On the basis of following features identify the correct option:
These rays travel in straight line. These rays consist of positively charged particles.

These rays are deflected by electric and magnetic fields. \( \mathrm{e} / \mathrm{m} \) values for the particles are not same
for all gases.
A. cathode rays
B. Anode rays
c. Both (1) and (2)
D. Neither (1) nor (2)


Why do off springs formed by asexual reproduction shares remarkable similarities?


Which metal is suitable to use to make
a permanent magnet?
A. Aluminium
B. Brass
c. Iron
D. stee


If \( A B C D \) is a rectangle, \( E, F \) are the
mid-points of \( B C \) and \( A D \) respectively and \( G \) is any point on \( E F, \) then \( \triangle G A B \) equals.
\( ^{\mathbf{A}} \cdot \frac{1}{2}(\square A B C D) \)
в. \( \frac{1}{3}(\square A B C D) \)
c \( \cdot \frac{1}{4}(\square A B C D) \)
D \( \cdot \frac{1}{6}(\square A B C D) \)


Linear momentum of the planet is
This question has multiple correct options
A. Different for different points of the orbitt
B. Conserved
c. Not conserved
D. None of these


A car runs at constant speed on a circular track of radius \( 100 \mathrm{m} \) taking
\( 62.8 \mathrm{s} \) on each lap. What is the average speed and average velocity on each complete lap? \( (\boldsymbol{\pi}=\mathbf{3 . 1 4}) \)
A. Velocity 10 \( \mathrm{m} / \mathrm{s} \), speed \( 10 \mathrm{m} / \mathrm{s} \)
B. Velocity zero, speed 10 m/s
c. Velocity zero, speed zero
D. Velocity 10 \( \mathrm{m} / \mathrm{s} \), speed zero


we do not get crushed by the atmospheric pressure as the out internal pressure and the atmospheric
pressure are?
A. equal
B. gretaer
c. lower
D. none of the above


An example of disaccharide, made up of two units of the same monosaccharide,
is:
A. maltose
B. sucrose
c. lactose
D. none


Explain with chemical equation-what happen when white phosphorous is heated at \( 473 K \) and very high
pressure?


Several spherical drops of a liquid of radius coalesce to form a single drop to
radius \( R \). If the surface tension and \( V \) is
volume and \( r \) consideration, then the
release of energy is :
\( ^{\mathbf{A}} \cdot_{3 V T}\left(\frac{1}{r}+\frac{1}{R}\right) \)
B. \( \quad 3 V T\left(\frac{1}{r}-\frac{1}{R}\right) \)
\( ^{\mathrm{c}} \cdot_{V T}\left(\frac{1}{r}-\frac{1}{R}\right) \)
D. \( V T\left(\frac{1}{r^{2}}+\frac{1}{R^{2}}\right) \)


Which of the following physiological effects is caused in plants by gibberellic acid?
A. Shortening of genetically tall plants
B. Elongation of genetically dwarf plants
c. Rooting in stem cuttings
D. Yellowing of young leaves


The vertical displacement of the particle of the string at \( x=7 \mathrm{cm} \) and \( t \)
\( =0.01 s \) will be
A. \( 0.75 \mathrm{cm} \)
B. \( 0.5 \mathrm{cm} \)
c. \( 0.25 \mathrm{cm} \)
D. zero


Which of the following hormones regulate stomatal colour?
A . Auxins
B. GAA
c. АВА
D. Cytokinin


\( A B C \) and \( D B C \) are two isosceles
triangle on the same side of \( B C . \) Then, \( \angle B D A=\angle C D A \)
A. True
B. False


Assertion
\( \mathbf{A} \)
p-njunction with reverse bias can be used as a photodiode to measure light intensity.
Reason
In a reverse bias condition the current
is small but it is more sensitive to
changes in incident light intensity.
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 optical rotation of the \( \alpha- \) form of
a pyramose is \( +150.7^{\circ}, \) that of the \( \beta- \)
form is \( +52.8^{\circ} . \) In solution an
equilibrium mixture of these anomers
has an optical rotation of \( +80.2^{\circ} . \) The percentage of the \( \alpha \) form in equilibrium
mixture is:
A . \( 28 \% \)
B. \( 32 \% \)
c. \( 68 \% \)
D. 72\%


The median of the observations
arranged in increasing order is \( 26 . \) Find
the value of \( x \)
\( \mathbf{1 0}, \mathbf{1 7}, \mathbf{2 2}, \boldsymbol{x}+\mathbf{2}, \boldsymbol{x}+\mathbf{4}, \mathbf{3 0}, \mathbf{3 6}, \mathbf{4 0} \)


An angiospermic male plant with 24 chromosomes in its pollen mother cells is crossed with female plant bearing 24 chromosomes in its root cells. What
would be the ploidy of embryo and endosperm respectively formed after this cross?
A. 24 and 48
B. 24 and 24
c. 48 and 72
D. 24 and 36


Two sides of a triangle are \( 64 \mathrm{m} \) and 48
m. If height of the triangle corresponding to \( 48 \mathrm{m} \) side is \( 6 \mathrm{m} \), then the height of the triangle corresponding to \( 64 \mathrm{m} \) side is \( 4.5 \mathrm{m} \)
If true then enter 1 and if false then
enter 0


An X-ray of lower abdomen shows a shades in the region of the ureter
suspected to be a uretelic calculus. A possible clinical symptom would be
A. Active renal failure
B. Anuria and haematuria
c. Motor aphasia
D. Chronic renal failure (CRF)


Define Pteridophyta


The age of our solar system is approximately
A . 4600 million years
B. 4.6 million years
c. 460 million years
D. 460 billion years


The number of vectors of unit length perpendicular to vectors \( \overline{\boldsymbol{a}}=(\mathbf{1}, \mathbf{1}, \mathbf{0}) \& \)
\( \bar{b}=(0,1,1) \) is:
\( A \)
B. 2
\( c \cdot 3 \)
D. \( \infty \)


\( \left[\begin{array}{ll}\boldsymbol{x}+\boldsymbol{y} & \boldsymbol{2} \\ \boldsymbol{5}+\boldsymbol{z} & \boldsymbol{x} \boldsymbol{y}\end{array}\right]=\left[\begin{array}{ll}\boldsymbol{6} & \boldsymbol{2} \\ \boldsymbol{5} & \boldsymbol{8}\end{array}\right] \)
Find \( \boldsymbol{x} \boldsymbol{y} \boldsymbol{z} ? \)


The Giant Metrewave Radio Telescope
(GMRT) is related to
A. Superconductivity
B. Generation, propagation and detection of electromagnetic waves
c. Detection of cosmic radio waves
D. Trapping and cooling of atoms by laser beams and magnetic fields


Two small identical conducting balls \( A \) and \( \mathrm{B} \) of charges \( +10 \mu \mathrm{C} \) and \( +30 \mu \mathrm{C} \) respectively, are kept at a separation of \( 50 \mathrm{cm} . \) These balls have been connected by a wire for a short time. The final
charge on each of the balls \( A \) and \( B \) will
be:
A \( . \) 10 \( \mu \mathrm{C} \) and \( 30 \mu \mathrm{C} \), respectively
B. 20 \muC on each ball
c. \( 30 \mu \mathrm{c} \) and \( 10 \mu \mathrm{C} \), respectively
D. -40 \muC and 80 \muC, respectively


An urn contains 2 white and 2 black
balls. A ball is drawn at random. If it is
white, it is not replaced into the urn. Otherwise, it is replaced with another ball of the same colour. The process is
repeated. Find the probability that the third ball drawn is black.


Show that each of the given three
vectors is a unit vector:
\( \frac{1}{7}(2 \bar{i}+3 \bar{j}+6 \bar{k},) \frac{1}{7}(3 \bar{i}+6 \bar{j}+\overline{2} k) \)
\( \frac{1}{7}(6 \bar{i}+2 \bar{j}+3 \bar{k}) \)


Assertion
In the dicot root, the vascular cambium
İs secondary in origin.
Reason
Secondary growth occurs in stems and
roots of gymnosperms also.
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


\( S_{2} O_{8} \) have :
A. S-S bond
B. S-O bridge
c. o-o bridge
D. None of the above


The radius of proton is \( 0.6 \times 10^{-15} m \)
What is the order of magnitude of it volume?
A \( \cdot 10^{-47} m^{3} \)
B . \( 10^{-44} m^{3} \)
D. \( 10^{-46} m^{3} \)


if \( \int f(x) d x=f(x), \) then \( \int\left(\frac{f(x)}{f^{\prime}(x)}\right) . d x \)
is equal to
A. \( x+c \)
B. \( \log f(x)+c \)
\( c \cdot \log F(x)+c \)
D. \( e^{f(x)}+c \)


State whether the following statement is true or false.
The rational numbers are whole
numbers, fractions, mixed numbers, and decimals, together with their
negative images.
A. True
B. False


\( A B C \) and \( D B C \) are two isosceles
triangles on the same base \( B C . \) Then
\( \angle A B D=\angle A C D \)
A. True
B. False


The thermodynamical variable temperatures is defined by:
A. zeroth law
B. I law
c. ॥ law
D. III law


\( \operatorname{Let} A=\left[\begin{array}{ll}1 & 0 \\ 1 & 1\end{array}\right] . \) Then which of following
is not true?
This question has multiple correct options
A \( \cdot \lim _{n \rightarrow \infty} \frac{1}{n^{2}} A^{-n}=\left[\begin{array}{cc}0 & 0 \\ -1 & 0\end{array}\right] \)
B \( \lim _{n \rightarrow \infty} \frac{1}{n} A^{-n}=\left[\begin{array}{cc}0 & 0 \\ -1 & 0\end{array}\right] \)
\( ^{\mathrm{c}},_{A^{-n}}=\left[\begin{array}{cc}1 & 0 \\ -n & 1\end{array}\right] \forall n \neq N \)
D. none of these


An electron and a proton equal momenta, enter a uniform magnetic filed at right angles to the field lines.
What will be the ratio of the radii of an
vature of three trajectories.
A . 1: 1
B. 1: 2
c. 2: 3
D. 3: 4


A graph of concentration versus time
data for a first-order reaction gives a
straight line in which of the following plots of the data?
A \( \cdot[A]_{t}=-k t+[A]_{0} \)
B \( \cdot \ln [A]_{t}=-k t+\ln [A]_{0} \)
c. \( \frac{1}{[A]_{t}}=k t+\frac{1}{[A]_{0}} \)
D. All of the above
E. None of the above


De-Broglie wavelength of an atom at absolute temperature \( \boldsymbol{T} \boldsymbol{K} \) will be
A \( \cdot \frac{h}{\sqrt{3 m K T}} \)
в. \( \frac{h}{m K T} \)
c. \( \frac{\sqrt{2 m K T}}{h} \)
D. \( \sqrt{2 m K T} \)


Phosphorus undergoes slow combustion and glows in dark. The process is called:
A. photochemical change
B. chemiluminescence
c. flourescence
D. phosphorescence


Fill in the blank
All \( \dots \dots \dots \dots \dots \) triangles are similar
A. equilateral
B. scalene
c. isoceles
D. None of these


\( (A)+\operatorname{tap} \) water \( \rightarrow \)
white turbidity soluble in aq. \( N H_{3} \)
\( (\boldsymbol{A}) \stackrel{\Delta}{\longrightarrow} \mathbf{r e s i d u e}(\mathbf{B})+\boldsymbol{N} \boldsymbol{O}_{2}+\boldsymbol{O}_{2} \)
Aqueous (A) gives brown ring on adding \( F e S O_{4} \) and conc.\( H_{2} S O_{4} . \) Identify \( (A) \)
as:
A. \( N a N O_{3} \)
в. \( A g N O_{3} \)
c. \( N a N O_{2} \)
D. \( A g N O_{2} \)


In a standing wave, node is a point of
A. maximum strain
B. maximum pressure
c. maximum density
D. All of these


A rectangular coil \( A B C D \) is rotated
anticlockwise with a uniform angular velocity about the axis shown in figure.
The axis of rotation of the coil as well as
the magnetic field \( B \) is horizontal. The
induced emf in the coil would be
minimum when the plane of the coil
A. is horizontal
B. makes and angle \( 45^{\circ} \) with direction of magnetic field
\( \mathrm{c} \). is at right angle to the magnetic field
D. makes and angle of \( 30^{\circ} \) with the magnetic field
E. answer required


The products are :
Products \( P, Q, \) and \( R \) are:
\( (\mathrm{I}) \)
A. \( P \Rightarrow I, Q \) and \( R \Rightarrow \| \)
B. P and Q both I and II, \( R \Rightarrow \) II
C. \( P \) is both I and II, \( Q \) and \( R \Rightarrow 1 \)
D. \( P, Q, \) and \( R \Rightarrow A \| \) II


The length of the latus rectum of the parabola
\( \mathbf{1 6 9}\left\{(\boldsymbol{x}-\mathbf{1})^{2}+(\boldsymbol{y}-\mathbf{3})^{2}\right\}=(\mathbf{5} \boldsymbol{x}- \)
\( 12 y+17)^{2} \) is
A \( \cdot \frac{14}{11} \)
в. \( \frac{12}{13} \)
c. \( \frac{28}{13} \)
D. none of these


Volume of \( 0.1 \mathrm{M} K M n O_{4}, \) required to
oxidise completely \( 50 \mathrm{ml} \) of \( 0.5 \mathrm{M} \) ferrous oxalate solution in acidic
medium will be:
A . \( 100 \mathrm{mL} \)
B . \( 120 \mathrm{mL} \)
\( c .150 \mathrm{mL} \)
D. \( 200 \mathrm{mL} \)


Rain water harvesting is:
A. storing ground water by not using water from the well
B. stop growing crops to save water
C. allowing water to go into rivers and lakes
D. collecting rainwater and storing it for later use


Refraction of light in the eye occurs at
A. The pupil only
B. The cornea only
c. The lens only
D. Both the cornea and the lens


8
8
8
8


Dialysis fluid contain all the constituents as in plasma except


A gas in a cylinder held at a constant pressure of \( 1.7 \times 10^{5} P a \) and is cooled
and compressed from \( 1.20 m^{3} \) to \( 0.8 m^{3} \) The internal energy of the gas decreses by \( 1.1 \times 10^{5} J . \) The magnitude of the
heat flow into or out of the gas is given
as \( x \times 10^{4} \) J. Find \( x \) ( \( x \) is a two digit
integer)


In the calender method, mating should be avoided from day - ....... to ............ of the cycle.
A. 9 to 21 days
B. 3 to 15 days
\( c .5 \) to 30 days
D. 12 to 15 days


Any ray which passes through the point is not deviated by the lens.
4
\( B \)
\( c .2 \)
Don


Rydberg constant is:
A. same for all elements
B. different for different elements
C . a universal constant
D. is different for lighter elements but same for heavier elements


The escape velocity of a body from earth is about \( 11.2 \mathrm{km} / \mathrm{s} \). Assuming the mass and radius of the earth to be about 81
and 4 times the mass and radius of the
moon, the escape velocity in \( \mathrm{km} / \mathrm{s} \) from the surface of the moon will be:
A . 0.54
B. 2.48
\( c \cdot 11 \)
D. 49.5


A die has 6 faces marked by the given numbers as shown below:
The die is thrown once. What is the
probability of getting a positive integer?
\( 1 3 \longdiv { 2 3 } \)


The momentum of a \( 225 g \) ball moving at \( 35 m / s \) is
\( \mathbf{A} \cdot 7875 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
B. \( 3.5 N \)
\( c .5 .0 m / s \)
D. \( 7.875 \mathrm{kg} \mathrm{m} / \mathrm{s} \)


Find the minimum value of
\( e^{(2 x-2 x+1) \sin ^{2} x} \)


toppr
Q Type your question.
from point A through point G in the
graphs directly below.
Which of the graphs shows the voltage
from point \( A \) to point \( G ? \)
\( A \cdot A \)
B. B
\( c \cdot c \)
\( D \cdot D \)
\( E . \)


Find the derivative of \( \boldsymbol{y}=(\boldsymbol{x}+ \)
1) \( (x+2)^{2} \)


The co-efficient of mutual induction
between primray and secondary coil is
2H. Calculate induced e.m.f. if current of
4A is cut off in \( 2.5 \times 10^{-4} \) seconds.


