot B e^{2} \)
в. \( M g^{2+} \)
c. \( C a^{2+} \)
\( D \cdot S r^{2} \)


The energy required to raise a given volume of water from a well can be
A. Mega watts
B. Mega newton
c. Mega joules
D. Kilo watts


Which of these can be one of the uses of
colloids?
A. Colloids act as transport vector
B. Colloids are used in intravenous therapy
C. Movement of enzyme molecules in water is because of colloid action
D. All of the above


A buffer solution made up of \( B O H \) and
\( B C l \) of total molarity \( 0.29 \mathrm{M} \) has \( p H= \) 9.6 and \( K_{b}=1.8 \times 10^{-5} \)
Concentration of salt and base
respectively is:
A. \( 0.09 \mathrm{M} \) and \( 0.2 \mathrm{M} \)
B. 0.2 M and 0.09 M
c. \( 0.1 \mathrm{M} \) and \( 0.19 \mathrm{M} \)
D. 0.19 M and 0.1 M


Keeping the number of moles, volume and pressure the same, which of the following are the same for all ideal gas?
A. rms speed of a molecule
B. density
c. temperature
D. average of magnitude of momentum


How many 3 -digit even numbers can be formed from the digits 1,2,3,4,5,6 if the digits can be repeated?
A \( \cdot 108 \)
B. 98
c. 72
D. 112


is a grade between lignite and anthracite.
A. Steam coal
B. Bituminous coal
c. Graphite
D. None of the above


If the position vector of a point (-4,-3)
be \( \vec{a}, \) find \( |\vec{a}| \)


Define RQ. What is its value for fats?


Orbital speed of an artificial satellite very close to earth's surface is V. Its orbital speed at a height equal to three
times the radius of the earth from the
earth's surface is:
\( A \cdot v \)
B. v/2
\( c \cdot 2 v \)
\( D \cdot v / 4 \)


In which of the following era man was originated?
A. Paleocene
B. Pliocene
c. Miocene
D. Devonian


If a simple harmonic motion is represent by \( \frac{d^{2} x}{d t^{2}}+a x=0, \) its time period is
A \( \cdot \frac{2 \pi}{\alpha} \)
в. \( \frac{2 \pi}{\sqrt{\alpha}} \)
\( c \cdot 2 \pi \alpha \)
D. \( 2 \pi \sqrt{\alpha} \)


The process used for purification of
\( A l_{2} O_{3} \cdot 2 H_{2} O \) is:
A . Magnetic separation
B. Froth flotation
c. Leaching
D. Liquation


In Ostwald process of manufacturing of \( H N O_{3} \) catalyst used is:
A. Mo
B. Fe
c. мn
D. Pt


If 10 million electrons are removed from a
neutral body, then the charge on the body
is :
A \( \cdot 1.2 \times 10^{-12} C \)
B. \( +1.6 \times 10^{-12} C \)
c. \( -1.6 \times 10^{-13} C \)
D. \( 10^{-12} C \)


Which of the following is used to adsorb
water?
A. Silica gel
B. Anhydrous \( C a C l_{2} \)
c. coal
D. coke


Calculate, \( \sqrt[4]{-1 \frac{1}{2}-i \frac{\sqrt{3}}{2}} \)


A mass of diatomic gas \( (\gamma=1.4) \) at a
pressure of 2 atm is compressed adiabatically so that its temperature
rise from \( 27^{\circ} \mathrm{C} \) to \( 927^{\circ} \mathrm{C} \). The pressure
of the gas is final state is
A .28 atm
B. 68.7 atm
c. 256 atm
D. 8 atm


An isosceles glass prism with angles
\( 40^{\circ} \) is clamped over a tray of water in a position such that the base is just dipped in water. A ray of light incident normally on the inclined face suffers
total internal reflection at the base. If
the refractive index of water is 1.33 then
the condition imposed on the refractive
index \( \mu \) of the glass is :
A \( . \quad \mu<2.07 \)
в. \( \mu>2.07 \)
c. \( \mu<1.74 \)
D. \( \mu>1.74 \)


