Find the mode of the following data.
\begin{tabular}{lllll}
\multirow{2}{*} { Number } & \( \mathbf{0}- \) & \( \mathbf{3}- \) & \( \mathbf{6}- \) & \( \mathbf{9}- \) \\
& \( \mathbf{3} \) & \( \mathbf{6} \) & \( \mathbf{9} \) & \( \mathbf{1 2} \)
\end{tabular}
Frequency \( \quad 4 \quad 18 \) 9
A . 19
B. 31
c. 26
D. 2


State and prove low of conservation of
momentum.


The perpendicular distance between the
straight lines \( 6 x+8 y+15=0 \) and
\( \mathbf{3} \boldsymbol{x}+\mathbf{4} \boldsymbol{y}+\mathbf{9}=\mathbf{0} \) is
A. \( 3 / 2 \) units
B. 3/10 units
c. \( 3 / 4 \) units
D. 2/7units


If the elastic deformation energy of a
steel rod of mass \( \boldsymbol{m}=\mathbf{3 . 1} \boldsymbol{k g} \) stretched
to a tensile strain \( \varepsilon=1.0 \times 10^{-3} \) is \( x \)
then value of \( 100 x \) is:


Find all real values of \( x \) such that
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{g}(\boldsymbol{x}) \) where \( \boldsymbol{f} \) and \( \boldsymbol{g} \) are
functions given by
\( \boldsymbol{f}(\boldsymbol{x})=\mathbf{3} \boldsymbol{x}+\sqrt{\boldsymbol{x}} \) and \( \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{2} \boldsymbol{x}+\boldsymbol{6} \)
This question has multiple correct options
A .4
B. 9
\( c .3 \)
D. 6


In Young's double slit experiment with monochromatic source of light of
wavelength \( 6000 A^{\circ} \), if the path
difference is \( 1.5 \times 10^{-6} m, \) the point
becomes:
A. bright band
B. dark band
c. sometimes bright and sometimes dark
D. data insufficient


Oak Tassar silkworm is
A. Bombyx mori
B. Antheraea ricini
C. Antheraea assama
D. Antheraea roylei, A pernyi.


Consider the process involving gaseous species,
Process \( \mid: C l+e^{-} \rightarrow C l^{-} \)
Process II: \( N a^{+}+e^{-} \rightarrow N a \)
Process III: \( \boldsymbol{S}^{-}+\boldsymbol{e}^{-} \rightarrow \boldsymbol{S}^{2-} \)
Process IV: \( \boldsymbol{K} \rightarrow \boldsymbol{K}^{+}+\boldsymbol{e}^{-} \)
The process in which size of product is
less than reactant?
\( A \)
B. ॥
c. ॥
D. IV


Evaluate: \( \int \frac{1}{x+\sqrt{x}} d x \)


Panmictic plant multiplies
A. Sexually
B. Asexually
c. Parthenogenetically
D. By stolons


Construct the matrix of order \( 3 \times 2 \)
whose elements are given by \( a_{i j}=2 i- \)
\( \boldsymbol{j} \)
A. \( \left[\begin{array}{ll}1 & 3 \\ 0 & 2 \\ -1 & 1\end{array}\right] \)
B. \( \left[\begin{array}{lll}1 & 3 & 5 \\ 0 & 2 & 4\end{array}\right] \)
\( \mathbf{c} \cdot\left[\begin{array}{ll}1 & 0 \\ 3 & 2 \\ 5 & 4\end{array}\right] \)
D. \( \left[\begin{array}{ccc}1 & 0 & -1 \\ 3 & 2 & 1\end{array}\right] \)


Given a line and a point, not on the line, there is one and only ...... line which passes through the given point and is to the given line. This question has multiple correct options
A. one, parallel
B. one, perpendicular
c. two, parallel
D. two, perpendicular


You are given benzene, conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
and \( N a O H . \) Write the equations for the preparation of phenol using these
reagents.


The bond in the formation of fluorine
molecule will be:
A. due to \( s-s \) overlapping
B. due to \( s-p \) overlapping
c. due to \( p-p \) overlapping
D. due to \( d-d \) hybridization


Assertion (A): The enthalpy of formation of gaseous oxygen molecules at \( 298 \mathrm{K} \) and under a pressure of 1 atm is zero. Reason (R): The entropy of formation of gaseous oxygen molecules under the same condition is zero.
A. Both assertion and reason are correct, reason is the correct explanation of the assertion
B. Both assertion and reason are correct, reason is the not correct explanation of the assertion
c. Assertion is correct, reason is incorrect
D. Assertion is incorrect, reason is correct


Sodium ions helps in:
This question has multiple correct options
A. transmission of nerve signals
B. transport of sugar and amino acids into cells
C. activation of different enzymes
D. oxidation of glucose to produce ATP


The number of neutrons in the parent
nucleus which gives \( ^{14} \mathrm{N} \) on beta emission is


How will crowding the wires of a solenoid, more closely together, will
affect the strength of the field inside it?
A. Field strength increases
B. Field strength decreases
c. Can't be said
D. Field strength will remain unchanged


What is dispersion? Which colour gets relatively more dispersed?


Mark the odd one in each of the
following series:
Human heart, fish heart, reptile heart, toad heart.


A body of mass \( 5 \mathrm{kg} \) is acted upon by two perpendicular forces \( 8 \mathrm{N} \) and \( 6 \mathrm{N} \) Given the magnitude and direction of the acceleration of the body.


Type of reflection in which images are
formed and reflection occurs from a
smooth surface like that of mirror is
known as:
A. diffused reflection
B. regular reflection
c. irregular reflection
D. none of these


The correct statement(s) about surface
properties is (are):
This question has multiple correct options
A. cloud is an emulsion type of colloid in which liquid is dispersed phase and gas is dispersion medium
B. adsorption is accompanied by decrease in enthalpy and decrease in entropy of the system
C. the critical temperatures of ethane and nitrogen are \( 563 K \) and \( 126 K, \) respectively. The adsorption of ethane will be more than that of nitrogen on same amount of activated charcoal at a given temperature
D. brownian motion of colloidal particles does not depend on the size of the particles but depends on viscosity of the solution


Construct a triangle \( X Y Z \) in which
\( X Y=5 c m, Y Z=5.5 c m \) and
\( \angle X Y Z=100^{\circ} \)


Phenol is used as:
A. an antiseptic
B. a disinfectant
C. both (A) and (B)
D. none of these


When two ice cubes are pressed over
each other they unites to form one cube. Which of the following forces are responsible to hold them together?
A. lonic interaction
B. Van der Waal's forces
c. covalent interaction
D. Hydrogen bond formation


The boiling point of liquid \( A, B, C \) and \( D \) \( \operatorname{are} 80^{\circ} C, 60^{\circ} C, 90^{\circ} C \) and \( 100^{\circ} C \)
respectively. Which will show highest vapour pressure at room temperature?
\( A \cdot A \)
B. B
\( c \cdot c \)
\( D . \) D


The value of the expression \( 2 \sec ^{-1} 2+ \) \( \sin ^{-1} \frac{1}{2} \) is
A \( \cdot \frac{\pi}{6} \)
в. \( \frac{5 \pi}{6} \)
c. \( \frac{7 \pi}{6} \)
D.


A tank of height \( 33.25 \mathrm{cm} \) is completely
filled with liquid \( (\mu=1.33) . \) An object
is placed at the bottom of tank on the
axis of concave mirror as shown in Fig.
Image of the object is formed at \( 25 \mathrm{cm} \)
below the surface of the liquid. Focal length of the mirror is
\( A \cdot 10 \mathrm{cm} \)
B. \( 15 \mathrm{cm} \)
\( c \cdot 20 \mathrm{cm} \)
D. 25 cm


In the given figure, if \( \boldsymbol{A B} \| \boldsymbol{C D} \)
\( \angle A P Q=50^{\circ} \) and \( \angle P R D=127^{\circ}, \) find
and \( y \)


Evaluate:
\( \int_{2}^{1}|\boldsymbol{x}-\mathbf{3}| \boldsymbol{d} \boldsymbol{x} \)


Over a number of years the average pH
of a stream changes from a pH of 6.9 to a pH of 5.9 due to acid rain. Which statement is true about the pH of the
stream?
A. The pH of the stream now is one times more acidic than it was years ago
B. The stream now has 10 times more hydroxide ions than it did years ago
c. The pH of the stream is now 10 times more acidic than it was years ago
D. The stream is more basic now than it was years ago
E. The concentration of hydronium ion in the stream has decreased over the years


Discuss the structure of
\( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{4} \)
A. Linear
B. Square Planar
c. Square Pyramidal
D. Tetrahedral


State Ampere's circuital law. Obtain an expression for magnetic induction along the axis of toroid.


Three substances are added to a mug to
make coffee : Coffee is at \( 65^{\circ} \mathrm{C} \), Milk at
\( 65^{\circ} \mathrm{C} \) and Sugar, which is in thermal
equilibrium with coffee. Then This question has multiple correct options
A. Heat will be transferred from sugar to coffee to reach equilibrium
B. The sugar is in equilibrium with the milk
c. Heat will be transferred from the coffee to the sugar to reach equilibrium
D. None of these conclusions are valid


According to Laplace correction, the propagation of sound in gas takes place under
A. isothermal condition
B. isobaric condition
c. isochoric condition
D. adiabatic condition


Assertion
Statement \( -1: C_{3} O_{2} \) has linear
structure.
Reason
Statement -2: Each \( C \) atom in \( C_{3} O_{2} \) is
sp - hybridised.
A. Statement - 1 is true, Statement - 2 is true and Statement - 2 is correct explanation for Statement -
1
B. Statement - 1 is true, Statement - 2 is true and Statement - 2 is NOT the correct explanation for Statement - 1
c. statement -1 is true, statement -2 is false
D. statement -1 is false, Statement - 2 is true


The angles of a triangle are in the ratio
\( 3: 4: 5 . \) Find the smallest angle.


The amount of heat required to increase the temperature of 1 mol of \( a \) triatomatic gas (non-linear) at constant volume is \( n \) times the amount of heat
required for 1 mol of monatomic gas. The value of \( n \) will be
A . 1
в. 1.3
c. 2
D. 2.5


Which of the following forms maximum
number of compounds?
A . Ne
B. Kr
c. \( x_{e} \)
D. Rn


Site of mRNA synthesis in lampbrush chromosomes is
A. Balbiani rings
B. Lateral loops
c. Dark bands
D. Light bands


If \( \boldsymbol{f}(\mathbf{1})=\mathbf{1}, \boldsymbol{f}(\boldsymbol{n}+\mathbf{1})=\mathbf{2} \boldsymbol{f}(\boldsymbol{n})+\mathbf{1}, \boldsymbol{n} \geq \)
1, then \( f(n) \) is:
\( \mathbf{A} \cdot 2^{n+1} \)
в. \( 2^{\text {г }} \)
c. \( 2^{n}-1 \)
D. \( 2^{n-1}-1 \)


The emf induced in the circuit is
A. \( 125 \mu V \)
B. \( 250 \mu V \)
c. \( 100 \mu V \)
\( \mathbf{D} \cdot 300 \mu V \)


D-fructose is used for sweetening cold drinks but not hot ones because:
A. it is not a true carbohydrate
B. on heating it is converted into pyranose form
c. on heating it is converted into furanose form
D. on heating it gets decomposed


Two resister \( \boldsymbol{R}_{1}=\mathbf{4 0 0 \Omega} \) and \( \boldsymbol{R}_{2}=\mathbf{2 0 \Omega} \)
are connected in parallel to a battery. If
heating power developed in \( R_{1} \) in \( 25 \mathrm{W} \)
find the heating power developed in \( \boldsymbol{R}_{2} \)


The equation \( 4_{1}^{1} H^{2} \rightarrow_{2}^{4} H e^{2+}+2 e^{+1}+ \)
\( 26 M e V \) represents
A. \( \beta- \) decay
B. \( \gamma- \) decay
c. fusion
D. fission


\( \ln \triangle A B C \) prove that \( \frac{b-C}{a}= \)
\( \frac{\tan (B / 2)-\tan (C / 2)}{\tan (B / 2)+\tan (C / 2)} \)


In a reaction, if \( \Delta H \) and \( \Delta S \) both are
more than zero, then in which of the
following cases, the reaction would not be
spontaneous? This question has multiple correct options
A \( . \Delta H>T \Delta S \)
в. \( T \Delta S>\Delta H \)
c. \( \Delta H=T \Delta S \)
D. All of the above


The current through the \( 10 \Omega \) resistor
shown in figure is
\( 4 \cdot 0.1 \)
B. \( 0.2 \mathrm{A} \)
\( c \cdot 0.3 \mathrm{A} \)
D. zer


Chalcogens are:
A. hydrocarbons
B. ore forming elements
C. oxide forming elements
D. those having ability to catenate


Assertion: The drift velocity of electrons in a metallic wire will decrease, if the
temperature of the wire is increased.
Reason: On increasing temperature, conductivity of metallic wire decreases.
A. Both (A) and (R) are true and
(R) is the correct explanation of
B. Both (A) and (R) are true but (R) is not the correct explanation of A
c. (A) is true but (R) is false
D. (A) is false but (R) is true


On reflection from a plane surface, the following two characteristics get changed:
This question has multiple correct options
A. wavelength
B. Frequency
c. velocity
D. Amplitude


\( \boldsymbol{H}_{2} \boldsymbol{O}_{2}+\boldsymbol{O}_{3} \rightarrow \boldsymbol{H}_{2} \boldsymbol{O}+\mathbf{2} \boldsymbol{O}_{2}, \) in this
reaction \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) acts as:
A. oxidising agent
B. reducing agent
c. dehydrating agent
D. bleaching agent


Two long parallel wires carrying currents \( 2.5 \mathrm{A} \) and I A in the same
direction (directed Into the plane of the paper) are held \( \mathrm{M} \mathrm{P} \) and \( \mathrm{Q} \) respectively such that they are perpendicular to the
plane of the paper. The points \( P \) and \( Q \) are located at a distance of \( 5 \mathrm{m} \) and 2
\( \mathrm{m}, \) respectively, from a collinear point \( \mathrm{R} \) as shown in figure. An electron moving with a velocity of \( 4 \times 10^{5} m s^{-1} \) along
the positive \( X \) -direction experiences a
force of magnitude \( 3.2 \times 10^{-20} \mathrm{N} \) at the
point \( R \) The current lin wire Q is
\( A \cdot 1 A \)
B. 2 A
\( c \cdot 3 A \)
\( D \cdot 4 A \)


\( \cos \frac{\pi}{7}+\cos \frac{2 \pi}{7}+\cos \frac{3 \pi}{7}+\cos \frac{4 \pi}{7}+ \)
\( \cos \frac{5 \pi}{7}+\cos \frac{6 \pi}{7}+\cos \frac{7 \pi}{7}= \)
\( A \)
в.
c.
D.


