Assertion
Functional groups are specific groups of atoms or bonds within molecules
that are responsible for the characteristic chemical reactions of
those molecules.
Reason
The same functional group will undergo the same or similar chemical
reaction(s) regardless of the size of the molecule.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Match the species in List 1 with their corresponding properties in List 2


Which of the following is the best
preparation of \( 2- \) methyl pentanoic
acid?
A \( \cdot \) 2 - chloropentane \( \stackrel{N a C N(a q)}{\longrightarrow} \stackrel{H^{+} / H_{2} O}{\longrightarrow} \)
B・ \( _{2-\text { pentanone }} \stackrel{N a C N(a q)}{\longrightarrow} \stackrel{H^{+} / H_{2} O}{\longrightarrow} \)
c. 2 - bromopentane \( \frac{M g}{\text {Ether}} \) (ii) (i) \( C O_{2} \) \( \overline{H C I} \) H \( _{2} \) O
D. \( 1- \) chloropentane \( \stackrel{N a C N(a q)}{\longrightarrow} \stackrel{H^{+} / H_{2}}{\longrightarrow} \)


Which of the following represents obligate anaerobes.
A. Spirogyra
B. Pisum sativum
c. onion
D. Methane bacteria


Choose the correct answer among the alternatives given:
In the following reaction, product \( (P) \) is:
\( \boldsymbol{R}-\stackrel{\|}{\boldsymbol{C}}-\boldsymbol{C l} \frac{\boldsymbol{H}_{2}}{\boldsymbol{p} \boldsymbol{d} / \boldsymbol{B a S O}_{4}} \boldsymbol{P} \)
A. \( R C H O \)
в. \( R C H_{3} \)
c. \( R C O O H \)
D. \( R C H_{2} O H \)


Assertion(A): Smaller particles (size <5 microns) cause fibrosis of the lung
lining. Reason
(R): They are more likely to
penetrate into the lungs.
A. Both A and R are true and R is the correct explanation of A
B. Both A and R are true but R is not correct explanation of
c. \( A \) is true and \( R \) is false
D. A is false and R is true.


A circular coil of cross-sectional area
\( 200 c m^{2} \) and 20 turns is rotated about
the vertical diameter with angular
speed of 50 rads\( ^{-1} \) in a uniform
magnetic field of magnetic \( 3.0 \times 10^{-2} \) T
Calculate the maximum value of the
current in the coil.


The distances traversed during equal intervals of time by a freely falling body from rest are in the ratio
A. \( 1: 3: 5: 7 . \)
B. \( 2: 4: 6: 8 . . \)
c. \( 1: 4: 9: 25 . . \)
D. \( 1: 9: 25: 49 \ldots \)
E. 1: 2: 3: 4


IN the figure \|\| and \( n \) is a ttansversal
such that \( \angle 3: \angle 8=1: 2 . \) Find \( \angle 4 \) and
\( \angle 3 \)


One of these have no specific function in a rabbit.
A. Caecum
B. Colon
c. vermiform appendix
D. sacculus rotundus


A certain weak acid has \( K_{a}=10^{-5} . \) If
the equilibrium constant for its reaction with a strong base is
represented by \( y \times 10^{10}, \) then find the
value of \( \boldsymbol{y} \)


If the mass of a body is \( 12.1 g \) and the
density is \( 2.2 g / c c, \) its volume is
\( \mathbf{A} \cdot 5.5 \mathrm{cm}^{3} \)
в. \( 8 c c \)
\( c .11 c c \)
D. \( 55 c c \)


The water conducting tissue in Bryophyta is
A. Parenchyma
B. Sclerenchyma
c. Trachieds
D. Sieve tubes


Van't Hoffs factor for a solution is less
than one, what is the conclusion drawn
from it.


For a given gas, which of the following relationships is correct at a given temp?
\( \mathbf{A} \cdot u_{r m s}>u_{a v}>u_{m p} \)
B . \( u_{r m s}<u_{a v}<u_{m p} \)
c. \( u_{r m s}>u_{a v}<u_{m p} \)
D. \( u_{r m s}<u_{a v}>u_{m p} \)


For non zero vectors \( a, b \) and \( c, \) if \( a+ \) \( b+c=0 \) then which relation true:
A \( a=b=c=0 \)
0
В. \( a . b=b . c=c . a \)
\( \mathbf{c} \cdot a \times b=b \times c=c \times a \)
D. None


A man can see objects clearly up to \( 3 m \) What type of lens he should use in order
to see clearly up to \( 12 m ? \)
A. Convex lens, \( f=4 m \)
B. Concave lens, \( f=4 m \)
c. convex lens, \( f=-4 m \)
D. Concave lens, \( f=-4 m \)


\( (-5)+6=? \)
A \( \cdot(-1) \)
в.
c. 11
D. (-11)


\( \frac{G}{S} \)


Solve
\( \frac{-3}{5}+\frac{-12}{20} \)


The increase in the \( \ldots \). factor greatly
the rate of photosynthesis.
A. Slowest, increases
B. Slowest, decreases
c. fastest, increases
D. None of the above


A tank is filled up to a height \( 2 \mathrm{H} \) with a
liquid and is placed on a platform of
height H from the ground. The distance
\( x \) from the ground where a small hole is
punched to get the maximum range
is
\( A \cdot H \)
B . \( 1.25 \mathrm{H} \)
c. \( 1.5 \mathrm{H} \)
D. 2


Assertion
The phloem present in the xylem elements is called protophloem.
Reason
The phloem elements develop in the middle of xylem elements are secondary in nature
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 angles of a pentagon are in the ratio \( 4: 8: 6: 4: 5 . \) Find each angle of
the pentagon.
A \( \cdot 40^{\circ}, 160^{\circ}, 120^{\circ}, 80^{\circ} \)and \( 100^{\circ} \)
B . \( 60^{\circ}, 160^{\circ}, 120^{\circ}, 80^{\circ} \) and \( 100^{\circ} \)
c. \( 80^{\circ}, 160^{\circ}, 120^{\circ}, 80^{\circ} \) and \( 100^{\circ} \)
D. \( 30^{\circ}, 160^{\circ}, 120^{\circ}, 80^{\circ} \) and \( 100^{\circ} \)


Which one of the following has phosphoric acid anhydride bonds?
A. Deoxy ribonucleic acid
B. Ribonucleic acid
c. dNTPs
D. Phospholipids


Which of the following statement is not
true?
A. metals produce a ringing sound when struck hard
B. copper doesn't get rusted
C. coal and sulphur are soft and dull in appearance
D. magnesium and phosphorous burn vigorously in air


A man cannot see objects distinctly at a distance less than 1 metre. He is
suffering from
A. old age sight
B. Short-sightedness
c. Long-sightedness
D. Opaqueness of the lens


The ratio of the number of ketonic
groups in cytosine, thymine and uracil is:
A \( \cdot 1: 2: 2 \)
B. 2: 1: 2
c. 2: 2: 1
D. 1: 1: 1


Find the square root of 33453


The compound (A) will be:
\( A \)
B.
\( c \)
D. none


Assertion
It is important that organism have cells.
Reason
A cell keeps its chemical composition
steady within its boundary.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The correct relation between
interatomic force constant \( K, \) Young
modulus \( Y \) and interatomic distance \( r_{0} \)
is
A. \( K=Y r_{0} \)
в. \( K=\frac{r_{0}}{Y} \)
\( c \cdot K=\frac{Y}{r_{0}} \)
D. \( K=r_{0}^{2} Y^{2} \)


Solve : \( \int \frac{x^{2}}{(4+x)^{3 / 2}} d x \)


You are riding in an automobile of mass 3000 kg. Assuming that you are examining the oscillation characteristics of its suspension system. The suspension sags \( 15 \mathrm{cm} \) when the entire automobile is places on ¡t. Also the amplitude of oscillation decreases by 50\% during one complete oscillation. Estimate the values of
(a) the spring constant \( k \) and
(b) the damping constant b for the
spring and shock absorber system of one wheel, assuming that each wheel supports \( 750 \mathrm{kg} \)


Evaluate \( \sin 29^{\circ}-\cos 61^{\circ} \)


Evaluate the integral \( \int_{\pi / 4}^{\pi / 2} \log (1+\cot x) d x \)
A \( \cdot \frac{\pi}{4} \log 2 \)
в. \( \frac{\pi}{8} \log 2 \)
c. \( \pi \log 2 \)
D.


Which force of friction which does not
allow one body to slide upon another is called
A. Kinetic friction
B. Static friction
c. Both
D. none


Find the area of the sector of a circle
with radius \( 4 \mathrm{cm} \) and of angle \( 30^{\circ} \). The
answer is \( \frac{x n}{3} \) then \( x= \)


Express \( \frac{-1+i}{\sqrt{2}} \) in the polar form


Which of the following statement is
correct?
A. Sigma bond is weaker than pie-bond
B. \( H F \) is less polar than \( H I \)
\( \mathrm{C} \cdot \ln N H_{4}^{+} \) ions 4 coordinate bond is present
D. \( \ln S F_{6} \) all \( S-F \) bond length are same


Hydrogen burns with:
A. smoky flame
B. yellow flame
c. blue flame
D. pale yellow flame


In a village, an enumerator has surveyed for 25 households. The size of
the family (number of family members) and the number of families is tabulated
as follows:
Size of
\[
\begin{array}{lcccc}
\begin{array}{l}
\text { the family } \\
\text { (No. of } \\
\text { members) }
\end{array} & \begin{array}{c}
1- \\
3
\end{array} & \begin{array}{c}
3- \\
5
\end{array} & \begin{array}{c}
5- \\
7
\end{array} & \begin{array}{c}
7- \\
9
\end{array} \\
\begin{array}{l}
\text { No. of } \\
\text { families }
\end{array} & 6 & 7 & 9 & 2
\end{array}
\]
Find the mode of the data.


\( 100 \mathrm{ml} \) of \( 0.5 \mathrm{N} \) NaOH solution is added
to \( 10 \mathrm{ml} \) of \( 3 \mathrm{N} H_{2} \mathrm{SO}_{4} \) solution and 20
\( \mathrm{ml} \) of \( 1 \mathrm{N} \) HCl solution. The mixture is :
A . acidic
B. alkaline
c. neutral
D. none of these


The converse of \( \boldsymbol{p} \Rightarrow \boldsymbol{q}, \) is
\( \mathbf{A} \cdot p \Rightarrow q \)
в. \( q \Rightarrow p \)
c. \( \sim p \Rightarrow \sim q \)
D. \( q \Rightarrow \sim p \)


Assertion
Respiratory pathway is an amphibolic pathway.
Reason
In respiration there is breakdown of many substance (catabolism) and
synthesis of many substance (anabolism) by respiratory intermediates.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A manometer connected to a closed tap reads \( 3.5 \times 10^{5} N / m^{2} . \) When the value
is opened,the reading of manometer fall
to \( 3.0 \times 10^{5} N / m^{2}, \) then velocity of flow
of water is
A. \( 100 \mathrm{m} / \mathrm{s} \)
в. \( 1 \mathrm{m} / \mathrm{s} \)
\( c \cdot 10 m / s \)
D. \( 10 \sqrt{10} \mathrm{m} / \mathrm{s} \)


Cyclic alkanes are simply prefixed with
A. alphabet
B. cyclo
c. ring
D. numbers


Application of adsorption is/are:
A. In separation of inert gas
B. As adsorption indicator
c. Production of high vacuum
D. All of the above


Arrange the following in decreasing
order of their boiling points.
(1) n-Butane
(II) 2-Methylbutane
(III) n-Pentane
(IV) 2,2 -Dimethylpropane
\( A \cdot|>||>|||>\mid V \)
B. ॥>॥I>IV>1
c. IV> |||>||>1
D. III > || > |V >


A tent is of the shape of a right circular
cylinder upto height of 3 metres and then becomes a right circular cone with
maximum height of 13.5 metres above the ground. Calculate the cost of
painting the inner side of the tent at the
rate of Rs.2 per square metre, if the
radius of the base is 14 metres.
A . Rs. 2068
B. Rss.1988
c. Rs. 1268
D. Rs 2248


How much eater should be filled in a
container of height \( 21 \mathrm{cm} \) so that it will appear half filled when viewed along
normal to water surface. (Take \( \left.\mu_{\omega}=4 / 3\right) \)


The protein part of enzyme is known as
A. Holoenzyme
B. Apoenzyme
c. Isoenzyme
D. All of the above


To explain ferromagnetism, we use
A. orbital electron hypothesis
B. spinning electron hypothesis
C. domain theory
D. Langevin theory


Find the value of \( \frac{6}{\sqrt{5}-\sqrt{3}}, \) it being given that \( \sqrt{3}=1.732 \) and \( \sqrt{5}=2.236 \)
A . 11.9304
B. 11.3904
c. 11.904
D. None of the above


A metallic rod of mass \( 20 \mathrm{kg} \) and of uniform thickness rests against a wall while the lower end of rod is in contact
with rough floor. The rod makes an
angle \( 60^{0} \) with floor. If the weight of
rod produces a torque \( 150 \mathrm{Nm} \) about its lower end, the length of rod \( (g= \)
\( \left.10 m s^{-2}\right) \) is:
\( \mathbf{A} \cdot 1.5 m \)
B. \( 2 m \)
\( c .3 m \)
D. \( 4 m \)


An electron of kinetic energy \( \boldsymbol{E}_{\mathbf{0}} \) is scattered by an atomic hydrogen sample in ground state. The minimum
value of \( E_{0}, \) so that a photon of
wavelength 656.3 nm may be emitted
by \( \boldsymbol{H}- \) atom is :
A. 12.09 eV
в. 13.6 eV
c. \( 14.6 e V \)
D. none of these


A box contains 60 eggs. Out of which \( 16 \frac{2}{3} \% \) are rotten ones. How many eggs are rotten?


Identify the decimal and whole number
from the following.
\( \mathbf{9 9 9 9 9 . 9 9} \)


Equivalent weight of \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{2} \) when it
disproportionates into \( P H_{3} \) and
\( H 3 P O_{3}(\text { mol. wt. }=M) \) is :
\( \mathbf{A} \cdot M \)
в. \( \frac{M}{2} \)
c. \( \frac{M}{4} \)
D. \( \frac{3 M}{4} \)


Explain the following giving an appropriate reason in each case
(i) \( O_{2} \) and \( F_{2} \) both stabilize higher
oxidation states of metals but \( \boldsymbol{O}_{2} \)
exceeds \( F_{2} \) in doing so
(ii) Structures of xenon fluorides cannot be explained by valence bond approach.


Which of the following is a displacement reaction?
\( A \cdot \operatorname{cacos} \rightarrow c a 0+c O \)
B . Ca0+2HCI \( \rightarrow \) CaCl \( _{2}+H_{2} \) O
\( \mathrm{c} \cdot \mathrm{Fe}+\mathrm{CuSO}_{4} \rightarrow \mathrm{FeSO}_{4}+\mathrm{Cu} \)
D. NaOH+HCI \( \rightarrow \) Nacl \( +H_{2} \) 0


Suppose a manufacturer of printed circuits has a stock of 200 resistors,
120 transistors and 150 capacitors and is required to produce two types of circuits.
Type A requires 20 resistors, 10 transistors and 10 capacitors
Type B requires 10 resistors, 20 transistors and 30 capacitors. If the profit on type \( A \) circuits is \( E 5 \) and
that on type \( B \) circuits is \( E 12 \), how
many of each circuit should be
produced in order to maximize profit?


