Two liquids \( A \) and \( B \) are miscible over the whole range of composition and may be treated as ideal (obeying Raoult's Law). At \( 350 \mathrm{K} \) the vapour pressure of pure \( A \) is \( 24.0 \mathrm{kPa} \) and of pure B is 12.0 kPa. A mixture of 60\% A
and \( 40 \% \mathrm{B} \) is distilled at this
temperature; what is the pressure in a closed distillation apparatus from which air is excluded? in KPa


The direction ratios of \( \overrightarrow{A B} \) are (-2,2,1)
If \( \boldsymbol{A}=(\mathbf{4}, \mathbf{1}, \mathbf{5}) \) and \( l(\mathbf{A B})=\mathbf{6} \) units, find
the coordinates of \( \boldsymbol{B} \).


Following two equilibrium is simultaneously established in a
container: \( \boldsymbol{P C l}_{5}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{P C l}_{3}(\boldsymbol{g})+ \)
\( \boldsymbol{C l}_{2}(\boldsymbol{g}) \) and \( \boldsymbol{C O}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) \rightleftharpoons \)
\( \boldsymbol{C O C l}_{2}(\boldsymbol{g}) \)
If some \( \mathrm{Ni}(\mathrm{s}) \) is introduced in the
container forming \( N i(C O)_{4}(g), \) then at new equilibrium:
A. \( P C l_{2} \) concentration will increase
B. \( P C l_{3} \) concentration will decrease
c. \( C l_{2} \) concentration will remain same
D. \( C O \) concentration will remain same


By increasing the temperature of a
liquid is:
A. Volume and density decrease
B. Volume and density increase
C. Volume increases and density decreases
D. Volume decreases and density increases


Atoms in \( P_{4} \) molecule of white
phosphorus are arranged regularly in the following way:
A. at the corners of a cube
B. at the corners of an octahedron
\( c . \) at the corners of a tetrahedron
D. at the center and corners of a tetrahedron


A negatively charged particle is situated on a straight line joining two other stationary particles each having charge \( +q . \) The direction of the motion
of the negatively charged particle will
depend on:
A. the magnitude of charge
B. the position at which it is situated
c. both magnitude of charge and its position.
D. the magnitude of \( +q \)


The formula \( v=R \omega \) relating linear and
angular velocity is true, only if
A. The velocities are instantaneous velocities
B. The velocities are average velocities
c. The velocities are initial velocities and the particle is moving with constant acceleration
D. The velocities are initial velocities and the particle is moving with constant retardation


ABCD is a parallelogram. The position vectors of \( A \) and \( C \) are respectively, \( 3 \hat{i}+ \) \( 3 \hat{j}+5 \hat{k} \) and \( \hat{i}-5 \hat{j}-5 \hat{k} . \) If \( \mathrm{M} \) is the
mid-point of the diagonal DB, then the magnitude of the projection of \( \boldsymbol{O} \boldsymbol{M} \) on \( \overrightarrow{O C}, \) where 0 is the origin is?
A \( \cdot \frac{7}{\sqrt{50}} \)
B . \( 7 \sqrt{50} \)
c. \( \frac{7}{\sqrt{51}} \)
D. \( 7 \sqrt{51} \)


The process in which a parent body
divides to form two daughter cells is called as
A. Fragmentation
B. Budding
c. Binary fission
D. Regeneration


A solution of \( \mathrm{SO}_{2} \) in water reacts with \( \mathrm{H}_{2} \)
S precipitating sulphur. Here, \( \mathrm{SO}_{2} \) acts
as:
A. an oxidising agent
B. a reducing agent
\( c . \) an acid
D. a catalyst


Out of the following functions representing motion of particle which
represents SHM?
\( x=\sin ^{3} \omega t \)
2. \( x=1+\omega t+\omega^{2} t^{2} \)
3. \( \boldsymbol{x}=\cos \omega \boldsymbol{t}+\cos \boldsymbol{3} \boldsymbol{\omega} \boldsymbol{t}+\boldsymbol{c} \boldsymbol{o} \boldsymbol{s} \boldsymbol{5} \boldsymbol{t} \)
4. \( x=\sin \omega t+\cos \omega t \)
A. Only 1
B. Only 1 and 3
c. only 1 and 4
D. only 4


Which of the following is not a food additive?
A. Preservatives
B. Sweetening agents
c. Flavours
D. Oxidants


For the reaction, \( A+B \rightleftharpoons 3 C, \) if \( ^{\prime} a^{\prime} \)
mole/litre of each 'A' \& 'B' are taken
initially then at equilibrium the incorrect relation is:
A \( \cdot[A]-[B]=0 \)
B . \( 3[B]+[C]=3 a \)
c. \( 3[A]+[C]=3 a \)
D . \( [A]+[B]=3[C] \)


A proton is accelerated through \( 225 V \)
Its de Brogile wavelength is:
A . \( 1.91 p m \)
B. \( 0.2 \mathrm{pm} \)
\( \mathrm{c} .3 \mathrm{pm} \)
D. \( 0.4 n m \)


Sets of travelling waves are given as shown in above figure. Identify which of
the following set of the wave will soon
show destructive interference?
\( A \cdot A \)
B. B
\( c \cdot c \)
D.
E.


Mushroom or utricular gland of male cockroach takes part in
A. Nourishing of sperms
B. Storing of sperms
c. Formation of inner membrane of spermatophore
D. All the above


The least value of magnetic moment
(where \( m \) is the mass of the electron, \( e \) is
the charge of electron) is :
A \( \cdot \frac{e h}{m} \)
в. \( \frac{e h}{4 \pi m} \)
c. \( \frac{2 e h}{\pi m} \)
D. \( \frac{e h}{\pi m} \)


Five identical parallel conducting
plates each of area A have separation 'd between successive surface. The plates
are connected to the terminal of a
battery as shown in the figure. The effective capacitance of the circuit is
A \( \cdot \frac{A \varepsilon_{0}}{4 d} \)
в. \( \frac{4 A \varepsilon_{0}}{d} \)
c. \( \frac{A \varepsilon_{0}}{3 d} \)
D. \( \frac{3 A \varepsilon_{0}}{4 d} \)


The place where the value of 'g' is unaffected by the increase (or) decrease in the speed of rotation of the earth about its own axis is poles
A. True
B. False


Find the square root of a given number by the prime factorization method. 529


Plane polarized light is passed through a Polaroid. Now the Polaroid is given one complete rotation about the direction of light propagation. When viewed through another Polaroid (analyser), one of the following is observed:
A. The intensity of light gradually decreases to zero and then remains zero
B. The intensity of light becomes twice maximum and twice zero
c. The intensity of light becomes maximum and stays maximum
D. The intensity of light does not change


Find \( n \) if the given value of \( x \) is the \( n \) th
term of the given A.P.
\( 5 \frac{1}{2}, 11,16,16 \frac{1}{2}, 22, \dots . ; x=550 \)


Crossing over takes place on
A. Two stranded stage
B. Three stranded stage
c. one stranded stage
D. Four stranded stage


If the points of local extremum of
\( f(x)=x^{3}-3 a x^{2}+3\left(a^{2}-1\right) x+1 \)
lies between \( -2 \& 4, \) then \( ^{\prime} a^{\prime} \) belongs to
A. (-2,2)
B \( \cdot(-\infty,-1) \cup(3, \infty) \)
c. (-1,3)
\( D \cdot(3, \infty) \)


Newton's second law of motion and work
done in rotation of a rigid body can be
expressed as
A. Newton's law cannot be expressed in rotation, work done in rotation is \( W=\tau \) theta
B. Force and work done are expressed as \( \tau=I \alpha \) and \( W=\tau \) theta
c. Force can be expressed as \( \tau=I \alpha, \) while work done will
be zero
D. Force will be zero, since no net displacement is present


n the give reaction, the product(s) obtained is/are:
нн,ссн \( _{z} \) сн, о dect
\( \mathrm{CH}_{2}=\mathrm{C}-\mathrm{CH}_{2}-\mathrm{CH}_{3} \)
\( \mathrm{CH}_{3}-\mathrm{C}=\mathrm{CH}-\mathrm{CH}_{3} \)
\( \mathrm{CH}_{3}-\mathrm{CH}-\mathrm{CH}=\mathrm{CH}_{2} \)


The relationship between the value of
Osmotic pressure \( (\pi) \) of the solution
obtained by dissolving \( 6 g . \mathrm{L}^{-1} \) of acetic
\( \operatorname{acid}\left(\pi_{1}\right) \) and 7.45 g.L \( ^{-1} \) of \( \mathrm{KCl}\left(\pi_{2}\right) \) is :
A \( \cdot \pi_{1}<\pi_{2} \)
В. \( \pi_{1}>\pi_{2} \)
\( \mathbf{c} \cdot \pi_{1}=\pi_{2} \)
D. \( \frac{\pi_{1}}{\pi_{1}+\pi_{2}}=\frac{\pi_{2}}{\pi_{1}+\pi_{2}} \)


On what sum will the compound
interest at \( 5 \% \) p.a.for 2 years compounded annually be Rs. \( 1,640 ? \)
A . 16,000
B. 630.50
c. 425.76
D. 1,640


A scrubber in the exhaust of a chemical
industrial plant removes
A. Gases like Sulphur dioxide
B. Particulate matter of the size 5 micrometers or above
c. Gases like ozone or methane
D. Gases like Nitrous oxide


For the precipitation reaction of \( \boldsymbol{A} \boldsymbol{g}^{+} \) ions with \( N a C l, \) the correct relation is
A. \( \Delta H=0 \)
в. \( \Delta G=0 \)
c. \( \Delta G=-v e \)
\( \mathbf{D} \cdot \Delta G=\Delta H \)


The cell division in blue green algae similar to that in
A. Bacteria
B. Brown algae
c. Green algae
D. Higher plants


A body of mass \( \mathrm{M} \) is situated in a
potential field \( \boldsymbol{U}(\boldsymbol{x})=\boldsymbol{U}_{0}(\mathbf{1}-\cos \boldsymbol{d} \boldsymbol{x}) \)
where \( U_{0} \) and \( d \) are constants. The time
period of small oscillations will be
в. \( 2 \pi \sqrt{\frac{M}{U_{0} d^{2}}} \)
\( ^{\mathbf{C}} \cdot 2 \pi \sqrt{\frac{U_{0} d^{2}}{M}} \)
D. \( 2 \pi \sqrt{\frac{U_{0}}{M d^{2}}} \)


The quantum numbers of most energetic electron in Ar atom when it is in first excited state is:
A \( \cdot_{2,1,0, \pm} \frac{1}{2} \)
в. \( _{4,1,1, \pm} \frac{1}{2} \)
c. \( _{4,0,0, \pm} \frac{1}{2} \)
D. \( _{4,1,0, \pm} \frac{1}{2} \)


A force \( F=10 \sqrt{2} N \) acts an angle of
\( 45^{\circ} \) above the horizontal on a \( 2 k g \) block
placed on a rough horizontal surface. The coefficient of friction between the
block and surface is 0.2 Find the work
done by the force \( F \) on the block in \( 5 s \)
initially the block is at rest. [Take \( g= \)
\( \left.\mathbf{1 0} / \boldsymbol{s}^{2}\right] \)
\( \mathbf{A} \cdot 250 J \)
В. \( 2500 J \)
c. \( 500 J \)
D. \( 50 J \)


If \( A \subset B \) then show that \( A \cup B=B \)
(use Venn diagram)


Number of peptide bonds present in Ala-Gly-Ser-Tyr
A . 4
B. 3
\( c \cdot 2 \)
\( D \)


Leaf fall occurs when
A. Auxin content is more in lamina than in the stem
B. Auxin content is low in the lamina as compared to stem
C. Abscisic acid is formed
D. Morphactins are produced


For what triplets of real numbers \( (a, b, \)
c) with \( a \neq 0 \) the function \( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{cc}\boldsymbol{x} & \boldsymbol{x} \leq \mathbf{1} \\ \boldsymbol{a} \boldsymbol{x}^{2}+\boldsymbol{b} \boldsymbol{x}+\boldsymbol{c} & \text { otherwise }\end{array}\right. \)
differentiable for all real x?
A \( \cdot\{(a, 1-2 a, a) / a \in R, a \neq 0\} \)
в. \( \{(a, 1-2 a, c) / a, c \in R, a \neq 0\} \)
c. \( \{(a, b, c) / a, b, c \in R, a+b+c=1\} \)
D. \( \{(a, 1=2 a, 0) / a \in R, a \neq 0\} \)


If the same force is applied to the surface area which reduced by half, the
pressure
A. remains the same
B. becomes half
c. becomes double
D. becomes zero


\( \mathbf{f} \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{3} & \boldsymbol{a} \\ \mathbf{- 4} & \mathbf{8}\end{array}\right], \boldsymbol{B}= \)
\( \left[\begin{array}{cc}\boldsymbol{c} & \boldsymbol{4} \\ -\boldsymbol{3} & \boldsymbol{0}\end{array}\right], \boldsymbol{C}=\left[\begin{array}{cc}-\mathbf{1} & \boldsymbol{4} \\ \boldsymbol{3} & \boldsymbol{b}\end{array}\right] \& \boldsymbol{3} \boldsymbol{A}- \)
\( 2 B=6 C, \) find the values of \( a, b \) and \( c \)


In the compound
\[
\boldsymbol{C H}_{3}
\]
the
\[
\boldsymbol{H C} \equiv \boldsymbol{C}-\boldsymbol{C}=\boldsymbol{C H}_{2}
\]
hybridisation of \( C-2 \) and \( C-3 \)
carbons are respectively:
A \( \cdot s p^{3} \) and \( s p^{3} \)
B. \( s p^{2} \) and \( s p^{3} \)
\( \mathbf{c} \cdot s p^{2} \) and \( s p \)
D. \( s p^{3} \) and \( s p \)


Which of the statements are correct?
This question has multiple correct options
A. Unit of work is \( \mathrm{kgm}^{2} \mathrm{s}^{-2} \)
B. Unit of force is \( k g m s^{-2} \)
C. Unit of work is \( k g m s^{-2} \)
D. Unit of force is \( k g m^{2} s^{-2} \)


A capacitor 'C', a variable resistor'R' and
a bulb 'B' are connected in series to the
ac mains in circuit as shown. The bulb
glows with some brightness. How will the glow of the bulb change if (i) a dielectric slab is introduced between
the plates of the capacitor, keeping resistance \( R \) to be the same; (ii) the
resistance \( R \) is increased keeping the
same capacitance?


Ultrasonics are useful for.
A. Bats only
B. Human beings only
C. Bats and human beings
D. Neither bats nor human beings


The ratio of RBC to WBC in man is
A. 6:
B. 60: 1
c. 600: 1
D. 6000:


If the sides of a triangle are produced, then the sum of the exterior angle i.e. \( \angle a+\angle b+\angle c \) is equal to
A \( .180^{\circ} \)
В. \( 360^{\circ} \)
\( c \cdot 90^{0} \)
D. \( 270^{\circ} \)


A point charge is brought in an electric field. The electric field at a nearby point:
This question has multiple correct options
A. Will increase if the charge is positive
B. Will decrease if the charge is negative
c. May increase if the charge is positive
D. May decrease if the charge is negative


Natural cytokinins are synthesized in tissues for
A. Differentiating
B. Senescent
c. Dividing
D. Storing food


Under what conditions algae enter the
palmella stage?


