Why is zinc not extracted from zinc
oxide through reduction using \( C O ? \)


Dynamos is a device that
A. reduces electric power
B. generates electricity
c. step down the voltage
D. the voltage


Assertion
The concepts of atom was firstly used by Dalton.
Reason
Atom is the smallest particle of matter
that takes part in a chemical reaction. Atom is also defined as the small-est
particle of an element that retains all
the properties of an element.
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


A particle starts performing simple
harmonic motion. Its amplitude is \( A \). At one time its speed is half that of the maximum speed. At this moment the displacement is:
A \( \cdot \frac{\sqrt{2} A}{3} \)
B. \( \frac{\sqrt{3} A}{2} \)
c. \( \frac{2 A}{\sqrt{2}} \)
D. \( \frac{3 A}{\sqrt{2}} \)


Evaluate the determinant to the closest nteger: \( \boldsymbol{A}=\left[\begin{array}{cc}\log _{3} \mathbf{5 1 2} & \log _{4} \mathbf{3} \\ \log _{3} \mathbf{8} & \log _{4} \mathbf{9}\end{array}\right] \)


A gas absorbs a photon of \( 355 n m \) and
emits two wavelengths. If one of the emission is at \( 680 n m \), the other is at:
\( \mathbf{A} .518 n m \)
в. \( 1035 n m \)
c. \( 325 n m \)
D. \( 743 n m \)


Cardiac output is determined by
A . Heart rate
B. Stroke volume
c. Both A and B
D. None of these


By selling pens at 4 for \( R s .10 \), a shopkeeper makes a profit of \( 20 \% \) on the cost price. If he sells them at \( R s . x \)
per dozen, he loses \( 10 \% \) on the cost
price. Calculate \( \boldsymbol{x} \)
A. \( R s .18 .50 \)
B. \( R s .22 .50 \)
c. \( R s .20 \)
D. \( R s .18 .75 \)


\( \boldsymbol{C u}^{+}+\boldsymbol{e}^{-} \longrightarrow \boldsymbol{C u}, \quad \boldsymbol{E}^{o}=\boldsymbol{x}_{1} \) volt
\( \boldsymbol{C u}^{2+}+\mathbf{2} e^{-} \longrightarrow \boldsymbol{C u}, \quad \boldsymbol{E}^{o}=\boldsymbol{x}_{2} \) volt
then for
\( \boldsymbol{C u}^{+}+\boldsymbol{e}^{-} \longrightarrow \boldsymbol{C u}^{+}, \quad \boldsymbol{E}^{o}(\text { volt }) \) will be
A. \( x_{1}-2 x_{2} \)
В. \( x_{1}+2 x_{2} \)
c. \( x_{1}-x_{2} \)
D. \( 2 x_{2}-x_{1} \)


If the S.P. of an article is 240 and the
discount given on it is \( 28, \) then the M.P. is
A . 212
B . 228
c. 268
D . 258


Compare the usefulness of solid, liquid and gaseous fuels.


Solve the following differential equation
\( \frac{d y}{d x}+2 x=e^{3 x} \)


A girl viewed an object and found that it is not clearly visible to her. It was found that the image was formed by her eye lens \( 3 \mathrm{cm} \) away from the pupil of her
eyes.The girl can correct this defect by using a:
A. concave lens
B. convex lens
c. bi-focal lens
D. plano-convex lens


The air pollutant NO is produced in
automobile engines from the high
temperature reaction \( N_{2}(g)+ \)
\( O_{2}(g) \rightleftharpoons 2 N O(g) ; K_{c}=1.7 \times 10^{-3} \mathrm{at} \)
2300K. If the initial concentrations of
\( N_{2} \) and \( O_{2} \) at \( 2300 K \) are both \( 1.40 M \)
what are the concentrations of \( N O, N_{2} \)
and \( O_{2} \) when the reaction mixture
reaches equilibrium?
A \( \cdot[N O]=0.056 M,\left[N_{2}\right]=\left[O_{2}\right]=1.37 M \)
B . \( [N O]=0.045 M,\left[N_{2}\right]=0.23 M,\left[O_{2}\right]=1.37 M \)
C \( \cdot[N O]=0.367 M,\left[N_{2}\right]=\left[O_{2}\right]=2.03 M \)
D \cdot \( [N O]=0.056 M,\left[N_{2}\right]=0.57 M,\left[O_{2}\right]=0.12 M \)


\( \ln \) a circuit \( L C=10^{-3} H, C=10^{-3} F \)
Find angular frequency.
A. 1000 rad \( / \) sec
B. 100 rad/sec
c. 10 rad \( / \) sec
D. \( 10^{-3} \)rad\( / \)sec


"All matter is made up of very small particles which cannot be further broken down. These particles are called atoms". This statement is one of the
assumptions of :
A. Rutherford's nuclear theory
B. Bohr's theory
c. Dalton's atomic theory
D. Kinetic theory of gases


The value of intensity of magnetic field at a point due to a current carrying conductor depends
A. on the value of current
B. On a small part of length of conductor
c. on angle between the line joining the given point to the mid point of small length and the distance between the small length of the point
D. On all and the above


Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \) where \( \boldsymbol{x}^{\mathbf{3}}+\boldsymbol{y}^{\mathbf{3}}+\mathbf{3} \boldsymbol{x} \boldsymbol{y}=\mathbf{7} \)


Find the square of the following
numbers using the identity \( (a-b)^{2}= \)
\( a^{2}-2 a b+b^{2}: \)
\( \mathbf{9 9 9} \)


How will you convert Benzene to acetophenone?


An ion \( M^{2+} \) contains 10 electrons and 12
neutrons. What is the atomic number
and mass number of element M?
A .10,24
B. 10,22
c. 12,24
D. 12, 22


Short / Long type answer type questions. Why can you palpate the pulse on an artery in each heart beat?


If \( \sum_{n=1}^{5} \frac{1}{n(n+1)(n+2)(n+3)}=\frac{k}{3} \)
then k is equal to?
A \( \frac{55}{336} \)
в. \( \frac{17}{105} \)
c. \( \frac{19}{112} \)
D.


If a toroid uses bismuth for its core, the
field in the core compared to that in empty core will be slightly
A. greater
B. smaller
c. equal
D. None of these


Equation of motion of a body is \( \frac{\boldsymbol{d v}}{\boldsymbol{d t}}= \) \( 6-3 v, \) where \( v \) is the velocity in \( m s^{-1} \)
and \( t \) is the time in second. Assuming
particle at rest initially. Then This question has multiple correct options
A. velocity of the body when its acceleration is zero is \( 2 m s^{-1} \)
B. initial acceleration of the body is \( 6 m / s^{2} \)
c. the velocity of the body when the acceleration is half the initial value is \( 1 \mathrm{m} / \mathrm{s} \)
D. the body has a uniform acceleration


The mass of \( _{92}^{235} \mathrm{U} \) which must go nuclear fission to produce the same mass of energy as produced by 1 ton of coal. Given the heat of combustion of
coal is \( 8 \times 10^{3} \) cal \( / \) g. The fission of \( _{92}^{235} \mathbf{U} \)
produces 200 MeV energy per fission. Use \( \left.1 c a l=4.2 J ; 1 t o n=10^{6} g\right) \)
A. \( 0.5165 \mathrm{g} \)
B. 0.2345 g
c. \( 0.8185 \mathrm{g} \)
D. 0.4145 g


The frequency of SHM is 100 Hz. Its time period is
A . \( 0.01 \mathrm{s} \)
B. \( 0.1 \mathrm{s} \)
\( c \cdot 1 s \)
D. 100 s


When iron pyrite is burnt,the gas evolved is:
\( A \cdot O_{2} \)
в. \( C O_{2} \)
\( c \cdot s O_{2} \)
D. \( H_{2} S_{S} \)


The peak voltage in the output of a halfwave diode rectifier fed with a
sinusoidal signal without filter is \( 10 \mathrm{V} \) The d.c. component of the output voltage is
A. \( 10 / \sqrt{2} V \)
в. \( 10 / \pi V \)
\( c \cdot 10 v \)
D. \( 20 / \pi V \)


Compute \( \left[\begin{array}{cc}\cos ^{2} x & \sin ^{2} x \\ \sin ^{2} x & \cos ^{2} x\end{array}\right]+ \)
\( \left[\begin{array}{cc}\sin ^{2} x & \cos ^{2} x \\ \cos ^{2} x & \sin ^{2} x\end{array}\right] \)


How does the sound produced by a vibrating object in a medium reach
your ear?
A. Through electron transfer
B. Through the vibration of particles
c. Sound waves don't need a medium
D. Not enough data


The straight lines \( A B \) and \( C D \) intersect
at \( E . \) If \( E F \) and \( E G \) are bisectors of
\( \angle D E A \) and \( \angle A E C \)
respectively and if \( \angle A E F=x \) and
\( \angle A E G=y, \) then
A \( \cdot x+y>90^{\circ} \)
В . \( x+y<90^{\circ} \)
c. \( x+y=90^{\circ} \)
D. \( x+y=180^{\circ} \)


In the given figure, co-ordinates of the
midpoint of \( \boldsymbol{A B} \) are
A . (0,2)
в. (0,3)
c. (1,2)
D. (3,1)


The equation of the base of an equilateral triangle is \( x+y=2 \) and
the vertex is \( (2,-1) . \) Length of its side
is
A \( \cdot \sqrt{\frac{1}{2}} \)
в. \( \sqrt{\frac{3}{2}} \)
c. \( \sqrt{\frac{2}{3}} \)
D. \( \sqrt{2} \)


The displacement of the particle varies with time \( x=12 \sin \omega t-16 \sin ^{3} \omega t . \) If its
motion is SHM, then maximum
acceleration is
A \( \cdot 12 \omega^{2} \)
B. 36 \( \omega^{2} \)
c. \( 144 \omega^{2} \)
D. \( \sqrt{192} \omega^{2} \)


Say true or false.
Derivative of \( x^{n} \) is \( n x^{n-1} \)
A. True
B. False


simple harmonic motion, then correct
graph for acceleration \( ^{\prime} a^{\prime} \) and
corresponding linear velocity' \( v^{\prime} \) is :
\( A \)
B.
\( c \)
\( D \)


What force and weight act on a mass of
10.5kg being pulled by earth? Take \( g= \)
\( 10 m s^{-2} \)
A . 105 N, 10.5
B. 105 N, 105 N
c. \( 100 \mathrm{N}, 105 \mathrm{N} \)
D. 10.5 N, 10.5 N


Find the instantaneous axis of rotation
of a rod of length \( l \) when its end \( A \) moves with a velocity \( \overrightarrow{\boldsymbol{v}}_{\boldsymbol{A}}=\boldsymbol{v} \hat{\boldsymbol{i}} \) and the
rod rotates with an angular velocity
\( \omega=-\frac{v}{2 l} \hat{k} \)


The area of the figure bounded by \( y^{2}= \)
\( 2 x+1 \) and \( x-y-1=0 \) is:
\( A \cdot 2 / 3 \)
B . \( 4 / 3 \)
\( c \cdot 8 / 3 \)
D. \( 11 / 3 \)


Define hydroxyl functional group.


Write the uses of Lanthanides.


Xenon reacts directly with
\( A \cdot F_{2} \)
в. \( C l_{2} \)
c. \( B r_{2} \)
D. \( I_{2} \)


The best solution to combat greenhouse
effect is
A. To use diesel vehicles
B. To stop infra-red from entering the earth
c. Afforestation and grow abundant plants
D. All of the above


On the basis of the following \( E^{o} \) values, the strongest oxidising agent is:
\( \left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{\boldsymbol{6}}\right]^{4-} \longrightarrow\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{\boldsymbol{6}}\right]^{\boldsymbol{3}+}+ \)
\( \boldsymbol{e}^{-}, \boldsymbol{E}^{o}=-\mathbf{0 . 3 5} \boldsymbol{V} \)
\( \boldsymbol{F} \boldsymbol{e}^{2+} \rightarrow \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{3}+}+\boldsymbol{e}^{-1} \)
\( \boldsymbol{F} \boldsymbol{e}^{2+} \rightarrow \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{3}+}+\boldsymbol{e}^{-1} ; \boldsymbol{E}^{\boldsymbol{o}}=-\boldsymbol{0 . 7 7} \boldsymbol{V} \)
A \( \cdot F e^{3} \)
в. \( \left[F e(C N)_{6}\right]^{3-} \)
\( \mathrm{c} \cdot\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4} \)
D. \( F e^{2} \)


The force of friction acting on a body
when velocity is \( 4 m s^{-1} \) is \( 8 N . \) The force
of friction when the velocity is \( 8 m s^{-1} \) is
\( A \cdot 4 N \)
B. 8 N
\( c \cdot 16 N \)
D. 32 N


A car travels with a uniform velocity of
\( 25 m s^{-1} \) for 5 s. The brakes are then
applied and the car is uniformly retarded and comes to rest in further 10
s. Find the acceleration.
\( \mathbf{A} \cdot 5 m s^{-2} \)
B. \( -2.5 \mathrm{m} \mathrm{s}^{-2} \)
c. \( 25 \mathrm{m} \mathrm{s}^{-2} \)
D. \( 10 \mathrm{m} \mathrm{s}^{-2} \)


Solve: \( \left[\begin{array}{ccc}\mathbf{5} & \mathbf{1 0} & \mathbf{8} \\ \mathbf{3} & \mathbf{2} & \mathbf{6} \\ \mathbf{8} & \boldsymbol{x}+\mathbf{9} & \mathbf{9}\end{array}\right]=\mathbf{1 0 0} \)


For a gas having molar mass \( \mathrm{M} \), specific heat at constant pressure can be given
as:
A \( \frac{\gamma R}{M(\gamma-1)} \)
в. \( \frac{\gamma}{R M} \)
c. \( \frac{M}{R(\gamma-1)} \)
D. \( \frac{\gamma R M}{\gamma+1} \)


Reciprocal of \( 2 \frac{1}{4} \)
\( \mathbf{A} \cdot-\frac{9}{4} \)
B. \( -\frac{4}{9} \)
c. \( \frac{9}{4} \)
D. \( \frac{4}{9} \)


An experiment is conducted where droplets of liquid are placed on the surface of a penny. Which of the following substances would you expect to the able to place the maximum
number of drops of on the surface of the
penny?
A . \( H F \)
в. \( H_{2} \) О
c. \( C H_{3} C H_{2} C H O \)
D. \( C C l_{4} \)


How will you obtain pure potassium
permanganate \( \left(\boldsymbol{K} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4}\right) \) crystals from
its ore, pyrolusite? Give the steps involved and the reactions.


