If \( \boldsymbol{x}=\frac{\mathbf{1}}{\mathbf{1}^{2}}+\frac{\mathbf{1}}{\mathbf{3}^{2}}+\frac{\mathbf{1}}{\mathbf{5}^{2}}+\ldots ., \boldsymbol{y}=\frac{\mathbf{1}}{\mathbf{1}^{2}}+ \)
\( \frac{3}{2^{2}}+\frac{1}{3^{2}}+\frac{3}{4^{2}}+\ldots \) and \( z=\frac{1}{1^{2}}- \)
\( \frac{1}{2^{2}}+\frac{1}{3^{2}}-\frac{1}{4^{2}}+\ldots ., \) then
A. \( x, y, z \) are in A.P.
B. \( \frac{y}{6}, \frac{x}{3}, \frac{z}{1} \) are in A.P.
c. \( \frac{y}{6}, \frac{x}{3}, \frac{z}{2} \) are in A.P
D. \( 6 y, 3 x, 2 z \) are in H.P


How does air trapped by the woolen
fabric help?
A. Air is a good conductor of heat and allows warm air to come near body
B. Air is a bad conductor of heat and allows body heat to escape into atmosphere
C. Air is a bad conductor of heat and doesn't allow body heat to escape into atmosphere
D. Air is a good conductor of heat and doesn't allow cool air to come near body.


If \( x=\cos ^{2}\left(\tan ^{-1}\left(\sin \left(\cot ^{-1} 3\right)\right)\right), \) then
\( 1331 x^{3}-3630 x^{2}+3300 x+7369= \)
\( m \) then find the sum of the second and
third digits of \( \boldsymbol{m} \)


What is electrophoresis? Why is it shown by a certain type of solution?


Angle between lines whose direction
\( \operatorname{cosine} \operatorname{satisfy} l+m+n=0, l^{2}+ \)
\( \boldsymbol{m}^{2}-\boldsymbol{n}^{2}=\mathbf{0} \)


the number of turn of primary and secondary coil of the transformer is 5 and 10 respectively ad the mutual inductance is 25 H. if the number \( f \)
turns of the primary and secondary is made 10 and \( 5, \) then the mutual
inductance of the coils will be
A . \( 6.25 \mathrm{H} \)
B. 12.5
c. 25
D. 50


In a parallelogram \( A B C D, \) if \( A B= \) \( \mathbf{2} \boldsymbol{x}+\mathbf{5}, \boldsymbol{C} \boldsymbol{D}=\boldsymbol{y}+\mathbf{1}, \boldsymbol{A} \boldsymbol{D}=\boldsymbol{y}+\mathbf{5} \) and
\( B C=3 x-4, \) what is the ratio of \( A B \)
and \( B C ? \)
A .71: 21
B. 12: 11
c. 31: 35
D. 4: 7


Range of \( \boldsymbol{f}(\boldsymbol{x})=\left(\sin ^{-1} \boldsymbol{x}+\tan ^{-1} \boldsymbol{x}+\right. \)
\( \left.\sec ^{-1} x\right) \) is
A \( \cdot\left(\frac{\pi}{4}, \frac{3 \pi}{4}\right) \)
В. \( \left[\frac{\pi}{4}, \frac{3 \pi}{4}\right] \)
c. \( \left\{\frac{\pi}{4}, \frac{3 \pi}{4}\right\} \)
D \( \cdot\left\{0, \frac{\pi}{4}\right\} \)


Calculate osmotic pressure of a solution (write only integer part) obtained on mixing \( 100 \mathrm{mL} \) of \( 3.4 \% \) (mass/vol) solution of urea (molar
mass 60 ) and \( 50 \mathrm{mL} \) of \( 1.6 \% \) (mass/vol)
solution of cane sugar (molar mass 342
\( \operatorname{at} 27^{\circ} C \)


If \( \boldsymbol{a}+\boldsymbol{b}+\boldsymbol{c}=\mathbf{0}, \) then \( \boldsymbol{a}^{3}+\boldsymbol{b}^{3}+\boldsymbol{c}^{3}= \)
\( k a b c, \) the value of \( ^{\prime} k^{\prime} \) is


Smoke particles are actually electrically charged colloidal particles
of :
A. carbon in air
B. water droplets in air
c. sulphur in air
D. titanium oxide in air


The area enclosed between the curves
\( \boldsymbol{y}=\boldsymbol{a} \boldsymbol{x}^{2} \) and \( \boldsymbol{x}=\boldsymbol{a} \boldsymbol{y}^{2}(\boldsymbol{a}>\boldsymbol{0}) \) is
1 sq.unit. then \( a= \)
A \( \cdot \frac{1}{\sqrt{3}} \)
в. \( \frac{2}{\sqrt{3}} \)
c. \( \frac{4}{\sqrt{3}} \)
D. \( \sqrt{3} \)


Which of the following match is correct?
A. last natural element- Uub
B. General electronic configuration of IA group - \( n s^{2} \)
C. inert gas lies in \( 2^{n d}-6^{t h} \) period
D. Typical elements - \( 3^{r d} \) period elements


Calculate the velocity of a body of a mass 2 kg whose linear momentum is 5
N s.
A \( .2 .5 \mathrm{ms}^{-1} \)
B. \( 10 \mathrm{ms}^{-1} \)
c. \( 5 m s^{-1} \)
D. \( 2 m s^{-1} \)


Which one of the following statements
about \( \boldsymbol{H}_{3} \boldsymbol{B} \boldsymbol{O}_{3} \) is not correct?
A. It is a strong tribasic acid
B. It is prepared by acidifying an aqueous solution of borax
c. It has a layer structure in which planar BO, units are joined by hydrogen bonds.
D. It does not act as proton donor as it acts as a Lewis acid by accepting hydroxyl ions.


The side of a square is increased by \( 20 \% . \) Find the \( \% \) change in its area.
A. \( 44 \% \) increase
B. \( 40 \% \) increase
c. No change
D. None of these


Differentiate \( x^{\sin x}+(\sin x)^{\cos x} \) w.r.t \( x \)


A rectangular plot is 125 m long and
\( 72 m \) broad. Find the cost of fencing it
at \( R s 27 \) per metre.


Identify the products.


Give reasons When \( C l_{2} \) reacts with
excess of \( F_{2}, C l F_{3} \) is formed and not
\( \boldsymbol{F} \boldsymbol{C l}_{3} \)


How many significant figures are in \( 54,050 ? \)
A. 5
B. 2
\( c \cdot 4 \)
D.
E. 3


Find the total number of possible
isomers of \( \left[\mathrm{CrCl}_{3}\left(\mathrm{NH}_{3}\right)_{3}\right] \)


In which of the following reactions of
\( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) sulphur retains its oxidation
state?
This question has multiple correct options
A. Reaction of dilute \( H_{2} S O_{4} \) with sulphur
B. Reaction of conc. \( H_{2} S O_{4} \) with sulphur
c. Reaction of conc. \( H_{2} S O_{4} \) with glucose
D. Reaction of dilute \( H_{2} S O_{4} \) with zinc


Alicyclic compounds are:
A. aromatic compounds
B. aliphatic cyclic compounds
C . heterocyclic compounds
D. none of the above


The hybrid orbital having equal amounts of \( s \) and \( p \) - characters is:
\( \mathbf{A} \cdot s p \)
B \( \cdot s p^{3} \)
\( c \cdot s p^{2} \)
D. none of the above


The cell wall is impermeable to water and deposition of suberin is also found in
A . Leaf
B. cork
c. Bark
D. xylem


Atomic number of Bismuth is:
\( A \cdot 84 \)
B. 85 5
\( c \cdot 83 \)
D. 82


The process of addition of sulphur to rubber is called
A. vulcenization
B. vulcanization
c. valcanization
D. vulcanisation


Which of the two orbitals have lower
energy among \( 4 s \) and \( 3 d ? \)


What is the odor of \( \boldsymbol{P C l}_{3} \) ?
A. Pungent
B. Fishy
c. sweet
D. None of the above


Calculate the electric potential at point
\( R \) on the \( x- \) axis
A . 0
B. \( V=\frac{q}{4 \pi \epsilon_{o} \sqrt{a^{2}+y^{2}}} \)
c. \( V=\frac{q}{4 \pi \epsilon_{o}}\left(\frac{1}{x+a}-\frac{1}{x-a}\right) \)
\( V=\frac{q}{4 \pi \epsilon_{o}}\left(\frac{1}{x+a}+\frac{1}{x-a}\right) \)


An electric cell of e.m.f. E is connected
across a copper wire of diameter d and length I. The drift velocity of electrons in
the wire is \( v_{d} \). If the length of the wire is changed to 21, the new drift velocity of electrons in the copper wire will be
\( \mathbf{A} \cdot v_{d} \)
в. \( 2 v_{d} \)
c. \( v_{d} / 2 \)
D. \( v_{d} / 4 \)


The compound \( C_{7} H_{8} \) undergoes the following reactions:
\( \boldsymbol{C}_{7} \boldsymbol{H}_{8} \frac{3 C l_{2} / \Delta}{\longrightarrow} \boldsymbol{A} \frac{B r_{2} / \boldsymbol{F} e}{\longrightarrow} \boldsymbol{B} \frac{\boldsymbol{Z} \boldsymbol{n} / \boldsymbol{H} C l}{\longrightarrow} \boldsymbol{C} \)
The product \( C \) is:
A. 3 -bromo -2,4,6 -trichlorotoluene
B. \( m \) -bromotoluene
c. \( p \) -bromotoluene
D. \( o \) -bromotoluene


The biggest snake in venomous snakes is
A. King cobra
B. Ptyas
C. Python
D. Pit viper


Draw the structure of the stable
positive ion formed when an acid dissolves in water.


f \( \boldsymbol{A}=\left|\begin{array}{cc}2 & \mathbf{3} \\ -\mathbf{1} & \mathbf{2}\end{array}\right| \) Find \( \boldsymbol{A} \)


Which of the following is/are true regarding the following linear equation:
\( \boldsymbol{y}=\mathbf{4} \boldsymbol{x}-\frac{\mathbf{5}}{\mathbf{2}} \)
A . It passes through (2.5,0) and \( m=-4 \)
B. It passes through (2.5,0) and \( m=4 \)
C. It passes through (0,2.5) and \( m=-4 \)
D. It passes through (0,-2.5) and \( m=4 \)


A person bring a mass of \( 1 k g \) from
infinite to point \( A \). Initially the mass was at rest but is moves a speed of \( 2 m / s \) as it reaches to \( A \). The workdone
by the person on mass is \( -3 J \) the gravitational potential at \( \boldsymbol{A} \) is
A. \( -3 J / k g \)
в. \( -2 J / k g \)
\( \mathbf{c} .-5 J / k g \)
D. \( -7 J / k g \)


Stool of a person is whitish grey coloured due to malfunction of which of
the following organs?
A. Pancreas
B. Spleen
c. Kidney
D. Liver


Which of the following property shows the property of ferromagnetic
substances?
A. The ferromagnetic property depends on temperature
B. The ferromagnetic property does not depend on temperature.
c. At high enough temperature ferromagnet becomes a diamagnet
D. At low temperature ferromagnet becomes a paramagnet


Which of the following statements gives
the correct distinction between the
burning of carbon compounds and
respiration?
A. The burning of carbon compounds is a slow process while respiration is spontaneous.
B. Burning of carbon compounds releases energy in form of ATP while respiration releases in form of light.
C. Burning of carbon compounds is a fast process while respiration is slow.
D. All the above statements are correct


will form chlorides
with the formula \( M C l_{2} \)
A. alkali metals
B. Alkaline earth metals
c. Transition metals
D. Halogens
E. Noble or inert gases


Point out the wrong statement about the magnetic properties of soft iron and
steel
A. Retentivity of soft iron is more than retentivity of steel
B. Coercivity of soft iron is less than coercivity of steel.
c. Area of B-H loop in soft iron is smaller than the area of B-H loop for steel
D. Area of B-H loop in soft iron is greater than the area of B-H loop for steel


\( A=3 \hat{i}+4 \hat{j} . \) Find a vector perpendicular to \( \vec{A} \) in the plane of \( \vec{A} \)
\( A \cdot \hat{k} \)
B. \( -3 \hat{i}-4 \hat{j} \)
c. \( 4 \hat{j}-3 \hat{i} \)
D. \( 4 \hat{i}-3 \hat{j} \)


Assertion
In YDSE, if a film is introduced in front
of the upper slit, then the fringe pattern shifts in the downward direction
Reason
In YDSE if the slit widths are unequal,
the minima will be completely dark
A. Both Assertion and Reason are incorrect
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 correct


If \( x=2 \) and \( x=3 \) are the roots of the
equation \( 3 x^{2}-2 m x+2 n=0, \) find the
values of \( m \) and \( n \)


List in tubular form three difference
between arteries and veins.


A particle of mass \( 10 g \) lies in a
potential field \( v=50 x^{2}+100 . \) The
value of frequency of oscillations in \( \mathrm{Hz} \)
is:
\( A .5 H z \)
в. \( 50 / \pi H z \)
\( \mathbf{c} \cdot 10 \pi / 3 H z \)
D. none of these


If \( \boldsymbol{A}=\left[\begin{array}{cc}\cos 2 \boldsymbol{\theta} & -\sin 2 \boldsymbol{\theta} \\ \sin 2 \boldsymbol{\theta} & \cos 2 \boldsymbol{\theta}\end{array}\right] \) and \( \boldsymbol{A}+ \)
\( A^{T}=I, \) where \( I \) is the unit of matrix of
\( 2 \times 2 \) and \( A^{T} \) is the transpose of \( A, \) then
the value of \( \theta \) is equal to
A \( \cdot \frac{\pi}{6} \)
в.
c. \( \pi \)
D. \( \frac{3 \pi}{2} \)


A triangle is formed by joining three points whose coordinates are integers. If the \( x \) -unit and the \( y \) -unit are each 1 \( \mathrm{cm}, \) then the area of the triangle, in sq.
\( \mathrm{cm} \)
A. must be an integer
B. may be irrational
c. must be irrational
D. must be rational
E. will be an integer only if the triangle is equilatera


Find the value of \( ^{\prime} a^{\prime} \) for which the vector
\( \boldsymbol{A}=\mathbf{3} \hat{\mathbf{i}}+\mathbf{3} \hat{\boldsymbol{j}}+\mathbf{9} \hat{\boldsymbol{k}} \) and \( \overline{\boldsymbol{B}}=\hat{\boldsymbol{i}}+\boldsymbol{a} \hat{\boldsymbol{j}}+\boldsymbol{3} \hat{\boldsymbol{k}} \)
are parallel


Heat of dissociation of benzene to
elements is \( 5535 \mathrm{KJ} \) mol \( ^{-1} \). The bond
enthalpies of \( \boldsymbol{C}-\boldsymbol{C}, \boldsymbol{C}=\boldsymbol{C} \) and \( \boldsymbol{C}-\boldsymbol{H} \)
are 347.3,615.0 and \( 416.2 \mathrm{KJ} \)
respectively. Resonance energy of benzene is:
A. \( 1.51 \mathrm{KJ} \)
в. 15.1 К.
c. \( 151 \mathrm{KJ} \)
D. \( 1511 \mathrm{KJ} \)


