Which of the following statement(s)
is/are false?
This question has multiple correct options
\( \mathbf{A} \cdot \Delta_{r} S \) for \( \frac{1}{2} C l_{2}(g) \rightarrow C l(g) \) is positive
B. \( \Delta E<0 \) for combustion of \( C H_{4}(g) \) in a sealed
container with rigid adiabatic system
C. \( \Delta G \) is always zero for a reversible process in a closed
system
D. \( \Delta G^{0} \) for an ideal gas reaction is a function of pressure


Henles loop plays an important role in concentrating the urine.
A. True
B. False


\( E D T A^{-4} \) is a \( X \) dentate ligand. \( X \) is :
A. mono
в. hexa
c. tetra
D. tertary


A man has 7 relatives, 4 of them are
ladies and 3 gentlemen; his wife has 7 relatives and 3 of them are ladies and 4
gentlemen. The number of ways they can invite a dinner party of 3 ladies and 3 gentlemen so that there are 3 of men's relatives and 3 of wife's relative is
A . 455
B. 565
c. 485
D. None of these


The Sl unit of electric flux is
A. Voltmetre
B. Joule/Metre
c. Newton
D. None


Expand the expression \( (2 x-3)^{6} \)


A block of mass \( 10 k g \) is pulled by force \( F=100 N . \) It covers a distance \( 500 m \)
in 10 sec. From initial point. This motion is observed by three observers \( A, B \) and C as shown in figure.

Find out work done by the force \( F \) in \( 10 s \)
as observed by \( \mathrm{C} \)
A . \( 0 . J \)
в. \( 50000 J \)
c. \( 20000 J \)
D. \( 40000 J \)


Name the compound mentioned above.
\[
\begin{array}{c}
\mathrm{H} \\
\mathrm{H}-\mathrm{C}=\mathrm{O}
\end{array}
\]
A. methanol
B. ethanal
c. ethanol
D. methanal


The probable element El can be:
\( A \cdot B \)
\( B \)
\( c \)
\( D \)


Which law of motion deals with inertia:
A. Third law of motion
B. Second law of motion
c. First law of motion
D. All of these


Solve the given inequalities graphically:
\( \boldsymbol{x}+\boldsymbol{y} \leq \mathbf{9}, \boldsymbol{y}>\boldsymbol{x}, \boldsymbol{x} \geq \mathbf{0} \)


What is the shape of the equipotential surface for the line charge?
A. Sphere
B. Cylinder
c. It will depend upon the type of charge
D. can't say


If \( m \) and \( n \) are order and degree of the
equation \( \left(\frac{d^{2} y}{d x^{2}}\right)^{5}+4 \frac{\left(\frac{d^{2} y}{d x^{2}}\right)}{\left(\frac{d^{3} y}{d x^{3}}\right)}+\left(\frac{d^{3} y}{d x^{3}}\right)=x^{2}- \)
1 then \( (\boldsymbol{m}, \boldsymbol{n})= \)
A \( \cdot(3,3) \)
в. (3,2)
\( c .(3,5) \)
D. (3,1)


Electromagnetic induction is not used
in :
A. Transformer
B. Room heater
c. AC generator
D. Choke coil


J J Thomson Model could not able to
explain the following?
A. Stability of Atom
B. electrical neutrality of atom
c. stability of nuclcus
D. all of these


Solve
\( 2 x+3 y=8 \)
\( 2 x=2+3 y \)


Identify the wrong statements regarding post-fertilization development.
A. The ovary wall develops into pericarp
B. The outer integument of ovule develops into tegmen
C. The fusion nucleus (triple nucleus) develops into endosperm.
D. The ovule develops into seed.
E. The ovary develops into fruit


In the figure, find the area of \( \triangle \boldsymbol{P Q R} \)
and the height \( P S \).


Which of these is not a fossil fuel?
A. coal
B. LPG
c. Bio gas
D. All are fossil fuel


In the diagram:
\( A B \) is parallel to \( E D \) the points \( \mathrm{B}, \mathrm{C} \) and \( \mathrm{E} \) lie on a straight
line, and
the points \( A, C \) and \( D \) also lie on a straight line. What is the value of e (the length of CD)
7
A . 14.5
в. 16.
\( c \cdot 17.5 \)
\( D \cdot 18 \)


Following chemical reaction involves a
heterogeneous catalyst \( \mathbf{2} \boldsymbol{S} \boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{O}_{2}(\boldsymbol{g}) \stackrel{N O(\boldsymbol{g})}{\longrightarrow} \boldsymbol{2} \boldsymbol{S} \boldsymbol{O}_{3}(\boldsymbol{g}) \)
If true enter 1 , else enter 0 .
\( A \)


In the reaction \( \boldsymbol{C H}_{3} \boldsymbol{C N} \frac{\text {heat}}{\boldsymbol{H}_{3} \boldsymbol{O}^{+}} \)
\( C H_{3} C O O H \) the hybridisation state of
the functional carbon changes from:
A \( \cdot s p^{3} \) to \( s p^{2} \)
В \( \cdot s p^{2} \) to \( s p^{3} \)
\( \mathbf{c} \cdot s p \) to \( s p^{2} \)
D. \( s p^{2} \) to \( s p \)


Which one of the following statements
is correct?
\( \mathbf{A} \cdot \) If \( g(x)(\neq 0) \) and \( f(x) \) are two polynomials \( \epsilon F(x), \) then there exists unique polynomials \( q(x) \) and \( r(x) \epsilon F(x) \) such that \( f(x)=g(x) q(x)+r(x), \) where deg. \( r(x)< \) \( \operatorname{deg} . g(x) \)
B. If \( g(x)(\neq 0) \) and \( f(x) \) are two polynomials \( \epsilon F(x) \), then there exists unique polynomials \( q(x) \) and \( r(x) \epsilon F(x) \) such that \( f(x)=g(x) q(x)+r(x), \) where deg. \( r(x) \leq \)
\( \operatorname{deg} . g(x) \)
C . If \( g(x)(\neq 0) \) and \( f(x) \) are two polynomials \( \epsilon F(x) \), then there exists unique polynomials \( q(x) \) and \( r(x) \epsilon F(x) \) such that \( f(x)=g(x) q(x)+r(x), \) where either \( r(x)=0 \)
or deg. \( r(x)<\operatorname{deg} . g(x) \)
D. If \( g(x)(\neq 0) \) and \( f(x) \) are two polynomials \( \epsilon F(x) \), then there exists unique polynomials \( q(x) \) and \( r(x) \epsilon F(x) \) such that \( f(x)=g(x) q(x)+r(x), \) where either \( r(x)=0 \) or deg. \( r(x)>\operatorname{deg} . g(x) \)


What is the main function of white
blood corpuscle?


\( \operatorname{Let} f(x)=\left\{\begin{array}{ll}2 x+3 & ,-3 \leq x<-2 \\ x+1, & -2 \leq x<0 \\ x+2, & 0 \leq x \leq 1\end{array}\right. \)
At what points the function is/are not differentiable in the interval (-3,1)
This question has multiple correct options
A . -2
B.
\( c .1 \)
D. \( 1 / 2 \)


The vectors \( \overrightarrow{A B}=3 \hat{i}+4 \hat{k} \) and \( \overrightarrow{A C}= \) \( \mathbf{5} \hat{\mathbf{i}}-\mathbf{2} \hat{\mathbf{j}}+\mathbf{4} \hat{\boldsymbol{k}} \) are the sides of a triangle
\( A B C, \) then the length of the median
through \( \boldsymbol{A} \) is:
A. \( \sqrt{72} \)
B. \( \sqrt{33} \)
c. \( \sqrt{45} \)
D. \( \sqrt{18} \)


Which of the following statements on the atomic wave function \( \Psi \) is not
correct?
A. \( \Psi \) may be a real valued wave function
B. \( \Psi \) may be in some cases be a complex function
c. \( \Psi \) has a mathematical significance only
D. \( \Psi \) is proportional to the probability of finding an electron


Which one of the following is not a synthetic auxin?
\( A \cdot 2,4-D \)
в. 2, 4, 5- -
c. NAA
D. IAA


\( 0.2 g \) of an organic compound on Kjeldahls analysis gives enough ammonia to neutralize \( 20 \mathrm{cm}^{3} \) of \( 0.1 \mathrm{N} \)
\( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} . \) The percentage of nitrogen in
the compound is:
A \( \cdot 14 \)
B. 20
c. 70
D. 24


The differential coefficient of \( f(\sin x) \)
with respect to \( x \) where \( f(x)=\log x \) is:
A . \( \tan x \)
B. \( \cot x \)
c. \( f(\cos x) \)
D.


\( \boldsymbol{C}(s)+\boldsymbol{O}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{C} \boldsymbol{O}_{2},(\boldsymbol{g}) ; \boldsymbol{\Delta} \boldsymbol{H}= \)
\( -\mathbf{9 4 . 3} \) kcal/mol \( C O(g)+\frac{1}{2} O_{2}(g) \rightarrow C O_{2}(g) ; \Delta H= \)
\( -\mathbf{6 7 . 4} \) kcal/mol
\( O_{2}(g) \rightarrow 2 O(g) ; \Delta H=117.4 \mathrm{kcal} / \mathrm{mol} \)
\( \boldsymbol{C O}(\boldsymbol{g}) \rightarrow \boldsymbol{C}(\boldsymbol{g})+\boldsymbol{O}(\boldsymbol{g}) ; \boldsymbol{\Delta} \boldsymbol{H}=\mathbf{2 3 0 . 6} \)
kcal/mol
Calculate \( \Delta \boldsymbol{H} \) for \( \boldsymbol{C}(\boldsymbol{s}) \rightarrow \boldsymbol{C}(\boldsymbol{g}) \) in
kcal/mol
A . 17.1
В. 154
\( c \cdot 117 \)
D. 145


If the molar concentration of \( \boldsymbol{P b I}_{2} \) is
\( 1.5 \times 10^{-3} \) mol \( L^{-1}, \) then the
concentration of iodide ions in \( g \) ion \( L^{-1} \)
is:
A. \( 3.0 \times 10^{-3} \)
В. \( 6.0 \times 10^{-3} \)
D. \( 0.6 \times 10^{-6} \)


Based on VBT, \( \left[\boldsymbol{F} \boldsymbol{e} \boldsymbol{C l}_{\mathbf{6}}\right]^{3-} \) has \( \boldsymbol{C l}^{-} \) as
weak ligands. Fe is \( s p^{3} d^{2} \) hybridized
(outer orbital complex) having five
unpaired electrons. \( \left[\boldsymbol{F e}(\boldsymbol{C N})_{\boldsymbol{6}}\right]^{3-} \) has
\( C N^{-} \) as strong ligand. Fe is \( d^{2} s p^{3} \) hybridized (inner orbital complex) having only one unpaired electron.
Hence, \( \left[\boldsymbol{F} e C l_{6}\right]^{3-} \) is more paramagnetic
\( \operatorname{than}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{\boldsymbol{8}}\right]^{\boldsymbol{3}-} \)
If true enter 1 , else enter 0 .


Mole fraction of ethanol \( \left(C_{2} H_{5} O H\right) \) in
ethanol-water system is \( 0.25 . \) Thus, it has:
This question has multiple correct options
A. \( 25 \% \) ethanol by weight of solution
B. \( 75 \% \) water by weight of solution
c. \( 46 \% \) ethanol by weight of solution
D. 54\% water by weight of solution


The process by which the energy of glucose is released under aerobic respiration was discovered by
A. Hopkins
B. Lister
c. Krebs
D. Pasteur


Write two important limitations of Rutherford nuclear model of the atom.


The law of minimum was proposed by
A. Priestly
B. Liebig
c. ні|
D. Blackman


Br \( F_{3} \) is a liquid which considerably undergoes self ionization to form cationic and anionic species.
\( 2 B r F_{3} \rightleftharpoons\left[B r F_{2}\right]^{+}+\left[B r F_{4}\right]^{-} \)
Based on \( V S E P R \) theory, how many
\( 90^{\circ} F-B r-F \) bond angles are
there in anionic species?
\( A \cdot 4 \)
B. 5
\( c \cdot 3 \)
D.


Two unbiased coins whose faces are
marked 1 and 2 are tossed. The mean
value of the total of the numbers is
A . 3
B. 4
\( c .5 \)
D.


The photons from Blamer series in
hydrogen spectrum having wavelength between \( 450 \mathrm{nm} \) to \( 700 \mathrm{nm} \) are incident
on a metal surface of work function 2
eV. Find the maximum kinetic energy of
one photo electron.


Boiling points of aldehydes and ketones
are:
A. higher than hydrocarbons and ethers
B. higher than hydrocarbons but lower than ethers
C. higher than ethers but lower than hydrocarbons
D. lower than hydrocarbons and ethers


A molecule of \( \boldsymbol{H} \boldsymbol{X} \) can form stronger
hydrogen bond than another molecule
\( \boldsymbol{H}_{2} \boldsymbol{Y} . \) But \( \boldsymbol{H} \boldsymbol{X} \) boils at a lower
temperature than \( \boldsymbol{H}_{2} \boldsymbol{Y} \). Identify \( \boldsymbol{H} \boldsymbol{X} \)
and \( H_{2} Y \) and give a reason for the
peculiar behavior.


Let \( \boldsymbol{f}(\boldsymbol{x})=\cos \left[\boldsymbol{\pi}^{2}\right] \boldsymbol{x}+\cos \left[-\boldsymbol{\pi}^{2}\right] \boldsymbol{x} \)
where \( [x] \) is the greatest integer
function, then find \( f\left(\frac{\pi}{2}\right) \) and \( f(\pi) \)


Which of the following is paramagnetic
in nature?
A. \( N_{2} O_{4} \)
в. \( N_{2} \)
\( c \cdot N O_{2} \)
D. \( N_{2} O_{5} \)


Arrangement of ear ossicles, starting from ear drum is
A. Stapes, malleus, incus
B. Malleus, incus, stapes
c. Incus, stapes, malleus
D. Stapes, incus, malleus


Three identical positive charges each of value \( Q \) are arranged at the vertices of an equilateral triangle of side length a.
The intensity of the electric field at the
vertex of a regular tetrahedron of which the triangle is the base is:
A \( \cdot \frac{\sqrt{6} k Q}{a^{2}} \)
B. \( \frac{\sqrt{2} \text { КQ }}{\frac{a^{2}}{2}} \)
c. \( \frac{\sqrt{3} \kappa Q}{a^{2}} \)
D. None


If the ionic product of \( M(O H)_{2} \) is \( 5 \times \) \( 10^{-10}, \) then the molar solubility of
\( M(O H)_{2} \) in \( 0.1 M N a O H \) is:
A \( .5 \times 10^{-12} \mathrm{M} \)
В. \( 5 \times 10^{-8} \) М
c. \( 5 \times 10^{-10} M \)
D. \( 5 \times 10^{-9} M \)
E \( .5 \times 10^{-16} M \)


A list of animals is given below. Identify the animals with open circulatory system and choose the correct answer.
(A) Squid
(B) Cockroach
(C) Earthworm
(D) Prawn
(E) Silverfish
(F) Snail
\( A \cdot B, D, F \)
B. A, B, D, F
c. \( \mathrm{c}, \mathrm{D}, \mathrm{E}, \mathrm{G} \)
D. B, D, E, F
E. \( A, B, D, F, G \)


In a circle with centre \( 0, O D \perp \) chord \( A B \)
If BC is the diameter, then
\( \mathbf{A} \cdot A C=B C \)
В \( . O D=B D \)
c. \( A C=2 O D \)
D. none of these


Describe the criteria for classification
considering the number of Germinal
layers.


