Consider the following statements:
1. The general solution of \( \frac{d y}{d x}=f(x)+ \) \( x \) is of the form \( y=g(x)+c, \) where \( c \) is
an arbitrary constant.
2. The degree of \( \left(\frac{d y}{d x}\right)^{2}=f(x) \) is 2 Which of the above statements is/are
correct?
A. 1 only
B. 2 only
c. Both 1 and 2
D. Neither 1 nor 2


In the figure above, \( A C=6 \) and \( B C= \)
3. Point \( P(\text { not shown }) \) lies on \( A B \)
between \( A \) and \( B \) such that \( C P \perp A B \)
Which of the following could be the
length of \( C P ? \)
\( A \cdot 2 \)
B. 4
\( c .5 \)
D.
\( E \)


Magnetic field at point 'P'due to
following current distribution is
A \( \cdot \frac{\mu_{0} I}{\pi r^{2}} \sqrt{r^{2}-a^{2}} \)
В \( \cdot \frac{\mu_{0} i}{2 \pi a} \)
C \( \cdot \frac{\mu_{0} I}{2 \pi r^{2}} \sqrt{r^{2}-a^{2}} \)
D. \( \frac{\mu_{0} l a}{2 \pi r^{2}} \)


The value of \( \boldsymbol{f}^{\prime}(\boldsymbol{3}) \) is
\( A \cdot 8 \)
B. 10
c. 12
D. 18


Fossil of Cro-Magnon Man was found in
A. Shivalik-Hille - - India
B. Neander-Valley - Germany
c. Africa
D. France


Two identical circular loops PP.


Find the order of the matrix
\( \left[\begin{array}{ccc}1 & 1 & 3 \\ 5 & 2 & 6 \\ -2 & -1 & -3\end{array}\right] \)


\( P \) represents the variable complex
number \( z . \) Find the locus of \( P, \) if \( \operatorname{lm} \) \( \left[\frac{2 z+i}{i z-1}\right]=-1 \)


How is lightening beneficial to plants?
A. It brings rain,
B. It increases the amount of nitrates in the soil,
C. It increases the minerals in the soil,
D. It provides the chemical energy required by plants,


What are diamagnetic substances?


\( \frac{1}{16} \) part of a radioactive material is left after one hour. It's half life is ?
A. 45 min
B. 30 min
c. 20 min
D. 15 min


A stationary ball weighing \( 0.25 k g \) acquires a speed of \( 10 \mathrm{m} / \mathrm{s} \) when hit by a hockey stick. The impulse imparted to the ball is :
A. \( 0.25 \mathrm{N} \) s
B. 2.5 N s
c. \( 2.0 \mathrm{N} \) s
D. \( 0.5 \mathrm{N} \) s


A conducting straight wire \( P Q \) of length
is fixed along a diameter of a nonconducting ring as shown in the figure. The ring is given a pure rolling motion
on a horizontal surface such that its
centre of mass has a veleocity \( v \). There
exists a uniform horizontal magnetic field \( B \) in horizontal direction
perpendicular to the plane of ring. The magnitude of induced emf in the wire
\( P Q \) at the position shown in the figure
will be :
A. \( B v \)
в. 2 Ву
c. \( 3 B v l / 2 \)
D. zer


\( \left(3 a-\frac{1}{a}\right)^{3} \)


A constant force \( \boldsymbol{F}=(\hat{\boldsymbol{i}}+\boldsymbol{3} \hat{\boldsymbol{j}}+\boldsymbol{4} \hat{\boldsymbol{k}}) \boldsymbol{N} \)
acts on a particle and displace it from \( (-1 m, 2 m, 1 m) \) to \( (2 m,-3 m, 1 m) \)
Then the work done by the force is:
\( \mathbf{A} \cdot 12 J \)
в. \( -10 J \)
c. \( -12 J \)
D. \( 15 J \)


DDT stands for:
A. Difluorodiphenyltrichloroethane
B. Dibromodiphenyltrichloroethane
C. Dichlorodiphenyltrichloroethane
D. Dichlorodiethyltrichloroethane


The sales have increase by nearly \( 99.9 \% \)
from 2007 to 2010 in the case of?
A. Rexona
3. Dettol
\( c \cdot \operatorname{Lux} \)
\( D . \) Dove


On moving a charge of 20 coulombs by \( 2 \mathrm{cm}, 2 \mathrm{J} \) of work is done, then the potential difference between the points is:
A . \( 0.1 \mathrm{v} \)
B. 8
\( c \cdot 2 v \)
D. 0.5


Discuss the applicapibility of Rolle's Theorem to the function \( f(x)=x^{2 / 3} \) in
(-1,1)
A. Yes Rolle's theorem is applicable and the stationary point \( x=0 \)
B. Yes Rolle's theorem is applicable and the stationary point \( x=\frac{1}{2} \)
c. No Rolle's theorem is not applicable in the given interval
D. none of these


against their corresponding description given in 1,2,3,4 and 5
A. Astronomical telescope
B. Galilean Telescope
C. Simple Microscope
D. Compound Microscope
1. Contains one convex lens
2. Contains one concave lens
3. Contains a convex lens of large foca
length in the objective and a convex lens of small focal length in the eye-
piece
4. Contains a convex lens of small foca
length in the objective and a convex Iens of large focal length in the eye-
piece
5. Contains a convex lens of large focal
length in the objective and a concave lens of small focal length in the eyepiece.
\( \begin{array}{llll}\text { A. } 2 & 3 & 1 & 5\end{array} \)
\( \begin{array}{llll}\text { В. } 3 & 2 & 4 & 1\end{array} \)
\( \begin{array}{llll}\text { C } .2 & 5 & 3 & 4\end{array} \)
D. 4


Assume that each atom in a copper
wire contributes one free electron.
Estimate the number of free electrons
in a copper wire having a mass of \( 6.4 \mathrm{g} \)


In the system \( : \boldsymbol{F e}(\boldsymbol{O H})_{3(s)} \rightleftharpoons \boldsymbol{F e}_{(a q)}^{3+}+ \)
\( 3 O H_{(a q)}^{-}, \) decreasing the conc. of \( O H^{-} \) ions \( \frac{1}{3} \) times will cause the equilibrium
conc of \( F e^{3+} \) to increase
times.
\( A \cdot 3 \)
B. 9
c. 18
D. 27


If the solution of the differential
equation \( x \frac{d y}{d x}+y=x e^{x} \) be, \( x y= \)
\( e^{x} \varphi(x)+c \) then \( \varphi(x) \) is equal to:
A. \( x+1 \)
B. \( x-1 \)
c. \( 1-x \)
D.


Laspeyres Price Index \( =? \)
\begin{tabular}{|c|c|c|c|c|}
\hline \multirow{2}{*} { Items } & \multicolumn{2}{|c|} {2005} & \multicolumn{2}{|c|} {2010} \\
\cline { 2 - 5 } & \( \mathrm{P}_{0}(₹) \) & \( \mathrm{Q}_{0} \) & \( \mathrm{P}_{1}(₹) \) & \( \mathrm{Q}_{1} \) \\
\hline \( \mathrm{A} \) & 2 & 5 & 3 & 4 \\
\( \mathrm{B} \) & 1 & 2 & 2 & 3 \\
\( \mathrm{C} \) & 3 & 1 & 4 & 1 \\
\hline
\end{tabular}
A. 157.33
B. 153.14
\( \mathbf{c} \cdot 153.33 \)
D. 157.14


5 mol of liquid water is compressed
from 1 bar to 10 bar at constant
temperature. Change in Gibb's energy \( (\Delta G) \) in Joule is: (Density of water \( = \)
\( \left.1000 k g / m^{3}\right) \)
A . 18
B. 225
\( c \cdot 450 \)
D. 900


Find the slope of the line perpendicular
to the line joining the points (2,-3) and \( (\mathbf{1}, \mathbf{4}) \)


Polypropylene can be obtained by polymerisation of :
A \( \cdot C H_{2}=C H-C H_{3} \)
в. \( C H_{2}=C H_{2} \)
\( \mathrm{c} \cdot \mathrm{CH}_{4} \)
D. \( C H_{3}-C H_{3} \)


Soaps are and
salts of certain
acids.
A. potassium and calcium
B. sodium and calcium
c. sodium and potassium
D. calcium and magnesium


Evaluate \( : \int \frac{e^{2 x}-1}{e^{2 x}+1} d x \)


Mass of an atom expressed in grams is known as:
A. atomic mass
B. gram atomic mass
c. molecular mass
D. None of the above


Using vectors, find the value of \( \lambda \) such
that the points \( (\boldsymbol{\lambda},-\mathbf{1 0}, \mathbf{3}),(\mathbf{1},-\mathbf{1}, \mathbf{3}) \)
and (3,5,3) are collinear.


Zone-refining has been employed for preparing ultra-pure samples of:
A. cu
B. zn
c. Ge
D. Agg


The scientist who coined the term
protista' to include both plant and animal like unicellular organism was
A. Robert Koch
B. E.F. Haeckel
c. L. Pasteur
D. Joseph Lister


Name the ion(s) obtained when \( H C l \)
dissociates in aqueous solution.
A. \( H_{3} O^{+} \)
в. \( C l \)
c. Both \( A \) and \( B \)
D. None of these


The most negative oxidation state of an atom of group 15 (VA) element is equal to the number of electrons required to fill the valence shell of the neutral
atom. If true enter 1 ,if false enter 0


\( \lim _{n \rightarrow \infty} \sum_{r=1}^{n} \frac{1}{\sqrt{4 n^{2}-r^{2}}}= \)
A \( \cdot \frac{\pi}{2} \)
в.
c.
D. \( \frac{\pi}{5} \)


If \( 1.3+2.3^{2}+3.3^{3}+\ldots+n .3^{n}= \)
\( \frac{(2 n-1) 3^{a}+b}{4} \) then \( a \) and \( b \) are respectively
A \( . n, 2 \)
в. \( n, 3 \)
c. \( n+1,2 \)
D. \( n+1,3 \)


The electrophilic aromatic substitution
of a compound \( C_{6} H_{5} Y \) produces
mainly a meta -disubstituted product. Among the following which one could be the substituent Y?
\( \mathbf{A} \cdot-N H_{2} \)
в. \( -C O O H \)
\( \mathrm{c} \cdot-C H_{3} \)
D. \( -O C H_{3} \)


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


\( f e^{i \theta}=\cos \theta+i \sin \theta, \) find the value of
\( -\left|\begin{array}{ccc}\mathbf{1} & \boldsymbol{e}^{i \boldsymbol{\pi} / \mathbf{3}} & \boldsymbol{e}^{i \boldsymbol{\pi} / \mathbf{4}} \\ \boldsymbol{e}^{-i \boldsymbol{\pi} / \mathbf{3}} & \mathbf{1} & \boldsymbol{e}^{\boldsymbol{i} \mathbf{2} \boldsymbol{\pi} / \mathbf{3}} \\ \boldsymbol{e}^{-\boldsymbol{i} \boldsymbol{\pi} / \mathbf{4}} & \boldsymbol{e}^{-\boldsymbol{i} \mathbf{2} \boldsymbol{\pi} / \mathbf{3}} & \mathbf{1}\end{array}\right|-\mathbf{2}^{\frac{1}{2}} \)


The displacement \( y \) of a particle in a medium can be expressed asy \( = \) \( \mathbf{1 0}^{-6} \sin \left(\mathbf{1 1 0 t}+\mathbf{2 0 x}+\frac{\boldsymbol{\pi}}{\mathbf{4}}\right) \mathbf{m}, \) where \( \mathbf{t} \) is
in second and \( x \) in metre. The speed of
the wave is
A \( .2000 \mathrm{m} / \mathrm{s} \)
B. \( 5 \mathrm{m} / \mathrm{s} \)
c. \( 20 \mathrm{m} / \mathrm{s} \)
D. \( 5 \pi \mathrm{m} / \mathrm{s} \)


Which of the following is the correct electronic configuration of potassium?
A .2,8,9
B. 8,2,9
c. 2,8,8,1
D. 1, 2,8, 8


Give reasons for the following Opening of auricles into ventricles are puarded by valves.


Determine the domain and range of the following relations. \( \boldsymbol{S}=\{(\boldsymbol{a}, \boldsymbol{b}): \boldsymbol{b}=|\boldsymbol{a}-\mathbf{1}|, \boldsymbol{a} \in \boldsymbol{Z} \) and
\( |a| \leq 3\} \)


Out of first 100 elements no.of elements
having electrons in \( 3 d \) orbital (in their complete electronic configuration) are:-
A . 80
в. 100
c. 40
D. 60


Find out the total number of products
(including stereoisomers) in the given
reaction:


In a reversible reaction, the enthalpy change and the activation energy in the forward direction are respectively \( -\boldsymbol{x} \boldsymbol{k} \boldsymbol{J} \boldsymbol{m o l}^{-1} \) and \( \boldsymbol{y} \boldsymbol{k} \boldsymbol{J} \boldsymbol{m o l}^{-1} \)
Therefore, the energy of activation in the
backward direction, in \( k J \) mol \( ^{-1} \) is:
A \( \cdot(y-x) \)
в. \( (x+y) \)
c. \( (x-y) \)
D. \( -(x+y) \)


What is the angle between \( \vec{P} \) and the resultant of \( (\vec{P}+\vec{Q}) \) and \( (\vec{P}-\vec{Q}) ? \)
A. zero
в. \( \tan ^{-1} \frac{P}{Q} \)
c. \( \tan ^{-1} \frac{Q}{P} \)
D. \( \tan ^{-1}\left(\frac{P-Q}{P+Q}\right) \)


Fill in the blank:
The uppermost layer of the Earth is called
A. mantle
B. outer core
c. crust
D. none of the above


Which of the following polymer is formed by cationic addition polymerisation reaction?
A. ButyI rubber
B. Poly styrene
c. Teflon
D. PVC


A bulb of \( 40 \mathrm{W} \) is producing a light of wavelength \( 620 \mathrm{nm} \) with \( 80 \% \) of efficiency, then the number of photons emitted by the bulb in 20 seconds are \( \left.\mathbf{1} e \boldsymbol{V}=\mathbf{1 . 6} \times \mathbf{1 0}^{-\mathbf{1 9}} \mathbf{J}, \boldsymbol{h} \boldsymbol{c}=\mathbf{1 2 4 0 0} e \boldsymbol{V}\right) \)
\( \mathbf{A} \cdot 2 \times 10^{18} \)
B . \( 10^{18} \)
c. \( 10^{21} \)
D. \( 2 \times 10^{11} \)


A ring of radius \( R \) rolls without sliding with a constant velocity with respect to ground. The radius of curvature of the path followed by any particle of the ring at the highest point of its path will be
A. \( R \)
в. \( 2 R \)
\( c .4 R \)
D. None


Choose the correct combination of
labelling of stomatal apparatus of dicot
and monocot leaves.
A. A-epidermal cells, B-subsidiary cells, C-chloroplast, D-guard cells, E-stomatal aperture
B. A-epidermal cells, B-guard cells, C-chloroplast, Dsubsidiary cells, E-stomatal aperture
C. A-epidermal cells, B-subsidiary cells, C-chloroplast,
D-stomatal cells, E-guard cells
D. A-subsidiary cells, B-epidermal cells, C-chloroplast,
D-stomatal aperture, E-guard cells
E. A-guard cells, B-epidermal cells, C-stomatal aperture, D-subsidiary cells, E-chloroplast


Which of the following molecules/species have identical bond order and same magnetic properties?
(I) \( \boldsymbol{O}_{2}(\|) \boldsymbol{N} \boldsymbol{O}(\| \text { I }) \boldsymbol{N}_{2}^{+} \)
\( A \cdot(1),(11) \) only
B. (I) and (III) only
c. (I), (II) and (III)
D. (II) and (III) only


Agonist can mimic natural chemical
messengers If this is true enter 1 , if false enter 0 .


