When \( x \geq 2, \) then function \( f(x)= \)
\( \mathbf{2}|\boldsymbol{x}-\mathbf{2}|-|\boldsymbol{x}+\mathbf{1}|+\boldsymbol{x} \) is reduced to
A. \( f(x)=-2 x+3 \)
в. \( f(x)=2 x-5 \)
\( \mathbf{c} \cdot f(x)=5 \)
D. \( f(x)=-1 \)
E. \( f(x)=2 x+4 \)


If \( \boldsymbol{f}(\boldsymbol{x})=\mathbf{3} \boldsymbol{x}-\boldsymbol{2} \) and \( \boldsymbol{g}(\boldsymbol{x})=\frac{\boldsymbol{x}+\mathbf{1}}{\mathbf{2}} \)
then \( \boldsymbol{g} \boldsymbol{o} \boldsymbol{f}(\boldsymbol{3})= \)


Find the sum of 70 terms of A.P
\( 7,9,11, \dots \)


The ether when treated with \( H I \)
produces:
A. alcohol + alkyl iodide
B. alkyl iodide only
c. alcohol only
D. one hydrogen in ether is substituted by iodide


The height of water level in a tank is \( \boldsymbol{H} \)
The range of water stream coming out of a hole at depth \( \frac{\boldsymbol{H}}{\mathbf{4}} \) from upper water level will be.
A. \( \frac{\sqrt{3} H}{2} \)
в. \( \frac{2 H}{\sqrt{3}} \)
c. \( \frac{H}{\sqrt{3}} \)
D. \( \sqrt{3} H \)


Which of the following is a true
statement:
A. The ionisation constant and ionic product of water are same.
B. Water is a strong electrolyte.
C. The value of ionic product of water is less than that of its ionisation constant
D. At \( 298 K \), the number of \( H^{+} \) ions in a litre of water is \( 6.023 \times 10^{16} \)


Buffer solution \( A \) of a weak monoprotic
acid and its sodium salt in the
concentration ratio \( \boldsymbol{x}: \boldsymbol{y} \) has \( \boldsymbol{p} \boldsymbol{H}= \)
\( (p H)_{1} . \) Buffer solution \( B \) of the same
acid and its sodium salt in the
concentration ratio \( \boldsymbol{y}: \boldsymbol{x} \) has \( \boldsymbol{p} \boldsymbol{H}= \)
\( (p H)_{2} . \) If \( (p H)_{2}-(p H)_{1}=1 \) unit and
\( (p H)_{1}+(p H)_{2}=9.5 \) units, then:
This question has multiple correct options
\( \mathbf{A} \cdot p K_{a}=4.75 \)
В. \( \frac{x}{y}=2.36 \)
c. \( \frac{x}{y}=3.162 \)
D \cdot \( p K_{a}=5.25 \)


Match the items of Column I with
suitable items in Column II


The amount of oxygen used by microorganisms present in water for
five days at \( 20^{\circ} \mathrm{C} \) is called :
A. \( \operatorname{cod} \)
B. DO
c. TLV
D. BOD


Arrange the following compounds in the increasing order of their boiling points.
\( \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{H} \boldsymbol{O}, \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{H} \)
\( \boldsymbol{O}-\boldsymbol{C}_{2} \boldsymbol{H}_{5}, \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{C}_{2} \boldsymbol{H}_{5} \)
A \( \cdot C H_{3} C H_{2} C H_{2} C H_{2} C H_{3}<H_{5} C_{2}-O-C_{2} H_{5}< \)
\( C H_{3} C H_{2} C H_{2} C H O<C H_{3} C H_{2} C H_{2} C H_{2} O H \)
в. \( C H_{3} C H_{2} C H_{2} C H_{2} C H_{3}>H_{5} C_{2}-O-C_{2} H_{5}> \)
\( C H_{3} C H_{2} C H_{2} C H O<C H_{3} C H_{2} C H_{2} C H_{2} O H \)
c. \( C H_{3} C H_{2} C H_{2} C H_{2} C H_{3}<H_{5} C_{2}-O-C_{2} H_{5}< \)
\( C H_{3} C H_{2} C H_{2} C H O>C H_{3} C H_{2} C H_{2} C H_{2} O H \)
D. \( C H_{3} C H_{2} C H_{2} C H_{2} C H_{3}>H_{5} C_{2}-O-C_{2} H_{5}< \)
\( C H_{3} C H_{2} C H_{2} C H O>C H_{3} C H_{2} C H_{2} C H_{2} O H \)


A spring \( \left(k=100 N m^{-1}\right) \) is suspended
in vertical position having one end fixed at top \( \& \) other end joined with a \( 2 \mathrm{kg} \) block. When the spring is in non deformed shape, the block is given initial velocity \( 2 \mathrm{m} / \mathrm{s} \) in downward direction. The maximum elongation of the spring is \( \left(\frac{\sqrt{3}+1}{n}\right) \) meter. Find \( n \)


The ratio between the difference
between the highest and the lowest of
the surplus countries to the difference
between Bangladesh and Oman is?
A. 3.44
B. 2.96
\( c \cdot 4.5 \)
D. 3.83


Which of the following does not contain nitrogen?
A. Proteins in plants and animals
B. Members of apatite family
C. Indian saltpetre
D. Chile saltpetre


One litre of a samle of hard water
contains \( 1 \mathrm{mg} \) of \( \mathrm{CaCl}_{2} \) and \( 1 \mathrm{mg} \) of
\( M g C l_{2} \). Then the total hardness in
terms of parts of \( C a C O_{3} \) per \( 10^{8} \) parts
of water by mass is:
A. \( 1.954 \mathrm{ppm} \)
B. 1.260
c. 0.946
D. none of these


The sum of first \( n \) terms of an G.P. is
A \( \cdot s_{n}=\frac{a_{1}\left(1-r^{n}\right)}{1-r} \)
B. \( s_{n}=\frac{a_{1}\left(1+r^{n}\right)}{1-r} \)
\( ^{\mathbf{c}} \cdot_{S_{n}}=\frac{a_{1}\left(1-r^{n}\right)}{1+r} \)
D. \( _{S_{n}}=\frac{a_{1}\left(1-r^{n}\right)}{r-1} \)


How many number of faces are there in
\( P_{4} \) molecule?


Write down the chemical equations for
metallurgical process to represent Roasting of galena (PbS)
Chemical equation:
\( 2 P b S+3 O_{2} \rightarrow 2 P b O+2 S O_{2} \)
\( \boldsymbol{P b S}+\mathbf{2 O}_{2} \rightarrow \boldsymbol{P b S O}_{4} \)
If true enter 1 else 0
\( A \)


A radioactive isotope has a \( t_{1 / 2} \) of 10
days. If today there is \( 125 g \) of it left then its weight 40 days earlier is
A . 6009
в. \( 1000 g \)
c. \( 1250 g \)
D. 2000g


Identify the true statements(s).
This question has multiple correct options
A. The electron density in the xy plane in \( 3 d_{y z} \) orbital is
zero
B. The electron densities in the xy and xz planes in \( 3 d_{y z} \)
orbital are zero
C. Paulis principle states that the total wave function of two identical fermions is anti-symmetric with respect to exchange of particles
D. Paulis principle is not obeyed by bosons


The decay constant of a radio active
element, which disintegrates to \( 10 g \) ms
from \( 20 g m s \) in 10 minutes is :
A .0 .00693 min\( ^{-1} \)
B. 6.93 min \( ^{-1} \)
c. 0.693 min \( ^{-1} \)
D. 0.0693 min \( ^{-1} \)


Which of the following is a mineralocorticoid?
A. Testosterone
B. Progesterone
c. Adrenaline
D. Aldosterone


What is total internal reflection?


Assertion
When fluids flow, there is some loss of
energy due to friction.
Reason
Different layers of the fluid exert forces
on each other.
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


\( \int(a x+b)^{2} d x \)


\( \boldsymbol{C H}_{3}-\boldsymbol{C} \equiv \boldsymbol{C H}+\boldsymbol{H}_{2} \boldsymbol{O} \frac{\boldsymbol{H} \boldsymbol{g} \boldsymbol{S O}_{4}}{\boldsymbol{H}_{2} \boldsymbol{S O}_{4}}(\boldsymbol{A}) \)
The product \( A \) in above reaction is:
A. propanal
B. propanone
c. propene
D. both (a) and (b)


In dicot stem, xylem is
A. Polyarch
B. Endarch
c. Exarch
D. Mesarch


Evaluate in standard form: \( \frac{(2-3 i)}{(2-2 i)} \)
where \( i^{2}=-1 \)
A \( \cdot \frac{5}{4}-\frac{i}{4} \)
в. \( \frac{5}{4}+\frac{i}{4} \)
c. \( -\frac{5}{4}-\frac{i}{4} \)
D. \( -\frac{5}{4}+\frac{i}{4} \)


Kidney stone is produced due to
A. Deposition of sand particles
B. Precipitation of proteins
C . Crystallisation of oxalates
D. Blockage of fat


In the given circuit find out :
(i) maximum value of current in the
circuit,
(ii) root mean square value of current in
the circuit,


The number of occupied subshell in
\( C r^{3+} \) ions is:
\( A \cdot 3 \)
B. 4
\( c \cdot 5 \)
D. 6


A geo-stationary satellite is orbiting around earth at height of \( 30,000 \mathrm{km} \) in circular orbit. The radius of the earth is
taken as \( 6000 \mathrm{km} . \) The geo-stationary satellite comes back to its position
after one revolution in exactly 24 hours.
Let the acceleration due to gravity \( (g) \) \( 10 m / s^{2} \) and mass of satellite be 1000
kg; calculate the work done in 12 hours when moving under gravitational force.
A \( \left..3 .6 \pi \times 10^{14}\right\rfloor \)
В \( \cdot 2 \pi \times 7.2 \pi \times 10^{14} \)
C \( .1 .8 \pi \times 10^{14} \mathrm{J} \)
D. 0


\( \sec ^{2}\left(\tan ^{-1} 2\right)+\operatorname{cosec}^{2}\left(\cot ^{-1} 3\right) \)


Q Type your question-
Given \( : \boldsymbol{E}_{\boldsymbol{L i} \oplus \mid \boldsymbol{L} i}^{\ominus}=-\mathbf{3 . 0 5} \boldsymbol{V} \)
\[
\begin{array}{l}
\boldsymbol{E}_{N a \oplus \mid N a}^{\ominus}=-2.71 V \\
\boldsymbol{E}_{\boldsymbol{K}^{\oplus} \mid \boldsymbol{K}}^{\ominus}=-\mathbf{2 . 9 3} \boldsymbol{V}
\end{array}
\]
Alkali metals react with water
according to the following reaction \( (\mathrm{M}= \) Alkali metals):
\[
\mathbf{2} \boldsymbol{M}+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \mathbf{2} \boldsymbol{M} \boldsymbol{O} \boldsymbol{H}+\boldsymbol{H}_{2}
\]
It is found that Li reacts gently with
water, whereas K reacts violenly with
water.
Statements
\( \Delta G \) values have nothing to do with kinetics of the reaction.
The metal having large standard oxidation potential will have lesseer reactivity

Potassium (K) has low melting point and heat of reaction which is sufficient to make it melt or even vapourize. This leads to expotential increase in its surface area.
The ionization potential of \( K \) is
d. smaller than that of Li.


Three badies \( A, B \) and \( C \) having masses \( 10 k g, 5 k g \) and \( 15 k g \) representively are projected from top of a tower with \( A \) vertically upwards with
\( \mathbf{1 0} \boldsymbol{m} / \boldsymbol{s}, \boldsymbol{B} \) with \( \mathbf{2 0} \boldsymbol{m} / \boldsymbol{s} \mathbf{5 3}^{\boldsymbol{o}} \) above east
horizontal and \( C \) horizontally southward
with \( 15 ~ m / s . \) Find
(a) Velocity of centre of mass of the
systrem.


Which property is shown by the alkali
sodium hydroxide?
A. It has a pH less than pH 7
B. It produces a gas when it is warmed with ammonium chloride
C. It turns blue litmus red
D. It turns Universal Indicator green


If \( \theta \) is in the first quadrant and \( \cos \theta= \)
\( \frac{3}{5}, \) then the value of \( \frac{5 \tan \theta-4 \operatorname{cosec} \theta}{5 \sec \theta-4 \cot \theta} \) is
A \( \cdot \frac{5}{34} \)
в. \( \frac{5}{16} \)
c. \( \frac{5}{-34} \)
D. \( \frac{-5}{16} \)


Match the terms listed with the
structures where they occur. Choose the
answer, which gives the correct
combination of alphabets of the two
columns.
\( \begin{array}{ll}\text { Structure } & \text { Occurrence } \\ \text { A. Haversian canal } & \text { p. Kidney } \\ \text { B. Dendrites } & \text { q. Cartilage } \\ \text { C. Sarcolemma } & \text { r. Muscle } \\ \text { D. Chondrocytes } & \text { s. Nerve cells } \\ & \text { t. Bone }\end{array} \)
\( A \)
\( A-q, B-r, C-s, D-t \)
c. \( A-t, B-s, C-r, D-q \)
D. A-s.B-t. C- a \( D- \)


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


\( x \)
\( x \)
0
\( w \)


The major organic product in the reaction:
\( \boldsymbol{C H}_{3}-\boldsymbol{O}-\boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right)_{2}+\boldsymbol{H I} \rightarrow \)
Product is:
A \( \cdot C H_{3} O H+\left(C H_{3}\right) C H I \)
в. \( \operatorname{ICH}_{2} \mathrm{OCH}\left(\mathrm{CH}_{3}\right)_{2} \)
\( ^{\mathrm{c}} \cdot_{C H_{3}} O C\left(C H_{3}\right)_{2} \)
D. \( \left.C H 3_{3} I+\left(C H_{3}\right)_{2}\right) C H O H \)


If \( \boldsymbol{z}(\mathbf{2}-\boldsymbol{i})=\mathbf{3}+\boldsymbol{i}, \quad \boldsymbol{z}^{20}= \)
A. \( 1-i \)
B. -1024
\( c \cdot 1024 \)
D. \( 1+i \)


\( \triangle-C O O H \stackrel{H B r}{\rightarrow} ? \)
Which of the following is the major product?
\( \mathbf{A} \cdot H_{3} C-C H_{2}-\underset{B r}{C} H-C H_{3} \)
в. \( B r-C H_{2}-C H_{2}-C H_{2} C O O H \)
c. \( H_{3} C-C H-C H_{2}-B r \)
Coot
D. \( H_{3} C-C_{\text {। }} H-C H_{2} \) COCH


The potential energy of a conservative
system is given by \( V(x)=\left(x^{2}-3 x\right) \)
joule where \( x \) is measured in metre. Then its equilibrium position is at
A . \( 1.5 \mathrm{m} \)
B. 2 \( m \)
\( c \cdot 3 m \)
\( D \cdot 1 \mathrm{m} \)
E. 5 m


The phase common in aerobic and anaerobic respiration is
A. Krebs cycle
B. Glycolysis
c. Glycogenolysis
D. ETC


f \( a=x(y-z), b=y(z-x) \) and \( c= \)
\( z(x-y) . \) What is the value of
\( \frac{x y z}{a b c}\left(\frac{a^{3}}{x^{3}}+\frac{b^{3}}{y^{3}}+\frac{c^{3}}{z^{3}}\right) ? \)


\( \int \frac{x d x}{(x-1)(x-2)} \) equals
\( ^{\mathbf{A}} \cdot \log \left|\frac{(x-1)^{2}}{x-2}\right|+C \)
\( ^{\mathbf{B}} \cdot \log \left|\frac{(x-2)^{2}}{x-1}\right|+C \)
\( ^{\mathrm{c}} \log \left(\left(\frac{x-1}{x-2}\right)^{2} \mid+C\right. \)
D. \( \log |(x-1)(x-2)|+C \)


Explain why interhalogen compounds are more reactive than their constituent
elements?