In a heterolytic bond fission of \( 2- \) methyl1-phenylpropane, which of the following stable carbocation will form?
A \( \cdot C_{6} H_{5}-C H_{2}^{+} \)
в. \( \left(C H_{3}\right)_{2} C H^{+} \)
\( \mathbf{c} \cdot C H_{3}^{+} \)
D. \( C_{6} H_{5}^{+} \)


Calculate reduction potential of the
following half-cell reaction at \( 25^{\circ} \mathrm{C} \)
\[
\begin{array}{rl}
2 H_{2} O+2 e & H_{2}+2 O H^{-} \\
& (1 \operatorname{atm})\left(10^{-7}\right)
\end{array}
\]


An uncharged conducting sphere of radius \( 2 R \) is joined to a charged
conducting sphere of radius \( R \) carrying
charge \( Q . \) The charge which flows between them is:
A \( \cdot \frac{Q}{3} \)
в. \( \frac{Q}{4} \)
c. \( \frac{Q}{5} \)
D. \( \frac{Q}{2} \)


Solve: \( (2 a+3 b)^{3}-(2 a-3 b)^{3} \)


Assertion
Two balls of different masses are
thrown vertically upward with same speed. They will pass through their point of projection in the downward direction with the same speed.
Reason
The maximum height and downward velocity attained at the point of
projection are independent of the mass of the ball.
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


Function \( f(x)=\frac{x}{1+x} \) defined from
\( [0, \infty) \rightarrow[0, \infty), f(x) \) is:
A. one-one and onto
B. one-one but not onto
c. not one- one but onto
D. neither one one nor onto


Construct the cells in which the
following reactions are taking place. Which of the electrodes shall act as
anode (negative electrode) and which one as cathode (positive electrode)?
(a) \( Z n+C u S O_{4}=Z n S O_{4}+C u \)
(b) \( \boldsymbol{C u}+\mathbf{2 A g} \boldsymbol{N O}_{3}=\boldsymbol{C u}\left(\boldsymbol{N O}_{3}\right)_{2}+ \)
\( \mathbf{2} \boldsymbol{A} \boldsymbol{g} \)
\( (c) Z n+H_{2} S O_{4}=Z n S O_{4}+H_{2} \)
(d) \( \boldsymbol{F} \boldsymbol{e}+\boldsymbol{S} \boldsymbol{n} \boldsymbol{C l}_{2}=\boldsymbol{F} \boldsymbol{e} \boldsymbol{C l}_{2}+\boldsymbol{S} \boldsymbol{n} \)


At the angle of polarisation, the angle of inclination between the reflected and
refracted rays is
\( A \cdot \frac{\pi}{8} \)
в. \( \frac{\pi}{6} \)
\( c \cdot \frac{\pi}{4} \)
0.5


\( \mathrm{G}_{2} \) phase takes
A. \( 50 \% \) time of cell cycle
B. 25 to 33\% time of cell cycle
c. 12 to \( 22 \% \) time of cell cycle
D. \( 4 \% \) time of cell cycle


Which of the following is/are correct?
This question has multiple correct options
A. Area of a circle with radius \( 6 \mathrm{cm} \), if angle of sector is \( 60^{\circ}, \) is \( \frac{132}{14} \mathrm{cm}^{2} \)
B. If a chord of circle of radius \( 14 \mathrm{cm} \) makes an angle of
\( 60^{\circ} \) at the centre of the circle, then area of major sector is \( 512.87 \mathrm{cm}^{2} \)
C. The ratio between the circumference and area of a
circle of radius \( 5 \mathrm{cm} \) is 2: 5
D. Area of a circle whose radius is \( 6 \mathrm{cm} \), when the length
of a arc is \( 22 \mathrm{cm}, \) is \( 66 \mathrm{cm}^{2} \)


An isosceles triangle has perimeter 30 \( \mathrm{cm} \) and length of its congruent sides is \( 12 \mathrm{cm} . \) Find the area of the triangle.


| vidnu nas decided to create a triangular
flower bed border. He plans to use 3
pieces of rectangular wooden plates
with lengths 4,5 and 6 feet, as shown in
the figure.

Manu plans to cut the 3 pieces of plate for the flower bed border from a single
piece of plate. If \( \frac{1}{8} \) inch wood is wasted
in every cut, calculate the shortest
single piece of plate which can be used
by Manu.
A . 178
B. 179
c. 180
D. 181
E . 182


The freezer in a refrigerator is located at the top section so that
A. The entire chamber of the refrigerator is cooled quickly due to convection
B. The motor is not heated
C. The heat gained from the environment is high
D. The heat gained from the environment is :ow


A family of lines is given by \( (1+ \)
\( 2 \lambda) x+(1-\lambda) y+\lambda=0, \lambda \) being the
parameter. The line belonging to this family at the maximum distance from
the point (1,4) is
A. \( 4 x-y+1=0 \)
B. \( 33 x+12 y+7=0 \)
c. \( 12 x+33 y=7 \)
D. none of these


Find the equation of the curve passing
through the point \( (0,1), \) if the slope of
tangent to the curve at each of its point is equal to the sum of the abscissa and the product of the abscissa and
ordinate of the point.


Cube of 1.5 is:
\( \mathbf{A} \cdot 3.375 \)
B. 33.75
c. 3.125
D. 31.25


Bond dissociation energy of \( \boldsymbol{X} \boldsymbol{Y}, \boldsymbol{X}_{2} \)
and \( Y_{2} \) (all diatomic molecules) are in
the ratio of 1: 1: 0.5 and \( \Delta H_{f} \) of \( X Y \) is
\( -100 k J m o l^{-1} . \) The bond dissociation
energy of \( X_{2} \) is \( 100 x . \) Find the value of \( x \)
\( A \cdot 4 \)
B.
\( c \cdot 8 \)
D. 10


A sound source emits two sinusoidal
sound waves. both of wavelength \( \lambda \)
along paths \( A \) and \( B \) as shown in figure
The sound travelling along path \( B \) is
reflected from five surfaces as shown
and then merges at point \( Q \), producing
minimum intensity at that point. Find
the minimum value of \( d \) in terms of \( \lambda \)


Each stomata is surrounded by
A. Passage cells
B. Guard cells
C. Parenchyma cells
D. Lenticels


Which one is non-biodegradable?
A . DDT
B. Sewage
c. Livestock waste
D. Market garbage


Phosphine is a reducing agent
If true enter 1 , else enter 0 .


A satellite is revolving in a circular orbit at a distance of \( 2620 \mathrm{km} \) from the
surface of the earth. The time period of
revolution of the satellite is
(Radius of the earth \( =\mathbf{6 3 8 0} \) km, mass
of the earth \( =\mathbf{6} \times \mathbf{1 0}^{\mathbf{2 4}} \mathbf{k g}, \mathbf{G}=\mathbf{6 . 6 7} \times \)
\( \left.\mathbf{1 0}^{-11} \mathbf{N}-\boldsymbol{m}^{\mathbf{2}} / \boldsymbol{k g}^{2}\right) \)
\( \mathbf{A} \cdot 2.35 \) hours
B. 23.5 hours
c. 3.25 hours
D. 32.5 hours


Setting of plaster of paris involves:
A. oxidation with atmospheric oxygen
B. combination with atmospheric \( C O_{2} \)
c. dehydration
D. hydration to yield another hydrate


A thin rod is bent in the shape of a small circle of radius r. If the charge per unit
length of the rod is \( \sigma, \) and if the circle is rotated about its axis at a rate of
rotations per second, the magnetic induction at a point on the axis at a
large distance y from the centre is?
A \( \cdot \mu_{0} \pi r^{3} n \frac{\sigma}{y^{3}} \)
В \( \cdot 2 \mu_{0} \pi r^{3} n \frac{\sigma}{y^{3}} \)
c. \( \left(\frac{\mu_{0}}{4 \pi}\right) r^{3} n \frac{\sigma}{y^{3}} \)
D \( \cdot\left(\frac{\mu_{0}}{2 \pi}\right)^{r^{3}} n \frac{\sigma}{y^{3}} \)


A reaction mixture containing \( \boldsymbol{H}_{2}, \boldsymbol{N}_{2} \)
and \( N H_{3} \) has partial pressures 2 atm
1 atm and 3 atm respectively at \( 725 K \)
If the value of \( K_{p} \) for the reaction,
\( N_{2(g)}+3 H_{2(g)} \rightleftharpoons 2 N H_{3(g)} \) is \( 4.28 \times \)
\( 10^{-5} a t m^{-2} \) at \( 725 K \), in which direction
the net reaction will go?
A. Forward
B. Backwardd
c. No net reaction
D. Direction of reaction cannot be predicted


0.1M of \( \boldsymbol{H} \boldsymbol{A} \) is titrated with \( \mathbf{0 . 1} \boldsymbol{M} \)
\( N a O H, \) calculate \( p H \) at end point \( \operatorname{Given} K(H A)=5 \times 10^{-6} \) and \( \alpha \ll 1 \)


The equilibrium constant \( \boldsymbol{K}_{\boldsymbol{p}} \) for a
homogeneous gaseous reaction is \( 10^{-8} \) The standard Gibbs free energy change \( \Delta G^{\ominus} \) for the reaction (using \( \boldsymbol{R}= \)
\( \left.2 c a l K^{-1} m o l^{-1}\right) \) is:
A. \( 10.98 k c a l \)
B. - 1.8kcal
c. \( -4.1454 k c a l \)
D. \( +4.1454 k c a l \)


Prove work energy theorem for a constant force.


A particular force propels a particle in such a way that the force can be
represented by the function \( \boldsymbol{F}(\boldsymbol{x})= \)
\( \sin 2 x, \) where \( x \) is in meters and \( F \) is in
Newtons (the proper conversion of input
and output units and dimensions is implied). When the particle moves from \( x=\frac{\pi}{2} \) to
\( x=\pi, \) by how much does its potential
energy change?
\( \mathbf{A} \cdot \mathbf{2} \)
B. 1
c. 0
D. -
E. -2


Assertion
According to Bronsted Lowry theory \( B F_{3} \)
is an acid.
Reason
\( B F_{3} \) is an electron deficient 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. Assertion is incorrect but Reason is correct


Choose the correct answer from the
alternatives given :
Watson and Crick (1953) proposed DNA
double helix model and won the Nobel
Prize; their model of DNA was based on
(i) X-ray diffraction studies of DNA done by Wilkins and Franklin
(ii) Chargaffs base equivalence rule
(iii) Griffiths transformation
experiment
(iv) Meselson and Stahls experiment.
A. (i), (ii) and (iv)
B. (i) and (ii)
c. (iii) and (iv)
D. (i), (ii), (iii) and (iv)


Which form of carbon is used in public address microphone systems?
A. Graphite
B. Charcoal
c. coke
D. Lamp black


Find the angular velocity of the rod after the collision.
A \( \cdot \omega=\frac{3 v}{(4+\eta) l} \)
B. \( \omega=\frac{12 v}{(4+\eta) l} \)
c. \( \omega=\frac{3 v}{(4-\eta) l} \)
D. \( _{\omega}=\frac{12 v}{(4-\eta) l} \)


Which set of human teeth help in cutting food?
A. Canine
B. Incisor
c. Molar
D. Premolar


If a complex number \( z \) and \( z+\frac{1}{z} \) have
same argument then-
A. z must be purely real
B. z must be purely imaginary
c. z cannot be imaginary
D. z must be raal


When pressure exerted on fluids by container, then the force is always parallel to the wall. Is the statement true or False
A. True
B. False


In which mode of transfer of heat
molecules pass on heat energy to neighbouring molecules without actually moving from their positions?
A. convection
B. radiation
c. conduction
D. none of these


Find the value of \( x \)
if \( \tan ^{-1} x+2 \cot ^{-1} x=\frac{2 \pi}{3} \)


The surface area of a cube is \( 600 \mathrm{cm}^{2} \)
Find its volume
A \( \cdot 1000 \mathrm{cm}^{3} \)
в. \( 729 \mathrm{cm}^{3} \)
\( c \cdot 512 c m^{3} \)
D. None of these


An investigator interviewed 100 students to determine their preferences for the three drinks: milk ( \( M \) ), coffee
\( (C) \) and tea \( (T) . \) He reported the following: 10 students had all the three drinks \( M, C, T ; 20 \) had \( M \) and \( C \) only; \( \mathbf{3 0} \) had \( \boldsymbol{C} \) and \( \boldsymbol{T} ; \mathbf{1 2} \) had \( \boldsymbol{M} \) only \( ; \mathbf{5} \) had \( C \) only; 8 had \( T \) only. Then how many did not take any of three drinks is
A . 20
B. 30
\( c .36 \)
D. 42


A mixture containing 2 moles of \( N_{2} \) and
3 moles of \( \boldsymbol{H}_{2} \) gas is brought to equilibrium in a 3 L vessel.lf the molar
concentration of \( N H_{3} \) at equilibrium is
\( 1 / 3 \) mol/L, calculate the \( K_{c} \) for the
formation of \( \boldsymbol{N} \boldsymbol{H}_{2} \cdot \boldsymbol{N}_{2}(\boldsymbol{g})+\boldsymbol{3} \boldsymbol{H}_{2}(\boldsymbol{g}) \rightleftharpoons \)
\( \mathbf{2} \boldsymbol{N} \boldsymbol{H}_{3}(\boldsymbol{g}) \)


A property of the progressive wave that
does not depend upon other characteristics mentioned below is
A. wavelength
B. amplitude
c. frequency
D. wave velocity


Chlorine exists in two isotopic forms, \( C l-37 \) and \( C l-35 \) but its atomic
mass is \( 35.5 . \) This indicates the ratio of
\( C l-37 \) and \( C l-35 \) is approximately:
A .1: 2
B. 1: 1
c. 1: 3
D. 3: 1


A coil of \( 10^{-2} H \) inductance carries a
current \( \boldsymbol{I}=2 \sin (\mathbf{1 0 0} \boldsymbol{t}) \boldsymbol{A} . \) When current
is half of its peak value then at that instant the induced emf in coil :-
A . \( 1 V \)
B. \( \sqrt{2} V \)
c. \( \sqrt{3} V \)
D. 2


