Today, the concentration of greenhouse gases is very high because of
A. Use of refrigerator
B. Increased combustion of oils and coal
c. Deforestation
D. All of the above


If \( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{ll}\boldsymbol{a} \boldsymbol{x}^{2}-\boldsymbol{b}, & \boldsymbol{i} \boldsymbol{f} \quad|\boldsymbol{x}|<-1 \\ -\frac{1}{|\boldsymbol{x}|} \boldsymbol{i} \boldsymbol{f} & |\boldsymbol{x}| \geq-1\end{array}\right. \)
differential at \( x=1 . \) Find the values of
\( a \) and \( b \)
A \( . a=1 / 2 ; b=3 / 2 \)
В. \( a=1 / 2 ; b=-3 / 2 \)
c. \( a=-1 / 2 ; b=3 / 2 \)


Suppose that a function \( f \) satisfies the following conditions for all real values of
\( x \) and \( y \)
\( (i) f(x+y)=f(x) \cdot f(y) \)
\( (i i) f(x)=1+x g(x), \) where
\( \lim _{x \rightarrow 0} g(x)=1 . \) The value of \( \log f(8) \) is


A calorimeter has mass 100 g and
specific heat \( 0.1 \mathrm{kcal} / \mathrm{kg}^{\circ} \mathrm{C} \). It contains
250 gm of liquid at \( 30^{\circ} C \) having
specific heat of \( 0.4 \mathrm{kcal} / \mathrm{kg}^{\circ} \mathrm{C} \). If we
drop a piece of ice of mass \( 10 \mathrm{g} \) at \( 0^{\circ} \mathrm{C} \)
What will be the temperature of the mixture?


Which of the following product(s) is/are obtained during the reaction of ethanoic acid with chlorine?
A. Monochloroacetic acid
B. Dichloroacetic acid
c. Trichloroacetic acid
D. All of the above


"Polarising power of \( L i^{+} \) ion is nearly
the same as that of \( M g^{2+} \) ion."

Answer whether the above statement is
true or false.
If true enter 1 , else enter 0 .


If \( i^{2}=-1, \) then find the odd one out of
the following expressions.
\( \mathbf{A} \cdot-i^{2} \)
B \( \cdot(-i)^{2} \)
\( c \cdot i^{4} \)
D. \( (-i)^{4} \)
\( E \cdot-i^{6} \)


In order for the blood to flow from right ventricle to left ventricle in mammalian
heart, it must flow through
A. Right ventricle, pulmonary arteries, lungs, pulmonary veins and left atrium
B. Right ventricle, pulmonary arteries, lungs, pulmonary arteries and left atrium
c. Right ventricle, right atrium, , lungs, pulmonary veins and left atrium
D. Right ventricle, systemic aorta, Iungs, pulmonary veins and left atrium


Sum of two angles of a triangle is \( 90^{\circ} \)
Find the third angle. What type of triangle is this.


Let \( I_{A} \) and \( I_{B} \) be the moments of inertia
of two solid cylinders of identical geometrical shape and size about their axes, the first made of aluminum and
the second of iron then:
A \( \cdot I_{A}<I_{B} \)
в. \( I_{A}=I_{B} \)
с. \( I_{A}>I_{B} \)
D. The relation between \( I_{A} \) and \( I_{B} \) depends on the actual shape of the bodies


A closed organ pipe and an open pipe of
same length produce 4 beats when they are set into vibrations simultaneously. If the length of each of them were twice their initial lengths, the number of
beats produced will be
\( A \cdot 2 \)
B. 4
\( c \)
\( D \)


For each of the following pair, deduce the stereochemical relationship, i.e., whether they are enantiomers, diastereomers or identical.


two players \( A \) and \( B \) play a series of games of chess. The winning players in any games gets 1 points while the losing plays get 0 points. The player who achievers 4 point first, wins the series. If no game ends in draw, find the Number
of ways in which the series is can be won
by \( A \)


A solid sphere is rolling without slipping on a level surface at a constant
speed of \( 2.0 m s^{-1} . \) How far can it roll up
a \( 30^{\circ} \) ramp before it stops?
\( \mathbf{A} \cdot 56 \mathrm{cm} \)
B . \( 26 \mathrm{cm} \)
\( c .53 \mathrm{cm} \)
D. 84


State Kirchoff's rules. Use these rules to
find the values of current \( \boldsymbol{I}_{1}, \boldsymbol{I}_{2}, \boldsymbol{I}_{3} \) in
the circuit diagram given
\begin{tabular}{|l|l|}
\hline\( I_{1} \) & \( 1 / 2 V \) & \( \gamma_{1}=4 \Omega \) \\
& \\
\( \vdots \) & 11 \\
\hline\( I_{2} \) & \\
\( I_{3} \) & \( 4 V \) & \( \gamma_{3}=3 \Omega \) \\
\hline
\end{tabular}


Glycolysis (EMP Pathway) takes place in
A. Mitochondria
B. Cytoplasm
c. Both mitochondria and cytoplasm
D. vacuole


Mitosis and meiosis take place
respectively in
A. Meristem and gametangia
B. Gametangia and meristem
C. Permanent tissues and secretory tissues
D. Secretory tissues and permanent tissues


If the displacement of a particle executing SHM is given by \( \boldsymbol{y}= \)
\( 0.30 \sin (220 t+0.64) \) in metre, then the
frequency and maximum velocity of the particle are
A \( .35 H z, 66 m / s \)
B. \( 45 H z, 66 m / s \)
\( \mathbf{c} .58 H z, 113 m / s \)
D. \( 35 H z, 132 m / s \)


The resistances in left and right gap of a meter bridge are \( 20 \Omega \) and \( 30 \Omega \) respectively. When the resistance in the
left gap is reduced to half its value, the balance point shifts by
A. \( 15 \mathrm{cm} \) to the right
B. \( 15 \mathrm{cm} \) to the left
c. \( 20 \mathrm{cm} \) to the right
D. \( 20 \mathrm{cm} \) to the left


If \( f(x)=x^{3}+3 x^{2}+12 x-2 \sin x \)
such that \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) then
A. \( f(x) \) is one-one and onto
B. \( f(x) \) is many one onto
c. \( f(x) \) is one-one and into
D. \( f(x) \) is many one into


The heat of atomization of methane and
ethane are \( 360 \mathrm{kJ} / \mathrm{mol} \) and \( 620 \mathrm{KJ} / \mathrm{mol} \)
respectively. The longest wavelength of light capable of breaking the \( C-C \)
bond is:
(Avogadro number \( =6.02 \times 10^{23}, h= \)
\( 6.62 \times 10^{-34} \mathrm{Js} \)
A \( \cdot 2.48 \times 10^{4} \mathrm{nm} \)
B . \( 1.49 \times 10^{3} \) nm
c. \( 2.48 \times 10^{3} \mathrm{nm} \)
D. \( 1.49 \times 10^{4} \) nm


Find the equation of a plane which is
parallel to the plane \( x-2 y+2 z=5 \)
and whose distance from the point (1,2,3) is 1


Long answer type questions:
Define soil erosion, It's cause and a few
remedial steps that can be taken to control soil erosion.


\( \int \frac{(2 x+1)}{(x+2)(x-3)} d x \)


How many different isomers are possible for a hydrocarbon with the molecular formula \( C_{4} H_{10} \)
A
B. 2
\( c \cdot 3 \)
D. 5


An ac source of emf \( V=V_{0} \sin \omega t \) is
connected to a capacitor of capacitance
C. Deduce the expression for the current
(I) flowing in it. Plot the graph of (i) \( \mathrm{V} \) vs
\( \omega t, \) and
(ii) I vs. \( \Omega t \)


ff \( y \sqrt{1-x^{2}}+x \sqrt{1-y^{2}}=1 \) then \( \frac{d y}{d x}= \)
A \( \cdot-\sqrt{\frac{1-y^{2}}{1-x^{2}}} \)
B. \( \sqrt{\frac{1-y^{2}}{1-x^{2}}} \)
c. \( \sqrt{\frac{1-x^{2}}{1-y^{2}}} \)
D. None of these


State expression for acceleration due to gravity at depth 'd' and altitude 'h' Hence show that ratio is equal to \( \frac{\boldsymbol{R}-\boldsymbol{d}}{\boldsymbol{R}-\mathbf{2} \boldsymbol{h}}, \) assuming that \( \boldsymbol{h}<\mathbf{R}, \) where \( \mathbf{R} \)
is radius of the earth.


Choose the correct answer from the
alternatives given.
A capacitor made of two circular plates
each of radius \( 12 \mathrm{cm} \) and separated by 5 mm. The capacitor is being charged by
an external source. The charging
current is constant and equal to 0.15 A.
The capacitance of the parallel plate
capacitor is:
\( A \cdot 40 \mathrm{pF} \)
B. \( 45 \mathrm{pF} \)
c. \( 70 \mathrm{pF} \)
D. 80 pF


The radial part of the Schrodinger wave equation for hydrogen atom is given below:
\( \gamma(r)=\frac{1}{16 \sqrt{4} a_{0}^{3 / 2}}(\sigma-1)\left(\sigma^{2}-8 \sigma+\right. \)
\( \mathbf{1 2}) \boldsymbol{\theta}^{-\boldsymbol{\sigma} / \mathbf{2}} \)
Here, \( a_{0}= \) constant, \( \sigma=\frac{2 r}{n a_{0}} \) and \( n= \)
principal quantum number.
With respect to the above-given data,
select the correct statements.
This question has multiple correct options
A. Distance of the nearest radial node from the nucleus is
\( 2 a_{0} \)
B. Distance of the farthest radial node from the nucleus
is \( 12 a_{0} \)
c. Number of maxima in the curve \( \gamma(r) \) vs \( r \) is 4
D. The given equation of \( \gamma(r) \) represents \( 4 p \) orbital.


The wave number for the shortest
wavelength transition in the Balmer series of atomic hydrogen is :
A . \( 8225714 \mathrm{m}^{-1} \)
В. \( 1523693 m^{-1} \)
\( \mathbf{c} \cdot 5333 c m^{-1} \)
D. \( 27419 \mathrm{cm}^{-1} \)


Elevation of boiling point of 1 molar aqueous glucose solution (density \( =1.2 \) \( g / m !) \) is
A . \( K_{b} \)
в. \( 1.20 K_{b} \)
c. \( 1.02 K_{b} \)
D. \( 0.98 K_{b} \)


The materials suitable for making electromagnets should have:
A. High retentivity and high coercivity
B. Low retentivity and low coercivity
c. High retentivity and low coercivity
D. Low retentivity and high coercivity


\( \boldsymbol{O}_{3}+\boldsymbol{K}_{4}\left[\boldsymbol{F} \boldsymbol{e}\left(\boldsymbol{C} \boldsymbol{N}_{6}\right)\right] \)
What is the product formed?


Barrier potential of a p-njunction diode does not depend on -
A. diode design
B. temperature
c. forward bias
D. doping density


What is the function of thyrocalcitonin hormone?
A. Sugar control in blood
B. Calcium control in blood
c. cholesterol control in blood
D. Proteins control in blood


The number of solutions of equations \( \left|\begin{array}{ccc}\sin 3 \theta & -1 & 1 \\ \cos 2 \theta & 4 & 3 \\ 2 & 7 & 7\end{array}\right|=0 \) in \( [0,2 \pi] \) is
A .2
B. 3
\( c \cdot 4 \)
D. 5


Assertion
When \( H C l \) in a jar is poured into a jar
containing burning candle, the candle
is put out.
Reason
\( H C l \) is a fire extinguisher.
A. If both assertion and reason are CORRECT and reason is the CORRECT explanation of the assertion.
B. If both assertion and reason are CORRECT, but reason is NOT THE CORRECT explanation of the assertion.
c. If assertion is CORRECT, but reason INCORRECT
D. If assertion is INCORRECT, but reason is CORRECT


Water gas is produced by:
A. Passing steam over red hot coke
B. Passing steam and air over red hot coke
C. Burning coke in excess of air
D. Burning coke in limited supply of air
E. Both (passing steam over red hot coke) and (passing steam and air over red hot coke)


A car initially travelling eastwards turns north by travelling in a quarter circular path of radius R metres at uniform speed as shown in figure. The
car completes the turn in T second.
(a) What is the acceleration of the car
when it is at \( \mathrm{B} \) located at an angle of \( 37^{\circ} \)
Express your answers in terms of unit vectors \( \hat{i} \) and \( \hat{j} \)
(b) The magnitude of car's average acceleration during T second period.


Arrange the following reducing agents in the order of increasing strength under standard state condition. Justify
the answer.
Element Al(s)
\( \mathrm{Cu}(\mathrm{s}) \quad \mathrm{cl}(\mathrm{aq}) \)
\( E^{o} \quad v^{-1.66} \) \( 1.36 \mathrm{v} \) \( 0.34 \mathrm{V} \)


Two coils each of 100 turns are held
such that one lies in vertical plane and the other in the horizontal plane with
their centers coinciding. The radius of
the vertical coil is \( 0.20 m \) and that of the
horizontal coil is 0.30 m. How will you
neutralize the magnetic field of the earth at their common center? If the
summation of current to be passed
through each coil is \( i_{\text {total}}=x A . \) Find
\( x^{*} 10 \)
Horizontal component of earth's magnetic field \( =0.35 \times 10^{-4} T \) and
angle of \( \operatorname{dip}=30^{\circ} \)


Consider the following salts:
\( N a C l, H g C l_{2}, H g_{2} C l_{2}, C u C l_{2}, C u C l \)
and \( A g C l \). Identify the correct set of insoluble salts in water.
A. \( H g_{2} C l_{2}, C u C l, A g C l \)
в. \( H g C l_{2}, C u C l, A g C l \)
c. \( H g_{2} C l_{2}, C u C l_{2}, A g C l \)
D. \( H g_{2} C l_{2}, C u C l, N a C l \)


Which of the following is not a general characteristic of equilibrium involving physical processes?
A. Equilibrium is possible only in a closed system at a given temperature.
B. All measurable properties of the system remain constant
C. All the physical processes stop at equilibrium
D. The opposing processes occur at the same rate and there is dynamic but stable condition


Find the second derivative of the
function \( \log x \)


Wobble hypothesis for genetic code was
given by
A. Bernfield and Nirenberg
B. Crick
c. creighton
D. Hedges


By what percentage should the pressure of a given mass of gas be increased, so as to decrease its volume by \( 10 \% \) at a
constant temperature?
A . \( 11.1 \% \)
B. \( 10.1 \% \)
c. 9.1\%
D. 8.1\%


The electronegativity of \( C s \) is 0.7 and that of \( F \) is 4.0 The formed between the
two is ?
A. Covalent
B. Electrovalent
c. coordinate
D. Metallic


Gravitational force acts
A. only between the sun and the planets moving around it.
B. only between the earth and the bodies on it.
C. between all bodies in the universe.
D. only between the Sun and the earth.


