Assertion
Dolly was a female domestic sheep, and the first mammal cloned by somatic
cell nuclear transfer
Reason
Cell nucleus from an adult somatic cell
is transferred into an unfertilized oocyte
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


One mole of an ideal monoatomic gas is
mixed with 1 mole of an ideal diatomic
gas. The molar specific heat of the mixture at constant volume is :
A. 3 cal
B. 4 cal
\( c \cdot 8 \) cal
D. 9 cal


Find the mean of the first 10 natural
numbers.


Which of the followings are not lyophobic in nature?

This question has multiple correct options
A. Gelatin
B. Sulphur
c. starch
D. Protein


Which of the following are the products
in the following reaction?
A . 2-chloro toluene
B. 3-chloro toluene
c. 4 -chloro toluene
D. Both A and


When phenol is treated with excess bromine water, it gives:
A. m-Bromophenol
B. o- and p-bromophenol
c. 2,4 -Dibromophenol
D. 2,4,6-Tribromophenol


topp
iven b


Find 'c', so that \( \boldsymbol{f}^{\prime}(\boldsymbol{c})=\frac{\boldsymbol{f}(\boldsymbol{b})-\boldsymbol{f}(\boldsymbol{a})}{\boldsymbol{b}-\boldsymbol{a}} \)
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{e}^{\boldsymbol{x}} \) at \( \boldsymbol{a}=\mathbf{0}, \boldsymbol{b}=\mathbf{1} \)


Select the most ionic and most covalent
compounds respectively from the following.
\( \boldsymbol{C r} \boldsymbol{O}_{5}, \boldsymbol{M n}_{2} \boldsymbol{O}_{7}, \boldsymbol{P b O}, \boldsymbol{P}_{4} \boldsymbol{O}_{10}, \boldsymbol{S n O}_{2} \)
A. \( C r O_{5}, M n_{2} O_{7} \)
в. \( P b O, M n_{2} O_{7} \)
\( \mathrm{c} \cdot \mathrm{Cr} \mathrm{O}_{5}, P_{4} \mathrm{O}_{1} \)
D. \( S n O_{2}, C r O_{5} \)


Write all pairs of angles of linear pair.


A constituent of gasoline is:
A. \( N a H C O_{3} \)
в. \( H_{2} S O_{4} \)
c. \( C H_{4} \)
D. \( \operatorname{Ca}(O H)_{2} \)
E \( . C_{8} H_{18} \)


The order of magnitude of seconds in a
day is \( 10^{x} \). What is \( x \)


Figure shows a capacitor made of two
circular plates each of radius \( 12 \mathrm{cm} \)
and separated by \( 5.0 \mathrm{cm} . \) The capacitor
is being charged by an external source (not shown in the figure). The charging
current is constant and equal to 0.15 A.
(a) Calculate the capacitance and the
rate of change of potential difference
between the plates.
\( (b) \)
Obtain the displacement current across
the plates.
\( (c) \)
Is
Kirchhoffs first rule (junction rule) valid
at each plate of
the capacitor Explain.


n the given figure, \( \boldsymbol{A B}=\boldsymbol{A C} \)
Then \( A D \) does not bisects angle \( A \)
\( A \). True
B. False


\( d \)
\( d \)
\( d \)
\( x \)


If the source of light used in a Young's double slit experiment is changed from red to violet
A. the fringes will become brighter
B. consecutive fringes will come closer
c. the intensity of minima will increase
D. the central bright fringe will become a dark fringe


The common name for propan-2-ol is :
A . n-Propyl alcohol.
B. iso-Propyl alcohol.
c. ethyl alcohol.
D. methyl alcohol.


Two equal point charges are fixed at \( x=-a \) and \( x=+a \) on the \( X- \) axis
Another point charge \( Q \) is placed at the
origin. The change in electrical potential energy \( Q \) when it is displaced by a smal
distance \( x \) along the \( X \) -axis, is approximately proportional to
\( A \cdot x \)
в. \( x^{2} \)
c. \( x^{3} \)
D. \( 1 / x \)


Why is agriculture the cause of water
scarcity?
A. Because a large amount of crops require quality water in huge quantities.
B. Because agriculture is the largest user of water.
C. Both A and B.
D. None of these.


A condenser of capacity \( C \) is charged to
a potential difference of \( V_{1} \). The planes
of the condenser are then connected to
an ideal inductor of inductance \( L \). The
current through the inductor when the
potential difference across the
condenser reduces to \( V_{2} \) is ?
A \( \cdot \frac{C\left(V_{1}^{2}-V_{2}^{2}\right)}{L} \)
B. \( \frac{C\left(V_{1}^{2}+V_{2}^{2}\right)}{L} \)
\( \left(\frac{C\left(V_{1}^{2}-V_{2}^{2}\right)}{L}\right)^{1 / 2} \)
\( \left(\frac{C\left(V_{1}-V_{2}\right)^{2}}{L}\right)^{1 / 2} \)


A railway carriage has its centre of gravity at a height of \( 1 m \) above the rails
which are \( 1.5 m \) apart.The maximum
safe speed at which it could travel round an unbanked curve of radius
\( 100 m \) is
\( \mathbf{A} \cdot 12 m / s \)
в. \( 18 \mathrm{m} / \mathrm{s} \)
c. \( 22 m / s \)
D. \( 27 m / s \)


Pasteur effect is concerned with the
shifting of environmental conditions from
A. Light to dark
B. Aerobic to anaerobic
c. Anaerobic to aerobic
D. Light to anaerobic


\( C O_{2} \) and \( S i O_{2} \) is a solid or gas?
A. \( C O_{2} \) gas and \( S i O_{2} \) solid
B. \( C O_{2} \) solid and \( S i O_{2} \) gas
c. \( C O_{2} \) gas and \( S i O_{2} \) gas
D. \( C O_{2} \) solid and \( S i O_{2} \) solid


The given sample of lathers easily with water, it is :
A. hard water.
B. soft water.
c. permanent hard water.
D. temporary hard water.


The quantity of heat required to raise the temperature of a body through one degree Celsius is known as:
A. Latent heat of body
B. Specific latent heat of body
c. Heat capacity of a body
D. None


If \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \boldsymbol{a} \boldsymbol{n} \boldsymbol{d} \boldsymbol{f}(\boldsymbol{x})=\frac{\boldsymbol{x}}{1+|\boldsymbol{x}|} \cdot \) then
\( f(x) \) is
A. injective but not surjective
B. surjective but not injective
c. injective as well as surjective
D. neither injective nor surjective


Which of the following is not a disadvantage of using hard water?
A. In production of steam in boilers
B. Formation of scales in cooking utensils
c. In cooking,bathing and washing
D. In ion exchanges


What is tissues?


What happens when white phosphorous
is heated with conc. \( N a O H \) solution in
an inert atmosphere of \( \boldsymbol{C O}_{2} \) ?


A particle experiences a positiondependent force given by
\[
\boldsymbol{F}(\boldsymbol{x})=-\boldsymbol{6} \boldsymbol{x}^{2}+\boldsymbol{4} \boldsymbol{x}+\boldsymbol{3} / \boldsymbol{x}^{2}
\]
where \( x \) is in meters and \( F \) is in
Newtons (units have been abbreviated).
At \( x=1 m, \) what is the potential energy
of the particle relative to the potential energy at the origin?
A . \( +5 J \)
в. \( +3 J \)
\( c .-3 J \)
D. \( -5 . J \)
E. Cannot be determined


Find the total surface area of cube
having side \( 3.4 \mathrm{cm} ? \)


For a critical study of secondary growth in the plant, which of the following pairs is suitable?
A. Sugarcane and sunflower
B. Teak and pine
c. Deodar and fern
D. Wheat and maiden hair fern


In the given figure, \( \frac{P K}{K S}=\frac{P T}{T R} \) and
\( \angle P K T=\angle P R S . \) Prove that \( \Delta P S R \) is
an isosceles triangle.


Maximum force exerted by the bat on the ball is:
A \( .2500 N \)
в. \( 5000 N \)
c. \( 7500 N \)
D. \( 1250 N \)


The foci of an ellipse are located at the points (2,4) and \( (2,-2) . \) The points (4,2) lies on the ellipse. If \( a \) and \( b \)
represent the lengths of the semi-major and semi-minor axes respectively, then
the value of \( (a b)^{2} \) is equal to
A. \( 68+22 \sqrt{10} \)
В. \( 6+22 \sqrt{10} \)
c. \( 26+10 \sqrt{10} \)


Which of the following is a natural indicator?
A. China rosa
B. Blueberry
C. Morning glory
D. All of above


Choose correct squence for the
following species.
\( \mathbf{A} \cdot F_{2}>C l_{2}>B r_{2}>I_{2}(\text { Reducing power }) \)
B. \( C l_{2}<F_{2}<B r_{2}<I_{2} \) (Reactivity)
\( \mathbf{C} \cdot I_{2}>B r_{2}>F_{2}>C l_{2}(\text { Bond length }) \)
D. \( C l_{2}>B r_{2}>F_{2}>I_{2} \) (Bond dissociation enthalpy)


Find the volume and surface area of a sphere of radius \( 8.4 \mathrm{cm} .\left(\pi=\frac{22}{7}\right) \)


Dimensions of specific heat are :
A \( \cdot\left[M L^{2} T^{-2} K\right] \)
\( \mathbf{B} \cdot\left[M L^{2} T^{-2} K^{-1}\right] \)
C \( \cdot\left[M L^{2} T^{2} K^{-1}\right] \)
D・ \( \left[L^{2} T^{-2} K^{-1}\right] \)


Find the value \( \frac{\left(x^{2}-4\right)}{(x+2)} \)
A \( .2 x-2 \)
B. \( x-2 \)
c. \( x+2 \)
D. None of these


Find the components of a vector \( \overrightarrow{\boldsymbol{A}}= \) \( 2 \hat{i}+3 \hat{j} \) along the directions of \( \hat{i}+ \) \( \hat{j} \) and \( \hat{i}-\hat{j} \)
A \( \cdot \frac{5}{\sqrt{2}}, \frac{-1}{\sqrt{2}} \)
B. \( \frac{-5}{\sqrt{2}}, \frac{-1}{\sqrt{2}} \)
c. \( \frac{5}{\sqrt{2}}, \frac{1}{\sqrt{2}} \)
D. \( \frac{-5}{\sqrt{2}}, \frac{1}{\sqrt{2}} \)


The curved face of a plano-convex lens
is silvered. If \( \mu \) be the refractive index
and \( r \) the radius of curvature of this
curvature surface, then the system behaves like a concave mirror of radius
\( A \cdot \frac{r}{\mu} \)
в. \( \frac{r}{\mu-1} \)
c. \( r \)
D \( \cdot r(\mu-1) \)


Study the graph carefully and answer
the question given below it.

In which year did the import register
highest increase over its preceding year
A .1973
В. 1974
\( c .1975 \)
D. 1978


Which of the folowing is incorrect?
A. Nitric oxide depletes ozone layer in upper atmosphere
B. \( O_{3} \) is a powerful oxidising agent
C . Acidic strength increases from \( H_{2} \) Te to \( H_{2} O \)
D. \( S O_{2} \) is redusing agent while \( T e O_{2} \) is an oxidising
agent


Give a non-empty set \( X . \) Consider \( P(X) \) which is the set of all subsets of \( \boldsymbol{X} \)
Define the relation \( R \) in \( P(X) \) as follows:
For subsets \( \boldsymbol{A} \) and \( \boldsymbol{B} \) in \( \boldsymbol{P}(\boldsymbol{X}), \boldsymbol{A} \boldsymbol{R} \boldsymbol{B} \) if
\( \boldsymbol{A} \subset \boldsymbol{B}, \) is \( \boldsymbol{R} \) an equivalence relation on
\( \boldsymbol{P}(\boldsymbol{X}) ? \)
Justify your answer.


Beryllium, when combined with trace of chromium forms a gemstone called
A. Ruby
B. Sapphire
c. Emerald
D. None of the above


If the bisectors of the angles \( \angle A B C \) and
\( \angle A C B \) of a triangle \( A B C \) meet at a point
0, then Prove that \( \angle B O C=90^{\circ}+ \)
\( \frac{1}{2} \angle B A C \)


The correct order of acidic strength of
oxy - acids of chlorine is:
\( \mathbf{A} \cdot H C l O<H C l O_{2}<H C l O_{3}<H C l O_{4} \)
B \( \cdot H C l O_{4}<H C l O_{3}<H C l O_{2}<H C l O \)
\( \mathbf{c} \cdot H C l O>H C l O_{4}>H C l O_{3}>H C l O_{2} \)
D. \( H C l O_{4}<H C l O_{2}>H C l O_{3}>H C l O \)


When a ball is \( h \) metre high from a point
\( O, \) its velocity is \( v . \) When it is \( h m \) below
\( O, \) its velocity is \( 2 v . \) Find the maximum
height from \( O \) it will acquire.
\( ^{A} \cdot \frac{2 h}{3} \)
в. \( \frac{5 h}{3} \)
c. \( \frac{3 h}{2} \)
D. \( 2 h \)


The type of hybrid orbitals used by the
chlorine atom in \( C l O_{2}^{-} \) is:
\( A \cdot s p^{3} \)
B . \( s p^{2} \)
\( c \cdot s p \)
D. none of these


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


In the diagram
Write the sum of coordinates of \( \boldsymbol{U} \)


\( \ln a \Delta A B C, \) if \( A B=A C \) and \( \angle A=70^{\circ} \)
find \( \angle B \) and \( \angle C \)


Force is directly proportional to
A. Rate of change in distance
B. Rate of change in velocity
C. Momentum
D. Rate of change in momentum


What name is given to the elements belonging to the third period of Mendeleev's periodic table?


Calculate the number of moles of
methyl alcohol in 2 molal solution in 5 L. The density of solution is \( 0.981 \mathrm{kg} . \mathrm{dm}^{-3} \)
Given that, molar mass of methyl alcohol is 32 g.mol \( ^{-1} \).


Atomic numbers of Cr and Fe are
respectively 24 and \( 26 . \) Which of the following is paramagnetic with spin of electron?
A \( \cdot C r(C O)_{6} \)
в \( \cdot\left[F e(C O)_{5}\right] \)
c. \( \left[F e(C N)_{6}\right]^{4} \)
D. \( \left[C r\left(N H_{3}\right)_{6}\right]^{3+} \)


At. N.T.P. \( 28 ~ g \) of Nitrogen occupies 22.4 litres. What is the mass of 5.6 litres of Nitrogen at \( 38 \mathrm{cm} \) Hg pressure and \( 273^{0} C \) temperature is then
A \( .1 .87 \mathrm{g} \)
в. 48 g
c. \( 1.75 \mathrm{g} \)
D. \( 1.5 \mathrm{g} \)


If the straight lines \( A B \) and \( X Y \) intersect at the point 0 and \( \angle A O X=3 \angle X O B \)
then the four angles formed at 0 are:
A \( \cdot 30^{\circ}, 30^{\circ}, 90^{\circ}, 210^{\circ} \)
В. \( 30^{\circ}, 30^{\circ}, 150^{\circ}, 150^{\circ} \)
c. \( 45^{\circ}, 135^{\circ}, 90^{\circ}, 90^{\circ} \)
D . \( 45^{\circ}, 45^{\circ}, 135^{\circ}, 135^{\circ} \)


If the two straight lines \( \boldsymbol{y}=\boldsymbol{m}_{1} \boldsymbol{x}+\boldsymbol{c}_{1} \)
and \( y=m_{2} x+c_{2} \) are perpendicular to
each other then \( \boldsymbol{m}_{1} \boldsymbol{m}_{2}= \)
A . -
B.
\( c \cdot 1 / 2 \)
D.


