Find the values of \( A, B \) and \( C \) in the
following table for the reaction \( X+ \)
\( \boldsymbol{Y} \rightarrow Z . \) The reaction is of first order
w.r.t \( X \) and zero w.r.t. \( Y \)
Exp. \( [\boldsymbol{X}]\left(\boldsymbol{m o l} \boldsymbol{L}^{-1}\right) \quad[\boldsymbol{Y}]\left(\boldsymbol{m o l} \boldsymbol{L}^{-1}\right) \)
1
2
\begin{tabular}{ccc}
0.1 & 0.1 \\
\( A \) & 0.2 \\
0.4 & 0.4 \\
\( C \) & 0.2 \\
\hline
\end{tabular}
3
4
\( \mathbf{A} \cdot A=0.2 \mathrm{mol} L^{-1}, B=8 \times 10^{-2} \mathrm{mol} L^{-1} \mathrm{s}^{-1}, C= \)
\( 0.1 \mathrm{mol} L^{-1} \)
B . \( A=0.4 \) mol \( L^{-1}, B=4 \times 10^{-2} \) mol \( L^{-1} s^{-1}, C= \)
\( 0.2 \mathrm{mol} L^{-1} \)
C \( . A=0.2 \) mol \( L^{-1}, B=2 \times 10^{-2} \) mol \( L^{-1} s^{-1}, C= \)
\( 0.4 \mathrm{mol} L^{-1} \)
D. \( A=0.4 \) mol \( L^{-1}, B=2 \times 10^{-2} \) mol \( L^{-1} s^{-1}, C= \)
\( 0.4 \mathrm{mol} L^{-1} \)


Find remainder, if \( f(x)=x^{2}-5 x+6 \) is
divided by \( \boldsymbol{x}-\mathbf{5} \)


At two points separated by a distance of \( 3 \mathrm{cm}, \) the magnetic field strength due to a short magnet on its axial line are in the ratio 512:125. Then the distance of magnet from the first point is:
A. \( 8 \mathrm{cm} \)
B. \( 11 \mathrm{cm} \)
\( c \cdot 4 c m \)
D. 5cm


The oxide of chlorine having the maximum oxidizing power is :
A. \( C l_{2} O_{7} \)
в. \( C l_{2} O_{6} \)
c. \( C l_{2} O \)
D. \( C l O_{2} \)


If \( z_{1}=\frac{1}{a+i}, a \neq 0 \) and \( z_{2}= \)
\( \frac{1}{1+b i}, b \neq 0 \) are such that \( z_{1}=\bar{z}_{2} \)
then
В. \( a=1, b=-1 \)
c. \( a=2, b=1 \)
D. \( a=1, b=2 \)
2


The S.I. unit of pole strength is
A \( . A m^{2} \)
в. \( A m \)
c. \( A m^{-1} \)
D. \( A m^{-2} \)


I. An endothermic reaction process
cannot occur spontaneously.
II. The enthalpy change for an
endothermic process is negative.
A. Statement \( I \) is true, Statement \( I I \) is true
B. Statement I is true, Statement II is false
c. statement \( I \) is false, statement \( I I \) is true
D. Statement I is false, Statement II is false


Assertion
Nitrogen in unreactive at room temperature but becomes reactive at elevated temperatures (on heating or in the presence of catalysts).
Reason
In nitrogen molecule, there is extensive delocalisation of electrons.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The e.m.f. of the cell \begin{tabular}{l|c||c|c}
\( \boldsymbol{P t} \boldsymbol{H}_{2} \) & \( \boldsymbol{H O C N} \) & \( \boldsymbol{A} \boldsymbol{g}^{+} \) \\
\( \boldsymbol{1} \boldsymbol{a} \boldsymbol{t m} \) & \( \boldsymbol{1} . \boldsymbol{3} \times \mathbf{1 0}^{-\boldsymbol{3}} \boldsymbol{M} \) & \( \boldsymbol{0 . 8} \boldsymbol{M} \)
\end{tabular} \mid \( \boldsymbol{A} \boldsymbol{g}(s) \) is
\( 0.982 \mathrm{V} . \) The \( \mathrm{K}_{a} \) for HOCN is :
\( \boldsymbol{A} \boldsymbol{g}^{+}+\boldsymbol{e} \rightarrow \boldsymbol{A} \boldsymbol{g}(\boldsymbol{s}) ; \boldsymbol{E}^{o}=\mathbf{0 . 8 0} \boldsymbol{V} \)
A. \( 3.33 \times 10^{-4} \)
B . \( 2.22 \times 10^{-4} \)
c. \( 4.44 \times 10^{-4} \)
D. \( 1.6 \times 10^{-3} \)


A steady current is set up in a metallic wire of nonuniform cross-section How is
the rate of flow of electrons
(R) related
the area of cross-section


If two equal chords of a circle intersect
within the circle, prove that the chords and line joining the point of intersection to the centre makes angles which are
A. Complementary to each other
B. Suplimentary to each other
c. Equal to each other
D. Not equal to each other


Integrate \( : \int \frac{1+\tan x}{x+\log \sec x} d x \)


Which of the following statement is
true?
A. A nylon thread is stronger than a steel wire
B. Rayon is a natural fibre made from wood pulp
C. Cotton is not a polymer
D. Fabric made from polyester can get wrinkles easily


reproduction causes greater diversity.
A. Sexual
B. Asexual
c. Both A and B
D. None of the above


Protons are accelerated from rest by a potential difference \( 4 \mathrm{kV} \) and strike a
metal target. If a proton produces one photon on impact of minimum
wavelength \( \lambda_{1} \) and similarly an electron accelerated to \( 4 \mathrm{kV} \) strikes the target
and produces a minimum wavelength
\( \lambda_{2} \) then
A \( \cdot \lambda_{1}=\lambda_{2} \)
B. \( \lambda_{1}>\lambda_{2} \)
\( c \cdot \lambda_{1}<\lambda_{2} \)
D. no such relation can be established


Bile pigments are formed in
A . Liver
B. Spleen
c. Every body partt
D. Both A and B


An AP has the property that the sum of
first ten terms is half the sum of next
ten terms. If the second term is \( 13, \) then
the common difference is
A . 3
B. 2
c. 5
D. 4
E . 6


Identify the correct pair of characters with reference to Pteris.
(I) Neck canal cell is uninucleated.
(II) Stem grows vertically in the soil.
(III) Apogamously produced sporophytes are haploids.
(IV) Open dichotomous venation in
leaflets.
The correct answer is
\( A \cdot(11),(1 \vee) \)
в. (III), (IV)
c. (।), (॥)
D. (I), (III)


According to Henry's law, the partial
pressure of \( \operatorname{gas}\left(P_{g}^{\prime}\right) \) is directly proportional to mole fraction of gas in
dissolved state, i.e., \( P_{g a s}^{\prime}=K_{H} . X_{g a s} \)
where, \( \boldsymbol{K}_{\boldsymbol{H}} \) is : Henry's constant. Which
are correct?
This question has multiple correct options
A . \( K_{H} \) is characteristic constant for a given gas-solvent system
B. Higher is the value of \( K_{H} \), lower is solubility of gas for given partial pressure of gas
C. \( K_{H} \) has temperature dependance
D. \( K_{H} \) increases with temperature


Solve \( 2 x+3 y=11 \) and \( 2 x-4 y=-24 \)


The Young's modulus of a wire of length
\( L \) and radius \( r \) is \( Y \). If the length is
reduced to \( \frac{L}{2} \) and radius is \( \frac{r}{2}, \) then the Young's modulus will be
A \( \frac{Y}{2} \)
в. \( Y \)
\( c .2 Y \)
D. \( 4 Y \)


Given \( \boldsymbol{f}(\boldsymbol{x})=\cos ^{2} \boldsymbol{x}, \) find whether \( \boldsymbol{f}(\boldsymbol{x}) \)
is increasing or decreasing in the range \( \left[0, \frac{\pi}{2}\right] \)


Cells of quiescent centre are characterized by
A. Dense cytoplasm and prominent nuclei
B. Light cytoplasm and small nuclei
c. Dividing regularly to add to the corpus
D. Dividing regularly to add to tunica


If \( 3^{n-2}=\frac{1}{81}, n= \)
A .
B.
\( c \cdot 2 \)
D. -
E. -4


Degree of \( 1+\left(\frac{d^{2} y}{d x^{2}}\right)^{2}=K\left(\frac{d y}{d x}\right)^{2} \)
\( A \cdot 4 \)
B. 3
\( c \cdot 2 \)
D.


Show that the points
\( \boldsymbol{A}(\mathbf{1}, \mathbf{2}, \mathbf{7}), \boldsymbol{B}(\mathbf{2}, \mathbf{6}, \mathbf{3}) \) and \( \boldsymbol{C}(\mathbf{3}, \mathbf{1 0},-\mathbf{1}) \)
are collinear.


The velocity of a particle executing a
simple harmonic motion is \( 13 m s^{-1} \)
when its distance from the equilibrium position \( (Q) \) is \( 3 m \) and its velocity is
\( 12 m s^{-1}, \) when it is \( 5 m \) away from \( Q \)
The frequency of the simple harmonic motion is:
\( \mathbf{A} \cdot \frac{5 \pi}{8} \)
В. \( \frac{5}{8 \pi} \)
c. \( \frac{8 \pi}{5} \)
D. \( \frac{8}{5 \pi} \)


A swimmer while jumping into water
from a height easily forms a loop in air, if
A. He pulls his arms and leg in
B. He spreads legs and his arms
C . He keeps himself straight
D. His body is so formed


The least value of \( 5^{\sin x+1}+5^{-\sin x+1} \) is
\( \mathbf{A} \cdot \mathbf{5} \)
B. 10
c. 15
D. 11


Chloroform is kept in brown bottles because:
A. It evaporates easily
B. It reacts with \( C O_{2} \) of the air
c. It easily oxidize to poisonous substance.
D. It absorbs moisture


The angles of a triangle are \( (2 x+ \) \( \left.30^{\circ}\right),\left(3 x-110^{\circ}\right) \) and \( \left(\frac{5}{2} x+20^{\circ}\right), \) find
the value of \( x \)
A \( \cdot 16^{\circ} \)
В. \( 32^{\circ} \)
\( c \cdot 40^{\circ} \)
\( D \cdot 50^{\circ} \)


The carbon-based reduction method is
not used for the extraction of :
This question has multiple correct options
A. tin from \( S n O_{2} \)
B. iron from \( F e_{e} O_{3} \)
C. aluminium from \( A l_{2} O_{3} \)
D. magnesium from \( M g C O_{3}, C a C O_{3} \)


Who proposed the double helical
structure of the DNA?


\( \boldsymbol{C}_{6} \boldsymbol{H}_{6}+\boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3}+\boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \frac{50^{0}-\boldsymbol{6} \boldsymbol{0}^{0}}{\longrightarrow} \)
\( \boldsymbol{A} \stackrel{\boldsymbol{S n}+\boldsymbol{H} C l}{\longrightarrow} \boldsymbol{B} \frac{\boldsymbol{C H}_{3} \boldsymbol{C O C l}}{\boldsymbol{N}} \boldsymbol{C} \). Then \( \boldsymbol{C} \) is:
A . aniline
B. nitro benzene
c. acetanilide
D. benzedine aniline


if \( \sec \theta+\tan \theta=x, \) then what is the
value of \( \sec \theta ? \)


The figure above shows a parallelogram
\( A B C D \) with \( A C=3 \) and \( A D=5 \)
Calculate the area of parallelogram
\( A B C D \)
A . 12
B. 15
c. 18
D. 2


A solid cylinder of glass whose diameter is \( 1.5 \mathrm{m} \) and height \( 1 \mathrm{m} \) is melted an recasted into a sphere then the radius of the sphere is
\( A \cdot 1 m \)
B. 0.75 \( m \)
c. \( 1.25 \mathrm{m} \)
D. \( 1.5 \mathrm{m} \)


The composition of a sample of Wustite
is \( F e_{0.93} \) O. What is the percentage of
iron present as \( F e^{3+} \) in total iron?
A . \( 15.05 \% \)
B. 25\%
\( c .35 \% \)
D. \( 45 \% \)


Which of the following plant's seeds are used as 'Jeweller's weight'?
A. Cajanus cajan
B. Lens culinariss
c. Glycine \( \max \)
D. Abrus precatorius


You are given four sources of light each
one providing a light of a single colour
red, blue, green and yellow. Suppose the
angle of refraction for a beam of yellow light corresponding to a particular
angle of incidence at the interface of
two media is \( 90 . \) Which of the following
statements is correct, if the source of
yellow light is replaced with that of
other lights without changing the angle
of incidence?
A. The beam of red light would undergo total internal reflection.
B. The beam of red light would bend towards normal while it gets refracted through the second medium.
C. The beam of blue light would undergo total internal reflection.
D. The beam of green light would bend away from the normal as it gets refracted through the second medium.


A solution contains \( 75 \mathrm{mg} \) of \( \mathrm{NaCl} \) per mL. To what extent must it be diluted to
give a solution of concentration \( 15 \mathrm{mg} \)
of \( N a C l \) per mL of solution?


The angles of triangle are arranged in ascending order of magnitude. If the difference between two consecutive
angles is \( 15^{\circ}, \) find the three angles.


Purine derivative among the bases is:
A. thymine
B. uraci
c. guanine
D. cytosine


The capacitance of a capacitor is \( 10 F \)
The potential difference on it is \( 50 V \). If the distance between its plate is halved, What will be the potential difference
now?
\( \mathbf{A} \cdot 100 V \)
в. \( 50 V \)
\( c .25 V \)
D. \( 75 V \)


Ammonia forms a complex ion \( \left[\boldsymbol{C u}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\right]^{2+} \) with copper ions in
alkaline solutions but not in acidic
solutions. What is the reason for it?
A. Copper hydroxide is an amphoteric substance.
B. In acidic solutions, hydration protects copper ions.
C. In acidic solutions, protons coordinate with ammonia molecules forming \( N H_{4}^{+} \) ions and \( N H_{3} \) molecules are no longer available for co-ordination to metal ions.
D. In alkaline solutions, insoluble \( C u(O H)_{2} \) is precipitated out which is soluble in excess of any alkali


How many electrons flow when a current
of 5 amperes is passed through a conductor for 200 seconds?
A \( \cdot 6.25 \times 10^{21} \)
B. \( 6.025 \times 10^{21} \)
c. \( 6.25 \times 10^{22} \)
D. \( 6.025 \times 10^{22} \)


The cause of the potential barrier in a \( \mathrm{p} \)
n diode is
A. depletion of positive charges near the junction
B. concentration of positive charges near the junction
c. depletion of negative charges near the junction
D. concentration of positive and negative charges near the junction


This process in which nutrient enriched
water bodies support a dense plant population, which kills animal life by depriving it of oxygen and results in subsequent loss of biodiversity is known as
A. green-house effect
B. eutrophication
c. land pollution
D. none of above


Consider the following two statements:
\( P: \) If 7 is an odd number, then 7 is
divisible by 2.
Q: If 7 is a prime number, then 7 is an odd number
If \( V_{1} \) is the truth value of the
contrapositive of \( \mathrm{P} \) and \( V_{2} \) is the truth value of contrapositive of \( Q, \) then the ordered pair \( \left(V_{1}, V_{2}\right) \) equals:
A. \( (F, F) \)
в. \( (T, T) \)
c. \( (T, F) \)
D. \( (F, T) \)


According to Moore's Law:
A. The memory capacity of a chip is constant.
B. The memory capacity of a chip doubles every one and a half-years.
C. The memory capacity of a chip increases by ten times every one and a half-years.
D. The memory capacity of chip decreases with time.


