Carbon-dating uses carbon isotope with
number of neutrons eight
if true enter 1 , else enter 0


A small particle of mass \( m \) moves in such a way that \( P . E=-\frac{1}{2} m k r^{2}, \) where
\( k \) is a constant and \( r \) is the distance of
the particle from origin. Assuming Bohr's model of quantization of angular momentum and circular orbit, \( r \) is
directly proportional to:
\( \mathbf{A} \cdot n^{2} \)
в.
c. \( \sqrt{n} \)
D. none of these


An object shaped as a hemisphere rests with its flat surface on a table. The
object has radius \( r \) and density \( \rho \) The volume of a sphere is \( \frac{4}{3} \pi r^{3} \) Which average pressure does the object exert on the table?
\( A \)
B.
c. \( \frac{2}{3} \rho r \)
D. \( \frac{2}{3} \rho r g \)


Aestivation found in pea flowers is
A. Twisted
B. Valvate
c. Imbricate
D. Vexillary


In man, small intestine is the place for
A. Digestion
B. Elimination
c. Degradatin
D. Absorption


Give the relation between focal length and radius of carvature


If \( \lim _{x \rightarrow c} \frac{f(x)-f(c)}{x-c} \) exists finitely, then
\( \mathbf{A} \cdot \lim _{x \rightarrow c} f(x)=f(c) \)
B. \( \lim _{x \rightarrow c} f^{\prime}(x)=0 \)
\( \mathbf{C} \cdot \lim _{x \rightarrow c} f(x) \) does not exist
D. \( \lim _{x \rightarrow c} f(x) \) may or may not exist


Can deceleration of car exceed'g'?
A. yes
B. no
c. depends upon friction coefficient
D. none


Instead of excreting, these can store urea in the tissues
A. Birds
B. Fish
c. Elephants
D. camels


\( \frac{8}{8} \)


In the binomial expansion of \( (1+y)^{n} \)
where \( n \) is a natural number, the
coefficients of the \( 5^{t h}, 6^{t h} \) and \( 7^{t h} \) terms
are in A.P, find \( n \)
This question has multiple correct options
\( \mathbf{A} \cdot n=7 \)
B . \( n=14 \)
c. \( n=8 \)
D. \( n=16 \)


Which of the following are used as food preservative? This question has multiple correct options
A. Table salt
B. Sodium hydrogen carbonate
c. cane sugar
D. Benzoic acid


The eccentricity of the conic section
\( 4\left(x^{2}-y^{2}\right)=1 \) is
A \( \cdot \sqrt{2} \)
B.
\( c \cdot 4 \)
D.


According to Dalton, atoms of different elements combine with one another to
form:
A. compounds
B. elements
c. solution
D. All of the above


Assertion
In a gas any rapid change must be adiabatic whereas a slow change may be adiabatic.
Reason
In a P-V diagram, the magnitude of the slope is greater for an adiabatic process than for an isothermal process.
A. Both statements 1 and 2 are true and statement 2 is the correct explanation of statement 1
B. Both statements 1 and 2 are true but statement 2 is not the correct explanation of statement 1
c. statement 1 is true but statement 2 is false
D. Statement 1 is false but statement 2 is true


Electroplating can done by
A. copper
B. Silver
c. Chromium
D. All of these


Choose the correct answers from the
alternatives given :
The period in mitosis in which daughter chromosomes separate from each other and get to opposite poles is known as
A. interphase
B. anaphase
c. metaphase
D. prophase


Construct the following quadrilaterals. Quadrilateral PLAN \( P L=4 \mathrm{cm} \)
\( \boldsymbol{L} \boldsymbol{A}=\mathbf{6 . 5} \boldsymbol{c m} \)
\( \angle P=90^{\circ} \)
\( \angle A=110^{\circ} \)
\( \angle N=85^{\circ} \)


\( a C u^{2+}(a q)+b I^{-}(a q) \rightarrow c C u I(s)+d I_{2}(s) \)
When the equation above is balanced and
all coefficients are reduced to lowest
whole-number terms, what will be the
coefficient for \( I^{-} \) ?
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 3 \)
\( D \cdot 4 \)
\( E \cdot 5 \)


All free electric charges can be
\( (e=\operatorname{single} \) unit of charge i.e. the
magnitude of charge on electron
This question has multiple correct options
A. odd multiples of \( e \)
B. fractional multiples of \( e \)
c. even multiples of \( e \)
D. negative multiples of \( e \)


The expansion \( \left[\boldsymbol{x}+\left(\boldsymbol{x}^{\mathbf{3}}-\mathbf{1}\right)^{\mathbf{1} / \mathbf{2}}\right]^{\mathbf{5}}+[\boldsymbol{x}- \)
\( \left.\left(x^{3}-1\right)^{1 / 2}\right]^{5} \) is a polynomial of degree
A. 5
B. 6
\( c \cdot 7 \)
\( D \)


Which expression has the same SI base
units as pressure?
A. \( \frac{\text { force }}{\text { length } \times \text { speed }} \)
в. \( \frac{\text { force }}{\text { length } \times \text { time }} \)
c. \( \frac{\text { mass }}{\text { length } \times(\text { time })^{2}} \)
D. \( \frac{\text { mass } \times(\text { time })^{2}}{\text { length }} \)


Starting with an expression for refraction at a single spherical surface, obtain Lens Maker's Formula.


The ratio between the sum of \( n \) terms of
two A.P.'s is \( 7 n+1: 4 n+27 . \) Find the
ratio between their nth terms.


Verify that:
\( \cos 60^{\circ}=\frac{1-\tan ^{2} 30^{\circ}}{1+\tan ^{2} 30^{\circ}}=\frac{1}{2} \)


Find the smallest positive values of \( x \) and y satisfying \( \boldsymbol{x}-\boldsymbol{y}=\frac{\boldsymbol{\pi}}{\boldsymbol{4}} \) and \( \cot \boldsymbol{x}+ \)
\( \cot \boldsymbol{y}=2 \)
A ' the least positive values of \( x \) and \( y \) are \( \frac{\pi}{6} \) and \( \frac{5 \pi}{12} \) respectively
B. The least positive values of \( x \) and \( y \) are \( \frac{5 \pi}{12} \) and \( \frac{\pi}{6} \) respectively
c. the least positive values of \( x \) and \( y \) are \( \frac{5 \pi}{6} \) and \( \frac{\pi}{3} \) respectively
D ' The least positive values of x and y are \( \frac{\pi}{3} \) and \( \frac{5 \pi}{6} \) respectively


If the radius of a sphere is measured as \( 9 \mathrm{cm} \) with an error of \( 0.02 \mathrm{cm}, \) then find
the approximate error in calculating its
volume


Among the following species, the diamagnetic molecule is:
\( A \cdot O_{2} \)
в. \( N O \)
c. \( B_{2} \)
D. \( C O \)


While a collector to emitter voltage is constant in a transistor, the collector
current changes by \( 8.2 m A \) when the
emitter current changes by \( 8.3 m A \). The
value of forward current ratio \( \boldsymbol{h}_{f e}(\text { or } \boldsymbol{\alpha}) \)
is
A .0 .9879
B. 8.30
c. 8.2158
D. 8.0123


The pH of blood is
A. 7.4
B. 8.4
\( c \cdot 6.4 \)
D. 6.0


Find the electric field in the region
labelled 2.
\( \mathbf{A} \cdot k_{e} \frac{q}{r^{2}} \)
\( \mathbf{B} \cdot 2 k_{e} \frac{q}{r^{2}} \)
\( c \cdot 3 k_{e} \frac{q}{r^{2}} \)
D. \( 4 k_{e} \frac{q}{r^{2}} \)


Which of the following statements are
correct about Mendeleev's periodic table?
i) It is based on increasing order of
atomic numbers.
ii) Mendeleev corrected the atomic
weight of some elements like Be, In etc.
iii) \( \left(\boldsymbol{A} \boldsymbol{r}, \boldsymbol{H}_{2}\right),\left(\boldsymbol{C o}, \boldsymbol{C l}_{2}\right),\left(\boldsymbol{T} \boldsymbol{e}, \boldsymbol{F}_{2}\right) \) are
three inverted pairs.
iv) It is based on increasing order of atomic weights.
A. only (i) correct
B. (ii) and (iv) are correct
c. only (iii) correct
D. (i) and (iv) are correct


Arrange the following compounds in order of their Molar conductance:
(।) \( \boldsymbol{K}\left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{O}_{2}\right)_{4}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{2}\right] \)
\( (\|)\left[\boldsymbol{C r}(\boldsymbol{O} \boldsymbol{N} \boldsymbol{O})_{3}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{3}\right] \)
\( (\|\|)\left[\boldsymbol{C r}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right] \boldsymbol{C l}_{3} \)
\( (\mathrm{IV}) M g\left[C r\left(N O_{2}\right)_{5}\left(N H_{3}\right)\right] \)
\( A \cdot\|<I<I V<\| 1 \)
B. II IV \( <1<11 \)
c. \( \|<1=1 V<\| \)
D. IV <III <II<I


Two bodies of mass \( 1 \mathrm{kg} \) and \( 3 \mathrm{kg} \) have position vectors \( \hat{\mathbf{i}}+\hat{\mathbf{2}} \boldsymbol{j}+\hat{\boldsymbol{k}} \) and \( -\hat{\mathbf{3}} \boldsymbol{i}- \)
\( \hat{\mathbf{2}} \boldsymbol{j}+\hat{\boldsymbol{k}}, \) respectively. The center of mass of this system has a position vector:
\( \mathbf{A} \cdot-\hat{i}+\hat{j}+\hat{k} \)
\( \mathbf{B} \cdot-\hat{2} i+\hat{2 k} \)
c. \( -\hat{2} i-\hat{j}+\hat{k} \)
D. \( 2 i-\hat{j}-\hat{2} k \)


Formula for argentite, horn silver and
pyragyrite are respectively?
\( \mathbf{A} \cdot A g_{2} S, A g C l \) and \( A g_{3} S b S_{3} \)
B. \( A g C l, A g_{3} S b S_{3} \) and \( A g_{2} S \)
\( \mathbf{c} \cdot A g_{3} S b S_{3}, A g_{2} S \) and \( A g C l \)
D. \( A g C l A g_{2} S \) and \( A g_{3} S b S_{3} \)


An oligotrophic lake is characterised by
A. great changes in water level
B. long food chains
c. low nutrient contents and little life
D. high nutrient levels and abundant flora and fauna


The nuclear model of the atom was
suggested by:
A. Bohr
B. Rutherford
c. Pauli
D. Mendeleef


Electric lines of forces.
A. May form closed path
B. Must form closed path
C. May be discontinuous
D. Both (a) and
(c) are correct


Which battery is used in aeroplanes?
A. Dry cell battery.
B. Lead acid battery.
c. Edission cell.
D. None of them.


In Mendeleev periodic table few elements that are chemically similar are placed in separate


State True or False:
Two atoms can be isotones and isobars
simultaneously.
A. True
B. False


Which component present in human hair?
A. Cellulose
B. Keratin
c. Mayoglobin
D. Albumin


In the arrangement shown in the figure,
the ends \( P \) and \( Q \) of an un-stretchable
string move downwards with uniform
speed \( U \). Pulleys \( A \) and \( B \) are fixed. The
mass \( M \) moves upwards with a speed:
\( \mathbf{A} \cdot 2 U \cos \theta \)
B. \( \frac{U}{\cos \theta} \)
c. \( \frac{2 U}{\cos \theta} \)
\( D . U \cos \theta \)


In which of the following cases the net force is not equal to zero?
A. A kite skillfully held stationary in the sky.
B. A ball falling freely from a height.
c. A helicopter hovering above the ground.
D. A cork floating on the surface of water.


When making repayments on a lease, the profit and loss account will contain
which items relevant to the lease?
A. Instalment charges only
B. Interest only
c. Interest and instalment charges
D. Neither interest or instalment charges


\( \mathbf{f} \boldsymbol{A}=\{\mathbf{1}, \mathbf{2}\}, \) from the \( \operatorname{set} \boldsymbol{A} \times \boldsymbol{A} \times \boldsymbol{A} \)


AZT stands for:
A. azidothymidine
B. azidothyroxine
c. azidothiol
D. both \( A \) and \( B \)


Consider two sealed jars of equal volume. One contains 2 g of hydrogen at \( 200 \mathrm{K} \) and the other contains \( 28 \mathrm{g} \) of nitrogen at \( 400 \mathrm{K} \). The gases in the two jars will have
A. the same pressure
B. the same average kinetic energy.
c. the same number of molecules
D. the same average molecular speed


Find Order of matrix : \( \left[\begin{array}{lll}\mathbf{1} & \mathbf{2} & \mathbf{6} \\ \mathbf{2} & \mathbf{4} & \mathbf{3}\end{array}\right] \)


Let \( A=\{0,1\} \) and \( N \) the set of all
natural numbers. Then show the
mapping \( \boldsymbol{f}: \boldsymbol{N} \rightarrow \boldsymbol{A} \) defined by
\( \boldsymbol{f}(\boldsymbol{2 n}-\mathbf{1})=\mathbf{0}, \boldsymbol{f}(\boldsymbol{2 n})=\mathbf{1} \forall \boldsymbol{n} \in \boldsymbol{N} \) is
many-one onto.


The potential and electric field in the
above set up if the consecutive charges
have opposite sign is :
A \( \cdot \frac{q}{6 \pi \epsilon_{0}} \) and \( \frac{q}{5 \pi \epsilon_{0}} \)
B. \( \frac{q}{6 \pi \epsilon_{0}} \) and \( \frac{q}{6 \pi \epsilon_{0}} \)
c. \( \frac{q}{5 \pi \epsilon_{0}} \) and \( \frac{q}{6 \pi \epsilon_{0}} \)
D. \( \frac{q}{4 \pi \epsilon_{0}} \) and \( \frac{q}{6 \pi \epsilon_{0}} \)


Which of the following mixture can be separated by magnetic separation?
A. Iron filings, sand and iodine
B. Common salt, sand and marbles
c. chalk powder, grain and chaff
D. Stone, salt and water


While measuring the thermal conductivity of liquids, the upper part is kept hot and lower one cool so that:
A. convectional flow is stopped
B. radiation is stopped
c. conduction is easier
D. it is easier to perform the experiment


Which of the following is not a longitudinal wave?
A. Seismic P-wave
B. Light
c. sound
D. Ultrasound


A hemisphere of lead of radius \( 7 \mathrm{cm} \) is cast into a right circular cone of height \( 49 \mathrm{cm} . \) Find the radius of the base in
\( \mathrm{cm} \)


In given figure \( P \) and \( Q \) are points on
sides \( A B \) and \( A C \) respectively of \( \triangle A B C \)
If \( A P=3 \mathrm{cm}, P B=6 \mathrm{cm}, A Q=5 \mathrm{cm} \) and
\( \mathrm{QC}=10 \mathrm{cm}, \) show that \( \mathrm{BC}=3 \mathrm{PQ} \)


The value of \( a \) for which one root of the
quadratic equation \( \left(a^{2}-5 a+3\right) x^{2}+ \)
\( (3 a-1) x+2=0 \) is twice as large as the other is
A \( \cdot-\frac{2}{3} \)
в. \( \frac{1}{3} \)
\( c \cdot-\frac{1}{3} \)
D. \( \frac{2}{3} \)


What is the effect of sexual
reproduction?
A. Offspring is weak.
B. offspring is like the parent.
c. offspring is more vigorous.
D. Offspring is diseased.


