\( \ln \) an ac circuit, the resistance of \( \mathrm{R} \Omega \) is connected in series with an inductance
I. If phase angle between voltage and
current be \( 45^{\circ}, \) the value of inductive
reactance will be:
A. \( R / 2 \)
B. \( R / \sqrt{2} \)
\( c . R \)
D. Insufficient data


Which of the following is not a proper fraction?
\( A \cdot \frac{2}{3} \)
B. \( _{4} \)
\( c \cdot \frac{5}{7} \)
D. \( \frac{6}{5} \)


A man standing in a lift falling under gravity releases a ball from his hand. As
seen by him, the ball:
A. Falls down
B. Remains stationary
c. Goes up
D. Executes SHM


Equanil is a/an:
A. tranqulizer
B. antifertility drug
c. artificial sweetner
D. antihistaamine


Charge \( Q \), is divided into two parts which are then kept some distance
apart. The force between them will be
maximum if the two parts are having the charge.
\( ^{\text {A }} \cdot \frac{Q}{2} \) each
в. \( \frac{Q}{4} \) and \( \frac{3 Q}{4} \)
c. \( \frac{Q}{3} \) and \( \frac{2 Q}{3} \)
D. \( e \) and \( (Q-e) \), where \( e= \) electronic charge


A body weighs \( 36 k g \) on the surface of the Earth. How much would it weights
on the surface of a planet,whose mass is \( \frac{1}{9} \) and radius \( \frac{1}{3} \) of that of earth?


The speed of the bicycle is
\( \begin{array}{ll}\text { A. } 6.4 \pi m & s^{-1}\end{array} \)
B. \( 3.5 \pi m \quad s^{-1} \)
\( \mathbf{c} \cdot 2.8 \pi m \quad s^{-1} \)
\( \begin{array}{ll}\text { D. } 5.6 \pi m & s^{-1}\end{array} \)


In which quadrant or on which axis each of the following points lies. Write abscissa and ordinate each of the
following:
(i) (3,-4)
(ii) (-3,5)
(iii) (-10,0)
(iv) (-2,-7)


Unit vector perpendicular to the plane passing through the points \( \hat{\mathbf{i}}-\hat{\mathbf{j}}+ \) \( 2 \hat{k}, 2 \hat{i}-\hat{k} \) and \( 2 \hat{j}+\hat{k} \) is
A \( \cdot \frac{2 \hat{i}-\hat{j}+\hat{k}}{\sqrt{6}} \)
\( ^{\text {В } \cdot \frac{2 \hat{i}+\hat{j}+\hat{k}}{\sqrt{6}}} \)
c. \( \frac{2 \hat{i}+\hat{j}-\hat{k}}{\sqrt{6}} \)
D. None of these


Subtract \( 24 a b-10 b-18 a \) from
\( 30 a b+12 b+14 a \)


Which of the following is the first compound that accepts carbon dioxide during dark phase of photosynthesis?
\( A \). NADP
B. RuBP
c. Ferredoxin
D. cytochrome


Javed was given \( \frac{5}{7} \) of a basket of oranges.What fraction of oranges was
left in the basket?


Heat is not transferred by the process of convection in:
A. solid
B. liquid
c. gas
D. none of the above


Evaluate the given integral. \( \int e^{x} \frac{x-4}{(x-2)^{2}} d x \)


1 volt is equivalent to:
A \( \cdot \frac{\text { newton }}{\text { second }} \)
B. \( \frac{\text { newton }}{\text { coulomb }} \)
c. \( \frac{\text { joule }}{\text { coulomb }} \)
D. \( \frac{\text { joule }}{\text { second }} \)


Formation of \( \boldsymbol{O}^{-} \) is
whereas formation of \( \boldsymbol{O}^{-2} \) is
A. exothermic, endothermic
B. endothermic, exothermic
c. endothermic, endothermic
D. exothermic, exothermic


Conversion of sulphur to \( \boldsymbol{S O}_{3} \) has
\( \triangle H=2 x K c a l \) and conversion of \( S O_{2} \)
to \( S O_{3} \) involves \( \triangle H=-y k c a l \). The
correct thermochemical equation for
formation of \( \boldsymbol{S} \boldsymbol{O}_{2} \) is:
A \( . S+O_{2} \rightarrow S O_{2} \triangle H=(y-2 x) \)
B. \( S+O_{2} \rightarrow S O_{2} \triangle H=-(y-2 x) \)
c. \( S+O_{2} \rightarrow S O_{2} \triangle H=(x+y) \)
D. \( S+O_{2} \rightarrow S O_{2} \triangle H=2 y-3 x \)


Relation between hydrolysis constant and dissociation constant are given.
Which is the correct formula for \( M g C l_{2} \)
\( ? \)
A \( \cdot K_{h}=\frac{K_{w}}{K_{a}} \)
в. \( K_{h}=\frac{K_{w}}{K_{b}} \)
\( ^{\mathrm{c}} \cdot_{K_{h}}=\frac{K_{w}}{K_{a} \times K_{b}} \)
D. \( _{K_{w}}=\frac{K_{h}}{K_{b}} \)


In the periodic table, the metallic
character of element:
A. decreases from left to right across a period and on descending a group
B. decreases from left to right across a period and increases on descending a group
C. increases from left to tight across a period and on descending a group
D. increases from left to right across a period and decreases on descending a group


Atto is used as prefix in SI system. If
true enter 1 else enter 0


A ball of mass \( 1 k g \) dropped from \( 9.8 m \) height strikes the ground and rebounds to a height of \( 4.9 m \). If the time of
contact between ball and ground is \( 0.1 s \)
then find impulse and average force acting on ball.


Phloem always flows from
\( \mathbf{a} \)
A. Sugar source to sugar sink
B. Sugar sink to sugar source
c. Leaf to root
D. None of these


3 moles of \( \boldsymbol{P} \) and 2 moles of \( \boldsymbol{Q} \) are
mixed, what will be their total vapour pressure in the solution if their partial
vapour pressures are 80 and 60 respectively.
A. 80 torr
B. 140 torr
\( c .720 \) torr
D. 70 torr


\( D- \) mannose \( \stackrel{H O^{-}}{\rightleftharpoons} D-g l u c o s e \stackrel{H O}{\rightleftharpoons} \)
A Product \( (A) \) of above reaction is:
A . \( D- \) fructose
B. \( D- \)talose
\( \mathbf{C} \cdot D-i d o s e \)
D. \( D- \) glucose


Match the following
1
Eutrophication
I. Rise in sea level
2
II. Water hyacinth Biomagnification
III. Increase of quantity of
3. Terror of Bengal pollutant at successive trophic levels
4. Green house \( \quad \) IV. Enrichment with nutrients effect
\( A \cdot 1-1 V, 2-111,3-1,4-11 \)
B. 1- -।, 2- ||, 3- |II, 4- IV
c. \( 1- \) ॥, \( 2- \) ॥ᅵ, \( 3-1 V, 4-1 \)
D. 1- -IV, 2- |II, 3- ||, 4-1


By selling a product for Rs. 100 how much profit was earned?
(1) \( 20 \% \) profit would have been earned if
it had been sold for Rs. 90 .
(II) The profit was one-third of the cost price
A. Statement (I) ALONE is sufficient, but statement (II) alone is not sufficient
B. Statement (II) ALONE is sufficient, but statement (I) alone is not sufficient
c. BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient
D. EACH statement ALONE is sufficient


The atomicity of neon gas is :
A . two
B. one
c. four
D. three


Which of the following processes is responsible for the relatively low
concentrations of \( C O_{2} \) in bowls 2 and \( 3 ? \)
A. Respiration
B. Fermentation
c. Photosynthesis
D. Photoperiodism
E. Transpiration


A scooterist sees a bus \( 1 k m \) ahead of
him moving with a velocity of \( 10 m s^{-1} \)
With what speed the scooterist should
move so as to overtake the bus in \( 100 s ? \)
A \( \cdot 10 m s^{-1} \)
B. \( 20 m s^{-1} \)
\( \mathrm{c} \cdot 50 \mathrm{ms}^{-1} \)
D. \( 30 m s^{-1} \)


Solve the following equation and check
your answer.
\( \boldsymbol{x}+(\boldsymbol{x}+\mathbf{2})=(\boldsymbol{x}+\mathbf{4})+\mathbf{3 1} \)


Q Type your question
which the first step is slowest and the
last step is fastest? (Assume that
reaction is exothermic)
\( A \)
B.
\( c \)
None of these


Mr. Gupta purchased an article for Rs.
702 including Sales Tax. If the rate of Sales Tax is \( 8 \% \), find the sale price of
the article.


Arrange the following in increasing
order of oxidation states of \( M n \)
\( \boldsymbol{K}_{2} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4}, \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{2}, \boldsymbol{K} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4} \)


Complete the following nuclear
equation:
\( _{26}^{69} \mathrm{Fe} \rightarrow \beta+_{-}- \)
\( \mathbf{A} \cdot_{25}^{58} \mathrm{Mn} \)
B . \( \frac{58}{27} \mathrm{Co} \)
\( \mathbf{C} \cdot_{25}^{59} \mathrm{Mn} \)
\( D \cdot \frac{59}{27} \mathrm{Co} \)
E \( . \begin{array}{c}60 \mathrm{Mn} \\ 25\end{array} \)


Differentiate w.r.t \( x, \) the following function:
\( \log \sqrt{\frac{1+\cos x}{1-\cos x}} \)


Euclid's division lemma states that for
two positive integers a and b, there exist unique integers \( q \) and \( r \) such that \( \boldsymbol{a}=\boldsymbol{b} \boldsymbol{q}+\boldsymbol{r}, \) where \( r \) must satisfy
\( A \cdot 1<r<b \)
B. \( 0<r \leq b \)
c. \( 0 \leq r<b \)
\( D \cdot 0<r<b \)


The moment directed along
positive \( x- \) axis of electric field at
point \( (2,2 \sqrt{2}, 0) \)
A. Along positive \( x- \) axis
B. Along positive \( y- \) axis
c. Along negative \( x- \) axis
D. along negative y-axis


The distance \( x \) covered by a particle
varies with time \( t \) as \( x^{2}=2 t^{2}+6 t+1 \)
Its acceleration varies with \( x \) as :
A . \( x \)
B . \( x^{2} \)
\( c \cdot x^{-1} \)
D. \( x^{-3} \)
E . \( x^{-2} \)


What happens in synthesis phase during cell cycle?
A. DNA synthesis
B. Chromosome number becomes double
c. Formation of two nuclei
D. synthesis of proteins \& RNA


\[
\begin{aligned}
\operatorname{Let} \boldsymbol{f}(\boldsymbol{x})=&\{\boldsymbol{x}+\boldsymbol{\lambda}, \boldsymbol{x}<1\\
& \boldsymbol{2} \boldsymbol{x}-\boldsymbol{3}, \boldsymbol{x} \geq 1, \text { if } \lim _{\boldsymbol{x} \rightarrow 1} \boldsymbol{f}(\boldsymbol{x})
\end{aligned}
\]
exists, then find value of \( \lambda \)


A mass \( \mathrm{m} \) is suspended form a sensitive spring balance kept in a satellite. The reading of the balance is
\( W_{1} \) when the satellite is in an orbit of
radius \( \mathrm{R} \) and is \( W_{2} \) when it is in an orbit
of radius \( 2 \mathrm{R} \). Then
A. \( W_{1}>W_{2} \)
в. \( W_{1}<W_{2} \)
c. \( W_{1}=W_{2} \)
D. cannot be predicted


For a transistor, \( \alpha_{d c} \) and \( \beta_{d c} \) are the
current ratios, then the value of \( \frac{\beta_{d c}-\alpha_{d c}}{\alpha_{d c} \cdot \beta_{d c}} \) is
A . 1
в. 1.5
\( c \cdot 2 \)
D. 2.5


If \( a=3+\sqrt{23}, \) then find \( \frac{-14}{a} \)


Mass of \( 12.044 \times 10^{23} \) atoms of
hydrogen is:
A . \( 1 g \)
в. \( 2 g \)
\( \mathrm{c} \cdot 3 g \)
D. \( 4 g \)


Write the units digit of the cube for
\( \mathbf{4 4 4 4 7} \)
A . 3
B. 7
c. 9
\( D \)


\( 25 \mathrm{mL} \) samples of distilled water, tap
water and boiled water required,
respectively, \( 1 \mathrm{mL}, 13 \mathrm{mL} \) and \( 5 \mathrm{mL} \) of soap solution to form a permanent
lather. The ratio of temporary to permanent hardness in the tap water is :
A .3: 2
B . 2: 3
\( c \cdot 1: 2 \)
D. 2: 1


A body of mass \( 50 k g \) is suspended using a spring balance inside a lift at rest. If the lift starts falling freely, the reading of the spring balance is
\( A \cdot=0 \)
в. \( <50 k g \)
\( \mathbf{c} .=50 k g \)
D. \( >50 k g \)


\( \boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{S}+\boldsymbol{N} \boldsymbol{a} \boldsymbol{C} \boldsymbol{N} \longrightarrow(\boldsymbol{A}),(\boldsymbol{A})+ \)
\( \boldsymbol{Z} \boldsymbol{n} \longrightarrow(\boldsymbol{B}) \)
(B) is a metal. Hence (A) and (B) are:
A \( \cdot \operatorname{Na}_{2}\left[\operatorname{Zn}(C N)_{4}\right], Z n \)
B . \( N a_{2}\left[A g(C N)_{2}\right], A g \)
c. \( N a_{2}\left[A g(C N)_{4}\right], A g \)
D. \( N a_{3}\left[A g(C N)_{4}\right], A g \)


Solve:
\( \frac{\boldsymbol{x}+\mathbf{5}}{\mathbf{5}}=\mathbf{6} \)


Petiole is modified into tendril in
A . Passiflora
B. Gloriosa
c. Pisum
D. Clematis


Explain homogenous and heterogenous
conditions with an example.


decimeter is \( _{--} \) megameter.
A \( \cdot 10^{-7} \)
B. \( 10^{-6} \)
\( \mathrm{c} \cdot 10^{-5} \)
D. \( 10^{-8} \)


Find the value of \( x \)


The molality \( (\mathrm{m}) \) of each ion \( \left(\mathrm{N} \boldsymbol{H}_{4}^{+} \) and \right.
\( \left.C l^{-}\right), \) respectively, present in the
aqueous solution of \( 2 M N H_{4} C l \)
assuming \( 100 \% \) dissociation according to given reaction is,
\( N H_{4} C l(a q) \rightarrow N H_{4}^{+}(a q)+C l^{-}(a q) \)
Given that density of solution \( =3.107 \)
\( \mathrm{g} / \mathrm{ml} \)
A \( .0 .45 \mathrm{m}, 0.67 \mathrm{m} \)
в. \( 0.67 \mathrm{m}, 0.45 \mathrm{m} \)
\( c .0 .67 m, 0.67 m \)
\( m \)
D. \( 0.45 \mathrm{m}, 0.45 \mathrm{m} \)


Calculate mole of \( I_{2} \) at equilibrium.