Compare a step-up transformer with a step-down transformer based on the number of loops in the primary and secondary coils.


Prove that the triangle, whose position vectors of the vertices are \( 2 \hat{i}+4 \hat{j}- \) \( \hat{\boldsymbol{k}}, \boldsymbol{4} \hat{\boldsymbol{i}}+\mathbf{5} \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \) and \( \boldsymbol{3} \hat{\boldsymbol{i}}+\boldsymbol{6} \hat{\boldsymbol{j}}-\boldsymbol{3} \hat{\boldsymbol{k}} \)
respectively, is an isosceles right angled triangle.


When \( 5 V \) potential difference is applied across a wire length \( 0.1 m \), the drift
speed of electron is \( 2.5 \times 10^{-4} m s^{-1} . \) If
the electron density in the wire is 8 \( \times 10^{28} m^{-3}, \) the resistivity of the material is close to
A \( \cdot 1.6 \times 10^{-8} \Omega \mathrm{m} \)
В. \( 1.6 \times 10^{-7} \Omega \mathrm{m} \)
c. \( 1.6 \times 10^{-6} \Omega \mathrm{m} \)
D. \( 1.6 \times 10^{-5} \Omega \) m


A body travels uniformly a distance of \( (13.7 \pm 0.2) m, \) in time \( (4.0 \pm 0.3) s \)
The velocity of particle is?
A \( .(3.45 \pm 0.31) m / s \)
в. \( (3.4 \pm 0.3) \mathrm{m} / \mathrm{s} \)
c. \( (3.68 \pm 0.4) \mathrm{m} / \mathrm{s} \)
D. \( (3.6 \pm 0.42) \mathrm{m} / \mathrm{s} \)


Cut leaves remain green for longer time if dipped in
A . Auxin
B. Cytokinins
c. Ethylene
D. Gibberellins


If a glass rod is rubbed on silk cloth and
then brought near the bits of paper it.....
then
A. Attracts
B. Repel
c. Both
D. None


Which quantity is zero for a crystalline
solid that is elementally pure at \( 0 \mathrm{K} ? \)
A. Standard voltaic potential
B. Entropy
c. Enthalpy
D. Reaction rate
E. Gibbs free energy


Forces between electric charges in relative motion are called:
A. Electromagnetic force
B. Electrostatic force
c. Both a and
D. None of these


Consider the above sequence of reactions. Find \( \boldsymbol{A}, \boldsymbol{B} \) and \( \boldsymbol{C} \)
\( \overbrace{\mathrm{CH}}_{2} \mathrm{OH} \stackrel{\mathrm{HBr}}{\longrightarrow} \mathrm{A}^{\mathrm{O}_{3} / \text { reduction }}>\mathrm{B}+\mathrm{c} \)
\( \mathbf{A} \)
\( \overbrace{\mathrm{CH}}_{2} \mathrm{Br}, \mathrm{CH}_{2}=\mathrm{O}, \mathrm{O}=\mathrm{CH}-^{*} \mathrm{CH}_{2} \mathrm{Br} \)
B. \( \overbrace{x}_{\mathrm{CH}_{2} \mathrm{Br}}, \stackrel{*}{\mathrm{CH}_{2}=} 0, \mathrm{O}=\mathrm{CH}-\mathrm{CH}_{2} \mathrm{Br} \)
\( c \)
\( \overbrace{x}_{\mathrm{CH}_{2} \mathrm{Br}}, \) HCOOH \( , \mathrm{O}=\mathrm{CH}-\dot{\mathrm{CH}}_{2} \mathrm{Br} \)
D. \( \overbrace{x}_{\mathrm{CH}_{2} \mathrm{Br}}, \) HCOOH \( , \mathrm{HOOC}-\stackrel{*}{\mathrm{CH}_{2}} \mathrm{Br} \)


Which of the following contains prokaryote organisms capable of surviving in extreme conditions of heat
and salt concentration?
A. Bacteria
B. Virus
c. Fungi
D. Plants


A wall 5 m long, \( 30 \mathrm{cm} \) wide and \( 4 \mathrm{cm} \)
height is made of bricks, each measuring \( (22 c m \times 12.5 c m \times \)
12.5cm \( ) . \) If \( \frac{1}{12} \) of the total volume of the
wall consists of motor, how many bricks
are there in the wall?


A dielectric is introduced in a charged
and isolated parallel plate capacitor, which of the following remains unchanged?
A. Energy
B. Charge
c. Electric field
D. Potential difference


Explain why ArOR ethers are cleaved to give RI and rather than Arl and ROH.


Protons and neutrons are heavier than
electrons and reside in the center of the
atom, which is called
A. the nucleus
B. the Orbit
c. the orbitals
D. none of the above


A satellite is going around the earth. Which of the following statement is not
correct?
A. It is freely falling body
B. It experiences no acceleration
c. It is moving with constant speed
D. Its angular momentum is constant


Atoms of eight elements \( A, B, C, D, E, F \) G and H have the same number of
electronic shells but different number
of electrons in their outermost shell. It
was found that elements \( A \) and \( G \)
combine to form an ionic compound which can also be extracted from sea
water. This compound is added in a small amount to almost all vegetable dishes during cooking. Oxides of elements A and B are basic in nature
while those of \( \mathrm{E} \) and \( \mathrm{F} \) are acidic. The
oxide of \( \mathrm{D} \) is almost neutral. Based on
the above information answer the
following question.
To which group or period of the periodic table do the listed elements belong?


A magnetic field \( B=2 t+4 t^{2} \) (where
\( t=\text { time }) \) is applied perpendicular to
the plane of a circular wire of radius \( r \)
and resistance \( R \). If all the units are in
\( S I, \) the electric charge that flows
through the circular wire during \( t=0 s \)
to \( t=2 s \) is:
\( \mathbf{A} \cdot \frac{6 \pi r^{2}}{R} \)
В. \( \frac{20 \pi r^{2}}{R} \)
\( ^{\mathrm{c}} \cdot \frac{32 \pi r^{2}}{R} \)
D. \( \frac{48 \pi r^{2}}{R} \)


Which of the following methods is employed to prevent rusting?
A. Annealing
B. Alloying
c. Enamelling
D. both (b) and (c)


A magnifying glass is used to read the newspaper. As it is moved far away from
the newspaper
A. Text becomes blurred and magnification reduces
B. Text becomes more focussed and magnification reduces
c. Text becomes more focused and magnification increases
D. Text becomes blurred and magnification increases


The oxide of aluminium has a chemical
formula \( A l_{2} O_{3} . \) State the valency of \( A l \)


\( \boldsymbol{E}_{\boldsymbol{g}}(\boldsymbol{T})=\boldsymbol{E}_{\boldsymbol{g}}(\boldsymbol{m})-\frac{\boldsymbol{\alpha} \boldsymbol{T}^{2}}{\boldsymbol{T}+\boldsymbol{\beta}} \) is
the Varshni's empirical expression,then
the value of \( m \) is


A particle moves in a way such that its
position can be expressed with \( \boldsymbol{x}(\boldsymbol{t})= \) \( t^{2}+t-3 \) and with \( y(t)=t^{3}-\frac{1}{t-1} \)
with being time in seconds. \( x(t) \) and
\( \boldsymbol{y}(t) \) are both in meters.
Initially, how far away is the particle from the origin?
A. \( 0.00 m \)
в. \( 1.00 m \)
c. \( 1.56 m \)
D. \( 2.83 m \)
E. \( 3.16 m \)


If a rigid body acted upon by a system of coplanar parallel forces is to be in
equilibrium, then :
A. vector sum of the forces must be zero
B. vector sum of the moments of the forces taken about a point in their plane must be zero
c. one of the conditions
(A) or
(B) must be satisfied
D. Both the conditions (A) and
(B) must be satisfied


Draw rough sketches for the following.
\( \ln \Delta \mathrm{PQR}, \mathrm{PQ} \) and PR are altitudes of the
triangle.


Differentiate the following functions
with respect to \( \boldsymbol{x} \)
\( \log \{x+2+\sqrt{x^{2}+4 x+1}\} \)


In Mendeleev table, the triad of VIII group is :
\( A \cdot \) Ru, Rh, Pd
B. Cu, Ag, Au
c. \( N, \) О, \( F \)
D. TI, Pb, Bi


Evaluate \( \int x^{2} \log x d x \)
A. \( \frac{x^{2}}{2} \log x-\frac{1}{9} x^{2}+c \)
B \( \cdot \frac{x^{3}}{3} \log x-\frac{1}{9} x^{2}+c \)
c. \( \frac{x^{3}}{3} \log x-\frac{1}{9} x^{3}+c \)
D. \( \frac{x^{3}}{3} \log x+\frac{1}{9} x^{3}+c \)


Which one is an accessory excretory organ?
A. Liver
B. Stomach
c. Intestine
D. Heart


The remainder when \( 2 x^{3}-3 x^{2}+7 x+ \)
5 is divided by \( 2 x+3 \) is :
\( A \cdot 0 \)
в. -13
c. -19
D. -16


In the circuit shown in figure, El and E2
are two ideal sources of unknown emfs.
Some currents are shown. Potential
difference appearing across \( 6 \Omega \)
resistance is \( \boldsymbol{V}_{\boldsymbol{A}}-\boldsymbol{V}_{\boldsymbol{B}}=\mathbf{1 0} \boldsymbol{V} \)
This question has multiple correct options
A. The current in the 4.00 resistance between \( c \& B \) is \( 5 A \)
B. The unknown emf \( E_{1} \) is 36 V.
C. The unknown emf \( E_{2} \) is 54 V.
D. The resistance R is equal to \( 9 \Omega \)


Coagulation of colloids can be achieved
by:
This question has multiple correct options
A . centrifugation
B. adding electrolyte
c. change in \( p H \)
D. adding water


Which among following is electron pair acceptor?
A. Arrhenius acid
B. Arrhenius base
c. Lewis acid
D. Lewis base
E. Bronsted-Lowry acid


The density of water is:
A \( \cdot 1 g / c m^{3} \)
В. \( 20 g / c m^{3} \)
\( \mathrm{c} \cdot 2 g / \mathrm{cm}^{3} \)
D. \( 0.1 g / c m^{3} \)


\( \ln 1932 \)
discovered an
electrically neutral particle in the atom named as neutron.
A. Rutherford
B. James chadwick
c. J.J. Thompson
D. none of the above


Calculate number of electrons present
\( \operatorname{in} 9.5 g \) of \( P O_{4}^{3-} \)
\( A \cdot 6 N_{A} \)
в. \( 4.7 \mathrm{N}_{\mathrm{A}} \)
\( c \cdot 5 N_{A} \)
D. \( 0.1 \mathrm{N}_{A} \)


\( \mathrm{IF} \mathrm{A}=\left|\begin{array}{ll}\mathbf{5} & \boldsymbol{x} \\ \boldsymbol{y} & \boldsymbol{6}\end{array}\right| \mathrm{B}=\left|\begin{array}{cc}-\boldsymbol{4} & \boldsymbol{y} \\ -\boldsymbol{4} & -\mathbf{5}\end{array}\right| \) and \( \mathbf{A}+\mathrm{B}=\mathbf{I} \) then
the values of \( x \) and \( y \) respectively are
A \( .-4,4 \)
B. -4,-4
\( c \cdot 4,4 \)
D. 4,-4


Three different objects \( m_{1}, m_{2} \) and \( m_{3} \)
are allowed to fall from rest and from
the same point \( \boldsymbol{O} \) along three different
frictionless paths. The speeds of the three objects, on reaching the ground will be in the ratio of
\( \mathbf{A} \cdot m_{1}: m_{2}: m_{3} \)
B. 1: 1: 1
c. \( m_{1}: 2 m_{2}: 3 m_{3} \)
D. \( \frac{1}{m_{1}}: \frac{1}{m_{2}}: \frac{1}{m_{3}} \)


\( \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{- 3} & \mathbf{- 4} \\ \mathbf{- 1} & \mathbf{3} & \mathbf{4} \\ \mathbf{1} & \mathbf{- 3} & \mathbf{- 4}\end{array}\right] \) and \( \mathbf{A}^{2}=\boldsymbol{\lambda} \boldsymbol{I} \) then
\( \boldsymbol{\lambda}= \)
\( A \cdot 0 \)
B.
\( c \cdot \frac{1}{2} \)
D. -


Arrange the following species in order of increasing stability: \( \boldsymbol{L} \boldsymbol{i}_{2}, \boldsymbol{L} \boldsymbol{i}_{2}^{+}, \boldsymbol{L} \boldsymbol{i}_{2} \)
A \( \cdot L i_{2}^{+}<L i_{2}^{-}<L i_{2} \)
c. \( L i_{2}<L i_{2}^{+}=L i_{2} \)
D. \( L i_{2}^{+}=L i_{2}^{-}<L i_{2} \)


\( \mathbf{A} \)
\( 2 \Omega \) resistor is connected in series
with \( R \Omega \) resistor. This combination is
connected across a cell. When the
potential difference across \( 2 \Omega \) resistor is balanced on potentiometer wire, null
point is obtained at length of 300cm.
When the same procedure is repeated for \( R \Omega \) resistor, null point is obtained at
length \( 350 \mathrm{cm}, \) value of \( \mathrm{R} \) is:
A. 5
в. 3.33
c. 4.6
D. 2.83


Assertion
Earthworms enhance porosity as they
move through the soil and this enriches the growth of a plant.
Reason
Roots take up air from the air spaces present between the soil particles.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The atomic number of a halogen element in the fourth period is \( 35 . \) If true
enter \( 1, \) else enter 0


The energy of the electron in the second
and third Bohr orbits of the hydrogen atom is \( -5.42 \times 10^{-12} \) erg and \( -2.41 \times 10 \)
-12 erg, respectively. The wave length of the emitted radiation when the electron
drops from third to second orbit will be :
\( A \cdot 6.6 \times 10^{3} \)
B. \( 6.6 \times 10^{-3} \)
c. \( 13.2 \times 10^{3} \)
D. 13.2 \( \times 10^{-3} \)


The roots of the equation \( 2 x^{2}+x- \)
\( 4=0 \) are
\( \mathbf{A} \cdot 1,-4 \)
в. \( -3, \frac{1}{\sqrt{3}} \)
c. \( \frac{\sqrt{33}-1}{4}, \frac{-\sqrt{33}-1}{4} \)
D. None