Match the following columns.
Column Column I n II
1. \( \alpha \)
\( A \)
Molecular roxygen ketoglutaric acid
B. Electron acceptor
2. Hydrogen acceptor
C. Pyruvate
3. Cytochrome-C dehydrogenase
D. Decarboxylation
4. Acetyl Co-A
\( \mathbf{A} \cdot 2,3,4,1 \)
\( \mathbf{B} \cdot 3,4,2,1 \)
\( \mathrm{C} \cdot 2,1,3,4 \)
D. 4,3,1,2


The spring of the winding knob of a watch has
A. mechanical energy
B. only kinetic energy
c. only potential energy
D. kinetic or potential energy


The Xenon compound which has more number of lone pairs in its central atom is :
A. \( X e F_{6} \)
в. \( X e O F_{4} \)
c. \( X e F_{4} \)
D. \( X e O_{3} \)


f \( f(x)= \) \( \left|\begin{array}{ccc}\mathbf{1} & \mathbf{1} & \mathbf{1} \\ \mathbf{2} \boldsymbol{x} & \boldsymbol{x}-\mathbf{1} & \boldsymbol{x} \\ \mathbf{3} \boldsymbol{x}(\boldsymbol{x}-\mathbf{1}) & (\boldsymbol{x}-\mathbf{1})(\boldsymbol{x}-\mathbf{2}) & \boldsymbol{x}(\boldsymbol{x}-\mathbf{1})\end{array}\right| \)
then \( \boldsymbol{f}(\mathbf{5 0})= \)
4.0
B. 2
\( c_{1} \)
\( D \)
\( E \)


The angle between vectors \( (\bar{M} \times \bar{N}) \) and \( (\overline{\boldsymbol{N}} \times \overline{\boldsymbol{M}}) \) is then
\( \mathbf{A} \cdot 0^{\circ} \)
B . \( 60^{\circ} \)
\( c .90^{\circ} \)
D. \( 180^{\circ} \)


In the adjoining figure \( D E \| B C \), if
\( A C=18 c m, A D=6 c m, A B=12 c m \)
find \( \boldsymbol{E C} \) ?


Evaporation of water occurs at all temperature How is eveporation dependent on temperature?


How many terms of \( \boldsymbol{A P}: 27,24,21, \ldots . \)
should be taken so that their sum is
zero? What is the value of that last term


Which of the following is used as \( \mathrm{S} \) I prefix:
This question has multiple correct options
A . Mega
B. Hecto
c. Tera
D. Mara


Find the minor of \( \left[\begin{array}{ccc}2 & 7 & 3 \\ -4 & 3 & -1 \\ 0 & -3 & 7\end{array}\right] \)


What is metallic corrosion? Give one
example


In genetics, a reference is made to an abbreviated expression AUG. Write any three points of scientific information embodied in this
combination of three letters.


A galvanometer having a coil resistance of \( 60 \Omega \) shows full scale deflection when a current of 1.0 amp passes through it. It can be converted into an ammeter to
read currents upto 5.0 amp by :
A. Putting in parallel a resistance of \( 15 \Omega \)
B. Putting in parallel a resistance of \( 240 \Omega \)
c. Putting in series a resistance of \( 15 \Omega \)
D. Putting in series a resistance of \( 240 \Omega \)


If the perimeter of an isosceles triangle is 36 and the altitude to the base is 6
find the length of the altitude to one of the legs.
A . 4.8
B. 6
c. 9.6
D. 10
E. cannot be found on the basis of the given data


The equation of the plane passing through the intersection of the planes \( \mathbf{3} \boldsymbol{x}-\boldsymbol{y}+\mathbf{2} \boldsymbol{z}-\mathbf{4}=\mathbf{0} \) and \( \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}- \)
\( \mathbf{2}=\mathbf{0} \) and passing through the point
\( A(2,2,1) \) is given by?
A. \( 7 x+5 y-4 z-8=0 \)
в. \( 7 x-5 y+4 z-8=0 \)
c. \( 5 x-7 y+4 z-8=0 \)
D. \( 5 x+7 y-4 z+8=0 \)


Match the following.


When two bodies move uniformly towards each other, the distance
decreases by \( 6 m s^{-1} \). If both bodies
move in the same direction with the
same speed as above the distance
between them increases by \( 4 m s^{-1} \)
Then the speed of the two bodies are
\( \mathbf{A} \cdot 3 m s^{-1} \) and \( 3 m s^{-1} \)
B. \( 4 m s^{-1} \) and \( 2 m s^{-1} \)
\( \mathbf{c} \cdot 5 m s^{-1} \) and \( 1 m s^{-1} \)
D. \( 7 m s^{-1} \) and \( 3 m s^{-1} \)


Arrange the following in the decreasing order of hydrogen bonding.
\( \boldsymbol{C H}_{4}, \boldsymbol{C H}_{3}-\boldsymbol{O H}, \boldsymbol{C H}_{3}-\boldsymbol{F}, \boldsymbol{C H}_{3}- \)
\( N H_{2} \)
A \( \cdot C H_{3},-O H>C H_{3}-N H_{2}>C H_{3}-F>C H_{4} \)
в. \( C H_{3},-O H>C H_{3}-F>C H_{3}-N H_{2}>C H_{4} \)
c. \( C H_{3},-F>C H_{3}-O H>C H_{3}-N H_{2}>C H_{4} \)
D. \( C H_{4},>C H_{3}-F>C H_{3}-N H_{2}>C H_{3}-O H \)


A large hollow metal sphere of radius has a small opening at the top through which drops of mercury each of radius \( r \) and charged to a potential V fall into the
sphere and the potential becomes \( V^{\prime} \)
after \( \mathrm{N} \) drops fall into it. Then:
A. \( \mathrm{V}^{\prime}<\mathrm{V} \) for any value of \( \mathrm{N} \)
B. \( \mathrm{V}^{\prime}=\mathrm{V} \) for \( \mathrm{N}=1 \)
c. \( \mathrm{v}^{\prime}=\mathrm{v} \) for \( \mathrm{N}=\frac{\mathrm{R}}{\mathrm{r}} \)
D


\( C l F_{3} \) is a............ in the reaction
\( \boldsymbol{C I F}_{3}+\boldsymbol{A s F}_{3} \longrightarrow\left[\boldsymbol{C l F}_{2}\right]^{+}\left[\boldsymbol{A} \boldsymbol{s} \boldsymbol{F}_{4}\right]^{-} \)
and is a \( \ldots \ldots . . . . . . . . . . \) in the reaction
\( \boldsymbol{C l F}_{3}+\boldsymbol{N O F} \ldots \rightarrow[\boldsymbol{N O}]^{+}\left[\boldsymbol{C l} \boldsymbol{F}_{4}\right]^{-} \)
A . Lewis base, Lewis base
B. Lewis acid, Lewis acid
c. Lewis acid, Lewis base
D. Lewis base, Lewis acid


A stone is released from the top of
tower. it covers \( 24.5 \mathrm{m} \) distance in the
last second of its journey.what is the height of tower?


The value of \( \frac{\tan 45^{\circ}}{\sin 30^{\circ}+\cos 30^{\circ}} \) is:
This question has multiple correct options
A. \( \frac{2}{\sqrt{3}+1} \)
B.
\( \frac{1+\sqrt{3}}{2} \)
D. \( \sqrt{3}-1 \)


The number of electrons to be put on a
spherical conductor of radius \( 0.1 m \) to
produce an electric field of \( 0.036 N / C \)
just above its surface is
A \( \cdot 2.7 \times 10^{5} \)
В. \( 2.6 \times 10^{5} \)
c. \( 2.5 \times 10^{5} \)
D. \( 2.4 \times 10^{5} \)


The de-Broglie wavelength of a tennis
ball of mass \( 60 g \) moving with a velocity of \( 10 \mathrm{m} / \mathrm{s} \) is approximately (planck's
constant, \( \boldsymbol{h}=\mathbf{6 . 6 3} \times \mathbf{1 0}^{-\mathbf{3 4}} \boldsymbol{J}-\boldsymbol{s} \)
A \( \cdot 10^{-33} m \)
В. \( 10^{-31} \) m
c. \( 10^{-16} m \)
D. \( 10^{-25} \mathrm{m} \)


Write the negative (additive inverse) of each of the following:
\( \frac{-5}{1} \)


A compound microscope has an objective and eye piece of focal lengths \( 2.5 \mathrm{cm} \) and \( 6.0 \mathrm{cm} \) respectively. The
lenses are \( 20 \mathrm{cm} \) apart. A small object is kept at \( 3 \mathrm{cm} \) from the objective. Find the distance of final image from
eyepiece and the magnifing power of microscope.


Which body part is useful to make basic sound of the voice in humans?
A. Vocal folds in larynx
B. Lungs
c. wind pipe
D. Throat


There is no
generator.
A. ship rings
B. electromagnets
c. commulator
D. generator coil


An object \( 2 \mathrm{cm} \) high is placed at a distance of \( 16 \mathrm{cm} \) from a concave
mirror, which produces a real image 3 \( \mathrm{cm} \) high. What is the focal length of the mirror?
A . - \( 9.6 \mathrm{cm} \)
B. -3.6 ст
\( c .-6.3 \mathrm{cm} \)
D. - 8.3 cm


The ratio of the volumes of two spheres is \( 8: 27 . \) The ratio of their radii is
A .3: 2
B. 2: 3
c. 4: 3
D. 2: 9


\( \boldsymbol{A}=(\mathbf{1},-\mathbf{1}, \mathbf{2}) \) and \( \boldsymbol{B}=(\mathbf{2}, \mathbf{3}, \mathbf{7}) \) are two
points. If \( \boldsymbol{P}, \boldsymbol{O} \) divide \( \boldsymbol{A B} \) in the ratios
2: 3,-2: 3 respectively then \( P_{x}+ \)
\( \boldsymbol{Q}_{\boldsymbol{y}}= \)
A \( \cdot \frac{-38}{5} \)
в. \( \frac{38}{5} \)
c. \( \frac{-2}{5} \)
D. \( \frac{-47}{6} \)


What does the term point to correspondence in the paragraph refer
to?
A. Waves having constant amplitude
B. Waves having constant phase relation
c. Waves having same frequency
D. Wave having same amplitude,frequency and constant phase relation


What will be the wave velocity, if the
radar gives 54 waves per min and wavelength of the given wave is \( 10 m ? \)
\( \mathbf{A} \cdot 4 m s^{-1} \)
B. \( 6 m s^{-1} \)
\( \mathrm{c} \cdot 9 m s^{-1} \)
D. \( 5 m s^{-1} \)


Assertion
The electrical resistance of a column of
\( 0.05 \mathrm{M} \) NaOH solution of diameter \( 1 \mathrm{cm} \)
and length \( 50 \mathrm{cm} \) is \( 5.55 \times 10^{3} \) ohm.
Reason

Its resistivity is equal to 76.234 ohm
\( \mathrm{cm} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which material is used for
vulcanisation of rubber?
A. Iron
B. Sulphur
c. Chlorine
D. Calcium Carbonate


Assertion
The temperature coefficient of resistance is always positive.
Reason
On increasing the temperature the resistance of metals and alloys
increase.
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


A simple harmonic motion along the \( x- \)
axis has the following properties:
amplitude \( =0.5 m, \) the time to go from
one extreme position to other is, 2 s and
\( \boldsymbol{x}=\mathbf{0 . 3} \boldsymbol{m} \) at \( \boldsymbol{t}=\mathbf{0 . 5} \boldsymbol{s} . \) The general
equation of the simple harmonic
motion is
A \( \cdot x=(0.5 m) \sin \left[\frac{\pi t}{2}+8^{\circ}\right] \)
B. \( x=(0.5 m) \sin \left[\frac{\pi t}{2}-8^{\circ}\right] \)
\( \mathbf{c} \cdot_{x}=(0.5 m) \cos \left[\frac{\pi t}{2}+8^{\circ}\right] \)
D. \( x=(0.5 m) \cos \left[\frac{\pi t}{2}-8^{\circ}\right] \)


Treatment of conc. \( \boldsymbol{H} \boldsymbol{I} \) with ethyl ether
will give the product:
\( \mathbf{A} \cdot C_{2} H_{5} O H \)
в. \( C_{2} H_{5} I \)
c. Both the above
D. None of the above


If \( \sin x+\sin y=a \) and \( \cos x+ \)
\( \cos y=b \) show that
\( \sin (x+y)=2 a b /\left(a^{2}+b^{2}\right) \)


Balance the question
\( M g_{(a q)}+H N O_{3(a q)} \rightarrow \)
\( M g\left(N O_{3}\right)_{2(a q)}+N_{2} O_{(g)}+H_{2} O_{(l)} \)


If \( 3 \sin \alpha=5 \sin \beta, \) then \( \frac{\tan \frac{\alpha+\beta}{2}}{\tan \frac{\alpha-\beta}{2}}= \)
A.
B. 2
\( c \cdot 3 \)
D. 4


n the circuit shown, the value of
currents \( I_{1}, I_{2} \) and \( I_{3} \) are.
' \( \quad 3 A, \frac{-3}{2} A, \frac{9}{2} A \)
3. \( \frac{9}{2} A, 3 A, \frac{-3}{2} A \)
c. \( 5 A, 4 A,-3 A \)
\( 7 A, \frac{5}{4} A, \frac{9}{2} A \)


Evaluate the given integral.
\( \int e^{x}(\cot x+\log \sin x) d x \)


Three resistance coils have same
resistance. How many possible combinations can be obtained by connecting all the above coils in any
manner:-
A . 3
B. 7
\( c \cdot 6 \)
D. 5


The pyramid of numbers in grassland
ecosystem will be
A. Upright
B. Inverted
c. I rregular
D. Linear


Maximum depression in freezing point is caused by:
A. potassium chloride
B. sodium sulphate
c. magnesium sulphate
D. magneisum carbonate


Name the body structure concerned
with the given functional activity:
Helps to increase the volume of the
chest cavity lengthwise


Post mitotic gap phase and synthetic phase refers to?
A. \( G_{2} \) and \( M \)
B. \( G_{1} \) and \( s \)
\( c \cdot G_{2} \) and \( s \)
D. \( \operatorname{sand} G_{1} \)


During the oscillations of a simple pendulum, the string takes the same
path as that of the bob, then:
A. motion of the bob and string are in SHM
B. motion of the bob is SHM and that of the string is s angular SHM
c. motion of the bob and string are angular SHM
D. None of the above


Find \( x \)


If \( \cos \theta+\sin \theta=\sqrt{2}, \) find the value of
\( \cos \theta-\sin \theta \)


The masses in figure slide on a
frictionless table. \( m_{1} \) but not \( m_{2}, \) is
fastened to the spring. If now \( m_{1} \) and
\( m_{2} \) are pushed to the left, so that the
spring is compressed a distance \( \mathrm{d} \) what will be the amplitude of the
oscillation of \( m_{1} \) after the spring
system is released?
\( ^{\mathrm{A}} \cdot_{A}=(\sqrt{\frac{m_{1}}{m_{1}+m_{2}}}) \)
B. \( A=(\sqrt{\frac{m_{2}}{m_{1}+m_{2}}}) d \)
\( ^{\mathbf{c}} \cdot_{A}=(\sqrt{\frac{m_{1}}{m_{1}+m_{2}}}) d \)
D. None


\( 500 m L \) of a glucose solution contains \( 6.02 \times 10^{22} \) molecules. The
concentration of the solution is
\( \mathbf{A} \cdot 0.1 M \)
в. \( 1.0 M \)
\( \mathbf{c} \cdot 0.2 M \)
D. \( 2.0 M \)


The migration of colloidal particles
under the influence of an electric field
is known as:
A. electro-osmosis
B. cataphoresis
c. electrodialysis
D. ultrafiltration


A block of mass \( m=0.1 \mathrm{kg} \) is released
from a height of \( 4 \mathrm{m} \) on a curved smooth
surface. On the horizontal surface, path
AB is smooth and path BC offers
coefficient of friction \( \mu=0.1 . \) If the
impact of block with the vertical wall at \( \mathrm{C} \) be perfectly elastic, the total distance covered by the block on the horizontal
surface before coming to rest will be :
\( \left.\operatorname{take} g=10 m / s^{2}\right) \)
A \( .29 m \)
в. \( 49 m \)
\( \mathbf{c} .59 m \)
\( \mathbf{D} \cdot 109 m \)


The angle between force \( \overrightarrow{\boldsymbol{F}}=(\mathbf{3} \hat{\boldsymbol{i}}+ \)
\( 4 \hat{j}-5 \hat{k}) \) unit and displacement \( \overrightarrow{\boldsymbol{d}}= \) \( (5 \hat{i}+4 \hat{j}+3 \hat{k}) \) unit is
\( A \cdot \cos ^{-1}(0.16) \)
B. \( \cos ^{-1}(0.32) \)
\( \mathbf{c} \cdot \cos ^{-1}(0.24) \)
D \( \cdot \cos ^{-1}(0.64) \)


Resolve into partial fractions:
\( \frac{\mathbf{7}+\boldsymbol{x}}{(\mathbf{1}+\boldsymbol{x})\left(\mathbf{1}+\boldsymbol{x}^{\mathbf{2}}\right)} \)


Draw a ray diagram of reflecting type telescope and hence give the advantage of reflecting type telescope.


