Why can't we see clearly through fog? Name the phenomenon responsible for it.


To coagulate \( [A g I] A g^{+}: N O_{3}^{-} S o I ; \) The decreasing order of coagulation power in following is -
\( \boldsymbol{N} \boldsymbol{a} \boldsymbol{C} \boldsymbol{I} \)
\( \boldsymbol{K}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
\( \boldsymbol{C} \boldsymbol{a}_{3}\left(\boldsymbol{P} \boldsymbol{O}_{4}\right)_{2} \)
\( \boldsymbol{K}_{4}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{6}\right] \)
A \( \cdot(a)>(b)>(c)>(d) \)
в. \( (d)>(c)>(b)>(a) \)
c. \( (a)>(d)>(c)>(b) \)
D. \( (d)>(c)>(a)>(b) \)


A rectangular solid box of length \( 0.3 m \) is held horizontally, with one of its sides on the edge of a platform of height \( 5 \mathrm{m} \) When released, it slips off the table in a very short time \( \tau=0.01 s, \) remaining
essentially horizontal. The angle by which it would rotate when it hits the
ground will be (in radians) close to :-
A. 0.02
2
в. 0.28
\( c .0 .5 \)
D. \( 0 . \)


\( \lim _{x \rightarrow 0} \frac{\log (a+x)-\log (a-x)}{x}, a>0 \)


Function of nucleases is to
A. Break the polynucleotide chain by breaking the each terminal nucleotide
B. Break phosphodiester bond
C . Break peptide bonds
D. Break ester bonds


From the adjacent circuit, the output
voltage is
\( \mathbf{A} \cdot 10 V \)
B. \( 100 V \)
\( \mathrm{C} \cdot 90 \mathrm{V} \)
D. zero


What is the coefficient of coupling for a
transformer in which \( 4 \% \) of the total flux
generated in the primary does not pass through the secondary?
A . 0.4
B. 4
\( c .9 .6 \)
D. 0.96


Which of the following statements is
true?
A. The reciprocals 1 and -1 are themselves
B. Zero has no reciprocal
C. The product of two rational numbers is a rational number
D. All the above


The sides of a rectangle are \( 7.01 m \) and 12 \( m . \) Taking the significant figures into account, the area of the rectangle
is
B. \( 84.00 m^{2} \)
c. \( 84.12 \mathrm{m}^{2} \)
D. \( 84 m^{2} \)


Find the distance of the point (2,12,5) from the point of intersection of the line \( \vec{r}=2 \hat{i}-4 \hat{j}+2 \hat{k}+\lambda(3 \hat{i}+4 \hat{j}+2 \hat{k}) \)
and the plane \( \vec{r}(\hat{i}-2 \hat{j}+\hat{k})=0 \)


How does \( K_{2}\left[P t C l_{4}\right] \) get ionized when
dissolved in water? Will it form
precipitate when \( A g N O_{3} \) solution is added to it? Give a reason for your
answer


Which property of water is used while
washing clothes?
A. Odour
B. Colour
c. solubility
D. sand


Homeothermic animals are
A. Toadd
B. Lizard
c. Rabbit
D. Frog


Which of the following statements is NOT TRUE in respect of hydrophilic sols?
A. They are quite stable and are not easily coagulated
B. There is considerable interaction between dispersed phase and a dispersion medium (water)
c. The sol particles are hydrated
D. They are very sensitive to coagulation by a small concentration of electrolytes


Assertion
Arteries carry blood from various body
organs to heart.
Reason
Veins carry blood from various body
organ to heart.
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


If \( \frac{1+3 p}{3}, \frac{1-2 p}{2} \) are probabilities of two mutually exclusive event, then \( p \) lies in the interval
\( ^{A} \cdot\left[-\frac{1}{3}, \frac{1}{2}\right] \)
B \( \cdot\left(-\frac{1}{2}, \frac{1}{2}\right) \)
\( ^{\mathbf{C}} \cdot\left[-\frac{1}{2}, \frac{2}{3}\right] \)
D. \( \left(-\frac{1}{3}, \frac{2}{3}\right) \)


Liquation process is used for the concentration of which ore?
A. Stibinite
B. Tinstone
c. limestone
D. Haematite


Metal which emits photo-electrons very easily is :
\( A \cdot A \)
B.
\( c \cdot c s \)
D. cu


Sunlight is present for only a short span
of time in
A. Polar regions
B. Subtropial regions
c. Desert regions
D. Himalayan region


Which among of the following pairs has
the bond angle \( 109^{\circ} 28^{\prime} ? \)
\( \mathbf{A} \cdot\left[N H_{4}^{+}\right],\left[B F_{4}^{-}\right] \)
B \( \cdot\left[N H_{4}^{+}\right],\left[B F_{3}\right] \)
C. \( N H_{3},\left[B F_{4}^{-}\right] \)
D. \( \left[N H_{3}\right],\left[B F_{3}\right] \)


The myelin sheath around the axon is
produced by which type of neurogical
cells?
A. Satellite glial cells
B. Radial glial cells
c. Dendrocytes
D. Schwann cells


Construct a triangle \( A B C \) in which
\( B C=7 c m, \angle B=75^{\circ} \) and \( A B+ \)
\( \boldsymbol{A C}=\mathbf{1 3} \boldsymbol{c m} \)


The group of islands formed by corals is
A. Andaman
B. Nicobar
C. Lakshadweep
D. st. Mary's


A train \( S 1, \) moving with a uniform
velocity of \( 108 \mathrm{km} / \mathrm{h} \), approaches
another train \( S 2 \) standing on a platform. An observer 0 moves with a
uniform velocity of \( 36 \mathrm{km} / \mathrm{h} \) towards \( S 2 \)
as shown in figure. Both the trains are
blowing whistles of same frequency 120
Hz. When 0 is 600 m away from \( S 2 \) and
distance between \( S 1 \) and \( S 2 \) is \( 800 m \)
the number of beats heard by 0 is
(Speed of the sound \( = \)
\( 330 \mathrm{m} / \mathrm{s} \)


Which of the following salts is not soluble in water?
A. \( K_{2} C O_{3} \)
в. \( R b_{2} S O_{4} \)
\( \mathrm{c} . B a C O_{3} \)
D. \( N a I O_{3} \)


Among VA group elements, the element which has highest ionization energy?
A. \( N \)
в. \( P \)
\( c \cdot S b \)
D. \( B i \)


The bone of a mammal contains
Haversian canals, which are connected
by transverse canals known as
A. Semi-circular canals
B. Inguinal canals
c. volkmann's canals
D. Bidder's canals


The correct match between Item(l) and
Item(II)
is :
\( \begin{array}{ll}\text { Item-I } & \text { Item-II } \\ \text { Nortehindrone } & \text { Anti-biotic } \\ \text { Ofloxacin } & \text { Anti-fertility } \\ \text { Equanil } & \text { Hypertension } \\ & \text { Analgesics }\end{array} \)
A. A-R, B-P, C-S
B. A-Q, B-P, C-R
c. \( A-R, B-P, C-R \)
D. A-Q, B-R, C-S


An organic compound gives orange precipitate with \( 2,4-D N P H . \) What is
the functional group in the compound?


Maximum oxidation state of \( O s \) is :
\( A \cdot+6 \)
B. +7
\( c \cdot+8 \)
D. +5


Which of the following substances are
formed when lithium is heated in air?
A \( . L i_{2} O+L i O_{2} \)
в. \( L i_{2} O_{2} \)
c. \( L i O_{2} \)
D. \( L i_{2} O+L i_{3} N \)


In the absence of an electric field, the mean velocity of free electrons in a
conductor at absolute temperature \( (\boldsymbol{T}) \)
is
A . zero
B. independent of \( T \)
c. proportional to \( T \)
D. proportional to \( T^{2} \)


An example of food preservative is:
A. Sodium benzoate
B. Adipic Acid
c. Calcium Benzoate
D. Alcohol


Madhuri went to a supermarket. The
price changes are as follows. The price
of rice reduced by \( 5 \% \), jam and fruits reduced by \( 8 \% \) and oil and dal
increased by \( 10 \% \). Help Madhuri to find the changed prices in the given table.
Original Item \( \quad \) Changed price price/kg
Rice
\[
\text {Rs.30}
\]
\( m \)
\[
\begin{array}{l}
\text {Rs.100} \\
\text {Rs.} 280
\end{array}
\]
Apples
\[
\text {Rs.120}
\]
Dal Rs.80


How does tendency to lose electrons
change in a period and why?


Write a note on pericardium.


Which one of the following statements
is not correct?
A. Oxidation state of \( S \) in \( \left(N H_{4}\right)_{2} S_{2} O_{8} \) is +6
B. Oxidation number of \( O s \) in \( O s O_{4} \) is +8
C. Oxidation state of \( S \) in \( H_{2} S O_{5} \) is +8
D. oxidation number of \( O \) in \( K O_{2} \) is \( -\frac{1}{2} \)


Which one of the following is employed as antihistamine?
A. Omeprazole
B. Chloramphenicol
c. Diphenhydramine
D. Norethindrone


A square hole of side a is made at a
depth \( h \) below water surface and to the
side of a water container another
circular hole of radius \( r \) is made to the
same container at a depth of \( 4 h . \) It
is found that volume flow rate of water
through both the holes is found to be same then:
A \( \cdot r=\frac{a}{2 \sqrt{\pi}} \)
В \( \cdot a=\frac{r}{2 \sqrt{\pi}} \)
c. \( a=\frac{r}{\sqrt{2 \pi}} \)
D. \( r=\frac{a}{\sqrt{2 \pi}} \)


A metallic wire of length \( L \) metre
extends by \( \ell \) metre when stretched by suspending a weight \( M g \) from it. The mechanical energy stored in the wire is
\( \mathbf{A} \cdot 2 M g \ell \)
в. \( M g \ell \)
c. \( \frac{M g \ell}{2} \)
D. \( \frac{M g \ell}{4} \)


Which of the following statements is wrong about gymnosperm?
A. They have naked seeds
B. They are perennial
c. Their xylem consists of vessels
D. They are xerophytic


Find the co-ordinates of the points on
the ellipse \( x^{2}+2 y^{2}=9 \) at which tangent has slope \( \frac{1}{4} . \) Also find the equation of normal.


A plant showing reticulate venation is
A . Ficus
B. Canna
c. Musa
D. zea


Draw neat diagrams showing the line (or lines) of symmetry and give the specific name to the quadrilateral having: only one line of symmetry. How many quadrilaterals are there?


Voltmeters \( V_{1} \) and \( V_{2} \) are connected in
series across a \( D . C . \) line. \( V_{1} \) reads \( 80 V \)
and has a per volt resistance of \( 200 \Omega \)
\( V_{2} \) has a total resistance of \( 32 k \Omega \). The
line voltage is
\( \mathbf{A} \cdot 120 V \)
в. \( 160 V \)
\( \mathbf{c} \cdot 220 V \)
D. \( 240 V \)


The kinetic energy of electrons ejected by using light having frequency equal to threshold frequency \( \left(\nu_{0}\right) \) is:
A \( . h v_{0} \)
B. almostzero
c. very large
D. \( h / v_{0} \)


In what respect is the electronic
configuration of hydrogen and halogens
similar?
A. Hydrogen and halogens have one electron in their outermost shell
B. Hydrogen and halogens have one electron less than noble gas configuration
C. Hydrogen and halogens can lose one electron
D. Hydrogen and halogens show noble gas configuration


The coefficient of \( x \) in the expansion of \( (1-a x)^{-1}(1-b x)^{-1}(1-c x)^{-1} \) is?
A \( . a+b+c \)
B. \( a-b-c \)
c. \( -a+b+c \)
D. \( a-b+c \)


If \( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{cl}\boldsymbol{x}^{a} \cos (\mathbf{1} / \boldsymbol{x}), & \text { if } \quad \boldsymbol{x} \neq \mathbf{0} \\ \text { 0, } & \text { if } \quad \boldsymbol{x}=\mathbf{0}\end{array}\right. \)
continuous at \( x=0 \) then
\( \mathbf{A} \cdot \alpha<0 \)
B \( . \alpha>0 \)
\( \mathbf{c} \cdot \alpha=0 \)
D. \( \alpha \geq 0 \)


The time period of a second's pendulum inside a satellite will be
A . zero
B. \( 1 \mathrm{sec} \)
\( c \cdot 2 \sec \)
D. infinite


Removal of gonads cannot be
considered as a contraceptive option
why?


A container is partially filled with hot water, sealed and left to cool. Which
statements are correct?
1. As the temperature decreases, water molecules lose kinetic energy.
2. As the temperature decreases, more water molecules move from vapour to
liquid.
3. As the temperature decreases, the
vapour pressure of the water decreases.
A. 1,2 and 3 are correct
B. 1 and 2 only are correct
C. 2 and 3 only are correct
D. 1 only is correct


Chlorine is used to purify drinking water. Excess of chlorine is harmful. The
excess of chlorine is removed by treating with sulphur dioxide. Present a balanced equation for the redox change taking place in water


Which of the hydrated species can exist?
I. \( \boldsymbol{H}_{\mathbf{5}} \boldsymbol{O}_{\mathbf{2}}^{+} \)
II. \( \boldsymbol{H}_{3} \boldsymbol{O}^{+} \)
III. \( \boldsymbol{H}_{3} \boldsymbol{O}_{2}^{-} \)
IV. \( \boldsymbol{H}_{7} \boldsymbol{O}_{3}^{+} \)
Select alternate from.
A. Il only
B. I and II
c. I, II and IV
D. I, II, II and IV


For \( \mathbf{r}=\mathbf{0}, \mathbf{1}, \dots, 10, \) let \( \mathbf{A}_{\mathbf{r}}, \mathbf{B}_{\mathbf{r}} \) and \( \mathbf{C}_{\mathbf{r}} \)
denote, respectively, the coefficient of \( x^{r} \) in the expansions of \( (1+x)^{10},(1+ \)
\( \mathbf{x})^{20} \) and \( (\mathbf{1}+\mathbf{x})^{30} \) Then \( \sum_{r=1}^{10} \boldsymbol{A}_{r}\left(\boldsymbol{B}_{10} \boldsymbol{B}_{r}-\right. \)
\( \left.C_{10} A_{r}\right) \) is equal to
A. \( \mathrm{B}_{10}-\mathrm{C}_{10} \)
B . \( A_{10}\left(B_{10}^{2}-C_{10} A_{10}\right) \)
c. 0
D. \( C_{10}-B_{10} \)


A massive ball moving with a speed \( \boldsymbol{v} \)
collide with a tiny ball having a very small mass, immediately after the impact the second ball will move at
speed approximately equal to :
\( A \cdot \infty \)
B. \( \frac{v}{2} \)
\( c \)
D. \( 2 v \)


