The area common to the circle \( x^{2}+ \)
\( y^{2}=16 a^{2} \) and the parabola \( y^{2}=6 a x \) is
A \( \cdot 4 a^{2}(8 \pi-\sqrt{3}) \)
B. \( \frac{4 a^{2}(4 \pi+\sqrt{3})}{3} \)
c. \( \frac{8 a^{2}(4 \pi-\sqrt{3})}{5} \)
D. none of these


The specific latent heat of fusion of ice
is:
A \( \cdot 4.2 J g^{-1} 0 C^{-1} \)
B. 4200 Jkg \( ^{-10} C^{-1} \)
c. з36 \( J g^{-1} \)
D. 336,000 Jg \( ^{-1} \)


Aluminium \( \left(\boldsymbol{\alpha}=\mathbf{4} \times \mathbf{1 0}^{-\mathbf{3}} \boldsymbol{K}^{-1}\right) \)
resistance of \( 60 \Omega \) and carbon
\( \left(\alpha=0.5 \times 10^{-3} K^{-1}\right) \) resistance \( 40 \Omega \)
are connected in parallel. The combination is heated. The effective
resistance is
A. Greater than \( 24 \Omega \)
B. Less than \( 24 \Omega \)
c. Greater than \( 40 \Omega \)
D. Greater than \( 100 \Omega \)


Which of the following is correct for \( \boldsymbol{S} \boldsymbol{F}_{4} \)
?
A. It has a see-saw shape
B. It has two lone pairs of electrons
C. It has a square planar geometry
D. It has five bonding pairs


Choose the correct answer among the alternatives given :
2-Chloro-2methylpropane on reaction
with alc. \( K O H \) gives \( X \) as the product \( x \) is \( ? \)
A. but-2-ene
B. 2-methylbut-1-ene
c. 2-methylprop-1-ene
D. 2-methylbutan-2-01


The rubber cord of a catapult has cross-
section area \( 2 m m^{2} \) and a total
unstretched length \( 15 \mathrm{cm} \). It is stretched
to \( 18 c m \) and then released to project a
particle of mass \( 3 g \). Calculate the
velocity of projection if \( Y \) for rubber is
\( 8 \times 10^{8} N / m^{2} \)
A \( .56 .5 m s^{-1} \)
B. \( 10 m s^{-1} \)
\( \mathrm{c} \cdot 20 \mathrm{ms}^{-1} \)
D. \( 40 m s^{-1} \)


How many unpaired electrons are there
in \( \mathrm{Ni}^{2+} \) ?
\( A \cdot O \)
B. 2
\( c \cdot 4 \)
D. 8


Find the radius of a \( H e^{+} \) ion in the
state \( \boldsymbol{n}=\mathbf{1} \)


Three \( 100 W, 150 V \) lamps are
connected across \( 150 V \) line.Find
voltage across each and power
disseminate in 3 bulbs.


A force of \( 600 N \) acts on the bullet of the
\( \operatorname{area~of~cross~section~} 0.6 \mathrm{cm}^{2} . \) The
pressure exerted is \( 10^{x} \). What is \( X ? \)


The coefficient of thermal expansion, \( \alpha \)
is nearly constant for a liquid \( \boldsymbol{\alpha}= \) \( \frac{1}{V}\left(\frac{d V}{d T}\right)_{P} \)
At \( 293 K \) and \( 1 a t m \) for water \( \alpha= \)
\( 2.1 K^{-1} \)
What is the approximate work done when 1 mole of liquid is heated from \( 288 K \) to \( 298 K \) at 1 at \( m \) (Molar volume
of liquid \( =18 m l \) )?
A. \( -78.25 k J \)
в. \( 78.15 J \)
c. \( -37.8 J \)
D. \( -83.14 J \)


\( s_{1} \) and \( s_{1} \) are two sources of sound
emitting sine waves. The two sporces
are in phase. The source emittied by the two sources interfere at point F. The
waves of wavelength:
A . \( 1 \mathrm{m} \) will result in constructive interference
B . \( \frac{2}{3} m \) will result in constructive interference
c. \( 2 \mathrm{m} \) will result in destructive interference
D. \( 4 \mathrm{m} \) will result in destructive interference


What do you mean by refraction of light
? What is the basic cause of refraction?


Synergic back-bonding is absent in transition metal carbonyls.
If true enter 1 , else enter 0 .


f \( 20: 28=x: 7=10: y \)
The values of \( x \) and \( y \) in the box
respectively are
A .5,14
в. 14,5
\( c .8,10 \)
D. 10,8


Name the process represented below:
\( (\text { a })_{92}^{235} U+_{0}^{1} n \longrightarrow_{56}^{141} B a+_{36}^{92} K r+ \)
\( \mathbf{3}_{0}^{1} \boldsymbol{n}+\mathbf{2 0 0} \boldsymbol{M} \boldsymbol{e} \boldsymbol{V} \)
(b) \( _{1}^{2} \boldsymbol{H}+_{1}^{3} \boldsymbol{H} \longrightarrow_{2}^{4} \boldsymbol{H} \boldsymbol{e}+_{0}^{1} \boldsymbol{n}+ \)
\( \mathbf{1 7 . 6} M e V \)
\( (c)_{29}^{63} C u+_{2}^{4} H e+400 M e V \longrightarrow_{17}^{37} \)
\( \boldsymbol{C l}+\mathbf{1 4}_{\mathbf{1}}^{\mathbf{1} \boldsymbol{H}}+\mathbf{1 6}_{\mathbf{0}}^{\mathbf{1}} \boldsymbol{n} \)
\[
\begin{array}{rl}
10 & \mathrm{B}+_{2}^{4} \mathrm{He} \longrightarrow_{7}^{13} \mathrm{N}+_{0}^{1} \mathrm{n} \\
& _{6}^{13} \mathrm{C}+_{1}^{0} \mathrm{e}
\end{array}
\]


A rigid body in the shape of a \( V \) has two equal arms made of uniform rods.What must the angle between the two rods be so that when the body is suspended from one end, the other arm is horizontal?
\( ^{A} \cdot \cos ^{-1}\left(\frac{1}{3}\right) \)
B. \( \cos ^{-1}\left(\frac{1}{2}\right) \)
c. \( \cos ^{-1}\left(\frac{1}{4}\right) \)
D. \( \cos ^{-1}\left(\frac{1}{6}\right) \)


Differentiate the following functions
with respect to \( x \) :
If \( y=\tan ^{-1}\left(\frac{2 x}{1-x^{2}}\right), x>0, \) prove
that \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\frac{\boldsymbol{4}}{\boldsymbol{1}+\boldsymbol{x}^{2}} \)


If \( \boldsymbol{x}^{m} \cdot \boldsymbol{y}^{n}=(\boldsymbol{x}+\boldsymbol{y})^{\boldsymbol{m}+\boldsymbol{n}}, \) then \( \frac{d \boldsymbol{y}}{d \boldsymbol{x}} \) is :
A \( \cdot \frac{y}{2 x} \)
в. \( \frac{2 y}{x} \)
\( c \cdot-\frac{y}{x} \)
D. \( \frac{y}{x} \)


Separation of o- nitrophenol from the mixture of \( o \) - and \( p \) - nitrophenol can be achieved by:
This question has multiple correct options
A. sublimation
B. steam distillation
c. crystallisation.
D. fractional distillation


Define electromagnetic induction?


The only plant cells without nucleus among the following is
A. Cambium cells
B. Root hair
c. companion cells
D. Xylem vessels


During the discharge of a lead storage battery, the density of sulphuric acid fell from 1.294 to \( 1.139 \mathrm{gm} L^{-1} \). Sulphuric acid
of density \( 1.294 \mathrm{gm} L^{-1} \) is \( 39 \% \) by weight
and that of density 1.139 gm \( L^{-1} \) is \( 20 \% \) by
weight. The battery holds 3.5 litres of acid and the column practically remained
constant during the discharge.

Calculate the number of ampere-hours for which the battery must have been used. The charging and discharging reactions are :
\( P b+S O_{4}^{2-} \rightarrow P b S O_{4}+2 e^{-}(\text {charging }) \)
\( P b O_{2}+4 H^{+}+S O_{4}^{2-}+2 e^{-} \rightarrow P b S O_{4}+ \)
\( 2 H_{2} O(\text { discharging }) \)
\( \mathbf{A} \cdot 297 \)
B. 189
c. 274
D. 200


The sum of the first three terms of an
increasing geometric progression is 13 and their product is \( 27 . \) Calculate the sum of the first five terms of the
progression.


A rod of length \( l \) rotates with a uniform
angular velocity \( \omega \) rad/s about an axis passing through its middle point but normal to its length in a uniform magnetic field of induction \( B \)
with its direction parallel to the axis of rotation. The induced emf between the
two ends of the rod is :
\( ^{A} \cdot \frac{B l^{2} \omega}{2} \)
в. zero
c. \( \frac{B l^{2} \omega}{4} \)
D \( \cdot 2 B l^{2} \omega \)


Find the sum of:
1. The first 50 multiples of 11
2. The multiples of 7 between 0 and
\( \mathbf{1 0 0 0} \)
3. The integers between 1 and 100 which are not divisible by 3 and 7


How many significant figures are there in \( 0.030100 \times 10^{6} ? \)
\( A \)
B. 3
\( c .5 \)
D.


\( \boldsymbol{y}=\boldsymbol{a} \boldsymbol{x}^{2}+\boldsymbol{b}, \) a,b being constants.
A \( \cdot x \frac{d^{2} y}{d x^{2}}-\frac{d y}{d x}=0 \)
в. \( x \frac{d^{2} y}{d x^{2}}+\frac{d y}{d x}=0 \)
c. \( 2 x \frac{d^{2} y}{d x^{2}}-\frac{d y}{d x}=0 \)
D. \( x \frac{d^{2} y}{d x^{2}}-2 \frac{d y}{d x}=0 \)


The difference between the different
permutation of the word BANANA and rank of the word BANANA is
A. 60
B. 35
\( c \cdot 24 \)
D. None of these


Write the fraction whose numerator is one and equivalent to \( \frac{\mathbf{9}}{\mathbf{3 6}} \) ?


A compound which does not give a positive test inLassaigne's testfor nitrogen is :
A . Glycine
B. Hydrazine
c. urea
D. Phenyl hydrazine


Barbiturates acts as:
A. hypnotic i.e., sleep producing agents
B. non-narcotic analgesics
C. activator of neurotransmitters
D. antiallergic drugs


Which of the following solutions shows Tyndall effect?
A. A solution of common salt
B. A solution of sodium carbonate
c. starch solution
D. sugar solution


Explain the process used to convert
carbonates in to oxides.


Two monochromatic (wavelength \( =\boldsymbol{a} / \mathbf{5} \)
and coherent source of
electromagnetic waves are placed on the \( x \) -axis at the point \( (2 a, 0) \) and
\( (-a, 0) . \) A detector moves in a circle of radius \( R(>>2 a) \) whose Centre is at
the origin. The number of maximas detected during one circular revolution by the detector are:
A . 60
в. 15
c. 64
D. None


Assertion (A): Stability of \( N H_{3} \) is
greater than \( \boldsymbol{P H}_{3} \)
Reason (R): M - H bond energy increases down the group in the hydrides of pnicogens.
A. Both (A) and (R) are true and (R) is the correct explanation of (A)
B. Both (A) and (R) are true and (R) is not the correct explanation of (A)
\( c \cdot(A) \) is true and
(R) is false
D. (A) is false but (R) is true


A car states from rest and acquires a velocity of \( 54 k m / h r \) in 2 minutes. Find(i) acceleration and(ii) distance
travelled by car in this time. Assume, that the motion of the car is uniform.


Floret is
A. Small fruit
B. Small flower
C. Small sessile flower
D. Small neuter flower


toppr LoGin Joln Now
Q Type your question
two classes of alphabets as in the two matrices given below. The columns and
rows of Matrix I are numbered from 0 to
4 and that of Matrix II are numbered
from 5 to \( 9 . \) A letter from these matrices
can be represented first by its row and
next by its column, e.g., \( ^{\prime} \boldsymbol{R}^{\prime} \) can be
represented by 04,42 etc., and \( ^{\prime} D^{\prime} \) can
be represented by 57,76 etc. Similarly, you have to identify the set for the word \( \mathrm{ROAD}^{\prime} \) Matrix
1 \begin{tabular}{cc|c|c|c|c}
& 0 & 1 & 2 & 3 & 4 \\
\hline 0 & \( F \) & \( O \) & \( M \) & \( S \) & \( R \) \\
1 & \( S \) & \( R \) & \( F \) & \( O \) & \( M \) \\
2 & \( O \) & \( M \) & \( S \) & \( R \) & \( F \) \\
3 & \( R \) & \( F \) & \( O \) & \( M \) & \( S \) \\
4 & \( M \) & \( S \) & \( R \) & \( F \) & \( O \)
\end{tabular}
Matrix I
\begin{tabular}{cccc|cc}
& 5 & 6 & 7 & 8 & 9 \\
5 & \( A \) & \( T \) & \( D \) & \( I \) & \( P \) \\
6 & \( I \) & \( P \) & \( A \) & \( T \) & \( D \) \\
7 & \( T \) & \( D \) & \( I \) & \( P \) & \( A \) \\
8 & \( P \) & \( A \) & \( T \) & \( D \) & \( I \) \\
9 & \( D \) & \( I \) & \( P \) & \( A \) & \( T \)
\end{tabular}
\( A \)
42,32,49,58
B. 23,32,98,99
\( c \)
11,13,67,69 13,67,69
00
\( D \)


Only few selected noble gas element reacts with halogen, it is:
\( A \cdot A r \)
в. не
c. \( x_{e} \)
D. kr


Chemically similar compounds
differing by \( -C H_{2} \) unit are called?
A. allotrops
B. homologues
\( \mathbf{C} \). isomers
D. tautomers


A compound \( X \) was treated with \( Z n \)
dust with simultaneous heating.This resulted in the formation of an aromatic
compound \( (X) \) and a white powder \( (A) . A \) was found to be insoluble in
water.ldentify correct combination of \( \boldsymbol{X} \)
and \( A \) respectively.
A. Toluene and \( C a O \)
B. Chlorobenzene and \( Z n O \)
c. Phenol and \( C a O \)
D. Phenol and \( Z n O \)


Solve:8 \( \boldsymbol{x}+\mathbf{5}>\mathbf{1 3} \)


When the momentum of a body decreases by \( 10 \% \), its \( \mathrm{K.E.} \) decreases by
A . 20\%
B. 40\%
c. 36\%
D. None of these


