Calculate \( K_{C} \) for the reaction:
\( 2 H_{2}(g)+S_{2}(g) \rightleftharpoons 2 H_{2} S(g) \) if \( 1.58 \mathrm{mol} \)
\( \boldsymbol{H}_{2} \boldsymbol{S}, 1.27 \mathrm{mol} \boldsymbol{H}_{2}, \) and \( \mathbf{2 . 7 8} \times \mathbf{1 0}^{-\mathbf{6}} \) mol
of \( S_{2} \) are in equilibrium in a flask of capacity \( 180 \mathrm{L} \) at \( 750 \mathrm{C} \)
A \( \cdot K_{C}=124 \times 10^{8} L \) mol \( ^{-1} \)
B. \( K_{C}=1 \times 10^{8} L \) mol\( ^{-1} \)
c. \( K_{C}=1 \times 10^{-8} L \mathrm{mol}^{-1} \)
D. \( K_{C}=1 \times 10^{7} L \mathrm{mol}^{-1} \)


Green fuel is the fuel obtained from:
A. Bio-waste
B. Metal waste
c. Plastic waste
D. Chemical waste
E. Electronic waste


The action of \( A l C l_{3} \) in Friedel Craft's
reaction is:
A. to absorb HC
B. to release HC
c. to generate electrophile
D. to produce nucleophile


Find the direction cosines of a line
which is perpendicular to the lines whose direction ratios are (1,-1,2) and (2,1,-1)


Amino acids are classified as acidic, basic or neutral depending upon the relative number of amino and carboxyl groups in their molecule. Which of the following are acidic?
(i) \( \left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{C H}-\boldsymbol{C}_{\boldsymbol{I} \boldsymbol{H}_{2}} \boldsymbol{H}-\boldsymbol{C O O H} \)
(ii) \( H O O C-C H_{2}-C H_{2}-C_{I H_{2}} H \)
COOH
(iii) \( \boldsymbol{N} \boldsymbol{H}_{2}-\boldsymbol{C} \boldsymbol{H}_{2}-\boldsymbol{C} \boldsymbol{H}_{2}-\boldsymbol{C} \boldsymbol{H}_{2}- \)
COOH
(iv) \( H O O C-C H_{2}-C_{\mid} H-C O O H \)
\( A \cdot \) (ii) and (iv)
B. (iii) and (iv)
c. (i) and (ii)
D. (ii) and (iii)


Observe the following Lists
List-I
A: \( \int_{-2}^{2} \frac{1}{4+x^{2}} d x \)
List-II
B: \( \int_{1}^{2} \frac{1}{x \sqrt{x^{2}-1}} d x \quad \) 1) \( \frac{\pi}{3} \)
C: \( \int_{0}^{\pi} \cos 3 x \cdot \cos 2 x d x \quad \) 2) 0
4) \( \frac{\pi}{2} \)
A. A-3, B-1, C-4
B. A-3, B-1, C-2
C. A-1, B-3, C-2
D. A-4, B-1, C-2


The sum of all the integers from 1 to 100 which are divisible by 2 or 5 is
A. 3000
B. 3050
\( c .3600 \)
D. 3250


The number of candy bars students
brought to school the day after Halloween are given in the table. What
is the mode?
\begin{tabular}{|c|c|}
\hline Number of Candy Bars & Number of Students \\
\hline 0 & 1 \\
\hline 1 & 1 \\
\hline 2 & 1 \\
\hline 3 & 3 \\
\hline 4 & 0 \\
\hline 5 & 4 \\
\hline 7 & 2 \\
\hline 8 & 2 \\
\hline
\end{tabular}
4
\( B \)
\( c \)
\( D \)


A part of the monthly expenses of a family is constant and the remaining varies with the price of wheat. When the price of wheat is Rs. 250 per quintal, the total monthly expenses are Rs. 1000 and when it is Rs. 240 per quintal, the total monthly expenses are Rs. 980 per quintal. The total monthly expenses of the family when the cost of wheat is Rs.
350 per quintal, will be:
A . Rs. 500
B. Rs. 1200
c. Rs. -1200
D. Rs. - 500


"Lithium is the only metal among alkali
metals that can form nitride."

Answer whether the above statement is
true or false.
If true enter 1 , else enter 0


The length of air column in a capillary glass tube closed at one end containing mercury pellet \( 10 \mathrm{cm} \) long are \( 43 \mathrm{cm} \) and \( 33 \mathrm{cm} \) respectively with the closed end up and down. The atmospheric
pressure is :
A. \( 75 \mathrm{cm} \) of \( \mathrm{Hg} \)
B. 76 \( \mathrm{cm} \) of \( \mathrm{Hg} \)
c. \( 70 \mathrm{cm} \) of \( \mathrm{Hg} \)
D. \( 100 \mathrm{cm} \) of \( \mathrm{Hg} \)


NCERT
Autecology is the
A. relation of heterogeneous population to its environment
B. relation of an individual to its environment
C. relation of a community to its environment
D. relation of a biome too its environment


On which basis later researches proved
that Dalton's atomic theory was not wholly correct :
A. An atom is the ultimate
B. Discrete particle of matter
c. Indivisible particle of matter
D. All of the above


Which of the following is responsible for soil erosion in farms?
A. Rivers and wind work
B. Defective methods of farming
c. Flowing water
D. Moving glaciers


Which of the following species are hypervalent?
1. \( C l O_{4}^{-} \)
2. \( \boldsymbol{B F}_{\mathbf{3}} \)
\( \mathbf{3} . \boldsymbol{S} \boldsymbol{O}_{\boldsymbol{4}}^{2-} \)
4. \( \boldsymbol{C O}_{3}^{2-} \)
\( \mathbf{A} \cdot 1,2,3 \)
B. 1,3
\( c .3,4 \)
D. 1,2


Find the oxidation number of elements
in each case.
\( O \) in \( O_{2}, O_{3}, O F_{2} \) and \( B a O_{2} \)
в. 0,0,+2,+1
c. 0,0,+1,0
D. None of the above


Column I represent the size of the soil
particles and Column I represents type of solid components. Which of the following is correct match for the Column I and
Column II.
Column I
A. 0.2 to \( 2.00 \mathrm{mm} \)
(i) Slit
B. Less than 0.002 \( \mathrm{mm} \)
(ii) Clay
\[
\begin{array}{l}
\text { C. } 0.02 \text { to } 0.2 \mathrm{mm} \\
\text { m }
\end{array}
\]
(iii) Coarse and particle
D. 0.002 to \( 0.02 \mathrm{mm} \)
(iv) Fine sand particle
B. (A) - (iv), (B) - (i), (C) - (iii), (D) - (ii)
c. (A) - (iii), (B) - (ii), (C)-(iv), (D) - (i)
D. None of the above


If \( z_{1}, z_{2}, z_{3}, z_{4} \) be the vertices of
rhombus in argand palne and
\( \angle C B A=\pi / 3, \) then prove that
\( \mathbf{2} z_{2}=z_{1}(\mathbf{1}+i \sqrt{\mathbf{3}})+z_{3}(1-i \sqrt{\mathbf{3}}) \)
and \( 2 z_{4}=z_{1}(1-i \sqrt{3})+z_{3}(1+ \)
\( \boldsymbol{i} \sqrt{\boldsymbol{3}}) \)


Statement I: The most important factor in determining the chemical properties of an element is the number of electrons
in the outermost shell.

Statement II: The number of electrons in
the outer shell determines the bonding characteristics of the element.
A. Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement
B. Both the Statement 1 and Statement 2 are correct and statement 2 is NOT the correct explanation of Statement
c. statement 1 is correct but Statement 2 is not correct
D. statement 1 is not correct but Statement 2 is correct
E. Both the Statement 1 and Statement 2 are not correct


A rope is wound around a hollow
cylinder of mass \( 3 k g \) and radius \( 40 c m \) What is the angular acceleration of the cylinder if the rope is pulled with a force
of \( 30 N ? \)
\( \mathbf{A} \cdot 5 m / s^{2} \)
B . \( 25 \mathrm{m} / \mathrm{s}^{2} \)
c. \( 0.25 \mathrm{rad} / \mathrm{s}^{2} \)
\( \mathbf{D} \cdot 25 \mathrm{rad} / \mathrm{s}^{2} \)


If the distance between two particles is doubled,then the gravitational force becomes
A . Half
B. One fourth
c. Double
D. one eighth


The length of similar components
produced by a company is approximated by a normal distribution model with a mean of \( 5 \mathrm{cm} \) and a
standard deviation of \( 0.02 \mathrm{cm} . \) If a
component is chosen at random.what
is the probability that the length of this component is between 4.98 and 5.02
\( \mathrm{cm} ? \)
\( \mathbf{A} \cdot 0.5826 \)
B . 0.6826
c. 0.6259
D. 0.6598


The range of the function, \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left(1+\sec ^{-1} x\right)\left(1+\cos ^{-1} x\right) \) is
\( A \cdot(-\infty, \infty) \)
В \( \cdot(-\infty, 0] \cup[4, \infty) \)
\( ^{c} \cdot\left\{0,(1+\pi)^{2}\right\} \)
D. \( \left[1,(1+\pi)^{2}\right] \)


State and explain laws of chemical combination.


In exothermic reaction
\( \mathbf{A} \cdot H_{R}=H_{P} \)
В \( \cdot H_{R}>H_{P} \)
\( \mathbf{c} \cdot H_{R}<H_{P} \)
D. \( \Delta H=0 \)


Assertion
\( H_{2} S O_{4} \) cannot act as reducing agent
Reason

Sulphur cannot increase its oxidation
number beyond +6
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


If the point \( (x, y) \) is equidistant from the points \( (a+b, b-a) \) and \( (a- \)
\( b, a+b), \) prove that \( b x=a y \)


A man is standing on a boat in still water. If he walks towards the shore, the boat will:
A. move away from the shore
B. remain stationary
c. move towards the shore
D. sink


Rainbow is an example of dispresion of sunlight.Expalin its formation.


Coulomb is an unit of charge while ampere is the rate at which it flows.
If true enter 1 , else enter 0 .


\( f(x)=\frac{\cos x}{\left[\frac{2 x}{\pi}\right]+\frac{1}{2}}, \) where \( x \) is not an
integral multiple of \( \pi \) and [.] denotes the
greatest integer function, is
A. an odd function
B. an even function
c. neither odd nor even
D. none of these


The target used in a Coolidge tube for the production of \( X \) -rays is made up of
A. manganese
B. molybdenumm
c. uranium
D. radium


The locus of the feet of perpendiculars drawn from the point \( (a, 0) \) on tangents
to the circle \( x^{2}+y^{2}=a^{2} \) is
A \( \cdot a^{2}\left(x^{2}+y^{2}+a x\right)^{2}=a^{2}\left(y^{2}+(x+a)^{2}\right) \)
B \( \cdot a^{2}\left(x^{2}+y^{2}-a x\right)^{2}=y^{2}+(x-a)^{2} \)
C \( \cdot\left(x^{2}+y^{2}-a x\right)^{2}=a^{2}\left(y^{2}+(x-a)^{2}\right) \)
D \cdot a \( ^{2}\left[\left(x^{2}+y^{2}\right)-a^{2} x^{2}\right]=\left(y^{2}+(x-a)^{2}\right) \)


A horizontal straight wire \( 10 \mathrm{m} \) long extending from east to west is falling
with a speed of \( 5.0 m s^{-1}, \) at right angles
to the horizontal component of the
earth's magnetic field 0.30 \( \times 10^{-4} W B m^{-2} . \) (a) What is the
instantaneous value of the emf induced
in the wire?(b) What is the direction of
the emf?(c) Which end of the wire is at
the higher electrical potential?


\( P H_{3} \) has lower boiling point than \( N H_{3} \)
Why?


Following are the car parking charges near railway station upto
\( 4 \mathrm{hrs} \quad \) Rs 60
\( \mathbf{8} \) hrs \( \quad \boldsymbol{R} \boldsymbol{s} \mathbf{1 0 0} \)
\( \mathbf{1 2} \) hrs \( \quad \boldsymbol{R} \boldsymbol{s} \mathbf{1 4 0} \)
\( \mathbf{2 4} \) hrs \( \quad \boldsymbol{R} \boldsymbol{s} \mathbf{1 8 0} \)
Check if the parking charges are in direct proportion to the parking time.


If the equation of family of curves be
\( \boldsymbol{y}=\boldsymbol{a} \cos (\boldsymbol{x}+\boldsymbol{b}), \) where \( a, \boldsymbol{b} \) are arbitrary
constants,and \( \boldsymbol{y}^{\prime}=\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}, \boldsymbol{y}^{\prime \prime}=\frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}^{\prime}} \) etc
then their differential equation is :
A \( \cdot y^{\prime \prime}=y \)
B \( \cdot y^{\prime \prime}=y y^{\prime} \)
C \( \cdot y^{\prime \prime}+y=0 \)
\( \mathbf{D} \cdot y^{\prime \prime}=y+y^{\prime} \)


Which of the following terms does not go well with the motion of a bus on a
crowded road.
A. Uniform velociity
B. Variable velocity
c. Variable acceleration
D. Variable speed


In order to prepare a 1 amine from an alkyl halide with simultaneous addition
of one \( C H_{2} \) group in the carbon chain, the reagent used as source of nitrogen is:
A. Sodium amide \( N a N H_{2} \)
B. Sodium azide \( N a N_{3} \)
c. Potassium cyanide \( K C N \)
D. Potassium phthalimide \( C_{6} H_{4}(C O)_{2} N^{-} K \)


The family of curves passing through (0,0) and satisfying the differential equation \( \left.\frac{\boldsymbol{y}_{2}}{\boldsymbol{y}_{1}}=1 \text { (where }\left(\boldsymbol{y}_{n}=\frac{\boldsymbol{d}^{n} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{n}}\right)\right) \)
is
A. \( y=k \)
в. \( y=k x \)
c. \( y=k\left(e^{x}+1\right) \)
D. \( y=k\left(e^{x}-1\right) \)


Wave front formed by the collimator of a spectrometer
A . Plane
B. Spherical
c. cylindrical
D. Paraboloidal


The least distance of distinct vision for
a normal person is:
\( A \cdot 1 m \)
B. 25 cm
c. \( 10 \mathrm{cm} \)
D. None of these


electron of hydrogen atom in a spherical shell of infinitesimal thickness \( d r, \) at a
distance r from the nucleus. The volume
of this shell is \( 4 \pi r^{2} d r . \) The qualitative
sketch of the dependence of P on r is:
\( \mathbf{A} \)
B.
\( c \)
D.


