The correct IUPAC name of the following compound is
\( \left[\boldsymbol{C r}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{5}(\boldsymbol{N} \boldsymbol{C S})\right]\left[\boldsymbol{Z n C l}_{4}\right] \)
A. pentaammine isothiocyanato chromium(III) tetrachlorozincate(II)
B. pentammine isothiocyanate zinc chloridechromate(III)
c. pentaammine isothiocyanato chromate(II)
D. isothiocyanato pentaammine chromium(II) zinc chloride(IV).


The equation of the transverse wave travelling in a rope is given by \( \mathbf{y}= \) \( 5 \sin (4 t-0.02 x) \) where \( y \) and \( x \) are in
meters and \( t \) is in seconds. Calculate
the intensity of the wave if the density
of rope material is \( 1250 \mathrm{kg} / \mathrm{m}^{3} \)
A. \( 2000 \mathrm{kJm}^{-2} \mathrm{s}^{-1} \)
B. \( 10 \mathrm{kJm}^{-2} \mathrm{s}^{-1} \)
c. \( 40 \mathrm{kJm}^{-2} \mathrm{s}^{-1} \)
D. 3 \( k J m^{-2} s^{-1} \)


Which of the following expressions for \( \% \) ionization of a monoacidic base
\( (B O H) \) in aqueous solution is not correct at appreciable concentration?
A \( \cdot_{100} \times \sqrt{\frac{K_{b}}{c}} \)
В. \( \frac{1}{1+10\left(p K_{b}-p O H\right)} \)
с. \( \frac{K_{w}\left[H^{+}\right]}{K_{b}+K_{w}} \)
D. \( \frac{K_{b}}{K_{b}+\left[O H^{-}\right]} \)


In G.P \( 3 r d \) term is 24 and 6 th term is 192
then find 10 th term


A projectile is thrown in the upward direction making an angle of 60 with the horizontal direction with a velocity
of 47 Then the time after which its
inclination with the horizontal is 45


Which of the element is most poisonous to human?
A. \( O \)
в. \( S \)
c. \( S e \)
D. None of above


When a coil rotated in magnetic field
induced current in it :
A. continuously changes
B. remains same
c. becomes zero
D. becomes maximum


In the circuit shown in the fig the heat
produced in resistance \( R_{1} \) can be
measured by
A. connecting both voltmeter and an ammeter in parallel to \( R_{1} \)
B. connecting ammeter in series with \( R_{1} \) and voltmeter in parallel to both \( R_{1} \) and \( R_{2} \)
C. connecting ammeter in parallel to \( R_{1} \) and voltmeter in
series with \( R_{1} \)
D. connecting voltmeter in parallel to \( R_{1} \) and ammeter in
series with \( R_{1} \)


The modal class of the following frequency distribution is
class \( \begin{array}{cc}0- & 10- \\ 10 & 20\end{array} \) 30 40
Frequency
15
17
A . \( 20-30 \)
в. \( 10-20 \)
c. \( 30-40 \)
D. \( 40-50 \)


A toroidal coil has 3000 turns. The
inner and outer radii are \( 10 \mathrm{cm} \) and 14
cm respectively. If current flowing is \( 5 A \) then the magnetic field inside the toroid will be.
A \( .2 .5 \times 10^{-5} T \)
В . \( 2.5 \times 10^{-2} T \)
c. \( 0.25 T \)
D. \( 2.5 \times 10^{-4} T \)


Name the process usually employed for the purification of nickel?


SD region in prokaryotic mRNA is a part of
A. TATA BOX
B. RBS (Ribosome Binding Site)
c. ASD region
D. Promoter


What is the name for the horizontal
rows of the periodic table?
A. Groups
B. Periods
c. Families
D. sets


Given \( 300.0 \mathrm{mL} \) of a gas at \( 17^{0} \mathrm{C} \). What
is its volume at \( 10^{0} \) C?


Days are shorter in winter than in
summer because
A. The tilt of the earth's axis
B. The tilting of the sun
C. The climate results in shortening of days
D. None of the above


(a) What is enzyme catalysis? Write an
example.
(b) Which type of emulsion is milk? Explain.
(c) Explain Electrophoresis with labelled diagram.


Dimensions of 'ohm' are same as that
of:
(Given \( : h \) is Planck's constant and \( e \) is
charge)
\( A \cdot \frac{h}{e} \)
в. \( \frac{h^{2}}{e} \)
\( c \cdot \frac{h}{e^{2}} \)
D. \( \frac{h^{2}}{e^{2}} \)


If \( A \) is a square matrix, then \( A-A^{T} \) is
A. unit matrix
B. null matrix
\( c . A \)
D. a skew symmetric matrix


10 g mixture of \( N a H C O_{3} \) and
\( N a_{2} C O_{3} \) has 1.68 g \( N a H C O_{3} . \) It is
heated at 400 K. Weight of the residue will be :
A. \( 9.38 \mathrm{g} \)
B. 8.32 g
c. \( 10.0 \mathrm{g} \)
D. 1.68 g


The closest distance of the origin from a curve given as \( \boldsymbol{a} \overline{\boldsymbol{z}}+\overline{\boldsymbol{a}} \boldsymbol{z}+\boldsymbol{a} \overline{\boldsymbol{a}}=\mathbf{0}(\boldsymbol{a} \) is a
complex number
A . 1
в. \( \frac{|a|}{2} \)
c. \( \frac{\operatorname{Re}(a)}{|a|} \)
D. \( \frac{\operatorname{Im}(a)}{|a|} \)


On dividing the polynomial \( 3 x^{3}+ \) \( 4 x^{2}+5 x-13 \) by a polynomial \( g(x), \) the
quotient and the remainder were \( (3 x+ \)
10) and \( (16 x-43) \) respectively. Find
\( \boldsymbol{g}(\boldsymbol{x}) \)


Enzyme causing lysis of fibrin during fibrinolysis is
A. Fibrinogen
B. Plasmin
c. Thrombin
D. VIII Platelet factor


The correct sequence of increasing covalent character is represented by :
A \( \cdot \operatorname{Becl}_{2}< \) Nacl \( < \) Lic
B. NaCI<LiCI <BeCla
\( \mathrm{c} \cdot \mathrm{BeCl}_{2}<\mathrm{LiCl}<\mathrm{NaCl} \)
D. LiCI<NaCI<BeCI


Sum of \( (267+345)+21 \) and \( 267+ \)
\( (345+21) \) will be same
A. True
B. False


R.Q. of a germinating ground nut and castor seed is
A . 1
B. \( <1 \)
\( c \cdot>1 \)
D.


How many play cricket only?


\( (a+b)^{3}=? \)
\( \mathbf{A} \cdot a^{3}+3 a^{2} b+3 a b^{2}+b^{3} \)
B \( \cdot a^{3}+a^{2} b+a b^{2}+b^{3} \)
c. \( a^{3}-3 a^{2} b+3 a b^{2}-b^{3} \)
D \( \cdot a^{3}+3 a^{2} b-3 a b^{2}+b^{3} \)


3 faraday of electricity are passed through molten \( A l_{2} O_{3}, \) aqueous
solution of \( C u S O_{4} \) and molten NaCl
taken in three different electrolytic
cells. The amount of \( \mathrm{Al}, \mathrm{Cu}, \) and \( \mathrm{Na} \)
deposited at the cathodes will be in the ratio of
A. 1 mole : 2 mole : 3 mole
B. 3 mole:2 mole:1 mole
c. 1 mole : 1.5 mole : 3 mole
D. 1.5 mole : 2 mole : 3 mole


\( \boldsymbol{I}=\int_{0}^{3} \frac{\boldsymbol{x} \boldsymbol{d} \boldsymbol{x}}{1+\boldsymbol{x}^{2}} \)


The table shows a five-day forecast indicating high (H) and Low(L) temperatures in Fahrenheit. Organise the temperatures in a matrix where the
first and second rows represent the High and Low temperatures respectively and identify which day will be the
warmest?
\begin{tabular}{|c|c|c|c|c|}
\hline Mon & Tue & wed & Thu & Fri \\
\hline\( \sum_{i}^{m} \) & \( \sum_{i}^{m} \) & \( \sum_{i}^{m} \) & \( \sum_{i}^{m} \) & \( \sum_{j}^{m} \) \\
\hline \( \mathrm{H} 88 \) & \( \mathrm{H} 90 \) & \( \mathrm{H} 86 \) & \( \mathrm{H} 84 \) & \( \mathrm{H} 85 \) \\
\hline \( \mathrm{L} 54 \) & \( \mathrm{L} 56 \) & \( \mathrm{L} 53 \) & \( \mathrm{L} 52 \) & \( \mathrm{L} 52 \) \\
\hline
\end{tabular}


If a continuous function \( \boldsymbol{f} \) satisfies \( \int_{0}^{x^{2}} f(t) d t=x^{2}(1+x) \operatorname{then} f(4) \) is
equal to
\( A \cdot 7 \)
B. 4
c. 5
\( D \)


The work done in an open vessel at 300
K, when \( 112 g \) iron reacts with dilute
\( H C l \) to give \( F e C l_{2}, \) is nearly:
A. 1.1 kcal
B. 0.6 kcal
c. 0.3 kcal
D. 0.2 kcal


Which one of the following is less polluting fuel?
A. Natural gas
B. coal
c. Kerosene
D. Petrol


If the range of \( 5 \cos \theta+3 \cos \left(\theta+\frac{\pi}{3}\right)+ \)
\( \mathbf{3} \) is \( [\boldsymbol{a}, \boldsymbol{b}], \forall \boldsymbol{\theta} \in \mathbf{R} \) then \( \boldsymbol{a}+\boldsymbol{b} \) is equal to
\( \mathbf{A} \cdot \mathbf{6} \)
B. 2
c. 8
D. 4


The value of \( \int x^{3} \log x d x \) is
A \( \cdot \frac{1}{16}\left(4 x^{4} \log x-x^{4}+c\right) \)
B \( \cdot \frac{1}{8}\left(x^{4} \log x-4 x^{4}+c\right) \)
c. \( \frac{1}{16}\left(4 x^{4} \log x+x^{4}+c\right) \)
\( \frac{x^{4} \log x}{4}+c \)


The dot products of a vector with the vectors \( (\hat{i}+\hat{j}-3 \hat{k}),(\hat{i}+3 \hat{j}-2 \hat{k}) \) and
\( (2 \hat{i}+\hat{j}+4 \hat{k}) \) are 0,5,8 respectively
Find the vector.


How many of the following compound on
thermal decomposition gives \( N_{2} \) gas?
\( \left(N H_{4}\right)_{2} C r_{2} O_{7}, N H_{4} N O_{3}, N H_{4} I O_{3} \)
\( N H_{4} N O_{2}, B a\left(N_{3}\right)_{2}, B a\left(N O_{3}\right)_{2} \)
\( \left(N H_{4}\right)_{2} S O_{4},\left(N H_{4}\right)_{2} C O_{3} \)
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 5


A neutron in a nuclear reactor collides
head on elastically with the nucleus of a carbon atom initially at rest. The fraction of kinetic energy transferred from the neutron to the carbon atom is
A \( \cdot \frac{11}{12} \)
B. \( \frac{2}{11} \)
c. \( \frac{48}{121} \)
D. \( \frac{48}{169} \)


If \( (x+1), 3 x \) and \( (4 x+2) \) are first
three terms of an AP then its 5th term
is
A . 14
B. 19
c. 24
D. 28


19 boys turn out for baseball. Of these
11 are wearing baseball shirts and 14 are wearing baseball pants. There are no boys without one or the other. The
number of boys wearing full uniform is
\( \mathbf{A} \cdot \mathbf{8} \)
B. 6
c. 5
D. 3


Damaged parts and organs can be repaired by
A. Reparative regeneration
B. Restorative regeneration
c. Physiological regeneration
D. Heteromorphic regeneration


Evaluate \( (\sqrt{\mathbf{3}}-\sqrt{\mathbf{2}})^{\mathbf{6}}+(\sqrt{\mathbf{3}}+\sqrt{\mathbf{2}})^{\mathbf{6}} \)
A. 678
в. 950
\( c .970 \)
D. 670


In a right angled triangle if an angle
measures then \( 35^{0} \) the measure of
other angle is
A \( .65^{\circ} \)
B. 55
c. \( 45^{\circ} \)
D. 30


The electric field at a distance \( 2 \mathrm{cm} \) from the centre of a hollow spherical conducting shell of radius \( 4 \mathrm{cm} \) having a charge of \( 2 \times 10^{-3} \mathrm{C} \) on its surface is :
This question has multiple correct options
A . \( 1.1 \times 10^{10} V / m \)
B . \( 4.5 \times 10^{-10} V / m \)
C \( .4 .5 \times 10^{10} V / m \)
D. zero


Find the angle which is supplementary of itself


Which of the following is not included under optical aids?
A. Contact lenses
B. Tinted lenses
c. Magnifiers
D. None of these


Calculate the cost of using four 500 W air-conditioners for eight hours each
day for a 30 day month. The unit cost of electrical energy is Rs. 1.50 per \( \mathrm{kWh} \)


Find the standard deviation of 40,42
and \( 48 . \) If each value is multiplied by 3 find the standard deviation of the new
data


If \( |\vec{A}+\vec{B}|=|\vec{A}|=|\vec{B}|, \) then angle
between \( \vec{A} \) and \( \vec{B} \) is
A \( \cdot 0^{\circ} \)
B. \( 60^{\circ} \)
\( c .90^{\circ} \)
D. \( 120^{\circ} \)


The floor of a building consists of around 3000 tiles which are rhombus
shaped and each of its diagonals are \( 45 c m \) and \( 30 c m \) in length. Find the total
\( \operatorname{cost} \) of flooring if each tile costs rupees
20 per \( m^{2} \)


Prove that:
\[
\left|\begin{array}{ccc}
\boldsymbol{a}-\boldsymbol{b}-\boldsymbol{c} & \boldsymbol{2} \boldsymbol{a} & \boldsymbol{2} \boldsymbol{a} \\
\boldsymbol{2} \boldsymbol{b} & \boldsymbol{b}-\boldsymbol{c}-\boldsymbol{a} & \boldsymbol{2} \boldsymbol{b} \\
\boldsymbol{2} \boldsymbol{c} & \boldsymbol{2} \boldsymbol{c} & \boldsymbol{c}-\boldsymbol{a}-\boldsymbol{b}
\end{array}\right|=
\]
\( (a+b+c)^{3} \)


If \( \vec{a}=i+j-k, \vec{b}=1-j+k, \vec{c} \) is a
unit vector such that \( \vec{c} . \vec{a}=0,[\vec{c} \vec{a} \vec{b}]=0 \)
then a unit vectors perpendicular to both \( \vec{a} \) and \( \vec{c} \) is
A \( \cdot \frac{1}{\sqrt{6}}(2 i-j+k) \)
B. \( \frac{1}{\sqrt{2}}(j+k) \)
c. \( \frac{1}{\sqrt{2}}(i+j) \)
D. \( \frac{1}{\sqrt{2}}(i+k) \)


What is the ability of the eye lens to
adjust its focal length called?


The principal value of \( \tan ^{-1}\left(\cot \frac{43 \pi}{4}\right) \) is
A \( \cdot-\frac{3 \pi}{4} \)
B. \( \frac{3 \pi}{4} \)
\( c \cdot-\frac{\pi}{4} \)
\( D \cdot \frac{\pi}{4} \)


a) Write the mechanism of acid
catalysed dehydration of ethanol to ethene.
b) Between phenol and alcohol which is
more acidic? Why?