\( \ln S O_{2} \) and \( S O_{3}, \) the ratio of weight of oxygen that combines with a fixed
weight of sulphur is \( 2: 3 . \) This
illustrates the law of:
A. constant proportions
B. conservation of mass
c. multiple proportions
D. reciprocal proportions


For the function \( f(x)=a(x-h)^{2}+k \)
which of the following statements is
wrong?
A. The value of \( a \) is negative
B. \( f(x) \) is symmetrical across the line \( y=3 \)
c. The function \( g(x)=\frac{2 x}{3} \) intersects \( f(x) \) at its vertex
D. The value of \( h \) is positive


Magnification for erect and invented
image is
A. \( + \) ve and \( -v e \) respectively
B. - -ve and + ve respectively
\( c .+v e \)
D. \( -v e \)


What is correct 'sequence of Man, taxonomically starting from super family to subfamily
A. Hominoidea, hominidae, homininae
B. Homininae, Hominoidea, hominidae
c. Hominidae, homoninae, Hominoidea
D. Hominoidea, homininae, hominidae


Identify \( (X),(Y) \) and \( (Z) \) in the given
reaction. \( \boldsymbol{X}+\boldsymbol{Y} \stackrel{Z}{\longrightarrow} \boldsymbol{C} \boldsymbol{H}_{3}-\stackrel{\boldsymbol{C} \boldsymbol{H}}{\boldsymbol{3}-\boldsymbol{H} \boldsymbol{y} d r o x y} \boldsymbol{H}-\boldsymbol{C} \boldsymbol{H}_{2}- \)
\( C H O \)
A \( \cdot X=H C H O Y=C H_{3} C H O Z=K O H \)
В . \( X=C H_{3} C H O Y=C H_{3} C H O Z=N a O H \)
c. \( X=C H_{3} C H_{2} \) OH \( Y=H C H O Z=H_{2} S O_{4} \)
D. \( X=C H_{3} C H_{2} C H O Y=H C H O Z= \)Dryether


Find the charge appearing on the inner face of the left plate:
A \( \cdot C V-Q_{1} \)
в. \( C V+Q_{1} \)
c. \( _{C V}-\frac{Q_{1}}{2} \)
D. \( C V \)


Sum of the two binary number
\( (100010)_{2} \) and \( (11011)_{2} \) is
\( \mathbf{A} \cdot(111101)_{2} \)
B. \( (111111)_{2} \)
\( \mathbf{c} \cdot(101111)_{2} \)
D. \( (111001)_{2} \)


Which of the following geometry is not possible when the central atom is
having \( s p^{3} d \) - hybridization?
A. TBP
B. Trigonal planar
c. Linear
D. T-shaped


For the given circuit diagram; the
equivalent resistance across battery is :
\( A .5 \Omega \)
B. \( 10 \Omega \)
\( c .20 \Omega \)
D. \( 15 \Omega \)


A plane electromagnetic wave of frequency \( 25 ~ M H z \) travels in free space along \( x \) -direction. At a particular
point in space and time, electric field
\( \boldsymbol{E}=\mathbf{6 . 3} \boldsymbol{V} \boldsymbol{m}^{-1}, \) the magnitude of
magnetic field B at this point is:
A . \( 1.2 \times 10^{-6} T \)
В . \( 1.2 \times 10^{-8} T \)
c. \( 2.1 \times 10^{-6} T \)
D. \( 2.1 \times 10^{-8} T \)


In the given figure, if AL is the bisector
of \( \Delta B A C, \) then \( A B \) is
\( A .7 c m \)
B. \( 10 \mathrm{cm} \)
\( c .15 c m \)
D. \( 22.50 \mathrm{cm} \)


The value of \( i^{2}+i^{4}+i^{6}+\ldots i^{2(2 n+1)}=? \)
A . -1
B.
\( c \cdot-i \)
\( D \)


Find the angle between the lines whose
direction cosines satisfy the equation \( \ell+\boldsymbol{m}+\boldsymbol{n}=\mathbf{0}, \ell^{2}+\boldsymbol{m}^{2}-\boldsymbol{n}^{2}=\mathbf{0} \)


Two nonideal batteries are connected in
parallel consider the following statements :-
(A) The equivalent emf is smaller than either of the two emfs
(B) The equivalent internal resistance is
smaller than either of the two internal
resistnaces
A. both A and B are correct
B. A is correct but B is wrong
C. b is correct but A is wrong
D. both A and B are wrong


The different colours of litmus in acidic,
neutral and basic solutions are
respectively:
A. red, orange and blue
B. blue, violet and red
c. red, colourless and blue
D. red, violet and blue


Which gas will be adsorbed on a solid to
greater extent?
A. A gas having non polar molecule.
B . A gas having highest critical temperature \( \left(T_{c}\right) \)
c. A gas having lowest critical temperature.
D. A gas having highest critical pressure.


Write a brief account of sericulture.


During meiosis I, the number of chromosomes is
A. Quadrupled
B. Tripledd
c. Doubled
D. Halved


Which among the following compounds will not give effervescence with sodium bicarbonate?
A. \( C_{6} H_{5} C O_{2} H \)
в. \( C_{6} H_{5} S O_{3} H \)
\( \mathbf{c} \cdot C_{6} H_{5} O H \)
D. \( C_{6} H_{3} N_{3} O_{7} \)


According to valence bond theory, the
predicted bond angle for \( \boldsymbol{H}_{2} \boldsymbol{O} \) is:
A \( \cdot 90^{\circ} \)
B. \( 109^{\circ} 28 \)
\( \mathbf{c} \cdot 107^{\circ} 18 \)
D. \( 104^{\circ} 28 \)


Specific heat of a substance depends
on its.
A. Mass
B. Volume
c. Temperature
D. colour


Differentiate between a Scalar and a
Vector quantity.


When \( C \) passes \( A \), where is B?


The \( V \) -I characteristic of a diode is
shown in the figure. The ratio of forward
to reverse bias resistance is :
4.10
\( 3 \cdot 10^{-6} \)
\( c .1 \)
0.10


Construct a \( 2 \times 2 \) matrix \( A=\left[a_{i j}\right] \)
whose elements are given by \( a_{i j}=2 i- \)
\( \boldsymbol{j} \)


The half life of a radioactive substance,
as compared to its mean life, is
A . \( 30 \% \)
B. 60 \%
c. \( 70 \% \)
D. 100 \%


Protein synthesis in an animal cell
occurs
A. Only on the ribosomes present in cytosol
B. On ribosomes present in cytoplasm as well as in mitochondria
c. only on ribosomes attached to the nuclear envelope and endoplasmic reticulum
D. On ribosomes present in the nucleolus as well as in cytoplasm


The number of possible monobromo products is (excluding stereoisomers):
\( A \cdot 4 \)
B. 5
\( c \cdot 8 \)
D. 10


The number of days so that half the population have flu is
\( \mathbf{A} \cdot 50 \)
B. 40
c. 45
D. 25


what is the steam engine?


Which is not a method of preparing
carbon monoxide on a commercial
scale?
\( \left.\text { A }\left.\cdot C_{(} S\right)+H_{2} O_{(g)} \frac{473-1273 K}{\longrightarrow} C O_{(} g\right)+H_{2(g)} \)
B . \( \left.2 C(s)+O_{2(g)}+4 N_{2(g)} \stackrel{1273 K}{\longrightarrow} 2 C O_{(} g\right)+4 N_{2(g)} \)
\( \mathbf{c} \cdot 2 C_{(s)}+O_{2(g)} \stackrel{\Delta}{\longrightarrow} 2 C O_{(g)} \)
D. \( H C O O H \frac{373 K}{\operatorname{coc} H F s O_{1}} \rightarrow H_{2} O+C O \)


The aluminium metal is obtained by the
reduction of aluminium oxide with:


The value of the determinant
\( \left[\begin{array}{lll}x^{2} & 1 & y^{2}+z^{2} \\ y^{2} & 1 & z^{2}+x^{2} \\ z^{2} & 1 & x^{2}+y^{2}\end{array}\right] \) is:
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( x^{2}+y^{2}+z^{2} \)
c. \( x^{2}+y^{2}+z^{2}+1 \)
D. None of the above


Location of the double bond in
unsaturated hydrocarbons can be detected by
A. Ozonolysis reaction
B. Baeyers reagent
c. \( B r_{2} \) in \( C C l_{4} \)
D. Tollen's reagent


A ray deviates at \( 90^{\circ} \) after suffering reflection from a mirror. The angle of incidence is:
A \( \cdot 90^{\circ} \)
B. 30
\( c \cdot 60 \)
\( D \cdot 45 \)


What is the angle of incidence of a ray if
the reflected ray is at an angle of \( 90^{\circ} \) to the incident ray?


Are the points (1,1),(2,3) and (8,11) collinear?
A. collinear
B. Non collinear
c. coplaner
D. None of above


\( \boldsymbol{A}: \mathbf{2} \boldsymbol{C}_{\boldsymbol{6}} \boldsymbol{H}_{\boldsymbol{5}} \boldsymbol{C H} \boldsymbol{O}+\boldsymbol{K} \boldsymbol{O H} \longrightarrow \)
\( \boldsymbol{C}_{6} \boldsymbol{H}_{5} \boldsymbol{C O O K}+\boldsymbol{C}_{6} \boldsymbol{H}_{5} \boldsymbol{C H}_{2} \boldsymbol{O H} \)
\( \boldsymbol{B}: \mathbf{3} \boldsymbol{C l}_{2}+\boldsymbol{6} \boldsymbol{K O H} \longrightarrow \mathbf{5} \boldsymbol{K} \boldsymbol{C l}+ \)
\( \boldsymbol{K} \boldsymbol{C l O}_{3}+\boldsymbol{3} \boldsymbol{H}_{2} \boldsymbol{O} \)
Select the correct statement.
A. Both are redox reactions
B. Both are disproportionation reaction
c. \( A \) is a disproportionation reaction and \( B \) is a redox reaction
D. \( A \) is a redox reaction and \( B \) is a disproportionation reaction.


Identyfy oxidation and reduction process for the reaction-
\( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{s})+\boldsymbol{F}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{H} \boldsymbol{F}(\boldsymbol{g})+\boldsymbol{H} \boldsymbol{O} \boldsymbol{F}(\boldsymbol{g}) \)


Using both Charles's law and Boyle's
law, we get :
A \( \cdot \frac{T V}{P}=K \)
В. \( \frac{V P}{T}=K \)
c. \( \frac{T P}{V}=K \)
D. none of the above


\( 30 g m \) of ethanoic acid present in 100 \( g m \) of water, determine molality of ethanoic acid in water?


A garden is 24 m long and 14 m wide.
There is a path \( 1 ~ m \) wide outside the
garden along its sides. If the path is to be constructed with square marble tiles \( 20 \mathrm{cm} \times 20 \mathrm{cm}, \) find the number of tiles
required to cover the path?
A. 1800
в. 200
c. 2000
D. 2150


A metal oxide has the formula \( X_{2} O_{3} \). It
can be reduced by hydrogen to give free
metal and water. \( 0.1596 g \) of metal oxide
requires \( 6 m g \) of hydrogen for complete
reduction. The atomic mass of metal in
amu is:
A . 15.58
B. 155.8
c. 5.58
D. 55.8


Q Type your question
unırormiy aıstrıbutea tnrougnout ırs
volume

Which of the following expressions
gives the electric field strength at point
\( P, \) a point that lies inside the sphere
and is a distance \( r \) from the center of
the sphere?
\( ^{\mathrm{A}} \cdot_{E}=\frac{Q r}{4 \pi \epsilon_{0} R^{3}} \)
B. \( \quad E=\frac{Q}{4 \pi \epsilon_{0} r^{2}} \)
c. \( E=0 \) (Point \( P \) is inside of a conductor.
'D \( \quad E=\frac{3 Q r}{4 \pi \epsilon_{0} R^{3}} \)
\( E=\frac{3 Q}{4 \pi \epsilon_{0} r^{3}} \)


the radius of a sphere increases at a rate of \( 2 \mathrm{cm} / \mathrm{sec} . \) Find the rate at which
its volume and area increases when
radius is \( 4 \mathrm{cm} \)


If \( a_{1}, a_{2}, \dots, a_{n} \) are positive real numbers
whose product is a fixed number \( c \), the
minimum value of \( \boldsymbol{a}_{\mathbf{1}}+\boldsymbol{a}_{\mathbf{2}}+\ldots+ \)
\( \boldsymbol{a}_{\boldsymbol{n}-\mathbf{1}}+\boldsymbol{2} \boldsymbol{a}_{\boldsymbol{n}} \) is
A \( \cdot n(2 c)^{1 / n} \)
B \cdot \( (n+1) c^{1 / n} \)
\( \mathbf{c} \cdot 2 n c^{1 / n} \)
D・ \( (n+1)(2 c)^{1 / n} \)


Statement 1: A wheel moving down frictionless inclined plane will slip and not roll on the plane. Statement 2 : It is the frictional force
which provides a torque necessary for a body to roll on a surface.
A. Statement 1 is false, Statement 2 is true
B. Statement 1 is true, Statement 2 is true; Statement 2 is correct explanation for Statement 1
c. statement 1 is true, statement 2 is true; Statement 2 is not a correct explanation for Statement
D. Statement 1 is true, Statement 2 is false


Assertion
In the coagulation of negatively charged arsenic sulphide sol, the coagulating power decreases in the order \( A l^{3+}> \)
\( \boldsymbol{B} \boldsymbol{a}^{2+}>\boldsymbol{N} \boldsymbol{a}^{+} \)
Reason
Generally, greater the valency of coagulating ion, the greater is its power
of coagulation.
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 incorrect but Reason is correct
D. Both Assertion and Reason are correct


\( 0.301 g \) of an organic compound gave \( 0.282 g \) of \( A g B r \) by Carius method. The
\( \% \) of Br is:
A . 39.87
B. 42.34
c. 36.20
D. 30.24


The hardness of a water sample
containing \( 10^{-3} \mathrm{M} M g S O_{4} \) expressed
as \( C a C O_{3} \) equivalents(in ppm) is
[molar mass of \( M g S O_{4} \) is 120.37 g/mol]


Two distinct lines in a plane
A. always intersect
B. always either intersect or are parallel
C . always have two common points
D. none of these


An aqueous solution involving charge species is used to melt ice on a frozen
walkway. The most effective melting at temperatures below the freezing point of water will be produced by an aqueous solution of which of the following?
A. Pure aluminum
B. Benzene
c. Carbon dioxide
D. Potassium chloride


Which formula represents an alkene?
A \( . C H_{4} \)
в. \( C_{2} H_{4} \)
\( \mathbf{c} \cdot C_{2} H_{6} \)
D. \( C_{2} H_{5} O H \)


\( \int x^{3} \tan ^{-1} x d x \)


An ideal gas undergoes a
thermodynamic cycle as shown in
figure. Which of the following
statements are correct?
A. Straight line \( A B \) cannot pass through \( O \)
B. During process \( A B \), temperature decreases while during process \( B C \) it increases
C. During process \( B C, \) work is done by the gas against external pressure and temperature of the gas increases.
D. During process \( C A \), work is done by the gas against external pressure and heat supplied to the gas is exactly equal to this work.


