A small spherical drop fall from rest in viscous liquid. Due to friction, heat is produced. The correct relation between the rate of production of heat and the radius of the spherical drop at terminal velocity will be
A \( \cdot \frac{d H}{d t} \propto \frac{1}{r^{5}} \)
в. \( \frac{d H}{d t} \propto r^{4} \)
c. \( \frac{d H}{d t} \propto \frac{1}{r^{4}} \)
D. \( \frac{d H}{d t} \propto r^{5} \)


A force \( \boldsymbol{F}=-\boldsymbol{K}(\boldsymbol{y} \hat{\boldsymbol{i}}-\boldsymbol{x} \hat{\boldsymbol{j}}), \) (where \( \boldsymbol{K} \) is
a positive constant) acts on a particle moving in the \( X Y \) -plane. Starting from the origin, the particle is taken along the positive \( X \) -axis to the plane
\( (a, 0) \) and then parallel to the \( Y \) -axis to the point \( (a, a) . \) The total work done by the force \( F \) on the particle is
A \( .-2 K a^{2} \)
B \( .2 K a^{2} \)
c. \( -K a^{2} \)
D. \( K a^{2} \)


Among the following statements, which
one is not correct?
A. Aspirin is both an analgesic and an antipyretic.
B. Ampicillin is a natural antibiotic.
c. sulphadiazine is a synthetic antibacterial
D. Some disinfectants can be used as antiseptics
at low concentration


In a city \( 20 \% \) of the total population is student community which is not employed, if the number of students who are unemployed is 14000 , then find the population of the city?
\( \mathbf{A} .56000 \)
B. 70000
c. 40000
D. 60000
E. None of these


If \( \boldsymbol{f}:[-\boldsymbol{2}, \boldsymbol{2}] \rightarrow \boldsymbol{R} \) is defined by \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{ll}\frac{\sqrt{1+e x}-\sqrt{1-e x}}{x} & \text { for }-2 \leq x< \\ \frac{x+3}{x+1} & \text { for } 0 \leq x \leq\end{array}\right. \)
is continuous on \( [-2,2], \) then \( e= \)
A \( \cdot \frac{2}{\sqrt{3}} \)
B. 3
\( c \cdot \frac{3}{2} \)
D. \( \frac{3}{\sqrt{2}} \)


In uniform circular motion
A. acceleration is variable.
B. acceleration is uniform.
C. the direction and magnitude of acceleration both vary.
D. if force applied is doubled in circular motion, then angular velocity becomes double.


The point of intersection of the line
joining the points (-3,4,-8) and (5,-6,4) with the \( X Y \) -plane is
\( \mathbf{A} \cdot\left(\frac{7}{3},-\frac{8}{3}, 0\right) \)
в. \( \left(-\frac{7}{3},-\frac{8}{3}, 0\right) \)
\( ^{\mathbf{c}} \cdot\left(-\frac{7}{3}, \frac{8}{3}, 0\right) \)
D. \( \left(\frac{7}{3}, \frac{8}{3}, 0\right) \)


Assertion
The images formed by total internal reflections are much brighter than those formed by mirrors or lenses
Reason

There is no loss of intensity in total
internal reflection.
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


Taking constant of integration as zero, find \( f(1) \) \( \int \frac{x e^{x}}{(x+1)^{2}} d x \)


\( 35 C l \) and \( _{17}^{37} C l \) are examples of ' \( X \) '. What \( 177^{\text {t }} \)
is ' \( \boldsymbol{X} \) '?
A. Isobars
B. Isotopes
c. Isotones
D. Isomers


Which of following forms net-like structure during bleeding?
A. Platelets
в. RВС
c. wвс
D. None of the above


Which of the following solution will not make the bulb glow?
A. Copper sulphate
B. Sodium chromate
c. Potassium dichromate
D. Sugar


Sector area of a circle in radians is
A \( \cdot 2 \times \frac{\theta}{2} r^{2} \)
в. \( \frac{\theta}{2} \times r^{2} \)
c. \( _{\pi \times \frac{\theta}{2} r^{2}} \)
D. \( _{2 \times \frac{\theta}{2} \pi r} \)


A liquid does not wet the solid surface if the angle of contact is then
A. zero
B . equal to \( 45^{\circ} \)
c. equal to \( 90^{\circ} \)
D. greater than \( 90^{\circ} \)


A lake receiving domestic sewage
shows
A. Drying up due to algal bloom
B. Increased fish production due to higher nutrient availability
C. Death of fish due to oxygen depletion
D. Increased food web organisation


The alkaline earth metal that has
greatest affinity for nitrogen is
A. sr
в. мв
\( c \cdot c a \)
D. Ba


If \( \boldsymbol{y}=\sec ^{-1}\left(\frac{\boldsymbol{x}^{2}+\mathbf{1}}{\boldsymbol{x}^{2}-\mathbf{1}}\right) \) then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=? \)
A \( \cdot \frac{-2}{\left(1+x^{2}\right)} \)
B. \( \frac{2}{\left(1+x^{2}\right)} \)
c. \( \frac{-1}{\left(1-x^{2}\right)} \)
D. none of these


toppr \( E \)
Q Type your question
field at \( t=0 \) and completely emerges
out at \( t=T \) sec. The current in the ring
varies as
A.
B.
\( c \)
D.


The IUPAC name for the complex
compound \( \boldsymbol{L} \boldsymbol{i}\left[\boldsymbol{A l} \boldsymbol{H}_{4}\right] \) is:
A. Lithium aluminium hydride
B. Hydride aluminium lithium (III)
C. Lithium tetrahydridoaluminate (III)
D. Llithium tetrahydridoaluminate (I)


Draw the graph of equation2 \( y+x=7 \)
and \( 2 x+y=8 \) on the same \( c o \)
ordination system. Write the pt of intersection.


If a back cell take 20 min to divide \( \& \) if
with this rate it take 10 hrs. To fill a cup
of cells. What time it will take to fill it
half?


State whether given statement is True or False
Sonar make use of ultrasound.
A. True
B. False


Carbon dioxide is associated with:
A . Elements
B. Mixture
c. compound
D. None of these


What is the difference in the greatest and the least fractions out of \( \frac{6}{7}, \frac{7}{8}, \frac{8}{9} \) and \( \frac{\mathbf{9}}{\mathbf{1 0}} \) ?
\( A \cdot \frac{3}{70} \)
в. \( \frac{1}{56} \)
c. \( \frac{1}{40} \)
D. \( \frac{1}{72} \)


An electron is moving with a speed of \( 10^{3} m / s \) in a straight line enters a
magnetic field where it experiences a
constant acceleration of \( 500 m / s^{2} \) in a direction opposite to its motion. The electron will come back to its initial
point after a time.
\( \mathbf{A} \cdot 2 \mathbf{s} \)
B. 4 s
c. \( 1 \mathrm{s} \)
D. 3s


A system absorbs \( 10^{3} \) cal of heat and
the system does \( 1677.3 J \) work. The
internal energy of the system increases by \( 2515 . J . \) The value of J is
A. \( 4.19 \mathrm{J} / \mathrm{cal} \)
в. 4.18 cal \( / J \)
c. \( 42 J / \) cal \( l \)
D. \( 420 J / c a l \)


Khadin is?
A. Earthen embankment down the slope
B. Check dam
C. Underground dam
D. Roof top water collecting system.


Which of the following is most covalent
\( ? \)
A \( . C u C l \)
в. \( N a C l \)
c. \( A g C l \)
D. \( A u C l \)


At 4: 24 p.m., how many degrees has the hour hand of a clock moved from its
position at noon?
A \( \cdot 135^{\circ} \)
B. 134
\( \mathrm{c} \cdot 133^{\circ} \)
D. \( 132^{\circ} \)


In Young's double slit experiment the distance between two slits is \( 2 m m \) and
screen is at a distance of \( 120 \mathrm{cm} \) from
the plane of slits. The smallest distance from the central maxima where the
bright fringe due to light of wavelength
\( 6500 A^{\circ} \) and \( 5200 A^{\circ} \) would coincide?
A \( .0 .156 \mathrm{cm} \)
B. \( 0.186 \mathrm{cm} \)
c. \( 0.486 \mathrm{cm} \)
D. \( 0.456 \mathrm{cm} \)


A wave travelling on a string at a speed of \( 10 \mathrm{m} / \mathrm{s} \) causes each particle of the string to oscillate with a time period of
\( 20 \mathrm{ms} \). what is the wavelength of the
wave?


\( \mathbf{f} \mathbf{\Delta}=\left|\begin{array}{ccc}\mathbf{1} & \mathbf{2} & \mathbf{3} \\ \mathbf{2} & \mathbf{0} & \mathbf{1} \\ \mathbf{5} & \mathbf{3} & \mathbf{8}\end{array}\right|, \) write the minor of the
elements \( a_{22} \)


A \( 100 \mathrm{W} \) bulb produces an electric field of \( 2.9 \mathrm{V} / \mathrm{m} \) at a point \( 3 \mathrm{m} \) away. If the bulb is replaced by \( 400 \mathrm{W} \) bulb without disturbing other conditions, then the electric field produced at the same point is
A \( .2 .9 \mathrm{V} / \mathrm{m} \)
в. \( 3.5 V / m \)
c. \( 4 V / m \)
D. \( 5.8 V / m \)


Secondary amines are derivatives of ammonia.
A. di-alky
B. alkyl-en
c. alk-en
D. none of the above


Starting from rest a particle is first
accelerated for time \( t_{1} \) with constant
acceleration \( a_{1} \) and then stops in time
\( t_{2} \) with constant retardation \( a_{2} . \) Let \( v_{1} \)
be the average velocity in this case and
\( s_{1} \) the total displacement. In the second
case
it is accelerated for the same time \( t_{1} \)
with constant acceleration \( 2 a_{1} \)
and come to rest with constant
retardation \( a_{2} \) in time \( t_{3} . \) If \( v_{2} \) is the
average velocity in this case and \( s_{2} \) the total displacement, then This question has multiple correct options
A \( \cdot v_{2}=2 v_{1} \)
В . \( 2 v_{1}<v_{2}<4 v_{1} \)
c. \( S_{2} 2=S_{1} \)
D. \( 2 S_{1}<S_{2}<4 S_{1} \)


If \( x \) is an even number then the
consecutive even number is
\( A \cdot x+1 \)
B. x+2
\( c \cdot 2 x \)
D. x-2


A piece of steel has a volume of \( 12 \mathrm{cm}^{3} \) and a mass of 96 g. Find its density in \( \mathrm{kg} / \mathrm{m}^{3} \)
Density \( =x \times 10^{3} k g / m^{3} . \) What is the
value of \( x ? \)
\( A \cdot 9 \)
B. 10
\( c \cdot 11 \)
D. 8


Which of the following acts as middle
man?
A. W.B.C
B. Plasma
c. Blood
D. Lymph


The sum of the squares of 2 numbers is
156. If the one number is 5 , the square of the other number is
\( \mathbf{A} \cdot 81 \)
в. 131
c. 11
D. 123


Simplify:
\( \frac{\mathbf{2 . 3} \times \mathbf{2 . 3}}{\mathbf{2 . 3} \times \mathbf{2 . 3 - 2} \times \mathbf{2 . 3} \times \mathbf{2 . 3}+\mathbf{2 . 3} \times \mathbf{2 . 3}+} \)
\( A \)
B. 3.24
c. 1.96
D. 5.29


If the 3 rd and the sth term of an AP are 4
and - 8 respectively, which term of this AP is zero?


How many peroxy linkages are present
in \( C r O_{5} ? \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c .3 \)
D. 4
E . 5


Assertion
According to Dobernier's, a group of three similar elements arranged in their increasing atomic weights so that atomic weight of middle is equal to the
arithmetic mean of the other two
elements.
Reason
Atomic weight is equal to one twelfth of mass of a carbon atom.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


The correct order of increasing \( \boldsymbol{C}-\boldsymbol{O} \)
bond length in \( C O, C O_{3}^{-2} \) and \( C O_{2} \) is:
A \( \cdot C O_{3}^{-2}<C O_{2}<C O \)
в. \( C O_{2}<C O_{3}^{-2}<C O \)
c. \( C O<C O_{3}^{-2}<C O_{2} \)
D. \( C O<C O_{2}<C O_{3}^{-2} \)


Which of the following induces morphogenesis in tissue culture?
A . Gibberellin
B. Cytokinin
\( c \cdot \) ।АА
D. Ethylene


\( 10^{-3} \) mol of \( C u S O_{4} \cdot 5 H_{2} O \) is
introduced in a \( 1.9 L \) vessel maintained
at a constant temperature of \( 27^{\circ} \mathrm{C} \) containing moist air at relative
humidity of \( 12.5 \% . \) What is the final molar composition of solid mixture?
For \( \boldsymbol{C u} \boldsymbol{S O}_{4} \cdot \boldsymbol{5} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{s}) \rightleftharpoons \boldsymbol{C u} \boldsymbol{S} \boldsymbol{O}_{4}(\boldsymbol{s})+ \)
\( \mathbf{5} H_{2} O(\boldsymbol{g}), \boldsymbol{K}_{p}(\boldsymbol{a} \boldsymbol{t m})=\mathbf{1 0}^{-10} . \) Take vapor
pressure of water at \( 27^{\circ} \mathrm{C} \) as 28 torrs.


Calculate the \% change in temperature
if \( \% \) change in volume of heat is \( 10 \% \)


Dobereiner was the first person to
illustrate the relationship between the of elements and
their properties.
A. atomic masses
B. electron negativity
c. molecular masses
D. number of protons


For a dilute solution, mole fraction of solute is given as \( (n= \) no. of moles of solute and \( N=\text { no. of moles of solvent }) \)
A \( \cdot \frac{n}{N} \)
в. \( \frac{N}{n} \)
c. \( \frac{N}{n+N} \)
D. Both B and C


Solubility of \( K B r \) shows slow rise in
solubility with increase in temperature
A. True
B. False


Differentiate the following functions
with respect to \( x: \) \( \mathbf{f} \boldsymbol{y}=\mathbf{s e c}^{-1}\left(\frac{\boldsymbol{x}+\mathbf{1}}{\boldsymbol{x}-\mathbf{1}}\right)+ \)
\( \sin ^{-1}\left(\frac{\boldsymbol{x}-\mathbf{1}}{\boldsymbol{x}+\mathbf{1}}\right), \boldsymbol{x}>\mathbf{0} . \) Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \)


A star like body with a long tail is called:
A. Comet
B. Meteor
c. Meteorite
D. Pluton


The essential organs of the flower are
A. Calyx and Corolla
B. Androecium and Gynoecium
c. calyx and Androecium
D. Corolla and Gynoecium


Explain the cleaning action of soap. Why
do soap not work in hard water?