To ensure almost 100 per cent
transmittivity, photographic lenses are often coated with a thin layer of dielectric material. The refractive index
of this material is intermediated between that of air and glass (which makes the optical element of the lens)
A typically used dielectric film is \( M g F_{2} \) \( (n=1.38) . \) What should the thickness of the film be so that at the center of the
visible spectrum \( (5500 A) \) there is maximum transmission.
A \( \cdot 5000 \) a
в. 2000 А
c. 1000 a
D. 3000 ,


Rhombic, monoclinic and plastic sulphur are?
A. isomers
B. isotopes
c. allotropes
D. hydrides of sulphu


What is the \( 5^{t h} \) term of this sequence?
\( \mathbf{5}, \mathbf{1 0}, \mathbf{2 0}, \dots \)
A . 30
B . 40
c. 50
D. 80


The paint in a certain container is sufficient to paint an area equal to
\( 9.375 m^{2} . \) How many bricks of
dimensions \( 22.5 \times 10 \times 7.5 c m \) can be
painted out of this container?


Magnetic lines of force due to a long straight conductor carrying current are
A. straight lines
B. elliptical
c. circular
D. parabolic


Short / Long type answer type
questions. How does the blood differ in its
components in a mammal when it enters the lungs and when it leaves them?


Which of the following statement is
correct
A. The motion of earth around the sun is vibratory
B. The motion of a mosquito in a room is in a straight line
C. The motion of moon around the earth is periodic
D. None of these


A current carrying ring is placed in a magnetic field. The direction of the field
is perpendicular to the plane of the ring. Which of the following correct for this? This question has multiple correct options
A. There is no net force on the ring
B. The ring will tend to expand
c. The ring will tend to contract
(b) or
D. Either
(c) depending on the directions of the current in the ring and the magnetic field


Draw a schematic ray diagram reflecting telescope showing how rays coming from a distant object are received at eye piece. Write its two important advantages over a refracting telescope


The correct order of acidities of the
following is :
A. III>IV > || > |
B. IV>|||>|>1|
c. \( \||>\|>|>\mid V \)
D. ॥> ||| > IV >


since the origin of life on earth, there
are five episodes of mass extinction of species. Who is mainly responsible for the sixth extinction?


Assertion
\( \left[A l\left(H_{2} O\right)_{6}\right]^{3+} \) is a stronger acid than
\( \left[\boldsymbol{M} \boldsymbol{g}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right]^{2+} \)
Reason
Size of \( \left[A l\left(H_{2} O\right)_{6}\right]^{3+} \) is smaller than
\( \left[M g\left(H_{2} O\right)_{6}\right]^{2+} \) and possesses more
effective nuclear charge.
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


With the help of which of the following
will you describe the position of a pen
on a table?
A. Coordinate geometry
c. Trignometry
D. Proportions


Which of the following acids is a vitamin?
A. Aspartic acid
B. Ascorbic acid
c. Adipic acid
D. Saccharic acid


The energy of a photon is \( 3 \times 10^{-12} \)
ergs. Its wavelength (in nm) will be:
A .662
в. 1324
c. 66.2
D. 6.62


Which one feature is correctly
described?
A. Salivary glands - secretes saliva - replication
B. Pupil of the eyes - dilate - constricts- regulates entry of light
C. Heart rate - decreases - tachycardia
D. Intestinal peristalsis - stimulates - inhibits - heart rate


The ratio in which the plane \( 2 x+3 y- \)
\( \mathbf{2} z+\mathbf{7}=\mathbf{0} \) divides the line segment
joining the points (-1,1,3),(2,3,5) is
A .3: 5
B. 7: 5
\( \mathbf{c} \cdot 9: 11 \)
D. 1: 5 externally


Which of the following floral parts forms pericarp after fertilization?
A. Nucellus
B. Outer integument
c. ovary wall
D. Inner integument


Total number of orbitals associated
with third shell will be
A .2
B. 4
\( c \cdot 9 \)
D.


Heavy water is:
A. water with mercury compounds
B. water with chlorides and sulphates of Ca and Mg
C. water with bicarbonates of Ca and Mg
D. deuterium oxide


Which is not true for \( _{1} H^{1} ;_{1} H^{2} ;_{1} H^{3} ? \)
A. They are isotopes of each other
B. They have similar electronic configurations
C. They exist in the nature in the ratio of 1: 2: 3
D. Their atomic masses are in the ratio of 1: 2: 3


The type of overlapping in \( B r-F \) bond
in \( B r F_{3} \) molecule is:
A \( \cdot s p^{3}-p \)
B \( \cdot s p^{2}-p \)
\( \mathbf{c} \cdot s p^{3} d-p \)
\( \mathbf{D} \cdot s p^{3} d^{2}-p \)


On a smooth surface there are five
identical equally spaced balls \( A, B, C, D \) and E present with initial velocities \( 10 \mathrm{m} / \mathrm{s},-5 \mathrm{m} / \mathrm{s}, 2 \mathrm{m} / \mathrm{s},-3 \mathrm{m} / \mathrm{s} \)
\( 3 \mathrm{m} / \mathrm{s} \) respectively, Collision between any two ball assumed to be elasitc.
Then after all possible collision which pair of balls will have same speed as of initial
\( A \cdot A \& D \)
B. B \&
\( c \cdot c \& D \)
\( D \cdot A \& C \)


Which of the following acids is commonly used in batteries for cars?
A. Sulphuric acid
B. Nitric acid
c. Hydrochloric acid
D. Acetic acid


The inert gas atom in which the total number of d-electrons is equal to the
difference in numbers of total \( p- \) and
\( s \) -electrons, is:
A. \( H e \)
в. \( N e \)
\( c . A r \)
D. \( K r \)


The value of \( \sum_{n=1}^{13}\left(i^{n}+i^{n+1}\right), i=\sqrt{-1}, \) is
\( \mathbf{A} \cdot i \)
B . \( i-1 \)
\( c \cdot 1 \)
D.


How frequently we should wear spectacles if it is advised by doctor if our eyes are damaged?
A. Sometimes
B. Always
c. Rarely
D. Never


Anisole is an example of:
A. aromatic ether
B. symmetrical ether
C . unsymmetrical open chain ether
D. symmetrical open chain ether


The significance of \( \boldsymbol{T} \boldsymbol{\Delta} \boldsymbol{S} \) in \( \boldsymbol{\Delta} \boldsymbol{G}= \)
\( \Delta H-T \Delta S \) is a quantitative measure
of the randomness of the:
B. space
c. both of the above
D. none of the above


If a rigid body rolls on a surface without
slipping, then:
A. linear speed is maximum at the highest point but minimum at the point of contact
B. linear speed is minimum at highest point but maximum at the point of contact
C. linear speed is same at all points of the rigid body
D. angular speed is different at different points of a rigid body


An aeroplane is flying in a horizontal direction at \( 600 k m / h r \) at a height of \( 6 k m s \) and is advancing towards a point
which is exactly over a target on earth. At that instant the pilot releases a ball which on descending the earth strike
the target. The falling ball appears-
A. To the pilot in the aeroplane, as falling along a parabolic path
B. To a person standing near the target, as falling exactly vertical
c. To a person standing near the target, as describing a parabolic path
D. To the pilot sitting in the aeroplane, as falling in a zigzag path


In fig \( 9.18, \) tangents PQ and PR are drawn to a circle such that
\( \angle R P Q=30^{0} . \) A chord RS is drawn
parallel to the tangent PQ. Find the
\( \angle R Q S \) in degrees.Hint: Draw a line
through \( Q \) and perpendicular to \( Q P \)


A man has a concave shaving mirror of focal length \( 0.2 \mathrm{m} \). How far should the mirror be held from his face in order to
give an image of two fold magnification?
\( \mathbf{A} \cdot 0.1 \mathrm{m} \)
B. \( 0.2 \mathrm{m} \)
c. \( 0.3 \mathrm{m} \)
D. \( 0.4 \mathrm{m} \)


What will be \( \Delta H \) for the reaction,
\( \boldsymbol{C H}_{2} \boldsymbol{C l}_{2} \rightarrow \boldsymbol{C}+\mathbf{2} \boldsymbol{H}+\mathbf{2} \boldsymbol{C l} ? \)
(B.E. of \( C-H \) and \( C-C \) ) bonds are 416 kJ
\( m o l^{-1} \) and 325 kJmol \( ^{-1} \) respectively
A . 832 k
B . 1482 k
c. \( 650 \mathrm{kJ} \)
D. 1855 k


Explain chemiosmotic hypothesis for ATP synthesis.


When a hole is produced in P-type semiconductor, there is
A. Extra electron in valence band
B. Extra electron in conduction band
c. Missing electron in valence band
D. Missing electron in conduction band


"Ingredients of baking powder are corn starch, sodium bicarbonate, calcium hydrogen phosphate and sodium aluminum sulfate." Therefore, baking powder is a:
A. mixture
B. molecule
c. mixture of elements
D. compound


What is the equivalent capacitance
between \( A \) and \( B \) in the diagram below?
A . \( 10 F \)
в. \( 5 F \)
\( c .2 .5 F \)
D. \( 0 F \)


When the mean value theorem does
apply?
This question has multiple correct options
A. Function needs to be continuous
B. Function needs to be differentiable
C. Function needs to be non-differentiable
D. None of the above


Prove that \( : 1+3+3^{2}+\ldots+3^{n-1}= \)
\( \frac{\left(3^{n}-1\right)}{2} \)


Evaluate \( \int_{0}^{\pi / 4} \sec ^{2} x d x \)


Among \( \left(C H_{3}\right)_{3} N \) and \( C H_{3} N H_{2}, \) amine
with \( _{\text {一一一一一一一一 }} \) methyl groups attached has the higher boiling point.


(a) Write names of any two conventional
sources of energy.
(b) Write any two limitations in harnessing wind energy.


\( H_{2} O_{2} \) is added to acidified \( \mathrm{KMnO}_{4} . \) In
this reaction \( H_{2} O_{2} \) acts as:
A. oxidising agent
B. reducing agent
c. a salt
D. a base


Two wires are as follows. The
resistivities, lengths and radii are in the ratio 2: 3,3: 5 and 2: 7 respectively
Their resistances are in the ratio of
A . 49: 10
B. 7: 2
\( c \cdot 2: 4 \)
D. 1: 2


Match the following:
\( \begin{array}{lll}\text { S.No } & \text { Scientists } & \text { Inventions } \\ 1 & \text { Michael Faraday } & \text { First battery } \\ 2 . & \text { George Simon Ohm } & \text { Radioactivity } \\ 3 . & \text { Volta } & \text { Dynamo } \\ 4 . & \text { Henry Becquerel } & \text { Ohm's law }\end{array} \)


Find the coefficients of \( x^{2} \) and \( x^{3} \) in the
expansion of \( (2-x)^{6} \)


If \( n \) arithmetic means are inserted
between 1 and 31 such that ratio of first
and \( n^{t h} \) mean is \( 3: 29, \) then what is the
value of \( n ? \)
A . 10
B. 14
c. 18
D. 23


Which of the following process is not
used in the concentration of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) ?
A. Distillation under reduced pressure
B. Evaporation on a water bath
c. Fractional crystallization
D. Sublimation


The strongest bond is present in:
A. \( B r_{2} \)
в. \( I_{2} \)
\( c \cdot C l_{2} \)
D. \( F_{2} \)


\( \sqrt{(12+\sqrt{12+\sqrt{12+\ldots}})}=x, \) then
the value of \( x \) is
\( A \cdot 3 \)
B. 4
\( c \cdot 6 \)
D. Greater than 6


Select incorrect statement.
A. Double bond is shorter than a single bond.
B. \( \sigma \) -bond is weaker than a \( \pi \) -bond.
C. Double bond is stronger than a single bond.
D. Covalent bond is stronger than a hydrogen bond.


Find the max.value of the total surface
of a right circular cylinder which can be inscribed in a sphere of radius a.
A \( \cdot \pi a^{2}(1+1 / \sqrt{5}) \)
B \( \cdot \pi / 2 a^{2}(1+\sqrt{5}) \)
c. \( \pi a^{2}(1+\sqrt{5}) \)
D \cdot \( \pi a^{2}(2+\sqrt{5}) \)


\( 4+8+16+32+\ldots . . \) What is the
common ratio?
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D. 4


A spring accelerates a \( 2 k g \) cart from
rest in a time of .8 seconds, giving it a momentum of \( 4 k g m / s \$ . \) With what
force did the spring accelerate the cart?
\( A \ldots 5 N \)
в. 1.6 N
c. \( 3.2 N \)
D. \( 5 N \)
\( E \cdot 8 N \)


\( H_{3} O^{+}+O H^{-} \rightarrow 2 H_{2} O, \) is an example
of:
A. Arrhenius neutralisation
B. Bronsted neutralisation
c. Lewis neutralisation
D. Both Lewis and Bronsted neutralisation


If a person is adviced to intake ORS, it
means he is suffering from
A. Typhoid
B. Jaundice
c. Diarrhoea
D. Measles


What is the process, of converting the air pressure from lungs into audible vibrations, called?
A. Excitation
B. Vibration
c. Phonation
D. None


A sonar echo takes 8.8 s to return from a
shark. How far away is the shark
\( \mathbf{A} \cdot 348 m \)
в. \( 5720 m \)
\( c .6745 m \)
D. 13490 m


If \( \boldsymbol{A}_{1}, \boldsymbol{A}_{3}, \dots \dots A_{2 n-1} \) are \( \boldsymbol{n} \) skew
symmetric matrices of same order, then \( \boldsymbol{B}=\sum_{r=1}^{n}(2 r-1)\left(A_{2 r-1}\right)^{2 r-1} \) will be
A. symmetric
B. skew-symmetricç
c. neither symmetric nor skew-symmetric
D. data not adequate


During the formation of sodium chloride, chlorine accepts one electron from sodium to attain the configuration of which noble gas?
A. Neon
B. Helium
c. Argon
D. xenon


Give a brief account of the mechanism
of water absorption by plants


The internal energy of a gas is given by
\( U=2 P V . \) it expands from \( V_{o} \) to \( 2 V_{o} \)
against a constant pressure \( P_{o} . \) The
heat absorbed by the gas in the process
is
A \( \cdot 2 P_{o} V_{o} \)
в. \( 4 P_{o} V_{o} \)
\( \mathrm{c} \cdot 3 P_{o} V_{\mathrm{o}} \)
D. \( P_{o} V_{o} \)


Only one element of forms
hydride.
A. group 6
в. group 7
c. group 8
D. group


Which of the following light has the combination of all frequencies of visible light?
A. white light
B. black light
C. ultraviolet light
D. infrared light
E. transparency


If a solute under goes dimerization and trimerization, the minimum values
of the vant Hoff factors are:
A. 0.50 and 1.50
B. 1.50 and 1.33
\( c .0 .50 \) and 0.33
D. 0.25 and 0.67