Find the area of \( \triangle P Q R \) whose vertices \( \operatorname{are} \boldsymbol{P}(-1,1) Q(0,5) R(3,2) \)


The Sl unit of specific latent heat is
A. cal \( g^{-1} \)
B . cal \( g^{-1} \mathrm{K}^{-1} \)
\( c \cdot J \operatorname{kg}^{-1} \)
D. J kg \( ^{-1} \mathrm{K}^{-1} \)


The bent-shape of the molecule may
develop from which of the following hybridization(s)? This question has multiple correct options
\( A \cdot s p^{3} d \)
B \( \cdot s p^{3} \)
\( c \cdot s p \)
\( D \cdot s p^{2} \)


Choose the correct answers from the
alternatives given Which of the following show embryonic development by the deuterostome pathway?
A. Annelids
B. Chordates
c. Molluscs
D. Arthropods


Above transformation can be carried
out by :
A \( \cdot H^{+} / \Delta, \quad Z n(H g), H C l \)
в. \( H I O_{4}, \) LiAlH\( _{4} \)
c. \( H I O_{4}, H^{+} / \Delta \)
D. \( H^{+} / \Delta, H I O_{4} \)


Observe the following statements:
1. The solubility of group \( V \) hydrides in
water decreases from \( N H_{3} \) to \( B i H_{3} \)
2. Phosphorous does not exhibit allotropy.
3. The stability of group V hydrides
decreases from \( N H_{3} \) to \( B i H_{3} \)
The correct statement(s) is/are:
A .2
B. 1 and 2
c. 1,2 and 3
D. 1 and 3


The following are the wages of 8 workers in a factory. Find the range and coefficient of range. Wages are in
dollars: 1400,1450,1520,1380,1485
1495,1575,1440
A .0 .0231
в. 0.03112
c. 0.66
D. 0.02314


The length of the diagonals of a
rhombus are \( 24 \mathrm{cm} \) and \( 18 \mathrm{cm} \). Find the
length of each side of the rhombus


Value of the expression \( (1-\cos \Theta)(1+ \)
\( \cos \Theta)\left(1+\cot ^{2} \Theta\right) \) is
A .
B.
\( c \cdot \sin ^{2} \theta \)
D. \( \operatorname{cosec}^{2} \Theta \)


The yellow coloured solution of chromate salt changes to orange colour on acidification due to the formation of :
A \( \cdot C r^{3} \)
B. \( C r_{2} O_{7}^{2} \)
\( \mathrm{c} \cdot \mathrm{Cr} \mathrm{O}_{4} \)
\( \mathrm{D} \cdot \mathrm{Cr}_{2} \mathrm{O}_{3} \)


Fill in the blanks with approriate words. ... node may be regarded as a remnant of sinus, venosus in mammalian heart.


The magnetic field intensity due to a magnet is \( \frac{100}{4 \pi} \mathrm{A} / \mathrm{m} \). The induction field strength due to it is :
\( \mathbf{A} \cdot 1 \times 10^{-5} T \)
в. \( \frac{4 \pi}{10^{3}} T \)
c. \( \frac{10^{3}}{4 \pi} \times 100 T \)
D. \( \frac{10^{-5}}{4 \pi} T \)


Determine \( n \) if \( ^{2 n} C_{2}:^{n} C_{3}=11: 1 \)


An inductor and resistor are connected
in series with an ac source. In this
circuit.
A. The current and the PD across the resistance lead the
PD across the inductance
B. The current and the PD across the resistance lag behind the PD across the inductance by an angle \( \pi / 2 \)
C. The current and the PD across the resistance lag behind the PD across the inductance by an angle \( \pi \)
D. The PD across the resistance lags behind the PD across the inductance by an angle \( \pi / 2 \) but the current in resistance leads the PD across the inductance by \( \pi / 2 \)


\( X, Y, Z, U \) are four points in a straight
line. If distance from \( X \) to \( Y \) is \( 15, Y \) to
\( Z \) is \( 5, Z \) to \( U \) is 8 and \( X \) to \( U \) is \( 2, \) what
is the correct sequence of the points?
A. \( X-Y-Z-U \)
в. \( X-Z-Y-U \)
c. \( X-U-Z-Y \)
D. \( X-Z-U-Y \)


When \( n \) number identical cell of emf \( E \)
and internal resistance, \( r \) is connected
in parallel, the net internal resistance of the system will be
\( A \)
B . \( n r \)
c. \( r / n \)
D. \( n / r \)


A magnetic substance is kept in a magnetic field, it will be thrown out of the field if it is a
substance.
A. paramagnetic
B. ferromagnetic
c. diamagnetic
D. antiferromagnetic


Select the correct statements regarding
the final product \( (Y) \)
This question has multiple correct options
A. It can be identified with neutral \( F e C l_{3} \) solution
B. On treatment with Zn-dust it yields a product having degree of unsaturation \( =4 \)
C. It undergoes coupling reaction with benzene diazonium chloride at low temperature \( \left(0-5^{\circ} \mathrm{C}\right) \) in slightly basic medium
D. It liberates \( H_{2} \) gas with Na


Where do charges reside in the case of a charged conductor?
A. Inside the conductor
B. on the outer surface of the conductor
c. on the inner surface of the conductor
D. Anywhere outside the conductor


On removing the dielectric from a charged condenser, its energy
A. increase
B. remains unchanged
c. decreases
D. none of these


(a) Consider an arbitrary electrostatic field configuration. A small test charge is placed at a null point (i.e., where \( \mathrm{E}= \)
0) of the configuration. Show that the equilibrium of the test charge is necessarily unstable.
(b) Verify this result for the simple configuration of two charges of the same magnitude and sign placed a certain distance apart.


\( \int \frac{d x}{\sqrt{2 e^{x}-1}} \) equals to
A \( \cdot \sec ^{-1} \sqrt{2 e^{x}}+c \)
B・sec-1 \( \left(\sqrt{2} e^{x}\right)+c \)
\( \mathbf{c} \cdot 2 \sec ^{-1}\left(\sqrt{2} e^{x}\right)+c \)
D. \( 2 \sec ^{-1} \sqrt{2 e^{x}}+c \)


Find the sum of the series: \( 1^{2}-2^{2}+ \)
\( 3^{2}-4^{2}+\ldots \) to \( n \) terms.


A thin wire of length \( L \) and uniform
linear mass density \( \rho \) is bent into a
circular loop with center \( 0 . \) The moment of inertia of the loop about the axis
which is tangent to this loop is:
This question has multiple correct options
A \( \cdot \frac{\rho L^{3}}{8 \pi^{2}} \)
B. \( \frac{\rho L^{3}}{16 \pi^{2}} \)
\( \mathbf{c} \cdot \frac{5 \rho L^{3}}{16 \pi^{2}} \)
D. \( \frac{3 \rho L^{3}}{8 \pi^{2}} \)


A uniform solid cylindrical roller of mass 'm' is being pulled on a horizontal surface \( F \) parallel to the surface and applied at its centre. If the acceleration
of the cylinder is 'a' and it is rolling
without slipping then the value of 'F' is
A . ma
B . \( \frac{5}{3} m a \)
\( c \cdot 2 m a \)
\( D \cdot \frac{3}{2} m a \)


A small cannon 'A' is mounted on a
platform (which can be rotated so that cannon can aim at any point) and is adjusted for maximum range \( R \) of
shells. It can throw shells on any point on the shown circle (dotted) on ground.
Suddenly a windstorm starts blowing in horizontal direction normal to AB with
speed \( \sqrt{2} \) times the velocity of shell. At what least distance can the shell land
from point B. (Assume that the velocity of projection. Also assume that the
platform is kept stationary while projecting the shell.)
A \( \cdot R(\sqrt{5}-1) \)
B . \( R(\sqrt{3}-1) \)
\( \mathbf{c} . R \sqrt{5} \)
D. \( R \sqrt{3} \)


The side of a square of metal is increasing at the rate of \( 5 \mathrm{cm} / \) minute. At what are its area is increasing when
the side is \( 20 \mathrm{cm} \) long?


A uniform magnetic field \( \vec{B}=(3 \hat{i}+ \)
\( 4 \hat{j}+\hat{k}) \) exists in region of space.
semicircular wire of radius 1 m
carrying current \( 1 A \) having its centre \( \operatorname{at}(2,2,0) \) is placed in \( x-y \) plane as
shown in figure. The force on semicircular wire will be
\( \mathbf{A} \cdot \sqrt{2}(\hat{i}+\hat{j}+\hat{k}) \)
B. \( \sqrt{2}(\hat{i}-\hat{j}+\hat{k}) \)
\( \mathbf{c} \cdot \sqrt{2}(\hat{i}+\hat{j}-\hat{k}) \)
D. \( \sqrt{2}(-\hat{i}+\hat{j}+\hat{k}) \)


The dip at the poles is
\( \mathbf{A} \cdot 80 \)
B. 60
c. 90
D. 0


A nucleus \( z X^{A} \) emits \( 9 \alpha \) -particles and 5 \( p \) particle. The ration of total protons
and neutrons in the final nucleus is:
A \( \frac{(Z-13)}{(A-Z-23)} \)
B. \( \frac{(Z-18)}{(A-36)} \)
c. \( \frac{(Z-23)}{(A-Z-8)} \)
D. \( \frac{(Z-13)}{(A-Z-13)} \)


Which of the following electronic configuration is associated with the highest stable oxidation state?
\( \mathbf{A} \cdot[A r] 3 d^{1} 4 s^{2} \)
B \cdot \( [A r] 3 d^{5} 4 s^{1} \)
\( \mathbf{c} \cdot[A r] 3 d^{5} 4 s^{2} \)
D \cdot \( [A r] 3 d^{6} 4 s^{2} \)


Find the name of the triangle.
A. isosceles
B. equilateral
\( c . \) scalene
D. acute


A body is moving with a constant speed
\( v \) in a circle of radius \( r . \) Its angular acceleration is:
A . \( v r \)
B. \( \frac{v}{r} \)
c. zero
D. \( v r^{2} \)


The binding energies per nucleon for
deuteron \( \left(_{1} H^{2}\right) \) and helium \( \left(_{2} H e^{4}\right) \) are
\( 1.1 \mathrm{MeV} \) and \( 7.0 \mathrm{MeV} \), respectively. Calculate the energy released when two deuterons fuse to form a helium
nucleus \( \left(_{2} \boldsymbol{H} e^{4}\right) \)


Choose the wrong statement about
equipotential surfaces.
A. It is a surface over which the potential is constant
B. The electric field is parallel to the equipotential surface
C. The electric field is perpendicular to the equipotential surface
D. The electric field is in the direction of steepest decrease of potential
E. They are concentric spheres for a point charge


In the given figure, \( \triangle A B C \) is right
angled at \( B \). If \( B D \perp A C \), which of the
following is/are true?
A. \( \triangle A B C \sim \triangle A D B \)
B. \( \triangle A B C \sim \triangle B D C \)
c. \( \triangle A D B \sim \triangle B D C \)
D. \( \triangle A B C \sim \triangle D B C \)


The Inverse expression of \( x+\frac{1}{x} \) will be:
A \( \frac{x^{2}+1}{x} \)
B. \( \frac{1}{x}-x \)
c. \( \frac{x}{x^{2}+1} \)
D. \( \frac{x}{x^{2}-1} \)


Resolve \( \frac{x^{4}}{(x-1)^{4}(x+1)} \) into partia
fractions.
A \( \cdot \frac{1}{2(x-1)^{4}}-\frac{7}{4(x-1)^{3}}+\frac{17}{8(x-1)^{2}}+\frac{15}{16(x-1)}+\frac{1}{16} \)
\( \frac{1}{(x+1)} \)
B. \( \frac{1}{2(x-1)^{4}}+\frac{7}{4(x-1)^{3}}+\frac{17}{8(x-1)^{2}}+\frac{15}{16(x-1)}+\frac{1}{16} \)
\( \frac{1}{(x+1)} \)
C \( \frac{1}{2(x-1)^{4}}+\frac{5}{4(x-1)^{3}}+\frac{17}{8(x-1)^{2}}+\frac{15}{16(x-1)}+\frac{1}{16} \)
\( \frac{1}{(x+1)} \)
D \( \frac{1}{2(x-1)^{4}}+\frac{7}{4(x-1)^{3}}+\frac{13}{8(x-1)^{2}}+\frac{15}{16(x-1)}+\frac{1}{16} \)
\( \frac{1}{(x+1)} \)


Bleaching powder loses its power on keeping for long time because:
A. it changes to calcium hypochlorite.
B. it changes to calcium chloride and calcium hydroxide.
c. it absorbs moisture.
D. it changes to calcium carbonate and chlorine


Which of the following process is not involved in manufacturing of steel?
A. Bessemer process
B. Open hearth process
c. вор
D. Thermite process


Consider a hypothetical atom where
\( \boldsymbol{p}_{\boldsymbol{x}}, \boldsymbol{p}_{\boldsymbol{y}}, \boldsymbol{p}_{\boldsymbol{z}}, \boldsymbol{d}_{\boldsymbol{x} \boldsymbol{y}}, \boldsymbol{d}_{\boldsymbol{x} z}, \boldsymbol{d}_{\boldsymbol{y} \boldsymbol{z}} \boldsymbol{a} \boldsymbol{n} \boldsymbol{d} \boldsymbol{d} \boldsymbol{x}^{2}-\boldsymbol{y}^{2} \)
orbital are present for principal quantum number \( n=3 \) Find the number of other orbitals whose
lobes are fully present in the nodal
plane of \( \boldsymbol{p}_{\boldsymbol{x}} \) orbital:
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 5


An alcohol on oxidation gives
\( C H_{3} C O O H \) and \( C H_{3} C H_{2} C O O H . \) The
alcohol is :
A \( \cdot C H_{3} C H_{2} O H \)
в. \( C H_{3} C H(O H) C H_{2} C H_{3} \)
c. \( \left(C H_{3}\right)_{2} C(O H) C H_{2} C H_{3} \)
D. \( C H_{3} C H(O H) C H_{2} C H_{2} C H_{3} \)


Charges \( 1 \mu C \) are placed at each of the four corners of a square of side \( 2 \sqrt{2} m \)
The potential at the point of intersection of the diagonals is \( _{-}-_{-}-_{-}(K=9 \times \)
\( \left.\mathbf{1 0}^{\mathbf{9}} \boldsymbol{S} \boldsymbol{I} \text { unit }\right) \)
\( \mathbf{A} \cdot 18 \times 10^{3} V \)
в. \( 1800 \mathrm{V} \)
\( \mathbf{c} \cdot 18 \sqrt{2} \times 10^{3} V \)
D. None of these