Find the roots of the quadratic equation
(i) \( 4 x^{2}+4 \sqrt{3} x+3=0 \)
(i) \( 2 x^{2}+x+4=0 \)


Which of the following is a rapid type of absorption?
A. Passive absorption
B. Active absorption
c. Salt absorption
D. Root absorption


Lewis dot symbol indicates the number of electrons of inner shell.
A. True
B. False


Let a function \( \boldsymbol{f}(\boldsymbol{x})= \)
a relation between \( b \) and \( c \) such that
\( \lim _{x \rightarrow 1} f(x) \) exists is
B. \( 3 b+2 c-1=0 \)
c. \( 3 b-2 c-1=0 \)
D. \( b-2 c+1=0 \)


Let \( S_{n}=\sum_{k=1}^{n} \frac{n}{n^{2}+k n+k^{2}} \) and \( T_{n}= \)
\( \sum_{k=0}^{n-1} \frac{n}{n^{2}+k n+k^{2}}, \) for \( n=1,2,3, \dots \)
Then,
This question has multiple correct options
A \( \cdot S_{n}<\frac{\pi}{3 \sqrt{3}} \)
в. \( S_{n}>\frac{\pi}{3 \sqrt{3}} \)
c. \( T_{n}<\frac{\pi}{3 \sqrt{3}} \)
D \( \cdot T_{n}>\frac{\pi}{3 \sqrt{3}} \)


The Poisson's ratio of the material of a
wire is0.25. If it is stretched by a force \( F \) the longitudinal strain produced in the
wire is \( 5 \times 10^{-4} \). What is the
percentage increase in its volume?
A . 0.2
B. \( 2.5 \times 10^{-2} \)
c. zero
D . \( 1.25 \times 10^{-6} \)


A astronomical telescope has objective
and eyepiece of focal lengths \( 40 \mathrm{cm} \) and
\( 4 \mathrm{cm} \) respectively. To view an object
\( 200 \mathrm{cm} \) away from the objective, the lenses must be separated by a distance:
A . \( 54.0 \mathrm{cm} \)
в. \( 37.3 \mathrm{cm} \)
c. \( 46.0 \mathrm{cm} \)
D. \( 50.0 \mathrm{cm} \)


A hemispherical bowl is made up of stone whose thickness is \( 5 \mathrm{cm} \). If the
inner radius is \( 35 \mathrm{cm}, \) find the total surface area of the bowl


Arrange the following in increasing order of boiling points


A given length of wire can be bent to form a circle or a square of single turn and a current may be established in it. The ratio of magnetic field at the centre of circle to that at the centre of square is :
A \( \cdot \frac{\pi^{2}}{8 \sqrt{2}} \)
B. \( \frac{4 \sqrt{2}}{\pi^{2}} \)
c. \( \frac{\pi}{2 \sqrt{2}} \)
D.


Which law is referred to as the law of
inertia?
A. First law of motion
B. Second law of motion
c. Third law of motion
D. None of these


Ram prasad saved \( R s .10 \) in the first
week of the year and then increased his
weekly saving by \( R s .2 .75 . \) If in the \( n^{t h} \)
week, his savings become \( R s .59 .50 \) find \( n \)


Very short answer type.
What happens to plasma proteins during hemodialysis?


1.2348 is:
A. An integer
B. A rational number
C. An irrational number
D. A natural number


Equatorial plate is found in which of the following stages?
A. Metaphase
B. Prophase
c. Telophase
D. Anaphase


\( H_{2} O_{2} \) solution turns blue litmus red
If this is true enter 1 , if false enter 0 .


Elements of which of the following groups do not form hydrides?
A. 1,2,3
в. 3,4,5
c. 7,8,9
D. 6,7,8


Photorespiration occurs in
A. Mitochondria
B. Chloroplast
c. Peroxisome
D. Cytoplasm


Evaluate the following integrals:
\( \int \sqrt{2 x-x^{2}} d x \)
A \( \cdot(x-1) \sqrt{2 x-x^{2}}+\frac{1}{2} \sin ^{-1}(x-1)+C \)
B. \( \frac{1}{2}(x-1) \sqrt{2 x-x^{2}}+2 \sin ^{-1}(x-1)+C \)
c. \( \frac{1}{2}(x-1) \sqrt{2 x-x^{2}}+\frac{1}{2} \sin ^{-1}(x-1)+C \)
D. none of these


A ray of light is incident at the glass-
water interface at an angle \( i \). It merges finally parallel to the surface of the water. Then, the value of \( \mu_{g} \) would
be(where \( \mu_{g} \) is the refractive index of glass with respect to water)
A \( \cdot(4 / 3) \sin i \)
B. 1/ \( \sin i \)
\( c \cdot 4 / 3 \)
\( D \)


Find variance for following data:
\( \begin{array}{lllll}\text { Class } & \mathbf{3 0}- & \mathbf{4 0}- & \mathbf{5 0 -} & \mathbf{6} \\ \text { interval } & \mathbf{4 0} & \mathbf{5 0} & \mathbf{6 0} & \mathbf{7}\end{array} \)
Frequency \( \quad 3 \) What is and 12
A. 14.17
B. 18.17
c. 16.17
D. 15.17


The magnetic susceptibilty for diamagnetic materials is
A. small and negative
B. small and positive
c. large and positive
D. large and negative


A block is placed on a rough floor and a
horizontal force \( \boldsymbol{F} \) is applied on it. The
force of friction \( \boldsymbol{f} \) by the floor on the
block is measured for different values
of \( F \) and a graph is plotted between
them.
This question has multiple correct options
A. The graph is a straight line of slope \( 45^{\circ} \)
B. The graph is a straight line parallel to the \( F \) -axis.
C. The graph is a straight line of slope \( 45^{\circ} \) for small \( F \) and a straight line parallel to the \( F \) -axis for large \( F \)
D. There is a small kink on the graph.


If the straight line joining two points \( P(5,8) \) and \( Q(8, k) \) is parallel to \( x- \)
axis, then write the value of \( k \)


\( (x, y) \) and \( (p, q) \) are two ordered pairs. Find the values of \( p \) and \( y, \) if \( (4 y+ \)
\( \mathbf{5}, \mathbf{3} \boldsymbol{p}-\mathbf{1})=(\mathbf{2 5}, \boldsymbol{p}+\mathbf{1}) \)
A. \( p=0, y=5 \)
В. \( p=1, y=5 \)
c. \( p=0, y=1 \)
D. \( p=1, y=1 \)


\( \operatorname{Given} f(x)=\frac{a x+b}{x+1}, \lim _{x \rightarrow \infty} f(x)=1 \) and
\( \lim _{x \rightarrow 0} f(x)=2, \) then \( f(-2) \) is
\( A \cdot 0 \)
B.
\( c \cdot 2 \)
\( D \)


Write the functions of the following
vitamins:
(i) Vitamin A
(ii) Vitamin D
(iii) Vitamin E
(iv) Vitamin K


An atom of an element has \( 4^{t h} \) shell as
the valence shell with an electron pair in
it. The number of electrons in \( 3^{r d} \) shell
is 2 times more than the number of
electrons in \( 2^{n d} \) shell. Identify atomic
number.
A .24
B. 25
c. 27
D. 28


lodine is used as an antiseptic in the
form of


Which of the following is homogeneous?
A. Milk
B. Paint
c. shampoo
D. None of these


Which of the following graphs would yield a straight line?
A. x/m vs p
B. \( \log _{x} / \) m vs p
c. \( x / m \) vs \( \log p \)
D. \( \log _{x} / m \) vs \( \log p \)


The normal operating voltage and current for a light-emitting diode are:
\( \mathbf{A} \cdot 60 V \) and \( 20 m A \)
B. \( 5 V \) and \( 50 m A \)
c. \( 1.7 V \) and \( 20 m A \)
D. \( 0.7 V \) and \( 60 m A \)


On a two lane road, car A is travelling with a speed of \( 36 \mathrm{km} h^{-1} \). two cars \( \mathrm{B} \) and \( C \) approach car \( A \) in opposite directions with a speed of \( 54 \mathrm{km} h^{-1} \) each. At a certain instant, when the distance \( A B \) is equal to \( A C, \) both being 1 \( \mathrm{km}, \mathrm{B} \) decides to overtake \( \mathrm{A} \) before \( \mathrm{C} \)
does. What minimum acceleration of
car B is required to avoid an accident?
\( A \cdot 9.8 \mathrm{m} s^{-2} \)
B \( \cdot 10 \mathrm{m} \mathrm{s}^{-2} \)
\( \mathrm{c} \cdot 1 \mathrm{m} s^{-2} \)
D. 2.0 \( \mathrm{m} s^{-2} \)


In the figure, \( O \) is the center of the circle \( \angle R P S=40, \) then \( \angle O Q P \) is equal to
A .140
в. 130
\( c .90 \)
\( D \)


Which order is coorect about auidity?
\( \mathbf{A} \cdot C H_{3} C O O H>C_{6} H_{5} C O O H>C_{6} H_{5} O H \)
B \( \cdot C_{6} H_{5} C O O H>C H_{3} C O O H>C_{6} H_{5} O H \)
\( \mathbf{c} \cdot C_{6} H_{5} O H>C_{6} H_{5} C O O H>C H_{3} C O O H \)
\( \mathbf{D} \cdot C_{6} H_{5} O H>C H_{3} C O O H>C_{6} H_{5} C O O H \)


consider the following species, when
attached to \( s p^{3} \) hybridized carbon, their
leaving group ability in nucleophilic substitution reactions decreases in the
order.
(I) \( C F_{3}-\underbrace{S}_{\|}^{O}-O^{\ominus} \)
\( (\|) C_{6} H_{5}-\prod_{\| \atop O}^{O}-O^{\ominus} \)
\( (\| I) C_{6} H_{5}-O^{\ominus} \)
\( O \)
\( (I V) C H_{3}-C^{\|}-O^{\ominus} \)


Each pair forms ideal solution except :
A \( \cdot C_{2} H_{5} B r \) and \( C_{2} H_{5} \)
B . \( C_{6} H_{5} C l \) and \( C_{6} H_{5} B r \)
c. \( C_{6} H_{6} \) and \( C_{6} H_{5} \cdot C H_{3} \)
D. \( C_{2} H_{5} I \) and \( C_{2} H_{5} O H \)


With respect to the figure which of the
following statement is correct?
\( A \cdot E_{A} \) for forward reaction is \( E_{A}-E_{B} \)
B. \( E_{A} \) for forward reaction is \( E_{C}-E_{A} \)
\( \mathrm{c} \cdot E_{A} \) for reverse reaction is greater than \( E_{A} \) for forward reaction
D. \( E_{A} \) for forward reaction is greater than \( E_{A} \) for
backward reaction


\( 100 \mathrm{ml} \) of \( 2 \mathrm{M} \) NaOH solution is diluted
by water and the final molarity becomes
0.5. The volume of water added to the
solution is:
A . \( 400 \mathrm{ml} \)
B. 300 m
c. \( 500 \mathrm{ml} \)
D. 200 m1


The maximum probability of finding
electron in the \( d_{x y} \) orbital is
A. Along with \( x \) - axis
B. Along the \( y \) - axis
C. At an angle of \( 45^{0} \) from the \( X \) and Y axis
D. At an angle of \( 90^{0} \) from the \( x \) and \( y \) axis


Time period of oscillation for given combination will be
A \( \cdot 2 \pi \sqrt{\frac{m\left(K_{1}+K_{2}\right)}{K_{1} K_{2}}} \)
в. \( 2 \pi \sqrt{\frac{m}{K_{1}+K_{2}}} \)
c. \( 2 \pi \sqrt{\frac{m K_{1} K_{2}}{K_{1}+K_{2}}} \)
D. \( 2 \pi \sqrt{\frac{m K_{1}}{K_{2}}} \)


Which \( P \) reacts with caustic soda, the
products are \( P H_{3} \) and \( N a H_{2} P O_{2} \). This
reaction is an example of:
A. Hydrolysis
B. Reduction
c. Disproportionation
D. Neutralisation


\( A, B, C \) and \( D \) have position vectors \( \vec{a}, \vec{b}, \vec{c} \) and \( \vec{d}, \) respectively, such that \( \vec{a}- \) \( \vec{b}=2(\vec{d}-\vec{c}), \) then
A. \( A B \) and \( C D \) bisect each other
B. \( A B \) and \( C D \) trisect each other
c. \( B D \) and \( A C \) bisect each other
D. \( B D \) and \( A C \) trisect each other


0
0
0
0
0


Exine modified to wings thereby strongly suggesting anemophily is exceptional to
A. Cycas
B. Pinus
c. All gymnosperms


Higher animals are capable of producing sounds with active
A. Vocal cords
B. Mammary glands
c. oil glands
D. Trachea


Students \( A, B \) and \( C \) measure the diameter
of a copper ball using the same screw gauge. A takes 5 readings, \( \mathrm{B} \) takes 9 readings and C takes 8 readings. The measured value will be most accurate for
\( A \cdot B \)
B. A
\( c \cdot c \)
D. all


The unit of length convenient on the nuclear scale is a fermi : \( 1 \mathrm{f}=10^{-15} \mathrm{m} \)
Nuclear sizes obey roughly the following empirical relation \( : r=r_{0} A^{1 / 3} \)
where, \( r \) is the radius of the nucleus, \( A \)
its mass number, and \( r_{o} \) is a constant
equal to about \( 1.2 \mathrm{f} \). Show that the rule implies that nuclear mass density is nearly constant for different nuclei Estimate the mass density of sodium
nucleus.


lodine gives blue colour with:
A . glucose
B. lactose
c. starch
D. heparin


Earth revolves around sun in 365
days.Calculate its angular speed.