Insectivorous plants grow in areas deficient in
A. Phosphorus
B. Nitrogen
c. sulphur
D. Iron


Name the four stages of life span.


A student named an alkane as \( 2- \)
ethylpropane the correct
IUPAC Name of the alkane is
A. \( 2- \) Methylbutane
B. 2,2 - Dimethylbutane
c. 2,3 Dimethylpentane
D. 2,3 - Dimethylbutane


is 0 a term of the \( A P: 31,28,25, \ldots ? \)
If true then enter 1 and if false then
enter 0


If \( \boldsymbol{y}=\boldsymbol{e}^{-\boldsymbol{x}} \cos \boldsymbol{x}, \) show that \( \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}= \)
\( 2 e^{-x} \sin x \)


Weight of oxygen in \( F e_{2} O_{3} \) and FeO is in
the ratio of :
A .3: 2
B. 1: 2
c. 2: 1
D. 3: 1


Find the smallest number by which a given number must be divided to obtain
a perfect cube 704


\( \chi_{1} \) and \( \chi_{2} \) are susceptibilities of \( a \)
diamagnetic substance at
temperatures \( T_{1} K \) and \( T_{2} K \)
respectively, then,
A \( \cdot \chi_{1} T_{1}=\chi_{2} T_{2} \)
B . \( x_{1}=x_{2} \)
c. \( \chi_{1} \sqrt{T_{1}}=\chi_{2} \sqrt{T_{2}} \)
D. \( \chi_{1} T_{2}=\chi_{2} T_{1} \)


How do you differentiate a butterfly
from a moth?
A. Moth has feathery antennae but butterfly has dub shaped antennae.
B. Moth has one pair of wings but butterfly has two pairs of wings
C. Moth is diurnal but butterfly is nocturnal.
D. Moth has simple eyes but butterfly has compound
eyes.


Which of the following solution contains approximately equal hydrogen ion concentration?
This question has multiple correct options
A. \( 100 \mathrm{mL} \) of \( 0.1 \mathrm{M} \mathrm{HCl}+50 \mathrm{mL} \mathrm{H}_{2} \mathrm{O} \)
B. \( 75 \mathrm{mL} \) of \( 0.1 \mathrm{M} \mathrm{HCl}+75 \mathrm{mL} \mathrm{H}_{2} \mathrm{O} \)
c. \( 50 \mathrm{mL} \) of \( 0.1 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}+100 \mathrm{mL} \mathrm{H}_{2} \mathrm{O} \)
D. \( 100 \mathrm{mL} \) of \( 0.1 \mathrm{N} \mathrm{H}_{2} \mathrm{SO}_{4}+50 \mathrm{mL} \mathrm{H}_{2} \mathrm{O} \)


Moment of inertia of a uniform rod of mass \( m \) and length \( l=\sqrt{2} \) is \( \frac{7}{12} m l^{2} \) about a line perpendicular to the rod. Find the distance of this line from the
middle point of the rod.


The conductivity of a Super conductor is
A. zero
B. Infinity
c. Dependson temp
D. Depends on free election


The IUPAC name of the following compound is 4 -(ethoxycarbonyl) benzoic acid.
A . True
B. False


In floating leaved plants, stomata occur
on.
A. Lower surface
B. Upper surface
c. Both surfaces
D. Absent


There are 60 terms in an A.P. of which
the first term is 8 and the last term is
185. The \( 31^{s t} \) term is
A . 56
B. 94
c. 85
D. 98


As shown in above figure, a uniform
magnetic field B, direction of magnetic
field is outward of the plane of the page.
Calculate the potential difference
between point a and b if metal rod is
pulled upward with constant velocity.
A .
B. \( \frac{1}{2} v B L \), with point a at the higher potential
C \( \cdot \frac{1}{2} v B L, \) with point \( b \) at the higher potential
D. vBL, with point a at the higher potential
E. vBL, with point b at the higher potential


What are the types of thermodynamic equilibrium?
A. Thermal equilibrium
B. Mechanical equilibrium
c. chemical equilibrium
D. All above


Let \( \boldsymbol{f}(\boldsymbol{x}), \boldsymbol{g}(\boldsymbol{x}) \) and \( \boldsymbol{h}(\boldsymbol{x}) \) be continuous
function on \( [0, a] \) such that \( f(x)= \)
\( \boldsymbol{f}(\boldsymbol{a}-\boldsymbol{x}), \boldsymbol{g}(\boldsymbol{x})=-\boldsymbol{g}(\boldsymbol{a}-\boldsymbol{x}), \boldsymbol{3} \boldsymbol{h}(\boldsymbol{x})- \)
\( 4 h(a-x)=5 \) then
\( \int_{0}^{a} f(x) g(x) h(x) d x \) is equal to
A . 1
B.
\( c \)
D. -


What questions you will ask a
paleantologist about fossils?


The domain of the function \( f(x)=\log _{10} \)
\( 4-x^{2} \mid \) is.


Calculate mole fraction of solute in its 2
molal aqueous solution.


f \( a=2, b=-2, \) find the value of:
\( a^{2}+a b+b^{2} \)


What is coulomb?


Simplify and give reasons:
\( (-3)^{-4} \)
\( ^{A} \cdot \frac{1}{81} \)
в. \( \frac{-1}{81} \)
c. \( \frac{3}{81} \)
D. None of these


What transformation of energy takes place when current is drawn from a cell
?
A. Chemical energy changes to electrical energy
B. Chemical energy changes to heat energy
c. mechanical energy changes to electrical energy
D. Chemical energy changes to mechanical energy


Which of the following has lowest boiling point?
A . \( N a C l \)
в. \( C u C l \)
c. \( C u C l_{2} \)
D. \( C s C l \)


If \( \log _{e} 5, \log _{e}\left(5^{x}-1\right) \) and
\( \log _{e}\left(5^{x}-\frac{11}{5}\right) \) are in \( A P, \) then the
values of \( x \) are :
A \( \cdot \log _{5} 4 \) and \( \log _{5} 3 \)
B. \( \log _{3} 4 \) and \( \log _{4} 3 \)
\( \mathbf{c} \cdot \log _{3} 4 \) and \( \log _{3} 5 \)
D. \( \log _{5} 6 \) and \( \log _{5} 7 \)
E . 12,6


If \( 1 \mathrm{mg} \) n \( s^{-1}=10^{x} \mu g p s^{-1}, \) then the value
of x is
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot-1 \)
D.


Which of the following is not a member of 3d-transition series?
\( A \cdot F e \)
B. co
c. Au
D. cu


Dihydrogen reacts with dioxygen \( O_{2} \) to form water. Write the name and formula
of the product when the isotope of hydrogen which has one proton and one neutron in its nucleus is treated with
oxygen. Will the reactivity of both the isotopes be the same towards oxygen? Justify your answer.


The argument of every complex number
is
A. Double valued
B. single valued
c. Many valued
D. Triple valued


The drama of human evolution was
dramatised in
A. Asia and Java
B. China and Asia
C. Africa and Java
D. Asia and Africa


What is the main differences between a
step-up transformer and a step-down transformer?


Write the name and structure of any five
oxy acids of phosphorus?


In a certain store, the profit is \( 320 \% \) of the cost. If the cost increases by \( 25 \% \)
but the selling price remains constant, approximately what percentage of the selling price is the profit?
A . \( 30 \% \)
B. \( 100 \% \)
\( c .70 \% \)
D. 250\%


A charge \( Q \) is to be distributed on two
objects, \( A \) and \( B \). The values of the
charges on the objects are such that the force between the objects will be
maximum. The ratio \( Q_{A}: Q_{B} \) will be
A . 1: 1
B. 1: 2
c. 1: 3
D. 1: 4


Displacement-time graph depicting an oscillatory motion is
A. cos curve
B. sine curve
c. tangent curve
D. straight line


The formula of the compound is
\( N a_{4} S_{4} O_{6} . \) Find the empirical formula of the compound.
A. \( N a S O \)
в. \( N a_{2} S_{2} O_{3} \)
c. \( N a_{2} S_{2} O \)
D. \( N a_{2} S_{4} O_{3} \)


Prefix giga means:
A \( \cdot 10^{-9} \)
B . \( 10^{9} \)
\( c \cdot 10^{6} \)
D. \( 10^{-6} \)


A player kicks a ball at a speed of 20 \( m s^{-1} \) so that its horizontal range is
maximum. Another player 24 m away in the direction of kick starts running in the same direction at the same instant
of hit. If he has to catch the ball just before it reaches the ground, he should run with a velocity equal to (Take \( g=10 \) \( m s-2) \)
A \( \cdot 2 \sqrt{2} \mathrm{ms}^{-1} \)
B. \( 4 \sqrt{2} \mathrm{ms}^{-1} \)
\( c \cdot 6 \sqrt{2} m s^{-1} \)
D. \( 10 \sqrt{2} \mathrm{ms}^{-1} \)


A 2 MeV proton is moving perpendicular to uniform magnetic field of 2.5 T. The magnetic force on the proton.
A \( \cdot 8 \times 10^{-12} \mathrm{N} \)
B . \( 4 \times 10^{-12} \mathrm{N} \)
c. \( 16 \times 10^{-12} \mathrm{N} \)
D. \( 2 \times 10^{-12} \mathrm{N} \)


A small disc of radius \( 2 \mathrm{cm} \) is cut from
a disc of radius \( 6 \mathrm{cm} \). If the distance
between their centres is \( 3.2 \mathrm{cm}, \) what is
the shift in the centre of mass of the
disc?
A. \( 0.4 \mathrm{cm} \)
B. 2.4 \( \mathrm{cm} \)
c. \( 1.8 \mathrm{cm} \)
D. \( 1.2 \mathrm{cm} \)


The inhibition of an enzyme controlling an early stage of a series of biochemical reactions by the end product, when it reaches a critical concentration is
called as
A. Allosteric inhibition
B. Feedback inhibiton
c. competitive inhibition
D. Non-competitive inhibition


What happens?
A) When bleaching powder is kept open
in air.
B) Chlorine gas is passed through dry slaked lime.


What is dialysis? State the condition in which dialysis treatment is given? Will
this be able to replace all kidney functions. Explain.


How many moles of \( N i(C O)_{4} \) could be
obtained from the CO produced by the
reaction of \( 75.0 \mathrm{g} \) of carbon? [Assume \( 100 \% \) reaction and \( 100 \% \)
recovery in both steps and molar mass of \( \mathrm{Ni}=59 \mathrm{g} / \mathrm{mol}] \)
A . 6.25
B. 1.5625
c. 3.125
D. 25.0


Area lying between the curve \( y^{2}=4 x \)
and \( \boldsymbol{y}=\mathbf{2} \boldsymbol{x} \) is :
A \( \cdot \frac{2}{3} \)
B. \( \frac{1}{3} \)
\( c \cdot \frac{1}{4} \)
D. \( \frac{3}{4} \)


Choose the incorrect statement
regarding DNA structure.
A. Base stacking destabilise DNA double helical structure.
B. Each chain in DNA constitute sugar-phosphate backbone
C. Two chains are coiled in right handed fashion
D. The pitch of the helix has roughly 10 bp.


Calamine is an ore of :
A. Iron
B. copper
c. Aluminium
D. zinc


Check whether the relation \( R \) in the set
\{1,2,3\} given by \( R=\{(1,2),(2,1) \) is transitive.


Oils on treating with hydrogen in the presence of palladium or nickel catalyst form fats. This is an example
of
A. addition reaction
B. substitution reaction
c. displacement reaction
D. oxidation reaction


A wedge of mass \( m \), having a smooth
semi circular part of radius R is resting on smooth horizontal surface.Now a
particle of mass \( m / 2 \) is released from
the top point of the semicircular part.
Then
This question has multiple correct options
A. The maximum displacement of the wedge will be R
B. The maximum displacement of the wedge will be \( \frac{2 R}{3} \)
c. The wedge will perform simple harmonic motion of amplitude
D. The wedge will perform oscillatory motion of amplitude \( \frac{R}{3} \)


If \( \frac{(1+i)(2+3 i)(3-4 i)}{(2-3 i)(1-i)(3+4 i)}=a+i b, \) then
\( a^{2}+b^{2} \) is equal to
A. 132
B . 25
\( c \cdot 144 \)
D. 128
\( E \)


Euchlorine is a mixture of.
A \( \cdot C l_{2} \) and \( S O_{2} \)
B. Free chlorine and \( C l O_{2} \)
c. \( C l_{2} \) and \( c o \)
D. None of the above


At the vicinity of absolute zero:
A. \( C_{p}+C_{v}=0 \)
B. \( C_{p}<C_{v} \)
c. \( C_{p}-C_{v}=0 \)
D. \( C_{p}>C_{v} \)


Find the value of
i) \( 2^{6} \)
ii) \( 9^{3} \)
iii) \( 11^{2} \)


The reaction which is taking place in
nickel- cadmium battery can be represented by which of the following equation?
A \( \cdot C d+N i O_{2}+2 H_{2} O \rightarrow C d(O H)_{2}+N i(O H)_{2} \)
B. \( C d+N i O_{2}+2 O H^{-} \rightarrow N i+C d(O H)_{2} \)
c. \( N i+C d(O H)_{2} \rightarrow C d+N i(O H)_{2} \)
D. \( N i(O H)_{2}+C d(O H)_{2} \rightarrow N i+C d+2 H_{2} O \)


Number of intramolecular aldol
condensation product is:
\[
\begin{array}{c}
\stackrel{0}{\|} \\
\mathrm{CH}_{3}-\mathrm{C}-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\mathrm{I}-\mathrm{H} \\
\mid \mathrm{KOH}
\end{array}
\]
\( A \)
B.
\( c \cdot 3 \)
\( D \)


A short bar magnet has a magnetic
moment of \( 0.65 \mathrm{JT}^{-1} \), then the
magnitude and direction of the magnetic field produced by the magnet at a distance \( 8 \mathrm{cm} \) from the centre of
magnet on the axis is:
A \( \cdot 2.5 \times 10^{-4} T, \) along NS direction
B . 2.5 \times \( 10^{-4} T \), along SN direction
c. \( 4.5 \times 10^{-4} T \), along NS direction
D. 4.5 \times \( 10^{-4} T \), along SN direction


Calculate the mass of ice needed to cool
\( 150 g \) of water contained in a
calorimeter of mass \( 50 \mathrm{g} \) at \( 32^{\circ} \mathrm{C} \) such
that the final temperature is \( 5^{\circ} \mathrm{C} \) Specific heat capacity of calorimeter \( = \)
\( \mathbf{0 . 4} \boldsymbol{J} / \boldsymbol{g}^{\boldsymbol{o}} \boldsymbol{C} \)
Specific heat capacity of water=
\( 4.2 J / g^{o} C \)
Latent heat capacity of ice \( =\mathbf{3 3 0} \boldsymbol{J} / \boldsymbol{g} \)


Find the cube of 49


Factorise the following expressions:
\( a x^{2} y+b x y^{2}+c x y z \)
A. \( x y(a x+b y+c z) \)
B. \( \operatorname{axy}(x+b y+c z) \)
\( c \cdot b x y(a x+y+c z) \)
D. \( x y(a x+b y-c z) \)


A biconvex lens of focal length \( \boldsymbol{f} \) and
radii of curvature of both the surfaces \( \boldsymbol{R} \)
is made of a material of refractive index
\( \boldsymbol{n}_{1} . \) This lens is placed in a liquid of
refractive index \( n_{2} . \) Now this lens will
behave like:
This question has multiple correct options
A. either as convex or as a concave lens depending solely on \( R \)
B. a convex lends depending on \( n_{1} \) and \( n_{2} \)
C . a concave lends depending on \( n_{1} \) and \( n_{2} \)
D. a convex lens of same focal length irrespective of
\( R, n_{1} \) and \( n_{2} \)


A bullet moving with a speed of
\( 100 m s^{-1} \) canjust penetrate two
planks of equal thickness. Then, the number of such planks penetrated by the same bullet when the speed is
doubled will be:
\( A \cdot 6 \)
B. 10
\( c \cdot 4 \)
D.