Among the statements \( (a)-(d), \) the incorrect ones are:
(a) Octahedral \( C o(I I I) \) complexes with strong field ligands have very high magnetic moments
(b) When \( \Delta_{0}<P, \) the d-electron
configuration of \( \operatorname{Co}(I I I) \) in an octahedral complex is \( t_{e g}^{4} e_{g}^{2} \)
(c) Wavelength of light absorbed by \( \left[\boldsymbol{C o}(\boldsymbol{e n})_{3}\right]^{3+} \) is lower than that of
\( \left[\boldsymbol{C o F}_{6}\right]^{3-} \)
(d) If the \( \Delta_{0} \) for an octahedral complex
of \( C o(I I I) \) is \( 18,000 \mathrm{cm}^{-1}, \) the \( \Delta_{t} \) for
its tetrahedral complex with the same
ligand will be \( 16,000 \mathrm{cm}^{-1} \)
\( A \cdot(b) \) and \( (c) \) only
B. (a) and (d) only
C. (a) and (b) only
D. (c) and (d) only


Conductance of \( \boldsymbol{A l}^{+\mathbf{3}} \) is \( \boldsymbol{x} \boldsymbol{S} \boldsymbol{m}^{2} \boldsymbol{g} \boldsymbol{e q}^{-1} \)
and that of \( S O_{4}^{-2} \) is \( y S m^{2} g e q^{-1} . \) Molar conductance of Aliminium sulphate is \( \boldsymbol{S m}^{2} \boldsymbol{m} \boldsymbol{o l} \boldsymbol{e}^{-1} \)
A. \( \frac{x+y}{6} \)
B. \( x+y \)
c. \( 6(x+y) \)
D. \( 2 x+3 y \)


The larger value of \( K \) indicates that the product is more stable relative to
reactants.
A. True
B. False


The gold leaves of a gold-leaf electroscope are enclosed in a glass
bottle
A. to protect the gold leaves from drafts of air.
B. to protect the gold leaves from rusting.
c. To protect the gold leaves from wear and tear.
D. All of the above


Which of the following noble gas is the most polarized?
A. Radon
B. Krypton
c. xenon
D. Neon


Two changes are stated below:
(i) A piece of magnesium gives of bright flames when burnt
(ii) A piece of iron glows red when heated strongly. Which of these is a chemical change?
A. i only
B. ii only
D. None of the above


The bakane disease of the rice seedling was caused by a pathogen known as
A. Gibberella fujikuroi
в. тму
c. RNA virus
D. None of the above


What is the maximum number of
electrons that the third energy level can hold?
A .2
B. 8
c. 18
D. 32


Explain co-ordination in plants with the
help of suitable examples.


A steel rod is clamped at its two ends and rests on a fixed horizontal base. The
rod is in natural length at \( 20^{\circ} \mathrm{C} \). Find the longitudinal strain developed in the
rod if the temperature rises to \( 50^{\circ} \mathrm{C} \)
Coefficient of linear expansion of steel
\( =1.2 \times 10^{-6} /^{\circ} \mathrm{C} \)
A \( .3 .6 \times 10^{-4} \)
B . \( 3.6 \times 10^{-5} \)
\( \mathbf{c} \cdot 6 \times 10^{-4} \)
D. \( 2.4 \times 10^{-5} \)


Find \( \boldsymbol{y} \) if \( \boldsymbol{x}=\mathbf{4} \) when \( \boldsymbol{y}=\boldsymbol{x}^{3} \)


Assertion
In free expansion of an ideal gas, the
entropy increases.
Reason
Entropy increases in all natural
processes.
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


During day time air blows-
A. from the land to the sea
B. from the sea to the land
C. from one sea to another
D. none of these


The first aldehyde is:
A. formaledehyde
B. acetaldehyde
\( c . \) acetone
D. acetal


Find the term independent of \( ^{\prime} x^{\prime} \) in the expansion of the expression, \( (1+x+ \)
\( \left.2 x^{3}\right)\left(\frac{3}{2} x^{2}-\frac{1}{3 x}\right)^{9} \)


In an organic compound \( P \) is estimated
as:
A. \( M g_{2} P_{2} O_{7} \)
в. \( M g_{3}\left(P O_{4}\right)_{2} \)
\( \mathrm{c} \cdot H_{3} P O_{4} \)
D. \( P_{2} O_{5} \)


Enzymes are:
A. proteins
B. lipids
C . carbohydrates
D. nucleic acids


A body of mass \( 0.1 \mathrm{kg} \) is dropped from a
height of \( 10 \mathrm{m} \) at a place wheres \( g= \)
\( 10 m s^{-2} . \) Its KE just before its strikes
the ground is:
A . 1
B. 1.04 J
c. 3.5
D. 10J


What is the minimum distance
between two crests called?
A. Wavelength
B. Amplitude
c. Displacement
D. wave pulse


n right angled triangle \( A B C \), right angled at \( C, M \) is the mid-point of hypotenuse \( A B . C \) is joined to \( M \) and
produced to a point \( D \) such that
\( D M=C M . \) Point \( D \) is joined to point
B. Show that:
(i) \( \triangle A M C \cong \triangle B M D \)
(ii) \( \angle D B C \) is a right angle.
(iii) \( \triangle D B C \cong \triangle A C B \)
\( (\mathrm{iv}) C M=\frac{1}{2} A B \)


Which of the following acts as a circuit protecting device?
A. Conductor
B. Inductor
c. switch
D. Fuse


The elastic limit of steel cable is \( 3.0 \times \)
\( 10^{8} N / m^{2} \) and the cross-section area is
\( 4 c m^{2} . \) Find the maximum upward
acceleration that can be given to a \( 900 k g \) elevator supported by the cable if the stress is not to exceed one-third of
the elastic limit.lf your answer is \( x, \) then mark the value of \( \frac{x}{5} \)


Assertion
If no external force acts on a system of
particles, then the centre of mass will
not move in any direction.
Reason
If net external force is zero, then the
linear momentum of the system
changes.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A steel wire, when bent in the form of a
square, encloses an area of 121 sq. \( \mathrm{cm} \)
The same wire is bent in the form of a
circle. Find the area of the circle.


Find the mean \( S . D \) of 1,2,3,4,5,6


Considering entropy(s) as a thermodynamic parameter, the criterion for the spontaneity of any
process is:
A \( \cdot \Delta S_{\text {system}}+\Delta S_{\text {surroundings}}>0 \)
B. \( \Delta S_{\text {system}}-\Delta S_{\text {surroundings}}>0 \)
C. \( \Delta S_{\text {system}}>0 \) only
D. \( \Delta S_{\text {surroundings}}>0 \) only


Verify the following:
\( \left(\frac{5}{7} \times \frac{12}{13}\right) \times \frac{7}{18}=\frac{5}{7}\left(\frac{12}{13} \times \frac{7}{18}\right) \)


Q Type your question
sy piocuris
equal area A are use dat the four
opening to keep the water in
equilibrium Now an additional force \( F \) is
applied at each piston. The increase
in the pressure at the centre of the
container due to this addition is
\( A \cdot F \)
\( \bar{A} \)
B. \( \frac{2 F}{A} \)
\( c \cdot \frac{4 F}{A} \)
2


According to Charles law,
A. At constant pressure, volume of gas is proportional to its absolute temperature.
B. At constant pressure, the volume of a gas is not proportional to its absolute temperature.
C. At constant gauge pressure, the molecular volume of a gas is proportional to its absolute temperature.
D. At constant volume, the absolute pressure is proportional to absolute temperature.


Which of the following statements about nucleosome is true?
A. It consists of only DNA.
B. It is a nucleus-like structure found in prokaryotes
c. It consists of DNA and proteins
D. It consists of only histone proteins


In the given figure, \( A B=A C \). Then
\( \angle B O C=\angle A C D \)
If the above statement is true then
mention answer as 1 . else mention 0


Coelom is formed by the splitting of
A. Mesoderm
B. Ectoderm
c. Endoderm
D. All the above


For the given potentiometer circuits,
potential gradient is \( 0.025 V / m \) and the
ammeter reading is 0.1 A. Now, when
terminals 1 and 2 are connected
balance point is obtained at \( 40 \mathrm{cm} \). Also
when terminals 1 and 3 are connected
balance point in obtained at \( 100 \mathrm{cm} \). If
\( 3 R=k X, \) then the value of \( k \) will be


If \( x^{2}+y^{2}=R^{2} \) and \( K=\frac{1}{R} \) then \( K= \)
A. \( \frac{y_{1}}{x \sqrt{1+y_{1}^{2}}} \)
в. \( \frac{\left|y_{2}\right|}{\sqrt{\left(1+y_{1}^{2}\right)^{3}}} \)
c. \( \frac{2\left|y_{2}\right|}{\sqrt{1+y_{1}^{2}}} \)
D. \( \frac{3\left|y_{2}\right|}{\sqrt{\left(1+y_{1}^{3}\right)^{3}}} \)


In an experiment \( 3 g \) of hydrogen was obtained. If hydrogen and oxygen combine in the ratio of \( 1: 8 . \) Prove the law
of constant proportion.


Find the inverse of \( \left[\begin{array}{ccc}3 & -1 & -2 \\ 2 & 0 & -1 \\ 3 & -5 & 0\end{array}\right] \)
using elementary row transformations.


The more negative the standard potential, the \( \ldots \) is its ability to
displace hydrogen from acids.
A. Greater
B. Lesser
c. Negetivity of the satndard potential has nothing to do with displacement of hydrogen
D. Depends on the acid


Moving with uniform acceleration a
body covers \( 150 m \) in \( 10 s, \) so that it
covers \( 24 m \) during the tenth second. Then the acceleration of the body is
A \( \cdot 2 m / s^{2} \)
B . \( 3 m / s^{2} \)
\( \mathrm{c} \cdot 4 \mathrm{m} / \mathrm{s}^{2} \)
D. \( 6 m / s^{2} \)


Charges -q and +q are fixed at the ends of a light rod of length \( l \). The rod is clamped at one end with axis of the dipole along the electric field. The rod is slightly displaced and then released, Neglecting gravity find the time period of small oscillations. Mass of charges is
meach.
\( ^{\mathbf{A}} \cdot_{2 \pi} \sqrt{\frac{m l}{q E}} \)
в. \( \quad 2 \pi \sqrt{\frac{m l}{3 q E}} \)
\( ^{\mathbf{c}} \cdot_{2 \pi} \sqrt{\frac{m l}{2 q E}} \)
D. \( 2 \pi \sqrt{\frac{2 m l}{q E}} \)


Cathode rays get deflected in an electric
field towards


The degree of the differential equation satisfying \( \sqrt{1-x^{2}}+\sqrt{1-y^{2}}= \)
\( a(x-y) \) is:
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D. none of these


The overall process of carbon nitrogen fusion cycle results in the fusion of 4 protons to yield helium nucleus and:
A. positron
B. two electrons
c. two positrons
D. an electron


Amperes circuital law is given by
A \( \cdot \oint \bar{H} \cdot \overline{d l}=\mu_{0} I_{e n c} \)
B . \( \oint \bar{B} . \overline{d l}=\mu_{0} I \)
C \( . \oint \bar{B} . \overline{d l}=\mu_{0} J \)
D \( \cdot \oint \bar{H} \cdot \bar{d} l=\mu_{0} J \)


The relation \( R \) in \( N \times N \) such that
\( (a, b) R(c, d) \Leftrightarrow a+d=b+c \) is
A. reflexive but not symmetric
B. reflexive and transitive but not symmetric
c. an equivalence relation
D. none of these


The bond disssociation energies of
\( \operatorname{gases} H_{2}, C l_{2} \) and \( H C l \) are 104,58 and
\( \mathbf{1 0 3} \) kcal \( m o l^{-1} \) respectively.

Calculate the enthalpy of formation of \( \boldsymbol{H} \boldsymbol{C l}(\boldsymbol{g}) \)


A chord of a circle is \( 12 \mathrm{cm} \) which is at a distance of \( 8 \mathrm{cm} \) from center. Find the length of the chord of the same circle
which is at a distance of \( 6 \mathrm{cm} \) from the
centre
\( A \cdot 20 \mathrm{cm} \)
B. \( 24 \mathrm{cm} \)
\( c .16 \mathrm{cm} \)
D. \( \mathrm{cm} \)


An electric bulb is rated ' \( 100 W, 250 V^{\prime} \)
How much current will the bulb draw if
connected to a \( 250 V \) supply
A . \( 0.6 A \)
в. \( 2.5 A \)
\( c .5 A \)
D. \( 0.4 A \)


Let in \( \Delta A B C, \angle A=\frac{\pi}{2} . \) Then value of \( \tan ^{-1} \frac{b}{a+c}+\tan ^{-1} \frac{c}{a+b} \) equals
A \( \cdot \frac{\pi}{2} \)
в.
\( c \cdot \frac{\pi}{3} \)
D. None of these


What happen when \( C l \) reacts with dry slaked lime?


Nitrogen in an organic compound can be estimated by:
A. Kjeldahl's method
B. Duma's method only
c. both the methods
D. none of these


Which of the following statements is true for hydra?
A. It provides asexual gemmules
B. It produces unicellular budd
c. It produces multicellular bud
D. None of these


What is fractional change in the
resistance of a filament of \( \boldsymbol{\alpha}=\mathbf{1 0} \times \)
\( 10^{-4} /^{\circ} \mathrm{C}, \) when temperature changes
from \( 25^{\circ} \mathrm{C} \) to \( 40^{\circ} \mathrm{C} ? \)


An element with atomic number 21 is a:
A. halogen
B. representative element
c. transition element
D. alkali element


Describe an experiment to verify the
Boyles law.


Two blocks of mass 5 kg and 10 kg are kept on a rough horizontal surface as
shown in figure A force \( F \) is applied on
upper block of mass 10 kg Now choose
the correct statement(s) regarding the
system
This question has multiple correct options
A. If magnitude of applied force is \( 2 \mathrm{N} \) then frictional force between the blocks is also 2 N
B. The acceleration of 10 kg block is 2 \( m / s^{2} \) when applied force is \( 30 \mathrm{N} \)
C. The minimum value of F for which 5 kg block begin to slide if coefficient of friction between blocks is
changed to 0.5 is \( 45 \mathrm{N} \)
D. 5 kg block will never move on the ground for any value of F if coefficient of friction between blocks is 0.1 and
between block and surface is 0.3


Which has maximum \( p K_{a} \) value?
\( A \cdot H_{2} O \)
в. \( H_{2} \).
\( \mathbf{c} \cdot H_{2} S e \)
D. \( H_{2} T e \)


A colloidal system having a solid substance as a dispersed phase and a
liquid as a dispersion medium are
classified as:
A. solid sol
B. gel
c. emulsion
D. sol


Smoke is colloidal system of dispersed in \( \ldots \)
1. water; air
2. air ; carbon
3. carbon ; air
4. none of the above
Fill in the blanks with correct answer.