The standard free energy change (in kJ) for the reaction,
\[
\begin{array}{c}
\mathbf{3} \boldsymbol{F} \boldsymbol{e}^{2+}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{2} \boldsymbol{C r}(\boldsymbol{s})=\boldsymbol{2} \boldsymbol{C r}^{3+}(\boldsymbol{a} \boldsymbol{q})+ \\
\boldsymbol{3} \boldsymbol{F} \boldsymbol{e}(\boldsymbol{s})
\end{array}
\]
\( \operatorname{given} E_{F e^{2+} / F e}^{o}=-0.44 \mathrm{V} \) and
\[
\boldsymbol{E}_{C r^{3+} / \boldsymbol{C r}}^{o}=-\mathbf{0 . 7 4 V} \text { is }(\boldsymbol{F}=\mathbf{9 6 5 0 0 C})
\]
A .57,900
В. -57,900
c. -173,700
D. 173,700


If atleast one child in a family with 3 children is a boy then the probability that 2 of the children are boys, is
\( A \cdot \frac{3}{7} \)
B. \( \frac{4}{7} \)
\( c \cdot \frac{1}{3} \)
D. \( \frac{3}{8} \)


The smallest bryophyte of \( 0-5 \mathrm{cm} \) in length is
A. cryptothallus
B. Radulla
c. zoopsis
D. Polytrichium


Find the fringe width of the fringe
pattern
A . \( 0.05 \mathrm{cm} \)
B. \( 0.25 \mathrm{cm} \)
\( c .0 .01 c m \)
D. \( 0.1 \mathrm{cm} \)


A man of mass \( 50 ~ k g \) carries a bag of
weight \( 40 N \) on his shoulder. The force
with which the floor pushes up his feet
will be
\( \mathbf{A} \cdot 882 N \)
в. \( 530 N \)
\( \mathbf{c} .90 N \)
D. \( 600 N \)


Complete nucleic acid hydrolysis yields all the following, except
A. Phosphoric acid
B. Purines
c. Pentoses
D. Adenosine


The reaction \( : \boldsymbol{X} \rightarrow \) product, follows first-order kinetics in 20 minutes, the
concentration of \( \boldsymbol{X} \) changes from \( \mathbf{0 . 1} \boldsymbol{M} \)
to \( 0.05 M \) then rate of reaction when
concentration of \( \boldsymbol{X} \) is \( \mathbf{0 . 0 2} \boldsymbol{m o l} / \boldsymbol{L} \) is:
A. \( 1.73 \times 10^{-4} \mathrm{M} / \min \)
B. \( 3.47 \times 10^{-5} \mathrm{M} / \mathrm{min} \)
c. \( 6.94 \times 10^{-4} \mathrm{M} / \min \)
D. \( 1.73 \times 10^{-5} \mathrm{M} / \mathrm{min} \)


Hydrogen shows similar properties with halogens. Which of the following properties does not match with the halogens?
A. Electronic configuration
B. Valency
c. Atomicity
D. None of the above


The instantaneous acceleration
(a) of a
particle executing a linear SHM is given by \( a=-4 x \) where \( x \) is the displacement from the mean position. The period of the particle is given by


A particle is revolving in a circle of radius \( r . \) Its displacement after
completing half the revolution will be
\( \mathbf{A} \cdot \pi r \)
B . \( 2 r \)
c. \( 2 \pi r \)
D. \( \frac{r}{2} \)


Which of the following has pungent odour?
A \( \cdot H_{2} S O_{4} \)
в. \( C H_{3} \) СООН
c. нс।
D. Both (a) and (b)


Sometimes you see a fountain of water rucshing out of the leaking joints (or holes) in the pipes of main water supply line in the city. Why does it happen?


Select out the odd one with respect to relative amount?
A.
в. Мв
\( c . \) мп
D.


Formation of cork cambium from fully
differentiated parenchyma cell is an example of
A. Differentiation
B. Dedifferentiation
c. Redifferentiation
D. None of the above


Which of the following cannot be dissolved in alcohol?
A. Dyes and drugs
B. Soaps and varnishes
c. Resins and varnishes
D. Rubber and plastics


Value of \( c \) using Rolle's theorem for
\( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{ll}\boldsymbol{x}^{2}+\mathbf{1} & , \mathbf{w h e n} \mathbf{0} \leq \boldsymbol{x} \leq \mathbf{1} \\ \mathbf{3}-\boldsymbol{x} & , \mathbf{w h e n} \mathbf{1}<\boldsymbol{x} \leq \mathbf{2}\end{array}\right. \)
\( A \)
B.
\( c \)
D. does notexis


Find all pairs of \( x, y \) that satisfy the
equation \( \cos x+\cos y+\cos (x+y)=-3 / 2 \)


STATEMENT-1: The boiling point of
\( C_{2} H_{5} O H \) is less than that of \( H_{2} O \)
though the molecular weight of
\( C_{2} H_{5} O H \) is more than that of water.
STATEMENT-2: \( C_{2} H_{5} O H \) molecules are
not highly associated through hydrogen
bonding as in water.
A. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-
B. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1
C. STATEMENT-1 is True, STATEMENT-2 is False
D. STATEMENT-1 is False, STATEMENT-2 is True


Establish the formula for area and
circumference of circle.


The average power dissipated in a pure inductor is
A \( \cdot \frac{1}{2} V I \)
B. \( V I^{2} \)
c. \( \frac{V I^{2}}{4} \)
D. zero


A uniform solid cylinder is rolling down
a rough inclined plane of inclination \( \boldsymbol{\theta} \)
Then?


A seven digit number is formed by using 0,1,2,3,4,8,9 without repetition. Then the probability that it is divisible by 4 is
A \( \cdot \frac{53 \times 4 !}{5 \times 6 !} ! \)
в. \( \frac{53}{180} \)
c. \( \frac{53}{6 \times 6 !} \)
D. None of these


The mid points of two small magnetic dipoles of length \( d \) in end-on positions, are separated by a distance \( \boldsymbol{x},(\boldsymbol{x}>>\boldsymbol{d}) \)
The force between them is proportional
to \( x^{-n} \) where \( n \) is :
\( A \)
в.
\( c \)
\( D \)


The sum of two numbers is \( \frac{-1}{3} . \) If one of the number is \( \frac{-12}{3}, \) find the other


The cost \( C \) of sending a parcel post
package weighing \( P \) gms, \( P \) an integer
is Rs.10 for the first grams and Rs.3 for
each additional grams. The formula for the cost is
A. \( C=10+3 P \)
B. \( C=10 P+3 \)
c. \( C=10+3(P-1) \)
E . \( C=10 P-7 \)


What should be taken away from \( 3 x^{2}- \) \( 4 y^{2}+5 x y+20 \) to \( \operatorname{get}-x^{2}-y^{2}+ \)
\( 6 x y+20 \)
A \( \cdot x^{2}-y^{2}-x y \)
в. \( x^{3}-3 y^{2}-x y \)
c. \( x^{2}-y^{3}-x y \)
D. \( 4 x^{2}-3 y^{2}-x y \)


For a body moving with uniform acceleration \( a \), initial and final
velocities in a time interval \( t \) are \( u \) and
\( \boldsymbol{v} \) respectively. Then, its average velocity
in the time interval \( t \) is :
This question has multiple correct options
A \( \cdot\left(v+\frac{a t}{2}\right) \)
B. \( \left(v-\frac{a t}{2}\right) \)
c. \( (v-a t) \)
D. \( \left(u+\frac{a t}{2}\right) \)


Genetic identity of human male is known by
A. Nucleolus
B. Cell organelles
c. Autosomes
D. sex chromosomes


What is the similarity between DNA and
RNA?
A. Both are polymer of nucleotides
B. Both have similar pyrimidine
c. Both have similar sugar
D. Both are genetic material


The number of corners in a cylinder is
\( A \cdot 1 \)
B. 2
\( c .3 \)
D. None


Charges \( Q_{1} \) and \( Q_{2} \) lie inside and outside respectively of a closed surface
S. Let \( \mathrm{E} \) be the field at any point on \( \mathrm{S} \) and
\( \phi \) be the flux of E over \( S \)
This question has multiple correct options
A \( \cdot \) If \( Q_{1} \) changes, both \( \mathrm{E} \) and \( \phi \) will change
B . If \( Q_{2} \) changes, E will change but \( \phi \) will not change
C. If \( Q_{1}=0 \) and \( Q_{2} \neq 0, \) then \( E \neq 0 \) but \( \phi=0 \)
D. If \( Q_{1} \neq 0 \) and \( Q_{2}=0, \) then \( \mathrm{E}=0 \) but \( \phi \neq 0 \)


Solve the following equations:
\( (a+x)^{\frac{2}{3}}+4(a-x)^{\frac{2}{3}}=5\left(a^{2}-x^{2}\right)^{\frac{1}{3}} \)


Two protons move parallel to each other,
keeping distance r between them, both moving with same velocity \( \overrightarrow{\mathrm{v}} \). Then the ratio of the electric and magnetic force of interaction between them is:
(c - Velocity of light)
A \( \cdot \mathrm{c}^{2} / \mathrm{v}^{2} \)
B \( \cdot 2 c^{2} / v^{2} \)
c. \( c^{2} / 2 v^{2} \)
D. none


Which scientist established the name
Hydrogen' meaning 'water producer'?
A. Robert Boyle
B. Henry Cavendish
c. Lavoiser
D. None of the above


How much more than \( 2 x^{2}+4 x y+2 y^{2} \)
is \( 5 x^{2}+10 x y-y^{2} ? \)
State True or False: The answer is \( 3 x^{2}+ \)
\( 6 x y-3 y^{2} \)
A . True
B. False


What is the mass of an object whose weight is 980 N?
\( A \cdot 980 \mathrm{kg} \)
B. 98 kg
\( c \cdot 100 \mathrm{kg} \)
D. zero


A godown building is in the form as shown in figure. The vertical crosssection parallel to the width side of the building is a rectangle \( 7 m \times 3 m \)
mounted by a semi-circle of radius
\( 3.5 m . \) The inner measurements of the
cuboidal portion of the building are
\( 10 m \times 7 m \times 3 m . \) Find the volume of
the godown and the total interior
surface area excluding the floor (Base) (Take \( \boldsymbol{\pi}=\mathbf{2 2} / \mathbf{7}) \)


Which of the following balanced equation correctly represents the formation of ammonia using Haber's
process?
A. \( N_{2}+H_{2} \rightarrow 2 N H_{3} \)
в. \( N_{2}+3 H_{2} \rightarrow N H_{3} \)
c. \( N_{2}+3 H_{2} \rightarrow 2 N H_{3} \)
D. \( 2 N_{2}+3 H_{2} \rightarrow 4 N H_{3} \)


A die is thrown, write a sample space
\( (S) \) and \( n(S) . \) If event \( A \) is getting a number greater than \( 4, \) write event \( A \) and \( n(A) \)


In a right triangle \( \Delta A B C \), right angled
at \( B . \) If \( \tan A=1, \) then verify that
\( 2 \sin A \cdot \cos A=1 \)


How should a thermometer be dipped inside beaker containing water
A. Vertically
B. Tilted
c. Any of the above way
D. None of the above way


A thermometer is used to measure
A . heat
B. thermal capacity
c. water equivalent
D. temperature


A block of mass \( M_{1}=10 \mathrm{kg} \) is placed
on a slab of mass \( M_{2}=30 \mathrm{Kg} \). The slab
lies on a frictionless horizontal surface
as shown in figure. The coefficient of
static friction between the block and
slab is \( \mu_{s}=0.25 \) and that of dynamic
friction is \( \mu_{k}=0.12 . \) A force \( F=40 \mathrm{N} \) acts
on block \( M_{1} \). The acceleration of the
slab will be \( \left(g=10 \mathrm{m} / \mathrm{s}^{2}\right) \)
A \( \cdot 0.5 \mathrm{m} / \mathrm{s}^{2} \)
B. \( 0.4 \mathrm{m} / \mathrm{s}^{2} \)
\( \mathrm{c} \cdot 1 \mathrm{m} / \mathrm{s}^{2} \)
D. \( \frac{5}{6} m / s^{2} \)


Choose the correct answers from the
alternatives given Which one of the following is not true of prokaryotes?
A. They are living cells
B. They lack a nucleus
c. They are either archaebacteria or eubacteria
D. All are parasitic


The line through point \( (\boldsymbol{m},-\mathbf{9}) \) and \( (7, m) \) has slope \( m . \) The \( y \) -intercept of this line, is?
A . -18
B. -6
\( c .6 \)
D. 18


The angle of dip at a place on the earth
gives:
A. The horizontal component of the earth's magnetic field.
B. The location of geograhical meridian.
C. The vertical component of the earth's magnetic field.
D. The direction of the earth's magnetic field.


n the given figure, \( A T \) is a tangent
\( A C=B C \) and \( \angle A B C=50^{\circ} . \) Find the
\( \angle B A T \)


Which of the following is a taxon?
A. species
B. Genus
c. Phylum
D. All of the above


n Fig, \( P Q \) and \( P R \) are the two light rays
emerging from an object \( \boldsymbol{P} \). The ray \( \boldsymbol{P Q} \)
is refracted as \( Q \) S. The ray \( P R \) suffers
partial reflection and refraction on the water-air interface. This is because:
A. the angle of incidence is more than the critical angle
B. the angle of incidence is equal to the critical angle
c. the angle of incidence is less than the critical angle
D. the angle of incidence is \( 90^{\circ} \)


In water treatment plants, the gas used
A. Ozone
B. Carbon dioxide
c. Nitrogen
D. oxygen


When a glass rod is rubbed with silk
cloth, it acquires charge because:
A. Electrons are added to it
B. Electrons are removed from it
c. Protons are added to it
D. Protons are removed from it


The area enclosed between the curves
\( \boldsymbol{y}=\boldsymbol{x}^{3} \) and \( \boldsymbol{y}=\sqrt{\boldsymbol{x}} \) is (in square units)
A \( \cdot \frac{5}{3} \)
B. \( \frac{5}{4} \)
c. \( \frac{5}{12} \)
D. \( \frac{12}{5} \)


Assertion: The more negative the standard reduction potential, the more is its ability to displace hydrogen from acids.