Determine whether the following polynomial has \( (x+1) \) as a factor. \( x^{3}-x^{2}-(3-\sqrt{3}) x+\sqrt{3} \)


In MKS, the gravitational unit of force is
A. \( k g f \)
в. \( g f \)
\( c . N \)
D. dyne


f the lattice constant of this
semiconductor is decreased, then
\( \mathbf{A} \cdot \) all \( E_{c}, E_{g}, E_{v} \) increases
B. \( E_{c} \) and \( E_{v} \) increases, but \( E_{g} \) decreases
\( \mathrm{C} \cdot E_{c} \) and \( E_{v} \) decreases, but \( E_{g} \) increases.
D. all \( E_{c}, E_{g}, E_{v} \) decreases.


If \( (x-a)^{2}+(y-b)^{2}=c^{2}, \) then prove
that \( \frac{\left[1+\left(\frac{d y}{d x}\right)^{2}\right]^{3 / 2}}{\frac{d^{2} y}{d x^{2}}} \) is a independent
of \( \boldsymbol{C} \)


A material has poisson's ratio \( 0.5 . \) If \( a \) uniform rod of it suffers a longitudinal
strain of \( 3 \times 10^{-3}, \) what will be
percentage increase in volume?
A . २\%
B. 3\%
c. 5\%
D. 0\%


The area of a rhombus is \( 48 \mathrm{cm}^{2} \). and its
perimeter is \( 20 \mathrm{cm} . \) What is its length?


Give expressions in the following cases. 11 added to \( 2 m \)


Select the best combination of reagents
which will bring the above conversion.
\( \mathbf{A} \cdot B r_{2} / F e B r_{3} ; H N O_{3} / H_{2} S O_{4} ; N a O H ; H_{2} / P t \)
B . \( C H_{3} C O C l / A l C l_{3} ; B r_{2} / F e B r_{3} ; N a B H_{4} / C H_{3} O H \)
c. \( C H_{3} C l / A l C l_{3} ; K M n O_{4} ; C H_{3} C l / A l C l_{3} ; N B S / h v \)
\( \operatorname{LiAlH}_{4} / H_{2} O ; N a O H \)
D. \( C H_{3} C l / A l C l_{3} ; H N O_{3} / H_{2} S O_{4} ; N B S / h v / N a O H \)


Solve the equations using elimination method:
\( x-y=2 \) and \( -x y=-10 \)
A. (6,-4)
()
в. (6,4)
c. (-6,-4)
D. (-6,4)


The phenomenon of nuclear fission can be carried out both in a controlled and
in an uncontrolled way. Out of the following, the correct statements vis-
avis these phenomena are
This question has multiple correct options
A. the fission energy released per reaction is much more than conventional nuclear reactions and one of the products of the reaction is that very particle which initiates the reaction
B. it is the "surface to volume" ratio of the sample of nuclear fuel used which determines whether or not the reaction would sustain itself as a "chain reaction"
c. the "control rods" in a nuclear reactor must be made of material that absorbs neutrons effectively
D. the energy released per fission as well as energy released per unit mass of the fuel in nuclear fission are both greater than the corresponding quantities for nuclear fusion


If \( x=a t^{2} \) and \( y=2 a t, \) then \( \frac{d y}{d x} \) is equal
to
\( \mathbf{A} \cdot t \)
B.
\( c . \)
D. \( t^{2} \)


In the figure, \( \angle A=90^{\circ}=\angle D \) and
\( A B=D C . \) Then \( \Delta A B O \cong \Delta D C O \) by
the congruence postulate
A . ASA
B. SAS
\( c . \) sss
D. RHS


Convert : Chloro benzene to phenol.


Solve: \( \frac{\mathbf{2} \boldsymbol{x}-\mathbf{3}}{\mathbf{4}}+\mathbf{8} \geq \mathbf{2}+\frac{\mathbf{4} \boldsymbol{x}}{\mathbf{3}} \)


Evaluate each of the following:
\( \frac{-4}{13}-\frac{-5}{26}=\frac{x}{26} \) what is 'x'?


Sex factor of bacteria is
A. Replicon
B. F-factor
c. sex pil
D. sRNA


The resistance of a wire of \( 100 \mathrm{cm} \)
length is \( 10 \Omega . \) Now, it is cut into 10 equal parts and all of them are twisted to form a single bundle. Its resistance is:
A . \( 1 \Omega \)
B. \( 0.5 \Omega \)
\( c .5 \Omega \)
D. \( 0.1 \Omega \)


Two particles start moving from the same position on a circle of radius 20 \( \mathrm{cm} \) with speed \( 40 \pi \mathrm{m} / \mathrm{s} \) and \( 36 \pi \mathrm{m} / \mathrm{s} \)
respectively in the same direction. Find
the time after which the particles will meet again.


A, \( \mathrm{B}, \mathrm{C} \) are three elements with atomic numbers, Z-1, Z, and Z+1 respectively. B is an inert gas. Identify the elements having same valence shell.
\( A \cdot A, B \)
B. В, С
c. \( A, C \)
D. A, B, C


Which of the following statements are
true with respect to electronic displacement in a covalent bond?
I. Inductive effect operates through \( \pi \)
bond.
II. Resonance effect operates through \( \sigma \) bond.
III. Inductive effect operates through \( \sigma \)
bond.
IV. Resonance effect operates through \( \pi \)
-bond
V. Resonance and inductive effects
operate through \( \sigma \) -bond.
A. III and IV
B. I and II
c. Il and IV
D. I and


If the each of the vertices of a triangle has integral coordinates, then the triangle may be This question has multiple correct options
A. right angled
B. equilateral
c. isosceles
D. none of these


The percentage errors in the measurement of the length (L) and breadth (B) of a rectangle are \( \ell \) and \( b \% \) respectively. Then the percentage error in the calculation of the area will be
\( A \cdot(\mid b) \% \)
B. (1+b)\%
\( c \cdot(L+1)(B+b) \)
D. Lb+BL


The region in atmosphere containing water vapour is:
A. thermosphere
B. stratosphere
c. troposphere
D. mesosphere


If \( \boldsymbol{f}(\boldsymbol{x})=\left|\boldsymbol{x}^{2}-\mathbf{5} \boldsymbol{x}+\boldsymbol{6}\right|, \) then \( \boldsymbol{f}^{\prime}(\boldsymbol{x}) \)
equals
A. \( 2 x-5 \) for \( 2<x<3 \)
B. \( 5-2 x \) for \( 2<x<3 \)
c. \( 2 x-5 \) for \( x>2 \)
D. \( 5-2 x \) for \( x<3 \)


Which one of the following pairs of compounds illustrate the law of multiple proportions?
A. \( H_{2} O \) and \( N a_{2} O \)
B. \( M g O \) and \( N a_{2} O \)
c. \( N a_{2} O \) and \( B a O \)
D. \( \operatorname{SnCl}_{2} \) and \( \operatorname{SnCl}_{4} \)


Only one semicircular canal is present
in
A. Bony fish
B. Cartilaginous fish
c. Hagfish
D. Amphibians


The melting points and solubility in water of amino acids are generally higher than of corresponding halo acids.


f maximum and minimum values of \( \boldsymbol{D}=\left|\begin{array}{ccc}\mathbf{1} & -\cos \boldsymbol{\theta} & \mathbf{1} \\ \cos \boldsymbol{\theta} & \mathbf{1} & -\cos \boldsymbol{\theta} \\ \mathbf{1} & \cos \boldsymbol{\theta} & \mathbf{1}\end{array}\right| \) are \( p \) and
respectively, then the value of \( 2 p+3 q \)
is
A . 16
B. 6
\( c .14 \)
\( D \)


The equation of a progressive wave is \( \boldsymbol{y}=\mathbf{0 . 5} \sin 2 \pi\left(\frac{\boldsymbol{t}}{\mathbf{0 . 0 0 4}}-\frac{\boldsymbol{x}}{\mathbf{5 0}}\right), \) where \( \boldsymbol{x} \) is
in \( c m . \) The phase difference between two points separated by a distance \( 5 \mathrm{cm} \) at any instant is :
A \( \cdot \frac{\pi}{5} \)
в.
c. \( \frac{\pi}{2} \)
D.


The nucleus of the atom \( (Z>1) \)
consists of:
A. Proton and neutron.
B. Proton and electron
c. Neutron and electron
D. Proton, neutron and electrons


For creating a \( \boldsymbol{p}-\boldsymbol{n} \) junction,
A. we take one slab of p-type semiconductor and physically join it to another n-type semiconductor
B. continuous contact at the atomic level is necessary.
C. two macroscopic smooth flat slabs can be used
D. None of these


Consider two different metallic strips
and 2 ) of same dimensions (length \( l \)
width \( \boldsymbol{w} \) and thickness \( \boldsymbol{d} \) ) with carrier
densities \( n_{1} \) and \( n_{2} \) respectively. Strip 1
is placed in magnetic field \( B_{1} \) and strip
2 is placed in magnetic field \( B_{2}, \) both
along positive y-directions. Then \( V_{1} \) and
\( V_{2} \) are the potential differences
developed between K and M in strips
and \( 2, \) respectively.
This question has multiple correct options
A \( \cdot \) If \( B_{1}=B_{2} \) and \( n_{1}=2 n_{2} \), then \( V_{2}=2 V_{1} \)
B. If \( B_{1}=B_{2} \) and \( n_{1}=2 n_{2} \), then \( V_{2}=V_{1} \)
C. If \( B_{1}=2 B_{2} \) and \( n_{1}=n_{2}, \) then \( V_{2}=0.5 V_{1} \)
D. If \( B_{1}=2 B_{2} \) and \( n_{1}=n_{2} \), then \( V_{2}=V_{1} \)


In a conductor, a point \( P \) is at a higher potential than another point \( Q . \) In which
direction do the electrons move?


Two copper wires having the length in ratio 4: 1 and their radii ratio as 1: 4
are stretched by the same force. Then the ratio of the longitudinal strain in the two will be
\( \mathbf{A} \cdot 1: 16 \)
B. 16: 1
\( \mathbf{c} \cdot 1: 64 \)
D. 64: 1


Define:
(i) Radial vascular bundle
(ii) Rigor mortis
(iii) Root pressure


If the molar concentration of \( \boldsymbol{P b I}_{2} \) is
\( 1.5 \times 10^{-3} \) mol \( L^{-1}, \) then the
concentration of iodide ions of \( g \) ion \( L^{-1} \)
is ?
A. \( 3.0 \times 10^{-3} \)
В. \( 6.0 \times 10^{-3} \)
c. \( 0.3 \times 10^{-3} \)
D. \( 0.6 \times 10^{-6} \)


If the electric flux entering and leaving
an enclosed surface respectively is \( \phi_{1} \)
and \( \phi_{2}, \) the electric charge inside the surface will be :
\( \mathbf{A} \cdot\left(\phi_{2}-\phi_{1}\right) \varepsilon_{0} \)
B. \( \frac{\left(\phi_{2}+\phi_{1}\right)}{\varepsilon_{0}} \)
c. \( \frac{\left(\phi_{2}-\phi_{1}\right)}{\varepsilon_{0}} \)
\( \mathbf{D} \cdot\left(\phi_{2}+\phi_{1}\right) \varepsilon_{0} \)


Among the following species which two have a trigonal pyramidal shape?
(I) \( \boldsymbol{N} \boldsymbol{I}_{\mathbf{3}} \)
(II) \( I_{3}^{-} \)
\( (\| I) \boldsymbol{S} \boldsymbol{O}_{3}^{2-} \)
\( (\mathrm{IV}) N O_{3}^{-} \)
A. \( I \) and \( I I I \)
B. III and \( I V \)
c. \( I \) and \( I V \)
D. II and III


Let \( G \) be the centroid of \( \triangle A B C \). If \( A B=\vec{a} \) and \( \overrightarrow{A C}=\vec{b}, \) then \( \overrightarrow{A G}, \) in
terms of \( \vec{a} \) and \( \vec{b} \) is
A \( \cdot \frac{2}{3}(\vec{a}+\vec{b}) \)
в. \( \frac{1}{6}(\vec{a}+\vec{b}) \)
c. \( \frac{1}{3}(\vec{a}+\vec{b}) \)
D. \( \frac{1}{2}(\vec{a}+\vec{b}) \)


Melting of iron is \( _{--}-_{-}- \) than sulphur.
A . higher
B. lower
c. equal
D. none of the baove


Suppose a girl throws a die. If she gets a
5 or \( 6, \) she tosses a coin 3 times and
notes the number of heads. If she gets
1,2,3 and 4 she tosses a coin once and
notes whether a head or tail is obtained.
If she obtained exactly one head. What
is the probability that she threw 1,2,3 or 4 with the die?