The hydrogen bond is absent in:
A \( . H_{2} O \)
в. \( H F \)
c. \( N H_{3} \)
D. Ge


Prove the assertions of the following
problems Prove that the expression \( n^{3}-n \) is
divisible by 24 for any odd \( n \)


Find the mean and variance for the data
6,7,10,12,13,4,8,12


Write the following equation in ionic form:
a) \( M n O_{2}+4 H C l \rightarrow M n C l_{2}+ \)
\( \mathbf{2} \boldsymbol{H}_{\mathbf{2}} \boldsymbol{O}+\boldsymbol{C} \boldsymbol{l}_{\mathbf{2}} \)
b) \( 2 N a H C O_{3}+H_{2} S O_{4} \rightarrow \)
\( N a_{2} S O_{4}+H_{2} O+C O_{2} \)
A \( \cdot \) a) \( M n O_{2}+4 H^{+}+4 C l^{-} \rightarrow M n^{2+}+2 C l^{-}+2 H_{2} O+ \)
\( C l_{2} \)
b) \( 2 N a^{+}+2 H C O_{3}^{-}+2 H^{+}+S O_{4}^{2-} \rightarrow 2 N a^{+}+ \)
\( S O_{4}^{2-}+2 H_{2} O+C O_{2} \)
B. a) \( 2 M n O_{2}+8 H^{+}+4 C l^{-} \rightarrow 2 M n^{2+}+2 C l^{-}+ \)
\( 4 H_{2} O+C l_{2} \)
b) \( 2 N a^{+}+2 H C O_{3}^{-}+2 H^{+}+S O_{4}^{2-} \rightarrow 2 N a^{+}+ \)
\( S O_{4}^{2-}+2 H_{2} O+C O_{2} \)
c. a) \( M n O_{2}+4 H^{+}+3 C l^{-} \rightarrow M n^{2+}+C l^{-}+2 H_{2} O+ \)
\( C l_{2} \)
b) \( 2 N a^{+}+2 H C O_{3}^{-}+2 H^{+}+S O_{4}^{2-} \rightarrow 2 N a^{+}+ \)
\( S O_{4}^{2-}+2 H_{2} O+C O_{2} \)
D. None of these


Core of electromagnets are made of ferromagnetic materials which have.
A. Low permeability and low retentivity
B. High permeability and high retentivity
c. High permeability and low retentivity
D. Low permeability and high retentivity


The vascular layer of the eye is
A. Choroid
B. Sclera
c. cornea
D. Retina


An ecosystem resists change because it is in a state of
A. Imbalance
B. Homeostasis
c. shortage of components
D. Deficiency of light


A convex lens forms a real image of a point object placed on its principal axis. If the upper half of the lens is painted black
(i) The image will be shifted downward
\( (i i) \) The image will be shifted upward
\( (i i i) \) The image will not be shifted
\( (i v) \) The intensity of the image will decrease
A. (i) and ( \( (i) \) )
B. (ii) and (iii)
c. \( (i i i) \) and \( (i v) \)
D. only \( (i v) \)


\( \sin ^{-1} x+\sin ^{-1} \frac{1}{x}+\cos ^{-1} x+ \)
\( \cos ^{-1} \frac{1}{x}= \)
A . \( \pi \)
в.
c. \( \frac{3 \pi}{2} \)
D. None of these


Find the change in the potential energy of the proton in the displacement.
A. \( -6.4 \times 10^{-15} J \)
В. \( 6.4 \times 10^{-15} \mathrm{J} \)
c. \( -6.4 \times 10^{-19} J \)
D. \( 6.4 \times 10^{-19} \mathrm{J} \)


A horse continues to apply a force in
order to move a cart with a constant
speed. This is because:
A. the force applied by the horse balances the gravitational force.
B. the force applied by the horse balances the force of friction
c. Horse does not apply any force
D. None of these


Assertion
Magnesium has two isotopes \( _{12}^{24} M g \) and \( _{12}^{26} M g . \) According to which isotopes of magnesium have different mass
numbers.
Reason
Different mass number of isotopes is due to the difference in neutrons no.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


An insulating rod of length \( l \) carries a charge \( q \) distributed uniformly on it. The rod is pivoted at its mid-point and is rotated at a frequency \( f \) about a fixed axis perpendicular to the rod and passing through the pivot. The magnetic moment of the rod system is
A \( \cdot \frac{1}{12} \pi q f l^{2} \)
В . \( \pi q f l^{2} \)
c. \( \frac{1}{6} \pi q f l^{2} \)
D. \( \frac{1}{3} \pi q f l^{2} \)


Calculate the energy of photon of light
having frequency \( 3 \times 10^{5} \) Hz. If wavelength of light is \( \lambda(0.50 A A), \) then
calculate its energy.


Urotropine is formed by the action of ammonia on:
A. Acetaldehyde
B. Formaldehyde
c. Acetone
D. Pheno


Curved surface area of solid sphere is \( 24 c m^{2} . \) If the sphere is divided into two hemispheres, then the total surface area of one of the hemispheres is :
\( \mathbf{A} \cdot 12 c m^{2} \)
в. \( 8 c m^{2} \)
\( \mathbf{c} \cdot 16 \mathrm{cm}^{2} \)
D. \( 18 \mathrm{cm}^{2} \)


Heat energy transferred in bodies at thermal equilibrium is
A. Very high and positive
B. Very low and positive
c. zero
D. negative


\( A B C \) is an isosceles triangle with
\( A B=A C \) and \( A D \) is one of its altitude
A. State the three pairs of equal parts in \( \triangle A D B \) and \( \triangle A D C \)
B. Is \( \triangle A D B \cong A D C \) ? Why or why not?
c. Is \( \angle B=\angle C \) ? Why or why not?
D. Is \( B D=C D \) ? Why or why not?


An electron moving at right angle to a uniform magnetic field completes a circular orbit in 1 micro - second. Find
the magnetic field.
Ans. \( 3.53 \times 10^{-5} T \)


Nonstoichiometry is shown
A. due to variable valency of transition elements
B. due to to defects in solid structures
C. due to both (a) and (b)
D. due to none of the above


esistance is connected across a uniform
wire of length \( 1 m \). The positive terminal of
another battery of e.m.f. \( 4 V \) and internal
resistance \( 1 \Omega \) is joined to the point \( A \) as
shown in the figure. The ammeter shows
zero deflection when the jockey touches
the wire at the point \( C \)
The length AC is equal to
\( A \cdot 2 / 3 m \)
\( 3.1 / 3 \mathrm{m} \)
\( c \cdot 3 / 5 m \)
12


If a line makes angles \( \frac{\pi}{12}, \frac{5 \pi}{12} \) with \( \boldsymbol{o} \boldsymbol{y}, \boldsymbol{o} \boldsymbol{z} \) respectively where \( \boldsymbol{0}=(\boldsymbol{0}, \boldsymbol{0}, \boldsymbol{0}) \)
then the angle made by that line with ox
is
A \( \cdot 45^{\circ} \)
B. \( 90^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 30^{\circ} \)


In which of the following devices, the eddy current effect is not used?
A. Induction furnace
B. Magnetic breaking in train
c. Electromagnet
D. Electric heater


Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be defined as \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \frac{2 x-3}{4} . \) Find \( f o\left(f^{-1}\right) \)


Amylopectin is a polymer of:
A. \( \beta \) -D-glucose
B. \( \alpha \) -D-glucose
c. \( \beta \) -D-fructose
D. \( \alpha \) -D-fructose


A \( 1 M e V \) proton is sent against a gold
leaf \( (Z=79) . \) Calculate the distance of
closest approach for head-on collision.


Offset occurs in
A. Strawberry
B. Colocasia
c. Pistia
D. chrysanthemumumummnmmen


Two blocks \( A \) and \( B \) of mass \( m \) and \( 2 m \)
respectively are moving towards a massive (mass \( >>2 m \) ) cliff with
velocities \( 2 v \) and \( v \) respectively. The cliff moves with a velocity \( v \). If the
coefficient of restitution of collision at the surface of the cliff is \( e=\frac{1}{2} . \) If the velocity of the block \( B \) just after colliding with the cliff is \( \frac{v}{x}, \) find the
value of \( \boldsymbol{x} \)


In a CRT the acceleration of electrons is
controlled by changing between the cathode and anode.
A. potential difference
B. space
c. temperature
D. none of these


Assertion
The precision of a measurement depends on least count of measuring instrument.
Reason
Smaller the least count greater is number of significant figures in
measurement value
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


In a \( 500 \mathrm{ml} \) capacity vessel \( C O \) and \( C l_{2} \)
are mixed to form \( C O C l_{2} \) at
equilibrium, it contains 0.2 moles of
\( C O C l_{2} \) and 0.1 mole each of \( C O \) and
\( C l_{2} . \) The equilibrium constant \( K_{c} \) for
reaction
\( \boldsymbol{C O}+\boldsymbol{C l}_{2} \leftrightharpoons \boldsymbol{C O C l}_{2}, \) is :
A . 20
B. 15
\( c \cdot 10 \)
D. 5


The device used to measure the
distance and direction of underwater
substances using ultrasonic waves is


Ratio between 2 -carbon and 3 -carbon
intermediate having \( \mathrm{NH}_{2} \) group formed
in photosynthetic oxidation cycle is
A. 2:
B. 1:
\( c \cdot 3: 2 \)
D. 3: 4


Find the median for the following data
shows that distance covered by 200
people to perform their IT project.
\( \begin{array}{ccc}\mathbf{5}- & \mathbf{1 5}- & \mathbf{2 5}- \\ \mathbf{1 5} & \mathbf{2 5} & \mathbf{3 5}\end{array} \) Distance(km)
Number of people 60 40
A. \( 12 \mathrm{km} \)
B. \( 13 \mathrm{km} \)
\( \mathbf{c} .14 \mathrm{km} \)
D. \( 15 \mathrm{km} \)


In a ripple tank,15 full ripples are produced in one second. if the distance between a trough and the next crest is 20 c.Calculate frequency
A . 2 н \( z \)
B. 12 Hz
\( c \cdot 15 \mathrm{Hz} \)
D. 22 Hz


A juggler tosses a ball up in the air with speed \( u \). At the instant it reaches its
maximum height \( \boldsymbol{H}, \) he tosses up a second ball with the same initial speed. The two balls will collide at a height.
A \( \cdot \frac{H}{4} \)
в. \( \frac{H}{2} \)
c. \( \frac{3 H}{4} \)
D. \( \sqrt{\frac{3}{4}} H \)


A man of mass \( m_{1} \) is standing on a
platform of mass \( m_{2} \) kept on a smooth horizontal surface. The man starts
moving on the platform with a velocity
\( v_{r} \) relative to the platform. Find the
recoil velocity of platform.


Equation of chord \( \mathrm{AB} \) of circle \( x^{2}+ \)
\( \boldsymbol{y}^{2}=\boldsymbol{2} \) passing through (2,2) such
that \( \boldsymbol{P B} / \boldsymbol{P A}=\mathbf{3}, \) is given by
A \( . x=3 y \)
В. \( y-2=\sqrt{3}(x-2) \)
c. \( x=y \)
D. none of these


Order and degree of a differential
equation \( \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}=\left\{\boldsymbol{y}+\left(\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}\right)^{2}\right\}^{1 / 4} \) are
A. 4 and 2
B. 1 and 2
\( c \cdot 1 \) and 4
D. 2 and 4


The change in orbital angular
momentum corresponding to an electron transition inside a hydrogen
atom can be:
A \( \frac{h}{4 \pi} \)
в. \( \frac{h}{p i} \)
\( c \cdot \frac{h}{2 \pi} \)
D. \( \frac{h}{8 \pi} \)


For a travelling wave match the
following two columns.


If \( A=\left|\begin{array}{ccc}3 & -1 & 0 \\ -1 & 2 & 3\end{array}\right| \) and \( B=\left|\begin{array}{ccc}-1 & 1 & 2 \\ 0 & 2 & -1\end{array}\right| \)
then find \( \left(A B^{T}\right)^{T} \)
A \( \cdot\left|\begin{array}{cc}2 & -5 \\ 1 & 6\end{array}\right| \)
в. \( \left|\begin{array}{cc}3 & -4 \\ 7 & -6\end{array}\right| \)
с. \( \left|\begin{array}{cc}-4 & 9 \\ -2 & 1\end{array}\right| \)
D \( \cdot\left|\begin{array}{cc}-3 & 8 \\ 4 & 2\end{array}\right| \)


Although each eye perceives a separate image, we do not see everything double because.
A. The inverted image formed by one eye is re-inverted by the other
B. The optic nerve fuses the two images
c. one eye works at one time
D. None of these


Unpolarized light of intensity \( \boldsymbol{I}_{0} \) is incident on surface of a block of a glass
of Brewster's angle. In that case, which one of the following statement is true?
A. transmitted light is partially polarized with intensity \( I_{0} / 2 \)
B. transmitted light is completely polarized with intensity less than \( I_{0} / 2 \)
C . reflected light is partially polarized with intensity \( I_{0} / 2 \)
D. reflected light is completely polarized with intensity less than \( I_{0} / 2 \)


Define the principal focus of a convex lens and that of a concave lens.


The induced emf developed across the
rod must be
A. \( 4.5 \mathrm{V} \) with b at higher potential
B. 1.5 V with a at higher potential
c. 1.5 V with b at higher potential
D. 4.5 V with a at higher potential


The cathode ray particles originates in a discharge tube from the
A. Cathode
B. Anode
c. source of high voltage
D. Residual gas


The national wealth of a country
increases by \( 4 \% \) of its value at the beginning of every year. Find the
national wealth of the country in \( 1985, \) if
was estimated at INR \( 3.125 \times 10^{12} \) in
1983


A driver takes 0.3 s to fully apply the brakes of truck. The truck moving with velocity of \( 54 \mathrm{km} / \mathrm{h} \) stops in \( 20 \mathrm{s} \) with a
deceleration of \( 6 m / s^{2} . \) Find the distance for where the driver must
apply the brakes without collision from the first obstacle?


