Dissolution of salt in water is a
change


Substance which give good conducting aqueous solution are called:
A. weak electrolytes
B. strong electrolytes
c. non-electrolytes
D. catalysts


Hydrogen can't be produced by the
action of dil. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) on:
A. \( C u \)
в. \( Z \) и
c. \( F e \)
D. \( A l \)


Q Type your question
shown in Fig. The cross sectional area of
\( A \) is half that of \( B \) and the Youngs
modulus of \( A \) is twice that of \( B . A \)
weight \( \mathrm{W} \) is hung as shown. The value of
\( x \) so that \( W \) produces equal stress in
wires \( A \) and \( B \) is
\( A \cdot \frac{L}{3} \)
в. \( L \) \( \overline{2} \)
c. \( \frac{2 L}{3} \)
D. \( \frac{3 L}{4} \)


An insulating sphere with radius a has
a uniform charge density \( \rho . \) The sphere
is not centered at the origin but at \( r=b \)
Find the electric field at any point inside sphere is \( \boldsymbol{E}=\frac{\boldsymbol{\rho}(\boldsymbol{x}-\boldsymbol{b})}{\boldsymbol{n} \varepsilon_{0}} . \) what is
the value of \( n \)


The reaction \( \boldsymbol{H}_{2} \boldsymbol{S}+\boldsymbol{H}_{2} \boldsymbol{O}_{2} \rightarrow \boldsymbol{S}+ \)
\( 2 H_{2} O \) describes:
A . acidic nature of \( H_{2} O_{2} \)
B. alkaline nature of \( H_{2} O_{2} \)
C . oxidizing nature of \( H_{2} O_{2} \)
D. reducing nature of \( H_{2} O_{2} \)


Factorise \( \left(3-4 y-7 y^{2}\right)^{2}-(4 y+1)^{2} \)
A \( \cdot\left(4-7 y^{2}\right)\left(2-8 y-7 y^{2}\right) \)
B \( \cdot\left(7 y^{2}-4\right)\left(2-8 y-7 y^{2}\right) \)
c. \( \left(4-7 y^{2}\right)\left(7 y^{2}+8 y-2\right) \)
D \( \cdot\left(7 y^{2}-4\right)\left(7 y^{2}-8 y-2\right) \)


The radius of a hydrogen atom is \( 0.5 \dot{A} \) Find the order of magnitude of volume
of 1 mole hydrogen in \( m^{3} . \) Given that 1
mole of hydrogen has \( 6.02 \times 10^{23} \)
hydrogen atoms.
A \( \cdot 2 \times 10^{-4} m^{3} \)
B. \( 10^{-3} m^{3} \)
\( \mathbf{c} \cdot 10^{-7} m^{3} \)
D. \( 10^{-2} m^{3} \)


The source of ultraviolet light is:
A . electric bulb
B. red hot iron ball
C. sodium vapour lamp
D. carbon arc-lamp


Two runners start simultaneously from
the same point on a circular \( 200 m \)
track in the same direction. Their
speeds are \( 6.2 m s^{-1} \) and \( 5.5 m s^{-1} . \) How
far from the starting point the faster and the slower runner would be side by
side again?
A. \( 150 \mathrm{m} \) away from the starting point
B. \( 170 m \) away from the starting point
c. \( 120 m \) away from the starting point
D. none


Complex inflorescence of which plant is
used as food?
A. Rhaphanus sativus
B. Brassica rapa
c. Brassica oleracea
D. Mustard


Inside human body,which of the following is responsible for heat transfer,
A. conduction
B. forced convection
c. free convection
D. none of the above


Define cryoscopic constant.


Which of the following statements are
correct?
A. Nylon 2-nylon 6 is a poly-amide copolymer of alanine
B. 3-Hydroxy pentanoic acid is a monomer of Nylon 2nylon 6
C. \( P H B V \) can never be used in the manufacture of orthopedic devices
D. None of these


The embryo of fish is covered by
A. Amnion
B. Chorion
C. Allantois
D. None of the above


Aluminium is much more reactive than
iron because its standard reduction
potential is higher than iron. Still, aluminium is less easily corroded than
iron because:
A. aluminium reacts with atmospheric carbon dioxide to form a self-protective layer of \( A l_{2} O_{3} \)
B. it has a higher reducing power and forms a self protective layer of \( A l_{2} O_{3} \)
C. it has a higher reducing power and does not react with oxygen so easily
D. both A and B.


\( \sin ^{-1}|\sin x|=\sqrt{\sin ^{-1}|\sin x|} \) then \( x= \)
This question has multiple correct options
A \( . n \pi-1 \)
в. \( n \pi \)
c. \( n \pi+1 \)
D. \( n \frac{\pi}{2}+1 \)


In the matrix, lies the bone cells, called
A. Chondroclasts
B. Osteoclasts
c. osteoblasts
D. osteocytes


Write short note on solar spectrum or
continuous spectrum


If \( \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{0} & \boldsymbol{c} & -\boldsymbol{b} \\ -\boldsymbol{c} & \boldsymbol{0} & \boldsymbol{a} \\ \boldsymbol{b} & \boldsymbol{-} \boldsymbol{a} & \boldsymbol{0}\end{array}\right] \) and \( \boldsymbol{B}= \)
\( \left[\begin{array}{lll}a^{2} & a b & a c \\ b a & b^{2} & b c \\ c a & c b & c^{2}\end{array}\right] \) then \( A B \) is equal to
\( A \)
B.
c. \( 2 I \)
D. none of these


Select the correct statements.
This question has multiple correct options
A. Oxides of boron \( \left(B_{2} O 3\right) \) and silicon \( \left(S i O_{2}\right) \) are acidic in nature.
B. Oxides of aluminium \( \left(A l_{2} O_{3}\right) \) and gallium \( \left(G a_{2} O_{3}\right) \) are amphoteric in nature.
C. Oxides of indium \( \left(I n_{2} O_{3}\right) \) and thallium \( \left(T l_{2} O_{3}\right) \) are basic in nature.
D. Oxides of germanium \( \left(G e O_{2}\right) \) and tin \( \left(S n O_{2}\right) \) are acidic in nature.


A uniform metal rod of \( 2 m m^{2} \) cross
section is heated from \( 0^{\circ} \mathrm{C} \) to \( 20^{\circ} \mathrm{C} \). The
coefficient of linear expansion of the rod is \( 12 \times 10^{-6 / 0} \mathrm{C} \). Its Young's modulus of
elasticity is \( 10^{11} \mathrm{N} / \mathrm{m}^{2} \). The
energy stored per unit volume of the rod
is :
\( \mathbf{A} \cdot 2880 J / m^{3} \)
B . \( 1500 J / m^{3} \)
c. \( 5760 J / m^{3} \)
D. \( 1440 J / m^{3} \)


toppr
Q Type your question_
move in the direction of current and
return to P. The potential \( V \) at every
point of the conductor is plotted against
the distance covered (x). Which of the
following best represents the resulting
Curve?
\( \mathbf{A} \)
\( B \)
\( \mathbf{C} \)
\( D \)


Consider the following equations for a cell reaction, then:
\( \boldsymbol{A}+\boldsymbol{B} \rightleftharpoons \boldsymbol{C}+\boldsymbol{D}, \quad \boldsymbol{E}^{o}=\boldsymbol{x} \) volt, \( \boldsymbol{K}_{e q}= \)
\( \boldsymbol{K}_{\mathbf{1}} \)
\( \mathbf{2 A}+\mathbf{2 B} \rightleftharpoons \mathbf{2 C}+\mathbf{2 D}, \quad \boldsymbol{E}^{o}=\boldsymbol{y} \) volt
\( \boldsymbol{K}_{e q}=\boldsymbol{K}_{2} \)
A \( \cdot x=y, K_{1}=K_{2} \)
B . \( x=2 y, K_{1}=2 K_{2} \)
C \( . x=y, K_{1}^{2}=K_{2} \)
D. \( x^{2}=y, K_{1}^{2}=K_{2} \)


What is the formula for spherical mirrors for object distance p and image distance q?
A \( \cdot \frac{1}{p}+q=\frac{1}{f} \)
в. \( \frac{1}{p}+\frac{1}{q}=\frac{1}{f} \)
c. \( \frac{1}{p}+\frac{1}{q}=f \)
D. \( p+\frac{1}{q}=\frac{1}{f} \)


Identify the median class.
\( \begin{array}{lllll}\text { Farm } & \mathbf{2 0}- & \mathbf{5 0}- & \mathbf{8 0}- & \mathbf{1 1 0} \\ \text { size } & \mathbf{5 0} & \mathbf{8 0} & \mathbf{1 1 0} & \mathbf{1 4 0}\end{array} \)
Rooms \( 4 \quad 8 \quad 12 \)
A. \( 20-50 \)
B . \( 50-80 \)
c. \( 80-110 \)
D. \( 110-140 \)


Enthalpy of sublimation of iodine is
\( 24 \operatorname{cal} g^{-1} \) at \( 200^{\circ} \mathrm{C} . \) If specific heat of
\( I_{2}(s) \) and \( I_{2}(\text { vap ) are } 0.055 \) and \( 0.031 \mathrm{cal} \mathrm{g}^{-1} \mathrm{K}^{-1} \) respectively, then
enthalpy of sublimation of iodine at
\( 250^{\circ} \mathrm{C} \) in \( \operatorname{cal} g^{-1} \) is :
A . 2.85
B. 11.4
\( c .5 .7 \)
D . 22.8


The droplets of water arranged at the
edges of leaves of roses in the morning
are
A. Water drops condensed from the atmosphere during night at low temperatures
B. Water transpired from the stomata and lenticels
C. Water produced on the leaves from the reaction of hydrogen and atmospheric oxygen
D. None of the above


Find the coordinates of the points where
the graph of the equation \( 3 x+4 y=21 \)
intersect \( x- \) axis and \( y- \) axis.


Distinguish between 'paramagnetic' and 'ferromagnetic' substances.


Give reason as to why a newly made
quilt is warmer than an old one.


In the given diagram, \( O \) is the centre of
the circle and \( P Q R \) is a straight line.
The value of \( x \) is
A \( \cdot 110^{\circ} \)
B. \( 120^{\circ} \)
\( c \cdot 130^{\circ} \)
D. \( 140^{\circ} \)


The unit of rate constant for a zero order
reaction is:
A \( \cdot \operatorname{mol} L^{-1} s^{-1} \)
B. \( L \) mol \( ^{-1} s^{-1} \)
c. \( L^{2} \) mol \( ^{-2} s^{-1} \)
D. \( s^{-1} \)


Find the solution of the given equation:
\( \frac{[9 x-(3+4 x)]}{[2 x-(7-5 x)]}=\frac{6}{7} \)


Select the incorrectly matched pair.
A. Leukopenia - Fall in WBCs count
B. Polycythemia - Abnormal rise in RBCs count
C. Thrombocytosis - Decrease in number of platelets
D. Erythrocytopenia - Decrease in number of RBCs


Shape of the nucleus of WBC is usually
A. Spherical
B. Irregular
c. oval
D. spindle shaped


Two magnetic poles of strengths \( 10 \mathrm{Am} \) and 20 Am are separated by a distance of \( 10 \mathrm{cm} . \) The ratio of force on them is
A . 1:
B. 1: 2
\( c \cdot 2: \)
D. 1: 4


The quantum number which
determines the energy of a sublevel is:
\( A \cdot n \)
B. \( l \)
c. both \( A \) and \( B \)
D. neither A nor B


Carbon can not be used i the reduction
of \( A l_{2} O_{3} \) because:
A. its is expensive.
B. the enthalpy of formation of is \( C O_{2} \) more than that of \( A l_{2} O_{3} \)
c. pure carbon is not easily available.
D. the enthalpy of formation of \( A l_{2} O_{3} \) is too high


A semiconductor is a material with a
small but non-zero band gap that
behaves as an insulator at absolute
zero but allows thermal excitation of
electrons into its
temperatures that are below its melting point.
A. номо
B. valence band
c. conduction band
D. LUMO


A car weighs 1800 kg. The distance
between its front and back axles is 1.8
m. Its centre of gravity is 1.05 m behind the front axle. Determine the force
exerted by the level ground on each front wheel and each back wheel.


Unpolarized light falls on two polarizing sheets placed one on top of the other.
What must be the angle between the characteristic directions of the sheets.
If the intensity of the final transmitted
light is one-third the maximum, intensity of the first transmitted beam?
\( \mathbf{A} \cdot 75^{\circ} \)
B . \( 55^{\circ} \)
\( c \cdot 35^{\circ} \)
D. \( 15^{\circ} \)


The concentration of \( O H^{-} \) ions in a
solution with the \( \boldsymbol{H}^{+} \) ions
concentration of \( 1.3 \times 10^{-4} \mathrm{M} \) is?
A \( .7 .7 \times 10^{-4} \)
B . \( 1.3 \times 10^{-4} \) М
c. \( 2.6 \times 10^{-8} \) М
D. \( 7.7 \times 10^{-11} \) М


The PDF of variable x: number of times
sum 6 appears on in two throw of a pair of dice is
\[
\begin{array}{cc}
\mathbf{0} & \mathbf{1}
\end{array}
\]
\( p(x) \)
then values of \( a, b, c \) are.
A \( \cdot a=\frac{2}{36}, b=\frac{3}{36}, c=\frac{5}{36} \)
В. \( a=\frac{961}{36}, b=\frac{310}{36}, c=\frac{25}{36} \)
\( ^{\mathbf{C}} \cdot_{a}=\frac{961}{1269}, b=\frac{310}{1296}, c=\frac{25}{1296} \)
D. \( a=\frac{91}{36}, b=\frac{30}{36}, c=\frac{25}{36} \)


The point (0,3) is nearest to the curve \( x^{2}=2 y \) at
A \( \cdot(2 \sqrt{2}, 0) \)
в. (0,0)
D. none of these


What is the incorrect option for
sucrose?
\( A \cdot \) It is also named as invert sugar
B. It is a non reducing sugar.
C. The glycosidic linkage present is \( \beta-1,4^{\prime}-g l y \) cosidic bond
D. One of the hydrolysis product is glucose


A beam of light of wavelength 600 nm from a distance source falls on a single
slit 1 mm wide and a resulting
diffraction pattern is observed on a
screen 2 m away. The distance between
the first dark fringes on either side of central bright fringe is
\( \mathbf{A} \cdot 1.2 \mathrm{cm} \)
B. \( 1.2 m m \)
c. \( 2.4 c m \)
D. \( 2.4 m m \)


A copper wire of resistance \( 4 \Omega \) is
stretched to thrice its original length.
The resistance of stretched
wirebecomes x times. Find the value of
\( \mathbf{x} \)


Which are the following consequences of deforestation?
A. Decrease in rainfall
B. Decrease in fertility of soil
c. Increased global warming
D. All of the above


square centimetres = 1
square decimetre \( \left(d m^{2}\right) \)
A . 100
B . 10
c. 1000
D. \( 0 . \)


Determine, graphically, the vertices of the triangle formed by the lines
\( \boldsymbol{y}=\boldsymbol{x}, \mathbf{3} \boldsymbol{y}=\boldsymbol{x}, \boldsymbol{x}+\boldsymbol{y}=\mathbf{8} \)
B . (0,0),(4,4),(0,2)
D. (0,0),(4,4),(6,2)


The 120 days is the life span of
A. Red blood cells
B. White blood cells
C. Platelets
D. Red blood cells and Platelets


What is the name of \( h \& \) what is the
value?


