In a cathode ray tube, what is the effect on the beam of particles if the anode voltage is increased?
A. Kinetic Energy of electron beam increase
B. Rate of electron emission increase
c. Kinetic energy of electron beam remains unchanged
D. Rate of electron emission decrease


\( \int e^{x}(\sin x+2 \cos x) \sin x d x \) is equal to
A \( \cdot e^{x} \cos x+C \)
B. \( e^{x} \sin x+C \)
\( \mathbf{c} \cdot e^{x} \sin ^{2} x+C \)
D. \( e^{x} \sin 2 x+C \)
E \( \cdot e^{x}(\cos x+\sin x)+C \)


Two identical current carrying coaxial
loops, carry current I in opposite sense. A simple amperian loop passes through both of them once. Calling the loop as \( C \)
then which statement is correct?
This question has multiple correct options
\( \mathbf{A} \cdot \oint \bar{H} \cdot \overline{d l}=\mp 2 \mu_{0} I \)
B. the value of \( \oint \bar{H} . \bar{d} l \) is independent of sense of \( C \).
C. there may be a point on C where B and \( d l \) are parallel.
D. none of these


One \( k g \) of water, at \( 20^{\circ} C \), is heated in an
electric kettle whose heating element has a mean (temperature averaged) resistance of \( 20 \Omega \). The rms voltage in the mains is \( 200 \mathrm{V} \). Ignoring heat loss from the kettle. time taken for water to
evaporate folly. is close to:
[Specific heat of water \( =4200 J / k g^{o} C \)
, Latent heat of water \( =\mathbf{2 2 6 0} \boldsymbol{k} \boldsymbol{J} / \boldsymbol{k g}] \)
A. 3 minutes
B. 22 minutes
c. 10 minutes
D. 16 minutes


Form 2 digit number using 0,1,2,3,4,5 without repeating the digits. Write the
sample space \( S, \) number of sample points \( n(S), U, n(U) \) for \( U \) is the event that the number so formed is divisible
by 5


The shortest distance between the
motorcyclist and the car is
A . \( 10 m \)
B. 20m
\( c .30 m \)
D. \( 40 m \)


(a) Six lead-acid type of secondary cells
each of emf \( 2.0 \mathrm{V} \) and
internal resistance \( 0.015 \Omega \) are joined in series to provide a supply to a resistance of \( 8.5 \Omega . \) What are the
current drawn from the supply and its terminal voltage?
(b) A secondary cell after long use has an emf of \( 1.9 \mathrm{V} \) and a large internal resistance of \( 380 \Omega . \) What maximum
current can be drawn from the cell?
Could the cell drive the starting motor of a car?


A convergent doublet of separated lenses, corrected for spherical aberration, has resultant focal length of
10cm. The separation between the two
lenses is \( 2 \mathrm{cm} \). The focal lengths of the
component lenses
A. \( 18 \mathrm{cm}, 20 \mathrm{cm} \)
в. \( 10 \mathrm{cm}, 12 \mathrm{cm} \)
c. \( 12 \mathrm{cm}, 14 \mathrm{cm} \)
D. \( 16 \mathrm{cm}, 18 \mathrm{cm} \)


In biprism experiment a source of wavelength \( 6500 A \) is replaced by
source of wavelength \( 5500 A \). Calculate change in fringe width if the screen is
at, \( 1 \mathrm{m} \) distance from the slits which are
1 mm apart.


Round up the following upto three significant figures:
(i) 34.216
(ii) 10.4107
(iii) 0.04597
(iv) 2808


When a sphere of radius \( 2 \mathrm{cm} \) is
suspended at the end of a wire,
elongation is 'e'. When the same wire is loaded with a sphere of radius \( 3 \mathrm{cm} \) and made of the same material,
the elongation would be :
A \( \cdot \frac{8}{27} e \)
в. \( \frac{27}{8} e \)
c. \( \frac{4}{9} e \)
D. \( \frac{9}{4} \)


According to electrochemical theory of
corrosion involves:
A. cathodic dissolution of metal
B. cathodic deposition of metal
c. anodic dissolution of metal
D. anodic deposition of meta


lodobenzene as the major organic
product?

This question has multiple correct options
\( A \)
\( B \)
\( c \)
\( D \)


Assertion
Reason
A. assertion is true, reason is true; reason is correct explanation for assertion.
B. assertion is true, reason is true; reason is NOT a correct explanation for assertion.
C. assertion is true, reason is false.
D. assertion is false, reason is true.


Resistivity is
A. an extensive property
B. intensive property
C . elastic property
D. none of the above


A light ray in passing from water to a medium. In which medium light ray
speeds up?
A . glass
B. air
c. wood
D. none of these


Transition elements have high MP \& BP
due to:
A. use of ns electrons
B. use of (n-1)d electrons only
c. both ns and (n-1)d electrons
D. use of np electrons


Find the measure of an angle which measures same as its complement


Which is the first phase of the moon
cycle?
A. Waxing Cresent
B. Waning Crescent
c. New Moon
D. Full Moon


Atomic number of strontium \( (S r) \) is
equal to:
A . 28
B. 38
\( c \cdot 42 \)
D. 34


Which of the following is not a green house gas?
A. Carbon dioxide
B. Water vapour
c. oxygen
D. Methane


Find the vector and Cartesian equations
of the plane passing through the points with position vectors \( 3 \vec{i}+4 \vec{\jmath}+ \) \( 2 \vec{k}, 2 \vec{i}-2 \vec{j}-\vec{k} \) and \( 7 \vec{i}+\vec{k} \)


The degree and order of differential
equation \( \left(\frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}\right)^{2}=\left(\boldsymbol{y}+\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}\right)^{\frac{1}{2}} \)
which of the following?


The area bounded by the curves \( y= \)
\( \log _{e} x \) and \( y=\left(\log _{e} x\right)^{2} \) is
\( \mathbf{A} \cdot 3-e \)
B . \( e-3 \)
C \( \cdot \frac{1}{2}(3-e) \)
D. \( \frac{1}{2}(e-3) \)


Making a light wave vibrate in only one plane is known as:
A. refraction
B. reflection
c. Interference
D. diffraction
E. polarization.


Find the distances between the
following pair of parallel lines:
\( \mathbf{3} \boldsymbol{x}+\mathbf{4} \boldsymbol{y}=\mathbf{1 3}, \mathbf{3} \boldsymbol{x}+\mathbf{4} \boldsymbol{y}=\mathbf{3} \)


Find matrix \( \boldsymbol{X}, \) if \( \left[\begin{array}{ccc}\mathbf{3} & \mathbf{5} & -\mathbf{9} \\ -\mathbf{1} & \mathbf{4} & -\mathbf{7}\end{array}\right]+\boldsymbol{X}= \)
\( \left[\begin{array}{lll}\mathbf{6} & \mathbf{2} & \mathbf{3} \\ \mathbf{4} & \mathbf{8} & \mathbf{6}\end{array}\right] \)


\( 60 \% \) of first order reaction was
completed in 60 min. The time taken for
reactants to decompose to half of their original amount will be :
\( \mathbf{A} \cdot \approx 30 \min \)
в. \( \approx 60 \) min
\( \mathbf{c} . \approx 90 \min \)
\( \mathbf{D} \cdot \approx 45 \min \)


The site from where the nerve impulse for hearing originates in mammals is
A. Ear ossicles
B. Cochlea
c. Tympanum
D. Vestibule


0
0
0
0


The element with atomic number 9
resembles with the element having atomic number:
\( A \cdot 8 \)
B. 17
\( c . \) 36
D. 27


Bloom occurs in
A. Oligotrophic lake
B. Eutrophic lake
C. Fast flowing river
D. Rain water


A solution is \( 0.1 \mathrm{M} \) with respect to
\( A g^{+}, C a^{2+}, M g^{2+} \) and \( A l^{3+} \) which will precipitate at lowest concentration of \( \left[\boldsymbol{P} \boldsymbol{O}_{4}^{3-}\right] \) when solution of \( \boldsymbol{N} \boldsymbol{a}_{3} \boldsymbol{P} \boldsymbol{O}_{4} \) is
added?
A \( \cdot A g_{3} P O_{4}\left(K_{s p}=1 \times 10^{-6}\right) \)
B. \( C a_{3}\left(P O_{4}\right)_{2}\left(K_{s p}=1 \times 10^{-33}\right) \)
C. \( M g_{3}\left(P O_{4}\right)_{2}\left(K_{s p}=1 \times 10^{-24}\right) \)
D. \( A l P O_{4}\left(K_{s p}=1 \times 10^{-20}\right) \)


The solution of differential equation
\( \left(e^{x}+1\right) y d y=(y+1) e^{x} d x \) is
A \( \cdot\left(e^{x}+1\right)(y+1)=C e^{y} \)
B . \( \left(e^{x}+1\right)|(y+1)|=C e^{-y} \)
C \( \cdot\left(e^{x}+1\right)(y+1)=\pm C e^{y} \)
D. None of these


List at least three gaseous air pollutants that are emitted from automobiles and industries.


A vertical metal cylinder of radius \( 2 \mathrm{cm} \)
and length \( 2 m \) is fixed at the lower end and a load of \( 100 k g \) is put on it. Find \( (a) \)
the stress
(b) the strain and
(c) the
compression of the cylinder. Young modulus of the metal \( =2 \times 10^{11} N m^{-2} \)


Complete the following:
\( \left(\boldsymbol{C H}_{3} \boldsymbol{C O O}\right)_{2} \boldsymbol{P b}+\boldsymbol{N} \boldsymbol{a}_{2} \boldsymbol{S} \stackrel{\boldsymbol{H}+}{\longrightarrow} \)
\( \mathbf{H} \)


Form the differential equation corresponding to \( y^{2}-2 a y+x^{2}=a^{2} b y \)
eliminating a.


Identify the true expression:
A \( \cdot V=J C^{-1} \)
B. \( V=J C \)
\( \mathbf{c} \cdot V=J C^{-2} \)
D. \( V=J C^{-3} \)


An electric circuit requires a total
capacitance of \( 2 \mu F \) across potential of
\( \mathbf{1 0 0 0} V \). Large number 1 \( \mu \boldsymbol{F} \)
capacitances are available each of which would breakdown if the potential is more than \( 350 V \) How many
capacitances are required to make the
circuit.
A .24
B . 20
c. 18
D. 12


The phosphate of a metal has the
formula \( M H P O_{4} . \) The formula of its
chloride would be:
A . \( M C l \)
в. \( M C l_{2} \)
c. \( M C l_{3} \)
D. \( M_{2} C l_{3} \)


Assertion: An orbital designated by \( n= \) \( \mathbf{3}, l=\mathbf{1} \) has double dumb-bell shape
Reason: It belongs to p-subshell.
A. Both assertion and reason are true and the reason is a correct explanation of the assertion.
B. Both assertion and reason are true but reason is not a correct explanation of the assertion
c. Assertion is true but reason is false
D. Both the assertion and reason are false
E. Assertion is false but the reason is true


Calculate the oxidation number of the
underlined elements.
a. \( \underline{P H}_{3} \)
b. \( \underline{S} O_{2} \)
\( \boldsymbol{H} \underline{\boldsymbol{N}} \boldsymbol{O}_{3} \)
d. \( \boldsymbol{H}_{3} \underline{\boldsymbol{P}} \boldsymbol{O}_{\mathbf{4}} \)
\( \begin{array}{llll}\text { A. } \text { a. }-3 ; & \text { b. }+4 ; & \text { c. }+5 ;\end{array} \) +5
В. а. \( -3 ; \quad \) b. \( +2 ; \quad \) с. \( +5 ; \)
d. +5
c. a. \( -3 ; \) b. +4
c. +5 +4
D. None of these


State whether the following statements are true or false. Give reasons for your
answers.

Square numbers can be written as the sum of two odd numbers.


What is the \( K_{b} \) for \( N H_{2} \) group in glycine?
\( \mathbf{A} \cdot 4 \times 10^{-3} \)
в. \( 1.6 \times 10^{-10} \)
c. \( 6.25 \times 10^{-5} \)
D. \( 2.5 \times 10^{-12} \)


According to Freundlich adsorption isotherm, which of the following is/are
correct?
A \( \cdot \frac{x}{m} \propto p^{1 / 2} \)
в. \( \frac{x}{m} \propto p^{\text {। }} \)
c. \( \frac{x}{m} \propto p^{1 / n} \)
D. All the above


is said to be done
when an electric charge flows through a conductor at some potential difference.


Assertion
\( K_{p} \) can be equal to or less than or even
greater than the value of \( \boldsymbol{K}_{c} \)
Reason
\( \boldsymbol{K}_{\boldsymbol{p}}=\boldsymbol{K}_{\boldsymbol{c}}(\boldsymbol{R} \boldsymbol{T})^{\boldsymbol{\Delta} \boldsymbol{n}} \)
the relation between \( \boldsymbol{K}_{\boldsymbol{p}} \) and \( \boldsymbol{K}_{\boldsymbol{c}} \)
depends on the change in the number of moles of gaseous reactants and
products.
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


Which linkage joins monosaccharide
units in sucrose?


Orthocentre of an equilateral triangle
\( A B C \) is the origin O. If \( A=\bar{a}, B= \) \( \boldsymbol{b}, \boldsymbol{C}=\overline{\boldsymbol{c}} \) then \( \overline{\boldsymbol{A} \boldsymbol{B}}+\mathbf{2} \overline{\boldsymbol{B} \boldsymbol{C}}+\boldsymbol{3} \overline{\boldsymbol{C} \boldsymbol{A}}= \)
A . \( 3 \bar{c} \bar{c} \bar{c} \)
B. \( 3 \bar{a} \bar{a} \bar{a} \) a
\( c \cdot 0 \)
\( D .3 \bar{b} \bar{b} \)


The differential equation which
represents the family of curves given by
\( \tan y=c\left(1-e^{x}\right) \) is
A \( \cdot e^{x} \tan y d x+\left(1-e^{x}\right) d y=0 \)
B . \( e^{x} \) tan \( y d x+\left(1-e^{x}\right) \sec ^{2} y d y=0 \)
C \( \cdot e^{x}\left(1-e^{x}\right) d x+\tan y d y=0 \)
D. \( e^{x} \tan y d y+\left(1-e^{x}\right) d x=0 \)


Greater the current in the wire strong will be the \( _{\text {一一一一一一一一一 }} \) produced


A uniform stationary sphere starts
rolling down from the upper end of the
surface as shown in the figure, and it
reaches the lower right end. Given, \( \boldsymbol{H}= \)
\( 27 m \) and \( h=20 m . \) The sphere will fall
on the ground level at the following
distance from \( C . \) (Assume horizontal
projection)
\( A \cdot 12 m \)
B. \( 24 m \)
\( c .36 m \)
D. 48 m


Which one has the electronic
configuration given below? \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{1} \)
A . \( N a^{+} \)
в. \( A l \)
\( c . F \)
D. \( T i \)
E . \( B r \)


At constant temperature \( 250 m L \) of
argon at a 760 mm \( H g \) pressure and
\( 60 m L \) of nitrogen at 500 mm pressure are put together in one litre flask. The
final pressure is mm Hg


Write the principle behind the Hydrogen bomb.