If the Arithmetic Mean of two numbers
is twice their Geometric Mean, then the ratio of larger number to the smaller
number is
This question has multiple correct options
A. \( 7-4 \sqrt{3}: 1 \)
B. \( 7+4 \sqrt{3}: 1 \)
c. 21: 1
D. 5: 1


In Bohr's model of the hydrogen atom, let \( R, V, T \) and \( E \) represent the radius of the orbit, speed of the electron, time period of revolution of electron and the total energy of the electron respectively. The quantity proportional to the quantum number n is
\( \mathbf{A} \cdot V R \)
в. \( E \)
\( c \)
D. \( T \)


What is the harm from the depletion of
Earth's ozone layer?
A. The average temperature of earth's surface will increase gradually
B. The oxygen content of the atmosphere will decrease
C. Increased amount of Ultra violet radiation will reach earth's surface
D. Sea levels will rise as the polar ice caps will gradually melt


Ten gram of a fairly concentrated solution of cupric sulphate is
electrolysed using 0.01 faraday of electricity. Calculate:
(i) The mass of the resulting solution.
(ii) The number of equivalents of acid or alkali in the solution.


How is co-dominance different from
incomplete dominance and dominance?


a) Draw a graph between spring force
\( \boldsymbol{F}_{s} \) displacement \( \mathbf{x} \) and
(b) Also find an expression for the P.E. of an elastic stretched spring.


Which letter shows the potential energy
of the products?
\( A \cdot A \)
\( B \)
\( c \)
\( D \)
\( E \)


The \( d \) and \( l \) forms of an optically
active compound differ in
A. boiling point
B. melting point
c. specific rotation
D. specific gravity


A uniform vertical field \( E \) is established
between two parallel plates. In this field, a small conducting sphere of mass \( \boldsymbol{M} \)
is suspended from a string of length \( l \). If the sphere is given a charge \( +q \) (statcoulomb) and if lower plate is charged
positively, the period of the simple pendulum is:
A \( .2 \pi \sqrt{l / g} \)
\( ^{\mathrm{B}} \cdot 2 \pi \sqrt{\frac{l}{\left(g+\frac{q E}{m}\right)}} \)
c.
\[
\sqrt[2 \pi]{\frac{l}{\left(g-\frac{q E}{m}\right)}}
\]
\( D \)
\[
\sqrt{\frac{l}{\left(\frac{q E}{m}-g\right)}}
\]


Which one of the following triplet codes, is correctly matched with its specificity for an amino acid in protein synthesis or as 'start' or 'stop' codon?
A . UCG - Start
B. UUU - Stop
c. UGU - Leucine
D. UAC - tyrosine


During the process of digestion, the protein present in food materials are hydrolysed to amino acids. The two enzymes involved in the process are:
Proteins

Enzyme \( \quad(A) \) Polypeptides
Enzyme\( ^{(B)} \) Amino acids
A. Invertase and zymase
B. Amylase and maltase
c. Diastase and lipase
D. Pepsin and trypsin


Common name of sodium chloride is
salt.


A wire of length \( 1 m \) is made into a
circular loop and it carries a current of \( 3.14 A . \) The magnetic dipole moment of the current loop (in \( A m^{2} \) ) is :
\( \mathbf{A} \cdot \mathbf{1} \)
B. 0.5
c. 0.25
D. 0.314


State True or False.
Polystyrene and PVC are thermoplastics


Select the correct IUPAC name for
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right]^{2+} \)
A. Hexammoniacobaltate(II) ion
B. Hexaamminecobaltate(II) ion
c. Hexammoniacobalt(II) ion
D. Hexaamminecobalt(II) ion


How is the arrangement of Mendel's
selected seven characters on four
chromosomes?
A. One in chromosome no. 1,4 in chromosome no. \( 4, \) one in chromosome no. 5 , and one in chromosome no. 7
B. 2 in chromosome no. 1 , 3 in chromosome no. 4 , one in chromosome no. 5 and one in chromosome no. 6
C. 3 in chromosome no. 1,1 in chromosome no. 4,2 in chromosome no. 5 and one in chromosome no. 7
D. 2 in chromosome no. 1,3 in chromosome no. 4,1 in
chromosome no. 5 and 1 in chromosome no. 7


If there is increased in RBC's count in
Ramesh's blood, then he is suffering from which condition?


Find the greatest value of \( x y z \) for
positive value of \( x, y, z \) subject to the
condition \( \boldsymbol{x} \boldsymbol{y}+\boldsymbol{y} \boldsymbol{z}+\boldsymbol{z} \boldsymbol{x}=\mathbf{1 2} \)


Radial symmetry is not found in
A. Hydra
B. Asterias
c. starfish
D. Araneae


Abnormal condition where mammary
gland of man become female like is called as
A. Gynosism
B. Gynochorism
c. Feminization
D. Gynaecomastia


A black body (heat capacity \( =\mathrm{C} \) ) at absolute temperature \( T \) is kept in a surrounding of absolute temperature
T/2. Its rate of cooling is :
\( (\sigma \) is stefan's constant)
\( ^{\mathrm{A}} \cdot \frac{\sigma A}{C}\left(\frac{T}{2}\right)^{4} \)
в. \( \frac{\sigma A T^{4}}{C^{2}} \)
\( ^{\mathrm{c}} \cdot \frac{_{15 \sigma A T^{4}}}{C^{2}} \)
\( ^{\mathrm{D}} \frac{15 \sigma A}{C}\left(\frac{T}{2}\right)^{4} \)


A particle revolving in a circular path completes first one third of the
circumference in \( 2 s, \) while next on third
in \( 1 s . \) Calculate its average velocity.


A very loud sound
A. damages the hair cells of the inner ear
B. damages the outer ear
C . damages the middle ear
D. reflects back from the ear


A double convex lens of glass of
refraction index \( \mu \) is immersed in a
medium of refractive index \( \mu_{1} \). If a
parallel beam emerges undeviated through the lens, then:
A \( \cdot \mu=\mu_{1} \)
в. \( \mu=\frac{1}{\mu_{1}} \)
c. \( \mu>\mu_{1} \)
D . \( \mu<\mu_{1} \)


If 90 g of water is electrolyzed completely with \( 50 \% \) current efficiency.
1) 10 Faraday of electricity will be consumed
2) 20 faraday of electricity will be consumed
3) \( 168 \mathrm{L}(\mathrm{STP}) \) of gases will be produced
4) \( 84 \mathrm{L}(\mathrm{STP}) \) of gases will be produced. Select the correct options.
A .2,3
В. 1,2,3
c. 1,3,4
D. 1,2,3,4


The fuel gas with the highest calorific value among the following is:
A. water gas
B. producer gas
c. carburetted water gas
D. semi water gas


Find the angles of a triangle whose
sides are \( \boldsymbol{x}+\mathbf{2} \boldsymbol{y}-\mathbf{8}=\mathbf{0}, \mathbf{3} \boldsymbol{x}+\boldsymbol{y}- \)
\( \mathbf{1}=\mathbf{0} \) and \( \boldsymbol{x}-\mathbf{3} \boldsymbol{y}+\mathbf{7}=\mathbf{0} \)


The differential equation for the family of curves \( \mathbf{x}^{2}+\mathbf{y}^{2}-\mathbf{2} \mathbf{a y}=\mathbf{0}, \) where \( \boldsymbol{a} \) is
an arbitrary constant is:
A \( \cdot 2\left(\mathrm{x}^{2}-\mathrm{y}^{2}\right) \mathrm{y}^{\prime}=x y \)
B \( \cdot 2\left(\mathrm{x}^{2}+\mathrm{y}^{2}\right) \mathrm{y}^{\prime}=x y \)
C \( \cdot\left(x^{2}-y^{2}\right) y^{\prime}=2 x y \)
D. \( \left(x^{2}+y^{2}\right) y^{\prime}=2 x y \)


Rational numbers are commutative
under
A. subtraction
B. multiplication
c. division
D. none of these


Find the equation of the set of points \( P \) the sum of whose distances from
\( \boldsymbol{A}(\mathbf{4}, \mathbf{0}, \mathbf{0}) \) and \( \boldsymbol{B}(-\mathbf{4}, \mathbf{0}, \mathbf{0}) \) is equal to
10


Find graphically, the maximum value of \( z=2 x+5 y, \) subject to constraints
given below:
\( 2 x+4 y \leq 8 \)
\( \mathbf{3} \boldsymbol{x}+\boldsymbol{y} \leq \mathbf{6} \)
\( \boldsymbol{x}+\boldsymbol{y} \leq \mathbf{4} \)
\( \boldsymbol{x} \geq \mathbf{0}, \boldsymbol{y} \leq \mathbf{0 . 6} \)


If the standard deviation of the numbers
\( -1,0,1, k \) is \( \sqrt{5} \) where \( k>0, \) then \( k \) is
equal to?
A \( \cdot 2 \sqrt{\frac{10}{3}} \)
в. \( 2 \sqrt{6} \)
c. \( 4 \sqrt{\frac{5}{3}} \)
D. \( \sqrt{6} \)


\( \int a^{m x} b^{n x} d x \)


toppr
Q Type your question
the \( x- \) coordinate.
\( A \)
B.
\( c \)
\( D \)
\( E \)


The number of 5 digit telephone numbers having least one of their digits repeated is
A .90,000
в. 100,000
c. 30,240
D. 69,760


\( \boldsymbol{H}_{2} \boldsymbol{O}_{(g)} \rightarrow \boldsymbol{H}_{(g)}+\boldsymbol{O H}_{(g)}: \boldsymbol{\Delta} \boldsymbol{H}_{1}=\boldsymbol{x}_{1} \)
\( \boldsymbol{O H}_{(g)} \rightarrow \boldsymbol{H}_{(g)}+\boldsymbol{O}_{(g)}: \boldsymbol{\Delta} \boldsymbol{H}_{2}=\boldsymbol{x}_{2} \)
Based on the above given data, determine the bond energy (BE) of \( \boldsymbol{O}- \)
\( \boldsymbol{H} \) bond :
A \( \cdot \frac{x_{1}+x_{2}}{2} \)
в. \( x_{1}+x_{2} \)
c. \( \frac{x_{1}-x_{2}}{2} \)
D. \( x_{1}-x_{2} \)


Cards marked with the numbers 2 to
101 are put in a box and mixed thoroughly. One card is drawn from this box. Find the probability that the number on the card is less than 14
A \( \cdot \frac{3}{27} \)
в. \( \frac{3}{29} \)
\( c \cdot \frac{3}{25} \)
D. \( \frac{3}{22} \)


Define magnifying power of a microscope in terms of visual angle.


Assertion
Simple distillation can help in separating a mixture of propan-1-ol
(boiling point 97 ) and propanone (boiling point \( 56) \)
Reason
Liquids with a difference of more than
\( 20^{0} C \) in their boiling points can be separated by simple distillation.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A raindrop falls near the surface of the earth with almost uniform velocity because:
A. its weight is negligible.
B. the force of surface tension balances its weight
c. the force of viscosity of air balances its weight.
D. the drops are charged and atmospheric electric field balances its weight


In carboxylate ion \( \left(C O O^{-}\right), \) both \( C-O \)
bond lengths are equal while in carboxyl \( \operatorname{group}(-C O O H), \) both \( C-O \) bond
lengths are different, why?


Identify the relation between molecular mass and boiling point in aldehydes and ketones.


Distinguish between the following pairs of compounds using the test given within brackets:

Ethane and ethene (using alkaline permanganate solution)


Which one of the following reacts with
conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} ? \)
A . Au
B. Agg
\( c \cdot P t \)
D. All


The IUPAC name of the compound is:
A. Chloromethylbenzene
B. Chlorophenylmethane
C. (a) and (b) both
D. none of these


If \( \quad A=\left(\begin{array}{ll}1 & 3 \\ 4 & 5\end{array}\right) \) then \( A^{-1} \) equals
\( ^{\mathrm{A}} \cdot \frac{1}{7}(A+6 I) \)
в. \( \frac{1}{7}(A-6 I) \)
c. \( \frac{1}{7}(6 I-A) \)
D. None of these


Evaluate \( : \int_{0}^{1} e^{2-3 x} d x \)
\( \mathbf{A} \cdot e^{2}-e \)
B. \( \frac{1}{3}\left(e^{2}-e\right) \)
c. \( \frac{1}{3}\left(e^{2}-\frac{1}{e}\right) \)
D. \( \frac{1}{2}\left(e^{2}-\frac{1}{e}\right) \)


In the figure, there are shown sectors of
two concentric circles of radii \( 7 \mathrm{cm} \) and
\( 3.5 \mathrm{cm} . \) Find the area of the shaded region. \( \left(\boldsymbol{U} \boldsymbol{s e} \boldsymbol{\pi}=\frac{\boldsymbol{2} \boldsymbol{2}}{\boldsymbol{7}}\right) \)
A. 10.425 sq. \( \mathrm{cm} \)
B. 10.125 sq. \( \mathrm{cm} \)
c. 9.625 sq. \( \mathrm{cm} \)
D. 9.152 sq. \( \mathrm{cm} \)


Which one of the following molecule is planar?
A. \( N F_{3} \)
в. \( N C l_{3} \)
c. \( P H_{3} \)
D. \( B F_{3} \)


The value of \( \sin ^{-1}\left(\cos \frac{33 \pi}{5}\right) \) is
A \( \cdot \frac{3 \pi}{5} \)
в. \( \frac{7 \pi}{5} \)
c. \( \frac{\pi}{10} \)
D. \( -\frac{\pi}{10} \)


Which of the following is a property of a Light Emitting Diode (LED)?
A. Low Threshold Voltage and High Reverse Breakdown Voltage
B. High Threshold Voltage and High Reverse Breakdown voltage
c. High Threshold Voltage and Low Reverse Breakdown Voltage
D. Low Threshold Voltage and Low Reverse Breakdown voltage


Evaluate: \( \lim _{x \rightarrow 2} \frac{x^{2}+5}{x^{2}-3} \)


What is the color of \( \boldsymbol{P C l}_{3} \) ?
A. White
B. Colorless
c. Brown
D. Bright yellow


A force acts on a \( 20 g \) particle in such a
way that the position of the particle as a function of time is given by \( \boldsymbol{x}=\mathbf{3} \boldsymbol{t}- \)
\( 4 t^{2}+t^{3}, \) where \( x \) is in meters and \( t \) is in
seconds. The work done during the first \( 4 \sec \) is:
A . \( -1.6 .5 \)
в. \( -1600 J \)
c. 2.6 .5
D. \( 1600 J \)


Give two example of water-soluble vitamins.


