The average breathing rate of human beings
A . \( 15-18 \) times
B. 15- 25 times
c. 10 -20 times
D. None of the above


If the product of two integers is 72 and one of them is \( -9, \) then the other
integer is.
A. -8
B. 8
c. 81
D. 63


\( \mathbf{f}_{\mathbf{0}}=\left|\begin{array}{lll}\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} \\ \boldsymbol{x} & \boldsymbol{y} & \boldsymbol{z} \\ \boldsymbol{p} & \boldsymbol{q} & \boldsymbol{r}\end{array}\right| \) and \( \boldsymbol{\Delta}_{2}=\left|\begin{array}{lll}\boldsymbol{y} & \boldsymbol{b} & \boldsymbol{q} \\ \boldsymbol{x} & \boldsymbol{a} & \boldsymbol{p} \\ \boldsymbol{z} & \boldsymbol{c} & \boldsymbol{r}\end{array}\right| \)
then \( \Delta_{1} \) is equal to
\( A \cdot 2 \Delta_{2} \)
в. \( \Delta_{2} \)
\( c \cdot-\Delta_{2} \)
D. none of these


The present age of a man is twice that of his son.After Eight years their ages will be in the ratio 7: 4 . Find the son's
present age.
A. 24years
B. 34years
c. 44years
D. 54years


Find the total surface area of cubes
having the following sides.
\( 6.8 m \)


You travel on the highway at a rate of \( 60 m p h \) for 1 hour and at \( 50 m p h \) for 2
hours and 40 mph for 3 hours. What is
your average speed during the trip?
A \( .48 m p h \)
в. 47 три
c. \( 46 m p h \)
D. \( 45 \mathrm{mph} \)


Choose the correct answer from the
alternatives given What is name of the iron-containing protein that gives red blood vessels
their colour?
A. Haemoglobin
B. Hemocyanin
c. Pyrite
D. Lymphocytes


If masses of three wires of copper are in the ratio of 1: 3: 5 and there lengths are in the ratio of \( 5: 3: 1, \) then ratio of their
electrical resistance is
A .1: 3: 5
B. 5: 3: 1
c. 1: 15: 125
D. 125 : 15 : 1


Evaluate the following:
\( \left|\begin{array}{ccc}1 & a & b c \\ 1 & b & c a \\ 1 & c & a b\end{array}\right| \)


A solution contaming \( N H_{4} C l \) and \( N H_{4} O H \) has \( [\stackrel{\ominus}{O} H]=10^{-6} m o l L^{-1} \)
which of the following hydroxides would be precipitated when this solution in added in equal volume to a solution containing \( 0.1 \mathrm{M} \) of metal ions?
A \( \cdot M g(O H)_{2},\left(K_{s p}=3 \times 10^{-11}\right) \)
B. \( F e(O H)_{2}\left(K_{s p}=8 \times 10^{-16}\right) \)
c. \( C d(O H)_{2}\left(K_{s p}=8 \times 10^{-6}\right) \)
D. \( \operatorname{AgOH}\left(K_{s p}=5 \times 10^{-3}\right) \)


Frictional force always reduces:
A. Speedd
B. Velocity
c. Acceleration
D. Time


Lower and upper mantle is separated
with help of :
A. territorial zone
B. transition zone
c. terrestrial zone
D. inner zone


The ionisation energy of a hydrogen like
Bohr atom is 4 Rydberg. What is the wavelength of the radiation emitted when the electronjumps from the first excited state to the ground
state?


Kidney of adult rabbit is
A. Pronephros
B. Metanephros
c. Mesonephros
D. Opisthonephros


When a mass is suspended from the end of a wire the top end of which is attached to the roof of the lift, the
extension is \( e \) when the lift
is stationary. If the lift moves up with a constant acceleration \( \boldsymbol{g} / \mathbf{2}, \) the
extension of the wire would be
A \( \cdot \frac{2 e}{3} \)
в. \( \frac{3 e}{2} \)
\( c \cdot 2 e \)
D. \( 3 e \)


Explain the temporary and permanent
methods to be adopted for kidney
failure (ESRD) persons.


Planets do not twinkle as stars, because
A. Planets are much closer to earth than stars
B. Planets are smaller in size than stars
C. A planet is not surrounded by gaseous atmosphere
D. A star is not surrounded by gaseous atmosphere


The important characteristic that
distinguishes uniform from non
uniform circular motion are
A. Uniform circular motion has radial acceleration and radial velocity, while non uniform motion lacks it
B. Uniform circular motion has radial acceleration and tangential velocity, while non uniform motion lacks it
C. Non uniform circular motion has tangential acceleration, while uniform circular motion lacks it
D. Non uniform circular motion has tangential acceleration and radial velocity, while uniform circular motion lacks it


Out of \( \boldsymbol{H}_{2} \boldsymbol{S}_{2} \boldsymbol{O}_{3}, \boldsymbol{H}_{2} \boldsymbol{S}_{2} \boldsymbol{O}_{4}, \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{5} \) and
\( \boldsymbol{H}_{2} \boldsymbol{S}_{2} \boldsymbol{O}_{8} \) peroxy acids are:
A. \( H_{2} S_{2} O_{3}, H_{2} S_{2} O_{8} \)
в. \( H_{2} S O_{5}, H_{2} S_{2} O_{8} \)
c. \( H_{2} S_{2} O_{4}, H_{2} S O_{5} \)
D. \( H_{2} S_{2} O_{3}, H_{2} S_{2} O_{4} \)


When light is incidence on a diffraction
grating, then the zero order maximum will be
A. spectrum of the colours
B. White
c. one of the component colours
D. Absent


The intensity of the
atmospheric electric field is, normally,
A. greater in the middle of the day than at morning
B. smaller in the middle of the day than at morning
C. same in the middle of the day as at morning
D. zero in the middle of the day and at morning


The magnetic field in the cylindrical region shown in figure increases at a
constant rate of \( 10.0 m T s^{-1} \). Each side
of the square loop abcd and defa has a
length of \( 20.0 \mathrm{cm} \) and a resistance of
\( 2.00 \Omega . \) Correctly match the current in
the wire \( a d \) in four different situations
as listed in column I with the values
given in column II.


In the reaction, \( C(s)+C O_{2}(g) \leftrightharpoons \)
\( 2 C O(g), \) the equilibrium pressure is 12
atm. If \( 50 \% \) of \( C O_{2} \) reacts, calculate \( K_{p} \)
A. 1.6 atm
B. 0.16 atm
\( c \cdot 16 \operatorname{atm} \)
D. 160 atm


Which of the following is true for
cornea?
A. It allows light to enter the eye
B. Most of the refraction of light occurs on the outer surface of cornea
C. It forms a transparent bulge on the outer surface of the eyeball.
D. All of the above


'Entomophagous fungi' is
A. Colletotrichum
B. Cercospora
c. Dactylella
D. Rhizopus


is continuously formed by the action of UV rays on molecular oxygen and also degraded into molecular oxygen in the stratosphere.


\( \mathbf{f} \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{- 1} & \mathbf{2} \\ \mathbf{3} & \mathbf{0} & -\mathbf{2} \\ \mathbf{1} & \mathbf{0} & \mathbf{3}\end{array}\right] \) verify that
\( \boldsymbol{A}(\boldsymbol{a} \boldsymbol{d} \boldsymbol{j} \boldsymbol{A})=|\boldsymbol{A}| \boldsymbol{I} \)


Match the column - I with Column - II
and pick up the correct answer:
\( \begin{array}{ll}\text { Column - - } & \text { Column -II } \\ \text { (I) Nickel } & \text { A. Conversion }\end{array} \)
(II) ZSM-5 \( \quad \) B. Alkylation of benzene I) ZSM-5
(III) \( S i O_{2} \quad \) C. Hydrogenation 'on
A.
B. I-A II - B III - C
c. \( 1-\mathrm{C} \) ॥ \( -\mathrm{B} \) III \( -\mathrm{A} \)
D. I - B II - C III - B


The following four wires are made of the same material. Which of these will have
the largest extension when the same tension is applied?
A. Length \( =50 \mathrm{cm}, \) diameter \( =0.5 \mathrm{mm} \)
B. Length = 100 cm, diameter = 1 mm
c. Length\( =200 \mathrm{cm}, \) diameter \( =2 \mathrm{mm} \)
D. Length \( =300 \mathrm{cm}, \) diameter \( =3 \mathrm{mm} \)


The scalar matrixis
\( \mathbf{A} \cdot\left[\begin{array}{cc}-1 & 3 \\ 2 & 4\end{array}\right] \)
\( \mathbf{B} \cdot\left[\begin{array}{ll}0 & 3 \\ 2 & 0\end{array}\right] \)
\( \mathbf{C} \cdot\left[\begin{array}{ll}4 & 0 \\ 0 & 4\end{array}\right] \)
D. None of these


Black precipitate in the detection of sulphur with lead acetate and acetic
acid is due to formation of:
A \( \cdot P b_{2} S \)
в. \( P b S \)
c. \( P b S_{2} \)
D. \( P b S O_{4} \)


The pair whose both species are used in antacid medicinal preparation is
в. \( N a_{2} C O_{3} \) and \( C a\left(H C O_{3}\right) \)
c. \( C a\left(H C O_{3}\right)_{2} \) and \( M g(O H)_{2} \)
D. \( C a(O H)_{2} \) and \( N a H C O_{3} \)


When an object is in a bond state in a field, its total energy is
A. positive
B. negative
c. zero
D. infinite


A man running with a uniform speed 'u' on a straight road observed a stationary bus at a distance 'd' ahead of him. At
that instance, the bus starts with an
acceleration 'a'. The condition that he
would be able to catch the bus is:


Name the stage of cell cycle at which one of the following events occurs. (i) Chromosomes are moved to spindle
equator.
(ii) Centromere splits and chromatids separate.
(iii) Pairing between homologous chromosomes
takes place
(iv) Crossing over between homologous chromosomes takes place.


Household electrical appliances are joined using combination
of resistors
A. Parallel
B. Alternating
c. continuous
D. Series


The epoch of human civilization is
A. Pliocene
B. Holocene
c. Pleistocene
D. Palaeocene


Statement \( I: H_{2} S O_{4} \) is not used during
the reaction of alcohols with \( K I \)
Statement II : \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) oxidises \( \boldsymbol{K} \boldsymbol{I} \) to \( \boldsymbol{I}_{2} \)
and will prevent reaction of alcohol with
\( \boldsymbol{K} \boldsymbol{I} \)
A. Statement I \& Statement II are correct and statement I is correct explanation of statement
B. Statement I \& Statement II are correct and statement
Il is not correct explanation of statement
c. Statement lis correct and Statement II is wrong
D. Statement I is wrong and Statement II is correct


For the half reaction
\( \boldsymbol{B}(\boldsymbol{s}) \rightarrow \boldsymbol{B}^{2+}+\boldsymbol{2} \boldsymbol{e}^{-} \quad \boldsymbol{E}_{1}^{\circ}=-\mathbf{0 . 4 4} \boldsymbol{V} \)
and \( B_{2}+\rightarrow B^{3+}+e^{-} \quad E_{2}^{\circ}=1.3 V \)
What is \( E^{\circ} \) for the reaction,
\( \boldsymbol{3} \boldsymbol{e}^{-}+\boldsymbol{B}^{+\boldsymbol{3}} \rightarrow \boldsymbol{B}(\boldsymbol{s}) \)
A . \( 0.86 \mathrm{v} \)
B. \( 0.14 \mathrm{v} \)
c. -0.14 v
D. - 0.28 v


A person is suffering from frequent episodes of nasal discharge, nasal
congestion, reddening of eyes and watery eyes. These are the symptoms of
A. Cyanosis
B. Bronchitis
c. Rhinitis
D. Bronchial carcinoma


The figure shows an estimated force
time graph for a baseball stuck by a bat From the curve determine:
(i) impulse delivered to the ball
(ii) force exerted on the ball
(iii) the max. force on the ball.


A fuse wire is always connected to the
A. earth wire
B. neutral wire
C. live wire
D. none of these


Feasible region's optimal solution for a linear objective function always includes
A. downward point
B. upward point
c. corner point
D. front point


Distinguish between the terms homopolymer and copolymer and give an example of each.


Let \( O \) be the origin and \( P \) be the point at a distance 3 units from origin. If d.x.s' of OP are \( 1,-2,-2, \) then coordinates of \( P \) is
given by
A. 1,-2,-2
в. 3,-6,-6
c. \( \frac{1}{3},-\frac{2}{3},-\frac{2}{3} \)
D. \( \frac{1}{9},-\frac{2}{9},-\frac{2}{9} \)


Use the test for symmetry to determine
if the graph of \( y-5 x^{2}=4 \) is
symmetric about the x-axis.
A. Symmetrical about x-axis
B. Not symmetrical about x-axis
c. Can't be determined
D. None of these


Evaluate \( \int_{1}^{3}(3 x-2) d x \)


If the roots of \( \left(a^{2}+b^{2}\right) x^{2}-2 b(a+ \)
\( c) x+\left(b^{2}+c^{2}\right)=0 \) are equal, then
\( a, b, c \) are in
A. A.P
в. G.P.
c. н.P.
D. none of these


Optical fibers works on the principle of
A. Reflection
B. Refraction
c. Total internal reflection
D. All


A buffer solution can be prepared from a
mixture of:
(i) Sodium acetate and acetic acid in
water
(ii) Sodium acetate and hydrochloric
acid in water
(iii) Ammonia and ammonium chloride
in water
(iv) Ammonia and sodium hydroxide in
water
\( A \cdot(i),(\text { ii }) \)
B . (ii), (iii)
c. (iii), (iv)
D. (i), (iii)


Cerium \( (z=58) \) is an important member of the lanthanides. Which of
the following statements about cerium is incorrect?
A. The common oxidation states of cerium are +3 and +4
B. The +3 oxidation state of cerium is more stable than the +4 oxidation state
c. The +4 oxidation state of cerium is not known in solutions
D. Cerium (IV) acts as an oxidising agent.


The probability \( (P) \) of survival of \( a \) radioactive nucleus in its mean life is:
\( A \cdot \frac{1}{e} \)
B. \( \frac{1}{\lambda} \)
c. \( \frac{0.633}{\lambda} \)
D.


plating is done on
objects such as car parts, bath taps, kitchen gas burners, bicycle handlebars, wheel rims because of its
shiny appearance
A. Chromium
B. Nickel
c. carbon
D. None of these


What are natural fibres ? Give two
examples.