Which of the following equations
represents parametrically, parabolic
profile?
\( \mathbf{A} \cdot x=3 \cos t ; y=4 \sin t \)
B \( x^{2}-2=-\cos t ; y=4 \cos ^{2} \frac{t}{2} \)
\( \mathbf{c} \cdot \sqrt{x}=\tan t ; \sqrt{y}=\sec t \)
D. \( x=\sqrt{1-\sin t} ; y=\sin \frac{t}{2}+\cos \frac{t}{2} \)


The shape of acetylene molecule is?
A. Linear
B. Planar
c. Pyramidal
D. Tetrahedral


If \( a=\frac{3+\sqrt{5}}{2}, \) then find the value of \( a^{2}+\frac{1}{a^{2}} \)
\( \mathbf{A} \cdot \mathbf{5} \)
B. 6
\( c \cdot 7 \)
\( D \)


Two particles of equal mass \( m \) go around in a circle of radius \( R \) under the action of
their mutual gravitational attraction. The
speed of each particle is \( v \). Find value of \( v \)
\( ^{\mathrm{A}} \cdot_{v}=\frac{1}{2 R} \sqrt{\left(\frac{1}{G m}\right)} \)
в. \( v=\sqrt{\left(\frac{G m}{2 R}\right)} \)
c. \( v=\frac{1}{2} \sqrt{\left(\frac{G m}{R}\right)} \)
D. \( v=\sqrt{\left(\frac{4 G m}{R}\right)} \)


Which of the following is the correct order of the solubility in water?
A. propane < ethylamine < ethyl alcohol
B. propane < ethyl alcohol < ethylamine
c. ethyl alcohol < propane < ethylamine
D. ethyl alcohol < ethylamine < propane


The conducting cells of xylem
are
A. Tracheary elements
B. Sieve elements
c. companion cells
D. All of the above


For the reaction, \( \left[\boldsymbol{A} \boldsymbol{g}(\boldsymbol{C} \boldsymbol{N})_{2}\right]^{-} \rightleftharpoons \)
\( A g^{+}+2 C N^{-}, \) the equilibrium
constant \( \boldsymbol{K}_{c} \) at \( \mathbf{2 5}^{\boldsymbol{o}} \boldsymbol{C} \) is \( \mathbf{4} \times \mathbf{1 0}^{-\mathbf{1 9}} \). Then
\( A g^{+} \) concentration in a solution which
has \( 0.1 M K C N \) and \( 0.03 M A g N O_{3} \)
is:
A. \( 7.5 \times 10^{18} \)
B . \( 7.5 \times 10^{-18} \)
c. \( 7.5 \times 10^{19} \)
D. \( 7.5 \times 10^{-19} \)


Find the resultant of three vectors
\( \boldsymbol{O A}, \overrightarrow{\boldsymbol{O B}} \) and \( \overrightarrow{\boldsymbol{O C}} \) shown in figure.
Radius of circle is 'R'.
A \( \cdot R(1+\sqrt{2}) \)
B . \( R(1+\sqrt{3}) \)
c. \( R(2+\sqrt{3}) \)
D \cdot \( R(1+\sqrt{5}) \)


f \( \boldsymbol{m}(\boldsymbol{a} \boldsymbol{r} \boldsymbol{c} \boldsymbol{B} \boldsymbol{C})=\boldsymbol{8} \boldsymbol{0}^{o}, \) find \( \boldsymbol{m}(\boldsymbol{a} \boldsymbol{r} \boldsymbol{c} \boldsymbol{C} \boldsymbol{D}) \)
A \( \cdot 40^{\circ} \)
B. \( 80^{\circ} \)
\( c \cdot 120^{\circ} \)
D. \( 140^{\circ} \)


Incorrect about alkyl halides is/ are:
This question has multiple correct options
A . tertiary alkyl halides undergo \( S_{N} 2 \) substitutions
B. alkyl iodides on exposure to sunlight gradually darken
C . alkyl chlorides do not give Beilstein test
D. a nucleophilic substitution is most difficult in alkyl iodides


The volume of a gas is reduced adiabatically to \( \frac{1}{4} \) of its volume at \( 27^{\circ} C \) If \( \gamma=1.4 \) the new temperature is :
A \( \cdot(300) 2^{0.4} K \)
В . (300) \( 2^{1.4} K \)
c. \( 300(4)^{\text {) }-4} K \)
D. \( 300(2)^{0.4} K \)


In the situation of resonance, frequency
of L-C circuit is:
\( ^{\mathrm{A}} \cdot \frac{1}{2 \pi} \sqrt{\frac{1}{L C}} \)
в. \( 2 \pi \sqrt{\frac{1}{L C}} \)
c. \( 2 \pi \sqrt{L C} \)
D. \( \frac{1}{2 \pi} \sqrt{L C} \)


Catalytic poison in Rosenmund's reduction is :
A. quinoline
в. \( H_{2} \)
c. \( C H_{3} \) COCl
D. \( C H_{3} C H O \)


The IUPAC name of is :
A. 1-Phenyl ethanone
B. Methyl phenyl ketone
c. Acetophenone
D. Phenyl methyl ketone


When an electron and a proton are
placed in an electric field
A. The electric forces acting on them are equal in magnitude as well as direction
B. Only the magnitudes of forces are same
C. Accelerations produced in them are same
D. Magnitudes of accelerations produced in them are same


A circular loop of mass \( \mathrm{m} \) and \( \mathrm{R} \) rests
flat on a horizontal frictionless
surface.A bullet also of mass \( \mathrm{m} \), and
moving with a velocity v, strikes the loop and gets embedded in it. The thickness of the hoop is much smaller than R. The anguler velocity with system rotates after the bullet strikes the hoop is


The energy supplied to Kolkata by the state electricity board during an average November week day was 40 GWh. If this energy could be obtained by the conservation of matter, how much
mass would have to be annihilated?
A \( .1 .6 g \)
B. \( 2.2 \mathrm{g} \)
c. \( 4.0 \mathrm{g} \)
D. \( 1.6 \mathrm{kg} \)


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


Assertion
The pressure at the bottom of two tanks of different area of cross sections are
equal if they contain same liquid to
same height
Reason
Pressure of a liquid is hdg and is
independent of shape and width of the
container
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


Using the concept of force between two
infinitely long parallel current carrying conductors, define one ampere of
current


The correct relationship between free energy change in a reaction and the corresponding equilibrium constant Kc
is:
\( \mathbf{A} \cdot \Delta G=R T \ln K c \)
в. \( -\Delta G=R T \ln K c \)
c. \( \Delta G^{0}=R T l n K c \)
D. \( -\Delta G^{0}=R T l n K c \)


An article in the newspaper reports that 'Refrigerants like Chloroflurocarbons (CFCs) pose threat to the environment'.
How CFCs are harmful to the
environment?


Table salt is contaminated with
\( N a H C O_{3} \) due to presence of \( M g C l_{2} \) as impurity (from sea).
If true enter 1 , else enter 0 .


A semipermeable membrane allows the diffusion of
A. Solutes
B. Solvent
c. Both solvent and solutes
D. None of above


The inverse of "If \( x \) has courage, then \( x \)
will win", is
\( \mathbf{A} \cdot \) If \( x \) will win, then \( x \) has courage.
B. If \( x \) has no courage, then \( x \) will not win.
C. If \( x \) will not win, then \( x \) has no courage.
D. If \( x \) will not win, then \( x \) has courage.


The number of values of \( x \) in the interval
\( [0,5 \pi] \) satisfying the equation \( 3 \sin ^{2} x-7 \sin x+2=0 \) is
A .
B. 5
\( c \cdot 6 \)
D. 10


The temperature of a normal human
being is
A \( \cdot 31^{\circ} \mathrm{C} \)
В. \( 37^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 20^{\circ} C \)
D. \( 50^{\circ} \mathrm{C} \)


A positive point charge is released from
rest at a distance \( r_{0} \) from a positive line charge with uniform density. The speed
(v) of the point charge, as a function of instantaneous distance r from line
charge, is proportional to :-
A \( \cdot v \propto e^{+r / r_{0}} \)
В \( \cdot v \propto \ln \left(\frac{r}{r_{0}}\right) \)
c. \( v \propto\left(\frac{r}{r_{0}}\right) \)
D.


The potential across the metal and the aqueous solution of its ions of unit
activity at \( 298 \mathrm{K} \) is known as:
A . electrode potential
B. standard electrode potential
c. formal electrode potential
D. oxidation potential


The first terms of a \( G . P . \) is 27 and its
\( 8^{t h} \) term is \( \frac{1}{81} . \) Find the sum of its first
10 terms.


In which of the following compounds manganese has an oxidation number
equal to that of iodine in \( K I O_{4} ? \)
A. Potassium manganate
B. Potassium permanganate
c. Manganous chloride
D. Manganese chloride


Consider the following relation \( R \) on the
set of real square matrices of order 3
\( \boldsymbol{R}=\{(\boldsymbol{A}, \boldsymbol{B}), \mid \boldsymbol{A} \boldsymbol{B}=\boldsymbol{B} \boldsymbol{A}\} \)
STATEMENT-1: Relation R is
equivalence.
STATEMENT-2: Relation R is symmetric.
A. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-
B. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1
C. STATEMENT -1 is True, STATEMENT-2 is False
D. STATEMENT-1 is False, STATEMENT-2 is True


Examine the graph of \( y=f(x) \) as
shown and evaluate the following limits
(i) \( \lim _{x \rightarrow 1} f(x) \)
(ii) \( \lim _{x \rightarrow 2} f(x) \)
(iii) \( \lim _{x \rightarrow 3} f(x) \)
(iv) \( \lim _{x \rightarrow 199} f(x) \)
\( (v) \lim _{x \rightarrow 3^{+}} f(x) \)


Hydrogen is the most abundant element
in the universe
If this is true enter 1 , if false enter 0 .


Given that \( r=0.4 \sum(x-\bar{x})(y-\bar{y})= \)
\( \mathbf{1 0 8}, \boldsymbol{\sigma}_{\boldsymbol{y}}=\mathbf{3} \) and \( \sum(\boldsymbol{x}-\overline{\boldsymbol{x}})^{2}=\mathbf{9 0 0} . \) Find
the number of pairs of observations.


Genetic dwarfness can be overcome by
treating the plant with
A. Cytokinin
B. Gibberellic acid
c. Auxin
D. Antigibberellin


Find the measure of an angle, if four
times of its complement is \( 12^{\circ} \) more
than twice the difference between its
supplement and complement.
A . 36
B . 45
c. 42
D. 24


Which of the following statements are true (T) and which are false (F)?
Sum of any two sides of a triangle is greater than the third side.
A . True
B. False


If \( \boldsymbol{x}=\mathbf{5}-\mathbf{2} \sqrt{\mathbf{6}}, \) find the value of \( \boldsymbol{x}+\frac{\mathbf{1}}{\boldsymbol{x}} \)


\( \lim _{x \rightarrow 0} \frac{1}{x^{2}} \frac{1}{\sin ^{2} x} \)
A \( \cdot \infty \)
B. \( -\frac{1}{3} \)
\( c \cdot \frac{1}{3} \)
D. does not exist


Which of these is a bisexual flower?
A. Petunia
B. corn
c. Papaya
D. None of these


If the forward voltage in a
semiconductor is doubled, the width of
depletion layer will
A. become half
B. become one-fourth
c. remain unchanged
D. become double


Two hail stones with radii in the ratio of
1: 2 fall from a great height through the atmosphere. Then the ratio of their momenta after they have attained terminal velocity is
A . 1: 1
B. 1: 4
c. 1: 16
\( \mathbf{D} \cdot 1: 32 \)


f a current lis flowing in a loop of
radius r as shown in adjoining figure,
then the magnetic field induction at the
centre 0 will be
A. zero
в. \( \frac{\mu_{0} I \theta}{4 \pi r} \)
c. \( \frac{\mu_{0} I \sin \theta}{4 \pi r} \)
D. \( \frac{2 \mu_{0} I \sin \theta}{4 \pi r^{2}} \)


Why do polarized sun glasses block out some reflected light (glare), but do not block out light that has not been reflected?
A. Some reflected light is at least partially polarizedd
B. Some reflected light changes frequency
c. Some reflected light is red-shifted
D. Some reflected light is at least partially diffracted
E. Some reflected light splits into multiple photons


Find the derivatives of the following functions at the indicated points.
\( \boldsymbol{f}(\boldsymbol{x})=\sin 4 \boldsymbol{x} \cos \mathbf{4} \boldsymbol{x}, \boldsymbol{f}^{\prime}(\boldsymbol{\pi} / \mathbf{3})=? \)


A mixture of \( S O_{3}, S O_{2} \) and \( O_{2} \) gases is
maintained at equilibrium in 10 litre. flask at a temperature at which Kc for
the reaction, \( 2 S O_{2}(g)+ \)
\( O_{2}(g) \rightarrow \neg 2 S O_{3}(g) \) is \( 100 m o l^{-1} \) litre
At equilibrium.
A. If no. of mole of \( S O_{3}, S O_{2} \) in the flask are same, how many moles of \( O_{2} \) are present 0.1
B. If no. of mole of \( S O_{3} \) in the flask are twine the no.of
mole of \( S O_{2} \), how many moles of \( O_{2} \) are present \( 0 . \)
c. Both A and B
D. None


If \( A \) and \( B \) are events such that
\( \boldsymbol{P}(\boldsymbol{A})=\mathbf{0 . 6}, \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 3} \) and \( \boldsymbol{P}(\boldsymbol{A} \cap \)
\( \boldsymbol{B})=\mathbf{0 . 2}, \) find \( \boldsymbol{P}(\boldsymbol{A} / \boldsymbol{B}) \) and \( \boldsymbol{P}(\boldsymbol{B} / \boldsymbol{A}) \)


The atomic number of an element \( ^{\prime} M^{\prime} \)
is \( 26 . \) How many electrons are present in
the M-shell of the element in its \( M^{3+} \)
state?
A . 11
B . 15
c. 14
D. 13


The minimum value of \( |\boldsymbol{x}|+\left|\boldsymbol{x}+\frac{\mathbf{1}}{\mathbf{2}}\right|+ \)
\( |\boldsymbol{x}-\mathbf{3}|+\left|\boldsymbol{x}-\frac{\mathbf{5}}{\mathbf{2}}\right| \) is
\( A \cdot 2 \)
B. 4
\( c \cdot 6 \)
D.


Distillation under reduced pressure is used to purify liquids which:
A. are highly volatile
B. have high boiling points
C. are explosives
D. decomposes below their boiling points


The monomers of Buna-S rubber are:
A. isoprene and butadiene
B. butadiene and phenol
c. styrene and butadiene
D. vinyl chloride and sulphur


Why does boron not form \( B^{3+} \) ion?