Calculate the normality of 10 volume
\( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \)
A . \( 1.78 N \)
в. 12 N
c. \( 30.3 N \)
D. \( 0.0303 N \)


Percentage of water present in oceans
and seas is
A. \( 60 \% \)
B. 70\%
\( c \cdot 80 \% \)
D. 95 \%


What is the derivative of \( |x-1| \) at \( x= \)
\( \mathbf{2} ? \)
A . -1
B. 0
c. 1
D. Derivative does not exist


Lightning strikes building when induced charge on top building is too high. This statement is:
A. True
B. False


A boy rolls a rubber ball on a wooden surface. The ball travels a short
distance before coming to rest. To make the same ball travel longer distance before coming to rest, he may
A. spread a carpet on the wooden surface.
B. cover the ball with a piece of cloth
c. sprinkle talcum powder on the wooden surface.
D. sprinkle sand on the wooden surface


If \( \boldsymbol{m}=\mathbf{2} \) and \( \boldsymbol{n}=\mathbf{1}, \) then find the value
of following polynomials:
\( m+3 n \)


The difference between \( a_{30} \) and \( a_{20} \) for
the \( A P-3,-7,-11 \) is \( ^{\prime} d^{\prime}, \) then \( \frac{|d|}{10} \)
equals


Write the converse and contrapositive of the following statement:
f \( x+3=9, \) then \( x=6 \)


A time varying current \( i \) in passed
through a resistance \( R \) as shown in
figure. The total heat generated in the
resistance is:
A \( \cdot 11 i_{0}^{2} R t_{0} \)
B. \( 13 i_{0}^{2} R t_{0} \)
\( \mathbf{c} \cdot 17 i_{0}^{2} R t_{0} \)
D. \( 15 i_{0}^{2} R t_{0} \)


\( f(x)=\left|\begin{array}{ccc}\sin x & \cos x & \tan x \\ x^{3} & x^{2} & x \\ 2 x & 1 & 1\end{array}\right|, \) then
\( \lim _{x \rightarrow 0} \frac{f(x)}{x^{2}} \) is
\( A \)
B. 3
\( c \cdot 1 \)
D. zero


Which of the following statement is
incorrect? Choose answer:
A. The acid insoluble fraction, has only four types of organic compounds, proteins, polysaccharides nucleic acids and lipids
B. Chemical compounds found in living organisms are of two types, acid soluble and acid insoluble
C. The compounds which are found in the acid insoluble fraction are called micromolecules
D. The acid soluble pool represents roughly the cytoplasmic composition


The formula that relates Bulk's
modulus with poisson's ratio is
В. \( Y=3 B(1-\sigma) \)
c. \( Y=3 B(1-2 \sigma) \)
D. \( Y=3 B(1+\sigma) \)


Nitrogen is an important component of
A . Lipids
B. Carbohydrates
c. Polyphosphates
D. Proteins


The e/m value of positive particles:
A. is constant
B. depends on the gas taken in the discharge
C. depends on the natures of cathode and anode taken
D. depends on fluorescent material coated on screen


Match the following.


The distance covered by a body in time \( (\mathbf{5 . 0} \pm \mathbf{0 . 6}) \) is \( (\mathbf{4 0 . 0} \pm \mathbf{0 . 4}) \mathrm{m} . \) Calculate
the speed of the body. Also determine
the percentage error in the speed.


A particle goes from \( A \) to \( B \) with a speed
of \( 40 \mathrm{km} / \mathrm{h} \) and \( \mathrm{B} \) to \( \mathrm{C} \) with a speed of 60
\( \mathrm{km} / \mathrm{h} . \) If \( \mathrm{AB}=6 \mathrm{BC}, \) then the average
speed in \( \mathrm{km} / \mathrm{h} \) between \( \mathrm{A} \) and \( \mathrm{C} \) is
(40+x). The value of x is:


Why Liquid nitrogen is used as a refrigerant to preserve biological specimens?


Assertion
In Chlorophyceae, plant body is usually
grass green
Reason
Members of Chlorophyceae, possess chlorophyll a, c, carotenoids and
xanthophyll.
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


Assertion
Chlorine water must be stored in dark
colored bottles.
Reason
Hypochlorous acid on exposure to sunlight decomposes to \( H_{2} \) and \( C l_{2} \)
gas.
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


Find the coordinate of point which divides \( A(5,6) \) and (5,10) in 2: 3


An emulsion is a colloidal system of
A. two solids
B. two liquids
c. one gas and one solid
D. one gas and one liquid


Given a square matrix \( \boldsymbol{A}=\left[\boldsymbol{a}_{\boldsymbol{g}}\right], \) where
\( a_{g}=\hat{i}^{2}-\hat{j}^{2} . \) Then matrix \( A \) is a unit
matrix or null matrix or a symmetric matrix a skew symmetric matrix. Select with a reason.


The reaction between \( A \) and \( B \) is first
order with respect to A and zero order with respect to B. Fill in the blanks in
the following table:
\( \begin{array}{lll}\text { Experiment } & {[\boldsymbol{A}] / \boldsymbol{m o l} \boldsymbol{L}^{-1}} & \boldsymbol{B}] / \boldsymbol{m o l} \boldsymbol{L}^{-1} \\ 1 & 0.1 & 0.1 \\ 11 & - & 0.2 \\ 111 & 0.4 & 0.4 \\ & & \\ & & \\ & & \\ & & \\ & & \end{array} \)


Chloramphenicol is used as an:
A. analgesic
B. antibiotic
c. anaesthetic
D. antiseptic


Consider the following two equations \( A \) and B.
Equation A Glucose \( \rightarrow \) Pyruvate \( \rightarrow C O_{2}+H_{2} O+ \)
Energy Equation B
Glucose \( \rightarrow \) Pyruvate \( \rightarrow C_{2} H_{5} O H+ \)
\( \boldsymbol{C O}_{2}+ \) Energy
Which one of the following is correct with respect to both the equations \( A \)
and B?
A. A is aerobic respiration consisting of glycolysis and Krebs cycle, B is anaerobic fermentation reaction
B. A is anaerobic respiration and B is aerobic fermentation reaction
c. A is aerobic respiration B is anaerobic lactic acid fermentation
D. In both A and B reactions, pyruvate undergoes complete oxidation.


M is the midpoint of the straight line PQ If \( P \) is (-2,9) and \( M \) is \( (4,3), \) find the coordinates of \( Q \)
A . (1,6)
в. (10,-3)
c. (10,6)
D. (8,-3)


Statement 1: The isotope \( \mathrm{Cl} \) -37 has 17 protons, 17 neutrons, and 17 electrons.
Statement 2: The atomic mass of
chlorine is 35.43 amu.
A. Both Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement
B. Both Statement 1 and Statement 2 are correct and Statement 2 is not the correct explanation of Statement
c. statement 1 is correct but Statement 2 is not correct
D. Statement 1 is not correct but Statement 2 is correct
E. Both the Statement 1 and Statement 2 are not correct


Arrange the following objects in the order of the intermolecular force of
attraction.
( Oxygen, Sugar, Water)
A. Oxygen > Water> Sugar
B. Sugar> Water> Oxygen
c. water > sugar > Oxygen
D. None of the above


For \( \boldsymbol{a} \in[\boldsymbol{\pi}, \boldsymbol{2} \boldsymbol{\pi}] \) and \( \boldsymbol{n} \in \boldsymbol{Z}, \) the critical
points of \( \boldsymbol{f}(\boldsymbol{x})=\frac{1}{\mathbf{3}} \sin \boldsymbol{a} \tan ^{3} \boldsymbol{x}+ \)
\( (\sin a-1) \tan x+\sqrt{\frac{a-2}{8-a}} \) are
A . \( x=n \pi \)
B. \( x=2 n \pi \)
c. \( x=(2 n+1) \pi \)
D. None of these


BOD is related with
A . Organic matter
B. Microbes
c. Both A and B
D. None of the above


Write the common difference of the A.P.
\( 7,5,3,1,-1,-3, \dots \)


Which force opposes the inter ionic
forces of attraction between the
oppositely charged ions during the formation of an ionic crystal?


A polarizer -analyser set is adjusted such that the intensity of light coming out of the analyser is just \( 10 \% \) of the original intensity. Assuming that the polarizer-analyser set does not absorb any light, the angle by which the analyser need to be rotated further to
reduce the output intensity to be zero, is:
A . \( 90^{\circ} \)
в. \( 71.6^{\circ} \)
c. \( 18.4^{\circ} \)
D. \( 45^{\circ} \)


Name the joint, label part \( A \) and \( B \) and write their functions.


Work is function.
A . path
B. state
c. both path and state
D. none of these


The bond dissociation energies of \( \boldsymbol{H}- \)
\( \boldsymbol{H}, \boldsymbol{C}-\boldsymbol{C} \) and \( \boldsymbol{C}-\boldsymbol{H} \) bonds
respectively are 104.2,83.1 and 98.8
kcal \( m o l^{-1} . \) The electronegativity of
carbon is:
A . 2.53
B . 2.51
c. 2.57
D. 2.52


Identify the correct ascending order of \( \boldsymbol{\alpha}, \boldsymbol{\beta} \) and \( \gamma \) with reference to their
ionizing power:
I) \( \alpha \) -ray
II) \( \gamma \) -ray III) \( \beta \) -ray
A . "।,॥,।,
в. ।,॥।,
c. ॥,।,॥|
D. I,II,II


Which logic gates mentioned below have the output value 'O' when both the inputs are 1
\( A \cdot O R, N A N D \)
B. AND, NOR
c. AND, OR
D. NOR, NAND


A reflecting surface is curved outwards. The mirror formed will be :
A. Concave
B. Plane
c. convex
D. None of these


Ant bite is treated by application of
A. washing soda
B. baking soda
c. neutral solution
D. acidic solution


Which of the following plot is correct for an ideal binary solution of liquids \( A \) and
B with \( \boldsymbol{P}_{A}^{o}>\boldsymbol{P}_{B}^{o} \)
\( A \)
в.
\( c \)
D.


From above compounds select two of
which are achiral and does not contain
chiral centres.
\( A \cdot b, g \)
B. a,e
\( c \cdot d, f \)
D. None of these


A resonant A.C. circuit contains a
capacitor of capacitance \( 10^{-6} \mathrm{F} \) and an inductor of \( 10^{-4} \) H. The frequency of oscillations will be :
\( \mathbf{A} \cdot 10^{5} \) Нz
в. 10 Н \( z \)
\( ^{\mathrm{c}} \cdot \frac{10^{5}}{2 \pi} \mathrm{Hz} \)
D. \( \frac{10}{2 \pi} \) нг


The complex number \( x+i y \) whose
modulus is unity, \( y \neq 0, \) can be represented as \( \boldsymbol{x}+\boldsymbol{i} \boldsymbol{y}=\frac{\boldsymbol{a}+\boldsymbol{i}}{\boldsymbol{a}-\boldsymbol{i}}, \) where \( \boldsymbol{a} \)
is real number.
A . True
B. False


Which of the following is paramagnetic in nature?
A \( \cdot V(C O)_{6} \)
в. \( F e C O_{5} \)
c. \( F e_{2}(C O)_{9} \)
D. \( \operatorname{Cr}(\text {CO})_{6} \)


A telegraph has 5 arms and each arm is
capable of 4 distinct positions, including the position of first; what is the total number of signals that can be
made?


What is the angle between \( \hat{i}+\hat{j}+\hat{k} \) and \( \hat{i} ? \)
A \( \cdot \frac{\pi}{3} \)
в. \( \frac{\pi}{4} \)
c.
D. none of these


Which of the following is a best nuclear
fuel?
A. Thorium 236
B. Plutonium 239
c. Uranium 236
D. Neptunium 239


Assuming Z-axis as molecular axis, the molecular orbitals formed by the following combination of atomic orbitals is labeled as:
\( 2 p_{z}+2 p_{z}: \pi 2 p_{z} \)
\( A \)


Corrosion occurs due to:
a) action of water on the metal.
b) action of air on the metal.
c) action of temperature on the metal
\( A \cdot a, b \)
в. b,
\( c \cdot \) а,
D. all of the above


Wool is obtained from
sheep.
A. skin
B. toes
c. fleece
D. All of the above


The magnetic field intensity due to a solenoid at end point \( \boldsymbol{P} \) is :
A. \( \mu_{0} n I \)
в. \( \frac{\mu_{0} n I}{2} \)
c. \( \frac{\mu_{0} n I}{2}(\cos \theta-\cos \phi) \)
D. \( \frac{\mu_{0} n I}{2}(\sin \theta-\sin \phi) \)


Assertion: An object falling through a viscous medium eventually attains terminal velocity Reason: All the rain drops hit the
surface of the earth with the same
constant velocity
A. Both assertion and reason are true and reason is 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. Both assertion and reason are false


\( \mathbf{0 . 1} \boldsymbol{g} \boldsymbol{C a} \boldsymbol{C O}_{3} \) will contain:
A. \( 0.1 N_{A} C a^{2-} \) ion
B. \( 0.01 N_{A} C a^{2+} \) ion
c. \( 0.001 N_{A} C a^{2+} \) ion
D. \( N_{A} C a^{2+} \) ion


'The parallax angle in radians is: \( \boldsymbol{\theta}= \) \( \left(1+\frac{54}{60}\right) \times \frac{\pi}{180}=0.03316 \mathrm{rad} \)
Hence, the distance between moon and earth:
A. \( \frac{\text { Diameter of Earth }}{\theta} \)
в. \( \frac{1.276 \times 10^{7} m}{0.03316} \)
c. \( 3.84 \times 10^{8} m \)
D. nnone of these


Let the formula relation the exterior
angle and number of sides of a polygon
be given as \( n A=360 \)
The measure \( A, \) in degrees, of an
exterior angle of a regular polygon is
related to the number of sides, \( n \), of the
polygon by the formula above. If the measure of an exterior angle of a
regular polygon is greater than \( 50, \) what is the greatest number of sides it can
have?
A. 5
B. 6
\( c .7 \)
D. 8


Mass of moon is \( 7.34 \times 10^{22} k g \). If the
acceleration due to gravity on the moon is \( 1.4 m s^{-2}, \) the radius of the moon is:
\( \left[G=6.667 \times 10^{-11} N m^{2} k g^{-2}\right] \)
A \( \cdot 0.56 \times 10^{4} m \)
В. \( 1.87 \times 10^{6} \mathrm{m} \)
c. \( 1.92 \times 10^{6} m \)
D. \( 1.01 \times 10^{8} \mathrm{m} \)


The real and imaginary parts of \( \frac{a+i b}{a-i b} \)
are:
A \( \cdot a^{2}-b^{2}, 2 a b \)
B. \( \frac{a^{2}+b^{2}}{a^{2}-b^{2}}, \frac{2 a b}{a^{2}-b^{2}} \)
c. \( \frac{a^{2}-b^{2}}{a^{2}+b^{2}}, \frac{2 a b}{a^{2}+b^{2}} \)
D. \( \frac{a^{2}+b^{2}}{a^{2}-b^{2}}, \frac{2 a b}{a^{2}+b^{2}} \)


Two protons attract each other when the distance between them is
A \( \cdot 10^{-18} \mathrm{m} \)
m \( \mathrm{r}^{-18} \mathrm{m}^{-} \)
B. \( 10^{-20} \mathrm{m} \)
\( \mathbf{c} \cdot 10^{-15} \mathrm{m} \)
D. \( 10^{-22} \mathrm{m} \)


Find the molecular mass of sulphuric acid.