Dalda (Vanaspathi) is prepared by:
A. hydrogenation of triolien
B. hydrogenation of soap
c. hydrogenation of tristearine
D. electrolysis of potassium acetate


A gas is enclosed in a vessel of volume
\( V \) at a pressure \( P . \) It is being pumped out of the vessel by means of a piston pump with a stroke volume \( \frac{V}{100} . \) What is the final pressure in the vessel after \( n \) strokes of the pump? Assume no change in temperature during pumping out of gas.


If there are three possible values
\( (-1 / 2,0,+1 / 2) \) for the spin quantum,
then electronic configuration of \( \boldsymbol{K}(\mathbf{1 9}) \)
will be:
A \( \cdot 1 s^{3}, 2 s^{3} 2 p^{9}, 3 s^{3} 3 p^{\text {th }} \)
B . \( 1 s^{2}, 2 s^{2} 2 p^{6}, 3 s^{2} 3 p^{6}, 4 s^{1} \)
C \( \cdot 1 s^{2}, 2 s^{2} 2 p^{9}, 3 s^{2} 3 p^{4} \)
D. None of these


Find the differential equation corresponding to the family of curves
\( y=k(x-k)^{2} \) where \( k \) is an arbitrary
constant.
\( ^{\mathbf{A}} \cdot\left(\frac{d y}{d x}\right)^{3}-4 x y \frac{d y}{d x}+8 y^{2}=0 \)
\( ^{\mathrm{B}}\left(\frac{d y}{d x}\right)^{3}+4 x y \frac{d y}{d x}+8 y^{2}=0 \)
\( ^{\mathrm{c}}\left(\frac{d y}{d x}\right)^{3}-2 x y \frac{d y}{d x}+8 y^{2}=0 \)
\( ^{\mathrm{D} \cdot}\left(\frac{d y}{d x}\right)^{3}+2 x y \frac{d y}{d x}+8 y^{2}=0 \)


A \( 6.0 g \) sample of carbon is burned to produce carbon dioxide. The yield from the reaction is only \( 60 \% . \) How much carbon dioxide was actually produced?


Amplitude of \( \frac{1+\sqrt{3} i}{\sqrt{3}+i} \) is
A \( \cdot \frac{\pi}{3} \)
в. \( \frac{\pi}{2} \)
\( c \cdot 0 \)
D.


In which one of the following compounds of xenon, highest number of lone pair of electrons is present in
xenon?
A. \( X e F_{6} \)
в. \( X e F_{4} \)
\( \mathrm{c} . \mathrm{XeOF}_{4} \)
D. \( X e O_{3} \)
E . \( X e F_{2} \)


In the following reaction, how is the rate
of appearance of \( B r_{2} \) related to the rate
of disappearance of the \( B r^{-} ? \)
\( \boldsymbol{B} \boldsymbol{r} \boldsymbol{O}^{3-}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{5} \boldsymbol{B} \boldsymbol{r}^{-}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{6} \boldsymbol{H}^{+} \rightarrow \)
\( \mathbf{3} \boldsymbol{B} \boldsymbol{r}_{2}(\boldsymbol{l})+\boldsymbol{3} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) \)
A \( \cdot \frac{\left.d B r_{2}\right]}{d t}=-\frac{d\left[B r^{-}\right]}{d t} \)
B. \( \frac{d\left[B r_{2}\right]}{d t}=+\frac{3}{5} \frac{d\left[B r^{-}\right]}{d t} \)
C. \( \frac{\left.d B r_{2}\right]}{d t}=-\frac{3}{5} \frac{d B r-1}{d t} \)
D. \( \frac{d\left[B r_{2}\right]}{d t}=-\frac{5}{3} \frac{d\left[B r^{-}\right]}{d t} \)


Consider the list of the things given
below.
salt, pepper, chilli, soap, turmeric How many of the following can be classified in the same group?
\( A \cdot 4 \)
B. 3
\( c \cdot 2 \)
D. none of these


Which hydrogen halides has maximum
ionic character?
\( \mathbf{A} \cdot H F \)
в. \( H C l \)
c. \( H I \)
D. \( H B r \)


In myopia or short sightedness,
A. Image is formed slightly in front of retina because eye ball is longer
B. Eye ball is normal but image is formed over blind spot
C. Eye ball is normal but images is formed slightly behind the retina due to faulty lens
D. Curvature of cornea becomes irregular


Evaluate \( : \frac{\operatorname{cosec}^{2} \mathbf{6 3}^{\mathbf{0}}+\tan ^{2} \mathbf{2 4}^{\mathbf{0}}}{\cot ^{2} \mathbf{6 6}^{\mathbf{0}}+\mathbf{s e c}^{\mathbf{2}} \mathbf{2 7}^{\mathbf{0}}}+ \)
\( \frac{\mathbf{s i n}^{2} \mathbf{6 3}^{\mathbf{0}}+\cos \mathbf{6 3}^{\mathbf{0}} \sin \mathbf{2 7}^{\mathbf{0}}+\sin \mathbf{2 7}^{\mathbf{0}} \mathbf{s e c 6}}{\mathbf{2}\left(\operatorname{cosec}^{\mathbf{2}} \mathbf{6 5}^{\mathbf{0}}-\mathbf{t a n}^{\mathbf{2}} \mathbf{2 5}^{\mathbf{0}}\right)} \)


\( \lim _{x \rightarrow \infty}\left\{\left(e^{x}+\pi\right)^{\frac{1}{x}}\right\} \) ( where \{\} denotes the
fractional part of \( x \) ) is equal to:
\( \mathbf{A} \cdot \pi-e \)
B . \( \pi-3 \)
\( \mathbf{c} \cdot e-2 \)
D. \( 3-e \)


Which of the following molecule has intramolecular H-bonding?
A. Ortho-nitrophenol
B. Ortho-boric acid
c. Both (a) and (b)
D. None of these


If three dice are thrown, then the
probability that they show the numbers in A.P.is
A \( \cdot \frac{1}{36} \)
в. \( \frac{1}{18} \)
\( c \cdot \frac{2}{9} \)
D. \( \frac{5}{18} \)


The velocity-position graph of a particle is shown in figure. Obtain the relation between acceleration and displacement
and plot it.


When a spinning top slows down, it begins to wobble. This phenomenon can be explained by
A. gyroscopic precession
B. inertia of motion
c. force of gravity
D. more complicated types of motion are coming into play


The number of lines of symmetry in a
square is
A . 4
B. 3
\( c \cdot 2 \)
D. Infinite


The ratio of amplitudes of radiation emitted by a cylindrical source at distances \( 2 r \) and \( 18 r \) from its axis will
be
A . 1: 3
B. 2:
c. 1:
D. 9: 1


Simplify \( \left[i^{17}+\left(\frac{1}{i}\right)^{25}\right]^{3} \)


The main product obtained when a solution of sodium carbonate reacts
with mercuric chloride is :
\( \mathbf{A} \cdot H g(O H)_{2} \)
в. \( H g C O_{3} . H g O \)
\( \mathrm{c} . \mathrm{Hg} \mathrm{CO}_{3} \)
D. \( H g C O_{3} . H g(O H)_{2} \)


If \( f(x)=2 x-1, \) if \( x>1 ;=x^{2}+1, \) if
\( -1 \leq x \leq 1, \) then
\( \frac{f(1)+f(3)+f(0)}{f(2)+f(-1)+f\left(\frac{1}{2}\right)} \) is?
A \( \cdot \frac{32}{5} \)
в. \( \frac{32}{25} \)
c. \( \frac{5}{32} \)
D. \( \frac{25}{32} \)


Variations in organisms lead to diversity in living organisms. State
reasons.


\( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3}+\boldsymbol{C} \longrightarrow-----+ \)
\( \mathbf{A} \cdot C O_{2}, N O_{2}, H_{2} O \)
B. \( C O, N O, H_{2} O \)
\( \mathbf{c} \cdot C O_{2}, N H_{2}, H_{2} O \)
\( \mathbf{D} \cdot C O_{2}, N O, H_{2} O \)


Construct a right angle triangle \( A B C \) in
which \( \angle B=90^{\circ}, A B=5 \mathrm{cm} \) and
\( \boldsymbol{A C}=\mathbf{7} \boldsymbol{c m} \)


At what time, there will be 6400 bacteria in the flask?
A. \( 150 \mathrm{min} \)
B. 90 min
c. \( 160 \min \)
D. \( 120 \mathrm{min} \)


While conversion of phosphoglyceric acid into phosphoglyceraldehyde during photosynthesis one of the following reactions occur
A. Oxidation
B. Reduction
c. Electrolysis
D. Hydrolosis


The branch of chemistry that applies Physics to Chemistry is called as:
A. Agrochemistry
B. Biochemistry
c. Physical Chemistry
D. Inorganic Chemistry


The S.D. of 1,2,3,4,5,6,7 is
A .4
B. 2
\( c \cdot \sqrt{7} \)
D. none of these


For a general reaction \( \boldsymbol{X} \rightarrow \boldsymbol{Y}, \) the plot
of conc. of \( \boldsymbol{X} \) vs time is given in the
figure. What is the order of the reaction
and what are the units of rate constant?
A. zero, mol \( L^{-1} s^{-1} \)
B. First, \( \operatorname{mol} L^{-1} s^{-1} \)
\( c . \) First, \( s^{-1} \)
D. zero, L mol- \( s_{s}^{-} \)


State True or False.
Ethyne is a linear molecule.
A. True
B. False


During fermentation alcohol is formed from
A. Sugar
B. Protein
c. carbon dioxide and water
D. None of the above


An electric field can just support a
water droplet \( 1.0 \times 10^{-6} \mathrm{m} \) in diameter
carrying one electron charge. The magnitude of electric field strength is
A \( \cdot 3.21 \times 10^{4} V / m \)
В. \( 2.31 \times 10^{4} V / m \)
C \( .1 .32 \times 10^{4} V / m \)
D. \( 6.42 \times 10^{4} V / m \)


section \( A \) and length \( 2 l \) is clamped
firmly at two points \( A \) and \( B \), which are
\( 2 l m \) apart and in the same plane. \( A \)
body of mass \( m \) is hung from
the middle point of the wire such that
the middle point sags by x lower from
the original position. If Young's modulus
is \( Y, \) then \( m \) is given by:
A \( \cdot \frac{1}{2} \frac{Y A x^{2}}{g l^{2}} \)
B \( \cdot \frac{1}{2} \frac{Y A l^{2}}{g x^{2}} \)
c. \( \frac{Y A x^{3}}{g l^{3}} \)
D \( \cdot \frac{Y A l^{2}}{g x^{2}} \)


The function \( f(x)=[x], \) at \( x=5 \) is:
A. Ieft continuous
B. right continuous
c. continuous
D. cannot be determined


Assertion (A) : The elastic potential energy of a spring increases when it is elongated and decreases when it is
compressed
Reason
(R) : Work done on spring is stored in it as elastic potential energy.
A. Both assertion and reason are true and the reason is correct explanation of the assertion
B. Both assertion and reason are true, but reason is not correct explanation of the assertion
c. Assertion is true, but the reason is false
D. Assertion is false, but the reason is true


Prove that, \( [\boldsymbol{x}]+[\mathbf{5} \boldsymbol{x}]+[\mathbf{1 0 x}]+[\mathbf{2 0 x}]= \)
\( 36 k+35 . k \varepsilon I \) does not have any real
solution. Here [.] denotes greatest integer function.


n given figure, AD and CE are two altitudes of \( \triangle A B C \). Prove that
(i) \( \triangle A E F \sim \triangle C D F \)
(ii) \( \triangle A B D \sim \triangle C B E \)
(iii) \( \triangle A E F \sim \triangle A D B \)
(iv) \( \triangle \boldsymbol{F} \boldsymbol{D} \boldsymbol{C} \sim \triangle \boldsymbol{B} \boldsymbol{E} \boldsymbol{C} \)


\( \int \frac{d x}{x\left(x^{7}+1\right)} \)
is equal to:
\( ^{\mathbf{A}} \cdot \log \left(\frac{x^{7}}{x^{7}+1}\right) \)
в. \( \frac{1}{7} \log \left(\frac{x^{7}}{x^{7}+1}\right)+c \)
\( ^{\mathbf{c}} \cdot \log \left(\frac{x^{7}+1}{x^{7}}\right)+c \)
D \( \cdot \frac{1}{7} \log \left(\frac{x^{7}+1}{x^{7}}\right)+c \)


Which of the given statements is incorrect for the complex
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right]^{3+} ? \)
A. It is a low spin complex
B . It is \( d^{2} s p^{3} \) hybridised
c. It is paramagnetic
D. None of these


Answer the following question in one
word or one sentence or as per exact
requirement of the question. Write the value of \( \lim _{x \rightarrow a} \frac{x f(a)-a f(x)}{x-a} \)


Expand \( (x-2)^{3} \)


A conductor rod AB moves parallel to Xaxis in a uniform magnetic field,
pointing in the positive Z-direction. The end \( A \) of the rod gets-
A. positively chargedd
B. negatively charge
c. neutral
D. first positively charged and then negatively chrged


Artificial ripening of fruits/banana is accomplished by treatment with
A. Sodium chloride
B. IAA
c. Ethylene gas
D. Kinetin


What is nucleosome? Draw diagram of double stranded polynucleotide chain of DNA and explain its structure.


A digestive enzyme, named amylase, in the saliva begins digestion of -
A. carbohydrates
B. fats
C. proteins
D. nucleic acids


When borax is dissolved in water:
\( \mathbf{A} \cdot B(O H)_{3} \) is formed only
\( \mathbf{B} \cdot\left[B(O H)_{4}\right]^{-} \) is formed only
\( \mathbf{c} \cdot \operatorname{both} B(O H) 3 \) and \( \left[B(O H)_{4}\right]^{-} \) are formed
D. \( \left[B_{3} O_{3}(O H)_{4}\right]^{-} \) is formed only


An ideal resistance \( R \), ideal inductance
\( L, \) ideal capacitance \( C \) and \( A C \) volt
meters \( V_{1}, V_{2}, V_{3} \) and \( V_{4} \) are
connected to an AC source as shown. At
resonance,
A. Reading in \( V_{3}= \) reading in \( V_{1} \)
B. Reading in \( V_{1}= \) reading in \( V_{2} \)
c. Reading in \( V_{2}= \) reading in \( V_{4} \)
D. Reading in \( V_{2}= \) reading in \( V \)


Which of the following element is not in the liquid state at room temperature?
A. \( H g \)
в. \( L i \)
\( c . G a \)
D. \( B r \)


\( \operatorname{Inthe} A \underline{H B r} \quad \) B \( \underline{a l c K O H} \quad c \frac{Z n / H_{2} O}{O_{3}} \)
\( \boldsymbol{C H}_{3} \boldsymbol{C H O}+\boldsymbol{H C H O} \) the compound \( \mathbf{A} \)
is :
A. ethylene
B. acetic acid
c. propene
D. 1- butene


Calculations show that an angle is \( 37 \frac{1}{2}^{\circ} \) The size obtained by drawing and
measurement is \( 35^{\circ} \). Find the error in
percent.