Rubber is very soft. Therefore, it is
vulcanized and used in tires.
Vulcanised rubber resists:
A. drops of acid rain
B. cold temperatures
c. jerking movement
D. wear and tear due to friction


If from the point \( \boldsymbol{P}(\boldsymbol{f}, \boldsymbol{g}, \boldsymbol{h}) \)
perpendiculars \( P L, P M \) be drawn to \( y z \)
and \( z x \) planes, then the equation to the
plane \( \boldsymbol{O} \boldsymbol{L} \boldsymbol{M} \) is
A \( \cdot \frac{x}{f}+\frac{y}{g}-\frac{z}{h}=0 \)
В \( \cdot \frac{x}{f}+\frac{y}{g}+\frac{z}{h}=0 \)
c. \( \frac{x}{f}-\frac{y}{g}+\frac{z}{h}=0 \)
D. \( -\frac{x}{f}+\frac{y}{g}+\frac{z}{h}=0 \)


In a hierarchial scheme of taxonomic
classification, the grouping just below order is
A. Family
B. Genes
c. Phylum
D. class


The name 'second messenger' is given to which of the following?
A. ATP
B. Cyclic AMP
c. GTP
D. Both ATP and AMP


Phototropic and geotropic movements are linked to
A . Gibberelins
B. Cytokinins
c. Auxin
D. None of the above


Living herbaria is
A. Museum
B. Botanical garden
c. Forest
D. Parks


Ideal function of vermiform appendixin human body is
A. Digestion of cellulose
B. Decrease the digestion
c. Produce more energy
D. Increase the weight


Identify the type of reaction taking place in \( \boldsymbol{F e}+\boldsymbol{C u S O}_{4} \rightarrow \boldsymbol{C u}+\boldsymbol{F e} \boldsymbol{S O}_{4} \)
A. Redox reaction
B. Displacement reaction
c. Neutralization reaction
D. Precipitation reaction


Two particles of equal mass go around a circle of radius \( R \) under the action of
their mutual gravitational attraction. The speech of each particle is
\( ^{\mathbf{A}} \cdot_{v}=\frac{1}{2 R} \sqrt{\left(\frac{1}{G M}\right)} \)
в. \( v=\sqrt{\left(\frac{G M}{2 R}\right)} \)
\( ^{\mathrm{c}} \cdot_{v}=\frac{1}{2} \sqrt{\left(\frac{G M}{R}\right)} \)
D. \( v=\sqrt{\left(\frac{4 G M}{R}\right)} \)


In a hostel \( 60 \% \) of the students read
Hindi news paper, \( 40 \% \) read English news paper and \( 20 \% \) read both Hind
and English news papers. A students is selected at random.
Find the probability that the reads neither Hindi nor English news papers


A number is chosen at random among
the first 120 natural numbers, The probability of the number chosen being
a multiple of 5 or 15 is
A . \( 1 / 5 \)
в. 1 18
c. \( 1 / 6 \)
D. none of these


Two stars \( S_{1} \) and \( S_{2} \) are located at
distances \( d_{1} \) and \( d_{2} \) respectively. Also if
\( d_{1}>d_{2} \) then which of the following
statements is true?
A. The parallax of \( S_{1} \) and \( S_{2} \) are same
B. The parallax of \( S_{1} \) is twice as that of \( S_{2} \)
C. The parallax of \( S_{1} \) is greater than parallax of \( S_{2} \)
D. The parallax of \( S_{2} \) is greater than parallax of \( S_{1} \)


The function \( f: R / 0 \rightarrow R \) given by \( f(x)= \) \( \frac{1}{x}-\frac{2}{e^{2 x}-1} \) can be made continuous at
\( x=0 \) by
defining \( f(0) \) as
A .
B.
\( c \cdot 2 \)
D. -


If \( \int \frac{f(x)}{1-x^{3}} d x= \)
\( \log \left|\frac{x^{2}+x+1}{x-1}\right| \frac{A}{948 \sqrt{3}} \tan ^{-1} \frac{2 x+1}{\sqrt{3}}+ \)
\( C \) then \( A=_{-}- \)
where \( f(x) \) is a polynomial of second
degree in \( x \) such that \( f(0)=f(1)= \)
\( \mathbf{3} f(\mathbf{2})=\mathbf{3} \)


Factorise:
\( y^{2}-5 y-24 \)


Characteristic of epithelial tissues is
A. They never produce glands
B. Cells can undergo rapid divisions
C. They have abundant vascularisation
D. They have large intercellular spaces


The monomers of biodegradable polymer, nylon 2-nylon 6 are:
A. glycine + adipic acid
B. glycol + phthalic acid
c. phenol + urea
D. glycine + amino caproic acid


Consider the following statements are arrange in the order of true/false as given in the codes. Select the correct
arrangement.
\( S_{1}: \) Ammonia on heating with concentrated solution of sodium
hypochlorite gives nitrogen gas.
\( S_{2}: \) The phosphine gas dissolves in
water in presence of sunlight and produces phosphonium hydroxide like ammonium hydroxides.
\( S_{3}: \) Barium azide on heating gives pure
nitrogen gas.
\( S_{4}: \) The oxo-acids of phosphorus in which phosphorus has lower oxidation state less than +5 contain either \( \boldsymbol{P}-\boldsymbol{P} \)
or \( P-H \) bonds but not both in addition
to \( P=O \) and \( P-O H \) bonds.
A. TF TT
B. F FTT
c. тт T \( F \)
D. TFTF


Simplify:
\( a^{6}-b^{6} \)


The mean deviation about the mean of
the set of first \( n \) natural numbers when
\( n \) is an odd number.
A \( \cdot \frac{n^{2}-1}{4 n} \)
B. \( \frac{n}{4} \)
c. \( \frac{n^{2}+1}{4 n} \)
D. \( \frac{n^{2}-1}{12} \)


What is the center of mass of an object?
A. The mean position of the mass in an object.
B. The geometric center of an object.
C. The furthest away position of the mass in an object.
D. The same as the center of gravity.
E. The closest position of the mass in an object.


Three charges all of \( +q \) are brought
together so that they form an equilateral triangle, with a distance \( r \)
between them.

Determine the electrostatic potential
energy needed to bring the system together from infinity:
\( A \)
B. \( \frac{3 q^{2}}{4 \pi \epsilon_{0} r} \)
c. \( \frac{5 q^{2}}{4 \pi \epsilon_{0} r} \)
D. \( \frac{7 q^{2}}{4 \pi \epsilon_{0} r} \)


slit separation dis \( 0.3 \mathrm{mm} \) and the
screen distance D is 1 m. A paralle
beam of light of wavelength 600 nm is
incident on the slits at angle \( \alpha \) as
shown in figure. On the screen, the point O is equidistant from the slits and
distance PO is \( 11.0 \mathrm{mm} \). Which of the
following statement (s) is/are correct?
A. For \( \alpha=0 \), there will be constructive interference at
point P.
B. For \( \alpha=\frac{0.36}{\pi} \) degree, there will be destructive
interference at point P.
C \( \cdot_{\text {Fro } \alpha}=\frac{0.36}{\pi} \) degree, there will be destructive
interference at point 0
D. Fringe spacing depends


Find real values of \( \theta \) for which
\( \left(\frac{4+3 i \sin \theta}{1-2 i \sin \theta}\right) \) is purely real


is produced by passing
air over red-hot coke.
A. Natural gas
B. Producer gas
c. Biomass
D. Biogas


Branch of 'botany' connected with heredity and variations is
A. Genetics
B. Eugenics
c. Palaeobiology
D. Euthenics


The lamprey (Petromyzon) is included in the same taxonomic class as the
A. Chamaeleon (Anolis)
B. Hag fish (Myxine)
c. Salamander (Ambystoma)
D. Lung fish (Neoceratodus)


A coil made of insulated copper wire is
connected to a galvanometer. What will
happen if a bar magnet is kept close to the wire ?
outside opposite


Draw a ray diagram for concave mirror when object is placed between focus
and centre curvature. Also write
position, nature and size of image.


Impulse originating from sino-atrial node are transmitted to the
A. Atrio-ventricular node
B. Bundle of Hiss
c. Pacemaker
D. Purkinje system


Glucose solution is an electrolyte and hence conducts electricity.
A. True
B. False


Two different compounds have the
formula \( X e F_{2} C l_{2} . \) Write Lewis
structure for these two compounds, and describe how measurement of dipole might be used to distinguish between them.


A \( 120 \mathrm{m} \) long train is moving towards west at a speed of \( 10 m s^{-1} \). A small bird
flying towards east at a speed of \( 5 m s^{-1} \)
crosses the train. What is time taken by
the bird to cross the train?
A \( .4 \mathrm{s} \)
B. 8 s
\( c \cdot 12 s \)
D. 24 s


If \( f(x)=\frac{x}{\sqrt{1-x^{2}}}, \) then \( (f o f)(x)= \)
A \( \cdot \frac{x}{\sqrt{1-x^{2}}} \)
в. \( \frac{x}{\sqrt{1-2 x^{2}}} \)
c. \( \frac{x}{\sqrt{1-3 x^{2}}} \)
D.


A student sitting at the back of the classroom cannot read clearly the letters written on the blackboard. What
advice will a doctor give to her? Draw ray diagram for the correction of this defect.


A cylinder of length \( l \) and radius \( R \) is placed in a uniform electric field \( \boldsymbol{E} \)
parallel to the cylindrical axis. The total flux through the surface of the cylinder is given by
\( \mathbf{A} \cdot 2 \pi R^{2} E \)
в. \( \frac{\pi R^{2}}{E} \)
c. \( \pi\left(R^{2}-R l\right) E \)
\( D \)


A particle is executing SHM with an amplitude \( 4 \mathrm{cm} . \) What time does it take to reach the distance equal to
amplitude, if the particle starts from rest at \( t=0 \) from the mean position
\( A \cdot T \)
в. \( T / 2 \)
\( c \cdot T / 4 \)
D. 3T/4


In the figure(not drawn to scale), ABCD
is a rhombus, ABE is a straight line.
Find \( \angle \mathrm{DBE} \)
A . 150
B. \( 152^{\circ} \)
\( \mathbf{c} \cdot 153^{\circ} \)
D. \( 156^{\circ} \)


Write an A.P. having 4 as the first term and -3 common difference.


The potential energy function associated with the force \( \overrightarrow{\boldsymbol{F}}=\mathbf{4 x y} \hat{\mathbf{i}}+ \)
\( 2 x^{2} \hat{j} \) is
A \( \cdot U=-x^{2} y \)
B . \( U=-2 x^{2} y+ \) constant
C. \( U=2 x^{2} y+ \) constant
D. Not defined


(a) Explain the addition polymer by an example.
(b) Write the equation of preparation of synthetic rubber.
(c) Give the names of monomers used
for obtaining dacron


Rainwater can be used to recharge the groundwater. This is referred to as:
A . Infiltration
B. water harvesting
c. rainwater harvesting
D. both \( B \) and \( C \)


\( |\overline{\mathbf{a}} \cdot \overline{\mathbf{b}}|^{2}-|\overline{\mathbf{a}} \times \overline{\mathbf{b}}|^{2}= \)
\( \mathbf{A} \cdot a b \cos \theta \)
B \( \cdot a^{2} b^{2} \cos \theta \)
C \( \cdot a^{2} b^{2} \cos 2 \theta \)
\( \mathbf{D} \cdot a b \cos 2 \theta \)


An alternating voltage \( \boldsymbol{E}= \) \( 200 \sqrt{2} \sin (100 t) \) is connected to 1
microfarad capacitor through \( A C \) ammeter. The reading of ammeter shall be
\( A \cdot 10 m A \)
B. \( 20 \mathrm{mA} \)
c. \( 40 \mathrm{mA} \)
D. \( 80 \mathrm{mA} \)


The kinetic energy (in keV) of the alpha particle, when the nucleus \( _{84}^{210} \) Po at rest undergoes alpha decay, is
\( A .5319 \)
в. 5422
c. 5707
D. 5818


Which of the following substances can be assimilated unchanged?
A. Vitamin
B. Proteins
c. starch
D. Lipids


Which among the following is the
correct sequence of prophase I of meiosis?
A. Leptotene, pachytene, zygotene, diplotene, diakinesis
B. Leptotene, diplotene, pachytene, zygotene, diakinesis
c. Leptotene, zygotene, pachytene, diplotene, diakinessis
D. Leptotene, zygotene, diakinesis, diplotene


Silver is displaced when zinc is added to aqueous sodium argentocyanide. This method of extracting silver is an example of :
A. leaching
B. hydrometallurgy
c. pyrometallurgy
D. liquation


Agar-agar is obtained from
A. Red algae
B. Brown algae
c. Green algae
D. Blue-green algae


The action of bleaching powder on ethyl alcohol gives:
A \( \cdot \mathrm{CCl}_{4} \)
B. CHCls
c. cocl
D. Ether


In a Helium gas discharge tube every second \( 40 \times 10^{18} H e^{+} \) (ions) move
towards the right through a cross section of the tube, while n electrons
move to the left in the same time. If the
current in the tube is \( 8 A \) towards right
then \( n=? \)
A \( \cdot 10 \times 10^{18} \)
B. 3 \( \times 10^{19} \)
\( c \cdot 3 \times 10^{20} \)
D. 3 \( \times 10^{2} \)


Find the arithmetic mean of numbers
from 1 to 9
A . 9
B. 5
c. 8
\( D \)


Write the colour code for \( 4.7 ~ K \Omega \pm \)
\( 10 \% \)


Define conductors and insulators. Give
one example of each.


The final image formed by a compound microscope is :
A. Real and erect
B. Virtual and erect
c. Real and inverted
D. Virtual and inverted


Eliminate the arbitrary constant \( \boldsymbol{A}, \boldsymbol{B} \) from \( V=\frac{A}{r}+B \) to form a differential
equation.


The Indian name of the Little Bear
constellation is:
A. Dhruv Tara
B. Bichchhu
c. Laghu saptarishi
D. Krittika


Natural gas occurs:
A. above the petroleum oil
B. below the petroleum oil
C . along with the petroleum oil
D. none of these


State whether true or false:
The degree of convergence of divergence of light rays achieved by a lens is expressed in terms of its power
A. True
B. False


Human fetal haemoglobin differs from the adult haemoglobin in that it has
A. Higher affinity for oxygen
B. Lower affinity for oxygen
c. Two subunits only
D. Is glycosylated.