A wire of length \( L \) and cross-sectional area \( A \) is constructed of a material
whose Young's modulus of elasticity is
Y. The energy density stored in the wire when stretched by \( x \) meter will be
A. \( Y \times x^{2} \)
в. \( \frac{Y \times x^{2}}{L} \)
c. \( \frac{Y \times x^{2}}{2 L^{2}} \)
D. \( \frac{Y \times x^{2}}{L^{2}} \)


Bad conductor of heat is
A. copper
B. Steel
c. Silver
D. none of these


An electron moving with a velocity of \( 5 \times 10^{4} m s^{-1} \) enters into a
uniform electric field and acquires a
uniform acceleration of \( 10^{4} m s^{-2} \) in the
direction of its initial motion. Calculate
the time(in \( s \) ) in which the electron
would acquire a velocity double of its initial velocity
A . 10
B. 8
\( c \cdot 5 \)
\( D \)


Power of accomodation of eye implies:
A. control intensity
B. prevent internal reflection of light
c. change of focal length of eye lens
D. all of the above


The correct order of magnetic moments (spin only values in (B.M.) among the following is:
[Atomic numbers \( M n=25, F e=26, C o= \)
27]
\( \left.\mathbf{A} \cdot\left[\mathrm{MnCl}_{4}\right]^{2-}>\left[\mathrm{CoCl}_{4}\right]^{2-}>\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4} \)
B . \( \left[\mathrm{MnCl}_{4}\right]^{2-}>\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4-}>\left[\mathrm{CoCl}_{4}\right]^{2} \)
C \( \cdot\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4-}>\left[\mathrm{MnCl}_{4}\right]^{2-}>\left[\mathrm{CoCl}_{4}\right]^{2} \)
D \cdot \( \left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4-}>\left[\mathrm{CoCl}_{4}\right]^{2-}>\left[\mathrm{MnCl}_{4}\right]^{2-} \)


Cantres of the three circles
\( x^{2}+y^{2}-4 x-6 y-14=0 \)
\( \boldsymbol{x}^{2}+\boldsymbol{y}^{2}+\boldsymbol{2} \boldsymbol{x}+\boldsymbol{4} \boldsymbol{y}-\boldsymbol{5}=\mathbf{0} \)
and \( x^{2}+y^{2}-10 x-16 y+7=0 \)
A. Are the vertices of a right triangle
B. The vertices of an isosceles triangle which is not regular
c. vertices of a regular triangle
D. Are collinear


Define a sere.


8
8
8


What happens to the moon after full
moon day?


In fig., ABCD is a rhombus
Is \( \angle B A C=\angle D A C ? \)
A. True
B. False


Next homologue of ethane is?
A. propane
B. methane
c. ethene
D. ethyne


For \( \mathbf{3} \times \mathbf{3} \) matrices \( \boldsymbol{A} \) and \( \boldsymbol{B}, \) if \( |\boldsymbol{B}|=\mathbf{1} \)
and \( A=2 B \) then find \( |A| \)
A .
B. 4
\( c \cdot 2 \)
D. 8


Evaluate \( \left(x^{3}+2 x^{2}+3 x\right) \div 2 x \)
A \( \cdot\left(x^{2}+2 x-3\right) \div 2 \)
B. \( \left(x^{2}-2 x+3\right) \div 2 \)
c. \( \left(x^{2}+2 x+3\right) \div 2 \)
D. \( \left(x^{2}+x+3\right) \div 2 \)


\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left(\tan ^{-1}\left(\frac{\boldsymbol{a}-\boldsymbol{x}}{\mathbf{1}+\boldsymbol{a} \boldsymbol{x}}\right)\right) \) equals if \( \mathbf{a x}>-1 \)
\( \mathbf{A} \cdot \frac{a}{1+x^{2}} \)
B. \( \frac{1}{1+x^{2}} \)
C \( \cdot-\frac{a}{1+x^{2}} \)
D. \( -\frac{1}{1+x^{2}} \)


Heavy water reacts with
\( \boldsymbol{C O}_{2}, \boldsymbol{S O}_{3}, \boldsymbol{P}_{2} \boldsymbol{O}_{5} \) and \( \boldsymbol{N}_{2} \boldsymbol{O}_{5} \)
respectively, to give the compounds:
A. \( D_{2} C O_{3}, D_{2} S O_{4}, D_{3} P O_{2} \) and \( D N O_{2} \)
в. \( D_{2} C O_{3}, D_{2} S O_{4}, D_{3} P O_{4} \) and \( D N O_{2} \)
c. \( D_{2} C O_{3}, D_{2} S O_{3}, D_{3} P O_{4} \) and \( D N O_{2} \)
D. \( D_{2} C O_{3}, D_{2} S O_{4}, D_{3} P O_{4} \) and \( D N O_{3} \)


Photosynthesis occurs in the
A . Root
B. Stem
c. Leaf.
D. Fruit


n the given figure, the value of \( x \text { (in } c m) \)
is :
4
B.
\( c \)
\( D \)


When mercuric iodide is added to an
aqueous solution of \( K I \) then:
A. boiling point increase
B. boiling point decrease
c. freezing point increase
D. osmotic pressure increase


A surface has work function \( 3.3 e V \)
Which of the following will cause
emission?
A. \( 100 W \) incandascent lamp
B. 40 \( W \) flouroscent lamp
c. \( 20 W \) sodium lamp
D. 20 \( W \) Hg lamp


Among \( K O_{2}, A l O_{2}^{-}, B a O_{2} a n d N O_{2}^{+} \)
unpaired electron is present in:
A. \( N O_{2}^{+} \) and \( B a O_{2} \)
B. \( K O_{2} \) and \( A l O_{2}^{-} \)
c. \( K O_{2} \) only
D. \( B a O_{2} \) only


An aquarium is in the form of a cuboid whose external measures are \( 80 \mathrm{cm} \times \)
\( 30 c m \times 40 c m . \) The base side faces and
back face are to be covered with a
coloured paper. Find the area of the paper needed?
A. \( 3000 \mathrm{cm}^{2} \)
B . \( 5000 \mathrm{cm}^{2} \)
c. \( 8000 \mathrm{cm}^{2} \)
D. \( 7000 \mathrm{cm}^{2} \)


The oxidation state of oxygen of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) in the final products when it reacts with \( C l O_{3}^{\ominus} \) is :
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot-1 \)
D. - -


In the fig; we have \( X \) and \( Y \) are the mid-
points of \( A C \) and \( B C \) and \( A X=C Y \)
then
This question has multiple correct options
A. \( A C=B C \)
B. \( A B=B C \)
\( \mathbf{c} . A C=A B \)
\( \mathbf{D} \cdot C X=C Y \)


Pyramid of numbers in a pond
ecosystem is
A. I rregular
B. Inverted
c. upright
D. Spindle shaped


Assertion
Forest influences local air circulation
and may thus retain solid suspensions and gaseous elements.
Reason
Forests control the wind velocity and air
flows.
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 rotational movement in humans is
brought about by
A. Slightly moveable joint
B. Ball and socket joint
c. Pivot joint
D. Plane joint
E. Both B and C


The pure form of carbon is found in :
A . jute
B. diamond
c. methane gas
D. All of the above


Two conducting plates \( A \) and \( B \) are
parallel. A is given a charge \( Q_{1} \) and \( B \) is
given a charge \( Q_{2} \). The charge on inner
side of B is :
\( A \)
\[
\frac{Q_{2}-Q_{1}}{2}
\]
в.
\[
\frac{\left(Q_{1}-Q_{2}\right)}{2}
\]
\( c \)
\[
\frac{\left(Q_{1}+Q_{2}\right)}{2}
\]
\( D \)
\[
\frac{-\left(Q_{1}+Q_{2}\right)}{2}
\]


Electrons of energies \( 10.20 e V \) and \( 12.09 e V \) can cause radiation to be
emitted from hydrogen atoms. Calculate, in each case, the principal quantum of the orbit to which electron in the hydrogen atom is raised and the
wavelength of the radiation emitted if it
drops back to the ground state. Find the sum of these numbers.


Draw a rough sketch of the curve \( y^{2}= \)
\( 4 x \) and find the area of the region
enclosed by the curve and the line \( y=x \)


The question is refer to image.
8


Assertion
The average mass of one Mg atom is
24.305 amu, which is not equal to the actual mass of one Mg atom.
Reason Three isotopes, \( ^{24} M g,^{25} M g \) and \( ^{26} M g \) of Mg can be found in nature.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


(a) \( \boldsymbol{H}_{2} \boldsymbol{O}_{2}+\boldsymbol{O}_{3} \rightarrow \boldsymbol{H}_{2} \boldsymbol{O}+\mathbf{2} \boldsymbol{O}_{2} \)
(b) \( \boldsymbol{H}_{2} \boldsymbol{O}_{2}+\boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{O} \rightarrow \boldsymbol{2} \boldsymbol{A} \boldsymbol{g}+\boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{O}_{2} \)
Role of hydrogen peroxide in the above reactions is respectively:
A. Oxidizing in (a) and reducing in (b)
B. Reducing in (a) and oxidizing in (b)
c. Reducing in (a) and (b)
D. Oxidizing in (a) and (b)


\( A \) box \( B_{1} \) contains 1 white ball, 3 red
balls and 2 black balls. Another box \( B_{2} \)
contains 2 white balls, 3 red balls and 4
black balls. A third box \( B_{3} \) contains 3
white balls, 4 red balls and 5 black balls If 2 balls are drawn (without replacement) from a randomly selected box and one of the balls is white and the other ball is red, the probability that
these 2 balls are drawn from box \( B_{2} \) is
A \( \cdot \frac{116}{181} \)
в. \( \frac{126}{181} \)
c. \( \frac{65}{181} \)
D. \( \frac{55}{181} \)


The ends of a coil are connected to a
galvanometer. When current suddenly I starts flowing in a neighbouring circuit, the instantneous deflection in the
galvanometer is \( +7^{\circ} . \) If now the coil be
quickly rotate through \( 180^{\circ}, \) what will be the maximum deflection in the
galvanometer?
A \( \cdot 7^{\circ} \)
B. \( 14^{\circ} \)
\( c \cdot 21^{0} \)
\( D \cdot 28^{\circ} \)


Evaluate \( \int_{-\sqrt{2}}^{2 \pi} \frac{2 x^{7}+3 x^{6}-10 x^{5}-7 x^{3}-12 x^{2}+}{x^{2}+2} \)
\( ^{\mathrm{A}} \cdot \frac{\pi}{2 \sqrt{2}}+\frac{16 \sqrt{2}}{5} \)
B. \( \frac{\pi}{4 \sqrt{2}}-\frac{8 \sqrt{2}}{5} \)
c. \( \frac{\pi}{4 \sqrt{2}}+\frac{8 \sqrt{2}}{5} \)
D. \( \frac{\pi}{2 \sqrt{2}}-\frac{16 \sqrt{2}}{5} \)


When a number is added to another number, the total becomes \( 333 \frac{1}{3} \) percent of the second number. What is the ratio between the first number and second number?
A. 3: 7
в. 7: 4
c. 7: 3
D. 4: 7


Assertion
In the following reaction,
\( \boldsymbol{S O}_{2}+\boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{S} \longrightarrow \boldsymbol{3} \boldsymbol{S}+\boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{O} \)
1 mole \( S O_{2} \) and 1 mole \( H_{2} S \) forms 3
moles sulphur.
Reason
1 mole \( S O_{2} \) and 2 mole \( H_{2} S \) form 3
moles sulphur and 2 moles \( H_{2} O \)
A. Both Assertion and Reason are are true and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation for Assertion
C. Assertion is true but Reason is false
D. Assertion is false but Reason is true


A neutral oxide which is slightly heavier than air and slightly soluble in water is:
\( A \cdot S O_{2} \)
в. \( O_{2} \)
c. \( N a_{2} \) Q
D. \( F e_{2} O_{3} . x H_{2} O \)


A catapult with a basket of mass \( 50 \mathrm{kg} \) launches a \( 200 \mathrm{kg} \) rock by swinging around from a horizontal to a
vertical position with an angular velocity of 2.0 rad/s. Assuming the rest of the catapult is massless and the catapult arm is \( 10 \mathrm{m} \) long, what is the velocity of the rock as it leaves the catapult?
\( A \cdot 10 \mathrm{m} / \mathrm{s} \)
B. 20 \( \mathrm{m} / \mathrm{s} \)
\( c \cdot 25 m / s \)
D. \( 50 \mathrm{m} / \mathrm{s} \)
E. \( 100 \mathrm{m} / \mathrm{s} \)


Find mode for given data:
\( \begin{array}{llll}\text { Class } & 20- & 30- & 40- \\ 29 & 39 & 49\end{array} \)
3. 20 Frequency 15


Write three methods of preventing rusting of iron.


Why does HF has the maximum boiling point amongst all hydrogen halides?
A. Due to hydrogen bonding
B. Due to Vander Waal's forces
c. Due to minimum molecular mass
D. None of these


\( f\left|\begin{array}{ccc}\mathbf{6} i & -\mathbf{3} i & \mathbf{1} \\ \mathbf{4} & \mathbf{3} i & -\mathbf{1} \\ \mathbf{2 0} & \mathbf{3} & \boldsymbol{i}\end{array}\right|=\boldsymbol{x}+\boldsymbol{i} \boldsymbol{y}, \) then
A \( . x=3, y=0 \)
B. \( x=1, y=3 \)
c. \( x=0, y=3 \)
D. \( x=0, y=0 \)


Number of moles of \( \boldsymbol{K}_{2} \boldsymbol{C r}_{2} \boldsymbol{O}_{7} \) reduced
by one mole of \( S n^{2+} \) ions is :
A \( \cdot \frac{1}{3} \)
B. 3
\( c \cdot \frac{1}{6} \)
D. 6


Which one of the following group of taxa does not represent similar category in hierarchy?
A. Potato and tomato
c. Monocots and angiosperms
D. Wheat and mango


Find the area of parallelogram in which base is \( 2.5 \mathrm{cm}, \) and altitude is \( 1.4 \mathrm{cm} \)


\( P b\left(I O_{3}\right)_{2} \) is a springly soluble salt
\( \left(K_{s p}=2.6 \times 10^{-13}\right) . \) To \( 35 \mathrm{mL} \) of \( 0.15 \mathrm{M} \)
\( P b\left(N O_{3}\right)_{2} \) solution, \( 15 \mathrm{mL} \) of \( 0.8 \mathrm{M} \)
\( K I O_{3} \) solution is added, and a
precipitate of \( \boldsymbol{P b}\left(\boldsymbol{I} \boldsymbol{O}_{3}\right)_{2} \) is formed
What will be the molarity of \( I O_{3}^{\Theta} \) ions in the solution after completion of the
reaction?
A. 0.152
B. 0.081
c. 0.4
D. 0.03


The elements of \( \boldsymbol{A} \cap \boldsymbol{B}^{\prime} \) are:


Two sounds can differ only by the difference in their loudness.
A. True
B. False


The gravitational potential is a
A. scalar
B. vector
C. scalar based on the mass of the particle
D. scalar or vector depending on the situation


The points (0,4) and (0,2) are
respectively the vertex and focus of a parabola. Then find the equation of the parabola.