Which of the following undergoes nucleophilic substitution exclusively by
\( \boldsymbol{S} \boldsymbol{N}^{1} \) mechanism:
A. ethyl chloride
B. isopropyl chloride
c. benzyl chloride
D. chlorobenzene


Differentiate the following function
w.r.t.x.
\( \frac{1}{\left(x^{2}+3^{2}\right)} \)


Which of the following pairs of linear equations has unique solution, no solution, or infinitely many solutions. In case there is a unique solution, find it by using cross multiplication method?
\( 3 x-5 y=20,6 x-10 y=40 \)
A. No solutions
B. Unique solutions, \( x=0 \) and \( y=1 \)
c. Infinitely many solutions
D. Data insufficient


The population of a place increased to 54000 in 2003 at a rate of \( 5 \% \) per
annum. Its population in 2005 will be \( P \)
What is the sum of the digits in \( \boldsymbol{P} \)


The freezing point of a solution containing 5.85 g of \( N a C l \) in \( 100 g \) of
water is \( -3.348^{\circ} \mathrm{C} . \) Calculate van't Hoff
factor 'i' for this solution. What will be
the experimental molecular weight of NaCl?
\( \left(K_{f} \text { for water }=1.86 K k g m o l^{-1}, \) at. wt. \right. \( \mathrm{Na}=23, \mathrm{Cl}=35.5) \)


(a) Give reasons for the following.
(i) Bond enthalpy of \( F_{2} \) is lower than
that of \( C l_{2} \)
(ii) \( P H_{3} \) has lower boiling point than
\( N H_{3} \)
(b) Draw the structures of the following molecules.
(i) \( B r F_{3}\left(\text { ii) }\left(H P O_{3}\right)_{3}\right. \)
(iii) \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{\mathbf{4}} \)


Work done in splitting a drop of water of
1 mm radius into 64 droplets is
(surface tension of water \( 72 \times \)
\( \left.10^{-3} J / m^{2}\right) \)
A . \( 2.0 \times 10^{-6} J \)
в. \( 2.4 \times 10^{-6} J \)
C \( .4 \times 10^{-6} J \)
D. \( 5.4 \times 10^{-6} J \)


a) Explain Rosenmund reduction with
equation
b) How does propanone \( \left(C H_{3} C O H_{3}\right) \) reacts with hydrazine? Give equation.
c) Name an oxidising agent used in the Etard's reaction.


Degree of \( \boldsymbol{y} \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}=\left[\boldsymbol{3}+\left(\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}\right)^{2}\right]^{\frac{2}{3}} \) is:
\( A \cdot 4 \)
в. 3
\( c \cdot 2 \)
\( D \)


A policeman fires four bullets at a dacoit. The probability that the dacoit will be killed by one bullet is \( 0.6 . \) What is the probability that the dacoit is still alive?
A .0 .064
B. 0.0256
c. 0.32
D. 0.16


A trapezium PQRSPQRS. Meassuremnt
in centimeters are given as shown in
the figure. Find the area of the
trapezium.


The equivalent conductance of NaCl at concentration \( C \) and at infinite dilution
\( \operatorname{are} \lambda_{C} \) and \( \lambda_{\infty} \) respectively. The correct
relationship between \( \lambda_{C} \) and \( \lambda_{\infty} \) is
given as: (Where the constant B is positive)
A \( \cdot \lambda_{C}=\lambda_{\infty}-(B) \sqrt{C} \)
в. \( \lambda_{C}=\lambda_{\infty}+(B) \sqrt{C} \)
c. \( \lambda_{C}=\lambda_{\infty}+(B) C \)
D. \( \lambda_{C}=\lambda_{\infty}-(B) C \)


If \( f(x)=\frac{x^{2}+2}{x-1} \) when \( x<3, f(x)= \)
\( \frac{\sin x}{x-3} \) when \( x>3, \) for what values of
is the function not defined
\( A \cdot 3 \)
B. 4
\( c \cdot 5 \)
D. 6


Select correct statement(s):
A. \( S i \) uses all of its valence electrons in an \( s p^{3}- \) hybridization and crystallizes in an fcc structure similar to diamond.
B. Diamond is an electrical insulator, graphite is an electrical conductor but silicon is a semiconductor.
C. Most common silica is quartz.
D. All of the above are correct statements.


\( a \)
\( a \)
\( b \)
\( a \)


The path of a beam of light is invisible in which solution?
A. Colloidal solution
B. True solution
c. Heterogenous solution
D. All of the above


The sum of the distances of any point on the ellipse \( 3 x^{2}+4 y^{2}=24 \) from its foci
is :
\( A \cdot 8 \sqrt{2} \)
B. 8
c. \( 16 \sqrt{2} \)
D. \( 4 \sqrt{2} \)


In any binomial expansion, the number
of terms are
\( A \cdot \geq 5 \)
B. \( \geq 2 \)
\( c \cdot \geq 3 \)
\( D \cdot \geq 4 \)


Sodium burns in dry air to ordinarily
give:
A. \( N a_{2} O \)
в. \( N a_{2} \mathrm{O}_{2} \)
c. \( N a O_{2} \)
D. \( N a_{3} N \)


Determine the electrostatic potential energy of a system consisting of two
charges \( 7 \mu C \) and \( -2 \mu C \) separated by distance of \( 20 \mathrm{cm} \)


There is a small black dot at the centre
\( C \) of a solid glass sphere of refractive index \( \mu . \) When seen from outside, comment on the location of the dot.
A. away from \( C \) for all values of \( \mu \)
B. at \( C \) for all values of \( \mu \)
\( \mathbf{c} . \) at \( C \) for \( \mu=1.5, \) but away from \( C \) for \( \mu \neq 1.5 \)
D. at \( C \) only for \( \sqrt{2} \leq \mu \leq 1.5 \)


A rectangle \( P Q R S \) is inscribed in a
quadrant of a circle, with \( P \) at the
centre and \( R \) on the circumference. If
\( P S \) is \( 12 \mathrm{cm} \) and \( Q P \) is \( 5 \mathrm{cm} \) then the
diameter of the circle is
\( \mathbf{A} \cdot 26 \mathrm{cm} \)
B. \( 29 \mathrm{cm} \)
\( \mathbf{c} .28 \mathrm{cm} \)
D. none of these


A linear object \( A B \) is placed along the axis of a concave mirror. The object is moving towards the mirror with speed
\( U . \) The speed of the image of the point \( A \)
is \( 4 U \) and the speed of the image of \( B \)
is also \( 4 U \) but in opposite direction. If
the center of the line \( A B \) is at a
distance \( L \) from the mirror then find out
the length of the object.
A \( \cdot \frac{3 L}{2} \)
в. \( \frac{5 L}{2} \)
\( c . L \)
D. None of these


Figure shows three circular arcs, each
of radius \( R \) and total change as
indicated. The net electric potential at
the center of curvature is :-
\( A \)
в. \( \frac{Q}{2 \pi \epsilon_{0} R} \)
с. \( \frac{2 Q}{\pi \epsilon_{0} R} \)
D. \( \frac{Q}{\pi \epsilon_{0} R} \)


(a) How would you account for the following:
(i) Actinoid contraction is greater than lanthaniod contraction.
(ii) Transition metals form coloured
compounds.
(b) Complete the following equation:
\( \mathbf{2} M \boldsymbol{n} \boldsymbol{O}_{4}^{-}+\boldsymbol{6} \boldsymbol{H}^{+}+\mathbf{5} \boldsymbol{N} \boldsymbol{O}_{2}^{-} \rightarrow \)


What is the difference between an
exocrine gland and an endocrine gland
\( ? \)


In a photoelectric effect, the anode
potential is plotted against the plate
current
A. A and B will have different intensities while B and
will have different frequencies
B. B and C will have different intensities while A and will have different frequencies
C. \( A \) and \( B \) will have different intensities while \( A \) and \( C \) will have equal frequencies
D. A and B will have equal intensities while B and C will have different frequencies


Assertion
When variable frequency a.c. source is connected to a capacitor, displacement current increases with increase in
frequency
Reason
As frequency increases conduction current also increases.
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


Evalaute the integral \( \int_{0}^{1} \sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right) d x \)
A \( \cdot \frac{\pi}{4}-\log 2 \)
B \( \cdot \frac{\pi}{2}+\log 2 \)
c. \( \frac{\pi}{2}-\log 2 \)
D. \( \frac{\pi}{4}+\log 2 \)


Two cells of the same emf \( e \) but
difference internal resistances \( r_{1} \) and
\( r_{2} \) are connected in series with an
external resistance \( R \). The potential
drop across the first cell is found to be
zero. The external resistance \( \boldsymbol{R} \) is
A \( \cdot r_{1}-r_{2} \)
в. \( r_{1} / r_{2} \)
\( c \cdot r_{1} r_{2} \)
D. \( r_{1}+r_{2} \)


Radiations from a nuclear power plant is harmful to:
A. environment
B. human civilization
c. wildlife
D. all of the above


Ten charges having charge \( \mathbf{1} \mu C, 8 \mu C, 27 \mu C, \dots \dots 1000 \mu C \) are
placed on the \( x \) -axis with co-ordinates \( \boldsymbol{x}=\mathbf{1} \boldsymbol{m}, \mathbf{2} \boldsymbol{m}, \mathbf{3} \boldsymbol{m}, \mathbf{4} \boldsymbol{m}, \dots . . \mathbf{1 0} \boldsymbol{m} . \) The
net electric field intensity at the origin is:
A \( \cdot 9 \times 10^{5} N / C \)
в. \( 9 \times 10^{4} N / C \)
C \( .4 .95 \times 10^{-5} \mathrm{N} / \mathrm{C} \)
D. \( 4.95 \times 10^{5} N / C \)


If the pressure of a gas is increased then its mean free path becomes:
A . zero
B. less
c. more
\( D \cdot \alpha \)


If \( \boldsymbol{x} \sqrt{\mathbf{1}+\boldsymbol{y}}+\boldsymbol{y} \sqrt{\mathbf{1}+\boldsymbol{x}}=\mathbf{0} \quad, \) for \( -\mathbf{1}< \)
\( \boldsymbol{x}<1, \) prove that \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=-\frac{\mathbf{1}}{(\mathbf{1}+\boldsymbol{x})^{2}} \)


\( (n-10)^{2}+(10-n) \)


Tangents drawn at the end points of the diameter of a circle are
A. Parallel
B. Perpendicular
c. Intersecting
D. None


The physical quantity having dimensions 2 in length is:
A. Power
B. Acceleration
c. Force constant
D. Stress


The reaction between which of the
following reactants produces hydrogen?
\( \mathbf{A} \cdot Z n+H C I \)
B \( . B a O_{2}+H C I \)
\( \mathbf{c} \cdot K_{2} S_{2} O_{8}+H_{2} O \)
D. \( N a_{2} O_{2}+H C I \)


A spring with force content \( k \) is initially
stretched by \( x_{1} . \) If it is further stretched
by \( x_{2}, \) then the increase in its potential
energy is.
A \( \cdot \frac{1}{2} k\left(x_{2}^{2}-x_{1}^{2}\right) \)
B \( \cdot \frac{1}{2} k x_{2}\left(x_{2}-2 x_{1}\right) \)
\( \mathbf{c} \cdot \frac{1}{2} k x_{1}^{2}-\frac{1}{2} k x_{2}^{2} \)
D・\frac{ } { \frac { 1 } { 2 } } x _ { 1 } ( x _ { 1 } + x _ { 2 } ) ^ { 2 }


Methanal and Phenol react in the
presence of base to give:
A. Bakelite
B. Polyethylene
c. Dacron
D. Nylon - 6, 6


Assertion
\( F_{2} \) undergoes disproportionation
reaction.
Reason
Fluorine shows both positive and
negative oxidation states.
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


Bromine can be liberated from
potassium bromide solution by the
action of :
A. iodine solution
B. chlorine water
c. sodium chloride
D. potassium iodide


If the \( C O_{2} \) content of the atmosphere is
as high as 300 parts per million
A. All plants would be killed
B. The plants would not grow properly
C. Plants would grow for some time and then die
D. The plants would thrive well


In Reimer Tiemann reaction
dichlorocarbene acts as:
A. nucleophile
B. electrophile
c. free radical
D. all of these


What is rainbow?


The direction of force on a current
carrying conductor placed in a magnetic field can be reversed by
reversing the direction of current flowing in the conductor. True/False?


A body at rest is acted upon by a constant force. What is the nature of the displacement-time graph?
A. Straight line
B. Symmetric parabola
c. Asymmetric parabola
D. Rectangular hyperbola


If a long straight wire carries a current
of \( 40 \mathrm{A} \), then the magnitude of the field B at a point \( 15 \mathrm{cm} \) away from the wire is:
A \( \cdot 5.34 \times 10^{5} \mathrm{T} \)
B. \( 8.34 \times 10^{5} \mathrm{T} \)
c. \( 9.6 \times 10^{5} \mathrm{T} \)
D . 10.2 \( \times 10^{5} \) न


ICZN was adopted in
A . 1960
B . 1970
\( c \cdot 1964 \)
D. 1974


The slag formed in the extraction of iron
from haematite in the blast furnace is:
A \( . F e S i O_{3} \)
в. \( \operatorname{casi} O_{3} \)
\( \mathbf{c} \cdot M g S i O_{3} \)
D. \( C a_{3}\left(P O_{4}\right)_{2} \)


Solution of differential equation \( x^{2}= \) \( 1+\left(\frac{x}{y}\right)^{-1} \frac{d y}{d x}+\frac{\left(\frac{x}{y}\right)^{-2}\left(\frac{d y}{d x}\right)^{2}}{2 !}+ \)
\( \frac{\left(\frac{x}{y}\right)^{-3}\left(\frac{d y}{d x}\right)^{3}}{3 !}+\ldots \)


Six particles situated at the corners of a regular hexagon of side a move at a constant speed v. Each particle maintains a direction towards the
particle at the next corner. If the time taken by the particles to meet each other is \( \frac{n a}{v} . \) Then \( n \) is given by


Energy required for the electron
excitation in \( \mathrm{Li}^{+} \) from the first to the
third Bohr orbit is
A. \( 12.1 \mathrm{eV} \)
B. 36.3 eV
c. \( 108.8 \mathrm{eV} \)
D. \( 122.4 \mathrm{eV} \)


State and explain Avogadro's law


Chromyl chloride gives yellow ppt. when it reacts with respectively
A \( \cdot C u(O H)_{2}, P b N O_{3} \)
в. \( N a O H,\left(C H_{2} C O O\right)_{2} C a \)
с. \( _{N a O H},\left(C H_{3} C O O O\right)_{2} P b \)
D. КОН \( , \)Рь SО О\( _{4} \)


The change in density from the maximum value to the minimum value,
again to the maximum value makes:
A. 2 complete oscillations
B. half oscillation
c. 3 complete oscillations
D. 1 complete oscillation


Transitional stage of physical and physiological development that occurs in the period between puberty and adulthood is called as
A. Adolescence
B. Puberty.
c. senescence
D. Maturity.


