Assertion
If a charged particle enters from outside at right angles in uniform
magnetic field.The maximum time spent in magnetic field may be \( \frac{\pi m}{B q} \)
Reason

It can complete only semi-circle in the magnetic field.
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


State the approximate value of the critical angle for (a) glass-air surface,
(b) water-air surface (Given \( \mu_{\text {glass}}= \)
\( \left.\mathbf{1 . 5}, \boldsymbol{\mu}_{\boldsymbol{w} \boldsymbol{a} \boldsymbol{t} e r}=\mathbf{1 . 3 3}\right) \)
A \( \cdot \) (a) \( 49^{\circ},(b) 49^{\circ} \)
B . (a) \( 42^{\circ},(b) 42^{\circ} \)
\( \mathbf{c} \cdot(\mathbf{a}) 42^{o},(\mathbf{b}) 49^{\circ} \)
D \( \cdot \) (a) \( 49^{\circ},(b) 42^{\circ} \)


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


On passing through a glass slab, red light suffers a change of:
A. wavelength
B. frequency
c. amplitude
D. both frequency and wavelength


If \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) satisfies \( |\boldsymbol{f}(\boldsymbol{x})-\boldsymbol{f}(\boldsymbol{y})| \leq \)
\( |x-y|^{3} \) and \( f(4)=192 \) then \( f(7) \) is
equal to


Two inductance's connected in parallel are equivalent to a single inductance of
\( 1.5 H, \) and when connected in series
are equivalent to a single inductance of
\( 8 H . \) The difference in their inductance
is:-
\( \mathbf{A} \cdot 3 H \)
в. \( 7.5 ~ H \)
c. \( 2 H \)
D. \( 4 H \)


The equation of the plane which is parallel to the \( x y- \) plane is
A. \( x=y \)
B. \( z=c \)
\( \mathbf{c} \cdot y=c \)
D. \( z=x y \)


Rearrange the following in a proper logical sequence.

Epidermis, Cortex, Root Hair, Xylem, Endodermis.


Define Growth rate


Draw Venn diagrams to illustrate \( A \backslash \)
\( (\boldsymbol{B} \cap \boldsymbol{C}) \)


When solid \( K C l \) is added to a saturated
solution of \( \boldsymbol{A} \boldsymbol{g} \boldsymbol{C} \boldsymbol{I} \) in \( \boldsymbol{H}_{2} \boldsymbol{O} \)
A. Nothing happens
B. Solubility of \( A g C l \) decreases
c. Solubility of \( A g C l \) increases
D. Solubility product of \( A g C l \) increases


In a saturated solution:
A. dissolved solute \( >>> \) undissolved solute
B. dissolved solute \( <<< \) undissolved solute
C. dissolved solute and undissolved solutes are in equilibrium with each other
D. none of the above


In which of the following, the reaction proceeds towards completion?
\( \mathbf{A} \cdot K=1 \)
В. \( K=10^{-2} \)
c. \( K=10 \)
D. \( K=10^{3} \)


A solid cylinder of mass \( 10 k g \) is rolling
perfectly on a plane of inclination \( 30^{0} \) The force of friction between the
cylinder and surface of the inclined
plane is :
A . \( 49 N \)
в. \( 24.5 \mathrm{N} \)
c. \( \frac{49}{3} N \)
D. \( 12.25 N \)


Which of the following compounds has greatest ionic character?
A \( \cdot P C l_{5} \)
в. \( \operatorname{si} C l_{4} \)
c. \( C C l_{4} \)
D. \( B C l_{3} \)


The mean deviation of
\( \frac{a+b}{2} \) and \( \frac{a-b}{2}(\text { where a and } b>0) \) is?
\( A \cdot \frac{b}{2} \)
в. \( \frac{a}{2} \)
\( c \cdot a \)
D.


Two soap bubbles of radii \( x \) and \( y \)
coalesce to constitute a bubble of
radius \( z . \) Then \( z \) is equal to:
\( \mathbf{A} \cdot \sqrt{x^{2}+y^{2}} \)
B. \( \sqrt{x+y} \)
c. \( x+y \)
\( \frac{x+y}{2} \)


The wavelength associated with a golf ball weighing \( 200 \mathrm{g} \) and moving at a speed of \( 5 m h^{-1} \) is of the order:
B . \( 10^{-20} m \)
\( \mathbf{c} \cdot 10^{-30} m \)
D. \( 10^{-40} m \)


If \( A=\left(\begin{array}{ccc}1 & -1 & 3 \\ 5 & -4 & 7 \\ 6 & 0 & 9 & 8\end{array}\right), \) Find the order of the
matrix


The idea of quantum nature of light has emerged in an attempt to explain:
A . interference
B. diffraction
c. black body radiation
D. polarisation


Without expanding at any stage,
evaluate the value of determinant


The focus of an ellipse is at the origin. The directrix is the line \( x=4 \) and its
eccentricity is \( \frac{1}{2} \) then length of its semi major axis is
A \( \cdot \frac{2}{3} \)
B. \( \frac{4}{3} \)
\( c \cdot \frac{5}{3} \)
D. \( \frac{8}{3} \)


These organisms are fungus like in one
phase of their life cycle and Amoeba like in another phase of their life cycle
A. Diatoms
B. Slime molds
c. Dinoflagellates
D. water molds


A thin spherical shell lying on a rough horizontal surface is hit by a cue in such a way that line of action passes
through the center of the shell. As a result, shell starts moving with a linear
speed \( \nu \) without any initial angular
velocity. Find the linear velocity of the shell when it starts pure rolling.
A \( \cdot \frac{3}{5} \nu \)
B. \( 2_{-\nu} \)
\( c \cdot 4 \)
D. None


Is the given Progression arithmetic progression?Why \( 2,3,5,7,8,10,15, \dots \dots \dots \)


The equation for the reaction of burning
Mg with \( N O_{2} \) is
\( \boldsymbol{x} \boldsymbol{M} \boldsymbol{g}+\boldsymbol{y} \boldsymbol{N} \boldsymbol{O}_{2} \longrightarrow \boldsymbol{x} \boldsymbol{M} \boldsymbol{g} \boldsymbol{O}+\boldsymbol{z} \boldsymbol{N}_{2} \)
Then \( \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}=? \)


Evaluate the following integral:
\( \int \frac{x^{3}-3 x^{2}+5 x-7+x^{2} a^{x}}{2 x^{2}} d x \)


A current is induced in a coil by
electromagnetic induction.
A. Only when coil moves in the magnetic field
B. Only when a magnetic is moved into a coil
C. Only when the coil and magnet move with respect to each other
D. None of the above


Define capillary water, hydroscopic water and combined water.


For the following differential equation, find the general solution.
\( \frac{d y}{d x}+x=1 \)


What are Detergents? How are they considered better than soap?


The equation of sound wave is \( y= \) \( 0.0015 \sin (62.4 x+316 t) . \) Find the
wavelength of this wave:
A. 0.2 unit
B. 0.1 unit
c. 0.3 unit
D. none of these


The best starting substrate to prepare
\( 2- \) Bromobenzoic acid?
\( A \)
B.
\( \mathbf{c} \)
D.


The term inertia was first used by
A. Newton
B. Galileo
C. Aristotle
D. Kepler


The iron formed in the blast furnace is
called:
A. pig iron
B. wrought iron
c. steel
D. cast iron


The substance not likely to contain
\( \boldsymbol{C a C O}_{3} \) is:
A. dolamite
B. sea shell
c. calcined gypsum
D. marble statue


Choose the correct answer from the
alternatives given. If a cell is placed in an isotonic solution, what will occur?
A. Salts will move into the cell from the surrounding solution
B. Water will move into the cell from the surrounding solution
c. Salts will move out of the cell into the surrounding solution
D. None of the above will occur


Limiting molar conductivity of NaBr is:
\( \mathbf{A} \cdot \Lambda_{m}^{o} N a B r=\Lambda_{m}^{o} N a C l+\Lambda_{m}^{o} K B r \)
B. \( \Lambda_{m}^{o} N a B r=\Lambda_{m}^{o} N a C l+\Lambda_{m}^{o} K B r-\Lambda_{m}^{o} K C l \)
\( \mathbf{C} \cdot \Lambda_{m}^{o} N a B r=\Lambda_{m}^{o} N a O H+\Lambda_{m}^{o} N a B r-\Lambda_{m}^{o} N a C l \)
\( \mathbf{D} \cdot \Lambda_{m}^{o} N a B r=\Lambda_{m}^{o} N a C l-\Lambda_{m}^{o} N a B r \)


Give an example of 'a narcotic'
analgesic.


Two particles of mass \( m \) and \( 2 m \) have equal kinetic energy. Their De Broglie wavelengths are in the ratio:
A . 1: 1
B. 1: 2
c. \( 1: \sqrt{2} \)
D. \( \sqrt{2}: 1 \)


stands at the end of diving board, as
shown. The board is uniform, massive
and solid. There is no vibration or
motion of any kind. The board is firmly
attached to two supports at point \( \boldsymbol{P}_{1} \)
and \( P_{2} . \) The professor now begins to walk slowly in (right) from the end of
the board towards \( P_{1} . \) While he is
walking, how should you describe the force on the board by the support at
point \( P_{2} ? \) (i.e. Over at the far right hand
end)
A. upwards and increasing magnitude.
B. upwards and decreasing magnitude
c. downwards and increasing magnitude.
D. downwards and decreasing magnitude


The range of function \( \boldsymbol{f}(\boldsymbol{x})= \) \( \sqrt{e^{\cos ^{-x}\left(\log _{4} x^{2}\right)}} \) is


A proton of charge \( e \) moving at speed \( v_{0} \) is placed midway between two parallel wires \( a \) distance a apart, each carrying
current \( I \) in the same direction.
The force on the proton is:
A . 0
в. \( \quad e v_{0} \frac{I_{0}}{2 \pi a} \)
\( ^{\mathrm{c}} \cdot \operatorname{ev}_{0} \frac{I_{0}}{2 \pi(2 a)} \)
D. \( _{e v_{0}} \frac{I_{0}}{2 \pi \frac{a}{2}} \)
E. Unable to be determined


A \( 10 \% \) (mass/mass) solution of cane sugar undergoes partial conversion into glucose and fructose to show an inversion of cane sugar as:
Sucrose\( + \)Water\( \rightarrow \)Glucose\( + \)
Fructose
The solution boils at \( 100.27^{\circ} \mathrm{C} \) at this
state. What fraction of the sugar has
inverted? \( \left(\text { Given } \boldsymbol{K}_{\boldsymbol{b}} \text { for } \boldsymbol{H}_{\mathbf{2}} \boldsymbol{O} \) is \right.
\( \left.0.512 K m o l^{-1} k g\right) \)
Multiply answer with 10 and write the nearest integer value.


The logic expression which is NOT true in Boolean algebra is
\( \mathbf{A} \cdot[\overline{1}+\overline{1}] \cdot 1=0 \)
В. \( [\overline{1}+0] .1=0 \)
c. \( [\overline{1}+0] . \overline{1}=0 \)
D. \( [1+1] .1=0 \)


A Carnot engine used first an ideal monoatomic gas and then an ideal diatomic gas. If the source and sink
temperature are \( 411^{\circ} \mathrm{C} \) and \( 69^{\circ} \mathrm{C} \)
respectively and the engine extracts \( 1000 \mathrm{J} \) of heat in each cycle, then area
enclosed by \( p V \) diagram is
A . 100 J
B. 300 J
c. 500
D. 700 J


Two angles of a triangle measure \( 52^{\circ} \)
and \( 72^{\circ} . \) Find the measure of the third
angle of the triangle.
A \( .36^{\circ} \)
B . 46
\( c \cdot 56^{\circ} \)
D. \( 66^{\circ} \)


What are the advantages of sexual reproduction over asexual reproduction?
A. Variation in gene pool leading to generation of new species
B. Exponential growth
c. Selective adaptation
D. Both A and C


A physician wishes to prepare a buffer solution at \( p H=3.58 \) that efficiently
resists a change in \( p H \) yet contains only small conc. of the buffereing agents. Which one of the following weak acid together with its sodium salt would be best to use?
A. \( m \) -chloro benzoic acid \( \left(p K_{a}=3.98\right) \)
B. \( p \) -chlorocinnamic acid \( \left(p K_{a}=4.41\right) \)
C. 2,5-dihydroxy benzoic acid ( \( p K_{a}=2.97 \) )
D. Acetoacetic aced ( \( p K_{a}=3.58 \) )


No. of double bond present in the Lewis
structure of \( \boldsymbol{P} \boldsymbol{F}_{\boldsymbol{6}}^{-} \) is


Specific resistance of all metals is
mostly affected by
A. volume
B. pressure
c. temperature
D. magnetic field


When chlorine is passed over dry slaked
lime at room temperature, the main reaction product is:
A \( \cdot C a\left(C l O_{2}\right)_{2} \)
в. \( C a C l_{2} \)
c. \( C a O C l \)
D. \( \operatorname{Ca}\left(O C l_{2}\right)_{2} \)


Identify the products.
\[
\underset{\mathrm{Me}}{\longrightarrow} \underbrace{\Gamma=\mathrm{O}+2 \mathrm{Me}-\equiv-\mathrm{H} \frac{\mathrm{M}_{\mathrm{CO}}}{_{\mathrm{MCOH}}}^{+}}_{(\mathrm{B})}(\mathrm{C})
\]


Joseph Lister discovered 'carbolic acid
for use in antiseptic surgery in 1834 which saved many mothers during
childbirth in those days. 'Carbolic acid was the name used for:
A. benzene
B. phenol
c. iodoform
D. chloroform


\( \Delta G^{0} \) for the reaction \( : X+Y \rightleftharpoons C \) is
-4.606 kcal at \( 1000 \mathrm{K} . \) The equilibrium
constant for the reverse mode of the
reaction is :
A . 100
B. 10
c. 0.01
D. 0.1


Eutrophication is found in
A. Agricultural land near thermal plant
B. Saline soil
c. Lake
D. Mountain


Evaluate: \( \int \frac{2 x}{(x+5)^{2}} d x \)


Superphosphate of lime is manufactured by the action of \( 70 \% \)
conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) on
A. phosphate
B. powdered phosphorite
c. powdered phosphorus
D. bone ash


Select correct statement(s).
\( \mathbf{A} \cdot P u^{4+} \) disproportionates to \( P u^{3+} \) and \( P u O_{2}^{2+} \) in strongly acidic solution
B. Maximum oxidation state of Np is +7
\( \mathrm{C} \cdot U \mathrm{O}_{2}^{2+} \) is stable
D. All of the above are correct statement


The safest general anaesthesia used at
present is:
A. chloroform
B. diethyl ether
c. acetylene
D. halothane


Assuming \( z- \) axis inter nuclear axis. In
which of the following orbitals overlap to
form \( \sigma \) bond
\( \boldsymbol{s}+\boldsymbol{p}_{\boldsymbol{x}} \)


For the data given, calculate the energy
deficit in the formation \( B e C l_{2} \) (it is a
stable molecule)
I. \( \boldsymbol{E}_{1} \) for \( \boldsymbol{B e}=\mathbf{8 9 9 k J} / \boldsymbol{m o l} \)
I. \( \boldsymbol{E} \). for \( \boldsymbol{B e}=\mathbf{1 7 5 7 k J} / \boldsymbol{m o l} \)
I.A. for \( C l=-348 k J / \) mol


Two water droplets combine to from a
large drop in this process energy is


Which of the following reactions will yield propan-2-ol? This question has multiple correct options
A \( \cdot C H_{2}=C H-C H_{3}+H O H \stackrel{H}{\rightarrow} \)
B. \( C H_{3}-C H O^{C H_{3} M g B r / H O H} \rightarrow^{C H} \)
\( \mathrm{c} \cdot \mathrm{CH}_{2} \mathrm{O}^{C_{2} \mathrm{H}_{5} \text { МуТ } / \text {НОН}} \)
D. None of the above


Define (a) Optical activity
(b) Asymmetric carbon atom
(c) Enantiomers
(d) Racemates.