What is the area of the plates of a 2 F parallel plate capacitor, given that the separation between the plates is 0.5 \( \mathrm{cm} ?[ \) You will realise from your answer
why ordinary capacitors are in the range of F or less. However, electrolytic capacitors do have a much larger capacitance (0.1 \( F \) ) because of very minute separation between the conductors.


Find \( \frac{\boldsymbol{a} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}, \) if \( \boldsymbol{y}= \)
\( \boldsymbol{e} \sin ^{2} \boldsymbol{x}\left\{\boldsymbol{2} \tan ^{-1} \sqrt{\frac{\boldsymbol{1}+\boldsymbol{x}}{1-\boldsymbol{x}}}\right\} \)


Which of the following is correct for a spontaneous reaction at any temperature?
A. \( \Delta H=-v e, \Delta S=+v e, \Delta G=-v e \)
B. \( \Delta H=-v e, \Delta S=-v e, \Delta G=-v e \)
c. \( \Delta H=+v e, \Delta S=+v e, \Delta G=-v e \)
D. \( \Delta H=-v e, \Delta S=+v e, \Delta G=+v e \)


A large quantity of urban sewage is drained to a nearby river. Which among the given conditions would happen after mixing of sewage into the river?
(i) BOD of receiving water body increases.
(ii) DO of receiving water body decreases.
(iii) It will not cause mortality among fishes and other aquatic creatures.
(iv) It will lead to nutrient enrichment of
receiving water body.
A. i, ii and iii
B. i, ii and iv
c. ii and iii
D. iii and iv


Two identical mercury drops, each of
radius r are charged to the same
potential V.If the mercury drops coalesce to form a big drop, each of radius \( R \) then the potential of the combined drop will be
\( \mathbf{A} \cdot(3)^{1 / 2} V \)
B . \( (3)^{2 / 3} V \)
c. \( (2)^{2 / 3} V \)
D. \( (2)^{3 / 2} V \)


On connecting a battery to the two corners of a diagonal of a square
conductor frame of side \( a \) the
magnitude of the magnetic field at the centre will be:
A . zero
в. \( \frac{\mu_{0}}{\pi a} \)
c. \( \frac{2 \mu_{0}}{\pi a} \)
D. \( \frac{4 \mu_{0}}{\pi a} \)


\( \lim _{x \rightarrow 0} \frac{x^{3}+3 x^{2}-9 x-2}{x^{3}-x-6} \)


The differential equation representing
the family of curves \( \boldsymbol{y}^{2}=\mathbf{2 c}(\boldsymbol{x}+\sqrt{\boldsymbol{c}}) \)
where \( c \) is a positive perimeter, is of
A. order 1 , degree 3
B. order 2 , degree 3
c. Degree 1 , order 2
D. None of these


10 g of ice at \( 0^{\circ} C \) absorbs 5460 J of heat energy to melt and change to water
at \( 50^{\circ} \mathrm{C} \). Calculate the specific latent heat of fusion of ice. Specific heat capacity of water is \( 4200 J k g^{-1} K^{-1} \)
A \( \cdot 2168 J g^{-1} \)
B. \( 336 J g^{-1} \)
\( \mathbf{c} \cdot 43.36 J g^{-1} \)
D. \( 21.68 J g^{-1} \)


Ethanoic acid +3 -methyl-1-butanol \( \underset{\mathbf{H}_{2} \boldsymbol{S O}_{4}}{\rightleftharpoons} \)
(A) ;Compound (A) is:
A.
B.
\( c \)
D.


State two uses each of : plane mirror


A rhombus has sides of length \( 1 \mathrm{cm} \) and the area \( \frac{1}{2} c m^{2} \). Find the angle between the two adjacent sides of the rhombus.
\( \mathbf{A} \cdot 60^{\circ} \)
B . 75
\( c \cdot 45 \)
D. \( 30^{\circ} \)


Match the column:
List I

List II
I) Cells possess highly thickened
A) Tracheids walls with oblilateral central
human
II) Elongated tube like cells with
B) Vessels \( \quad \) thick lignified walls and tapering ends
III) Individual members are
C) Xylem \( \quad \) interconnected through parenchyma perorations in their common walls
D) Xylem
IV) Cells are living with thin fibers
A. A-II B-III C-IV D-I
B. A-II B-IV C-I D-III
C \( . \) A-III B-II C-IV D-I
D. A-II B-III C-I D-IV


\( \lim _{x \rightarrow \infty}(\sin \sqrt{x+1}-\sin \sqrt{x})= \)
A .
B. - -
\( c \cdot 0 \)
D. None of these


An aeroplane of mass \( 6000 \mathrm{kg} \) is flying at an altitude of \( 3 k m . \) If the area of the
wings is \( 30 m^{2} \) and the pressure at the lower surface of wings is \( 0.6 \times 10^{5} p a \)
the pressure on the upper surface of wings is : ( in pascal) \( \left(g=10 m s^{-2}\right) \)
A \( \cdot 5.8 \times 10^{4} \)
B. \( 6.8 \times 10^{4} \)
\( \mathbf{c} \cdot 7.8 \times 10^{4} \)
D. \( 8.8 \times 10^{4} \)


Write the name of any four waves (radiations) produced in electromagnetic spectrum.


In the experimental arrangement shown
in figure, the areas of cross-section of the wide and narrow portions of the tube
are \( 5 \mathrm{cm}^{2} \) and \( 2 \mathrm{cm}^{2} \) respectively. The
rate of flow of water through the tube is
\( 500 \mathrm{cm}^{3} \mathrm{s}^{-1} . \) The difference of
mercury levels in the U-tube is:
A. \( 0.97 \mathrm{cm} \)
в. 1.97 ст
\( \mathrm{c} .0 .67 \mathrm{cm} \)
D. \( 4.67 \mathrm{cm} \)


Assume that the nuclear binding energy
per nuclear \( (B / A) \) versus mass
number \( (A) \) as shown in the figure. Use
this plot to choose the correct choice \( (s) \)
given below.
A. Fusion of two nuclei with mass number lying in the range of \( 51<A<100 \) will release energy
B. Fission of a nucleus lying in the mass range of \( 200< \) \( A<260 \) will release energy when broken into two
equal fragments
c. Both (a) and (b)
D. None of the above


Isotopes are the atoms of
element having the atomic
number but \( _{-}-\ldots-_{-} \) mass number


Which of the following statements about a catalyst is/are true?
This question has multiple correct options
A. A catalyst accelerates the reaction by bringing down the energy of activation.
B. A catalyst does not take part in the reaction.
C. A catalyst makes the reaction more feasible by making the \( \Delta G^{\circ} \) more negative.
D. A catalyst makes the equilibrium constant of the reaction more favourable for the forward reaction.


Which of the following relation is
correct.
A \( .3(x-9)=3 x-27 \)
B. \( 3(x-9)=3 x-24 \)
c. \( 3(x-8)=3 x-27 \)
D. None


\( \mathbb{R} \) 4
4
6


A \( 2 \mathrm{KW} \) heater of capacity 10 litres is
used for heating water. The time required to raise the temperature of water by \( 10 \mathrm{K} \) is
\( A \cdot 210 S \)
B. 180 s
c. 240 s
D. 150


\( \operatorname{Given} \vec{P}=2 \hat{i}-3 \hat{j}+4 \widehat{k} \) and \( Q=\hat{j}- \)
2 \( \widehat{k} \). The magnitude of their resultant is:
A. \( \sqrt{3} \)
B. \( 2 \sqrt{3} \)
c. \( 3 \sqrt{3} \)
D. \( 4 \sqrt{3} \)


Find \( \left|\begin{array}{ll}\cos \alpha & -\sin \alpha \\ \sin \alpha & \cos \alpha\end{array}\right| \)


Factorize the following expression \( 9 x^{2}+y^{2}+1-6 x y+6 x-2 y \)
A \( \cdot(3 x-y+1)^{2} \)
в. \( (3 x-y+1)^{3} \)
c. \( (3 x-y-1)^{2} \)
D. None of these


In the following gaseous phase first order reaction
\( \boldsymbol{A}(\boldsymbol{g}) \rightarrow \boldsymbol{2} \boldsymbol{B}(\boldsymbol{g})+\boldsymbol{C}(\boldsymbol{g}) \)
initial pressure was found to be 400
\( \mathrm{mm} \) of \( \mathrm{Hg} \) and it changed to \( 1000 \mathrm{mm} \) of \( H g \) after \( \$ \$ 20 \$ 4 \) min. Then:
This question has multiple correct options
A. half life for \( A \) is 10 min
B. rate constant is \( 0.0693 \mathrm{min}^{-1} \)
c. partial pressure of \( C \) at 30 min is 350 mm of \( H g \)
D. total pressure after 30 min is 1100 mm of \( H g \)


Which life process is classified as
autotrophic in some organisms and heterotrophic in others?
A. Hormonal regulation
B. Nutrition
c. Anaerobic respiration
D. Transport


If \( \frac{7}{2} x+\frac{5}{2} y=5 ; 4 x+2 y=7, \) then
what is the value of \( \boldsymbol{x}-\boldsymbol{y} ? \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. 4
c. 2
D. -


The number of ways in which a mixed
doubles tennis game can be arranged between 10 players consisting of 6 men and 4 women is
A . 180
B. 90
\( c \cdot 48 \)
\( D \cdot 12 \)


One joule is approximately equal to:
A. 0.28 call \( l \)
в. 0.32 сад \( l \)
c. 0.24 call \( l \)
D. 4.2 call \( l \)


Trans-form of rubber is called
A. Isoprene
B. Neoprene
c. Gutta percha
D. Glyptal


The amplitudes \( E_{0} \) and \( B_{0} \) of electric
and the magnetic component of an electromagnetic wave respectively are
related to the velocity \( c \) in vacuum as
A \( \cdot E_{0} B_{0}=\frac{1}{c} \)
B \( \cdot E_{0}=\frac{c}{B_{0}} \)
c. \( B_{0}=c E_{0} \)
D. \( E_{0}=c B_{0} \)
E \( . E_{0}=c^{3} B_{0} \)


When a tree with a flexible stem is
shaken vigorously,its fruits and leaves fall own.This phenomenon can be
explained by making use of
A. Newton's first law of motion
B. Newton's second law of motion
c. Newton's third law of motion
D. Law of conservation of momentum


For the standardization of \( B a(O H)_{2} \) solution, 0.204 g of potassium acid phthalate was weighed which was then
titrated with \( B a(O H)_{2} \) solution. The titration indicated equivalence at 25.0
\( \mathrm{ml} \) of \( B a(O H)_{2} \) solution. The reaction involved is:
\( \boldsymbol{K} \boldsymbol{H} \boldsymbol{C}_{8} \boldsymbol{H}_{4} \boldsymbol{O}_{4}+\boldsymbol{B} \boldsymbol{a}(\boldsymbol{O} \boldsymbol{H})_{2} \rightarrow \boldsymbol{H}_{2} \boldsymbol{O}+ \)
\( \boldsymbol{K}^{+}+\boldsymbol{B} \boldsymbol{a}^{2+}+\boldsymbol{C}_{8} \boldsymbol{H}_{4} \boldsymbol{O}_{4}^{2-} \)
The molarity of the base solution is \( (K= \)
39)
A. \( 0.04 \mathrm{M} \)
в. о.озм
c. о.о२м
D. 0.01M


What is the percentage of pyridine
\( \left(C_{5} H_{5} N\right) \) that forms pyridinium ion
\( \left(C_{5} H_{5} N^{+} H\right) \) in a 0.10 M aqueous
pyridine solution \( \left(\boldsymbol{K}_{\boldsymbol{b}} \text { for } \boldsymbol{C}_{\mathbf{5}} \boldsymbol{H}_{\mathbf{5}} \boldsymbol{N}=\right. \)
\( \left.1.7 \times 10^{-9}\right) ? \)
A . 0.77\%
B . 1.6\%
c. \( 0.0060 \% \)
D. 0.013\%


The Indian goat breeds Jamunapari is
found in:
A. Uttar Pradesh
B. Madhya Pradesh
c. Himachal Pradesh
D. Haryana


In reflex action, the reflex arc is formed
by
A. Brain \( \rightarrow \) spinal cord \( \rightarrow \) muscles
B. Receptor \( \rightarrow \) spinal cord \( \rightarrow \) muscles
c. Muscle \( \rightarrow \) receptor \( \rightarrow \) brain
D. Muscles \( \rightarrow \) spinal cord \( \rightarrow \) receptor


Evaluate \( \int_{0}^{2}\left(x^{2}+2\right) d x \)


A first order reaction takes 40 min for
\( 30 \% \) decompsoition. The value of \( t_{1 / 2} \) will be:
A. \( 97.7 \mathrm{min} \)
B. 77.7 min
c. \( 80.5 \mathrm{min} \)
D. \( 70.7 \mathrm{min} \)


The magnification of an image by a convex lens is positive only when the project is placed:
A. at its focus \( F \)
B. between \( F \) and \( 2 F \)
c. at \( 2 F \)
D. between \( F \) and optical centre
E. beyond \( 2 F \)


Spleen and thymus are haematopoietic
for
A. RBC
в. wвс
c. Platelets
D. All of the above


The value of wavelength of radiation emitted due to transition of electrons
from \( n=4 \) to \( n=2 \) state in hydrogen atom
will be
A \( \cdot \frac{5 R}{36} \)
в. \( \frac{16}{3 R} \)
c. \( \frac{36}{5 R} \)
D. \( \frac{3 R}{16} \)


India does not share land frontier with
the following country
A. Myanmar
B. Pakistan
c. Nepal
D. Srilanka


Which of the following is a chemical change?
A. Breaking of a brick
B. Evaporation of a liquid
c. Burning of a candle
D. Moving of a wheel


The value of expression \( \frac{(2 \tan 4+3 \cot 4)(2 \cot 4+3 \tan 4)}{24 \cot ^{2} 8+25} \) is
\( A \)
B. 2
\( c \cdot 3 \)
\( D \)


The most appropriate definition for neuroglial cells are that, they
are
A. Nonsensory supporting cells
B. Secretory cells
c. sensory cells
D. Sensory and supporting cells
E. Nonsensory supporting or secretory cells


Atomic spectrum should be:
A. Pure line spectrum
B. Emission band spectrummm
D. Absorption band spectrum


Water enters through end \( A \) with a
speed \( v_{1} \) and leaves through end \( B \) with
a speed \( v_{2} \) of a cylindrical tube \( A B \). The
tube is always completely filled with
water In case \( I \) the tube is horizontal,
in case \( I I \) it is vertical with the end \( A \)
upward and in case \( I I I \) it is vertical
with the end \( B \) upward. We have \( v_{1}= \)
\( \boldsymbol{v}_{2} \) for
A . case I
B. case II
c. case \( I I I \)
D. each case


The type of soil suitable for growing masoor dal is:
A. sandy soil
B. loamy soil
c. clayey soil
D. bricks


Which instrument converts mechanical
energy into electrical energy?
A. Electric motor
B. Electric iron
c. Electric generator
D. Electric oven


Solve \( \frac{1}{1+i} \)


If \( \boldsymbol{x}=\boldsymbol{m}+\mathbf{1} \) and \( \frac{\mathbf{1}}{\mathbf{3}}(\mathbf{6} \boldsymbol{x}-\mathbf{3})-(\mathbf{8}- \)
\( \mathbf{3} \boldsymbol{x})=\mathbf{1 1} ; \) find the value of \( \mathbf{m} \)
A \( . m=2 \)
в. \( m=3 \)
c. \( m=7 \)
D. \( m=5 \)


A dorsal horn is present on the of mulberry silk worm (caterpillar)
A. Head
B. \( 8^{\text {th}} \) abdominal segment
c. \( 5^{t h} \) abdominal segment
D. \( 2^{n d} \) thorasic segment


Suppose you have focused on a screen the image of candle flame placed at the farthest end of the laboratory table using a convex lens. If your teacher suggests you to focus the parallel rays of the sun, reaching your laboratory table, on the same screen, what you are expected to do is to move the:
A. Lens slightly towards the screen
B. Lens slightly away from the screen
c. Lens slightly towards the sun
D. Lens and screen both towards the sun


Choose the correct statements from the
following:
This question has multiple correct options
A. the general form of Newton's second law of motion is \( \vec{F}_{e x t}=\vec{m} a \)
B. a body can have energy and get no momentum.
C. a body having momentum must necessarily have kinetic energy.
D. the relative velocity of two bodies in a head-on elastic collision remains unchanged in magnitude and direction.