Interference fringes are produced by a double-slit experiment and a piece of
plane parallel glass refractive index 1.5 is interposed in one of the interfering beams. If the fringes are displaced
through 30 fringe widths for light of wavelength \( 6 \times 10^{-5} \mathrm{cm}, \) if the
thickness of the plate is \( 3.6 \times 10^{-X} \mathrm{cm} \)
Find \( X ? \)


\( \sin \theta+\cos \theta=1 \) where \( \theta= \)
A \( \cdot 30^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 90^{\circ} \)


Give the IUPAC name and molecular
formula of a substance which is used
as a solvent in paint and in lacquer industries:


Newtons law are not valid in
A. Both inertial as well as non- inertial frame of
reference.
B. A frame moving with constant velocity w.r.t. an inertial frame.
C. All reference frames which are at rest w.r.t. an inertial
frame
D. The reference frame attached to the earth.


Let \( A(-1,0) \) and \( B(2,0) \) be two points.
A point \( M \) moves in the plane in such a
way that \( \angle M B A=2 \angle M A B \). Then the
point \( M \) moves along
A. A straight line
B. A parabola
c. An ellipse
D. A hyperbola


\( K O_{2} \) is an example of:
A. normal oxide
B. super oxide
c. sub oxide
D. peroxide


\( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4} \rightleftharpoons \boldsymbol{H}^{\oplus}+\boldsymbol{H}_{2} \boldsymbol{P} \boldsymbol{O}_{4}^{\ominus} ; \boldsymbol{K}_{a_{1}} \)
\( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4}^{\ominus} \rightleftharpoons \boldsymbol{H}^{\oplus}+\boldsymbol{H} \boldsymbol{P} \boldsymbol{O}_{4}^{2-} ; \boldsymbol{K}_{a_{2}} \)
\( \boldsymbol{H} \boldsymbol{P} \boldsymbol{O}_{4}^{2-} \rightleftharpoons \boldsymbol{H}^{\oplus}+\boldsymbol{P} \boldsymbol{O}_{4}^{3-} ; \boldsymbol{K}_{a_{3}} \)
Mark out the incorrect statements
This question has multiple correct options
\( \mathbf{A} \cdot K_{a_{1}}>K_{a_{2}}>K_{a_{3}} \)
B. \( _{p H\left(H_{2} P O_{4}^{\circ}\right)=\frac{p K_{a_{1}}+p K_{a_{2}}}{2}} \)
C. Both \( H_{3} P O_{4} \) and \( H_{2} P O_{4}^{\odot} \) are more acidic than \( H P O_{4}^{2} \)
D. only \( H P O_{4}^{2-} \) is amphiprotic anion in the solution


In resonance column experiment, the velocity of sound is given by \( v= \) \( 2 n\left(l_{2}-l_{1}\right) . \) Where \( n \) is frequency \( =325 \)
Hz measured accurately. \( l_{1}, l_{2} \) are
resonating length and are measured as \( l_{1}=25.0 c m, l_{2}=75.0 c m \) then speed of
sound is
A. \( 350 m / s \)
в. \( 327 m / s \)
c. \( 325 m / s \)
D. \( 400 \mathrm{m} / \mathrm{s} \)


A neutral water molecules \( \left(H_{2} O\right) \) in its
vapour state has an electric dipole moment of \( 6 \times 10^{-30} \mathrm{Cm} . \) If the
molecule is placed in an electric field of \( 1.5 \times 10^{4} N C^{-1}, \) the maximum torque
that the field can exert on it is nearly:
A \( .4 .5 \times 10^{-26} \mathrm{Nm} \)
B. \( 4 \times 10^{-34} \mathrm{Nm} \)
c. \( 9 \times 10^{-26} \mathrm{Nm} \)
D. \( 6 \times 10^{-26} \mathrm{Nm} \)


If \( A=\left|\begin{array}{cc}2 & -3 \\ 3 & 2\end{array}\right| \) and \( B=\left|\begin{array}{cc}3 & -2 \\ 2 & 3\end{array}\right| \) then \( 2 A-B= \)
A. 11
\( \begin{array}{ll}1 & 4 \\ 4 & 1\end{array} \)
в. \( \mid \begin{array}{ll}1 & 4 \\ 1 & 4\end{array} \)
c. \( \left|\begin{array}{cc}1 & -4 \\ 4 & 1\end{array}\right| \)
D. \( \mid \begin{array}{ll}4 & 1 \\ 1 & 4\end{array} \)


The dual of the following statement "Reena is healthy and Meena is beautiful"' is
A. Reena is not beaufiful and Meena is not healthy
B. Reena is not beautiful or Meena is not healthy.
c. Reena is not healthy or Meena is not beautiful.
D. None of these.


Assertion
Formation of petroleum occurs from hydrocarbon by the process called pyrolysis.
Reason
Hydrocarbon pyrolysis involves
exothermic reactions.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A particle of mass M kg describes a circle of radius \( 1 \mathrm{m} \). The centripetal acceleration of the particle is \( 4 m / s^{2} \) What will be the momentum of the
particle ?
\( A \cdot 4 M \)
B. 2 M
\( c \cdot 8 M \)
D. M


Calculate the number of molecules in 11
gof \( C O_{2} \)


State whether the given statement is True or False :
To process nitrogen, lightning and other processes help in life existence.
A. True
B. False


Different materials have
A. different resistivityyyy
B. same resistivity
c. O resistivity
D. none of the above


What are antipyretics? Give an example.


The price of a dress was INR \( 500 . \) In December 2006 the price was increase by \( 10 \% \). during October 2007 it was reduced by \( 10 \% \). what is the new price of the shirt?


One mole of \( \boldsymbol{H}_{2} \boldsymbol{O} \) and one mole of \( \boldsymbol{C O} \)
are taken in 10 L vessel and heated to
725 K. At equilibrium, \( 40 \% \) of water (by mass) reacts with \( C O \) according to the
equation.
\( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g})+\boldsymbol{C O}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{H}_{2}(\boldsymbol{g})+ \)
\( \boldsymbol{C O}_{2}(\boldsymbol{g}) \)
Calculate the equilibrium constant for the reaction.


Represent the following complex number in trigonometric form:
\( 1+i \tan \alpha \)


The area of a square is numerically equal to the perimeter of the square, then the side of square is
A . 2 units
B. 3 units
c. 4 units
D. 5 units


The velocity vector of a particle moving in the xy plane is given by \( \vec{v}=t \hat{i}+x \hat{j} \). If
initially, the particle was at origin then
the equation of trajectory of the projectile is?


Express as product :
\( \sin 6 x-\sin 2 x \)


along a diameter of a conducting ring of
radius \( 0.1 m \) and lies on \( x \) -y plane. There
is a magnetic field \( \vec{B}=(50 T) \hat{K} . \) The
ring rotates with an angular velocity
\( \omega=20 r a d s^{-1} \) about its axis. An
external resistance of \( 10 \Omega \) is connected
across the center of the ring and rim.
The current through external resistance
is:
\( \mathbf{A} \cdot \frac{1}{4} \)
B. \( \frac{1}{2} \)
\( c \cdot \frac{1}{3} \)
D. zero


Thiamine is a
A. Enzyme
B. Vitamin
C. Protein
D. Hormone


Least active electrophile is
A. \( C H_{3}-_{\|}^{C}-O C H_{3} \)
B. \( _{\text {I }}^{o} \)
\[
C H_{3}-C-C l
\]
c. \( C H_{3}-\underset{d}{\|}_{O}-N M e_{2} \)
D.
\[
C H_{3}-C-S C H_{3}
\]


Find the distance between the points
(3,4,-2),(1,0,7)


A circle of radius 5 units touches the
coordinate axes in the first quadrant. If the circle makes one complete roll on \( x \) axis along the positive direction of \( x \) axis, find its equation in new position.


What are the oxidation states of
phosphorus in the following:
(i) \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3} \)
(ii) \( \boldsymbol{P C l}_{3} \)
(iii) \( \boldsymbol{C a}_{3} \boldsymbol{P}_{2}(\text { iv }) \)
\( N a_{3} P O_{4}(v) P O F_{3} ? \)


If \( ^{n} C_{r} \) denotes the number of
combinations of \( n \) things taken \( r \) at a
time, then the expression \( ^{n} C_{r+1}+^{n} \)
\( C_{r-1}+2 \times^{n} C_{r} \) equals
A. \( ^{n+2} C_{r} \)
B. \( ^{n+2} C_{r+1} \)
c. \( ^{n+1} C_{r} \)
D. \( n+1 C_{r+1} \)


How does sound is produced by
humans?
A. In humans sound is produced by the voice box.
B. In humans sound is produced by the larynx.
C. In humans sound is produced by the upper part of the wind pipe.
D. All


If \( \int x \frac{\ln (x+\sqrt{1+x^{2}})}{\sqrt{1+x^{2}}} d x= \)
\( \boldsymbol{a} \sqrt{\mathbf{1}+\boldsymbol{x}^{2}} \ln (\boldsymbol{x}+\sqrt{\mathbf{1}+\boldsymbol{x}^{2}})+\boldsymbol{b} \boldsymbol{x}+\boldsymbol{c} \)
then
A \( . a=1, b=-1 \)
В. \( a=1, b=1 \)
c. \( a=-1, b=1 \)


Assertion
lonic compounds have high melting and boiling points.
Reason
lonic compounds are solids and hard due to strong force of attraction between positive and negative ions in their molecules.
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


Two point masses 1 and 2 move with
uniform velocities \( \boldsymbol{v}_{1} \) and \( \boldsymbol{v}_{2} \)
respectively. Their initial position
vectors are \( r_{1} \) and \( r_{2}, \) respectively.
Which of the following should be satisfied for the collision of the point
masses?
A \( \cdot \frac{r_{1}-r_{2}}{\left|r_{2}-r_{1}\right|}=\frac{v_{1}-v_{2}}{\left|v_{2}-v_{1}\right|} \)
В. \( \frac{r_{2}-r_{1}}{\left|r_{1}-r_{1}\right|}=\frac{v_{2}-v_{1}}{\left|v_{2}-v_{1}\right|} \)
c. \( \frac{r_{2}-r_{1}}{\left|r_{2}+r_{1}\right|}=\frac{v_{2}-v_{1}}{\left|v_{2}+v_{1}\right|} \)
D. \( \frac{r_{2}+r_{1}}{\left|r_{2}+r_{1}\right|}=\frac{v_{2}-v_{1}}{\left|v_{2}+v_{1}\right|} \)


Draw Venn diagrams to illustrate \( (A \cup \)
\( B)^{\prime} \)


Ovules are naked in gymnosperm,
because
A. Fertilisation is absent
B. True carpels are absent
c. Archegonia are absent
D. Endosperm is absent


Two particles of mass \( m_{1} \) and \( m_{2} \) in projectile motion have velocities \( \vec{v}_{1}< \)
\( \vec{v}_{2} \) respectively at tine \( t=0 . \) They collide at time \( t_{0} . \) Their velocities become \( \overrightarrow{v_{1}^{\prime}} \) and \( \vec{v}_{2}^{\prime} \) at time \( 2 t_{0^{\prime}} \) while still moving in
air. The value of
\( \left|\left(m_{1} \vec{v}_{1}^{\prime}+m_{2} \overrightarrow{v_{2}^{\prime}}\right)-\left(m_{1} \vec{v}_{1}+m_{2} \vec{v}_{2}\right)\right| \)


Evaluate each of the following using suitable identities:
\( (99)^{3} \)


A sinusoidal voltage of peak value \( \mathbf{2 0 0} V \) is connected to a diode
and resistor \( R \) in the circuit shown so
that halfwave rectification occurs. If the
forward resistance of the diode is
negligible compared to it, the r.m.s.
voltage (in volt) across \( R \) is approximately
A . 200
в. 100
c. \( \frac{200}{\sqrt{2}} \)
D. 280


The temperature of a gas is T K. What would be the temperature at which volume and pressure, both will reduce to half of the initial values?
A . T/2
B. T/4
\( c \cdot T / 3 \)
D. T/


In Kjeldahl's method of estimation of nitrogen, copper sulphate acts as:
A. an oxidising agent
B. a reducing agent
c. a catalytic agent
D. a hydrolysing agent


Let the co - ordinates of the point where the line joining the points
(2,-3,1),(3,-4,-5) cuts the plane
\( \mathbf{2} \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}=\mathbf{7} \) be \( (\boldsymbol{x}, \boldsymbol{y}, \boldsymbol{z}) . \) Find \( \boldsymbol{x}+ \)
\( \boldsymbol{y}+\boldsymbol{z} ? \)


A chord of a circle of radius \( 15 \mathrm{cm} \)
subtends an angle of \( 120^{\circ} \) at the centre. Find the area corresponding minor sector of the circle.


Name an electromagnetic wave which
is used in the radar system used in aircraft navigation. Give another use of
the wave.