Which organ is part of circulatory system but does not take part in
pumping?
A . Heart
B. Liver
c. spleen
D. Kidney


Evaluate
\( \left|\begin{array}{ccc}\cos \alpha \cos \beta & \cos \alpha \sin \beta & -\sin \alpha \\ -\sin \beta & \cos \beta & 0 \\ \sin \alpha \cos \beta & \sin \alpha \sin \beta & \cos \alpha\end{array}\right| \)


Solve for \( \boldsymbol{x}: \cos ^{-1}\left(\frac{\boldsymbol{x}^{2}-\mathbf{1}}{\boldsymbol{x}^{2}+\mathbf{1}}\right)+ \)
\( \frac{\mathbf{1}}{\mathbf{2}} \tan ^{-1} \frac{\mathbf{2} \boldsymbol{x}}{\mathbf{1}-\boldsymbol{x}^{2}}=\frac{\mathbf{2} \boldsymbol{\pi}}{\mathbf{3}} \)


Maximum area of rectangle whose two
sides are \( \boldsymbol{x}=\boldsymbol{x}_{0}, \boldsymbol{x}=\boldsymbol{\pi}-\boldsymbol{x}_{0} \) and which
is inscribed in a region bounded by \( \boldsymbol{y}= \)
\( \sin x \) and \( x- \) axis is obtained, when \( x_{0} \in \)


\( \mathbf{a}=\left|\begin{array}{lll}\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} \\ \boldsymbol{c} & \boldsymbol{a} & \boldsymbol{b} \\ \boldsymbol{b} & \boldsymbol{c} & \boldsymbol{a}\end{array}\right|, \) then the value of
\( \left|\begin{array}{ccc}a^{2}-b c & b^{2}-c a & c^{2}-a b \\ c^{2}-a b & a^{2}-b c & b^{2}-c a \\ b^{2}-c a & c^{2}-a b & a^{2}-b c\end{array}\right| \)
\( A \cdot \Delta^{2} \)
B \( .2 \Delta^{2} \)
\( c \cdot \Delta^{3} \)
D. none of these


\( \mathrm{O}=\langle\overrightarrow{\quad}\rangle=\mathrm{O}+\mathrm{HBr} \longrightarrow(\mathrm{A}) \)
\( A \)
B.
\( c \)
D.


In a right angled triangle, if the square of the hypotenuse is twice the product of the other two sides, then one of the
angles of the triangle is:
A \( \cdot 15^{\circ} \)
B . \( 30^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 60^{\circ} \)


Check the existance of the limit \( \lim _{x \rightarrow 0} \frac{|x|}{x} \)


A crack in a glass vessel often shines
like a mirror because of
A. Total reflecting surface
B. Reflection
c. Refraction
D. All


Which of the following pollutant is released in larger quantity from the exhaust emission of a petrol/diesel automobile?
A . \( c o \)
B. \( \mathrm{cO}_{2} \)
c. \( \mathrm{NO}_{2}, \mathrm{SO}_{2} \) and \( \mathrm{Pb} \)
D. Hydrocarbons


In the given diagram CE is parallel to
AD and the measures of two angles at \( \mathrm{B} \)
and \( C \) have been indicated.Then \( \angle D A B \)
is equal to
\( A \cdot 30 \)
B. 35
\( c \cdot 40 \)
D. cannot be determined


\( \boldsymbol{H}_{3} \boldsymbol{C}-\boldsymbol{C H}_{2}-\underset{\boldsymbol{H}}{\boldsymbol{C}}^{\boldsymbol{C H}_{3}}-\boldsymbol{C H}_{2} \boldsymbol{C H}_{3} \)
Maximum numbers of isomers(during stereoisomers) that are possible on monochlorination of following compound is:
A .2
B. 4
\( c \cdot 6 \)
D.


Given: \( 1= \) Natural selection; \( 2= \)
Variations and their inheritance; \( 3= \)
Survival of the fittest; \( 4= \) Struggle for existence.

According to Darwinism, which of the following represents the correct sequence of events in the origin of new
species?
A .3,4,1,2
в. 2,3,1,4
c. 1,2,3,4
D. 4,2,3,1


Solve:
\( \frac{d y}{d x}=x+1 ; \) find \( y \) when \( x=2 \)


Prove that \( : \tan ^{-1}\left[\frac{6 x-8 x^{3}}{1-12 x^{2}}\right]- \)
\( \tan ^{-1}\left[\frac{4 x}{1-4 x^{2}}\right]=\tan ^{-1} 2 x,|2 x|<\frac{1}{\sqrt{3}} \)


The graph drawn between pressure and
volume in Boyle's law experiment is
shown in figure for different masses of
same gas at same temperature then
\( \mathbf{A} \cdot m_{2}>m_{1} \)
В \( \cdot m_{1}>m_{2} \)
\( \mathbf{c} \cdot m_{1}=m_{2} \)
\( \mathbf{D} \cdot m_{1}^{3}>m_{2} \)


If \( \Delta A B C \sim \Delta D E F, B C=3 c m E F= \)
\( 4 c m \) and area of \( \Delta A B C=54 c m^{2} \) then
find the area of \( \Delta D E F ? \)


Find the ordinate of point whose abcissa is 4 and which is at a distance
5 from (0,5)
A .1,2
B. 2,4
c. 2,8
D. None


When Ammonical common salt solution
is saturated with carbon dioxide we
obtain ?
A. \( N H_{4} H C O_{3} \)
B. \( \left(N H_{4}\right)_{2} C O_{3} \)
с. \( _{N a H C O_{3}} \)
D. \( N a_{2} C O_{3} \)


The smallest value of \( x^{2}-3 x+3 \) in the interval \( \left(-3, \frac{3}{2}\right) \) is
A \( \cdot \frac{3}{4} \)
B. 5
\( c .-15 \)
D . -20


\( K_{a} \) for \( H C N \) is \( 5 \times 10^{-10} \) at \( 25^{\circ} C . \) For
maintaining a constant \( p H=9 \), the volume of \( 5 M K C N \) solution required
to be added to \( 10 \mathrm{ml} \) of \( 2 M H C N \)
solution is:
\( \left[\text { Given } \log _{10} 5=0.69: \) antilog \right.
\( (-0.3010)=0.5] \)
A. \( 4 m l \)
B. 2 ml
c. \( 7.95 \mathrm{ml} \)
D. \( 9.3 \mathrm{ml} \)


If \( a x+b\left(\sec \left(\tan ^{-1} x\right)\right)=c \) and \( a y+ \)
\( b\left(\sec \left(\tan ^{-1} y\right)\right)=c, \) then the value of
\( \frac{\boldsymbol{x}+\boldsymbol{y}}{\mathbf{1}-\boldsymbol{x} \boldsymbol{y}} \) is,
A \( \cdot \frac{2 a b}{a^{2}-c^{2}} \)
в. \( \frac{2 a c}{a^{2}-c^{2}} \)
c. \( \frac{c^{2}-b^{2}}{a^{2}+b^{2}} \)
D. none of these


\( \underbrace{E}_{i=} \)


For the displacement-time graph shown
in the figure above, find the velocity at
point \( \mathbf{A} \)
A. \( 4 \mathrm{m} \mathrm{s}^{-1} \)
B. 3 \( \mathrm{m} \) s \( ^{-1} \)
\( c \cdot 5 m s^{-} \)
D. \( 6 \mathrm{m} \) s \( ^{-1} \)


How long does it take for the ball to
strike the ground?
A . \( 4.52 s \)
B . \( 5 s \)
\( c \cdot 6 s \)
D. \( 7 s \)


How much 5 is less than -2 is.
\( A \cdot 3 \)
в. -3
\( c \cdot-7 \)
D. 7


What do you mean by motion? Explain different type of motion.


Which of the following cannot be used in electronic devices?
A. Aluminium gallium arsenide
B. Indium gallium arsenide
c. Gallium arsenide
D. Quasicrystals.


The maximum current in the inductor
is:
A \( \cdot \frac{3 V_{0}}{2} \sqrt{\frac{3 C}{L}} \)
3. \( V_{0} \sqrt{\frac{3 C}{L}} \)
\( ^{c} \cdot 2 V_{0} \sqrt{\frac{3 C}{L}} \)
\( v_{0} \sqrt{\frac{C}{I}} \)


If \( y=\tan ^{-1} \sqrt{\frac{1-\cos x}{1+\cos x}}, \) then for \( 0< \)
\( \boldsymbol{x}<\frac{\boldsymbol{\pi}}{\mathbf{2}}, \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}= \)
\( \mathbf{A} \cdot 2 \sec ^{2}(x / 2) \)
B \( \cdot \frac{1}{2} \sec ^{2}(x / 2) \)
\( c \cdot \frac{1}{2} \)
D. \( -\frac{1}{2} \sec ^{2}(x / 2) \)


A solid ball of volume \( V \) is dropped in a viscous liquid. It experiences a viscous force F. If the solid ball of volume \( 2 V \) of
same material is dropped in the same fluid, then the viscous force acting on it will be
\( \mathbf{A} \cdot n F / 2 \)
B. \( F / 2 \)
\( c .2 F \)
D. \( 2 n F \)


Let \( S \) be a square with sides of length \( x \)
If we approximate the change in size of the area of \( S \) by \( \left.h \cdot \frac{d A}{d x}\right|_{x=x_{0}}, \) when the sides are changed from \( x_{0} \) to \( x_{o}+h \)
then the absolute value of the error in
our approximation, is
\( \mathbf{A} \cdot h^{2} \)
B. \( 2 h x_{0} \)
c. \( x_{0}^{2} \)
D. \( h \)


Consider the van der Waals constants, \( a \)
and \( b, \) for the following gases.
Gas What is and \( A r \) \( N e \)
\( \boldsymbol{K} \boldsymbol{r} \)
\( \mathrm{a} / \mathrm{catm} \)
\( d m^{6} m o l^{-2} \)
5.1
0.2
1.3
\( \begin{array}{lll}\text { 3.2 } & \text { 1.7 } & \text { 1.0 }\end{array} \) \( \mathrm{b} / \mathrm{c} \)
\( 10^{-2} \mathrm{dm}^{3} \mathrm{mol}^{-1} \)
Which gas is expected to have the highest critical temperature?
\( \mathbf{A} \cdot K r \)
B. \( N e \)
c. \( A r \)
D. \( X e \)


Cooking oil should not be thrown down
the drain because
A. They do not allow free flow of oxygen
B. They do not allow bacteria to decompose waste.
c. They block the drainage pipes.
D. None of the above


Consider \( \boldsymbol{f}: \boldsymbol{N} \rightarrow \boldsymbol{N}, \boldsymbol{g}: \boldsymbol{N} \rightarrow \boldsymbol{N} \)
defined as \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{2} \boldsymbol{x}, \boldsymbol{g}(\boldsymbol{x})=\mathbf{3} \boldsymbol{x}+\boldsymbol{4} \)
find \( \boldsymbol{f} \boldsymbol{o} \boldsymbol{g}(\boldsymbol{x}) \)


The armature of de motor has \( 20 \Omega \)
resistance .It draws current of 1.5
ampere when run by 220 volts dc supply. The value of back e.m.f. induced in it will be
\( A \cdot 190 V \)
B. 150 V
c. \( 170 v \)
D. \( 120 \mathrm{V} \)


Calculate the amount and compound interest for Rs. 10,000 for \( 1 \frac{1}{2} \) years at \( 5 \% \) compounded half-yearly.


The activity present after 50 minutes.
A \( \cdot 4.1 \times 10^{4} B q \)
в. \( 3.6 \times 10^{5} \) В \( q \)
c. \( 7.5 \times 10^{5} \) В \( q \)
D. \( 1.4 \times 10^{6} \) В \( q \)


\( \boldsymbol{P h}-\boldsymbol{C} \equiv \boldsymbol{C}-\boldsymbol{C H}_{3} \stackrel{\boldsymbol{H} \boldsymbol{g}^{2+} / \boldsymbol{H}^{+}}{\longrightarrow} \boldsymbol{A} \)
The product A is:
\( A \)
в.
\( c \)
D.


If \( \boldsymbol{E} \) and \( \boldsymbol{F} \) are independent events such
that \( \boldsymbol{P}(\boldsymbol{E})=\mathbf{0 . 7} \) and \( \boldsymbol{P}(\boldsymbol{F})=\mathbf{0 . 3}, \) then \( \mathrm{P} \)
\( (\boldsymbol{E} \cap \boldsymbol{F}) \)
A . 0.4
B.
c. 0.21
D. None


The top of the atmosphere is about
\( 400 k V \) with respect to the surface of earth, corresponding to an electric field that decreases with altitude. Near the
surface of earth the field is about
\( 100 V m^{-1}, \) but still don't get an electric
shock, as we set out of our houses in to open because (assume the house is
free from electric field)
A. our body is a perfect insulator
B. our body and ground form an equipotential surface
c. the original euipotential surfaces of open air remain same
D. none of these


What describes a non-spontaneous
reaction?
A. Positive \( \Delta H \)
B. Negative \( \Delta H \)
c. Positive \( \Delta G \)
D. Negative \( \Delta G \)


Assertion
In YDSE, if separation between the slits is less than wavelength of light, then no interference pattern can be observed.
Reason

For interference pattern to be observed, light sources have to be coherent.
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


Position of Q is
A. Interior of curve
B. Exterior of curve
c. on the curve
can not be said


\( f\left(\begin{array}{ccc}2 & 3 & 4 \\ 5 & -3 & 8 \\ 9 & 2 & 16\end{array}\right], \) then trace of \( A \) is
A . 17
B. 25
\( c \cdot 8 \)
D. 15


One milligram of matter convert into
energy will give
A. 90 joule
B. \( 9 \times 10^{3} \) joule
c. \( 9 \times 10^{5} \) joule
D. \( 9 \times 10^{10} \) joule


Which of the following is NOT a physical process of digestion?
A. Deglutition
B. Churning
c. Peristalsis
D. Emulsification


In the modern periodic table, periods and groups are given. Periods and Groups indicate:
A. rows and Columns
B. columns and Rows
c. only rows
D. only columns


Find the sum of the series \( 3+7+11+ \)
\( 15+19+\ldots \) up to 10 terms
A . 210
в. 201
\( c \cdot 120 \)
D. 102


Picric acid is a yellow coloured compound. Its chemical name
is
A. m-nitrobenzoic acid
B. 2,4,6 -trinitropheno
c. 2,4,6 -tribromophenol
D. p-nitrophenol.


