Assertion
According to Rutheford's atomic model, electron should fall into the nucleus
Reason

Electron is a charged particle and it emits radiation while in motion and
lose energy
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


\( \mathbf{f} \mathbf{\Delta}=\left|\begin{array}{ccc}\boldsymbol{x}+\mathbf{1} & \boldsymbol{x}+\mathbf{2} & \boldsymbol{x}+\boldsymbol{a} \\ \boldsymbol{x}+\mathbf{2} & \boldsymbol{x}+\mathbf{3} & \boldsymbol{x}+\boldsymbol{b} \\ \boldsymbol{x}+\mathbf{3} & \boldsymbol{x}+\boldsymbol{4} & \boldsymbol{x}+\boldsymbol{c}\end{array}\right|=\mathbf{0}, \) then
the family of lines \( a x+b y+c=0 \)
passes through
A. (1,-1)
B. (1,-2)
c. (2,-3)
D. (0,0)


A1 \( \mu F \) capacitor and a \( 2 \mu F \) capacitor
are connected in series across a \( 1200 \mathrm{V} \)
supply line. The charged capacitors are
disconnected from the line and from
each other and reconnected with
terminals of like sign together. Find the final charge on each and the voltage
across them:
A \( \cdot \frac{1600}{13} V \)
В. \( \frac{1600}{32} V \)
c. \( \frac{1600}{3} V \)
D. \( \frac{160}{3} V \)


In common emitter amplifier, the current gain is \( 62 . \) The collector resistance and input resistance are \( 5 k \Omega \) an \( 500 \Omega \)
respectively. If the input voltage is \( 0.01 V, \) the output voltage is
A. \( 0.62 V \)
V
B. \( 6.2 V \)
\( c .62 V \)
D. \( 620 V \)


Select the wrong statement
A. The walls of diatoms are easily destructible
B. 'Diatomaceous earth' is formed by the cell walls of diatoms
C. Diatoms are chief producers in the oceans
D. Diatoms are microscopic and float passively in water


Let a function \( \boldsymbol{f}:[\mathbf{0}, \mathbf{5}] \rightarrow \boldsymbol{R} \) be
continuous, \( \boldsymbol{f}(1)=\boldsymbol{3} \) and \( \boldsymbol{F} \) be defined
as:
\( \boldsymbol{F}(\boldsymbol{x})=\int_{1}^{x} \boldsymbol{t}^{2} \boldsymbol{g}(\boldsymbol{t}) \boldsymbol{d} t, \) where \( \boldsymbol{g}(\boldsymbol{t})= \)
\( \int_{1}^{t} \boldsymbol{f}(\boldsymbol{u}) \boldsymbol{d} \boldsymbol{u} \)
Then for the function \( F \) the point \( x=1 \)
is
A. a point of local minima
B. a point of local maxima
c. not a critical point
D. a point of inflection


Is it true that the every relation which is
symmetric and transitive is also reflexive ? Give reasons.


The wheels of a car are of diameter
\( 80 \mathrm{cm} \) each. How many complete
revolutions does each wheel make in 10
minutes when the car is travelling at a speed of \( 66 k m \) per hour


A wave creates disturbance and
transmits matter from one place to
another.
A. True
B. False


Under which congruence condition the following figure are said to be congruent:
(a) Two Line Segments
(b) Two squares
(c)Two rectangles
\( (d) \) Two circles


Find \( P Q, \) if \( A B=150 m, \angle P=30^{\circ} \)
and \( \angle Q=45^{\circ} \)
.978 .8
8
3,524.4
\( c .279 .9 \)
D. 409.8


The water of crystallisation is the fixed number of
one formula unit of salt
A. hydrogen
B. water
c. oxygen
D. hydroxide


A parallel beam of light is incident from
air at an angular \( \alpha \) on the side PQ of a right - angled triangular prism of refractive index \( n=\sqrt{2} \)
Light undergoes total internal reflection
in the prism at the face PR when \( \alpha \) has
a minimum value of \( 45^{\circ} . \) The angle \( \theta \) of
the prism is
A \( \cdot 15^{\circ} \)
В \( \cdot 22.5^{\circ} \)
\( c \cdot 30^{\circ} \)
D. \( 45^{\circ} \)


Determine \( k \) for which the quadratic
equation has equal roots \( k x^{2}-5 x+ \)
\( \boldsymbol{k}=\mathbf{0} \)


\( \int e^{x}\left(\frac{1+\sin x}{1+\cos x}\right) d x \) is
A \( \cdot e^{x} \tan \left(\frac{x}{2}\right)+C \)
B \cdot \( \tan \left(\frac{x}{2}\right)+C \)
\( \mathbf{c} \cdot e^{x}+C \)
D. \( e^{x} \sin x+C \)


1 L oxygen gas at STP will weigh:
A \( .1 .43 \mathrm{g} \)
B. 2.24g
c. \( 11.2 g \)
D. 22.4g


The domain of \( f(x)=\sqrt{\log _{x^{2}-1}(x) \text { is }} \)
\( \mathbf{A} \cdot(\sqrt{2},+\infty) \)
B. \( (0,+\infty) \)
\( c \cdot(1,+\infty) \)
D. none of these


If \( \sin x+\sin y=\sqrt{3}(\cos y-\cos x) \)
then value of \( \sin 3 x+\sin 3 y \) equals
\( A \cdot 3 \)
B. \( \sqrt{3} \)
\( c \cdot 0 \)
D.


Which of the following shapes of \( S F_{4} \) is
more stable and why?
(i)
A. (i) Lone pair at axial position is stable
B. (ii) Lone pair at equatorial position is stable
c. Both are equally stable due to \( l p \) -bp repulsion
D. Both are unstable since \( S F_{4} \) has tetrahedral shape


The final product of the following sequence of reaction is? \( \left(\boldsymbol{C H}_{3} \boldsymbol{O}\right)_{2} \boldsymbol{C H} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{B r} \stackrel{M g}{\longrightarrow} \)
\( \stackrel{\boldsymbol{H}_{2} \boldsymbol{C}=\boldsymbol{O}}{\longrightarrow} \underset{\boldsymbol{h e a t}}{\boldsymbol{H}_{3}} \stackrel{\boldsymbol{\rho}}{_{\boldsymbol{h e a t}}} \)
\( ^{\text {A. }} \quad_{C H_{3} O C C H_{2} C H_{2} C H_{2} C H_{2} O H}^{0} \)
в. \( _{\|}^{o} \)
\( C H_{3} C C H_{2} C H_{2} C H_{2} C H_{2} O H \)
\( c \)
\( _{\mathrm{H}}^{\mathrm{O}} \)
\( \mathrm{CCH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{OH} \)


Fill in the blanks:
A functional group is an atom or in a molecule that gives the
molecule its characteristic


How many \( \mathrm{P}-\mathrm{H} \) bonds are there in
\( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{2} ? \)


The group has \( +R \) and \( -I \) effects are:
A. \( C H O \)
в. \( -O H \)
c. \( N C \)
D. \( C N \)


State which of the following are infinite
sets
\( (i) A=\left\{x: x \in Z: x^{2} \text { is even }\right\} \)
\( (i i) B=\{x: x \in R:-4<x<-2\} \)
A . (i) only y
B. (ii) only
c. \( (i) \) and \( (i i) \) both
D. Neither \( (i) \) nor \( (i i) \)


Biotic component of biosphere is not constituted by
A. Producers
B. Consumers
c. Decomposer
D. Air


The accompanying graph of position \( x \)
versus time represents the motion of a
particle. If \( p \) and \( q \) are positive
constants, the expression that best
describes acceleration \( a \) of the particle
is
A. \( a=-p-q t \)
B \( . a=-p+q t \)
\( \mathbf{c} \cdot a=p+q t \)
D. \( a=p-q t \)


If \( \boldsymbol{f}\left(\frac{\boldsymbol{x}-\boldsymbol{4}}{\boldsymbol{x}+\mathbf{2}}\right)=\mathbf{2} \boldsymbol{x}+\mathbf{1},(\boldsymbol{x} \in \boldsymbol{R}-\mathbf{1},-\mathbf{2}) \)
then \( \int f(x) d x \) is equal to:
(where \( C \) is constant of integration)
A \( \cdot 12 \log _{e}|1-x|+3 x+C \)
B. \( -12 \log _{e}|1-x|-3 x+C \)
C. \( 12 \log _{e}|1-x|-3 x+C \)
D. \( -12 \log _{e}|1-x|+3 x+C \)


Match the Lists I and II and pick the
correct matching from the codes given
below.
List I
(i) Peroxy acetyl nitrate
1. Carcinogens
(ii) Polycyclic aromatic \( \quad \) 2. Global warming hydrocarbons
3. Photochemical
(iii) IR active molecules
4. Waste
(iv) Dioxins \( \quad \) incineration
A. \( (i)-3, \) (ii) \( -1, \) (iii) \( -4, \) (iv) -2
B. (i) - 3, (ii) - 2, (iii) - 4, (iv) - 1
C. (i) - 3, (ii) - 1, (iii) - 2, (iv) - 4
D. (i) - 4, (ii) - 2, (iii) - 1, (iv) - 3


Maximum value of \( \frac{\log x}{x} \) is
\( A \cdot \frac{2}{e} \)
B.
\( c \cdot \frac{1}{e} \)
D.


Match the terms to these definitions.
Conjugation, transformation, transduction, phototrophs, saprotrophs, archaebacteria, actinomycetes, mycoplasma, thermoacidophiles, methanogens, halophiles, vibrio, Bacillus, micrococcus, helical, staphylococcus. a kind of archaebacteria, found in
hot sulphur springs.


Find the number of terms of the AP
\( 121,117,113, \dots,-3 ? \)
A . 32
B. 30
c. 28
D . 26


A buffer solution with \( p H=9 \) is to be
prepared by mixing \( N H_{4} C I \) and
\( N H_{4} O H . \) Calculate the number of
moles of \( N H_{4} C I \) that should be added
to one litre pf \( 1.0 M N H_{4} O H .\left[K_{b}=\right. \)
\( \left.1.8 \times 10^{-5}\right] \)
A . 3.4
B . 2.
c. 1.5
D. 1.8


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


A student wants to use two p-njunction
diodes to convert alternating current into direct current. Draw the labelled
circuit diagram he/she would use and explain how it work


The probability that it will rain on a
particular day is 0.64 what is the probability that it will not rain on that day?


Choose the correct options.
A. If the incident rays are converging, we have a real object
B. If the final ray are converging, we have a real image.
C. The image of a virtual object is called a virtual image.
D. If the image is virtual, the corresponding object is called a virtual object


Which of the following pairs has not the same dimension?
A. Stress; pressure
B. Force; surface tension
c. Impulse; linear momentum
D. Frequency; angular velocity


Assertion: The solubility of
\( \boldsymbol{C H}_{3} \) COOAg in water considering
hydrolysis of \( C H_{3} C O O^{-} \) ions would be
greater than that ignoring the hydrolysis. Reason: During hydrolysis, the concentration of acetate ions decrease
as they combine with hydrogen ions to
form acetic acid.
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


Using (iiii) above the best upper bound of \( \int_{0}^{1} \sqrt{1+x^{4}} d x \)
A . 1.2
B. \( \sqrt{1.22} \)
c. \( \sqrt{1.2} \)
D. \( \sqrt{1.4} \)


A body is projected vertically upwards. The times corresponding to height \( h \) while ascending and while descending
are \( t_{1} \) and \( t_{2} \) respectively. Then the
velocity of projection is \( (g \) is acceleration due to gravity)
A. \( g \sqrt{t_{1} t_{2}} \)
an \( t_{2} \)
в. \( \frac{g t_{1} t_{2}}{t_{1}+t_{2}} \)
c. \( \frac{g \sqrt{t_{1} t_{2}}}{2} \)
D. \( \frac{g\left(t_{1}+t_{2}\right)}{2} \)


Which elements occur in the native
state?


Which reactions usually release energy that is used to drive chemical reactions.
A. Anabolic
B. Catabolic
c. Photosynthesis
D. None of the above


The mass of proton is \( _{---}-- \) times the
mass of an electron.
A . 1822
в. 1857
\( c \cdot 1869 \)
D. 1837


Figure shows the shape of a string, the pairs of points which are in opposite phase is
A. A and B
B. B and C
\( c \cdot c \) and \( E \)
D. A and E


In the given diagram circle A represents
teachers who teach Physic circle B represents teachers who can teach
Chemistry and circle C represents teachers who can teach Mathematics
Amount the regions marked
\( \boldsymbol{p}, \boldsymbol{q} \cdot \boldsymbol{r}, \boldsymbol{s}, \boldsymbol{t}, \boldsymbol{u}, \boldsymbol{v} \) the one that represents
teacher who can teach Physics and
Mathematics but not Chemistry is
\( A \)
B.
\( c \)
\( D \)


Three measurement are made as
\( 18.425 \mathrm{cm} 7.21 \mathrm{cm} \) and \( 5.0 \mathrm{cm} . \) The
addition should be written as then:
A. \( 30.635 \mathrm{cm} \)
B . \( 30.64 c m \)
c. \( 30.63 c m \)
D. \( 30.6 \mathrm{cm} \)


\( \int \frac{3 x^{2}}{\sqrt{\left(9-16 x^{6}\right)}} d x \)
A. \( \frac{1}{4} \sin ^{-1} \frac{4}{3} x^{3} \)
B \( \cdot \frac{1}{2} \sin ^{-1} \frac{4}{3} x^{3} \)
c. \( \frac{1}{4} \sin ^{-1} \frac{2}{3} x^{3} \)
D. \( \frac{1}{4} \sin ^{-1} \frac{4}{3} x^{6 .} \)


For two data sets, each size \( 5, \) the
variances are given to be 4 and 5 and the corresponding means are given to be 2 and \( 4, \) respectively. The variance of the combined data set is
A \( \cdot \frac{5}{2} \)
B. \( \frac{11}{2} \)
c. \( \sqrt{\frac{11}{2}} \)
D. \( \frac{13}{2} \)


How many arrangements of the word \( A R R A N G E \) can be made
\( (i) \) If the two \( R^{\prime} s \) are not allowed to
come together, let it be \( k ? \)
\( (i i) \) If neither the two \( R^{\prime} s \) nor the two
\( A^{\prime} s \) are allowed to come together, let it
be \( \mathrm{m} \)
Find the sum of digits of \( \mathrm{m}+\mathrm{k} \) ?


The ionization constant of
dimethylamine is \( 5.4 \times 10^{-4} \). Calculate
its degree of ionization in its \( 0.02 \mathrm{M} \) solution. What percentage of dimethylamine is ionized if the solution
is also 0.1M in NaOH?