3 mol of a mixture of \( F e S O_{4} \) and
\( \boldsymbol{F} \boldsymbol{e}_{2}\left(\boldsymbol{S} \boldsymbol{O}_{4}\right)_{3} \) required \( \mathbf{1 0 0 m} \boldsymbol{L} \) of \( \boldsymbol{2} \boldsymbol{M} \)
\( K M n O_{4} \) solution in acidic medium.
Hence, mole fraction of \( F e S O_{4} \) in the
mixture is:
A \( \cdot \frac{1}{3} \)
B. \( \frac{2}{3} \)
c. \( \frac{2}{5} \)
D. \( \frac{3}{5} \)


Which of the following would show deflection in the compass needle, the
moment you dip the free ends of the
tester?
A. Tap water, vinegar
B. Tap water, vegetable oil
c. tap water, honey
D. vegetable oil, honey


The angle of minimum deviation for a
\( 75^{\circ} \) prism of dense glass is found to be
\( 45^{\circ} \) when in air and \( 15^{\circ} \) when immersed in certain liquid. The refractive index of the liquid is :
A. \( \sqrt{\frac{2}{3}} \)
B. \( \frac{3}{2} \)
c. \( \sqrt{\frac{3}{2}} \)
D. \( \sqrt{3} \)


Images formed on retina of human eye
are:
A. Real
B. Virtual
c. Human eye adapts to form the image suitable
D. Both real and virtual


Find the range of the following function \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}+\boldsymbol{2}, \boldsymbol{x} \in \boldsymbol{R} \)


According to WHO, the soft water has 0 to \( _{--}--_{-} \) milligram per litre as
\( \boldsymbol{C a C O}_{3} \)
A . 60
B. 120
c. 180
D. 150


A beam of specific kind of particles of
velocity, \( 2.1 \times 10^{7} m / s \) is scattered by
a gold \( (Z=79) \) nuclei. Find out specific charge (charge/mass) of this particle if this distance of closest approach is \( 2.5 \times 10^{-14} m ? \)
\( \mathbf{A} \cdot 4.84 \times 10^{7} C / k g \)
B . \( 4.84 \times 10^{-7} \mathrm{C} / \mathrm{kg} \)
c. \( 2.42 \times 10^{7} \mathrm{C} / \mathrm{kg} \)
\( \mathbf{D} \cdot 3 \times 10^{-12} C / k g \)


Let then \( \boldsymbol{f}(\boldsymbol{x})= \)
\( (x-4)(x-5)(x-6)(x-7) \) then
A \( \cdot f^{\prime}(x)=0 \) has four real roots
\( \mathbf{B} \cdot \) three roots of \( f^{\prime}(x)=0 \) lie in (4,5)\( \cup(5,6) \cup(6,7) \)
C \( \cdot \) the euation \( f^{\prime}(x)= \) has only two roots \( >d \). three roots
of \( f^{\prime}(x)=0(3,4) \cup(4,5) \cup(5,6) \)
D. three roots of \( f^{\prime}(x)=0(3,4) \cup(4,5) \cup(5,6) \)


If the values of inductance and
frequency in an AC circuit are 2 henry and \( \frac{10^{3}}{2 \pi} \) Hz respectively then the value of inductive reactance will be
A \( \cdot \frac{2 \times 10^{3}}{\pi} \Omega \)
B . \( 2 \times 10^{2} \Omega \)
\( c \cdot 10^{3} \Omega \)
D. \( 2 \times 10^{3} \Omega \)


\( \boldsymbol{C}+\boldsymbol{O}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{C} \boldsymbol{O}_{2}(\mathrm{i}) ; \quad \boldsymbol{\Delta} \boldsymbol{H}=-\boldsymbol{3} \boldsymbol{9} \boldsymbol{3} \mathbf{k} \)
\( m o l^{-1} \)
\( \boldsymbol{H}_{2}+\mathbf{1} / \mathbf{2} \boldsymbol{O}_{2} \rightarrow \boldsymbol{H}_{2} \boldsymbol{O},(\mathbf{i} \mathbf{i}) ; \quad \boldsymbol{\Delta} \boldsymbol{H}= \)
\( -287.3 \mathrm{kJ} \) mole\( ^{-1} \)
\( 2 C O_{2}+3 H_{2} O \rightarrow C_{2} H_{5} O H+3 O_{2} \)
(iii); \( \Delta \boldsymbol{H}=\mathbf{1 3 6 6 . 8} \) kJ \( \boldsymbol{m o l}^{-1} \)
Find the standard enthalpy of formation of \( C_{2} H_{5} O H(l) \)
A \( \cdot 281.1 \) kJ \( m o l^{-1} \)
в. \( -281.1 \mathrm{kJ} \) тог
\( \mathrm{c} \cdot_{562.2 \mathrm{kJ}} \mathrm{mol}^{-1} \)
D. \( -562.2 \mathrm{k} \) s \( \mathrm{mol}^{-1} \)


If the angles of a triangle are in the ratio
\( 2: 3: 4, \) find the three angles.
A \( \cdot 80^{\circ}, 120^{\circ}, 160^{\circ} \)
\( ^{\circ} 00^{\circ}, 166^{\circ} 0^{\circ} \)
В. \( 20^{\circ}, 30^{\circ}, 40^{\circ} \)
c. \( 40^{\circ}, 60^{\circ}, 80^{\circ} \)
D. None of these


\( 10.0 \mathrm{cm} \) from the centre of the pipe (half
way between the centre and the walls)


If the entries in a \( 3 \times 3 \) determinant are
either 0 or 1 , then the greatest value of their determinats is:
A
B. 2
\( c \cdot 3 \)
D.


Three flasks of identical volume are filled
separately by
(a) 1 gram of \( H_{2} \)
(b) 1 gram of \( O_{2} \)
(c) 1 gram of \( C O_{2} \)
They are immersed in a tank of water so
that all of them attain same
temperature. The pressures \( P_{1}, P_{2} \) and \( P_{3} \)
have the on.
\( \mathbf{A} \cdot P_{1}>P_{2}>P_{3} \)
\( \mathbf{B} \cdot P_{1}=P_{2}=P_{3} \)
\( \mathbf{c} \cdot P_{1}<P_{2}<P_{3} \)
\( \mathbf{D} \cdot P_{3}>P_{1}>P_{2} \)


If 3 charges are placed at the vertices of
equilateral triangle of charge \( ^{\prime} \boldsymbol{q}^{\prime} \) each
What is the net potential energy, if the side of equilateral triangle is \( 1 c m \)
A. \( \frac{1}{4 \pi \epsilon_{0}} \frac{q^{2}}{l} \)
B. \( \frac{1}{4 \pi \epsilon_{0}} \frac{2 q^{2}}{l} \)
c. \( \frac{1}{4 \pi \epsilon_{0}} \frac{3 q^{2}}{l} \)
D. \( \frac{1}{4 \pi \epsilon_{0}} \frac{4 q^{2}}{l} \)


What is the unit of electric potential difference?
A. volt
B. Coulamb
c. Joul
D. watt


How many terms of the series \( 54,51,48, \dots \dots \) be taken so that their
sum is \( 513 ? \)
A . 18
B . 19
c. 20
D. \( A \) and \( B \)


A pendulum bob is held stationary by a horizontal force H. The three forces
acting on the bob are shown in the
diagram.
The tension in the string of the pendulum is T. The weight of the pendulum bob is W.The string is held at
an angle of \( 30^{\circ} \) to the vertical.
Which statement is correct?
A. \( H=T \cos 30 \)
B. \( T=H \sin 30 \)
c. \( W=T \sin 30 \)
D. \( W=T \cos 30 \)


Which of the following relation is not correctly matched with the formula?
A \( \cdot \ln \) case of association, \( \alpha=\frac{i-1}{\frac{1}{n}-1} \)
B. \( _{\text {In case of dissociation, } \alpha}=\frac{i-1}{n+1} \)
\( i \frac{n_{B}}{n_{A}+n_{B}} \)
Devation in boiling point, \( \Delta T=K_{b} \times \frac{W_{B} \times 1000}{M_{B} \times W_{A}} \)


Which of the following molecule has
\( O-O \) bond?
This question has multiple correct options
\( \mathbf{A} \cdot H_{2} S_{2} O_{8} \)
\( \mathbf{B} \cdot H_{2} S_{2} O_{7} \)
\( \mathbf{c} \cdot H_{2} S O_{5} \)
\( \mathbf{D} \cdot H_{2} S_{2} O_{6} \)


Solve the differential equation \( \left(x^{2}-\right. \) \( \left.\boldsymbol{y}^{2}\right) \boldsymbol{d} \boldsymbol{x}-\boldsymbol{x} \boldsymbol{y} \boldsymbol{d} \boldsymbol{y}=\mathbf{0} \)
A \( \cdot y^{2}\left(x^{2}-2 y^{2}\right)=k \)
B . \( x^{2}\left(x^{2}-2 y^{2}\right)=k \)
C \( \cdot y^{2}\left(2 x^{2}-y^{2}\right)=k \)
D. \( x^{2}\left(2 x^{2}-y^{2}\right)=k \)


Why should the height of lightning conductor is more than that of the walls
of the building?
A . Lightning get attracted towards the tallest target
B. Lightning get repelled
c. Lightning get attracted by the walls of building
D. None of the above


Each wire in Fig. has cross-section area
\( 5 \times 10^{-3} c m^{2} \) and \( Y=2 \times 10^{11} P a . P, Q \)
and R have mass \( 3 k g \) each. Find the
strain developed in A. Assume surface
to be smooth.
A \( \cdot 10^{-5} \)
B. \( 10^{-6} \)
c. \( 10^{-4} \)
D. none


State whether given statement is True or False.
It's possible to have motion in the absence of a force
A. True
B. False


For positive integers \( n_{1}, n_{2} \) the value of
the expression \( (1+i)^{n_{1}}+\left(1+i^{3}\right)^{n_{1}}+ \)
\( \left(1+i^{5}\right)^{n_{2}}+\left(1+i^{7}\right)^{n_{2}}, \) where \( i=\sqrt{-1} \)
is a real number if
A \( \cdot n_{1}=n_{2}+1 \)
В . \( n_{1}=n_{2}-1 \)
c. \( n_{1}=n_{2} \)
D \( . n_{1}>0, n_{2}>0 \)


During respiration there is
A. gain in dry weight
B. loss in dry weight
C. no change in dry weight
D. increase in the overall weight


Select the correct statement:
This question has multiple correct options
A. Chelation effect is maximum for five and six
membered rings
B. Greater the charge on the central metal cation, greater the value of \( \Delta(\mathrm{CFSE}) \)
C. In complex ion \( \left[\mathrm{CoF}_{6}\right]^{3-}, F^{-} \) is a weak field ligand, so that \( \Delta_{\text {oct}}<P \) (Pairing energy) and it is low spin
complex.
D. \( \left[\operatorname{CoCl}_{2}\left(N H_{3}\right)_{2}(e n)\right]^{\oplus} \) complex ion will have four different isomers.


A card is drawn from a well shuffled
pack of 52 cards. Events A and B are defined as follows:
\( A: \) Getting a card of spade
B : Getting an ace, then \( A \) and \( B \) are
A. mutually exclusive and independent events
B. not mutually exclusive but independent events
c. mutually exclusive and not independent events
D. neither mutually exclusive nor independent events


A particle is moving along a circular path with a constant speed of \( 10 m s^{1} \) What is the magnitude of the change is velocity of the particle, when it moves
through an angle of 60 around the centre of the circle?
A .
в. \( 10 \mathrm{m} / \mathrm{s} \)
\( \mathbf{c} \cdot 10 \sqrt{3} m / s \)
D. \( 10 \sqrt{2} \mathrm{m} / \mathrm{s} \)


The area bounded by \( \frac{|\boldsymbol{x}|}{\boldsymbol{a}}+\frac{|\boldsymbol{y}|}{\boldsymbol{b}}=\mathbf{1} \)
where \( a>0 \) and \( b>0 \) is
A \( \cdot \frac{1}{2} a b \)
в. \( a b \)
c. \( 2 a b \)
D. \( 4 a b \)


Consider an "L"-shaped object where the vertical leg extends from the origin to
(0,5) and the horizontal segment
extends from the origin to (3,0)
Assume that the object has uniform
linear density throughout. Where is the location of the center of
\( \operatorname{mass}(\boldsymbol{C o} \boldsymbol{M}) ? \)
A \( \cdot(1.5,1.5) \)
B . (1.5,2.5)
\( \mathbf{c} \cdot(2.5,2.5) \)
D. The center of mass for an "L" is undefined because there is no single point on the object where it can be supported, such that it will not rotate
E. None of these


The process \( S o l i d \rightarrow G a s \) is known as:
A. sublimation
B. condensation
c. evaporation
D. deposition
E. melting


A compound microscope has on objective of focal length \( 0.5 \mathrm{cm} \) and a tube length of \( 15 \mathrm{cm} . \) If it produces and angular magnification of 225 in normal adjustment, find the focal length of the
eyepiece.
A. \( 3.33 \mathrm{cm} \)
B. \( 15 \mathrm{cm} \)
c. \( 2.25 \mathrm{cm} \)
D. 3.5 cm


Rearrange the following steps of constructing a triangle when the base angle say \( \angle B \) and \( \angle C \) and its
perimeter \( \boldsymbol{B C}+\boldsymbol{C A}+\boldsymbol{A B} \) is given:
1. Draw perpendicular bisectors \( \boldsymbol{P Q} \) of
\( A X \) and \( R S \) of \( A Y \)
2. Draw a line segment, say \( X Y \) equal to \( B C+C A+A B \)
3. Let \( P Q \) intersect \( X Y \) at \( B \) and \( R S \)
intersect \( X Y \) at \( C . \) Join \( A-B \) and
\( A-C \)
4. Make \( \angle L X Y \) equal to \( \angle B \) and
\( \angle M Y X \) equal to \( \angle C \)
5. Bisect \( \angle L X Y \) and \( \angle M Y X \). Let these
bisectors intersect at a point \( \boldsymbol{A} \)
\( \mathbf{A} \cdot 1 \rightarrow 3 \rightarrow 5 \rightarrow 4 \rightarrow 2 \)
В. \( 2 \rightarrow 4 \rightarrow 5 \rightarrow 1 \rightarrow 3 \)
c. \( 5 \rightarrow 4 \rightarrow 3 \rightarrow 2 \rightarrow 1 \)
D. \( 2 \rightarrow 3 \rightarrow 5 \rightarrow 4 \rightarrow 1 \)


What is the difference between
Dispersed phase and Dispersion medium?