Arrange the following compounds in increasing order of their acid strength:
Propan-1-ol, 2, 3, 6 - trinitrophenol, 3nitrophenol,
3. 5-dinitrophenol, phenol, 4-methyl phenol.


Use the following system of naming elements in which first alphabets of the digits are written collectively,
0
2
uni
bi rri quad pent
Write three-letter symbol for the elements with atomic number 106
A . un
B. unh
c. uunhe
D. unhex


Result of ozone hole is
A. Green house effect
B. Global warming
C. Acid rain
D. UV radiations reach the earth


In a diode, when there is a saturation
current, the plate resistance will be
A. data insufficient
B. zero
c. some finite quantity
D. infinite


f graphs are possible then, in which of
the following cases external impulse must be acting on the box?
\( \mathbf{A} \)
3.11
\( c \)
\( 0 . v \)


A body is thrown vertically upwards and rises to a height of \( 10 \mathrm{m} \). The velocity with which the body was thrown
upwards is \( \left(g=9.8 m / s^{2}\right) \)
\( A \cdot 10 \mathrm{m} / \mathrm{s} \)
B. 20 \( \mathrm{m} / \mathrm{s} \)
\( c \cdot 14 \mathrm{m} / \mathrm{s} \)
D. none of these


The nature of image of a candle flame located \( 40 \mathrm{cm} \) from a concave spherical mirror is real, inverted and magnified
four times. Then the radius of curvature
of the mirror is:
\( A .32 \mathrm{cm} \)
B. \( 64 \mathrm{cm} \)
c. \( 48 \mathrm{cm} \)
D. \( 80 \mathrm{cm} \)


On chlorination of propane, the number of products of the formula \( C_{3} H_{6} C l_{2} \) is only structural isomers \( ) \)
\( A \cdot 3 \)
B. 4
\( c .5 \)
D.


An aeronautical engineer observed that on the upper and lower surfaces of the wings of an aeroplane, the speed of the air are \( 90 m / s \& 72 m / s \) respectively. What is the left on the wing if its area is
\( 3.2 m^{2} \) density of air is \( 0.29 k g / m^{3} \)


Consider the following reaction
\( \boldsymbol{A}+\boldsymbol{B} \rightleftharpoons \boldsymbol{E} ; \boldsymbol{K}_{c}=\mathbf{6} \)
\( \mathbf{2} \boldsymbol{B}+\boldsymbol{C} \rightleftharpoons \mathbf{2} \boldsymbol{D} ; \boldsymbol{K}_{c}=\mathbf{4} \)
What will be the equilibrium constant
\( \left.K_{c}\right) \) for the following reaction? \( \boldsymbol{A}+\boldsymbol{D} \rightleftharpoons \boldsymbol{E}+\frac{\mathbf{1}}{\mathbf{2}} \boldsymbol{C} \)


The temperature coefficient of
resistance of a wire is 0.00125 per
degree celcius. At \( 300 K \) its resistance
is 1 ohm. The resistance of the wire will
be 2 ohm at following temperature :-
A . \( 1154 K \)
в. \( 400 K \)
\( c .600 K \)
D. \( 1400 K \)


Statement 1: Novolac is soft and has a
low melting point.

Statement 2: It is highly cross-linked
polymer.
A. Statement 1 is true; statement 2 is true; statement 2 is the correct explanation of statement
B. Statement 1 is true; statement 2 is true; statement 2 is not the correct explanation of statement 1
c. Statement 1 is true; statement 2 is false
D. Statement 1 is false; statement 2 is true


The diagrams given below represent the relationship between a mouse and a
physiological process that occurs in
green plants. Study the diagrams and answer the questions that follow:
Why did the mouse die in bell jar \( B \) ?


Which one of the following is responsible for the soil erosion in farms?
A. Rivers and wind work
B. Defective methods of farming
c. Flowing water
D. Moving glaciers


The specific resistance \( \rho \) of a circular wire of radius \( r, \) resistance \( R, \) and length
is given by \( \rho=\pi r^{2} R / l . \) Given: \( r= \)
\( \mathbf{0 . 2 4} \pm \mathbf{0 . 0 2 c m}, \boldsymbol{R}=\mathbf{3 0} \pm \mathbf{1 \Omega}, \) and \( \boldsymbol{l}= \)
\( 4.80 \pm 0.01 c m . \) The percentage error in
\( \rho \) is nearly:
A . \( 7 \% \)
в. \( 9 \% \)
c. \( 13 \% \)
D. 20\%


Two small balls \( A \) and \( B \) are made of
same material. \( \boldsymbol{A} \) is solid but \( \boldsymbol{B} \) is
hollow. These are connected by an ideal spring and this whole system is kept
over a smooth plank such that center of mass of two balls coincide with mid
point of the plank. Initially the spring is
compressed by certain amount and the plank is in horizontal position. Now we
release the system. Then:
A. Plank will rotate clock wise
B. Plank will rotate anti clock wise
c. Plank will not rotate
D. It will depend upon string constant


Evaluate the following limits. \( \lim _{x \rightarrow 2}(3-x) \)


Mark the correct alternative of the
following. An angle is double of its supplement. The measure of the angle is?
A \( .60^{\circ} \)
B. \( 120^{\circ} \)
\( c \cdot 40^{\circ} \)
D. \( 80^{\circ} \)


Which of them is a mineral of
lanthanum?
A. Monazite
B. Xenotime
c. Euxenite
D. All of the above


If \( f(x)=\frac{x^{3}+x^{2}-16 x+20}{(x-2)^{2}}, \) if \( x \neq 2 \)
\[
=k, \quad \text { if } x=2
\]
is continuous at \( x=0 \) then
\( \mathbf{A} \cdot k=2 \)
B. \( k=0 \)
c. \( k=20 \)
\( \mathbf{D} \cdot k=7 \)


What is the percentage of the total sales of laptop in the state of Haryana and Rajasthan for both the years?
Sales of laptop
A . \( 23.13 \% \)
B . \( 26.54 \% \)
c. \( 27.4 \% \)
D. \( 31.34 \% \)


Pyruvate kinase enzyme catalyses
A. First irreversible step of glycolysis
B. Second irreversible step of glycolysis
C. Third irreversible step of glycolysis
D. Fourth irreversible step of glycolysis


\( \int \frac{1}{(x-2)\left(x^{2}+1\right)} d x= \)
A. \( \frac{1}{5}\left[\log |x-2|-\frac{1}{2} \log \left(x^{2}+1\right)+2 \tan ^{-1} x\right]+c \)
B. \( \frac{1}{5}\left[\log |x-2|-\frac{1}{2} \log \left(x^{2}+1\right)-2 \tan ^{-1} x\right]+c \)
C \( \cdot \frac{1}{5}\left[\log |x-2|-\frac{1}{2} \log \left(x^{2}+1\right)-2 \tan ^{-1} x\right]+c \)
D. \( -\frac{1}{2}\left[\log |x+2|+\frac{1}{2} \log \left|x^{2}-1\right|-2 \tan ^{-1} x\right]+c \)


The percentage composition of sodium phosphate as determined by analysis is 42.1\% sodium, 18.9 \% phosphorus and 39 \( \% \) oxygen. Find the empirical formula of the compound \( [\mathrm{Na}=23, \mathrm{P}=31,0=16] \)
A. \( N a_{3} P O_{3} \)
в. \( N a P O_{4} \)
\( \mathbf{c} \cdot N a_{2} P O_{4} \)
D. \( N a_{3} P O_{4} \)


Solve the following pair of equations
graphically; \( 2 x-3 y=1, \& 4 x-3 y+ \)
\( \mathbf{1}=\mathbf{0} \)
A. \( x=1 y=-1 \)
В. \( x=-1 y=-1 \)
c. \( x=-1 y=1 \)
D. \( x=1 y=1 \)


Solve: \( \frac{x}{3}>\frac{x}{2}+1 \)


Which statement about enzymes is not
correct?
A. Enzymes are in colloidal state
B. Enzymes are catalysts
c. Enzymes can catalyse any reaction.
D. Urease is an enzymes


A compound microscope has a magnification of \( 30 . \) The focal length of the eye-piece is \( 5 \mathrm{cm} . \) If the final image is formed at the least distance of
distinct vision \( 25 c m, \) the magnification produced by the objective is
A . 5
B. 7.5
c. 10
D. 15


We do not clean ponds or lakes, but an
aquarium needs to be cleaned because
A. An aquarium is an artificial and incomplete ecosystem.
B. Pond/lake are natural, self-sustaining and complete ecosystems.
c. Both A and B
D. None of the above


An object is placed \( 0.40 \mathrm{m} \) from one of
the two lenses \( L_{1} \) and \( L_{2} \) of focal
lengths \( 0.20 \mathrm{m} \) and \( 0.10 \mathrm{m} \) respectively
as depicted in the figure. The
separation between the lenses is 0.30
\( \mathrm{m} \)
The final image formed by this two lens
system is at
A. \( 0.13 \mathrm{m} \) to the right of the second lens
B. \( 0.05 \mathrm{m} \) to the right of the second lens
c. \( 0.13 \mathrm{m} \) to the left of the second lens
D. Infinity


Spore dissemination in some liverworts
is aided by
A. Elaters
B. Indusium
c. calyptra
D. Peristome teeth


\( \ln \Delta A B C \)
\( a^{2}, b^{2}, c^{2} \) are in A.P.
Show cot \( A, \cot B, \cot C \) are in A.P


A group of N cells whose emf varies
directly with the internal resistance as
per the equation \( \boldsymbol{E}_{N}=\mathbf{1 . 5 r}_{N} \) are
connected as shown in the figure. The current I in the circuit is :-
A . 5.1 A
B. 0.51 A
\( c \cdot 1.5 \mathrm{A} \)
D. 0.15 A


Find the area of a quadrilateral \( \boldsymbol{P Q R S} \)
in which \( \angle Q P S=\angle S Q R= \)
\( 90^{\circ}, P Q=12 \mathrm{cm}, P S=9 \mathrm{cm}, Q R= \)
\( 8 c m \) and \( S R=17 \mathrm{cm} \)


The gas law \( \left[\frac{P V}{T}\right]= \) constant is true for
A. isothermal change only
B. adiabatic change only
c. both isothermal \& adiabatic
D. neither isothermal nor adiabatic


Which of the following expressions corresponds to simple harmonic motion along a straight line, where \( x \) is the displacement and a, b, c are positive constants?
A \( \cdot a+b x-c x^{2} \)
B. \( b x^{2} \)
c. \( a-b x+c x^{2} \)
D. \( -b x \)


The molar conductances of HCl, NaCl and
\( C H_{3} C O O N a \) are \( 426,12691 \Omega^{-1} c m^{2} m o l^{-1} \)
respectively. The molar conductances of
\( C H_{3} C O O H \) is :
A \( \cdot 561 \Omega^{-1} \mathrm{cm}^{2} \mathrm{mol}^{-1} \)
B. \( 391 \Omega^{-1} c m^{2} \) mol \( ^{-1} \)
c. \( 261 \Omega^{-1} c m^{2} m o l^{-1} \)
D. \( 612 \Omega^{-1} c m^{2} m o l^{-1} \)


A ball thrown vertically upwards with a velocity of \( 25 \mathrm{m} / \mathrm{s} \) reaches its highest point of at \( 35 \mathrm{m} \) in 1.5 sec. Find the total
distance travelled by the ball and its position after 2 sec respectively.
A. Total distance \( =50 \mathrm{m}, \) After \( 2 \mathrm{sec}=25.4 \mathrm{m} \)
B. Total distance \( =35 \mathrm{m} \), After \( 2 \mathrm{sec}=28 \mathrm{m} \)
c. Total distance \( =37.5 \mathrm{m}, \) After \( 2 \mathrm{sec}=50 \mathrm{m} \)
D. Total distance = 70 \( \mathrm{m} \), After 2 \( \mathrm{sec}=30.4 \mathrm{m} \)


In the figure below, the diagonal \( \boldsymbol{A C} \) of
quadrilateral \( A B C D \) bisects \( \angle B A D \)
and \( \angle B C D . \) Then \( B C=m D C \).Find \( m \)


If there is a fault in the function of the
'Bowman's capsule, what will happen?


Explain how an unpolarised light gets polarised when incident on the interface separating the two transparent media.


Calamine solution is applied on the skin when an ant bites. Explain why?


f \( \boldsymbol{x}=\mathbf{1} ; \boldsymbol{y}=\mathbf{2} \) find the values:
\( \boldsymbol{x}^{2}+\boldsymbol{y}^{2} \)


stage of cell division occurs after
\( G_{2} \) phase
A. Prophase
B. Metaphase
c. Anaphase
D. Diakinesis


An air bubble is inside water. The
refractive index of water is \( 4 / 3 . \) At what distance from the air bubble should a
point object be placed so as to form a
real image at the same distance from the bubble?
A \( .2 . R \)
в. \( 3 R \)
\( c .4 R \)
D. The air bubble cannot image


The following data gives the distribution of total monthly household
expenditure of 200 families of a village. Find the modal monthly expenditure of
the families. Also, find the mean
monthly expenditure:
Expenditure (in C) \( \quad \) Number of families 4 \( 1000-1500 \) 24 The line 1 1 \( 1500-2000 \) 40
33 \( 2000-2500 \) A 3 \( \begin{array}{lll}2500-3000 & 28 \\ 3000-3500 & 30 \\ 3500-4000 & 22 \\ 4000-4500 & 16 \\ 4500-5000 & 7\end{array} \)


Which of the following statements is
incorrect?
A. Transition elements exhibit higher enthalpies of atomization as they have stronger interatomic interaction
B. Second ionisation energy of \( _{23} V<_{24} C r>_{25} M n \) and
\( _{28} N i<_{29} C u>_{30} Z n \)
C \( . N i(I I) \) compounds are more stable than \( P t(I I) \) whereas \( P t(I V) \) compounds are more stable than nickel \( (I V) \)
D. The elements which give the greatest number of oxidation states do not occur in or near the middle of the series


Write chemical equations for metallurgical processes to represent roasting of Galena \( (\boldsymbol{P b S}) \)
A. \( 2 P b S+3 O_{2} \rightarrow P b_{2} O_{2}+2 S O_{2} \)
в. \( P b S+2 O_{2} \rightarrow P b O+S O_{3} \)
\( \mathrm{c} \cdot 2 P b S+3 O_{2} \rightarrow 2 P b O+2 S O_{2} \)
D. None of these


A circus tent is cylindrical to a height of \( 4 \mathrm{m} \) and conical above it If its diameter
is \( 105 \mathrm{m} \) and the slant height of the cone is \( 80 \mathrm{m} \) then the total surface area of the canvas required is
A. \( 15540 m^{2} \)
В. \( 30880 m^{2} \)
c. \( 46020 m^{2} \)
D. \( 14520 m^{2} \)


An ideal gas having initial pressures \( \boldsymbol{P} \)
volume \( V \) and temperature \( R \) is allowed
to expand adiabatically until its volume
becomes \( 5.66 V \) while its temperature falls to \( \boldsymbol{T} / \mathbf{2} \)
Obtain the work done by the gas during the expansion as a function of initial pressure \( \boldsymbol{P} \) and volume \( \boldsymbol{V} \)


The principle of independent
assortment means
A. Separation of characters of one parent
B. Non-Separation of characters of one parent
C. Separation of characters of both parents together
D. Combination of both parental characters


A soap film of thickness \( t \) is surrounded
by air and is illuminated at near normal
incidence by monochromatic light with wavelength \( \lambda \) in the film. With respect
to the wavelength of the monochromatic light in the film, what film thickness will produce maximum constructive interference?
A \( \cdot \frac{1}{4} \lambda \)
B. \( \frac{1}{2} \lambda \)
c. \( 1 \lambda \)
D. \( 2 \lambda \)


If the sum of first 8 and 19 terms of an
A.P. are 64 and 361 respectively, find the common difference.