Assertion
Superoxides contain the \( O_{2}^{-} \) ion which has one unpaired electron.
Reason
Superoxides contain the \( O_{2}^{-} \) ion which
has one unpaired electron in its antibonding orbital
A. Assertion is true, Reason is true and Reason is correct explanation for Assertion
B. Assertion is true, Reason is true and Reason is NOT the correct explanation for Assertion
c. Assertion is true, Reason is false
D. Assertion is false, Reason is true


\( \int \cos (\log x) d x=\ldots \ldots \ldots \ldots \quad+\quad c \)
A. \( \frac{x}{2}[\cos (\log x)+\sin (\log x)] \)
B \( \cdot \frac{x}{4}[\cos (\log x)+\sin (\log x)] \)
c. \( \frac{x}{2}[\cos (\log x)-\sin (\log x)] \)
D. \( \frac{x}{2}[\sin (\log x)+\cos (\log x)] \)


\( * \)
\( \vdots \)
\( * \)
\( * \)


Match the items of column I and
column I
\( \begin{array}{llll}\text { Column } & & \text { Column II } & \\ & \text { I } & & \\ \text { a } & \text { Mitchell } & \text { p } & \begin{array}{l}\text { Steps of dark reaction } \\ \text { to photosynthesis }\end{array} \\ \text { b } & \text { Gibbs } & \text { q } & \text { Photophosphorylation } \\ \text { c } & \text { Arnon } & \text { r } & \text { Concept of free energy } \\ \text { d } & \text { Calvin } & \text { s } & \begin{array}{l}\text { Chemiosmotic } \\ \text { hypothesis }\end{array} \\ & \text { t } & \text { Mass flow hypothesis }\end{array} \)
\( A \cdot a-s, b-t, c-r, d-q \)
B. \( a-s, b-r, c-p, d-q \)
\( c \cdot a-r, b-s, c-p, d-q \)
D. a-s, b-r, c-q, d-p


Lanthanoids contraction is observed in:
A. \( H f \)
в. \( A t \)
\( c \cdot X e \)
D. \( A c \)


has the highest specific latent heat of vaporisation.
A. steam
B. constant
c. can't say
D. none of the above


If \( P Q \) and \( R S \) intersect at point \( T, \) such
that \( \angle P R T=40^{\circ}, \angle R P T=95^{\circ} \) and
\( \angle T S Q=75^{\circ} . \) Find \( \angle S Q T \)


Write the set of values of \( a \) for which
\( \boldsymbol{f}(\boldsymbol{x})=\cos \boldsymbol{x}+\boldsymbol{a}^{2} \boldsymbol{x}+\boldsymbol{b} \) is strictly
increasing on \( \boldsymbol{R} \)


The roots of \( x^{2}+k x+k=0 \) are real
and equal, find \( k \)


The wrong statement among the
following is:

This question has multiple correct options
A. nitrogen atom, nitride ion have same atomic number
B. aluminium atom and its ion have same mass number
C. iron atom, ferrous ion have same electron configuration
D. effective nuclear charge is same in both chlorine atom, chloride ion


The sine of the angle between the vectors \( \bar{i}+3 \bar{j}+2 \bar{k} \) and \( 2 \bar{i}-\overline{4 j}+\bar{k} \) is
A. \( \sqrt{\frac{155}{1.56}} \)
В. \( \sqrt{\frac{115}{116}} \)
c. \( \sqrt{\frac{115}{147}} \)
D. \( \sqrt{\frac{\sqrt{5}}{188}} \)


The A.M. of the series \( 1,2,4,8,16, \dots . ., 2 \)
is
A \( \cdot \frac{2^{n}-1}{n} \)
B. \( \frac{2^{n+1}-1}{n+1} \)
c. \( \frac{2^{n}-1}{n+1} \)
\( \frac{2^{n+1}-1}{n} \)


Find any ten rational numbers between
\( \frac{-5}{6} \) and \( \frac{5}{8} \)


Six identical resistors are connected as
shown in the figure. The equivalent
resistance will be:
A. Maximum between P and R
B. Maximum between Q and R
c. Maximum between P and Q
D. All are equal


Which of the following results in more energy in a wave?
A. a smaller wavelength
B. a lower frequency
c. a shallower amplitude
D. a lower speed


What is the duration of one cardiac
cycle in man when the heart beats for 75
times per minute?
A. 0.4 seconds
B. 0.8 seconds
c. 0.5 seconds
D. 0.3 seconds


The amount of heat energy given out by a given body when its temperature rises
or falls by \( 1^{\circ} C \) is called:
A. latent heat of fusion
B. specific heat capacity
c. heat capacity
D. latent heat of vaporisation


What does lac refer to in the lac operon?
A . Lactase
B . 1,00,000
c. Lac insect
D. Lactose


Why first ionization enthalpy of nitrogen
is more than oxygen?


The most common oxidation state of
actinide is:
\( A \cdot+2 \)
B. +1
\( c \cdot+3 \)
D. +4


Which of the following does not give silver mirror test with Tollen's reagent?
A. sucrose
B. Glucose
c. Fructose
D. Lactose


The angle of elevation of the top of a
tower from a point \( 20 m \) away from its
base is \( 60^{\circ} . \) The height of the tower is-
\( A \cdot 2 \sqrt{3} m \)
В. \( -20 \sqrt{3} \mathrm{m} \)
c. \( \sqrt{3} m \)
D. \( 20 \sqrt{3} \) m


The uses of plaster of paris are:
A. it is used as plaster for supporting fractured bones
B. for making toys and material for decoration
C. for making smooth surface
D. all of the above


Assertion
\( \boldsymbol{P}(\boldsymbol{H} / \boldsymbol{E})>\boldsymbol{P}\left(\boldsymbol{E} / \boldsymbol{H}_{i}\right) \boldsymbol{P}\left(\boldsymbol{H}_{i}\right), \boldsymbol{i}= \)
\( \mathbf{1}, \mathbf{2}, \mathbf{3}, \dots, \boldsymbol{n} . \operatorname{Let} \boldsymbol{H}_{1}, \boldsymbol{H}_{2}, \boldsymbol{H}_{3}, \dots . . \boldsymbol{H}_{n} \) be \( \mathbf{n} \)
mutually exclusive \& exhaustive
events with probability \( \boldsymbol{P}\left(\boldsymbol{H}_{\boldsymbol{i}}\right)>\mathbf{0}, \boldsymbol{i}= \)
\( 1,2,3, \dots n . \) Let \( E \) be any other event with
\( \mathbf{0}<\boldsymbol{P}(\boldsymbol{E})<\mathbf{1} \)
Reason
\( \sum_{i=1}^{n} \boldsymbol{P}\left(\boldsymbol{H}_{i}\right)=\mathbf{1} \)
A. Both Assertion \& Reason are individually true \& Reason is correct explanation of Assertion
B. Both Assertion \& Reason are individually true but Reason is not the , correct (proper) explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true


A disk with
radius R has uniform surface cha
disk as a sereis of thin concer
potential \( V \) at a point on the di the disk.Assume that the potent
A \( \cdot \frac{\sigma}{2 \varepsilon_{0}} \)
B \( \cdot \frac{\sigma}{30} \)
\( c \cdot \frac{\sigma R}{24 c-c} \)
D. \( \frac{\sigma}{66} \)


If the compound interest on a certain
sum for 2 years is Rs \( 21 . \) What could be the simple interest?
\( \mathbf{A} \cdot \operatorname{Rs} 20 \)
B. Rs 16
c. Rs 18
D. Rs 20.50


The gas phase decomposition of
dimethyl ether follows first order kinetics,
\( \boldsymbol{C H}_{3} \boldsymbol{O C H}_{3}(\boldsymbol{g}) \rightarrow \boldsymbol{C H}_{2}(\boldsymbol{g})+\boldsymbol{H}_{2}(\boldsymbol{g})+ \)
\( \boldsymbol{C O}(\boldsymbol{g}) \)
The reaction is carried out in a constant
volume container at \( 500^{\circ} \mathrm{C} \) and has a
half-life of 14.5 minute. Initially only dimethyl ether is present at a pressure of 0.40 atmosphere. The total pressure
of the system after 12 minutes
assuming ideal gas behaviour in atm
is (write answer as the
first integer after decimal, e.g., if answer is 2.56 then answer should be 5 )


The area lying in the first quadrant between the curves \( x^{2}+y^{2}=\pi^{2} \) and
\( y=\sin x \) and \( y- \) axis is
\( ^{A} \cdot \frac{\pi^{3}-8}{4} \) sq. units
B. \( \frac{\pi^{3}+8}{4} \) sq. units
c. \( 4\left(\pi^{3}-8\right) \) sq. units
D. \( \frac{\pi-8}{4} \) sq. units


There have been certain objectives
against food preservation by
irradiations. These are:
This question has multiple correct options
A. irradiated food may itself become radioactive
B. irradiation can destroy the the nutrients such as vitamins and amino acids
C. ionising radiation produces reactive species such as the hydroxyl radical which then react with organic molecules to produce potentially harmful substances.
D. irradiated food may be much costlier


The synthetic steroid ethynylestardiol
(1) is a compuond used in the birth control pill.
How many \( s p \) hybridised carbon atoms
are present in compound (1) ?
\( A \cdot 2 \)
B.
\( c \)
D. 8
E. 10


The total number of all the numbers
divisible by \( 5, \) lying between 4000 and 5000 and can be formed using the digits 4,5,6,7 and 8 is :
A . 125
B. 9
c. 25
D. 625


\( \sin ^{-1} \frac{2 a}{1+a^{2}}+\sin ^{-1} \frac{2 b}{1+b^{2}}= \)
\( 2 \tan ^{-1} x, \) then find the value of \( x \)


Name the transition element of highest density


If \( \boldsymbol{y}=\cos \sqrt{\boldsymbol{x}} \) find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \)


The anode mud in the electrolyte refining of silver contains:
A. \( Z n, C u, A g, A u \)
в. \( Z n, \) А\( g, \) Аи
c. \( C u, A g, A u \)
D. \( A u \)


How much energy in watt-hour is required for an electric heater to convert
\( 2 \mathrm{kg} \) of ice at \( 0^{\circ} \mathrm{C} \) to water \( 25^{\circ} \mathrm{C} \)
Assume the water equivalent of the given heater to be 10 g. (Assume that initially the heater and the ice are in thermal equilibrium).


Characteristic of simple epithelium is
A. They are arranged indiscriminately.
B. They make a definite layer.
c. continue to devide and help in organ function.
D. None of the above


How soil testing helps the farmer? Write your opinion.


The escape velocity for a planet is \( \boldsymbol{v} . \mathbf{A} \)
particle starts from rest at large
distance from the planet The planet only under gravitational attraction and passes through a smooth tunnel through its centre, speed at the centre of the planet will be:


A chemical reaction in which energy is
liberated is called :
A. exothermic reaction
B. physical change
c. endothermic reaction
D. photochemical reaction


Express as kilogram (kg) using decimals:
\( 2750 g \)


The waves which are produced by accelerated electrons in electronic
circuits are
A . '-'-waves
B. '+'waves
c. Radio waves
D. Infrared rays


A beam of white light traveling in medium \( A \) strikes the interface to
another transparent medium, medium
B. If the speed of white light is less in
medium \( B \) than in medium \( A \), the
beam will
A. refract toward the normal
B. refract away from the normal
c. undergo total internal reflection
D. have an angle of reflection smaller than the angle of incidence
E. have an angle of reflection greater than the angle of incidence


If \( |a|<1 \) and \( |b|<1 \) then
\( \boldsymbol{S}=\mathbf{1}+(\mathbf{1}+\boldsymbol{a}) \boldsymbol{b}+\left(\mathbf{1}+\boldsymbol{a}+\boldsymbol{a}^{2}\right) \boldsymbol{b}^{2}+\dots \)
\( = \)
A \( \cdot \frac{1}{(1-b)(1-a b)} \)
B. \( \frac{1}{(1+b)(1-a b)} \)
c. \( \frac{1}{(1-b)(1+a b)} \)
D. \( \frac{1}{(1+b)(1+a b)} \)


An inorganic compound contains \( 5.88 \% \)
of hydrogen and \( 94.11 \% \) oxygen. The empirical formula of the compound is:
A. \( H O \)
B. \( H_{2} O_{2} \)
c. \( H_{2} O \)
D. Both A and B


\( 4.0 \mathrm{kg} \) of a gas occupies 22.4 litres at NTP. The specific heat capacity of the
gas at constant volume is \( 5.0 J K^{-1} \)
mol \( ^{-1} \) If the speed of sound in this gas
at NTP is \( 952 \mathrm{ms}^{-1} \) then the heat
capacity at constant pressure is (Take gas constant \( \mathrm{R}=8.3 \mathrm{JK}^{-1} \) mol \( ^{-1} \)
A \( \cdot 8.5 \mathrm{JK}^{-1} \mathrm{mol}^{-1} \)
в. \( 8.0 \mathrm{JK}^{-1} \mathrm{mol}^{-1} \)
\( \mathbf{c} \cdot 7.5 \mathrm{JK}^{-1} \mathrm{mol}^{-1} \)
D. \( 7.0 \mathrm{JK}^{-1} \mathrm{mol}^{-1} \)


If the switch at point \( P \) is opened
(shown in the figure) choose the correct
option
A. the current in \( R_{1} \) would not change
B. the potential difference between point \( X \) and the ground would increas
c. the current provided by the battery would increase
D. the emf produced by the battery (assumed to have internal resistance) would change


The amount of heat required to convert 1 g of ice at \( -10^{0} C \) into steam at \( 100^{0} C \) is (approximately): (specific
heat of water \( =4.187 \mathrm{J} / \mathrm{g}^{0} \mathrm{C}, \) latent heat of fusion \( =334 \) J/g , latent heat of
vaporization \( =2260 \) J/g, specific heat of ice \( =\mathbf{2 . 0 3} \mathrm{J} / \mathrm{g} \) ):
A . 3034 J
B. 735 J
c. 1000
D. 4200 J


A car of mass \( 1000 \mathrm{kg} \) rounds a curve of radius \( 250 \mathrm{m} \) at \( 90 \mathrm{km} / \mathrm{hr} \). Cpmpute its,
A. Angular speed
B. Centripal accelearation
c. centripetal accele ration
D. Centripetal force.