Which of the following is present both in animals as well as fungi?
I. Autotrophic mode of nutrition
Il. Extracellular digestion
III. Lack of cell walls
IV. Membrane-bound organelles
A. I and III
B. I and IV
c. II and III
D. II and IV
E. IV only


At what price should a shopkeeper
mark a radio that costs him Rs.1200 in
order that he may offer a discount of
\( 20 \% \) on the marked price and still make
a profit of \( 25 \% ? \)


The acceleration of a particle is increasing linearly with time \( t \) as \( b t \). The particle starts from the origin with an
initial velocity \( v_{0} . \) The distance
travelled by the particle in time \( t \) will be:
A \( \cdot v_{0} t+\frac{1}{6} b t^{3} \)
B. \( v_{0} t+\frac{1}{3} b t^{3} \)
c. \( v_{0} t+\frac{1}{3} b t^{2} \)
D. \( v_{0} t+\frac{1}{2} b t^{2} \)


Among the following, which one is isotope
A. \( N H_{3} \) and \( N_{2} H_{4} \)
B. 160 and \( ^{17} O \)
c. \( N H_{4} C l \) and \( N H_{4} N O_{3} \)
D. \( C H_{3} O C H_{3} \) and \( C H_{3} C H_{2} O H \)
E. \( O_{2} \) and \( O_{3} \)


Show that the differential equation of the family of circles having their centre
at the origin and radius \( a \) is
\[
\boldsymbol{x}+\boldsymbol{y} \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\mathbf{0}
\]


If \( \boldsymbol{x}, \boldsymbol{y} \in[\mathbf{0}, \mathbf{2} \boldsymbol{\pi}], \) then find the total
number of ordered pairs \( (\boldsymbol{x}, \boldsymbol{y}) \)
satisfying the equation \( \sin x \cos y=1 \)


Which of the following expression gives the de-Broglie relationship?
A \( \cdot p=\frac{h}{m v} \)
B. \( \lambda=\frac{h}{m v} \)
c. \( \lambda=\frac{h}{m p} \)
D \( \cdot \lambda m=\frac{v}{p} \)


A material upon heavy stress undergoes a deformation and lands a part of permanent set. Upon removal of the stress, the material will
A. return to its original position
B. become permanently plastic
c. start oscillating about the elastic point
D. start oscillating about the yield point


Assertion
We apply paint on iron articles.
Reason
Iron is a metal, metals rust when they
come in contact of direct air so to
prevent rusting.
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 terminal velocity \( \left(V_{c}\right) \) of a small
sphere falling under gravity in a viscous liquid is related to its radius as
A. \( V_{c} \propto r \)
B. \( V_{c} \propto \frac{1}{r} \)
c. \( V_{c} \propto r^{2} \)
D. \( V_{c} \propto r^{3} \)


A particle is moving along a circular path of radius \( 5 m \) with a uniform
speed \( 5 m s^{-1} . \) What will be the average
acceleration when the particle completes half revolution?
A. Zero
B. \( 10 \mathrm{ms}^{-2} \)
\( \mathbf{c} \cdot 10 \pi \mathrm{ms}^{-2} \)
D. \( \frac{10}{\pi} m s^{-2} \)


A uniform magnetic field parallel to the
plane of paper, existed in space initially directed from left to right. When a bar of soft iron is placed in the field parallel to
it, the lines of force passing through it will be represented by figure.
\( \mathbf{A} \)
B.
\( c \)
D.


Which of the following is the correct product for the compound when treated
with \( \boldsymbol{B} \boldsymbol{r}_{2} / \boldsymbol{C C l}_{4} \)
A \( \cdot C H_{3}-C H=C H_{2} \rightarrow C H_{3}-C H_{2}-C H_{2} B r \)
В. \( C H_{3}-C H=C H_{2} \rightarrow B r C H_{2}-C H=C H_{2} \)
c. \( C H_{3}-C H=C H_{2} \rightarrow C H_{3}-C H B r-C H_{3} \)
D. \( C H_{3}-C H=C H_{2} \rightarrow C H_{3}-C H B r-C H_{2} B r \)


\( [\mathrm{AS} 1] \) If \( \boldsymbol{A}=\frac{1}{3} \boldsymbol{B} \boldsymbol{a} \boldsymbol{n} \boldsymbol{d} \boldsymbol{B}=\frac{1}{2} \boldsymbol{C}, \) then \( \boldsymbol{A} \)
\( B: C= \)
A .1: 3: 6
B. 2:3:6
\( c \cdot 3: 2: 6 \)
D. 3: 1: 2


Three coins are tossed once. Describe
the following events associated with this random experiment. \( \boldsymbol{A}= \) Getting three heads, \( \boldsymbol{B}= \) Getting
two heads and one tail
\( \boldsymbol{C}= \) Getting three tails, \( \boldsymbol{D}= \) Getting a head on the first coin.
Which events are compound events


Find :
\( \lim _{x \rightarrow 0^{+}} x^{x} \)


Iron carbonyl, \( \boldsymbol{F e}(\boldsymbol{C O})_{5} \) is
A . trinuclear
B. tetranuclear
c. dinuclear
D. mononuclear


A body weighs \( 900 \mathrm{N} \) on the earth. Find its weight on a planet whose density is \( \mathbf{1}^{s} \)
\( \frac{1}{3} \) the density of earth and radius is 1
\( t h \)
\( \frac{1}{4} \) that of the earth.
A . \( 75 \mathrm{N} \)
в. 500 N
c. 62 N
D. 320N


On approximately how many days was
the 2 p.m temperature above \( 70^{\circ} \) F?
A. Approx. 12
B. Approx. 39
C. Approx. 93
D. None of these


Suppose that a hypothetical atom gives
a red, green, blue and violet line
spectrum. Which jump according to the
figure would give off the red spectral
line?
\( A \cdot 3 \rightarrow 1 \)
B \( .2 \rightarrow 1 \)
\( c \cdot 4 \rightarrow 1 \)
\( D \cdot 3 \rightarrow 2 \)


The average value of acceleration due to gravity on the surface of the earth is
equal to:
A. \( 9.8 \mathrm{ms}^{-2} \)
B. \( 9.8 \mathrm{ms}^{-1} \)
c. \( 19.6 \mathrm{ms}^{-2} \)
D. \( 9.8 s^{-2} \)


If the price of a book is reduced by Rs. 5 a person can buy 5 more books for Rs.
300. Find the original list price of the book.


Name the region beyond the violet end,
of the spectrum
A. infraviolet
B. ultraviolet
c. darkviolet
D. lightviolet


\( f \int_{0}^{2 \pi} \log (1+\sin x) d x=k \pi \log \frac{1}{2} \)
then find the value of \( k \)


A body is released from the top of a smooth inclined plane at height h above the ground. Simultaneously another body is pushed up with a velocity u from the bottom. If they meet after time \( t, \) an inclination of that inclined plane to the horizontal is
A \( \cdot \sin ^{-1}\left(\frac{t}{h u}\right) \)
B. \( \cos ^{-1}\left(\frac{t}{h u}\right) \)
c. \( \sin ^{-1}\left(\frac{h}{u t}\right) \)
D. \( \cos ^{-1}\left(\frac{h u}{t}\right) \)


Calculate the area of the adjoining
figure shown


Set of molecules which are
isoelectronic is :
a) \( N_{2} \) and \( C O \)
b) \( C O_{2} \) and laughing gas \( \left(N_{2} O\right) \)
c) \( \mathrm{CaO} \) and \( \mathrm{MgS} \)
d) Benzene and Borazole \( \left(B_{3} N_{3} H_{6}\right) \)
\( A \cdot a, b, d \)
B. b, c, d
c. \( c, d \)
D. \( a, b, c, d \)


Collect information about
electroplating. Make a list of articles in day-to-day life, where this technique is used.


If \( a \neq R \) and the equation \( -3(x- \)
\( [\boldsymbol{x}])^{2}+\mathbf{2}(\boldsymbol{x}-[\boldsymbol{x}])+\boldsymbol{a}^{2}=\mathbf{0}(\text { where }[\boldsymbol{x}] \)
denotes the greatest integer \( \leq x \) ) has
no integral solution, then all possible values of a lie in the interval:
A \( \cdot(-2,-1) \)
B . \( (-\infty,-2) \cup(2, \infty) \)
c. (-1,0)\( \cup(0,1) \)
D. (1,2)


A loop of magnetic moment \( \overrightarrow{\boldsymbol{M}} \) is placed in the orientation of unstable equilibrium position in uniform magnetic field \( \vec{B} \). The external work
done in rotating it through an angle \( \theta \) is
A. \( -M B(1-\cos \theta) \)
B. \( -M B(\cos \theta) \)
\( \mathbf{c} \cdot M B \cos \theta \)
D. \( M B(1-\cos \theta) \)


Which of the following is an insulator?
A. woodd
B. Iron
c. carbon
D. Silver


Find the oxidation state of sulphur in
\( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
\( A \cdot+6 \)
\( B \cdot+4 \)
\( c \cdot+2 \)
\( D \cdot+3 \)


Which of the following is a macronutrient?
A. Mn
в. Мв
\( c \cdot c u \)
D. zn


The maximum range of a rifle bullet on
the horizontal ground is \( 6 \mathrm{km} \). Find its
maximum range on an inclined of \( 30^{\circ} \)
A. 5
B. 6
\( c \cdot 4 \)
D.


What is swarming?


The value of \( x=\sqrt{2}+\sqrt{2+\sqrt{2+\ldots}} \) is


Raffinose on hydrolysis forms
A. Glucose
B. Fructose
c. Galactose
D. All of these


Consider the two gaseous equilibrium involving \( S O_{2} \) and the corresponding
equilibrium constant at \( \mathbf{2} 99 K S O_{2}(g)+^{1 / 2} O_{2}(g) \rightleftharpoons S O_{3}(g) ; K_{1} \)
\( \mathbf{4} \boldsymbol{S} \boldsymbol{O}_{3}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{4} \boldsymbol{S} \boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{2} \boldsymbol{O}_{2}(\boldsymbol{g}) ; \boldsymbol{K}_{2} \)
The value of the equilibrium constant are related by :
A \( \cdot K_{2}=\frac{1}{\left(K_{1}\right)^{4}} \)
B \( . K_{2}=K_{1}^{4} \)
\( \mathrm{C} \cdot_{\mathrm{K}_{2}}=\left(\frac{1}{K_{1}}\right)^{1 / 4} \)
D. \( K_{2}=\frac{1}{K_{1}} \)


In a bolt factory, three machines \( A, B \)
and \( C \) manufacture \( 25 \%, 35 \% \) and \( 40 \% \)
of the total production respectively. Of
their respective outputs, \( 5 \%, 4 \% \) and \( 2 \% \) are defective. A bolt is drawn at random
from the total production and it is found to be defective. Find the probability that
it was manufactured by machine \( C \)


Compare thermal stability of \( L i_{2} C O_{3} \)
and \( B e C O_{3}: \)
A. \( L i_{2} C O_{3}>B e C O_{3} \)
в. \( L i_{2} C O_{3}<B e C O_{3} \)
c. \( L i_{2} C O_{3}=B e C O_{3} \)
D. None of these


Closed circulatory system is found in
A. Fishes
B. Amphibians
c. Birds
D. All of the above


The compound (A) is:
(D) \( \quad(\mathrm{C})+\mathrm{CO}_{2} \)
\( \left(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}\right) \)
\( A \)
B.
\( c \)
D.


Evaluate:
\( (a+b)(a-b)\left(a^{2}+b^{2}\right) \) is \( a^{4}-b^{4} \)
If true then enter 1 and if false then
enter 0


Give the structural differences between
saturated and unsaturated
hydrocarbons with two examples each.


Which of the following are true for
hydrophilic solution?
This question has multiple correct options
A. They do not require electrolytes for stability
B. Their coagulation is irreversible
C. Their surface tension is usually lower than water
D. Their viscosity is of the order of water


\( C_{6} H_{4} C l_{2}+C l_{2} \frac{F e}{(x)} C_{6} H_{5} C l_{3} \) Only one
structural isomer of \( Y \) is formed. Hence
\( (X) \) is:
(doclorobenzeme ) (Trichlorobenzeme)
A . o-isomer
B. p-isomer
c. m-isomer
D. any of this


Which of the following is not the advantage of Carbon resistors?
A. It is small in size and is light in weight.
B. It has low-temperature coefficient value.
c. using it high-value resistor can easily be made.
D. It has high power rating with a low tolerance value.


In a YDSE with identical slits, the
intensity of the central bright fringe is
\( I_{0} . \) If one of the slits is covered, the intensity at the same point is
A \( \cdot 2 I_{0} \)
в. \( I_{0} \)
\( c \cdot I_{0} / 2 \)
D. \( I_{0} / 4 \)


A quantity of 10 g of a gas at 1 atm pressure is cooled from \( 273^{\circ} \mathrm{C} \) to \( 273 \mathrm{K} \)
keeping its volume constant, the final
pressure of the gas will be?
A. 273 atm
B. 0.5 atm
c. 0.2 atm
D. 0.1 atm


Assertion: Reactions happen faster at higher temperatures.
Reason: As temperatures increase, there is also an increase in the number
of collisions with the required
activation energy for a reaction to occur
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false


Define Mole fraction


Which of the following statement is
correct?
A \( \cdot D_{2} O, \) is more viscous than \( H_{2} O \)
B. \( D_{2} O, \) is less viscous than \( H_{2} O \)
\( \mathrm{C} \cdot D_{2} \mathrm{O}, \) is as viscous as \( \mathrm{H}_{2} \mathrm{O} \)
D. Viscosity of heavy water depends on temperature


What are the total number of orbitals
and electrons for \( m=0, \) if there are 30 protons in an atom?
A. 6 orbitals, 12 electrons
B. 5 orbitals, 10 electrons
c. 7 orbitals, 14 electrons
D. 4 orbitals, 8 electrons


The resultant of \( \vec{A} \times \overrightarrow{0} \) will be equal to:
A . zero
в. \( A \)
c. zero vector
D. unit vector


A \( 50 ~ k g \) man is runing at a speed of
\( 18 k m h^{-1} . \) If all the kinetic energy of the
man can be used to increase the
temerature of water from \( 20^{0} C \) to \( 30^{0} C \)
how much after can be heated with this
energy?


By passing a certain amount of charge through NaCl solution, 9.2 litre of \( C l_{2} \)
were liberated at STP when the same
charge is passed through a nitrate solution of metal \( \mathrm{M}, 7.467 \mathrm{g} \) of the metal was deposited. If the specific heat of metal is 0.216 cal/g, the formula of metal nitrate will be:
\( \mathbf{A} \cdot M\left(N O_{3}\right)_{3} \)
B . \( M\left(N O_{3}\right) \)
\( \mathbf{c} \cdot M\left(N O_{3}\right)_{2} \)
D. None of these


Which of the following sets has different dimensions?
A. Pressure, Young's modulus, stress
B. Emf, potential difference, electric potential
c. Heat, work done, energy
D. Dipole moment, electric flux, electric field


Out of
\( \boldsymbol{C H}_{2} \boldsymbol{C l}_{2}, \boldsymbol{C H}_{4}, \boldsymbol{C C l}_{4}, \boldsymbol{H}_{2} \boldsymbol{O}, \boldsymbol{C H C l}_{3}, \boldsymbol{d}- \)
dichlorobenzene, \( o \) -cresol, \( p \) -xylene,
\( S C l_{2}, B F_{3}, I B r \) and \( C H_{2} O, \) non zero
value of dipole moment are:


Three bodies \( A, B \) and \( C \) are in thermal
equilibrium.