Effect of temperature on internal
resistance of a battery is:
A. directly proportional
B. inversely proportional
c. no effect
D. none of these


As the principal quantum number increases, the difference of distance of
separation between consecutive energy
levels:
A . Decreases
B. Remains the same
c. Increases
D. Sometimes increases and sometimes decreases


What conditions are responsible for stimulation of juxtaglomerular
apparatus?
A. An increase in blood pressure or blood volume in heart
B. An increase in the solute concentration the blood plasma.
C. A decrease in the solute concentration oil the blood
plasma.
D. Decrease in blood pressure or blood volume in afferent arteriole.


Solve :
\( \int \frac{x}{2 x-3} d x \)


In the given figure, \( A O B \) is a diameter
of the circle with center \( \boldsymbol{O} \) and \( \boldsymbol{A} \boldsymbol{C} \) is a
tangent to the circle at \( A \). If \( \angle B O C= \)
\( 130^{\circ}, \) then find \( \angle A C O \)


In humans, sex is determined by
A. Y-chromosome
B. X-chromosome
c. A and X-chromosome
D. A and Y-chromosome


Fertilization is necessary even in asexual reproduction
A. True
B. False


Volume (in litres) of \( 0.1 \mathrm{M} \boldsymbol{H}_{2} \boldsymbol{S O}_{4} \)
required to completely neutralize 1 litres of \( 0.5 \mathrm{M} \) NaOH is:
\( \mathbf{A} \cdot \mathbf{5} \)
в. 2.
c. 0.5
D. 10


For the given data, \( S D=10, A M=20, \) the coefficient
of variation is
A . 47
B. 24
\( c \cdot 44 \)
D. 50


Which of the following substance enters our body when a red ant bites us?
A. Melittin
B. Calcium Formate
c. Formic acid
D. Magnesium hydroxide


Assertion
Charge can neither be created nor
destroyed.
Reason
Positive Charge attracts negative
charge.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A block of mass \( m k g \) is sliding from
rest on an inclined rough surface of
inclination \( \theta \) as shown in the figure
under the action of three forces, weight normal and frictional force only. The
magnitude of force are \( 20 N, 40 N \) and
\( \mathbf{5 0} N \) not necessarily in the same order The value of \( g \) is \( 10 m / s^{2} . \) Now match
the physical quantity in \( L i s t-I \) with
their magnitude in \( L i s t-I I \) in \( S I \) unit
and select the correct answer using the
codes given below the lists: (assume
that the coefficient of kinetic friction is
less than 1 ).


Electric Potential on the surface of a
charged spherical shell of radius \( 10 \mathrm{cm} \)
is 50 volt. Find the value of electric
potential at a distance of \( 20 \mathrm{cm} \) from the center of spherical shell.


Which of the following occurs in simple
reflex arc?
A. The sensory neuron synapses directly with the motor neuron
B. Sensory and motor neurons can synapse outside of the spinal cord
C. Sensory neurons synapse in the brain
D. The motor response occurs without synaptic delay
E. A minimum of three neurons must participate


When a ray of light enters glass from
water, it bends:
A. Away from the normal due to increase in the speed of light
B. Away from the normal due to decrease in the speed of light
C. Towards the normal due to decrease in the speed of light.
D. Towards the normal due to increase in the speed of light.


For any two events \( A \) and \( B \) in a sample
space
This question has multiple correct options
\( ^{\mathbf{A}} \cdot p(A / B) \geq \frac{P(A)+P(B)-1}{P(B)}, P(B) \neq 0, \) is always true
B \( \cdot P(A \cap B)=P(A)-P(\bar{A} \cap \bar{B}) \) does not hold.
\( \mathbf{c} \cdot P(A \cup B)=1-P(\bar{A}) P(\bar{B}), \) if \( A \) and \( B \) are independent
D \( \cdot P(A \cup B)=1-P(\bar{A}) P(\bar{B}) \), if \( A \) and \( B \) are disjoint.


In a particular section of class \( 1 X, 40 \) students were asked about the month
of their birth and following graph was prepared for data so obtained:

Find the probability that a student of
the class was born in August.


If \( \overrightarrow{D A}=\vec{a}, \overrightarrow{A B}=\vec{b}, \overrightarrow{C B}=\overrightarrow{k a} \) where
\( k>0 \mathrm{X}, \mathrm{Y} \) are the mid points of \( \mathrm{DB} \) and
AC respectively, such that \( |\vec{a}|=17 \) and \( |\vec{X} Y|=4, \) then k equal to \( ? \)


Boron can be obtained by various methods but not by:
A. thermal decomposition of \( B_{2} H_{6} \)
B. pyrolysis of \( B I_{3} \) (van Arkel)
C . reducing \( B C l_{3} \) with \( H_{2} \)
D. electrolysis of fused \( B C l_{3} \)


What is the centripetal acceleration of the ball if the instantaneous velocity of the ball is doubled?
\( A \cdot a / 4 \)
B. a/2
\( c \)
D. 2a
E. \( 4 a \)


\( \int 5^{5^{5^{x}}} \cdot 5^{5^{x}} \cdot 5^{x} d x \) is equal to


Equipotential surfaces
A. are closer in regions of large electric fields compared to regions of lower electric fields
B. will be more crowded near sharp edges of a conductor
C . will always be equally spaced
D. both
(a) and
(b) are correct


The disease 'witch's broom' of
leguminosae family is caused by a
A. Virus
B. Mycoplasma
c. Protozoan
D. Fungus


\( 100 \mathrm{ml} \) of a hydrocarbon on combustion gave \( 300 \mathrm{ml} \) of \( C O_{2} \) and \( 400 \mathrm{ml} \) of
water vapor measured under similar conditions of temperature and pressure. Find out the molecular
formula of hydrocarbon.
A \( \cdot C_{2} H_{4} \)
в. \( C_{3} H_{6} \)
\( \mathbf{c} \cdot C_{3} H_{8} \)
D. \( C_{3} H_{4} \)


Cell division can not be stopped in which phase of the cell cycle?
A. Gi phase
B. Ga phase
c. s phase
D. All of the above


Name the phenomenon which shows the
quantum nature of electromagnetic radiation.


Figure shows a container filled with a liquid of density \( \rho . \) Four points \( A, B, C \) and D lie on the vertices of a vertical
square. Points A and C lie on a vertical
line and points \( \mathrm{B} \) and \( \mathrm{D} \) lies on a
horizontal line. Choose the correct
statement(s) about the pressure at the
four points
This question has multiple correct options
A \( \cdot P_{D}=P_{B} \)
B . \( P_{A}<P_{B}=P_{D}<P_{C} \)
\( \mathbf{c} \cdot P_{D}=P_{B}=\frac{P_{c}-P_{A}}{2} \)
D \( \cdot P_{D}=P_{B}=\frac{P_{c}+P_{A}}{2} \)


Choose the correct option about a - d.
A. a - eosinophil, b - - lymphocyte, c- neutrophil, d monocyte
B. a - erythrocyte, b - basophil, c- neutrophil, d ymphocyte
c. a - eosinophil, b - monocyte, c- neutrophil, dymphocyte
D. a - eosinophil, b - erythrocyte, c- neutrophil, dbasophi


A municipal corporation wall on road side has dimensions as shown in figure
The wall is to be used for
advertisements and it yields an earning
of \( R s .400 \) per \( m^{2} \) in a year. Find the
total amount of revenue earned in a
year.


During reflection of sound waves against a wall, which of the following properties not change?
A. Frequency
B. Speed
c. wavelength
D. All of them


Two liquids \( A \) and \( B \) form an ideal solution. The vapour pressure of pure \( \mathbf{A} \) and pure B are 66mm of Hg and 88mm of Hg, respectively. Calculate the composition of vapour \( A \) in the solution which is equilibrium and whose molar volume is \( 36 \% \)
A. 0.43
B. 0.70
c. 0.30
D. 0.50


Let \( \left\{a_{n}\right\} \) and \( \left\{b_{n}\right\} \) are two sequences
given by \( a_{n}=(x)^{1 / 2^{n}}+ \)
\( (\boldsymbol{y})^{1 / 2^{n}} \) and \( \boldsymbol{b}_{n}=(\boldsymbol{x})^{1 / 2^{n}}-(\boldsymbol{y})^{1 / 2^{n}} \) for
all \( n \epsilon \) N. The value of \( a_{1} a_{2} a_{3} \dots a_{n} \) is equal to
\( A \cdot x-y \)
в. \( \frac{x+y}{b_{n}} \)
c. \( \frac{x-y}{b_{n}} \)
D. \( \frac{x y}{b_{n}} \)


The compound having lowest melting point is:
A. Licl
в. \( C s C l \)
c \( . R b C l \)
D. KCl


Give suitable chemical terms for the
following:
A definite number of water molecules
bound to some salts.


Fountain pen leak at high altitude.Type 1
for true and 0 for false


Which of the following statement is true
about mole?
A. It is quantity having mass equal to its atomic/ molecular mass
B. It is equal to \( 6.023 \times 10^{23} \)
C. It is the chemist's counting unit
D. All of the above


The A.M. of the first ten odd numbers is
A . 10
B. 100
c. 1000
D.


Explain the formation of energy bands in solids. On the basis of energy bands distinguish between a metal, a semiconductor and an insulator.


\( ^{10} C_{3}=^{10} C_{2 r} \) then \( r=? \)


In a rabbit, the RBCs are formed from
A. Myeloblast
B. Agranulocyte
c. Thymocyte
D. Lymphoblast


placed in the group 17 of the long from periodic table. Element with atomic
number 9 is placed above and with
atomic number 35 is placed below it.
Element with atomic number 16 is
placed left and with atomic number 18
is placed right to it. Which of the following statements are correct?
a) Valency of the element with atomic
number 18 is zero.
b) Elements with same valency will have atomic number 16,17 and 18
c) Valency of element with atomic
number 9,17 and 35 is one.
d) Element with atomic number 17 is
more electronegative than element with atomic number 16 and 35
\( A \cdot(a),(b) \) and \( (c) \)
B. (a), (c) and (d)
\( c \cdot(b),(c) \) and \( (d) \)
D. \( (a),(b) \) and \( (d) \)


To step \( 110 V \) ac down to \( 20 V \) ac, the
turns ratio must be
A . 5.5
B . 18
c. 0.18
D. 0.018


In the equation of the motion of a particle \( \boldsymbol{y}=\mathbf{0 . 5} \sin (\mathbf{0 . 3} \boldsymbol{t}+\mathbf{0 . 1}), \) the
initial phase of motion is
A. \( (0.3 t+0.1) \)
B. 0.3
c. \( 0.3 t \)
D. \( 0 . \)


The Vander waal's equation for ideal gas is given by \( \left(p+\frac{a}{V^{2}}\right)(V-b)=R T \)
where \( P \) is pressure, \( V \) is volume \( a \) and
\( b \) are constants, \( R \) is universal gas
constant and \( \boldsymbol{T} \) is
absolute temperature. Then the dimensions of \( \frac{a}{b} \) are same as that of:
A. Force
B. Momentum
c. Energy
D. Power


A thermometer placed under the armpit always shows a lower value than the actual body temperature. Which type of error is demonstrated in its
measurement.


If a body mass \( 36 g m \) moves with \( \mathrm{S}, \mathrm{H}, \mathrm{M} \)
of amplitude \( A=13 \) and period \( T= \)
12 \( \sec \) At a time \( t=0 \) the displacement
is \( x=+13 c m . \) The shortest time of
passage from \( \boldsymbol{x}=+\mathbf{6 . 5} \mathrm{cm} \) to \( \boldsymbol{x}=-\mathbf{6 . 5} \)
is
\( A \cdot 4 \sec \)
B. 2 sec
\( c \cdot 6 \sec \)
D. 3 sec


The load versus elongation graph for four wires of the same materials is
shown in the figure The thinnest wire is
represented by the line
A. \( 0 c \)
B. OD
\( c \cdot O A \)
D. OB


Which number line correctly shows the
rational number \( \left(-\frac{2}{9}+\frac{1}{9}\right) ? \)
\( A \)
B.
\( c \)
\( D \)


For the curve \( f(x)=\frac{1}{1+x^{2}}, \) let two
points on it be \( \boldsymbol{A}(\boldsymbol{\alpha}, \boldsymbol{f}(\boldsymbol{\alpha})), \boldsymbol{B}\left(-\frac{1}{\boldsymbol{\alpha}}, \boldsymbol{f}\left(-\frac{1}{\boldsymbol{\alpha}}\right)\right)(\boldsymbol{\alpha}>\mathbf{0}) \)
Find the minimum area bounded by
the line segments \( 0 A, O B \) and \( f(x) \) where 'O' is the origin.
A \( \cdot \frac{(\pi-1)}{2} \)
в. \( \frac{\pi}{2} \)
c. \( \frac{(\pi-2)}{2} \)
D. Maximum area is always infinitt


The foci of the ellipse \( \frac{x^{2}}{16}+\frac{y^{2}}{b^{2}}=1 \) and the hyperbola \( \frac{x^{2}}{144}-\frac{y^{2}}{81}=\frac{1}{25} \) coincide
then the value of \( b^{2} \) is:
A . 5
B. 7
c. 9
D. 4


Which of the following pairs of species could be a buffer?
\( A \cdot H^{+} \) and \( \left.C\right|^{-} \)
B. \( \mathrm{H}_{2} \mathrm{CO}_{3} \) and \( \mathrm{HCO}_{3}^{-} \)
c. \( \mathrm{Na}^{+} \) and \( \mathrm{NO}_{3}^{-} \)
D. Nat and OH
E. \( \mathrm{HNO}_{3} \) and \( \mathrm{NO}_{3}^{\text {. }} \)


Which method is used in the refining of Titanium metal?
A. zone refining
B. Mond carbonyl
c. Frasch
D. Van Arkel


What is the order of rotational
symmetry of this star?
\( A \)
3.4
\( c \)
\( D \)


Blood vessel carrying blood from the lungs to the heart is
A. Pulmonary artery
B. Pulmonary vein
c. Coronary artery
D. None of the above


Let us assume that for every 1000 feet
of altitude, the temperature falls 3.5 F.
the temperature at sea level is \( 78 \mathrm{F} \)
what would you expect the temperature to be at 10,000 feet in \( C ? \)
A . 6.11
B. 43
c. 41
D. 7.01


Match the column and choose the
a ppropriate match
\begin{tabular}{lllll}
List I & \multicolumn{3}{l} { List II } \\
A & 4C Compound & 1 & Acetyl Co-A \\
B & 2C Compound & 2 & Pyruvate \\
C & 5C Compound & 3 & Citric acid \\
D & 3C Compound & 4 acid & \( \alpha \) -keto glutaric Malic acid
\end{tabular}
\( A \)
\( A-5, B-1, C-4, D-2 \)
2
B. \( A-5, B-4, C-1, D-2 \)
C. \( A-1, B-5, C-4, D-2 \)
D. A- 5, B-1, C- 2, D-


Which of the following is not a part of
the acid-growth hypothesis?
A. Auxin stimulates proton pumps in cell membranes
B. Lowered pH activates enzymes in the cell walls
C. pH-sensitive enzymes break cross-links between cellulose microfibrils
D. Auxin-activated proton pumps stimulate cell division in meristems


For the coagulation of \( 200 \mathrm{mL} \) of \( A s_{2} S_{3} \)
solution, 10 mL of 1 \( M \) NaCl is
required. What is the coagulating value of \( N a C l ? \)
A . 200
в. 100
c. 50
D. 25


In calcium fluoride, having the fluorite structure, the coordination numbers for
calcium ion \( \left(C a^{2+}\right) \) and fluoride ion
\( \left(\boldsymbol{F}^{-}\right) \) are:
A. 8 and 4
B. 4 and 8
\( c \cdot 4 \) and 2
D. 6 and 6


In uniform circular motion, the velocity vector and acceleration vector are:
A. perpendicular to each other
B. in the same direction
c. opposite in direction
D. not related to each other


The number of elements in each of the
inner transition series is :
\( A \cdot 2 \)
B. 8
c. 10
\( D \cdot 14 \)


Kepler's second law is based on
A. Newton's first law
B. Newton's second law
c. special theory of relativity
D. conservation of angular momentum


Each month a store owner can spend at
most \( \$ 100,000 \) on PC's laptops. A PC
costs the store owner \( \$ 1000 \) and \( a \)
laptop costs him \( \$ 1500 . \) Each PC is sold for a profit of \( \$ 400 \) while laptop is sold for a profit of \( \$ 700 . \) The store owner
estimates that at least 15 PC's but no
more than 80 are sold each month. He
also estimates that the number of
laptops sold is at most half the PC's. How many PC's and how many laptops should be sold in order to maximize the
profit?