8 mol of a gas \( A B_{3} \) are introduced into a \( 1.0 d m^{3} \) vessel. It dissociates as
\( \mathbf{2} \boldsymbol{A} \boldsymbol{B}_{3}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{A}_{2}(\boldsymbol{g})+\boldsymbol{3} \boldsymbol{B}_{2}(\boldsymbol{g}) \)
At equilibrium, 2 mol of \( A_{2} \) is found to be present. The equilibrium constant for the reaction is :
A \( \cdot 2 m o l^{2} L^{-2} \)
B. \( 3 m o l^{2} L^{-2} \)
c. \( 27 m o l^{2} L^{-2} \)
D. \( 36 m o l^{2} L^{-2} \)


What is the power dissipated by each
lamp of resistance \( 60 \Omega ? \)
\( A \cdot 1 w \)
\( 3.2 \mathrm{w} \)
\( c \cdot 6 w \)
\( D \cdot 12 \mathrm{w} \)


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


The system of giving one name to the
individual is called
A. Quasibinomial system
B. Semibinomial system
c. Mononomial system
D. Uninomial system


HOTS
The various types of hydrides and
examples of each type are given below:
Hydride type Compound A Electron deficient
B Saline \( \quad \) ii \( \quad \boldsymbol{C H}_{4} \)
C Electron-precise iii \( \quad N H_{3} \)
D Interstitial \( \quad \) iv \( \quad B_{2} H_{6} \)
E Electron rich
\( \mathbf{v} \quad \mathbf{C r H} \)
Choose the correct matching from the
code given below:
\( A \cdot(A)-(i i),(B)-(i v),(C)-(v),(D)-(i i i),(E)-(i) \)
B. (A)-(iv), (B) - (i), (C) - (ii), (D) - (v), (E) - (iii)
\( c \cdot(A)-(i v),(B)-(i i i),(C)-(v),(D)-(i i),(E)-(i) \)
\( D \cdot(A)-(v),(B)-(i i i),(C)-i(v),(D)-(i i),(E)-(i) \)


In the circuit shown below, all the
resistances are equal, each equal to \( \mathrm{R} \)
The equivalent resistance
between points \( A \) and \( C \) is :
\( A \)
8. 4 R
\( c \cdot R / 2 \)
D. None of the above


If \( \boldsymbol{P}(\boldsymbol{A})=\frac{\mathbf{7}}{\mathbf{1 3}}, \boldsymbol{P}(\boldsymbol{B})=\frac{\mathbf{9}}{\mathbf{1 3}}, \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B})= \)
2
- then find \( (\mathrm{A} \mid \mathrm{B}) \) 13


Assertion
Hydrolysis of sucrose brings about a change in sign of rotation from dextro to laevo.
Reason
Hydrolysis always changes the optical
rotation of a compound.
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


Evaluate \( \int \frac{\cos ^{2} x}{\sin ^{3} x\left(\sin ^{5} x+\cos ^{5} x\right)^{\frac{3}{5}}} d x \)


The acid dissociation constant of uric
\( \operatorname{acid} \) is \( \boldsymbol{K}_{\boldsymbol{a}}=\boldsymbol{4} \cdot \boldsymbol{0} \times \mathbf{1 0}^{-\boldsymbol{6}} \boldsymbol{M} \cdot \) The \( \boldsymbol{p} \boldsymbol{H} \) of
a sample is \( 6.0 . \) What is the ratio of urate ion to uric acid in the urine?
A . 2.0
в. 4.0
\( c .6 .0 \)
D. 0.25


In submerged hydrophytes Ceratophyllum and Vallisneria, stomata
are
A. On the upper surface of leaves
B. On the lower surface of leaves
c. Both A and B
D. Absent


\( P C l_{3} \) reacts with water, then formed
acid of phosphorous, what is the basicity of acid of phosphorous?


Name the following:
a) An element which forms the triple
covalent bond.
b) An element which obtains the noble
gas configuration of neon by losing three electrons.
c) An element which gains two electrons to obtain the noble gas configuration of neon.
d) Name a compound which is an exception to the octet rule.
e) \( \ln S O_{2} \) molecule, which element is a
donor of electrons.


Two dice each numbered from 1 to 6 are
thrown together. Let \( A \) and \( B \) be two
events given by
\( A: \) even number on the first die
\( B: \) number on the second die is greater
than 4
Find the value of \( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B}) \)
A \( \cdot \frac{1}{2} \)
B. \( \frac{1}{4} \)
\( c \cdot \frac{2}{3} \)
D. \( \frac{1}{6} \)


Wavelength of light used in an optical instrument are \( \lambda_{1}=4000 \hat{A} \) and \( \lambda_{2}= \) \( \mathbf{5 0 0 0} \boldsymbol{A} \) then ratio of their respective
resolving powers(corresponding to \( \lambda_{1} \)
and \( \lambda_{2} \) ) is
A. 16: 25
B. 9:
\( c \cdot 4: 5 \)
D. 5:


Roasting is carried out to:
1) convert sulphide to oxide and
sulphate.
2) remove the water of hydration.
3) melt the ore
4) remove arsenic and sulphur impurities.
Choose the correct options.
A. \( 1.2, \) and 3 are correct
B. 1 and 4 are correct
c. \( 1,2, \) and 4 are correct
D. \( 2,3, \) and 4 are correct


How many of the following are taxa?
Dogs, Cats, Mammals, Wheat, Rice, Plants, Wood, Mango, Leaves, Jointed legs.
A. Eight
B. Six
c. Seven
D. one


Which of the following will lead to a change in kinetic energy of a body?
A. change in its mass
c. change in its velocity
D. all of the above


Cannizzaro reaction will be given by:
(iv) \( \mathrm{cH}_{3} \) сно
\( A \cdot(i),(\text { ii) }, \) (iii)
B. (i) and (ii)
c. (ii) and (iii)
D. (i) and (iv)


Which of the following orbitals can not undergo hybridisation amongst themselves?
\( (I) 3 d, 4 s \)
\( (I I) 3 d, 4 d \)
\( (I I I) 3 d, 4 s \& 4 p \)
\( (I V) 3 s, 3 p \& 4 s \)
\( \mathbf{A} \cdot I I \)
B. II and III
c. \( I, I I \) and \( I V \)
D. II and \( I V \)


Evaluate:
\( \tan \frac{1}{2}\left[\sin ^{-1} \frac{2 y}{1+y^{2}}+\cos ^{-1} \frac{1-y^{2}}{1+y^{2}}\right] \)


A uniform metre scale is in equilibrium position. Calculate the mass of the
ruler.


Name one halogen of period.


Above Curie temperature, ferromagnetic substances become
A. diamagnetic
B. paramagnetic
c. ferrimagnetic
D. none of these


1 kg of water under a nitrogen pressure of 1 atmosphere dissolves 0.02 gm of nitrogen at \( 293 \mathrm{K} \) Calculate Henry's law constant.
A \( \cdot 7.2 \times 10^{-4} \) atm
B . \( 7.5 \times 10^{4} \) atm
\( c \cdot 7.4 \times 10^{4} \operatorname{atm} \)
D. \( 7.2 \times 10^{4} \) atm


The atomic number of an element that
belongs to the IVA (or 14) group and 4th period is:
A . 32
B. 30
\( c \cdot 34 \)
D. 36


If \( R=r a d i u s \) of the earth and \( g= \) acceleration due to gravity on the
surface of the earth, the acceleration
due to gravity at a distance
A \( . r \)
B \( \cdot r^{2} \)
\( c \cdot r^{-2} \)
D. \( r^{-1} \)


A moves with constant velocity u along
then \( x \) -axis. \( B \) always has velocity
towards A. After how much time will B
meet \( A \) if \( B \) moves with constant speed
V? What distance will be travelled by A
and B?


The terminal voltage of a cell is equal to
A. potential across external resistance.
B. potential across internal resistance.
C . potential across sum of external resistance and internal resistance.
D. emf of cell.


300 gm of water at \( 25^{\circ} \mathrm{C} \) is added to 100
\( \mathrm{gm} \) of ice at \( 0^{\circ} \mathrm{C} \). Final temperature of the mixture is:
A \( \cdot-\frac{5^{\circ}}{3} C \)
В. \( -\frac{5^{\circ}}{2} C \)
\( \mathbf{c} \cdot-5^{\circ} C \)
D. \( 0^{\circ} \mathrm{C} \)


Find out which of the following
sequences are arithmetic progressions. For those which are arithmetic
progressions, find out the common difference. \( 1^{2}, 5^{2}, 7^{2}, 73, \dots \)


The sum of first \( n \) terms of \( A . P . \) is \( 3 n+ \)
\( n^{2} \) then Find second, third and \( 15^{t h} \)
term.
This question has multiple correct options
A. 6
B. 8
c. 32
D. 45


An element necessarily have same
A. No. of protons
B. No. of electrons
c. No. of nuetrons
D. All


Although F is more electronegative than
H, the resultant dipole moment of \( \boldsymbol{N} \boldsymbol{H}_{3} \)
is much more than that of \( N F_{3} \). It can
be explained as:
A. the lone pair of nitrogen opposes the dipole moment of \( N F_{3} \) while it is added to the dipole moment of \( N H_{3} \)
B. all the dipoles of \( N F_{3} \) are in same direction
c. all the dipoles of \( N H_{3} \) are in opposite direction
D. \( N H_{3} \) has a regular geometry while \( N F_{3} \) has irregular geometry which makes dipole moment of \( N H_{3} \) more than \( N F_{3} \)


Given are some organisms.
(I) Fowl
(II) Humans (III) Grasshopper Following alphabets related to the given
animals.
Male homogametic - \( A \) Female heterogametic - \( \mathrm{B} \) Male heterogametic - \( C \) Female homogametic - D Which of the following options correctly describes the given animals in terms of sex determination?
\( A \cdot(\text { () } A, B \text { (II) } C, D \text { (III) } C, D \)
B. (I) C, D (II) A, B (III) C, D
C . (I) A, D (II) C, D (III) A, D
D. (I) B, C (II) C, D (III) A, B


The figure shows an infinite line charge of density \( C / m . \) The work done by the
electrostatic force on a unit charge,
when it is moved along the path \( \boldsymbol{A B C} \)
is (plane of the curve \( A B C \) contains the
line charge)
\( A \cdot \) zero
B. \( \frac{-\sigma}{2 \pi \epsilon_{o}} \ln 2 \)
c. \( \frac{-\sigma}{2 \pi \epsilon_{o}} \ln 3 \)
D. \( \frac{\sigma}{2 \pi \epsilon_{o}} \ln 2 \)


Direction cosines of ray from
\( \boldsymbol{P}(\mathbf{1},-\mathbf{2}, \mathbf{4}) \) to \( \boldsymbol{Q}(-\mathbf{1}, \mathbf{1},-\mathbf{2}) \) are
в. 2,-3,6
\( \mathbf{c} \cdot 2,3,6 \)
D. \( \frac{-2}{7}, \frac{3}{7}, \frac{-6}{7} \)


The coordinates of the point on the
curve \( \left(x^{2}+1\right)(y-3)=x \) where a
tangent to the curve has the greatest slope are given by This question has multiple correct options
A \( \cdot(\sqrt{3}, 3+\sqrt{3} / 4) \)
B \( \cdot(-\sqrt{3}, 3-\sqrt{3} / 4) \)
c. (0,3)
D. none of these


Product of the reactions is :
\( A \)
B.
\( c . \) both (a) and (b)
D. None of these


An electric dipole of moment \( p \) is lying along a uniform electric field \( \boldsymbol{E} \). The
work done in rotating the dipole by \( 90^{\circ} \) is:
A \( . p E \)
B . \( \sqrt{2} p E \)
c. \( \frac{p E}{2} \)
D. \( 2 p E \)


The static frictional force is
A. self adjustable.
B. not self adjustable.
C . scalar quantity.
D. equal to the limiting force.


In which condition plant cell become
flacid?


State the following statements are true
or false.
In metaphase, the sister chromatids move towards the opposite poles of the spindle.
A. True
B. False


The sides \( A B, B C, C A \) of a triangle \( A B C \) have 3,4 and 5 interior points respectively on them. The number of triangles that can be constructed using these points as vertices is-
A . 205
в. 210
\( c .315 \)
D. 216


Which of the following lens is used to minimise myopia?
A. Convex lens
B. Concave lens
c. Cylindrical lens
D. Planar lens


Which of the following is/are correct
matches?
(Trend)
(Characteristic/Property)


In the potentiometer arrangement shown in figure, null point is obtained
at length \( l \)
Table Table - 2
(a) If \( E_{1} \) is increased
(p) \( l \) should increase
(b) If \( \mathrm{R} \) is increased
(q) \( l \) should
decrease
(c) If \( E_{2} \) is increased
(r) \( l \) should
remain the same to again get the null point
A. a \( -q, b-q, c-p \)
\( c \cdot a-p, b-p, c-r \)
D. a - q, b-p, c-p


Which of the follwoing does not have \( \boldsymbol{S}-\boldsymbol{S} \) linkage \( ? \)
A \( \cdot H_{2} S_{2} O_{5} \)
в. \( H_{2} S_{2} O_{7} \)
c. \( H_{2} S_{2} O_{3} \)
D. \( H_{2} S_{2} O_{6} \)


The area enclosed between the curves
\( \boldsymbol{y}^{2}=\boldsymbol{x} \) and \( \boldsymbol{y}=|\boldsymbol{x}| \boldsymbol{i} \boldsymbol{s} \)
A \( \cdot \frac{2}{3} \)
B.
\( c \cdot \frac{1}{6} \)
\( D \)


What is octet rule? How do you
appreciate role of the 'octet rule' in explaining the chemical properties of elements?