The temperature of \( B \) is \( 45^{\circ} C . \) Then the
temperature of \( ^{\prime} C^{\prime} \) is
\( \mathbf{A} \cdot 45^{\circ} C \)
B \( .50^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 40^{\circ} C \)
D. Any temperature


The formula of exhausted permutit
is
A. \( C a A l_{2}, S i_{2} O_{8} . x H_{2} O \)
B. \( N a A l_{2}, S i_{2} O_{8} . x H_{2} O \)
\( \mathrm{c} \cdot \mathrm{CaB}_{2} \mathrm{Si}_{2} \mathrm{O}_{8} \cdot x \mathrm{H}_{2} \mathrm{O} \)
D. \( K_{2} A l_{2}, S i_{2} O_{8} . . x H_{2} O \)


The collection of tickets for the three
different show (1 \( s t \) shows, \( 2 n d \) show, \( 3 r d \) show) of circus on a particular day are in the ratio 2: 4: 5 if the \( 2 n d \) show
collection is \( R s .15,000 \) find the total
collection and collection of the
remaining two shows:


High frequency sound waves vibrate basilar membrane
A. Near helicotrema
B. In middle of cochlea
C. From oval window to helicotrema
D. Near oval window


Prove that:
\( \left|\begin{array}{ccc}\mathbf{0} & \boldsymbol{a} & -\boldsymbol{b} \\ -\boldsymbol{a} & \boldsymbol{0} & -\boldsymbol{c} \\ \boldsymbol{b} & \boldsymbol{c} & \boldsymbol{0}\end{array}\right|=\mathbf{0} \)


A man \( 1.5 ~ m \) tall walks away from a
lamp post \( 4.5 ~ m \) high at a rate of
\( 4 k m / h r( \) i) How fast is his shadow lengthening?(ii)How fast is the farther end of shadow moving on the
pavement??


A modified discharge tube is used as a
A. cathode ray oscilloscope
B. fluorescent tube
c. x-ray tube
D. all the above


For three non-zero vectors \( \vec{a}, \vec{b}, \vec{c} \) the elation \( |(\vec{a} \times \vec{b}) \cdot \vec{c}|=|\vec{a}||\vec{b}||\vec{c}| \) will hold
true if and only if:
\( \mathbf{A} \cdot \vec{a} \cdot \vec{b}=0, \vec{b} \cdot \vec{c}=0 \)
В . \( \vec{c} . \vec{a}=0, \vec{a} . \vec{b}=0 \)
C \( . \vec{a} . \vec{c}=0, \vec{b} . \vec{c}=0 \)
D. \( \vec{a} . \vec{b}=\vec{b} . \vec{c}=\vec{c} . \vec{a}=0 \)


Law of conservation of energy
states that :
A. energy cannot be destroyed but can be created and transformed from one form to another
B. enerry exists in only one form
C. energy exists in many forms but it cannot be transformed
D. energy can neither be created nor be destroyed but can be transformed from one form to another


If \( A \) is a \( 3 \times 3 \) matrix such that \( |A| \neq 0 \) and \( |3 A|=k|A|, \) then write the value of
\( \boldsymbol{k} \)


Two parallel wires on of length 1 m and
other is infinitive, are lying at a
distance of \( 2 m . \) If the current flowing in
each wire is 1 ampere then the force between them will be-
A \( \cdot 2 \times 10^{-7} N \)
В. \( 10^{-7} N \)
c. \( 0.5 N \)
D. \( 10^{7} N \)


Find the area of a square park whose
perimeter is \( 320 \mathrm{m} \)


A police jeep is chasing with velocity of \( 45 k m / h \) a thief in another jeep moving with velocity \( 153 k m / h . \) Police fires a
bullet with muzzle velocity of \( 180 m / s \) The velocity it will strike the car of the
thief is?
A. \( 150 \mathrm{m} / \mathrm{s} \)
в. \( 27 \mathrm{m} / \mathrm{s} \)
c. \( 450 m / s \)
D. \( 250 \mathrm{m} / \mathrm{s} \)


The flow of blood in a large artery of an anesthetised dog is diverted through a venturi meter. The wider part of the
meter has a cross-sectional area equal
to that of the artery \( A=8 m m^{2} \). The
narrower part has an area \( a=4 m m^{2} \)
The pressure drop in the artery is 24 Pa. What is the speed of blood in the artery?
Density of blood is \( 1.06 \times 10^{3} k g / m^{3} \)
A . \( 13.5 \times 10^{-2} \mathrm{ms}^{-1} \)
B . \( 12.5 \times 10^{-2} \mathrm{ms}^{-1} \)
C \( .26 .5 \times 10^{-3} \mathrm{ms}^{-1} \)
D . \( 32.5 \times 10^{-} \mathrm{ms}^{-1} \)


A boy weighing 25 kg \( f \) climbs up from
the first floor at a height \( 3 m \) above the
ground to the third floor at a height \( 9 m \) above the ground. What will be the increase in his gravitational potential energy? (Take \( \boldsymbol{g}=\mathbf{1 0} \boldsymbol{N} \boldsymbol{k} \boldsymbol{g}^{-1} \mathbf{)} \)
\( \mathbf{A} \cdot 1500 J \)
в. \( 0 . J \)
\( c .150 J \)
D. 2250J


The value of which of the following
determinants can be non-zero?
\( \mathbf{A} \cdot\left|\begin{array}{lll}a_{1}+a_{2} & a_{2} & a_{1} \\ a_{4}+a_{5} & a_{5} & a_{4} \\ a_{7}+a_{8} & a_{8} & a_{7}\end{array}\right| \)
\( \mathbf{B} \cdot\left|\begin{array}{lll}a_{1}+2 a_{2} & a_{2} & a_{3} \\ a_{4}+2 a_{5} & a_{5} & a_{6} \\ a_{7}+2 a_{8} & a_{8} & a_{9}\end{array}\right| \)
\( \mathbf{C} \cdot\left|\begin{array}{lll}k a_{4} & k a_{5} & k a_{6} \\ a_{4} & a_{5} & a_{6} \\ a_{7} & a_{8} & a_{9}\end{array}\right| \)
D. None of these


The area of parallelogram with
diagonals \( 6 \mathrm{cm}, 10 \mathrm{cm} \) is


The last element of lanthanide series is
A. lawrencium
B. lutetium
c. cerium
D. thorium


Prove that \( ^{n-1} C_{r}+^{n-1} C_{r-1}=^{n} C_{r} \)


Compare metallic character of
following:
\( \boldsymbol{S} \boldsymbol{e}, \boldsymbol{A} \boldsymbol{s} \)


The equilibrium constant \( \boldsymbol{K}_{\boldsymbol{p}}(\text { in atm }) \) for the reaction is 9 at 7 atm and \( 300 \mathrm{K} \)
\( \boldsymbol{A}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{B}_{2}(\boldsymbol{g})+\boldsymbol{C}_{2}(\boldsymbol{g}) \cdot \) Calculate the
average molar mass (in gm/mol)of an equilibrium mixture. Given: Molar mass
of \( A_{2}, B_{2} \) and \( C_{2} \) are \( 70,49 \& 21 \mathrm{gm} / \mathrm{mol} \)
respectively.
\( \mathbf{A} \cdot 50 \)
B . 45
c. 40
D. 37.5


White light is normally incidents on a soap film. The thickness of the film is \( 0.5 \mu m \) and its refractive index is 1.33 Which wave length will be reflected maximum in the visible region?
A \( .26600 A^{\circ} \)
B . \( 8860 A^{\circ} \)
\( \mathrm{c} .5320 A^{\circ} \)
D. \( 3800 A^{\circ} \)


In a sphere, that is fully submerged in a İiquid,
A. Force is applied along one of the diameter to determine the volume stress
B. Force is applied along two perpendicular diameters to determine the volume stress
C. Force is applied along the entire surface to determine the volume stress
D. Force is applied along the hemispherical surface to determine the volume stress


In the expansion of \( \left(x^{2}-\frac{1}{4}\right)^{n}, \) the coefficient of third term is \( 31, \) then the
value of \( n \) is-
A . 30
B. 31
c. 29
D. 32


If the position vectors of the points \( \boldsymbol{A}(\mathbf{3}, \mathbf{4}), \boldsymbol{B}(\mathbf{5},-\mathbf{6}) \) and \( \boldsymbol{C}(\mathbf{4},-\mathbf{1}) \) are
\( \vec{a}, \vec{b}, \vec{c} \) respectively, compute \( \vec{a}+2 \vec{b}- \)
\( \mathbf{3} \overrightarrow{\boldsymbol{c}} \)
B. \( \hat{i}-5 \hat{j} \)
c. \( \hat{i}+5 \hat{j} \)
D. none of these


Which of the following statement is
correct?
A. Carbon form oxides which are in nature
B. Metal can form only acidic oxides
c. Sodium metal is stored under kerosene
D. White phosphorus is kept under kerosene to avoid oxidation


What is the magnitude of angular
velocity of the stick plus puck after the collision?
A \( \cdot \frac{6 v_{i}}{5 l} \)
в. \( \frac{5 v_{i}}{6 l} \)
c. \( \frac{v_{i}}{l} \)
D. \( \frac{v_{i}}{\sqrt{2} i} \)


In which of the following molecule dipole dipole interaction is absent:
A . HCl
B. water
c. carbon dioxide
D. нF


Explain the term 'sharpness of resonance' in ac circuit.


In Whittaker's five kingdom system of classification, eukaryotes are distributed among
A. two kingdoms
B. three kingdoms
c. four kingdoms
D. all the five kingdoms


\( C O_{2} \) is:
A . pyramidal
B. trigonal planar
C. linear
D. tetrahedral


Without actually performing the long division, state whether the following rational numbers will have a
terminating decimal expansion or a non-terminating repeating decimal expansion:
(i) \( \frac{\mathbf{1 3}}{\mathbf{3 1 2 5}} \)
(ii) \( \frac{17}{8} \)
(iii) \( \frac{\mathbf{6 4}}{\mathbf{4 5 5}} \) (iv) \( \frac{\mathbf{1 5}}{\mathbf{1 6 0 0}}(\mathbf{v}) \)
\( \frac{\mathbf{2 9}}{\mathbf{3 4 3}} \)
(vi) \( \frac{\mathbf{2 3}}{\mathbf{2}^{3} \mathbf{5}^{2}} \)
(vii) \( \frac{\mathbf{1 2 9}}{\mathbf{2 ^ { 2 }} \mathbf{5}^{7} \mathbf{7}^{\mathbf{5}}} \)
(viii) \( \frac{\mathbf{6}}{\mathbf{1 5}}(\text { ix }) \frac{\mathbf{3 5}}{\mathbf{5 0}} \)
(x) \( \frac{77}{210} \)


Assertion
Phenolphthalein is used as indicator
during the titration of oxalic acid against sodium hydroxide.
Reason
The pH range of phenolphthalein is from
\( 8 \operatorname{tog} .6 \)
Choose the correct option.
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


If a ball is thrown upwards from the
Surface of earth:
A. The earth remains stationary while the ball moves upwards
B. The ball remains stationary while the earth moves downwards
C. The ball and earth both move towards each other
D. The ball and earth both move away from each other


Find \( p \) for which given equation has
unique solution
\( 4 x+p y+8=0 \)
\( 2 x+2 y+2=0 \)


The first 3 terms in the expansion of \( (1+a x)^{n}(n \neq 0) \) are \( 1,6 x \) and \( 16 x^{2} \)
Then the value of \( a \) and \( n \) are
respectively
A . 2 and 9
B. 3 and 2
c. \( 2 / 3 \) and 9
D. \( 3 / 2 \) and 6


Common to kidney and skeleton in mammals is
A. cortex
B. Medulla
c. Radius
D. Pelvis


Two different dice are tossed together
Find the probability:
(i) of getting a doublet
(ii) of getting a sum 10 , of the number on the two dice.


The part of the electromagnetic spectrum which is suitable for radar systems used in aircraft navigation:
A. X-Rays
B. Gamma Rays
c. Microwaves or short radiowaves
D. Ultraviolet


Complete the electronic configuration
of a chloride ion.
\( \mathbf{1} s^{2} \)


Arrange the following compounds in decreasing order of reactivity towards nucleophilic addition reaction. \( \begin{array}{cc}o & o \\ \boldsymbol{C H}_{3}-\stackrel{\|}{\boldsymbol{C}}-\boldsymbol{C H}_{3} & \boldsymbol{C H}_{3}-\underset{I I}{C}-\boldsymbol{C l}\end{array} \)
\( \boldsymbol{C H}_{3}-\underset{\boldsymbol{I} I I}{\boldsymbol{C}}-\boldsymbol{N} \boldsymbol{H}_{2} \quad \boldsymbol{C H}_{3}-\underset{\boldsymbol{I} \boldsymbol{V}}{\boldsymbol{C}}-\boldsymbol{O} \boldsymbol{H} \)
\( \boldsymbol{C H}_{3}-\stackrel{\|}{\boldsymbol{C}}-\underset{\boldsymbol{V}}{\boldsymbol{O}}-\stackrel{\|}{\boldsymbol{C}}-\boldsymbol{C H}_{3} \)
A \( . I I>V>I>I V>I I I \)
В. \( I I I>I V>I>V>I I \)
c. \( I I>I>V>I I I>I V \)
D. \( I V>I I I>V>I>I I \)


How much momentum will a dumb-bel
of mass \( 10 \mathrm{kg} \) transfer to the floor if it falls from a height of \( 80 \mathrm{cm} \) ? Take its
downward acceleration to be \( 10 \mathrm{m} \mathrm{s}^{-2} \)


Given that the vectors \( \bar{a} \) and \( \bar{b} \) are non-
collinear, the value of \( x \) and \( y \) for which
the vector quantity \( 2 \bar{u}-\bar{v}=\bar{w} \) holds true if \( \bar{u}=x \bar{a}+2 y \bar{b}, \bar{v}=-2 y \bar{a}+ \)
\( \mathbf{3} \boldsymbol{x} \overline{\boldsymbol{b}}, \overline{\boldsymbol{w}}=\mathbf{4} \overline{\boldsymbol{a}}-\mathbf{2} \overline{\boldsymbol{b}} \) are
A \( \cdot x=\frac{4}{7}, y=\frac{6}{7} \)
в. \( x=\frac{10}{7}, y=\frac{4}{7} \)
c. \( x=\frac{8}{7}, y=\frac{2}{7} \)
D. \( x=2, y=3 \)


A solid cylinder of mass 2 Kg and radius
\( 0.2 \mathrm{m} \) is rotating about its own
axis without friction with angular
velocity 3 rad/s. A particle of mass 0.5
Kg and moving with a velocity of \( 5 \mathrm{m} / \mathrm{s} \) strikes the cylinder and sticks to it as
shown in. The angular momentum of the
cylinder before collision will be
A. 0.12 Joule/s
B. 12 Joule/s
c. 1.2 Joule/s
D. 1.12 Joule/s


Using information given in the adjacent
figure, find the values of \( x \) and \( y \)


Calculate the coefficient of variation of
the following data: 20,18,32,24,26
A . 20.41
в. 2041
c. 204.1
D. None of these


The arithmetic mean of the nine
numbers in the given set
\( \{9,99,999, \dots \dots . .999999999\} \) is a 9
digit number \( N, \) all whose digits are distinct, The number \( N \) does not
contain the digit
\( \mathbf{A} \cdot \mathbf{0} \)
B. 2
c. 5
D.