Vapour pressure of \( C C l_{4} \) at \( 25^{\circ} \mathrm{C} \) is 143
\( \mathrm{mm} \) of Hg. \( 0.5 \mathrm{g} \) of a non-volatile solute (mol. Mass \( =\mathbf{6 5} \) ) is dissolved in \( 100 \mathrm{mL} \)
\( \boldsymbol{C C l}_{4} . \) Find the vapour pressure of the
solution: (Density of \( \boldsymbol{C} \boldsymbol{C l}_{4}= \)
\( 1.58 g / c m^{3} \)
\( \mathbf{A} \cdot 141.93 \mathrm{mm} \)
B. \( 94.39 \mathrm{mm} \)
c. \( 199.34 \mathrm{mm} \)
D. \( 143.99 \mathrm{mm} \)


The ratio of electric force between two
electrons to that between two protons
separated by the same distance in air is
A \( \cdot 10^{\circ} \)
B. \( 10^{6} \)
\( c \cdot 10^{4} \)
D. None of the above


Which of the following is true regarding atoms according to Rutherford's gold foil experiment?
A. Are mostly space
B. Are in continuous motion
c. Have negative orbitals
D. Have diffuse charge distribution
E. Have dense crystalline structure


\( \mathbf{I f A}=\left\{\begin{array}{ccc}\mathbf{2} & \boldsymbol{x}-\mathbf{3} & \boldsymbol{x}-\mathbf{2} \\ \mathbf{3} & \mathbf{- 2} & \mathbf{- 1} \\ \mathbf{4} & \mathbf{- 1} & \mathbf{- 5}\end{array}\right\} \) is a
symmetric matrix then
\( A \cdot 0 \)
B. 3
\( c .6 \)
\( D \)


A longer conducting cylinder carrying a
charge \( +q \) is surrounded by a
conducting cylindrical shell having
charge \( -2 q . \) The charge on the inner
and outer side of conducting shell is:
\( \mathbf{A} \cdot q,-q \)
B. \( -q,-3 q \)
\( \mathbf{c} .-q,+3 q \)
\( \mathbf{D} \cdot-q,-q \)


How aquatic animals survive is cold
countries when temperature fall below
\( \mathbf{0}^{\circ} \mathbf{C} ? \)


The Marina trench is located in the
Pacific Ocean, and at one place it is nearly eleven km beneath the surface of
water. The water pressure at the bottom
of the trench is about \( 1.1 \times 10^{8} \) Pa.
steel ball of initial volume \( 0.32 m^{3} \) is
dropped into the ocean and falls to the bottom of the trench. What is the
change in the volume of the ball when it reaches to the bottom?


A stone is projected vertically up to
reach maximum height ' \( h^{\prime} . \) The ratio of
its kinetic energy to potential energy, at a height \( \frac{4 h}{5} \) will be:
A . 5: 4
в. 4: 5
\( c \cdot 1: 4 \)
D. 4: 1


2 grams of monoatomic gas occupies a volume of 2 litres at a pressure of \( 8.3 \times \) \( 10^{5} P a \) and \( 127^{0} \mathrm{C} \). Find the molecular
weight of the gas. (R=8.3 joule/mole/K)
A. 2 gram/mole
B. 16 gram/mole
c. 4 gram/mole
D. 32 gram/mole


The decreasing order of bond dissociation energies of \( \boldsymbol{C}-\boldsymbol{C}, \boldsymbol{C}-\boldsymbol{H} \)
and \( H-H \) bonds is:
A. \( H-H>C-H>C-C \)
в. \( C-C>C-H>H-H \)
c. \( C-H->C-C>H-H \)
D. \( C-C>H-H>C-H \)


Give the two-two examples of the living being performing asexual and sexual reproduction.


The \( p H \) of blood is maintained by \( C O_{2} \)
and \( H_{2} C O_{3} \) in the body and chemical constituents of blood. This phenomenon is called:
A. colloidal
B. buffer action
c. acidity
D. salt balance


Assertion
The magnetic poles of earth do not coincide with the geographic poles.
Reason
The discrepancy between the orientation of a compass and true north-south direction is known as
magnetic declination.
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 uniform disc of radius \( R \) is put over
another uniform disc of radius \( 2 R \) of
the same thickness and density. The peripheries of the two discs touch each other. Locate the centre of mass of
the system from the centre of large disc


The diagram below shows a cathode ray
tube in which the arrow indicates a
beam of charged particles approaching an electric field between the plates \( A \)
and B. State the amount of charge on each particle.
A \( \cdot 1.6 \times 10^{-19} \mathrm{C} \)
в. \( -1.6 \times 10^{-19} \mathrm{C} \)
\( c \)
D. \( -1.16 \times 10^{-19} C \)


Given that \( i z^{2}=1+\frac{2}{z}+\frac{3}{z^{2}}+\frac{4}{z^{3}}+\frac{5}{z^{4}}+ \)
\( \ldots . \) and \( z=n \pm \sqrt{-i}, \) find \( \lfloor 100 n\rfloor \)


E.A.N. of \( \left[\boldsymbol{F e}\left(\boldsymbol{\eta}^{\boldsymbol{5}}-\boldsymbol{C}_{\boldsymbol{5}} \boldsymbol{H}_{\boldsymbol{5}}\right)(\boldsymbol{C O})_{2} \boldsymbol{C l}\right] \)
A . 36
B. 35
c. 37
D. 34


A projectile is fired with a speed \( u \) at an angle \( \theta \) with horizontal. Its speed when
its direction of motion makes an angle
\( \alpha^{\prime} \) with the horizontal is
A . u \( \sec \theta \cos \alpha \)
B. u \( \sec \theta \sin \alpha \)
\( c \cdot u \cos \theta \sec \alpha \)
D. u \( \sin \theta \sec \alpha \)


What will be the path of a charged
particle moving along the direction of a uniform magnetic field?


Number of lines is space which are equally inclined to three co-ordinate
axes are?
A .2
B. 4
\( c .6 \)
D. 8


The capacitance \( C_{A B} \) in the given network
is:
\( \mathbf{A} \cdot 7 \mu F \)
B. \( \frac{50}{7} \mu F \)
\( \mathbf{c} .7 .5 \mu F \)
D. \( \frac{7}{50} \mu F \)


Nylon threads are made of
A. polyethylene polyemer
B. polyvinyl polymer
C . polyester polymer
D. polyamide polymer


Summarise the rules for writing of
distribution of electrons in various
shells for the first eighteen elements.


A liquid does not wet the surface of a solid if the angle of contact is
A. zero
B. An acute one
\( c \cdot 45^{\circ} \)
D. An obtuse one


A liquid \( P \) if specific heat capacity
\( 2400 J k g^{-1} K^{-1} \) and \( a t 70^{\circ} C \) is mixed
with another liquid \( \mathrm{R} \) of specific heat capacity \( 1000 J k g^{-1} K^{-1} \) at \( 30^{\circ} C . \) After mixing, the final temperature of the
mixture is \( 40^{\circ} \mathrm{C} \). Find the ratio of the
mass of the liquids mixed?
A .4: 5
B. 8: 5
\( c \cdot 40: 5 \)
D. 48 : 5


Two charges \( 2 \mu C \) and \( -2 \mu C \) are placed
at points \( A \) and \( B 6 \mathrm{cm} \) apart.
(a) Identify an equipotential surface of the system.
(b) What is the direction of the electric field at every point on this surface?


In which of the following class of Reptilia, the skull posses a solid roof?
A. Anapsida
B. Diapsida
c. Parapsida
D. synapsida
E. Both c and


How is chlorine manufactured by
Deacon's method?


What is activated sludge?


If the d.c's of a line are \( \left(\frac{1}{c}, \frac{1}{c}, \frac{1}{c}\right), \) find \( c . \)


A soap bubble of radius R has been
formed at normal temperature and pressure under isothermal conditions.
Compute the work done. The surface
tension of soap solution is \( \mathrm{T} \).


Four consecutive terms of a progression are \( 38,30,24,20 . \) The next term of the
progression is
\( A \cdot 18 \)
B \( \cdot 17 \frac{1}{7} \)
\( c \cdot 16 \)
D. none of these


An organic compound contains a
functional group, multiple bonds, and a side chain then what will be the order of
preference?
A. Double bond \( > \) Triple bond \( > \) Side chain \( > \) Functional group
B. Functional group > Double bond > Triple bond > Side chain
c. Triple bond > side chain > Double bond > Functional group
D. Functional group > Triple bond > Double bond > Side chain


Use of \( _{--}-_{-}-_{-}- \) helps in water purification.
A. Sodium
B. Alum
c. chlorine
D. Both B and C


If there are \( N \) nuclear particles in a
nucleus of radius \( R \) then the number of
nuclear particles in radius \( 3 R \) will be
A . \( N \)
в. \( 2 N \)
c. \( 27 N \)
D. \( \frac{21}{3} N \)


Which of the following is logically equivalent to \( \sim(\sim p \Rightarrow q) ? \)
A \( \cdot p \wedge q \)
В . \( p \wedge \sim q \)
\( \mathrm{c} \cdot \sim p \wedge q \)
D \( . \sim p \wedge \sim q \)


Which of the following compound is responsible for catching fire spontaneously in Holme's singal?
\( \mathbf{A} \cdot P_{2} H_{4} \)
в. \( P H_{3} \)
\( \mathbf{c} \cdot C_{2} H_{4} \)
D. All of these


Which lens has the greater in the focal
plane of which lens?


If the general solution of some
differential equation is \( \boldsymbol{y}=\boldsymbol{a}_{1}\left(\boldsymbol{a}_{2}+\right. \)
\( \left.\boldsymbol{a}_{3}\right) \cdot \cos \left(\boldsymbol{x}+\boldsymbol{a}_{4}\right)-\boldsymbol{a}_{5} \boldsymbol{e}^{x+\boldsymbol{a}_{6}} \quad \) then order
of differential equation is
\( \mathbf{A} \cdot \mathbf{6} \)
B. 5
\( c \cdot 4 \)
D. 3


Write any one solution of equation \( \boldsymbol{x}+ \)
\( 2 y=7 \)


State whether the given statement is true or false:
\( \Delta H_{f}^{\circ}(\mathrm{C}, \text { diamond }) \neq 0 \)
A. True
B. False


If you touch your ear with right hand in front of a plane mirror it will be seen in the mirror that your right ear is touched with hand.
A. right, left
B. left, left
c. right, right
D. left, right


At constant temperature when pressure of gas decreased by \( 50 \% \) than since percentage change in volume.


The function of leghemoglobin in the root nodules of legumes is
A. Oxygen removal
B. Inhibition of nitrogenase activity
c. Expression of nif gene
D. Nodule differentiation


Which has the same electronic
configuration as of inert gas?
A \( \cdot \mathrm{Ag}^{3} \)
B. \( \mathrm{Cu}^{2} \)
\( c \cdot P b^{4} \)
D. \( \mathrm{Ti}^{4} \)


Write the balanced Chemical equation with condition involved in manufacture
of nitric acid by ostwald's process.


Name the sound producing organ of human being?


What is the volume in cubic cm of a
pyramid whose area of the base is
25 sq cm height \( 9 c m ? \)
A \( \cdot 75 \mathrm{cm}^{3} \)
B. \( 70 \mathrm{cm}^{3} \)
\( \mathrm{c} \cdot 100 \mathrm{cm}^{3} \)
D. None of these


The carbohydrate used as storage
molecule in animal is:
A. sucrose
B. glycogen
c. maltose
D. glucose
E. fructose


A true breeding plant producing red flowers is crossed with a pure plant producing white flowers. Allele for red colour of flower is dominant. After
selfing the plants of first filial generation, the proportion of plants producing white flowers in the progeny would be
\( A \cdot \frac{3}{4} \)
B.
\( c \cdot \frac{1}{3} \)
\( D \)


For the galvanic cell pictured below, determine the electrochemical
potential for the system at \( 25^{\circ} \mathrm{C} \)
Note: \( \boldsymbol{C u}_{(a q)}^{2+}+\boldsymbol{2} \boldsymbol{e}^{-} \rightarrow \boldsymbol{C u}_{(s)} \boldsymbol{E}^{\circ}= \)
\( \mathbf{0 . 3 3 7} \mathbf{V} \)
\( Z n_{(a q)}^{2+}+2 e^{-} \rightarrow Z n_{(s)} E^{\circ}=-0.763 V \)
A. \( -0.426 V \)
В. \( -1.10 v \)
\( \mathbf{c} .+0.426 V \)
D. \( +1.10 v \)


Two types of nucleic acids are DNA and
A. RNA
B. chromosome
c. Ribosome
D. mRNA


What is the atomic number of the
element with \( M^{2+} \) ion having electronic
configuration \( [\boldsymbol{A} \boldsymbol{r}] \boldsymbol{3} \boldsymbol{d}^{8} ? \)
A . 25
B . 28
c. 27
D. 26


A man is going in a topless car with a velocity of \( 10.8 k m / h . \) It is raining vertically downwards. He has to hold the
umbrella at an angle of \( 53^{\circ} \) to the vertical to protect himself from rain. The
actual speed of the rain is \( \left(\cos 53^{\circ}=\right. \) \( \left.\frac{3}{5}\right) \)
A \( .2 .25 \mathrm{ms}^{-1} \)
B. \( 3.75 \mathrm{ms}^{-1} \)
c. \( 0.75 \mathrm{ms}^{-1} \)
D. \( 2.75 \mathrm{ms}^{-1} \)


Find the average weight using direct
method.
\( \mathbf{A} \cdot 81.15 k g \)
B. \( 82.50 k g \)
\( \mathbf{c} .86 .26 \mathrm{kg} \)
D. \( 80.21 k g \)


has the highest boiling
point.
A. \( 0.2 \mathrm{m} \mathrm{CaCl}_{2} \)
B. 0.2 \( \mathrm{m} \) NaCl
c. \( 0.1 \mathrm{m} \) Al \( C l_{3} \)
D. \( 0.2 \mathrm{m} \mathrm{CH}_{3} \mathrm{OH} \)
E. \( 0.2 \mathrm{m} \mathrm{NaC}_{2} \mathrm{H}_{3} \mathrm{O}_{2} \)


Assertion
Incoming light reflected by earth is
partially polarized.
Reason
Atmospheric particle polarize the light.
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


DNA is a polymer of nucleotides which
are linked to each other by \( 3-5 \) phosphodiester bond. To prevent polymerisation of nucleotides, which of the following modifications would you choose?
A. Replace purines with pyrimidines.
B. Remove/Replace 3 OH group in deoxyribose.
c. Remove/Replace 2 OH group with some other group in deoxyribose.
D. Both (b) and (c)


A series of concentric ellipses
\( \epsilon_{1}, \epsilon_{2}, \epsilon_{3}, \cdots \in_{n} \) are drawn such that \( \epsilon_{n} \)
touches the extremities of the major
axis of \( \epsilon_{n-1} \) and the focii of \( \epsilon_{n} \) coincides
with the extremities of the minor axis of
\( \epsilon_{n-1} \) if the \( e \) of the ellipse is independent on \( n, \) then the value of \( e ? \)


How many \( 2^{\circ} \) Hydrogen atoms are
present in the given following
compound?
A .2
B. 5
\( c \)
\( D \)