The half-life of a radioactive material is
693 years. Find its decay constant.


Sl unit of G in Newton's law of
Gravitation is :
A \( \cdot N^{2} m^{2} / k g \)
в. \( N m^{2} / k g \)
c. \( N m / k g \)
D. \( N m^{2} / k g^{2} \)


Which of the following rejector circuit (symbols have their usual meaning)?
\( A \)
B.
\( c \)
D.


An electromagnetic wave has energy in
the form of
A. variable electric field
B. variable magnetic field
c. both A and B
D. none of the above


\( \int_{1}^{2} x^{2} \log x d x_{=} \)
A. \( \frac{8}{3} \log 2-\frac{7}{9} \)
в. \( \frac{8}{3} \log 2+\frac{7}{9} \)
c. \( \frac{8}{3} \log \frac{1}{3}-\frac{7}{9} \)
D. \( \frac{8}{3} \log \frac{1}{3}+\frac{7}{9} \)


The perimeter of one face of a cube is 24
\( \mathrm{cm} . \) Find the total area of the 6 faces in
\( \mathrm{cm}^{2} \)


A crane pulls up a car of mass \( 500 \mathrm{kg} \) to a vertical height of \( 4 m . \) So, work done by
the crane is:
A. \( 19.6 J \)
в. \( 19.6 k J \)
c. \( 19600 k J \)
D. \( 4900 J \)


Which of the following statement is true for laws of reflection?
A. The incident ray, reflected ray and the normal lie in the same plane.
B. Angle of incidence is equal to the angle of reflection
c. Both A and B
D. None


Differentiate with respect to \( x \) :
\( e^{-3 x} \log (1+x) \)


Which of the following is used for purification of aldehydes from impurities?
\( \mathbf{A} \cdot H C N \)
в. \( \operatorname{NaHSO}_{3} \)
c. \( C H_{3} M g B r \)
D. \( N a_{2} S O_{4} \)


A mass m starting from A reaches B of
frictionless track. On reaching B, it pushes the track with a force equal to \( x \)
times its weight, then the applicable relation is :
A \( n=\frac{(5-x)}{2} \)
в. \( h=\frac{x}{2} R \)
\( c \cdot h=R \)
' \( h=\left(\frac{x+1}{2}\right) R \)


Energy is released during the formation
of:
A. hydride ion
B. oxide ion
c. ferrous ion
D. ferric ion


Draw a labelled diagram of a step-up transformer. Obtain the ratio of
secondary to primary voltage in terms of number of terns and current in the
two coil.


What is the angular velocity of rotation of this rigid body?
A \( \cdot \frac{V_{0}}{5 d} \)
B. \( \frac{V_{0}}{d} \)
c. \( \frac{V_{0}}{3 d} \)
D.


Which type of reaction in the reduction
of carbonyl compound with \( L A H \) and
\( N a B H_{4} \) occurs, and which nucleophile takes part in the reaction?
A . Nucleophilic addition and \( A l H_{4}^{\ominus} \) or \( B H_{4}^{\text {d }} \)
B. Nucleophilic addition and \( H^{\ominus} \)
C. Nucleophilic substitution and \( A l H_{4}^{\ominus} \) or \( B H_{4}^{\text {d }} \)
D. Nucleophilic substitution and \( H^{\ominus} \)


Use or storage of acetylene in the form of liquid is prohibited by law.
A. True
B. False


Which of the following are green lungs?
A. Green coloured lungs
B. Lungs with green alga
c. Lungs in Green coloured animals
D. Forests


Statement \( (A): \) The reactance offered by an inductance in A.C. circuit decreases with the increase of \( A C \)
frequency. Statement \( (\mathrm{B}): \) The reactance offered
by a capacitor in AC circuit increases with the increase of AC frequency.
A. A is true but B is false
B. Both A and B are true
c. A is false but B is true
D. Both A and B are false


It is known that \( 60 \% \) mice inoculated
with a serum are protected from a
certain disease. If 5 mice are
inoculated, find the probability that none contact the disease.


The electron pairs involved in hybridisation and not involved in bonding are called


If \( \int \frac{2 \sin x+3 \cos x}{3 \sin x+4 \cos x} d x=A \log \)
\( |3 \sin x+4 \cos x|+B x+c, \) then \( A= \)
\( \ldots \ldots \ldots, B=\ldots \ldots \ldots . . \)
A. \( -\frac{1}{25}, \frac{18}{25} \)
8. \( -\frac{1}{5},-\frac{1}{5} \)
c. \( \frac{1}{25}, \frac{18}{25} \)
D. \( \frac{1}{25}, \frac{3}{25} \)


Consider the following in respect of the function \( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{ll}2+\boldsymbol{x}, & \boldsymbol{x} \geq 0 \\ 2-\boldsymbol{x}, & \boldsymbol{x}<0\end{array}\right. \)
1. \( \lim _{x \rightarrow 1} f(x) \) does not exist.
2. \( f(x) \) is differentiable \( a t x=0 \)
3. \( f(x) \) is continuous at \( x=0 \)
Which of the above statements is/are
correct?
A. 1 only
B. 3 only
c. 2 and 3 only
D. 1 and 3 only


If \( f(x)=x+7 \) and \( g(x)=x-7, x \in R \)
find \( (f o g)(7) . \) function \( f: R \rightarrow R \)
defined by \( f(x)=\frac{3 x+5}{2} \) is an invertible
function, find \( \boldsymbol{f}^{-1} \)


The truth-table given below is for which gate?
\( \begin{array}{lll}A & B & C \\ 0 & 0 & 1 \\ 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0\end{array} \)
A. xor
B. OR
c. AND
D. NAND


Figure \( (a) \) below shows a Wheatstone
bridge in which \( P, Q, R, S \) are fixed
resistances, \( G \) is a galvanometer and \( B \)
is a battery. For this particular case the galvanometer shows zero deflection.
Now, only the positions of \( B \) and \( G \) are
interchanged, as shown in figure ( \( b \) ).
The new deflection of the galvanometer.
A. Is to the left
B. Is to the right
\( c . \) Is zero
D. Depends on the values of \( P, Q, R, S \).


The IUPAC name of \( \boldsymbol{X} \boldsymbol{e}\left[\boldsymbol{P} \boldsymbol{t} \boldsymbol{F}_{\boldsymbol{6}}\right] \) is:
A. Hexafluoridoplatinate (VI) xenon
B. Xenon xenon hexafluoroplatinate (V)
c. xenon hexafluoridoplatinate (VI)
D. xenonium hexafluoridoplatinum ( V )


There are 5 cards in a box with numbers
1 to5 written on them. If 2 cards are
picked out from the box, write all the possible outcomes and find the probpossible ability of getting both even numbers.


Here is another look at the reaction of
crystal violet with sodium hydroxide, a
first-order reaction \( (\ln A \mathbf{v} \text { time }) \)

What is the significance of the slope?
A. The slope represents the change in concentration over time
B. The slope represents the inverse of change in concentration over time
c. The slope represents the negative value of the rate constant
D. The slope represents the negative rate of product concentration over time


Which one of the following is a disaccharide?
A. Starch
B. Lactose
c. Cellulose
D. Fructose


ENERGY OF AN ORBITING SATELLITE
A comet orbits the sun in a highly elliptical orbit. Which of the following quantities remains constant throughout its orbit?
(i) Linear speed
(ii) Angular speed (iii) Angular momentum (iv) Kinetic energy
(v) Potential energy (vi)Total energy
\( A \cdot(i),(\text { ii) },( \text { iii) } \)
B. (iii), (iv), (v)
c. (iii) and (vi)
D. (ii), (iii) and (vi)


State whether True or False:
Facatorization of \( 9 x^{2}-\frac{1}{16} \) is \( (3 x- \) \( \left.\frac{1}{4}\right)\left(3 x+\frac{1}{4}\right) \)
A. True
B. False


Which of the following is most common pathogen pollutant?
A . Coliform
B. E. coli bacteria
c. Psedumonas
D. Both A and B


Q Type your question
\[
\underset{\mathbf{M e} \atop \mathbf{P r o p e n}}^{\mathbf{S}}+\mathbf{P} \mathrm{d} \mathrm{Cl}_{2}+\mathbf{H}_{2} \mathbf{O} \frac{\mathbf{C u C l}_{2}}{\mathbf{O}_{2}} \underbrace{\mathbf{O}}_{\mathbf{M e}} \|_{\mathbf{M e}}+\mathbf{P} \mathbf{d}+\mathbf{3 H C l}
\]
(The reaction proceeds via the addition of \( \mathbf{H}^{\oplus} \) and \( \mathbf{O} \mathbf{H} \) by Markovnikov's rule followed by oxidation.
(or)
(iii) \( \mathrm{BH}_{3}+\mathrm{THF}+\mathrm{CH}_{3} \mathrm{COOH} \)
OH
(Wacker process)
This question has multiple correct options
\( \mathbf{A} \cdot H_{2} / P t \quad M M P P \quad \) Coldalk. \( K M n O_{4} \quad O_{2}+ \)
\[
P d C l_{2}+C u C l_{2}+H_{2} O
\]
\( \mathbf{B} \cdot H_{2} / P d+B a S O_{4}+ \)
quinoline\( \quad H C O_{3} H \quad \)Hotalk. \( K M n O_{4} \)
\( H \)
\( H g^{2+} \)
\( \mathbf{c} \cdot \sin _{2} B H+ \)
\( C H_{3} C O O H \quad P h C O_{3} H \quad O s O_{4} / N a H S O_{3} \)
\[
P d C l_{2}+C u C l_{2}+H_{O}
\]
\( \mathbf{D} \cdot B H_{3}+T H F+ \)
\[
\begin{array}{llll}
C H_{3} C O O H & M C P B A & O s O_{4} / H_{2} O_{2} & i
\end{array}
\]


Assign structures to \( A, B, C \) and \( D \) in
the following:
\( \mathbf{A} \cdot C H_{2} C H_{2} C H_{2} C H_{2}+a l c \cdot K O H \rightarrow A \)
\( B r \)
B \cdot \( \left(C H_{3}\right)_{3} C B r+C H_{3} C O O^{-} \rightarrow B \)
c. \( \left(C H_{3}\right)_{2} C H \underset{O_{H}}{C H} C H_{3}+H_{2} S O_{4} \triangleq C \)
\( D \)


How much positive and negative charge
is there in a cup of water?


\( \frac{d}{d} \)


Macrocystis is a
A. Red algae
B. Fungi
C . Bryophyta
D. Brown algae


Choose the correct statement
A. Any charged particle in rest is accompanied by matter waves.
B. Any uncharged particle in rest is accompanied by matter waves.
C. The matter waves are waves of zero amplitude.
D. The matter waves are waves of probability amplitude.


Structure present in a cell which is responsible for determination of the sex of a baby is
A . Cytoplasm
B. Cell membrane
c. Nucleus
D. chromosome


The ratio of the value of any colligative property for \( N a C l \) solution of that of an
equimolal solution of sugar is nearly
\( \mathbf{2}: \mathbf{1} \)
A. True
B. False


The lightening conductor is connected to interface with ground or "earth" through
\( A \cdot \) a cathode
B. an anode
c. an electrode
D. a semiconductor


Six X's have to be placed in the square
of given figure such that each row
contains at least one X. Then number of
ways doing so are
A . 28
B. 26
\( c .6 \)
D. \( 8 ! .6 \)


The incorrect statement in respect of chromyl chloride test is
A. Formation of Red vapour
B. Liberation of chlorine
c. Formation of chromyl chloride
D. All statements are wrong


A 0.02 M solution of pyridinium
hydrochloride has \( p H=3.44 . \) Calculate
the ionization constant of pyridine.


A current of 5 A is passing through a metallic wire of cross-sectional area
\( 4 \times 10^{-6} m^{2} . \) If the density of charge
carriers of the wire is \( 5 \times 10^{26} m^{-3}, \) then
the drift velocity of the electrons will be
A \( \cdot 1 \times 10^{2} m / s \)
B . \( 1.56 \times 10^{-2} \mathrm{m} / \mathrm{s} \)
c. \( 1.56 \times 10^{-3} \mathrm{m} / \mathrm{s} \)
D. \( 1 \times 10^{-2} \mathrm{m} / \mathrm{s} \)


Crystallisation is an example of chemical change.
A. True
B. False


Displacement current goes through the gap between the plates of a capaitor when the charge of the capacitor:
(i) does not change
(ii) change with time
(iii) increases
(iv) decreases
\( A \cdot(i),(\text { iii }) \) and \( (\text { iv }) \)
B. (i), and (ii) and (iv)
c. ( ii ), (iii) and (iv)
D. (i), (ii) and (iii)


In which of the following reaction pair of
diastereomers will form?
4
B
D. All of these


In the replacement reaction:
The reaction will be most favourable if
M happens to be:
\[
\frac{\lambda}{\nearrow} \mathrm{CI}+\mathrm{MF} \rightarrow \frac{\searrow}{/} \mathrm{CF}+\mathrm{MI}
\]
\( A \cdot K \)
B. Rb
\( c \cdot L \)
D. Na a


In a question on division if four times the divisor is added to the dividend then how will the new remainder change in comparison with the original remainder?
A. Remainder remains unchanged.
B. Remainder increases by 4
c. Remainder decreases by 4.
D. Remainder becomes 4 times the older remainder


\( 4.4 C O_{2} \) gas and 2.24 litre of \( H_{2} \) gas at
S.T.P are taken in a 1 litre container at
27. The total pressure of gases in container will be ?
\( A \cdot 4.926 \) atm
B. 3743.76 mm of Hg
c. \( 1871.88 \mathrm{mm} \) of \( \mathrm{Hg} \)
D. 2.463 atm


Give chemical name, formula, and uses
of Washing soda.