The soft-iron core of an electromagnet loses its magnetism once the current passing through the electromagnetic coil stops because
A. Domains lose their alignment when the current is stopped
B. Iron cannot hold alignment for longer time even when the current is passing through the coil
c. Magnetic properties of iron are weak
D. Domains inside the iron get aligned in north to south direction


A circular coil of radius \( 10 \mathrm{cm}, 500 \)
turns and resistance \( 2 \Omega \) is placed with
its plane perpendicular to the horizontal component of the earth's magnetic field
If is rotated about its vertical diameter
through \( 180^{\circ} m \) in \( 0.25 s . \) The current induced in the coil is
(Horizontal component of the earth's magnetic field at that place is \( 3.0 \times \) \( \left.10^{-5} T\right) \)
A \( \cdot 1.9 \times 10^{-3} A \)
A \( .1 .9 \times 10^{-3} \)
B . \( 2.9 \times 10^{-3} A \)
\( \mathbf{c} \cdot 3.9 \times 10^{-3} A \)
D. \( 4.9 \times 10^{-3} A \)


a parallel glass slab at a point \( A, \) as
shown in the given figure. It undergoes partial reflection and
refraction. At each reflection \( 25 \% \) of
incident energy is reflected. The rays
\( A B \) and \( A^{\prime} B^{\prime} \) undergo interference. The
1 max ratio \( \frac{\text { nunce is }}{\text { : }} \) is \( \boldsymbol{I}_{m i} \)
\( A \cdot 4: 1 \)
B. 8: 1
c. 7:
29


\( 92 U^{238} \rightarrow 82 p b^{206}+8_{2}^{4} H e . \) The number
of \( \beta \) particles released in this reaction
is :
\( \mathbf{A} \cdot \mathbf{6} \)
B. 3
c. 1
D. 10


State whether true or false.
The line drawn perpendicular to the mirror at the point of incidence is called the reflected ray.
A. True
B. False


For the three events \( A, B \) and \( C, P \)
(exactly one of the events \( \boldsymbol{A} \) or \( \boldsymbol{B} \) occurs \( )=P(\text { exactly one of the events } B \) or \( C \text { occurs })=P( \) exactly one of the events \( C \text { or } A \text { occurs })=p \) and \( P( \) all the
three events occur simultaneously) \( = \)
\( p^{2}, \) where \( 0<p<1 / 2 . \) Then the
probability of at least one of the three events \( A, B \) and \( C \) occurring is
\( ^{\mathrm{A}} \cdot \frac{3 p+2 p^{2}}{2} \)
\( ^{\text {В } \cdot \frac{p+3 p^{2}}{4}} \)
c. \( \frac{p+3 p^{2}}{2} \)
\( \frac{3 p+2 p^{2}}{4} \)


Rhombus PQRB is inscribed in \( \triangle \boldsymbol{A B C} \)
such that \( \angle B \) is one of the its angle, \( P, Q \)
and \( \mathrm{R} \) lie on \( \mathrm{AB}, \mathrm{AC} \) and \( \mathrm{BC} \) respectively. If \( A B=12 \mathrm{cm} \) and \( B C=6 \mathrm{cm} \) find the
sides of rhombus PQRB.


Let \( A=\{1,2,3\} . \) Then number of
relations containing (1,2) and (1,3) which are reflexive and symmetric but not transitive is
A .
B. 2
\( c \cdot 3 \)
D. 4


Which among the following is/are natural source(s) of organic
compounds?
A . coal
B. natural gas
c. petroleum
D. all of the above


When does the truth value of the
statement \( (\boldsymbol{p} \vee \boldsymbol{r}) \Leftrightarrow(\boldsymbol{q} \vee \boldsymbol{r}) \) become
true?
A . p is true, q is true
B. p is false, q is false
c. p is true, r is true
D. Both (1) and (3)


what could be the possible values of \( x \)
when, \( [\mathbf{2 x}]=[\boldsymbol{x}] \)


Differentiate the following with respect
to \( \boldsymbol{x} \)
\( \cos ^{-1}[\sqrt{\frac{1+x}{2}}],-1<x<1 \)


Two cells of emf \( 4 V \) and \( 2 V \) and
internal resistance \( 2 \Omega \) and \( 1 \Omega \)
respectively are connected in parallel so
as to send the current in the same
direction through an external resistance of \( 10 \Omega \). Find the potential difference across \( 10 \Omega \) resistor.