The stiochiometry of the following
reaction is:
\( \boldsymbol{K}_{2} \boldsymbol{S}_{2} \boldsymbol{O}_{8}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{2} \boldsymbol{K} \boldsymbol{I}(\boldsymbol{a} \boldsymbol{q}) \rightarrow \)
\( \mathbf{2} K_{2} \boldsymbol{S} \boldsymbol{O}_{4}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{I}_{2}(\boldsymbol{a} \boldsymbol{q}) \)
A .2: 1
B. 1: 2
c. 2: 2
D. 1: 3


Fill in the blanks using the correct word given in brackets:
Two polygons of the same number of sides are similar, if (a) their corresponding angles are and
(b) their
corresponding sides are \( \ldots \) proportional).


Amoeba consists of
A. Many cells
B. One cell
C. Two cells
D. Four cells


Calculate the critical angle between glass and air. (Given \( \left._{a} \mu_{g}=\frac{3}{2}\right) \)
A . 41.8
в. 45.8
c. 45
D. 30


The length of a potentiometer wire is 10m. The distance between the null
points on its wire corresponding to two cells comes out to be \( 60 \mathrm{cm} \). If the difference of emf's of the cells is 0.4 volt
then the potential gradient on potentiometer wire will be
\( A \cdot 0.67 \mathrm{V} / \mathrm{m} \)
B. \( 0.5 \vee / \) m
c. \( 2.5 \mathrm{V} / \mathrm{m} \)
D. ov \( / \mathrm{m} \)


Assertion
A cloth covers a table. Some dishes are
kept on it. The cloth can be pulled out without dislodging the dishes from the
table
Reason
For every action, there is an equal and opposite reaction.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Which among the following is true regarding alpha particles?
A. They posses low ionising power
B. They posses high penetrating power
C. They produce scintillation on fluorescent screen
D. Alpha particle is the lightest particle emitted by radioactive substance


Find \( x, y \) satisfying the matrix
equations \( \left[\begin{array}{ccc}\boldsymbol{x}-\boldsymbol{y} & \boldsymbol{2} & -\boldsymbol{2} \\ \boldsymbol{4} & \boldsymbol{x} & \boldsymbol{6}\end{array}\right]+\left[\begin{array}{ccc}\boldsymbol{3} & -\boldsymbol{2} & \boldsymbol{2} \\ \boldsymbol{1} & \boldsymbol{0} & \boldsymbol{-} \boldsymbol{1}\end{array}\right]= \)
\( \left[\begin{array}{ccc}\mathbf{6} & \mathbf{0} & \mathbf{0} \\ \mathbf{5} & \mathbf{2} \boldsymbol{x}+\boldsymbol{y} & \mathbf{5}\end{array}\right] \)


Brass is an element.
A. True
B. False


A current of 0.24 A flows through a
circular coil of 72 turns, the average diameter of the coil being \( 20 \mathrm{cm} . \) What is the strength of field produced at the centre of the coil?


Enter 1 if true else 0 .
The direction cosines of the vector \( 3 \hat{i}- \) \( 4 \hat{k} \) are
\( \frac{3}{5}, 0, \frac{-4}{5} \)


Find the solution of the differential
equation \( (x \log x) \frac{d y}{d x}+y= \)
\( 2 x \log x,(x \geq 1) \)


A number when increased by \( 30 \% \) becomes \( 78 . \) Find the number.
A . 60
B. 70
\( c \cdot 40 \)
D. 48


Assertion
Assertion: In physics, we attempt to derive the properties of a bigger, more complex system from the properties and interactions of its constituent
simpler parts.
Reason
Reason: This approach is called unification and is at the heart of
physics.
A. both assertion and reason are true and reason is the correct explanation of assertion
B. both assertion and reason are true and reason is not the correct explanation of assertion
c. assertion is true but reason is false
D. both assertion and reason are false.


Chlorine is called as a saviour as well as
killer. Explain.


Use Venn diagrams to verify De Morgan's law for set difference \( \boldsymbol{A} \backslash \)
\( (\boldsymbol{B} \cap \boldsymbol{C})=(\boldsymbol{A} \backslash \boldsymbol{B}) \cup(\boldsymbol{A} \backslash \boldsymbol{C}) \)


\( \mathbf{f} \boldsymbol{A}=\left[\begin{array}{lll}\mathbf{1} & \mathbf{4} & \mathbf{0} \\ \mathbf{2} & \mathbf{5} & \mathbf{0} \\ \mathbf{3} & \mathbf{6} & \mathbf{0}\end{array}\right] \) and \( \boldsymbol{B}=\left[\begin{array}{lll}\mathbf{3} & \mathbf{2} & \mathbf{1} \\ \mathbf{1} & \mathbf{2} & \mathbf{3} \\ \mathbf{4} & \mathbf{5} & \mathbf{6}\end{array}\right] \)
and \( C=\left[\begin{array}{lll}3 & 2 & 1 \\ 1 & 2 & 3 \\ 7 & 8 & 9\end{array}\right], \) Then evaluate
\( \boldsymbol{A B}-\boldsymbol{B C} \)


\( \int_{\pi / 6}^{\pi / 3} \frac{\sin ^{3} x}{\sin ^{3} x+\cos ^{3} x} d x= \)
A \( \cdot \frac{\pi}{2} \)
в.
\( c \cdot \frac{\pi}{12} \)
D. \( \frac{\pi}{6} \)


A wire of radius r and another wire of
radius \( 2 r, \) both of same material and
length are connected in series to each other. The combination is connected
across a battery. The ratio of the heats produced in the two wires will be
A . 4.00
B . 2.00
c. 0.50
D. 0.25


0
the starting material for the oxidation
shown below?
\( A \)
B.
\( c \)
D.


Evaluate: \( [\sqrt[3]{\sqrt[6]{5^{9}}}]^{4}[\sqrt[6]{\sqrt[3]{5^{9}}}]^{4} \)
\( A \cdot 5^{2} \)
в. \( 5^{4} \)
\( c \cdot 5^{8} \)
D. \( 5^{12} \)


When \( _{3}^{7} \mathrm{Li}\left(M_{L i}=7.016004 \mu\right) \) is
bombarded by a proton two \( \alpha \) - particles
result. \( \left(M_{H e}=4.002603 \mu\right) . \) Find the reaction energy
A . 13.35 MeV
B. 14.85 MeV
c. \( 16.08 \mathrm{MeV} \)
D. 17.35 MeV


The variance of the data
6,8,10,12,14,16,18,20,22,24 is
A . 15
B . 20
c. 30
D. 33


Two small equal point charges of magnitude \( q \) are suspended from a
common point o the ceiling by insulating massless strings of equal lengths. They come to equilibrium with
each string making angle \( \theta \) from the
vertical. If the mass of each charge is \( m \)
\( \mathrm{m}, \) then the electrostatic potential at
the center of line joining them will be \( \left(\frac{1}{4 \pi \epsilon_{0}}=K\right) \)
A \( .2 \sqrt{k / m g \tan \theta} \)
B . \( \sqrt{k m g \tan \theta} \)
c. \( 4 \sqrt{k / m g \tan / \theta} \)
D. \( 4 \sqrt{k m g \tan \theta} \)


Food poisoning and gas forming rodshaped bacterium is
A. Shigella
B. Salmonella
c. clostridium
D. Escherichia coli


A hollow metal ball carrying an electric charge produces no electric field at points.
A. outside the sphere
B. on its surface
c. Inside the sphere
D. At a distance more than twice


An electron is moving in a cyclotron at a speed of \( 3.2 \times 10^{7} m s^{-1} \) in a magnetic
field of \( 5 \times 10^{-4} \) T perpendicular to it.
What is the frequency of this electron? \( \left(\boldsymbol{q}=\mathbf{1 . 6} \times \mathbf{1 0}^{-\mathbf{1 9}} \boldsymbol{C}, \boldsymbol{m}_{\boldsymbol{e}}=\mathbf{9 . 1} \times\right. \)
\( \left.10^{-31} k g\right) \)
A \( .1 .4 \times 10^{5} \mathrm{Hz} \)
B. \( 1.4 \times 10^{7} \mathrm{Hz} \)
c. \( 1.4 \times 10^{6} \mathrm{Hz} \)
D. \( 1.4 \times 10^{9} \mathrm{Hz} \)


If current \( \boldsymbol{I}_{1}=\mathbf{3} \boldsymbol{A} \sin \omega \boldsymbol{t} \) and \( \boldsymbol{I}_{2}=\boldsymbol{4} \boldsymbol{A} \)
\( \cos \omega t, \) then \( I_{3} \) is :
A .5 Asin \( \left(\omega t+53^{\circ}\right) \)
B. 5 Asin \( \left(\omega t+37^{\circ}\right) \)
c. 5 Asin \( \left(\omega t+45^{\circ}\right) \)
D. 5 Asin \( \left(\omega t+30^{0}\right) \)


Among the electrolytes
\( N a_{2} S O_{4}, C a C l_{2}, A l_{2}\left(S O_{4}\right)_{3} \quad \) and
\( N H_{4} C l, \) the most effective coagulating
agent for \( S b_{2} S_{3} \) sol is:
A. \( N a_{2} S O_{4} \)
в. \( C a C l_{2} \)
c. \( A l_{2}\left(S O_{4}\right)_{3} \)
D. \( N H_{4} C l \)


Let \( R \) be the relation over the set of all
straight lines in a plane such that \( l_{1} R \)
\( l_{2} \Leftrightarrow l_{1} \perp l_{2} . \) Then, \( R \) is
A. symmetric
B. reflexive
c. transitive
D. an equivalence relation


Explain the process of formation of complex proteins.


Which of the following are exothermic processes?
(i) The reaction of water with quicklime
(ii) Dilution of an acid
(iii) Evaporation of water
(iv) Sublimation of camphor (crystals)
\( A \cdot \) (i) and (ii)
B. (ii) and (iii)
c. (i) and (iv)
D. (iii) and (iv)


The string of a violin emits a note of 205
\( \mathrm{Hz} \) at its correct tension. The string is tightened slightly and then it produces six beats in 2 seconds with tuning fork of the frequency \( 205 \mathrm{Hz} \). The frequency of the note emitted by the taut string is


If \( ^{18} \boldsymbol{C}_{\boldsymbol{r}}=^{18} \boldsymbol{C}_{\boldsymbol{r}+\mathbf{2}}, \) find \( ^{r} \boldsymbol{C}_{\boldsymbol{5}} \)


In a circle of diameter \( 10 \mathrm{cm} \), the length of each of 2 equal and parallel chords is \( 8 \mathrm{cm}, \) then the distance between these
two chords is
A. \( 4 \mathrm{cm} \)
B. \( 5 \mathrm{cm} \)
\( c \cdot 6 \mathrm{cm} \)
D. \( 7 \mathrm{cm} \)


Which of the following changes will cause the free energy of a cell reaction
to decrease?
\( \boldsymbol{Z} \boldsymbol{n} \mid \boldsymbol{Z} \boldsymbol{n} \boldsymbol{S} \boldsymbol{O}_{4}(\boldsymbol{a} \boldsymbol{q})\left(\boldsymbol{x}_{1} \boldsymbol{M}\right) \| \boldsymbol{H} \boldsymbol{C l}(\boldsymbol{a} \boldsymbol{q})\left(\boldsymbol{x}_{2} \boldsymbol{N}\right. \)
This question has multiple correct options
A. Increase in the volume of HCI solution from \( 100 \mathrm{mL} \) to \( 200 \mathrm{mL} \)
B. Increase in the pressure of hydrogen from 1 atm to 2 \( \operatorname{atm} \)
C . Increase in molarity \( x_{2} \) from 0.1 to 1 M
D. Decrease in molarity \( x_{1} \) from 1 M to 0.1 M


In a regular pentagon \( A B C D E ; A C \)
and \( B E \) intersect at \( P . \) Calculate the
angles \( C B E \) and \( B P A \)
\( A \cdot 30^{\circ} \) and \( 60^{\circ} \)
B. \( 72^{\circ} \) and \( 108^{\circ} \)
c. \( 54^{\circ} \) and \( 108^{\circ} \)
D. \( 72^{\circ} \) and \( 72^{\circ} \)


The following table shows the interest paid by a company (in lakhs):
\( \begin{array}{lll}\text { 1995- } & \text { 1996- } & \text { 1997- }\end{array} \) Year
Interest
in lakhs
\[
20
\]
25
of rupees)
Draw the bar graph to represent the above information.


State differences between acids and
bases.


Which of the following quantities remain constant during projectile
motion?
A. Average velocity between two points
B. Average speed between two points
c. \( \frac{d \bar{v}}{d t} \)
D. \( \frac{d \vec{y}}{d t} \) where y is vertical displacement


select the correct option from the given
codes.
\( \mathbf{A} \)
\( A-(i), B-(i i) ;(i v) ;(i x), C-(i i i) ;(v i), D-(v i i) \) ; (viii), , E-(V)
\( B \)
\( A-(i), B-(i i) ;(i v), C-(i i i) \) ; (vi); ; (ix), D-(vii);(viii), E-(v)
\( ;(i x), D-(v i i) \)
\( \mathbf{C} \cdot A-(i), B-(i i) ;(i v) ;(i x), C-(i i i) \)
; (viii), , E-(v); (vi)
D. \( A-(i) \) \( \mathrm{B}-(\mathrm{iv}) ;(\mathrm{i} \mathrm{x}), \mathrm{C}-(\mathrm{ii}) ;(\mathrm{iii}) ;(\mathrm{vi}), \mathrm{D}-(\mathrm{vii}) ;(\mathrm{viii}), \mathrm{E}-(\mathrm{v}) \)


How many men must be engaged to do
a piece of work in 16 days which 24 men can do in 40 days?


Sound travels the fastest through vacuum. State whether true or false.
A. True
B. False


The difference between a two-digit number and the number obtained by interchanging the position of the digits is \( 45 . \) What is the difference between
the digits of that number?
\( A \cdot 4 \)
B. 5
c. 6
D.


An infinite number of charges, each of
charge \( 1 \mu C \) are placed on the \( x \) -axis with co-ordinates \( x=1,2,4,8, \dots \dots \dots \) an charge of \( 1 \mathrm{C} \) is kept at the origin, then what is the net force acting on \( 1 \mathrm{C} \) charge
A. 9000 N
B. 12000 N
c. \( 24000 \mathrm{N} \)
D. 36000 N


Inversion of sugar is pseudo first order reaction. Explain.