If \( A=60^{\circ} \) verify the following.
\( \sin 2 A=2 \sin A . \quad \cos A \)


The equilibrium constant for the
ionization of \( \boldsymbol{R} \boldsymbol{N} \boldsymbol{H}_{2}(\boldsymbol{g}) \) in water as
\( \boldsymbol{R} \boldsymbol{N} \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{H}_{2} \boldsymbol{O}(l) \rightleftharpoons \)
\( \boldsymbol{R} \boldsymbol{N} \boldsymbol{H}_{3}^{+}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{O} \boldsymbol{H}^{-}(\boldsymbol{a} \boldsymbol{q}) \)
is \( 8 \times 10^{-6} \) at \( 25^{\circ} \mathrm{C} \). Find the pH of a
solution at equilibrium when pressure
of \( \boldsymbol{R} \boldsymbol{N} \boldsymbol{H}_{2}(\boldsymbol{g}) \) is \( \boldsymbol{0} . \boldsymbol{5} \) bar:
\( \mathbf{A} \cdot \approx 12.3 \)
в. \( \approx 11.3 \)
c. \( \approx 11.45 \)
D. None of the above


Q Type your question-
thermodynamic properties during the formation of 1 mol of an ideal binary solution.
\( A \)
\( (\mathbf{A}) \)
B.
\( (\mathbf{A}) \)
\( c \)
\( (\mathbf{A}) \)
\( D \)
(A)


In scattering experiment, find the distance of closest approach, if a \( 6 \mathrm{MeV} \) \( \alpha \) -particle is used
A . \( 3.2 \times 10^{-16} \mathrm{m} \)
В. \( 2 \times 10^{-14} \mathrm{m} \)
c. \( 4.6 \times 10^{-15} \mathrm{m} \)
D. \( 3.2 \times 10^{-15} \mathrm{m} \)


The conductivity of N/10 KCl solution at
\( 20^{\circ} \mathrm{C} \) is \( 0.0212 \mathrm{Scm}^{-1} \) and the
resistance of cell containing this
solution at \( 20^{\circ} C \) is 55 ohm. The cell
constant is:
A \( .2 .173 \mathrm{cm}^{-1} \)
B. \( 1.166 \mathrm{cm}^{-1} \)
c. \( 4.616 \mathrm{cm}^{-1} \)
D. \( 3.324 c m^{-1} \)


is present among the molecules of \( \boldsymbol{H} \boldsymbol{C l} \)
A. Electrostatic force
B. Hydrogen bond
c. Dipole-dipole attraction
D. All of the above


Two liquids have the densities in the ratio of 1: 2 and specific heats in the
ratio of \( 2: 1 . \) The ratio of thermal
capacity of equal volume of those liquids is:
A . 1: 1
B. 1: 4
c. 4: 1
D. 2: 1


A large mixing tank currently contains
200 gallons of water into which 10 pounds of sugar have been mixed. A tap
will open pouring 20 gallons per minute
of water into the tank at the same time
sugar is poured into the tank at a rate
of 2 pound per minute. Find the concentration (pounds per gallon) of sugar in the tank after 14 minutes.
Then
A. the concentration is greater than at the beginning?
B. the concentration lesser than at the beginning?
c. the concentration equal to the concentration at the beginning?
D. None of the above


toppr
Q Type your question
same straight line
Which of these objects is experiencing
a non-zero net force?
4
B.
\( c \)
\( D \)
\( E \)


What is Geminal dihalide?


\( \begin{array}{ll}\text { List-I } & \text { List-II } \\ \text { (A) } O_{3}+C_{2} N_{2} & \text { (1) Black colour } \\ \text { (B) } H_{2} O_{2}+O_{3} & \text { (2) Rocket fuel } \\ \text { (C) } A g+O_{3} & \text { (3) Tailing } \\ \text { (D) } O_{3}+H g & \text { (4) } O_{2}+H_{2} O\end{array} \) The correct match is:
A. A-1, B-3, C-2, D-4
B. A-2, B-4, C-1, D-3
C. \( A-3, B-2, C-3, D-1 \)
D. \( A-4, B-1, C-4, D-2 \)


A person is suffering from frequent episodes of nasal discharge, nasal congestion, reddening of eyes and
watery eyes. These are the symptoms of
A. Cyanosis
B. Bronchitis
c. Rhinitis
D. Bronchial carcinoma


Prove that if the mid-points of the opposite sides of a quadrilateral are joined, they bisect each other.


Soil which is carried by air, known as
A. Alluvial
B. Colluvial
c. Eolian
D. Glacial


In Millikan's oil drop experiment, what is the terminal speed of an uncharged drop of radius \( 2.0 \times 10^{-5} m \) and density
\( 1.2 \times 10^{3} k g m^{-3} . \) Take the viscosity of
air at the temperature of the experiment to be \( 1.8 \times 10^{-5} \) Pa s. How
much is the viscous force on the drop at
that speed ? Neglect buoyancy of the drop due to air.


topp
ом ком
Q туре уочr question
\( \mathrm{CH}_{3}-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\mathrm{O}-\mathrm{CH}_{3} \)
\( \mathrm{CH}_{3}-\mathrm{CH}_{2}-\mathrm{CH}-\mathrm{O}-\mathrm{CH}_{3} \)
\( \mathrm{CH}_{3} \)
\( \mathrm{CH}_{3} \)
\( \mathrm{CH}_{3}-\mathrm{C}-\mathrm{O}-\mathrm{CH}_{3} \)
\( \mathrm{CH}_{3} \)
D.
\( \mathrm{CH}_{3}-\mathrm{CH}-\mathrm{CH}_{2}-\mathrm{O}-\mathrm{CH}_{3} \)
\( \mathrm{CH}_{3} \)


The real value of \( k \) for which \( f(x)= \) \( x^{2}+k x+1 \) is increasing on \( (1,2), \) is
A . -2
B. - 1
\( c .1 \)
D. 2


Bowmans capsule is constituent of
A. Renal artery
B. Ureter
c. Uriniferous tubule
D. Renal portal vein


The Venn diagram shows sets \( P, Q \) and \( R \) with regions labelled, I, II, III and IV.
State the region which represents set
\( \left[\boldsymbol{P} \cap(\boldsymbol{Q} \cup \boldsymbol{R})^{\prime}\right] \)
4
B.
\( c \)
\( D \cdot|v| \)


Reaction of magnesium ribbon with dilute sulphuric acid to form magnesium sulphate and hydrogen is a combination reaction.
A. True
B. False


Which of the following is an example of rapid combustion?
A. Burning of wood
B. Burning of LPG
c. Burning of coal
D. Burning of a candle


\( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{3} \stackrel{\boldsymbol{B r}_{2} / \boldsymbol{h} \boldsymbol{v}}{\boldsymbol{A}} \)
\( \boldsymbol{B} \stackrel{\boldsymbol{B r}_{2} / \boldsymbol{h} \boldsymbol{v}}{\longrightarrow} \boldsymbol{C} \stackrel{\boldsymbol{N a} / \text {ether}}{\boldsymbol{D}} \)
The compound \( D \) is :
\( \mathbf{A} \cdot C H_{3}-C H_{2}-C H_{2}-C H_{3} \)
B \( \cdot C H_{3}-C H_{2}-O-C H_{2}-C H_{3} \)
\( \mathbf{c} \cdot C H_{3}-C H\left(C H_{3}\right)-C H\left(C H_{3}\right)-C H_{3} \)
\( \mathbf{D} \cdot C H_{3}-C H_{2}-C H_{3} \)


The blood vessel which supply oxygenated blood to cardiac tissue is
A. Coronary artery
B. Coronary vein
c. coronary sinus
D. Pulmonary vein


The relation between the time of flight of projectile \( T, \) and the time to reach the
maximum height \( t_{m} \) is
A \( \cdot T_{f}=2 t_{m} \)
B . \( T_{f}=t_{m} \)
c. \( T_{f}=t_{m} / 2 \)
\( \mathbf{D} \cdot T_{f}=\sqrt{2} t_{m} \)


An organic compound (A) of molecular
formula \( C_{2} H_{6} O \) on oxidation with
alkaline \( K M n O_{4} \) solution gives an acid (B) with the same number of
carbon atoms. Compound A is used as an antiseptic to sterilize wounds, in hospitals. Identify A and
B. Write the
chemical equation involved in the formation of B from A.


Which of the following statements are
true?

Of the two integers, if one is negative, then their product must be positive.
A. True
B. False


The slope of a straight line passing through \( A(-2,3) \) is \( -4 / 3 . \) The points on the line that are 10 units away from \( A \)
are
A \( .(-8,11),(4,-5) \)
B. (-7,9), (17-1)
c. (7,5)(-1,-1)
D. (6,10),(3,5)


Which of the following option could represent the ball being thrown upward before it begins falling back down?
\( \mathbf{A} \)
(A)
B.
(B) \( \ldots . \)
\( c \)
(C)
D.
(D)
E
(E)


The geometric mean of the first n terms
of the series \( a, a r, a r^{2}, \dots, \) is
A \( \cdot a r^{n / 2} \)
2
B \( . a r^{n} \)
c. \( a r^{(n-1) / 2} \)
D. \( a r^{n-1} \)


Find the direction cosines of
perpendicular from the origin to the plane \( \bar{r}(2 \hat{i}+3 \hat{j}+6 \hat{k})+7=0 \)


Find the circulation of the vector \( \vec{B} \)
around the square path \( \Gamma \) with side \( l \)
located as shown in the figure above.
\( \mathbf{A} \cdot \oint \vec{B} d r=2(1-\mu) B l \sin \theta \)
в. \( \oint \vec{B} d r=(1+\mu) B l \sin \theta \)
c. \( \oint \vec{B} d r=2(1-+\mu) B l \sin \theta \)
D. \( \oint \vec{B} d r=(1-\mu) B l \sin \theta \)


A body of mass \( 5 k g \) is acted on by a net
force \( \boldsymbol{F} \) which varies with time \( t \) as
shown in graph. Then the net
momentum in \( S I \) units gained by the
body at the end of 10 seconds is
\( A \)
в. 100
\( c .140 \)
D. 200


Calculate percentage of water of
crystallization in \( : M g S O_{4} .7 H_{2} O \) [Atomic masses of \( M g=24, S= \)
\( \mathbf{3 2}, \boldsymbol{O}=\mathbf{1 6}, \boldsymbol{H}=\mathbf{1}] \)


In the given figure a piano-concave lens is placed on a paper on which a flower is drawn. how far above its actual position
does the flower appear to be?
\( A \cdot 10 \mathrm{cm} \)
B. \( 15 \mathrm{cm} \)
\( c \cdot 50 \mathrm{cm} \)
D. none of these


The number of basic layers of inner wall of the alimentary canal is
A. one
B. Two
c. Three
D. Four


An audible sound has the frequency
range of


The value of \( \sec ^{2} A \tan ^{2} B- \)
\( \tan ^{2} A \sec ^{2} B \) is
\( \mathbf{A} \cdot \tan ^{2} B-\tan ^{2} A \)
B \( \cdot \sec ^{2} B+\sec ^{2} A \)
c. \( \tan ^{2} B-\sec ^{2} A \)
\( \mathbf{D} \cdot \sec ^{2} B-\tan ^{2} A \)


Tidal volume of air in a normal healthy man during inspiration is about
A. 300-400 m1
в. 500-700 m1
c. \( 900-1000 \mathrm{ml} \)
D. 100-250 m1


\( \int_{0}^{\pi} \frac{\phi d \phi}{1+\sin \phi} \) is equal to
A . \( -\pi \)
в. \( \frac{\pi}{2} \)
c. \( \pi \)
D. None of these


Which of the following is not the name of a physical quantity?
A. Displacement
B. Momentum
c. Meter
D. Torque


\( \boldsymbol{A}_{(g)} \stackrel{\Delta}{\longrightarrow} \boldsymbol{P}_{(g)}+\boldsymbol{Q}_{(g)}+\boldsymbol{R}_{(g)}, \) follows first
order kinetics with a half life of \( 69.3 s \) at
\( \mathbf{5 0 0} \mathrm{K} . \) Starting from the \( \operatorname{gas}^{\prime} \boldsymbol{A}^{\prime} \)
enclosed in a container at \( 500 \mathrm{K} \) and at
a pressure of 0.4 atm, the total
pressure of the system after \( 230 s \) will
be:
A. 1.32 atm
B. 1.12 atm
c. 1.15 atm
D. 1.22 atm


Maya bought a television for 14,500
rupees and spent 500 rupees on transportation. she sold that television
for 12,000 rupees. Calculate her loss
percent
A . \( 12.22 \% \)
B. \( 32.23 \% \)
c. \( 22.22 \% \)
D. 20\%


\( j_{j}^{j} \)


If each edge of cuboid of surface area \( \boldsymbol{S} \)
is doubled, then surface area of the new
cuboid is
A . \( 2 S \)
B. \( 4 S \)
\( c \cdot 6 S \)
D. \( 8 S \)


Divide 32 into two parts such that 5
times one part added to 6 times the
other part gives 164


Find the unit vector in the direction of \( \mathbf{3} \hat{\mathbf{i}}-\mathbf{6} \hat{\mathbf{j}}+\mathbf{2} \widehat{\mathbf{k}} \)


If we switch on a fan heater, it blow hot
air through a grille into the room, then
A. Cold air rises upwards
B. Hot air rises upwards
C. Neither A nor B
D. None


Difference between diastole and systole
pressure is
A . 40
B. 60
c. 80
D. 120


If \( \boldsymbol{x}=\frac{1}{2}, \boldsymbol{y}=1, \boldsymbol{z}=2 \operatorname{then} \boldsymbol{x}^{100} \boldsymbol{y}^{99} \boldsymbol{z}^{99}+ \)
\( \boldsymbol{x}^{99} \boldsymbol{y}^{100} \boldsymbol{z}^{99}+\boldsymbol{x}^{99} \boldsymbol{y}^{99} \boldsymbol{z}^{100}= \)
\( A \cdot \frac{5}{2} \)
B. \( \frac{7}{2} \)
\( c \cdot \frac{3}{2} \)
D.


The mode of reproduction in which an individual produces offspring without the help of another individual is called
as
A. Sexual reproduction
B. Tissue culture
c. Fertilisation
D. Asexual reproduction


Match the following catalyst with their
products
\( -B ;(i i)-A ;(i i i)-D ;(i v)-C \)
\( \mathbf{A} \cdot(i) \)
B \( \cdot(i)-C ;(i i)-D ;(i i i)-B ;(i v)-A \)
\( \mathbf{c} \cdot(i)-D ;(i i)-A ;(i i i)-B ;(i v)-C \)
D. \( (i)-A ;(i i)-B ;(i i i)-C ;(i v)-D \)


The correct order in the processing of
wool is:
A. Shearing-sorting-scouring - fiberspinning fiberdying - rolling
B. Shearing-scouring-sorting - fiberspinning fiberdying - rolling
c. Shearing - scouring - sorting - fiberdying
fiberspinning - rolling
D. Shearing-sorting - scouring - fiberspinning rolling - fiberdying


Who proposed the wave theory of light?