If \( f(x)=\frac{1}{1-x}, x \neq 0,1 \) then the graph
of the function \( \boldsymbol{y}=\boldsymbol{f}\{\boldsymbol{f}(\boldsymbol{f}(\boldsymbol{x}))\}, \boldsymbol{x}>1 \)
is
A . a circle
B. an ellipse
c. a straight line
D. a pair of straight lines


A flow of \( 10^{6} \) electrons per second in a
conducting wire constitutes a flow of
current
A . \( 1.6 \times 10^{-15} A \)
В. \( 1.6 \times 10^{-11} \) А
c. \( 1.6 \times 10^{-12} A \)
D. \( 1.6 \times 10^{-19} A \)
E . \( 1.6 \times 10^{-13} A \)


Two half life radioactive substance is
20 minutes. The approximate time
interval \( \left(t_{2}-t_{1}\right) \) between the time \( t_{2} \)
when \( \frac{2}{3} \) of it has decayed and time \( t_{1} \) and \( \frac{1}{3} \) of it had decayed is:
A . 14 min
B. 20 min
\( c .28 \) min
D. 7 min


Chlorination of toulene in the presence
of light and heat followed by the treatment with aqueous \( N a O H \) gives:
A. o-cresol
B. p-Cresol
c. 2,4 -Dihydroxy toulene
D. Benzoic acid


Consider a neutral conducting sphere. A positive point charge is placed outside the sphere. The net charge on the sphere is then,
A. negative and distribute uniformly over the surface of the sphere
B. negative and appears only at the sphere closest to the point charge
c. negative and distribute non-uniformly over the entire surface of the sphere
D. zero


Onions are modified
A. Stem
B. Leaves
\( c . \) Root
D. All of the above


The angular momentum of an electron depends on:
A. principal quantum number
B. azimuthal quantum number
c. magnetic quantum number
D. all of the above


Evaluate the definite integral \( \int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{\sin x+\cos x}{\sqrt{\sin 2 x}} d x \)


The correct decreasing order of boiling points of petroleum fractions is:
A. petrol > lubricating oil > diesel > LPG
B. lubricating oil > diesel > petrol> LPG
c. petrol > diesel > LPG > lubricating oil
D. lubricating oil > petrol> diesel > LPG


Consider the situation shown in figure. Show that if the blocks are displaced slightly in opposite directions and released, they will execute simple harmonic motion. Calculate the time
period.
uculate


In intrinsic semiconductors;
A. holes or electrons are supplied by a foreign atom acting as an impurity
B. holes in the valence band are vacancies created by electrons that have been thermally excited to the conduction band
C. has high amount of impurities
D. none of the above


When potassium dichromate is heated, one of the products are:
в. \( C r_{2} O_{5} \)
\( c \cdot O_{3} \)
D. \( O_{2} \)


In the \( \Delta A B C, A=(1,3,-2) \) and \( G(-1,4, \)
2) is the centroid of the triangle. If D is the mid point of \( \mathrm{BC} \) then \( \mathrm{AD}= \)
A \( \cdot \frac{\sqrt{21}}{2} \)
B. \( \frac{3 \sqrt{21}}{2} \)
\( c \cdot \sqrt{21} \)
D. \( \frac{63}{2} \)


If the probability of selecting a bolt from
400 bolts is \( 0.1, \) then the mean for the
distribution is
A . 0.09
B . 40
\( c .36 \)
D. 360


The production of saleable steel in some of the steel plants of our country during 1999 is given below:

Plant \( \quad \) Bhilai \( \quad \) Durgapur \( \quad \) Rourkel
Production
In thousand tonnes
Construct a bar graph to represent the above data on a graph paper by using the scale 1 big divisions \( =20 \) thousand
tonnes.


The displacement of \( S \) of a particle at time \( t(O<t<\pi) \) is given by \( S= \)
\( \sin 2 t-6 \cos t . \) Then the acceleration for
the value of \( t \) for which its velocity is
zero is
A .0 unit/ \( \sec ^{2} \)
B. 3 unit/ sec \( ^{2} \)
c. 2 unit \( \mid \sec ^{2} \)
D. 4 unit/ \( \sec ^{2} \)


Which is the correct sequence of planets in increasing order of size?
A. Saturn, Jupitar, Uranus, Neptune
B. Jupitar, Saturn, Uranus, Neptune
c. Jupitar, Uranus, Neptune, Saturn
D. Neptune, Uranus, Saturn, Jupitar


Find the time dependence of the velocity of the particle.
A \( \cdot v=\frac{\alpha t}{4} \)
B. \( v=\frac{\alpha^{2} t}{2} \)
\( ^{\mathrm{C}} \cdot_{v}=\frac{\alpha^{2} t}{4} \)
D. \( v=\frac{\alpha t}{2} \)


In the region of only gravitational fields of mass ' \( M^{\prime} \) a particle is shifted from \( \boldsymbol{A} \)
to \( B \) via three different paths of length
\( 5 m, 10 m \) and \( 25 m . \) The work done in
different paths is \( W_{1}, W_{2}, W_{3} \) respectively then:
A. \( W_{1}=W_{2}=W_{3} \)
В. \( W_{1}>W_{2}>W_{3} \)
C \( . W_{1}=W_{2}>W_{3} \)
D. \( W_{1}<W_{2}<W_{3} \)


Capacity of a parallel capacitor with dielectric constant 5 is \( 40 \mu F . \) Calculate
the capacity of the same capacitor when dielectric material is removed.


Which of the following statements
is/are correct?
This question has multiple correct options
\( \mathbf{A} \cdot\left[C o(p n)_{2} C l_{2}\right]^{+} \) forms cis-trans isomers
B . \( \left[\operatorname{Co}\left(N H_{3}\right)_{4}\left(H_{2} O\right) C l\right] B r_{2} \) exhibits both ionization as well as hydrate isomerism.
\( \mathbf{c} \cdot\left[C r\left(g l y_{3}\right] \) exhibits both geometrical and optical \right. isomerism.
D. \( \left[\operatorname{Co}\left(N H_{3}\right)_{4} C l_{2}\right] N O_{2} \) exhibits both ionization as well as linkage isomerism.


Figure shows the electric field lines
around three point charges \( A, B \) and \( C \)
Which charge has the largest
magnitude then?
\( \mathbf{A} \cdot A \)
B. \( B \)
\( c \cdot C \)
D. \( B \) and \( C \) have equal magnitude


Give some examples of Tyndall effect
observed in your surroundings? This question has multiple correct options
A. Sunbeam coming from ventilation
B. Milk in a glass appearing faint blue
C. Sunbeam coming from behind the clouds
D. Flour suspended in water


In Hall-Heroult process \( C O_{2} \) is released
at ?


Express the matrices as the sum of
systemmetric \( \& \) a skew- symmetric
\[
\text { matrices }\left[\begin{array}{ccc}
\mathbf{6} & -\mathbf{2} & \mathbf{2} \\
-\mathbf{2} & \mathbf{3} & -\mathbf{1} \\
\mathbf{2} & -\mathbf{1} & \mathbf{3}
\end{array}\right]
\]


A block is thrown with a velocity of \( 2 m / s \) (relative to ground) on a belt,
which is moving with velocity \( 4 m / s \) in
opposite direction of the initial velocity
of block. If the block stops slipping on
the belt after \( 4 s \) of the throwing then
choose the correct statement(s)
This question has multiple correct options
A. Displacement with respect to ground is zero after 2.66 and displacement with respect to ground is \( 12 \mathrm{m} \) after \( 4 s \)
B. Displacement with respect to ground in \( 4 s \) is \( 4 m \).
C. Displacement with respect to belt in \( 4 s \) is \( -12 m \).
D. Displacement with respect to ground is zero in \( \frac{8}{3} s \)


Find the time period of meeting of minute hand and second hand of a
clock?
A. 60 min
в. \( \frac{59}{60} \) min
c. \( \frac{60}{59} \) min
D. 59 min


Evaluate the integral \( \int_{0}^{\pi / 2} \sin 2 x \log (\tan x) d x \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( -1 / 2 \)
c. \( 1 / 3 \)
D. \( 1 / 4 \)


Which of the following equation does
not represent a SHM?
\( \mathbf{A} \cdot \cos \omega t+\sin \omega t \)
\( \mathbf{B} \cdot \sin \omega t-\cos \omega t \)
c. \( 1-\sin 2 \omega t \)
\( \mathbf{D} \cdot \sin \omega t+\cos (\omega t+\alpha) \)


The total number of electrons in 4.2 g of \( N^{3-} \) ion is: \( \left(N_{A} \) is the Avogadro's \right.
number
A \( \cdot 2.1 N_{A} \)
в. \( 4.2 N_{A} \)
\( c \cdot 3 N_{A} \)
D. \( 3.2 N_{A} \)


Expand:
\( \frac{1}{\sec A-\tan A}-\frac{1}{\cos A} \)


Two separate monochromatic light beams \( A \) and \( B \) of the same intensity
are falling normally on a unit area of a metallic surface. Their wavelengths are
\( \boldsymbol{\lambda}_{A} \) and \( \boldsymbol{\lambda}_{B}, \) respectively. Assuming that
all the incident light is used in ejecting the photoelectrons, the ratio of the number of photoelectrons from beam \( \boldsymbol{A} \)
to that from \( B \) is:
A. \( \frac{\lambda_{A}}{\lambda_{B}} \)
в. \( \frac{\lambda_{B}}{\lambda_{A}} \)
\( ^{c}\left(\frac{\lambda_{B}}{\lambda_{A}}\right)^{2} \)
\( ^{\mathrm{D}}\left(\frac{\lambda_{A}}{\lambda_{B}}\right)^{2} \)


Find the ratio in which the straight line segment joining (-2,-3) and (5,6) is divided by (i) x-axis (ii) y-axis. Also, find the coordinates of the point of division in each case.


Evaluate: \( \lim _{x \rightarrow 0}\left[\tan \left(\frac{\pi}{4}+x\right)\right]^{\frac{1}{\sin 2 x}} \)


Match the Column I with Column II
Column
(A) A body which regains its original shape after the removal of external forces
(B) A body which does not regain its original shape after the removal Elastic of external forces.
(C) A body which does not show any deformation on applying external forces
(D) The property of the body to regain
(s) Rigid its original configuration when the deforming forces are removed
A. A-q, B-r, C-s, D-p
B. A-p, B-q, C-r, D-s
\( c \cdot A-r, B-s, c-p, D-q \)
D. A-s, B-p, C-q, D-r


Cells which lose their nucleus during differentiation are
A. Nerve cells
B. Muscle cells
c. Erythrocytes
D. Leucocytes


For a dilute solution containing \( 2.5 g m \) of a non-volatile non-electrolyte solute in \( 100 g m \) of water, the elevation in boiling point at 1 atm pressure is \( 2^{\circ} C \) Assuming concentration of solute is much lower than the concentration of
solvent, the vapour pressure (mm of \( \boldsymbol{H} \boldsymbol{g} \)
of the solution is \( \left(\boldsymbol{K}_{\boldsymbol{b}}=\right. \)
\( \left.0.76 K k g m o l^{-1}\right) \)
A .724
в. 740
\( c .736 \)
D. 718


Variegated coloration of leaves, first studied by K.Correns in 1909 is inherited only from the female parent. The genes coding for this trait are located in
A . ER
B. Nucleus
c. Plastids
D. Plasma membrane


The solution of \( \left(x^{3}-2 y^{3}\right) d x+ \)
\( 3 x y^{2} d y=0 \) is:
A \( \cdot x^{3}-y^{3}=c x^{2} \)
в. \( x^{3}=y^{3} \)
c. \( x^{3}-y^{3}=c x \)
D. \( x^{3}+y^{3}=c x^{2} \)


n figure, \( A B \| C D \) and a transversal
\( P Q \) cuts them at \( L \) and \( M \) respectively.
f \( \angle Q M D=100^{\circ} \), find all other angles


When a sample of compound is considered to be optically pure:
A. if only one enantiomer is present
B. no enantiomer is present
c. if the compound is having racemic mixture
D. none


Toricelli's barometer used mercury. Pascal duplicated it using French wine
of density \( 984 \mathrm{kg} \mathrm{m}^{-3} . \) Determine the height of the wine column for normal
atmospheric pressure.


If voltage \( V=(100 \pm 5) \vee \) and current \( I= \)
\( (10 \pm 0.2) A, \) the percentage error in resistance R is
A . \( 5.2 \% \)
B . 25\%
c. \( 7 \% \)
D. 10\%


Q Type your question
4
B.
\( c \)
D


Differentiate between.
Hemopoiesis and hemolysis.


Find the maximum possible percentage
error in the measurement of force on an
object(on mass \( \mathrm{m} \) ) travelling at velocity vin a circle of radius \( r, \) if \( m=(4.0 \) plus minus 0.1 ) \( \mathrm{kg}, \mathrm{v}=(10 \text { plus minus } 0.1) \mathrm{m} / \mathrm{s} \) and \( r=(8.0 \text { plus minus } 0.2) m \)
A. \( (50 \pm 1) \mathrm{N} \)
B. ( 50 ±2.5 ) N
c. \( (50 \pm 1.5) \mathrm{N} \)
D. \( (50 \pm 3.5) \) N


The perimeters of a circular field and a square field are equal. If the area of the square field is \( 12100 m^{2} \), then the area
of the circular field will be
A. \( 15500 m^{2} \)
В. \( 15400 m^{2} \)
c. \( 15200 m^{2} \)
D. \( 15300 m^{2} \)


The maximum value of the function
\( y=\frac{1}{4 x^{2}+2 x+1} \) is
A \( \cdot \frac{4}{3} \)
в. \( \frac{5}{2} \)
c. \( \frac{13}{4} \)
D. None of these


Which of the following is true regarding law of total probability?
A. It is a fundamental rule relating marginal probabilities to conditional probabilitities.
B. It expresses the total probability of an outcome which can be realized via several distinct events
c. Both are correct
D. None of these


What is the most suitable catalyst for reducing vinyl cyanide \( (\boldsymbol{C H}= \) \( \boldsymbol{C H C N} \) to propanenitrile?
A. \( H_{2} / N i \)
в. \( H_{2} / P t \)
C \( \cdot\left(P h_{3} P\right)_{3} R h C l \) (Wilkinson's catalyst)
D. LiAlH\( _{4} \)


Area bounded by the curves \( y=x e^{x} \)
and \( y=x e^{-x} \) and the line \( |x|=1 \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B. \( \frac{4}{e} \)
\( c \)
D. -


The bouncing of a beam of light from a polished surface in some other direction is called -
\( A \). refraction
B. reflection
c. dispersion
D. scattering


An anticoagulant is
A. Heparin
B. Hirudin
c. ЕDTA
D. All of the above


Which of the following is/are correct?
This question has multiple correct options
A. The vibration of drilling machine depends on a force from outside
B. The vibration of drilling machine does not depend on a force from outside
C. When a pendulum vibrates it is free vibration because it does not depend on any outside force to vibrate
D. When a pendulum vibrates it is free vibration because it depends on any outside force to vibrate


The ionization potential of hydrogen is \( 13.6 V . \) How much energy need to be supplied to ionize the hydrogen atom in the first excited state?
A . \( 13.6 e V \)
B. 27.2eV
c. \( 3.4 e V \)
D. \( 6.8 e V \)


\( C l_{2} \) gas is obtained by various reaction
select the reactions from the
following(s):
This question has multiple correct options
A. \( K M n O_{4}+ \) conc.HCl \( \triangleq \)
B . \( K C l+K_{2} C r_{2} O_{7}+ \) conc.H \( _{2} S O_{4} \stackrel{\Delta}{\longrightarrow} \)
c. \( M n O_{2}+ \) conc.HCl \( \Delta \)
D. \( K C l+F e_{2}\left(S O_{4}\right)_{3} \rightarrow \)


Given, \( P(A)=\frac{3}{5} \) and \( P(B)=\frac{1}{5} . \) Find
\( P(A \text { or } B), \) if \( A \) and \( B \) are mutually exclusive events.