The cell potential of \( \mathbf{A} \mathbf{g}|\mathbf{A} \mathbf{g} \mathbf{B} \mathbf{r}(\mathbf{s})| \mathbf{H} \mathbf{B} \mathbf{r}_{(0.02 \mathrm{M})}\left|\mathbf{H}_{\mathbf{2}(\mathbf{0 . 5} \mathrm{atm})}\right| \mathbf{P} \mathbf{t}(\mathbf{G} \mathbf{i} \)
is:
A . \( 0.26 v \)
B. -0.26V
c. \( 0.16 v \)
D . -0.16v


Figure shows three spherical shells in
separate situations, with each shell having the same uniform positive net
charge. Points 1,4 and 7 are at the same radial distances from the centre
of the their respective shells; so are
points 2,5 and \( 8 ; \) and so are points 3,6 and \( 9 . \) With the electric potential taken equals to zero at an infinite distance,
choose correct statement.
A. Point 3 has highest potential
B. Point 1,4 and 7 are at same potential
C. Point 3 has lowest potential
D. Point 5 and 8 are at same potential


The circuit shown in Figure contains
three resistors \( \boldsymbol{R}_{1}=\mathbf{1 0 0} \boldsymbol{\Omega}, \boldsymbol{R}_{2}=\mathbf{5 0} \boldsymbol{\Omega} \)
and \( R_{3}=20 \Omega \) and cells of emfs \( E_{1}= \)
\( 2 V \) and \( E_{2} . \) The ammeter indicates a
current of 50 mA. Determine the
currents in the resistors and the emf of
the second cell. The internal resistance
of the ammeter and of the cells should
be neglected


If the energy difference between the
electronic states is \( 214.68 \mathrm{kJ} \mathrm{mol}^{-1} \)
calculate the frequency of light emitted when an electron drops form the higher to the lower state Plank's constant?
\( h=39.79 \times k J \mathrm{mol}^{-1} \)
A \( \cdot 5.39 \times 10^{14} \) cps
B. \( 5.99 \times 10^{15} \) cps
C. \( 5.99 \times 10^{14} \) cps
D. 5.39 \( \times 10^{15} \mathrm{cps} \)


A current \( i \) is flowing through the wire of
diameter \( d \) having drift velocity of
electrons \( v_{d} \) in it. What will be new drift
velocity when diameter of wire is made \( \frac{\boldsymbol{d}}{\boldsymbol{4}} \)
\( \mathbf{A} \cdot 4 V_{d} \)
в. \( \frac{V_{d}}{4} \)
\( \mathbf{c} \cdot 16 V_{d} \)
D. \( \frac{V_{d}}{16} \)


From the below-given pairs, which is more stable?
\( \boldsymbol{C r} \boldsymbol{O}_{4}^{2-}-\ldots-\boldsymbol{M o} \boldsymbol{O}_{4}^{2-} \)
A \( \cdot C r O_{4}^{2-}=M o O_{4}^{2-} \)
B . \( C r O_{4}^{2-}<M o O_{4}^{2} \)
c. \( C r O_{4}^{2-}>M o O_{4}^{2-} \)
D. None of these


A circuit element shown in the figure as
box is having either a capacitor or an
inductor. The power factor of the circuit
is \( 0.8, \) which current lags behind the
voltage. The source voltage \( V \)


A coconut of mass \( m \) falls from its tree
through a vertical distance of \( s \) and
could reach ground with a velocity of \( v \)
\( m s^{-1} \) due to air resistance. The work
done by air resistance is:


What is transmitted from parent cells to daughter cells during cell division?
A. DNA
B. tRNA
c. mRNA
D. rRNA
E. RNA polymerase


Write a linear equation in two variables to represent the following statement Two numbers are such that 2 times of
one is same as 3 times of the other.
A. \( 2 x=3 y, \) where \( x= \) first number and \( y=\operatorname{second} \)
number
B. \( 2 x=-3 y \), where \( x= \) first number and \( y=\operatorname{second} \) number
c. \( 2 x=7 y \), where \( x= \) first number and \( y=\operatorname{second} \) number
D. \( x=3 y \), where \( x= \) first number and \( y=\operatorname{second} \) number


A car covers first \( 2 k m \) of the total
distance of \( 4 k m \) with a speed of
\( 30 k m / h \) and the remaining distance of \( 2 k m \) with a speed of \( 20 k m / h \). The
average speed of the car is:
\( \mathbf{A} \cdot 24 k m / h \)
в. \( 25 k m / h \)
\( c .50 k m / h \)
D. \( 26 k m / h \)


The flux linked with a coil changes with
time according to the equation \( \phi=a t^{2} \) \( +b t+c . \) Then Sl unit of a is
A. volt
B. Volt/sec
c. volt.sec
D. weber


A group of students while coming from
the school noticed a box marked

"Danger H.T. 2200 \( V \) " at a substation in
the main street. They did not understand the utility of a such a high voltage, while they argued the supply was only \( 220 \mathrm{V} \). They asked their
teacher this question the next day. The teacher thought it to be an important question and therefore explained to the whole class.
(i) What device is used to bring the high voltage down to low voltage of a.c. current and what is the principle of its working?
(ii) Is it possible to used this device for bringing down the high dc voltage to the
low voltage? Explain.
(iii) Write the values displayed by the
students and the teacher


What is correct acidic strength of nitrogen oxides?
A. \( N_{2} O>N O>N_{2} O_{3}>N O_{2} \)
в. \( N_{2} O<N O<N_{2} O_{3}<N O_{2} \)
c. \( N O>N_{2} O_{3}>N_{2} O_{4}>N_{2} O_{5} \)
D. \( N O<N_{2} O_{3}<N_{2} O_{4}<N_{2} O_{5} \)


Two metallic spheres, one hollow and the other solid, have same diameter.
The hollow sphere will hold charge
A. Same as the solid sphere
B. 2 times as the solid sphere
\( \mathrm{c} \cdot \frac{1}{2} \) times as the solid sphere
D. zero


A uniform conduction wire of length
\( 10 g \) and resistance \( R \) is wound up into
four turns as a current carrying coil in
the shape of equilateral triangle of side
\( a . \) If current \( I \) is flowing through the coil
then the magnetic moment of the coil is
A \( \cdot \frac{\sqrt{3}}{2} a^{2} I \)
B. \( \frac{a^{2} I}{\sqrt{3}} \)
c. \( \sqrt{3} a^{2} I \)
D. \( \frac{2 a^{2} I}{\sqrt{3}} \)


freely slide on a pair of parallel smooth
horizontal rails placed in vertical
magnetic field \( B \). The rails are
connected by a capacitor of
capacitance \( C . \) The electric resistance
of the rails and the wire is zero. If a
constant force \( F \) acts on the wire as
shown in the figure. Then, the
acceleration of the wire can be given as
\( ^{\mathbf{A}} \cdot_{a}=\frac{C^{2} B^{2} l-F}{m} \)
\( ^{\mathbf{B}} \cdot_{a}=\frac{F}{m+C B l} \)
\( ^{\mathbf{C}} \cdot_{a}=\frac{F C^{2} B^{2} l}{m} \)
D. \( a=\frac{F}{m+C B^{2} l^{2}} \)


Identify the pair of alkanes which can exhibit chain isomerism and has a neo
isomer respectively? This question has multiple correct options
A. \( C_{3} H_{8}, C_{4} H_{10} \)
B. \( C_{4} H_{10}, C_{5} H_{12} \)
c. \( C_{5} H_{12}, C_{6} H_{14} \)
D. \( C_{6} H_{14}, C_{7} H_{16} \)


In a reaction, a substance undergoes decomposition which is catalyzed in the presence of finely divided nickel. If there
are enough sites on the surface of catalysts so that 20 molecules of
substance react per second, the rate of reaction for a \( 1.0 \mathrm{M} \) solution is:
A \( .3 .34 \times 10^{-23} \) mol \( L^{-1} s^{-1} \)
B . 3.14 \( \times 10^{-23} \) mol \( L^{-1} s^{-1} \)
c. \( 3.68 \times 10^{-23} \) mol \( L^{-1} s^{-1} \)
D. None of these


which term of the A.P.
\( \mathbf{1 0 0}, \mathbf{9 7}, \mathbf{9 4}, \mathbf{9 1}, \ldots \) is its first negative
term?


Calculate the area between two curves:
\( \boldsymbol{y}=\boldsymbol{x}^{2} \)
\( \boldsymbol{y}=\boldsymbol{x}+1 \)


Human eye:
A. can detect polarized light
B. cannot detect polarization of light
C. can detect only circularly polarized light
D. can detect only linearly polarized light


Photographic paper is developed with
alkaline hydroquinone
Select correct statement
A. Hydroquinone is the oxidant
B. \( A g^{+} \) is the oxidant
\( \mathrm{c} \cdot B r^{-} \) is the oxidant
D. \( A g^{+} \) is the reductant


An experiment in which \( \alpha \) - particles were deflected by a gold foil produced new insights into the structure of the
atom

Which conclusion can be drawn from
the results of the experiment?
A. Atomic nuclei occupy a very small fraction of the volume of an atom
B. Electrons orbit the atomic nucleus
c. Some atoms of the same element contain different numbers of neutrons
D. The atomic nucleus contains protons and neutrons


If the set \( A \) has 3 elements and the set
\( \boldsymbol{B}=(\mathbf{3}, \mathbf{4}, \mathbf{5}) \) find the number of
elements in \( (\boldsymbol{A} \times \boldsymbol{B}) \) ?


In crystalline form sulphur existing in
\( \boldsymbol{S}_{8} \) molecule has :
A. crown shaped structure
B. tetrahedral structure
c. pyramidal structure
D. angular structure


State whether the following number is rational,

If rational then enter 1 and if false then
enter 0
\( \left(\frac{\sqrt{7}}{6 \sqrt{2}}\right)^{2} \)


The method of extraction of silver by
cyano complex formation followed by metal displacement is called as:
A. Parke's method
B. MacArthur-Forest method
c. Serpeck method
D. Hall's method


If \( \boldsymbol{A}=[\mathbf{1} \mathbf{2} \mathbf{3}], \) then the set of elements of
\( A \) is
\( A \cdot\{1,2,3\} \)
в. \{2,0\}
c. only 2
D. None of these


The value of \( \frac{1}{i}+\frac{1}{i^{2}}+\frac{1}{i^{3}}+\ldots+\frac{1}{i^{102}} \) is
equal to
A \( .-1-i \)
в. \( -1+i \)
\( \mathrm{c} \cdot 1-i \)
D. \( 1+i \)


Strongest cartilage is
A. Hyaline cartilage
B. Fibrous cartilage
C . Elastic cartilage
D. None of the above


Differentiate between male and female
heterogamety.


The force acting on a pole of strength of \( 20 \mathrm{Am} \) is \( 8 \times 10^{-4} \mathrm{N}, \) when placed in a
magnetic field. The magnetic induction field strength is :
A. \( 4 \times 10^{-6} \) т
B. \( 0.4 \times 10^{4} \mathrm{T} \)
\( c \cdot 4 G \)
D. \( 4 \times 10^{-5} \mathrm{T} \)


\( 1.00 \mathrm{g} \) of a hydrated salt contains \( 0.2014 \mathrm{g} \) of iron, \( 0.1153 \mathrm{g} \) of sulphur \( 0.2301 \mathrm{g} \) of oxygen and 0.4532 g of water of crystallisation. If its empirical formula \( (\boldsymbol{F e}=\mathbf{5 6} ; \boldsymbol{S}=\mathbf{3 2} ; \mathbf{0}=\mathbf{1 6}) \) is
\( F e S O_{x} \cdot y H_{z} O, \) then find the value of
\( x, y \) and \( z \)
A. \( x=4, y=7, z=2 \)
в. \( x=3, y=6, z=2 \)
c. \( x=4, y=6, z=3 \)
D. None of these


Describe the criteria for animal
classification.


If a clock strikes once at 1 o'clock,
twice at 2 o'clock and so on, how many
times will it strike in a day?


Select the correct statements about
greenhouse gases:
A. Carbon dioxide is the only gas in the atmosphere which causes global warming.
B. The greenhouse gases trap heat and do not allow heat to escape into outer
space
C. Water vapours do not contribute to the greenhouse effect.
D. The presence of excessive greenhouse gases in the atmosphere is responsible for global warming.
A. A and B
B. B and D
c. \( c \) and \( B \)
D. D and A


Assertion
The flux of electric field through a spherical surface of radius 1.5 a is more
than flux of electric field through a
spherical surface of radius 0.5 a. (Both
centred at origin)
Reason
The electric field at \( x=1.5 \) a is more than
electric field at 0.5 a
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 \( \frac{d y}{d x} \) for \( y=e^{x}(a \cos x+b \sin x) \)


The decomposition of \( C l_{2} O_{7} \) at \( 400 K \)
in the gas phase to \( C l_{2} \) and \( O_{2} \) is a first
order reaction.
(i) After 55 seconds at \( 400 K \), the
pressure of \( \boldsymbol{C l}_{2} \boldsymbol{O}_{7} \) falls from \( \mathbf{0 . 0 6 2} \) to
0.044 at \( m . \) Calculate the rate constant.
(ii) Calculate the pressure of \( C l_{2} O_{7} \) after 100 seconds of decomposition at this temperature.


A certain \( 120 \mathrm{Hz} \) wave on a string has an amplitude of \( 0.160 \mathrm{mm} . \) The amount of energy exists in an 80 g length of the \( \operatorname{string} \) is \( 58 \times 10^{-x} \) m \( J \). Find \( x \)


\( \lim _{x \rightarrow 0} \frac{\sin \left(x^{3}\right)}{x} \) is equal to
A
B. 3
\( c \cdot 0 \)
D. None of these


Which of the following statements is
correct for \( \left[M n(C N)_{6}\right]^{3-} \) according to
valence bond theory?
\( \mathbf{A} \cdot d^{2} s p^{3}, \) inner orbital complex, paramagnetic, 2.87 B.M.
B. \( d^{2} s p^{3}, \) inner orbital complex, diamagnetic, zero magnetic moment.
C \( \cdot d^{2} s p^{3} \), outer orbital complex, paramagnetic, 3.87 B.M.
D. \( d s p^{2} \), outer orbital complex, diamagnetic, zero magnetic moment.


The force between two magnetic poles
reduces to \( a N, \) if distance between
them is increased to \( n \) times and it
increases to \( b N \) if the distance between
them is \( 1 / n^{t h} \) the original value. Then
\( a: b \) is :
\( A \cdot 1 \cdot n^{2} \)
B \( \cdot n^{2}: \)
\( c \cdot n^{4} \cdot 1 \)
\( D \cdot 1: n^{4} \)


A closed system can exchange:
A. matter with the surroundings
B. energy with the surroundings
C. both \( A \) and \( B \)
D. none of the above


Prove that \( \int_{\log 2}^{x} \frac{1}{e^{x}-1} d x=\log \frac{3}{2} \) when
\( \boldsymbol{x}=\log 4 \)


How many number of atoms are present
in 50 grams of iron?
B. \( 0.537 \times 10^{20} \)
C. \( 5.37 \times 10^{24} \)
D. \( 1.537 \times 10^{24} \)


Why should electrostatic field be zero
inside a conductor?