Reason: Ability to displace hydrogen from acids translates to the strength of the reductant.
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false


To make the following reduction process
spontaneous, temperature should be \( Z n O+C \longrightarrow Z N+C O \)
\( \mathbf{A} \cdot<1000^{\circ} \mathrm{C} \)
B \( \cdot>1100^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot<500^{\circ} \mathrm{C} \)
\( \mathrm{D} \cdot>500^{\circ} \mathrm{C} \) but \( <1000^{\circ} \mathrm{C} \)


Two short electric dipoles are placed as
shown. The energy of electric interaction
between these dipoles will be:
A \( \cdot \frac{2 k P_{1} P_{2} \cos \theta}{r^{3}} \)
B. \( \frac{-2 k P_{1} P_{2} \cos \theta}{r^{3}} \)
c. \( \frac{-2 k P_{1} P_{2} \sin \theta}{r^{3}} \)
D. \( \frac{-4 k P_{1} P_{2} \cos \theta}{r^{3}} \)


\( \frac{k}{k} \)


In the Millikan's oil drop experiment the oil drop is subjected to a horizontal electric field of \( 4 \mathrm{N} / \mathrm{C} \) and the drop moves with a constant velocity
making an angle \( 45^{0} \) to the horizontal. If
the weight of the drop is W. The charge on the drop is (neglect buoyancy)
A. w
B. W/4
c. w/2
D. 3W/4


If the zeros of the polynomial \( \boldsymbol{f}(\boldsymbol{x})= \) \( x^{3}-3 x^{2}+x+1 \) are \( a-b, a, a+b, \) find \( a \)
and b.


toppr
Q Type your question
Those of which not regaining are called
plastic. There may be delay in the
regaining in some materials. They are
said to have got elastic aftereffect,
since they have gone beyond the elastic
limit. Repeated application and removal
of force break at any point time and so
a re avoided.
The stress strain graph for two
materials \( A \) and \( B \) is shown in the
following figure:

The time in which the two materials
regain their original status is \( t_{A} \) and \( t_{B} \)
related as \( t_{B}=2 t_{B} . \) Then the materia
under elastic aftereffect (relatively) is
\( \mathbf{A} \cdot B \)
B. \( A \)
\( c \cdot \operatorname{Both} A \) and \( B \)
D. Neither \( A \) nor \( B \)


The quantity of electricity required to reduce 12.3 g of nitro benzene to aniline assuming 50\% current efficiency is:
\( A \cdot 115800 C \)
B. 57900 C
c. 231600 \( c \)
D. 28950 C


A solution of hydrogen chloride gas was named as:
A . blue vitriol
B. green vitriol
c. muriatic acid
D. none of the above


Fill in the blank:
A G.L.E. gets \( _{\text {一一一一一一一一 }} \) charged when its disc is touched with a positively charged glass rod.


The name of the compound is isobuty
alcohol.
If true enter 1 , else enter 0 .


The smallest natural number by which 36 must be multiplied to get a perfect cube is
\( A \cdot 6 \)
в. 216
\( c \cdot 45 \)
D.


The following compounds may exist as two or more stereoisomers. These may
be classified as enantiomer pairs or
meso compounds.
What are total number of
stereoisomers(A) of each of the given
compounds?
(b)
\( \mathrm{c}\left(\mathrm{CH}_{3} \mathrm{CHCl}_{4}\right. \)
\( (g) \)
\( (\mathbf{h}) \)


In a stationary wave,
A. Energy is carried away throughout the infinite medium
B. Energy is confined to a limited region of the medium.
C. Different particles in a loop have different amplitudes
D. Both (2) and (3)


Find the least positive value of \( k \) for
which the equation \( x^{2}+k x+4=0 \)
has real roots.


The conversion of primary aromatic amines into diazonium salts is known
as:
A. diazotisation
B. displacement
c. acylation
D. alkylation


What type of isomerism is exhibited by \( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C H} \boldsymbol{O} \) and \( \boldsymbol{C} \boldsymbol{H}_{3}-\underset{\boldsymbol{O}}{\boldsymbol{V}}- \)
\( \boldsymbol{C H}_{3} \)


For a given value of degree of dissociation,which of the following have correct Van't Hoff factor?
This question has multiple correct options
A. \( N a C l, i=2+\alpha \)
в. \( C a\left(N O_{3}\right)_{2}, i=1+2 \alpha \)
C . \( K_{4}\left[F e_{3}(C N)_{6}\right], i=1+4 \alpha \)
D. \( \left(N H_{3}\right)_{3} P O_{4}, i=3+\alpha \)


The vapour pressure of two pure liquids \( A \) and \( B, \) that form an ideal solution are
100 and 900 torr respectively at temperature T. This liquid solution of \( \mathbf{A} \) and B is composed of 1 mole of A and 1 mole of B. What will be the pressure,
when 1 mole of mixture has been
vapourized?
A. 800 torr
B. 500torr
c. 300 torr
D. None of these


Represent on number line \( \frac{2}{3} \)


If a vector \( 2 \hat{i}+3 \hat{j}+8 \hat{k} \) is perpendicular to the vector \( 4 \hat{i}-4 \hat{j}+\alpha \hat{k}, \) then value of
\( \boldsymbol{\alpha} \) is:
A . -1
в. \( \frac{1}{2} \)
\( c \cdot-\frac{1}{2} \)
D. 1


is malleable and ductile.
A . Metal
B. Compound
c. Non-metal
D. Solution


The condensed form of ethyl acetylene
is:
A \( \cdot H_{3} C-C \equiv C \)
в. \( H_{3} C-C H=C H_{2} \)
\( \mathbf{c} \cdot H_{3} C-C H_{2}-C \equiv C H \)
D. none of the above


The voltage of clouds is \( 4 \times 10^{6} \) volt
with respect to round. In a lightening strike lasting 100 m sec , a charge of 4 coulombs is delivered to the ground. The power of lightening strike is:
A. \( 160 M W \)
в. 80 М \( W \)
\( \mathrm{c} .20 \mathrm{MW} \)
D. \( 500 K W \)


In the given figure, \( \ln \Delta P Q R \quad X Y \| \)
\( Q R, P X: Q X=1: 3 Y R=4.5 \mathrm{cm} \) and \( Q R=9 \)
\( \mathrm{cm} . \) Find \( \mathrm{XY} \). Further if \( \operatorname{ar}(\Delta P X Y)=A \)
\( c m^{2}, \) find in terms of \( A \) the area of
\( \Delta P Q R \) and the area of trapezium
XYRQ.


When a catalyst increases the rate of a chemical reaction, the rate constant:
A. increases
B. decreases
c. remains constant
D. becomes infinite


Assertion
Boiling point of pentane is higher than 2,2-dimethylpropane.
Reason
There is steady increase in boiling point with increase in molecular mass.
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


For a satellite to be geostationary, which of the following are essential conditions?
This question has multiple correct options
A. It mu always be stationed above the equator.
B. It must rotate from west to east
c. It must be about \( 36,000 \mathrm{km} \) above the earth.
D. Its orbit must be circular, and not elliptical


The de Broglie wavelength of a particle with mass \( 1 \mathrm{gm} \) and velocity \( 100 \mathrm{m} / \mathrm{s} \) is:
A \( \cdot 6.63 \times 10^{-33} m \)
B. \( 6.63 \times 10^{-34} m \)
D. \( 6.635 \times 10^{-35} m \)


Position vector of a particle is given by \( \vec{r}=a \cos \omega t \hat{i}+a \sin \omega t \hat{j} . \) Which of the
following is/are true? This question has multiple correct options
A. velocity vector is parallel to position vector
B. velocity vector is perpendicular to position vector
c. acceleration vector is directed towards the origin
D. acceleration vector is directed away from the origin


A reaction continues even after the
attainment of equilibrium.
A. True
B. False


A scooter going to the east at 10
\( \mathrm{m} / \mathrm{s} \) turns right through an angle of \( 90^{\circ} \)
If the speed of the scooter remains unchanged in taking this turn, the change in the velocity of the scooter is:
A. 20 \( \mathrm{m} / \mathrm{s} \) in south-west direction
B. zero
c. \( 10.0 \mathrm{m} / \mathrm{s} \) in south direction
D. 14.14 m/s in south-western direction


A circle touches the sides of a
quadrilatieral ABCD at P, Q, R, S respectively. The angles subtended at the centre by a pair of opposite sides have theirs sum as:


Assertion
Red phosphorous on heating changes its colour to black.
Reason
Black phosphorus contain \( P_{4} \) units.
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


GM of the numbers \( 3,3^{2}, 3^{3}, \ldots . ., 3^{n} \) is.
\( A \cdot 3^{2 / n} \)
B. \( 3^{n / 2} \)
\( c \cdot 3^{(n+1) / 2} \)
D. \( 3^{(n-1) / 2} \)


polymerization of styrene and
acrylonitrile in the presence of peroxide
ss
4
\[
\left[\begin{array}{c}
\mathbf{c} \\
\mathbf{C H}-\mathbf{C H}_{2}-\mathbf{C H}_{2}-\mathbf{I} \mathbf{H} \\
\mathbf{C}_{\mathbf{6}} \mathbf{H}_{\mathbf{5}}
\end{array}\right]
\]
3
\[
\left[\begin{array}{l}
\mathbf{C}_{6} \mathbf{H}_{5} \mathbf{C} \mathbf{N} \\
\mathbf{C}-\mathbf{C} \mathbf{H}-\mathbf{C} \mathbf{H}_{2} \\
\mathbf{C} \mathbf{H}_{3}
\end{array}\right]
\]
\( c \)
\[
\left[\begin{array}{cc}
\mathbf{C H}_{2}-\mathbf{C H}-\mathbf{C H}_{2}-\mathbf{C H} & \\
\mathbf{C}_{\mathbf{6}} \mathbf{H}_{\mathbf{5}} & \mathbf{C} \mathbf{N}
\end{array}\right]
\]
)
\[
\left[\begin{array}{c}
\mathbf{C}_{6} \mathbf{H}_{5} \mathbf{C N} \\
\mathbf{C H}_{2}-\mathbf{C H}-\mathbf{C} \mathbf{H}-\mathbf{C H}_{2}
\end{array}\right]
\]


If Velocity of flow is \( 4 \mathrm{m} / \mathrm{s} \), then velocity
head is
A. \( 0.2 m \)
в. \( 0.4 m \)
\( \mathrm{c} .0 .6 \mathrm{m} \)
D. \( 0.8 m \)


Friction reduces efficiency of machines
due to:
A. production of heat
B. wearing out of moving parts
C. increase in energy consumption
D. all of the above


Which blood vessels carry blood from different parts of your body to the heart?
A. Capillaries
B. Arteries
c. veins
D. All of the above


If \( f(x)=(x)^{\frac{1}{x-1}} \) for \( x \neq 1 \) and \( f \) is
continuous at \( \mathbf{x}=1 \) then \( \mathbf{f}(\mathbf{1})= \)
\( A \)
B . e-
\( c \cdot e^{-2} \)
D. e \( ^{2} \)


Look at the following figure of
chloroplast and choose the correct
combination of statements.
. Light reaction of photosynthesis
occurs in \( Y \)
ii. Dark reaction of photosynthesis
occurs in \( x \)
iii. \( X \) is known as thalakoid.
¡v. Y is known as granum.
v. \( Z \) is known as granum.
\( A \). i, ii, and iv
B. ii, iii, and iv
c. iii, iv and \( v \)
D. ii, iii, iv, and v


A car is accelerated on a leveled road
and attains a velocity 4 times of its initial velocity. In this process the potential energy of the car
A. does not change
B. becomes twice to that of initial
c. becomes 4 times that of initial
D. becomes 16 times that of initial


Which of the following is a branch of chemistry?
A. Analytical
B. organic
c. Biochemistry
D. All of the above


The secondary structure of a protein
refers to:
A \( . \alpha \) -helical back bone
B. hydrophobic interations
C. Sequence of \( \alpha \) -amino acids
D. fixed configuration of the polypeptide backbone


What specific name can be given to the following sequence of steps: \( H g+h v \rightarrow \)
\( H g^{*} \)
\( H g^{*}+H_{2} \rightarrow H_{2}^{*}+H g \)
A. Fluorescence
B. Phosphorescence
c. Photosensitization
D. Chemilumionescence


Division of cytoplasm is called
A. Karyokinesis
B. crossing over
c. cytokinesis
D. Kinesiss


The point \( (0,0),(16,0),(12,12), \) and (4,12) are the corners of a
A. Rhombus
B. Rectangle
c. Parallelogram
D. Trapezium


toppr
Q Type your question
magnitude of linear magnification \( (\boldsymbol{m}) \)
versus distance of the object from the
mirror \( (x) \) is correctly given by
(Graphs are drawn schematically and
are not to scale)
\( A \)
B.
\( c \)
D.


A catalyst:
This question has multiple correct options
A. Increases the average kinetic energy of the reacting molecules.
B. Decreases the activation energy
C. Alters the reaction mechanism
D. Increases the frequency of the collisions of the reacting species


A capacitor has a capacitance of \( \boldsymbol{C} \)
when a potential difference of \( V \) is
across it.
The potential difference is increased to \( 2 V, \) what is the new capacitance?
A. \( C \)
B. \( 2 C \)
\( c .3 C \)
D. \( 5 C \)


An aromatic compound \( (\boldsymbol{X})\left(\boldsymbol{C}_{\mathbf{8}} \boldsymbol{H}_{\mathbf{8}} \boldsymbol{O}\right) \)
gives positive 2,4 -DNP test. It gives a yellow precipitate of compound \( (Y) \) on
reaction with iodine and sodium
hydroxide solution. \( (X) \) does not give
Tollen's test on oxidation under drastic
conditions. It gives a carboxylic acid
\( (Z)\left(C_{7} H_{6} O_{2}\right) \cdot(Z) \) is also formed with
\( (Y) \) during the reaction. \( (X),(Y) \) and
\( (Z) \) respectively are:
\( \mathbf{A} \cdot C_{6} H_{5} C O C H_{3}, C H I_{3}, C_{6} H_{5} C O O H \)
в. \( C H_{3} C O C H_{3}, C H I_{3}, C H_{3} C O O H \)
\( \mathbf{c} \cdot C_{6} H_{5} C O C H_{3}, C H I_{3}, C H_{3} C O O H \)
D. \( C H_{3} C H O, C H I_{3}, C_{6} H_{5} C O O H \)


A ball of mass \( 50 \mathrm{g} \) is dropped from a height of 20 m.A boy on the ground hits the ball vertically upwards with a bat with an average force of \( 200 \mathrm{N}, \) so that it attains a vertical height of 45 m.The time foe which the ball remains in
contact with the bat is
A \( \cdot 1 / 20^{\operatorname{th}} \) of a second
B . \( 1 / 40^{\text {th }} \) of a second
c. \( 1 / 80^{\text {th }} \) of a second
D. \( 1 / 20^{\text {th }} \) of a second


A \( 10.0 \mu F \) parallel-plate capacitor with
circular plates is connected to a \( 12.0 \mathrm{V} \)
battery. What is the charge on each plate \( (\operatorname{in} \mu C) ? \)


The base of a parallelogram is twice its
height.lf the area of a parllelogram is 72 sq cm ,find the height.