When a regular pentagon is cut along any one of its lines of symmetry, the quadrilaterals so formed are
A. parallelograms
B. trapeziums
c. triangles
D. trapezium and triangle


let \( f(x)=\sin x, g(x)=[x+1] \) and \( g(f(x))=h(x) \)
then \( h^{\prime}\left(\frac{\pi}{2}\right) \)


A catapult throws a stone of mass 0.10 kg with a velocity of \( 30 \mathrm{m} / \mathrm{s} \). If \( 25 \% \) of the PE of the elastic band is wasted
during transmission, find the magnitude of PE.


Which one is not an example for hydrolases?
A. Dehydrogenase
B. Protease
c. Amylase
D. Esterase
E. Sucrase


\( \mathbf{A} \)
girl throws a ball with velocity at an
inclination of \( 45^{\circ} \). The ball strikes the
smooth vertical wall at a horizontal
distance d from the girl and after reboundig returns to her hand. What is the coefficient o restitution between
wall fand the ball.
A \( \cdot v^{2}-g d \)
в. \( \frac{g d}{v^{2}-g d} \)
c. \( \frac{g d}{v^{2}} \)
D. \( \frac{v^{2}}{g d} \)


Write the formulae of the following compounds:
a. Sodium hexanitrito N cobaltate (III)
b. Tetraaquodichlorochromium (III) chloride


The angle which subtends the periphery of the spherical mirror at the centre of curvature is called:
A. angular aperture
B. glancing angle
c. critical angle
D. none of these


Consider the graph Identify correct option:
A \( \cdot \Delta U_{a}=\Delta_{b}, Q_{b}>Q_{a} \)
В . \( \Delta_{a}>\Delta U_{b}, Q_{a}=Q_{b} \)
C \( \cdot \Delta U_{a}=\Delta U_{b}, Q_{a}<Q_{b} \)
D. \( \Delta U_{a}=\Delta U_{b}, Q_{a}=Q_{b} \)


The given IUPAC name is 1,1 dimethylcyclohexane-3-ol
Is the above statement correct?


The potential of live wire is:
A. ov
B. 300V
c. \( 220 v \)
D. 1000v


\( \mathbf{0 . 0 0 1} \) molal solution of \( \left[\boldsymbol{P t}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4} \boldsymbol{C l}_{4}\right] \)
in water had a freezing point depression
of \( 0.0054 \quad^{o} C . \) If \( K_{f} \) for water is 1.80 the correct formula of the compound is :
\( \mathbf{A} \cdot\left[P t\left(N H_{3}\right)_{4} C l_{3}\right] C l \)
\( ^{\mathbf{B}} \cdot\left[P t\left(N H_{3}\right)_{4} C l_{4}\right] \)
c. \( \left[P t\left(N H_{3}\right)_{4} C l_{2}\right] C l_{2} \)
D. \( \left[P t\left(N H_{3}\right)_{4} C l\right] C l_{3} \)


A sound wave has a frequency of \( 1 k H z \)
and wave length \( 25 c m \), to travel \( 2.2 k m \) it takes:
A \( \cdot 2 \frac{3}{7} s \)
B. \( 80 \frac{2}{5} \) min
c. \( \frac{5}{4} \) min
D. \( 8 \frac{4}{5} s \)


Triangles \( A B C \) and \( P Q R \) are similar
Find the angle \( B \)
\( A \cdot 30^{\circ} \)
B. \( 60^{\circ} \)
\( c \cdot 90^{\circ} \)
0.70


For the transition from \( \boldsymbol{n}=\mathbf{2} \rightarrow \boldsymbol{n}=\mathbf{1} \)
which of the following will produce shortest wavelength?
A. H atom
B. D atom
\( \mathbf{c} \cdot H e^{+} i o n \)
D. \( L i^{2+} \) ion


Water consumption in a city depends on
A. Size of the city.
B. Population of the city.
c. Demand of water.
D. All of the above.


Consider the optical system shown in the figure that follows. The point source
of light \( S \) is having wavelength equal to
\lambda. The light is reaching screen only after
reflection. For point \( \boldsymbol{P} \) to be \( 2^{n d} \) maxima
the value of \( \lambda \) would be \( (D>>d \) and
\( \boldsymbol{d}>>\boldsymbol{\lambda}) \)
A \( \cdot \frac{12 d^{2}}{D} \)
B. \( \frac{6 d^{2}}{D} \)
c. \( \frac{3 d^{2}}{D} \)
D. \( \frac{24 d^{2}}{n} \)


Find the dimensions and units of \( \varepsilon_{0} ? \)


The order of rotational symmetry for the given figure is
\( A \cdot 4 \)
B. 3
\( c \cdot 2 \)
\( D \)


A wire of length ' \( l^{\prime} \) and radius ' \( r^{\prime} \) is
clamped rigidly at one end. When the other end of the wire is pulled by a force
\( F^{\prime}, \) its length increases by \( ^{\prime} x^{\prime} . \) Another wire of same material of length '2l
and radius \( ^{\prime} 2 r^{\prime} \) is pulled by a force \( ^{\prime} 2 F^{\prime} \) the increase in its length will be :
\( A \)
B. \( 2 x \)
c. \( x / 2 \)
D. \( 4 x \)


Oxidation that leads to formation of
sulphuric acid is catalysed by:
A. ozone
B. hydrogen peroxide
c. oxygen
D. All of the above


Explain the refection of transverse and longitudinal waves from a denser medium and a rarer medium.


Caustic soda is chemically sodium hydroxide \( (N a O H) \)
A. True
B. False


For what value of \( n \) are the \( n^{t h} \) terms of
the following two A.P's the same?
(i) \( 1,7,13,19, \dots \)
(ii) \( 69,68,67, \dots \)


The inferior vena cava
A. Divides into hepatic portal veins
B. Opens into the left auricle
C. Commences at the kidney
D. Begins at the hind end of abdomen


If the latus rectum of an ellipse \( \boldsymbol{x}^{2} \tan ^{2} \varphi+\boldsymbol{y}^{2} \sec ^{2} \varphi=1 \) is \( 1 / 2, \) then \( \varphi \)
is
\( \mathbf{A} \cdot \pi / 2 \)
в. \( \pi / 6 \)
c. \( \pi / 3 \)
D. \( 5 \pi / 12 \)


Which of the following is/are the characteristics of the family whose floral diagram is given?
(i) Aloe, Asparagus and Colchicum belong to this family
(ii) Flower is zygomorphic.
(iii) Floral formula is \( 0+P 3+3 A 3+3 G 3 \)
(Fruits are berry or capsule.
A . (i),(ii) and (iii)
B. (iii) only
c. (i) only
D. (i), (iii) and (iv)


Which one of these configurations belongs to unstable configuration?
\( A \cdot 2,8,1 \)
B. 2, 8, 8
c. 2,8
\( D \)


Gibberellins can promotes seed germination because of their influence
on
A. Rate of cell division
B. Production of hydrolyzing enzymes
c. synthesis of absicisic acid
D. Absorption of water through hard seed coat


Assuming that the number of maximum permissible shells is \( 5, \) how many elements would be there in the
periodic table?


The Coefficient of Variation is given by:
A. \( \frac{\text { Mean }}{\text { Standard deviation }} \times 100 \)
B. \( \frac{\text { Standard deviation }}{\text { Mean }} \)
c. \( \frac{\text { Standard deviation }}{\text { Mean }} \times 100 \)
D. \( \frac{\text { Mean }}{\text { Standard Deviation }} \)


If the dielectric constant of a substance
is \( K=\frac{4}{3}, \) then the
electric susceptibility \( \Psi_{e} \) is:
A \( \cdot \frac{1}{3} \)
B. 3
\( c \cdot \frac{4}{3} \)
D. \( \frac{3}{4} \)


Oxidation of pyruvate is accompanied by
A . oxidation of \( N A D^{+} \)
B. Reduction of \( N A D^{+} \)
c. oxidation of CoA
D. Reduction of CoA


Cotton fibres dipped in water absorb water through
A. Endosmosis
B. Exosmosis
c. capillarity
D. Imbibition


Prove that \( 1+2+3+\ldots .+n= \)
\( \frac{n(n+1)}{2} . \) for \( n \) being a natural
numbers.


A tangent to the curve \( y=f(x) \) at
\( \boldsymbol{p}(\boldsymbol{x}, \boldsymbol{y}) \) meets \( \boldsymbol{x}-\boldsymbol{a} \boldsymbol{x} \boldsymbol{i} \boldsymbol{s} \) at \( \boldsymbol{A} \) and \( \boldsymbol{y}- \)
axis at \( B . \) If \( \overline{A P}: \overline{B P}=1: 3 \) and
\( f(1)=1 \) then the curve also passes
through the point.
\( ^{\mathbf{A}} \cdot\left(\frac{1}{2}, 4\right) \)
B \( \cdot\left(\frac{1}{3}, 24\right) \)
c. \( \left(2, \frac{1}{8}\right) \)
D. \( \left(3, \frac{1}{28}\right) \)


Point \( A \) is at a lower electrical potential than point B. An electron between them
on the line joining them will
A. move towards A
B. move towards B
c. move at right angles to the line joining \( A \) and \( B \)
D. remain at rest


Is the given sequence an AP? If it forms
an \( A P, \) find the common difference \( d \)
and write the next three terms.
\( \mathbf{0},-\mathbf{4},-\mathbf{8},-\mathbf{1 2} \dots \)


Ray \( A O \) in medium \( I \) emerges as \( O B \) in
medium \( I I \) then refractive index of
medium \( I I \) with respect to medium \( I \)
is:
\( A \)
в. \( \frac{\partial \vec{O} A \times N_{1}^{\rightarrow} O}{O B \times N_{2} \vec{\rightarrow}} \)
c. \( \frac{\overrightarrow{A O} \cdot \overrightarrow{O P}}{\overrightarrow{O B} \cdot \overrightarrow{O P}} \)
D \( \frac{\overrightarrow{O A} \times \overrightarrow{O P}}{\overrightarrow{O B} \times \overrightarrow{O P}} \)


The plane which passes through the point (-1,0,-6) and perpendicular to the line whose direction ratios is
(6,20,-1) also passes through the point:
в. (0,0,0)
c. (2,1,-32)
D. (1,1,1)


Which of the following could be an empirical formula?
A. \( C_{4} H_{8} \)
в. \( C_{2} H_{6} \)
c. \( C H \)
D. \( C_{3} H_{6} \)


Which one of the following dienes would
you expect to be the most stable?
\( A \)
в.
\( c \)
D.


A bullet of mass \( 1 \times 10^{-2} k g \) moving
horizontally with a velocity of \( 2 \times \) \( 10^{2} m s^{-1} \) strikes a block of mass
\( 1.99 k g \) and gets embedded into it. If the
coefficient of kinetic friction between
the block and the horizontal surface is
\( 0.25, \) then the distance moved by the block with the bullet before coming to rest is
A. \( 0.4 \mathrm{m} \)
в. \( 0.8 \mathrm{m} \)
\( c \cdot 0.6 m \)
D. \( 0.2 \mathrm{m} \)


A rod PQ of mass 'm' and length 'I'
rotated about and axis through 'p' as
shown in figure.Find the moment of
inertia about axis of Rotation
A \( \cdot \frac{3 g}{2 L} \)
B. \( \frac{m l^{2}}{3} \)
c. \( \frac{m l^{2}}{3} \cos ^{2} \theta \)
D. \( \frac{m l^{2}}{3}+m l^{2} \)


\( \alpha-D-g l u \cos e \) undergoes mutarotation to
\( \alpha-D \) -glucose in aqueous solution. If at
\( 298 \mathrm{K} \) there is \( 60 \% \) conversion,
calculate \( \Delta G^{o} \) of the reaction.
\( \boldsymbol{\alpha}-\boldsymbol{D}-\boldsymbol{G} \boldsymbol{l} \boldsymbol{u} \operatorname{cose} \rightleftharpoons \boldsymbol{\beta}-\boldsymbol{D}-\boldsymbol{G} \boldsymbol{l} \boldsymbol{u} \operatorname{cose} \)
A. 0.525 kJ/mol
B. 1.005 kJ/mol
c. \( 2.45 \mathrm{kJ} / \mathrm{mol} \)
D. None of these


Find the value of \( x, y \) and \( z \) in the figure.
\( \mathbf{A} \cdot x=60^{\circ}, y=120^{\circ}, z=60^{\circ} \)
B \( \cdot x=60^{\circ}, y=60^{\circ}, z=120^{\circ} \)
\( \mathbf{C} \cdot x=120^{\circ}, y=60^{\circ}, z=60^{\circ} \)
D \( \cdot x=70^{\circ}, y=100^{\circ}, z=70^{\circ} \)


Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be a differentiable
function for all values of \( x \) and has the
peoperty that \( f(x) \) and \( f^{\prime}(x) \) have opposite signs for all values of \( x \). Then
A. \( f(x) \) is an increasing function
B. \( f(x) \) is a decreasing function
C \( \cdot f^{2}(x) \) is a decreasing function
D. \( |f(x)| \) is an increasing function


Spraying of DDT produces pollution of
A. Air
B. Air and water
c. Air and soil
D. Air, water and soil


There are 20 points on a plane, with no 3 being collinear. The number of triangles that can be formed by connecting the points is
A . 1140
в. 940
c. 380
D. 220


\( \mathrm{f} \mathrm{A}=\left[\begin{array}{lll}\mathbf{1} & \mathbf{2} & \mathbf{3} \\ \mathbf{4} & \mathbf{5} & \mathbf{6}\end{array}\right], \mathbf{B}=\left[\begin{array}{l}\mathbf{1} \\ \mathbf{0} \\ \mathbf{5}\end{array}\right] \) then \( \mathbf{A B}= \)
\( \mathbf{A} \cdot\left[\begin{array}{lll}1 & 0 & 15\end{array}\right] \)
В. \( \left[\begin{array}{lll}4 & 0 & 30\end{array}\right] \)
\( c \cdot \mid 1 \)
[34]
\( \mathbf{D} \cdot\left[\begin{array}{ll}16 & 34\end{array}\right] \)


What is activation energy?


Simplify \( x^{2}-2 x y+y^{2}=0 \)


Find the product of the roots of equation \( \left(\frac{x}{\sqrt{2}}-2\right)(x-\sqrt{2})=0 \)
\( \mathbf{A} \cdot \mathbf{4} \)
B. 3
c. 2
\( D \)


What is main difference between
angina pectoris, heart failure, cardiac arrest and heart attack? Explain.