Law of limiting factor is
A. Law of maximum
B. Law of minimum
C. Law of optimum
D. All of the above


Evaluate \( \sqrt[3]{\left(\frac{1}{64}\right)^{-2}} \)
\( A \)
B . 16
\( c .32 \)
D. 64


How will you design a shaving mirror
assuming that a person keeps it \( 10 \mathrm{cm} \) from his face and view the magnified image of the face of the closest
comfortable distance of \( 25 \mathrm{cm} \). The
radius of curvature of the mirror would
then be:
\( \mathbf{A} \cdot 24 \mathrm{cm} \)
B. \( -60 c m \)
\( c .-24 c m \)
D. \( 30 \mathrm{cm} \)


If the geometric progression
\( 162,54,18, \dots \) and \( \frac{2}{81}, \frac{2}{27}, \frac{2}{9}, \dots . . \) here
their nth term equal. Find the value of \( n \)


A metal nitrate A on heating gives yellowish brown coloured metal oxide with brown gas \( \mathrm{B} \) and a colourless gas
C. aqueous solution of A on reaction with potassium iodide forms a yellow precipitate of compound
D. Identify \( A, B \)
C, D. Also identify the types of both the reactions.


Mark correct answer


The function
\[
\boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{r}
\boldsymbol{x}^{2}-\boldsymbol{a} \boldsymbol{x}+\mathbf{3}, \boldsymbol{x} \text { is ratio } \\
\boldsymbol{2}-\boldsymbol{x}, \quad \boldsymbol{x} \text { is irratio }
\end{array}\right.
\]
is continuous at exactly two points then
the possible values of ' \( a \) ' are
\( A \cdot(2, \infty) \)
В \( \cdot(-\infty, 3) \)
c. \( (-\infty,-1) \cup(3, \infty) \)
D. \( R \)


Phosphorus trichloride, \( \boldsymbol{P} \boldsymbol{C l}_{3} \) undergoes hydrolysis to produce an oxoacid. The formula of oxoacid is :
A \( . H P O_{3} \)
в. \( H_{3} P O_{3} \)
\( \mathrm{c} \cdot H_{3} P O_{4} \)
D. \( H_{3} P O_{2} \)


Two identical equiconcex lenses made of glass of refractive index \( 1.5, \) placd in contact has power P. When a liquid of refractive index \( \mu \) is filled in the gap between the lenses, the power becomes \( \boldsymbol{P} \)
\( \overline{\mathbf{3}} \)
\( i f \mu=\frac{x}{3} . \) Find the value of \( x \)


Study the following table.
Compound Compound Mass of the wmpound Compound Mass
(mol. mass)
\( C O_{2}(44) \) 4.4
॥. \( N O_{2}(46) \) 2.3
\( \| \)
\( H_{2} O_{2}(34) \) 6.8
\( V \)
\( S O_{2}(64) \)
Which two compounds have least mass
of oxygen? (Molecular masses of compounds are given in brackets)
A. II and IV
B. I and III
c. I and II
D. III and IV


A compound \( X \) is obtained by the
reaction of alkaline \( \boldsymbol{K} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4} \) with
another compound \( Y \) followed by
acidification. Compound \( X \) also reacts with compound \( Y \) in presence of few
drops of \( H_{2} S O_{4} \) to form a sweet
smelling compound \( Z \). The compound
\( X, Y \) and \( Z \) are respectively:
A. ethanol, ethene, ethanoic acid
B. ethanoic acid, ethanol, ethylethanoate
c. ethanoic acid, ethanal, ethene
D. ethanol, ethanoic acid, sodium ethanoate


What is the phase difference between
AC e.m.f and current in the following? Pure resistor and pure inductor.


Who was the first woman to fly in space?
A. Valentina Tereshkova
B. Rhea Seddon
c. sally Ride
D. Anna Fisher


Statement 1: Gas-phase elements
absorb or emit only specific wavelengths of visible light when
excited by an electric current.
Statement 2: The energy levels that
electrons can occupy in gas-phase
atoms and molecules are continuous.
A. Both Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement 1
B. Both Statement 1 and Statement 2 are correct and Statement 2 is not the correct explanation of Statement 1.
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.


Members of which of the following have similar chemical properties?
A. Isotopes
B. Isobars
c. Allotropes
D. Both isotopes and allotropes


Which of the following is the IUPAC name of the aromatic monomer is
present in melmac?
B. Methanal
c. 1,3,5 - Triamine -2,4,6 - triazine
D. Melamine


In India, a nuclear power plant is
located in
A. Rampur
B. Tarapur
c. sahranpur
D. Kanpur


Mean deviation for \( n \) observations
\( x_{1}, x_{2}, \ldots . . x_{n} \) from their mean \( \bar{X} \) is given
by:
A \( \cdot \sum_{i=1}^{n}\left(x_{i}-\bar{X}\right) \)
B \( \cdot \frac{1}{n} \sum_{i=1}^{n}\left|x_{i}-\bar{X}\right| \)
C \( \cdot \sum_{i=1}^{n}\left(x_{i}-\bar{X}\right)^{2} \)
D \( \cdot \frac{1}{n} \sum_{i=1}^{n}\left(x_{i}-\bar{X}\right)^{2} \)


The magnetic moment of a thin round loop with current, if the radius of the loop is equal to \( R=100 m m \) and the
magnetic field at its centre is equal to \( B=6.0 \mu T, \) is \( 30 \times 10^{-x} A-m^{2} \). Find
the value of \( x \)


\( \mathbf{a}=\left|\begin{array}{ccc}\boldsymbol{a} & \mathbf{5}-\boldsymbol{i} & \mathbf{7}+\boldsymbol{i} \\ \mathbf{5}+\boldsymbol{i} & \boldsymbol{b} & \mathbf{3}+\boldsymbol{i} \\ \mathbf{7}-\boldsymbol{i} & \boldsymbol{3}-\boldsymbol{i} & \boldsymbol{c}\end{array}\right|, \) then \( \boldsymbol{\Delta} \) is
always
A . real
B. imaginary
\( c \cdot 0 \)
D. None of these


A \( 10.0 \mu F \) parallel-plate capacitor with
circular plates is connected to a \( 12.0 \mathrm{V} \)
battery. How much charge \( (\text { in } \mu C) \)
would be on the plates if their separation were doubled while the capacitor remained connected to the
battery?


Among the following pairs of compounds, the one that illustrates the law of multiple proportions is:
A. \( N H_{3} \) and \( N C l_{3} \)
B. \( H_{2} S \) and \( S O_{2} \)
c. \( C u O \) and \( C u_{2} O \)
D. \( C S_{2} \) and \( F e S O_{4} \)


Which of the following phenomena is related to the formation of rainbows?
This question has multiple correct options
A . Reflection
B. Refraction
c. Dispersion
D. Scattering


The most effective resource for visually challenged person is
A. Telescopic aid
B. Auditory aid
c. Lenses
D. Braille system


A shiny brown-coloured element 'X' on heating in air becomes black in colour
Name the element 'X'?
A. Sodium
B. Calcium
c. copper
D. Aluminium


What is the minimum pH necessary to
cause a precipitate of
\( \boldsymbol{P b}(\boldsymbol{O} \boldsymbol{H})_{2}\left(\boldsymbol{K}_{s p}=1.2 \times 10^{-5}\right) \) to form
in a \( 0.12 M P b C l_{2} \) solution?
A . 12.4
B. 10.0
c. 12.0
D. 11.1


An electric current is flowing through a circular coil of radius \( \mathrm{R} \). The ratio of the
magnetic field at the center of the coil and that at a distance \( 2 \sqrt{2} R \) from the
center of the coil and on its axis is:


Oxidation number of bromine in
sequence in \( B r_{3} O_{8} ? \)
\( \mathbf{A} \cdot+8,+6,+8 \)
B. +6,+4,+6
c. 0,0,0
\( \mathbf{D} \cdot+8,+4,+8 \)


Find union of \( A \) and \( B \) by representing
using Venn diagram:
\( \boldsymbol{A}=\{\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}, \boldsymbol{d}\}, \boldsymbol{B}=\{\boldsymbol{b}, \boldsymbol{d}, \boldsymbol{e}, \boldsymbol{f}\} \)
\( \mathbf{A} \cdot\{a, b, c, d\} \)
B \( \cdot\{b, d, e, f\} \)
\( \mathbf{c} \cdot\{b, d\} \)
D. None of these


Q Type your question
between its plates that covers \( 1 / 3 \) of the
area of its plates, as shown in the figure. The total capacitance of the capacitor is \( C \) while that of the portion
with dielectric in between is \( \mathrm{C}_{1} \). When
the capacitor is charged, the plate area
covered by the dielectric gets charge \( Q_{1} \)
and the rest of the area gets charge \( Q_{2} \)
The electric field in the dielectric is \( \mathrm{E}_{1} \)
and that in the other portion is \( \mathrm{E}_{2} \)
Choose the correct option/options, ignoring edge effects:
This question has multiple correct options
A \( \cdot \frac{E_{1}}{E_{2}}=1 \)
В. \( \frac{E_{1}}{E_{2}}=\frac{1}{K} \)
C. \( \frac{Q_{1}}{Q_{2}}=\frac{3}{K} \)
D. \( \frac{C}{C_{1}}=\frac{2+K}{K} \)


In Mirablilis jalapa, red flowered plant is crossed with white flowered plant. What
will the phenotypic ratio in \( \boldsymbol{F}_{2} \) generation?
A. 1: 1: 1
B. 1: 2: 1
c. 3: 1
D. 1: 1


A closed system shows exchange of mass and not energy with surroundings
A. True
B. False


During protein synthesis in an
organism, at one point the process comes to a halt. Select the group of the three codons from the following from which any one of the three could bring about this halt?
A. UUU, UCC, UAU
B. UUC, UAC
c. UAG, UGA, UAA
D. UUG, UCA, UCG


The year of publication of "Species Plantarum" is
A . 1853
в. 1857
\( c \cdot \) 1753
D. 1786


If a first order reaction is completed to the extent of \( 75 \% \) and \( 50 \% \) in time
interval, \( t_{1} \) and \( t_{2}, \) what is the ratio \( t_{1} \)
\( t_{2} ? \)
A . \( \ln 2 \)
B. \( \frac{\ln (3 / 4)}{\ln 2} \)
\( c \cdot 2 \)
D. \( 1 / 2 \)


Evaluate:
\( \int e^{x^{3}+x^{2}-1}\left(3 x^{4}+2 x^{3}+2 x\right) d x \)


In which phase of the cell cycle DNA doubles and chromosomes replicate?
A. S period
B. \( G_{1} \) phase
\( \mathrm{c} \cdot G_{2} \) phase
D. metaphase


Frog's kidneys for communication with
the coelom has
A. Nephridiopores
B. Septal nephridia
c. Nephrostomes
D. Renal pores


The optical instrument which is used in every cricket match is.:
A. simple microscope
B. Compound microscope
c. Astronomical telescope
D. Binocular


Which of the following statements is
not true about the complex ion
\( \left[\boldsymbol{C r} \boldsymbol{C l}\left(\boldsymbol{N} \boldsymbol{O}_{2}\right)(\boldsymbol{e n})_{2}\right]^{+} ? \)
This question has multiple correct options
A. it has two geometrical isomers cis and trans.
B. cis and trans forms are not diastereomers to each other
c. only the cis isomers displays optical activity.
D. it has three optically active isomers: d, land trans forms


Find the value of \( x \)


For two data sets, each of size of \( 5, \) the
variances are given to be 4 and 5 and the corresponding means are given to be 2 and \( 4, \) respectively. The variance of the combined data set is :
A \( \cdot \frac{11}{2} \)
B. 6
c. \( \frac{13}{2} \)
D.


The empty space above mercury in a simple barometer is called
vaccum
A . pressure
B. barometric
c. torricellian
D. mercuric


Find the area of the triangle with vertices at the points:
(3,8),(-4,2) and \( (5,-1) . \) If the area is \( \left(\frac{a}{2}\right) \) sq. units, then what will be the value of
\( \boldsymbol{a} ? \)


Write the overall reaction taking place
in Daniel Cell.


ff \( \boldsymbol{y}=\tan ^{-1} \frac{1}{1+x+x^{2}}+ \)
\( \tan ^{-1} \frac{1}{x^{2}+3 x+3}+ \)
\( \tan ^{-1} \frac{1}{x^{2}+5 x+7}+\ldots+ \) upto \( n \) terms
then \( y^{\prime}(0) \) is equal to
A \( \cdot-\frac{1}{1+n^{2}} \)
B. \( -\frac{n^{2}}{1+n^{2}} \)
c. \( \frac{n}{1+n^{2}} \)
D. none of these


Two condensers of capacities \( 10 \mu F \) and \( 20 \mu F \) have potential differences of \( 20 \mathrm{V} \)
and \( 10 \mathrm{V} \) respectively. The total charge is
A \( .200 \mu C \)
в. \( 600 \mu C \)
c. \( 400 \mu C \)
D. zero


Th coordinates of three consecutive
vertices of a parallelogram are (1,3),(-1,2) and \( (2,5) . \) The
coordinates of the fourth vertex are
A \( \cdot(6,4) \)
B. (4,6)
c. (-2,0)
D. none of these


The isotope of carbon used extensively
for studies in photosynthesis is
\( \mathbf{A} \cdot^{13} C \)
B. \( ^{14} C \)
\( \mathbf{c} \cdot^{15} C \)
D. \( ^{16} C \).