Integrate \( \int e^{\sin x} \cdot \cos x d x \)


If \( f(x)=|\cos 2 x| \) then \( f^{\prime}\left(\frac{\pi}{4}+0\right) \) is
equal to
A .2
B.
c. -2
D. none of these


Which of the following gas is used in bleaching of paper?
A. Hydrogen peroxide
B. Sulphur dioxide
c. Methane
D. None of the above


Assertion
Intrinsic semiconductors are undoped
Reason

Holes in the valence band are vacancies
created by electrons that have been thermally excited to the conduction
band
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


Solve the inequalities:
\( \tan x=-\sqrt{3} \)


When stationary waves are produced in a medium, which physical
characteristic change at antinodes?
A. Density only
B. Pressure only
c. Density and pressure
D. Neither density nor pressure


A plant with epidermis specialised to absorb mositure from air is?
A. Avicennia
B. Vanda
c. Rhizophora
D. Jussiaea


Which of the following oxides is amphoteric in character?
A. \( C a O \)
в. \( C O_{2} \)
\( \mathrm{c} \cdot \operatorname{si} 0_{2} \)
D. \( \operatorname{sn} O_{2} \)


A meteor is:
A . a rapidly moving star
B. a piece of matter which has entered the Earth's atmosphere from outer space
C. part of a constellation
D. a comet without a tail


Which one of the following elements is required for photosynthetic oxygen evolution?
A. copper
B. Iron
c. Manganese
D. zinç


Mark correct option.
A. The laws of reflection of light hold only for plane surfaces
B. The size of virtual image can be measured by receiving it on screen
C. Plane mirror alongs form an erect image
D. Plane mirror may form inverted image


Integrate \( \int \frac{d x}{x^{4}+1} \)


Which logic gate is represented by the following logic gates?
A. NOR
B. NAND
\( c . \) AND
D. on


What is the formula for refraction
through spherical Lens when the refractive index of the medium on two
sides of lens are different?


Find \( \boldsymbol{A B} \)
A. 57.34
В. 71.94
\( c .54 .64 \)
0.50 .0


If the altitudes of a triangle be 3,4,6
then find its in-radius.


Assertion
In alpha decay of different radioactive nuclides, the energy of alpha particles has been compared. It is found that as the energy of alpha particle increases the half-life of the decay goes on decreasing.
Reason
More is the energy in any decay process, more is the probability of decaying the nuclide which leads to faster rate of
decay.
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


Fill in the blanks:
An electron emitter must have
work function and \( \ldots . . . . . . . . . . . . . . . . \) melting point.
A. high, high
B. low, low
c. high, low
D. low, high


The ratio of the outer and inner
perimeters of a circular path is 23: 22
If the path is \( 5 \mathrm{m} \) wide what is the diameter of the circle? Also find the
area of path enclosed between the two
circles.
A. 3535.71 sq. \( \mathrm{m} \)
B . 1232.23 sq. \( \mathrm{m} \)
c. 2727.53 sq. \( \mathrm{m} \)
D. 4343.12 sq. \( \mathrm{m} \)


A thin horizontal disc of radius \( R= \)
\( 10 \mathrm{cm} \) is located within a cylindrical
cavity filled with oil whose viscosity \( \boldsymbol{\eta}=\mathbf{0 . 0 8} \boldsymbol{P} \) (figure shown above). The
clearance between the disc and the
horizontal planes of the cavity is equal
to \( h=1.0 m m . \) Find the power
developed by the viscous forces acting on the disc when it rotates with the
angular velocity \( \omega=60 \mathrm{rad} / \mathrm{s} \). The end
effects are to be neglected. Round off to closest integer.


Indicate the point of the complex plane
\( z \) which satisfy the following equation. \( |z|^{3}+z=0 \)


Two capacitors of \( 1 \mu F \) and \( 2 \mu F \) are connected in series and this
combination is changed upto a potential difference of 120 volt. What will be the potential difference across \( 1 \mu F \) capacitor:
A . \( 40 v o l t \)
B. 60 volt
c. \( 80 v \) olt
D. \( 120 v o l t \)


State the following statement is True or False
If \( k^{2} x^{2}-2(k-1) x+4=0 \) has
equal roots, then \( \boldsymbol{k}=-\mathbf{1} \) or \( \boldsymbol{k}=\frac{\mathbf{1}}{\mathbf{3}} \)
A. True
B. False


The peak voltage of an ac supply is \( 300 V . \) What is the rms voltage?


Show that the points \( A(2,-2), B(8,4), C(5,7), D(-1,1) \) are the
vertices of a rectangle.


Tangents \( P A \) and \( P B \) are drawn from
an external point \( P \) to two concentric
circle with centre \( O \) and radii \( 8 \mathrm{cm} \) and
5 \( \mathrm{cm} \) respectively, as shown in figure. If
\( A P=15 \mathrm{cm}, \) then find the length of
\( \boldsymbol{B P} \)


The arrangement of
\( \left(\boldsymbol{C H}_{3}\right)_{3} \boldsymbol{C}-,\left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{C H}-, \boldsymbol{C H}_{3} \boldsymbol{C H}_{2}- \)
when attached to benzene or an
unsaturated group in increasing order of inductive effect is
A \( \cdot\left(C H_{3}\right)_{3} C-<\left(C H_{3}\right)_{2} C H-<C H_{3} C H_{2}- \)
в. \( C H_{3} C H_{2}-<\left(C H_{3}\right)_{2} C H-<\left(C H_{3}\right)_{3} C- \)
c. \( \left(C H_{3}\right)_{2} C H-<\left(C H_{3}\right)_{4} C-<C H_{3} C H_{2}- \)
D. \( \left(C H_{3}\right)_{3} C-<C H_{3} C H_{2}-<\left(C H_{3}\right)_{2} C H- \)


\( \Delta H_{r} \) of which of the following reactions
is zero?
A \( \cdot H_{2}(g) \rightarrow 2 H^{+}(g)+2 e^{-} \)
B . \( 2 H(g)+a q \rightarrow 2 H^{+}(a q)+2 e^{-} \)
C \( \cdot 2 H(g) \rightarrow 2 H^{+}(g)+2 e^{-} \)
D \( \cdot H_{2}(g)+a q \rightarrow 2 H^{+}(a q)+2 e^{-} \)


Three numbers whose sum is 45 are in
A.P. If 5 is subtracted from the first
number and 25 is added to third
number, the numbers are in G.P. Then
numbers can be
A. 10,15,20
B. 8,15,22
c. 5,15,25
D. 12,15,18


Find the inclination of the line \( ( \) in
degrees ) whose slope is 1


Given the following bond energies, \( \boldsymbol{C}-\boldsymbol{H}=\mathbf{4 1 4} \boldsymbol{K} \boldsymbol{J} / \boldsymbol{m o l} \)
\( \boldsymbol{C}-\boldsymbol{C l}=\mathbf{1 5 0} \boldsymbol{K} \boldsymbol{J} / \boldsymbol{m o l} \)
\( C l-C l=243 K J / m o l \)
\( \boldsymbol{H}-\boldsymbol{C l}=\mathbf{4 3 2} \boldsymbol{K} \boldsymbol{J} / \boldsymbol{m o l} \)
How much energy would be required in the reaction?
\( \boldsymbol{C H}_{4(\boldsymbol{g})}+\boldsymbol{2} \boldsymbol{C l}_{2(\boldsymbol{g})} \rightarrow \boldsymbol{C H}_{2} \boldsymbol{C l}_{2(\boldsymbol{g})}+ \)
\( 2 H C l_{(g)} \)
A. -150 KJ
J
в. -130 Кл
с. -228 Кл
D. -571 Кл


The quantity of charge flowing per unit time is called
A . capacitance.
B. charge density.
c. current
D. potential difference


Given \( A=\{x: x \in N \text { and } 3<x \leq 6\} \)
and \( \mathrm{B}=\{x: x \in W \text { and } x<4\}, \) then
find \( : B-A \)


A wire of stretched \( 50 \% \), calculate
percentage change in its resistance.
A . 0.50\%
B. 25\%
\( c \cdot 100 \% \)
D. 125\%


Which among the following is a competitive inhibitor of succinic
dehydrogenase?
A . \( \alpha \) -ketoglutarate
B. Malate
c. Malonate
D. Oxaloacetate


Zygospore is formed from :
A. Gamentangial copulation
B. Gametic union
c. zygote
D. Oogamy


Ceratium is a
A. Dinoflagellate
B. Diatom
c. Slime mold
D. Sporozoan


Line segment joining the centre to any point on the circle is
A. radius of the circle
B. diameter of the circle
c. secant of the circle
D. tangent of the circle.


What is the maximum range up to
which fiber optic can be used without repeater in communication systems?
\( A \cdot 4 \mathrm{km} \)
B. 10 km
\( c \cdot 100 \mathrm{km} \)
D. 500 km


A nitrogenous fertilizers having more nitrogen is :
\( \mathbf{A} \cdot\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4} \)
B. \( C a\left(N O_{3}\right)_{2} \)
c. \( N H_{2} C O N H_{2} \)
D. \( N H_{4} N O_{3} \)


A train, blowing a whistle of frequency \( f \) is standing in the railway yard. A person is running towards the engine.
The frequency of the sound of the whistle as heard by the personn will be
A. greater than \( f \)
B. less than \( f \)
c. equal to \( f \)
D. greater or less than \( f \) depending on the speed of the train


Conceptual Question Three elements \( X, Y, Z \) form a Dobernier traid. The difference in atomic weights
between elements \( Y, Z \) is \( 45 . \) If atomic
weight of \( X \) is 35 find atomic weight of elements X, Y and Z.


The distillation of phenol with zinc dust gives:
\( \mathbf{A} \cdot C_{6} H_{6} \)
в. \( C_{6} H_{5}-C_{6} H_{5} \)
c. \( C_{6} H_{1} \)
D. \( C_{6} H_{5}-O-C_{6} H_{5} \)


A body of mass 40 gram is moving with a constant velocity of \( 20 \mathrm{ms}^{-1} \) on a
horizontal frictionless table. The force
acting on the body in horizontal direction is:
A. 39.200 dyne
B. 160 dyne
c. 80 dyne
D. zero


Which statement about aspirin is not
true?
A. Aspirin belongs to narcotic analgesics.
B. It is effective in relieving pain.
c. It has antiblood clotting action
D. It is a neurologically active drug.


Parkinsonia is good example of
A. Phylloclade
B. Parachute mechanism
c. Phyllode
D. winged fruit


Find the smallest number which should
be multiplied to 15625 to get a perfect
cube.


The baking soda formula is :
A. \( K_{2} C O_{3} \)
в. \( N a H C O_{3} \)
c. both a and
D. none of these


The length of a tangent from a point \( \boldsymbol{A} \)
at distance \( 5 \mathrm{cm} \) from the centre of the
circle is \( 4 \mathrm{cm} \). Find the radius of the
circle.


Echo is a type of
A. Reflected sound
B. Refracted sound
C. Neither reflected nor refracted sound
D. None of these


Match the following.
List-II List-I
(A) Simple squamous
(I) Ureters epithelium
(B) Simple cuboidal
(II) Epididymis epithelium
\( (C) \)
Non-ciliated simple
(III) Lining of columnar epithelium \( \quad \) alveoli of lungs
Lining of
(D) Transitional epithelium (IV) Li
thyro thyroid vesicles
\( (E) \)
Pseudostratified non-
(V) Mucosa of stomach ciliated columnar and epithelium intestine
\( \mathbf{A} \cdot A-(1), B-(11), C-(1 V), D-(111), E-(V) \)
B. \( A-(V), B-(111), C-(11), D-(I V), E-(1) \)
C \( \cdot A-(11), B-(1 V), C-(111), D-(V), E-(1) \)
D. \( A-(111), B-(I V), C-(V), D-(1), E-(11) \)


The hybrdisation of the complex \( \left[C u\left(N H_{3}\right)_{4}\right]^{+2} \) is :
\( A \cdot s p^{3} \)
B \( \cdot s p^{3} d \)
c. \( d s p^{2} \)
D. \( s p^{3} d^{2} \)


A coil of insulated Copper wire is connected to a Galvanometer.
What happens, if a bar magnet is:
(i) pushed into the coil?
(ii) withdrawn from inside the coil?
(iii) held stationary inside the coil?


Classify the following as linear, circular, vibratory or oscillatory motion.
¡) The motion of a swing.
ii) The motion of earth around the sun
iii) The motion of a cyclist on a plain
road.
iv) The motion of a falling stone
v) The motion of a plucked string of a sitar.