Suppose an orbital may accommodate three electrons then the number of
elements in 4 th period will be?
A \( \cdot 12 \)
B. 27
\( c \cdot 18 \)
D. 32


An electron is accelerated through a
potential difference of \( 200 V . \) If e / m for the electron be \( 1.6 \times 10^{11} \) coulomb \( k g^{-1} \)
then the velocity acquired by the electron will be
\( \mathbf{A} \cdot 8 \times 10^{6} m s^{-1} \)
В. \( 8 \times 10^{5} \mathrm{ms}^{-1} \)
C . \( 5.9 \times 10^{6} \mathrm{ms}^{-1} \)
D. \( 5.9 \times 10^{5} \mathrm{ms}^{-1} \)


Factorise the expression: \( (x-2 y+ \)
\( 3 z)^{2} \)
\( \mathbf{A} \cdot x^{2}+y^{2}+9 z^{2}-4 x y+12 y z+6 z x \)
B . \( x^{2}+y^{2}+9 z^{2}-4 y-12 y z+6 z x \)
\( \mathbf{c} \cdot x^{2}+4 y^{2}+9 z^{2}-4 x y-12 y z+5 z x \)
D. \( x^{2}+4 y^{2}+9 z^{2}-4 x y-12 y z+6 z x \)


A capacitor has a capacitance of
\( 7.28 \mu F . \) What amount of charge in \( (\mu C \) must be placed on the plates to make the potential difference between its
plates equal to \( 25.0 \mathrm{V} ? \)


In a cathode ray tube, why is the
filament made of tungsten?


Two dice are thrown simultaneously.
The probability of getting a multiple of 2 on one die and a multiple of 3 on the other is
A \( \cdot \frac{5}{36} \)
в. \( \frac{5}{12} \)
c. \( \frac{11}{36} \)
D. \( \frac{1}{12} \)


Construct a quadrilateral ABCD in which \( A B=3.8 \mathrm{cm}, \mathrm{BC}=3.4 \mathrm{cm}, \mathrm{CD}=4.5 \)
\( \mathrm{cm}, \mathrm{AD}=5 \mathrm{cm} \) and \( \angle \mathrm{B}=80^{\circ} \)


If \( M=\{b, h, i\} ; N=\{b, c, d, e\} \) and
\( \boldsymbol{S}=\{\boldsymbol{e}, \boldsymbol{f}, \boldsymbol{g}\}, \) determine \( \boldsymbol{M} \cap \boldsymbol{N} \cap \boldsymbol{S} \)
and represent it in a Venn diagram.


According to Bohr's model, the minimum energy (in eV) required to remove an electron from the ground state of doubly ionised Li atom \( (z=3) \) is
A . 40.8
B. 13.6
c. 122.4
D. 1.5


The cartesian equation of the plane \( \overline{\boldsymbol{r}}=(\mathbf{1}+\boldsymbol{s}-\boldsymbol{t}) \hat{\boldsymbol{i}}+(\boldsymbol{2}-\boldsymbol{s}) \hat{\boldsymbol{j}}+ \)
\( (3-2 s+2 t) \hat{k} \)
A. \( 2 x-y=5 \)
B. \( 2 x+z=5 \)
c. \( 2 x+y=5 \)
D. \( 2 x-z=5 \)


(a) Write the name and electronic
configuration of the third element from the top in group 15
(b) Draw the structure of ammonia
molecule.
(c) Why does \( N H_{3} \) act as a Lewis base?
(d) Give equations for the reactions of
dilute and concentrated \( H N O_{3} \) and \( Z n \)


Maximum digestion takes place in which part of cockroach?
A . In crop
B. In gizzard
c. In mesenteron
D. In oesophagous


A body is moving with constant acceleration from \( A \) to \( B \) in a straight line. \( C \) is the mid-point of \( A B . \) If \( u \) and \( v \) are the speeds at \( A \) and \( B \) respectively. The speed at \( C \) is
A \( \cdot \frac{u+v}{2} \)
B. \( \frac{u v}{2} \)
c. \( \sqrt{\frac{u^{2}+v^{2}}{2}} \)
D. \( \sqrt{\frac{u^{2}-v^{2}}{2}} \)


For natural polymers, PDI is generally
\( \mathbf{A} \cdot \mathbf{0} \)
B.
c. 100
D. 1000


Assertion
\( \boldsymbol{P C l}_{5} \) and \( \boldsymbol{P C l}_{4} \) are thermally unstable
Reason
They produce same gas on thermal
decomposition
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


What is the mass of a positron?
A. Equivalent to the sum of a neutron and an electron
B. Equivalent to a proton
C. Equivalent to a neutron
D. Equivalent to an electron


Area of a rhombus is \( 256 \mathrm{cm}^{2} \). One of
the diagonal is twice of the other diagonal. The sum of the diagonals is:
\( \mathbf{A} \cdot 38 \mathrm{cm} \)
в. \( 48 \mathrm{cm} \)
c. \( 28 \mathrm{cm} \)
D. \( 56 \mathrm{cm} \)


ff \( 4^{x+3}=112+8 \times 4^{x} \); find the value
of \( (18 x)^{3 x} \)


Among \( N a, H g, S, P t \) and graphite, which can be used as electrodes in
electrolytic cells having aqueous solutions?
A. \( H g \) and \( P t \)
в. \( H g, P t \) and graphite
c. \( N a \) and \( S \)
D. \( N a, H g \) and \( S \)


Sulphurous smog is
A. Photochemical smog
B. Oxidising smog
c. classical smog
D. Los Angeles smog


Gold and platinum do not dissolve
either in conc. \( H C l \) or conc. \( H N O_{3} \) but
dissolves in the mixture of 3 parts of
conc. \( H C l \) and 1 part of conc. \( H N O_{3} \)
Give reason and write the necessary chemical equations.


Give few example where displacement
of an object is in the direction opposite
to the force acting on the object \( \left(A S_{1}\right) \)


If true enter 1 , else enter 0 .
The formation of ionic solid from ions of
the elements is an endothermic
process.
A.


Give reasons:
It is possible to enjoy a rainbow at fountains in any season.


A child stands inside a large charged metal sphere. Will her hair stand on
end?
A. Yes
B. No
c. Incomplete information
D. No guess about her hair style


If in a Wheatstone bridge the battery and Galvanometer are interchanged, the condition for balance
A. is disturbed
B. is not disturbed
c. depends on the internal resistance of the bridge
D. depends on the values of the resistances in the bridge


A ray of light is normally incident on one face of an equilateral glass prism. What is the angle of refraction from the
first face of the prism?
A \( .90^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 30^{\circ} \)
D. \( 0^{\circ} \)


Solve : \( \int \frac{1-\cot x}{1+\cot x} d x \)


The sun revolves around galaxy with speed of \( 250 k m / s \) around the center of
milky way and its radius is \( 3 \times 10^{4} \)
light year. The mass of milky way in \( k g \)
is
A \( \cdot 6 \times 10^{4} \)
В \( .5 \times 10^{4} \)
\( c \cdot 4 \times 10^{4} \)
D. \( 3 \times 10^{4} \)


Correct IUPAC name of the given
compound is
A. Anthranilic acid
B. 2-carboxylbenzamine
c. 2-Aminobenzoic acid
D. 2-Aminocarboxylic acid


What is the function of aqueous
humour?
A. Helps in transmitting impulses to the brain
B. Protect the eyeball from collapsing
C. Keeps the cornea moist and give definite shape to the eyeball
D. All


The number of pi bond/s in a benzene
molecule is/are:
A. \( 3 \pi \) bonds
B. \( 6 \pi \) bonds
c. \( 12 \pi \) electrons
D. \( 1 \pi \) bond


If \( C_{\text {diamond }} \longrightarrow C_{\text {graphite }} ; \Delta H=-v e \)
This means:
A. Graphite is more stable form than diamond.
B. Graphite has more energy than diamond.
C . Both are equally stable form.
D. Stability of form cannot be predicted by \( \Delta H \) values.


The marks obtained by the students of
class 6 are shown:
\( \mathbf{0}-\mathbf{1 0} \quad \mathbf{1 0}-\mathbf{2 0} \quad \mathbf{2 0}-\mathbf{3 0} \) \( \mathbf{3 0}-\mathbf{4 0} \)
15
32 55
Find the mean of the data.


If \( \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{9} & \mathbf{- 7} \\ \boldsymbol{i} & \boldsymbol{\omega}^{\boldsymbol{n}} & \mathbf{8} \\ \mathbf{1} & \boldsymbol{6} & \boldsymbol{\omega}^{\mathbf{2 n}}\end{array}\right] \) where \( \boldsymbol{i}=\sqrt{-\mathbf{1}} \)
and \( \omega \) is complex cube root of unity, then \( \operatorname{tr}(A) \) will be
This question has multiple correct options
A. \( 1, \) if \( n=3 k, k \in N \)
B. \( 3, \) if \( n=3 k, k \in N \)
c. \( 0, \) if \( n \neq 3 k, k \epsilon \in N \)
D. \( -1, \) if \( n \neq 3 k, k \epsilon \in N \)


The \( p H \) of pure water at \( 25^{\circ} C \) and \( 60^{\circ} C \)
are 7 and 6.5 respectively. \( H C l \) gas is
passed through water at \( 25^{\circ} C \) till the
resulting 1 litre solution which aquires a \( p H \) of \( 3 . \) Now \( 4 \times 10^{-3} \) mole of \( N a C N \)
are added into this solution. Also a fresh
\( 0.1 M H C N \) solution has \( p H 5.1936 \)
Now in the one part of solution obtained
after addition of \( N a C N \), one milli mole
of \( N a O H \) are added and in the second
part of this solution 0.5 miili mole of
HCl are added.

The dissociation constant of \( \boldsymbol{H} \boldsymbol{C} \boldsymbol{N} \) is:
A \( \cdot 4.1 \times 10^{-10} \)
B . \( 4.1 \times 10^{-6} \)
c. \( 4.1 \times 10^{-3} \)
D . \( 4.1 \times 10^{-8} \)


Given that \( x \) and \( y \) satisfy the relation. \( \boldsymbol{y}=\mathbf{3}[\boldsymbol{x}]+\mathbf{7} \)
\( \boldsymbol{y}=\mathbf{4}[\boldsymbol{x}-\mathbf{3}]+\mathbf{4} \) then find \( [\boldsymbol{x}+\boldsymbol{y}] \)


Identify the finite geometric progression.
A \( .3,6,12,24 . \)
в. \( 81,27,9,3 . \)
c. \( 10-5+2.5-1.25 \dots \)
D. \( 1+0.5+0.25+0.125 \)


Choose the correct option.
A. Testis - posses \( 3-4 \) testicular lobule
B. Seminal vesicle - storage of sperm
c. vas deferens - help in sperm transfer
D. Prostate gland - secretes seminal fluid


Which of the following substance is not a covalent polymer?
A . Silica
B. Diamond
c. Glucose
D. Silicon carbide


A compound microscope has an objective of focal length \( 2 \mathrm{cm} \) and an eye-piece of focal length \( 6.25 \mathrm{cm}, \) which are separated by 15 cm.fr the final image is formed at the least distance of distinct vision \( 25 \mathrm{cm}, \) distance to the object from the objective is
A. \( 20 \mathrm{cm} \)
B. 8.75 cm
\( c .1 .50 \mathrm{cm} \)
D. 2.5 \( \mathrm{cm} \)


Mention the desired properties of
magnetic materials used in making
electromagnets.


The duration of cardiac cycle is
A. \( 0.8 \mathrm{sec} \)
B. \( 0.8 \mu \) sec
c. \( 0.08 \mathrm{sec} \)
D. \( 0.008 \mathrm{sec} \)


What is mean by drift velocity?
current of 0.5 ampere flows in a wire of
radius \( 0.5 m m . \) If the number of free
electrons in the wire be \( 4 \times 10^{28} \) per \( m^{3} \)
calculate their drift velocity.


A capacitor of capacitance \( C_{1} \) charged
at a certain potential v. It is connected
with another uncharged capacitor \( C_{2} \) What is the final p.d. of this new system.
A \( \cdot \frac{C_{2} V}{C_{1} C_{2}} \)
в. \( \frac{C_{1} V}{C_{1} C_{2}} \)
c. \( \left(1+\frac{C_{2}}{C_{1}}\right) \)
D. \( D\left(1-\frac{C_{2}}{C_{1}}\right) V \)


\( \boldsymbol{K}_{s p} \) of \( \boldsymbol{C u} \boldsymbol{S}, \boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{S} \) and \( \boldsymbol{H} \boldsymbol{g} \boldsymbol{S} \) are
\( 10^{-31}, 10^{-44} \) and \( 10^{-54} \) mol \( ^{2} \) litre \( ^{-2} \)
respectively. Select the correct order for their solubility in water
\( \mathbf{A} \cdot A g_{2} S>H g S>C u S \)
B. \( H g S>C u S>A g_{2} S \)
c. \( H g S>A g_{2} S>C u S \)
D. \( A g_{2} S>C u S>H g S \)


The snow on mountains does not melt
all at once


State whether True or False:
A man slip when he steps on a
banana peel thrown on the road.


If \( l, m, n \) are d.c's of vector \( \overline{O P} \) then
maximum value of \( l \) mn is
A \( \cdot \frac{1}{\sqrt{3}} \)
B. \( \frac{1}{2 \sqrt{3}} \)
c. \( \frac{1}{3 \sqrt{3}} \)
D. \( \frac{2}{\sqrt{3}} \)


Which one of the following molecules is paramagnetic?
\( \mathbf{A} \cdot F_{2} \)
в. \( B_{2} \)
c. \( L i_{2} \)
D. \( N_{2} \)


The figure represented the velocity-time graph of body moving in a straight line.
How much distance does it travel
during the last 10 seconds?
A. \( 40 \mathrm{m} \)
в. 80 т
c. \( 100 m \)
D. \( 220 m \)


Which of the following shows similarity with first man/human hominid?
A. Homo neanderthalensis
B. Australopithecus
c. Homo erectus
D. Homo habilis


\( \operatorname{Given} \boldsymbol{A} \boldsymbol{g}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{2}^{+} \rightleftharpoons \boldsymbol{A} \boldsymbol{g}^{+}+\boldsymbol{2} \boldsymbol{N} \boldsymbol{H}_{3} \)
\( \boldsymbol{K}_{c}=\mathbf{6 . 2} \times \mathbf{1 0}^{-8} \) and \( \boldsymbol{K}_{s p} \) of \( \boldsymbol{A} \boldsymbol{g} \boldsymbol{C l} \) is
\( 1.8 \times 10^{-10} \) at \( 298 K . \) Calculate
concentration of the complex in \( 1 M \)
aqueous ammonia.