\( \boldsymbol{O} \)
\( \boldsymbol{P h}-\hat{\boldsymbol{C}}-\boldsymbol{O}-\boldsymbol{C P h}_{3} \frac{\boldsymbol{H}_{3}^{18} \boldsymbol{O} \oplus}{\longrightarrow} \)
Product of this reaction is:
B. \( o^{18} \)
\( P h-C-O H+P h_{3} C-O H \)
c. \( _{\text {I }}^{o} \)
Ph \( -C-O H+P h_{3} C-O H \)
D.
\[
P h-C-O H+P h_{3} C-O H
\]


The equation of motion of a rocket are:
\( \boldsymbol{x}=\mathbf{2} \boldsymbol{t}, \boldsymbol{y}=-\boldsymbol{4} \boldsymbol{t}, \boldsymbol{z}=\boldsymbol{4} \boldsymbol{t}, \) where the time
\( t \) is given in seconds and the coordinate
of a moving point in kilometers. At what distance will the rocket be from the
starting point \( O(0,0,0) \) in 10 seconds?
\( \mathbf{A} \cdot 60 \mathrm{km} \)
B. \( 30 \mathrm{km} \)
c. \( 45 \mathrm{km} \)
D. None of these


A hollow sphere of radius 5 cm is
charged such that the potential on its
surface is \( 10 \mathrm{V} \). The potential at the
center of the sphere will be:
\( \mathbf{A} \cdot 0 V \)
B. \( 10 V \)
C. same as at a point \( 5 \mathrm{cm} \) away from the surface
D. same as at point \( 25 \mathrm{cm} \) away from the center


2,4-hexadiyne \( \left(C_{6} H_{6}\right) \) is allowed to
react with \( L i \) in \( N H_{3}(\text { liq }) . \) The product obtained is treated with 1 equivalent of \( C l_{2} C C l_{4} . \) Which of the following constitutional isomers are possible products?
A . I and II
B. II and II
c. I and IV
D. I and III


The displacement of a particle is given by \( \boldsymbol{y}=\left(6 t^{2}+3 t+4\right) m, \) where \( t \) is in
seconds. Calculate the instantaneous
speed of the particle.
A . 12
B. \( 12 t+3 \)
c. \( 12 t+4 \)
D. \( 3 t+3 \)


Interstitial compounds are:
A. non-stoichiometric and are ionic in nature
B. non-stoichiometric and are covalent in nature
C. non-stoichiometric and are neither typically ionic nor covalent in nature
D. stoichiometric and are neither ionic nor covalent in
nature


Which of the following options correctly
represents the lungs conditions in
asthma and emphysema respectively?
A. Increased respiratory surface and inflammations of bronchioles
B. Inflammations of bronchioles, and decreased respiratory surface
C. Decreased respiratory surface, and inflammations of bronchioles
D. Increased number of bronchioles, and increased respiratory surface


The speed of sound in solid, liquid and gas can be correctly compared as:
A. solid >liquid > gas
B. liquid>gas>solidd
c. liquid > solid > gas
D. gas >liquid > gas


Knowing the properties of \( \boldsymbol{H}_{2} \boldsymbol{O} \) and
\( D_{2} O . \) Do you think that \( D_{2} O \) can be
used for drinking purposes?


In above fig. \( 2, \) if \( D \) is mid-point of \( B C \) the value of \( \frac{\cot y^{\circ}}{\cot x^{\circ}} \) is:
\( A \)
B. \( \frac{1}{4} \)
\( c \cdot \frac{1}{3} \)
D. 1


Set up equations and solve them to find the unknown numbers in the following
cases:
lbenhal thinks of a number. If she adds
19 to it divides the sum by 5, she will get
8


Which of the following statements concludes that ruminants are
multicellular animals?
A. They have specialized organs for digestion
B. They can reproduce
c. They have lungs for breathing
D. Both A and C


The emissivity of a body of surface area
\( 5 c m^{2} \) and radiating \( 300 \mathrm{J} \) of energy per
minute at temperature \( 727^{\circ} C \) is :
A. 0.48
B. 0.38
\( c \cdot 0.28 \)
D. 0.18


Three moving coil galvanometer \( \boldsymbol{A}, \boldsymbol{B} \) and \( C \) are made of coils of three
different material having torsional constant \( 1.8 \times 10^{-8}, 2.8 \times 10^{-8} \) and
\( 3.8 \times 10^{-8} \) respectively. If the three
galvanometers are identical in all other respect, then in which of the above cases, current sensitivity is maximum?
A. \( A \)
в. \( C \)
\( c . B \)
D. same in each case


A wire of length L and of cross-sectional area A is made of a material of Young's modulus Y. The work done in stretching the wire by an amount \( x \) is given by :
A \( \cdot \frac{Y A x^{2}}{L} \)
в. \( \frac{Y A x^{2}}{2 L} \)
c. \( \frac{Y A L^{2}}{x} \)
D. \( \frac{Y A L^{2}}{2 x} \)


Which of these configuration are
achiral?
\( A \cdot e, \)
B. a,
\( c \cdot d, \)
D. None of these


The amorphous form of silica is:
A. Quartz
B. Kieselguhr
c. Cristobalite
D. Tridymite


Show that \( \cot ^{-1}\left(\frac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}}\right)= \)
\( \frac{x}{2} \) for \( x \in\left(0, \frac{\pi}{2}\right) \)


Using the properties of determinants \& without expanding \( \left[\begin{array}{ccc}\boldsymbol{b}+\boldsymbol{c} & \boldsymbol{q}+\boldsymbol{r} & \boldsymbol{y}+\boldsymbol{z} \\ \boldsymbol{c}+\boldsymbol{a} & \boldsymbol{r}+\boldsymbol{p} & \boldsymbol{z}+\boldsymbol{x} \\ \boldsymbol{a}+\boldsymbol{b} & \boldsymbol{p}+\boldsymbol{q} & \boldsymbol{x}+\boldsymbol{y}\end{array}\right]=\boldsymbol{2}\left[\begin{array}{ccc}\boldsymbol{a} & \boldsymbol{p} & \boldsymbol{x} \\ \boldsymbol{b} & \boldsymbol{q} & \boldsymbol{y} \\ \boldsymbol{c} & \boldsymbol{r} & \boldsymbol{z}\end{array}\right] \)


The flying of birds is a proof of
Newton's:
A. First law
B. Second law
c. Third law of motion
D. Both second and third law


m-bromotoluene is prepared by:
This question has multiple correct options
A. bromination of toluene
B. Friedel Craft's reaction of bromobenzene with \( C H_{3} C l \)
C. bromination of nitrobenzene and subsequent replacement of \( -N O_{2} \) group with methyl group
D. bromination of aceto-p-toluidine followed by hydrolysis and deamination


Following are the marks obtained by 9 students in Mathematics test:
\( \mathbf{5 0 , 6 9}, \mathbf{2 0 , 3 3 , 5 3 , 3 9 , 4 0 , 6 5 , 5 9 \text { The }} \)
mean deviation from the median is
A . 9
B. 10.5
c. 12.67
D. 14.76


Rusting of iron is an example of
reaction.


R.Q. is zero, when the respiratory
substrate is
A. Completely oxidized
B. Incompletely oxidized
c. Not oxidized at all
D. Reduced


On the interval \( \boldsymbol{I}=[-2,2] \),for the
function \( \left\{\begin{array}{ll}(x+1) e^{-\left[\frac{1}{[x]}+\frac{1}{x}\right]} & (x \neq 0) \\ 0 & (x=0)\end{array}\right. \)
(where []\( \text { is } G I F) \) which one of the
following hold good?
This question has multiple correct options
A. is continuous for all values of \( x \in I \)
B. is continuous for all values of \( x \in I-(0) \)
c. assumes all intermediate values from \( f(-2) \) \& \( f(2) \)
D. has a maximum value equal to


If \( \tan \alpha=\frac{m}{m+1} \) and \( \tan \beta=\frac{1}{2 m+1} \)
find the possible values of \( (\boldsymbol{\alpha}+\boldsymbol{\beta}) \)
\( A \cdot 30 \)
B. 90
\( c \cdot 60 \)
D. \( 45^{\circ} \)


Factorize:
\( a^{4}-343 a \)
\( \mathbf{A} \cdot a(a-7)\left(a^{3}+a+36\right) \)
B \( \cdot a(a-7)\left(a^{2}+7 a+49\right) \)
\( \mathbf{c} \cdot a(4 a-7)\left(a^{2}-a+49\right) \)
D. \( a(4 a-7)\left(a^{3}+7 a-36\right) \)


The weakest reducing agent among the following is :
A. hydrogen Gas
B. coke
c. carbon monoxide gas
D. aluminium metal


In \( \triangle A B C \) is on isosceles \( \triangle \) with \( A B= \)
\( A C \) and \( D \) in a point on BC such that
\( A D \perp B C . \) Prove that \( \angle B A D=\angle C A D \)


A particle moves along a curve so that
its coordinates at time \( t \) are \( \boldsymbol{x}=\boldsymbol{t}, \boldsymbol{y}= \) \( \frac{1}{2} t^{2}, z=\frac{1}{3} t^{3} \) acceleration at \( t=1 \) is
\( \mathbf{A} \cdot j+2 k \)
B. \( j+k \)
\( c \cdot 2 j+k \)
D. none of these


Define temperature coefficient of
resistance.


A force acts on a body and displaces it
in it's direction. The graph shows the
relation between the force and
displacement. The work done by the force is:
\( \mathbf{A} \cdot 420 J \)
B. \( 360 J \)
c. \( 840 J \)
D. \( 720 J \)


The angular frequency of motion whose equation is \( 4 \frac{d^{2} y}{d t^{2}}+9 y=0 \) is \( (y= \)
displacement and \( t= \) time
A \( \cdot \frac{9}{4} \)
в. \( \frac{4}{9} \)
\( c \cdot \frac{3}{2} \)
D. \( \frac{2}{3} \)


In glycolysis, the end product is
A. Protein is converted into glucose
B. Glucose is converted into glycogen
c. starch is converted into glucose
D. Glucose is converted into pyruvic acid


The potential energy of a particle of
mass \( m \) is given by \( V(x)= \) \( \left\{\begin{array}{cc}\boldsymbol{E}_{0} \mathbf{0} & \leq \boldsymbol{x} \leq \mathbf{1} \\ \mathbf{0} & \boldsymbol{x}>\mathbf{1}\end{array}\right\} \)
\( \lambda_{1} \) and \( \lambda_{2} \) are the de-Broglie
wavelengths of the particle, when \( 0 \leq \)
\( x \leq 1 \) and \( x>1 \) respectively.

If the total energy of particle is \( 2 E_{0} \)
find \( \left(\lambda_{1} / \lambda_{2}\right) \)


The value of the determinant
\( \left|\begin{array}{lll}a_{1} & m a_{1} & b_{1} \\ a_{2} & m a_{2} & b_{2} \\ a_{3} & m a_{3} & b_{3}\end{array}\right| \) is
\( \mathbf{A} \cdot \mathbf{0} \)
В. \( m a_{1} a_{2} a_{3} \)
\( \mathrm{c} \cdot m a_{1} b_{2} a_{2} \)
D. \( m b_{1} b_{2} b_{3} \)


If \( E=16 \) volts, \( r=4 \Omega \) and distance of
balance point \( P \) from end \( A \) is \( 90 \mathrm{cm} \)
then the value of \( X \) is
A . \( 3 \Omega \)
B. \( 6 \Omega \)
\( c .9 \Omega \)
D. \( 12 \Omega \)


The polarising angle for a medium is
found to be \( 60^{\circ} . \) The critical angle of the medium is
A \( \cdot \sin ^{-1}\left(\frac{1}{2}\right) \)
B. \( \sin ^{-1}\left(\frac{\sqrt{3}}{2}\right) \)
\( ^{c} \cdot \sin ^{-1}\left(\frac{1}{\sqrt{3}}\right) \)
D. \( \sin ^{-1}\left(\frac{1}{4}\right) \)
E \( \cdot \sin ^{-1}\left(\frac{2}{\sqrt{3}}\right) \)


Write two difference between
conduction and convection


The order of the differential equation is
\( A \cdot 3 \)
B. 2
\( c \cdot 1 \)
D. None of these


A particle is vibrating simple harmonically with an amplitude \( a \). The
displacement of the particle when its energy is half kinetic and half potential.
A \( \cdot a \)
B. \( \frac{a}{\sqrt{2}} \)
\( c \cdot a \)
D. zero


soil holds highest water capacity
A. sandy
B. Clayey
c. Loamy
D. Both A and C


Name of the process is cyanide process, in which we added Zn to soluble
\( \left[\boldsymbol{A} \boldsymbol{g}(\boldsymbol{C N})_{2}\right]^{-} \) to get Ag. If true enter 1
else 0.


Calculate \( \left[\boldsymbol{S}^{-2}\right] \) in a solution originally
having \( 0.1 \mathrm{M} H C l \) and \( 0.2 M H_{2} S . \) For
\( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{K} \boldsymbol{a}_{1}=\mathbf{1} . \boldsymbol{4} \times \mathbf{1 0}^{-\mathbf{7}} \) and \( \boldsymbol{K} \boldsymbol{a}_{2}= \)
\( 1.0 \times 10^{-14} \)
A \( .2 .8 \times 10^{-22} M \)
M
В. \( 3 \times 10^{-15} \mathrm{M} \)
\( \mathbf{c} .2 .8 \times 10^{-21} M \)
D. \( 4 \times 10^{-10} M \)


If \( \boldsymbol{A}=\left[\begin{array}{rr}\mathbf{4} & \boldsymbol{x}+\mathbf{2} \\ \mathbf{2} \boldsymbol{x}-\mathbf{3} & \boldsymbol{x}+\mathbf{1}\end{array}\right] \) is symmetric
then what is x equal to?
\( \mathbf{A} \cdot \mathbf{5} \)
B. 3
\( c \cdot-1 \)
D. -


Calculate the efficiency of a Carnot engine operating between temperatures of \( 900 \mathrm{K} \) and \( 300 \mathrm{K} \)
A . \( 87 \% \)
B. \( 67 \% \) \%
c. \( 100 \% \)
D. 45 \%


Which of the following acid is used by goldsmiths for cleaning gold and silver
ornaments?
A. \( H C l \)
в. \( H_{2} S O_{4} \)
c. \( H N O_{3} \)
D. \( H_{3} P O_{4} \)


If a metal is irradiated with light of
frequency \( 3 \times 10^{19} \mathrm{sec}^{-1}, \) the electron
is emitted with a kinetic energy of \( 6.625 \times 10^{-15} \) J. The threshold
frequency of the metal is
A \( \cdot 2 \times 10^{19} \sec ^{-1} \)
B. \( 1.25 \times 10^{19} \mathrm{sec}^{-1} \)
c. \( 6.625 \times 10^{35} \mathrm{sec}^{-1} \)
D. \( 6.625 \times 10^{19} \sec ^{-1} \)


Basement membrane is formed of
A. Epidermal cells
B. Endodermal cells
c. Both A and B
D. None of the above


Which two orbitals are located along the
axis, not between the axis?
\( \mathbf{A} \cdot d_{x^{2}-y^{2}}, d_{z^{2}} \)
B . \( d_{x y}, p_{z} \)
\( \mathbf{c} \cdot d_{y z}, p_{x} \)
D \( \cdot p_{x}, d_{x^{2}-y^{2}} \)


The \( I_{1}, I_{2}, I_{3}, I_{4} \) values of an element \( M \)
are \( 120 \mathrm{kJ} / \mathrm{mole}, 600 \mathrm{kJ} / \mathrm{mole}, 1000 \)
kJ/mole and \( 8000 \mathrm{kJ} / \) mole. Then the
formula of its sulphate is:
A. \( M S O_{4} \)
в. \( M_{2}\left(S O_{4}\right)_{3} \)
\( \mathrm{c} \cdot M_{2} \mathrm{SO}_{4} \)
D. \( M_{3}\left(S O_{4}\right)_{2} \)


\( \boldsymbol{H}_{2(g)}+\frac{1}{2} \boldsymbol{O}_{2(g)} \rightarrow \boldsymbol{H}_{2} \boldsymbol{O}_{(l)} ; \boldsymbol{\Delta} \boldsymbol{H}= \)
\( -286.2 k J ; H_{2} O_{(l)} \rightarrow H_{(a q)}^{+}+O H_{(a q)}^{-} \)
\( \Delta H=+57.3 k J . \) Enthalpy of ionisation
of \( O H^{-} \) in aqueous solution is:
B . \( +228.5 k J \)
c. \( -343.5 k J \)
D. zero


Find the mean deviation about the
median for the following data:
\( \boldsymbol{x}_{i} \quad 3 \quad 6 \quad 9 \quad 12 \)
\[
f_{i} \quad 3 \quad 4 \quad 5 \quad 2
\]