The value of the expansion \( (\sqrt{3}+1)^{5}+ \)
\( (\sqrt{3}-1)^{5} \)
\( \mathbf{A} \cdot 88 \)
B . 40
c. \( 88 \sqrt{3} \)
D. \( 40 \sqrt{3} \)


Transform the ratio given below into
percentage.
\( \frac{5}{16} \) in percentage form is \( 31.25 \%, \) if true then enter 1 and if false then enter 0


Find distance of point \( \boldsymbol{A}(2,3) \) measured
parallel to the line \( x-y=5 \) from the
line \( 2 x+y+6=0 \)
\( ^{\mathrm{A}} \cdot \frac{13 \sqrt{2}}{3} \) units
B. \( \frac{13}{3} \) units
\( ^{\mathrm{C}} \cdot \frac{13 \sqrt{2}}{6} \) units
D. None of these


What is the value of \( \int_{-\pi / 4}^{\pi / 4}(\sin x-\tan x) d x \)
\( ^{\mathbf{A}} \cdot-\frac{1}{\sqrt{2}}+\ln \left(\frac{1}{\sqrt{2}}\right) \)
B. \( \frac{1}{\sqrt{2}} \)
c. 0
D. \( \sqrt{2} \)


Find the length of the latus rectum, the eccentricity and the coordinates of the foci of the ellipse \( x^{2}+3 y^{2}=a^{2} \)


Select the correct statement about \( G_{1} \)
phase.
A. Cell is metabolically inactive
B. DNA in the cell does not replicate
C. It is not a phase of synthesis of macromolecules
D. Cell stops growing


The strength of magnetic field around a
bar magnet:
A. decrease with the decrease in distance from the magnet
B. decrease with the increase in distance from the magnet
c. remain constant with increase in distance from magnet
D. becomes zero with decrease in distance from magnet


A smooth sphere \( A \) is moving on a
frictionless horizontal plane with
angular speed \( \omega_{a} \) and \( \omega_{b} \)
respectively.Then: \( \omega_{a}=\omega_{b} \) Type 1 for true
and 0 for flase


Which are isomers?
A. Ethanol and ethoxy ethane
B. Methanol and methoxy methane
C. Propionic acid and ethyl acetate
D. Propanal and acetone


Nucleic acid are
A. mega molecules
B. macro molecules
C. micro molecules
D. meso molecules


\( \left(\frac{4}{3} x-\frac{3}{4} y\right)^{3} \) is equal to
A \( \cdot \frac{64}{27} x^{3}+\frac{27}{64} y^{3}+4 x^{2} y+\frac{9}{4} x y^{2} \)
B. \( \frac{64}{27} x^{3}+\frac{27}{64} y^{3}-4 x^{2} y-\frac{9}{4} x y^{2} \)
C \( \frac{64}{27} x^{3}-\frac{27}{64} y^{3}-4 x^{2} y+\frac{9}{4} x y^{2} \)
D. \( \frac{64}{27} x^{3}-\frac{27}{64} y^{3}+4 x^{2} y-\frac{9}{4} x y^{2} \)


Mean of 5 observation is \( 7 . \) If four of
these observation are 6,7,8,10 and one
is missing then the variance of of all the five observations is :
A . 4
B. 6
\( c \cdot 8 \)
D. 2


\( \left[5\left\{\left(\frac{1}{8}\right)^{\frac{-1}{3}}+\left(\frac{1}{27}\right)^{\frac{-1}{3}}\right\}\right]^{\frac{1}{2}} \)
\( \mathbf{A} \cdot 5 \)
B. \( \sqrt{13} \)
\( \mathbf{c} .25 \)
D. 13


Select the hormone-releasing IntraUterine Devices.
A. Vaults, LNG-20
B. Multiload 375, Progestasert
c. Progestasert, LNG-20
D. Lippes Loop, Multiload 375


Assertion
Hydrolysis of ethyl acetate in the
presence of acid is a reaction of first
order whereas in presence of alkali, it is
reaction of second order.
Reason
Acid only acts as a catalyst whereas
alkali acts as one of the reactants.
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


Let \( f: N \rightarrow N \) defined by \( f(n)= \)
\( \left\{\begin{array}{cc}\frac{n+1}{2} & \text { if } n \text { is odd } \\ \frac{n}{2} & \text { if } n \text { is even }\end{array}\right. \)
then \( \boldsymbol{f} \) is.
A. Many-one and onto
B. One-one and not onto
c. onto but not one-one
D. Neither one-one nor onto


When \( N a \) and \( L i \) placed in dry air we
get :
A. \( N a O H, N a_{2} O, L i_{2} O \)
в. \( N a_{2} C O_{3}, N a_{2} O_{2}, L i_{2} O \)
c. \( N a_{2} O, L i_{3} N, N H_{3} \)
D. \( N a_{2} O, L i_{2} O, L i_{3} N \)


toppr \( t \)
Q Type your question-
Which of the diagrams shown In
\( (\overline{4}) \)
figure correctly shows the change in kinetic and potential energy of the drop
during its fall up to the ground?
\( A \)
B.
\( c \)
\( D \)


Write the different oxidation states of
manganese.Why +2 oxidation state of
manganese is more stable?


When the normal to a coil points in the direction of magnetic field (B), then flux is
A. a scalar quantity
B. a vector quantity
c. neither scalar nor vector
D. uncertain


The book 'Descent of Man and Selection
in Relation to Sex' was written by
A. Charles Darwin
B. J B. Lamarck and C. Darwin
c. F.B. Sumner and E. Darwin
D. Robert Brown


A shopkeeper buys some books for
Rs.80. If he had bought 4 more books
for the same amount, each book would
have cost \( R s .1 \) less. Find the number of
books he bought.


Arrange the following compounds in increasing order of solubility in water:
\( \boldsymbol{C}_{6} \boldsymbol{H}_{5} \boldsymbol{N} \boldsymbol{H}_{2},\left(\boldsymbol{C}_{2} \boldsymbol{H}_{5}\right)_{2} \boldsymbol{N} \boldsymbol{H}, \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{N} \boldsymbol{H}_{2} \)


\( \underbrace{L_{k}} \)


Which curve in figure represents the
curve of ideal gas?
\( A \cdot B \) only
3. \( C \) and \( D \) only
c. \( E \) and \( F \) only
D. \( A \) and \( B \) only


The eartesian equations of the line are
\( \mathbf{3} \boldsymbol{x}+\mathbf{1}=\mathbf{6} \boldsymbol{y}-\mathbf{2}=\mathbf{1}-\boldsymbol{z} . \) Find its
equation in vector form and find direction ratios of the line.


Which is not true for dicot root
A. Less developed pith or absent
B. Secondary growth
\( c \cdot \) Both
D. \( 15-20 \) vascular bundles


A wire of length \( 1 \mathrm{m} \) fixed at one end has a sphere attached to it at the other end.
The sphere is projected horizontally with a velocity of \( \sqrt{9 g} \). When it describes a vertical circle, the ratio
of elongations of the wire when the sphere is at the top and bottom of the circle is:
A .2: 5
B. 5: 2
c. 3: 5
D. 5: 3


In \( X e O_{3} F_{2}, \) the number of bond pair(s),
\( \pi \) -bond(s) and lone pair(s) on Xe atom
respectively are.
\( \mathbf{A} \cdot 5,3,0 \)
B. 5,2,0
c. 4,2,2
D. 4,4,0


If the function \( \left\{\begin{array}{cc}\frac{k \cos x}{(\pi-2 x)}, & \text { when } x \neq \frac{\pi}{2} \\ 3, & x=\frac{\pi}{2}\end{array}\right. \)
be continue at \( x=\frac{\pi}{2}, \) then the value of
\( k \) is
A . 3
в. -3
c. -5
D. 6


A lens is placed between the source of light and a wall. It forms images of area
\( A_{1} \) and \( A_{2} \) on the wall for its two different positions. The area of the source of light is :
в. \( \frac{A_{1}+A_{2}}{2} \)
\( ^{\mathrm{c}}\left(\frac{\sqrt{A_{1}}+\sqrt{A_{2}}}{2}\right)^{2} \)
D. None of these


Holotype is a specimen
A. Nomenclature type used by author
B. Nomenclature type when the original is missing
C. Nomenclature type when the lectotype is missing
D. Synonym of paratype


In given figure, If PSIIQR, prove that
\( \triangle P O S \sim \triangle R O Q \)


Name the largest planet of the solar
system.


Indicate which pairs of angles are:
Vertically opposite angles.
\( A \cdot 184 \)
\( B \cdot 2 \& 4 \)
\( c \cdot 1 \& 3 \)
\( D \cdot 5 \& 4 \)


Equations of a stationary wave and a
travelling wave are \( \boldsymbol{y}_{1}=\boldsymbol{a} \) sink \( \boldsymbol{x} \) coswt
and \( y_{2}=a \sin (\omega t-k x) . \) The phase
difference between two points \( \boldsymbol{x}_{1}= \) \( \frac{\pi}{3 k} \) and \( x_{2}=\frac{3 \pi}{2 k} i s \phi_{1} \) for the first
wave and \( \phi_{2} \) for the second wave. The
ratio \( \frac{\phi_{1}}{\phi_{2}} \) is :
A. 1
в. \( \frac{5}{6} \)
\( c \cdot \frac{3}{4} \)
D. \( \frac{6}{7} \)


Write an anti derivative for each of the
following functions using the method of inspection:
i) \( \cos 2 x \)
ii) \( 3 x^{2}+4 x^{3} \)
iii) \( \frac{1}{x}, x \neq 0 \)


Which of the following is thermosetting polymer?
A. Nylon
B. Sealing wax
c. Polysiloxanes
D. Both B and C


When moderate amount of sodium
metal is dissolved in liquid \( N H_{3} \) at low
temperature, which one of the following \( \operatorname{occur}(s) ? \)
This question has multiple correct options
A. Blue colored solution is obtained
B. \( N a^{+} \) ions are formed in the solution
C . Liquid \( N H_{3} \) becomes good conductor of electricity
D. Liquid \( N H_{3} \) remains diamagnetic.


\( A B C D \) is a rectangle in which diagonal
\( B D \) bisects \( \angle B . \) Show that \( A B C D \) is a
square.


A box contains 100 tickets numbered
\( 1,2,3, \dots, 100 . \) two tickets are chosen at random. If it is given that the maximum
number on the two chosen tickets is not
more than 10 , then the probability that the minimum number on them is not
less than 5 is
A \( \cdot \frac{1}{3} \)
B. \( \frac{1}{5} \)
c. \( \frac{152}{165} \)
D. None of these


Describe a method for refining nickel


Figure shows a square loop of resistance \( 1 \Omega \) of side \( 1 m \) being moved towards right at a constant speed of 1 \( \boldsymbol{m} / \boldsymbol{s} \). The front edge enters the \( \boldsymbol{3} \boldsymbol{m} \)
wide magnetic field \( (B=1 T) \) at \( t=0 \)
Draw the graph of current induced in
the loop as time passes. (Take anticlockwise direction of current as
positive)
\[
x
\]


Solve the differential equation:
\( \sqrt{1+x^{2}} d x+\sqrt{1+y^{2}} d y=0 \)
A \( . x \sqrt{1+x^{2}}+y \sqrt{1+y^{2}}+ \)
\( \log [(x+\sqrt{1+x^{2}})(y+\sqrt{1+y^{2}})]=c \)
B . \( \sqrt{1+x^{2}}+\sqrt{1+y^{2}}=c \)
c. \( \frac{1}{\sqrt{1+x^{2}}}+\frac{1}{\sqrt{1+y^{2}}}=c \)
D \( \cdot \log \{(\sqrt{1+x^{2}})+(\sqrt{1+y^{2}})\}=x+c \)


If the points \( (a, 0),(0, b) \) and (1,1) are collinear, then \( \frac{1}{a}+\frac{1}{b} \) equal to -
A . 1
B. 2
\( c \cdot 3 \)
D. 4


Even through carbon and silicon are non metals, they have higher melting points than others because:
A. they exist as covalent solids in 3D networks
B. the bonds in their molecules are strong
c. they exhibit multiple bonding
D. they are highly electronegative


Age at which puberty begins in individuals generally is
A . \( 10-13 \)
B. 15 - 25
\( c \cdot 2-4 \)
D. 50 - 70


One ampere equals
A \( \cdot 10^{6} \mu A \)
В \( \cdot 10^{-6} \mu A \)
\( \mathbf{c} \cdot 10^{-3} \mu A \)
D. 10 A


If the complex numbers \( z_{1}, z_{2} \) and \( z_{3} \)
denote the vertices of an isosceles
triangle, right angled at \( z_{1}, \) then \( \left(z_{1}-\right. \)
\( \left.z_{2}\right)^{2}+\left(z_{1}-z_{3}\right)^{2} \) is equal to
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( \left(z_{2}+z_{3}\right)^{2} \)
\( c \cdot 2 \)
D. 3
E \( \cdot\left(z_{2}-z_{3}\right)^{2} \)


Two cars of masses \( m_{1} \) and \( m_{2} \) are
moving along the circular paths of
radius \( r_{1} \) and \( r_{2} \) respectively. The speeds are such that they complete one round at the same time. The ratio of
angular speeds of two cars is
В. \( r_{1}: r_{2} \)
c. 1:
D. \( m_{1} r_{1}: m_{2} r_{2} \)


The compounds \( A \) and \( B \) are mixed in equimolar proportion to form the products, \( \boldsymbol{A}+\boldsymbol{B} \rightleftharpoons \boldsymbol{C}+\boldsymbol{D} . \) At
equilibrium, one-third of \( A \) and \( B \) are
consumed. The equilibrium constant for the reaction is:
A . 0.5
в. 4.0
c. 2.5
D. 0.25


Pick out the wrong statement.
A. Amino acids are substituted methanes.
B. Is a trihydroxy propane.
C. Lysine is a neutral amino acid.
D. Lecithin is a phospholipid.
E. Adenosine is a nucleoside.


\( \ln \) a \( G . P \) sum of \( n \) terms is 255 , the last
term is 128 and the common ratio is 2 .
Find \( n \)


Two cars \( c_{1}, \) and \( c_{2} \) moving in the same
direction on a straight single lane road
with velocities \( \boldsymbol{v}_{1}=12 m s^{-1} \) and \( \boldsymbol{v}_{2}= \)
\( 10 m s^{-1}, \) respectively. When the
separation between the two was \( d=200 \)
\( \mathrm{m}, \mathrm{c}_{2} \) started accelerating to avoid
collision. What is the minimum
acceleration of car \( c_{2} \) so that they do not
collide?