\( \Delta_{f} H^{\ominus} \) per mole of \( N H_{3}(g), N O(g) \) and \( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) \) are \( -\mathbf{1 1 . 0 4},+\mathbf{2 1 . 6 0} \) and
\( -68.32 K c a l, \) respectively. Calculate
the standard heat of reaction at
constant pressure and at a constant volume for the reaction:
\( \mathbf{4} \boldsymbol{N} \boldsymbol{H}_{3}(\boldsymbol{g})+\mathbf{5} \boldsymbol{O}_{2}(\boldsymbol{g}) \longrightarrow \boldsymbol{4} \boldsymbol{N} \boldsymbol{O}(\boldsymbol{g})+ \)
\( \mathbf{6} \boldsymbol{H}_{\mathbf{2}} \boldsymbol{O}(\boldsymbol{l}) \)
A. \( \Delta H=-279.36 K c a l \Delta U=-276.38 K c a l \)
В. \( \Delta H=+279.36 K c a l \Delta U=-276.38 K \) сад.
c. \( \Delta H=-279.36 K c a l \Delta U=+276.38 K c a l \)
D. None of these


Write the vector equation of the line equation \( \frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4} \)


Weber \( / m^{2} \) is equal to
A. dyne
B. tesla
c. watt
D. henry


The spreading of living pteridophytes is
limited and is restricted to narrow
geographical areas
A. Gametophytic growth needs cool, damp and shady places
B. Requirement of water for fertilization
c. Absence of stomata in leaf and absence of vascular tissue
D. a and


If the above radial probability curve
indicates '2s' orbital, the distance
between the peak points \( \boldsymbol{X}, \boldsymbol{Y} \) is:
A \( .2 .07 \hat{k} \)
в. 1.59 .
\( .0 .53 \AA \)
\( .2 .12 \hat{k} \)


From the list of alkenes given below, identify the alkenes which on ozonolysis give only ketones.
(a) 2 methyl-1-butene
(b) 1-butene
(c) 2,3 -dimethyl-2-butene
(d) 3 -methyl-2-pentene
(e) 3,4 -dimethyl-3-hexene
(f) 2,5-dimethyl-2,4-hexadiene
\( A \cdot a, b \) and \( c \)
B. \( c \) and \( e \) only
c. \( d, e \) and \( f \)
D. \( c, d \) and \( e \)


If \( f \) is differentiable at \( x=1 \) and
\( \lim _{h \rightarrow 0} \frac{1}{h} f(1+h)=5, f^{\prime}(1)= \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 3 \)
D. 4
\( E \)


Describe the mechanism of mineral
absorption by ion-exchange method.


The family of curves represented by \( \frac{d y_{1}}{d x}=\frac{x^{2}+x+1}{y^{2}+y+1} \) and the family
represented by \( \frac{\boldsymbol{d} \boldsymbol{y}_{2}}{\boldsymbol{d} \boldsymbol{x}}+\frac{\boldsymbol{y}^{2}+\boldsymbol{y}+\mathbf{1}}{\boldsymbol{x}^{2}+\boldsymbol{x}+\mathbf{1}}=\mathbf{0} \)
A. touch each other
B. orthogonal to each other
c. identical
D. intersect at an angle of \( \frac{\pi}{4} \)


Let \( a_{1}, a_{2}, a_{3}, \dots \) be terms of an A.P. If \( \frac{\boldsymbol{a}_{1}+\boldsymbol{a}_{2}+\ldots . .+\boldsymbol{a}_{p}}{\boldsymbol{a}_{1}+\boldsymbol{a}_{2}+\ldots . .+\boldsymbol{a}_{\boldsymbol{q}}}=\frac{\boldsymbol{p}^{2}}{\boldsymbol{q}^{2}}, \boldsymbol{p} \neq \boldsymbol{q}, \) then
\( \frac{u_{6}}{2} \) equals


Perform the division: \( 2 x^{2}+2 x+11 \) by
\( \boldsymbol{x}+\mathbf{3} \)


A charge of \( +4 \mu C \) is kept at a distance
of \( 50 \mathrm{cm} \) from a charge of \( -6 \mu C \). Find the two points where the potential is
zero
A. Internal point lies at a distance of \( 20 \mathrm{cm} \) from \( 4 \mu \mathrm{C} \) charge and external point lies at a distance of \( 100 \mathrm{cm} \) from \( 4 \mu C \) charge
B. Internal point lies at a distance of \( 30 \mathrm{cm} \) from \( 4 \mu C C \) charge and external point lies at a distance of \( 100 \mathrm{cm} \) from \( 4 \mu C \) charge
c. Potential is zero only at \( 20 \mathrm{cm} \) from \( 4 \mu \mathrm{C} \) charge between the two charges
D. Potential is zero only at \( 20 \mathrm{cm} \) from \( -6 \mu \mathrm{C} \) charge between the two charges


The dispersed phase and dispersion medium in soap lather are respectively:
A. gas and liquid
B. liquid and gas
c. solid and gas
D. solid and liauid


Which of the following is the correct representation of electron dot structure of nitrogen?
A \( \ldots \ddot{N}: \ddot{N} \)
B . : \( \dot{N}:: \dot{N} \)
\( \mathrm{c} \cdot \ddot{N}: \dot{N} \)
D・: \( N: \)


In Argand diagram, O, P, Q represents the origin, \( z \) and \( z+i z \)
respectively. then \( \angle O P Q= \)
A.
в.
\( c \cdot \frac{\pi}{2} \)
D.


A plano-convex lens fits exactly into plano-concave lens as shown in figure. Their plane surfaces are parallel to each
other. If the lens are made of different
materials of refractive indices 1.6 and
1.5 respectively. If \( R \) is the radius of
curvature of curved surfaces of lenses.
Then the focal length of the combination
A \( \frac{R}{0.2} \)
в. \( \frac{R}{6.2} \)
c. \( \frac{R}{3.1} \)
D. \( \frac{R}{0.1} \)


Which of these four numbers \( \sqrt{\boldsymbol{\pi}^{2}}, \sqrt[3]{\boldsymbol{0 . 8}}, \sqrt[4]{.00016}, \sqrt[3]{-1} \cdot \sqrt{(.09)^{-1}} \) is
(are) rational:
A. none
B. all
c. the first and fourth
D. only the fourth
E. only the first


What is the center of gravity of an
object?
A. The point where gravity appears to act.
B. The point where gravity doesn't act.
C. The point where the force of gravity is strongest.
D. The point where the force of gravity is weakest.


An isotone of \( _{32}^{76} \) Ge is:
This question has multiple correct options
\( \mathbf{A} \cdot_{32}^{77} G e \)
\( \mathbf{B} \cdot_{33}^{77} A s \)
\( \mathbf{c} \cdot_{34}^{77} S e \)
\( \mathbf{D} \cdot_{34}^{78} S e \)


Assertion
(A) :When the radius of a
copper wire is doubled, its specific resistance increases
Reason
(R) :Specific resistance is independent of cross-section of
material used
A. Both A \& R are true and R is the correct explanation of \( A \)
B. Both A \& R are true and R is not a correct explanation of
c. A is true but R is false
D. A is false but R is true


List the hormones secreted by ovary.


The mass of chlorine \( \left(_{17} C l^{35}\right) \) atom is
34.98 amu, mass of proton \( =1.007825 \) amu, mass of neutron= 1.008665 amu
Then binding energy is :
\( \mathbf{A} \cdot 287.83 \mathrm{Mev} \)
B. 287.83 joules
c. 8.22 Mev
D. 8.22 joule


In the circuit shown in the figure, the
heat produced in the \( 5 \Omega \) resistor due to
a current flowing in it, is 10 calories per
second. The heat produced in the \( 4 \Omega \)
resistor is?
A \( \cdot 1 \) cal \( s^{-} \)
B . 2 cal \( s^{-1} \)
\( c \cdot 3 \) cal \( s^{-1} \)
D. 4 cal \( s^{-} \)


Read the assertion and reason carefully to mark the correct option out of the options given below:

Assertion : Radius of circular orbit of a
satellite is made two times, then it
areal velocity will also become two
times.

Reason: Areal velocity is given as \( \frac{\boldsymbol{d} \boldsymbol{A}}{\boldsymbol{d} \boldsymbol{t}}=\frac{\boldsymbol{L}}{\boldsymbol{2 m}}=\frac{\boldsymbol{m} \boldsymbol{v} \boldsymbol{r}}{\boldsymbol{2} \boldsymbol{m}} \)
A. If both assertion and reason are true and the reason is the correct explanation of the assertion
B. If both assertion and reason are true but reason is not the correct explanation of the assertion
c. If assertion is true but reason is false
D. If assertion is false but reason is true


Name the factors affecting the turning effect of a body


Which of the following pairs constitutes a buffer?
A. \( H N O_{2} \) and \( N a N O_{2} \)
в. \( N a O H \) and \( N a C l \)
c. \( H N O_{3} \) and \( N H_{4} N O_{3} \)
D. \( H C l \) and \( K C l \)


Differentiate between.
Inspiration and expiration.


Which of the following chemicals starts the combustion process in the matchstick?
A. antimony sulphide
B. potassium chlorate
c. phosphorous
D. starch and wool


Froth floatation process for the concentration of sulphide ores is an illustration of the practical application of:
A. adsorption
B. absorption
c. sedimentation
D. coagulation


The pressure on a square plate is measured by measuring the force on the plate. If the maximum error in the measurement of force and length are respectively \( 4 \% \) and \( 2 \% \), then the maximum error in the measurement of
pressure is :
A . \( 1 \% \)
B. 2\%
c. \( 4 \% \)
D. \( 8 \% \)


Let \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{3} \) and \( \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{3}^{x} \). The values
of \( \boldsymbol{A} \) such that \( \boldsymbol{g}[\boldsymbol{f}(\boldsymbol{A})]=\boldsymbol{f}[\boldsymbol{g}(\boldsymbol{A})] \) are
A . 0.2
в. 1,3
c. 0,±3
D. 1,±2
E. \( 0, \pm \sqrt{3} \)


The leaching of chemical fertilizers into
rivers and ponds causes:
A. the rapid growth of algae
B. air pollution
c. an increase in the oxygen concentration of the water
D. an increase in number of aquatic organisms


Solve:-sin \( x \frac{d y}{d x}+3 y=\cos x \)


Factorise:
\( 2 x^{2}-9 x+9 \)


Function \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R}, \boldsymbol{f}(\boldsymbol{x})=[\boldsymbol{x}] \) is
A. one-one
B. onto
c. one-one onto
D. Many one into


Select the correct I.U.P.A.C name for
\( \left[\boldsymbol{C u}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\right]\left[\boldsymbol{P t} \boldsymbol{C l}_{4}\right]: \)
(II) tetrachloridoplatinum (II)
A. Tetraamminecopper
B. Tetraamminecopper
(II) tetrachloridoplatinum (IV)
c. Tetraamminecopper(II) tetrachloridoplatinate (II)
D. Tetraamminecuprate(II) tetrachloridoplatinate (II)


Find the amount on a deposit of Rs.
\( 2100, \) earning \( 4 \% \) interest compounded quarterly for 2 years(approx.).
A .2272
в. 2372
c. 2472
D. 2572


A semi conductor device with both
active and passive electronic elements
diffused into a silicon water to form a
functional circuit is called.
A. Thin-film circuit
B. Integrated circuit
c. Hybrid-circuit
D. Thick-film circuit


Differentiate the following expression
\( \boldsymbol{w} \cdot \boldsymbol{r} \cdot \boldsymbol{t} \cdot \boldsymbol{x} \)
\( \boldsymbol{y}=\csc ^{2}\left(\boldsymbol{x}^{2}\right) \)


The substance which undergoes combustion is called
A . fue
B. non-inflammable
c. combustible
D. Both \( A \& C \)


Oxygen is transported in blood mainly by
A. Leucocytes
B. Erythrocytes
c. Thrombocytes
D. Blood plasma


Perhydrol is:
\( \mathbf{A} \cdot 10 \% H_{2} O_{2} \)
B. \( 30 \% \mathrm{H}_{2} \mathrm{O}_{2} \)
\( \mathbf{c} \cdot 3 \% H_{2} O_{2} \)
D. \( 100 \% \mathrm{H}_{2} \mathrm{O}_{2} \)


Identify which of the following quantity describe object's resistance to change
in motion.
A. acceleration
B. velocity
c. mechanics
D. force
E. inertia


Solve the following system of equations:
\( \boldsymbol{x}+\boldsymbol{y}=\boldsymbol{a}-\boldsymbol{b} \)
\( \boldsymbol{a} \boldsymbol{x}-\boldsymbol{b} \boldsymbol{y}=\boldsymbol{a}^{2}+\boldsymbol{b}^{2} \)


The vertical limbs of a \( U \) shaped tube
are filled with a liquid of density \( \boldsymbol{p} \) upto
a height \( h \) on each side. The horizontal
portion of the \( U \) tube having length \( 2 h \) contains a liquid of density \( 2 p . \) The \( U \) is moved horizontally with an accelerator
\( \boldsymbol{g} / 2 \) parallel to the horizontal arm. The
difference in heights in liquid levels in th two vertical limbs, at steady state
will be
A \( \cdot \frac{2 h}{7} \)
B. \( \frac{8 h}{7} \)
\( c \cdot \frac{4 h}{7} \)
D. None of these


When oleum \( \left(H_{2} S_{2} O_{7}\right) \) is completely hydrolyzed, then how many acidic
hydrogens are present in the final product?
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
\( D \)


t-butyl methyl ether on reaction with
anhydrous \( H I \) gives an alcohol \( (A) \) and
halide (B). Which of the following
statement is correct?