Fe, Ti and Sn metals are found in
nature as?
A. Sulphide ores
B. Oxide ores
c. Native
D. Silicate ores


Which alkane, having a molecular weight of \( 86, \) will form only two monobromo alkanes? If the alkane is
\( C_{n} H_{m}, \) find \( n ? \)
A . 4
B. 5
\( c \cdot 6 \)
\( D \)


Denial of a statement is called its
A. negation
B. converse
c. inverse
D. truth value


Let \( f(x)=\left[\begin{array}{cc}e^{x}, & x \leq 0 \\ |1-x| & x>0\end{array}\right], \) then which
one of the following statement is incorrect ?
A. continuous and differentiable at \( x=0 \)
B. \( \lim _{x \rightarrow-\infty} f(x)=0 \)
c. one local maxima and one local minima
D. Decreasing function in (0,1)


Solubility of \( M X_{2} \) type electrolytes is
\( 0.5 \times 10^{-4} \) mole/lit. Then find out \( K_{s p} \) of
electrolytes.
В. \( 25 \times 10^{-10} \)
c. \( 1.25 \times 10^{-13} \)
D. \( 5 \times 10^{-13} \)


Three aluminium rods of equal length
form an equilateral triangle \( A B C \). Take \( O \)
(mid point of \( \operatorname{rod} B C \) ) as the origin. The
increase in Y-coordinate of center
of mass per unit change in temperature of the system is given as \( x \times 10^{-6} \mathrm{m} /^{\circ} \mathrm{C} \)
Find \( x \). Assume the length of each rod is
\( 2 m, \) and \( \alpha_{a l}=4 \sqrt{3} \times 10^{-6} /^{\circ} \mathrm{C} \)


In an electromagnetic wave in free space the root mean square value of the electric filed is \( \boldsymbol{E}_{r m s}=\boldsymbol{6} \boldsymbol{V} / \boldsymbol{m} . \) The peak
value of the magnetic field is:
A \( \cdot 4.23 \times 10^{-8} T \)
B. \( 1.41 \times 10^{-8} T \)
c. \( 2.83 \times 10^{-8} T \)
D. \( 0.70 \times 10^{-8} T \)


Give two example of intrinsic semiconductor?
A . aluminum
B. Silicon, germanium
c. copper
D. nitrogen


In an experiment to trace the path of a ray of light through a glass prism for different values of angle of incidence a student would find that the emergent
ray:
A. is parallel to the incident ray
B. perpendicular to the incident ray
C. is parallel to the refracted ray
D. bends at an angle to the direction of incident ray


Three point charges, each \( +q \) are placed at the vertices of an equilateral triangle. What charge should be placed at its centroid so that all four charges
are in equilibrium?
A \( \cdot \frac{q}{\sqrt{2}} \)
B. \( \frac{q}{\sqrt{3}} \)
c. \( \frac{\sqrt{3} q}{2} \)
D. \( \frac{2 q}{\sqrt{3}} \)


A machine part is shown in cross
section in figure consists of two homogeneous solid, coaxial cylinders \( A B \) as the common axis. Where is its
centre of mass from A? (in \( \mathrm{m} \) )
\( A \)
\( \overline{7} \)
B. 2 \( \overline{7} \)
c. \( \frac{52}{7} \)
D. 5


Black diamonds are called:
A. carnado
B. carbonado
C . carbond
D. arnold


The median of an arranged series of \( n \) even observations, will be
A \( \cdot\left(\frac{n+1}{2}\right) \) th term
B. \( \left(\frac{n}{2}\right) \) th term
c. \( \left(\frac{n}{2}+1\right) \)
D. Mean of \( \left(\frac{n}{2}\right) \) th and \( \left(\frac{n}{2}+1\right) \) th terms


An experiment is performed to find the refractive index of glass using a travelling microscope. In this experiment distances are measured by:
A. a screw gauge provided on the microscope
B. a standard laboratory scale
c. a vernier scale provided on the microscope
D. a meter scale provided on the microscope


\( 0.303 \mathrm{g} \) of the organic compound in Duma's method on combustion gave
\( 32.27 \mathrm{ml} \) of moist nitrogen at \( 27^{\circ} \mathrm{C} \) and
at P mm of Hg pressure. The vapour
pressure at \( 27^{\circ} \mathrm{C} \) is \( 21 \mathrm{mm} \) of Hg. Find
the value of P.
A. \( 725 \mathrm{mm} \) of \( \mathrm{Hg} \)
B. \( 746 \mathrm{mm} \) of \( \mathrm{Hg} \)
c. \( 710 \mathrm{mm} \) of \( \mathrm{Hg} \)
D. \( 760 \mathrm{mm} \) of \( \mathrm{Hg} \)


A deuterium is:
A. an electron with a positive charge
B. a nucleus havng two protons
C . a nucleus containing a neutron and two protons
D. a nucleus containing a neutron and a proton


The pressure on a swimmer \( 10 \mathrm{m} \) below the surface lake is:(Atmospheric
pressure \( =1.01 \times 10^{5} \) Pa,Density of
water \( \left.=1000 k g / m^{3}\right) \)
A . 10 atm
B. 5 atm
c. 15 atm
D. 2 atm


Write the structure of \( \mathrm{p} \)
methylbenzaldehyde molecule.


Assertion (A): The half life of a radioactive isotope is equal to \( \frac{\mathbf{0 . 6 9 3}}{\boldsymbol{\lambda}} \) Reason (R): Radioactivity is a first order reaction
The correct answer is
A. Both A and R are true and R is correct explanation of A
B. Both A and R are true and R is not the correct explanation of
C. A is true but R is false
D. A is false but R is true


Set up an equation of a tangent to the graph of the following function.

A sector with a central angle \( \alpha \) is cut off
from a circle. A cone is made of the
remaining part of the circle. At what
value of \( \alpha \) is the capacity of the cone
the greatest?


Exchange of gases takes place through
the
A. Wall of trachea and blood capillaries
B. Wall of alveoli and blood capillaries
C. Wall of pleura and diaphragm
D. Wall of alveoli and bronchioles


How many terms are there in the G.P \( \mathbf{3}, \mathbf{6}, \mathbf{1 2}, \mathbf{2 4}, \dots \dots \dots, \mathbf{3 8 4} ? \)
\( \mathbf{A} \cdot \mathbf{8} \)
B. 9
c. 10
D. 11
E. 7


Which of the following statements is
not true?
\( \mathbf{A} \cdot C O_{2} \) is the best fire extinguisher
B. Global warming can cause acid rain
C. Burning of coal and diesel releases sulphur dioxide gas
D. LPG has higher calorific value than biogas


If the function \( \mathbf{f}(\boldsymbol{x})= \) \( \left\{\begin{array}{ll}\frac{\sin 3 x}{x} & (x \neq 0) \\ \frac{k}{2} & (x=0)\end{array} \) is continuous at \right.
\( x=0, \) then \( k \) is:
\( A \cdot 3 \)
B. 6
\( c \cdot 9 \)
\( D \)


A sealed bottle containing some water
is made up of two cylinders \( A \) and \( B \) of
radius \( 1.5 \mathrm{cm} \) and \( 3 \mathrm{cm} \) respectively, as
shown in the figure. When the bottle is
placed right up on a table, the height of
water in it is \( 15 \mathrm{cm}, \) but when placed
upside down, the height of water is \( 24 \mathrm{cm} . \) The height of the bottle is
A \( .25 \mathrm{cm} \)
B. \( 26 \mathrm{cm} \)
c. \( 27 \mathrm{cm} \)
D. 28 cm


An object is placed at a distance of 15 \( \mathrm{cm} \) from a convex lens of focal length 10 \( \mathrm{cm} . \) On the other side of the lens, a convex mirror is placed such that its distance from the lens equals focal length of the lens. The focal length of the convex mirror is
A. 20 cm
B. \( 10 \mathrm{cm} \)
c. \( 15 \mathrm{cm} \)
D. 30 cm


\( \boldsymbol{y}=\sqrt{\frac{\boldsymbol{1}-\boldsymbol{x}}{\mathbf{1}+\boldsymbol{x}}} \)
Prove that \( \left(\mathbf{1}-\boldsymbol{x}^{2}\right) \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}+\boldsymbol{y}=\mathbf{0} \)


State True or False.
Dipole moment of \( B H_{3} \) is zero.
A. True
B. False


Two thin lenses of focal lengths
\( f_{1} \) and \( f_{2} \) are in contact and co-axial.
the combination is equivalent to single lens of power
A \( \cdot f_{1}+f_{2} \)
в. \( \frac{f_{1} f_{2}}{f_{1}+f_{2}} \)
c. \( \frac{f_{1}+f_{2}}{2} \)
D. \( \frac{f_{1}+f_{2}}{f_{1} f_{2}} \)


(a) Identify the given diagram. Name
the parts 1 to 5 .
(b) What is contraception? List three
advantages of adopting contraceptive
measures.


The force responsible for the union of
two ice blocks into a single block is:
A. van der waals force
B. hydrogen bonds
c. dipole interaction
D. van der waals repulsion


ABCD is a parallelogram with sides \( A B=12 \mathrm{cm}, B C=10 \mathrm{cm} \) and
diagonal \( \boldsymbol{A C}=\mathbf{1 6} \mathrm{cm} . \) Find the
approximate area of the parallelogram.
\( \mathbf{A} \cdot 119.8 \mathrm{cm}^{2} \)
B. \( 103.7 \mathrm{cm}^{2} \)
\( \mathrm{c} \cdot 15.7 \mathrm{cm}^{2} \)
D. None of these


Rennin and lactase, the enzymes required to digest milk, disappear in the human body by the age of
A . Five
B. Three
c. Two
D. Eight


A step down transformer is used on
\( 1000 V \) line to deliver \( 20 A \) at \( 120 V \) at
the secondary coil. If the efficiency of
the transformer is \( 80 \% \) the current
drawn from the line is
\( \mathbf{A} \cdot 3 A \)
в. 30 А
\( \mathbf{c} \cdot 0.3 A \)
D. 2.4 \( A \)


As shown in fig., an object \( O \) is at the
position (-10,2) with respect to the
origin \( P . \) The concave mirror \( M_{1} \) has
radius of curvature \( 30 \mathrm{cm} . \) A plane
mirror \( M_{2} \) is kept at a distance of
\( 40 \mathrm{cm} \) in front of the concave mirror


A laser used to weld detached retains
emits light with a wavelength 652 nm in
pulses that are of \( 20 m s \) duration. The average power during each pulse is \( 0.6 W . \) The energy in each pulse and in a single photon are :
A \( .7 .5 \times 10^{15} e V, 2.7 e V \)
В . \( 6.5 \times 10^{16} e V, 2.9 e V \)
\( c \cdot 6.5 \times 10^{16} e V, 2.7 e V \)
\( V \)
D. \( 7.5 \times 10^{16} e V, 1.9 e V \)


The parabola \( y^{2}=4 x+1 \) divides the
\( \operatorname{disc} x^{2}+y^{2} \leq 1 \) into two regions with
\( \operatorname{areas} A_{1} \) and \( A_{2} . \) Then \( \left|A_{1}-A_{2}\right| \) equals
A \( \cdot \frac{1}{3} \)
B. \( \frac{2}{3} \)
c.
D. \( \frac{\pi}{3} \)


Hybridised states of carbon in graphite and diamond are respectively:
\( \mathbf{A} \cdot s p^{3}, s p^{3} \)
в. \( s p^{3}, s p^{2} \)
c. \( s p^{2}, s p^{2} \)
D. \( s p^{2}, s p^{3} \)


In the given figure, if parallelogram
ABCD and rectangle ABEF are of equal
area then:
A. Perimeter of ABCD=Perimeter of ABEF
B. Perimeter of ABCD < Perimeter of ABEF
C. Perimeter of ABCD > Perimeter of ABEF
D. Perimeter of \( A B C D=\frac{1}{2} \) (Perimeter of ABEF)


If \( f(x)=\frac{x^{2}}{2}, 0 \leq x<1 \) and \( f(x)= \)
\( \frac{2 x^{2}-2 x+3}{2} ; 1 \leq x \leq 2, \) then
\( \lim _{x \rightarrow 1} f(x)= \)
A \( \cdot \frac{1}{2} \)
B. \( \frac{3}{2} \)
c. does not exist
D. \( -\frac{1}{2} \)


The density of a gas at N.T.P. is \( 1.5 \mathrm{gm} / \) lit its density at a pressure of \( 152 \mathrm{cm} \) of \( \mathrm{Hg} \) and temperature \( 27^{0} \mathrm{C} \)
A \( \cdot \frac{273}{100} g m / l t r \)
B . \( \frac{150}{233} \mathrm{gm} / \mathrm{ltr} \)
\( \mathbf{c} \cdot \frac{1}{273} g m / l t r \)
D. \( 1.5 \mathrm{gm} / \) lit


For each the differential equations given, find the general solution:
\( \left(1+x^{2}\right) d y+2 x y d x=\cot x d x(x \neq 0) \)


What is the probability that you will get admission in atleast two colleges?


Refrigeration helps in food reservation by:
A. killing the germs
B. reducing the rates of biochemical reactions
c. destroying enzyme action
D. decreasing the size of bacteria


Sun ray are incident at an angle of \( 24^{\circ} \)
with the horizontal. How can they be directed parallel to the horizon using a plane mirror?


Let \( A \) and \( B \) be events such that \( \boldsymbol{P}(\overline{\boldsymbol{A}})=\frac{4}{5}, \boldsymbol{P}(\boldsymbol{B})=\frac{1}{3}, \boldsymbol{P}\left(\frac{\boldsymbol{A}}{\boldsymbol{B}}\right)=\frac{1}{6} \)
then:
A \( . P(A \cap B) \)
в. \( P(A \cup B) \)
\( ^{\mathrm{c}} \cdot_{P}\left(\frac{B}{A}\right) \)
D. Are \( A \) and \( B \) independent


The surface that have zero flux are
\( \mathbf{A} \cdot S_{2}, S_{4}, \) and \( S_{5} \)
B. \( S_{1}, S_{3}, S_{4} \) and \( S_{6} \)
\( c \cdot S_{1}, S_{2}, \) and \( S_{3} \)
\( \mathrm{D} \cdot S_{2}, S_{3}, \) and \( S_{4} \)


Differentiate w.r.t \( x \)
\( \boldsymbol{y}=\log \left(\boldsymbol{4} \boldsymbol{e}^{\boldsymbol{3} \boldsymbol{x}}\right) \)


When the radius of earth is reduced by
\( 1 \% \) with out changing the mass, then the acceleration due to gravity will
A. increase by \( 2 \% \)
B. decrease by 1.5\%
C. increase by \( 1 \% \)
D. decrease by 1\%


Prothrombin required for blood clotting is produced in
A. Stomach
B. Liver
c. spleen
D. Pancreas


In Yeast, anaerobic respiration produces
A. \( C O_{2} \) and ethanol
B. \( C O_{2} \) and water
\( \mathrm{c} \cdot O_{2} \) and lactic acid
D. \( O_{2} \) and pyruvic acid


Combustion is
A. exothermic reaction
B. endothermic reaction
C. addition reaction
D. None of these


Mendeleev arranged the known elements in a/an order of
their atomic masses.
A. increasing
B. decreasing
c. random
D. none of the above


Which of the following pairs is not
correct?
A. strain-dimensionless
B. stress-N/m \( ^{2} \)
c. modulus of elasticity- \( N / m^{2} \)
D. poisson's ratio- \( N / m^{2} \)


The molecular formula of Baking soda
is:
A. \( N a H C O_{3} \)
в. \( N a H C O_{3} .6 H_{2} O \)
\( \mathbf{c} \cdot N a_{2} C O_{3} \)
D. \( N a_{2} C O_{3} .10 H_{2} O \)


What devices are used to locate
underwater objects and to determine
depths of water beneath the ship?


The liquefied metal expanding on solidification is :
A . Ga
в. А।
\( c \cdot z n \)
D. c


Explain with the help of a circuit diagram the working of a photo diode. Write briefly how it is used to detect the optical signals.