Consider a huge charge reservoir at potential \( V=200 \) volts. A spherical
capacitor \( C_{1}=40 n F \) is brought in
contact with the charge reservoir and
then removed.
Afterwards, another spherical capacitor
\( C_{2}=30 n F \) is brought in contact with
\( C_{1} \) and removed. This process is
repeated many times. Assume that potential of reservoir does not change during this exercise. Then the charge in
\( (\mu C) \) on \( C_{2} \) after a very long time is :
A . 6
B. 3
\( c .9 \)
D. 12


\( \left.\left[\begin{array}{cc}\mathbf{2 x}+\boldsymbol{y} & \boldsymbol{y} \\ \mathbf{1 - x} & \mathbf{4 x}\end{array}\right]=\mid \begin{array}{cc}\mathbf{1} & \mathbf{- 1} \\ \mathbf{0} & \mathbf{4}\end{array}\right], \) find the
values of \( \boldsymbol{x}+\boldsymbol{y} \)


Which of the following is a general form of geometric sequence?
\( \mathbf{A} \cdot\{2,4,6,8,10\} \)
B . \{-1,2,4,8,-2\}


consider the following statements each with one or two blanks.
(i) The ascending limb of loop of Henle is impermeable to (1) but allows transport of (2)
(ii) (3) and
(4) play a significant role in producing a concentrated urine.
(iii) A fall in glomerular blood flow/glomerular blood pressure/GFR can activate the JG cells to release (5)
Which one of the following options correctly fills the blanks in any two of the statements?
A. (1)-water, (2)-electrolytes, (5)-renin
B. (3)-Henle's loop, (4)-vasa recta,
(5)-angiotensin
c. (1)-electrolytes,
(2)-water,
\( (3)- \) РСТ, \( (4)- \) DCT
D. (3)-Henle's loop, (4)-vasa recta, (5)-angiotensinogen


A solution containing \( 0.1 M Z n^{2+} \) and \( 0.01 M C u^{2+} \) saturated with \( H_{2} S . \) The \( S^{2-} \) concentration is \( 8.1 \times 10^{-31} M \)
Will \( Z n S \) and \( C u S \) precipitate? \( \boldsymbol{K}_{s p}(\boldsymbol{Z} \boldsymbol{n} \boldsymbol{S})=\boldsymbol{3} \cdot \boldsymbol{0} \times \boldsymbol{1 0}^{-2 \boldsymbol{3}} \) and
\( \boldsymbol{K}_{s p}(\boldsymbol{C u S})=\mathbf{8 . 0} \times \mathbf{1 0}^{-\mathbf{4}} \)


Find the correctly matched pair.
A. Pepsinogen - Zymogenic cells
B. HCI - Goblet cells
C. Mucous - Oxyntic cells
D. Pancreatic juice - Salivary gland
E. Ptyalin - Acinar cells


Assertion
In the acid-base titration involving a strong base and a weak acid, methyl orange can be used as an indicator
Reason
Methyl orange changes its colour in pH range 3 to 5
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which of the following are the best
methods for the preparation of cumene
\( (A) ? \)
This question has multiple correct options
\( A \)
\[
\bigcirc+\mathrm{Me} \frown^{\mathrm{Cl}}+\mathrm{AlCl}_{3} \longrightarrow(\mathrm{A})
\]
B.
\[
\left.\bigcirc+\sum_{\mathrm{Me}}^{\mathrm{Me}}\right\rangle-\mathrm{Cl}+\mathrm{AlCl}_{3} \longrightarrow(\mathrm{A})
\]
\( c \)
\[
\left.\bigcirc+\frac{\mathrm{Me}}{\mathrm{Me}}\right\rangle-\mathrm{OH}+\mathrm{BF}_{3} \longrightarrow(\mathrm{A})
\]
\( D \)
\[
\widehat{\bigcirc}+\underbrace{\mathrm{Me}}_{\mathrm{Me}}\rangle=-\frac{\mathrm{H}_{3} \mathrm{PO}_{4}}{\longrightarrow}(\mathrm{A})
\]


In three element group \( \{e, a, b\} \) where \( e \)
is the identity, \( a^{5} b^{4} \) is equal to
\( \mathbf{A} \cdot \boldsymbol{a} \)
в.
\( c \cdot a b \)
D. \( b \)


If \( \frac{\sin x}{1+\sec x}+\frac{\sin x}{\sec x-1}=2 \) where
\( 0^{\circ}<x<90^{\circ} \) then cosec \( x \) has the value
equal to
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
c. \( \sqrt{2} \)
D. \( \sqrt{3} \)


In which one of the following organisms its excretory organs are correctly stated?
A. Frog - kidneys, skin and buccal epithelium
B. Human - kidneys, sebaceous glands and tear glands
c. Earthworm - pharyngeal, integumentary and septal nephridia
D. cockroach - Malpighian tubules and enteric caeca


Evaluate \( \int_{0}^{2} x \sqrt{x+2} d x \)


Glycerol does not contain
alcoholic group.
A . \( 1^{\circ} \)
B . \( 2^{\circ} \)
\( c \cdot 3^{0} \)
D. \( 1^{0} \) and \( 2^{0} \)


Infrared radiations are used in
A. Microwave ovens
B. Long distance photography
c. Microscopes
D. Treatment of cancer


Ozonolysis of
2,5 -dimethyl-2,4-hex-diene gives total number of carbonyl compounds:


Chlorine is a bleaching agent used for bleaching cotton fabrics
A. True
B. False


Component of smog is
\( A \cdot O_{3} \)
B. PAN
c. PPN and PBN
D. Both A and B


As the concentration of reactants
increases:
A. rate of the reaction decreases
B. rate of the reaction increases
c. rate of the reaction remains the same
D. reaction stops


Keplers second law regarding constancy of arial velocity of a planet is a consequence of the law of conservation
of
A. energy
B. angular momentum
c. linear momentum
D. none of these


Pick out the two scalar quantities in the following list :force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, relative velocity


People living at sea level have around 5
million RBC per cubic millimetre of their blood whereas those living at an altitude of 5400 metres have around 8
million. This is because at high altitude
A. people eat more nutritive food, therefore more RBCs are formed
B. people get pollution-free air to breathe and more oxygen is available
C. atmospheric \( O_{2} \) level is less and hence more RBCs are needed to absorb the required amount of \( O_{2} \) to survive
D. there is more UV radiation which enhances RBC production


The enthalpies of formation of \( N_{2} O \) and
\( N O \) are 28 and \( 90 k J m o l^{-1} \)
respectively. The enthalpy of the
reaction, \( 2 N_{2} O(g)+O_{2}(g) \longrightarrow \)
\( 4 N O(g) \) is equal to :
\( A \cdot 8 k J \)
B. 88 kJ
c. \( -16 k J \)
D. 304 kJ


\( \lim _{n \rightarrow \infty}\left(\frac{(n+1)(n+2) \dots 3 n}{n^{2 n}}\right)^{\frac{1}{n}} \)
equal to :-


Prove
\[
\left|\begin{array}{ccc}
x^{2} & y^{2} & z^{2} \\
(x+1)^{2} & (y+1)^{2} & (z+1)^{2} \\
(x-1)^{2} & (y-1)^{2} & (z-1)^{2}
\end{array}\right|=
\]
\( -4(x-y)(y-z)(x-z) \)


f \( A+B+C=\pi \), then
\( \left|\begin{array}{ccc}\sin (\boldsymbol{A}+\boldsymbol{B}+\boldsymbol{C}) & \sin \boldsymbol{B} & \cos \boldsymbol{C} \\ -\sin \boldsymbol{B} & \boldsymbol{0} & \boldsymbol{t a n} \boldsymbol{A} \\ \cos (\boldsymbol{A}+\boldsymbol{B}) & -\boldsymbol{t a n} \boldsymbol{A} & \boldsymbol{0}\end{array}\right| \)
equals
A .
B. 2 \( \sin B \tan A \cos C \)
\( c \)
D. none of these


Wien's displacement law fails at:
A. low temperature
B. high temperature
c. short wavelength
D. Iong wavelength


Solve:
\( \lim _{x \rightarrow 0} \frac{(1-\cos 3 x)}{x \sin 2 x} \)


The balancing point in a meter bridge is \( 44 \mathrm{cm} . \) If the resistances in the
are gaps are inchanged the new balance point is
A. \( 44 \mathrm{cm} \)
B. 56 \( \mathrm{cm} \)
c. \( 50 \mathrm{cm} \)
D. 22 \( \mathrm{cm} \)


\( \angle A O B \) is
\( \mathbf{A} \cdot 54^{\circ} \)
B. \( 72^{\circ} \)
\( c \cdot 90^{\circ} \)
\( D \cdot 108^{\circ} \)


Which of these is not a base quantity in mechanics?
A. Charge
B. Length
c. Mass
D. Time


Find the coordinates of focus, the
equation of the directrix and length of the latus rectum of the conic
represented by the equation \( x^{2}=-y \)


In the relation, \( \boldsymbol{P}=\frac{\boldsymbol{\alpha}}{\boldsymbol{\beta}} \boldsymbol{e}^{\boldsymbol{\alpha} \boldsymbol{z} / k \boldsymbol{\theta}} \boldsymbol{P} \) is
pressure, \( Z \) is distance, \( K \) is Boltzmann
constant and \( \theta \) is the temperature. The
dimensions of \( \beta \) will be
A \( \cdot\left[M^{\circ} L^{2} T^{0}\right] \)
в. \( \left[M L^{2} T\right] \)
\( \mathbf{c} \cdot\left[M L^{\circ} T^{1}\right] \)
D. \( \left[M^{\circ} L^{2} T^{-1}\right] \)


A person sitting in an artificial satellite of earth feels weightlessness but a person standing on Moon has weight though Moon is also a satellite of earth.
Why?


A characteristic feature of ovary of Brassica campestris is
A. Presence of replum.
B. Axile placentation
c. Epigynous.
D. Multilocular nature


Which of the following is an example of
convection?
A. The heat of the sun warming our planet
B. The heat from an electric stove warming a frying pan
C . Ice cubes cooling a drink
D. A microwave oven cooking a meal
E. An overhead fan cooling a room


In the above figure, if DE \( \| \mathrm{BC} \), then \( x \)
equals:
\( A \cdot 6 \mathrm{cm} \)
B. \( 7 \mathrm{cm} \)
\( c \cdot 3 \mathrm{cm} \)
D. \( 4 \mathrm{cm} \)


The reagent used for converting benzene to ethyl benzene is:
\( \mathbf{A} \cdot C_{2} H_{5} C l, \) anhydrous \( A l C l_{3} \)
в. \( C_{2} H_{5} C l \), а \( q A l C l_{3} \)
c. \( C_{2} H_{5} O H \), anhydrous \( A l C l_{3} \)
D. \( C_{2} H_{5} C l, S O C l_{2} \)


The de-Broglie wavelength of a proton and alpha particle is same, the ratio of their velocities is :
A . 1: 2
B. 2:
\( c \cdot 1: 4 \)
D. 4:


The area of a traingle is 5 square units, two of its verices are (2,1) and \( (3,-2) . \) The
third vertex lies on \( y=x+3 \).The third vertex is
\( ^{\mathbf{A}} \cdot\left(\frac{7}{2}, \frac{3}{2}\right) \)
в. \( \left(-\frac{3}{2}, \frac{3}{2}\right) \)
c. \( \left(-\frac{3}{2}, \frac{13}{2}\right) \)
D \( \cdot\left(\frac{7}{2}, \frac{5}{2}\right) \)


Assertion
STATEMENT 1 (Assertion)- The oxidizing
power is maximum for \( \boldsymbol{H} \boldsymbol{C l O}_{4} \) and
least for HCIO.
Reason
STATEMENT 2 (Reason)-With increase
in oxidation number of chlorine,the
thermal stability of the anion of the oxyacid increases.
A. Statement 1 is True, statement 2 is True; 'statement 2 is a correct explanation for statement 1
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


Let \( \boldsymbol{f}(\boldsymbol{x}) \) be a differentiable function in
\( [2,7] . \) If \( f(2)=3 \) and \( f^{\prime}(x) \leq 5 \) for all \( x \)
in \( (2,7), \) then the maximum possible
value of \( f(x) \) at \( x=7 \) is
\( A \cdot 7 \)
B. 15
c. 28
D. 14


The radius of a circle is increasing uniformly at the rate of \( 5 \mathrm{cm} / \mathrm{sec} \). Find
the rate at which the area of the circle is
increasing when the radius is \( 6 \mathrm{cm} \)


When the earth is far away from the
sun, its travels slower. This is due to
A. Potential energy is higher, hence it travels slower
B. Inertia of the earth make it to go in straight line
C. Kinetic energy is lower and hence it travels slower
D. tend to get attracted by other planets and hence it becomes slower


\( \left[\begin{array}{ccc}-\boldsymbol{C H}_{2}- & \boldsymbol{C H}-\boldsymbol{C H}_{2}- & \boldsymbol{C H}-\boldsymbol{C I} \\ & \boldsymbol{O H} & \boldsymbol{O H}\end{array}\right. \)
Polyvinyl alcohol (as shown above) is a unique polymer having high affinity for water. Which of the following procedures would be most suitable for
its preparation?
A . radical chain polymerisation of \( C H_{2}=C H-C H_{2} \)
\( O H \)
B. radical chain polymerisation of \( C H_{2}=C H-O H \)
c. radical chain polymerisation of \( C H_{2}=C H- \) \( C O_{2} C H_{3}, \) following by base catalysed hydrolysis
D. radical chain polymerisation of \( C H_{2}=C H- \) \( O C O C H_{3}, \) followed by acid catalysed hydrolysis
E. radical chain polymerisation of \( C H_{2}=C H- \) \( O C O C H_{3}, \) followed by base catalysed hydrolysis


In figure, DE||BC, then the value of \( x \)
equals to:
A. \( 2.5 \mathrm{cm} \)
B. \( 2 \mathrm{cm} \)
c. \( 1.4 \mathrm{cm} \)
D. \( 4 \mathrm{cm} \)


A fuse is always connected in the live wire of the circuit. Explain the reason


Evaluate:
\( \int \frac{x^{3}}{\sqrt{1+x^{2}}} d x \)


Two exactly similar wires of steel \( (\mathrm{y}=20 \) \( x 10^{11} \) dyne \( / \mathrm{cm}^{2} \) ) and copper \( (\mathrm{y}=12 \times 10 \)
11 dyne /cm \( ^{2} \) )are stretched by equal forces. If the total elongation is \( 1 \mathrm{cm} \) elongation of copper wire is
\( \mathbf{A} \cdot 3 / 5 \mathrm{cm} \)
в. \( 5 / 3 c m \)
\( \mathbf{c} \cdot 3 / 8 c m \)
D. \( 5 / 8 c m \)


Classify the following as physical or chemical change.
Metallic sodium is soft enough to be cut
with a knife.
A. Chemical
B. Physical
c. Both \( A \) and \( B \)
D. None of these


What is ten times the square root of the
following decimal number:
\( \mathbf{7 . 2 9} \)


Decide whether set \( A \) and \( B \) are equal
sets. Given reason for your answer
\( A= \) Even prime number \( \mathrm{B}=\{\boldsymbol{x}, \mathbf{7} \boldsymbol{x}-\mathbf{1}=\mathbf{3}\} \)


Microwaves are detected by
A. barometer
B. point contact diodes
C. thermopiles
D. the eye


The reaction between \( H_{2} \) and \( C l_{2} \) in
direct sun light is explosive.
A. True
B. False


The 'lubb' and "dubb" heart sound are
due to
A. Opening of heart valves
B. Action of papillary muscles
c. closing of heart valves
D. Activity of pacemaker


The temperature on the Celsius scale is
\( 25^{\circ} C . \) What is the
corresponding temperature on the Fahrenheit scale?
\( \mathbf{A} \cdot 40^{\circ} F \)
В \( \cdot 77^{\circ} \)
\( \mathbf{c} \cdot 50^{\circ} F \)
D. \( 45^{\circ} \) F


The displacement (s) of a particle moving along a straight line is related
to time \( t \) as \( s=a t^{3}+b t^{3}+c t, \) where
\( a, b \) and \( c \) are constants. What is the ratio of its initial velocity and initia
acceleration?
\( A \cdot \infty \)
в. \( \frac{b}{2 c} \)
c. \( \frac{c}{2 c} \)
D.