\( \sum_{s=1}^{n}\left\{\sum_{r=1}^{s} r\right\}=a n^{3}+b n^{2}+c n \)
then find the value of \( a+b+c \)
\( A \)
B.
\( c \cdot 2 \)
\( D \)


Some water in a tin with lid which can
be tightly screwed on its open mouth. The water is heated to boil and the
steam from boiling water is allowed to escape for sometime. The open mouth is sealed with air-tight cap and the can is cooled under tap-water. The sides of the can are crushed and get deformed.


The electric potential at a point in free space due to a charge \( Q \) coulomb is
\( Q \times 10^{11} \) volts. The electric field at that
point is -
\( \mathbf{A} \cdot 4 \pi \epsilon_{0} \times 10^{20} \) volt \( / \mathrm{m} \)
B . \( 12 \pi \epsilon_{0} \times 10^{22} \)volt\( / m \)
C . \( 4 \pi \epsilon_{0} \times 10^{22} \) volt \( / m \)
D . \( 12 \pi \epsilon_{0} \times 10^{20} \) volt \( / m \)


Define experiment


Which of the following reacts with water to form very stable product?
A. \( C H_{3} C l \)
в. \( C C l_{4} \)
c. \( C C l_{3} C H O \)
D. \( C H_{2} C l C H_{2} C l \)


The present system of Braille was adopted in :
A . 182
в. 1932
c. 191
D. 1852


Which set of rational numbers is
arranged in ascending order?
A \( \cdot-\frac{5}{14},-\frac{25}{28},-\frac{3}{7},-\frac{1}{2} \)
B. \( -\frac{25}{28}, \frac{-5}{14}, \frac{-3}{7},-\frac{1}{2} \)
c. \( -\frac{25}{28},-\frac{1}{2},-\frac{3}{7},-\frac{5}{14} \)
D. \( -\frac{1}{2}, \frac{-3}{7}, \frac{-5}{14}, \frac{-25}{28} \)


net acceleration of block \( \mathrm{B}, \) when
extension in the spring is \( \boldsymbol{x}=\frac{\boldsymbol{x}_{\boldsymbol{m}}}{\boldsymbol{4}} \)
A \( \cdot \frac{g}{2}(\text {downwards}) \)
B. \( \frac{g}{3}(\text {downwards}) \)
c. \( \frac{g}{4}(\text {downwards}) \)
D. \( \frac{g}{6}(\text {downwards}) \)


Electrochemical cells are also called:
This question has multiple correct options
A. electrolytic cells
B. galvanic cells
c. fuel cells
D. voltaic cells


In the given circle \( A B C D, O \) is the centre
and \( \angle B D C=42^{\circ} . \) The \( \angle A C B \) is equal to
A \( \cdot 42^{\circ} \)
B. \( 45^{\circ} \)
\( c \cdot 48^{\circ} \)
\( D \cdot 60 \)


Give the dimensional formula for
Gravitational constant \( G \)


A fork of frequency 256 Hz resonates with a closed organ pipe of length 25.4 \( \mathrm{cm} . \) If the length of pipe be increases by \( 2 \mathrm{mm}, \) the number of beats/sec will be :
\( A \cdot 4 \)
B.
\( c \cdot 2 \)
D.


Which of the following is used in making textiles and ropes?
A. Dacron
B. Perlon - L
c. Rayon
D. None of the above


How far will the car have traveled in the
time? (in km)
\( \mathbf{A} \cdot \mathbf{6} \)
B. 6.75
c. 7.75
D. 8.75


An object is said to be in equilibrium
when:
1. there is no net force acting on the
object
2. the total clockwise moments about
any point is equal to the total anti-
clockwise moments about the same
point
3. the object moves with constant
velocity
A . 1 only
B. 2 only
c. 1 and 2 only
D. 1,2 and 3


Fossils are
A. Fovea in the retina of vertebrate eye
B. Remains of organisms present in the rocks
C. The fossa present in the bones
D. Foramen through which nerves pass


Which of the following devices can be used as a square law device for modulation.
A. p-n-p transistor in active region
B. p-n junction diode near threshold voltage
c. superconductor
D. Inductor


For a reaction, calculate value of ratio, \( \frac{[x]_{t}}{[y]+[z]} \) at any given instant \( t \)


Mark the incorrect statement.
A. The direction of the magnetic field is taken to be the direction in which a north pole of the compass needle moves inside it.
B. The magnetic field lines are closed curves.
C. No two field-lines are found to cross each other.
D. None


The symbols \( F . H . S . V_{m} \) and \( E^{o} \) denote
Helmholtz free energy, enthalpy, entropy, molar volume and standard
electrode potential, respectively. The correct classification of the properties
is:
A. \( F . H . S \) are intensive; \( V_{m} \) and \( E^{o} \) are extensive
B. F.H.S are extensive; \( V_{m} \) and \( E^{\circ} \) are intensive
c. \( F . H . S \) and \( V_{m} \) are intensive; \( E^{o} \) are extensive
D. \( F . H . S \) and \( E^{o} \) are extensive; \( V_{m} \) are intensive


Find any two rational numbers \( \frac{1}{4} \) and \( \frac{3}{4} \)


Which of the following is the most stable form of cyclohexane?
A. Boat
B. Planar
c. Twist boat
D. chair


Apparent weight at bottom most line is
A . 2 mg
в. \( m g \)
\( \mathrm{c} .3 \mathrm{mg} \)
D. \( 4 \mathrm{mg} \)


\( N^{\prime} \) moles of a diatomic gas in a
cylinder are at a temperature \( ^{\prime} \boldsymbol{T}^{\prime} . \) Heat
is supplied to the cylinder such that the
temperature remains constant but \( n \)
moles of the diatomic gas get converted
into monatomic gas.What is the change in the total kinetic energy of the
gas?
A \( \cdot \frac{5}{2} n R T \)
B. \( \frac{1}{2} n R T \)
c. 0
D. \( \frac{3}{2} n R T \)


An example of double salt is:
A. potash alum
B. hypo
c. \( K_{4}\left[F e(C N)_{6}\right. \)
D. bleaching powder


A wire is cut in to 4 pieces, which are put together by sides to obtain one conductor. If the original resistance of
wire was \( R, \) the resistance of the bundle
will be:
A \( \cdot \frac{R}{4} \)
в. \( \frac{R}{8} \)
c. \( \frac{R}{16} \)
D. \( \frac{R}{32} \)


What is the first component of an ordered pair (1,-1)\( ? \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. -
\( c \cdot 2 \)
\( D \)


Which of the following combinations is correctly matched?
\( ^{\mathbf{A}} \cdot_{C H_{3}-C_{D}^{H}-C l, S_{N^{2}} W a l d e n i n v e r s i o n} \)
\( ^{\text {B. }} C H_{3}-_{J}^{\text {I }} C-C l, S_{N 1} \) Waldeninversion
\( \mathrm{c}_{C_{6} H_{5}-} \stackrel{c_{2}, \text { Нь}}{C}-\mathrm{Cl}, S_{N 1} \) Only retension
\( ^{\mathrm{D}} C_{6} H_{5}-\begin{array}{c}c_{2}, H_{5} \\ C_{H} \\ C H_{3}\end{array}-C l, S_{N^{1}} O n l y \) inversion


Name a prism required for obtaining a spectrum of ultraviolet light.


The reaction \( \boldsymbol{A}(\boldsymbol{g})+\mathbf{2} \boldsymbol{B}(\boldsymbol{g}) \rightarrow \boldsymbol{C}(\boldsymbol{g})+ \)
\( D(g) \) is an elementary process. In an
experiment, the initial partial pressure
of \( A \) and \( B \) are \( P_{A}=0.40 \) and \( P_{B}= \)
0.60 atm. When \( P_{C}=0.2 a t m \) and the
rate of reaction relative to the initial
rate is ?
A \( \cdot 1 / 48 \)
B. 1/24
c. \( 9 / 16 \)
D. 1/18


The boiling points of neon and krypton
\( \operatorname{are}-245.9^{\circ} \mathrm{C} \) and \( -152.9^{\circ} \mathrm{C} \)
respectively. Using these data estimate the boiling point of argon. (report answer as the negative of the closest integer)
A \( \cdot-289^{\circ} C \)
в. \( -299^{\circ} \mathrm{C} \)
c. \( -199^{\circ} \mathrm{C} \)
D. \( -189^{\circ} \mathrm{C} \)


Obtain a differential equation by
eliminating the arbitrary constants \( a \)
and \( b \) from the equation \( y=a \cos n t+ \)
\( \boldsymbol{b} \sin \boldsymbol{n} \boldsymbol{t} \)


If spin quantum number are \( -\frac{1}{2}, 0,+\frac{1}{2} \) based on the above assumption electronic configuration of the elements with atomic number 30 is:
B . \( 1 s^{3} 1 p^{15} 2 s^{3} 1 d^{9} \)
C \( \cdot 1 s^{9} 1 p^{15} 2 s^{6} \)
D \cdot \( 1 s^{3} 19^{p} 2 s^{3} 2 p^{9} 1 d^{6} \)


How many colors are present in the rainbow?
A. 5
B. 6
c. 7
\( D \)


f at a particular temperature, the density of \( 18 ~ M ~ H_{2} S O_{4} \) is \( 1.8 ~ g c m^{-3} \)
then calculate the molality of the
solution:


Integrate:
\( \int \frac{1}{\sqrt{x}+x} d x= \)


If total sum of square is 20 and sample
variance is 5 then total number of
observations are
A . 15
B. 35
c. 25
D. 4


In studying diffraction pattern of different obstacles, the effect of:
A. full wave front is studied
B. portion of a wave front is studied
c. waves from two coherent sources is studied
D. waves from one of the coherent source is studied


Excretory material are formed in
A. Kidney
B. Rectum
c. Liver
D. Every cell of the body


Find the maximum and minimum
values, if any of the following function given by
¡) \( \boldsymbol{f}(\boldsymbol{x})=|\boldsymbol{x}+\mathbf{2}|-\mathbf{1} \)
ii) \( \boldsymbol{g}(\boldsymbol{x})=-|\boldsymbol{x}+\mathbf{1}|+\mathbf{3} \)
iii) \( \boldsymbol{f}(\boldsymbol{x})=|\sin 4 \boldsymbol{x}+\boldsymbol{3}| \)


Two boxes \( A \) and \( B \) weighing 5 kg and 10 kg respectively, have to be pushed along the same slope. In which case will the frictional force be more?
\( A \cdot B O x A \)
B. Box B
c. same for both
D. Unsure


What are indicators? Name any two
natural and two synthetic indicators.


Which of these is not an ore of Iron?
A . Haematite
B. Limonite
c. cassiterite
D. Magnetite


Does a new substance form when a
solute dissolves in a solvent?


In a DC generator,the induced e.m.f in the armature is
A. DC
B. AC
c. Fluctuating DC
D. Both AC and DC


n Fig. \( \boldsymbol{A D} \perp \boldsymbol{C D} \) and \( \boldsymbol{C B} \perp \boldsymbol{C D .} \) If
\( A Q=B P \) and \( D P=C Q, \) prove that
\( \angle D A Q=\angle C B P \)


decreases to \( 6 \% \)


Two radio stations broadcast their
program at the same amplitude \( A \) but
at slightly different frequencies \( n_{1} \) and \( n_{2} \) such that \( \left(n_{1}-n_{2}\right)=10^{3} H z . \)
detector receives signals from both the stations simultaneously but only when
intensity of signal is greater than \( 2 A^{2} \) The time interval between two
successive maxima will be :
в. \( 10^{-2} \) s
\( \mathrm{c} \cdot 10^{-3} s \)
D. \( 10^{\circ} \)


If the density of materials of two strings of same length, tension and area of cross-section are 2 kgm \( ^{-3} \) and
\( 4 k g m^{-3} \) respectively then the ratio of their frequencies will be
A. \( 1: \sqrt{2} \)
2 \( : \sqrt{2} \cdot \sqrt{2} \)
B . 2: 1
c. 1: 2
D. \( \sqrt{2}: 1 \)


The pressure on a square plate is measured by measuring the force on the plate and the length of the sides of
the plate. If the maximum errors in the
measurement of force and length are respectively \( 4 \% \) and \( 2 \% \), then the maximum error in the measurement of
pressure is?
A . \( 1 \% \)
B. 2\%
\( c .6 \% \)
D. \( 8 \% \)


If \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) is defined by \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}- \)
\( [\boldsymbol{x}]-\frac{1}{2} \forall \boldsymbol{x} \in \boldsymbol{R}[\boldsymbol{x}] \) is the greatest
integer not exceeding \( x \) then \( \{x \in R: \) \( \left.\boldsymbol{f}(\boldsymbol{x})=\frac{1}{2}\right\}= \)
A. the set of all integers
B. N, the set of all natural numbers
c. \( \phi \), the empty set
\( D \)


The effect of an impulse force on the body is measured only in terms of its
A. Force
B. Moment of momentum
c. Impulse
D. None of these


At room temperature \( \left(20^{\circ} \mathrm{C}\right) \) orange juice gets spoilt in about 64 hours. In a
refrigerator at \( 3^{\circ} C \) juice can be stored
three times as long before it gets spoilt. The activation energy of the reaction that causes the spoiling of juice is :
A \( .43 .46 \mathrm{kJmol}^{-1} \)
B . \( 46.76 \mathrm{kJmol}^{-1} \)
c. \( 49.54 \mathrm{kJmol}^{-1} \)
D. 50.23 kJmol\( ^{-1} \)


Factorise the following:
\( x^{2}+8 x+24 y-9 y^{2} \)
A \( .(x+y)(x-3 y+8) \)
в. \( (x+3 y)(x-3 y+8) \)
c. \( (x+2 y)(x-3 y+8) \)
D. \( (2 x+3 y)(x-3 y+8) \)


If y varies inversely with the fourth root
of \( x, \) and \( y=4 \) when \( x=\frac{1}{16}, \) then what
is the value of \( y \) when \( x=\frac{1}{81} \)


Explain the steps involved in the
sewage treatment.