The potential of the following cell at
\( 25^{\circ} C \) is:
\( \boldsymbol{P t}\left|\begin{array}{c|c|c}\boldsymbol{H}_{2} & \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} & \boldsymbol{N a O H} & \boldsymbol{H}_{2} \\ (\boldsymbol{1} \boldsymbol{a} \boldsymbol{t m}) & \boldsymbol{0} . \boldsymbol{1} \boldsymbol{M} & \mid & \left(\boldsymbol{1 0}^{-3} \boldsymbol{M}\right)\end{array}\right|(\boldsymbol{1} \boldsymbol{a} \boldsymbol{t m}) \)
A. \( -0.059 V \)
B. \( 0.059 V \)
\( c .-0.59 V \)
D. \( 0.5 V \)


Generally ornaments are usually made
up of 24 karat gold.
A. True
B. False


If the four angles of a quadrilateral are equal, what will be the measure of each angle ? What is the special name of this figure?


Which of the following lacks proteins?
A. Pancreatic juice
B. Saliva
c. Bile
D. Intestinal juice


If
\( f(x) \) is monotonic in \( (a, b) \) then prove that the area bounded by the ordinates
at \( \boldsymbol{x}=\boldsymbol{a}: \boldsymbol{x}=\boldsymbol{b}: \boldsymbol{y}=\boldsymbol{f}(\boldsymbol{x}) \) and \( \boldsymbol{y}= \)
\( f(c), c \epsilon(a, b) \) is minimum when \( c= \) \( \frac{a+b}{2} \)
Hence if the area bounded by the graph of \( f(x)=\frac{x^{3}}{3}-x^{2}+a, \) the straight
lines \( x=0, x=2 \) and the \( x \) -axis is
minimum then find the value or 'a'.
\( A \cdot \frac{2}{3} \)
B. \( \frac{2}{5} \)
\( c \cdot \frac{7}{3} \)
D. \( \frac{4}{3} \)


What is the oxidation state of central
\( \operatorname{atom} \operatorname{in} C a\left[P t C l_{4}\right] ? \)
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D. 4


\( A \) and \( B \) are two independent events. The probability that both \( A \) and \( B \) occur is \( \frac{1}{6} \)
and the probability that neither of them occurs is \( \frac{1}{3} . \) The probability of
occurrence of A is?
A \( \cdot \frac{1}{2} \)
B. \( \frac{1}{3} \)
\( c \cdot \frac{5}{6} \)
D.


Q Type your question
Who did
at the four corners of a square with
sides of length D.

What is the electric potential at the
center of the square? (k is Coulomb constant.)
\( A \cdot \frac{4 k Q}{D} \)
в.
c. \( \frac{2 k Q}{\left(D \cos 45^{\circ}\right)} \)
\( D \)
\( E \)


Residence time of water in the
atmosphere is
A . 10 days
B. 20 days
c. 28 days
D. 35 days


Use of chemicals for therapeutic effect
is called :
A. medicine
B. chemotherapy
c. drug-target intereaction
D. Photography


Dimensional formula for electric field is
A \( \cdot\left[M L^{2} T^{-3} A^{-1}\right] \)
B \( \cdot\left[M L^{2} T^{-3} A^{-2}\right] \)
\( \mathbf{c} \cdot\left[M L T^{-3} A^{-1}\right] \)
D \cdot \( \left[M^{0} L^{0} T^{0} A^{0}\right] \)


A charged particle of mass \( 5 \times 10^{-6} \mathrm{kg} \)
is held stationary in space by placing it
in an electric field of strength \( 10^{6} N C^{-1} \) directed vertically downwards. The charge of the particle is \( \left(\boldsymbol{g}=\mathbf{1 0 m} \boldsymbol{s}^{-\mathbf{2}}\right): \)
A. \( -20 \times 10^{-4} \mu C \)
B. \( -5 \times 10^{-5} \mu C \)
c. \( 5 \times 10^{-11} \mu C \)
D. \( 20 \times 10^{-5} \mu C \)


A square loop, carrying a steady current
Is placed in a horizontal plane near a
long straight conductor carrying a
steady current \( I_{1} \) at a distance d from
the conductor as shown in figure. The loop will experience:
A. a net repulsive force away from the conductor
B. a net torque acting upward perpendicular to the horizontal plane
C. a net torque acting downward normal to the horizontal plane
D. a net attractive force towards the conductor


The negative of the statement "he is rich and happy" is given by
A. He is not rich and not happy
B. He is not rich or not happy
c. He is rich and happy
D. He is not rich and happy


Who carried out discharge tube
experiments?
A. Rutherford
B. Bohr
c. Goldstein
D. Einstein


Dissolution of carbon dioxide gas in
water is \( -\ldots-\ldots- \) change.
A . chemical
B. physical
c. both of \( A \) and \( B \)
D. none of the above


If a capillary tube is tilted to \( 45^{\circ} \) and
\( 60^{\circ} \) from the vertical then the ratio
of length \( l_{1} \) and \( l_{2} \) of liquid columns in
it will be -
A. \( 1: \sqrt{2} \)
B. \( \sqrt{2}: 1 \)
c. 1: 2
D. 2:


Which phase of mitosis is responsible for uncoiling of chromosomes followed by nuclear membrane formation?
A. Interphase
B. Prophase
c. Metaphase
D. Anaphase
E. Telophase


The standard reduction potential of
\( E_{B i^{3+} / B i}^{o} \) and \( E_{C u^{2+} / C u}^{o} \) are \( 0.226 \mathrm{V} \) and
\( 0.344 \mathrm{V} \) respectively. A mixture of salts of Bi and Cu at unit concentration each
is electrolysed at \( 25^{\circ} \mathrm{C} \). To what value
\( \operatorname{can}\left[C u^{2+}\right] \) be brought down before bismuth starts to deposit during electrolysis?
В. \( 10^{-3} M \)
c. \( 10^{-5} M \)
D. \( 10^{-2} M \)
E \( \cdot 10^{-6} M \)
F. \( 10^{-1} M \)
G. \( 10^{-7} M \)


How is RQ slightly more than unity?


Which of the following isomerism can be exhibited by the given compound?
A. Tautomerism
B. Optical isomerism
c. Geometrical isomerism
D. Geometrical and optical isomerism


\( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{3} \) and
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}=\boldsymbol{C H}-\boldsymbol{C H}_{3} \) are they
constitutional isomers or not?


Kinetic energy of a particle moving in a straight line is proportional to the time
\( t . \) The magnitude of the force acting on the particle is:
This question has multiple correct options
A. directly proportional to the speed of the particle
B. inversely propotional to \( \sqrt{t} \)
c. inversely proportional to the speed of the particle
D. directly proportional to \( \sqrt{t} \)


1 mole of \( H N O_{3} \) absorbs 4 moles of
electrons in a redox reaction. The
reduced product of this reaction is :
A. 1 mole \( N_{2} \)
B. 1 mole \( N_{2} \) O
c. 1 mole \( N O_{2} \)
D. 1 mole \( N H_{3} \)


Find the uncertainty in mass.
A \( \cdot 1.4 \times 10^{-35} \mathrm{kg} \)
в. \( 2.6 \times 10^{-11} \mathrm{kg} \)
c. \( 2.6 \times 10^{-13} k g \)
D. \( 8 \times 10^{-14} \mathrm{kg} \)


Find the vector equation of the line passing through the point (3,1,2) and perpendicular to the plane \( \vec{r} \cdot(2 \hat{i}-\hat{j}+\widehat{k})=8 \) Also find the point
of intersection of line and plane.


Assume that \( P(A)=P(B) . \) Show that
\( A=B \) Is it true that for any sets \( A \) and
\( \boldsymbol{B}, \boldsymbol{P}(\boldsymbol{A}) \cup \boldsymbol{P}(\boldsymbol{B})=\boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B}) ? \) Justify


When lead storage battery is charged:
A. lead dioxide dissolves
B. sulphuric acid is regenerated
C. the lead electrode becomes coated with lead sulphate
D. the amount of sulphuric acid decreases


The formula of discriminant of
quadratic equation \( a x^{2}+b x+c=0 \) is
\( D= \)


Which of the following gases is used for the qualitative analysis of metal ions?
A. \( C O_{2} \)
в. \( H_{2} \).
\( c \cdot s O_{2} \)
D. \( S O_{3} \)


Commercial detergent contains mainly:
A. \( R C O O N a \)
в. \( R O N a \)
c. \( R S N a \)
D. \( R S O_{3} N a \)


In carnot cycle to increase efficiency which of the following parameter need to be changed?
A. Decrease source temperature
B. Decrease sink Temperature
C. No effect
D. None of these


Rh factor may be responsible for which of the following disease?
A. Turner's syndrome
B. AlDS
c. sickle cell anaemia
D. Erythroblastosis foetalis


The position vectors of the points \( A, B, C \) and \( D \) are \( 3 \hat{i}-2 \hat{j}-\hat{k}, 2 \hat{i}+ \)
\( \mathbf{3} \hat{\boldsymbol{j}}-\mathbf{4} \hat{\boldsymbol{k}},-\hat{\mathbf{i}}+\hat{\boldsymbol{j}}+\mathbf{2} \hat{\boldsymbol{k}} \) and \( \mathbf{4} \hat{\boldsymbol{i}}+\mathbf{5} \hat{\boldsymbol{j}}+\boldsymbol{\lambda} \hat{\boldsymbol{k}} \)
respectively. If the points \( A, B, C \) and \( D \)
lie on a plane, find the value of \( \lambda \)


The following relation is defined on the set of real numbers. \( \boldsymbol{a} \boldsymbol{R} \boldsymbol{b} \) if \( |\boldsymbol{a}-\boldsymbol{b}|>\mathbf{0} \)


If \( \boldsymbol{I}=\int_{\boldsymbol{\pi} / \mathbf{6}}^{\boldsymbol{\pi} / \mathbf{3}} \frac{\boldsymbol{d} \boldsymbol{x}}{\mathbf{1}+\sqrt{\tan \boldsymbol{x}}} \) then \( \boldsymbol{I} \) equals
A \( \cdot \frac{\pi}{12} \)
в. \( \frac{\pi}{6} \)
\( c \cdot \frac{\pi}{4} \)
D. \( \frac{\pi}{3} \)


Write the names of isotopes of hydrogen.What is the mass ratio of these isotopes?


Differentiable \( \log _{7}(\log x) \) with respect
to \( \boldsymbol{x} \)


Which of the following does not contributes to greenhouse effect?
A. Carbon dioxide
B. Carbon monoxide
c. chloro-fluoro carbon and Methane
D. Refrigerant freon


The photoelectric effect was experimentally studied by
A. Einstein
B. Lennard
c. Hertz
D. Rutherford


Can we perform Young's double slit experiment with sound waves? To get a reasonable "fringe pattern", what should be the order of separation between the slits? How can the bright fringes and the dark fringes be detected in this case?


Reduce the equation \( 2 x-3 y-5=0 \)
to slope-intercept form and find its slope and \( y- \) intercept


The equilibrium constant for the
reaction, \( \boldsymbol{H}_{2}+\boldsymbol{I}_{2} \rightarrow 2 \boldsymbol{H} \boldsymbol{I} \) at \( 700 \mathrm{K} \) is
56. If 0.5 mole of hydrogen and 1 mole of iodine are added to the system at equilibrium, the value of the
equilibrium constant will be
A . 25
B. 100
c. 56
D. 0.25


Find the length of the medians of a \( \triangle A B C \) having vertices at \( \boldsymbol{A}(\mathbf{0},-\mathbf{1}), \boldsymbol{B}(\mathbf{2}, \mathbf{1}) \) and \( \boldsymbol{C}(\mathbf{0}, \mathbf{3}) ? \)


In each of the following figure, find the
value of \( x: \)


Which of the following statements is true for a solution containing
components \( A \) and \( B \) and following
Raoult's law:
A. \( A-B \) attraction force is greater than \( A-A \) and \( B- \) \( B \)
B. \( A-B \) attraction force is less than \( A-A \) and \( B-B \)
c. \( A-B \) attraction force remains same as \( A-A \) and \( B-B \)
D. Volume of solution is different from sum of volume of solute and solvent


In the given figure, the position-time
graph of a particle of mass \( 0.1 \mathrm{kg} \) is
shown. The impulse at \( t=2 \) sec is:
A. \( 0.2 \mathrm{kg} \mathrm{m} \mathrm{sec}^{-1} \)
B. \( -0.2 \mathrm{kg} \mathrm{m} \mathrm{sec}^{-1} \)
C. \( 0.1 \mathrm{kg} \mathrm{m} \mathrm{sec}^{-1} \)
D. \( -0.4 \mathrm{kg} \mathrm{m} \mathrm{sec}^{-1} \)


The masses \( 4 m \) and \( m \) are connected
by a light string passing over a frictionless pulley fixed at inclined
plane of inclination \( 45^{\circ} \) as shown in
figure. The coefficient of friction
between \( 4 m \) and inclined plane is \( \frac{1}{\sqrt{2}} \)
When two blocks are released, then
This question has multiple correct options
A. the tension in the string is mg
B. the frictional force on the block of \( 4 \mathrm{m} \) will be \( 2 \mathrm{mg} \)
c. the block of \( \mathrm{m} \) will move in upward direction
D. the frictional force on block of mass \( 4 \mathrm{m} \) has magnitude \( (2 \sqrt{2}-1) \mathrm{mg} \)


Inner side of the cylindrical tube of a periscope is blackened to avoid:
A. unwanted refraction
B. unwanted reflection
c. diffusion
D. both a and


If \( A=\operatorname{diag}\left[d_{1}, d_{2}, d_{3}\right] \) then \( a^{n} \) is equal to
A \( \cdot \operatorname{diag}\left[d_{1}^{n-1}, d_{2}^{n-1}, d_{3}^{n-1}\right] \)
B. A
c. \( \operatorname{diag}\left[d_{1}^{n}, d_{2}^{n}, d_{3}^{n}\right] \)
D. none


Choose the correct mirror image for the
word SHARE
\( A \cdot A \)
B. B
\( c \cdot c \)
\( D \)


Oxyhaemoglobin is converted into haemoglobin during the internal respiration because
A. An enzyme splits oxyhaemoglobin
B. Oxygen tension in tissues is less than capillary blood reaching tissues
\( \mathrm{c} \cdot \mathrm{c} \mathrm{O}_{2} \) tension is low in blood that reaches tissues
D. Oxyhaemoglobin is unstable


said that cathode
rays consist of negatively charged particles and these were named as
electrons.
A . Goldstein
B. Thomson
c. chadwick
D. Rutherford


toppr
Q Type your question
\( \mathbf{A} \)
B.
\( c \)
D.


Use the identity and expand the following \( (2 x+y)^{2} \)


The osmotic pressure of a solution containing 40 g of solute (molecular mass 246 ) per litre at \( 27^{\circ} C \) is:
\( \left[\boldsymbol{R}=\mathbf{0 . 0 8 2 2} \boldsymbol{\operatorname { a t m }} \boldsymbol{L} \boldsymbol{m o l}^{-\mathbf{1}}\right] \)
A. 3.0 atm
B. 4.0 atm
c. 2.0 atm
D. 1.0 atm


If \( \frac{z-1}{z+1} \) is purely imaginary then
в. \( |z|>1 \)
c. \( |z|<1 \)
D. |z|<2


Answer in one word or one line.
(i) Give the common name of Periplanata
americana.
(ii) How many spermathecae are found in earthworm?
(iii) What is the position of ovaries in cockroach?
(iv) How many segments are present in the abdomen of cockroach?
(v) Where do you find Malpighian tubules?