If the polynomial \( f(x) \) is such that \( f(-43)=0, \) which of the following is
the factor of \( \boldsymbol{f}(\boldsymbol{x}) \) ?
A . \( x-43 \)
B.
c. \( x-7 \)
D. \( x+43 \)


If the order of \( \mathbf{A} \) is \( \mathbf{4} \times \mathbf{3}, \) the order of \( \mathbf{B} \)
is \( 4 \times 5 \) and the order of \( C \) is \( 7 \times 3 \), then
the order of \( \left(\mathbf{A}^{T} \mathbf{B}\right)^{T} \mathbf{C}^{T} \) is
A. \( 4 \times 5 \)
в. \( 3 \times 7 \)
c. \( 4 x 3 \)
D. \( 5 \times 7 \)


Bond energy of covalent \( \boldsymbol{O}-\boldsymbol{H} \) bond in
water is:
A. greater than bond energy of hydrogen bond
B. equal to bond energy of hydrogen bond
c. less than bond energy of hydrogen bond
D. half of the bond energy of hydrogen bond


The majority charge carriers in the emitter of an NPN transistor are
A. pentavalent atoms
B. trivalent atoms
c. electrons
D. holes


In comparing e.m.f.s of 2 cells with the
help of potentiometer, at the balance point, the current flowing through the wire is taken from:
A. 1 ) Any one of these cells
B. 2) both of these cells
c. 3 ) Battery in the main circuit
D. 4 ) From an unknown source


The herbicide DCMU kills the weeds
because it inhibits
A. respiration
B. \( C O_{2} \) fixation
c. cell division
D. \( N O_{3}^{2-} \) uptake


Solve the following equation: \( \frac{5}{2} x=\frac{25}{4} \)


Which of the following reasons corresponds to decrease in IP value
from top to bottom in a group?
A. Decrease in screening effect
B. Increase in atomic number
c. Increase in screening effect
D. Decrease in nuclear charge


What is the weight of oxygen that is required for the complete combustion of \( 2.8 \mathrm{kg} \) of ethylene?
A. \( 9.6 \mathrm{kg} \)
в. 96.0 kg
c. \( 6.4 \mathrm{kg} \)
D. 2.8 kg


The bacteria that commonly live in animal and human intestine is
A. Vibrio cholerae
B. Bacillus anthracis
c. corynebacterium
D. Escherichia coli


In an electrochemical process, a salt
bridge is used:
A. as a reducing agent.
B. as an oxidizing agent.
c. to complete the circuit so that current can flow.
D. None of these


A \( 20 \mathrm{kg} \) block is in motion on a rough horizontal surface. A horizontal force of
\( 60 \mathrm{N} \) is requited to keep the body moving with constant speed. Then the coefficient of kinetic friction is \( 3 \times \)
\( 10^{-x} . \) Find the value of \( x .\left(g=10 m s^{-2}\right) \)


Vector is represented by directed line segment where length of line gives
of vector.
A. Direction
B. Magnitude
c. Both (A) and (B)
D. None of the above


What is the relative lowering in vapour pressure of \( 10 \% \) aqueous solution of glucose :
A \( .1 / 10 \)
B. 1/90
c. \( 1 / 20 \)
D. 1/30


How many wavelengths of \( K r^{86} \) are
contained in one meter?
A . 1553164.13
B. 652189.63
c. 2347127.23
D. 1650763.73


Which Semiconductors are created by
doping an intrinsic semiconductor with acceptor impurities?
A . p-type
B. n-type
c. both of them
D. none of them


\( \frac{1}{2} \sin (2 x)\left(1+\cot ^{2}(x)\right) \) is equal to
\( \mathbf{A} \cdot \tan (x) \)
B. \( \sin (x) \)
\( \mathbf{c} \cdot \cos (x) \)
D. \( \cot (x) \)
E. \( \sec (x) \)


Assertion
Insulin is a globular protein.
Reason
It has two polypeptide chains with 21
and 30 amino acids joined by sulphur
bridges connecting cysteine amino acid
on the two chains.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Which out of these have genetic
complement \( 44+X ? \)
\( A \cdot A \)
B. B
\( c \cdot c \)
D.


In silicon dioxide:
A. each silicon atom is surrounded by four oxygen atoms and each oxygen atom is bonded to two silicon atoms
B. each silicon atom is surrounded by two oxygen atom and each oxygen atom is bonded to two silicon atoms
C. silicon atom is bonded to two oxygen atoms
D. there are double bonds between silicon and oxygen
atoms


The order, degree of the \( D . E \)
corresponding to the family of curve
\( \boldsymbol{y}=\boldsymbol{a}(\boldsymbol{x}+\boldsymbol{a})^{2} \) where \( \boldsymbol{a} \) is an arbitrary
constant is
A . 1,2
в. 2,4
\( c .3,1 \)
D. 1,3


a. Redraw the diagram!
b. This diagram represents
c. Label the parts of the diagram.
d. Mention the principle used in the device denoted by this diagram


Enthalpy of formation of \( \boldsymbol{C}_{2} \boldsymbol{H}_{\mathbf{6}}= \)
\( -83 k J / m o l \)
Enthalpy of sublimation of graphite = \( \mathbf{7} 19 k J / m o l \)
Enthalpy of bond dissociation of \( \boldsymbol{H}_{2}= \) \( 435 k J / m o l \)
\( \mathrm{C}-\mathrm{H} \) bond enthalpy \( =414 k J / m o l \)
Calculate the bond enthalpy of \( C-C \)


Radius of \( 2 n d \) shell of \( H e^{+} \) (where \( a_{0} \)
Bohr radius)
A \( .3 a_{0} \)
в. \( a_{0} \)
c. \( \frac{3}{2} a_{0} \)
D. \( 2 a_{0} \)


Give Reason
Amount of insolation decreases from
equator towards poles?


What will be the next number in this
sequence \( 21 \frac{1}{3}, 16,12,9, ? \)
\( A \cdot 7 \)
B. 6
c. 6.75
D. 5


Define open and closed type of circulatory systems.


A block of mass \( m \) slides down a
smooth vertical circular track. During the motion, the block is in.
A. Vertical equilibrium
B. Horizontal equilibrium
c. Radial equilibrium
D. None of these.


On moving from left to right in any period valence electrons keeps on increasing and period gets over when that valence shell gets filled.
A . True
B. False


There are total of orbitals
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 5


Find the point on the curve \( y=x^{2} \)
where rate of change of \( x \) -co ordinate is
equal to the rate of change of \( y-c o \)
ordinate.


A circular copper disc \( 10 \mathrm{cm} \) in diameter rotates at 1800 revolution per minute about an axis through its centre and at right angles to disc. A uniform
field of induction \( B \) of 1 Wh \( m^{2} \) is
perpendicular to disc. What potential difference is developed between the axis of the disc and the rim?
A. 0.023 v v vas
B. 0.23
\( c \cdot 23 v \)
D. 230 V


The de-Broglie wavelength of a proton \( \left(\text {mass}=\mathbf{1 . 6} \times \mathbf{1 0}^{-\mathbf{2 7}} \mathbf{k g}\right) \) accelerated
through a potential difference of \( 1 \mathrm{kV} \) is :
B . \( 0.9 \times 10^{-12} \mathrm{m} \)
\( c .7 \dot{h} \)
D. \( 0.9 \times 10^{-19} n m \)


Assertion
Physically, if a dielectric with a high value of \( \mathrm{k} \) is placed in an electric field, the electric field will be greatly reduced
inside.
Reason
Dielectrics are very useful in modern electronics as it is possible to to precisely control their permittivity by doping them with other types of
materials.
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 room has \( A C \) run hours a day at a
voltage of \( 220 \mathrm{V} \). The wirng of the room consists of Cu of \( 1 \mathrm{mm} \) radius and a length of \( 10 \mathrm{m} . \) Power consumption per day is 10 commercial units. The fraction of it goes in the joule heating in wires is: \( \rho_{c u}=1.7 \times 10^{-8} \Omega m \)
A . \( 0.32 \% \)
B. \( 0.2 \% \)
c. \( 2 \% \)
D. \( 3.2 \% \)


The sum of coordination number and
oxidation number of the metal \( M \) in the
complex \( \left[M(e n)_{2}\left(C_{2} O_{4}\right)\right] C l \) (where \( e n \) is ethylenediamine) is :
A. 7
B. 8
\( c \cdot 9 \)
D.


A uniform electric field 'E' is directed
towards positive X-axis. If at \( X=0, \) the electric potential is zero, then the
potential at \( \boldsymbol{X}=+\boldsymbol{X}_{0}, \) would be
A \( \cdot \frac{E}{X_{0}} \)
в. \( \frac{-E}{X_{0}} \)
c. \( -E X_{0} \)
D. \( E X_{0} \)


Lysine is used as:
This question has multiple correct options
A. disinfectant
B. germ killer
C . treating eye disease
D. anti-cancer drug


I ne retractıve index of the materıal of a
concave lens is \( \mu . \) It is immersed in a
medium of refractive index \( \mu_{1} . A \)
parallel beam of light is incident on the
lens. The path of the emergent rays
when \( \mu_{1}>\mu \) is :
\( \mathbf{A} \)
B.
\( \mathbf{c} \)
D.


The reference standard used for the
measurement of a physical quantity is called:
A. standard quality
B. Dimension
c. constant
D. Unit


The type of lens used as a simple microscope.
A. Binocular lens
B. Plano concave lens
c. concave convex lens
D. Convex lens


The pressure of a gas in a \( 100 \mathrm{mL} \) container is \( 200 \mathrm{kPa} \) and the average
translation kinetic energy of each gas particle is \( 6 \times 10^{-21} \). Find the number
of gas particles in the container. How many moles are there in the container?


In hydrogen-like atom \( (z=11), n^{t h} \) line of
Lyman series has wavelength \( \lambda \) equal to the de-Broglie's wavelength of an electron in the level from which it
originated. What is the value of n?
A . 20
B. 25
c. 22
D. 24


The equation of a stationary wave is \( Y= \) \( 10 \sin \sin \frac{\pi x}{4} \cos 20 \pi t . \) The distance
between two consecutive antinodes in
meters is -
A . 4
B. 2
\( c \cdot 5 \)
D. 8


Find the point of intersection of the plane \( \bar{r} .(1,1,1)=2 \) and the line \( \bar{r}= \) \( (4,5,3)+k(2,2,1), k \in R \)


Find the area bounded by curves
\( (x-1)^{2}+y^{2}=1 \) and \( x^{2}+y^{2}=1 \)


An intense stream of water of cross
sectional area A strikes a wall at an
angle \( \theta \) with the normal to the wall and
returns back elastically. If the density of
water is \( \rho \) and its velocity is \( v \), then the
force exerted on the wall will be :
A. \( 2 A v \rho \cos \theta \)
B. \( 2 A v^{2} \rho \cos \theta \)
c. \( 2 A v^{2} \rho \)
D. 2Av


Find the distance of the point (1,2,-1) from the plane \( \boldsymbol{x}-\mathbf{2} \boldsymbol{y}+\mathbf{4} \boldsymbol{z}-\mathbf{1 0}= \)
\( \mathbf{0} \)


the \( x y \) -plane along the lines \( x=\pm R \)
The wire located at \( x=+R \) carries a
constant current \( I_{1} \) and the wire located
at \( x=-R \) carries a constant current \( \boldsymbol{I}_{2} \)
A circular loop of radius \( \boldsymbol{R} \) is
suspended with its centre at \( (0,0, \sqrt{3} R) \) and in a plane parallel to the
\( \boldsymbol{x} \boldsymbol{y} \) -plane. This loop carries a constant
current \( I \) in the clockwise direction as
seen from above the loop. The current in the wire is taken to be positive if it is in the \( +\hat{\boldsymbol{j}} \) direction. Which of the following statements regarding the magnetic field \( \vec{B} \) is (are) true?
This question has multiple correct options
A \( \cdot \) If \( I_{1}=I_{2} \), then \( \vec{B} \) cannot be equal to zero at the origin
(0,0,0)
B. If \( I_{1}>0 \) and \( I_{2}<0 \), then \( \vec{B} \) can be equal to zero at the origin (0,0,0)
C \( \cdot \) If \( I_{1}<0 \) and \( I_{2}>0, \) then \( \vec{B} \) can be equal to zero at the origin (0,0,0)
D. If \( I_{1}=I_{2} \), then the \( z \) -component of the magnetic field at the centre of the loop is \( \left(-\frac{\mu_{0} I}{2 R}\right) \)


A spherical ball of mass \( 20 k g \) is stationary at the top of a hill of height 100 \( m \). It rolls down a smooth surface to
the ground, then climbs up another hill of height \( 30 m \) and finally rolls down to a
horizontal base at a height of \( 20 m \)
above the ground. The velocity attained
by the ball is
\( \mathbf{A} \cdot 40 m / s \)
в. \( 20 \mathrm{m} / \mathrm{s} \)
c. \( 10 m / s \)
D. \( 10 \sqrt{30} \mathrm{m} / \mathrm{s} \)


f \( \log _{10} 2, \log _{10}\left(2^{x}-1\right) \) and \( \log _{10}\left(2^{x}+\right. \)
3) be three consecutive terms of an A.P.
then \( x=\log _{2} 5 \)


A parallel plate capacitor of plate separation 2 mm is connected in an
electric circuit having source voltage
\( 400 V . \) If the plate area is \( 60 \mathrm{cm}^{3} \) then
the value of displacement current for time period of \( 10^{-6} \) sec will be
A. 1.062 amp
В. \( 1.062 \times 10^{-2} \) атр
c. \( 1.062 \times 10^{-1} \) amp
D. \( 1.602 \times 10^{-2} \) amp


Who proposed the law of traids?


\( 2+2^{2}+2^{3}+\ldots \ldots+2^{9}=? \)
\( \mathbf{A} \cdot 2044 \)
B. 1022
c. 1056
D. None of these


What is the limit of temperatures human body can achieve?
\( \mathbf{A} \cdot 25^{\circ} C \) to \( 42^{\circ} C \)
B . \( 35^{\circ} \mathrm{C} \) to \( 42^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 35^{\circ} C \) to \( 62^{\circ} C \)
D. \( 5^{\circ} C \) to \( 42^{\circ} C \)


Convert given percents to decimal fractions and also to fractions in
simplest forms:
\( \mathbf{2 0 \%} \)


Mumps is caused by ............ virus.


The charge to mass ratio is highest for:
A. proton
B. electron
c. neutron
D. alpha


Which of the following best define the term hyperconjugation?
A. Transfer of \( \mathrm{H} \) from \( \sigma_{C-H} \) bond to the \( \pi \) system.
B. Participation of an H-atom on terminal carbon in the electron sharing.
C. Delocalisation of electron density from a proper oriented \( \sigma \) -bond into \( \pi \) system.
D. Interaction between a' properly aligned, electron pair with the empty \( \pi \) system.


Assuming that petrol is octane \( \left(C_{8} H_{18}\right) \)
and has a density of \( 0.8 g m L^{-1}, 1.425 \)
litre of petrol on combustion will
consume:
A. 100 mole of oxygen
B. 125 mole of oxygen
c. 150 mole of oxygen
D. 175 mole of oxygen


Give the formula for Step up deviation
method.


A system is shown in the figure. A man
a standing on the block is pulling the rope. Velocity of the point of string in contact with the hand of the man is
\( 2 m / s \) downwards. The velocity of the
block will be: [Assume that the block
does not rotate \( ] \)
A. \( 3 m / s \)
B. \( 2 m / s \)
c. \( \frac{1}{2} m / s \)
D. \( 1 \mathrm{m} / \mathrm{s} \)


Compare metals and non-metals with
particular emphasis on solubility:
A. Both dissolve in solvent
B. None of them dissolve in solvent
C. Metal dissolve while non-metal do not dissolve in solvent
D. Non-metal dissolve while metal do not dissolve in solvent


The value of zero kelvin on Celsius scale
is :
\( \mathbf{A} \cdot 0^{0} C \)
B. \( -32^{0} C \)
c. \( 100^{\circ} \mathrm{C} \)
D. \( -273^{\circ} \mathrm{C} \)


Angle of incidence is equal to the angle
of reflection. This is true:
A . always
B. sometimes
c. under special conditions
D. never


The value of \( 4-\frac{5}{1+\frac{1}{3+\frac{1}{2+\frac{1}{4}}}} \) is
A \( \cdot \frac{40}{31} \)
B. \( \frac{4}{9} \)
\( c \cdot \frac{1}{8} \)
D. \( \frac{31}{40} \)


What is reflection? Write the laws of
reflection.