How many stereoisomers are possible for B?
A . 2
B. 4
\( c .6 \)
\( D \)


Normal cardiac output is
A. 15 litres/min
B. 520 litres/min
c. 5 litres/min
D. None of the above


Find the points of local maxima or local minima of the following function, using the first derivative test. Also, find the
local maximum or local minimum
values, as the case may be. \( \boldsymbol{f}(\boldsymbol{x})=(\boldsymbol{x}-\mathbf{5})^{4} \)


Solve the equation: \( -4 x+8 y=12 \) and
\( -2 x+4 y=6 \) and then identify the
system of equation. This question has multiple correct options
A. Consistent
B. Inconsistent
c. Dependent
D. None the above


A half meter rod is pivoted at the centre
with two weights of \( 20 g f \) and \( 12 g f \)
suspended at a perpendicular distance of \( 6 \mathrm{cm} \) and \( 10 \mathrm{cm} \) from the pivot respectively
as shown below.
¡) Which of the two force acting on the
rigid rod causes clockwise moment?
ii) is the rod in equilibrium?


Find the area of the region bounded by
the curve \( x y=c^{2}, \) the \( X \) -axis, and the
\( \operatorname{lines} x=c, x=2 c \)


Prove that:
(i) \( 2 \tan ^{-1} \sqrt{\frac{b}{a}}=\cos ^{-1}\left(\frac{a-b}{a+b}\right) \)
(ii) Find the principal value of \( \cos ^{-1}\left(-\frac{1}{\sqrt{2}}\right) \)


In the titration of ferrous ammonium
sulphate and potassium dichromate, the external indicator used is:
A. \( K C N S \)
в. \( N H_{4} C N S \)
c. \( K_{3}\left[F e(C N)_{6}\right] \)
D. \( K_{4}\left[F e(C N)_{6}\right] \)


The kidneys are located in the
space.
A. Pelvic cavity
B. Peritoneal cavity
c. Abdominal
D. Retroperitoneal


Who is the discoverer of Proton?
A. J. J. Thomson
B. James Chadwick
c. Ernest Rutherford
D. None of the above


Compound apocarpous gynoecium is found in
A . Lily
B. Hollyhock
c. Lotus or Ranunculus
D. Pumpkin


Kidney of fish is of type
A. Pronephros
B. Opisthonephros
c. Metanephros
D. Nephridia


Ootheca of cockroach has fertilized
eggs, this numbers is
A. 6
B. 8
\( c \cdot 16 \)
D. 24


Which of the following is used for making optical
instruments:
A. \( \operatorname{si} 0_{2} \)
в. \( s \)
c. \( \operatorname{si} H_{4} \)
D. sic


A male rabbit of genotype AABBDDEE is crossed with a female rabbit of
genotype aabbddee to produce \( \boldsymbol{F}_{1} \) hybrid offspring. How many genetically different gametes can be produced by
this \( F_{1} \) hybrid
\( A \cdot 4 \)
B. 8
\( c \cdot 16 \)
D. 32


The compound \( C_{6} H_{12} \) shows optical isomerism. Draw the structural formula
of the compound and name it.


There is a small block in the centre \( C \) of
solid glass sphere of refractive index \( \mu \) When seen from outside the block will
appear to be located:
A. Away from C for all values of \( \mu \)
B. at C for all values of \( \mu \)
c. at \( \mathrm{C} \) for \( \mu=1.5 \) but away from c for \( \mu \neq 1.5 \)
D. at c only for \( \sqrt{2} \leq \mu \leq 1.5 \)


Assertion
\( C H_{3}-C H_{2} I \) reacts more rapidly with
strong base in comparison to
\( \boldsymbol{C} \boldsymbol{D}_{3} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{I} \)
Reason
The elimination of \( H I(\text { or } D I) \) in
presence of strong base shows \( \boldsymbol{E}_{2} \) elimination.The rate determining step involves breaking up of \( C-H \) or \( (C- \)
\( D \) ) bond.The \( C-D \) bond being stronger
than \( C-H \) and thus elimination is
faster in case of \( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2} \boldsymbol{I} \)
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


Give an expression for magnetic field on the axis of a circular current loop.
(Expression only). What is the value of
\( B \) at the center of the loop?


The colour of methyl orange indicator in an acid solution is


If the function \( f \) defined on \( \left(-\frac{1}{3}, \frac{1}{3}\right) \) by \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{ll}\frac{1}{x} \log _{e}\left(\frac{1+3 x}{1-2 x}\right), & \text { when } x \neq 0 \\ k, & \text { when } x=0\end{array}\right. \)
is continuous, then k is equal to


\( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{2} \boldsymbol{H} \boldsymbol{C l}(\boldsymbol{g}) \)
Which of the following alternative is
correct?
\( \mathbf{A} \cdot \Delta H=\Delta U \)
в. \( \Delta H>\Delta U \)
c. \( \Delta H<\Delta U \)
D. \( \Delta \)Hand\DeltaU bear no relation with each other


Solve the linear equation:
\( \mathbf{1 5}(\boldsymbol{y}-\mathbf{4})-\mathbf{2}(\boldsymbol{y}-\mathbf{9})+\mathbf{5}(\boldsymbol{y}+\mathbf{6})=\mathbf{0} \)
A \( y=\frac{1}{7} \)
B. \( y=\frac{3}{5} \)
c. \( y=\frac{5}{2} \)
D. \( y=\frac{2}{3} \)


Two radioactive substances \( X \) and \( Y \)
emit \( \alpha \) and \( \beta \) particles respectively. Their disintegration constants are in the ratio \( 2: 3 . \) To have equal probabilities of getting emission of \( \alpha \) and \( \beta \) particles,
find the ratio of number of atoms of \( X \) to
that of \( Y \) at any time instant.


Two particles start moving from the
same point along the same stright line.
The first moves with constant velocity \( \mathbf{v} \) and the second with constant
acceleration a. During the time that
elapses before the second catches the first, the greater distance between the
particles is
A \( \cdot \frac{v^{2}}{a} \)
B. \( \frac{v^{2}}{2 a} \)
c. \( \frac{2 v^{2}}{a} \)
D. \( \frac{v^{2}}{3 a} \)


A reaction is \( 50 \% \) complete in 2 hours and \( 75 \% \) complete in 4 hours. The order
of reaction is:
\( A \cdot 0 \)
B.
\( c \cdot 2 \)
D. 3


\( \lim _{x \rightarrow 0} 4 x^{2}+3 x+2 \) is equal to
\( A \cdot 2 \)
B \( \cdot e^{2} \)
c. 1
D.


When a vector of magnitude 12 units is added to a vector of magnitude 8 units, the magnitude of the resultant vector will be:
A. exactly 4 units
B. exactly 20 unit
c. exactly 2 unitt
D. O units, 10 units, or some value between them
E. 4 units, 20 units, or some value between them


Which of the following is a use of metal gold?
A. Health supplement
B. Protection from the sun
c. Making jewellery
D. All of above


To obtain p-type Si semiconductor, we need to dope pure Si with
A. Aluminium
B. Phosphorous
c. oxygen
D. Germanium


Which part is not included in Cochlear
duct?
A. Tectorial membrane
B. Macula of utricle
c. Scala media
D. Reissner's membrane


This polygon is one-half of a shape. Use a vertical line through 5 on the \( x \) -axis as a line of symmetry to complete the shape by drawing its other half. Write the coordinates of the larger shape
formed by PQRS and its image.


The efficiency of fuel cell is given by the
expression, \( \eta \) is:
A \( \quad \eta=-\frac{n F E_{c l l}}{\Delta H} \times 100 \)
B. \( \eta=-\frac{n F E_{c l l l}}{\Delta S} \times 100 \)
c. \( _{\eta}=-\frac{n F E_{c l l}}{\Delta A} \times 100 \)
D. None of the above


1,2,3 and 4 are the four stages of \( a \) rotating armature coil placed between the poles of a filed magnet.
(a) In which stage / stages will the emf be maximum?
(b) Represent graphically the relation between induced emf and angle of
rotation of the coils in stages 1,2,3 and
4


The thyroid gland is the largest endocrine gland of the body
A. True
B. False


Let PQR is a right angled prism with
other angles as \( 60^{\circ} \) and \( 30^{\circ} . \) PQ has a
thin layer of liquid and light falls normally on the face PR as shown in
figure. If the refractive index of prism is
1.5, then for total internal reflection,
maximum refractive index of liquid will
be
A . 1.2
B. 1.3
\( c .1 .4 \)
D. 1.5


The two adjacent sides of a parallelogram are \( 5 \mathrm{cm} \) and \( 4 \mathrm{cm} \) respectively and if the respective diagonal is \( 7 \mathrm{cm}, \) then find the area of the parallelogram?
\( A \cdot 8 \sqrt{6} \)
B. \( 6 \sqrt{6} \)
c. \( 4 \sqrt{6} \)
D. \( 8 \sqrt{3} \)


\( \begin{array}{lllll}\mathbf{0} & & \mathbf{c o s} \boldsymbol{\alpha} & \mathbf{c o s} & \boldsymbol{\beta} \\ \mathbf{c o s} & \boldsymbol{\alpha} & \mathbf{0} & \mathbf{c o s} & \gamma \\ \mathbf{c o s} & \boldsymbol{\beta} & \mathbf{c o s} \boldsymbol{\gamma} & \mathbf{0} & \end{array} \mid= \)
A \( \cdot \cos \alpha+\cos \beta+\cos \gamma \)
\( \mathbf{B} \cdot \cos \alpha \cos \beta \cos \gamma \)
c. \( 2 \cos \alpha \cos \beta \cos \gamma \)
D. \( 2 \sum \cos \alpha \cos \beta \)


\( \boldsymbol{A}=\left[\begin{array}{rrr}\mathbf{1} & \mathbf{- 2} & \mathbf{3} \\ \mathbf{7} & -\mathbf{8} & \mathbf{9} \\ \mathbf{4} & \mathbf{- 5} & \mathbf{6}\end{array}\right] \) the new matrix
formed by adding \( 2^{n d} \) row to \( 1^{s t} \) row will be
A. \( \left[\begin{array}{ccc}8 & -10 & 12 \\ 7 & -8 & 9 \\ 4 & -5 & 6\end{array}\right] \)
В. \( \left[\begin{array}{lll}6 & 6 & 6 \\ 7 & 8 & 9 \\ 4 & 5 & 6\end{array}\right] \)
c. \( \left[\begin{array}{ccc}1 & 2 & 3 \\ 7 & 8 & 9 \\ 11 & -13 & 14\end{array}\right] \)
D. \( \left[\begin{array}{ccc}1 & -2 & 3 \\ 7 & 8 & -29 \\ 4 & -2 & 6\end{array}\right] \)


If the zeroes of the polynomial \( 5 x^{2}- \)
\( 7 x+k \) are reciprocal of each other, then
find the value of \( k \)


The solubility of \( \mathrm{CaF}_{2}\left(\mathrm{K}_{s p}=5.3 \times 10^{-9}\right. \)
in \( 0.1 \mathrm{M} \) solution of NaF would be :
(Assume no reaction of cation/anion).
B. \( 5.3 \times 10^{-8} \) М
c. \( 5.3 \times 10^{-7} \) М
D. \( 5.3 \times 10^{-11} \) М


For a branched unsaturated acyclic hydrocarbon, the parent chain is the longest carbon chain that contains the :
A. Maximum number of double bonds
B. Maximum number of triple bonds
c. Both A and B
D. None of above


\( f x \neq 0 \) and \( \left|\begin{array}{ccc}1 & x & 2 x \\ 1 & 3 x & 5 x \\ 1 & 3 & 4\end{array}\right|=0, \) then \( x= \)
\( A \)
B. -
\( c \cdot 2 \)
\( D \ldots-2 \)


For hyperbola \( \frac{x^{2}}{\cos ^{2} a}-\frac{y^{2}}{\sin ^{2} a}=1 \)
which of the following remains constant with change in 'a'?
A. Abscissae of vertices
B. Abscissae of foci
c. Eccentricity
D. Directrix


At what height above the ground must a mass of \( 5 \mathrm{kg} \) be to have its P.E. equal in value to the K.E. possessed by it when it moves with a velocity of \( 10 \mathrm{m} / \mathrm{s} ? \)
(Assume \( \boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} / \boldsymbol{s}^{2} \)
A. \( 1 \mathrm{m} \)
B. \( 5 \mathrm{m} \)
\( c \cdot 10 m \)
D. 50 \( m \)


Which of the following is/are the value of \( \cos \left[\frac{1}{2} \cos ^{-1}\left(\cos \left(-\frac{14 \pi}{5}\right)\right)\right] ? \)
This question has multiple correct options
A \( \cdot \cos \left(-\frac{7 \pi}{5}\right) \)
B \cdot \( \sin \left(\frac{\pi}{10}\right) \)
c. \( \cos \left(\frac{2 \pi}{5}\right) \)
D. \( \cos \left(-\frac{3 \pi}{5}\right) \)


A metal forms two oxides. The higher oxide contains \( 80 \% \) metal. \( 0.72 g \) of the
lower oxide gave \( 0.8 g \) of higher oxide when oxidized. Then the ratio of the weight of oxygen that combines with the fixed weight of the metal in the two oxides will be:
A .2: 3
B . 2: 1
c. 4: 5
D. 3: 2


Choose the correct statement from the
following
This question has multiple correct options
A. Distance between earth and nearest star is of order in
parsec.
B. Thousand millimetre make one metre.
C. 1 tonne is equal to \( 10^{6} \) g.
D. A simple pendulum is used to measure the mass of a bob


In which of the following groups, would you place a plant which produces seeds but lacks flower and fruits?
A. Fungi
B. Bryophytes
c. Pteridophytes
D. Gymnosperms


The farthest objects in our universe discovered by modern astronomers are so distant that light emitted by them takes billions of years to reach the Earth. These objects (known as quasars) have many puzzling features, which have not yet been satisfactorily explained. What is the distance in \( k m \) of a quasar from which light takes 3.0
billion years to reach us?