Which of the following is an antacid?
A. Rantidine
B. Histamine
c. Cimetidine
D. All of the above


The acceleration due to gravity on the surface of a planet, whose mass and diameter are double that of the earth,
is \( \times 10^{-1} \) times the acceleration due to gravity on the surface of the earth.
A. 5
B. 3
\( c \cdot 0.5 \)
D. 50


If you made a map of magnetic field lines at Melbourne in Australia, then the magnetic field lines seem to be
A. go into the ground
B. come out of the ground
c. maintain a spiral path on the surface of earth
D. move on helical path above the surface of ground


How many atoms of oxygen are present
in 300 grams of \( C a C O_{3} ? \)
B . \( 18.06 \times 10^{23} \)
c. \( 36.12 \times 10^{23} \)
D. \( 12.04 \times 10^{23} \)


rectangular conductor \( L M N O \) is placed in a uniform magnetic field of \( 0.5 T . \) The field is directed
perpendicular to the plane of the conductor. When the arm \( M N \) of length \( 20 \mathrm{cm} \) is moved towards left with
velocity of \( 10 m s^{-1} \) calculate the emf
induced in the arm. Given the
resistance of the arm to be \( 5 \Omega \) assuming that other arms are of regligible resistance) find the value of
the current in the arm
\( \left.\begin{array}{l}\mathbf{X}_{\mathrm{L}} \mathbf{X}^{\overrightarrow{\mathbf{B}}} \mathbf{X} & \mathbf{X} \times \mathbf{X} \\ \mathbf{X} \\ \mathbf{X} \\ \mathbf{X} & \mathbf{X} & \mathbf{X} \\ \mathbf{X} & \mathbf{X} & \mathbf{X} \mathbf{X} \\ \mathbf{X} & \mathbf{X} & \mathbf{X} \mathbf{X} \\ \mathbf{X} & \mathbf{X} & \mathbf{X} \\ \mathbf{X} & \mathbf{X} & \mathbf{X} & \mathbf{X} \\ \mathbf{X}^{\mathbf{o}} & \mathbf{X} & \mathbf{X} & \mathbf{X}\end{array}\right] \underset{\mathbf{X}}{\mathbf{X}}_{\mathbf{X}} \mathbf{X}_{\mathbf{X}} \mathbf{X}_{\mathbf{X}} \mathbf{X} \)


Rate of substitution reaction in phenol
is:
A. slower then the rate of benzene
B. faster than the rate of benzene
c. equal to the rate of benzene
D. none of these


Find the equation to the circle :
Whose radius is \( \sqrt{a^{2}-b^{2}} \) and whose
center is \( (-a,-b) \)


Balance the following equation by ion electron method.
\( \boldsymbol{C r}_{2} \boldsymbol{O}_{7}^{2-}+\boldsymbol{H}^{+}+\boldsymbol{C}_{2} \boldsymbol{O}_{4}^{2-} \rightarrow \boldsymbol{C r}^{3+}+ \)
\( \boldsymbol{C O}_{2}+\boldsymbol{H}_{2} \boldsymbol{O} \)


Assertion
\( H_{2} O \) is stronger acid than \( D_{2} O \)
Reason
At \( 25^{\circ} \mathrm{C} \) ionic product of water is \( 1.0 \times \)
\( 10^{-14} \) and that of \( D_{2} O \) is \( 1.35 \times 10^{-15} \)
Read the above assertion and reason
and choose the correct option regarding
¡t.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


\( S O_{2} \) is a dangerous air pollutant and harms plant life. What changes in the plant indicates its toxic effects?
A. Darkening of leaves
B. Withering of leaves
c. Falling of leaves
D. Bleaching of leaves


Find the electric flux through each of
the six cube faces \( S_{1}, S_{2}, S_{3}, S_{4}, S_{5} \) and
\( \boldsymbol{S}_{6} \)


Which of the following statements are
true about the alkali metals?
This question has multiple correct options
A. All alkali-metal salts impart a characteristic colour to the Bunsen flame.
B. Among LiOH, CsOH, KOH, and RbOH, CsOH has the highest solubility in water.
C. Among the alkali metals, cesium is the most reactive.
D. The reducing character of the alkali metal hydrides follow the order: \( L i H>N a H>K H>R b H>C s H \)


A stone of mass \( m \) is tied to an elastic
string of negligble mass and spring constant k. The unstretched length of
the string is \( L \) and has negligible mass. The other end of the string is fixed to a
nail at a point P. Initially the stone is at the same level as the point P. The stone is dropped vertically from point P.
(a) Find the distance y from the top
when the mass comes to rest for an
instant, for the first time.
(b) What is the maximum velocity
attained by the stone in this drop?
(c) What shall be the nature of the
motion after the stone has reached its
lowest point?


If the line passing through the origin
makes angles \( \theta_{1}, \theta_{2}, \theta_{3} \) with the planes
\( X O Y, X O Z \) and \( Z O X \) respectively
then prove that \( \cos ^{2} \theta_{1}+\cos ^{2} \theta_{2}+ \)
\( \cos ^{2} \theta_{3}=2 \)


The electricity tariff in a town is \( R s .3 .00 \)
per unit. Calculate the cost of running
an \( 80 W \) fan for \( 10 h \) a day for the month
of June.
A . \( R s .12 .00 \)
в. \( R s .52 .00 \)
c. \( R s .72 .00 \)
D. Rs.92.00.


Assertion
\( (A): \) If \( A=(300)^{600}, B=600 !, C= \)
\( (200)^{600}, \) then \( A>B>C \)
Reason
\( (\mathrm{R}):\left(\frac{n}{2}\right)^{n}>n !>\left(\frac{n}{3}\right)^{n} \) for \( n>6 \)
A. Both (A) \& (R) are individually true \& (R) is correct explanation of (A).
B. Both (A) \& (R) are individually true but (R) is not the correct (proper) explanation of (A)
c. (A) is true but (R) is false.
D. (A) is false but (R) is true.


Photorespiration is a characteristic of
A. CAM plants
B. \( C_{3} \) plants
C \( . C_{4} \) plants
D. None of the above


Which of the following is the only natural satellite sent by ISRO to moon?
A. PSVL
B. GSLV
c. chandrayaan- -
D. None of the above


The mean deviation of the numbers
\( \mathbf{3}, \mathbf{4}, \mathbf{5}, \mathbf{6}, \mathbf{7} \) from mean is
A . 25
B. 5
c. 1.2
\( D \)


The image of an object form at the distance of distinct vision from the lens
of a simple microscope of focal length \( 2.5 \mathrm{cm} . \) It magnifying power is


The potential difference between points \( A \) and \( B \) in the circuit shown in figure
is \( 16 \mathrm{V} \). Then,
This question has multiple correct options
A. the current through the \( 2 \Omega \) resistance is 3.5 A
B. the current through the \( 4 \Omega \) resistance is 2.5 A
c. the current through the \( 3 \Omega \) resistance is 1.5 A
D. the potential difference between the terminals of the V battery is 7 V


Find solution for \( D E \Rightarrow\left(\frac{d y}{d x}\right)^{2} \) \( \boldsymbol{y} \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}+\boldsymbol{x}=\mathbf{0} \)


In the silver plating of copper,
\( \boldsymbol{K}\left[\boldsymbol{A} \boldsymbol{g}(\boldsymbol{C} \boldsymbol{N})_{2}\right] \) is used instead of
\( A g N O_{3} . \) The reason is :
\( A \). a thin layer of \( A g \) is formed on \( C u \)
B. more voltage is required
C. \( A g^{+} \) ions are completely removed from solution
D. less availability of \( A g^{+} \) ions, as \( C u \) cannot displace
\( A g \) from \( \left[A g(C N)_{2}\right]^{-} \) ion


The functional group present in organic acid is:
\( \mathbf{A} \cdot-O H \)
в. \( -C H O \)
\( \mathrm{c} .-\mathrm{COOH} \)
\( \mathbf{D} \cdot>C=O \)


With due regards to significant figures
\( 5.4 \times 0.125 \) is equal to:
A. 0.7
B. 0.68
c. 0.667
D. none of these


A liquid with coefficient of volume
expansion \( \gamma \) is filled in a container of a
material having coefficient of linear
expansion \( \alpha \). If the liquid overflows on
heating, then:
A \( \cdot \gamma=3 \alpha \)
в. \( \gamma>3 \alpha \)
c. \( \gamma<3 \alpha \)
D . \( \gamma=a^{3} \)


Nuclear membrane disappears in
A. Late prophase
B. Early prophase
c. Metaphase
D. Telophase


Full form of OCTEC is:
A. Ocean Thermal Energy Conversion Power Plant.
B. Ocean Thermal Consumer Energy Power Plant.
C. Ocean Current Thermal Energy Cycle.
D. Ocean Current Thermal Electric Plant.


Which term of the sequence 72,70,68
\( 66, \dots \) is \( 40 ? \)
A . 14
B. 15
\( c \cdot 16 \)
\( D \cdot 17 \)


State true or false:
In triangle \( A B C, P \) is the mid-point of
side \( B C . \) A line through \( P \) and Parallel to \( C A \) meets \( A B \) at point \( Q ; \) and a line through \( Q \) and parallel to \( B C \) meets
median \( A P \) at point \( R \). Can it be
concluded that,
\( \boldsymbol{A P}=\boldsymbol{2} \boldsymbol{A} \boldsymbol{R} ? \)
A. True
B. False


Evaluate the determinant :
\( \left|\begin{array}{cc}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta\end{array}\right| \)


Construct \( \triangle A B C \) such that \( A B= \)
\( 2.5 c m, B C=6 c m \) and \( A C=6.5 c m \)
Measure \( \angle B \)


The basic building unit of protein is:
A. polypeptide
B. amino acids
\( c . \) amines
D. carboxylic acids


Chlorine cannot be used for
delicate materials.


Integrate the rational function \( \frac{1}{x^{4}-1} \)


Nitrogen molecule, in which each nitrogen atom has electrons
in its valence shell and required three electrons to complete the octet.
A. 5
B. 4
\( c \cdot 3 \)
\( D .2 \)


How many grams of concentrated sulphuric acid \( (80 \% w / w) \) should be
used to prepare \( 100 m L \) of one molar
\( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} ? \)
A . \( 10 g \)
в. 12.25 g
c. \( 15 g \)
D. \( 17.5 g \)


Where does the center of gravity of the
atmosphere of the earth lie?


f an annular disc of radii \( r_{1} \) and \( r_{2} \) is
heated, then
A \( \cdot r_{1} \) increases, \( r_{2} \) decreases
B. \( r_{2} \) increases, \( r_{1} \) decreases
\( c \cdot \operatorname{both} r_{1} \) and \( r_{2} \) increase
\( \mathrm{D} \cdot r_{2} \) increases, \( r_{1} \) remains unchanged


Roots of the equation \( \boldsymbol{x}^{3}-(\boldsymbol{a}+\boldsymbol{b}+ \)
\( c) x^{2}+(a b+b c+c a) x-a b c=0 \)
\( x^{2}+2 x+7=0 \) and \( a x^{2}+b x+c=0 \)
have a common root, where \( a, b, c \in R, \) can
be
A .4,8,28
В. 1,2,7
c. 1,4,36
D. None of the above


\( \lim _{x \rightarrow 0}\left(1+\frac{2}{x^{2}}\right)^{x^{2}}= \)
\( A \)
B. e
\( c \cdot e^{2} \)
D. None of these


Nitrobenzene can be prepared by heating with a mixture of concentrated
\( H N O_{3} \) and concentrated \( H_{2} S O_{4} . \) In
this nitrating mixture, \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3}, \) acts as
A. A base
B. An acid
c. A catalys
D. A reducing agent


The force of attraction between the
plates of a charged condenser is :
A \( \cdot q^{2}\left(2 \varepsilon_{0} A\right) \)
B \( \cdot q^{2}\left(2 \varepsilon_{0} A^{2}\right) \)
\( \mathbf{c} \cdot q^{2} /\left(2 \varepsilon_{0} A\right) \)
D. none of these


Write the principle of working of a meter
bridge


If \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R}, \boldsymbol{g}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) are defined by
\( \boldsymbol{f}(\boldsymbol{x})=\mathbf{5} \boldsymbol{x}-\boldsymbol{3}, \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{x}^{2}+\boldsymbol{3}, \) then
\( \left(g o f^{-} 1\right)(3)= \)
A \( \cdot \frac{25}{7} \)
в. \( \frac{111}{25} \)
c. \( \frac{9}{25} \)
D. \( \frac{25}{111} \)


The light enters our eye through the transparent through the and is focused
on the The is
sensitive to light and sends images to our brain through
A. cornea, lens, retina, retina, optic nerve
B. retina,cornea, lens, retina, optic nerve
c. retina, cornea, lens, optic nerve , retina
D. cornea,retina, lens, retina, optic nerve


Arrange the following lengths in their increasing magnitude:
1 metre, 1 centimetre, 1 kilometre,
1 millimetre.


Sum of measures of angles of a
Nonagon is \( 1260^{\circ} . \) Find how much each
angle is measured.
A \( \cdot 100^{\circ} \)
B . \( 140^{\circ} \)
\( c \cdot 108^{\circ} \)
D. \( 90^{\circ} \)


In which of the following entropy
increases?