The immpurity atoms with which pure silicon should be doped to make a \( \mathrm{p} \) type semiconductor are those
This question has multiple correct options
A. Boron
B. Aluminium
c. Phosphorus
D. Antimony


In Earthworm, ovary is situated in
segment
\( A \cdot 13 \)
B. 9
c. 10
D. 26


Which of the following compound is used in detection of metal ions such as
\( \boldsymbol{C u}^{+\mathbf{2}}, \boldsymbol{A} \boldsymbol{g}^{+} ? \)
A \( . P H_{3} \)
в. \( N H_{3} \)
c. \( N_{2} \)
D. \( F e C l_{3} \)


In the given figure 'O' is the centre of the
circle and \( A B, C D \) are equal to chords. If
\( <A O B=70^{\circ} k . \) Find the angles of
\( \triangle O C D \)


Highly resistant thick walled spores produced by bacterial cells during unfavourable conditions are called as
A. Endospores
B. Heterocyst
c. Gemmules
D. zoospores


Find \( \boldsymbol{a}^{3} \) if \( \left(\frac{2}{\mathbf{7}}\right)^{\boldsymbol{a}}=\left(\frac{\mathbf{1 6}}{\mathbf{2 1}}\right)^{-\mathbf{5}} \times\left(\frac{\mathbf{3}}{\mathbf{8}}\right)^{-5} \)


In conductors electrons can flow
because their
A . ions are free
B. electrons are free and mobile
c. protons are free
D. negative ions are free


A man bought a goat for Rs. \( 2000 . \) He sold at a loss of \( 20 \%, \) the sell price of the goat which was sold at a loss was
A. Rs. 1,648
B. Rs. 1, 600
c. Rs. 1,048
D. Rs. 2,048


If \( l=50 \mathrm{kg}-m^{2}, \) then how much torque
will be applied to stop it in 10 sec. Its initial angular speed is 20 rad sec.
A . \( 100 \mathrm{N}-\mathrm{m} \)
B . \( 150 \mathrm{N}-\mathrm{m} \)
c. \( 200 \mathrm{N}-\mathrm{m} \)
D. \( 250 \mathrm{N}-\mathrm{m} \)


How many grams of concentrated nitric acid solution should be used to prepare
\( 250 \mathrm{mL} \) of \( 2.0 \mathrm{M} H N O_{3} ? \)
The concentrated acid is \( 70 \% H N O_{3} \)
A \( \cdot 45.0 \mathrm{g} \) conc. \( \mathrm{H} \mathrm{NO}_{3} \)
B. 90.0 g conc. H NO
c. \( 70.0 \mathrm{g} \) conc. \( \mathrm{H} \mathrm{NO}_{3} \)
D. 54.0 g conc. \( H N O_{3} \)


The number of atoms present in 0.5 mole of nitrogen is same as the atoms in:
(a)12 g of \( \mathrm{C} \)
(b) 64 g of \( s \)
\( (c) 8 g \) of 0
(d) 48 g of mg


In the figure, it is given that \( B R=P C \)
and \( \angle A C B=\angle Q P R \) and \( A B \| P Q \)
Prove that \( \boldsymbol{A C}=\boldsymbol{Q} \boldsymbol{R} \)


Water is a resource
A. Degradable maintainable
B. Non-degradable maintainable
C. Renewable
D. Non-renewable


An object \( 20 \mathrm{cm} \) from a concave mirror form an image, double the size of the object, on a screen. How far should the screen be placed from the mirror?
A. -40 cm
B. 40 cm
c. \( 20 \mathrm{cm} \)
D. -20 cm
E. 30 \( \mathrm{cm} \)


A wheel of radius R rolls without
slipping on the ground with a uniform
velocity v. The relative acceleration of
the top most point ofthe wheel with
respect to the bottom most point is
\( \mathbf{A} \cdot \frac{v^{2}}{R} \)
B. \( \frac{2 v^{2}}{R} \)
c. \( \frac{v^{2}}{2 R} \)
D. \( \frac{4 v^{2}}{R} \)


(i) What type of isomers are
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{5} \boldsymbol{B r}\right] \boldsymbol{S} \boldsymbol{O}_{4} \) and
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{5} \boldsymbol{S O}_{4}\right] \boldsymbol{B r} ? \) Give a chemical
test to distinguish between them.
(ii) Write the structures of optical isomers of the complex ion
\( \left[\boldsymbol{C o}(\boldsymbol{e n})_{2} \boldsymbol{C l}_{2}\right]^{+} \)


DNA differs from RNA in the nature of
A. Sugar alone
B. Purines alone
c. sugar and pyrimidines
D. sugar and purines


Q Type your question_
charge of \( +5 q . \) Which diagram best
represents the charge distribution on
the sphere?
\( \mathbf{A} \)
Solid Conducting Sphere
Stand
B. Solid Conducting Sphere
Stand
\( c \)
Solid Conducting Sphere
Stand
D. Solid Conducting Sphere
Stand


Position of a body moving along a
straight line is given by \( s=p t+q t^{2} \)
where \( p \) and \( q \) are constant. State
whether the body is moving with
constant velocity or constant acceleration.


Hydrochloric acid reacts with metals to produce:
A. hydrogen
B. chlorine
c. carbon dioxide
D. oxygen


Write the value of
\( \tan ^{-1}\left[2 \sin \left(2 \cos ^{-1} \frac{\sqrt{3}}{2}\right)\right] \)


product in each of the following
reactions:
(i) \( C H_{3} C H_{2} C H_{2} C l+N a I \frac{\text { acetone }}{h e a t} \)
(ii) \( \left(C H_{3}\right)_{3} C B r+K O H \frac{e \text {thanol}}{\text {heat}} \)
(iii) \( C H_{3} C H(B r) C H_{2} C H_{3}+ \)
\( N a O H \stackrel{w a t e r}{\longrightarrow} \)
(iv) \( \left(C H_{3}\right)_{3} C B r+K O H \frac{\text {ethanol}}{\text {heat}} \)
(v) \( C_{6} H_{5} O N a+C_{2} H_{5} C l \longrightarrow \)
\( (\mathrm{vi}) C H_{3} C H_{2} C H_{2} O H+S O C l_{2} \longrightarrow \)
(vii) \( C H_{3} C H_{2} C H=C H_{2}+ \)
\( \boldsymbol{H} \boldsymbol{B} \boldsymbol{r} \stackrel{\text {peroxide}}{\longrightarrow} \)
\( \left(\text { viii) } \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C H}=\boldsymbol{C}\left(\boldsymbol{C H}_{3}\right)_{2}+\right. \)
\( \boldsymbol{H} \boldsymbol{B} \boldsymbol{r} \longrightarrow \)


If a magnet is suspended at an angle
\( 30^{\circ} \) to the magnetic meridian, the dip
needle makes angle of \( 45^{\circ} \) with the horizontal. The real dip is :
A \( \cdot \tan ^{-1}(\sqrt{3} / 2) \)
B. \( \tan ^{-1}(\sqrt{3}) \)
\( \mathbf{c} \cdot \tan ^{-1}(\sqrt{3} / \sqrt{2}) \)
D. \( \tan ^{-1}(2 / \sqrt{3}) \)


Reticulate venation is found in the
plants with
A. Tap root system
B. Fibrous root system
c. Branched root system
D. Both A and C


In a thermodynamic process pressure of a fixed mass of a gas is changed in such a manner that the gas releases
\( 20 J \) of heat and \( 8 J \) of work is done on
the gas. If initial internal energy of the gas was \( 30 J \), what will be the fixed
internal energy?
\( \mathbf{A} \cdot 9 J \)
B. \( 27 J \)
c. \( 18 J \)
D. \( 12 J \)


Charging by friction can be explained by
A . electrostatic conduction
B. electrostatic induction
c. ionisation
D. All of the above


The highest score of a certain data exceeds in lowest score by 16 and coefficient of range is \( \frac{1}{3} . \) The sum of the highest score and the lowest score is
A . 36
B. 48
c. 24
D. 18


In the case of different rolling bodies
match the ratio of rotational kinetic
energy to the total kinetic energy
\( \begin{array}{ll}\text { List-I } & \text { List-II } \\ \text { a) hollow sphere } & \text { e) } 2: 5 \\ \text { b) solid cylinder } & \text { f) } 1: 2\end{array} \) c) solid sphere
d) hollow cylinder
\( A \)
\( a-h ; b-g ; c-e ; d-f \)
в. \( a-h ; b-g ; c-f ; d-e \)
c. \( a-e ; b-g ; c-h ; d-f \)
D. \( a-e ; b-g ; c-f ; d-h \)


Give the structural formulae for the
following:
2-propanol


The lubricant mucin of saliva is made
up of
A. Unsaturated fats
B. Polysaccharides
c. Glycoproteins
D. Phospholipids


Express \( 2 \frac{1}{5} \) as a fraction of \( 7 \frac{2}{9} \)
A \( \cdot \frac{99}{325} \)
в. \( \frac{143}{9} \)
c. \( \frac{67}{200} \)
D. \( \frac{143}{18} \)


In a square room ABCD a small plane
mirror \( \mathrm{M} \) is rotating with \( \omega=\pi / 60 \)
rad/sec about a vertical axis through
the centre of the room. The source \( S \)
directs a thin parallel beam of ray at the
centre of the mirror. Time taken by reflected spot of light to cross the wall
DA is?
A . 10 sec
B. \( 12.5 \mathrm{sec} \)
c. \( 15 \sec \)
D. 20 sec


A tension of \( 20 N \) is applied to a copper
wire of cross sectional area \( 0.01 c m^{2} \)
Young's Modulus of copper is \( 1.1 \times \)
\( 10^{11} N / m^{2} \) and Poisson's ratio is 0.32
The decrease in cross sectional area of
the wire is:
\( \mathbf{A} \cdot 1.16 \times 10^{-6} \mathrm{cm}^{2} \)
В. \( 1.16 \times 10^{-5} \mathrm{m}^{2} \)
c. \( 1.16 \times 10^{-4} m^{2} \)
D. \( 1.16 \times 10^{-3} \mathrm{cm}^{2} \)


Using \( \varepsilon=-\frac{d \phi}{d t} \) and \( \varepsilon=i R \) find the
current in the loop after the external
field has stopped changing.
A \( \cdot \frac{d i}{d t}=-\left(\frac{2 R}{\mu_{0} \pi a}\right) \)
в. \( \frac{d i}{d t}=-\frac{R}{\mu_{0} a} \)
c. \( \frac{d i}{d t}=\frac{-2 R}{\mu_{0} a} i \)
D. \( \frac{d i}{d t}=\frac{-2 R}{3 \mu_{0} \pi a} \)


In reverse biasing
A. large amount of current flows
B. potential barrier across junction increases
C. depletion laver resistance increases
D. no current flows


5 pencils and 7 pens together cost Rs.
\( \mathbf{5 0}, \) whereas \( \mathbf{7} \) pencils and \( \mathbf{5} \) pens together cost Rs. \( 46 . \) The cost of one pencil is
A. Rs.
в. Rs.
c. Rs.
D. Rs.


Calculate force per unit length acting
on the wire B due to the current flowing
in the wire \( A \)


\( \lim _{x \rightarrow 0} \frac{(1-\cos 2 x)(3+\cos x)}{x \tan 4 x} \) is equal to:
A. \( -\frac{1}{4} \)
B.
c.
D.


Which of the following quantities are always negative?
A \( \cdot \vec{F} \cdot \vec{r} \)
в. \( \vec{v} \cdot \vec{r} \)
c. \( \vec{a} \cdot \vec{r} \)
D. Both \( A \) and \( C \)


Wasp stings can be treated with:
A. baking soda
B. vinegar
c. washing soda
D. milk of magnesia


Formula of oleum is:
\( \mathbf{A} \cdot H_{2} S O_{3} \)
\( \mathbf{B} \cdot H_{2} S O_{4} \)
\( \mathbf{c} \cdot H_{2} S O_{5} \)
D. \( H_{2} S_{2} O_{7} \)


Electric field in a region is given by \( \overrightarrow{\boldsymbol{E}}=-4 \boldsymbol{x} \hat{\boldsymbol{i}}+\boldsymbol{6} \boldsymbol{y} \hat{\boldsymbol{j}}, \) find the charge
enclosed in cube of side 1 m oriented as
shown in figure.
\( 4 \cdot 2 \varepsilon \)
B.
\( c \cdot \varepsilon \)
D. \( 6 \varepsilon \)


The equation of the straight line cutting off an intercept 8 on \( x \) -axis and making
an angle of \( 60^{\circ} \) with the positive
direction of \( y- \) axis is
A \( . x-\sqrt{3} y-8=0 \)
B. \( x+\sqrt{3} y=8 \)
c. \( y-\sqrt{3} x=8 \)
D. \( y+\sqrt{3} x=8 \)


toppr
Q Type your question
An opaque plate with a triangular
aperture, side \( 1 \mathrm{cm} \), is in contact with
the lens. (see Figs.).

Which one of the following diagrams
best shows to appearance of the patch
of light seen on the screen?
\( \mathbf{A} \)
B.
\( \mathbf{c} \)
D.


\( \boldsymbol{K}_{a 1}, \boldsymbol{K}_{a 2} \) and \( \boldsymbol{K}_{a 3} \) are the respective
ionisation constants for the following reactions;
\( \boldsymbol{H}_{2} \boldsymbol{S} \rightleftharpoons \boldsymbol{H}^{+} \boldsymbol{H} \boldsymbol{S}^{-} \)
\( \boldsymbol{H} \boldsymbol{S}^{-} \rightleftharpoons \boldsymbol{H}^{+} \boldsymbol{S}^{2-} \)
\( \boldsymbol{H}_{2} \boldsymbol{S} \rightleftharpoons \mathbf{2} \boldsymbol{H}^{+} \boldsymbol{S}^{2-} \)
The correct relationship between
\( \boldsymbol{K}_{a 1}, \boldsymbol{K}_{a 2} \) and \( \boldsymbol{K}_{a 3} \) is:
В. \( K_{a 3}=K_{a 1}+K_{a 2} \)
C \( . K_{a 3}=K_{a 1}-K_{a 2} \)
D. \( K_{a 3}=K_{a 1} / K_{a} \)


In the following, figure, seg DE II side BC
n \( \triangle A B C . \) If \( 3 A(\triangle A D E)= \)
\( A(D E C B), \) then find the ratio \( B C \)
\( D E ? \)
\( A \cdot 1: 2 \)
в. 16:
\( c \cdot 1: 16 \)
D.