When a body starts to roll on an inclined plane, its potential energy is converted into
A. Translation kinetic energy only
B. Translation and rotational kinetic energy
C. Rotational energy only
D. None of these


STATEMENT-1: Dumas method is more
applicable to nitrogen containing
organic compounds than Kjeldahl's
method.
STATEMENT-2:Kjeldahl's method does
not give satisfactory results for compounds in which nitrogen is linked
to oxygen.
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


What is the aim of water harvesting?


The pendulum bob has a speed of \( 3 \mathrm{m} / \mathrm{s} \)
at its lowest position. The pendulum is \( 0.5 \mathrm{m} \) long. The speed of the bob, when
the bob makes an angle of \( 60^{\circ} \) to the vertical will be \( \left(\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2}\right) \)
\( A \cdot 1 \mathrm{m} / \mathrm{s} \)
B. \( 1.5 \mathrm{m} / \mathrm{s} \)
\( c \cdot 3 m / s \)
D. \( 2 \mathrm{m} / \mathrm{s} \)


In order to convert aniline to
chlorobenzene, the reagent(s) needed is/are:
A. \( C u C l \)
в. \( \operatorname{NaNO}_{2} / \mathrm{HCl} \) and \( \mathrm{Cu}_{2} \mathrm{Cl}_{2} \)
c. \( C l_{2} / C C l_{4} \)
D. \( C l_{2} / A l C l_{3} \)


In the reaction, \( \boldsymbol{N} \boldsymbol{H}_{3}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{I})= \)
\( N H_{4}^{+}+O H^{-} \) the water is a
A. bronsted acid
B. bronsted base
c. conjugate acid
D. conjugate base


Assertion
Sound shadows are generally not so well defined as those of light.
Reason
The wavelength of sound waves are very large in comparison to that of light
waves.
A. Statement 1 is True and Statement 2 is True and is correct explanation of statement 1
B. Statement 1 is True and Statement 2 is True but not correct explanation for Statement
c. Statement 1 is True and Statement 2 is False.
D. Statement 1 is False and Statement 2 is True


A ball of radius \( R \) and with bulk
modulus of elasticity \( K \) is kept in a liquid inside a cylindrical container. It is pressed by putting a mass \( \mathrm{m} \) on a massless piston of cross-sectional area
A, then the fractional decrease in the
radius of ball will be
A \( \cdot \frac{M g}{3 K R} \)
в. \( \frac{M g}{3 K A} \)
c. \( \frac{M g}{K A} \)
D. \( \frac{M g K}{3 A R} \)


For all values of \( x, \) the values of \( 3- \) \( \cos x+\cos \left(x+\frac{\pi}{3}\right) \) lie in the interval
A \( .[-2,3] \)
B. [-2,1]
c. [2,4]
D. [1,5]


Which of the following is the chemical formula for washing soda?
A. \( C a O \)
в. \( N a_{2} C O_{3} \)
c. \( N H_{2} C l \)
D. \( M g C l_{2} \)


Which one of the following cannot form an amphoteric oxide?
A . \( A l \)
в. \( S n \)
\( c \cdot S b \)
D. \( P \)


Write down the co-ordinates of the points
\( A \) to \( J \) marked in the following diagram:


Evaluate:
\( \int \frac{x}{\sqrt{\left(1-x^{2}\right)} \cos ^{2} \sqrt{\left(1-x^{2}\right)}} d x \)
A \( \cdot \tan \sqrt{1-x^{2}} \)
\( \mathbf{B} \cdot-\tan \sqrt{1-x^{2}} \)
c. \( -\tan \left(1-x^{2}\right) \)
D. \( -\sec ^{2} \sqrt{1-x^{2}} \)


If a reaction gets completed in finite time then its order can be :
\( A \cdot 3 \)
B. 2
\( c \)
D. zero


Acidophils of pituitary secrete
A. STH and FSH
B. STH and PL
c. stH and Tsh
D. STH and GTH


Find the angle between the lines
represented by \( 3 x^{2}+4 x y-3 y^{2}=0 \)


The value of \( \cos ^{2} 30^{0}-\cos ^{2} 60^{0}- \)
\( \cos 60^{0} \) is
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( \frac{1}{2} \)
\( c \cdot \frac{3}{4} \)
D.


Which of the following exhibit simple harmonic motion?
I. A pendulum
II. A mass attached to a spring
III. A ball bouncing up and down, in the absence of friction
A. I only
B. II only
c. ॥ only
D. I and II only
E . ।, ॥।, and III


Which of the following plants has high water retention capacity and is used to provide moisture to plants?
A. Sphagnum
B. Botrychium
c. Marsilea
D. Marchantia


Electronic configuration of Gd(64) is
written as: \( [\boldsymbol{X} \boldsymbol{e}]_{54} \boldsymbol{4} \boldsymbol{f}^{x} \boldsymbol{5} \boldsymbol{d}^{1} \boldsymbol{6} \boldsymbol{s}^{2}, \) then
the value of \( x \) is \( 7 . \) If true enter 1 , else
enter 0


Show that it is not possible for a photon to be completely absorbed by a free
electron.


Write four difference between
heterogeneous and homogeneous
mixtures.


The internal resistance of a primary cell
is 4 \Omega. It generates a current of \( 0.2 \mathrm{A} \) in
an external resistance of \( 21 \Omega \). The rate
of chemical energy consumed in providing the current is
A \( \cdot 0.42 \mathrm{J} \mathrm{s}^{-} 1 \)
B. 0.84 J \( s^{-1} \)
c. \( 1 J s^{-1} \)
D. 5 J \( s^{-1} \)


Write down the characteristics of the
elements having atomic number 17 Electronic configuration
Period number
Group number
Element family
No. of valence electrons
Valency
Metal or non-metal


Oleum on hydrolysis gives sulphuric
acid.
A . True
B. False


if \( \alpha \) and \( \beta \) are angles in the first quadrant, \( \tan \alpha=\frac{1}{7}, \sin \beta=\frac{1}{\sqrt{10}}, \) then
using the formula \( \sin (A+B)= \)
\( \sin A \cos B+\cos A \sin B, \) one can find
the value of \( (\boldsymbol{\alpha}+\mathbf{2} \boldsymbol{\beta}) \) to be
\( A \cdot 0^{\circ} \)
B. 45
\( c \cdot 60 \)
\( D \cdot 90^{\circ} \)


Stephen's reduction is used to prepare
aldehyde from :
A. Alcohol
B. Alkyl cyanide
c. Alkanone
D. Acid chloride


Due to the presence of nambidentate ligands coordination compounds show isomerism. Palladium complexes of the
type \( \left[\boldsymbol{P} \boldsymbol{d}\left(\boldsymbol{C}_{6} \boldsymbol{H}_{5}\right)_{2}\left(\boldsymbol{N} \boldsymbol{O}_{2}\right)_{2}\right] \) and
\( \left[\boldsymbol{P d}\left(\boldsymbol{C}_{6} \boldsymbol{H}_{5}\right)_{2}(\boldsymbol{O} \boldsymbol{N} \boldsymbol{O})_{2}\right] \) are?
A. Linkage isomers
B. Coordination isomers
c. lonisation isomers
D. Geometrical isomers


Measure of the opposition to the flow the free electron is known as
A. current
B. Resistance
c. conductance
D. Capacitance


What is the oxidising agent in the following reaction? \( \mathbf{2} \boldsymbol{F} \boldsymbol{e}_{\boldsymbol{a} \boldsymbol{q}}^{\mathbf{2}+}+\boldsymbol{C l}_{\mathbf{2}(\boldsymbol{g})} \rightarrow \mathbf{2} \boldsymbol{F} \boldsymbol{e}_{(\boldsymbol{a q})}^{\mathbf{3}+}+\mathbf{2} \boldsymbol{C l}_{(\boldsymbol{a} \boldsymbol{q})}^{-} \)
A \( \cdot F e^{2} \)
в. \( C l_{2} \)
\( \mathrm{c} \cdot F e^{3} \)
D. \( C l^{-} \)


Acetone can not be obtained from:
A. hydrolysis of isopropylidene chloride
B. hydration of propyne
C. dehydrogenation of isopropyl alcohol
D. hydrolysis of ester


Study the given reaction and identify the process which is carried out.
\[
\left.\rangle \mathrm{c}=\mathrm{O}+\mathrm{NaHSO}_{3} \rightarrow \lambda_{\mathrm{SO}_{3} \mathrm{Na}}^{/ \mathrm{OH}} \frac{\mathrm{Na}_{2} \mathrm{CO}_{3}}{\rightarrow}\right\rangle \mathrm{C}=0
\]
A. It is used for purification of aldehydes and ketones
B. It is used to distinguish aldehydes from ketones
c. It is used to prepare cyclic aldehydes and ketones
D. It is used to study polar nature of aldehydes and ketones


Which of the following is a living fossil?
A . Pinus
B. Ginkgo biloba
c. Thuja
D. Deodar


For a unimolecular reaction:
A. The order and molecularity of the slowest step are equal to one
B. Molecularity of the reaction can be zero, one or two
C. More than one reacting species are involved in one step
D. Molecularity of the reaction can be determined only experimentally


Sound requires a medium to travel
A. True
B. False


The reaction of \( K M n O_{4} \) and \( \mathrm{HCl} \)
results in
A. Oxidation of \( \mathrm{Mn} \) in \( \mathrm{KMnO}_{4} \) and production of \( \mathrm{Cl}_{2} \)
B. Reduction of Mn in \( K M n O_{4} \) and production of \( H_{2} \)
C. Oxidation of \( \mathrm{Mn} \) in \( \mathrm{KMnO}_{4} \) and production of \( \mathrm{H}_{2} \)
D. Reduction of Mn in \( K M n O_{4} \) and production of \( C l_{2} \)


The equivalent resistance between \( A \) and B in the network in
A \( \cdot \frac{4}{3} \Omega \)
B . \( \frac{3}{2} \Omega \)
\( c .3 \Omega \)
D. \( 2 \Omega \)


The current in the rod is \( \left(\boldsymbol{I}_{o}=\frac{V_{o}}{R_{o}}\right) \)
A \( \cdot I_{o} e^{x / L} \)
В . \( \frac{I_{0}}{L}(L-X) \)
c. \( I_{o} e^{-x / L} / L \)
D \( \cdot \frac{I_{0}}{L}(L+X) \)


A uniform metre rule of weight \( 10 g f \) is
pivoted at its 0 mark. What moment of force depresses the rule?
\( A .5 g f c m \)
в. \( 10 g f \) ст
c. \( 100 g f \mathrm{cm} \)
D. \( 500 g f \mathrm{cm} \)


In general, the number of electrons in
the outermost shell of a metal atom is:
\( \mathbf{A} \cdot \mathbf{1} \)
B. 1-3
\( c \cdot 1-8 \)
\( D \)


What is disadvantage of building large dams?
A. Natural ecosystem in the surrounding forest areas get disturbed
B. Plants and animals' life get disrupted
C. People are displaced on a large scale.
D. All of the above.


The molal elevation constant is the ratio
of the elevation in boiling point to:
A. molarity
B. molality
c. mole fraction of solute
D. mole fraction of solvent


Find a quadratic equation with real coefficient whose one root is \( 3-2 i \)


If \( N a^{+} \) ion is larger than \( M g^{2+} \) ion, and
\( S^{2-} \) ion is larger than \( C l^{-} \) ion, which of the following will be less soluble in water?
A. \( N a C l \)
B. \( N a_{2} S \)
c. \( M g C l_{2} \)
D. \( M g S \)


State whether the given statement is
true or false :

Gravity and friction are both contact forces.
A. True
B. False


Which is wrong according to kinetic
theory of gases?
A. Average \( K E \) of molecules is proportional to the absolute temperature
B. Collisions between molecules are perfectly elastic
C. Pressure is due to collisions between molecules
D. There are no attractive forces between the molecules of gas


Name the rays or waves of wavelength
nearly \( 0.1 n m \)
A . IR rays
B. UV rays
c. Gamma rays
D. x-rays


For \( \boldsymbol{A} \rightarrow \boldsymbol{B}, \boldsymbol{\Delta} \boldsymbol{H}=\boldsymbol{4} \boldsymbol{k} c a l \boldsymbol{m} \boldsymbol{o} \boldsymbol{l}^{-1}, \boldsymbol{\Delta} \boldsymbol{S}= \)
\( 10 c a l m o l^{-1} k^{-1} \) is spontaneous when
temperature can be:
\( \mathbf{A} \cdot 400 K \)
B. \( 300 K \)
\( \mathbf{c} .500 K \)
D. \( 200 K \)


The given structure represents bondline formula of Heptan-4-one. Is it True or False.
A. True
B. False


In the figure, \( \angle \boldsymbol{E} \boldsymbol{F B}=\mathbf{6 6}^{\circ}, \angle \boldsymbol{B F O}= \)
\( 43^{\circ}, \angle O G F=23^{\circ}, \angle O G D=y . \) Find
the value of \( y \)


Charges \( 5 \mu \mathrm{C} \) and \( 10 \mu \mathrm{C} \) are placed \( 1 \mathrm{m} \)
a part. Workdone to bring these charges
at a distance \( 0.5 \mathrm{m} \) from each other is
\( \left(k=9 \times 10^{9} S I\right) \)
\( \mathbf{A} \cdot 9 \times 10^{4} J \)
B . \( 18 \times 10^{4} J \)
c. \( 45 \times 10^{2} J \)
D. \( 9 \times 10^{-1} J \)


The area bounded by \( y^{2}=4 x \) and \( x^{2}= \)
\( 4 y \) is
A \( -\frac{20}{3} \) sq. units
B. \( \frac{16}{3} \) sq. units
\( ^{\mathrm{c}} \cdot \frac{14}{3} \mathrm{sq} . \) units
D. \( \frac{10}{3} \) sq. units


(a) Write Fleming's left-hand rule for the direction of force on a current carrying conductor placed in a magnetic field.
(b) Draw a diagram to show lines of magnetic field inside and around a current carrying solenoid.
(c) Write the names of four devices
where current carrying conductor is used along with magnetic fields


Name one element, one compound and
one mixture.