State whether true or false:
When light passes through a prism the colour that suffers minimum deviation
is violet.
A. True
B. False


Which is more stable in the below
given pair?
\( V^{2+}-- \)
\( \boldsymbol{V} \boldsymbol{O}_{4}^{3-} \)
A \( \cdot V^{2+}=V O_{4}^{3-} \)
B . \( V^{2+}<V O_{4}^{3-} \)
c. \( V^{2+}>V O_{4}^{3-} \)
D. None of these


Let \( P Q R \) be a right angled isosceles traingle, right angled at \( P(2,1) . \) If the
equation of the line \( Q R \) is \( 2 x+y=3 \)
then the equation represnting the pair
of lines \( P Q \) and \( P R \) is
A \( \cdot 3 x^{2}-3 y^{2}+8 x y+2 x+10 y+25=0 \)
B . \( 3 x^{2}-3 y^{2}+8 x y-20 x-10 y+25=0 \)
c. \( 3 x^{2}-3 y^{2}+8 x y+10 x+15 y+20=0 \)
D. \( 3 x^{2}-3 y^{2}-8 x y-10 x-15 y-20=0 \)


Mark the correct options
A. Gauss law is valid only for unsymmetrical charge distributions
B. Gauss law is valid only for charge placed in vacuum
C. The electric field calculated by Gauss law is the field due to the charges outside the Gaussian surface
D. The flux of the electric field through a closed surface due to all the charges is equal to the flux due to the charges enclosed by the surface


Deoxyribonuclease and ribonuclease
are secreted by
A. Liver
B. Stomach
c. Pancreas
D. Kidney


The magnetic field of the earth can be modelled by that of a point dipole placed at the centre of the earth. The
dipole axis makes an angle of \( 11.3^{\circ} \) with the axis of the earth. At mumbai
declination is nearly zero. Then
A. the declination varies between \( 11.3^{\circ} \) W to \( 11.3^{\circ} \) E
B. the least declination is \( 0^{\circ} \)
c. the plane defined by dipole and the earth axis posses through greenwich
D. declination average over the earth must be always negative


\( \frac{\tan \theta}{\left(1+\tan ^{2} \theta\right)^{2}}+\frac{\cot \theta}{\left(1+\cot ^{2} \theta\right)^{2}}=\sin \theta \)
\( \cos \theta \quad, \) then \( \theta \) is
\( \mathbf{A} \cdot 2 \pi \)
в. \( \frac{\pi}{56} \)
\( c \cdot \frac{\pi}{2} \)
D.


A uniform rod of length \( L \) and density \( \rho \)
is being pulled along a smooth floor with a horizontal acceleration \( a \). Find
the magnitude of the stress at the transverse cross section through the mid-point of the rod.


A mixture of ethanol and propanol has
vapor pressure \( 279 \mathrm{mm} \) of \( \mathrm{Hg} \) at \( 300 \mathrm{K} \) The mol fraction of ethanol in the
solution is 0.6 and vapour pressure of pure propanol is \( 210 \mathrm{mm} \) of Hg. Vapour pressure of pure ethanol will be:
\( \mathbf{A} \cdot 336.6 \mathrm{mm} \)
B . \( 325 \mathrm{mm} \)
c. \( 375 \mathrm{mm} \)
D. \( 415 \mathrm{mm} \)


The centre of the circle \( (x-a)(x- \)
\( \boldsymbol{b})+(\boldsymbol{y}-\boldsymbol{c})(\boldsymbol{y}-\boldsymbol{c})=\mathbf{0} \) is
\( \mathbf{A} \cdot(a+b, c+d) \)
В. \( 9-a-b,-c-d) \)
\( ^{\mathbf{c}} \cdot\left(\frac{a+b}{2}, \frac{c+d}{2}\right) \)
D. none of these


A helical spring is stretched by a force, the resultant strain produced in the spring is:
A. volume strain
B. shearing strain
c. longitudinal strain
D. all the above


The width of a slit is \( 0.012 \mathrm{mm} \)
Monochromatic light is incident on it. The angular position of first bright line
is \( 5.2^{\circ} . \) The wavelength of incident light is : \( \left(\operatorname{given} \sin 5.2^{0}=0.0906\right) \)
A \( \cdot 6040 \),
в. 4026 \( ^{\circ} \)
\( c \cdot 5890 \stackrel{\circ}{A} \)
D. 7248 , \( ^{\circ} \)


In triangle \( P Q R \), right angled at \( Q \), if \( \tan P=\frac{1}{\sqrt{3}} \) find the value of \( \sin P+ \)
\( \cos R+\cos P \sin R \)


Two small glass spheres of masses 10 g and 20 g are moving in a straight line in the same direction with velocities of
\( 3 m s^{-1} \) and \( 2 m s^{-1} \) respectively. They collide with each other. After collision,
glass sphere of mass 10 g moves with a velocity of \( 2.5 m s^{-1} . \) Find the velocity of the second ball after collision.
A \( .2 .25 m s^{-1} \)
B. \( 5.5 m s^{-1} \)
\( \mathbf{c} \cdot 2.75 m s^{-1} \)
D. \( 7.5 m s^{-1} \)


Which rule determines the direction of
current induced in a coil due to the
rotation in a magnetic field.
A. Maxwell right hand grip rule
B. Fleming's left hand rule
c. Fleming's right hand rule
D. None


A very long straight wire carries a
current I. At the instant when a charge \( +Q \) at point \( P \) has velocity \( \vec{V}, \) as shown, the force on the charge is
A. Along ox
B. Opposite to oy
c. Along oy
D. Opposite to ox


The following equilibrium are given below:
\( \boldsymbol{A}_{2}+\mathbf{3} \boldsymbol{B}_{2} \rightleftharpoons \mathbf{2} \boldsymbol{A} \boldsymbol{B}_{3} \ldots \boldsymbol{K}_{\mathbf{1}} \)
\( \boldsymbol{A}_{2}+\boldsymbol{C}_{2} \rightleftharpoons \mathbf{2} \boldsymbol{A} \boldsymbol{C} \ldots \boldsymbol{K}_{2} \)
\( \boldsymbol{B}_{2}+\frac{1}{2} \boldsymbol{C}_{2} \rightleftharpoons \boldsymbol{B}_{2} \boldsymbol{C} \ldots \boldsymbol{K}_{3} \)
The equilibrium constant of the reaction
\( 2 A B_{3}+\frac{5}{2} C_{2} \rightleftharpoons 2 A C+3 B_{2} C . \) in terms
of \( K_{1}, K_{2} \) and \( K_{3} \) is:
\( ^{\text {A } \cdot \frac{K_{1} K_{2}}{K_{3}}} \)
в. \( \frac{K_{1} K_{3}^{2}}{K_{2}} \)
c. \( \frac{K_{2} K_{3}^{3}}{K_{1}} \)
D. \( K_{1} K_{2} K_{3} \)


A reaction is catalysed by \( \boldsymbol{H}^{+} \) ion. In presence of HA, rate constant is \( 2 \times \)
\( 10^{-3} \) min \( ^{-1} \) and in presence of HB rate
constant is \( 1 \times 10^{-3} \) min \( ^{-1} \), HA and HB
both being strong acids, we may conclude that:

This question has multiple correct options
A . equilibrium constant is 2
B. HA is stronger acid than HB.
c. relative acidic strength of HA and HB is 2.
D. HA is weaker acid than HB and relative strength is 0.5


Blood is isotonic with.
A. \( 0.16 M \) NaCl
\( l \)
B. Conc.NaCl
c . \( 30 \% \) NaCl \( l \)
D. \( 50 \% \) NaCl


I. A \( 2 M \) solution of urea \( \left(C H_{4} N_{2} O\right) \)
can be prepared by dissolving 1 mole of
urea in \( 500 m L \) of water.
II. Urea is a non-polar molecular compound
A. Statement \( I \) is true, Statement \( I I \) is true
B. Statement I is true, Statement II is false
c. statement \( I \) is false, statement \( I I \) is true
D. Statement I is false, Statement II is false


Acromion process is found in
A. Coxal bone
B. Scapula
c. Sternum
D. Clavicle


U' or 'V' or 'J' shaped chromosomes are
seen in \( \ldots \ldots . . . . . \) the phase of cell division.
A. Prophase
B. Metaphase
c. Telophase
D. Anaphase


Conversion of precipitate into colloidal solution is known as


A wheel of mass \( 10 k g \) and radius \( 20 c m \)
is rotating at an angular speed pf 100 revolution/min when the motor is
turned off. neglecting the friction at the axle, Calculate the force that must be applied tangentially to the wheel to bring it to rest in 10 revolutions?
A . 0.02
B. 0.23
\( c \cdot 0.05 \)
D. 0.87


Which of the following elements shown as pairs with their atomic numbers
belong to the same period?
A. \( Z=19 \) and \( z=38 \)
B. \( Z=12 \) and \( Z=17 \)
C \( . \quad Z=11 \) and \( Z=21 \)
D. \( z=16 \) and \( z=35 \)


Succession is
A. Orderly process of community change till stability.
B. Gradual convergent, directional and continuous
process.
C. Series of biotic communities that appear generally in barren area.
D. All of the above.


Assertion
Peroxisomes alone can carry the
photorespiration.
Reason
Peroxisome contain all enzymes to
carry out photorespiration.
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


0
0
0
0
0
0
0


1,4-dimethylbenzene on heating with
anhydrous \( A l C l_{3} \) and \( H C l \) produces :
A. 1,2 -dimethylbenzene
B. 1, 3-dimethylbenzene
c. 1,2,3 -trimethylbenzene
D. ethylbenzene


The second law of thermodynamics
states that
This question has multiple correct options
A. all spontaneous processes are thermodynamically irreversible.
B. entropy of the universe is continuously increasing.
C. energy can neither be created nor destroyed.
D. energy of the universe remain constant.


If the vapour pressure of solutions of two liquids are less than those expected from ideal solution they are said to have:
A. negative deviation from ideal behaviour
B. positive deviations from ideal behaviour
c. ideal behaviour
D. positive deviation for lower concentration and negative deviations for higher concentration


The distance of point \( A(-2,3,1) \) from
the PQ through \( P(-3,5,2), \) which makes equal angles with the axes is-
A \( \cdot \frac{2}{\sqrt{3}} \)
в. \( \sqrt{\frac{14}{3}} \)
c. \( \frac{16}{\sqrt{3}} \)
D. \( \frac{5}{\sqrt{3}} \)


Chlorine on reaction with hot and
concentrated sodium hydroxide gives:
\( \mathbf{A} \cdot C l^{-} \) and \( C l O_{2}^{-} \)
в. \( C l^{-} \) and \( C l O_{3}^{-} \)
c. \( C l^{-} \) and \( C l O^{-} \)
D. \( C l O_{3}^{-} \) and \( C l O_{2}^{-} \)


When an ideal gas expands isothermally, its internal energy will
A. increases
B. decreases
c. remains constant
D. becomes zero


Assertion
Degree of a zero polynomial is not
defined.
Reason
Degree of a non-zero constant
polynomial is 0
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


Three point charges \( -q, q \) and \( Q \) are arranged as given in figure:

If \( d \) is distance from centre of \( -q \) and \( +\boldsymbol{q} \) to \( \boldsymbol{Q} \) and \( \boldsymbol{d}>>>\boldsymbol{a}, \) then the
potential energy of given system is:
\[
\mathbf{q}
\]
\( A \)
\[
\left(\frac{k q Q a}{d^{2}}\right)
\]
в.
\[
\left(\frac{+k q^{2}}{a}+\frac{k q Q a}{d^{2}}\right)
\]
c.
\[
\left(\frac{-k q^{2}}{a}+\frac{k q Q a}{2 d^{2}}\right)
\]
D.
\[
\left(\frac{-k q^{2}}{a}+\frac{k q Q a}{d^{2}}\right)
\]


A photo diode is made from a
semiconductor \( I n_{0.53} . \) As, with \( E_{g}=0.73 \)
eV. What is the maximum wavelength
which it can detect? \( \boldsymbol{h}=\mathbf{6 . 6 3} \times \)
\( 10^{-34} J_{s} \)


lce is used in a cooler in order to cool its
contents.Which of the following will speed up the cooling process
A. Wrap the ice in a metal foil
B. Drain the water from the cooler periodically
c. Put the ice as a single block
D. Crush the ice


Consider the following alkane and answer the following questions.
\( \left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{C H C H}_{2} \boldsymbol{C H}\left(\boldsymbol{C}_{2} \boldsymbol{H}_{5}\right) \boldsymbol{C H}(\boldsymbol{C H} \)
(a) Write the complete structural formula of the alkane.
(b) What is its molecular formula?
(c) Write its bond line formula and give
IUPAC name.
(d) How many methyl, methylene and methine groups are present in this alkane?
(e) How many ethyl and isopropyl groups are present in this alkane?
(f) How many carbon atoms are
\( 1^{\circ}, 2^{\circ}, 3^{\circ}, 4^{\circ} ? \)


The area of the triangle whose adjacent sides are represented by the vector \( (4 \bar{i}+3 \bar{j}+4 \bar{k}) \) and \( 5 \bar{i} \) in square units
is:
A . 25
в. 12.5
c. 50
D. 45


Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}: \)
\( \boldsymbol{x}+\boldsymbol{y}^{2}=\log \boldsymbol{y}+\boldsymbol{x}^{2} \)


Two identical plano convex lenses are arranged in three different
combinations as:
I) the plane surfaces touching each
other
II) the curved surfaces touching each
other
III) the plane surface of one lens touching the curved surface of the
other.
Then the focal lengths of the combinations are in the ratio:
A \( \cdot 1: 2: 3 \)
B. 1: 1: 1
c. 3: 2: 1
D. 2: 2: 1


The first two terms in a GP as 3 and 6
what is the \( 10^{t h} \) term?
A . 1536
B . 2536
\( c .3536 \)
D. 4536


Rank the bond length of the bond below
in the molecules on the left column with
longest as 1 and shortest as 4 Match the following.