Using trigonometric table, the value of
\( \tan 60^{\circ}+1 \) is approximately
A . 2.73
в. 4.56
c. 1.678
D. None of these


A count rate meter shows a count of 240
per minute from a given radioactive
source. One hour later the meter shows
a count rate of 30 per minute. The half life of the source is:
A. 80 min
B. 120 min
\( c .20 \) min
D. 30 min


At time \( t=0, N_{1} \) nuclei of decay
constant \( \lambda_{1} \) and \( N_{2} \) nuclei of decay
constant \( \lambda_{2} \) are mixed. The decay rate of
mixture is
\( \mathbf{A} \cdot N_{1} N_{2} e^{-\left(\lambda_{1}+\lambda_{2}\right) t} \)
B. \( -\left(\frac{N_{1}}{N_{2}}\right) e^{-\left(\lambda_{1}+\lambda_{2}\right) t} \)
C. \( -\left(N_{1} \lambda_{1} e^{-\lambda_{1} t}+N_{1} \lambda_{2} e^{-\lambda_{2} t}\right) \)
D. \( -N_{1} \lambda_{1} N_{2} \lambda_{2} e^{\left(-\lambda_{1}+\lambda_{2}\right) t} \)


\( \int \sqrt{\frac{\cos x-\cos ^{3} x}{1-\cos ^{3} x}} d x \) is equal to
A \( \cdot \frac{2}{3} \sin ^{-1}\left(\cos ^{3 / 2} x\right)+C \)
B \( \cdot \frac{3}{2} \sin ^{-1}\left(\cos ^{3 / 2} x\right)+C \)
C \( \cdot \frac{2}{3} \cos ^{-1}\left(\cos ^{3 / 2} x\right)+C \)
D. none of these


In series LCR circuit, the phase difference between applied voltage and current is
A. Positive when \( X_{L}>X_{C} \)
B. Positive when \( X_{C}>X_{L} \)
\( c \cdot 90^{\circ} \)
D. 0


Simplify, using trigonometric tables
\( \sin 30^{\circ} 30^{\prime}+\cos 40^{\circ} 20^{\prime} \)


The displacement of a particle moving in a straight line is given by \( \boldsymbol{x}=\mathbf{1 6 t} \)
\( 2 t^{2} \) (where, \( x \) is in meters and \( t \) is in
second). The distance traveled by the particle in 8 seconds [starting from \( t= \)
O] is
A \( .24 m \)
в. \( 40 m \)
\( c .64 m \)
D. \( 80 m \)


Value of \( n \) that satisfies the equation \( \frac{7}{8}(n-6)=\frac{21}{2} \) is
A . 28
B. 18
c. 14
D. 22


State whether the statement is True or
False.
\( (\boldsymbol{m}+\boldsymbol{n})^{-1}\left(\boldsymbol{m}^{-1}+\boldsymbol{n}^{-1}\right)=(\boldsymbol{m} \boldsymbol{n})^{-1} \)
A. True
B. False


What is a transistor? Mention any two
uses of transistor.


Nitrite ion \( \left(N O_{2}^{-}\right) \) is said to interfere
in the ring-test of nitrate ion \( \left(N O_{3}^{-}\right) \)
Urea can decompose \( N O_{2}^{-} \)
If true enter 1 , else 0


In an AC circuit, electrical energy is consumed in
A .
B.
\( c \cdot R \)
D. Land


What are the distance and the
displacement of the race car drivers in the \( 500 \mathrm{m} \) race in a circular path?
A . 500,0
B. 0,0
c. 0,500
D. None of these


\( \boldsymbol{a}_{\boldsymbol{n}}=\frac{\boldsymbol{n}(\boldsymbol{n}-\boldsymbol{2})}{\boldsymbol{n}+\boldsymbol{3}} ; \boldsymbol{a}_{20} \)


Find the average velocity of a projectile
between the instants it crosses half the
maximum height. It is projected with a
speed \( u \) at an angle \( \theta \) with the horizontal.


The \( x \% \) dissociation of \( H_{2} S \) if 1 mole of
\( H_{2} S \) is introduced into a 1.10 litre vessel
at \( 100 K ? K_{c} \) for the reaction:
\( 2 H_{2} S(g) \rightleftharpoons 2 H_{2}(g)+S_{2}(g) \) is \( 10^{-6} \)
Then value of \( 10 x \) is:


Explain hydrogen exist on earth in atomic form or molecular form?


Which types of clothes are more suitable for the winter season?
A. cotton clothes
B. Sweater
c. Raincoats
D. All of the above


In the figure, the displacement time graph of a body is shown at different time-intervals. Calculate the velocity of
the body as it moves for
\( (i) 0 \) to \( 5 s \)
\( (i i) 5 s t o 7 s \) and
\( (i i i i) 7 s t o 9 s \)
A \( \cdot(i) 1.2 m s^{-1}(i i) 0 m s^{-1}(i i i) 1 m s^{-1} \)
В \( \cdot(i) 0.6 m s^{-1}(i i) 0 m s^{-1}(i i i) 2 m s^{-1} \)
C \( \cdot(i) 0 m s^{-1}(i i) 0.6 m s^{-1}(i i i) 4 m s^{-1} \)
D. \( (i) 0.3 m s^{-1}(i i) 1 m s^{-1}(i i i) 1.2 m s^{-1} \)


An \( \alpha \) -particle, a deuteron and a proton
are moving with same momentum in a uniform magnetic field. The ratio of their speeds will be
A . 1: 2: 4
B. 4:2:
\( c \cdot 1: 1: 1 \)
D. 2:2:4


\( \boldsymbol{K} \boldsymbol{O} \boldsymbol{H}(\boldsymbol{a} \boldsymbol{q}) \rightleftharpoons \)
A \( \cdot K^{-}+O H^{+} \)
B. \( K^{+}+O H^{+} \)
\( \mathbf{c} \cdot K^{-}+O H^{-} \)
\( \mathbf{D} \cdot K^{+}+O H^{-} \)


Calculate the ratio of radii of first,
second and third orbits of a hydrogen
atom


The wavelength of first line of the Lymen
series for hydrogen is \( 1216 A^{\circ} . \) The wavelength for the first line of this
series for a 10 time ionised sodium
atom \( (z=11) \) will be :
A \( \cdot 1000 A^{\circ} \)
B . \( 100 A^{\circ} \)
c. \( 10 A^{\circ} \)
D. \( 1 A^{\circ} \)


toppr
Q Type your ques
to the processes that occur in living organisms. This primarily because the functioning of enzymes-catalysts for these processes - is sharply pH dependent. The normal pH value of blood plasma is \( 7.4 . \) Severe illness or death
can result from sustained variations of
a few tenths of pH unit.
Among the factors that lead to a condition of acidosis, in which there is a
decrease in the pH of blood are heart failure, kidney failure diabetes mellitus
persistent diarrhoea or a long term high protein diet.A temporary condition of acidosis may result from prolonged, intensive exercise. Alkalosis, which
causes increase in pH of blood may occur as a result of severe vomiting over breathing or exposure to high altitudes.

Several factors are involved in the
control of the pH of blood. A particularly important one is the ratio of dissolved \( H C O_{3}^{-} \) to \( H_{2} C O_{3} . C O_{2}(g) \) is
moderately soluble in water and in aqueous solution reacts only to a
limited extent to produce \( \boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{O}_{3} \)
\( \boldsymbol{C O}_{2}+\boldsymbol{H}_{2} \boldsymbol{O} \rightleftharpoons \boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{O}_{3}(\boldsymbol{a} \boldsymbol{q}) \)
\( \boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{O}_{3}+\boldsymbol{H}_{2} \boldsymbol{O} \rightleftharpoons \boldsymbol{H} \boldsymbol{C} \boldsymbol{O}_{3}^{-}+\boldsymbol{H}_{3} \boldsymbol{O}^{+} \)
\( \boldsymbol{p} \boldsymbol{K}_{\boldsymbol{a}_{1}}=\mathbf{6 . 1 1} \)
\( \boldsymbol{H} \boldsymbol{C O}_{3}^{-}+\boldsymbol{H}_{2} \boldsymbol{O} \rightleftharpoons \boldsymbol{C} \boldsymbol{O}_{3}^{2-}+\boldsymbol{H}_{3} \boldsymbol{O}^{+} \)
\( \boldsymbol{p} \boldsymbol{K}_{\boldsymbol{a}_{2}}=\mathbf{1 0 . 2 5} \)
In the \( H_{2} C O_{3}, H C O_{3}^{-} \) buffer system, we deal only with the first ionization
\( \operatorname{step}\left(\boldsymbol{K}_{a_{1}}\right): \boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{O}_{3} \) is a weak acid and
\( H C O_{3}^{-} \) is the conjugate base (salt)
\( C O_{2} \) enters the blood from tissues as
the by -product of a metabolic reaction.
In the lungs, \( C O_{2}(g) \) is exchanged for \( O_{2}(g), \) which is transported throughout the body by the blood.Important diagnostic analysis in the blood is :
A \( \cdot\left[H_{2} P O_{4}^{-}\right] /\left[H P O_{4}^{-}\right. \)
в \( \cdot\left[H C O_{3}^{-}\right] /\left[C O_{2}\right] \)
c. \( \left[C O_{3}^{2-}\right] /\left[H C O_{3}^{2-}\right] \)
D \cdot \( \left[P O_{4}^{3-}\right] /\left[H P O_{4}^{2-}\right] \)


Which of the following is not a member of the solar system?
A . Artificial Satellite
B. Shooting star
c. sun
D. Asteroids


Goods were bought for \( R s .600 \) and sold
the same for \( R s .688 .50 \) at a credit of 9
months and thus gaining \( 2 \% \). The rate of interest per annum is:
A \( \cdot 16 \frac{2}{3} \% \)
в. \( 14 \frac{1}{2} \% \)
c. \( _{13} \frac{1}{3} \% \)
D. 15\%


Explain with the help of a labelled diagram the distribution of a magnetic field due to a current through a circular loop. Why is it that if a current carrying loop has n turns the field produced
at any point is \( n \) times as large as that produced by a single turn?


If the maximum permissible orbits of elements in nature are limited to \( n=4 \)
what are the number of possible elements?


Histogen theory was proposed by
A. Nageli
B. Schmidt
C. Hanstein
D. wolf


The pole strength of \( 12 \mathrm{cm} \) long bar magnet is 20 A m having Magnetic moment \( 20 \times 0.12 A m^{2} \). The magnetic
induction at a point \( 10 \mathrm{cm} \) away from the centre of the magnet on its axial line is \( \left[\frac{\mu_{0}}{4 \pi}=10^{-7} H m^{-1}\right] \)
A \( \cdot 1.17 \times 10^{-3} \mathrm{T} \)
В . \( 2.20 \times 10^{-3} \mathrm{T} \)
c. \( 1.17 \times 10^{-2} \mathrm{T} \)
D. 2.20 \( \times 10^{-2} \) न


A parallel beam of light falling on the eye gets focused on the retina because of refraction at
A. the cornea
B. the crystalline lens
c. the vitreous humor
D. various surfaces in the eye


Deciduous forests have
A. Variety of grasses
B. Broad-leaved trees
C. Narrow-leaved trees
D. Variety of crocodiles


Integrate: \( \int_{0}^{\frac{\pi}{4}} \log (1+\tan x) d x \)


Let L be the length and d be the
diameter of cross-section of a wire.
Wires of the same material with
different L and d are subjected to the same tension along the length of the wire. In which of the following cases, the extension of wire will be the maximum?
A. \( L=200 \mathrm{cm}, d=0.5 \mathrm{mm} \)
в. \( L=300 \mathrm{cm}, d=1.0 \mathrm{mm} \)
c. \( L=50 \mathrm{cm}, d=0.05 \mathrm{mm} \)
D. \( L=100 \mathrm{cm}, d=0.2 \mathrm{mm} \)


\( H_{2} S \) is acidic in nature while \( H_{2} O \) is
neutral in nature. Give reason.
A. Oxygen is more electronegative than sulphur
B. \( H-S \) bond is weaker than \( O-H \) bond
c. Bond angle in \( H_{2} \) S is less than that in \( H_{2} \) O
D. \( H-S \) bond is stronger than \( O-H \) bond.


In the figure, a block of weight \( 60 N \) is
placed on a rough surface. The
coefficient of friction between the block
and the surface is \( 0.5 . \) What should be
the weight \( W \) such that the block does
not slip on the surface?


The given diagrammatic representation of reflex action shows knee jerk reflex.
Identify the parts labelled as \( A \) to \( E \) and
select the correct option.
A. A - Dorsal root ganglion, B - White matter, C - Grey matter, D - Afferent pathway, E - Efferent pathway
B. A - Dorsal root ganglion, B - White matter, C - Grey matter, D - Efferent pathway, E - Afferent pathway
C. \( A \) - Ventral root ganglion, \( B \) - Grey matter, \( C \) - White matter, D - Efferent pathway, E - Afferent pathway
D. A - Ventral root ganglion, B - White matter, C - Grey matter, D - Efferent pathway, E - Afferent pathway


How many moles of electrons wil
together contribute to the charge of 289500 coulomb?


SONAR is based on the principle of
A. echo
B. resonance
c. reverberation
D. anyone of the above


Nuclear fusion is a
A. thermonuclear reaction
B. thermochemical reaction
c. electrochemical reaction
D. none of these


Assertion
Hydroxylamine \( \left(N H_{2} O H\right) \) contains \( N \)
and hence gives Prussian blue colour in
Lassaigne's test.
Reason
Hydroxylamine does not contain \( C, \) so
with Na metal, \( C N^{\ominus} \) ion is not formed
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


Formula of rate of percolation is
A \( \cdot \) Percolation rate \( (\mathrm{mL} / \mathrm{min})=\frac{\text {amount of water}(\mathrm{mL})}{\text {percolation time}(\min )} \)
B. \( \quad \) Percolation rate \( (\mathrm{mL} / \mathrm{min})=\frac{\text {percolation time}(\min )}{\text {amount of water}(\mathrm{mL})} \)
C. Both A and B
D. None of these


A ray of light traveling in water is
incident on its surface open to the air.
The angle of incidence is \( \theta, \) which is
less than the critical angle. Then there
will be
A. Only a reflected ray and no refracted ray
B. Only a refracted ray and no reflected ray
C. A reflected ray and a refracted ray and the angle between them would be less than \( 180^{\circ}-2 \theta \)
D. A reflected ray and a refracted ray and the angle between them would be greater than \( 180^{\circ}-2 \theta \)


Two waves are propagating with same amplitude and nearly same frequency, they result in
A. beats
B. stationary wave
c. resonance
D. wave packet


Fill in the blanks with suitable words:
Newtons first law of motion is also
called law of


The ends \( A \) and \( B \) of a rod of length \( \sqrt{5} \)
are sliding along the curve \( y=2 x^{2} \). Let
\( x_{A} \) and \( x_{B} \) be the \( x \) -coordinate of the
ends. At the moment when \( A \) is at (0,0) and \( \mathrm{B} \) is at (1,2) the derivative \( \frac{d x_{B}}{d x_{A}} \) has the value equal to
\( A \cdot 1 / 3 \)
B. 1/5
\( c \cdot 1 / 8 \)
D. \( 1 / 9 \)


Let for \( \boldsymbol{a} \neq \boldsymbol{a}_{1} \neq \mathbf{0}, \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{a} \boldsymbol{x}^{2}+\boldsymbol{b} \boldsymbol{x}+ \)
\( c, g(x)=a_{1} x^{2}+b_{1} x+c_{1} \) and \( p(x)= \)
\( f(x)-g(x) \). If \( p(x)=0 \) only for \( x=-1 \)
and \( p(-2)=2, \) then the value of \( p(2) \) is
A . 3
B. 9
\( c \cdot 6 \)
D. 18


The skeletal structure of \( C H_{3} C O O H \)
as shown above is correct but some of
the bonds are shown incorrectly. Write the correct Lewis structure for acetic
acid.
\[
\mathrm{H}=\frac{\mathrm{H}}{\mathrm{C}}-\mathrm{C}-\mathrm{O}-\mathrm{H}
\]


A resistor and an inductor are
connected to an ac supply of \( 120 \mathrm{V} \) and \( \mathbf{5 0} \boldsymbol{H} z . \) The current in the circuit is \( \mathbf{3} \boldsymbol{A} \)
If the power consumed in the circuit is \( 108 W, \) then the resistance in the
circuit is
A. \( 12 \Omega \)
в. \( 40 \Omega \)
c. \( \sqrt{(52 \times 28)} \),
D. \( 360 \Omega \)


The elements \( \mathrm{Na}, \mathrm{Mg}, \mathrm{Al}, \mathrm{Si}, \mathrm{P}, \mathrm{S}, \mathrm{Cl} \) and
Ar are arranged in the periodic table in the increasing order of their atomic numbers.