Fructose on reduction gives a mixture
of two alcohols which are related as:
A. Diastereomers
B. Epimers
c. Both (a) and (b)
D. Anomers


The relation between frequency \( v \)
wavelength \( \lambda \) and velocity of
propagation of wave \( \nu \) is
A \( \cdot v=\frac{\lambda}{\nu} \)
B . \( v=\lambda \nu \)
c. \( v=\frac{\nu}{\lambda} \)
D. None of these


"Sodium metals when dissolved in
ammonia gives a non-conducting solution."
Answer whether the above statement is
true or false.
If true enter 1 , else enter 0


State whether the following statements
are true or false?
(i) the pressure inside our body is equal to the atmospheric pressure
(ii) pressure is inversely proportional to the area.
A. Both are true
B. Both are false
c. (i) True
(ii) False
D. (i) False
(ii) True


A man earns \( x \% \) on the first Rs. 2,000
and \( y \% \) on the rest of his income. If he
earns Rs.700 from Rs. 4,000 and Rs. 900
from Rs. 5,000 of income, find \( x \% \)
A . 20 \%
B . 15 \%
c. 25 \%
D. None of these


The number of vibrations exhibited by a vibrating particle in one second is called its frequency. True or false.
A. True
B. False


In the reaction \( \boldsymbol{F e}(\boldsymbol{O} \boldsymbol{H})_{3}, \boldsymbol{F} \boldsymbol{e}_{\boldsymbol{a} \boldsymbol{q}}^{3+}+ \)
\( 3 O H_{a q}^{-}, \) if the concentration of \( O H^{-} \) is decreased by \( \frac{1}{4} \) times then the equilibrium concentration of \( \boldsymbol{F} \boldsymbol{e}^{\mathbf{3}+} \)
increased by how many times??


The critical temperature is the
temperature:
A. below which the gas undergoes cooling when expanded into vacuum
B. at which a gas liquefies at 1 at \( m \)
C. at which the average kinetic energy of the molecules is \( \operatorname{minimum} \)
D. above which the gas cannot be liquefied how so ever high pressure may be applied


The product of the d.r's of a line perpendicular to the plane passing through the points (4,0,0),(0,2,0) and (1,0,1) is
A. 6
B . 2
\( c .0 \)
\( D \)


A small particle travelling with a
velocity v collides elastically with a
smooth spherical body of equal mass
and of radius \( r \) initially kept at rest. The
centre of this spherical body is located
a distance
8


The velocity vector of a particle moving in the xy plane is given by \( v=t i+x j \). If initially, the particle was at origin then the equation of trajectory of the projectile is:
A \( \cdot 4 x^{2}-9 y=0 \)
B. \( 9 x^{2}-2 y^{3}=0 \)
c. \( 16 x^{3}-9 y^{2}=0 \)
D. \( 9 x^{3}-2 y^{2}=0 \)


State your observation when nitric acid is added to saw dust colour appears is :
A. black
B. grey
c. grey gold.
D. brown


Oxygen haemoglobin dissociation curve will shift to right on decrease of
A. Acidity
B. Carbon dioxide concentration
c. Both A and B
D. ph


Give reason for the higher boiling point
of ethanol in comparison to
methoxymethane.


If \( a+b+c+d+e+f=12 \) then the
maximum value of \( a b+b c+c d+d e+ \)
\( e f+f a \) is \( (a, b, c, d, e, f \) are non
negative real numbers)
A . 36
B . 24
c. 30
D. none of these


State the properties and uses of a
Junction transistor


Two planes intersect each other to form
\( \mathbf{a}: \)
A. plane
B. point
c. straight line
D. angle


In plant succession, the net productivity of climax community
A. Continuous to increase
B. Becomes stable
c. Becomes halvedd
D. Reduced to \( 10 \% \)
E. Becomes zero


What is the average adult female speaking voice range?
A . \( 125 \mathrm{Hz} \)
в. 210нz
c. 300 н \( z \)
D. 400нz


(a) A rod of length I is moved horizontally with a uniform velocity 'v' in a direction perpendicular to its length
through a region in which a uniform magnetic field is acting vertically downward. Derive the expression for the
emf induced across the ends of the rod.
(b) How does one understand this
motional emf by invoking the Lorentz force acting on the free charge carriers of the conductor? Explain.


The life span of red blood cells is about
A. 100 days
B. 80 years
c. 120 days
D. 10 days


For which cell e.m.f. is independent of
the concentrations of electrolytes used?
\( \mathbf{A} \cdot F e|F e O(s)| K O H(a q)|N i O(s)| N i_{2} O_{3}(s) \mid N i \)
\( \mathbf{B} \cdot P t\left(H_{2}\right)|H C l| P t\left(C l_{2}\right) \)
\( \mathbf{c} \cdot Z n\left|Z n\left(N O_{3}\right)_{2}\right|\left|C u S O_{4}\right| C u \)
D. \( H g, H g C l_{2}\left|K C l \| A g N O_{3}\right| A g \)


Assertion
\( N_{2} O \) supports combustion more
vigorously than air
Reason
Both nitrogen and oxygen contribute for combustion
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


For a given reaction \( \boldsymbol{A} \rightarrow \) Products, rate
is \( 1 \times 10^{-4} M s^{-1} \) when \( [A]=0.01 \mathrm{M} \)
and rate is \( 1.41 \times 10^{-4} M s^{-1} \) when
\( [\boldsymbol{A}]=\mathbf{0 . 0 2} \) M. Hence, rate law is:
A \( \cdot-\frac{d[A]}{d t}=k[A]^{2} \)
B. \( -\frac{d[A]}{d t}=k[A] \)
\( ^{\mathrm{c}}-\frac{d[A]}{d t}=\frac{k}{4}[A] \)
D. \( -\frac{d[A]}{d t}=k[A]^{1 / 2} \)


English Braille has how many levels of encoding?
\( \mathbf{A} \cdot \mathbf{1} \)
B. 5
\( c \cdot 3 \)
\( D \)


A force \( \overrightarrow{\boldsymbol{F}}=(2 \hat{\boldsymbol{i}}+\boldsymbol{3} \hat{\boldsymbol{j}}-\boldsymbol{5} \hat{\boldsymbol{k}}) \boldsymbol{N} \) acts at a
point \( \vec{r}_{1}=(2 \hat{i}+4 \hat{j}+7 \hat{k}) m . \) The
torque of the force about the point \( \vec{r}_{2}= \) \( (\hat{\mathbf{i}}+\mathbf{2} \hat{\mathbf{j}}+\mathbf{3} \hat{\boldsymbol{k}}) \boldsymbol{m} \) is :
A \( .17 \hat{j}+5 \hat{k}-3 \hat{i}) N m \)
B . \( 2 \hat{i}+4 \hat{j}-6 \hat{k}) N m \)
c. \( 12 \hat{i}-5 \hat{k}+7 \hat{k}) N m \)
D. \( 13 \hat{j}-22 \hat{i}-\hat{k}) N m \)


Write the formula of :
Tetraamineaquachloridocobalt (III)
chloride.


A \( 5 \% \) solution (w/v) of cane-sugar (Mol. weight \( =342 \) ) is isotonic with \( 0.877 \% \) \( (w / v) \) of urea solution. Find molecular
weight of urea (round off to the nearest integer).


Two masses \( M_{1} \) and \( M_{2} \) are attached
to the end of a light string which passes
over a massless pulley attached to the
top of a double inclined smooth plane of
angles of inclination \( \boldsymbol{\alpha} \) and \( \boldsymbol{\beta} \). If \( \boldsymbol{M}_{\mathbf{2}}> \)
\( M_{1} \) and \( \beta>\alpha \) then the acceleration of
block \( M_{2} \) down the inclined will be:
A \( \cdot \frac{M_{2} g(\sin \beta)}{M_{1}+M_{2}} \)
В. \( \frac{M_{1} g(\sin \alpha)}{M_{1}+M_{2}} \)
\( c \)
D. Zero


toppr 5
Q type your question
(b) \( \frac{4}{20} \)
\( (c) \frac{1}{2} \)
(d) \( \frac{2}{3} \)
\( (e) \frac{3}{5} \)
(f) \( 2 \frac{1}{7} \)
\( (g) \frac{1}{5} \)
(h) \( \frac{4}{15} \)
(i) \( \frac{1}{6} \)
(j) \( 4 \frac{3}{8} \)
(k) \( \frac{8}{9} \)
(।) \( 1 \frac{1}{9} \)


Which of the following Earth's plates is responsible for causing an earthquake?
A. The crust of the earth
B. The mantle of the earth
c. The inner core of the earth
D. The outer core of the earth


The equation of motion of particle is
given by dp \( / \mathrm{dt}+\mathrm{m} \omega^{2} \mathrm{y}=0 \) where p is momentum and y is its position. Then the particle :
A. moves along a straight line
B. moves along a parabola
c. executes simple harmonic motion
D. falls freely under gravity


If \( f(x)=a x^{2}+b x+c, \) show that \( \lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}=2 a x+b \)


Some meta - directing substituent in aromatic substitution is given.Which one is most deactivating?
A \( . C N \)
в. \( S O_{3} \) Н
c. со ОН
D. \( N O_{2} \)


Force generated by transpiration can create pressure to lift water upto
A. 130 feet
B. 130 metres
c. 230 feet
D. 230 metres


Find the distance of the point (-1,1) from the line \( 12(x+6)=5(y-2) \)


Prove that \( 4\left[\sin ^{4} 30^{\circ}+\cos ^{4} 60^{\circ}\right]- \)
\( 3\left[\cos ^{2} 45^{\circ}-\sin ^{2} 90^{\circ}\right]=2 \)


When pure semimconductor is doped
then its electrical conductivity
A. increases
B. decreases
c. remains constant
D. initially increases and then decreases


Cis-dicholoroethylene can be converted to trans-dicholorethylene by irradiations. During the interconversion.
A. Both the \( \pi \) and \( \sigma \) bonds are broken and reformed
B. Only the \( \pi \) bond is broken and reformed
c. The \( C-C l \) and \( C-H \) bonds are broken, \( H \) and \( C l \)
atoms interchanges their positions and new bonds are formed
D. Both the \( \pi \) and \( \sigma \) bonds rotate along with the groups


Carbon reduction process is not commercially applicable for which of the following set of oxides to extract the respective metal?
(I) \( Z n O \)
\( (\|) \boldsymbol{F} \boldsymbol{e}_{2} \boldsymbol{O}_{3} \)
\( (\| I) A l_{2} O_{3}(I V) \)
\( \boldsymbol{S} \boldsymbol{n} \boldsymbol{O}_{2}(\vee) \boldsymbol{M} \boldsymbol{g} \boldsymbol{O} \)
A. \( Z n O, F e_{2} O_{3}, S n O_{2} \)
в. \( Z n O, S n O_{2}, M g O \)
\( \mathrm{c} \cdot \mathrm{Mg} \mathrm{O}, \mathrm{Al}_{2} \mathrm{O}_{3} \)
D. \( M g O, S n O_{2}, A l_{2} O_{3} \)


Find the order and degree of the given
differential equation: \( y^{\prime}=\sin y . \) The
order of this equation is the same as its degree. If true enter 1 else enter 0


Read the following bar graph (Fig. 23.12) and answer the following questions:
State each of the following whether true
or false.

The number of government companies in 1957 is that of 1982 is 1: 9
A. True
3. False


toppr
Q Type your question
conductivity of theses reactions is
given in List II. Match List I with List II
and select the correct using the code
given below the lists:
List-A
\( (P) \)
(1) Conductivity decreases and
\[
\left(\begin{array}{cc}
\left.C_{2} H_{5}\right)_{3} N+ & \text { then increases } \\
X &
\end{array}\right.
\]
\[
C H_{2} C O O H
\]
(Q)
(2) Conductivity decreases and
\[
\begin{array}{c}
K I(0.1 M)+ \\
X
\end{array}
\]
\[
\begin{array}{c}
A g N O_{3}(0.01 M) \\
Y
\end{array}
\]
(R)
(3) Conductivity increases and \( C H_{2} C O O+\quad \) then does not change much \( K_{Y}^{O H} \)
(4) Conductivity does not
(S) \( N a O H+\quad \) change much and then \[ X \] \( H I \)
\( Y \)\( \quad \) increases
A. 3,4,2,1
B. 4,3,2,1
C. 2,3,4,1
D. 1,4,3,2


In a swimming pool measuring \( 90 \mathrm{m} \) by \( 40 \mathrm{m}, 150 \) men take a dip. If the average
displacement of water by a man is \( 8 m^{3} \) what will be the rise in water level?
A. \( 33.33 \mathrm{cm} \)
B. \( 30 \mathrm{cm} \)
c. \( 20 \mathrm{cm} \)
D. \( 25 \mathrm{cm} \)


Which compound is obtain on
hydrolysis of \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{\boldsymbol{6}} \) ?
A. \( X e O_{3} \)
в. \( X e O_{2} F_{2} \)
c. \( X e O F_{3} \)
D. \( X e O_{3} F \)


Which congruence criterion do you use
in the following?
Given: \( \angle \mathrm{MLN}=\angle \mathrm{FGH}, \angle \mathrm{NML}=\angle \mathrm{HFG}, \mathrm{ML} \)
= FG. So \( \Delta \) LMN \( \equiv \Delta G F H \)


Motion of a bus moving on a crowded road is an example of
A. uniform motion
B. non-uniform motion
c. either uniform or non-uniform motion
D. neither uniform nor non-uniform motion


Imagine a planet with an atmosphere
that contains \( O_{2} \) and \( S O_{2} \) but no \( C O_{2} \)
The chemical composition of the minerals you would expect to find the
alkaline earth metals on such a planet
is/ are:
This question has multiple correct options
A \( . M S O_{4} \)
в. \( M_{2} S O_{3} \)
c. \( M S O_{3} \)
D. \( M_{2} S O_{4} \)


The value of \( x \) for which
\( \sin \left(\cot ^{-1}(1+x)\right)=\cos \left(\tan ^{-1} x\right) \) is
\( A \cdot \frac{1}{2} \)
B.
\( c \)
D. \( -\frac{1}{2} \)


Absolute zero (OK) is that temperature
at which
A. Matter ceases to exit
B. Ice melts and water freezes
c. volume and pressure of a gas become zero
D. None of the above


What are nucleic acids?


Enough \( N a_{2} S O_{4} \) is dissolved in water
at \( 40^{\circ} C \) to saturated the solution. When
this occurs heat is given off. All of the following statements are true EXCEPT:
A. The enthalpy change of this process is negative
B. The boiling point of the solution is higher than that of pure water
C. The freezing point of the solution is lower than that of pure water
D. If the temperature of the water is lowered, then the solubility of \( N a_{2} S O_{4} \) decreases


Two masses \( m_{1} \) and \( m_{2} \) are connected
by a spring of spring constant k and are placed on a smooth horizontal surface. Initially the spring is stretched through a distance 'd' when the system is
released from rest. Find the distance
moved by the two masses when spring is compressed by a distance 'd'.


In Figure, identify the following vectors.
(i) Coinitial
(ii) Equa
(iii) Collinear but not equal


Find the maximum possible number of
hydrogen bonds in which \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \)
molecule can participate.