A calorimeter of water equivalent 6 g has water of mass 64 gup to a certain volume. Another identical calorimeter
has liquid of mass 50 g and
specific heat \( 0.6 \mathrm{cal} / \mathrm{g}^{-0} \mathrm{C} \) up to same
level. If both of them cool in the same
surroundings through same range of temperature and the time taken for the water to cool is 140 s, then the time taken for the liquid to cool will be :
A. 72 s
B. 140 s
\( c \cdot 36 s \)
D. 120


The time required for the
decomposition of \( N_{2} O_{5}, \) so that the total pressure becomes 0.15 atm is
(Given \( \log 1.8=0.255) \)
A . \( 25.5 \mathrm{sec} \)
B. 35.5 sec
c. \( 45.5 \mathrm{sec} \)
D. \( 55.5 \mathrm{sec} \)


Write any two Maxwell's equation.


The vapour pressure of pure water at
\( 26^{\circ} \mathrm{C} \) is 25.21 torr. The vapour pressure
of a solution which contains 20.0 g glucose, \( C_{6} H_{12} O_{6}, \) in 70 g water is :
A .22 .5 torr
B . 23.4 torr
c. 24.4 torr
D. 24.5 torr


Nitration of benzene is:
A. Nucleophilic substitution
B. Nucleophilic addition
C. Electroohilic substitution
D. Free radical substitution


A long horizontal rigidly supported wire
carries a current \( i_{a}=96 A . \) Directly
above it and parallel to it at a distance,
another wire of \( 0.144 N \) weight per
metre is carrying a current \( i_{b}=24 A, \) in
a direction same as the lower wire. If the
weight of the second wire is balanced
by the force due to magnetic repulsion, then its distance (in mm) from the
lower wire is:
A . 9.6
B. 4.8
c. 3.2
D. 1.6


ff \( \boldsymbol{y}=\boldsymbol{a} \boldsymbol{l} \boldsymbol{n}|\boldsymbol{x}|+\boldsymbol{b} \boldsymbol{x}^{2}+\boldsymbol{x} \) has its
extremum values at \( x=-1 \) and \( x=2 \)
then
A \( . a=2, b=-1 \)
в. \( a=2, b=-\frac{1}{2} \)
c. \( a=-2, b=\frac{1}{2} \)
D. none of these


If \( a+b+c=1 \) and \( a, b, c \) are all distinct positive reals, then prove that (1- a)
b) \( (1-c)>8 \) abc.


How many atom(s) of \( B F_{2}- \) lie in the
same plane?


IUPAC name of \( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{C H}- \)
\( \mathcal{H}_{2} O H \)
\( \boldsymbol{C H}_{2} \boldsymbol{C H}_{3} \) is:
A. 3-propylbutan-1-ol
B. 2-Ethylpentan-1- 이
c. 3- methyl hydroxyhexane
D. 2- ethyl-2 - propyl ethanol


Explain the process of nutrition in
human?


Muddy water can be purified through coagulation by using:
A. common slat
B. alums
\( c . \) sand
D. lime


The multiplicative inverse of \( \frac{-13}{19} \) is \( \frac{-19}{q}, \) then the value of \( q \) is equal to \( ? \)


Assertion
The plots of \( \log \frac{x}{m} \) vs \( \log P \) are linear
Reason

Adsorption increases linearly with increase in pressure at lower range.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


A ball is thrown vertically upwards. After some time, it returns to the thrower
Draw the velocity-time graph and speed-time graph.


Find the lengths of, and the equations to, the focal radii drawn to the point \( (4 \sqrt{3}, 5) \) of the ellipse \( 25 x^{2}+16 y^{2}= \)
\( \mathbf{1 6 0 0} \)


Which of the following is not a polymer?
A. Cholestrol
B. Oxytocin
c. Amylose
D. RNA


Assertion
First seven pairs of ribs are called true
ribs.
Reason
These ribs are connected ventrally to
the sternum.
A. If both assertion and reason are true and reason is the
correct explanation of assertion.
B. If both assertion and reason are true but reason is not the correct explanation of assertion.
C. If assertion Is true but reason is false
D. If both assertion and reason are false.


Find the difference between the mean
and the median of the \( \operatorname{set} 3,8,10,15 \)
A . 0
B.
\( c \cdot 4 \)
\( D \)


A glass rod when rubbed with silk cloth
acquires a charge \( 1.6 \times 10^{-13} C . \) What
is the charge on the silk cloth?
A \( .-1.6 \times 10^{-19} C \)
В. \( 1.6 \times 10^{-13} C \)
c. \( -1.6 \times 10^{-13} C \)
D. \( 1.6 \times 10^{-19} C \)


The quantum numbers of \( +1 / 2 \) and
\( -1 / 2 \) for the electron spin
represents
A. rotation of electron in clockwise and anticlockwise direction respectively
B. rotation of electron in anticlockwise and clockwise
direction respectively
C. two quantum mechanical states having classical analogue
D. two quantum mechanical states having no classical analogue


True or False
A person stands at a point A due south of a tower and observes his elevation is
\( 60^{\circ} . \) He then walks westwards towards
where the elevation is \( 45^{\circ} . \) At a point \( C \)
on \( A B \) produced he finds it to be \( 30^{\circ} \)
then \( A B=2 B C \)
A. True
B. False


The line \( x \cos \theta+y \sin \theta=p \) meets the
axes of co-ordinates at \( A \) and \( B \)
respectively. Through A and B lines are drawn parallel to axes so as to meet the perpendicular drawn from origin to given line in \( P \) and \( Q \) respectively; then show that \( |P Q|=\frac{4 p|\cos 2 \theta|}{\sin ^{2} 2 \theta} \)


Assertion
For adsorption \( \Delta G, \Delta S \) and \( \Delta H \) all have negative values.
Reason
Adsorption is a spontaneous process accompanied by decrease in randomness.
A. If both (A) and (R) are true and (R) is the correct explanation of (A).
B. If both (A) and (R) are true, but (R) is not the correct explanation of (A).
c. If (A) is correct, but (R) is incorrect.
D. If (A) and (R) are both incorrect


Construct a quadrilateral \( P Q R S \) in
which \( P Q=4.5 c m, Q R=5.2 \mathrm{cm} \)
\( R S=5.5 c m, P S=4 c m \) and
\( \angle P Q R=120^{\circ} \)


On the basis of Rutherford's model of an
atom, which sub-atomic particle is
present in the nucleus of an atom?
A. Protons
B. Electrons
c. Neutrons
D. All of the above


A light bulb is constructed from \( 2 \mathrm{cm} \) of
tungsten wire of diameter \( 50 \mu m \) and is
enclosed in an evacuated glass bulb. What temperature does the filament reach when it is operated at a power of 1 watt. (Assume the emissivity of the
tungsten surface is 0.35 Stefan's constant \( =\mathbf{5 . 6 7} \times \mathbf{1 0}^{-4} \mathbf{c m}^{-\mathbf{2}} \mathbf{K}^{-\mathbf{4}} \)
A . \( 2000 K \)
в. \( 4000 K \)
\( c .2500 K \)
D. \( 1200 K \)


Which of the following is more reactive?
A. \( H g \)
B. \( A l \)
\( c . A g \)
D. \( C a \)


Arrange the given set of compounds in order of increasing boiling point:
I. 1 -chloropropane
II. Isopropyl chloride
III. 1 -chlorobutane
A. \( I I<I I I<I \)
B. \( I<I I<I I I \)
c. \( I I<I<I I I \)
D. \( I I I<I<I I I \)


Oxalic acid is found in:
A. spinach
B. amla
c. grapes
D. unripe mangoes


How long after the beginning of motion is the displacement of a harmonically oscillating particle equal to one half its amplitude if the period is 24 s and particle starts from rest.
A . 12 s
B. 2s
\( c \cdot 4 s \)
D. \( 6 s \)


More is the specific heat capacity of a substance, \( \ldots \) the temperature for a given amount of heat energy
A. more
B. less
c. same
D. cant say


The electrolysis of aqueous solution of
\( \boldsymbol{C u B r _ { 2 }} \) using platinum electrode would
leads to:
This question has multiple correct options
A. \( B r_{2} \) gas at anode
B. \( B r_{2} \) gas at anode and \( O_{2} \) gas at cathode
c. copper(s) at cathode
D. \( H_{2} \) gas at cathode


Prove that \( : 4-5 \sqrt{3} \) is irrational


Simplify \( :(a+2 b+3 c)^{2}- \)
\( (a-2 b+3 c)^{2}-6 b^{2}-9 b c \)


The oxidation state of the most
electronegative element in the products
of the reaction between \( B a O_{2} \) and
\( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) is:
A. 0 and -1
B. - - 1 and - 2
c. - - a and o
D. - 2 and +1


Explain the term 'solubility product'. How does it differ from ionic product?


The length and breadth of a rectangle (in \( \mathrm{cm} \) ) are \( \mathrm{x} \) and \( \mathrm{y} \) respectively \( \boldsymbol{x} \leq \) \( \mathbf{3 0}, \boldsymbol{y} \leq \mathbf{2 0}, \boldsymbol{x} \geq \mathbf{0} \) and \( \boldsymbol{y} \geq \mathbf{0} . \) If \( \mathbf{a} \)
rectangle has a maximum perimeter, then its area is \( \ldots \ldots \)


The role of mitosis is not merely, to
divide a cell into two daughter cells but
to ensure genetic continuity, from one cell generation to another cell generation. The mechanism ensuring genetic continuity is
A. Formation of cells with new chromosomes
B. Formation of two daughter cells
c. Formation of two cells with identical DNA
D. Halving the chromosome number between the two new cells


The expression \( 21 x^{2}+a x+21 \) is to be
factored into two linear prime binomial factors with integer coefficients. This
can be done if a is:
A. odd number
B. zero
c. even number
D. None


Uncertainly principle is valid for:
A. Proton
B. Methane
C. Both (proton) and (methane)
D. \( 1 \mu m \) sized platinum particles
E . \( 1 \mu m \) sized \( N a C l \) particles


Two loudspeakers are emitting sound
waves of wavelength \( \mu \) with an initial
phase difference of \( \frac{\pi}{2} . \) At what minimum distance from 0 on line AB
will one hear a maxima?
A \( .25 \lambda \)
B. \( \frac{100 \lambda}{\sqrt{15}} \)
\( c \cdot \frac{25 \lambda}{3} \)
D. \( 50 \lambda \)


At two different places the angles of dip
are respectively \( 30^{0} \) and \( 45^{0} . \) At these
two places the ratio of horizontal component of earths magnetic field is
A. \( \sqrt{3}: \sqrt{2} \)
B. \( 1: \sqrt{2} \)
c. 1: 2
D. \( 1: \sqrt{5} \)


Which of the following electromagnetic waves is used in medicine to destroy
cancer cells?
A . IR-rays
B. Visible rays
c. Gamma rays
D. Ultraviolet rays


The equivalent mass of an element is 4
Its chloride has vapour density 59.25 Then the valency of the element is:
\( A \cdot 4 \)
B. 2
\( c \cdot 3 \)
D.


Iron is ferromagnetic:
A. at all temperatures
B. at NTP only
C . above \( 770^{\circ} \mathrm{C} \)
D. below \( 770^{\circ} \mathrm{C} \)


Find the direction cosines of two lines
which are connected by the relations \( l+m+n=0 \) and \( m n-2 n l-2 l m= \)
\( \mathbf{0} \)


Assertion
Size of the hydrated ion is in order \( \boldsymbol{L} \boldsymbol{i}^{+}>\boldsymbol{N} \boldsymbol{a}^{+}>\boldsymbol{K}^{+}>\boldsymbol{R} \boldsymbol{b}^{+} \geq \boldsymbol{C} \boldsymbol{s}^{+} \)
which is just reverse of ionic size
Reason
Greater the charge or charge density smaller the ionic size, greater the hydration hence, greater the size of the hydrated ion
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


On suspending a mass M from a spring of force constant K,frequency of vibration \( f \) is obtained If a second spring as shown in the figure. is arranged then the frequency will be :
A \( . f \sqrt{2} \)
B. \( f / \sqrt{2} \)
\( c . \) २
D.


How many times will light travel around
the Earth in one second?
A. 7 times
B. 5 times
c. 3 times
D. 9 times


Pick the correct name of
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{5} \boldsymbol{C l}\right] \boldsymbol{C l}_{2} \)
a) Chloropentammine cobalt (III)
b) Pentammine cobalt (III) chloride
c)Chloropentammine cobalt (III) chloride
d)Pentaamminechloridocobalt(III)dichl
oride.


Two unbiased dice are thrown together
at random. Find the expected value of
the total number of points shown up.