Calculate the sum of first 20 terms of
the G.P. \( -1,1,-1,1 \dots \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. 3


A current I flows in a circular arc of
radius R, which subtends an angle \( \frac{\pi}{6} \) radian at the center. The magnetic induction B at the center is
\( A \cdot \frac{I_{l d}}{4 R_{D}} \)
B. \( \frac{I_{\mu}}{2_{R}} \)
c. \( \frac{I \mu_{0}}{24 R_{0}} \)
D. \( \frac{I \mu_{0}}{12 R_{R}} \)


\( H_{2} S_{2} O_{8} \) and \( H_{2} S O_{5} \) both have +6
oxidation state of sulphur. It is due to
the:
A. presence of peroxy group
B. presence of superoxo group
c. presence of neutral group
D. presence of ozone


Standard molar enthalpy of combustion
of glucose is \( -2880 k J . \) If only \( 25 \% \) of energy is available for muscular work
and \( 1.0 k m \) walk consume \( 90 k J \) of
energy, what is the maximum distance
(in \( \mathrm{km} \) ) a person can walk after eating \( 90 g \) of glucose.


The argument of \( \frac{(1-i \sqrt{3})}{(1+i \sqrt{3})} \) is
A \( \cdot 60^{\circ} \)
B . \( 120^{\circ} \)
\( c \cdot 210^{\circ} \)
D. \( 240^{\circ} \)


The primary pollutant that leads to photochemical smog is :
A. sulphur dioxide
B. acrolein
c. ozone
D. nitrogen oxides


The area of the top of the table
\( \mathbf{A} \cdot 8478 \mathrm{cm}^{2} \)
B \( .65478 \mathrm{cm}^{2} \)
\( c \cdot 7678 c m^{2} \)
D. None


Which of the following gases has the greatest density at STP conditions?
A. \( N e \)
в. \( A r \)
c. \( H e \)
D. \( K r \)
ह. \( X e \)


Displacement of a person moving from \( x \) to \( Y \) along a semicircular path of
radius r is \( 200 \mathrm{m} \). What is the distance
travelled by him?


What is the oxidation number of gold in
the complex \( \left[A u C l_{4}\right]^{1-} ? \)
\( A \cdot+4 \)
B. +3
\( c \cdot+2 \)
D. +1


Find the value of the following:
\( \left(\frac{3}{8}\right)^{5} \times\left(\frac{3}{8}\right)^{4} \div\left(\frac{3}{8}\right)^{9} \)


A random variable \( X \) has the following probability distribution
\[
\begin{array}{llll}
\boldsymbol{X}= & -2 & -1 & 0
\end{array}
\]
\[
\begin{array}{c}
P(x) \\
\text { Then } \boldsymbol{E}(\boldsymbol{x})=
\end{array}
\]
\( \begin{array}{llll}0.1 & 0.2 & 0.2\end{array} \)
A . 0.8
в. 0.9
c. 0.7
D. 1.


Find the values of \( x, \) for which the
function \( f(x)=x^{3}+12 x^{2}+36 x+6 \) is
increasing.


A fixed cylindrical vessel is filled with water up to height \( H . A \) hole is bored in
the wall at a depth \( h \) from the free surface of water. For maximum
horizontal range \( h \) is equal to :
A. \( H \)
в. \( 3 H / 4 \)
c. \( H / 2 \)
D. \( H / 4 \)


What role does light play in photosynthesis?
A. Provides heat energy for leaves to convert into light energy
B. Excites electron from carotene which is taken up for photophosphorylation
c. catalyse synthesis of ATP
D. Both A and B


Sounds having frequency more than \( 20,000 \mathrm{Hz} \) are called -
A. sonic sound
B. ultrasonic sound
c. infrasonic sound
D. none of these


At resonance, the amplitude of forced oscillations is
A. minimum
B. maximum
c. zero
D. none of these


IUPAC name is 2-propoxycyclohexane.
Is the above statement correct?
A. True
B. False


Draw a scientifically correct labelled diagram of a human eye and answer the questions based on it:
Name the screen at which the
maximum amount of incident light is refracted ?


Let air be at rest at the front edge of a wing and air passing over the surface of wing at a fast speed v. If density of air is
\( \rho, \) the highest value for \( v \) in streamline flow when atmospheric pressure is
\( \boldsymbol{P}_{\text {atmosphere}} \) is:
\( ^{\mathrm{A}}\left[\frac{P_{\text {atnosphere}}}{\rho}\right]^{\frac{1}{2}} \)
\( \left[\frac{P_{a t m o s p h e r e}}{\rho}\right]^{2} \)
\( ^{\mathrm{c}}\left[\frac{P_{\text {atmosphere}}}{\rho}\right]^{\frac{1}{2}} \)
D. \( \frac{P_{\text {atmosphere }}}{\rho} \)


An object is placed \( 20 \mathrm{cm} \) to the left of a convex lens of focal length \( 10 \mathrm{cm} \). If a concave mirror of focal length \( 5 \mathrm{cm} \) is placed \( 30 \mathrm{cm} \) to the right of the lens, find the magnification.
A . 1.5
B. 1
c. 2
D. 2.5


\( \int \tan ^{4} x \sec ^{2} x d x \)


Find the volume and surface area of a
sphere of radius \( 6.3 \mathrm{cm} \)


Vectors \( \vec{A}, \vec{B} \) and \( \vec{C} \) are such that \( \vec{A} \) \( \vec{B}=0 . \) Then the vector parallel to \( \vec{A} \) is
A. \( \vec{B} \) and \( \vec{C} \)
в. \( \vec{A} \times \vec{B} \)
c. \( \vec{B}+\vec{C} \)
D. \( \vec{B} \times \vec{C} \)


Centripetally arranged sessile flowers on a flattened convex axis are found in
A. Hibiscus
B. Helianthus
c. Holoptelea
D. All of the above


Solve :
\( \frac{\boldsymbol{x}+\mathbf{2}}{\mathbf{9}}=\frac{\boldsymbol{x}+\mathbf{4}}{\mathbf{1 1}} \)


Given, a circle with designated center
designated perpendicular and radius 5
units. Find the length of the segment
labeled \( \boldsymbol{x} \)
\( A \cdot 4 \)
B. 5
\( c \cdot 8 \)
D. \( \sqrt{10} \)
E \( . \sqrt{3} \)


The focal length of a plane mirror is
A. positive
B. negative
c. zero
D. infinite


\( 1+\frac{1}{4 \times 3}+\frac{1}{4 \times 3^{2}}+\frac{1}{4 \times 3^{3}} \) is equal
to
A . 1.120
B. 1.250
c. 1.140
D. 1.160


The half life of \( ^{58} \) Co is 72 days. The time taken for \( \frac{3}{4} t h \) of the initial mass to disintegrate is:
A. 144 days
B . 235 days
c. 344 days
D. 433 days


are drawn on light rays to show the direction in which light travels.


Which of the following wires of the same material will have higher resistance :-
A. radius is 1 \( \mathrm{mm} \) and the length is 40 \( \mathrm{m} \)
B. radius is 2 \( \mathrm{mm} \) and the length is 40 \( \mathrm{m} \).
c. radius is \( 1 \mathrm{mm} \) and the length is \( 80 \mathrm{m} \)
D. radius is 2 \( \mathrm{mm} \) and the length is 80 \( \mathrm{m} \).


Rank the following points from greatest to least Electric field.
\( \mathbf{A} \cdot 1>2>3 \)
B. \( 3>1>2 \)
c. \( 3=2>1 \)
D. \( 1=2=3 \)


Find the vector and cartesian equations of the plane passing through the points \( A(1,1,-2), B(1,2,1) \) and \( C(2,-1,1) \)


What happens at the synapse between
two neurons?


\( \operatorname{Let} \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{ll}\boldsymbol{x}+\mathbf{1}: & \boldsymbol{x} \leq \mathbf{1} \\ \boldsymbol{3}-\boldsymbol{a} \boldsymbol{x}^{2}: & \boldsymbol{x}>1\end{array}\right. \)
Find the value of \( a \) if \( f \) is continuous at
\( \boldsymbol{x}=\mathbf{1} \)


A particle is dropped from the top of a
tower. It covers \( 40 \mathrm{m} \) in last \( 2 \mathrm{s} \). Find the
height of the tower.


The potential of a hydrogen electrode in
a solution with \( p O H=4 \) at \( 25^{\circ} C \) is:
A . -0.059
B. 0.059
c. -0.59
D. 0.59


toppr
Q Type your question
(A)
\( (\mathrm{C}) \)
This question has multiple correct options
A \( \cdot(B) \) and \( (D) \) are the same product as given
B. \( (B) \) is as shown in figure
C. \( (D) \) is as shown in figure
D. The above reaction is called ipso substitution


When white light is passed through prism and glass slab separately then
we get seven colours as emergent ray in former while same white light in latter.
As both are made up of same glass but why getting different results?


An aqueous solution of an unknown
compound (X) gives the following reactions
(i) It gives a brown precipitate with
alkaline \( K M n O_{4} \) solution
(ii) It forms \( H C l \) and evolves \( O_{2} \) when
reacted with \( C l_{2} \) gas.
(iii) It liberates \( I_{2} \) from an acidified \( \mathrm{K} \)
solution
(iv) It gives orange yellow color with acidified titanic sulfate solution.
Identify \( \boldsymbol{X} \)


Two uniform rods of equal lengths \( \left(l_{0}\right) \) and equal masses have coefficient of linear expansion \( \alpha \) and \( 2 \alpha \) are placed in contact on a smooth horizontal surface
as shown. The temperature of system is
\( \theta^{0} C . \) Now the temperature is increased by \( \Delta \theta^{0} C \) The junction of the rods will shift from its initial position by?
initial temperature \( =\theta^{\circ} \mathrm{C} \)
A \( \cdot \frac{\log _{2} \Delta \theta}{2} \)
B. \( \frac{\log _{3} \Delta \theta}{3} \)
\( c \cdot \frac{\log _{4} \Delta \theta}{_{4}} \)
D. \( \frac{\log _{6} \Delta \theta}{6} \)


What are the measures used to record
description of organisms?


A plant virus is found to consist of
uniform symmetrical particles of \( 150 A \)
in diameter and 5000 A long. The
specific volume of the virus is 0.75
\( c m^{3} / g . \) The virus is considered to be a
single particle. If its molecular weight is
\( x \times 10^{7}, \) find \( x \)


The value of determinant \( \left|\begin{array}{ccc}\mathbf{1 9} & \mathbf{6} & \mathbf{7} \\ \mathbf{2 1} & \mathbf{3} & \mathbf{1 5} \\ \mathbf{2 8} & \mathbf{1 1} & \mathbf{6}\end{array}\right| \)
is :
A. 150
B. -110
\( c \cdot 0 \)
D. None of these


Write correct sequence of four steps of
method for the preperation of temparary mount of stained leaf peel.


A compound \( (X) \) gives brick red flame and breaks down on heating giving
oxygen brown gas \( (A) \) and \( (B) \). Identify \( (X),(A) \) and \( (B) \) respectively
A \( \cdot C a\left(N O_{3}\right)_{2}, N O_{2}, C a O \)
в. \( C a\left(N O_{3}\right)_{2}, C a O, N O_{2} \)
c. \( M g\left(N O_{3}\right)_{2}, M g O, N O_{2} \)
D. \( M g\left(N O_{3}\right)_{2}, N O_{2}, M g O \)


Find the mean of first six natural
numbers.
A . 3.6
B. 7
\( c .3 .5 \)
D. None of these


A block is gently placed at the top of a inclined plane \( 6.4 \mathrm{m} \) long. Find the time taken by the block of slide down to the
bottom of plane. The plane makes an
angle 30 with the horizontal. coefficient
of friction between the block and the
plane is \( 0.2 .\left[\mathrm{g}=10 \mathrm{m} / \mathrm{sec}^{2}\right] \)


The solubility of \( C a C O_{3} \) is \( 7 \mathrm{mg} / \mathrm{L} \)
Calculate the \( K_{s p} \) of \( B a C O_{3} \) when
\( N a_{2} C O_{3} \) is added slowly a solution
containing equimolar concentration of
\( C a^{+2} \) and \( B a^{+2} \) and no precipitate is
formed until \( 90 \% \) of \( B a^{+2} \) has been
precipitated as \( B a C O_{3} \)
A \( \cdot 1.1 \times 10^{-10} \)
В. \( 55 \times 10^{-10} \)
c. \( 2.5 \times 10^{-10} \)
D. \( 4.9 \times 10^{-10} \)


What is called as Warburgs effect
on photosynthesis?
A . Low rate of process due to \( O_{2} \) supply
B. Low rate of process due to \( C O_{2} \) supply
c. Both A and B
D. None of the above


The instrument used for measuring
humidity of air is called
A. Calorimeter
B. Hygrometer
c. Pyrometer
D. Hydrometer


Two thin rods each of mass \( m \) and
length 1 are joined to form L shape as
shown. The moment of inertia of rods
about an axis passing through free end
(O) of a rod end and perpendicular to
both the ends is
A \( \cdot \frac{5 m l^{2}}{3} \)
B. \( \frac{m l^{2}}{6} \)
c. \( \frac{5}{7} M R^{2} \)
D. \( \frac{7}{12} M R^{2} \)