\( \frac{1}{1-\cos \theta+2 i \sin \theta}=\frac{1-2 i \cot (\theta / 2)}{5+3 \cos \theta} \)
f this is true enter 1 , else enter 0


f \( 2 s=a+b+c, \) prove that \( \left|\begin{array}{ccc}a^{2} & (s-a)^{2} & (s-a)^{2} \\ (s-b)^{2} & b^{2} & (s-b)^{2} \\ (s-c)^{2} & (s-c)^{2} & c^{2}\end{array}\right| \)
\( =2 s^{3}(s-a)(s-b)(s-c) \)


Two elastic bodies \( P \) and \( Q \) having equal masses are moving along the same line with velocities of \( 16 \mathrm{m} / \mathrm{s} \) and \( 10 \mathrm{m} / \mathrm{s} \)
respectively. Their velocities after the elastic collision will be in \( \mathrm{m} / \mathrm{s} \)
A. 0 and 25
B. 5 and 20
c. 10 and 16
D. 20 and 5


Represent the following families of curves by forming the corresponding differential equation.(a, b being parameters). \( x^{2}-y^{2}=a^{2} \)


Cells are connected in series in order to:
A. increase the voltage rating
B. increase the electric current rating.
c. increase the life of cells.
D. none of above.


The hydrolysis constant Kh of a salt of NaOH anda weak acid (HX) if the Ka of
the acid is \( 2 \times 10^{-6} \) is:
A \( .5 \times 10^{-8} \)
B . \( 5 \times 10^{-6} \)
c. \( 5 \times 10^{-9} \)
D. \( 5 \times 10^{-7} \)


An unknown transistor needs to be
identified as a \( n p n \) or \( p n p \) type.
multimeter, with \( + \)ve and -ve
terminals, is used to measure resistance between different terminals
of transistor. If terminal 2 is the base of
the transistor then which of the
following is correct for a \( p n p \) transistor?
A. \( + \)ve terminal
\( 1,-v e \) terminal
2 , resistance high
\( 2,-v e \) terminal
B. \( + \)ve terminal
\( 3, \) resistance low
c. \( + \)ve terminal
\( 3,-v e \) terminal
2 , resistance high
D. \( + \)ve terminal \( 2, \) -ve terminal \( 1, \) resistance high


A block of mass 1 gm executes an
oscillatory motion (sliding) on a
concave surface of radius of curvature
2m. If the particle starts its motion from
a point at a height of I cm from the
horizontal and the coefficient of friction
is \( 0.01, \) then the total distance covered
by the particle before it comes to rest,
will be (approx)
A. \( 5.001 \mathrm{m} \)
B. 0,015 m
\( c \cdot 1.005 \mathrm{m} \)
D. none of these


At a certain point in a pipeline the
velocity is \( 1 m / s \) and gauge pressure is
\( \mathbf{3} \times \mathbf{1 0}^{\mathbf{5}} \quad \boldsymbol{N} / \boldsymbol{m}^{2} . \) Find the gauge
pressure at a second point in the line \( 20 m \) lower than the first, if the cross-
section at the second point is half that at the first. The liquid in the pipe is
water


Solve the following:
n \( \Delta M N P, \angle M N P= \)
\( 90^{\circ}, \operatorname{seg} N Q \perp \operatorname{seg} M P . \) If \( M Q= \)
\( \mathbf{9}, \boldsymbol{Q} \boldsymbol{P}=\mathbf{4}, \) then find \( \boldsymbol{N} \boldsymbol{Q} \)


Examine the table.
(Each figure is divided into triangles
and the sum of the angles deduced from that.)

What can you say about the angle sum of a convex polygon with number of sides?
(a) \( 7(b) 8 \)
\( (c) 10(d) n \)


Assertion
Slime moulds show alternation of
generation.
Reason
The sporangia bearing slime moulds
represent haplophase.
A. Both the assertion and the reason are true and the
reason is a correct explanation of the assertion
B. Both the assertion and reason are true but the reason
is not a correct explanation of the assertion
C. The assertion is true but the reason is false
D. Both the assertion and reason are false


The value of the expression \( ^{47} C_{4}+ \) \( \sum_{j=1}^{5} 52-j C_{3} \) is
\( \mathbf{A} .^{51} C_{4} \)
B. \( ^{52} C_{4} \)
c. \( ^{52} C_{3} \)
D. \( ^{53} C_{4} \)


f \( \boldsymbol{y}=\log \sin \boldsymbol{x}+\boldsymbol{e}^{\boldsymbol{x}} \tan \boldsymbol{x}, \) then find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \)


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


Assuming that the behavior of ammonia is correctly described by the van der Waal's equation near the critical point, and knowing the critical
molar volume of \( 0.72500 \mathrm{mol} L^{-1} \) and
critical temperature of \( 405.3 \mathrm{K} \) determine the critical pressure of
ammonia.
\( A \cdot 109.8 \) atm
B. 141.3 atm
c. 152.6 atm
D. 17.20 atm


The Newland's law of octaves for the
classification of elements was found to
be applicable only up to the element
A. potassium
B. calcium
c. cobalt
D. phosphorous


The specific charge for cathode rays is
A. Constant
B. Variable
c. Depend upon the material of the cathode
D. Depend upon the nature of the gas in the discharge tube


A ball is dropped from a bridge \( 122.5 \mathrm{m} \) above a river. After 2 s, a second ball is
thrown down after it. What must its
initial velocity be so that both hit the water at the same time?
A. \( 49 \mathrm{m} / \mathrm{s} \)
B. \( 55.5 \mathrm{m} / \mathrm{s} \)
c. \( 26.1 \mathrm{m} / \mathrm{s} \)
D. \( 9.8 \mathrm{m} / \mathrm{s} \)


The slope of voltage (V) versus current
(I) is called
A. resistance
B. conductance
C . resistivity
D. conductivity


Minimum value of the polynomial \( \boldsymbol{p}(\boldsymbol{x})=\mathbf{4} \boldsymbol{x}^{2}-\boldsymbol{6} \boldsymbol{x}+\mathbf{1} \)
A. \( -\frac{3}{4} \)
B. \( -\frac{5}{4} \)
\( c \cdot-\frac{5}{16} \)
D. - œ


\( A \) is :
\( A \)
B.
\( c \)
\( D \)


The value of
\( \lim _{|x| \rightarrow \infty} \cos \left(\tan ^{-1}\left(\sin \left(\tan ^{-1} x\right)\right)\right) \) is
equal to
A . -1
B. \( \sqrt{2} \)
c. \( -\frac{1}{\sqrt{2}} \)
D. \( \frac{1}{\sqrt{2}} \)


Heart lacks sinus venosus in
A. Fishes
B. Mammals
c. Amphibians
D. Echinoderms


Evaluate the magnitude and direction
of magnetic field at point \( \boldsymbol{O} \)
A \( \cdot \frac{3 \mu_{0} i}{8 a}, \) с
в. \( \frac{\mu_{0} i}{2 \sqrt{2} b}, \) с
с. \( \frac{3 \mu_{0} i}{8 a}+\frac{\mu_{0} i}{2 \sqrt{2} b}, \) с
D. \( \frac{3 \mu_{0} i}{8 a}+\frac{\mu_{0} i}{2 \sqrt{2} b}, \otimes \)


Are the following name correct according to IUPAC system of nomenclature? If not, give the correct
names.
Hexa-1,6-diene


If \( \left(a_{1}+i b_{1}\right)\left(a_{2}+i b_{2}\right) \dots\left(a_{n}+i b_{n}\right)= \)
\( A+i B \) then \( \left(a_{1}^{2}+b_{1}^{2}\right)\left(a_{2}^{2}+b_{2}^{2}\right) \dots\left(a_{n}^{2}+\right. \)
\( \left.b_{n}^{2}\right)= \)
A. \( A^{2}-B^{2} \)
B. \( A^{2}+B^{2} \)
c. \( A-B \)
D. \( A+B \)


A monovalent cation which has atomic
number \( 11, \) makes a compound with a
monovalent anion whose atomic
number is 17. The popular name of the compound is:
A. plaster of paris
B. chilli salt peter
c. common salt
D. TNT


Oxidation state of oxygen in \( C r O_{5} \) is
A . -
B. - -
\( c . \) Both (1) \& (2)
D. \( -\frac{1}{2} \)


\( \sum_{m=1}^{n} \tan ^{-1}\left(\frac{2 m}{m^{4}+m^{2}+2}\right) \) is equal
to
A \( \cdot \tan ^{-1}\left(n^{2}+n+1\right)-\frac{\pi}{4} \)
B \cdot \( \tan ^{-1}\left(n^{2}+n+1\right)+\frac{\pi}{4} \)
c. \( \tan ^{-1}\left(n^{2}+n-1\right)-\frac{\pi}{4} \)
D \( \cdot \tan ^{-1}\left(n^{2}-n-1\right)-\frac{\pi}{4} \)


Write the converse and contrapositive of
the statement
"If two traingles are congruent, then their areas are equal."


Why are protozoa called early animals?


Which of the following statement is
correct?
A. Vitreous fluid helps to maintain the shape of the retina
B. Crystalline eye lens helps in focusing the image
C. Aqueous humour helps to maintain the pressure in the
eye
D. All of the above


Generally non-metals are non-lustrous.
Exception to this property is-
A. Flourine
B. Chlorine
c. Bromine
D. lodine


If \( y=\cos ^{3} x, \) then \( \frac{d y}{d x}= \)


Given two independent events \( A \) and \( B \) such that \( \boldsymbol{P}(\boldsymbol{A})=\mathbf{0 . 3}, \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 6} \)
Find
(i) \( P(A \text { and not } B) \)
(ii) P(neither A nor
B)


The oxoacid of sulphur that does not contain bond between sulphur atoms is:
A \( \cdot H_{2} S_{4} O_{6} \)
в. \( H_{2} S_{2} O_{7} \)
c. \( H_{2} S_{2} O_{3} \)
D. \( H_{2} S_{2} O_{4} \)


An oxide of a metal (M) contains \( 40 \% \) by mass of oxygen. Metal (M) has atomic
mass of 24.The empirical formula of the oxide is :
A. \( M_{2} O \)
в. \( M O \)
c. \( M_{2} O_{3} \)
D. \( M_{3} O_{4} \)


The fact that lightning and spark are essentially the same phenomena, was discovered in:
A . 1882
B. 1752
c. 177
D. 1802


Find the derivative of \( \frac{\tan ^{-1} x}{1+\tan ^{-1} x} \) w.r.t.
\( \tan ^{-1} x \)
A \( \cdot \frac{1}{\sec ^{-1} x} \)
в. \( \frac{1}{\left(\tan ^{-1} x\right)^{2}} \)
c. \( \frac{1}{1+\tan ^{2} x} \)
D. \( \frac{1}{\left(1+\tan ^{-1} x\right)^{2}} \)


n right triangle \( A B C \), right-angled at
\( C, M \) is the mid-point of hypotenuse
\( A B . C \) is joined to \( M \) and produced to a
point \( D \) such that \( D M=C M . \) Point \( D \)
is joined to point \( B \).Which of the
following is correct.

This question has multiple correct options
A. \( \Delta \mathrm{AMC} \cong \Delta \mathrm{BMD} \)
B. \( \angle D B C \) is a right angle.
c. \( \Delta D B C \equiv \Delta A B C \)
D. \( \mathrm{CM}=\frac{1}{2} \mathrm{AB} \)


The dimensions of a rectangle ABCD are
\( 51 \mathrm{cm} 25 \mathrm{cm} . \) A trapezium \( P Q C D \) with
its parallel sides \( \mathrm{QC} \) and \( \mathrm{PD} \) in the ratio
\( 9: 8, \) is cut off from the rectangle as
shown in the figure. If the area of the
trapezium PQCD is \( \frac{5}{6} \) th part of the area of the rectangle, find the length \( Q C \)


Define the atomic mass unit.
A. Mass unit equal to exactly one-twelfth the mass of a carbon-12 atom
B. Mass unit equal to exactly the mass of a carbon-12 atom
C. Mass unit equal to exactly one-twelfth the mass of a hydrogen atom
D. All of the above


Rewrite the following equation in terms
of \( \boldsymbol{a} \)
\( s=u t+\frac{1}{2} a t^{2} \)


The ellipse cuts \( x \) axis at \( A \) and \( y \) axis at \( \mathrm{B} \) and the line joining the focus \( \mathrm{S} \) and B makes an angle \( \frac{3 \pi}{4} \) with \( x \) -axis, then the eccentricity of the ellipse is:
A \( \cdot \frac{1}{\sqrt{2}} \)
B. \( \frac{1}{2} \)
c. \( \frac{\sqrt{3}}{2} \)
D. \( \frac{1}{3} \)


is liberated when acetic
acid reacts with sodium metal.
A. Hydrogen
B. Chloride
c. oxygen
D. Nitrogen


Q Type your question
uniformly distributed over its circumference is hanging by an
insulated thread with the help of a
small smooth ring (not rigidly fixed with bigger ring). A time varying
magnetic field \( B=B_{0} \sin \omega t \) is
switched on at \( t=0 \) and the ring is
released at the same time. The induced
EMF in loop at time \( t=2 \pi / \omega \) is:
A . 0
в. \( \frac{B_{0} \pi \omega R^{2}}{2} \)
\( \mathbf{c} \cdot B_{0} \pi \omega R^{2} \)
D. \( -\frac{B_{0} \pi \omega R^{2}}{2} \)


Define the focal length of a spherical mirror. A concave mirror produces 3 times a real image of an object placed
at a distance of \( 10 \mathrm{cm} \) in front of it. Find
the radius of curvature of the mirror.