A large rimmed hoop with a bowling bal inside it rolls down an incline plane.
Identify the statements which best
describes the relationship between the
hoop and the bowling ball?
A. Their angular accelerations are the same
B. Their angular displacements are the same
c. Their angular velocities are the same
D. Their tangential displacements are the same
E. Their centripetal accelerations are the same


Explain the manner in which light travels with the help of an activity.


Assertion
Detergents and soaps both are different.
Reason

Soap contains an aliphatic or straight chain carbon skeleton, with a carboxylic
acid group at its end. Instead of a carboxylic acid group, the detergent may contain a sulphate or sulphonate group. In addition, detergents can
contain an aromatic ring or rings.
Read the above assertion and reason
and choose the correct statement
regarding it.
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


What do you understand by the term tissue?


When the atmospheric pressure of the earth falls suddenly then
A. there is a clear weather
B. there may be a slow wind
c. there may be storms and strong winds
D. none of these


The molecules of a given mass of a gas have root mean square speeds of \( 100 \mathrm{m} \)
\( s^{-1} \) at \( 27^{\circ} C \) and 1 atmospheric
pressure. The root mean square speeds
of the molecules of the gas at \( 127^{\circ} \mathrm{C} \)
and 2 atmospheric pressure is?
A \( \cdot \frac{20}{\sqrt{3}} \)
в. \( \frac{100}{\sqrt{3}} \)
c. \( \frac{400}{3} \)
D. \( \frac{200}{3} \)


Assertion
Static frictional force is self adjusting, for the given two surfaces.
Reason
Sliding frictional force between two given solid surfaces is independent of
surface area of contact
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


\( \tan ^{-1}\left[\frac{a \cos x-b \sin x}{b \cos x+a \sin x}\right]=\tan ^{-1}\left(\frac{a}{b}\right) \)
\( \mathcal{L} \)
A. True
B. False


Student A and student B sit in identical
office chairs facing each other, as
shown in figure. Student A is heavier
than student B. Student A suddenly pushes with his feet. Which of the following statements related to
momentum is correct?
A. Momentum of A is greater than momentum of
B. Momentum of A and B are equal but opposite in direction
9 mentum of of B is greater than momentum of
D
direction


From which part of Atropa belladonna, the drug belladonna is obtained?
A . Roots
B. Bark
c. stem
D. All parts of the plant


Ab is \( 47.32 \mathrm{cm} \)
f true then enter 1 and if false then
enter 0


If reaction \( A \) and \( B \) are given with Same temperature and same concentration but rate of \( A \) is double than \( B \). Pre
exponential factor is same for both the reaction then difference in activation
energy \( \boldsymbol{E}_{\boldsymbol{A}}-\boldsymbol{E}_{\boldsymbol{B}} \) is?
\( \mathbf{A} \cdot-R T \ln 2 \)
в. \( R T \ln 2 \)
c. \( 2 R T \)
D. \( \frac{R T}{2} \)


The percentage of \( F e(I I I) \) present in
iron ore \( F e_{0} .9301 .00 \) is \( (F e=56) \)
A . 94
B. 6
c. 21.5
D. 15


Glass wool is a ..... conductor of
electricity.
A . goodd
B. badd
c. very good
D. None of the above


Silk is obtained from which of these
stages?
A. cocoon
B. Larva
c. Adult
D. Pupa


In flowering plants, water in conducted through
A. vessels
B. Tracheids
c. cork
D. Both A and B


A bus driver is reversing his bus at a
speed \( 8 m s^{-1} . \) The rear view mirror of a
bus is a plane mirror. The driver sees in
his rear view mirror the image of a car
parked behind his bus. The speed at which the image of the car appears to approach the driver will be
\( \mathbf{A} \cdot 2 m s^{-1} \)
B. \( 4 m s^{-1} \)
\( \mathrm{c} \cdot 8 \mathrm{ms}^{-1} \)
D. \( 16 m s^{-1} \)


Bile juice is secreted from
A. Salivary glands
B. Intestinal glands
c. Stomach
D. Liver


An equation that defines \( y \) as a function
of \( x \) is given. Solve for \( y \) in terms of \( x \)
and replace \( y \) with the function notation
\( \boldsymbol{f}(\boldsymbol{x}) \)
\( \boldsymbol{x}-\boldsymbol{2} \boldsymbol{y}=\mathbf{1 8} \)
A \( \cdot f(x)=\frac{1}{2} x-18 \)
B \( \cdot f(x)=\frac{1}{2} x-9 \)
c. \( f(x)=-x+9 \)
D. \( f(x)=-\frac{1}{2} x+9 \)


Which of the following reagents can reduce acetyl chloride to acetaldehyde?
A \( \cdot N a / C_{2} H_{5} O H \)
в. LiАlH\( _{4} \)
c. \( H_{2} / N i \)
D. \( H_{2} / P d-B a S O_{4} \)


A cylinder of radius \( \boldsymbol{R} \) full of liquid of
density \( \rho \) is rotated about its axis at
wrad/s. The increase in pressure at the centre of the cylinder will be
A \( \cdot \frac{\rho \omega^{2} R^{2}}{2} \)
в. \( \frac{\rho \omega^{2} R}{2} \)
c. \( \frac{\rho^{2} \omega R}{2} \)
D. \( \frac{\rho^{2} \omega^{2} R^{2}}{2} \)


Assertion
Atomic size decreases in a period due
to increase of atomic number.
Reason
The nuclear charge is increasing and size of valence shell remains same as
we move from left to right. Hence, in any
period, the atomic size of the element decreases from left to right.
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 reactance of a condenser of
capacity \( 50 \mu \mathrm{F} \) for an \( A C \) of frequency
\( 2 \times 10^{3} \) Hertz will be
\( A .5 \) ohm
B. \( \frac{2}{\pi} \)
\( c \cdot \frac{3}{\pi} \)
D. \( \frac{5}{\pi} \)


Find four numbers in G.P in which the
sum of the extreme terms is 112 and
sum of middle terms is 48 .


Syngas is a mixture of ?
A. \( C O_{2}+H_{2} \)
в. \( C O+H_{2} \)
\( \mathrm{c} \cdot \mathrm{CO}+\mathrm{CO}_{2} \)
D. \( C O+O_{2} \)


Which of the following element shows only +3 oxidation state?
A. \( B \)
в. \( A l \)
\( c . G a \)
D. In


IAA and serotonin are derived (formed)
from which of the following?
A. Tryptophan
B. Tyrosine
c. Phenylalanine
D. None of these


Raffinose is:
A. trisaccharide
B. disaccharide
C. monosaccharide
D. polysaccharide


Q Type your question
sheets:
I. Plants should be collected in the
flowering stage.
II. Every detail regarding the plant such as locality, ecological conditions, plants vegetative and floral characters,
etc should be noted.
III. Plants are evenly pressed by unfolding a plant part between blotting papers (or newspapers) with the help of
plant presser.
IV. Blotting paper need not be changed
until plants get dried.
V. After drying, the plant's specimen is carefully mounted/pasted on the herbarium sheets.
VI. The herbarium sheet is labeled on
the lower right hand corner representing the number of plant specimen, date of collection, etc.

Which of the above statement(s) is/are
incorrect?
A. Only I
B. Only IV
c. I and IV
D. III and IV


Give one equation each to show the following properties of sulphuric acid:
As a non-volatile acid.


A disaccharide may contain different types of monosaccharide units.
A. True
B. False


Fill in the blanks with the correct words:
The distance of an object from one end
to the other is called
(length/kilometer)


On the curve \( x^{3}=12 y, \) the abscissa
changes at faster rate than the ordinate. Then \( x \) belongs to the interval
\( A \cdot(-2,2) \)
B. (-1,1)
\( c \cdot(0,2) \)
D. none of these


\( B r_{2}+H_{2} O_{2} \rightarrow \) (in acidic medium)
Complete the reaction.


If \( \boldsymbol{A}-\boldsymbol{B}=\emptyset, \) then relation between \( \mathbf{A} \)
and B is :
\( \mathbf{A} \cdot A \neq B \)
в. \( B \subset A \)
\( c . A \subset B \)
D. \( A=B \)


Which of the following is an atom of
tritium?
\( A \)
в.
\( c \)
D.


Heat of combustion of glucose at
constant pressure at \( 17^{\circ} \mathrm{C} \) was found to
be \( -651,000 c a l . \) Calculate the heat of
combustion of glucose at constant
volume considering water to be in the
gaseous state.


Which of the following is considered as pioneer community in xerarch?
A. Annual herbs
B. Perennial herbs
c. Shrubs
D. Lichens


When the distance an object travels is directly proportional to the time, it is said to travel with
A. Constant speed
B. Zero velocity
c. Constant acceleration
D. Uniform velocity


toppr 유데
Q Type your question-
straight line as shown in the image. He
now puts a candle in front of the first
cardboard piece and looks at it from
behind the third piece. He is able to see
the candle. He puts the third cardboard piece aside and now tries to look at the
candle. But this time, he is not able to
see it.
What can be concluded from this
experiment?
A. The visibility of candle depends on the position of candle with respect to Rajesh
B. The visibility of candle depends on the position of Rajesh
C. The visibility of candle depends on the relative alignment of 3 cardboards
D. The candle is visible only when the 3 cardboards are in a line because light from the candle travels only in a straight line, to reach Rajesh's eyes


The contrapositive of the statement "If it is raining, then I will not come", is :
A. If I will come, then it is not raining.
B. If I will not come, then it is raining.
c. If 1 will come, then it is raining
D. If I will not come, then it is not raining


Draw Venn diagrams to illustrate \( \boldsymbol{A} \cap \) \( (B \backslash C) \)


If heart of a mammal is injected with
\( 2 \% \mathrm{CaCl}_{2} \) solution, then
A. Heart beat will increase
B. Heart beat will decrease.
c. Heart beat will stop
D. No effect


The stipules are modified into tendrils
in
A. Smilax
B. Asphodelus
c. Gloriosa
D. Asparagus


For a game in which a every pair play
with every other pair, 6 men are available.
find the number of games which can be played.


Light rays of wavelengths \( 6000 A \) and of
photon intensity 39.6 watts \( / m^{2} \) incidents on a metal surface. If only \( 1 \% \) of photons incident on the surface emit photoelectrons, then the number of electrons emitted per second per
unit area from the surface will be
approximately:
[Planck constant \( \boldsymbol{h}=\mathbf{6 . 6 4} \times \mathbf{1 0}^{-\mathbf{3 4} \mathbf{J}} \boldsymbol{s} \)
Velocity of light \( \left.=\mathbf{3} \times \mathbf{1 0}^{\mathbf{8}} \boldsymbol{m} \boldsymbol{s}^{-\mathbf{1}}\right] \)
A \( \cdot 12 \times 10^{18} \)
В. \( 10 \times 10^{18} \)
C \( .12 \times 10^{17} \)
D. \( 12 \times 10^{15} \)


If \( \boldsymbol{x} \times \mathbf{1 0}^{-\mathbf{2}} \) moles of helium at
temperature \( 300 \mathrm{K} \) and 1.00 atm pressure are needed to make the
internal energy of the gas 100 J. Find \( x \)
(Round off to the nearest integer)


The orbital having minimum \( l \) value is:
A. spherical in shape
B. dumbell in shape
c. double dumbell in shape
D. tetrahedral in shape


If a charged particle is projected perpendicular to a uniform magnetic field, then
a) it revolves in circular path
b) its K.E. remains constant
c) its momentum remains constant
d) its path is spiral
A. only a, bare correct
B. only a, c are correctt
c. only b, dare correct
D. only a, dare correctt


If \( \boldsymbol{A}^{\prime}=\left[\begin{array}{cc}-2 & 3 \\ 1 & 2\end{array}\right] \) and \( \boldsymbol{B}=\left[\begin{array}{cc}-1 & 0 \\ 1 & 2\end{array}\right] \)
then find \( (\boldsymbol{A}+\mathbf{2} \boldsymbol{B})^{\prime} \)


Anaerobic respiration, that occurs after glycolysis is also called as
A. Fermentation.
B. Fragmentation.
c. Restoration.
D. Multiplication.


Assertion (A): To protect any
instrument from external magnetic field, it is put inside an iron box Reason (R) : Iron is a ferromagnetic
substance
A. Both A and R are true and R is the correct explanation of A
B. Both A and R are true and R is not correct explanation of
c. A is true, but R is false
D. A is false, but R is true


Assertion
If \( \boldsymbol{P}(\boldsymbol{A} / \boldsymbol{B})=\boldsymbol{P}(\boldsymbol{B} / \boldsymbol{A}) \cdot \mathbf{A}, \mathrm{B} \) are two non
mutually exclusive events then
\( \boldsymbol{P}(\boldsymbol{A})=\boldsymbol{P}(\boldsymbol{B}) \)
Reason
For non mutually exclusive events
\( (A \cap B) \neq \phi \) and \( P(A / B)= \)
\( \frac{\boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})}{\boldsymbol{P}(\boldsymbol{B})}, \boldsymbol{P}(\boldsymbol{B} / \boldsymbol{A})=\frac{\boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})}{\boldsymbol{P}(\boldsymbol{A})} \)
A. Both Assertion \& Reason are individually true \& Reason is correct explanation of Assertion
B. Both Assertion \& Reason are individually true but Reason is not the , correct (proper) explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true


Potassium-argon dating can determine the age of the fossils
A. of about 5,00,000 years old
B. 2 billion years old
c. of all ages
D. of azoic era only


Which radioactive series do not show
the formation of radon atom as one of
the intermediate?
A. \( T h \) series
B. Np series
c. \( U \) series
D. \( A c \) series


Nitrolim is a mixture of:
A \( \cdot \mathrm{Ca} \mathrm{C}_{2}+\mathrm{N}_{2} \)
B. \( \mathrm{CaCN}_{2}+ \) graphite
c. \( \mathrm{Ca} \) NCN \( + \) diamond
D. \( \mathrm{Ca}(\mathrm{CN})_{2}+\mathrm{C} \)


Find the distance between the points \( \boldsymbol{A}(\mathbf{2}, \mathbf{1}, \mathbf{5}) \) and \( \boldsymbol{B}(\mathbf{3}, \mathbf{4}, \mathbf{3}) \)


In an n-p-n transistor circuit, the
collector current is \( 9 \mathrm{mA} \). If \( 90 \% \) of the
electrons emitted reach the collector.
Then the emitter current is
\( A \cdot 8.1 \mathrm{mA} \)
B. 8 mA
\( c \cdot 9 m A \)
D. \( 10 \mathrm{mA} \)


Europium is
A. s-block element
B. p-block element
c. d-block element
D. f-block element


Rutherford's \( \alpha \) -scattering experiment
led to the following conclusions:
A. atom has largely completely filled space
B. the centre of the atom has negatively charged nucleus
C. the size of the nucleus is very small as compared to the size of the atom
D. electrons revolve around the proton


Which of the following has least bond
energy?
A. \( F_{2} \)
в. \( H_{2} \)
\( c \cdot N_{2} \)
D. \( O_{2} \)


Find the median for the following data:
\( \begin{array}{ccccc}\mathbf{x} & \mathbf{6} & \mathbf{1 2} & \mathbf{1 8} & \mathbf{2 4} \\ \mathbf{F} & 2 & 4 & 6 & 8\end{array} \)
A . 17
B . 18
c. 19
D. 20


Assertion
A monocistronic mRNA can
produce several types of polypeptide
chains.
Reason
The terminator codon is present on
the mRNA.
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 incorrect but Reason is correct
D. Both Assertion and Reason are incorrect


The acid ionization constant of \( Z n^{2+} \) is
\( 1.0 \times 10^{-9} . \) Calculate the \( p H \) of a
\( 0.001 M \) solution of \( Z n C l_{2} \)
A . 5
B. 6
c. 8
D.