Which one of the following statements
is correct?
A. The planets twinkle at night due to atmospheric refraction of light
B. The stars appear higher in the sky than they actually are, due to scattering of light
C. The blue colour of sky is due to scattering of light
D. The rainbow is produced by the reflection of white sunlight by water drops in the atmosphere.


If the curve \( y=|x-3| \) touches the parabola \( \boldsymbol{y}^{2}=\boldsymbol{\lambda}(\boldsymbol{x}-\mathbf{4}), \boldsymbol{\lambda}>\mathbf{0}, \) then
latus rectum of the parabola, is
\( A \cdot 2 \)
B. 4
\( c \cdot 8 \)
\( D \cdot 16 \)


Two bodies move uniformly towards each other. They become \( 4 m \) nearer in
every 1 second. After crossing each
other they get \( 4 m \) farther every 10
second. If their speeds are constant,
their values would be
A . \( 1.8 m s^{-1}, 1.8 m s^{-1} \)
B . \( 2.2 m s^{-1}, 2.0 m s^{-1} \)
c. \( 2.2 m s^{-1}, 1.8 m s^{-1} \)
D. \( 1.5 m s^{-1}, 2.5 m s^{-1} \)


If each observation of a dist., whose
variance is \( \sigma^{2}, \) is multiplied by \( \lambda, \) then
the \( S . D . \) of the new new observations is
A . \( \sigma \)
B. \( \lambda \sigma \)
c. \( |\lambda| \sigma \)
D. \( \lambda^{2} \sigma \)


Internal reflections of light is prevented
in human eye by:
A . iris
B. pupil
c. choroid
D. blind spot


Evaluate \( \int \frac{d x}{\sqrt{5 x^{2}-2 x}} \)


Assertion: When an electric current is
passed through the copper sulphate electrolyte, the impure copper anode gradually dissolve and pure copper is deposited on the cathode. Reason: Pure metals are deposited in electroplating techniques.
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false


Aldehydes upto are colourless
liquids.
A \( . C_{11} \)
в. \( C_{12} \)
\( c \cdot C_{13} \)
D. \( C_{1} \)


The area of cross-section of the wider
tube shown in figure is \( 800 \mathrm{cm}^{2} . \) If \( \mathrm{a} \)
mass of \( 12 \mathrm{kg} \) is placed on the massless piston, the difference in heights h in the level of water in the two tubes is :
\( A \cdot 10 \mathrm{cm} \)
B. 6 cm
\( c \cdot 15 \mathrm{cm} \)
D. \( 2 \mathrm{cm} \)


Assertion
In the metallurgy of iron, limestone is
added to the ore
Reason
In the metallurgy of iron, limestone
\( \left(\mathrm{CaCO}_{3}\right) \) acts as a flux and forms
calcium silicate \( \mathrm{CaSiO}_{3}(\mathrm{slag}) \)
Read the above assertion and reason
and choose the correct option regarding
¡t.
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


Find \( x \), if the given numbers are in A.P. 5
\( (x-1), 0 \)


The amount of energy required to change \( 1 k g \) of a solid into liquid at atmospheric pressure at its melting point is known as
A. latent heat of fusion
B. latent heat of boiling
c. latent heat of freezing
D. melting energy


Use Gauss's law to show that due to a
uniformly charged spherical shell of radius \( \mathrm{R} \), the electric field at any point
situated outside the shell at a distance
r from its centre is equal to the electric field at the same point, when the entire charge on the shell were concentrated
at its centre. Also plot the graph showing the variation of electric field
with \( r, \) for \( r \leq R \) and \( r \geq R \)


Which of the following equations
represents reducing property of \( \boldsymbol{S O}_{2} \) ?
A \( \cdot 2 H_{2} S+S O_{2} \rightarrow 3 S+2 H_{2} O \)
в. 3 Fe \( +S O_{2} \rightarrow 2 F e O+F e S \)
c. \( K_{2} C r_{2} O_{7}+S O_{2}+H_{2} S O_{4} \rightarrow K_{2} S O_{4}+C r_{2}\left(S O_{4}\right)_{3}+ \)
\( H_{2} O \)
D. All of these


The area bounded by the curve \( y= \) \( \sin ^{-1} x \) and \( \operatorname{lines} x=0,|y|=\frac{\pi}{2} \) is 2
sq.unit
A . True
B. False


The molarity of a NaOH solution by dissolving \( 4 g \) of it on \( 250 m L \) water is:
A \( .0 .4 M \)
B. \( 0.8 M \)
c. \( 0.2 M \)
D. \( 0.1 M \)


If the quotient on dividing, \( 8 x^{4}-2 x^{2}+ \)
\( 6 x-7 \) by \( 2 x+1 \) is \( 4 x^{3}+p x^{2}-q x+3 \)
then find \( \boldsymbol{q}-\boldsymbol{p} \)


An electron with an initial speed of
\( 4.0 \times 10^{6} m s^{-1} \) is brought to rest by an
electric field. The mass and charge of an
electron are \( 9 \times 10^{-31} \mathrm{kg} \) and \( 1.6 \times \)
\( 10^{-19} \mathrm{C}, \) respectively. Identify the correct
statement.
A. The electron moves from a region of lower potential to higher potential through a potential difference of 11.4
\( v \)
B. The electron moves from a region of higher potential to lower potential through a potential difference of \( 11.4 \mu \mathrm{V} \)
C. The electron moves from a region of lower potential to higher potential through a potential difference of \( 45 \mathrm{v} \)
D. The electron moves from a region of higher potential to lower potential through a potential difference of 45
\( V \)


Take some clean iron nails and place them in the three test tubes prepared as
under:

Test tube A: Contains boiled water and a
thin layer of oil

Test tube B: Contains a small cloth bag
containing soda lime Test tune C: Contains ordinary water. Some nails are kept under water and
some more are suspended above the
water surface
All the test tubes are tightly closed after
placing the nails. After some time what
will you observe?
This question has multiple correct options
A. Nail A rusts
B. Nail B rusts
C. Nail C rusts
D. Nail A does not rust


Say true or false. Every solution of the equation is a point on the line representing it.
A. True
B. False


Which of the following statements(s)
is/are correct?
This question has multiple correct options
\( \mathbf{A} \cdot B_{2} H_{6} \) is non-planar
B. \( B_{2} H_{6} \) is polar
\( \mathbf{C} \cdot B_{2} H_{6} \) is \( e^{-} \) deficient
D. \( B_{2} H_{6} \) has two \( 3 C-2 e^{-} \) bond


The set of all points of differentiability of the function \( \mathbf{f}(\mathbf{x})=\frac{\sqrt{\mathbf{x}+\mathbf{1}}-\mathbf{x}}{\sqrt{\mathbf{x}}} \) for \( \mathbf{x} \)
\( \neq 0 \) and \( \mathrm{f}(0)=0 \) is
\( \mathbf{A} \cdot(-\infty, \infty) \)
B. \( [0, \infty) \)
\( c \cdot(0, \infty) \)
D. \( (-\infty, \infty) \sim\{0\} \)


Assertion
\( \boldsymbol{K}_{2} \boldsymbol{C r}_{2} \boldsymbol{O}_{7} \) is generally preferred over
\( N a_{2} C r_{2} O_{7} \) in volumetric analysis
although both are oxidizing agents.
Reason
\( N a_{2} C r_{2} O_{7} \) is deliquescent in nature.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


An electron is moving in a uniform
horizontal electric field. If the
acceleration of electron is \( 45^{\circ} \)
downward to the horizontal, then the field intensity in newton/coloumb will
be


In sun, the important source of energy
is
A. proton-proton cycle
B. carbon-nirtogen cycle
c. carbon-caron cycle
D. nitrogen-nitrogen cycle


Assertion
Boron can only form \( \left[\boldsymbol{B} \boldsymbol{F}_{4}\right]^{-}, \) whereas
aluminum forms \( \left[A l F_{6}\right]^{3-} \)
Reason
The first member of a group of elements in the \( s- \) and \( p- \) blocks shows
anomalous behavior
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 one roots of the polynomial \( k x^{2}- \)
\( 15 x+18=0 \) is 2 then \( k= \)


Weak zones of plates are also known as:
A. seismic zones
B. faultzones
c. danger zones
D. both A and B


The three laws of planetary motion were given by:
A. Einstein
B. Kepler
c. copernicus
D. Tycho Brahe


Which of the following are correct?
This question has multiple correct options
A. Silica gel adsorbs \( H_{2} O_{2} \)
B. Anhydrous \( C a C l_{2} \) absorbs \( \mathrm{H}_{2} \mathrm{O} \)
C. Gas masks works on the principle of selective adsorption.
D. zeolites are shape selective catalyst and water softners


A catalyst decrease \( E_{a} \) from \( 100 \mathrm{kJ} \)
\( m o l^{-1} \) to \( 80 \mathrm{kJ} \) mol\( ^{-1} . \) At what
temperature the rate of reaction in the absence of the catalyst at \( 500 \mathrm{K} \) will be equal to rate reaction in the presence of the catalyst:
\( A \cdot 400 K \)
B. 200 K
c. \( 625 \mathrm{k} \)
D. None of these


If \( \boldsymbol{P}(\boldsymbol{n})=\mathbf{1}+\mathbf{2}+\mathbf{3}+\cdots+\boldsymbol{n} \) is a
perfect square, \( N \) is less than 100 , then
possible values of \( n \) is/are
A. only 1
B. 1 and 8
c. only 8
D. 1,8,49


Assertion
Vertebrate blood can carry larger
volumes of \( \boldsymbol{O}_{2} \% \)
Reason
The presence of respiratory pigment in
blood enables it to carry more \( O_{2} \) than
the same blood could carry without it.
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


Identify the correct sequence of taxonomical categories?
(a) Species - Order - Phylum - Kingdom
(b) Genus - Species - Order - Kingdom
(c) Species - Genus - Order- Phylum


\( C H_{3} C O O H \) is titrated with \( N a O H \)
solution. Which of the following
statement is true?
A. Conductance decreases upto equivalence point, after which it increases.
B. conductance increases upto equivalence point, after which it decreases.
c. conductance first increases (but not rapidly) upto equivalence point and then increases rapidly after equivalence point.
D. None of the above


A body is dropped from a certain height.
When it loses \( U \) amount of its energy it
acquires a velocity' \( v^{\prime} . \) The mass of the
body is:
A \( \cdot 2 U / v^{2} \)
B \( \cdot 2 v / U^{2} \)
c. \( 2 v / U \)
D. \( U^{2} / 2 v \)


Convert in \( \frac{\boldsymbol{p}}{\boldsymbol{q}} \) form:
(i) \( 0 . \overline{47} \)
(ii) \( 0 . \overline{001} \)
(iii) \( 0 . \overline{9} \)
(iv) \( 2.3 \overline{5} \)


The first steps of \( S N^{1} \) and \( S N^{2} \)
reactions are, respectively:
A. Both exothermic
B. Both endothermic
c. Endothermic and exothermic
D. Exothermic and endothermic


Gases referred to as 'green house gases'
are
\( \mathbf{A} \cdot \mathrm{CO}_{2}, \mathrm{O}_{2}, \mathrm{NO}_{2}, \mathrm{NH}_{3} \)
B. Chlorofluoro carbon, \( \mathrm{CO}_{2}, \mathrm{NH}_{3}, \mathrm{N}_{2} \)
\( \mathbf{C} \cdot \mathrm{CH}_{4}, \mathrm{N}_{2}, \mathrm{CO}_{2}, \mathrm{NH}_{3} \)
D. Chlorofluoro carbon, \( \mathrm{CO}_{2}, \mathrm{CH}_{4}, \mathrm{NO}_{2} \)


In young's double slit experiment \( \beta \) is
the fringe width and \( I_{o} \) is the intensity of the central bright fringe. What will be the intensity at a distance \( x \) from the central bright fringe?
\( \mathbf{A} \cdot_{\mathrm{l}_{o}} \cos \left(\frac{x}{\beta}\right) \)
B \( \cdot \cos ^{2}\left(\frac{x}{\beta}\right) \)
\( ^{\mathrm{c}} \cdot_{1_{0} \cos ^{2}}\left(\frac{\pi x}{\beta}\right) \)
D. \( \left(\frac{I_{o}}{4}\right) \cos ^{2} \frac{\pi x}{\beta} \)


The point for the curve \( y=x e^{x} \) is
A. \( x=-1 \) is minimum
B. \( x=0 \) is minimum
c. \( x=-1 \) is maximum
D. \( x=0 \) is maximum


Which is not a carbon compound?
This question has multiple correct options
A. woodd
B. Chalk
c. Paper
D. Cement


Assertion
Heavier bodies fall with greater
acceleration.
Reason
Gravitational force is stronger on
heavier bodies.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The actinide contraction is due to:
A. perfect shielding of \( 5 f \) election
B. imperfect shielding of \( 4 f \) election
C. imperfect shielding of \( 5 f \) electron
D. perfect shielding of \( 4 f \) election


The area where medullary sheath is absent in the nerve fibre is
A. Nissl granules
B. Schwann cells
c. Node of Ranvier
D. Schwann node


The magnetic moment of an ion is close to \( 36 \times 10^{-24} \) Joule /Tesla. The number of
unpaired electrons of the ion are
\( A \cdot 4 \)
B. 2
\( c \cdot 1 \)
D. 3


Write the IUPAC name of the compound:
\[
\begin{array}{cc}
\boldsymbol{C H}_{3}-\boldsymbol{C H}-\boldsymbol{C H}_{2}-\boldsymbol{C}-\boldsymbol{C H}_{3} \\
\mid & \| \\
\boldsymbol{O H} & \boldsymbol{O}
\end{array}
\]


Globular proteins are present in?
A. blood
B. eggs
\( c . \) milk
D. all of these


If \( y=a^{\frac{1}{2} \log _{a} \cos x} . \) Find \( \frac{d x}{d} \)


When the angle between two plane
mirrors is \( 60^{\circ} \), how many images will be formed by the mirrors?
A. 5
B. 6
\( c \cdot 7 \)
D. 8


The magnitude of the force between a pair of conductors, each of length 110 \( \mathrm{cm}, \) carrying a current of \( 10 \mathrm{A} \) and separated by a distance of \( 10 \mathrm{cm} \) is
A \( \cdot 55 \times 10^{-5} N \)
B . \( 44 \times 10^{-5} N \)
c. \( 33 \times 10^{-5} N \)
D. \( 22 \times 10^{-5} N \)


Two plane mirrors are at right angles to each other. A man stands between them and combs his hair with his right hand. In how many of the images will he be seen using his right hand :
A. Zero
B. 1
c. 2
D. 3


Find an angle \( \theta, 0<\theta<\frac{\pi}{2}, \) which
increases twice as fast as its sine.