A ray of light from denser medium strikes a rarer medium at angle of incidence \( i . \) The reflected and refracted
rays make an angle of \( 90^{\circ} \) with each
other. The angle of reflection and
refraction are \( r \) and \( r^{\prime} . \) The critical
angle is
A \( \cdot \sin ^{-1}(\tan r) \)
B. \( \sin ^{-1}(\tan i) \)
c. \( \sin ^{-1}\left(\tan r^{\prime}\right) \)
D. \( \sin ^{-1}(\tan (i+r)) \)


Which of the following statement can be related to puberty?
A. Is never ending
B. Is only for girls
c. Is only for boys
D. Ends at a certain age


Mean of the first \( n \) terms of the A.P.
\( \boldsymbol{a},(\boldsymbol{a}+\boldsymbol{d}),(\boldsymbol{a}+\boldsymbol{2} \boldsymbol{d}), \ldots \ldots . . \) is
A \( \cdot a+\frac{n d}{2} \)
в. \( a+\frac{(n-1) d}{2} \)
c. \( a+(n-1) d \)
D. \( a+n d \)


The balance point in a meterbridge is 60cm. The ratio of the resistance in the
gaps is:
A. 3: 5
B. 5: 3
\( c \cdot 3: 2 \)
D. 2:3


If \( C_{p} \) and \( C_{v} \) are the molar specific
heats of a gas at constant pressure and volume respectively then the ratio of
adiabatic and isothermal modulii of
elasticity will be
A. \( \frac{C_{p}-C_{v}}{C_{p}} \)
B. \( C_{p} C_{v} \)
c. \( \frac{C_{v}}{C_{p}} \)
D. \( \frac{C_{p}}{C_{v}} \)


A particle of mass \( m \) moving with a velocity \( (3 \hat{\hat{i}}+2 \hat{j}) m s^{-1} \) collides with stationary body of mass \( M \) and finally moves with a velocity \( (-2 \hat{i}+\hat{j}) m s^{-1} \) If \( \frac{M}{m}=\frac{1}{13}, \) then:
A \( \cdot \) the impuse received by \( M \) is \( m(5 \hat{i}+\hat{j}) \)
B. The velocity of the \( M \) is \( \frac{1}{13}(5 \hat{i}+\hat{j}) \)
c. the coefficient of restitutions \( \frac{11}{17} \)
D. All of the above are correct


A car moving along a straight highway with speed of \( 126 k m h^{-1} \) is brought to a stop within a distance of \( 200 \mathrm{m} \). What
is the retardation of the car
(assumed uniform), and how long does
it take for the car to stop?


The type of hybrid orbitals used by
chlorine atom in \( C l O_{2}- \) is:
\( A \cdot s p^{3} \)
B . \( s p^{2} \)
\( c \cdot s p \)
D. \( d s p^{2} \)


If \( f(x)=\frac{1-\tan x}{1-\sqrt{2} \sin x}, \) for \( x \neq \)
\( \frac{\pi}{4} \) is continous \( \boldsymbol{a t} \quad \boldsymbol{x}= \)
\( \frac{\pi}{4}, \quad \) find \( \quad f\left(\frac{\pi}{4}\right) \)


Simplify: \( (3 a-5 b)^{3}-(3 a+5 b)^{3} \)


Define the following:
Threshold frequency and work function.


Find the \( 9^{t h} \) term of an A.P
\( \mathbf{2}, \mathbf{5}, \mathbf{8}, \mathbf{1 1}, \dots \dots \)


Identify the product(s) which will be formed by using the information provided about the reactants.
\( N a C l(a q)+A g N O_{3}(a q) \rightarrow \)
A. \( N a A g+C l N O_{3} \)
в. \( N a C l+A g N O_{3} \)
c. \( A g C l+N a N O_{3} \)
D. \( N a N O_{3}+A g N O_{3} \)


Carry out the following division. \( 28 x^{4} \div 56 x \)


Draw quadrilateral ABCD with the following measurements. Also find its
area.
\( A B=6 \mathrm{cm}, \mathrm{BC}=6 \mathrm{cm}, \angle \mathrm{BAC}=50^{\circ}, \angle \)
\( A C D=30^{\circ} \) and \( \angle C A D=100^{\circ} \)


The oldest museum in India is
A. Indian museum
c. National museum of India
D. Uffizi gallery


In the adjoining potentiometer circuit, the resistance of uniform cross section
the potentiometer wire \( A B \) of Length \( 1 \mathrm{m} \)
is \( 10 \Omega . \) When the variable resistance \( R= \)
\( 10 \Omega, \) the balance point is obtained for length I as shown. If the variable resistance is doubled, the new balance
length is
\( A \)
B. \( 1.5 l \)
\( c \cdot 2 l \)
\( D \)
\( \mathbf{?} \)


By blowing between two balloons hanging close to each other you observe that come closer. A similar phenomenon
is seen in
A. the lifting of an aeroplane.
B. kite flying
c. the lifting of balloon filled with
D. take off of rocket


Which of the following pair of element
has same property? This question has multiple correct options
A \( \cdot 10,12 \)
B. 11,20
c. 20,38
D. 13, 31


Which of the following cycloalkanes has
lowest heat of combustion per- \( C H_{2} \)
group per mole?
\( A \)
в.
\( c \)
D.


\( 12 g \) of carbon combines with \( 64 g \)
sulphur to form \( C S_{2} .12 g \) carbon also
combines with \( 32 g \) oxygen to form \( C O_{2} \)
10 \( g \) sulphur combines with \( 10 g \) oxygen
to form \( S O_{2} . \) These data illustrate the
A. Law of multiple proportions
B. Law of definite proportions
c. Law of reciprocal proportions
D. Law of gaseous volumes


\( \left(25 x^{5}-15 x^{4}\right) \div 5 x^{3} \)
A. \( x(5 x+3) \)
в. \( (5 x-3) \)
c. \( x(5 x-3) \)
D. None


Two sound waves emerging from a source reach a point simultaneously along two paths. When the path difference is \( 12 \mathrm{cm} \) or \( 36 \mathrm{cm} \) then there
is silence at that point. If the speed of sound in air is \( 330 \mathrm{m} / \mathrm{s} \) then calculate
least possible frequency of the source in Hz


Two liquid jets coming out of the small
holes at \( P \) and \( Q \) intersect at the point \( R \)
Find the position of \( R \) if we maintain the
liquid level constant
A \( \cdot \sqrt{2} h \)
B. \( 2 \sqrt{2} h \)
\( c \cdot 3 \sqrt{2} h \)
D. \( 5 \sqrt{2} h \)


The square root of a perfect square containing 'n' digits has ............... digits.
A \( \cdot \frac{n+1}{2} \)
в. \( \frac{n}{2} \)
c. A or B
D. None of these


Which of the following represents the
given mode of hybridisation \( s p^{2}- \)
\( s p^{2}-s p \) from left to right?
A. \( C H_{2}=C H-C \equiv N \)
в. \( C H \equiv C-C \equiv C H \)
c. \( C H_{2}=C=C=C H_{2} \)
D. \( C H_{2}=C H-C H=C H_{2} \)


\( \$ \$ \text { lbegin\{array }\}\{\mid\} A=\mid \) left [ lbegin\{array \( \}[1332-4115 \& 2 \) \( \mathrm{~ l e n d \{ a r r a y \} ~ | r i g h t ] ~ | , ~ | , ~ B = | l e f t [ ~} \)
\[
\begin{array}{cc}
1 & -3 \\
5 & 8
\end{array}
\]
|right] \( \|=3 \) left Then find \( 3 A-5 B+ \)
\( 4 I \) by using matrix


Carbon, Silicon and Germanium atoms
have limn valence electrons each. Their
valence and conduction bands
are separated by energy band gaps
represented by \( \left(\boldsymbol{E}_{\boldsymbol{g}}\right)_{\boldsymbol{c}},\left(\boldsymbol{E}_{\boldsymbol{g}}\right)_{\boldsymbol{s i}} \) and \( \left(\boldsymbol{E}_{\boldsymbol{g}}\right)_{\boldsymbol{G} \boldsymbol{e}} \)
respectively. Which one of the following relationship is true in their
case?
A \( \cdot\left(E_{g}\right)_{C}>\left(E_{g}\right)_{s i} \)
B. \( \left(E_{g}\right)_{C}<\left(E_{g}\right)_{s i} \)
\( \mathbf{c} \cdot\left(E_{g}\right)_{C}=\left(E_{g}\right)_{s i} \)
D \cdot \( \left(E_{g}\right)_{C}<\left(E_{g}\right)_{G e} \)


\( \int \frac{3 x-1}{(x+2)^{2}} d x= \)


The distance between the parallel lines
\( 5 x-12 y-14=0 \) and \( 5 x-12 y+ \)
\( 12=0 \) is equal to
A \( \cdot \frac{1}{13} \)
B. 2
c. \( \frac{2}{13} \)
D. 4
E \( \cdot \frac{4}{13} \)


The inverse of the statement "if Abbey is not injured, she will win the race." is
A. If Abbey is injured, she will not win the race
B. If Abbey is not injured, she will not win the race.
c. If Abbey is injured, she will win the race."
D. None of these


Evaluate:
\( +5-6=? \)
A . -1
B.
\( c \cdot 2 \)
D. - 2


\( \lim _{n \rightarrow \infty}\left[\frac{1}{3 n+1}+\frac{1}{3 n+2}+\dots+\right. \)
\( \left.\frac{1}{3 n+n}\right] \)
A \( \cdot \log (2 / 3) \)
and 5
B. \( \log (3 / 2) \)
\( c \cdot \log (4 / 3) \)
\( \mathbf{D} \cdot \log (3 / 4) \)


A \( 50 \mathrm{cm} \) long conductor \( \mathrm{AB} \) moves with
a speed \( 4 m / s \) in a magnetic field \( B= \)
\( 0.01 W b / m^{2} \) as shown. Find the emf
generated and power delivered if
resistance of the circuit is \( 0.1 \Omega \)


Anju buys a book for Rs. 375 and sells it at a loss of \( 18 \% \) for how much does she
sell it?
A. Rs. 37.50
B. Rs. 107.50
c. Rs. 307.50
D. Rs. 442.50


The period of revolution of planet \( \mathbf{A} \) around the sun is 8 times that of B. The
distance of A from the sun is how many
times greater than that of B from the sun?
A . 4
B. 5
c. 2
D. 3


A stationary body explodes into four identical fragments such that three of them fly off mutually perpendicular to each other, each with same kinetic
energy, \( \boldsymbol{E}_{\mathbf{0}} \). The minimum energy of
explosion will be
\( \mathbf{A} \cdot 6 E_{0} \)
в. \( \frac{4 E_{0}}{3} \)
c. \( 4 E_{0} \)
D. \( 8 E_{0} \)


Write structure of Aspartame.


Find the mean of the following
frequency distribution:
\( \begin{array}{lll}\text { Marks obtained } & \text { Number of students } \\ \text { 10-20 } & 6 \\ \text { 20-30 } & 8 \\ \text { 30-40 } & 13 \\ \text { 40-50 } & 7 \\ \text { 50-60 } & 3 \\ \text { 60-70 } & 2 \\ \text { 70-80 } & 1\end{array} \)


A block of mass \( 0.5 k g \) is moving with a speed of \( 2.0 m / s \) on smooth surface. It
strikes another mass of \( 1.0 k g \) and then they move together as a single body. The energy loss during collision is (in J)
A . 0.16
B. 0.67
c. 1.0
D. 6.7


When metal XX is treated with sodium
hydroxide, a white ppt. of AA is obtained
which is soluble in excess
of NaOHNaOH to form soluble
complex BB.Compound AA is soluble in dilute HCIHCl to form compound CC.The compound AA when strongly heated gives compound DD which is used to
extract metals.
Compound \( D \) is :
\( \mathbf{A} \cdot A l_{2} O_{3} \)
в. \( C u O \)
c. \( H g O \)
D. \( M g O \)


A jet plane is travelling towards west at a speed of \( 1800 \mathrm{km} / \mathrm{h} . \) What is the
voltage difference developed between the ends of the wing having a span of 25 \( \mathrm{m}, \) if the Earth's magnetic filed at the
location has a magnitude of \( 5 \times 10^{-4} T \)
and the dip angle is \( 30^{0} ? \)


State whether true or false:
In Carnot cycle there are total 4 processes which takes place?
A. True
B. False


Which of the following will shift the equilibrium in the forward direction for the following equilibrium?
\( N_{2}(g)+O_{2}(g) \rightleftharpoons 2 N O(g) ; \Delta H^{0}= \)
\( +181 k J \)
A. Increase of pressure
B. Increase in the concentration of \( N O \)
c. Decrease in pressure
D. Increase in temperature


Primary succession on land occurs as:
A. lichen \( \rightarrow \) mosses \( \rightarrow \) annual grass \( \rightarrow \) shrubs \( \rightarrow \) trees
B. mosses \( \rightarrow \) lichen \( \rightarrow \) annual grass \( \rightarrow \) shrubs \( \rightarrow \) trees
C. plankton \( \rightarrow \) submerged \( \rightarrow \) floating stage \( \rightarrow \) marsh stage \( \rightarrow \) climax stage
D. all of these


The displacement \( y \) of a executing Periodic motion is given by \( y=4 \cos ^{2}\left(\frac{1}{2} t\right) \sin (1000 t) \)
This expression may be considered to be a result of the superposition of independent harmonic motions.
A. two
B. three
c. four
D. five


The hydrolysis of \( N C l_{3} \) by water molecules produces:
A. \( N H_{2} O H+H O C l \)
B. \( N H_{2} N H_{2}+H O \)
c. \( N H_{4} O H+H O C l \)
D. \( N H_{2} C l+H O C l \)


Match the expression/statements on the left with the expression on the right.


In the given molecule, which
atom/group is below the plane of the
paper?
A. Hydroxy
B. lodine
c. chlorine
D. Ethy


Construct a triangle \( A B C \), given the
following \( B C=4.8 \mathrm{cm}, A B=5.7 \mathrm{cm} \) and \( \angle A= \)
45


One mole of calcium phosphide on reaction with excess of water gives:
A. Three moles of phosphine
B. One mole of phosphoric acid
c. Two moles of phosphinc
D. one mole of \( P_{2} O_{5} \)


Briefly explain any three disorders of
digestive system?