When \( S_{2} O_{8}^{2-} \) oxidise \( F e^{2+} \) then product formed is:
\( \mathbf{A} \cdot S_{2} O_{6}^{2} \)
B \( . S O_{4}^{2-} \)
\( \mathrm{c} \cdot S_{2} O_{3}^{2} \)
D. \( S O_{5}^{2-} \)


Which substance could not be used as
a fuel to heat water in a boiler?
A. ethanol
B. hydrogen
c. methane
D. oxygen


Give the balanced reaction for the
manufacture of the ammonia gas.
A. \( 3 N_{2}+3 H_{2} \rightarrow 6 N H_{3} \)
в. \( N_{2}+3 H_{2} \rightarrow 2 N H_{3} \)
c. \( N_{2}+3 H_{2} \rightarrow N H_{3} \)
D. \( N_{2}+6 H_{2} \rightarrow 4 N H_{3} \)


Cladonia rangiferina is,
A. Lichen
B. Alga
c. Fungus
D. Angiosperm


Ruchi noticed a major problem in her state. She found that more and more
land area in her state is turning into desert. What is the condition called?
A. Deforestation
B. Barren land
c. Desertification
D. Afforestation


What is the dominant intermolecular
force or bond that must be overcome in
converting liquid \( C H_{3} O H \) to a gas?
A. London dispersion force
B. Hydrogen bonding
c. Dipole-dipole interaction
D. Covalent bonds


The reaction, \( 2 S O_{2(g)}+O_{2(g)} \rightleftharpoons \)
\( 2 S O_{3(g)} \) is carried out in a \( 1 d m^{3} \) vessel
and \( 2 d m^{3} \) vessel separately. The ratio of the reaction velocities will be:
A . 1: 8
B. 1: 4
c. 4: 1
D. 8: 1


Which periods were not divided into two series in the Mendeleev's periodic
table?
A .4
B. 5
\( c .6 \)
D. None of the above


Fill in the blanks.
Nitrogen is a of
combustion.


Evaluate: \( \int_{0}^{\frac{\pi}{2}} \cos ^{2} x d x \)


Serule is
A. Hydrosere
B. Biosere
c. Microbial succession
D. Lithosphere


A light of wavelength \( \lambda \) is incident on an object of size b. If a screen is at a
distance D from the object. Identify the correct condition for the observation of
different phenomenon:
a) if \( b^{2}=D \lambda \), Fresnel diffraction is
observed
b) if \( b^{2}>>D \lambda \), Fraunhoffer diffraction
is observed
c) if \( b^{2}<<D \lambda \), Fraunhoffer diffraction
is observed
d) if \( b^{2}=D \lambda, \) Fraunhoffer diffraction is
observed
A. a, b and d are true
B. a,c and d are true
\( c \cdot \) a and c are true
D. a and d are true


RBCs have
A. Antigen (agglutinogen) on their surface
B. Carbonic anhydrase
C. Antibody on their surface
D. Both A and B


A current of \( 10^{-7} \) ampere produces 50
division deflection in a galvanometer. Then its figure of merit will be
A \( \cdot 10^{-4} \) amp \( / d i v \)
B . \( 10^{-8} \) amp / div
\( \mathbf{c} \cdot 10^{-10} \mathrm{amp} / \mathrm{div} \)
D. \( 2 \times 10^{-9} \) amp/div


How much water has he to consume in
30 min running if the heat is eliminated through perspiration?
A . \( 0.6 L \)
в. \( 0.7 L \)
c. \( 0.8 L \)
D. \( 0.9 L \)
E. none of these


The middle terms, if four different
numbers are in proportion are called
A. Antecedents
B. Means
C. Extremes
D. consequents


The wave number of the radiation whose
quantum 1 erg is:
A. \( 5 \times 10^{15} \mathrm{cm}^{-1} \)
B. \( 15 \times 10^{5} \mathrm{cm}^{-1} \)
c. \( 1.5 \times 10^{15} \mathrm{cm}^{-1} \)
D. \( 5 \times 10^{5} \mathrm{cm}^{-1} \)


The radius of the circle \( x^{2}+y^{2}-5 x+ \)
\( 2 y+5=0 \) is
\( A \cdot 2 \)
B.
\( c \cdot \frac{3}{2} \)
D. \( \frac{2}{3} \)


Find the integral \( \int \frac{\sin x}{\cos ^{2} x} d x \)


Which of the following can be used for protection of carbonyl group:
This question has multiple correct options
A. \( C H_{2} O H-C H_{2} O H / H \)
в. \( C H_{2} O H-C H_{2}-C H_{2} O H / H \)
c. \( H S-\left(C H_{2}\right)_{3}-S H \)
D. \( C H_{2} O H-C H_{2}-C H O \)


Which of the following patterns of reproduction involves the exchange of genetic material?
A. Sexual reproduction
B. Asexual reproduction
c. Both A and B
D. None of these


\( A \) block \( A, \) whose weight is \( 200 N, \) is
pulled up a slope of length \( 5 m \) by
means of a constant force \( \boldsymbol{F}(=\mathbf{1 5 0} \boldsymbol{N}) \)
as illustrated in the figure.The difference in work done by the force and the increase in potential energy of the block is :
A . \( 0 . \)
в. \( 150 J \)
\( c .750 J \)
D. \( 600 J \)


Find the inverse of the following matrices by the adjoining method \( \left[\begin{array}{ccc}1 & 0 & 0 \\ 3 & 3 & 0 \\ 5 & 2 & -1\end{array}\right] \)


I: The real number x when added to its
inverse gives the minimum positive
value of the sum at \( x=1 \)
Il: If product of the two positive numbers is 400 , then the minimum value of their
sum is 20
which of the above statements are true
A . only lis true
B. only II is true
c. both I and II are true
D. niether I nor II are true


Let \( \alpha \) and \( \beta \) be the distinct roots of
\( a x^{2}+b x+c=0, \) then
\( \lim _{x \rightarrow \alpha} \frac{1-\cos \left(a x^{2}+b x+c\right)}{(x-\alpha)^{2}} \) is equal to
\( \mathbf{A} \cdot \mathbf{0} \)
B \( \cdot \frac{1}{2} a^{2}(\alpha-\beta)^{2} \)
c. \( \frac{1}{2}(\alpha-\beta)^{2} \)
D. \( -\frac{1}{2} a^{2}(\alpha-\beta)^{2} \)


The angle between the pair of lines whose equation is \( 4 x^{2}+10 x y+ \)
\( m y^{2}+5 x+10 y=0 \) is
A \( \cdot \tan ^{-1}\left(\frac{3}{8}\right) \)
B. \( \tan ^{-1} \frac{2 \sqrt{25-4 m}}{m+4} \)
\( ^{\mathbf{c}} \cdot \tan ^{-1}\left(\frac{3}{4}\right) \)
D. \( \tan ^{-1} \frac{\sqrt{25-4 m}}{m+4} \)


Find the value of the constant \( k \) so that
the function given below is continuous
at \( \boldsymbol{x}=\mathbf{0} \)
\( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\frac{1-\cos 2 x}{2 x^{2}}, x \neq 0 \quad k x=0\right\} \)


Find out the increase in temperature of
\( 50 g \) block of solid marble (specific heat
\( =\mathbf{0 . 9 k J} / k g), \) originally at 20 if it
absorbs \( 100 \mathrm{J} \) of heat \( ? \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 4 \)
D. 10
E. 20


Vocal cords in men are about
long.
A. 20 mm
B. 20 cm
\( c \cdot 20 m \)
D. \( 15 \mathrm{cm} \)


Both of the gas samples represented
above are at the same temperature and
pressure. The mass of \( \boldsymbol{H}_{2} \) in the one
liter container is 0.20 gram. The mass
of \( X \) in the two-liter container is 8
grams. The molecular weight of \( \boldsymbol{X} \) is :
A. \( 10 \mathrm{g} / \mathrm{mol} \)
B. 20 g/mol
c. 40 g/mol
D. \( 60 g / \) mol
E . 80 g/mol


\( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R}, \boldsymbol{g}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) and \( \boldsymbol{f}(\boldsymbol{x})=\sin \boldsymbol{x} \)
\( \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{x}^{2} \) then \( \boldsymbol{f o g}(\boldsymbol{x})= \)
A \( \cdot x^{2}+\sin x \)
B. \( x^{2} \sin x \)
\( \mathbf{c} \cdot \sin ^{2} x \)
\( D \cdot \sin x^{2} \)


A ball is dropped on the floor from a height of \( 10 \mathrm{m} \). It rebounds to a height of \( 2.5 \mathrm{m} \).If the ball is in contact with the
floor for 0.01 sec, then average acceleration during contact is
\( \mathbf{A} \cdot 2100 m / s^{2} \)
B. \( 1400 \mathrm{m} / \mathrm{s}^{2} \)
\( \mathbf{c} \cdot 700 m / s^{2} \)
D. \( 400 \mathrm{m} / \mathrm{s}^{2} \)


Pick out the correct statement(s) above
a universal indicator.
This question has multiple correct options
A. It is a mixture of some indicators.
B. It shows the change in colour at different pH with altogether different colours for a change in pH by units
C. Phenolphthalein is an universal indicator.
D. a mixture of methyl red, \( \alpha \) -naphthol, phthalein blue shows different colours between pH range 4 to 11


Predict product (s) in the following reaction,
\( \boldsymbol{P}+\boldsymbol{O H}^{-} \rightarrow \boldsymbol{P r o d u c t s} \)
This question has multiple correct options
A \( . P H_{3} \)
B \( \cdot P O_{4}^{2} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{PO}_{2} \)
D. \( P O_{2}^{-} \)


Number of possible isomers for the
complex \( \left[\text { Co }(e n)_{2} C l_{2}\right] C l \) will be
A .
B. 3
\( c \cdot 4 \)
D. 2


A metal conductor of length \( 1 \mathrm{m} \) rotates vertically about one of its ends at angular velocity 5 radians per second. If
the horizontal component of earth's magnetic field is \( 0.2 \times 10^{-4} T \), then the
e.m.f developed between the two ends of
the conductor is
\( A \cdot 5 m v \)
B. \( 50 \mu V \)
c. \( 5 \mu V \)
D. 50 mv


Find the number of S-S linkage in \( \gamma- \)
\( \boldsymbol{S O}_{3} \) molecule


A sample consisting of 1 mol of a
monoatomic perfect gas \( \left(C_{v}=\frac{3}{2} R\right) \) is
taken through the cycle as shown:
\( \Delta H \) for the overall cycle is :
A \( \cdot+5.67 \times 10^{3} J \)
B \( .-5.67 \times 10^{3} J \)
c. \( -11.34 \times 10^{3} J \)
\( D \)


Select correct statement regarding
\( \left[N i(D M G)_{2}\right] \) complex compound.
\( A \cdot \) It acts as oxidising agent because \( N i^{2+} \) cation is having EAN 34.
B. It is extra-stabilized by hydrogen bonding.
C. Its IUPAC name in bis(dimethylglyoximato)nickel(II)
D. It's ligand contains two different donar site.


Heat always flows from
temperature to \( _{-}-_{-}-_{-}- \) temperature


When light is incident on the interface of glass and air as shown in the figure, the green light is just totally internally reflected. Then the emerging ray in air contains:
A . yellow, orange, redd
B. violet, indigo, blue
c. all colours
D. all colours except green


A circular coil of 250 turns and
diameter \( 18 \mathrm{cm} \) carries a current of \( 12 A \)
What is the magnitude of magnetic moment associated with the coil?


State, whether the following number is rational,

If rational then enter 1 and if false then
enter 0 \( (5+\sqrt{5})(5-\sqrt{5}) \)


Prove that:
\( \int_{0}^{2 a} f(x) d x=\int_{0}^{a} f(x) d x+\int_{0}^{a} f(2 a- \)
\( \boldsymbol{x}) \boldsymbol{d} \boldsymbol{x} \)


The product which is not formed on the heating of potassium permanganate is
A. \( K_{2} M n O_{4} \)
в. \( M n O_{2} \)
\( c \cdot O_{2} \)
D. \( M n O_{4} \)


\( \left[(13)^{2}+\sqrt[3]{1728}-\sqrt{441}\right] \div 4^{2} \times 15^{3} \)
equals
A \( \cdot \frac{2}{675} \)
B. 33750
\( c \cdot \frac{2}{45} \)
D. 485


In India the family planning program officially started in
A . 1958
B. 1991
c. 2000
D. 1951


Electric field intensity at a point due to a charge \( Q \) is \( 24 \mathrm{N} / \mathrm{C} \) and electric potential at \( A^{\prime} \) due to charge \( Q \) is \( =12 \mathrm{j} / \mathrm{C} \) The distance between the charges and magnitude of \( Q \) are
A \( \cdot 0.4 m, 0.667 \times 10^{-9} \mathrm{C} \)
B . \( 0.4 m, 6.67 \times 10^{-4} \mathrm{C} \)
c. \( 0.5 m, 2.67 \times 10^{-9} \mathrm{C} \)
D. \( 0.5 m, 7.66 \times 10^{-9} \mathrm{C} \)


State whether the given statement is true or false. If true enter 1 or else enter
\( \mathbf{0} \)
\( (x, y) \) is an ordered pair, whose first component is \( x \) and the second
component is \( \boldsymbol{y} \)


Pick out the wrong statement from the following
A. The Sl unit of universal gravitational constant is \( N m^{2} k g^{-2} \)
B. The gravitational force is a conservative force
C. The force of attraction due to a hollow spherical shell of uniform density on a point mass inside it is zero
D. The centripetal acceleration of the satellite is equal to acceleration due to gravity
E . Gravitational potential energy \( =\frac{\text { gravitation potential }}{\text { mass of the body }} \)


A neutral atom has a total of
17 electrons. The electron configuration
in the outermost principle energy level will look closest to:
A \( \cdot 1 s^{2}, 2 s^{2}, 2 p^{5} \)
B . \( 3 s^{2}, 3 p^{5} \)
\( \mathbf{c} \cdot s^{2}, p^{5} \)
D. \( s^{2}, p^{8}, d^{7} \)
E \( . s, p^{7} \)


Assertion
\( N O_{2} \) is reddish brown and its dimer
\( N_{2} O_{4} \) is colourless
Reason
There is a dative bond formation
between two \( N O_{2} \) molecules.
A. Both assertion and reason are CORRECT and reason is the CORRECT explanation of the assertion
B. Both assertion and reason are CORRECT, but reason is NOT THE CORRECT explanation of the assertion
c. Assertion is CORRECT, but reason is INCORRECT
D. Assertion is INCORRECT, but reason is CORRECT


The standard heats of formation at
\( 298 K \) for \( C C l_{4}(g), H_{2} O(g), C O_{2}(g) \)
and \( H C l(g) \) are -25.5,-57.8,-94.1
and \( -22.1 k c a l \) mol \( ^{-1} \) respectively
Calculate \( \Delta H_{298}^{o} \) for the reaction. \( \boldsymbol{C C l}_{4}(\boldsymbol{g})+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \longrightarrow \boldsymbol{C O}_{2}(\boldsymbol{g})+ \)
\( 4 H C l(g) \)


The ratio of the weight of a body to its
mass gives the at the given place
A. acceleration due to gravity
B. velocity due to gravity
c. force due to gravity
D. displacement due to gravity


Read the statements and mark the
correct one:
i. It has 63 dot patterns or characters.
ii. through Braille system,visually challenged people can only read the languages.
iii. It is a coded language based on logical system
B. i, ii
c. ii, ii
D. All are true


A function \( \boldsymbol{f}:(-\mathbf{3}, \mathbf{7}) \rightarrow \boldsymbol{R} \) is defined as
follows:
\( f(x)=\left\{\begin{array}{cc}4 x^{2}-1 ; & -3 \leq x<2 \\ 3 x-2 ; & 2 \leq x \leq 4 \\ 2 x-3 ; & 4<x \leq 6\end{array}\right. \)
Find: \( \boldsymbol{f}(\boldsymbol{5})+\boldsymbol{f}(\boldsymbol{6}) \)


f \( A+2 B=\left[\begin{array}{cc}2 & -4 \\ 1 & 6\end{array}\right], A^{\prime}+B^{\prime}= \)
\( \left[\begin{array}{cc}1 & 2 \\ 0 & -1\end{array}\right], \) then \( A= \)


Fill in the blanks with approriate words. ... valves prevent backflow of blood
into the heart.