Annual number of deaths in Delhi
believed to be due to air pollution is
A. 1000
B. 5000
\( c .7500 \)
D. 15000


If \( \vec{E}_{a x} \) and \( \vec{E}_{e q} \) represents electric field at a point on the axial and equatorial line of a dipole. If points are at a distance \( r \) from the centre of the dipole,
for \( \boldsymbol{r} \gg \boldsymbol{a} \)
\( \mathbf{A} \cdot \overrightarrow{E_{a x}}=\overrightarrow{E_{e q}} \)
B . \( \overrightarrow{E_{a x}}=-\overrightarrow{E_{e q}} \)
c. \( \overrightarrow{E_{a x}}=-2 \overrightarrow{E_{e q}} \)
D. \( \overrightarrow{E_{e q}}=2 \overrightarrow{E_{a x}} \)


Which of the following reaction produces hydrogen?
A. \( M g+H_{2} O \)
в. \( H_{2} S_{2} O_{8}+H_{2} O \)
\( \mathrm{c} \cdot B a O_{2}+H C l \)
D. \( N a_{2} O_{2}+2 H C l \)


Sacroiliac joint is
A. Movable
B. Immovable
c. Imperfect
D. None of the above


The temperature of a conductor is increased. The product of resistivity and conductivity:
A . increases
B. decreases
c. remains constant
D. may increase or decrease


Q Type your question.
perween I nomson's model ana
Rutherford's model better.
(a) Is the average angle of deflection of \( \alpha \) -particles by a thin gold foil predicted by Thomson's model much less, about
the same, or much greater than that predicted by Rutherford's model?
(b) Is the probability of backward scattering (i.e., scattering of \( \alpha \) -particles
at angles greater than \( 90^{\circ} \) ) predicted by
Thomsons model much less, about the
same, or much greater than that predicted by Rutherfords model?
(c) Keeping other factors fixed, it is found experimentally that for small thickness \( t, \) the number of \( \alpha \) -particles
scattered at moderate angles is proportional to t. What clue does this linear dependence on t provide?
(d) In which model is it completely wrong to ignore multiple scattering for the calculation of average angle of
scattering of \( \alpha \) -particles by a thin foil?


In a step-down transform the turn ratio is 1: 2 and output power is \( 2.2 k W \). if
output current is \( 10 A \) then the value of
input voltage and input current:
A. \( 100 V, 20 A \)
в. \( 110 V, 10 A \)
c. \( 440 V, 5 A \)
D. \( 440 V, 20 A \)


If the value of \( y \) is 3 then find value of \( x \) if \( \frac{1}{x}+\frac{1}{y}=\frac{5}{6} \)


The Poisson's ratio of a material is \( 0.8 . \) If
a force is applied to a wire of this material decreases its cross-sectional
area by \( 4 \%, \) then the percentage increase in its length will be.
A . \( 1 \% \)
B. 2\%
\( c .2 .5 \% \)
D. \( 4 \% \)


Least chemical activity is shown by:
A. nitrogen
B. argon
c. methane
D. oxygen


Non-cyclic photophosphorylation produces
A. NAD
B. NADH
c. NADPH
D. NADP'


The increasing order of the strength of hydrogen bond in the following mentioned linkages is
(i) \( \boldsymbol{O}-\boldsymbol{H}-\boldsymbol{S} \) (ii) \( \boldsymbol{S}-\boldsymbol{H}-\boldsymbol{O} \)
\( \boldsymbol{F}-\boldsymbol{H}-\boldsymbol{O}(\text { iv }) \boldsymbol{F}-\boldsymbol{H}-\boldsymbol{O} \)
A \( \cdot(i)<(i i)<(i v)<(i i i) \)
B. \( (i i)<(i)<(i v)<(i i i) \)
c. \( (i)<(i i)<(i i i)<(i v) \)
D. \( (i i)<(i)<(i i i)<(i v) \)


Which statement below is
false regarding empirical formulas?
A. The empirical formula for butyne is \( \mathrm{CH} \)
B. The empirical formula for ammonia is \( N H_{3} \)
C. The empirical formula of \( C H_{2} O \) is \( C_{6} H_{12} O_{6} \)
D. Ionic compounds are written as empirical formulas
E. The empirical and molecular formulas for methane are the same


Assertion
Derivative of \( \frac{x^{n}-a^{n}}{x-a} \) for some
constant \( n \) is
\( \frac{(n-1) x^{n}-n a x^{n-1}+a^{n}}{(x-a)^{2}} \)
Reason \( \frac{\boldsymbol{d}}{\boldsymbol{x}}\left(\frac{\boldsymbol{u}}{\boldsymbol{v}}\right)=\frac{\boldsymbol{u}^{\prime} \boldsymbol{v}-\boldsymbol{u} \boldsymbol{v}^{\prime}}{\boldsymbol{v}^{2}} \)
where \( u \) and \( v \) are two distinct
functions.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


In a photo-emissive cell with exciting wavelength \( \lambda \), the fastest electron has
speed \( v \). If the exciting wavelength is
changed to \( 3 \lambda / 4 \) the speed of the fastest emitted electron will be :
A \( \cdot v(3 / 4)^{1 / 2} \)
B \( \cdot v(4 / 3)^{1 / 2} \)
c. less than \( v(4 / 3)^{1 / 2} \)
D. greater than \( v(4 / 3)^{1 / 2} \)


Ionic hydrides are usually:
A. good electrical conductors when solid
B. easily reduced
C . good reducing agents
D. liquid at room temperature


A converging lens of focal length \( f_{1} \) is
placed in front of and coaxially with a
convex mirror of focal length \( f_{2} \). Their
separation is d and whole arrangement
is in air. A parallel beam of light
incident on the lens returns as a
parallel beam from the arrangement.
Then
This question has multiple correct options
A. The diameter of incident and emergent beam is the same
B. The distance d can be \( f_{1} \)
C. The distance d can be \( f_{2} \)
D. The distance d can be \( f_{1}-2 f_{2} \)


The height of a barometer filled with a
liquid of density \( 3.4 g / c c \) under normal condition is approximately -
\( \mathbf{A} \cdot 8 m \)
B. \( 5 m \)
\( c .3 m \)
D. \( 1 m \)


The slope of the curve \( y=\sin x+\cos ^{2} x \)
is zero at the point where -
A \( \cdot x=\frac{\pi}{4} \)
B. \( x=\frac{\pi}{2} \)
c. \( x=\pi \)
D. No where


If 6 arithmetic means are inserted
between 1 and \( \frac{9}{2}, \) then find the \( 4^{t h} \) arithmetic mean.


statement-l: rrom a poınt \( \boldsymbol{r} \) on tne
circle with centre \( \boldsymbol{O} \) the chord \( \boldsymbol{P} \boldsymbol{A}=\mathbf{8} \)
\( \mathrm{cm} \) is drawn. The radius of the circle is
\( 24 \mathrm{cm} . \) Let \( P B \) be drawn parallel to \( O A \)
Suppose \( B O \) extended meet \( P A \)
extended at \( M . \) The length of \( M A \) is 9
\( \mathrm{cm} \)
Reason
Statement-2: \( O A \) is a radius of a circle
with centre at \( O . R \) is a point on \( O A \)
through which a chord \( C D \)
perpendicular to \( \boldsymbol{O} \boldsymbol{A} \) is drawn. Let a chord through A meet the chord \( C D \) at
\( M \) and the circle at \( B \). Also \( O S \) is
perpendicular from \( \boldsymbol{O} \) on chord \( \boldsymbol{A} \boldsymbol{B} \). The radius of the circle is \( 18 \mathrm{cm} . R \) is the mid point of \( \boldsymbol{A O} \) and \( \boldsymbol{A} \boldsymbol{M} / \boldsymbol{M} \boldsymbol{B}=\frac{\mathbf{1}}{\mathbf{2}} \)
The length of \( \boldsymbol{O} \boldsymbol{S} \) is \( \boldsymbol{9} \mathrm{cm} \)
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


\( M w_{N}= \) Normal molecular mass of
solute
\( M w_{2}=0 \) bserved molecular mass of
solute from colligative property
measurement.


Alkynes are more reactive than alkene towards catalytic hydrogenation. State whether the statement is True or False


Negetive of Discriminant of the following quadratic equation is :
\( x^{2}-x+1=0 \)


The starting material for the
manufacture of polyvinyl chloride is obtained by reacting HCl with:
A. \( C_{6} H_{6} \)
в. \( C_{2} H_{4} \)
\( \mathbf{c} \cdot C_{2} H_{2} \)
D. \( C H_{3} C l \)


Find the unit vector in the direction of
sum of the vectors (1,1,1),(2,-1,-1) and \( (\mathbf{0}, \mathbf{2}, \mathbf{6}) \)


Aspirin is given for minor heart stroke because
A. It reduces oedema
B. It is a painkiller.
c. It has ability to inhibit the production of blood platelet aggregatess
D. All of the above


Differentiate the following w.r.t. \( x \)
\( \left(2 x^{2}+9\right)^{3} \)
A \( \cdot 4\left(2 x^{2}+9\right)^{2} x \)
B. \( 12\left(2 x^{2}+9\right)^{2} x \)
c. \( 12\left(2 x^{2}+9\right)^{3} x \)
D. \( 6\left(2 x^{2}+9\right)^{2} x \)


The value of \( \cos ^{2} 10^{\circ}- \)
\( \cos 10^{\circ} \cos 50^{\circ}+\cos ^{2} 50^{\circ} \) is?
A \( \cdot \frac{3}{2}\left(1+\cos 20^{\circ}\right) \)
в. \( \frac{3}{4} \)
c. \( \frac{3}{4}+\cos 20^{\circ} \)
D. \( \frac{3}{2} \)


is a couple of layers thick, made of narrow, thin walled and nearly
rectangular cells. It cuts derivatives on both sides. The outer cells differentiate
into while the
inner cells differentiate into
or \( _{\text {十一一一一一一一. }} \) The three together is called

Select the right sequence of words to complete the above given paragraph.
A. Phellogen, cork, phellem, secondary cortex, phelloderm, periderm
B. Phellem, phelloderm, cork, secondary cortex, phellogen, periderm
c. Phellogen, cork, periderm, secondary cortex, phellem, phelloderm
D. Phellem, secondary cortex, periderm, cork, phellogen, phelloderm


Watson and Crick are credited for the
discovery that DNA
A. Is a double stranded helì
B. Is responsible for the synthesis of tRNA
c. Is a carrier of genetic information
D. Provides proof for the \( x \) -y chromosomal theory of sex determination


Which one of the following order is not
in accordance with the property stated
against it?
\( \mathbf{A} \cdot F_{2}>C l_{2}>B r>I_{2}: \) Electronegativity
B \( \cdot F_{2}>C l_{2}>B r_{2}>I_{2}: \) Bond dissociation energy
\( \mathbf{C} \cdot F_{2}>C l_{2}>B r_{2}>I_{2}: \) Oxidizing power
D. \( H I>H B r>H C l>H F \) : acidic property in water


A force acts on a \( 3 g \) particle in such a way that the position of the particle as a function of time is given by \( \boldsymbol{x}=\mathbf{3} \boldsymbol{t}- \)
\( 4 t^{2}+t^{3}, \) where \( x \) is in meters and \( t \) is in
second. The work done during the first 4 second is:
A. \( 490 m J \)
J
в. \( 450 m J \)
\( \mathrm{c} .528 \mathrm{mJ} \)
D. \( 530 m J \)


In the Arrhenius equation for a certain reaction, the value of \( A \) and \( E \) (energy of
activation) are \( 4 \times 10^{-13} \mathrm{sec}^{-1} \) and
\( 98.6 k J \) mol\( ^{-1} \) respectively. If the
reaction is of the first order,
the temperature at which its half-life period will be 10 minutes in \( K \) will be \( x \)
then find the value of \( x / 6 \) to the nearest
integer.


The hyperbola \( \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 \) has its
conjugate axis of length 5 and passes
through the point \( (2,1) . \) The length of latus rectum is :
A \( \cdot \frac{5}{4} \sqrt{29} \)
B. \( \frac{5}{8} \sqrt{29} \)
c. \( \sqrt{29} \)
D. \( \frac{\sqrt{29}}{4} \)


Which of the following is not a correct match?
A. Butter - Oil in water type emulsion
B. Vanishing cream - Oil in water type emulsion
c. Milk - Oil in water type emulsion
D. Cream - water in oil type emulsion


Can the phenomenon of resonance be
exhibited in RL or RC circuit?


\( \frac{1+i}{1-i}-\frac{1-i}{1+i} \)
\( \mathbf{A} \cdot-2 i \)
B.
\( c \cdot 2 i \)
\( D \)


In wheatstone's bridge \( \boldsymbol{P}=\mathbf{9} \) ohm, \( \boldsymbol{R}= \)
4 ohm and \( S=6 \) ohm. How much
resistance must be put in parallel to the resistance \( S \) to balance the bridge?
A .24 ohm
B. 13.5 ohm
c. 7.2 ohm
D. 18.7 ohm


The bond formed between the two
atoms by mutual sharing of electrons so as to complete their octets or duplets gives:
A. Covalent Compounds
B. Metallic Compound
c. lonic compound
D. none of these


Nitric oxide becomes brown when
released into air. Explain.


Group the following as nitrogenous
bases and nucleosides:
Adenine, Cytidine, Thymine, Guanosine, Uracil and Cytosine.


State True or False.
The diameter of molecules are much
smaller than the average distance travelled between collisions.
A. True
B. False


Sucrose is not a reducing sugar since:
A. it is chemically stable.
B. it contains no free aldehyde or keto group adjacent to
a \( \backslash C H O H \) group.
C . it is built up of a fructose unit.
D. it is optically active.