\( N O_{2} \) is released by heating:
A \( \cdot P b\left(N O_{3}\right)_{2} \)
в. \( K N O_{3} \)
c. \( N a N O_{2} \)
D. \( N a N O_{3} \)


The force of friction always opposes
motion or the tendency of motion
A. True
B. False


For each value of \( 1, \) the possible values
of \( \boldsymbol{m}_{l} \) are
A . (21 + 1)
в. 2
c. (२ᅵ - 1)
\( D \cdot 2(1+1) \)


John bought a car for a certain sum of money. He spent \( 10 \% \) of the cost on
repairs and sold the car for a profit of
Rs. 11000. How much did he spend on
repairs, if he made a profit of \( 20 \% ? \)
A. Rs. 4000
B. Rs. 4400
c. Rs. 5000
D. Rs. 5500


If the coefficient of variation and
standard deviation of a distribution are
\( 50 \% \) and 20 respectively, the its mean is
A .40
B. 30
c. 20
D. None of these


Name the product obtained when
alcohol is added to a carbonyl group in
presence of dry \( \boldsymbol{H} \boldsymbol{C l} \)


An electron enters an electric field with
its velocity in the direction of the electric lines of field then:
A. the path of the electron will be a circle
B. the path of the electron will be a parabola
c. the velocity of the electron will decrease just after entry
D. the velocity of the electron will increase just after entry


For a gas Van der Waal constant, \( b= \)
\( 0.04281 L m o l e^{-1} . \) Calculate its critical
volume


\( H_{2} O_{2} \) and heavy water was discovered
by respectively:
A. Thenard, Urey
B. Urey, Rutherford
c. Aston, Urey
D. Aston, Chadwick


The Born Haber cycle below represents
the energy changes occurring at \( 298 \mathrm{K} \) when \( \mathrm{KH} \) is formed from its elements
\( \mathbf{v}: \Delta \boldsymbol{H}_{\text {atomisation}} \mathbf{K}=\mathbf{9 0} \mathbf{k J} / \mathrm{mol} \)
\( \mathbf{w}: \mathbf{\Delta} \boldsymbol{H}_{\text {ionisation}} \mathbf{K}=\mathbf{4 1 8} \mathbf{k} \mathbf{J} / \mathrm{mol} \)
\( \mathbf{x}: \boldsymbol{\Delta} \boldsymbol{H}_{\text {dissociation}} \mathrm{H}=\mathbf{4 3 6} \mathrm{kJ} / \mathrm{mol} \)
\( \mathbf{y}: \boldsymbol{\Delta} \boldsymbol{H}_{\text {electronaffinity}} \mathbf{H}=\mathbf{7 8} \mathbf{k J} / \mathrm{mol} \)
\( \mathbf{z}: \boldsymbol{\Delta} \boldsymbol{H}_{\text {lattice}} \mathrm{KH}=710 \mathrm{kJ} / \mathrm{mol} \)
In terms of the letters \( v \) to \( z \) the
expression for
\( \boldsymbol{\Delta} \boldsymbol{H}_{\text {electronaffinity}} \) of H is
\( \boldsymbol{\Delta} \boldsymbol{H}_{\text {electronaffinity}} \) is \( _{--} \)
A . \( y \)
в. \( y / 2 \)
\( c \cdot 2 y \)
D. \( y / 3 \)


Where should a horizontal tube B
connected, without causing any flow
between the tanks?


The cause of mirage in desert areas is
A. The refractive index of atmosphere decreases with height
B. The refractive index of atmosphere increases with height
C. The refractive index of atmosphere does not change with height
D. Scattering


If the light from star \( A \) takes 15 min to
reach star \( \boldsymbol{B} \) and the speed of light is \( 3 \times 10^{8} m / s, \) then what is the distance
between the stars?
A \( .2 .7 \times 10^{8} k m \)
В . \( 2,9 \times 10^{11} k m \)
c. \( 2.7 \times 10^{8} m \)
D. \( 36 \times 10^{9} k m \)


\( \frac{3 \frac{1}{4}-\frac{4}{5} o f \frac{5}{6}}{4 \frac{1}{3} \div \frac{1}{5}-\left(\frac{3}{10}+21 \frac{1}{5}\right)} \)
\( \left(1 \frac{2}{3} o f 1 \frac{1}{2}\right) \) is equal to:
\( A \cdot 9 \)
B \( \cdot 11 \frac{1}{2} \)
c. 13
D. \( 15 \frac{1}{2} \)


The vapour pressure of water at \( 20^{\circ} \mathrm{C} \) is 17 mm Hg. Calculate the vapour pressure of a solution containing 2.8 g
of urea \( \left(N H_{2} C O N H_{2}\right) \) in 50 g of water
\( \mathrm{N}=14, \mathrm{C}=12,0=16, \mathrm{H}=1(16.71 \mathrm{mm} \mathrm{Hg}) \)


Pressure is increased in the Haber
process for making ammonia. It favors:
A. the reverse reaction
B. the forward reaction
c. neither reaction
D. none


Obtain the differential equation from
the relation \( A x^{2}+B y^{2}=1, \) where \( A \)
and B are constants.


Which of the following can be used for controlling Gaseous Pollutant?
A . Arrestor
B. Incineration
c. Absorption
D. None of above


The state of a thermodynamic system is represented by:
A. Pressure only
B. Volume only
C. Pressure, volume and temperature
D. number of moles


The axis of inflorescence is known as
A. Petiole
B. Pedicle
c. Peduncle
D. Pinna


A point object is placed at a distance \( 10 c m \) and its real image is formed at a
distance of \( 20 \mathrm{cm} \) from concave mirror
If the object is moved by \( 0.1 \mathrm{cm} \) towards the mirror, the image will shift by about
A. \( 0.4 \mathrm{cm} \) away from the mirror
B. \( 0.4 \mathrm{cm} \) towards the mirror
c. \( 0.8 c m \) away from the mirror
D. \( 0.8 \mathrm{cm} \) towards the mirror


Reproduction is the characteristics of
living organisms, but it cannot be regarded as defining property because
A. Asexual reproduction involves only single parent
B. Lower organisms do not reproduce under stressful environmental conditions
c. All living beings do not have the capacity to reproduce
D. For lower plants growth and reproduction are mutually inseparable phenomenon


Fill in the blanks so as to make the
statement true:

Two rational numbers with different
numerators are equal, if their numerators are in the same
as their denominators.


Product \( (A) \) is :
\( \sim \frac{\mathrm{B}_{\mathrm{T}_{2}}}{\mathrm{CCl}_{4}} \quad \frac{(\mathrm{i}) \mathrm{alc} \cdot \mathrm{KOH}}{(\mathrm{ii}) \mathrm{NaNH}_{2}}(A) \)
\( \mathbf{A} \cdot H_{2} C=C H-C H=C H_{2} \)
B \( \cdot C H_{3}-C \equiv C-C H_{3} \)
\( \mathbf{c} \cdot C H_{3}-C H_{2}-C \equiv C H \)
\( \mathbf{D} \cdot C H_{3}-C H=C \equiv C H_{2} \)


When the plane of the armature of an
a.c generator is parallel to the field, in which it is rotating
A. both the flux linked and induced emf in the coil are zero
B. the flux linked with it is zero, while induced emf is maximum
c. flux linked is maximum while induced emf is zero
D. both the flux and emf have their respective maximumm values


A series combination of two
capacitances of value 0.1 mu \( F \) and
\( 1 \mu F \) is connected with a source of voltage 500 volts. The potential difference in volts across the capacitor of value 0.1 mu \( F \) will be :
\( \mathbf{A} \cdot 50 \)
в. 500
c. 45.5
D. 454.5


Enzyme helping in oxidative decarboxylation of pyruvic acid is
A. Pyruvate kinase
B. Pyruvic dehydrogenase
c. Malate dehydrogenase
D. succinic dehydrogenase


Which one is smallest?
A. Eosinophil
B. Basophil
C . Neutrophil
D. Monocyte


Find \( m \) if the following equation holds true \( 1.2+2.3+3.4+. .+n(n+1)= \)
\( \frac{1}{m} n(n+1)(n+2) \)


A current of \( 4 A \) flows through 5 turn coil
of a tangent galvanometer having a diameter of \( 30 \mathrm{cm} . \) If the horizontal
component of Earth's magnetic induction is \( 4 \times 10^{-5} T \), find the
deflection produced in the coil. \( \left[\text { Given } \mu_{0}=4 \pi \times 10^{-7} H m^{-1}\right] \)


The composition of turbid suspension
(B) and the white precipitate (C) are respectively.
A \( \cdot \operatorname{Sn} C l_{2}, \operatorname{Sn}(O H)_{2} \)
в. \( \operatorname{Sn}(O H) C l, \quad N a_{2} Z n O_{2} \)
c. \( \operatorname{Sn}(O H) C l, \operatorname{Sn}(O H)_{2} \)
D. \( \operatorname{Sn}(O H) C l, \) SnCl \( _{4} \)


For a given cell, its terminal voltage depends on and
A. external resistance, internal resistance
B. internal resistance only
c. external resistance only
D. none of these


Number of oxygen molecule that bind to a molecule of haemoglobin are
A .2
B. 3
\( c \cdot 4 \)
D.


A magnetic needle makes an angle of 45 with the thread from which it is
suspended then
A. Dip at that place is 45
B. Inclination at that place is 45
c. Declination angle at that place is 45
D. Both (1) and (2)


Fill up the blank with suitable
Acceleration due to gravity is independent of


The Henle's loop of nephron is mainly responsible for reabsorption of water in the kidney. Which of the following has a long loop of Henle in its nephrons to
conserve water?
A. Polar bear
B. Camel
c. Frog
D. whale


Which of the following statements is
not correct?
A. Whenever the amount of magnetic flux linked with a circuit changes, an emf is induced in the circuit.
B. The induced emf lasts so long as the change in magnetic flux continues.
C. The direction of induced emf is given by Lenz's law.
D. Lenz's law is a consequence of the law of conservation of momentum.


A cell sends a current through a resistance \( R \) for time \( t ; \) next the same
cell sends current through another resistance \( r \) for the heat is developed in
both the resistance, then the internal
resistance of the cell is:
A. \( (R+r) / 2 \)
в. \( (R-r) / 2 \)
c. \( \sqrt{R r} \)
D. \( \sqrt{R r} / 2 \)


In Young's double slit experiment, the fringe width is \( \beta . \) If the entire
arrangement is placed in a liquid of refractive index \( \mu, \) the fringe width will become
A. \( \mu \beta \)
в. \( \frac{\beta}{\mu} \)
\( c \cdot \frac{\beta}{\mu+1} \)
D. \( \frac{\beta}{\mu-1} \)


If \( \frac{3 x+7}{5}=11, \) then \( x \) is equal to
A . 16
B . 15
c. -16
D. -15


Primary succession takes much longer
than secondary succession because it
involves:
A. time for development of the soil horizons
B. more time for development of a seed.bank
C. colonization by organisms that are farther away
D. redevelopment of the atmospheric gases


In each of the following circuit diagrams, identify which diode(diodes) is(are) forward biased
\( A \cdot \) Only \( D_{2} \)
B. only \( D_{1} \)
c. Both \( D_{1} \) and \( D_{2} \)
D. Neither \( D_{1} \) nor \( D_{2} \)


Find \( a_{1}+a_{6}+a_{11}+a_{16} \) if it is known
that \( a_{1}, a_{2} \dots . \) is an A.P. and \( a_{1}+a_{4}+ \)
\( \boldsymbol{a}_{\boldsymbol{7}}+\ldots+\boldsymbol{a}_{\mathbf{1 6}}=\mathbf{1 4 7} \)


\( f(\alpha, \beta, \gamma \) are the zeroes of the cubic
polynomial \( x^{3}+4 x+2, \) then find the
value of:
\( \frac{1}{\alpha+\beta}+\frac{1}{\beta+\gamma}+\frac{1}{\gamma+\alpha} \)


One litre of a sample of hard water
contains \( 55.5 \mathrm{mg} \) of \( \mathrm{CaCl}_{2} \) and \( 4.75 \mathrm{mg} \)
of \( M g C l_{2} . \) The total harness in terms of
ppm of \( C a C O_{3} \) is :
\( A \cdot 9 \) ppm
B. 10 ppm
c. 20 ppm
D. none of these


Imagine a light planet revolving around a very massive star in a circular orbit of
radius R with a speed of revolution T. If the gravitational force of attraction between the planet and the star is proportional to \( \boldsymbol{R}^{-5 / 2}, \) then
A \( \cdot T^{2} \) is proportional to \( R^{2} \)
B . \( T^{2} \) is proportional to \( R^{7 / 2} \)
c. \( T^{2} \) is proportional to \( R^{3 / 2} / 2 \) proportional
D. \( T^{2} \) is proportional to \( R^{3.75} \)


If \( \sin x+\sin ^{2} x=1 \) then the value of
\( \cos ^{2} x+\cos ^{4} x \) is equal to
\( A \)
B. \( \frac{1}{2} \)
c. \( \frac{1}{3 \sqrt{3}} \)
D. \( \frac{3 \sqrt{5}-5}{2} \)


Choose the redox reaction from the
following.
\( \mathbf{A} \cdot C u+2 H_{2} S O_{4} \rightarrow C u S O_{4}+S O_{2}+2 H_{2} O \)
B \( \cdot B a C l_{2}+H_{2} S O_{4} \rightarrow B a S O_{4}+2 H C l \)
\( \mathbf{c} \cdot 2 N a O H+H_{2} S O_{4} \rightarrow N a_{2} S O_{4}+2 H_{2} O \)
\( \mathbf{D} \cdot K N O_{2}+H_{2} S O_{4} \rightarrow 2 H N O_{2}+K_{2} S O_{4} \)


Consider the following statements:
1. The general solution of \( \frac{d y}{d x}=f(x)+ \) \( x \) is of the form \( y=g(x)+c, \) where \( c \) is
an arbitrary constant.
2. The degree of \( \left(\frac{d y}{d x}\right)^{2}=f(x) \) is 2 Which of the above statements is/are
correct?
A. 1 only
B. 2 only
c. Both 1 and 2
D. Neither 1 nor 2


The enery of loss of an electron from \( N e \)
and \( N a^{+} \) ion(both isoelectronic) are:
A \( \cdot 4562 \) k) \( m o l^{-1}, 2081 \) k) \( m o l^{-1} \)
-
B . 2081 kJ mol-1, 4562 kJ mol-1
\( \mathbf{c} .2081 \mathrm{kJ} \mathrm{mol}^{-1} \) each
D. 4562 kJ \( m o l^{-1} \) each


If \( \boldsymbol{A}=\left[\begin{array}{ll}2 & 3 \\ 5 & 7\end{array}\right], B=\left[\begin{array}{cc}0 & 4 \\ -1 & 7\end{array}\right], C= \)
\( \left[\begin{array}{cc}1 & 0 \\ -1 & 4\end{array}\right], \) find \( A C+B^{2}-10 C \)


If \( \boldsymbol{v}_{1}= \) Speed of light in media \( \mathbf{1} \)
\( v_{2}= \) Speed of light in media 2
then, refractive index of media with
respect to media 1 is,


Calculate the mass number of atoms
\( X, Y \) and \( Z ? \)
A . 5,11,18
B. 10,18,31
c. 11,18,3
D. 11,19,30


There are two concentric spherical
shells of radii \( r \) and \( 2 r . \) Initially a
charge \( Q \) is given to the inner shell and
both the switches are open. If switch \( S_{1} \) is closed and then opened, charge on
the outer shell will be
\( A \cdot Q \)
в. \( \frac{Q}{2} \)
c. \( -Q \)
D. \( \frac{-Q}{2} \)