The velocity of train increase uniformly from \( 20 \mathrm{km} / \mathrm{h} \) to \( 60 \mathrm{km} / \mathrm{h} \) in 4 hour.The
distance traveled by the train during this period is


Q Type your question
paluic invitg in a suaigil line is shown in given figure. During the nterval \( O A, A B, B C \) and \( C D, \) the
acceleration of the particle is
CD \( \mathrm{BC} \) \( \begin{array}{cc}\mathrm{OA} & \mathrm{AB} \\ + & 0\end{array} \) \( + \) \( t \)
B \( \mathrm{CD} \) \( \begin{array}{ccc}\text { OA } & \text { AB } & \text { BC } \\ - & 0 & +\end{array} \) 0
\( \begin{array}{cccc}\text { OA } & \text { AB } & \text { BC } & \text { CD } \\ + & 0 & - & +\end{array} \)
D \( \begin{array}{cccc}\mathrm{OA} & \mathrm{AB} & \mathrm{BC} & \mathrm{CD} \\ - & 0 & - & 0\end{array} \)


Which compound is used as an
antacid?
A. Soda ash
B. Baking soda
c. Nitrous oxide
D. Magnesium carbonate


The heights of trees in a forest are given as follows. Draw a histogram to represent the data.
\( \begin{array}{llll}\text { Heights } & \mathbf{1 6}- & \mathbf{2 1}- & \mathbf{2 6}- \\ \text { in } & \mathbf{2 0} & \mathbf{2 5} & \mathbf{3 0} \\ \text { metre } & & & \end{array} \)
Number
of trees
10
15
25


Find the mean deviation from the
median for the following ungrouped data 20,25,30,18,15,40
\( \mathbf{A} \cdot \mathbf{6} \)
B. 4
\( c \cdot 7 \)
D. 5


Two resistors of resistances \( 2 \Omega \) and \( 6 \Omega \)
are connected in parallel. This
combination is then connected to a
battery of emf \( 2 \mathrm{V} \) and internal
resistance \( 0.5 \Omega . \) What is the current
flowing through the battery?
A. 4 A
в. \( \frac{4}{3} A \)
c. \( \frac{4}{17} A \)
D. 1A


Screen S is illuminated by two point
sources \( A \) and \( B \). Another source
C sends a parallel beam of light towards
point \( P \) on the screen. Line \( A P \) is normal
to the screen and the lines \( A P, B P \)
and \( \mathrm{CP} \) are 6,3 and \( 3 \mathrm{m} \) respectively. The
radiant powers of sources A and B are 45 and \( 90 \mathrm{W} \) respectively. The beam
from \( C \) is of intensity \( 0.4 ~ W / m^{2} . \) The total incident intensity at \( \mathrm{P} \) is


How many molecules of ammonia are
required to form 8 molecules of urea?
A . 24
B. 8
\( c \cdot 16 \)
\( D \)


The average power transmitted through a given point on a string supporting a
sine wave is 0.40 watt when the
amplitude of wave is 2 mm. What average power will be transmitted
through this point if its amplitude is increased to 4 mm?


If \( G_{1} \) and \( G_{2} \) are geometric mean of two
series of sizes \( n_{1} \) and \( n_{2} \) respectively
and \( G \) is geometric mean of their
combined series, then \( \log G \) is equal to
A \( \cdot \log G_{1}+\log G_{2} \)
в. \( n_{1} \log G_{1}+n_{2} \log G_{2} \)
\( c \cdot \frac{\log G_{1}+\log G_{2}}{n_{1}+n_{2}} \)
D. \( \frac{n_{1} \log G_{1}+n_{2} \log G_{2}}{n_{1}+n_{2}} \)


Which molecular geometry is least likely to result from a trigonal bipyramidal electron geometry?
A. Trignoal planer
B. See-saw
c. Linear
D. T-shaped


Which of the following occurs as a deposit of river bed?
A. Sand
B. Clay
c. silt
D. Silica


Rhizophora possesses
A. Pneumatophores
B. Prop roots
C . Stilt roots
D. Modified roots


Let \( \boldsymbol{P}=\left[\boldsymbol{a}_{i j}\right] \) be a \( \boldsymbol{3} \times \boldsymbol{3} \) matrix and let
\( Q=\left(b_{i j}\right) \) where \( b_{i j}=2^{i+j} a_{i j} \) for \( 1 \leq \)
\( i, j \leq 3 . \) If the determinant of \( P \) is 2 then
the determinant of the matrix \( Q \) is?
A \( \cdot 2^{10} \)
B . \( 2^{11} \)
\( c \cdot 2^{12} \)
D. \( 2^{13} \)


If to a stationary observer the apparent frequency appear to be \( 6 / 5 \) times the actual frequency of the moving source then the speed and direction of the sound source is : (velocity of sound = \( 360 \mathrm{m} / \mathrm{sec}) \)
A. \( 60 \mathrm{m} / \mathrm{s} \) towards the observer
B. 60 m/s away from the observer
c. \( 55 \mathrm{m} / \mathrm{s} \) towards the observer
D. 55 m/s away from the observer


Assertion: Substances which at room
temperature retain their ferromagnetic
property for a long period of time are
called permanent magnets.

Reason: Permanent magnet can be
made by placing a ferromagnetic rod in
a solenoid and passing current through
¡t.
A. If both assertion and reason are true and reason is the
correct explanation of assertion.
B. If both assertion and reason are true and reason is not the correct explanation of assertion.
C. If assertion is true but reason is false.
D. If both assertion and reason are false.


Three different wavelengths of light (1,2 and 3 ) are shined onto the same
sodium metal surface. Light 1 and 2 produced photoelectrons while Light 3 did not produce any photoelectrons.
Light 2 was able to produce photoelectrons with higher velocities
than Light 1
Arrange the lights in order of decreasing wavelength.
\( \mathbf{A} \cdot 3>1>2 \)
В. \( 2>1>3 \)
c. \( 1>2>3 \)
D. \( 3>2>1 \)


A direct current of \( 5 A \) is superimposed
on an alternating current \( \boldsymbol{I}=\mathbf{1 0} \sin \boldsymbol{\omega} \boldsymbol{t} \)
flowing through a wire. The effective value of the resulting current will be
\( \mathbf{A} \cdot(15 / 2) A \)
B. \( 5 \sqrt{3} A \)
c. \( 5 \sqrt{5} \) A
D. 15 A


A body has its center of mass at the origin. The \( x \) -axis coordinates of the
particles:
A. may be all positive
B. may be all negative
c. should be all at zero
D. may be positive for some case and negative in other cases


When a solenoid is activated, the force
that moves the plunger is
A. an electromagnetic field
B. a permanent magnetic field
c. varying voltage
D. a steady current


Which of the following do not have
linear structure?
A. \( C O_{2} \)
в. \( N_{2} \),
\( \mathbf{c} \cdot B e F_{2} \)
D. \( \operatorname{SnCl}_{2} \)


The construction of \( \Delta L M N \) when
\( M N=6 \mathrm{cm} \) and \( m \angle M=45^{\circ} \) is not
possible when difference between \( L M \)
and \( L N \) is equal to:
\( \mathbf{A} \cdot 6.9 \mathrm{cm} \)
B. \( 5.2 \mathrm{cm} \)
\( c .5 \mathrm{cm} \)
D. 4 ст


Given \( \boldsymbol{A}=\{\boldsymbol{b}, \boldsymbol{c}, \boldsymbol{d}\} \) and \( \boldsymbol{B}=\{\boldsymbol{x}, \boldsymbol{y}\} \)
find element of \( \boldsymbol{A} \times \boldsymbol{B} \)
A \( \cdot\{b, x\} \)
в. \( \{b, y\} \)
c. \( \{c, x\} \)
D. All of the above


Let \( \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{2} & \mathbf{3} \\ \mathbf{- 1} & \mathbf{5}\end{array}\right] \cdot \) If \( \boldsymbol{A}^{-\mathbf{1}}=\boldsymbol{x} \boldsymbol{A}+\boldsymbol{y} \boldsymbol{I} \)
find \( \boldsymbol{x}+\mathbf{2} \boldsymbol{y} \)


A very dilute saturated solution of a
sparingly soluble salt \( A_{3} B_{4} \) has a vapour pressure of \( 20 \mathrm{mm} \) of Hg at temperature \( T, \) while pure water exerts a pressure of \( 20.0126 \mathrm{mm} \) Hg at the same temperature. Calculate the
solubility product constant of \( \boldsymbol{A}_{3} \boldsymbol{B}_{4} \) at the same temperature.
A. \( 2.7 \times 10^{-13} \)
В. \( 4.45 \times 10^{-7} \)
c. \( 6.8 \times 10^{-12} \)
D. \( 13.6 \times 10^{-7} \)


Show that the function \( f \) in \( A=R=\frac{2}{3} \) defined by \( f(x)=\frac{3 x+2}{5 x+3}, \neq \frac{-3}{5} \) is
one-one and onto.Hence find \( \boldsymbol{f}^{-1}(\boldsymbol{x}) \)


The \( x \) -t plot shown in the figure below
describes the motion of the particle,
along \( x \) -axis, between two positions \( A \)
and B. The particle passes through two
intermediate points \( P_{1} \) and \( P_{2} \) as shown
in the figure.
A. The instantaneous velocity is positive as \( P_{1} \) and
negative at \( P_{2} \)
B. The instantaneous velocity is negative at both \( P_{1} \) and
\( P_{2} \)
C. The instantaneous velocity is negative at \( P_{1} \) and
positive at \( P_{2} \)
D. The instantaneous velocity is positive at both \( P_{1} \) and
\( P_{2} \)
E. The instantaneous velocity is always positive


The set \( \{x: x \neq x\} \) may be equal to
\( A \cdot\{0\} \)
B. \{1\}
\( c \cdot\{3\} \)
\( D \cdot\{\phi\} \)


Three dimensional polymers with cross links formed in case of:
A. Thermoplastic
B. Thermosetting plastic
c. Both a) and b)
D. None of these


A terpene has molecular formula
\( A\left(C_{10} H_{16} O\right) \) and it is a major
constituent of lemongrass oil. \( \boldsymbol{A} \) on
treatment with acidified \( K M n O_{4} \)
solution produces acetone, Oxalic acid
and \( \boldsymbol{C H}_{3} \boldsymbol{C O C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{C O O H} . \boldsymbol{A} \| \mathbf{s o}, \boldsymbol{A} \)
does not give silver mirror test with Tollen's reagent. The correct deduction regarding \( \boldsymbol{A} \) is/are:
A. \( A \) gives positive iodoform test
B. \( A \) has two stereoismers
c. \( A \) has one chiral carbon
D. \( A \) on treatment with \( N H_{2} O H \) gives six pair of diastereomers


Draw a right angle and construct its bisector.


The centre of mass of a system of
particles is at the origin. From this we
conclude that:
A. The numberof particles on positive x-axis is equal to the number of particles on negative x-axis
B. The total mass of the particles on positive x-axis is same as the total mass on negative x-axis
C. The number of particles on X-axis may be equal to the number of particles on Y-axis
D. If there is a particle on the positive \( X \) -axis, there must be at least one particle in the negative \( X \) -axis.:


Structures of nuclei of three atoms \( A, B \) and \( C \) are given below :
A has 90 protons and 146 neutrons
B has 92 protons and 146 neutrons
C has 90 protons and 148 neutrons Based on the above data, which of these
atoms are isotopes and which are isobars?
A. A and C are isotopes; B and C are isobars
B. A and B are isotopes; A and C are isobars
c. B and C are isobars; A and B are isotopes
D. A and C are isotopes; A and B are isobars


Two conducting rings \( P \) and \( Q \) of radi and \( r \) and \( 2 r \) rotate uniformly in opposite directions with centre of mass
velocities \( 2 \mathrm{v} \) and \( \mathrm{v} \) respectively on a conducting surface S. There is a uniform magnetic field of magnitude B perpendicular to the plane of the rings.
The potential difference between the
highest points of the two rings is
\( A \cdot(a) \) zer
\( B \cdot(b) 4 B v \)
\( c \cdot(c) 8 \) Bv
D. (d)16 Bv


The given equation \( (x+1)^{2}=2(x-3) \)
is
A . linear
B. quadratic
c. cubic
D. none of these


Tritium emits:
\( \mathbf{A} \cdot \alpha- \) particle
B. positron
\( \mathbf{c} \cdot \beta- \) particle
D. neutron


Assertion
When \( A g N O_{3} \) is treated with excess of
potassium iodide, colloidal particles
gets attracted towards anode.
Reason
Precipitate adsorb common ions (excess) and thus, become charged.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


The work done to increase the radius of
orbit of a satellite of mass \( \boldsymbol{m} \) revolving around a planet of mass \( M \) from orbit of radius \( R \) into another orbit of radius
\( 3 R \) is :
\( ^{\mathrm{A}} \cdot \frac{2 G M m}{3 R} \)
в. \( \frac{G M m}{R} \)
c. \( \frac{G M m}{6 R} \)
D. \( \frac{G M m}{24 R} \)


chambered heart helps
separation of the right side and left side of the heart useful in mammals and
birds?