In which quadrant \( 196^{\circ} \) lies?
B. quadrant III
c. quadrantı
D. quadrant IV


How fast should a girl of \( 40 \mathrm{kg} \) run so that her kinetic energy is 320 J?
\( A \cdot 64 \mathrm{m} / \mathrm{s} \)
B. \( 8 \mathrm{m} / \mathrm{s} \)
\( c \cdot 16 m / s \)
D. \( 4 \mathrm{m} / \mathrm{s} \)


Assertion
Detergents can easily remove oil and
dirt from soiled garments.
Reason
Detergents increase the surface tension
of water.
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


\( \cdot\left[\begin{array}{l}1 \\ 1\end{array}\right]_{1}^{1}, \quad \)
\( a_{-1 / 1}^{11}[1]_{1} \)
\( \therefore \sum_{i=1}^{\infty} z_{k} \)


Construct a tangent to a circle of radius
\( 4 c m \) from a point on the concentric
circle of radius \( 6 \mathrm{cm} \) and measure its
length. Also verify the measurement by actual calculation.


Bright colour of petals is due to the
presence of
A. Chloroplast
B. Anthocyanin
c. Elaioplast
D. Amyloplast


A wire \( 50 \mathrm{cm} \) long and \( 1 \mathrm{mm}^{2} \) in cross
section carries a current of 4 A when
connected to a 2 V battery. The resistivity of the wire is
A. \( 2 \times 10^{-7} \Omega m \)
В. \( 5 \times 10^{-7} \Omega m \)
c. \( 4 \times 10^{-6} \Omega m \)
D. \( 1 \times 10^{-6} \Omega m \)


Electro negativity is expressed in
Scale.
A. paulings
B. sorensens
c. rutherford
D. none of these


When you are holding a ball in your hand, the reaction force to the force of
gravity on the ball is, the force exerted by the:
A. ball on the earth
B. ball on the hand
c. hand on the ball.
D. earth on the ball


Which of the following is a pythagorean triplet?
в. (5,7,9)
\( \mathbf{D} \cdot(8,15,17) \)


Assertion
Molten \( I_{2} \) is conducting in nature.
Reason
Bond dissociation energy increases in
the order, \( \boldsymbol{B r}_{2}<\boldsymbol{C l}_{2}<\boldsymbol{I}_{2} \)
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.


Imagine a cannon being fired on the
surface of the moon. Then
A. the sound will be heard at the surface of the earth during all seasons
B. the sound will not be heard at the surface of the earth
c. the sound will be heard at the surface of the earth during the rainy season
D. no sound will be heard on the earth or on the moon


Ordinary tap water conducts electric
current due to :
A. the dissolved salts in it it
B. higher purity of the water
c. the bacteria present in it it
D. none of these


The products formed when an aqueous solution of \( N a B r \) is electrolysed in a
cell having inert electrodes are :
A. \( N a \) and \( B r_{2} \)
B. \( N a \) and \( O_{2} \)
\( \mathrm{c} \cdot \mathrm{H}_{2}, \mathrm{Br}_{2} \) and \( \mathrm{NaOH} \)
D. \( H_{2} \) and \( O_{2} \)


The Coefficient of \( x^{n} \) in the expansion of
\( (1+x)(1-x)^{n} \) is
A. \( (n-1) \)
B \( \cdot(-1)^{n-1} n \)
C \( \cdot(-1)^{n-1}(n-1)^{2} \)
D・ \( (-1)^{n}(1-n) \)


The corresponding sides of two similar triangles are in the ratio \( 1: 3 . \) If the area
of the smaller triangle in \( 40 \mathrm{cm}^{2} \), find
the area of the larger triangle.


On the basis of Bohrs model, the radius
of the \( 3 r d \) orbit is:
A. equal to the radius of first orbitt
B. three to the radius of first orbit
c. five to the radius of first orbit
D. nine to the radius of first orbit


Describe the drawback of Rutherford's
model of atom.


Whose bicentenary is the year \( 2009 ? \)
A. Darwin
B. Edward Jenner
c. stanley Miller
D. T.H. Morgan


Heat is a form of \( _{-}-\ldots-_{\text {and }} \)
temperature is a of amount
of heat energy in a body
A. energy, measure
B. mass, measure
c. energy, instrument
D. mass, experiment


For a capacitor, distance between the plates \( =d, \) p.d between the plates \( = \)
\( \boldsymbol{V}, \boldsymbol{k}=\mathbf{1}, \) area of each plate \( =\boldsymbol{A} \) and
electric field between the plates \( =E \)
For another capacitor distance between
plates \( =\boldsymbol{d}, \) p.d between plates \( = \)
\( V, k=2, \) area of each plate \( =2 A \) and
electric field between the plates \( =\boldsymbol{E}^{1} \)
Relation between \( E \) and \( E^{1} \) is:
\( \mathbf{A} \cdot E^{1}=E / 4 \)
B . \( E^{1}=E / 2 \)
c. \( E^{1}=E \)
D. \( E^{1}=4 E \)


The following table of grouped data
represents the weight (in kg) of 100 gas
cylinders. Calculate the mode weight of
a cylinder.
Weight \( \begin{array}{cccc}\mathbf{3}- & \mathbf{5}- & \mathbf{7}- & \mathbf{9}- \\ \mathbf{5} & \mathbf{7} & \mathbf{9} & \mathbf{1 1}\end{array} \)
\( (\%) \)
Number of gas
16
13
15
cylinders
A. 12.96
B. 15.96
\( \mathbf{c} .9 .96 \)
D. 10.96


The number of solutions of the equation \( \tan ^{-1}\left(\frac{1}{2 x+1}\right)+\tan ^{-1}\left(\frac{1}{4 x+1}\right)= \)
\( \tan ^{-1}\left(\frac{2}{x^{2}}\right) \) is
\( A \)
B.
\( c \cdot 2 \)
D. 3


three idntical spherical ball \( A, B, C \) are placed on a table as shown in the figure along a straight line. \( \mathrm{B} \) and \( \mathrm{C} \) are at rest initilly. the ball \( A \) hits \( B \) head -on with a speed of \( 10 \mathrm{ms}^{-1} \).then after all collision
s( assumed to be elastic )A and B are brought to rest and \( C \) takes off with a
velocity of
\( \mathbf{A} \cdot 5 m s^{-1} \)
B. \( 10 m s^{-1} \)
c. \( 2.5 m s^{-1} \)
D. \( 7.5 m s^{-1} \)


Construct \( A B C, \) an isosceles triangle
with \( A B=A C=13 \mathrm{cm} \) and \( B C=10 \)
cm. Calculate the length of perpendicular from \( \boldsymbol{A} \) to \( \boldsymbol{B C} \)


Nitric acid is yellow in colour when freshly prepared.
A. True
B. False


What is series?
A. adding all the numbers
B. subtracting all the numbers
C. multiplying all the numbers
D. dividing all the numbers


The apparatus which is used at \( C \) is
known as
A. Anode
B. Cathode
c. Salt bridge
D. Ion bridge
E. Osmotic bridge


Fungi which occur on wood are
A. Epibiotic
B. Eucarptic
c. Epixylic
D. Epigeon


A waveform has a baseline of \( 3 V \), a duty
cycle of \( 20 \%, \) and an amplitude of \( 8 V \)
The average voltage value is
A . \( 4 V \)
в. \( 4.6 V \)
c. \( 1.6 V \)
D. \( 11 V \)


Which of the following does not show octahedral geometry?
A. \( S F_{6} \)
в. \( I F_{5} \)
\( \mathbf{c} \cdot \operatorname{si} F_{6}^{2} \)
D. \( S F_{4} \)


If \( 70 \% \) of the students in a school are
boys and the number of girls is \( 540, \) find the number of boys in the school


Give reasons
(a) Water is not used to control fires
involving electrical equipment.
(b) LPG is a better domestic fuel than
wood.
(c) Paper by itself catches fire easily whereas a piece of paper wrapped around an aluminium pipe does not.


Work function of three metals \( A, B, C \) are
\( 4.5 \mathrm{eV}, 4.3 \mathrm{eV} ., 3.5 \) ev respectively. If a light of wavelength 4000 A is incident on the metals, then
A. photoelectron are emitted from \( c \)
B. photoelectrons are emitted from A
c. photoelectrons are emitted from B
D. photoelectron will not emitted from all the surfaces


Four cubes of side 'a' each of mass 40 g. 20 \( g, \) 10 \( g \) and 20 g are arranged in \( x Y \) plane as shown in the figure. The coordinates of COM of the combination
with respect to point 0 is:
A \( \frac{19 a}{18}, \frac{17 a}{18} \)
в. \( \frac{17 a}{18}, \frac{11 a}{18} \)
с. \( \frac{17 a}{18}, \frac{13 a}{18} \)
". \( \frac{13 a}{18}, \frac{17 a}{18} \)


A ray of light passes from a medium \( \mathbf{A} \) having refractive index 1.6 to the medium B having refractive index 1.5 The value of critical angle of medium \( A \)
is
\( ^{\mathbf{A}} \cdot \sin ^{-1}\left(\frac{16}{15}\right) \)
B. \( \sin ^{-1} \sqrt{\frac{16}{15}} \)
\( ^{\mathbf{c}} \cdot \sin ^{-1}\left(\frac{1}{2}\right) \)
D. \( \sin ^{-1}\left(\frac{15}{16}\right) \)


A body falling freely from rest covers \( \frac{7}{16} \) of the total height in the last second of its fall. What is the height from which it falls?
\( \mathbf{A} \cdot 24.2 m \)
в. \( 40 m \)
c. \( 80 m \)
D. \( 46.8 m \)


Moon is revolving in a circular orbit with
a uniform velocity \( V_{0} \). If the
gravitational force suddenly disappears, the moon will
A. continue to move in the same orbit
B. move with a velocity \( V_{0} \) tangentially to the orbitt
c. fall down freely
D. ultimately comes to rest


The sum of 12 observations is \( 600, \) then
their mean is
A . 20
B. 30
c. 40
D. 50


A magnet has a pole strength of 1000 milli amp.m. The magnetic field intensity at a distance of \( 10 \mathrm{cm} \) from its North pole
is
\( \mathbf{A} \cdot \frac{25}{\pi} A / m \)
B . \( \frac{\pi}{25} A / m \)
\( \mathbf{c} \cdot \frac{100}{\pi} A / m \)
D \( \cdot \frac{\pi}{100} A / m \)


The process of formation of polymers
from respective monomers is called:
A. Polyacrylonitrile
B. Co-polymerization
c. Polymerization
D. None of these


Two bodies of mass \( 1 \mathrm{kg} \) and \( 4 \mathrm{kg} \) are massing with equal kinetic energies. The ratio of their linear momantum is-
A . 1: 2
B. 2:
\( c \cdot 4: \)
D. 1:


For which of the following, 'Wharton's jelly' term is used?
A. Elastic tissue
B. Mucoid tissue
c. Reticular tissue
D. All of the above


\( \frac{5}{6} \)
\( \frac{6}{8} \)
in


Which of the following statements is
true?
A. The image formed by a pinhole camera is inverted because light travels in a straight line.
B. Light does not change its direction on reflection.
C. As we move the object away from the light source, the shadow of the object becomes smaller.
D. Reflection is possible only from polished surface.


The solubility products of \( A g C l \) and \( A g I \) are \( 1.1 \times 10^{-10} \) and \( 1.6 \times 10^{-16} \)
respectively. If \( A g N O_{3} \) is added drop by drop the solution containing both chloride and iodide ions, then
precipitated first is:
\( A \cdot A g I \)
в. \( A g N O_{3} \)
c. \( A g C l \)
D. Both \( A g I \) and \( A g C l \)


A given quantity of an ideal gas is at pressure \( P \) and absolute temperature
T. The isothermal bulk modulus of the
gas is:
A. \( 2 P / 3 \)
в. \( P \)
c. \( 3 P / 2 \)
D. \( 2 P \)


Which of the following is not a structure of nitromethane molecule?
\( A \)
B.
c.
D.


Match the four starting materials (P, Q,
R, S) given in List I with the corresponding reaction schemes (I, II, III, IV) provided in List II and select the correct answer using the code given below the lists.
A. P-1, Q- 4, R- 2, S- 3
B. P- 3, Q-1,R- 4, S-2
c. \( P-3, Q-4, R-2, S-1 \)
D. P- \( 4,0-1, R-3, S-2 \)


Add the following rational numbers:
\( \frac{-7}{27} \) and \( \frac{11}{18} \)


State the exact location of the following
structures.
Proximal convoluted tubule.


The moon's distance from the earth is
\( 360000 \mathrm{kms} \) and its diameter subtends
an angle of \( 31^{\prime} \) at the eye of the
observer. Find the diameter of the moon.
A . \( 3246.33 \mathrm{km} \)
в. \( 3747.62 \mathrm{kms} \)
c. \( 3400.52 \mathrm{km} \)
D. 3244.72 kms


A liquid flow through a horizontal tube.
The velocities of the liquid in the two sections, which have areas of cross
section \( \boldsymbol{A}_{\mathbf{1}} \) and \( \boldsymbol{A}_{\mathbf{2}} \) are \( \boldsymbol{v}_{\mathbf{1}} \) and \( \boldsymbol{v}_{\mathbf{2}} \)
respectively. The difference in the levels
of the liquid in the two vertical tubes is
\( h . \) Then
This question has multiple correct options
A. The volume of the liquid flowing through the tube in unit time is \( A_{1} v_{1} \)
\( \mathbf{B} \cdot v_{2}-v_{1}=\sqrt{2 g h} \)
\( \mathbf{c} \cdot v_{2}^{2}-v_{1}^{2}=2 g h \)
D. The energy per unit mass of the liquid is the same in both section of the tube


For a first order reaction, the time
required for \( 99.9 \% \) of the reaction to take place in nearly:
A. 10 times that required for half the reaction
B. 100 times that required for two-third of the reaction
c. 10 times that required for one-fourth of the reaction
D. 20 times that required for half of the reaction.