This question has multiple correct options
A. rusting of iron
B. melting of ice
c. crystallisation of sugar from solution
D. vaporisation of camphor


Which of the following lines is parallel
to the line \( 3 x-2 y+6=0 ? \)
A. \( 3 x+2 y-12=0 \)
в. \( 4 x-9 y=6 \)
c. \( 12 x+18 y=15 \)
D. \( 15 x-10 y-9=0 \)


If nth term of an A.P is \( (2 n+1), \) what is the sum of its first three terms?


The domain of \( \boldsymbol{f}(\boldsymbol{x})=\frac{1}{\sqrt{(\boldsymbol{x}-\mathbf{1})(\boldsymbol{x}-\mathbf{2})(\boldsymbol{x}-\mathbf{3})}} \)
is
\( \mathbf{A} \cdot(-\infty, 1) \cup(3, \infty) \)
B. (1,2)\( \cup(3, \infty) \)
\( \mathbf{c} \cdot(-\infty, 2) \)
D. R


The ratio of angular velocity of rotation of minute hand of a clock with the
angular velocity of rotation of the earth
about its own axis is
A \( \cdot 12 \)
B. 6
\( c \cdot 24 \)
D. none of these


In a race of 12 cars, the probability that \( \operatorname{car} A \) will win is \( \frac{1}{5} \) and of \( \operatorname{car} B \) is \( \frac{1}{6} \)
and that of car \( C \) is \( \frac{1}{3} . \) Find the probability that only one of them won the race.


Plants which are shorter than trees and
have a bushy appearance, called as
A. Short trees
B. Shrubs
c. Bushes
D. sporophytes


A block of mass 2 kg rests on a rough
inclined plane making an angle of \( 30^{\circ} \)
with the horizontal. The coefficient of
static friction between the block and
the plane is \( 0.7 . \) The frictional force on
the block is
\( \mathbf{A} \cdot 9.8 N \)
в. \( 0.7 \times 9.8 \times \sqrt{3} N \)
c. \( 9.8 \times \sqrt{3} N \)
D. \( 0.7 \times 9.8 N \)


Energy possessed by a body by virtue of its motion is :
A. Potential energy
B. Kinetic energy
c. Chemical energy
D. Electrical energy


Aqua regia consists of:
A. hydrochloric acid
B. carbonic acid
C. nitric acid
D. both \( A \) and \( C \)


Explain why:
Hydride of sulphur is a gas while
hydride of oxygen is a liquid.


The drift velocity of the electron in a
copper wire of length \( 2 \mathrm{m} \) under the application of a potential difference of
\( 200 \mathrm{V} \) is \( 0.5 \mathrm{ms}^{-1} \).Their mobility is (in
\( \left.m^{-2} V^{-1} s^{-1}\right) \)
\( \mathbf{A} \cdot 5 \times 10^{-3} \)
B. \( 2.5 \times 10^{-2} \)
c. \( 5 \times 10^{2} \)
D. \( 10^{-3} \)


The value of \( 2 \frac{1}{2} \times 10-4 \frac{1}{3} \times 10 \) is
A \( \cdot \frac{-3}{55} \)
в. \( \frac{3}{55} \)
c. \( \frac{55}{3} \)
D. \( \frac{-55}{3} \)


If \( \vec{a}, \vec{b}, \vec{c} \) are mutually perpendicular vectors of equal magnitudes, then the angle between the vectors \( \vec{a} \) and \( \vec{a}+ \) \( \vec{b}+\vec{c} \) is
A \( \cdot \frac{\pi}{3} \)
в.
\( ^{\mathrm{c}} \cdot \cos ^{-1}\left(\frac{1}{\sqrt{3}}\right) \)
D.


Which of the following are main requirements for vapour phase refining?
(i) Metal should form a volatile
compound with the reagent.
(ii) The volatile compound should be easily decomposable to give back pure
metal.
(iiii) Metal should be very reactive and form a stable compound with the
reagent.
A. (i), (ii) and (iii)
B. (i) and (ii)
c. (ii) and (iii)
D. (i) and (iii)


In which one of the followings, expenditure of energy is required?
A. Osmosis
B. Diffusion
c. Active transport
D. Passive transport


In diborane, the banana bond is formed
between:
A. 2 electrons, 3 atoms
B. 2 electrons, 1 atom
c. 1 electron, 2 atoms
D. 2 electrons, 2 atoms


A mark placed on the surface of a sphere is viewed through glass from a position directly opposite as shown in
the figure. The diameter of the sphere is
\( 30 \mathrm{cm} \) and refractive index of glass is
1.5. The position of the image is


A ray of light is normally incident on one face of an equilateral glass prism. Will the light ray suffer minimum deviation
by the prism?
A . True
B. False


Which of the following reactions can take place in the reverberatory furnace?
A. \( z n 0+c \rightarrow z n+c 0 \)
B. \( 2 \mathrm{Cu}_{2} \mathrm{S}+3 \mathrm{O}_{2} \rightarrow 2 \mathrm{Cu}_{2} \mathrm{O}+2 \mathrm{SO}_{2} \)
\( \mathrm{c} \cdot \mathrm{HgS}+\mathrm{O}_{2} \rightarrow \mathrm{Hg}+\mathrm{SO}_{2} \)
D. \( \mathrm{PbCO}_{3} \rightarrow \mathrm{PbO}+\mathrm{CO}_{2} \)


How many different words can be
formed from the letters of the word
GANESHPURI when:
The vowels are always together


The mean and S.D of 100 observations
are 50 and 4 respectively. Find the sum of squares of observation.


The angular momentum of a system as
particle is conserved
A. when no external force acts upon the system
B. when no external torque acts upon the system
C. when no external impulse acts upon the system
D. when axis of rotation remains same


Banking of roads is done due to
A. provide enough friction for circular motion of the vehicle
B. provide necessary centripetal force required for circular motion of the vehicle
C. provide enough radius of curvature for circular motion of the vehicle
D. provide enough area for navigating in the circular motion of the vehicle


Phenolphthalein and methyl orange are themselves:
A. weak acid and weak base respectively
B. both weak acid
c. both weak base
D. weak base and weak acid respectively


Complere the reaction.
(ii)
fin


A mixture of \( N_{2} \) and \( H_{2} \) is the molar
ratio 1: 3 at 50 atm and 650 is allowed
to react till equilibrium is obtained. The
\( N H_{3} \) present at equilibrium is \( 25 \% \) by
weight, \( \boldsymbol{K}_{\boldsymbol{p}} \) for
\[
\begin{array}{r}
\boldsymbol{N}_{2}+\mathbf{3} \boldsymbol{H}_{2} \rightleftharpoons \mathbf{2} \boldsymbol{N} \boldsymbol{H}_{3} \\
\text { is } \boldsymbol{X} \times \mathbf{1 0}^{-4} \boldsymbol{a} \boldsymbol{t m}^{-2} \cdot(\mathbf{1 0 0 0} \boldsymbol{X})
\end{array}
\]
is
A \( \cdot 1434 \)
B. 35844
c. 21370
D. none of these


Sudha finds out that the sharp image of the window pane of her science laboratory is formed at a distance of \( 15 c m \) from the lens. She now tries to
focus the building visible to her outside the window instead of the window pane
without disturbing the lens. In which direction will she move the screen to
obtain a sharp image of the building? What is the approximate focal length of this lens?


Alveoli increase the surface area of the
human lung which is approximately the size of a:
A. tennis court
B. dining table
c. dinner plate
D. small bowl


ff \( f(x)+f(1-x)=10, \) then the value
of \( \boldsymbol{f}\left(\frac{1}{10}\right)+\boldsymbol{f}\left(\frac{2}{10}\right)+\ldots \ldots \ldots+\boldsymbol{f}\left(\frac{9}{10}\right) \) is
A . 45
B . 50
\( c .90 \)
D. Cannot be determined


\( \operatorname{Let} \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{l}\sin \boldsymbol{x}, \boldsymbol{x} \neq \boldsymbol{n} \boldsymbol{\pi} \\ \boldsymbol{2}, \boldsymbol{x}=\boldsymbol{n} \boldsymbol{\pi}\end{array}, \text { where } \boldsymbol{n} \boldsymbol{\epsilon} \mathbb{Z}\right. \)
and
\( \boldsymbol{g}(\boldsymbol{x})=\left\{\begin{array}{l}\boldsymbol{x}^{2}+\mathbf{1}, \boldsymbol{x} \neq \mathbf{2} \\ \boldsymbol{3}, \boldsymbol{x}=\mathbf{2}\end{array}\right. \)
Then \( \lim _{x \rightarrow 0} g(f(x)) \) is
\( A \)
B.
\( c \cdot 3 \)
D. none of these


Show that \( y=\log (1+x)-\frac{2 x}{2+x}, x> \)
\( -1, \) is an increasing function of \( x \)
throughout its domain.


The sequence that correctly represents the increasing order of bond angles in
\( O F_{2}, O C l_{2}, C l O_{2} \) and \( H_{2} O \) is :
A. \( O F_{2}<H_{2} O<O C l_{2}<C l O_{2} \)
в. \( H_{2} O<F_{2} O<C l_{2} O<C l O_{2} \)
c. \( O F_{2}<C l_{2} O<H_{2} O<C l O_{2} \)
D. \( C l O_{2}<C l_{2} O<O F_{2}<H_{2} O \)


Which labelled parts of the heart pump
deoxygenated blood to lungs?
A .1,2 and 6
B. 1,2 and 7
\( c \cdot 2,4 \) and 6
D. 3,4 and 5
E. 3, 4 and 8


The enzyme responsible for primary
carboxylation in \( C_{3} \) plants is
A. Hexokinase
B. Succinic dehydrogenase
c. Pyruvate carboxylase
D. RuBP carboxylase oxygenase


For adsorption of a gas on solid surface, the plot of \( \log \frac{x}{m} \) vs \( \log P \) is linear with
slope equal to:
\( \mathbf{A} \cdot K \)
в. \( \log K \)
c. \( \frac{1}{n K} \)
D. \( \frac{1}{n}(n \text { being integer }) \)


The equation of the circle passing
through (3,6) and whose centre is (2,-1) is
A \( \cdot x^{2}+y^{2}-4 x+2 y=45 \)
B . \( x^{2}+y^{2}-2 y+45=0 \)
c. \( x^{2}+y^{2}+4 x-2 y=45 \)
D. \( x^{2}+y^{2}+2 y+45=0 \)


An object is placed at \( 20 \mathrm{cm} \) in front of a concave mirror produces three times magnified real image. What is focal length of the concave mirror?
\( A \cdot 15 \mathrm{cm} \)
B. 6.6 \( \mathrm{cm} \)
c. \( 10 \mathrm{cm} \)
D. 7.5 cm


\( \int x \cdot\left(x^{x}\right)^{x}(2 \log x+1) d x \)
\( \mathbf{A} \cdot x^{\left(x^{x}\right)}+c \)
B. \( \left(x^{x}\right)^{x}+c \)
c. \( x^{x} \cdot \log x+c \)
D. does not exist


Suppose a lot of \( n \) objects having \( n_{1} \)
objects of one kind, \( n_{2} \) objects are of
second kind, \( n_{3} \) objects of third kind, \( \dots \)
\( n_{k} \) objects of \( k^{t h} \) kind satisfying the
condition \( n_{1}+n_{2} \dots+n_{k}=n, \) then the
number of possible arrangements/permutation of \( \mathrm{m} \) objects out of this lot is the coefficient
of \( x^{m} \) in the expansion of \( m ! \prod\left\{\sum_{\lambda=0}^{a_{1}} \frac{x^{\lambda}}{\lambda !}\right\} \)
The number of permutations of the letters of the word SURITI taken 4 at a
time is
A . 360
B. 240
c. 216
D. 192


\( _{3} L i^{7}+_{1} H^{2} \rightarrow_{4} B e^{8}+_{o} n^{1}+Q \)
Mass of \( _{3} L i^{7}=7.01823 a m u \)
Mass of \( _{1} H^{2}=2.01474 a m u \)
Mass of \( _{4} B e^{8}=8.00785 a m u \)
Mass of \( _{o} n^{1}=1.00899 a m u \)
Then, the value of Q is
A. 5 MeV
в. \( 10 \mathrm{MeV} \)
c. 15 MeV
D.


Assuming the formation of an ideal
solution, the boiling point of a mixture
containing 1560 g benzene (molar mass =78) and 1125 g chlorobenzene (molar" mass \( =112.5)^{\prime} \) using the given vapour
pressure vs. temperature diagram against anexternal pressure of 1000
torr, is :
\( \mathbf{A} \cdot 90^{\circ} C \)
B. \( 100^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 110^{\circ} C \)
D. \( 120^{\circ} \mathrm{C} \)


Starch undergoes hydrolysis in presence of mineral acids to form:
A. glucose
B. fructose
c. maltose
D. sucrose


Statement I: Above reaction is
exothermic.
Because
Statement II: Energy difference B is
greater than energy difference \( \mathbf{A} \)
A. true, true, correct explanation
B. true, true, not correct explanation
c. true, false
D. false, true
E. false, false


Red cell count is carried out by
A. Haemocytometer
B. Haemoglobinometer
c. Electro cardiogram
D. Sphygmomanometer


State the following statements are true
or false.

During \( G_{2} \) phase a cell contains double the amount of DNA (4n) present in the original diploid cell.
A. True
B. False


The dissolution of copper sulfate in
water is a physical change where as
that of granulated zinc in dilute hydrochloric acid is a Chemical Change.


The major product in the following
conversion is
\( A \)
\( B \)
\( c \)
\( D \)


Versene, a chelating agent has chemical formula
\( C_{2} H_{4} N_{2}\left(C_{2} H_{2} O_{2} N a\right)_{4} . \) If each mole of
this compound could bind 1 mole of
\( C a^{2+}, \) then the rating of pure versene
expressed as \( \mathrm{mg} \) of \( \mathrm{CaCO}_{3} \) bound per \( \mathrm{g} \) of chelating agent is:
A. \( 100 \mathrm{mg} \)
в. \( 163 \mathrm{mg} \)
c. \( 200 \mathrm{mg} \)


Consider the following transformations
\( \boldsymbol{I} \cdot \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{6}+\boldsymbol{N} \boldsymbol{a} \boldsymbol{F} \longrightarrow \boldsymbol{N} \boldsymbol{a}^{+}\left[\boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{7}\right]^{-} \)
\( \boldsymbol{I} \boldsymbol{I} \cdot \boldsymbol{2} \boldsymbol{P} \boldsymbol{C l}_{5}(\boldsymbol{s}) \longrightarrow\left[\boldsymbol{P} \boldsymbol{C l}_{4}\right]^{+}\left[\boldsymbol{P} \boldsymbol{C l}_{6}\right]^{-} \)
\( \boldsymbol{I I I} \cdot\left[A l\left(H_{2} O\right)_{6}\right]^{3+}+H_{2} O \longrightarrow \)
\( \left[A l\left(H_{2} O\right)_{5} O H\right]^{2+}+H_{3} O^{+} \)
Possible transformations are:
A. \( I, I I, I I I \)
В. \( I, I I I \)
c. \( I, I I \)
D. II, III


A bag contains 4 identical red balls and
3 identical black balls. The experiment consists of drawing one ball, then putting it into the bag and again drawing a ball. What are the possible outcomes of the experiment?