Divide the given polynomial by the given monomial
\( 8\left(x^{3} y^{2} z^{2}+x^{2} y^{3} z^{2}+x^{2} y^{2} z^{3}\right) \div \)
\( 4 x^{2} y^{2} z^{2} \)


A long slender rod of mass \( 2 \mathrm{kg} \) and
length 4 m is placed on a smooth
horizontal table. Two particles of
masses \( 2 k g \) and \( 1 k g \) strike the rod
simultaneously and stick to the rod
after collision as shown in Figure. Velocity of the centre of mass of the rod
after collision is
A \( .12 \mathrm{m} / \mathrm{s} \)
B. \( 9 \mathrm{m} / \mathrm{s} \)
c. \( 6 m / s \)
D. \( 3 \mathrm{m} / \mathrm{s} \)


Define trial


Chromatography is based on the:
A. Different rate of movement of the solvent in the
column
B. Different rate of movement of the solute in a column
C. Separation of one solute from other constituents by being captured on the adsorbent
D. None of the above


A parallel plate capacitor with plate area A and separation between the
plates \( d, \) is charged by a constant
current \( i . \) Consider a plane surface of area \( \frac{\boldsymbol{A}}{\mathbf{2}} \) parallel to the plate and down symmetrically between the plates. Find the displacement current through this
area.
A \( \cdot i_{d}=\frac{i}{8} \)
B. \( i_{d}=\frac{i}{2} \)
\( \mathbf{c} \cdot_{i_{d}=\frac{i}{3}} \)
D \( i_{d}=\frac{i}{4} \)


The differential equation by eliminating \( A, B, C \) from \( y=A e^{2 x}+B e^{3 x}+C e^{2 x} \)
is


Which of the following sets of side lengths form a triangle?
A. \( 4 \mathrm{m}, 3 \mathrm{m}, 11 \mathrm{m} \)
B. 7 \( \mathrm{mm}, 4 \mathrm{mm}, 4 \mathrm{mm} \)
\( c .3 \mathrm{cm}, 1.23 \mathrm{cm}, 5 \mathrm{cm} \)
D. 3 \( m, 10 \mathrm{m}, 8 \mathrm{m} \)


Explain the industrial production of phenol of high purity and less production cost and also explain the bromination of phenol.


State any two properties of magnetic lines of force.


is the common pathway for aerobic and anaerobic respiration.
A. Krebs' cycle
B. ETS
c. calvin cycle
D. Glycolysis


Statement 1: Leaching is employed in the extraction of aluminium, silver and
gold. Statement 2: During leaching, the impurities in the ore are chemically removed by dissolving them in a suitable reagent.
A. Statement 1 and statement 2 are true and statement 2 is a correct explanation of statement 1
B. Statement 1 and statement 2 are true but statement 2 is not a correct explanation of statement 1
c. statement 1 is true and statement 2 is false.
D. Statement1 is false and statement 2 is true


which of the following pairs of nitrates gives the same gaseous products on thermal decomposition? This question has multiple correct options
A. \( K N O_{3} \) and \( P b\left(N O_{3}\right)_{2} \)
в. \( K N O_{3} \) and \( N a N O_{3} \)
c. \( P b\left(N O_{3}\right)_{2} \) and \( C u\left(N O_{3}\right)_{2} \)
D. \( \operatorname{NaNO}_{3} \) and \( \operatorname{Ca}\left(N O_{3}\right)_{2} \)


Which among the following is not a weak electrolyte?
\( \mathbf{A} \cdot C a(O H)_{2} \)
B. \( M g(O H)_{2} \)
c. \( L i O H \)
D. \( N H_{4} O H \)


Why \( N O_{2}^{+} \) and \( I_{3}^{-} \) are linear species?


A metal \( M \) readily forms water-soluble
sulphate \( M S O_{4}, \) water-insoluble
hydroxide \( M(O H)_{2} \) and oxide \( M O . \) The
oxide and hydroxide are soluble in NaOH. The \( M \) is:
\( A . B e \)
в. \( M g \)
\( c . C a \)
D. \( S r \)


(a) Explain the Pauling scale for the determination of electronegativity. Give the disadvantages of Pauling scale.
(b) How does Fluorine differ from other
halogens?


Among the quantities, density \( (\rho) \) temperature(T), enthalpy(H), heat
capacity \( \left(C_{\rho}\right), \) volume (V) and pressure
(P), a set of intensive variables are :
A. \( (\rho, T, H) \)
в. \( (H, T, V) \)
\( \mathbf{c} \cdot\left(V, T, C_{\rho}\right) \)
D. \( (\rho, T, P) \)


Mitosis can be studied in
A. Onion root trip
B. Garlic root tip
c. Tendril tip
D. All the above


The temperature coefficient of
resistance of a wire at \( 0^{\circ} \mathrm{C} \) is
\( 0.00125^{\circ} \mathrm{C}^{-1} . \) At \( 25^{\circ} \mathrm{C} \) its resistance is
one ohm. The resistance of the wire will
be 1.2 ohm at
A . \( 225 K \)
B . \( 190^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 260^{\circ} C \)
D. \( 185 K \)


What is true about Ichthyosaurs?
A. It is the 20 feet tall biggest dinosaur
B. It is a fish like reptile
C. It is the first animal to invade land
D. It is jawless fish


The pH of an \( H C l \) solution is 2
Sufficient water is added to make the pH of new solutions. The hydrogen ion concentration is reduced:
A. ten fold
B. seven fold
c. thousand fold
D. hundred fold


A line \( y=x \) is rotated through \( 60^{\circ} \)
Find the new angle made by line with \( x \)
axis.
A . \( 105^{\circ} \)
B. \( 135^{\circ} \)
\( \mathbf{c} \cdot 155^{\circ} \)
D. \( 120^{\circ} \)


Two bodies of masses \( 20 k g \) and \( 15 k g \) are dropped from the top of a building. At any instant during the fall, which of the following properties that both the bodies posses is equal in magnitude?
A. Potential energy
B. Kinetic energy
c. Momentum
D. Acceleration


An intrinsic semiconductor is:
A. undoped
B. dopedd
c. can be undoped or doped
D. semi-doped


Select the correct I.U.P.A.C name for
\( \left[\boldsymbol{P t}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\right]\left[\boldsymbol{P t C l}_{4}\right]: \)
A. Tetraammineplatinum(II) tetrachloridoplatinate(II)
B. Tetraammineplatinate(II) tetrachloridoplatinate(II)
C. Tetraammineplatinate(II) tetrachloridoplatinum(II)
D. All are correct


Do the following as directed.
From \( 21 v \) subtract \( -v \)
A \( .22 v \)
в. 200
\( c \cdot-20 v \)
D. \( -22 v \)


A signal which can be green or red with probability \( \frac{4}{5} \) and \( \frac{1}{5}, \) respectively, is received at station \( A \) and then
transmitted to station B. The probability of each station receiving the signal correctly is \( \frac{3}{4} . \) If the signal received at station B is green, then the probability that the original signal was green is
\( A \cdot \frac{3}{5} \)
B. \( \frac{6}{7} \)
c. \( \frac{20}{23} \)
D. \( \frac{9}{20} \)


The negation of the statement, "l go to school everyday", is
A. I never go to school.
B. Some days, I do not go to school.
c. Not all the days I do not go to school.
D. All days I go to school.


If two stars of masses in the ratio 2: 3
become black holes, their radii will be in
the ratio of:
A .4: 9
B. 3: 2
c. 2: 3
D. 9: 4


There exists a non-uniform electric field
along \( x \) -axis as shown in the figure
below. The field increases at a uniform
rate along +ve x-axis. A dipole is placed inside the field as shown.Which one of
the following is correct for the dipole?
A. Dipole moves along positive x-axis and undergoes a clockwise rotation
B. Dipole moves along negative x-axis and undergoes a clockwise rotation
c. Dipole moves along positive x-axis and undergoes a anticlockwise rotation
D. Dipole moves along negative x-axis and undergoes a anticlockwise rotation


Determine the nature of the roots of the
given equation from their discriminants.
\( 2 y^{2}+11 y-7=0 \)
A. Real and equal
B. Real and unequal
c. one real and one imaginary
D. Both imaginary


A helicopter flies horizontally with
constant velocity in a direction \( \boldsymbol{\theta} \) east of
north between two points \( \boldsymbol{A} \) and \( \boldsymbol{B}, \) at distance d apart. Wind is blowing from south with constant speed u; the speed of helicopter relative to air is nu, where
\( \mathbf{n}>1 . \) Find the speed of the helicopter along AB. The helicopter returns from B
to A with same speed nu relative to air in same wind. Find the total time for the
journeys.


The Principle of Uncertainty was introduced by


Fill in the blank: \( (-12)+\left(4+\frac{1}{8}\right)= \) \( [(-12)+\ldots . .]+\frac{1}{8} \)
A. (-12)
B. 4
c. 1
D.


The valency of noble gases is generally:
A . zero
B. one
c. three
D. two


Make h the subject of the formula given
above.
A \( \quad h=\frac{s+2 \pi r^{2}}{2 \pi r} \)
B. \( h=\frac{s-2 \pi r^{2}}{2 \pi r} \)
c. \( h=\frac{s-2 \pi r^{2}}{4 \pi r} \)
D. none of the above


n Fig. \( \angle \boldsymbol{P}=\mathbf{5} \mathbf{2}^{\circ} \boldsymbol{a} \boldsymbol{n} \boldsymbol{d} \angle \boldsymbol{P} \boldsymbol{Q} \boldsymbol{R}=\boldsymbol{6} \boldsymbol{4}^{\circ}, \) i
\( Q O \) and \( R O \) are the angle bisectors of
\( \angle P Q R \) and \( \angle P R Q \) respectively, then
find the values of \( \angle x \) and \( \angle y \)


Equal volume of two immiscible liquids
of densities \( \rho \) and \( 2 \rho \) are filled in a
vessel as shown in the figure. Two smal
holes are punched at depths h/2 and 3h/2 from the surface of lighter liquid. If
\( v_{1} \) and \( v_{2} \) are the velocities of efflux at
these two holes, then \( v_{1} / v_{2} \) is:
\( ^{A} \cdot \frac{1}{2 \sqrt{2}} \)
B. \( \frac{1}{2} \)
\( c \cdot \frac{1}{4} \)
D. \( \frac{1}{\sqrt{2}} \)


Colour of crude oil is:
A. brownish black
B. light yellow
c. transparent
D. white


Find the area of the smaller region bounded by the ellipse \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 \)
and the line \( \frac{x}{a}+\frac{y}{b}=1 \)


There are 4 white and 3 black balls in a
box. In another box there are 3 white and
4 black balls. An unbiased dice is rolled.
If it shows a number less than or equal
to
\( 3, \) then a ball is drawn from the first
box, but if it shows a number more than
3 , then a ball is drawn from the second
box. If the ball drawn is black, then the
probability that the ball was drawn from the first box is
A \( \cdot \frac{1}{2} \)
B. \( \frac{6}{7} \)
\( c \cdot \frac{4}{7} \)
D. 3 7


Any physical and chemical process by which low grade ores are concentrated,
is
A. froth flotation
B. crushing and then screening
c. hand picking
D. washing in zigs


An alpha particle after passing through a potential difference of \( 2 \times 10^{6} \) volt
falls on a silver foil. The atomic number
of silver is \( 47 . \) Calculate \( (I) \) the \( K . E \) of the alpha-particle at the time of falling on the foil. \( (I I) K . E \) of the alpha-
particle at a distance of \( 5 \times 10^{-14} m \)
from the nucleus, \( (I I I) \) the shortest
distance from the nucleus of silver to
which the alpha-particle reaches.


Assertion
If the postman delivers 1332 card to the students then number of students are
36.
Reason
If there are n students then total
number of cards are \( n(n-1) \)
A. Both (A) \& (R) are individually true \& (R) is correct explanation of (A),
B. Both (A) \& (R) are individually true but (R) is not the correct (proper) explanation of (A)
c. (A)is true but (R) is false
D. (A)is false but (R) is true.


An angle is \( 14^{\circ} \) more than its
complementary angle, then angle is:
\( A \cdot 38^{\circ} \)
B. \( 52^{\circ} \)
\( c .50^{\circ} \)
D. none of these


The collision between both blocks
shown in figure is completely inelastic. The total energy of oscillation after collision is:
A \( \cdot \frac{1}{2} m v^{2} \)
B. \( \frac{m v^{2}}{8} \)
c. \( \frac{m v^{2}}{4} \)
D. None of these


A body moves at a speed of \( 100 \mathrm{ms}^{-1} \) for
10 s and then moves at a speed of 200
\( m s^{-1} \) for 20 s along the same direction The average speed is


Calculate the period and frequency for
the second hand, minute hand, and hour
hand of a clock.
A. For second hand, period \( =1 \min =60 \mathrm{s} ; \) frequency \( =0 \)
For minute hand, period \( =1 \mathrm{hr}=3600 \mathrm{s} ; \) frequency \( =2 \)
\( 10^{-4} \mathrm{Hz} \)
For hour hand, period \( =12 \mathrm{hrs}=43200 \mathrm{s} ; \) frequency \( =2 \)
\( 10^{-5} \mathrm{Hz} \)
B. For second hand, period \( =1 \min =360 \) s; frequency \( =0 \)
For minute hand, period \( =1 \mathrm{hr}=600 \mathrm{s} ; \) frequency \( =2.7 \)
\( 10^{-4} \mathrm{Hz} \)
For hour hand, period \( =12 \mathrm{hrs}=3200 \mathrm{s} ; \) frequency \( =2 . \) \( 10^{-5} \mathrm{Hz} \)
C. For second hand, period \( =1 \min =0 \) s; frequency \( =0.0 \)
For minute hand, period \( =1 \mathrm{hr}=36 \mathrm{s} ; \) frequency \( =2.7^{\circ} \)
\( 10^{-4} \mathrm{Hz} \)
For hour hand, period \( =12 \mathrm{hrs}=43200 \mathrm{s} ; \) frequency \( =2 \)
\( 10^{-5} \mathrm{Hz} \)
D. For second hand, period \( =1 \) min \( =3660 \) s; frequency \( = \)
For minute hand, period \( =1 \mathrm{hr}=3600 \mathrm{s} ; \) frequency \( =2 \)
\( 10^{-4} \mathrm{Hz} \)
For hour hand, period \( =12 \mathrm{hrs}=4300 \mathrm{s} ; \) frequency \( =2 \)
\( 10^{-5} \mathrm{Hz} \)


If \( L, C \) and \( R \) represent inductance, capacitance and resistance respectively, than which of the following
does not represent dimensions of frequency?
\( ^{A} \cdot \frac{1}{R C} \)
в. \( \frac{R}{L} \)
c. \( \frac{1}{\sqrt{L C}} \)
D. \( \frac{c}{L} \)


The resistivity of a wire depends on its
A. length
B. area of cross-section
c. material
D. all of the above three factors


Identify a non-terminating repeating decimal.
A \( \cdot \frac{24}{1600} \)
в. \( \frac{171}{800} \)
c. \( \frac{123}{2^{2} \times 5^{3}} \)
D. \( \frac{145}{2^{3} \times 5^{2} \times 7^{2}} \)


Which of the following hormone is correctly matched with it's source and
function?
A. Vasopressin - Anterior pituitary - Induces reabsorption of water in nephron
B. Oxytocin - Anterior pituitray - Contraction in uterine muscles during birth (parturation)
C. Thymosin - Thymus - Helps in differentiation of \( T \) Lymphocyte
D. Glucagon - Pancreatic \( \alpha \) cells- Induces the uptake of utilization of glucose inside cells


\( \boldsymbol{A}= \)
\( \{x: x \text { is a perfect square, } x<50, x \in \lambda \)
\( \boldsymbol{B}= \)
\( \{x: x=8 m+1, \text { where } m \in W, s<5 \)
then find \( A \cap B \) and display it with
Venn diagram.