Which element shows +6 oxidation
state?


In an AC generator, a coil with \( N \) turns,
all of the same area \( A \) and total
resistance \( \boldsymbol{R}, \) rotates with frequency in
a magnetic field \( B \). The maximum
value of emf generated in the coil is:
\( \mathbf{A} . N . A . B \)
в. \( N . A . B . R \)
\( ^{\mathbf{C}} \cdot \frac{1}{10} N \cdot A \cdot B \)
D. \( \frac{1}{10} N . A . B . R \)


An electric heater and a fan marked
\( 1000 \mathrm{W}, 220 \mathrm{V} \) and \( 100 \mathrm{W}, 220 \mathrm{V} \)
respectively. The resistance of fan is
A. equal to that of heater.
B. greater than that heater.
c. less than that of heater
D. zero


The set of values of parameter \( a \) so that the equation \( \left(\sin ^{-1} x\right)^{3}+\left(\cos ^{-1} x\right)^{3}= \)
\( a \pi^{3} \) has a solution.
\( \mathbf{A} \cdot\left[\frac{-1}{32}, \frac{7}{8}\right] \)
в. \( \left[\frac{1}{32},, \frac{9}{8}\right] \)
\( ^{\mathbf{c}} \cdot\left[0, \frac{7}{8}\right] \)
D. \( \left[\frac{1}{32}, \frac{7}{8}\right] \)


In
\( Z, \) the set of all integers, the inverse
of -7 w.r.t. defined by \( a \times b=a+b+7 \)
for all \( a, b, \in Z \) is :
A . -14
B. 7
c. 14
D. -


Adsorption of a gas follows the equation
\( \frac{x}{m}=k P^{1 / 2} \)
Then the effect of pressure \( \& \) temperature on physical adsorption of gas on solid is:
A. increase with pressure increase, decrease with temperature increase
B. increase with both temperature \& pressure increase
c. decrease with pressure increase, increase with temperature increase
D. decrease with both temperature \& pressure increase


Form a differential equation representing the given family of curves by eliminating arbitrary constant a and b.
\( y=e^{x}(a \cos x+b \sin x) \)


Sakshi can do a piece of work in 20 days. Tanya is \( 25 \% \) more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is:
A . 15
B. 16
c. 18
D. 25


Expand the polynomial: \( \left(3 x^{2}-1\right)\left(x^{2}+\right. \)
\( \boldsymbol{x}+\mathbf{1}) \)
A \( \cdot 3 x^{4}+3 x^{3}+3 x^{2}+x^{2}-x-1 \)
B. \( 3 x^{4}+3 x^{3}+x^{2}-x^{2}-x-1 \)
c. \( 3 x^{4}+3 x^{3}+2 x^{2}-x-1 \)
D. \( 3 x^{4}-3 x^{3}+3 x^{2}-x^{2}-x-1 \)


An exterior angle of a triangle is 100 and its interior opposite angles are equal to each other. Find the measure of each
angle of the triangle.


what is tangent of a circle and
definition?


If \( f(x) \) is continuous such that
\( |\boldsymbol{f}(\boldsymbol{x})| \leq \mathbf{1}, \forall \boldsymbol{x} \in \boldsymbol{R} \) and \( \boldsymbol{g}(\boldsymbol{x})= \)
\( \frac{e^{f(x)}-e^{|f(x)|}}{e^{f(x)}+e^{|f(x)|}} \) then range of \( g(x) \) is
A \( \cdot[0,1] \)
B. \( \left[0, \frac{e^{2}+1}{e^{2}-1}\right] \)
\( ^{\mathbf{C}} \cdot\left[0, \frac{e^{2}-1}{e^{2}+1}\right] \)
D. \( \left[\frac{1-e^{2}}{1+e^{2}}, 0\right] \)


Submucosa is thickest in
A. Stomach
B. Oesophagus
c. Pancreas
D. Rectum


Solve \( : 3 x+11=6 x-13 \)


Drones in a colony of honey bees originate by
A. Thelytoky
B. Arrhenotoky
c. Amphitoky
D. Deuterotoky


Match the following:
PART-A

PART-B
a)
e) All types of waves Polarisation
\( b \)
interference
f) longitudinal waves
\( c \)
diffraction
g) transverse waves
d) reflection
h) only with transverse waves
i) stationary waves produced in stretched strings
\( \mathbf{A} \cdot \mathbf{a} \rightarrow g ; \mathbf{b} \rightarrow \mathbf{e}, \mathbf{f}, \mathbf{g}, \mathbf{i} ; \mathbf{c} \rightarrow \mathbf{e}, \mathbf{f}, \mathbf{g} ; \mathbf{d} \rightarrow \mathbf{e}, \mathbf{f}, \mathbf{g} \)
\( \mathbf{B} \cdot \mathbf{a} \rightarrow \mathbf{h}, \mathbf{g} ; \mathbf{b} \rightarrow \mathbf{f}, \mathbf{g} ; \mathbf{c} \rightarrow \mathbf{g} ; \mathbf{d} \rightarrow \mathbf{h} \)
\( \mathbf{C} \cdot \mathbf{a} \rightarrow \mathbf{e}, \mathbf{f}, \mathbf{g} ; \mathbf{b} \rightarrow \mathbf{g} ; \mathbf{c} \rightarrow \mathbf{e}, \mathbf{f}, \mathbf{g} ; \mathbf{d} \rightarrow \mathbf{g} \)
\( \mathbf{D} \cdot \mathbf{a} \rightarrow \mathbf{e} ; \mathbf{b} \rightarrow \mathbf{h}, \mathbf{i} ; \mathbf{c} \rightarrow \mathbf{g}, \mathbf{h} ; \mathbf{d} \rightarrow \mathbf{e} \)


In the reaction of \( H I \) with \( H_{2} S O_{4} \) the
oxidation state of sulphur is changed to
-2. Identify the correct balanced
equation
A \( \cdot H_{2} S O_{4}+2 H I \rightarrow S O_{2}+2 H_{2} O+I_{2} \)
в. \( H_{2} S O_{4}+6 H I \rightarrow S+4 H_{2} O+3 I_{2} \)
c. \( H_{2} S O_{4}+8 H I \rightarrow H_{2} S+4 H_{2} O+4 I_{2} \)
D. All of the above


For a longitudinal sound wave, \( (B \) is the engineering modulus of the medium
and \( \rho \text { is the density }) \)
A \( \cdot \frac{d^{2} y}{d x^{2}}=\frac{B}{\rho} \frac{d^{2} y}{d t^{2}} \)
в. \( \frac{d y}{d x}=\frac{B}{\rho} \frac{d y}{d t} \)
c. \( \frac{d^{2} y}{d t^{2}}=\frac{B}{\rho} \frac{d^{2} y}{d x^{2}} \)
D. \( \frac{d y}{d t}=\frac{B}{\rho} \frac{d y}{d x} \)


(i) Two sets \( A \) and \( B \), of three bulbs
each, are glowing in two separate rooms.When one of the bulbs in set A is
fused, the other two bulbs also cease to glow. But in set \( \mathrm{B} \), when one bulb fuses, the other two bulbs continue to glow.
explain why this phenomenon occurs.
(ii) Why do we prefer arrangements of Set B for house circuiting?


The pH of an aqueous solution of
\( B a(O H)_{2} \) is \( 10 . \) If the \( K_{s p} \) of \( B a(O H)_{2} \)
is \( 1 \times 10^{-9} \), then the concentration of
\( B a^{2+} \) ions in the solution in mol \( L^{-1} \) is:
A. \( 1 \times 10^{-2} \)
B. \( 1 \times 10^{-4} \)
C \( .1 \times 10^{-1} \)
D. \( 1 \times 10^{-5} \)


The temperature of liquid hydrogen is 20 K. What is this temperature on the Fahrenheit scale?
A \( \cdot 495.4^{\circ} \mathrm{F} \)
B . \( -423.4^{\circ} F \)
c \( .-108.56^{\circ} \mathrm{F} \)
D. \( -487.4^{\circ} F \)


Identify the triplet codons which code for amino acids serine and proline.
(a) UCC
(d) \( \mathrm{AAG} \)
(b) \( \mathrm{CCA}(\mathrm{c}) \mathrm{GGG} \)
The correct answer is
A. a and c
B. b and d
\( c \cdot c \) and \( d \)
D. a and


Inflorescence of sunflower is
A. Umbel
B. Cyathium
c. Hypanthodium
D. Capitulum


The algebraic sum of deviations of ten observations about 15 is \( 70 . \) The mean is
A . 22
B. 25
c. 20
D. none of these


With the increase in quantum number the energy difference between consecutive energy levels
A. remains constant
B. decreases.
c. increases
D. sometimes increases sometimes decreases


When viewed in white light, soap bubble show colors because of
A . Interference
B. Scattering
c. Diffraction
D. Dispersion


A sound wave travels at a speed of \( 340 m / s . \) If its wavelength is \( 2 c m, \) what
is the frequency of the wave? Will it be in the audible range?


Fill in the blank.
\( \left[N i(C N)_{4}\right]^{2-} \) is \( _{-}-_{-}- \) in shape
whereas the shape of \( \left[N i(C l)_{4}\right]^{2-} \) is


Two charges are at a distance \( d \) apart. If
\( \boldsymbol{d} \)
a copper plate of thickness \( \frac{u}{2} \) is kept
between them, the effective force will be
A. \( F / 2 \)
B. zero
\( c \cdot 2 F \)
D. \( \sqrt{2} F \)


The distance from the origin to the centroid of the tetrahedron formed by
the points (0,0,0),(3,0,0),(0,4,0),(0,0,5) is
A. \( \frac{\sqrt{3+4+5}}{4} \)
B. \( \frac{\sqrt{3+4+5}}{3} \)
c. \( \frac{\sqrt{3^{2}+4^{2}+5^{2}}}{16} \)
D. \( \frac{\sqrt{3^{2}+4^{2}+5^{2}}}{4} \)


In one second, a particle goes from
point \( A \) to point \( B \) moving in a semicircle. Find the magnitude of the
average velocity.
\( A \cdot 1 \mathrm{m} / \mathrm{s} \)
B. 2 m/s
c. \( 0.5 \mathrm{m} / \mathrm{s} \)
D. None of the above


The effective capacitance between the
point \( \mathrm{P} \)
and \( Q \) in the given figure is
\( \mathbf{A} \cdot 4 \mu F \)
B. \( 16 \mu F \)
c. \( 26 \mu F \)
D. \( 10 \mu F \)


During photosynthesis
\( A \cdot O_{2} \) evolved comes from \( C O_{2} \)
B. ATP is formed
C. ATP is not formed
D. Water is required as medium but it does not take part in photosynthesis


\( f(x)=\left\{\begin{aligned} 4 x, & x<0 \\ 1, & x=0 \text { then } \lim _{x \rightarrow 0} f(x) \\ 3 x^{2}, & x>0 \end{aligned}\right. \)
equals
A .
B.
\( c \cdot 3 \)
D. does not exist


Inert gases are mixed in iodine vapours. Then there are \( _{-1-}-\ldots- \) between
them.
A. H-bonding
B. Vander Waal's forces
c. Electrostatic forces
D. Metallic bonds


Assertion
Electromotive force is a force which
help the electrons to flow and produce
current.
Reason
Electromotive force is independent of
the voltage across the cell
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


When HF reacts with glass, the compound formed is:
A \( . F_{2} \)
в. NaF
c. \( N a_{3} A l F_{3} \)
D. \( N a_{2} \) SiF \( _{6} \).


Identify the salts which on heating produce mixture of gases. This question has multiple correct options
A. \( N a N O_{3} \)
B. \( P b\left(N O_{3}\right)_{2} \)
c. \( C u\left(N O_{3}\right)_{2} \)
D. \( K N O_{3} \)


The inductive reactance of a coil of
\( 0.2 H \) inductance at a frequency of
\( \mathbf{6 0} \boldsymbol{H} \boldsymbol{z} \) is:
A . \( 7.54 \Omega \)
в. \( 0.754 \Omega \)
c. \( 75.4 \Omega \)
D. \( 7.54 \times 10^{-3} \Omega \)


A ray of light is incident on a plane
mirror and the angle of reflection is \( 50^{\circ} \)
Calculate the angle between the incident and the reflected ray.
A \( .50^{\circ} \)
B . \( 25^{\circ} \)
\( c \cdot 90^{\circ} \)
D. \( 100^{\circ} \)


Write the IUPAC name of \( \boldsymbol{C H}_{3}- \)
\( \left(\boldsymbol{C H}_{2}\right)_{5}-\boldsymbol{C H O} \)


Find the \( 19^{t h} \) term of the following A.P.
\( \mathbf{7}, \mathbf{1 3}, \mathbf{1 9}, \mathbf{2 5}, \dots \)


The moon is observed from two
diametrically opposite points \( A \) and \( B \) on earth. The angle \( \theta \) subtended at the
moon by the two directions of
observation is \( 1^{0} 54^{\prime} . \) Given the diameter
of the earth to be about \( 1.276 \times 10^{7} m \)
compute the distance of the moon from
the earth.