Check the validity of the following
statement:
\( \boldsymbol{p}: \boldsymbol{6} \boldsymbol{0} \) is a multiple of \( \boldsymbol{3} \) and \( \boldsymbol{5} \)
A. True
B. False


When six fair coins are tossed
simultaneously, in how many of the outcomes will at most three of the coins
turn up as heads?
A . 25
B. 41
\( c \cdot 22 \)
D. 42


If
[.] denotes the greatest integer function, then find the value of \( \lim _{n \rightarrow \infty} \frac{[x]+[2 x]+\ldots \ldots \ldots . .+[n x]}{n^{2}} \)


If \( \boldsymbol{y}=\tan ^{2}\left(\log \boldsymbol{x}^{3}\right), \) find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \)


A \( 1.5 \mu F \) capacitor is charged of \( 60 V \) The charging battery is then disconnected and a \( 15 \mathrm{mH} \) coil is
connected in series with the capacitor so that LC oscillations occurs. Assuming that the circuit contains no
resistance. The maximum current in
this coil shall be close to
A . 1.4 A
B. \( 1.2 A \)
\( c .0 .8 A \)
D. 0.6 A


The number of values of \( k \) for which the
system of equations \( (k+2) x+10 y=k \)
\( \boldsymbol{k} \boldsymbol{x}+(\boldsymbol{k}+\boldsymbol{3}) \boldsymbol{y}=\boldsymbol{k}-\mathbf{1} \)
has infinitely many solutions, is?
\( \mathbf{A} \cdot \mathbf{0} \)
B. 1
c. 2
D. infinite


When a hydrogen atom is in its first
excited level, its radius is
A. four times its ground state radius
B. twice times its ground state radius
c. same times its ground state radius
D. half times its ground state radius


The coefficient of \( x^{18} \) in the expansion of
\( (1+x)(1-x)^{10}\left\{\left(1+x+x^{2}\right)^{9}\right\} \) is?
\( \mathbf{A} \cdot 84 \)
в. 126
\( c \cdot-42 \)
D. 42


Which of the following reduction
reactions are actually employed in
commerical extraction of metals?
This question has multiple correct options
\( \mathbf{A} \cdot F e_{2} O_{3}+2 A l \rightarrow A l_{2} O_{3}+2 F e \)
B. \( C r_{2} O_{3}+2 A l \rightarrow A l_{2} O_{3}+2 C r \)
\( \mathbf{c} \cdot 2 N a\left[A u(C N)_{2}\right]+Z n \rightarrow N a_{2}\left[Z n(C N)_{4}\right]+2 A u \)
\( \mathbf{D} \cdot C u_{2} S+P b \rightarrow C u+P b S \downarrow \)


A sink, that is the system where heat is rejected, is essential for the conversion of heat into work. From which law does
the above inference follow?
A. zeroth
B. First
c. second
D. Third


If \( 2 A-\left[\begin{array}{ll}1 & 2 \\ 7 & 4\end{array}\right]=\left[\begin{array}{cc}3 & 0 \\ 0 & -2\end{array}\right], \) then \( A \) is
equal to
\( \mathbf{A} \cdot\left[\begin{array}{cc}2 & 1 \\ 7 / 2 & 1\end{array}\right] \)
В. \( \left[\begin{array}{cc}4 & 4 \\ 7 / 2 & 1\end{array}\right] \)
c. \( \left[\begin{array}{ll}3 & -1 \\ 7 & 2\end{array}\right] \)
D. None of these


Show that \( (\sqrt{3}+\sqrt{5})^{2} \) is an irrational.


More than \( 70 \% \) of world's freshwater is
contained in
A. Polarice
B. Glaciers and mountains
C. Antartica
D. Greenland


Living cells of xylem are
A. Xylem parenchyma
B. Xylem fibres
c. Vessels
D. Tracheids


Who discovered Java ape man?
A . Leakey
B. Mayr
C. Davidson Black
D. Dubois


What is acid rain?


A radioactive element X disintegrates successively as under:
\( \boldsymbol{X} \stackrel{\boldsymbol{\alpha}}{\rightarrow} \boldsymbol{X}_{1} \stackrel{\boldsymbol{\beta}}{\rightarrow} \boldsymbol{X}_{2} \stackrel{\boldsymbol{\alpha}}{\rightarrow} \boldsymbol{X}_{3} \stackrel{\gamma}{\rightarrow} \boldsymbol{X}_{4} \)
If the atomic number and atomic mass.
Number of \( X \) are 72 and \( 180 . \) What are
the corresponding values for \( \boldsymbol{X}_{\mathbf{4}} \)
A .69,176
B. 69,172
c. 71,176
D. 71,172


The numerator of the rational number is
less than its denominator by 3 . If the numerator becomes three times and
the denominator is increased by \( 20, \) the new number becomes \( \frac{1}{8} . \) Find the original number.


The velocity-time graph of a linear
motion is shown in Fig. The distance
from the origin 0 after 8 seconds is :
\( \mathbf{A} \cdot 18 m \)
B. \( 16 m \)
\( c .8 m \)
D. \( 6 m \)


Given a uniform electric field \( \overrightarrow{\boldsymbol{E}}=\mathbf{5} \times \)
\( \mathbf{1 0}^{3} \hat{\mathbf{i}} \mathbf{N} / \mathbf{C}, \) find the flux of this field
through a square of \( 10 \mathrm{cm} \) on a side whose plane is parallel to the \( \boldsymbol{Y}-\boldsymbol{Z} \)
plane. What would be the flux through the same square if the plane makes a
\( 30^{\circ} \) angle with the \( \$ \$ X \) -axis?


The probability distribution function of a random variable \( \boldsymbol{X} \) is given by
\( \boldsymbol{x}_{i}: \quad 0 \quad 1 \quad 2 \)
\[
\begin{array}{lll}
3 c & 4 c & c-1
\end{array}
\]
where \( c>0 . \) Find \( c \)


When a test charge is brought in from infinity along the perpendicular bisector of an electric dipole, the work done is
A. positive
B. zero
c. Negative
D. None of theses


Which one of the following noble gas has an unusual property of diffusing through the materials such as rubber,
glass or plastic?
A. не
B. Kr
c. Ne
D. Ar


Green house effect is due to
A. X-rays
B. UV rays
c. Green rays
D. Infra-red rays


The tenth term in the expansion of
\( \left(2 x^{2}+\frac{1}{x}\right)^{12} \)
A \( \cdot \frac{1760}{x^{3}} \)
в. \( -\frac{1760}{x^{3}} \)
c. \( \frac{1760}{x^{2}} \)
D. none of the above


\( \boldsymbol{a} \neq \boldsymbol{p}, \boldsymbol{b} \neq \boldsymbol{q}, \boldsymbol{c} \neq \boldsymbol{r} \) and \( \left|\begin{array}{lll}\boldsymbol{p} & \boldsymbol{b} & \boldsymbol{c} \\ \boldsymbol{a} & \boldsymbol{q} & \boldsymbol{c} \\ \boldsymbol{a} & \boldsymbol{b} & \boldsymbol{r}\end{array}\right|=0 \)
then the value of \( \frac{\boldsymbol{p}}{\boldsymbol{p}-\boldsymbol{a}}+\frac{\boldsymbol{q}}{\boldsymbol{q}-\boldsymbol{b}}+ \)
\( \frac{r}{r-c} \) is equal to
\( A \)
B. 2
\( c \cdot 3 \)
D.


Wavelength is expressed in:
A . \( N \)
в. \( e \) го \( g \)
c. dyne
D. \( A^{0} \)


The presence or absence of hymen is not reliable indicator of virginity or sexual experience.
A. True
B. False


In the given figure, two identical regular
hexagons are placed side by side as
shown.
Find the value z.
\( \mathbf{A} \cdot 60^{\circ} \)
\( \mathbf{B} \cdot 90^{\circ} \)
\( \mathbf{C} \cdot 120^{\circ} \)
D. \( 160^{\circ} \)


Construct a \( \triangle \boldsymbol{A B C}, \boldsymbol{A B}= \)
\( \mathbf{6 c m}, \boldsymbol{B C}=\mathbf{7} \mathbf{c m} \) and \( \angle \boldsymbol{A}=\mathbf{6 0}^{\circ} \)


Choose the correct answer from the
alternatives given By anticlinal divisions, an organ increases in:
A. circumference
B. volume
c. area
D. length


Fibres can be classified as natura
fibres and synthetic fibres.
A. True
B. False


Three coins are tossed. Find the
probability of getting atleast two head.


Which among the following group 15 element forms most stable pentavalent compound?
A. Phosphorus
B. Antimony
c. Bismuth
D. Arsenic


If 10 g of ice at \( 0^{\circ} \mathrm{C} \) mixes with 10 g of water at \( 10^{\circ} \mathrm{C} \), then the final
temperature \( t \) is given by
A \( \cdot(10 \times 80)+10(t-0)=10(10-t) \)
в. \( 10 \times 80=10(10-t)+10(t-0) \)
\( \mathbf{c} \cdot t=5^{\circ} C \)
D. \( t=0^{\circ} \mathrm{C} \)


Which of the following is an antihistamine?
A. Brompheniramine
B. Rantidine
c. cimetidine
D. None of the above


Male heterogametic, XX-XO type of sex determination is found in
A. Butterflies
B. Moth
c. Grasshoppers
D. Drosophila


Calculate the force of gravitation between the earth and the sun, given that the mass of the earth \( =6 \times 10^{24} k g \)
and of the \( \operatorname{Sun}=2 \times 10^{30} k g . \) The
average distance between the two is
\( 1.5 \times 10^{11} m \)


What is ecological succession?


Factorise \( : 8 x^{3}-27 y^{3}-2 x+3 y \)
A \( \cdot(2 x+3 y)\left(4 x^{2}-x y+9 y^{2}+1\right) \)
В \( \cdot(2 x+y)\left(4 x^{2}-6 x y-9 y^{2}\right) \)
C \( \cdot(x-3 y)\left(4 x^{2}-3 x y+9 y^{2}\right) \)
D \( \cdot(2 x-3 y)\left(4 x^{2}+6 x y+9 y^{2}-1\right) \)


\( \mathbf{f} \boldsymbol{A}=\left[\begin{array}{lll}\boldsymbol{i} & \boldsymbol{0} & \boldsymbol{0} \\ \boldsymbol{0} & \boldsymbol{i} & \boldsymbol{0} \\ \boldsymbol{0} & \boldsymbol{0} & \boldsymbol{i}\end{array}\right] \) then \( \boldsymbol{n} \in \boldsymbol{N}, \boldsymbol{A}^{4 n+1}= \)


For \( x, t \in R \) let
\( \boldsymbol{p}_{1}(\boldsymbol{x})=(\sin t) \boldsymbol{x}^{2}-(2 \cos \boldsymbol{t}) \boldsymbol{x}+\sin \boldsymbol{t} \)
be a family of quadratic polynomials in \( x \) with variable co efficients. Let \( A(t)= \) \( \int_{0}^{1} p_{t}(x) d x . \) Which of the following
statements are true?
(I) \( A(t)<0 \) for all \( t \)
(II) \( A(t) \) has infinitely many critica points.
(III) \( A(t)=0 \) for infinitely many t.
(IV) \( A^{\prime}(t)<0 \) for all \( t \)
A. (I) and (II) only
B. (II) and (III) only
C. (III) and (IV) only
\( D \cdot(I V) \) and (1) only


A man standing on the road has to ho!d his umbrella at \( 30^{\circ} \) with the vertical to
keep the rain away. He throws the umbrella and starts running at 10 k \( m / h r . \) He find that rain drops are
hitting his head vertically, then the speed of the rain drops with respect to moving man.
A. \( 20 k m / h r \)
в. \( 10 \sqrt{3} k m / h r \)
c. \( \frac{10}{\sqrt{3}} k m / h r \)
D. \( 10 k m / h r \)


Identify the products.
\[
\mathrm{NaBH}_{4} \quad \mathrm{Me}-\mathrm{CONH}_{2} \quad \mathrm{LiAlH}_{4}
\]


Substances that break just after elastic
limit is reached are known as
A. brittle substances
B. breakable substances
c. ductile substances
D. elastic substances


The domain of \( f(x)=\log (\sin x) \) is
A \( \cdot(-\pi, \pi) \)
В. \( (2 n \pi,(2 n+1) \pi) \) and \( n \in Z \)
с. \( [0,2 \pi] \)
]
D. \( \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \)


The reference electrode is made from
which of the following?
A. \( Z n C l_{2} \)
в. \( \mathrm{CuSO}_{4} \)
c. \( H g_{2} C l_{2} \)
D. \( H g C l_{2} \)


Write Chemical equation when \( X e F_{4} \) disproportionates to \( \mathrm{Xe}(0) \) and \( \boldsymbol{X} e(\boldsymbol{V} \boldsymbol{I}) \)
compounds through \( X e(I I) \) and \( \boldsymbol{X} \boldsymbol{e}(\boldsymbol{V} \boldsymbol{I} \boldsymbol{I} \boldsymbol{I}) \)


Describe briefly the underlying principle of a transistor amplifier working as an oscillator. Hence, use the necessary circuit diagram to explain how self sustained oscillations are achieved in
the oscillator.


If \( 1 \mathrm{kg} \) wt \( =10 \mathrm{N}, \) the value of gravitational intensity will be
A \( \cdot 10 m / s^{2} \)
в. \( \frac{1}{10} m / s^{2} \)
c. \( 1 m / s^{2} \)
D. \( \frac{1}{100} m / s^{2} \)


Given that \( A \subset B, \) then identify the
correct statement
\( \mathbf{A} \cdot P(A / B)=P(A) \)
B \( . P(A / B) \leq P(A) \)
\( \mathbf{c} \cdot P(A / B) \geq P(A) \)
D \( \cdot P(A / B)=P(A)-P(B) \)


The decision of cell division occurs at
A. starting of \( G_{1} \)
B. End of G \( _{1} \)
c. Initial stage of prophase
D. End of telophase


What is common between given cations
and anions :
\( \boldsymbol{O}^{2-}, \boldsymbol{F}^{-}, \boldsymbol{N} \boldsymbol{a}^{+}, \boldsymbol{M} \boldsymbol{g}^{2+}, \boldsymbol{A} \boldsymbol{l}^{3+} ? \)
A. All have same ionic radii
B. All are isoelectronic species having 10 electrons
c. All of them belong to the third period
D. The nature of oxides of all the ions is basic


The given structure show bondline
formula of 2, 3-Dimethylbutanal
A. True
B. False


Let \( \boldsymbol{f}(\boldsymbol{x}) \) be a continuous function
whose range is \( [2,6,5] . \) If \( h(x)= \) \( \left[\frac{\cos x+f(x)}{\lambda}\right], \lambda \in N \) be continuous
where [.] denotes the greatest integer
function, then the least value of \( \lambda \) is
\( A \cdot 6 \)
B. 7
c. 8
D. None of these


Assertion
In any transition series, the magnetic
moment of \( M^{2+} \) ion first increases and
then decreases.
Reason
In any transition series, the number of unpaired electrons first increases, afterwards decrease
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The convex lens used in a simple microscope produces a magnification of
5. The image is formed at the least
distance of distinct vision. What is the
focal length of the lens?


A thin circular loop of radius R rotates about its vertical diameter with an angular frequency \( \omega . \) Show that a small bead on the wire loop remains at its lower most point for \( \omega \leq \sqrt{g / R} \). What
is the angle made by the radius vector joining the centre to the bead with the vertical downward direction for \( \omega= \)
\( \sqrt{2 g / R} ? \) Neglect friction.


At what distance should an object be
placed in front of a convex lens of focal length \( 0.4 m \) so that the image is thrice the size ofthe object?