Write the equation for the formation of ammonia by the action of water on magnesium nitride.
A \( \cdot 2 M g_{3} N_{2}+6 H_{2} O \rightarrow 2 N H_{3}+6 M g(O H)_{2} \)
В \( \cdot M g_{3} N_{2}+3 H_{2} O \rightarrow N H_{3}+3 M g(O H)_{2} \)
\( \mathrm{c} \cdot_{3 M g_{3} N_{2}+6 H_{2}} O \rightarrow 6 N H_{3}+3 M g(O H)_{2} \)
D. \( M g_{3} N_{2}+6 H_{2} O \rightarrow 2 N H_{3}+3 M g(O H)_{2} \)


Shaving cream produces foam. What kind of colloid is shaving cream?
A. Liquid dispersed in a gas
B. Gas dispersed in a liquid
c. solid dispersed in a liquid
D. solid dispersed in a gas


According to the ideal gas law, what is the approximately volume that will be occupied by 0.5 mole of an ideal gas at
\( 30^{\circ} \mathrm{C} \) and 3 atm pressure (gas constant
\( \boldsymbol{R}=\mathbf{0 . 0 8 2 1} \mathrm{L} \operatorname{atm} \mathrm{mol}^{-1} \mathrm{K}^{-1} \) )?
A. Less than 1 L
в. 5 L
\( c .10 L \)
D. 15 L
E. More than \( 20 L \)


Starting with 1- butyne, how could you make 3-hexanone?


No two equipotential surface intersect each other ?why?


The radius of sphere is measured to be
\( (2.1 \pm 0.5) \mathrm{cm} \)
Calculate its surface area with error
limits.
\( \mathbf{A} \cdot S=(55.4 \pm 26.4) \mathrm{cm}^{2} \)
B . \( S=(55.4 \pm 26.4) \mathrm{mm}^{2} \)
\( \mathbf{c} \cdot S=(55.4 \pm 13.2) \mathrm{cm}^{2} \)
D. None of these


The concentration of \( N H_{3} \) solution
whose one litre can dissolve 0.10 mole
AgCl is:
\( \left[\boldsymbol{K}_{s p} \text { of } \boldsymbol{A} \boldsymbol{g} \boldsymbol{C l} \text { and } \boldsymbol{K}_{\boldsymbol{f}} \text { of } \boldsymbol{A} \boldsymbol{g}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{2}^{+}\right. \)
\( \operatorname{are} 10^{-10} M^{2} \) and \( 1.6 \times 10^{7} M^{-2} \)
respectively].
\( \mathbf{A} \cdot 2.5 M \)
B. \( 3.0 M \)
c. \( 2.8 M \)
D. none of these


The S.I. unit of specific heat capacity is
A. \( J k g^{-1} K^{-1} \)
в. \( J m o l^{-1} K^{-1} \)
c. \( J k g^{-1} \)
D. \( J K^{-1} \)


Fill in the blanks:
When light falls on the junction of a photo diode, the number of charge carriers and hence the
conductivity of the junction
A. increases, decreases
B. decreases, increases
c. decreases, decreases
D. increases, increases


When a bar magnet is broken into two pieces:
A. we will have a single pole on each piece
B. each piece will have two unlike poles
c. each piece will have two like poles
D. none of these


Assertion
The variance of the series \( \boldsymbol{a}, \boldsymbol{a}+\boldsymbol{d}, \boldsymbol{a}+ \)
\( \mathbf{2} \boldsymbol{d}, \boldsymbol{a}+\mathbf{3} \boldsymbol{d}, \ldots \boldsymbol{a}+\boldsymbol{2 n d} \) is \( \frac{\boldsymbol{n}(\boldsymbol{n}+\mathbf{1})}{\mathbf{3}} \boldsymbol{d}^{2} \)
Reason
The sum and the sum of squares of first
\( n \) natural numbers \( \frac{n(n+1)}{2} \) and \( \frac{n(n+1)(2 n+1)}{6} \) respectively
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


Which of the following instruments is used to check whether electricity is flowing through a substance or not?
A. Ammeter
B. Voltmeter
c. Tester
D. None of these


The binary compounds of metallic or non-metallic elements with oxygen are called
A . oxoacid
B. oxide
\( c \cdot \) oxo
D. none of these


Find the derivative of \( f(\log x) \) with
respect to \( x \) where \( f(x)=\log x \)


Find the equivalent resistance across
\( A B \) for the given circuit:
A . \( 1 \Omega \)
B. \( 2 \Omega \)
\( c .3 \Omega \)
D. \( 4 \Omega \)


A potentiometer wire of length \( 1.0 \mathrm{m} \) has a resistance of \( 15 \Omega \). It is connected to a
\( 5 V \) battery in series with a resistance of
5 \Omega. Determine the emf of the primary cell which gives a balance point at 60
\( \mathrm{cm} \)


Which is not true about \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{2} \) ?
A . It is tribasic acid
B. one mol is neutralised by 0.5 mol \( C a(O H) \) )
c. \( N a H_{2} P O_{2} \) is normal salt
D. It disproportionates to \( H_{3} P O_{3} \) and \( P H_{3} \) on heating


A liter of air at \( 20^{\circ} \mathrm{C} \) is heated until both
the pressure and the volume are tripled, what is the tempertare then.
В . \( 927^{\circ} \) К
\( \mathbf{c} \cdot 200^{\circ} K \)
D. \( 977^{\circ} K \)


The D.E of the family of parabolas with vertex at (0,-1) and having axis along the y axis is
A. \( x y^{1}-2 y-2=0 \)
В. \( x y^{1}+y+1=0 \)
c. \( x y^{1}-y-1=0 \)
D. \( x y^{1}+2 x y+1=0 \)


Phototropism is because of unequal distribution of auxin under the
influence of unilateral (one sided)
¡Illumination as auxin
A. Moves from illuminated side to shaded side
B. Synthesis is checked on illuminated side
c. Destroyed on illuminated and not on shaded side
D. All of the above


Assertion (A): According to Newton's third law sum of action and reaction is
not equal to zero Reason (R) : The forces
action and reaction acts on different
bodies.
A. A and R are correct and R is the correct
explanation of
B. A and R are correct and R is not the correct
explanation A
c. \( A \) is true and \( R \) is false
D. A is false and R is true


Scale less fish is
A. Torpedo
B. Catfish
\( c . \) Both A and B
D. Raja


If \( A \) is a square matrix of order 3 with
\( |A|=4, \) then write the value of \( |-2 A| \)


A body of mass \( 10 k g \) at rest is acted upon simultaneously by two forces \( 4 N \)
and \( 3 N \) at right angles to each other.
The kinetic energy of the body at the end
of \( 10 s \) is
\begin{tabular}{l}
A. \( 50 \mathrm{J} \) \\
\hline
\end{tabular}
в. \( 100 J \)
c. \( 125 J \)
D. \( 144 J \)


What are amines?


If volume of cube is \( 64 \mathrm{cm}^{3} \), find its
surface area.


The value of \( \sqrt{10+\sqrt{25+\sqrt{108+\sqrt{154+\sqrt{225}}}}} \)
is:
A . 4
B. 6
\( c \cdot 8 \)
D. 10


The range of \( y=\sin 3 x+\sin x \) is-
A \( \cdot\left[\frac{-8}{3 \sqrt{3}}, \frac{8}{3 \sqrt{3}},\right] \)
в. \( \left[\frac{-4}{3 \sqrt{3}}, \frac{4}{\sqrt[3]{3}}\right] \)
c. \( \left[\frac{-3}{\sqrt{2}}, \frac{3}{\sqrt{2}},\right] \)
D. \( \left[\frac{-3}{3 \sqrt{2}}, \frac{3}{2 \sqrt{2}},\right] \)


What is the electronic configuration of elements of \( I I I \) rd group
A \( \cdot 1 s^{2}, 2 s^{2} 2 p s^{3} \)
В \( \cdot 1 s^{2}, 2 s^{2} 2 p^{6}, 3 s^{2} 3 p^{1} \)
C \( \cdot 1 s^{2}, 2 s^{2} 2 p^{6} \)
D. \( 1 s^{2}, 2 s^{2} 2 p^{6}, 3 s^{1} \)


If \( a, b, c \) are distincts \( \& w(\neq 1) \) is a cube of unity then minimum value of
\( \boldsymbol{x}=\left|\boldsymbol{a}+\boldsymbol{b} \boldsymbol{w}+\boldsymbol{c} \boldsymbol{w}^{2}\right|+\left|\boldsymbol{a}+\boldsymbol{b} \boldsymbol{w}^{2}+\boldsymbol{c} \boldsymbol{w}\right| \)
A \( \cdot 2 \sqrt{3} \)
B. 3
\( c \cdot 4 \sqrt{2} \)
D.


If \( x_{0} \) is the \( x \) -coordinate of the point of
inflection of curve \( y=f(x) \) then
(assume second derivative exists)
A \( \cdot f\left(x_{0}\right) \neq 0 \)
В \( \cdot f\left(x_{0}\right)=0 \)
C \( \cdot f^{\prime \prime}\left(x_{0}\right)=0 \)
D. \( f^{\prime \prime}\left(x_{0}\right) \neq 0 \)


Differentiate the following from first principle. \( f(x)=\cos \left(x-\frac{\pi}{8}\right) \)


1 g of helium gas is confined in a two
litre flask under a pressure of 2.05 atm.
What is its temperature?


Evaluate \( \int \frac{x^{5} d x}{\sqrt{\left(1+x^{3}\right)}}= \)
A. \( \frac{2}{3} \sqrt{\left(1+x^{3}\right)+\left(x^{2}+2\right)} \)
B. \( \frac{2}{9} \sqrt{\left(1+x^{3}\right)-\left(x^{3}-4\right)} \)
c. \( \frac{2}{9} \sqrt{\left(1+x^{3}\right)\left(x^{3}+4\right)} \)
D. \( \frac{2}{3} \sqrt{\frac{\left(1+x^{3}\right)^{3}}{3}-\left(1+x^{3}\right)} \)


Integrate the function \( e^{x}(\sin x+ \)
\( \cos x \)


Complete the missing components/variables given as \( x \) and \( y \) in the following reactions.
\( P b\left(N O_{3}\right)_{2}(a q)+2 K I(a q) \rightarrow \)
\( \boldsymbol{P b I}_{2}(\boldsymbol{x})+\boldsymbol{2} \boldsymbol{K} \boldsymbol{O}_{3}(\boldsymbol{y}) \)
A \( . x \rightarrow s ; y \rightarrow g \)
в. \( x \rightarrow s ; y \rightarrow a q \)
c. \( x \rightarrow a q ; y \rightarrow g \)
D. None of these


Predict the product (T) for the following
reaction sequence. \( \boldsymbol{C}_{6} \boldsymbol{H}_{5}-\boldsymbol{C H}=\boldsymbol{O} \stackrel{\boldsymbol{K C N} / \boldsymbol{O H}^{-}}{\longrightarrow} \)
\( \boldsymbol{R} \frac{\boldsymbol{C r} \boldsymbol{O}_{2} / \boldsymbol{H}^{\oplus}}{\longrightarrow} \boldsymbol{S} \frac{(i) \operatorname{conc} K \boldsymbol{O} \boldsymbol{H}}{(i i) \text { Acidification }} \boldsymbol{T} \)
A. cinnamic acid
B. Mandelic acid
c. Benzilic acid
D. Benzoic acid \& Benzyl alcohol


If \( l \| \boldsymbol{m} \) and \( \boldsymbol{m} \| \boldsymbol{n} \) then:
A . \( l \| \)
в. \( l \| \)
c. \( m \| \) n
D. \( l \| n \)


Area of the field is
\( \mathbf{A} \cdot a^{2} \sin \alpha \cos \alpha+c^{2} \sin \beta \cos \beta+e^{2} \sin \gamma \cos \gamma \)
B. \( (a \cos \alpha+c \cos \beta+d+e \cos \gamma)(a \sin \alpha+b+c \sin \beta+ \)
\( e \sin \gamma) \)
C \( \cdot a^{2}+b^{2}+c^{2}+d^{2}+e^{2} \)
D. none of these


Consider elastic collision of a particle of mass \( m \) moving with a velocity \( u \) with
another particle of the same mass at rest. After the collision the projectile and the stuck particle move in
directions making angles \( \theta_{1} \) and \( \theta_{2} \)
respectively with the initial direction
of motion. The sum of the angles \( \boldsymbol{\theta}_{1}+\boldsymbol{\theta}_{2} \)
is


What is the degree of the differential quation \( \left(\frac{d^{3} y}{d x^{3}}\right)^{3 / 2}=\left(\frac{d^{2} y}{d x^{2}}\right)^{2} ? \)
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c \cdot 3 \)
\( D \)


If coefficient of variation is 60 and
standard deviation is \( 24, \) then
Arithmetic mean is
A . 40
B. \( \frac{1}{40} \)
c. \( \frac{7}{20} \)
D. \( \frac{20}{7} \)


Construct a triangle \( A B C \), in which
\( A B=5.5 c m, A C=6.5 c m \) and
\( \angle B A C=70^{\circ} \)
Steps for its construction is given in a jumbled form.Identify its correct
sequence
1) At \( A, \) construct a line segment \( A E \)
sufficiently large, such that \( \angle B A C \) at
\( 70^{\circ}, \) use protractor to measure \( 70^{\circ} \)
2) Draw a line segment which is sufficiently long using ruler.
3) With \( A \) as centre and radius \( 6.5 \mathrm{cm} \)
draw the line cutting \( A E \) at \( C \), join \( B C \),
then \( A B C \) is the required triangle.
4) Locate points \( A \) and \( B \) on it such that
\( A B=5.5 c m \)
A. 2,4,1,3
B. 2,1,4,3
c. 1,2,4,3
D. 4,2,1,3


\( A t 817^{\circ} C, K_{p} \) is 10 atm for the reaction
between pure \( C O_{2} \) and excess hot graphite to form \( 2 \mathrm{CO}(\mathrm{g}) \) Then at what total pressure will the gas
mixture analyze \( 6 \%, C O_{2} \) by volume?
A \( \cdot P_{\text {Total }}=0.34 a t m \)
B. \( P_{\text {Total}}=0.68 a t m \)
C \( . P_{\text {Total}}=1.3 a t m \)
D. None of these


Thecost of 3 televisions and \( 2 V . C . R . s \) is
Rs. 35,000 . The shop-keeper wants profit
of \( R s .1,000 . \) per television and \( R s .500 \)
per \( V . C . R . \) He can sell 2 televisions and
\( 1 V . C . R \) and he gets the total revenue as
Rs. 21,500 . Find the cost and the selling
price of a television and a \( V . C . R \)


f two equal chords of a circle intersect
within the circle, prove that the line
joining the point of intersection to the centre makes equal angles with the
chords.