What will be the abnormal molecular
\( \operatorname{mass} \) of \( \mathrm{K}_{3}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right] . \) If in a aqueous
solution it is \( 40 \% \) dissociated? (Given, normal molecular weight of
\( \left.\mathbf{K}_{3}\left[\mathbf{F e}(\mathbf{C N})_{6}\right] \text { is } 329\right) \)
A . 149.54
B. 723.8
c. 82.25
D. 329.0


Cause of positive charge on a body is an excess of electrons.
A . True
B. False


Calculate the values of the
determinants:
\( \left|\begin{array}{cccc}\mathbf{7} & \mathbf{1 3} & \mathbf{1 0} & \mathbf{6} \\ \mathbf{5} & \mathbf{9} & \mathbf{7} & \mathbf{4} \\ \mathbf{8} & \mathbf{1 2} & \mathbf{1 1} & \mathbf{7} \\ \mathbf{4} & \mathbf{1 0} & \mathbf{6} & \mathbf{3}\end{array}\right| \)


An ammonia solution has a density of
\( 0.910 \mathrm{g} \mathrm{cm}^{-3} \) and is \( 25.0 \% \mathrm{NH}_{3} \) by mass.
What is the molarity of the solution?
A . \( 12.1 \mathrm{M} \)
B. 13.4 M
c. \( 14.5 \mathrm{M} \)
D. 15.5 M


If the volume of a sphere increases by \( 72.8 \%, \) then its surface area increases by
A . 20\%
B. 44\%
c. 24.3\%
D. 48.6\%


Closed circulatory system occurs in
A. Cockroach
B. Tadpole and fish
c. Mosquito
D. Housefly


f \( \sin \theta+2 \cos \theta=1 \) then prove that
\( 2 \sin \theta-\cos \theta=0 \)


Arrange the following in increasing order of boiling points.
¡) \( \left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{C H} \boldsymbol{C H}_{2} \boldsymbol{I} \)
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{C l} \)
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{I} \)


Are nuclear reactions more energetic
than chemical reactions?


Autotrophs and heterotrophs differ in
A. How they obtain their carbon.
B. Whether they are prokaryotic or eukaryotic.
C . How they reproduce, sexually or asexually.
D. Whether they use chemicals or light as a source of energy.


At constant pressure, the heat of
formation of a compound is not dependent on temperature, when:
\( \mathbf{A} \cdot \Delta C_{p}=0 \)
В. \( \Delta C_{v}=0 \)
\( \mathbf{c} \cdot \Delta C_{p}>0 \)
D. \( \Delta C_{p}<0 \)


Which of the following is a product of the incomplete combustion of hydrocarbons?
A \( . H_{2} \)
в. \( S O_{2} \)
c. \( C O \)
D. \( H C l \)
E. \( O_{3} \)


Sulphides ores are converted to oxides
before reduction. This is explained on
the basis of which of the following?
A. Sulphides cannot be reduced easily while oxides can be reduced easily.
B. Sulphides decompose on reduction hence they are fixed converted to oxides.
C. Sulphide ores have higher melting points than oxides.
D. Oxides are more stable than sulphides hence easy to reduce.


The net torque on the body is zero that
means the distance between the force
and the rotational axis is zero
A. The first part of the statement is false and other part is true
B. The first part of the statement is false and other part is false too
C. The first part of the statement is true and other part is false
D. The first part of the statement is true and other part is true too


If \( \tan \theta+\sec \theta=2 x \) then prove that
\( \sec \theta=x+\frac{1}{4 x} \)


Find the degree of the following polynomial \( x^{3}+2 x^{2}-5 x-6 \)


An die is tossed twice. Find the
probability of getting 4,5 or 6 on the toss and 1,2,3 or 4 on the second toss.


(i) Name the device used to protect the electric circuits from overloading and short circuits.
(ii) On what effect of electricity does the above device work?


Take any point \( O \) in the interior of a
\( \triangle P Q R \) Is \( O R+O P>R P ? \)


Codon for Glutamine is:
A. CAGG
в. АМР
c. ADP
D. ATP


What is the tension between her ears?
A \( .2 .1 k N \)
B. \( 2.6 k N \)
c. \( 2.9 k N \)
D. None


Which of the following are the symptoms of diarrhoea?
A. skin tenting and abdominal pain
B. Pain in legs
c. Heart attack
D. All of the above


What is common between parrot,
platypus and kangaroo?
A. Mammary glands
B. Homeothermy
c. Toothless jaws
D. Functional post-anal tail


A steel wire of length \( 5 \mathrm{m} \) is pulled to have an extension of \( 1 \mathrm{mm} \). Its \( \mathrm{Y} \) is \( 1.9 \mathrm{x} \)
\( 10^{4} \mathrm{N} / \mathrm{m}^{2} . \) The energy per unit volume stored in it is
A \( .3 .8 \times 10^{-4} \mathrm{J} / \mathrm{m}^{3} \)
B . \( 7.6 \times 10^{-4} J / m^{3} \)
C \( .1 .9 \times 10^{-4} J / m^{3} \)
D. \( 0.95 \times 10^{-4} \mathrm{J} / \mathrm{m}^{3} \)


A ball is dropped from a height of \( 19.6 m \) The distance covered by it in the last second is
A . 19.6
B. \( 14.7 m \)
\( c .4 .8 m \)
D. \( 9.8 m \)


Diameter of capillaries for RBC to pass
should be
\( A \cdot 4 \mu \)
B. Less than \( 5 \mu \)
c. More than \( 5 \mu \)
D. More than \( 10 \mu \)


The indicator used in iodometric
titrations is
A. Phenolphthalein
B. Litmus
c. Potassium iodide
D. starch


\( \operatorname{Let} \boldsymbol{P}(\boldsymbol{n})=\boldsymbol{x}^{2 n-1}+\boldsymbol{y}^{2 n-1} \) is divisible
by \( \boldsymbol{x}+\boldsymbol{y} \) as \( \boldsymbol{P}(1) \) is true, then truth of
\( \boldsymbol{P}(\boldsymbol{k}+\mathbf{1}) \) indicates
A \( \cdot P(n) \) s divisible by \( x+y \) only for odd positive integer
B . \( P(n) \) is divisible by \( x+y \) only for positive even integer
c. \( P(n) \) is true \( \forall n \in N \)
D \cdot \( P(k) \) is true


Methanol is never stored in aluminium
vessel because:
A. it reacts with aluminium forming toxic gas
B. it results in explosion
c. it corrodes the the metal by destroying its oxide layer
D. aluminium reduces methanol to methane


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


Gurmit wanted to perform activity 16.8
using a laser torch. Her teacher advised
her not to do so. Can you explain the basis of the teachers advise?


The equilibrium constant for the
reaction is 9.40 at \( 900^{\circ} \mathrm{C} . S_{2}(g)+ \)
\( C(s) \rightleftharpoons C S_{2}(g) \)
The pressure of two gases at
equilibrium, when 1.42 atm of \( S_{2} \) and excess of \( C(s) \) come to equilibrium is :
A \( \cdot P_{C S_{2}}=1.284 a t m, P_{S_{2}}=0.1365 a t m \)
B . \( P_{C S_{2}}=0.1365 a t m, P_{S_{2}}=1.284 a t m \)
C . \( P_{C S_{2}}=1.345 a t m, P_{S_{2}}=0.1456 a t m \)
D. \( P_{C S_{2}}=1.444 a t m, P_{S_{2}}=0.1857 a t m \)


The number of possible arrangements of letters of the word \( R E V I S I O N \) such
that there are exactly two vowels
between \( E \) and \( V \) is
A. 4032
в. 480
\( c .600 \)
D. 720


Bacteria have been put in the kingdom Monera because they are
A. Prokaryotic
B. Eukaryotic
c. Acellular
D. None of the above


The vapour pressure in \( \mathrm{mm} \) of \( \boldsymbol{H} \boldsymbol{g} \), of an aqueous solution obtained by adding 18 g of glucose \( \left(C_{6} H_{12} O_{6}\right) \) to 180 gof water at \( \left(100^{\circ} \mathrm{C}\right) \) is:
A . 7.60
B. 76.0
c. 759
D. 752.4


A jet plane is travelling towards west at a speed of \( 1600 \mathrm{km} / \mathrm{h} \). What is the voltage difference developed between
the ends of the wing having a span of 25 \( \mathrm{m}, \) if the Earths magnetic field at the
location has a magnitude of \( 5 \times 10^{-4} \mathrm{T} \)
and the dip angle is \( 30^{\circ} \)
A . 4.1
B. 2.2 V
c. \( 3.2 v \)
D. 3.8 V


In which of the following cases, a force is not being applied?
A. A man standing behind a stationary car.
B. A car being pushed by a man.
c. A man trying to stop a sliding car.
D. A man standing on a car


The food stored in the ripening fruit is derived from
A . Roots
B. Farthest leaves
c. Nearest leaves
D. Aerial stem


Domain formation is the necessary
feature of
A. ferromagnetism
B. diamagnetism
c. paramagnetism
D. all of these


Thomson atomic theory proved that the stream in cathode ray tube is made up of small particles which is piece of the atom and is :
A. neutral
B. negatively chargedd
c. positively charged
D. both A and B


In a right-angled, triangle the area of the square drawn on the Hypotenuse is \( 289 c m^{2} \) and the area of the
square drawn on the Base is \( 225 \mathrm{cm}^{2} \)
What will be the area of the square
drawn on the Height of the triangle in
\( c m^{2} ? \)


f \( z=2-3 i, \) then show that, \( z^{2}-4 z+ \)
\( \mathbf{1 3}=\mathbf{0} \)


The distance or origin from the point \( P(3,2) \) is :
A \( \cdot \sqrt{2} \)
B. \( \sqrt{15} \)
c. \( \sqrt{13} \)
D. \( \sqrt{11} \)


The value of \( f(0) \) so that the function \( f(x)=\frac{\sqrt{1+x}-\sqrt[3]{1+x}}{x} \)
becomes continuous, is equal to
A \( \cdot \frac{1}{6} \)
B. \( \frac{1}{4} \)
\( c \cdot 2 \)
D.


The number of positive integral
solutions of the equation \( \left|\begin{array}{ccc}\boldsymbol{x}^{\boldsymbol{3}}+\mathbf{1} & \boldsymbol{x}^{\boldsymbol{2}} \boldsymbol{y} & \boldsymbol{x}^{\boldsymbol{2}} \boldsymbol{z} \\ \boldsymbol{x} \boldsymbol{y}^{\boldsymbol{2}} & \boldsymbol{y}^{\boldsymbol{3}}+\boldsymbol{1} & \boldsymbol{y}^{\boldsymbol{2}} \boldsymbol{z} \\ \boldsymbol{x} \boldsymbol{z}^{\boldsymbol{2}} & \boldsymbol{y} \boldsymbol{z}^{\boldsymbol{2}} & \boldsymbol{z}^{\boldsymbol{3}}+\mathbf{1}\end{array}\right|=\mathbf{1 1} \) is
A.
B. 3
\( c \cdot 6 \)
D. 12


What is the distribution of electrons in
nitrogen atom?
A. (2,4)
B. (2, 5)
c. (2,6)
D. (2,15)


Two thin lenses of focal lengths \( 20 \mathrm{cm} \) and \( 25 \mathrm{cm} \) are placed in contact. The effective power of the combination is :
\( A \cdot 1 \)
\( \frac{1}{9} \) diopters
B. 45 diopters
c. 6 diopters
D. 9 diopters


The number of moles of sodium oxide in
620 g of it is:
A. 1 moles
B. 10 moles
c. 19 moles
D. 20 moles


How do the functions of cytokinins differ from gibberellins?


Find the value of \( x \) in each of the
following figure :


What will be the product when \( C_{10} H_{22} \) is used in a cracking process?


A boy standing on an open car throws a ball vertically upwards with a velocity of
\( 9.8 m / s, \) while moving horizontally with
uniform acceleration of \( 1 \mathrm{m} / \mathrm{s}^{2} \) starting from rest. The ball will fall behind the
boy on the car at a distance of
\( \mathbf{A} \cdot 1 m \)
B. \( 2 m \)
\( c .3 m \)
D. \( 4 m \)


Give two important uses of washing soda and baking soda.


Multiply 107.88 by 0.610 and express the result with a correct number of
significant figures.
A. 65.8068
B. 65.807
\( c .65 .81 \)
D. 65.8


Let \( Q \) be a non empty subset of \( N \)
and \( q \) is a statement as given below:
\( \boldsymbol{q}: \) There exists an even number \( \boldsymbol{a} \in \boldsymbol{Q} \)
Negation of the statement \( \boldsymbol{q} \) will be :
A. There is no even number in the set \( Q \)
B. Every \( a \in Q \) is an odd number
c. \( (a) \) and \( (b) \) both
D. None of these


\( \ln \operatorname{an} A \cdot P \) sum of first ten terms is
-150 and the sum of its next ten terms
is \( -550, \) Find the \( A . P \)


What happens when phosphine is
passed over copper sulphate solution.


et \( \frac{\boldsymbol{d} \boldsymbol{f}(\boldsymbol{x})}{\boldsymbol{d} \boldsymbol{x}}=\frac{\boldsymbol{e}^{\sin \boldsymbol{x}}}{\boldsymbol{x}}, \boldsymbol{x}>\mathbf{0} \)
\( \int_{1}^{4} \frac{3 e^{\sin x^{3}}}{x} d x=f(k)-f(1) \) then one
of the possible values of \( k \) is
A . 16
B. 63
c. 64
D. 15


The value of \( \cos \left(36^{\circ}-A\right) \cos \left(36^{\circ}+\right. \)
\( A)+\cos \left(54^{\circ}+A\right) \cos \left(54^{\circ}-A\right) \) is?
\( \mathbf{A} \cdot \sin 2 A \)
B. \( \cos 2 A \)
\( c \cdot \cos 3 A \)
\( \mathbf{D} \cdot \sin 3 A \)


The speed of a longitudinal wave in a mixture of hellium and neon at \( 300 \mathrm{k} \)
was found to be \( 758 \mathrm{m} / \mathrm{s} \). The
composition of the mixture would then
be
\( \mathbf{A} \cdot 13: 3 \)
B . 4: 3
c. 2: 1
D. 4: 1


What is the power gain?


State Biot-Savart law.