The compound which does not possess a peroxide linkage is:
A. \( N a_{2} O_{2} \)
в. \( C r O_{5} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{SO}_{5} \)
D. \( P b O_{2} \)


In double strand helix structure of DNA,
heterocyclic base cytosine forms hydrogen bond with:
A. adenine
B. guanine
c. purine
D. thymine
E. uraci


For the function \( f(x)=e^{\cos x}, \) Rolle's
theorem is
A \( \cdot \) applicable, when \( \frac{\pi}{2} \leq x \leq \frac{3 \pi}{2} \)
B. applicable, when \( 0 \leq x \leq \frac{\pi}{2} \)
C . applicable, when \( 0 \leq x \leq \pi \)
D. applicable, when \( \frac{\pi}{4} \leq x \leq \frac{\pi}{2} \)


Evaluate:
\( \frac{1}{(216)^{\frac{-2}{3}}} \div \frac{1}{(27)^{\frac{-4}{3}}} \) is equal to \( \frac{4}{m} \)
value of \( m \) is


The EMF of the cell
\( Z n\left|Z n^{2+}(0.01 M) \| F e^{2+}(0.001 M)\right| F e \) at
\( 298 K \) is 0.2905 then the value of
equilibrium constant for the cell reaction
is :
B. \( 10^{\frac{1.33}{35}} \)
\( \mathbf{c} \cdot 10 \frac{0.25}{15} \)
D. \( 10^{\frac{0.32}{0.539}} \)


Which of the following elements is placed just after actinide series? This question has multiple correct options
A. Rutherfordium
B. Unnilpentium
c. Unnilquadium
D. Ununbium


Materials that allow electrons to flow
through them are known as
A. Insulator
B. Conductors
c. Electrolytes
D. Bases


Convert into fraction :-
\( 10 \% \)


The ratio of magnetic moments of \( \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{3}+} \)
\( \& C o^{3+} \) is:
B. \( \sqrt{35}: \sqrt{24} \)
\( c \cdot 7: 3 \)
D. \( \sqrt{24}: \sqrt{15} \)


If the ordered pairs \( (x,-1) \) and \( (5, y) \)
belong to the set \( (a, b): b=2 a-3, \) find the values of \( x \) and \( y ? \)


Which one of the following ions has
electronic configuration \( [\mathrm{Ar}] 3 \mathrm{d}^{6} ? \)
\( A \cdot N i^{3} \)
B. \( \mathrm{Mn}^{3+} \)
\( \mathbf{c} \cdot \mathrm{Fe}^{3} \)
\( D \cdot c_{0}^{3} \)


The stages in proper sequence of
prophase I are
A. Diplotene \( \rightarrow \) diakinesis \( \rightarrow \) pachytene \( \rightarrow \) zygotene \( \rightarrow \) leptotene
B. Leptotene \( \rightarrow \) zygotene \( \rightarrow \) pachytene \( \rightarrow \) diplotene \( \rightarrow \) diakinesis
C. Leptotene \( \rightarrow \) pachytene \( \rightarrow \) zygotene \( \rightarrow \) diakinesis \( \rightarrow \) diplotene
D. Zygotene \( \rightarrow \) leptotene \( \rightarrow \) pachytene \( \rightarrow \) diakinesis \( \rightarrow \) diplotene


The acidity of the compounds
\( \boldsymbol{R} \boldsymbol{C O O H}, \boldsymbol{H}_{2} \boldsymbol{C O}_{3}, \boldsymbol{C}_{6} \boldsymbol{H}_{5} \boldsymbol{O H}, \boldsymbol{R O H} \)
decreases in the order:
A \( \cdot R C O O H>H_{2} C O_{3}>C_{6} H_{5} O H>R O H \)
в. \( C_{6} H_{5} \)ОН\( > \)RСООН\( >H_{2} \)СО\( _{3}> \)ВОН
c. \( R O H>C_{6} H_{5} O H>R C O O H>H_{2} C O_{3} \)
D. \( H_{2} C O_{3}>R C O O H>C_{6} H_{5} O H>R O H \)


Find the order and the degree of the
differential equation:
\( \left[1+\left(\frac{d y}{d x}\right)^{2}\right]^{\frac{3}{2}}=5 \frac{d^{2} y}{d x^{2}} \)


Which forms an equal number of moles
of ions, when one mole of it is dissolved
in excess of water?
A. Ferrous ammonium sulphate, Carnallite
B. Carnallite, Alum
c. Alum, Potassium ferrocyanide
D. Potassium ferrocyanide, Potassium ferricyanide


Structure of propanone is:
A \( \cdot C H_{3}-C H_{2}-C H_{3} \)
в. \( C H_{3}-C-O H \)
॥
О
c. \( C H_{3}-O-C_{3} H_{7} \)
D. \( C H_{3}-C-C H_{3} \)
I
O
E \( \cdot C H_{3}-C H_{2}-N H_{2} \)


Find the image of (1,5,1) in the plane
\( \boldsymbol{x}-\mathbf{2} \boldsymbol{y}+\boldsymbol{z}+\mathbf{5}=\mathbf{0} \)


If the radius of the sphere is increased by \( 100 \% \), the volume of the
corresponding sphere is increased by-
\( \mathbf{A} \cdot 200 \% \)
B. \( 500 \% \)
c. \( 700 \% \)
D. \( 800 \% \)


The approximate percentage of silica in cement is :
A . 5-10\%
B. 15-20\%
c. 17-25\%
D. 25-30\%


toppr
Q Type your question
circuited and the current i is measured.
Which of the following graphs give
correct relationship between i and n?
\( A \)
\( B \)
\( c \)
\( D \)


Particles move randomly in
A. nitrogen
B. sugar
\( c . \) ice
D. water


A \( 90 \mathrm{cm} \) long barometer tube contains some air above the mercury. The reading is \( 74.5 \mathrm{cm} \) when the true pressure is \( 76 \mathrm{cm} \) at the temperature \( 15^{0} C . \) If the reading is observed to be \( 75.8 \mathrm{cm} \) on a day when the temperature
is \( 5^{0} C \), then the true pressure is:
A. \( 77.38 \mathrm{cm} \) of \( \mathrm{Hg} \)
B. 75.8 cm of Hg
c. \( 74 \mathrm{cm} \) of \( \mathrm{Hg} \)
D. \( 80 \mathrm{cm} \) of \( \mathrm{Hg} \)


A real image, equal in size to the object, is obtained when the object is placed at the centre of curvature in front of a:
A. Concave mirror
B. Plane mirror
c. Convex mirror
D. None of these


Normal force is a
A. Action force
B. Reaction force
c. Both
D. None


Circulation of blood was discovered by and father of blood circulation is
A. William Harvey
B. Karl Landsteiner
c. watson and crick
D. Bose


When a ray of light passes from an optically less dense medium to a more
dense medium, it :
A. goes undeviated
B. bends towards the normal
c. bends away from the normal
D. none of these


A rectangular parallelopiped is formed by drawing planes through the points (-1,2,5) and (1,-1,-1) and paralle to the coordinate planes. the length of the diagonal of the parallelopiped is
\( A \cdot 2 \)
B. 3
c. 6
D.


The reagent(s) required for the following
conversion is:
A \( \cdot\left(\text { i) } N a B H_{4} \text { (ii) Raney } N i / H_{2} \text { (iii) } H_{3} O^{+}\right. \)
B \( \cdot\left(\text { i) } B_{2} H_{6} \text { (ii) } \operatorname{SnCl}_{2} / H C l \text { (iii) } H_{3} O^{+}\right. \)
C . (i) \( \operatorname{LiAlH}_{4} \) (ii) \( H_{3} O^{+} \)
\( \mathbf{D} \cdot(\mathbf{i}) B_{2} H_{6} \)
(ii) DIBAL-H (iii) \( H_{3} O^{+} \)


When current is passed through calculated water, the Hydrogen and
Oxygen separates. The hydrogen gets accumulated on the negative electrode. Why does it not deposit on positive electrode?
A. Hydrogen is positive charge
B. Hydrogen is negatively charged
c. That is because, it is the characteristic of acidulated
water
D. None of the above


If \( E^{o} \) denotes reduction potential, then
which is true?
\( \mathbf{A} \cdot E_{c e l l}^{0}=E_{r i g h t}^{o}-E_{l e f t}^{o} \)
B \( \cdot E_{\text {cell }}^{0}=E_{\text {left }}^{o}+E_{\text {right }}^{o} \)
\( \mathbf{c} \cdot E_{c e l l}^{0}=E_{l e f t}^{o}-E_{r i g h t}^{o} \)
D. \( E_{c e l l}^{0}=-\left(E_{l e f t}^{o}+E_{r i g h t}^{o}\right) \)


Evaluate: \( \lim _{x \rightarrow 0} \frac{6^{x}-1}{\sqrt{3-x}-\sqrt{3}} \)


Which of the following Benzene rings contain o-p directing groups?


A balloon gets negatively charged by rubbing ceilings of a wall.
A. The balloon sticks to the ceiling forever.
B. The balloon eventually fall off the ceiling
C. The balloon does not stick to the ceiling at all
D. The balloon charges the ceiling negatively


A solid body is heated upto very high temperature As we go on heating its brightness increases and it appears
white at the end The sequence of the
colour observed as the temperature of the body increases will be-
A. Yellow, green, red, white
B. Green, yellow, red, white
c. Red, green, yellow, white
D. Red, yellow, green, white


Suggest measures in the following
situations:
Bursting fire crackers in festivals and processions.


A flywheel of moment of inertia
\( 0.4 K g / m^{2} \) and radius \( 0.2 m \) is free to
rotate about a central axis. If a string is wrapped around it and it is pulled with a force of \( 10 N \) then its angular velocity
after \( 4 s \) will be
A. \( 5 r a d / s \)
в. 20rad/s
c. \( 10 r a d / s \)
D. \( 0.8 \mathrm{rad} / \mathrm{s} \)


A girl brings a positively charged rod
near a thin neutral stream of water from
a tap. She observes that the water
stream bends towards her. Instead, if
she were to bring a negatively charged rod near to the stream, it will :
A. Bend in the same direction
B. Bend in the opposite direction
c. Not bend at all
D. Bend in the opposite direction above and below the rod


A man, of mass \( m \), standing at the bottom of the staircase, of height \( \boldsymbol{L} \)
climbs it and stands at its top.
This question has multiple correct options
A. Work done by all forces on man is equal to the rise in potential energy mgL
B. Work done by all forces on man is zero
c. work done by the gravitational force on man is mgL
D. The reaction force from a step does not do work because the point of application of the force does not move while the force exists


Neutron is not present in the nucleus of:
A . helium
B. protium
c. tritium
D. lithium


If the equation \( k x^{2}+4 x+1=0 \) has
real and distinct roots, then:
\( \mathbf{A} \cdot k<4 \)
B. \( k>4 \)
\( \mathbf{c} \cdot k \leqslant 4 \)
D. \( k \geqslant 4 \)


Coal can be used as a:
A. purifier
B. fuel
c. insecticide
D. fertilizer


The angle of the dip at a place is \( 40.6^{\circ} \) and
the vertical component of the earths
magnetic field \( B_{V}=6 \times 10^{-5} T . \) The total
intensity of the earth's magnetic field at this place is:
\( \mathbf{A} \cdot 7 \times 10^{-5} \mathbf{T} \)
В. \( 6 \times 10^{-5} \mathrm{T} \)
c. \( 5 \times 10^{-5} \mathrm{T} \)
D. \( 9.2 \times 10^{-5} \mathrm{T} \)


Describe the following:
Layer test for bromine and iodine in an
organic compound.


Write down four differences between
interference and diffraction.


The number of moles of \( \boldsymbol{H}_{2} \) in \( \mathbf{0 . 2 2 4} \) Lof
hydrogen at STP is:
\( \mathbf{A} \cdot \mathbf{1} \)
B. 0.1
c. 0.01
D. 0.001


Find the Standard Deviation of the
following data:
\( \mathbf{5}, \mathbf{9}, \mathbf{8}, \mathbf{1 2}, \mathbf{6}, \mathbf{1 0}, \mathbf{6}, \mathbf{8} \)
A . 2.14
B . 2.16
c. 2.15
D. 2.17


Ellingham diagram in the extraction of
zinc.


Radical leaves are found in
A. Radish
B. Wheat
c. Maize
D. Mustard


How it is helpful to locate submarines of enemies through SONAR?
A. It produces ultrasound in water
B. It produces infrasonic in water
c. It produces ultrasound and infrasound in water
D. None


Two open pipes of length \( 50 \mathrm{cm} \) and 51
cm produce 6 beats when sounded together, find the speed of sound:
A \( \cdot 330 m s^{-1} \)
B. \( 316 \mathrm{ms}^{-1} \)
c. \( 306 m s^{-1} \)
D. \( 360 \mathrm{ms}^{-1} \)


Razia conducted an experiment in the
field related to the rate of percolation. She observed that it took 40 min for 200
mL of water to percolate through the soil sample. Calculate the rate of
percolation.


In the process of extraction of gold, Roastedgoldore \( +C N^{-}+H_{2} O \stackrel{O_{2}}{\rightarrow} \)
\( [X]+O H^{-}[X]+Z n \rightarrow[Y]+A u \)
Identify the complexes [X] and [Y]
A \( \cdot x=\left[A u(C N)_{2}^{-}\right], Y=\left[Z n(C N)_{4}\right]^{2} \)
B . \( x=\left[A u(C N)_{4}\right]^{3-}, Y=\left[Z n(C N)_{4}\right]^{2-} \)
C \( \cdot x=\left[\operatorname{Zn}(C N)_{2}\right]^{-}, \mathrm{Y}=\left[\operatorname{Zn}(C N)_{6}\right]^{4-} \)
D. \( x=\left[Z n(C N)_{4}\right]^{-}, Y=\left[Z n(C N)_{4}\right]^{2-} \)


Two events \( A \) and \( B \) are such that
\( P(A)=\frac{1}{4}, P(B)=\frac{1}{2} \) and \( P(B \mid A)=\frac{1}{2} \)
Consider the following statements
\( (I) P(\bar{A} \mid \bar{B})=\frac{3}{4} \)
\( (I I) A \) and \( B \) are mutually exclusive
\( (I I I) P(\bar{A} \mid \bar{B})+P(A \mid \bar{B})=1 \)
Then
A. Only I is correct
B. Only I and II are correct
c. only \( I \) and \( I I I \) are correct
D. only II and III are correct


Let \( X \) and \( Y \) be two random variables.
The relationship \( \boldsymbol{E}(\boldsymbol{X} \boldsymbol{Y})=\boldsymbol{E}(\boldsymbol{x}) \cdot(\boldsymbol{Y}) \)
holds.
A. Always
B. If \( E(X+Y)=E(X)+E(Y) \) is true
c. If \( X \) and \( Y \) are independent
D. If \( X \) can be obtained from \( Y \) by a linear transformation


When a natural number \( x \) is divided by
\( 5, \) the remainder is \( 2 . \) When a natural number y is divided by 5, the remainder is \( 4 . \) The remainder is \( z \) when \( x+y \) is divided by 5. The value of \( \frac{2 z-5}{3} \) is
A . -
в.
\( c \cdot-2 \)
D.