When a Dobereiner's triad is
considered, the sum of atomic weights of the terminal elements \( X \) and \( Z \) is
162.5. The atomic weight of \( Z \) is 50 units
less than 5 times that of \( X \). Identify the
periods of \( X, Y \) and \( Z \) respectively in the present periodic table.
A. 3,4,5
в. 4,5,6
c. 2,3,4
D. 3,5,4


\( \int_{0}^{\pi / 2} \frac{d x}{1+\tan x} \)
This question has multiple correct options
A . a multiple of \( \pi / 4 \)
B. a multiple of \( \pi / 2 \)
c. equal to \( \pi / 4 \)
D. a multiple of \( \pi \)


A parallel plate capacitor is charged by a battery and the battery remains connected, a dielectric slab is inserted
in the space between the plates. Explain what changes if any, occur in the values of the
(i) potential difference between the plates
(ii) electric field between the plates
(ii) energy stored in the capacitor


The diversity in the type of beaks of finches adapted to different feeding habits on the Galapagos Islands, as observed by Darwin, provides evidence for
A. Intraspecific competition
B. Interspecific competition
c. origin of species by natural selection
D. Origin of species by mutation


Which of the following metal is used in atomic energy and space projects?
A . Titanium
B. Zirconium
c. sodium
D. All of above


The impurity in white bauxite is:
A. \( F e O \)
в. \( F e_{2} O_{3} \)
\( \mathrm{c} \cdot \operatorname{sio}_{2} \)
D. \( A l C l_{3} \)


Describe the primary structure of monocot root.


Atmosphere maintain the temperature on the surface of earth because
A. It contains water vapour in it
B. It holds air, which is a bad conductor of heat
c. It reflects the heat rays.
D. It absorbs the heat rays


The transfer of pollens from anther to stigma of the same flower is called as
A. Cross pollination
B. Self-fertilization
c. cross breeding
D. Hybridization


The slopes of two line segments are equal. Which of the following is correct?
A. The line segments are parallel.
B. The end points of the line segments are collinear
c. The line segments are perpendicular.
D. The ends points of the line segments are n


Assertion
Angle of repose is equal to the angle of
limiting friction.
Reason
When the body is just at the point of motion, the force of friction in this stage
is called limiting friction
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


Two circular rings of equal mass \( (\boldsymbol{m}) \) and radius \( (r) \) are placed side by side, touching each other. The moment of inertia of the system about tangential axis in the plane of system passing through point of contact of the rings is:
A \( \cdot \frac{3}{2} m r^{2} \)
B. \( 6 m r^{2} \)
c. \( \frac{5}{2} m r^{2} \)
\( D \cdot 3 m r^{2} \)


The lanthanide series starts from and
ends in which atomic number?
\( \mathbf{A} \cdot 55,68 \)
B. 56,69
c. 57,70
D. 58,71


It is better to wear , wered clothes in
summer.
A . black
B . light
C. neither A nor B
D. either A or B


Which of the following equation is not a balanced chemical reaction?
A \( \cdot P_{4}+20 H N O_{3} \rightarrow 4 H_{3} P O_{4}+20 N O_{2}+4 H_{2} O \)
B . \( I_{2}+10 H N O_{3} \rightarrow 2 H I O_{3}+10 N O_{2}+4 H_{2} O \)
c. \( S+6 H N O_{3} \rightarrow H_{2} S O_{4}+6 N O_{2}+2 H_{2} O \)
D. None of these


A uniform circular disc of radius is taken. A circular portion of radius b has
been removed from its as shown in the
figure. If the centre of hole is at a
distance c from the centre of the disc,
the distance \( x_{2} \) of the centre of mass of
the remaining part from the initial
centre of mass 0 is given by :
A \( \cdot \frac{\pi b^{2}}{a^{2}-c^{2}} \)
B. \( \frac{b^{2} c}{\left(a^{2}-b^{2}\right)} \)
c. \( \frac{\pi e^{2}}{a^{2}-b^{2}} \)
D. \( \frac{c a^{2}}{c^{2}-b^{2}} \)


Ray optics is valid when characteristic dimension are
A. much smaller than wavelength of light.
B. of same order as wavelength of light
c. much larger than wavelength of light
D. none of the above


A cyclist bends while taking turn to
A. Reduce friction
B. Generate required centripetal force
c. Reduce apparent weight
D. Reduce speed


The ratio between the curved surface
area and the total surface area of a
right circular cylinder is \( 1: 2 . \) Find the
volume of the cylinder if its total surface area is \( 616 \mathrm{cm} \) sq.


What are the coordinates of \( \boldsymbol{S} \) ?
\( A \cdot(3,2) \)
B. (3,-2)
\( c \cdot(-2,3) \)
D. (-3,-2)


A small, flat coil of resistance \( r \) is
placed at the centre of a large, closed coil of resistance \( R \). The coils are
coplanar and their mutual inductance
is \( M . \) Initially, a constant current \( i \) was
flowing in the inner coil. If this current is suddenly switched off, what charge will circulate in the other coil?
A. \( \operatorname{Mir} / R^{2} \)
в. \( M i R / r^{2} \)
с. \( M i / R \)
D. \( M i / r \)


Assertion
We can live very happily if the friction is
not present in nature.
Reason
Aeroplane shape is stream lined to
reduce the effort of frictional force.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


The Vant Hoff factor (i) for a dilute
solution of \( \boldsymbol{K}_{\mathbf{3}}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{\boldsymbol{6}}\right] \) is (Assuming
\( 100 \% \text { ionsation }) \)
A . 10
B. 4
c. 5
D. 0.25


Assertion
Galvanic cell convert chemical energy into electrical energy.
Reason
Redox reactions are those in which
oxidation takes place at anode and reduction at cathode.
A. If both Assertion and Reason are correct and Reason is the correct explanation of assertion
B. If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion
C. If Assertion is correct but Reason is incorrect
D. If Assertion is incorrect but Reason is correct


Give one example each of Iyophobic sol and lyophillic sol.


Who had introduced the binomial
system of naming living beings?


In an experiment on photoelectric effect, Light of wavelength 800 nm (less than threshold wavelength) is incident
on a cesium plate at the rate of \( 5.0 \mathrm{W} \) The potential of the collector plate is made sufficiently positive with respect on the emitter so that the current
reaches its saturation value. Assuming
that on the average one of every \( 10^{6} \)
photons is able to eject a photoelectron,
find the photo current in the circuit.


The energy currency of the cell is


Which of the following molecules contain odd electron bonds?
This question has multiple correct options
\( A \cdot H_{2} O \)
B. \( N O \)
\( c \cdot N O_{2} \)
D. \( C l O_{2} \)


Point \( P(2,3) \) lines on the \( 4 x+3 y=17 \)
Then find the co-ordinated of points
farthest from the line which are at 5
units distance from the P.
A. (6,6)
(年) 6,6,6
в. (6,-6)
D. (-2,0)


The differential equation whose solution is \( (\boldsymbol{x}-\boldsymbol{h})^{2}+(\boldsymbol{y}-\boldsymbol{k})^{2}=\boldsymbol{a}^{2} \) is
\( (a \text { is a constant }) \)
\( ^{\mathbf{A}} \cdot\left[1+\left(\frac{d y}{d x}\right)^{2}\right]^{3}=a^{2} \frac{d^{2} y}{d x^{2}} \)
B \( \cdot\left[1+\left(\frac{d y}{d x}\right)^{2}\right]^{3}=a^{2}\left(\frac{d^{2} y}{d x^{2}}\right)^{2} \)
\( ^{\mathbf{c}} \cdot\left[1+\left(\frac{d y}{d x}\right)\right]^{3}=a^{2}\left(\frac{d^{2} y}{d x^{2}}\right)^{2} \)
D. None of these


The value of \( \boldsymbol{K}_{\boldsymbol{p}} \) is \( 1 \times 10^{-3} \boldsymbol{a} \boldsymbol{t m}^{-1} \) at \( \boldsymbol{2 5} \)
for the reaction \( : 2 N O+C l_{2} \rightleftharpoons \)
2 NOCl. A flask contains \( N O \) at
\( 0.02 a t m \) at \( 25^{0} C . x \times 10^{-2} \) mole of \( C l_{2} \)
must be added if \( 1 \% \) of the \( N O \) is to be
converted to \( N O C l \) at equilibrium. The
volume of the flask is such that 0.2
mole of gas produce 1 atm pressure at
25. Also \( y \times 10^{-5} \) mole of \( C l_{2} \) used.
(lgnore probable association of \( N O \) to
\( N_{2} O_{2} . \)
Then calculate the value of \( x \) and \( y \)


Lines \( \mathrm{PQ} \) and \( \mathrm{RS} \) intersect at \( \mathrm{O} \). If
\( \angle P O S=2 \angle S O Q, \) then the four angles
at 0 are:
A \( \cdot 30^{\circ}, 30^{\circ}, 120^{\circ}, 180^{\circ} \)
B . \( 60^{\circ}, 60^{\circ}, 120^{\circ}, 120^{\circ} \)
c. \( 60^{\circ}, 90^{\circ}, 90^{\circ}, 120^{\circ} \)
D. \( 30^{\circ}, 60^{\circ}, 90^{\circ}, 180^{\circ} \)


At constant temperature, the
equilibrium constant \( \left(\boldsymbol{K}_{\boldsymbol{p}}\right) \) for the
decomposition reaction. \( N_{2} O_{4} \rightleftharpoons \)
\( 2 N O_{2} \) is expressed by
\[
\begin{array}{c}
\boldsymbol{K}_{\boldsymbol{p}}=\frac{\left(\boldsymbol{4} \boldsymbol{x}^{2} \boldsymbol{P}\right)}{\left(\mathbf{1}-\boldsymbol{x}^{2}\right)} \\
\text { where, } \boldsymbol{P}=\text { pressure, } \boldsymbol{x} \text { =extent of }
\end{array}
\]
decomposition. Which of the following
statements is true?
\( \mathbf{A} \cdot K_{p} \) increases with increase of \( P \)
B. \( K_{p} \) increases with increase of \( x \)
C. \( K_{p} \) increases with decrease of \( x \)
D. \( K_{p} \) remains constant with change in \( P \) and \( x \) decreases with pressure


How many structures are possible for \( C_{5} H_{8} \) with one triple bond?
\( A \cdot 4 \)
B. 3
\( c \cdot 2 \)
D.


The graph between temperature and
pressure of a perfect gas is
A. hyperbola.
B. parabola.
C . a straight line parallel to pressure axes at \( 73^{0} C \).
D. a straight line intercepting the temperature axes at \( 273^{0} C \)


Which wavelength of sun is used finally as electric energy?
A. Radio waves
B. Infrared waves
c. visible light
D. Micro waves


Destruction of large eco-systems occurs during the harnessing of
A. geothermal energy
B. tidal energy
c. wind energy
D. hydroelectric energy


Let \( V_{s} \) be the speed of the source
emitting sound waves, \( n \) the actual
frequency of the source of sound, \( V \) the speed of the sound in the medium and
\( n_{1} \) the frequency of sound waves as
perceived by a stationary observer to whom the source of sound is
approaching. The formula for
calculating \( n_{1} \) is :
\( \mathbf{A} \cdot \mathbf{n}_{1}=\mathbf{n}\left(1-\mathbf{V}_{\mathbf{s}} / \mathbf{V}\right) \)
B. \( n_{1}=n\left(\frac{V}{V-V_{s}}\right) \)
\( \mathbf{c} \cdot \mathbf{n}_{1}=\mathbf{n} /\left(1+\mathbf{V}_{\mathbf{s}} / \mathbf{V}\right) \)
\( \mathbf{D} \cdot \mathbf{n}_{1}=\mathbf{n} \)


Which of the following give \( \boldsymbol{S}_{\boldsymbol{N}} \mathbf{1} \)
reaction?
Select the correct answer.
I.
II.
III.
\( \mathbf{I V} \)
\( \mathbf{A} \cdot(I),(I I) \) and \( (I I I) \)
B. \( (I) \) and \( (I I) \)
C \( .(I I),(I I I) \) and \( (I V) \)
D. \( (I),(I I I) \) and \( (I V) \)


Triangles \( A B C \) and \( P Q R \) are similar
What is the length of PQ?
\( A \)
B. 10.5
\( c \cdot 13 \)
D. 15


A man spends \( \frac{1}{5} \) of his salary to meet pocket expenses and \( \frac{4}{5} \) of the
remainder to meet other expenses If his
monthly savings amount to Rs 1200 his monthly salary is
\( A \cdot R s 3,750 \)
B. Rs 8,500
c. \( R s 7,000 \)
D. Rs 7,500


When acetone in treated with
sodium bisulphite, the compound formed is :
\( A \)
\[
\mathrm{CH}_{3}-\underset{\mathrm{SO}_{3}^{\prime} \mathrm{Na}}{\mathrm{C}}^{\mathrm{OH}}-\mathrm{CH}_{3}
\]
в.
\[
\mathrm{CH}_{3}-\begin{array}{c}
\text { он } \\
\mathrm{C} \\
\mathrm{s} 0_{3}^{\prime} \mathrm{Na}
\end{array}-\mathrm{H}
\]
\( c \)
\[
\mathrm{CH}_{3}-\stackrel{\mathrm{O}_{3}^{\mathrm{Na}}}{\mathrm{C}}-\mathrm{CH}_{3}
\]
D.
\[
\mathrm{CH}_{3}-\stackrel{\mathrm{O}_{3}}{\mathrm{C}}-\mathrm{H}
\]


The frequency of a sound wave is
\( 250 H z \) and its wavelength is \( 100 c m \)
The distance travelled by a sound wave
in the time taken to produce 100 waves is


\( \boldsymbol{f}:(-\infty, \infty) \rightarrow(-\infty, \infty) \) is defined by
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{a} \boldsymbol{x}+\boldsymbol{b} ; \boldsymbol{a}, \boldsymbol{b} \in \boldsymbol{R}(\boldsymbol{a} \neq \mathbf{0}) \) then \( \boldsymbol{f} \)
is
A. injective but not surjective
B. surjective but not injective
c. bijective
D. neither injective nor surjective


The solution of \( \frac{d y}{d x}=\frac{\sqrt{x^{2}-y^{2}}+y}{x} \)