Evaluate \( \left(\frac{a}{2 b}+\frac{2 b}{a}\right)^{2} \)
\( \left(\frac{a}{2 b}-\frac{2 b}{a}\right)^{2}-4 \)
\( A \cdot 2 \)
B. \( a b \)
\( c \)
\( D \)


A tangent to the curve \( y=x^{2}+3 x \)
passes through a point (0,-9) if it drawn at the point-
A. (-3,0)
в. (1,4)
c. (0,0)
(年. \( 0,0,0,0) \)
D. (-4,4)


The correct order of enthalpy of vaporisation of noble gases is :
A. \( H e<N e<A r<K r<X e \)
в. \( H e>N e>A r>K r>X e \)
c. \( H e<A r<K r<N e<X e \)
D. \( H e<X e<A r<N e<K r \)


\( \begin{array}{ll}\text { List-I } & \text { List-II } \\ \text { A) } S_{8}+N a_{2} S O_{3} \rightarrow & \text { 1) } M \text { ustard gas } \\ \text { B) } 2 C_{2} H_{4}+S_{2} C l_{2} \rightarrow & \text { 2) } H_{2} S O_{3} \\ \text { C) } S+3 F_{2} \rightarrow & \text { 3) } N a_{2} S_{2} O_{3} \\ \text { D) } S C l_{4}+H_{2} O \rightarrow & \text { 4) } S F_{6}\end{array} \) The correct match is:
\( A \cdot(A)-4,(B)-2,(C)-1,(D)-3 \)
B. \( (A)-3,(B)-1,(C)-4,(D)-2 \)
C \( \cdot(A)-1,(B)-3,(C)-2,(D)-4 \)
D. \( (A)-2,(B)-4,(C)-3,(D)-1 \)


200 g of \( 25 \% \) sulphuric acid solution was added to 300 g of \( 40 \% \) sulphuric acid solution. Find the concentration of
the acid in the mixture.


Calculate the magnitifying power of a simple microscope of focal length \( 2.5 \mathrm{cm} . \) The least distance of distinct
vision is \( 25 \mathrm{cm} \)


An air bubble in water shines because
of the phenomenon of:
A. reflection
B. refraction
c. diffraction
D. total internal reflection


Which of the following condition is not followed for an ideal solution?
A \( \cdot \Delta H_{\text {mixing}}=0 \)
B. \( \Delta S_{\text {mixing}}=0 \)
C. \( \Delta v_{\text {mixing}}=0 \)
D. All A, B, and C are followed


The magnifying power of an astronomical telescope is 8 , then the ratio of the focal length of the objective to the focal length of the eyepiece is :
(final image is at \( \infty) \)
\( \mathbf{A} \cdot \mathbf{8} \)
B. \( \frac{1}{8} \)
c. 0.45
D. None of these


A person travels in a car from his village to a town at a speed of \( 50 \mathrm{km} / \mathrm{hr} \) for four hours. There he spends an hour moving about \( 20 \mathrm{kms} \). He then returns to his
village at a speed \( 40 \mathrm{km} / \mathrm{hr} \). His average speed over the whole journey (in \( \mathrm{km} / \mathrm{hr}) \) is :
A . 44
в. 42
c. \( 44 \frac{4}{9} \)
D. \( 46 \frac{2}{3} \)


A particle moves in x-y under the action of the force \( \overrightarrow{\mathbf{F}} \) Such that \( \mathbf{x} \) and \( \mathbf{y} \)
components of linear momentum, \( \overrightarrow{\mathbf{P}} \) at any time \( t \) are 2 cos \( t \) and \( 2 \sin t . \) Find the angle between \( \overrightarrow{\mathbf{F}} \& \overrightarrow{\mathbf{P}} \) at a given time
\( A \cdot 60^{\circ} \)
B. 300
\( c \cdot 0^{0} \)
D. \( 90^{\circ} \)


In Young's double-slit experiment \( \boldsymbol{d} / \boldsymbol{D}=\mathbf{1 0}^{-4}(\boldsymbol{d}= \) distance between
slits, \( D= \) distance of screen from the
slits). At point \( P \) on the screen resulting intensity is equal to the intensity due to the individual slit \( \boldsymbol{I}_{0} \) Then, the distance of point \( P \) from the central maximum is \( (\boldsymbol{\lambda}=\mathbf{6 0 0 0} \boldsymbol{\boldsymbol { A }}) \)
\( \mathbf{A} \cdot 2 m m \)
B. \( 1 \mathrm{mm} \)
\( \mathrm{c} .0 .5 \mathrm{mm} \)
D. \( 4 \mathrm{mm} \)


The following graph represents
the energy consumption of a
reaction. What kind of change is it?
A. Periodic change
B. Physical change
C. Endothermic reaction
D. Exothermic reaction


In which graph, rectangle bars are separated?
A . line
B. pie
\( c . \) bar
D. histogram


Which of the following sets of compounds follow law of multiple proportions?
A. \( N O, N O_{2} \) and \( N_{2} O_{5} \)
в. \( C O, C O_{2} \) and \( C H_{4} \)
c. \( N H_{3}, H_{2} O \) and \( N O_{2} \)
D. \( H_{2} O, C O_{2} \) and \( C H_{4} \)


\( \int x \sec ^{2} 2 x d x \)
A. \( \frac{1}{4} x \tan 2 x-\frac{1}{2} \log \sec 2 x \)
B. \( \frac{1}{2} x \tan 2 x+\frac{1}{4} \log \sec 2 x \)
C \( \frac{1}{4} x \tan 2 x-\frac{1}{4} \log \sec 2 x \)
D. \( \frac{1}{2} x \tan 2 x+\frac{1}{4} \log \cos 2 x \)


If two angles of a triangle are acute angles, then third angle
A. is less than the sum of the two angles
B. is an acute angle
c. is the largest angle of the triangle
D. may be an obtuse angle


Let \( g \) is the inverse function of \( f \) and \( \boldsymbol{f}^{\prime}(\boldsymbol{x})=\frac{\boldsymbol{x}^{\mathbf{1 0}}}{\left(\mathbf{1}+\boldsymbol{x}^{2}\right)} \cdot \) If \( \boldsymbol{g}(\boldsymbol{2})=\boldsymbol{a} \) then \( \boldsymbol{g}^{\prime}(\boldsymbol{2}) \)
is equal to
A \( \cdot \frac{5}{2^{10}} \)
в. \( \frac{1+a^{2}}{a^{10}} \)
c. \( \frac{a^{10}}{1+a^{2}} \)
D. \( \frac{1+a^{10}}{a^{2}} \)


Dark reaction of photosynthesis is called so, because
A. It can also occurin dark
B. It does not require light.
c. cannot occur during day time
D. It occurs more rapidly in night


Q Type your question-
\( \bigcirc\rangle-\mathbf{C}=\mathbf{C H} \frac{\mathbf{H B r} / \mathbf{R}_{2} \mathbf{O}_{2}}{(\text { 1equivalent })} \)
\( A \)
B.
\( c \)
\( D \)


A swimmer wishes to cross a \( 500 \mathrm{m} \)
wide river flowing at \( 5 \mathrm{km} / \mathrm{h} \). His speed with respect to water is \( 3 \mathrm{km} / \mathrm{h} \). (a) If he
heads in a direction making an angle \( \theta \)
with the flow, find the time he takes to
cross the river.(b) Find the shortest
possible time to cross the river.


Find the angles in each of the following:
The angles are complementary and the
smaller is \( 40^{\circ} \) less than the larger.


Titanium shows the magnetic moment of 1.73 B.M. in its compound. What is the oxidation number of \( \boldsymbol{T} \boldsymbol{i} \) in the
compound?
\( A \cdot+1 \)
\( B .+4 \)
\( c \cdot+3 \)
\( D \cdot+2 \)


The greatest value of \( \boldsymbol{f}(\boldsymbol{x})= \)
\( (x+1)^{1 / 3}-(x-1)^{1 / 3} \) on [0,1] is
\( A \)
B. 2
\( c \cdot 3 \)
D. \( 1 / 3 \)


A radio transmitter operates at a frequency of \( 880 \mathrm{kHz} \) and power of 10 kW. The number of photons emitted per second is :
\( \mathbf{A} \cdot 13.27 \times 10^{4} \)
B. \( 13.27 \times 10^{3} \)
c. \( 1327 \times 10^{34} \)
D. \( 1.71 \times 10^{31} \)


An inductance of \( 2.0 \mathrm{H} \),a capacitance of 18 and a resistance of 10 are connected
to an \( A C \) source of 20 with adjustable frequency
(a) What frequency should be chosen to maximum the current (RMS)
in the circuit?
(b) What is the value of
this maximum current (RMS)?


A yo-yo is relased from your hand with the string wrapped around your finger. If you hold your hand still, the
acceleration of the yo-yo is :
A. downward, much greater than g
B. downward, much less than g
c. upward, much less than \( g \)
D. upward, much greater thang


Solubility in water is very high for :
A. \( N e \)
в. \( H e \)
c. \( A r \)
D. \( x e \)


Assertion
A large dry cell has higher emf.
Reason
The emf of a dry cell is independent of its size.
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


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


Number of vertical columns in the
modern periodic table are:
A. 7
B. 8
c. 10
D. 18


Express the following as a rational number i.e. in the form \( \frac{a}{b} ; \) where \( a, b \in I \) and \( \boldsymbol{b} \neq \mathbf{0} \)
\( \mathbf{0 . 8 6} \)
A \( \cdot \frac{43}{50} \)
в. \( \frac{13}{50} \)
c. \( \frac{91}{50} \)
D. \( \frac{83}{50} \)


Assertion
Bond order for \( C O^{+} \) is more than bond
order in \( C O \) whereas bond order in \( N_{2}^{+} \)
is less than \( N_{2} \) whereas both are
isoelectronics.
Reason
Both have same bond order.
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 value of \( \lim _{x \rightarrow a} \frac{\sqrt{x-b}-\sqrt{a-b}}{x^{2}-a^{2}}(a> \)
\( b) \) is
A \( \cdot \frac{1}{4 a} \)
B. \( \frac{1}{a \sqrt{a-b}} \)
c. \( \frac{1}{2 a \sqrt{a-b}} \)
D. \( \frac{1}{4 a \sqrt{a-b}} \)


Sixty-five percent of a number is 21 less than four-fifth of that number. what is
the number?
A . 100
B. 120
\( c \cdot 140 \)
D. 160


Which of the following devices has a source of emf inside it?
A. Voltmeter
B. Ammeter
c. ohm-meter
D. Rectifier


A binary liquid solution is prepared by mixing n-heptane and ethanol. Which one of the following statement is correct regarding the behavior of the solution?
A. The solution formed is an ideal solution
B. The solution is non-ideal, showing +ve deviation from Raoults Law
c. The solution is non-ideal, showing ve deviation from Raoults Law
D. n-heptane shows +ve deviation while ethanol shows ve deviation from Raoults Law


A charged particle moving with constant velocity passes through a region of space without any change in its velocity. If \( \mathrm{E} \) and \( \mathrm{B} \) represent electric and magnetic fields in that region respectively,what is the \( \mathrm{E} \) and \( \mathrm{B} \) in this space?
A \( . E=0 \) and \( B=0 \)
B. \( E=0 \) and \( B \neq 0 \)
c. \( E \neq 0 \) and \( B=0 \)
D. \( E \neq 0 \) and \( B \neq 0 \)


A unit magnetic pole is that pole which
repels an identical pole at a 1 meter distance with a force of
В. \( 10^{-7} N \)
\( \mathbf{c} \cdot 10^{-5} N \)
D. \( 10^{-4} N \)


n the figure measure of two angles are
given. If line ED \( \| \operatorname{seg} A B \) and \( E-C-D \) then
find the values of \( x \) in degrees.
\( A \cdot 35 \)
B. \( 55^{\circ} \)
\( c \cdot 65^{\circ} \)
\( D .95 \)


Which of the following organelle is responsible for differentiation?
A. Nucleus
B. Mitochondria
c. Ribosomes
D. Centrioles


Which of the following statements
regarding nitrogen sesquioxide is not
correct?
A. Nitrogen sesquioxide is stable only in the liquid state. It dissociated in the vapour phase
B. Dinitrogen sesquioxide is a neutral oxide
C. Dinitrogen sesquioxide contains a weak \( N-N \) bond
D. Dinitrogen sesquioxide exists in two different crystalline forms


Standard Gibbs Free energy change
\( \Delta G^{o} \) for a reaction is zero. The value of
equilibrium constant of the reaction will be:
\( A \cdot O \)
B.
\( c \cdot 2 \)
\( D \cdot 3 \)


Two charges of magnitudes \( -2 Q \) and
\( +Q \) are located at points \( (a, 0) \) and
\( (4 a, 0) \) respectively. What is the electric
flux due to these charges through a
sphere of radius \( ^{\prime} 3 a^{\prime} \) with its centre at
the origin?


The graphs in figure show that a quantity y varies with displacement d in a system undergoing simple harmonic motion. The unbalanced force acting on the system.
\( A \)
B. I
\( c \)
\( D . \) iv


Bernoulli's equation includes as a special case:
A. Archimede's principle
B. Pascal's law
c. Toricelli's law
D. Hooke's law


Calculate the value of \( \frac{\left(290 K \times 300^{\circ} C\right)}{0^{o} C} \) in Kelvin scale.
\( \mathbf{A} \cdot 608.681 K \)
B. \( 615.234 K \)
c. \( 655.344 K \)
D. Not defined


A variable point \( \boldsymbol{P} \) on the ellipse of eccentricity is joined to the foci \( S \) and
\( s^{\prime} . \) The eccentricity of the locus of the in
cetre of the triangle \( P S S^{1} \) is
A \( \cdot \sqrt{\frac{2 e}{1+e}} \)
B. \( \sqrt{\frac{e}{1+e}} \)
c. \( \sqrt{\frac{1-e}{1+e}} \)
D. \( \frac{e}{2(1+e)} \)


The wavelength of a spectral line in Lyman series, when electronjumps back from 2nd orbit, is:
в. 1216 А
c. \( 1362 \dot{h} \)
D. None of the above


The work functions of lithium and
copper are \( 2.3 e V \) and \( 4.0 e V \)
respectively. Out of these, the one which is suitable for the photoelectric cell that works with the visible light is
A. lithium
B. copper
c. both lithium and copper
D. neither lithium nor copper.


The distance of point (4,4) from \( Y \) -axis is
A . 4 units
B. \( \sqrt{32} \) units
c. -4 units
D. None of the above


If one side of an equiateral triangle is \( 3 x+4 y=7 \) and its vertex is (1,2)
then the length of the side of the triangle is
A \( \cdot \frac{4 \sqrt{3}}{17} \)
B. \( \frac{3 \sqrt{3}}{16} \)
\( c \cdot \frac{8 \sqrt{3}}{15} \)
D. \( \frac{4 \sqrt{3}}{15} \)


Write the formulae of the following compounds. Sodium hexanitrito-N-cobaltate


Which of the following statements are
true?
This question has multiple correct options
A. When the mass of a body is doubled then the momentum of a body is also doubled, provided the body maintains the same velocity.
B. We feel pain in the hand on hitting the wall, this is a consequence of Newton's third law of motion.
C. A table cloth can be pulled from a table without dislodging the dishes. This is due to inertia of rest.
D. Momentum is a vector quantity.