Which substance does not possess a
peroxy cyclic ring?
\( \mathbf{A} \cdot \mathrm{CrO}_{5} \)
\( \mathbf{B} \cdot B a O_{2} \)
\( \mathbf{c} \cdot H_{2} S_{2} O_{8} \)
D. All have peroxy linkage


Asexual reproduction is the method of reproduction in organisms that have a relatively simple organisation like and
Fill in the blank in the above statement.
A. Rare, plant, bacteria
B. Common, plant, bacteria
c. common, algae, fungi
D. Rare, algae, fungi


The runs secored in a cirect match by
11 players is as follows:
\( \mathbf{9}, \mathbf{1 5}, \mathbf{1 2 1}, \mathbf{5 1}, \mathbf{1 0 1}, \mathbf{8 1}, \mathbf{5 0}, \mathbf{1 6}, \mathbf{8 2}, \mathbf{1 1}, \mathbf{1 1} \)
Find the mean, mode and median
respectively of this data.
A .48,11,51
в. 49,81,11,51
c. 49,90,11,50
D. 49,81,11,50


Write the mechanism involved in the
esterification of a carboxylic acid with alcohol


An azeotropic solution of two liquids has boiling point lower than either of them when it:
A. shows negative deviation from Raoult's law
B. shows no deviation from Raoult's law
c. shows positive deviation from Raoult's law
D. is saturated


If \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{3} & \mathbf{1} \\ \mathbf{7} & \mathbf{5}\end{array}\right], \) find the values of \( \boldsymbol{x} \) and
\( y \) such that \( A^{2}+x I_{2}=y A \)


The set of all real numbers satisfying \( e^{\left(\frac{1}{x}-1\right)}<1 \)
A. \( (0, \infty) \)
)
B . \( (-\infty, 0) \cup(1, \infty) \)
\( c \cdot(-\infty, \infty) \)
D. (0,1)


Two wires of the same radius and
material and having length in the ratio 8.9: 7.6 are stretched by the same
force. The strains produced in the two cases will be in the ratio:
A . 1: 1
B. 8.9: 1
c. 1: 7.6
D. 1: 3.2


A sphere, cylinder \( \& \) a cone gave the same radius \( \& \) same height, find the ratio of their curved surface areas.


Assertion: The more negative is the standard reduction potential, greater is its ability to displace \( \mathrm{H}_{2} \) from acid. Reason: Strength of reducing agent increases with the increase in the
negative value of the standard reduction potential.
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


Tell what is the profit or loss in the following transaction. Also find profit per cent or loss per cent in the case.
A refrigerator bought for \( R s 12,000 \) and
sold at \( R s 13,500 \)


Find the sum of terms of the sequence
till \( n \) terms \( : 6+9+16+27+42+ \)
\( \ldots+n \) terms.


Which one of the following hormones never reaches to the cytoplasm?
A. Estrogen
B. FSH
c. Progesterone
D. Testosterone


A car travels a distance of \( 60 k m \) in
10min. Find its speed in SI.
\( \mathbf{A} \cdot 6 m s^{-1} \)
B. \( 0.17 m s^{-1} \)
\( \mathrm{c} \cdot 10 \mathrm{ms}^{-1} \)
D. \( 100 \mathrm{ms}^{-1} \)


Chemical properties of of an
element are same, but their physical properties may be different
A. isotopes
B. isobars
c. neutron
D. proton


If \( a_{1}, a_{2}, a_{3} \dots \dots \dots a_{n} \) are in A.P.with
common difference \( d, \) then
\( \tan \left[\tan ^{-1}\left(\frac{d}{1+a_{1} a_{2}}\right)+\tan ^{-1}\left(\frac{d}{1+a_{2} a_{3}}\right)+\right. \)
\( \dots \dots \dots \dots \dots+ \)
\( \left.\tan ^{-1}\left(\frac{d}{1+a_{n-1} a_{n}}\right)\right]=? \)
A \( \cdot \frac{(n-1) d}{a_{1}+a_{n}} \)
B. \( \frac{(n-1) d}{1+a_{1} a_{n}} \)
c. \( \frac{n d}{1+a_{1} a_{n}} \)
D. \( \frac{a_{n}-a_{1}}{a_{n}+a_{1}} \)


A wire fixed at the upper end stretches by length \( l \) by applying a force \( F \). The work done in stretching is:
\( ^{A} \cdot \frac{F}{2 l} \)
в. \( F l \)
c. \( \frac{2 F}{l} \)
D. \( \frac{F l}{2} \)


Why is the upper slide of the leaf more
green than the lower slide?


Complete the following statements with an appropriate word /term be filled in
the blank space(s).

The equivalent capacitance \( C \) for the series combination of three
capacitance \( C_{1}, C_{2} \) and \( C_{3} \) is given by
\( \frac{1}{C}= \)
A. \( C_{1}+C_{2}+C_{3} \)
\( ^{\text {В }} \cdot\left(\frac{1}{C_{1}+C_{2}+C_{3}}\right) \)
\( \left(\frac{1}{\frac{1}{C_{1}}+\frac{1}{C_{2}}+\frac{1}{C_{3}}}\right) \)
D \( \cdot\left(\frac{1}{C_{1}}+\frac{1}{C_{2}}+\frac{1}{C_{3}}\right) \)


Nuclear spindle has ........... types of fibres
A. one
B. Two
c. Three
D. Four


Calculate the ratio of the number of
metal atoms to the total number of
constituents in aluminium carbonate.
\( A \cdot 1: 4 \)
B. 7:6
\( c \cdot 71: 6 \)
D. 1:7


\( 00= \)
80
000


Which of the following statements is
wrong?
A. Sound travels in a straight line
B. Sound travels as a wave
C. Sound is a form of energy
D. Sound travels faster in vacuum than in air


How many grams of \( C u \) and what
volume of \( O_{2} \) gas will be obtained at
STP by passing 20 ampere current for 96.5 minutes from an aqueous solution
of \( C u S O_{4} ? \) The efficiency of the electrolytic cell is \( 90 \% .(C u=63.5) \)


What type of attraction occurs between the partial positively charged hydrogen atom in one water molecule and the
partial negatively charged oxygen atom in another water molecule?
A. Covalent bond
B. Dipole moment
c. lonic bond
D. van der Waals interaction
E. Hydrogen bond


There are 15 tickets in a box, each
bearing one of the numbers from 1 to 15 One ticket is drawn from the box. Find
the probability of event that the ticket drawn -
(1) shows an even number.
(2) shows a number which is a multiple
of 5.


During an experiment, a signal from a spaceship reached the ground station in five minutes. What was the distance
of the spaceship from the ground station? The signal travels at the speed
of light, that is, \( 3 \times 10^{8} m s^{-1} \)


Using slope concept show that the points \( P(-2,3), Q(7,-4) \) and \( R(2,1) \)
A. are not collinear
B. cannot be plotted
c. are not defined
D. are collinear


State true or false.
Coal gas, coke and producer gas are examples of fossil fuel.
A. True
B. False


A car accelerates from rest at a
constant rate \( \alpha \) for some time, after
which it decelerates at a constant rate
\( \beta \) and comes to rest. If the total time
elapsed is \( t, \) then the maximum velocity acquired by car is
\( ^{\mathbf{A}} \cdot\left(\frac{\alpha^{2}+\beta^{2}}{\alpha \beta}\right) t \)
\( ^{\mathrm{B}}\left(\frac{\alpha^{2}-\beta^{2}}{\alpha \beta}\right) t \)
c. None of these
D. \( \left(\frac{\alpha \beta r}{\alpha \beta}\right) \)


In the statement of Fleming's left hand rule, force acting on the conductor is is
represented by
A. thumb
B. fore finger
c. middle finger
D. none


Which of the following is an example of polyatomic gas?
A. Ozone
B. Hydrogen
c. Helium
D. oxygen


Composting is carried out from
A. Sewage sludge
B. Rubbish
C . Garbage and sewage sludge
D. Industrial wastes


\( \boldsymbol{A} \rightarrow \boldsymbol{B} \)
\( \boldsymbol{K}_{\boldsymbol{A}}=\mathbf{1 0}^{\mathbf{1 5}} \boldsymbol{e}^{\mathbf{2 0 0 0} / \boldsymbol{T}} \)
\( \boldsymbol{C} \rightarrow \boldsymbol{D} \quad \boldsymbol{K}_{\boldsymbol{C}}=\mathbf{1 0}^{14} \boldsymbol{e}^{\mathbf{1 0 0 0} / \boldsymbol{T}} \)
Temperature \( \mathrm{T} \mathrm{K} \) at which \( \left(\boldsymbol{K}_{\boldsymbol{A}}=\boldsymbol{K}_{\boldsymbol{C}}\right) \)
is :
\( A \cdot 1000 K \)
B. 2000 K
D. (1000 / 2.303) K


In the given figure, \( \triangle D A \) and \( \triangle C A B \)
are on the same base \( A B \). Prove that
\( \triangle D A B \equiv \triangle C A B \)


The structures that develops into the fruit once fertilization has occurred is
A. Integument
B. cotyledon
c. Ovule
D. Ovary
E. Endosperm


Construct a quadrilateral ABCD, when:
\( \boldsymbol{B C}=\mathbf{7 . 5} \mathrm{cm}, \boldsymbol{A C}=\mathbf{5 . 8} \mathrm{cm}, \boldsymbol{A D}=\mathbf{3 . 6} \)
\( \mathrm{cm} \)
\( C D=4.2 \mathrm{cm} \) and \( A=120^{\circ} \)


Find the principal value of:
\( \cot ^{-1}(-\sqrt{3}) \)


Ship A is located \( 4 k m \) north and \( 3 k m \)
east of ship B. Ship A has a velocity of
\( 20 \mathrm{kmh}^{-1} \) towards the south and ship \( \mathrm{E} \)
is moving at \( 40 \mathrm{kmh}^{-1} \) in a direction
\( 37^{\circ} \) north of east. \( X \) and \( Y \) axes are along east and north directions, respectively. This question has multiple correct options
A. Velocity of A relative to B is \( -32 \hat{i}-44 \hat{j} \)
B. Position of A relative to B as a function of time is given by \( \vec{r}_{A B}=(3-32 t) \hat{i}+(4-44 t) \hat{j} \)
c. Velocity of A relative to B is \( 32 \hat{i}-44 \hat{j} \)
D. Position of A relative to B as a function of time is given by \( (32 t \hat{i}-44 t \hat{j}) \)


The solubility of diethyl ether in water is comparable with that of:
A. ethanamine
B. chlorobutane
c. 1-butanol
D. ethanol


toppr
Q Type your question
height 1 m above the ground. The
particle is thrown from some point in
such a way that it strikes the ground
(perfectly inelastic) with velocity \( v_{0} \) at
an angle \( 37^{\circ} \) with vertical just below \( O \)
List
(P) Radius of curvature of particle just before striking the ground
(Q) Minimum value of \( v_{0} \) such that at highest point in vertical circle tension in the string \( T=0 \)
(R) Negative of work done by gravity after it strikes the ground to the topmost point in frame moving with constant acceleration on ground is (assume that after collision the particle complete the vertical loop)
(S) Power delivered by the gravity at highest point is (assume that after
\[
\frac{5}{3} \frac{v_{0}^{2}}{g}
\]
collision the particle complete the vertical loop)
A. P- \( 2 ; Q-3 ; R-1 ; S-4 \)
B. P- 3; Q- 2; R- 4; S-1
\( \mathrm{C} \cdot \cdot \mathrm{Q}-1 ; \mathrm{R}-2 ; \mathrm{S}-3 \)
D. P- 2; Q- 3; R-4; S-1


Which of the following shows differential coloring in acidic and basic solutions?
A. Arrhenius acid
B. Arrhenius base
c. Buffer
D. Indicator
E. Salt


A loop made of straight edges has six corners at \( A(0,0,0), B(L, 0,0), c(L, L, 0) \)
\( \mathrm{D}(0, \mathrm{L}, 0), \mathrm{E}(0, \mathrm{L}, \mathrm{L}) \) And \( F(0,0, \mathrm{L}) \)
A magnetic field \( \bar{B}=B_{0}(\hat{i}+\hat{k}) T \) is
present in the region.The flux passing through the loop ABCDEFA (in the order)
is
A. \( B_{0} L^{2} W b \)
В \( \cdot 2 B_{0} L^{2} W b \)
c. \( \sqrt{2} B_{0} L^{2} W b \)
D. \( 4 B_{0} L^{2} W b \)


C-C bond length is maximum in?
A. diamond
B. graphite
c. naphthalene
D. fullerene


A man carries a load on his headd
through distance of \( 5 \mathrm{m} \). The maximum
amount of work done when he
A. Move it over an inclined plane
B. Moves it over a horizontal surface
c. Lifts it vertically upwardd
D. None of these


\( \ln a G P \) the \( 3^{r d} \) term is 24 and the \( 6^{t h} \)
term is \( 192 . \) Find the \( 10^{t h} \) term.


If a ball is thrown vertically upwards with speed \( u, \) the distance covered during the last \( t \) seconds of its ascent is
\( \mathbf{A} \cdot u \)
в. \( \frac{1}{2} g t^{2} \)
c. \( u t-\frac{1}{2} g t^{2} \)
D. \( (u+g t) t \)


The value of \( \int_{0}^{\pi / 4} \frac{\sin ^{\frac{1}{2}} x}{\cos ^{\frac{5}{2}} x} d x \)
\( \mathbf{A} \cdot \mathbf{0} \)
в.
c.
D.


Could this reaction occur?
Proton \( \rightarrow \) neutron \( + \) other particles
A. Yes, if the other particles have much more kinetic energy than mass energy.
B. Yes, but only if the proton has potential energy (due to interactions with other particles)
C. No, because a neutron is more massive than a proton.
D. No, because a proton is positively charged while a neutron is electrically neutral.


A magnet is moved towards the coil
(i) quickly in one case, and
(ii) slowly in another case.
Then the induced emf is :
A. larger in case (i)
B. smaller in case (i)
c. equal in both
D. larger or smaller depending upon the radius of the coil


Which of the following compounds show hydrogen bonding?
A. \( H C l \)
в. \( C_{2} H_{6} \)
c. \( R C H_{2} C H O \)
D. \( R C H_{2} N H C H_{3} \)


A galvanometer having a resistance of \( 120 \Omega \) is shunted by \( 5 \Omega \) resistance.
What is the ratio of current in shunt to
the current in galvanometer?


Show that \( 7-\sqrt{5} \) is irrational given that \( \sqrt{5} \) is irrational.