Enzymes concerned with transfer of electrons are
A. Hydrolase
B. Dehydrogenase
c. Transaminase
D. Deoxygenase


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


According to the graph, what are the
three biggest threats to the biodiversity
of the Mediterranean Sea?
A. Aquaculture, invasions, and climate change
B. Exploitation, eutrophication, and pollution
C. Exploitation, habitat degradation, and pollution
D. Exploitation, habitat degradation, and climate change
E. Maritime traffic, eutrophication, and invasions


\( \left\{x^{2}+10 x+25\right\} \div(x+5) \)


Two sound waves move in the same
direction in the same medium. The
pressure amplitude of the waves are equal but the wavelength of the first wave is double that of the second. Let
the average power transmitted across a
cross section by the two waves be \( \boldsymbol{P}_{1} \)
and \( P_{2} \) and their displacement
amplitudes be \( s_{1} \) and \( s_{2} \) then
\( A \cdot P_{1} / P_{2} \)
B . \( P_{1} / P_{2}=2 \)
c. \( s_{1} / s_{2}=1 / 2 \)
D. \( s_{1} / s_{2}=2 / 1 \)


Q Type your question
fixed to a mount B of mass \( m_{2}(\text { fig }) . \) A
constant horizontal force \( F \) is applied to
the end \( \mathrm{K} \) of a light thread tightly wound on the cylinder. The friction between the
mount and the supporting horizontal plane is assumed to be absent. Find:
(a) the acceleration of the point \( K \)
(b) the kinetic energy of this system
seconds after the beginning of motion.
\( ^{\mathbf{A}} \cdot_{a_{k}}=\frac{F\left(3 m_{1}+2 m_{2}\right)}{2 m_{1}\left(m_{1}+m_{2}\right)} ; K \cdot E=\frac{1}{2} \frac{F^{2}\left(3 m_{1}+m_{2}\right)}{m_{1}\left(m_{1}+m_{2}\right)} t^{2} \)
B. \( a_{k}=\frac{F\left(3 m_{1}+2 m_{2}\right)}{m_{1}\left(m_{1}+m_{2}\right)} ; K \cdot E=\frac{1}{2} \frac{F^{2}\left(3 m_{1}+2 m_{2}\right)}{m_{1}\left(m_{1}+m_{2}\right)} t^{2} \)
\( a_{k}=\frac{F\left(3 m_{1}+2 m_{2}\right)}{2 m_{1}\left(m_{1}+m_{2}\right)} ; K \cdot E=\frac{1}{2} \frac{F^{2}\left(3 m_{1}+2 m_{2}\right)}{m_{1}\left(m_{1}+m_{2}\right)} t^{2} \)
\( ^{\mathrm{D}} a_{k}=\frac{F\left(3 m_{1}+2 m_{2}\right)}{m_{1}\left(m_{1}+m_{2}\right)} ; K \cdot E=\frac{1}{2} \frac{F^{2}\left(3 m_{1}+m_{2}\right)}{m_{1}\left(m_{1}+m_{2}\right)} t^{2} \)


Give laboratory method for preparation of phosphine.


a) Define atomic mass unit
b) Distinguish between molecular mass
and molar mass
c) Give an example of
(i) diatomic, (ii) triatomic molecule of compounds.


A charged particle oscillates about its mean (equilibrium) position with a frequency of \( 10^{9} H z . \) What is the
frequency of the electromagnetic waves produced by the oscillator?


If the point object is moved away from
mirror normal to screen then
A. fringe width will increase
B. fringe width will decrease
c. fringe width will first increase then decrease
D. Remain unchanged


Which of the following statements
is/are correct for potentiometer circuit?
A. Sensitivity doesn't depend on the length of the potentiometer wire.
B. Sensitivity is inversely proportional to potential difference applied across the potentiometer wire.
C. Accuracy of potentiometer can be increased, only by increasing length of the wire.
D. Range is independent of potential difference applied across the potentiometer wire.


The sides of a triangle \( A B C \) are
positive integers. The smallest side has
length \( l . \) What of the following
statements is true?
A. The area of ABC is always a rational number
B. The area of ABC is always an irrational number
c. The perimeter of ABC is an even integer.
D. The information provided is not sufficient to conclude any of the statements A, B or C above


Which statement(s) is/are not correct
about the reaction?
\( \boldsymbol{H}_{2} \boldsymbol{O}_{2}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{2} \boldsymbol{I}^{-}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{2} \boldsymbol{H}^{+}(\boldsymbol{a} \boldsymbol{q}) \rightarrow \)
\( \boldsymbol{I}_{2}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{O}(l) \boldsymbol{I}_{2}(\boldsymbol{a} \boldsymbol{q})+ \)
\( \mathbf{2} N a_{2} S_{2} O_{3} \rightarrow N a_{2} S_{4} O_{6}+2 N a I ? \)
This question has multiple correct options
A. The \( I_{2} \) formed is consumed completely in the second state is confirmed by addition of starch just before its complete consumption
B. The reaction process is called clock reaction because the appearance of blue colour on addition of starch is like an alarm given by clock
c. Sulphur is oxidised whereas iodine is oxidised and reduced during whole process
D. \( H_{2} O_{2} \) acts as reducing agent


A sphere is rolled on a rough horizontal
surface. It gradually slows down and stops. The force of friction tries to
This question has multiple correct options
A. decreases the linear velocity.
B. increase the angular velocity.
c. increase the linear momentum
D. decreases the angular velocity


Assertion
For the reaction \( R C l+N a O H(a q) \rightarrow \)
ROH \( + \) Na \( C l \), the rate of reaction is
reduced to half on reducing the concentration of RCl to half.
Reason
The rate of the reaction is represented by k[RCl], i.e., it is a first order reaction.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


The boiling point \( T_{b}^{*} \) of a solvent becomes \( T_{b} \) on addition of \( X_{1} \) mole
fraction of solute. Heat of vaporisation
of solvent is \( \Delta \boldsymbol{H}_{\boldsymbol{v} \boldsymbol{a} \boldsymbol{p}} . \) The relation
between elevation in b.pt. \( \Delta T_{b}\left(=T_{b}-\right. \)
\( \left.T_{B}^{*}\right) \) can be given by:
\( \frac{\Delta T_{b}}{T_{b} \times T_{b}^{*}}=-\frac{R I n X_{1}}{\Delta H_{v a p}} \)
A graph plotted between \( \log _{10} X_{1} \) vs. \( \frac{1}{T_{b}} \) gives:
A.
\[
\text { straight line with slope } \frac{R}{\Delta H_{v a p}} \text { and intercept } T_{b}^{*}
\]
B. a straight line with slope \( \frac{2.303 R}{\Delta H_{v a p}} \) and intercept \( \frac{1}{T_{b}} \)
c. a straight line with slope \( \frac{\Delta H_{v a p}}{2.303 R} \) and intercept \( \frac{1}{T_{b}^{*} \times 2.303} \)
D. a straight line with slope \( \frac{\Delta H_{v a p}}{2.303 R} \) and intercept \( -\frac{\Delta H_{v a p}}{2.303 R T_{b}^{*}} \)


A car is travelling at \( 30 \mathrm{m} / \mathrm{s} \) on a circular road of radius \( 300 \mathrm{m} \). It is
increasing its speed at the rate of \( 4 m / s^{2} . \) The acceleration of the car is
A \( \cdot 3 m / s^{2} \)
B. \( 4 m / s^{2} \)
c. \( 5 m / s^{2} \)
D. \( 1 \mathrm{m} / \mathrm{s}^{2} \)


Out of the three characteristics,
monocots show
A. I only
B. II only
c. I and ॥
D. I and III
E . II and III


Determine the values of \( x \) and \( y \)
A .2,5
B . 2,4
\( \mathrm{c} \cdot 1,5 \)
D. 1,3


If \( \left|\frac{z_{1}}{z_{2}}\right|=1 \) and \( \arg \left(z_{1} z_{2}\right)=0, \) then
A \( \cdot z_{1}=z_{2} \)
B . \( \left|z_{2}\right|^{2}=z_{1} z_{2} \)
\( \mathbf{c} \cdot z_{1} z_{2}=1 \)
D. None of these


Coefficient of \( \boldsymbol{x}^{r} \) in \( \mathbf{1}+(\mathbf{1}+\boldsymbol{x})+(\mathbf{1}+ \)
\( x)^{2}+\ldots \ldots+(1+x)^{n} \) is
A. \( ^{n+3} C_{r} \)
B. \( ^{n+1} C_{r+1} \)
\( \mathbf{c} \cdot^{n} C_{r} \)
D. \( (n+2) C_{r} \)


Semicircles are drawn outside by taking every side of regular hexagon as a diameter. The perimeter of hexagon is \( 60 \mathrm{cm} . \) Find the area of complete figure formed as such. \( (\pi=3.14)(\sqrt{3}=1.73) \)
A \( .495 \mathrm{cm}^{2} \)
B. 259.5cm \( ^{2} \)
c. \( 235.5 \mathrm{cm}^{2} \)
D. \( 695.5 \mathrm{cm}^{2} \)


To which organ does femoral artery supply blood
A. Dorsal part of thighh
B. All parts of hind limb
c. Ventral part of hind limb
D. Rectum


The diagram shows four different cells. Which cells provide a large surface area for absorption?
A . 1 and 2
B. 1 and 3
\( c \cdot 2 \) and 4
D. 3 and


The distance between the lower and
upper fixed points of a Fahrenheit
thermometer is \( 90 \mathrm{mm} \). If mercury rises \( 30 \mathrm{mm} \) above the lower fixed point then find the corresponding temperature.
A \( \cdot 65^{\circ} \)
В \( \cdot 92^{\circ} \)
\( \mathbf{c} \cdot 62^{\circ} F \)
D. \( 60^{\circ} \mathrm{F} \)


An equilateral triangle whose each side
is \( 4.5 \mathrm{cm} . \) How many lines of symmetry
does it has????????
\( A \cdot 3 \)
B. 2
\( c \)
D. infinite


Which of the following ray diagrams are
correct?
This question has multiple correct options
\( A \)
в.
\( c \)
D.


The product of photosynthesis is
transported from source of production
to the storage organs through
A. Palisade tissue
B. Phloem tissue
c. spongy tissue
D. xylem tissue


Smith invested \( \$ 5000 \) for two years. For
the first year, the rate of interest was \( 7 \% \) and the second year it was \( 8.5 \% \)
How much interest did he earn at the
end of the two year period?
A . \( \$ 804.75 \)
в. \( \$ 604.54 \)
\( c . \$ 304.54 \)
D. None of these


Under 3 atm, 12.5 litres of a certain gas
mass 15 g. The average speed of the
gaseous molecules is \( 8.03 \times \)
\( 10^{n} \) cmsec\( ^{-1} \). The value of \( n \) is


The kinetic energy of \( 2.8 g \) of nitrogen
\( \operatorname{gas} \operatorname{at} 127^{\circ} C \) is nearly
A \( .2 \times 249.3 J \)
В. \( 2 \times 200.4 J \)
C . \( 2 \times 25 J \)
D. \( 20.5 J \times 2 \)


One mapping is selected at randon from
all mappings of the set \( S= \)
\( \{1,2,3, \dots,, n\} \) into itself. If the
probability that mapping is one-one is \( 3 / 32 \) then the value of \( n \) is
A .2
B. 3
\( c \cdot 4 \)
D. None of these


A piece of wire of resistance \( 4 \Omega \) is bent
through \( 180^{\circ} \) at its mid point and the
two halves are twisted together, then
resistance is :
A . \( 1 \Omega \)
B. 2\Omega
c. \( 5 \Omega \)
D. 8\Omega


Consider the function \( \boldsymbol{f}(\boldsymbol{x})= \)
\[
\begin{array}{cl}
\sqrt{\boldsymbol{x}} \ln \boldsymbol{x} \text { when } & \boldsymbol{x}>\mathbf{0} \\
\mathbf{0} \text { for } & \boldsymbol{x}=\mathbf{0}
\end{array}
\]
Let the inflection points of the graph of
\[
\boldsymbol{y}=\boldsymbol{f}(\boldsymbol{x}) \text { be } \boldsymbol{x}=\boldsymbol{k} \text { .Find } \boldsymbol{k} ?
\]


Why do the passengers fall forward when a fast moving bus stops suddenly?


In our number system the base is ten. If the base were changed to four you would count as follows:
\( 1,2,3,10,11,12,13,20,21,22,23,30, \dots \)
The twentieth number would be:
A . 20
B. 38
c. 44
D. 104
E. 110


Use of charkha was popularized by Mahatma Gandhi as part of the Independence movement.
A. True
B. False


The relative atomic mass of an element \( A \) is \( 16.2 . \) There are two isotopes \( _{8}^{16} A \) and \( _{8}^{18} A \) of the element. Calculate the percentage of \( _{8}^{16} A \) present in the
element.
A. 90\%
в. 60 \%
c. \( 45 \% \)
D. 80\%


What should be subtracted from \( x^{3}- \)
\( 7 x^{2}+17 x+17 \) so that the difference is
a multiple of \( x-3 ? \)
A . 5
B. 32
\( c \cdot 7 \)
D. 43


How can we change a camera from \( \boldsymbol{F} / \mathbf{4} \)
\( \operatorname{to} F / 5.6 ? \)
A. Increase the aperture to 2 time keeping the focal distance constant
B. Increase the aperture to \( \sqrt{2} \) time keeping the focal distance constant
C . Increase the aperture to \( \frac{1}{2} \) time keeping the focal
distance constant
D. Increase the aperture to \( \frac{1}{\sqrt{2}} \) time keeping the focal
distance constant


In the figure at right, \( A B \) and \( C D \) are
straight lines through the centre 0 of a
circle. If \( \angle A O C=98^{\circ} \) and \( \angle C D E= \)
\( \mathbf{3 5}^{\circ} \)
Find (i) \( \angle D C E \)
(ii) \( \angle A B C \)


Find the remainder using remainder
theorem, when:
\( x^{3}-a x^{2}-5 x+2 a \) is divided by \( x-a \)


Metal X form 2 oxide. Formula of 1 \( ^{s t} \) is
\( X O_{2} 1^{s t} \) oxide contain \( 50 \% O_{2} . \) If \( 2^{n d} \)
oxide contain \( 60 \% O_{2} \). Formula of \( 2^{n d} \)
oxide?
A. \( X_{2} O \)
в. \( X O_{3} \)
\( c \cdot X_{2} O_{3} \)
D. \( X_{3} O_{2} \)


Two Faraday of electricity is passed
through a solution of \( C u S O_{4} . \) The mass of copper deposited at the cathode is
at. mass of \( \mathrm{Cu}=63.5 \text { amu }) \)
\( A \cdot O g \)
в. \( 63.5 \mathrm{g} \)
\( c \cdot 2 g \)
D. 127 g


In an expression of the equilibrium constant, units for concentrations are:
A. mol/mL
B. mol/L
\( c \cdot g / L \)
D. gram-equivalents/L


Capitulum is considered most perfect (advanced) type of inflorescence because aggregation of florets ensures
A. Enhancement of attraction
B. Maximum prorection of flowers
c. Pollination of many flowers in a single visit by insects
D. All of the above


If \( g \) is inverse function of \( f \) where
\( f(x)=\int_{0}^{\pi} \frac{1}{\sqrt{1+t^{2}}} d t \quad \) and
\( \int g\left(g^{\prime}(x)\right)^{2} d x=\frac{\left[1+(g(x))^{\alpha}\right]^{\beta}}{\gamma}+c \)
Then the value of \( \alpha \beta \gamma \) is equal to [where \( \boldsymbol{\alpha}, \boldsymbol{\beta}, \boldsymbol{\gamma} \in \boldsymbol{R}] \)
A . 9
B. 6
\( c .3 \)
D.