The nuclear radius is of the order of
B. \( 10^{-6} \) m
\( \mathbf{c} \cdot 10^{-15} m \)
D. \( 10^{-14} m \)


Select correct statement(s).
A \( . \) Equivalent mass of \( X e O_{3}= \) \( \frac{\text {molar mass}}{6} \) and Equivalent mass of \( H X e O_{4}^{-}= \)
\( \frac{\text { molar mass }}{6} \)
B. As reaction I or II goes to forward side, pressure increases
C. Both are correct statements
D. None of the above is correct statement


Determine the area of the shaded
segment
A . 10
B. 11
\( c .12 \)
D. 13


Two electric lines of force never
intersect.
A . True
B. False


Identify the semiconductor devices
whose characteristics are given above
in the order \( (a),(b),(c),(d): \)
(a)
\( (b) \)
\( (c) \)
A. Simple diode, Zener diode, Solar cell, Light dependent resistance
B. Zener diode, Simple diode, Light dependent resistance, Solar cell
C. Solar cell, Light dependent resistance, Zener diode Simple diode
D. Zener diode, Solar cell, Simple diode, Light dependent resistance


If \( \int_{a}^{b} \frac{f(x)}{f(a)+f(a+b-x)} d x=10, \) then
This question has multiple correct options
A. \( b=22, a=2 \)
В. \( b=15, a=-5 \)
c. \( b=10, a=-10 \)
D. \( b=10, a=-2 \)


Assertion: When radius of a circular wire
carrying current is doubled, its magnetic
moment becomes four times
Reason: Magnetic moment is
directly proportional to area of the loop
A. Both A and R are true and R is the correct explanation of A.
B. Both \( A \) and \( R \) are true and \( R \) is not correct explanation of A.
C. \( A \) is true, but \( R \) is false
D. A is false, but R is true


Which aqueous solution has minimum
freezing point?
в. 0.005 М \( C_{2} \) Н \( _{5} \) ОН
c. 0.005 М \( M g I_{2} \)
D. \( 0.005 \mathrm{M} \mathrm{MgSO}_{4} \)


A ladder of length \( 20 m \) is resting
against a wall \( 10 m \) high such that the
top of the ladder touches the top edge of the wall. Find the distance of the foot of the ladder from the foot of the wall?
A \( \cdot \frac{10}{\sqrt{3}} m \)
в. \( 10 m \)
c. \( 10 \sqrt{3} \mathrm{m} \)
.
D. 30 \( m \)


What is the angle of deviation produced
by a glass slab? Explain with ray diagram.


Which of the following does not have \( s-s \) linkage?
\( A \cdot S_{2} O_{8}^{2-} \)
B. \( S_{2} O_{6}^{2-} \)
\( \mathrm{c} \cdot S_{2} O_{5}^{2} \)
D. \( S_{2} O_{3}^{2-} \)


Identify the functional group in Product
B?
\[
\sqrt{ }+\mathrm{NBS} \longrightarrow \mathrm{A}-\frac{(\mathrm{i}) \mathrm{Mg} / \mathrm{ether}}{(\mathrm{ii}) \mathrm{CO}_{2} / \mathrm{H}_{3} \mathrm{O}^{\oplus}}
\]
A. Ketone
B. Carboxylic acid
c. aldehyde
D. none


A simple pendulum is vibrating with an
angular amplitude of \( \frac{r}{2} . \) The value of \( \alpha \)
for which the resultant acceleration has
a direction along the horizontal is :
\( \mathbf{A} \)
\( \frac{\pi}{2} \)
B. \( 180^{\circ} \)
c. \( \cos ^{-1}\left(\frac{1}{\sqrt{3}}\right) \)
D. \( \cos ^{-1}\left(\frac{1}{\sqrt{2}}\right) \)


Let \( f(x) \) be a polynomial of degree four
having extreme values at \( x=1 \) and \( c=2 . \) If \( \lim _{x \rightarrow 0}\left[1+\frac{f(x)}{x^{2}}\right]=3, \) then \( f(2) \)
is equal to
A . -8
B. -4
c. 0
D. 4


Fill in the blanks with correct word(s) to
make the statement true:
A radius of a circle is a line segment with one end point at and the
other end point on


In an electrolytic cell, the current flows
from:
A. cathode to anode in outer circuit
B. anode to cathode outside the cell
c. cathode to anode inside the cell
D. current does not flow


If \( x \) is increased by \( k \) then \( \sigma \) changes to
\( \mathbf{A} \cdot k+\sigma \)
в. \( k \sigma \)
c. \( k \sqrt{\sigma} \)
D. remains unchanged


Test scores out of 100 for a class of 20
students are as follows:
93,84,97,98,100,78,86,100,85,92,55
Find the interval that contains the
median
A. \( 81-90 \)
В. \( 71-80 \)
c. \( 71-90 \)
D. None of these


Nitrogen (I) oxide is produced by:
A. thermal decomposition of sodium nitrite at low temperature
B. thermal decomposition of ammonium nitrite
C. disproportionation of \( N_{2} O_{4} \)
D. interaction of hydroxyl amine and nitrous acid


\( (148) \div(-4)= \)
\( A \cdot+37 \)
B. -37
\( c \cdot-38 \)
D. None of these


If \( \boldsymbol{f}(\boldsymbol{x})=\sqrt{1}+\sqrt{\boldsymbol{x}}, \boldsymbol{x}>0, \) then \( \boldsymbol{f}(\boldsymbol{x}) \)
\( f^{\prime}(x) \) is equal to
A \( \cdot \frac{1}{2 \sqrt{x}} \)
B. \( \frac{1}{2} \)
c. \( \frac{1}{4 \sqrt{x}} \)
D. \( \frac{2 \sqrt{x}+1}{4 \sqrt{x}} \)


A mass of \( 30 \mathrm{kg} \) is supported on a spring of stiffness \( 60000 \mathrm{N} / \mathrm{m} \). The system is damped and the damping ratio is \( 0.4 . \) The mass is raised \( 5 \mathrm{mm} \)
and then released. Calculate the
damped frequency in Hz.
A. 6.235
B. 6.352
c. 6.523
D. 6.325


Nitrolim is obtained by heating calcium carbide in :
A. \( \mathrm{H}_{2} \)
в. \( \mathrm{O}_{2} \)
\( c \cdot N_{2} \)
D. NH


Assertion
Alkenes usually undergo electrophilic addition reaction at carbon-carbon
double bond.
Reason
Electrophilic addition at double bond produces carbocation intermediate.
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


Write the IUPAC name of the given
compound


Construct a perpendicular line from
point \( p \) to any line \( A B \)


\( \mathrm{ff}=\left[\begin{array}{ccc}\boldsymbol{a} & \mathbf{0} & \mathbf{0} \\ {[\mathbf{0 . 3 e m}] \mathbf{0}} & \boldsymbol{a} & \mathbf{0} \\ {[\mathbf{0 . 3 e m}] \mathbf{0}} & \mathbf{0} & \boldsymbol{a}\end{array}\right], \) then the value
of IAdj. Al is equal to
A \( \cdot a^{3} \)
в. \( a^{6} \)
\( c \cdot a^{9} \)
\( \mathbf{D} \cdot a^{2} \)


The complex ion \( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right]^{+2} \) is
readily oxidized to \( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right]^{+3} \)
A . True
B. False


How many time will the wheel of a can
rotation in a iorrney of \( 88 \mathrm{km} \), given that the diameter of the wheel is \( 56 \mathrm{cm} \) ?


Assertion
In metallurgy calcination use for
purification of metals
Reason
Calcination is a chemical process wherein a carbonate ore or an oxide ore
is strongly heated in the absence of air, to decompose it to remove volatile
matter and moisture.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is incorrect but Reason is correct
D. Both Assertion and Reason are incorrect


A biconvex lens of focal length f forms a circular image of radius r of sun in focal plane. Then which option is correct?
A \( \cdot \pi r^{2} \propto f \)
В \( \cdot \pi r^{2} \propto f^{2} \)
c. If lower half part is covered by black sheet, then area of the image is equal to \( \pi r^{2} / 2 \)
D. If fis doubled, intensity will increase


The electric field in the region \( r<a \) is
\( \boldsymbol{E}=\frac{\boldsymbol{Y} \boldsymbol{Q} \boldsymbol{r}}{\boldsymbol{a}^{3}} . \) Find \( \boldsymbol{Y} ? \)


In which major group of fungi is the common black bread mould placed?
A. zygomycetes
B. Ascomycetes
c. Basidiomycetes
D. Sporomycetes


Compound with the geometry square pyramidal and \( s p^{3} d^{2} \) hybridisation is:
A \( . \quad X e O F_{2} \)
в. \( X e O F_{4} \)
\( \mathbf{c} \cdot X e O_{4} \)
D. \( X e O_{2} F_{2} \)


The supply voltage to room is 120 \( V \). The
resistance of the lead wires is \( 6 \Omega . \) A
\( 60 W \) bulb is already switched on. What
is the decrease of voltage across the bulb, when a \( 240 W \) heater is switched
on in parallel to the bulb?
A . zero
в. 2.9 volt
c. 13.3 volt
D. 10.04 Volt


A parallel plate condenser of capacity \( 10 \mu F \) is connected to an A.C. supply
voltage \( e=4 \sin (100 \pi t) . \) The
maximum displacement current:
A. \( 4 \pi \mu A \)
в. \( 4 \pi m A \)
c. \( 2.8 \pi \mu A \)
D. \( 2 \pi \mu A \)


The value of \( \cos ^{-1}\left(\cos \frac{5 \pi}{3}\right)+ \)
\( \sin ^{-1}\left(\sin \frac{5 \pi}{3}\right) \) is
A \( \cdot \frac{\pi}{2} \)
В. \( \frac{5 \pi}{2} \)
\( c \cdot \frac{10 \pi}{2} \)
D.


What is a uriniferous tubule? How does
it function?


Generate a polynomial equation if \( \boldsymbol{A} \) is
singular. \( \boldsymbol{A}=\left[\begin{array}{ccc}\boldsymbol{x}-\mathbf{1} & \mathbf{1} & \mathbf{1} \\ \mathbf{1} & \boldsymbol{x}-\mathbf{1} & \mathbf{1} \\ \mathbf{1} & \mathbf{1} & \boldsymbol{x}-\mathbf{1}\end{array}\right] \)


Study of physico-chemical nature of bio-molecules is
A. Biochemistry
B. Physiology
c. Oenology
D. Biotechnology.


The figure shows the field lines of a
positive point charge. The work done by
the field in moving a small positive
charge from \( Q \) to \( P \) is:
A. zero
B. Positive
c. Negative
D. Data insufficient


The potentiometer is more appropriate
for measuring potential difference than
a voltmeter because
A. the resistance of voltmeter is high
B. the sensitivity of a potentiometer is higher than that of voltmeter
C. the resistance of potentiometer wire is very low
D. the potentiometer does not draw any current from the unknown source of emf


The amount of light reflected depends
upon
A. the nature of material of the object
B. the nature of the surface
c. the smoothness of the surface
D. all the above


\( \boldsymbol{S} \boldsymbol{i} \boldsymbol{O}_{2}(\boldsymbol{s})+\boldsymbol{N} \boldsymbol{a} \boldsymbol{O} \boldsymbol{H}(\boldsymbol{l}) \rightarrow \boldsymbol{N} \boldsymbol{a}_{2} \boldsymbol{S} \boldsymbol{i} \boldsymbol{O}_{3}(\boldsymbol{a} \boldsymbol{q}) \)
\( +? \)
A \( \cdot H_{2} O(l) \)
в. \( H_{2}(g) \)
c. \( H_{3} O^{+} \)
D. \( O H^{-} \)


The respiratory organs of silkworm is called as
A. Lungs
B. Tracheae
c. Malpighian tubules
D. skin


Limiting friction is
A. Directly proportional to the area of contact
B. Inversely proportional to the area of contact
C. Independent on the area ofcontact
D. All of these


A ray of light passing through a prism having \( \mu=\sqrt{2} \) suffer minimum deviation. It is found that angle of incidence is double the angle of
refraction within the prism. Find angle of the prism.


The 17 th term of an \( A . P . \) is 5 more than
twice its \( 8 t h \) term. If the \( 11 t h \) term of
the \( A . P \) is 43 , find the \( n t h \) term.


In a mononuclear tetrahedral complex,
optical isomerism cannot arise, unless:
A. all ligands are same
B. all ligands are different
c. the ligands are of two types
D. the ligands are of three types


\( \boldsymbol{K}_{c} \) for the reaction \( \boldsymbol{A}+\boldsymbol{B} \stackrel{\frac{\boldsymbol{K}_{1}}{\boldsymbol{K}_{2}}} \boldsymbol{C}+\boldsymbol{D}, \) is
equal to:
A \( \cdot \frac{K_{1}}{K_{2}} \)
в. \( K_{1} K_{2} \)
\( \mathbf{c} \cdot K_{1}-K_{2} \)
D. \( K_{1}+K_{2} \)


Two numbers \( b \) and \( c \) are chosen at
random (with replacement) from the
numbers 1,2,3,4,5,6,7,8 and \( 9 . \) The probability that \( x^{2}+b x+c>0 \) for all
\( c \in \boldsymbol{R} \) is \( \frac{\mathbf{4} k}{81} . \) Find the value of \( \boldsymbol{k} ? \)


Read carefully the sequence of codons
in the mRNA unit and answer the
questions.
(a) What change is needed in the first codon to start the translation process?
(b) If translation starts by that change, till which codon it can continuous?
Why?


A laser lamp is of \( 9 m W \) diameter \( = \)
\( 2 m m . \) Then what is the amplitude of
magnetic field associated with it?
A \( .49 \mu T \)
B. \( 98 \mu T \)
c. \( 9.8 \mu T \)
D. \( 4.9 \mu T \)


Calculate the values of the
determinants:
\( \left|\begin{array}{ccc}\boldsymbol{b}+\boldsymbol{c} & \boldsymbol{a} & \boldsymbol{a} \\ \boldsymbol{b} & \boldsymbol{c}+\boldsymbol{a} & \boldsymbol{b} \\ \boldsymbol{c} & \boldsymbol{c} & \boldsymbol{a}+\boldsymbol{b}\end{array}\right| \)


Of the following species, one which is non-existent :
A. \( X e F_{6} \)
в. \( X e F_{5} \)
c. \( X e F_{4} \)
D. \( X e F_{2} \)


Let \( y=f(x) \) be the solution of \( \frac{d y}{d x}=\frac{y}{x}+ \) \( \tan \frac{\boldsymbol{y}}{\boldsymbol{x}}, \boldsymbol{y}(1)=\boldsymbol{\pi} / 2 \) then


Write two slogans to spread awareness
about biodiversity


Plot a graph showing variation of current versus voltage for the material
Ga.