Give balanced equations for the following reactions?
Ozone and mercury.


resistances are connected as shown in
the figure. Initially resistance \( \boldsymbol{P}=4 \Omega \)
and the neutral point \( N \) is at \( 60 c m \)
from \( A . \) Now an unknown resistance \( \boldsymbol{R} \)
is connected in series to \( \boldsymbol{P} \) and the new
position of the neutral point is at \( 80 c m \)
from \( A \). The value of unknown
resistance \( \boldsymbol{R} \) is :
\( \mathbf{A} \cdot 6 \Omega \)
B. \( 7 \Omega \)
c. \( \frac{33}{5} \Omega \)
D. \( \frac{20}{3} \Omega \)


What is the approximation made in
the parallax method?
A. All distances measured between two points on earth is zero
B. All distances measured between two points on earth is constant
c. Distance between a point on the earth and the planet is very large as compared to the distance between two points on earth's surface.
D. No approximation is made


\( 11.6 g \) of an organic compound having
formula \( C_{n} H_{2 n+2} \) is burnt in excess of
\( O_{2}(g) \) initially taken in a 22.41 litre
steel vessel. Before reaction the
gaseous mixture was at \( 273 K \) with
pressure reading 2atm. After complete
combustion and loss of consideration
amount of heat, the mixture of product
and excess of \( O_{2} \) had a temperature of
\( 546 K \) and \( 4.6 a t m \) pressure. The
formula of organic compound is:
A. \( C_{2} H_{6} \)
в. \( C_{3} H_{8} \)
c. \( C_{5} H_{12} \)
D. \( C_{4} H_{10} \)


Identify most suitable options for the following vacant space. The visible light spectrum sits between the and
regions of the electromagnetic spectrum
A. infrared; ultraviolet
B. infrared; X-ray
c. infrared; gamma ray
D. microwave; ultraviolet
E. radio; ultraviolet


In an SHM, the total energy of a particle
is
A . a constant
B. increases with time
c. decreases with time
D. oscillates with time


Find the value of \( \lambda \) in the unit vector
\( \mathbf{0 . 4} \hat{\mathbf{i}}+\mathbf{0 . 8} \hat{\mathbf{j}}+\boldsymbol{\lambda} \hat{\boldsymbol{k}} \)


Construct the quadrilaterals with the given measurements.And write steps of construction.
quadrilateral ABCD with \( A B=5.5 c m \)
\( B C=3.5 c m, C D=4 c m, A D=5 c m \)
and \( \angle A=45^{\circ} \)


Which of the one is not true about redox
reactions?
A. Share of electrons
B. Transfer of electrons
c. Gain of oxygen
D. Loss of Hydrogen


Aspartame is unstable at cooking temperature. Where would you suggest
aspartame to be used for sweetening?
A. Soft drinks
B. Cold drinks
c. Both of them
D. None of these


Find the general solution of \( (x+ \) \( \left.2 y^{3}\right) \frac{d y}{d x}=y \)


A proton (mass \( 1.67 \times 10^{-27} \mathrm{kg} \) ) on striking a neutron (mass nearly equal to the proton ) forms a deutron. What would be the velocity of the deutron if it is formed by a proton moving left with a velocity of \( 7.0 \times 10^{6} \mathrm{m} / \mathrm{s} \) and a neutron
moving right with a velocity of \( 4.0 \times 10^{6} \) \( \mathrm{m} / \mathrm{s} \)


Potassium selenate is isomorphous
with potassium sulphate and contains \( 50.0 \% \) of Se. Find the atomic weight of
\( \mathbf{S e} \)
A \( \cdot 142 \)
в. 71
c. 47.33
D. 284


A ray \( O P \) of monochromatic light is
incident on the face \( A B \) of prism
\( A B C D \) near vertex \( B \) at an incident
angle of \( 60^{\circ} \) (see figure). If the refractive
index of the material of the prism is \( \sqrt{3} \) which of the following is (are) correct?
This question has multiple correct options
A. The ray gets totally internally reflected at face \( C D \)
B. The ray comes out through face \( A D \)
c. The angle between the incident ray and the emergent
ray is 90
D. The angle between the incident ray and the emergent ray is \( 120^{\circ} \)


Prove by method of induction, for all
\( \boldsymbol{n} \in \boldsymbol{N} \)
\( \mathbf{2}+\mathbf{4}+\mathbf{6}+\ldots+\mathbf{2} \boldsymbol{n}=\boldsymbol{n}(\boldsymbol{n}+\mathbf{1}) \)


1) State the law of magnetism.
2) State the law of charges.
3) What happens when a straw is rubbed with a sheet.


If the surface tension of water is \( \mathbf{0 . 0 6} N / \boldsymbol{m}, \) then the capillary rise in a
tube of a diameter 1 m \( m \) is \( :\left(\theta=0^{\circ}\right) \)
A . \( 1.22 \mathrm{cm} \)
B. 2.44 ст
\( c .3 .12 c m \)
D. \( 3.86 \mathrm{cm} \)


If \( A \) is any skew-symmetric matrix of
odd order then \( |\boldsymbol{A}| \) equals
A . -1
B. 0
c. 1
D. none of these


The voluntary muscles are known as
A. Striated muscles
B. Cardiac muscles
C. Unstriated muscles
D. None of the above


For two figures to be congruent, they need to be:
A. exactly alike
B. smaller
c. bigger
D. none of these


Multiply the given matrices:
\[
\left[\begin{array}{cc}
1 & -2 \\
2 & 3
\end{array}\right]\left[\begin{array}{ccc}
1 & 2 & 3 \\
-3 & 2 & -1
\end{array}\right]
\]


The magnetic field inside a \( 2 m H \)
inductor becomes 0.8 of its maximum
value in \( 20 \mu s \) when the inductor is
joined to battery. Find resistance of the circuit.
A . \( 160 \Omega \)
B. \( 80 \Omega \)
\( c .320 \Omega \)
D. \( 240 \Omega \)
E. none of these


Two different masses \( m \) and \( 2 m \) are
fallen from height \( \boldsymbol{H}_{1} \) and \( \boldsymbol{H}_{2} \) respectively. First mass takes t second and another takes \( 2 t \) second, then the
ratio of \( \boldsymbol{H}_{1} \) and \( \boldsymbol{H}_{2} \) is?
A .2: 1
B. 4: 1
c. 0.25: 1
D. None of these


Is this possible \( a \neq \)
\( \mathbf{0} \cdot\left|\begin{array}{ccc}\boldsymbol{x}+\mathbf{1} & \boldsymbol{x} & \boldsymbol{x} \\ \boldsymbol{x} & \boldsymbol{x}+\boldsymbol{a} & \boldsymbol{x} \\ \boldsymbol{x} & \boldsymbol{x} & \boldsymbol{x}+\boldsymbol{a}^{2}\end{array}\right|=\mathbf{0} \)
represents a straight line parallel to the
y-axis
A. True
B. False


Extranuclear inheritance (cytoplasmic inheritance) is a consequence of presence of genes in
A. Ribosomes and chloroplasts
B. Lysosomes and ribosomes
c. Mitochondria and chloroplasts
D. Endoplasmic reticulum and mitochondria


If the mid point of the line joining the points \( P(6, b-2) \) and \( Q(-2,4) \) is (2,-3) Find the value of 'b'


Using the given materials design the experiment to illustrate the change in speed of chemical reaction with temperature. Materials: Sodium thiosulphate, water,
dilute \( H C l \) boiling tubes, beaker, spirit
\( \operatorname{lamp} \)


A plot of land has a shape of a
parallelogram. It is to be covered by mud. Find the cost of speeding mud at the rate of \( R s 100 \) per square meter
while the adjacent sides of the plot are
\( \mathbf{3 9} \boldsymbol{m} \) and \( \mathbf{2 5} \boldsymbol{m} \) and the diagonal is
\( \mathbf{5 6} \boldsymbol{m} \)


\( \operatorname{Let} \theta \epsilon[0,4 \pi] \) satisfy the equation
\( (\sin \theta+2)(\sin \theta+3)(\sin \theta+4)=6 . \) If
the sum of all the values of \( \theta \) is of the
form \( k \pi \) then the value of \( k \) is


In a fraction, if numerator is increased
by 2 and denominator is decreased by 3 then the fraction becomes \( 1 . \) Instead, if
numerator is decreased by 2 and denominator is increased by 3 , then the fraction becomes \( \frac{3}{8} . \) Find the fraction.


Read the bar graph as given in above
figure and answer the following
questions:
Which Doordarshan centres are in U.P.
State? What are the areas covered by
them?
Bar of


Find the term independent of \( x \) in the expansion of \( \left(\sqrt{\frac{\boldsymbol{x}}{\mathbf{3}}}+\frac{\mathbf{3}}{\mathbf{2} \boldsymbol{x}^{2}}\right)^{10} \)
\( \mathbf{A} \cdot T_{3} \)
в. \( T_{4} \)
c. \( T_{5} \)
D. No term will be independent of \( x \)


\( P, Q \) and \( R \) are three sets and \( \xi P \cup Q \cup \)
\( R . \) Given that \( n(\xi)=60, n(P \cap Q)=5 \)
\( n(Q \cap R)=10, n(p)=20 \) and \( n(Q)=23 \)
find \( n\left(P^{\prime} \cup Q\right) \)
A. 37
3. 38
\( c \cdot 45 \)
D. 52


Which of the following will given maximum number of isomers?
\( \mathbf{A} \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{4} C l_{2}\right]^{+} \)
B . \( \left[N i(e n)\left(N H_{3}\right)_{4}\right]^{2+} \)
\( \mathbf{c} \cdot\left[\operatorname{Cr}(S C N)_{2}\left(N H_{3}\right)_{4}^{+}\right] \)
D. \( \left[N i\left(C_{2} O_{4}\right)(e n)_{2}\right]^{2} \)


The volume of \( C O_{2} \) produced at STP by
decomposition of \( 4.2 g \) of \( N a H C O_{3} \)
according to the reaction:
\( 2 N a H C O_{3} \rightarrow N a_{2} C O_{3}+H_{2} O+C O_{2} \)
\( \mathbf{A} \cdot 150 \mathrm{m} \)
B. \( 569 \mathrm{ml} \)
c. \( 1.68 L \)
D. \( 5.6 L \)


The sum of 11 terms of an A.P. Whose
middle term is 30 is \( ? \)
A. 320
в. 330
\( c \cdot 340 \)
D. 350


Find the co-ordinates of the foci, the
vertices, the length of major axis, latus rectum and the eccentricity of the conic
represented by the equation \( 3 x^{2}+ \)
\( 5 y^{2}=15 \)


Match the reactions of the List I with the
relations in the List II.


The oxidation number of \( P t \) in
\( \left[\boldsymbol{P t}\left(\boldsymbol{C}_{2} \boldsymbol{H}_{4}\right) \boldsymbol{C l}_{3}\right]^{-} \) is :


If the angle of incidence is twice the angle of refraction in a medium of refractive index \( \mu, \) then the angle of
incidence is :
A \( \cdot 2 \cos ^{-1} \frac{\mu}{2} \)
B \( \cdot 2 \sin ^{-1} \frac{\mu}{2} \)
\( \mathrm{c} \cdot 2 \cos ^{-1} \mu \)
D. \( 2 \sin ^{-1} \mu \)


A simple circuit consisting of three
resistors is shown above. \( \boldsymbol{R}_{1} \) has twice
the resistance of \( R_{2} \). If the switch
remains open, determine the ratio of
heat dissipated of \( \boldsymbol{R}_{1} \) to \( \boldsymbol{R}_{2} \)
A . 1: 3
B. 1:
\( c \cdot 1: 1 \)
D. 2:
E. 3:


When \( N a O H \) is used in making of soap, it is called as:
A . alkali soap
B. soft soap
c. hard soap
D. none of above


Mass of one molecule of glucose is(in \( \operatorname{grams} \)
A . 180
в. 270
c. \( 180 \times 1.66 \times 10^{-24} \)
D. \( 180 \times 1.66 \times 10^{-23} \)


Using the formula for the moment of
inertia of a uniform sphere, the moment
of inertia of a thin spherical layer of
mass \( m \) and radius \( R \) relative to the
axis passing through its centre is \( \boldsymbol{I}= \) \( \frac{2}{x} m r^{2} . \) Find the value of \( x \)


Which of the following among the
visible colours has the minimum
wavelength?
A. Red
B. Blue
c. Green
D. Violet


In which of the following complexes
more than one type of structural isomerism is possible? This question has multiple correct options
\( \mathbf{A} \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{5}\left(N O_{2}\right)\right] C l \)
B . \( \left[\operatorname{Co}\left(N H_{3}\right)_{5}\left(H_{2} O\right)\right]\left(N O_{2}\right)_{3} \)
\( \mathbf{c} \cdot\left[P t\left(N H_{3}\right)_{4}\right]\left[P t(S C N)_{4}\right] \)
\( \mathbf{D} \cdot\left[C r(D M G)_{3}\right] \)


The power of a lens is inversely proportional to :
A. image distance
B. object distance
c. focal length
D. none of these


When fuel is added to the exhaust
(burnt) gases in a jet engine combustion takes place. Some facts are mentioned here about this combustion.
Pick the false one?
A. It increases the intake of oxygen from the air
B. It reduces fuel consumption
c. It gives additional thrust
D. It is known as 'after burning'


The amplitude of \( \frac{1+\sqrt{3 i}}{\sqrt{3}+1} \) is
\( ^{A} \cdot \frac{\pi}{3} \)
в. \( -\frac{\pi}{3} \)
\( c \cdot \frac{\pi}{6} \)
D. \( -\frac{\pi}{6} \)


A colourless salt (X) has \( 50 \% N a_{2} S O_{3} \)
and \( 50 \% H_{2} O . \) Then (a)The formula of
\( (X) \) is
(b)The amount of \( S O_{2} \) at NTP obtained
when 2.52 g of \( (X) \) reacts with excess of
dil. \( \boldsymbol{H}_{2} \boldsymbol{S O}_{4} \) is
A \( \cdot N a_{2} S O_{3} \cdot 7 H_{2} O, 0.224 \mathrm{L} \) at \( \mathrm{NTP} \) from \( 2.52 \mathrm{g} \) of \( (\mathrm{X}) \)
B. \( N a_{2} S O_{3} \cdot 6 H_{2} O, 0.224 \mathrm{L} \) at \( \mathrm{NTP} \) from \( 2.52 \mathrm{g} \) of \( (\mathrm{X}) \)
C. \( N a_{2} S O_{3} \cdot 7 H_{2} O, 2.24 \mathrm{L} \) at NTP from 2.52 g of \( (x) \)
D. \( N a_{2} S O_{3} \cdot 6 H_{2} O, 2.24 \mathrm{L} \) at NTP from \( 2.52 \mathrm{g} \) of \( (\mathrm{X}) \)


Maximum number of unpaired electrons
are present in:
A . Tit'
B. \( s c^{+3} \)
\( c \cdot c r^{+} \)
\( D \cdot M n^{+2} \)


Sterile jacket cells around reproductive cells is characteristic of
A. Algae
B. Bryophyta
c. Fungi
D. Thallophyta


Calculate simultaneous solubility of AgCNS and AgBr in a solution of water.
[Ksp of \( A g B r=5 \times 10^{-13} \) and Ksp of
\( \left.A g C N S=1 \times 10^{-12}\right] \)
A \( \cdot 8.1610^{-7} M, 4.0810^{-7} M \)
B . \( 5.78 \times 10^{-8} M, 0.037 M \)
C. \( 0.04 M, 6.25 \times 10^{-8} M \)
D. \( 1.58 \times 10^{-3} M, 1.26 \times 10^{-5} M \)


If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that it is a rectangle.