\( f\left(\begin{array}{lll}1 & 0 & 1 \\ 0 & 1 & 2 \\ 0 & 0 & 4\end{array}\right], \) then show that
\[
|\mathbf{3} \boldsymbol{A}|=\mathbf{2 7}|\boldsymbol{A}|
\]


Formation of gametophyte directly from spore mother cell, without meiosis is
called as
A. Apospory
B. Apogamy
c. Apomictic
D. Apomixis


The magnitude of electric field intensity E, such electron, placed in the field, would experience an electric force equal to its weight is :
A \( \cdot 5.6 \times 10^{-7} N C^{-1} \)
B . \( 5.6 \times 10^{-8} N C^{-1} \)
c. \( 5.6 \times 10^{-10} N C^{-1} \)
D. \( 5.6 \times 10^{-11} \mathrm{NC}^{-1} \)


The ratio of the radius difference
between \( 4 t h \) and \( 3 r d \) orbit of H-atom
and that of \( L i^{2+} \) ion is:
A . 1: 1
B. 3: 1
\( c .3: 4 \)
D. 9: 1


An electrovalent compound forms
between
A. metal and nonmetal
B. nonmetal and nonmetal
c. metal and metalloid
D. metal and metal


\( \int \frac{d t}{(6 t-1)} \) is equal to:
A \( \cdot \frac{1}{6} \ln (6 t-1)+C \)
B. \( \ln (6 t-1)+C \)
\( c \cdot-\frac{1}{6} \ln (6 t-1)+C \)
D. None of these


An allotropic form of carbon used for
cutting and drilling is :
A. charcoal
B. bone charcoal
c. graphite
D. diamond


If \( \left(x^{2}+4 x-21\right) \) is divided by \( x+7 \)
then the quotient is
\( \mathbf{A} \cdot x+3 \)
B. \( x-3 \)
c. \( x^{2}-2 \)
D. \( x-4 \)


At the centre \( (t=0) \) of Newton's ring
arrangement, we observe a
A. dark spot
B. bright spot
c. coloured spot
D. None of these


Q Type your question
school 0 to their homes \( P \) and \( Q \)
respectively are shown in Fig. above.
Choose the correct entries in the
brackets below :
(a) (A/B) lives closer to the school than
\( (\mathrm{B} / \mathrm{A}) \)
(b) (A/B) starts from the school earlier
\( \operatorname{than}(\mathrm{B} / \mathrm{A}) \)
(c) \( (\mathrm{A} / \mathrm{B}) \) walks faster than \( (\mathrm{B} / \mathrm{A}) \)
(d) \( A \) and \( B \) reach home at the
(same/different) time
(e) \( (\mathrm{A} / \mathrm{B}) \) overtakes \( (\mathrm{B} / \mathrm{A}) \) on the road
(once/twice).


In which of the following molecules
atom does not assume \( s p^{3} \)
hybridsation?
A. \( S O_{4}^{2} \)
в. \( S F_{4} \)
\( \mathrm{c} \cdot S F_{2} \)
D. \( S_{8} \)


For a prism kept in air, it is found that
for an angle of incidence \( 60^{\circ} \), the angle
of refraction \( ^{\prime} \boldsymbol{A}^{\prime}, \) angle of deviation \( ^{\prime} \boldsymbol{\delta}^{\prime} \)
and angle of emergence \( ^{\prime} e^{\prime} \) become equal. The minimum angle of incidence of a ray that will be transmitted through the prism is
A . 1.73
в. 1.15
c. 1.5
D. 1.33


Assertion \( : H C O_{3}^{-} \) can act as a Bronsted acid or a Bronsted base.
Reason \( : H C O_{3}^{-} \) can donate a proton to
form \( C O_{3}^{2-} \) or accept a proton to form
\( \boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{O}_{3} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
E. Both Assertion and Reason are incorrect


If the \( n^{t h} \) term of an A.P. is \( 4 n+1 \), then
the common difference, \( d \) is equal to
A . 3
B. 4
\( c .5 \)
D. 6


The fundamental frequency of a vibrating string fixed at both the ends is
f. Will the 5 th harmonic vibrate with the
same wavelength as that of the fundamental?
A. Yes
B. No
c. Depends on the tension in the string
D. Depends on the linear density of the string


Value of \( 1+\frac{1^{3}+2^{3}}{1+2}+\frac{1^{3}+2^{3}+3^{3}}{1+2+3}+ \)
\( \ldots+\frac{1^{3}+2^{3}+\ldots \ldots 15^{3}}{1+2+\ldots .+15}-\frac{1}{2}(1+2+ \)
\( \ldots+15) \) is?
A \( \cdot 840 \)
в. 720
\( c .680 \)
D. 620


Pyruvate (pyruvic acid) dehydrogenase is used in converting
A. Pyruvate to glucose
B. Glucose to pyruvate
c. Pyruvic acid to lactic acid
D. Pyruvate to acetyl CoA


Find the coefficient of range for the following data.
size \( \quad \begin{array}{lll}\mathbf{1 0}- & \mathbf{1 5}- & \mathbf{2 0}- \\ \mathbf{1 5} & \mathbf{2 0} & \mathbf{2 5}\end{array} \)
Frequency


The equilibrium constant of the
\[
\text { reaction } 2 C_{3} H_{6}(g) \rightleftharpoons C_{2} H_{4}(g)+
\]
\( C_{4} H_{8}(g) \) is found to fit the expression:
\[
\ln K=-1.04-\frac{1088}{T}
\]
Calculate the standard reaction
enthalpy and entropy at \( 400 \mathrm{K} \)
A \( \cdot \Delta H^{o}=4.5 k J / m o l ; \Delta S^{o}=4.32 J / m o l^{1} K^{1} \)
В . \( \Delta H^{o}=9.04 k J / m o l ; \Delta S^{o}=-8.64 J / m o l^{1} K^{1} \)
C . \( \Delta H^{o}=18.08 k J / \) mol; \( \Delta S^{o}=17.28 J / \) mol \( ^{1} K^{1} \)
D. None of these


For a zero-order reaction \( \boldsymbol{A} \rightarrow \) product
the rate constant is \( 10^{-2} \) mol \( L^{-1} s^{-1} \)
Starting with 10 moles of \( A \) in a 1 L
vessel, how many moles of \( A \) would be left unreacted after 10 minutes?
A. 5 moles
B. 6 moles
c. 4 moles
D. 10 moles


Net charge within an imaginary cube drawn in a uniform electric field is
always zero. Is this statement true or false.


How much time the man has to board
the boat comfortably during each cycle of up and down motion?
A . 0.585 s
в. 1.17 s
\( c \cdot 2.33 \mathrm{s} \)
D. 0.293 s


There are two concentric metal shells of
radii \( r_{1} \) and \( r_{2}\left(>r_{1}\right) . \) If the outer shell
has a charge \( q \) and the inner shell is grounded, the charge on the inner shell is
A. zero
B. \( -\left(r_{1} / r_{2}\right) \) q
c. \( r_{1} r_{2} \) q
D. None of thee


\( F e^{3+} \) is reduced to \( F e^{2+} \) by using:
This question has multiple correct options
\( \mathbf{A} \cdot H_{2} O_{2} \) is presence of \( N a O H \)
B. \( N a_{2} O_{2} \) in water
\( \mathrm{C} \cdot \mathrm{H}_{2} \mathrm{O}_{2} \) in presence of \( \mathrm{H}_{2} \mathrm{SO}_{4} \)
D. \( N a_{2} O_{2} \) in presence of \( H_{2} S O_{4} \)


There are ' \( m^{\prime} \) copies each of \( ^{\prime} n^{\prime} \)
different books in a university library. The number of ways in which one or more than one book can be selected is
A \( \cdot m^{n}-1 \)
B . \( (m+1)^{n}-1 \)
C \( \cdot(m+1)^{n}-m^{n} \)
D. \( (m+1)^{n}-m \)


An open vessel full of water is falling freely under gravity. There is a small hole in one face of the vessel as shown
in the figure. The water which comes out from the hole at the instant when
hole is at height H above the ground, strikes the ground at a distance of \( x \) from P.


The order of a matrix \( \left[\begin{array}{lll}2 & 5 & 7\end{array}\right] \) is
\( A \cdot 3 \times 3 \)
B. \( 1 \times 1 \)
\( c \cdot 3 \times 1 \)
D. \( 1 \times 3 \)


Consider the complex numbers \( z= \) \( \frac{(1-i \sin \theta)}{(1+i \cos \theta)} . \) The value of \( \theta \) for which \( z \) is
purely imaginary are-
A \( \cdot n \pi-\frac{\pi}{4}, n \epsilon I \)
В \( \cdot n \pi+\frac{\pi}{4}, n \epsilon I \)
c. \( n \pi, n \epsilon I \)
D. No real values of \( \theta \)


Shooting star is another name for
A . comet
B. meteor
c. nubulae
D. solar flare


The number of nodes of s orbital
increases with
A. the increase in n value.
B. the decrease in n value
c. the increase in 1 value.
D. the decrease in 1 value


Figure shows two conducting spheres separated by large distance and of
radius \( 2 \mathrm{cm} \) and \( 3 \mathrm{cm} \) containing
charges \( 10 \mu \mathrm{C} \) arc \( 20 \mu \mathrm{C} \) respectively
When the spheres are connected by a conducting wire then find out following:
¡)Ratio of the final charge.
ii)Final charge on each sphere.
iii)Ratio of final charge densities.


A circle, having radius "r" has line charge distribution over its
circumference having linear charge
density \( \lambda=\lambda_{0} \cos ^{2} \theta . \) Calculate the
total electric charge residing on the
circumference of the circle.
\( \left[\int_{0}^{2 \pi} \cos ^{2} \theta d \theta=\pi\right] \)


What are polar and non polar molecules


Which of the following are correct for purification by steam distillation?
A. Impurities must be non - volatile.
B. The liquid must be completely immiscible with water.
c. The vapor pressure of the liquid must be sufficiently high
D. All are correct


What is a rectifier? With a suitable
circuit diagram, describe the action of
a full wave rectifier by drawing input and output waveforms.


Two wires of same material are having length \( L \) and \( 2 L . \) Compare their resistance and resistivity.


Newton's second law gives a measure of
A. Acceleration
B. Force
c. Momentum
D. Angular momentum


The length of latus rectum of \( \frac{x^{2}}{9}+ \) \( \frac{\boldsymbol{y}^{2}}{2}=1 \) is
\( A \cdot \frac{7}{4} \)
B. \( \frac{3}{4} \)
\( c \cdot \frac{4}{3} \)
D. None.


The standard electrode potential of the half cells is given below:
\( Z n^{2+}+2 e^{-} \rightarrow Z n ; E=-0.76 V \)
\( \boldsymbol{F} \boldsymbol{e}^{2+}+\boldsymbol{2} \boldsymbol{e}^{-} \rightarrow \boldsymbol{F} \boldsymbol{e} ; \boldsymbol{E}=-\mathbf{0 . 4 4} \boldsymbol{V} \)
The emf of the cell \( F e^{2+}=Z n^{-} \rightarrow \)
\( Z n^{2+}+F e \)
A . \( 1.54 V \)
в. \( -1.54 V \)
c. \( 0.32 V \)
D. \( +0.19 V \)


Root hairs are
A. Always unicellular
B. Sometimes unicellular
c. Sometimes multicellular
D. Always multicellular


Lattice energy (numerical value) of choride of alkali metals is in order:
A . LiCI > NaCI>KCI> RbCI> Cscl
B. LiCI<NaCI<KCI<RbCI<CsCI
C. NaCI<KCI <LiCI <RbCI <CsC
D. NaCI<KCI<RbCI<CsCI<Lic


Given ordered pairs :(5,4),(5,5),(5,6) \( (6,4),(6,5),(6,6),(6,7),(8,4),(8,5),(8, \)
6), (8,8)
Use these ordered pairs to find the following relation:
\( R_{3}= \) "is one less than"


Prove the following by using the principle of mathematical induction for
all \( \boldsymbol{n} \in \boldsymbol{N}: \mathbf{1 . 2}+\mathbf{2 . 2}^{\mathbf{2}}+\mathbf{3 . 2}^{\mathbf{2}}+\ldots \ldots . \)
\( \boldsymbol{n} \cdot \boldsymbol{2}^{n}=(\boldsymbol{n}-\mathbf{1}) \mathbf{2}^{n+\mathbf{1}}+\mathbf{2} \)


Urea is prepared by the chemical reaction of:
A. acetamide and ethyl alcochol
B. ammonium sulphate and calcium chloride
c. ammonia and Carbon dioxide
D. chlorine and water


Find solution of following inequality also show it graphically.
\( \boldsymbol{x}<\mathbf{5}, \boldsymbol{x} \in \boldsymbol{Z} \)
\( A \)
в.
\( c \)
\( D \)


Assertion
In a varying magnetic field the induced currents exhibit diamagnetic-like repulsion effects. A conductive object
will experience a repulsion force.
Reason
Eddy currents produced in conductor will produce magnetic field to oppose the varying magnetic field according to faradays law
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


An industrial plant reduces its number of employees, which was originally \( \mathbf{3}, \mathbf{7 6 0}, \) by \( \mathbf{5 \%} \). How many employees now work at the plant?
A . 3542
в. 3565
c. 3525
D. 3572


Choose the correct answer from the
alternatives given. A radio can tune to any station in 7.5 MHz to 12 MHz band. The corresponding wavelength band is
A. \( 40 \mathrm{m} \) to \( 25 \mathrm{m} \)
B. 30 m to 25 \( \mathrm{m} \)
\( c .25 \mathrm{m} \) to \( 10 \mathrm{m} \)
D. \( 10 \mathrm{m} \) to \( 5 \mathrm{m} \)


\( C r^{2+} \) is reducing in nature while the
same \( d- \) orbital configuration
\( \left(d^{4}\right) M n^{+3} \) is an oxidising agent


With reference to Valence Bond Theory in coordination compounds which of the following statements is/are, correct?
I. VBT does not explain the colour exhibited by co-ordination compounds.
II. VBT explains and gives a quantitative interpretation of magnetic data.
III. VBT does not distinguish between weak field ligand and strong field ligand.
A . ।, ॥, ॥
B. ।, ॥
c. ॥, ॥
D. ।, II


State whether the given statement is
True or False:

Consider a sinusoidal travelling wave
shown in figure. The wave velocity is \( +40 c m / s . \) The phase difference
between points \( 2.5 \mathrm{cm} \) apart will be \( \frac{\mathrm{b} \pi}{4} \)
rad
A. True
B. False


Light enters an isosceles right triangular prism at normal incidence through face \( A B \) and undergoes total
nternal reflection at face BC as shown
below:

The minimum value of the refractive
index of the prifsm is close to:
A .1 .10
в. 1.55
\( c \cdot 1.42 \)
0.1 .7


\( \cos ^{-1}\left(\cos \left(2 \cot ^{-1}(\sqrt{2}-1)\right)\right) \) is equal
to
A \( \cdot \sqrt{2}-1 \)
B.
\( c \cdot \frac{3 \pi}{4} \)
D. none of these


Lustre is a property of:
A. metals.
B. non-metals.
c. metalloids.
D. none of the above.