Alkyl halide can be converted into alkene by:
A. nucleophilic substitution reaction
B. elimination reaction
c. both nucleophilic substitution and elimination reaction
D. rearrangement


Thermal pollution causes a decrease in dissolved oxygen Is the above statement true?
A. True
B. False


The projection of \( \vec{a}=\hat{i}+2 \hat{j}+3 \hat{k} \) on the vector \( \overrightarrow{\boldsymbol{b}}=\hat{\boldsymbol{i}}+2 \hat{\boldsymbol{j}}-\hat{\boldsymbol{k}} \) is :
A. \( \sqrt{\frac{2}{3}} \)
B. \( \sqrt{\frac{3}{2}} \)
c. \( \sqrt{\frac{4}{21}} \)
D. \( \sqrt{\frac{25}{21}} \)


If true enter 1 , else enter 0 .
Multiple bonds repel single bond more
strongly than single bond repel other single bond


What is the difference between the
production of Company \( Z \) in 1998 and
Company Y in \( 1996 ? \)
A. 2,00,000 tons
B. 20,00,000 tons
c. 20,000 tons
D. 2,00,00,000 tons


A one litre flask is full of reddish brown
bromine fumes. The intensity of brown colour of vapour will decrease appreciably on adding to the flask \( x \) number of species from the following
find \( x \)
(i) Marble pieces
(ii) Animal charcoal powder
(iii) \( \mathbf{C} \boldsymbol{C l}_{\mathbf{4}} \)
(iv) \( \mathbf{C} \boldsymbol{S}_{2} \)
(v) Water
\( A \cdot(3) \)
B. (2)
c. (1)
\( D \cdot(4) \)


For an elementary reaction, \( \boldsymbol{X}(\boldsymbol{g}) \rightarrow \) \( \boldsymbol{Y}(\boldsymbol{g})+\boldsymbol{Z}(\boldsymbol{g}): \) the half life period is
10 min. In what period of time would
the concentration of \( X \) be reduced to
\( 10 \% \) of original concentration?
A . 20 min
B. 33 min
\( c .15 \) min
D. 25 min


Solve: \( \frac{\cos ^{2} 25^{\circ}+\cos ^{2} 65^{\circ}}{\sin ^{2} 59^{\circ}+\sin ^{2} 31^{\circ}}=? \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
c. 2
\( D \)


Identify the hybridisation of underline \( \operatorname{atom} \operatorname{in} \boldsymbol{H}_{3} \boldsymbol{O}^{+} \)
\( \mathbf{A} \cdot s p \)
B . \( s p^{2} \)
\( c \cdot s p^{3} \)
D. \( d^{2} s p^{3} \)


Determine the average velocity of the
car.


Determine the domain and range of the following relation.
\( \boldsymbol{R}=\{(\boldsymbol{a}, \boldsymbol{b}): \boldsymbol{a} \in \boldsymbol{N}, \boldsymbol{a}<\mathbf{5}, \boldsymbol{b}=\mathbf{4}\} \)


Assertion: Inert gases are monoatomic.
Reason: Inert gases have stable configuration.
A. Both assertion and reason are true and the reason is a
correct explanation of the assertion
B. Both assertion and reason are true but reason is not a
correct explanation of the assertion
C. The assertion is true but reason is false
D. Both the assertion and reason are false
E. The assertion is false but the reason is true


f \( \boldsymbol{y}=\tan ^{-1}\left(\frac{\sqrt{1+\boldsymbol{a}^{2} \boldsymbol{x}^{2}}-\mathbf{1}}{\boldsymbol{a} \boldsymbol{x}}\right), \) then
\( \left(1+a^{2} x^{2}\right) y^{\prime \prime}+2 a^{2} x y^{1}= \)
A . \( -2 a^{2} \)
B \( \cdot a^{2} \)
\( c \cdot 2 a^{2} \)
\( D \)


melting points and boiling points due to
relatively weak intermolecular
attractions that hold the molecules in
their solid form.
\( t^{\circ}(C) \) Molecular Solid \( \quad \) Boiling Point
\( H_{2} T e \) 0
\( H_{2} S e \) -50
\( H_{2} S \) -75
\( H_{2} O \) 100
Which of the following reasons explain
why \( H_{2} O \) does not appear to follow this
fact?
\( \mathbf{A} \cdot H_{2} O \) is relatively small compared to the other molecules
B. \( H_{2} O \) is not a molecular solid
C. \( H_{2} O \) have hydrogen bonding
D. \( H_{2} O \) is ionicly bonded while the others are covalently bonded


Which of the following is/are examples of linear motion?
A. Motion of a molecule of a gas
B. Motion of a stone falling from a certain height
c. Motion of a swing
D. Motion of a clock hand


A current of 8 A flows through a 25 V car headlight bulb. Calculate the electric
power (in Watts).


A copper rod of length \( l \) is suspended from the ceiling by one of its ends. Find the elongation \( \Delta l \) of the rod
due to its own weight.
A \( \quad \Delta l=\frac{1}{2} \frac{\rho g l^{2}}{E} \)
B. \( \Delta l=\frac{1}{3} \frac{\rho g l^{2}}{E} \)
c. \( \Delta l=\frac{1}{4} \frac{\rho g l^{2}}{E} \)
D. \( \Delta l=\frac{1}{5} \frac{\rho g l^{2}}{E} \)


A uniform rod is resting freely over a
smooth horizontal plane. A particle
moving horizontally strikes at one end
of the rod normally and gets stuck. Then
This question has multiple correct options
A. the momentum of the particle is shared between the particle and the rod and remains conserved
B. the angular momentum about the mid-point of the rod before and after the collision is equal
C. the angular momentum about the centre of mass of the combination before and after the collision is equal
D. the centre of mass of the rod particle system starts to move translationally with the original momentum of the particle


How much amount of \( C u S O_{4} \cdot 5 H_{2} O \) is
required for liberation of \( 2.54 g \) of \( I_{2} \) when titrated with \( K \) I?
A . \( 2.5 g \)
в. \( 4.99 g \)
\( c .2 .4 g \)
D. \( 1.2 g \)


Find the intersection of the line \( x- \)
\( \mathbf{2} \boldsymbol{y}+\mathbf{4} \boldsymbol{z}+\mathbf{4}=\mathbf{0}, \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}-\mathbf{8}=\mathbf{0} \)
with the plane \( \boldsymbol{x}-\boldsymbol{y}+\mathbf{2} \boldsymbol{z}+\mathbf{1}=\mathbf{0} \)


If the \( p^{t h}, q^{t h}, r^{r h} \) terms of a G.P. be \( a, b, c \)
respectively, then
\( \mathbf{A} \cdot a^{q-r} b^{r-p} c^{p-q}=1 \)
B . \( a^{q-r} b^{r-p} c^{p-q}=-1 \)
\( \mathbf{c} \cdot a^{q-r} b^{r-p} c^{p-q}=0 \)
D. none of these


Give an example of a cartilaginous fish.


\( \left|z_{1}+z_{2}\right|=\left|z_{1}\right|+\left|z_{2}\right| \) is possible if
A \( \cdot z_{2}=\overline{z_{1}} \)
в. \( _{z_{2}}=\frac{1}{z_{1}} \)
\( \mathbf{c} \cdot \arg z_{1}=\arg z_{2} \)
D \( \cdot\left|z_{1}\right|=\left|z_{2}\right| \)


Which statement is incorrect about
\( \boldsymbol{O} \)
peptide bond \( -\stackrel{\|}{C}-\stackrel{\bullet}{N} H-? \)
A. \( C-N \) bond length in proteins is longer than usual bond length of \( N \) -bond
B. Spectroscopic analysis shows planar structure \( o- \) \( C_{0}-N H-\operatorname{grou} \)
0
c. \( C-N \) bond length in proteins is smaller than usual bond length of \( C-N \) bond
D. None of the above


Prove the following identitie:
\[
\left|\begin{array}{ccc}
\boldsymbol{a}+\boldsymbol{b}+\mathbf{2} \boldsymbol{c} & \boldsymbol{a} & \boldsymbol{b} \\
\boldsymbol{c} & \boldsymbol{b}+\boldsymbol{c}+\mathbf{2} \boldsymbol{a} & \boldsymbol{b} \\
\boldsymbol{c} & \boldsymbol{a} & \boldsymbol{c}+\boldsymbol{a}+\boldsymbol{2} \boldsymbol{b}
\end{array}\right|=
\]
\( 2(a+b+c)^{3} \)


The phase difference between alternating emf and current in a purely capacitive circuit will be
A . zero
в. \( \pi \)
\( c \cdot-\frac{\pi}{2} \)
D.


How would you account for the following:
(i) Many of the transition elements are known to form interstitial compounds.
(ii) The metallic radii of the third (5d)
series of transition metals are virtually the same as those of the corresponding group members of the seconds \( (4 d) \) series.
(iii) Lanthanoids form primarily +3 ions, while the actinoids usually have higher oxidation states in their compounds, +4 or even +6 being typical


Let \( z \) and \( w \) be two nonzero complex
numbers such that \( |z|=|w| \) and
\( \arg (z)+\arg (w)=\pi \)
Then prove that \( z=-\bar{w} \)


An example for saprophytic angiosperm
is
A. Drosera
B. Vanda
C. Monotropa
D. cuscuta


Cell wall of diatom consists of
A. Silica only
B. Pectic substances
c. Both A and B
D. None of the above


Imagine an atom made of a proton and a hypothetical particle of double the mass of the electron but having the same charge as the electron. Apply Bohr atom model and consider all possible transitions of this hypothetical particle to the first excited level. The longest
wavelength photon that will be emitted has wavelength [Rydberg Constant = R] equal to
A. \( \frac{9}{5 R} \)
в. \( \frac{36}{5 R} \)
c. \( \frac{18}{5 R} \)
D. \( \frac{4}{R} \)


The domain of the function \( \mathbf{f}(\boldsymbol{x})=\sqrt{\frac{\boldsymbol{x}-\mathbf{2}}{\boldsymbol{x}+\mathbf{2}}}+\sqrt{\frac{\mathbf{1}-\boldsymbol{x}}{\mathbf{1}+\boldsymbol{x}}} \) is
A. \( R \)
B. [-2,2]
c. [-1,1]
D.


\( \ln \) a shop \( X, 30 \) tin pure ghee and 40 tin adultered ghee are kept for sale while in
shop \( Y, 50 \) tin pure ghee and 60 tin adultered ghee are there. One tin of ghee is purchased from one of the shops randomly and it is found to be adultered. Find the probability that it is
purchased from shop B.


The process Glycolysis occurs in
A . Cytoplasm
B. Mitochondria
c. chloroplast
D. Golgi Complex


If \( z=\frac{-1}{2}+i \frac{\sqrt{3}}{2}, \) then \( 8+10 z+7 z^{2} \) is
equal to:
A \( \cdot-\frac{1}{2}-i \frac{\sqrt{3}}{2} \)
B \( \cdot \frac{1}{2}+i \frac{\sqrt{3}}{2} \)
\( ^{\mathrm{C}}-\frac{1}{2}+i \frac{3 \sqrt{3}}{2} \)
D. \( \frac{\sqrt{3}}{2} \)
E \( -\frac{\sqrt{3}}{2} i \)


Specific reaction rate is rate of reaction at unit concentration of reactants.
A. True
B. False


Find \( \frac{n_{1}}{2} \) and \( \frac{n_{2}}{\longrightarrow} \) in terms of \( k \) \( \boldsymbol{R}_{2} \)
\( \boldsymbol{R}_{3} \)


For an angle \( x^{2} \), find:
The supplementary angle.


Which one of the following reactions
does not form gaseous product?
A. \( P b O_{2}+H_{2} O_{2} \rightarrow \)
в. \( N a_{2} C O_{3}+H_{2} O_{2} \rightarrow \)
\( \mathbf{c} \cdot P b S+H_{2} O_{2} \rightarrow \)
D. \( C l_{2}+H_{2} O_{2} \rightarrow \)


Triphasic life cycle is present in
A. Red alga
B. Brown algae
c. Diatom
D. Dinoflagellate


\( \Delta G_{f}^{o} \) (standard free energy of formation) of \( Z n O \) and \( C O \) are \( -318.2 \mathrm{kJ} \)
\( \mathrm{mol}^{-1} \) and \( -137.3 \mathrm{kJ} \mathrm{mol}^{-1} \) respectively.
\( Z n O+C \longrightarrow Z n+C O \)
The approximate value of \( \Delta G_{f}^{o} \) in kJmol
-1 for the above reaction is
\( \mathrm{kJ} \mathrm{mol}^{-1} \)
[Write your answer in form of inearest integer]


Noble gas compounds are formed only
with \( O_{2} \) and \( F_{2} \)
If true enter 1 , else enter 0 .


At the poles, the air is colder than that at latitudes about?
A. 30 degrees
B. 60 degrees
c. 90 degrees
D. 80 degrees


The points \( \boldsymbol{A}(\boldsymbol{a}, \boldsymbol{b}+\boldsymbol{c}), \boldsymbol{B}(\boldsymbol{b}, \boldsymbol{c}+\boldsymbol{a}) \) and
\( \boldsymbol{C}(\boldsymbol{c}, \boldsymbol{a}+\boldsymbol{b}) \) are:
A. collinear
B. doesn'tt lie in the same plane
c. doesn't lie on the same line
D. nothing can be said


The normal to the curve \( y(x-2)(x- \)
\( \mathbf{3})=\boldsymbol{x}+\boldsymbol{6} \) at the point where the curve
intersects the y-axis passes through the point.
\( ^{A} \cdot\left(-\frac{1}{2},-\frac{1}{2}\right) \)
в. \( \left(\frac{1}{2}, \frac{1}{2}\right) \)
\( ^{\mathrm{c}} \cdot\left(\frac{1}{2},-\frac{1}{3}\right) \)
D \( \cdot\left(\frac{1}{2}, \frac{1}{3}\right) \)


Using Binomial Theorem, evaluate \( (101)^{4} \)


The projection of the line segment joining (0,0,0) and (5,2,4) on the line whose direction ratios are 2,-3,6 is
A . 28
B. 4
c. \( \frac{40}{7} \)
D. \( \sqrt{45} \)


Every point is located in one of the four quadrants.


The image of an object is formed 3 times by a convex lens. On interchanging the positions of object and screen, what will be the
magnification in that case?


The element placed with nickel in the table formed by Newlands was:
A . iron
B. cobalt
c. chromium
D. copper


A first order reaction follows the
expression:
A \( \cdot C_{t} e^{k_{1} t}=C_{0} \)
B. \( C_{t}=C_{t} e^{k_{1} t} \)
\( \mathbf{c} \cdot \ln \frac{C_{o}}{C_{t}}=-k_{1} t \)
\( \mathbf{D} \cdot \ln \frac{C_{t}}{C_{o}}=k_{1} t \)


Find equation of latus rectum of the
parabola \( (x+1)^{2}=32 y \)
A \( . y=32 \)
B . \( x-8=0 \)
\( \mathbf{c} \cdot y-8=0 \)
D. \( x=32 \)


Calculate. \( \arctan 1+\arccos \left(-\frac{1}{2}\right)+ \)
\( \arcsin \left(-\frac{1}{2}\right)=? \)


Carbonisation is
A. Slow conversion of dead vegetation Into coal
B. Deposition of soil
C. Falling of trees
D. None of these


Flux associated with coil of unit area
placed int he magnetic field of
induction \( B \) is doubled in \( 0.2 s . \) The emf
induced in the coil is:
A . \( 5 V \)
B. \( 10 B V \)
\( \mathrm{c} .5 B V \)
D. \( 10 V \)


f \( \vec{a} \) and bare unit vectors and \( \theta \) is the
angle between them, show that \( \sin \frac{\boldsymbol{\theta}}{\mathbf{2}}=\frac{\mathbf{1}}{\mathbf{2}}|\overrightarrow{\boldsymbol{a}}-\overrightarrow{\boldsymbol{b}}| ? \)


Amines are almost colourless but
develop colour on keeping in the air for a long time, because:
A. they are readily oxidised in air to form coloured oxidation product.
B. they react with oxygen present in air in very less amount
c. they regain color in presence of air
D. none of these


Divide: \( 2 x^{4}+x^{3}+8 x^{2}+14 x+5 \) by
\( (2 x+1) \) (use division algorithm method).