Electric charge is due to the loss or gain
of
A. protons
B. neutrons
c. electrons
D. none of these


Mention three methods of reducing friction in a machine


Let \( U_{a} \) and \( U_{d} \) be the energy densities in air and in a dielectric of constant k for
same field. Then
\( \mathbf{A} \cdot U_{a}=U_{d} \)
в. \( U_{a}=k U_{d} \)
\( \mathbf{c} \cdot U_{d}=k U_{a} \)
D. \( U_{a}=(k-1) U_{d} \)


A particle moves along a straight line
according to the law \( s=16-2 t+3 t^{3} \)
where \( s \) metres is the distance of the
particle from a fixed point at the end of \( t \) second. The acceleration of the particle
at the end of 2 s is
A \( \cdot 3.6 m / s^{2} \)
B. \( 36 m / s^{2} \)
c. \( 36 k m / s^{2} \)
D. \( 360 m / s^{2} \)


Number of species growing in botanical gardens world wide is
A. 7500
B. 25,000
c. 57,000
D. 80,000


A midpoint of a thin uniform rod \( A B \) of
mass \( m \) and length \( l \) is rigidly fixed to a
rotation axle \( O O^{\prime} \) as shown in figure
above. The rod is set into rotation with a
constant angular velocity \( \omega . \) If the
resultant moment of the centrifugal
forces of inertia relative to the point \( \boldsymbol{C} \)
in the reference frame fixed to the axle
OO' and to the rod is given by \( N= \) \( \frac{1}{x} m \omega^{2} l^{2} \sin 2 \theta, \) then the value of \( x / 4 \) is :


Alcohols containing only up to carbon atoms are
completely miscible with water
A. three
B. four
c. five
D. two


Incorrect statement about Ge is:
\( \mathbf{A} \cdot G e O_{2} \) is weakly acidic
B. \( G e(O H)_{2} \) is amphoteric
C \( \cdot G e C l_{2} \) is more stable than \( G e C l_{4} \)
D. \( G e-G e \) bond energy is lesser than that of \( S i-S i \)


If \( y=3 e^{2 x}+2 e^{3 x} . \) prove that \( \frac{d^{2} y}{d x^{2}}- \)
\( \mathbf{5} \frac{d y}{d x}+6 y=0 \)


\( \frac{x^{2}}{\left(x^{2}+a^{2}\right)\left(x^{2}+b^{2}\right)}= \)
\( k\left[\frac{a^{2}}{x^{2}+a^{2}}-\frac{b^{2}}{x^{2}+b^{2}}\right] \Rightarrow k= \)
\( A \)
в. \( \frac{1}{a^{2}+b^{2}} \)
c. \( \frac{1}{a^{2}-b^{2}} \)
D. \( \frac{1}{b^{2}-a^{2}} \)


Energy is not propagated by
A. stationary waves
B. electromagnetic waves
C. longitudinal progressive waves
D. transverse progressive Waves


A block of mass ' \( m^{\prime} \) is placed on floor of a lift which is rough. The coefficient of friction between the block and the floor
is \( \mu . \) When the lift falls freely, the block
is pulled horizontally on the lift floor. The force of friction is:
A . zero
в. \( 2 \mu m g \)
c. \( \frac{1}{2} \mu m g \)
D. \( \mu m g \)


The function \( f(x)= \) \( \frac{\log (1+a x)-\log (1-b x)}{x} \) is not
defined at \( x=0 . \) The value of which
should be assigned to \( f \) at \( x=0 \), is
\( \mathbf{A} \cdot a-b \)
B. \( a+b \)
\( \mathbf{c} \cdot \log a+\log b \)
D. None of these


are the ways of family planning.
A. To take contraceptive tablets
B. To use Nirodh (Condoms)
c. To install copper -
D. All of the above


Assertion
Hydrogen peroxide acts only as
oxidising agent. \( \left(\boldsymbol{H}_{2} \boldsymbol{O}_{2} \rightarrow \boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{O}\right) \)
Reason
All peroxides behave as the oxidising
agent only.
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 temperature of water at the bottom
of a large waterfall is higher than that of the water at the top, because
A. the falling water absorbs heat from the sun
B. the KE of the falling water is converted into heat
c. the water at the bottom has greater PE
D. rocks on the bed of the river give out heat


In an atomic explosion, a temperature of about 10 million degrees is developed at the moment of explosion. The wavelengths of light corning from the hot region of the atomic explosion lie in
the
A . Ultraviolet region
B. Visible region
c. Infrared region
D. x-ray region


A glass vessel of volume \( v_{0} \) is completely filled with a liquid and its temperature is raised by \( \triangle \boldsymbol{T} . \) What volume of the liquid will overflow? Coefficient of linear expansion of glass
\( =\alpha_{g} \) and coefficient of volume
expansion of the liquid \( =\gamma \)


Murugan measured the electric current
What unit should he use?


In the shown circuit, \( \boldsymbol{R}_{1}=\mathbf{1 0 \Omega}, \boldsymbol{L}= \)
\( \frac{\sqrt{3}}{10} H, R_{2}=20 \Omega, C=\frac{\sqrt{3}}{2} \) milli
farad and \( t \) is time in seconds. Then at
the instant current through
\( \boldsymbol{R}_{1} \boldsymbol{i} \boldsymbol{s} \mathbf{1} \boldsymbol{0} \sqrt{\boldsymbol{2}} \boldsymbol{A} \)
find the current through resistor \( \boldsymbol{R}_{2} \) in
amperes.


\( \frac{\sqrt{2}}{2} \)


How many medians are there in a
triangle \( P Q R ? \)
4
B. 2
\( c \)
\( D \)


When a circle is cut into fourths, those
sectors are called as,
A . semicircle
B. quadrant
c. major sector
D. None of these


A body of mass \( x k g \) is moving with
velocity of \( 100 m \) sec \( ^{-1} \). Its de Broglie wavelength is \( 6.62 \times 10^{-35} \) m. Hence \( x \)
is:
\( \left[\boldsymbol{h}=\mathbf{6 . 6 2} \times \mathbf{1 0}^{-\mathbf{3 4}} \boldsymbol{J}-\boldsymbol{s e c}\right] \)
A. \( 0.25 k g \)
B. \( 0.15 k g \)
c. \( 0.2 k g \)
D. \( 0.1 k g \)


State whether given statement is True or False.
Are forces acting on block actionreaction pair.
A. True
B. False


Consider the wave and choose the
correct option
A. blue wave has higher frequency
B. red wave has higher frequency
C. blue wave has higher time period
D. none of the above


Reverberations in a room is minimized
by
A. talking softly
B. using an extra layer of paint
c. use of curtains
D. none of the above


The conditions for the discharge of electricity in a discharge tube are :
A. high temperature and high potential
B. low pressure and high potential
c. low pressure and high temperature
D. low potential and high pressure


What are the important factors that bring about biological diversity?
A. Temperature
B. Enviornment
c. climatic conditions
D. All of the above


What occurs in germinal cells during gamete formation?
A. One reduction division and one equational division
B. Two successive equational divisions
c. Two successive reduction divisions
D. Short prophase in division I


f \( a, b, c, d \) are in a \( G . P ., \) then show that
\( (a-d)^{2}=(b-c)^{2}+ \)
\( (c-a)^{2}+(d-b)^{2} \)


A particle of mass \( 2 m \) is connected by
an inextensible string of length \( 1.2 m \) to a ring of mass \( m \) which is free to slide on a horizontal smooth rod. Initially the
ring and the particle are at the same level with the string, taut. Both are then released simultaneously. What is the distance in meters moved by the ring when the string becomes vertical?


You will find metals on the extreme
right side of the periodic table.
A. True
B. False


Evaluate \( \int_{-1}^{1} \log \frac{2-x}{2+x} d x \)


is a mixed type of gland
A. Thymus
B. Salivary gland
c. Intestinal glands
D. Pancreas


The diagram shows equipotential lines
from an unknown charge configuration.
Determine where in the diagram, the
electric field is the strongest:
\( A \cdot A \)
B. B
\( c \cdot c \)
\( D \)


The electrical resistance of a mercury
column in a cylindrical container is 'R',
The mercury is poured into another cylindrical container with half the radius of cross-section. The resistance
of the mercury column is
\( A \cdot R \)
B. 2R
\( c \cdot \) 16R
D. 5R


State True or False, Differentiating the equation of the curve at a point gives the slope of the tangent to the curve at that point.
A . True
B. False


Locus of a point \( \boldsymbol{P} \) which such that
\( \boldsymbol{P A}=\boldsymbol{P B} \) where \( \boldsymbol{A}=(\mathbf{0}, \boldsymbol{3}, \boldsymbol{2}) \) and \( \boldsymbol{B}= \)
(2,4,1) is
A. \( 2 x+y-z=4 \)
B. \( x-2 y+z+1=0 \)
c. \( 9 x-2 y+4 z-5=0 \)
D. None of these


\( \int \frac{3 \sin x+2 \cos x}{\sin x+\cos x} d x \)


Hydrogen resembles halogen in many respect for which several factors are
responsible. Of the following factors which one is the most important in this respect?
A. Its tendency to lose electron
B. Its tendency to gain electron in its valence shell
c. Its low negative electron gain enthalpy
D. Its small size


Consider the following concentration cell
\( Z n(s)\left|Z n^{2+}(0.024 M) \| Z n^{2+}(0.480 M)\right| Z \)
which of the following statements
is/are correct?

This question has multiple correct options
A. The EMF of the cell at \( 25^{\circ} \mathrm{C} \) is nearly \( +0.039 \mathrm{V} \)
B. The EMF of the cell at \( 25^{\circ} C \) is nearly -0.039 V.
C. If water is added in LHE, so that the \( \left[Z n^{2+}\right] \) is reduced to \( 0.012 \mathrm{M} \), the cell voltage increases.
D. If water is added in LHE, so that the \( \left[Z n^{2+}\right] \) is reduced to \( 0.012 \mathrm{M} \), the cell voltage decreases.


Potential difference between two points
is equal to
A. electric charge / time
B. work done/time
c. work done/charge
D. work done \( \times \) charge


Solutions distilled without change in
composition at a temperature are called
A. Amorphous
B. Azeotropic mixture
c. Ideal solution
D. Super saturated solution


If \( |\bar{A}+\bar{B}|=|\bar{A}|+|\bar{B}| \) then the angle
between \( \bar{A} \) and \( \bar{B} \) is:
\( A \cdot 0^{0} \)
B . \( 90^{\circ} \)
\( c \cdot 180^{\circ} \)
D. \( 60^{\circ} \)


A loud speaker converts:
A. electrical energy into sound energy
B. sound energy into electrical energy
C. mechanical energy into sound energy
D. sound energy into mechanical energy


In compound \( X \), all the bond angles are
exactly \( 109^{\circ} 28^{\prime} . \$ \$ \times \$ \$ \) is
A. Chloromethane
B. lodoform
c. Carbon tetrachloride
D. chloroform


\( = \)
0
0
0


The degree of dissociation of
\( \boldsymbol{C a}\left(\boldsymbol{N O}_{3}\right)_{2} \) in a dilute aqueous
solution containing \( 7 g \) of the salt per \( 100 g \) of water at \( 100^{\circ} C \) is \( 70 \% \). If the vapour pressure of water at \( 100^{\circ} \mathrm{C} \) is
\( \mathbf{7 6 0} \boldsymbol{m m}, \) calculate the vapour pressure of the solution.
\( \mathbf{A} .378 .5 \mathrm{mm} \)
В. \( 492.8 \mathrm{mm} \)
c. \( 746.10 m m \)
D. \( 985.6 \mathrm{mm} \)


In a transformer, the number of turns of
primary coil and secondary coil are 5 and 4 respectively. If \( 220 \mathrm{V} \) is applied on the primary coil, then the ratio
of primary current to the secondary current is :
A .4: 5
B. 5: 4
\( c \cdot 5: 9 \)
D. 9 : 5


The inverse of statement is " If you grew
in Alaska, then you have seen snow."
A. "If you did not grow up in Alaska, then you have not seen snow."
B. "If you grow up in Alaska, then you have not seen snow."
C. "If you did not grow up in Alaska, then you have seen snow."
D. None of these


Fill in the blanks:
Human eye has maximum luminous efficiency to light
A . yellow
B. red
c. violet
D. green


Potential Energy(U) of a body of unit mass moving in a one-dimension conservative force field is given by \( U= \)
\( \left(x^{2}-4 x+3\right) . \) All units are in S.I.
(i) Find the equilibrium positions of the body
(ii) Show that oscillations of the body
about this equilibrium positions is simple harmonic motion \& find its time period.
(iii) Find the amplitude of oscillations if speed of the body at equilibrium position is \( 2 \sqrt{6} \mathrm{m} / \mathrm{s} \)


The angle made by incident ray of light with the reflecting surface is called
A. Glancing angle
B. Angle of incidence
c. Angle of deviation
D. Angle of refraction


Suppose that \( f \) is differentiable for all
\( \boldsymbol{x} \in \boldsymbol{R} \) and that \( \boldsymbol{f}^{\prime}(\boldsymbol{x}) \leq 2 \) for all \( \boldsymbol{x} . \) If
\( f(1)=2 \) and \( f(4)=8, \) then \( f(2) \) has
the value equal to
A . 3
B. 4
\( c \cdot 6 \)
D. 8


In the Merck's process, the reagents involved in the preparation of hydrogen peroxide are:
A. \( B a O_{2}, H C l \)
в. \( N a_{2} O_{2}, H_{2} S O_{4} \)
с. Ва Од\( _{2}, \)На\( _{2} \)СО\( _{3} \)
D. \( P b O_{2}, H_{2} O \)


Select the correct statements.
This question has multiple correct options
A. Contraction of bond angle in \( H_{2} O \) relative to methane
is \( 4^{\circ} \)
B. The molecules having cation with 18 electron valence shell are more covalent than those having 8 electron valence shell
C. \( C o^{3+} \) ion is less stable than \( F e^{3+} \) ion
D. \( S n^{4+} \) is less stable than \( S n^{2+} \)


Give the missing product of the following reaction in same order of reaction order:
\( \boldsymbol{C a}+\boldsymbol{a i r} \rightarrow \boldsymbol{C a O}+_{--}- \)
\( \boldsymbol{C a} \boldsymbol{C O}_{3}(\boldsymbol{s}) \stackrel{\Delta}{\longrightarrow} \boldsymbol{C a O}(\boldsymbol{s})+_{--} \)
(2)
\( \boldsymbol{C a}(\boldsymbol{O} \boldsymbol{H})_{2} \stackrel{\text {calcination}}{\longrightarrow} \boldsymbol{C a O}+_{--} \)
\( \ldots(3) \)
A. \( C a_{3} N_{2} ; C O_{2} ; H_{2} O \)
в. \( C a_{3} N_{2} ; C O_{2} ; H_{2} \)
c. \( C a_{a} N_{2} ; \operatorname{CO} ; H_{2} O \)
D. \( C a F_{2} ; C O_{2} ; H_{2} O \)


Which quantity remains same in isobars?
A. Number of neutrons
B. Number of protons
c. Mass number
D. All of the above


Explain the important aspects of
resonance with reference to the \( \boldsymbol{C} \boldsymbol{O}_{3}^{2-} \)
ion.