A vector \( \vec{V} \) is given in a rectangular coordinates system as \( \boldsymbol{V}=\boldsymbol{6} \overrightarrow{\boldsymbol{i}}+\boldsymbol{8} \overrightarrow{\boldsymbol{j}} \)
where \( \vec{i} \) and \( \vec{\jmath} \) are the unit vectors along \( x \) and \( y \) axes, then the angle \( \theta \) which the vector \( \vec{V} \) makes with the \( x- \)
axis is
A. \( \tan \theta=8 / 6 \)
B. \( \tan \theta=6 / 8 \)
\( \mathbf{c} \cdot \tan \theta=6 \)
\( \mathbf{D} \cdot \tan \theta=8 \)


Which equation has the solution shown on the number line?
в. \( -5<x<-2 \)
c. \( -2>x>0 \)
D. \( -1>x>-6 \)


Which of the following groups contain typically coenocytic forms?
A. Lichens
B. Phycomycetes
c. Liverworks
D. Chlorophyceae


The equilibrium constant for the reaction
\( \boldsymbol{P C l}_{5(g)} \rightleftharpoons \boldsymbol{P} C l_{3(g)}+\boldsymbol{C l}_{2(g)} \) is \( 2.4 \times \)
\( 10^{-3} . \) Determine the equilibrium
constant for the reverse reaction at
same temperature


In a region of space, the electric field is given by \( \overrightarrow{\boldsymbol{E}}=\mathbf{8} \hat{\mathbf{i}}+\mathbf{4} \hat{\mathbf{j}}+\mathbf{3} \hat{\boldsymbol{k}} . \) The electric
flux through a surface of area 100 units in the xy plane is :
A. 800 units
B. 300 units
c. 400 units
D. 1500 units


A Zener diode when used as a voltage
regulator, is connected
(a) in forward bias.
(b) in reverse bias.
(c) in parallel to the load.
(d) in series to the load.
A. (a) and (b) are correct
B. (b) and (c) are correct
c. (a) only is correct
D. (d) only is correct


Which of the following is a secondary amine?
A. \( H_{2} N-N H_{2} \)
в. \( C H_{3}-N H_{2} \)
c. \( \left(C H_{3}\right)_{2} N C_{6} H_{5} \)
D. \( C_{6} H_{5}-N H-C H_{3} \)


A current of \( 10 A \) is flowing in a
equilateral triangle of side length \( \ell= \)
\( 1 m \) as shown in figure. The magnetic
field at centre of triangle is :
A \( \cdot 8 \times 10^{-6} T \)
В. \( 9 \times 10^{-5} T \)
c. \( 9 \times 10^{-6} T \)
D. \( 10^{-5} T \)


Angle of incidence is equal to the angle
of reflection.
A . Always
B. Sometimes
c. Under special condition
D. Never


An electron of mass \( M_{e}, \) initially at rest moves through a certain distance in a uniform electric field in time \( t_{1} . A \)
proton of mass \( M_{p}, \) also initially at rest,
takes time \( t_{2}, \) to move through an equal distance in this uniform electric field.
Neglecting the effect of gravity, the ratio \( t_{2} / t_{1} \) is nearly equal to?
A . 1
в. \( \sqrt{\frac{M_{p}}{M_{e}}} \)
c. \( \sqrt{\frac{M_{e}}{M_{p}}} \)
D. 1836


How will you carry out the following reactions? Write relevant balanced
equations and name the reactions.
(i) Acetyl chloride to acetaldehyde
(ii) Acetamide to methyl-amine


The value of \( \lim _{\boldsymbol{x} \rightarrow \boldsymbol{\pi} / 2} \frac{\sin (\boldsymbol{x} \cos \boldsymbol{x})}{\cos (\boldsymbol{x} \sin \boldsymbol{x})} \) is
equal to
A . 0
в. \( \frac{\pi}{2} \)
\( c . \pi \)
D . 2 \( \pi \)


Moon is a satellite of the Earth, but
weightlessness is not experienced at the surface of the Moon because
A. its distance from the Earth is more
B. it is a natural satellite
c. its size is big but density is very low.
D. its own mass is more


ldentify the noble gas in the \( 4^{t h} \) period.


Chemistry of carbon compounds is known as:
A. organic chemistry
B. inorganic chemistry
c. physical chemistry
D. biochemistry


\( A \) and \( B \) are two fixed points in a plane. If Pis a moving point in the plane such that \( P A=P B, \) then the:
A. locus of P is the line AB itself.
B. locus of P is a line parallel to AB
c. point P always makes equilateral triangles with A, B.
D. triangle PAB is isosceles for all positions of P.


Sodium carbonate softens permanent
hard water.
A. True
B. False


Using the standard half-cell potential listed, calculate the equilibrium constant for the reaction:
\( \boldsymbol{C o}(s)+\mathbf{2} \boldsymbol{H}^{+}(\boldsymbol{a q}) \longrightarrow \boldsymbol{C o}^{2+}(\boldsymbol{a q})+ \)
\( \boldsymbol{H}_{2}(\boldsymbol{g}) \quad \boldsymbol{a t} \quad \boldsymbol{2} \boldsymbol{9} \boldsymbol{8} \boldsymbol{K} \)
\( \boldsymbol{C o}^{2+}(\boldsymbol{a q})+\boldsymbol{2 e}-\longrightarrow \boldsymbol{C o}(\boldsymbol{s}) \boldsymbol{E}^{0}= \)
\( -0.277 V \)
A \( \cdot 2.3 \times 10^{9} \)
B . \( 4.8 \times 10^{4} \)
C \( .4 .8 \times 10^{7} \)
D. \( 4.8 \times 10^{11} \)


A body of mass \( \mathbf{m}=\mathbf{3 . 5 1 3} \mathbf{k g} \) is moving along the x-axis with a speed of 5.00
\( \mathrm{ms}^{-1} . \) The magnitude of its momentum
is recorded as :
A \( \cdot 17.56 \mathrm{kg} \mathrm{ms}^{-1} \)
B . 17.57 kg ms \( ^{-1} \)
c. \( 17.6 \mathrm{kg} \mathrm{ms}^{-1} \)
D. 17.565 kg ms \( ^{-1} \)


\( \boldsymbol{f}(\boldsymbol{x})=\cos [\boldsymbol{2} \boldsymbol{\pi}] \boldsymbol{x}+\cos [-2 \boldsymbol{\pi}] \boldsymbol{x}, \) where
\( [x] \) stands for the greatest integer function, then

This question has multiple correct options
A. \( f(\pi / 2)=-1 \)
B. \( f(\pi)=+1 \)
c. \( f(-\pi)=0 \)
D. \( f(\pi / 4)=1 \)


The correct order of increasing basicity
of the given conjugate bases \( \left(R=C H_{3}\right. \)
is:
A \( \cdot \mathrm{RCOO}^{-}<\mathrm{HC}=\mathrm{C}^{-}<\mathrm{R}^{-}<\mathrm{NH}_{2}^{-} \)
B . \( \mathrm{R}^{-}<\mathrm{HC} \equiv \mathrm{C}^{-}<\mathrm{RCOO}^{-}<\mathrm{NH}_{2}^{-} \)
C. \( \mathrm{RCOO}^{-}<\mathrm{NH}_{2}^{-}<\mathrm{HC} \equiv \mathrm{C}^{-}<\mathrm{R} \)
D. \( \mathrm{RCOO}^{-}<\mathrm{HC} \equiv \mathrm{C}^{-}<\mathrm{NH}_{2}^{-}<\mathrm{R} \)


Sewage gases are produced by the decomposition of :
A. organic household
B. industrial wastes
c. both A and B
D. none of these


\( \boldsymbol{Y}, \boldsymbol{k}, \boldsymbol{n} \) represent respectively the
young's modulus,bulk modulus and rigidity modulus of a body. If rigidity modulus is twice the bulk
modulus, then:
A. \( Y=5 k / 18 \)
в. \( Y=5 n / 9 \)
c. \( Y=9 k / 5 \)
D. \( Y=18 k / 5 \)


The wall of rectum lacks
A. Muscularis mucosa
B. Lamina propria
C. Multicellular glands
D. taeniae


For a P-Njunction diode.
A. Forward current in \( \mathrm{mA} \) and reverse current is in \( \mu A \)
B. Forward current is in \( \mu A \) are reverse current is in \( \mathrm{mA} \)
C. Both forward and reverse currents are in \( \mu A \)
D. Both forward and reverse currents are in \( \mathrm{mA} \)
E. No current flows in any direction


If \( \boldsymbol{x}=\boldsymbol{2} \boldsymbol{p}, \) then find the value of \( \boldsymbol{p} \) from
the equation \( : 2(3 p+3)-\frac{2}{5}(3+ \)
\( 4 x)=\frac{9}{2} \)


Solve :
\( (-2)+8+(-4) \)


A cell in mitotic prophase can be distinguished from a cell in meiotic
prophase by?
A. Formation of tetrad in a meiotic cell
B. The terminalisation of chiasmata in late prophase of mitosis
c. zipping in early prophase of mitosis
D. Presence of only half as many chromosomes in the meiotic cell


The rate of disintegration of a radioactive substance falls from
800dpm to 100dpm in 6 hours. The halflife of the radioactive substance is
\( \mathbf{A} \cdot 6 / 7 h r s \)
B. 2 hrs
c. 3 hrs
D. \( 1 h r \)


Compound formed on reaction of nitrogen with oxygen at very high temperature is:
A \( . N O_{2} \)
в. \( N_{2} O_{4} \)
c. \( N O \)
D. \( N_{2} O_{3} \)


At a place the value of \( B_{H} \) and \( B_{V} \) are \( 0.4 \times 10^{-4} \) and \( 0.3 \times 10^{-4} \) respectively.
The resultant earths magnetic field is :
A \( .0 .5 \times 10^{-4} T \)
в. \( 10^{-4} T \)
c. \( 2 \times 10^{-4} T \)
D. \( 5 \times 10^{-4} T \)


A ladder \( ^{\prime} A B^{\prime} \) of weight \( 300 N \) and length \( 5 m \) is lying on a horizontal surface. Its centre of gravity is at a distance of \( 2 m \) from end \( A . \) A weight of
\( 80 N \) is attached at end \( B \). The work
done in raising the ladder to the vertical
position with end \( ^{\prime} \boldsymbol{A}^{\prime} \) in contact with the ground is.
A. \( 500 J \)
в. \( 1000 J \)
c. \( 1150 J \)
D. \( 1900 J \)


Which of the following will have maximum covalent character?
A . \( N a C l \)
в. \( N a B r \)
c. \( N a I \)
D. \( N a F \)


No. of magnetic lines of force present per unit volume is called
A. Magnetic flux
B. Magnetic line of force
c. Magnetic Induction
D. None of these


Consider a jet traveling at \( 1000 \mathrm{km} / \mathrm{hr} \). If the jet shoots a laser in the same
direction it is traveling, how fast will the laser be traveling relative to the jet?
A. \( 300,000 \mathrm{km} / \mathrm{sec} \)
B. 1000 km/hr minus 300,000 km/sec
c. \( 300,000 \mathrm{km} / \mathrm{sec} \) plus \( 1000 \mathrm{km} / \mathrm{hr} \)
D. cannot determine with information available
E. \( 300,000 \mathrm{km} / \mathrm{sec} \) minus \( 1000 \mathrm{km} / \mathrm{hr} \)


Which destroy antigens?
A. Insulin
B. Antibodies
C. Chromoprotein
D. Phosphoprotein


A \( 7 k g \) object is accelerating to the right at \( 2 k m / s \).what is the rightward net force acting on it?
A . \( 1400 N \)
в. \( 2000 N \)
c. \( 670 N \)
D. \( 890 N \)


Hair wigs are made from a co-polymer of vinyl chloride and acrylonitirile and is called:
A. PVC
B. dynel
c. polyacrylonitrile
D. cellulose


The gas thermometer are more sensitive than liquid thermometers because gases
A. expand more than liquid
B. are easily obtained
c. are much lighter
D. do not easily change their states


Assertion
White phosphorus exhibits phenomenon of phosphorescence.
Reason

Phosphorescence means glow after illumination and this glow itself originates from oxidation of white
phosphorous and shows a faint flow on
exposure to oxygen.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


If \( I \) is the intensity of absorbed light
and 'C' is the concentration of AB for the
photochemical process, \( A B+h v \rightarrow \)
\( A B, \) the rate of the formation of \( A B \) is
directly proportional to:
A.
B. \( I \)
c. \( I^{2} \)
D. \( C, I \)


A thin brass sheet at \( 10^{\circ} C \) and thin
steel sheet at \( 20^{\circ} C \) have the same
surface area.The common temperature at which both would have the same area (Coefficient of linear expansion for
brass and steel are respectively \( 19 \times \)
\( \left.10^{-6} /^{\circ} \mathrm{C} \text { and } 11 \times 10^{-6} /^{\circ} \mathrm{C} .\right) \)
\( \mathbf{A} \cdot-3.75^{\circ} \mathrm{C} \)
B . \( -2.75^{\circ} \mathrm{C} \)
c. \( 2.75^{\circ} \mathrm{C} \)
D. \( 3.75^{\circ} \mathrm{C} \)


Assertion
The center of mass of a body may lie where there is no mass.
Reason
Centre of mass of a body is a point, where the whole mass of the body is
supposed to be concentrated.
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


For two data sets, each of size 5 , the
variances are given to be 4 and 5 and the corresponding means are given to
be 2 and \( 4, \) respectively. The variance of the combined data set is
A \( \cdot \frac{11}{2} \)
B. 6
c. \( \frac{13}{2} \)
D.


In an exothermic reaction if \( \Delta H \) is the
enthalpy, then activation energy is:
\( A . \) more than \( \Delta H \)
B. less than \( \Delta H \)
c. equal to \( \Delta H \)
D. none of the above


The filaments of myofibril are made up of
A. Actin, troponin, tropomyosin
B. Actin, troponin
c. Myosin, troponin
D. Actin, tropomyosin


For \( \boldsymbol{A} \longleftrightarrow \boldsymbol{B} \) equilibrium constant at
total pressure \( p_{1} \) is \( k_{p_{1}} \) and for \( C \rightleftharpoons \) \( D+E \) equilibrium constant at total
pressure \( p_{2} \) is \( k_{p_{2}} . \) If both reaction are gaseous homogeneous reations and degree of dissociation of \( A \) and \( C \) are
same, then the ratio of \( p_{1} / p_{2} \) if \( k_{p_{1}}= \)
\( 2 k_{p_{2}} \) is:
A \( .1 / 2 \)
B. \( 1 / 3 \)
\( c \cdot 1 / 4 \)
D.