The ratio of radii of fourth to third orbits
for an atom will be :
\( A \cdot \frac{4}{3} \)
в. \( \frac{16}{9} \)
\( c \cdot \frac{8}{3} \)
D. \( \frac{16}{3} \)


Which statement is incorrect?
A. Colloidal state is a particular state and not a class of compounds
B. The dispersed phase may consists of a single macro molecule or an aggregate of atoms or ions
C. The sol particles can be seen under microscope
D. Colloidal state is an intermediate (but heterogeneous) state between true solution and suspension state


A function \( f \) is defined for all positive
integers and satisfies \( \boldsymbol{f}(\mathbf{1})=\mathbf{2 0 0 5} \) and
\( \boldsymbol{f}(1)+\boldsymbol{f}(2)+\ldots+\boldsymbol{f}(\boldsymbol{n})=\boldsymbol{n}^{2} \boldsymbol{f}(\boldsymbol{n}) \) for
all \( n>1 . \) Find the value of \( f(2004) \)


Find the degree measure of the angle
subtended at the centre of a circle of
radius \( 10 \mathrm{cm} \) by an arc of length \( 22 \mathrm{cm} \) \( \left(\boldsymbol{U} \boldsymbol{s e} \boldsymbol{\pi}=\frac{\boldsymbol{2} \boldsymbol{2}}{\mathbf{7}}\right) \)


The Muscular physique of a male is due to the influence of the Hormone is called
A. testosterone
B. estradiol
c. progesterone
D. estrone


In a sample, electronjumps from \( 5^{t h} \) excited state to ground state then number of spectral lines in visible
range will be:
A . 4
B. 3
c. 2
\( D \)


State whether the statement is True or
False.
\( (x+8)(x+3) \) is equal to \( x^{2}+11 x+ \)
\( \mathbf{2 4} \)
A. True
B. False


Find the locus of the point of intersection of the lines \( \sqrt{3} x-y- \) \( 4 \sqrt{3} \lambda=0 \) and \( \sqrt{3} \lambda x+\lambda y-4 \sqrt{3}=0 \)
for different values of \( \lambda \)
A \( \cdot 4 x^{2}-y^{2}=48 \)
B . \( x^{2}-4 y^{2}=48 \)
c. \( 3 x^{2}-y^{2}=48 \)
D. \( y^{2}-3 x^{2}=48 \)


Let \( S_{1}, S_{2}, \dots . S_{n} \) be squares such that
for each \( n \geq 1, \) the length of a side of \( S_{n} \) equals the length of the diagonal of
\( S_{n+1} . \) If the length of a side of \( S_{1} \) is \( 10 \mathrm{cm}, \) then the least value of \( n \) for
which the area of \( S_{n} \) less than 1 sq \( c m \)
A. 7
B. 8
c. 9
D. 10


Fractional distillation is used to
separate liquids which differ in their boiling points by?
A \( \cdot 0-10^{\circ} \mathrm{C} \)
B . \( 10-20^{\circ} \mathrm{C} \)
c. \( 20-40^{\circ} \mathrm{C} \)
D. \( 40-80^{\circ} \mathrm{C} \)


What information could not explained by Bohr, after observing Hydrogen
spectrum?


In the figure, the line segment \( X Y \) is
parallel to the side \( A C \) of \( \triangle A B C \) and it
divides the triangle into two parts of equal areas, then match the column.


The refractive index of water with
respect to air is \( 1.33 . \) Calculate the critical angle for water air interface
A \( \cdot 26^{\circ} \)
В \( \cdot 22^{\circ} 6^{1} \)
\( \mathbf{c} \cdot 48^{\circ} 45 \)
D. \( 76^{\circ} 5^{1} \)


If the arithmetic mean of \( 6,8,5,7, x \) and
4 is \( 7, \) then \( x \) is
A . 12
B. 6
\( c \cdot 8 \)
D.


Arrange the following elements in increasing order of their size.
Be, Ca, Ba, Ra
A. Be <Ca<Ba<Ra
B. \( \mathrm{Ca}<\mathrm{Be}<\mathrm{Ba}<\mathrm{Ra} \)
c. \( \mathrm{Be}<\mathrm{Ca}<\mathrm{Ra}<\mathrm{Ba} \)
D. None of these


Assertion
Failure of secretion of somatotropin from an early age causes dwarfism in the patient.
Reason
Somatotropin hormone stimulates the body growth and elongation of long
bones
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The forces at the support point
A. 780 N
B. 220 N
c. \( 1920 \mathrm{N} \)
D. 1140 N


The acceleration of a freely falling body
does not depend on the mass of the
body.
A. True
B. False


From a deck of 52 cards, four cards are
drawn simultaneously, find the chance that they will be the four honours of the
same suit.


The potential difference \( \left(V_{A}-V_{B}\right) \)
between the points \( A \) and \( B \) in the given figure is.
\( A \cdot+9 v \)
B. - 3 V
\( c \cdot+3 v \)
\( D \ldots+6 v \)


Ursa Major resembles:
A. a bear
B. a bowl
C. a hunter
D. a dog


\( \left(x^{3}+x^{2}-3 x+5\right)+(x-1) \)


A hammer exerts a force of \( 1.5 N \) on
each of the two nails \( A \) and \( B \). The area
of cross section of tip of nail \( \boldsymbol{A} \) is
\( 2 m m^{2} \) while that of nail \( B \) is \( 6 m m^{2} \)
Let the pressure on nail \( A \) be \( x \) and that on nail \( B \) be \( y, \) then find \( \frac{x}{y} \)
A \( \cdot \frac{1}{3} \)
в. 3
c. 9
D. \( \frac{1}{9} \)


Calculate M.D about Mean for the given
data
\begin{tabular}{lcccc}
Size of item & 4 & 6 & 8 & 10 \\
\hline
\end{tabular}
\[
\text { Frequency } \quad 2 \quad 1 \quad 3
\]
6
A . 6.12
в. 5.12
c. 2.44
D. 3.44


Show that the diagonals of a
parallelogram divide it into four triangles of equal area.


Which of the following is an artificial edible colour?
A. Saffron
B. Carotene
c. Tetrazine
D. Melamine


The speed at which the current travels,
in conductor, is nearly equal to:
\( \mathbf{A} \cdot 3 \times 10^{4} m / s \)
B \( .3 \times 10^{5} \mathrm{m} / \mathrm{s} \)
\( \mathbf{c} \cdot 3 \times 10^{6} m / s \)
D. \( 3 \times 10^{8} \mathrm{m} / \mathrm{s} \)


The plane side of a thin plano-convex
lens with radius of curvature \( 20 \mathrm{cm} \) is
silvered to obtain a concave mirror. An
object is located at a distance of \( 25 \mathrm{cm} \) in front of this mirror. The distance of
the image from the mirror is \( (\mu=1.5) \)
A . \( 100 \mathrm{cm} \)
в. \( \frac{100}{11} \mathrm{cm} \)
\( c \cdot 6.25 c m \)
D. \( \frac{100}{9} \mathrm{cm} \)


There are n points on a circle. The number of straight lines formed by joining them is equal to
\( A \cdot^{n} C_{2} \)
в. \( ^{n} P_{2} \)
\( \mathrm{c} \cdot^{n} C_{2}-1 \)
D. None of these


Two mirrors \( A \) and \( B \) are placed at right
angles to each other as shown in figure. A ray of light incident on mirror \( A \) at an
angle of \( 25^{\circ} \) falls on mirror \( \mathrm{B} \) after
reflection. The angle of reflection for the ray reflected from mirror B would be:
\( \mathbf{A} \cdot 25^{\circ} \)
B. \( 50^{\circ} \)
\( \mathbf{c} \cdot 65^{\circ} \)
D. \( 115^{\circ} \)


Aarati bought 10 dresses at Rs 6300 She paid Rs 200 extra as expenses. If she sold all the dresses at the cost of Rs
780 per dress, how much percentage profit or loss does she make?
A. 20\% profit
B. 20\% loss
c. \( 40 \% \) profit
D. 30\% profit


In the reaction \( S n C l_{2}+C l_{2} \rightarrow \)
\( \boldsymbol{S} \boldsymbol{n} \boldsymbol{C l}_{4}+\boldsymbol{2} e^{-}, \) the lewis acid is:
A. \( S n C l_{4} \)
в. \( \operatorname{SnCl}_{3} \)
\( \mathrm{c} \cdot \operatorname{Sn} C l_{2} \)
D. \( S n C l \)


Assertion
\( C_{P}-C_{V}=R \) for an ideal gas.
Reason
\( \left[\frac{\partial E}{\partial V}\right]_{T}=0 \) for an ideal gas.
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 car travelling with a velocity of
\( 80 k m / h \) slowed down to \( 44 k m / h \) in
15s. The retardation is
A \( \cdot 0.67 m / s^{2} \)
в. \( 1 m / s^{2} \)
\( \mathbf{c} \cdot 1.25 m / s^{2} \)
D. \( 1.5 \mathrm{m} / \mathrm{s}^{2} \)


\( \lim _{x \rightarrow 0}\left(\frac{1^{1 / x}+2^{1 / x}+3^{1 / x}+\ldots . . n^{1 / x}}{n}\right)^{n x} \)
is equal to
A . \( n \)
B.
c. \( \frac{1}{n !} \)
\( D \)


If \( y=\sqrt{\frac{\sec x-1}{\sec x+1}} \) then \( \frac{d y}{d x}= \)
A. \( \frac{1}{2} \sec ^{2} \frac{x}{2} \)
B. \( \sec ^{2} \frac{x}{2} \)
c. \( \frac{1}{2} \tan \frac{x}{2} \)
D. \( \tan \frac{x}{2} \)


The disc of radius \( r \) is confined to roll
without slipping at \( A \) and \( B \). If the plates have the velocities shown, then
This question has multiple correct options
A. angular velocity of the disc is \( 2 V / r \)
B. linear velocity, \( V_{0}=V \)
c. angular velocity of the disc is \( 3 V / 2 r \)
D. none of these


A ray of light is incident at an angle i on a glass slab of refractive index \( \mu . \) The angle between reflected and refracted
light is \( 90^{\circ} . \) Then the relationship
between i and \( \mu \) is.
A \( \cdot_{i}=\tan ^{-1}\left(\frac{1}{\mu}\right) \)
B. \( \tan i=\mu \)
\( \mathrm{c} \cdot \sin i=\mu \)
D. \( \operatorname{cosi}=\mu \)


The correct order of boiling point of
1,2,3 alcohol is:
\( \mathbf{A} \cdot 1>2>3 \)
В. \( 3>2>1 \)
c. \( 2>1>3 \)
D \( .2>3>1 \)


Assertion
Density is expressed as \( g m L^{-1} \) whereas specific gravity is dimensionless.
Reason
Specific gravity is ratio of the masses of solution and solvent.
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 cyclotron is operated at an oscillator frequency of \( \frac{80}{\pi} M H z \) and has a Dee of radius \( R=60 \mathrm{cm} . \) The magnitude of
magnetic field \( B \) (in Tesla) to accelerate deuteron is \( \frac{x}{10} \) Tesla. Find \( x ? \)
(charge on deuteron \( e=1.6 \times 10^{-19} \)
mass of deuteron \( =\mathbf{3 . 2 4} \times \mathbf{1 0}^{-\mathbf{2 7}} \mathbf{K} \boldsymbol{g} \)
A . 32.4
в. 16.2
\( c \cdot 64 \)
D.


an infinite number of tangents can be
drawn from (1,2) to the circle \( x^{2}+y^{2}- \)
\( 2 x-4 y+\lambda=0 \) then \( l a m b d a \) is
A . -20
B. 0
c. 5
D. can no be determined


Identify each part in a flowering plant and write whether it is haploid (n) or diploid (2n).
(a) Ovary
(b) Anther
(c) Egg
(d) Pollen
(e) Male gamete
(f) Zygote


The transmission of traits from parents to offspring is called
A. Characteristic
B. Heredity
c. Donation
D. Both A and B


\( R \) and \( r \) are the radii of the Earth and
the Moon respectively and \( \rho_{e} \) and \( \rho_{m} \) are
the densities of the Earth and Moon
respectively. The ratio of acceleration due to gravity on the surface of the
Earth to the Moon is:
A \( \cdot \frac{R}{r} \cdot \frac{\rho_{e}}{\rho_{m}} \)
в. \( \frac{r}{R} \cdot \frac{\rho_{e}}{\rho_{m}} \)
c. \( \frac{r}{R} \cdot \frac{\rho_{m}}{\rho_{e}} \)
D. \( \frac{R}{r} \cdot \frac{\rho_{m}}{\rho_{e}} \)


Group of animals which gives wool are:
A. Sheep, goat, camel and yak
B. Sheep camel, lion and rabbitt
c. Rabbit, silkworm, buffalow and cow
D. Goat, cat, sheep and camel


The type of elements present in group to \( 12[\mathrm{IB} \text { to } \mathrm{V} \| \mathrm{B} \text { and } \mathrm{V} \text { III }] \) are :
A . alkal
B. alkaline
c. transition
D. halogen


A particle moving with certain velocity collides elastically with another particle at rest. If it were head on collision, the
K.E. transferred by the colliding particle is \( 100 \% \) when its mass is equal to the
A. the mass of the stationary particle
B. twice the mass of the stationary particle
c. half the mass of the stationary particle
D. \( 1 / 4 \) times the mass of the stationary particle


Assertion
To move a body uniformly in a circular
path, an external agent has to apply a force.
Reason
To more a body uniformly in a circular path, an external agent has to do work.
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 and Reason is correct


A point mass of \( 10 k g \) is placed at the
centre of Earth. The weight of the point mass will be
A. zero
B. Infinite
c. Less than zero
D. \( 10 k g \)


Which of the following can give a buffer solution?
\( \mathbf{A} \cdot H C I+N a O H \)
в. \( C H_{3} \) СОО Na
c. \( H C O O H+H C O O N a \)
D. \( H_{2} S O_{4}+N a_{2} S O_{4} \)


The distances travelled by a body falling freely from rest in the first, second and third seconds are in the ratio:
A .1: 2: 3
B. 1: 3: 5
\( c \cdot 1: 4: 9 \)
D. None of the above


This is a complex, non-carbohydrate polymer found in cell walls Its function is to provide stiffening to the cell as in xylem vessels and bark fibres. Name it
A. Opsonin
B. Saponin
c. Lignin
D. Plant Polypeptide


\( \ln H N C, \) which element has least value of formal charge?
\( \mathbf{A} \cdot H \)
в. \( N \)
\( c . c \)
D. All have same value


Find 10 th term of the \( A . P .1,4,7,10, \dots \)


Which of the following compound will give Walden inversion?
A \( \cdot C_{4} H_{9}-C H(D)-B r \)
в. \( C_{6} H_{5}-C H_{2}-B r \)
c. \( C H_{2}=C H-C H_{2}-B r \)
D. All of the above


Assertion
Melting point of \( M n \) is more than that
of \( \boldsymbol{F e} \)
Reason
Mn has higher number of unpaired \( e^{-} \)
than \( F e \) in atomic state
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


For the reaction
\[
\begin{array}{r}
\boldsymbol{S n O}_{2}(\boldsymbol{s})+\mathbf{2} \boldsymbol{H}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{S} \boldsymbol{n}(\boldsymbol{l})+ \\
\boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g})
\end{array}
\]
the equilibrium mixture of steam and
hydrogen contained \( 45 \% \) and \( 24 \% H_{2} \) at
\( 900 K \) and \( 1100 K \) respectively. The sum
of \( K_{p} \) at both temperatures for better
reduction of \( S n O_{2} \) is (nearest integer
value).