The width of B-DNA is
each turn of its helix has
nucleotides.
A. 34 A; 11
B. 20 \( \dot{A} ; 12 \)
c. \( 40 \AA ; 8 \)
D. \( 20 \AA ; 10 \)


The DNA strands are antiparallel because of the presence of
A. H-bonds
B. Peptide bonds
c. Disulphide bonds
D. Phosphate-diester bonds
E. None of the above


A circular disc of area \( A_{1} \) is given with
its radius as diameter of a circular disc
of area \( A_{2} \) is cut out of it. The area of the
remaining disc is denoted by \( A_{3} . \) Then
\( \mathbf{A} \cdot A_{1} A_{3}<16 A_{2}^{2} \)
B. \( A_{1} A_{3}>16 A_{2}^{2} \)
\( \mathbf{c} \cdot A_{1} A_{3}=16 A_{2}^{2} \)
D. \( A_{1} A_{3}>2 A_{2}^{2} \)


Very short answer type.
In what way pulmonary vein is different
from other veins?


A metal used to recover copper from a
solution of \( \boldsymbol{C u} \boldsymbol{S O}_{4} \) is
\( A \cdot F e \)
в. нв
c. Na
D. Ag


What are the difference between
dispersion and scattering


When an a.c source is connected across
a resistor:
A. the current leads the voltage in phase
B. the current lags behind the voltage in phase
C. the current and voltage are in same phase
D. the current and voltage are out of phase


What will be the vapour pressure of a
solution containing 5 moles of sucrose
\( \left(C_{12} H_{22} O_{11}\right) \) in \( 1 k g \) of water, if the vapour pressure of pure water is \( 4.57 m m \) of \( H g ?[C=12, H=1, O= \)
\( \mathbf{1 6}] \)


A wheel is rolling without slipping on a horizontal plane with velocity \( \boldsymbol{v} \)
and acceleration a of centre of mass as
shown in figure. Acceleration at
This question has multiple correct options
A. \( A \) is vertically upwards
B. \( B \) may be vertically downwards
c. \( C \) cannot be horizontal
D. a point on the rim may be horizontal leftwards


All possible values of \( x \) for which the
function
\( f(x)=x \ln x-x+1 \) is positive is
A. \( (1, \infty) \)
(n)
B. \( \left(\frac{1}{e}, \infty\right) \)
c. \( [e, \infty) \)
D. \( (0, \infty)-\{1\} \)


A prism \( (\mu=1.5) \) has the refracting
angle of \( 60^{\circ} . \) The deviation of a monochromatic ray incident normally on its one surface will be \( \left(\sin 48^{\circ} 36^{\prime}=\right. \) \( \mathbf{0 . 7 5}) \)
\( \mathbf{A} \cdot 36^{\circ} 72 \)
B . \( 20^{\circ} 30^{\prime} \)
\( c \cdot 18^{\circ} \)
D. \( 22^{\circ} 1^{\prime} \)


Two light rays having the same
wavelength \( \lambda \) in vacuum are in phase initially. Then the first ray travels a path \( L_{1} \) through a medium of refractive
index \( n_{1} \) while the second ray travels a
path of length \( L_{2} \) through a medium of
refractive index \( n_{2} \). The two waves are
then combined to produce interference. The phase difference between the two
waves is:
A \( \cdot \frac{2 \pi}{\lambda}\left(L_{2}-L_{1}\right) \)
в. \( \frac{2 \pi}{\lambda}\left(n_{1} L_{1}-n_{2} L_{2}\right) \)
c. \( \frac{2 \pi}{\lambda}\left(n_{2} L_{1}-n_{1} L_{2}\right) \)
D \( \cdot \frac{2 \pi}{\lambda}\left(\frac{L_{1}}{n_{1}}-\frac{L_{2}}{n_{2}}\right) \)


An object is placed at a distance of 40 \( \mathrm{cm} \) in front of a concave mirror of focal
length \( 20 \mathrm{cm} . \) Determine the ratio of the size of the image and the size of object
A . 2:
B. 1:
\( c \cdot 1: \)
D. 4:


Find the area of a rhombus, each side of
which measures \( 20 \mathrm{cm} \) and one of
whose diagonals is \( 24 \mathrm{cm} \)


At what temperature will the resistance of a copper wire become three times its value at \( 0^{\circ} \mathrm{C} \) [Temperature coefficient of
resistance for copper \( =4 \times 10^{-3} \) per \( ^{\circ} \mathrm{C} \)
]:
\( \mathbf{A} \cdot 400^{\circ} \mathrm{C} \)
B . \( 450^{\circ} \mathrm{C} \)
c. \( 500^{\circ} \mathrm{C} \)
D. \( 550^{\circ} \mathrm{C} \)


The IUPAC name of dimethyl ether is :
A. ethoxymethane
B. methoxymethane
c. methoxyethane
D. ethoxyethane


Select the molecule that has one
pi bond?
This question has multiple correct options
\( \mathbf{A} \cdot C H=C H \)
B. \( C H_{2}=C H-C H O \)
c. \( C H_{3}-C H=C H_{2} \)
D. \( C H_{3}-C H=C H-C O O H \)


Solve:3 \( x+8>2 \) when \( x \) is an real
number.


A circular disc of radius \( 10 \mathrm{cm} \) is free to
rotate about an axis passing through its centre without friction and its moment of inertia is \( \frac{1}{2} \pi k g m^{2} . A \) tangential force of \( 20 N \) is acting on the
disc along its rim. Starting from rest, the number of rotations made by the disc in \( 10 s \) is:
A . 50
в. 100
\( c .150 \)
D. 200


An inorganic compound contains \( 5.88 \% \) of hydrogen and \( 94.11 \% \) oxygen. Find out the empirical formula of the compound and predict the molecular formula.
\( A \cdot H_{2} O \)
в. \( H O \)
\( \mathrm{c} \cdot \mathrm{H}_{3} \mathrm{O}_{2} \)
D. \( H_{5} O_{2} \)


Q Type your question-
with their correct arrangements.
List List - II
(i) Random Copolymer
1) \( (A- \)
\( A-A-A)-(B-B-B-B)-(A-A-A) \)
(ii) Block Copolymer
2) - A -
B-A-B-A.
(iii) Graft Copolymer
3) -A-
B-A-A-A-B-B-A-B-A-A-
B-B-B-B-
(iv) Alternating Copolymer
4)- \( A \)
\( \mathbf{A}-\mathbf{A}-\mathbf{A}-\mathbf{A}-\mathbf{A}-\mathbf{A}-\mathbf{A}-\mathbf{A}- \)
B-
A. (i)-1, (ii)-2, (iii)-3, (iv) -4
B. (i)-2, (ii)-4, (iii)-3, (iv)- -
c. (ii)-3, (ii)-1, (iii)-4, (iv)-2
D. (i)-4, (ii)-3, (iii)-1, (iv)-2


The set of all values of 'a' for which
\( \lim _{x \rightarrow a}[x] \) does not exist is \( ([x] \)
denotes greatest integer function)
A. a is any integer
B. a is a positive rational number
C. a is a negative rational integer
D. a is complex number


Name the three important blood
proteins are seen in the plasma. Add a note, on their functions.


The energy required to blow a bubble of radius \( 4 \mathrm{cm} \) and \( 3 \mathrm{cm} \) in the same
liquid is in the ratio of
A .4: 3
B. 3:4
\( c \cdot 16: 9 \)
D. 64 : 27


If \( A(2,2,-3), B(5,6,9), C(2,7,9) \) be
the vertices of a triangle. The internal bisector of the angle \( A \) meets \( B C \) at the
point \( D, \) then find the coordinates of \( D \)
A \( \cdot\left(\frac{13}{2}, \frac{7}{2}, 9\right) \)
В \( \cdot\left(\frac{7}{2}, \frac{13}{2}, 9\right) \)
c. \( \left(\frac{9}{2}, \frac{7}{2}, 9\right) \)
D. \( \left(\frac{13}{2}, \frac{9}{2}, 9\right) \)


In the series LCR circuit shown the
impedance is:
A. \( 200 \Omega \)
B. \( 100 \Omega \)
c. \( 300 \Omega \)
D. \( 500 \Omega \)


In the equilibrium \( 4 H_{2} O(g)+ \)
\( \mathbf{3} F e(s) \leftrightharpoons F e_{3} O_{4}(s)+4 H_{2}(g), \) the yield
of \( H_{2} \) can be increased by:
A. increasing the pressure
B. passing more steam
c. increasing the mass of iron
D. decreasing the pressure


Four resistances of 20 ohms each are
connected in parallel. Four such combinations are connected in series.
What is the total resistance?
\( A \cdot 80 \) ohms
B. 40 ohms
c. 20 ohms
D. 10 ohms


Actual efficiency of fuel cell is only around:
A. 60-70\%
в. 20-30\%
c. \( 100 \% \)
D. 30-40\%


Which of the following element is present as the impurity to maximum extent in pig iron?
\( A \cdot P \)
в. мп
\( c \cdot c \)
D. si


Number of oxygen atoms present in 1 gram of calcium carbonate is:
A \( \cdot 6 \times 10^{2} \)
1
B . \( 1.8 \times 10^{22} \)
\( c \cdot 6 \times 10^{2} \)
2
D. \( 8 \times 10^{22} \)


When an object can be seen with one eye, why is it that we have a pair of eyes?


Which of the following represents a linear polynomial?
A \( \cdot p(x)=3 x+4 \)
В \( \cdot p(x)=3 x^{3}+4 \)
C \( \cdot p(x)=4 x^{3}+3 \)
D \( \cdot p(x)=2 x^{2} \)


\( C u S O_{4} \) when reacts with \( K C N \) forms
\( C u C N \) which is insoluble in water. It is
soluble in excess of \( K C N, \) due to
formation of the following complex:
A \( \cdot K_{2}\left[C u(C N)_{4}\right] \)
в. \( K_{3}\left[C u(C N)_{4}\right] \)
c. \( C u C N_{2} \)
\( \mathbf{D} \cdot \operatorname{cu}\left[K C u(C N)_{4}\right] \)


Ammonium hydrogen sulphide dissociates according to the equations:
\( N H_{4} H S(s) \rightleftharpoons N H_{3}(g)+H_{2} S(g) \)
If the observed pressure at equilibrium is \( 1.12 a t m \) at \( 380 K, \) what is the
equilibrium constant \( \boldsymbol{K}_{\boldsymbol{p}} \) of the
reaction?


Which of the following are the reasons for population explosion?
(i) Increased health facilities
(ii) Rapid increase in MMR
(iii) Rapid increase in IMR
(iv) Rapid decrease in MMR
(v) Decrease in number of people
reaching reproductive age
\( A \cdot \) (i) and (iv)
B. (iii) and (v)
c. (ii) and (iii)
\( D \cdot \) (i) and (v)


The distance between two particle is decreasing at the rate of \( 6 \mathrm{m} / \mathrm{sec} \). If these particles travel with same speeds and in the same direction, then the separation increase at the rate of 4 m/sec. The particle have speed as
A. \( 5 \mathrm{m} / \mathrm{sec} ; 1 \mathrm{m} / \mathrm{sec} \)
B. \( 4 \mathrm{m} / \mathrm{sec} ; 1 \mathrm{m} / \mathrm{sec} \)
c. \( 4 \mathrm{m} / \mathrm{sec} ; 2 \mathrm{m} / \mathrm{sec} \)
D. \( 5 \mathrm{m} / \mathrm{sec} ; 2 \mathrm{m} / \mathrm{sec} \)


Hail storms are observed to strike the
surface of the frozen lake at 30 with the
vertical and rebiund at 60 with the
vertical. Then:


\( 660 J \) heat energy is supplied to a solid
of mass \( 275 g . \) When its temperature rises by \( 1^{\circ} \mathrm{C} \), calculate specific heat capacity of the solid:
A \( \cdot 1.2 J / g^{o} C \)
в. \( 4.8 \mathrm{J} / \mathrm{g}^{\circ} \mathrm{C} \)
c \( \cdot 2.4 J / g^{\circ} C \)
D. \( 9.6 J / g^{o} C \)


The hydrogen bonding is strongest in which one of the following set?
\( \mathbf{A} \cdot F-H---F \)
B. \( O-H---S \)
c. \( S-H---F \)
D. \( F-H---O \)


Assertion
\( H_{3} P O_{4} \) and \( H_{3} P O_{3} \) both are present in fertilizers.
Reason
\( H_{3} P O_{3} \) increases the solubility of fertilizers.
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 region of the nephron found in the
renal medulla is
A. Malpighian corpuscle
B. Proximal convoluted tubule
c. Distal convoluted tubule
D. Henle's loop
E. Glomerulus


Which one of the following gives only one monochloro derivative?
A. neo-Pentane
B. n-Hexane
c. 2-Methylpentane
D. 3-Methylpentane


heated on the flame directly. It crumbled to give white powder of calcium oxide. After cooling, when water is added to it a hissing sound is heard and water started boiling. If it is allowed to stay over night, a clear solution (top layer) is taken and for this experiment below as lime water.

When carbon dioxide is bubbled into
testtube a clear solution of lime water, turbidity appears first and later a white precipitate of calcium carbonate is formed. Carbon dioxide is continued to
passed into the same solution and the solution again became clear because of
formation of calcium bicarbonate. On
heating the contents of the tube, white precipitate of calcium carbonate
reappears. Heating of calcium bicarbonate gave the following:
A. Calcium oxide and carbon dioxide
B. Calcium carbonate, water and \( C O_{2} \)
c. calcium bicarbonate and \( C O_{2} \)
D. Calcium hydroxide and carbon dioxide


Choose the correctly paired sets from
the following
\( \begin{array}{lll}\text { SET I } & \text { SET II } & \text { SET III } \\ \begin{array}{l}\text { (A) Sphenoid } \\ \text { bone }\end{array} & \begin{array}{l}\text { Keystone } \\ \text { bone }\end{array} & \text { Cranium } \\ \begin{array}{l}\text { (B) Acromion } \\ \text { process }\end{array} & \text { Collar bone } & \text { Scapula } \\ \begin{array}{l}\text { (C) Xipioid } \\ \text { process }\end{array} & \text { Breastbone } & \text { Thorax } \\ \begin{array}{l}\text { (D) Odontoid } \\ \text { process }\end{array} & \text { Atlas } & \begin{array}{l}\text { Cervical } \\ \text { vertebra }\end{array}\end{array} \)
\( A \cdot A, D \)
B. B, D
\( c \cdot B, c \)
D. A.