Which of the following mixtures will be
buffer?
This question has multiple correct options
\( \mathbf{A} \cdot C H_{3} C O O H+C H_{3} C O O N H_{4} \)
B . \( H C l+N a C l \)
C. Borax+boric acid
D. \( C H_{3} C O O H+C H_{3} C O O N a \)


If the circumference of a circle is
increased by \( 50 \% \), by what percent will its area be increased?
A . \( 75 \% \)
B. \( 100 \% \)
c. \( 125 \% \)
D. \( 150 \% \)


Petromyzon and Myxine are not regarded as true fishes, because
A. They lack unpaired fins
B. They have circular mouth
c. In them operculum is absent
D. There is absence of paired fins and jaws


Evaluate \( : \sqrt{-\mathbf{1 6}}+\mathbf{3} \sqrt{-\mathbf{2 5}}+\sqrt{-\mathbf{3 6}}- \)
\( \sqrt{-\mathbf{6 2 5}} \)


The relationship between band gap
energy and temperature can be described by
A. supersymmetric quantum mechanics
B. hyperuniformity.
c. phonons theory.
D. Varshni's empirical expression


Give two rational numbers lying between \( 0.232332333233332 \ldots . \) and
0.2121121112111122
Enter 1 if the answer is 0.221,0.222
otherwise enter 0


Let \( \boldsymbol{A}=(\mathbf{1}, \mathbf{2}, \mathbf{3}) \boldsymbol{B}= \)
\( (-1,-2,-1) C=(2,3,2) \) and \( D= \)
\( (4,7,6) . \) Then \( A B C D \) is a
A. rectangle
B. square
c. parallelogram
D. none of these


\( \mathrm{CH}_{3} \mathrm{COCl}+\mathrm{H}_{2} \stackrel{(A)}{\longrightarrow}(\mathrm{B}) \)
The given reaction is an example of Rosenmund's reaction. Identify the
product \( \mathbf{B} \)
A. Formaldehyde
B. cloroethane
c. Acetaldehyde
D. Ethanol


Using Euclid's division algorithm find the HCF of the following numbers.
\( \mathbf{2 6 6 7 6} \) and \( \mathbf{3 3 7 5 5 4} \)


Equation of a straight line meeting the circle \( x^{2}+y^{2}=100 \) in two points each
point at a distance of 4 from the point (8,6) on the circle is
A. \( 4 x+3 y-50=0 \)
B. \( 4 x+3 y-100=0 \)
c. \( 4 x+3 y-46=0 \)
D. none of these


In order of prepare fluorobenzene from
benzene diazonium chloride, which of
the folowing reagents is used?
A. Fluorine
в. \( H F \)
c. Hydrofluorosilic acid
D. Fluoroboric acid


Match the List-I with List-II and List-III:
List - I
(Ouantity) List - II
(Symbol) (Quantity)
(a) Conductivity
\( (p) \)
\( \wedge_{m} \)
\( (b) \)
Cell
constant
\( (q) \)
\( K \)
(c) Molar
conductance \( \quad(\mathrm{r}) \quad \wedge_{e} \)
(d) Equivalent
conductance \( \quad(\mathrm{s}) \)
\( \mathbf{A} \cdot(a-q, u),(b-s, v),(c-d, w),(d-r, x) \)
B . \( (a-q, u),(b-s, v),(c-p, w),(d-r, x) \)
C \( .(a-b, u),(b-s, v),(c-p, w),(d-r, x) \)
D . \( (a-p, u),(b-s, v),(c-p, w),(d-r, x) \)


\( \boldsymbol{A} \boldsymbol{g} \mid \boldsymbol{A} \boldsymbol{g}^{\oplus}(\boldsymbol{1} \boldsymbol{M})\left\|\boldsymbol{A} \boldsymbol{g}^{\oplus}\right\| \boldsymbol{A} \boldsymbol{g} \)
\( 0.5 F \) electricity in this LHS (anode) and
1 F of electricity in the RHS (cathode) is first passed making them independent electrolytic cells at \( 298 \mathrm{K} \). EMF of the cell after electrolysis will be:
A. increased
B. remain same
c. decreased
D. None of these


Solve the following linear inequality:
\( \frac{8 x-5}{2 x+11} \geq 4 \)


The electronegativity difference
between \( N \) and \( F \) is greater than \( N \) and
\( \boldsymbol{H}, \) yet the dipole moment of \( \boldsymbol{N} \boldsymbol{H}_{3}(1.5 \)
D) is greater than that of \( N F_{3}(0.2 D) \)
This is because:
A \( \cdot \) in \( N H_{3} \) as well as \( N F_{3} \), the atomic dipole and bond dipole are in the opposite direction
B. in \( N H_{3} \), the atomic dipole and bond dipole are in the
opposite direction, whereas in \( N F_{3} \) these are in the same direction.
C. in \( N H_{3} \) as well as in \( N F_{3} \) the atomic dipole and bond dipole are in the same direction
D. in \( N H_{3} \) the atomic dipole and bond dipole are in the
same direction, whereas in \( N F_{3} \) these are in the opposite direction.


Suggest two methods to find out wind
direction at a give place.


The vapour pressure of pure benzene at
a certain temperature is 0.850 bar. \( A \) non-volatile, non-electrolyte solid weighing \( 0.5 g \) is added to \( 39.0 g \) of benzene (molar mass \( 78 g / \)mol ). The vapour pressure of the solution then is
\( \mathbf{0 . 8 4 5} \) bar. What is the molecular mass
of the solid substance?
\( \mathbf{A} .58 \)
в. 180
\( c .170 \)
D. 145


Difference between atomic number and
mass number.


The cost of fencing a circular field at the
rate of \( R s .24 \) per meter is \( R s .5280 /- \) The field is to be ploughed at the.


Write on expression for vector from of magnetic force on a moving charge.


Which of the following match is correct?
A. Emphysema - Reduction of surface area of alveoli and bronchi.
B. Pneumonia - Occupational disease with asbestos.
C. Silicosis - Inflammation of alveoli.
D. Asthma - Excessive secretion of bronchial mucus.


The subnormal at any point on the curve
\( x y^{n}=a^{n+1} \) is constant for
\( \mathbf{A} \cdot n=0 \)
B . \( n=1 \)
c. \( n=-2 \)
D. \( n=2 \)


The vector \( \vec{a}+\vec{b} \) bisects the angles between the vectors \( \vec{a} \) and \( \vec{b} \) if
A. \( |\vec{a}|=1 \)
1 \( 1==1=1 \)
в. \( |\vec{b}|=1 \)
c. \( |\vec{a}|=\mid \vec{b} \)
D. \( \vec{a} \vec{b}=0 \)


If \( z_{1}=2 \sqrt{2}(1+i) \) and \( z=1+i \sqrt{3} \)
then \( z_{1}^{2} z_{2}^{3} \) is equal to
\( \mathbf{A} \cdot 128 \)
в. \( 64 i \)
\( c .-64 \)
D. \( -128 i \)
E . 256


The property of metals which allows them to be drawn readily into thin wires is:
A. elasticity
B. ductility
c. hardness
D. malleability


Name the kind of meniscus formed in
case of water.
A. Concave
B. convex
c. Both \( A \& B \)
D. None


Evaluate the following determinant:
\( \left|\begin{array}{ccc}1 & 3 & 5 \\ 2 & 6 & 10 \\ 31 & 11 & 38\end{array}\right| \)


A Zener diode is connected to a battery
and a load as shown below: The current
\( \boldsymbol{I}, \boldsymbol{I}_{Z} \) and \( \boldsymbol{I}_{\boldsymbol{L}} \) are respectively :
A \( .12 .5 \mathrm{mA}, 735 \mathrm{mA}, 5 \mathrm{mA} \)
B. \( 12.5 \mathrm{mA}, 5 \mathrm{mA}, 7.5 \mathrm{mA} \)
c. \( 15 \mathrm{mA}, 7.5 \mathrm{mA}, 7.5 \mathrm{mA} \)
D. \( 15 \mathrm{mA}, 5 \mathrm{mA}, 10 \mathrm{mA} \)


Give balanced equations for the following reactions?
Acidifed potassium permanganate and oxalic acid.


toppr
Q Type your question-
rate. In that case, which of the following graphs, drawn schematically, correctly shows the variation of the induced
electric field \( \boldsymbol{E}(\boldsymbol{r}) \) ?
\( A \)
B.
\( c \)
\( D \)


The kinetic energy of a simple
pendulum may be decreased by:
A. increasing the mass of the bob
B. increasing the thickness of the string
C. decreasing the length of the string
D. increasing the length of the string
E. decreasing the displacement of the string


Find the equation of the plane through the points \( \boldsymbol{A}(\mathbf{2}, \mathbf{2}-\mathbf{1}), \boldsymbol{B}(\mathbf{3}, \mathbf{4}, \mathbf{2}) \) and
\( \boldsymbol{C}(\boldsymbol{7}, \boldsymbol{0}, \boldsymbol{6}) \)
A. \( 5 x+2 y-3 z=17 \)
B. \( 5 x+2 y+3 z=17 \)
c. \( 5 x+y-3 z=7 \)
D. \( 5 x+y+3 z=7 \)


When ethanol react with sodium,which
gas will produce?
A. hydrogen
B. oxygen
c. sodium ethoxide
D. carbon dioxide


An element has 8 electrons in \( 4 d- \)
subshell. Show the distribution of 8
electrons in the \( d \) -orbitals of the
element within small rectangles.


\( ^{57} \) Co decays by electron capture. Its half life is 272 days. Find the activity left after a year if present activity is \( 2 \mu C i \)
A. \( 0.788 \mu \) Ci
B. \( 0.431 \mu C i \)
\( \mathbf{c} .0 .39 \mu \mathrm{Ci} \)
D. none of these


Determine the order and degree(if defined) of the following differential equation.
\( \boldsymbol{y}^{\prime \prime}+\left(\boldsymbol{y}^{\prime}\right)^{2}+\mathbf{2} \boldsymbol{y}=\mathbf{0} \)


Check the continuity of the function \( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{ll}\frac{|\boldsymbol{x}|}{\boldsymbol{x}}, & \boldsymbol{x} \neq \mathbf{0} \\ \mathbf{0}, & \boldsymbol{x}=\mathbf{0}\end{array} \quad \mathbf{a t} \boldsymbol{x}=\mathbf{0}\right. \)


\( \boldsymbol{C H}_{2}=\boldsymbol{C H}_{2}+\boldsymbol{S}_{2} \boldsymbol{C l}_{2} \rightarrow \boldsymbol{X} \)
Then, which are the correct statements
about X?
This question has multiple correct options
A. \( x \) is mustard gas
B. \( x \) is used as war gas
c. \( x \) has two \( s \) atoms
D. \( x \) has only one \( S \) atom


Figure shows the elliptical path of a
planet around the sun. The two shaded
parts have equal areas. If \( t_{1} \) and \( t_{2} \) be
the time taken by the planet to go from
\( a \) to \( b \) and from \( c \) to \( d \) respectively, then
\( \mathbf{A} \cdot t_{1}<t_{2} \)
B \( \cdot t_{1}=t_{2} \)
\( \mathbf{C} \cdot t_{1}>t_{2} \)
D. Insufficient information to deduce the relation
between \( t_{1} \) and \( t_{2} \)


One atomic mass unit (a.m.u) is equal
to:
A \( \cdot 1 \) ev of energy
B. 931 eV of energy
c. 1 Mev of energy
D. 931 MeV of energy


Sound requires a for
propagation.
A. medium
B. companion
c. lot of energy
D. liquid


Without teats, mammary glands are found in
A. Prototheria
B. Metatheria
c. Eutheria
D. Theria


A ball of mass 10 g moving perpendicular to the plane of the wall strikes it and rebounds in the same line
with the same velocity. lithe impulse experienced by the wall is \( 0.54 \mathrm{N} \) -s, the velocity of the ball is
A \( \cdot 27 m s^{-1} \)
B . \( 2.7 \mathrm{ms}^{-1} \)
\( \mathrm{c} \cdot 54 \mathrm{ms}^{-1} \)
D. \( 37 m s^{-1} \)
E . \( 5.4 \mathrm{ms}^{-1} \)


Differentiate with respect to \( x \) :
\( \boldsymbol{y}=\cos \boldsymbol{x}+\sin 2 \boldsymbol{x} \)


The difference between the greatest and the least value of \( \boldsymbol{f}(\boldsymbol{x})= \) \( \cos ^{2} \frac{x}{2} \sin x, x \in[0, \pi] \) is
\( A \cdot \frac{3 \sqrt{3}}{8} \)
в. \( \frac{\sqrt{3}}{8} \)
\( c \cdot \frac{3}{8} \)
D. \( \frac{1}{2 \sqrt{2}} \)


Evaluate the definite integral:
\( \int_{1}^{2} \frac{1}{x} d x \)


Two capacitors of caacity \( C_{1} \) and \( C_{2} \) are connected in series and potential difference V is applied across it. Then
the potential difference across \( C_{1} \) will
be
\( ^{\mathrm{A}} \cdot \frac{C_{2} V}{C_{1}+C_{2}} \)
в. \( \frac{C_{1} V}{C_{1}+C_{2}} \)
\( ^{c} \cdot\left(1+\frac{C_{2}}{C_{1}}\right) V \)
D. \( \left(1-\frac{C_{2}}{C_{1}}\right) v \)


What are Emulsions? How are they
classified?