When the temperature of an iron sphere
of mass \( 1 \mathrm{kg} \) falls from \( 30^{\circ} \mathrm{C} \) to \( 25^{\circ} \mathrm{C} \) the 550 calories of heat are released The
heat capacity of iron sphere will be in
cal/o \( _{C} \)
A . 110
B. 220
\( c \cdot 330 \)
D. 440


Construct a \( \triangle A B C, \) when \( A B= \)
\( A C, B C=6.0 \mathrm{cm} \) and \( \angle B=45^{\circ} \)


If \( f(x)=\left(a x^{2}+b\right)^{3} \) then a function
\( g(x) \) such that \( f(g(x))=g(f(x)) \) is given by
A \( , \quad g(x)=\left(\frac{b-x^{1 / 3}}{a}\right)^{1 / 2} \)
B. \( g(x)=\frac{1}{\left(a x^{2}+b\right)^{3}} \)
c. \( g(x)=\left(a x^{2}+b\right)^{1 / 3} \)
\( g(x)=\left(\frac{x^{1 / 3}-b}{a}\right)^{1 / 2} \)


Find:
\( \lim _{x \rightarrow 0} \frac{\sin x-x+\frac{1}{6} x^{3}}{x^{3}} \)


The number of different 7 -digit telephone numbers that can be formed
by using 0,1,2,3,4,5,6,7,8,9 is :
A \( \cdot 10^{7} \)
B. \( 9 \times 10^{6} \)
\( c .9 ! \)
D. None of these


Separation of isotopes can be made by:
This question has multiple correct options
A. gaseous diffusion
B. thermal diffusion
c. distillation
D. ultra centrifuge
E. electromagnetic separation
F. laser spectrata


The element which could be extracted
by electrolytic reduction of its oxide dissolved in a high temperature melt is:
A. sodium
B. magnesium
C. flourine
D. aluminium


Molecule which contains only sigma bonds in it is:
A. Pentene
B. Pentane
c. Pentadiene
D. Pentyne


Following are the ionisation potential values of :
\( \left(I_{1}\right) 899 k J m o l^{-1},\left(I_{2}\right) 1757 k J m o l^{-1},\left(I_{3}\right. \)
A. Na
B.
c. Ве
D. Ne


The specific heat of a metal is 0.16 cal/g approximate atomic weight would be:
A . 40
B. 16
\( c .32 \)
D. 64


Find the value of \( x \) if \( a \) and \( b \) are in
direct proportion
\( \begin{array}{ccccc}a & 2 & 3 & 4 & 5 \\ b & 14 & 21 & x & 35\end{array} \)
A . 16
в. 25
c. 27
D. 28


The equations \( a x+b y+c=0 \) and
\( \boldsymbol{d} \boldsymbol{x}+\boldsymbol{e} \boldsymbol{y}+\boldsymbol{f}=\boldsymbol{0} \) represent the same
straight line if and only if
A \( \cdot \frac{a}{d}=\frac{b}{c} \)
в. \( c=f \)
c. \( \frac{a}{d}=\frac{b}{e}=\frac{c}{f} \)
D. \( a=d, b=e, c=f \)


The heat of combustion of \( C H_{4}(g), C \)
(graphite) and \( H_{4}(g) \) are respectively \( -20 k . c a l,-40 k . c a l \) and \( -10 k . c a l . \) The heat
of formation of \( \mathrm{CH}_{4} \) is
A. \( -40 K \). cal
в. \( +40 K . c a l \)
c. \( -80 K . c a l \)
D. \( +80 K . c a l \)