Consider two perfectly elastic spheres
having velocities \( u_{1} \) and \( u_{2} \) in the same
direction and masses \( m \) and \( m^{\prime} . \) When
these two spheres collide, the impulse of the blow on the spheres is
A \( \cdot \frac{2 m m^{1}}{m+m^{1}}\left(u_{1}-u_{2}\right) \)
в. \( \frac{2 m m^{1}}{m-m^{1}}\left(u_{1}-u_{2}\right) \)
c. \( \frac{2 m m^{1}}{m+m^{1}}\left(u_{1}+u_{2}\right) \)
D. \( \frac{2 m m^{1}}{m-m^{1}}\left(u_{1}+u_{2}\right) \)


Addition of \( B H_{3} \) followed by \( H_{2} O_{2} \) to trans - 2 - butene would give you a
product which is:
A . achiral
B. racemic
c. meso
D. optically active


\( \cos ^{2} \frac{3 \pi}{5}+\cos ^{2} \frac{4 \pi}{5} \) is equal to
A \( \cdot 4 / 5 \)
B. \( 5 / 2 \)
c. \( 5 / 4 \)
D. \( 3 / 4 \)


On a linear escalator running between
two points \( A \) and \( B, \) a boy takes time \( t_{1} \)
to move from \( A \) to \( B \), if the boy runs with a constant speed on the escalator.
If the boy runs from \( B \) to \( A \), he takes
time \( t_{2} \) to reach \( B \) from \( A \). The time
taken by the boy to move from \( \boldsymbol{A} \) to \( \boldsymbol{B} \) if he stands still on the escalator will be
(The escalator moves from \( \boldsymbol{A} \) to \( \boldsymbol{B} \) )
A \( \cdot \frac{t_{1} t_{2}}{t_{2}-t_{1}} \)
В. \( \frac{2 t_{1} t_{2}}{t_{2}-t_{1}} \)
c. \( \frac{t_{1}^{2}+t_{2}^{2}}{t_{1} t_{2}} \)
D. \( \frac{t_{1}^{2}-t_{2}^{2}}{t_{1} t_{2}} \)


If the radius of a sphere is measured as \( 7 m \) with an error of \( 0.02 m, \) then find the approximate error in calculating its volume


Solve
\( \left|\begin{array}{ccc}1 & 1 & -1 \\ 6 & 4 & -5 \\ -4 & -2 & 3\end{array}\right| \)


The point (2,1) lies in the region of the solution of linear
inequations \( x-2 y \leq 0, \) and \( x-y>0 \)
This question has multiple correct options
A. feasible
B. non-feasible
c. unbounded
D. bounded


Specific heat of a monoatomic gas at
constant volume is \( 315 J k g^{-1} K^{-1} \) and
at a constant pressure is \( 525 J k g^{-1} K^{-1} . \) Calculate the molar
mass of the gas.


Endotherms or warm blooded animals
maintain a constant temperature by
A. Insulating coat
B. Changing cutaneous circulation
c. Both A and B
D. Disposing off extra energy as heat


In a dc circuit the power generated per unit volume of the conductor is directly proportional to:
A. current
B. electric filed inside the conductor
c. resistivity of the condutor
D. square of the electric field


Two soap bubbles of different radii are
in contact with each other. Then
A. air follows from the larger bubble into smaller bubble till both bubbles acquire same size
B. air follows from the smaller bubble into larger bubble and the larger bubble grows in size of the smaller bubble
C. air does not flow but the sizes of the bubbles changes
D. sizes of the bubbles remain unchanged


\( \int \frac{1}{1-\cos \frac{x}{2}} d x \)


How many EDTA molecules are required to make an octahedral complex with a
\( C a^{2+} \) ion?
A. Six
B. Three
c. one
D. Two


A method for charging a conductor without bringing a charged body in contact with it is called:
A. Magnetization
B. Electrification
c. Electrostatic induction
D. Electromagnetic induction


Which blood vessels carry blood from
heart to body parts?


Which of the following type of life cycle is observed in Saccharomyces cerevisiae?
A. Haplontic
B. Diplontic
c. Haplo-diplontic
D. Diplo-haplontic


In the adjoining figure \( \triangle P Q R \sim \)
\( \triangle \boldsymbol{T} \boldsymbol{S} \boldsymbol{R} \)
ldentify the corresponding vertices, corresponding sides and their ratios.


In which compound oxygen atom take part in conjugation of phenol \( (\boldsymbol{P h}- \)
\( O H) \) and Benzyl alcohol \( \left(P h C H_{2} O H\right) ? \)
A \( . P h O H \)
в. \( P h C H_{2} O H \)
c. Both A and B
D. None of these


The height at which the acceleration due to gravity becomes \( g / 9 \) (where \( g= \) the acceleration due to gravity on the
surface of the earth) in terms of \( R \), the
radius of the earth, is
A. \( R / 2 \)
в. \( \sqrt{2} R \)
\( c .2 R \)
D. \( \frac{R}{\sqrt{2}} \)


Which is an incorrect order of basic
strength?
A \( \cdot N H_{2}^{-}>P H_{2} \)
B \( . H_{2} O>H_{2} \)
\( c \)
\( D \)
\( \mathrm{E} \cdot \mathrm{CO}_{3}^{2-}>\mathrm{HCO}_{3}^{-} \)


A transparent medium of the angle of
polarisation is \( 60^{\circ} . \) Find the angle of
refraction.


\( _{7} N^{15} \) and \( _{8} O^{16} \) are a pair of :
A. isotopes
B. isobars
c. isotones
D. none of them


The function \( x^{5}-5 x^{4}+5 x^{3}-10 \) has a
maximum, when \( \boldsymbol{x}= \)
\( A \cdot 3 \)
B . 2
\( c .1 \)
D.


Transuranic elements begin with:
\( A \cdot N p \)
в. \( \mathrm{cm} \)
c. Pu
D.


Pancreas is absent in which group of
vertebrates
A. Reptiles
B. Cyclostomates
c. Birds
D. Mammals


What is global warming? Mention any four measures to control global warming.


The graph of \( x=8 \) represents:
A. line parallel to \( y \) -axis and at a distance of 8 units
B. line parallel to \( x \) -axis and at a distance of 8 units
c. line parallel to \( y \) -axis and at a distance of 0 units
D. None of these


Which of the following is true about
and II?
A. I is eclipsed, II is staggered
B. II is eclipsed, lis staggered
c. both are eclipsed
D. both are staggered


Atom bomb consists of pieces of \( ^{92} U_{235} \)
and a source of
A. Proton
B. Neutron
c. Meson
D. Electron


The purpose of the Contact process is to
A. manufacture sulphuric acid
B. manufacture nitric acid
c. manufacture hydrochoric acid
D. manufacture sulphonic acid


Give Reasons
A histogram is not a diagram.


\( S O_{2} \) reacts with \( C l_{2} \) to form


Inverse of a diagonal non-singular matrix is
A. Scalar matrix
B. Skew symmetric matrix
c. zero matrix
D. Diagonal matrix


If earth is a homogeneous solid sphere
of mass \( M \) and radius \( R \), then
gravitational self potential energy of earth is
\( ^{\mathrm{A}} \cdot-\frac{G M^{2}}{R} \)
в. \( -\frac{G M^{2}}{2 R} \)
c. \( -\frac{3 G M^{2}}{5 R} \)
D. None of these


The minimum mass of water needed to
slake \( 1 k g \) of quicklime, assuming no loss by evaporation, is:
A \( .243 .2 g \)
в. \( 642.8 g \)
c. \( 160.7 g \)
D. \( 321.4 g \)


Describe an activity to show that thermoplastic is a poor conductor of
electricity.


If \( \boldsymbol{M}=\int_{0}^{\pi / 2} \frac{\cos \boldsymbol{x}}{\boldsymbol{x}+\mathbf{2}} \boldsymbol{d} \boldsymbol{x}, \boldsymbol{N}= \)
\( \int_{0}^{\pi / 4} \frac{\sin x \cos x}{(x+1)^{2}} d x \quad, \) then the value of
\( M-N \) is \( ? \)
\( A \)
в.
c. \( \frac{2}{\pi-4} \)
D. \( \frac{2}{\pi+4} \)


Evaluate
\( \int \frac{d x}{\left(x^{2}+1\right) \sqrt{x^{2}+1}} \)


When we look towards the pole star, it
appears stationary because
A. it is very far from Earth as compared to other stars.
B. it moves with much lesser speed than others stars.
C. it is pointing exactly in the south direction.
D. it is pointing exactly in the north direction.


according to Ruther-fordis atomic
model, the mass of the atom is evenly distributed throughout the atom
A. True
B. False


Protein synthesis commences when
A. mRNA binds to the smaller subunit of Ribosomes
B. mRNA bind to the larger subunit f Ribosome
C. Both smaller and larger sub units binds each other over the mRNA molecule.
D. The adapter RNA recognises the enzymes from cytoplasm.


At large distances from source \( \vec{E} \) and \( \vec{B} \)
are in phase and the decrease in their magnitude is comparatively slower with distance r as per
A \( \cdot r^{-1} \)
B.
\( c \cdot r^{-3} \)
D \( \cdot r^{2} \)


\( f\left(x-\frac{x^{2}}{4}+\frac{x^{3}}{4}-\dots \dots \infty\right)+ \)
\( \cos ^{-1}\left(x^{2}-\frac{x^{4}}{4}+\frac{x^{6}}{4}-\ldots \ldots . . \infty\right)=\frac{\pi}{2} \)
and \( 0<x<\sqrt{2} \) then \( x= \)
A \( \cdot \frac{1}{2} \)
B.
\( c \cdot-\frac{1}{2} \)
D. -


The Bulk modulus for an
incompressible liquid is :
A. zero
B. Unity
c. Infinty
D. Between O and 1


Total number of faces in a cuboid is


Assertion \( (A) \). The direction ratios of the line joining origin and point \( (x, y, z) \) must be \( x, y, z \)

Reason (R): If \( P(x, y, z) \) is a point in space and \( |O P|=r, \) then the direction cosines of \( O P \) are \( \frac{x}{r}, \frac{y}{r}, \frac{z}{r} \)
A. Both A and R are individually true and R is the correct explanation of
B. Both A and R individually true but R is not the correct explanation of A
c. A is true but R is false
D. A is false but R is true


Which one is correct for fuse wire?
A. low resistance and low melting point
B. high resistance and high melting point
C . high resistance and low melting point
D. low resistance and high melting point


A transition element \( X \) has a
configuration \( [A r] 3 d^{4} \) in its +3 oxidation state.
Its atomic number is not:
This question has multiple correct options
A . 25
B . 26
c. 22
D. 19


Write in proper sequence the name of
all the parts of the human eye through which the light rays coming from an object pass before they form an image
on the retina.


In figure the segment \( S T \) is parallel to
side \( P R \) of \( \triangle P Q R \) and it divides the
triangle into two parts of equal area.Find the ratio \( \frac{\boldsymbol{P S}}{\boldsymbol{P Q}} \)
\( \mathbf{A} \cdot 1: 2 \)
B. 1: 8
\( c \cdot 1: 4 \)
D. 1: 10


\( 2 \tan ^{-1}\left(\frac{3}{4}\right)= \)
A \( \cdot \sin ^{-1} \frac{24}{25} \)
B \( \cdot \sin ^{-1} \frac{12}{13} \)
c. \( \cos ^{-1}\left(\frac{24}{25}\right) \)
D. \( \cos ^{-1}\left(\frac{12}{13}\right) \)


A pulley has a light rope running over it, with a \( 10 N \) weight on one side and a
\( 20 N \) weight on the other. Ropes always
pull with equal force on each end; this is called tension. If the masses are
allowed to fall, what is the tension, \( \boldsymbol{T} \) in
the rope?
A . \( 0 N \)
В. \( 1 N<T<10 N \)
\( c \cdot 10 N \)
D. None of these


Find the inverse function of \( f(x)= \)
\( 2 x-3 \)


If \( x=\sec \theta-\cos \theta \) and \( y=\sec ^{3} \theta- \)
\( \sec ^{3} \theta-\cos ^{3} \theta, \) then the value of
\( \left(\frac{d y}{d x}\right)^{2} \) at \( x=0 \)
A . 0
B. 2
\( c \cdot 4 \)
D.


\( \lim _{x \rightarrow 0} \frac{\sin 3 x \tan 4 x}{x \sin 5 x}= \)
\( A . \)
B. \( \frac{5}{12} \)
c. 0
D. \( \frac{12}{5} \)


Main ore of aluminium is:
A. \( A l_{2} S \)
B. Bauxite
c. cinnabar
D. Aluminium glance


Expand the following binomial \( \left(1+\frac{x}{2}\right)^{7} \)


The sound waves are the longitudinal
waves. The electromagnetic waves are


Identify open curve.
\( \mathbf{A} \cdot 1 \) only
B. 2 only
\( \mathrm{C} \cdot 1,2 \) only
D. 3only


Lt is known that the decay rate of radium is directly proportional to its quantity at each given instant Find the law of variation of a mass of radium
as a function of time if at \( t=0, \) the
mass of the radius was \( m_{0} \) and
during time \( t_{0} \alpha \% \) of the original mass of radium decay, if \( m=m_{0} e^{-k t}, \) then
\( k=? \)
A \( \cdot k=\frac{1}{t_{0}} \ln \left(1-\frac{\alpha}{100}\right) \)
В \( \cdot k=\frac{-1}{t_{0}} \ln \left(1-\frac{\alpha}{100}\right) \)
C \( \cdot k=\frac{1}{t_{0}} \ln (1-\alpha) \)
D・ \( k=\frac{-1}{t_{0}} \ln (1-\alpha) \)


Tangents TP and TO are drawn from a
point \( \mathbf{T} \) to the circle \( \boldsymbol{x}^{2}+\boldsymbol{y}^{2}=\mathbf{a}^{2} . \) If the
point \( \mathbf{T} \) lies on the line \( \mathbf{p x}+\mathbf{q y}=\mathbf{r} \)
then the locus of centre of the
circumcircle of \( \Delta \) TPO is
A \( \cdot p x+q y=\frac{r}{3} \)
B. \( p x+q y=\frac{r}{2} \)
c. \( p x+q y=2 r \)
D. \( p x+q y=r \)


Which of the following is not a linear molecule?
A. \( C O_{2} \)
в. \( C_{2} H_{2} \)
c. \( H C N \)
D. \( H_{2} O \)


A particle is moving uniformly in a
circular path of radius 10 m. When it moves through a displacement \( 5 m \) then the magnitude of the corresponding angular displacement will be:
A \( \cdot 20^{\circ} \)
B . \( 30^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 90^{\circ} \)


Hertz is the unit of
A. Wavelength
B. Amplitude
c. Frequency
D. None of these


What type of bond does \( M g \) form with
\( C l ? \)
A. Covalent
B. Ionic
c. co-ordinate
D. None of these


What is the mathematical equation for the rate constant for the decomposition
of nitrous oxide in presence of platinum catalyst?


Solve:
\( \frac{1}{3}(x-2)+\frac{1}{4}(x+3)=\frac{1}{5} \)


Is it possible to construct a triangle
with lengths of its sides as \( 4 \mathrm{cm} .3 \mathrm{cm} \)
and \( 7 \mathrm{cm} ? \) Give reason for your answer.


