Which statements is/are correct for the
given molecule?
(S)
A. Molecule is optically inactive
B. Plane of symmetry is present in molecule
C \( . S_{4} \) alternative axis of symmetry is present in the molecule
D. If all the four \( C D C l \) carbon have \( R \) configuration then molecule is optically acitve


Metameric segmentation is the characteristic of
A. Platyhelminthes and Arthropoda
B. Echinodermata and Annelida
c. Annelida and Arthropoda
D. Mollusca and Chordata


The formal charge on carbon atom in
carbonate ion is?


The momentum of a body of mass 0.5 kg dropped from a certain height (h),
when reaches the ground is \( 10 \mathrm{N} \) s. The value h is \( _{---} \) m. \( \left(g=10 m s^{-2}\right) \)
A . 20
B . 40
c. 10
D. 80


Atomic masses of two isobars \( _{29}^{64} C u \) and
\( _{30}^{64} Z n \) are \( 63.9298 u \) and \( 63.9292 u \)
respectively. It can be concluded from this data that
A. both the isobars are stable
B. \( 64 Z n \) is radioactive, decaying to \( ^{64} C u \) through \( \beta- \) decay
C. \( ^{64} C u \) is radioactive, decaying to \( ^{64} Z n \) through \( \beta- \) decay
D. \( ^{64} C u \) is radioactive, decaying to \( ^{64} Z n \) through \( \gamma \) decay


Factorise: \( 36 x^{2}+24 x+4 \)
A. \( 4(3 x-1)(3 x+1) \)
B. \( (3 x-1)(3 x+1) \)
c. \( (3 x+1)(3 x+1) \)
D. \( 4(3 x+1)(3 x+1) \)


An electron is projected from a distance
\( d \) and with initial velocity \( u \) parallel to a uniformly charged flat conducting plate
as shown. It strikes the plate after
travelling a distance \( \ell \) along the direction of projection. The surface
charge density of the conducting plate is equal to
A \( \cdot \frac{2 d \varepsilon_{0} m u^{2}}{e \ell^{2}} \)
B. \( \frac{2 d \varepsilon_{0} m u}{e \ell^{2}} \)
c. \( \frac{d \varepsilon_{0} m u^{2}}{e \ell} \)
D. \( \frac{d \varepsilon_{0} m u}{e l} \)


What is the median for the following
data?
\( \begin{array}{lllll} & 2- & 4- & 6- & 8- \\ x & 4 & 6 & 8 & 10\end{array} \)
4 frequency \( \quad 1 \quad 3 \quad 2 \)
\( \mathbf{A} \cdot \mathbf{6} \)
B. 6.5
c. 7
D. 7.5


For a given material, the Young's modulus is 2.4 times that of rigidity modulus. Its poisson's ratio is.
A . 2.4
B. 1.2
\( c .0 .4 \)
D. 0.2


Pick the odd ones in each of the
following groups and select the correct
option.
(i) Renal pelvis, Medullary pyramid, Renal cortex, Renal papilla
(ii) Afferent arteriole, Henle's loop, Vasa
recta, Efferent arteriole
(iii) Glomerular filtration, Antidiuretic
hormone, Hypertonic urine, Collecting
duct
(iv) Proximal convoluted tubule, Distal
convoluted tubule, Henle's loop, Renal
corpuscle
A. (i)Renal pelvis (ii)Henle's loop (iii)Collecting duct tubule (iv)Distal convoluted tubule
B. (i)Renal papilla (ii)Afferent arteriole (iii)Antidiuretic hormone (iv)Henle's loop
C. (i)Medullary pyramid (ii)Efferent arteriole
(iii)Hypertonic urine (iv)Proximal convoluted tubule
D. (i)Renal cortex (ii)Vasa recta (iii)Glomerular filtration (iv)Renal corpuscle


Find the smaller area enclosed by the
circle \( x^{2}+y^{2} \) and the line \( x+y=2 \)


The IUPAC name for Teflon is:
A. polytrifluoroethane
B. polytetrafluoroethane
c. polytrifluoroethylene
D. polytetrafluoroethylene


The plane \( a x+b y+c z+(-3)=0 \)
meet the co-ordinate axes in \( A, B, C \)
The centroid of the triangle is
B \( \cdot\left(\frac{3}{a} \cdot \frac{3}{b}, \frac{3}{c}\right) \)
c. \( \left(\frac{a}{3} \cdot \frac{b}{3}, \frac{c}{3}\right) \)
D. \( \left(\frac{1}{a} \cdot \frac{1}{b}, \frac{1}{c}\right) \)