The reaction quotient ( \( Q \) ) predicts
A. the direction of equilibrium to be attained
B. the ratio of activities at equilibrium, i.e., \( K_{c} \)
C. the ratio of activities at any time
D. all of the above


The density of a gas at \( 27^{\circ} C \) and 1 atm is 'd'. Pressure remaining constant, the temperature at which its density
becomes 0.75 d is :
A \( \cdot 20^{\circ} \mathrm{C} \)
B. \( 30^{\circ} \mathrm{C} \)
\( c \cdot 400 k \)
D. 300k


The material mixed before ore is
subjected for smelting in the extraction of iron are:
A. cake and silica
B. coke and limestone
c. limestone and silica
D. coke, limestone and silika


The incorrect IUPAC name is:
\( \mathbf{A} \cdot C H_{3}-C O-C H\left(C H_{3}\right)-C H_{3}: 2- \) methyl-3-butanone
\( \mathbf{B} \cdot C H_{3}-C H\left(C H_{3}\right)-C H\left(C H_{2} C H_{3}\right)-C H_{3}: 2,3 \)
dimethylpentane
\( \mathbf{c} \cdot C H_{3}-C \equiv C-C H\left(C H_{3}\right) \quad \) 2,4-Methyl-2-pentyne
D. \( C H_{3}-C H(C l)-C H(B r)-C H_{3}: 2- \) bromo-3
chlorobutane


A tank contains \( 40 l \) of solution
containing \( 2 g \) of substance per liter.
Salt water containing \( 3 g \) of this
substance per liter runs in at the rate of \( 4 l / m i n \) and the well-stirred mixture
runs out at the same rate. Find the
amount of substance in the tank after
15minutes (in grams).
A. 110.075
в. 121.075
c. 111.075
D. 211.075


Find the square root of 8100 by the
prime factorisation method.
\( A \cdot 80 \)
B. 90
\( c .30 \)
D. 70


Solve for \( x \) :
\( \mathbf{3} \boldsymbol{x}-\boldsymbol{4}>\boldsymbol{6}, \) where \( \boldsymbol{x} \in \boldsymbol{N} \)
A \( \cdot\{1,2,3, \ldots \ldots . . .\} \)
в. \( \{4,5,6, \dots . . . . . .\} \)
c. Data insufficient
D. None of these


The alpha particles get deflected by :
A. very small amounts
B. very large amount
c. same amount
D. \( 90^{\circ} \)


Find the radian measure corresponding
to the degree \( -47^{\circ} 30^{\prime} \)
A \( \cdot \frac{-19 \pi}{72} r a d \)
В \( \cdot \frac{19 \pi}{72} r a d \)
c. \( \frac{13 \pi}{72} \) rad
D. None of these


Identify the mistakes and correct them. An optical fibre is a device based on the principle of refraction.


\( \int(x+2) \sqrt{x^{2}+1} d x \)


Metallurgy involves steps:-
This question has multiple correct options
A. Concentration of ore
B. Oxidation of ore
C. Purification
D. Reduction of ore


Which of the following have highest
energy of electron?
\( \mathbf{A} \cdot_{1} H^{1} \)
В . \( _{1} H^{2} \)
\( \mathbf{c} \cdot_{1} H^{3} \)
D. All have equal energy


Fill in the blank with appropriate word
to complete the sentence. The Greek word which is the origin of
the word "planets" means


The \( \triangle S \) for the reaction
\( \mathbf{2} \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{O}_{2}(\boldsymbol{g}) \rightarrow \mathbf{2} \boldsymbol{H}_{2} \boldsymbol{O}(l) \) at \( \boldsymbol{3 0 0} \boldsymbol{K} \)
when
\( \boldsymbol{S}_{\boldsymbol{H}_{2}}^{\boldsymbol{o}}(\boldsymbol{g})=\mathbf{1 2 6 . 6}, \boldsymbol{S}_{\boldsymbol{O}_{2}}^{o}(\boldsymbol{g})=\mathbf{2 0 1 . 2 0} \)
\( S_{H_{2}} o(l)=68.0 J K^{-1} m o l-1 \)
respectively is:
A. \( -318.4 J K^{-1} \) mol \( ^{-1} \)
B. \( 318.4 J K^{-1} \) mol \( ^{-1} \)
c. \( 31.84 J K^{-1} \) mol \( ^{-} \)
D. 3.184 J K \( ^{-1} \) mol \( ^{-1} \)


\( 4,9,25, ?, 121,169 \)
A . 36
B . 49
\( c .64 \)
D. 81


Pictured above is a red point charge and
a blue point charge. The blue point charge is moved from loication 1 to location 2. The force
between the point charges is \( 5.00 \mathrm{N} \)
when blue charge is at location 1
How much force exist between the point charges when the blue charges is at
location 2?
A . 25.0
B. 30.0 N
c. \( 125 \mathrm{N} \)
D. \( 180 \mathrm{N} \)
E . \( 1.0 \mathrm{N} \)


The given quadratic equations have real roots and the roots are \( -\sqrt{2}, \frac{-5}{\sqrt{2}} \) \( \sqrt{2} x^{2}+7 x+5 \sqrt{2}=0 \)
A. True
B. False


The force experienced on an electric charge of \( 10 \mathrm{C} \) placed at a point in the electric field is 50 N. The strength of the electric field at the point is
A \( \cdot 25 \mathrm{N} \mathrm{C}^{-1} \)
B. 5 N \( c^{-1} \)
c. \( 10 \mathrm{N} \mathrm{c}^{-1} \)
D. 30 N C \( ^{-1} \)


A mixture of barium sulphate and \( \mathrm{H}_{2} \mathrm{O} \)
can be separated by the method of


\( \Delta L M N \Delta L M N \)
(2) Area of any one of the sectors.
(3) Total area of all the three sectors.
(4) Area of the shaded region.


Which of the following does not contain chlorine?
A. Rock salt
B. sylvine
c. cryolite
D. carnallite


Which of these equations represents a line parallel to the line \( 2 x+y=6 ? \)
A. \( y=2 x+3 \)
в. \( y-2 x=4 \)
c. \( 2 x-y=8 \)
D. \( y=-2 x+1 \)


A staircase has a large number of steps each of width \( 25 \mathrm{cm} \) and height \( 20 \mathrm{cm} \) A sharp sound is made at a distance in front of the staircase. The frequency of the musical note produced by the echelon effect is (take speed of sound in air as \( 350 \mathrm{m} / \mathrm{s} \) )
A. 700 Hz
в. 350 нz
c. 437.5 Нz
D. 875 нz


Large volumes of C.N.G is available in
small cylinders due to its property of
A. high density
B. low density
c. high compressibility
D. easy availability


In the given figure given below \( P Q \) is a
diameter chord \( S R \) is parallel to \( P Q \)
Given \( \angle P Q R=58^{\circ}, \) calculate \( \angle R P Q \)
\( A \cdot 30^{\circ} \)
B. 32
\( c \cdot 34 \)
\( D .36 \)


Pentane has the molecular formula
\( C_{5} H_{12} . \) It has:
A. 10 covalent bonds
B. 12 covalent bonds
c. 16 covalent bonds
D. 17 covalent bonds


The distance between the points \( (\cos \theta, \sin \theta) \) and \( (\sin \theta-\cos \theta) \) is
A. \( \sqrt{3} \)
B. \( \sqrt{2} \)
\( c \cdot 2 \)
D.


Write the cathodic and anodic cell
reactions of a Hydrogen-Oxygen fuel
cell.


The position and velocity of a particle executing simple harmonic motion at \( t=0 \) are given by \( 3 \mathrm{cm} \) and \( 8 \mathrm{cm} / \mathrm{s} \)
respectively. If the angular frequency of the particle is \( 2 r a d / s \), then the amplitude of oscillation, in centimeters
is?
A . 3
B. 4
c. 5
D. 6
\( E \)


A partial food web is shown here:
Which of the following changes is most
likely to occur if the sparrow population
decreases?
A. The fox population increases.
B. The hawk population increases
c. The grasshopper population competes less with the praying mantis
D. The hawk population and the fox population prey more heavily on rabbit


Which show \( \boldsymbol{H} \) -bonding? This question has multiple correct options
A . o-Nitrophenol
B. water
c. \( H C l \)
D. Ethyl acetoacetate


\( p H \) of a \( 0.1 M \) monobasic acid is found to be \( 2 . \) Hence its osmotic pressure at a
given temp. \( \boldsymbol{T} \boldsymbol{K} \) is:
A. \( 0.1 R T \)
\( T \)
в. \( 0.11 R T \)
c. \( 1.1 R T \)
D. \( 0.01 R T \)


The continuous cytoplasmic system running through the sieve tubes is called as
A. Symplast
B. Ectoplast
c. Protoplast
D. Endoplast


What is the trick to memorize periodic
table?


In a glass of water, we cannot
dissolve sugar more than a certain
limit. At this stage, the solution is said
to be:
A. saturated
B. unsaturated
c. supersaturated
D. complete solution


Monochromators are seen in:
A . centrifuges
B. potentiometers
c. spectrophotometers
D. densitometers


The oxidation states of iodine in
\( H I O_{4}, H_{2} I O_{5} \) and \( H_{5} I O_{6} \) are
respectively
A. +1,+3,+7
B. +7,+7,+3
\( c \cdot+7,+7,+7 \)
\( D \cdot+7,+5,+3 \)


\( \theta \)
\( \theta \)
町 再 \( \theta \)


The most stable conformational isomer
of cis-1-bromo-2-chlorocyclohexane will have:
A. both halide atoms in axial positions
B. both halide atoms in equatorial positions
c. bromine atom in an axial position and the chlorine atom in an equatorial position
D. bromine atom in an equatorial position and the chlorine atom in an axial position


The decomposition of an equal mole of two reactants \( P \) and \( Q \) obey 1 st order kinetics with half-life 54 and 18
minutes respectively. If both are allowed to run for 54 minutes. The ratio of mole of \( Q \) and \( P \) left after decomposition will
be:
A . 3
B. \( \frac{1}{4} \)
\( c \cdot 4 \)
D. 16


The maximum and the minimum
magnitude of the resultant two vectors
are 17 and 7 units respectively. Then the magnitude of the resultant vector when they act perpendicular to each other is:
A . 14
B. 16
c. 18
D. 13


\( \frac{\sqrt{2}}{8} \)


Calculate the partial pressure of \( B \) at equilibrium in the following equilibrium. \( \boldsymbol{A}(s) \rightleftharpoons \boldsymbol{B}(\boldsymbol{g})+\mathbf{2} \boldsymbol{C}(\boldsymbol{g}) ; \quad \boldsymbol{K}_{\boldsymbol{p}}=\mathbf{3} 2 \boldsymbol{a} \boldsymbol{t} \boldsymbol{m}^{3} \)


The metal with the lowest density is :
\( \mathbf{A} \cdot M g \)
B. \( L i \)
\( c . A g \)
D. \( A u \)


Solve: \( x^{2} \frac{d y}{d x}=\frac{y(x+y)}{2} \)


Write first four terms of the AP,when the
first term \( a \) and the common difference
\( d \) are given as follows:
\( \boldsymbol{a}=-\mathbf{1 . 2 5}, \boldsymbol{d}=-\mathbf{0 . 2 5} \)


\( \left\{\begin{array}{cl}\text { Evaluate } \lim _{x \rightarrow 2^{+}} f(x), \text { where } f(x)= \\ (x-[x], \quad x<2 \\ 4, & x=2 \\ 3 x-5, & x>2\end{array}\right. \)


Baking powder contains baking soda and:
A. potassium hydrogen tartarate
B. calcium bicarbonate
c. sodium carbonate
D. vinegar


Light a Bunsen burner and adjust the
air hole at the base to get different types of flames/presence of smoke. When do you get a yellow, sooty flame? When do you get a blue flame?


What external changes are visible after the last moult of a cockroach nymph?
A. Mandibles becomes harder
B. Anal cerci develop
c. Both fore wings and hind wings develop
D. Labium develops


Complete the following reactions:
(i) \( C_{6} H_{5} N H_{2}+C H C l_{3}+ \)
alc.KOH\( \longrightarrow \)
(ii) \( C_{6} H_{5} N_{2} C l+H_{3} P O_{2}+H_{2} O \rightarrow \)
(iii) \( C_{6} H_{5} N H_{2}+H_{2} S O_{4}(\text { conc. }) \rightarrow \)
(iv) \( C_{6} H_{5} N_{2} C l+C_{2} H_{5} O H \rightarrow \)
\( (v) C_{6} H_{5} N H_{2}+B r_{2}(a q) \rightarrow \)
\( (v i) C_{6} H_{5} N H_{2}+\left(C H_{3} C O\right)_{2} O \rightarrow \)
\( \left(\text { vii) } C_{6} H_{5} N_{2} C l \frac{(i) H B F_{4}}{(i i) N a N O_{2} / C u, \Delta}\right. \)


Which of the above represents the formula for the most common
compound of \( A \) and \( B, \) where \( A \) and \( B \) represent given pairs of elements or polyatomic ions as indicated below?
A) \( \boldsymbol{H} \)
B) \( \boldsymbol{S} \)
\( \mathbf{A} \cdot A B \)
в. \( A B_{2} \)
c. \( A_{2} B \)
D. \( A B_{3} \)
E . \( A_{2} B_{3} \)


The projection of a directed line segment on the co-ordinate axes are
\( 12,4,3, \) the DC's of the line are
A \( \cdot \frac{-12}{13}, \frac{-4}{13}, \frac{-3}{13} \)
B. \( \frac{12}{13}, \frac{4}{13}, \frac{3}{13} \)
c. \( \frac{12}{13}, \frac{-4}{13}, \frac{3}{13} \)
D. \( \frac{12}{13}, \frac{4}{13}, \frac{-3}{13} \)


Form two digit numbers using the digit
0,1,2,3,4,5 without repeating the digits.
\( P \) is the event that the number so
formed is even
\( Q \) is the event that the number so
formed is divisible by 3
\( R \) is the event that the number so
formed is greater than 50 . \( S \) is the sample space.
Which of the following options is
correct?
A \( . n(S)=25, n(P)=13, n(Q)=9, n(R)=5 \)
в. \( n(S)=25, n(P)=13, n(Q)=9, n(R)=2 \)
C. \( n(S)=25, n(P)=13, n(Q)=9, n(R)=4 \)
D. \( n(S)=25, n(P)=13, n(Q)=9, n(R)=8 \)


A particle performs SHM with period and amplitude A. The mean velocity of the particle averaged over quarter oscillation, starting from right extreme position is
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( \frac{2 A}{T} \)
c. \( \frac{4 A}{T} \)
D. \( \frac{3 A}{T} \)


When most fuels burn, the products include carbon dioxide and X. What is
X?
A. Hydrocarbons
B. Hydrogen
c. water
D. Hydroxide
E. Hydrogen peroxide


A parallel plate capacitor is charged and then disconnected from the
charging battery. If the plates are now moved farther apart by pulling at them by means of insulating handles, then:
A. the energy stored in the capacitor decreases
B. the capacitance of the capacitor increases
c. the charge on the capacitor decreases
D. the voltage across the capacitor increases


Evaluate the following limits. \( \lim _{x \rightarrow 3}\left(\frac{1}{x-3}-\frac{3}{x^{2}-3 x}\right) \)
A \( \cdot \frac{1}{3} \)
B. \( \frac{1}{2} \)
\( c \cdot-\frac{1}{3} \)
D. None of these


A biased coin (with probability of
obtaining a Head equal to \( p>0 \) ) is tossed repeatedly and independently until the first head is observed.