Chipko movement was launched for the protection of
A. Wet lands
B. Grasslands
c. Forests
D. Livestock


The length of the latus rectum of the
parabola \( \boldsymbol{x}=\boldsymbol{a} \boldsymbol{y}^{2}+\boldsymbol{b} \boldsymbol{y}+\boldsymbol{c} \) is
A \( \cdot \frac{a}{4} \)
B. \( \frac{a}{3} \)
\( c \cdot \frac{1}{a} \)
D. \( \frac{1}{4 a} \)


The factor which does not affect the rate
of alveolar diffusion is
A. solubility of gases
B. thickness of the membranes
c. pressure gradient
D. reactivity of the gases.


An AC generator is a device which
converts:
A. Electrical energy to mechanical energy.
B. Heat energy to electrical energy
c. Heat energy to light energy.
D. Mechanical energy to electrical energy


Last digit in \( 2^{2^{n}}+1, n \in N, n \neq 1 \) is
This question has multiple correct options
\( A \cdot 7 \)
B. 3
\( c .5 \)
D.


Fill up the blank with suitable words. Value of universal gravitational
constant \( G= \)


\( 10 \mathrm{ml} \) of \( \mathrm{CO} \) is mixed with \( 25 \mathrm{ml} \) air
having 20 per cent \( O_{2} \) by volume. What would be the final volume if none of \( \mathrm{CO} \)
and \( O_{2} \) is left after the reaction?
A . 30 \( m 1 \)
B. 40 \( m \)
c. \( 43 \mathrm{ml} \)
D. 49 \( m \)


A radioactive material of half-life \( \boldsymbol{T} \) was
produced in a nuclear reactor at different instants, the quantity
produced second time was twice of that produced first time. If now their present
activities are \( A_{1} \) and \( A_{2} \) respectively then their age difference equals:
\( ^{\mathbf{A}} \cdot \frac{T}{\ln 2}\left|\ln \frac{A_{1}}{A_{2}}\right| \)
\( ^{\mathbf{B}} \cdot \quad^{ }\left|\ln \frac{A_{1}}{A_{2}}\right| \)
\( c \)
\[
\frac{T}{\ln 2}\left|\ln \frac{A_{2}}{2 A_{1}}\right|
\]
D.
\[
T \mid \ln \frac{A_{2}}{2 A_{1}}
\]


f the line \( x \cos \alpha+y \sin \alpha=p \)
represents the common chord \( A P Q B \) of
the circles \( x^{2}+y^{2}=a^{2} \) and \( x^{2}+y^{2}= \)
\( b^{2}(a>b) \) as shown in the figure, then
\( A P \) is equal to
A \( \cdot \sqrt{a^{2}+p^{2}}+\sqrt{b^{2}+p^{2}} \)
B. \( \sqrt{a^{2}-p^{2}}+\sqrt{b^{2}-p^{2}}^{2} \)
c. \( \sqrt{a^{2}-p^{2}}-\sqrt{b^{2}-p^{2}} \)
D. \( \sqrt{a^{2}+p^{2}}-\sqrt{b^{2}+p^{2}}^{2} \)


Assertion
Dipole moment of \( C-C l \) bond is more
than that of \( \boldsymbol{C}-\boldsymbol{F} \)
Reason
Size of \( \boldsymbol{F} \) is very small.
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 vectors \( \bar{a}, \bar{b}, \bar{c} \) are equal in length and taken pairwise they make equal angles. If \( \bar{a}=\bar{i}+\bar{j}, \bar{b}=\bar{j}+\bar{k} \) and \( \bar{c} \)
makes an obtuse angle with \( x \) -axis
then \( \bar{c}= \)
A. \( \bar{i}+\bar{k} \)
the
B . \( -\bar{i}+4 \bar{j}-\bar{k} \)
c. \( \frac{1}{3}(-\bar{i}+4 \bar{j}-\bar{k}) \)
D \( \frac{1}{3}(\bar{i}-4 \bar{j}+\bar{k}) \)


In the manufacture of ammonia by the
Haber Process the chemical reaction
depends upon Pressure


The standard deviation of a data is 6
when each observation is increased by
1, then the S.D. of the new data is
A . 5
B. 7
\( c .6 \)
D.


Choose the correct answers from the
alternatives given Which of the following is not grouped
with archaebacteria?
A. Methanogens
B. Cyanobacteria
c. Thermophiles
D. Halophiles


(B) \( \overbrace{\operatorname{Ph} C H}^{N a B H_{4}} \operatorname{CH} \)
\( \boldsymbol{C H O} \frac{1 . L A H, \text { ether }}{2 . H_{3} O^{+}}(A) \) The products \( (A) \)
and (B) are:
\( A \)
\( A \)
в.
\( c \)
D.


By melting down 3 spherical balls of
radius \( 6 \mathrm{cm}, 8 \mathrm{cm} \) and \( 10 \mathrm{cm} \) one big solid sphere is made. Calculate the radius of the new solid sphere.


A body starts from rest and moves with
a uniform acceleration. The ratio of the
distance covered in the \( n^{t h} \) second to
the distance covered in \( n \) seconds is
given by
A \( \cdot \frac{2}{n}-\frac{1}{n^{2}} \)
B. \( \frac{1}{n^{2}}-\frac{1}{n} \)
c. \( \frac{2}{n^{2}}-\frac{1}{n} \)
D. \( \frac{2}{n}+\frac{1}{n^{2}} \)


In the following reactions \( \boldsymbol{M} \boldsymbol{g}+\boldsymbol{a i r} \underset{\rightarrow}{\longrightarrow}(\boldsymbol{A})+(\boldsymbol{E}) \)
\( (A)+H_{2} O \rightarrow(B) C O_{2}(C) \)
\( (\boldsymbol{E})+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow(\boldsymbol{D})+(\boldsymbol{B}) \)
mole of (B) neutralises 2 moles of HCl.
(A) to (E) are \( (A): M g O(B) \)
\( \boldsymbol{M} \boldsymbol{g}(\boldsymbol{O} \boldsymbol{H})_{2}(\boldsymbol{C}): \boldsymbol{M} \boldsymbol{g} \boldsymbol{C} \boldsymbol{O}_{3}(\boldsymbol{D}) \)
\( \boldsymbol{N} \boldsymbol{H}_{3}(\boldsymbol{E}): \boldsymbol{M} \boldsymbol{g}_{3} \boldsymbol{N}_{2} \)
If true enter \( 1, \) else enter 0


The complete balanced equation is:
\( \boldsymbol{H}_{2} \boldsymbol{S}+\boldsymbol{K}_{2} \boldsymbol{C r} \boldsymbol{O}_{4}+\boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \rightarrow \)
A \( \cdot 3 \mathrm{H}_{2} S+2 \mathrm{K}_{2} \mathrm{CrO}_{4}+5 \mathrm{H}_{2} \mathrm{SO}_{4} \rightarrow \mathrm{Cr}_{2}\left(\mathrm{SO}_{4}\right)_{3}+ \)
\( 2 K_{2} S O_{4}+8 H_{2} O+3 S \)
B. \( 3 H_{2} S+K_{2} C r O_{4}+5 H_{2} S O_{4} \rightarrow C r_{2}\left(S O_{4}\right)_{3}+ \)
\( K_{2} S O_{4}+8 H_{2} O+3 S \)
c. \( H_{2} S+2 K_{2} C r O_{4}+3 H_{2} S O_{4} \rightarrow C r_{2}\left(S O_{4}\right)_{3}+ \)
\( 2 K_{2} S O_{4}+8 H_{2} O+3 S \)
D. none of these


What is the alternative term used for
metre bridge?


Heavy water can be used as:
A. Neutron moderator
B. Production of deuterium
C. Tracer compound
D. All of above


A steamer moves with velocity \( 3 \mathrm{km} / \mathrm{h} \) in and against the direction of river water whose velocity is \( 2 \mathrm{km} / \mathrm{h} \). Calculate the total time for the total journey if the boat travels \( 2 \mathrm{km} \) in the direction of a stream
and then back to its place:
A. 2 hrs
B. 2.5 hrs
c. 2.4 hrs
D. 3 hrs


Assuming \( z- \) axis inter nuclear axis.
which orbitals overlap to form \( \sigma \) bond
\( \boldsymbol{s}+\boldsymbol{P}_{\boldsymbol{Y}} \)


A volume 'V' and temperature 'T' was
obtained, as shown in the diagram, when
a given mass of gas was heated. During
the heating process, the pressure is
A . increased
B. decreased
c. remains constant
D. changed erratically


Successive discounts of \( 10 \% \) and \( 20 \% \)
are equivalent to a single discount of
A . \( 30 \% \)
B. 15\%
c. \( 72 \% \)
D. 28\%
E. None of these


Two chords of lengths \( 30 \mathrm{cm} \) and \( 16 \mathrm{cm} \) are on the opposite side of the centre of the circle. If the radius of the circle is 17
\( \mathrm{cm}, \) find the distance between the
chords.


Find the charge in coulomb on
1 gram ion of \( N^{3-} \)


Resolve \( \frac{2 x^{2}-11 x+5}{(x-3)\left(x^{2}+2 x+5\right)} \) into
partial fractions.
A \( \frac{1}{2(x-3)}-\frac{(5 x-5)}{2\left(x^{2}+2 x+5\right)} \)
B. \( \frac{1}{2(x-3)}+\frac{(5 x-5)}{2\left(x^{2}+2 x+5\right)} \)
C \( \frac{1}{(x-3)}+\frac{(5 x-5)}{\left(x^{2}+2 x+5\right)} \)
D \( \frac{1}{2(x+3)}+\frac{(5 x-5)}{2\left(x^{2}+2 x+5\right)} \)


Which one of the following is correct?
A. An event having no sample point is called an elementary event
B. An event having one sample point is called an elementary event
C. An event having two sample point is called an elementary event
D. An event having many sample point is called an elementary event


Number of neutrons in a parent nucleus \( X, \) which gives \( _{7}^{14} \mathrm{N} \) after two
successive \( \beta \) -emission would be :
\( A \cdot 6 \)
B. 7
\( c \cdot 8 \)
D.


Fill the most suitable option. Mosquitoes and some snakes find their food using vision in the \( _{---} \) range
A. infrared
B. ultraviolet
c. radio
D. microwave
E. visible light


A circular loop of radius \( 0.3 \mathrm{cm} \) lies parallel to a much bigger circular loop of radius \( 20 \mathrm{cm} . \) The centre of the small
loop is on the axis of the bigger loop. The distance between their centres is \( 15 \mathrm{cm} \)
If a current of 2.0 A flows trough the smaller loop, then the flux linked with bigger loop is
A. \( 9.1 \times 10^{-11} \) weber
B. \( 6 \times 10^{-11} \) weber
c. \( 3.3 \times 10^{-11} \) weber
D. \( 6.6 \times 10^{-9} \) weber


Whenever a mixture of gases is allowed
to come in contact with a particular
adsorbent under the same conditions,
the more strong adsorbate is adsorbed
to a greater extent irrespective of its
amount present. For example, \( \boldsymbol{H}_{2} \boldsymbol{O} \) is
adsorbed to more extent on silica gel
than \( N_{2} \) and \( O_{2} . \) This shows that some
adsorbates are preferentially adsorbed. It is also observed that preferentially adsorbable adsorbents can displace a
weakly adsorbed substance from the surface of an adsorbent.
When temperature is increased:
A. extent of adsorption increases
B. extent of adsorption decreases
C. no effect on adsorption
D. extent of adsorption first decreases, then increases


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


The value of \( \lim _{x \rightarrow 0} \frac{(1-\cos 2 x) \sin 5 x}{x^{2} \sin 3 x} \) is
A . \( 10 / 3 \)
B. 3/10
c. \( 6 / 5 \)
D. \( 5 / 6 \)


A car moving on a straight path covers a distance of \( 1 k m \) due east in 100 s. What
is the velocity of the car?
\( \mathbf{A} \cdot 10 m s^{-1} \) due east
B . \( 10 m s^{-1} \) due west
c. \( 100 m s^{-1} \) due west
D. \( 100 m s^{-1} \) due east


Which of the following is the biodegradable polymer of polyamide class ?
A. Nylon - 6,6
B. Nylon - 2 - nylon - 6
c. Dextran
D. PHBV


Number of solutions of the equation \( \sin \left(\frac{1}{3} \cos ^{-1} x\right)=1 \) are
A. only one
B. no solution
c. only three
D. at least two


The correct relation between the
following two of the shown compounds
is:
A. both are identical
B. pair of enantiomers
C. pair of diasteriomers
D. pair of mesoisomers


Name the following.
Cortical portions projecting between the
medullary pyramids in the human kidney.


Which one of the following is aromatic?
A. cyclopentadienyl cation
B. cyclooctatetraene
c. cycloheptatriene
D. cycloheptatrienylcation


Find the relation between potential
difference V and separation between the
plates z:
\( ^{\mathrm{A}} \cdot_{V^{2}}=\frac{K_{z}\left(z_{0}-z\right)^{2}}{A \varepsilon_{0}} \)
B. \( V^{2}=\frac{2 K_{z}\left(z_{0}-z\right)^{2}}{A \varepsilon_{0}} \)
c. \( V^{2}=\frac{4 K_{z}\left(z_{0}-z\right)^{2}}{A \varepsilon_{0}} \)
D. \( V^{2}=\frac{K_{z}\left(z_{0}-z\right)^{2}}{4 A \varepsilon_{0}} \)


Insulin is dissolved in a suitable solvent
and the osmotic pressure \( \pi \) in atm of
solutions of various concentrations \( C \) in
\( g / c m^{3} \) is measured at \( 27^{\circ} \mathrm{C} \). The slope of plot of \( \pi \) against \( C \) is found to be
\( 4.1 \times 10^{-3} \operatorname{atm} \mathrm{cm}^{3} g^{-1} . \) The molecular
mass of insulin is?
A \( .6 \times 10^{3} \)
B. \( 3 \times 10^{6} \)
\( c \cdot 6 \times 10^{5} \)
D. \( 3 \times 10^{3} \)


\( _{d} \)


The product of two middle terms in the
expansion of \( \left(\frac{3 x^{2}}{2}-\frac{1}{3 x}\right)^{9} \) is
\( ^{\mathrm{A}} \cdot\left(^{9} C_{4}\right)^{2} \cdot \frac{x^{9}}{512} \)
в. \( -9_{C_{4}} .^{9} C_{5}, \frac{x^{8}}{512} \)
c. \( _{-9}^{\text {g }} q_{4} .^{9} C_{5} \). \( \frac{x^{9}}{512} \)
D・ \( _{9} C_{4} .^{9} C_{5}, \frac{x^{9}}{256} \)


The e.m.f of a cell is \( 2.0 \mathrm{V} \) and the
internal resistance is \( 0.1 \Omega \). It is
connected with a resistance of \( 3.9 \Omega \)
Then potential difference across the cell is :-
\( \mathbf{A} \cdot 0.20 V \)
B. \( 1.90 V \)
c. \( 1.95 V \)
D. \( 2.00 V \)


The number of optically active optical
isomers of compound is :
\( A \)
B. 2
\( c \cdot 0 \)
\( D \)