Which of the following is correctly matched?
A. Momentum of H-atom when electrons return from
\( n=2 \) to \( n=1: \frac{3 R h}{4} \)
B. Momentum of proton: Independent of wavelength of light
c. e/m ratio of anode rays : Independent of gas in the discharge tube
D. Radius of nucleus :: (Mass no.) \( ^{1 / 2} \)


Which of the following should a heart patient firmly avoid?
A. Cream
B. Mango
c. Rice
D. Milk


The following reaction is at equilibrium, \( \boldsymbol{F} \boldsymbol{e}_{(a q)}^{3+}+\boldsymbol{S C} \boldsymbol{N}_{(a q)}^{-} \rightleftharpoons \)
\( \left[\boldsymbol{F e}(\boldsymbol{S C N})_{(a q)}^{2+} ; \boldsymbol{K}_{c}=\frac{[\boldsymbol{F e}(\boldsymbol{S C N})]^{2+}}{\left[\boldsymbol{F e}^{3+}\right]\left[\boldsymbol{S C N}^{-}\right]}\right. \)
In the above reaction, color intensity of
red colour can be increased by:
A. addition of KSCN
B. addition of oxalic acid which reacts with \( F e^{3+} \) ions
C. addition of \( H g^{2+} \) ions which reacts with \( S C N^{-} \) ions
D. red colour intensity cannot be changed.


The standard deviation of
\( \mathbf{9}, \mathbf{1 6}, \mathbf{2 3}, \mathbf{3 0}, \mathbf{3 7}, \mathbf{4 4}, \mathbf{5 1} \) is
A. 7
B. 9
c. 12
D. 14
E . 16


Carbon atom is
A. monovalent
B. divalent
C . trivalent
D. tetravalent


A potential barrier of \( 0.50 \mathrm{V} \) exists across of PN Junction. If the depletion region is \( 5.0 \times 10^{-7} m \) wide, the
intensity of the electric field in this
region is
A \( \cdot 1.0 \times 10^{9} \mathrm{V} / \mathrm{m} \)
в. \( 2.0 \times 10^{5} \mathrm{V} / \mathrm{m} \)
c. \( 1.0 \times 10^{6} \mathrm{V} / \mathrm{m} \)
D. 2.0 \( \times 10^{6} \mathrm{V} / \mathrm{m} \)


Differentiate with respect to \( x: e^{(5 x+2)} \)
\( A \cdot 5 e^{5 x+2} \)
B. \( 10 e^{5 x+2} \)
\( \mathbf{c} \cdot 25 e^{5 x+2} \)
D. \( e^{5 x+2} \)


\( Z n S \) is not precipitated by passing
\( \boldsymbol{H}_{2} \boldsymbol{S} \) in acidic medium but \( \boldsymbol{C} \boldsymbol{u} \boldsymbol{S} \)
precipitated. The reason for it is:
\( \mathbf{A} \cdot K_{s p} C u S<<K_{s p} Z n S \)
B . \( K_{s p} C u S>>K_{s p} Z n S \)
c. \( K_{s p} C u S=K_{s p} Z n S \)
D. None of these


In Dumas' method for estimation of
nitrogen, \( 0.3 g \) of an organic compound
gave \( 50 m L \) of nitrogen collected at
\( 300 K \) temperature and \( 715 m m \)
pressure. Calculate the percentage composition of nitrogen in the compound. (Aqueous tension at \( 300 K=15 m m) \)


Bond angle in structure of diamond is:
A \( \cdot 109.5^{\circ} \mathrm{C} \)
B . \( 210^{\circ} \mathrm{C} \)
c. \( 200^{\circ} \mathrm{C} \)
D. \( 154^{\circ} \mathrm{C} \)


In an isosceles triangle, one angle has
the angle measure of \( 110^{\circ} . \) Find sum of two other angles of the triangle.
A \( .70^{\circ} \)
B . \( 30^{\circ} \)
\( \mathbf{c} \cdot 25^{\circ} \)
D. 26


A ball is dropped from a bridge \( 122.5 \mathrm{m} \) above a river. After the ball has been
falling for \( 2 s, \) a second ball is thrown straight down after it. What must the initial velocity of the second ball be so that both hit the water at the same
time?
A. \( 40 \mathrm{m} / \mathrm{s} \)
В. \( 55.5 \mathrm{m} / \mathrm{s} \)
c. \( 26.1 \mathrm{m} / \mathrm{s} \)
D. \( 9.6 \mathrm{m} / \mathrm{s} \)


\( A+2 B \rightarrow C+D \) the equilibrium
constant is:
A \( \cdot \frac{[C][D]}{[A][B]^{2}} \)
в. \( \frac{[C][D]}{[A][B]} \)
\( ^{\mathbf{c}} \frac{[A][B]^{2}}{[C][D]} \)
D. \( \frac{[A][C]}{[B][D]} \)


Jeshu purchased a bike by paying Rs. \( 52,000 . \) If the value depreciates by \( 2 \% \) every year, find the value of the bike
after 3 years.


Area of the region bounded by \( \boldsymbol{y}=|\boldsymbol{x}| \)
and \( \boldsymbol{y}=\mathbf{1}-|\boldsymbol{x}| \) is
A \( \cdot \frac{1}{3} \) sq. units
B. 1 sq. units
c. \( \frac{1}{2} \) sq. unit
D. 2 sq. units


\( A \) compound \( C \) (molecular formula,
\( \left.C_{2} H_{4} O_{2}\right) \) reacts with \( N a \) metal to form
a compound \( \boldsymbol{R} \) and evolves a gas which
burns with a pop sound. Compound \( C \)
on treatment with an alcohol \( A \) in
presence of an acid forms a sweet smelling compound \( S \) (molecular formula, \( C_{3} H_{6} O_{2} \) ). On addition of
NaOH to \( C, \) it also gives \( R \) and water.
S on treatment with \( N a O H \) solution
gives back \( \boldsymbol{R} \) and \( \boldsymbol{A} \)
Identify \( \boldsymbol{R} \) and \( \boldsymbol{A} \) ?
A . Compound \( R \) is \( C H_{3} C O O N a \) Compound \( A \) is \( C H_{3} O H \)
B. Compound \( A \) is \( C H_{3} O H \) Compound \( R \) is \( C H_{3} C O O C H_{3} \)
C. Compound \( A \) is \( C H_{3} C O O H \) compound \( R \) is \( C H_{3} C O O N a \)
D. Compound \( A \) is \( C H_{3} C O O N a \) Compound \( R \) is \( C H_{3} O H \)


At what height from the ground will be the value of \( g \) be the same as
that in \( 10 k m \) deep mine below the
surface of earth.
\( A \cdot 20 \mathrm{km} \)
B. 7.5 km
\( c \cdot 5 k m \)
D. 2.5 km


Which of the following is not the derivative of Petroleum?
A . Petrol
B. Kerosene
c. Asphalt
D. Acetone


Explain why propanol has higher boiling point than that of the hydrocarbon, butane?


Life cycle of Saccharomyces cerevisiae is
A. Haplontic
B. Diplontic
C . Haplodiplontic
D. None of the above


The heat required (in \( c a l \) ) to change 10 g
ice at \( 0^{\circ} \mathrm{C} \) to steam at \( 100^{\circ} \mathrm{C} \) is:

I Heat of fusion and heat of vaporization
for \( \boldsymbol{H}_{2} \boldsymbol{O} \) are \( \boldsymbol{8} \boldsymbol{0} \boldsymbol{c} \boldsymbol{a} \boldsymbol{l} / \boldsymbol{g} \) and \( \boldsymbol{5} \boldsymbol{4} \boldsymbol{\theta} \boldsymbol{g} \)
respectively. Specific heat of water is \( \mathbf{1} \boldsymbol{c a l} / \boldsymbol{g}] \)


The degree of the differential equation \( \left(1+\left(\frac{d y}{d x}\right)^{2}\right)^{3 / 4}=\left(\frac{d^{2} y}{d x^{2}}\right)^{1 / 3} \) is:
\( A \)
B.
\( c \cdot 9 \)
\( D \)


Size of the nucleus is:
\( \mathbf{A} \cdot 1 A^{0} \)
B. \( 10^{-16} m \)
\( \mathbf{c} \cdot 10^{-15} m \)
D. \( 10^{-14} m \)


Consider two solid uniform spherical
objects of the same density \( \rho . \) One has
radius \( R \) and the other has radius \( 2 R \)
They are in outer space where the
gravitational fields from other objects are negligible. If they are arranged with their surface touching, what is the contact force between the objects due to their traditional attraction?
\( \mathbf{A} \cdot G \pi^{2} R^{4} \)
B. \( \frac{128}{81} G \pi^{2} R^{4} \rho^{2} \)
\( ^{\mathbf{C}} \cdot \frac{128}{81} G \pi^{2} \)
\( \stackrel{128}{87} G \pi^{2} R^{2} \)


n figure, lines \( l_{1} \) and \( l_{2} \) intersect at \( O \)
forming angles as shown in the figure. I
\( x=45^{\circ}, \) find the values of \( y, z \) and \( u \)


A flower which can be divided into two
equal halves by only one plane is
A. zygomorphic
B. Actinomorphic
c. Regular
D. Perfect


The forward biased diode connection is:
\( A \)
B.
c.
D.


In the circuit shown in the figure the
heat produced in the 5 ohm resistor due
to the current flowing through it is 10
calories per second. The heat generated
in the 4 ohm resistor is
A. 1 calorie \( / \)per
B. 2 calorie/sec
c. 3 calorie \( / \)per
D. 4 calorie / per


Find the distance of the point (-1,-5,-10) from the point of intersection of the line
\( \boldsymbol{r}=\mathbf{2} \overline{\boldsymbol{i}}-\overline{\boldsymbol{j}}+\mathbf{2} \overline{\boldsymbol{k}}+\overline{\boldsymbol{\lambda}}(\mathbf{3} \overline{\boldsymbol{i}}+\mathbf{4} \overline{\boldsymbol{j}}+\mathbf{2} \overline{\boldsymbol{k}}) \) and
the plane \( \bar{r} .(\bar{i}-\bar{j}+\bar{k})=5 \)


The first element of a group in many ways differs from the other heavier
members of the group. This is due to:
A. the small size
B. the high electronegativity and high ionisation potential
c. the unavailability of d-orbitals
D. all of the above


What do you understand by the internal resistance of a cell? The potential difference of a cell becomes \( 1.8 \mathrm{V} \) when
\( 0.5 A \) current is drown and when \( 1.0 A \)
current is drawn, it becomes \( 1.6 \mathrm{V} \). Find
the internal resistance of the cell and
its e.m.f.


Some dog breeds have more potential to cause injuries than other breeds and thus, they are said to be dangerous. Which among the following is the most dangerous breed of dogs?
A. Siberian Husky
B. German Shepherd
c. Pit bull
D. Rottweiler


Which of the following statement is
correct regarding container B?
Container \( (\mathbf{A}) \)

Container
\( (\mathbf{B}) \)
A. Water will migrate from Glass (i) to Glass (ii) and no equilibrium will establish
B. Water will migrate from Glass (i) to Glass (ii) and equilibrium will establish after some time
c. Water will not migrate to any side
D. None of these


Let \( n_{r} \) and \( n_{b} \) be respectively the number of photons emitted by a red bulb and a blue bulb of equal power in a given time, then:
A \( \cdot n_{r}=n_{b} \)
в. \( n_{r}<n_{b} \)
\( \mathrm{c} \cdot n_{r}>n_{b} \)
D. data insufficient


The minimum and maximum values of \( \mathbf{f}(\mathbf{x})=\sin (\cos \mathbf{x})+\cos (\sin \mathbf{x}) \forall-\frac{\boldsymbol{\pi}}{\mathbf{2}} \leq \)
\( x \leq \frac{\pi}{2} \) are respectively
A . \( \cos 1 \) and \( 1+\sin 1 \)
B. \( \sin 1 \) and \( 1+\cos 1 \)
c. \( \cos 1 \) and \( \cos \left(\frac{1}{\sqrt{2}}\right)+\sin \left(\frac{1}{\sqrt{2}}\right) \)
D. \( \frac{1}{\sqrt{2}} \)


If \( \epsilon_{0} \) and \( \mu_{0} \) represent the permittivity and permeability of vaccum and \( \epsilon \) and \( \mu \) represent the permittivity and permeability of medium, then refractive index of the medium is given by
A. \( \sqrt{\frac{\epsilon_{0} \mu_{0}}{\epsilon \mu}} \)
в. \( \sqrt{\frac{\epsilon \mu}{\epsilon_{0} \mu_{0}}} \)
c. \( \sqrt{\frac{\epsilon_{0} \mu_{0}}{\epsilon}} \)
D. \( \sqrt{\frac{\epsilon_{0} \mu_{0}}{\mu}} \)


A bullet of mass m moving with a
velocity \( v_{1} \) strikes a suspended wooden
block of mass \( \mathrm{M} \) as shown in the figure
and sticks to it. If the block rises to a
height h the initial velocity of the bullet
is-
A \( \cdot \frac{m+M}{m} \sqrt{2 g h} \)
\( \mathbf{B} \cdot \sqrt{2 g h} \)
c. \( \frac{M+m}{m} \sqrt{g h} \)
D. \( \frac{m}{M+m} \sqrt{2 g h} \)


Read the following statements and
answer as true or false.