Q Type your question
\( \mathbf{A} \cdot 2 C H_{3} C O O H+N a_{2} C O_{3} \rightarrow 2 C H_{3} C O O N a+H_{2} O+ \)
\( C O_{2} \) (Test tube \( B \) )
\( \left.C a(O H)_{2}+C O_{2} \rightarrow C a C O_{3}+H_{2} O \text { (Test tube } A\right) \)
B \( \cdot 2 C H_{3} C O O H+N a_{2} C O_{3} \rightarrow 2 C H_{3} C O O N a+H_{2} O+ \)
\( C O_{2}(\text { Test tube } A) \)
\( \left.C a(O H)_{2}+C O_{2} \rightarrow C a C O_{3}+H_{2} O \text { (Test tube } B\right) \)
\( \mathbf{c} \cdot C H_{3} C O O H+N a_{2} C O_{3} \rightarrow C H_{3} C O O N a+H_{2} O+ \)
\( C O_{2}(\text { Test tube } A) \)
\( \left.C a(O H)_{2}+C O_{2} \rightarrow C a C O_{3}+H_{2} \text { (Test tube } B\right) \)
D \( \cdot 2 C H_{3} C O O H+N a_{2} C O_{3} \rightarrow 2 C H_{3} C O O N a+H_{2} O+ \)
\( C O \text { (Test tube } A) \)
\( \left.\mathrm{Ca}(\mathrm{OH})_{2}+\mathrm{CO}_{2} \rightarrow \mathrm{CaCO}_{3}+\mathrm{H}_{2} \mathrm{O} \text { (Test tube } B\right) \)


Substances that are not broken down by
biological processes are said to be


A capacitor consists of two metal plates each \( 10 \mathrm{cm} \) by \( 20 \mathrm{cm} ; \) they are separated by a 2.0 mm thick insulator
with dielectric constant 4.1 and
dielectric strength \( 6.0107 \mathrm{V} / \mathrm{m} . \) What is
the capacitance in \( \boldsymbol{p} \boldsymbol{F}\left(\mathbf{1 0}^{-12} \boldsymbol{F}\right) ? \)
A . 75
B. 100
\( c \cdot 240 \)
D. 360


What is the cellulose made part that
encircle the cell?


Find the equation of line passing through \( (5,0,5) \&(2,1,3) . \) Also show that \( (5,0,5),(2,1,3) \&(-4,3,-1) \) are
collinear.


A device used for detecting small currents due to changing magnetic field is known as:
A. Galvanometer
B. Ammeter
c. Voltmeter
D. Potentiometer


\( S_{1}, S_{2} \) are two coherent sources (having
initial phase difference zero) of sound
located along \( x- \) axis separated by \( 4 \lambda \)
where \( \lambda \) is wavelength of sound emitted
by them. Number of maxima located on
the elliptical boundary around it will be :
A . 16
B. 12
\( c \)
\( D .4 \)


The burning of fossil fuels is the main source of which of the following pollutants?
A. Nitrogen
B. Carbon monoxide
c. Sulphur dioxide
D. Particulate matter


A magnetic moment of \( 1.73 B M \) will be
shown by one among of the following compounds:
\( \mathbf{A} \cdot\left[C u\left(N H_{3}\right)_{4}\right]^{2+} \)
B : \( \left[N i(C N)_{4}\right]^{2-} \)
\( \mathrm{c} \cdot \operatorname{Ti} \mathrm{Cl}_{4} \)
D \( \cdot\left[\mathrm{CoCl}_{6}\right]^{-3} \)


The solubility of \( N a C l(s) \) in water at
\( 298 K \) is about 6 moles per litre.