In forced vibration \( \boldsymbol{m}=\mathbf{1 0 g m}, \boldsymbol{f}= \)
\( 100 H z \) and driver force \( F= \)
\( 100 \cos (20 \pi t) \) then what amplitude of
particle.


A beam of ultraviolet radiation having wavelength between \( 100 n m \) and
\( 200 n m \) is incident on a sample of atomic hydrogen gas. Assuming that the atoms are in ground state, which wavelengths will have low intensity in the transmitted beam?
A . \( 104 n m \)
в. \( 103 n m \)
c. \( 105 n m \)
D. 100 nm


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


Assertion
In angiosperms, the ovule develops into
a seed after fertilization.
Reason
Fertilization is not essential for the
development of fruit.
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


Amongst the primary alkyl halides the order of reactivity is:
\( \boldsymbol{C H}_{3} \boldsymbol{X}>\boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{X}>\boldsymbol{C}_{3} \boldsymbol{H}_{7} \boldsymbol{X}, \) etc.


Which of the following is a pentose
sugar?
A. Glucose
B. Fructose
c. Ribose
D. Cellulose


If \( 6^{t h} \) term of a G.P. is \( \frac{1}{32} \) and \( 9^{t h} \) term is \( \frac{1}{256}, \) then \( 11^{t h} \) term \( = \)
A . 1024
в. \( \frac{1}{1024} \)
c. \( \frac{1}{256} \)
D. \( \frac{1}{512} \)


The area bounded by the parabola \( y^{2}= \)
\( 4 x \) and its latusrectum is:
A \( \cdot \frac{8}{3} \) sq. units
B. \( \frac{3}{8} \) sq. units
c. 12 sq. units
D. \( \frac{1}{3} \) sq. units


(a) Given reasons for the following:
(i) \( M n^{3+} \) is a good oxidising agent
(ii) \( E_{M^{2+} / M}^{\circ} \) values are not regular for
fist row transition metals (3 \( \boldsymbol{d} \) series).
(iii) Although \( F \) is more electronegative than \( O \), the highest \( M n \) fluoride is
\( M n F_{4}, \) whereas the highest oxide is
\( \boldsymbol{M} \boldsymbol{n}_{2} \boldsymbol{O}_{7} \)
(b) Complete the following equations:
(i) \( 2 C r O_{4^{-}}^{2}+2 H^{+} \rightarrow \)
(ii) \( \boldsymbol{K} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4} \stackrel{\boldsymbol{\Delta}}{\longrightarrow} \)


Prahlad invests a sum of money in a bank and gets \( R s .3307 .5 \) and
Rs.3472.87 in 2-nd and 3-rd years
respectively. Find the sum he invested.


A circular disc of mass \( M_{1} \) and radius
\( R, \) initially moving with a constant
angular speed \( \omega_{0} \) is gently placed coaxially on a stationary circular disc of
mass \( M_{2} \) and radius \( R \), as shown in
Figure. There is a frictionless force
between the two discs
f disc \( M_{2} \) is placed on a smooth surface, then determine the final
angular speed of each disc.


Which of the following unit is not a fundamental unit:
A . Meter
B. Litre
c. second
D. Kilogram


The frequency of the output signal becomes \( _{-}--_{-}-_{-}- \) times by doubling the value of the capacitance in the LC oscillator circuit.
A \( \cdot \sqrt{2} \)
B. \( \frac{1}{\sqrt{2}} \)
\( c \cdot \frac{1}{2} \)
D. 2


How many integers, greater than 999
but not greater than \( 4000, \) can be
formed with the digits 0,1,2,3 and \( 4, \) if repetition of digits is allowed?
A . 376
в. 375
\( c .500 \)
D. 673


If \( 8 g \) mol of \( P C l_{5} \) heated in a closed vessel of \( 10 L \) capacity and \( 25 \% \) of its
dissociates into \( P C l_{3} \) and \( C l_{2} \) at the
equilibrium then value of \( \boldsymbol{K}_{\boldsymbol{p}} \) will be equal to:
A. \( P / 30 \)
в. \( P / 15 \)
c. \( 2 / 3 P \)
D. \( 3 / 2 P \)


Balance the following equation:
\( N H_{3}+O_{2} \rightarrow N O+H_{2} O \)


If the uncertainty in the position of proton is \( 6 \times 10^{-8} m, \) then the
minimum uncertainty in its speed will
be:
A \( \cdot 1 \mathrm{cms}^{-1} \)
В. \( 0.52 \mathrm{ms}^{-1} \)
\( \mathbf{c} \cdot 1 \mathrm{mms}^{-1} \)
D. \( 100 \mathrm{ms}^{-1} \)


Reduce the equation \( 3 x+4 y-5=0 \)
to intercept form.Hence find the length of the segment intercepted between the
axes.


The value of coefficient of mutual
induction for the arrangement of two coils shown in the figure will be :
A. zero
B. Maximum
c. Negative
D. Positive


Which one of the following is known as energy currency of cell?
A. Adenosine diphosphate
B. Adenosine triphosphate
c. Pyruvate
D. Glucose


State one appropriate observation for each of the following: Concentrated sulphuric acid is added drop wise to a crystal of hydrated copper sulphate.


Match the columns and choose the
correct combination


The value of \( \mid \begin{array}{cc}\mathbf{2} & \boldsymbol{a}+\boldsymbol{b}+\boldsymbol{c}+\boldsymbol{d} \\ \boldsymbol{a}+\boldsymbol{b}+\boldsymbol{c}+\boldsymbol{d} & \boldsymbol{2}(\boldsymbol{a}+\boldsymbol{b})(\boldsymbol{c}+\boldsymbol{d}) \\ \boldsymbol{a} \boldsymbol{b}+\boldsymbol{c} \boldsymbol{d} & \boldsymbol{a} \boldsymbol{b}(\boldsymbol{c}+\boldsymbol{d})+\boldsymbol{c} \boldsymbol{d}(\boldsymbol{a}+\boldsymbol{b})\end{array} \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c .-1 \)
D. None of these


Metals have .......... electronegativity.
A. moderate
B. low
c. high
D. All of the above


Show that \( \frac{\sqrt{8}+i \sqrt{2}}{\sqrt{8}-i \sqrt{2}}+\frac{\sqrt{8}-i \sqrt{2}}{\sqrt{8}+i \sqrt{2}} \) is
real.


\( O^{\prime} \) is a point inside of \( \triangle A B C . \) The
bisector of \( \angle A O B, \angle B O C, \angle C O A \) meet
the sides \( A B, B C \) and \( C A \) in points
\( D, E \) and \( F \) respectively, then
\( \boldsymbol{A} \boldsymbol{D} \cdot \boldsymbol{B} \boldsymbol{E} \cdot \boldsymbol{C} \boldsymbol{F}= \)
A. \( D B . E C . F A \)
в. \( A D . E C . F A \)
c. \( D B . B \) E.FA
D. DB.BE.CF


Given that \( \vec{A}+\vec{B}+\vec{C}=0, \) out of three
vectors two are equal in magnitude and the magnitude of third vector is \( \sqrt{2} \) times that of either of two having equal magnitude. Then angle between vectors are given by
A \( \cdot 30^{\circ}, 60^{\circ}, 90^{\circ} \)
В . \( 45^{\circ}, 135^{\circ}, 150^{\circ} \)
c. \( 90^{\circ}, 135^{\circ}, 150^{\circ} \)
D. \( 90^{\circ}, 135^{\circ}, 135^{\circ} \)


Solve:
\( \sin ^{-1}(\cos x) \)


Assertion
Small liquid drops assume a spherical
shape.
Reason
Due to surface tension liquid drops tend to have minimum surface area.
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


During an experiment, an ideal gas is found to obey a condition \( \frac{\boldsymbol{P}^{2}}{\boldsymbol{\rho}}= \)
constant \( [\rho=\text { density of the gas }] \) The gas is initially at temperature \( T \) pressure \( P \) and density \( \rho . \) The gas expands such that density changes to
\( \frac{\rho}{2} \)
This question has multiple correct options
A. The pressure of the gas changes to \( \sqrt{2} P \)
B. The temperature of the gas changes to \( \sqrt{2} T \)
C. The graph of the above process on the P-T diagram is parabola.
D. The graph of the above process on the P-T diagram is hyperbola.


Pasteur's effect is
A. Stoppage of fermentation in the presence of oxygen
B. Increase of fermentation in the presence of oxygen
C. Decrease of fermentation in the presence of oxygen
D. No effect on fermentation


Five charges of equal values placed at
corners of a regular pentagon of side 'a'.
The force on \( q_{0} \) which is placed at
centroid 'O' is?
A. zero
B. \( \frac{2 k Q q \text { , along OE }}{r_{2}}, \) E
C. \( \frac{2 k Q q \text { , along }}{r_{2}} \) EO
\( \mathbf{D} \cdot \frac{k Q_{q 0}}{r_{2}}, \) along OE


Assertion
Metals are good conductors of heat and
electricity.
Reason
The positive nuclei are surrounded by a
"sea" of mobile electrons.
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 female
hormones
are released by the


Match the column I with Column II:
\( \begin{array}{llll} & \text { Column I } & & \text { Column } \\ & & & \text { II } \\ \text { a. } & \begin{array}{l}\text { Royal Botanical } \\ \text { Garden }\end{array} & \text { 1. } & \text { Howrah } \\ \text { b. } & \begin{array}{l}\text { Indian botanical } \\ \text { garden }\end{array} & \text { 2. } & \text { Lucknow } \\ \text { c. } & \begin{array}{l}\text { National botanical } \\ \text { research institute }\end{array} & \text { 3. } & \begin{array}{l}\text { Kew } \\ \text { (England) }\end{array}\end{array} \)
\( \mathbf{A} \)
\( a \rightarrow 3 ; b \rightarrow 2 ; c \rightarrow 1 \)
B \( . a \rightarrow 3 ; b \rightarrow 1 ; c \rightarrow 2 \)
\( \mathbf{c} \cdot a \rightarrow 1 ; b \rightarrow 2 ; c \rightarrow 3 \)
\( \mathbf{D} \cdot a \rightarrow 1 ; b \rightarrow 3 ; c \rightarrow 2 \)


The current sensitivity of a moving coil galvanometer depends on
A. the number of turns in the coil
B. moment of inertia of the coil
c. current sent through galvanometer
D. eddy current in A1 frame


\( \triangle H \) of which of the following reaction is
zero?
\( \mathbf{A} \cdot H_{2}(g) \rightarrow 2 H^{+}(g)+2 e^{-} \)
B \( \cdot 2 H(g)+a q \rightarrow 2 H^{+}(a q)+2 e^{-} \)
\( \mathbf{c} \cdot 2 H(g) \rightarrow 2 H^{+}(g)+2 e^{-} \)
D \( \cdot H_{2}(g)+a q \rightarrow 2 H^{+}(a q)+2 e^{-} \)


State whether true or false.
Regular reflection is produced when light falls on the rough walls.
A. True
B. False


If three positive numbers \( a, b \) and \( c \) are
in \( A . P . \) such that \( a b c=8 \), then the
minimum possible value of \( b \) is
\( A \cdot 2 \)
B. \( 4^{\frac{1}{5}} \)
\( \mathbf{c} \cdot 4^{\frac{2}{5}} \)
D.


What would be the radius of second
orbit of \( \boldsymbol{H} \boldsymbol{e}^{+} \) ion?
A . \( 1.058 \AA \)
в. \( 3.023 \AA \)
c. \( 2.068 \hat{h} \)
D. \( 4.458 \dot{h} \)


Two flasks of equal volume are connected by a narrow tube (of
negligible volume) all at \( 27^{0} \mathrm{C} \) and
contain 0.70 mole of \( H_{2} \) at 0.5 atm. One
of the flask is then immersed into a
bath kept at \( 127^{0} \mathrm{C} \), while the other
remains at \( 27^{0} \mathrm{C} \). The final pressure in
each flask is :
A. Final pressure \( =0.5714 \) atm
B. Final pressure = 1.5714 atm
C. Final pressure \( =0.5824 \mathrm{atm} \)
D. None of these


\( C l_{3} C H O \rightarrow \stackrel{H_{2} O}{\rightarrow} \)
Find the final product


Which one of the following is wrongly
matched?
A. Transcription - Writing information from DNA to t-RNA
B. Translation - Using information in mRNA to make protein
C. Repressor protein - Binds to a operator to stop enzyme synthesis
D. Operon - Structural genes, Operator and Promoter


If \( 3 x-\frac{1}{2 x}=6, \) then the value of \( 9 x^{2}+ \)
\( \frac{1}{4 x^{2}} \)
A . 36
B. 33
c. 30
D. 39


The excess pressure inside an air bubble of radius \( R \) inside the liquid:
\( ^{A} \cdot \frac{2 T}{R} \)
в. \( \frac{4 T}{R} \)
c. \( \frac{T}{R} \)
D. \( \frac{8 T}{R} \)


If \( \boldsymbol{A}\left(\mathbf{1}, \boldsymbol{p}^{2}\right), \boldsymbol{B}(\mathbf{0}, \mathbf{1}) \) and \( \boldsymbol{C}(\boldsymbol{p}, \mathbf{0}) \) are the
coordinates of three points, then the
value of \( p \) for which the area of the
triangle \( A B C \) is minimum is
A \( \cdot \frac{1}{\sqrt{3}} \)
B. \( -\frac{1}{\sqrt{3}} \)
c. \( \frac{1}{\sqrt{2}} \) or \( -\frac{1}{\sqrt{3}} \)
D. none


Moss sporophyte is diffentiated in
A. Stem and leaves
B. Root, stem and leaves
c. Rhizoids, stem and leaves
D. None of the above


A string of length \( 2 m \) is fixed at two ends. It is in resonance with a tuning
fork of frequency \( 240 H z \) in its third harmonic. Than speed of sound wave in string and its fundamental frequency
is:
\( \mathbf{A} \cdot 240 m / s, 80 H z \)
В. \( 320 \mathrm{m} / \mathrm{s}, 80 \mathrm{Hz} \)
c. \( 640 m / s, 80 H z \)
D. \( 120 \mathrm{m} / \mathrm{s}, 40 \mathrm{Hz} \)


Which one of the following correctly describes AGNI?
A. A long range gun
B. A long range missile
c. A versatile tank
D. A fighter plane


Choose the correct answers from the
alternatives given

Succus entericus is the name given to
A. a junction between ileum and large intestine
B. intestinal juice
c. swelling in the gut
D. appendix


State whether true or false:
Water cannot be converted into ice by adding ice to it.
A. True
B. False


Glomerular capillaries are times more permeable to water
A . 5000
B. 6000
\( c .9000 \)
D. 10,000


The largest interval lying in \( \left(\frac{-\pi}{2}, \frac{\pi}{2}\right) \) for which the function \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{4}^{-\boldsymbol{x}^{2}}+ \)
\( \cos ^{-1}\left(\frac{x}{2}-1\right)+\log (\cos x) \) is defined
A \( \cdot\left[-\frac{\pi}{4}, \frac{\pi}{2}\right) \)
в. \( \left(0, \frac{\pi}{2}\right) \)
\( \mathbf{c} \cdot[0, \pi] \)
D. \( \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \)


Structural isomers possess the same
molecular formula but a different
arrangement of atoms or groups within the molecule.
A. True
B. False


One mole of calcium phosphide on
reaction with excess of water gives how
many moles of phosphine?