Among the following the least thermally stable is:
A. \( K_{2} C O_{3} \)
B. \( N a_{2} C O_{3} \)
\( \mathrm{c} . B a C O_{3} \)
D. \( L i_{2} C O_{3} \)


If the dielectric constant is \( K \) then, find the electric field at equator of dipole?


The couple developed in the suspension wire and the loose spring in a suspension type of moving coil galvanometers called:
A. Deflecting couple
B. Restoring couple
c. Twisting couple
D. None of these


The value of \( \triangle= \)
\( \begin{array}{cc}\mathbf{2} & \boldsymbol{a}+\boldsymbol{r}+\mathbf{2} \\ \boldsymbol{a}+\boldsymbol{r}+\mathbf{2} & \mathbf{2}(\boldsymbol{a}+\mathbf{1})(\boldsymbol{r}+\mathbf{1}) \\ \boldsymbol{a}+\boldsymbol{r} & \boldsymbol{a}(\boldsymbol{r}+\mathbf{1})+\boldsymbol{r}(\boldsymbol{a}+\mathbf{1})\end{array} \)
\( A \)
в. \( -2 a(r+1) \)
c. \( a(a r+r+a) \)
D. -1


If \( l \| \boldsymbol{m} \) and \( \mathrm{CD} \) is transversal, \( \angle \mathbf{1} \) and \( \angle \mathbf{2} \)
represents
A. Co-interior angles
B. Corresponding angles
c. Alternate interior angles
D. Exterior angles


A block of mass \( m \) is pushed against a
spring of spring constant \( k, \) fixed to one
end of the wall. The natural length of the
spring is / and it is compressed to half
its natural length when the block is
released. The velocity of the block as a
function of its distance \( x \) from the wall
is
\( \sqrt[A \cdot]{\frac{k}{m}\left(\frac{l^{2}}{4}-(l-x)^{2}\right)} \)
B. \( \sqrt{\frac{k}{m}(l-x)^{2}} \)
c. \( \sqrt{\frac{k}{m}\left(\frac{l^{2}}{4}+(l+2 x)^{2}\right.}) \)
D. \( \sqrt{\frac{k}{m}(l+x)^{2}} \)


A proton and a neutron are both shot at
\( 100 m s^{-1} \) towards a \( \frac{12}{6} C \) nucleus. Which
particle, if either, is more likely to be absorbed by the nucleus?
A. The proton
B. The neutron
C. Both particles are about equally likely to be absorbedd
D. Neither particle will be absorbed


An aircrafts executes a horizontal loop at a speed of \( 720 k m / h \) with its wings
banked at \( 15^{\circ} . \) What is the radius of the
loop?


For the process,
\( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l})(\mathbf{1} \boldsymbol{b} \boldsymbol{a} \boldsymbol{r}, \boldsymbol{3} \boldsymbol{7} \boldsymbol{3} \boldsymbol{K}) \rightarrow \)
\( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g})(\boldsymbol{1} \boldsymbol{b} \boldsymbol{a} \boldsymbol{r} ; \boldsymbol{3} \boldsymbol{7} \boldsymbol{3} \boldsymbol{K}) \)
The correct set of thermodynamics
parameters is:
A. \( \Delta G=0, \Delta S=+v e \)
в. \( \Delta G=0, \Delta S=-v e \)
c. \( \Delta G=+v e, \Delta S=0 \)
D. \( \Delta G=-v e, \Delta S=+v e \)


(a) Describe how the following properties vary on descending group IA and IIA (alkali and alkaline earth
metals) and state how these properties differ between the two groups?
(i) \( (I E)_{1} a n d(I E)_{2} \)
(ii) cationic radii
(iii) rates of reaction with cold water
(b) For the same s-block elements,
discuss:
(i) the action of heat on their nitrates
(ii) the crystal structures of their chlorides, XY type only.


Using the Gibbs change, \( \Delta G^{o}= \)
\( +63.3 k J, \) for the following reaction, the
\( \boldsymbol{K}_{s p} \) of \( \boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{C} \boldsymbol{O}_{3}(s) \) in water at \( \boldsymbol{2} \boldsymbol{5}^{o} \boldsymbol{C} \) is :
\( A g_{2} C O_{3}(g) \rightleftharpoons 2 A g^{+}(a q)+C O_{3}^{2-}(a q) \)
\( \left(\boldsymbol{R}=\mathbf{8 . 3 1 4} \boldsymbol{J} \boldsymbol{K}^{-1} \boldsymbol{m o l}^{-1}\right) \)
A. \( 3.2 \times 10^{-26} \)
B. \( 8.0 \times 10^{-12} \)
c. \( 2.9 \times 10^{-3} \)
D. \( 7.9 \times 10^{-2} \)


What must be the matrix \( \boldsymbol{X} \) if \( 2 \boldsymbol{X}+ \) \( \left[\begin{array}{l}12 \\ 34\end{array}\right]=\left[\begin{array}{l}38 \\ 72\end{array}\right] ? \)
A \( \cdot\left[\begin{array}{l}13 \\ 2-1\end{array}\right] \)
в. \( \left[\begin{array}{l}1-3 \\ 2-1\end{array}\right] \)
c. \( \left[\begin{array}{l}26 \\ 4-2\end{array}\right] \)
D. \( \left[\begin{array}{l}2-6 \\ 4-2\end{array}\right] \)


Solve: \( 3 x+4 y \geq 12, x \geq 0, y \geq 1 \) and
\( 4 x+7 y \leq 28 \)


If selling price is doubled, the profit triples. Find the profit percent.
A \( \cdot 66 \frac{2}{3} \)
в. 100
c. \( _{105} \frac{1}{3} \)
D. 120


The pH of blood does not appreciably change by a small addition of acid or a base because blood:
A. contains serum protein which acts as buffer
B. contains iron as a part of the molecule
c. can be easily coagulated
D. is body fluid


Hydrogen is present in the form
in free state.
\( \mathbf{A} \cdot H \)
в. \( H_{2} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{O} \)
D. \( H^{+} \)


A plant that has well differentiated
body, special tissues for transport of water and other substances, but does
not have seed or fruits is a example of
A. Bryophyte
B. Angiosperm
c. Gymnosperm
D. Pteridophyte


Evaluate the following:
\( (99)^{3} \)


In a parallel plate capacitor, the
capacitance:
A. increases with increase in the distance between the
plates
B. decreases if a dielectric material is put between the plates
C. increases with decrease in the distance between the plates
D. increases with decrease in the area of the plates


Assertion
\( H_{2} S O_{4} \) is a strong acid
Reason
\( H_{2} S O_{4} \) undergoes almost complete ionization 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


Which synthetic fibre is used in making ropes for rock climbing and parachutes
?
A . Nylon
B. Rayon
c. Polycot
D. Jute


Spiral valve is present in
A. Right auricle
B. Left auricle
c. Right ventricle
D. Truncus arteriosus


A mature male gametophyte of
angiosperm is
A. Very developed structure
B. Develops completely in pollen sac
C. Consist of a tube nucleus and two non motile male
gametes
D. Develops on style


In the following reaction \( \boldsymbol{H}_{2}+\boldsymbol{I}_{2} \rightleftharpoons \boldsymbol{H} \boldsymbol{I} \)
the amount of \( \boldsymbol{H}_{2}, \boldsymbol{I}_{2} \) and \( \boldsymbol{H} \boldsymbol{I} \) are \( \boldsymbol{0} . \boldsymbol{2} \boldsymbol{g} \)
\( 9.525 g \) and \( 44.8 g \) respectively at equilibrium at a certain temperature. Calculate the equilibrium constant of
the reaction.


A luminous object is placed at a distance of \( 30 \mathrm{cm} \) from a convex lens of
focal length \( 20 \mathrm{cm} . \) On the other side of the lens, at what distance from the lens
must a convex mirror of radius of
curvature \( 10 \mathrm{cm} \) be placed in order to have an upright image of the object coincident with it?
\( A . \) 30 \( \mathrm{cm} \)
B. 40 cm
\( c .50 \mathrm{cm} \)
D. \( 12 \mathrm{cm} \)


Which of the following statements is
incorrect?
A. Mammals have the ability to produce concentrated urine
B. Counter current is due to the flow of filtrate in two limbs of Henle's Loop in opposite direction.
C. Henle's loop and vasa recta play a significant role in concentrating the urine.
D. Flow of fitrate through vasa recta also follow the counter current pattern.


In froth floatation process, gangue articles are wetted by pine oil
A. True
B. False


A particle is performing S.H.M. with
acceleration \( a=8 \pi^{2}-4 \pi^{2} x \) where \( x \) is
coordinate of the particle w.r.t. the origin. The parameters are in S.I. units. The particle is at \( x=-2 a t t=0 \) then
find the coordinate of the particle \( \boldsymbol{w} . \boldsymbol{r} . \boldsymbol{t} \)
origin at any time \( t \)


Which of the following is a nonrenewable source of energy?
A. woodd
B. Sun
c. Fossil fuels
D. wind


Which of the following statements
about hydrogen is incorrect?
A. Hydrogen has three isotopes of which tritium is the most common
B. Hydrogen never acts as cation in ionic salts
C. Hydronium ion, \( H_{3} O^{+} \) exists freely in solution
D. Dihydrogen does not act as a reducing agent


The point \( C=\left(\frac{12}{5}, \frac{-1}{5}, \frac{4}{5}\right) \) divides the
line segment \( A B \) in the ratio \( 3: 2 . \) If
\( B=(2,-1,2) \) then \( A \) is
A . (3,1,1)
В. (3,1,-1)
D. (-3,1,-1)


Two polaroids are kept crossed to each other. If one of them is rotated an angle
\( 60^{\circ}, \) the percentage of incident light now transmitted through the system is
A . 10\%
B. 20\%
c. 25\%
D. 12.5\%


A point mass \( m \) is rigidly attached at
the circumference of uniform Ring of same mass. It is at same horizontal
position as centre of ring. The minimum coefficient of friction between ring and
ground so that there is pure rolling of
ring on surface just after system is
released is:
A . \( 3 / 5 \)
B. 2/3
\( c \cdot 1 / 3 \)
D. \( 2 / 7 \)


State true or false:
In the given figure, the diagonals \( \boldsymbol{A C} \)
and \( B D \) intersect at point \( O . \) If \( O B= \)
\( O D \) and \( A B / / D C, \) then
Area\( (\triangle D C B)= \)Area\( (\triangle A C B) \)
A. True
B. False


\( \mathbf{2} C_{6} \boldsymbol{H}_{5} \boldsymbol{C l}+\mathbf{2} \boldsymbol{N} \boldsymbol{a} \rightarrow \boldsymbol{X} \)
In the given reaction \( \boldsymbol{X} \) is:
A. toulene
B. biphenyl
c. phenyl ethane
D. 1-chloro-2-phenyl ethane


Assertion
Sulphide ores are converted to oxides before reduction.
Reason
Oxides are easier to reduce.
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


Write balanced equation for : Acetic
acid is warmed with ethanol in the
presence of conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)


Choose the correct answers from the
alternatives given :
In the meiotic cell division four
daughter cells are produced by two successive divisions in which
A. first division is equational and second is reductional
B. first division is reductional and second is equational
c. both divisions are reductional
D. both divisions are equational


\( \boldsymbol{A}=\left[\begin{array}{ll}\boldsymbol{a} & \boldsymbol{b} \\ \boldsymbol{b} & \boldsymbol{a}\end{array}\right] \) and \( \boldsymbol{A}^{2}=\left[\begin{array}{ll}\boldsymbol{\alpha} & \boldsymbol{\beta} \\ \boldsymbol{\beta} & \boldsymbol{\alpha}\end{array}\right] \) then
\( \mathbf{A} \cdot \alpha=a^{2}+b^{2}, \beta=2 a b \)
B . \( \alpha=a^{2}+b^{2}, \beta=a^{2}-b^{2} \)
C \( \cdot \alpha=2 a b, \beta=a^{2}+b^{2} \)
D . \( \alpha=a^{2}+b^{2}, \beta=a b \)


A ball is released from the top of a
height \( h \). It takes time \( T \) to reach the
ground. What is the position of the ball
(from ground) after time \( \frac{T}{3} \)
A \( \cdot \frac{h}{9} m \)
в. \( \frac{7 h}{9} m \)
c. \( \frac{8 h}{9} m \)
D. \( \frac{17 h}{18} \mathrm{m} \)


You remove four fresh tobacco leaves of
similar size and age. Leave "leaf \( 1 " \) as it is, smear "leaf \( 2^{\prime \prime} \) with vaseline on the
upper surface, "leaf \( 3^{\prime \prime} \) on the lower
surface and "leaf \( 4 " \) on both the
surfaces. Hang the leaves for a few hours and you observe that leaf 1 wilts
the most, leaf 2 has wilted, leaf 3 wilted
less than leaf 2 and leaf 4 remains
fresh. Which of the following conclusion is most logical?
A. Tobacco leaf has more stomata on the upper surface
B. Tobacco leaf has more stomata on the lower surface
c. Stomata are equally distributed in upper and lower surfaces
D. No conclusion on stomatal distribution can be drawn from this experiment


Nylon-66 is an example of:
A. polypropylene
B. polyester
c. polyamide
D. polystyrene


Force applied by a lady is \( 2 \mathrm{N} \) and moment of force is \( 16 \mathrm{Nm} \), distance of pivot from effort would be
A. 32
B. 8 m
\( c \cdot 14 m \)
D. 18


Which one among the following is a strong acid?
A . NaOH
в. \( \csc \)
c. нвт
D. \( C H_{3} C O O H \)
E. \( O_{2} \)