The characteristics and an example of a
synovial joint in humans is:
A. Characteristics - Fluid cartilage between two bones, limited movements, Examples - Knee joint
B. Characteristics - Fluid filled between two joints, provides cushion, Examples - Skull bones
C. Characteristics - Fluid filled synovial cavity between two bones, Examples - Joint between atlas and axis
D. Characteristics - Lymph filled between two bones, limited movement, Examples - Gliding joint between carpals


Assertion
When a metal is treated with
cone.H \( N O_{3} \) it generally yields a
nitrate, \( N O_{2} \) and \( H_{2} O \)
Reason
Conc. \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \) reacts with metal and
first produces a metal nitrate and
nascent hydrogen. The nascent
hydrogen then further reduces \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \)
to \( N O_{2} \)
A. If both Assertion and Reason are correct and Reason is the correct explanation of Assertion
B. If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion
C. If Assertion is correct but Reason is incorrect
D. If Assertion is incorrect but Reason is correct


First strand of cDNA can be synthesized
by
A. Transaminase
B. DNA ligase
c. RNA dependent DNA polymerase
D. DNA dependent DNA polymerase


If an adding of \( F e C l_{3} \) solution to acidified Lassaigne s solution, a red colouration is produced, it indicates the presence of:
A . \( S \)
в. \( N \)
c. \( N \) and \( S \)
D. \( S \) and \( C l \)


If \( l_{1}=\frac{d}{d x}\left(e^{\sin x}\right), l_{2}= \)
\( \lim _{h \rightarrow 0} \frac{e^{\sin (x+h)}-e^{\sin x}}{h} \) and \( l_{3}= \)
\( \int e^{\sin x} \cos x d x, \) then which one of the
following is correct?
A. \( l_{1} \neq l_{2} \)
в. \( \frac{d}{d x}\left(l_{3}\right)=l_{2} \)
\( \mathbf{c} \cdot \int l_{3} d x=l_{2} \)
D. \( l_{2}=l_{3} \)


Consider the below diagram of heat
transfer and work transfer for a system.
What will be the first law equation for
the below system?
A \( \cdot(Q 1-Q 2)=E(W 2+W 3+W 1) \)
B . \( (Q 1+Q 2)=E+(W 2+W 3+W 1) \)
c. \( (Q 1-Q 2)=E+(W 2+W 3-W 1) \)
D. None of the above


Which one is not a property of ozone?
A. it acts as an oxidising agent in dry state.
B. oxidation of \( K I \) into \( K I O_{2} \)
C \( . P b S \) is oxidised to \( P b S O_{4} \)
D. \( H g \) is oxidised to \( H g_{2} O \)


If a new planet is discovered rotating around sun with the orbital radius
double that of the earth, then what will
be its time period? (in earth's days)
A . 1032
B. 1023
\( c \cdot 1024 \)
D. 1043


Neutrons are discovered by:
A. J.J. Thomson
B. Goldstein
C. Crookes
D. Chadwick


Unpolarised and Polarised Light.


Complete and balance the following chemical equations:
(i) \( \boldsymbol{K} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4}+\boldsymbol{K} \boldsymbol{I}+\boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \rightarrow \)
\( t \)
(ii) \( K_{2} C r_{2} O_{7}+H_{2} S O_{4}+H_{2} S \rightarrow \)
(iii) \( K M n O_{4}+H_{2} S O_{4}+F e S O 4 \rightarrow \)


The half-life of a radiosotope is four hours. If the initial rate of the isotope was 200 dpm, the rate after 24 hours
is:
A. 6.25 dpm
B. 2.084 dpm
c. 3.125 dpm
D. 4.167 dpm


Property of sulphuric acid accounts for its use as a dehydrating agent :
A . high a ffinity for water
B. low affinity for water
c. high avidity for water
D. low avidity for water


\( \boldsymbol{A}=\left[\boldsymbol{a}_{i j}\right]_{m \times n} \) is a square matrix , if
\( \mathbf{A} \cdot m<n \)
в. \( m>n \)
c. \( m=n \)
D. None of these


Out of the following numbers, which cannot be represented on a number line? \( \mathbf{0}, \frac{\mathbf{5}}{6}, 1, \frac{2}{4} \)
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( \frac{5}{6} \)
c. 1
D. None of these


The maximum current flowing long time after the switch \( \mathrm{S} \) is moved to \( \mathrm{B} \)
should be
A. 0.707 A
B. 1.0 \( A \)
\( c \cdot 0.5 \mathrm{A} \)
D. 1.414 A


A lot contains 20 articles. The
probability that the lot contains exactly
2 defective articles is 0.4 and the
probability that the lot contains exactly
3 defective articles is \( 0.6 . \) Article are
drawn from the lot at random one by one
without replacement and are tested till all defective articles are found. What is
the probability that the testing procedure ends at the twelfth testing?


Find the common difference and write
the next three terms of the A.P.
\( \mathbf{3},-\mathbf{2},-\mathbf{7},-\mathbf{1 2}, \dots \)


A uniform electric field and a uniform
magnetic field are acting along the same direction in a certain region. If an
electron is projected along the direction of the fields with a certain velocity then
A. its velocity will increase
B. its velocity will decrease
c. it will turn towards left of its motion
D. it will turn towards right of its motion


In a test an examine either gusses or copies or knows the answer to a
multiple choice question with \( m \) choices out of which exactly one is correct. The probability that he makes a guess is \( 1 / 3 \) and the probability that he copies the answer is 1/6. The probability that his answer is correct given that the copied it, is \( 1 / 8 . \) If the probability that he knew the answer to the question given that he correctly answered it is \( 120 / 141 \)
find \( \boldsymbol{m} \)


Write the molecular formula for
aluminium
(III) nitrate?


\( \ln \) a \( \triangle A B C \) in which \( A C=5 \mathrm{cm} \) and
\( \angle B A C=60^{\circ} \) and \( B C-A B=1.2 \mathrm{cm} \)
The, \( A B \) is
A . 3.18
в. 4.32
\( c .5 .12 \)
D. None of these


\( \lim _{x \rightarrow 0} \frac{x \tan 2 x-2 x \tan x}{(1-\cos 2 x)^{2}}= \)
\( A \cdot 2 \)
B.
\( c .-2 \)
D. \( -\frac{1}{2} \)


Which reaction is most spontaneous?
A \( \cdot G a^{3+}+2 e^{-} \rightarrow G a^{+} \)
B. \( I n^{3+}+2 e^{-} \rightarrow I n^{+} \)
\( \mathbf{c} \cdot T l^{3+}+2 e^{-} \rightarrow T l^{+} \)
D. cannot be predicted


An electron with kinetic energy 5 eV is
incident on a hydrogen atom in its ground state. The collision
A. must be elastic
B. may be partially elastic
c. must be completely inelastic
D. may be completely inelastic


If \( \sqrt{\frac{\boldsymbol{v}}{\boldsymbol{\mu}}}+\sqrt{\frac{\boldsymbol{\mu}}{\boldsymbol{v}}}=\boldsymbol{6}, \) then \( \frac{\boldsymbol{d} \boldsymbol{v}}{\boldsymbol{d} \boldsymbol{\mu}}= \)
A. \( \frac{17 \mu-v}{\mu-17 v} \)
в. \( \frac{\mu-17 v}{17 \mu-v} \)
c. \( \frac{17 \mu+v}{\mu-17 v} \)
D. \( \frac{\mu+17 v}{17 \mu-v} \)


If \( a_{1}, a_{2}, a_{3}, \dots a_{n} \in R \) then \( (x- \)
\( \left.a_{1}\right)^{2}+\left(x-a_{2}\right)^{2}+\ldots\left(x-a_{n}\right)^{2} \)
assumes least value at \( \boldsymbol{x}= \)
A \( \cdot a_{1}+a_{2}+a_{3}+\ldots+a_{n} \)
В . \( a_{n} \)
\( \mathbf{c} \cdot n\left(a_{1}+a_{2}+\ldots+a_{n}\right) \)
D. \( \frac{\left(a_{1}+a_{2}+\ldots+a_{n}\right)}{n} \)


Voltmeter is an instrument used to
measure
A . Electric current
B. Electric charge
c. Resistance
D. Potential difference


The value of
\( \int_{-\pi / 2}^{\pi / 2}\left(\operatorname{psin}^{3} x+q \sin ^{4} x+r \sin ^{5} x\right) \) does
not depend on
\( A \cdot p, q, r \)
B. p, ronly
c. ponly
D. \( q \), ronly


Sulphur dioxide gas turns acidified potassium dichromate paper
A . red
B. green
c. white
D. yellow


Choose the correct experiment to
demonstrate the transfer of heat by the
process of conduction.
A. Take two metal blocks of same size \& shape and heat one of them to a considerable temperature, then allow both the blocks to touch each other, after a while, you will see the other block gets heated due to contact
B. Take two metal blocks of same size \& shape and heat one of them to a considerable temperature, then keep the blocks separate, after a while you will see the other block gets heated due to contact.
C. Take two metal blocks of same size \& shape and heat one of them to a considerable temperature, then allow both the blocks to touch each other after the block get cooled down, after a while you will see the other block gets heated due to contact
D. None of above


\( \int_{0}^{\pi / 2} \frac{d x}{\sin x} \) equals
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( \frac{1}{2} \)
\( c \cdot 1 \)
D. \( 3 / 2 \)


The high-energy bonds of ATP are between
A . C-C
B. C-O
c. \( c-N \)
D. P- -


The specific charge of electrons is less than the specific charge of protons.
A. True
B. False


State whether true or false.
A moving body can have non-uniform velocity and uniform speed at the same
time.
A. True
B. False


A spherical balloon is being inflated so that its volume increases uniformly at
the rate of \( 40 \mathrm{cm}^{3} / \) min. When \( r=8 \)
then the increase in radius in the next
\( 1 / 2 m i n \) is
A \( .0 .025 \mathrm{cm} \)
B . \( 0.050 \mathrm{cm} \)
c. \( 0.075 \mathrm{cm} \)
D. \( 0.01 \mathrm{cm} \)


Two bulbs, one of \( 200 W \) and the other
of \( 100 W, \) are connected in series with a
\( 100 V \) battery which has no internal
resistance. Then,
A. The current passing through the \( 200 W \) bulb is more than that through the \( 100 \mathrm{W} \) bulb
B. The power dissipation in the \( 200 W \) bulb is less than that In the \( 100 \mathrm{W} \) bulb
c. The voltage drop across the \( 200 W \) bulb is more than that across the \( 100 \mathrm{W} \) bulb
D. The power dissipation In the \( 100 W \) bulb is more than that in the \( 200 \mathrm{W} \) bulb


With ethoxyethane which compound is miscible to almost the same extent?
A. Formaldehyde
B. Bhutanone
c. Butan-1-ol
D. Propan-1-ol


A strong magnetic field is applied on a stationary electron. Then
A. the electron moves in the direction of the field
B. the electron moves in an opposite
c. the electron remains stationary
D. the electron starts spinning


A circular coil of conducting wire has an area \( A \) and number of turns \( N . \) It is lying in a vertical plane in a region where uniform magnetic field B exist with field direction normal to the coil plane. If the coil is rotated about a vertical axis
by an angle \( \pi \) in 0.5 seconds, then the value of the emf induced at the ends of
the coil is
\( A \). 4 NAB
B. \( 4 \pi \) NAB
c. 8 NAB
D. 8 \( \pi \) NAB


I.U.P.A.C name for \( \boldsymbol{F e}(\boldsymbol{C O})_{2}(\boldsymbol{\sigma}- \)
\( \left.\boldsymbol{C}_{5} \boldsymbol{H}_{5}\right)\left(\boldsymbol{\pi}-\boldsymbol{C}_{5} \boldsymbol{H}_{5}\right) \) complex
A . Dicarbonyl ( \( \eta^{5} \) - cyclopentadienyl) (cyclopentadienyl)ferrate(II)
B. Dicarbony! ( \( \eta^{5} \) - cyclopentadiene) (cyclopentadiencyl)iron(II)
C. Dicarbonyl ( \( \eta^{5} \) - cyclopentadienyl) ( \( \eta^{5} \) cyclopentadienyl)iron(II)
D. Dicarbonyl ( \( \eta^{5} \) - cyclopentadieny!) (cyclopentadienyl)iron(II)


On the sides \( A B \) and \( A C \) of triangle \( A B C \), equailateral triangle \( A B D \) and \( A C E \) are drawn, then \( \angle C A D=\angle B A E \)
If true then enter 1 and if false then
enter 0


If the system is not in free fall, which of
the following statements is true about
hydrostatic pressure?
This question has multiple correct options
A. In a liquid, point at different depth can never be at the
same pressure.
B. In a liquid, point at different depth may be at the same pressure.
C. In different liquids, points at different depths can be at the same pressure.
D. In different liquids, points at the same depths can never be at the same pressure.


Fluorides and phosphates of alkali metals are:
A. completely soluble in water
B. sparingly soluble in water
C. completely soluble in water except \( L i \) and \( M g \)
D. completely insoluble in water except \( L i \) and \( M g \)


The work done in turning a magnet of
magnetic moment \( M \) by an angle of \( 90^{\circ} \)
from the meridian is \( n \) times the
corresponding work done to turn it
through an angle of \( 60^{\circ} . \) Where \( n \) is
given by
A \( \cdot 1 / 2 \)
B. 2
c. \( 1 / 4 \)
D.


One end of a string of length L and cross-sectional area A is fixed to a
support and the other end is fixed to a
bob of mass \( \mathrm{m} \). The bob is revolved in a
horizontal circle of radius \( r, \) with an
angular velocity \( \omega, \) such that the string
makes an angle \( \theta \) with the vertical. The increase \( \Delta L \) in length of the string is
A \( \cdot \frac{M L}{A Y} \)
В. \( \frac{M g L}{A Y \cos \theta} \)
c. \( \frac{M g L}{A Y \sin \theta} \)
D. \( \frac{M g L}{A Y} \)


The mass of deutron \( \left(_{1} H^{2}\right) \) nucleus is
2.013553 a.m.u. If the masses of proton and neutron are 1.007275 a.m.u. and
1.008665 a.m.u. respectively. Calculate the mass defect, the packing fraction, binding energy and binding energy per
nucleon.


Two identical parallel plate capacitance
C each are connected in series with a
battery of emf, \( E \) as shown, If one of the
capacitors is now filled with a dielectric of dielectric constant \( \mathrm{k} \), the amount of
charge which will flow through the
battery is ?(neglect internal resistance of the battery)
A \( \cdot \frac{k+1}{2(k-1)} C E \)
В \( \cdot \frac{k-1}{2(k+1)} C E \)
c. \( \frac{k-2}{k+2} C E \)
D. \( \frac{k+2}{k-2} C E \)


In a glass sphere, there is a small
bubble \( 22 \times 10^{-2} \mathrm{m} \) from its centre. If the
bubble is viewed along a diameter of the sphere, from the side on which it lies. The distance from the surface
where it appears is
(The radius of glass sphere is \( 25 \times 10^{-2} \)
\( \mathrm{m} \) and refractive index of glass is 1.5
A . 22.5 \( \times 10^{-2} \mathrm{m} \)
B. 23.2 \( \times 10^{-2} \mathrm{m} \)
\( c \cdot 26.5 \times 10^{-2} \mathrm{m} \)
D. 20.2 \( \times 10^{-2} \mathrm{m} \)


Explain why sportsmen use shoes with spikes.