This question has multiple correct options
A. Alcohol (A) performs Lucas test immediately at room temperature
B. Halide
(B) undergoes \( S_{N} 1 \) reaction most readily
C. Alcohol (A) on heating with copper gives formaldehyde
D. Halide
(B) on reaction with \( K C N \) undergoes \( S_{N} 2 \) reaction


If \( A \) and \( B \) are two events such that
\( \boldsymbol{P}(\boldsymbol{A})=\frac{1}{4}, \boldsymbol{P}(\boldsymbol{B})=\frac{1}{2} \) and \( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})= \)
\( \frac{1}{8} \) find \( P A \cup B \)


A bacterium has a generation time of
50 minutes. A culture containing \( 10^{8} \) cells \( m L \) is incubated for 300 minutes.
What will be the number of cells after
300 minutes?
A \( \cdot 64 \times 10^{3} \) cells
B . \( 64 \times 10^{8} \) cells
c. \( 64 \times 10^{9} \) cells
D. \( 64.4 \times 10^{9} \) cells


The level formed due to impurity atom,in the forbidden energy gap,very near to the valence band in a p-type
semiconductor is called
A. acceptor level
B. donor level
c. conduction level
D. forbidden level


In the following reaction, which compound/s corresponds to \( (\boldsymbol{X}) \) ?
\( \boldsymbol{C a} \boldsymbol{C}_{2}+\mathbf{2} \boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \boldsymbol{C}_{2} \boldsymbol{H}_{2}+(\boldsymbol{X}) \)
A \( . \) CaOH
В \( \cdot C a(O H)_{2} \)
\( \mathbf{c} \cdot C a O+H_{2} \)
D. none of the above


The electrons in the atom of an element
which determine its chemical and
electrical properties are.
A. Valence electrons
B. Revolving electrons
c. Excess electrons
D. Active electrons


All of the following are the functions of the mammalian kidney, except
A. Elimination of urea and other nitrogenous wastes
B. Maintenance of water balance
c. Manufacture of antibodies
D. Regulation of salt excretion
E. Formation of urine from glomerular filtrate


The solution of \( (x+y+1) \frac{d y}{d x}=1 \) is:
A \( . x=-(y+2)+c e^{y} \)
B . \( y=-(x+2)+c e^{x} \)
c. \( x=-(y+2)+c e^{x} \)
D. \( x=(y+2)+c e^{-y} \)


Major product of this reaction will be:
A . o-xylene
B. p-xylene
c. cumen
D. m-xylene


In nuclear fusion, \( 1 g m \) hydrogen is
converted into \( 0.993 g m \) Helium in one hour. If the efficiency of the generator is
\( 5 \%, \) the energy obtained in \( K W h \) is:
\( \mathbf{A} \cdot 8.75 \times 10^{3} \)
B . \( 4.75 \times 10^{3} \)
c. \( 5.75 \times 10^{3} \)
D. \( 3.73 \times 10^{3} \)


Assertion
According to Newton's law, good conductors of electricity are also good conductors of heat.
Reason
At a given temperature, \( e_{\lambda} \propto a_{\lambda} \) for any
body
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


What are extrinsic semicunductors?
Name the two types of extrinsic semiconductors.


What value should come in place of
question mark (?) in the questions given below? \( 29+729=? \)
A. 758
B. 763
\( c \cdot 741 \)
D. 75


How many mL of a solution of
concentration \( 100 \mathrm{mg} \) Co\( ^{2+} \) per mL is
needed to prepare \( 10 \mathrm{mL} \) of a solution of
concentration \( 20 \mathrm{mg} \mathrm{Co}^{2+} \) per \( \mathrm{mL} \) ?


If a boat can travel with a speed of \( v \) in
still water, which of the following trips will take the least amount of time?
A. travelling a distance of \( 2 d \) in still water.
B. travelling a distance of \( 2 d \) across (perpendicular to) the current w.r.t. in a stream
C. travelling a distance \( d \) downstream and returning a distance \( d \) upstream
D. travelling a distance \( d \) upstream and returning a distance \( d \) downstream


For the angle in standard position if the
Initial arm rotates \( 130^{\circ} \) in
anticlockwise direction, then state the
quadrant in which terminal arm lies. (Draw the figure and write the answer).


How many moles of \( N_{2} \) are needed to
produce 18 moles \( N H_{3} \) in the reaction?
\( N_{2}+3 H_{2} \rightarrow 2 N H_{3} ? \)
\( A \cdot 9 \)
B. 18
\( c \cdot 3 \)
\( D \cdot 2 \)
\( E \)


A reaction will never be spontaneous at
any temperature and pressure provided.
\( \mathbf{A} \cdot \Delta \) S positive and \( \Delta \) H positive
B. \( \Delta \) S positive and \( \Delta \) H negative
C. \( \Delta \) S negative and \( \Delta \) H positive
D. \( \Delta \) S negative and \( \Delta \) H negative


The least electro positive alkali metal
is:
A. Sodium
B. Lithium
c. Potassium
D. Caesium


The product formed when ethene gas
reacts with water in the presence of sulphuric acid is :
A. ethanol
B. ethanal
c. ethanoic acid
D. ethanoate


Number of \( C l^{-} \) ions satisifying both
primary and secondary valency are in \( C o C l_{3} .5 N H_{3} \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 3 \)
D. 4


If \( f(x)=\frac{x+1}{x-1} \) the show that \( f(x)+ \) \( f\left(\frac{1}{x}\right)=0 \)


What would happen to hydrogen and
magnetic oxide of iron if they are kept
in closed vessels at \( 400^{\circ} \mathrm{C} \) ?


In compound \( A, 1.0 \) g nitrogen combines with 0.57 g oxygen. In compound \( \mathrm{B}, 2.0 \mathrm{g} \) nitrogen unite with 2.24 g oxygen and in compound \( C, 3.0 \) g nitrogen combine with \( 5.11 \mathrm{g} \) oxygen. These results obey
the law of:
A. multiple proportions
B. constant proportions
C. reciprocal proportions
D. none of these


An intrinsic semiconductor has
\( 10^{18} / m^{3} \) free electron and is doped with
pentavalent impurity of \( 10^{24} / m^{3} . \) Then the free electrons density order increase by
A .4
B. 3
c. 5
D. 6


Match column I and column II and
select the correct answer using the codes given below:


Two mirrors meet at right angles. A ray
of light is incident on one end at an
angle of \( 30^{\circ} \) as shown in figure. Draw
the reflected ray from the second
mirror.


Find the sum of -9,+14,+21,+19,+7


Solve the following Simple Equation:
\( 13-6 n=7 \)


If the vectors \( \overrightarrow{\mathbf{a}}+\overrightarrow{\mathbf{b}}+\overrightarrow{\mathbf{c}}, \overrightarrow{\mathbf{a}}+\boldsymbol{\lambda} \overrightarrow{\mathbf{b}}+ \)
\( \mathbf{2} \overrightarrow{\mathbf{c}},-\overrightarrow{\mathbf{a}}+\overrightarrow{\mathbf{b}}+\overrightarrow{\mathbf{c}} \) are linearly dependent
\( \operatorname{then} \lambda= \)
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c \cdot 3 \)
D. 4


Which of the following statement(s)
is/are true?
This question has multiple correct options
A. The apoplastic movement of water occurs exclusively through the cell wall without crossing any membranes
B. Solutes present in a cell (or in any solution) increase the free energy of water or water potential.
C. The symplastic movements occurs from cell to cell through the plasmodesmata.
D. Membrane permeability depends on the membrane composition, as well as the chemical nature of the solute.


A mixture of \( N a_{2} C_{2} O_{4}(A) \) and
\( K H_{2} C_{2} O_{4} \cdot 2 H_{2} O(B) \) required equal
volumes of \( 0.1 \mathrm{M} K M n O_{4} \) and \( 0.1 \mathrm{M} \)
NaOH separately. Molar ratio of \( A \) and
\( B \) in the mixture is :
A . 1: 1
B. 1: 5.5
c. 5.5: 1
D. 3.1 : 1


In Wedge-Dash Notation for threeDimensional Representation of an
organic molecule, how many bonds are represented in the plane of the paper?
A. one
B. Two
c. Three
D. Four


toppr
Q Type your question
below. For which figure the net force on
the charge may be zero
\( A \)
B.
\( c \)
\( D \)


Megaphones or loudhailers, horns,
musical instruments such as trumpets
and shehnais, are all designed to
A. send sound in a particular direction without spreading it in all directions.
B. send sound in a particular direction spreading it in all directions.
C. collect sound from all directions spreading it in all directions.
D. all of the above


Define Ventilation of air.


The expression \( y=a \sin b x \sin \omega t \)
represents a stationary wave. The distance between two consecutive
nodes is -
\( A \cdot \frac{\pi}{b} \)
в. \( \frac{\pi}{2 b} \)
\( c \cdot \frac{2 \pi}{b} \)
D.


A current carrying infinitely long wire is kept along the diameter of a circular wire loop, without touching it. The correct statement(s) is(are)
This question has multiple correct options
A. The emf induced in the loop is zero if the current is constant
B. The emf induced in the loop is finite if the current is constant
c. The emf induced in the loop is zero if the current decreases at a steady rate.
D. The emf induced in the loop is finite if the current decreases at a steady rate


A satellite moving in a circular path of radius \( r \) around earth has a time period
T. If its radius slightly increases by \( 4 \% \) then percentage change in its time period is:
A . \( 1 \% \)
B. \( 6 \% \)
c. \( 3 \% \)
D. \( 9 \% \)


\( s_{n}=5 n^{2}+11 n \) Find \( s_{5} \)


8
田
田
田田


When you lower a book of mass \( \mathrm{m} \) down
slowly through a distance h from yourself, the work done by you on the book is :
A. mgh
B. -mgh
c. zero
D. \( > \) mgh


ff \( \boldsymbol{y}=\boldsymbol{A} \boldsymbol{e}^{-\boldsymbol{k} t} \cos (\boldsymbol{p} \boldsymbol{t}+\boldsymbol{c}), \) then prove
that \( \frac{d^{2} y}{d t^{2}}+2 k \frac{d y}{d t}+n^{2} y=0, \) where
\( \boldsymbol{n}^{2}=\boldsymbol{p}^{2}+\boldsymbol{k}^{2} \)


Name the tissue that forms inner lining
of mouth.


For a zero order reaction, \( \boldsymbol{A} \longrightarrow \boldsymbol{P}, \boldsymbol{t}_{1 / 2} \)
is:
(k is the rate constant, \( [A]_{0} \) is the initial
concentration of \( \boldsymbol{A} \) )
\( ^{A} \cdot \frac{[A]_{0}}{2 k} \)
B. \( \frac{\ln 2}{k} \)
c. \( \frac{1}{k[A]_{0}} \)
D. \( \frac{\ln 2}{[A]_{0} k} \)


Enthalpy of atomisation of a diamond is \( 600 k J / \) mol
\( \boldsymbol{C}(\text {diamond}) \rightarrow \boldsymbol{C}(\boldsymbol{g}) \)
Find the bond energy of the \( \boldsymbol{C}-\boldsymbol{C} \)
bond.
Give your answer in \( k J / \) mol.


Assertion
The reaction of zinc with hydrochloric acid goes to completion in an open container.
Reason
Hydrogen gas is evolved from the reaction of zinc and hydrochloric acid.
A. Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement
B. Both the Statement 1 and Statement 2 are correct and Statement 2 is not the correct explanation of Statement 1.
c. statement 1 is correct but Statement 2 is not correct
D. Statement 1 is not correct but Statement 2 is correct


An electron in \( n \) th excited state in a
hydrogen atom comes down to first excited state by emitting ten different
wavelengths. Find the value of \( n \) (an integer)


What do you mean by Biochemical Oxygen Demand (BOD)?


What is the moment of inertia of each of
the following uniform objects about the
axes indicated?
A. \( A \) 2.50-kg sphere, 31.0 -cm in diameter about an axis through its center, if the sphere is solid.
B. A 2.50-kg sphere, 31.0-cm in diameter about an axis through its center, if the sphere is a thin-walled hollow shell.
C. An 8.00 -kg cylinder of length 17.0 -cm and diameter \( 20.0-\mathrm{cm} \) about the central axis of the cylinder, if the cylinder is thin-walled and hollow.
D. An 8.00-kg cylinder of length 17.0-cm and diameter 20.0-cm about the central axis of the cylinder, if the cylinder is solid.


For the given parabola find the coordinates of focus, axis, the equation of the directrix and the length of the
latus rectum.
\( x^{2}=6 y \)


Obtain the expression for the radius of the \( n^{t h} \) dark ring in Newton's rings
experiment.


Let \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}+\boldsymbol{x}+\mathbf{1} \) and \( \boldsymbol{g}(\boldsymbol{x})=\sin \boldsymbol{x} \)
Show that \( \boldsymbol{f} \circ \boldsymbol{g} \neq \boldsymbol{g} \circ \boldsymbol{f} \)


The solution of \( \frac{d y}{d x}+a y=e^{m x} \) is (where \( a+m=0 \) ) is:
A \( \cdot e^{a x} y=x+c \)
B . \( e^{a x} y=y+c \)
c. \( e^{a y} x=y+c \)
D. \( e^{a y} y=x+c \)


Q Type your question
to determine the effect of each
substance on normal body variables. An
appropriate amount of time was allowed between injections and the
substances did not interfere with one
another
Values
Baseline after Variable \( \quad \) injecting values \( \quad \) substance
\( \mathbf{A} \)
Serum
\[
C a^{+}
\]
\( 2.3 \mathrm{mmol} / \mathrm{L} \)
\( 2.3 \mathrm{mmol} / \mathrm{L} \)
Serum \( \quad 135 \mathrm{mmol} / \mathrm{L} \quad 135 \mathrm{mmol} / \mathrm{L} \)
\( N a^{+} \)
Serum \( \quad 5.6 \mathrm{mmol} / \mathrm{L} \quad 3.3 \mathrm{mmol} / \mathrm{L} \quad 5.6 \mathrm{n} \)
glucose
The normal release of substance D will
be
A. Soon after a meal.
B. When blood pressure is low.
C . Between meals.
D. When there has been limited intake of dietary calcium.
E. When dietary calcium is in excess.


The measured resistance of a
conductance cell was \( 100 \Omega .\left(M_{K C l}=\right. \)
\( 74.5 g m o l^{-1} \) and cell constant \( = \)
\( 1.25 \mathrm{cm}^{-1} \) ). If the specific conductance
\( \operatorname{in} \operatorname{oh} m^{-1} c m^{-1} \) is \( 125 \times 10^{-x}, \) then
what is the value of \( x ? \)


Water if often used as a coolant, a liquid to remove heat from things like hot
engines. One reasons is that water can absorb a lot of heat without changing temperature too much.

What property of water allows it to do this?
A. Water has a high latent heat of fusion
B. Water has a low latent heat of fusion.
c. water has a high specific heat capacity.
D. Water has a low specific heat capacity.
E. Water has a low latent heat of vaporization


Which of the following is the weakest base?
A. Ethyl amine
B. Ammonia
c. Dimethyl amine
D. Methyl amine


If a gas has \( R M S \) velocity \( 5.2 \times \)
\( 10^{4} \mathrm{cm} / \mathrm{s} . \) Find the average and M.P
velocity of the gas.


The escape velocity on the surface of a
planet is \( V_{e} \) what would be the escape
velocity on the planet having the same radius but mass 4 times that of it.
\( A \cdot 2 V_{e} \)
B. \( 4 V_{e} \)
c. \( V_{c} \)
\( D \cdot \frac{V_{c}}{2} \)


The electrons are filled in various sub
levels according to the order of their energies, is known as:
A. Aufbau principle
B. Pauli's principle
c. Hund's rule
D. \( n l^{x} \) principle


The reaction \( _{1}^{2} \boldsymbol{H}+_{1}^{2} \boldsymbol{H} \rightarrow_{2}^{3} \boldsymbol{H} \boldsymbol{e}+_{0}^{1} \boldsymbol{n} \)
is called
A. Fusion
B. Fission
c. Endothermic reaction
D. Spontaneous reaction


Draw the typical input and output characteristic of an \( n-p-n \)
transistor in \( C E \) configuration. Show
how these characteristics can be used
to determine (a) the input resistance
\( \left(r_{i}\right), \) and
(b) current amplification
factor \( (\boldsymbol{\beta}) \)


In a triangle \( A B C \) with vertices \( A(2,3) \)
\( B(4,-1) \) and \( C(1,2) \) Find the length of
altitude, from the vertex \( \boldsymbol{A} \)


If true then enter 1 and if false then
enter 0
Can two adjacent angles be
complementary?