Suppose you add 1 mole of \( N a C l(s) \) to a litre of water. For the reaction:
\( N a C l(s)+H_{2} O \rightarrow N a C l(a q) \)
A. \( \Delta G>0, \Delta S>0 \)
в. \( \Delta G<0, \Delta S>0 \)
c. \( \Delta G>0, \Delta S<0 \)
D. \( \Delta G<0, \Delta S<0 \)


The area enclosed by a hysteresis loop is a measure of
A. retentivity
B. susceptibility
c. permeability
D. energy loss per cycle


The radial probability distribution curve obtained for an orbital wave function
\( (\mathbf{\Psi}) \) has \( \mathbf{3} \) peaks and 2 radial nodes. The
valence electron of which one of the
following metals does this wave
function \( (\Psi) \) correspond to?
A . \( C o \)
в. \( L i \)
c. \( K \)
D. Na


Find the number of sides of a regular polygon whose each exterior angle has a
measure of:
\( 45^{\circ} \)


The point at which the tangent to the
curve \( y=x^{3}+5 \) is perpendicular to
the line \( x+3 y=2 \) are
A. (6,1),(-1,4)
В. (6,1)(4,-1)
c. (1,6),(1,4)
D. (1,6),(-1,4)


Factorise the following: \( (5 x-6 y)^{3}+ \)
\( (7 z-5 x)^{3}+(6 y-7 z)^{3} \)
A. \( 3(5 x-6 y)(7 z-5 x)(6 y-7 z) \)
в. \( (x-6 y)(7 z-x)(y-7 z) \)
c. \( 3(x-6 y)(z+5 x)(8 y-z) \)
D. \( (x-y)(7 z+5 x)(6 y-7 z) \)


In Rutherford's atomic model, the electrostatic force of attraction between
the positively and negatively charged particles is counter balanced by:
A. The centripetal force exerted on the electrons moving in circular path
B. The high velocity of the electrons moving in a circular path
c. The linear movement of the nucleus
D. None of these


\( \boldsymbol{p} \leftrightarrow \boldsymbol{q} \) is equivalent to
\( \mathbf{A} \cdot p \rightarrow q \)
\( \mathbf{B} \cdot q \rightarrow p \)
\( \mathbf{c} \cdot(p \rightarrow q) \vee(q \rightarrow p) \)
D. \( (p \rightarrow q) \wedge(q \rightarrow p) \)


Simplify the following:
\( \left(\frac{1+i}{1-i}\right)^{4 n+1} \)
\( \mathbf{A} \cdot \mathbf{1} \)
B.
c.
D. None of these


Three particles having charges in the
ratio of 2: 3: 5 produce the same point on the photographic film in Thomson
experiment. Their masses are in the ratio of
A .2: 3: 5
B. 5: 3: 2
c. 15: 10: 6
D. 3: 5: 2


Assertion
The number of unpaired electrons in the
following gaseous ions:
\( M n^{3+}, C r^{3+}, V^{3+} \) and \( T i^{3+} \) are 4,3,2
and 1 respectively.
Reason
Among these \( \mathrm{Cr}^{3+} \) is most stable in
aqueous solution.
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


Chlorine has electron in
outer orbit. It needs
electron to become stable.
A. seven, one
B. seven, two
\( c . \) six, two
D. five, three


Consider the cell:
\( \boldsymbol{Z} \boldsymbol{n} \mid \boldsymbol{Z} \boldsymbol{n}^{2+}(\boldsymbol{a q})(\boldsymbol{1} . \boldsymbol{0} \boldsymbol{M}) \| \boldsymbol{C u}^{2+}(\boldsymbol{a q}) \)
The standard reduction potential are \( 0.350 \mathrm{V} \) for \( \boldsymbol{C u}^{2+}(\boldsymbol{a q})+\boldsymbol{2} \boldsymbol{e}^{-} \rightarrow \boldsymbol{C u} \)
and \( -0.763 \mathrm{V} \) for \( \mathrm{Zn}^{2+}(a q)+2 e^{-} \rightarrow \)
\( Z n \)
The EMF (in V) of the cell is (write your answer as nearest integer):


The distance between the straight lines \( 5 x+12 y+11=0,5 x+12 y+37=0 \)
is
A .2
B. 3
\( c \cdot 26 \)
D. 48


What is the name of the strings which vibrate in our voice box when we talk?
A. Oesophagus
B. Pharyngeal slits
c. vocal cords
D. None of these


distance Travelled by an object in 4 th \( \sec \) is twice the distance travelled by it in 2 nd second. If the acceleration of the object
\( 3 m s^{-2} n \) is calculate
(i) its initial velocity
(ii) the distance travelled in 7th second.