When \( N a N O_{2} \) is heated in absence of
air the products is/are? This question has multiple correct options
A \( \cdot \) NaNO \( _{3} \)
В. \( N a_{2} O \)
\( c \cdot N_{2} \)
D. \( O_{2} \)


For the given parabola find the coordinates of focus, axis, the equation of the directrix and the length of the
latus rectum.
\( \boldsymbol{x}^{2}=\mathbf{1 6} \boldsymbol{y} \)


A \( 4- \) kilograms ball slides over horizontal friction less surface with velocity of meter per second ball strike the post
and rebounds upward perpendicular to the initial direction with same speed.
Calculate the change of momentum of
the ball in initial direction.
A. \( -4 \mathrm{kg}, \mathrm{m} / \mathrm{s} \)
B. - - 1 kg.m/s
c. \( 0 \mathrm{kg} . \mathrm{m} / \mathrm{s} \)
D. \( 1 \mathrm{kg} . \mathrm{m} / \mathrm{s} \)
E . \( 4 \mathrm{kg} . \mathrm{m} / \mathrm{s} \)


\( f(x)=x^{3}-6 x^{2}+12 x-16 \) is strictly
decreasing for
\( \mathbf{A} \cdot x \in R \)
в. \( x \in R-\{1\} \)
c. \( x \in R^{+} \)
D. \( x \in \phi \)


In Question above, what is the angle between the incident and the reflected
rays?
A \( .90^{\circ} \)
B. \( 100^{\circ} \)
\( c \cdot 110^{\circ} \)
D. none of these


An ice cube of size \( a=10 \mathrm{cm} \) is
floating in a tank (base \( =50 \mathrm{cm} \times \)
50cm ) partially filled with water. The
change in gravitational potential energy, when ice completely melts is [Density of ice is \( 900 k g m^{-3} \) and \( g=10 m s^{-2} \)
A. \( -0.0455 J \)
в. \( -0.016 J \)
c. \( -0.24 J \)
D. \( -0.072 J \)


Peroxydisulphuric acid and its salts are powerful oxidizing agents. Thus it can be estimated reducing agents and also study the kinetics of the reaction.
Peroxydisulphuric acid:
A. is also called Marshall's acid
B. has two peroxy linkages
C. liberates \( I_{2} \) with \( K I \) I in a fast reaction
D. has oxidation number of sulphur as +7


the mass of a planet is \( 10 \% \) less than
that of the Earth and the radius \( 20 \% \)
greater than that of Earth, the acceleration due to gravity on the planet will be:
A . 5 \( \frac{5}{8} \) times that on the surface of the Earth
B. 3 \( \frac{3}{4} \) times that on the surface of the Earth
c. \( \frac{1}{2} \) times that on the surface of the Earth
D. \( \frac{9}{10} \) times that on the surface of the Earth


The product, other than carbon dioxide,
formed when a candle burns in air is:
A. \( C O \)
в. \( S O_{2} \)
c. water vapor
D. \( N_{2} \)


An enclosure of volume 3 litre contains 16
\( \mathrm{gms} \) of oxygen, \( 7 \mathrm{gms} \) of nitrogen and 11 gms of carbon di-oxide at \( 27^{\circ} \mathrm{C} \). The
pressure exerted by the mixture is approximately
A. 1 atmosphere
B. 3 atmosphere
c. 9 atmosphere
D. 8.3 atmosphere


The image of an object formed by a concave lens is:
A. Virtual, inverted and diminished
B. Virtual, upright and diminished
c. Virtual, inverted and enlarged
D. Virtual, upright and enlarged


Kerosene is a mixture of:
A. alkanes
B. aromatic compounds
c. alcohols
D. aliphatic acid


The length of a wire is \( l_{1} \) when tension is
\( T_{1} \) and \( l_{2} \) when tension is \( T_{2} \). The natura length of the wire is
A \( \cdot \frac{l_{1}+l_{2}}{2} \)
B. \( \sqrt{l_{1} l_{2}} \)
c. \( \frac{l_{1} T_{2}-l_{2} T_{1}}{T_{2}-T_{1}} \)
D. \( \frac{l_{1} T_{2}+l_{2} T_{1}}{T_{2}+T_{1}} \)
E \( \cdot \frac{l_{1} T_{1}-l_{2} T_{2}}{T_{1}-T_{2}} \)


A body dropped freely from a height h onto a horizontal plane, bounces up and down and finally comes to rest. The coefficient of restitution is e, the ratio
of distance travelled in two consecutive
rebounds
A \( .1: e \)
B . \( e: 1 \)
\( \mathbf{c} \cdot 1: e^{2} \)
D. \( e^{2}: 1 \)


Two particles of charges and masses
\( \left(+q_{1}, m_{1}\right) \) and \( \left(-q_{2}, m_{2}\right) \) are released at
two different points in a uniform electric field E established in free
space. If their separation remains unchanged find the separation \( l \) between them


Which lipids are present in essential
oils?


If \( 10,000 V \) are applied across an \( X \) -ray tube, find the ratio of wavelength of the incident electrons and the shortest
wavelength of \( X \) -ray coming out of the X-ray tube, given \( e / m \) of electron \( = \) \( 1.8 \times 10^{11} C k g^{-1} \)
\( \mathbf{A} \cdot 1: 10 \)
B. 10: 1
c. 5: 1
D. 1: 5


Praveen wanted to make a temporary shelter for her car, by making a box-like structure with tarpaulin that covers all
the four sides and the top of the car (with the front face as a flap which can be rolled up). Assuming that the stitching margins are very small, and therefore negligible, how much tarpaulin would be required to make the shelter of height 2.5 m, with base
dimensions \( 4 m \times 3 m ? \)


If the relative rates of abstraction of 2
and \( 1 \mathrm{H} \) atoms 3.8 and \( 1.0, \) respectively,
then the percentage ratios of the products 1-chloro-, 2- chloro-, and 3-
chloro- are obtained in the
photochlorination of n-hexane would be
A. 17\%, 41.5\%, 41.5\% respectively
в. 17\%, 17\%, 66\% respectively
c. 30\%, 40\%, 30\% respectively
D. 15\%, 15\%, 70\% respectively


Is the motion of the ball simple harmonic?


Work out the following divisions.
\( 96 a b c(3 a-12)(5 b+30) \div 144(a- \)
4)\( (b+6) \)
\( \mathbf{A} \cdot 96 a b c \)
B. \( 10 a b c \)
c. \( 144 a b c(b-12) \)
D. \( 24(a-b+c) \)


In the circuit shown below in Fig.
the value of \( x \) if the equivalent
resistance between \( A \) and \( B \) is \( 4 \Omega \) will
be:
\( A \cdot 2 \Omega \)
B. \( 1 \Omega \)
c. \( 1.5 \Omega \)
D. \( 3 \Omega \)


Calculate the surface area of
hemisphere having the radius of \( 1.4 \mathrm{cm} \)
A \( \cdot 1.232 \mathrm{cm}^{2} \)
B . \( 12.32 \mathrm{cm}^{2} \)
\( \mathbf{c} \cdot 123.2 \mathrm{cm}^{2} \)
D. \( 1232 c m^{2} \)


Draw excretory system in human beings and label the following organs of excretory system which perform
following functions.
(i) form urine
(ii) is a long tube which collects urine from kidney
(iii) store urine until it is passed out


What is meant by producers in an
ecosystem?


The value of \( \left(\sin \frac{\pi}{8}+\right. \)
\( \left.i \cos \frac{\pi}{8}\right)^{8}\left(\sin \frac{\pi}{8}-i \cos \frac{\pi}{8}\right)^{8} \) is
\( A \cdot-1 \)
B.
\( c \)
\( D \cdot 2 \)


Which of the following ligands form a chelate?
A. Acetate
B. Oxalate
c. cyanide
D. Ammonia


In the figure given, \( O \) is the centre of the
circle. \( A B \) and \( C D \) are two chords of the
circle. \( O M \) is perpendicular to \( A B \) and \( O N \) is perpendicular to \( C D . A B= \)
\( \mathbf{2 4} c \boldsymbol{m}, \boldsymbol{O} \boldsymbol{M}=\mathbf{5} \boldsymbol{c m}, \boldsymbol{O} \boldsymbol{N}=\mathbf{1 2} c \boldsymbol{m} . \) Finc
the
Length of chord \( C D \)


\( \boldsymbol{y}=\boldsymbol{A} \cos \boldsymbol{n} \boldsymbol{x}+\boldsymbol{B} \sin \boldsymbol{n} \boldsymbol{x} \)
Prove that \( \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}+\boldsymbol{n}^{2} \boldsymbol{y}=\mathbf{0} \)


The primary phenomenon in the working of lens is
A. Reflection
B. Refraction
c. Scattering
D. Diffusion


State whether True or False.
Ozone is the oxidising agent in the following reaction:
\( \boldsymbol{O}_{3}(\boldsymbol{g})+\boldsymbol{H}_{2} \boldsymbol{O}_{2}(l) \rightarrow \boldsymbol{H}_{2} \boldsymbol{O}(l)+ \)
\( \mathbf{2} \boldsymbol{O}_{\mathbf{2}}(\boldsymbol{g}) \)


Raman effect is an example of
A. coherent scattering of light
B. Incoherent scattering of light
c. coherent interference of light
D. Incoherent interference of light


\( \lim _{x \rightarrow 0} \frac{x e^{x}-\log (1+x)}{x^{2}} \) equals


One of the most extensively studied enzymes of photosynthesis is
A. Carboxypeptidase
B. Hexokinase
c. carboxydismutase
D. Dehydrogenase


Microwaves from a transmitter are
directed normally toward a plane reflector. A detector moves along the normal to the reflector. Between
positions of 14 successive maxima the
detector travels a distance 0.14 m. The
frequency of the transmitter is \( (c= \) \( 3 \times 10^{8} m s^{-1} \)
A. \( 1.5 \times 10^{10} \mathrm{Hz} \)
в. \( 10^{10} \mathrm{Hz} \)
c. \( 3 \times 10^{10} H z \)
D. \( 6 \times 10^{10} \mathrm{Hz} \)


if \( y=5 x^{2}+8 x \) find \( \frac{d y}{d x} \)
A. \( 10 x+8 \)
B. \( 5 x+8 \)
c. \( 10 x^{2}+8 x \)
D. none of these


Foetal passage between aortic and pulmonary arches is
A. Foramen rotundum
B. Foramen caecum
c. Ductus arteriosus
D. Ligamentum arteriosum


Hydrolysis of sucrose gives glucose and fructose. The reaction takes place as:
Sucrose \( +\boldsymbol{H}_{2} \boldsymbol{O} \rightleftharpoons \) Glucose \( + \) Fructose
The equilibrium constant \( K_{c} \) for this
reaction is \( 2 \times 10^{13} \) at \( 300 K . \) The \( \Delta G^{\circ} \)
at \( 300 K \) is:
A . \( 7.64 \times 10^{4} \mathrm{J} \mathrm{mol}^{-} \)
В. \( 7.64 \times 10^{-4} \) Л то \( l^{-1} \)
c. \( -7.64 \times 10^{-4} \mathrm{J} \mathrm{mol}^{-1} \)
D. \( -7.64 \times 10^{4} \mathrm{J} \) mol \( ^{-1} \)


Given below are the three statements
each with two blanks. Select the option
which correctly fills up the blank in any two statements. (A) Each seminiferous
tubule is lined on Its inside by two types of cells called_(i)_and_(ii).
(B) The seminiferous tubules open into the \( (\mathrm{i})_{-} \) through \( (\mathrm{i} \mathrm{i}) \)
(C) The enlarged end of penis called the \( \underline{\text { (i) }} \) is covered by a loose fold of skin called the \( (\text { ii }) \)
A. (A)-(i)spermatogonia,(ii) follicular cells
(B)-(i) vas deferens,
(ii) urethral meatus
B. (B)-(i) vasa efferentia, (ii) rete testis
(C)-(i) glans penis
(ii) foreskin
C. (A)-(i) spermatogonia,
(ii) Sertoli cells
(C)-(i) urethral meatus,
(ii) scrotum
D. (A)-(i) spermatocytes, (ii) oogonia
(B)-(i) rete testis, (ii) vasa efferentia


If the compound interest of an amount,
at the rate of \( 5 \% \) per annum, for two years is Rs. \( 123.00, \) then the principal is
A. Rs. 1000
B. Rs. 1100
c. Rs.1200
D. Rs.1300


Which of the following structures are
not observed in a cell at the end of
prophase, when viewed under the microscope?
A. Golgi complex
B. Nucleolus
c. Nuclear envelope
D. All of the above


What is the name of the phase transition that occurs when a solid is converted
directly into a gas (without going through the liquid phase)?
A. vaporisation
B. sublimation
c. boiling
D. melting


What is plasmalemma?