Statement(A): Negative charges always
move from a higher potential to lower potential point Statement (B): Electric potential is
vector.
A. A is true but B is false
B. B is true but A is false
c. Both A and B false
D. Both A and R are true


Electrostatic force is also a force
A. contact
B. muscular
c. non-contact
D. gravitational


The rational number that is equal to its
negative.


A uniform metre rule of weight \( 10 g f \) is
pivoted at its 0 mark. How can it be
made horizontal by applying a least force?
A. By applying a force \( 10 g f \) downwards at the \( 100 \mathrm{cm} \) mark
c. By applying a force \( 5 g f \) upwards at the 100 cm mark.
D. By applying a force \( 5 g f \) downwards at the 100 cm mark.


\( A, B \) and \( C \) are the three coils of
conductor having different number of
turns, wound around a soft iron ring as
shown in the figure. Ends of coils \( B \) and
\( C \) are connected to the galvanometers.
The observation that can be made when
ends of coil \( A \) are connected to an A.C.
source is
A. Same electric current is induced in \( B \) and \( C \)
B. No electric current is induced in \( B \) and \( C \)
c. Induced electric current is more in \( B \) than in \( C \)
D. Induced electric current is less in \( B \) than in \( C \)


Assertion
\( E_{c e l l}^{0}=0 \) for a chloride ion concentration cell.
Reason
For this concentration cell: \( \boldsymbol{E}_{\boldsymbol{c e l l}}= \) \( \frac{\boldsymbol{R} \boldsymbol{T}}{\boldsymbol{n} \boldsymbol{F}} \boldsymbol{l} \boldsymbol{n} \frac{\left[\boldsymbol{C l}^{-}\right]_{L H S}}{\left[\boldsymbol{C l}^{-}\right]_{R H S}} \)
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


Distinguish between Para, Ferro and Diamagnetism.


Are the equations of motion applicable to bodies projected vertically up with
any velocity, say \( 8 k m s^{-1}, \) for
determining the maximum height? And why?


Let \( \boldsymbol{P}(\boldsymbol{n}): \boldsymbol{2}^{n}>\boldsymbol{n}, \forall \boldsymbol{n} \in \boldsymbol{N} \) and \( \boldsymbol{2}^{k}> \)
\( k, \forall n=k, \) then which of the following is
true \( \forall k \geq 2 ? \)
\( \mathbf{A} \cdot 2^{k}>5 k>1 \)
В \( \cdot 2^{k+1}>2 k>k+1 \)
C \( \cdot 2^{k}>2(k+1)>k \)
D. None of these.


The metal which does not react with
water or dilute \( H_{2} S O_{4} \) but reacts with
concentrated \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) is
\( (A l / C u / Z n / F e) \)


Brunner's gland are characteristic of
A. Submucosa of duodenum
c. Submucosa of stomach
D. Mucosa of colon


A person sells a table at a profit of \( 20 \% \) If he had bought it at \( 10 \% \) less cost and
sold for Rs. 105 more, he would have
gained \( 35 \% \). The cost price of the table
is
A. Rs. 7000
B. Rs. 7350
c. Rs. 9200
D. Rs. 8140


Ten grams of \( C o^{57} \) kept in open
container beta-decays with half life of 270 days. The weight of the material in container after 540 days will be very nearly.
\( A \cdot 10 g m \)
B. \( 5 \mathrm{gm} \)
c. \( 2.5 \mathrm{gm} \)
D. \( 1.25 \mathrm{gm} \)


All resistance are connected in the
series. The current is flowing through
circuit is \( 2 A \) and battery is of 20 Volts. What is the power dissipated through one of the \( 4 \Omega \) :
\( A \cdot 4 w \)
B. 8 w
\( c \cdot 16 w \)
D. 32 \( w \)
E. 36


Calculate the oxidation number of \( F e \) in
\( \boldsymbol{K}_{\mathbf{4}}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{6}\right] \)


\( _{1} H^{1},_{1} H^{2},_{1} H^{3} \) are :
A. isotopes
B. isotones
c. isobars
D. isotherms


The number of line symmetries that the given figure have- -
\( A \cdot 2 \)
B. 4
\( c .3 \)
D.


Heat produced by burning \( 2 k g \) of a fuel,
whose calorific value is \( 22000 k J k g^{-1} \) is utilized to boil certain mass of water
which is at \( 34^{\circ} \mathrm{C} \). Find the mass of
water taken.
(Specific heat capacity of water is \( \left.4200 J k g^{-1} K^{-1}\right) \)
A . \( 159 \mathrm{kg} \)
в. \( 172 \mathrm{kg} \)
c. \( 183 \mathrm{kg} \)
D. \( 100 \mathrm{kg} \)


Order of rate of reaction with \( A g N O_{3} \) or
rate of \( \boldsymbol{S}_{N} \mathbf{1} \) is:
A . ।>III>II
B. ||>|||>|
c. ।>II>III
D. III>>>II


At what temperature the rms velocity of
helium molecules will be equal to that of
hydrogen molecules at NTP?
A . \( 844 k \)
B. 64 K
c. \( 273^{0} \mathrm{C} \)
D. 273k


Which of the following is commonly known as "chilgoza pine"?
A. Pinus roxburghii
B. Pinus strobus
c. Pinus gerardiana
D. Pinus sylvestris


Capacitance is best described as the:
A. Rate of flow of charge
B. Energy per unit charge
C. Change in electric potential per unit length
D. Charge per unit of electric potential difference
E. Electric potential difference per unit of electric current


The total vapour pressure, \( \mathbf{P}_{\text {total }} \) (in torr)
for a mixture of thwo volatile
components, \( A \) and \( B \) is given by \( P_{\text {total }} \)
\( =220-110 X_{B} \)
Where, \( \mathbf{X}_{\mathbf{B}} \) is mole fraction of
component, \( B \) is mixture. Hence,
pressure (in torr) of pure components,
\( A \) and \( B \) are respectively:
A \( \cdot 220,110 \)
В. 110,220
\( c \cdot 220,330 \)
D. 220,150


The number of possible surjection from \( \boldsymbol{A}=\{1,2,3, \dots n\} \) to \( B=\{1,2\} \) (where
\( \boldsymbol{n} \geq \mathbf{2}) \) is \( \mathbf{6 2}, \) then \( \boldsymbol{n}= \)
\( \mathbf{A} \cdot \mathbf{5} \)
B. 6
\( c \cdot 7 \)
D.


Which of the these are
disproportionation reactions?
I. \( 2 \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CHO}-^{\mathrm{A}\left(\mathrm{CC}_{2} \mathrm{H}_{5}\right)_{3}} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOCH}_{2} \mathrm{C}_{6} \mathrm{H}_{5} \)
III. \( \mathrm{Cl}_{2}+2 \mathrm{OH}^{-} \longrightarrow \mathrm{Cl}^{-}+\mathrm{ClO}^{-}+\mathrm{H}_{2} \mathrm{O} \)
IV. \( 2 \mathrm{KClO}_{3} \longrightarrow 2 \mathrm{KCl}+3 \mathrm{O}_{2} \)
\( \mathbf{A} \cdot \) ।, ॥।, ॥ ॥
в. ॥, IV
c. ॥, ॥ा, । v
D. I, IV


Which of the following is not a part of hindbrain?
B. Thalamus
c. Cerebellum
D. Pons


Platinum, palladium and iridium are
called noble metals because:
A. Alfred Nobel discovered them
B. They are inert towards many common reagents
C. They are shining, lustrous and pleasing to look at
D. They are found in active state


Incorrect statement about given
carbohydrate is
A. Above compound is a reducing sugar
B. Above compound undergo mutaritation
C. Above compound is a non-reducing sugar
D. Above compound has a glycosidic linkage


An object is placed at a distance \( 2 f \)
from the pole of a convex mirror of focal
length \( f . \) The linear magnification is:
A \( \cdot \frac{1}{3} \)
B. \( \frac{2}{3} \)
\( c \cdot \frac{3}{4} \)
D.


Current is induced in a coil by
electromagnetic induction when:
A. Only the coil moves in a magnetic field.
B. Only the magnet moves towards the coil.
C. Coil and the magnet move with respect to each other
D. None of the above


Choose the correct answer from the
alternatives given :

Directions for questions 71 to 75: The
graph shows the production of wheat in different years of a particular State
The year which had the percentage of
decrease vis-a-vis its previous year
in production
A. \( 1996-1997 \)
B. \( 1995-1996 \)
c. \( 1999-2000 \)
D. \( 2000-2001 \)


In the fractional evaporation of liquid air, we use :
A. Dewar flask
B. Kjeldahl flask
c. claude's apparatus
D. Ramsay apparatus


The following table gives the distribution of 45 students across the
different levels of intelligent quotient. Draw the histogram for the data.
\begin{tabular}{|l|c|c|c|c|c|c|c|}
\hline IQ Level & \( ^{60-70} \) & \( 70-80 \) & \( 80-90 \) & \( 90-100 \) & \( 100-110 \) & \( 110-120 \) & \( 120-130 \) \\
\hline No of Sudents & 2 & 5 & 6 & 10 & 9 & 8 & 5 \\
\hline
\end{tabular}


Organisms which obtain energy by oxidation of reduced inorganic
compounds are
A. Photoautotrophs
B. Saprotrophs
c. coproheterotrophs
D. chemoheterotrophs


The displacement of a particle varies according to the relation \( \boldsymbol{X}= \) \( 4(\cos \pi t+\sin \pi t) \)
The amplitude of the particle is
A . -4
B. 4
c. \( 4 \sqrt{2} \)
D.


A 2 MeV proton is moving perpendicular to a uniform magnetic field of 2.5 tesla. The force on the proton is
В. \( 7.6 \times 10^{-11} N \)
c. \( 2.5 \times 10^{-11} N \)
D. \( 7.6 \times 10^{-12} N \)


A magnet makes 40 oscillation per minute at a place having magnetic intensity of \( 0.1 \times 10^{-5} \) Tesla. At another
place it takes 2.5 sec to complete one oscillation. The value of earth's
horizontal field at that place is
A \( .0 .76 \times 10^{-6} T \)
В. \( 0.18 \times 10^{-6} T \)
\( \mathbf{c} \cdot 0.09 \times 10^{-6} T \)
D. \( 0.36 \times 10^{-6} T \)


If \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) and \( \boldsymbol{g}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) are defined
by \( f(x)=2 x+3 \) and \( g(x)=x^{2}+7 \)
then the values of \( x \) such that
\( g(f(x))=8 \) are:
A . 1,2
в. -1,2
c. -1,-2
D. 1,-2


Which is not a characteristic of free
radical chain reaction?
A. It produces a mole of product for a mole of free radical initiated
B. It gives the product derived from the most stable radica
C. It may be initiated by peroxides
D. It may be initiated by light or heatt


What is observed when nitric acid is
kept in a reagent bottle for a long time?
A. Brown vapours are seen in the bottle
B. The nitric acid turns yellowish in colour
c. The nitric acid turns black in colour
D. both A and


In terms of period and group where would you locate the element with \( z= \)
\( 114 ? \)


State true or false:
Sum of two sides of a triangle is greater than the third side.
A. True
B. False


Self inductance of a long solenoid is directly proportional to \( (N \) is no. of turns in solenoid)
A . \( N \)
B . \( N^{2} \)
\( c \cdot 1 / N \)
D. \( 1 / N^{2} \)


In Young's double slit experiment, one of the slit is wider than another, so that
amplitude of the light from one slit is
double of that from other slit. If \( \boldsymbol{I}_{m} \) be
the maximum intensity, the resultant intensity I when they interfere at phase difference \( \phi \) is given by
A \( \cdot \frac{I_{m}}{9}(4+5 \cos \phi) \)
в. \( \frac{I_{m}}{3}\left(1+2 \cos ^{2} \frac{\phi}{2}\right) \)
c. \( \frac{I_{m}}{5}\left(1+4 \cos ^{2} \frac{\phi}{2}\right) \)
D. \( \frac{I_{m}}{9}\left(1+8 \cos ^{2} \frac{\phi}{2}\right) \)


Explain Mean Value Theorem


\( \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{1} & \boldsymbol{\omega} & \boldsymbol{\omega}^{2} \\ \boldsymbol{\omega} & \boldsymbol{\omega}^{2} & \mathbf{1} \\ \boldsymbol{\omega}^{2} & \mathbf{1} & \boldsymbol{\omega}\end{array}\right] \) Find Det \( \mathbf{A} \)


Which of the following compounds will be most easily attacked by an electrophile?
\( A \)
в.
\( c \)
D.


There are 50 marbles of 3 colors: blue
yellow and black The probability of picking up a blue marble is \( 3 / 10 \) and that of picking up a yellow marble is \( 1 / 2 \) The probability of picking up a black ball is
A \( .1 / 5 \)
B. 1/10
\( c \cdot 1 / 4 \)
D. \( 4 / 5 \)


Nephridiopores present over the body of
earthworm belong to
A. Integumentary nephridia
B. Septal nephridia
c. Pharyngeal nephridia
D. Peptonephridia


The bacteria in a a culture grows by \( 10 \% \)
in the first hour, decreases by \( 10 \% \) in the second hour and again increases by \( 10 \% \) in the third hour.lf the count of
bacteria in the sample is 121000000 what will be the count of bacteria after 3
hours?