Assertion: AgCl is less soluble in aqueous sodium chloride solution than
in pure water.
Reason: AgCl dissociates completely
and more rapidly than NaCl
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false


A thermostat is?
A. A device used to maintain a constant temperature of a water bath or an oven
B. A modern type of thermoflask which work on the principle of equipartition of heat energy
C. An instrument by which the accuracy of thermometers is determined
D. A device which varies the temperature of a both


\( 6 x-3=4 x+5 \) is a simple equation
give reason


If \( y=\frac{\sin x+\cos x}{\sin x-\cos x} \) find \( \frac{d y}{d x} \) at \( x=\frac{\pi}{4} \)


What is NAND gate? Write its truth
table.


The following bodies are made to roll up
(without slipping) the same inclined plane from a horizontal plane: (i) a ring of radius \( R, \) (ii) a solid cylinder of radius \( \frac{\boldsymbol{R}}{\mathbf{2}} \) and (iii) a solid sphere of radius \( \frac{R}{4} . \) If in each case, the speed of the centre of mass at the bottom of the
incline is same, the ratio of the
maximum heights they climb is:
A .4: 3: 2
B. 14: 15: 20
c. 10: 15: 7
D. 2: 3: 4


Assertion
\( 14 C \) is an isotope of carbon.
Reason
\( 14 C \) and \( 14 N \) have the same mass
number.
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 incorrect but Reason is correct
D. Both Assertion and Reason are incorrect


Density of \( H_{2} O \) is \( 1 g m L^{-1} . \) If we have
\( 1 m L H_{2} O \) then:
This question has multiple correct options
A . It is 55.55 mol \( L^{-1} \)
B . It has \( 3.33 \times 10^{22} \mathrm{H}_{2} \mathrm{O} \) molecules
c. It has \( 3.33 \times 10^{22} \) H-atoms
D. It has \( 6.66 \times 10^{22} \) O-atoms


Suppose refractive index \( \mu \) is given as \( \boldsymbol{\mu}=\boldsymbol{A}+\frac{\boldsymbol{B}}{\boldsymbol{\lambda}^{2}} \)
where \( A \) and \( B \) are constants and \( \lambda \) is
wavelength, then dimensions of B are
same as that of
A. Wavelength
B. volume
c. Pressure
D. Area


If the position vectors of the points \( \boldsymbol{A}, \boldsymbol{B}, \boldsymbol{C}, \boldsymbol{D} \operatorname{are}(\boldsymbol{0}, \boldsymbol{2}, \boldsymbol{1}),(\boldsymbol{3}, \boldsymbol{1}, \boldsymbol{1}) \)
(-5,3,2),(2,4,1) respectively and if \( \boldsymbol{P A}+\boldsymbol{P B}+\boldsymbol{P C}+\boldsymbol{P D}=\mathbf{0} \) then the
position vector of \( \mathrm{P} \) is
A \( \cdot\left(0, \frac{5}{2}, \frac{5}{4}\right) \)
в. \( \left(\frac{5}{2}, \frac{5}{2}, \frac{5}{4}\right) \)
c. \( \left(\frac{5}{2}, 0, \frac{5}{4}\right) \)
D \( \left(\frac{5}{2}, \frac{5}{4}, 0\right) \)


The wire loop PQRSP formed by joining
two semi-circular wires of radii \( \boldsymbol{R}_{1} \) and
\( R_{2} \) carries a current I as shown. The
magnitude of the magnetic induction at
the centre \( C \) is
A \( \cdot \frac{\mu_{0} I}{4} \frac{R_{2}-R_{1}}{R_{2}} \)
В \( \cdot \frac{\mu_{0} I}{4} \frac{R_{2}-R_{1}}{R_{1}} \)
C \( \cdot \frac{\mu_{0} I}{4} \frac{R_{2}-R_{1}}{R_{2} R_{1}} \)
D. None of these


If \( (\boldsymbol{x} \boldsymbol{y})^{\boldsymbol{a}-1}=\boldsymbol{z} \)
\( (\boldsymbol{y} \boldsymbol{z})^{\boldsymbol{b}-1}=\boldsymbol{x} \)
\( (\boldsymbol{z} \boldsymbol{x})^{c-1}=\boldsymbol{y} \)
then \( \boldsymbol{a} \boldsymbol{b}+\boldsymbol{b} \boldsymbol{c}+\boldsymbol{c} \boldsymbol{a}=? \)


A redox reaction simply involves the transfer of electrons from reductant to
oxidant
If true enter 1 , else enter 0 .
\( A \)


A mixture is made from different
substances that are
A. not chemically joint
B. chemically joint
c. physically joint
D. not physically joint


The half life of a reaction is 46 minutes
when the initial concentration of the
reactant is 0.4 mole/lit and 92 minutes
when the initial concentration is 0.2
mole/lit. The order of the reaction is:
A.
B. 0.5
c. 2
\( D \)


Find the approximate error in the volume of a cube with edge \( x \mathrm{cm}, \) when the edge is increased by \( 2 \% \)
A . \( 4 \% \)
в. \( 2 \% \)
\( c .6 \% \)
D. \( 8 \% \)


The mean of the numbers obtained on
throwing a die having written 1 on three faces, 2 on two faces and 5 on one face
is:
A .
B. 2
c. 5
D. \( \frac{8}{3} \)


Anti hemorrhagic vitamin is:
\( A \cdot A \)
B. B \( _{1} \)
\( c \cdot k \)
D.


The maximum number of electrons in a
shell with the principal quantum number \( =4 \) is :
A .2
B. 10
c. 16
D. 32


When inert gas at constant pressure is added to the given reversible process then the equilibrium will:
A. be unaffected
B. shift in backward direction
c. shift in forward direction
D. cannot predicted


The element which cannot form a cation
is:
A . \( A l \)
в. \( B \)
c. \( C s \)
D. \( B i \)


PR, side of the triangle PQR.


Sensory cells are found in which part of
eye?
A. Cornea
B. Pupil
c. Retina
D. Choroid


Given a triangle with unequal sides, if is the set of all points which are equidistant from \( \mathrm{B} \) and \( \mathrm{C} \), and \( \mathrm{Q} \) is the set of all points which are equidistant from sides \( A B \) and \( A C, \) then what is the
intersection with \( \mathrm{Q} \) equal to?


When white light enters a prism, it gets split into its constituent colours. This is
due to:
A. High density of prism material
B. Value of \( \mu \) is different for different \( \lambda \)
c. Diffraction of light
D. velocity changes for different frequencies


Sequence of ond energy in \( N O, N O^{+} \)
and \( N O^{-} \) is:
A. \( N O>N O^{+}>N O^{-} \)
В. \( N O^{-}>N O^{+}> \) NO
c. \( N O^{+}>N O>N O^{-} \)
D. \( N O^{+}>N O^{-}>N O \)


0
0
0
0
0


\( \boldsymbol{K}_{(\boldsymbol{5})} \boldsymbol{C}_{\boldsymbol{5}} \boldsymbol{A}_{(\infty)} \boldsymbol{G}_{(\boldsymbol{5}-\infty)} \) floral formula is
related is to which of the following
family?
A. Liliaceae
B. Malvaceae
c. cruciferae
D. Leguminosae


If \( a^{2} \) ends in \( 9, \) then \( a^{3} \) will end in:
\( A \cdot 7 \)
B. 3
c. 5
D. none of the above


The solution set of \( 6 x-1>5 \) is
\( \mathbf{A} \cdot\{x \mid x<1, x \in R\} \)
B . \( \{x \mid x<1, x \in N\} \)
\( \mathbf{c} \cdot\{x \mid x>1, x \in W\} \)
D \cdot \( \{x \mid x>1, x \in R\} \)


For any integer \( n \) the integral \( \int_{0}^{\pi} e^{\cos ^{2} x} \cos ^{3}(2 n+1) x d x \) has the
value
A . \( \pi \)
B.
c. 0
D. none of these


Show that the function \( \boldsymbol{f}(\boldsymbol{x})= \) \( \left\{\begin{array}{cll}3-x, & \text { if } & x<1 \\ 2, & \text { if } & x=1 \text { is continuous at } \\ 1+x, & \text { if } & x>1\end{array}\right. \)
\( \boldsymbol{x}=\mathbf{1} \)


A screw gauge has positive error of 4 divisions. When the screw gauge holds a sphere the main scale reading is 4 \( \mathrm{mm} \) and the head scale coinciding division is \( 24 . \) If its least count is 0.01
\( \mathrm{mm}, \) the volume of the sphere is \( m m^{3} \)
A . 24.456
B. 38.808
c. 62.378
D. 40.567


A hollow spherical shell is made of
metal of density \( 4.8 \mathrm{g} / \mathrm{cm}^{3} . \) If its
internal and external radii are \( 10 \mathrm{cm} \)
and \( 12 \mathrm{cm} \) respectively, find the weight of the shell
A. \( 15.24 \mathrm{kg} \)
B . \( 12.84 \mathrm{kg} \)
c. \( 14.64 \mathrm{kg} \)
D. None of these


Spherical mirror with reflecting surface curved inwards is called
A. convex mirror
B. concave mirror
c. curved mirror
D. None of these


When a solid directly turns into
gaseous state, it is called:
A. sublimation
B. condensation
c. polymerisation
D. melting


Which statement is incorrect for ion-
channels?
A. They are protein
B. Movement through them is simple diffusion
C. Movement through them is from high to low concentration
D. All ions pass through the same type of channel


Which pair of substances will have the most similar geometry?
\( A \cdot S O_{3}, S O_{3}^{2-} \)
в. \( S O_{3}, S O_{4}^{2-} \)
\( \mathrm{c} \cdot \mathrm{SO}_{3}, \mathrm{CO}_{3}^{2} \)
D. \( S O_{4}^{2-}, C O_{3}^{2} \)


The increasing order of base strength of
\( \boldsymbol{C l}^{-} \boldsymbol{C H}_{3} \boldsymbol{C O O}^{-},^{-\boldsymbol{O H}} \) and \( \boldsymbol{F}^{-} \) is
A \( \cdot C l^{-}<F^{-}<C H_{3} C O O^{-}<^{-} O H \)
в. \( C l^{-}>F^{-}>C H_{3} C O O^{-}>^{-} O H \)
c. \( C H_{3} C O O^{-}<C l^{-}<F^{-}<^{-} O H \)
D. None of these


Azolla has a symbiotic relationship with
A. Chlorella
B. Anabaena
c. Nostoc
D. Tolypothrix


Evalaute the integral \( \int_{0}^{\pi} x f(\sin x) d x \)
\( \mathbf{A} \cdot 2 \pi \)
\( ^{\mathbf{B}} \cdot \pi \int_{0}^{\pi / 2} f(\cos x) d x \)
\( ^{\mathbf{c}} \cdot_{\pi} \int_{0}^{\pi} f(\cos x) d x \)
D. \( \pi \int_{0}^{\pi} f(\sin x) d x \)


Steel is preferred over iron in construction of ships because:
A. melting point of steel is higher than iron
B. steel is more uniform than iron
c. steel does not rust
D. tensile strength of steel is not high


The equilibrium constant for the reaction
\( \boldsymbol{S} \boldsymbol{r}(\boldsymbol{s})+\boldsymbol{M} \boldsymbol{g}^{+2}(\boldsymbol{a} \boldsymbol{q}) \rightleftharpoons \boldsymbol{S} \boldsymbol{r}^{+2}(\boldsymbol{a} \boldsymbol{q})+ \)
\( M g(s) \) is \( 4 \times 10^{12} \) at \( 25^{\circ} C \)
The \( E^{o} \) for a cell made up of the
\( \boldsymbol{S} \boldsymbol{r} \mid \boldsymbol{S} \boldsymbol{r}^{+2} \) and \( \boldsymbol{M} \boldsymbol{g}^{+2} \mid \boldsymbol{M} \boldsymbol{g} \) half cells \( (\log \)
\( \mathbf{2}=\mathbf{0 . 3}) \)
A. \( 0.3717 V \)
в. \( 0.7434 \mathrm{V} \)
c. \( 0.1858 V \)
D. \( 0.135 V \)


Following table gives frequency distribution of time (in minutes) taken
by a person in watching T.V. on a day.
Time \( \quad \) 30 \( \quad 40 \quad 50 \quad 60 \) ne
in \( \min \)
\( \begin{array}{llll}\text { 40 } & \text { 50 } & \text { 60 } & \text { 70 }\end{array} \)
No. of 19
14
persons
Obtain modal time taken for watching a
T.V. by persons on a day.
A. \( 51.22 . \) minutes
B . 53.22 . minutes
c. 57.22 . minutes
D. \( 59.22 . \) minutes


If \( \boldsymbol{y}=4 \boldsymbol{x}^{4}+\boldsymbol{2} \boldsymbol{x}^{3}+\frac{\mathbf{5}}{\boldsymbol{x}}+\boldsymbol{9}, \) then find
\( \boldsymbol{d} \boldsymbol{y} / \boldsymbol{d} \boldsymbol{x} \)


Which of the following metal is present in native state?
A. platinum
B. iron
c. potassium
D. copper


Define:-
Electromagnetic induction.


State whether true or false.
Motion of an ant on a floor along the edges is an example of translatory motion.
A. True
B. False


The number of primary, secondary and tertiary amines which possible with the molecular formula \( C_{3} H_{9} N \) are :
\( A \cdot 1,2,2 \)
B. 1, 2,
c. \( 2,1, \)
D. 3, 0,


The slope and intercept respectively of the graph drawn between \( \log \frac{x}{m} \) and \( \log \) \( P \) in respect of the logarithmic form of Freundlich adsorption isotherm are :
A \( \cdot \)n.log\( \frac{1}{K} \)
в. \( \frac{1}{n}, \log K \)
c. \( \log n, \frac{1}{K} \)
D. \( n, \log K \)


A block of \( A \) of \( \operatorname{mass} M_{A}=1 \) kg is kept
on a smooth horizontal surface and
attached by a light thread to another
block B of mass \( M_{B}=2 k g . \) Block B is
resting on ground, and thread and pulley are massless and frictionless. A
bullet of mass \( m=0.25 \mathrm{kg} \) moving
horizontally with velocity of \( u= \)
\( 200 m / s \) penetrates through block \( A \)
and comes out with a velocity of 100 \( \mathrm{m} / \mathrm{s} \)


Transform \( 2 x+3 y+6=0 \) to the
parallel axes through the point (4,-3)


The energy of the electron of hydrogen
atom in its nth orbit is given by \( \boldsymbol{E}_{\boldsymbol{n}}= \) \( -\frac{13.6}{n^{2}} \) electron volt(eV). Based on this
formula
(i) Draw different energy levels corresponding to \( n=1,2,3,4,5,6 \) and
\( \infty \)
(ii) Show Lyman and Baler series of
emission spectrum of hydrogen atom by drawing various electronic transitions.
(iii) Find the ionisation energy of
hydrogen atom.