The change in the P.E., when a body of mass \( m \) is displaced from Earth's surface to a vertical height equal to radius of earth \( (\mathrm{g}= \) acceleration due to gravity on earth surface) is:
A \( \cdot \frac{m g R}{2} \)
в. \( \frac{2 m g R}{3} \)
c. \( \frac{3 m g R}{4} \)
D. \( \frac{m g R}{3} \)


Chloroform reacts with conc. \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \) to
give \( X . \) This \( X \) is used as
This question has multiple correct options
A. war gas
B. insecticide
c. drug
D. preservative


Which of the following is not a method of removing impurities from a colloidal
sol?
A. Electrodialysis
B. Ultrafiltration
c. Ultra centrifugation
D. Distillation


Consider the following statements and state true(T) or false(F).
(A) In Phycomycetes members, coenocytic mycelium is found.
(B) The common asexual spores in Basidiomycetes are conidia and
zoospores.
(C) Mycelium of Ascomycetes is branched and septate.
A \( \cdot(A)-T,(B)-T,(C)-T \)
B. (A)-T, (B)-F, (C)-T
c. \( (A)-T,(B)-T,(C)-F \)
D. (A)-F, (B)-T, (C)-F


f the balanced reaction is as given
below, find the value of \( x, y \) and \( z \)
\( \boldsymbol{C u}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}^{2+}(\boldsymbol{a q})+\boldsymbol{S}_{2} \boldsymbol{O}_{4}^{2-}(\boldsymbol{a q})+ \)
\( \boldsymbol{x} \boldsymbol{O} \boldsymbol{H}^{-} \rightarrow \boldsymbol{y} \boldsymbol{S} \boldsymbol{O}_{3}^{2-}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{C} \boldsymbol{u}(\boldsymbol{s}) \)
\( +z N H_{3}(a q)+2 H_{2} O \)
A. \( x=4, y=2, z=4 \)
в. \( x=3, y=2, z=3 \)
c. \( x=4, y=3, z=4 \)
D. None of the above


In cell division, spindle fibres are made up of protein
A. Myoglobin
B. Tubulin
c. Albumin
D. Myosin


An iron ball and a wooden ball of the
same radius are released from a height
\( H \) in vacuum. The times taken by both of them to reach the ground are
A. Roughly equal
B. Unequal
c. Exactly equal
D. In the inverse ration of their diameters


If the acceleration due to gravity on the surface of the earth is \( 9.8 ~ m / s^{2}, \) what
will be the acceleration due to gravity
on the surface of a planet whose mass and radius both are two times the
corresponding quantities for the earth
\( ? \)
A. \( 4.9 \mathrm{m} / \mathrm{s}^{2} \)
B. \( 9.8 \mathrm{m} / \mathrm{s}^{2} \)
C \( \cdot 19.8 \mathrm{m} / \mathrm{s}^{2} \)
D. None of the above


Which of the following statement is NOT
true?
A. lightning and spark from wollen clothing are essentially the same phenomena.
B. when you rub a plastic scale on your dry hair, it acquires a charge.
C. charge acquired by a glass rod when it is rubbed with silk is called as negative charge
D. static charges are called so, because they donot move by themselves


f \( p, q, r \) are real and \( p \neq q, \) then roots of
the equation \( (\boldsymbol{p}-\boldsymbol{q}) \boldsymbol{x}^{2}+\mathbf{5}(\boldsymbol{p}+\boldsymbol{q}) \boldsymbol{x}- \)
\( \mathbf{2}(\boldsymbol{p}-\boldsymbol{q})=\mathbf{0} \) are
A. Real and equal
B. Complex
c. Real and unequal
D. None of these


A system of springs with their springs constants are as shown in figure. The
frequency of oscillation of the mass \( m \)
will be (assuming the springs to be massless
A \( \cdot \frac{1}{2 \pi} \sqrt{\frac{k_{1} k_{2}\left(k_{3}+k_{4}\right)}{\left[\left(k_{1}+k_{2}\right)+\left(k_{3}+k_{4}\right)+k_{1} k_{4}\right] m}} \)
B \( \cdot \frac{I}{2 \pi} \sqrt{\frac{k_{1} k_{2}\left(k_{3}+k_{4}\right)}{\left[\left(k_{1}+k_{2}\right)+\left(k_{3}+k_{4}\right)+k_{1} k_{2}\right] m}} \)
c. \( \frac{1}{2 \pi} \sqrt{\frac{k_{1} k_{2}\left(k_{3}+k_{4}\right)}{\left[\left(k_{1}+k_{2}\right)+\left(k_{3}+k_{4}\right)+k_{1} k_{2}\right] m}} \)
D \( \frac{1}{2 \pi} \sqrt{\frac{\left(k_{1}+k_{2}\right)+\left(k_{3}+k_{4}\right)+k_{1} k_{2}}{\left[\left(k_{1}+k_{2}\right)+\left(k_{3}+k_{4}\right)+k_{1} k_{2}\right] m}} \)


Find the value of \( \frac{\sin x}{1+\cos x} \) at \( x=\frac{\pi}{4} \)


State true or false:
In a parallelogram, the diagonals are of equal length.
A. True
B. False


For what value of \( x, \) will the points \( (-1, x) \) (-3,2) and (-4,4) lie on a line?
\( A \cdot-3 \)
B. 3
\( c \cdot-2 \)
D.


\( X \) follows a binomial distribution with
parameters \( n \) and \( p, \) and \( Y \) follows a binomial distribution with parameters
\( \boldsymbol{m} \) and \( \boldsymbol{p} . \) Then, if \( \boldsymbol{X} \) and \( \boldsymbol{Y} \) are independent \( \boldsymbol{P}\left(\frac{\boldsymbol{X}=\boldsymbol{r}}{\boldsymbol{X}+\boldsymbol{Y}=\boldsymbol{r}+\boldsymbol{s}}\right)= \)
A \( \cdot \frac{\left(^{m} C_{r}\right)\left(^{n} C_{s}\right)}{m+n C_{r+s}} \)
В. \( \frac{\left(^{m} C_{s}\right)\left(^{n} C_{r}\right)}{m+n C_{r+s}} \)
c. \( \frac{\left(^{m} C_{s}\right)}{m+n C_{r}} \)
D. none of these


Is the following pair of sets equal? Give
reasons.
\( A=\{2,3\}, B=\{x: x \) is a solution of
\( \left.\boldsymbol{x}^{2}+\mathbf{5} \boldsymbol{x}+\boldsymbol{6}=\mathbf{0}\right\} \)
A. True
B. False


Material 1 has an index of refraction of
1.15.
Material 2 has an index of refraction of
\( \mathbf{2 . 3 0} \)
If light passes from air into each of these materials at the same angle of
incidence, how will the angle of
refraction in material 1 compare to the
angle of refraction in material \( 2 ? \)
A. The angle of refraction in material 1 will be half as much as the angle of refraction in material 2
B. The angle of refraction in material 1 will be greater than the angle of refraction in material 2
C. The angle of refraction in material 1 will be less than the angle of refraction in material 2 but not necessarily half as much as the angle of refraction in material 2
D. The angle of refraction in material 1 will be less than the angle of refraction in material 2 but not necessarily twice as much as the angle of refraction in material 2
E. The angle of refraction in material 1 will be one-fourth as much as the angle of refraction in material 2


A proton is moving with velocity \( 10^{4} m / s \) parallel to the magentic field of
intensity 5 tesla.The force on the proton
is
A. \( 8 \times 10^{-15} N \)
B . \( 10^{4} N \)
c. \( 1.6 \times 10^{-19} N \)
D. zero


Which of the following can be used to prepare hydrogen gas in the laboratory?
A. Mercuric oxide
B. Acid plus zinç
c. Potassium chlorate
D. Carbon disulfide
E. Benzene


Passengers in the jet transport \( \boldsymbol{A} \) flying east at a speed of \( 800 k m / h \) observe a
second jet plane \( B \) that passes under
the transport in horizontal flight

Although the nose of \( B \) is pointed in the
\( 45^{\circ} \) northeast direction, plan \( B \) appears
to the passengers in \( A \) to be moving
away from the transport at the \( 60^{\circ} \)
angle as shown in the fig. The true
velocity of \( \boldsymbol{B} \) is
A. \( 586 k m / h \)
в. \( 400 \sqrt{2} k m / h \)
c. \( 717 k m / h \)
D. \( 400 k m / h \)


\( C_{3} H_{9} N \) cannot represent:
A \( \cdot 1^{0} \) amine
B . \( 2^{0} \) amine
\( \mathbf{c} \cdot 3^{0} \) amine
D. quaternary salt


The isomer of propyne is:
A. allene
B. propene
c. cyclo propane
D. propane


Planets rotate around the Sun in a path
best described as
A. elliptical
B. circular
c. parabola
D. none of the above


Auxospore formation is seen in
A. Nostoc
B. Yeast
c. Diatoms
D. Agaricus


The most common oxidation states of
cerium are:
\( A \cdot+2 \) and +4
\( B \cdot+3 \) and +4
\( c \cdot+3 \) and +5
D. +2 and +3


A quadrilateral is a parallelogram
if
A. opposite angles are equal.
B. opposite angles aren't obtuse, neither acute.
c. opposite sides are not equal.
D. none


The temperature of gas is increased
from \( 27^{\circ} \mathrm{C} \) to \( 127^{\circ} \mathrm{C} \). The ratio of its mean
kinetic energies will be
A \( \cdot \frac{3}{4} \)
B. \( \frac{4}{3} \)
c. \( \frac{9}{16} \)
D. \( \frac{16}{9} \)


Gravitational potential energy is
A. the product of force and velocity
B. the product of force and momentum
C. the product of weight and height lifted by an object
D. the product of force and displacement, if the particle is moving in a cirlce


Which of the following molecules have zero dipole moment and tetrahedral
structure ?
This question has multiple correct options
A \( \cdot C C l_{4} \)
в. \( \operatorname{SnCl}_{2} \)
\( \mathrm{c} \cdot \operatorname{Sn} C l_{4} \)
D. \( C O_{2} \)


Let \( f(x)=1+|\sin x| . \) Then
This question has multiple correct options
\( \mathbf{A} \cdot f(x) \) is continuous nowhere
B . \( f(x) \) is continuous everywhere
\( \mathbf{C} \cdot f(x) \) is differentiable nowhere
D. \( f^{\prime} \)
(0) does not exist


If Michael Jordan has a vertical leap of 1.29 \( m \), then what is his hang time (total time to move upwards to the peak and then return to the ground)?
A. \( 2.03 s \)
B. \( 1.03 s \)
c. \( 0.03 s \)
D. \( 1.0 s \)


The latent heat of vaporization of a substance is always
A. greater than its latent heat of fusion
B. greater than its latent heat of sublimation
c. equal to its latent latent heat of sublimation
D. less than its latent heat of fusion


State whether the following statement is true or false.

If two squares have equal areas, they
are congruent.
A. True
B. False


toppr
Q Type your question
inspection should convince you that they are indeed different. Now, how their
physical and chemical properties differ? Generally,
i) Cis-isomer has more dipole moment than trans-isomer.
ii) Cis is less stable than trans.
iii) The boiling points of cis isomers are more than those of trans isomers
(remember boiling points are directly related to polarity which is determined by dipole moment).
iv) Chemical reactivities of cis and
trans also differ from each other.
Which of the following statements best explain(s) the relationship between two
isomers of \( \boldsymbol{C H}_{3}-\boldsymbol{C H}=\boldsymbol{C H}-\boldsymbol{C H}_{3} ? \)
You are given two compounds
This question has multiple correct options
A. They are diastereomers
B. They are enantiomers.
C. They are geometrical isomers.
D. Their melting points are same.


A uniform thin rod of length L is moving
in a uniform magnetic field \( B_{0} \) such
that velocity of its centre of mass is \( \mathbf{v} \) and angular velocity is \( \omega=\frac{4 v}{L} \) Then
A. e.m.f. between end \( \mathrm{P} \) and \( \mathrm{Q} \) of the rod is \( B_{0} l v \)
B. end P of the rod is at higher potential than end Q of the rod
C. end \( Q \) of the rod is at higher potential than end P of the rod
D. the electrostatic field induced in the rod has same direction at all points along the length of rod


The mean marks got by 300 students in the subject of statistics was \( 45 . \) The
mean of the top 100 of them was found
to be 70 and the mean of the last 100
was known to be 20 , then the mean of
the remaining 100 students is
A . 45
B. 58
c. 68
D. 88


The atomic number is identical to the
amount of \( _{---}-_{--} \) in the atom
nucleus.
A. Protons
B. Neutrons
c. Both a and
D. None of above


E.O. Lawrence was awarded the 1939
Physics Nobel Prize for invention and development of
A. diode
B. microwave transmitter
c. cyclotron
D. none of these


Find the middle term of the AP
\( 6,13,20, \dots \dots, .216 \)


The length of each of the equal sides of
an isosceles triangle is \( 4 \mathrm{cm} \) longer than the base. If the perimeter of the
triangle is \( 62 \mathrm{cm}, \) find the length of the sides of the triangles.


The variance of the series
\( \boldsymbol{a}, \boldsymbol{a}+\boldsymbol{d}, \boldsymbol{a}+\boldsymbol{2} \boldsymbol{d}, \ldots \ldots \boldsymbol{a}+(\boldsymbol{2} \boldsymbol{n}-\mathbf{1}) \boldsymbol{d}, \boldsymbol{a}+ \)
2nd is
\( ^{\text {A } \cdot} \frac{n(n+1)}{2} d^{2} \)
\( ^{\text {В }} \cdot \frac{n(n-1)}{6} d^{2} \)
c. \( \frac{n(n+1)}{6} d^{2} \)
D. \( \frac{n(n+1)}{3} d^{2} \)


Match the following:


2
\( y \)


In a chemical change:
A. Molecules of substance do not change
B. Molecules of substance change
C. Substance remain the same
D. Change is reversible


Why do we need to group materials?
Give one reason.


Pneumatophores are found in
A. Orchid
B. Piper
c. Ficus
D. Rhizophora


Which one of the following statements
is correct for secondary succession?
A. It begins on a bare rock
B. It occurs on a deforested site
C. It follows primary succession
D. It is similar to primary succession except that primary succession has a relatively fast pace


Construct a quadrilateral \( \boldsymbol{A B C D} \)
where \( A B=4 c m, B C=5 c m, C D= \)
\( 6.5 \mathrm{cm} \) and angle \( B=75^{\circ} \) and angle
\( C=60^{\circ} \)


A conducting sphere is enclosed by a
hollow conducting shell. Initially the
inner sphere has a charge \( Q \) while the
outer one is uncharged. The potential difference between the two spherical
surface is found to be \( V \). Later on the
outer shell is given a charge \( -4 Q \). The
new potential difference between the
two surface is:
A. \( V \)
B. \( -V \)
c. \( -2 V \)
D. \( 2 V \)


Let three matrices \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{2} & \mathbf{1} \\ \mathbf{4} & \mathbf{1}\end{array}\right] ; \boldsymbol{B}= \)
\( \left[\begin{array}{ll}\mathbf{3} & \mathbf{4} \\ \mathbf{2} & \mathbf{3}\end{array}\right] \) and \( \boldsymbol{C}=\left[\begin{array}{cc}\mathbf{3} & -\mathbf{4} \\ -\mathbf{2} & \mathbf{3}\end{array}\right] \) then find
\( \operatorname{tr}(A)+\operatorname{tr}\left(\frac{A B C}{2}\right) \operatorname{tr}\left(\frac{A(B C)^{2}}{4}\right)+ \)
\( \operatorname{tr}\left(\frac{A(B C)^{3}}{8}\right)+\ldots+\infty, \) where \( t r(A) \)
represents trace of matrix \( \boldsymbol{A} \)
\( \mathbf{A} \cdot \mathbf{6} \)
B.
c. 12
D. 15


Write the nature of the ionic solids.