How many mole \( C O_{2} \) molecules are
represented by \( 1.8 \times 10^{24} \) atoms?
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 3 \)
D. 4
E. 5


Suppose \( A \) is any \( 3 \times 3 \) non-singular
matrix and \( (\boldsymbol{A}-\mathbf{3} \boldsymbol{I})(\boldsymbol{A}-\mathbf{5} \boldsymbol{I})=\boldsymbol{O} \)
where \( \boldsymbol{I}=\boldsymbol{I}_{3} \) and \( \boldsymbol{O}=\boldsymbol{O}_{3}, \) If \( \boldsymbol{\alpha} \boldsymbol{A}+ \)
\( \beta A^{-1}=4 I, \) then \( \alpha+\beta \) is equal to
A . 8
B. 7
c. 13
D. 12


Find the derivative of the following (it is to be understood that \( a, b, c, d, p, q, r \)
and \( s \) are fixed non-zero constants and
\( m \text { and } n \text { are integers }): \frac{\sin x+\cos x}{\sin x-\cos x} \)


If electronegativity values of element \( \boldsymbol{X} \)
and \( Y \) are 3.8 and 1.8 respectively, then
an ionic percentage of compound \( \boldsymbol{X} \boldsymbol{Y} \) is:
A . 50
B. 46
\( c \cdot 64 \)
D. 36


Which of the following pairs is
mismatch?
A. Pedology - Study of soil
B. Kinesiology - Study of fossils
C. limnology - Study of fresh water ecosystem
D. Physiology - Study of processes and functions of life


The type of bond formed between \( \boldsymbol{H}^{+} \)
and \( N H_{3} \) in \( N H_{4}^{+} \)
A. covalent
B. ionic
c. dative
D. hydrogen


Current in the circuit will be
\( A \cdot \frac{5}{A 0} \)
\( B \cdot \frac{5}{50} A \)
\( c \cdot \frac{5}{10} A \)
\( D \cdot \frac{5}{20} A \)


Match the column:
Column-I Column-II
(p) Complex having lowest
(a) \( \left[F e(C O)_{4}\right]^{2-} \quad \) bond length of CO ligand
(q) Follow Sidgwick's rule of
(b) \( \left[V(C O)_{6}\right]^{-} \quad \) E.A.N.
(r) Synergic bonding is
(c) \( K\left[P t C l_{3}\left(C_{2} H_{4}\right)\right] \) involved in complex/ion
\( (d) \)
(s) Complex having highest \( \left[F e\left(H_{2} O\right)_{5} N O\right] S O_{4} \) bond length of CO ligand
(t) Oragnometallic compound
\( \mathbf{A} \cdot(\mathrm{a}) \mathrm{q}, \mathrm{r}, \mathrm{s}, \mathrm{t} ;(\mathrm{b}) \mathrm{p}, \mathrm{q}, \mathrm{r}, \mathrm{t} ;(\mathrm{c}) \mathrm{r}, \mathrm{r} ;(\mathrm{d}) \mathrm{r} \)
B. (a)s,t; (b) p,q,r,t; (c) r; (d) r
C. \( (a) q, s, t ;(b) q, r, t ;(c) r, t ;(d) r \)
D. \( (a) q, r, t ;(b) q, r, t ;(c) r \)


For the reaction, \( 2 N_{2} O_{5}(g) \longrightarrow \)
\( 4 N O_{2}(g)+O_{2}(g), \) if the concentration
of \( N O_{2} \) increases by \( 5.2 \times 10^{-3} M \) in
100 sec, then the rate of reaction is:
A \( \cdot 1.3 \times 10^{-5} M s^{-1} \)
В \( \cdot 5 \times 10^{-4} \mathrm{M} s^{-1} \)
c. \( 7.6 \times 10^{-4} M s^{-1} \)
D. \( 2 \times 10^{-3} M s^{-1} \)
E \( .2 .5 \times 10^{-5} M s^{-1} \)


Find the sum of first 51 terms of an AP
whose second and third terms are 14
and 18 respectively.


Mark the following rational numbers on the number line.
\( \frac{10}{3} \)


Which of the following disease increase due to greenhouse effect?
A. Malaria
B. Dengue
c. Yellow Fever
D. All of the above


Which of the following statement is correct for a galvanic cell?
A. Reduction occurs at cathode
B. Oxidation occurs at anode
c. Electrons flow anode to cathode
D. All the statements are correct


Prove that \( \frac{\cos 9^{0}+\sin 9^{0}}{\cos 9^{0}-\sin 9^{0}}=\cot 36^{0} \)


Calculate the following integral:
\( \int_{0}^{\pi} \frac{d x}{\cos ^{2} \frac{x}{5}} \)


Neoprene is:
A. Polyster
B. Polyamide
C . Polysaccharide
D. Polyhalodiene


\( x^{2}-256=0 \) find \( x \)


A circle of 'a' radius is divided into 6
equal sectors An equilateral triangle is drawn on the chord of each sectors to lie
outside the circle. The area of the
resulting figure is


\( f(x)=\frac{a \sin x+b \cos x}{c \sin x+d \cos x} \) is an
increasing funtion if
A \( . a d-b c=0 \)
B. \( a d-b c<0 \)
c. \( a d-b c>0 \)
\( \mathbf{D} \cdot a b+c d=0 \)


The alkaline earth metal ion that has
least electrical conductivity in aqueous solutions is:
\( \mathbf{A} \cdot B a^{++} \)
B. \( C a^{+} \)
\( \mathbf{c} \cdot B e^{++} \)
D. \( C s^{+}+ \)


When balanced using smallest, wholenumber coefficients, the correct
coefficients for the following equation
are:
\( -A l C l_{3}+_{-} H_{2} S O_{4} \rightarrow_{-} A l_{2}\left(S O_{4}\right)_{3}+_{-} \)
\( \boldsymbol{H} \boldsymbol{C l} \)
в. 2,3,1,6
\( \mathrm{c} .1,3,1,3 \)
D. 2,3,1,3


\( a^{-1}+b^{-1}+c^{-1}=0 \) such that
\( \left|\begin{array}{ccc}1+a & 1 & 1 \\ 1 & 1+b & 1 \\ 1 & 1 & 1+c\end{array}\right|=\triangle \) then the
value of \( \triangle \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B. abco
\( \mathrm{c} .-a b c \)
D. None of these


If the variance of the random variable \( \boldsymbol{X} \)
is \( 5, \) then the variance of the random
variable \( -\mathbf{3} \boldsymbol{X} \) is
A . 15
B . 45
c. -45
D. 60


Match the columns


\( \frac{\boldsymbol{d}^{20}(2 \cos \boldsymbol{x} \cos \mathbf{3} \boldsymbol{x})}{\boldsymbol{d} \boldsymbol{x}^{20}}= \)
A \( \cdot 2^{20}\left(\cos 2 x-2^{20} \cos 4 x\right) \)
B . \( -2^{20}\left(\cos 2 x+2^{20} \cos 4 x\right) \)
C \( \cdot 2^{20}\left(\sin 2 x+2^{20} \sin 4 x\right) \)
D. \( 2^{20}\left(\sin 2 x-2^{20} \sin 4 x\right) \)


Diamond on burning in oxygen gives:
A \( . C O \)
в. \( C a(O H)_{2} \)
\( c \cdot C O_{2} \)
D. \( C a O \)


Draw a triangle whose side are
represented by \( \boldsymbol{x}=\mathbf{0}, \boldsymbol{y}=\mathbf{0} \) and \( \boldsymbol{x}+ \)
\( \boldsymbol{y}=\mathbf{3} \) in the Cartesian system Also find
the coordinates of its vertices.


The function which represents the height, \( h(t), \) of a ball \( t \) seconds after it is kicked into the air is
\( \boldsymbol{h}(\boldsymbol{t})=-\mathbf{1 6} \boldsymbol{t}^{2}+\boldsymbol{6} \boldsymbol{4} \boldsymbol{t} \)
What does \( t \) represent if \( h(t) \) is zero?
A time that ball reaches \( \frac{3^{t h}}{4} \) its maximum height
B. TIme that ball reaches one- - half its maximum height
c. The time at which the ball is on the ground
D. Time that ball reaches its maximum height


Direction angle of a vector is \( 30^{\circ}, \) then
find the vector.
B. \( \sqrt{3} a \hat{i}+b \hat{j} \)
c. \( a \hat{i}+b \hat{j} \)
D. \( \sqrt{3} a \hat{i}+\sqrt{3} 3 \hat{j} \)


A sample of HCl gas is placed in an electric field of \( 2.5 \times 10^{4} N C^{-1} \). The
dipole moment of each HCl molecule is
\( 3.4 \times 10^{-30} \mathrm{Cm} . \) Find the maximum
torque that can act on a molecule.


The number of \( 1^{0}, 2^{0} \) and \( 3^{0} \) alcoholic
groups in Mannitol or Sorbitol are:
\( A \cdot 2,4 \) and 0
B. 1,4 and 0
c. 2,2 and 0
D. 2, 1 and 1


An example of bactericidal drug is:
A. Penicillin
B. Clindamycin
c. Tigecycline
D. Nitrofurantoin


Match the physical quantities given in
column A to their Sl units given in
column B:


Assertion
We can calculate angular momentum of bodies of all shapes by the product of moment of inertia and angular velocity
Reason The basic equation of torque i.e.,torque is equal to rate of change of angular momentum is valid for both inertial and
non inertial frames.
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


If \( \vec{a}=4 \hat{i}-\hat{j}+\hat{k} \) and \( \vec{b}=2 \hat{i}-2 \hat{j}+\hat{k} \)
then find a unit vector parallel to the vector \( \overrightarrow{\boldsymbol{a}}+\overrightarrow{\boldsymbol{b}} \)


\( \int_{-\pi}^{\pi} x^{3} \cos x d x \)
A . \( \pi \)
в. \( \pi / 2 \)
c. \( -\pi / 3 \)
D.


When is water said to be polluted?
A. If a person can't swim
B. If water dries out
C. If it is unfit for drinking
D. All of the above


At what rate precent will Rs 2000 amount to Rs 2315.25 in 3 years at compound interest?


Magnetic field strength at the centre of
regular pentagon made of a conducting wire of uniform cross section area as
shown in figure is : (i amount of current
enters at A and leaves at E)
\( \mathbf{A} \cdot \frac{5 \mu_{0} i}{4 \pi a}\left[2 \sin \frac{72^{0}}{2}\right] \)
\( B . \quad 0 \)
C \( \cdot \frac{3 \mu_{0} i}{4 \pi}\left[2 \sin \frac{72^{0}}{2}\right] \)
D. \( \frac{\mu_{0} i}{4 \pi a}\left[2 \sin \frac{72^{0}}{2}\right] \)


The correct IUPAC name of the following
hydrocarbon is :
A. 4,5 -diisopropyl-3-methylheptane
B. 3-methyl-4,5-diisopropylheptane
C. 5 -ethyl-4-isopropyl-3,6-dimethylheptane
D. 3-Ethyl-4-isopropyl-2,5-dimethylheptane


If \( A \) is \( 3 \times 4 \) matrix and \( B \) is a matrix
such that \( A^{\prime} B \) and \( B^{\prime} A \) are both
defined, then the order of \( B \) is
\( \mathbf{A} \cdot 4 \times 4 \)
B. \( 3 \times 3 \)
c. \( 3 \times 4 \)
D. \( 4 \times 3 \)


\( f l \| \boldsymbol{m} \) and \( \boldsymbol{p} \| \boldsymbol{q}, \) find \( \boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}, \boldsymbol{d} \)


The figure formed by four points \( 1+ \)
\( 0 i ;-1+0 i, 3+4 i \) and \( \frac{25}{-3-4 i} \) on the argand plane is
A. parallelogram but not a rectangle
B. a trapesium which is not equilateral
c. cyclic quadrilateral
D. none of these


When particles moves in a circle at a constant speed then the motion is said
to be
A. Uniform motion
B. Non uniform motion
c. Projectile motion
D. All


The phase difference between two
points is \( \pi / 3 . \) If the frequency of wave is \( 50 \mathrm{Hz}, \) then what is the distance between two points? \( (\operatorname{given} v=330 \mathrm{m} / \mathrm{s}) \)
\( A \cdot 2.2 \mathrm{m} \)
в. \( 1.1 \mathrm{m} \)
c. \( 0.6 \mathrm{m} \)
D. \( 1.7 \mathrm{m} \)


Aquaporins are integral proteins of the plasma membrane whose role is to
allow the passage of water molecules
down its concentration gradient. Recent observations have shown an
interesting arrangement of charged amino acid residues along the inner
surface of the channel resulting in the entry of water via its oxygen, then flipping to lead with its hydrogens half way through the channel. How might this explain aquaporins specificity for water and not cations or protons?
A. Cations such as \( K^{+} \) and \( N a^{+} \) would be repelled at the opening of the channel
B. Water gains access because it is electrically neutral.
c. Protons cannot cross since they do not interact with water
D. Water, being a small polar molecule, is able to interact with both negative and positive residues in the channel.


Which is the set of amphiprotic
species?
A \( \cdot H_{3} O^{+}, H P O_{4}^{2-}, H C O_{3} \)
B. \( H_{2} O, H P O_{3}^{2-}, H_{2} P O_{2}^{-} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{PO}_{4}^{-}, \mathrm{H}_{2} \mathrm{PO}_{3}^{-}, \mathrm{H}_{2} \mathrm{O} \)
D. All of these


The Henry's law constant for the solubility of oxygen in water is \( 3.3 \times \)
\( 10^{-4} \) M \( / \) atm at \( 12^{\circ} \mathrm{C} \). Air is \( 21 \mathrm{mol} \% \)
oxygen. How many grams of oxygen can be dissolved in one litre of a trout
stream at \( 12^{\circ} \mathrm{C} \) at an air pressure of 1.00
atm?
A. 0.222 g
gg \( . . .222 \)
В. 0.11222 g
c. 0.333 g
D. 0.422 g


topp
Q rpesour


The probability of a radioactive nucleus to survive one mean life is \( \frac{1}{e+x}, \) then \( x \) is


Orion nebula glows brightly because the gas in it is energised by the stars that have already formed within it, such
types of nebula are called
as
A. planetary nebula
B. dark nebula
c. reflection nebula
D. emission nebula


ff \( y=f\left(x^{2}+2\right) \) and \( f^{\prime}(3)=5, \) then \( \frac{d y}{d x} \)
at \( x=1 \) is
\( \mathbf{A} \cdot \mathbf{5} \)
B . 25
c. 15
D. 10


Range of \( \boldsymbol{y}=\log _{\frac{3}{4}}(\boldsymbol{f}(\boldsymbol{x})) \)
\( A \cdot(-\infty, 1] \)
в. \( \left[\frac{3}{4}, \infty\right) \)
\( c \cdot(-\infty, \infty) \)
D. \( R \)


The height of a waterfall is \( 50 m . \) If \( g= \)
\( 9.8 m s^{-2} \) the difference between the
temperature at the top and the bottom of the waterfall is
A . 1.17
в. 2.17
c. 0.117
D. 1.43


Total number of equivalence relations defined in the \( \operatorname{set} S=\{a, b, c\} \) is ?


If \( \boldsymbol{y}=\mathbf{s e c}^{-1}\left[\frac{\sqrt{\boldsymbol{x}}+\mathbf{1}}{\sqrt{\boldsymbol{x}}-\mathbf{1}}\right]+ \)
\( \sin ^{-1}\left[\frac{\sqrt{\boldsymbol{x}}-1}{\sqrt{\boldsymbol{x}}+1}\right] \) then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}= \)
\( A \)
в.
c.
D.