The value of \( \int_{2}^{3} \frac{\sqrt{x}}{\sqrt{5-x}+\sqrt{x}} d x \) is
A . 1
B.
\( c \cdot 2 \)
D. None of these


Maximum kinetic energy of the emitted photoelectrons depends upon
A. Intensity of incident light
B. Frequency of incident light
c. Total number of photons of incident light
D. Both (2) and (3)


Light of two different frequencies whose photons have energies leV and \( 2.5 \mathrm{eV} \) successively illuminate a metal of work
function 0.5 eV.The ratio of the
maximum speeds of the emitted
electrons will he
A .1: 5
B. 1: 4
\( c \cdot 1: 2 \)
D. 1:


ff \( P(E)=0.05, \) what is the probability
of not \( ^{\prime} \boldsymbol{E}^{\prime} \) ?


An \( \alpha \) -particle and proton are
accelerated from rest through same potential difference and both enter into a uniform perpendicular magnetic field. Find the ratio of their radii of curvature.
A. \( \sqrt{7}: 1 \)
B. \( \sqrt{5}: 1 \)
c. \( \sqrt{2}: 1 \)
D. \( \sqrt{3}: 1 \)


From a rectangular metal sheet of sides
\( 25 \mathrm{cm} \) and \( 20 \mathrm{cm} \) a circular sheet as
large as possible is cut off What is the area of the remaining metal sheet?
\( A \cdot 186 c m^{2} \)
В. \( 144 \mathrm{cm}^{2} \)
\( c \cdot 185 c m^{2} \)
\( \mathbf{D} \cdot 72 c m^{2} \)


The standard error of two means is
equal to
\( ^{\mathrm{A}} \cdot \sqrt{\frac{\sigma_{1}^{2}}{n_{1}}+\frac{\sigma_{2}^{2}}{n^{2}}} \)
в. \( \frac{\sigma}{\sqrt{n-1}} \)
c. \( \frac{\sigma}{\sqrt{n+1}} \)
D. \( \sqrt{\frac{P_{1} Q_{1}}{\sqrt{n_{1}}}+\frac{P_{2} Q_{2}}{n_{2}}} \)


If \( 2 \sinh ^{-1}\left(\frac{a}{\sqrt{1-a^{2}}}\right)=\log \left(\frac{1+X}{1-X}\right) \)
then \( X= \)
\( A \)
B.
c. \( \sqrt{1-a^{2}} \)
D. \( \frac{1}{\sqrt{1-a^{2}}} \)


A man 2 metres high walks at a uniform speed of \( 6 \mathrm{km} / \mathrm{h} \) away from a lamp-post 6 metres high. Find the rate at which the length of his shadow increases. (in
\( \boldsymbol{k} \boldsymbol{m} / \boldsymbol{h} \boldsymbol{r}) \)


lonic mobility of \( \mathrm{Li}^{+} \) is greater than that
of \( \mathrm{Na}^{+} \)
A. True
B. False


A small object \( Q \) of length 1 mm lies
along the principal axis of a spherical glass of radius \( \mathrm{R}=10 \mathrm{cm} \) and refractive
index is \( 3 / 2 . \) The object is seen from air
along the pricipal axis from left. The distance of object from the center \( P \) is 5
cm. Find the size of the image. Is it real,
inverted?
\( A \)
B.
c. \( \frac{8}{3} m m ; \) virtual
D. Noneofthese


\( \lim _{\boldsymbol{\pi} \atop \boldsymbol{x} \rightarrow \frac{\pi}{\boldsymbol{4}}} \frac{\sec \boldsymbol{x} \cdot \tan (\boldsymbol{4} \boldsymbol{x}-\boldsymbol{\pi})}{\sin (\boldsymbol{4} \boldsymbol{x}-\boldsymbol{\pi})}= \)
A \( \cdot \sqrt{2} \)
B. \( \frac{1}{\sqrt{2}} \)
\( c \cdot-\sqrt{2} \)
D. \( \frac{-1}{\sqrt{2}} \)


In the reaction \( : \boldsymbol{C l}_{2}+\boldsymbol{O H}^{-} \rightarrow \boldsymbol{C l}^{-}+ \)
\( \boldsymbol{C l O}_{\boldsymbol{4}}^{-}+\boldsymbol{H}_{2} \boldsymbol{O} ? \)
A. Chlorine is oxidised
B. Chlorine is reduced
C. Chlorine is oxidised as well as reduced
D. Chlorine is neither oxidised nor reduced


By row transformation find \( \boldsymbol{A}^{-1} \) if:
\( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{2} & \mathbf{1} \\ \mathbf{4} & \mathbf{2}\end{array}\right] \)


Which term of the A.P., \( 84,80,76, . . \) is \( 0 ? \)
A \( \cdot 18^{\text {th}} \) term
B. \( 20^{\text {th }} \) term
c. \( 22^{\text {nd }} \) term
D. \( 24^{t h} \) term


\( 1000 \mathrm{g} \) aqueous solution of \( \mathrm{CaCO}_{3} \) contain \( 10 g \) of calcium carbonate
concentration of the solution is?
A. 10 ppm
B. 100 ppm
c. 1000 ppm
D. 10,000 ppm


The length of a side of a square garden \( A B C D \) is \( 70 m . A \) minor segment of
\( \odot(O, O A) \) is drawn on each of two
opposite sides for developing lawn, as shown in the figure. Find the area of the lawn.


Find \( \mathbf{x} \) and \( \mathbf{y} \) if \( \left[\begin{array}{cc}\mathbf{2} \boldsymbol{x} & \boldsymbol{x} \\ \boldsymbol{y} & \boldsymbol{3} \boldsymbol{y}\end{array}\right]\left[\begin{array}{l}\mathbf{3} \\ \mathbf{2}\end{array}\right]=\left[\begin{array}{c}\mathbf{1} \mathbf{6} \\ \mathbf{9}\end{array}\right] \)


Calculate the number of coulombs
required to deposit \( 5.4 g \) of \( A l \), when the electrode reaction is \( A l^{3+}+3 e^{-} \rightarrow A l \)
(At.mass of \( A l=27, F=96500 \)
coulomb per mole)


Which one of the following gases can deplete ozone layer in the upper atmosphere?
\( A \). Ammonia
B. Methane
c. Carbon monoxide
D. None of the above


Find the value of
\[
\tan \left\{\frac{1}{2} \sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right)+\frac{1}{2} \cos ^{-1}\left(\frac{1-}{1+}\right.\right.
\]
if \( \boldsymbol{x}>\boldsymbol{y}>1 \)


For any two events \( A \) and \( B \), the
conditional probability \( \boldsymbol{P}(\boldsymbol{B} / \boldsymbol{A})= \)
\( \frac{P(B \cap A)}{P(A)} \) and ifAand \( B \) are independent
\( \boldsymbol{P}(\boldsymbol{B} \cap \boldsymbol{A})=\boldsymbol{P}(\boldsymbol{B}) \cdot \boldsymbol{P}(\boldsymbol{A}) \) So,
\( \boldsymbol{P}(\boldsymbol{B} / \boldsymbol{A})=\boldsymbol{P}(\boldsymbol{B}) \)
A lot contains 50 defective and 50 non-
defective bulbs. Two bulbs are drawn at
random one at a time with replacement. The events \( A, B, C \) are defined as:
\( \mathbf{A}: \) 1st bulb is defective
\( \mathrm{B}: \) 2nd bulb is non-defective
\( \mathrm{C}: \) both are defective or both are non-
defective
then,
A. A, B, C are pair-wise independent as well as mutually independent
B. A, B, C are pair-wise independent but mutually not
c. \( A, B, C \) are mutually independent but pair-wise not
D - of these


8064 is resolved into all possible product of two factors. Find the number of ways in which this can be done?
A .24
B . 21
c. 20
D. None of these


The radii of two circles are \( 8 \mathrm{cm} \) and
\( 6 \mathrm{cm} \) respectively. Find the radius of the
circle having area equal to the sum of the areas of the two circles


Which is true for the combustion of
\( \operatorname{sucrose}\left(C_{12} H_{22} O_{11}\right) \) at \( 25^{\circ} C ? \)
\( \mathbf{A} \cdot \Delta H>\Delta E \)
в. \( \Delta H<\Delta E \)
c. \( \Delta H=\Delta E \)
D. None


The final product obtained when toluene is subjected to side chain chlorination followed by hydrolysis at 373 K is
A. phenol
B. benzaldehyde
c. acetophenone
D. chlorobenzene


If \( \alpha \) is only real root of the equation
\( \boldsymbol{x}^{3}-(\cos 1) \boldsymbol{x}^{2}+(\sin 1) \boldsymbol{x}+1=\mathbf{0}, \) then
\( \left(\tan ^{-1} \alpha+\tan ^{-1} \frac{1}{\alpha}\right) \) cannot be equal
to
his question has multiple correct options
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( \frac{\pi}{2} \)
\( c \cdot-\frac{\pi}{2} \)
D.


Express the following angles in degrees.
\( \begin{array}{ll}\text { (1) } & \left(\frac{5 \pi}{12}\right)^{\circ}\end{array} \)
(2) \( -\left(\frac{7 \pi}{12}\right)^{\circ} \)
(3) \( \frac{\pi}{3} \)
(4) \( \frac{5 \pi^{\circ}}{6} \)
(5) \( \frac{2 \pi^{\circ}}{9} \)
(6) \( \frac{7 \pi^{\circ}}{24} \)


A thermodynamic system undergoes a
cyclic process as shown in the figure. In
each of the loops 1 and 2 , does the heat flow into or out of the system?
A. into loop 1 and out of loop 2
B. into loop 2 and out of loop 1
\( c . \) into loop 1 and into loop 2
D. out of loop 1 and loop 2 both


Prove that:
\( \cos 2 \alpha \cos 2 \beta+\sin ^{2}(\alpha-\beta)-\sin ^{2}(\alpha+ \)
\( \boldsymbol{\beta})=\cos 2(\boldsymbol{\alpha}+\boldsymbol{\beta}) \)


The defective condition of eye in which distant objects are seen distinct but near objects are indistinct is called
A. Myopia
B. Astigmatism
c. Presbyopia
D. Hypermetropia


Which of the following metal oxides are reduced by CO? This question has multiple correct options
A. zno
B. \( F e_{2} O_{3} \)
\( c . \) сао
D. \( \left.A\right|_{2} O_{3} \)


What is(are) true regarding free radical
iodination of the alkane?
This question has multiple correct options
A. It occur very rapidly because of very small value of bond energy of \( I_{2} \)
B. Direct iodination of alkane with \( I_{2} \) in presence of light is impractical
c. lodination of alkane can be achieved successfully using an oxidizing agent catalyst
D. Presence of some \( H C I \) active the free radical
iodination


When a sound wave travels from water
to air, it
A. bends towards normal
B. bends away from normal
c. may bend in any direction
D. data insufficient


If the roots of the equation
\( (x-a)(x-b)+(x-b)(x-c)+ \)
\( (x-c)(x-a)=0 \) are equal, then
\( a^{2}+b^{2}+c^{2} \) is equal to
\( \mathbf{A} \cdot a+b+c \)
B . \( 2 a+b+c \)
c. \( 3 a b c \)
D. \( a b+b c+c a \)
E \( . a b c \)


In each of the following state if the statement is true (T) or false (F):
Every acute triangle is equilateral.
A. True
B. False


The empirical formula of a hydrocarbon is \( C H_{3} . \) It's molecular weight is 30
What is molecular formula of the
compound.
A \( . C H_{4} \)
B. \( C_{2} H_{6} \)
\( \mathbf{c} \cdot C_{3} H_{8} \)
D. \( C_{4} H_{10} \)


Find the moment of inertia of a uniform
square plate of mass \( m \) and edge \( a \) about one of its diagonals.


The AM range of radiowaves has frequency:
A. less than 30 MHz
B. more than 30 Мн н
c. less than 20000 Hz
D. more than 20000Hz


An alternating voltage given as \( \boldsymbol{V}= \) \( \mathbf{1 0 0} \sqrt{\mathbf{2}} \sin 100 t \quad \) is applied to a
capacitor of \( 1 \mu F \). The current reading of
the ammeter will be equal to \( \mathrm{mA} \)
A . 10
B . 20
c. 40
D. 80


\( \left|\begin{array}{ccc}(\boldsymbol{b}+\boldsymbol{c})^{2} & \boldsymbol{a}^{2} & \boldsymbol{a}^{2} \\ \boldsymbol{b}^{2} & (\boldsymbol{c}+\boldsymbol{a})^{2} & \boldsymbol{b}^{2} \\ \boldsymbol{c}^{2} & \boldsymbol{c}^{2} & (\boldsymbol{a}+\boldsymbol{b})^{2}\end{array}\right| \) is equal
to
\( \mathbf{A} \cdot a b c(a+b+c)^{2} \)
B \( \cdot 2 a b c(a+b+c)^{2} \)
\( \mathbf{c} \cdot 2 a b c(a+b+c)^{3} \)
\( \mathbf{D} \cdot 2 a b c(a+b+c) \)


Define the term : isotonic solution


The phragmoplast is organised
A. At the beginning of anaphase
B. At the end of anaphase
C. At the beginning of telophase
D. At the end of telophase


Find the principal value of:
\( \sec ^{-1}\left(2 \tan \frac{3 \pi}{4}\right) \)


How many \( \sigma \) - and \( \pi \) -bonds are present in each of the following molecules?
(a) \( \boldsymbol{H} \boldsymbol{C} \equiv \boldsymbol{C}-\boldsymbol{C H}=\boldsymbol{C H}-\boldsymbol{C H}_{3} \)
(b) \( \boldsymbol{C H}_{2}=\boldsymbol{C}=\boldsymbol{C H}-\boldsymbol{C H}_{3} \)


Write the order of magnitude of mass of an electron \( 9.1 \times 10^{-31} \mathrm{kg} \)


Which reaction shows oxidising nature
of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} ? \)
A. \( A g_{2} O+H_{2} O_{2} \rightarrow A g+H_{2} O+O_{2} \)
в. \( M n O_{2}+H_{2} O_{2}+H_{2} S O_{4} \rightarrow M n S O_{4}+2 H_{2} O+O_{2} \)
\( \mathbf{c} \cdot P b S+4 H_{2} O_{2} \rightarrow P b S O_{4}+4 H_{2} O \)
D. \( K_{2} C r_{2} O_{7}+H_{2} S O_{4}+4 H_{2} O_{2} \rightarrow K_{2} S O_{4}+2 C r O_{5}+ \)
\( 5 H_{2} O \)


The mean and variance of 7
observations are 8 and 16 respectively. If 5 of the observations are
\( 2,4,10,12,14, \) find the remaining two observations.
\( \mathbf{A} \cdot 3,6 \)
в. 6,8
c. 1,5
D. None of these


If the points \( A, B, C, D \) are collinear and \( C, D \) divide \( A B \) in the ratios 2:
3,-2: 3 respectively, then the ratio in
which \( A \) divides \( C D \) is
A . 5: 1
B. 2: 3
c. 3: 2
D. 1: 5


The absolute minimum \& maximum
values of \( f(x)=\frac{x^{2}-3 x+4}{x^{2}+3 x+4} \) are
respectively
A \( \cdot \frac{1}{7} \) and 7
B. \( 5 \& 7 \)
c. \( \frac{1}{7} \& 1 \)
D. None of these


If \( \boldsymbol{A}-\boldsymbol{B}=\boldsymbol{\phi} \) and \( \boldsymbol{B}-\boldsymbol{A}=\boldsymbol{\phi}, \) then \( \mathbf{A} \)
and B are
A. Overlapping
B. Equivalent
c. Disjoint
D. Equal


In a certain \( A . P ., 5 \) times the 5 th term
is equal to 8 times the 8 th term, then
find its 13 th term.