A body of mass \( m \) moving with a
velocity \( v \) strikes a stationary body of
mass \( m \) and sticks to it. What is the
speed of the system
A \( .2 v \)
B.
c. \( \frac{v}{2} \)
D. \( \frac{v}{3} \)


How does the force of gravitation between two objects change when the distance between them is reduced to
half?
\( \mathbf{A} \cdot F^{\prime}=4 F \)
В . \( F^{\prime}=8 F \)
\( \mathbf{c} \cdot F^{\prime}=2 F \)
D. \( F^{\prime}=F \)


A free charge is placed at a point at
which there is no charge, then
A. The charge must be in stable equilibrium
B. The charge may be in stable equilibrium
C. The charge must not be in stable equilibrium
D. The potential energy of the charge is minimum


For a number of years, it was not clear whether mercury (I) ion existed in solution as \( H g^{\oplus} \) or as \( H g_{2}^{2+} . \) To distinguish between these two possibilities, the following set up was
made:

Hg(I) I Solution A II Solution B I Hg(I) where solution A contained 0.263 g mercury
(I) nitrate per liter and solution B contained 2.63 g mercury
(I) nitrate per litre. If the measured EMF of such a
cell is \( 0.0289 \mathrm{V} \) at \( 18^{\circ} \mathrm{C} \), then mercury
(I) ions exist in the form of \( \boldsymbol{H} \boldsymbol{g}_{2}^{2+} \)
f true enter 1 , else enter 0


Which acid helps in the digestion of food without harming the stomach?
A. \( H_{2} S O_{4} \)
в. НС l
c. \( C H_{3} \) СООН
D. \( H_{3} P O_{4} \)


Insert three rational numbers between
\( \frac{2}{3} \) and \( \frac{3}{5} \)


Aryl halides are less reactive in nucleophilic substitution reactions.
(i) Write any two reasons for less reactivity.
(ii) Give one example for nucleophilic substitution reactions of aryl halides.


Glucose and fructose are both
monosaccharides.
A. True
B. False


Which one of the following relations is
true?
\( A \cdot \cos ^{2} \Theta-\sin ^{2} \Theta=1 \)
B. \( \operatorname{cosec}^{2} \Theta-\sec ^{2} \Theta=1 \)
\( \mathbf{c} \cdot \cot ^{2} \Theta-\tan ^{2} \Theta=1 \)
\( \mathrm{D} \cdot \sec ^{2} \Theta-\tan ^{2} \Theta=1 \)


Atomic number (Z) of a neutral atom and mass number (A) of an atom are
equal to:
(Here \( n= \) number of neutrons and \( p= \)
number of protons)
\( A \cdot Z=n \) and \( A=n+p \)
B. \( z=e \) and \( A=n+e \)
c. \( z=p \) and \( A=n+p \)
D. \( z=n \) and \( A=p+e \)


(a) Tabulate the differences in the
characteristics of states of matter.
(b) Comment upon the following:
Rigidity, compressibility, fluidity, filling a gas container, shape, kinetic energy and density


Explain the mechanism of alkaline hydrolysis of t-butyl bromide with energy profile diagram.


Maximum value of frictional force is
called:
A. limiting frictional force
B. static frictional force
c. kinetic friction force
D. rolling friction force


If the equations \( k x+4 y+1=0, x+ \)
\( k y+1=0 \) and \( 2 x-3 y+1=0 \) are
consistent, then show that the value of
\( k \) is not a real number.


A ball of mass \( 4 \mathrm{kg} \) moving on a smooth horizontal surface makes an elastic collision with another ball of mass \( \mathrm{m} \) at
rest in the line of motion of first ball, if
after collision first ball moves in the
same direction with one fourth of its
velocity before collision, then mass of
second ball is :
\( A \cdot 4 \mathrm{kg} \)
B. 4.4 kgg \( g g \)
c. \( 2.4 \mathrm{kg} \)
D. \( 2 \mathrm{kg} \)


Let \( A B C \) be a triangle, the position vectors of whose vertices are \( 7 \widehat{j}+ \) \( \mathbf{1 0} \widehat{\boldsymbol{k}},-\hat{\mathbf{i}}+\mathbf{6} \hat{\boldsymbol{j}}+\mathbf{6} \widehat{\boldsymbol{k}} \) and \( -\mathbf{4} \hat{\boldsymbol{i}}+\mathbf{9} \hat{\boldsymbol{j}}+\boldsymbol{6} \widehat{\boldsymbol{k}} \)
Then \( \Delta A B C \) is
This question has multiple correct options
A. isosceles
B. equilateral
c. right angled
D. none of these


Which of the following numbers lies between \( 2 \frac{1}{7} \) and \( 3 \frac{1}{7} ? \)
A \( \frac{37}{7} \)
B. \( \frac{14}{7} \)
\( c \cdot \frac{37}{14} \)
D. 2


Pulmonary veins are those which
A. Carry impure blood from lungs to heart
B. Carrying pure blood from lungs to heart
C. Carry impure blood from heart to lungs
D. Carry pure blood from heart to lungs


If an object is placed symmetrically between two plane mirrors, inclined at
an angle of \( 72^{0}, \) then the total number of
images formed is:
A. 5
B. 4
\( c \cdot 2 \)
D. Infinite


Green chemistry means such reactions
which:
A. produce colour during reactions
B. reduce the use and production of hazardous chemicals
C. are related to the depletion of ozone layer
D. study the reactions in plants


The process of losing water by plants is called:
A. evaporation
B. transpiration
c. condensation
D. translocation


Which of the following quantities do not change when an ohmic resistor connected to a battery is heated due to
the current?
A. drift speedd
B. resistivity
c. resistance
D. number of free electrons


Find the equation of the plane that contains the point (1,-1,2) and is
perpendicular to both the planes \( 2 x+3 y- \) \( 2 z=5 \) and \( x+2 y-3 z=8 \)


In these colloids, a large number of
small atoms or smaller molecules of a
substance aggregate to form colloidal particles having size in colloidal range. These colloids are known as:
A. multimolecular colloids
B. macromolecular colloids
c. associated colloids
D. Iyophilic colloids


Which of the following isoelectronic ions have lowest ionisation energy?
A . \( K^{+} \)
в. \( C a^{2} \)
c. \( C l^{-} \)
\( D \cdot S^{2} \)


State whether True or False:
Motion in 3-Dimension can't be
represented with the help of vectors.
A. True
B. False


The bond between hydrogen and fluorine
in a molecule of hydrogen fluoride. \( \boldsymbol{H} \boldsymbol{F} \)
is sometimes considered an ionic bond
and other times is considered a
covalent bond.
What is the reason for this confusion?
A. The electronegativity difference between the two atoms is not high enough to be considered an ionic bond even though \( H \) is a metal.
B. The hydrogen atoms is sometimes considered a metal and in other considered a non-metal.
C. The electronegativity difference between the two atoms is high enough to be considered an ionic bond even though \( H \) is a non-metal.
D. The fluorine atoms are sometimes considered a metal and in other times considered a non-metal.


Figure shows a network of three
resistances.When some potential
difference is applied across the network, thermal powers dissipated by
A, \( B, \) and \( C \) are in the ratio
\( A \cdot 2: 3: 4 \)
B. 2: 4: 3
\( c \cdot 4: 2: 3 \)
D. 3: 2: 4


The unit of equilibrium constant for the following reaction is:
\( \mathbf{2} N \boldsymbol{O}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{N}_{2} \boldsymbol{O}_{4}(\boldsymbol{g}) \)
A \( . \) mol \( L^{-1} \)
B. \( L \) mol \( ^{-1} \)
c. \( m o l^{-1} L^{-1} \)
D. Equilibrium constant is unitless


The binding energies of the atoms of
elements \( \boldsymbol{P} \) and \( \boldsymbol{Q} \) are \( \boldsymbol{E}_{\boldsymbol{p}} \) and \( \boldsymbol{E}_{Q} \)
respectively. Three atoms of element \( \boldsymbol{Q} \)
fuse to form one atom of element \( P . \) In
this process, the energy released is \( e \)
The correct relation between \( \boldsymbol{E}_{\boldsymbol{P}}, \boldsymbol{E}_{\boldsymbol{Q}} \)
and \( e \) will be
\( \mathbf{A} \cdot E_{Q}=3 E_{P}+e \)
B . \( E_{Q}=3 E_{P}-e \)
\( \mathbf{c} \cdot E_{P}=3 E_{Q}+e \)
D. \( E_{P}=3 E_{Q}-e \)


For \( M K_{3} A \) (potassium salt of a
tribasic acid \( \boldsymbol{H}_{3} \boldsymbol{A} \) ) solution:
(Dissociation constants of acid are
\( \left.k_{a_{1}} k_{a_{2}} \& k_{a_{3}} ; h<<1\right) \)
A \( \cdot p H=\frac{1}{2}\left(p K_{w}+p K_{a_{3}}-\log c\right) \)
B・ \( p H=\frac{1}{2}\left(p K_{w}+p K_{a_{2}}+\log c\right) \)
C・ \( p H=\frac{1}{2}\left(p K_{w}+p K_{a_{1}}+\log c\right) \)
D \( \cdot p H=\frac{1}{2}\left(p K_{w}-p K_{a_{3}}-\log c\right) \)


Prove that each angle of an equilateral
triangle is \( 60^{\circ} \)


If the sum of squares of the zeroes of the polynomials \( 6 x^{2}+x+k \) is \( \frac{25}{36} \) find
the value of k?


toppr
Q Type your question
inkage.
\( \mathbf{A} \)
\( B \)
\( \mathbf{C} \)
\( D \)
\( E \)


Which one of the following is correct?
A. Left atrium and left ventricle - oxygenated blood, right atrium and right ventricle - deoxygenated blood
B. Left atrium and left ventricle - deoxygenated blood, right atrium and right ventricle - oxygenated blood
C. Both A and B
D. None of the above


Which of the molecules is trigonal bipyramidal?
A. \( B F_{3} \)
в. \( C H_{4} \)
c. \( P C l_{5} \)
D. \( S F_{6} \)


Fairly concentrated solution of \( A g N O_{3} \)
weighing \( 108 g \) is electrolyzed using \( 0.1 F \) of electricity. The weight of resulting solution is:
A .949
в. \( 11.6 g \)
c. \( 97.2 g \)
D. None of these


In the figure below, the plane drawn behind the peptide bond indicates the:
A. absence of rotation around \( C-N \) bond because of its
partial-double bond character
B. plane of rotation around the \( C-N \) bond
c. region of steric hindrance determined by the large \( C=O \) group
D. none of the above


If \( \frac{\mathbf{3} \boldsymbol{x}^{2}+\mathbf{1 0 x}+\mathbf{1 3}}{(\boldsymbol{x}-\mathbf{1})^{4}}=\frac{\boldsymbol{A}}{(\boldsymbol{x}-\mathbf{1})^{2}}+ \)
\( \frac{B}{(x-1)^{3}}+\frac{C}{(x-1)^{4}} \) then descending
order of \( \boldsymbol{A}, \boldsymbol{B}, \boldsymbol{C} \)
A. \( A, B, C \)
в. \( C, B, A \)
c. \( A, C, B \)
D. \( C, A, B \)


the blanks by choosing an appropriate
option.

In the given cell, hydrogen and oxygen
are bubbled through porous \( (i) \) electrodes into concentrated aqueous
\( (i i) \) solution. Catalysts like finely
divided \( (i i i) \) or \( (i v) \) metal are
incorporated into the electrodes for increasing the rate of electrode
reactions.
A. (i)- Hydrogen, (ii)-Potassium hydroxide, (iii)palladium, (iv)-platinum
B. (i)- Oxygen
(ii)- Hydrogen chloride
(iii)- Manganese, (iv)- Iron
c. (i)- Carbon
(ii)- sodium hydroxide
(iii)- Platinum, (iv) palladium
D. (i)- Graphite,
(ii)- Sodium Chloride
(iii)- Nickel, (iv)Platinum


ff \( \boldsymbol{A}=\left(\begin{array}{cc}\mathbf{3} & \mathbf{1} \\ -\mathbf{9} & -\mathbf{3}\end{array}\right) \) then
\( \left(1+2 A+3 A^{2}+\ldots . \infty\right)^{-1} \) equals
\( ^{A} \cdot\left(\begin{array}{cc}-5 & -2 \\ 18 & 7\end{array}\right) \)
B. \( \left(\begin{array}{rr}-5 & 18 \\ -2 & 7\end{array}\right) \)
c. \( \left(\begin{array}{cc}7 & -2 \\ 18 & -5\end{array}\right) \)
D. None of these


The human sperm consist of head,
middle piece and tail. What purpose does the tail in a sperm serve?


Write the principle behind the froth floatation process. What is the role of collectors in this process?


Using elementary transformations find
the inverse of
\( \left[\begin{array}{ccc}3 & 2 & 1 \\ 2 & 4 & 3 \\ 2 & -1 & 2\end{array}\right] \)


Write any four characteristic of an ideal
fuel.


Find the distance between the centre of
gravity and centre of mass of a twoparticle system attached to the ends of
light rod. Each particle has the same
mass. Length of the rod is \( R \), where \( R \) is the radius of the earth.
\( A \cdot R \)
в. \( \frac{R}{2} \)
\( c . \) zer
D. \( \frac{R}{4} \)


The figure shows a surface \( \boldsymbol{X} \boldsymbol{Y} \)
separating two transparent media, medium - 1 and medium - 2. The lines
\( a b \) and \( c d \) represent wavefronts of \( a \)
light wave travelling in medium - 1 and incident on \( X Y . \) The lines \( e f \) and \( g h \)
represents wavefronts of the light wave
in medium - 2 after refraction.
Light travels as a:
A. Parallel beam in each medium
B. Convergent beam in each medium
c. Divergent beam in each mediu
D. Divergent beam in one medium and convergent beam in the other medium


\( \left[N i C l_{4}\right]^{2-} \) is diamagnetic in nature
A. True
B. False


Which of the following is a Pythagorean triplet?
A. 3,4,5
в. 5,12,14
c. 6,8,11
D. 8,5,17


The remainder of
\( \frac{(5 m+1)(5 m+3)(5 m+4)}{5} \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 3 \)
\( D \)


A situation may be described by using different sets of co-ordinate axes
having different orientations. Which of the following do not depend on the orientation of the axes -
(a) The value of a scalar
(b) Component of a vector
(c) A vector
(d) The magnitude of a vector
A \( \cdot \) a, \( d \)
B. a, b, d
\( c \cdot a, b, c \)
D. a, c, d


The term photosynthesis was coined by
A. Fiescher
B. Priestley.
c. Blackman
D. Barnes


The plane of a dip circle is set in the geographical meridian and the apparent dip is \( \theta_{1} \). If it is set in a vertical plane perpendicular to the geographical meridian, then the
apparent dip becomes \( \theta_{2} \). The angle of declination \( \alpha \) at the given place is given by :
A. \( \tan \alpha=\sqrt{\left(\tan \theta_{1} \tan \theta_{2}\right)} \)
B. \( \tan \alpha=\frac{\tan \theta_{1}}{\tan \theta_{2}} \)
\( c \cdot \tan \alpha=\tan \theta_{1}+\tan \theta_{2} \)
D. \( \tan \alpha=\frac{\tan \theta_{2}}{\tan \theta_{1}} \)


3 equal cubes are placed adjacently in a row find the ratio of TSA of new cuboid
to that of the sum of surface area of 3
cubes.