Compute the probability that the first head appears at an even numbered
toss.
A \( \cdot \frac{2-p}{3-p} \)
в. \( \frac{1-p}{3-p} \)
c. \( \frac{1-p}{2-p} \)
D. none of these


Define magnetic inclination or angle of
dip.


Which of the following is not a component of electric bell?
A. Gong
B. Ferromagnetic strip
C. Low magnetic field permanent magnet to attract ferromagnetic strip
D. None of the above


There are three set of animals \( C, D \) and
E. Which symmetry gets cephalization?
A. Type C- Bilateral symmetry
B. Type D- Radial symmetry
c. Type E- No symmetry
D. Both B and C


A person connects four \( \frac{1}{4} \Omega \) cells in
series but one cell has its terminal
reversed. The external resistance is \( 1 \Omega \)
If each cell has an emf of \( 1.5 \mathrm{V} \), the
current flowing is
A \( \cdot \frac{4}{3} A \)
B . \( \frac{3}{4} A \)
\( c \cdot 1.5 \mathrm{A} \)
D. zero


In semiconductor physics, what is meant by an amplifier?


Figure shows a square with total area of
121 square units. Calculate the value of
\( \boldsymbol{x} \)
\begin{tabular}{|c|c|}
\hline & \\
\( 7 x \) & 49 \\
\hline\( x^{2} \) & \( 7 x \) \\
\hline
\end{tabular}
\( A \)
B.
\( c \)
D. 1
\( E \)


Heat of a reaction \( (Q) \) at constant
pressure is equal to:
\( \mathbf{A} \cdot E_{P}-E_{R} \)
B . \( E_{R}-E_{P} \)
\( \mathbf{c} \cdot H_{P}-H_{R} \)
D. \( H_{R}-H_{P} \)


\( \boldsymbol{K}_{4}\left[\boldsymbol{F} e(\boldsymbol{C} \boldsymbol{N})_{6}\right] \) is called:
A. potassium hexacyano ferrate (II)
B. potassium hexacyano ferrate (III)
c. potassium ferricyanide
D. prussian blue


In the hydrogen peroxide molecule:
A. two hydrogen atoms are connected to one of the oxygen
B. all the four atoms are in the same plane
C. the four atoms are arranged in a non-linear and nonplanar manner
D. \( O-H \) bonds are polar but molecule is non-polar


Ejection of stomach contents through the mouth is called
A. diarrhoea
B. constipation
c. vomiting
D. indigestion


A bag contains 5 red balls and some
blue balls. If the probability of drawing a blue ball at random from the bag is
three times that of a red ball, find the
number of blue balls in the bag.


If the ratio in the amplitudes for two waves of equal frequencies is 1: 3 then the ratio of the energies carried out by
the waves will be
A \( .1 ; 3 \)
B. 1: 9
\( c \cdot 9: \)
D. None of these


Choose the incorrect reaction.
\( \mathbf{A} \cdot 2 C_{2} H_{5} I+2 N a \frac{\left(C_{2} H_{5}\right)_{2} O}{\longrightarrow} C_{4} H_{10}+2 N a I \)
B \( \cdot 2 C_{2} H_{5} B r+Z n \stackrel{E t O H}{\longrightarrow}\left(C_{2} H_{5}\right)_{2} Z n+B r_{2} \)
\( \mathbf{c} \cdot_{2 C_{2}} H_{5} I+N a_{2} S \longrightarrow\left(C_{2} H_{5}\right)_{2} S+2 N a I \)
D \( \cdot 2 C_{2} H_{5} B r+N a I \frac{\left(C H_{3}\right)_{2} C=O}{\longrightarrow} C_{2} H_{5} I+N a B r \)
E. All are correct reations


A convex lens of focal length \( f \) is cut into two halves as shown. Light rays parallel to the principal axis are incident on one
half of the lens \( \left(\operatorname{say} L_{1}\right) . \) This will
form an image at :
\( A \cdot f \)
B. \( f / 2 \)
\( c \cdot 2 f \)
D. \( f / \)


Which of the following metals occurs in nature principally oxide ores.
A . \( C a \)
в. \( C o \)
\( c \cdot C r \)
D. \( C u \)


A man is moving away from a tower 41.6 \( \mathrm{m} \) high at a rate of \( 2 \mathrm{m} / \mathrm{s} \). If the eye level of the man is \( 1.6 \mathrm{m} \) above the ground,
then the rate at which the angle of elevation of the top of the tower changes, when he is at a distance of 30
\( \mathrm{m} \) from the foot of the tower, is
\( A \cdot-\frac{4}{125} \mathrm{rad} / \mathrm{s} \)
B. \( -\frac{2}{25} \) rad/s
c. \( -\frac{1}{625} \) rad/s
D. none of these


The electrochemical cell stops working
after some time because:
A. electrode potentials of both electrodes becomes zero
B. electrode potentials of both electrodes becomes equal
C. temperature of the cell increases
D. the reaction starts proceeding in opposite direction


Why is sulphuric acid not used during the reaction of alcohols with KI?


A fair coins is tossed 8 times. Find the
probability that:
(i) it shows no head
(ii) it shows head at least once.


How do we separate two sulphide ores
by froth floatation method?
A. By using excess of pine oil.
B. By adjusting proportion of oil to water or using depressant.
C. By using collectors and froth stabilities like xanthates.
D. By using some solvent in which one of the sulphides is soluble.


f \( \log _{e} 4=1.3868, \) then \( \log _{e} 4.01= \)
A . 1.3968
B . 1.3898
c. 1.3893
D. none of these


If \( a \hat{i}+b \hat{j}+c \hat{k} \) is the position vector of
the mid - point of the vector joining the points \( \boldsymbol{P}(\mathbf{2} \hat{\boldsymbol{i}}-\boldsymbol{3} \hat{\boldsymbol{j}}+\boldsymbol{4} \hat{\boldsymbol{k}}) \) and \( \boldsymbol{Q}(\boldsymbol{4} \hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}- \)
\( 2 \hat{k}) \) then \( a+b+c \) is equal to


Assertion(A): Atmosphere plays an important role in maintaining the heat balance on earth.

Reason(R): Atmosphere absorbs a portion of electromagnetic
radiation coming from the sun
and transmits near UV, visible
and near IR radiation.
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not correct explanation of Assertion
c. Assertion is true and Reason is false
D. Assertion is false and Reason is true


\( \ln \) G.P. \( (p+q) \) th term is \( m,(p-q) \) th term is
n, then pth term is
A . \( n m \)
B. \( \sqrt{n m} \)
\( \mathrm{c} \cdot m / n \)
D. \( \sqrt{m / n} \)


The molar heat capacity of water at
constant pressure \( P, \) is \( 75 \mathrm{JK}^{-1} \mathrm{mol}^{-1} \) When \( 1.0 \mathrm{kJ} \) of heat is supplied to \( 100 \mathrm{g} \) of water which is free to expand, the increase in temperature of water is:
A . \( 1.2 k \)
B. 2.4 K
c. \( 4.8 \mathrm{k} \)
D. 6.6 K


Identify disproportionation reaction
A. \( C H_{3}+2 O_{2} \rightarrow C O_{2}+2 H_{2} O \)
в. \( C H_{4}+4 C l_{2} \rightarrow C C l_{4}+4 H C l \)
c. \( 2 F_{2}+2 O H^{-} \rightarrow 2 F^{-}+O F_{2}+H_{2} O \)
D. \( 2 N O_{2}+2 O H^{-} \rightarrow N O_{2}^{-}+N O_{3}^{-}+H_{2} O \)


Out of the following statements, which
one is true?
A. DNA is single stranded, RNA is double stranded
B. There is only one type of RNA, whereas there are many types of DNA.
c. DNA synthesizes RNA, but RNA generally cannot synthesize DNA.
D. DNA bases are adenine, guanine, cytosine, uracil and RNA has adenine, guanine, cytosine, thymine


If \( \boldsymbol{x} \sqrt{\mathbf{1}+\boldsymbol{y}}+\boldsymbol{y} \sqrt{\mathbf{1}+\boldsymbol{x}}=\mathbf{0} \) and \( \boldsymbol{x} \neq \boldsymbol{y} \)
then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}= \)
A. \( \frac{1}{1+x} \)
B. \( \frac{1}{(1+x)^{2}} \)
c. \( \frac{-1}{(1+x)^{2}} \)
D. \( \frac{-1}{1+x} \)


Q Type your question
behaviour of one mole of an ideal gas at
one atmosphere?
\( A \)
B.
\( c \)
\( D \)


The equation of a wave is given by \( Y= \) \( 4 \sin \omega\left(\frac{x}{v}-k\right) \) where \( \omega \) is the angular
velocity and \( v \) is the linear velocity. The
dimensions of \( k \) is \( ? \)
\( A \cdot[L T] \)
в. \( [T] \)
\( \mathbf{c} \cdot\left[T^{-1}\right] \)
D・[T']


The "butterfly" like structure surrounding the central region of human's spinal cord is called as
A. Funiculus
B. Horn
c. White matter
D. Grey matter


Fluorine molecules is formed by:
\( \mathbf{A} \cdot \) the axial \( p-p \) orbital overlap
B. the sideways \( p \) -porbital overlap
C . the \( s-s \) orbital overlap
D. the \( s-p \) orbital overlap


In the Boolean algebra : \( \boldsymbol{A}+\boldsymbol{B}= \)
A. \( \bar{A}+\bar{B} \bar{\hline} \bar{B} \)
в. А.
c. \( \overline{\bar{A}}+\overline{\bar{B}} \)


Find the general solution of each of the following equations. \( \sin \left(x+\frac{\pi}{5}\right)=0 \)


\( 1.00 g \) of \( E u C l_{2} \) is treated with excess
of aqueius \( A g N O_{3} \) and all the chlorine
is recovred as \( 1.29 \mathrm{g} \) of \( A G c L . \) Calculate the atomic weight of \( \boldsymbol{E u}(\boldsymbol{C l}= \) \( \mathbf{3 5 . 5}, \boldsymbol{A} \boldsymbol{g}=\mathbf{1 0 8}) \)


Solve for \( -\boldsymbol{x} \)
\( \frac{\mathbf{5}}{\boldsymbol{x}}=\frac{\mathbf{7}}{\boldsymbol{x}-\mathbf{4}} \)


Name three constituents of an atom
and state mass and charge of each.


Which one is not produced by basophils of pituitary?
A. Prolactin
в. TSH
c. FSH
D. LH


To maintain a rotor at a uniform angular
speed of 200 rad \( s^{-1}, \) an engine needs to transmit a torque of \( 180 \mathrm{N} \) m. What is the power required by the engine
? (Note: uniform angular velocity in the absence of friction implies zero torque. In practice, applied torque is needed to counter frictional torque). Assume that the engine is \( 100 \% \) efficient.


f \( \boldsymbol{I}=\int \frac{\boldsymbol{d} \boldsymbol{x}}{\boldsymbol{x}^{3} \sqrt{\boldsymbol{x}^{2}-1}}, \) then I equals
A \( \cdot \frac{1}{2}\left(\frac{\sqrt{x^{2}-1}}{x^{3}}+\tan ^{-1} \sqrt{x^{2}-1}\right)+C \)
B. \( \frac{1}{2}\left(\frac{\sqrt{x^{2}-1}}{x^{2}}+x \tan ^{-1} \sqrt{x^{2}-1}\right)+C \)
\( ^{c} \cdot \frac{1}{2}\left(\frac{\sqrt{x^{2}-1}}{x}+\tan ^{-1} \sqrt{x^{2}-1}\right)+C \)
D \( -\frac{1}{2}\left(\frac{\sqrt{x^{2}-1}}{x^{2}}+\tan ^{-1} \sqrt{x^{2}-1}\right)+C \)


In intrinsic semiconductor at room
temperature number of electrons and holes are:
A. Equal
B. zero
c. Unequal
D. Infinite


If a piece of iron gains \( 10 \% \) of its weight
due to partial rushing into \( F e_{2} O_{3} \) the
percentage of total iron that has rusted is:
A . 23
B. 13
c. 23.3
D. 90


Assertion
A step up transformer can also be used as a step down transformer
Reason
This is because \( \frac{\boldsymbol{E}_{\boldsymbol{p}}}{\boldsymbol{E}_{\boldsymbol{s}}}=\frac{\boldsymbol{n}_{\boldsymbol{s}}}{\boldsymbol{n}_{\boldsymbol{p}}} \)
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 oxidation number of underlined
element in \( \underline{M} \boldsymbol{n}_{3} \boldsymbol{O}_{4} \) compound is :
\( A \cdot \frac{8}{3} \)
B. \( \frac{7}{3} \)
\( c \cdot \frac{8}{5} \)
D. none of these


Simplify: \( i^{2}+i^{3}+i^{4}+i^{5} \)


Which of the following is true for a
plane?
This question has multiple correct options
A. A locus is called a plane if the line joining any two arbitrary points on the locus is also a part of the locus.
B. Value of \( y \) in a \( z x \) plane is non-zero.
C. Value of \( z \) in a \( x y \) plane is zero.
D. None of the above


In electric dipole what is the locus of Zero potential?