Water cannot be used as a liquid in a thermometer because it has:
A. higher freezing point and lower boiling point than other thermometric liquids
B. lower freezing point and higher boiling point than other thermometric liquids
c. low specific heat capacity
D. transparent colour


one end has a small block of mass \( m \)
and charge \( q \) is attached at the other
end. The block rests over a smooth
horizontal surface. A uniform and
constant magnetic field \( B \) exists
normal to that plane of paper as shown in figure. An electric field \( \overrightarrow{\boldsymbol{E}}=\boldsymbol{E}_{0} \hat{\boldsymbol{i}}\left(\boldsymbol{E}_{\mathbf{0}}\right. \)
is a positive constant) is switched on at
\( \boldsymbol{t}=\mathbf{0} \) sec. The block moves on horizontal
surface without ever lifting off the
surface. Then the normal reaction
acting on the block is
A. Maximum at extreme position and minimum at mean position
B. Maximum at mean position and minimum at extreme position
C. is uniform throughout the motion
D. is both maximum and minimum at mean position


An electric dipole is placed in nonuniform electric field, then it
experiences
A . only torque
B. force and torque
c. only force
D. neither force nor torque


\( \operatorname{Let} f(x)=\frac{\sin 4 \pi[x]}{1+[x]^{2}}, \) where \( [x] \) is the
greatest integer less than or equal to \( x \)
then
A. \( f(x) \) is not differentiable at some points
B. \( f(x) \) exists but is different from zero
c. \( L H D(a t x=0)=0 . R H D(a t x=1)=0 \)
D. \( f(x)=0 \) but \( f \) is not a constant function


Which one of the following will be most
reactive for \( \boldsymbol{E}_{1} \) reactions?
\( \mathbf{A} \)
B.
c. \( B r-C H=C H-C H_{2}-C H_{3} \)
D.


An imbalance of electric charges within or on the surface of a material is
A. current electricity
B. an electromagnetic wave
c. static electricity
D. None of these


An inductor of reactance \( X_{L}=4 \Omega \) and
resistor of resistance \( \boldsymbol{R}=\mathbf{3} \Omega \) are
connected in series with a voltage
source of emf \( \varepsilon= \)
\( (20 V)[\sin (100 \pi r a d / s) t] . \) The current in
the circuit at any time t will be?
A \( \cdot I=(4 A)\left[\sin (100 \pi r a d / s) t+37^{\circ}\right] \)
B . \( I=(4 A)\left[\sin (100 \pi r a d / s) t-37^{\circ}\right. \)
C \( \cdot I=(4 A)\left[\sin (100 \pi r a d / s) t+53^{\circ}\right. \)
D. \( I=(4 A)\left[\sin (100 \pi r a d / s) t-53^{\circ}\right. \)


The largest term of the sequence \( a_{n}= \) \( \frac{n}{\left(n^{2}+10\right)} \) is
A \( \cdot \frac{3}{19} \)
B. \( \frac{2}{13} \)
c. 1
D.


Name the taxonomic term given to an organism which falls in the same class but not in the same family.
A. Family
B. Genus
c. species
D. Order


The set of values of \( p \) for which the roots
of the equation \( 3 x^{2}+2 x+p(p-1)= \)
0 are of opposite sign is
\( A \cdot(-\infty, 0) \)
B. (0,1)
c. \( (1, \infty) \)
D. \( (0, \infty) \)


Micelle formation take place when soap
is added to water? Will a micelle be
formed in other solvents like ethanol
also?
A. True
B. False


\( \mathbf{A} \)
300 pound fullback carrying the football towards the goal line encounters a 150 pound defensive back
near the goal line. The two are moving at the same speed when they both leave their feet and collide head-on in mid-air.
The defensive back goes flying backward, and the fullback continues
forward, scoring a touchdown. As a result of the collision. How do the
player's changes in momentum compare?
A. The amount of the defensive back's momentum changes is twice as much as the fullback's
B. The amount of the fullback's momentum changes is twice as much as the back's
c. The amount of the defensive back's momentum changes is more than twice as much as the fullback's
D. The amount of the fullback's momentum change is more than twice as much as the fullback's
E. The amount of momentum change for each player is the same


Difference in the number of protons of the largest element of the fourth period
and the smallest element of the third
period is:
\( A \)
B. 2
c. 20
D. 12


A sphere of mass \( \mathrm{M} \) and radius \( \mathrm{R} \) is falling in a viscous fluid. The terminal velocity attained by the falling object will be proportional to
\( \mathbf{A} \cdot M R^{2} \)
B. M/R
c. мк
D. \( M / R^{2} \)


Calculate the pH of \( 0.1 M \) solution of
\( N H_{4} O C N . K_{b} \) for \( N H_{3} \) is \( 1.75 \times 10^{-5} \)
and \( K_{a} \) for \( H O C N \) is \( 3.3 \times 10^{-4} \)


The hormone secreted by kidney is
A. Gastrin
B. Secretin
c. Erythropoietin
D. Aldosterone


Assertion
When a person walks on a rough surface, the frictional force exerted by surface on the person is opposite to the
direction of his motion.
Reason
It is the force exerted by the road on the
person that causes the motion.
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


Is the given sequence \( 3,3+\sqrt{2}, 3+ \) \( 2 \sqrt{2}, 3+3 \sqrt{2} \) form an APs? If it forms
an \( A P, \) find the common difference \( d \)
and write the next three terms.


In the expression of \( \left(2^{x}+\frac{1}{4^{x}}\right)^{n} \) ratio of
2nd and third terms is given by \( t_{3} / t_{2}= \)
7 and the sum of the co-efficients of 2 nd
and \( 3 \mathrm{rd} \) term is \( 36, \) then the value of \( x \)
is
A \( \frac{-1}{3} \)
в. \( \frac{-1}{2} \)
\( c \cdot \frac{1}{3} \)
D.


Which type of fertilization is found in
Bryophytes?
A. Siphonogamous
B. Zoidogamous
c. zoodio-siphonogamous
D. Fertilization is not found


Order and degree of \( \left(x^{2}+2 x\right) y_{2}^{2}+\left(x^{2}-2\right) y_{1}^{3}-2(x+ \)
\( \mathbf{3}) \boldsymbol{y}=\mathbf{0} \) are:
A . 2,3
B. 2,
c. 3,1
D. 3,


LPG is liquefied petroleum gas which is a compound of butane and propane and
used as:
A. cooking fue
B. motor fue
c. refrigeration
D. All of these


How many moles of acetic anhydride
\( \left(A c_{2} O\right) \) is needed to react completely
with sucrose?
\( A \cdot 8 \)
B. 6
\( c \cdot 4 \)
D.


If the distance is increased after
disconnecting the power source, then electric field inside the capacitor is:
A \( \cdot 6 \times 10^{3} V / m \)
B . \( 3 \times 10^{3} V / m \)
c. \( 12 \times 10^{3} V / m \)
D. \( 15 \times 10^{3} V / m \)


At the time of fertilization, sperm head
enters in the egg from
A. Any where
B. Animal pole
c. vegetal pole
D. Lateral side of egg


A spherical lens has a focal length \( 2 \mathrm{cm} \)
The lens will be
A. concave lens
B. Convex lens
c. concavo convex lens
D. None


Find the maximum velocity with which
a train can be moved on a circular track
of radius \( 200 m . \) The banking of the
track is \( 5.71^{\circ}\left(\text { given, } \tan 5.71^{\circ}=0.1\right) \)
A \( .1 .4 m / s \)
в. \( 14 \mathrm{m} / \mathrm{s} \)
c. \( 140 m / s \)
D. \( 0.14 m / s \)


Is the given Progression arithmetic progression?Why \( 2,6,7,10,12,15, \dots \dots \dots \)


Fill in the blanks.
\begin{tabular}{llll}
S.No. & Molecular formula & Common name & IUPA nam \\
\hline \( 1 . \) & \( \mathrm{CH}_{3} \mathrm{COOH} \) & \( \ldots \) & Ethan acid \\
\hline \( 2 . \) & \( \mathrm{HCHO} \) & Formaldehyde & \( \ldots \) \\
\hline
\end{tabular}


From the displacement-time graph
shown here, find the velocity of the body
as it moves from \( A \) to \( B \)
A. \( 0.8 \mathrm{m} / \mathrm{s} \)
B. \( 1.2 \mathrm{m} / \mathrm{s} \)
c. \( 10 \mathrm{m} / \mathrm{s} \)
D. \( 20 \mathrm{m} / \mathrm{s} \)


The length of the latus rectum of the parabola \( \boldsymbol{x}=\boldsymbol{a} \boldsymbol{y}^{2}+\boldsymbol{b} \boldsymbol{y}+\boldsymbol{c} \) is \( \frac{\boldsymbol{k}}{\boldsymbol{a}} . \) Find \( \boldsymbol{k} \)


How many moles of \( N a^{+} \) ions are
present in \( 20 \mathrm{mL} \) of \( 0.40 \mathrm{M} N a_{3} P O_{4} ? \)
A . 0.0080
B. 0.024
c. 0.050
D. 0.20


From a motorboat moving downstream
with a velocity \( 2 m / s \) with respect to
river, a stone is thrown. The stone falls
on an ordinary boat at the instant when
the motorboat collides with the ordinary boat. The velocity of the ordinary boat with respect to the river is equal to zero.
The river flow velocity is given to be \( \mathbf{1} \boldsymbol{m} / \boldsymbol{s} . \) The initial velocity vector of the stone with respect to earth is
A \( .2 \hat{i}+20 \hat{j} \)
B . \( 3 \hat{i}+40 \hat{j} \)
c. \( 3 \hat{i}+50 \hat{j} \)
D . \( 2 \hat{i}+50 \hat{j} \)


When an energetic \( \gamma \) -ray photon falls on heavy substance, an electron and positron produced. The least energy required for t process is
A .4 .8 Mav
B. 1.02 Mev
c. 7.3 Mev
D. 10 Mev


Which of the following are reasons for depletion of underground water of a particular place?
A. Population explosion
B. Extensive urbanization
c. Building concrete structures
D. All of the above


Threshold wavelength of tungsten is 2300 angstrom. If ultraviolet light of wavelength 1800 angstrom is incident on it, then the maximum kinetic energy of photoelectrons would be?
A . 1.5 ev
B. 2.5ev
c. 3.0 ev
D. \( 5.0 \mathrm{eV} \)


f mean of given data is 21 then value of
p is
\( \begin{array}{llllll}\mathrm{x} & 10 & 15 & 20 & 25 & 36 \\ \mathrm{f} & 6 & 10 & \mathrm{p} & 10 & 8\end{array} \)
A . 24
B . 10
c. 26
D. none of the above


A charged rod is brought near a
negatively charged pith ball electroscope. What conclusion would you draw about the charge on the rod if pith ball moves away from the rod?
A. Positive
B. Negative
c. No charge
D. can't say


Show that subtraction are not binary operation on natural number \( N \)


A gas container observes Maxwellian
distribution law of speed. If the number
of molecules between the speed 5.0 and 5.1 km per sec at \( 298 \mathrm{K} \) is N, what would be number of molecules between this
range of speed if the total number of molecules in the vessel are doubled?
A . \( 2 N \)
в.
\( c \cdot 2 N^{2} \)
D. \( N^{2} / 2 \)


A bar magnet for dipole moment \( 10^{4} J T^{-1} \) is free to rotate around a
horizontal plane. A horizontal magnetic field \( 4 \times 10^{-5} T \) exists on the space.
Find the work done in rotating the magnet slowly from a direction parallel
to the field to a direction \( 60^{0} \) from the
field.
A. \( 0.1 J \)
\( J \)
B. \( 0.2 J \)
\( c .0 .45 \)
D. \( 0.5 J \)


\( \ln \) an \( \mathrm{AC} \) circuit, \( V \) and \( I \) are given below,
then the power dissipated in the circuit:
\( V=50 \sin (50 t) V, I=50 \sin \left(50 t+\frac{\pi}{3}\right) m A \)
A. \( 0.625 W \)
В. \( 1.25 \mathrm{W} \)
c. \( 2.50 W \)
D. \( 5.0 W \)


Assertion
Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be any function. Define
\( \boldsymbol{g}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) by \( \boldsymbol{g}(\boldsymbol{x})=|\boldsymbol{f}(\boldsymbol{x})| \) for all \( \boldsymbol{x} \)
Then, \( g \) is continuous is \( \boldsymbol{f} \) is
continuous.
Reason
Composition of two continuous functions is a continuous function
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A square metal loop of side \( 10 \mathrm{cm} \) and
resistance \( 1 \Omega \) is moved with a
constant velocity partly inside a uniform magnetic field of \( 2 W b m^{-2} \)
directed into the paper, as shown in the
figure. The loop is connected to a
network of five resistors each of value
\( 3 \Omega \). If a steady current of 1 m \( A \) flows in
the loop, then the speed of the loop is
A \( \cdot 0.5 \mathrm{cms}^{-1} \)
B. \( 1 \mathrm{cms}^{-1} \)
\( \mathrm{c} \cdot 2 \mathrm{cms}^{-1} \)
D. \( 4 \mathrm{cms}^{-1} \)


The outcomes of a random experiment are called \( _{--}-_{-}- \) connected with the
experiment
A . space
B. events
c. experiment
D. random


\( \frac{2 \tan 45^{\circ}}{1+\tan ^{2} 45^{\circ}} \)


Active transport of ions by a cell requires
A. High temperature
B. Low temperature
c. Alkaline ph
D. ATP


If \( a, b, c, d \) and \( p \) are distinct real
number such that \( \left(a^{2}+b^{2}+c^{2}\right) p^{2}- \)
\( \mathbf{2}(\boldsymbol{a} \boldsymbol{b}+\boldsymbol{b} \boldsymbol{c}+\boldsymbol{d} \boldsymbol{c}) \boldsymbol{p}+\left(\boldsymbol{b}^{2}+\boldsymbol{c}^{2}+\boldsymbol{d}^{2}\right) \geq \mathbf{0} \)
then \( a, b, c, d: \)
\( A \cdot \operatorname{arein} A \cdot P \)
B. are in G.P.
c. are in \( H . P \)
D. satisfy \( a b=c d \)


Respiratory quotient is expressed as which of the following equations?
A. \( O_{2} / C O_{2} \)
в. \( C O_{2} / O_{2} \)
\( \mathrm{c} \cdot O_{2} / \mathrm{H}_{2} \mathrm{O} \)
D. \( C O_{2}-O_{2} \)


Fill in the blanks.
Linear movement of the piston in a heat engine is converted into circular motion
by


In what time, will the simple interest on
a certain sum of money at \( 6 \frac{1}{4} \% \) p.a be \( \frac{3}{8} \) of the sum itself?