The focus of a conic is the origin and its
corresponding directrix is \( 7 x-y- \)
\( \mathbf{1 0}=\mathbf{0 .} \) If length of its latus rectum is 2
then its eccentricity is:
A \( \cdot \sqrt{2} \)
B. 1
c. \( \frac{1}{\sqrt{2}} \)
D. \( \frac{1}{2} \)


An ideal gas with adiabatic exponent \( =1.5 \) ) undergoes a process in which work done by the gas is same as increase in internal energy of the gas. The molar heat capacity of gas for the process is:
\( A \cdot C=4 R \)
B. \( c=0 \)
\( c \cdot c=2 R \)
D. \( c=R \)


A tunnel is dug along a chord of the earth at a perpendicular distance R/2
from the earth's centre. The wall of the
tunnel may be assumed to be frictionless. Find the force exerted by the wall on a particle of mass \( \mathrm{m} \) when it is at a distance \( x \) from the centre of the
tunnel.


The precipitate of \( M_{2} S_{3} \) obtained on
mixing equal volumes of solutions \( \boldsymbol{S}_{1} \)
having \( \left[M^{3+}\right]=4 \times 10^{-5} M \) and \( S_{2} \)
having \( \left[S^{2-}\right]=2 \times 10^{-3} M . \) Calculate
its solubility product.


A child is standing in tront ot a straight plane mirror. His father is standing
behind him, as shown in the fig. The
height of the father is double the height
of the child. What is the minimum
length of the mirror required so that the
child can completely see his own image
and his fathers image in the mirror?
Given that the height of father is \( 2 H \)
\( \mathbf{A} \cdot H / 2 \)
B. \( 5 H / 6 \)
c. \( 3 H / 2 \)
D. None of these


If \( X=\{2,3,5,7,11\} \) and \( Y=\{4,6,8,9,10\} \) then find the number of one-one functions
from \( X \) to \( Y \)
A . 720
B. 120
\( c \cdot 24 \)
\( D \cdot 12 \)


Differentiate \( \sin ^{2} 3 x \cdot \tan ^{3} 2 x \)


If \( I_{0} \) is the intensity of the principal maximum in the single slit diffraction pattern, then what will be its intensity
when the slit width is doubled
A. \( I_{0} \)
B. \( \frac{I_{0}}{2} \)
\( c \cdot 2 I_{0} \)
D. \( 4 I_{0} \)


Evaluate \( \lim _{x \rightarrow 0} \frac{\sin ^{-1}[\cos x]}{1+[\cos x]} \)
denotes the greatest integer function)
A . 0
B. -
\( c . \)
D. \( \infty \)


The ultra-high frequency band of radio waves in electromagnetic wave is used
as in:
A. television waves
B. cellular phone communication
c. commercial FM radio
D. both (a) and (c)


The frequency of light of wave length
\( 5000 A^{\circ} \) is :
A \( \cdot 1.5 \times 10^{3} \mathrm{Hz} \)
B \( \cdot 6 \times 10^{8} \mathrm{Hz} \)
c. \( 6 \times 10^{14} \mathrm{Hz} \)
D. \( 7.5 \times 10^{15} \mathrm{Hz} \)


Find \( \boldsymbol{f}^{\prime}(\boldsymbol{3}) \) if \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{3}+\mathbf{5} \boldsymbol{x}^{2}-\boldsymbol{3} \boldsymbol{x}+\mathbf{5} \)
A . 28
B. 54
\( c .32 \)
D. None


Assertion
Pulling a lawn roller is easier than
pushing it.
Reason
Pushing increases the apparent weight
and hence the force of friction.
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


Ketone bodies are byproducts in the metabolism of
A. carbohydrate
B. Protein
\( c . \) Fat
D. All the above


The wavelength associated with 1 Me \( V \)
proton is
A. \( 28.6 p m \)
B. 2.86 \( p m \)
c. \( 2.86 \mathrm{fm} \)
D. 28.6 \( f m \)


With due regard to significant figures, add the following:
a. 953 and 0.324
b. 953 and 0.625
c. 953.0 and 0.324
d. 953.0 and 0.374
A . a. \( 953 ; \) b. 954 c. 953.3 d. 953.4
B. a. \( 953 ; \) b. 955 c. 953.3 d. \( 953 . \)
c. a. \( 952 ; \) b. 954 с. 953.3 d. 953.4
D. a. \( 953 ; \) b. 954 c. 953.3 d. 952.4


If \( a \neq 0 \) and \( a-\frac{1}{a}=4, \) find:
\( a^{3}-\frac{1}{a^{3}} \)
A . 76
B. 71
c. 45
D. 16


Muscles of heart are
A. Striated and voluntary
B. Nonstriated and voluntary
C. Striated unbranched and involuntary
D. Nonstriated and involuntary
E. Striated, branched and involuntary


If \( x \) and \( y \) are positive integers, the
value of \( p \) in the equation \( p x=y \) is
always
A. positive
B. negative
c. one
D. zero


For a weak electrolyte molar conductance in dilute solution
increases sharply as its concentration in solution is decreased. Give reason.


The magnetic materials having negative magnetic susceptibility are
A. non-magnetic
B. para magnetic
c. dia magneticc
D. ferro magnetic


A point on the line \( \frac{\boldsymbol{x}-\mathbf{1}}{\mathbf{1}}=\frac{\boldsymbol{y}-\mathbf{2}}{\mathbf{2}}= \)
\( \frac{z+1}{3} \) at a distance \( \sqrt{6} \) from the origin
is
This question has multiple correct options
\( \mathbf{A} \cdot\left(\frac{-5}{7}, \frac{-10}{7}, \frac{13}{7}\right) \)
в. (1,2,-1)
\( ^{\mathbf{C}} \cdot\left(\frac{5}{7}, \frac{10}{7}, \frac{-13}{7}\right) \)
D. (-1,-2,1)


The nuclear reactor at Kaiga is a :
A. research reactor
B. fusion reactor
c. breedor reactor
D. power reactor


What is the name given to energy which must be provided in order for a chemical change to occur?
A. Gibbs free energy
B. Activation energy
c. Potential energy
D. Bond energy
E. Kinetic energy


The circumference of a circle is \( 22 \mathrm{cm} \)
Then the area is


A compound \( X \) on heating gives a colorless gas. The residue is dissolved
in water to obtain \( Y . \) Excess \( C O_{2} \) is
bubbled through aqueous solution of \( Y \) and \( Z \) is formed. \( Z \) on gentle heating
gives back \( X . \) The \( X \) is:
A \( \cdot C a C O_{3} \)
в. \( C a\left(H C O_{3}\right)_{2} \)
c. \( N a_{2} C O_{3} \)
D. \( N a H C O_{3} \)


Find the ratio in which the line \( 2 x+ \)
\( 3 y-5=0 \) divides the line segment
joining the points (8,9) and \( (2,1) . \) Also, find the coordinates of the point of
division.


The first element of group number 15 is:
A. carbon
B. nitrogen
c. oxygen
D. beryllium


The resistance of an iron wire is \( 10 \Omega \)
and its temperature coefficient of
resistance is \( 5 \times 10^{-3} /^{o} C . \) A current of
\( 30 \mathrm{mA} \) is flowing in it at \( 20^{\circ} \mathrm{C} \). Keeping potential difference across its ends constant, if its temperature is
increased to \( 120^{\circ} \mathrm{C} \) then the current
flowing in the wire will be (in \( \mathrm{mA} \) )
A . 20
B . 35
c. 10
D. 40


Which of the following conclusions can be drawn from the Rutherford alpha
scattering model?
I. The atom is mostly empty space.
II. Electrons orbit the nucleus of the
atom.
III. The atom has a dense, positively charged nucleus.
A. I only
B. Il only
c. I and II only
D. II and III only
E. I, II, and III


Expand the following using identities \( (x+7)(y+5) \)


What is the black circular aperture in
our eyes and why does it appear black?
A. The aperture is known as iris and it appears black as no light is reflected from it.
B. The aperture is known as pupil and it appears black as all light is reflected from it.
C. The aperture is known as iris and it appears black as all light is reflected from it.
D. The aperture is known as pupil and it appears black as no light is reflected from it.


\( \operatorname{Let} f(x)=\cos 2 x \cdot \cot \left(\frac{\pi}{4}-x\right) \) If \( f \) is
continuous at \( x=\frac{\pi}{4} \) then the value of \( f\left(\frac{\pi}{4}\right) \) is equal to
A . 2
B. -
c. \( \frac{-1}{2} \)
D.


If \( f(x)=\sin 2 x-\cos 2 x, \) find \( f^{\prime}\left(\frac{\pi}{6}\right) \)


A force \( \overrightarrow{\boldsymbol{F}}=\mathbf{3} \hat{\mathbf{i}}+\mathbf{4} \hat{\mathbf{j}}-\mathbf{3} \hat{\boldsymbol{k}} \) is applied at
the point \( P, \) whose position vector is \( \vec{r}=2 \hat{i}-2 \hat{j}-3 \hat{k} . \) What is the
magnitude of the moment of the force about the origin?
A . 23 units
B. 19 units
c. 18 units
D. 21 units


Which condition is not satisified by an
ideal solution?
A \( \cdot \Delta H_{\operatorname{mixing}}=0 \)
B. \( \Delta V_{\text {mixing}}=0 \)
C. \( \Delta S_{\text {mixing}}=0 \)
D. obeyance of Raoult's law


Tidal energy works using:
A. average of sea levels of high and low tides.
B. resisting the formation of tides.
C. difference in sea levels between high and low tides
D. using heat energy in tides.


Angular momentum of the disc will be
conserved about
A. centre of mass
B. point of contact
C. a point at a distance \( 3 R / 2 \) vertically above the point of contact
D. a point at a distance \( 4 R / 3 \) vertically above the point of contact


Find the general solution of the
equation \( 4 \cos ^{2} x=1 \)


If \( \left(x^{2}+x y+3 y^{2}\right)=1, \) what will be the
value of \( (x+6 y)^{3} \cdot \frac{d^{2} y}{d x^{2}} ? \)


The sporophyte of Bryophyte is
A. Parasitic
B. Autotrophic
c. Saprophytic
D. Semiparasitic or parasitic


Sum of all the values of \( x \) in the interval
\( [0,100 \pi] \) satisfying the equation
\( \sin x=0 \) is
\( \mathbf{A} \cdot 4950 \pi \)
B. \( 5050 \pi \)
c. \( 5151 \pi \)
D. none of these


\( A D \) is an altitude of an isosceles
triangle \( A B C \) in which \( A B=A C \)
Show that, \( A D \) bisects \( B C \)


Which of the elements below is most
likely to form compounds in which it has an incomplete octet?
A. \( B \)
в. \( C \)
c. \( N \)
D.
E. \( F \)


Select correct options.
This question has multiple correct options
A. In hitting or kicking a ball we decrease the time of contact so that large force acts on the ball producing greater acceleration.
B. In catching a ball by drawing hands backwards, increases the time of contact and so, lesser force acts on hands and hands are saved from getting hurt.
C. An athlete is advised to come to stop slowly after finishing a fast race. So that time of stop increases and hence force experienced by him decreases.
D. None of these


The potential energies of first, second
and third Bohr's orbits of \( H e^{+} \) cation
are \( E_{1}, E_{2} \) and \( E_{3} . \) The correct sequence
of these energies is:
A \( . E_{1}>E_{2}>E_{3} \)
B . \( E_{1}=E_{2}>E_{3} \)
c. \( E_{1}=E_{2}=E_{3} \)
D. \( E_{3}>E_{2}>E_{1} \)


Let \( [t] \) denote the greatest integer \( \leq t \) and \( \lim _{x \rightarrow 0} x\left[\frac{4}{x}\right]=A . \) Then the function,
\( f(x)=\left[x^{2}\right] \sin (\pi x) \) is discontinuous,
when \( x \) is equal to:
\( A \cdot \sqrt{A} \)
B. \( \sqrt{A+1} \)
c. \( \sqrt{A+5} \)
D. \( \sqrt{A+21} \)


In funaria, the meiosis occurs in
A. capsule/sporangium
B. Gametophore
c. Protonema
D. Gametangia


The sex ratio is the highest in
A. Punjab
B. Harayana
c. Kerala
D. Karnataka


Which of the following is an example of
weak electrolyte?
A \( \cdot C H_{3} C O O H \rightarrow C H_{3} C O O^{-}+H^{+} \)
в. \( K O H \rightarrow K^{+}+O H^{-} \)
\( \mathrm{c} \cdot A g N O_{3} \rightarrow A g^{+}+N O_{3} \)
D. all of the above


A buffer solution of \( 0.80 M N a_{2} H P O_{4} \)
and \( 0.020 M N a_{3} P O_{4} \) is prepared. The
electrolytic oxidation of 1.0 milli mole RNHOH is carried out in \( 100 m L \)
buffer to give.
\( \boldsymbol{R} \boldsymbol{N} \boldsymbol{H} \boldsymbol{O} \boldsymbol{H}+\boldsymbol{H}_{2} \boldsymbol{O} \longrightarrow \boldsymbol{R} \boldsymbol{N} \boldsymbol{O}_{2}+ \)
\( 4 H^{+}+4 e \)
Calculating approximate \( p H \) (nearest integer) of the solution after oxidation
is complete. \( \boldsymbol{p} \boldsymbol{K}_{\boldsymbol{a}_{1}}, \boldsymbol{p} \boldsymbol{K}_{\boldsymbol{a}_{2}} \) and \( \boldsymbol{p} \boldsymbol{K}_{\boldsymbol{a}_{3}} \) of
\( H_{3} P O_{4} \) are 2.12,7.20 and 12.0
respectively.


Calculate the mean deviation from the
median of the following data.
\[
\begin{array}{llll}
\begin{array}{l}
\text { Wages } \\
\text { per } \\
\text { week }
\end{array} & \begin{array}{l}
\mathbf{1 0}- \\
\mathbf{2 0}
\end{array} & \begin{array}{l}
\mathbf{2 0}- \\
\mathbf{3 0}
\end{array} & \begin{array}{l}
\mathbf{3 0}- \\
\mathbf{4 0}
\end{array} \\
\begin{array}{l}
\text { No. of } \\
\text { workers }
\end{array} & 4 & 6 & 10
\end{array}
\]


A wave of frequency 500 Hz has a phase velocity of \( 360 \mathrm{m} / \mathrm{s} \). The phase difference between the two displacements at a certain point in a time interval of \( 10^{-3} \) seconds will be
how much?
A \( \cdot \frac{\pi}{2} \) radian
B. \( \pi \) radian
c. \( \frac{\pi}{4} \) radian
D. \( \frac{\pi}{8} \) radian


Match following


For the reaction \( \boldsymbol{P} \boldsymbol{C l}_{5}_{5} \rightleftharpoons \boldsymbol{p} \boldsymbol{C l}_{3(g)}+ \)
\( C l_{2(g)}, \) the forward reaction at constant
temperature is favoured by:
A. introducing an inert gas at constant volume
B . introducing \( C l_{2} \) at constant volume
C . introducing \( P C l_{5} \) at constant volume
D. reducing the volume of the container


A centrifuge starts rotating from rest
and reaches a rotational speed of 8,000 radians/sec in 25 seconds. Calculate
the angular acceleration of the
centrifuge?
A. 160 radians \( / \)sec\( ^{2} \)
B. 320radians/sec^
c. 640 radians / sec \( ^{2} \)
D. 10,000 radians \( / \)sec\( ^{2} \)
E .20,000 radians / sec \( ^{2} \)


The electron in a hydrogen atom makes
a transition \( n_{1} \rightarrow n_{2} \) where \( n_{1} \) and \( n_{2} \)
are principal quantum numbers of two states. Assume the Bohr model to be
valid. The time period of the electron in the initial state is eight times that in
the final state. Then the possible value
of \( n_{1} \) and \( n_{2} \) is/are:
\( \mathbf{A} \cdot n_{1}=2, n_{2}=1 \)
B \( . n_{1}=1, n_{2}=2 \)
\( \mathbf{c} \cdot n_{1}=4, n_{2}=2 \)
D \( . n_{1}=6, n_{2}=3 \)
E \( . n_{1}=6, n_{2}=4 \)


If \( n^{t h} \) term of an A.P. is \( 2 n+1 \), then find
its common difference.