Energy currency/coin of cell is
A . ATP
B. NAD
c. ADP
D. GDP


If \( x \) is real, then \( \frac{x^{2}+2 x+c}{x^{2}+4 x+3 c} \) can take all real values if?
A. \( 0<c<2 \)
В. \( 0<c<1 \)
c. \( -1<c<1 \)
D. None of the above


Explain the bonding on \( C o C l_{2} .3 N H_{3} \)
and \( \operatorname{CoCl}_{2} \cdot 5 N H_{3} \) structure on the
basis at Werner's theory.


The critical checkpoints that control the
cell cycle are at the
\( \mathbf{A} \cdot G_{1} \) to \( \mathrm{S} \) stage and \( G_{2} \) to \( \mathrm{M} \) stage
B. \( \mathrm{S} \) to \( G_{2} \) stage and \( G_{2} \) to M stage
\( \mathbf{C} \cdot \mathbf{M} \) to \( G_{1} \) stage and \( G_{2} \) to \( \mathbf{M} \) stage
D. M to \( G_{1} \) stage and \( \mathrm{S} \) to \( G_{2} \) stage


The shape of \( X e O_{2} F_{2} \) molecule is:
A. trigonal bipyramidal
B. square planar
c. tetrahedral
D. see-saw


A black body calorimeter filled with hot
water cools from \( 60^{\circ} \mathrm{C} \) to \( 50^{\circ} \mathrm{C} \) in 4 min
and \( 40^{\circ} \mathrm{C} \) to \( 30^{\circ} \mathrm{C} \) in 8 min. The
approximate temperature of surrounding is :
A \( \cdot 10^{\circ} \mathrm{C} \)
В. \( 15^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 20^{\circ} C \)
D. \( 25^{\circ} \mathrm{C} \)


Find the equation of the ellipse whose
vertices are \( (\pm \mathbf{2}, \mathbf{0}) \) and foci are
(±1,0)


Two waves \( \boldsymbol{y}_{1}=\boldsymbol{A} \sin [\boldsymbol{k}(\boldsymbol{x}-\boldsymbol{c} \boldsymbol{t})] \) and
\( \boldsymbol{y}_{2}=\boldsymbol{A} \sin [\boldsymbol{k}(\boldsymbol{x}+\boldsymbol{c} \boldsymbol{t})] \) are superimposed
on a string. The distance between adjacent nodes is


Which of the following reactions will
yield 2,2 -dibromopropane?
A. \( C H_{3}-C \equiv C H+2 \mathrm{HBr} \rightarrow \)
B. \( C H_{3} C H=C H B r+\mathrm{HBr} \rightarrow \)
c. \( C H \equiv C H+2 \mathrm{HBr} \rightarrow \)
D. \( C H_{3}-C H=C H_{2}+ \) HBr \( \longrightarrow \)


The line segment joining the points \( (-3, \)
-4 ) and (1,-2) is divided by the \( y \) -axis in the ratio
\( A \cdot 1: 3 \)
B. 3:1
\( c \cdot 2: 3 \)
D. 3:2


An unhappy mouse of mass \( m_{0}, \) moving on the end of a spring of spring constant p is acted upon by a damping force
\( F_{x}=-b v_{x} . \) For what value of \( b \) the
motion is critically damped?
A \( \cdot b=\sqrt{\frac{p}{m_{0}}} \)
B. \( b=2 \sqrt{p m_{0}} \)
\( ^{\mathrm{c}}_{b}=\sqrt{\frac{p^{2}}{2 m_{0}}} \)
D. \( b=\sqrt{\frac{p}{2 m_{0}}} \)


The \( \% \) loss in mass after heating a pure sample of potassium chlorate (Mol. mass \( =122.5 \) ) will be:
A . 12.25
B. 24.50
c. 39.17
D. 49.0


If the Neanderthals are not the direct
ancestors of humans, is it still possible for humans and Neanderthals to be
related?
A. Yes, because we share a common ancestor
B. Yes, but only if humans and Neanderthals could have interbred
c. No, because the human evolutionary tree is strictly linear and without branches
D. No, because this means that Neanderthals evolved from an entirely different branch of organisms than humans did


Factorise :
\( (2 a+b)^{3}-(a+3 b)^{3} \)
A \( \cdot(a+b)\left(7 a^{2}+13 a b+13 b^{2}\right) \)
B . \( (a-2 b)\left(7 a^{2}+17 a b+13 b^{2}\right) \)
C \( \cdot(a-b)\left(7 a^{2}+13 a b+17 b^{2}\right) \)
D. \( (2 a-b)\left(7 a^{2}+17 a b+17 b^{2}\right) \)


Show that the Modulus Function \( \boldsymbol{f} \) \( \boldsymbol{R} \rightarrow \boldsymbol{R}, \) given by \( \boldsymbol{f}(\boldsymbol{x})=|\boldsymbol{x}|, \) is neither
one-one nor onto, where \( |x| \) is \( x, \) if \( x \) is
positive or 0 and \( |x| \) is \( -x, \) if \( x \) is
negative.


The effective nuclear charge for the outermost electron of oxygen atom is
A . 4.55
B. 5.35
\( c \cdot 6.68 \)
D. None of these


In the expansion of \( \left(x^{3}-\frac{1}{x^{2}}\right)^{2}, \) where n is a positive integer, the sum of the
coefficients of \( \boldsymbol{x}^{\boldsymbol{6}} \) is \( \mathbf{1} \)


Write the IUPAC name of the complex
\( \left[\boldsymbol{A} \boldsymbol{g}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{2}\right]\left[\boldsymbol{A} \boldsymbol{g}(\boldsymbol{C} \boldsymbol{N})_{2}\right] \)


f \( \boldsymbol{f}(\boldsymbol{x})=\sin \boldsymbol{x} \forall \boldsymbol{x} \in[\mathbf{0}, \boldsymbol{x} / 2], \boldsymbol{f}(\boldsymbol{x})+ \)
\( \boldsymbol{f}(\boldsymbol{\pi}-\boldsymbol{x})=\boldsymbol{2} \forall \boldsymbol{x} \in[\boldsymbol{x} / 2, \boldsymbol{\pi}] \) and
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{f}(\boldsymbol{2} \boldsymbol{\pi}-\boldsymbol{x}) \forall \boldsymbol{x} \in[\boldsymbol{\pi}, \boldsymbol{2} \boldsymbol{\pi}] \) then
find the area bounded by \( y=f(x) \) and
the \( x- \) axis.


A rectangle ABCD is inscribed in a circle
with centre 0. If AC is the diagonal and
\( \angle B A C=30^{\circ}, \) then radius of the circle
will be equal to
A \( \cdot \frac{\sqrt{3}}{2} B C \)
B. BC
\( c \cdot \sqrt{3} B C \)
D. 2BC


The cost of a refrigerator is \( R s .9000 . \) Its
value depreciates at the rate of \( 5 \% \) every year. The total depreciation in its value at the end of 2 years 877.5
A. True
B. False


Explain Huygen's construction of spherical wavefront


A material has Poisson's ratio 0.5 . if a
uniform rod of it suffers a longitudinal
strain of \( 2 \times 10^{3}, \) then the percentage
change in volume is
A . 0.6
B. 0.4
\( c .0 .2 \)
D. zero


The melting point of \( M g C l_{2} \) is greater
than that of \( B a C l_{2} \). Give reason?


Pictured above are four disks rotating
counter-clockwise (as viewed from
above) at a constant speed. Which disk
is experiencing greatest acceleration?
A. green
B. red
c. blue
D. yellow
E. All disks are experiencing the same acceleration


For the situation shown in figure, match the entries of Column I with Column II.
Assume thickness of films to be very
small compared towavelenght of incident light.


A ray of light is incident on the plane mirror at rest. The mirror starts turning
at a uniform acceleration of \( 2 \pi r a d / s^{2} \) about an axis in plane of mirror. The reflected ray at the end of \( \frac{1}{4} \) s must have turned through:
A . 90
B. 45
c. 22.5
D. 11.25


\[
\begin{aligned}
\operatorname{Let} x &=111 \ldots 11(20 \text { digits }) \\
y &=333 \ldots 33(10 \text { digits }) \\
\text { and } z &=222 \ldots 22(10 \text { digits })
\end{aligned}
\]
The value of \( \frac{\boldsymbol{x}-\boldsymbol{y}^{2}}{\boldsymbol{z}} \)


If a planet of given density were made larger, its force of attraction for an object on its surface would increase
because of the greater distance from the object to the centre of the planet. Which effect predominates?


Two liquids \( X \) and \( Y \) from an ideal
solution. At \( 300 K, \) a vapour pressure of
the solution containing 1 mol of \( X \) and
3 mol of \( Y \) is 550 mm \( H g . \) At the same
temperature, if 1 mol of \( Y \) is further
added to this solution, a vapour
pressure of the solution increased by 10
mm Hg. Vapour pressure ( in mmHg) of
\( X \) and \( Y \) in their pure states will be
respectively:
A. 300 and 400
B. 400 and 600
c. 500 and 600
D. 200 and 300


Distinguish between centre of mass and centre of gravity?


Fill in the blanks:
The process of loss of an electron is known as
A. oxidation
B. reduction
c. enthalphy
D. entropy


The area bounded by the two curves \( \boldsymbol{y}=\sin \boldsymbol{x}, \boldsymbol{y}=\cos \boldsymbol{x} \) and the X-axis in
the first quadrant \( \left[0, \frac{\pi}{2}\right] \) is
A \( .2-\sqrt{2} \) sq. units
B . \( 2+\sqrt{2} \) sq. units
c. \( 2(\sqrt{2}-1) \) sq. units
D. 4 sq. units


Which joint is more flexible in males than females?
A. Public symphysis
B. Deltoid ridge
c. Deltoid tuberosity
D. sacroiliac joint


The tremendous pressure exerted by air can be demonstrated by :
A. crushing can experiment
B. Hydraulic press
c. Altimeter
D. All


The coefficient of volume expansion of mercury is \( 5.4 \times 10^{-4} \) o \( C . \) What is the
fractional change in its density for a
\( 80^{\circ} \mathrm{C} \) rise in temperature?


As we move from left to right in a period, which of the periodic properties decreases?

This question has multiple correct options
A. electronegativity
B. atomic size
c. electropositivity
D. metallic character


State whether true or false:
Bakelite is the first synthetic thermosetting plastics.
A. True
B. False


If \( \boldsymbol{y}=\log \sqrt{\frac{1-\cos 3 x}{1+\cos 3 x}}, \) find \( \frac{d y}{d x} \)


\( H_{2} O_{2} \) solution used for hair bleaching
is sold as a solution of approximately
\( 5.0 \mathrm{g} H_{2} \mathrm{O}_{2} \) per \( 100 \mathrm{mL} \) of the solution
The molecular mass of \( H_{2} O_{2} \) is \( 34 . \) The
molarity of this solution is approximately:
A \( .0 .15 M \)
B. \( 1.5 M \)
c. \( 3.0 M \)
D. 3.4 \( M \)


The non-viable particulate among the following is:
A. dust
B. bacteria
c. moulds
D. fungi


When 2 dice are thrown simultaneously what is the probability that there is exactly one \( 5 ? \)
A \( \cdot \frac{4}{36} \)
в. \( \frac{5}{18} \)
c. \( \frac{6}{23} \)
D. \( \frac{7}{24} \)


Ammonia and oxygen reacts at higher
temperature as
\( 4 N H_{3}(g)+5 O_{2}(g) \rightarrow 4 N O(g)+ \)
\( \mathbf{6} \boldsymbol{H}_{\mathbf{2}} \boldsymbol{O}(\boldsymbol{g}) \)
In an experiment, the concentration of NO increases by \( 1.08 * \) \( 10^{-2} \) mol \( \operatorname{litr} e^{-1} \) in 3 seconds.
Calculate,
(1) rate of reaction
(2) rate of disappearance of ammonia
(3) rate of formation of water


Which is used to produce smoke
screens?
A. zinc sulphide
B. Calcium phosphide
c. zinc phosphide
D. Sodium carbonate


A current of \( 19.3 \mathrm{mA} \) is passed for 9375 seconds through \( 500 \mathrm{ml} \) of \( 2 \mathrm{mM} \)
\( Z n S O_{4} \) solution. If the final molarity of
\( Z n^{2+} \) is \( 0.5 \mathrm{mM} \), then the current efficiency of the source is (assume volume remains constant during this process):
A . 80\%
B. 75\%
c. 72\%
D. 65\%


In a division operation the divisor is 5 times the quotient and twice the remainder. If the remainder is \( 15, \) then
what is the dividend?
A . 175
в. 185
c. 195
D. 205


A tank initially holds 10 lit. of fresh
water. \( A t t=0, \) a brine solution containing \( \frac{1}{2} \) kg of salt per lit. is poured into tank at a rate 1 lit/min while the
well-stirred mixture leaves the tank at
the same rate. Find the amount of salt
in a tank at a particular time
A \( \cdot-5 e^{-t}+5 \)
B. \( 5 e^{-t}+5 \)
\( \mathbf{c} \cdot 5 e^{-t}-5 \)
D. \( -5 e-5 \)


A body subjected to three concurrent forces is found to be in equilibrium. The resultant of any two forces then will be
A. Is equal to third force
B. Is opposite to third force
c. Is collinear with the third force
D. All of these


Hydrargyrum is the latin name of:


Which of the following is NOT true for
supernova?
A. A supernova is stellar explosion.
B. Supernova can produce elements like titanium, iron, cobalt and nickel.
C. The Sun is likely to become a supernova.
D. The core collapse that causes some supernovas may result in the formation of a black hole remnant.
E. Supernovas can outshine an entire galaxy for a brief period of time.


Cinchona bark is used to extract:
A. penicillin
B. quinine
c. sulpha drugs
D. chloromycetin


Find the equivalent capacitance of three capacitors of capacitance \( 3 \mu F \)
\( 10 \mu F \) and \( 15 \mu F \) connected in (1) series
(2) parallel.