With what minimum acceleration can a
fireman slide down a rope whose
breaking strength is two third of his weight ?
\( \mathbf{A} \cdot g / 2 \)
в. \( 2 g / 3 \)
\( c \cdot g / 3 \)
D. \( 3 g / 4 \)


The balanced chemical equation for the
reaction of iron \( (I I I) \) oxide and carbon
monoxide is :
A \( \cdot F e_{2} O_{3}+3 C O \rightarrow 2 F e O+2 C O_{2} \)
в. \( F e_{2} O_{3}+3 C O \rightarrow 2 F e+3 C O \)
c. \( F e_{2} O_{3}+3 C O \rightarrow 2 F e+3 C O_{2} \)
D. \( 2 F e_{2} O_{3}+3 C O \rightarrow 4 F e O+3 C O_{2} \)


Proteins are biopolymers. Their monomeric units are:
A. Carbohydrates
B. Amino acids
c. Fatty acids
D. Alkenes


Corrosion is a chemical reaction that
involves:
A. The inside of the object changing from an element to a compound
B. The surface of the object changing from an element to a compound
C. Nothing happens
D. The surface of the object changes from one element into another element


Which of the following statements
is/are true in case of rainbow?
This question has multiple correct options
A. In the morning a rainbow can be seen in the east.
B. In the morning a rainbow can be seen in the west.
C. In the evening a rainbow can be seen in the east.
D. In the evening a rainbow can be seen in the west.


Car \( A \) and car \( B \) start moving simultaneously in the same direction along the line joining them. Car \( A \) with a
constant acceleration \( \boldsymbol{a}=\mathbf{4} \boldsymbol{m} / \boldsymbol{s}^{2} \)
while car \( B \) moves with a constant
velocity \( \boldsymbol{v}=\mathbf{1} \boldsymbol{m} / \boldsymbol{s} . \) At time \( \boldsymbol{t}=\mathbf{0}, \) car \( \boldsymbol{A} \)
is \( 10 m \) behind car \( B \). Find the time
when car \( A \) overtakes car \( B \)


Draw the ray diagram of image formation in case of compound microscope.


Which of the following statements is
the inverse of
"lf you do not understand geometry, then you do not know how to reason deductively." ?
A. If you reason deductively, then you understand geometry.
B. If you understand geometry, then you reason deductively
c. If the do not reason deductively, then you understand geometry
D. None of the above


Mention the advantage of alternating current over direct current


What happens when zinc or iron react with dilute sulphuric acid.Explain your answer by giving suitable chemical
equation. Why does copper not show similar behaviour?


The angle between \( \overrightarrow{\boldsymbol{R}}=\mathbf{2} \hat{\mathbf{i}}+\mathbf{3} \hat{\boldsymbol{j}}-\mathbf{4} \hat{\boldsymbol{k}} \)
and y-axis is
\( ^{\mathrm{A}} \cdot \cos ^{-1}\left(\frac{2}{\sqrt{29}}\right) \)
в. \( \cos ^{-1}\left(\frac{3}{\sqrt{29}}\right) \)
\( ^{\mathrm{c}} \cdot \sin ^{-1}\left(\frac{3}{\sqrt{29}}\right) \)
D \( \cdot \tan ^{-1}\left(\frac{3}{\sqrt{29}}\right) \)


Find the sum to n terms of the
sequence, \( 8,88,888,8888, \dots \)


An object falling freely from rest reaches ground in \( 2 s . \) If acceleration
due to gravity is \( 9.8 m s^{-2}, \) the velocity of object on reaching the ground will be
\( \mathbf{A} \cdot 9.8 m s^{-1} \)
B. \( 4.9 \mathrm{m} \mathrm{s}^{-1} \)
c. \( 19.6 \mathrm{m} \mathrm{s}^{-1} \)
D. zero


The conductivity of 0.001028 mol \( L^{-1} \)
acetic acid is \( 4.95 \times 10^{-5} \mathrm{Scm}^{-1} \)
Calculate its dissociation constant if
\( \boldsymbol{\Lambda}_{\mathbf{m}}^{\mathbf{o}} \) for \( \mathbf{3} \mathbf{9 0 . 5} \mathbf{S} \mathbf{c m}^{2} \mathbf{m o l}^{-\mathbf{1}} \)


In physics, the mean free path is the average distance traveled by a moving particle (such as an atom, a molecule, a photon) between successive impacts (collisions), which modify its direction or energy or other particle properties. In which of the following mean free path is used ?
A. to estimate the resistivity of a material
B. to design a chemical apparatus
c. It can be used in optics and in acoustics
D. All of the above


The solubility product of \( \boldsymbol{A l}_{2}\left(\boldsymbol{S O}_{4}\right)_{3} \) is
given by the expression:
A \( \cdot\left[A l^{+3}\right] \cdot\left[S O_{4}^{-2}\right] \)
B \( \cdot\left[A l^{+3}\right]^{2} \cdot\left[S O_{4}^{-2}\right] \)
\( ^{\mathbf{C}} \cdot\left[A l^{+3}\right]^{3} \cdot\left[S O_{4}^{-2}\right]^{2} \)
D \( \left[A l^{+3}\right]^{2} \cdot\left[S O_{4}^{-2}\right]^{3} \)


Assertion (A) : Zeroth law of thermodynamics gives us the concept
of energy Reason
(R) : Internal energy is
dependent on temperature
A. 1) Both Assertion and Reason are true and reason is correct explanation of Assertion
B. 2) Both Assertion and Reason are true but reason is not correct explanation of Assertion
C. 3 ) Assertion is true but reason is false
D. 4 ) Assertion is false but reason is true


Write the method of preparation,
chemical name and chemical formula
of Plaster of Paris.


Identify \( Y \) in the following reaction. \( \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{N} \boldsymbol{H}_{2} \frac{\boldsymbol{H} C l}{N a N O_{2}}[\boldsymbol{X}] \stackrel{\boldsymbol{H}_{2} \boldsymbol{O}}{\longrightarrow} \boldsymbol{Y} \)
A. \( C_{2} H_{5} N_{2} C l \)
в. \( C_{2} H_{5} C l \)
с. \( C_{2} H_{5} O H \)
D . \( C_{2} H_{6} \)


Let \( \boldsymbol{f}(\boldsymbol{x}) \) be polynomial in \( \boldsymbol{x} \) of degree
not less than 1 and \( ^{\prime} a^{\prime} \) be a real number.
If \( f(x) \) is divided by \( (x-a), \) then the
remainder is \( \boldsymbol{f}(\boldsymbol{a}) \). If \( (\boldsymbol{x}-\boldsymbol{a}) \) is a factor
of \( f(x), \) then \( f(a)=0 . \) Find the remainder of \( x^{4}+x^{3}-x^{2}+2 x+3 \)
when divided by \( \boldsymbol{x}-\mathbf{3} \)
A. 108
B. 98
c. 165
D. 170


If the Rydberg constant for hydrogen
atom is \( R, \) then the Rydberg constant for positronium atom is
A \( .2 R \)
в. \( R \)
c. \( R / 2 \)
D. \( 4 . R \)


Catalyst used in Rosenmund reaction
is:
\( A \cdot S n \)
в. \( Z n / H C l \)
\( \mathbf{c} \cdot P d / B a S O_{4} \)
D. \( N i \)


STATEMENT: All cabbages are red. Which of the following statements shows that the statement above is
FALSE?
A. David is eating a red apple
B. Bill is eating a green apple
c. Alice is not eating a red cabbage
D. Ted is eating a red cabbage
E. Keisha is eating green cabbage


In a \( \triangle A B C, \angle A \) is greater than \( \angle B \). If
the measures of \( \angle A \) and \( \angle B \) satisfy the
equation \( 2 \tan x-k\left(1+\tan ^{2} x\right)=0 \)
where \( k \epsilon(0,1), \) then the measure of the
\( \angle C \) is
A.
в.
\( c \cdot \frac{5 \pi}{12} \)
D.


The Sl unit of electron mobility is :
A \( . M^{2} S^{-1} V-1 \)
В. \( =m^{2} s^{-1} V^{-1} \)
\( \mathbf{c} \cdot m s^{-1} V \)
D. \( m^{2} s^{-2} V \)


What is the area of a plane figure bounded by the points of the lines max \( (x, y)=1 \) and \( x^{2}+y^{2}=1 ? \)


For positive integers \( n_{1}, n_{2} \) the value of
the expression \( (1+i)^{n_{1}}+\left(1+i^{3}\right)^{n_{1}}+ \)
\( \left(1+i^{5}\right)^{n_{2}}+\left(1+i^{7}\right)^{n_{2}}, i=\sqrt{-1} \) is a
real number if and only if
\( \mathbf{A} \cdot n_{1}=n_{2}+1 \)
В . \( n_{1}=n_{2}-1 \)
c. \( n_{1}=n_{2} \)
D \( . n_{1}>0, n_{2}>0 \)


In the ground state of \( C u^{+}, \) the number
of shells occupied, sub-shells occupied, filled orbitals and unpaired electrons respectively are:
[Atomic no. of copper \( =29 \)
A .4,8,15,0
В. 3,6,15,1
c. 3,6,14,0
D. 4,7,14,2


Differentiate:
\( \boldsymbol{y}=\boldsymbol{c}^{2}+\frac{\boldsymbol{c}}{\boldsymbol{x}} \)


To observe diffraction, the size of an
obstacle:
A. should be of the same order as wave length
B. should be much larger than the wave length
c. has no relation to wave length
D. may be greater or smaller than the wave length


A box contains 32 coloured marbles. 8 of
them are red marbles and the rest are
either blue or green marbles. A marble is drawn at random. Calculate the
probability of drawing a marble which is not red in colour.
\( A \cdot \frac{2}{3} \)
в. \( \frac{5}{8} \)
\( c \cdot \frac{3}{4} \)
D. \( \frac{7}{16} \)


What is oxidation number of \( C r \) in
\( \left(N H_{3}\right)_{3} C r O_{4} \) or \( \left(N H_{3}\right)_{3} C r\left(O_{2}\right)_{2} ? \)


The equation of a simple harmonic motion is \( \boldsymbol{x}=\mathbf{0 . 3 4} \cos (\mathbf{3 0 0 0 t}+\mathbf{0 . 7 4}) \)
where \( x \) and \( t \) are in \( \mathrm{mm} \) and \( \mathrm{sec} \)
respectively. The frequency of the motion is :
A. 3000
B. 3000/2\pi
c. \( 0.74 / 2 \pi \)
D. 3000/ \( \pi \)


Which of the following has been arranged in order of decreasing dipole
moment?
A. \( C H_{3} C l>C H_{3} F>C H_{3} B r>C H_{3} I \)
B. \( C H_{3} F>C H_{3} C l>C H_{3} B r>C H_{3} \)
c. \( C H_{3} C l>C H_{3} B r>C H_{3} I>C H_{3} F \)
D. \( C H_{3} F>C H_{3} C l>C H_{3} I>C H_{3} B r \)


Which of the following is not the allotropic form of sulphur?
A. Roll sulphur
B. Monoclinic sulphur
c. Plastic sulphur
D. Rhombic sulphur


Oxides which show both acidic and
basic nature are called as
oxides
A. dual
B. amphoteric
c. aprotic
D. none of these


Find the magnetic field due to
conducting wire at point \( O, \) at centre of
semicircle of radius \( r \) and carrying a
current \( i \) as shown in the figure.
\( ^{A} \cdot \frac{\mu_{0}}{4 r} \)
в. \( \frac{\mu_{0} i}{4 r}(1+2 \pi) \)
c. \( \frac{\mu_{0} i}{4 r}(\pi-2) \)
D. \( \frac{\mu_{0} i}{4 \pi r}(\pi+2) \)


There are 6 books of Economics, 3 of Mathematics and 2 of Accountancy. In how many ways can these be placed on
a shelf, if:
1. Books on the same subject are together?
2. Books on the same subject are not together?


Basal metabolism disorders are caused
by
A. Impairment of the pituitary
B. Impairment of the gonads
c. Impairment of the thyroid
D. Impairment of the thymus
E. Impairment of the parathyroid


\( f(x-2)(x-3)^{3}=\frac{A}{x-2}+\frac{B}{x-3}+ \)
\( \frac{C}{(x-3)^{2}}+\frac{D}{(x-3)^{3}} \) then \( B= \)
\( A \)
B.
c. \( \frac{1}{25} \)
\( D \)


Which pair(s) of liquids on mixing is/are expected to show no net volume
change and no heat effect? This question has multiple correct options
A. Acetone and ethanol.
B. Chlorobenzene and bromobenzene
c. chloroform and benzene
D. n-Butyl chloride and n-butyl bromide


Which of the following does not reflect the periodicity of elements?
A. Bonding behaviour
B. Electronegativity
c. lonisation potential
D. Neutron/proton ratio


The vapour prerssure of pure liquids \( A \) and B are 400 and \( 600 m m H g \) respectively at \( 298 K . \) On mixing the two liquids, the sum of their initial volumes is equal to the volume of the final mixture. The mole fraction of liquids B
is 0.5 in the mixture. The vapour pressure of the final solution,the mole fraction of components \( A \) and \( B \) in
vapour phase, respectively are:
A. \( 500 \mathrm{mmHg}, 0.5,0.5 \)
в. 450 ттН \( g, 0.4,0.6 \)
c. 450 mmHg \( , 0.5,0.5 \)
D. \( 500 \mathrm{mmHg}, 0.4,0.6 \)


The stage of cell cycle after DNA replication is
\( A \cdot G_{1} \)
B. \( G_{2} \)
\( c \cdot s \)
D. M
E. Cytokinesis


The amount of heat (in calories)
required to convert 10 g of ice at \( -10^{0} C \)
into steam at \( 100^{0} C \) is nearly:
(Specific heat of steam is
\( \mathbf{5 3 6} \) cal \( / \mathbf{g m}-\mathbf{K} \)
A \( . \quad 5400 \) cal
B. 6400 cal
c. 7210 cal
D. 8250 cal


The conjugate acid of \( \boldsymbol{O H}^{-} \) is:
\( \mathbf{A} \cdot H_{3} O^{+} \)
B. \( O^{2-} \)
\( \mathbf{c} \cdot O H^{-} \)
D. \( H_{2} O \)


Write an essay on Indian space
programme


Reagents used for industrial
preparation of methanol are:
A. \( C O+H_{2} \)
в. \( H C H O+H_{2} \)
c. \( C O_{2}+H_{2} \)
D. \( H C O O H+H_{2} \)


A person pushing a wall hard is liable to fall back. Which law is related for this?
A. Newton's first law
B. Newton's second law
c. Newton's third law
D. Newton's gravitational law


If the coordinates of the points \( A, B, C, D \) be
(1,2,3),(4,5,7),(-4,3,-6) and
(2,9,2) respectively, then find the angle between the lines \( A B \) and \( C D \)


Why are the group I metals soft, low melting and of low density?


The largest of 50 measurements is 3.84
kg. If the range is \( 0.46 \mathrm{kg} \), find the smallest measurement.
A . \( 3.38 \mathrm{kg} \)
B. 2.38kg.
c. \( 6.38 \mathrm{kg} \)
D. None of these


The shortest distance of the point
(1,2,3) from \( x^{2}+y^{2}=0 \) is
\( \mathbf{A} \cdot \mathbf{5} \)
B. \( \sqrt{5} \)
\( c \cdot 2 \)
D. \( \sqrt{14} \)


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


If the last term in the binomial
expansion of \( \left(2^{\frac{1}{3}}-\frac{1}{\sqrt{2}}\right)^{n} \quad \) is \( \quad\left(\frac{1}{3^{\frac{5}{3}}}\right)^{\log _{3} 8} \)
then the 5 th term from the beginning
is
A. 210
B. 420
\( c \cdot 105 \)
D. none of these


Find the sum of oxidation state of \( S \) -
atom(s) in thio-sulphuric acid.