\( \int \frac{d x}{(x-1) \sqrt{x^{2}-1}}= \)
A \( -\sqrt{\frac{x-1}{x+1}}+C \)
в. \( \sqrt{\frac{x-1}{x^{2}+1}}+C \)
c. \( -\sqrt{\frac{x+1}{x-1}}+C \)
D. \( \sqrt{\frac{x^{2}+1}{x-1}}+C \)


The value of \( (1+i)^{5} \times(1-i)^{5} \)


Wearing black clothes in summer is
more preferable. True or false.
A. True
B. False


A charge \( q \) is moving with a velocity \( \bar{v}_{1}= \) 1 ìm / \( s \) at a point in a magnetic field and experiences a force \( \overline{\boldsymbol{F}}_{\mathbf{1}}=\boldsymbol{q}[-\mathbf{1} \hat{\boldsymbol{j}}+ \)
\( \mathbf{1} \hat{\boldsymbol{k}}] \boldsymbol{N} . \) If the charge is moving with a
velocity \( \bar{v}_{2}=1 \hat{j} m / s \) at the same point
it experiences a force \( \overline{\boldsymbol{F}}_{2}=\boldsymbol{q}[\mathbf{1} \hat{\boldsymbol{i}}-\mathbf{1} \hat{\boldsymbol{k}}] \boldsymbol{N} \)
The magnetic induction \( \bar{B} \) at that
point is
\( \mathbf{A} \cdot(\hat{i}+\hat{j}+\hat{k}) W b / m^{2} \)
B \( \cdot(\hat{i}-\hat{j}+\hat{k}) W b / m^{2} \)
\( \mathbf{c} \cdot(-\hat{i}+\hat{j}-\hat{k}) W b / m^{2} \)
D. \( (\hat{i}+\hat{j}-\hat{k}) W b / m^{2} \)


The Young's modulus of a material is
\( 2 \times 10^{11} N / m^{2} \) and its elastic limit is
\( 1.8 \times 10^{8} N / m^{2} . \) For a wire of \( 1 m \) length
of this material, the maximum elongation achievable is
\( \mathbf{A} \cdot 0.2 m m \)
в. \( 0.3 m m \)
\( c .0 .4 m m \)
D. \( 0.5 m m \)


Assertion
On cooling, the brown colour of nitrogen dioxide disappears.
Reason
On cooling, \( N O_{2} \) undergoes dimerisation resulting in the pairing of
odd electrons of \( N O_{2} \)
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


(i) Define ampere in terms of force
between two current carrying
conductors.
(ii) What is an ideal transformer?


If in a triangles \( \mathrm{XYZ}, \mathrm{P}, \mathrm{Q} \) are points on XY, YZ respectively such that \( X P=2 P Y \) \( \mathrm{XQ}=2 \mathrm{QZ}, \) then the ratio, area of \( \Delta \boldsymbol{X P Q} \)
\( \operatorname{area~of} \Delta X Y Z, \) is
A .4: 9
B. 2:3
\( c \cdot 3: 2 \)
\( D \cdot 9: 4 \)


The contrapositive of \( \sim \boldsymbol{p} \rightarrow(\boldsymbol{q} \rightarrow \sim \boldsymbol{r}) \)
is
\( \mathbf{A} \cdot(q \wedge r) \rightarrow p \)
в. \( (q \rightarrow r) \rightarrow p \)
c. \( (q \vee r) \rightarrow p \)
D. None of these


Explain how heat losses due to conduction, convection and radiation are minimized in a Thermos Flask.


Equal volume of two solution having pH \( =2 \) and \( p H=10 \) are mixed together at 90C. Then pH of resulting solution is :
(Take \( \left.K w \text { at } 90 C=10^{-12}\right) \)
A. \( 2+\log 2 \)
B. 10 \( \log 2 \)
c. 7
\( D \cdot 6 \)


Prove that:
\( \frac{\sin A-2 \sin ^{3} A}{2 \cos ^{3} A-\cos A}=\tan A \)


Find \( x, \) if the matrix \( \left|\begin{array}{ccc}-1 & 2 & 3 \\ 2 & 5 & 6 \\ 3 & x & 7\end{array}\right| \) is a
symmetric matrix.


In the given equation
\( \boldsymbol{a}=\frac{\boldsymbol{2}}{\boldsymbol{3}} \boldsymbol{b}+\mathbf{5} \)
At what value \( a \) becomes equal to \( b \) ?
A . 5
B. 7
c. 10
D. 15


Find the area of the minor segment of a circle of radius \( 14 \mathrm{cm}, \) when its central angle is \( 60^{\circ} \). Also find the area of the
corresponding major segment. \( \left[\boldsymbol{U s e} \boldsymbol{\pi}=\frac{\mathbf{2 2}}{\mathbf{7}}\right] \)


Two forces which are perpendicular to each other, act on a body. The resultant
force \( F_{1} \) makes an angle of \( 60^{\circ} \) with one force. The magnitude of the other force is?
A \( \cdot \sqrt{3} F / 2 \)
B . \( F / \sqrt{2} \)
c. \( F / 2 \)
D. \( 2 F \)


Evaluate: \( \int \frac{1}{x^{2}\left(x^{4}+1\right)^{\frac{3}{4}}} d x ; x=0 \)
\( ^{\mathrm{A}} \frac{\left(x^{4}-1\right)^{\frac{1}{4}}}{x}+c \)
B. \( -\frac{\left(x^{4}+1\right)^{\frac{1}{4}}}{x}+c \)
c. \( \frac{\sqrt{x^{4}+1}}{x}+c \)
D. None of these


A myopic person cannot see clearly:
A. near objects
B. objects placed at the least distance of distinct vision
C. very far objects
D. none


A spherical capacitor consists of two concentric spherical conductors of
inner one of radius \( R_{1} \) maintained at
potential \( V_{1} \) and the outer one of radius
\( \boldsymbol{R}_{2} \) at potential \( \boldsymbol{V}_{2} . \) The potential at a
point \( p \) at a distance \( x \) from the centre
\( \left(R_{2}>x>R_{1}\right) \) is:
A \( \cdot \frac{V_{1}-V_{2}}{R_{2}-R_{1}}\left(x-R_{1}\right) \)
B. \( \frac{V_{1} R_{1}\left(R_{2}-x\right)+V_{2} R_{2}\left(x-R_{1}\right)}{x\left(R_{2}-R_{1}\right)} \)
C \( \cdot V_{1}+\frac{V_{2} x}{R_{2}-R_{1}} \)
D. \( \frac{V_{1}+V_{2}}{R_{2}+R_{1}} x \)


The displacement of a body at a particular second \( n \) is given by the expression \( S_{n^{t h}}=u+\frac{a}{2}(2 n-1) . \) The
dimensional formula of \( S_{n^{t h}} \) in this
equation is
\( \mathbf{A} \cdot\left[M^{2} L^{0} T^{1}\right] \)
B \( \cdot\left[M^{0} L^{1} T^{0}\right] \)
\( \mathbf{c} \cdot\left[M^{0} L^{1} T^{-1}\right] \)
\( \mathbf{D} \cdot\left[M^{0} L^{0} T^{0}\right] \)


The convex surface of a plano-convex
lens is silvered and the radius of
curvature of this surface is \( R \). Find the
focal length of the system.


Write the difference between absorption and adsorption


The population of Delhi State in different census years is as given below:

Census \( \quad 1961 \quad \) 1971 \( \quad 1981 \) year
population
in akhs 30
55
Represent the above information with the help of a bar graph.


A body at maximum height possesses:
A. kinetic energy
B. potential energy
c. solar energy
D. heat energy


There are four kinds of trees in an
orchard. Four part of total trees are Neem trees. Half of the remaining trees
are Mango trees. Half of the remaining trees are Drumstick trees and the
remaining 6 trees are Peepel trees. Find the total number of trees in the orchard.


The potential across a 25.0 microfarad capacitor is \( 5.0 \mathrm{V} \). What is the charge on the capacitor?
A. 0.20 microcoulombs
B. 5.0 microcoulombs
c. 125 microcoulombs
D. 30.0 microcoulombs
E. we cannot determine the charge on the capacitor with the given information.


If a particle moves with an acceleration, then which of the following can remains
constant
A. Both speed and velocity
B. Neither speed nor velocity
c. only the velocity
D. Only the speed


Which of the following are the uses of medicines?
A. Cure disease
B. Maintain health
c. Modify body characterisitics
D. All of the above


When sulphur ( in the form of \( S_{8} \) ) is
heated to temperature \( T, \) at
equilibrium, the pressure of \( S_{8} \) falls by
\( 30 \% \) from 1.0 atm, because \( S_{8}(g) \) is
partially converted into \( S_{2}(g) \). Find the
value of \( K_{p} \) for this reaction.
A .2 .96
B. 6.14
c. 204.8
D. None of these


Draw the structure of the hexanal
molecule.


The major product obtained in the
reaction of aniline with acetic
anhydride is:
\( A \)
B
\( c \)
\( D \)


What would have been happened if any
of the cells in nature had not been
divided by meiosis?


If \( \boldsymbol{I}_{n}=\int_{0}^{\sqrt{3}} \frac{\boldsymbol{d} \boldsymbol{x}}{1+\boldsymbol{x}^{n}},(\boldsymbol{n}=\mathbf{1}, \mathbf{2}, \mathbf{3}, \boldsymbol{4} \dots \dots \dots) \)
then find the value of \( \lim _{n \rightarrow \infty} I_{n}, \) is
A .
B. 1
c. 2
D. \( \frac{1}{2} \)


Which of the following B-group vitamins can be stored in our body?
A. Vitamin \( B_{1} \)
B. Vitamin \( B_{2} \)
c. vitamin \( B_{6} \)
D. Vitamin \( B_{12} \)


Why is aluminium metal not used in
the lab preparation of hydrogen?


The multiplicative inverse of a positive rational number is
A. always positive.
B. may be positive.
c. always negative.
D. maybe negative.


Sucrose is converted to glucose and
fructose of acidic solution which is first
order reaction.


In a dry cell containing a
moist paste of plaster of Paris, \( \boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{C l} \)
and \( Z n C l \) acts as
A. copper vessel, Cathode
B. zinc vessel, Cathode
c. zinc vessel, Anode
D. copper vessel, Anode


Which of the following species will not exhibit disproportionation reaction?
A \( \cdot C l O^{-} \)
B. \( C l O_{2}^{-} \)
\( \mathrm{c} \cdot \mathrm{ClO}_{3}^{-} \)
D. \( C l O_{4}^{-} \)


If a signal passing through a gate is inhibited by sending a LOW into one of the inputs, and the output is HIGH, the gate is \( a(n) \)
A. AND
B. NAND
c. NOR
D. or


Solve \( : \frac{9}{x}-\frac{4}{y}=8 \) and \( \frac{13}{x}+\frac{7}{y}= \)
\( \mathbf{1 0 1} \)
A \( \cdot x=\frac{1}{7} y=\frac{1}{6} \)
В. \( x=\frac{3}{4} y=\frac{1}{6} \)
c. \( x=\frac{1}{4} y=\frac{1}{7} \)
D. \( x=\frac{2}{7} y=\frac{1}{7} \)


Which of the following is secreted at ends of nerve fibres?
A. Ascorbic acid
B. Acetic acid
c. Acetyl CoA
D. Acetylcholine


In an area undergonle process of succession, which community has highest rate of organic matter storage
after consumption of heterotrophs:-
\( A \cdot w \)
B. x
\( c \cdot Y \)
\( D \cdot z \)


In Young's double slit experiment the separation between the slits is halved and the distance between the slits and
screen is doubled. The fringe width is:
A. unchanged
B. halvedd
c. doubled
D. quadrupled


During preparation of soap, sodium is used as:
A. precipitate the soap
B. dehydration of soap
c. as a catalyst
D. for smoothness of soap


The IUPAC name of the compound with
formula \( \mathrm{C}_{n} \mathrm{H}_{2 n+2} \) having the lowest
possible molecular mass and capable of showing enantiomerism, is :
A. 3-Methyl hexane
B. 2,3-Dimethyl pentane
c. Methane
D. Both (a) and (b)


If the solubility product of a sparingly
soluble salt \( M X_{2} \) at \( 25^{\circ} C \) is \( 1.0 \times \)
\( \mathbf{1 0}^{-11}, \) the solubility of the salt in moles
\( L^{-1} \) at this temperature will be:
A \( .2 .46 \times 10^{14} \)
B . \( 1.36 \times 10^{-4} \)
c. \( 2.60 \times 10^{-7} \)
D. \( 1.20 \times 10^{-10} \)


Which of the following is/are correct statement(s) regarding agricultural
activities as a reason for water
scarcity? This question has multiple correct options
A. A majority of farmers in India depend upon rains for irrigating their crops.
B. Irrigation systems such as canals are there only in a few places
c. Even these systems may suffer from lack of water due to erratic rainfall
D. Farmers have to use groundwater for irrigation


Number of \( C l^{-} \) ions satisifying both primary and secondary valency are in
\( \boldsymbol{C o C l}_{3} \mathbf{5} \boldsymbol{N} \boldsymbol{H}_{3} \)


n Fig \( , A C=A E, A B=A D \) and
\( \angle B A D=\angle E A C . \) Show that \( B C=D E \)


State four points of differences between a Concave mirror and a Convex mirror.


A \( 20 \mathrm{cm} \) tall object is placed
perpendicular to the principal axis of a convex lens of focal length \( 10 \mathrm{cm} \). If
object distance is \( 15 \mathrm{cm} . \) Find the
image distance.
A. \( -30 \mathrm{cm} \)
B. \( 30 \mathrm{cm} \)
\( \mathrm{c} \cdot 15 \mathrm{cm} \)
D. -15 cm


The substance added in water in the
froth floatation process is
A. Olive oil
B. Pine oil
c. coconut oil
D. None of the above


What is the degree of the following differential equation?
\( \mathbf{5} x\left(\frac{d y}{d x}\right)^{2}-\frac{d^{2} y}{d x^{2}}-6 y=\log x \)


Diff: \( \cos ^{-1}\left(\frac{2 x}{1+x^{2}}\right) \) w.r.t. \( x \)


a) The diagram below shows the
excretory system of a human being.
Study the same and then answer the
questions that follow.
i) Name the parts labelled 1,2,3 and 4
ii) Give the main function of the parts
labelled 5,6,7 and 8
iii) Name the endocrine gland which
could be added in the diagram and
state its location/position.


Consider the given lewis dot structure:
The formal charges on \( B \) and \( F \) are
respectively.
4. \( -1 . \)
3. -1,-1
\( c \cdot 0,- \)
\( D \)


In given figure \( A B \) is a line-segment. \( P \)
and \( Q \) are points on either side of \( A B \)
such that each of them is equidistant
from the points \( A \) and \( B . \) Show that the
line \( P Q \) is the perpendicular bisector of
\( A B \)


All of the following are isotopes of hydrogen except:
A. tritium
B. hydronium
c. protium
D. deuterium


In Carius method of estimation of halogen, 0.15 g of an organic compound gave 0.12 g of AgBr. What is the percentage of bromine in the compound?
A. 68.08\%
B. 34.04\%
c. 42.1\%
D. 50\%


The value of \( \tan ^{-1}\left(2 \sin \left(\sec ^{-1}(2)\right)\right) \) is
A \( \cdot \frac{\pi}{6} \)
в.
\( c \cdot \frac{\pi}{3} \)
D.