Explain the differences between emission and absorption spectra.


An electron in a hydrogen atom makes a
transition from \( n=n_{1} \) to \( n=n_{2} . \) The
time period of the electron in the initial state is eight times that in the final
state. The possible values of \( n_{1} \) and \( n_{2} \)
are
This question has multiple correct options
\( \mathbf{A} \cdot n_{1}=4, n_{2}=2 \)
B \( . n_{1}=8, n_{2}=2 \)
c. \( n_{1}=8, n_{2}=1 \)
D \( \cdot n_{1}=6, n_{2}=3 \)


\( \mathbf{1 3 8}-\mathbf{2 3 4}=? \)
A . 60
в. 372
c. 96
D. -96


The possible values of orbital quantum numbers are:
\( [n \text { is the principle quantum number }] \)
\( A \cdot \) from 0 to \( (n-1) \)
B. from 0 to \( n \)
\( c \cdot \) from 0 to \( (n+1) \)
D. all of the above


The energy released during the transition of \( 3^{r d} \) orbit to \( 2^{n d} \) orbit is
equal to the difference of energy of the two levels.
A. True
B. False


The Interaction energy between an electron and proton is very small when they are far apart.
A. True
B. False


Leaf fall can be prevented by
A. Florigen
B. Auxin
c. Cytokinins
D. Abscisic acid


The large muscular sheet which forms
the floor of the chest cavity is known as
A. Diaphragm
B. Lungs
c. Ribcage
D. None of the above


State True or False.
Nucleons are just like electrons, which
possess spin and act as tiny magnets.
A. True
B. False


If the normal reactional force is
doubled, the coefficient of friction is :
A. doubled
B. halved
c. not charged
D. tripled


Choose the correct answer from the
allternatives given
In cockroach, the ovary consists
of ovarioles formed of
A. 6 groups
B. 8 groups
c. 10 groups
D. 4 groups


We can easily move our hand in air
because
A. the particles of air have high force of attraction
B. the particles of air have less space between them
C. the particles of air are highly compressible
D. the particles of air are loosely bound


Find the order and degree of \( (1+ \)
\( \left.\boldsymbol{y}^{\prime}\right)^{1 / 2}=\boldsymbol{y}^{\prime \prime} \)
A .2,2
в. 1,1
c. 1,2
D. 2,


Fruit drop is caused by
A. Less auxin in fruit than in stem.
B. More auxin in fruit than in stem.
C. Equal distribution of auxin in stem and fruit.
D. Absence of auxin in stem and fruit.


Which cartilage is present on the end of long bone?
A. Hyaline cartilage
B. Fibrous cartilage
c. Calcified cartilage
D. Elastic cartilage


A particle is moving in a straight line such that its distance at any time t is given by \( \mathbf{S}=\frac{\boldsymbol{t}^{4}}{\mathbf{4}}-\mathbf{2} \boldsymbol{t}^{\mathbf{3}}+\mathbf{4} \boldsymbol{t}^{2}+\mathbf{7} \) then
its acceleration is minimum at \( t= \)
\( A \)
B. 2
\( c \cdot 1 / 2 \)
D. 3/2


Write the causes of energy loss and ways to reduce them in transformer
(any four)


The correct order of decreasing bond
energy is:
A. \( O-O>S-S>S e-S e \)
в. \( C-C>S i-S i>G e-G e \)
c. \( F-F>O-O>N-N \)
D. \( F-F>C l>B r-B r \)


Oxidation state of oxygen in \( F_{2} O \) is:
\( A \cdot+1 \)
B. -
\( c \cdot+2 \)
D. - -


Which of the following is not a correct
postulate of kinetic theory of gases?
A. The molecules of a gas are continuously moving in different directions with different velocities.
B. The average kinetic energy of the gas molecules is directly proportional to the absolute temperature of the gas.
C. The volume of the gas is due to the large number of molecules present in it.
D. The pressure of the gas is due to the collision of the molecules on the walls of the container.


In an experiment it was found that when a sonometer in its fundamental mode of
vibration and a tuning fork gave 5 beats when length of wire is 1.05 metre or 1 metre. The velocity of transverse waves in sonometer wire when its length is \( 1 \mathrm{m} \)
A. \( 400 \mathrm{m} / \mathrm{s} \)
B. 210 \( \mathrm{m} / \mathrm{s} \)
c. \( 420 \mathrm{m} / \mathrm{s} \)
D. \( 450 \mathrm{m} / \mathrm{s} \)


Let \( \boldsymbol{f}(\boldsymbol{x})=|\boldsymbol{x}-\mathbf{1}|, \) then
\( \mathbf{A} \cdot f\left(x^{2}\right)=(f(x))^{2} \)
B. \( f(x+y)=f(x)+f(y) \)
\( c . f(|x|)=\mid f(x) \)
D. None of these


Find the length of chord of circle with
radius \( 5 c m \) and distance from center
\( 2 c m \)


\( \boldsymbol{P H}_{4} \boldsymbol{I}+\boldsymbol{N a O H} \) forms:
A \( . P H_{3} \)
в. \( N H_{3} \)
\( \mathrm{c} \cdot P_{4} O_{6} \)
D. \( P_{4} O_{10} \)


Correct order of electronegativity of \( N, P, C \) and \( S i \) is:
A. \( N<P<C<S \) i
в. \( N>C>S i>P \)
c. \( N=P>C=s i \)
D. \( N>C>P>S i \)


Knowing that the chemistry of lanthanoids \( (L n) \) is dominated by its
+3 oxidation state, which of the
following statements is incorrect?
A. \( L n(I I I) \) hydroxides are mainly basic in character
B. The ionic sizes of \( \operatorname{Ln}(I I I) \) decrease in general with increasing atomic number
c. Because of the large size of the \( L n(I I I) \) ions the bonding in its compounds is predominantly ionic in character
D. \( L n(I I I) \) compounds are generally colourless


Work done in an isothermal reversible
expansion of 1 mole \( C l_{2} \) from 1 ltr to 50
litre at \( 273 K \) for \( C l_{2}, a= \)
\( \mathbf{0 . 6 5 5} \) litre \( ^{\mathbf{2}} \) MPa mol \( ^{-\mathbf{2}}, \boldsymbol{b}= \)
\( \left.0.055 \text { litre } m o l^{-1}\right) \)
\( \mathbf{A} \cdot-8.365 k J / m o l \)
в. \( 32.55 k J / \) mol
c. \( 8.365 k J / m o l \)
D. \( 83.65 k J / \) mol


The count rate of a radioactive source
at \( t=0 \) was 1600 counts/s and at \( t=8 s, \) it
was 100 counts/s. The count rate (in
counts) at \( t=6 s \) will be
A . 150
B. 200
\( c .300 \)
D. 400


Amongst the following hydroxides, the
one which has the highest value of \( \boldsymbol{K}_{s p} \)
\( \operatorname{at} 25^{\circ} C \) is:
A \( . \) КОН
в. \( C s O H \)
c. LiOH
D. \( R b O H \)


\( \boldsymbol{3} \boldsymbol{A} \longrightarrow \boldsymbol{B}+\boldsymbol{C} \)
It would be a zero-order reaction when:
A. The rate of reaction is proportional to square of concentration of \( A \)
B. The rate of reaction remains the same at any concentration of \( A \)
C. The rate remains unchanged at any concentration of \( B \) and \( C \)
D. The rate of reaction doubles if concentration of \( B \) is
increased to double


There are four men and six women on
the city councils. If one council number
is selected for a committee at random,
how likely that it is a woman


\( a \)
\( d \)
\( d a \)
\( \cos \)


\( 3 x-1=9-2 x \)


Assertion: When two solutions are
mixed, if the ionic product has a small value, precipitates won't be formed.
Reason: If an ionic product is less than
\( k_{s} p, \) no precipitation will occur
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but the Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false


A cell of emf \( E \) is connected across a
resistance \( R \). The potential difference
across the terminals of the cell is \( V \)
What is the internal resistance of the
cell?
A \( \cdot E-\frac{V}{R} \)
в. \( \frac{E-V}{V} \)
c. \( \frac{E-V}{R} \times V \)
D. \( \frac{E-V}{V} \times R \)


The potential energy of a two particle
system separated by a distance \( r \) is \( \operatorname{givenby} U(r)=\frac{A}{r}, \) where \( A \) is a
constant. Find the magnitude of radial
force \( F_{r}, \) that each particle exerts on the other.
A \( \cdot \frac{A}{r^{2}} \)
в. \( \frac{A}{r} \)
c. \( A r^{2} \)
D. \( A r \)


Fern gametophyte is
A. Homothallic
B. Monoecious
c. Heterothallic
D. Both A and B


If in two triangles \( \Delta A B C \) and \( \Delta P Q R \)
\( A B=Q R, B C=P R \) and \( C A=P Q \)
then :
A. \( \Delta A B C \cong \Delta P Q R \)
в. \( \Delta C B A \cong \Delta P R Q \)
c. \( \Delta B A C \cong \Delta R P Q \)
D. \( \Delta P Q R \cong \Delta B C A \)


The total surface area of cube is
\( 100 \mathrm{cm}^{3} . \) Find its volume.
\( ^{\mathbf{A}} \cdot\left(\frac{100}{6}\right)^{\frac{2}{3}} \)
\( ^{\mathrm{B}}\left(\frac{100}{6}\right)^{\frac{1}{2}} \)
\( ^{\mathrm{C}}\left(\frac{100}{6}\right)^{\frac{3}{2}} \)
D. None


Assertion
Let \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{ll}1+x & x<0 \\ 1+[x]+\sin x & 0 \leq x \leq \pi / 2 \\ 3 & x \geq \pi / 2\end{array}\right. \)
is continuous on \( \mathrm{R}-\{1\} \)
Reason
The greatest integer function is
discontinuous at every integer.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which of the following statement is TRUE for the electrochemical Daniel cell
A. Electron flow from Zinc electrode to copper electrode.
B. Current flows from zinc electrode to copper electrode
c. cation moves towards copper electrode.
D. cation moves towards zinc electrode


The solubility product of iron (III) hydroxide is \( 1.6 \times 10^{-39} . \) If \( X \) is the
solubility of iron(III) hydroxide, then which one of the following expressions
can be used to calculate \( X ? \)
\( \mathbf{A} \cdot K_{s p}=X^{4} \)
B. \( K_{s p}=9 X^{4} \)
C \( . K_{s p}=27 X^{3} \)
D. \( K_{s p}=27 X^{4} \)


Choose the correct order of nucleophilic substitution reaction:
\( (\mathrm{III}) \)
\( A \cdot(1)<(11)<(11) \)
B. (II) <(I) <(III)
\( c \cdot(111)<(11)<(1) \)
D. (1) <(III) <(II)


Rearrange the following stages of Calvin cycle in correct order.
1. Reduction during which carbohydrate
is formed at the expense of the
photochemically made ATP and NADPH.
2. Regeneration, during which the carbon dioxide acceptor ribulose- 1,5
biphosphate is formed.
3. Carboxylation during which carbon dioxide combines with ribulose- 1,5
biphosphate.
\( A \cdot 3-\rightarrow 1->2 \)
B. 3->>2
c. \( 1->2-\rightarrow 3 \)
D. \( 2-->1->3 \)
\( E \cdot 1-\rightarrow 3-\rightarrow>2 \)


Which one has the highest number of species?
A. Birds
B. Angiosperms
c. Fungi
D. Insects


A letter Lock consists of three rings
each marked with 5 different letters
Number of maximum attempts to open
the lock is:
A . 124
в. 125
c. 120
D. 75


What number divided by two is equal to that same number minus \( 15 ? \)
A . 30
B. 34
c. 15
D. 60


The percentage of metals in a mine of zinc ore is \( 60 \% \). Now the percentage of silver is \( \frac{3}{4} \% \) of metals and the rest is zinc. If the mass of ore extracted from
the mine is 8000 kg, then find the mass (in \( \mathrm{kg} \) ) of zinc?


Out of the total percentage, of water present as ground water is
A . 0.1\%
в. 0.3\%
c. \( 0.5 \% \)
D . 0.75\%


Which of the following monomers are unsuitable for condensation
polymerization?
A. hydroxy acids
B. butane-dioic acid and glycol
c. diamines and dicarboxylic acids
D. propanoic acid and ethanol


Given is an animal followed by three terms or features. Choose the term
which does not match with the animal.
Amoeba.
A. Nucleus
B. Tentacle
c. Food vacuole
D. None of the above


The period of a particle in SHM is 8
seconds. At \( t=0 \) it is at the mean
position. The ratio of the distance traveled by it in the 1 st and the 2nd seconds is
A \( \cdot \frac{1}{2} \)
B. \( \frac{1}{\sqrt{2}} \)
\( c \cdot \sqrt{2} \)
D. \( \sqrt{2}+1 \)


Two equal charges \( q \) are placed at a
distance \( 2 a \) and a third charge \( -2 q \) is
placed at the midpoint. The potential energy of the system is
A \( \cdot \frac{9 q^{2}}{8 \pi \epsilon_{0} a} \)
В. \( \frac{q^{2}}{8 \pi \epsilon_{0} a} \)
c. \( \frac{-7 q^{2}}{8 \pi \epsilon_{0} a} \)
D. \( \frac{6 q^{2}}{8 \pi \epsilon_{0} a} \)


If sum of \( n \) terms of A.P. is \( 476, \) last
term \( =20, n=17, \) then the first term is
A .32
B. 34
c. 36
D. 38 8


The magnetic induction at a point at a large distance d on the axial line of
circular coil of small radius carrying
current is \( 120 \mu T . \) At a distance 2 d the
magnetic induction would be:
A. \( 60 \mu T \)
в. зод \( T \)
\( c \cdot 15 \mu T \)
D. 240\muT


How can we save the environment from
degradation by reducing the number of fossil fuels to be burned?
A. By using public mode of transportation
B. By conserving energy
c. By using efficient device
D. All of these


Medicine, which is an antibiotic, is:
A. ampicillin
B. aspirin
c. chloroquine
D. None of these


Two coils are placed close to each other. The mutual inductance of the pair of
coils depend upon:
A. the currents in the two coils
B. the rates at which currents are changing in the two coils
c. relative position and orientation of the two coils
D. the materials of the wires of the coil


\( \ln \operatorname{an} L C R \) circuit as shown in figure,
both switches are open initially. Now
switch \( S_{1} \) is closed, \( S_{2} \) kept open. \( (q \) is
charge on the capacitor and \( 4 \tau=R C \) is
capacity time constant).
Which of the following statement is
correct?
A \( \cdot \operatorname{At} t=\frac{\tau}{2}, q=C V\left(1-e^{-1}\right. \)
B. Work done by the battery is half of the energy dissipated in the resistor
c. At \( t=\tau, q=C V / 2 \)
D. At \( t=2 \tau . q=C V\left(1-e^{-2}\right) \)


Discuss on how to make orally active protein pharmaceutical. What is the major problem to be encountered?