(i) For a Searle's experiment, in the
graph shown, there are two readings a
and b that are not lying on the straight
line
(ii) Experiment is not performed
precisely
A. Both (i) and (ii) are true and (ii) is reason for (i)
B. Both (i) and (ii) are true but (ii) is not reason for (ii)
c. only (i) is true
D. only (ii) is true


In maize, sugar, beet etc., the translocation of carbohydrate is
A. Apolar
B. Polar
c. Basipetal
D. None of the above


Write the name of acid secreted from
sting of ant


For a chemical reaction \( A \rightarrow \) Products the rate of reaction doubles when the concentration of \( A \) is increased by 4
times.
The order of reaction is:
\( A \cdot 4 \)
B. 0
\( c \cdot 1 / 2 \)
\( D \)


A straight wire of length \( 50 \mathrm{cm} \) carrying
a current of \( 2.5 A \) is suspended in mid-
air by a uniform magnetic field of \( 0.5 T \)
(as shown in figure). The mass of the
wire is \( \left(\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2}\right) \)
\( \mathbf{A} \cdot 100 g m \)
В. \( 125 g m \)
\( \mathbf{c} \cdot 62.5 g m \)
D. \( 250 g m \)


Area of region bounded by \( \boldsymbol{x}=\mathbf{0}, \boldsymbol{y}=\mathbf{0} \)
\( \boldsymbol{x}=\mathbf{2}, \boldsymbol{y}=\mathbf{2}, \boldsymbol{y} \leq \boldsymbol{e}^{x} ; \boldsymbol{y} \geq \ln \boldsymbol{x} \) is
A \( .6-4 \ln 2 \)
B. \( 4 \ln 2-2 \)
c. \( 2 \ln 2-4 \)
D. \( 6-2 \ln 2 \)


Evaluate: \( \lim _{x \rightarrow 2}\left\{\frac{1}{x-2}-\frac{4}{x^{2}-4}\right\} \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. 4
\( c \cdot \frac{1}{4} \)
D. \( -\frac{1}{4} \)


A parallel plate capacitor is charged. If the plates are pulled apart
A. The capacitance increases
B. The potential difference increases
c. The total charge increases
D. The charge and potential difference remain the same


Two moles of an ideal monoatomic gas
occupies a volume \( V \) at \( 27^{\circ} \mathrm{C} \). The gas expands adiabatically to a volume \( 2 \mathrm{V} \) Calculate (a) the final temperature of the gas and (b) change on its internal
energy.
B. (a) \( 195 K \) (b) 2.7 k
\( c .(a) 189 K(b) 2.7 k J \)
D. (a) \( 195 \mathrm{k} \) (b) \( -2.7 \mathrm{kJ} \)


An oscillating circuit contains an inductor of inductance \( 10^{-6} \mathrm{H} \) and two
capacitor each of capacitance \( 5 \times 10^{-6} \)
farad connected in parallel. Then the
resonance frequency of the circuit is
A \( \cdot \frac{10^{5}}{2 \pi} \)
B. \( \frac{10^{5}}{\pi} \)
c. \( \frac{3 \times 10^{5}}{2 \pi} \)
D. \( \frac{\sqrt{2 \times 10^{5}}}{\pi} \)


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


Let \( \boldsymbol{A}=\{\mathbf{1}, \mathbf{2}, \mathbf{3}, \mathbf{4}, \mathbf{5}\}, \boldsymbol{B}=\{\mathbf{2}, \mathbf{3}, \mathbf{6}, \mathbf{7}\} \)
Then the number of elements in
\( (\boldsymbol{A} \times \boldsymbol{B}) \cap(\boldsymbol{B} \times \boldsymbol{A}) \) is
A . 18
B. 6
\( c \cdot 4 \)
\( D \)


\( f\left(\frac{1+i}{1-i}\right)^{m}=1, \) then find the least positive integral value of \( \mathrm{m} \)


Which of the following compounds will be dissociated into its constituent
ions?
This question has multiple correct options
A. Aqueous \( K C l \)
B. Solid KCl
c. Aqueous \( M g C l_{2} \)
D. solid \( M g C l_{2} \)


Generally sulphide ores are concentrated by which of the following
process?
A. Hand picking
B. Washing with water
c. Leaching
D. Froth floatation


State whether the given statement is
True or False :

Gauss' law is useful for the calculation
of electrostatic field when the system
doesn't possess any symmetry.
A. True
B. False


The device used to provide electricity in the instruments of artificial satellites
is


Which type of polynomial, the given
expression \( 5 x^{2}+x-7 \) is?


Solve \( \int \frac{d x}{\sqrt{5 x^{2}-2 x}} \)
\( \mathbf{A} \cdot_{I}=\frac{1}{\sqrt{5}} \log \left|x-\frac{1}{5}-\frac{1}{\sqrt{5}} \sqrt{5 x^{2}-2 x}\right|+c \)
B. \( I=-\frac{1}{\sqrt{5}} \log \left|x-\frac{1}{5}+\frac{1}{\sqrt{5}} \sqrt{5 x^{2}-2 x}\right|+c \)
\( ^{\mathbf{C}} I=\frac{1}{\sqrt{5}} \log \left|x-\frac{1}{5}+\frac{1}{\sqrt{5}} \sqrt{5 x^{2}-2 x}\right|+c \)
D. None of these


A fuel cell is:
I.A voltaic cell in which continuous supply of fuels are sent at anode to perform oxidation.
II. A voltaic cell in which fuels such as:
\( C H_{4}, H_{2} \) and \( \mathrm{CO} \) are used up at anode.
III. One which involves the reaction of
\( H_{2} O_{2} \) fuel cell such as:
Anode \( : 2 H_{2}+4 \stackrel{\ominus}{O} H \rightarrow 4 H_{2} O(l)+4 e^{-} \)
Cathode \( : O_{2}+2 H_{2} O(l)+4 e^{-} \rightarrow 4 \stackrel{\ominus}{O} H \)
IV. The efficiency of \( H_{2}-O_{2} \) fuel cell is 70
to \( 75 \% \)
A. \( I, I I I \)
в. \( I, I I I, I V \)
c. \( I, I I, I I I, I V \)
D. \( I, I I, I I I \)


Which of the following is not true about
LED?
A. There are two wires (called leads) attached to an LED.
B. While connecting to a circuit, the longer lead of LED is always connected to the positive terminal of the battery.
C. While connecting to a circuit, the shorter lead of LED is always connected to the positive terminal of the battery.
D. LED can be used to detect weak current.


The author of the book "The book on
game of chance" based on probability theory is-
A. J.Cardon
B. R.S.Woodwards
c. P.S.Laplace
D. P.D.Pherma


\( \ln \) an oscillating \( L-C \) circuit in which
\( C=4.00 \mu F, \) the maximum potential
across the capacitor during the
oscillations is \( 1.50 V \) and the maximum
current through the inductor is \( 50.0 m A \)
What is the inductance \( L ? \)
\( \mathbf{A} \cdot 8.6 m H \)
в. \( 3.6 m H \)
c. \( 6.6 m H \)
D. \( 4.6 m H \)


Describe Rutherford's atomic model


Solve:
\( \operatorname{Tan}(\boldsymbol{A}-\boldsymbol{B})+\boldsymbol{\operatorname { T a n }}(\boldsymbol{B}-\boldsymbol{C})+ \)
\( \operatorname{Tan}(C-A) \) is equal to
A. \( \operatorname{TanA} \) TanB \( \operatorname{TanC} \)
B. CotA CotB CotC
c. \( \operatorname{Tan}(A-B) \operatorname{Tan}(B-C) \operatorname{Tan}(C-A) \)
D.


\( \frac{1}{y} \)
\( \frac{8}{8} \)
\( x \)


If \( \cos x=\tan y, \cot y=\tan z \) and
\( \cot z=\tan x ; \) then \( \sin x= \)
A. \( \frac{\sqrt{5}+1}{4} \)
B. \( \frac{\sqrt{5}-1}{4} \)
c. \( \frac{\sqrt{5}+1}{2} \)
D. \( \frac{\sqrt{5}-1}{2} \)


Calculate the scalar product of the following vectors. Find the vector a which is collinear with
the vector \( b=\{2,-1,0\} \) if \( a \cdot b=10 \)


Assertion
\( \mathrm{CaCO}_{3} \) is prepared by passing carbon
dioxide gas through slaked lime.
Reason
Passing excess of \( C O_{2} \) through slaked lime leads to the formation of quick
lime.
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 potentiometer wire AB shown in the figure is \( 40 \mathrm{cm} \) long. Where should the
free end of the galvanometer be connected on AB so that the
galvanometer may show zero deflection?


\( H-C-H \) bond angle in ethene and
ethane are \( _{-}-_{-}-_{-}- \) respectively
\( \mathbf{A} \cdot 120^{0} \) and \( 109.5^{0} \)
B. \( 180^{\circ} \) and \( 109.5^{\circ} \)
C . \( 109.5^{\circ} \) and \( 120^{\circ} \)
D. \( 120^{\circ} \) and \( 180^{\circ} \)


Out of \( N i(C O)_{4}, N i(C N)_{4}^{2-} \) and
\( N i C l_{4}^{2-} \) select paramagnetic and diamagnetic.
A \( \cdot N i(C O)_{4} \) and \( N i(C N)_{4}^{2-} \) are diamagnetic
B . \( N i C l_{4}^{2-} \) is paramagnetic
c. Both (A) and
(B) Correct
D. None of these


Arrange the following set of atoms in the order of increasing atomic radius:
\( \boldsymbol{F}, \boldsymbol{C l}, \boldsymbol{C}, \boldsymbol{O} \)
A. \( F, C l, O, C \)
в. \( C, O, F, C l \)
c. \( O, C, F, C l \)
D. \( F, O, C, C l \)


If the number of bivalents are 8 in
metaphase I, what shall be the number of chromosomes in daughter cells after meiosis I and meiosis II respectively.
A. 8 and 4
B. 4 and 4
\( c \cdot 8 \) and 8
D. 16 and 8


Latent heat of vaporization of liquid at
\( \mathbf{5 0 0} \boldsymbol{K} \) and \( \mathbf{1} \) atm pressure is \( 10 \mathrm{kcal} / \) mol. What is the change in internal energy when 3 moles of the liquid is vaporized at the same
temperature?
A . \( 27 \mathrm{kcal} \)
B. \( 7 k c a l \)
c. 33 k call \( l \)


In a syncarpous unilocular ovary, ovules develop from two opposite lines on the wall. The placentation is
A. Superficial
B. Marginal
c. Axile
D. Parietal


The reaction \( \boldsymbol{A}(s) \rightarrow 2 B(g)+C(g) \) is
first order. The pressure after 20 min. and after a very long time are \( 150 \mathrm{mm} \) Hg and 225 mm Hg. The value of rate
constant and pressure after 40 min are?
A. 0.05 In 1.5 min \( ^{-1}, 200 \) mm men
B. 0.5 In 2 min \( ^{-1}, 300 \) mm
c. 0.05 In 3 min\( ^{-1} \), 300 mm
D. \( 0.05 \operatorname{In} 3 \) min\( ^{-1}, 200 \mathrm{mm} \)


The compound of the formula
\( \boldsymbol{C H}_{3} \boldsymbol{C O}\left(\boldsymbol{C H}_{2}\right)_{5} \boldsymbol{C H}=\boldsymbol{C H}-\boldsymbol{C O O H} \)
would be expected to:
I rotate the plane polarised light
II : contain chiral centre
III : contain three stereocentres
IV: show geometrical isomerism
A. Only I, II, II are correct.
B. Only II, IV are correct.
c. ।, ॥, ॥I, IV are correct.
D. only IV is correct.


The food stocks in a hostel are
sufficient for 1200 students for 20 days
If 400 more students joined the hostel,
the stocks just for ... days.
A \( \cdot 12 \)
B. 15
\( c \cdot 18 \)
D. 2


Which of the following sets of reactants is used for preparation of paracetamol from phenol?
A \( \cdot H N O_{3}, H_{2} / P d,\left(C H_{3} C O\right)_{2} O \)
B \( \cdot H_{2} S O_{4}, H_{2} / P d,\left(C H_{3} C O\right)_{2} O \)
\( \mathrm{c} \cdot C_{6} H_{5} N_{2} C l, \operatorname{Sn} C l_{2} / H C l,\left(C H_{3} C O\right)_{2} O \)
D \( \cdot B r_{2} / H_{2} O, Z n / H C l,\left(C H_{3} C O\right)_{2} O \)


Decomposition of organic wastes in
water causes
A. Eutrophication
B. Desertification
c. soil erosion
D. Both A and B


If \( \boldsymbol{I}=\int \frac{\boldsymbol{x}^{2}+\boldsymbol{a}^{2}}{\boldsymbol{x}^{4}-\boldsymbol{a}^{2} \boldsymbol{x}^{2}+\boldsymbol{a}^{4}} \boldsymbol{d} \boldsymbol{x} \)
A \( \cdot \frac{1}{a} \tan ^{-1}\left(\frac{a x}{x^{2}-a^{2}}\right)+C \)
B. \( \frac{1}{a} \tan ^{-1}\left(\frac{x^{2}-a^{2}}{a x}\right)+C \)
c. \( \log |x+\sqrt{x^{2}-a^{2}}|+x+C \)
D. none of these


State the characteristics of magnetic
lines of force.


Auerbach's plexus are found in
A. Below dermis and made up of muscles
B. Outer to muscularis externa and made up of nerves
C. Below muscularis interna
D. Layer of podocytes in glomerulus of kidney


Where do plant roots take up oxygen
from?
A. Atmospheric air
B. Air spaces between soil particles
C. Water in soil particles
D. None of the above


Two similar boxes \( B_{i}(i=1,2) \) contains \( (i+1) \) red and \( (5-i-1) \) black balls.
One box is chosen at random and two
balls are drawn randomly. What is the probability that both the balls are of
different colours?
A \( \cdot \frac{1}{2} \)
B. \( \frac{3}{10} \)
\( c \cdot \frac{2}{5} \)
D.


Rutherfords alpha-particles dispersion
experiment concludes
A. all positive ions are deposited at small part
B. all negative ions are deposited at small part
C. proton moves around the electron
D. neutrons are charged particles


You are given two convex lenses of focal lengths \( 5 \mathrm{cm} \) and \( 25 \mathrm{cm} \). Which one of
these would you like to use as an objective in a telescope? Give reasons
for your answer.


Which of the following units can be
used to express G?
\( A \cdot N K g^{-2} \)
B. \( \mathrm{Nm}^{-2} \mathrm{Kg}^{2} \)
\( \mathrm{C} \cdot \mathrm{Nm}^{2} \mathrm{Kg}^{-2} \)
D. \( \mathrm{Nm}^{-2} \mathrm{Kg}^{-3} \)


A \( 13 f t . \) ladder is leaning against a wall when its base starts to slide away At the instant when the base is 12 ft. away from the wall, the base is moving away from the wall at the rate of 5 ft/sec. The
rate at which the angle \( \theta \) between the ladder and the ground is changing is
A \( \cdot-\frac{12}{13} r a d / \sec \)
B. - 1 rad\( / \)sec.
c. \( -\frac{13}{12} r a d / s e c \)
D. \( -\frac{10}{13} \) rad/sec


The value of the integral \( \int_{\frac{1}{3}}^{1} \frac{\left(x-x^{3}\right)^{\frac{1}{3}}}{x^{4}} d x \) is?
\( A \cdot 6 \)
B.
\( c .3 \)
D.