Construct \( \square \) DEFG such that \( l(\mathrm{DE})=4.5 \)
\( \mathrm{cm}, l(\mathrm{EF})=6.5 \mathrm{cm}, l(\mathrm{DG})=5.5 \mathrm{cm}, l(\mathrm{DF}) \)
\( =\mathbf{7} . \mathbf{2} \mathrm{cm}, l(\mathrm{EG})=\mathbf{7 . 8} \mathrm{cm} \)


The motion of a dust particle in air is an example of -
A. rectilinear motion
B. curvilinear motion
c. oscillatory motion
D. random motion


Assertion
Both Grinard reagent and dialkyl cadmium react with acid chlorides to
form tert. alcohols.
Reason
Grignard reagents are as reactive as diakyl cadmium.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Give a balanced equation for thermal dissociation of a solid [both containing the chloride ion].
A \( \cdot 2 N H_{4} C l(s) \rightleftharpoons N_{2} H_{6}(g)+2 H C l(g) \)
B. \( N H_{4} C l(s) \rightleftharpoons N H_{3}(g)+C l_{2}(g) \)
c. \( N H_{4} C l(s) \rightleftharpoons N H_{3}(g)+H_{2}(g) \)
D. \( N H_{4} C l(s) \rightleftharpoons N H_{3}(g)+H C l(g) \)


The number of real solutions of the
equation \( e^{|x|}-|x|=0 \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. None of these


In aqueous solution, the ionization
constants for carbonic acid \( \left(\boldsymbol{H}_{2} \boldsymbol{C O}_{3}\right) \)
\( \operatorname{are} \mathbf{K}_{\mathbf{1}}=\mathbf{4} . \mathbf{2} \times \mathbf{1 0}^{-\mathbf{7}} \) and \( \mathbf{K}_{\mathbf{2}}=\mathbf{4 . 8} \times \)
\( 10^{-11} . \) Select the correct statement for a
saturated \( 0.034 \mathrm{M} \) solution of the
carbonic acid.
A. The concentration of \( \mathrm{CO}_{3}^{2-} \) is \( 0.034 \mathrm{M} \)
B. The concentration of \( \mathrm{CO}_{3}^{2-} \) is greater than that of \( \mathrm{HCO}_{3}^{-} \)
C. The concentration of \( \mathrm{H}^{+} \) and \( \mathrm{HCO}_{3}^{-} \) are approximately equal
D. The concentration of \( \mathrm{H}^{+} \) is double that of \( \mathrm{CO}_{3}^{2-} \)


R. Hill used which of the following dye for his famous Hill-reaction?
A. Dichlorophenolindophenol (DCPIP)
B. Sulphur green
c. Methylene blue
D. Eosine


Two bodies of different masses
\( m_{1} \) and \( m_{2} \) are dropped from two
different heights \( h_{1} \) and \( h_{2} \). What is the ratio of time taken by the two to reach the ground?
\( \mathbf{A} \cdot \sqrt{h_{1}}: \sqrt{h_{2}} \)
B \( \cdot \sqrt{h_{2}}: \sqrt{h_{1}} \)
c. \( m_{1} h_{2}: m_{2} h_{1} \)
D. \( m_{1} h_{1}: m_{2} h_{2} \)


A pond is
A. Biome
B. Natural ecosystem
C. Artificial ecosystem
D. Community of plants and animals


Mirror nuclei are those which have:
A. the same number of protons
B. the same number of neutrons
C. the number of protons equal to number of neutrons
D. the number of neutrons in one equal to the number of protons in the other


As one considers orbits with higher values of \( n \) in a hydrogen atom, the electric potential energy of the atom
A . decreases
B. increases
c. remains the same
D. does not increase


\( \mathbf{2} \boldsymbol{C a}_{3}\left(\boldsymbol{P} \boldsymbol{O}_{4}\right)_{2}+\boldsymbol{6} \boldsymbol{S} \boldsymbol{i} \boldsymbol{O}_{2}+\mathbf{1 0} \boldsymbol{C} \rightarrow \boldsymbol{P}_{4}+ \)
\( \ldots . \mathrm{CaSiO}_{3}+\mathbf{1 0 C O} \)
Which coefficient balances the reaction
given above?
A . 2
B. 4
c. 5
D. 6
E . 8


A metal present in vitamin \( B_{12} \) is:
A. aluminium
B. zinç
\( c \). iron
D. cobalt


Interval between two events is called
A. Solar day
B. Hour
c. Time
D. Duration


Stone wort is common name of
A. Chara
B. Chlorella
c. Laminaria
D. Polysiphonia


If \( A+B+C=180^{\circ} \) then \( a \sin (B-C)+b \sin (C- \)
\( A)+c \sin (A-B) \) is :
\( A \cdot O \)
B. 1
\( c \cdot 2 \)
D. 3


The value of the variable which satisfies
the equation is called the
A . coefficient
B. degree
c. variable
D. solution of the equation


Give balanced chemical equations for the following reactions. Potassium iodide treated with acidified
potassium permanganate solution


Show that the determinant \( \boldsymbol{a}^{2}+\boldsymbol{b}^{2}+\boldsymbol{c}^{2} \quad \boldsymbol{b} \boldsymbol{c}+\boldsymbol{c} \boldsymbol{a}+\boldsymbol{a} \boldsymbol{b} \quad \boldsymbol{b} \boldsymbol{c}+\boldsymbol{c} \boldsymbol{a} \)
\( \boldsymbol{b} \boldsymbol{c}+\boldsymbol{c} \boldsymbol{a}+\boldsymbol{a} \boldsymbol{b} \quad \boldsymbol{a}^{2}+\boldsymbol{b}^{2}+\boldsymbol{c}^{2} \quad \boldsymbol{b} \boldsymbol{c}+\boldsymbol{c} \boldsymbol{a} \)
\( \boldsymbol{b} \boldsymbol{c}+\boldsymbol{c} \boldsymbol{a}+\boldsymbol{a b} \quad \boldsymbol{b c}+\boldsymbol{c a}+\boldsymbol{a b} \quad \boldsymbol{a}^{2}+\boldsymbol{b}^{2} \)
is always non-negative.


An arsenious sulphide sol carries a negative charge. The maximum precipitating power of this sol is possessed by :
A. \( K_{2} S O_{4} \)
в. \( C a C l_{2} \)
\( \mathbf{c} \cdot N a_{3} P O_{4} \)
D. \( A l C l_{3} \)


If \( I \) excitation energy for the \( H- \) like
(hypothetical) sample is \( 24 e V \), then binding energy in \( I I I \) excired state is:
A .2 eV
в. 3 eV
\( c .4 e V \)
D. 5 eV


Ambergris is the secretion from the
intestine of ................ used in the
manufacture of perfumes and cosmetics.
A. Tachyglossus
B. Physeter
c. Musk deer
D. Kangaroo


Find the next term
\( \mathbf{3}, \mathbf{5}, \mathbf{7}, \mathbf{1 0}, \mathbf{1 1}, \mathbf{1 5}, \mathbf{1 5}, \mathbf{2 0}_{\mathbf{-}} \)


A proton of mass \( m \) and charge \( q \) is
moving in a plane with kinetic energy \( \boldsymbol{E} \) If there exists a uniform magnetic field
\( B, \) perpendicular to the plane of the motion the portion will move in a circular path of radius
A \( \cdot \frac{2 E m}{q B} \)
в. \( \frac{\sqrt{2 E m}}{q B} \)
c. \( \frac{\sqrt{E m}}{2 q B} \)
D. \( \sqrt{\frac{2 E q}{m B}} \)


ABCD is a trapezium. Further if \( \mathrm{CD}=4.5 \) \( \mathrm{cm} ; \) find the length of \( 2 \mathrm{AB} \) in \( \mathrm{cm} \)


Find the principal value of the following
\( \cot \left(\tan ^{-1} x+\cot ^{-1} x\right) \)


An athlete runs a distance of \( 1500 \mathrm{m} \) in
the following manner.
(i) Starting from rest, he accelerates himself uniformly
at \( 2 m s^{-2} \) till he covers a distance of
\( (i i) \) He, the run remaining \( 900 m \)
distance of \( 600 \mathrm{cm} \) at the uniform
speed developed. Calculate the time
taken by the athlete to cover the two parts of the distance covered. Also find the time, when he is at the centre of the
track.


For the reaction taking place at certain
temperature \( N H_{2} C O O N H_{4}(s) \rightleftharpoons \)
\( \mathbf{2} N \boldsymbol{H}_{3}(\boldsymbol{g}) \) if equilibrium pressure is \( \mathbf{3} \boldsymbol{X} \)
bar then \( \Delta G^{\circ} \) would be:
A. \( -R T \ln 9-3 R T \ln X \)
B. \( R T \ln 4-3 R T \ln X \)
c. \( -3 R T \ln 4 X \)
D. none of these


Regarding \( N_{2} O, \) the wrong statement
is :
A. It is called laughing gas
B. It is called nitrous oxide
c. It is a linear molecule
D. It is a more reactive oxide


Which plant hormone causes fruit
ripening?
A. Indole acetic acid
B. Cytokinin
c. Ethylene
D. Gibberellic acid


Find the coefficient of \( x^{-17} \) in the
expansion of \( \left(x^{4}-\frac{1}{x^{3}}\right)^{15} \)
A. 1200
B. -1331
c. -1365
D. -2016


Who proposed the cycle of events
leading to the fixation of \( C O_{2} \) in mesophyll and its reduction in bundle sheath?
A. Emerson
B. Melvin Calvin
c. Hatch and Slack
D. Hill and Bendall


Find the area of the sector of a circle
whose radius is \( 14 \mathrm{cm} \) and angle of
sector is \( 45^{\circ} \)


Pradeep is a Section Chief for an electric utility company. The employees in his section cut down tall trees or
climb poles. Pradeep recently reported the following information to the
management of the utility Out of 100 employees in my section, 55 can cut tall trees, 50 can climb poles, 1
can do both, 6 can't do any of the two. Is this information correct?


Find the value of \( p \) and \( q \) for which
\[
\boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{c}
\frac{1-\sin ^{3} x}{\cos ^{2} x}, i f x<\pi / 2 \\
\boldsymbol{p}, \quad i \boldsymbol{f} \quad \boldsymbol{x}=\boldsymbol{\pi} / 2 \\
\frac{\boldsymbol{q}(1-\sin x)}{(\pi-2 x)^{2}}, \boldsymbol{i} \boldsymbol{f} \quad \boldsymbol{x}>\pi / 2
\end{array}\right.
\]
is continuous at \( \boldsymbol{x}=\boldsymbol{\pi} / \mathbf{2} \)


Two short bar magnets with magnetic
moments 400 ab-amp \( c m^{2} \) and 800 ab
amp \( c m^{2} \) are placed with their axis in
the same straight line with similar poles facing each other and with their
centres at \( 20 \mathrm{cm} \) from each other. Find
the force of repulsion.


n figure, line \( n \) is a transversal to lines \( l \)
and \( m . \) Identify the following angles
alternate to \( \angle d \) and \( \angle g \) and angles
corresponding to angles \( \angle f \) and \( \angle h \) in
figure


\( \int \sec x \ln (\sec x+\tan x) d x \)


Two cards are drawn simultaneously
from a well shuffled pack of 52 cards.
The expected number of aces is
A \( \cdot \frac{4}{13} \)
в. \( \frac{3}{13} \)
c. \( \frac{2}{13} \)
D. \( \frac{1}{13} \)


The number of nodal planes in a \( \boldsymbol{P}_{\boldsymbol{x}} \) orbital is:
A. one
B. Two
c. Three
D. zero


A tuning fork produces 4 beats per second with another tuning fork of
frequency 256 Hz. The first one is now loaded with a little wax and the beat
frequency is found to increase to 6 per second. What was the original frequency of the first tuning fork. (in Hz)


A certain radioisotope \( _{Z}^{A} X \) (Half life \( = \) \( 10 \text { days }) \) decays to \( _{Z-2}^{A-4} Y . \) If \( 1 g \) atom of
\( A X \) is kept in sealed vessel, how much \( Z^{\text {}} \) helium will accumulated in 20 days?


The graph of \( x=2 \) is a line parallel to
axis.
\( A \)
в. \( y=2 \)
c. \( y \)
D. None of these


1 Horse power \( = \) watt.


\( C r O_{5} \) forms addition compound with
pyridine in the ethereal layer. The addition product is pentagonal pyramidal.
A. True
B. False


If \( \sin \theta=\frac{7}{25}, \) where \( \theta \) is an acute, find
the value of \( \cos \theta \) using identity


Which of the following oxides is not expected to react with sodium hydroxide?
A. \( B e O \)
в. \( B_{2} O_{3} \)
\( c . C a O \)
D. \( \operatorname{si} 0_{2} \)


Which one of the following contains P- -
-0 - - -P bond?
A. Hypophosphorus acid
B. Phosphorus acid
c. Pyrophosphoric acid
D. orthophosphoric acid


The IUPAC name of :
A. 5 -oxopentanoic acid
B. 4 -oxopentanoic acid
C. 6 -oxopentanoic acid
D. 5 -oxopentenoic acid


Express the rate for the following reaction in terms of concentration of
reactants and products.
\( 5 B r^{-}(a q)+B r O_{3}^{-}(a q)+6 H^{+} \rightarrow \)
\( \mathbf{3} \boldsymbol{B} \boldsymbol{r}_{2}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{3} \boldsymbol{H}_{2} \boldsymbol{O}(l) \)


The unit of the coefficient of viscosity in
S.I. system is:
\( \mathbf{A} \cdot m / k g s \)
B . \( m s / k g^{2} \)
c. \( k g / m s^{2} \)
D. \( k g / m s \)


Assertion
A solid sphere and a hollow sphere when allowed to roll down on an inclined
plane, the solid sphere reaches the bottom first.
Reason
Moment of inertia of solid sphere is greater than that of hollow sphere.
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


Root hair helps in better absorption of air and water
A. It increases the surface area for absorption
B. It helps in growth and developement
C. It increases the rate of flowering in plants.
D. All of the above


At what separation should two equal charges, \( 1.0 C \) each, be placed so that
the force between them equals the
weight of a \( 50 k g \) person?


A bullet of mass \( 0.1 \mathrm{kg} \) moving horizontally with a velocity of \( 20 \mathrm{m} / \mathrm{s} \) strikes a target and brought to rest in
0.1 s. Find the impulse and average force of impact.


Describe the construction of direct
current dynamo drawing labelled diagram. Explain its working. What is the difference between direct current
and alternating current? Explain it.


For \( \boldsymbol{H} \) -like atoms:
\[
\boldsymbol{E}_{\boldsymbol{n}}=-\frac{\boldsymbol{Z}^{2} \boldsymbol{R} \boldsymbol{h}}{\boldsymbol{n}^{2}} ; \boldsymbol{u}_{\boldsymbol{n}}=\frac{\boldsymbol{u}_{1} \boldsymbol{Z}}{\boldsymbol{n}} \text { and }
\]
\( r_{n}=\frac{r_{1} \times n^{2}}{Z} ; \) where \( R h \) is Rydberg.
What is the potential energy of electron
\( \operatorname{in} 2^{n d} \) orbit of \( H \) -atom?
\( A \cdot-\frac{R h}{2} \)
B. \( -2 R h \)
c. \( -4 R h \)
D. - Rh


Elevation in boiling point of \( \boldsymbol{C a}\left(\boldsymbol{N} \boldsymbol{O}_{3}\right)_{2} \)
gives molar mass as \( 131.2 . \) The degree of
dissociation of \( \boldsymbol{C a}\left(\boldsymbol{N} \boldsymbol{O}_{3}\right)_{2} \) is:
A. \( 100 \% \)
B. \( 75 \% \)
\( c .50 \% \)
D. \( 12.5 \% \)


If you dip your open palm in a bucket full of water, you feel your hand being pushed up? Why?


Hydrogen atom excites energy level
from fundamental state to \( n=3 \)
Number of spectral lines according to Bohr, is
A . 4
B. 3
c. 1
D.