Assertion
A reaction between \( F e \) and \( I_{2} \) occurs,
but a reaction between \( F e^{2+} \) and \( I^{\ominus} \)
does not occur.
Reason
Fe is a better reducing agent than \( \boldsymbol{I}^{\ominus} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A solution of 10 g of a nonvolatile binary electrolyte (mat. wt. \( =100 \) ) in 500 g of
water freezes at \( -0.74^{\circ} \mathrm{C} \). What is the
degree of ionisation? \( \left[k_{f} \text { of water }=1.85 K \text { molality }^{-1}\right] \)
A . 50\%
B. 75\%
c. \( 100 \% \)
D. 0\%


Eutrophication in lakes is caused due
to
A. A lack of oxygen
B. A lack of sunlight
c. A lack of nutrients
D. An excess of oxygen
E. An excess of nutrients


Solution \( A, B \) and \( C \) of the same strong electrolyte offered resistance of \( 50 \Omega \) \( 100 \Omega \) and \( 150 \Omega \) in a given conductivity cell. The resistance observed if they are
mixed in a volume proportion which is reciprocal of their resistances and tested in the same conductivity cell would be:
\( \mathbf{A} \cdot 67.3 \Omega \)
B. \( 81.8 \Omega \)
c. \( 100 \Omega \)
D. 300\Omega


Find the value of \( x \) in the
diagram below


Suppose we define definite integral using the formula \( \int_{a}^{b} f(x) d x= \) \( \frac{b-a}{2}\{f(a)+f(b)\} . \) For more
accurate result, we have \( \int_{a}^{b} f(x) d x= \) \( \frac{b-a}{4}\{f(a)+f(b)+2 f(c)\}, \) when
\( c=\frac{a+b}{2} \cdot \) Also, let \( F(c)= \)
\( \frac{c-a}{2}\{f(a)+f(c)\}+ \)
\( \frac{b-c}{2}\{f(b)+f(c)\}, \) when \( c \epsilon(a, b) \)
(i) \( \int_{0}^{\pi / 2} \sin x d x \) equals
A \( \cdot \frac{\pi}{8}(1+\sqrt{2}) \)
в. \( \frac{\pi}{4}(1+\sqrt{2}) \)
c. \( \frac{\pi}{8 \sqrt{2}} \)
D. \( \frac{\pi}{4 \sqrt{2}} \)


The value of \( \int_{0}^{\frac{\pi}{2}} \frac{\sqrt{\tan x}}{\sqrt{\tan x}+\sqrt{\cot x}} d x \) is


A uniform electric field \( \overrightarrow{\boldsymbol{E}} \) exists
between 2 plates, a charged particle enters the space between the plates and perpendicular to \( \vec{E} \). The path of the particle between the plates is a:
A. straight line
B. hyperbola
c. parabola
D. circle


Divide
\( \frac{x^{2}-36}{x^{2}-49} \div \frac{x+6}{x+7} \)


The differential equation representing
the family of curves \( y^{2}=a(a x+b) \)
where \( a \) and \( b \) are arbitrary constants, is of
A. order 1, degree 1
B. order 1, degree 3
c. order 2 ,degree 3
D. order \( 1, \) degree 4
E. order 2, degree 1


Positive charge flow from a body at to a body at Fill
in the blanks.
A. higher potential, lower potential
B. lower potential, higher potential
c. higher charge, , lower charge
D. higher force, lower force


Which of the following conclusions
cannot be drawn on Rutherford's atomic
model?
A. The total mass of an atom is concentrated at the
centre of the atom
B. Nucleus is located inside the atom containing positively charged particles
C. Most of the atom is empty in space
D. Electrons revolve around the nucleus in stationary, circular orbits


According to Rutherford's atomic model, electron:
A. are not stationary
B. revolve around the nucleus
C. feels force of attraction by nucleus
D. all of these


Classify the following polynomial based on their degrees:
\( \boldsymbol{y}+\mathbf{3} \)


Find out \( \% \) strength of \( 11.2 V H_{2} O_{2} \)
A . \( 34 \% \)
B. 3.4\%
c. \( 1.7 \% \)
D . 13.8\%


\( \boldsymbol{C} \boldsymbol{u}_{2} \boldsymbol{S}+\mathbf{2} \boldsymbol{C} \boldsymbol{u}_{2} \boldsymbol{O} \rightarrow \boldsymbol{6} \boldsymbol{C} \boldsymbol{u}+\boldsymbol{S} \boldsymbol{O}_{2} \)
In which process of metallurgy of copper, above equation is involved -
A. roasting
B. self reduction
c. refining
D. purification


Graph showing the variation of current
versus voltage for a material Ga As is
shown in the figure, Identify the region
of:
(i) negative resistance
(ii) where Ohm's law is obeyed


Identify the formula for the \( n^{t h} \) term of
the sequence \( 54,18,6 \dots \)
\( ^{\mathrm{A}} \cdot_{54}\left(\frac{1}{3}\right)^{n-1} \)
\( ^{\text {В }} \). \( _{6}\left(\frac{1}{3}\right)^{n-1} \)
c. \( _{3}\left(\frac{1}{3}\right)^{n} \)
D. \( _{54}\left(\frac{1}{3}\right)^{n} \)


The maximum number of electrons in a
subshell is given by the expression \( \ldots \)
\( \mathbf{A} \cdot n^{2} \)
B \( \cdot 2 n^{2} \)
c. \( 2(21+1) \)
D. n-


Halogen can be estimated by:
A. Dumas method
B. Carius method
C . Leibig's method
D. All of the above


Mass of one atom of \( \boldsymbol{X} \) is \( \mathbf{6 . 6 6} \times \mathbf{1 0}^{-\mathbf{2 3}} \)
g. Hence, number of mole of atom \( X \) in
\( 40 \mathrm{kg} \) is :
\( \mathbf{A} \cdot 10^{3} \mathrm{mol} \)
B . \( 10^{-3} \) mol
c. \( \frac{40 \times 10^{3}}{6.66 \times 10^{-23}} \mathrm{mol} \)
D. \( \frac{40 \times 10^{3}}{6.022 \times 10^{23}} \mathrm{mol} \)


Who is credited with study of external respiration for the first time?
A. Dutrochet
B. Pasteur
c. cruickshank
D. Lavosier


The lines \( \frac{x-2}{1}=\frac{y-3}{1}=\frac{z-4}{-k} \) and
\( \frac{\boldsymbol{x}-\mathbf{1}}{\boldsymbol{k}}=\frac{\boldsymbol{y}-\boldsymbol{4}}{\mathbf{2}}=\frac{\boldsymbol{z}-\mathbf{5}}{\mathbf{1}} \) are coplanar if
A. \( k=1 \) or -1
B. \( k=0 \) or -3
c. \( k=3 \) or -3
D. \( k=0 \) or -1


Define the term heat:
A. the condition or quality of being hot
B. the sensation of warmth or hotness
C. the degree of hotness; temperature
D. all of the above


An organism is in the same class but not in the same family. It may belong to
same
A. Genus
B. species
c. variety
D. Order


If you have to purchase 100 kg weight of gold, which place would you prefer-the
Earth or the Moon?

Similarly, if you have to sell gold, which place you prefer - The earth or the moon? Explain.
A. earth, moon
B. moon, moon
c. earth, earth
D. moon, earth


Short / Long answer type questions. Intramembranous ossification involves
the formation of bone directly on or within loose fibrous connective
tissue membranes.Which bones of the
body develop by intramembranous ossification?


If \( z=f \) of \( (x) \) where \( f(x)=x^{2}, \) then what
is \( \frac{d z}{d x} \) equal to?
\( \mathbf{A} \cdot x^{3} \)
В. \( 2 x^{3} \)
\( c \cdot 4 x^{3} \)
D. \( 4 x^{2} \)


Variation of \( \log _{10} K \) with \( \frac{1}{T} \) is shown by
the following graph in which straight
line is at \( 45^{\circ}, \) hence \( \Delta H \) is :
A \( .+4.606 \) cal
B . -4.606 ca
\( c .+2 \) cal
D. \( -2 \mathrm{ca} \)


Who is the greatest enemy of nature
and organism?


The value if power \( \boldsymbol{P}_{2} \) is
A. \( 10000 W \)
B. \( 975 W \)
\( c .25 W \)
D. \( 200 W \)


Two charged objects are brought close
to each other. Choose the most
appropriate statement from the following options:
A. they may attract
B. they may repel
c. they may attract or repel depending on the type of charges they carry
D. there will be no effect


The disc of the radius \( R \) is confined to
roll without slipping at \( A \) and \( B \). If the
plates having the velocities as shown
determine the angular velocity of disc.


Copper and silicon is cooled from \( 300 \mathrm{K} \) to \( 60 \mathrm{K} \), the specific resistance :
A. decreases in copper but increase in silicon
B. increases in copper but decrease in silicon
c. increase in both
D. decrease in both


Glycolysis pathway was invented by
A. Calvin
в. Kreb
c. J.C Bose
D. None of the above


Which are good insulators?
This question has multiple correct options
A. wood
B. copper
c. human body
D. glass


If \( l=\lim _{x \rightarrow 0} \frac{\sin a x-\sin x-x}{x^{3}} \) exists, and
is finite, then the values of ' \( l \) ' and 'a' are
respectively equal to
A \( \cdot \frac{7}{6}, 2 \)
в. \( -\frac{4}{3}, 2 \)
c. \( -\frac{7}{6},-2 \)
D. \( -\frac{7}{6}, 2 \)


How Iymph acts as middle man in the
body?
A. It transports food materials, oxygen, hormones etc. to the body cells and brings carbon dioxide and other metabolic wastes from the body cells to blood and then finally pours the same into venous system.
B. It transports metabolic wastes, carbon dioxide, hormones etc. to the body cells and brings oxygen and other food materials from the body cells to blood and then finally pours the same into venous system.
C. It transports metabolic wastes, carbon dioxide, hormones etc. to the body cells and brings oxygen and other food materials from the body cells to blood and then finally pours the same into arterial and capillary system.
D. All of the above


Which ore does not contain carbonate?
A. Calamine
B. ciderite
c. Malachite
D. zincite


For the gas phase decomposition \( \boldsymbol{A} \rightarrow \)
\( 2 B, \) the rate constant is \( 6.93 \times 10^{-3} \)
\( \min ^{-1} \) at \( 300 \mathrm{K} . \) The percentage of \( \mathrm{A} \)
remaining at the end of 300 minutes is :
A . 75
B. 50
\( c \cdot 25 \)
D. 12.5


A storage battery contains a solution of
\( H_{2} S O_{4}, 38 \% \) by mass. At this
concentration, van't Hoff factor is 2.50
The temperature at which battery contents freeze will be:
\( \left(\boldsymbol{K}_{f}=\mathbf{1 . 8 6} \boldsymbol{K} \boldsymbol{m o l}^{-1} \boldsymbol{k g}\right) \)
A \( .-29.08^{\circ} \mathrm{C} \)
B . \( -25.18^{\circ} \mathrm{C} \)
c. \( -17.25^{\circ} \mathrm{C} \)
D. none of these


How many 3 digit numbers can be formed from the digits 2,3,5,6,7,9
which are divisible by 5 and none of the digits is repeated?
A . 5
B. 10
c. 15
D. 20


Form the differential equation of the family of curves represented by the equation(a being the parameter). \( (x-a)^{2}+2 y^{2}=a^{2} \)


A train has a speed of \( 60 \mathrm{km} / \mathrm{h} \) for the first one hour and \( 40 \mathrm{km} / \mathrm{h} \) for the next half hour.lts average speed in \( k m / h \) is
A . 50
B. 53.33
c. 48
D. 70


Which one contains one pair of electrons in the ground state of the lithium atom among the following
A . \( 1 s \)
B . \( 2 s \)
c. \( 3 s \)
D. \( 3 p \)
E . \( 3 d \)


If \( \boldsymbol{x}-\boldsymbol{i} \boldsymbol{y}=\sqrt{\frac{\boldsymbol{a}-\boldsymbol{i} \boldsymbol{b}}{\boldsymbol{c}-\boldsymbol{i} \boldsymbol{d}}} \) prove that \( \left(\boldsymbol{x}^{2}+\right. \)
\( \left.\boldsymbol{y}^{2}\right)^{2}=\frac{a^{2}+b^{2}}{c^{2}+d^{2}} \)


Ritu ate \( \frac{3}{5} \) part of an apple and the
remaining apple was eaten by her
brother Sam. How much part of the
apple did Sam eat? Who had the larger share? by how much?


If \( A \) and \( B \) are independent events such
\( \operatorname{that} P(A)=0.3 \) and \( P(B)=0.4, \) then find
(i) \( P(A \text { and } B) \)
(ii) \( P(A \text { or } B) \)


When a die is thrown, list the outcomes
of an event of getting: a prime number.
A. 2,3,5
в. 1,3,5
c. 3,5,7
D. 1,2,5


Assertion
The number of significant figures depends on the least count of measuring instrument.
Reason
Significant figures define the accuracy of measuring instrument.
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


The following is not a noble metal
A. Au
B. cu
c. \( A g \)
D. Pt


The bond length (pm) of \( F_{2}, H_{2}, C l_{2} \) and
\( I_{2}, \) respectively is:
A . 144,74,199,267
В. 74,144,199,267
c. 74,267,199,144
D. 144,74,267,199


\( \int x^{2} e^{x^{3}} d x \) equals
A \( \cdot \frac{1}{3} e^{x^{3}}+C \)
B \( \cdot \frac{1}{3} e^{x^{2}}+C \)
c. \( \frac{1}{2} e^{x^{3}}+C \)
D. \( \frac{1}{2} e^{x^{2}}+C \)


The S.D. of \( 1,2,3, \cdots 23 \) is
A \( \cdot 2 \sqrt{11} \)
B. \( \sqrt{11} \)
c. \( \frac{\sqrt{11}}{2} \)
D. None of these


All minerals are not the ore but all ores
are minerals. The extraction of a
particular metal depends upon several
factors and overall it has to be
convenient and economical.
Which of the following statement is
true?
A. Na-ethyl xanthate is used as frother exclusively.
B. Levigation cannot be applied for sulphide in any condition.
C. Froth floatation can be applied for non-sulphide ore also using suitable activator
D. Impurities like \( S \) and \( A \) s are removed as elemental vapor in roasting.