Induced charge resides at/in the
A. bulk of the object
B. centre of the object
c. surface of the object
D. All of the above


In which of the following acetic acid is used?
A. Antibiotics
B. To remove nail polish
c. Antiseptic
D. White lead


Three charged particles are in equilibrium under their electrostatic forces only. which of the following statements is true for the system. This question has multiple correct options
A. the particles have the same charge
B. all the charges cannot have the same magnitude
c. all the charges cannot have the same sign
D. the equilibrium is unstable


When at rest, a liquid stands at the
same level in the tubes as shown in the
figure. But as indicated, a height
difference \( h \) occurs when the system is given an acceleration \( a \) towards the
right. Then \( h \) is equal to
\( ^{A} \cdot \frac{a L}{2 g} \)
в. \( \frac{g L}{2 a} \)
c. \( \frac{g L}{a} \)
D. \( \frac{a L}{q} \)


When \( H g I_{2} \) is added to aqueous
solution of \( \mathrm{KI} \), why there is an increase
in vapour pressure of solution?


The number of marble slabs of size
\( 20 \mathrm{cm} \times 30 \mathrm{cm} \) required to pave the
floor of a square room of side 3 metres
is
A. 100
в. 150
\( c .225 \)
D. 25


\( \int \frac{e^{x}}{x}\left(x \cdot(\log x)^{2}+2 \log x\right) d x \)


In fuel cells, the reaction that takes
place at the anode is:
A \( \cdot H_{2}(g)+2 O H^{-}(a q) \rightarrow 2 H_{2} O(l)+2 e^{-} \)
в. \( O_{2}(g)+2 H_{2} O(l)+4 e^{-} \rightarrow 4 O H^{-}(a q) \)
c. \( 4 O H^{-} \rightarrow O_{2}+2 H_{2} O+4 e^{-} \)
D. \( 2 H^{+}+2 e^{-} \rightarrow H_{2} \)


Fill in the blanks with appropriate
words.
In mitotic metaphase centromeres of chromosomes remain directed towards
the \( \ldots . . . . . . \) and the arms of chromosomes
remain directed towards the


Assertion
If a light body and a heavy body possess the same momentum, the lighter body
will possess more kinetic energy.
Reason
The kinetic energy of a body varies as
the square of its velocity.
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 objects pictured above are coins moving around on a record player. The coins are not sliding on the record player surface. Which coins is moving faster and how many times faster it is moving than the other one? The space between each vertical line along the horizontal arrow is one-
seventh the radius of the circular record
player surface.
A. 1-three times faster than slowest
B. 3-five-seventh's faster than slowest
c. 3-five times faster than slowest
D. 1-five-seventh's faster than slowest
E. 2 -three-seventh's faster than slowest


The organic acid that can be made from ethanol is:
A . acetic acid
B. formic acid
\( \mathbf{c} \cdot C_{3} H_{7} O H \)
D. valeric acid
E. butanoic acid


The necessary condition for a compound to form fibre is that
A. its molecules must be linear
B. its molecules must be spherical
c. its molecules must be rectangular
D. its molecules must be hexagonal


When a symbol is used to represent a unit named after a person, lower-case letters are used.
A. True
B. False


In the synthesis of sodium carbonate, the recovery of ammonia is done by
treating \( N H_{4} C l \) with \( C a(O H)_{2} \)
The by-product obtained in this process is:
A. \( C a C l_{2} \)
в. \( N a C l \)
c. \( N a O H \)
D. \( \operatorname{NaH} \mathrm{CO}_{3} \)


A block of mass \( m \) is pulled slowly by a
minimum constant force \( (\boldsymbol{F}) \) on a
horizontal surface through a distance \( x \)
The coefficient of kinetic friction is \( \mu \)
Find the work done by the force \( (\boldsymbol{F}) \)


In the Castner process for the extraction of sodium, the anode is made of:
A. copper
B. iron
c. sodium
D. nickel


If \( I=\int_{3}^{5} \frac{\sqrt{x}}{\sqrt{8-x}+\sqrt{x}} d x \) then \( I \) equals
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D. 3.5


Technique for detecting and screening the nutritional mutants in Neurospora crassa was developed by
A. Beadle and Tatum
B. Bateson and Punnet
c. Luria Dulbecco
D. Knoll and Ruska


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


What would be the output of the circuit whose boolean expression \( \boldsymbol{Y}=\boldsymbol{A} \overline{\boldsymbol{B}}+ \)
\( A B \) when \( A=1, B=0 ? \)
\( A \)
B.
c. Both (A) \& (B)
D. None of these


The minimum work which must be done
to compress \( 16 g \) of oxygen isothermally, at \( 300 K \) from pressure of \( 1.01325 \times \) \( \mathbf{1 0}^{3} \boldsymbol{N} / \boldsymbol{m}^{2} \) to \( \mathbf{1 . 0 1 3 2 5} \times \mathbf{1 0}^{\mathbf{5}} \boldsymbol{N} / \boldsymbol{m}^{\mathbf{2}} \) is
\( \mathbf{n} \mathbf{1 0 0}=\mathbf{4 . 6}, \boldsymbol{R}=\mathbf{8 . 3} \boldsymbol{J} / \boldsymbol{K}-\boldsymbol{m o l} \)
\( \mathbf{A} \cdot 5727 J \)
в. \( 11.454 k J \)
c. \( 123.255 k J \)
D. \( 1232.55 J \)


The intensities of two notes are equal. If frequency of one note is one-fourth that of the other then the ratio of their
amplitudes is
A . 16
B. 4
\( c \cdot 2 \)
\( D \)


Which of the following statements are
correct?
This question has multiple correct options
\( A \cdot A \) plot of \( \log K_{P} \) vs. \( 1 / T \) is linear.
B. A plot of log [X] vs. time is linear for I order reaction \( X \rightarrow P \)
C. A plot of log P vs. 1/T is linear at constant volume.
D. A plot of P vs. 1/V is linear at constant temperature.


If the angle between the unit vectors \( \vec{a} \) and \( \vec{b} \) is \( 60^{\circ}, \) then \( |\vec{a}-\vec{b}| \) is
A. 0
B. 2
\( c \)
D. 4


Match the following:
\( \begin{array}{ll}\text { Column I } & \text { Column II } \\ \text { A. Sphalerits } & \text { p. } F e C O_{3} \\ \text { B. Malachite } & \text { q. } Z n C O_{3} \\ \text { C. Calamine } & \text { r. } N a_{3} A l F_{8} \\ \text { D. Cryolite } & \text { s. } C u C O_{3} \cdot C u(O H)_{2} \\ \text { E. Siderite } & \text { t. } Z n S\end{array} \)
A. A-r B-p C-t D-q E-s
B. A-t B-s C-q D-p E-r
C. A-t B-r C-q D-p E-s
D. A-t B-s C-q D-r E-p
\( E \cdot A-r B-r C-p D-t E-s \)


The domain of the function \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \log _{x} e \) is given by \( [0, \infty]-k \)
What is \( k \)
This question has multiple correct options
A . 1
B. \( e \)
c. 0
D. 10


A particle moves with an initial velocity
\( \boldsymbol{v}_{0} \) and retardation \( \boldsymbol{\alpha} \boldsymbol{v}, \) where \( \boldsymbol{v} \) is its initial velocity at any time \( t \) and \( \alpha \) is a
constant
This question has multiple correct options
A \cdot The particle will cover a total distance \( \frac{v_{0}}{\alpha} \)
B. The particle will come to rest after a time \( \frac{1}{\alpha} \)
c. The particle will continue to move for a very long time.
D. The velocity of the particle will become \( \frac{v_{0}}{2} \) after a time \( \frac{1}{\alpha} \)


Find the angle between the following pair of lines:
(i) \( \vec{r}=2 \hat{i}-5 \hat{j}+\hat{k}+\lambda(3 \hat{i}-2 \hat{j}+6 \hat{k}) \)
and \( \vec{r}=\mathbf{7} \hat{\boldsymbol{i}}-\boldsymbol{6} \hat{\boldsymbol{k}}+\boldsymbol{\mu}(\hat{\boldsymbol{i}}+\mathbf{2} \hat{\boldsymbol{j}}+\mathbf{2} \hat{\boldsymbol{k}}) \)
(ii) \( \vec{r}=3 \hat{i}+\hat{j}-2 \hat{k}+\lambda(\hat{i}-\hat{j}-2 \hat{k}) \)
and \( \vec{r}=2 \hat{i}-\hat{j}-56 \hat{k}+ \)
\( \mu(\hat{\mathbf{3}} \mathbf{i}-\mathbf{5} \hat{\mathbf{j}}-\mathbf{4} \hat{\boldsymbol{k}}) \)


The ratio 2: 3 expressed as percentage
is
A. \( 401 \% \)
B. \( 60 \% \)
c. \( 66 \frac{2}{3} \% \)
D. \( 33 \frac{1}{3} \% \)


Name a compound of chlorine that is
used as:
(A) An disinfectant
(B) An anesthetic
(C) A bleaching agent


Formation of RNA on DNA template is called as
A. Transduction
B. Transformation
c. Transcription
D. Translation


If the galvanometer shows no deflection
then the value of \( \mathrm{R} \) for the circuit shown
in the figure is ( length \( A B=100 \mathrm{cm} \) )
A. 30 ohms
B. 60 ohms
\( c .10 \) ohms
D. 120 ohms


A ray of light is incident normally on one refracting surface of an equilateral
prism. If the refractive index of the
material of the prism is \( 1.5, \) then:
A. the emergent ray is deviated by \( 30^{\circ} \)
B. the emergent ray is deviated by \( 60^{\circ} \)
C. the emergent ray just graces the second reflecting surface
D. the ray undergoes total internal reflection at second refracting surface
E. the ray emerges normally from the second refracting surface


Why do we lose hearing while yawning?
A. Muscles around middle ear contracts
B. Muscles around middle ear expands
C. Muscles around inner ear contracts
D. Muscles around inner ear expands


Why is RNA required to undergo splicing?


For \( \boldsymbol{x} \in(\mathbf{0}, \boldsymbol{\pi}), \) the equation \( \sin \boldsymbol{x}+ \)
\( 2 \sin 2 x-\sin 3 x=3, \) has
A. infinitely many solutions
B. three solutions
c. one solution
D. no solution


Shown below is an animal cell. Label the
parts \( A \) and \( B \)
A. Cell wall and cell membrane
B. Chloroplast and cell wall
c. Cytoplasm and cell membrane
D. Chloroplast and cell membrane


The diameter of zinc atom is \( 2.6 A \) Calculate (a) radius of zinc atom in pm
and (b) number of atoms present in a length of \( 1.6 \mathrm{cm} \) if the zinc atoms are arranged side by side lengthwise.


The equation of the progressive wave is \( \boldsymbol{Y}=\mathbf{3} \sin \left[\boldsymbol{\pi}\left(\frac{\boldsymbol{t}}{\mathbf{3}}-\frac{\boldsymbol{x}}{\mathbf{5}}\right)+\frac{\boldsymbol{\pi}}{\boldsymbol{4}}\right] \) where \( \boldsymbol{x} \)
and \( Y \) are in metre and time in second.
Which of the following is correct?
A. Velocity \( V=1.5 \mathrm{m} / \mathrm{s} \)
B. Amplitude \( A=3 \mathrm{cm} \)
c. Frequency \( F=0.2 \mathrm{Hz} \)
D. Wavelength \( \lambda=10 m \)


If the two sides and the \( _{----} \) angle of
one triangle are respectively equal to two sides and the included angle of the
other triangle, then the triangles are
congruent.
A. Included
B. Excluded
c. Adjacent
D. Any


A positively charged particle of \( 2.0 C \)
moves upward into an area where both a magnetic field and an electric field
are acting. The magnetic field has a
magnitude of \( 4.0 \times 10^{4} T \) and the
electric field has a magnitude of
\( 0.1 N / C . \) At what velocity must the particle be moving if it is not deflected when it enters this area?
A \( \cdot 4.0 \times 10^{-3} \mathrm{m} / \mathrm{s} \)
в. \( 125 \mathrm{m} / \mathrm{s} \)
\( c \cdot 250 m / s \)
D. \( 500 \mathrm{m} / \mathrm{s} \)
E. The particle will be deflected to the left regardless its velocity


Consider the following elementary
reaction
\[
\mathbf{2 A}+\boldsymbol{B}+\boldsymbol{C} \rightarrow \boldsymbol{\text {Products.}}
\]
All reactant are present in the gaseous
state and reactant \( C \) is taken in excess.
What is the unit of rate constant of the
reaction?
\( \mathbf{A} \cdot \operatorname{mol} L^{-1} \operatorname{tim} e^{-1} \)
B. \( \operatorname{time}^{-1} \)
\( \mathbf{c} \cdot m o l^{-1} L^{2} \operatorname{time}^{-1} \)
D. \( m o l^{-2} L^{2} \)time\( ^{-1} \)


The term mole was accepted in the year
\( ? \)
A . 1962
в. 1965
\( c \cdot \) 1967
D. 1969


The diagonal of a rhombus are \( 15 \mathrm{cm} \) and \( 18 \mathrm{m} . \) Find its area and side.


A closed vessel contains a mixture of
two diatomic gases \( A \) and \( B \). Molar mass \( A \) is 16 times that of \( B \) and mass
of gas \( A \) contained in the vessel is 2
times that of \( B \). The following
statements are given:
A. Average kinetic energy per molecule of \( B \) is equal to that of \( A \)
B. Root mean square value of translation velocity of \( B \) is four times of \( A \)
C. Pressure exerted by \( B \) is eight times of that exerted by \( A \)
D. Number of molecules of \( B \) in the cylinder is eight time that of \( A \)


Reptiles like mammals originated in
A. Jurassic
B. Cretaseus
c. Triassic
D. Permian


\( A B C \) is a right isosceles triangle right
angled at \( B . \) Then \( \sin ^{2} A+\cos ^{2} C= \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( \frac{1}{2} \)
c. \( \frac{1}{\sqrt{2}} \)
D.


Assertion
Statement-1: \( \boldsymbol{f}(\boldsymbol{x})=\frac{\mathbf{1}}{\{\boldsymbol{x}\}} \) is
discontinuous for integral values of \( \boldsymbol{x} \) where \( \vartheta \) denotes the fractional part
function.
Reason
Statement-2: For integral values of \( \boldsymbol{x} \) \( f(x) \) is not defined.
A. Statement-1 is true, Statement-2 is true and Statement-2 is correct explanation for Statement-1
B. Statement-1 is true, Statement-2 is true and Statement-2 is NOT the correct explanation for Statement-1
c. statement-1 is true, Statement-2 is false.
D. Statement-1 is false, Statement-2 is true.