A wire elongates by 1 m \( m \) when a load
\( W \) is hung from it. If the wire goes over
a pulley and the two weights \( W \), each are hung at the two ends, then the elongation of the wire will be:
A. \( 0.5 m m \)
в. \( 1 \mathrm{mm} \)
\( \mathbf{c} \cdot 2 m m \)
D. \( 4 m m \)


Given a relation \( \boldsymbol{R}=(\mathbf{1}, \mathbf{2}),(\mathbf{2}, \mathbf{3}) \) on the
set of natural numbers, add a minimum
number of ordered pairs so that the enlarged relation is symmetric, transitive and reflexive.


In the reaction, \( \boldsymbol{C r} \boldsymbol{O}_{\boldsymbol{5}}+\boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \rightarrow \)
\( \boldsymbol{C r}_{2}\left(\boldsymbol{S O}_{4}\right)_{3}+\boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{O}_{2}, \) one mole of
\( C r O_{5} \) will liberate how many moles of
\( O_{2} ? \)
A. \( 5 / 2 \)
B. 5/4
\( c \cdot 9 / 2 \)
D. None of the above


Cell organelles are the parts of a living cell. All cells have a cell membrane and
some cells have a cell wall.

Which of the following has a cell wall?
I. Plants
II. Bacteria
III. Fungi
A. I only
B. II only
c. I and II only
D. Il and III only
E. I, II and III


Which of the following voices is likely to have minimum frequency?
A. Baby girl
B. Baby boy
c. A man
D. A woman


Show that:
\( \left(\frac{1+i}{\sqrt{2}}\right)^{8}+\left(\frac{1-i}{\sqrt{2}}\right)^{8}=2 \)


Marshall's acid \( \frac{H_{2} O}{\longrightarrow} A+B \)
\( \boldsymbol{A} \stackrel{\boldsymbol{H}_{2}}{\rightarrow} \boldsymbol{O} \boldsymbol{B}+\boldsymbol{C} \)
If \( P \) and \( Q \) represent a maximum number of atoms that can lie in a plane of compound \( A \) and \( C \) respectively. Then, find the value of \( (\boldsymbol{P}-\boldsymbol{Q}) \)


\( \tan ^{-1}\left(\frac{5-x}{6 x^{2}-5 x-3}\right) \)


More than four bonds are made by how many elements in carbon family?
A .
B. 2
\( c .3 \)
D. 4
E. 5


Assertion
The stability of peroxides and
superoxides increases in passing from
Li to CS.
Reason
The electropositive character of the
elements in the periodic table increases
on moving down a group.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
C. Assertion is correct but Reason is incorrect.
D. Assertion is incorrect but Reason is correct.


\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}} \cot \left(\frac{x}{2}\right)= \)


If two forces \( \boldsymbol{F}_{1}=\mathbf{2} \hat{\mathbf{i}}+\mathbf{4} \hat{\boldsymbol{k}} \boldsymbol{F}_{2}=\mathbf{3} \hat{\boldsymbol{j}}+ \)
\( 2 \hat{k} \) acts on one body and displaces it from (1,0,0) to (2,1,1) find net work done


\( 10^{22} \) particle each of mass \( 10^{-26} \mathrm{Kg} \) are
striking perpendicularly on a wall of \( \operatorname{area} 1 m^{2} \) with speed \( 10^{4} m / s \) in 1 sec
The pressure on the wall if collisions are
perfectly elastic is:
A \( \cdot 2 N / m^{2} \)
в. \( 4 N / m^{2} \)
\( \mathrm{c} \cdot 6 N / m^{2} \)
D. \( 8 N / m^{2} \)


Differentiate between the following pairs on the basis of what is mentioned
in brackets:
Active Transport and Diffusion [significance in plants]


Give the IUPAC name of the following compound


Which of the following has highest relative density?
A. water
B. oil
c. mercury
D. glass