Prove that \( : \frac{1-\tan ^{2}\left(45^{\circ}-A\right)}{1+\tan ^{2}\left(45^{\circ}-A\right)}=\sin 2 A \)


Negation of the statement "Every natural number is an integer""
A. All natural numbers are whole numbers.
B. Every natural number is not an integer.
c. Every natural number is not a real number.
D. none of the above


A malfunction of the lymph nodes would most likely interfere with the
A. Release of carbon dioxide into the lymph.
B. Filtering of glucose from the lymph.
c. Release of oxygen into the lymph.
D. Filtering of bacteria from the lymph,


Linear overlapping of any two pure atomic \( p \) - orbitals lead to sigma bond formation.
A. True
B. False


Iron is not found naturally in the form of the free metal. Gold can be found naturally as the free metal. Explain.


Removal of gonads cannot be
considered as a contraceptive option.
Why?


One similarity between sound and light
waves is that
A. Both can propagate in vacuum
B. Both have same speedd
c. Both can show polarization
D. Both can show interference


Q Type your question
opuion gıven below:
\( \mathbf{A} \)
b-iv, c-iii, d\( a-i i \)
B. a-i, b-iv, c-iii, d-ii
c. a-iii, b-iv, c-i, d-ii
D. \( a-i i i \) b-ii, c-i, d-iv


Power of a lens of focal length \( 1 \mathrm{cm} \) is
A . 10
B. 10
\( c \cdot 100 D \)
D. \( \frac{1}{100} D \)


Find the order of rotational symmetry of rhombus.
A . 4
B. 3
\( c \cdot 2 \)
\( D \)


Draw the structure of the following compounds:
4-Methylpent-3-en-2-one


If \( \mathrm{m} / \mathrm{n} \), in lowest terms, be the
probability that a randomly chose
positive divisor of \( 10^{99} \) is an integral
multiple of \( 10^{88} \) than find the value of
\( (\boldsymbol{m}+\boldsymbol{n}) \)


Maximum value of a second order
determinant whose every element is either 0,1 or 2 only is:
A.
B.
\( c \cdot 2 \)
D. 4


The carbon \% in Pig iron?


Let \( f(x) \) be defined as follows:
\[
\boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{l}
\boldsymbol{x}^{\boldsymbol{6}}, \boldsymbol{x}^{2}>\mathbf{1} \\
\boldsymbol{x}^{3}, \boldsymbol{x}^{2} \leq \mathbf{1}
\end{array}\right.
\]
Then \( \boldsymbol{f}(\boldsymbol{x}) \) is?
This question has multiple correct options
A. continuous everywhere
B. differentiable everywhere
c. discontinuous at \( x=-1 \)
D. not differentiable at \( x=1 \)


The vapour pressure of a pure liquid \( \mathbf{A} \) is \( 80 \mathrm{mmHg} \) at \( 300 K . \) It forms an ideal solution with liquid B. When the mole fraction of \( \mathrm{B} \) is \( 0.4, \) the total pressure
was to be \( 88 \mathrm{mmHg} \). The vapour pressure of liquid B would be?


Which of the following sets cannot enter into the list of fundamental quantities in any system of units?
A. length, mass and velocity
B. length, time and velocity
c. mass, time and velocity
D. length, time and mass


Draw a circle with centre \( O \) and radius
\( 6 \mathrm{cm} . \) Take a point \( P \) outside the circle
at a distance of \( 10 \mathrm{cm} \) from \( 0 . \) Draw
tangents to the circle from point \( P . \) Let the tangents intersect the circle in
points \( A \) and \( B \). Find the area of triangle
OBPin sq.cm.
A .24
B . 26
c. 25
D. None of these


Write two advantages of a reflecting telescope over a refracting telescope.


If \( \boldsymbol{\alpha}+\boldsymbol{i} \boldsymbol{\beta}=\tan ^{-1} \boldsymbol{z}, \boldsymbol{z}=\boldsymbol{x}+\boldsymbol{i} \boldsymbol{y} \) and \( \boldsymbol{\alpha} \) is
constant then the locus of \( z \) is
A \( \cdot x^{2}+y^{2}+2 x \cot 2 \alpha=1 \)
B \cdot \( \cot 2 \alpha\left(x^{2}+y^{2}\right)=1+x \)
c. \( x^{2}+y^{2}+2 y \tan 2 \alpha=1 \)
D. \( x^{2}+y^{2}+2 x=1 \)


Examine if 398 is a perfect cube. If not,
then find the smallest number that
must be subtracted from 398 to obtain
a perfect cube


Assertion
If \( \boldsymbol{y}= \)
\( (1+x)\left(1+x^{2}\right)\left(1+x^{4}\right) \ldots\left(1+x^{2^{n}}\right) \)
then \( \frac{d y}{d x} \) at \( x=0 \) is 1
Reason
\( y=\frac{1-x^{2^{n+1}}}{1-x} \)
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


Match the following.
A. Gave the concept of
1. John Ray \( \quad \) Systematics
B. First described species as a
2. C. Linnaeus \( \quad \) unit of classification
3. Augustin Pyrame de
C. Coined the term, taxonomy candolle
D. Introduced binomial
4. Julian Huxley \( \quad \) nomenclature
A. \( 1-B, 2-C, 3-D, 4-A \)
B. \( 1-A, 2-C, 3-D, 4-B \)
\( c \cdot 1-c, 2-B, 3-D, 4-A \)
D. \( 1-B, 2-D, 3-C, 4-A \)


Prove that the relation \( R \) on \( Z \) defined
by \( (a, b) \in R \Leftrightarrow 5 \) divides \( a-b, \) is an
equivalence relation on \( Z \)


Plastics are mainly used by everyone because:
This question has multiple correct options
A. They are cheap
B. Easy to handle
c. Do not break
D. Light weight


The thalloid body of a slime mould (Myxomycetes) is known as
A. Fruiting body
B. Mycelium
c. Protonema
D. Plasmodium


Two different ideal diatomic gases \( A \)
and B are initially in the same state. A and \( \mathrm{B} \) are then expanded to the same
final volume through adiabatic and isothermal processes respectively. If
\( P_{A}, P_{B} \) and \( T_{A}, T_{B} \) represents the final
pressure and temperature of \( A \) and \( B \) respectively then
A \( \cdot P_{A}<P_{B} \) and \( T_{A}<T_{B} \)
В \( \cdot P_{A}>P_{B} \) and \( T_{A}>T_{B} \)
\( \mathbf{c} \cdot P_{A}>P_{B} \) and \( T_{A}<T_{B} \)
D. \( P_{A}<P_{B} \) and \( T_{A}>T_{B} \)


The core of a transformer is laminated
to reduce
A. flux leakage
B. hysteresis
c. copper loss
D. eddy current


What is the cell reaction occurring in
Daniell cell (galvanic cell)?
\( \mathbf{A} \cdot C u(s)+Z n S O_{4}(a q .) \rightarrow C u S O_{4}(a q .)+Z n(s) \)
B \( \cdot Z n(s)+C u S O_{4}(a q .) \rightarrow C u(s)+Z n S O_{4}(a q .) \)
\( \mathbf{c} \cdot N i(s)+Z n S O_{4}(a q .) \rightarrow N i S O_{4}(a q .)+Z n(s) \)
\( \mathbf{D} \cdot 2 N a(s)+C d S O_{4}(a q .) \rightarrow N a_{2} S O_{4}(a q .)+C d(s) \)


The vapour pressure of a solvent
decreased by \( 10 \mathrm{mm} \) of mercury when a
non-volatile solute was added to the
solvent. The mole fraction of the solute
in the solution is \( 0.2 . \) What should be the mole fraction of the solvent, if the
decrease in the vapour pressure is to be
20 mm of mercury?
A . 0.8
B. 0.6
\( c .0 .4 \)
D. 0.2


If \( \operatorname{cosec} x=\frac{25}{15}, \sin x= \)


The correct set of reagents for the
following conversion is :
\( \mathbf{A} \cdot P_{2} O_{5} / \Delta, P_{4} / I_{2}, N a \)
\( \mathbf{B} \cdot P_{4} / I_{2}, N a, P_{2} O_{5} / \Delta \)
\( \mathbf{c} \cdot P_{2} O_{5}, N a B H_{4} \)
D. \( P_{4} / I_{2}, \) Na, conc. \( H_{2} S O_{4} \)


A light ray passes from a material of low refractive index to one of high refractive index. Which of the pairs of quantities listed below describes the light ray as it
strikes and passes through the interface between the two materials?
Match the descriptions below with the
statement that best describes the
situation.
A part of the light ray remains inside
the low refractive index material:
A. the angle of refraction is larger than the angle of incidence
B. the angle of refraction is equal to the angle of incidence
C. the angle of reflection is larger than the angle of incidence
D. the angle of incidence equals the angle of reflection
E. the angle of reflection is smaller than the angle of incidence


State True or False:
On subtracting \( \boldsymbol{x}^{\mathbf{3}}-\mathbf{4} \boldsymbol{x}-\mathbf{1} \) from \( \mathbf{3} \boldsymbol{x}^{\mathbf{3}}- \)
\( x^{2}+6, \) the answer is \( 2 x^{3}-x^{2}+4 x+7 \)
A. True
B. False


Concentrated nitric acid is converted to
sulphuric acid by the reaction with
A. sulphuric dioxide
B. conc. Sulphuric acid
c. sulphur
D. sulphur trioxide


\( \left[P t(G l y)_{2}\right] \) can exist as \( c i s-, \) and
trans- isomers. If true enter 1 , else
enter 0


Show that \( \left|\begin{array}{lll}\boldsymbol{x} & \boldsymbol{x}^{2} & \boldsymbol{y} \boldsymbol{z} \\ \boldsymbol{y} & \boldsymbol{y}^{2} & \boldsymbol{z} \boldsymbol{x} \\ \boldsymbol{z} & \boldsymbol{z}^{2} & \boldsymbol{x} \boldsymbol{y}\end{array}\right|=(\boldsymbol{x}-\boldsymbol{y})(\boldsymbol{y}- \)
\( z(z-x)(x y+y z+z x) \)


A design is made on a rectangular tile
of dimensions \( 50 \mathrm{cm} 70 \mathrm{cm} \) as shown in
Fig. \( 12.7 . \) The design shows 8 triangles,
each of sides \( 26 \mathrm{cm}, 17 \mathrm{cm} \) and \( 25 \mathrm{cm} \) os
cut out. Find the total area of the design
in \( c m^{2} \)


What is the maximum number of
orbitals that can be identified with the
following quantum numbers?
\( n=3, l=+1, m_{l}=0 \)
\( A \)
B. 2
\( c \cdot 3 \)
D. 4


Define renewable sources of energy.
A. A source whose energy supplied can be renewed is called renewable source of energy.
B. A source of energy which will exhaust in future is called renewable source of energy.
C. A natural source providing us energy which takes long time to replenish.
D. A source of energy which causes environmental pollution is called renewable source of energy.


\( \boldsymbol{N} \boldsymbol{i}\left|\boldsymbol{N} \boldsymbol{i}^{2+} \| \boldsymbol{C} \boldsymbol{u}^{2+}\right| \boldsymbol{C} \boldsymbol{u} \)
The standard EMF of the above cell is
\( 0.59 \mathrm{V} . \) The standard electrode potential (reduction potential) of the copper electrode is 0.34 V. Calculate the
standard electrode potential of nicke
electrode.
A . \( -0.5 V \)
B. \( 0.25 V \)
c. \( 0.93 V \)
D. - \( 0.25 V \)


The general name of the elements of
17th group are:
A. hydrides
B. halogens
c. chacogens
D. noble gases


Find the domain of the real valued
square root function \( f \) given below \( \boldsymbol{f}(\boldsymbol{x})=\sqrt{(\mathbf{2} \boldsymbol{x})} \)


A straight wire carries conventional
current toward the sky. What is the direction of the magnetic
field due to the current west of the wire?
A. North
B. South
c. East
D. west
E. Up


Chemical passivity is possible with:
A. conc. \( H N O_{3} \)
B. air
c. both A and B
D. none of the above


"Water is a compound, not a mixture."
Explain this condition.


Describe the extraction of Mercury metal from its ore Cinnabar \( (\boldsymbol{H} \boldsymbol{g} \boldsymbol{S}) \)


The functional group of carboxylic acid
is:
\( \mathbf{A} \cdot-O H \)
в. \( -C H O \)
\( \mathbf{c} .>C=O \)
D. \( -C O O H \)


A long straight wire is carrying current
\( \boldsymbol{I}_{1}=\mathbf{2} / \mathbf{5} \boldsymbol{A} \) in \( +\mathbf{z} \) direction.The \( \mathbf{x}-\mathbf{y} \) plane
contains a closed circular loop carrying
current \( \boldsymbol{I}_{2}=\mathbf{5} / \mathbf{2} \boldsymbol{A} \) and not encircling
the straight wire, then the force (in newton) on the loop will be ? (Radius of
the circular loop \( \boldsymbol{R}=\mathbf{3} / \mathbf{4 m} \) ).


a) What are monosaccharides? Write
the definition?
b) i) Name the products yields from the complete hydrolysis of DNA?
ii) Write the structural formula of sugar
moiety in DNA \& RNA?
c) Write the name of method related
with DNA to identify the dead body in any accident?


(a) In the following diagram, which bulb
out of \( B_{1} \) and \( B_{2} \) will glow and why?
(b) Draw a diagram of an illuminated \( p \)
n junction solar cell.
(c) Explain briefly the three processes
due to which generation of emf takes place in a solar cell.


In case of oxygen family (Group 16):
A. The tendency for catenation decreases markedly as we go down the group.
B. Maximum coordination of oxygen is four due to lack of \( d \) -orbital but that of other elements is six due to
presence of \( d \) -orbital
C. The tendency to form multiple bonds with \( C, N \) and \( O \) decreases as going down the group from \( S \) to \( T e \)
D. All of the above are correct statements.