Which of the following relationship is incorrect?
A \( \cdot \frac{\Delta H-\Delta E}{\Delta n T}= \) constant
B. \( \Delta G=\Delta H-T \Delta S \)
c. \( q=\Delta U+W \)
D. \( \Delta G^{o}=-R T \ln K \)


A water jet, whose cross sectional are is
'a' strikes a wall making an angle ' \( \boldsymbol{\theta}^{\prime} \)
with the normal and rebounds
elastically. The velocity of water of
density 'd' is v. Force exerted on wall is
A \( \cdot 2 a v^{2} d \cos \theta \)
B. \( 2 a v^{2} d \sin \theta \)
c. 2 avd \( \cos \theta \)
D. avd cose


The correct relation between \( S, \theta, L \) and
\( C \) for an optically active solution is:
\( \mathbf{A} \cdot S=\theta L C \)
B. \( \theta=S L C \)
\( \mathbf{c} . L=\theta S C \)
\( \mathbf{D} \cdot C=\theta L S \)


Evaluate the following:
i. \( \sin \left(\cot ^{-1} x\right) \)
ii. \( \sin \left(\frac{\pi}{2}-\sin ^{-1}\left(-\frac{\sqrt{3}}{2}\right)\right) \)
\( ^{\mathbf{A}} \cdot(\mathrm{i}) \frac{1}{\sqrt{x^{2}+1}},(\mathrm{ii}) \frac{1}{2} \)
B. \( \quad(i) \frac{1}{\sqrt{x^{2}-1}},\left(\text { ii) } \frac{-\sqrt{3}}{2}\right. \)
\( c \cdot(i) \frac{-1}{\sqrt{x^{2}+1}},\left(\text { ii) } \frac{1}{2}\right. \)
D. \( \left(\text { i) } \frac{-1}{\sqrt{x^{2}-1}} \text { , (ii) } \frac{+\sqrt{3}}{2}\right. \)


Which of the following groups are metadirecting? This question has multiple correct options
\( \mathbf{A} \cdot-N H_{2} \)
в. \( -O H \)
\( \mathrm{c} \cdot-N O_{2} \)
D. \( -C N \)


The compound in which all the bond
angles around every atom are 109.28 is:
\( \mathbf{A} \cdot H C O O H \)
B \( \cdot\left(N H_{2}\right)_{2} C O \)
с. \( \left(C H_{3}\right)_{3} C O H \)
D. \( \left(C H_{3}\right)_{3} C C H O \)


\( \boldsymbol{f}: \boldsymbol{N} \rightarrow \boldsymbol{N}, \) then show that \( \boldsymbol{f}(\boldsymbol{n})= \)
\( 2 n+3 \forall n \in N \)
This question has multiple correct options
A. many one, into.
B. one-one, into
c. one-one, not onto
D. many-one, onto


You are provided with two similar bars. One is magnet and the other is a soft iron. How will you distinguish between
them without the use of any other magnet or bar?


The differential equation of all straight lines in a plane passing through (0,1) is:
A \( . y-1=m x \)
в. \( y=m(x-1) \)
c. \( y=x y_{1} \)
D. \( y=x y_{1}+1 \)


The equilibrium position of the particle
is
A. \( x=4 \)
B. \( x=6 \)
\( c \cdot x=2 \)
D. x = 3


A man uses a concave mirror for
shaving. He keeps his face at a distance of \( 25 \mathrm{cm} \) from the mirror and gets an
image which is 1.4 times enlarged. Find the focal length of the mirror.


Velocity - time graphs of two bodies \( \boldsymbol{A} \)
and \( B \) are as shown in the figure. The
ratio of, their acceleration is
A .1: 3
B. 3: 1
c. \( 1: \sqrt{3} \)
D. \( \sqrt{3}: 1 \)


Which is/are used as an anaesthetic?
в. \( C_{2} H_{4} \)
c. \( C H C I_{3} \)
D. All of these


Find the terminal velocity of the
connector?


The maidenhair tree is
A . Pinus
B. Adiantum
c. Ginkgo biloba
D. Gnetum ula


If the mean deviation of number \( 1,1+ \)
\( \boldsymbol{d}, \mathbf{1}+\mathbf{2} \boldsymbol{d}, \dots, \mathbf{1}+\mathbf{1 0 0} \boldsymbol{d} \) from their mean
is \( 255, \) then the \( d \) is equal to :-
A . 20.0
B. 10.1
c. 20.2
D. 10.0


One end of a horizongal thick copper wire of length \( 2 L \) and radius \( 2 R \) is welded to an end of another horizontal
thin copper wire of length \( L \) and radius
\( R \) When the arrangement is stretched by applying forces at two ends, the ratio of the elongation in the thin wire to that in the thick wire is then
A . 0.25
B. 0.50
\( c .2 .00 \)
D. 4.00


Which of the following compound is used in gas lighter?
A. Pyrophoric Misch metal
в. \( C e O_{2} \)
c. Nichrome
D. Nitinol


What type of force is applied in kicking a football?
A. Magnetic force
B. Muscular force
c. Electrical force
D. Nuclear force


Analgin is a derivative of:
A. phenol
B. benzoic acid
c. pyrazole
D. pyridine


What is a rate constant?
A. Equality constant
B. Shows relation between rate of reaction and pressure
C. Proportionality constant between rate of reaction and concentration
D. None of above


Sodium carbonate exists as(in):
A \( \cdot N a_{2} C O_{3} \cdot 10 H_{2} O(s) \)
B . \( N a_{2} C O_{3} \cdot H_{2} O(s) \)
c. \( N a_{2} C O_{3} \)
D. All of the above


Two Mark Questions:
Explain mechanism of sex determination in birds.


Three lines are given by \( \vec{r}=\lambda \hat{i}, \lambda \epsilon R \) \( \overrightarrow{\boldsymbol{r}}=\boldsymbol{\mu}(\hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}), \boldsymbol{n} \boldsymbol{\epsilon} \boldsymbol{R} \) and \( \overrightarrow{\boldsymbol{r}}=\boldsymbol{v}(\hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}+ \)
\( \hat{\boldsymbol{k}}), \boldsymbol{v} \boldsymbol{\epsilon} \boldsymbol{R} \)
Let the lines cut the plane \( \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}= \)
1 at he points \( A, B \) and \( C \) respectively.
If the area of the triangle \( A B C \) is \( \triangle \)
then the value of \( (6 \triangle)^{2} \) equals
A . 0.75
в. \( 0 . \)
\( c .0 .85 \)
D. 0.65


Number of photons emitted in 10 hours
by \( 60 \mathrm{W} \) sodium lamp is \( \left(\lambda=5983 A^{\circ}\right) \)
A. \( 6.40 \times 10^{22} \)
B. \( 6.40 \times 10^{24} \)
c. \( 4.60 \times 10^{22} \)
D. \( 4.60 \times 10^{42} \)


Which one of these units would you use
to measure the length of a handbag?
A. Centimeter
B. Pounds
c. Miles
D. None


Write the ratio of the heights of
highest peak and the lowest peak.
A .22: 15
B . 15: 22
\( c, 20: 13 \)
D. 13: 22


In a winter season, a heat pump is used to warm the room. A heat pump works \( 60 \mathrm{J} \) on the pump while it absorbs \( 90 \mathrm{J} \)
of heat. How much heat is delivered to
the house?
A. 5,400 J
B. 150 J
c. 30 J
D. 1.5 J
E . 0.67 J


Let \( \boldsymbol{f}(\boldsymbol{x})=\sin ^{-1} \boldsymbol{x}+\cos ^{-1} \boldsymbol{x}, \) then \( \frac{\boldsymbol{\pi}}{2} \) is
equal to This question has multiple correct options
A \( \cdot f\left(-\frac{1}{2}\right) \)
B . \( f\left(k^{2}-2 k+3\right), k \in R \)
c. \( f\left(\frac{1}{1+k^{2}}\right), k \in R \)
D. \( f(-2) \)


The displacement of a particle varies
according to the relation \( \boldsymbol{y}= \)
\( 4(\cos \pi t+\sin \pi t) . \) The amplitude of the
particle is:
A. 8 units
B. 2 units
c. 4 units
D. \( 4 \sqrt{2} \) units


The \( n^{t h} \) term of a GP is given by
A \( \cdot t_{n}=a r^{n+1} \)
В . \( t_{n}=a r^{n-1} \)
C \( \cdot t_{n}=a r^{n \div 1} \)
D. \( t_{n}=a r^{2 n-1} \)


Why anabolic reactions are endergonic
reactions?


The resultant of two resistances
connected in parallel is 2 oh \( m \) and when
connected in series, the resultant
becomes 9 oh \( m \). The values of the
resistance are:
A. 7 ohm, 2 ohm
B. 11ohm, 7ohm
c. 4.5 and 8 ohm
D. 3ohm, 6ohm


Chemisorption needs activation energy.
A. True
B. False


In an insulator, the energy gap
between conduction band and valence
band is about
A. 0 eV
B. 6 eV
\( c \cdot 1 e V \)
D. 0.6 eV


Consider the reaction,
\( 4 \mathrm{NO}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \rightarrow \)
\( \mathbf{2} \mathbf{N}_{2} \mathbf{O}_{5}(\mathbf{g}), \mathbf{\Delta}_{r} \boldsymbol{H}=-\mathbf{1 1} \mathbf{1} \mathbf{k} \mathbf{J} \)
If \( N_{2} O_{5}(s) \) is formed instead of
\( N_{2} O_{5}(g) \) in the above reaction, the
\( \Delta_{r} H \) value will be
(Given, \( \Delta H \) of sublimation for \( N_{2} O_{5} \)
is \( \left.54 k J m o l^{-1}\right) \)
A. \( -165 k J \)
в. \( +54 k J \)
\( \mathrm{c} \ldots+219 k J \)
D. \( -219 k J \)


A trian of length \( 200 m \), travelling at \( 30 m s^{-1} \) overtakes another train of
length \( 300 m \) travelling at \( 20 m s^{-1} . \) The time taken by the first train to pass the second train is
A .30 sec
B. 50 sec
c. 10 sec
D. 40 sec


Which of the following oxides cannot be reduced to metal by carbon? This question has multiple correct options
A. \( Z n O \)
в. \( A l_{2} O_{3} \)
c. \( C u O \)
D. \( \mathrm{CaO} \)


In the given circuit find the ratio of \( i_{1} \) to
\( i_{2} . \) Where \( i_{1} \) is the initial \( (\text { at } t=0) \)
current, and \( i_{2} \) is steady state \( (\text { at } t= \)
\( \infty) \) current through the battery.
A . \( 1 . \)
В. 0.8
c. 1.2
D. 1.5


By which reaction ketal is formed?
A. Glycol with acetone
B. Hydration of glycol
c. condensation of glycol
D. Glycol with acetaldehyde


Find the derivative of \( \frac{x+\cos x}{\tan x} \)


The value of \( \Delta H \) and \( \Delta S \) for a reaction
are respectively \( 30 k J \) mol \( ^{-1} \) and \( 100 J K^{-1} \) mol \( ^{-1} . \) Then temperature above which the reaction will become
spontaneous is:
\( \mathbf{A} \cdot 300 K \)
в. \( 30 K \)
c. \( 100 K \)
D. \( 300^{\circ} \mathrm{C} \)


If \( S=\frac{1}{1^{2}}+\frac{1}{2^{2}}+\frac{1}{3^{2}}+\frac{1}{4^{2}}+\dots \dots \dots \dots \) to \( \infty \)
then find \( \frac{1}{1^{2}}+\frac{1}{3^{2}}+\frac{1}{5^{2}}+\frac{1}{7^{2}}+\dots \dots \dots \dots \)
\( \infty \) in terms of \( S \)


Formation of non-functional
methaemoglobin causes blue-baby syndrome. This is due to
A. Excess of arsenic concentration in drinking water.
B. Excess of nitrates in drinking water.
c. Deficiency of iron in food
D. Increased methane content in the atmosphere


Assertion
A beam of light rays has been reflected
from a rough surface.
Reason
Amplitude of incident and reflected rays
would be different.
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


What percent of \( 160 \mathrm{m} \) is \( 80 \mathrm{m} \) ?
A . \( 40 \% \)
B. 50\%
c. 30\%
D. 20\%


The diagram shows four charges
\( q_{1}, q_{2}, q_{3}, \) and \( q_{4} \) all lying in the plane of the page. The diagram also shows the dotted circle that represents the crosssection of a spherical Gaussian surface
Point \( P \) is a single point on that surface
Which of the charges contributes to the
electric field at point \( P ? \)
\( \mathbf{A} \cdot q_{1} \) and \( q_{3} \)
\( \mathbf{B} \cdot q_{2} \) and \( q_{4} \)
\( \mathbf{c} \cdot q_{1} \) and \( q_{2} \)
\( \mathbf{D} \cdot q_{3} \) and \( q_{4} \)
E \( . q_{1}, q_{2}, q_{3}, \) and \( q_{4} \)


Evaluate the following limits. \( \lim _{x \rightarrow 4} \frac{x^{3}-64}{x^{2}-16} \)


If \( \boldsymbol{n}(\boldsymbol{A})=\boldsymbol{4}, \boldsymbol{n}(\boldsymbol{B})=\boldsymbol{3}, \boldsymbol{n}(\boldsymbol{A} \times \boldsymbol{B} \times \)
\( \boldsymbol{C})=\boldsymbol{2} 4, \) then \( \boldsymbol{n}(\boldsymbol{C})= \)


The extraction of metal from the ore is :
A. an oxidation process
B. a reduction process
C . a hydration process
D. a neutralisation process


Hydrogen bomb is based on the principle
of


Waves on water surface are
A. Longitudinal
B. Transverse
C. Combination of longitudinal and transverse
D. None of these


Passiflora is the examples of
A. Stem tendril
B. Phylloclade
c. Thorn
D. Cladode


A set of genetic material for both daughter cells are provided by the replication of chromosomes at
A. Mitosis
B. Prophase
c. cytokinesis
D. Interphase
E. Metaphase


Natural rubber is a polymer of:
A . 1, 1-dimethylbutadiene
B. 2-methy|-1, 3-butadiene
c. 2-chlorobuta-1, 3-diene
D. 2-chlorobut-2-ene


\( \lim _{n \rightarrow \infty} \sum_{r=1}^{4 n} \frac{1}{n+r} \)
\( \mathbf{A} \cdot \log _{e} 5 \)
B. 0
\( \mathbf{c} \cdot \log _{e} 4 \)
D. none of these


If \( y=\tan ^{-1}\left(\frac{2^{x}}{1+2^{2 x+1}}\right) \) then \( \frac{d y}{d x} \) at
\( \boldsymbol{x}=\mathbf{0} \) is
A \( \cdot \frac{1}{10} \log 2 \)
B. \( \frac{1}{5} \log 2 \)
c. \( -\frac{1}{10} \log 2 \)
D. \( \log 2 \)


Define a symmetric relation.