Among i-iii the boiling point follows the
order.
(i)
(ii)
(iii)
A \( . i i<i< \) ii \( i \)
B . \( i i i<i i<i \)
c. \( i<i i< \) ii \( i \)
D. \( i i<i i i<i \)


Which one of the following properties is not generally exhibited by ionic compounds?
A. Solubility in water
B. Electrical conductivity in solid state
c. High melting and boiling points
D. Electrical conductivity in molten state


Light of wavelength \( \lambda_{1} \) enters a medium
with refractive index \( n_{2} \) from a medium
with refractive index \( n_{1} \). What is the
wavelength of light in second medium?


Magnetic lines of force around any
current carrying conductor are circular in nature.


An object is displaced from point \( \mathrm{A}(2 \mathrm{m} \) \( 3 m, 4 m) \) to a point \( B(1 m, 2 m, 3 m) \) under a constant force \( \overrightarrow{\boldsymbol{F}}= \) \( (2 \hat{i}+3 \hat{j}+4 \hat{k}) N . \) Find the work done by this force in this process.
A. \( -9 J \)
\( J \)
B. \( 9 J \)
c. \( -18 J \)
D. \( 18 J \)


If \( \boldsymbol{A}+\boldsymbol{B}+\boldsymbol{C}=\boldsymbol{\pi} \) and \( \boldsymbol{A}, \boldsymbol{B}, \boldsymbol{C} \) are
angles of \( \triangle ; \) then \( \sin A+\sin B+\sin C \)
is
\( ^{A}=\frac{3 \sqrt{3}}{2} \)
B. \( <\frac{3 \sqrt{3}}{2} \)
\( ^{c}>\frac{3 \sqrt{3}}{2} \)
D. none of these


The base current of a transistor is
\( 105 \mu A \) and the collector current is
\( 2.05 m A . \) Then \( \beta \) of the transistor is
\( \mathbf{A} \cdot 1.952 \)
B. 19.52
c. 195.2
D. 1952


Construct a \( 2 \times 2 \) matrix \( A=\left[a_{i j}\right] \) whose element \( a_{i j} \) is \( a_{i j}=\frac{(i-2 j)^{2}}{2} \)


A brown coloured mixture of two gases
is obtained by the reduction of 6N nitric acid with metallic copper. This mixture on cooling condenses to a blue liquid which on freezing \( \left(-30^{\circ} \mathrm{C}\right) \) gives a blue solid. The correct choice for blue liquid
or solid is :
A. it is referred to as the anhydride of nitrous acid
B. it is an acidic oxide and hence dissolves in alkalies producing nitrites.
C . it can also be prepared by the action of 50\% \( \mathrm{H} \mathrm{NO}_{3} \) on arsenious oxide and then cooling to \( 250 \mathrm{K} \)
D. all of the above


Which of the following do not have stomata?
A. Xerophytes
B. Mesophytes
c. Hydrophytes
D. Submerged hydrophytes


Which of the following statements
is/are correct?
This question has multiple correct options
A. Spontaneous adsorption of gases on solid surface is an exothermic process as entropy decreases during adsorption.
B. Formation of micelles takes place when temperature is below Kraft temperature ( \( T_{k} \) ) and concentration is above critical micelle concentration (CMC)
C. A colloid of \( \mathrm{Fe}(\mathrm{OH})_{3} \) is prepared by adding a little excess (required to completely precipitate \( F e^{3+} \) ion as \( F e(O H)_{3} \) ) of \( N a O H \) in \( F e C l_{3} \) solution. The particles of this sol will move towards cathode during electrophoresis
D. According to Hardy-Schulze rule, the coagulation (flocculating) value of \( F e^{3+} \) ion will be more than \( B a^{2+} \) or \( N a^{+} \)


A bullet is fired vertically upwards with velocity \( v \) from the surface of a
spherical planet. When it reaches its maximum heights, its acceleration due
to the planet's gravity is \( 1 / 4 \) th of its value at the surface of the planet. If the
escape velocity from the planet is \( \boldsymbol{v}_{e s c}=\boldsymbol{v} \sqrt{\boldsymbol{N}}, \) then the value of \( \mathrm{N} \) is
(ignore energy loss due to atmosphere)


The maximum value of \( \sin ^{2} x \cos ^{3} x \) is
A \( \cdot \frac{6 \sqrt{3}}{25 \sqrt{5}} \)
В. \( \frac{9 \sqrt{3}}{25 \sqrt{5}} \)
c. \( \frac{9 \sqrt{2}}{6 \sqrt{5} / 5} \)
D. \( \frac{\sqrt{2}}{\sqrt{5}} \)


Account for the following:
(a) \( N i(C O)_{4} \) is tetrahedral
(b) \( \left[\boldsymbol{N} \boldsymbol{i}(\boldsymbol{C} \boldsymbol{N})_{4}\right]^{2-} \) is square planar
(c) \( \left[N i\left(N H_{3}\right)_{6}\right]^{2+} \) is octahedral


\( A B C D \) is a rectangle with \( A(-1,2) \) \( B(3,7) \) and \( A B: B C=4: 3 . \) If \( P \) is
the centre of the rectangle then the distance of \( P \) from each corner is equal
to
A \( \cdot \frac{\sqrt{41}}{2} \)
B. \( \frac{3 \sqrt{41}}{4} \)
c. \( \frac{2 \sqrt{41}}{3} \)
D. \( \frac{5 \sqrt{41}}{8} \)


Which is/are correct representation of boranes?
This question has multiple correct options
\( \mathbf{A} \cdot B_{n} H_{n+4} \)
В. \( B_{n} H_{n+6} \)
\( \mathbf{c} \cdot B_{n} H_{2 n+2} \)
D. None of these


For the hydrolysis of methyl acetate in aqueous solution, the above tabulated results were obtained:
(i) Show that it follow pseudo first order
reaction as the concentration of water
remains constant.
(ii) Calculate the average rate of reaction between the time interval 30 to
60 seconds.
(Given log \( 2=0.3010, \) log \( 4=0.6021 \) )
\begin{tabular}{|c|c|c|c|}
\hline \( \mathrm{t} / \mathrm{s} \) & 0 & 30 & 60 \\
\hline \( \mathrm{c} \mathrm{CH}_{3} \mathrm{COOH}_{3} \) & \( / \mathrm{moll}^{-1} \) & 0.60 & 0.30 & 0.15 \\
\hline
\end{tabular}


An electron in an atom revolves around
0
the nucleus in an orbit of radius \( 0.53 A \)
Calculate the equivalent magnetic moment, if the frequency of revolution of electron is \( 6.8 \times 10^{9} M H z( \) Given :
\( \left.e=1.6 \times 10^{-19}\right) \)


If two sides of an isosceles \( \Delta \) are \( 3 \mathrm{cm} \)
and \( 8 \mathrm{cm}, \) then the length of the third side is :
\( \mathbf{A} \cdot 3 \mathrm{cm} \)
B. \( 8 \mathrm{cm} \)
\( c .3 \mathrm{cm} \) or \( 8 \mathrm{cm} \)
D. none


When a body is stationary, then:
A. there is no force acting on it.
B. the body is in vacuum.
C. the forces acting on it are not in contact with it.
D. the net forces acting on it balance each other.


An aqueous solution of \( 2 \% \) non-volatile
solute exerts a pressure of 1.004 bar at the normal boiling point of the solvent.
What is the molecular mass of the
solute?
A \( .23 .4 \mathrm{gmol}^{-1} \)
B . \( 41.35 \mathrm{gmol}^{-1} \)
c. \( 10 \mathrm{gmol}^{-1} \)
D. 20.8 gmol-


Arun and Tarun appeared for an
interview for two vacancies. The
probability of Arun's selection is \( \frac{1}{4} \) and that of Tarun's rejection is \( \frac{2}{3} . \) Find the probability that at least one of them will
be selected.


An ideal aqueous solution containing liquid \( \boldsymbol{A}(M \cdot W \boldsymbol{t}=\mathbf{1 2 8}) \mathbf{6 4 \%} \) by weight
has a vapour pressure of \( 145 m m H g \). If
the vapour pressure of \( \boldsymbol{A} \) is \( \boldsymbol{x} \) mm of \( H g \) and that of water is \( 155 m m H g \) at the same temperature. Then find \( \frac{x}{5} . \) The solutions is ideal.


One reaction that occurs in producing steel from iron ore is the reduction of
iron ore(II) by carbon monoxide to give iron metal and carbon dioxide. The
equilibrium constant \( \boldsymbol{K}_{\boldsymbol{p}} \) for the
reaction at \( 1000 \mathrm{K} \) is \( 0.259 . F e O+ \)
\( \boldsymbol{C O} \leftrightharpoons \boldsymbol{F} \boldsymbol{e}+\boldsymbol{C O}_{2} . \) If the initial partial
pressure of \( \mathrm{CO} \) and \( C \mathrm{O}_{2} \) are 1 atm and
0.5 atm respectively, the equilibrium
partial pressures of \( \mathrm{CO} \) and \( \boldsymbol{C O}_{2} \) at
1000K are :
A. 1.191 atm, 0.309 atm
B. 0.309 atm, 1.191 atm
c. 1.191 atm for both
D. 0.309 atm for both


A liquid P of specific heat capacity \( 1800 J k g^{-1} K^{-1} \) and at \( 80^{\circ} \mathrm{C} \) is mixed
with liquid \( R \) of specific heat capacity \( 1200 J k g^{-1} K^{-1} \) and at \( 30^{\circ} \mathrm{C} . \) After
mixing, the final temperature of
mixture is \( 50^{\circ} \mathrm{C} . \) In what proportion by weight are the liquids mixed?


The distance between two consecutive
points in the same phase is called
A. Pitch
B. Velocity
c. wavelength
D. Period


The distance AC is :
A . \( 20 \mathrm{m} \)
B. 30 \( m \)
\( c \cdot 40 m \)
D. \( 50 \mathrm{m} \)


Formation of ammonium sulphate from ammonia and dil sulphuric acid is given by :
\( \mathbf{A} \cdot 3 N H_{3}+H_{2} S O_{4} \rightarrow\left(2 N H_{4}\right)_{2} S O_{4} \)
B \( \cdot 2 N H_{3}+H_{2} S O_{4} \rightarrow\left(N H_{4}\right)_{2} S O_{4} \)
\( \mathbf{c} \cdot 2 N H_{3}+3 H_{2} S O_{4} \rightarrow\left(N H_{4}\right)_{2} S O_{4} \)
\( \mathrm{D} \cdot 2 \mathrm{NH}_{3}+2 \mathrm{H}_{2} \mathrm{SO}_{4} \rightarrow\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4} \)


An electron of mass 'm' and charge 'w' initially at rest gets accelerated by a constant electric field 'E'. The rate of
change of de-Broglie wavelength of this electron at time 't' ignoring relativistic effects is
\( ^{A} \cdot-\frac{h}{e E t^{2}} \)
B. \( -\frac{e h t}{E} \)
c. \( -\frac{m h}{e E t^{2}} \)
D. \( \frac{h}{e E} \)


Select the correct statements:
This question has multiple correct options
A. The value of \( Q_{c} \) for a given reaction is constant.
B. A change in the physical state of a gaseous product shows a change in the value of equilibrium constant of that reaction.
C the value of ratio \( \frac{Q_{c}}{K_{c}} \) can be used to predict the direction in which a system will proceed spontaneously towards equilibrium.
D. The rate constants for forward and backward reaction
for a reversible reaction always increases with temperature but their ratio \( \left(i . e ., \frac{K_{f}}{K_{b}}\right) \) may increase or decrease with temperature.


Select the correct option(s) for ab ideal
gas:
This question has multiple correct options
A. Most probable speed increases with increases in temperature
B. Fraction of particles moving with most probable speed increase with increases in temperature
C. Fraction of particles moving with most probable speed are more for \( C l_{2} \) than \( H_{2} \) under similar condition of \( T \)
\( P \& V \)
D. Most probable speed is more for \( C l_{2} \) than \( H_{2} \) at same temperature


Find the value of \( (27)^{-\frac{2}{3}}+ \)
\( \left(\left(2^{-\frac{2}{3}}\right)^{-\frac{5}{3}}\right)^{-\frac{9}{10}} \)
A \( \cdot \frac{1}{9} \)
B. \( \frac{2}{9} \)
c. \( \frac{11}{18} \)
\( D \)


1 L of \( 0.15 M H C l \) and 1 L of \( 0.3 M \)
\( H C l \) is given. What is the maximum
volume of \( 0.2 M H C l \) which one can
make from these two solutions? No
water is added.
\( \mathbf{A} \cdot 1.2 L \)
B. \( 1.5 L \)
c. \( 1.3 L \)
D. \( 1.4 L \)


A short bar magnet of magnetic
moment \( 0.4 J T^{-1} \) is place in a uniform
magnetic field of 0.16 T. The magnet is stable equilibrium when the potential energy is
\( \mathbf{A} \cdot-0.064 J \)
B. zero
c. \( -0.082 J \)
D. 0.064


For the equation \( \boldsymbol{x}^{2}-(\boldsymbol{k}+\mathbf{1}) \boldsymbol{x}+\left(\boldsymbol{k}^{2}+\right. \)
\( k-8)=0 \) if one root is greater then 2
and other is less than 2 , then \( k \) lies
between
A . \( -2 \& 3 \)
B. 2 \& - 2
c. \( 2 \&-3 \)
D. None of these


Solve \( 2 \cos ^{2} \theta+\sin \theta \leq 2 \) where \( \pi / 2 \leq \)
\( \theta \leq 3 \pi / 2 \)


Sum \( 1, \sqrt{3}, 3, \dots \) to 12 terms.