Which of the following show the correct arrangement of different layers of the soil?
A. Topsoil, Subsoil, Bedrock
B. Subsoil, Bedrock, Topsoil
c. Bedrock, Topsoil, Subsoil
D. subsoil, Topsoil, Bedrock


The blood groups of 30 students of Class VIII are recorded as follows:
\( \boldsymbol{A}, \boldsymbol{B}, \boldsymbol{O}, \boldsymbol{O}, \boldsymbol{A} \boldsymbol{B}, \boldsymbol{O}, \boldsymbol{A}, \boldsymbol{O}, \boldsymbol{B}, \boldsymbol{A}, \boldsymbol{O}, \boldsymbol{B}, \boldsymbol{A}, \boldsymbol{O} \)
\( \boldsymbol{A}, \boldsymbol{A B}, \boldsymbol{O}, \boldsymbol{A}, \boldsymbol{A}, \boldsymbol{O}, \boldsymbol{O}, \boldsymbol{A B}, \boldsymbol{B}, \boldsymbol{A}, \boldsymbol{O}, \boldsymbol{B}, \boldsymbol{A} \)
Use this table to determine the
probability that a student of this class, selected at random, has blood group
\( A B \)


In which of the following, the oxidation number of oxygen has been arranged in increasing order?
A. \( B a O_{2}<K O_{2}<O_{3}<O F_{2} \)
в. \( O F_{2}<K O_{2}<B a O_{2}<O_{3} \)
c. \( B a O_{2}<O_{3}<O F_{2}<K O_{2} \)
D. \( K O_{2}<O F_{2}<O_{3}<B a O_{2} \)


Solve: \( \int_{0}^{\pi / 4} \frac{\sin x \cos x}{\cos ^{4} x+\sin ^{4} x} d x \)


\( N H_{3} \quad P H_{3} \)
The bond angle in \( N H_{3} \) is larger than, in \( P H_{3} \) because the \( P-H \) bonds are
longer and the lower electronegativity of P permits electron-density to be displaced towards hydrogen to a greater
extent than in the case of \( N H_{3} \). Both of these effects diminish the repulsion
due to bond-pairs.
If true enter 1 , else enter 0 .


Acetic acid has \( K_{a}=1.8 \times 10^{-5} \) while
formic acid has \( K_{a}=2.1 \times 10^{-4} . \) What
would be the magnitude of the emf of the cell? \( \boldsymbol{P t}\left(\boldsymbol{H}_{2}\right)\left|\begin{array}{c}\boldsymbol{0 . 1} \text {Maceticacid}+ \\ \boldsymbol{0 . 1 M s o d i u m a c e t a t e}\end{array}\right| \mid \begin{array}{c}\mathbf{0 . 1 N} \\ \mathbf{0 . 1 M s}\end{array} \)
A. 0.032 vol
B. 0.063 volt
c. 0.0456 volt
D. 0.055 volt


Function \( \boldsymbol{f}(\boldsymbol{x})=(\boldsymbol{x}+\mathbf{2}) \boldsymbol{e}^{-\boldsymbol{x}} \) is
A. decreasing
B. decreasing in \( (-\infty,-1) \) and increasing in \( (-1, \infty) \)
c. increasing
D. decreasing in \( (-1, \infty) \) and increasing in \( (-\infty,-1) \)


When water flows through a pipe, which
layer moves fastest?


PUC certificate is omitted to the
vehicles which
A. Run under low consumption of fuel
B. Has low emission
C. Greater acceleration power
D. None of the above


A screen is placed \( 2 \mathrm{m} \) away from a single narrow slit. The slit width if the first minimum lies \( 5 \mathrm{mm} \) on either side
of the central maximum is:
(wave length \( =5000 A^{\circ} \) )
A . \( 0.01 \mathrm{cm} \)
B. \( 0.02 \mathrm{cm} \)
\( c .0 .03 c m \)
D. \( 0.04 \mathrm{cm} \)


A body explodes in mid-air. Does its momentum remain conserved?


Using Euclid's division algorithm, find
the HCF of 56,96 and 404


The fees structure for one-day
admission to a swimming pool is as follows
Daily Admission Fees in Rs.
\( \begin{array}{lll}\text { Member } & \text { Children } & \text { Adult } \\ \text { Before 2.00 p.m. } & 20 & 30 \\ \text { After 2.00 p.m. } & 30 & 40 \\ \text { Non-Member } & & \\ \text { Before 2.00 p.m. } & 25 & 35 \\ \text { After 2.00 p.m. } & 40 & 50\end{array} \) Write the matrix that represents the
additional cost for non-membership.


An object is placed at a distance of 30 \( \mathrm{cm} . \) from a concave mirror. The magnification produced is \( 1 / 2 . \) where should the object be placed to get the magnification of \( 1 / 3 \)


Fructose \( \frac{B r_{2} / H_{2} O}{?} ? \)


According to Kohlrausch law, the limiting value of molar conductivity of
an electrolyte \( A_{2} B \) is:
\( \mathbf{A} \cdot \Lambda_{A}^{\infty}+\Lambda_{B}^{\infty} \)
B \( \cdot \Lambda_{A}^{\infty}-\Lambda_{B}^{\infty} \)
\( \mathbf{C} \cdot \Lambda_{A}^{\infty}+\frac{1}{2} \Lambda_{B}^{\infty} \)
\( \mathbf{D} \cdot 2 \Lambda_{A}^{\infty}+\Lambda_{B}^{\infty} \)


Aqueous solutions of
\( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3}, \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C O O H} \) and \( \boldsymbol{C H}_{3} \boldsymbol{C O O K} \)
of identical concentrations are given
The pair(s) of the solution which may form a buffer upon mixing is(are):
This question has multiple correct options
A. \( N a O H \) and \( C H_{3} C O O H \)
в. \( H N O_{3} \) and \( C H_{3} C O O K \)
c. \( C H_{3} C O O H \) and \( C H_{3} C O O K \)
D. \( H N O_{3}+C H_{3} C O O H \)


Heights of students of class \( X \) are given in the following frequency distribution. Find the modal height.


Find \( (\boldsymbol{a}+\boldsymbol{b})^{4}-(\boldsymbol{a}-\boldsymbol{b})^{4} \). Hence,
evaluate \( (\sqrt{\mathbf{3}}+\sqrt{\mathbf{2}})^{4}-(\sqrt{\mathbf{3}}-\sqrt{\mathbf{2}})^{4} \)


\( C l_{2} O \) is a yellowish-red gas at room
temperature. The strongest
intermolecular forces present in \( C l_{2} O \)
are:
A. dipole-dipole forces
B. landon forces
c. hydrogen bonds
D. covalent bonds


Evaluate
\( \int \frac{(\log x)^{2}}{x} d x \)


State whether the given statement is
True or False :
A uniform linear motion is
unaccelerated, while a uniform circular
motion is an accelerated motion
A. True
B. False


A stone is dropped from the top of a tall cliff and \( n \) seconds later another stone
is thrown vertically downwards with velocity u. Then the second stone overtakes the first, below the top of the
cliff at a distance given by:
[Assume u sufficiently enough to overtake the first stone]
\( A \)
\( \left(\frac{g}{2}\right)\left[n \frac{\left(\frac{g n}{2}-u\right)}{g n-u}\right]^{2} \)
B.
\( \left(\frac{g}{2}\right)\left[n \frac{\left(g n-\frac{u}{2}\right)}{g n-u}\right]^{2} \)
c.
\( (g)\left[\frac{(g n-u)}{g n-(u / 2)}\right]^{2} \)
D.
\( \left(\frac{g}{5}\right)\left[\frac{(g n-u)}{g n-(u / 2)}\right]^{2} \)


Assertion
Complexity of classification increases from kingdom to species.
Reason
Common characters increase from
kingdom to species.
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 body of mass 5 kg rests on a rough horizontal surface of friction coefficient
0.2. The is pulled through a distance 10
\( \mathrm{m} \) by a horizontal force of \( 25 N . \) The kinetic energy acquired by it is
A . \( 200 J \)
в. \( 150 J \)
\( c \cdot 100 J \)
D. \( 50 J \)


The value of \( \cos \left[\frac{1}{2} \cos ^{-1} \cos \left(-\frac{14 \pi}{5}\right)\right] \) is
\( \mathbf{A} \cdot \cos \left(-\frac{7 \pi}{5}\right) \)
B \cdot \( \sin \left(-\frac{\pi}{10}\right) \)
\( \mathbf{c} \cdot \cos \left(\frac{2 \pi}{5}\right) \)
D. \( -\cos \left(\frac{3 \pi}{5}\right) \)


An organic compound \( \boldsymbol{A}\left(\boldsymbol{C}_{4} \boldsymbol{H}_{9} \boldsymbol{C l}\right) \) on
reaction with \( N a / \)diethyl ether gives a
hydrocarbon which on monochlorination gives only one chloro derivative. \( A \) is:
A. t-butyl chloride
B. sec-butyl chloride
c. isobutyl chloride
D. n-butyl chloride


The equation of .a wave, travelling with
amplitude \( A, \) linear \( u, \) angular velocity \( \omega \) is given by
\( \boldsymbol{y}=\boldsymbol{A} \sin \boldsymbol{\omega}\left(\frac{\boldsymbol{x}}{\boldsymbol{v}}-\boldsymbol{k}\right) \)
The dimensions of 'k' are
A . \( [T] \)
B \( \cdot\left[T^{-1}\right] \)
\( \mathbf{c} \cdot\left[T^{-2}\right] \)
D・ \( \left[T^{2}\right] \)


Enzymes, vitamins and hormones can
be classified into a single category of biological chemicals, because all of
these
A. Are exclusively synthesized in the body of a living organism as at presentttt
B. Enhance oxidative metabolism.
c. Are conjugated proteins
D. Help in regulating metabolism


Which one of following is not a longitudinal wave?
A. Ultrasonic wave
B. Infrasonic wave
c. Infrared wave
D. Seismic wave


Vessels differ from tracheids
A. In being living
B. In being derived from a single cell
C. In having vertical row of cells with cross walls dissolved
D. Because they conduct water


Two large vertical and parallel metal
plates having a separation of \( 1 \mathrm{cm} \) are
connected to a \( D C \) voltage source of
potential difference \( X . \) A proton is released at rest midway between the
two plates. It is found to move at \( 45^{\circ} \) to
the vertical JUST after release. Then \( \boldsymbol{X} \)
is nearly
A. \( 1 \times 10^{-5} V \)
В . \( 1 \times 10^{-7} V \)
c. \( 1 \times 10^{-9} V \)
D. \( 1 \times 10^{-10} V \)


Which of the following are the correct examples of matter?
A. Glass bottle, water and noise.
B. Air, wood and vacuum
c. Silver foil, hot air and chalk.
D. sand, oxygen and light flash


Subtract -6 from 3


Write the Faraday's law of
electromagnetic induction.


Sodium hexa-metaphosphate is known
as:
A . calgon
B. permutit
c. natalite
D. nitrolim


Which of the following mixtures
constitute a buffer?

This question has multiple correct options
A. \( H C O O H+H C O O N a \)
в. \( N a_{2} C O_{3}+N a H C O_{3} \)
c. \( N a C l+H C l \)
D. \( N H_{4} C l+\left(N H_{4}\right)_{2} S O_{4} \)


Evaluate \( \int \frac{\cos x-\sin x}{\cos x+\sin x} \cdot(2+ \)
\( 2 \sin 2 x) d x \)


What does the negative sign indicate in Lenz's law?


How many three digit numbers can be
formed that are divisible by 5 by using the digits 0,2,5,8,9 such that repetition is strictly not allowed
A . 21
B . 25
c. 30
D. none of these


At equilibrium, if \( \boldsymbol{K}_{\boldsymbol{p}}=\mathbf{1}, \) then:
\( \mathbf{A} \cdot \Delta G^{o}>1 \)
В. \( \Delta G^{o}<1 \)
c. \( \Delta G^{o}=0 \)
D. \( \Delta G^{o}=1 \)


The pd a cross terminals of a cell is
found to be 29 volt and 28 volt
respectively when it delivers a current of 1 ampere and 2 ampere respectively. The emf and internal resistance of a cell
are respectively
A. \( 30 \mathrm{V}, 2 \Omega \)
B. 30V,1\Omega
c. \( 29 v, 1 \Omega \)
D. \( 28 \mathrm{V}, 2 \Omega \)


The energy possessed by the fast moving air or storm is called:
A. hydro energy
B. kinetic energy
c. geothermal energy
D. wind energy


State whether true or false:
The magnetic polarity of an electromagnet does not change with the change in the direction of current in its coil.
A. True
B. False


Find the derivative of
\( \frac{2}{x+1}-\frac{x^{2}}{3 x-1} \)


Find the principal value of:
\( \cot ^{-1}\left(-\frac{1}{\sqrt{3}}\right) \)


What should a gardener do to induce flowering in Chrysanthemum?
A. Apply gibberellins
B. Cut off tip
c. Apply 2,4 D
D. Supply lot of water


What is the correct sequence from least
complex to most complex in terms of the amount of information they carry?
. Chromosomes
II. Base pair
III. Codon
IV. Gene
\( \mathbf{A} \cdot \mid \rightarrow\|\rightarrow\| \rightarrow \rightarrow \) ।
B. \( \|\rightarrow\| \dashv \rightarrow \perp \rightarrow \) ।
c. \( \|! \rightarrow\| \rightarrow 1 \rightarrow \) ।V
D. II \( \rightarrow \| \perp \rightarrow I V \rightarrow 1 \)
E . \( \|\rightarrow \mid V \rightarrow\| \rightarrow \) ।


Sometimes it is possible to separate
two sulphide ores by adjusting the
proportion of oil to water by using
depressants. When a depressant
NaCN is added to an ore containing
\( Z n S \) and \( P b S, \) what is the correct
observation?
A. \( N a C N \) prevents \( P b S \) from coming to the froth but allows \( Z n S \) to come with froth
B. \( N a C N \) prevents \( Z n S \) from coming to the froth but allows \( P b S \) to come with froth
C. \( N a C N \) prevents frothing of both \( Z n S \) and \( P b S \), hence no froth is formed
D. \( N a C N \) does not act as depressant hence a mixture of \( P b S \) and \( Z n S \) is found in the froth


Which of the following processes leads to formation of germ layers?
A. Embryogenesis
B. Gastrulation
c. Fertilization
D. None of the above


Is there anything that can block the effects or decrease the effect of gravity? Any experiments that tested it?

Magnetism can be blocked and why not gravity?


Evaluate the integral \( \int_{1}^{3}\left(3 x^{2}+1\right) d x \)


When methane is heated with dioxygen
in the presence of \( M o_{2} O_{3} \) catalyst, the
organic product obtained is:
A. methanal
B. ethanol acid
c. methanol
D. ethanol
E. 2-methyl propar-2-ol


A line a passes through (3,-4) and is parallel to y - axis find its equation.