Which of the following is NOT a member of the solar system?
A. An asteroid
B. A satellite
c. A constellation
D. A comet


The above-given model of t-RNA was
explained by
A. Watson and crick
B. Friedrick meischer
c. Clover leaf
None of the above


In which of the following, iron is present
in its lowest oxidation state?
A \( \cdot \) FeSO\( _{4} \cdot 7 \mathrm{H}_{2} \) O
в. \( F e(C O)_{5} \)
\( \mathrm{c} . F e_{e, 94} \mathrm{O} \)
D. \( F e_{3} O_{4} \)


Given : A and B are input terminals.
\( \operatorname{Logic} 1=>5 V \)
\( \operatorname{Logic} \mathbf{0}=<\mathbf{1} \boldsymbol{V} \)
Which logic gate operation, the following circuit does?
\( A \). AND Gate
B. OR Gate
c. XOR Gate
D. NOR Gate


State whether true or false:
A concave lens forms a magnified or diminished image depending on the distance of object from it.
A. True
B. False


ff \( i z^{3}+z^{2}-z+i=0, \) then \( |z| \) is equal
to
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. None of these


Which one of \( \mathrm{K}, \mathrm{I}, \mathrm{Cl} \) and \( \mathrm{Li} \) Will display the highest first ionisation energy?
\( A \cdot K \)
B.
c. \( c \)
D. L


Which of the following will show more intensity of scattering?
A. Protein sol
B. Starch sol
c. Gold sol
D. Milk


Which of the above statements is(are)
correct?
This question has multiple correct options
A. Atomic hydrogen is obtained by passing hydrogen through an electric arc.
B. Hydrogen gas will not reduce heated aluminium oxide.
C. Finely divided palladium adsorbs large volume of hydrogen gas.
D. None of the above


A hemisphere and a solid cone have a common base. The centre of mass of the
common structure coincides with the
centre of the common base. If \( \mathrm{R} \) is the
radius of hemisphere and h is the height of the cone, then :
A \( \cdot \frac{h}{R}=\sqrt{3} \)
в. \( \frac{h}{R}=\frac{1}{\sqrt{3}} \)
c. \( \frac{h}{R}=3 \)
D. \( \frac{h}{R}=\frac{1}{3} \)


The value of \( x \) satisfying the equation 2 \( \left|\begin{array}{cc}\mathbf{3} & \mathbf{1} \\ \mathbf{1} & \mathbf{2}\end{array}\right|+\left|\begin{array}{cc}\boldsymbol{x}^{\mathbf{2}} & \mathbf{9} \\ -\mathbf{1} & \mathbf{0}\end{array}\right|=\left|\begin{array}{cc}\mathbf{5} \boldsymbol{x} & \mathbf{6} \\ \mathbf{0} & \mathbf{1}\end{array}\right|+\left|\begin{array}{cc}\mathbf{0} & \mathbf{5} \\ \mathbf{1} & \mathbf{3}\end{array}\right| \) are
\( A \cdot 1,2 \)
B. 2,3
\( c .\pm 2 \)
\( \mathrm{D} \cdot \pm 3 \)


The scalar product and the magnitude of vector products of two vectors are \( 48 \sqrt{3} \) and 144 respectively. Then the angle between the two vectors is
A. 54.7
B. 60
c. 90
D. 120


Simmond's disease is
A. Hyperthyroidism
B. Hypothyroidism
c. Hypopituitarism
D. Hyperpituitarism


The mean deviation of an ungrouped data is \( 50 . \) If each observation is
increased by \( 2 \% \), then the new mean deviation is
A . 50
B. 51
c. 49
D. 50.5


Explain hybridization of central atom in
\( : \boldsymbol{C H}_{\mathbf{4}} \)


Differentiate the given function w.r.t. \( x \) \( \frac{\cos ^{-1} \frac{x}{2}}{\sqrt{2 x+7}},-2<x<2 \)


\( \ln \) a \( \Delta A B C, \) if \( \angle A=53^{\circ} \) and \( \angle C=44^{\circ} \)
then the value of \( \angle B \) is
\( A \cdot 73^{\circ} \)
в. \( 83^{\circ} \)
c. \( 103^{\text {। }} \)
D. \( 46^{\circ} \)


Describe the main features of
Mendeleev's Periodic Table.


If \( \boldsymbol{x}\left[\begin{array}{l}2 \\ \mathbf{3}\end{array}\right]+\boldsymbol{y}\left[\begin{array}{c}-\mathbf{1} \\ \mathbf{1}\end{array}\right]=\left[\begin{array}{c}\mathbf{1 0} \\ \mathbf{5}\end{array}\right] \)
Find values of \( x \) and \( y \)


\( S O_{2} \) gas is used as a bleaching agent. Its bleaching action is
A. temporary and due to its oxidizing nature
B. temporary and due to its reducing action
c. permanent and due to its oxidizing action
D. permanent and due to its reducing action


Equilibrium constant, \( \boldsymbol{K}_{c} \) for the
reaction
\( N_{2}(g)+3 H_{2}(g) \rightleftharpoons 2 N H_{3}(g) \) at \( 500 K \)
is 0.061
At a particular time, the analysis shows that composition of the reaction
mixture is 3.0 mol \( L^{-1} N_{2}, 2.0 \) mol \( L^{-1} \)
\( \boldsymbol{H}_{2} \) and \( \mathbf{0 . 5 m o l} \boldsymbol{L}^{-1} \boldsymbol{N} \boldsymbol{H}_{3} . \) Is the
reaction at equilirbium? IF not in which direction does the reaction tend to
proceed to reach equilibrium?


A bag contains 8 red balls, 11 blue balls
and 6 green balls. Find the percentage of blue balls in the bag.


The subatomic particle which remains unchanged during the chemical reaction is/are

This question has multiple correct options
A. proton
B. electron
c. neutron
D. All of the above


The continuous medium in a colloid is
called :
A. dispersed phase
B. dispersion medium
c. gel
D. none of the above


If \( P(A)=\frac{1}{8} \) and \( P(B)=\frac{5}{8} . \) Which of the
following statements is correct?
A \( \cdot P(A \cup B) \leq \frac{3}{4} \)
B \( \cdot P(A \cap B) \leq \frac{5}{8} \)
\( \mathbf{c} \cdot P(\bar{A} \cap B) \leq \frac{5}{8} \)
D \( \cdot P(A \cap B) \geq \frac{5}{8} \)


Nutrients which are required in large
quantities are called as
A. Macronutrients
B. Micronutrients
c. Secondary nutrients
D. None of the above


Let the p.m.f. of a random variable \( \boldsymbol{X} \) be
\( P(x)=\frac{3-x}{10} \) for \( x=-1,0,1,2 \)
otherwise
Then \( \boldsymbol{E}(\boldsymbol{X}) \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
c. 0
D. -


In corals, the gonads are
A. Endodermal
B. Ectodermal
c. Mesodermal
D. Mesogleal


A solenoid of inductance \( L \) and length \( l \)
and mass \( m, \) whose windings are made
of material of density \( D \) and resistivity
is \( \rho, \) (the winding resistance is \( \boldsymbol{R} \) ). Find out the inductance in terms of others.
A \( \cdot \frac{\mu_{0}}{4 \pi l} \frac{R m}{\rho D} \)
В. \( \frac{\mu_{0}}{4 \pi R} \frac{l m}{\rho D} \)
c. \( \frac{\mu_{0}}{4 \pi l} \frac{R^{2} m}{\rho D} \)
D. \( \frac{\mu_{0}}{2 \pi R} \frac{l m}{\rho D} \)


\( P \) and \( Q \) are two points whose coordinates are \( \left(a t^{2}, 2 a t\right) a n d\left(\frac{a}{t^{2}}, \frac{-2 a}{t}\right) \) respectively
and \( \mathrm{S} \) in the point \( (\mathrm{a}, 0) . \) show that \( \frac{1}{S P}+\frac{1}{S Q} \) is independent of \( t \)


Find 'c' of the mean value theorem,if
\( f(x)=x(x-1)(x-2) \)
\( \boldsymbol{a}=\mathbf{0}, \boldsymbol{b}=\frac{\mathbf{1}}{\mathbf{2}} \)
\( ^{\mathrm{A}} \cdot_{C}=1-\frac{\sqrt{21}}{5} \)
в. \( \quad C=1-\frac{\sqrt{21}}{6} \)
\( ^{\mathrm{c}} \cdot_{C}=2-\frac{\sqrt{21}}{6} \)
D. \( c=1+\frac{\sqrt{21}}{6} \)


Differentiate the following functions
with respect to \( \boldsymbol{x} \) \( \frac{e^{2 x}+e^{-2 x}}{e^{2 x}-e^{-2 x}} \)


If \( f(x)=\frac{a \cos x-\cos b x}{x^{2}}, x \neq 0 \) and
\( \boldsymbol{f}(\mathbf{0})=\mathbf{4} \) continuous at \( \boldsymbol{x}=\mathbf{0}, \) then the
ordered pair \( (a, b) \) is
\( A \cdot(\neq 1,3) \)
в. \( (1, \neq 3) \)
c. (-1,-3)
D. (1,±3)


If \( D\left(-\frac{1}{5}, \frac{5}{2}\right), E(7,3) \) and \( F\left(\frac{7}{2}, \frac{7}{2}\right) \)
are the mid-points of sides of \( \Delta A B C \)
find the area of \( \Delta A B C \)


An automobile and a truck start from
rest at the same instant, with the automobile initially at some distance behind the truck. Then truck has a
constant acceleration of \( 2.2 m / s^{2} \) and the automobile has an acceleration of
\( 3.5 m / s^{2} . \) The automobile overtakes the truck when it (truck) has moved 60 \( \mathrm{m} \).
(a) How much time does it take to automobile to overtake the truck?
(b) How far was the automobile behind the truck initially?
(c) What is the speed of each during overtaking?


A moving charge can produce a magnetic field. How does a current loop behaves like a magnetic dipole?


A ball is projected vertically upwards with a velocity of \( 25 m s^{-1} \) from the
bottom of a tower. A boy who is standing at the top of a tower sees it passes by him in the upward direction. He sees
ball again at same height after 3 sec when it is falling. Then the height of the tower is : \( \left(\boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} \boldsymbol{s}^{-2}\right) \)
A . \( 5 m \)
в. \( 10 m \)
c. \( 15 m \)
D. \( 20 m \)


The chemical name for melamine is:
A . 1,3,5 -Triamino- 2,4,6 -triazine
B. 1,3,5-Triazine-2,4,6-triamine
c. 2-Amino-1,3,5-triazine
D. 2,4-Diamino 1,3,5-triazine


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


\( \lim _{x \rightarrow 0} \frac{\sin \left(\pi \cos ^{2} x\right)}{x^{2}} \) equals
A . \( -\pi \)
B.
\( c \cdot \frac{\pi}{2} \)
\( D \)


The changes in a function y and the independent variable \( x \) are related as \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\boldsymbol{x}^{2} . \) Find \( y \) as a function of \( \boldsymbol{x} \)


A body is thrown vertically upwards with
an initial velocity \( u \). The expression for the maximum height attained by the body is
A \( \cdot \frac{u}{2 g g} \)
в. \( \frac{g^{2}}{2 u} \)
c. \( \frac{u^{2}}{g} \)
D. \( \frac{u^{2}}{2 g} \)


If the value of the resistance of carbon
resistance is \( 0.2 k \Omega \pm 10 \% \) write the
color code for the same.


Motion which repeats itself after regular intervals.
A. oscillatory motion
B. vibratory motion
c. periodic motion
D. none


If the function
\( \left\{\begin{array}{l}\boldsymbol{x}, \quad \text { if } \quad \boldsymbol{x} \leq \mathbf{1} \\ \boldsymbol{c x}+\boldsymbol{k}, \quad \text { if } \quad \mathbf{1}<\boldsymbol{x}<\mathbf{4} \\ -\mathbf{2} \boldsymbol{x}, \quad \text { if } \quad \boldsymbol{x} \geq \mathbf{4}\end{array}\right. \)
is contionus everywhere, then the value
of \( c \) and \( k \) are respectively:
A. -3,-5
в. -3,5
c. -3,-4
D. -3,4
E . -3,3


Primary and secondary active
transports, both.
A. Generate ATP
B. Use ATP
c. can move solutes against their concentration gradients
D. Include passive movement of glucose molecule


The power of a lens is - \( 5 D \)
(i) find its focal length.
(ii) name the type of lens.


If the decomposition of nitrogen oxides
as \( 2 N_{2} O_{5} \rightarrow 4 N O_{2}+O_{2} \)
Calculate the rate constant for a \( 0.05 M \)
solution if the instantaneous rate is
\( \mathbf{1 . 5} \times \mathbf{1 0}^{-\mathbf{6}} \mathbf{m o l} / \mathbf{l} / \mathbf{s} \)
A \( .3 \times 10^{-5} \)
В. \( 3 \times 10^{-4} \)
c. \( 3 \times 10^{-2} \)
D. \( 2 \times 10^{-4} \)


Evaluate: \( \int \frac{1}{x\left(x^{2}+1\right)} d x \)


A particle moves along the X-axis
according to the equation \( \boldsymbol{x}= \)
\( 10 \sin ^{3}(\pi t) . \) the amplitudes and
frequencies of component SHMs are
A . amplitude \( 30 / 4,10 / 4 ; \) frequencies3 \( / 2,1 / 2 \)
в. amplitude30/4,10/4; frequencies1/2,3/2
c. amplitude10, \( 10 ; \) frequencies1/2,1/2
D. amplitude30/4,10; frequencies3/2,


A number decreased by 30 is the same as 14 decreased by 3 times the number. Find the number.
A . 11
B. 9
c. 8
D. 12


If \( y=\sin \left\{\tan ^{-1}\left[\frac{1-x}{1+x}\right]\right\} \) find
\( \frac{d y}{d x} \)


Usually the atmospheric pressure is
equal to
A . \( 1.013 \times 10^{5} \) Pascal
В. \( 1.013 \times 10^{5} N / m^{2} \)
c. \( 101.3 k P a \)
D. all of the above


A conducting circular loop is placed in a uniform magnetic field \( B=0.020 T \)
with its plane perpendicular to the field. Somehow, the radius of the loop starts
shrinking at a constant rate of 1 m \( m / s \) Find the induced current in the loop at
an instant when the radius is \( 2 \mathrm{cm} \)


In the reaction, \( C l_{2}+O H^{-} \rightarrow C l^{-}+ \)
\( C l O_{4}^{-}+H_{2} O, \) chlorine is?
A. Oxidised
B. Reduced
c. Oxidised as well as reduced
D. Neither oxidised nor reduced


A battery of e.m.f. \( 15 \mathrm{V} \) and internal resistance \( 2 \Omega \) is connected to two
resistors of resistance 4 ohm and 6 ohm
joined in series. What is the electrical energy spent per minute in 6 ohm
resistor?
A . 562.5
B. 180 J
c. 456.5 J
D. 360 J


A loop carrying current \( I \) lies in the \( x \)
\( \boldsymbol{y} \) plane as shown in figure. The unit
vector \( \hat{k} \) is coming out of the plane of the paper. The magnetic moment of the
current loop is
\( \mathbf{A} \cdot a^{2} I \hat{k} \)
B \cdot \( \left(\frac{\pi}{2}+1\right) a^{2} I \hat{k} \)
c. \( -\left(\frac{\pi}{2}+1\right) a^{2} I \hat{k} \)
D. \( (2 \pi+1) a^{2} I \hat{k} \)


Suggest any four methods that are used
for birth control. State the basic
principles involved in each.