Express the following as a rational number i.e. in the form \( \frac{a}{b} ; \) where \( a, b \in I \) and \( \boldsymbol{b} \neq \mathbf{0} \)
\( 0.81 \overline{3} \)
A \( \cdot \frac{11}{75} \)
в. \( \frac{61}{75} \)
c. \( \frac{51}{75} \)
D. \( \frac{31}{75} \)


The angular frequency of small
oscillations of the system shown in the
figure is
A \( \cdot \sqrt{(K / 2 m)} \)
B . \( \sqrt{(2 K / m)} \)
c. \( \sqrt{(K / 4 m)} \)
D. \( \sqrt{(4 K / m)} \)


Image on the retina remains for:
A . 20 s
B. 10 s
c. \( \frac{1}{100} s \)
D. \( \frac{1}{20} s \)


\( \operatorname{In} \operatorname{an} \operatorname{SHM} x=\operatorname{asin} \omega t, \) the minimum
0.5 second what is the minimum time
A . \( 0.3 \mathrm{s} \)
B. \( 0.4 \mathrm{s} \)
\( c \cdot 0.2 s \)
D. \( 0.1 \mathrm{s} \)


If the solubility of \( A g C l \) (formula mass
\( =143) \) in water at \( 25^{\circ} \mathrm{C} \) is \( 1.43 \times 10^{-4} \)
g/100 mL of solution then the value of
\( \boldsymbol{K}_{s p} \) will be:
A \( \cdot 1 \times 10^{-5} \)
В. \( 2 \times 10^{-5} \)
c. \( 1 \times 10^{-10} \)
D. \( 2 \times 10^{-10} \)


The frequency of A.C. (alternating current) provided to a household in USA
is


Calculate simultaneous solubility of \( A g C N S \) and \( A g B r \) in a solution of
water.
\( \left[\text { Given: } \boldsymbol{K}_{s p} \text { of } \boldsymbol{A} \boldsymbol{g} \boldsymbol{C} \boldsymbol{N} \boldsymbol{S}=\mathbf{1} \times \mathbf{1 0}^{-12}\right. \)
\( \boldsymbol{K}_{s p} \) of \( \boldsymbol{A} \boldsymbol{g} \boldsymbol{B} \boldsymbol{r}=\boldsymbol{5} \times \mathbf{1 0}^{-13} \)


Quiescent centre theory for demonstrating apical organisation in root was proposed by
A. Schuepp
B. Hanstein
c. clowes
D. Nageli


A \( 200 \mathrm{Hz} \) wave with amplitude \( 1 \mathrm{mm} \) travels on a long string of linear mass density 6 g/m kept under a tension of 60N. Find the average power transmitted across a given point on the string.


0
0
0
0


The direction of impulse in a typical
neuron is
A. Axon to dendron
B. Dendron to axon
c. Both A and B
D. None of these


Find how the volume density of the elastic deformation energy is distributed in a steel rod depending on
the distance \( r \) from its axis. The length
of the rod is equal to \( l \), the torsion angle
to \( \varphi \)
A. \( u=\frac{1}{2} \frac{G \varphi^{2} r^{2}}{l^{2}} \)
B. \( u=\frac{3}{2} \frac{G \varphi^{2} r^{2}}{l^{2}} \)
c. \( _{u=\frac{5}{2} \frac{G \varphi^{4} r^{2}}{l^{2}}} \)
D. None of these


In a circuit two or more cells of the
same e.m.f are connected in parallel in
order to:
A. increase the P.D across a resistance in the circuit
B. decrease the P.D across a resistance in the circuit
C. facilitate drawing more current from the battery system
D. change the e.m.f across the system of batteries


Brilliance of diamond is due to:
A. shape
B. cutting
c. reflection
D. total internal reflection


The sum of coordination number and
oxidetion number of the metal M in the
\( \operatorname{complex}\left[M(e n)_{2}\left(C_{2} O_{4}\right)\right] \) CI (where en
is ethylenediamine) is:
\( A \cdot 6 \)
B. 7
\( c \cdot 8 \)
D.


Two spheres of the same size are made of the same metal, but one is hollow but
the other is solid.When, they are heated
to the same temperature then
A. the hollow sphere will expand more
B. the solid sphere will expand more
c. both spheres will expands almost equally
D. only the solid sphere will expand


What will be the current drawn by an
electric fan of \( 805 \mathrm{W} \), when it is connected to a source of \( 230 \vee ? \)
\( A \cdot 3 A \)
B. 4 A
\( c .3 .5 \mathrm{A} \)
D. 4.5 A


A metallic wire bent in form of a semi-
circle of radius \( 0.1 \mathrm{m} \) is moved in a
direction parallel to its plane, but perpendicular to a magnetic field \( \boldsymbol{B}= \)
\( 20 \mathrm{mT} \) with a velocity of \( 10 \mathrm{m} / \mathrm{s} \). What is
the induced e.m.f. in wire?
A \( \cdot 4 \times 10^{-3} \) volts
B. \( 4 \times 10^{-2} \) volts
\( \mathrm{c} \cdot 4 \times 10^{-1} \mathrm{v} \) olts
D. None of these


Find the sum of 32 terms of an
A.P. whose third terms is 1 and 6 th
term is -11


A radioactive nucleus A finally transforms into a stable nucleus B.
Then, A and B may be
A. isobars
B. isotones
c. isotopes
D. none of these


If \( \boldsymbol{A}=(\boldsymbol{6}, \boldsymbol{7}, \boldsymbol{8}, \boldsymbol{9}), \boldsymbol{B}=(\boldsymbol{4}, \boldsymbol{6}, \boldsymbol{8}, \boldsymbol{1 0}) \) and
\( \boldsymbol{C}=\{\boldsymbol{x}: \boldsymbol{x} \boldsymbol{\epsilon} \boldsymbol{N}: \boldsymbol{2}<\boldsymbol{x} \leq 7\} ; \) find :
\( \boldsymbol{A}-(\boldsymbol{B} \cup \boldsymbol{C}) \)


The functional group present in acyl chlorides is:
A. \( -C l \)
в.
\[
\begin{array}{c}
0 \\
-C-C l
\end{array}
\]
\( c \)
\[
\begin{array}{c}
0 \\
-C-O C l
\end{array}
\]
D. \( -C H_{2}- \) OCl


Closed system is
A . Perfectly sealed
B. Perfectly insulated
C. Both perfectly insulated and sealed
D. Neither insulated nor sealed


(A). The reverberation time is
dependent on the shape of the enclosure, position of the sources and observer.
(B) The unit of absorption coefficient in
S.I. system in metric is sabine
A. both (A) and (B) are true
B. both (A) and (B) are false
c. (A) is true but (B) is false
D. (A) is false but (B) is true


A plane mirror of length \( 8 \mathrm{cm} \) is moving
with speed of \( 3 m / s \) towards a wall in
situation as shown in figure. Size of spot formed on the wall is \( 32 / x \) cm. Find
the value of \( x \).


A non-zero vector \( \vec{a} \) is parallel to the line
of intersection of the plane \( \boldsymbol{P}_{1} \) determined by \( \hat{i}+\hat{j} \) and \( \hat{i}-2 \hat{j} \) and plane \( P_{2} \) determined by vector \( 2 \hat{i}+ \) \( \hat{j} \) and \( 3 \hat{i}+2 \hat{k}, \) then angle between \( \vec{a} \) and vector \( \hat{i}-2 \hat{j}+2 \hat{k} \) is
A \( \cdot \frac{\pi}{4} \)
в.
\( c \cdot \frac{\pi}{3} \)
D. \( \pi \)


Define Young's modulus.


State whether True or False:
The shape of the wave front originating from a line is spherical
A. True
B. False


When P reacts with caustic soda, the
products are \( \boldsymbol{P H}_{3} \) and \( \boldsymbol{N a H}_{2} \boldsymbol{P O}_{2} . \) The
reaction is an example of
A. Oxidation
B. Reduction
c. Both oxidation and reduction
D. Neutralisation


\( \begin{array}{ccc}(\boldsymbol{b}+\boldsymbol{c})^{2} & \boldsymbol{a}^{2} & \boldsymbol{a}^{2} \\ \boldsymbol{b}^{2} & (\boldsymbol{c}+\boldsymbol{a})^{2} & \boldsymbol{b}^{2} \\ \boldsymbol{c}^{2} & \boldsymbol{c}^{2} & (\boldsymbol{a}+\boldsymbol{b})^{2}\end{array} \mid= \)


Plant hormone associated with
climacteric respiration is
A . Auxin
B. Cytokinin
c. Ethylene
D. Gibberellin


Hydrogenation of vegetable ghee at \( 25^{\circ} \)
C reduces the pressure of \( \boldsymbol{H}_{2} \) from 2 \( \operatorname{atm} \) to 1.2 atm in 50 minute. Calculate
the rate of reaction in terms of change:
(a) In pressure per minute.
(b) In molarity per second.


Succession is
A. Orderly process of community change till stability
B. Gradual, directional and continuous process
C. Series of biotic communities that appear gradually in a barren area
D. All of the above


In which of the following reaction
hydrogen peroxide acts as reducing
agent?
\( \mathbf{A} \cdot P b S+4 H_{2} O_{2} \rightarrow P b S O_{4}+4 H_{2} O \)
B. \( N a_{2} S O_{3}+H_{2} O_{2} \rightarrow N a_{2} S O_{4}+H_{2} O \)
\( \mathbf{c} \cdot A g_{2} O(\text { moist })+H_{2} O_{2} \rightarrow 2 A g+H_{2} O+O_{2} \)
D. \( 2 K I+H_{2} O_{2}+H_{2} S O_{4} \rightarrow K_{2} S O_{4}+I_{2}+H_{2} O_{2} \)


Calculate the product of boiling point of water and melting point of water in Celsius scale.
\( \mathbf{A} \cdot 0^{\circ} C \)
B. \( 273^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 100^{\circ} \mathrm{C} \)
D. \( 373^{\circ} \mathrm{C} \)


Check whether \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be a function defined by \( f(x)=\frac{x^{2}+2 x+5}{x^{2}+x+1} \) is one
one or not.


The rough, reddish-brown strip on a safety matchbox is used for lighting a match by striking against it. It is made of powdered glass mixed with:
A. Mercury
B. White phosphorous
c. Red lead
D. Potash


A microscope is having objective of
focal length \( 1 \mathrm{cm} \) and eyepiece of focal
length \( 6 \mathrm{cm} \). If tube length is \( 30 \mathrm{cm} \) and image is formed at the least distance of distinct vision, what is the
magnification produced by the microscope? Take \( D=25 \mathrm{cm} \)
\( \mathbf{A} \cdot \mathbf{6} \)
в. 150
c. 25
D. 125


Ozone layer absorbs \( 93-99 \% \) of sun's
high frequency \( _{-}-_{-}-_{-}- \) light.


Which of the following statement is true about a rational number \( \frac{-2}{3} ? \)
A . It lies to the left side of \( ^{\prime} 0^{\prime} \) on the number line
B. It lies to the right side of ' \( 0^{\prime} \) on the number line
c. It is not possible to represent on the number line.
D. It cannot be determined on which side the number lies


Solve:3 \( -2 x \geq x-32 \) for \( x \in I \)


Which one of the following complexes is an outer orbital complex?
\( A \)
\( \left[F e(C N)_{4}\right]^{6-} \)
в. \( \left[F e(C N)_{6}\right]^{4} \)
c. \( \left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+} \)
D. \( \left[N i\left(N H_{3}\right)_{6}\right]^{2+} \)


Perimeter of a rectangular garden is \( 1.2 \times 10^{5} k m \) and length is \( 0.2 \times \)
\( 10^{5} k m . \) Find the area of the garden in
standard form.
\( \mathbf{A} \cdot 8 \times 10^{6} k m^{2} \)
B . \( 0.8 \times 10^{8} k m^{2} \)
c. \( 80 \times 10^{8} k m^{2} \)
D. \( 8.0 \times 10^{8} k m^{2} \)


\begin{tabular}{llllll}
C.I. & \( 0- \) 4 & 4 8 & \( 8- \) 12 & \( 12- \) 16 & 16 20 \\
\hline
\end{tabular}
19
Find the mode of the following data
A. 10.6
B. 12
c. 12.6
D. 8


Velocity-time curve for a body projected vertically upwards is:
A. Parabola
B. Ellipse
c. Hyperbola
D. Straight line


Assertion
Light year and wavelength have same
dimensional formula.
Reason
Both have the dimensions of time
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which of the following statement is
wrong for acceleration due to gravity.
A. \( g \) decreases on going above the surface of earth
B. \( g \) increases on going below the surface of earth
\( \mathrm{C} \cdot g \) is maximum at pole
D. \( g \) increases on going from equator to poles


Which of the following is thermoresistant polymer?
A. Orlon
B. Polythene
c. Teflon
D. Bakelite


In evolutionary terms, can we say which among bacteria, spiders, fish and chimpanzee have a better body design? Why or why not?


Toss a coin for number of times as
shown in the table. And record your findings in the table.

Number of heads heads
10
\[
\begin{array}{l}
20 \\
30
\end{array}
\]
40
50
What happens if you increase the
number of tosses more and more.


Evaluate \( \left|\begin{array}{ccc}\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} \\ -\mathbf{1} & \mathbf{1} & -\mathbf{1} \\ \mathbf{1} & \mathbf{- 1} & \mathbf{1}\end{array}\right| \)


When the sun is directly overhead, the surface of the earth receives \( 1.4 \times \)
\( 10^{3} W m^{-2} \) of sunlight. Assume that the
light is monochromatic with average wavelength \( 500 n m \) and that no light is
absorbed in between the sun and the
earth's surface. The distance between
the sun and the earth is \( 1.5 \times 10^{11} m \) (a)
Calculate the number of photons falling per second on each square metre of
earth's surface directly below the sun
(b) How many photons are there in each cubic metre near the earth's surface at
any instant?
(c) How many photons does the sun emit per second?


For \( k=1,2,3 \) the box \( B_{k} \) contains \( k \) red
balls and \( (k+1) \) white balls, let
\( P\left(B_{1}\right)=\frac{1}{2}, P\left(B_{2}\right)=1 \) and \( P\left(B_{3}\right)= \)
\( \frac{1}{6} \cdot A \) box is selected at random and \( a \) ball is drawn from it. If a red ball is
drawn, then the probability that it has
come from box \( B_{2} \) is
A \( \cdot \frac{35}{78} \)
в. \( \frac{14}{39} \)
c. \( \frac{10}{13} \)
D. \( \frac{12}{13} \)


The major product of the reaction is:
\( A \)
в.
\( c \)
D.