Which of the following properties are common to the elements manganese,
iron, cobalt, nickel and copper?
(I) Coloured ions in aqueous solution
(II) Oxides of nitrogen on reaction with
concentrated \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \)
(III) Chlorides of formula \( M C l_{2} \) and
\( M C l_{3} \)
A. ।, ॥।, ॥।
B . ।, ॥
c. ॥, ॥ा
D. I only


Find the charge on the inner surface of
the conducting concentric shell
\( A \cdot Q \)
B. \( 2 Q \)
\( c .-2 Q \)
D. \( -Q \)


Evaluate the following limits. \( \lim _{x \rightarrow a} \frac{x^{2 / 7}-a^{2 / 7}}{x-a} \)


The D.E whose solution is \( y=c(x-c)^{2} \)
is
\( ^{\mathbf{A}} \cdot\left(\frac{d y}{d x}\right)^{3}=4 y\left(x \frac{d y}{d x}-2 y\right) \)
В. \( y_{1}^{3}=2 y\left(x y_{1}-y\right) \)
\( ^{\mathbf{c}}\left(\frac{d y}{d x}\right)^{3}=4 y\left(2 x \frac{d y}{d x}-y\right) \)
D. \( \left(\frac{d y}{d x}\right)^{3}=2 y\left(x \frac{d y}{d x}-4 y\right) \)


How many delocalised \( \pi \) - electrons are
there in the following compound?
\( A \)
B. 2
\( c \cdot 4 \)
D.


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


There is no life on moon because there
is no
A. carbon
B. Nitrogen
c. water
D. silicates


What is the sum of G.P. \( 1+p+p^{2}+ \)
\( \boldsymbol{p}^{3}+\boldsymbol{p}^{4}+\boldsymbol{p}^{5} ? \)
\( ^{\mathbf{A}} \cdot_{S_{6}}=\frac{1-p^{6}}{1-p} \)
в. \( s_{5}=\frac{1-p^{5}}{1-p} \)
\( ^{\mathbf{c}} \cdot_{S_{4}}=\frac{1-p^{4}}{1-p} \)
D. \( s_{6}=\frac{1-p^{6}}{1+p} \)


A solution contains \( 20 \% \) solute by
weight at \( 60^{\circ} \mathrm{C} \). Whencooled to \( 30^{\circ} \mathrm{C} \)
the solution contains \( 10 \% \) solute by
weight. When \( 45 g \) solution is cooled
from \( 60^{\circ} \mathrm{C} \) to \( 30^{\circ} \mathrm{C} \), the mass of solute
deposited is:


Imagine a light planet revolving around a very massive star in a circular orbit of
radius \( R \) with a period of revolution \( T . \) If the gravitational force of attraction between the planet and the star is proportional to \( R^{-5 / 2}, \) then \( T^{2} \) is
proportional to:
\( \mathbf{A} \cdot R^{3} \)
B. \( R^{7 / 12} \)
c. \( R^{3 / 2} \)
D. \( R^{3.75} \)


A ray of light is reflected by a plane
mirror.
Which row shows the angle of incidence
and the angle of reflection?
A. Angle of incidence - \( P \), Angle of reflection - \( Q \)
B. Angle of incidence - \( P \), Angle of reflection - \( S \)
C. Angle of incidence - \( Q \), Angle of reflection - \( R \)
D. Angle of incidence - \( R \), Angle of reflection - \( S \)


To a germanium sample, traces of gallium are added as an impurity. The resultant sample would behave like
A. a conductor
B. a p-type semiconductor
c. an n-type semiconductor
D. a insulator


\( \operatorname{Let} \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{5} & \mathbf{5} \boldsymbol{\alpha} & \boldsymbol{\alpha} \\ \mathbf{0} & \boldsymbol{\alpha} & \mathbf{5} \boldsymbol{\alpha} \\ \mathbf{0} & \mathbf{0} & \mathbf{5}\end{array}\right] \) If \( \left|\boldsymbol{A}^{2}\right|=\mathbf{2 5} \)
then \( |\boldsymbol{\alpha}| \) equals
\( \mathbf{A} \cdot 5^{2} \)
B.
\( c \cdot \frac{1}{5} \)
D. 5


Identify the correct statement regarding
enzymes.
A. Enzymes are specific biological catalysts that possess well defined active sites.
B. Enzymes are normally heterogeneous catalysts that are very specific in their action.
C. Enzymes are specific biological catalysts that cannot be poisoned
D. Enzymes are specific biological catalysts that can normally function at very high temperature (T=1000K)


Which of the following has more inertia
\( ? \)
A five-rupee coin or a one-rupee coin.


Which one of the following is a secondary alkylhalide?
A \( \cdot\left(C H_{3}\right)_{3} C C l \)
B \( \cdot C_{2} H_{5} C l \)
c. \( \left(C H_{3}\right)_{2} C H C l \)
D. \( \left(C H_{3}\right)_{2} C H C H_{2} C l \)


If \( I \) is regarded as the fourth dimension, then the dimensional formula of charge
in terms of current \( \boldsymbol{I} \) is
\( \mathbf{A} \cdot\left[I T^{2}\right] \)
B . \( \left[I^{0} T^{0}\right] \)
c. \( \left[I^{-1} T^{0}\right] \)
D. [IT]


Chromosomal morphology (structure) is best observed at
A. Prophase
B. Metaphase
c. Interphase
D. Anaphase


Assertion \( \operatorname{Let} \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{0} & \boldsymbol{c} & -\boldsymbol{b} \\ -\boldsymbol{c} & \boldsymbol{0} & \boldsymbol{a} \\ \boldsymbol{b} & \boldsymbol{-} \boldsymbol{a} & \boldsymbol{0}\end{array}\right] \) and \( \boldsymbol{t} \in \boldsymbol{C} \)
\( \boldsymbol{a} \boldsymbol{d} \boldsymbol{j}(\boldsymbol{t} \boldsymbol{I}-\boldsymbol{A})=\boldsymbol{t}^{2} \boldsymbol{I}+\boldsymbol{t} \boldsymbol{A}+\boldsymbol{A}^{2}+\left(\boldsymbol{a}^{2}+\right. \)
\( \left.b^{2}+c^{2}\right) I \)
Reason
\( \boldsymbol{a} \boldsymbol{d} \boldsymbol{j} \boldsymbol{A}=\boldsymbol{A}^{2}+\left(\boldsymbol{a}^{2}+\boldsymbol{b}^{2}+\boldsymbol{c}^{2}\right) \boldsymbol{I} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Given three vectors \( \vec{a}=6 \hat{i}-3 \hat{j}, \vec{b}= \) \( 2 \hat{i}-6 \hat{j} \) and \( \vec{c}=-2 \hat{i}+21 \hat{j} \) such that
\( \overrightarrow{\boldsymbol{\alpha}}=\overrightarrow{\boldsymbol{a}}+\overrightarrow{\boldsymbol{b}}+\overrightarrow{\boldsymbol{c}}, \) then the resolution of
the vector \( \vec{\alpha} \) into components with respect to \( \vec{a} \) and \( \vec{b} \) is given by
A \( .3 \vec{a}-2 \vec{b} \)
в. \( 3 \vec{b}-2 \vec{a} \)
c. \( 2 \vec{a}-3 \vec{b} \)
D. \( \vec{a}-2 \vec{b} \)


Let the statement \( P(n): 2^{n} \geq 3 n \), the
truth of \( \boldsymbol{P}(\boldsymbol{k}), \forall \boldsymbol{k} \in \boldsymbol{N} \Rightarrow \) truth of
\( \mathbf{A} \cdot P(1) \)
B \( \cdot P(2) \)
\( \mathbf{c} \cdot P(3) \)
D \( \cdot P(k+1) \)


Assertion
Perfectly ideal solution is not possible with respect to binary solution of two liquids.
Reason
No two substances can have exactly the same nature of intermolecular forces
and also of the same magnitude.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


The correct order for reducing nature of
\( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4}, \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3} \) and \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{2} \) is :
A. \( H_{3} P O_{2}<H_{3} P O_{3}<H_{3} P O_{4} \)
в. \( H_{3} P O_{4}<H_{3} P O_{3}<H_{3} P O_{2} \)
c. \( H_{3} P O_{3}<H_{3} P O_{4}<H_{3} P O_{2} \)
D. \( H_{3} P O_{4}<H_{3} P O_{2}<H_{3} P O_{3} \)


Carbohydrates are
A. used to make a paper
B. produced as an intermediate in the synthesis of proteins
C. the polyhydroxy aldehyde or polyhydroxy ketone
D. all of these


The amplitude and the time period in a
S.H.M. is \( 0.5 \mathrm{cm} \) and 0.4 see respectively If the initial phase is \( r / 2 \) radiam,then the equaction of S.H.H. will be
A \( \cdot y=0.5 \sin 5 / \pi \)
B. \( y=0.5 \sin 4 / \pi \)
c. \( y=0.5 \sin 2.5 / \pi \)
D. \( y=0.5 \cos 5 \pi t \)


Papillary muscles are located in
A. Ventricle of rabbit
B. Dermis of mammalian skin
c. orbit of vertebrate eyes
D. Pylorus of vertebrate stomach


For the equilibrium of the reaction:
\( N H_{4} C l(s) \rightleftharpoons N H_{3}(g)+ \)
\( \boldsymbol{H} \boldsymbol{C l}(\boldsymbol{g}) ; \boldsymbol{K}_{\boldsymbol{p}}=\boldsymbol{8} 1 \boldsymbol{a} \boldsymbol{t} \boldsymbol{m}^{2} \)
Total pressure at equilibrium will be \( x \)
times the pressure of \( \boldsymbol{N} \boldsymbol{H}_{3} \)
The value of \( x \) will be:


Arrange giving the sequence order to \( B r, C l, F \) and \( H \) combined with
asymmetric carbon
A. \( H, C l, B r, F \)
в. \( H, C l, F, B r \)
c. \( B r, C l, F, H \)
D. \( H, F, B r, C l \)


Two equal positive charges \( Q \) are fixed at points \( (a, 0) \) and \( (-a, 0) \) on the \( x \) axis. An opposite charge \( -q \) at rest is released from point \( (0, a) \) on the \( y \) -axis.
The charge \( -\boldsymbol{q} \) will
A. move to infinity
B. Move to origin and rest there
c. Undergo SHM about the origin
D. Execute oscillatory periodic motion but not SHM


How many transition states and
intermediates will be formed during the
course of following reaction?
\( A . \quad 3 \) transition states and 3 intermediates
B. 4 transition states and 3 intermediates
C. 3 transition states and 2 intermediates
D. 5 transition states and 4 intermediates


Reduce the equation \( x+2 y-5=0 \) to
slope-intercept form and find its slope
and \( \boldsymbol{y}- \) intercept.


Amplitude of oscillation of a particle that executes S.H.M. is 2 cm. Its
displacement from its mean position in a time equal to \( 1 / 6 \) th of its time period
is
A \( \cdot \sqrt{2} \mathrm{cm} \)
B. \( \sqrt{3} \mathrm{cm} \)
c. \( 1 / \sqrt{2} \mathrm{cm} \)
D. \( 1 / \sqrt{3} \mathrm{cm} \)


If the sum of two adjacent angles is
\( 100^{\circ} \) and one of them is \( 35^{\circ}, \) then the
other is :
A \( .70^{\circ} \)
B . 65
c. \( 135^{\circ} \)
D. 145


1-phenylethyne gives \( C_{6} H_{5} C H_{2} C H O \) as a product on hydroboration-oxidation reaction.
Enter 1 if true else 0


A silver article generally turns black when kept in the open for a few days.
The article when rubbed with
toothpaste again starts shining. Silver articles turn black when kept in the open for a few days because of


Two rods of the same weight and equal
length have different thickness. They are held vertically on the surface of sand as shown in Figure. Which one of them will sink more? Why?
\( A \)
B. B
c. both sink same
D. cant say


A man wearing a wingsuit glides through the air with a constant velocity
of \( 47 m s^{-1} \) at an angle of \( 24^{\circ} \) to the horizontal. The path of the man is shown
in Fig.
The total mass of the man and the
wingsuit is \( 85 k g . \) The man takes a time
of 2.8 minutes to glide from point \( A \) to
point \( \boldsymbol{B} \)

For the movement of the man from \( A \) to
\( B, \) determine:
the decrease in gravitational potential energy decrease in gravitational potential energy \( = \)


Two fishes are \( 1 m \) apart underwater
The gravitational force between them is
\( F_{1}, \) Theyjump above the surface of water keeping the same distance (i.e 1 m)
between them. The new gravitational
force between them is \( F_{2} \). The
relationship between \( \boldsymbol{F}_{1} \) and \( \boldsymbol{F}_{2} \) is
A \( \cdot F_{1}>F_{2} \)
B. \( F_{1}<F_{2} \)
c. \( F_{1}=F_{2} \)
D. \( F_{1}: F_{2}=1: 2 \)


The pupil of the eye changes its size to adjust for
A. objects at different distances
B. different amount of light
c. objects of different sizes
D. different colours


The integer next above \( (\sqrt{3}+1)^{2 n} \)
contains
\( \mathbf{A} \cdot 2^{n+1} \) as a factor
B. \( 2^{n+2} \) as a factor
\( \mathbf{c} \cdot 2^{n+3} \) as a factor
D. \( 2^{n} \) as a factor


ff \( y \) varies inversely as \( x, \) and \( y=9 \) when \( x=2, \) find \( y \) when \( x=3 \)


Water absorption through roots can be increased by keeping the plants
A. In the shade
B. In dim light
c. under the fan
D. Covered with a polythene bag


If a car is moving forward, what is the
direction of the moment of the moment
caused by the rotation of the tires
A. It is heading inwards, i.e. the direction is towards inside of the car
B. It is heading outwards, i.e. the direction is towards outside of the car
c. It is heading forward, i.e. the direction is towards the forward direction of the motion of the car
D. It is heading backward, i.e. the direction is towards back side of the motion of the car


The main raw materials required for the manufacture of portland cement are:
A. limestone and clay
B. limestone and gypsumm
c. limestone and calcium chloride
D. limestone and silica


Which of the following statements is
false?
A. Glycine is amphoteric in nature.
B. Hydrolysis of sucrose is known as inversion of cane sugar.
C. Sucrose undergoes mutarotation.
D. Maltose and Lactose both are reducing sugars.


Column I Column II


To convert mechanical energy into
electrical energy, one can use This question has multiple correct options
A. \( D C \) dynamo
B. \( A C \) dynomo
c. motor
D. transformer


A wave completes 20 vibrations in 2.5 s.
Its frequency is
\( A \cdot 20 H z \)
в. 8 н \( z \)
c. 200 н \( z \)
D. 50 Hz


Find the square of the following number
\( \mathbf{9 7} \)


Magnesium is manufactured by electrolysing fused magnesium chloride using.
A. A nickel cathode and a graphite anode
B. The iron container as anode and a nickel cathod
C. The iron container as cathode and a graphite anode
D. The nickel container as cathode and iron anode


NaOH can't be stored in
\( \mathbf{A} \cdot \) Al vessel
B. Zn vessel
c. Both a and
D. None of these


The first term of an A.P. is 2 and ninth
term is \( 58 . \) What is the common
difference?
A . 5
B. 6
\( c \cdot 7 \)
D.