Match the columns.
Column 1 1 Columr
A. Waste product of respiration
1. Resin
B. Waste product of \( \quad \) 2. \( \mathrm{CO}_{2} \) photosynthesis
3. Essential
\( \mathrm{C} \)
Leaves of \( 1 € \) flemon I
o oil
D. Stem of conifers 4. \( O_{2} \)
\( A \cdot A-2, B-4, C-1, D-3 \)
B. \( A-2, B-4, C-3, D-1 \)
C. \( A-4, B-2, C-3, D-1 \)
D. \( A-2, B-3, C-4, D-1 \)


If \( \boldsymbol{A}=\{1,2,3\} \) and \( \boldsymbol{B}=\{4,5,6\} \) then
which of the following sets are relation from \( \boldsymbol{A} \) to \( \boldsymbol{B} \)
(i) \( R_{1}=\{(4,2)(2,6)(5,1)(2,4)\} \)
(ii) \( \boldsymbol{R}_{2}=\{(1,4)(1,5)(3,6)(2,6)(3,4)\} \)
(iii) \( R_{3}=\{(1,5)(2,4)(3,6)\} \)
(iv) \( \boldsymbol{R}_{4}=\{(\mathbf{1}, \mathbf{4})(\mathbf{1}, \mathbf{5})(\mathbf{1}, \mathbf{6})\} \)
A. \( R_{1}, R_{2}, R_{3} \)
в. \( R_{1}, R_{3}, R_{4} \)
\( \mathbf{c} \cdot R_{2}, R_{3}, R_{4} \)
D. \( R_{1}, R_{2}, R_{3}, R_{4} \)


Which of the following are associated with a consensus sequence and a signal sequence?
A. Translation, hnRNAs
B. DNA, translation
c. Transcription, a snurp
D. hnRNA, a snurp
E. Spliceosomes, translation


A particle is projected up an inclined plane of inclination \( \beta \) at an elevation a
to the horizon. Show that
a. \( \tan \alpha+\cot \beta+2 \tan \beta, \) if the particle
strikes the plane at right angles
b. \( \tan \alpha=2 \tan \beta \) if the particle strikes
the plane horizontally.


An electric dipole is placed at the origin and is directed along the \( x \) -axis. At a point \( P, \) far away from the dipole,the electric field is parallel to the y-axis. OP makes an angle \( \theta \) with the \( x \) -axis. Then,
A \( \cdot \tan \theta=\sqrt{3} \)
B. \( \tan \theta=\sqrt{2} \)
\( \mathbf{c} \cdot \tan \theta=1 \)
D. \( \tan \theta=\frac{1}{\sqrt{2}} \)


Find the shortest distance between the
following pair of lines. \( \overline{\boldsymbol{r}}=(\overline{\boldsymbol{i}}+\mathbf{2} \overline{\boldsymbol{j}}+\overline{\boldsymbol{k}})+\boldsymbol{\lambda}(\mathbf{2} \overline{\boldsymbol{i}}-\overline{\boldsymbol{j}}+\mathbf{3} \overline{\boldsymbol{k}}) \& \)
\( \overline{\boldsymbol{r}}=(\overline{\boldsymbol{i}}-\mathbf{3} \overline{\boldsymbol{j}}-\overline{\boldsymbol{k}})+\boldsymbol{\mu}(\mathbf{3} \overline{\boldsymbol{i}}+\mathbf{2} \hat{\boldsymbol{j}}-\mathbf{5} \overline{\boldsymbol{k}}) \)


Unsaturated hydrocarbon among the following is:
A. ethane
B. methane
c. ethylene
D. propane


The \( r . m . s . \) velocity of hydrogen is \( \sqrt{7} \) times the \( r . m . s . \) velocity of nitrogen. If
\( \boldsymbol{T} \) is the temperature of the gas:
\( \mathbf{A} \cdot T\left(H_{2}\right)=T\left(N_{2}\right) \)
B \( \cdot T\left(H_{2}\right)>T\left(N_{2}\right) \)
C \( \cdot T\left(H_{2}\right)<T\left(N_{2}\right) \)
D. \( T\left(H_{2}\right)=\sqrt{7} T\left(N_{2}\right) \)


Calomel is:
A \( . H g_{2} C l_{2} \)
в. \( \mathrm{HgCl}_{2} \)
\( \mathrm{c} . H g_{2} C l_{2}+H g \)
D. \( H g+H g C l_{2} \)


How many moles of \( A g C l \) will be
precipitated when an excess of \( A g N O_{3} \)
solution is added to one molar solution
of \( \left[\boldsymbol{C r} \boldsymbol{C l}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{5}\right] \boldsymbol{C l}_{2} ? \)


Inverse circular functions,Principal values of \( \sin ^{-1} x, \cos ^{-1} x, \tan ^{-1} x \)
\[
\begin{aligned}
\tan ^{-1} x+\tan ^{-1} y=\tan ^{-1} \frac{x+y}{1-x y} \\
x y<1 \\
\pi+\tan ^{-1} \frac{x+y}{1-x y}, & x>1
\end{aligned}
\]
Solve
(a) \( \cos \left(2 \sin ^{-1} x\right)=1 / 9 \)
(b) \( \cos ^{-1}(3 / 5)-\sin ^{-1}(4 / 5)=\cos ^{-1} x \)
(c) If \( \sin \left(\sin ^{-1} \frac{1}{5}+\cos ^{-1} x\right)=1, \) then
prove that \( x \) is equal to \( 1 / 5 \)


The number of lobes in most of the d-
orbitals are:
A. 6
B. 8
c. 10
\( D \)


Which of the following is not true about
deforestation?
A. Population explosion is one of the reasons for deforestation
B. Cleaning of forest for agriculture causes deforestation
C. Deforestation is taking place only in developing courtiers
D. Cash crop economy of third world is a cause of deforestation


Discuss the general characteristics of Group 15 elements with reference to their electronic configuration, oxidation state, atomic size, ionisation enthalpy and electronegativity


The angle between the lines whose direction cosines are \( \left(\frac{\sqrt{3}}{4}, \frac{1}{4}, \frac{\sqrt{3}}{2}\right) \)
and \( \left(\frac{\sqrt{3}}{4}, \frac{1}{4},-\frac{\sqrt{3}}{2}\right) \) is :
\( A \)
в. \( \frac{\pi}{2} \)
c. \( \frac{\pi}{3} \)
D.


Formula of Heisenberg uncertainty
principle is:


Evaluate: \( \lim _{x \rightarrow 0} \frac{x\left(e^{\sin x}-1\right)}{1-\cos x} \)
A \( \cdot \frac{1}{2} \)
B . 2
\( c \cdot 0 \)
D.


Show an experiment which proves light always travels in a straight line.


The Figure 26.67 shows variation of \( R \)
\( X_{L} \) and \( X_{C} \) with frequency fin a series
L, C, R circuit. Then, for
what frequency point, the circuit is inductive?
\( A \)
B.
\( c \)
'. all point


Assertion
Ratio of isothermal bulk modulus and
adiabatic bulk modulus for a
monoatomic gas at a glven pressure is \( \frac{3}{5} \)
Reason This ratio is equal to \( \gamma=\frac{C_{p}}{C_{v}} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


If a cylinder of diameter \( 1.0 \mathrm{cm} \) at \( 30^{\circ} \mathrm{C} \)
is to be slid into a hole of diameter
\( 0.9997 \mathrm{cm} \) in a steel plate at the same temperature, the minimum required rise in the temperature of the plate is: (Coefficient of linear expansion of \( \left.\operatorname{steel}=12 \times 10^{-6} /^{\circ} C\right) \)
A \( \cdot 25^{\circ} \mathrm{C} \)
В \( \cdot 35^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 45^{\circ} \mathrm{C} \)
D. \( 55^{\circ} \mathrm{C} \)


A body has an acceleration of \( -4 m s^{-2} \) Then its retardation is equal to :
A \( .-4 m s^{2} \)
B. \( 4 m s^{-2} \)
c. zero
D. Nothing can be decided


Explain ion-dipole interaction with suitable example.


\( K_{P} \) for reaction \( A+B \rightleftharpoons C+D \) is 1.34
\( \operatorname{at} 60^{\circ} \mathrm{C} \) and 6.64 at \( 100^{\circ} \mathrm{C} . \) Determine
the free energy change of this reaction at each temperature and \( \Delta H^{o} \) for the reaction over this range of
temperature?
A. 405J/mol ; 5872 J/mol and 41.3 kJ/mol
B. 810 J/mol ; 5870 J/mol and 41.3 kJ/mol
c. \( 405 J / \mathrm{mol} \); \( 5 \mathrm{J} / \mathrm{mol} \) and \( 20.56 \mathrm{kJ} / \mathrm{mol} \)
D. 810 J/mol; 29362 J/mol and 20.56 kJ/mo


A body starts moving with a velocity \( v_{0}=10 m s^{-1} . \) It experiences a retardation equal to \( \frac{1}{5} v^{2} \). Its velocity after \( 2 s \) is given by
\( \mathbf{A} \cdot-3.33 m s^{-1} \)
B. \( +4 m s^{-1} \)
c. \( +3.33 m s^{-1} \)
D. \( +6 m s^{-1} \)


If \( x=\phi(t), y=\psi(t), \) then \( \frac{d^{2} y}{d x^{2}} \) is
A \( \cdot \frac{\phi^{\prime} \psi^{\prime \prime}-\psi^{\prime} \phi^{\prime \prime}}{\left(\phi^{\prime}\right)^{2}} \)
B. \( \frac{\phi^{\prime} \psi^{\prime \prime}-\psi^{\prime} \phi^{\prime \prime}}{\left(\phi^{\prime}\right)^{3}} \)
c. \( \frac{\phi^{\prime \prime}}{\psi^{\prime \prime}} \)
D. \( \frac{\psi^{\prime \prime}}{\phi^{\prime \prime}} \)


The arithmetic mean of two numbers is
17 and their geometric mean is \( 15 . \) Find
the numbers.


Denominator of a Fraction exceeds its
numeration by \( 6 . \) If 1 is added to the
numerator and 3 is substracted from
the denominater, the new friction is
\( \frac{3}{4} . \) find the orignal fraction


Which of the following is not a physical change?
A. Melting of wax
B. Tearing a piece of paper
c. cutting wood
D. Digestion of food


Venation is monocots in
A. Pinnate reticulate
B. Palmate reticulate
C . Pinnate parallel
D. Parallel


Consider the hydrogen atom to be a
proton embedded in a cavity of radius
\( a_{0} \) (Bohr's radius), whose charge is
neutralized by the addition of an electron to the cavity in vacuum, infinitely slowly. Then the wavelength of the electron when it is at a distance of
\( a_{0} \) from the proton will be
A \( \cdot \lambda=\sqrt{\frac{4 \pi \varepsilon_{0} a_{0}}{h^{2} e^{2} m}} \)
B. \( \lambda=\sqrt{\frac{4 \pi \varepsilon_{0} a_{0} h^{2}}{e m}} \)
\( ^{\mathbf{c}} \cdot_{\lambda}=\sqrt{\frac{4 \pi \varepsilon_{0} a_{0} h^{2}}{e^{2} m}} \)
D. \( \lambda=\sqrt{\frac{4 \pi \varepsilon_{0} a_{0} h^{2}}{e^{5} m}} \)


A body of mass \( 5 k g \) is taken from a
height of \( 5 m \) to \( 10 m . \) Find the increase
in its potential energy. Take \( \boldsymbol{g}= \) \( 10 m s^{-2} \)
A . \( 50 J \)
в. \( 150 J \)
\( c .250 J \)
D. \( 300 J \)


Give the IUPAC name of the following:


Which of the following metals dissolves in \( K O H \) with the evolution of
hydrogen?
A. \( C a \)
в. \( M g \)
\( c \cdot S r \)
D. \( B e \)


\( \triangle A B C \) is an isosceles triangle. If the
coordinates of the base are \( \boldsymbol{B} \equiv(\mathbf{1}, \mathbf{3}) \) and \( C \equiv(-2,7), \) the coordinates of vertex \( A \) can be This question has multiple correct options
A. (1,6)
(年) (1,66)
в. \( \left(-\frac{1}{2}, 5\right) \)
\( ^{c} \cdot\left(\frac{5}{6}, 6\right) \)
D. \( \left(-7, \frac{1}{8}\right) \)


An electron is in an excited state in a
hydrogen like atom. It has a total energy of \( -3.4 e V . \) The kinetic energy of the
electron is \( \boldsymbol{E} \) and its de Broglie
wavelength is \( \lambda \)
A \( . E=6.8 \mathrm{eV}, \lambda=-6.6 \times 10^{-10} \mathrm{m} \)
B . \( E=3.4 \mathrm{eV}, \lambda=-6.6 \times 10^{-10} \mathrm{m} \)
C . \( E=3.4 \mathrm{eV}, \lambda=-6.6 \times 10^{-11} \mathrm{m} \)
D. \( E=6.8 e V, \lambda=-6.6 \times 10^{-11} \mathrm{m} \)


In long form of periodic table, the total number of periods is:
A. 5
B. 7
\( c \cdot 8 \)
D.


Ammonia is not produced in the
reaction of
A. \( N H_{4} C l \) with кон
B. AlN with water
c. \( N H_{4} C l \) with \( N a N O_{2} \)
D. \( N H_{4} C l \) with \( C a(O H)_{2} \)


Young's modulus of rubber is \( 10^{4} N / m^{2} \)
and area of cross section is \( 2 \mathrm{cm}^{-2} \). If
force of \( 2 \times 10^{5} \) dyn is applied along its
length, then its initial \( l \) becomes.
A . \( 3 l \)
в. \( 4 l \)
\( c \cdot 2 l \)
D. None of these


Which of the following involves in formation of mitotic spindle?
A . ca
B. s
c. мg
D.


A point particle moves along a straight line such that \( x=\sqrt{t}, \) where \( t \) is time.
Then, ratio of acceleration to cube of the
velocity is
A . -1
в. -0.5
c. -3
D. -


Find \( \lim _{x \rightarrow \pi / 4} \frac{\sin x-\cos x}{x-\pi} \)


A ray of light is travelling from a denser
medium to rarer medium. For these
media critical angle is C. The maximum possible deviation of the ray is
\( \mathbf{A} \cdot \pi-2 \)
B . \( \pi-2 C \)
\( c \cdot 2 C \)
D. \( \pi_{/ 2}+C \)


A sonar device fitted in a submarine
receives an echo \( 4 s \) later the signal is transmitted towards another
submarine \( 3060 m \) away. Find the speed of sound in water.
\( \mathbf{A} \cdot 1530 m s^{-1} \)
B . \( 1342 \mathrm{ms}^{-1} \)
c. \( 1600 m s^{-1} \)
D. \( 1250 m s^{-1} \)


Anhydrous \( H_{2} S O_{4} \) has high viscosity
due to strong hydrogen bonding. If true enter 1 , else enter 0 .


Solve the equations
\( 3\left(\sec ^{2} \theta+\tan ^{2} \theta\right)=5 \)


An n-p-n transistor power amplifier in \( \mathrm{C} \) E configuration gives
A. Voltage amplification only
B. Current amplification only
c. Both current and voltage amplification
D. only power gain of unity


A \( 20 \mathrm{kg} \) object is being lifted through a
height of \( \mathrm{m} \) when \( 484 \mathrm{J} \) of
work is done on it.