Which of the following metals is obtained by leaching the ore with dilute cyanide solution?
A. Silver
B. Titanium
c. Vanadium
D. zinç


Which of the following is not a method of refining of metals?
A. Electrolysis
B. Smelting
c. Poling
D. Liquation


The current birth rate per thousand is
\( 32, \) whereas the corresponding death
rate is 11 per thousand. The net growth rate in terms of population increase in per cent is given by,
A. \( 0.0021 \% \)
and \( 6.0021 \% \)
B. \( 0.021 \% \)
\( c \cdot 2 \cdot 1 \% \)
D. \( 21 \% \)


Multiple Correct Answers Type The values of measurement of a
physical quantity in five trials were found to be 1.51,1.53,1.53,1.52 and
\( \mathbf{1 . 5 4} . \) Then
A. Average absolute error is 0.01
B. Relative error is 0.01 .
c. Percentage error is \( 0.01 \% \)
D. Percentage error is \( 1 \% \).


If \( \frac{a}{b}=\frac{2}{3}, \) then find the value of \( \frac{4 a+3 b}{3 b} \)


A balanced chemical equation
supports
A. Law of chemical equilibrium
B. Law of conservation of energy
C. Law of conservation of mass
D. None of these


A solid fuel formed by heating coal in the absence of air is:
A. hydrogen
B. coke
c. methane
D. coal tar


Theory of chemiosmosis was
propounded by
A. Mitchell
B. Kok
c. Arnold
D. Calvin


A vector \( \vec{r} \) is equally inclined with the
coordinate axes. If the tip of \( \vec{r} \) is in the
positive octant and \( |\boldsymbol{r}|=\mathbf{6}, \) then \( \overrightarrow{\boldsymbol{r}} \) is
A \( \cdot 2 \sqrt{3}(\hat{i}-\hat{j}+\widehat{k}) \)
B \( \cdot 2 \sqrt{3}(-\hat{i}+\widehat{j}+\widehat{k}) \)
c. \( 2 \sqrt{3}(\hat{i}+\widehat{j}-\widehat{k}) \)
D \( \cdot 2 \sqrt{3}(\hat{i}+\hat{j}+\widehat{k}) \)


Solve for a
\( \frac{3 a-2}{7}-\frac{a-2}{4}=2 \)


Old tin plates can be reused by removing the coating of tin on the metal. This saves a lot of money on
buying new metal. The tin is removed
with the help of:
A. Solvents
B. Metal brushes
c. oxygen
D. Chlorine


\( \lim _{x \rightarrow \infty} \frac{\sqrt{x^{2}+1}-\sqrt[3]{x^{3}+1}}{\sqrt[4]{x^{4}+1}-\sqrt[5]{x^{4}+1}} \) is
equals to
A .
B.
c. -1
D. None of these


In the formula of brown ring complex
\( \left[\boldsymbol{F e}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{5}(\boldsymbol{N O})\right] \boldsymbol{S} \boldsymbol{O}_{4}, \) the magnetic
moment is 3.87 B.M. The oxidation state
of Fe and number of unpaired electrons present respectively are :
\( \mathbf{A} \cdot 1+, 3 \)
в. \( 2+, 3 \)
c. \( 3+, 3 \)
D. \( 3+, 5 \)


Which one carries extra nuclear genetic material?
A. Plastid
B. Ribosomes
c. chromosomes
D. Golgi complex


Simplify:
\( (8 a-5 b)^{2} \)


Second and fourth term of on A.P. is 12
and 20 respectively. Find the sum of
first 25 terms of the A.P.


A particle undergoes SHM. When its displacement is \( 8 \mathrm{cm}, \) it has speed 3 \( \mathrm{m} / \mathrm{s} \) and a speed \( 4 \mathrm{m} / \mathrm{s} \) at displacement of \( 6 \mathrm{cm} . \) Find time period of oscillation.
A . \( 4 \pi \)
в. \( 6 \pi \)
c. \( 7 \pi \)
D. \( 8 \pi \)


Expand using Binomial Theorem \( \left(1+\frac{x}{2}-\frac{2}{x}\right)^{4}, x \neq 0 \)


Find the distance the rain drop has fallen in \( t=3 s: \)
A. \( 12 \mathrm{m} \)
в. 22.5 m
c. \( 2.5 \mathrm{m} \)
D. 7.2 \( m \)


Assertion
Archaebacteria are able to survive in
harsh habitats.
Reason
Presence of peptidoglycan in cell wall
help archaebacteria to survive in extreme conditions.
A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true but reason is not the correct explanation of assertion.
c. If assertion is true but reason is false.
D. If both assertion and reason are false


A \( 6 k g \) block is kept over a rough surface
with coefficients of friction \( \mu_{s}= \)
0.6 and \( \mu_{4}=0.4 \) as shown in figure.
time varying force \( \boldsymbol{F}=\mathbf{4} \boldsymbol{t}(\boldsymbol{F} \) in newton
and \( t \) in \( \operatorname{second} \) ) is applied on the block
as shown. Plot a graph between acceleration of block and time. (Take
\[
\begin{array}{c}
\left.\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2}\right) \\
\boldsymbol{6} \mathbf{k g} \quad \boldsymbol{6} \mathbf{k g} \\
\boldsymbol{\mu}_{\mathbf{5}}=\mathbf{0 . 6} \\
\boldsymbol{\mu}_{\mathbf{k}}=\mathbf{0 . 4}
\end{array}
\]


If the straight line \( a x+b y+p=0 \) and
\( x \cos \alpha+y \sin \alpha=p \) enclosed an angle
of \( \frac{\pi}{4} \) and the line \( x \sin \alpha-y \cos \alpha=0 \)
meets them at the same point, the
\( a^{2}+b^{2} \) is
A .4
B. 3
\( c \cdot 2 \)
D.


Find the value 'p' so that the equation
\( 4 x^{2}-8 p x+9=0 \) has roots whose
difference is 4


Hydrogen atom will be in its ground state, if its electron is in
A. any energy level
B. the lowest energy state
c. the highest energy state
D. the intermediate state


Prove that a triangle \( A B C \) is equilateral
if and only if \( \tan A+\tan B+\tan C= \)
\( \mathbf{3} \sqrt{\mathbf{3}} \)


One number is to be chosen from
Numbers 1 to \( 100, \) the probability that it is divisible by 3 or 7 is.....
A \( \frac{33}{100} \)
в. \( \frac{7}{100} \)
c. \( \frac{4}{100} \)
D. \( \frac{43}{100} \)


Let \( \boldsymbol{f}(\boldsymbol{x})=[\boldsymbol{x}]+[-\boldsymbol{x}] . \) Then for any
integer \( n \) and \( k \in R-I \)
This question has multiple correct options
A \( \cdot \lim _{x \rightarrow n} f(x) \) exists
B. \( \lim _{x \rightarrow k} f(x) \) exists
c. f is continuous at \( x=n \)
D. f is continuous at \( x=k \)


Warm ocean currents make the
climate?
A. warm
B. wet
c. warm and wet
D. cold


Plaster of paris in contact with water sets to a hard mass whose composition
is :
A. \( \operatorname{CaSO}_{4} \)
в. \( \operatorname{CaSO}_{4} . \mathrm{H}_{2} \mathrm{O} \)
\( \mathrm{c} \cdot \operatorname{CaSO}_{4} \cdot 2 \mathrm{H}_{2} \mathrm{O} \)
D. \( \operatorname{CaSO}_{4} \cdot \operatorname{Ca}(O H)_{2} \)


What will happen if there are no platelets in the blood?


If \( f(x) \) is continuous on \( [a, b] \) and \( \boldsymbol{f}(\boldsymbol{a}) \neq \boldsymbol{f}(\boldsymbol{b}), \) then for
any value \( c \) belongs \( (f(a), f(b)), \) there is at least one number
\( \boldsymbol{x}_{o} \) in \( (\boldsymbol{a}, \boldsymbol{b}) \) for which \( \boldsymbol{f}\left(\boldsymbol{x}_{\boldsymbol{o}}\right)=\boldsymbol{c} \)
A. \( f\left(x_{o}\right)=b \)
В. \( f\left(x_{o}\right)=c \)
c. \( f\left(x_{o}\right)=f(c) \)
D. \( f\left(x_{o}\right)=0 \)


Constant DC voltage is required from a variable AC voltage. Which of the following is correct order of operation?
A. Regulator, Filter, Rectifier
B. Rectifier, Regulator, Filter
c. Rectifier, Filter, Regulator
D. Filter, Regulator, Rectifier


Hockey handle is prepared from the wood of
A. salix
B. Morus
c. Picea
D. Phytelephas


\( \mathrm{C} \) is the centre of an equilateral triangle
PQR. \( f_{1}, f_{2} \) and \( f_{3} \) are the three forces acting along the sides as shown. For the
total torque about \( C \) to be zero,
\( ^{\mathrm{A}} \cdot f_{3}=\frac{\left(f_{1}+f_{2}\right)}{2} \)
3. \( f_{3}=\frac{\left(f_{1}+f_{2}\right)}{4} \)
\( \mathbf{c} \cdot f_{3}=f_{1}+f_{2} \)
D. \( f_{3}=f_{1}-f_{2} \)


A cyclist riding a bicycle fitted with dynamo to a tyre gets bright light from the bulb connected when he s fast. this
is because
A. magnet becomes powerful, when wheel rotates faster and current flows fast
B. current flows easly when cycle goes down
c. more magnetic lines of force change with respect to the coil and leading more current
D. coil become hot due to friction and produces more current


Find the smallest number by which 33275 must be multiplied so that the product is a perfect cube.


ACCELERATION DUE TO GRAVITY OF THE
EARTH

Radius of earth is \( 6400 \mathrm{km} \) and that of
mars is \( 3200 \mathrm{km} \). Mass of mars is 0.1
that of earth's mass. Then the acceleration due to gravity on mars is nearly.
A \( \cdot 1 \mathrm{m} / \mathrm{s}^{2} \)
B \( .2 .5 m / s^{2} \)
c. \( 4 m / s^{2} \)
D. \( 5 m / s^{2} \)


A muscle which is spindle shaped and
lacks striations are known as
A. Smooth muscle
B. Cardiac muscle
c. striated muscles
D. None of the above


The mode from the following table will
be:
Term \( \quad \mathbf{2 5} \quad \mathbf{3 5} \quad \mathbf{4 5} \) Frequency \( \quad 14 \quad 16 \quad 24 \quad 20 \)
A . 24
B. 45
c. 65
\( D \)


\( B r C H_{2} C H_{2} C H_{2} B r \) reacts with Na in
the presence of ether at \( 100 \mathrm{C} \) to produce:
A \( \cdot B r C H_{2} C H=C H_{2} \)
B. \( C H_{2}=C=C H_{2} \)
c. cyclopropane
D. All of these


Mica is a \( _{---} \) conductor of electricity
A. good
B. badd
c. positive
D. None of the above


Charging by friction is used to develop charges on
A. metals
B. conductors
c. insulators
D. Non of these


Assertion
If \( ^{n} C_{r-1}=36,^{n} C_{r}=84 \) and \( ^{n} C_{r+1}= \)
\( 126, \) then \( ^{r} C_{2}=8 \)
Reason
\( n C_{r}=^{n} C_{n-r} \)
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 and Reason is correct


Which one of the following animals has
a nervous system but no brain?
A. Earthworm
B. Hydra
c. Amoeba
D. cockroach


Extraction of metals from its ores
contain the following stages such as calcination and:
A. Roasting
B. Smelting
c. Both (a) and (b)
D. None of these


Write the male part of flower.


\( \cos 18^{\circ}-\sin 18^{\circ}= \)


\( A \) is a set containing \( n \) elements. Two subsets \( P \) and \( Q \) of \( A \) are chosen at
random. (P and Q may have elements in
common). The probability that \( \boldsymbol{P} \cup \boldsymbol{Q} \neq \)
\( A \) is
A \( \cdot(3 / 4)^{n} \)
B. 1/4n
c. \( ^{n} C_{2} / 2^{n} \)
D. \( 1-(3 / 4)^{n} \)


If the coefficient of variation of some
observation is 60 and their standard
deviation is 20 , then their mean is
A . 35
B. 34
\( c \cdot 33 \)
D. 33.33(nearly)


Which of the following shafts is stronger
A. solid
B. hollow
c. cylindrical
D. circular


ABCD is a parallelogram \( P \) and \( R \) are two points on AB such that the area of parallelogram ABCD is 8 times the are
of \( \Delta D P R \) If \( P R=5 c m \) then \( C D \) is equal
to
\( A \cdot 10 \mathrm{cm} \)
B. \( 5 \mathrm{cm} \)
\( c .20 \mathrm{cm} \)
D. \( 12 \mathrm{cm} \)


In non-resonant circuit, the nature of
circuit for frequencies greater than the
resonant frequency is :
A . resistive
B. capacitive
c. inductive
D. both 1 and 2


A bomb is dropped from a flying
aeroplane. Its path will be
A. an arc of a circle
B. a parabola
c. a zig-zag path
D. a straight vertical path in the do rection


Choose the incorrect statement among
the following:
A. the chemistry of different lanthanoids is very similar
B. \( 4 f- \) and \( 5 f- \) orbitals are equally shielded
C. \( d- \) block element show irregular and erratic chemical properties among themselves
D. \( L a \) and \( L u \) have partially filled d-orbitals


Identify a possible graph for function \( \boldsymbol{f} \)
given by
\( \boldsymbol{f}(\boldsymbol{x})=-\sqrt{(\boldsymbol{x}-\mathbf{1})}-\mathbf{1} \)
A. graph a
B. graph b
c. graph c
D. graph d


\( \int_{0}^{\pi / 2} \frac{\sin ^{6} x}{\cos ^{6} x+\sin ^{6} x} d x \) is equal to
A . 0
в. \( \pi \)
c. \( \frac{\pi}{4} \)
D . \( 2 \pi \)


Two resistances are connected in two
gaps of a metre bridge. The balance point is \( 20 \mathrm{cm} \) from the zero end. \( A \)
resistance of \( 15 \Omega \) is connected in series with the smaller of the two. The null
point shifts to \( 40 \mathrm{cm} . \) The value of the smaller resistance in ohms is.
A . 3
B. 6
c. 9
D. 12


Evaluate: \( \lim _{\boldsymbol{\pi}} \frac{\boldsymbol{c o t}^{3} \boldsymbol{x}-\boldsymbol{t a n} \boldsymbol{x}}{\cos (\boldsymbol{x}+\boldsymbol{\pi} / \mathbf{4})} \)
\( \boldsymbol{x} \rightarrow \boldsymbol{\boldsymbol { 4 }} \)
\( A \)
B. \( 8 \sqrt{2} \)
\( c \cdot 4 \)
D. \( 4 \sqrt{2} \)


In zone-refining method, the molten
zone:
A. consists of impurities only
B. contains more impurity than the original metal
c. contains the purified metal only
D. moves to either side


The figure shows a bar magnet coil.
Consider four situations.
(I) Moving the magnet away from the
coil.
(II) Moving the coil towards the magnet.
(III) Rotating the coil about the vertical
diameter
(IV) Rotating the coil about its axis.
An emf in the coil will be generated for the following situations.
\( A \cdot(1) \) and (11) only
B. (I), (II) and (IV) only
C. (I), (II) and (III) only
D. (I), (II), (III) and (IV) only