\( \int \frac{1}{(2 x+1) \sqrt{x^{2}-x-2}} d x= \)
A. \( -\frac{1}{\sqrt{5}} \sin ^{-1} \frac{7+4 x}{3(2 x+1)}+c \)
B. \( -\frac{1}{\sqrt{5}} \cos \frac{7+4 x}{3(2 x+1)}+c \)
c. \( -\frac{1}{\sqrt{5}} \sinh ^{-1} \frac{7+4 x}{3(2 x+1)}+c \)
D. \( -\frac{1}{\sqrt{5}} \cosh ^{-1} \frac{7+4 x}{3(2 x+1)}+c \)


\( \operatorname{Prove} \frac{1}{\sec \theta-1}-\frac{1}{\sec \theta+1}=2 \cot ^{2} \theta \)


Statement 1: The reaction of hydrogen
with oxygen to form water is an
exothermic reaction
Statement 2: Water molecules have
polar covalent bonds.
A. Both Statement 1 and Statement 2 are correct and
Statement 2 is the correct explanation of Statement 1
B. Both Statement 1 and Statement 2 are correct and Statement 2 is not the correct explanation of Statement 1.
c. Statement 1 is correct but Statement 2 is not correct.
D. Statement 1 is not correct but Statement 2 is correct.
E. Both the Statement 1 and Statement 2 are not correct.


Which is called chromic acid?
A. \( C r O \)
в. \( C r_{2} O_{3} \)
\( \mathrm{c} \cdot \mathrm{CrO}_{3} \)
D. \( C r O_{2} \)


Find the degree of the polynomial given
below:
\( \boldsymbol{x}^{5}-\boldsymbol{x}^{4}+\mathbf{3} \)


An element \( X \) has number of protons \( =4 \)
What will be its mass number if it has 3
neutrons?
\( A \cdot 4 \)
B. 3
c. 7
D. 5


Which of the following polymers can be made by condensation polymerisation reaction?
This question has multiple correct options
A. Dacron
B. Nylon - 6, 6
c. Bakelite
D. Polyethylene


The centre of a square is at the origin
and vertex is \( A(2,1) . \) Find the \( c 0 \)
ordinates of other vertices of the square
A. \( B(1,-2), C(-2,-1), D(-1,-2) \)
B. \( B(-1,-2), C(-2,-1), D(-1,-2) \)
c. \( B(-1,2), C(-2,-1), D(1,-2) \)
D. \( (-1,-2), C(-2,-1), D(1,2) \)


What does the following sequence represent?
Blue-Green Algae \( \rightarrow \) Crustose Lichens
\( \rightarrow \) Foliose Lichens \( \rightarrow \) Mosses \( \rightarrow \) Shrubs
\( \rightarrow \) Dicotyledonous trees
A. A food pyramid
B. Ecological succession
c. Genetic drift
D. Phylogenetic trend


The Kirchhoff's first \( \operatorname{law}\left(\sum i=0\right) \) and second law \( \left(\sum i R=\sum E\right), \) where the symbols have their usual meanings, are respectively based on
A. conservation of charge, conservation of energy
B. Conservation of charge, conservation of momentum
c. conservation of energy, conservation of charge
D. conservation of momentum, conservation of charge


General representation of alkyl halides is:
A. \( R-X_{2} \)
в. \( R_{2} X \)
c. \( R-X \)
D. none of these


Which of the following is not a characteristic of chemisorption?
A . It is irreversible
B. It is specific.
c. It is a multi-layer phenomenon
D. Heat of adsorption is about -400 k.


Sulfuric acid has a charring action because, it is:
A. a strong acid
B. a dehydrating agent
c. an oxidizing agent
D. a reducing agent


Which of the following statements is
incorrect in case of equilibrium state?
A. It is dynamic in nature
B. It readjust itself on the changing conditions
\( \mathrm{C} \). It can be attained from the side of reactants only
D. It can be attained from either side of the reaction


The physical adsorption of gases on the solid surface is due to:
A. covalent bond
B. hydrogen bond
c. ionic bond
D. van der wal's force


If \( \vec{a}+\vec{b} \perp \vec{a} \) and \( |\vec{b}|=\sqrt{2}|\vec{a}| \), then?
\( \mathbf{A} \cdot(2 \vec{a}+\vec{b} \| \vec{b} \vec{b} \)
B . \( (2 \vec{a}+\vec{b}) \perp \vec{b} \)
c. \( (2 \vec{a}-\vec{b}) \perp \vec{b} \)
D. \( (2 \vec{a}+\vec{b}) \perp \vec{a} \)


Two parallel wires are suspended in vacuum. When the potential difference between the wires is 30 V then the
charge on the wires is \( 140 \mu C \). The capacitance of the system of wires will be:
A \( .4 .66 \mu F \)
в. \( 5 \mu F \)
c. \( 10.21 \mu F \)
\( \mathbf{D} \cdot 50 \mu F \)


The work that has to be done in
transferring unit positive charge from one point to the other is called
A. electric potential energy
B. electrical potential
c. electric potential difference
D. electric field


Aldehydes on oxidation gives
A. Alcohol
B. Acid
c. Ketone
D. Ether


Which of the following statements
corresponds to Kepler's laws of planetary motion?
A. A planet moves around the sun in a circular orbit
B. A planet moves around the sun in an elliptical orbit with the sun at the geometrical centre
c. A planet moves around the sun in an elliptical orbit with the sun at the focus
D. A planet moves around the sun in an elliptical orbit with uniform speed


A box contains 6 pens, 2 of which are
defective. Two pens are taken randomly
from the box. If r.v. \( X: \) Number of
defective pens obtained, then standard deviation of \( \boldsymbol{X}= \)
\( ^{\mathrm{A}}: \pm \frac{4}{3 \sqrt{5}} \)
B. \( \frac{8}{3} \)
\( c \cdot \frac{16}{45} \)
D. \( \frac{4}{3 \sqrt{5}} \)


Which of the following is non-existing?
A. \( \mathrm{H}_{2} \)
в. \( \mathrm{O}_{2} \)
c. \( \mathrm{N}_{2} \)
D. He \( _{2} \)


Consider the following equilibrium:
\( 2 N O_{2} \rightleftharpoons 2 N O_{3} ; \Delta H=-v e \) If \( O_{2} \) is
added and volume of there action vessel
is reduced, the equilibrium
A. shifts in the product side
B. shifts in the reactant side
c. cannot be predicted
D. remains unchanged


Two condensers of capacitance \( 4 \mu F \) and \( 5 \mu F \) are joined in series. If the potential difference across \( 5 \mu F \) is \( 10 V \), then the
potential difference across \( 4 \mu F \)
condenser is :
\( \mathbf{A} \cdot 22.5 V \)
B. \( 10 V \)
c. \( 12.5 V \)
D. \( 25 V \)


The angle of reflection is
\( A \cdot 25 \)
B \( .12 .5^{\circ} \)
\( c \cdot 50^{\circ} \)
D. None of these


Carbon and oxygen forms two compounds. Carbon content in one of them is \( 42.9 \% \) while in the other is
27.3\%. The given data is in support with:
A. Law of definite proportions
B. Law of reciprocal proportions
c. Law of multiple proportion
D. Law of conservation of mass


A red LED emits light at \( 0.1 W \) uniformly around it. The amplitude of the electric filed of the light at a
distance of \( 1 ~ m \) form the diode is:
A. \( 1.73 \mathrm{V} / \mathrm{m} \)
в. \( 2.45 \mathrm{V} / \mathrm{m} \)
c. \( 5.48 \mathrm{V} / \mathrm{m} \)
D. \( 7.75 V / m \)


\( \left(x^{2}+y^{2}-z^{2}\right)^{2}-\left(x^{2}-y^{2}+z^{2}\right)^{2}= \)
\( A \cdot O \)
B \( \cdot 4 x^{2} z^{2} y^{2} \)
C \( .-4 x^{2} z^{2}+4 x^{2} y^{2} \)
D・ \( x^{4}+y^{4}+z^{4} \)


A gas is filled in a container at any
temperature and at pressure \( 76 \mathrm{cm} \) of Hg. If at the same temperature the
mass of gas is increased by \( 50 \% \) then the resultant pressure will be
\( A .38 \mathrm{cm} \) of \( \mathrm{Hg} \)
B. 76 \( \mathrm{cm} \) of \( \mathrm{Hg} \)
c. \( 114 \mathrm{cm} \) of \( \mathrm{Hg} \)
D. \( 152 \mathrm{cm} \) of \( \mathrm{Hg} \)


The coefficient of self inductance and
the coefficient of mutual inductance
have
A. same units but different dimensions
B. different units but same dimensions
c. different units and different dimensions
D. same units and same dimensions


State whether given statement is True or False.
A ray of light which passes through principal focus of a lens, does not suffer any refraction.
A. True
B. False


Whay would be the \( C . I \) obtained on an
amount of 12500 at the rate of 12
p.c.p.a. after 2 years?
A. Rs. 3180
B. Rs. 3360
c. Rs. 3540
D. Rs. 3720


\( \$ \$ \) lbegin \( \{\text { matrix }\} \lim || x \) \( \mathrm{~ | x r i g h t a r r o w l q u a d ~ 1 ~ l e n d \{ m a t r i x \} \$ \$ ~} \)
\( \left(\frac{1}{x-1}-\frac{2}{x^{2}-1}\right) \)


A uniform ladder of length \( 5 m \) is placed against the wall as shown in the figure. If coefficient of friction \( \mu \) is the same for
both the walls. what is the minimum
value of \( \mu \) for it not to slip?
A \( \cdot \mu=1 / 2 \)
B. \( \mu=1 / 4 \)
c. \( \mu=1 / 3 \)
D. \( \mu=1 / 5 \)


An object is thrown vertically upward with a speed of \( 30 m / s . \) The velocity of
the object half a second before it reaches the maximum height is
A \( .4 .9 \mathrm{m} / \mathrm{s} \)
в. \( 9.8 \mathrm{m} / \mathrm{s} \)
c. \( 19.6 m / s \)
D. \( 25.1 \mathrm{m} / \mathrm{s} \)


toppr
Q Type your question
following steps. Step 1: First of all we find the successive
difference (first difference, second
difference, third difference \( \ldots \text { so on }) \)
Step 2: If first successive difference is
in A.P, then general term can be taken \( \operatorname{as} t_{n}=a n^{2}+b n+c\left(\text { i.e.consider } t_{n} \) as \right.
quadratic polynomial in the decreasing power of \( n \text { with constants } a, b, c) \)
Step 3: If the second, third successive
differences are in \( \mathbf{A} . \mathbf{P}, \) then \( \boldsymbol{t}_{\boldsymbol{n}}=\boldsymbol{a} \boldsymbol{n}^{\boldsymbol{3}}+ \)
\( b n^{2}+c d+d \) for second successive
difference in A.P and so on where
\( a, b, c, d \) are constants whose order can be changed. Step 4: If the first difference in step 1 is
in G.P, then take \( t_{n}=a r^{n-1}+b n+c \)
Similarly if second, third difference are in \( G . P, \) then general terms are considered by \( t_{n}=a r^{n-1}+b n^{2}+ \)
\( \boldsymbol{c n}+\boldsymbol{d} \) and \( \boldsymbol{t}_{\boldsymbol{n}}=\boldsymbol{a} \boldsymbol{r}^{\boldsymbol{n}-\mathbf{1}}+\boldsymbol{b} \boldsymbol{n}^{\boldsymbol{3}}+\boldsymbol{c n}^{\boldsymbol{2}}+ \)
\( \boldsymbol{d} \boldsymbol{n}+\boldsymbol{e} \) respectively where \( \boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}, \boldsymbol{d}, \boldsymbol{e} \ldots \)
are constants whose orders can be
changed. Now consider the sequences
\( P: 9,16,29,54,103, \dots \)
\( Q: 4,14,30,52,80,114, \dots \)
\( R: 2,12,36,80,150,252, \dots \)
\( \boldsymbol{S}: \mathbf{2}, \mathbf{5}, \mathbf{1 2}, \mathbf{3 1}, \mathbf{8 6}, \dots \)
On the basis of above data
(information) answer the following questions:If \( t_{n}=A+B n+C n^{2} \) for
sequence \( Q \), then the value of \( A^{2}+ \)
\( B^{2}+C^{2} \) equals
A. 10
B. 8
\( c . \)
D. None of these


Error in B is
\( \mathbf{A} \cdot \pm 0.9 T \)
В. \( \pm 0.09 m T \)
\( \mathbf{c} . \pm 0.9 m T \)
D. ±0.097


As the depth of the river increases, the velocity of flow:
A. increases
B. decreases
c. remains unchanged
D. may increase or decrease


Which type of force caused this fault to
form?
A. compression
B. tension.
c. shear
D. divergent.


The boiling point of water at 735 torr is
\( 99^{\circ} \mathrm{C} . \) The mass of \( \mathrm{NaCl} \) added in 100
\( \operatorname{gmof} \sin \operatorname{tar}\left(K_{b}=0.51 K k g m o l^{-3}\right) \) to
make its boiling point at \( 100^{\circ} \mathrm{C} \) is:
A \( .10 .68 \mathrm{g} \)
B. \( 5.34 \mathrm{g} \)
c. 2.67 g
D. 26.7 g


Green algae are considered as
ancestors of higher plants due to their resemblance with higher plants in
A. Pigments
B. Cell wall
c. Stored food
D. All of the above


A triangle and a parallelogram have the
same base and the same area. If the
sides of the triangle are \( 26 \mathrm{cm}, 28 \mathrm{cm} \) and \( 30 \mathrm{cm}, \) and the parallelogram stands on the base \( 28 \mathrm{cm}, \) find the height of the parallelogram.


The ratio of momentum of an electron
and an alpha particle which are accelerated from rest by potential difference of \( 100 \mathrm{V} \) is:
A \( \cdot \sqrt{\frac{m_{\alpha}}{m_{e}}} \)
В. \( \sqrt{\frac{m_{e}}{m_{\alpha}}} \)
c. \( \frac{2 m_{e}}{m_{\alpha}} \)
D. \( \sqrt{\frac{m_{e}}{2 m_{\alpha}}} \)


Which one of the following platinum complexes is used in cancer
chemotherapy?
\( A \cdot \operatorname{cis}-\left[P t C l_{2}\left(N H_{3}\right)_{2}\right. \)
B. trans \( -\left[P t C l_{2}\left(N H_{3}\right)\right] \)
\( \mathrm{c} \cdot\left[P t\left(N H_{3}\right)_{4}\right]^{2+} \)
\( \mathbf{D} \cdot\left[P t C l_{4}\right]^{2-} \)


Evaluate:
\( \lim _{x \rightarrow \infty} \frac{3 \sqrt{x}+5 \sin ^{2} x-10 \log x}{5 \sqrt{x}+7 \cos ^{2} x+100 \log x} \)
A . 3 5
в. \( \frac{5}{3} \)
c. 15
D. \( \frac{1}{15} \)


Active transport involves the transport of molecules across a cell membrane.
In order to establish and maintain a
concentration gradient, which of the following condition is suitable?
A. Free energy is used to drive molecules back-and-forth across the transmembrane protein
B. Free energy is used to drive molecules and across a transmembrane protein against the concentration gradient.
c. No free energy is required
D. There must be an equal quantity of molecules on both sides of the membrane


Find the cube root of the number
704969 by looking at the last digit and using estimation


The \( Q \) factor of an ac circuit lies
between:
A. 0 and 1
B. - 1 and 1
c. -1 and 0
D. none of these


Let \( \left[\varepsilon_{o}\right] \) denote the dimensional formula
of the permittivity of the vacuum, and
\( \left[\mu_{o}\right] \) that of the permeability of the vacuum. If \( \mathrm{M}= \) mass, \( \mathrm{L}= \) length, \( \mathrm{T}= \) time
and I = electric current.
This question has multiple correct options
A \( \cdot\left[\mu_{o}\right]=M^{-1} L^{-3} T^{2} I \)
B . \( \left[\varepsilon_{o}\right]=M^{-1} L^{-3} T^{4} I^{2} \)
c. \( \left[\mu_{o}\right]=M L T^{-2} I^{-2} \)
\( \mathbf{D} \cdot\left[\mu_{o}\right]=M L^{2} T^{-1} I \)


A motion which repeats itself after a fixed interval of time is called
A. vibratory motion
B. curvilinear motion
c. linear motion
D. straight line motion


Which of the following is true about the angular momentum of a cylinder down a slope without slipping?
A. its magnitude changes but the direction remains same
B. both magnitude and direction change
c. only the direction change
D. neither change


The force at the end that is held down.
A . 780 N
B. 220 N
c. \( 1920 \mathrm{N} \)
D. 1140 N


According to the law of triads:
A. the properties of the middle element were in between those of the other two members.
B. three elements arranged according to increasing weights have similar properties.
C. the elements can be grouped in the groups of six elements.
D. every third element resembles the first element in periodic table.