The polysaccharide among the following
is :
This question has multiple correct options
A. Glucose
B. Cellulose
c. starch
D. sucrose


(R)-2-Chlorobutane is represented by:
\( A \)
B. I
\( c \)
\( D \cdot|v| \)


Zeroth law of thermodynamics gives the
concept of
A. Pressure
B. Volume
c. Temperature
D. Heat


The hollow sphere, in which the circus motorcyclist performs his stunts, has diameter of 7 m. Find the area available
to motorcyclist for riding.
A \( .154 \mathrm{m}^{2} \)
B. \( 144 \mathrm{m}^{2} \)
c. \( 38.5 \mathrm{m}^{2} \)
D. \( 176 m^{2} \)


is known as heavy hydrogen.
A. Protium
B. Deuterium
c. Tritium
D. Proton


Evaluate: \( \int_{0}^{\pi / 2} \cos ^{2} x d x \)


buy 40 animals consisting of rams at 4
pounds, pigs at 2 pounds, and oxen at
17 pounds. if I spend 301 pounds, how many of each do I buy?


A piston cylinder device initially contains \( 0.2 m^{3} \) neon (assume ideal) at
\( 200 \mathrm{kPa} \) inside at \( T_{1}^{0} C . A \) value is now
opened and neon is allowed to escape until the volume reduces to half the
initial volume. At the same time heat
transfer with outside at \( T_{2}^{0} C \) ensures a constant temperature inside. Select the statement(s) for given process:
A. \( \Delta U \) must be zero
B. \( \Delta U \) may not be zero
c. \( q \) may be \( + \) ve
D. q may not be -ve


Hydrolysis of which of the following does
not occur?
A \( \cdot V C l_{4} \)
в. \( T i C l_{4} \)
\( \mathrm{c} \cdot \operatorname{siCl}_{4} \)
D. \( C C l_{4} \)


Find derivative of \( f(x) \)
\( f(x)=x \sin x \)


The correct pair is
A. RNA: thymine
B. DNA: uracil
C . RNA: replication
D. mRNA: picks up amino acids
E . RNA: ribose sugars


Mark the following statements as true
(T) or false (F):
(a) Pole Star is a member of the solar
system.
(b) Mercury is the smallest planet of the solar system.
(1)
(c) Uranus if the farthest planet in the solar system.
()
(d) INSAT is an artificial satellite.
(1)
(e) There are nine planets in the solar
system.
()
(f) Constellation Orion can be seen only with a telescope.


The inverse of "If two angles are
congruent, then they have the same measure" is
A. If two angles have the same measure, then they are congruent
B. If two angles are not congruent, then they do not have the same measure
C. If two angles do not have the same measure, then they are not congruent
D. None of these


ATP synthesis in cell requires
\( \mathbf{A} \cdot H^{+} \) gradient across the membrane
B. \( K^{+} \) gradient across the membrane
C \( \cdot P O_{4}^{3-} \) gradient across the membrane
D. \( C a^{2+} \) gradient across the membrane


By which optical phenomena the splitting of white light into seven
constituent colours occur?
A. Refraction
B. Dispersion
c. Reflection
D. Interference


If the perpendicular distance of a point \( P \) from the \( x \) -axis is 5 units and the foot
of the perpendicular lines on the negative direction of \( x \) -axis, then the
point P has?
A. \( x \) coordinate \( =5 \)
B. \( y \) coordinate \( =5 \) only
c. \( y \) coordinate \( =-5 \) only
D. \( y \) coordinate \( =5 \) or -5


Which one is an epiphyte?
A. Cuscuta
B. Orchid
c. Drosera
D. corypha


The incorrect statement about
deuterium is:
\( A \cdot \) it is an isotope of hydrogen
B \( \cdot \) it contains \( \left[\left(1 e^{-}\right)+\left(1 p^{+}\right)+(1(n)]\right. \)
C \cdot it contains \( \left[\left(1 p^{+}\right)+(1(n)]\right. \)
D. \( D_{2} O \) is called heavy water


Which gland is concerned with salt equilibrium in body?
A. Anterior Pituitary
B. Pancreas
c. Adrenal
D. Thyroid


When the earth completes one revolution around the sun, the
displacement of the earth is zero. True
or false.
A. True
B. False


A sphere of mass \( m_{1}=2 k g \) collides
with a sphere of mass \( m_{2}=3 k g \) which
is at rest. Mass \( m_{1} \) will move at right angles to the line,joining centres at the time of collision, if the coefficient of
restitution is :
\( A \cdot 4 / 9 \)
в. \( 1 / 2 \)
\( c \cdot \frac{2}{3} \)
D. \( \sqrt{2 / 3} \)


Assertion
The sensitivity of a moving coil galvanometer is increased by placing a
suitable magnetic material as a core
inside the coil.
Reason
Soft iron has a high magnetic
permeability and cannot be easily magnetized or demagnetized.
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 \( f \) be a function such that \( f(3)=1 \)
and \( f(3 x)=x+f(3 x-3) \) for all \( x \)
Then find the value of \( \boldsymbol{f}(\boldsymbol{3 0 0}) \)
A . 5500
B. 10100
\( c .5050 \)
D. 1,71,700


Multiply:
\( (a b+b c+c a) \) by \( (a b-b c-c a) \)


Consider a light source placed at a
distance of \( 1.5 m \) along the axis facing the convex side of a spherical mirror of
radius of curvature 1 m. The position \( \left(s^{\prime}\right. \)
nature and magnification \( (m) \) of the image are
A \( \cdot s^{\prime}=0.375 m, \) Virtual, upright, \( m=0.25 \)
B . \( s^{\prime}=0.375 m \), Real, inverted, \( m=0.25 \)
C . \( s^{\prime}=3.75 m, \) Virtual, upright, \( m=2.5 \)
D. \( s^{\prime}=3.75 m \), Real, upright, \( m=2.5 \)


List two reasons for the appearance of
variations among the progeny formed by sexual reproduction


Which lens are used to correct myopia or short sightedness?
A. Convex lens
B. Concave lens
c. Bipolar lens
D. Cylindrical lens


The total spin and paramagnetism
(B.M.) of ferrocyanide ion are respectively:
\( A \cdot 0,2 \sqrt{6} \)
B . \( 5 / 2, \sqrt{35} \)
\( c \cdot 4, \sqrt{24} \)
D. \( 1,2 \sqrt{2} \)


\( \mathbf{1}-\mathbf{1}+\mathbf{1}-\mathbf{1}+\mathbf{1}-\mathbf{1}+ \)
\( \dots \dots \dots(\mathbf{1} \mathbf{0} \mathbf{1} t i m e s)= \)


ff \( f(x)=\left\{\begin{array}{lll}\frac{e^{3 x}-1}{4 x} & \text { for } & x \neq 0 \\ \frac{k+x}{4} & \text { for } & x=0\end{array}\right. \)
continuous at \( x=0, \) then \( k= \)
\( A \cdot \)
B. 3
\( c \cdot 2 \)
\( D \)


Which of the following is(are) example(s) of Sandmeyer reaction? This question has multiple correct options
A \( \cdot C_{6} H_{5} N_{2}^{+} C l^{-} \rightarrow C_{6} H_{5} C l \)
в. \( C_{6} H_{5} N_{2}^{+} C l^{-} \rightarrow C_{6} H_{5} O H \)
c. \( C_{6} H_{5} N_{2}^{+} C l^{-} \rightarrow C_{6} H_{5} C N \)
D. \( C_{6} H_{5} N_{2}^{+} I^{-} \rightarrow C_{6} H_{5} I \)


Evaluate: \( \int\left(3 x^{2}-5\right)^{2} d x \)


\( \int \frac{\boldsymbol{d} \boldsymbol{x}}{\cos \boldsymbol{x}-\sin \boldsymbol{x}}= \)
A. \( \frac{1}{\sqrt{2}} \log \left|\tan \left(\frac{x}{2}-\frac{\pi}{8}\right)\right|+c \)
в. \( \frac{1}{\sqrt{2}} \log \left|\tan \left(\frac{x}{2}+\frac{3 \pi}{8}\right)\right|+c \)
c. \( \frac{1}{\sqrt{2}} \log \left|\tan \left(\frac{x}{2}-\frac{3 \pi}{8}\right)\right|+c \)
D. \( \frac{1}{\sqrt{2}} \log \left|\cot \left(\frac{x}{2}\right)\right|+c \)


In urinary system, aldosterone takes part in retention (reabsorption) of
A . \( K^{+} \)
в. \( N a^{\text {t }} \)
c. water
D. both (b) and (c)


A solution of \( 8 \% \) boric acid is to be
diluted by adding a \( 2 \% \) boric acid solution to it. The resulting mixture is to be more than \( 4 \% \) but less than \( 6 \% \)
boric acid. If we have 640 litres of the
\( 8 \% \) solution, how many litres of the \( 2 \% \) solution will have to be added?


The maximum kinetic energy of
photoelectrons
A. depends on collector plate
B. is independent of emitter plate material
C. is independent of frequency of incident radiation
D. depends on the frequency of light source and the nature of emitter plate material
E. depends on intensity of incident radiation


What is calorific value?
A. Amount of heat energy produced on complete combustion of 1 Kg of fuel.
B. Amount of heat energy produced on complete combustion of \( 100 \mathrm{Kg} \) of fuel.
C. Amount of heat energy produced on complete combustion of 1 g of fuel.
D. Amount of heat energy lost on complete combustion of \( 1 \mathrm{Kg} \) of fuel.


(a) Complete the following equations:
(i) \( C r_{2} O_{7}^{2-}+2 O H^{-} \rightarrow \)
\( M n O_{4}^{-}+4 H^{+}+3 e^{-} \rightarrow \)
(b) Account for the following:
(i) \( Z n \) is not considered as a transition
element.
(ii) Transition metals form a larger number of complexes.
(iii) The \( E^{0} \) value for the \( M n^{3+} / M n^{2+} \)
couple is much more positive than that for \( \boldsymbol{C r}^{3+} / \boldsymbol{C r}^{2+} \) couple.


If an electron describes half a revolution
in a circle of radius \( r \) in a magnetic field
B, the energy acquired by it is
A. zero
B. \( \frac{1}{2} m v^{2} \)
c. \( \frac{1}{4} m v^{2} \)
\( \mathbf{D} \cdot \mu_{r} \times B e v \)


What is refraction of light?


Golgi apparatus is specialized for all the following except:
A. Glycosylation of proteins
B. Secretion
c. Intracellular digestion
D. Formation of acrosome


Sulphuric acid is \( 95.8 \% \) by mass.
Calculate mole fraction of \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) of
density \( 1.91 \mathrm{cm}^{-3} .(H=1, S= \)
\( \mathbf{3 2}, \boldsymbol{O}=\mathbf{1 6}) \)
A . 0.8950
B. 0.2982
c. 0.2056
D. 0.8075


A neutron, with kinetic energy KE and moving with velocity \( v, \) collides head on
with a nucleus of mass number \( \boldsymbol{A} \)
perfectly elastically. The fraction of total
energy possessed by the neutron transferred to nucleus is
A \( \cdot \frac{4 A}{(A+1)^{2}} \)
\( ^{\mathrm{B}}\left(\frac{A-1}{A+1}\right)^{2} \)
\( \left(\frac{A+1}{2 A}\right)^{2} \)
\( \left(\frac{A-1}{2 A}\right)^{2} \)


If a car is travelling westwards with a constant speed of \( 20 m / s, \) what is the
resultant force acting on it?
\( A \)
B.
\( c \cdot 2 \)
D. 3


The additive identify of rational number
is
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot-1 \)
\( D \)


Sodium alkyl benzene sulphonate is
used as:
A. Soap
B. Fertilizer
c. Detergent
D. Pesticide


\( O_{3} \) in ozone layer is formed by action of
A. IR radiation
B. Blue radiation
c. uv radiation
D. Other radiations


Two cards are drawn simultaneously (or successively without replacement) from a well shuffled pack of 52 cards. Find the Probability that both are king.


If \( 8 \tan A=15, \) then the value of \( \frac{\sin A-\cos A}{\sin A+\cos A} \) is:
A \( \cdot \frac{7}{23} \)
в. \( \frac{11}{23} \)
c. \( \frac{13}{23} \)
D. \( \frac{17}{23} \)


Which of the following equations represents a particle performing simple harmonic motion
A \( \cdot x=3 \)
B. \( x=4 \sin 2 t \)
\( c \cdot x=1 / t \)
D. \( x=3 \log 2 t \)


Name the types of isomerism shown by the following pairs of compounds:
(i) \( \left[\boldsymbol{C u}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\right]\left[\boldsymbol{P t} \boldsymbol{C l}_{4}\right] \) and
\( \left[\boldsymbol{P t}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\right]\left[\boldsymbol{C u} \boldsymbol{C l}_{4}\right] \)
(ii) \( \left[\boldsymbol{C o}(\boldsymbol{P n})_{2} \boldsymbol{C l}_{2}\right]^{+} \) and \( \left[\boldsymbol{C o}(\boldsymbol{t n})_{2} \boldsymbol{C l}_{2}\right]^{+} \)


If \( \boldsymbol{\alpha} \leq 2 \sin ^{-1} \boldsymbol{x}+\cos ^{-1} \boldsymbol{x} \leq \boldsymbol{\beta}, \) then
A \( \cdot \alpha=\frac{\pi}{2}, \beta=\frac{\pi}{2} \)
B. \( \quad \alpha=\frac{\pi}{2}, \beta=\frac{3 \pi}{2} \)
c. \( \alpha=0, \beta=\pi \)


Assertion Derivative of \( (\boldsymbol{p} \boldsymbol{x}+\boldsymbol{q})\left(\frac{\boldsymbol{r}}{\boldsymbol{x}}+\boldsymbol{s}\right) \) is \( \boldsymbol{p s}+ \)
\( \frac{\boldsymbol{q} \boldsymbol{r}}{\boldsymbol{x}^{2}} \)
Reason
\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}(\boldsymbol{u} \boldsymbol{v})=\boldsymbol{u}^{\prime} \boldsymbol{v}+\boldsymbol{u} \boldsymbol{v}^{\prime} \)
where \( u \) and \( v \) are two distinct
functions.
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


Examine the following structures:
Which of the following statement is
correct:
\( (A) C H_{3}-C-O H \)
\( (B) C H_{3}-C-N H_{2} \)
(A) \( \mathrm{CH}_{3}-\frac{\mathrm{CH}_{3}}{\mathrm{C}}-\mathrm{OH} \)
(B) \( \mathbf{C H}_{3}-\underbrace{\mathbf{C H}_{\mathbf{3}}}_{\mathbf{C H}_{\mathbf{3}}}-\mathbf{N H}_{\mathbf{2}} \)
A. \( A \) is tertiary alcohol while \( B \) is tertiary amine
B. \( A \) is primary alcohol while \( B \) is primary amine
C. \( A \) is tertiary alcohol while \( B \) is primary amine
D. \( A \) is primary alcohol while \( B \) is tertiary amine


Assertion (A): Balloons made by nylon films are better for containing helium than the conventional rubber balloons. Reason (R): R.M.S. velocity of helium is very high. So helium atoms can effuse out through rubber balloons.
A. Both \( A \) and \( R \) are correct and \( R \) is the correct explanation of \( A \)
B. Both \( A \) and \( R \) are correct and \( R \) is not the correct explanation of \( A \)
c. \( A \) is true but \( R \) is false
D. \( A \) is false but \( R \) is true.