The percentage of \( C, H \) and \( N \) in an
organic compound are \( 40 \%, 13.3 \% \) and \( 46.7 \% \) respectively then its empirical
formula is:
A. \( C_{3} H_{13} N_{3} \)
в. \( C H_{2} N \)
c. \( C H_{4} N \)
D. \( C H_{6} N \)


Which of the following metal is used in
ornaments?
This question has multiple correct options
A . Silver
B. Gold
c. Sodium
D. Mercury


Identify the wrong statement
A. Eddy currents are produced in a steady magnetic field
B. Eddy currents can be minimized by using laminated core
C. Induction furnace uses eddy current to produce heat
D. Eddy current can be used to produce breaking force in moving vehicles
E. Power meters are working on the principle of eddy currents


The ratio of the radii of two planets \( r_{1} \)
and \( r_{2} \) is \( k . \) The ratio of acceleration due
to gravity on them is \( r . \) Then the ratio of the escape velocities from them, will be:
A. \( \sqrt{\frac{r}{k}} \)
в. \( \sqrt{\frac{k}{r}} \)
\( c . k r \)
D. \( \sqrt{k s} \)


Bond enegry of \( (N \equiv N)=948 k J M o l^{-1} \)
\( (\boldsymbol{P} \equiv \boldsymbol{P})=\mathbf{4 8 1} \boldsymbol{k} \boldsymbol{J} \boldsymbol{M} \boldsymbol{o l}^{-1} \)
\( (N-N)=160 k J M o l^{-1} \)
\( (\boldsymbol{P}-\boldsymbol{P})=\mathbf{2} \mathbf{1 5} \boldsymbol{k} \boldsymbol{J} \boldsymbol{M} \boldsymbol{o l}^{-1} \)
Which molecules do not exist?
This question has multiple correct options
A \( \cdot P_{4} \)
B. \( N_{4} \)
c. \( N_{2} \)
D. \( P_{2} \)


When 280 gm of ethylene polymerises to polyethene according to the equation.
\( \boldsymbol{n} \boldsymbol{C H}_{2}=\boldsymbol{C H}_{2} \longrightarrow-\left(\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}\right)_{n} \)
The weight and mole of polyethylene formed will be:
A \( .280,10 n \)
в. \( \frac{280}{n}, \) n
c. \( \frac{280}{n}, \) 280
D. \( 280, \frac{10}{n} \)


Find the unit vector perpendicular to each of the vectors \( 6 \hat{i}+2 \hat{j}+3 \hat{k} \) and \( \mathbf{3} \hat{\mathbf{i}}-\mathbf{2} \hat{\boldsymbol{k}} \)


A circular coil of one turn in formed by a \( 6.28 \mathrm{m} \) length wire, which carries a current of 3.14 A. the magnetic field at the center of coil is :-
A \( \cdot 1 \times 10^{-6} T \)
В. \( 4 \times 10^{-6} T \)
c. \( 0.5 \times 10^{-6} T \)
D. \( 2 \times 10^{-6} T \)


An \( L E D \) is constructed from a pn
junction based on a certain semiconducting material whose energy gap is \( 1.9 e V . \) Then the wavelength of the emitted light is
A \( .2 .9 \times 10^{-9} \mathrm{m} \)
в. \( 1.6 \times 10^{-8} \mathrm{m} \)
c. \( 6.5 \times 10^{-7} m \)
D. \( 9.1 \times 10^{-5} m \)


Desmosomes
A. Connect the epithelial cells
B. Types of lysosomes
C. Granules of muscle fibres
D. Found in bone


Let ABCD be a parallelogram. The diagonals bisect in E.
(i) If \( A B=6 \mathrm{cm} \) and \( A D=4 \mathrm{cm}, \) find \( C D \)
and BC.
(ii) If \( \mathrm{DE}=5 \mathrm{cm} \) and \( \mathrm{AE}=7 \mathrm{cm}, \) find \( \mathrm{BD} \)
and AC.
(iii) If \( \angle D A B=72^{\circ}, \) find the measure
of \( \angle C B A \)
\( (\text { iv ) If } \boldsymbol{A} \boldsymbol{D}=(\boldsymbol{x}+\boldsymbol{2} \boldsymbol{y}), \boldsymbol{B} \boldsymbol{C}=(\boldsymbol{2} \boldsymbol{x}+ \)
\( \mathbf{3}), \boldsymbol{D} \boldsymbol{C}=(\boldsymbol{x}+\boldsymbol{7}) \) and \( \boldsymbol{A} \boldsymbol{B}=(\boldsymbol{3} \boldsymbol{y}+\boldsymbol{2}) \)
find \( A B \) and \( B C \).


Jyoti secured 35 marks out of 50 in English and 25 marks out of 30 in Mathematics. In which subject did she get better marks and by how much?


Given \( \boldsymbol{f}(\boldsymbol{x})=\frac{\boldsymbol{x}+\mathbf{2}}{\mathbf{5}} \) for \( \operatorname{gof}(\boldsymbol{x})=\boldsymbol{x}-\mathbf{3} \)
find \( \boldsymbol{g} \)


Which of the following forms the most basic hydroxide?
A. \( C u \)
в. \( A l \)
\( c . N a \)
D. \( Z \) n


Kjeldahl's method can not be used for estimation of nitrogen in:
A. pyridine
B. azobenzene
c. nitrobenzene
D. all of these


The order of size is:
A. \( S^{2-}>C l^{-}>O^{2-}>F^{-} \)
B. \( C l^{-}>S^{2-}>O^{2-}>F^{-} \)
c. \( S^{2-}>O^{2-}>C l^{-}>F^{-} \)
D. \( S^{2-}>O^{2-}>F^{-}>C l^{-} \)


The units of \( K_{c} \) for the decomposition of potassium nitrate is same as the units
of \( K_{c} \) for the:
A. decomposition of sulphur trioxide
B. decomposition of hydrogen iodide
c. decomposition of ammonium nitrite
D. formation of nitrogen dioxide from nitric oxide and oxygen


Concentrated nitric acid, upon long standing, turns yellow-brown due to the formation of :
A . \( N O \)
в. \( N O_{2} \)
\( \mathrm{c} \cdot N_{2} \mathrm{O} \)
D. \( N_{2} O_{4} \)


There are 6 multiple choice questions in an examination. How many sequences of answers are possible, if the first three
questions have 4 choices each and the
next three have 2 each?


Number of moles of the solute per
kilogram of the solvent is:
A. mole fraction
B. molality
c. molarity
D. molar mass


Internal resistance of a battery cell
decreases with:
A. an increase in area of the plates inside the electrolyte
B. an increase in distance between the two electrodes
c. a decrease in size of the electrodes
D. an increase of age of the battery


Which of the following is not correct?
This question has multiple correct options
A. Hydrolysis of \( 4 \mathrm{NC}_{3} \) gives \( \mathrm{NH}_{3} \) and \( \mathrm{HOC} \)
B. \( \mathrm{NH}_{3} \) is less stable than \( \mathrm{PH}_{3} \)
\( \mathrm{C} \cdot \mathrm{NH}_{3} \) is weak reducing agent compared to \( \mathrm{PH}_{3} \)
D. Nitric Oxide in solid state exhibitsdiamagnetic property.


The name of the figure formed by the points (3,-5,1),(-1,0,8) and
(7,-10,-6) is
A. a triangle
B. a straight line
c. an isosceles triangle
D. an equilateral triangle


Assertion
On cooling, the brown colour of nitrogen dioxide disappears.
Reason
On cooling \( N O_{2} \) undergoes dimerisation resulting in the pairing of
odd electrons of \( N O_{2} \)
Read the above assertion and reason
and choose the corret option regarding
¡t.
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


Assertion
Nitric oxide is paramagnetic while \( N_{2} O \)
is diamagnetic.
Reason
Nitrogen exhibits variable valency in
\( N O \) and \( N_{2} O \)
A. Both assertion and reason are CORRECT and reason is
the CORRECT explanation of the assertion.
B. Both assertion and reason are CORRECT, but reason is NOT THE CORRECT explanation of the assertion.
C. Assertion is CORRECT, but reason is INCORRECT.
D. Assertion is INCORRECT, but reason is CORRECT.


If \( \sum_{r=1}^{n}(r)(r+1)(2 r+3)=a n^{4}+ \)
\( b n^{3}+c n^{2}+d n+e, \) then
This question has multiple correct options
A \( . a+c=b+d \)
В. \( e=0 \)
c. \( a, b-\frac{2}{3}, c-1 \) are in A.P
D. \( \frac{c}{a} \) is an integers


If one angle of a triangle is \( \frac{\pi}{4} \) and other
angle is \( 90^{\circ} \) then find the third angle in
degree measure.


Evaluate:
\( \int \frac{1}{4+9 x^{2}} d x \)


If an element A is present in group I of the periodic table, the formula of its chloride should be:
A \( \cdot A_{2} C l \)
в. \( A C l_{2} \)
c. \( A C l \)
D. \( A C l_{3} \)


Progesterone present in contraceptive pill is meant for
A. Checking ovulation
B. Preventing fertilisation
c. Preventing implantation of zygote
D. Preventing cleavage


Which one of the following is a xerophytic plant in which the stem is modified into a flat, green and
succulent structure?
A. Acacia
B. opuntia
c. casuarina
D. Hydrilla


The degree of \( 3 x^{2} y^{4} z^{6} \) is
\( A \cdot 2 \)
B. 12
\( c \cdot 4 \)
D. 6


Identify \( (X),(Y) \) and \( (Z) \) in the given
reaction.
\( C H_{3} C H O \frac{K_{2} C r_{2} O_{7}}{H_{2} S O_{4}}(X) \stackrel{P C l_{5}}{ } \)
\( (Y) \frac{C_{6} H_{6}}{a n h . A l C l_{3}}(Z): \)
\( \mathbf{A} \cdot(X)=H C O O H, \quad(Y)=C O C l_{2}, \quad(Z)=C_{6} H_{5} C l \)
B \( \cdot(X)=C H_{3} C O O H, \quad(Y)=C H_{3} C O C l, \quad(Z)= \)
\( C_{6} H_{5} C O C H_{3} \)
\( \mathbf{c} \cdot(X)=C H_{3} C O O H, \quad(Y)=C H_{3} C H_{2} C H_{2} C l, \quad(Z)= \)
\( C_{6} H_{5} C H_{2} C H_{2} C H_{3} \)
\( \mathbf{D} \cdot(X)=C H_{3} C O C H_{3}, \quad(Y)=C H_{3} C H(C l) C H_{3}, \quad(Z)= \)
\( C_{6} H_{5} C O C H_{3} \)


Gravitational force between two point
masses \( m \) and \( M \) separated by a
distance \( r \) is \( F \). now if a point mass \( 3 m \)
is placed very next to \( \mathrm{m} \), the total force
on \( \boldsymbol{M} \) will be
A. \( F \)
в. \( 2 F \)
\( c .3 F \)
D. \( 4 F \)


Which among the following elements
shown in the table forms amphoteric
oxide?
\( A \cdot A \)
B. \( B \)
\( c \cdot C \)
\( D . D \)
E . \( E \)
\( F . F \)
\( \mathrm{G} \). \( G \)


\( M_{2} O_{3} \) (sesquoxides) is paramagnetic
in nature. It is due to presence of :
A. peroxide ion.
B. superoxide ion.
c. oxide ion
D. all of these


A p-type semiconductor is
A. positively charged
B. negatively charged
C. uncharged
D. uncharged at \( 0 K \) but charged at higher temperatures.


What is common in common pathway of
aerobic respiration
A. Glycolysis in both aerobic and anaerobic respiration
B. Krebs cycle common with HMP
C. Terminal oxidation in both aerobic and anaerobic respiration
D. Krebs cycle in both aerobic and anaerobic respiration


1 mole of \( A l \) is deposited by \( X \) coulomb of electricity passing through aluminium nitrate solution. Calculate
the number of moles of silver deposited by \( \mathrm{X} \) coulomb of electricity from silver
nitrate solution
A . 3
B. 4
\( c \cdot 2 \)
\( D \)


Phenol on sulphonation at \( 100^{\circ} \mathrm{C} \) gives:
A. o-phenol sulphonic acid
B. p-phenol sulphonic acid
c. m-phenol sulphonic acid
D. o- and p-phenol sulphonic acid


Let \( A_{1}, A_{2} \) be two arithmetic means,
\( G_{1}, G_{2} \) be two geometric means and
\( \boldsymbol{H}_{1}, \boldsymbol{H}_{2} \) be two harmonic means
between two positive numbers a and b. The value of \( \frac{\boldsymbol{G}_{1} \boldsymbol{G}_{2}}{\boldsymbol{H}_{1} \boldsymbol{H}_{2}} \cdot \frac{\boldsymbol{H}_{1}+\boldsymbol{H}_{2}}{\boldsymbol{A}_{1}+\boldsymbol{A}_{2}} \) is
A \( \cdot 1 / 2 \)
B.
\( c \cdot 3 / 2 \)
\( D \)


\( A B C \) is a triangular park with \( A B= \) \( A C=100 \) metres. A vertical tower is
situated at the mid-point of \( B C . \) If the
angles of elevation of the top of the tower at \( A \) and \( B \) are \( \cos ^{-1}(3 \sqrt{2}) \) and \( \operatorname{cosec}^{-1}(2 \sqrt{2}) \) respectively, then the height of the tower (in metres is):
A. \( 10 \sqrt{5} \)
the \( 6 \sqrt{55} \)
в. \( \frac{100}{3 \sqrt{3}} \)
c. 20
D. 25


If the current is flowing through a \( 10 \Omega \) resistor, then in which case the
maximum heat will be generated?
A. 5 ampere in 2 minutes
B. 4 ampere in 3 minutes
c. 3 ampere in 6 minutes
D. 2 ampere in 5 minutes


Maximum number of chambers-13 are
found in heart of
A. cockroach
B. Frog
c. Human
D. Fish