The displacement time graphs of two particles \( A \) and \( B \) are straight lines
making angles of respectively \( 30^{\circ} \) and
\( 60^{\circ} \) with the time axis. If the velocity of
\( A \) is \( v_{A} \) and that of \( B \) is \( v_{B}, \) then the value of \( \frac{v_{A}}{v_{B}} \) is:
A \( \cdot \frac{1}{2} \)
в. \( \frac{1}{\sqrt{3}} \)
\( c \cdot \sqrt{3} \)
D.


\( \operatorname{Let} O P=5 \) and \( P M=4 \) Find \( O M \)
\( A \cdot 3 c m \)
B. \( 4 \mathrm{cm} \)
\( c .5 \mathrm{cm} \)
D. \( 8 c m \)


Find the square root of the following number by Division method.
\( \mathbf{3 1 3 6} \)


Explain how you can take care of your
eyes.


If for a matrix \( \boldsymbol{A}, \boldsymbol{A}^{2}+\boldsymbol{I}=\boldsymbol{O} \) where \( \boldsymbol{I} \) is
the identity matrix, then \( A \) equals
\( \mathbf{A} \cdot\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right] \)
В. \( \left[\begin{array}{cc}i & 0 \\ i & -i\end{array}\right] \)
c. \( \left[\begin{array}{cc}1 & 2 \\ -1 & 1\end{array}\right] \)
D. \( \left[\begin{array}{cc}-1 & 0 \\ 0 & -1\end{array}\right] \)


Which of the following are not compounds?
A. Potassium chlorid
B. Carbon monoxide
c. Iron sulphide
D. Sulphur powder


Chlorine is:
A. Oxidising agent
B. bleaching agent
C . disinfectant
D. all of the above


A step-down transformer has a coil ratio of 1.5 to \( 17 . \) The voltage applied at the
primary side of the transformer is \( 136 V \)
What is the output voltage of the transformer?
A . \( 1.2 V \)
в. \( 1.5 V \)
c. \( 5.25 V \)
D. \( 12 V \)
E . \( 18.75 V \)


When there is a current in a circuit, the
electrons:
A. Move through the circuit slower than the average person would walk.
B. Move through the circuit at nearly the speed of light.
C. Move through the circuit at the speed of light.
D. Do not actually move through the circuit, this is just an analogy people use.


How many lines does a spectrum contain in an electronic transition from
\( \boldsymbol{n}=\mathbf{1} \) to \( \boldsymbol{n}=\mathbf{5} \) in hydrogen atom?
A . 10
B. 8
\( c \cdot 1 \)
D. 5


Find the degree of the following polynomial \( x^{3}+17 x-21-x^{2} \)


Find the first three terms in the
expansion of :
\( \frac{1}{(1+x)^{2} \sqrt{1+4 x}} \)


Match the column-


Mendel was lucky in the choice of the material of his experiments, which of the following contributed to his success?
A. He observed distinct inherited traits
B. He qualitatively analysed his date.
c. He liked pea plants
D. He considered only one character at one time.


Two long parallel conductors carry currents of \( 12 \mathrm{A} \) and \( 8 \mathrm{A} \) respectively in the same direction. If the wires are 10
cm apart, find where the third parallel
wire also carrying a current must be
placed so that the force experienced by
it shall be zero. Answer in the form of
\( x \times 10^{-2} m . \) Find \( x \)


f the diagonal of a quadrilateral shaped field is \( 24 m \) and the perpendiculars
dropped on it from the remaining
opposite vertices are \( 8 m \) and \( 13 m \)
then the area of the field is


The ratio of the intensities at minima to
the maxima in the Young's double slit experiment is \( 9: 25 . \) Find the ratio of the widths of the two slits.


The equation of tangent to the curve
\( \boldsymbol{y}=3 x^{2}-x+1 \) at the point (1,3) is
A. \( y=5 x+2 \)
в. \( y=5 x-2 \)
c. \( _{y=\frac{1}{5} x+2} \)
D. \( _{y=\frac{1}{5} x-2} \)


A person drops the ball from the top of a
building. Taking air resistance into account, which of the following best describes the speed of the ball during its downward motion?
A. It will increase until it reaches the speed of light
B. It will increase at a steady rate
c. It will remain constant
D. It will decrease
E. Its rate of acceleration will decrease until the ball moves at a constant speed


In reaction \( \boldsymbol{C O}(\boldsymbol{g})+\mathbf{2} \boldsymbol{H}_{2}(\boldsymbol{g}) \rightleftarrows \)
\( \boldsymbol{C H}_{3} \boldsymbol{O H}(\boldsymbol{g}) ; \boldsymbol{\Delta}_{f} \boldsymbol{H}^{o}=-\mathbf{9 2 . 0} \boldsymbol{k J} / \boldsymbol{m o l} \)
What will happen if:
A. volume of the rection vessel in which reactants is reduced to half
B. some amount of \( C H_{3} O H \) is removed
c. the partial pressure of hydrogen is suddenly doubled
D. an inert gas is added to the system under constant volume conditions


Three of the exterior angles of a hexagon are \( 40^{\circ}, 51^{\circ} \) and \( 86^{\circ} . \) If each of
the remaining exterior angles is \( x^{\circ}, \) find
the value of \( x \)
A . 58
B. 61
c. 65
D. none of the above


A molal solution is one that contains
one mole of a solute in :
A. 1000 g of the solvent
B. 1000 \( \mathrm{mL} \) of the solution
c. 1 litre of the solvent
D. 1000 g of the solution


Represent graphically by two separate diagrams in the case where two sound
waves having the same amplitude but different frequencies:


A line makes the same angle \( \theta \) with
each of the \( x \) and \( z \) -axes. If the angle \( \beta \)
which it makes with \( y \) -axis, is such that \( \sin ^{2} \beta=3 \sin ^{2} \theta, \) then \( \cos ^{2} \theta \) is equal to
A \( \cdot \frac{2}{3} \)
B. \( \frac{1}{5} \)
\( c \cdot \frac{3}{5} \)
D.


What is the base of the cone?
A. Square
B. Triangle
c. Circle
D. None of these


A certain vector in the \( x y \) plane has an
\( x \) component of \( 4 m \) and a \( y \) component
of \( 10 m . \) It is then rotated in the \( x y \)
plane so that its \( x \) -component is doubled. Then its new \( y \) component is (approximately):
A. \( 20 m \)
B. \( 7.2 m \)
c. \( 5.0 m \)
D. \( 4.5 m \)


Cornea is a transparent spherical structure which :
A. Reflects light
B. Scatters light
c. Refracts light
D. None of these


The characteristic oxidation number of
atoms in free metals is:
A . -1
B. +1
c. any number
D.


The clouds consists of charged particles of water dispersed in air. Some of them are positively charged, others are negatively charged. When positively charged clouds come closer, they cause lightening and thundering whereas when positive and negative charged colloids come closer, they cause heavy rain by aggregation of minute particles. It is possible to cause artificial rain by throwing electrified sand or silver iodide from an
aeroplane and thus, coagulation the mist hanging in air.
Clouds are colloidol solution of :
A. liquid in gas
B. gas in liquid
c. liquid in liquid
D. solid in liquid


For \( n=5, \) the types of orbitals found in
shell is?
\( A \cdot s \)
B. s, p
\( c \cdot s, p, d, f \)
D. \( s, p, d, f, g \)


The velocity of sound in a gas in which two waves of wavelengths \( 50 \mathrm{cm} \) and
\( 50.5 \mathrm{cm} \) produces 6 beats per second is?
A. \( 303 \mathrm{m} / \mathrm{s} \)
B. \( 332 \mathrm{m} / \mathrm{s} \)
c. \( 296 \mathrm{m} / \mathrm{s} \)
D. \( 228 \mathrm{m} / \mathrm{s} \)


The kinetic energy (in keV) of the alpha particle, when the nucleus at rest undergoes alpha decay, is
A. 5319
B. 5422
c. 570
D. 5818


Explain the following with one example
(a) Aldol condensation
(b) Cannizzaro reaction
(c) Esterification
(d) Decarboxylation


Find \( A M \) of 12 and 14


Elements after atomic number 103
have not been discovered till now. If an
element with atomic number 106 were
ever discovered which of the following electronic configuration will it possess.
\( \mathbf{A} \cdot[R n] 5 f^{14} 6 d^{4} 7 s^{1} \)
B \( \cdot[R n] 5 f^{14} 6 d^{5} 7 s^{1} \)
\( \mathbf{c} \cdot[R n] 5 f^{14} 6 d^{6} 7 s^{0} \)
D \cdot \( [R n] 5 f^{14} 6 d^{1} 7 s^{2} 7 p^{3} \)


In the given figure, \( m \| n \) and \( \angle 1=50^{\circ} \)
then find \( \angle \mathbf{5} \)
A \( \cdot 130^{\circ} \)
В. \( 60^{\circ} \)
\( c \cdot 70^{\circ} \)
D. \( 180^{\circ} \)


Given \( -51 \times x=204 \) and \( -33 \times y= \)
\( -297, \) then find the value of \( -x \times y \)
A . -36
B. 33
\( c .36 \)
D. -33


A metal oxide having formula \( Z_{2} O_{3} \)
gives free metal and water on reduction
with hydrogen. 0.2 g of the metal oxide can be completely reduced by \( 12 \mathrm{mg} \) of hydrogen. The atomic weight of the metal is:
A . 12
B. 13
\( c \cdot 26 \)
D. 78


Bacteria show anoxygenic photosynthesis.Why?


If an incident light ray is reflected back along its original path by a plane mirror, then its angle of incidence is:
A \( \cdot 0^{\circ} \)
B. \( 90^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 30^{\circ} \)


The electric flux over a sphere of radius
\( 1 m \) is \( \phi . \) If radius of the sphere were
doubled without changing the charge
enclosed, electric flux would become
\( \mathbf{A} \cdot 2 \phi \)
B. \( \phi / 2 \)
c. \( \phi / 4 \)
D.


Given : AB || CD.
What type of angle is formed by adding
together \( \angle 4 \) and \( \angle 6 ? \)
A . Acute
B. Right
c. obtuse
D. Supplimentry


A stationary source is emitting sound
at a fixed frequency \( f_{0}, \) which is reflected by two cars approaching the source. The difference between the
frequencies of sound reflected from the
cars in \( 1.2 \% \) of \( f_{0} . \) What is the
difference in the speed of the cars (in km per hour) to nearest integer? The
cars are moving at constant speeds much smaller that the speed of sound
which is \( 330 m s^{-1} \)
A .2
B. 3
c. 5
D. 7


Which of the following species is diamagnetic in nature?
A \( \cdot H_{2}^{-} \)
в. \( H_{2}^{+} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \)
D. \( H e_{2}^{+} \)


What is the order of basic nature of
hydrides of VA group elements?
A \( \cdot \mathrm{AsH}_{3}>\mathrm{SbH}_{3}>\mathrm{PH}_{3}>\mathrm{NH}_{3} \)
В. \( \mathrm{NH}_{3}>\mathrm{SbH}_{3}>\mathrm{PH}_{3}>\mathrm{AsH}_{3} \)
C. \( \mathrm{NH}_{3}>\mathrm{PH}_{3}>\mathrm{AsH}_{3}>\mathrm{SbH}_{3} \)
D. \( \mathrm{PH}_{3}>\mathrm{NH}_{3}>\mathrm{SbH}_{3}>\mathrm{AsH}_{3} \)


A coin is tossed 1000 times with the
following frequencies:
Head: \( 445, \) Tail: 555
When a coin is tossed at random, what
is the probability of getting a head?


In moving from \( A \) to \( B \) along an electric
field line, the electric field does \( 1.28 \times \)
\( 10^{-18} J \) of work on an electron. If \( \phi_{1}, \phi_{2} \)
are equipotential surface, then
potential difference \( V_{E}-V_{D} \) is equal
to:
A. -8 volt
B. +8 volt
\( c \). zero
D. 64 volt


The determinant \( \Delta= \) \( \left|\begin{array}{ccc}a^{2}(1+x) & a b & a c \\ a b & b^{2}(1+x) & b c \\ a c & b c & c^{2}(1+x)\end{array}\right| \) is
divisible by
This question has multiple correct options
A. \( (x+3) \)
B \( \cdot(1+x)^{2} \)
\( c \cdot x^{2} \)
D. \( \left(x^{2}+1\right) \)


toppr
Q Type your question-
the rails is \( 1 m . \) A conducting rod of
mass \( 0.5 k g \) can slide on the rails
frictionlessly. The rod is tied at
midpoint to a light string passing over a smooth pulley fixed to the edge of the
table. A mass of 0.5kg tied to the other
end of the string hangs vertically as shown in the Figure. A uniform magnetic field of \( 0.5 T \) can be applied in
vertically downward direction. If the system is released from rest, then, point out incorrect statements from the
following:
I be the acceleration due to gravity]
This question has multiple correct options
A. When the magnetic field is put on, the acceleration of the system increases from \( \frac{g}{3} \) to \( \frac{g}{2} \)
B. Due to induction, the change in the acceleration of the system is same as that obtained by increasing the mass of the rod by \( 0.5 k g \) in the absence of the magnetic field.
c. Due to induction, the change in the acceleration of the system is same as that obtained by decreasing the mass of the rod by \( 0.25 \mathrm{kg} \) in the absence of magnetic field
D. When the magnetic field is put on, the acceleration of the system decreases from \( \frac{g}{2} \) to \( \frac{g}{3} \)


Consider the following statements:
When two straight lines intersect,
(i) adjacent angles are complementary
(ii) adjacent angles are supplementary
(iii) opposite angles are equal
(iv) opposite angles are
supplementary
\( A \cdot \) (i) and (iii)
B. (ii) and (iii)
c. (i) and (iv)
D. (ii) and (iv)


Explain why the planets do not twinkle.


In a potentiometer arrangement, a cell of emf \( 1.5 V \) gives a balance point at
\( 27 \mathrm{cm} \) length of wire. If the cell is replaced by another cell and balance
point shifts to \( 54 c m, \) the emf of the second cell is
A . \( 3 V \)
в. \( 1.5 V \)
c. \( 0.75 V \)
D. \( 2.25 V \)


What is the similarity between
glycolysis and Krebs cycle?
A. Formation of intermediate \( 5 C \) compound
B. Substrate level phosphorylation
c. oxidative phosphorylation
D. Decarboxylation.