The flux of electric field \( \mathrm{E}=200 \) iNC
through a cube of side \( 10 \mathrm{cm}, \) oreinted so that its faces are parallel to the coordinate axes is


As per Bohr's model, an electron in an uni-electronic species revolves around
the nucleus in circular orbits. What is
the radius of the 3 rd orbit of \( \boldsymbol{H} \boldsymbol{e}^{+} \) ion?
A \( .2 .38 \AA \)
В. \( 1.19 \dot{A} \)
c. \( 0.7 \dot{h} \)
D. \( 4.76 \AA \)


What is the wavelength of light emitted when the electron in hydrogen atom undergoes transition from the energy
level with \( n=4 \) to energy level \( n=2 ? \)
\( \left(\operatorname{given} R_{n}=109678 c m^{-1}\right) \)
A. 786 nm
B. 486 nm
c. \( 586 \mathrm{nm} \)
D. 986 nm


Triangle \( A \) has a base of \( x \) and a height of \( 2 x . \) Triangle \( B \) is similar to triangle \( A \) and has a base of \( 2 x \). What is the ratio
of the area of triangle \( A \) to triangle \( B ? \)
A . 1: 2
B. 2:
\( c \cdot 2: 3 \)
D. 1: 4


A plane mirror \( 50 \mathrm{cm} \) long, is hung on a vertical wall of a room,with its lower
edge \( 50 \mathrm{cm} \) above the ground.A man stands infront of the mirror at a
distance \( 2 \mathrm{m} \) away from the mirror. If his eyes are at a height \( 1.8 \mathrm{m} \) above the ground,then the length (distance between the extreme points of the visible region perpendicular to the mirror) of the floor visible to him due to reflection from the mirror is \( \frac{x}{26} \) m. Find the value of \( x \).


The perimeters of two similar triangles
are \( 25 \mathrm{cm} \) and \( 15 \mathrm{cm} \) respectively. If one side of first triangle is \( 9 \mathrm{cm}, \) then the corresponding side of the other triangle is
\( A \cdot 6.2 \mathrm{cm} \)
B. \( 3.4 \mathrm{cm} \)
c. \( 5.4 \mathrm{cm} \)
D. \( 8.4 \mathrm{cm} \)


Give the essential postulates of Bohr's
model of an atom. How did it Explain
i) the stability of an atom?
ii) origin of spectral lines in the Hydrogen atom?


State whether given statement is True or False

Resistivity of semiconductor depends on atomic nature of semiconductor.
A. True
B. False


Can you tell which metabolic pathway is taking place resulting in the formation
of \( \mathrm{CO}_{2} \) ? Where do you think the bacteria for these fermentations came from?


Which of the following is a derivative of amino acid?
A. Thyroxine
B. Estradiol
c. Estrone
D. Progesterone


RNA synthesis is controlled by
A. Rho factor
B. Sigma factor
c. Endonuclease
D. RNA polymerase


Radial probability distribution curve is
shown for \( s \) -orbital. The curve is:
A . \( 1 s \)
B . \( 2 s \)
\( c .3 s \)
D. \( 4 s \)


Mass \( m_{1} \) hits and sticks with \( m_{2} \) while
sliding horizontally with velocity \( v \) along the common line of centres of the three
\[
\text { equal masses }\left(\boldsymbol{m}_{1}=\boldsymbol{m}_{2}=\boldsymbol{m}_{3}=\boldsymbol{m}\right)
\]
Initially masses \( m_{2} \) and \( m_{3} \) are stationary and the spring is unstretched. Minimum kinetic energy of
\( m_{2} \) is \( y m v^{2} / 36 . \) Find \( y \)


A solution is prepared by dissolving 9.8
\( g \) of \( H_{2} S O_{4} \) in 54 g of water. What is the
mole fraction of \( \boldsymbol{H}_{2} \boldsymbol{S O}_{4} ? \)
A. 0.03
B. 0.04
c. 0.01
D. 0.02


The median of the following data is :
\begin{tabular}{|c|c|c|c|c|c|}
\hline\( x: \) & 10 & 20 & 30 & 40 & 50 \\
\hline\( f: \) & 2 & 3 & 2 & 3 & 1 \\
\hline
\end{tabular}
A . 30
B. 40
\( c .35 \)
\( D \cdot 3 \)


ff \( P=\left[\begin{array}{lll}1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4\end{array}\right] \) is the adjoint of
\( \mathbf{3} \times \mathbf{3} \) matrix \( \boldsymbol{A} \) and \( |\boldsymbol{A}|=\mathbf{4} \) then \( \boldsymbol{\alpha} \) is
\( A \cdot 4 \)
B. 1
\( c \cdot 5 \)
\( D \)


For an ideal solution containing a nonvolatile solute, which of the followig expressions represents the vapour
pressure of the solution? \( \left(x_{1} \rightarrow\right. \) mole fraction of solvent
A \( . p=x_{2} p_{2} \)
В . \( p=x_{1} p_{2}^{*} \)
c. \( p=x_{1} p_{1}^{*} \)
D. \( p_{1}^{*}-p=x_{2} \)


Arrange \( C e^{3+}, L a^{3+}, P m^{3+} \) and \( Y b^{3+} \) in
increasing order of their ionic radii
A \( \cdot Y b^{3+}<P m^{3+}<C e^{3+}<L a^{3+} \)
B. \( C e^{3+}<Y b^{3+}<P m^{3+}<L a^{3+} \)
c. \( Y b^{3+}<P m^{3+}<L a^{3+}<C e^{3+} \)
D. \( P m^{3+}<L a^{3+}<C e^{3+}<Y b^{3} \)


The concept of stabilizing selection is described by
0
A. Graph I only
B. Graph II only
c. Both Graph I and Graph II
D. Graph III only
E. Both Graph II and Graph III


A swimmer's speed in the direction of
flow of river is \( 16 k m h^{-1} . \) Against the
direction of flow of river, the swimmer's
speed is \( 8 k m h^{-1} \) Calculate the
swimmer's speed in still water and the velocity of flow of the river.
\( \mathbf{A} \cdot 12 k m / h, 4 k m / h \)
B. \( 10 k m / h, 3 k m / h \)
c. \( 10 k m / h, 4 k m / h \)
D. \( 12 k m / h, 3 k m / h \)


Let \( P(x) \) be a polynomial of degree 4
with \( \boldsymbol{P}(\mathbf{2})=-\mathbf{1}, \boldsymbol{P}^{\prime}(\mathbf{2})=\mathbf{0}, \boldsymbol{P}^{\prime \prime}(\mathbf{2})=\mathbf{2} \)
\( \boldsymbol{P}^{\prime \prime \prime}(2)=-12 \) and \( \boldsymbol{P}^{i v}(2)=24, \) The
value of \( \boldsymbol{P}^{\prime \prime}(1) \) is


A block moving in air breaks in two
parts and the parts separate
A. the total momentum must be conserved
B. the total kinetic energy must be conserved
c. the total momentum must change
(B) both are correct
D. option (A) and


If \( f\left(x_{1}\right)-f\left(x_{2}\right)=f\left(\frac{x_{1}-x_{2}}{1-x_{1} x_{2}}\right) \) for
\( \boldsymbol{x}_{1}, \boldsymbol{x}_{2} \in[-1,1] \) then \( \boldsymbol{f}(\boldsymbol{x}) \) is
This question has multiple correct options
\( ^{\mathbf{A}} \cdot \log \left(\frac{1-x}{1+x}\right) \)
B. \( \tan ^{-1}\left(\frac{1-x}{1+x}\right) \)
\( ^{\mathrm{c}} \cdot \log \left(\frac{1+x}{1-x}\right) \)
D. \( \tan ^{-1}\left(\frac{1+x}{1-x}\right) \)


In \( \triangle A B C, \) angle \( A \) is \( 120^{\circ}, B C+C A=20 \)
and \( A B+B C=21 . \) Find the length of the
side BC.


Derive Lens maker formula \( \frac{\mathbf{1}}{\boldsymbol{f}}=\mathbf{( n}- \)
1) \( \left(\frac{1}{R_{1}}-\frac{1}{R_{2}}\right) . \) The lower half of the concave mirror's reflecting surface is covered with an opaque material. What
will be the effect on the image formed by the mirror?


"Human population grows in geometric ratio while food materials increase in
arithmetic proportion." It is a statement
from
A. Darwin
B. Bateson
c. Amartya sen
D. Malthus


Red pepper is
A. Capsicum annuum
B. Solanum nigrum
C . Lycopersicum esculentum
D. Physalis peruviana


A possible explanation for a smoker cough that develops when the tracheal epithelium changes from pseudostratified columnar to stratified
squamous is that
A. This change is accompanied by tumours that irritate the upper respiratory tractt
B. Stratified squamous epithelium secretes more mucin than pseudostratified columnar.
C. The stratified squamous epithelium has no cilia to remove accumulating mucus
D. The two events are unrelated


At \( 300 \mathrm{K}, 36 \mathrm{g} \) of glucose present per litre in its solution has an osmotic
pressure of 4.98 bar. If the osmotic
pressure of the solution is 1.58 bar at
the same temperature, what would be its concentration?


Find the number of four letter words,
with meaning or without meaning, that can be formed by using the letters of the
word' \( C H E M I S T R Y^{\prime} \)
A . 1024
B. 3251
\( c .3024 \)
D. 24


If the function \( \boldsymbol{f}:[\mathbf{0}, \mathbf{8}] \rightarrow \boldsymbol{R} \) is
differentiable and \( 0<\alpha<1<\beta<2 \)
then \( \int_{0}^{8} f(t) d t \) is equal to?
A \( \cdot 3\left[a^{3} f\left(a^{2}\right)+\beta^{2} f\left(\beta^{2}\right)\right] \)
B・3 \( \left[a^{3} f(a)+\beta^{3} f(\beta)\right. \)
c \( \cdot 3\left[a^{2} f\left(a^{2}\right)+\beta^{2} f\left(\beta^{3}\right)\right] \)
D \( \cdot 3\left[a^{2} f\left(a^{3}\right)+\beta^{2} f\left(\beta^{3}\right)\right] \)


When an atom undergoes \( \beta^{+} \) decay
A. a neutron changes into a proton
B. a proton changes into a neutron
C . a neutron changes into an antiproton
D. a proton changes into an antineutron


\( M g \) can be used to reduce \( T i C l_{4} \) into
Ti in
1. Monds
2. van Arkel
3. Hall
4. Kroll


A 60 -kg person on a merry-go round is travelling in a circle with a radius of \( 3 m \) at a speed of \( 6 m / s . \) What is the magnitude of the net force experienced by this person?
A . zero
B. \( 60 N \)
c. \( 180 N \)
D. \( 600 N \)
E. \( 720 N \)


Cuticle is secreted by
A. Hypodermis
B. Endodermis
C. Epidermis
D. Both B and C


Find the interval of increase and
decrease of the following functions. \( f(x)=x^{2} e^{-x} \)


Hg sticks to the surface of glass when it
comes into contact with:
A. \( H_{2} O \)
в. \( H N O_{3} \)
c. \( g \)rease
D. \( O_{3} \)


One calorie is defined as the heat
required to raise the temperature of 1
\( \mathrm{gm} \) of water by \( 1^{\circ} \mathrm{C} \) in a certain interval
of temperature and at certain pressure. The temperature interval and pressure is?
A \( \cdot 13.5^{\circ} \mathrm{C} \) to \( 14.5^{\circ} \mathrm{C} \& 76 \mathrm{mm} \) of \( \mathrm{Hg} \)
B . \( 6.5^{\circ} \mathrm{C} \) to \( 7.5^{\circ} \mathrm{C} \& 76 \mathrm{mm} \) of \( \mathrm{Hg} \)
C. \( 14.5^{\circ} \mathrm{C} \) to \( 15.5^{\circ} \mathrm{C} \& 760 \mathrm{mm} \) of \( \mathrm{Hg} \)
D. \( 98.5^{\circ} \mathrm{C} \) to \( 99.5^{\circ} \mathrm{C} \& 760 \mathrm{mm} \) of \( \mathrm{Hg} \)


A small amount of solution containing \( ^{24} \mathrm{Na} \) radio nuclide with activity \( \boldsymbol{A}= \) \( 2 \times 10^{3} \) dps was administered into
blood of a patient in hospital. After 5 hour, a sample of the blood drawn out from the patient showed an activity of 16 dpm per cc. \( t_{1 / 2} \) for \( ^{24} \mathrm{Na}=15 \) hr. The
activity of blood sample drawn after a further time of 5 hr is :
A. 0.2118 dpm per \( m L \)
B. 0.4232 dps per \( m L \)
c. 0.4232 dpm per \( m L \)
D. 0.2118 dps per \( m L \)


In a series combination of two
capacitances \( C^{\prime} \) and \( C(C>C) \) (as
shown in the circuit)
A. C' stores more energy than \( C \)
B. \( C \) stores more energy than \( C^{\prime} \)
c. potential difference across \( C \) is more than that across
\( C \)
D. potential difference across \( C^{\prime} \) is less than that across \( C \)


Give the equation which explains the different series of lines in the atomic
spectrum of hydrogen. who is the equation named after? Explain the various terms involved.


"LiI has greater solubility in water than
\( \boldsymbol{C} \boldsymbol{s} \boldsymbol{I} \)
Answer whether the above statement is
true or false.
If true enter 1 , else enter 0 .