Udxidı Canıt ILyplicaliy ustu IUI CdNIE
and satellite tv) has its signal run on a
copper wire surrounded by an insulator which is surrounded by the ground wire,
as opposed to the typical side by side
configuration.
What is the most logical reason for
this?
A. The energy held in the electric field between the inside wire and the outside allow for a clearer signal.
B. The outside wire prevents any magnetic field from the inside wire from leaking out of the wire
C. The outside wire prevents electric fields from interfering with the signal in the inside wire
D. The overall resistance of the wire is reduced using this configuration.


If 'n' identical water drops assumed spherical each charged to a potential energy U coalesce to a single drop, the potential energy of the single drop is:
(Assume that drops are uniformly charged).
A \( \cdot n^{2 / 3} U \)
B . \( n^{3 / 2} U \)
c. \( n^{4 / 3} U \)
\( \mathbf{D} \cdot n^{5 / 3} U \)


Electric field lines of force
A. exist everywhere
B. exist only in the immediate vicinity of electric charges
C. exist only when both positive and negative charges are near one another
D. are imaginary


Budding is a normal mode of asexual reproduction in
A. Starfish and Hydra
B. Hydra and sponges
c. tapeworm and Hydra
D. Sponge and starfish


Urea is preferred to ammonium sulphate soluble in water as a nitrogenous fertilizer because:
A. it is more soluble in water
B. it is cheaper than ammonium sulphate
C. it is quite stable
D. it does not cause acidity in the soil


Bond energy is maximum in?
A. \( O-O \)
B. \( C \equiv C \)
c. \( C \equiv N \)
D. \( N \equiv N \)


Which one is least ionic in the following compounds?
A. \( A g C l \)
в. КСl
c. \( B a C l_{2} \)
D. \( C a C l_{2} \)


A particle travels in a straight line, such that for a short time \( 2 s \leq t \leq 6 s \), its motion is described by \( \mathrm{v}=(4 / \mathrm{a}) \mathrm{m} / \mathrm{s} \)
where a is in \( m / s^{2} . \) If \( v=6 \mathrm{m} / \mathrm{s} \) when \( t= \)
2s, determine the particle's acceleration when \( t=3 s \)


If a body is sent with a velocity of \( \mathrm{km} \mathrm{sec}^{-1} \), it would leave the earth
forever.
A . 11.9
в. 11.6
c. 11.4
D. 11.2


\( \boldsymbol{C H}_{3} \boldsymbol{M} \boldsymbol{g} \boldsymbol{B r}+\boldsymbol{C O}_{2} \stackrel{\text {Dryether}}{\longrightarrow} \boldsymbol{Y} \frac{\boldsymbol{H}_{3} \boldsymbol{O}^{\oplus}}{\longrightarrow} \)
\( Z \)
What is product \( z \) in the given reaction?
A. Ethyl acetate
B. Acetic acid
c. Propanoic acid
D. Methyl acetate


The speed of sound in air is \( 5100 \mathrm{m} / \mathrm{s} \) True or false.
A . True
B. False


A plot of the kinetic energy \( \left(1 / 2 m v^{2}\right) \) of
ejected electrons as a function of the frequency (v) of incident radiation for
four alkali metals \( \left(M_{1}, M_{2}, M_{3}, M_{4}\right) \) is
shown below:

The alkali metals \( M_{1}, M_{2}, M_{3} \) and \( M_{4} \)
are respectively
A . Li, Na, K and Rb
B. Rb, K, Na and Li
C. Na, K, Li and Rb
D. Rb, Li, Na and K


Calculate the \( p H \) value of
\( \mathbf{0 . 0 0 4} N \mathbf{H}_{2} \mathbf{S O}_{4} \) solution:


What is the sum of all positive integers
up to \( 1000, \) which are divisible by 5 and are not divisible by \( 2 ? \)
A. 10,050
в. 5050
c. 5000
D. 50,000


Which of the following is regarded as an absolute contraindication of oral
contraceptive pill?
A. Eczema/Dermatitis
B. Lactating mother
c. Breast cancer
D. Both (B) and (C)


Find the common ratio of the G.P. 2,-6
\( 18, \dots \dots \)
\( A \cdot-2 \)
B . - -
\( c \cdot-4 \)
D. - -


Match the following:
\( \begin{array}{ll}\text { List- I } & \text { List - II } \\ \text { a) Resistivity } & \text { e) volt } \\ \text { b) Conductivity } & \text { f) siemen } \\ \text { c) emf } & \text { g) ohm-metre } \\ \text { d) conductance } & \text { h) mho / metre }\end{array} \)
\( A \cdot a-e, b-f, c-g, d-h \)
B. \( a-f, b-e, c-g, d-h \)
\( c \cdot a-g, b-h, c-e, d-f \)
\( D \cdot a-h, b-g, c-e, d-f \)


Force produced by shooting makes the bullet to move forwards, also equal
force in opposite direction is applied which recoils gun backwards. It is used
to refill gun in semi automatic weapons.
State True or False.


An air bubble of radius r rises from the
bottom of a tube of depth H. When it
reaches the surface, its radius becomes
3r. What is the atmospheric pressure in terms of height of water column?
A \( \cdot \frac{H}{2} \)
в. \( \frac{H}{4} \)
c. \( \frac{H}{8} \)
D. \( \frac{H}{26} \)


Estimate the average drift speed of
conduction electrons in a copper wire of
cross-sectional area \( 2.5 \times 10^{-7} m^{2} \)
carrying a current of 1.8 A. Assume the density of conduction electrons to be
\( 9 \times 10^{28} m^{-3} \)


In acidic medium the rate of reaction
between \( \left(B r O_{3}\right)^{-} \) and \( B r^{-} \) ion is given by the expression \( \frac{\boldsymbol{d}\left[\boldsymbol{B r} \boldsymbol{O}_{3}^{-}\right]}{\boldsymbol{d} \boldsymbol{t}}=\boldsymbol{k}\left[\boldsymbol{B r O}_{3}^{-}\right]\left[\boldsymbol{B r}^{-}\right]\left[\boldsymbol{H}^{+}\right]^{2} \)
it means:
A. rate constant of overall reaction is 4 sec"
B. rate of reaction is independent of the conc. of acid
c. the change in pH of the solution will not attect the rate
D. doubling the conc. of \( H^{+} \) ions will increase the reaction rate by 4 times


An element \( X \) has 7 electrons in its
shell. What is true about the element \( X \)
\( ? \)
This question has multiple correct options
A. It belongs to period 9 of modern periodic table.
B. Its atom contains 9 protons.
C. It has a valency of 7
D. It can accept an electron to acquire noble gas configuration.


Rocksalt is:
A. \( K C l \)
в. \( C a C l_{2} \)
c. \( M g C l_{2} \)
D. \( N a C l \)


\( \left[\left(\frac{x^{2}}{\sqrt{1+x^{2}}}+\frac{1}{\sqrt{1+x^{2}}}\right)^{2}\right] \)


Mark the correct alternative of the
following.
Two numbers are in the ration 3: 5 and
their sum is \( 96 . \) The larger number is?
A . 36
B. 42
c. 60
D. 70


Two bodies \( m_{1} \) and \( m_{2} \) are attached to
the two ends of a string figure. The
string passes over a pulley of mass \( M \)
and radius \( R \) If \( m_{1}>m_{2} \), then the
acceleration of the system is
A \( \cdot \frac{\left.m_{1}-m_{2}+m\right) g}{m_{1}+m_{2}+m} \)
B. \( \frac{\left(m_{1}-m_{2}\right) g}{m_{1}+m_{2}} \)
c. \( \frac{\left(m_{1}+m_{2}\right) g}{m_{1}-m_{2}} \)
D. \( \frac{\left(m_{1}-m_{2}\right) g}{m_{1}-m_{2}+m / 2} \)


The mean kinetic energy of gas
molecules is zero at
\( A \cdot O^{o} C \)
B. -273 \( ^{\circ} \mathrm{C} \)
c. \( 100 \mathrm{k} \)
D. \( 100^{\circ} \mathrm{C} \)


A progression of the form \( a, a r, a r^{2}, \dots \)
is a
A . geometric series
B. harmonic series
c. arithmetic progression
D. geometric progression


If \( f(x)=\sqrt{\frac{x-\sin x}{x+\cos ^{2} x} \text { then } \lim _{x \rightarrow \infty} f(x) \text { is }} \)
A.
B.
\( c \)
D. None of these


In the figure a long uniform
potentiometer wire \( A B \) is having a
constant potential gradient along its
length. The null points for the two
primary cells of emfs \( \varepsilon_{1} \) and \( \varepsilon_{2} \)
connected in the manner shown are
obtained at a distance of \( 120 \mathrm{cm} \) and
\( 300 c m \) from the end \( A . \) Find (i) \( \varepsilon_{1} / \varepsilon_{2} \)
and (ii) position of null point for the cell
\( \varepsilon_{1} \)
How is the sensitivity of a
potentiometer increased?


Choose the correct answers from the
alternatives given :
Which of these pairs of processes are
anaerobic?
A. Fermentation and glycolysis
B. Fermentation and the Krebs cycle
c. Glycolysis and the Krebs cycle
D. The Krebs cycle and the electron transport system


All animals and fungi are autotrophs.
A. True
B. False


A box is placed on an inclined plane and has to be pushed down. The angle of inclination is :
A. Equal to the angle of friction
B. More than the angle of friction
c. Equal to the angle of repose
D. Less than the angle of repose


Cellulose is a?
A. hexapolysaccharide.
B. pentapolysaccharide.
C . tripolysaccharide.
D. None of these.


Light of wavelength \( 6000 \mathrm{nm} \) falls on a
p-njunction photodiode. This photodiode is fabricated from a semiconductor with a band gap of 2.8
eV. Then, which of the following statement is true?
A. This wavelength is not detected by the photodode
B. This wavelength is detected by the photodiode
c. Light is reflected back completely
D. None of the above


For the function \( f(x)=\frac{x^{100}}{100}+\frac{x^{99}}{99}+ \)
\( +\frac{x^{2}}{2}+x+1, f^{\prime}(1)= \)
\( \mathbf{A} \cdot x^{100} \)
в. 100
\( c .10 \)
D. None of these


A cuboid has dimensions of \( 0.4 m \times \)
\( 0.6 m \times 0.2 m \) and a weight of \( 288 \mathrm{kg}-f . \)
What is the maximum pressure exerted by the cuboid?


What are the advantages of chlorofluorocarbons?
A. Excellent refrigerants
B. Very good propellants
c. Useful in firefighting
D. All of the above


The mechanism of urine formation in
nephron involves
A. (i)- Glomerular filtration
(i)- Reabsorption, (ii) Secretion, (iv)- Excretion
B. (i)- Glomerular filtration
(ii)- Secretion, (ii)Reabsorption,
(iv)- Excretion
c. (i)- secretion
(ii)- Reabsorption, (ii)- Glomerular filtration, (iv)- Excretion
D. (i)- Glomerular filtration
(ii)- Reabsorption, (ii) Excretion
(iv)- Secretion


The flow of liquid is laminar or steamline is determined by
A. Rate of flow of liquid
B. Density of fluid
c. Radius of the t ube
D. coeffiecient of visocity of liquid


f \( \sum_{i=1}^{2 n} \sin ^{-1} x_{i}=n \pi, \) then \( \sum_{i=1}^{2 n} x_{i} \) is
equal to
\( \mathbf{A} \cdot n / 2 \)
B. \( 2 n \)
c. \( \frac{n(n+1)}{2} \)
D. none of these


Which of the following is soluble in
water?
A. \( C S_{2} \)
в. \( C H_{3} O C H_{3} \)
c. \( C_{2} H_{5}-C O-C_{2} H_{5} \)
D. \( C C l \)


A resistor \( R, \) inductor \( L \) and a capacitor \( \mathrm{C} \) are connected in series to an
oscillator of frequency v. If the resonant
frequency is \( \boldsymbol{v}_{r}, \) then the current lags behind the voltage, when:
\( \mathbf{A} \cdot v=0 \)
В. \( v<v_{r} \)
с \( . v>v_{r} \)
D. \( v=v_{r} \)


Column I describe some situations in
which a small object moves. Column I
describes some characteristics of these
motions. Match the situation in Column
with the characteristics in Column I
and indicate your answer by darkening appropriate bubbles in the 44 matrix given in the ORS


Smallest particle in a chemical element or compound that has the chemical properties of that element or compound
is
\( A \). Atom
B. Molecule
c. Mixture
D. Element


Assertion
Solubility of sparingly soluble salt decreases due to common ion effect
Reason

Solubility product constant does not
depend on common ion effect.
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 variance of the following data is :
\[
\begin{array}{llll}
\text { Length } & \mathbf{7 2 . 0 -} & \mathbf{7 4 . 0 -} & \mathbf{7 6 . 0 -} \\
\text { of rod } & \mathbf{7 3 . 9} & \mathbf{7 5 . 9} & \mathbf{7 7 . 9}
\end{array}
\]
No. of
Rods
A .2
B. 13.45
c. 13.54
D. 13.40


Which of the following are the correct
statements regarding the catalyzed and
uncatalyzed reactions at constant
temperature?
This question has multiple correct options
A. Catalyzed reaction does not alter \( \Delta H \) of the reaction
B. At constant temperature, \( \Delta G^{0} \) of the catalysed and uncatalyzed reaction is same
C. Catalyzed reaction alters equilibrium constant even at constant temperature
D. Catalysed reaction alters \( r_{f} \) and \( r_{b} \) values equally at constant temperature


Both homosporous and heterosporous plants are found in the group.
A. Algae
B. Bryophytes
c. Pteridophytes
D. Gymnosperms


The distance between two places is 900 km. An ordinary express train takes 5
hours more than a superfast express train to cover this distance. If the speed of the superfast express train is 15 km/hr more than that of the ordinary express train, find the speed of the trains.