A man of weight mg is moving upwards in a rocket with acceleration 4 g. His
apparent weight in side the rocket will
be?
A. zero
B. \( 4 \mathrm{mg} \)
\( \mathrm{c} \cdot 5 \mathrm{mg} \)
D. \( 2 \mathrm{mg} \)


What is the empirical formula for a compound containing \( 25.9 \% \mathrm{N} \) and \( 74.1 \% \)
O?
\( A \cdot N_{2} O_{5} \)
В. \( N_{2} O_{3} \)
\( c \cdot N O_{2} \)
D. \( N O \)
E. \( N_{2} \) O


\( \mathbf{A} \mathbf{5} . \mathbf{8 5} \%(\mathbf{w} \mathbf{t} / \mathbf{v} \text { ol }) \mathbf{N} \boldsymbol{a} \boldsymbol{C l} \) solution will
exert an osmotic pressure closet to which one of the following.
A. \( 5.85 \% \) (wt/vol) sucrose solution
B. \( 5.85 \% \) (wt/vol) glucose solution
c. 2 m sucrose solution
D. \( 1 \mathrm{m} \) glucose solution


When enthalpy and entropy changes for a chemical reaction are \( 2.5 \times 10^{3} \) cals
and 7.4 cals \( \operatorname{deg}^{-1}, \) respectively. The reaction at \( 298 K \) will be :
A. spontaneous
B. reversible
c. irreversible
D. non-spontaneous


The graph between \( \log \left(\theta-\theta_{0}\right) \) and time \( (t) \) is a straight line in the experiment based on Newton's law cooling. What is the shape of graph between \( \theta \) and \( t ? \)
A. A straight line
B. A parabola
c. A hyperbola
D. A circle


Prove that the sum of \( n \) number of
terms of two different A.P.'s can be same
for only one value of \( n \) if they have same
value of \( \boldsymbol{d}, \boldsymbol{a} \)


Assertion
Work and internal energy are not state functions.
Reason
The sum of \( \boldsymbol{q}+\boldsymbol{w} \) is state 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. Assertion is incorrect but Reason is correct


Hydrotropism have seen in
A. Flowers
B. Seedlings
c. Stem
D. None of the above


Which one of the following is common to multicellular fungi,filamentous algae
and protonema of mosses?
A. Diplontic life cycle
B. Members of kingdom platoon
c. Mode of Nutrition
D. Multiplication by fragmentation


Coelom derived from 'blastocoel' is
known as
A. Enterocoelom
B. Haemocoel
c. Pseudocoelom
D. Schizocoel


Which of the following is true for the reaction?
\( \boldsymbol{H}_{2} \boldsymbol{O}(l) \rightleftharpoons \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \) at \( \mathbf{1 0 0}^{\circ} \mathbf{C} \) and \( \mathbf{1} \) atm
pressure.
A \( . \Delta S=0 \)
в. \( \Delta H=T \Delta S \)
c. \( \Delta H=\Delta U \)
D. \( \Delta H=0 \)


\( \sin ^{-1} x+\cos ^{-1} x= \)


Crocodile and penguin are similar to whale and Dogfish in which one of the following features?
A. Possess a solid single stranded central nervous
B. Lay eggs and guard them till they hatch
c. Possess bony skeleton
D. Have gill slits at some stage


A car covers \( 30 \mathrm{km} \) at a uniform speed
of \( 60 k m h^{-1} \) and the next \( 30 \mathrm{km} \) at a
uniform speed of \( 40 k m h^{-1} \). Find the
total time taken.
A. 30 min
B. 45 min
c. 75 min
D. \( 120 \mathrm{min} \)


\( \mathbf{1} \boldsymbol{k} \boldsymbol{m} / \boldsymbol{h} \boldsymbol{r}=\dots \dots \dots \dots \dots \)
A \( \cdot \frac{18}{5} \)
в. \( \frac{5}{18} \)
c. \( \frac{15}{18} \)
D. \( \frac{18}{15} \)


The probability of an event A occurring
is 0.5 and of B occuring \( s 0.3 . \) If \( A \) and \( B \) are mutually exclusive events, then the probability of neither A nor B occurring is
A . 0.6
B. 0.5
\( c .0 .7 \)
D. none of these


In electromagnetic induction, the induced E.M.F is independent of
A. Change of flux
B. Time
c. Tesla
D. weber


A field of strength \( 5 \times 10^{4} / \pi \) ampere
turns / meter acts at right angles to the
coil of 50 turns of area \( 10^{-2} m^{2} . \) The coil
is removed from the field in 0.1 second.
Then the induced e.m.f. in the coil is :
A . \( 0.1 V \)
B. \( 0.2 V \)
c. \( 1.96 V \)
\( \mathbf{D} \cdot 0.98 V \)


Draw the structure of hex-1-en-3-ol
compound.


Kinetic energy of a body depends upon its:
A. mass
B. velocity
c. density
D. both A and


Marcello Malpighi after whom Malpighian tubules are named was
born in
A. Germany
B. Australia
c. Austria
D. Italy


\( 9 x^{2}-y^{2}+4 y-4 \)


Find the equation of the circle which pass through the origin and cut off intercepts \( a \) and \( b \) respectively from the
\( x \) and \( y \) axes.


The distance of a galaxy is \( 56 \times 10^{25} m \)
Assume the speed of light to be \( 3 x \)
\( 10^{8} m s^{-1} . \) Express order of magnitude of
time taken by light travelled to the galaxy.


What is the energy in \( e V \) required to
excite the electron from \( n=1 \) to \( n=2 \)
state in hydrogen atom? \( (n= \) principal
quantum number)
A . 13.6
в. 3.4
c. 17
D. 10.2


The power of water pump is The power
of water pump is \( 4 k W . \) If
\( \left(g=10 m s^{-2}\right), \) the amount of water it
can raise in 1 minute to a height of \( 20 m \)
is:
A. 100 litre
B. 1000 litre
c. 1200 litre
D. 2400 litre


Give IUPAC name:
A. Bicyclo [2,1,0] pentane
B. 1,2 - cyclopropyl cyclobutane
C. 1,2 -cyclobutyl cyclopropane
D. 1,2- Methylene cyclobutane


Left auricle recieves pure blood from the
A. Pulmonary veins
B. Pulmonary artery
c. Superior vena cava
D. Inferior vana cava


A square park has each side \( 100 m \). At
each corner of the park there is a flower
bed in the form of a quadrant of radius
\( 14 m, \) as shown in the figure. The area of
the remaining part of the park is:


A battery lights a bulb. The electric energy on flowing through the filament of the bulb, first changes into energy and then into the
energy.
A. heat; light
B. light; heat
c. mechanical; heat
D. mechanical; light


What moves the food in the digestive organs? What is the other name for the
food pipe?


The alternating current in a circular is
described by the graph as shown in
figure. The rms current obtained from
the graph would be
A \( \cdot 1.4 \mathrm{A} \)
B. 2.2 A
\( c \cdot 1.6 A \)
D. 2.6 A


is a parasite which also causes waterborne disease.
A. Roundworm
B. Tapeworm
c. Both A and B
D. Earthworm


\( N a H C O_{3} \) can be used on its own to
make cakes or bread. Baking powder is more commonly used, and contains
\( N a H C O_{3}, C a\left(H_{2} P O_{4}\right)_{2} \) and starch. An
improved combination baking powder contains about \( 40 \% \) starch, \( 30 \% \)
\( N a H C O_{3} 20 \% N a A l\left(S O_{4}\right)_{2} \) and \( 10 \% \)
\( \boldsymbol{C a}\left(\boldsymbol{H}_{2} \boldsymbol{P} \boldsymbol{O}_{4}\right)_{2} \)
Answer the following questions based on above study.
\( \boldsymbol{C} \boldsymbol{a}\left(\boldsymbol{H}_{2} \boldsymbol{P} \boldsymbol{O}_{4}\right)_{2} \) in baking powder:
A. behaves as an acid in moist condition and decomposes \( N a H C O_{3} \) to give \( C O_{2} \)
B. behaves as a base in moist condition and gives \( H_{3} P O_{4} \)
c. behaves as a binder
D. behaves as a filler


Assertion
Lower parts of the ship or bridge is coated with tar.
Reason
It is to increase rusting.
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 Actinoid cannot have an electron in 5f-orbital?
A. Uranium
B. Thorium
c. Plutonium
D. Nobelium


A solution contains \( 20 \% \) solute by
weight at \( 60^{\circ} \) C. When cooled to \( 30^{\circ} \mathrm{C} \)
the solution contains \( 10 \% \) solute by weight. When 45 g solution is cooled from \( 60^{\circ} \mathrm{C} \) to \( 30^{\circ} \mathrm{C} \), the mass of solute
deposited is :
A. \( 4.5 \mathrm{g} \)
B. 48
\( c \cdot 5 g \)
D. \( 4.75 \mathrm{g} \)


What is A?


Among the following inert gas elements, the elements that show highest chemical reactivity is:
A. \( N e \)
в. \( A r \)
c. \( H e \)
D. \( x e \)


Q Type your question
\( \left.\begin{array}{lll}\mathbf{0} & \mathbf{0} & \mathbf{1}\end{array}\right], \mathbf{i} \mathbf{z}- \)
\( \left[\begin{array}{lll}\mathbf{1} & \mathbf{0} & \mathbf{0} \\ \mathbf{0} & \mathbf{0} & \mathbf{1} \\ \mathbf{0} & \mathbf{1} & \mathbf{0}\end{array}\right], \boldsymbol{P}_{\mathbf{3}}=\left[\begin{array}{lll}\mathbf{0} & \mathbf{1} & \mathbf{0} \\ \mathbf{1} & \mathbf{1} & \mathbf{0} \\ \mathbf{0} & \mathbf{0} & \mathbf{1}\end{array}\right] \)
\( \boldsymbol{P}_{4}=\left[\begin{array}{ccc}0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 1\end{array}\right], P_{5}= \)
\( \left[\begin{array}{lll}0 & 0 & 1 \\ 1 & 0 & 0 \\ 0 & 1 & 0\end{array}\right], P_{6}=\left[\begin{array}{lll}0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0\end{array}\right], \) and
\( \boldsymbol{X}=\sum_{\boldsymbol{k}=1}^{6} \boldsymbol{P}_{\boldsymbol{K}}\left[\begin{array}{lll}2 & 1 & 3 \\ 1 & 0 & 2 \\ 3 & 2 & 1\end{array}\right] \boldsymbol{P}_{K}^{T} \)
Where \( P_{K}^{T} \) denotes the transpose of
matrix \( P_{k} \). Then which of the following
option is / are correct?
This question has multiple correct options
A. \( X \) is symmetric matrix
B. The sum of the diagonal entries of \( X \) is 18
c.
If \( X\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right]=\alpha\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right] \) then \( \alpha=30 \)
D. \( X-30 I \) is an invertible matrix


Which selection is an example of a combustion reaction?
A \( \cdot 2 K+F_{2} \rightarrow 2 K F \)
в. \( 2 A l+6 H C l \rightarrow 2 A l C l_{3}+3 H_{2} \)
c. \( C_{3} H_{8}+5 O_{2} \rightarrow 3 C O_{2}+4 H_{2} O \)
D. \( N a C l+A g N O_{3} \rightarrow A g C l+N a N O_{3} \)


Q Type your question
precipitate with CaCl\( _{2} \) solution. This
precipitate is dissolved in dilute
\( H_{2} S O_{4} \) and decolourises \( K M n O_{4} \)
(acidified) solution as the following reactions:
\( N a_{2} C_{2} O_{4}+C a C l_{2} \rightarrow C a C_{2} O_{4} \downarrow+ \)
\( \mathbf{2} \boldsymbol{N} \boldsymbol{a} \boldsymbol{C l} \boldsymbol{l} \)
\( \boldsymbol{C a} \boldsymbol{C}_{2} \boldsymbol{O}_{4}+\boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \rightarrow \boldsymbol{C a} \boldsymbol{S O}_{4}+ \)
\( \boldsymbol{H}_{2} \boldsymbol{C}_{2} \boldsymbol{O}_{4} \)
\( \boldsymbol{K} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4}+\boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4}+\boldsymbol{H}_{2} \boldsymbol{C}_{2} \boldsymbol{O}_{4} \rightarrow \)
\( M n S O_{4}+K_{2} S O_{4}+H_{2} O+C O_{2} \)
If one mole of \( N a_{2} C_{2} O_{4} \) is taken and
reacted with sufficient amount of other
reactants such as to give \( 100 \% \) reaction yield at each step and the liberated
\( C O_{2} \) is kept in a container of volume \( V \)
at pressure \( P \), temperature T. Then \( U_{r m s} \)
of \( C O_{2} \) gas in container will be :
This question has multiple correct options
A \( \cdot \sqrt{\frac{3 P V}{2 M_{C O_{2}}}} \)
B. \( \sqrt{\frac{3 R T}{2 M_{C O_{2}}}} \)
c. \( \sqrt{\frac{3 p V}{M \sigma_{2}}} \)
D. \( \sqrt{\frac{3 R T}{M C_{22}}} \)


State whether the given statement is True or False

The boiling point of liquid increases with increase in pressure.
A. True
B. False


The correct IUPAC name of the
compound \( \boldsymbol{H} \boldsymbol{O O C}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}- \)
COOH is:
A. Butanedioic acid
B. Ethane-1,2-dicarboxylic acid
c. succinic acid
D. 1,2-Ethane dioic acid


Find the average sales of laptop of all
the states for the year 2004
\( A, 9,7 \)
3. 11.71
\( c .14 .45 \)
D. 15.23


Transition metals have the general
electronic configuration?
A \( \cdot n s^{2} n d^{1-10} \)
В \( \cdot n s^{2} n p^{1}(n-1) d^{1-10} \)
c. \( n s^{1-2}(n-1) d^{1-10} \)
D. \( n s^{2} n p^{6}(n-1) d^{1-1} \)


Plaster of paris is obtained by heating gypsum at controlled-temperature.
A. True
B. False


Rosalind Franklin produced an X-ray image that helped Watson and Crick determine the width of a DNA molecule.
What did this information help them
realize?
A. Bonding between two purines would be consistent witt the diameter of the DNA helix
B. Chargaffs Rule did not apply to the DNA molecule
c. Bonding between a purine and pyrimidine would be consistent with this width of a DNA helix since each rung has a three-ring molecular dimension.
D. Adenine must bond with cytosine, and guanine must bond with thymine on each rung of the DNA ladder to accommodate for proper diameter of the double helix


Prove that the distances traversed
during equal intervals of time by a body falling from rest, stand to one another in the same ratio as the odd numbers beginning from unity [namely 1: 3: 5:
\( 7 \ldots \ldots . .] \)


Which of the following is poor resistant
to weather?
A. Polyethene
B. Polystyrene
c. PVC
D. All


Let \( \boldsymbol{A}=\{1, \mathbf{3}, \mathbf{5}, \mathbf{7}, \dots .\} \) and \( \boldsymbol{B}= \)
\{1,2,3,4,5\}
Then \( A \) and \( B \) are
A. Finite and infinite set respectively
B. Infinite and finite set respectively
c. Both Infinite sets
D. Both finite sets


A mass \( M \) is split into two parts \( m \) and
\( (M-m), \) which are, then separated by
a certain distance. The ratio \( \boldsymbol{m} / \boldsymbol{M} \) which maximizes the gravitational force between the parts is
A . 1: 4
B. 1: 3
c. 1: 2
D. 1: 1


Smoke screens consist of :
A. fine particles of \( T i O_{2} \) dispersed in air by aeroplanes
B. fine particles of \( A g I \) dispersed in air by aeroplanes
C. fine particles of \( A l_{2} O_{3} \) dispersed in air by aeroplanes
D. none of the above


What is the width of DNA molecule?
A \( \cdot 15 \mathrm{A}^{\circ} \)
B. 20 A \( ^{\text {о }} \)
c. \( 25 \mathrm{A}^{\circ} \)
D. 34 A


G-6-P dehydrogenase deficiency is assoiciated with haemolysis of
A. Leucocytes
B. Lymphocytes
c. Platelets
D. RBCs


When a mass \( m \) is connected
individually to two springs \( S_{1} \) and \( S_{2} \),
the oscillation frequencies are \( \boldsymbol{v}_{1} \) and \( \boldsymbol{v}_{2} \)
If the same mass is attached to the two
springs as shown in figure, the
oscillation frequency would be:
A \( \cdot v_{1}+v_{2} \)
B. \( \sqrt{v_{1}^{2}+v_{2}^{2}} \)
\( \mathbf{c} \cdot\left[\frac{1}{v_{1}}+\frac{1}{v_{2}}\right]^{-1} \)
D. \( \sqrt{v_{1}^{2}-v_{2}^{2}} \)