A ray of light strikes a glass plate at an
angle of \( 60^{\circ} . \) If the reflected and refracted rays are perpendicular to each other, the refractive index of glass is
\( ^{A} \cdot \frac{\sqrt{3}}{2} \)
B. 3
\( c \cdot \frac{1}{2} \)
D. \( \sqrt{3} \)


Jacob and Monad studied lactose
metabolism in E.Coli and proposed
operon concept. Operon concept applicable for : -
A. All prokaryotes
B. All prokaryotes and some eukaryotes
c. All prokaryotes and all eukaryotes
D. All prokaryotes and some protozoanes


The line L given by \( \frac{x}{5}+\frac{y}{b}=1 \) passes
through the point \( (13,32) . \) The line \( \mathrm{K} \) is parallel to L and has the equation \( \frac{x}{e}+ \) \( \frac{y}{3}=1 . \) Then the distance between L and
K is
A. \( \frac{23}{\sqrt{15}} \)
в. \( \sqrt{17} \)
c. \( \frac{17}{\sqrt{15}} \)
D. \( \frac{23}{\sqrt{17}} \)


The magnetic moment of a complex is
4.9 B.M. Thus, unpaired electron(s)
maybe


The thermal conductivity of a rod depends on:
A. length
B. mass
c. area of cross-section
D. material of rod


Simplify: \( 3^{0}+2^{-2} \)


Interfascicular cambium develops from
cells of.
A. Pericycle
B. Medullary rays
c. xylem parenchyma
D. Endodermis


\( 100 \mathrm{ml} \) of \( 10 \mathrm{V} \mathrm{H}_{2} \mathrm{O}_{2} \) solution is heated.
The evolved gas is completely reacted with Ca to form CaO. The aqueous solution of Cao is neutralised by \( 50 \mathrm{m} \)
of \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) solution. The molarity of
\( \boldsymbol{H}_{2} \boldsymbol{S O} \mathbf{4} \) is:
A. 2.43 M
B. 1.78 M
c. \( 1.55 \mathrm{M} \)
D. 2.78 м


A two digit number is such that the product of its digits is \( 18 . \) When 63 is subtracted from the number, the digits interchange their places. Find the number


Green house effect is warming due to
A. Infra-red rays reaching earth
B. Moisture layer in atmosphere
C. Increase in temperature due to increase in carbon dioxide concentration of atmosphere
D. Ozone layer of atmosphere


One litre of a buffer solution contains
\( 0.01 \mathrm{M} N H_{4} C l \) and \( 0.1 \mathrm{M} N H_{4} O H . \) The
\( p^{k b} \) of base is \( 5 . p^{H} \) value of the solution
is:
\( A \cdot 9 \)
B. 10
\( c \cdot 4 \)
D. 6


The frequency of the 1 st harmonic of a sonometer wire is \( 160 H z \). If the length
of the wire is increased by \( 50 \% \) and the tension in the wire is decreased by
\( 19 \%, \) the frequency of its first overtone
is :
(Assume linear mass density to be constant
A. \( 180 H z \)
в. \( 192 \mathrm{Hz} \)
c. \( 220 H z \)
D. 232 Нг


To get maximum current in resistance of \( 3 \Omega, \) one can use \( n \) parallel rows of \( m \)
cells each connected in series. If the
total no. of cells is 24 and the internal
resistance is 0.5 ohm then:
A. \( m=12, n=2 \)
в. \( m=8, n=3 \)
c. \( m=2, n=12 \)
D. \( m=6, n=4 \)


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


Which of the following processes is NOT used to preserve the food?
A. Irradiation
B. Addition of salts
c. Addition of heat
D. Hydration


f \( P Q=P R, \) Show that \( P S>P Q \)


\( 20 \% \) of a mans salary is paid as rent, 60 \( \% \) are his living expenses and \( 10 \% \) is paid in LIC. If he spends the remaining
Rs. 3,000 on education of the children, his salary is
A. \( R s .9,000 \)
B. \( R s .90,000 \)
c. \( R s .35 .000 \)
D. Rs.30, 000


Two lens of focal length \( f_{1} \) and \( f_{2} \) are kept in contact coaxially. The resultant power of combination will be
A. \( \frac{f_{1} f_{2}}{f_{1}-f_{2}} \)
в. \( \frac{f_{1}+f_{2}}{f_{1} f_{2}} \)
c. \( f_{1}+f_{2} \)
D. \( \frac{f_{1}}{f_{2}}+\frac{f_{2}}{f_{1}} \)


A neutral atom of fluorine has a mass
number of 19 and an atomic number of
9. How many neutrons does it have?
A . 10
B. 9
c. 19
D . 28
E. It is impossible to determine from the information given


If \( \omega \) is cube root of unity, then \( \boldsymbol{\Delta}=\left|\begin{array}{cccc}\boldsymbol{x}+\mathbf{1} & \boldsymbol{\omega} & \boldsymbol{\omega}^{2} \\ \boldsymbol{\omega} & \boldsymbol{x}+\boldsymbol{\omega}^{2} & \mathbf{1} \\ \boldsymbol{\omega}^{2} & \boldsymbol{1} & \boldsymbol{x}+\boldsymbol{\omega}\end{array}\right|= \)
\( \mathbf{A} \cdot x^{3}+1 \)
B. \( x^{3}+\omega \)
c. \( x^{3}+\omega^{2} \)
D. \( x^{3} \)


The common oxidation state of
elements of lanthanide series is
\( A \cdot+1 \)
\( B \cdot+3 \)
\( c \cdot+4 \)
\( D \cdot+6 \)


Identify a possible graph for function
given by \( f(x)=-(x-2)^{3}+1 \)
A. graph a
B. graph b
c. grpah c
D. grpah d


The standard reduction potential of \( \boldsymbol{C u}^{2+} / \boldsymbol{C u} \) couple is \( \mathbf{0 . 3 4} \mathrm{V} \) at \( \mathbf{2 5}^{\mathbf{0}} \mathrm{C} \)
Calculate the reduction potential at
\( \boldsymbol{p} \boldsymbol{H}=\mathbf{1 4} \) for this couple.
\( \operatorname{Given} \boldsymbol{K}_{s p} \) of \( \boldsymbol{C u}(\boldsymbol{O H})_{2}=\mathbf{1 . 0} \times \mathbf{1 0}^{-\mathbf{1 8}} \mathbf{)} \)


The hybridization of \( X e \) -atom in \( X e O_{6}^{4-} \) is same with:
This question has multiple correct options
A \( \cdot x e \) in \( X e F_{6} \)
B. Te in \( T e O_{6}^{6} \)
\( \mathbf{c} \cdot \operatorname{Pin} P F_{6}^{-} \)
\( \mathbf{D} \cdot \sin S i F_{6}^{2} \)


The main cause of water depletion is
A. Over-pumping groundwater
B. Water Pollution
C. Global warming
D. None of the above


Which among the following statements is incorrect with regards to the features of population in India?
A. Birth rate per thousand is 20.97 as per Census 2011
B. According to Census 2011, the death rate per thousand stands at 7.48
C. As per Census 2011 , there are 940 females for every 1000 males
D. The density of population in India is 297 people per square kilometre


For an ideal solution, the correct option
is :
A \( \cdot \Delta_{\operatorname{mix}} S=0 \) at constant T and \( \mathrm{P} \)
B. \( \Delta_{\operatorname{mix}} V \neq 0 \) at correct T and P
C. \( \Delta_{\operatorname{mix}} H=0 \) at constant \( \mathrm{T} \) and \( \mathrm{P} \)
D. \( \Delta_{\text {mix}} G=0 \) at constant T and \( P \)


Evaluate \( -\mathbf{3 5}+\boldsymbol{x}=\mathbf{3 9} \)


\( R \) is a relation defined in \( R \times T \) by \( (a, b) R(c, d) \) iff \( a-c \) is an integer and
\( b=d . \) The relation \( R \) is
A. an identity relation
B. an universal relation
c. an equivalence relation
D. None of these


Matter has both
A. mass, volume
B. mass, weight
C. life, particle
D. None of the above


An investigator interviewed 100
students to determine their preferences for the three drinks milk coffee and tea.
He reported the following, 10 students had all the three drinks, 20 had milk
and coffee, 30 had coffee and tea \( , 25 \)
had milk and tea, 12 had milk only. 5
had coffee only, 8 had tea only. The
number of students that did not take
any of the three drinks is.


\( 420 J \) of energy supplied to \( 10 g m \) of water will raise its temperature by
\( \mathbf{A} \cdot 1^{\circ} C \)
в. \( 4.2^{\circ} \mathrm{C} \)
\( \mathrm{c} \cdot 10^{\circ} \mathrm{C} \)
D. \( 42^{\circ} \mathrm{C} \)


Given name for the following substituted alkanes:


For which colour is the fringe width minimum?
A . violet
B. red
c. green
D. yellow


A first-order reaction which is \( 30 \% \)
complete in 30 minutes has a half-life period of:
A .24 .2 min
B. 58.2 min
c. 102.2 min
D. 120.2 min


A block of mass \( m \) slides down an
inclined plane of slope angle \( \theta \) with constant velocity. Now, same block is
projected up an inclined plane with an
initial velocity \( u \). If the coefficient of
kinetic friction between the block and
the plane is \( \mu, \) the distance up to which the block will rise up the plane, before coming to rest is :-
\( ^{\mathrm{A}} \cdot \frac{u^{2} \mu}{2 g \sin \theta} \)
в. \( \frac{u^{2} \mu}{2 g \cos \theta} \)
c. \( \frac{u^{2}}{4 g \sin \theta} \)
D. \( \frac{u^{2}}{4 g \cos \theta} \)


A ball is thrown horizontally from a point \( 100 \mathrm{m} \) above the ground with a speed of \( 200 \mathrm{m} / \mathrm{s} \). Find (a) the time it takes to reach the ground,
(b) the horizontal distance it travels before
reaching the ground,
(c) the velocity (direction and magnitude) with which it strikes the ground.


\( \lim _{x \rightarrow \frac{\pi}{2}}\left(\lim _{x \rightarrow \infty} \cos \frac{x}{2} \cos \frac{x}{2^{2}} \cos \frac{x}{2^{3}} \ldots \ldots \cos \frac{x}{2^{n}}\right) \)
equals to


Photosynthesis is an oxidationreduction process, the material that gets oxidised is
\( A \cdot C O_{2} \)
B. NADP
\( c \cdot H_{2} 0 \)
D. PGAA


A long solenoid has 200 turns per \( \mathrm{cm} \) and carries a current \( i . \) The magnetic
field at its centre is \( 6.28 \times \) \( 10^{-2} W b m^{-2} . \) Another solenoid has 100
turns per \( c m \) and it carries a current \( \frac{i}{3} \) The value of the magnetic field at its
centre :
A . \( 1.05 \times 10^{-4} \mathrm{Wbm}^{-2} \)
B. \( 1.05 \times 10^{-2} \mathrm{Wbm}^{-2} \)
c. \( 1.05 \times 10^{-5} \mathrm{Wbm}^{-2} \)
D. \( 1.05 \times 10^{-3} \mathrm{Wbm}^{-2} \)


Root pressure does not take an active part in the ascent of sap because
A. It is not found in all the plants and water can rise in the absence of root
B. It is seen during most favourable periods like spring or rainy season.
c. It is never found to exist in the plants
D. Both A and B


Determine the nature of roots of the
following quadratic equation:
\( 2 x^{2}+5 x+5=0 \)


When does a moving charged particle
not experience any force while moving through a uniform magnetic field?


\( \int \frac{\log (x+1)-\log x}{x(x+1)} d x \) equals


A screw factory has two machines, the
M1, which is old, and does \( 75 \% \) of all the
screws, and the M2, newer but small,
that does \( 25 \% \) of the screws. The \( \mathrm{M} \)
does \( 4 \% \) of defective screws, while the
M2 just does \( 2 \% \) of defective screws. If we choose a screw at random: what is
the probability that it turns out to be
defective?
A. 0.035
в. 0.045
c. 0.015
D. None of these


Which of these belong to cartilaginous
fish?
\( A \)
\( A \)
B. B
\( c \cdot c \)
\( D \)


The value of \( K_{c} \) for the reaction \( \boldsymbol{A}+ \) \( B \leftrightharpoons C+D \) was found to be 0.0997 at a
certain temperature. If the initial
concentrations of \( A \) and \( B \) are both \( 1 M \)
What are the equilibrium concentrations of \( \boldsymbol{A}, \boldsymbol{B}, \boldsymbol{C} \) and \( \boldsymbol{D} \) ?


Which of the following electrons have little influence on the properties of elements?
A . outer electrons
B. electrons have no influence on properties of elements
c. inner electrons
D. Both A and C


Vitamin D is also known as:
A. growth vitamin
B. sunshine vitamin
c. reproductive vitamin
D. ascorbic acid


Two wires of same material and length
but cross-sections in the ratio 1: 2 are
used to suspend the same loads. The extensions in them will be in the ratio
A .1: 2
B . 2: 1
c. 4: 1
D. 1: 4


\( \sqrt{\mu_{0} \epsilon_{0}} \) has the dimensions
\( \mathbf{A} \cdot\left[M^{0} L T^{-1}\right] \)
В . \( \left[M^{0} L^{-1} T\right] \)
\( \mathbf{c} \cdot\left[M^{2} L^{3} T^{-1}\right] \)
D \cdot \( \left[M^{-1} L^{3} T^{-2}\right] \)