Digestion of starch in most of mammals start in
A. Stomach
B. Mouth
c. Duodenum
D. Oesophagus


A steady current i passes through a linear conductor of uniform cross-
section. Any given segment of the conductor has
A. a net negative charge
B. a net positive charge
c. a zero net charge of any kind
D. a net charge proportional to the volume of the segment


The thickness of a metal sheet is
measured to be \( 326 m m \). Express its
order of magnitude in \( \mathrm{mm} \)
A \( \cdot 10^{\circ} \)
B. \( 10^{\text {। }} \)
\( c \cdot 10^{2} \)
D. \( 10^{3} \)


Among the following the ambident nucleophile is:
A . iodide
B. alkoxy
c. hydroxyl
D. hybride
E . cyanide


Which of the following is/are true regarding Earthquake?
A. It refers to shaking of the Earth.
B. It occurs due to release of energy
c. It generates waves that travel in all direction.
D. All of the above.


\( i^{2}+i^{3}+i^{4}+i^{3} \) is equal to


If the error in the measurement of
radius of a sphere is \( 2 \% \) then the error in the determination of volume of the
sphere will be -
A . \( 8 \% \)
B. 2\%
\( c .4 \% \)
D. \( 6 \% \)


The population of a town was \( 59000 . \) In one year it was increased by 4536 due to new births. However, 9218 persons
died or left the town during the year
What was the population at the end of
the year?


Sodium sulphite is used in preserving squashes and other mildly acidic foods
due to:
A. potassium salt has preservative action
B. potassium metabisulphite prevents oxidation
c. potassium metabisulphite is not influenced by acid
D. sulphur dioxide and sulphurous acid formed kill bacteria and germs


Prove the following formulae to the
given latters:
\( \boldsymbol{v}=\boldsymbol{u}+\boldsymbol{a} \boldsymbol{t}, \boldsymbol{a} \)


If current in a source of e.m.f. is in the
direction of e.m.f., the energy of the
source
A. Increase
B. Decrease
c. Remains constant
D. zero


Which is the principal site for the development of ribosomal RNAs?


Which of the following is true in an ecosystem?
A. Animals can live without plants
B. Plants can live without animals
C. Animals can survive for long without plants
D. Plants can survive for long without animals


Find \( C_{A B} \) if each capacitor is \( C \) in the
figure shown :
A. 3C
B. 2C
\( c \cdot c \)
D. \( c / 2 \)


Find the radian measures
corresponding to the following degree measures:(i) \( 25^{\circ}\left(\text { ii) }-47^{\circ} 30^{\prime}\left(\text { iii) } 240^{\circ}\right.\right. \)
\( (i v) 520^{\circ} \)


What type of motion do the vehicles on a straight road perform?


The change in seasons on the Earth
occurs because
A. the distance between the Earth and the Sun is not
constant.
B. the axis of rotation of the Earth is parallel to the plane of its orbit.
C. the axis of rotation of the Earth is perpendicular to the plane of its orbit.
D. the axis of rotation of the Earth is tilted with respect to the plane of its orbit.


If two non-parallel lines are perpendicular to two other straight lines, each to each. Show that the acute
angle between the first pair of lines is
equal to the acute angle between the second pair of lines.


Find odd man out
Plastic, Rubber, Glass, Silver
A . Glass
B. Rubber
c. Silver
D. Plastic


A shopkeeper makes a profit of \( 20 \% \) on selling a transistor radio for Rs. \( 840 . \) For how much should he sell another
transistor radio, whose cost price is Rs.
25 more than the first one, to make the
same percentage profit ?


By what per cent, the volume of a cube increases, if the length of each edge was increased by \( 50 \% \) ?
A . \( 237.5 \% \)
в. 273.5\%
c. \( 125 \% \)
D. \( 50 \% \)


In which of the following reactions does
hydrogen act as an oxidising agent:
\( \mathbf{A} \cdot H_{2}+F_{2} \longrightarrow \)
B. \( H_{2}+S i C I_{2} \longrightarrow \)
\( \mathbf{c} \cdot N a_{2}+H_{2} \longrightarrow \)
\( \mathbf{D} \cdot C u O+H_{2} \longrightarrow \)


Suppose that \( f(n) \) is a real valued function whose domain is the set of
positive integers and that \( \boldsymbol{f}(\boldsymbol{n}) \) satisfies the following two properties:
\( \boldsymbol{f}(1)=23 \) and \( \boldsymbol{f}(\boldsymbol{n}+1)=\boldsymbol{8}+\boldsymbol{3} \cdot \boldsymbol{f}(\boldsymbol{n}) \)
for \( n \geq 1 \)
It follows that there are constant \( \boldsymbol{p}, \boldsymbol{q} \)
and \( r \) such that \( f(n)=p \cdot q^{n}-r, \) for
\( \boldsymbol{n}=\mathbf{1}, \mathbf{2}, \ldots \ldots \) then the value of \( \boldsymbol{p}+\boldsymbol{q}+\boldsymbol{r} \)
is:
A . 16
B. 17
c. 20
D. 26
E . 31


Normal calomel electrode has e.m.f. of
\( 0.67 \mathrm{V} \) at \( 25^{\circ} \mathrm{C} \). Calculate pH of solution.
The oxidation potential of calomel electrode on \( H \) scale is \( 0.28 V \) (nearest
integer).


Light of wavelength 589.3 nm is incident normally on a slit of width \( 0 . \) \( \mathrm{mm} . \) The angular width of the central diffraction maximum at a distance of
Im from the slit is
A \( \cdot 0.68 \)
В. \( 0.34^{\circ} \)
\( c .2 .05 \)
D. None of these


ldentify the largest side of the triangle. f the angles are given as:
\( \angle A=50^{\circ}, \angle B=10^{\circ} \) and \( \angle C=22^{\circ} \)
\( A \cdot \overline{A B} \)
8. \( \overline{B C} \)
\( c \cdot \overline{C A} \)
\( D . \overline{A C} \)


The gravitational force between two
particles is \( F, \) if the objects are stationary and separated by a distance of \( 1 \mathrm{m} \). If the objects starts moving in opposite directions, from rest with
uniform acceleration of \( a=1 m / s^{2} \)
then the force between them after 3 secs will be
A. 4 F/ 5
B. F/100
c. \( 4 F / 121 \)
D. F/2


The work function of a surface of a
photosensitive material is \( 6.2 e V . \) The wavelength of the incident radiation for
which the stopping potential is \( 5 V \) lies in the:
A. ultraviolet region
B. \( X \) -ray region
c. infrared region
D. none of these


In Young's experiment, the fringe width
was found to be \( 0.4 m m \). If the whole
apparatus is immersed in water of refractive index \( \frac{4}{3}, \) the new fringe width in mm is :
A. 0.25
B. 0.30
\( c \cdot 0.40 \)
D. 2.00


Which of the following characters is not found in the transverse section of
monocot stem?
A. Sclerenchymatous bundle sheath
B. Lysigenous cavity
c. Sclerenchymatous hypodermis
D. Starch sheath


In the absence of intermolecular forces
of attraction, the observed pressure \( \mathrm{P} \) will be:
\( A \cdot P \)
B. <P
\( c \cdot>p \)
D. zero


An electron is moving in an orbit of a hydrogen atom from which there can be
a maximum of six transitions. An
electron is moving in an orbit of another
hydrogen atom from which there can be
a maximum of three transitions. The
ratio of the velocity of the electron in
these two orbits is
\( \mathbf{A} \cdot \underline{5} \)
B. \( \frac{3}{4} \)
\( c \cdot \frac{1}{2} \)
D.


Integrating factor of \( \frac{\boldsymbol{x} \boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}-\boldsymbol{y}=\boldsymbol{x}^{4}-\boldsymbol{3} \boldsymbol{x} \)
is:


To reduce the light reflected by the glass surface of a camera lens, the surface is
coated with a thin layer of another material which has an index of
refraction \( (\mu=7 / 4) \) smaller than that of glass. he least thickness of the layer, to ensure that light falling
perpendicularly on the surface and
having wavelengths, \( \lambda_{1}=700 n m \) and
\( \lambda_{2}=420 n m \) will be weekly reflected for
both wavelengths is \( x \times 10^{-7} \) m. Find \( x ? \)


An ideal gas is one which obeys?
A. Boyle's law
B. Gas laws
c. charle's law
D. Avogadro law


The automobile emission can be
reduced by adding which of the following in the petrol?
A. Barium salts
B. Cadmium salts
c. cobalt salts
D. silicon 011


Maximum conductance is shown by:
A . \( 0.1 M \) NaCl
в. \( 0.1 M \) Н \( _{2} \) SO \( _{4} \),
c. \( 0.1 M \) sucrose
D. \( 0.1 M \) glucose


When the electric resistance are
connected in parallel, which one of the following quantities is not affected?
A. Potential difference
B. Resistance
c. Electric current
D. Capacity


A curve which has 2 end points is called
an
A. closed curve
B. simple curve
c. open curve
D. None of the above


The set of all points of differentiability of the function \( f(x)=\frac{\sqrt{x+1}-1}{\sqrt{x}} \) for
\( x \neq 0 \) and \( f(0)=0 \) is
\( \mathbf{A} \cdot(-\infty, \infty) \)
B. \( [0, \infty) \)
\( c \cdot(0, \infty) \)
\( \mathbf{D} \cdot(-\infty, \infty) \sim\{0\} \)


is a form of renewable
energy.
A. coal
B. Petroleum
c. wind
D. None of these


In a company, the average income of all the employees is \( R s .20000 \) per month
recently the company announced the increment of \( \boldsymbol{R} \boldsymbol{s} . \boldsymbol{2 0 0 0} \) per month for all
the employees, the new average is
A. \( R s .22000 \)
B . Rs.24000
c. \( R s .28000 \)
D. \( R s .26000 \)


powder sprinkled on a carrom board
A. magnifies friction.
B. reduces friction
c. removes friction.
D. does not affect friction


Derive the formula for the electric
potential energy of an electric dipole in a uniform electric field.


If \( \boldsymbol{x}=\mathbf{2} \cos ^{-1}\left[\frac{1}{2}\right]+\sin ^{-1}\left[\frac{\mathbf{1}}{\sqrt{\mathbf{2}}}\right]+ \)
\( \tan ^{-1}(\sqrt{3}) \) and \( y= \)
\( \cos \left[\frac{1}{2} \sin ^{-1}\left[\sin \frac{x}{2}\right]\right] \) then which of the
following statements holds good?
A \( \cdot y=\cos \frac{3 \pi}{16} \)
В. \( y=\cos \frac{5 \pi}{16} \)
c. \( x=4 \cos ^{-1} y \)
D. none of these


Why are coherent sources required to create interference of light?


The picture shows a wave generated in a laboratory. The wavelength of the wave is
A . \( 1.5 \mathrm{cm} \)
B. \( 1.7 \mathrm{cm} \)
c. \( 2.0 \mathrm{cm} \)
D. 2.7 cm


A disc of mass \( 100 g \) and radius \( 10 \mathrm{cm} \) has a projection on its circumference. The mass of projection is negligible. A \( 20 g \) bit of putty moving tangential to
the disc with a velocity of \( 5 m s^{-1} \) strikes the projection and sticks to it. The angular velocity of disc is
A \( \cdot 14.29 \) rad \( s_{1} \)
B. 17.3 rad \( s_{-1} \)
c. 12.4 rad \( s_{-1} \)
D. 9.82 rad \( s_{1} \)


A person with vibrating tuning fork of frequency \( 338 \mathrm{Hz} \) is moving towards a
vertical wall with a speed of \( 2 m s^{-1} \)
Velocity of sound in air is \( 340 m s^{-1} \). The
number of beats heard by that person per second is.
A . 2
B. 4
c. 6
D.


By increasing the temperature the resistance of a conductor
A. increases
B. decreases
c. remains constant
D. initially increases then decreases


Solve the following equations:
\( y+\sqrt{x^{2}-1}=2 \)
\( \sqrt{\boldsymbol{x}+\mathbf{1}}-\sqrt{\boldsymbol{x}-\mathbf{1}}=\sqrt{\boldsymbol{y}} \)
This question has multiple correct options
A. \( x=2 ; y=5 \)
в. \( x=1 ; y=2 \)
c. \( _{x}=\frac{5}{3} ; \frac{2}{3} \)
D. \( x=3 ; y=3 \)


A Gaussian surface in the figure is
shown by dotted line. The electric field
on the surface will be:
A. due to \( q_{1} \) and \( q_{2} \) only
B. due to \( q_{2} \) only
c. zero
D. due to all


What is the orbital period of halley's
comet?
A. 66 years
B. 76 years
c. 86 years
D. 96 years


Which of the following is a female sex hormone?
A. Adrenaline
B. Estrone
c. cortisone
D. Testosterone


Given that \( 0 \leq x \leq \frac{1}{2} \) the value of
\( \tan \left[\sin ^{-1}\left(\frac{x}{\sqrt{2}}+\sqrt{\frac{1-x^{2}}{2}}\right)-\sin ^{-1} x\right. \)
is
\( A \)
B.
\( c \cdot 1 \sqrt{3} \)
D. \( \sqrt{3} \)


A sphere A moving with a speed u and rotating with an angular velocity \( \omega \) makes a head-on elastic collision with
an identical stationary sphere B. There is no friction between the surface of \( A \)
and B. Disregard gravity. Then which of the following statements is/are true? This question has multiple correct options
A. A will stop moving but continue to rotate with an angular velocity \( \omega \)
B. A will come to rest and stop rotating.
c. B will move with a speed u without rotating
D. B will move with a speed u and rotate with an angular velocity \( \omega \)


The logic behind NOR gate is that which
gives
A. high output when both inputs are high
B. low output when both inputs are low
c. high output when both inputs are low
D. none of these


Find oxidation number of Magnese in
\( \boldsymbol{K}_{2} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4} \)


Let \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \lim _{n \rightarrow \infty} \frac{\left(x^{2}+2 x+3+\sin \pi x\right)^{n}-1}{\left(x^{2}+2 x+3+\sin \pi x\right)^{n}+1} . \) Then
A. \( f(x) \) is continuous and differentiable for all \( x \in R \)
B. \( f(x) \) is continuous but not differentiable for all \( x \in R \)
\( \mathrm{c} \cdot f(x) \) is discontinuous at infinite number of points
D. \( f(x) \) is discontinuous at finite number of points


If \( A \) and \( B \) are symmetric matrices,
then write the condition for which \( A B \) is
also symmetric


Choose the correct options for the following statements:
A) First law of thermodynamics specifies the conditions under which a body can use its heat energy to produce the work.
B) Second law of thermodynamics
states that heat always flows from hot body to cold body by itself
A. Both A and B are true
B. Both A and B are false
C. A is true but B is false
D. A is false B is true


The adjacent sides of a paralleleogram \( \operatorname{are} \vec{A}=2 \hat{i}-3 \hat{j}+\hat{k} \quad \) and \( \quad \vec{B}= \)
\( -2 \hat{i}+4 \hat{j}-\hat{k} \) What is the area of the
parallelogram?
A. 4 units
B. 7units
c. \( \sqrt{5} \) units
D. \( \sqrt{8} \) units


Solve :
\( \boldsymbol{I}=\int \sin ^{6} \boldsymbol{x} \boldsymbol{d} \boldsymbol{x} \)


Glacial phosphoric acid is :
A \( . H P O_{3} \)
в. \( H_{3} P O_{3} \)
\( \mathrm{c} \cdot H_{3} P O_{4} \)
D. \( H_{4} P_{2} O_{7} \)


A bullet passes past a person at a speed \( 220 \mathrm{m} / \mathrm{s} \). The fractional change in the frequency of the whistling sound
heard by the person as the bullet crosses the person is (Speed of sound = \( 330 \mathrm{m} / \mathrm{s}) \)
A. 0.67
B. 0.8
\( c \cdot 1.2 \)
D. 3.0


A molecule has a permanent electric dipole moment of \( 5 \times 10^{-30} C-m \). If it
is supposed to arise from net charge of
\( +e \) and \( -e \) in the two regions of the
molecule, what is their separation?