A type of ion found in sodium acetate
is :
A \( . x^{+} \)
B. \( X^{2+} \)
\( c \cdot X^{3+} \)
D. \( X O_{3}^{2-} \)
E \( \cdot X O_{4}^{2-} \)


The ratio of the measure of the angles in
a rhombus is \( 2: 7 . \) What is the measure
of the four angles?
В. \( 40^{\circ}, 140^{\circ}, 40^{\circ}, 140^{\circ} \)
C \( \cdot 65^{\circ}, 115^{\circ}, 65^{\circ}, 115^{\circ} \)
D. None of the above


Three small spheres, each carrying a
charge \( q \) are placed on the circumference of a circle of radius \( R \)
forming an equilateral triangle. If we
place another charge \( Q \) at the center of the circle, then the force on \( Q \) will be
A. zero
В. \( \frac{1}{4 \pi \epsilon_{0}} \times \frac{q Q}{R^{2}} \)
c. \( \frac{1}{4 \pi \epsilon_{0}} \times \frac{2 q Q}{R^{2}} \)
D. \( \frac{1}{4 \pi \epsilon_{0}} \times \frac{3 q Q}{R^{2}} \)


Two fixed, equal, positive charges, each of magnitude \( 5 \times 10^{-5} C \) are located at
point \( A \) and \( B \) separated by a distance
\( 6 m . \) An equal and opposite charge moves towards them along the line
COD, the perpendicular bisector of the
line \( A B . \) The moving charge, when it reaches the point \( C \) at a distance of \( 4 m \) from \( O, \) has a kinetic energy of 4
joules. Calculate the distance of the
farthest point \( D \) which the negative
charge will reach before returning
towards \( C \)


The IUPAC name of \( \boldsymbol{K}_{3}\left[\operatorname{Ir}\left(\boldsymbol{C}_{2} \boldsymbol{O}_{4}\right)_{3}\right] \) is:
A. Potassium trioxalatoiridium (III)
B. Potassium trioxalatoiridate (III)
c. Potassium tris (oxalato) iridium (III)
D. Potassium tris (oxalato) iridate (III)


A resistance col of \( 60 \Omega \) is immersed in
\( 42 \mathrm{kg} \) of water. What is the rise in temperature of water per minute if a steady current of \( 7 \mathrm{A} \) is made to flow
through the coli?
A \( \cdot 10.10^{\circ} \mathrm{C} \)
B. 9.51 \( ^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 1.0^{\circ} \mathrm{C} \)
D. \( 0.5^{\circ} \mathrm{C} \)


During aerobic respiration maximum ATP is synthesized by
A . ETS
B. Kreb's cycle
c. Glycolysis
D. Fermentation


Which of the following metals require radiation of highest frequency to cause emmission of electrons?
A. \( N a \)
в. \( M g \)
\( c . k \)
D. \( C a \)


A cord is used to lower vertically a block
of mass \( M \) by a distance \( d \) with constant downword acceleration \( \frac{g}{2} \) work done by the cord on the block is
\( ^{\mathbf{A}} \cdot \frac{-M g d}{2} \)
B. \( \frac{M g d}{4} \)
c. \( \frac{-3 M g d}{4} \)
D. \( M g d \)


Convert \( \frac{7}{20} \) to per cent.


A person driving a car with a speed 72 \( \mathrm{km} / \mathrm{h}, \) suddenly sees a boy crossing the road. If the distance moved by a car, before the person applies brakes is \( 5 \mathrm{m} \) the reaction time of the person is:
A . 0.5 s
B. 0.10
\( c \cdot 10 s \)
D. 0.25 s


The Universal gas constant may be
expressed as:
a) \( 8.31 \mathrm{J} / \mathrm{mole}-\mathrm{K} \)
c) \( 2.00 \mathrm{J} / \mathrm{mole}-\mathrm{K} \)
b) 8.31 cal/mole-K
d) 2.00 cal/mole-K
A . a,
в. а,
\( c \cdot b, c \)
D. b,


Write the given statement using numbers, literals and signs of basic
operations. State what each letter
represents. The selling price equals the sum of the cost price and the profit.


Determine the electric field everywhere
outside the sphere at a distance \( r(>> \)
\( \boldsymbol{a}) \) from the centre
A \( \cdot E=\frac{Q}{4 \pi \epsilon_{0} r^{2}} \)
B. \( \quad E=\frac{Q}{4 \pi \epsilon_{0} r} \)
c. \( \quad E=\frac{Q}{4 \pi \epsilon_{0} a^{2}} \)
D. \( \quad E=\frac{Q}{4 \pi \epsilon_{0} a} \)


Given a function \( \boldsymbol{f}(\boldsymbol{x})=\frac{1}{2} \boldsymbol{x}-\boldsymbol{4} \) and the
composite function \( \boldsymbol{f}(\boldsymbol{g}(\boldsymbol{x}))=\boldsymbol{g}(\boldsymbol{f}(\boldsymbol{x})) \)
determine which among the following
\( \operatorname{can} \operatorname{be} g(x): \)
\( 2 x-\frac{1}{4} \)
11. \( 2 x+8 \)
III. \( \frac{1}{2} x-4 \)
A. I only
B. II only
c. III only
D. II and III only
E . ।, II, and III


A metal rod having \( \boldsymbol{\alpha}=\mathbf{1 0} \times \mathbf{1 0}^{-\mathbf{6}} /^{\circ} \boldsymbol{C} \)
has a length of \( 250 \mathrm{cm} \) at \( 40^{\circ} \mathrm{C} \). The
temperature at which it can be shortened by \( 1 \mathrm{mm} \)
\( \mathbf{A} \cdot 80^{\circ} \mathrm{C} \)
в. \( -40^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 0^{\circ} C \)
D. \( 40^{\circ} \mathrm{C} \)


What type of forces are involed in binding of substrate to the active site of
enzyme?


Chemically least active element is :
\( A \cdot K r \)
B. Ne
\( c \cdot x e \)
D. Ar


Two wires of the same material have
lengths in the ratio 1: 2 and their radii are in the ratio \( 1: \sqrt{2} . \) If they are
stretched by applying equal forces, the increase in their lengths will be in the ratio :
A .2
B . \( \sqrt{2}: 2 \)
c. 1: 1
D. 1: 2


The Sl unit of magnetic permeability is:
A. \( A m^{-1} \)
B. \( A m^{-2} \)
c. \( H m^{-2} \)
\( \mathbf{D} \cdot H m^{-1} \)


Find the number of ordered pairs in
RoR?


Joule's Law for heat produced is valid for
A . Resistance
B. Inductance
c. capacitance
D. Battery


Which statements is/are correct?
i. \( \quad \) Me \( \overbrace{(\mathbf{A})}^{\wedge} C l \frac{N a N O_{2}}{E t O H} \)
ii. \( \mathbf{M e} \widehat{\mathbf{O}}^{\mathbf{N}} \mathbf{C l} \frac{\mathbf{N a N O}_{\mathbf{2}}}{\mathbf{E} \mathbf{t} \mathbf{O} \mathbf{H}} \)
\( (\mathrm{C}) \)
A. Both reactions ( \( i \) ) and
(ii) proceed via \( S_{N} 2 \) mechanism
B. Both reactions (i) and (ii) proceed via \( S_{N} 1 \) mechanism
C. Reactions ( \( i \) ) proceeds via \( S_{N} 1 \) and reaction (ii) proceed via \( S_{N} 2 \) mechanism
D. Reactions ( \( i \) ) proceeds via \( S_{N} 2 \) and reaction (ii) proceed via \( S_{N} 1 \) mechanism


Coke oven gas consists mainly of
A. \( H_{2} \) and \( C H_{4} \)
в. \( C O \) and \( C O_{2} \)
c. \( H_{2} \) and \( C O \)
D. \( C H_{4} \) and \( C O \)


Ozone hole enhances
A. UV radiations reaching earth
B. Number of cataracts
C. Skin cancers
D. All of the above


Identify the type of nutrition in Amoeba.
A. Saprotrophic
B. Parasitic
C. Holozoic
D. Holophytic


What does CNG mean?
A. Compressed Natural Gas
B. Coal Natural Gas
c. Carbon Natural Gas
D. Carbon Nitrogen Gas


John Newland arranged the element starting with hydrogen and ending at
A. cerium
B. calcium
c. thorium
D. rubidium


Show that \( (x-a) \) is a factor of
\( \left|\begin{array}{lll}\boldsymbol{x} & \boldsymbol{a} & \boldsymbol{a} \\ \boldsymbol{a} & \boldsymbol{x} & \boldsymbol{a} \\ \boldsymbol{a} & \boldsymbol{a} & \boldsymbol{x}\end{array}\right| \)


The DNA content of a diploid cell in the G1 phase of the cell cycle is measured If this DNA content is \( X \), then the DNA
content of the same cell at metaphase of meiosis I would be
\( A \cdot 0.5 x \)
B. 0.25 \( x \)
\( c \cdot x \)
D. \( 2 x \)


Acetabularia, a largest unicellular plant
belongs to
A. chlorophyta
B. Rhodophyta
c. Pyrrophyta
D. Phaeophyta


Which element can form positive ions by the loss of electrons?
A. Metals
B. Non metals
c. metalloids
D. None of these


If a machine is Iubricated with oil
A. The mechanical advantage of the machine increases
B. The mechanical efficiency of the machine increases
C. Both its mechanical advantage and efficiency increase
D. Its efficiency increases, but its mechanical advantage decreases


Bentham and Hooker classified dicots
into
A. Polypetalae, gamopetalae and glumiflorae
B. Polypetalae, gamopetalae and monochlamydae
C. Achlamydae, diclamydeae and metachlamydae
D. Archichlamydae, sympetalae and apetalae


Four dipoles each one having magnitudes of charges \( \pm \mathrm{e} \) are placed inside a sphere. The total flux of \( \vec{E} \) coming out of the sphere is :
A. zero
в. \( \frac{4 e}{\varepsilon_{0}} \)
\( c \cdot \frac{8 e}{\varepsilon_{0}} \)
D. None of these


When an ideal diatomic gas is heated
at constant pressure, the fraction of the heat energy supplied which increases
the internal energy of the gas is?
A. \( 2 / 5 \)
B. 3/5
c. \( 3 / 7 \)
D. \( 5 / 7 \)


Evaluate \( \int_{a}^{b} x \sin x d x \)


Amount of light entering the eye is controlled by:
A. Iriss
B. Cornea
c. Pupil
D. crystalline lens


Which among the following is not a natural polymer?
A. wool
B. Silk
c. Rubber
D. PVC


The aqueous solution of the following
salts will be colored in the case of
This question has multiple correct options
\( \mathbf{A} \cdot Z n\left(N O_{3}\right)_{2} \)
\( \mathbf{B} \cdot L i N O_{3} \)
\( \mathbf{c} \cdot \operatorname{Co}\left(N O_{3}\right)_{2} \)
\( \mathbf{D} \cdot C r C l_{3} \)


In a cyclotron, magnetic field of \( 3.5 W b / m^{2} \) is used to accelerate
protons.What should be the time interval in which the electric field
between the Dees be reversed?
(Mass of proton \( =1.67 \times 10^{-27} k g \)
charge on proton \( =\mathbf{1 . 6} \times \mathbf{1 0}^{-\mathbf{1 9}} \mathbf{C} \) ).


Define zygote.


\( \ln \Delta A B C, P, Q, R \) are points on
\( B C, C A, A B \) respectively, dividing them in the ratio 1: 4,3: 2 and 3: 7
The point \( S \) divides \( A B \) in the ratio 1: 3
Then \( \frac{|\overrightarrow{\boldsymbol{A P}}+\overline{\boldsymbol{B} Q}+\overline{\boldsymbol{C} \boldsymbol{R}}|}{|\overline{\boldsymbol{C S}}|} \) is
A \( \cdot \frac{1}{5} \)
B. \( \frac{2}{5} \)
\( c \cdot \frac{5}{2} \)
D. \( \frac{7}{10} \)


The ratio of the magnetic field at the
centre of a circular loop to the magnetic field at the centre of the square loop, which is made by a constant length current carrying wire is:
A \( \cdot \frac{\pi^{2}}{16} \)
в. \( \frac{\pi^{2}}{8 \sqrt{2}} \)
c. \( \frac{\pi^{2}}{4 \sqrt{2}} \)
D. \( \frac{\pi^{2}}{2 \sqrt{2}} \)


Mohan spent \( 25 \% \) of his monthly
earning on magazines. Out of the remaining amount amount he spent \( 75 \% \) on the hostel and college fees. If he had Rs. 120 at the end of the month, find how much money he has received from his father in that month?
A. Rs. 1000
B. Rs. 1260
c. Rs. 640
D. Rs. 850


The period of the SHM of a particle with
the maximum velocity \( 50 \mathrm{cm} / \mathrm{s} \) and maximum acceleration \( 10 \mathrm{cm} / \mathrm{s}^{2} \) is
A . \( 31.42 s \)
B. \( 6.284 s \)
c. \( 3.142 s \)
D. \( 0.3124 s \)


A body is lifted over route I and then
route II such that force is always
tangent to the path. Coefficient of
friction is same for both the paths. Work
done
A. on both routes is same
B. on route lis more
c. on route II is more.
D. on both routes is zero


\( \int \frac{d\left(x^{2}+1\right)}{\sqrt{x^{2}+2}} \) is equal to
A \( \cdot 2 \sqrt{x^{2}+2}+k \)
B . \( \sqrt{x^{2}+2}+k \)
\( \left(\frac{1}{x^{2}+2}\right)^{\frac{3}{2}}+k \)
D. none of these


Give Reason:
During the test for nitrogen in Lassaigne's filtrate, sometimes red colouration is obtained when ferric
chloride is added.


A charge \( q \) is placed at the centre of the open end of cylindrical vessel. The flux of electric field through the surface of
the vessel is
A . 0
в. \( \frac{q}{\epsilon_{0}} \)
c. \( \frac{q}{2 \epsilon_{0}} \)
D. \( \frac{2 q}{\epsilon_{0}} \)


The equation ot the line passing through the point (1,-2,3) and paralle to the \( \operatorname{linex}-y+2 z=5 \) and \( 3 x+y+ \)
\( z=6 \) is
A \( \cdot \frac{x-1}{-3}=\frac{y+2}{5}=\frac{z-3}{4} \)
B. \( \frac{x-1}{1}=\frac{y+2}{-1}=\frac{z-3}{2} \)
\( \mathbf{c} \cdot \frac{x-1}{3}=\frac{y+2}{1}=\frac{z-3}{6} \)
D. \( \frac{x-1}{3}=\frac{y+2}{-1}=\frac{z-3}{2} \)


A shopkeeper bought a cycle for Rs.1200 and sold it for Rs.1500. Find his profit
(or) loss percentage.


A die is thrown thrice. Find the
probability of getting an odd number
number at least once.