Which of the following will give \( \boldsymbol{S}_{N} \mathbf{2} \)
mechanism?
\( A \)
в.
\( c \)
D.


\( \int_{0}^{\frac{\pi}{2}} \frac{\sin x}{1+\cos ^{2} x} d x \)


Let \( s_{1}, s_{2}, s_{3} \) be the sums of \( n \) term of
each being 1 and the common
differences 1,2,3 respectively. If \( s_{1}+s_{3}= \)
\( \lambda s_{2}, \) then the value of \( \lambda \) is
A . 1
B . 2
\( c .3 \)
D. None of these


In a turbulent flow, the velocity of the liquid molecules in contact with the
walls of the tube is :
A. zero
B. Maximum
c. Equal to critical velocity
D. May have any value


The de Broglie wavelength of a tennis ball of mass 60 g moving with a velocity of \( 10 \mathrm{m} / \mathrm{sec} \) is approximately:
A. \( 10^{-33} \mathrm{m} \)
.
В . \( 10^{-31} \mathrm{m} \)
c. \( 10^{-16} \mathrm{m} \)
.
D. \( 10^{-25} \mathrm{m} \)


If \( \mathbf{f}(\boldsymbol{\theta})=\sin ^{99} \boldsymbol{\theta} \cos ^{94} \boldsymbol{\theta} ; \boldsymbol{\theta} \in\left(-\frac{\boldsymbol{\pi}}{2}, \frac{\boldsymbol{\pi}}{2}\right) \)
attains a maximum at \( \boldsymbol{\theta} \) equals
A \( \cdot \tan ^{-1} \sqrt{\frac{94}{99}} \)
B. \( \tan ^{-1} \sqrt{\frac{99}{94}} \)
c.
D.


In a metre-bridge experiment, when the resistances in the gaps are interchanged, the balance point did not shift at all. The ratio of resistances
must be
A. very large
B. very small
c. equal to unity
D. zero


Initially, it was believed that the atomic mass of beryllium was 13. But Mendeleev suggested that its atomic
mass should be 9
i) Was Mendeleev suggestion correct?
ii) How had he reached to this
conclusion?


During the formation of a chemical
bond:
A. electron-electron repulsion becomes more than the nucleus-electron attraction
B. energy of the system does not change
c. energy increases
D. energy decreases


Depletion of ozone layer causes:
A. blood cancer
B. Iung cancer
c. skin cancer
D. breast cancer


Carbide of calcium yields ethyne on
reaction with \( \boldsymbol{H}_{2} \boldsymbol{O} \)
If true enter 1 , else 0


Q Type your quest
Grignard's reagent?
B.
\( c \)
\( D \)


The degree of unsaturation in the
following compound is:
\( A \cdot 8 \)
B . 10
\( c \cdot 2 \)
\( D \)


A solution has \( p H \) 2. It contains:
A. \( C H_{3} \) СООН
в. \( H_{2} C O_{3} \)
c. \( H N O_{3} \)
\( \mathrm{D} \cdot \mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4} \)


Find the relation between \( x \) and \( y \) from
the following statement.
\( \boldsymbol{x}>-\mathbf{3} ;-\mathbf{6}>\boldsymbol{y} \)
A \( . x<y \)
в. \( x>y \)
c. \( x=y \)
D. none


Determine the number of significant figure in the following.
\( \mathbf{0 . 2 3 7 0} \mathbf{m} \)


What are the rules (sign conventions) to use \( S . I \) units?


If \( \boldsymbol{P}(\boldsymbol{A})+\boldsymbol{P}(\boldsymbol{B})=1 ; \) then which of the
following option explains the event \( \boldsymbol{A} \)
and \( B \) correctly?
A. Event \( A \) and \( B \) are mutually exclusive, exhaustive and complementary events
B. Event \( A \) and \( B \) are mutually exclusive and exhaustive events
C. Event \( A \) and \( B \) are mutually exclusive and complementary events
D. Event \( A \) and \( B \) are exhaustive and complementary events


Which of the following is a disaccharide?
A. Glucose
B. Fructose
c. sucrose
D. starch


A rectangle has
A. Two lines of symmetry
B. Four lines of symmetry
C. Three lines of symmetry
D. None of these


State True or False.
Molecular hydrogen consists of two forms, ortho- and para- hydrogen, which differ by the spins of the electrons and nuclei.
A. True
B. False


How are the following conversions carried out?
(i) Propene \( \longrightarrow \) Propan-2-ol
(ii) Benzyl chloride \( \longrightarrow \) Benzyl alcohol
(iii) Ethyl magnesium chloride \( \longrightarrow \) Propan-1-ol
(iv) Methyl magnesium bromide \( \longrightarrow 2 \) Methylpropan-2-ol


If \( \left(\frac{8}{15}\right)^{3}-\left(\frac{1}{3}\right)^{3}-\left(\frac{1}{5}\right)^{3}=\frac{x}{75}, \) Find
\( \boldsymbol{x} \)


Choose the correct answers from the
alternatives given.

When an earthworm secretes a slime
layer to receive eggs and sperm and form a cocoon, this secretion is
produced by the:
A . peritoneum
B. clitellum
c. nephridium
D. prostomium


Choose the option which describes best this statement:
"The modern periodic table is based upon".
A. Atomic mass of the elements
B. Number of neutrons in the nucleus
c. Number of isotopes of an element
D. Oxidation states
E. Number of protons in the nucleus


The molar conductivity of \( N a C l, H C l \)
and \( C H_{3} C O O N a \) at infinite dilution
are 126.45,426.16 and \( 91 S c m^{2} m o l^{-1} \)
respectively. The molar conductivity of
\( C H_{3} C O O H \) at infinite dilution is:
A \( .201 .28 S \mathrm{cm}^{2} \mathrm{mol}^{-1} \)
B. \( 698.28 S \mathrm{cm}^{2} \mathrm{mol}^{-1} \)
c. \( 390.71 S \mathrm{cm}^{2} \mathrm{mol}^{-1} \)
D. \( 540.48 S \mathrm{cm}^{2} \mathrm{mol}^{-1} \)


All dilute acids react with bleaching
powder, liberating:
A . chlorine gas
B. hydrogengas
c. nitrogen gas
D. \( H C l \) gas


The complex ion \( \left[\boldsymbol{C u}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\right]^{2+} \) is:
A. tetrahedral and paramagneticç
B. tetrahedral and diamagnetiç
c. square planar and paramagnetiç
D. square planar and diamagnetiç


Assertion
Auxins were the first growth hormones
discovered in plants.
Reason
In most of plant tip movements in
seedling stages led to the discovery of
auxins.
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 coins are tossed. Find the
conditional probability that two Heads will occur given that at least one occurs
A \( \cdot \frac{1}{3} \)
B. \( \frac{1}{2} \)
\( c \cdot \frac{1}{4} \)
D. none of these


If \( A, B \) and \( C \) are three sets such that
\( \boldsymbol{A} \cap \boldsymbol{B}=\boldsymbol{A} \cap \boldsymbol{C} \) and \( \boldsymbol{A} \cup \boldsymbol{B}=\boldsymbol{A} \cup \boldsymbol{C} \)
then
A \( . A=C \)
B. \( B=C \)
c. \( A \cap B=\phi \)
D. \( A=B \)


Which of the following compound is more acidic?
\( ^{\mathbf{A}} \cdot_{C H_{2}-C}^{\circ}-O H \)
No
в. \( _{C H_{2}}-C H_{2}-\stackrel{\circ}{C}-O H \)
\( N O_{2} \)
2
c.
\[
\begin{array}{l}C H_{2}-C H_{2}-C-O H \\ \text { I }\end{array}
\]
D.
\[
C H_{3}-\begin{array}{c}c_{1} \\ _{1} \\ C \\ C l\end{array}-C_{-} O H
\]


Match the List I with the List II.


An electron doesn't suffer any deflection
while passing through a region of uniform magnetic field What is the direction of magnetic field?


\( 9548+7314=8362+(?) \)
A .8230
В. 8410
\( c .8500 \)
D. 8600
E. None of these


Which compound exhibits hydrogen bonding when in the liquid state?
A \( \cdot N H_{3} \)
в. \( C s H \)
c. \( C H_{4} \)
D. \( G a H_{3} \)


Alveoli are tiny sacs in the lungs whose
average diameter is \( 5 \times 10^{-10} \) m. An
oxygen molecule is trapped in a sac. The uncertainty in the velocity of oxygen molecule within a sac is:
A. \( 2.0 m / \)sec
в. \( 3.0 \mathrm{m} / \mathrm{sec} \)
c. \( 1.0 m / s e c \)
D. \( 4.0 m / \)sec


Which satellite is launched by India for Direct to Home T.V. transmission?
A . IRS-P
B. INSAT-4A
c. INSAT- -
D. CARTOSAT


If molality of ethyl alcohol in aqueous
solution is 4.45 then the mole fraction of
ethyl alcohol in the solution is


Increasing order of equilibrium
constants for the formation of a hydrate.
A. \( |V<| I \mid<\|<1 \)
B. \( \mid V<\|I<I<\| \)
C. \( \mid<\|<\|<I V \)
D. \( \|<\| 1<1<I V \)


What will be the amount of DNA in
meiosis II products, if meiocyte contains 30 pg DNA in G phase?
A. 30 pg
B. 60 pg
c. \( 15 \mathrm{pg} \)
D. 120 pg


The scientist, who proved that bacteria
use \( H_{2} S \) gas and \( C O_{2} \) to synthesize
carbohydrate is
A. Van Niel
B. Ruben
c. Jean Senebier
D. Julius Robert Mayer


Two cells of internal resistances \( r_{1} \) and
\( r_{2} \) and of same emf are connected in
series, across a resistor of resistance \( \mathrm{R} \)
If the terminal potential difference
across the cells of internal resistance \( r_{1} \)
is zero, then the value of \( R \) is?
A \( \cdot R=2\left(r_{1}+r_{2}\right) \)
B. \( R=r_{2}-r_{1} \)
c. \( R=r_{1}-r_{2} \)
D. \( R=2\left(r_{1}-r_{2}\right) \)


In a group of 10 people, \( 70 \% \) take vitamins. If you randomly choose 2 of them, what is the probability
that neither person selected takes vitamins?
A \( . . .0677 \)
в \( \ldots .09 \)
\( c \ldots 30 \)
D \( \ldots 4 \)
\( E \ldots .49 \)


Zeroth law of thermodynamics
A. deals with mass and energy
B. deals with heat engines
C. states that if two systems are both in equilibrium with a third system, they are in thermal equilibrium with each other
D. does not exist


An infinite number of charges each equal to \( ^{\prime} q^{\prime} \) are placed along the \( X \) -axis at \( x=1 \)
\( x=2, x=4, x=8 \) The potential at the
point \( x=0 \) due to this set of charges is :
\( ^{A} \cdot \frac{Q}{4 \pi \epsilon_{0}} \)
в. \( \frac{2 Q}{4 \pi \epsilon_{0}} \)
с. \( \frac{3 Q}{4 \pi \epsilon_{0}} \)
D. \( \frac{Q}{\pi \epsilon_{0}} \)


Assertion
The electrostatic force on a charged
particle located on an equipotential surface is zero.
Reason
\( x \) component of electric field is given by,
\( \boldsymbol{E}_{\boldsymbol{x}}=-\frac{\boldsymbol{\delta} \boldsymbol{V}}{\boldsymbol{\delta} \boldsymbol{x}} \) and on equipotential
surface potential \( V \) is constant.
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 not correct but Reason is correct


Compare \( x \) and \( y \) bond lengths for the
above given molecule
A \( . x>y \)
В. \( y>x \)
c. \( x=y \)
D. None of these


The value of acceleration due to gravity at height \( h \) from earth surface will
become half its value on the surface if
\( (R=\text { radius of earth }) \)
\( \mathbf{A} \cdot h=R \)
в. \( h=2 R \)
c. \( h=(\sqrt{2}-1) R \)
D. \( h=(\sqrt{2}+1) R \)


The triangle PQR is inscribed in the circle \( x^{2}+y^{2}=25 . \) If \( Q \) and \( R \) have
coordinates \( (\mathbf{3}, \mathbf{4}) \) and \( (-\mathbf{4}, \mathbf{3}) \)
respectively, then \( \angle Q P R \) is equal to
A \( \cdot \frac{\pi}{2} \)
в.
c.
D.


The \( V-I \) characteristic of a silicon diode
is shown in the figure. Calculate the
resistance of the diode at
(a) \( I_{D}=15 m A \) and
(b) \( V_{D}=-10 V \)


Find the value \( (\sqrt{3}+1)^{4}+(\sqrt{3}-1)^{4}=? \)


The rate of transfer of charges through a circuit is called:
A. potential difference
B. resistance
c. energy
D. current


Superphosphate of lime is a good fertilizer because it is
A. calcium containing substance
B. soluble in water
C. containing gypsum
D. none of these


From a circular sheet of paper with
radius \( 20 \mathrm{cm}, 4 \) circles of radius \( 5 \mathrm{cm} \)
each are cut out. Find the ratio of the
uncut to the cut portions.
\( \mathbf{A} \cdot 1: 3 \)
B. 4: 1
\( \mathbf{c} \cdot 3: 1 \)
D. 4: 3


The sympathetic nervous system
causes
A. Constriction of the pupil
B. Decreased heart rate
C. Increased gastric secretion
D. Reduction of adrenaline secretion
E. Increased respiration


By which instrument we collect the
space information:
A. Convex lens
B. Microscope
c. Hubble Telescope
D. None of these


\( X e F_{6}+H_{2} O \rightleftharpoons X e O F_{4}+2 H F \)
constant \( =k_{1}, X e O_{4}+X e F_{6} \rightleftharpoons \)
\( X e O F_{4}+X e O_{3} F_{2} \) constant \( =K_{2} \)
Then equilibrium constant for the
following reaction will be:
\( \boldsymbol{X} \boldsymbol{e} \boldsymbol{O}_{4}+\boldsymbol{2} \boldsymbol{H} \boldsymbol{F} \rightleftharpoons \boldsymbol{X} \boldsymbol{e} \boldsymbol{O}_{3} \boldsymbol{F}_{2}+\boldsymbol{H}_{2} \boldsymbol{O} \)
A \( \cdot \frac{K_{2}}{K_{1}} \)
в. \( K_{1}+K_{2} \)
c. \( \frac{K_{1}}{K_{2}} \)
D. \( \frac{K_{1}}{\left(K_{2}\right)^{2}} \)