Identify the plant belonging to the reed swamp stage in hydrosphere
succession
A. Juncus
B. Sagittaria
c. Salix
D. Trapa


f \( \boldsymbol{A}=(\boldsymbol{6}, \boldsymbol{7}, \boldsymbol{8}, \boldsymbol{9}), \boldsymbol{B}=(\boldsymbol{4}, \boldsymbol{6}, \boldsymbol{8}, \boldsymbol{1} \boldsymbol{0}) \) and
\( C=\{x: x \in N: 2<x \leq 7\} ; \) find :
\( \boldsymbol{B}-(\boldsymbol{A} \cap \boldsymbol{C}) \)
The sum of the elements in the above
\( \operatorname{set} \) is?


A block od mass \( 10 \mathrm{kg} \) is moving up an
inclined plane of inclination \( 30^{\circ} \) with an initial speed of \( 5 \mathrm{m} / \mathrm{s} \). It stopes after 0.5
s, what is the value of coefficient of kinetic friction?
A . 0.5
B. 0.6
\( c \cdot \sqrt{3} \)
D. \( \frac{1}{\sqrt{3}} \)


Holes are charge carriers in
This question has multiple correct options
A. intrinsic semiconductors
B. ionic solids
C. p-type semiconductors
D. metals


If \( A=10 w^{3}+20 w^{2}-55 w+60 \)
\( \mathrm{B}=-25 w^{2}+15 w-10 \) and
\( \mathbf{C}=\mathbf{5} \boldsymbol{w}^{2}-\mathbf{1 0} \boldsymbol{w}+\mathbf{2 0} \)
then \( A+B-C \) is equal to
A \( \cdot 10 w^{3}+10 w^{2}+30 w+30 \)
B. \( 10 w^{3}+10 w^{2}-30 w+30 \)
c. \( 10 w^{3}-10 w^{2}-30 w+30 \)
D. None of these


ff \( i^{2}=-1 \), then the value of \( \sum_{n=1}^{200} i^{n} \) is
A . 50
B. - -50
\( c \cdot 0 \)
D. 100


Fifth period has elements.
\( A \cdot 18 \)
B. 32
\( c \cdot 26 \)
D. 16


A man weighing \( 1500 N \) exerts a
pressure of \( 105 N / m^{2} \) on the ground. Calculate his area of contact with the
ground.


\( \int \sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right) d x=f(x)-\log (1+ \)
\( \left.\boldsymbol{x}^{2}\right)+\boldsymbol{c} \) then \( \boldsymbol{f}(\boldsymbol{x})= \)
A \( \cdot 2 x \tan ^{-1} x \)
B. \( -2 x \tan ^{-1} x \)
c. \( x \tan ^{-1} x \)
D. \( -x \tan ^{-1} x \)


Acidic or enzymatic hydrolysis of sucrose to give an equimolar mixture of glucose and fructose, is called:
A. esterification
B. inversion
c. saponification
D. insertion


The technique used by bats to find their way or to locate food is
A. SONAR
B. RADAR
c. Echolocation
D. Flapping


Find density when a mass of \( 9.23 \mathrm{kg} \) occupies a volume of \( 1.1 m^{3} \) with due
regard to significant figures.
\( \mathbf{A} \cdot 8.4 k g / m^{3} \)
B. \( 8.39 k g / m^{3} \)
\( \mathbf{c} \cdot 8.3 k g / m^{3} \)
D. None of the above


Vitamins are generally involved in forming component of enzyme called
A. Apoenzyme
B. Holoenzyme
c. Prosthetic group
D. Coenzyme and prosthetic group


For given half cell; \( A l^{+3}+3 e^{-} \rightarrow A l ; \) on
increasing \( \left[A l^{+3}\right], \) the electrode
potential:
A. Increases
B. Decreases
c. No change
D. First increases then decreases


If the roots of the equation \( x^{2}+p x- \)
\( 6=0 \) are 6 and -1 then the value of \( p \)
is
A . 2
B. 3
\( c .-5 \)
D. 5


Spike of spikelets inflorescence commonly occurs in
A. Cruciferae
B. Papilionaceae
c. Poaceae
D. Solanaceae


Find the \( 15^{t h} \) term of the series
\( \mathbf{3}, \mathbf{9}, \mathbf{1 5}, \mathbf{2 1}, \mathbf{2 7}, \mathbf{3 3}, \dots \)


The sequence of bases in the nucleic acid strand is explained by:
A \( \cdot 1^{0} \) structures
B. 2 \( ^{0} \) structures
C. Both \( 1^{0} \) and \( 2^{0} \)
D. None


Figure below shows the distance-time
graph of three objects \( A, B \) and \( C \) Study the graph and answer the following questions: which of the three is travelling the fastest?
A. car \( C \)
B. car \( A \)
\( c \cdot \operatorname{car} B \)
Dan not be determine


What is a tidal volume? Find out the
tidal volume (approximate value) for a healthy human in an hour.


\( \sin 360^{\circ}=? \)


LED is a p-njunction diode which is
A. forward biased.
B. either forward biased or reverse biased.
C. reverse biased.
D. neither forward biased nor reverse biased.


Find the mean deviation about the
mean for the following data:
\( \begin{array}{ll}\text { Marks obtained } & \text { No. of students } \\ \text { 0-10 } & 5 \\ \text { 10-20 } & 8 \\ \text { 20-30 } & 15 \\ \text { 30-40 } & 16 \\ \text { 40-50 } & 6\end{array} \)


Assertion: A beam of white light gives a spectrum on passing through a hollow prism. Reason: Speed of light outside the prism is different from the speed of light inside the glass prism.
A. Both assertion and reason are correct and reason is the correct explanation of the assertion
B. Both assertion and reason are correct, but reason is not the correct explanation of the assertion
c. Assertion is correct, but reason is incorrect
D. Assertion is incorrect, but reason is correct
E. Both assertion and reason are incorrect.


The structure of \( I F_{7} \) is:
A. Trigonal bipyramidal
B. Octahedral
c. Pentagonal bipyramidal
D. Tetrahedral


\( \int \frac{\boldsymbol{x}+\boldsymbol{2}}{\mathbf{2} \boldsymbol{x}^{2}-\mathbf{7} \boldsymbol{x}+\mathbf{3}} \boldsymbol{d} \boldsymbol{x}= \)
A. \( \log \left|\frac{x-3}{2 x-1}\right|+c \)
в. \( \log \left|\frac{x-3}{\sqrt{2 x-1}}\right|+c \)
c. \( \frac{1}{2} \log \left|\frac{x-3}{2 x-1}\right|+c \)
D. \( \frac{1}{2} \log \left|\frac{x-3}{\sqrt{2 x-1}}\right|+c \)


If 2 nd, 3 rd and 6 th terms of an AP are the three consecutive terms of a GP
then find the common ratio of the GP.


The relation \( \left[\boldsymbol{H}^{+} \boldsymbol{O}\right]=\frac{\boldsymbol{K} \boldsymbol{w}}{\left[\boldsymbol{H}_{3} \boldsymbol{O}^{+}\right]}+ \)
\( [\boldsymbol{H} \boldsymbol{C l}]_{0} \) for an aqueous solution of \( \boldsymbol{H} \boldsymbol{C l} \)
can be reduced to:
This question has multiple correct options
\( \mathbf{A} \cdot\left[H_{3} O^{+}\right]=[H C l]_{0} \quad \) if \( \quad\left[H_{3} O^{+}\right] \geq 10^{-6} \)
\( ^{\mathrm{B}}\left[H_{3} O^{+}\right]=[H C l]_{0} \quad \) if \( \quad \frac{K_{w}}{\left[H_{3} O^{+}\right]} \geq 10^{-8} \)
\( \left[H_{3} O^{+}\right]=\frac{[H C l]_{0} \pm \sqrt{[H C l]_{0}^{2}+4 K_{w}}}{2} i f \quad\left[H_{3} O^{+}\right] \leq \)
\( 10^{-6} \)
\( \mathbf{D} \cdot\left[H_{3} O^{+}\right]=[H C l]_{0} \quad \) if \( \quad[H C l]_{0} \geq 10^{-6} \)


Which is the correct order of increasing ionic nature of following molecules?
I. \( L i F \)
Il. \( C l F_{3} \)
III. \( \boldsymbol{K}_{2} \boldsymbol{O} \)
IV. \( \boldsymbol{S O}_{2} \)
\( A \cdot||<|<| V<\| \)
B. II<IV<I<III
c. Ik IV<IIISI


Fill in the blank:
The Pole star can be located with the
help of
A. Ursa Major
B. Big Dipper
c. saptarshi
D. all of the above


If a copper wire is stretched to make it
\( 0.1 \% \) longer, the percentage increases in resistance will be
A . 0.2\%
B. 2\%
c. 1\%
D. 0.1\%


Distinguish between Uniform motion and non uniform motion.


In a compound microscope the focal
length of objective lens.
A. Is more than the focal length of eyepiece lens
B. Is less than the focal length of eyepiece lens
C. Is equal to the focal length of eyepiece lens
D. Is two times to the focal length of eyepiece lens


have equal number of
neutrons.
A. Isobars
B. Isotones
c. Isotopes
D. Mass Number


The mean of data 34,65,14,74,43 is


What is the order of rotational
symmetry of rectangle?
\( A \)
B. 2
\( c \cdot 3 \)
\( D \)


A secondary cell is one that:
A. can be recharged
B. can be recharged by passing current through it in the same direction
C. can be recharged by passing current through it in the opposite direction
D. can not be recharged


A simple harmonic oscillator has an
amplitude a and time period T. The time required by it to a travel from \( x=a \) to \( x= \) a/2 is
A. \( T / 6 \)
B. T / 4
\( c \cdot T / 3 \)
D. T/2


Find the number of combinations and
permutations of 4 letters taken from the word \( \boldsymbol{E} \boldsymbol{X} \boldsymbol{A} \boldsymbol{M} \boldsymbol{I} \boldsymbol{N} \boldsymbol{A} \boldsymbol{T} \boldsymbol{I} \boldsymbol{N} \)


Evaluate the following limits. \( \lim _{x \rightarrow \pi / 2} \frac{2^{-\cos x}-1}{x\left(x-\frac{\pi}{2}\right)} \)


Which of the following is/are redox reactions?
This question has multiple correct options
A. \( B a O_{2}+H_{2} S O_{4} \rightarrow B a S O_{4}+H_{2} O_{2} \)
в. \( 2 B a O+O_{2} \rightarrow 2 B a O_{2} \)
\( \mathbf{c} \cdot 2 K C I O_{3} \rightarrow 2 K C l+3 O_{2} \)
D. \( S O_{2}+2 H_{2} S \rightarrow 2 H_{2} O+3 S \)


Which of the following is an allylic
halide?

This question has multiple correct options
A. 3-bromo-2-methylpropene
B. 3-bromobut-1-ene
c. 3-bromopent-2-ene
D. 4 -bromobut- - -ene


Define Reference electrode.


Hydrogen is produced by the reaction:
A. \( N a_{2} O_{2}+2 H C l \)
в. \( M g+H_{2} O \)
\( \mathrm{c} \cdot B a O_{2}+H C l \)
D. \( H_{2} S_{4} O_{8}+H_{2} O \)


Function \( f(x) \) is defined as \( f(x)= \) \( \left\{\begin{array}{l}\frac{x-1}{2 x^{2}-7 x+5}, \quad x \neq 1 \\ -\frac{1}{3}, \quad x=1\end{array}\right. \)
Is \( f(x) \) differentiable at \( x=1 \) if yes find
\( \boldsymbol{f}^{\prime}(\mathbf{1}) \)


Asci is formed in :
A. Ascobolus
B. Saccharomyces
c. Penicillium
D. All of the above


A potentiometer has a driving cell of negligible internal resistance. The balancing length of a Daniel cell is \( 5 \mathrm{m} \) If the driving cell had internal resistance, the balancing length of the same Daniel cell would have been
A. More
B. Less
c. same
D. Cannot be said from the data


In the Ingen Hausz's experiment, the wax melts up to lengths \( 10 \mathrm{cm} \) and
\( 25 c m \) on two identical rods of different
materials. The ratio of thermal conductivities of the two materials is
A . 1: 6.25
B. 6.25: 1
c. \( 1: \sqrt{2.5} \)
D. 1: 2.5


\( P \) and \( Q \) are two objects with masses 5 kg and 30 kg respectively. Then
A. P has more inertia than \( Q \)
B. Q has move inertia than P
c. P and Q have the same inertia
D. neither P nor Q has any inertia


A marble of mass \( x \) and diameter \( 2 r \) is
gently released in tall cylinder containing honey. If the marble displace \( \operatorname{mass} \boldsymbol{y}(<\boldsymbol{x}) \) of the liquid, then the
terminal velocity is proportional to
\( \mathbf{A} \cdot x+y \)
в. \( x-y \)
c. \( \frac{x+y}{r} \)
D. \( \frac{x-y}{r} \)


The process by which protein synthesis takes pace based on genetic information is called:
A. Replication
B. Messenger hypothesis
c. Translation
D. Transcription


The ratio of wavelengths of the last line
of Balmer series and the last line of
Lyman series is
A .2: 1
B. 1: 2
c. 4: 1
D. 2: 6


A school has a hall which is 22 m long and \( 15.5 m \) broad. A carpet is laid
inside the hall leaving all around a margin of \( 75 \mathrm{cm} \) from the walls. Find the
area of the carpet and the area of the
strip left uncovered. If the width of the carpet is \( 82 \mathrm{cm}, \) find the cost at the rate
of \( \boldsymbol{R} \boldsymbol{s} \boldsymbol{6} \boldsymbol{0} \) per meter


Type of hybridisation in transition state
of \( S e F_{4}, \) when it undergoes in
hydrolysis:
B. \( s p^{3} d^{2} \)
\( \mathbf{c} \cdot d s p^{3} \)
D. \( s p^{3} \)


The point of intersection of the line \( \frac{x-1}{3}=\frac{y+2}{4}=\frac{z-3}{-2} \) and plane
\( 2 x-y+3 z-1=0 \) is.
B . (10,10,-3)
c. (-10,10,3)
D. None of these


When the distance covered by a moving object is directly proportional to the time duration, it is said to travel with:
A. Zero velocity
B. Constant speed
c. Constant acceleration
D. Uniform velocity