Is it safe for the electrician to carry out
electrical repairs outdoors during heavy downpour? Explain.


Draw the circuit diagram of a full wave rectifier using two p-njunction diodes and explain its working. Show the input
and output waveforms.


The characteristic differentiation of
pteridophytes from bryophytes is
A. Well formed stelar system
B. Circinate venation
c. Independent sporophyte
D. All of the above


The contrapositive of \( (\boldsymbol{p} \vee \boldsymbol{q}) \Rightarrow \boldsymbol{r} \) is
A \( \cdot r \Rightarrow(p \vee q) \)
в. \( r \Rightarrow(p \vee q) \)
c. \( r \Rightarrow \sim p \wedge \sim q \)
D. \( R \Rightarrow(q \vee r) \)


Evaluate \( : \int_{-\pi}^{\pi} \frac{\sin ^{2} x}{1+e^{x}} d x \)


One of the most common phenomenon related to rainfall is
A. Evaporation
B. Vaporization
c. Fusion
D. Solidification


The organic solvent is:
A. water
B. hydrogen peroxide
C. hydrochloric acid
D. carbon tetrachloride


A man can swim in still water at a
speed of \( 3 \mathrm{km} / \mathrm{h} \). he want to cross a river
that flows at \( 2 \mathrm{km} / \mathrm{h} \) and reach the point directly opposite to his starting point.
(a) In which direction should he try to
swim (that is, find the angle his bodys makes with the river flows??
(b) How
much time will he take to cross the river
if the is \( 500 \mathrm{m} \) wide?


Write 0,7,10,-4 in \( \frac{p}{q} \) form


Find the value of \( z \) using shortcut
method whose arithmetic mean is 2.5
A . 14
B . 15
c. 16
D. 17


In seas, mainly how do marine organism build their shells?


A P-V diagram is obtained by changing
the temperature of the gas as shown.
During this process the gas is :
A. heated continuously
B. cooled continuously
c. heated in the beginning but cooled towards the end
D. cooled in the beginning but heated towards the end


Fill in the blank spaces:
The amount of heat energy supplied to
boiling water at \( 100^{0} C \) is called latent heat of
A. Evaporation
B. Vaporisation
c. Both \( A \& B \)
D. None of these


What will be the approximate terminal velocity of a rain drop of diameter \( 1.8 \times \)
\( 10^{-3} \mathrm{m}, \) when density of rain water \( \approx \)
\( .10^{3} k g m^{-3} \) and the co=efficient of
viscosity of air \( \approx .1 .8 \times 10^{-5} N s m^{-2} ? \)
(Neglect buoyancy of air).
A \( \cdot 49 m s^{-1} \)
B. \( 98 m s^{-1} \)
c. \( 392 m s^{-1} \)
D. \( 980 \mathrm{ms}^{-1} \)


Assertion
Oxyhaemoglobin dissociates near the organ tissue due to Bohr effect and
oxygen is released.
Reason
Increased \( \mathrm{CO}_{2} \) concentration reduces
the affinity of haemoglobin for oxygen.
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


Prove that the vectors \( 2 \hat{i}-3 \hat{j}-\hat{k} \) and \( -6 \hat{i}+9 \hat{j}+3 \hat{k} \) are parallel.


Which of the following has the highest boiling point?
A. \( C_{3} H_{7} C l \)
в. \( C_{4} H_{9} C l \)
c. \( C H_{3} C H\left(C H_{3}\right) C H_{2} C l \)
D. \( \left(C H_{3}\right)_{3} C-C l \)


If two parallel chords on the same side
of the centre of a circle are \( 6 \mathrm{cm} \) and 8
\( \mathrm{cm}, \) and they are \( 1 \mathrm{cm} \) apart, then the diameter of the circle will be
\( \mathbf{A} \cdot 14 \mathrm{cm} \)
B. \( 10 \mathrm{cm} \)
c. \( 8 \mathrm{cm} \)
D. \( 5 \mathrm{cm} \)


If \( A \) is a square matrix of order \( n \times n \)
then adj(adj A) is equal to
\( \mathbf{A} \cdot|A|^{n} A \)
B \( \cdot|A|^{n-1} A \)
\( \mathbf{c} \cdot|A|^{n-2} A \)
D \( \cdot|A|^{n-3} A \)


Add the following rational numbers:
\( \frac{6}{13} \) and \( \frac{-9}{13} \)


Silver halides are used in photography because they are -
A. Photosensitive
B. Soluble in hypo solution
c. soluble in \( N H_{4} O H \)
D. Insoluble in acids


Hydrogen resembles alkali metals in
many respect for which several factors
are responsible. Of the following factors which one is the most important in this respect?
A. Its tendency to lose electron
B. Its tendency to gain electron in its valence shell
c. It has high ionisation enthalpy.
D. ts small size


Calculate \( \left[\boldsymbol{F}^{-}\right] \) in a solution saturated
with respect to both \( M g F_{2} \) and \( S r F_{2} \)
assuming no hydrolysis of \( \boldsymbol{F}^{-} . \boldsymbol{K}_{s p} \) of \( M g F_{2}=6.5 \times 10^{-9} ; K_{s p} \) of \( S r F_{2}= \)
\( \mathbf{2 . 9} \times \mathbf{1 0}^{-\mathbf{9}} \)
A \( \cdot 2.35 \times 10^{-3} M \)
В . \( 2.65 \times 10^{-3} M \)
\( \mathbf{c} \cdot 2.95 \times 10^{-3} M \)
D. None of the above


State True or False.
Elevation in boiling point is directly proportional to the molality of the solution.
A. True
B. False


Which of the following is essential minor element for the healthy growth of plants?
\( A \cdot A \)
в. Gа
\( c . \) в
\( D \cdot \ln \)


A fuse wire with a radius of \( 0.1 m m \)
blows up at \( 5 A \). The radius of another
fuse wire made of the same material
which will blow up at \( 40 A \) is
\( \mathbf{A} \cdot 0.8 m m \)
B. \( 0.6 m m \)
\( \mathrm{c} .0 .45 \mathrm{mm} \)
D. \( 0.4 m m \)


If \( \arg \left(\frac{z_{1}}{z_{2}}\right)=\frac{\pi}{2}, \) then find the value of
\( \left|\frac{z_{1}+z_{2}}{z_{1}-z_{2}}\right| \)


In the given figure, \( A P \) is bisector of \( \angle A \)
and \( \mathrm{CQ} \) is bisector of \( \angle C \) of
parallelogram ABCD
Prove that APCQ is a parallelogram


Find the sum to \( n \) terms of the series
\( \mathbf{1} \cdot \mathbf{2}^{2}+\mathbf{2} \cdot \mathbf{3}^{2}+\mathbf{3} \cdot \mathbf{4}^{2}+\dots \)


What is the amount of heat given off by
\( 100 g \) of \( O_{2} \) when it is used to burn an
excess of sulfur according to the following reaction?
\( S(s)+O_{2} \rightarrow S O_{2}(g) \Delta H= \)
\( -296 k J / \) mole
A. \( 925,000 \mathrm{J} \)
B. 29,000 J
c. 1,850 J
D . 296 J
E. 100


In which zone of a candle flame does
complete combustion take place?
A. Inner
B. Outer
c. Middle
D. All three zones


Ecosystem is
\( A \cdot \) Open
B. Closed
C. Both A and B
D. Neither open nor closed


Networks of nine conductors connects
six points \( A, B, C, D, E \) and \( F \) as shown
in figure. The figure denoted
resistances in ohms. Find the
equivalent resistance between A and D.


What is reflex action?


Find \( a \) and \( b, \) where \( a \) and \( b \) are real
numbers so that \( a+i b=(2-i)^{2} \)
A \( . a=3, b=-4 \)
В. \( a=-3, b=-4 \)
c. \( a=3, b=4 \)
D. \( a=-3, b=4 \)


\( \boldsymbol{P} \frac{1 . C H_{3} M g B r}{2 . H_{3} O^{+}} R \frac{1 . d i l . N a O H}{2 . \Delta} 4 \)
methylpent-3-en-2-one
\( \boldsymbol{P} \) is :
A. ethanamine
B. ethanal
c. propanone
D. ethanenitrile


Avena coleoptile test is for which of the following hormone?
A . GA
B. ABA
\( c \cdot \) ।АА
D. NAA


In an isosceles triangle, the vertex angle
is \( 50^{\circ} . \) What are the base angles of the
triangle?


Construct a \( 3 \times 2 \) matrix \( A=\left[a_{i j}\right] \) whose elements are given by \( a_{i j}=\frac{i}{j} \)


The perpendicular drawn at any point on a mirror is called:
A. incident ray
B. reflected ray
c. normal
D. image


Which is/are the characteristic(s) of
Diamond?
A. Opaque
B. Hardness
c. Both \( A \) and \( B \)
D. conductor of electricity


The correct order of pH is
A. Lemon juice < water < Milk of Magnesia
B. Lemonjuice> water> Milk of Magnesia
C. Water > lemon juice > milk of Magnesia
D. Milk of Magnesia > lemon juice > water


The \( p H \) values of certain substances
are given below.
\( \begin{array}{ll}\text { Substance } & \text { pH value } \\ \text { (1) Human blood } & 7.4 \\ \text { (2) Baking soda } & 8.2 \\ \text { (3) Vinegar } & 2.5 \\ \text { (4) Household Ammonia } & 12.0\end{array} \)
(a) Which of the substances are acidic
in nature?
(b) Which of the substances are basic
in nature?


In humans, the joint between bones of skull is
A. Fibrous joint
B. Hinge joint
c. synovial joint
D. None of the above


Two rods, one of iron and the other of aluminum, are heated to the same temperature difference. If the
coefficient of expansion of iron rod is more than that of aluminum, then:
A. the iron rod will expand less
B. the iron rod will expand more
c. both rods will expand equally
D. the iron rod will not expand at all


The electronic configuration of element with atomic no. 14 is:
A. (2,6,6)
в. (4,6,4)
c. (2,4,8)
D. (2,8,4)


The flow rate of a water from a tap of
diameter \( 1.25 \mathrm{cm} \) is \( 0.48 \mathrm{L} / \) min. If the
coefficient of viscosity of water is
\( 10^{-3} P a s, \) what is the nature of flow of
water?


Which statement is wrong from the
following?

Statement 1: METSAT is useful for
weather forecasting. Statement 2: INSAT is useful for Direct
To Home (DTH) transmission
Statement 3: CARTOSAT is useful
astronomical observation.
A. Statement
B. Statement 3
c. Statement 1 and 2
D. Statement 2


A Lanthanoid contraction is the gradual
decrease in the atomic and ionic radii
of lanthanoids with an increase in the
atomic number. If true press 1 else 0


\( \ln 4 t h, 5 t h \) and \( 6 t h \) segments of Earthworm, lying above the pharyngeal mass and connected with pharyngeal glands are found small, red coloured follicular bodies called
A. Septal glands
B. Blood glands
c. Salivary glands
D. Nephridia
E. Intestinal caecae


Why molality is preferred over moalarity in expressing the concentration of a solution?


Source and observer start moving simultaneously along \( x \) and \( y \) -axis
respectively. The speed of source is
twice the speed of observer, \( V_{0} . \) If the
ratio of observed frequency to frequency
of the source is \( 0.75, \) find the velocity of
sound
A \( \cdot \frac{11}{\sqrt{5}} v_{0} \)
B. \( \frac{17}{\sqrt{5}} v_{0} \)
c. \( \frac{16}{\sqrt{5}} v_{0} \)
D. \( \frac{19}{\sqrt{5}} v_{0} \)


A stream of water flowing horozintally with a speed of \( 15 \mathrm{ms}^{-1} \) gushes out of a
tube of cross-sectional area \( 10^{-2} m^{2} \)
and hits a vertical wall nearly. The force exerted on the wall by the impact of water assuming it does not rebound is
A \( \cdot 2.25 \times 10^{3} N \)
В. \( 2.5 \times 10^{3} N \)
c. \( 3.0 \times 10^{3} N \)
D. \( 35 \times 10^{3} N \)


A circular ring starts rolling down on an inclined plane from its top. Let \( \boldsymbol{V} \) be velocity of its centre of mass on
reaching the bottom of inclined plane. If a block starts sliding down on an identical inclined plane but smooth, from its top, then the velocity of block
on reaching the bottom of
inclined plane is:
\( \mathbf{A} \cdot \frac{V}{2} \)
B. \( 2 V \)
c. \( \frac{V}{\sqrt{2}} \)
D. \( \sqrt{2} V \)


Show that if a rod held at angle \( \theta \) to the horizontal and released, its lower end
will not slip if the friction coefficient
between rod and ground is greater than \( \frac{3 \sin \theta \cos \theta}{1+3 \sin ^{2} \theta} \)


How does a diode acts as a rectifier.


Teflon (tetrafluoroethylene) is a black material used in non-stick pans for frying chips and vegetables. The oil or
butter does not stick at all. In the
process of manufacture, one of the
technical problems is:
A. to make teflon stick to the metal of the pan
B. to make teflon that is non-sticky
c. to make teflon
D. to cut a round sheet of teflon that exactly fits


A copper wire of resistance \( R \) is cut in
to ten parts of equal length. Two pieces each are joined in series and then five such combinations are joined in parallel. The new combination will have
a resistance
A. \( R \)
в. \( \frac{R}{4} \)
c. \( \frac{R}{5} \)
D. \( \frac{R}{25} \)


Which one of the following is a series?
A. \( 1 \times 2 \times 3 \times 4 \times 5 \)
в. (0,1,2,3,4)
c. \{1,2,3,5,6\}
D. \( \sum_{n=1}^{10} n k^{2} \)


The net charge inside an isolated system is
A. conserved
B. variable
c. zero
D. infinite.


In 1930 , John Northrop crystallized which of the following enzyme as a protein?
A. Pepsin
B. Renin
c. Amylase
D. Trypsin


State whether the following statement
is True or False.

The magnetic lines of force around a bar magnet mutually attract each other.