A standard solution of potassium dichromate contains \( 5.442 g L^{-1} . \) The
amount is in terms of \( F e_{3} O_{4} \) per \( \mathrm{mL} \)
\( K_{2} C r_{2} O_{7}, \) expressed as \( x \times 10^{-4} . \) Here
\( x \) is :


Prove that \( \tan \left(2 \times 30^{\circ}\right)=\frac{2 \tan 30^{\circ}}{1-\tan ^{2} 30^{\circ}} \)


The orbital angular momentum of an electron is \( \sqrt{3} \frac{h}{\pi}, \) Which of the following
of angular momentum of this electron revolving in unknown Bohr orbit?
A \( \cdot \frac{h}{2 \pi} \)
в. \( \frac{h}{\pi} \)
\( \mathrm{c} \cdot_{3} \frac{h}{\pi} \)
D. none of the above


Electrical power \( P \) is given by the expression \( P=\frac{Q \times V}{t} . \) time. What does
\( Q \) and \( V \) stand for?
A. Charge, energy
B. Current, voltage
c. current, power
D. Charge, voltage


Which method is used to get pure
ethanol?
A. Membrane technology
B. Esterification
c. Fermentation
D. None of these


Acids produce \( \left(O H^{-}\right) \) ions when dissolved in water.
A. True
B. False


Given are two figures of Daniell cell(X) and (Y). Study the figures and mark the incorrect statement from the following.
A . In fig( \( (x) \) ) electrons flow from \( Z n \) rod to \( C u \) rod hence current flows from \( C u \) to \( Z n\left(E_{\text {ext}}<1.1 \mathrm{V}\right) \)
B. In fig (Y), electrons flow from \( C u \) to \( Z n \) and current flows from \( Z n \) to \( C u\left(E_{e x t}>1.1 \mathrm{V}\right) \)
\( c . \ln \operatorname{fig}(x), Z n \) dissolves at anode and \( C u \) deposits at cathode
D. In fig ( \( \gamma \) ), \( Z n \) is deposited at \( C u \) and \( C u \) is deposited at \( z_{n} \)


A girl in a swing is \( 2.5 m \) above ground
at the maximum height and at \( 1.5 m \)
above the ground at the lowest point. Her maximum velocity in the swing is
\( \left(g=10 m s^{-2}\right) \)
В. \( 2 \sqrt{5} \mathrm{ms}^{-1} \)
D. \( 3 \sqrt{2} \mathrm{ms}^{-1} \)
E \( \cdot 4 \sqrt{2} m s^{-1} \)


In the leaves, veins are useful for
A. Transport of water and minerals
B. Mechanical support
C. Transport of organic nutrients
D. All of the above


Identify the correct statements from the
following.
(I) A single male and a few female flowers are present in a flowers like inflorescence in poinsettia.
(II) Sessile or subsessile flowers formed
in the axils of leaves are crowded at the
nodes in Leonotis.
(III) In Ficus, a fruit like inflorescence is
present with all fertile flowers.
(IV) The floral axis is sympoidal in
Hamelia.
\( A \cdot(11),(1 \vee) \)
B. (1), (IV)
c. (॥), (॥I)
D. (I), (III)


The irregular shape of amoeba is attributed by the presence of
A. Food vacuole
B. Slimy cell membrane
c. Pseudopodia
D. contractile vacuole


Most recent man found as fossil was
A. Java mann
B. Peking man
c. Cro-magnon man
D. Heidelberg man


According to kircholf's second law:


A balloon, which always remains
spherical has a variable radius. Find the rate at which its volume is increasing with the radius when the later is \( 10 \mathrm{cm} \)


Which of the following pairs are
members of a Homologous series?
\( \mathbf{A} \cdot C H_{3} O C H_{3} ; C H_{3} C H_{2} O H \)
B. \( C H_{3} C H O ; C H_{3} C H_{2} C H O \)
\( \mathbf{c} \cdot C H_{3} C H_{2} C O O H ; C H_{3} C O O C H_{3} \)
D. \( \left(C H_{3}\right)_{2} C H O H ; C H_{3} C H_{2} O H \)


Let angle \( A, B \) and \( C \) of a triangle \( A B C \) be in arithmetic progression. If \( \frac{b}{c}=\sqrt{\frac{3}{2}} \) then the value of cosec \( 2 A \) is equal to
(Symbols used have usual meaning in a triangle \( A B C \) )


Give the IUPAC names of the following compounds:
Ethyl alcohol


Two particles having masses in \( \mathrm{m} \) and \( 2 \mathrm{m} \) are travelling along \( \mathrm{x} \) -axis on a
smooth surface with velocities \( u_{1} \) and
\( u_{2}, \) collide .If their velocities after
collision are \( v_{1} \) and \( v_{2}, \) then the ratio of
velocities of their centre of mass before
and after impact is
A. 2:
B. 2:3
\( c \cdot 1: \)
D. 1: 2


Acetylation of a secondary amine in alkaline medium yields:
A. N, N - dialkylacetamide
B. N, N - dialkylamide
c. acetyl dialkylamide
D. none of these


In the given reaction sequence \( \mathrm{X} \) will be:
A. Benzoic acid
B. Salicylic acid
C. Phenol
D. Aniline


The force exerted by a weird, stretch
cord at given displacements is shown in
the above table. Experimentally the force is found to vary proportionally to
the square of the displacement, i.e.
\( \boldsymbol{F}(\boldsymbol{x})=-\boldsymbol{h} \boldsymbol{x}^{2} \) where \( h \) is some
constant.
If the potential energy at \( x=0 m \) is
\( U_{0}=0 J \) as shown above, determine
the potential energy at \( x=1.5 m \)
\begin{tabular}{|c|c|}
\hline Displacement \( x \) & Force \( F \) \\
\hline \( 0 \mathrm{m} \) & \( 0 \mathrm{N} \) \\
\hline \( 1 \mathrm{m} \) & \( -2 \mathrm{N} \) \\
\hline \( 2 \mathrm{m} \) & \( -8 \mathrm{N} \) \\
\hline
\end{tabular}
\( \mathbf{A} \cdot 1.13 J \)
B. \( 2.25 J \)
c. \( 4.50 J \)
D. \( 6.75 J \)
E \( .7 .50 J \)


What do you mean by conservation charges?


If velocity of a satellite is half of escape velocity, then distance of the satellite from earth surface will be.
A. \( 6400 k m \)
B. \( 12800 k m \)
c. \( 6400 \sqrt{2} k m \)
D. \( \frac{6400}{\sqrt{2}} k m \)


Which of the following is not an allotrope of carbon?
A. Graphite
B. Granite
c. Diamond
D. Fullerene


Assertion
Catalyst is a substance which takes
part in a chemical reaction, undergoes chemical change and alters the rate of a
reaction
Reason
Catalyst is a substance which does not
take part in a chemical reaction, but changes the rate of reaction
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 absolute value of middle term in the
expansion of \( \left(1-\frac{1}{x}\right)^{n} \cdot(1-x)^{n} \) is
A \( \cdot 2^{n} \mathrm{C}_{n} \)
B. - \( ^{2 n} \mathrm{C}_{n} \)
\( \mathbf{c} \cdot-^{2 n} \mathbf{C}_{n-1} \)
D. none of these


Two spheres of the same material, but
radii \( \boldsymbol{R} \) and \( \boldsymbol{3} \boldsymbol{R} \) are allowed to fall
vertically downwards through a liquid of
uniform density. The ratio of their
terminal velocities is:
A . 1: 3
B. 1: 6
c. 1: 9
D. 1: 1


Electronic configuration of \( _{19} K^{39} \) is:
A \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{1} \)
B \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{1} \)
\( \mathbf{c} \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{3} 4 s^{1} 3 d^{1} \)
D. \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{3} 4 s^{2} 3 d^{1} \)


When \( S O_{2} \) is passed through acidified
\( K_{2} C r_{2} O_{7} \) solution
A. solution turns blue
B. solution decolorizes.
c. \( S O_{2} \) is reduced.
D. green \( C r_{2}\left(S O_{4}\right)_{3} \) is formed.


Moment of any force is equal to the algebraic sum of the component of that force. This statement is known as:
A. Principle of moment
B. Varignon's theorem
c. Both A and B
D. None


Adsorption is
1. exothermic process
2. endothermic process
3. species dependent
4. no heat change


Exothermic enthalpy changes are shown
as
negative values positive values
neutral
constant
\( A \)
B. 2
\( c \cdot 3 \)
D. 4


For the reaction \( : \boldsymbol{C l}_{2}(\boldsymbol{g}) \longrightarrow \boldsymbol{2} \boldsymbol{C l}(\boldsymbol{g}) \)
\( A \cdot \Delta H \) is positive, \( \Delta \) s is positive
B. \( \Delta \) H is positive, \( \Delta \) s is negative
c. \( \Delta \) H is negative, \( \Delta \) s is negative
D. \( \Delta \) H is negative, \( \Delta \) s is positive


The plane \( X O Z \) divides the join of (1,-1,5) and (2,3,4) in the ratio \( \lambda: 1 \)
then \( \lambda \) is
A . -3
B. \( -1 / 3 \)
\( c \cdot 3 \)
D. \( 1 / 3 \)


Amongst the following, the one which
can exist in free state as a stable
compound is:
A \( \cdot C_{7} H_{9} \),
в. \( C_{8} H_{12} O \)
c. \( C_{6} H_{11} O \)
D. \( C_{10} H_{17} O_{2} \)


The \( K_{c} \) for the reaction \( A+B \Leftrightarrow C \) is 4
and \( K_{c} \) for \( 2 A+D \Leftrightarrow C \) is 6 the value
of \( \boldsymbol{K}_{c} \) for \( \boldsymbol{C}+\boldsymbol{D} \Leftrightarrow \mathbf{2} \boldsymbol{B} \) is:


Which of the following does not give \( \mathrm{N} \) ethyl cyclopentyl amine as a major
product?
(1)
(2)


In the complex numbers, where \( i= \)
\( \sqrt{-1}, \) the conjugate of any value \( a+b i \)
is \( a- \) ib. What is the result when you
multiply \( 2+7 i \) by its conjugate?
A . 45
в. -45
\( c .45 i \)
D. 53
E. 53


In a triangle, there are 3 different angles.Which of the following statements is/are definitely true about the angles?
(i) Sum of all the angles is \( 100^{\circ} \)
(ii) One angle is obtuse and other two
are acute and right angle respectively.
(iii) Sum of any two angles is always
less than \( 180^{\circ} \)
A. (ii) only
B. (ii)and (iii) both
c. (iii) only
D. (i) and (iii) both


Which of the following is incorrect
A. When \( \Delta \mathrm{G}<0 \) process is spontaneous.
B. When \( \Delta G>0 \) process is non spontaneous.
C. when \( \Delta G=0 \) process is at equilibrium.
D. When \( \Delta G>0 \) process is spontaneous.


(a) Complete the reaction?
(b) Name the product formed if a large
number of \( \boldsymbol{C H}_{2}=\boldsymbol{C H}_{2} \) molecules are
added instead of \( \boldsymbol{H}-\boldsymbol{H} \) ?
\[
\begin{array}{l}
\mathbf{H} \\
\mathbf{C}=\mathbf{C}^{\prime}+\mathbf{H}-\mathbf{H} \rightarrow \\
\mathbf{H}
\end{array} \mathbf{H}
\]


Find the shortest distance between the
line \( \boldsymbol{x}=\mathbf{1}+\boldsymbol{t}, \boldsymbol{y}=\mathbf{1}+\boldsymbol{6} \boldsymbol{t}, \boldsymbol{z}=\boldsymbol{2} \boldsymbol{t}, \boldsymbol{t} \in \boldsymbol{R} \)
and \( \boldsymbol{x}=\mathbf{1}+\mathbf{2 k}, \boldsymbol{y}=\mathbf{5}+\mathbf{1 5 k}, \boldsymbol{z}= \)
\( -2+6 k, k \in R \)


A microscope makes use of
A. convex lenses
B. concave lenses
c. both convex and concave lenses
D. no lenses at all


\( X e F_{6} \) is hydrolysed to \( X e O_{3} \) as:
\( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{6}+\boldsymbol{H}_{2} \boldsymbol{O} \longrightarrow \ldots \ldots \ldots(\boldsymbol{I}) \)
A \( \cdot I: X e O F_{4} \)
в. \( I: X e_{2} O_{3} F_{6} \)
c. \( I: X e O_{2} F_{2} \)
D. none of these


Range of \( \boldsymbol{f}(\boldsymbol{x})=\sin ^{-1} \boldsymbol{x}+\tan ^{-1} \boldsymbol{x}+ \)
\( \cos ^{-1} x \) is
\( \mathbf{A} \cdot[0, \pi] \)
В. \( \left[\frac{\pi}{4}, \frac{3 \pi}{4}\right] \)
с. \( [-\pi, 2 \pi] \)
D. None of these


Given a sequence of 4 members, first three of which are in G.P. and the last
three are in A.P. with common difference
six. If first and last terms of this sequence are equal, then the last term is:
\( A \cdot 8 \)
B . 16
\( c \cdot 2 \)
D. 4


If the sequence if the nitrogenous bases on template strand is ATCTGGCGT, what
would be the sequence of mRNA transcribed from it?
A . AUCACCGCU
в. UUcUGGCGU
c. UAGACCGCA
D. AUGUccGCU


The enthalpy change involved in the
oxidation of glucose is \( -28850 \mathrm{KJ} \) mole\( ^{-1} \)
\( 25 \% \) of this energy is available for
muscular work. If \( 100 \mathrm{KJ} \) of muscular
work is needed to walk one kilometer
What is the maximum distance that a
person will be able to walk after
consuming 120 gm of glucose?
A \( .4 .8 \mathrm{km} \)
B. \( 9.6 \mathrm{km} \)
c. \( 2.4 \mathrm{km} \)
D. \( 7.2 \mathrm{km} \)