A body of mass \( m \) slides down an
incline and reaches the bottom with a
velocity \( V \). If the same mass were in the form of a ring which rolls down the same incline, the velocity of its centre of
mass at bottom of the plane is:
A. \( V \)
B. \( \sqrt{2} V \)
c. \( \frac{V}{\sqrt{2}} \)
D. \( \frac{V}{2} \)


For reactions involving gaseous reactants and products, the
equilibrium constant \( \boldsymbol{K}_{\boldsymbol{p}} \) is written
in terms of:
A. the pressure of the gases
B. the molar volumes of the gases
c. the partial pressures of the gases
D. the mole fraction of the gases


Sodium chloride, when heated with
conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) and solid potassium dichromate gives:
A. chromic chloride
B. chromyl chloride
c. chromous chloride
D. none of these


The mentioned equation is in which form?
\( (y-2)(y+2)=0 \)
A. cubic
B. quadratic
c. linear
D. none of these


A convex lens forms a e real image three times larger than the object on a screen Object and screen are moved until the image becomes twice the size of the object. If the shift of the object is \( 6 \mathrm{cm} \) The shift of screen is
A . 36 \( \mathrm{cm} \)
B. 72 cm
c. \( 18 \mathrm{cm} \)
D. \( 9 \mathrm{cm} \)


Let the magnetic field on the earth be modelled by that of a point magnetic dipole at the centre of the earth. The angle of dip at a point the geographical
equator This question has multiple correct options
A. is always zero
B. can be zero at specific points
c. can be positive or negative
D. is bounded


Shine at freshly cut sodium is because
of :
A. due to oscillations of free electrons.
B. due to weak metallic bonding
c. due to absorption of light in crystal lattice.
D. due to the presence offree valency at the surface


\( A B C D \) is a parallelogram and \( P \) is a
point on the segment \( \overline{A D} \) dividing it internally in the ratio 3: 1 the line \( \overline{B P} \)
meets the diagonal \( \overline{A C} \) in \( Q . \) Then the
ratio \( \boldsymbol{A} \boldsymbol{Q}: \boldsymbol{Q} \boldsymbol{C} \) is
A .3: 4
B. 4: 3
c. 3: 2
D. 2 : 3


What is the function of the iris in
human eye?
A. Iris restricts the light to pass through the eye over to the retina.
B. Iris provides protection to the eye from microorganisms.
C. Iris controls the size of the pupil and hence the amount of light entering the eye.
D. Iris allows colour detection in eye.


If \( A \) is any \( m \times n \) matrix, then show
that
\( (i)(1) A=A \)
\( (i i)(-1) A=-A \)


An oxygen-containing organic compound was found to contain 52\% carbon and \( 13 \% \) of hydrogen. Its vapour density is \( 23 . \) The compound reacts with sodium metal to liberate hydrogen. A functional isomer of this compound is :
A. ethanol
B. ethanal
c. methoxy methane
D. methoxy ethane


Which of the following is utilized by all living organisms?
A \( \cdot C O_{2} \)
B. A triplet genetic code to produce proteins
c. oxygen
D. ADP as cellular energy
E. Membrane-bound organelles


Two concentric shells carry charges \( q \)
and Q. Their radius are r and R. The potential difference between the two is :
A \( \cdot \frac{q}{4 \pi \varepsilon_{0} R^{2}}-\frac{Q}{4 \pi \varepsilon_{0} R} \)
в. \( \frac{Q-q}{4 \pi \varepsilon_{\Omega} R} \)
\( ^{\mathrm{c}} \cdot \frac{q}{4 \pi \varepsilon_{0}}\left[\frac{1}{r}-\frac{1}{R}\right] \)
D. \( \frac{(Q-q)}{4 \pi \varepsilon_{0}}\left[\frac{1}{r}-\frac{1}{R}\right] \)


If a charge is shifted from a high potential region to low potential region, the electrical potential energy
A. Increses
B. Decreses
c. May increase or decrease
D. Remains constant


If \( \boldsymbol{y}=|\cos \boldsymbol{x}|+|\sin \boldsymbol{x}|, \) then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \) at \( \boldsymbol{x}= \)
\( \frac{2 \pi}{3} \) is
A \( \cdot \frac{1-\sqrt{3}}{2} \)
B.
c. \( \frac{\sqrt{3}-1}{2} \)
D. None of these


The bar graph shown in above figure represents the circulation of
newspapers in 10 languages.
study the bar graph and answer the
following question:
Find the excess of the number of
newspapers published in English over
those published in Urdu.


In eubacteria, a cellular component that resembles eukaryotic cell is
A. Cell wall
B. Plasma membrane
c. Nucleus
D. Ribosomes


What, according to you, were the values
displayed by Asha and her mother?


an angle is \( 28^{\circ} \) less than its
complement, find its measure.


The rate of change of the volume of a sphere w.r.t. its surface area, when the radius is \( 2 \mathrm{cm} \) is
A . 1
B. 2
\( c .3 \)
D.


Fusion of \( M n O_{2}, \) with \( K O H \) in
presence of \( \boldsymbol{O}_{2} \) produces a salt \( \boldsymbol{W} \)
Alkaline solution of \( W \) upon
electrolytic oxidation yields another salt
\( X . \) The manganese containing ions
present in \( W \) and \( X, \) respectively are \( Y \)
and \( Z . \) Correct statement(s) is (are)
This question has multiple correct options
\( \mathbf{A} \cdot \operatorname{In} \operatorname{both} Y \) and \( Z, \alpha- \) bonding occurs between \( p- \)
orbitals of oxygen and d-orbitals of manganese
B. Both \( Y \) and \( Z \) are coloured and have tetrahedral shape
C. In aqueous acidic solution, \( Y \) undergoes disproportionation reaction to give \( Z \) and \( M n O_{2} \)
D. \( Y \) is diamagnetic in nature while \( Z \) is paramagnetic


Upton Chuck is riding the Giant Drop at Great America. If Upton free falls for 2.60 seconds, then how far will he fall?
\( (\operatorname{in} m) \)
A . \( 33.1 m \)
в. \( 33 m \)
\( c .3 .1 m \)
D. \( 63.1 m \)


In the circuit shown in figure, a
conducting wire \( H E \) is moved with a
constant speed \( \boldsymbol{v} \) toward left. The
complete circuit is placed in a uniform magnetic field \( \vec{B} \) perpendicular to the plane of the circuit inward. The current
in \( \boldsymbol{H} \boldsymbol{K} \boldsymbol{D} \boldsymbol{E} \) is
A . clockwise
B. anticloclwise
c. alternating
D. zero
E. answer required


The device which converts the
mechanical energy in to electric energy is
A . D.C. motor
B. A.C. dynamo
c. Transformer
D. starter


The number of moles of lead nitrate
needed to coagulate 2 mole of colloidal
\[
[\boldsymbol{A} \boldsymbol{g} \boldsymbol{I}] \boldsymbol{I}^{-} \text {is: }
\]
A .2
B.
c. \( \frac{1}{2} \)
D. \( \frac{2}{3} \)
E. 5 \( \overline{2} \)


The value of least distance of clear
vision is about.....................
A. \( 50 \mathrm{cm} \)
B. 40 cm
c. \( 20 \mathrm{cm} \)
D. 25 cm


The stability of ferric ion is due to
A. half filled f-orbitals
B. half filled d-orbitals
C. completely filled f-orbitals
D. completely filled d-orbitals


How many of the following have two \( \sigma \)
and two \( \pi \) bonds?
\( C_{3}^{4-}, C N_{2}^{2-}, C O_{2}, C_{2}^{2-}, C_{2} H_{4}, C N^{-} \)


\( 1- \) is a \( -\dots--- \) fraction 4
A. Proper
B. improper
c. mixed
D. None of the above


Which term of the sequence
\( 72,70,68,66, \dots \) is \( 40 ? \)


The number of solutions for \( 2 x+3 y= \)
10 and \( 4 x+6 y=25 \) are


a distance \( L \) in front of the centre of a
mirror of width \( d \), hung vertically on a
wall. A man walks in front of the mirror
along a line parallel to the mirror at a
distance \( 2 L \) from it as shown in the
figure. The greatest distance over which
he can see the image of the light source
in the mirror is :
\( \mathbf{A} \cdot d / 2 \)
B. \( d \)
c. \( 2 d \)
D. \( 3 d \)


A charge is distributed over two
concentric hollow spheres of radii \( \boldsymbol{R} \) and \( r, \) where \( R>r, \) such that the
surface densities of charges are equal
( \( \sigma \) ). What is the potential at their
common centre?
A \( \cdot \frac{\sigma}{\varepsilon_{0}}(R+r) \)
В \( \cdot \frac{\varepsilon_{0}}{\sigma}(R+r) \)
c. \( \frac{\sigma}{\varepsilon_{0}} R \)
D. \( \frac{\sigma}{\varepsilon_{0}} r \)


Decomposition of \( H_{2} O_{2} \) is prevented in
presence of :
A . acetanilide
B. glycol
c. oxygen
D. none of the above


A boy standing on a long railroad car throws a ball straight upwards. The car is moving on the horizontal road with an
acceleration of \( 1 \mathrm{ms}^{-2} \) and the
projection velocity in the vertical direction is \( 9 \cdot 8 m s^{-2} . \) How far behind
the boy will the ball fall on the car?


Galvanisation means:
A. decomposition of \( Z n \) on \( F e \)
B. decomposition of \( A l \) on \( F e \)
c. decomposition of \( S n \) on \( F e \)
D. decomposition of \( C u \) on \( F e \)


Choose the odd one out in each of the
following groups of four items each:
Ethyl alcohol, Carbon dioxide, Starch,
Oxygen absence


Paired copulatory organs are present in the reptilian order
A. Chelonia
B. Rhynchocephalia
c. squamata
D. crocodilia


Androecium is the whorl of
A. Anthers
B. Stamens
c. Filaments
D. Tepals


The function \( f(x)= \)
\( \left\{\begin{array}{l}\frac{\cos 3 x-\cos 4 x}{x^{2}}, \text { for } x \neq 0 \\ \frac{7}{2}, \text { for } x=0\end{array} \) at \right.
\( \boldsymbol{x}=\mathbf{0} \) is
A. right continuous only
B. discontinuous
c. left continuous only
D. continuous


If \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{n}, \boldsymbol{n} \in \boldsymbol{N} \) and \( (\boldsymbol{g} \boldsymbol{o} \boldsymbol{f})(\boldsymbol{x})= \)
\( \boldsymbol{n} \boldsymbol{g}(\boldsymbol{x}) \operatorname{then} \boldsymbol{g}(\boldsymbol{x}) \) can be
A \( . n|x| \)
B. \( 3 . \sqrt[3]{x} \)
\( c \cdot e^{x} \)
\( \mathbf{D} \cdot \log |x| \)


Solve:
\( \frac{91}{9}+2 a \frac{13}{3}=169 \)


Which of the compounds with
molecular formula \( C_{5} H_{10} \) yields acetone on ozonolysis?
A. 2-Methyl-1-butene
B. 2-Methyl-2-butene
c. 3-Methyl-1-butene
D. Cyclopentane


If the sum of \( n \) terms of an \( A . P . \) is
\( 3 n^{2}+5 n, \) then which of its term is 164
A . \( 26 t h \)
B. 27th
\( c .28 t h \)
D. None of these


What happens when a thermos flask containing liquid is vigorously shaken? Will there be any change in the temperature of the liquid?


Be \( O \) is almost insoluble but \( B e S O_{4} \) is
soluble in water. Explain.


How does gold react with aquaregia?


Assertion
Latent heat of fusion of ice is
\( 33600 J k g^{-1} \)
Reason
Latent heat refers to change of state without any change in temperature.
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


Both chromosome and gene (Mendelian factors) whether dominant or recessive
are transmitted from generation to generation in which form
A. changed
B. unaltered form
c. altered form
D. disintegrated


The first and last elements of the
longest period are
A. francium and Uuo
B. caesium and radon
c. francium and radon
D. caesium and Uuo


Casparian strip occurs in:
A. Pericycle
B. Endodermis
c. Epidermis
D. cortex


A vertical hollow cylinder of height \( 1.52 \mathrm{m} \) is fitted with a movable piston of
negligible mass and thickness. The lower
half portion of the cylinder contains an
ideal gas and the upper half is filled with
mercury. The cylinder is initially at \( 300 \mathrm{K} \)
When the temperature is raised half of
the mercury comes out of the cylinder. Then the temperature is (the thermal
expansion of mercury to be negligible)
\( A \cdot 437 \mathrm{K} \)
B. 337.5 K
c. \( 275 \mathrm{k} \)
D. 137.K


Which one of the following is of related type?
A. Catkin and Hypanthodium
B. Raceme and Cyathium
c. corymb and umbel
D. Verticillaster and spike


Primata and Carnivora are placed
together in the same?
A. Order
B. Division
c. Family
D. class


Why is meiosis essential in sexually
reproducing organisms?


Choose the correct answer out the given options.


Which of the following compounds has
phosphorus atom in +1 oxidation
state?
A \( . H_{3} P O_{3} \)
в. \( H_{3} P O_{4} \)
c. \( H_{3} P O_{2} \)
D. \( H_{4} P_{2} O_{7} \)


Which of the following is the most stable form of cyclohexane?
A. Boat form
B. Chair form
c. Half chair form
D. Half boat form


For the reaction, \( \boldsymbol{S n O}_{2}(\boldsymbol{s})+\boldsymbol{2} \boldsymbol{H}_{2}(\boldsymbol{g}) \rightleftharpoons \)
\( \boldsymbol{S} \boldsymbol{n}(l)+\boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \) the equilibrium
mixture of steam and hydrogen
contained \( 45 \% \) and \( 24 \% H_{2} \) at \( 900 \mathrm{K} \)
and \( 1100 \mathrm{K} \) respectively. Calculate \( \boldsymbol{K}_{\boldsymbol{P}} \)
at both the temperatures. Generally should it be higher or lower temperatures for better reduction of
\( \boldsymbol{S} \boldsymbol{n} \boldsymbol{O}_{2} ? \)
\( \mathbf{A} \cdot \therefore K_{C_{2}}=1.03 \)
\( \mathbf{B} \cdot \therefore K_{C_{2}}=5.02 \)
\( \mathbf{c} \cdot \therefore K_{C_{2}}=15.01 \)
\( \mathbf{D} \cdot \therefore K_{C_{2}}=10.03 \)


Why is water a bent molecule and not
İinear?
A. Water has four electron domains repelling each other, causing the molecule to be bent.
B. There are not enough electrons involved for the molecule to be linear.
C. Because the oxygen in water can only make bent molecules.
D. The molecule alternates in between a bent geometry and a linear geometry.