If \( A \) is a matrix of order \( 3 \times 4 \) and \( B \) is a
matrix of order \( 4 \times 3, \) find the order of
the matrix of \( \boldsymbol{A B} \)


\( \left.\left(\frac{1+i}{1-i}\right)^{2}+\frac{1-i}{1+i}\right)^{2} \) ) is equal to


Fill up the blanks in the following paragraph by selecting the correct
option.
(i) are the primary female sex organs that produce \( (\mathrm{i} \mathrm{i}) \) and \( (\mathrm{iii}) . \) Each primary
sex organ is about \( ( \) iv ) in length and is
connected to the pelvic wall and uterus
by \( (\underline{v}) \)
A. (i)-Testes, (ii)-sperms, (iii)-hormones, (iv)-4-5 \( \mathrm{cm},(\mathrm{v})- \) ligaments
B. (i)-Ovaries, (ii)-oogonia, (iii)-follicles, (iv)-2-4 \( \mathrm{cm},(\mathrm{v})- \) muscles
C . (i)-Ovaries, (ii)-ovum, (iii)-hormones, (iv)-2-4 cm, (v)ligaments
D. (i)-Testes, (ii)-sperms, (iii)-testosterone, (iv)-8-9 \( \mathrm{cm} \)
(v)-muscles


The middle term of expansion of \( \left(\frac{10}{x}+\frac{x}{10}\right)^{10} \)
A \( \cdot^{7} C_{5} \)
в. \( ^{8} C_{5} \)
\( \mathrm{c} \cdot^{9} \mathrm{C}_{5} \)
D. \( ^{10} C_{5} \)


Mark out the incorrect statement:
A. A free neutron can transform itself into photon
B. A free proton can transform itself into neutron
C. In beta minus decay, the electron originates from nucleus
D. All of the above


If \( n \) balls hit elastically and normally on a surface per unit area and all units has
mass \( \mathrm{m} \) and are moving with same velocity u, then force on surface is:
A. mun
B. 2 mun
c. \( \frac{1}{2} m u^{2} n \)
\( \mathbf{D} \cdot m u^{2} n \)


Let \( \boldsymbol{f}(\boldsymbol{x})=\sqrt{\log \left(2 \boldsymbol{x}-\boldsymbol{x}^{2}\right)} . \) Then, dom
\( (f)=? \)
A \( .(0,2) \)
B. [1,2]
\( c \cdot(-\infty, 1] \)
D. None of these


A wire of resistance \( 40 \Omega \) is bent into a
square. Then consider the following
statements:
a) resistance between opposite corners
is \( 20 \Omega \)
b) resistance between adjucent corners
is \( 7.5 \Omega \)
c) resistance between mid points of
opposite sides is \( 10 \Omega \)
d) resistance between mid points of
adjacent sides is \( 15 \Omega \)
A. a and dare correct
B. b and d are correct
C. \( b \) and \( c \) are correct
D. a and b are correct


The difference between he maximum
and the minimum observations in the
data is
A. class interval
B. frequency
c. cumulative frequency
D. range


Which of the following is the ore of \( C u ? \)
A. ciderite
B. Magnetite
c. Calamine
D. Malachite


Solution is made by dissolving 0.518 mol of nonelectrolyte solution in 887 g of benzene. Calculate the freezing point.
\( T_{f} \) and boiling point, \( T_{b} \) of the solution
\( T_{\mathrm{b}}=\sqrt{\square}^{\text {Number }} \circ \mathrm{C} \)


What is mechanics?


The boiling point of heavy water is?
\( \mathbf{A} \cdot 100^{0} C \)
в. \( 101.4^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 99^{0} C \)
D. \( 110^{\circ} \mathrm{C} \)


How much heat is required to raise the
temperature of 100 g of water of \( 5^{\circ} \mathrm{C} \) to
\( 95^{\circ} \mathrm{C} ? \)
A. 900 kcal
B. 90 kcal
c. 10 kcal
D. 9 kcal


In dicot root
A. Vascular bundles are scattered with cambium.
B. Vascular bundles are open and arranged in a ring.
C . Xylem and phloem are radial
D. Xylem is always endarch.


A liquid is contained in a vertical tube of a semi-circular cross section as
shown. If angle contact is zero, the
forces of surface tension on the curved
part and on the part are in ratio


Name the type of following triangle.
Triangle with lengths of sides \( 7 \mathrm{cm}, 8 \mathrm{cm} \)
and \( 9 \mathrm{cm} \)


Why all \( P-F \) bonds in \( P F_{5} \) are not
equivalent?
\( \mathbf{A} \cdot P F_{5} \) has \( s p^{3} d \) hybridisation, out of five \( P \) - \( F \) bonds three are equatorial which have different lengths.
B. \( P F_{5} \) has \( s p^{3} \) hybridisation, out of five \( P \) - \( F \) bonds two are equatorial which have different lengths.
C. Out of five \( P \) - \( F \) bonds two are axial and three equatorial. All five bonds have different bond lengths.
D. \( P F_{5} \) is made up of two types of bonds namely covalent and coordinate, hence are not equivalent.


If \( \boldsymbol{f}: \boldsymbol{A} \rightarrow \boldsymbol{B} \) and \( \boldsymbol{g}: \boldsymbol{B} \rightarrow \boldsymbol{C} \) are one-one
functions, show that gof is a one-one function.


\( D_{2} O \) is used as a moderator in nuclear
reactors to slow down the neutrons.
If this is true enter 1 , if false enter 0 .


A ball is dropped from a table-top. Air
resistance may be ignored.

Which row describes the velocity and
the acceleration of the ball at point \( X ? \)
A . acceleration - constant; velocity - constant
B. acceleration - constant; velocity - increasing
c. acceleration - increasing; velocity - constant
D. acceleration - increasing; velocity - increasing


If \( \sin ^{-1}(6 x)+\sin ^{-1}(6 \sqrt{3} x)=-\frac{\pi}{2} \)
then the value of \( x \) is
A \( \cdot \frac{1}{12} \)
B. \( -\frac{1}{12} \)
c. \( -\frac{1}{4 \sqrt{3}} \)
D. \( \frac{1}{4 \sqrt{3}} \)


If \( A_{1} A_{2} ; G_{1} G_{2} ; H_{1} H_{2} \) be two A.M.s
G.M.s and H.M.s between two numbers then prove: \( \frac{\boldsymbol{G}_{1} \boldsymbol{G}_{2}}{\boldsymbol{H}_{1} \boldsymbol{H}_{2}}=\frac{\boldsymbol{A}_{1}+\boldsymbol{A}_{2}}{\boldsymbol{H}_{1}+\boldsymbol{H}_{2}} \)


Which of the following devices can be used to detect a weak current?
A. Use of electric bulb in tester
B. Use of LED in tester
c. A tester using magnetic effects of current
D. Both B and C


\( C H_{3} C H_{2} O H+O_{2} \stackrel{X}{\longrightarrow} \) Vinegar
In the above reaction, \( \boldsymbol{X} \) is:
A \( \cdot\left(C H_{3} C O O\right)_{2} M n \)
в. \( C H_{3} \) СООН
c. mycoderma aceti
D. \( K_{2} C r_{2} O_{7} / H \oplus \)


A invested Rs 76000 in a business After
few months B joined him with Rs 57000 At the end of the year the total profit
was divided between them in the ratio
of 2: 1 After how many months did \( B \) join?
\( A \cdot 4 \)
B. 8
\( c \cdot 9 \)
D. None of these


Two circles of radii \( 10 \mathrm{cm} \) and \( 8 \mathrm{cm} \)
intersect each other and the length of the common chord is 12 m. Then the
distance between their centres is
\( \mathbf{A} \cdot(10+2 \sqrt{7}) \mathrm{cm} \)
B. \( (8+2 \sqrt{7}) \mathrm{cm} \)
\( \mathbf{c} \cdot(12+2 \sqrt{7}) \mathrm{cm} \)
D \( \cdot(6+2 \sqrt{7}) \) ст


The jaundice is a physiological liver dis ease. It is most commonly caused by a
A. Bacterium
B. Virus
c. Both A and B
D. Helminth


Pressure head in Bernoulli's equation
is:
A \( \cdot \frac{P \rho}{g} \)
в. \( \frac{P}{\rho g} \)
\( c \cdot \rho g \)
D. \( P \rho g \)


Which oxides cause acid rains?
A. Sulphur dioxide
B. Nitrogen oxide
C. Carbon dioxide
D. Both A and B


What is the IUPAC name of an element
with atomic number 107


The distance of origin from the image of (1,2,3) in plane \( x-y+z=5 \) is
A \( \cdot \sqrt{17} \)
B. \( \sqrt{29} \)
c. \( \sqrt{34} \)
D. \( \sqrt{41} \)


The earth shakes when
occurs.
A. Tsunami
B. Flood
c. Earthquake
D. Drought


In substance \( M g\left(H X O_{3}\right), \) the oxidation number of \( X \) is :
\( \mathbf{A} \cdot \mathbf{0} \)
B. +2
\( c \cdot+3 \)
D. +4


Which of the following represents
Freon?
A. Acetylene tetrachloride
B. Trichloroethylene
c. Dichlorodifluoromethane
D. Ethylene dichloride


A sphere of mass \( m \) moving with constant velocity hits another sphere of
same mass at rest. If \( e \) is the coefficient
of restitution. The ratio of their
velocities after collision is :
\( \mathbf{A} \cdot 1+e \)
B. \( \frac{1+e}{2} \)
\( c \cdot \frac{1+2 e}{1-2 e} \)
D. \( \frac{1-e}{1+e} \)


Which soil is used to make decorative
articles and pots used for growing plants?
A. Multani soil
B. Terracotta soil
c. shadu soil
D. Kaolin (china clay)


Carbohydrates containing more than 10 simple units of sugar are called:
A. Monosaccharides
B. Disaccharides
c. Trisaccharides
D. Polysaccharides


Q Type your question
school organised a seminar in which he invited parents and principle. They all resolved this issue by strictly banning junk food in schools and introducing healthy snacks and drinks like soup, lassi, milk etc. in school canteens. They
also decided to make compulsory half an hour of daily physical activities for the students in the morning assembly. After six months, Mr. Chopra conducted
the health survey in most of the schools and discovered a tremendous
improvement in the health of the
students.

After reading the above passage, answer the following questions:
(i) What are the values (at least two)
displayed by Mr. Chopra?
(ii) As a student, how can you spread awareness about this issue?
(iii) Why should antidepressant drugs not be taken without consulting a
doctor?
(iv) Give two examples of artificial
sweeteners.


\( \boldsymbol{P h}-\boldsymbol{N}=\boldsymbol{C O} \frac{(\boldsymbol{i}) C \boldsymbol{H}_{3} M \boldsymbol{g} \boldsymbol{B r}}{(\boldsymbol{i} i) \boldsymbol{H}_{2} \boldsymbol{O}} \boldsymbol{P} \frac{\boldsymbol{L} \boldsymbol{i} A \boldsymbol{l} \boldsymbol{H}_{4}}{\longrightarrow} \)
\( Q \)
A \( \cdot P \) is \( P h-N H-\underset{V}{\left.\right|_{V}}-C H_{3} \) and \( Q \) is \( P h-N H- \)
\( C H_{2}-C H_{3} \)
B \( \cdot P \) is \( P h-N H-C H_{3} \) and \( Q \) is \( N H_{3} \)
C.
\[
P \text { is } P h N=C-O H \text { and } Q \text { is } P h-N H-C H_{3}
\]
D \( \cdot P \) is \( P h-N H-C H-C H_{3} \) and \( Q \) is \( P h-N H- \)
\( P h-N H-\underset{O H}{C} H-C H_{3} \)
\( C H-C H_{3} \)
\( _{C H_{3}} \)


Which of the following characteristics should an aromatic compound exhibit?
This question has multiple correct options
A \( \cdot \) It should have \( (4 n+2) \pi \) -electrons in the ring
B. It should be planar and conjugated
c. It should have \( 4 n \pi \) -electrons in the ring
D. It should possess high resonance energy


What is reflection of light ? Also write the laws of reflection.


Which one of the following is the
complementary sequence for the DNA
with \( \mathbf{5}^{\prime} \) -CGTACTA-3' \( ^{\prime} \)
A . \( 5^{\prime} \) '-ТАGТАСG-3
B. 5'-ATCATGA-3
c. \( 5^{\prime} \) -UTCUTGC-3'
D. 3'-GCATGAT-5'


How many triangles can be formed by joining the vertices of a hexagon?


Which of the following connectives satisfy commutative law?
\( A \cdot \wedge \)
B.
\( c \cdot \Leftrightarrow \)
D. All the above


Forests take part in
A. Control of atmospheric pollution
B. Prevention of soil erosion
C. Maintenance of natural balance
D. All the above


During dry weather, clothes made of synthetic fibre often stick to the skin. Which type of force is responsible for this phenomenon?
A. Electrostatic force
B. Frictional force
c. Inter Molecular force
D. None of the above


8
0
0
0


Find the angle between the \( x \) -axis and
the line joining the points (3,-1) and
(4,-2)
A \( .115^{\circ} \)
B . \( 120^{\circ} \)
\( \mathbf{c} \cdot 135 \)
D. \( 140^{\circ} \)


Find the electric field in the region
labelled 3
\( A \cdot 0 \)
B \( \cdot k_{e} \frac{q}{r^{2}} \)
\( c \cdot 2 k_{e} \frac{q}{r^{2}} \)
\( \mathrm{D} \cdot 3 k_{e} \frac{q}{r^{2}} \)


Draw a circuit diagram of an electric circuit containing a cell, a key, an ammeter, a resistor of \( 4 \Omega \) in series with
a combination of two resistors \( (8 \Omega \)
each ) in parallel and a voltmeter across parallel combination. Each of them dissipate maximum energy and canwithstand a maximum power of
\( 16 W \) without melting. Find the
maximum current that can flow
through the three resistors.