For construction of a quadrilateral \( A B C D, \) where \( A B=4.2 \mathrm{cm}, B C=3.8 \)
\( \mathrm{cm}, C D=4.9 \mathrm{cm}, A D=5.4 \mathrm{cm} \) and
\( \angle B=72 . \) Its steps for construction is
given injumbled form. Identify the first step from the following:
1) From \( B \), set off \( B C=3.8 \mathrm{cm} \)
2) Draw \( A B=4.2 \mathrm{cm} \) and Make
\( \angle A B X=72^{\circ} \)
3) With \( A \) as center and radius equal to
\( \mathbf{5 . 4} \mathrm{cm} \) draw an arc.
4) With \( C \) as center and radius equal to \( 4.9 \mathrm{cm}, \) draw another arc, cutting the previous arc at \( D . \) Join \( A D \) and \( C D \)
\( A \)
в. 3
\( c \cdot 4 \)
\( D \)


Which of the following organisms reproduce by the fragmentation method?
A. Rhizopus and Penicillium
B. Hydra and Amoeba
c. Paramecium and Plasmodium
D. Spirogyra


The blue compound is formed in the
positive test for nitrogen with Lassaigne's solution of an organic compound is:
\( \mathbf{A} \cdot \operatorname{Na}_{4}\left[\mathrm{Fe}(\mathrm{CN})_{5}(\mathrm{NOS})\right. \)
в. \( N a_{3}\left[F e(C N)_{6}\right. \)
\( \mathbf{c} \cdot\left[F e(C N)_{3}\right. \)
D. \( F e_{4}\left[F e(C N)_{6}\right]_{3} \)


A point moves with uniform
acceleration and \( \boldsymbol{v}_{1}, \boldsymbol{v}_{2} \) and \( \boldsymbol{v}_{3} \) denote
the average velocities in the three
successive intervals of time \( t_{1}, t_{2} \) and \( t_{3} \)
Which of the following relation is
correct?
\( \mathbf{A} \cdot\left(v_{1}-v_{2}\right):\left(v_{2}-v_{3}\right)=\left(t_{1}-t_{2}\right):\left(t_{2}+t_{3}\right) \)
\( \mathbf{B} \cdot\left(v_{1}-v_{2}\right):\left(v_{2}-v_{3}\right)=\left(t_{1}+t_{2}\right):\left(t_{2}+t_{3}\right) \)
\( \mathbf{c} \cdot\left(v_{1}-v_{2}\right):\left(v_{2}-v_{3}\right)=\left(t_{1}-t_{2}\right):\left(t_{1}-t_{3}\right) \)
\( \mathbf{D} \cdot\left(v_{1}-v_{2}\right):\left(v_{2}-v_{3}\right)=\left(t_{1}-t_{2}\right):\left(t_{2}-t_{3}\right) \)


In the waste water treatment plant (WWTP), air is pumped into water to
A. Support the growth of anaerobic bacteria
B. Support the growth of aerobic bacteria
c. Disinfect water
D. Throw human waste


Fog is a solution of


What should be the maximum
acceleration of a train in order that an
object kept on its floor remains
stationary? \( \mu \) between the two surfaces
is \( 0.2, g=9.8 m / s^{2} \)


Which amino acid is achiral?
A. Alanine
B. Valine
c. Proline
D. Glycine


If two particles of masses \( 3 k g \) and \( 6 k g \)
which are at rest are separated by a distance of 15 m. The two particles are
moving towards each other under a
mutual force of attraction. Then the
ratio of distances travelled by the particles before collision is
A .2: 1
B. 1: 2
c. 1: 3
D. 3: 1


Which of the following compound may be optical active?
A \( \cdot C o(e n)_{2} C I_{2} \)
В・ \( \left[R h C I B r N H_{3} P H_{3}\right] \)
\( \mathbf{c} \cdot C u(e n)_{2} C I_{2} \)
D. All of these


Which of the following is a weed killer?
A. \( 2,4- \) D
B. NAA
\( c \cdot \) GА
D. ABA


Chloroplast involvement in photosynthesis was discovered by
A. Julius von Sachs
B. Mayer
c. Ingenhousz
D. Liebig


Basic stregth of \( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{N H}_{2} \) is
to that of \( \boldsymbol{C} \boldsymbol{H}_{2}= \)
\( \boldsymbol{C H} \boldsymbol{N} \boldsymbol{H}_{2} \)
A. stronger
B. weaker
c. equal
D. none of the above


\( \sim(p \vee q) \vee(\sim p \wedge q) \) is logically
equivalent to
\( \mathbf{A} \cdot \sim p \)
B.
\( c \cdot q \)
\( \mathrm{D} \cdot \sim q \)


In fig. \( A B C D \) is a field in the form of a
quadrilateral whose sides are indicated
in the figure. if \( \angle D A B=90^{\circ}, \) find the
area of the field.
Answer: \( 306 m^{2} \)
State whether answer given is true or
not
A. True
B. False


A boy fires a gun and another boy at a distance hears the sound of fire 2.5 s
after seeing the flash. If speed of sound
in air is \( 340 m s^{-1}, \) find the distance
between the boys:
\( \mathbf{A} .850 m \)
в. 8500 т
c. \( 1700 m \)
D. none of the above


Which of the following fungus can cause diseases in humans?
A. Penicillium
B. Ustilago
c. Puccinia
D. All of the above


If the radius of the earth is increased
by three times, keeping the mass constant, then the weight of a body on the earth surface will be
as compared to its previous value
A . one third
B. one ninth
c. three times
D. nine times


The displacement of a body along x-axis depends on time as \( x=\sqrt{t+1} . \) Then
the velocity of body
A. increases with time
B. decreases with time
c. independent of time
D. none of these


The most suitable property for molecular weight determination of
polymers is:
A . osmotic pressure
B. lowering of vapour pressure
c. elevation in boiling point
D. depression in freezing point


Assertion
In a common-emitter amplfier, the load
resistance of the output circuit is 1000 times the load resistance of the input
circuit. If \( \boldsymbol{\alpha}=\mathbf{0 . 9 8}, \) then voltage gain is
\( 49 \times 10^{3} \)
Reason
\( \boldsymbol{\alpha}=\frac{\beta}{1-\beta}( \) symbols have their usual
meaning).
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:
\( \int \frac{1+x+\sqrt{x+x^{2}}}{\sqrt{x}+\sqrt{1+x}} d x \) is equal to
A \( \cdot \frac{1}{2} \sqrt{1+x} C \)
B \( \cdot \frac{2}{3}(1+x)^{3 / 2}+C \)
\( \mathbf{c} \cdot \sqrt{1+x}+C \)
D \( \cdot \frac{3}{2}(1+x)^{32}+C \)


What is the oxidation number of Cl in
\( H C l O \) and \( H C l O_{2} ? \)


Potential energy of an object raised through a height h is \( (1 / 2 \)
\( \left.m v^{2}, m g h\right) \)


What the significance of negative electronic energy?


When \( \left[N i\left(H_{2} O\right)_{6}\right]^{3+} \) is mixed with ethylenediamine in excess,
ethylenediamine(en) displaces \( H_{2} O \) to
form a chelate.
If true enter 1 , else enter 0 .


Instead of \( 3, \) if it was 2 bases code for
an amino acid, the degeneracy of codons coding for the same amino acid
would have
A. Increased
B. Decreased
c. Remained the same
D. Been uncertair


Choose the correct options -
This question has multiple correct options
A. In a nuclear reactor, the function of the moderator, is to slow down neutrons
B. 1 MeV energy is \( 1.6 \times 10^{-13} J \)
C . A nucleus \( _{Z}^{A} X \) emits an \( \alpha- \) particle. The resultant nucleus emits a \( \beta^{+}- \) particle. The respective atomic
and mass nos. of the final nucleus will be \( z-3, A-4 \)
D. The mass equivalent of 931 MeV energy is \( 1.66 \times \) \( 10^{-27} k g \)


Give two examples of Liquid element


\( \boldsymbol{C H}_{3} \boldsymbol{C H O} \stackrel{\text {dil.NaOH}}{\longrightarrow} \boldsymbol{A} \stackrel{\boldsymbol{\Delta}, \text {dehydration}}{\longrightarrow} \)
\( \boldsymbol{B} \stackrel{\boldsymbol{N i} / \boldsymbol{H}_{2}}{\longrightarrow} \boldsymbol{C} \stackrel{\boldsymbol{N i} / \boldsymbol{H}_{2}}{\longrightarrow} \boldsymbol{D} \)
In the above sequence of reactions,
compound D is:
\( \mathbf{A} \cdot C H_{3} C H_{2} C H_{2} C H_{2} O H \)
в. \( C H_{3} C H_{2} C H_{2} C H O \)
c. O
\( C H_{3} C H_{2} C H_{2} C H-C H_{3} \)


toppr LoGın
Q Type your question
and was caught. Which reading helped
the teacher to arrive at the conclusion
that he cheated?
\( \begin{array}{lll}\text { S. No. } & \text { Value of rheostat } & \text { Null point } \\ \text { 1. } & R_{1} & \text { 50 cm } \\ \text { 2. } & R_{2} & \text { 60 cm } \\ \text { 3. } & R_{3} & \text { 70cm } \\ \text { 4. } & R_{4} & \text { 80 cm }\end{array} \)
This question has multiple correct options
A.
B. 2
\( c \cdot 3 \)
\( D \)


\( (a . c) c+(c . b) a \)
\( A \cdot-2 k \)
B . \( 2 k \)
c. \( i-j \)
D. \( i+j-2 k \)


Draw the Lewis structures for the
following molecules and ions:
\( \boldsymbol{H}_{2} \boldsymbol{S}, \boldsymbol{S} \boldsymbol{i} \boldsymbol{C l}_{4}, \boldsymbol{B} \boldsymbol{e} \boldsymbol{F}_{2}, \boldsymbol{C} \boldsymbol{O}_{3}^{2-} \) and
HCOOH


The oxidation number of \( C \) -atom in
\( C H_{2} C l_{2} \) and \( C C l_{4} \) are respectively
A. -2 and -4
B. 0 and -4
c. 0 and 4
D. 2 and 4


A hemispherical tank is made up of an
iron sheet \( 1 \mathrm{cm} \) thick. If the inner radius
is \( 1 \mathrm{m} \), then find the volume of the iron
used to make the tank.


toppr
Q Type your question
Superman arrives on the top of a cliff
and, due to some reason, Superman lost
his flying power immediately after arrival on cliff. Due to shortage of time,
somehow, Superman manages a strong and long straw and decided to drink
whole water of lake to save Bantu.
(Data:Atmospheric pressure \( =1.2 \times \)
\( 10^{5} P a, g=10 m / s^{2}, \) density of water \( = \)
1000 \( k g / m^{3} \) ) Assume Superman has
infinite power and ability to drink whole water. Which of the following statements is/are true?
(1) Superman cannot save Bantu by this
way.
(2) Superman can drink some water but not whole water.
(3) Superman will save Bantu by drinking whole water.
A. Only (1) \& (2)
B. Only (3)
c. Only (1)
D. AII (1), (2) \&
(3) are wrong


A diploid cell in human, where cell
division does not occur:
(a) Heart cell
(b) Muscle cell
(c) Nerve cell
A. Only c
B. b and c
\( c . \) a and \( c \)
D. a, b and c


Assertion
Kepler's second law can be understood by conservation of angular momentum principle.
Reason
Kepler's second law is related with areal
velocity which can further be proved to
be based on conservation of angular
momentum as \( (\boldsymbol{d A} / \boldsymbol{d t})=\left(\boldsymbol{r}^{2} \boldsymbol{\omega}\right) / 2 \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect and Reason is correct


Find the value of the determinant
without expansion \( \left|\begin{array}{ccc}b^{2}-a b & b-c & b c-a c \\ a b-a^{2} & a-b & b^{2}-a b \\ b c-a c & c-a & a b-a^{2}\end{array}\right| \)


Find the value of \( \int \sec ^{2} x \tan ^{3} x d x \)


Which of the following substances does not burn with a flame?
A . LPG
B. Camphor
c. Dry grass
D. Charcoal


The possible oxidation state of Tl are:
\( A \cdot+1 \) and +2
\( B \cdot+2 \) and +3
c. +1 and -1
\( D \cdot+1 \) and +3


Find the curve passing through the point (0,1) and satisfying the equation \( \sin \left(\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}\right)=\boldsymbol{a} \)


Which of the following equations are
correctly represented for \( 0.10 \mathrm{M} \) solution of acetic acid in water?
\( \mathbf{A} \cdot[H O A c]=[H O A c c]_{e q .}+\left[O A c^{-}\right]_{e q .}=0.10 \mathrm{M} \)
B . \( \left[H^{+}\right]_{e q .}=\left[O A c^{-}\right]_{e q .}+\left[O H^{-}\right]_{e q} \)
\( \mathbf{c} \cdot\left[H^{+}\right]>\left[O H^{-}\right] \)
D. All of the above


Divide \( x^{4}-y^{4} \) by \( x-y \)


Let \( f(x)=x^{2}-3 x+4, \) then the value
of \( \boldsymbol{x} \) which satisfies \( \boldsymbol{f}(\mathbf{1})+\boldsymbol{f}(\boldsymbol{x})= \)
\( \boldsymbol{f}(\mathbf{1}) \boldsymbol{f}(\boldsymbol{x}) \) is
A .
B.
c. 1 or 2
D. 1 and 0


Add: \( 6 a x-2 b y+3 c z, 6 b y-11 a x-c z \)
and \( 10 c z-2 a x-3 b y \)


When air beneath the piston is
completely pumped out, how much does
the atmospheric pressure cause the
spring to compress?


Write the hybridisation and number of unpaired electrons in the complex
\( \left[\boldsymbol{C o F}_{6}\right]^{3-} . \) (Atomic No. of \( \mathrm{Co}=\mathbf{2 7} \) ).


For the ionic reaction of hydrochloric acid with the following alkenes, predict the correct sequence of reactivity as measured by reaction rates:
\( (\boldsymbol{I}) \boldsymbol{C l C H}=\boldsymbol{C H}_{2} \)
\( (\boldsymbol{I I})\left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{C}=\boldsymbol{C H}_{2} \)
\( (I I I) O H C C H=C H_{2} \)
\( (\boldsymbol{I} \boldsymbol{V})(\boldsymbol{N} \boldsymbol{C})_{2} \boldsymbol{C}=\boldsymbol{C}(\boldsymbol{C} \boldsymbol{N})_{2} \)
A. IV > |> ||| > ||
B. |>IV> || > ||
c. \( \||>\|>| V> \)
D. II>1>111>1V


What properties of the bacteriophages made them ideal material for solving
the controversy regarding the genetic material to be protein or DNA ?