Ethanol is the first member of the
alcohol homologous series.
If true enter 1 , else enter 0


\( \lim _{x \rightarrow 0} \frac{\sqrt{1+x}-\sqrt{1-x}}{2 x} \) equals


The radius of a shell for \( \boldsymbol{H}- \) atom is
\( 4.761 A \). The value of \( n \) is:
\( A \cdot 3 \)
B. 9
\( c \cdot 5 \)
D. None of these


Prove:
\( 3 \cos ^{-1} x=\cos ^{-1}\left(4 x^{3}-3 x\right), x \in\left[\frac{1}{2}, 1\right] \)


Contraceptive pill contains -
A. Chemical that cause automatic abortion
B. Chemical that prevent fertilization of ovum
c. spermmicidal salt
D. Progesterone and estrogen


Which of the following quantities is
always negative in SHM?
This question has multiple correct options
\( \mathbf{A} \cdot \vec{F} \cdot \vec{a} \)
в. \( \vec{F} \cdot \vec{r} \)
c. \( \vec{v} . \vec{r} \)
D. \vecू.न


Write 5 equivalent fraction of \( \frac{7}{13} \)


A simple circuit consisting of three
resistors is shown above. \( \boldsymbol{R}_{1} \) has the
same resistance of \( \boldsymbol{R}_{2} \) and \( \boldsymbol{R}_{2} \) has twice
the resistance of \( \boldsymbol{R}_{3} \). If the switch
remains closed, determine the ratio of
heat dissipated of \( \boldsymbol{R}_{1} \) to \( \boldsymbol{R}_{2} \)
\( \mathbf{A} \cdot 1: 9 \)
B. 1: 3
c. 1:
D. 3:
E. 9: 1


Find the area of a triangle, two sides of
which are \( 8 \mathrm{cm} \) and \( 11 \mathrm{cm} \) and the
perimeter is \( 32 \mathrm{cm} \)


If \( \vec{a} \) is perpendicularto \( \vec{b} \) and \( \vec{r} \) is a nonzero vector such that \( \boldsymbol{p} \overrightarrow{\boldsymbol{r}}+(\overrightarrow{\boldsymbol{r}} \cdot \overrightarrow{\boldsymbol{b}}) \overrightarrow{\boldsymbol{a}}=\overrightarrow{\boldsymbol{c}} \)
\( \operatorname{then} \vec{r}= \)
A \( \cdot \frac{\vec{c}}{p}-\frac{(\vec{b} \cdot \vec{c}) \vec{a}}{p^{2}} \)
В \( \cdot \frac{\vec{a}}{p}-\frac{(\vec{c} \cdot \vec{a}) \vec{b}}{p^{2}} \)
c \( \cdot \frac{\vec{b}}{p}-\frac{(\vec{a} \cdot \vec{b}) \vec{c}}{p^{2}} \)
D \( \cdot \frac{\vec{c}}{p}-\frac{(\vec{b} \cdot \vec{c}) \vec{a}}{p} \)


State first law of motion and explain it


Vertical displacement of a plank with a
body of mass ' \( m \) ' on it is varying
according to law \( \boldsymbol{y}=\sin (\boldsymbol{\omega} \boldsymbol{t})+ \)
\( \sqrt{3} \cos (\omega t) . \) The minimum value of \( \omega \) for
which the mass just breaks off the plank and the moment this occurs first
\( \operatorname{after} t=0 \) are given by \( (y \) is positive
vertically upwards):
A \( \cdot \sqrt{\frac{g}{2}}, \sqrt{\frac{2}{g}} \frac{\pi}{6} \)
В \( \cdot \frac{g}{\sqrt{2}} \frac{2}{3}, \sqrt{\frac{\pi}{g}} \)
c. \( \sqrt{\frac{g}{2}} \frac{\pi}{3}, \sqrt{\frac{2}{g}} \)
D. \( \sqrt{2 g}, \sqrt{\frac{2 \pi}{3 g}} \)


The pH of water at \( 25^{\circ} C \) is close to:
A . 1
B. 7
c. 10
D. 6


If a charge \( -150 n C \) is given to a concentric spherical shell and a charge \( +50 n C \) is placed at its centre, then the
charge on inner and outer surface of the shell is
A. \( 50 n C, 100 n C \)
в. \( -50 n C,-100 n C \)
c. \( 50 n C, 200 n C \)
D. \( -50 n C,-200 n C \)


What is the common name of the
polymer obtained by the polymerization of caprolactum? Is it addition polymer or condensation polymer?


If \( p \) and \( p^{\prime} \) are the perpendiculars from
the origin upon the \( \operatorname{lines} x \sec \theta+ \)
\( \boldsymbol{y} \csc \boldsymbol{\theta}=\boldsymbol{a} \) and \( \boldsymbol{x} \cos \boldsymbol{\theta}-\boldsymbol{y} \sin \boldsymbol{\theta}= \)
\( a \cos 2 \theta \) respectively then
A \( \cdot 4 p^{2}+p^{\prime 2}=a^{2} \)
B \cdot \( p^{2}+4 p^{\prime 2}=a^{2} \)
C \( \cdot p^{2}+p^{\prime 2}=a^{2} \)
D. none of these


\( \boldsymbol{C}_{6} \boldsymbol{H}_{5}-\boldsymbol{O}-\boldsymbol{C}_{7} \boldsymbol{H}_{15}(\boldsymbol{n}) \) IUPAC name of
the compound is :
A. 1-Phenoxyheptane
B. 1-Heptoxybenzene
c. Both (a) and (b)
D. None of these


Correct sequence of different phases of
growth is
A. Cell division \( \rightarrow \) Cell differentiation \( \rightarrow \) Cell elongation
B. Cell differentiation \( \rightarrow \) Cell division \( \rightarrow \) Cell elongation
C. Cell elongation \( \rightarrow \) Cell division \( \rightarrow \) Cell differentiation
D. Cell division \( \rightarrow \) Cell elongation \( \rightarrow \) Cell differentiation


Two planets have radii \( r_{1} \) and \( r_{2} \) and
their densities are \( \rho_{1} \) and \( \rho_{2} \)
respectively. The ratio of acceleration due to gravity on them will be.
A \( \cdot r_{1} \rho_{1}: r_{2} \rho_{2} \)
B \( \cdot r_{1} \rho_{1}^{2}: r_{2} \rho_{2}^{2} \)
\( \mathbf{c} \cdot r_{1}^{2} \rho_{1}: r_{2}^{2} \rho_{2} \)
D \( \cdot r_{1} \rho_{2}: r_{2} \rho_{1} \)


The range of \( f(x)=\frac{1-\tan x}{1+\tan x} \) is
\( A \cdot(-\infty, \infty) \)
в. \( (-\infty, 0) \)
c. \( (0, \infty) \)
D. \( (-\infty,-1) \cup(-1, \infty) \)


Complete the following statement.
During meiosis, there is
A. One round of DNA replication and one division
B. Two round of DNA replication and one division
C. Two round of DNA replication and two division
D. One round of DNA replication and two division


Formaldehyde is used:
A. for preserving biological specimens
B. for the preparation of urotropine
C. in the manufacture of bakelite
D. all of these


The only one cell organelle seen in prokaryotic cell is
A. Mitochondria
B. Plastids
c. Ribosomes
D. Lysosomes


Students 2
Marks \( \quad 100 \quad \) 90 \( \quad \) 75 \( \quad \) 80
Find the mean for the following data using direct method.
A . 15.010
в. 14.520
c. 13.837
D. 16.127


A container is divided into two equal
parts I and II by a partition with a small
hole of diameter d. The two partitions are filled with same ideal gas, but held
at temperatures \( \boldsymbol{T}_{\boldsymbol{I}}=\mathbf{1 5 0 K} \) and \( \boldsymbol{T}_{\boldsymbol{I I}}= \)
\( 300 K \) by connecting to heat reservoirs.
Let \( \lambda_{I} \) and \( \lambda_{I I} \) be the mean free paths of the gas particles in the two parts such
that \( \boldsymbol{d}>>\boldsymbol{\lambda}_{\boldsymbol{I}} \) and \( \boldsymbol{d}>>\boldsymbol{\lambda}_{\boldsymbol{I} I} . \) Then
\( \boldsymbol{\lambda}_{I} / \boldsymbol{\lambda}_{I I} \) is close to.
\( \mathbf{A} \cdot 0.25 \)
B. 0.5
c. 0.7
D. 1.0


If \( \cot ^{-1}\left(\frac{1}{x+1}\right)+\cot ^{-1}\left(\frac{1}{x-1}\right)= \)
\( \tan ^{-1} 3 x-\tan ^{-1} x \)
then \( \boldsymbol{x}= \)
A. \( \pm 1 / 2 \)
B. \( -1, \pm 1 / 3 \)
c. 2,±1
D. \( -1 . \pm 1 / 2 \)


The number of permutations of \( \mathbf{M} \) things out of A things of one kind B things of the second kind and \( C \) things of other kinds is \( \frac{(A+B+C) !}{A ! B ! C !} \)
A . True
B. False


In which of the following reactions there is a change in the oxidation number of nitrogen atom?
A \( .2 N O_{2} \rightarrow N_{2} O_{4} \)
B. \( N H_{3}+4 N H_{3} \rightarrow\left[C u\left(N H_{3}\right)_{4}\right] S O_{4} \)
c. \( 2 N a_{2} S_{2} O_{3}+I_{2} \rightarrow N a_{2} S_{4} O_{6}+2 N a I \)
D. None of these


Fill in the blanks with appropriate
words.
Pseudostratified epithelium lines the tract while transitional epithelium
lines the \( \ldots \ldots \)..... tract.


With a neat circuit diagram, explain the working of an nPn transistor in CE mode
as an amplifier with input and output waveform.


A lens that has convex surface at one
side and concave surface at another
side behaves as:
a) convergent lens when the radius of curvature of convex surface is greater
than that of concave surface.
b) divergent lens when the radius of curvature of concave surface is greater
than that of convex surface.
c) convergent lens when the radius of
curvature of convex surface is less than
that of concave.
d) divergent lens when the radius of
curvature of concave surface is less
than that of convex surface.
\( \mathbf{A} \cdot \mathbf{a}, \mathbf{b} \) are true
B. a, dare true
c. \( c, d \) are true
D. b,c are true


Write L.H.S and R.H.S of the following simple equations:
\( 2 a-3=5 \)


In Young's double slit experiment, the
source \( S \) and two slits \( A \) and \( B \) are
lying in a horizontal plane. The slit \( \boldsymbol{A} \) is
above slit \( B \). The fringe are obtained on
a vertical screen \( K . \) The optical path
from \( S \) to \( B \) is increased by putting a
transparent material of higher refractive indices. The path from \( \boldsymbol{S} \) to \( \boldsymbol{A} \)
remains unchanged. As a result of this, the result fringe pattern moves some what
A. upwards
B. downwards
c. towards left horizontally
D. towards right horizontally


That 'Entropy of a system increases in all
spontaneous processes' is known as
A. 1 st law of Thermodynamics
B. 2nd law of Thermodynamics
C. Zeroth law of Thermodynamics
D. 3rd law of Thermodynamics


In figure, a ray of light \( P Q \) is incident
normally on the hypotenuse of an
isosceles right angle prism \( A B C . \) What
is the angle of deviation of the ray \( P Q ? \)
\( \mathbf{A} \cdot 90^{\circ} \)
B \( .45^{\circ} \)
\( c \cdot 180^{\circ} \)
\( D \cdot 30^{\circ} \)


The radius of any circle touching the \( \operatorname{lines} 3 x-4 y+5=0 \) and \( 6 x-8 y- \)
\( \mathbf{9}=\mathbf{0} \) is
A \( \cdot \frac{19}{10} \)
в. \( \frac{19}{20} \)
c. \( \frac{9}{20} \)
D. \( \frac{90}{20} \)


Identify the incorrect statement among
the following.
A. \( 4 f \) and \( 5 f \) orbitals are equally shielded.
B. 4 -Block elements show irregular and erratic chemical properties among themselves.
C. La and Lu have partially filled d-orbitals and no other partially filled orbitals.
D. The chemistry of various lanthanoids is very similar.


In floating leaved plants stomata occur
on
A. Lower surface
B. Upper surface
c. Both surfaces
D. Absent


Statement-1: When a travelling wave is sent along a particular string by
oscillating one end, the speed of the
wave will increase if we increase the
frequency of oscillations. Statement-2: If a travelling wave sent
along a particular string by oscillating
its one end, it is the wavelength of the
wave that decreases.
A. If both the statements are true and statement- 2 is the correct explanation of statement-
B. If both the statements are true but statement-2 is not the correct explanation of statement-
C. If statement-1 is true and statement-2 is false
D. If statement-1 is false and statement-2 is true


The displacement \( y \) of a particle executing periodic motion is given by \( y=4 \cos ^{2}\left(\frac{1}{2} t\right) \sin (1000 t) . \) This
expression may be considered to be a result of the superposition of independent harmonic motions
A. two
B. three
c. four
D. five


of of .


Sun spins around once every
A. 26 days
B. 27.4 days
\( c .27 \) cas
D. 30 days


Identify zero polynomial among the following.
A . 0
B. \( x \)
\( \mathbf{c} \cdot x^{2} \)
D. None of the above


Bohr's model of an atom is contradicted
by:
A. Paulis exclusive principle
B. Plancks quantum theory
c. Heisenbergs uncertainty principle
D. all the above


To stop bleeding from an injury ferric chloride can be applied Which comment about the statement is
justified?
A. It is not true, ferric chloride is a poison
B . It is true, \( F e^{3+} \) ions coagulate blood which is negatively charged so
C. It is not true, \( C l^{-} \) ions from positively charged sol profuse bleeding takes place
D. It is true, coagulation takes place because of formation of negatively charged sol with \( C l^{-} \) ions.
E. It is not true, ferric chloride is ionic and gets into blood stream


The addition of HBr is easiest with:
A \( \cdot C H_{2}=C H C l \)
в. \( C l C H=C H C l \)
c. \( C H_{3}-C H=C H_{2} \)
D \( \cdot\left(C H_{3}\right)_{2} C=C H_{2} \)


Regarding linear momentum of a body
a. It is a measure of quantity of motion
contained by the body
b. Change in momentum is the measure
of impulse
c. Impulse and acceleration act in
opposite direction to the change in
momentum
d. In the case of uniform circular motion
the linear momentum is conserved.
\( A \cdot \) a \( \& b \) are true
B. b \& c are true
c. \( c \& \) d are true
D. a, b \& c are ture


The correct structure of \( 7- \)
Hydroxyheptan - 2- one is:
\( \mathbf{A} \cdot H O-C H_{2}-\left(C H_{2}\right)_{4}-C H_{2}-C O C H_{3} \)
B \( \cdot H O-C H_{2}-\left(C H_{2}\right)_{3}-C H_{2}-C O C H_{3} \)
\( \mathbf{c} \cdot H O-C H_{2}-\left(C H_{2}\right)_{3}-C H_{2}-C O C H_{2} C H_{3} \)
\( \mathbf{D} \cdot C H_{3}-C H(O H)-\left(C H_{2}\right)_{3}-C H_{2}-C O C H_{3} \)


The ratio of the radii of the atom to
the nucleus is :
A \( \cdot 10^{4}: 1 \)
B . \( 10^{-4}: 1 \)
\( \mathrm{c} \cdot 10^{2}: 1 \)
D. \( 10^{3}: 1 \)


In which phase of mitosis the chromatids of chromosomes separate
from each other?
A. Anaphase
B. Telophase
c. Metaphase
D. Prophase


During the estimation of phosphorous present in an organic compound, phosphorous present in the organic compound is converted into
A. phosphoric acid
B. phosphorous acid
c. pyrophosphoric acid
D. hypophosphoric acid


A fair die is rolled. Consider the events
\( \boldsymbol{E}=\{1, \mathbf{3}, \mathbf{5}\} \) and \( \boldsymbol{F}=\{\mathbf{2}, \mathbf{3}\}, \) find
\( \boldsymbol{P}(\boldsymbol{E} \mid \boldsymbol{F}) \)


Write true(T) or false(F) for the
following.
Vasectomy is the surgical method of sterilisation in human males.
A. True
B. False


Mark the wrong statement about
enzymes
A. enzymes are biological catalysts
B. each enzyme can catalyse a number of similar reactions
C. enzymes are very efficient catalysts
D. enzymes are needed only in very small amounts for their action


The resistive force suffered by a motor
boat is \( \propto V^{2} . \) When the engine was
shutdown, the velocity is \( V_{0} . \) Find the
average velocity at any time \( t \)
A \( \cdot V_{a V}=\frac{V_{0}+V}{2} \)
B. \( \frac{V V_{0}}{2\left(V_{0}+V\right)} \)
\( c \)
\( \frac{2 V V_{0} \log _{e} \frac{V_{0}}{V}}{\left(V_{0}+V\right)} \)


The direction of magnetic field on the conductor in Fleming's left hand rule is represented by finger.