A particle moves with constant acceleration along a straight line starting from rest. The percentage increase in its displacement during the 4th second compared to that in the \( 3 r d \)
second is:
A . 33\%
B. 40\%
c. \( 66 \% \)
D. 77\%


A tank is filled with water of density 1 g \( c m^{-3} \) and oil of density \( 0.9 \mathrm{g} \mathrm{cm}^{-3} . \) The height of water layer is \( 100 \mathrm{cm} \) and of the oil layer is \( 400 \mathrm{cm} . \) If \( g=980 \mathrm{cm} s^{-2} \) then the velocity of efflux from an opening in the bottom of the tank is :
B . \( \sqrt{900 \times 980} \mathrm{cms}^{-1} \)
c. \( \sqrt{1000} \times 980 c \mathrm{cms}^{-1} \)
D. \( \sqrt{92 \times 980} \mathrm{cms}^{-1} \)


The figure shows the positions and
velocities of two particles. If the
particles move under the mutual attraction of each other, then the
position of the centre of mass at \( t=1 s \)
is


Which of the following represents the chemical equation involved in the
preparation of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) from barium
peroxide?
A \( \cdot B a O_{2} \cdot 8 H_{2} O+H_{2} S O_{4} \rightarrow B a S O_{4}+H_{2} O_{2}+8 H_{2} O \)
в. \( C H_{3} C H O H C H_{3} \rightarrow C H_{3} C O O C H_{3}+H_{2} O_{2} \)
\( \mathbf{c} \cdot B a O_{2}+C O_{2}+H_{2} O \rightarrow B a C O_{3}+H_{2} O_{2} \)
D. \( B a_{3}\left(P O_{4}\right)_{2}+3 H_{2} S O_{4} \rightarrow 3 B a S O_{4}+2 H_{3} P O_{4} \)


The nuclear radius is given by \( \boldsymbol{R}= \) \( r_{0} A^{1 / 3}, \) where \( r_{0} \) is constant and \( A \) is
the atomic mass number.
Then :
A. The nuclear mass density of \( U^{238} \) is twice that of \( S n^{119} \)
B. The nuclear mass density of \( U^{238} \) is thrice that of \( S n^{11} \)
C. The nuclear mass density of \( U^{238} \) is the same as that of \( S n^{11} \)
D. The nuclear mass density of \( U^{238} \) is half that of \( S n^{119} \)


Explain refining of nicket by mond
process. State kohlarausch's law


Word genetics comes from
A. Gene
B. Genesis
C. Genome
D. Genomics


A series of ocean waves, each \( 5.0 \mathrm{m} \)
from crest to crest, moving past the observer at a rate of 2 waves per second
What is the velocity of ocean waves?
A. \( 2.5 \mathrm{m} / \mathrm{s} \)
B. \( 5.0 \mathrm{m} / \mathrm{s} \)
\( c \cdot 8.0 \mathrm{m} / \mathrm{s} \)
D. \( 10.0 \mathrm{m} / \mathrm{s} \)


The susceptibility of magnetic material
is \( -4.2 \times 10^{-6} . \) Name the type of
magnetic material it represents.


Assertion
A small electric dipole is moved translationally from higher potential to lower potential in uniform electric field.
Work done by electric field is positive.
Reason

When a positive charge is moved from
higher potential to lower potential, work
done by electric field is positive.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which one of the following is a natural growth inhibitor?
A. NAA
B. ABA/Ethylene
\( c \cdot \) ।АА
D. GA


The angle at which the curve \( y=k e^{k x} \)
intersects the \( y \) - axis is This question has multiple correct options
A \( \cdot \tan ^{-1} k^{2} \)
B \( \cdot \cot ^{-1}\left(k^{2}\right) \)
\( \mathrm{c} \cdot_{\sin }^{-1}\left(\frac{1}{\sqrt{1+k^{4}}}\right) \)
D・sec- \( 1(\sqrt{1+k^{4}}) \)


Resistance of a conductivity cell filled with a solution of an electrolyte of concentration \( 0.1 M \) is 100 ohm. The
conductivity of this solution is \( 1.29 S m^{-1} . \) Resistance of the same cell
when filled with \( 0.2 ~ M \) of the same
solution is 520 ohm. The molar
conductivity of \( 0.02 M \) solution of the electrolyte will be:
A \( \cdot 124 \times 10^{-4} \mathrm{S} \mathrm{m}^{2} \mathrm{mol}^{-1} \)
В. \( 1240 \times 10^{-4} \mathrm{S} \) m \( ^{2} \) mol \( ^{-1} \)
c. \( 1.24 \times 10^{-4} \) S \( m^{2} \) "nol \( ^{-1} \)
D. \( 12.4 \times 10^{-4} \mathrm{S} \mathrm{m}^{2} \mathrm{mol}^{-} \)


An engine operates by taking n moles of
an ideal gas through the cycle ABCDA
shown in figure. The thermal efficiency
of the engine is :

Take \( C_{v}=1.5 \mathrm{R}, \) where \( \mathrm{R} \) is gas constant
4.0 .32
3.0 .24
\( c \cdot 0.15 \)
2


Explain the process of release of energy in the installation at Chernobyl.


Differentiate the following function with
respect to \( x \)
\( \frac{\boldsymbol{x}^{n}}{\sin \boldsymbol{x}} \)


A second pendulum clock having steel wire is calibrated at \( 20^{0} C . \) When
temperature is increased to \( 30^{0} C \), then
how much time does the clock lose or
\( \operatorname{gain} \) in one week \( ? \) \( \left[\boldsymbol{\alpha}_{\text {steel}}=\mathbf{1 . 2} \times \mathbf{1 0}^{-\mathbf{5}}\left(^{0} \boldsymbol{C}\right)^{-\mathbf{1}}\right] \)
B. \( 3.626 s \)
c. \( 362.8 s \)
D. 36.28S


A water drop in air reflects the light rays
as
\( A \)
в.
\( c \)
\( D \)


Find the multiplicative inverse of \( \frac{\mathbf{5}}{\mathbf{3}} \) \( +\frac{-17}{11} \)
A \( \cdot \frac{33}{4} \)
в. \( \frac{33}{23} \)
\( c \cdot \frac{3}{4} \)
D. None of these


A rod of negligible mass having length
\( l=2 m \) is pivoted at its centre and two
masses of \( \boldsymbol{m}_{1}=\mathbf{6 k g} \) and \( \boldsymbol{m}_{2}=\mathbf{3 k g} \) are
hung from the ends as shown in figure.
(a) Find the initial acceleration of the
rod if it is horizontal initially


The incorrect statement for L-R-C series
circuit is
A. The potential difference across the resistance and the appleid e.m.f. are always in same phase
B. The phase difference across inductive coil is \( 90^{\circ} \)
C. The phase difference between the potential difference across capacitor and potential difference across inductance is \( 90^{\circ} \)
D. The phase difference between potential difference across capacitor and potential difference across resistance is \( 90^{\circ} \)


Identify the correct sets of entries that
are rightly matched.

Column A
\( B \)
(A) Bridge elements Elements of group IA-VIIA
(B) Representative elements
(b) 2nd-
period elements
(C) Typical elements
(c) 7 th-
period elements
(D) Transition elements
(d) \( 3 r d- \)
period elements
(E) Transuranic elements
(e) Present
in 4 th, 5 th and 6 th periods
\( \mathbf{A} \cdot A-b, B-a, C-d, D-e, E-c \)
B . \( A-c, B-a, C-b, D-d, E-e \)
c. \( A-a, B-c, C-d, D-e, E-b \)
D. \( A-c, B-e, C-d, D-b, E-a \)


Two trains are each 50 m long moving parallel towards each other at speeds \( 10 m / s \) and \( 15 m / s \) respectively. After what time will they pass each other?
\( ^{\mathrm{A}} \cdot_{5} \sqrt{\frac{2}{3}} s e c \)
B. 4 sec
\( \mathbf{c} \cdot 2 \sec \)
D. 6 sec


\( \sum_{n=1}^{20}\left(i^{n}+i^{n+1}\right) \) where \( i=\sqrt{-1} \) is equal
to
\( A \)
B. -
\( c \cdot 0 \)
D.


\( \underbrace{k}_{k} \)


Statement-1: the two vectors \( a=1 i+ \)
\( \boldsymbol{P j}+\mathbf{2 k} \) and \( \boldsymbol{b}=\boldsymbol{3} \boldsymbol{i}+\boldsymbol{3} \boldsymbol{j}+\boldsymbol{Q} \boldsymbol{k} \) are
parallel only if \( \boldsymbol{P}=\mathbf{1} \) and \( \boldsymbol{Q}+\boldsymbol{6} \)
Statement-2: if two vectors \( \boldsymbol{a}=\boldsymbol{a}_{1} \boldsymbol{i}+ \)
\( a_{2} j+a_{3} k \) and \( b=b_{1} i+b_{2} j+b_{3} k \) are
parallel then \( \frac{\boldsymbol{a}_{1}}{\boldsymbol{a}_{2}}=\frac{\boldsymbol{b}_{1}}{\boldsymbol{b}_{2}} \)
A. Both statements are true and Statement-2 is correct explanation of Statement- -
B. Both statements are true and Statement-2 is not correct explanation of Statement-
c. statement-2 is false but other is true
D. Statement-1 is false but other is true


The system shown is in equilibrium in
vertical plane. All the rods and the supports \( A \& B \) are light and friction
coefficient between supports and
horizontal rod is \( \mu . \) If maximum value of
angle \( \alpha \) is \( 37^{0} \) then find the value of \( 4 \mu \)
Assume light rod exerts force only along
the rod.
\( A \cdot 2 \)
B. 3
\( c .5 \)
\( D \)


Area of parallelogram, whose diagonals \( \operatorname{are} 3 \hat{i}+\hat{j}-2 \hat{k} \) and \( \hat{i}-3 \hat{j}+4 \hat{k} \) will be
:
A. 14 unit
B. \( 5 \sqrt{3} \) unit
c. \( 10 \sqrt{3} \) unit
D. \( 20 \sqrt{3} \) unit


Which of the following compounds can exhibit both geometrical isomerism
and enantiomerism?
A. \( C H_{3} \)
\( C H_{3} C H_{2}-C=C H-C O O H \)
в. \( C H_{3}-C H O H- \) СООН
c. \( C H_{3}-C H=C H-C H_{3} \)
\( \mathrm{D} \)
\( C H_{3} C H_{2}-C H-H C=C H-C H_{3} \)


The casing of a rocket in flight burns up
due to friction. At whose expense is the heat energy required for burning obtained? The rocket or the atmosphere


The magnetic lines of force inside a current carrying solenoid are:
A. along the axis and parallel to each other
B. perpendicular to the axis and parallel to each other
c. circular and do not intersect each other
D. circular and intersect each other


Liquid ammonia is used in ice factory
for making ice from water. If water at
\( 20^{\circ} \mathrm{C} \) is to be converted to \( 2 \mathrm{kg} \) ice at
\( 0^{\circ} \mathrm{C}, \) how many grams of ammonia are to be evaporated? (Given:The latent heat of vapourization of ammonia \( = \) \( 341 \mathrm{cal} / \mathrm{g} \)


\( 28 g m \) of \( N_{2} \) gas is contained in a flask at
a pressure of 10 atm and at a temperature of \( 57^{0} \) C. It is found that due to leakage in
the flask, the pressure is reduced to half
and the temperature reduced to \( 27^{\circ} \mathrm{C} \). The
quantity of \( \mathrm{N}_{2} \) gas that leaked out is
\( \mathbf{A} \cdot \frac{5}{63} g m \)
В \( \cdot \frac{63}{5} g m \)
\( \mathbf{c} \cdot \frac{11}{20} g m \)
D. \( \frac{20}{11} g m \)


In which of the following way, the transportation of hydrogen gas do not take place?
A. Liquid
B. Gas
c. compressed gas
D. Pressurized gas


Select the correct option for contractile proteins from the given diagram labelled as (a) and
\( A \cdot a=G-a c \operatorname{tin} ; b=F-\operatorname{actin} \)
B. a = Meromyosin; b = Myosin
c. a = Tropomyosin; b = Troponin
D. a = Troponin; b = Tropomyonin


Evaluate the following as the limit of
sum :
\( \int_{0}^{2}(x+4) d x \)
A .4
B. 6
c. 8
D. 10


The power loss in an AC circuit can be minimized by.
A. Decreasing resistance and increasing inductance
B. Decreasing inductance and increasimg resistance
c. Increasing both inductance and resistance
D. Decreasing both inductance and resistance


Which of them are Non-biodegradable
waste?
A. Synthetic fibers
B. Pen refills
c. silver foil
D. All of above


What is the difference between
lyophobic sol and lyophilic sol?


The output of the combination of the
gates shown in the figure is
\( \mathbf{A} \cdot A+A \cdot B \)
B . \( (A+B) A+\bar{B} \)
c. \( (A . B)+(\bar{A} . \bar{B}) \)
D. \( (A+B)(\overline{A . B}) \)


The following diagram in figure shows a fixed coil of several turns connected to a
centre zero galvanometer \( G \) and \( a \)
magnet NS which can move in the direction shown in the diagram. How
would the observation alter if a more
powerful magnet is used?


In a wave motion \( y=\alpha \sin (K x-\omega t) \)
the equation represents:
A . electric field
B. magnetic field
c. displacement field
D. pressure wave


\( n \stackrel{L t}{\rightarrow} \infty\left\{\frac{1}{n+1}+\frac{1}{n+2}+\ldots+\frac{1}{6 n}\right\}= \)
\( A \cdot \log 2 \)
B. \( \log 3 \)
\( c \cdot \log 5 \)
\( D \cdot \log 6 \)


A student is standing at a distance of 50 metre from the bus. As soon as the
bus begins its motion with an acceleration of \( 1 m s^{-2}, \) the student starts running towards the bus with a uniform velocity \( u \). Assuming the motion to be along a straight road, the minimum value of \( u \), so that the
student is able to catch the bus is
\( \mathbf{A} \cdot 8 m s^{-1} \)
B. \( 5 m s^{-1} \)
\( \mathrm{c} \cdot 12 m s^{-} \)
D. \( 10 m s^{-1} \)


Match the following
\( \begin{array}{lll}\text { S.No } & \text { Source } & \text { Acid present } \\ 1 . & \text { Apple } & \text { Oxalic acid } \\ 2 . & \text { Lemon } & \text { Tartaric acid } \\ 3 . & \text { Grape } & \text { Malic Acid } \\ 4 . & \text { Tomato } & \text { Citric Acid }\end{array} \)


If \( \boldsymbol{A}=\left[\begin{array}{lll}\mathbf{1} & \mathbf{2} & \mathbf{3} \\ \mathbf{3} & \mathbf{2} & \mathbf{1}\end{array}\right] \) and \( \boldsymbol{B}=\left[\begin{array}{lll}\mathbf{3} & \mathbf{2} & \mathbf{1} \\ \mathbf{1} & \mathbf{2} & \mathbf{3}\end{array}\right] \)
find \( \mathbf{3} \boldsymbol{B}-\mathbf{2} \boldsymbol{A} \)


If \( f(x)=x^{\frac{1}{x}} \) then \( f^{\prime \prime}(e) \) is equal to
B \( \cdot e^{1 / e} \)
\( \mathbf{c} \cdot e^{1 /(e-2)} \)
D. \( \left.-e^{((1 / e)-3}\right) \)