Which among the following has highest boiling point?
A. \( C H_{3} C H_{2} C H_{2} C H_{2} C l \)
в. \( \left(C H_{3}\right)_{2} C H C H_{2} C l \)
c. \( \left(C H_{3}\right)_{3} C-C l \)
D. None of the above


At \( 90^{\circ} C \) pure water has \( \left[H_{3} O^{+}\right]=10^{-6} \)
mol/litre. The value of \( \boldsymbol{K}_{\boldsymbol{w}} \) at \( \mathbf{9 0}^{\circ} \boldsymbol{C} \) is
A \( \cdot 10^{-6} \)
\( ^{6}-10^{-6} \)
B . \( 10^{-12} \)
\( c \cdot 10^{-8} \)
D. \( 10^{-14} \)


Consider the experiment of throwing a die, if a multiple of 3 comes up, thrown the die again and if any other number comes, toss a coin. Find the conditional
probability of the event 'the coin shows a tail', given that 'at least one die shows
a 3 '.


Two complex numbers are represented by ordered pairs \( z_{1}:(3,4) \& z_{2}:(4,5) \)
which of the following is correct
representation for \( z_{1} \times z_{2}=? \)
A \( \cdot(-3,31) \)
в. (-8,31)
c. (-1,21)
D. None of these


In a triangle \( A B C, \) medians \( A D \) and \( B E \)
are drawn. If \( \mathrm{AD}=4, \angle D A B=\frac{\pi}{6} \) and
\( \angle A B E=\frac{\pi}{3}, \) then the area of \( \Delta A B C \) is
A \( \cdot \frac{8}{3} \)
в. \( \frac{16}{3} \)
c. \( \frac{32}{3 \sqrt{3}} \)
D. \( \frac{64}{3} \)


The compound that causes a genera
antidepressant action on the central
nervous system belongs to the class of:
A. analgasics
B. tranquilizers
c. nacrotic analgesics
D. antihistamines


Consider the following two statements A and B and identify the correct choice
in the given answers
A) Line spectra is due to atoms in
gaseous state
B) Band spectra is due to molecules
A. Both A and B are false
B. A is true but B is false
c. \( A \) is false but \( B \) is true
D. Both A and B are true.


In a transformer the number of turns of
primary coil and secondary coil are 2.5 and 2 respectively and \( 140 \mathrm{V} \) is applied on primary coil, then find the ratio of current in primary and secondary coils:
A \( \cdot I_{p}: I_{s}=4: 5 \)
B . \( I_{p}: I_{s}=5: 4 \)
\( \mathrm{c} \cdot I_{p}: I_{s}=4: 3 \)
D. \( I_{p}: I_{s}=3: 5 \)


A solution of urea (mol. mass 56
\( \left.g m o l^{-1}\right) \) boils at \( 100.18^{\circ} C \) at the
atmospheric pressure. If \( \boldsymbol{K}_{f} \) and \( \boldsymbol{K}_{\boldsymbol{b}} \) for
water are 1.86 and 0.52 Kkg.mol\( ^{-1} \)
respectively, the above solution will freeze at:
A. \( -6.54^{\circ} \)
B. \( 6.54^{\circ} \mathrm{C} \)
\( c \cdot 0.654^{\circ} C \)
D. \( -0.654^{\circ} \mathrm{C} \)


Integrate the rational function
\( \frac{x}{(x-1)^{2}(x+2)} \)


A \( 12 \Omega \) resistor, a \( 40 \mu F \) capacitor, and
an \( 8 m H \) coil are in series across an ac
source. The resonant frequency is
A \( .28 .1 H z \)
в. \( 281 \mathrm{Hz} \)
\( \mathbf{c} \cdot 2,810 H z \)
D. \( 10 H z \)


If the half life of a radioactive material
is 100 days then its half life after 10 days will become
A. 50 days
B. 200 days
c. 400 days
D. 100 days


The polar end in soap is called:
A. hydrophilic
B. hydrophobic
c. lipophilic
D. none of these


Ammonia evolved from the treatment of
\( 0.30 \mathrm{g} \) of an organic compound for the estimation of nitrogen was passed in 100 mL of 0.1 M sulphuric acid. The excess of acid required \( 20 \mathrm{mL} \) of \( 0.5 \mathrm{M} \) sodium hydroxide solution for complete neutralization. The organic compound is:
A. thiourea
B. benzamide
c. urea
D. acetamide


The angles are complementary and the larger is four times the smaller.


Assertion
We can live very happily if the friction is
not present in nature
Reason
Aeroplane shape is stream lined to
reducec the effort of frictional force.
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 incorrect but Reason is correct
D. Both Assertion and Reason are incorrect


Pituitary gland of adult rat is surgically removed. Which of the following endocrine glands will be less affected?
A. Thyroid
B. Gonads
c. Adrenal cortex
D. Adrenal medulla


If the dimension of a physical quantity is given by \( \left[M^{a} L^{b} T^{c}\right] \) then the physical
quantity will be
A. acceleration, if \( a=1, b=-1, c=-2 \)
B. velocity, if \( a=1, b=0, c=-1 \)
c. pressure, if \( a=1, b=-1, c=-2 \)
D. force, if \( a=0, b=-1, c=-2 \)


State whether the following statement is True or False?

In a circuit containing inductance \( L \)
resistance \( R \) and Voltage \( E \),the current in the circuit is given by \( L \frac{d i}{d t} R i=E \) The current \( i \) at time \( t \) is given by \( i= \) \( \frac{\boldsymbol{E}}{\boldsymbol{R}}\left(\mathbf{1}-\boldsymbol{e}^{-\boldsymbol{R} \boldsymbol{t} / \boldsymbol{L}}\right) \)
A . True
B. False


Newton's first law of motion leads to the
concept of
\( A \cdot \) force
B. inertia
c. both of the above
D. temperature


Two isosceles triangles have equal vertical angles and their areas are in
the ratio 36: 25 Find the ratio of their
corresponding heights.


\( A \) vendor bought 4 dozen eggs at
Rs. 4 each. 7 of these were broken. At
what price per dozen should he sell the
remaining eggs so as to gain \( 10 \% \) on the whole?


The product of two consecutive natural
numbers is \( 56 . \) Find their sum.


Show that if \( \boldsymbol{f}: \boldsymbol{A} \rightarrow \boldsymbol{B} \) and \( \boldsymbol{g}: \boldsymbol{B} \rightarrow \boldsymbol{C} \)
are one-one, then \( g \circ f: A \rightarrow C \) is also
one-one.


Assertion
Two bodies of unequal masses \( m_{1} \) and
\( \boldsymbol{m}_{2} \) are dropped from the same height. If the resistance force offered by air to the motion of both bodies is the same, the bodies will reach the earth at the same
time.
Reason
For equal air resistance, acceleration of
fall of masses \( m_{1} \) and \( m_{2} \) will be
different.
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 is incorrect but Reason is correct


A ray of light passing from glass of water is incident on the glass-water interface at \( 65^{0} . \) If the critical angle for
the pair of media is \( 63^{0}: \)
A. the ray will emerge into water with a deviation of \( 2^{\circ} \) from the normal
B. the ray will be refracted into water with a deviation of \( 2^{0} \)
c. the ray will be totally internally reflected back into glass with a deviation of \( 50^{\circ} \)
D. the ray will be totally internally reflected back into glass with a deviation of \( 2^{0} \)


The relative permittivity of water is \( 81 . \) If
\( \varepsilon_{0} \) and \( \varepsilon \) are permittivities of vaccum
and water respectively Then:
A \( \cdot \varepsilon_{0}=9 \varepsilon_{w} \)
В. \( \varepsilon_{0}=81 \varepsilon_{w} \)
\( \mathbf{c} \cdot \varepsilon_{w}=9 \varepsilon_{0} \)
D. \( \varepsilon_{w}=81 \varepsilon_{0} \)


Prove that \( : C_{0}+C_{1}+C_{2}+\ldots \ldots+ \)
\( C_{n}=2^{n} ? \)


A wire is subjected to a longitudinal
strain of \( 0.05 . \) If its material has a
Poisson's ratio \( 0.25, \) the lateral strain
experienced by it is
A. 0.00625
B. 0.125
c. 0.0125
D. 0.0625


With regard to the respiratory system and the process of respiration in man, answer the following questions:
What is meant by:
Dead air space


Discuss the continuity of the following function at the indicated point(s):
\[
\boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{l}
\frac{\boldsymbol{e}^{\boldsymbol{x}}-\mathbf{1}}{\log (\mathbf{1}+\mathbf{2} \boldsymbol{x})}, \boldsymbol{i} \boldsymbol{f} \boldsymbol{x} \neq \mathbf{0} \\
\boldsymbol{7}, \boldsymbol{i} \boldsymbol{f} \quad \boldsymbol{x}=\mathbf{0}
\end{array}\right.
\]
\( \boldsymbol{x}=\mathbf{0} \)


\( \boldsymbol{C}_{4} \boldsymbol{H}_{10}(\boldsymbol{g})+\boldsymbol{O}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g})+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) \)
Find the coefficient of \( C O_{2} \), when the
above equation is balanced using the lowest whole-number terms?
\( A \cdot 4 \)
B. 2
\( c \cdot 13 \)
D. 10
E. 8


Blocks P and R starts from rest and
moves to the right with acceleration
\( a P=12 t a P=12 t . \) Here \( f \) is in seconds. The
time when block \( Q \) again comes to rest
is?
\( A \cdot 1 \)
в. \( \frac{3}{2} s \)
\( c .2 s \)
D. \( \frac{1}{4} s \)


Find the value of \( k, \) if \( x=2, y=1 \) is a solution of the equation \( 2 x+3 y=k . \) Find two more solutions of the resultant
equation.


Assertion
A point charge \( q \) is placed in front of a
solid conducting sphere. Electric field due to induced charges at the centre of
sphere is zero.
Reason
Electric field at point inside the solid
body of conductor is zero.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Three coins are tossed. Describe two
events \( A \) and \( B \) which are not mutually
exclusive.


If \( \frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{1}{a+b+c} \) where \( (a+ \)
\( b+c) \neq 0 \) and \( a b c \neq 0 . \) What is the
value of \( (\boldsymbol{a}+\boldsymbol{b})(\boldsymbol{b}+\boldsymbol{c})(\boldsymbol{c}+\boldsymbol{a}) ? \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot-1 \)
\( D \)


How many meso isomers are possible for \( 2,3,4- \) pentanetriol
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D. none of these


A uniform chain has a mass \( m \) and
Iength \( l \). It is held on a frictionless table with one-sixth of its length hanging over the edge. The work done injust puling the hanging part back on the table is:
A \( \cdot m g \frac{l}{72} \)
в. \( \frac{m g l}{36} \)
c. \( \frac{m g l}{12} \)
D. \( \frac{m g l}{6} \)


A solution containing 8 g of a substances in 100 g of diethyl ether
boils at \( 36.86^{\circ} \mathrm{C} \). Where as pure ether
boils at \( 35.60^{\circ} \mathrm{C} \). Determine the
molecular mass of the solute. (For ether,
\( \boldsymbol{K}_{\boldsymbol{b}}=\mathbf{2 . 0 2 \mathrm { k }} \mathrm{kh} \boldsymbol{m o l}^{-1} \mathbf{)} \)


A series of ocean waves, each \( 5.0 \mathrm{m} \)
from crest to crest, moving past the observer at a rate of 2 waves per second
What is the velocity of ocean waves?
A. \( 2.5 \mathrm{m} / \mathrm{s} \)
B. \( 5.0 \mathrm{m} / \mathrm{s} \)
\( c \cdot 8.0 \mathrm{m} / \mathrm{s} \)
D. \( 10.0 \mathrm{m} / \mathrm{s} \)


The main difference between A.C.
generator and D.C. generator is
A. carbon brushes
B. magnets
c. coil
D. commutator


\( 10^{-1} M \) HCl is diluted to 100 times. Its
pHis:
\( A \cdot 3 \)
B. 8
\( c \cdot 6.98 \)
D. 7.02


What is the electron configuration of
\( \boldsymbol{V}^{2+} ? \)
\( \mathbf{A} \cdot[A r] 4 s^{2} 3 d^{3} \)
B . \( [A r] 4 s^{1} 3 d^{4} \)
\( \mathbf{c} \cdot[A r] 3 d^{3} \)
D \( \cdot[A r] 4 s^{2} 3 d^{1} \)


Assertion
The order of a reaction can have
fractional value.
Reason
The order of a reaction cannot be
written from balanced equation of a
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. Both Assertion and Reason are incorrect


With the help of labelled diagrams describe the structure of an artery, a
vein and a capillary. State how each of these are adapted for its functions.


In how many ways can the following prizes be given away to a class of 20 students, first and second in Mathematics, first and second in
physics, first in Chemistry and first in English?


The points \( O, A, B, C, D \) are such that \( \boldsymbol{O A}=\boldsymbol{a}, \boldsymbol{O B}=\boldsymbol{b}, \boldsymbol{O C}=\boldsymbol{2} \boldsymbol{a}+\boldsymbol{3 b} \) and
\( \boldsymbol{O} \boldsymbol{D}=\boldsymbol{a}-\boldsymbol{2 b} . \) If \( |\boldsymbol{a}|=\boldsymbol{3}|\boldsymbol{b}|, \) then the
angle between \( B D \) and \( A C \) is
A . \( \pi \)
в. \( \frac{\pi}{2} \)
\( c \cdot \frac{\pi}{3} \)
D. None of these


What will be the input of \( A \) and \( B \) for Boolean expression
\[
(\overline{A+B})(\overline{A \cdot B})=1
\]
A .0,0
в. 0,1
c. 1,0
D. \( 1, \)


Fill in the blanks with appropriate
words.
The cell cycle is divisible into two main
phases \( \ldots \ldots \ldots . . \) and


An \( \alpha \) - particle moves from \( \mathrm{E} \) to \( \mathrm{W} \) in a magnetic field perpendicular to the plane of the paper and into the paper. The particle is deflected towards:
A. East
B. west
c. south
D. North


If \( f(x)=3 x-2 \) and \( (g o f)^{-1}(x)=x- \)
2, then find the function \( g(x) \)