Calculate the amount of charge required to deposit 1.0 g of sodium metal(molar mass 23.0 g \( m o l^{-1} \) ) from sodium ion.
A . 2098
B. 96500
c. 193000
D. 4196


An oscillator circuit contains an
inductor \( 0.05 H \) and a capacitor
of capacity \( 80 \mu F \).When the maximum
voltage across the capacitor is \( 200 V \) the maximum current (in amperes) in the circuit is
\( A \cdot 2 \)
B. 4
c. 8
D. 10
E. 16


When a molecule of pyruvic acid is subjected to anaerobic oxidation and forms lactic acid, these are:
A. Loss of 3 ATP molecules
B. Loss of 6 ATP molecules
c. Gain of 2 ATP molecules
D. Gain of 4 ATP molecules


A farmer \( F_{1} \) has a land in the shape of a
triangle with vertices at \( \boldsymbol{P}(\mathbf{0}, \mathbf{0}), \boldsymbol{Q}(\mathbf{1}, \mathbf{1}) \)
and \( R(2,0) . \) From this land, a
neighbouring farmer \( F_{2} \) takes away the region which lies between the side PQ and a curve of the form \( \boldsymbol{y}=\boldsymbol{x}^{n}(\boldsymbol{n}>1) \)
If the area of the region taken away by the farmer \( F_{2} \) is exactly \( 30 \% \) of the area of \( \Delta P Q R, \) then the value of \( n \) is


What is the formula to find the value of
\( t_{1 / 2} \) for a zero order reaction?
A. \( \frac{k}{[R]_{0}} \)
в. \( \frac{2 k}{[R]_{0}} \)
c. \( \frac{[R]_{0}}{2 k} \)
D. \( \frac{0.693}{k} \)


Solve the following system of equation \( 2 x+3 y+8=0 \)
\( 4 x+5 y+14=0 \)


The principal axis is also called
of the lens.
A. optical axis
B. x-axis
c. y-axis
D. axis


The vertices of a triangle \( A B C \) are \( A(2,3, \)
1), \( B(-2,2,0) \) and \( C(0,1,-1) \).Find the
magnitude of the line joining mid points of the sides \( A C \) and \( B C \).
A \( \cdot \frac{1}{\sqrt{2}} \) unit
B. 1 unit
c. \( \frac{3}{\sqrt{2}} \) unit
D. 2 unit


Electronic configuration has violated :
仙 \( \left[\begin{array}{l}16 \\ 1 k\end{array}\right] \) 倪
A. Hund's rule
B. Pauli's principle
c. Aufbau principle
D. \( (n+l) \) rule


If \( \boldsymbol{A} \) is a \( \mathbf{3} \times \mathbf{3} \) matrix \( |\mathbf{3} \boldsymbol{A}|=\boldsymbol{k}|\boldsymbol{A}| \), then
write the value of \( k \)


\( H_{2} S \) is acidic in nature while \( H_{2} O \) is
neutral in nature. Give reason.
A. Oxygen is more electro negative than sulphur
B. \( H-S \) bond is weaker than \( O-H \) bond
c. Bond angle in \( H_{2} S \) is less than that in \( H_{2} O O \)
D. \( H-S \) bond is stronger than \( O-H \) bond


Which of the following is not s-block element?
В. \( 1 s^{2} 2 s^{2} 2 p^{1} \)
c. \( 1 s^{2} 2 s^{1} 2 p^{1} \)
D・ \( [A r] 4 s^{1} 4 p^{1} \)


With rise in temperature, resistance of
a semiconductor material (germanium or silicon)
A . increases
B. decreases
c. remains the same
D. first increases then decreases


An electron in the hydrogen atom is excited from \( 1^{s t} \) orbit to \( 5^{t h} \) orbit. Find
the change in energy of the electron in
\( e V: \)
A. (13.6 \( \times 24) / 25 \)
B. (13.6 \( \times 4) / 5 \)
\( c \cdot(0.529 \times 4) / 5 \)
D. (13.6 \( \times 4) / 9 \)


The rate constant, the activation energy
and the frequency factor of a chemical
reaction at \( 25^{\circ} \mathrm{C} \) are \( 3.0 \times 10^{-4} s^{-1} \)
\( 104.4 \mathrm{KJ} \) mol\( ^{-1} \) and \( 6.0 \times 10^{14} s^{-1} \)
respectively. The value of the rate constant as \( \boldsymbol{T} \rightarrow \infty \) is:
A . \( 2.0 \times 10^{18} s^{-1} \)
B. \( 6.0 \times 10^{14} s^{-1} \)
\( c \cdot \alpha \)
D. 3.6 \( \times 10^{20} s^{-1} \)


The pressure exerted by a column of liquid of height \( h \) and density \( p \) is
given by the hydrostatic pressure equation equal to
\( A \cdot p g h \)
B. \( p g \)
\( c \cdot g h \)
D. Cannot be calculated


A particle with a charge of 3 coulombs is taken from a point at a potential of 50 V to another point at a potential of \( 120 \mathrm{V} \) Calculate the work done.
A . 23.33 J
B. 2.4 J
c. 210
D. 40 J


The amount of \( \left(N H_{4}\right)_{2} S O_{4} \) having degree of dissocation \( 75 \% \) which should
be dissolved in \( 1500 \mathrm{ml} \) of \( 1 \mathrm{M} N H_{4} \mathrm{OH} \)
to decrease its degree of dissociation
by 200 times, is \( \left[k_{b} \text { of } N H_{4} O H=1.8\right. \)
\( \left.\times 10^{-5}\right]: \)
A . \( 112.1 \mathrm{gm} \)
B. 224.2 gm
c. \( 56.0 \mathrm{gm} \)
D. 65.4gm


A photon of wavelength \( 4 \times 10^{-7} \mathrm{m} \)
strikes on the metal surface, the work
function of the metal is 2.13 eV.

Calculate the energy of the photon (eV)
(ii) the kinetic energy of the emission and (iii) the velocity of the photoelectrons \( (1 e V= \) \( \left.1.6020 X 10^{-23} J\right) \)


The molecular weight of benzoic acid in benzene as determined by depression in the freezing point method corresponds
to:
A. ionization of benzoic acid
B. dimerization of benzoic acid
c. trimerization of benzoic acid
D. solvation of benzoic acid


Ordinary CuO is used in Liebig's combustion method for estimation of
carbon and hydrogen in organic compounds.
A. True
B. False


Describe with suitable diagram the Deacon process of manufacture of chlorine. Write its reaction with
ammonia.


\( \operatorname{Let} \boldsymbol{F}(\boldsymbol{x})=\boldsymbol{f}(\boldsymbol{x})+\boldsymbol{f}\left(\frac{1}{\boldsymbol{x}}\right) \) where
\( f(x)=\int_{1}^{x} \frac{\log t}{1+t} d t \)
Then \( F(e) \) is equal to?
\( A \)
B. 2
\( c \cdot 1 / 2 \)
\( D \)


In the given figure
\[
\angle Q R N=40^{\circ}, \angle P Q R=46^{\circ} \text { and } M N
\]
is a tangent at \( R \). What is the value
\( (\text {in degrees}) \)of \( \mathbf{x}, \) y and z respectively?
\( M \)
\[
\frac{y_{z}}{R} 40^{46^{\circ}}
\]


The hybridization of \( X e \) in \( X e F_{2} \) is:
\( A \cdot s p^{3} \)
B \( \cdot s p^{2} \)
\( \mathrm{c} \cdot s p^{3} d \)
D. \( s p^{3} d^{2} \)


This is not a part of the ear.
A. humerus
B. cochlea
c. labyrinth
D. stapes


In the circuit shown, the effective
capacitance between points \( X \) and \( Y \) is
\( A \cdot 3.33 \mu F \)
В. \( 1 \mu F \)
\( c .0 .44 \mu F \)
D. none of these


The ratio of the secondary to the primary turns in a transformer is 3: 2
and the output power is \( P . \) Neglecting
all power losses, the input power must be
A \( \cdot \frac{2 P}{3} \)
в. \( \frac{3 P}{2} \)
c. \( \frac{P}{2} \)
D. \( P \)


Write balanced chemical equations to
show:

The oxidizing action of conc. Sulphuric acid on Carbon.


\( F e^{3+} \) oxidises \( N H_{2} O H \) to
A \( \cdot N O_{2} \)
в. \( N_{2} \),
c. \( N_{2} \)
D. \( N_{3} \)


In \( \triangle \mathrm{PQR}, \mathrm{M} \) and \( \mathrm{N} \) are points on sides PQ and PR respectively such that PM = \( 15 \mathrm{cm} \) and \( \mathrm{NR}=8 \mathrm{cm} . \) If \( \mathrm{PQ}=25 \mathrm{cm} \) and
\( P R=20 \mathrm{cm} \) state whether MN \( \| \mathrm{QR} \)


Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \)
if \( \boldsymbol{y}=(\sin \boldsymbol{x})^{\boldsymbol{x}}+\sin ^{-1} \sqrt{\boldsymbol{x}} \)


The adjoining diagram shows the
energy levels for an electron in a certain,
which transition shown represents the
emission of a photon with the maximum energy
\( A \)
B. I
c. III
D. IV


Position \( x \) of a particle moving along a straight line with time \( t \) is given by \( x= \) \( \sqrt{t^{2}+2} . \) Acceleration of the particle is
given by.
A. \( \frac{1}{x^{3}} \)
в. \( \frac{2}{x^{3}} \)
c. \( \frac{1}{x}-\frac{t^{2}}{x^{2}} \)
D. \( \frac{1}{x}-\frac{t^{2}}{x} \)


Given, \( \vec{\omega}=2 \hat{k} \) and \( \vec{r}=2 \hat{i}+2 \hat{j} . \) Find the linear velocity.
A \( \cdot 4 \hat{i}+4 \hat{j} \)
B - \( 4 \hat{i}-4 \hat{k} \)
\( \mathbf{c} \cdot_{-4 \hat{i}+4 \hat{j}} \)
D. \( -4 \hat{i}-4 \hat{j} \)


If \( a^{2}=b^{2}+b c \) then \( b+c \) always equals
A \( \cdot \frac{a^{2}}{b} \)
в. \( \frac{1}{2} b c \)
\( c \cdot 1 \)
D. \( b c \)


The correct order of atomic size of Na,
Be and Mg is:
\( A \cdot B e>M g>N a \)
в. \( \mathrm{Na}>\mathrm{Mg}>\mathrm{Be} \)
c. \( \mathrm{Mg}>\mathrm{Na}>\mathrm{Be} \)
D. \( N a=M g>B e \)


Cotrell precipitator works on the
principle of:
A. distribution law
B. addition of electrolyte
C. neutralisation of charge on colloids
D. Le Chatelier's principle


Two satellites of identical masses orbit
the earth at different heights. The ratio of their distances from the centre of
earth is \( d: 1 \) and the ratio of the
acceleration due to gravity at those height is \( g: 1 . \) Then find the ratio of their orbital velocities.
A \( \cdot \sqrt{\frac{g}{d}} \)
B. \( \sqrt{g d} \)
\( \mathrm{c} \cdot \sqrt{g} \)
D. \( \sqrt{g} d \)


Find the focal length of a convex lens, if its power is \( +2.0 \mathrm{D} \)
A. \( 0.5 \mathrm{m} \)
B. -0.5 m
\( c \cdot 1 m \)
D. -1 m


IUPAC name of the compound is:
A. 2 -methylbenzoic acid
B. 3-methyl benzenecarboxilic acid
c. 2 -methylbenzeneoic acid
D. 3-methylbenzoic acid


Which of the following postulate can be used to prove \( \Delta K L M \) and \( \Delta R S T \) are similar?
This question has multiple correct options
A . AAS
B. sss
c. sas
D. AAA


The speed of sound in a gas is given by \( \boldsymbol{v}=\sqrt{\frac{\gamma \boldsymbol{R} \boldsymbol{T}}{\boldsymbol{M}}} \)
\( R= \) universal gas constant
\( \boldsymbol{T}= \) temperature
\( M= \) molar mass of gas The dimensional formula of \( \gamma \) is
\( \mathbf{A} \cdot\left[M^{0} L^{0} T^{0}\right. \)
B . \( \left[M^{0} L T^{-1}\right] \)
\( \mathbf{c} \cdot\left[M L T^{-2}\right] \)
D \cdot \( \left[M^{0} L^{0} T^{-1}\right] \)


Assertion: Paramagnetic substances get weakly attracted to a magnet. Reason : They have tendency to move from a region of strong magnetic field to weak magnetic field
A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true and reason is not the correct explanation of assertion
c. If assertion is true but reason is false
D. If both assertion and reason are false


The derivative of the function \( f(x)= \) \( \sqrt{x^{2}-2 x+1} \) in the interval [0,2] is
A . -1
B.
\( c \cdot 0 \)
D. does not exist


Factorize \( \left(1+\frac{1}{x}+\frac{1}{x^{2}}+\frac{1}{x^{3}}\right) \)


Cluster of molecules in which the
hydrophobic tails are in the interior of the clusterand the ionic ends are on the
surface of the cluster, are called:
A . scum
B. micelles
c. colloids
D. emulsion


In a parallel RC circuit, there is \( 100 m A \)
through the resistive branch and
100 \( m A \) through the capacitive branch.
The total rms current is
A \( .200 m A \)
в. \( 100 \mathrm{mA} \)
\( c .282 m A \)
D. \( 141 m A \)


What happens to the fringe pattern, if in the path of one of the slits a glass plate which adsorbs \( 50 \% \) energy is interposed?
A. brightness of fringes will decrease but the dark fringe will become brighter
B. No fringes are observedd
c. The frings width decrease
D. None of the above


The laws of reflection are true for:
A. the plane mirror only
B. the concave mirror only
C. the convex mirror only
D. all reflecting surfaces


What is the other name of Galileo's law
of falling bodies?
A. Law of motion
B. Newton's first law
c. Newton's second law
D. Newton's third law


Density of vitreous humour is equal to the?
A. Air
B. water
c. Lens
D. None of these


Nitrites and nitrates are added to food
to keep meat red for a longer time but
there are harmful effects. What are
these harmful effects?


The D.E whose solution is \( y=a x^{3}+b x^{2} \)
is
A \( \cdot x^{2} y_{2}-4 x y_{1}+6 y=0 \)
B . \( x^{2} y_{2}-4 y_{1}+6 y=0 \)
c. \( x^{2} y_{2}+4 x y_{1}-6 y=0 \)
D. \( x^{2} y_{2}-2 x y_{1}+6 y=0 \)


Probability is 0.45 that a dealer will sell
at least 20 television sets during a day, and the probability is 0.74 that he will
sell less that 24 televisions. The
probability that he will sell 20,21,22 or
23 televisions during the day, is
A . 0.19
в. 0.32
c. 0.21
D. None of these


How many words can be formed from the word "BHARAT"
A . 360
B. 180
\( c \cdot 90 \)
D. 45


Integrate the function \( \tan ^{-1}(\sqrt{\frac{1-\sin x}{1+\sin x}}) \) w.r.t d \( x \)


Which of the following is the correct value of \( \boldsymbol{R} \) in \( \boldsymbol{S} \boldsymbol{I} \) units?
A. 0.083 bar \( d m^{3} K^{-1} m o l^{-1} \)
-
B. 1.98 calK\( ^{-1} \)mol\( ^{-1} \)
c. \( 8.314 \times 10^{7} \) ergK\( ^{-1} \) mol \( ^{-1} \)
D. \( 8.314 J K^{-1} m o l^{-1} \)


Which of the following units is correctly
matched?
A. SI units of conductivity is \( S m^{-1} \)
B. \( S I \) units of molar conductivity is \( S \mathrm{cm}^{2} \mathrm{mol}^{-1} \)
c. \( S I \) unit of conductance is \( S^{-1} \)
D. All of these


In the decomposition of oxalic acid following data were obtained.
\[
\begin{array}{lcc}
\text { Time (second) } & 0 & 300 \\
\text { Volume of } K M n O_{4} & 22.0 & 17.0
\end{array}
\]
used in \( \mathrm{mL} \)
If reaction obeys 1 st order kinetics then
determine the rate constant K and half-
life period:
A \( \cdot 8.43 \times 10^{-4} \) sec \( , 13.7 \) minute
B . \( 86 \times 10^{-4} \) sec \( , 134.3 \) minute
c. \( 8.6 \times 10^{-5} \) sec \( , 1.343 \) minute
D. None of these


The matter-wave picture of electromagnetic wave/radiation elegantly incorporated the:
A. Heinsenbergs uncertainty principle
B. correspondence principle
c. cosmic theory
D. Hertzs observations


There are 15 buses running between two
towns. In how many ways can a man go
to one town and return by a different bus?