If \( A \) is a real skew-symmetric matrix
such that \( A^{2}+I=O, \) then
\( \mathbf{A} \cdot A \) is a square matrix of even order with \( |A|=\pm 1 \)
B. \( A \) is a square matrix of odd order with \( |A|=\pm 1 \)
C \( \cdot A \) can be a square matrix of any order with \( |A|=\pm 1 \)
D. \( A \) is a skew-symmetric matrix of even order with
\( |A|=1 \)


f \( \triangle \boldsymbol{D} \boldsymbol{E} \boldsymbol{F} \cong \triangle \boldsymbol{R} \boldsymbol{P} Q, \) then \( \angle \boldsymbol{D}=\angle \boldsymbol{Q} . \) If
true enter 1 else 0


What will happen when diethyl ether
treated with hot and conc. \( H \) I?
A. Ethyl alcoho
B. Ethyl iodide
c. Methyl iodide
D. Methanol


The center of gravity of an object
A. can never exist at a point where there is no mass.
B. can exist at a point where there is no mass.
C. may exist or may not exist.
D. none of the above


Example for an improper fraction is
A \( \cdot \frac{25}{26} \)
в. \( \frac{12}{13} \)
c. \( \frac{15}{14} \)
D. \( \frac{19}{20} \)


What does a Lewis dot diagram allow
you to show?
This question has multiple correct options
A. The valence electrons in an atom
B. All of the electrons in an atom
C. The valence protons in an atom
D. The neutrons, protons and electrons in an atom
E. How an atom bonds with other atoms


Transition elements form complexes
readily because :
A. Small size of cation
B. Large ionic Charge
c. vacant d orbitals
D. All the above


The elements with atomic numbers
2,10,18,36,54 and 86 are all
A. Light metals
B. Halogens
c. Rare earths
D. Noble gases


Which one of the following undergoes decay when exposed to air?
A. Sap wood
B. Hard wood
c. Heart wood
D. Light wood


Metal hydride on treatment with water gives
A. \( H_{2} O_{2} \)
в. \( H_{2} \) о
c. acid
D. hydrogen


A sessile plant is a plant
A. Which has modified leaves
B. Which has petioles
C. Which does not possess petioles
D. Which cannot synthesise its own food


Write definitions of plane of vibration and plane of polarization. Explain the working process to obtain plane polarized light by Nicole Prism. Draw necessary diagram.


Find a unit vector in the direction of \( \overrightarrow{A B} \)
where \( A(1,2,3) \) and \( B(4,5,6) \) are the given points.


Statement 1: Isotopes of a particular element have nearly identical chemical behavior.
Statement 2: They have identical electron configurations.
A. Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement 1
B. Both the Statement 1 and Statement 2 are correct, but 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


Two adjacent sides of a parallelogram are \( 5 \mathrm{cm} \) and \( 3.5 \mathrm{cm} . \) One of its
diagonals is \( 6.5 \mathrm{cm} . \) Then the area of parallelogram is
A \( \cdot 5 \sqrt{3} \mathrm{cm}^{2} \)
в. \( 10 \sqrt{3} \mathrm{cm}^{2} \)
\( \mathbf{c} \cdot 15 \sqrt{3} \mathrm{cm}^{2} \)
D. \( 20 \sqrt{3} \mathrm{cm}^{2} \)


If \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) defined by \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2} \) is
A. one-one but not onto
B. onto but not one-one
c. bijective
D. neither one-one nor onto


The three planes divides the space into
A. four parts
B. six parts
c. eight parts
D. sixteen parts


Hydrolysis of an ester gives acid \( A \) and alcohol B. The acid reduces Fehlings solution. Oxidation of alcohol B gives
acid A. The ester is:
A. Mehthyl formate
B. Ethyl formate
c. Methyl acetate
D. Ethyl acetate


If latus rectum of an ellipse \( \frac{x^{2}}{16}+ \) \( \frac{\boldsymbol{y}^{2}}{\boldsymbol{b}^{2}}=1\{0<\boldsymbol{b}<4\}, \) subtends angle \( \mathbf{2} \boldsymbol{\theta} \)
at farthest vertex such that \( \operatorname{cosec} \theta= \)
\( \sqrt{5} \) then which of the following options
are correct:
This question has multiple correct options
A \( \cdot e=\frac{1}{2} \)
B. no such ellipse exists
c. \( b=2 \sqrt{3} \)
D. area of \( \Delta \) formed by \( L R \) and nearest vertex is 6 sq units


Arrange the following in order of increasing reducing property.
\( N a H, M g H_{2} \) and \( H_{2} O \)


Which of the following laws of thermodynamics leads to the inference that it is difficult to convert whole of
heat into work:
A. zeroth
B. second
\( c . \) first
D. third


The absolute value of the determinant
\( \left|\begin{array}{ccc}-1 & 2 & 1 \\ 3+2 \sqrt{2} & 2+2 \sqrt{2} & 1 \\ 3-2 \sqrt{2} & 2-2 \sqrt{2} & 1\end{array}\right| \) is \( \frac{k}{\sqrt{2}} \) then
\( \boldsymbol{k}= \)


Two vitamins absorbed from intestines,
along with fats, are:
A. A and D
B. A and B
c. A and \( c \)
D. D and B


Find the area of the shaded region in the
following figure where \( \boldsymbol{P Q R S} \) is a
rectangle \( 30 \mathrm{cm} \) long and the two
circles have the same radii. \( (\pi=3.14) \)


Drugs which bind strongly to the active site of an enzyme and do not depend upon the concentration of natural
substrate are called as:
A. competitive inhibitors
B. non-competitive inhibitors
c. \( \beta \) -blockers
D. \( \alpha \) -blockers


When a voltage \( V_{s}=200 \sqrt{2} \sin (\omega t+ \)
\( \left.15^{\circ}\right) V \) is applied to an ac circuit, the
current in the circuit is found to be \( i= \)
\( 2 \sin [\omega t+(\pi / 4)] A . \) If the average power
consumed in the circuit is \( x \sqrt{6} W \). Find
\( \boldsymbol{x} \)


An organic compound undergoes firstorder decomposition. The time taken for
its decomposition to \( 1 / 8 \) and \( 1 / 10 \) of
its initial concentration are \( t_{1 / 8} \) and
\( t_{1 / 10} \) respectively. What is the value of \( \frac{\left[\boldsymbol{t}_{\mathbf{1} / \mathbf{8}}\right]}{\left[\boldsymbol{t}_{\mathbf{1} / \mathbf{1 0}}\right]} \times \mathbf{1 0} ?\left(\boldsymbol{t a k e} \log _{\mathbf{1 0}} \mathbf{2}=\mathbf{0 . 3}\right) \)


The magnifying power of a telescope with tube length \( 60 \mathrm{cm} \) is \( 5 . \) What is the
focal length of its eye piece?
\( \mathbf{A} \cdot 30 \mathrm{cm} \)
B. \( 20 \mathrm{cm} \)
c. \( 10 \mathrm{cm} \)
\( \mathbf{D} \cdot 40 \mathrm{cm} \)


A converging lens of focal length \( f_{1} \) is placed in front of and coaxially with a
convex mirror of focal length \( f_{2} \). Their separation is d and whole arrangement is in air. A parallel beam of light incident on the lens returns as a
parallel beam from the arrangement. This question has multiple correct options
A. The diameter of incident and emergent beam is the same
B. the distance d can be \( f_{1} \)
c. the distance d can be \( f_{2} \)
D. the distance d can be \( f_{1}-2 f_{2} \)


A straight coaxial cable of negligible active resistance is receiving energy
from a constant voltage source \( V \) Current consumed is \( I \). Find the energy
flux across the cross-section. Assume
conductive sheath to be thin.


Select the incorrect set of elements:
I. Work done by the surrounding in case of infinite stage expansion is more than single expansion
II. Ineversible work is always greater
than reversible work
III. \( 0 n \) an ideal gas in case of single stage expansion and compression system as well as surrounding are restored back to their original states
IV. If gas is in thermodynamic
equilibrium is taken from state \( \boldsymbol{A} \) to
state \( B, \) by four successive single stage
expansions. Then we can plot 4 points on the P.V indicator diagram
A . I
B. ।, ॥, ॥II, IV
\( \mathbf{C} \cdot \|, I V \)
D. I, II, IV


The shape of the string is drawn at \( t=0 \) and the area of the pulse enclosed by the string and the \( x \) -axis ismeasured. it
will be equal to
\( A \cdot 2 c m^{2} \)
B. \( 2.5 \mathrm{cm}^{2} \)
c. \( 4 c m^{2} \)
\( D \cdot 5 c m^{2} \)


State whether the following sentence is always true, always false or ambiguous. Justify your answer February has only 28 days.


Some students set up the circuit shown
to investigate how a variable resistor
affects an electrical circuit.

If the variable resistance is increased:
ariable 'esistor
A. Ammeter reading - decreases Voltmeter
reading - decreases
B. Ammeter reading - decreases Voltmeter
reading - increases
C. Ammeter reading - increases Voltmeter reading decreases
D. Ammeter reading - increases Inter reading increases


What was Mendeleev's basis of
classification of elements?


The number of solutions of the equation \( 2 \sin ^{-1}(\sqrt{x^{2}-x+1})+ \)
\( \cos ^{-1}(\sqrt{x^{2}-x})=\frac{3 \pi}{2} \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B. Infinite
\( c \cdot 2 \)
D.


The reduction potential of a \( 0.01 M \) hydrogen electrode is:
A. \( 0.059 V \)
\( V \)
в. \( -0.059 V \)
c. \( -0.118 V \)
D. \( 0.118 V \)


Equilibrium constant for two complexes
are:
\( \boldsymbol{A}: \boldsymbol{K}_{4}\left[\boldsymbol{F} e(\boldsymbol{C} \boldsymbol{N})_{6}\right] \quad ; \quad \boldsymbol{2} . \boldsymbol{6} \times 10^{37}( \) for
dissociation)
\( \boldsymbol{B}: \boldsymbol{K}_{3}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{6}\right] \quad ; \quad \mathbf{1 . 9} \times \mathbf{1 0}^{17} \) (for
dissociation)
A. \( A \) and \( B \) are equally stable
B. \( A \) is more stable than \( B \)
\( \mathrm{c} . B \) is more stable than \( A \)
D. The predictable stability


Magnetic lines of force :
A. Always intersect.
B. Are closed curves.
C. Tend to crowd far away from the poles of a magnet.
D. Do not pass through vacuum.


Find \( \alpha \) in order that \( x^{3}-7 x+5 \) may be
a factor of \( x^{5}-2 x^{4}-4 x^{2}+19 x^{2}- \)
\( 31 x+12+\alpha \)


An excess of \( \mathrm{AgNO}_{3} \) is added to \( 100 \mathrm{ml} \) of
a \( 0.1 \mathrm{M} \) solution of
dichlorotetraaquachromium (III) chloride
The number of mol of AgCl precipitate would be:
A. 0.001
B. 0.002
c. 0.003
D. 0.01


Find the remainder if \( x-1 \) is divided by
\( 5 x^{3}-2 x^{2}+3 x-22 \)


The inflorescences with indeterminate
growth of axis are found in
A. Raceme and cyathium
B. Umbel and verticillaster
c. capitulum and cnrymb
D. Cyathium and cymose


A letter is taken out at random from the
word ASSISTANT and an other from
STATISTICS. The probability that they
are the same letters is
A \( \cdot \frac{13}{90} \)
в. \( \frac{17}{90} \)
c. \( \frac{19}{90} \)
D. \( \frac{15}{90} \)


The given circuit has two ideal diodes
connected as shown in the figure below
The current flowing through the
resistance \( \boldsymbol{R}_{\mathbf{1}} \) will be
A \( .3 .13 A \)
B . \( 2.5 A \)
c. \( 10.0 A \)
D. \( 1.43 A \)


In the given circuit, the value of current
is
A . 12 ampere
B. 11 ampere
c. 0.5 ampere
D. zero


Three of the following statements about
enzymes are correct and one is wrong. Which one of the following is wrong?
A. Enzymes require optimum pH for maximal activity
B. Enzymes are denatured at high temperature but in certain exceptional organisms they are effective even at temperatures \( 80-90^{\circ} \mathrm{C} \)
c. Enzymes are highly specific.
D. Most enzymes are proteins but some are lipids


A particular atom has the 4 th shell as its valence shell. If the difference
between the number of electrons
between K and N shell and L and M shell
is zero, find the electronic configuration of its stable ion.
A. 2,8,8,2
B. 2, 8, 18,8
c. 2,8,8
D. 2, 8


A reaction is catalysed by \( \boldsymbol{H}^{+} \) ion. In the
presence of an acid \( \boldsymbol{H} \boldsymbol{A}, \) the rate
constant is \( 2 \times 10^{-3} \) min \( ^{-1} \) and in the
presence of an acid \( \boldsymbol{H} \boldsymbol{B}, \) the rate
constant is \( 1 \times 10^{-3} \) min \( ^{-1} \). Given \( H A \)
and \( H B \) both being strong acids, we
may conclude that:
This question has multiple correct options
A. equilibrium constant is 2
B. \( H A \) is stronger acid than \( H B \)
C. relative strength of \( H A \) and \( H B \) is 2
D. \( H A \) is weaker acid than \( H B \) and their relative strength is 0.5


Assertion
If water is heated to \( 50^{\circ} \mathrm{C} \) then \( p H \) will
increase
Reason
\( K_{w} \) increases with decrease in
temperature
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


\( \mathbf{3 0} \boldsymbol{m} \boldsymbol{L} \) of \( \boldsymbol{C H}_{3} \boldsymbol{O H}\left(\boldsymbol{d}=\mathbf{0 . 8} \boldsymbol{g} / \boldsymbol{c m}^{3}\right) \) is
mixed with \( 60 m L \) of \( C_{2} H_{5} O H(d= \)
\( \left.0.92 g / c m^{3}\right) \) at \( 25^{\circ} C \) to form a solution
of density \( 0.88 g / c m^{3} . \) Select the
correct option. This question has multiple correct options
A. Molarity and molality of resulting solution are 6.33 and 13.59 respectively
B. The mole fraction of solute and molality are 0.385 and 13.59 respectively
c. Molarity and \% change in volume are 13.59 and zero respectively
D. Mole fraction of solvent and molality are 0.615 and 13.59 respectively


Indicator is a substance which shows
different colors in acidic and basic
solutions.
A. True
B. False


Which layer is considered crucial for
the existence of the ecosystems on the planet which is depleting due to increased pollution?
A. Inner
B. Outer
c. Middle
D. Ozone


According to Tippo, BGA are included in
A. chrysophyta
B. Pyrrophyta
c. chlorophyta
D. cyanophyta


Hydrolysis of \( N C l_{3} \) gives \( N H_{3} \) and \( X \)
which of the following is \( X ? \)
A \( . H C l O_{4} \)
в. \( H C l O_{3} \)
c. НОС l
D. \( H C l O_{2} \)


Evaluate: \( \int_{0}^{\pi} \frac{x \tan x}{\sec x \cdot \operatorname{cosec} x} d x \)


Statement: Sodium, when heated in
excess of oxygen, gives sodium oxide.
State whether the given statement is
true or false.
A. True
B. False


Two particles \( P \) and \( Q \) describe simple harmonic motions of same period,
same amplitude, along thesame line about the same equilibrium position 0 When \( P \) and \( Q \) are on opposite sides of 0 at the samedistance from 0 they have the same speed of \( 1.2 \mathrm{m} / \mathrm{s} \) in the same direction, when their displacements arethe same they have the same speed of \( 1.6 \mathrm{m} / \mathrm{s} \) in opposite directions. The maximum velocity in \( \mathrm{m} / \mathrm{s} \) ofeither
particle is
A . 2.8
B. 2.5
\( c \cdot 2.4 \)
D. 2