Which of the following has high heat of vapourisation?
A. \( \mathrm{PH}_{3} \)
в. \( \mathrm{SbH}_{3} \)
c. \( \mathrm{NH}_{3} \)
D. AsH \( _{3} \)


n the adjoining figure (not drawn to scale)
\( \boldsymbol{P S}=\mathbf{4} \boldsymbol{c m}, \boldsymbol{S R}=\mathbf{2} \boldsymbol{c m}, \boldsymbol{P T}=\mathbf{3} c \boldsymbol{m} \)
and \( Q T=5 c m \)
(i) Show that \( \triangle P Q R \sim \triangle P S T \).
(ii) Calculate \( S T, \) if \( Q R=5 \cdot 8 \mathrm{cm} \)


Which of the following in relation to the energy of sublevels in H atom is incorrect?
A. \( 4 s<4 p<4 d<4 f \)
B. \( 3 s<4 s<5 s<6 s \)
c. \( 4 s=4 p<5 s<6 p \)
D. \( 2 s<3 s=3 p<4 d \)


\( \mathbf{3 5}, \mathbf{4 1}, \mathbf{4 7}, \mathbf{5 3}, \mathbf{5 9}, \dots \dots \)
For this sequence, write down
(a) the next term
(b) the \( n \) th term


Distinguish between Avalanche breakdown and Zener breakdown.


The main constituent of LPG is butane.
Then
(A) Butane can be liquefied easily under high pressure
(B) Butane is liquefied by chemically reacting with ethane and propane.
A. only A is true
B. Only B is true
c. Both \( A \) and \( B \) are true
D. Both A and B are false


If the matrix \( \left[\begin{array}{ccc}1 & 3 & \lambda+2 \\ 2 & 4 & 8 \\ 3 & 5 & 10\end{array}\right] \) is singular
\( \operatorname{then} \lambda= \)
A . -2
B. 4
\( c \cdot 2 \)
D. -


A metal ion \( M^{n+} \) having \( d^{4} \) valence electronic configuration combines with three bidentate ligands to form a complex compound. Assuming \( \triangle \boldsymbol{a}>\boldsymbol{p} \)
(i) Write the electronic configuration of
\( \boldsymbol{d}^{4} \) ion.
(ii) What type of hybridisation will \( M^{n+} \) ion has?
(iii) Name the type of isomerism exhibited by this complex.


The active constituent of bleaching
powder is:
\( \mathbf{A} \cdot C a(O C l)_{2} \)
в. \( C a(O C l) C l \)
c. \( C a\left(C l O_{2}\right)_{2} \)
D. \( \operatorname{Ca}\left(\text {ClO}_{2} \text { ) } \)Cl\right.


If the sum of measures of two angles of
a hexagon is \( 220^{\circ}, \) then what is the sum of the measures of other four angles?
A . \( 800^{\circ} \)
B. \( 700^{\circ} \)
\( c \cdot 600^{\circ} \)
D. \( 500^{\circ} \)


A fixed amount of dry air at
temperature of \( 27^{\circ} C \) is compressed to \( \frac{1}{9} t h \) of original volume. Its final temperature is \( (\gamma=\mathbf{1 . 5}) \)
\( \mathbf{A} \cdot 627^{\circ} C \)
B. \( 600^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 158^{\circ} \mathrm{C} \)
D. \( 527^{\circ} \mathrm{C} \)


A man starts his job with a certain monthly salary and a fixed increment
every year. If his salary will be Rs. 11000
after 2 years and Rs. 14000 after 4 years of his service. What is his starting salary and what is the annual increment?
A. Starting salary is Rs. 7500 and increment is Rs. 2500
B. Starting salary is Rs.5000 and increment is Rs. 1800
C. Starting salary is Rs. 8000 and increment is Rs. 1500
D. Starting salary is Rs. 7000 and increment is Rs. 1300


The atoms of various isotopes of a particular element differ from each other in the number of:
A. electrons in the outer shell only
B. protons in the nucleus
c. electrons in the inner shell only
D. neutrons in the nucleus


\( A \)
\( B \)
\( c \)
5


A particle is projected at time \( t=0 \) from a point 'O' with a speed 'u' at an angle ' \( \theta \)
to horizontal. Find the torque of a gravitational force on projectile about the origin at time 't'. (x, y plane is vertical plane)


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


A particle executes SHM given by the equation \( \boldsymbol{x}=\mathbf{4} \sin (\mathbf{2} \boldsymbol{\pi} \boldsymbol{t}+\boldsymbol{\pi} / \mathbf{4}), \) what
will be the velocity of the particle at \( t= \) (1/8)th sec;
A. velocity = 0
B. velocity = maximum
c. velocity = minimum
D. The particle's speed cannot be determined


The correct order of acidic strength is:
A. \( K_{2} O>C a O>M g O \)
в. \( C O_{2}>N_{2} O_{5}>S O_{3} \)
c. \( N a_{2} O>M g O>A l_{2} O_{3} \)
D. \( C l_{2} O_{7}>S O_{2}>P_{4} O_{10} \)


The products obtained when anisole is
heated in sealed tube with \( H I \) are:
\( A \)
B
\( c \)
D. \( C H_{3} O H+C H_{3} I \)


Define the term malleability


Total number of lone pair of electrons in
\( X e O F_{4} \) is :
A . 0
B.
\( c \cdot 2 \)
D. 3


Assertion
Internal energy of a system is an
extensive property.
Reason
The internal energy of a system depends
upon the amount and physical state of
the substance.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


A rectangle garden has a length \( 3 \frac{1}{5} \mathrm{m} \) and breadth \( 2 \frac{3}{4} \mathrm{m} \) what is its area?


Biochemical Oxygen Demand measures:
A. industrial pollution
B. air pollution
C . pollution capacity of effects
D. dissolved \( O_{2} \) needed by microbes to decompose organic waste.


Some of the major uses of heavy water
are given below. Which one is not
correct?
A. It is used as a moderator in nuclear.
B. It is used as a tracer compound for studying reaction mechanism
c. High concentration of heavy water accelerates the growth of plants
D. It is used in preparing deuterium


If the replacement set is the set of real numbers, solve \( :-4 x \geq-16 \)


Which is true statement about \( D_{2} O \)
and \( \boldsymbol{H}_{2} \boldsymbol{O} ? \)
A \( \cdot D_{2} O \) has lower dielectric constant than \( H_{2} O \)
B. \( N a C l \) is more soluble in \( D_{2} O \) than \( H_{2} O \)
c. Both are correct
D. None of these


How solubility of a gas in liquid varies with i) Temperature ii) pressure?


Let \( \boldsymbol{f}(\boldsymbol{x}+\boldsymbol{y})=\boldsymbol{f}(\boldsymbol{x}) \boldsymbol{f}(\boldsymbol{y}) \) and \( \boldsymbol{f}(\boldsymbol{x})= \)
\( 1+(\sin 2 x) g(x) \) where \( g(x) \) is
continuous, then \( f^{\prime}(x) \) equals
A \( . f(x) g(0) \)
B \( .2 f(x) g(0) \)
D. \( 2 f(0) \)


Which of the following is the correct order of chemical reactivity with water according to electrochemical series?
A. \( K>M g>Z n>C u \)
в. \( K>M g>C u>Z n \)
c. \( C u>Z n>K>M g \)
D. \( M g>K>C u>Z n \)


Which of the following contributes most to the transport of water, from the ground to the leaves of a tall tree?
A. Breakdown of ATP
B. Cohesion of water and transpiration pull
c. Root pressure
D. Capillary rise of water in xylem


The position of a particle is given by \( \vec{r}=(\hat{i}+2 \hat{j}-\hat{k}) \) and momentum \( \vec{P}= \)
\( (3 \hat{i}+4 \hat{j}-2 \hat{k}) . \) The angular momentum is perpendicular to
A. X-axis
B. Y-axis
c. z-axis
D. Line at equal angles to all the three axes


Green chemistry deals with:
A. study of plant physiology
B. study of extraction of natural products from plants
C. detailed study of reactions involved in the synthesis of chlorophyll
D. utilization of existing knowledge base for reducing the chemical hazards along with developmental activities
E. synthesis of chemical compounds using green light


Which of the following radiations have least effect on both the photographic plate and zinc sulphide screen?
A . \( \alpha \) -rays
B. \( \beta \) -rays
c. \( \gamma \) -rays
D. All have equal effect


The north poles of pole strengths, \( \boldsymbol{m}, \boldsymbol{9} \boldsymbol{m} \)
are kept apart by certain distance ' \( \boldsymbol{d} \) Find distance of null point from larger
pole
A \( .2 d / 4 \)
в. \( 2 d / 3 \)
c. \( 5 d / \)
D. \( 3 d / 2 \)


A disadvantage of nuclear power is -
A. it produces carbon dioxide which is responsible for global warming
B. it produces toxic waste
C . it affects the ozone layer
D. it requires large amounts of fuel to produce a small amount of energy


The volume of \( 20 V-H_{2} O_{2} \) solution
required to prepare 5 litres of oxygen at
STP is:
A . \( 125 \mathrm{ml} \)
B. 250 m1
c. \( 100 \mathrm{ml} \)
D. \( 50 \mathrm{m} \)


Which of the following is the least volatile?
A \( \cdot C H_{3}-C H_{2}-C H_{2}-F \)
в. \( C H_{3}-C H_{2}-C H_{2}-C l \)
c. \( C H_{3} C H-C H \)
D. \( C H_{3}-C H_{2}-C H_{2}-B r \)


A type of electromagnetic wave has
wavelength \( 50 A \)
What is the speed of the wave in
vacuum?


From which of the following crosses, \( \boldsymbol{F}_{1} \)
progeny showing maximum hybrid vigour can be obtained?
(1) \( A A b b \times a a B B \)
(II) \( A A b b \times a a b b \)
\( (\| I) \) aaBB \( \times \) aabb
\( (I V) A A B B \times \)
aabb
A \( . \) (II), (III)
B. (III), (IV)
\( c \cdot(1),(1 v) \)
D. (I), (II)


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


If the momentum of an electron is
changed by \( p_{m}, \) then the de Broglie wavelength associated with it
increased by \( 0.5 \% \). The initial momentum of electron will be
A \( \cdot p_{m} / 200 \)
в. \( p_{m} / 100 \)
c. \( 201 p_{m} \)
D. \( 100 p_{m} \)


Which of the following parts of the eye refracts light ?
A. Pupil
B. Iriss
c. Lens
D. Retina


How many mitotic divisions must occur in a cell of a root tip to form 256 cells?
A . 256
B. 8
\( c \cdot 128 \)
\( D \cdot 64 \)


If the line joining \( \boldsymbol{A}(\mathbf{1}, \mathbf{3}, \mathbf{4}) \) and \( \boldsymbol{B} \) is divided by the point (-2,3,5) in the ratio \( 1: 3, \) then \( B \) is
A. (-11,3,8)
(年) (-1,3,8)
в. (-11,3,-8)
D. (13,6,-13)


A convex lens of focal length \( 16 \mathrm{cm} \) is completely immersed in water.lf the refractive indices of material of lens
and water are 1.5 and 1.33 respectively, then its focal length be :
\( \mathbf{A} \cdot 16 \mathrm{cm} \)
B . \( 62.59 \mathrm{cm} \)
\( \mathbf{c} \cdot 18 c m \)
D. \( 24.24 \mathrm{cm} \)


A motorboat starting from rest on a lake
accelerates in a straight line at a constant rate of \( 3.0 m / s^{2} \) for 8.0 s. How far does the boat travel during this time?


\( \left(\frac{1}{4}+\frac{1}{4^{2}}+\frac{1}{4^{3}}----+\frac{1}{4^{n-1}}\right) \)


Three water samples namely river water, untreated sewage water and secondary effluent discharged from a sewage treatment plant were subjected to BOD test. The samples were labelled \( A, B \) and \( C ; \) but the laboratory attendant did not note which was which
The BOD values of the three samples \( A, B \) and \( C \) were recorded as \( \mathbf{2 0} \boldsymbol{m g} / \boldsymbol{L}, \mathbf{8 m g} / \boldsymbol{L} \) and \( \mathbf{4 0 0} \boldsymbol{m g} / \boldsymbol{L} \)
respectively. Which sample of the water is most polluted? Can you assign the correct label to each assuming the river water is relatively clean?


Which of the following ore contains both copper and iron?
A. Cuprite
B. Chalcocite
c. chalcopyrite
D. Malachite


Select whether the following combinations of reactants will react by
substitution \( \left(S_{N^{1}} \text { Or } S_{N^{2}} \) mechanism) \right.
elimination \( \left(E_{1} \text { or } E_{2} \) mechanism) \right.
A \( \cdot\left(S_{N^{1}}\right) \)
в. \( \left(S_{N^{2}}\right) \)
\( c \cdot E_{1} \)
D. \( E_{2} \)


A cell of emf \( ^{\prime} E^{\prime} \) and internal resistance
\( r^{\prime} \) draws a current \( ^{\prime} I^{\prime} . \) Write the relation
between terminal voltage \( ^{\prime} V^{\prime} \) in terms
of \( \boldsymbol{E}, \boldsymbol{I} \) and \( \boldsymbol{r} \)


A product costs a company Rs 60 to manufacture, and it sold the product to a dealer for Rs \( 70, \) who in turn sold it to
a shopkeeper for Rs \( 85, \) who sold to a
customer for Rs \( 102 . \) What is the
percentage of profit for the company and who made the highest profit on
selling the product?


A constant current of \( 30 A \) is passed
through an aqueous solution of \( N a C l \)
for a time of \( 1.00 h \). What is the volume
of \( C l_{2} \) gas at STP produced?
A . \( 30.00 L \)
B . \( 25.08 L \)
c. \( 12.54 L \)
D. \( 1.12 L \)


\( H_{2} O_{2} \) is an oxidant when it reacts with:
\( A \)
acidified \( K_{4}\left[\mathrm{Fe}(C N)_{6}\right. \)
B. alkaline \( K_{3}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right] \)
\( c \cdot C l_{2} \)
D. acidified \( K M n O_{4} \)


Which of the following shows the Lewis
dot formula for \( \boldsymbol{C O}_{2} \) ?
\( A \cdot: \ddot{O}:: C:: \ddot{O} \)
в. \( : \ddot{O}: \ddot{C}:: \ddot{O} \)
\( c \ldots \ddot{o}:: C: \ddot{O} \)
\( \mathrm{D} \cdot: \ddot{O}: C: \ddot{O} \)


The general electronic configuration of transition element is \( (\boldsymbol{n}-\mathbf{1}) \boldsymbol{d}^{1-\mathbf{1 0}} \boldsymbol{n s}^{\mathbf{1 - 2}} \)
A . True
B. False