A solid sphere is rotating in free space. If the radius of the sphere is increased keeping the mass same without applying any external force, which one of the following will not be affected?
A. Moment of inertia
B. Angular momentum
c. Angular velocity
D. Rotational kinetic energy


In complexes of weak field ligands,
\( \Delta_{o}<P(\text { pairing energy }), \) the energy
difference between \( t_{2 g} \) and \( e_{g} \) sets is relatively less. Under the influence of
strong field ligands, \( \Delta_{o}>P \) (pairing energy), the energy difference between
\( t_{2 g} \) and \( e_{g} \) sets is relatively high.
The correct statement regarding
\( \left[\boldsymbol{C r}(\boldsymbol{e n})_{2} \boldsymbol{C l}_{2}\right]^{+} \) and
\( \left[\boldsymbol{C o}\left(\boldsymbol{C}_{2} \boldsymbol{O}_{4}\right)_{2}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{2}\right]^{-} \) complex ions is :
A. both are equally stable complexes
B. both have equal number of stereoisomers
c. both are diamagnetic complexes
D. none of the above


The total current supplied to the circuit
by the battery is
\( \mathbf{A} \cdot 1 \mathbf{A} \)
B. 2 A
\( c \cdot 4 A \)
\( D \cdot 6 A \)


Find the length of the diagonal of a rectangle whose three vertices in order \( \operatorname{are} A(0,4), B(0,0) \) and \( C(5,0) \)


Find the cube of \( (4 a+5 b) \)


4 chloro 3, 5-dimethyl phenol is one of the constituent of called :
A. Chloramphenicol
B. Paracetamol
c. Barbital
D. Dettol


The half life of a first order reaction is
69.35 seconds, the value of rate constant of the reaction is:
A \( \cdot 1.0 s^{-1} \)
B. \( 0.1 s^{-1} \)
\( c \cdot 0.01 s^{-1} \)
D. \( 0.001 s^{-1} \)


Choose the correct statement(s)
A. Motion necessarily takes place along the direction of force
B. If no force acts, the body is at rest
C. \( A \) body in motion, need not be acted upon by a force
D. A change in speed is always there, whenever a force is applied on the moving body


The best solvent for the crystallization
of organic solid is in which:
A. organic compound is highly soluble
B. compound is soluble on warming
c. compound is soluble at \( 90^{\circ} \)
D. compound is insolubl


A conductor carries a current of \( 50 \mu A \) If the area of cross-section of the
conductor is \( 50 \mathrm{mm}^{2} \), then value of the
current density in \( A m^{-2} \) is
A . 0.5
B.
\( c \cdot 10^{-3} \)
D. \( 10^{-6} \)


Which of the following statements
is/are correct?
This question has multiple correct options
A. The common name of benzene- 1,2 -diol is catechol
B. The common name of benzene- 1,3 -diol is resorcinol.
C. The common name of benzene- 1,4 -diol is quinol,
D. The common name of benzene- 1,4 -diol is hydroquinone


An object is in equilibrium under four
concurrent forces in the directions
shown in figure. Find the magnitudes of \( \vec{F}_{1} \) and \( \vec{F}_{2} \)


Which of the following statement(s) is/are affect the stability of hydrates of carbonyl compounds? This question has multiple correct options
A. Steric hindrance
B. Presence of -I groups on carbonyl carbon's hydrate
c. Intramolcular hydrogen bonding
D. Angle strain in carbonyl compound


Which of the following substance is not present in clear water?
A \( \cdot \operatorname{Ca}\left(\mathrm{HCO}_{3}\right)_{2} \)
в. \( M g C l_{2} \)
\( \mathrm{c} \cdot \mathrm{CaSO}_{4} \)
D. \( C a C O_{3} \)


If a mirror has focal length of \( +15 \mathrm{cm} \)
then it is a
A. Convex mirror
B. Concave mirror
c. Plane mirror
D. None of these


A progressive wave moves with a velocity of \( 36 m / s \) in a medium with a
frequency of \( 200 H z . \) The phase difference between two particles
separated by a distance of \( 1 \mathrm{cm} \) is:
A . 40
B . 20
c.
D. \( \frac{\pi}{16} \)


Cooking is done fast in pressure cooker
because
A. The boiling point of water is lowered
B. The boiling point of water is increased
c. More pressure is the cooker cooks the food at 100 C
D. The boiling point remains the same but more steam cooks the food


Which of the following material is not ferromagnetic in nature?
A . \( F e \)
в. \( C o \)
c. \( N i \)
D. \( A l \)


An LED is forward-biased. The diode
should be on, but no light is showing. A possible trouble might be :
A. the diode is open.
B. the series resistor is too small
c. the power supply voltage is too high.
D. none of these


The mass number is the sum of the
number of protons and the number of
neutrons in an atom.

State whether the given statement is
true or false.
A. True
B. False


Which of the following processes is responsible for the existence of a stream free of pollutants within a few miles downstream of a point at which a small amount of sewage is dumped into
it?
A. succession
B. Biological magnification
c. Evaporation
D. Photosynthesis
E. Decomposition


State True or False:
I: Candles can be safely stored at room temperature/ even though their
reaction with air is spontaneous at
room temperature. The reaction that takes place when a candle is burned involves a decrease in
entropy
A . True
B. False


Which of the following is/are not radioactive elements(s)?

This question has multiple correct options
A. Sulphur
B. tellurium
c. Selenium
D. Polonium


Which term of the sequence
\( \mathbf{7 2}, \mathbf{7 0}, \mathbf{6 8}, \mathbf{6 6}, \dots \dots \) is \( \mathbf{4 0} ? \)


A system where there is exchange of energy but not of mass is called
system.
A. insulated
B. isolated
c. open
D. closed


Which of the following molecules is a chiral?
\( A \)
B. II
\( c \)
\( D \)


The expression \( 2 \cos 10^{\circ}+\sin 100^{\circ}+ \)
\( \sin 1000^{\circ}+\sin 10000^{\circ} \) is simplified
then it simplifies to?


Identify the error in the given statement Circle the incorrect word and write the
correct word in the blank.
Noble gas show some properties of metals and some properties of nonmetals.


Subtract \( : \frac{3}{2} x^{2} y+\frac{4}{5} y-\frac{1}{3} x^{2} y z \) from
\( \frac{3}{5} x y z-\frac{2}{3} x^{2} y \)


The pH of a compound is found to be 9
The compound can be:
A. \( H C l \)
в. ма а Н
\( \mathbf{c} \cdot N a_{2} C O_{3} \)
D. \( C H_{3} \) СООН


The diameter of a brass rod is \( 4 m m \) and
Youngs modulus of brass is \( 9 \times \) \( 10^{10} N / m^{2} \) The force required to stretch
it by \( 0.1 \% \) of its length is
A. \( 360 \pi N \)
Then
в. \( 36 N \)
c. \( 144 \pi \times 10^{3} N \)
D. \( 36 \pi \times 10^{5} N \)


Which of the following statements is
false?
A. Blood from the right side of the heart is carried to the lungs by the pulmonary artery
B. The term pleura refers to the double layered covering of the kidney.
c. Pancreas is both an exocrine and endocrine gland
D. Scurvy is caused by the deficiency of vitamin C


Reproductive shoot apex is
A. Conical or dome shaped
B. Broad
C. Broad and flat
D. Narrow


An electromagnet is a permanent
magnet.
A. True
B. False


A Zener diode having break-down voltage \( 5.6 V \) is connected in reverse
bias with a battery of emf \( 10 \mathrm{V} \) and a
resistance of \( 100 \Omega \) in series. The
current flowing through the Zener is
\( \mathbf{A} \cdot 88 m A \)
в. \( 0.88 m A \)
c. \( 4.4 m A \)
D. \( 44 m A \)


How many tiles with dimensions \( 5 c m \)
and \( 12 \mathrm{cm} \) will be required to fit a
region with length \( 100 \mathrm{cm} \) and breadth
\( 96 \mathrm{cm} \) respectively?


If \( y \) co-ordenate of a particle moving in
\( \boldsymbol{x}-\boldsymbol{y} \) plane is given as \( \boldsymbol{y}= \)
\( \sqrt{60-9 x^{2} m / s} \) then graph between \( y \)
and \( x \) is
A. Straight line
B. Circle
c. parabolic
D. Ellipse


\( \boldsymbol{A}=\left[\begin{array}{cc}-\mathbf{3} & -\mathbf{5} \\ -\mathbf{6} & \mathbf{0}\end{array}\right], \boldsymbol{A}-\boldsymbol{B}=\mathbf{2} \boldsymbol{I} . \) Find \( \boldsymbol{B} \)
\( \mathbf{A} \cdot\left[\begin{array}{cc}-5 & -5 \\ -6 & -2\end{array}\right] \)
в. \( \left[\begin{array}{cc}1 & 2 \\ -3 & -6\end{array}\right] \)
с. \( \left[\begin{array}{cc}5 & 5 \\ -3 & -6\end{array}\right] \)
О \( \cdot\left[\begin{array}{ll}1 & 2 \\ 3 & 6\end{array}\right] \)


Mendeleev arrange the elements in the increasing order of their atomic weight in his periodic table.
If true enter 1 , else enter 0 .


What do you mean by electric generator? Differentiate between a.c. and d.c generators on the basis of
construction.


Fill in the blanks with approriate words. The impulse for voluntary muscles during forced breathing starts in


Give the main characters of
Dinoflagellates.


Verify the following:
(0,7,-10),(1,6,-6) and (4,9,-6) are
the vertices of an isosceles triangle.


Identify the highest soluble amine from the following.
A. Primary amine
B. Secondary amine.
c. Tertiary amine
D. none of these


In an AC circuit we have a black box of
\( 200 \Omega, 60^{\circ} . \) Frequency of \( A C \) is \( 250 \mathrm{Hz} \)
When a capacitor of \( 2 n \mu F \) is added
maximum power is obtained. The values of components of black box are
A \( \cdot R=100 \Omega, X_{L}=100 \sqrt{3} \Omega \)
B. \( R=100 \sqrt{3} \Omega, X_{L}=100 \Omega \)
c. \( R=100 \Omega, X_{C}=100 \sqrt{3} \Omega \)
D. \( X_{C}=100 \Omega, R=100 \sqrt{3} \Omega \)


What are the components of the
common food chain of a pond
ecosystem?
A. Phytoplanktons, zooplanktons, aquatic plants, small aquatic animals
B. Phytoplanktons, zooplanktons, aquatic plants, small aquatic animals, small fishes, big fishes, birds
C. Phytoplanktons, zooplanktons
D. None of the above


Succession on sand dune is
A. Lithosere
B. Psychrosere
c. Psammosere
D. Halosere


Chlorine is liberated when we heat:
A. \( K M n O_{4}+N a C l \)
В \( \cdot P b_{2}\left(N O_{3}\right)_{4}+M n O_{2} \)
c. \( K_{2} C r_{2} O_{7}+M n O_{2} \)
D. \( K_{2} C r_{2} O_{7}+H C l \)


are rixed at separatıon or \( \boldsymbol{a} \) trom eacn
other as shown. The area of each plate is
A. Plate 1 is given charge \( +Q \) while
plate 2 and 3 are neutral and are
connected to each other through coil of inductances \( L \) and switch \( S . \) If
resistance of all connected wires is
neglected the maximum current flow, through coil after closing switch is
\( \left(\boldsymbol{C}=\varepsilon_{0} \boldsymbol{A} / \boldsymbol{d}\right) \) (neglect fringe effect)
A \( \cdot \frac{Q_{0}}{\sqrt{L C}} \)
в. \( \frac{Q_{0}}{\sqrt{2 L C}} \)
c. \( \frac{2 Q_{0}}{\sqrt{L C}} \)
D. \( \frac{Q_{0}}{2 \sqrt{L C}} \)


The electronic configuration \( 1 s^{2} 2 s^{2} 2 p x^{1} 2 p y^{1} 2 p z^{1} \) is of:
A.
B.
c. Na
D.


What are the renewable and non-
renewable sources of energy?


The mathematical study of randomness is called probability theory.
A. True
B. False
c. Partly true
D. None of above


Name the forces acting on a plastic bucket containing water held above ground level in your hand. Discuss why
the forces acting on the bucket do not bring a change in its state of motion.


In the AC circuit shown, \( X_{L}=7 \Omega, R= \)
\( 4 \Omega \) and \( X_{c}=4 \Omega . \) The reading of the
ideal voltmeter \( V_{2} \) is \( 8 \sqrt{2} \). The reading
of idea voltmeter \( V_{1} \) will be :
A. 20 volt
B. 7 volt
\( c \cdot 8 \) volt
D. 10 volt


order to calculate the binding energy
per nucleon of an element \( _{z} X^{A}, \) given
the actual mass of \( _{z} X^{A}(\mathrm{M}), \) mass of
proton \( \left(\boldsymbol{m}_{\boldsymbol{p}}\right) \) and mass of neutron \( \left(\boldsymbol{m}_{\boldsymbol{n}}\right) \)
(All the values are given in atomic mass units)
(a) Note the actual mass of the nucleus
(M), number of nucleons in \( _{z} \boldsymbol{X}^{\boldsymbol{A}}, \boldsymbol{m}_{\boldsymbol{p}} \)
and \( \boldsymbol{m}_{\boldsymbol{n}} \)
(b) Calculate the mass defect of the
given nucleus.
(c) Find the number of protons and number of neutrons in the nucleus.
(d) Determine the sum of the individual
masses of constituents in \( _{z} \boldsymbol{X}^{\boldsymbol{A}} \)
(e) Calculate the binding energy (B. E) of the nucleus.
(f) Divide it with the number of
nucleons present in the element to get
binding energy per nucleon.
A. a ed cb f
B. a c d bef
\( c \cdot a c b d e f \)
D. a d c be f


A comb run through ones hair attracts
small bits of paper. What happens, if
the hair are wet or if it is a rainy day?
A. The comb does not get charged and it will not attract small bits of paper
B. The comb does not get charged but it will attract small bits of paper.
C. The comb does gets charged and it will attract small bits of paper.
D. The comb does gets charged but it will not attract small bits of paper.


Write vector relation between angular velocity \( (\vec{\omega}), \) tangential velocity \( (\vec{V}) \) and position vector \( (\vec{r}) \)


Find out relation between I and II ?
A. Enantiomers
B. Diastereomers
c. Homomers
D. Structural isomers


In alternating current
A. The direction of current is always positive
B. The direction of current is always negative
C. The direction of current changes constantly
D. The direction of current is either positive or negative


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


Do all the stars in the sky move?
Explain.