The electronegativities of two elements are 0.7 and \( 3.0 . \) The bond formed
between them would be:
A . ionic
B. covalent
c. co-ordinate covalent
D. metallic


In an a.c. circuit, the instantaneous
e.m.f. and current are given by
\( e=100 \sin 30 t \)
\( i=20 \sin \left(30 t-\frac{\pi}{4}\right) \)
In one cycle of a.c., the average power consumed by the circuit and the wattless current are, respectively:
\( \mathbf{A} \cdot 50,10 \)
B. \( \frac{1000}{\sqrt{2}}, 10 \)
c. \( \frac{50}{\sqrt{2}}, 0 \)
D. 50,0


Which of the following has highest ratio of reducting hydrogen / OH?
A. Orthophosphroric acid
B. Hypophosphorus acid
c. Phosphorus acid
D. Pyrophosphoric acid


Needles \( N_{1}, N_{2} \) and \( N_{3} \) are made of a ferromagnetic, a paramagnetic and a diamagnetic substance respectively. A
magnet when brought close to them will?
A. Attract all three of them
B. Attract \( N_{1} \) strongly, \( N_{2} \) weakly and repel \( N_{3} \) weakly
C. Attract \( N_{1} \) strongly but repel \( N_{2} \) and \( N_{3} \) weakly
D. Attract \( N_{1} \) and \( N_{2} \) strongly but repel \( N_{3} \)


If the total amount of adenine and
thymine in a double-stranded DNA is \( 60 \% \) the amount of guainine in this DNA will be
A . 15\%
B. 20\%
c. 30\%
D. 40\%


Oxidation number of chromium in
potassium dichromate is:
\( A \cdot+4 \)
B. +5
\( c \cdot+6 \)
\( D \cdot+3 \)


What is the pH of \( 0.001 M H C l ? \)
\( A \cdot 1 \)
B. 2
\( c .3 \)
D. 4


Find the greatest and the least values of the following functions. \( \boldsymbol{y}=\boldsymbol{x}^{5}-\boldsymbol{x}^{3}+\boldsymbol{x}+\boldsymbol{2} \) on the interval
[-1,1]


Classify the given amines a primary, secondary or tertiary:
\( \mathrm{c}, \mathrm{H}_{2}, \mathrm{CHNH}_{2} \quad \) (iv \( \mathrm{CC}, \mathrm{H}_{2}, \mathrm{N} \)


Calculate standard enthalpy of
formation for benzene from the
following data. \( \boldsymbol{C}_{\boldsymbol{6}} \boldsymbol{H}_{\boldsymbol{6}(\ell)}+\frac{\mathbf{1 5}}{\mathbf{2}} \boldsymbol{O}_{\mathbf{2}(\boldsymbol{g})} \longrightarrow \boldsymbol{6} \boldsymbol{C} \boldsymbol{O}_{\boldsymbol{2}(\boldsymbol{g})}+ \)
\( \mathbf{3} \boldsymbol{H}_{2} \boldsymbol{O}_{(\ell)} \quad \boldsymbol{\Delta} \boldsymbol{H}^{o}=-\mathbf{3 2 6 7} \boldsymbol{K} \boldsymbol{J} \)
\( \Delta_{f} H^{o}\left(C O_{2}\right)=-393.5 K J m o l^{-1} \)
\( \Delta_{f} H^{o}\left(C_{2} O\right)=-285.8 K J m o l^{-1} \)


What is the common difference of an AP
in which the ratio of the product of the first and fourth term to the product of the second and third term is \( 2: 3 ? \) It
is given that the sum of the four terms
is 20
A . 3
B. 4
c. 1
\( D \)


All the capacitance in the figure are of capacitance \( C . \) The effective capacitance between \( P \) and \( Q \) is :
4.20
3. \( 3 C \)
\( c \cdot 4 C \)
D. \( 1.5 C \)


The maximum number of photons emitted by an H-atom,if atom is excited to states with principal quantum number four is
A .4
B. 6
\( c \cdot 2 \)
\( D \)


Cetyl trimethyl ammonium chloride is which type of detergent?
A. Cationic
B. Anionic
c. Biosoft
D. Non-ionic


In corrosion of iron:
A. an electrochemical reaction (galvanic cell) is formed in which Fe acts as anode and cathode is where \( O_{2} \) is
reduced
B. electrons flow from anode to cathode through the metal while ions flow through the waterdroplets
C. dissolved \( O_{2} \) oxidises \( F e^{2+} \) to \( F e^{3+} \) before it is
deposited as rust \( \left(\mathrm{Fe}_{2} \mathrm{O}_{3} \cdot \mathrm{H}_{2} \mathrm{O}\right) \)
D. all of the above take place


At a given temperature, the equilibrium
constant for the reaction \( \boldsymbol{P} \boldsymbol{C l} \boldsymbol{l}_{5}(\boldsymbol{g}) \leftrightharpoons \)
\( \boldsymbol{P C l}_{3}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) \) is \( \boldsymbol{2} . \boldsymbol{4} \times 10^{-3} . \) At the
same temperature, the equilibrium constant for the reaction
\( \boldsymbol{P C l}_{3}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) \leftrightharpoons \boldsymbol{P C l}_{5}(\boldsymbol{g}) \) is:
A \( .2 .4 \times 10^{-3} \)
В. \( -2.4 \times 10^{-3} \)
C \( .4 .2 \times 10^{2} \)


State and prove Bayes' theorem


State any two applications of baking
soda.


The gravitational force between two objects placed at a distance r is proportional to
\( \mathbf{A} \cdot r \)
в. \( r^{2} \)
c. \( \frac{1}{r^{2}} \)
D. \( \frac{1}{r} \)


Calcium carbide + heavy water \( \rightarrow ? \)
The product of the above reaction is:
A. \( C_{2} H_{2} \)
в. \( C a D_{2} \)
\( \mathbf{c} \cdot \operatorname{Ca}(O D)_{2} \)
D. \( C D_{4} \)


Mammals are characterized by the following features except
A. Presence of mammary glands
B. Presence of external ears of pinnae
c. cold blooded nature
D. Mostly viviparous


Say True or False. All the sides of a rhombus are of equal
length.
A. True
B. False


Number of ATP molecules required for regeneration phase of RuBP during synthesis of 1 glucose molecule is
\( A \cdot 6 \)
B. 12
\( c \cdot 18 \)
D. 30


A rectangular tank \( 28 m \) long and \( 22 m \) wide is required to receive entire water from a full cylindrical tank of internal
diameter \( 28 m \) and depth \( 4 m . \) Find the
least height of the tank that will serve
the purpose. (Take \( \boldsymbol{\pi}=\mathbf{2 2} / \mathbf{7}) \)
A. \( 4.0 \mathrm{m} \)
в. \( 4.5 \mathrm{m} \)
\( c .5 .0 m \)
D. \( 5.2 m \)


Show that the statement
\( \boldsymbol{p}: \) If \( \boldsymbol{x} \) is a real number such hat \( \boldsymbol{x}^{\mathbf{3}}+ \)
\( 4 x=0, \) then \( x \) is 0 is true by
direct method


If the mean deviation of the numbers
\( \mathbf{1}, \mathbf{1}+\boldsymbol{d}, \dots, \mathbf{1}+\mathbf{1 0 0} \boldsymbol{d} \) from their mean
is \( 255, \) then a value of \( d \) is:
A . 10.1
B. 20
c. 10
D. 20.2


Express \( -\overline{\mathbf{i}}-\mathbf{3} \overline{\mathbf{j}}+\mathbf{4} \overline{\mathbf{k}} \) as a linear
combination of \( 2 \bar{\imath}+\bar{\jmath}-4 \bar{k}, 2 \bar{\imath}-\bar{\jmath}+3 \bar{k} \)
and \( 3 \bar{\imath}+\bar{\jmath}-2 \bar{k} \)


The temperature at which the \( \boldsymbol{R} \boldsymbol{M} \boldsymbol{S} \)
velocity of \( C O_{2} \) is equal to the RMS
velocity of \( N_{2} O \) at \( 27^{\circ} C \) is:
\( \mathbf{A} \cdot 0^{\circ} C \)
В. \( 27^{\circ} \mathrm{C} \)
\( \mathrm{c} \cdot 273^{\circ} \mathrm{C} \)
D. \( -273^{\circ} \mathrm{C} \)


An organic compound which produces a bluish green coloured flame on heating in presence of copper is :
A. benzaldehyde
B. benzoic acid
c. aniline
D. chlorobenzene


The value of \( \int \sqrt{\frac{e^{x}}{e^{x}}+1} d x \) is equal
to
\( \mathbf{A} \cdot \ln \left(e^{x}+\sqrt{e^{2} x}-1\right)-\sec ^{-} 1\left(e^{x}\right)+c \)
B \( \cdot \ln \left(e^{x}+\sqrt{e^{2} x}-1\right)+\sec ^{-} 1\left(e^{x}\right)+c \)
C \( \cdot \ln \left(e^{x}-\sqrt{e^{2} x}-1\right)-\sec ^{-} 1\left(e^{x}\right)+c \)
D \( \cdot \ln \left(e^{x}+\sqrt{e^{2} x}-1\right)-\sin ^{-} 1\left(e^{-x}\right)+c \)


Which one of the following group 16 elements does not exist in -2 oxidation
state?
A . \( S \)
в. \( S e \)
\( c \cdot O \)
D. \( P o \)
E . \( T e \)


The function \( f(x)=\sin ^{-1}(\cos x) \) is :
A. discontinuous at \( =0 \)
B. continuous at \( =0 \)
c. differentiable \( =0 \)
D. none of these


Compute the value of \( x \) in the figure
given


Describe the process of respiration in the following part of a plant.
Stem.


The circle whose radius is \( 1 \mathrm{cm} \) then the
diameter of the circle is


Write two examples of metallic soilds.


A codon in mRNA has
A. 3 bases
B. 2 bases
c. 1 base
D. Number of bases vary


\( \operatorname{Let} \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{2} & \mathbf{0} & \mathbf{7} \\ \mathbf{0} & \mathbf{1} & \mathbf{0} \\ \mathbf{1} & \mathbf{- 2} & \mathbf{1}\end{array}\right] \) and \( \boldsymbol{B}= \)
\( \left[\begin{array}{ccc}-\boldsymbol{x} & \mathbf{1 4 x} & \mathbf{7 x} \\ \mathbf{0} & \mathbf{1} & \mathbf{0} \\ \boldsymbol{x} & \mathbf{- 4 x} & \mathbf{- 2 x}\end{array}\right] \) are two matrices
such that \( A B=(A B)^{-1} \) and \( A B \neq I \)
(where \( I \) is an identity matrix of order
\( 3 \times 3) \)
Find the value of
\( \boldsymbol{T} \boldsymbol{r} \cdot\left(\boldsymbol{A} \boldsymbol{B}+(\boldsymbol{A} \boldsymbol{B})^{2}+(\boldsymbol{A} \boldsymbol{B})^{3}+\ldots+(\boldsymbol{A} \boldsymbol{B}\right. \)
where \( T r .(A) \) denotes the trace of
matrix \( \boldsymbol{A} \)
A. 98
в. 99
\( c \cdot 100 \)
D. 10


Match the following.
\( \begin{array}{ll}\text { 1. Incisors } & \text { a. Grinding teeth } \\ \text { 2. Canines } & \text { b. Cracking teeth } \\ \text { 3. Premolars } & \text { c. Cutting teeth } \\ \text { 4. Molars } & \text { d. Tearing teeth }\end{array} \)
\( A \cdot 1-b, 2-d, 3-a, 4-c \)
B. \( 1-b, 2-a, 3-d, 4-c \)
\( c \cdot 1-c, 2-b, 3-d, 4-a \)
D. \( 1-c, 2-d, 3-b, 4-a \)


Describe reflex action and reflex arc


Which reaction is responsible for solar
energy? Name the major component of
solar energy that reaches us.


Solve it
\( \mathbf{2} \boldsymbol{I}=\int_{\boldsymbol{O}}^{\boldsymbol{Q}} \boldsymbol{d} \boldsymbol{x} \)


If \( \overrightarrow{\boldsymbol{A}}=\mathbf{2} \hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}-\hat{\boldsymbol{k}} \) and \( \overrightarrow{\boldsymbol{B}}=\sqrt{\mathbf{2}}(\hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}) \)
Find \( \vec{A} . \vec{B} \). Hence find the angle between \( \vec{A} \) and \( \vec{B} \). Also find the component of \( \overrightarrow{\boldsymbol{A}} \) along \( \overrightarrow{\boldsymbol{B}} \)


Write down the number of significant figures in the following value.
\( 62.00 \mathrm{m} \)
A. four
B. three
c. \( t w o \)
D. on


Name the part of the brain that
performs following functions:
Maintaining posture
Seeing

Sensation of hunger


Solvent dissolve large amount of solute
at
A. room temperature
B. boiling temperature
c. freezing temperature
D. less than room temperature but more than freezing temperature


A table.


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


The most important force which pulls the water in trees in
A. Cohesive force
B. Electromagnetic force
c. Imbibition force
D. osmotic force


One hormone hastens maturity period in juvenile conifers, a second hormone controls xylem differentiation, while the third increases the tolerance of plants
to various stresses. They are
respectively
A. Auxin, Gibberellins, cytokinin
B. Auxin, Gibberellins, ABA
c. Gibberellin, Auxin, Cytokinin
D. Gibberellin, Auxin, ABA


\( 75 \% \) of element \( \mathrm{M} \) exists as \( ^{214} M \) and 25
\( \% \) of it exists as \( ^{210} M . \) Find the atomic
weight of element M in amu?
A . 211
в. 214
c. 213
D. 212
E . 85


Find the number of metals from the
given metals which can be commercially purified by zone refining methods:
\( (\mathrm{Si}, \mathrm{Ge}, \mathrm{Ga}, \mathrm{Al}, \mathrm{Ti}, \mathrm{Zr}) \)


The silver salts like \( A g B r \) and \( A g I \) are coloured because of:
A. d-d transition of electrons
B. charge transfer
C. polirisation of halid \( A g^{+} \) by
D. both (b) and (c)


Given n real numbers \( a_{1}, a_{2}, \dots a_{n}, \) the
value of \( x \) for which sum of the square of
all the deviations is least is
A \( \cdot a_{1}+a_{2}+\ldots+a_{n} \)
В - \( 2\left(a_{1}+a_{2}+\ldots+a_{n}\right) \)
c. \( a_{1}^{2}+a_{2}^{2}+\ldots a_{n}^{2} \)
D. \( \frac{a_{1}+a_{2}+\ldots+a_{n}}{n} \)


By process of electrolysis chemical energy gets converted into electrical
energy.