A conductor \( A B \) carries a current \( i \) in a magnetic field \( \vec{B} . \) If \( \overrightarrow{A B}=\vec{r} \) and the force on the conductor is \( \vec{F} \). Then
This question has multiple correct options
A \( \cdot \vec{F} \) does not depend on the shape of \( A B \)
В \( \cdot \vec{F}=i(\vec{r} \times \vec{B}) \)
c. \( \vec{F}=i(\vec{B} \times \vec{r}) \)
D \( \cdot|\vec{F}|=i(\vec{r} \cdot \vec{B}) \)


A small sphere of radius \( r, \) falls from
rest in a viscous liquid. As a result, heat is produced due to viscous force. The rate of production of heat when the sphere attains its terminal velocity, is proportional to
A \( \cdot r^{5} \)
в. \( r^{3} \)
\( c \cdot r^{4} \)
D \( \cdot r^{2} \)


For the block under SHM shown in the
figure, which of the following quantities
is not constant?
vertica
oscillation
A. Amplitude
B. Frequency
c. Period
D. Position of block
E. Total mechanical energy of the block


The functional isomer of ethanenitrile
is:
A. ethyl carbylamine
B. methanenitrile
c. methyl isocyanide
D. propanenitrile


How is phenol (carbolic acid) prepared from Rasching's process?


The radius of curvature for a plane mirror is
A. Positive
B. Negative
c. Infinite
D. None of these


Mid-points of the sides \( A B \) and \( A C \) of \( a \) \( \triangle A B C \) are (3,5) and (-3,-3) respectively then the length of the side BC is:
A . 10
B . 20
c. 15
D. 30


Which of the following is the correct order of the magnitude of \( -I \) effect
among the groups given?
\( A \cdot-F>-N O_{2}>-C O O H>-O C H_{3} \)
B. - \( \mathrm{NO}_{2}>-\mathrm{F}>-\mathrm{COOH}>-\mathrm{OCH}_{3} \)
c. \( -\mathrm{NO}_{2}>-\mathrm{COOH}>-\mathrm{F}>-\mathrm{OCH}_{3} \)
D. - COOH > - NO \( _{2}>-\mathrm{OCH}_{3}>-\mathrm{F} \)


On which one of the following the emf of a cell does not depend:
A. The nature of the metal of electrodes
B. The size of the plates
c. Nature of the electrolyte
D. The nature of electrodes


A long straight conductor, carrying a
current \( I, \) is bent to form an almost
complete circular loop of radius \( r \) on it.
The magnetic field at the center of the
loop:
A. is directed into the paper
B. is directed out of the paper
C . has magnitude \( \frac{\mu_{0} I}{2 r}\left(1-\frac{1}{\pi}\right) \)
D. has magnitude \( \frac{\mu_{0} I}{2 r}\left(1+\frac{1}{\pi}\right) \)


Rat in any food chain would occupy the position of
A. Tertiary consumer
B. Secondary consumer
c. Primary consumer
D. Producer


A differential equation representing the
family of curves \( \boldsymbol{y}=\boldsymbol{a} \sin (\boldsymbol{\lambda} \boldsymbol{x}+\boldsymbol{\alpha}) \) is:
\( ^{A} \cdot \frac{d^{2} y}{d x^{2}}+\lambda^{2} y=0 \)
B. \( \frac{d^{2} y}{d x^{2}}-\lambda^{2} y=0 \)
c. \( \frac{d^{2} y}{d x^{2}}+\lambda y=0 \)
D. None of the above


Which of the following is monomer of natural rubber?
A. Isoprene
B. Chloroprene
c. caprolactum
D. styrene


Assertion
As long as the mother breast-feeds the
child fully, chances of conception are almost nil.
Reason
Lactational amenorrhea method is
based on the fact that ovulation does
not occur during the period of intense lactation.
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


Certain force acting on a \( 20 \mathrm{kg} \) mass
changes its velocity from \( 5 m s^{-1} \) to
\( 2 m s^{-1} . \) Calculate the work done by the
force
A. \( -210 J \)
B. \( 210 J \)
c. -105 J.
D. \( 420 J \)


Find the domain of the function defined
by \( f(x)=\frac{2}{3 x^{2}+1} \)
A. R-II
B.
c. R-(-1)
D. R-IO


A pnjunction conducts only in forward biased condition.
A. True
B. False


A body performs harmonic oscillations along the straight line \( A B C D E \) with \( C \) as a mid-point. of \( A E . \) Its kinetic
energies at \( B \) and \( D \) are each onefourth of its maximum value. If \( \boldsymbol{A} \boldsymbol{E}= \)
\( 2 R, \) the distance between \( B \) and \( D \) is:


A water drop is divided into 8 equal droplets. The pressure difference between the inner and outer side of the
big drop will be
A. same as for smaller droplet
B. \( 1 / 2 \) of that for smaller droplet
c. \( 1 / 4 \) of that for smaller droplet
D. twice that for smaller droplet


Unscramble the underlined words in the
following sentences.
The overgrowth of sclemus in ynxlar leads to the hoarse voice in
adolescent boys.
A. The overgrowth of scmusle in rylanx leads to the hoarse voice in adolescent boys
B. The overgrowth of mulescs in lanxyr leads to the hoarse voice in adolescent boys
c. The overgrowth of lesmcus in xylran leads to the hoarse voice in adolescent boys
D. The overgrowth of muscles in larynx leads to the hoarse voice in adolescent boys.


\( \boldsymbol{H}-\boldsymbol{C} \equiv \boldsymbol{C}-\boldsymbol{H}+ \)
\( \boldsymbol{H}_{2} \frac{P d-B a S O_{4} / Q u i n o l i n e}{ } \boldsymbol{A} \stackrel{\boldsymbol{H} C l}{\longrightarrow} \)
\( \boldsymbol{B} \stackrel{\boldsymbol{a q} \cdot \boldsymbol{K} \boldsymbol{O} \boldsymbol{H}}{\longrightarrow} \boldsymbol{C} \)
Here, \( C \) is :
A. propane
B. ethanol
c. ethyne
D. ethylene


Setting of mortar is the result of
reaction between slaked lime and \( C O_{2} \)
of air.
A. True
B. False


toppr
Q Type your question_
or \( x \) between the oralnates \( x=a \) メ \( x= \)
\( b, \) is given by definite integral
\( \int_{a}^{b} y d x \) or \( \int_{a}^{b} f(x) d x \) and the area
bounded by the curve \( x=f(y), \) the axis
of \( y \& \) two abscissae \( y=c \& y=d \) is
given by \( \int_{c}^{d} x d y \) or \( \int_{c}^{d} f(x) d y . \) Again if
we consider two curves \( \boldsymbol{y}=\boldsymbol{f}(\boldsymbol{x}), \boldsymbol{y}= \)
\( g(x) \) where \( f(x) \geq g(x) \) in the interval
\( [a, b] \) where \( x=a \& x=b \) are the
points of intersection of these two
curves Shown by the graph given
Then area bounded by these two curves
is given by
\( \int_{a}^{b}[\boldsymbol{f}(\boldsymbol{x})-\boldsymbol{g}(\boldsymbol{x})] \boldsymbol{d} \boldsymbol{x} \)
On the basis of above information
answer the following questions.
The area bounded by parabolas \( \boldsymbol{y}= \)
\( x^{2}+2 x+1 \& y=x^{2}-2 x+1 \) and the
line \( y=\frac{1}{4} \) is equal to
\( \mathbf{A} \)
square unit
B. \( \overline{3} \) square unit
\( c \)
\( \overline{2} \) square unit
D. 2 square unit


The distance between two parallel chords, each of length 10 units is 24 units then the radius of the circle is:
A . 5
B. 12
c. 13
D. 30


Construct \( \Delta A B C \) in which \( A B=4 \mathrm{cm} \)
\( \mathrm{BC}=7 \mathrm{cm} \) and \( \mathrm{CA}=3 \mathrm{cm} . \) Which type of
triangle is this?


Which of the following acids have the
lowest \( p K_{a} \) value?
\( A \)
\( C l \)
\[
\begin{array}{c}
\mid \\
C H_{3}-C H-C O O H
\end{array}
\]
в. \( C l-C H_{2}-C H_{2}-C O O H \)
c. \( C C l_{3} \) СООН
D. \( C H C l_{2} C O O H \)


Two vessels \( A \) and \( B \) of different shapes
have the same base area and are filled
with water up to the same height h (see figure). The force exerted by water on
the base is \( F_{A} \) for vessel \( A \) and \( F_{B} \) for
vessel B. The respective weights of the
water filled in vessels are \( W_{A} \) and \( W_{B} \)
Then:
\( \mathbf{A} \cdot F_{A}>F_{B} ; W_{A}>W_{B} \)
B \( \cdot F_{A}=F_{B} ; W_{A}>W_{B} \)
\( \mathbf{c} \cdot F_{A}=F_{B} ; W_{A}<W_{B} \)
D. \( F_{A}>F_{B} ; W_{A}=W_{B} \)


Thickness of the page on which you are writing is in the order of :
A . \( 0.1 \mathrm{cm} \)
B. 0.1 micrometer
c. 0.1 angstrom
D. \( 0.1 \mathrm{mm} \)


If \( [\sin x]+[\sqrt{2} \cos x]=-3, x \in[0,2 \pi] \)
([.] denotes the greatest integer function), then \( x \) belongs to
A \( \cdot\left(\pi, \frac{5 \pi}{4}\right) \)
B . \( \left[\pi, \frac{5 \pi}{4}\right] \)
c. \( \left(\frac{5 \pi}{4}, 2 \pi\right) \)
D・ \( \left[\frac{5 \pi}{4}, 2 \pi\right] \)


The solution of the equation \( 2 \cos ^{-1} x=\sin ^{-1}(2 x \sqrt{1-x^{2}}) \)
A \( \cdot[-1,0] \)
B \( \cdot[0,1] \)
c. [-1,1]
D. \( \left[\frac{1}{\sqrt{2}}, 1\right] \)


An example for homopolysaccharide is/are:
This question has multiple correct options
A. sucrose
B. cellulose
c. mannose
D. starch


If \( f(x)= \)
\[
\frac{\sin 3 x+A \sin 2 x+B \sin x}{x^{5}} \quad(x \neq 0)
\]
continuous at \( x=0, \) then find \( A+B \)


8
8
8
8


Combustion is a:
A. physical process
B. chemical process
C. biological process
D. mechanical process


Which of the following is not the feature of gymnosperms?
A. Parallel venation
B. Perennial plants
c. Distinct branches (long and short branches)
D. xylem with vessels


A change in the physical state can be
brought about:
A. only when energy is given to the system
B. only when energy is taken out from the system
c. when energy is either given to, or taken out from the
D. without any energy change


\( \left|\begin{array}{ccc}\boldsymbol{a}^{2}+\mathbf{1} & \boldsymbol{a} \boldsymbol{b} & \boldsymbol{a} \boldsymbol{c} \\ \boldsymbol{a} \boldsymbol{b} & \boldsymbol{b}^{2}+\mathbf{1} & \boldsymbol{b} \boldsymbol{c} \\ \boldsymbol{c} \boldsymbol{a} & \boldsymbol{c} \boldsymbol{b} & \boldsymbol{c}^{2}+\mathbf{1}\end{array}\right|=\mathbf{1}+\boldsymbol{a}^{2}+ \)


If voltage across zener diode is \( 6 V \) then
find out value of maximum resistance
in this condition.
\( A \cdot 2 k \Omega \)
3. \( 1 k \Omega \)
\( c .5 k \Omega \)
D. \( 4 k \Omega \)


A force \( \boldsymbol{F}=(\mathbf{1 0}+\mathbf{0 . 5} \boldsymbol{x}) \boldsymbol{N} \) acts on a
particle in \( X \) direction, where \( x \) is in meters. Find the work done by this force during a displacement from \( \boldsymbol{x}=\mathbf{0} \) to
\( \boldsymbol{x}=\mathbf{2} \)


Column 1
A) \( \wedge^{0}_{m}\left(N a N O_{3}\right) \)
(P) Can be
obtained by Kohlraush law
B) \( \wedge^{0}_{m} \)
(Q) Can be
obtained by
\( \left(\boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{C O O H}\right) \quad \) extrapolating
\( \wedge^{0} m \) vs
\( (\text {Molarity})^{1 / 2} \)
graph to zero molarity.
C) Ilonic conductance
(R) Contribution
by the ion to \( \wedge^{0}_{m} \)
D) \( \wedge^{0}_{m} \) of \( C H_{3} C O O H \)
(S) increases on
dilution
A. A-P,R: B-Q,S:C-S:D-S
B. A-P,Q: B-P,S:C-S:D-P,S
c. A-R: B-Q:C-R,S:D-P,Q
D a c. B-Q.R:C-P:D-Q


(a) What do you understand by corrosion?
(b) Write electro-chemical theory of corrosion (Rust).
(c) Write prevention (two) of corrosion.


Which hormone causes dilation of blood
vessels, increased oxygen consumption and gluconeogenesis?
A. Adrenaline
B. Glucagon
c. АСТН
D. Insulin


Why the nucleus is positively charged?


The wavelength of the gamma ray is
\( \mathbf{A} \cdot 0.02 \stackrel{\circ}{A} \)
B \( \cdot 0.03 \stackrel{\circ}{A} \)
c. \( 0.04^{\circ} \)
D. \( 0.05 \stackrel{\circ}{A} \)


Reactive dyes utilize a attached to a substituent that is capable
of directly reacting with the fibre substrate.
A. chromophore
B. auxochrome
c. chlorophyll
D. none of the above


A coin is tossed 100 times and tail is
obtained 10 times. Now, if a coin is
tossed at random, what is the
probability of getting a head?
A \( \cdot \frac{11}{10} \)
в. \( \frac{9}{10} \)
c. \( \frac{90}{10} \)
D. \( \frac{100}{10} \)


Write the general outer electronic
configuration of \( s-, p-, d- \) and \( f- \) block elements.


A man is known to speak the truth 3 out of 4 times. He throws a die and reports
that it is a six. The probability that it is
actually a six is
A \( \cdot \frac{3}{8} \)
в. \( \frac{1}{8} \)
\( c \cdot \frac{1}{4} \)
D.


Which of the following is not a rectifier
circuit?
4
3
\( c \)
. none of thes


Radioactivity of a sample \( (Z=22) \) decreases \( 90 \% \) after 10 yr. What will be the half-life of the sample?
A . 5 yr
B. 2 yr
\( c \cdot 3 y r \)
D. 10 yr


Prove that; \( a^{2}-b^{2}, b^{2}-c^{2}, c^{2}-d^{2} \) are
in \( G . P \)


Find the values of \( a \) and \( b \) such that the
function defined by
\( f(x)=\left\{\begin{array}{l}5, \text { if } x \leq 2 \\ a x+b, \text { if } 2<x<10 \text { is a } \\ 21, \text { if } x \geq 10\end{array}\right. \)
continuous function.


While measuring the length of a wooden box, the reading at one end is \( 1.5 \mathrm{cm} \) and the other end is \( 4.7 \mathrm{cm} . \) What is the
length of the wooden box?
A. \( 4.7 \mathrm{cm} \)
B. \( 1.5 \mathrm{cm} \)
c. 3.2 \( \mathrm{cm} \)
D. 6.2 cm