Which of the following is a double salt?
A. Carnallite
B. Potassium ferrocyanide
c. Potasium ferricyanide
D. Nesslers reagent


Two vectors \( \vec{A} \) and \( \vec{B} \) inclined at an
angle \( \theta \) have a resultant \( \vec{R} \) which makes an angle \( \alpha \) with \( \vec{A} \) and angle \( \beta \) with \( \vec{B} \). Let the magnitudes of the vectors \( \vec{A}, \vec{B} \) and \( \vec{R} \) be represented by \( A \) B and R respectively. Which of the following relations is not correct?
A . Asin\alpha \( =B \sin \beta \)
B. \( R \sin \alpha=B \sin (\alpha+\beta) \)
c. \( R \sin \beta=\operatorname{Asin}(\alpha+\beta) \)
D. None of these


A new flag is to be designed with six vertical strips using some or all of the colour yellow, green, blue and red. Then,
the number of ways this can be done such that no two adjacent strips have
the same colour is?
A. \( 12 \times 81 \)
B . \( 16 \times 192 \)
c. \( 20 \times 125 \)
D. \( 24 \times 216 \)


Draw \( \angle A B C \) of measure \( 115^{\circ} \) and
bisect it.


The displacement s of an object is given as a function of time \( t \) by the following equation \( s=2 t+5 t^{2}+3 t^{3} . \) Calculate
the instantaneous velocity of the object
at \( t=1 s \)


A neutron of energy 1 Me \( V \) and mass
\( 1.6 \times 10^{-27} \) kg passes a proton at such
a distance that the angular momentum of the neutron relative to the proton approximately equals \( 10^{-33} \mathrm{J} \) s. The distance of closest approach neglecting the interaction between particles is
A. \( 0.44 n m \)
B. \( 0.44 m m \)
c. \( 0.44^{\circ} \)
D. \( 0.44 f m \)


\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{O} \boldsymbol{H} \frac{c o \boldsymbol{c} \boldsymbol{c} \boldsymbol{H}_{2} \boldsymbol{S O}_{4}}{170^{\circ} \boldsymbol{C}} \)
\( \boldsymbol{A} \quad \frac{\boldsymbol{C l}_{2}}{500^{\circ} \boldsymbol{C}} \boldsymbol{B} \)
\( A \) and \( B \) are:
A \( \cdot A: C H_{3} C H_{2} C H_{3}, \quad B: C H_{3} C H_{2} C H_{2} C l \)
B. \( A: C H_{3} C H=C H_{2}, \quad B: C H_{2} C l C H=C H_{2} \)
c. \( A: C H_{2}=C H_{2}, \quad B: C H_{3} C H_{2} C l \)
D. \( A: C H_{3} C H_{2} C H_{3}, \quad B: C H_{3} C H=C H_{2} \)


Find \( n, \) if \( ^{2 n} C_{3}:^{n} C_{2}=52: 3 \)


The concentration of the \( A g^{+} \) ion in a
saturated solution of \( A g_{2} C r O_{4} \) at \( 20^{\circ} C \)
is \( 1.5 \times 10^{-4} \) mol \( \quad L^{-1} . \) The solubility
product constant of \( A g_{2} C r O_{4} \) at \( \$ \$\{20 \) \( 3 \wedge\{0\} C \$ \) is:
A. \( 3.4 \times 10^{-12} \)
В. \( 1.7 \times 10^{-10} \)
c. \( 1.7 \times 10^{-8} \)
D. \( 1.7 \times 10^{-12} \)


On the basis of Huygen's Wave theory of light, show that angle of reflection is equal to angle of incidence. You must
draw a labelled diagram for this derivation.


No work is said to have been done when
an object moves at an angle of with the direction of the
force.
A. 0
B. 90
\( c \cdot 180 \)
D. Between 90 and 180


Name a chelate. Why is iron added in
hydroponics along with chelating agent
\( ? \)


If \( \boldsymbol{x}+\boldsymbol{y}=\frac{\boldsymbol{\pi}}{2}, \) then prove that \( \cos (\boldsymbol{x}+ \)
\( \boldsymbol{y})=\mathbf{0} \)


\( \boldsymbol{D}(\mathbf{2}, \mathbf{1}, \mathbf{0}), \boldsymbol{E}(\mathbf{2}, \mathbf{0}, \mathbf{0}), \boldsymbol{F}(\mathbf{0}, \mathbf{1}, \boldsymbol{0}) \) are mid
point of the sides \( B C, C A, A B \) of \( \Delta \)
\( A B C \) respectively, The the centroid of \( \Delta \)
\( A B C \) is
A \( \cdot\left(\frac{1}{3}, \frac{1}{3}, \frac{1}{3}\right) \)
B. \( \left(\frac{4}{3}, \frac{2}{3}, 0\right) \)
\( ^{c} \cdot\left(-\frac{1}{3}, \frac{1}{3}, \frac{1}{3}\right) \)
D. \( \left(\frac{2}{3}, \frac{1}{3}, \frac{1}{3}\right) \)


Identify the common property for a chemical reaction at dynamic equilibrium.
A. The measurable properties like concentration, density colour, pressure etc remain constant at constant temperature.
B. The forward and backward reactions take place with the same rate
c. It can be achieved from both directions
D. All the above


The value \( \csc \left(\cos ^{-1}(-12 / 13)\right) \) is?
\( \mathbf{A} \cdot+12 / 5 \)
в. \( -12 / 5 \)
\( \mathbf{c} \cdot+13 / 5 \)
D. \( -13 / 5 \)


\( \int_{0}^{\frac{\pi}{2}} \frac{\sin x-\cos x}{1+\sin x \cdot \cos x} d x \) is equal to
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( \frac{\pi}{4} \)
\( c \cdot \frac{\pi}{2} \)
D.


What is \( \boldsymbol{v}-\boldsymbol{t} \) graph? Derive \( \boldsymbol{x}=\boldsymbol{v}_{0} \boldsymbol{t}= \)
\( \frac{1}{2} a t^{2} \) using \( v-t \) graph.


An object is 1 metre in front of a curved surface of a plano-convex lens whose flat surface is silvered. A real image is
forme \( 120 c m \) in front of the lens. What
is the focal length of the lens?
A. \( 9.1 \mathrm{cm} \)
B. \( 90.1 \mathrm{cm} \)
c. \( 109.1 \mathrm{cm} \)
D. none of these


The earth's atmosphere is transparent for the visible light.
A. True
B. False


Which of the following is true?
This question has multiple correct options
A. A configuration with the maximum spin multiplicity has the minimum energy and thus is most stable
B. The energy of 3d orbital may be grater than or lesser than, equal to that 4 s orbital depending upon the atomic number of the atom
C. All p orbital have the same type of angular dependence irrespective of the value of principal quantum number
\( n \)
D. In a given electrical field, \( \beta \) -particles are deflected more than \( \alpha \) -particles in spite of \( \alpha \) -particles having larger charge


Electrons move at right angles to a magnetic field of \( 0.03 \mathrm{T} \) and enter with a velocity \( 9 \times 10^{7} m / s . \) The value of e \( / \mathrm{m} \)
will be: (Given radius of circular path =
\( 1.764 \mathrm{cm} \)
A \( \cdot 1.7 \times 10^{11} \mathrm{Ckg}^{-1} \)
В . \( 2 \times 10^{11} \mathrm{Ckg}^{-} \)
c. \( 2.5 \times 10^{11} \mathrm{Ckg}^{-1} \)
D. none of these


Very short answer type. Define zero population growth.


Integrate the function \( \frac{x \cos ^{-1} x}{\sqrt{1-x^{2}}} \)


An organism without true nucleus is
A. Bacterium
B. Archaebacterium
c. Cyanobacterium
D. All the above


A \( 200 k m \) long telegraph wire has a capacitance of \( 0.014 \mu F / k m . \) If it carries an ac of \( 5 k H z, \) what should be the inductance required to be connected in series, so that the impedance is minimum? Take \( \pi=\sqrt{10} \)


In a clockwise system:
\( \mathbf{A} \cdot \hat{j} \times \hat{k}=\hat{i} \)
\( \mathbf{B} \cdot \hat{i} \hat{i}=0 \)
\( \mathbf{c} \cdot \hat{j} \times \hat{j}=1 \)
D. \( \hat{k} . \hat{i}=1 \)


The number of water molecules
differing in molecular mass formed by hydrogen isotopes and \( ^{1} \boldsymbol{H},^{2} \boldsymbol{H},^{3} \boldsymbol{H} \) and
oxygen isotopes \( ^{16} \boldsymbol{O},^{17} \boldsymbol{O},^{18} \boldsymbol{O} \) is
\( A \cdot 6 \)
B. 9
c. 12
D. 18


Study the following graph carefully and
answer the question given

The total production of \( C \) type tyres in
1992 and 1993 together was what
percentage of production of B types
tyres in \( 1994 ? \)
A . 50
B. 100
c. 150
D. 200


The types of bonds present in
\( \mathrm{CuSO}_{4} .5 \mathrm{H}_{2} \mathrm{O} \) are only:
A. electrovalent and covalent
B. electrovalent and coordinate covalent
C. electrovalent, covalent and coordinate covalent
D. covalent and coordinate covalent


\( \int(g(x)+1) \sin x d x \) is equal to
A \( \frac{e^{x}}{2}(\sin x-\cos x)+c \)
B. \( \frac{e^{2 x}}{5}(2 \sin x-\cos x)+c \)
c. \( \frac{e^{x}}{5}(\sin 2 x-\cos 2 x)+c \)
D. none of these


If \( E_{p} \) and \( E_{s} \) are the input and output voltages of a transformer, then:
(where \( n_{p} \) is the number of turns in
primary and \( n_{s} \) is the number of turns in secondary
A \( \cdot \frac{E_{s}}{E_{p}}=\frac{n_{p}}{n_{s}} \)
B . \( E_{s} E_{p}=n_{s} n_{p} \)
c. \( E_{s} n_{p}=E_{p} n_{s} \)
D. None of these


\( H_{2} O_{2} \) can not be concentrated easily because:
A . it is very volatile
B. it is insoluble in water
c. it decomposes at its boiling point
D. its boiling point is very high


Find the domain of the following
functions:
\( \boldsymbol{f}(\boldsymbol{x})=\sqrt{\mathbf{3}-\mathbf{2}^{\boldsymbol{x}}-\mathbf{2}^{\mathbf{1 - x}}} \)
A . [0,1]
B . [0,4]
c. [0,2]
D. None of these


If \( z=a+i b \) then its conjugate is \( a-i b \)
If \( 1, \omega, \omega^{2} \) are cube roots of unity then
(i) \( 1+\omega+\omega^{2}=\mathbf{0} \) (ii) \( \omega^{3}=1 \) The
conjugate of \( \frac{\mathbf{6}-\mathbf{3} i}{\mathbf{7}+\mathbf{i}} \) is
A \( \cdot \frac{39-27 i}{50} \)
в. \( \frac{-39+27 i}{50} \)
c. \( \frac{39+27 i}{50} \)
D. \( \frac{-39-27 i}{50} \)


A thermometer graduated according to
a linear scale reads a value \( x_{0} \) when in
contact with boiling water, and \( \boldsymbol{x}_{\mathbf{0}} / \mathbf{3} \) when in contact with ice. What is the
temperature of an object in \( 0^{\circ} \mathrm{C} \), if this thermometer in the contact with the
object reads \( \boldsymbol{x}_{0} / 2 ? \)
A . 35
B . 25
c. 60
D. 40


The order of reactivity of alkyl halides is
as follows:
A. \( R C l<R B r<R I \)
в. \( R I<R B r>R C l \)
c. \( R B r>R I>R C l \)
D. \( R I>R C l>R B r \)


Chlorine is non-metal used for
bleaching cotton fabrics
A. True
B. False


Heartwood differs from sapwood in
A. Absence of vessels and parenchyma
B. Having dead and non-conducting elements
C. Being susceptible to pests and pathogens
D. Presence of rays and fibers


Which of the following sequences of
reactions must be carried out
respectively to get a secondary alcohol
for primary alcohol?
A. Oxidation reaction with \( R-M g-I \), hydrolysis \( / H^{+} \)
B. Oxidation reaction with \( R-M g-C l \), hydrolysis/ \( H^{+} \)
C . Hydrolysis/ \( H^{+}, \) oxidation reaction with \( R-M g-O \)
D. Oxidation


Which of the following statements best
describes the data in the given table?
\( \begin{array}{cc}\boldsymbol{x} & \boldsymbol{y} \\ \frac{1}{2} & 4 \\ 1 & 5 \\ 3 & 9 \\ 4 & 11\end{array} \)
A \( \cdot \) The value of \( y \) is \( 3 \frac{1}{2} \) more than the value of \( x \)
B. The value \( y \) is 3 more than twice the value \( x \).
C. The value of \( y \) is 3 times the value of \( x \) increased by 1
D. The value of \( y \) is 3 less than twice the value of \( x \).