The resultant of two forces \( P \) and \( Q \) is \( R \)
If \( Q \) is doubled and when \( Q \) is reversed \( R \) is again doubled. Show that \( P: Q: \)
\( \boldsymbol{R}=\sqrt{\mathbf{2}}: \sqrt{\mathbf{3}}: \sqrt{\mathbf{2}} \)


Write equation for the reaction which take place when gas \( X \) reacts with lime water to form white precipitate \( Y \)


A glass sphere of radius \( 2 R \) and
refractive index \( n \) has a spherical cavity
of radius \( R \), concentric with it

When viewer is on left side of the hollow
sphere, what will be the shift in position
of the object?
A \( \cdot \frac{(n+1)}{(n-1)} R, \) right
B \( \cdot \frac{(n-1)}{(n+1)} R, \) right
c. \( \frac{(2 n-1)}{(2 n+1)} R, \) left
D. \( \frac{2(n-1)}{(n+1)} R \), left


Concentrated \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) cannot be used to
prepare HBr or HI from KBr or KI because
it
A. reacts too slowly with KBr or KI
B. reduces HBr or H
c. oxidises KBror KI
D. oxidises KBr to \( K B r O_{3} \) or \( K \) I to \( K I O_{3} \)


Glycosidic linkage is present in:
This question has multiple correct options
A. sucrose
B. starch
c. glucose
D. fructose


Total number of atoms represented by
the compound \( C u S O_{4} \cdot 5 H_{2} O \) is:
A . 20
B. 21
c. 6
D. 10


Show that the straight lines \( \left(A^{2}-\right. \) \( \left.\mathbf{3} \boldsymbol{B}^{2}\right) \boldsymbol{x}^{3}+\mathbf{8} \boldsymbol{A} \boldsymbol{B} \boldsymbol{x} \boldsymbol{y}+\left(\boldsymbol{B}^{2}-\boldsymbol{3} \boldsymbol{A}^{2}\right) \boldsymbol{y}^{2}=\mathbf{0} \)
form with the line \( A x+B y+C=0 \) an equilateral triangle whose area is \( \frac{C^{2}}{\sqrt{3}\left(A^{2}+B^{2}\right)} \)


The Sl unit of form factor is :
A. Ampere
B. volt
c. watt
D. none of the above


Find the point on Z-axis which are at a distance \( \sqrt{21} \) unit from the point
(1,2,3)


What is the correct representation of
reaction occurring when HCl is heated
with \( M n O_{2} ? \)
\( \mathbf{A} \cdot M n O_{4}^{-}+5 C l^{-}+8 H^{+} \rightarrow M n^{2+}+5 C l^{-}+5 H_{2} O \)
B. \( M n O_{2}+2 C l^{-}+4 H^{+} \rightarrow M n^{2+}+C l_{2}+2 H_{2} O \)
\( \mathbf{c} \cdot 2 M n O_{2}+4 C l^{-}+8 H^{+} \rightarrow 2 M n^{2+}+2 C l_{2}+4 H_{2} O \)
D. \( M n O_{2}+4 H C l \rightarrow M n C l_{4}+C l_{2}+H_{2} O \)


A ball is dropped from the top of a building. The ball takes 0.2 s to fall past the \( 3 \mathrm{m} \) length of a window some
distance from the top of the
building. Speed of the ball as it crosses the top edge of the window is \( (g= \)
\( \left.10 m s^{-2}\right) \)
A. \( 3.5 \mathrm{m} / \mathrm{s} \)
B. \( 8.5 \mathrm{m} / \mathrm{s} \)
\( c \cdot 5 m / s \)
D. \( 14 \mathrm{m} / \mathrm{s} \)


A body travelling in a straight line with
a uniformly increasing speed. Which
one of the plot represents the changes
in distance(s) travelled with time ( \( t \) )?
\( A \)
B.
\( c \)
D.


particular orbit, the electron does not lose its energy. Therefore, these orbits are called stationary orbits and the electrons are said to be in stationary energy states.
(b) Each orbit or shell is associated with
a definite amount of energy. Hence these are also called energy levels.
(c) An electron jumps from a lower energy level to a higher energy level, by absorbing energy. It jumps from a higher energy level to a lower energy level, by emitting energy in the form of electromagnetic radiation.
(d) Electrons move around the nucleus
in specified circular paths called orbits or shells or energy levels and are designated as \( \mathrm{K}, \mathrm{L}, \mathrm{M}, \mathrm{N} \) shells
respectively.
Arrange the above postulates of Bohr's theory in a correct sequence.
A. \( d \) a cb
B. \( d b \) a c
c. \( d \) a b c
D. b da c


If \( \mathbf{x} \in \mathbf{R} \) and the numbers \( \mathbf{5}^{(1-x)}+\mathbf{5}^{(x+1)} \)
a/2, \( \left(25^{x}+25^{-x}\right) \) form an A. P. then a
must lie in the interval
\( A \cdot[12, \infty] \)
в. [-5,5]
D. \( [8, \infty] \)


The ratio of the velocity of an electron in
the first Bohr's orbit of the hydrogen atom and the velocity of light is:
A . 1: 100
B. 1: 137
c. 1: 1000
D. 1: 10


Write the velocity function \( f(t) \) of the
particle for all time, where time \( t \) is in
hours.


Let \( z=1+i b=(a, b) \) be any complex
number, \( a, b, \epsilon R \) and \( \sqrt{-1}=i . \) Let \( z \neq \) \( 0+0 i, a r g z=\tan ^{-1}\left(\frac{I m z}{R e z}\right) w h e r e \)
\( -\pi<\arg z \leq \pi \)
\( \arg (\bar{z})+\arg (-z)= \)
\( \left\{\begin{array}{c}\pi, \text { if } \arg (z)<0 \\ -\pi, \text { if } \arg (z)>0\end{array}\right. \)
Let \( z \& w \) be non-zero complex numbers such that they have equal modulus
values and \( \arg z-a r g \bar{w}=\pi, \) then \( z \)
equals
\( \mathbf{A} \cdot-u \)
B.
\( \mathrm{c} \cdot-\bar{w} \)
D. \( \bar{w} \)


The dispersed phase in colloidal iron
(III) hydroxide and coltoidal gold is positively and negatively charged, respectively. Which of the following statements is not correct?
A. Sodium sulphate solution causes coagulation in both sols
B. Magnesium chloride solution coagulates, the gold sol more readily than the iron
(III) hydroxide sol.
c. the processes of electrophoresis provide charge on both the sols
D. colloidal iron is coagulated by \( M g^{+2} \) and coltoidal gold is coagulated by \( C l^{-} \)


An electric dipole is situated in an electric field of uniform intensity whose dipole moment is \( p \) and moment of inertia is I. If the dipole is displaced
then the angular frequency of its
oscillation is :
\( ^{\mathrm{A}} \cdot\left(\frac{p E}{I}\right)^{\frac{1}{2}} \)
B. \( \quad\left(\frac{p E}{I}\right)^{\frac{3}{2}} \)
\( \left(\frac{I}{p E}\right)^{\frac{1}{2}} \)
\( ^{\mathrm{D}}\left(\frac{p}{I E}\right)^{\frac{1}{2}} \)


Hard, lignified, thick-walled, long and pointed cells of a plant are
A. Parenchyma
B. Sclerenchyma
c. collenchyma
D. Sclereids


The events \( E_{1}, E_{2}, \ldots \ldots . . \) represents the
partition of the sample space \( S \), if they
are:
A. pairwise disjoint
B. exhaustive
c. have non-zero probabilities
D. All are correct


Heat transfer is done by:
A. convection
B. cooling
c. expansion
D. none of the above


Which one of the following is not a unit of Young's modulus?
\( \mathbf{A} \cdot N m^{-1} \)
B. \( N m^{-2} \)
c. Dyne \( c m^{-2} \)
D. Mega pascal


What is the degree of polynomial \( \boldsymbol{P} \)
defined by :
\( \boldsymbol{P}(\boldsymbol{x})=-\mathbf{5}(\boldsymbol{x}-\mathbf{2})\left(\boldsymbol{x}^{3}+\mathbf{5}\right)+\boldsymbol{x}^{5} ? \)
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 5


In order to be used as mirrors, glasses are coated with:
A . Silver
B. Copper
c. Aluminium
D. Platinum


The line \( A A^{\prime} \) is on a changed infinite conducting plane which is perpendicular to the plane of the paper. The plane has a surface density of
charge \( \sigma \) and \( \mathrm{B} \) is a ball of mass \( \mathrm{m} \) with
a like charge of magnitude \( q . B \) is connected by a string from a point on the line \( A A^{\prime} . \) The tangent of the angle \( (\theta) \) formed between the line \( A A^{\prime} \) and the
string is:
A \( \cdot \frac{q \sigma}{2 \epsilon_{c} m g} \)
В . \( \frac{q \sigma}{4 \pi \epsilon \theta} m g \)
c. \( \frac{q \sigma}{2 \pi \epsilon m g} \)
D. \( \frac{q \sigma}{\epsilon_{0} m g} \)


Find \( x \) if \( \tan ^{-1} x+2 \cot ^{-1} x=\frac{2 \pi}{3} \)


The weight of \( 350 m L \) of a diatomic gas
at \( 0^{\circ} \mathrm{C} \) and 2 atm pressure is \( 1 g \). The weight of one atom is:


Which of the following non-metal possess highest atomicity?
A. Oxygen
B. Sulphur
c. Phosphorus
D. Nitrogen


Explain why water stored in a dam has potential energy.


Many molecules can move briefly across the membrane without any
requirement of energy and special membrane proteins. This is called
A. Active transporttt
B. Passive transport
c. Facilitated diffusion
D. All of these


Find the remainder by using remainder
theorem when polynomial \( x^{3}-3 x^{2}+ \)
\( x+1 \) is divided by \( x-1 \)
\( A \cdot 8 \)
B.
\( c \cdot-2 \)
D. -7


What is green house effect? Why it is
named so?


A circuit is shown below.lf \( A \) is an ideal
ammeter, B an ideal Battery of voltae \( V \)
and \( C \) an ideal voltmeter, what will be
reading of the \( \frac{\text { eading of } \boldsymbol{A}}{\text { reading }} \) ?
\( A \)
в. 2 R
\( c \cdot \frac{R}{2} \)
\( D \)


The gravitational potential at the centre of a square of side a when four point masses m each are kept at its vertices will be
A \( \cdot 4 \sqrt{2} \frac{G m}{a} \)
в. \( -4 \sqrt{2} \frac{G m}{a} \)
c. \( _{2 \sqrt{2}} \frac{G m}{a} \)
D. \( -2 \sqrt{2} \frac{G m}{a} \)


If the distance between two successive
crests of a wave is \( 14 \mathrm{cm}, \) the distance between two successive troughs is 7
\( \mathrm{cm} \)
A. True
B. False


Using elementary transformation, find the inverse of the matrix \( \boldsymbol{A}= \) \( \left[\begin{array}{cc}\boldsymbol{a} & \boldsymbol{b} \\ \boldsymbol{c} & \left(\frac{1+\boldsymbol{b} c}{\boldsymbol{a}}\right)\end{array}\right] \)
\( ^{\mathbf{A}} \rightarrow A^{-1}=\left[\begin{array}{cc}\frac{1+b c}{a} & b \\ -c & a\end{array}\right] \)
\( \stackrel{\mathbf{B}}{\rightarrow} \Rightarrow A^{-1}=\left[\begin{array}{cc}\frac{1+b c}{a} & -b \\ c & a\end{array}\right] \)
\( \stackrel{\mathrm{c}}{*} \quad, A^{-1}=\left[\begin{array}{cc}\frac{1+b c}{a} & b \\ c & a\end{array}\right] \)
D. None of these.


\( \int \frac{1 d x}{1+\cot x} \)


Let \( f(x)= \) \( \left\{\begin{array}{l}1, \quad \text { if } x \text { is a rational number } \\ 0, \quad \text { if } x \text { is an irrational number }\end{array}\right. \)
be a function from \( R \) to \( R \) where \( R \) is
the set of real numbers. Find
(i) \( f\left(\frac{1}{3}\right) \)
(ii) \( f(\sqrt{7}) \)
(iii) \( f(\text { fof })(1.4327) \)
(iv) \( f(\text { fof })(\sqrt{3}) \)
A. 0,0,0,0
0
в. 1,1,1,1
c. 1,0,1,1
D. 0,1,0,1


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


If the number \( 93215 x 2 \) is completely divisible by \( 11, \) then \( x \) is equal to
\( A \cdot 2 \)
B. 3
\( c \cdot 1 \)
D. 4


In metre bridge experiment, with a standard resistance in the right gap
and a resistance coil dipped in water (in a beaker) in the left gap, the balancing length obtained is 'l'. If the temperature of water is increased, the new balancing length is
\( A \cdot> \)
B. none
\( c .=0 \)
\( D .= \)


Find the zeroes of the quadratic
polynomial \( x^{2}+14 x+48 \) and verify
them


A very long uniform helix is made of thin
metal wire. The axis of helix is vertical.
A small bead begins to slide down the
fixed helix starting from rest.

Considering friction between bead and
wire of helix to be non-zero, which of the
following statements is/ are true as
long as bead moves on helix.
This question has multiple correct options
A. The speed of bead keeps on increasing.
B. The magnitude of frictional force on bead remains constant
C. The speed of bead first increases and then remains constant
D. The magnitude of frictional force increases and then remains constant.


A particle is executing SHM with amplitude \( A \) and has maximum
vekocity \( v_{0} . \) Find its speed when it is located at distance of \( \frac{A}{2} \) from position.


The price of an article of \( R s 100 . \) Its
price is increased by \( 10 \% \), then again its is increased by \( 10 \% . \) How much is an increased in total price?
A . 20
B . 21
\( c .110 \)
D. 121


One die of red colour one of white colour
and one of blue colour are placed in a
bag. One die is selected at random and rolled
its colour and the number on its
uppermost face is noted. Describe the
sample space


The domain of \( \sin ^{-1}\left[\log _{2}\left(x^{2} / 2\right)\right] \) is
A . [2,1]
в. [1,2]
c. [-2,-1]\( \cup[1,2] \)
D. [-2,0]


The distribution below gives the weights of 30 students of a class. Find
the median weight of the students
\( \begin{array}{lllll}\text { weight } & 40- & 45- & 50- & 55- \\ (\text { in } \mathrm{kg}) & 45 & 50 & 55 & 60\end{array} \)
8 6 No. of
students \( \quad 2 \) \begin{tabular}{ll|l|l}
Weight tin & 60- & 65- & 70- \\
Kg) & 65 & 70 & 75 \\
Ma of & & &
\end{tabular} No. of
students 3 If
A .46 .67 g
в. 12.12 кв
\( c .75 .12 \mathrm{kg} \)
D. \( 56.67 \mathrm{kg} \)


Stomochord is found in
A. Urochordata
B. Hemichordata
c. cephalochordata
D. Both A and B


What do we name the device which
increases the emf?
A. electric generator
B. step-up transformer
c. electric motor
D. none of these


The full form of LDPE is low-density polyester, which is monomer of first grade unit.
A. ester
B. alcohol
c. ether
D. phenol


A rational number between \( \sqrt{2} \) and \( \sqrt{3} \)
is :
A \( \cdot \frac{3}{2} \)
B. \( \frac{2}{3} \)
c. 1
D. 5


The owner of a milk store finds that he
can sell 980 liters of milk each week at
Rs. 14 per lit. and 1220 liters of milk
each week at Rs. 16 per lit. Assuming a liner relationship between selling price and demand, how many liters could you sell weakly at Rs. 17 per liter?