1.8 g hydrogen atoms are excited to radiations. The study of spectra indicates that \( 27 \% \) of the atoms are in
3rd energy level and \( 15 \% \) of atoms in 2 nd
energy level and the rest in the ground
state. If I.P. of \( \mathrm{H} \) is \( 21.7 \times 10^{-12} \) erg. The
number of atoms present in III \& II energy level and total energy evolved
when all the atoms return to ground
state respectively are:
A . \( 292.68 \times 10^{21} \) atoms \( , 162.60 \times 10^{21} \) atoms and \( 823 k J \)
B . \( 292.68 \times 10^{34} \) atoms \( , 162.60 \times 10^{43} \) atoms and \( 990 k J \)
c. \( 292.68 \times 10^{36} \) atoms \( , 162.60 \times 10^{28} \) atoms and \( 594.1 k J \)
D . \( 292.68 \times 10^{28} \) atoms \( , 162.60 \times 10^{36} \) atoms and \( 594.1 k J \)


An electronic test circuit produced a
resonant curve of half power frequency points at \( 414 H z \) and \( 436 H z \). If \( Q \) factor
be \( 10, \) the resonant frequency of the circuit is:
A \( .220 H z \)
B. \( 22 H z \)
c. \( 2.2 H z \)
D. \( 0.22 H z \)


Integrate:
\( \int\left(a^{x}+x^{a}+a^{a}\right) d x \)
A. \( -\frac{a^{x}}{\ln a}-\frac{x^{a+1}}{a+1}+a^{a} x+c \)
B. \( a^{x}+\frac{x^{a+1}}{a+1}+a^{a} x+c \)
c. \( \frac{a^{x}}{\ln a}+x^{a+1}+a^{a} x+c \)
D. \( \frac{a^{x}}{\ln a}+\frac{x^{a+1}}{a+1}+a^{a} x+c \)


If the resistivity of copper is \( 1.7 \times \)
\( 10^{-6} \Omega c m, \) then the mobility of electrons
in copper, if each atom of copper contributes one free electron
for conduction, is
[The atomic weight of copper is 63.54 and its density is \( 8.96 g / c c] \)
A. \( 23.36 \mathrm{cm}^{2} / \mathrm{Vs} \)
B. \( 503.03 \mathrm{cm}^{2} / \mathrm{Vs} \)
c. \( 43.25 \mathrm{cm}^{2} / \mathrm{V} s \)
D. \( 88.0 \mathrm{cm}^{2} / \mathrm{Vs} \)


Alnico is used for making permanent
magnets because it has
A. High coercivity and high retentivity
B. high coercivity and low retentivity
C. low coercivity and low retentivity
D. low coercivity and high retentivity


Which of the following generates a plane wavefront?
A \( . \alpha- \) rays
B. \( \beta- \) rays
c. \( \gamma- \) rays
D. None of these


A rock is thrown vertically upward with
initial speed \( v_{0} . \) Assume a friction force
proportional to \( -v, \) where \( v \) is the
velocity of the rock and neglect the buoyant force exerted by air. Which of
the following is correct?
A. The acceleration of the rock is always equal to \( g \)
B. The acceleration of the rock is always equal to \( g \) only at the top of the flight
C. The acceleration of the rock is always less than \( g \)
D. The speed of the rock upon return to its starting point
is \( v_{0} \)
E. The rock can attain a terminal speed greater than \( v_{0} \) before it returns to its starting point


Determine the value of \( p \) if \( (x+3) \) is a
factor of \( x^{3}-3 x^{2}-p x+24 \)


The value of \( \vec{i} \times(\vec{a} \times \vec{i})+\vec{j} \times(\vec{a} \times \)
\( \vec{j})+\vec{k} \times(\vec{a} \times \vec{k}) \) is (where \( \vec{i}, \vec{j}, \vec{k} \) are
unit vectors
\( A \cdot \vec{a} \)
B . \( 2 \vec{a} \vec{a} \vec{a} \)
\( c \cdot 0 \)
D. - \( \vec{a} \)


In the diagram of T.S. monocot leaf, identify labellings a, b, c, d with their functions.
A. a-motor action, b-photosynthesis, c-conduction, transpiration
B. a-motor action, b-conduction, c-photosynthesis, dtranspiration
c. a-transpiration, b-photosynthesis, c-conduction, dtranspiration
D. a-transpiration, b-conduction, c-photosynthesis, dmotor action


A parabola with axis parallel to \( x \) axis
passes through \( (\mathbf{0}, \mathbf{0}),(\mathbf{2}, \mathbf{1}),(\mathbf{4},-\mathbf{1}) . \) Its
length of latus rectum is
A \( \cdot \frac{2}{3} \)
B.
\( c \cdot \frac{7}{3} \)
D. \( \frac{1}{3} \)


Equal volume of gases contain equal
number of moles.

State whether the above statement is
true or false.
A. The statement is True
B. The statement is False
C. Neither
D. Equal volume of gases contain equal number of moles, only when the temperature is increased


The differential equation representing the family of curves \( y^{2}=2 c(x+\sqrt{c}) \)
where \( c \) is a positive parameter is of
A . order 3
B. order 2
c. degree 3
D. degree 4


overlapping between
orbitals leads to \( \pi \) bond formation.


The persistence of hearing of human beings is not more than
A . \( 1 \mathrm{s} \)
в. \( \frac{1}{5} \) s
c. \( \frac{1}{10} \) s
D. \( \frac{1}{2} \) s


The amount of freshwater of the Earth
frozen as polar or glacial ice is
A . 0.5\%
B. 0.02\%
c. \( 0.01 \% \)
D . 1.97\%
E. 2.5\%


Pyrimidines have nitrogen atoms at positions.
A \( .1 ; 3 ; 7 ; 9 \)
B. \( 1 ; \) ', \( 7 ; \) ?
\( c \cdot 1 ; 3 \)
D. \( 1 ; 9 \)


\( \ln \Delta A B C, \) if \( \angle A+\angle B=90^{\circ}, \cot B= \)
\( \frac{3}{4}, \) then the value of \( \tan A \) is :
A \( \cdot \frac{4}{5} \)
в. \( \frac{3}{4} \)
\( c \cdot \frac{4}{3} \)
D. \( \frac{3}{5} \)


Which of the following is different from
the other three?
\( \mathbf{A} \)
\( B \)
\( \mathbf{C} \)
D.


What is the smallest number of squares
that must be added so that the line PQ
becomes a line of symmetry?
\( \mathbf{A} \cdot \mathbf{5} \)
B. 3
\( c \cdot 4 \)
\( D \)


A car starts from rest and accelerates
to a speed of \( 20 \mathrm{m} / \mathrm{s} \) in a time of \( 5 \mathrm{s} \)
Find out the average acceleration of
car?
A \( \cdot 100 m / s^{2} \)
в. \( 80 m / s^{2} \)
c. \( 40 m / s^{2} \)
D. \( 20 m / s^{2} \)
E \( \cdot 4 m / s^{2} \)


Which one of the following solutions will have the highest pH value?
A. \( 0.01 M \) NaOH
в. \( 0.02 M \) СН\( _{3} \) СОО Na .
c. \( 0.01 M \) NaHCO\( _{3} \)
D. \( 0.01 M H_{2} S O_{4} \)


The probability that a certain radioactive atom would get distance in
a time equal to the mean life of the radioactive sample is
A . 0.37
B. 0.63
\( c .0 .50 \)
D. 0.67


If \( f(x) \) is a polynomial function of the second degree such that \( \boldsymbol{f}(-\mathbf{3})= \) \( \mathbf{6}, \boldsymbol{f}(\mathbf{0})=\mathbf{6} \) and \( \boldsymbol{f}(\mathbf{2})=\mathbf{1 1}, \) then the
graph of the function \( f(x) \) cuts the
ordinate \( x=1 \) at the point:
B. (1,4)
c. (1,-2)
D. None of these


Derive Laplace's law for a spherical
membrane.


What is primary treatment of sewage?


Which of the following anions is most easily polarized?
A \( \cdot C l \)
B. \( S e^{2} \)
c. \( B r^{-} \)
D. \( T e^{2} \)


The value of \( \sqrt{214+\sqrt{130-\sqrt{88-\sqrt{44+\sqrt{25}}}}} \)
A . 14
B. 15
c. 16
D. 17


Structure of methyl propyl ether (methoxypropane) is:
A \( \cdot C H_{3}-C H_{2}-C H_{3} \)
в. \( C H_{3}-\underset{O}{\|}-O H \)
c. \( C H_{3}-O-C_{3} H_{7} \)
D. \( C H_{3}-C-C H_{3} \)
॥
监
\( o \)
E \( \cdot C H_{3}-C H_{2}-N H_{2} \)


R.Q. of fatty substances is generally
A. Unity
B. Less than one
c. Greater than one
D. zero


The process suitable for charging a glass rod is :
A. conduction
B. induction
c. rubbing against a suitable substance
D. all of the above


The time at which block will leave the
inclined plane is?
A . 1 s
B . 2 s
\( c \cdot 3 s \)
D. 4 s


Arrange the acids \( C H_{3} C H_{2} C O O H \) (I) \( C H_{2}=C H-C O O H \) (II) and \( H C \equiv \)
\( C-C O O H \) (III) in order of decrease in
acidity
A . ।>॥>॥
в. ॥॥>॥>
c. ॥>1>॥||
D. ॥ᅵ>1>1


The general formula for halo alkanes is :
A \( \cdot C_{n} H_{2 n+2} X \)
B. \( C_{n} H_{2 n-1} X \)
c. \( C_{n} H_{l n-2} X \)
D. \( C_{n} H_{2 n+1} X \)


A current-carrying ring is placed in a magnetic field. The direction of the field
is perpendicular to the plane of the
ring.Then:
A. there is no net force on the ring
B. the ring will tend to expand
C. the ring will tend to contract
D. either
(B) and
(C) depending on the directions of the current in the ring and the magnetic field


A block which is being raised against gravity with infinetisimally slow rate can be considered as (consider only the
given case)
A . Irreversible
B. Reversible
c. It depends on the rate of the motion.
D. none of the above


Assertion
While blowing a soap bubble, to increase the size of soap babble, we have to increase the air pressure within
the soap bubble.
Reason
To increase the size of soap bubble,
more air has to be pushed into the
bubble.
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


0.2 molal acid \( H X \) is \( 20 \% \) ionised in
solution. \( \boldsymbol{K}_{\boldsymbol{f}}=\mathbf{1 . 8 6 K} \) molality \( ^{-1} \). The
freezing point of the solution is:
A. \( -0.45^{\circ} \mathrm{C} \)
B . \( -0.90^{\circ} \mathrm{C} \)
c. \( -0.31^{\circ} \mathrm{C} \)
D. \( -0.53^{\circ} \mathrm{C} \)


Motion of artificial satellite around the
earth is powered by :
A . Liquid fuel
B. Solar energy
c. Atomic energy
D. None of these


If the density of a small planet is the same as that of earth, while the radius
of the planet is 0.2 times that the earth, the gravitational acceleration on the surface of that planet is:
A \( .0 .2 \mathrm{g} \)
в. 0.4 g
\( c \cdot 2 g \)
D. 4 g


Which is the major product obtained by hydrolysis of compound formed by
reaction between
formaldehyde and ethyl magnesium bromide?
A. Ethanol
в. Propan \( -2- \) ol
c. Propan \( -1- \) ol
D. \( 2- \) Methyl \( - \) propan \( -2- \) ol


Three concentric spherical metallic shells \( A, B \) and \( C \) of \( \operatorname{radii} a, b \) and \( c(a< \) \( b<c) \) have charge densities \( \sigma,-\sigma \) and
\( \sigma \) respectively. If the shells \( A \) and \( C \) are
at the same potential then the relation between \( a, b \) and \( c \) is :
A \( a+b+c=0 \)
0
B . \( a+c=b \)
\( \mathbf{c} \cdot a+b=c \)
\( \mathbf{D} \cdot a=b+c \)


\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}+\mathbf{3} \boldsymbol{x}+\mathbf{5} \) find \( \boldsymbol{f}(\boldsymbol{4}) \)


A uniform rod of mass \( 1 \mathrm{kg} \) is hanging from a thread attached at the midpoint of the rod. A block of mass \( m=3 \mathrm{kg} \) hangs at the left end of the rod and block of mass \( M \) hangs at the right side at \( 80 \mathrm{cm} \) from block \( m . \) If system is
in equilibrium. Calculate \( M \)
\( A \cdot 4 \) kg
в. 5 кв
\( c \cdot 6 \mathrm{kg} \)
\( D \cdot 8 \mathrm{kg} \)
E. 9 kg


The study of the kind and diversity of organisms and the existing relationship among them is called
A. systematics
B. Taxonomy
c. Classification
D. Nomenclature


Assertion
Li \( F \) has more covalent character than
\( C s F \)
Reason
Lattice energy of \( C s F \) is less than that
of \( \boldsymbol{L} \boldsymbol{i} \boldsymbol{F} \)
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 rate law for the dimerisation of
\( N O_{2} \) is \( \frac{-d\left[N O_{2}\right]}{d t}=k\left[N O_{2}\right]^{2} \)
Which of the following changes will change the value of the specific rate constant \( (\mathrm{k}) ? \)
A. Doubling the total pressure on the system
B. Doubling the temperature
c. Both A and B
D. None of these


Which of the following is not true?
A. The electrode which pushes electrons into external circuit is known as anode
B. The electrode which pulls electrons out of external circuit is known as cathode
C. Weak electrolytes conduct relatively small quantity of electricity than strong electrolytes
D. Effect of dilution on conductance of strong electrolyte can be explained by Arrhenius theory.