A person on the surface of the moon:
A. Does not feel the effect of earth's gravity because the gravity due to moon is such stronger.
B. Does not feel the effect of earth's gravity.
C. Does not feel the effect of earth's gravity and moon gravity he is freely towards the earth.
D. Feels only the combined effect of earth's and moon gravity which are comparable in magnet


Find the derivative of the following
function.
\( \log (\log x) \)


A point source of light is placed in front
of a plane mirror as shown in the fig.
Determine the length of reflected path
of light on the screen \( \left(\sum\right) \)
\( A . L \)
В. \( 2 L \)
\( c \cdot \frac{3 L}{2} \)
D. \( \frac{L}{2} \)


Assertion
If \( A, B, C \) are acute positive angles then \( \frac{(\sin A+\sin B)(\sin B+\sin C)(\sin C+s)}{\sin A \sin B \sin C} \)
8
Reason
\( \boldsymbol{A M} \geq \boldsymbol{G} \boldsymbol{M} \)
A. Statement-1 is false, statement-2 is true
B. Statement-1 is true, statement-2 is true,statement-2 is correct explanation for statement-
c. statement-1 is true, statement-2 is true,statement-2 is not a correct explanation for statement-
D. Statement-1 is true, statement-2 is false


What is the sum of 12 odd numbers
\( \mathbf{1}, \mathbf{3}, \mathbf{5}, \mathbf{7}, \mathbf{9} \ldots . . ? \)
A . 12
B. 144
\( c .141 \)
D. 124


The hydride ion is isoelectronic with:
A . \( H^{+} \)
в. \( H e^{+} \)
\( \mathrm{c} . \) Не
D. \( B e \)


Name two pentavalent impurities.


The specific conductance of a
\( 0.1 N K C l \) solution at \( 23^{\circ} C \) is
0.0112 oh \( m^{-1} c m^{-1} . \) The resistance of
the cell containing the solution at the
same temperature was found to be \( \mathbf{5 5} \) ohm. The cell constant will be:
A. \( 0.142 \mathrm{cm}^{-1} \)
B. \( 0.918 \mathrm{cm}^{-1} \)
c. \( 1.12 \mathrm{cm}^{-1} \)
D. \( 0.616 \mathrm{cm}^{-1} \)


Which of the following solutions shows positive deviation from Raoult's law?
A. Acetone + Aniline
B. Acetone + Ethanol
c. water + Nitric acid
D. Chloroform + Benzene


The following table gives the route length (in thousand kilometres) of the Indian Railways in some of the years:
Year
\( \begin{array}{lll}1960- & 1970- & 1980-\end{array} \)
is and 61
Route length (in \( \quad \) 56 \( \quad \) 60 thousand kilometres)
Represent the above data with the help of a bar graph.


What is the trend of boiling points of
hydrides of \( \mathrm{N}, \mathrm{O}, \) and \( \mathrm{F} \) ?
A. Due to lower molecular masses \( N H_{3}, H_{2} O \) and HF have lower boiling points than those of the subsequent group member hydrides
B. Due to higher electronegativity of \( \mathrm{N}, \mathrm{O} \) and \( \mathrm{F} \) \( N H_{3}, H_{2} O \) and HF show hydrogen bonding and hence higher boiling points than the hydrides of their subsequent group members.
C. There is no regular trend in the boiling points of hydrides
D. Due to higher oxidation states of \( \mathrm{N}, \mathrm{O} \) and \( \mathrm{F} \), the boiling points of \( N H_{3}, H_{2} O \) and HF are higher than the hydrides of their subsequent group members.


What is the oxidation number of Pt in
\( \boldsymbol{K}\left[\boldsymbol{P t} \boldsymbol{N} \boldsymbol{H}_{3} \boldsymbol{C l}_{5}\right] ? \)
\( A \cdot O \)
B. +1
\( c \cdot+2 \)
\( D \cdot+4 \)


The law of constant proportions was enunciated by:
A. Dalton
B. Berthelot
c. Avogadro
D. Proust


Pneumoconiosis is a type of?
A. Emphysema
B. Occupational renal disease
c. Occupational respiratory disease
D. coronary artery disease


\( \boldsymbol{C H}_{3}-\boldsymbol{O H} \stackrel{\boldsymbol{P}+\boldsymbol{I}_{2}}{\longrightarrow} \boldsymbol{A} \frac{\boldsymbol{H} \text {eating}}{\operatorname{alc} K C \boldsymbol{N}} \)
\( \boldsymbol{B} \frac{\boldsymbol{L i} A \boldsymbol{l} \boldsymbol{H}_{4}}{\boldsymbol{N a} / \text {alcohol}} \boldsymbol{C} \frac{\boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{2}}{\boldsymbol{N a N O _ { 2 }}+\boldsymbol{d i l} \boldsymbol{H C l}} \boldsymbol{D} \)
What is \( D ? \)
A. \( C H_{3} C H O \)
в. \( C H_{3} \)СООН
c. \( C H_{3} C H_{2} \) ОН
D. \( C H_{3}-O-C H_{3} \)


With the help of the given clues, unscramble the letters to make a
meaningful word. ETHZR (unit of frequency of sound wave)


\( (-\sqrt{-1})^{4 n+3}(n,+i v e \text { integer }) \)
\( \mathbf{A} \cdot-i \)
B.
\( c \cdot 1 \)
D. -


In the following electronic configuration
\( n s^{2}(n-1) d^{0-1}(n-2) f^{1-14} . \) If value
of \( (\boldsymbol{n}-\mathbf{1})=\mathbf{6} \) the configuration will be
of:
A. lanthanides
B. d- block
c. actinides
D. s - block


Which of the following is a property of nitrogen?
A. Supports combustion
B. Allows combustion
c. Supports but does not allow combustion
D. Neither supports nor allows combustion


The free energy for a reaction having \( \Delta H=31400 \mathrm{cal}, \Delta S= \)
32 cal \( K^{-1} \) mol \( ^{-1} \) at \( 1000^{\circ} \mathrm{C} \) is:
\( \mathbf{A} \cdot-9336 \mathrm{cal} \)
в. -7386 са\( l \)
\( \mathbf{c} .-1936 \mathrm{cal} \)
D. +9336 cal


The one which is the measure of the
central tendency is
A. mode
B. mean deviation
c. standard deviation
D. coefficient of correlation


An isosceles right angle triangle of side d is placed in a horizontal plane. A point charge \( \mathrm{q} \) is placed at a distance \( \mathrm{d} \) vertically above from one of the corner as shown in the figure. Flux of electric
field passing through the triangle is
A \( \cdot \frac{q}{36 \varepsilon_{0}} \)
в. \( \frac{q}{18 \varepsilon_{0}} \)
c. \( \frac{q}{24 \varepsilon_{0}} \)
D. \( \frac{q}{48 \varepsilon_{0}} \)


The excited state(n) of the atom is :


A high-altitude balloon is filled with 1.41
\( \times 10^{4} \mathrm{L} \) of hydrogen at a temperature of
\( 21^{\circ} \mathrm{C} \) and a pressure of 745 Torr. What is the volume of the balloon at a height of
\( 20 \mathrm{km}, \) where the temperature is \( -48^{\circ} \mathrm{C} \) and the pressure is 63.1 Torr.
A \( .1 .274 \times 10^{5} \mathrm{L} \)
В. \( 1.66 \times 10^{5} \mathrm{L} \)
c. \( 1.66 \times 10^{4} \mathrm{L} \)
D. None of these


There are only three hydrogen atoms in
a discharge tube. The analysis of spectrum shows that in all the hydrogen atoms, electrons are de-exciting from the fourth orbit. What should be the maximum number of spectral lines?
\( A \cdot 6 \)
B. 1
\( c \cdot 4 \)
D. 5


The value of current in two series \( L C R \)
circuits at resonance is same. Then
A. both circuits must be having same value of capacitance and inductance
B. in both circuits ratio of \( L \) and \( C \) will be same
c. for both the circuits \( X_{L} / X_{C} \) must be same at that frequency
D. both circuits must have same impedance at all frequencies


A uniform metal sphere of radius \( \boldsymbol{R} \) and
mass \( m \) is surrounded by a thin
uniform spherical shell of same mass
and radius \( 4 R \) The centre of the shell \( C \)
falls on the surface of the inner sphere.
Find the gravitational fields at points \( A \)
and B.


The most probable velocity for monoatomic gas is
A \( \cdot \sqrt{\frac{3 k T}{m}} \)
в. \( \sqrt{\frac{8 k T}{\pi m}} \)
c. \( \sqrt{\frac{2 k T}{m}} \)
D. zero


Assertion
The hierarchy includes seven obligate
categories.
Reason
Intermediate categories are used to make taxonomic position more informative.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The density of lake water is 1.3 g/cc. and
it contains 69 g of \( N a^{+} \) ions per kg of
water. What is molality of \( N a^{+} \) ion in the lake?
\( A \cdot 1 m \)
B. 3 \( m \)
\( c \cdot 2 m \)
D. \( 4 \mathrm{m} \)


Find the degree of the expression \( [x+ \) \( \left.\left(x^{3}-1\right)^{\frac{1}{2}}\right]^{5}+\left[x-\left(x^{3}-1\right)^{\frac{1}{2}}\right]^{5} \)


Tonic usually contains:
A. methanol
B. quinine
c. chloroform
D. ether


Assertion The angle between the two vectors \( (\hat{i}+ \)
\( \hat{\boldsymbol{j}}) \) and \( (\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}}) \) is \( \frac{\pi}{3} \) radian
Reason
Angle between two vectors \( \vec{A} \) and \( \vec{B} \) given by \( \boldsymbol{\theta}=\cos ^{-1}\left(\frac{\vec{A} \cdot \vec{B}}{A B}\right) \)
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


Calculate the force required to lift a load of \( 60 N, \) placed at a distance of
\( 3 m, \) from the fulcrum if the effort force
is applied at a distance of \( 6 \mathrm{cm} \) from
the fulcrum.
\( A .300 N \)
в. \( 3000 N \)
c. \( 1500 N \)
D. 30 \( N \)


What is a coefficient?
A. A whole number that appears in front of a formula in a balanced chemical equation
B. A whole number that appears as a subscript at the end of a formula in a balanced chemical equation
C. A whole number that appears as a subscript in front of a formula in a balanced chemical equation
D. A fraction that appears in front of a formula in a balanced chemical equation
E. A whole number that appears as a superscript at the end of a formula in a balanced chemical equation


In acidic medium the rate of reaction
between \( \left(B r O_{3}\right)^{-} \) and \( B r^{-} \) ion is given by the expression.
\( -\left[\boldsymbol{d}\left(\boldsymbol{B} \boldsymbol{r} \boldsymbol{O}_{3}^{-}\right) / \boldsymbol{d} \boldsymbol{t}\right]= \)
\( \boldsymbol{K}\left[\boldsymbol{B} \boldsymbol{r} \boldsymbol{O}_{3}^{-}\right]\left[\boldsymbol{B r}^{-}\right]\left[\boldsymbol{H}^{+}\right]^{2} . \) It means:
A. Rate constant of overall reaction is 4 sec\( ^{-1} \)
B. Rate of reaction is independent of the concentration of acid
C. The change in pH of the solution will not affect the rate
D. Doubling the concentration of \( H^{+} \) ions will increase the reaction rate by 4 times.


For magnification in spherical mirrors object height is :
A. Negative.
B. Positive.
c. For real images positive.
D. For virtual images negative


\( \int \frac{\sin x}{1+\cos ^{2} x} d x \)


Near point of an eye suffering from long sightedness is:
A. less than \( 25 \mathrm{cm} \)
B. greater than 25cm
c. equal to 25cm
D. infinity


Prove that:
\( 2 \sin ^{2} \frac{\pi}{6}+\operatorname{cosec}^{2} \frac{7 \pi}{6} \cos ^{2} \frac{\pi}{3}=\frac{3}{2} \)


A committee of two persons is selected from two men and two women. What is
the probability that the committee will
have no man


Choose the correct answer among the alternatives given :
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}-\boldsymbol{C H}_{3} \stackrel{[a l c K O \boldsymbol{H}]}{\longrightarrow} \)
\( B r \)
\( \boldsymbol{X} \frac{\text {peroxide}}{\boldsymbol{H B r}} \boldsymbol{Y} \frac{\text {acetone}}{\boldsymbol{N a I}} \boldsymbol{Z} \)
In the given reaction what will be the final product?
A. \( C H_{3} C H_{2} C H_{2} I \)
в. \( C H_{3} C H_{2} I \)
c. \( C H_{3} C H_{2} C H_{2} C H_{2} C H_{3} \)
D. \( C H_{3} C H_{2} C H I_{2} \)


When \( F e C l_{3} \) is ignited in an
atmosphere of pure oxygen, the following reaction takes place:
\( 4 F e C l_{3}(s)+3 O_{2}(g) \rightarrow \)
\( 2 F e_{2} O_{3}(s)+6 C l_{2}(g) \)
If 3 moles of \( F e C l_{3} \) are ignited in the
presence of 2 moles of \( O_{2} \) gas, how
much of which reagent is present in excess and therefore, remains
unreacted?
A. 0.33 mole \( F e C l_{3} \) remains unreacted
B. 0.67 mole \( F e C l_{3} \) remains unreacted
C. 0.25 mole \( O_{2} \) remains unreacted
D. 0.50 mole \( O_{2} \) remains unreacted


A vicinal diol has two alcoholic groups
present:
A. on the same carbon
B. on adjacent carbon atoms
c. anywhere along the carbon chain
D. none of the above


A particle starts with initial speed \( u \)
and retardation a to come to rest in
time t. The time taken to cover first half
of the total path travelled is


In a shotput event, an athlete throws the
shotput of mass \( 10 k g \) with an initial
speed of \( 1 m s^{1} \) at \( 45^{\circ} \) from a height
\( 1.5 m \) above ground. Assuming air resistance to be negligible and
acceleration due to gravity to be \( 10 m s^{2} \)
the kinetic energy of the shotput when it just reaches the ground will be:
A . 2.5 .5
в. \( 5.0 J \)
c. \( 52.5 J \)
D. \( 155.0 J \)


Let \( a, b, c \) be real numbers with \( a^{2}+ \)
\( b^{2}+c^{2}=1 \)
show that the equation \( \mid \begin{array}{ccc}\boldsymbol{a} \boldsymbol{x}-\boldsymbol{b} \boldsymbol{y}-\boldsymbol{c} & \boldsymbol{b} \boldsymbol{x}+\boldsymbol{a} \boldsymbol{y} & \boldsymbol{c} \boldsymbol{x}+ \\ \boldsymbol{b} \boldsymbol{x}+\boldsymbol{a} \boldsymbol{y} & \boldsymbol{-} \boldsymbol{a} \boldsymbol{x}+\boldsymbol{b} \boldsymbol{y}-\boldsymbol{c} & \boldsymbol{c} \boldsymbol{y}+ \\ \boldsymbol{c} \boldsymbol{x}+\boldsymbol{a} & \boldsymbol{c} \boldsymbol{y}+\boldsymbol{b} & \boldsymbol{-} \boldsymbol{a} \boldsymbol{x}-\boldsymbol{b}\end{array} \)
represents a straight line.


Assertion
The radio and TV signals from
broadcasting stations carry energy.
Reason
Electromagnetic waves are capable to
carry energy from one place to another.
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