All gasses deviate from gas laws at
A. high pressure and low temperature.
B. low pressure and high temperature.
C. high pressure and high temperature.
D. low pressure and low temperature.


The angle of intersection between the
curves \( \boldsymbol{x}^{2}=\mathbf{4}(\boldsymbol{y}+\mathbf{1}) \) and \( \boldsymbol{x}^{2}=-\mathbf{4}(\boldsymbol{y}+ \)
1) is.
A \( \cdot \frac{\pi}{6} \)
B. \( \frac{\pi}{4} \)
c. 0
D.


Which of the following reaction shows
reduction of water?
A \( \cdot 2 H_{2} O+2 N a \rightarrow 2 N a O H+H_{2} \)
B \( \cdot 6 C O_{2}+12 H_{2} O \rightarrow C_{6} H_{1} 2 O_{6}+6 H_{2} O+6 O_{2} \)
\( \mathbf{c} \cdot 2 F_{2}+2 H_{2} O \rightarrow 4 H^{+}+4 F^{-}+O_{2} \)
D. \( P_{4} O_{1} 0+6 H_{2} O \rightarrow 4 H_{3} P O_{4} \)


Assertion
For a particular reaction, heat of
combustion at constant pressure \( \left(\boldsymbol{q}_{\boldsymbol{P}}\right) \)
is always greater than that at constant
volume \( \left(\boldsymbol{q}_{V}\right) \)
Reason
Combustion reactions are invariably
accomplished by increase in number of
moles.
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


\begin{tabular}{l|l|l}
List & \multicolumn{1}{l} { List } \\
I & II \\
A. & A dusting of a carpet & Inertia of direction \\
B. & Provided with a mudguard & Inertia of motion \\
C. & Fan continues to rotate after switching off & Measure of inertia \\
\hline D. & Mass & Inertia of rest
\end{tabular}
\( \mathbf{A} \)
\( A-(4) ; B-(1) ; C-(3) ; D-(2) \)
\( \mathbf{B} \)
\( A-(4) ; B-(1) ; C-(2) ; D-(3) \)
C \( \cdot A-(4) ; B-(2) ; C-(1) ; D-(3) \)
D. \( A-(1) ; B-(4) ; C-(2) ; D-(3) \)


In the given figure, the work done in taking the charge q from M to N is
\( \mathbf{A} \cdot \frac{2 k q Q}{a} \)
B. \( \frac{2 \sqrt{2} k q Q}{a} \)
c. \( \frac{\sqrt{2} k q Q}{a} \)
D. zer


Solve:
\( \int \frac{2 x+1}{\left(x^{2}-1\right)} d x \)


One mole of an ideal gas in initial state
A undergoes a cyclic process \( A B C A, \) as
shown in the figure. Its pressure at \( A \) is
\( P_{0} . \) Choose the correct option(s) from
the following.
This question has multiple correct options
A. Internal energies at A and B are the same
B. Work done by the gas in process AB is \( P_{o} V_{o} \) In 4
c. pressure at \( c \) is \( \frac{P_{o}}{4} \)
D temperature at \( C \) is \( \frac{T_{o}}{4} \)


Convert \( 3 \frac{5}{6} \) into an improper fraction.


Give two differences between D.N.A. and
R.N.A.


The IUPAC name for the compound is:
A. 2-acetyl prop-1-ene
B. pent-1-en-4-one
c. Pent-4-en-2-one
D. formyl propene


Light : Ray : : Sound : ?
A. Hear
B. wave
c. Audio
D. Pitch


The diagram shows the changes in
state of water \( \left(H_{2} O\right) . \) What is the
process X called:
A. Melting
B. Freezing
c. Boiling
D. Evaporation


The acceleration of an electron in the
first orbit of the hydrogen atom \( (\boldsymbol{n}=\mathbf{1}) \)
is :
A \( \cdot \frac{h^{2}}{\pi^{2} m^{2} r^{3}} \)
B. \( \frac{h^{2}}{8 \pi^{2} m^{2} r^{3}} \)
c. \( \frac{h^{2}}{4 \pi m^{2} r^{3}} \)
D. \( \frac{2 \pi^{2} k m e^{2} Z}{\eta h} \)


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


The fuel formed by the marine animal and plant remnants is :
A. Petroleum
B. Electricity
c. Biogas
D. coal


If \( 50 \mathrm{N} \) force is applied on a liquid and it
experiences \( 25 N / m^{2} \) pressure. Find
out the area on which the force is
applied?


Our body irritates if it comes in contact with jelly fish. Give reasons.


Number of lone pair of electrons present
on the central atom of \( N O_{2}^{-} \) ion is?
A. zero
B. 1
\( c \cdot 2 \)
D. 3


The contrapositive of \( \boldsymbol{p} \rightarrow(\sim \boldsymbol{q} \rightarrow \sim \boldsymbol{r}) \)
is equivalent to
\( \mathbf{A} \cdot(\sim q \wedge r) \rightarrow \sim p \)
В \( \cdot(q \wedge \sim r) \rightarrow \sim p \)
c. \( p \rightarrow(\sim r \vee q) \)
D. \( p \wedge(q \vee r) \)


Due to low atmospheric pressure, the rate of transpiration will
A. Decrease slowly
B. Decrease rapidly
c. Increase
D. Remain unaffected


\( \lim _{x \rightarrow 0} \frac{2 \sin x-\sin 2 x}{x^{3}} \) is equal to :


Displacement versus time curve for a
particle executing SHM is as shown in
figure.
At what points the velocity of the
particle is zero?
\( A \cdot A, C, E \)
B. В, D, F
\( c \cdot A, D, F \)
D. \( \mathrm{C}, \mathrm{E}, \mathrm{F} \)


Find the rate percent, if the S.I on Rs 275 in 2 years is Rs 22.


If \( \mathrm{KE} \) of a given particle is doubled, its momentum will be:
A. Doubled
B. Tripled
C. Increases by \( \sqrt{2} \) times
D. Remains unchangedd


Suppose a pure \( \boldsymbol{S} \boldsymbol{i} \) crystal has \( \boldsymbol{5} \times \)
\( 10^{28} \) atoms \( m^{-3} . \) It is doped by 1 ppm
concentration of pentavalent \( \boldsymbol{A} \boldsymbol{s} \)

Calculate the number of electrons and
holes. Given that \( n_{i}=1.5 \times 10^{16} m^{-3} \)


The equation of the diameter of circle \( x^{2}+y^{2}+2 x-4 y-11=0 \) which
bisects the chords intercepted on the line \( 2 x-y+3=0 \) is
A. \( x+y-7=0 \)
В. \( 2 x-y-5=0 \)
c. \( x+2 y-3=0 \)
D. None of these


The floating roots in water absorbs the
air from
A. Dissolved oxygen in water
B. Dissolved oxygen in soil
c. Stomata
D. None of the above


Discuss the causes and effects of
global warming. What measure need to be taken to control global warming?


Order of \( \frac{1}{8 \times 10^{9}} \) is:
\( \mathbf{A} \cdot 1.77 \times 10^{-10} \)
B \( .1 .25 \times 10^{-10} \)
C \( .1 .55 \times 10^{-10} \)
D. \( 1.95 \times 10^{-10} \)


If \( \frac{x+a}{2}=b \cot ^{-1}(b \ln y), b>0, \) then
value of \( \boldsymbol{y} \boldsymbol{y}^{\prime \prime}+\boldsymbol{y} \boldsymbol{y}^{\prime} \ln \boldsymbol{y} \) equals
A \( \cdot y^{\prime} \)
B . \( y^{\prime} \)
\( c \cdot 0 \)
D.


Which one of the following is not a common component of Photochemical Smog?
A. Ozone
B. Acrolein
c. Peroxyacetyl nitrate
D. chloroflurocarbons


A substance \( X \) on heating gives \( Y \) and \( Z \) What is \( X ? \) Is it an element or a
compound? State two differences between an element and a compound. \( (1+1=2 \text { marks }) \)


Examine the data showing the percent identity of the GAPDH gene and protein sequences between humans and the
three species shown below.
Species G
lo \( \begin{array}{ll}\text { Gene } & \text { Protein } \\ \text { ldentity } & \text { ldentity }\end{array} \)
99.6\% \( \quad 100 \% \) Chimpanzee
Fruit Fly 72.4\% 76.7\%
Roundworm \( 68.2 \% \) 74.3\%
Provide a possible reason for why the percent identity between gene sequences is lower than the percent identity of protein sequences.
A. Multiple codons code for the same amino acid
B. Introns are likely to have different sequences.
c. Differences in DNA sequences are edited when the mRNA is transcribed
D. Amino acids cannot be substituted without consequence


The probability that Chakri passes in mathematics is \( \frac{2}{3} \) and the probability that he passes in English is \( \frac{4}{9} . \) If the probability of passing both courses is \( \frac{1}{4}, \) then the probability that Chakri wil pass in at least one of these subjects is \( \mathbf{3 1} \)
立 \( \overline{\mathbf{3 6}} \)
A . True
B. False
c. Ambiguous
D. Data Insufficient


Find a unit vector in the direction of the
vector \( \overrightarrow{\boldsymbol{a}}=\hat{\boldsymbol{i}}+\mathbf{2} \hat{\boldsymbol{j}}+\mathbf{3} \hat{\boldsymbol{k}} \)


(Kinetics/lonic equilibrium) studies of reactions involve molecular
reactions.


In an isosceles \( \triangle A B C \) is the \( A B=A C \)
\( D \) and \( E \) are points on \( B C \) such that
\( B E=C O \) show that \( A D=A E \)


\( \ln \operatorname{an} \mathrm{L}-\mathrm{C} \) circuit \( \boldsymbol{L}=\mathbf{0 . 7 5} \boldsymbol{H} \) and \( \boldsymbol{C}= \)
\( 18 \mu F . \) At the instant when the current
in the inductor is changing at a rate of \( 3.40 A / s, \) what is the charge on the capacitor?
A \( .45 .9 \mu C \)
B. \( 15.9 \mu C C \)
\( c .55 .9 \mu C \)
D. \( 35.9 \mu C \)


Disease caused by eating fish found in water contaminated with industrial
waste having mercury is:
A. minamata disease
B. brights disease
c. hashimotos disease
D. osteosclerosis


Is there ever an instant when the
velocity is \( 0 ? \) If \( s o, \) give the time.
A . \( 1.5 s \)
B . \( 2 s \)
\( c .3 s \)
D. \( 6 s \)


What are artificial Sweetening agents?
Give one example


In chickens, the female is the homogametic sex.
A. True
B. False


Which ion produces a small crystal field splitting (a weak ligand field)?
\( \mathbf{A} \cdot I^{-} \)
в. \( C I^{-} \)
\( c \cdot F^{-} \)
D. All of the above


Which of the following is/are examples of pseudo unimolecular reactions?
This question has multiple correct options
\( \mathbf{A} \cdot C H_{3} C O_{2} C_{2} H_{5}+H_{2} O \stackrel{H}{\rightarrow} C H_{3} C O_{2} H+C_{2} H_{5} O H \)
\( ^{\mathbf{B}} \cdot C_{12} H_{22} O_{11}+H_{2} O \stackrel{H}{\rightarrow}^{\oplus} \quad \begin{array}{ll}C_{6} H_{12} O_{6} & =C_{6} H_{12} O_{6} \\ & (G l u \operatorname{cose})\end{array}=\quad(\text {Fructose}) \)
\( \mathbf{c} \cdot C H_{3} C O C l+H_{2} O \rightarrow C H_{3} C O_{2} H+H C l \)
\( \mathrm{D} \cdot \mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{C}_{2} \mathrm{H}_{5}+\mathrm{H}_{2} \mathrm{O} \stackrel{\mathrm{OH}}{\rightarrow} \mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}+\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH} \)


Draw a sectional view of the human
heart and label the aorta, right ventricle,
and veins.


State and Explain Law of Multiple Proportions with the help of an example.


The time period of a simple harmonic motion is \( 8 s . \) At \( t=0, \) it is at its
equilibrium position. The ratio of distances transversed by it in the first and second seconds is:
A \( \cdot \frac{1}{\sqrt{2}} \)
в. \( \frac{1}{\sqrt{2}-1} \)
c. \( \frac{1}{\sqrt{3}} \)
D. \( \frac{1}{2} \)


The number of carbon atoms in Buckminsterfullerene is:
A . 50
B. 350
\( c \cdot 60 \)
D. 70


Charles's law is represented
mathematically as (symbols have their usual meanings)
\( \mathbf{A} \cdot V_{t}=K V_{o} t \)
в. \( v_{A}=\frac{K V_{o}}{t} \)
c. \( v_{t}=V_{o}\left(1+\frac{273}{t}\right) \)
D. \( V_{t}=V_{o}\left(1+\frac{t}{273}\right) \)


A graph of volume of hydrogen released
vs time for the reaction between zinc
and dil. \( H C l \) is given in figure. On the
basis of this mark the correct option.
' Average rate upto 40 seconds is \( \frac{V_{3}-V_{2}}{40} \)
B. Average rate upto 40 seconds is \( \frac{V_{3}-V_{2}}{40-30} \)
c. average rate upto 40 seconds is \( \frac{V_{3}}{40} \)
'Average rate upto 40 seconds is \( \frac{V_{3}-V_{1}}{40-20} \)


The stress-strain graphs for materials and B are shown in Fig. The graphs are drawn to the same scale.
(a) Which of the materials has the
greater Young's modulus?
(b) Which of the two is the stronger material?


Sublimation is used to purify:
A. plasma
B. gases
c. solids
D. liquids


Water is flowing in streamline motion through a horizontal tube. The pressure at a point in the tube is \( \boldsymbol{P} \) where the velocity of flow is \( v . \) At another point,
where the pressure is \( P / 2 \), the velocity
of flow is:
[Density of water \( =\rho \)
A \( \cdot \sqrt{v^{2}+\frac{P}{\rho}} \)
B. \( \sqrt{v^{2}-\frac{P}{\rho}} \)
c. \( \sqrt{v^{2}+\frac{2 P}{\rho}} \)
D. \( \sqrt{v^{2}-\frac{2 P}{\rho}} \)


State true or false:
In the figure, given below, \( 2 A D=A B \)
\( P \) is mid-point of \( A B . Q \) is mid-point of
DR and \( \boldsymbol{P R} \| \boldsymbol{B S}, \) then \( \boldsymbol{A Q} \| \boldsymbol{B S} \)
A. True
B. False


Factorize:
\( 2 x^{3} b^{2}-4 x^{5} b^{4} \)


Why HF acid is stored in plastic bottles?