The acidic hydrolysis of sucrose called
inversion reaction.
If true enter 1 , else enter 0 .


A potential difference across the terminals of a battery is \( 50 V \) when \( 11 A \)
current is drawn and \( 60 V, \) when \( 1 A \)
current is drawn. The emf and the
internal resistance of the battery are
A. \( 62 V, 2 \Omega \)
в. \( 63 V, 1 \Omega \)
\( \mathrm{c} \cdot 61 V, 1 \Omega \)
D. \( 64 V, 2 \Omega \)


\( \underbrace{\left[\begin{array}{l}E \\ L \\ L\end{array}\right.} \)


Plants are called
they fix carbon dioxide.


Using properties of determinants, the negative of \( \left|\begin{array}{ccc}18 & 40 & 89 \\ 40 & 89 & 198 \\ 89 & 198 & 440\end{array}\right| \) would be


What is the depletion region in pn
junction?


\( \left[\begin{array}{lll}0 & 0 & 0\end{array}\right] \) is
A. Identity matrix
B. diagonal matrix
c. scalar matrix
D. null matrix


The modern periodic table consists of periods.


Magnetically aligned atoms in a magnetic material forms a cluster. The cluster is called a:
A. Domain
B. Molecule
c. Pole
D. charge
E. Electron cloud


f \( n(A)=4 \) and \( n(B)=5, \) then \( n(A x \)
\( B)= \)
A . 20
B . 25
\( c \cdot 4 \)
D. 15


Solve the following differential eqauton
\( \boldsymbol{y}^{2} \boldsymbol{d} \boldsymbol{y}-\boldsymbol{x}^{2} \boldsymbol{d} \boldsymbol{x}=\mathbf{0} \)


A point sized sphere of mass \( ^{\prime} \boldsymbol{m}^{\prime} \) is
suspended from a point using a string
of length \( ^{\prime} l^{\prime} . \) It is pulled to a side till the string is horizontal and released. As the mass passes through the portion where the string is vertical, magnitude of its angular momentum is:
\( \mathbf{A} \cdot m l \sqrt{g l} \)
в. \( m l \sqrt{2 g} \)
c. \( m l \sqrt{\frac{g l}{2}} \)
D. \( m l \sqrt{3 g l} \)


(a) Write the products of the following reactions:
(ii) \( 2 C_{6} H_{5} C H O+ \) Conc.NaOH\( \longrightarrow \)
(iii) \( C H_{3} C O O H \quad C l_{2} / P \)
(b) Give simple chemical tests to distinguish between the following pairs of compounds:
(i) Benzaldehyde and benzoic acid
(ii) Propanal and propanone


If \( \boldsymbol{y}=\frac{\boldsymbol{x}^{4}+\boldsymbol{4}}{\boldsymbol{x}^{2}-\boldsymbol{2} \boldsymbol{x}+\boldsymbol{2}} \) then find \( \left.\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}\right|_{\boldsymbol{x}=\frac{1}{2}} \)


If \( \alpha, \beta, \gamma \) be the direction angles of a vector and \( \cos \alpha=\frac{14}{15}, \cos \beta=\frac{1}{3}, \) then
\( \cos \gamma= \)
This question has multiple correct options
\( A \cdot \pm \frac{2}{15} \)
в. \( \frac{1}{5} \)
\( c \cdot \pm \frac{1}{15} \)
D. None of these


thickness and refractive index \( n_{1}=1.4 \)
is coated on the convex spherical
surface of radius \( R \) at one end of a long
solid glass cylinder of refractive index
\( \boldsymbol{n}_{2}=1.5, \) as shown in the figure. Rays of
light parallel to the axis of the cylinder
traversing through the film from air to
glass get focused at distance \( f_{1} \) from
the film, while rays of light traversing from glass to air get focused at
distance \( f_{2} \) from the film. Then
This question has multiple correct options
\( \mathbf{A} \cdot\left|f_{1}\right|=3 R \)
B . \( \left|f_{1}\right|=2.8 R \)
\( \mathbf{c} \cdot\left|f_{2}\right|=2 R \)
D \cdot \( \left|f_{2}\right|=1.4 R \)


Natural radioactivity was discovered by
A. Marie Curie
B. Ernest Rutherford
C. Henri Becquerel
D. Enrico Fermi


A positive charge \( q \) at origin is moving with velocity \( v_{0} \hat{j} \). Magnetic field at point
\( (a,-a) \) is
A. zero
B. \( \frac{\mu_{0} q v_{0}}{16 \sqrt{2} \pi a^{2}} \hat{k} \)
c. \( \frac{-\mu_{0} q v_{0}}{8 \sqrt{2} \pi a^{2}} \hat{k} \)
D. \( \frac{-\mu_{0} q v_{0}}{4 \sqrt{2} \pi a^{2}} \hat{k} \)


The line which intersects two or more
lines at distinct points is called
transversal.lf true enter 1 else 0


Carbon dioxide contains \( 27.27 \% \) carbon
carbon disulphide contains \( 15.97 \% \) carbon and sulphur dioxide contains \( 50 \% \) sulphur. Show that these figures illustrate the law of reciprocal
proportions.


\( H_{2} S O_{4} \) is a stronger acid than \( H_{2} S O_{3} \)
If true enter 1 , else enter 0 .


Which of the following statements is
true about acid rain?
A. Acid rain will erode marble statues
B. Acid rain can change the pH of lakes and streams
C. Acid rain can be formed from carbon dioxide
D. Acid rain creates holes in the ozone layer
E. All of the above


The binding energies per nucleon of
deutreron \( \left(_{1} H^{2}\right) \) and helium \( \left(_{2} H e^{4}\right) \) atoms are \( 1.1 \mathrm{MeV} \) and \( 7 \mathrm{MeV} \). If two
deuteron atoms react to form a single
helium atom, then the energy released
is
A. \( 13.9 \mathrm{MeV} \)
в. \( 26.9 \mathrm{MeV} \)
c . \( 23.6 \mathrm{MeV} \)
D. \( 19.2 \mathrm{MeV} \)


Find the value of \( \tan ^{-1} \sqrt{3}-\sec ^{-1}(-2) \)
is equal to
\( A \)
B. \( -\frac{\pi}{3} \)
c.
D. \( \frac{2 \pi}{3} \)


\( n \stackrel{L t}{\rightarrow} \infty\left\{\frac{1}{2 n+1}+\frac{1}{2 n+2}+\right. \)
\( \left.\frac{1}{2 n+3} \cdots+\frac{1}{2 n+n}\right\} \)
A. \( \log _{e}\left(\frac{1}{3}\right) \)
B. \( \log _{e}\left(\frac{2}{3}\right) \)
c. \( \log _{e}\left(\frac{3}{2}\right) \)
D \( \cdot \log _{e}\left(\frac{4}{3}\right) \)


In the electronic configuration, outermost orbit number is considered
as:
A. period
B. group
c. octet
D. none of these


If \( \boldsymbol{\alpha} \in\left(\mathbf{0}, \frac{\boldsymbol{\pi}}{\mathbf{2}}\right) \) then \( \sqrt{\mathbf{x}^{2}+\mathbf{x}}+\frac{\tan ^{2} \boldsymbol{\alpha}}{\sqrt{\mathbf{x}^{2}+\mathbf{x}}} \)
is always greater than or equal to
\( A \cdot 2 \tan \alpha \)
B.
\( c \cdot 2 \)
\( D \cdot \sec ^{2} \alpha \)


When the specific heat of a metallic element is 0.214 cal the atomic mass
will be closest to which one of the
following?
\( A \)
B. 12
\( c . \) 30
D. 66


Name the products of hydrolysis of
sucrose.


Specific conductance of \( 0.1 \mathrm{M} \) NaC solution is \( 1.01 \times 10^{-2} \) ohm \( ^{-1} \mathrm{cm}^{-1} \)
Its molar conductance in ohm \( ^{-1} \mathrm{cm}^{2} \)
\( m o l^{-1} \) is:
A \( \cdot 1.01 \times 10^{2} \)
B . \( 1.01 \times 10^{3} \)
c. \( 1.01 \times 10^{4} \)
D. 1.01


State the following statement is True or False
\( \boldsymbol{D}=\left\{\boldsymbol{y} \mid \boldsymbol{y}=\boldsymbol{3}^{n}, \boldsymbol{n} \in \boldsymbol{N}\right\} \) is an example
of an infinite set.
A. True
B. False


A particle is executing \( S . H . M \) with amplitude \( A \) and has maximum
velocity \( v_{0} . \) Its speed at displacement \( \frac{3 A}{4} \) will be
A \( \cdot \frac{\sqrt{7}}{4} v_{0} \)
в. \( \frac{v_{0}}{\sqrt{2}} \)
c. \( \frac{\sqrt{3}}{2} v_{o} \)
D. \( v_{0} \)


The area (in sq. units) of the region
described by \( \boldsymbol{A}= \)
\( \left\{(x, y) \mid y \geq x^{2}-5 x+4, x+y \geq 1, y \leq\right. \)
is:
A \( \cdot \frac{17}{6} \)
в. \( \frac{13}{6} \)
c. \( \frac{19}{6} \)
D. \( \frac{7}{2} \)


Phenol reacts with bromine in \( C S_{2} \) at
low temperature to give:
A. m-bromophenol
B. p-bromophenol
c. o and p-bromophenol
D. 2,4,6-tribromophenol


The hydrolysis of 1 mol of
peroxodisulphuric acid produces
A. 2 mol of sulphuric acid
B. 2 mol of peroxomonosulphuric acid
c. 1 mol each of sulphuric acid and peroxomonosulphuric acid
D. 1 mol each of sulphuric acid, peroxomonosulphuric acid and hydrogen peroxide


What do you mean by limiting factors?
Explain effect of light on photosynthesis. Which hormone is
named as hormone of flight and flight?


Conversion of benzene to acetophenone
can be brought by:
A. Wurtz reaction
B. Wurtz-Fittig's reacton
c. Friedel Crafts alkylation
D. Friedel Crafts acylation


Select an option that shows the correct
sequence of the events involved in the
translation mechanism.
a. Binding of mRNA to a smaller subunit of ribosome
b. Aminoacylation of tRNA
c. Binding of initiator tRNA to the P-site
of the ribosome
d. Formation of polypeptide
e. Formation of a peptide bond between first and second amino acids at the \( A \)
site
A \( . a \rightarrow b \rightarrow c \rightarrow d \rightarrow e \)
B . \( b \rightarrow a \rightarrow e \rightarrow c \rightarrow d \)
\( \mathbf{c} \cdot b \rightarrow d \rightarrow a \rightarrow c \rightarrow e \)
D. \( b \rightarrow a \rightarrow c \rightarrow e \rightarrow d \)


Explain the term perianth.


\( \boldsymbol{f}(\boldsymbol{x})=\sqrt{\log _{1 / 2}\left(\frac{\mathbf{5} \boldsymbol{x}-\boldsymbol{x}^{2}}{\mathbf{4}}\right)} \)


A photon of energy 10.2 eV corresponds
to light of wavelength \( \lambda_{0} . \) Due to an electron transition from \( x=2 \) to \( x=1 \) in a
hydrogen atom, light of wavelength A is emitted. If we take into account the
recoil of the atom when the photon is
emitted, then :
\( A \cdot \lambda<\lambda_{0} \)
B. \( \lambda>\lambda_{0} \)
c. \( \lambda=\lambda_{0} \)
D. None of these


Which of the following are biodegradable polymers? This question has multiple correct options
A. Nylon - 6,6
B. PHBV
c. Nylon - 2 - Nylon - 6
D. Polychloroprene


The solution of the equation \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}= \)
\( \frac{y}{x}\left(\log \frac{y}{x}+1\right) \) is
\( ^{A} \cdot \log \frac{y}{x}=c x \)
в. \( \frac{y}{x}=\log y+c \)
c. \( y=\log y+1 \)
D. \( y=x y+c \)


What s the basis of triad formation of
elements?


A quantity of \( P C l_{5} \) was heated in
\( \mathbf{1 0} d \boldsymbol{m}^{3} \) vessel \( \mathbf{2 5 0}^{\mathbf{0}} \boldsymbol{C} \)
\( \boldsymbol{P C l}_{5} \) g) \( \square \boldsymbol{P} \boldsymbol{C l}_{3}(g)+\boldsymbol{C l}_{2}(g) \)
At equilibrium the vessel contains \( 0 . \)
mole of \( P C l_{5} \) and 0.2 mole of \( C l_{2} \). The
equilibrium constant of the reaction is
\( ? \)
A. 0.05
B. 0.02
c. 0.025
D. 0.04


Let \( A=\{1,2\} \) and \( B=\{3,4\} . \) Find the
total number of relations from A into B.


A cylinder of mass \( m \) and radius \( R \) rolls
down an incline plane of inclination \( \theta \) The linear acceleration of the axis of the
cylinder is given as \( a=\frac{x}{3} g \sin \theta . \) Find \( x \)


Maximum oxidation state exhibited by osmium is:
\( A \cdot+8 \)
B. +7
\( c \cdot+6 \)
D. + 5


A metal wire is connected in the left gap
and a semiconductor is connected in
the right gap of a meter bridge and the balancing point is found. Both are heated so that change of resistances in them are same. Then the
balancing point:
A. will not shift
B. shifts towards left
c. shifts towards right
D. depends on the rise of temperature


In the given loop the magnetic field at
the centre 0 is :
A \( \cdot \frac{\mu_{0} I}{4}\left(\frac{r_{1}+r_{2}}{r_{1} r_{2}}\right) \) out of the page
B. \( \frac{\mu_{0} I}{4}\left(\frac{r_{1}+r_{2}}{r_{1} r_{2}}\right) \) into the page
c. \( \frac{\mu_{0} I}{4}\left(\frac{r_{1}-r_{2}}{r_{1} r_{2}}\right) \) out of the page
D. \( \frac{\mu_{0} I}{4}\left(\frac{r_{1}-r_{2}}{r_{1} r_{2}}\right) \) into the page


Arrangement of the following group of orbitals in which they fill with electrons
\( (5 f, 6 p, 4 p, 6 s, 4 d, 4 f) \)
\( \mathbf{A} \cdot 4 p, 4 d, 6 s, 4 f, 6 p, 5 f \)
B. \( 6 s, 4 d, 4 f, 5 f, 4 p, 6 p \)
\( \mathbf{c} .6 s, 4 p, 4 d, 4 f, 5 f, 6 p \)
D. \( 4 d, 4 p, 4 f, 5 f, 6 s, 6 p \)


Riboflavin is the chemical name of:
A . Vitamin \( B_{1} \)
B. Vitamin \( B_{2} \)
C. Vitamin \( B_{6} \)
D. Vitamin B complex


State True or False.
The electron distribution is spherically symmetrical for \( l=2 \)
A. True
B. False