Vectors \( \bar{a}, \bar{b} \) are non-collinear find \( x, s \) o that the vectors \( (x-1) \bar{a}+\bar{b} \) and \( (2+ \) \( 3 x) \bar{a}-2 \bar{b} \) are collinear


Fill in the blank:
does not appear to move.
A. sirius
B. Pole star
c. vega
D. Rigel


Write an essay on soil erosion,


Alka spends \( 90 \% \) of the money that she
received every month, and saves Rs. 120. How much money does she get
monthly


Find the solution for the following
equations:
\( \frac{5}{2 x}+\frac{2}{3 y}=7 ; \frac{3}{x}+\frac{2}{y}= \)
\( \mathbf{1 2} \quad(\boldsymbol{x} \neq \mathbf{0}, \boldsymbol{y} \neq \mathbf{0}) \)


Sulphur trioxide can be obtained by which of the following reaction?
\( \mathbf{A} \cdot S+H_{2} S O_{4} \stackrel{\Delta}{\rightarrow} \)
в. \( H_{2} S O_{4}+P C l_{5} \) 오
\( \mathbf{c} \cdot \operatorname{CaSO}_{4}+C \triangleq \)
D. \( F e_{2}\left(S O_{4}\right)_{3} \Delta \)


If \( \vec{b}=3 \hat{i}+4 \hat{j} \) and \( \vec{a}=\hat{i}-\hat{j}, \) the vector
having the same magnitude as that of \( \vec{b} \) and parallel to \( \vec{a} \) is
A \( \cdot \frac{5}{\sqrt{2}}(\hat{i}-\hat{j}) \)
B. \( \frac{5}{\sqrt{2}}(\hat{i}+\hat{j}) \)
c. \( 5(\hat{i}-\hat{j}) \)
D. \( 5(\hat{i}+\hat{j}) \)


The valency of elements in the periodic table in respect of hydrogen:
A. increases regularly from 1 to 8
B. decreases regularly from 1 to 8
c. first increases from group I to group IV and then decreases
D. first decreases from group I to group IV and then increases


The main source of organic compounds
is :
A. coaltar
B. petroleum
c. both (a) and (b)
D. none of the above


Where in the classroom was the student
after 10 seconds?
Distance \( / m \) \( \mathbf{1} \) \( \mathbf{2} \) \( \mathbf{3} \)
Time \( / s \) 0 1 2


A uniform magnetic field is restricted
within a region of radius \( r . \) The
magnetic field changes with time at a rate \( \frac{d \vec{B}}{d t} . \) Loop 1 of radius \( R>r \) enclose the region \( r \) and loop 2 of radius \( R \) is
outside the region of magnetic field as shown in the figure below. Then the
e.m.f. generated is :
\( A \)
B. Zero in loop 1 and zero in loop 2
c. \( \quad \frac{d \vec{B}}{d t} \pi r^{2} \) in loop 1 and \( -\frac{d \vec{B}}{d t} \pi r^{2} \) in loop 2
D. \( -\frac{d \vec{B}}{d t} \pi R^{2} \) in loop 1 and zero in


The electronic configuration of actinides cannot be predicted with
degree of certainty because of :
A. small energy difference between 5f and 6d levels
B. overlapping of inner orbitals
C. free movement of electrons over all the orbitals
D. none of the above


In Young's double-slit experiment, 12 fringes are observed to be formed in a certain segment of the screen when light of wavelength 600 nm is used. If the wavelength of light is changed to \( 400 n m, \) number of fringes observed in the same segment of the screen is given by
A . 12
B . 18
\( c \cdot 24 \)
D. 30


Following are the car parking charges near a railway station up to
Time Parking chargess
4 hours \( \quad \) Rs. 60
Rours
12 hours \( \quad \) Rs. 140
24 hours \( \quad \) Rs. 180
Check if the parking charges are in direct proportion to the parking time.


If the wave equation is \( y= \)
\( 0.08 \sin \frac{2 \pi}{\lambda}(150 t-x) s . \) Then velocity of
the wave will be
A. 150 units
B. \( 150 \sqrt{2} \) units
c. 300 units
D. \( 300 \sqrt{2} \) units


Can a body have a charge of \( 4.8 \times 10^{-20} \)
coulomb?
A. Yes
B. No
c. мау be
D. only semiconductors can have


The rigid conducting thin wire frame carries an electric current \( I \) and this
frame is inside a uniform magnetic field \( \vec{B} \) as shown in fig. Then
A. the net magnetic force on the frame is zero but the torque is not zero
B. the net magnetic force on the frame and the torque due to magnetic field are both zero
c. the net magnetic force on the frame is not zero and the torque is also not zero
D. none of these


Assertion
A car moving on a horizontal rough road with velocity \( v \) can be stopped in a minimum distance \( d \). If the same car
moving with same speed \( v \) takes a circular turn, then minimum safe
radius can be \( 2 d \)
Reason
\( d=\frac{v^{2}}{2 \mu g} \) and minimum safe radius \( = \) \( \boldsymbol{v}^{2} \)
\( \mu g \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion is incorrect and Reason is correct


(a) What is anionic detergent? Write an example.
(b) Why are chemicals added to food?
Write any two reasons.
(c) Write any one difference between broad spectrum and narrow spectrum
antibiotics.


A particle executing SHM is described
by the equation \( \boldsymbol{x}=\boldsymbol{A} \boldsymbol{e}^{\boldsymbol{\omega} t} \). Will this
particle describe SHM.
A. It dosen't execute SHM
B. It executes SHM only for the first time
c. It executes SHM from \( x=0 \) to \( x=A \)
D. It executes SHM from \( x=0 \) to \( x=-A \)


The product \( C \) and \( D \) in above reaction
are:
\( \mathbf{A} \)
B.
and
\( c \)
and
D.
and


A light ray going through a prism with
the angle of prism \( 60^{\circ}, \) is found to
deviate at least by \( 30^{\circ} . \) What is the range of the refractive index of the
prism?


Simplify : \( (-13)-(+14) \)


The movement of stems and roots in
response to force of gravity is known as
A. Geotropism
B. Hydrotropism
c. Thigmotropism
D. chemotropism


Name the following:
Reaction when an alkyl halide is treated
with alcoholic potassium hydroxide.


Matter can be hard or soft
A. True
B. False


The value of \( \sin ^{-1} x+\cos ^{-1} x, \forall x \in \)
[-1,1] is
A \( \cdot \frac{\pi}{2} \)
в. \( \frac{-5 \pi}{3} \)
c. \( \frac{-3 \pi}{2} \)
D.


If 3 points \( A(1, a, b), B(a, 2, b), C(a, b, 3) \) are
collinear, then find \( a+b=? \)


Of the following quantities which one has the dimensions different from the
remaining three?
A. Energy density
B. Force per unit area
c. Product of charge per unit volume and voltage
D. Angular momentum per unit mass


To determine the Youngs modulus of a wire,the formula is \( \boldsymbol{Y}=\frac{\boldsymbol{F}}{\boldsymbol{A}} \times \frac{\boldsymbol{\Delta} \boldsymbol{L}}{\boldsymbol{L}} \)
where \( L= \) length, \( A= \) area of cross
section of the wire, \( \Delta \mathrm{L}= \) change in length of the wire when stretched with a force F. The conversion factor to change
it from CGS to MKS system is :
\( A \cdot 1 \)
B. 10
c. \( 0 . \)
D. 0.01


One kilogram of sugar has more volume than one kilogram of iron. True or false.
A. True
B. False


In the nuclear fusion reaction \( :_{1}^{2} \boldsymbol{H}+_{1}^{3} \) \( \boldsymbol{H} \rightarrow_{2}^{4} \boldsymbol{H} e+\boldsymbol{n}, \) given that the
repulsive potential energy between the two nuclei is \( \sim 7.7 \times 10^{-14} \mathrm{J} \), the
temperature to which the gases must be heated to initiate the reaction is
nearly (Boltzmann's constant \( \left.k=1.38 \times 10^{-23} \mathrm{J}\right) \)
\( \mathbf{A} \cdot 10^{7} K \)
B . \( 10^{5} K \)
\( \mathbf{c} \cdot 10^{3} K \)
D. \( 10^{9} K \)


If \( \boldsymbol{2} \boldsymbol{x}=\boldsymbol{y}^{\frac{1}{5}}+\boldsymbol{y}^{-\frac{1}{5}} \) and \( \left(\boldsymbol{x}^{2}-\mathbf{1}\right) \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}+ \)
\( \lambda x \frac{d y}{d x}+k y=0, \) then \( \lambda+k \) is equal to:
A . -23
в. -24
\( c \cdot 26 \)
D. -26


A train travels at a speed \( 50 \mathrm{km} / \mathrm{hr} \) for \( 0.5 \mathrm{hr}, \) at \( 30 \mathrm{km} / \mathrm{hr} \) for next \( 0.26 \mathrm{hr} \) and
then \( 70 \mathrm{km} / \mathrm{hr} \) for next \( 0.76 \mathrm{hr} \)
Determine the average speed of the train.


One mole of non volatile solute is
dissolved in two moles of water. The
vapour pressure of the solution relative to that of water is:
A \( \cdot \frac{2}{3} \)
в. \( \frac{1}{3} \)
\( c \cdot \frac{1}{2} \)
D. \( \frac{3}{1} \)


In Melandrium, the sex determination
type is
A. \( x x \) -XY type
B. XX-XO type
c. zz-zw type
D. xy-xo type
E. xo-zz type.


If \( \boldsymbol{A}=\{\boldsymbol{x}:-\mathbf{1} \leq \boldsymbol{x} \leq \mathbf{1}\}=\boldsymbol{B} . \) Discuss
the following function w.r.t one-one onto bijective and write their characteristics \( \boldsymbol{f}(\boldsymbol{x})=\frac{\boldsymbol{x}}{\boldsymbol{2}} \)
A. one one, into
B. one one, onto
c. many one, into
D. many one, onto


Which of the following is homogeneous?
A. Milk
B. Paint
c. shampoo
D. All of the above


Vitamin \( \mathrm{B}_{6} \) is known as:
A. pyridoxine
B. thiamine
c. tocopherol
D. riboflavin


Find the value of the following determinant:
\( \left|\begin{array}{cc}-4 & \frac{-6}{35} \\ 7 & \frac{35}{5} \\ 5 & 5\end{array}\right| \)
A \( \cdot \frac{15}{34} \)
в. \( \frac{32}{45} \)
c. \( \frac{25}{33} \)
D. \( \frac{38}{35} \)


Distinguish between orbit and orbital


List four characteristic of the images formed by plane mirrors.


Branch dealing with study of algae is
A. Phycology
B. Mycology
c. Microbiology
D. onchology


The plates of a parallel-plate capacitor are made of circular discs of radii 5.0
\( \mathrm{cm} \) each. If the separation between the plates is \( 1.0 \mathrm{mm}, \) what is the capacitance?


On electrolysis of NaH, hydrogen is
liberated at:
A. anode
B. cathode
c. inert electrode
D. none of these


Aluminium is more reactive than iron
but aluminium is less easily corroded than iron because:
A. aluminium is a noble metal
B. oxygen forms a protective oxide layer
c. iron undergoes reaction easily with water
D. iron forms mono and divalent ions


A \( 60 \mathrm{HP} \) car is moving with a uniform velocity of \( 54 \mathrm{km} / \mathrm{hr} \). Find the forward force exerted by its engine.


Which is/are true statements?
A. Diamond is unaffected by conc acids but graphite reacts with hot conc. \( H N O_{3} \) forming mellitic acid, \( C_{6}(C O O H)_{6} \)
B. \( C O \) is toxic because it forms a complex with hemoglobin in the blood
\( \mathrm{C} \cdot \mathrm{C}_{3} \mathrm{O}_{2}, \) carbon sub-oxide, is a foul-smelling gas
D. All the above


Two particles of masses are in the ratio
1: 2. The ratio of distance of the center of
mass of the system of these two particles from the lighter particle to that from the heavier particle is
\( A \cdot 1: 2 \)
B. 2:
\( c \cdot 1: 4 \)
\( D \cdot 4: \)


Assuming each salt to be \( 90 \% \) dissociated which of the followings will have highest osmotic pressure?
A. Decimolar \( A l_{2}\left(S O_{4}\right)_{3} \)
B. Decimolar \( B a C l_{2} \)
c. Decimolar \( N a_{2} S O_{4} \)
D. A solution obtained by mixing equal volumes of \( (b) \) and (c) and filtering


The range of \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \sec \left(\frac{\pi}{4} \cos ^{2} x\right) \cdot-\infty<x<\infty \) is
A \( \cdot[1, \sqrt{2}] \)
B . \( [1, \infty] \)
c. \( [-\sqrt{2},-1] \cup[1, \sqrt{2}] \)
D \( \cdot[-\infty,-1] \cup[1, \infty] \)


A sphere is released on a smooth
inclined plane from the top. When it
moves down its angular momentum is:
A. conserved about every point
B. conserved about the point of contact only
c. conserved about the centre of the sphere only
D. conserved about any point on a fixed line parallel to the inclined plane and passing through the centre of the ball


The atomic numbers of elements
\( A, B, C \) and \( D \) are \( Z-1, Z, Z+1 \) and
\( Z+2, \) respectively. If \( ^{\prime} B^{\prime} \) is a noble gas, choose the correct answers from the following statements
(1) \( ^{\prime} A^{\prime} \) has higher electron affinity
(2) ' \( C^{\prime} \) exists in +2 oxidation state
(3) ' \( D^{\prime} \) is an alkaline earth metal
A \( \cdot(1) \) and (2)
B. (2) and (3)
c. (1) and (3)
D. (1),(2) and (3)


Number of spectral line in hydrogen
atom is
A. 6
B. 8
c. 15
D. None of the above


\( B r F_{3} \) molecule is:
A. planar trigonal
B. tetrahedral
c. T-shaped
D. trigonal pyramidal


A capacitor and resistor are connected with an \( A C \) source as shown in figure.
Reactance of capacitor is \( X_{C}=3 \Omega \) and
resistance of resistor is \( 4 \Omega \). Phase
difference between current \( I \) and \( I_{1} \) is \( \left[\tan ^{-1}\left(\frac{3}{4}\right)=37^{\circ}\right] \)
A \( .90^{\circ} \)
B. zero
\( c \cdot 53^{\circ} \)
D. 37


The transfer ratio \( \beta \) of a transistor is 50 The input resistance of the transistor
when used in the common emitter
mode is \( 1 K \omega \).The peak value of the
collector alternating current for an
input peak voltage of \( 0.01 V \) is
A. \( 100 \mu A \)
в. \( 500 \mu A \)
c. \( 0.01 \mu A \)
D. \( 0.25 \mu A \)


Reducing power generated during light reaction is used during formation of
A. 3-phosphoglyceraldehyde from RuBP
B. Sucrose from triose phosphate
c. Glyceraldehyde 3-phosphate from 3-phosphoglycerate
D. RuBP from triose phosphate


Pick up the correct statement:
A. Boiling points of alkyl halides are greater than those of the corresponding alkanes.
B. In water, the solubility decreases as \( C H_{3} O H> \) \( C_{2} H_{5} O H>C_{6} H_{5} O H \)
C. Aniline is a weaker base than ammonia.
D. All of the above.


Find the volume of a hemisphere of radius 7 dm.
A \( \cdot 708.67 d m^{3} \)
B . \( 818.67 d m^{3} \)
c. \( 717.67 d m^{3} \)
D. \( 718.67 d m^{3} \)


Which of the following is incorrect
about \( \boldsymbol{H}_{\mathbf{4}} \boldsymbol{P}_{\mathbf{2}} \boldsymbol{O}_{\mathbf{5}} \) ?
A. It contains \( P \) in +5 oxidation state
B. It is dibasic acid
c. It is strongly reducing in nature
D. It contains one \( P-O-P \) bond


If \( \boldsymbol{K}_{s p} \) for \( \boldsymbol{H} \boldsymbol{g} \boldsymbol{S} \boldsymbol{O}_{4} \) is \( \boldsymbol{6} . \boldsymbol{4} \times 10^{-5}, \) then
solubility of this substance in mole per
\( m^{3} \) is:
A. \( 8 \times 10^{-3} \)
В. \( 6.4 \times 10^{-5} \)
c. \( 8 \times 10^{-6} \)
D. None of these


The best malleable metal is:
A. aluminium
B. silver
c. gold
D. leadd