When a substance \( A \) reacts with water, it produces a combustible gas \( B \) and a solution of substance \( C \) in water. \( D \)
reacts with this solution of \( C \) and
produces the same gas \( B \) on warming.
\( D \) can also produce gas \( B \) on reaction
with dilute \( H_{2} S O_{4} . A \) imparts a deep golden yellow colour to a smokeless flame. \( A, B, C \) and \( D \) are respectively:
A. \( N a, H_{2}, N a O H, Z n \)
в. \( K, H_{2}, \) КОН \( , \) Аг
c. \( C a, H_{2}, C a(O H)_{2}, S n \)
D. \( C a C_{2}, C_{2} H_{2}, C a(O H)_{2}, F e \)


The concentration of \( K^{+} \) ion in \( 0.1 \mathrm{M} \)
\( K_{2} C r_{2} O_{7} \) solution is \( x \) M. The value of
\( 10 x \) is


How much water must be added to 0.50
litre of \( 6.0 \mathrm{M} \) H \( C l \) to make the solution
2.0M ? Answer in liters.
A . 0.33
B. 0.50
c. \( 1 . \)
D. 1.5
E . 2.0


Borax is the sodium salt of:
A. Ortho boric acid.
B. Meta boric acid.
C. Tetra boric acid.
D. Pyro boric acid.


The process of mineralisation by microorganisms helps in the release of
A. Inorganic nutrients from humus
B. Both organic and inorganic nutrients from detritus
c. organic nutrients from humus
D. Inorganic nutrients from detritus and formation of humus


Find the area of the regular hexagon
PQRST in which each side measures
\( 17 \mathrm{m} \) and its height is \( 33 \mathrm{m} \)


Solve the following equations. \( \sin ^{-1} \frac{5}{x}+\sin ^{-1} \frac{x}{2}=\frac{\pi}{2} \)


A metal rod moves at a constant
velocity in a direction perpendicular to its length. A constant uniform magnetic
field exists in space in a direction perpendicular to the rod as well its
velocity. Select correct statements from the following
A. the entire rod is at the same potential
B. there is an electric field in the rod
c. the electric potential is highest at the centre
D. the electric potential is lowest at its centre and increases towards its ends


If a non-degradable and fat soluble pollutant, such as DDT enters the food
chain, the pollutant
A. Magnifies in concentraition at each tropic level
B. Degrades at first trophic level
c. Accumulates in the body fat of organism at first trophic level and does not pass to second trophic level
D. Decreases inconcentration at each trophic level


The constant speed with which the wire
slides after applying the external force
must be
\( 4.16 \mathrm{ms} \)
В. \( 8 m s^{\text {- }} \)
\( c \cdot 24 m s^{-} \)
. 32
2


The energy required to melt 1 g ice is \( 33 J . \) The number of quanta of radiation
of frequency \( 4.67 \times 10^{13} \) sec \( ^{-1} \) that
must be absorbed to melt \( 10 \mathrm{g} \) ice is:
A \( \cdot 1.065 \times 10^{22} \)
B. \( 3.205 \times 10^{23} \)
c. \( 9.076 \times 10^{20} \)
D. none of the above


A spring mass system oscillates with a
time period \( T_{1} \) when a certain mass is
attached to the spring. When a different mass is attached after removing the
first mass the time period becomes \( T_{2} \)
When both the masses are attached to
the free end of the spring with the other end fixed, the time period of oscillation is :
\( \mathbf{A} \cdot \sqrt{T_{1} T_{2}} \)
в. \( T_{1}+T_{2} \)
c. \( \frac{T_{1}+T_{2}}{2} \)
D. \( \sqrt{T_{1}^{2}+T_{2}^{2}} \)


What is the magnetomotive force \( (m m f) \) of a wire with 8 turns carrying three amperes of current?
A. 2,400 At
B. 240 At
\( c \cdot 24 \mathrm{At} \)
D. 2.4 At


A piece of thread folded 6 times is placed along a \( 15 \mathrm{cm} \) long measuring scale as shown in the figure. The length of the thread is between
A. \( 0.15-0.50 \mathrm{m} \)
B. \( 0.50 \mathrm{m}-1.0 \mathrm{m} \)
c. \( 1.0 \mathrm{m}-1.5 \mathrm{m} \)
D. \( 1.5 \mathrm{m}-2.0 \mathrm{m} \)


If the roots of the equation \( \frac{\alpha}{x-\alpha}+ \) \( \frac{\beta}{\boldsymbol{x}-\beta}=1 \) be equal in magnitude but
opposite in \( \operatorname{sign}, \) then \( \alpha+\beta \) is equal to:
A.
B. 1
\( c \cdot 2 \)
D.


Distance of \( 5^{t h} \) dark fringe from centres
is 4 mm. If \( D=2 m, \lambda=600 n m, \) then
distance between slits is
A. \( 1.35 \mathrm{mm} \)
B . \( 2.00 \mathrm{mm} \)
c. \( 3.25 \mathrm{mm} \)
D. \( 10.35 \mathrm{mm} \)


Show that the function \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left[\cos \left(x^{10}+1\right)\right]^{1 / 3}, x \in R \) is a continuous
function.


A solution that is at equilibrium and contains the maximum amount of
solute for a given amount of solvent at constant temperature and pressure. What type of solution is it?
A. Miscible
B. Suspension
c. colloid
D. Saturated


Which of the following is not an actinoid
\( ? \)
\( A \cdot A m \)
B. \( \mathrm{cm} \)
\( c . F m \)
D. Tm


\( \frac{\frac{\sqrt{1}}{12}}{\frac{11}{12}} \)


The coal tar fraction which contains
phenol is:
\( A . \) middle oil
B. green oil
c. heavy oil
D. light oil


Assertion
A rectangular current loop is in an arbitrary orientation in an external
uniform magnetic field. No work is
required to rotate the loop about an axis
perpendicular to its plane.
Reason
All positions represent the same level of
energy.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Bile secretion is proportional to the concentration of
A. Protein
B. Fatt
c. carbohydrate
D. None of the above


Sum of \( n \) terms of \( A \) is \( n^{2}+2 n . \) Find
the first term and common difference


\( \boldsymbol{C a}+\boldsymbol{C}_{2} \rightarrow \boldsymbol{C a} \boldsymbol{C}_{2} \stackrel{N_{2}}{\longrightarrow} \boldsymbol{A} \)
Compound \( (A) \) is used as a / an :
A. fertilizer
B. dehydrating agent
c. oxidising agent
D. reducing agent


The electric field outside the plates of
two oppositely charged plane sheets of charge density \( \sigma \) is :
A \( \cdot+\frac{\sigma}{2 \varepsilon_{0}} \)
В. \( -\frac{\sigma}{2 \varepsilon_{0}} \)
c. zero
D. \( \frac{\sigma}{\varepsilon_{0}} \)


Suppose that \( f(n+1)=\frac{2 f(n)+1}{2} \) for \( \boldsymbol{n}=\mathbf{1}, \mathbf{2}, \mathbf{3}, \ldots \) and \( (\mathbf{1})=\mathbf{2} \) Then \( \boldsymbol{f}(\mathbf{1 0 1}) \)
equals
A . 50
B. 52
c. 54
D. none of these


For which order reaction, the unit of rate
constant is \( \operatorname{tim} e^{-1} ? \)
A. Zero order
B. First order
c. Second order
D. Third order


Find the average of \( \frac{2}{3}, \frac{1}{5} \)


A baby boy aged two years is admitted to play school and passes through a dental check-up. The dentist observed that the boy had twenty teeth. Which teeth were absent?
A. Molars
B. Incisors
c. canines
D. Pre-molars


Expand to 4 terms the following expressions:
\( (1+x)^{\frac{2}{5}} \)


Non vascular land plants are called as
A. Bryophtyes
B. Pteridophytes
c. Fungi
D. Algae


The distances of the point \( \boldsymbol{P}(\mathbf{1}, \mathbf{2}, \mathbf{3}) \)
from the coordinates axes are:
A \( \cdot \sqrt{13}, \sqrt{10}, \sqrt{5} \)
в. \( \sqrt{11}, \sqrt{10}, \sqrt{5} \)
c. \( \sqrt{13}, \sqrt{20}, \sqrt{15} \)
D. \( \sqrt{23}, \sqrt{10}, \sqrt{5} \)


In a wind mill the electric energy is converted into mechanical energy.
A. True
B. False
c. Ambiguous
D. Data insufficient


Which of the two switches \( S_{1} \) and \( S_{2} \)
shown in figure will produce short-
circuiting?
\( A \cdot S_{1} \)
B. \( S_{2} \)
c. Both \( S_{1} \) and \( S_{2} \)
D. Neither \( S_{1} \) nor \( S_{2} \)


A particle having mass 1 g and electric
charge \( 10^{-8} \mathrm{C} \) travels from a point \( \mathrm{A} \)
having electric potential \( 600 \mathrm{V} \) to the point B having zero potential. What would be the change in its kinetic
energy?
A . \( -6 \times 10^{-6} \) erg
В. \( -6 \times 10^{-6} \) j
c. \( 6 \times 10^{-6} \) j
D. \( 6 \times 10^{-6} \) erg


Write a short note on gangue and anode
mud.


Fill in the blank.
The heat generated in calorie is equal to
A. \( V I t \)
B. \( (V I t) / 4.2 \)
C \( \cdot\left(V^{2} R t\right) / 4.2 \)
D. \( V I^{2} t \)


Diffusion current in a p-njunction is greater than the drift current in
magnitude
A. if the junction is forward-biased
B. if the junction is reverse-biased
c. if the junction is unbiased
D. in no case


Draw the structure which shows
synergic bonding interaction in a carbonyl complex?


If the density of earth increases by \( 20 \% \) and radius decreases by \( 20 \% \) then the new value of "g" on the surface of earth will be:
A. \( 0.8 \mathrm{g} \)
B. \( 0.90 \mathrm{g} \)
c. \( 0.96 \mathrm{g} \)
D.


Two person each of mass \( m \$ \) are
standing at the two extremes of a
railroad car of mass left \( M \) resting on a
smooth track. The person on the left
jumps to with a velocity \( u \). Find the velocity of the train when both the person have jumped off.
A \( \cdot \frac{m^{2} u}{m(m+M)} \) towards left
B. \( \frac{m^{2} u}{M(m+M)} \) towards left
c. \( \frac{m^{2} u}{M(m+M)} \) towards right
D. \( \frac{m^{2} u}{m(m+M)} \) towards right


Four charges \( +\boldsymbol{Q},-\boldsymbol{Q},+\boldsymbol{Q} \) and \( -\boldsymbol{Q} \) are
situated at the corners of a square; in a
sequence then at the centre of the
square:
A. \( E=0, V=0 \)
в. \( E=0, V \neq 0 \)
c. \( E \neq 0, V=0 \)
D. \( E \neq 0, V \neq 0 \)


If \( \boldsymbol{y}=\boldsymbol{a} e^{4 x}+\boldsymbol{b} e^{5 x}, \) then prove \( \boldsymbol{y}_{2}- \)
\( \mathbf{9} \boldsymbol{y}_{1}+\mathbf{2 0} \boldsymbol{y}=\mathbf{0} \)


Two thin wire rings each having a radius R are placed at a distance d apart with their axes coinciding. The charges on the two rings are \( +q \) and \( -q \) The potential difference between the centres of the two rings is -
A \( . Q R / 4 \pi \varepsilon 0 d^{2} \)
B. \( \frac{Q}{2 \pi_{c \theta}}\left[\frac{1}{R}-\frac{1}{\sqrt{R^{2}+\alpha^{2}}}\right. \)
c. zero
D. \( \frac{Q}{4 \pi \varepsilon_{0}}\left[\frac{1}{R}-\frac{1}{\sqrt{R^{2}+\bar{d}^{2}}}\right] \)


Examine whether the given function \( f(x) \) is continuous at \( x=3 \)
\[
\begin{array}{c}
\boldsymbol{f}(\boldsymbol{x})= \\
\frac{\boldsymbol{x}^{4}-\boldsymbol{8} \boldsymbol{x}}{\sqrt{\boldsymbol{x}^{2}+\mathbf{5}}-\mathbf{3}}, \quad \text { for } \quad \boldsymbol{x} \neq \boldsymbol{3} \\
\boldsymbol{3} \quad \text { for } \quad \boldsymbol{x}=\mathbf{3}
\end{array}
\]
\[
\boldsymbol{f}(\boldsymbol{x})=\mathbf{3}
\]


The equilibrium constant has no unit if \( \Delta n=\dots \dots \dots \dots \dots \)


If an ecosystem is composed of only three trophic levels, then how much
energy will be conserved at the III \( ^{r d} \)
trophic level?
A . 30\%
B. 20\%
c. \( 10 \% \)
D. 1\%


An incandescent lamp is operated at
\( 240 V \) and the current is \( 0.5 A . \) What is
the resistance of the lamp?


What is pseudocoelom? Where is it located?


Solve the following Linear programming problems graphically:
Maximize \( z=3 x+4 y \) subject to the
constraints \( : \boldsymbol{x}+\boldsymbol{y} \leq \mathbf{4}, \boldsymbol{x} \geq \mathbf{0}, \boldsymbol{y} \geq \mathbf{0} \)


\( \frac{\pi}{k} \)


Let \( E_{1}, E_{2}, E_{3} \dots E_{N} \) be the 'n' exhaustive
events in a random experiment then
\( \boldsymbol{p}\left(\boldsymbol{E}_{1}\right) \boldsymbol{p}\left(, \boldsymbol{E}_{2}\right), \boldsymbol{p}\left(\boldsymbol{E}_{3}\right) \ldots \boldsymbol{p}\left(\boldsymbol{E}_{N}\right) \) is
A. less than
B. equal to
c. greater than 1
D. none


Verify Lagrange's Mean Value Theorem for the following function:
\( \boldsymbol{f}(\boldsymbol{x})=2 \sin \boldsymbol{x}+\sin 2 \boldsymbol{x} \) on \( [\mathbf{0}, \boldsymbol{\pi}] \)


The incident photon involved in the photo-electric effect experiment
\( \nu>\nu_{o} \)
A. Completely disappears
B. Comes out with increased frequency
c. comes out with a decreased frequency
D. Comes out with out change in frequency


The value of \( \lim _{x \rightarrow 2} \frac{\sqrt{1+\sqrt{2+x}}-\sqrt{3}}{x-2} \) is
\( A \cdot \frac{1}{8 \sqrt{3}} \)
в. \( \frac{1}{4 \sqrt{3}} \)
c. 0
D. None of these


The intercept made by the plane \( \vec{r} \cdot \vec{n}= \) \( q \) on the \( x \) -axis is
A \( \cdot \frac{q}{\hat{i} \cdot \vec{n}} \)
в. \( \frac{\hat{i} \cdot \vec{n}}{q} \)
\( c \cdot \frac{\hat{i} \cdot q}{n} \)
D. \( \frac{q}{|\vec{n}|} \)