The Cartesian equation of line \( 6 x- \) \( \mathbf{2}=\mathbf{3} \boldsymbol{y}+\mathbf{1}=\mathbf{2} z-\mathbf{2} \) is given by
\( ^{\text {A } \cdot \frac{3 x-1}{3}}=\frac{3 y+1}{6}=\frac{z-1}{3} \)
B. \( \frac{3 x+1}{3}=\frac{3 y-1}{6}=\frac{z-1}{3} \)
c. \( \frac{3 x-1}{3}=\frac{3 y-1}{6}=\frac{z-1}{3} \)
D. \( \frac{3 x-1}{6}=\frac{3 y-1}{3}=\frac{z-1}{3} \)


A boy stands \( 85 \mathrm{m} \) infront of a high wall and then blows a whistle. Calculate the
time interval when he hears an echo.
(speed of sound \( =340 m s^{-1} \) )
A . \( 0.1 \mathrm{s} \)
B. \( 0.2 \mathrm{s} \)
c. \( 0.5 \mathrm{s} \)
D. 1 s


Check the incorrect statement: When a
magnet is moved into a coil the
strength of the current depends on:
A. The number of turns in the coil
B. The speed with which the magnet moves
c. The resistance of the coil
D. None of the above


A car falls off a bridge and drops to the
ground in \( 0.5 s . \) Let \( g=10 m / s^{2}, \) what is its speed on striking the ground?
A. \( 5 m / s \)
в. \( 10 m / s \)
\( \mathbf{c} \cdot 15 m / s \)
D. \( 20 \mathrm{m} / \mathrm{s} \)


How many atoms are contained in a
mole of acetic acid?
A \( \cdot 8 \times 6.02 \times 10^{23} \) atom \( \mathrm{mol}^{-1} \)
B . \( 4 \times 6.02 \times 10^{23} \) atom \( \mathrm{mol}^{-1} \)
C. \( 6 \times 6.02 \times 10^{23} \) atom \( \mathrm{mol}^{-1} \)
D. None of the above


If the angle of incidence is \( 70^{\circ}, \) then
calculate the angle between the incidence ray and the reflected ray.
A \( \cdot 40^{\circ} \)
B . \( 140^{\circ} \)
\( \mathrm{c} \cdot 130^{\circ} \)
D. \( 110^{\circ} \)


Define subset of a set.


Which of the following substances can
be compressed?
A. sponge
B. Stone
c. Magnettet
D. Diamond


Permanent magnet has properties retentivity and coercivity respectively
as:
A. high-high
B. low-low
c. low-high
D. high-low


Nitration of xylene gives only one mononitro derivative. Which xylene is it?
A. ortho
B. meta
c. para
D. Both o and


Simplify:\( \int\left(\frac{1}{(\ln x)}-\frac{1}{(\ln x)^{2}}\right) d x \)


The coordinates of the point(s) on the
graph of the function \( f(x)= \) \( \frac{x^{3}}{3}-\frac{5 x^{2}}{2}+7 x-4 \) where the tangent
drawn cut off intercepts from the
coordinate axes which are equal in
magnitude but opposite in sign is
This question has multiple correct options
\( \mathbf{A} \cdot\left(2, \frac{8}{3}\right) \)
B. \( \left(3, \frac{7}{2}\right) \)
\( \mathbf{c} \cdot\left(1, \frac{5}{6}\right) \)
D. none


What is hybridization of carbon atom
present in haloarenes?
\( A \cdot s p \)
B. \( s p^{2} \)
\( c \cdot s p^{3} \)
D. \( s p^{3} d \)


Discuss the endocrine system and its
functions.


Two cubes, each of side \( 4 \mathrm{cm} \) are joined end to end. Find the surface area of the
resulting cuboid


Why does fluorine shows anomalous
behaviour?


Two similar parallel plate capacitors
each of capacity \( C_{o} \) are connected in
series, The combination is connected
with a voltage source of \( V_{o} . \) Now
separation between the plates of one
capacitor is increased by a distance \( \boldsymbol{d} \)
and the separation between the plates of another capacitor is decreased by the
distance \( d / 2 \) The distance between the
plates of each capacitor was \( \boldsymbol{d} \) before the change in separation. Then, select the correct choice :
A. the new capacity of the system will increase
B. the new capacity of the system will decrease
c. the new capacity of the system will remain same
D. data insufficient


Solve :
\( \log \left(\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}\right)=\boldsymbol{a} \boldsymbol{x}+\boldsymbol{b} \boldsymbol{y} \)


Given the system of equation \( \boldsymbol{p} \boldsymbol{x}+\boldsymbol{y}+ \)
\( \boldsymbol{z}=\mathbf{1}, \boldsymbol{x}+\boldsymbol{p} \boldsymbol{y}+\boldsymbol{z}=\boldsymbol{p}, \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{p} \boldsymbol{z}=\boldsymbol{p}^{2} \)
then for what value of \( p \) does this system have no solution
A . -2
B. - 1
\( c .1 \)
D.


The bond formed between phosphate and pentose sugars of DNA is
A. Sulphide bond
B. Phosphodiester bond
c. Hydrogen bond
D. covalent bond


Which of the following statements is
not true?
The partial pressure of
A. Oxygen in deoxygenated blood is \( 40 \mathrm{mm} \) Hg
B. Oxygen in deoxygenated blood is \( 95 \mathrm{mm} \) Hg
c. oxygen in alveolar air is \( 104 \mathrm{mm} \) Hg
D. Carbon dioxide in the alveolar air is 40 \( \mathrm{mm} \) Hg


The heat energy emitted by sun reaches
the earth through:
A. Conduction
B. Convection
c. Radiation
D. None


A sphere, a cube and a thin circular plate have the same mass and are
made of the same material. All of them
are heated to the same temperature. The rate of cooling is
A. The maximum for the sphere and minimum for the plate
B. The maximum for the sphere and minimum for the cube
(a) and (b)
c. Both
D. None of the above


Derived Einstein's Photoelectric
equation. Explain photoelectric effect with help of this equation.


What is the chemical formula of rust?


Anabaena belongs to the kingdom
A. Monera
B. Protista
c. Animalia
D. None of the above


A line is perpendicular to the plane \( x+ \)
\( 2 y+2 z=0 \) and passes through
\( (0,1,0) . \) The perpendicular distance of this line from the origin is
A \( \frac{\sqrt{5}}{3} \)
B. \( \frac{\sqrt{7}}{3} \)
\( c \cdot \frac{2}{3} \)
D. 3


A tower stands at the top of a hill whose height is three times the height of the tower. The tower is found to subtend an
angle of \( \mid \tan ^{-1}(1 / 7) \) at a point \( 2 k m \) away on the horizontal throught the foot of the hill. Then the height of the tower is
\( ^{\mathbf{A}} \cdot \frac{1}{2} k m \) or \( \frac{1}{3} k m \)
B. \( \frac{1}{3} k m \) or \( \frac{2}{3} k m \)
c. \( \frac{2}{3} k m \) or \( \frac{1}{2} k m \)
D. \( \frac{3}{4} k m \) or \( \frac{1}{2} k m \)


If \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) satisfies \( \boldsymbol{f}(\boldsymbol{x}+\boldsymbol{y})= \)
\( \boldsymbol{f}(\boldsymbol{x})+\boldsymbol{f}(\boldsymbol{y}) \) for all \( \boldsymbol{x}, \boldsymbol{y} \in \boldsymbol{R} \) and
\( f(1)=7, \) then \( \sum_{r=1}^{n} f(r) \)
\( A \cdot \frac{7 n}{2} \)
B. \( \frac{7(n+1)}{2} \)
\( \mathbf{c} \cdot 7 n(n+1) \)
D. \( \frac{7 n(n+1)}{2} \)


Find the common ratio in the following
G.P. \( \sqrt{\mathbf{3}}, \mathbf{3}, \mathbf{3} \sqrt{\mathbf{3}} \)


Heavy water \( \left(D_{2} O\right) \) freezes at \( ? \)
A . \( -3.8^{0} \mathrm{C} \)
B . \( 3.8^{\circ} \mathrm{C} \)
\( c \cdot 0^{0} C \)
D. \( 38^{\circ} \mathrm{C} \)


\( d \)
0
\( d \)
\( d \)


A DNA segment has sequence ATC CAT CTA GTA, the sequence of RNA synthesized by this segment is
A. TUG GTU GUT CAU
в. GUT GтU GUT САU
c. сАU ятบ яUт сти
D. UAG GUA GAU CAU


The graph represents the motion of a
train travelling between two stations.
Which statement about the train is
correct?
A. Its acceleration takes a longer time than its deceleration
B. It travels at constant speed for less than half of its journey time
c. It travels \( 2000 m \) in the first 100 s
D. It travels \( 10000 m \) at constant speed


Study the bar graph representing the
number of persons in various age
groups in a town shown in above fig.
Observe the bar graph and answer the
following questions:
Whether the population in general
increases, decreases or remains
constant with the increase in the age-
group.


Electrophile that participates in
nitration of benzene is:
A . \( N O^{+} \)
в. \( N O_{2}^{\text {t }} \)
c. \( N O \)
D. \( N O_{3}^{-} \)


Find the equation of centre (1,1) and radius \( \sqrt{2} \)


Haemoglobin of the human blood forms
a stable compound with which of the
following gas, leads to death?
A. Oxygen
B. Carbon dioxide
c. Carbon monoxide
D. Nitrogen


What happens when dilute hydrochloric acid is added to iron fillings?
A. Hydrogen gas and iron chloride are produced
B. Chlorine gas and iron hydroxide are produced
c. No reaction takes place
D. Iron salt and water are produced


Let \( L \) be the set of all straight lines in
the Euclidean plane. Two lines \( l_{1} \) and \( l_{2} \)
are said to be related by the relation \( \boldsymbol{R} \) if
\( l_{1} \) is parallel to \( l_{2} \). Then the relation \( R \) is This question has multiple correct options
A. Reflexive
B. Symmetric
c. Transitive
D. Equivalence


The condition of erythroblastosis
foetalis occurs only when
A. The husband is \( R h^{+} \) and wife is \( R h^{-} \)
B. The husband is \( R h^{-} \) and wife is \( R h^{+} \)
C. The mother is \( R h^{+} \) and the foetus is \( R h^{-} \)
D. The mother is \( R h^{-} \) and the foetus is \( R h^{+} \)


In the given reaction,
\( \boldsymbol{C H}_{3}-\underset{C H_{3}}{C}=\boldsymbol{C H}-\boldsymbol{O}-\boldsymbol{C H}_{3}+ \)
\( \boldsymbol{C H}_{3}-\boldsymbol{O}-\boldsymbol{H}(\boldsymbol{e} \boldsymbol{x} \boldsymbol{c} \boldsymbol{e} \boldsymbol{s} \boldsymbol{s}) \frac{\boldsymbol{H} \boldsymbol{C I}}{d r \boldsymbol{y}} \)
\( \boldsymbol{X}(M \boldsymbol{a} \boldsymbol{j} \boldsymbol{o} \boldsymbol{r}) \)
Then \( X \) will be:
\( ^{\mathbf{A}} \cdot_{C H_{3}-} \stackrel{_{C H_{3}}^{O C H_{3}}}{C}-C H_{2}-O C H_{3} \)
B.
(2)
\( \mathrm{c} \cdot_{C H_{3}-C_{C H_{3}}^{I}-C H_{2}-\ddot{O}-C H_{3}} \)
\( ^{\mathrm{D}} \mathrm{CH}_{3}-\underset{_{C H_{3}}^{\mathrm{H}}}{C H}-C_{H}^{\text {сл }}-\ddot{O}-C H_{3} \)


Whenever the amount of urine
decreases the stage is called
A. Anuria
B. Polyuria
c. oliguria
D. Floating kidney


Fill in the blank.
Water offers fluid friction as
compared to honey.
A. higher
B. lower
c. same
D. zero


The largest set of values of 'x' for which
\( x \operatorname{in} x>x-1 \) is?
A \( .(0,1) \)
B. \( (1, \infty) \)
c. (0,1)\( \cup(1, \infty) \)
D. None


A stone is dropped into a quiet lake and
waves move in circles at the speed of 5 \( \mathrm{cm} / \mathrm{s} \) At the instant when the radius of
the circular wave is \( 8 \mathrm{cm} \) how fast is the
enclosed area increasing?
\( \mathbf{A} \cdot 84 \pi \mathrm{cm}^{2} / \mathrm{s} \)
B. \( 80 \pi \mathrm{cm}^{2} / \mathrm{s} \)
\( \mathbf{c} \cdot 90 \pi \mathrm{cm}^{2} / \mathrm{s} \)
D. \( 96 \pi \mathrm{cm}^{2} / \mathrm{s} \)


Can two angles be supplementary if both of them are: (i) acute (ii) obtuse
(iii) right?


The amplitude and time period of simple harmonic oscillator are \( a \) and \( T \)
respectively. The time taken by it in
displacing from \( \boldsymbol{x}=\mathbf{0} \) to \( \boldsymbol{x}=\boldsymbol{a} / \mathbf{2} \) will
be
A . \( T \)
в. \( \frac{T}{2} \)
c. \( \frac{T}{4} \)
D. \( \frac{T}{12} \)


At what distance ( from the left) on the
bottom face of the block will the normal
reaction act when \( F \) acts at the height \( \frac{\boldsymbol{H}}{\mathbf{2}} \) ? (here, assume no toppling happens)
A \( \cdot \frac{\mu_{k} H}{2} \)
в. \( \frac{b-\mu_{k} H}{2} \)
c. \( _{b-} \frac{\mu_{k} H}{2} \)
D. \( \frac{H}{2 \mu_{k}} \)