At magnetic poles, the angle of dip is
A \( \cdot 45^{\circ} \)
B . \( 30^{\circ} \)
c. zero
D. \( 90^{\circ} \)


Assertion
Changes in volume of thoracic cavity reflect on volume of pulmonary cavity.
Reason

We can alter the pulmonary volumes directly for breathing.
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


In a three litre vessel, 2 moles of \( N_{2} \) and
3 moles of length \( \boldsymbol{H}_{2} \) are taken. If at
equilibrium \( x \) moles of \( N_{2} \) were obtained then the concentration of
\( N H_{3} \) at equilibrium will be:
\( \mathbf{A} \cdot 2-x \)
B. \( 4-2 x \)
c. \( \frac{2 x}{3} \)
D. \( \frac{4-2 x}{3} \)


The sum of first \( n \) terms of an \( A . P \) is
\( 2 n+3 n^{2} . \) Find the common difference.


With a growth rate of about \( 5 \mathrm{mm} \) a minute, it is one of the fastest growing organisms in the world. It is also known as 'the lady of the white veil'. Identify it
A. Sphagnum moss
B. Stinkhorn fungus
c. Bamboo
D. Clubmoss


Solve:
\( \left|\begin{array}{ccc}\mathbf{0} & -\mathbf{3} & \boldsymbol{x} \\ \boldsymbol{x}+\mathbf{1} & \mathbf{3} & \mathbf{1} \\ \mathbf{4} & \mathbf{1} & \mathbf{5}\end{array}\right|=\mathbf{0} \)


State whether True or False.
Multiply: \( x^{2}+x+1 \) by \( 1-x \)
The answer is \( 1-x^{3} \)
A. True
B. False


Because of lanthanoid contraction, which of the following pairs of elements have nearly the same atomic radii?
A. \( z r(40) \) and \( H f(72) \)
B. \( \operatorname{Zr}(40) \) and \( \operatorname{Ta}(73) \)
c. \( \operatorname{Ti}(22) \) and \( z r(40) \)
D. \( z r(40) \) and \( N b(41) \)


Which of the following statements is the converse of "You cannot skateboard
if you do not have a sense of balance."?
A. If you cannot skateboard, then you do not have a sense of balance
B. If you do not have a sense of balance, then you cannot skateboard.
c. If you skateboard, then you have a sense of balance
D. None of these


The distance between (0,1,-1) and the point of intersection of the line \( \frac{x}{2}= \) \( \frac{\boldsymbol{y}-\mathbf{1}}{\mathbf{3}}=\frac{\boldsymbol{z}+\mathbf{1}}{\mathbf{4}} \) and the plane \( \boldsymbol{x}+\boldsymbol{y}+ \)
\( z=9 \) is
A. \( \sqrt{29} \)
в. \( \frac{1}{2} \sqrt{29} \)
\( c \cdot \frac{4}{9} \)
D. \( \frac{2}{9} \sqrt{29} \)


Solve the following equation \( \mathbf{2}(\mathbf{2} \boldsymbol{x}+\mathbf{4})-\mathbf{3}(\boldsymbol{x}-\mathbf{1})=\mathbf{1 1} \)


Hybridization and shape of \( \mathbf{X e F}_{4} \) is:
A \( \cdot \mathrm{sp}^{3} \mathrm{d} \), trigonal bipyramidal
B . sp \( ^{3} \), tetrahedral
c. \( s p^{3} d^{2}, \) square planar
D. \( \operatorname{sp}^{3} \mathrm{d}^{2} \), hexagonal


Two bodies have same mass and speed,
then:
A. their momentums are same
B. the ratio of momentums is not determined
C. the ratio of their magnitudes of momentum is one
D. both (B) and (C) are correct


Hydrogen and helium each having
volume \( V \) at same temperature \( T \) and
same pressure \( \boldsymbol{P} \) are mixed to have
same volume \( V \). The resulting pressure of the mixture will be:
A \( . R / 2 \)
в. \( P \)
\( c .2 P \)
D. depending on the relative mass of the gases


Find the expansion of \( (p+2)(p-4)(p+6) \)
A \( \cdot p^{3}+4 p^{2}-20 p-48 \)
в. \( p^{3}-4 p^{2}-20 p-48 \)
c. \( p^{3}+4 p^{2}+20 p-48 \)
D. None of these


A sphere rolls without sliding on a
rough inclined plane (only mg and contact forces are acting on the body).
The angular momentum, of the body:
A. about centre is conserved
B. is conserved about the point of contact
c. is conserved about a point whose distance from the inclined plane is greater than the radius of the sphere
D. is not conserved about any point


The temperature-time variation graphs,
as obtained by four students \( \boldsymbol{A}, \boldsymbol{B}, \boldsymbol{C} \)
and \( D \) are as shown. The graph, likely to
be correct is that of student
\( \mathbf{A} \cdot A \)
B. \( B \)
\( c \cdot C \)
\( \mathbf{D} \cdot D \)


A planet in a distant solar system is 10 times more massive than the earth and
its radius is 10 times smaller. Given
that the escape velocity from the earth is \( 11 \mathrm{kms}^{-1} \), the escape velocity from
the surface of the planet would be
A. \( 1.1 \mathrm{km} / \mathrm{s} \)
в. \( 11 \mathrm{km} / \mathrm{s} \)
c. \( 110 \mathrm{km} / \mathrm{s} \)
D. \( 0.11 \mathrm{km} / \mathrm{s} \)


What are introns?


A body falls freely from rest. It covers as much distance in the last second of its
motion as covered in the first three
seconds. The body has fallen for a time of
A . \( 3 s \)
B . \( 5 s \)
c. \( 7 s \)
D. \( 9 s \)


Acetic acid is obtained when:
A. methyl alcohol is oxidised with potassium permanganate
B. calcium acetate is distilled in the presence of calcium formate
C . acetaldehyde is oxidised with potassium dichromate and sulphuric acid
D. glycerol is heated with sulphuric acid


\( \lim _{x \rightarrow k}(x-[x]), \) where \( k \) is an integer
is equal to (where [.] denotes greatest integer function).
\( \mathbf{A} \cdot \mathbf{1} \)
B.
\( c \cdot-1 \)
D. Does not exist


Write 5 rational number between \( \frac{2}{5} \) and \( \frac{3}{5}, \) having the same denominators


A thin conducting strip of width \( h= \) \( 2.0 \mathrm{cm} \) is tightly wound in the shape of
a very long coil with cross-section radius \( R=2.5 \mathrm{cm} \) to make a single-
layer straight solenoid. A direct current \( \boldsymbol{I}=\mathbf{5 . 0} \boldsymbol{A} \) flows through the strip. Find
the magnetic induction inside and
outside the solenoid as a function of the
distance \( r \) from its axis.


A ray of light passes through a prism as
shown in the figure.
The angle \( \delta \) is known as:
A. Angle of deviation
B. Angle of dispersion
c. Angle of emergence
D. Angle of refraction


Two like parallel forces \( 20 N \) and \( 30 N \)
act at the ends \( A \) and \( B \) of a rod \( 1.5 m \)
long. The resultant of the forces will act
at the point:
A. \( 90 \mathrm{cm} \) from A
B. \( 75 \mathrm{cm} \) from \( \mathrm{B} \)
\( \mathrm{c} .20 \mathrm{cm} \) from \( \mathrm{B} \)
D. \( 85 \mathrm{cm} \) from \( \mathrm{A} \)


We have four substances \( \mathrm{P}, \mathrm{Q}, \mathrm{R}, \mathrm{S} \)
Substance \( P \) is dark coloured violet
solid having diatomic molecules.
Solution of \( P \) in alcohol is an Antiseptic 'T' Substance 'Q'is a white solid usually
recovered from sea on a large scale.
Substance 'R' is also a white solid
insoluble in water and used in the form
of small balls for safe storage of woolen
clothes. Substance 'S' is a white solid
too used in dry cell. P,Q,R,S,T, may be (choose correct option)
A. P-lodine, Q-Napthalene,R- \( R-N H_{4} C I \) S-Nacl, T-lodin
tincture
B. P-NaCI,Q-Napthalene, \( R-N H_{4} C I \)
S-lodine, T-lodine tincture
C. P-lodine tincture, Q- \( R-N H_{4} C I R \) - lodine, S-
Napthalene, T-NaCl
D. P-lodine, Q-Nacl, R- Napthalene
S- \( R-N H_{4} C I, \) T-lodine tincture


The graph between \( \log \frac{x}{m} v / s \log P \) is
straight line inclined at an angle \( 45^{\circ} \) with intercept \( 0.30 . \) What will be rate of
adsorption at pressure 0.4 atm?
A . 0.4
B. 0.6
c. 0.8
D. 0.9


The compound (A) is:
\( \mathbf{A} \)
B.
\( \mathbf{C} \)
D.


The differential equation by eliminating the arbitary constants from the equation \( \boldsymbol{y}=\boldsymbol{a} \cos \boldsymbol{x}+\boldsymbol{b} \sin \boldsymbol{x}+\boldsymbol{x} \sin \boldsymbol{x} \)
is
\( \mathbf{A} \cdot y_{2}+y=3 \cos x \)
В. \( y_{2}+2 y=2 \cos x \)
C \( \cdot y_{2}+y=2 \cos x \)
D. \( y_{2}+y=4 \cos x \)


Which of the following does not give a borax-bead test?
A. Ferrous salt
B. Chromium
c. cobalt
D. Sodium


Which of the following is volatile covalent liquid at room temperature
\( 25^{\circ} C \) ) and 1 atm?
A . \( N_{2} \)
в. \( K I \)
c. \( C C l_{4} \)
D. \( A g N O_{3} \)
ह. \( C a C O_{3} \)


Define Eccentricity?


The polynomial \( a x^{3}+b x^{2}+x-6 \) has
\( (x+2) \) as a factor and leaves a
remainder 4 when divided by \( (x-2) \)
Find \( a \) and \( b \)
This question has multiple correct options
\( \mathbf{A} \cdot a=0 \)
в. \( b=2 \)
\( \mathbf{c} \cdot a=2 \)
\( \mathbf{D} \cdot b=0 \)


Draw a neat labelled diagram of \( \boldsymbol{H}_{2}- \)
\( O_{2} \) fuel cell. Write the reaction occurs at
cathode of the cell.


The inhibitory effect of the presence of
\( O_{2} \) on anaerobic respiration is termed
as
A. Warburg effect
B. Pasteur effect
c. Emerson's effect
D. oxygen effect


Give one example each of 'oil in water' and 'water in oil' emulsion.


The compound which gives the most stable carbonium ion on dehydration is:
\( A \)
B.
c. \( C H_{3} C H_{2} C H_{2} C H_{2} O H \)
D.


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


NaCN used in the froth flotation method
for the purification of ore is:-
A. \( Z n S \) which contain \( P b S \)
B. \( C u_{2} S \) which contain \( F e_{e} S_{3} \)
c. \( P b S \) which contain \( Z n S \)
D. \( P b S \) which contain \( S i O_{2} \)


In which of the following secondary growth occurs:
(A) The root of cycas
(B) Stem of Pinus
(C) The root of maize
(D) Stem of
mango
(E) Stem of wheat
A. All except A and B
B. All except \( c \) and \( E \)
c. only D
D. Only A and B


Polymerisation in which two or more chemically different monomers take part is called
A. addition polymerisation
B. copolymerisation
c. chain polymerisation
D. homopolymerisation


What is Thermit Reaction? Explain its use and give equation.


ff \( x=a t^{4}, y=b t^{3}, \) then find \( \frac{d y}{d x} \)


toppr
Q Type your question.
as shown. At the same instant, a man \( P \) throws a ball vertically upwards with
initial velocity ' \( u^{\prime} \). Ball touches (coming
to rest) the base of the plane at point \( B \)
of plane's journey when it is vertically
above the mans. ' \( s^{\prime} \) is the distance of
point \( B \) from point \( A \). Just after the
contact of ball with the plane, acceleration of plane increases to \( 3 m / s^{2} . \) Find:
(i) Initial velocity \( ^{\prime} u^{\prime} \) of ball.
(ii) Distance \( ^{\prime} s^{\prime} \)
(iii) Distance between man and plane when the man catches the ball black.
\( \left.\boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} / \boldsymbol{s}^{2}\right) \) (Neglect the height of
\( \operatorname{man}) \)


Lichen is a pioneer in which succession?
A. Hydrosere
B. Lithosere
c. Psammosere
D. Xerosere


\( \frac{\pi}{\frac{\pi}{4}} \)


A disc of mass \( \mathrm{M} \) and radius \( \mathrm{R} \) is rolling
with angular speed \( \omega \) on a horizontal
plane as shown. The magnitude of
angular momentum of the disc about
the origin 0 is
A \( \cdot \frac{1}{2} M R^{2} \omega \)
B. \( M R^{2} \omega^{\omega} \)
c. \( \frac{3}{2} M R^{2} \omega \)
D. \( 2 M R^{2} \omega \)


Show that the circumference of the Bohr
orbit for the hydrogen atom is an integral multiple the de-Broglie wavelength associated with the
electron revolving around orbit.


Glauber's salt is:
A. hepta hydrate
B. deca hydrate
C. penta hydrate
D. dihydrate


Two particles one with constant velocity
\( 50 m / s \) and the other with uniform
acceleration \( 10 \mathrm{m} / \mathrm{s}^{2}, \) start moving simultaneously from the same place in the same direction. They will be at a distance of \( 125 \mathrm{m} \) from each other after
A . 5 sec
B. \( 5(1+\sqrt{2}) \) sec
c. 10 sec
D. \( 10(\sqrt{2}+1) \) sec


The lengths of two wires made of same material are \( 2 \mathrm{m} \) and \( 1 \mathrm{m} . \) Their radii are
\( 1 \mathrm{mm} \) and \( 2 \mathrm{mm} . \) The ratio of their
specific resistances is
A. 2:
B. 1: 1
\( c \cdot 4: \)
D. 8: 1


Select the correct order of bond angle in
following molecules.
A. \( x>z>y \)
в. \( x>y>z \)
c. \( z>y>x \)
D. \( y>x>z \)


A thin lens of focal length \( f \) and its aperture has a diameter d. It forms an image of intensity I. Now the central part of the aperture upto diameter (d/2)
is blocked by an opaque paper. The focal length and image intensity would change to
A \( \cdot \) f/2, \( 1 / 2 \)
B. f, \( 1 / 4 \)
c. \( 3 f / 4,1 / 2 \)
D. f, 31/4


Assertion
Corrosion of iron is commonly known as
rusting.
Reason
Corrosion of iron occurs in presence of
water and air.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
C. Assertion is correct but Reason is incorrect.
D. Both Assertion and Reason are incorrect.