In case of conductors and insulators, if an electric field is applied then conduction current density \( (\vec{J}) \) is:
This question has multiple correct options
A. in the direction of electron flow
B. in the direction of proton flow.
c. in the direction of electric field
D. against the direction of electric field


Show that the surface tension of a
liquid is numerically equal to the
surface energy per unit area.


Show how internal energy U varies with \( T \) in isochoric, isobaric and adiabatic
process?


Active mass of \( 5 g \) CaO is:
\( A \cdot 2 \)
B. 1
\( c \cdot 5 \)
D.


Q Type your question-
along \( x \) -axis. The equilibrium of a positive test charge placed at the point 0 midway
between them is stable for
displacements along the \( x \) -axis.
Reason: Force on test charge is zero.
A. If both Assertion arid Reason are correct and Reason is the correct explanation of Assertion.
B. If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion,
C. If Assertion is correct but Reason is incorrect.
D. If Assertion is incorrect but Reason is correct


The numerical value of energy involved in the given process \( K \rightarrow K^{-} \) is less
than that of which of the following
processes?
\( \mathbf{A} \cdot K^{-} \rightarrow K \)
В. \( K \rightarrow K^{+} \)
c. Both (a) and (b)
D. None of these


The given figure shows diagrammatic
representation of exchange of gases at
the alveolus and the body tissues with
blood and transport of oxygen and
carbon dioxide. Identify the blood
vessels \( A \) to \( D \)
A. Systemic vein Pulmonary artery Pulmonary vein Systemic artery
B. Systemic artery Pulmonary artery Pulmonary vein Systemic vein
C. Pulmonary artery Systemic vein Pulmonary vein Systemic artery
D. Systemic vein Pulmonary vein Pulmonary artery Systemic artery


In the electric field of charge \( Q \), another
charge is carried from \( \boldsymbol{A} \) to \( \boldsymbol{B} . \boldsymbol{A} \) to \( \boldsymbol{C}, \boldsymbol{A} \)
to \( D \) and \( A \) to \( E \), then work done will be
A. Minimum along path \( A B \).
B. Minimum along path \( A D \).
C. Minimum along path \( A E \).
D. zero along all the paths


A shopkeeper sells a badminton marked at Rs. 30 at \( 15 \% \) discount and
gives a shuttle cock costing Rs. 1.50 free with each badminton. He then
makes a profit of \( 20 \% . \) His cost price per badminton is
A . Rs. 35
B. Rs. 30
c. Rs. 25
D. Rs. 20


\( \boldsymbol{S} \boldsymbol{O}_{2} \) gas was prepared by
(i) burning sulphur in oxygen,
(ii) reacting sodium sulphite with
dilute \( H_{2} S O_{4} \) and
(iii) heating copper with conc. \( \boldsymbol{H}_{2} \boldsymbol{S O}_{4} \). It was found that in each case sulphur and oxygen combined in the ratio of 1: 1 The data illustrates the law of :
A. conservation of mass
B. multiple proportions
c. constant proportions
D. reciprocal proportions


Solve \( \boldsymbol{y}= \)
\( \tan ^{-1}\left(\frac{3 x-x^{3}}{1-3 x^{2}}\right),-\frac{1}{\sqrt{3}}<x<\frac{1}{\sqrt{3}} \)


The stele found in monocot is
A. Haplostele
B. Atactostele
c. Dictyostele
D. Actinostele


Mucus is secreted by the
A. Stomach
B. Duodenum
c. Large intestine
D. All of the above


Find the angle of the vector of the
angular velocity of the cone it forms
with the vertical.
\( \mathbf{A} \cdot 60^{\circ} \)
B \( .67^{\circ} \)
\( c \cdot 62^{\circ} \)
D. \( 50^{\circ} \)


A current is divided into two resistors
connected in parallel according to Kirchhoff's law, then the heat produced in the combination is
A. zero
B. Cannot be predicated
c. Minimum
D. Maximum


Consider the linear inequations and
solve them graphically:
\( \mathbf{3} \boldsymbol{x}-\boldsymbol{y}-\mathbf{2}>\mathbf{0} ; \boldsymbol{x}+\boldsymbol{y} \leq \mathbf{4} ; \boldsymbol{x}> \)
\( \mathbf{0} ; \boldsymbol{y} \geq \mathbf{0} \)
Which of the following are corner points of the convex polygon region of the
solution?
A. (0,0)
(年) \( 0,0,0,0,0,1, \)
B. (2,3)
c. (0,4)
(年. \( (0,4)) \)
D \( \cdot\left(\frac{3}{2}, \frac{5}{2}\right) \)


If \( \boldsymbol{A}_{\mathbf{3} \times \mathbf{3}} \) and \( |\boldsymbol{A}| \neq \mathbf{0} \Rightarrow \boldsymbol{A} \boldsymbol{d} \boldsymbol{j}(\boldsymbol{A} \boldsymbol{d} \boldsymbol{j} \boldsymbol{A})= \)
\( \mathbf{A} \cdot|A|^{2} A \)
B \( \cdot|A| A \)
c. \( \frac{A}{|A|} \)
D. \( \frac{A}{|A|^{2}} \)


\( \mu=\sqrt{15} \) is true for the pair:
A \( \cdot C o^{2+}, C r^{3+} \)
B. \( F e^{+2}, C r^{+3} \)
\( \mathbf{c} \cdot F e^{+3}, F e^{+2} \)
D. \( M n^{+2}, F e^{+2} \)


Which of the following does not belong to the group formed by the others?
A. Copper coin
B. Steel spoon
c. wooden ruler
D. Iron nail


Ionic compounds in general posses
both:
A. high melting points and non-directional bonds
B. high melting points and low boiling points
C. directional bonds and low boiling points
D. high solubilities in polar and non-polar solvents


The assembly of two discs as shown in figure is placed on a rough horizontal surface and the front disc is given an
initial angular velocity \( \omega_{0} \) Determine the final linear and angular velocity when both the discs start rolling. It is given that friction is sufficient 10
sustain rolling in the rear wheel from the starting of motion


a) Explain Heisenberg's uncertainly principle with mathematical derivation
b) Calculate the wavelength, frequency
and wave number of light wave whose period is \( 2.0 \times 10^{-10} \) sec


The density of an object that has a mass of 0.86 grams and a volume of \( 0.953 \mathrm{ml} \) will be:
A \( .1 .0 \mathrm{g} / \mathrm{m} \)
B. \( 0.90 \mathrm{g} / \mathrm{ml} \)
c. \( 0.902 \mathrm{g} / \mathrm{ml} \)
D. none of the above


A white salt is readily soluble in water and gives a colourless solution with \( \boldsymbol{p} \boldsymbol{H} \)
of about \( 9 . \) The salt would be:
A. \( N H_{4} N O_{3} \)
в. \( C H_{3} \) СОО Na а
\( \mathrm{c} \cdot \mathrm{CH}_{3} \mathrm{COONH}_{4} \)
D. \( C a C O_{3} \)


Arrange the following rational numbers in ascending order \( :-\frac{7}{8}, \frac{36}{-12}, \frac{5}{-4}, \frac{-2}{3} \)


The nuclear reaction that takes place in a nuclear reactor is
A. controlled fission reaction
B. uncontrolled fission reaction
c. nuclear fusion reaction
D. none of the above


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


Milk of sulphur finds its applications in
A. medicines
B. photography
c. head of match stick
D. vulcanization


How is phenol manufactured by
Cumene process?


A boy is moving on a straight road against a frictional force of \( 5 N . \) After
travelling a distance of \( 1.5 k m, \) he forgets the correct path at a round about (see fig.) of radius \( 100 m \) However, he moves on the circular path
for one and half cycle and then he moves
forward upto \( 2.0 k m . \) Calculate the work
done by him \( (\pi=3.14) \)


The process in which a simple permanent tissue like parenchyma and collenchyma regain their power of cell division and becomes lateral
meristems. It helps in the formation of secondary tissues known as
A. Dedifferentiation
B. Cell division
c. Autolysis
D. Totipotency


Let the H.M and G.M of two positive numbers be in the ratio 4: 5
then largest number divided by smallest number of the two numbers?


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


The ion exchange resins helps in:
A. Removing moisture
B. Controlling humidity
C. Removing hardness of water
D. All of the above


If \( \boldsymbol{A}=\left[\begin{array}{ccc}2 & -1 & 1 \\ -1 & 2 & -1 \\ 1 & -1 & 2\end{array}\right], \) verify that
\( \boldsymbol{A}^{3}-\mathbf{6} \boldsymbol{A}^{2}+\mathbf{9} \boldsymbol{A}-\mathbf{4} \boldsymbol{I}=\mathbf{0} . \) Hence find
\( \boldsymbol{A}^{-1} \)


A plant in your garden avoids photorespiratory losses, has improved water use efficiency, shows high rate of photosynthesis at high temperature and has improved efficiency of nitrogen utilisation. In which of the following physiological groups would you assign this plant?
A. \( C_{3} \)
в. \( C_{4} \)
c. сАм
D. Nitrogen fixer


Natural rubber is a polymer of:
A. Neoprene
B. Chloroprene
C. Isoprene
D. styrene


Histogen theory states that epidermis is derived from the
A. Periblem
B. Cambium
c. cortex
D. Dermatogen


The best method to prepare neopenty chloride is:
A \( \cdot\left(C H_{3}\right)_{3} C C H_{2} O H \stackrel{P C l_{5},}{\longrightarrow} \)
в. \( \left(C H_{3}\right)_{3} C C H_{2} O H \stackrel{\text {НС}, \text {А}}{\longrightarrow} \)
C. \( \left(C H_{3}\right)_{3} C C H_{2} O H^{S_{o} C l_{2}, p y r i d i n e} \)
D. \( \left(C H_{3}\right)_{3} C C H_{3} \stackrel{C l_{2}, h \nu \Delta}{\longrightarrow} \)


n fig if \( \boldsymbol{A B} \| \boldsymbol{D} \boldsymbol{E}, \angle \boldsymbol{B A C}=\mathbf{3 5}^{\circ} \) and
\( \angle C D E=53^{\circ}, \) find \( \angle D C E \) in degrees


The molecule which has zero dipole
moment is:
A \( . C H_{3} C l \)
в. \( N F_{3} \)
\( \mathrm{c} \cdot B F_{3} \)
D. \( C l O_{2} \)


Organic ion exchange resins purify hard
water to yield:
A. Distilled water
B. Only decalcified water
c. Deionised water
D. water having relatively high concentration of \( O H^{-} \) ion


Prove that \( \left|\begin{array}{ccc}a^{2} & b c & a c+c^{2} \\ a^{2}+a b & b^{2} & a c \\ a b & b^{2}+b c & c^{2}\end{array}\right| \)
\( =4 a^{2} b^{2} c^{2} \)


Determine the three planes through the intersection of the planes \( \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}=\mathbf{1} \)
and \( 2 x+3 y-z+4=0 \) which are
parallel to the three co - ordinate axes.
Also find the equation of the plane
perpendicular to the \( y z- \) plane and
passing through the point (2,3,1) and
(4,-5,3)
A \( \cdot y-3 z-6=0 ; x-4 z=7 \) and \( 3 x-4 y-3=0 \)
\( y+4 z+7=0 \)
B. \( y-3 z+6=0 ; x+4 z=7 \) and \( 3 x+4 y+3=0 \)
\( y-4 z+7=0 \)
c. \( y+3 z+6=0 ; x+4 z=7 \) and \( 3 x+4 y+3=0 \)
\( y-4 z-7=0 \)
D. \( y-3 z+6=0 ; x+4 z=7 \) and \( 3 x+4 y+3=0 \)
\( y+4 z-7=0 \)


Evaluate \( \int_{0}^{5} x^{4} d x \)


The value of \( n \) in \( M n O_{4}^{-}+8 H^{+}+ \)
\( \boldsymbol{n} e^{-} \longrightarrow \boldsymbol{M} \boldsymbol{n}^{2+}+\boldsymbol{4} \boldsymbol{H}_{2} \boldsymbol{O} \) is:
A. 5
B. 4
\( c \cdot 2 \)
D.


Identify the correct statement of Work-
Energy Theorem:
A. Work done by all the forces on a particle to displace it is equal to its change in kinetic energy.
B. Work done by all the forces on a particle is equal to its change in mechanical energy
C. Work done by all the forces acting on a particle is equal to change in its potential energy.
D. Work done by a force on a particle is equal to change in its kinetic energy.


Two metallic blocks \( P \) and \( Q \) of masses
in ratio 2: 1 are given same amount of
heat. If their temperature rise by same amount, compare their specific heat
capacities.
A . 1: 1
B . 2: 1
c. 1: 2
D. 1: 4


All the edges of a block with parallel faces are unequal. Its longest edge is twice its shortest edge. The ratio of the maximum to minimum resistance
between parallel faces is
A .2
B. 4
\( c \cdot 8 \)
D. indeterminate unless the length of the third edge is specified


The triangle formed by \( B C= \)
\( 5 c m, A C=3 c m, A B=5.8 c m \) is:
A. a right angled \( \Delta \)
B. an isosceles \( \Delta \)
c. an equilateral \( \Delta \)
D. a scalene \( \Delta \)


Pick the correct match.
A. Helicase
(i) To join nucleotides on DNA
B. Gyrase
(ii) To open DNA
C. Primase
(iii) Unwind DNA
D. DNA
(iv) For RNA printing polymerase III
A. A-ii, B-iii, C-iv, D-i
B. A-i, B-ii, C-iii, D-iv
c. A-ii, B-iv, C-iii, D-i
D. A-iv, B-iii, C-i, D-ii


Two moles of helium gas undergo a
cyclic process as shown in Figure.
Assuming the gas to be ideal, calculate
the following quantities in this process.
The net change in the heat energy


In the given sequence of reactions, predict \( (\boldsymbol{X}) \)
\( (\boldsymbol{X}) \frac{\boldsymbol{K O H}}{\boldsymbol{H}_{2} \boldsymbol{O}}(\boldsymbol{Y}) \frac{\boldsymbol{A l}_{2} \boldsymbol{O}_{3}}{4 \boldsymbol{3} \boldsymbol{3} \boldsymbol{K}}(\boldsymbol{Z}) \stackrel{[\boldsymbol{O}]}{\longrightarrow} \)
\( 2 m o l C H_{3} C O O H \)
\( \mathbf{A} \cdot C H_{3} C H_{2} C H(I) C H_{3} \)
в. \( C H_{3} C H_{2} C H_{2} C H_{2} I \)
c. \( C H_{3} C H(I) C H(I) C H_{3} \)
D. \( C H_{3} C H(I) C H_{2} C H_{2} I \)


Find the order and degree of the differential equation:
\( \sqrt{1+\left(\frac{d y}{d x}\right)^{2}}=1+x \)


Noble gases are chemically inert. Give
one reason.