Which of the following is not a decomposer?
A. Fungi
B. Bacteria
c. Hyenas
D. Earthworms
E. Dung beetles


Name the type of energy (kinetic energy
\( K \) or potential energy \( U \) ) possessed in a compressed spring:
A. \( U \)
в. \( K \)
c. Both \( U \) and \( K \)
D. None


Benzene has \( \ldots . . . . . . . . . . \) number of covalent
bonds.
\( \mathbf{A} \cdot \mathbf{6} \)
B. 9
c. 12
D. 15


\( d \) is parallel to \( e, \) as shown in the figure
above. Find the value of \( y \) in deg.


A chemical reaction is said to have
attained equilibrium when:
A. equal amounts of reactants and products are formed
B. reactants are completely converted to products
C. the rate of forward reaction is equal to the rate of backward reaction
D. the concentration of the reactants and products is the
same


The distance between two consecutive
waves is given by:
A. Frequency
B. Amplitude
c. wavelength
D. Velocity
E. Period


Spirit of wine contains:
\( \mathbf{A} \cdot C H_{3} O H \)
в. \( C_{2} H_{5} O H \)
с. НСН О
D. \( C H_{3} \) СОСН\( _{3} \)


In an examination \( 70 \% \) students
passed both in Mathematics and Physics \( 85 \% \) passed in Mathematics
and \( 80 \% \) passed in Physics If 30 students have failed in both the
subjects then the total number of students who appeared in the examination is equal to:
A . 900
в. 600
\( c .150 \)
D. 100


Systema Naturae is written
by


Which one of the following pairs of molecules will have a permanent dipole moments for both members?
A \( \cdot N O_{2} \) and \( O_{3} \)
B. \( \operatorname{SiF}_{4} \) and \( C O_{2} \)
c. \( \operatorname{SiF}_{4} \) and \( N O_{2} \)
D. \( N O_{2} \) and \( C O_{2} \)


Chlorine atoms in the upper
atmosphere cause the breakdown of
ozone.
\( \boldsymbol{C l}+\boldsymbol{O}_{3} \rightarrow \boldsymbol{O}_{2}+\boldsymbol{C l O} \)
\( \boldsymbol{C l O}+\boldsymbol{O} \rightarrow \boldsymbol{C l}+\boldsymbol{O}_{2} \)
Which statements about these chlorine
atoms are correct?
1. The chlorine atoms act as catalysts.
2. The chlorine atoms are free radicals.
3. The chlorine atoms are formed by heterolytic fission of a covalent bond in
chlorofluorocarbons.
A .1,2 and 3 are correct
B. 1 and 2 only are correct
c. 2 and 3 only are correct
D. 1 only is correct


Instantaneous rate and average rate of a reaction are same when \( \Delta \boldsymbol{t} \rightarrow \mathbf{0} \)
If true enter 1 , else enter 0


If \( A \) is a square matrix of order \( n \), then
\( |\mathbf{A} \mathbf{d} \mathbf{j} A| \) is
\( \mathbf{A} \cdot|A|^{2} \)
B \cdot \( |A|^{n} \)
C \( \cdot|A|^{n-1} \)
D・ |A|


The number of H bonds between
guanine and cytosine are
A. one
B. Two
c. Three
D. Four


An oil drop is negatively charged and weights \( 5 \times 10^{-4} N \). The drop is
suspended in an electric field intensity of \( 2.6 \times 10^{4} N / C \). The number of
electrons the oil drop is in \( \boldsymbol{x} \times \mathbf{1 0}^{\mathbf{1 0}} \)
Then \( x \) is
A. 8
B. 10
\( c \cdot 16 \)
D. 12


Which of following has a clover leaf shaped structure?
\( \mathbf{A} \cdot \) tRNA
B. rRNA
c. DNA
D. mRNA


If unit of mass, length and time are
tripled, then unit of energy becomes:
\( \mathbf{A} \cdot \mathbf{3} \)
B. \( \frac{1}{3} \)
c. 9
D.


The marked price of an article is Rs 200 A discount of \( 12 \frac{1}{2} \% \) is allowed on the
marked price and a profit of \( 25 \% \) is
made. What is the cost price of the article?
A . Rs 120
B. Rs 140
c. Rs 160
D. Rs 180


Which of following is not correctly matched?
A. d-block element: electronic configuration is \( n s^{0-2}(n-1) d^{1-1} \)
B. p-block element : electronic configuration is \( n s^{2} n p^{1-6} \)
C. s-block element: electronic configuration is \( n s^{1-2} \)
D. None of these


A cyclic molecule that is a
constitutional isomer of cyclohexane is
\( A \)
B.
\( c \)
D. all of the above


Formula unit mass of \( N a H C O_{3} \) is :
A . \( 84 u \)
в. 76
\( c .52 u \)
D. 64


Express the given complex number in the form \( a+i b:(5 i)\left(-\frac{3}{5} i\right) \)


The atmosphere between the heights
\( \mathbf{1 0} \) to \( \mathbf{5 0} \) kilometer above the sea level is
A. troposphere
B. stratosphere
c. mesosphere
D. ionosphere


In a potentiometer using two cells in series gives a balance length of \( 600 \mathrm{cm} \) When the same cells are connected
opposing each other then balance length is \( 100 \mathrm{cm} \). The ratio of
emf of larger to smaller cell is:
A .7: 5
в. 5: 7
\( c \cdot 6: 1 \)
D. 1: 6


Three flat mirrors are arranged mutually perpendicular to each other. The number of distinct images that will be formed due to a point object is?
\( A \cdot 6 \)
B. 7
c. 12
D. None of these


If two angles in a triangle are \( 65^{\circ} \) and
\( 85^{\circ}, \) then the third angle is:
\( A \cdot 30 \)
B . 45
\( c \cdot 60^{\circ} \)
D. \( 90^{\circ} \)


Reactivity of a double or a triple bond is due to the:
A. single bond
B. sigma bond
c. pi bond
D. covalent bond


Let \( \boldsymbol{A}=\{1,2,3,4\} \) and \( B= \)
\{2,3,4,5,6\} then \( A \triangle B \) is equal to
A \( \cdot\{2,3,4\} \)
B \cdot \{1\}
\( \mathbf{c} \cdot\{5,6\} \)
D \cdot \{1,5,6\}


If the radius of the earth decreases
by \( 10 \%, \) the mass remaining unchanged, what will happen to the acceleration due to gravity?
A. Decreases by 19\%
B. Increases by 19\%
c. Decreases by more than \( 19 \% \)
D. Increases by more than 19\%


\( \ln \) a hexagon \( A B C D E F ; \) side \( A B \) is
parallel to side \( \boldsymbol{F} \boldsymbol{E} \) and \( \angle \boldsymbol{B}: \angle \boldsymbol{C}: \angle \boldsymbol{D} \)
\( \angle E=6: 4: 2: 3 \)
Find the measure of \( \angle B \)
\( \mathbf{A} \cdot 108 \)
B . \( 216^{\circ} \)
\( c \cdot 244^{\circ} \)
D. None of these


The solution of \( \frac{d^{2} x}{d y^{2}}-x=k, \) where \( k \) is a non-zero constant, vanishes when
\( y=0 \) and tends of finite limit as \( y \)
tends to infinity, is
\( \mathbf{A} \cdot x=k\left(1+e^{-y}\right) \)
в. \( x=k\left(e^{y}+e^{-y}-2\right) \)
C \( . x=k\left(e^{-y}-1\right) \)
D. \( x=k\left(e^{y}-1\right) \)


The intensity of the light coming from
one of the slits in a Young's double slit
experiment is double the intensity from
the other slit. Find the ratio of the
maximum intensity to the minimum intensity in the interference fringe
pattern observed.


Meena draws magnetic field lines of the
field close to the axis of a current
carrying circular loop. As she moves away from the center of the circular loop she observes that the lines keep
A. on diverging
B. on converging
c. diappearing
D. none


Find the solution of \( \left(e^{y}+1\right) \cos x d x+ \)
\( e^{y} \sin x d y=0 \)
\( A \cdot \sin x\left(e^{y}+1\right)=c \)
B \cdot \( \sin x\left(e^{y}-1\right)=c \)
\( \mathbf{c} \cdot \sin x\left(2 e^{y}+1\right)=c \)
D・sin \( x\left(3 e^{y}-1\right)=c \)


The temperature of oxy-acetylene flame
is
\( \mathbf{A} \cdot 200^{\circ} \mathrm{C} \)
в. \( 1600^{\circ} \mathrm{C} \)
\( c \cdot 2000^{\circ} C \)
\( \mathbf{D} \cdot>2500^{\circ} \mathrm{C} \)


Bakelite is obtained from phenol by
reaction with:
A. \( H C H O \)
в. \( \left(C H_{2} O H\right)_{2} \)
\( \mathbf{c} \cdot C H_{3} C H O \)
D. \( C H_{3} \) COCH\( _{3} \)


The term independent of \( x \) in the expansion of \( \left(\boldsymbol{x}^{2}-\frac{\mathbf{1}}{\boldsymbol{x}}\right)^{\boldsymbol{6}} \) is
A . -12
B. 15
\( c \cdot 24 \)
D. -15


Find the condition on the complex
constants \( \alpha, \beta \) if \( z^{2}+\alpha z+\beta=0 \) has
two distinct roots on the line \( \operatorname{Re}(z)=1 \)


Lamprey (Petromyzon) belongs to
A. Chondrichthyes
B. Osteichythes
C. Agnatha
D. Amphibia


Evaluate \( \int_{\pi / 6}^{\pi / 3} \frac{d x}{1+\sqrt{\tan x}} \)
A. \( \frac{\pi}{12} \)
в. \( \frac{7 \pi}{12} \)
c. \( \frac{5 \pi}{12} \)
D. None of these


\( \frac{x^{3}}{x^{2}-x+2}=x+k-\left[\frac{x+2}{x^{2}-x+2}\right] \Rightarrow \)
\( \mathbf{k}= \)
\( \mathbf{A} \cdot \mathbf{4} \)
B . 2
\( c \cdot 1 \)
\( D \)


Solve the following systems of linear equations by using the method of elimination by equating the coefficients:
(i) \( 3 x+2 y=11 \)
(ii)2 \( \boldsymbol{x}+\mathbf{3} \boldsymbol{y}=\mathbf{4} \)


Which one of the following is a possibility for most of us with regards to breathing, by making a conscious effort?
A. One can consciously breathe in and breathe out by moving the diaphragm alone, without moving the ribs at all
B. The lungs can be made fully empty by forcefully breathing out all air from them.
c. One can breathe out air totally without oxygen
D. One can breathe out air through eustachian tubes by closing both the nose and the mouth.


In an uniform electric field \( \boldsymbol{E}=\mathbf{1 0} \boldsymbol{N} / \boldsymbol{C} \)
as shown in figure, find \( \boldsymbol{V}_{\boldsymbol{A}}-\boldsymbol{V}_{\boldsymbol{B}} \)
\( \mathbf{A} \cdot 10 V \)
B. \( -10 V \)
\( \mathbf{c} \cdot 20 V \)
D \( .-20 V \)


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


Ferrocene is:
\( \mathbf{A} \cdot F e\left(\eta^{2}-C_{6} H_{5}\right)_{2} \)
B \( \cdot F e\left(\eta^{5}-C_{5} H_{5}\right)_{2} \)
\( \mathbf{c} \cdot F e\left(\eta^{6}-C_{6} H_{6}\right)_{2} \)
D. \( F e\left(\eta^{3}-C_{3} H_{3}\right)_{2} \)


Among alpha, beta and gamma radiations, which are the ones affected by a magnetic field?


When \( K C l O_{3} \) is heated, it decomposes
into \( K C l \) and \( O_{2} . \) If some \( M n O_{2} \) is
added, the reaction goes much faster
because:
A. \( M n O_{2} \) decomposes to give \( O_{2} \)
B. \( M n O_{2} \) provides heat by reacting
C. better contact is provided by \( M n O_{2} \)
D. \( M n O_{2} \) acts as a catalyst


A particle executes SHM with a time period of 10 secs. At what times will the velocity of the particle be maximum, if at \( t=0, \) the particle starts from \( x=-A \)
B. (0,10)
c. (5,10)
D. (2.5,7.5)


Energy of the electron in hydrogen in its first orbit is:
A. \( -3.4 e V \)
B. 3.4eV
c. \( -13.6 e V \)
D. 13.6eV


Can a couple force acting on a body produce translatory motion?


Factors controlling regeneration seem
to be
A. Neural
B. Hormonal
c. Both neural and hormonal
D. Genetic


The median and standard deviation
(S.D.) of a distribution will be, If each term is increased by 2
A. median and S.D. will increased by 2
B. median will increased by 2 but S.D. will remain same
c. median will remain same but S.D. will increased by 2
D. median and s.D. will remain same


Correct order of number of outer most
electron is true for:
A. \( P d<N i>P t \)
B. \( N i=P d=P t \)
c. \( P d>N i>P t \)
\( \mathbf{D} \cdot P d>P t>N i \)


Choose the correct answer among the alternatives given :
Which of the following statements, is incorrect regarding the medical termination of pregnancy (MTP)?
A. These help in getting rid of unwanted pregnancies.
B. These help in aborting the pregnancies which may be harmful to either mother or foetus or both
c. These contribute in decreasing the human population
D. None of these


What is the dimensional formula of
universal gravitational'G'? The gravitational force of attraction between two objects of masses
\( m_{1} \) and \( m_{2} \) seperated by a distance \( \mathrm{d} \) is given by \( \boldsymbol{F}=\frac{\boldsymbol{G} \boldsymbol{m}_{1} \boldsymbol{m}_{2}}{\boldsymbol{d}_{2}} . \) Where 'G' is
the universal gravitational constant
B . \( \left[M^{-1} L^{2} T^{2}\right. \)
c. \( \left[M^{-1} L^{3} T^{-2}\right] \)
D. \( \left[M^{2} L^{2} T^{-2}\right. \)


Let \( p \) and \( E \) denote the linear
momentum and the energy of a photon. For another photon of smaller wavelength (in same medium)
A. Both \( p \) and \( E \) increase
B. \( p \) increases and \( E \) decreases
c. \( p \) decreases and \( E \) increases
D. Both \( p \) and \( E \) decrease


toppr
Q Type your question
This question has multiple correct options
A. Current at \( t=2 \sec \) is \( 5 A \)
B. Current at \( t=2 \sec \) is \( 10 A \)
c. Current vs time graph will be
D. Current vs time graph will be


What should be added in \( \frac{1}{x} \) so that the
result \( x: \)
A \( \cdot \frac{1-x^{2}}{x} \)
в. \( \frac{1-x}{x} \)
c. \( \frac{x^{2}-1}{x} \)
D.