The type of inflorescence in a plant showing polygamous condition and lateral styles is
A. Compound umbel
B. Compound headd
c. compound raceme
D. compound corymb


Why do most chemical reaction rates
increase rapidly as the temperature
rises
A. The fraction of molecular with kinetic energy grater than the activation energy increases rapidly with temperature
B. The average kinetic increases as temperature rises
C. The activation energy decreases as temperature rise
D. More collisions take place between particle so that the reaction can occur


is the nuclear process
that transmutes uranium-238 into
thorium-234.
A. Gamma decay
B. Nuclear fusion
c. Alpha decay
D. Positron emission
E. Nuclear fission


Find the roots of each of the
following quadratic equations by the method of completing the squares \( \sqrt{5} x^{2}+9 x+4 \sqrt{5}=0 \)
A. \( -\sqrt{7}, \frac{-17}{\sqrt{3}} \)
в. \( -\sqrt{5}, \frac{-4}{\sqrt{5}} \)
c. \( -\sqrt{5}, \frac{-14}{\sqrt{3}} \)
D. \( -\sqrt{7}, \frac{-13}{\sqrt{5}} \)


Which term of the \( \boldsymbol{A} . \boldsymbol{P} \mathbf{2 5}, \mathbf{2 0}, \mathbf{1 5} \dots \dots \)
is the first \( - \) ve term.


1.5\% glucose (mol. wt. =180) solution is isotonic with 7.65 g/L glycerine solution. Find out mol. wt. of glycerine.


When the hybridization state of carbon
atom changes from \( s p^{3} \) to \( s p^{2} \) and
finally to \( s p, \) the angle between the
hybridized orbitals?
A. Decreases gradually
B. Decreases considerably
c. Is not affected
D. Increases progressively


A body cools from a temperature \( 3 T \) to
\( 2 T \) in 10 minutes. The room
temperature is \( T . \) Assume that
Newton's law of cooling is applicable. The temperature of the body at the end
of next 10 minutes will be
A \( \cdot \frac{7}{4} T \)
в. \( \frac{3}{2} T \)
c. \( \frac{4}{3} T \)
D. \( T \)


How many equivalents of HCHO are formed by oxidative cleavage of one equivalent of D-glucose by excess of HIO
in water?


ff \( y=\tan \left(\frac{5}{2} \pi t+\frac{\pi}{6}\right) \) then find the
value of \( \frac{\boldsymbol{a} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{t}} \) at \( \boldsymbol{t}=\mathbf{0} \)


What is the partial pressure (in atm) of HI in theequilibrium mixture?
A . 6.37
в. 12.77
c. 40.76
D. 646.58


When sound travels from air to water,
the quantity that remains unchanged is:
A . speedd
B. wavelength
c. intensity
D. frequency


In a Young's double slit experiment, let
\( A \) and \( B \) be the two slits. A thin film of
thickness \( t \) and refractive index \( \mu \) is
placed in front of \( \boldsymbol{A} \). Let \( \boldsymbol{\beta}= \) fringe width The central maximum will shift
This question has multiple correct options
A. towards \( A \)
B. towards \( B \)
\( c \cdot \operatorname{byt}(\mu-1) \frac{\beta}{\lambda} \)
D. by \( \mu t \frac{\beta}{\lambda} \)


A metallic ring of radius 'r', cross sectional area 'A' is fitted into a wooden
circular disk of radius 'R' \( (R>r) . \) If the
Young's modulus of the material of the ring is 'Y', the force with which the metal ring expands is :
A. \( \frac{A Y R}{r} \)
в. \( \frac{A Y(R-r)}{r} \)
c. \( \frac{Y(R-r)}{A r} \)
D. \( \frac{Y R}{A r} \)


Name two processes which provide the best evidence for the motion of particles
in matter.


Which of the following compound has a directional bond?
A. Magnesium chloride
B. Solid neon
c. Hydrogen sulphide
D. caesiun fluoride


The mean of 100 observations is 50 and
their standard deviation is \( 5 . \) The sum of the squares of all the observations is
\( \mathbf{A} .50000 \)
B. 250000
c. 252500
D. 255000


Calculate the work required to be done
to stop a car of \( 1500 \mathrm{kg} \) moving at a
velocity of \( 60 \mathrm{kmh}^{-1} \)
в. 208333 Л
c. -209333 J
D. \( -207333 J \)


Magnitude of change of linear
momentum of the ball between \( t=0 \)
and \( t=t^{\prime}, t^{\prime} \) being the instant when the
ball hits the wall, is nearly
A. \( 3.2 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
в. \( 2.8 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
c. \( 4.6 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
D. \( 1.4 \mathrm{kg} \mathrm{m} / \mathrm{s} \)


For the reaction \( 4 N H_{3}+5 O_{2} \rightarrow \)
\( 4 N O+6 H_{2} O, \) the rate disappearance
of ammonia is \( 3.6 \times 10^{-3} \) mol \( L^{-1} s^{-1} \)
What is the rate of formation of water?


The reagent used to remove the traces of oxygen from a mixture of noble gases is:
A. ammonical cuprous chloride solution
B. potash solution
c. alkaline pyrogallol solution
D. caustic soda solution


A horizontal wire carries 200 amp
current below which another wire of
linear density \( 20 \times 10^{-3} k g m^{-1} \)
carrying a current is kept at \( 2 \mathrm{cm} \) distance. If the wire kept below hangs in air. The current in this wire is :
A. \( 100 A \)
B. \( 9.8 \mathrm{A} \)
\( c \cdot 98 A \)
\( D \cdot 48 A \)


A hydraulic automobile lift is designed to lift cars with a maximum mass of
3000 kg. The area of cross-section of
the piston carrying the load is \( 425 \mathrm{cm}^{2} \)
What maximum pressure would the smaller piston have to bear?


At \( 400^{\circ} \mathrm{C}, \) the following equilibrium is
established \( : \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{S}(s) \rightleftharpoons \boldsymbol{H}_{2} \boldsymbol{S}(\boldsymbol{g}) \)
\( \boldsymbol{K}_{\boldsymbol{p}}=\mathbf{6 . 8} \times \mathbf{1 0}^{-2} . \) If 0.2 mol of hydrogen
and 1.0 mol of sulphur are heated to \( 90^{\circ} \mathrm{C} \) in a 1.0 litre vessel, what will be
the partial pressure of \( \boldsymbol{H}_{2} \boldsymbol{S} \) at equilibrium?
\( \mathbf{A} \cdot 0.013 \mathrm{atm} \)
B. 0.345 atm
c. 0.456 atm
D. 0.564 atm


The depressions and elevations present on the surface of objects causes
friction.
A. True
B. False
c. Ambiguous
D. Data insufficient


Name the compound that does nit fit
into the formula \( C_{x}\left(H_{2} O\right)_{y}, \) but is a carbohydrate.


Metal oxide which show basic as well as
acidic behaviour are known as:
A. neutral oxide
B. amphoteric oxide
c. metalloid oxide
D. none of the above


A man walks on a straight road from his home to a marhet \( 3 \mathrm{Km} \) away with a speed of \( 6 \mathrm{Km} / \mathrm{h} \). The time taken by the
man to go from his home to market
equals


What is the significance of electric
field?


A measured temperature on the Fahrenheit scale is \( 200^{0} \) F.What will
this reading be on the Celsius scale?
A \( \cdot 40^{\circ} \mathrm{C} \)
В \( \cdot 94^{\circ} \mathrm{C} \)
c. \( 93.3^{\circ} \mathrm{C} \)
D. \( 30^{\circ} \mathrm{C} \)


Describe different components of
ecosystem in brief.


Give reasons for the following:
(i) \( \left(\boldsymbol{C H}_{3}\right)_{3} \boldsymbol{P}=\boldsymbol{O} \) exists but
\( \left(\boldsymbol{C H}_{3}\right)_{3} \boldsymbol{N}=\boldsymbol{O} \) does not.
(ii) Oxygen has less electron gain enthalpy with negative sign than sulphur.
(iii) \( H_{3} P O_{2} \) is a stronger reducing
agent than \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3} \)


The circumference of a circular track is
\( 400 \pi / m . \) If the optimum speed with which a vehicle can be driven along it is
to be \( 20 m / s \), the angle of banking of the road must be about
A \( \cdot \tan ^{-1}(0.02) \)
B. \( \tan ^{-1}(0.4) \)
c. \( \tan ^{-1}(0.8) \)
D. \( \tan ^{-1}(0.2) \)


Metals getting magnetised by orientation of atomic magnetic moments in external magnetic field are
called
A. diamagnetics
B. paramagnetics
c. ferromagnetics
D. antimagnetics


Soil contains
A. Air and water
B. Water and plants
C. Minerals, organic matter, air and water
D. Water, air and plants


The solution of the equation \( \frac{d y}{d x}= \) \( \frac{x(2 \log x+1)}{\sin y+y \cos y} \) is
A \( \cdot y \sin y=x^{2} \log x+C \)
B . \( y=x^{2}+\log x+C \)
C \( \cdot y \sin y=x^{2}+C \)
D. None of the above


\( N_{2}+O_{2}+H e a t \rightarrow 2 N O \)
\( (g) \)
\( \boldsymbol{q} \)
\( \boldsymbol{C}_{(\boldsymbol{s})}+\boldsymbol{O}_{\boldsymbol{2}(\boldsymbol{g})} \rightarrow \boldsymbol{C} \boldsymbol{O}_{\boldsymbol{2}(\boldsymbol{g})}+\boldsymbol{Q} \)
What information do you get from the above equations ? Comment. Write an activity about how you conduct an experiment to show that more
reactive metals replace less reactive metals from their compounds.


Shape of \( X e F_{2} \) molecule is :
A. Trigonal bi pyramidal
B. Tetrahedral
c. Square pyramidal
D. Linear


(a) A student suffering from myopia is not able to see distinctly the objects
placed beyond \( 5 m . \) List two possible
reasons due to which this defect of
vision may have arisen. With the help of ray diagrams, explain
(i) why the student is unable to see distinctly the objects placed beyond \( 5 m \) from his eyes.
(ii) the type of the corrective lens used
to restore proper vision and how this defect is corrected by the use of this lens.
(b) If, in this case, the numerical value of the focal length of the corrective lens is \( 5 m \), find the power of the lens as per the new Cartesian sign convention.


Which of the following case act as both oxidising and reducing agent?
A \( . H_{2} S \)
в. \( H_{2} S O_{4} \)
\( c \cdot S O_{2} \)
D. \( S O_{3} \)


Chelsy spends \( 40 \% \) of her monthly
earnings on rent and \( 10 \% \) of the remaining amount on entertainment. If
she spends \( \$ 800 \) for rent, how much does she use for entertainment?
A. \( \$ 120 \)
B. \( \$ 180 \)
\( c . \$ 200 \)
D. \( \$ 800 \)
E . \( \$ 2,000 \)


The specific rate constant of a first order reaction depends on the:
A. Concentration of the reactant
B. Concentration of the product
c. Time
D. Temperature


In photosynthesis, carbon dioxide is converted to carbohydrates. It is a
process
A . Reductive
B. Oxidative.
c. catabolic and exergonic
D. Reductive, anabolic and endergonic.


Write the conditions for intersecting the two lines \( \vec{r}=\overrightarrow{a_{1}}+l \overrightarrow{b_{1}} \) and \( \vec{r}=\overrightarrow{a_{2}}+l \overrightarrow{b_{2}} \)


Nitrogen differs from \( P, A s, \) Sb and Bi in
the following properties:
A. It forms diatomic molecule
B. It is not able to extent its coordination number beyond four
c. Nitrogen does not function as a Lewis acid whereas \( P \) As, Sb and Bi do so
D. In all the properties given above.


Which of the following is true for carbon resistors?
A. Resistance value does not get changed by change in temperature
B. Current carrying capacity and hence power wattage are limited to about 50 watts
c. It has low-temperature coefficient value.
D. stability and reliability are very good.


Let \( \left|z_{i}\right|=i, i=1,2,3,4 \) and
\( \mid 16 z_{1} z_{2} z_{3}+9 z_{1} z_{2} z_{4}+4 z_{1} z_{3} z_{4}+z_{2} z_{3} z_{4} \)
\( 48, \) then the value of \( \left|\frac{1}{z_{1}}+\frac{4}{\bar{z}_{2}}+\frac{9}{\bar{z}_{3}}+\frac{16}{\bar{z}_{4}}\right| \)
A . 1
B. 2
\( c \cdot 4 \)
\( D \)


Assertion
The process of filtration takes place in malpighian corpuscles
Reason
The total blood pressure is very high in glomerular capillaries
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


State True or False:
\( b^{2} y-9 b^{2} y+2 b^{2} y-5 b^{2} y \) is equal to
\( -11 b^{2} y \)
A. True
B. False


Fill in the blanks.
Sulphur extracted from natural sources
is called


Mammals are
A. cold
B. Warm
c. All are cold blooded with few exceptions of warm blooded
D. None of the above


The acceleration of a body in motion can
be known from slope of
A. Force-time graph
B. work-time graph
c. displacement-time graph
D. velocity-time graph


Describe the experiment conducted by Sir C.V. Raman to demonstrate Raman effect. What is the use of this effect?


Hydrogen atom, unipositive helium, dipositive lithium contain single
electron in the same shell. Is the radius
of the shell same in all cases? Give
reason.