The speed of light in dense flint glass is \( 3 / 5 \) of its speed in air : The refractive index of dense flint glass is
A . 1.5
B. 1.75
c. 1.67
D. 1.1


How much the surface of earth does the
acceleration due to gravity reduce by \( 36 \% \) of its value on the surface of earth?
Radius of earth \( =\mathbf{6 4 0 0 k m} \)


n the given fig 0 is a point in the
nterior of a triangle of a triangle \( A B C, O D \perp B C, O E \perp A C \) and
\( O F \perp A B \) show that
\( \mathbf{O} \mathbf{A}^{2}+\mathbf{O B}^{2}+\mathbf{O C}^{2}-\mathbf{O D}^{2}-\mathbf{O E}^{2}- \)
\( \mathrm{OF}^{2}=\mathrm{AF}^{2}+\mathrm{BD}^{2}+\mathrm{CE}^{2} \)


Cyanide resistant pathway is
A. Anaerobic respiration
B. Aerobic respiration
C. Both (A) and (B)
D. None of these


Hormones, enzymes and vitamins are included in same group of biochemicals because these all
A. Composed of proteins
B. Regulate oxidative metabolism
c. synthesized in animal body
D. Help to regulate the metabolism


Define the following terms with a
suitable example:
Polysaccharides


Electric field inside the cavity of any conductor is
A . Infinite
B \( \cdot \vec{E}=\frac{\epsilon_{0}}{\sigma} \)
c. zero
D・ \( \vec{E}=K \frac{\sigma}{\epsilon_{0}} \hat{n} \)


If \( O A B C \) is a tetrahedron such that the
\( \boldsymbol{O} \boldsymbol{A}^{2}+\boldsymbol{B} \boldsymbol{C}^{2}=\boldsymbol{O} \boldsymbol{B}^{2}+\boldsymbol{C} \boldsymbol{A}^{2}=\boldsymbol{O} \boldsymbol{C}^{2}+ \)
\( A B^{2}, \) then which of the following is/are
correct
A. \( A B \perp O C \)
в. \( O B \neq C A \)
c. \( O C=A B \)
D. \( A B \perp B C \)


Assertion
\( \mathrm{g} \) atom of \( \boldsymbol{O}_{2} \) and \( 1 \mathrm{g} \) atom of \( \boldsymbol{O}_{3} \) have equal number of molecules.
Reason
Mass of 1 mol atom is equal to its gram atomic mass.
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


Maximum velocity of block during
subsequent motion of the system after
release of ball is :
A \( \cdot[g L(1-\cos \theta)]^{1 / 2} \)
B \( \cdot[2 g L(1-\cos \theta)]^{1 / 2} \)
\( \mathbf{c} \cdot[g L(\cos \theta)]^{1 / 2} \)
D. insufficient information


The magnetic flux linked with a coil
setisfies the relation \( \phi=4 t^{2}+6 t+ \)
\( 9 W b, \) where \( t \) is the time (in \( s \) ). The
emf indused in the coilat \( t=2 s \) is, (in
\( \mathbf{V}) \)
\( \mathbf{A} \cdot 22 \)
B . 18
c. 16
D. 40


Solve \( \lim _{x \rightarrow \frac{\pi}{2}} \frac{2^{-\cos x-1}}{x\left(x-\frac{\pi}{2}\right)} \)


Match the following


In the experiment of rolling a dice, find the probability of getting an even number that is multiple of 3.
A \( \cdot \frac{2}{5} \)
B. \( \frac{2}{3} \)
\( c \cdot \frac{3}{5} \)
D. None of these


The balanced molecular equation is :
A. \( C l_{2}+H_{2} O+N a_{2} S_{2} O_{3} \rightarrow N a_{2} S O_{4}+S+2 H C l \)
в. \( C l_{2}+N a_{2} S_{2} O_{3} \rightarrow 2 N a C l+N a_{2} S O_{4} \)
c. \( \quad C l_{2}+S_{2} O_{3}^{2-} \rightarrow S O_{4}^{2-}+S+C l \)
D. none of these


What could be the limiting factor/s in
region A ?
A. Light
B. Concentration of \( C O_{2} \)
c. Both A and B
D. None of the above


According to Bohr's theory, the angular momentum for an electron of 5th orbit
is:
\( \mathbf{A} \cdot 10 h / \pi \)
в. \( 5 h / 2 \pi \)
\( \mathbf{c} \cdot 25 h / \pi \)
D. \( 5 \pi / 2 h \)


A convex mirror has a focal length f. A real object is placed at a distance of \( \frac{\boldsymbol{f}}{\mathbf{2}} \) from the pole. Find out the position, magnification and nature of the image.


Important constituent of Portland and high alumina cements is?
A. \( C a_{3} A l_{2} O_{6} \)
в. \( \operatorname{casi} O_{3} \)
\( \mathrm{c} \cdot \mathrm{CaSO}_{4} \cdot 2 \mathrm{H}_{2} \mathrm{O} \)
D. \( F e_{2} C O_{3} \)


Find the maximum value of \( \boldsymbol{y}= \)
\( 2 \sin ^{2} x-3 \sin x+1 \forall x \in R \)


A man stands at one end of the open
truck which can run on frictionless
horizontal rails. Initially, the man and the truck are at rest. Man now walks to
the other end and stops. Then which of the following is true?
A. The truck moves opposite to direction of motion of the man even after the man ceases to walk
B. The centre of mass of the man and the truck remains at the same point throughout the man's walk
C. The kinetic energy of the man and the truck are exactly equal throughout the man's walk.
D. The truck does not move at all during the man's walk


The area of the region, enclosed by the circle \( x^{2}+y^{2}=2 \) which is not common
to the region bounded by the parabola \( y^{2}=x \) and the straight line \( y=x, \) is:
A \( \cdot \frac{1}{3}(15 \pi-1) \)
в. \( \frac{1}{6}(24 \pi-1) \)
c. \( \frac{1}{6}(12 \pi-1) \)
D. \( \frac{1}{3}(6 \pi-1) \)


Which among the following is an inorganic compound?
A. Protein
B. Marble
c. waxes
D. Sugar


Electrostatic induction is used to
charge
A. Conductors
B. Semiconductors
c. Insulators
D. All of the above


If \( g(x) \) is defined on [-1,1] and the area
of the equilateral triangle with two of its vertices (0,0) and \( (x, g(x)) \) is \( \frac{\sqrt{3}}{4}, \) then
A \( . g(x)=\pm \sqrt{\left(1-x^{2}\right)} \)
в. \( g(x)=-\sqrt{\left(1-x^{2}\right)} \)
c. \( g(x)=\sqrt{\left(1-x^{2}\right)} \)
D. \( g(x)=\sqrt{\left(1+x^{2}\right)} \)


Find the area of a triangle \( : \boldsymbol{y}=\boldsymbol{x}, \boldsymbol{y}= \)
\( 2 x \) and \( y=3 x+4 ? \)


When zinc reacts with very dilute nitric acid it produces:
A. \( N H_{4} N O_{3} \)
B. \( N O \)
\( c \cdot N O_{2} \)
D. \( H_{2} \)


Temperature is a measure of :
This question has multiple correct options
A. the average kinetic energy of the particles in a substance.
B. the average potential energy of the particles in a substance.
C. the highest amount of kinetic energy the particles in a substance have.
D. the number of particles a substance has.
E. the amount of heat a substance has.


\( \lim _{x \rightarrow 0} \frac{\{\sin (\alpha+\beta) x+\sin (\alpha-\beta) x+\sin 2}{\cos ^{2} \beta x-\cos ^{2} \alpha x} \)


A hammer of mass \( M \) falls from a
height \( h \) repeatedly to drive a pile of
mass \( m \) into the ground. The hammer
makes the pile penetrate in the ground
to a distance \( d \) in single blow.

Opposition to penetration is given by:
A \( \cdot \frac{m^{2} g h}{M+m d} \)
B. \( \frac{m^{2} g h}{(M+m) d}+(M+m) g \)
c. \( \frac{M^{2} g h}{M+m d} \)
D. \( \frac{m^{2} g h}{(m+M) d}-(M+m) g \)


Which of the following insects is economically useful for us?
A . Musca
в. Вотыух
c. Pheretima
D. Periplaneta


The cartesian equation of a line is \( \frac{\boldsymbol{x}+\mathbf{3}}{\mathbf{2}}=\frac{\boldsymbol{y}-\mathbf{5}}{\mathbf{4}}=\frac{\boldsymbol{z}+\mathbf{6}}{\mathbf{2}} \) find the vector
equation of the line?


A force cannot be seen but the effect of
force can be felt
A. True
B. False
c. Ambiguous
D. Data insufficient


A \( 1 \mathrm{m} \) long uniform beam is being
balanced as shown. Calculate the force
\( F \)
\( A \cdot 2 N \)
B. 3 N
c. 7 n
\( D \)


The Indian Navy flight fly in a formation
that can be viewed as two triangles with
common side. Prove that \( \triangle \boldsymbol{S} \boldsymbol{R} \boldsymbol{T} \cong \)
\( \triangle Q R T, \) if \( T \) is the midpoint of \( S Q \) and
\( \boldsymbol{S} \boldsymbol{R}=\boldsymbol{R} \boldsymbol{Q} \)


Inter- halogen compounds can be:
A \( . I C l_{3} \)
B. \( B r F_{5} \)
c. \( I F_{7} \)
D. all of these


How many pair of spiracles are present in thorax region of cockroaches?
A . 10
B. 2
\( c \cdot 8 \)
\( D \)


Evaluate :
\( \lim _{n \rightarrow \infty} \frac{[1 . x]+[2 . x]+[3 . x]+\ldots \ldots+[n . x]}{n^{2}}, \) where
denotes the greatest integer function.


In electrolytic refining of any metal impure metal is taken as anode.
A. True
B. False


The common difference of the AP
\( \mathbf{5}, \mathbf{3}, \mathbf{1},-\mathbf{1}, \dots \) is
A . -2
B . 2
\( c \cdot-1 \)
\( D \)


Write the IUPAC names of the following ketone or aldehyde. If possible, give common name(s) also.
\( \mathrm{Ph}-\mathrm{CH} \equiv \mathrm{CH}-\mathrm{CHO} \)


According to Kohlrausch law, the limiting value of molar conductivity of
an electrolyte \( \boldsymbol{A}_{2} \boldsymbol{B} \)
\( \mathbf{A} \cdot \lambda_{A^{+}}+\lambda_{B^{2}} \)
в. \( \frac{1}{2} \lambda_{A+}+\lambda_{B^{2}} \)
c. \( _{2 \lambda_{A^{+}}+\frac{1}{2} \lambda_{B^{2}}} \)
D. \( 2 \lambda_{A^{+}}+\lambda_{B^{2}} \)


\( 2 H N O_{3}+C a C O_{3} \longrightarrow \)
A. \( C a\left(N O_{3}\right)_{2}+H_{2} O+C O_{2} \)
в. \( C a\left(N O_{3}\right)_{2}+C O_{2} \)
c. \( \operatorname{Ca}\left(N O_{3}\right)_{2}+H_{2} O \)
D. None of the above


Which gas is produced when compound
\( X \) reacts with washing soda?
A. Hydrogen
B. Oxygen
c. Methane
D. Carbon dioxide


The shape of gaseous \( S n C l_{2} \) is:
A . tetrahedral
B. linear
c. angular
D. T-shape


\( \mathrm{HX} \) is a weak acid \( \left(\boldsymbol{K}_{\boldsymbol{a}}=\mathbf{1 0}^{-\mathbf{5}}\right) . \) It forms
a salt \( \mathrm{NaX}(0.1 \mathrm{M}) \) on reacting with caustic soda. The degree of hydrolysis of NaX is:
A . 0.01 \%
B. 0.0001 \%
c. \( 0.1 \% \)
D. 0.5 \%


Consider the following equilibrium
reaction:
\( \boldsymbol{N} \boldsymbol{H}_{3}+\boldsymbol{N} \boldsymbol{H}_{3} \rightleftharpoons \boldsymbol{N} \boldsymbol{H}_{4}^{+}+\boldsymbol{N} \boldsymbol{H}_{2} \)
Find the ionic product of the above equilibrium reaction?


Write the dispersed phase and dispersion medium of the following colloidal systems:
(i) Smoke
(ii) Milk
What are Iyophilic and lyophobic colloids? Which of these sols can be
easily coagulated on the addition of small amounts of electrolytes?


The coordinates of a moving particle at time \( t \) are given by \( x=c t^{2} \) and \( y=b t^{2} \)
The speed of the particle is given by
A \( \cdot 2 t(c+b) \)
B . \( 2 t \sqrt{\left(c^{2}-b^{2}\right)} \)
c. \( t \sqrt{\left(c^{2}+b^{2}\right)} \)
D. \( 2 t \sqrt{\left(c^{2}+b^{2}\right)} \)


\( 7^{2 n}+2^{3 n-3} .3^{n-1} \) is divisible by 25 for
any natural number \( n \geq 1 . \) Prove that by
mathematical


Area enclosed by curves \( y=x^{2} \) and line
\( \boldsymbol{y}=\boldsymbol{x} \) is
A \( \cdot \frac{1}{6} \)
B. 1
\( c \cdot \frac{5}{2} \)
D.


A coil of insulated copper wire is connected to a galvanometer. What will happen if a bar magnet is
(i) pushed into the coil
(ii) withdrawn from inside
the coil (iii) held stationary inside the coil.


is a technique of watering plants by making use of narrow tubings which deliver
water directly at the base of the plant.
A. Sprinkler irrigation
B. Drip irrigation
c. center pivot irrigation
D. Localized irrigation


Match the items listed in column I with
Column II and mark the correct option.
Column I Column II
a. Glycosidic bond
(i) Protein detection
b. Tertiary structure
(ii) Dehydration reaction
c. Biuret test
(iii) Formation of
d. single alphabet catalytic site code 'P'
(iv) Proline
\( A \cdot a-(i), b-(i i), C-(i v), d-(i i i) \)
B. \( a-(\text { iii) }, b-(i i), C-(i v), d-(i) \)
C \( \cdot a-(\text { ii }), b-(\text { iii }), C-(i), d-(i v) \)
D. a - (iii), b - (iv), C - (ii), d - (i)


Amount of oxygen in \( 32.2 g \) of \( N a_{2} S O_{4} \cdot 10 H_{2} O \) is:
A \( .20 .8 g \)
B. \( 22.4 g \)
c. \( 2.24 g \)
D. \( 2.08 g \)


Magnitude of binding energy of satellite is \( \boldsymbol{E} \) and kinetic energy is \( \boldsymbol{K} \). The ratio \( \boldsymbol{E} / \boldsymbol{K} \) is :
A . \( 2 / 1 \)
B . \( 1 / 4 \)
\( c .1 \)
D. \( 1 / 2 \)


Which of the following is used for inducing sleep?
A. Paracetamol
B. chloroquine
c. Bithional
D. Barbituric acid derivatives