The path of projectile is represented by
\( \boldsymbol{y}=\boldsymbol{P} \boldsymbol{x}-\boldsymbol{Q} \boldsymbol{x}^{2} \)
\begin{tabular}{|l|l|l|l|}
\hline \multicolumn{2}{|c|} { Column I } & \multicolumn{2}{|c|} { Column II } \\
\hline i. & Range & a. & \( P / Q \) \\
\hline ii. & Maximum height & b. & \( P \) \\
\hline iii. & Time of flight & c. & \( P^{2} / 4 Q \) \\
\hline iv. & Tangent of angle of projection is & d. & \( \sqrt{\frac{2}{Q g}} \) P \\
\hline
\end{tabular}


The ionisation energy of 10 times ionized sodium atom is
\( \mathbf{A} \cdot \frac{13.6}{11} e V \)
B. \( \frac{13.6}{112} e V \)
C \( .13 .6 \times(11)^{2} e V \)
D. \( 13.6 e V \)


Vector \( C \) is the sum of two vectors \( A \)
and \( B \) and vector \( D \) is the cross product
of vectors \( A \) and \( B . \) What is the angle
between vectors \( C \) and \( D ? \)
A. zero
B. \( 60^{\circ} \)
\( c \cdot 90^{\circ} \)
D. \( 180^{\circ} \)


In the demographic transition, the birth as well as the death rates decline.
A. third
B. second
c. fourth
D. first


The total energy emitted when electrons
of \( 1.0 \mathrm{g} \) atom of hydrogen undergo transition giving the spectral line of lowest energy in the visible region of its atomic spectrum is:
\( \left[\text { Given }: \boldsymbol{E}_{\mathbf{1}(\boldsymbol{H})}=\mathbf{2 . 1 7 6} \times \mathbf{1 0}^{-\mathbf{1 8}}\right] \)
A . \( 1.82 \times 10^{5} \mathrm{J} / \mathrm{mol} \)
В. \( 1.96 \times 10^{5} \mathrm{J} / \mathrm{mol} \)
c. \( 2.01 \times 10^{5} \mathrm{J} / \mathrm{mol} \)
D. \( 2.06 \times 10^{5} \mathrm{J} / \mathrm{mol} \)


Law of Triad was proposed by:
A. Newland
B. Gay Lussac
C . Mendeleev
D. Dobereiner


Ashish took 4 test tubes \( P, Q, R \) and \( S \)
each containing \( 10 \mathrm{ml} \) of different solutions as shown in the figure. Few drops of methyl orange are added to each tube. The solution in which tube
will turn methyl orange to red?
'his question has multiple correct options
A . \( P \)
в. \( Q \)
\( c . R \)
D. \( S \)


Which of the following is a normal salt:
A. \( \mathrm{NaH}_{2} \mathrm{PO}_{2} \)
в. \( \mathrm{NaH}_{2} \mathrm{PO}_{3} \)
\( \mathbf{c} \cdot \mathrm{NaH}_{2} \mathrm{PO}_{4} \)
D. \( \mathrm{Na}_{3} \mathrm{PO}_{4} \)


Malleus is formed by modification of articular bone of lower vertebrates,
while incus is modification of
A. Quadrate
B. Jugal
c. Hyomandibularis
D. Both A and B


A convex lens of focal length \( 6.25 \mathrm{cm} \) is used as a simple microscope. To obtain maximum magnification, the object
distance should be
A \( .4 .25 \mathrm{cm} \)
в. \( 4.50 \mathrm{cm} \)
c. \( 5.00 \mathrm{cm} \)
D. \( 5.25 \mathrm{cm} \)


In a constant volume calorimeter, 3.5 g of a gas with molecular weight 28 was
burnt in excess oxygen at 298.0 K. The temperature of the calorimeter was found to increase from \( 298.0 \mathrm{K} \) to
\( 298.45 \mathrm{K} \) due to the combustion
process. Given that the heat capacity of
the calorimeter is \( 2.5 \mathrm{kJ} \mathrm{K}^{-1} \), the
numerical value for the enthalpy of combustion of the gas in \( \mathrm{kJmol}^{-1} \) is:


In the reaction:
\( \mathbf{2} \boldsymbol{A} \boldsymbol{l}_{(\boldsymbol{6})}+\boldsymbol{6} \boldsymbol{H} \boldsymbol{C l}(\boldsymbol{a q}) \rightarrow \boldsymbol{2} \boldsymbol{A l}^{3+}(\boldsymbol{a q})+ \)
\( 6 C l^{-}(a q)+3 H_{2}(g) \)
A. 6 L \( H C l(a q) \) is consumed for every 3 L \( H 2(g) \) produced
B. 33.6 し \( H_{2}(g) \) is produced regardless of temperature and pressure for every mole \( A l \) that reacts
C. 67.2 L \( H_{2}(g) \) at STP is produced for every mole \( A l \) that reacts
D. \( 11.2 \mathrm{L} H_{2}(g) \) at STP is produced for every mole \( H C l(a q) \) consumed


Show that
\( \sin ^{-1} \frac{4}{5}+\sin ^{-1} \frac{5}{13}+\sin ^{-1} \frac{16}{65}=\frac{\pi}{2} \)


Differentiate \( \boldsymbol{y}=\log (\log \sqrt{\boldsymbol{x}}) \)


The potential energy of the system of two identically charged spheres as shown in the figure is equal to (Assume the charge distribution to be uniform)
\( ^{\mathbf{A}} \cdot \frac{q^{2}}{4 \pi \varepsilon_{0}}\left[\frac{1}{R}+\frac{1}{r}\right] \)
в. \( \frac{1}{4 \pi \varepsilon_{0}} \frac{q^{2}}{r} \)
c. \( \frac{1}{4 \pi \varepsilon_{0}} \frac{q^{2}}{(R+r)} \)
D. None of these


The oxidation number of \( C \) atom in
\( C H_{2} C l_{2} \) and \( C C l_{4} \) are respectively
\( A \cdot-2 \) and -4
B. 0 and -4
\( c .0 \) and 4
D. 2 and 4


Match the List 1 with List 2 and choose
the correct option.


Mark the odd one w.r.t girdle bones
A. Clavicle
B. Ischium
c. lleum
D. Pubis


The parallel sides of a trapezium are \( x \) and y in length. The length of the line segement joining the mid points of the non parallel sides is
A. \( \frac{x+y}{2} \)
в. \( x+y \)
c. \( \frac{2 x+3 y}{2} \)
D. \( \frac{x y}{2} \)


The potential at point \( B, C \) and \( D \) in the following circuit will be
A . \( 12 \vee, 10 \vee, 6 v \)
B. \( 11 \vee, 9 \vee, 6 v \)
c. \( 11 \vee, 9 \vee, \) o \( v \)
D. \( 12 \vee, 10 \vee, \) o \( v \)


The initial concentrations or pressure of reactants and products are given for each of the following systems. The reaction quotient and the directions in which system will shift to reach equilibrium of the following reaction is:
\( \mathbf{2} N \boldsymbol{H}_{3}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{N}_{2}(\boldsymbol{g})+\mathbf{3} \boldsymbol{H}_{2}(\boldsymbol{g}), \boldsymbol{K}=\mathbf{1 7} \)
\( \left[\boldsymbol{N} \boldsymbol{H}_{3}\right]=\mathbf{0 . 2 0} \boldsymbol{M} ;\left[\boldsymbol{N}_{2}\right]= \)
\( \mathbf{1} . \mathbf{0 0} \boldsymbol{M} ;\left[\boldsymbol{H}_{\mathbf{2}}\right]=\mathbf{1 . 0 0} \boldsymbol{M} \)
A. 25, shifts left
B. 25, shifts right
c. 35 , shifts left
D. 35, shifts right


Which of the following contains up to 10
electrons.
A . \( 1 s \)
B . \( 2 s \)
\( c \cdot 3 s \)
D. \( 3 p \)
E . \( 3 d \)


In a Rutherford scattering experiment
when a projectile of charge \( Z_{1} \) and
mass \( M_{1} \) approaches a target nucleus
of charge \( Z_{2} \) and mass \( M_{2} \) the distance
to closest approached is \( r_{0} . \) The energy
of the projectile is
A . directly proportional to \( M_{1} \times M_{2} \)
B. directly proportional to \( Z_{1} Z_{2} \)
C. directly proportional to to \( Z_{1} \)
D. directly proportional to mass \( M_{1} \)


Identify less reactive element from the following:
\( \mathbf{A} \cdot_{8} Y^{16} \)
B. \( _{10} Y^{20} \)
C. \( _{11} Y^{23} \)
D. \( _{9} Y^{19} \)


dentify a possible graph for function \( \boldsymbol{f} \)
given by
\( \boldsymbol{f}(\boldsymbol{x})=\sqrt{(\boldsymbol{x}-\mathbf{2})}+\mathbf{1} \)
\begin{tabular}{|l|l|l|l|}
\hline \( \mathrm{a} \) & & & \( \mathrm{b} \) & \\
\hline & & & & \\
\hline & & & & \\
\hline \( \mathrm{c} \) & & & \( \mathrm{d} \) & \\
& & & & \\
\hline & & & & \\
& & & \\
\hline
\end{tabular}
A. graph a
B. graph b
c. graph c
D. graph d


The sum of \( \frac{1}{x+y} \) and \( \frac{1}{x-y} \) is
A \( \cdot \frac{2 y}{x^{2}-y^{2}} \)
в. \( \frac{2 x}{x^{2}-y^{2}} \)
c. \( \frac{2 x}{y^{2}-x^{2}} \)
D. \( -\frac{2 y}{x^{2}-y^{2}} \)


\( \left|\begin{array}{ccc}\mathbf{1}+\boldsymbol{i} & \mathbf{1}-\boldsymbol{i} & \mathbf{1} \\ \mathbf{1}-\boldsymbol{i} & \boldsymbol{i} & \mathbf{1}+\boldsymbol{i} \\ \boldsymbol{i} & \mathbf{1}+\boldsymbol{i} & \mathbf{1}-\boldsymbol{i}\end{array}\right| \) is a
A. real number
B. irrational number
c. complex member
D. Purely imaginary


Which of the following is always true
A \( \cdot(p \Longrightarrow q) \equiv \sim q \Longrightarrow \sim p \)
в. \( (p \Longrightarrow q) \equiv p \wedge \sim q \)
\( \mathbf{c} . \sim(p \vee q) \equiv \vee p \vee \sim q \)
D. \( (p \vee q) \equiv \sim p \wedge \sim q \)


A convex lens of focal length \( 15 \mathrm{cm} \) is placed on a plane mirror. An object is placed at \( 30 \mathrm{cm} \) from the lens. The
image will be
A. real, at \( 30 \mathrm{cm} \) in front of the mirror
B. real, at 30 cm behind the mirror
c. real, at \( 10 \mathrm{cm} \) in front of the mirror
D. virtual, at 10 cm behind the mirror


C.V Raman's major contribution was on
A. Inelastic scattering of light by molecules
B. Quantum statistics
c. Theory of super conductivity
D. Expanding universe


ff \( \boldsymbol{A}=\left[\begin{array}{cc}\cos \boldsymbol{\alpha} & -\sin \boldsymbol{\alpha} \\ \sin \boldsymbol{\alpha} & \cos \boldsymbol{\alpha}\end{array}\right] \) and \( \boldsymbol{A}+\boldsymbol{A}^{\boldsymbol{T}}= \)
\( I, \) find the value of \( a \) in \( \frac{\pi}{a} \in[0, \pi] \)


In the presence of manganese acetate, ethyne produces:
A . acetic acid
B. propanoic acid
c. butanoic acid
D. methanoic acid


There are five boys \( A, B, C, D, E . \) The order
of their height is \( A<B<C<D<E \)

Number of ways in which they have to be arranged in 4 seats in increasing order of their height such that \( C \& E \) are never adjacent, is
A . 10
B. 6
\( c \cdot 4 \)
\( D \)


Inspite of the validity of Ohm's law, it has some limitations. Give one
limitation of Ohm's law.


Which of the following is not a redox reaction?
A \( \cdot C a C O_{3} \rightarrow C a O+C O_{2} \)
в. \( O_{2}+2 H_{2} \longrightarrow 2 H_{2} O \)
c. \( N a+H_{2} O \longrightarrow N a O H+\frac{1}{2} H_{2} \)
D. \( M n C l_{3} \longrightarrow M n C l_{2}+\frac{1}{2} C l_{2} \)


It experiences an increase in energy through a mechanical influence \( A \) 50 \( g \)
bullet moving with a velocity of \( 10 \mathrm{ms}^{-1} \)
strikes a block of mass 950 g at rest and gets embedded in it. The percentage loss in kinetic energy is
A . \( 100 \% \)
B. 95\%
c. 5\%
D. 50\%


KCl easily dissolves in water because:
A . it is a salt of potassium
B. it reacts with water
c. it is an electrovalent compound
D. its ions are easily solvated


The present day abundances of the isotopes \( \bigcup^{238} \) and \( U^{235} \) are in the ratio
of \( 128: 1 . \) They have half lives of \( 4.5 \times \)
\( 10^{9} \) years and \( 7 \times 10^{8} \) years
respectively and assume that the equal amount of each isotope existed at the
time of formation of the earth. If age of earth is \( \frac{49 X}{76} \times 10^{9} \) years, then calculate \( X \)


Figure shows a uniformly charged
hemispherical shell. The direction of
electric field at point \( p, \) that is off-
centre (but in the plane of the largest
circle of the hemisphere), will be along
B. pb
\( c \cdot p c \)
D. pd


Meena had a big farm. On Sunday she went to her farm and was surprised to see a house being constructed and a wooden almirah being made out of a
tree
a. Reforestation
b. Desertification
c. Deforestation
d. Drought Which of the following is correct?
A. a and
B. a and d
c. conly
D. a only


The addition of two numbers is \( -36 . \) If
one number is twice the another
number. What are the two numbers
A. (-18,-18)
(i) (-18,-18,-18),(8)
B. (-2,-34)
c. (12,24)
D. (-12,-24)


Two coins are tossed. Find the
probability, if \( \boldsymbol{P} \) is the event of getting
two head


Which of the elements indicated by \( A, B \)
\( \mathrm{C} \) and \( \mathrm{D} \) is expected to be found in
native state?
\( A \cdot A \)
B. B
\( c \cdot c \)
\( D . \) D


A die is thrown 100 times and outcomes
are noted as given below:
\[
\text { Outcome: } \quad 1 \quad 2
\]
3 4
Frequency:
\( \begin{array}{llll}21 & 9 & 14 & 23\end{array} \)
If a die is thrown at random, find the probability of getting a/an. 4


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


For a tetrahedral complex \( \left[M C l_{4}\right]^{2-}, \) the
spin-only magnetic moment is 3.83 BM.
The element \( M \) is:
A. \( C o \)
в. \( C u \)
c. \( M n \)
D. \( F e \)


Reduction of \( C H_{3} C H_{2} N C \) with
hydrogen in presence of \( \boldsymbol{N} \boldsymbol{i} \) or \( \boldsymbol{P} \boldsymbol{t} \) as catalyst gives:
A \( \cdot C H_{3} C H_{2} N H_{2} \)
B. \( C H_{3} C H_{2} N H C H_{3} \)
c. \( C H_{3} C H_{2} N H C H_{2} C H_{3} \)
D. \( \left(C H_{3}\right)_{3} N \)


What type of oxide would aluminium
form ?
A. \( E O_{3} \)
в. \( E_{3} O_{2} \)
\( \mathrm{c} \cdot E_{2} \mathrm{O}_{3} \)
D. EO


Cell elongation in internodal region takes place due to
A . Gibberellins
B. Ethylene
c. cytokinins
D. Indole acetic acid


Choose the correct option:
Electrical conductivity of a semi conductor-
A. decreases with rise in its temperature.
B. increases with rise in its temperature.
c. does not changes with temperature.
D. first decreases and then increases with rise in temperature.