The cosine of the angle \( A \) of the triangle with vertices
\( \boldsymbol{A}(\mathbf{1},-\mathbf{1}, \mathbf{2}), \boldsymbol{B}(\mathbf{6}, \mathbf{1 1}, \mathbf{2}), \boldsymbol{C}(\mathbf{1}, \mathbf{2}, \boldsymbol{6}) \) is
\( ^{\text {A }} \cdot \frac{63}{65} \)
в. \( \frac{36}{65} \)
c. \( \frac{16}{65} \)
D. \( \frac{13}{64} \)


Nutritionally, Australopithecus was
A. Omnivorous
B. Carnivorous
c. Herbivorous
D. Frugivorous


A vibrating tuning fork of frequency \( v \) is
placed near the open end of a long cylindrical tube. The tube has side
opening and is also fitted with a
movable reflecting piston. As the piston
is moved through \( 8.75 c m, \) the intensity
of sound changes from a maximum to minimum. If the speed of sound is
\( 350 m s^{-1}, \) then, \( v \) is
A \( .500 H z \)
В. \( 1000 H z \)
c. \( 2000 H z \)
D. \( 4000 H z \)


\( = \)

\( L_{k} \)


If we dig a hole in the ground near a water body we may find that the soil is
A. oily
B. moist
\( c \cdot \) red
D. both \( A \) and \( B \)


In \( 1 g \) of a solid, there are \( 5 \times 10^{21} \)
atoms. If one electron is removed from
energy of \( 0.01 \% \) atoms of the solid, the charge gained by the solid is :
(electronic charge is \( \left.1.6 \times 10^{19} C\right) \)
\( \mathbf{A} \cdot+0.08 C \)
B. \( +0.8 C \)
\( c .-0.08 C \)
D. \( -0.8 C \)


Which of the following relation is true?
A. \( 3 Y=K(1+\sigma) \)
в. \( _{K}=\frac{9 \eta Y}{Y+\eta} \)
\( \mathbf{c} \cdot \sigma=(6 K+\eta) Y \)
D. \( \sigma=\frac{0.5 Y-\eta}{\eta} \)


From a pack of cards two are
accidentally dropped probability they are of opposite shade is
A \( \cdot \frac{13}{51} \)
в. \( \frac{1}{52 \times 51} \)
c. \( \frac{26}{51} \)
D. None of these


In modern periodic table, if two elements have the same number of
valence electrons, then they belong to
the same:
A. group
B. period
c. part
D. none of the above


Two supplementary angles differ by \( 22^{0} \)
Find the angles.


The bar graph shows the amount of
money Varun earned in a week by
selling fruits in his store
f he earned 20 paise for every orange
sold, how many oranges did he sell?
A. 1000
B. 1500
c. 1050
D. 1200


Water has maximum density at \( 4^{\circ} C \)
If true enter 1 , else enter 0 .
\( A \)


Let \( A \) be the set of all \( 3 \times 3 \) symmetric
matrices all of whose entries are either
0 or \( 1 . \) If five of these entries are 1 and
four of them are 0 , then the number of
matrices in \( A \) is
A . 12
B. 6
\( c .9 \)
D. 3


The length and area of cross -section of a conductor are doubled, then its
resistance is
A. halved
B. unchanged
c. doubled
D. quadrupled


Starting from a stationary position, Rahul paddles his bicycle to attain a velocity of \( 6 m s^{-1} \) in \( 30 s . \) Then he applies brakes such that the velocity of the bicycle cones down to \( 4 m s^{-1} \) in the
next \( 5 s . \) Calculate the acceleration of
the bicycle in both the cases.


Integrate: \( \int \frac{x^{4}-x^{3}+8 x-8}{x^{2}-2 x+4} d x \)


One angle of a triangle is \( \frac{2 x}{3} \) grad, another is \( \frac{3 x}{2} \) degrees, whilst the third is \( \frac{\pi x}{75} \) radians. Express all angles in
degress.
A. Hence three angles of the triangle are \( 43^{\circ}, 30^{\circ}, 30^{\circ} \)
B. Hence three angles of the triangle are \( 24^{\circ}, 60^{\circ}, 96^{\circ} \)
C. Hence three angles of the triangle are \( 74^{\circ}, 27^{\circ}, 98^{\circ} \)
D. Hence three angles of the triangle are \( 30^{\circ}, 60^{\circ}, 90^{\circ} \)


Super heating is minimized by stirring and indirect \( _{---} \) (heating/cooling)


Find it; \( \lim _{x \rightarrow 0}\left(\frac{x^{2}+x+1}{x+1}-a x-6\right)=4 \)


Find the domain and range of :-
(i) \( \sqrt{\boldsymbol{x}}-\mathbf{1} \)
(ii) \( (\boldsymbol{x}-\mathbf{1}) \)


The maximum no. of electrons
having parallel spin in the configuration \( 4 s^{2} 4 p^{5} \) are:
\( A \cdot 7 \)
B. 4
\( c .3 \)
D. 5


Find the values of \( \angle a \angle b \) in the figure
given below.


\( \ln \) an office 20 clerks get a salary of Rs. 2500 each and 10 officers get a salary
of Rs. 4000 each. The average salary of the employees in the office is
A. Rs.2800
B. Rs.3000
c. Rs. 3200
D. Rs.3600


Ocean thermal energy is a useful
source of energy when temperature difference between surface and depth of \( 2 \mathrm{km} \) is :
A \( \cdot \) Less than \( 10^{\circ} C \)
B. More than \( 10^{\circ} \mathrm{C} \)
c. Less than \( 20^{\circ} \mathrm{C} \)
D. More than \( 20^{\circ} \mathrm{C} \)


The value of \( \sin ^{-1}\left(\cos \frac{53 \pi}{5}\right) \) is
A \( \cdot \frac{3 \pi}{5} \)
в. \( \frac{-3 \pi}{5} \)
c. \( \frac{\pi}{10} \)
D. \( \frac{-\pi}{10} \)


A die has 6 faces marked by the given numbers as shown below:
The die is thrown once. What is the
probability of getting an integer greater
than \( -\mathbf{3} ? \)
\( 1 3 \longdiv { 2 3 } \)


For the preparation of hydrochloric acid in the laboratory.
(i) Why is direct absorption of hydrogen chloride gas in water is feasible?
(ii) What arrangement is done to dissolve hydrogen chloride gas in water?


During the Rutherford's \( \alpha \) -particle
scattering experiment, he concluded that:
(i) electrons have negative charge.
(ii) the mass and positive charge of the
atom is concentrated in the nucleus.
(iii) neutron exists in the nucleus.
(iv) most of the space in atom is empty.
Choose the correct statements.
\( A \). (i) and (iii)
B. (ii) and (iv)
c. (i) and (iv)
D. (iii) and (iv)


The velocity factor of a transmission
line is \( 0.62 . \) Calculate dielectric
constant of the insulation used
A . 2.6
B. 3
\( c \cdot 4 \)
D. 5


Melanin protects us from
A. \( x \) -rays
B. Infra-red rays
C. Visible rays
D. UV rays


Given below are some organic
compounds containing certain functional group.
¡. \( \boldsymbol{C H}_{3}- \) COOH
ii. \( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{O H} \)
iii. \( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2}-\boldsymbol{C H}_{2} \cdot \boldsymbol{N} \boldsymbol{H}_{2} \)
iv. \( \boldsymbol{C H}_{3}-\boldsymbol{C H O} \)
(a) Write the names of functional group of any of the two compounds given
above.
(b) Write the IUPAC name of \( \boldsymbol{C H}_{3}- \)
\( \boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{O H} \)
(c) Give the structural formula and
IUPAC name of functional group isomer
of \( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{O H} \)


An increase in temperature produces
A. an increase in the minority carrier current
B. an decrease in the minority carrier current
C. an increase in the majority carrier current
D. no carrier current


Very short answer type.
What does a plant hormone do at the
molecular level?


Statement 1: Paradichlorobenzene has
higher melting point and solubility than that of ortho and meta forms.
Statement
2: Para isomer has
symmetrical structure and can easily pack closely in crystal structure.
A. Both Statement 1 and Statement 2 are correct and Statement 2 is correct explanation for Statement 1
B. Both Statement 1 and Statement 2 are correct and Statement 2 is not correct explanation for Statement
c. statement 1 is correct and statement 2 is wrong
D. Statement 1 is wrong and statement 2 is correct.


Name the polygon. Make two more examples of same type.


Explain the term with example:Oxidant


The distance between the two charges
\( +q \) and \( -q \) of a dipole is \( r . \) The
intensity at a point on the axial line at a
distance \( x \) from the centre of dipole is
proportional to
A \( \cdot \frac{q}{x^{2}} \)
в. \( \frac{q r}{x^{2}} \)
c. \( \frac{q}{x^{3}} \)
D. \( \frac{q r}{x^{3} r} \)


In the graph below is given the variation
of force with time. Find out the net
change in momentum of the object
A. \( 24 k g m / s \)
B. \( 22 k g m / s \)
\( \mathbf{c} .6 \mathrm{kgm} / \mathrm{s} \)
D. \( 3 k g m / s \)


Which of the following other than planet is (are) member(s) of solar system?
A. Asteroids
B. Constellations
c. Meteors
D. Both A and C


The human intestine is long because
A. Bacteria in food can be killed gradually.
B. It provides more surface for food storage.
C. It increases surface area for absorption of food.
D. None of the above.


Screening effect of inner shells decreases the effective nuclear charge. The order of screening effect of subshells is \( s>p>d>f \) State whether the given statement is
true or false.
A. True
B. False


If a copper ring is moved towards the north pole of a bar magnet, then:
A. the ring will not be affected
B. the ring will become warm
c. an alternating current will flow in the ring
D. the ring will be positively charged


In how many ways 5 different balls can
be distributed into 3 boxes so that no
box remains empty?


A first order reaction takes 40 min for
\( 30 \% \) decomposition. Calculate \( t_{1 / 2} \)


\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2}-\boldsymbol{C l} \) undergoes homolytic
fission to produce :
\( \mathbf{A} \cdot C H_{3} C H_{2} \quad \) and \( \quad \dot{C} l \)
B. \( C H_{3} C H_{2} \) and \( C l^{\ominus} \)
\( \mathbf{c} \cdot c_{H_{3}} \stackrel{\oplus}{C H_{2}} \) and \( C l^{\ominus} \)
\( \mathrm{D} \cdot \mathrm{CH}_{3} \mathrm{CH}_{2} \quad \) and \( \quad \mathrm{Cl}^{\oplus} \)


Find the remainder when \( x^{3}+3 x^{2}+ \)
\( 3 x+1 \) is divided by \( x+1 \)


An ideal diatomic gas \( \left(\gamma=\frac{7}{5}\right) \) undergoes a process in which its
internal energy relates to the volume as \( U=\alpha \sqrt{V}, \) where \( \alpha \) is a constant. Find
the molar specific heat of the gas.


Which of the following molecule has a
see-saw geometry?
A \( \cdot I_{3}^{-} \)
в. \( I C l_{2}^{-} \)
\( \mathbf{c} \cdot C l F_{3}^{-} \)
D. \( I O_{2} F_{2}^{-} \)


In a meeting, \( 70 \% \) of the members favour and \( 30 \% \) oppose a certain proposal. A member is selected at
random and we take \( \boldsymbol{X}=\mathbf{0} \) if he
opposed, and \( X=1 \) if he is in favour.
Find \( \boldsymbol{E}(\boldsymbol{X}) \) and \( \boldsymbol{V} \boldsymbol{a} \boldsymbol{r}(\boldsymbol{X}) \)


State whether the statement is
true/false.
8 can be written as a rational number
with any integer as denominator.
A. True
B. False


Prove \( \sin \frac{8 \pi}{3} \cos \frac{23 \pi}{6}+ \)
\( \cos \frac{13 \pi}{3} \sin \frac{35 \pi}{6}=\frac{1}{2} \)


Feeding zooids of Physalia are called
A. Gastrozooids
B. Dactylozoids
c. Gonodendra
D. Gonopalpons


Nematocysts are activated by
A. water
B. Touch
c. Brain
D. None of the above


Choose the correct answers from the
alternatives given :
Which of these processes occurs in the cytosol?
A. Krebs cycle
B. Glycolysis
c. Electron transport system
D. Transition reaction


Determine \( p \) and \( q \) if \( p q=32 \) and \( p+ \)
\( \boldsymbol{q}=-\mathbf{1} \mathbf{2} \)


A certain substance 'A' tetramerises in
water to the extent of \( 80 \% \). A solution of
2.5 g of \( A \) in 100 g of water lowers the
freezing point by \( 0.3^{\circ} \mathrm{C} \). The molar mass of \( A \) is:
A .122
B. 31
c. 244
D. 62


The Bohr orbit radius for the hydrogen \( \operatorname{atom}(\boldsymbol{n}=\mathbf{1}) \) is approximately \( \mathbf{0 . 5 3 0} \boldsymbol{A} \)
The radius for the first excited state
\( (n=2) \) will be:
в. 1.06
c. 4.77 ,
D. \( 2.12 \dot{A} \)


What is a calorimeter? Name the
material of which it is made of. Give two
reasons for using the material stated by
you.


The probability of finding an electron in
\( a d_{x y} \) orbital is maximum:
A. parallel to x-axis
B. parallel to y-axis
c. parallel to x and y-axis
D. at an angle of \( 45^{0} \) from \( x \) and \( y \) axis


A circle of radius \( 4 \mathrm{cm} \) is cut into 6
equal pieces find area of each part


Distinguish between real and virtual images.


A person observes that rain strikes him
normally when he is moving with 2 kmph. When he reverses his direction and moves with the same speed, the
rain will strike him at an angle \( 45^{\circ} \) with the vertical. Determine the true velocity of rainfall is?
A \( \cdot 2 \sqrt{5} \) kmph
B. \( \sqrt{2} \) kmph
c. \( 5 \sqrt{2} \) kmph
D. \( \sqrt{5} \) kmph


"When aqueous \( K O_{2} \) solution reacts
with \( C O_{2}, O_{2} \) is formed and thus, \( K O_{2} \)
is used in submarines."

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


Which one has the maximum number
of chromosomes?
A. Marsilea
B. Equiserum
c. ophioglossum
D. Lycopodium


If \( P(E)=0 \) then \( E \) is a/an
A. sure event
B. impossible event
c. equally likely event
D. none of these


Work function of sodium is \( 2.3 e V \). Does
sodium show photo-electric emission for light wavelength 6800 A?


What is spectrochemical series? Explain the difference between a weak field ligand and a strong field ligand


cosine of an angle between the vectors \( \vec{a}+\vec{b} \) and \( \vec{a}-\vec{b} \) if \( |\vec{a}|=2,|\vec{b}|=1 \) and \( \vec{a} \)
\( \wedge \vec{b}=60^{\circ} \) is?
A \( \cdot \sqrt{\frac{3}{7}} \)
B. \( \frac{9}{\sqrt{21}} \)
c. \( \frac{3}{\sqrt{7}} \)
D. None


In electrophilic aromatic substitution reaction, the nitro group is meta directing because it:
A. Decreases electron density at meta position
B. Increases electron density at meta position
c. Increases electron density at ortho and para positions
D. Decreases electron density at ortho and para positions