\( f(x)=1, \) if \( x \) is rational and \( f(x)=0 \)
if \( x \) is irrational
then \( (\text { fof })(\sqrt{5})= \)
\( A \cdot 0 \)
B.
\( c \cdot \sqrt{5} \)
D. \( \frac{1}{\sqrt{5}} \)


Consider the reactions:
\( 2 S_{2} O_{3}^{2-}(a q)+I_{2}(s) \longrightarrow S_{4} O_{6}^{2-}(a q)+ \)
\( 2 I^{-}(a q) \)
\( \boldsymbol{S}_{2} \boldsymbol{O}_{3}^{2-}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{2} \boldsymbol{B} \boldsymbol{r}_{2}(\boldsymbol{l})+\boldsymbol{5} \boldsymbol{H}_{2} \boldsymbol{O}(l) \longrightarrow \)
\( \mathbf{2} \boldsymbol{S} \boldsymbol{O}_{4}^{2-}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{4} \boldsymbol{B} \boldsymbol{r}^{-}(\boldsymbol{a} \boldsymbol{q})+\mathbf{1 0} \boldsymbol{H}^{+}(\boldsymbol{a} \boldsymbol{q}) \)
Why does the same reductant
thiosulphate react differently with iodine and bromine?


A cubical block of mass \( m \) and side 'a
is moving horizontally on a smooth horizontal surface with a velocity \( v_{0} \)
The block collides with a ridge \( P \) and starts rotating about \( P \). Find the
minimum value of \( \boldsymbol{v}_{0} \) needed to
overcome the ridge.


A \( 30 \mathrm{kg} \) child climbs 15 meters up a tree when he stops to have a look around. What is the child's potential energy in joules? [Assume \( \left.g=10 m / s^{2}\right] \)
A . 1500
B. 3000
c. 4500
D. 6000


Japanese food 'kombu' is prepared from
A. Chlorella
B. Laminaria
c. Porphyra
D. All of the above


In fern sex organ are found on :-
A. Protonema
B. Prothallus
c. Sporophyte
D. sporophyll


The chromosome exhibit high level of coiling at which phase of karyokinesis?
A. Prophase
B. Metaphase
c. Telophase
D. Interphase


Many fungi display the phenomenon of heterothallism. What exactly
heterothallism?
A. Presence of different types of hyphae acting as male or female
B. Production of different kinds of spores
C. Presence of a net-like mycelium
D. Ability to produce both sexually as well as asexually


State the electronic configuration for Neon \( [p=10, n=10] \)
A. 2,6
в. 2,
c. 2,9
D. 2, 8


The hydrides of the first elements in
groups \( 15-17, \) namely \( N H_{3}, H_{2} O \) and \( H F \) respectively, show abnormally high
values for melting and boiling points. This is due to:
A. small size of \( N, O \) and \( F \)
B. the ability to form extensive intermolecular \( H \) bonding
c. the ability to form extensive intramolecular \( H \) bonding
D. effective van der Waal's interaction


Dielectric constant for a metal is:
A . zero
B. infinite
\( c \cdot 1 \)
D. 10


Which tissue is responsible for secondary growth in the plants?
A. vascular cambium
B. Xylem
c. Phloem
D. cork


Antibiotics kill or inhibits bacteria. The
real revolution in antibacterial therapy began with the discovery of Alexander Fleming. Antibiotics have either bactericidal effect or a
bacteriostatic effect on microbes. The
antibiotic given orally in case of
typhoid, dysentry, acute fever, etc. is:
A. penicillin
B. chloramphenicol
c. ofloxacin
D. ampicillin


If the different permutations of all letters of the word \( B H A S K A R A \) are
listed as in a dictionary, how many strings are there in this list before the
first word starting with \( \boldsymbol{B} \) ?


f \( \frac{14}{3}+\left(\frac{1}{2}\right)\left(x-\frac{7}{3}\right)=-\frac{2 x}{3}, \) then the
value of \( x \) is:
A . -3
B. 3
\( c \cdot 6 \)
D. - 6


An aeroplane pilot wishes to fly due
west. A wind of \( 100 \mathrm{km} h^{-1} \) is blowing
towards south.
a. If the speed of the plane (its speed in
still air) is \( 300 \mathrm{km} h^{-1}, \) in which
direction should the pilot head?
What is the speed of the plane with respect to ground? IIlustrate with a vector diagram.


Two objects that are moving along an xy-plane on a frictionless floor collide.
Assume that they form a closed, isolated system. The following table gives some of the momentum components (in kilogram meters per second) before and after the collision.
What are the mission values \( (a, b) \)
After Before
collision collision
Object \( \mathrm{P}_{x} \) \( P_{x} \)
-2
A. 10,11
B. 1,11
\( c \cdot 5,7 \)
\( D \cdot 6,4 \)


Select the correct IUPAC name for \( \left[\left(\mathrm{NH}_{3}\right.\right. \)
\( \left.\mathrm{T}_{4} \mathrm{Co}(\mathrm{OH})\left(\mathrm{NH}_{2}\right) \mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4}\right]^{4+} \)
A. \( \mu \text { -Amido- } \mu \text { -hydroxidobis (tetraammine cobalt }(4+)) \)
in
B. \( \mu \) -Amido- \( \mu \) -hydroxidobis (tetraarnmine cobalt(III)) ion
c. \( \mu \) -t-Amido- \( \mu \) -hydroxidobis (tetraarnmine cobaltate
\( (4+)) \) ion
D. \( \mu \) -Amido- \( \mu \) -hydroxidobis (tetraarnmine cobaltate (III))) ion


If for a gas \( \frac{\boldsymbol{R}}{\boldsymbol{C}_{\boldsymbol{v}}}=\mathbf{0 . 6 7}, \) then the gas is
made up of molecules which are :
A. Diatomic
B. Monoatomic
c. Polyatomic
D. Mixture of Diatomic \& Polyatomic


Impulse is a scalar quantity. State true or false.
A . True
B. False


Number of spectral lines in hydrogen
atom is
A . 8
B. 6
c. 15
D.


\( A C B \) is right-angled prism with other
angles as \( 60^{\circ} \) and \( 30^{\circ} . \) Refractive index
of the prism is \( 1.5 . A B \) has thin layer of
liquid on it as shown. Light falls
normally on the face \( A C . \) For total
internal reflections, maximum
refractive index of the liquid is
\( \mathbf{A} \cdot 1.4 \)
B. 1.3
c. 1.2
D. 1.6


Assertion
The number of electrons in a p-type
silicon semiconductor is less than the
number of electrons in a pure silicon semiconductor at room temperature
Reason
It is due to law of mass action.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


If \( A \) is a square matrix, \( B \) is a singular
matrix of same order, then for a positive integer \( n,\left(A^{-1} B A\right)^{n} \) equals
\( \mathbf{A} \cdot A^{-n} B^{n} A^{n} \)
B \( \cdot A^{n} B^{n} A^{-n} \)
c. \( A^{-1} B^{n} A \)
D. \( n\left(A^{-1} B A\right) \)


What normal to the curve \( y=x^{2} \) form
the shortest chord?
\( \mathbf{A} \cdot x+\sqrt{2} y=\sqrt{2} \) or \( x-\sqrt{2} y=-\sqrt{2} \)
B \( . x+\sqrt{2} y=\sqrt{2} \) or \( x-\sqrt{2} y=\sqrt{2} \)
c. \( x+\sqrt{2} y=-\sqrt{2} \) or \( x-\sqrt{2} y=-\sqrt{2} \)
D. \( x+\sqrt{2} y=-\sqrt{2} \) or \( x-\sqrt{2} y=\sqrt{2} \)


Which of the following set is not natural plant growth regulator?
A. \( G A_{3}, I A A, 2 I P \)
в. \( I A A, 2 I P, Z n \)
c. \( A B A, I B A, G A_{3} \)
D. \( A B A, G A_{3}, I A A \)


A parallel plate condenser with oil between the plates (dielectric constant
of oil \( K=2 \) ) has a capacitance \( C . \) If the oil is removed, then capacitance of the capacitor becomes:
A \( \cdot \sqrt{2} C \)
B. 2C
c. \( \frac{c}{\sqrt{2}} \)
D. \( \frac{c}{2} \)


Explain the followings:
Circle


Gauss is unit of which quantity?
A. \( H \)
в. \( B \)
\( c \cdot \phi \)
D. \( I \)


\( A \operatorname{soap}\left(C_{17} H_{35} C O O N a\right) \) solution
becomes a colloidal sol at a
concentration of \( 1.2 \times 10^{3} M . \) On the
average, \( 2.4 \times 10^{13} \) colloidal particles
are present in \( 1 \mathrm{mm}^{3} \). What is the
average number of stearate ions (in
multiples of \( 10^{6} \) ) in one colloidal particle (micelle)?
A . 30
B. 40
\( c .50 \)
D. 60


\( \lim _{x \rightarrow \pi / 4} \frac{\sqrt{2} \cos x-1}{\cot x-1} \) equals
A .
в. \( \frac{1}{2} \)
\( c \cdot \frac{1}{\sqrt{2}} \)
\( D \cdot \sqrt{2} \)


Three unbiased coins are tossed
together. Find the probability of getting
1. Two heads.
2. At least two heads.
3. No heads


When a ray of light strikes a plane
mirror at an angle of \( 15^{\circ} \) with the
mirror, what will be the angle through which the ray gets deviated?
A \( \cdot 15^{\circ} \)
B. \( 30^{\circ} \)
\( c \cdot 75^{\circ} \)
D. None of these


For the reaction:
\( \left[C r\left(H_{2} O\right)_{6}\right]^{3+}+\left[S C N^{\ominus}\right] \rightarrow \)
\( \left.\left[\mathrm{Cr} 9 \mathrm{H}_{2} \mathrm{O}\right)_{5} \mathrm{NCS}\right]^{2+} \mathrm{H}_{2} \mathrm{O} \)
The rate law is : \( r=k\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{3+}\left[\mathrm{SCN}^{\ominus}\right]\right. \)
The value of k is \( 2.0 \times 10^{-6} L m o l^{-1} s^{-1} \) at
\( 14^{0} \mathrm{C} \) and \( 2.2 \times 10^{-5} L m o l^{-1} s^{-1}, \) at \( 30^{0} \mathrm{C} \)
What is the value of \( E_{a} ? \)
A \( .26 k c a l m o l^{-1} \)
B. \( 2.6 k \)cal \( \mathrm{mol}^{-1} \)
c. \( 2600 k c a l \) mol\( ^{-1} \)
D. \( 260 k c a l \) mol\( ^{-1} \)


Insufficient light can cause:
A. headache
B. eye strain
c. both headache and eye strain
D. blindness


One body is dropped, while a second body is thrown downwards with an initial velocity of \( 1 \mathrm{m} / \mathrm{s} \) simultaneously the separation between these is \( 18 m \) after how much time?


Which chemical substance is emitted
in car exhaust and is a cause of acid
rain?
A. Nitrogen oxides
B. Leadd
c. Carbon dioxide
D. DDT
E. Nitrates


\( \frac{-1}{\frac{1}{4}} \)


Long pointed sclerenchyma cells are
A. Fibres
B. Tracheae.
c. wood parenchyma
D. Sclereids.


An astronaut who weighs 162 pounds on the surface of the earth is orbiting the earth at a height above the surface
of the earth of two earth radii \( (h=2 R \)
where \( R \) is the radius of the earth.
How much does this astronaut weigh while in orbit at this height (With how much force is the earth pulling on him while he is in orbit at this height?)
A. 81 pounds
B. 40.5 pounds
c. 18 pounds
D. 54 pounds
E. 0 pounds (astronaut is weightless


\( \boldsymbol{F} \boldsymbol{e o}(\boldsymbol{s}) \stackrel{\boldsymbol{H e a t}}{\rightarrow} \boldsymbol{F e O}(\boldsymbol{l}) \stackrel{\boldsymbol{H e a t}}{\rightarrow} \boldsymbol{F e O}(\boldsymbol{g}) \stackrel{\boldsymbol{H e a t}}{\rightarrow} \)
\( \boldsymbol{X}+\boldsymbol{Y} \)
The end products of the above heating processes may be?
A \( \cdot F e^{2+}(g) \) and \( O^{2-}(g) \)
B . \( F e^{2+}(g) \) and \( O^{+}(g) \)
C \( \cdot F e^{+}(g) \) and \( O^{2-}(g) \)
D. \( F e^{2-}(g) \) and \( O^{2-}(g) \)


A double convex lens is made of glass which has refractive index 1.55 for violet
rays and 1.50 for red rays. If the focal length of violet rays is \( 20 \mathrm{cm}, \) the focal length for red rays is :
A. \( 9 \mathrm{cm} \)
B. \( 18 \mathrm{cm} \)
c. \( 20 \mathrm{cm} \)
D. 22 cm


Convert \( \frac{15}{50} \) into percentage
A . \( 35 \% \)
B. 30\%
c. \( 25 \% \)
D. 20\%


If \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{x \sin \frac{1}{x}, x \neq 0 \quad k \quad, x=0\right\} \) is
continuous at \( x=0, \) then the value of \( k \)
is
\( A \cdot 1 \)
B. - 1
c.
D. 2


In a common -base amplifier, the phase difference between the input signal voltage and output voltage is :
A \( \cdot \frac{\pi}{4} \)
в. \( \pi \)
c. 0
D.


ampere current is passed for 60 seconds into an electrolytic cell. Number
of electrons that pass through the
solution is :
A. \( 6.0 \times 10^{23} \)
B. \( 1.2 \times 10^{24} \)
c. \( 37.5 \times 10^{19} \)
D. \( 7.48 \times 10^{21} \)


Which is the correct structural formula
for terylene?
\( A \)
B.
\( c \)
\[
\left.\left[\begin{array}{cc}
c & -\bigcirc \\
\| & \\
0 &
\end{array}\right)-\begin{array}{c}
c-o-c H_{2}-c H_{2}-o \\
\| \\
0
\end{array}\right]_{n}
\]
D.
\[
\left[\begin{array}{l}
\mathrm{c} \\
\| \\
\mathrm{o}
\end{array}\right] \underset{\mathrm{o}}{\mathrm{d}} \underset{\mathrm{n}}{\mathrm{d}}-\mathrm{cH}_{2}-\mathrm{o}-\mathrm{cH}_{2}-\mathrm{o}
\]