If \( \theta=\sin ^{-1} x+\cos ^{-1} x-\tan ^{-1} x, x \geq \)
\( 0, \) then the smallest interval in which \( \theta \)
lies is-
\( ^{\mathrm{A}} \cdot \frac{\pi}{2} \leq \theta \leq \frac{3 \pi}{4} \)
В. \( \quad 0 \leq \theta \leq \frac{\pi}{4} \)
\( ^{\mathrm{c}}-\frac{\pi}{4} \leq \theta \leq 0 \)
\( \stackrel{\pi}{4} \leq \theta \leq \frac{\pi}{2} \)


ne / \( m \) experiment we assume nature
of electron as
A. wave
B. particle.
c. photon
D. both a and b


Assertion: Reducing power of nascent hydrogen is more than atomic hydrogen Reason: Bond energy of hydrogen is maximum.
A. Both Assertion \& Reason are correct and Reason is correct explanation of Assertion
B. Both Assertion \& Reason are correct but Reason is not correct explanation of Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is wrong but Reason is correct


The segment of DNA which acts as the instrumental manual for the synthesis
of the protein is:
A . ribose
B. gene
c. nucleoside
D. nucleotide


The angular momentum of an electron
in the first orbit of \( L i^{++} \) ion is
A \( \cdot \frac{3 h}{2 \pi} \)
в. \( \frac{9 h}{2 \pi} \)
c. \( \frac{h}{2 \pi} \)
D. \( \frac{3 h}{6 \pi} \)


At \( 320 K, \) a gas \( A_{2} \) is \( 20 \% \) dissociated
to \( A(g) \). The standard free energy change at \( 320 K \) and 1 atm in \( J \) mol \( ^{-1} \)
is approximately:
\( \left[\boldsymbol{R}=\mathbf{8 . 3 1 4} \boldsymbol{J} \boldsymbol{K}^{-1} \boldsymbol{m o l}^{-1} ; \ln \mathbf{2}=\mathbf{0 . 6 9 3}\right. \)
A. 4763
B. 2068
c. 4281
D. 1844


Which element can show \( +2,+3,+4+6 \)
and +7 oxidation states?
A . cr
в. мп
\( c \cdot c_{0} \)
D.


A ray of light travels from ethanol into air. If the angle of incidence of the ray at the boundary is \( 30^{0} \) and the refractive
index of ethanol is \( 1.36, \) what is the
angle of refraction of the ray as it
emerges out of ethanol?
A \( \cdot 42.84^{0} \)
в. \( 21.5^{\circ} \)
\( c \cdot 46.8^{0} \)
D. None of the above


Hormogonia are the vegetatively reproducing structure of
A. Ulothrix
B. Spirogyra
c. oscillatoria
D. chlamydomonas


\( 2 K(s)+F_{2}(g) \rightarrow 2 K^{+} F^{-}(s) \) is a type
of reaction.
A. disproportionation
B. combustion
c. corrosion
D. redox


Which gas sample contains the fewest molecules?
A \( \cdot 1.00 d m^{3} \) of carbon dioxide at \( 27^{\circ} C \) and \( 2.0 k P a \)
B. \( 1.00 d m^{3} \) of hydrogen at \( 100^{\circ} \mathrm{C} \) and \( 2.0 \mathrm{kPa} \)
C \( \cdot 1.00 d m^{3} \) of nitrogen at \( 300^{\circ} \mathrm{C} \) and \( 4.0 k P a \)
D. \( 1.00 d m^{3} \) of oxygen at \( 250^{\circ} \mathrm{C} \) and \( 3.0 \mathrm{kPa} \)


Weight of a body on earth's surface is \( W . \) At a depth half way to the centre of
the earth, it will be (assuming uniform density in earth).
\( \mathbf{A} \cdot W \)
в. \( W / 2 \)
c. \( W / 4 \)
D. \( W / 8 \)


Find the point of intersection of the following pair of lines, assuming that the vectors \( \vec{a} \) and \( \vec{b} \) are not parallel. \( \vec{r}=\gamma(\vec{b}+\vec{a}), \vec{r}=\mu(\vec{b}-\vec{a}) \)
A . origin
в. \( \vec{b}+\vec{a} \)
\( c \cdot 2 b \)
D. no intersection point


The IUPAC name of the given compound
is :
A. \( 4- \) hydroxy-z-pentanone
B. 2-hydroxy-4-pentanone
c. 2-oxo-4-pentanol
D. 4-keto-2-pentanol


The correct structure of
ethylenediaminetetraacetic acid (EDTA)
is:
\( A \)
B.
\( c \)
\( D \)


Find the mean deviation about the
median for the data
\( \mathbf{1 3}, \mathbf{1 7}, \mathbf{1 6}, \mathbf{1 4}, \mathbf{1 1}, \mathbf{1 3}, \mathbf{1 0}, \mathbf{1 6}, \mathbf{1 1}, \mathbf{1 8}, \mathbf{1 2}, \mathbf{1} \)


An echo is simply a........of sound.
A. Reflection
B. Frequency
c. Amplitude
D. None of these


Integrate the rational function
\( \frac{3 x+5}{x^{3}-x^{2}-x+1} \)


At metaphase, chromosomes are attached to the spindle fibres by their
A. Kinetochores
B. Centromere
c. Satellites
D. Secondary constrictions


mass \( m \) is hanging in front of a large non-conducting sheet having surface charge density \( \sigma \). If suddenly a charge \( +q \) is given to the bob \( \& \) it is released
from the position shown in figure. The maximum angle through which the string is deflected from vertical is \( x \tan ^{-1}\left(\frac{\sigma q_{0}}{2 \varepsilon_{0} m g}\right) . \) Find \( x \)


Choose the wrong options
This question has multiple correct options
A. Translation kinetic energy of all ideal gases at same temperature is same
B. In one degree of freedom all ideal gases has internal energy \( =\frac{1}{2} R T \)
C. Translational degree of freedom of all ideal gases is three
D. Translational kinetic energy of one mole of all ideal gases is \( \frac{3}{2} R T \)


Difference in density is the basis of:
A . ultra filtration
B. molecular sieving
c. gravity separation
D. molecular attraction
E. atomic absorption


The phase difference between the
applied emf and the line current in an
anti resonant circuit at resonance is
A \( \cdot \frac{\pi}{2} \) radian
B. \( \pi \) radian
c. \( \frac{3 \pi}{2} \) radian
D. zero


State the characteristic of chemical
reaction which takes place when
1) Lead reacts with KI
2) Zinc reacts with HCl
3) Reaction of candle wax


Write a \( 2 \times 2 \) matrix which is both
symmetric and skew-symmetric.


A girl riding a bicycle with a speed of 5
\( m s^{-1} \) towards north direction, observes
rain falling vertically down. If she
increases her speed to \( 10 \mathrm{ms}^{-1}, \) rain
appears to meet her at \( 45^{\circ} \) to the
vertical. What is the speed of the rain?
A \( \cdot 5 \sqrt{2} \mathrm{ms}^{-1} \)
B. \( 5 m s^{-1} \)
D. \( 10 m s^{-1} \)


Can you explain why is bimolecular dehydran not appropriate for the preparation of ethyl methyl ether?


The real part of \( (1-\cos \theta+2 i \sin \theta)^{-1} \)
is
A. \( \frac{1}{3+5 \cos \theta} \)
B. \( \frac{1}{5-3 \cos \theta} \)
C. \( \frac{1}{3-5 \cos \theta} \)
D. \( \frac{1}{5+3 \cos \theta} \)


Currents of \( 10 A, 2 A \) are passed through two parallel wires \( A \) and \( B \) respectively in opposite directions. If the wire A is infinitely long and the length of the wire B is \( 2 m, \) the force on the conductor \( B \)
which is situated at \( 10 \mathrm{cm} \)
distance from A will be
\( \mathbf{A} \cdot 8 \times 10^{-5} N \)
B . \( 5 \times 10^{-5} N \)
c. \( 8 \pi \times 10^{-7} N \)
D. \( 4 \pi \times 10^{-7} N \)


Let \( ^{\prime} *^{\prime} \) be a binary operation on \( N \) defined by \( a * b=\mathrm{LCM}(a, b) \) for all
\( \boldsymbol{a}, \boldsymbol{b} \in \boldsymbol{N} . \) Find \( \boldsymbol{2} * \boldsymbol{4}, \boldsymbol{3} * \boldsymbol{5}, \boldsymbol{1} * \boldsymbol{6} \)


Construct a triangle of sides \( 5 \mathrm{cm}, 6 \mathrm{cm} \)
and \( 7 \mathrm{cm}, \) then construct a triangle
similar to it, whose sides are \( \frac{2}{3} \) of
corresponding sides of the first triangle.


The number of solutions of the equation
\( |\sin x|=|\cos 3 x| \operatorname{in}[-2 \pi, 2 \pi] \) is:
A . 32
B . 28
c. 24
D. 30


The silk from silk worm is softer as
compared to
A. Jute
B. cotton
c. Polyster
D. None of the above


A metallic sphere \( 1 \mathrm{cm} \) in diameter is beaten into a circular sheet of uniform
thickness equal to 1 mm. Find the
radius of the sheet


The IUPAC name of the following
compound is:
A. 1,2 -dimethyl-2-butenol
B. 3-methylpent-3-en-2-ol
C. 3,4 -dimethyl-2-buten-4-ol
D. none of the above


The number of all the possible selection
which a student can make for answering one or more questions out of eight given question in a paper, which each question has an alternative is
A . 255
B. 6560
\( c .6561 \)
D. none of these


In the figure, the disc D does not slip on
the surface S. The pulley P has mass,
and the string does not slip on it. The
string is wound around the disc. Then,
which of the following statement(s) is/are true?
his question has multiple correct options
A. The acceleration of the block B is double the acceleration of the centre of \( D \)
B. The force of friction exerted by D on S acts to the left
c. The horizontal and the vertical sections of the string have the same tension
D. The sum of the kinetic energies of D and B is less than the loss in the potential energy of B as it moves down


Calculate velocity at time


Find the sum of \( n \) terms of \( 1^{2}+ \)
\( \left(1^{2}+2^{2}\right)+\left(1^{2}+2^{2}+3^{2}\right)+ \)
\( \left(1^{2}+2^{2}+3^{2}+4^{2}\right)+\ldots \) from that find
the sum of the first 10 terms


A symmetric star-shaped conducting
wire loop is carrying a steady state
current I as shown the figure. The distance between the diametrically
opposite vertices of the star is \( 4 a . \) The magnitude of the magnetic field at the centre of the loop is


sources of energy:
A . Highly polluting
B. Unreliable supply
C. High running cost
D. High waste disposal cost


Assertion \( \mathbf{f}[\boldsymbol{x} \mathbf{1}]\left[\begin{array}{cc}\mathbf{1} & \mathbf{0} \\ -\mathbf{2} & \mathbf{3}\end{array}\right]\left[\begin{array}{c}\boldsymbol{x} \\ -\mathbf{5}\end{array}\right]=\mathbf{0}, \) then value
of \( x \) is either- 3 or 5
Reason Two matrices \( \left[\begin{array}{ll}\boldsymbol{x} & \boldsymbol{y} \\ \boldsymbol{u} & \boldsymbol{v}\end{array}\right] \) \& \( \left[\begin{array}{ll}\boldsymbol{a} & \boldsymbol{b} \\ \boldsymbol{c} & \boldsymbol{d}\end{array}\right] \) are
equal if \( \& \) only if their corresponding
entries are equal
\& only if their corresponding entries are equal
A. Both (A) \& (R) are individually true \& (R) is correct explanation of (A)
B. Both (A) \& (R) are individually true but (R) is not the correct (proper) explanation of (A).
c. (A)is true but (R) is false
D. (A)is false but (R) is true


Find the points on the line \( \frac{x+2}{3}= \) \( \frac{y+1}{2}=\frac{z-3}{2} \) at a distance of 5 units
from the point (1,3,3)


Which of the following is not a characteristic of image formed by Concave lens?
This question has multiple correct options
A. Virtual
B. Erect
c. Real
D. Magnified


The smallest positive integer for which
the statement \( 3^{n+1}<4^{n} \) holds is
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D. 4


The reaction, \( \boldsymbol{A}(\boldsymbol{g})+\mathbf{2} \boldsymbol{B}(\boldsymbol{g}) \rightarrow \boldsymbol{C}(\boldsymbol{g})+ \)
\( D(g), \) is an elementary process. In an
experiment involving this reaction, the initial partial pressures of \( A \) and \( B \) are
\( \boldsymbol{P}_{\boldsymbol{A}}=\mathbf{0 . 6 0} \) atm and \( \boldsymbol{P}_{\boldsymbol{B}}=\mathbf{0 . 8 0} \) atm
respectively. When \( P_{C}=0.20 \) atm, the rate of the reaction relative to the initial
rate is:
A \( \cdot 1 / 6 \)
B. 1/12
\( c \cdot 1 / 36 \)
D. 1/18


Which of the statements are the
drawbacks of Rutherford's model of an
atom?
A. The orbital revolution of the electron is not expected to be stable
B. Any particle in a circular orbit would undergo a acceleration and the charged particles would radiate energy
c. The revolving electron would lose energy and finally fall into the nucleus
D. All of the above


Explain oxy-acids of phosphorous.


Two identical magnetic dipoles are
placed, as shown separated by distance
d. The magnetic field, mid way between
the dipoles, is :
\( A \)
\[
\frac{\mu_{0} M \sqrt{2}}{4 \pi d^{3}}
\]
B.
\[
\frac{\mu_{0} M \sqrt{5}}{4 \pi d^{3}}
\]
\( c \)
\[
\frac{2 \mu_{0} M \sqrt{5}}{\pi d^{3}}
\]
D. none of these


\( X e F_{6} \) on hydrolysis gives:
A. \( X e O_{3} \)
в. \( X e O_{2} \)
\( c . X e O \)
D. \( x e \)


If four resistances, each of value 1 ohm,
are connected in series, what will be the
resultant resistance?
\( A . \) 3 ohm
B. 4 ohm
c. 5 ohm
D. 2 ohm


How is a rainbow formed?


Select the correct reaction(s) for \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \)
This question has multiple correct options
A. \( A g_{2} O+H_{2} O_{2} \rightarrow 2 A g+H_{2} O+O_{2} \)
в. \( C l_{2}+H_{2} O_{2} \rightarrow 2 H C l+O_{2} \)
c. \( O_{2}+H_{2} O_{2} \rightarrow H_{2} O+2 O_{2} \)
D. \( H_{2} O_{2}+2 K I \rightarrow 2 K O H+I_{2} \)


Which of the following statements does not show correct difference between
adsorption and absorption?
A. In adsorption, the substance is concentrated only at the surface while in absorption it is uniformly distributed in the bulk
B. Adsorption is instantaneous while absorption is a slow process
c. A substance can be adsorbed as well as absorbed simultaneously and the process is called sorption
D. only gases are adsorbed while solids and liquids are absorbed


In which of the following cases is the work done positive or zero or negative?
a) Work done by the porter on a suitcase in lifting it from the platform on to his head.
b) Work done by the force of gravity on suitcase as the suitcase falls from
porter's head.
c) Work done by the porter standing on platform with suitcase on his head.
d) Work done by force of gravity on a ball thrown up vertically up into the sky.
e) Work done by force applied by hands of a man swimming in a pond.