If the vectors \( a \hat{i}+\hat{j}+\hat{k}, \hat{i}+b \hat{j}+\hat{k} \) and
\( \hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}+\boldsymbol{c} \hat{\boldsymbol{k}}(\boldsymbol{a} \neq \boldsymbol{b} \neq \boldsymbol{c} \neq 1) \) are coplanar
then the value of \( \frac{1}{1-a}+\frac{1}{1-b}+ \) \( \frac{1}{1-c} \) is equal to
A . 1
B.
\( c \cdot 2 \)
D. none of these


\( \boldsymbol{R}=\lim _{\boldsymbol{x} \rightarrow \mathbf{0}^{+}} \boldsymbol{f}(\boldsymbol{x}) \) is equal to
A \( \cdot \frac{\pi}{2} \)
в. \( \frac{\pi}{2 \sqrt{2}} \)
c. \( \frac{\pi}{\sqrt{2}} \)
D. \( \sqrt{2} \pi \)


A basic solution has a pH of approximately:
A. more than 7
B. equal to 7
c. less than 7
D. between 4 to 5


Carbon, Silicon, and Germanium atoms have four valence electrons each. Their
valence and conduction bands are
separated by energy band gaps
represented by \( (E g)_{C},(E g)_{S i}, \) and
\( (E g)_{G e} \) respectively. Which one of the following relationships is true in their
case:
A \( \cdot(E g)_{C}<(E g)_{G e} \)
в. \( (E g)_{c}>(E g)_{S i} \)
c. \( (E g)_{C}=(E g)_{S i} \)
D. \( (E g)_{C}<(E g)_{S i} \)


If \( A=\{a, b, c\}, B=\{1,2\}, \) then find
\( \boldsymbol{A} \times \boldsymbol{B}, \boldsymbol{B} \times \boldsymbol{A} \boldsymbol{a} \boldsymbol{n} \boldsymbol{d} \boldsymbol{A} \times \boldsymbol{A} \)


The radius of the nearly circular orbit of mercury is \( 5.8 \times 10^{10} m \) and its orbital
period is 88 days. If a hypothetical planet has an orbital period of 55 days, what is the radius of its circular orbit?


Acetic acid is prepared from
A. formaldehyde
B. acetaldehyde
c. vinyl acetate
D. all of the above


Fill in the blanks.
sulphur has no sharp melting point.


Which one of the following is without
coenzyme activity?
A. Vitamin B
B. Thiamine
c. Biotin
D. Riboflavin


what is the formula of potassium amminetrichlorido platinate(ii)


If eight persons are to address a meeting, then the number of ways in which a specified speaker is to speak before another specified speaker is?
A . 2520
B. 20160
c. 40320
D. None of these


The acute angle between two lines such
that the direction cosines \( l, \boldsymbol{m}, \boldsymbol{n} \) of each of them satisfy the equation \( l+ \)
\( \boldsymbol{m}+\boldsymbol{n}=\mathbf{0} \) and \( l^{2}+\boldsymbol{m}^{2}-\boldsymbol{n}^{2}=\mathbf{0} \) is
\( A \cdot 30 \)
B . 45
\( c \cdot 60 \)
D. \( 15^{\circ} \)


\( f\left(\begin{array}{ccc}1 & -1 & 1 \\ 2 & -1 & 0 \\ 1 & 0 & 0\end{array}\right], \) then solve is \( A^{3}= \)
I?
If correct state true else false.
A. True
B. False


What is the work required to set up the four-charge configuration of the figure, assuming the charges are initially infinitely far apart?
A \( \cdot \frac{q^{2}}{4 \pi \epsilon_{0} a}(4+\sqrt{2}) \)
В \( \cdot \frac{q^{2}}{4 \pi \epsilon_{0} a}(4-\sqrt{2}) \)
c. \( \frac{q^{2}}{4 \pi \epsilon_{0} a}(-4+\sqrt{2}) \)
D. \( \frac{q^{2}}{4 \pi \epsilon_{0} a}(-4-\sqrt{2}) \)


Which impurity (as a salt) is associated with table salt obtained
from sea-water?
A. \( N a H C O_{3} \)
B. \( M g C O_{3} \)
c. \( M g C l_{2} \)
D. NaI


The magnetic field \( \overline{\boldsymbol{d} \boldsymbol{B}} \) due to a small
current element dl at a distance \( \vec{r} \) and
carrying current 'i' is
A \( \left.\cdot \frac{\mu_{0}}{d B}=\frac{\frac{d \bar{d}}{4 \pi} i}{r}\right) \)
В \( \cdot \frac{ }{d B}=\frac{\mu_{0}}{4 \pi} i^{2}\left(\frac{\overline{d l} \times \bar{r}}{r^{2}}\right) \)
\( ^{\mathbf{C}} \cdot \frac{\mu_{0}}{d B}=\frac{\frac{\mu}{4 \pi} i^{2}}{r} \)
D \( \cdot \frac{\mu_{0}}{d B} i\left(\frac{\overline{d l} \times \bar{r}}{r^{3}}\right) \)


What name is given to the type of astronomy having the following characteristics.
I. It is carried out in the waveband 300
nm to 10 nm.
II. The atmosphere is opaque to the incoming radiation from space
III. Observations are to be carried out
from above the earth's atmosphere.
A. X-ray astronomy
B. Ultra-violet astronomy
c. Infra-red astronomy
D. Gamma ray astronomy


Pig iron is the purest form of iron.
If true enter 1 , else enter 0 .


The IUPAC name for the compound
\( \boldsymbol{C H}_{3}-\boldsymbol{C}\left(\boldsymbol{C H}_{3}\right)=\boldsymbol{C H}-\boldsymbol{C O O H} \) is:
A. 2-Methyl-2-butenoic acid
B. 3-Methyl-3-butenoic acid
c. 3-Methyl-2-butenoic acid
D. 2-Methyl-3-butenoic acid


The emf of a cell is \( \epsilon \) and its internal
resistance is \( r . \) Its terminals are
connected to a resistance \( R \) The
potential difference between the terminals is \( 1.6 \mathrm{V} \) for \( \boldsymbol{R}=\mathbf{4} \Omega, \) and \( 1.8 \mathrm{V} \)
for \( \boldsymbol{R}=\mathbf{9} \Omega . \) Then
A. \( \epsilon=1 V, r=1 \Omega \)
В. \( \epsilon=2 V, r=1 \Omega \)
c. \( \epsilon=2 V, r=2 \Omega \)
D. \( \epsilon=2.5 V, r=0.5 \Omega \)


A bag contains 7 white, 5 black and 4
red balls. Four balls are drawn without
replacement. Find the probability that at least three balls are black.


The fruit formed from the fusion of
inflorescence is called as
A. Simple fruit
B. Aggregate fruit
c. Pseudo fruit
D. composite fruit


Three rods made of the same material
and having the same cross-section have been joined as shown in figure. Each rod is of the same length. The left and right
ends are kept at \( 0^{\circ} \mathrm{C} \) and \( 90^{\circ} \mathrm{C} \)
respectively. The temperature of the
junction of three
A \( \cdot 46^{\circ} \mathrm{C} \)
B. \( 60^{\circ} \mathrm{C} \)
\( c \cdot 30^{\circ} \mathrm{C} \)
D. \( 20^{\circ} \) C


IUPAC name of \( \boldsymbol{K}_{3}\left[\boldsymbol{F} \boldsymbol{e}\left(\boldsymbol{C}_{2} \boldsymbol{O}_{4}\right)_{3}\right] \) is:
A. Potassium dioxalatoferrate(1)
B. Potassium dioxalatoferrate(III)
c. Potassium trioxalatoferrate(III)
D. Potassium trioxalatoferate(II)


Assertion
Steel is more elastic than rubber.
Reason
For same strain, steel requires more stress to be produced in it
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which of the following conditions
guarantee a spontaneous reaction?
A. Positive \( \triangle H, \) positive \( \triangle S \)
B. Positive \( \triangle H, \) negative \( \triangle S \)
C. Negative \( \triangle H, \) negative \( \triangle S \)
D. Negative \( \triangle H, \) positive \( \triangle S \)
E. None of the above


If a current is passed in a spring it
A. gets compressed
B. gets expanded
c. oscillates
D. remains unchanged


If \( \left(\frac{1+i}{1-i}\right)^{n} \) is 1 find the least value of \( n \) where \( \boldsymbol{n} \in \boldsymbol{N} \)


During day period, ............ and .......... helps in the upward movement of sap from roots to the leaves.
A. Reverse osmosis and diffusion
B. Facilitated diffusion and osmosis
c. cohesive force and transpiration pull
D. None of the above


When you move from left to right across a period, or row, of the periodic table which one decreases?
A. Reactivity
B. Ionization energy
c. Electron affinity
D. Number of valence electrons
E. Atomic radius


How the gravitational constant will change if a brass plate is introduced between two bodies?
A. No change
B. Decreases
c. Increases
D. No sufficient data


\( \lim _{x \rightarrow 9} \frac{2 x-7 \sqrt{x}+3}{3 x-11 \sqrt{x}+6} \)
\( \mathbf{A} \cdot \frac{3}{4} \)
B. \( \frac{5}{3} \)
\( c \cdot \frac{5}{7} \)
\( D \cdot \frac{3}{7} \)


Ecosystem is an interacting system
made up of
A. Consumers and their physical surroundings
B. Producer and consumers
C. Producer and their physical surroundings
D. Organisms and their physical surroundings


Residual volume is
A. Lesser than tidal volume
B. Greater than inspiratory volume
C. Greater than vital capacity
D. Greater than tidal volume


The position \( x \) of a particle varies with
time \( t \) a \( a t^{2}-b t^{3} . \) The acceleration of
particle will be zero at time \( t \) is equal to
A \( \cdot \frac{a}{b} \)
в. \( \frac{2 a}{3 b} \)
c. \( \frac{a}{3 b} \)
D. zero


The S.I. unit of specific heat capacity is :
A. \( J k g^{-1} \)
B. \( J K^{-1} \)
c. \( J k g^{-1} K^{-1} \)
D. \( k c a l k g^{-1} \circ C^{-1} \)


Differentiate between simple epithelium and compound epithelium.


If \( g \) is acceleration due to gravity on the earth's surface, the gain in the potential energy of an object of mass \( m \) raised from the surface of earth to a height equal to the radius \( R \) of the earth is
\( ^{\mathbf{A}} \cdot \frac{1}{2}^{m g R} \)
в. \( 2 m g R \)
\( \mathrm{c} \cdot m g R \)
D. \( \frac{1}{4} m g R \)


\( 0.38 e v_{-1-}-n 6 \)
\( 0.54 e v_{-}--n 5 \)
\( 0.85 e v_{-}---n 4 \)
\( 1.52 e v_{-}--n 3 \)
\( 3.39 e v_{-1-}-n 2 \)
13.6ev \( \boldsymbol{n} \mathbf{1} \)
A hydrogen electron falls from the \( n=3 \)
to the \( n=1 \) energy level. Using the
chart above, determine how much
energy it must release:
\( \mathbf{A} \cdot+0.97 e V \)
B. \( +2.85 e V \)
\( \mathbf{c} \cdot+10.29 e V \)
D. +12.08 eV
E . \( +13.06 \mathrm{eV} \)


Find: \( (5 m+7 n)^{2} \)


Simplify:
\( (a+b+c)^{2}-(a-b+c)^{2} \)


Kolliker's pit' of protochordates is regarded as organ of
A. Smell
B. Taste
c. sight
D. None of the above


Write down the sequence of radiations
emitted in the following radioactive
processes. \( z+2 \boldsymbol{X}^{\boldsymbol{A}} \rightarrow_{z} \boldsymbol{Y}^{\boldsymbol{A}-\mathbf{4}} \rightarrow_{\boldsymbol{z}+\mathbf{1}} \boldsymbol{Y}^{\boldsymbol{A}-\mathbf{4}} \rightarrow_{\boldsymbol{z}-\mathbf{1}} \)
\( \boldsymbol{K}^{\boldsymbol{A}-\boldsymbol{8}} \)
A. \( \gamma-\beta-\alpha \)
B . \( \gamma-\alpha-\beta \)
c. \( \beta-\gamma-\alpha \)
D. \( \alpha-\beta-\alpha \)


Which one of the following statement(s)
is/are true about \( \operatorname{Ca}(\boldsymbol{O H})_{2} \) ?
This question has multiple correct options
A. It is used in the preparation of bleaching powder
B. It is a light blue solid
c. It is used in chromatography
D. Its solution in water is called lime water


Which of the following statement (s) is (are) true about heart?
(i) Left atrium receives oxygenated blood from different parts of the body while right atrium receives deoxygenated blood from lungs.
(ii) Left ventricle pumps oxygenated blood to different body parts while right ventricle pumps deoxygenated blood to lungs.
(iii) Left atrium transfers oxygenated
blood to right ventricle which sends it to
different parts of the body.
(iv) Right atrium receives deoxygenated blood from different parts of the body
while left ventricle pumps oxygenated blood to different parts of the body.
A . (i)
B. (ii)
c. (ii) and (iv)
D. (i) and (iii)


Solve \( \sin ^{4} x+\cos ^{4} x=5 / 8 \)


\( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}+\frac{\boldsymbol{y}}{\boldsymbol{x}}=\frac{\boldsymbol{y}^{2}}{\boldsymbol{x}^{2}} \)
Solve
\( \mathbf{A} \cdot y-2 x=k x^{2} y \)
B \( \cdot y+2 x=k x^{2} y \)
C \( \cdot 2 y-x=k x^{2} y \)
D. \( 2 y+x=k x^{2} y \)


The pathway of impulses in reflex action is called as
A. Stimulus
B. Action potential
c. Transportation
D. Reflex arc


Find the area of the triangle whose two adjecent sides are represented by the vectors \( \bar{a}=3 \bar{i}+4 \bar{j} \) and \( \bar{b}=-5 \bar{i}+7 \bar{j} \)


Fill in the blanks with approriate words. The maximum volume of inspirable air is called


To the nearest dollar, what does the
analyst believe the value of the stock will be at the end of three weeks? (Note:
Disregard the \( \$ \) sign when gridding your answer.)


Solve: \( a x+b=0 \)


Which of the following statement is/are
true?
(i) Sudden action in response to something in the environment is called
as a reflex action.
(ii) Sensory neurons carry signals from the spinal cord to muscles.
(iii) Motor neurons carry signals from receptors to the spinal cord.
(iv) The path through which signals are transmitted from a receptor to a muscle or a gland is called as reflex arc.
A \( \cdot \) (i) and (ii)
B. (i) and (iii)
c. (i) and (iv)
D. (i), (ii) and (iii)