A sphere of radius \( 3 \mathrm{cm} \) is dropped into a cylindrical vessel of radius \( 4 \mathrm{cm} \). If the sphere is submerged completely, then the height (in cm) to which the water
rises, is
A. \( 2.35 \mathrm{cm} \)
B . \( 2.30 \mathrm{cm} \)
c. \( 2.25 \mathrm{cm} \)
D. \( 2.15 \mathrm{cm} \)


Consider the following statements in respect of the function \( \boldsymbol{f}(\boldsymbol{x})=\sin \left(\frac{\mathbf{1}}{\boldsymbol{x}}\right) \)
for \( \boldsymbol{x} \neq \mathbf{0} \) and \( \boldsymbol{f}(\mathbf{0})=\mathbf{0} \)
1. \( \lim _{x \rightarrow 0} f(x) \) exists
2. \( f(x) \) is continuous at \( x=0 \)
Which of the above statements is/are
correct?
A. 1 only
B. 2 only
c. Both 1 and 2
D. Neither 1 nor 2


An electromagnet is a
A. Temporary magnet
B. Permanent magnet
C. Both (A) and (B)
D. None of the above


The Banker's discount on a sum of
money for 18 months is Rs600 and the
true discount on the same sum for 3
years is Rs750/- The percentage is:
A . \( 10 \% \)
B. 20\%
c. \( 15 \% \)
D. \( 12 \% \)


A ball is dropped from the top of a
building. The ball takes 0.5 s to fall past the window \( 3 \mathrm{m} \) in length at certain distance from the top of the building. \( \boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} \boldsymbol{s}^{-2} \mathbf{)} \)
Speed of the ball as it crosses the top edge of the window is
A. \( 3.5 \mathrm{ms}^{-1} \)
B. \( 8.5 \mathrm{ms}^{-1} \)
c. \( 5 m s^{-1} \)
D. \( 12 \mathrm{ms}^{-1} \)


Which one of the following forms micelles in aqueous solution above certain concentration?
A. Dodecyl trimethyl ammonium chloride
B. Glucose
c. urea
D. Pyridiniumchloride


A particle moves along a straight line such that it's displacement x changes with time \( t \) as \( x=\sqrt{a t^{2}+2 b t+c} \)
A \( \cdot \frac{1}{x} \)
B. \( \frac{1}{x^{2}} \)
c. \( \frac{1}{x^{3}} \)
D. \( \frac{1}{x^{4}} \)


Find the value of \( \frac{K N}{L M} \) from the given figure.
A
в. \( \frac{2}{5} \)
c. \( \frac{2}{3} \)
D. 5 \( \overline{3} \)


For the arrangement shown in figure,
pulleys and strings are ideal. Find out
the acceleration of \( 2 \mathrm{kg} \) block
A \( \cdot \frac{g}{3} \)
B. \( \frac{g \sqrt{2}}{3} \)
c. \( \frac{2 g}{3} \)
D. \( \frac{2 g}{\sqrt{2} g} \)


\( \operatorname{Let} f(x)=\sin \frac{1}{x}, x \neq 0 . \) Then \( f(x) \) can
be continuous at \( 4 x=0 \)
A. If \( f(0)=1 \)
B. If \( f(0)=0 \)
c. If \( f(0)=-1 \)
D. For no definite value of \( f(0) \)


Draw a diagram of nuclear power reactor and label the parts.


Which of the following statements is
incorrect regarding fermentation?
A. Propionibacterium is used to ferment the cheese.
B. The puffed-up appearance of dough is due to the production of \( C O_{2} \) gas.
C. Fermentation in muscle produces ethanol
D. Toddy is made by fermenting sap from palms.


\( f^{8} C_{r}=^{8} C_{r+2}, \) then the value of \( ^{r} C_{2} \) is:
\( A \cdot 8 \)
B. 3
\( c \cdot 5 \)
D. 2


At \( 300 \mathrm{K} \) the standard enthalpies of
formation of \( C_{6} H_{5} C O O H_{(s)}, C O_{2(g)} \)
and \( H_{2} O_{(l)} \) are -408,-393 and -286
kJ \( m o l^{-1} \) respectively. Calculate the heat of combustion of benzoic acid at
constant volume.
B. +3199.75 kJ
D. -3199.75 k


A metal sphere of radius a is having
charge \( +Q \) on it Now it is connected with
a metal wire to a concentric spherica
shell of radius 2 a Then the net potential
at the surface of outer shell is
\( ^{A} \cdot \frac{K Q}{a} \)
в. \( \frac{K Q}{2 a} \)
c. \( \frac{3}{2} \frac{K Q}{a} \)
D. \( \frac{2 K Q}{a} \)


For the given bond pairs, decide which is the more polar?
\( \boldsymbol{S} \boldsymbol{i}-\boldsymbol{O} \) and \( \boldsymbol{P}-\boldsymbol{P} \)
A \( . S i-O>P-P \)
в. \( S i-O<P-P \)
c. \( s i-O=P-P \)
D. None of these


Two identical calorimeters 'X' and 'Y', of water equivalent 10 g each, contain equal quantities of the same liquid. The mass, initial temperature and specific heat capacity of the liquid present in
both calorimeters are 50 g, \( 25^{\circ} \mathrm{C} \) and \( \frac{1}{2} c a l g^{-1 \circ} C^{-1} \) respectively.A 10 g metal
piece (say A) of specific heat capacity \( 0.4 c a l g^{-1 \circ} C^{-1} \) is dropped in calorimeter "X". and 25 g of metal piece (say B) of specific heat capacity " \( S_{B} \) "is dropped into calorimeter "Y". Due to this, the equilibrium temperature in 'X'
and 'Y' rises to \( 30^{\circ} \mathrm{C} \) and \( 40^{\circ} \mathrm{C} \)
respectively. If the initial temperature of B' is twice that of 'A', then find the value
of "S \( _{B} " \)


The trees growing in desert will
A. Show alternate rings of xylem and sclerenchyma
B. Have only conjunctive tissue and phloem formed by the activity of cambium
C. Show distinct annual rings
D. Not show distinct annual rings


Let \( \left(1+x^{2}\right)^{2} \cdot(1+x)^{n}=\sum_{K=0}^{n+4} a_{K} \cdot x^{K} \)
\( f\left(a_{1}, a_{2} \text { and } a_{3} \text { are in A.P, find } n\right. \)


In a long straight solenoid with cross-
sectional radius \( a \) and number of turns
per unit length, \( n \), the current varies
with the rate \( \boldsymbol{I} \boldsymbol{A} / \boldsymbol{s} \). The magnitude of
the induced current field strength as a function of distance \( r \) from the solenoid
axis is
A \( \cdot \frac{1}{2} \frac{n I a^{2}}{\mu_{0} r} \)
В \( \cdot \frac{1 I a^{2}}{2 \mu_{0} r} \)
С \( \cdot \frac{n I a^{2}}{\mu_{0} r} \)
D. \( \frac{1}{2} \frac{\mu_{0} n I a^{2}}{r} \)


When a sulphur sol is evaporated, solid sulphur is left. On mixing with water no colloidal sol is formed. The sulphur sol
is:
A. hydrophilic
B. hydrophobic
c. reversible
D. lyophilic


Magnetic susceptibility for a paramagnetic and diamagnetic materials is respectively
A. small, positive and small, positive
B. large, positive and small, negative
c. small, positive and small, negative
D. large, negative and large, positive


The electrons in the beam of a television
tube move horizontally from south to north. The vertical component of the
earths magnetic field points down. The electron is deflected towards
A . east
B. no deflection
c. west
D. north to south


A bullet of mass \( \mathrm{m} \) hits a block of mass
M. The transfer of energy is maximum
when:
\( A \cdot m=M \)
B. М=2m
c. мк
December 26, 2019
Poulomi Chotai
(8)
Share Save


What is a stress hormone? or The
hormone produced during adverse environmental conditions is
A. Benzyl aminopurine
B. Dichlorophenoxy acetic acid
c. Ethylene
D. Abscisic acid


Find \( b \lim _{x \rightarrow 2 a} \frac{\sqrt{(x-2 a)}+\sqrt{x}-\sqrt{2 a}}{\sqrt{\left(x^{2}-4 a^{2}\right)}} \) is
\( \frac{1}{b \sqrt{a}} \)


Contamination found in natural
environment is called as
A. Sewage
B. Distortion
c. spoilage
D. Pollution


A steel rod of length \( 1 \mathrm{m} \) is heated from
\( 25^{\circ} \) to \( 75^{\circ} \mathrm{C} \) keeping its length constant. The longitudinal strain developed in the rod is (Given coefficient of linear expansion of stee \( \left.=12 \times 10^{-6} /^{\circ} C\right) \)
A. \( 6 \times 10^{-4} \)
В. \( -6 \times 10^{-5} \)
c. \( -6 \times 10^{-4} \)
D. zero


If \( P(x, y, z) \) moves such that \( x=0, z= \)
\( 0, \) then the locus of \( P \) is the line whose
d.cs are
A . \( y \) -axis
B. 1,0,0
c. 0,1,0
D. 0,0,0


Statement -1: Carbon dioxide is
insoluble in water.
Staement -2 Haemoglobin has a high affinity for oxygen.
A. Both the statements are true
B. Both the statements are false
c. statement- - is true and Statement - 2 is false
D. Statement-1 is false and Statement-2 is true


A special lottery is to be held to select a student who will live in the only deluxe room in a hostel. There are 100 Year-III, 150 Year-II and 200 Year-I students who
applied. Each Year-III's name is placed in the lottery 3 times; each Year-II's name, 2 times and Year-l's name, 1 time.
What is the probability that a Year-III's name will be chosen?
\( A \cdot \)
B.
\( c \cdot \frac{3}{3} \)
\( D \)


Consider an optical system placed in
water \( (\mu=4 / 3) \) PQRS is a hollow glass
slab filled with air \( (\mu=1) \) This slab is
kept on the principle axis of a lens in
such a way that surface PS makes an
angle \( \theta \) with the axis of the lens.
\( \left(0<\theta<180^{\circ}\right), \) then
This question has multiple correct options
A. for transmission of light takes place through slab \( \theta_{\min }=\frac{\pi}{2}-\sin ^{-1}(0.75) \)
B \cdot for transmission of light through slab \( \theta_{\text {max }}=\frac{\pi}{2}+\sin \)
\( -1(0.75) \)
C. for \( x=50 \mathrm{cm} \) final image is at \( 3 \mathrm{m} \) distance from 0
D. for \( x=100 \mathrm{cm} \) final image is at \( 3 \mathrm{m} \) distance from 0


The experimental data for
decomposition of \( N_{2} O_{5}\left[2 N_{2} O_{5} \rightarrow\right. \)
\( \left.4 N O_{2}+O_{2}\right] \) in gas phase at \( 318 K \) are
given below:
\[
\text { t/s } \quad \mathbf{0} \quad \mathbf{4 0 0} \quad \mathbf{8 0 0}
\]
\[
10^{2}
\]
\[
\left[N_{2} O_{5}\right] / m o l L^{-1}
\]
(i) Plot \( \left[N_{2} O_{5}\right] \) against t.
(ii) Find the half-life period for the
reaction.
(iii) Draw a graph between \( \log \left[N_{2} O_{5}\right] \)
and t.
(iv) What is the rate law?
(v) Calculate the rate constant.
(vi) Calculate the half-life period from \( \mathbf{k} \) and compare it with (ii)


\( 2 \mathrm{gm} \) of oxygen contains number of atoms equal to that in:
A. \( 0.5 \mathrm{gm} \) of hydrogen
B. 4 gm of sulphur
c. \( 7 \mathrm{gm} \) of nitrogen
D. 2.3 gm of sodium


An element R belongs to IVA(14) group and 3rd period in the periodic table. Arrange the elements that are placed below 'R' in increasing order of atomic size.
A. \( G e>S n>P b \)
B. \( A s>S b>B i \)
c. \( G e<S n<P b \)
D. \( A s<S b<B i \)


The earth and the moon are attracted to
each other by gravitational force. Is the force with which the Earth attracts the
Moon greater, smaller or the same as
the force with which the Moon attracts
the Earth?
A. Same and opposite
B. Greater
c. Smaller
D. Data insufficient


An object is located \( 4 \mathrm{m} \) from the first of
two thin converging lenses of local lengths \( 2 \mathrm{m} \) and \( 1 \mathrm{m} \) respectively. The
lenses are separated by 3 m. The final image formed by the second lens is located from the source at a distance of
source.
\( \mathbf{A} \cdot 8.0 m \)
B. \( 7.5 m \)
\( \mathrm{c} \cdot 6.0 \mathrm{m} \)
D. 6.5 m


Incomplete breakdown of sugars in anaerobic respiration forms
A. Glucose and \( C O_{2} \).
B. Alcohol and \( C O_{2} \).
c. water and \( C O_{2} \)
D. Fructose and water


Measurement of water pollution is made by
A. Coliform count
B. Biological oxygen demand
c. pH
D. All of the above


A person walks up a stalled escalator in
\( \mathbf{9 0} \)
s. when standing on the same escalator, now moving, he is carried in
\( 60 s . \) The time he would take to walk up
the moving escalator will be
A \( .27 s \)
в. \( 72 s \)
\( c \cdot 18 s \)
D. \( 36 s \)


A charged particle is shot at an angle \( \theta \)
to a uniform magnetic field along directed X-axis. Duration its motion
along a helical path, whose pitch is equal to the maximum distance from \( x \) axis, the particle will :
This question has multiple correct options
A. Never move parallel to x-axis
B. \( \tan \theta=2 / p i \)
\( \mathbf{c} \cdot \sin \theta=1 / p i \)
D. \( \tan \theta=\pi \)


If \( \vec{a}=x \hat{i}+y \hat{j}+z \hat{k} \) makes equal angles with \( \vec{b}=y \hat{i}-2 z \hat{j}+3 x \hat{k} \) and \( \vec{c}=2 z \hat{i}+3 x \hat{j}-y \hat{k} \) and \( \vec{a} \perp \vec{d}, \) where
\( \vec{d}=\hat{i}-\hat{j}+2 \hat{k} . \) If \( |\vec{a}|=2 \sqrt{3}, \) then
\( \vec{a} \cdot \vec{b}= \)
A . 12
B. -12
\( c \cdot 24 \)
D. -24


A uniform plate of area \( 10 \mathrm{cm}^{2} \) is placed on a horizontal surface coated with an
oil layer of thickness \( 5 \mathrm{mm} \). The force
that must be applied horizontally on the plate to move it with a speed of \( 5 \mathrm{cm} / \mathrm{s} \) is
\( \mathbf{A} \cdot 3 \times 10^{-2} N \)
В. \( 2.5 \times 10^{-2} N \)
c. \( 2 \times 10^{-2} N \)
D. \( 1.5 \times 10^{-2} N \)


Which gland is concerned with salt equilibrium in body?
A. Anterior pituitary
B. Pancreas
c. Adrenal
D. Thyroid


Find \( A \triangle B \) and draw Venn diagram when:
\( \boldsymbol{A}=\{1,2,3,4,5\} \) and \( \boldsymbol{B}= \)
\{1,2,3,4,5,6\}


In the circuit diagram shown all the
capacitors are in \( \mu F . \) The equivalent
capacitance between points \( A \) and \( B \) is \( (\operatorname{in} \mu F) \)
A \( \cdot \frac{14}{5} \)
B. 7.5
\( c \cdot \frac{3}{7} \)
D. none of these


Sketch for \( \boldsymbol{y}=\sin ^{-1}\left(\frac{1+x^{2}}{2 x}\right) \)


The carbonate of a metal is
isomorphous (similar formula) with magnesium carbonate and contains 6.091 percent of carbon. The atomic weight of metal is:
A . 24
B. 56
\( c \cdot 137 \)
D. 260


Assertion
In a motion picture, the consecutive frames are almost the same and
quickly switched.
Reason
In the retina of human eyes these
continuous images get fused into one another
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


Pascal (Pa) is the unit of
A. Thrust
B. Pressure
c. Buoyant force
D. Momentum