Choose the correct answer form the
alternatives given. When alkaline earth metals dissolve in
ammonia, they form coloured solution like alkali metals. Which of the
following observations regarding the reaction are correct?
(i) Dilute solution are bright blue in
colour due to solvated electrons.
(ii) These solutions decompose to form amides and hydrogen.
(iii) From this solution the ammoniates
\( \left[M\left(N H_{3}\right)_{6}\right]^{2+} \) can be recovered by
evaporation
A. only (i) and (ii)
B. Only (i) and (ii) and (iii)
c. only (ii) and (iii)
D. only (i)


Electric power is defined as the
A. Product of resistance and current flowing through is
B. Product of Potential difference applied across the circuit and current flowing through it
C. Product of current and energy
D. None


Consider the expansion \( \left(x^{2}+\frac{1}{x}\right)^{15} \) Consider the following statements:
1. There are 15 terms in the given expansion.
2. The coefficient of \( x^{12} \) is equal to that
of \( x^{3} \)

Which of the statements is/are correct
\( ? \)
A. 1 only
B. 2 only
c. Both 1 and 2
D. Neither 1 nor 2


Every atom makes one free electron in
copper. If 1.1 ampere current is flowing in the wire of copper having \( 1 \mathrm{mm} \) diameter, then the drift velocity
(approx) will be (density of copper \( =9 \times \)
\( 10^{3} k g / m^{3} \) and atomic weight of copper
\( =\mathbf{6 3}) \)
A. \( 0.1 m m / s \)
B. \( 0.2 \mathrm{mm} / \mathrm{s} \)
\( \mathbf{c} \cdot 0.3 m m / s \)
D. \( 0.2 c m / s \)


Write the polynomial in standard form and also write down their degree. \( \left(p^{2}+2\right)\left(p^{2}+7\right) \)


Table sugar (Sucrose) is a:
A. disaccharide of \( \alpha \) -D Glucose and \( \beta \) -D Fructose
B. monosaccharide
C . disaccharide containing two glucose units
D. polysaccharide


STATEMENT-1
An astronaut in an orbiting space station above the Earth experiences weightlessness.
and

STATEMENT-2
An object moving around the Earth under the influence of Earths
gravitational force is in a state of freefall.
A. STATEMENT-1 is True, STATEMENT-2 is True:
STATEMENT-2 is a correct explanation for STATEMENT
B. STATEMENT-1 is True, STATEMENT-2 is True STATEMENT-2 is NOT a correct explanation for STATEMENT-1
C. STATEMENT-1 is True, STATEMENT-2 is False
D. STATEMENT-1 is False, STATEMENT-2 is True


Name the property of light, which is responsible for tyndall effect.


Carbylamine reaction is given by:
A . aliphatic \( 1^{\circ} \) amines only
B. aromatic \( 1^{\circ} \) amines only
C. both aliphatic and aromatic primary amines
D. all secondary amines and diazonium salts


For the reaction of one mole zinc dust
with one mole sulphuric acid in a bomb calorimeter, \( \triangle \boldsymbol{U} \) and \( \mathbf{w} \) correspond to?
A. \( \triangle U<0, w=0 \)
в. \( \triangle U<0, w<0 \)
\( \mathbf{c} . \triangle U>0, w=0 \)
D. \( \Delta U>0, w>0 \)


What the decrease in weight ofa body of mass 600 kg when it is taken in a mine of depth \( 5000 \mathrm{m} \) ? [Radius of earth a
\( 6400 \mathrm{km}, \mathrm{g}=9.8 \mathrm{m} / \mathrm{s}^{2} \)


Which among the following resists a rapid change of pH?
A. Buffer
B. Indicator
C. Arrhenius acid
D. Arrhenius base
E. Neutral condition


Assertion
Bakelite is first completely synthesized thermoplastic.
Reason
Thermosetting plastics are harder.
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


Arrange the following in increasing
order of pH value
A . ॥ < I < II
\( c .\|<\|< \)
D. II<IIIS


If \( \boldsymbol{z}_{1}=\mathbf{9}+\mathbf{5} \boldsymbol{i} \) and \( \boldsymbol{z}_{2}=\mathbf{3}+\mathbf{5} \boldsymbol{i} \) and if
\( \arg \left(\frac{\boldsymbol{z}-\boldsymbol{z}_{1}}{\boldsymbol{z}-\boldsymbol{z}_{2}}\right)=\frac{\boldsymbol{\pi}}{\boldsymbol{4}} \) then \( \mid \boldsymbol{z}-\boldsymbol{6}- \)
\( \mathbf{8 i} \mid=\mathbf{3} \sqrt{\mathbf{2}} \)


A small cube with mass \( M \) starts at
rest point 1 at a height \( 4 R, \) where \( R \) is
the radius of the circular part of the
track. The cube slides down the
frictionless track and around the loop.
The force that the track exerts on the
cube at point 2 is nearly
times the cube's
weight \( M g \)
\( A \)
в.
\( c .3 \)
D.


In earthworm, the segment bearing
mouth is called as
A. Deuterostomium
B. Prostomium
c. Peristomium
D. Stomium


The vapour pressure of a saturated solution of sparingly soluble salt
\( \left(X C l_{3}\right) \) was \( 17.20 \mathrm{mm} \) Hg at \( 27^{\circ} \mathrm{C} . \) If the
vapour pressure of pure \( \boldsymbol{H}_{2} \boldsymbol{O} \) is 17.25 \( \mathrm{mm} \mathrm{Hg} \) at \( 300 \mathrm{K}, \) what is the solubility of sparingly soluble salt \( X C l_{3} \) in
mole/L?
A . \( 4.02 \times 10^{-2} \)
в. \( 8.08 \times 10^{-2} \)
c. \( 2.02 \times 10^{-2} \)
D. \( 4.04 \times 10^{-3} \)


A trust fund has Rs. 30,000 that must
be invested in two different types of bonds. The first bond pays \( 5 \% \) interest per year, and the second bond pays \( 7 \% \) interest per year. Using matrix multiplication, determine how to divide
Rs. 30,000 among the two types of bonds. If the trust fund must obtain an
annual total interest of
A) Rs. 1800
B) Rs. 2000


A liquid is kept in a closed vessel. If a glass plate (negligible mass) with a small hole is kept on top of the liquid surface, then the vapour pressure of the liquid in the vessel is :
A. more than what would be if the glass plate were removed
B. same as what would be if the glass plate were removed
c. less than what would be if the glass plate were removed
D. cannot be predicted


Why specific heat is different from
different substance?


The colour of light emitted by an LED depends on
A. Its reverse bias
B. The amount of forward current
c. Its forward bias
D. Type of semiconductor material


Show that the following points form an isosceles triangle. (2,3),(5,7) and (1,4)


When a bus suddenly takes a turn, the passengers are thrown outwards because of
A. Inertia of motion
B. Acceleration of motion
c. speed of motion
D. Both (b) and (c)


\( ^{22} N e \) nucleus, after absorbing energy
decays into two \( \alpha \) -particles and an unknown nucleus. The unknown
nucleus is
A. nitrogen
B. carbon
c. boron
D. oxygen


The nucleodic masses of \( ^{14} \mathrm{N} \) and \( ^{15} \mathrm{N} \)
are mixed to give atomic mass of 14.1 What is the ratio of the two isotopes as a whole number


Calculate the wavelength of the wave as
Shown above:
\( A \cdot 1 m \)
\( B \cdot 2 m \)
\( c \cdot 3 m \)
\( D \cdot 6 m \)
\( E \cdot 9 m \)


In the following reaction:
\( \boldsymbol{x} \boldsymbol{Z} \boldsymbol{n}+\boldsymbol{y} \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3}(\boldsymbol{d} \boldsymbol{i} l) \longrightarrow \)
\( \boldsymbol{a} \boldsymbol{Z} \boldsymbol{n}\left(\boldsymbol{N} \boldsymbol{O}_{3}\right)_{2}+\boldsymbol{b} \boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{c} \boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{N} \boldsymbol{O}_{3} \)
What is the sum of the coefficients
\( (a+b+c) ? \)


What is the pattern of the veins in the leaves required for the conduction called ?
A. Vein distribution
B. Venation
c. vein morphology
D. Network system


Find the modulus and argument of \( z= \) \( \frac{3+2 i}{-2+i} \)


Sulphur on reaction with \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) gives


The angles of a triangle are arranged in ascending order of magnitude. If the difference between two consecutive
angles is \( 10^{\circ}, \) find the three angles.


A soap film of thikness \( 0.0011 \mathrm{mm} \)
appears dark when seen by the reflated light of wavelength 580 nm. What is the
index of refraction of the soap solution, if it is known to be between 1.2 and \( 1.5 ? \)


Which one of the following is mainly responsible for green house effect?
\( A \cdot S O_{2} \)
в. \( C O_{2} \)
c. \( C O \)
D. \( O_{2} \)


Boron has an extremely high melting point because of:
A. the strong van der Waals forces between its atoms
B. the strong binding forces in the covalent polymer
c. its ionic crystal structure
D. allotropy


A vector \( a \) can be written as
\( \mathbf{A} \cdot(a \cdot i) i+(a \cdot j) j+(a \cdot k) k \)
B. \( (a \cdot j) i+(a \cdot k) j+(a \cdot i) k \)
\( \mathbf{c} \cdot(a \cdot k) j+(a \cdot i) j+(a \cdot j) k \)
\( \mathbf{D} \cdot(a \cdot a) i+(i+j+k) k \)


How many commonly used hydraulic jacks are available?
A. 3
B. 4
\( c \cdot 2 \)
\( D \)


Find \( x \) satisfying \( |x-5| \leq 3 \)


The diagram shows a pump connected
to a glass jar. The volume of the glass jar is \( 400 \mathrm{cm}^{3} \) and it is filled with air.
When the piston is pushed in completely, \( 50 \mathrm{cm}^{3} \) of air is forced into
the jar. What is the final volume of air in the
jar?
\( \mathbf{A} \cdot 50 \mathrm{cm}^{3} \)
В. \( 100 \mathrm{cm}^{3} \)
c. \( 400 \mathrm{cm}^{3} \)
D. \( 450 \mathrm{cm}^{3} \)


Isotopes have same
A. atomic mass number
B. atomic number
C. number of neutrons
D. moles


The standard enthalpy of formation of water liquid is \( 285.76 \mathrm{kJ} \) at \( 298 \mathrm{K} \)
Calculate the value at \( 373 \mathrm{K} \). The molar
heat capacities at constant pressure
\( \left(C_{P}\right) \) in the given temperature range of
\( \boldsymbol{H}_{2}(\boldsymbol{g}), \boldsymbol{O}_{2}(\boldsymbol{g}) \) and \( \boldsymbol{H}_{2} \boldsymbol{O}(l) \) are
respectively 38.83,29.16 and 75.312 \( \$ \$ J K^{\wedge}\{1\} \operatorname{mol}^{\prime}\{1\} \)
A \( \cdot \Delta H_{373}^{\circ}\left(H_{2} O,(l)\right)=-284.11 k J \)
B. \( \Delta H_{3^{\prime 3}}\left(H_{2} O,(l)\right)=+284.11 k J \)
C . \( \Delta H_{373}^{\circ}\left(H_{2} O,(l)\right)=28.411 k J \)
D. None of these


For the curve \( y=3 \sin \theta \cos \theta, x= \)
\( e^{\theta} \sin \theta, 0 \leq \theta \leq \pi ; \) the tangent is
parallel to \( x \) -axis when \( \theta \) is
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( \frac{\pi}{2} \)
c.
D.


A transparent sphere of radius \( 20 \mathrm{cm} \) and refractive index 1.6 is fixed in a hole
of the partition separating the two
media: A(refractive index \( n_{1}=1.2 \) ) and B
(refractive index \( n_{3}=1.7 \) ). A luminous point object is placed \( 120 \mathrm{cm} \) from
surface of sphere in medium A. It is viewed from D in medium B in a
direction normal to the sphere. Find the
position of the image formed by the rays, from point \( \mathrm{N} \)


A game of number has cards marked
with \( 11,12,13, \ldots .40 . \) A card is drawn at
random. Find the Probability that the number on the card drawn is a perfect
square


Smudge in certain colored varieties of
onions is prevented by.
A. Fumeric acid
B. Ferulic acid
c. chlorogenic acid
D. Protocateuchuic acid


Which of the following has a higher boiling point?
A. Butanol
B. Butanal
c. Both of them have similar boiling point
D. Cannot say anything


The mass and density of a solid are
measured to be \( (12.4 \pm 0.1) \mathrm{kg} \) and
\( (4.6 \pm 0.2) k g / m^{3} . \) Calculate the
volume of the sphere with error limits.
\( \mathbf{A} \cdot \therefore V \pm \Delta V=(2.7 \pm 0.14) m^{3} \)
B \( \ldots V \pm \Delta V=(5.4 \pm 0.14) m^{3} \)
\( \mathbf{c} \cdot \therefore V \pm \Delta V=(2.7 \pm 0.28) m^{3} \)
D. None of these


Looking at the Venn diagram list the
elements of the following sets:
\( \boldsymbol{B} \backslash \boldsymbol{C} \)


Show that \( \int \sqrt{4+8 x-5 x^{2}} d x= \)
\( \sqrt{5}\left[\frac{5 x-4}{10 \sqrt{(5)}} \sqrt{4+8 x-5 x^{2}}+\frac{18}{25} \sin ^{-1} 1\right. \)


RCH stands for
A. Routine check-up of health
B. Reproduction cum hygiene
C. Reversible contraceptive hazards
D. Reproductive and child health care


State whether the following statements
are true or false.
There are about seventy chemical forms of the hormone group called thegibberellins.
A. True
B. False


The IUPAC name of acryldehdye is:
A. Prop-2-en-1-al
B. Propenylaldehyde
c. But-2-en-1-al
D. Propenal


What happens when
An iron rod is placed in \( C u S O_{4} \)
solution?


is a better domestic fuel than
wood.
A. cNG
B. LPG
c. Petrol
D. All of above


If the roots of the equation \( \frac{1}{x+p}+ \) \( \frac{1}{x+q}=\frac{1}{r} \) are equal in magnitude and opposite in \( \operatorname{sign}, \) then This question has multiple correct options
A. \( p+q=r \)
в. \( p+q=2 r \)
c. product of roots \( =-\frac{1}{2}\left(p^{2}+q^{2}\right) \)
D. Sum of roots \( =1 \)


Check the continuity of the function \( \boldsymbol{f}(\boldsymbol{x})=|\boldsymbol{x}-\mathbf{2}|+\boldsymbol{x} \)


In the Bohr's model of hydrogen atom, the electron moves around the nucleus
in a circular orbit of-radius \( 5 \times 10^{-11} \)
meters. If its time period is \( 1.5 \times 10^{-16} \)
sec, then current associated with the
electron motion is
A. zero
B. \( 1.6 \times 10^{-19} A \)
c. 0.17 А
D. \( 1.07 \times 10^{-3} A \)


Prove that
\[
\frac{\sin \mathbf{A}+\sin 3 A+\sin 5 A+\sin 7 A}{\cos A+\cos 3 A+\cos 5 A+\cos 7 A}=
\]
\( \tan 4 A \)