The lightest gas which is noninflammable is:
A \( . H_{2} \)
в. \( H e \)
c. \( N_{2} \)
D. \( A \) r


In the following \( V-T \) diagram, what is
the relation between \( P_{1} \) and \( P_{2} ? \)
\( A \cdot P_{2}=P_{1} \)
В \( \cdot P_{2}>P_{1} \)
\( c \cdot P_{2}<P_{1} \)
D. cannot be predicted


Evaluate:
\( \left|\begin{array}{cc}x^{2}-x+1 & x-1 \\ x+1 & x+1\end{array}\right| \)


Very short answer type. What type of tissue is the main
component of teeth?


If \( L \) has the dimensions of length, \( V \)
that of potential and \( \epsilon_{0} \) is the permittivity of free space then quantity
\( L V \epsilon_{0} \) has the dimensions of:
A . current
B. charge
c. resistance
D. voltage


A freely falling body starting from rest, travel \( _{--}-_{-} \) of total distance in 5 th
Second
A. \( 8 \% \)
B. \( 12 \% \)
c. \( 25 \% \)
D. \( 36 \% \)


The given bar graph shows the favourite breakfast items of the students of Class
V. Read the bar graph and answer the
questions

Which two breakfast items are equally
liked by the students?
A. Cornflakes \& milk, Sandwich
B. Paratha, Boiled egg
c. Paratha, Toast \& butter
D. Boiled egg, sandwich


\( \frac{3 x-2}{5}=4-\left(\frac{x+2}{3}\right), \) find \( x \)


Anode in the galvanic cell is :
A. Negative electrode
B. Positive electrode
c. Neutral electrode
D. None of the above


The number of atoms contained in a fcc
unit cell of a monatomic substance is


Electrolysis is carried out in three cells:
\( (A)-1.0 M C u S O_{4}, \) Pt electrodes;
\( (B)-1.0 M C u S O_{4}, \) Copper electrodes;
\( (C)-1.0 M K C I, \) Pt electrodes. If volume
of
electrolytic solution is maintained
constant in
each of the cells, which is correct set of
\( \mathrm{pH} \)
changes in \( (A),(B) \) and \( (C) \) cells respectively:
A. increase in all the three
B. decrease in all the three
c. increase, constant, increase
D. decrease, constant, increase


Combustion is a process involving:
A. oxidation
B. reduction
c. liberation of heat
D. all of the above


The area of a quadrant of a circle whose
circumference is \( 44 \mathrm{cm} \) is
A \( \cdot 144 \mathrm{cm}^{2} \)
В. \( 175.76 \mathrm{cm}^{2} \)
c. \( 38.5 \mathrm{cm}^{2} \)
D. \( 154 \mathrm{cm}^{2} \)


Hormone involved in photoperiodism is
A . IAA
B. Gibberellin
c. Kinetin
D. 2, 4-D


Burning \( C a \) in air give \( C a_{3} N_{2} \) as the major side product because:
A. air contains oxygen and nitrogen only
B. percentage of nitrogen gas in air is maximum
c. oxygen is inert in atmosphere
D. none of these


The enthalpy of combustion of \( \boldsymbol{H}_{2} \)
cyclohexene \( \left(C_{6} H_{10}\right) \) and cyclohexane
\( \left(C_{6} H_{12}\right) \) are -241,-3800 and -3920
kJ/mol respectively. Heat of hydrogenation of cyclohexene is:
A. -121 kJ per mol
B. +121 kJ per mol
c. +242 kJ per mol
D. -242 kJ per mol


Select the correct option:
Select the right option regarding the
given graph.
A. \( x \) - axis = Rate of reaction \( Y \) - axis = Enzymatic activity
B. \( x \) -axis = Enzymatic activity \( Y \) - axis = Rate of reaction
c. \( x \) -axis = Enzymatic activity \( Y \) - axis = pH/Temperature
D. \( x \) - axis = pH/Temperature
Y-axis = Enzymatic activity


What is kinetic energy? Derive an
equation for the kinetic energy of a body of mass ' \( m \) ' moving at a speed ' \( v \) '


Two identical p-njunctions may be connected in series with battery in
three ways as shown in the adjoining
figure. The potential drop across the p-n junctions are equal in
A. Circuit 1 and circuit 3
B. Circuit 1 and circuit 2
c. circuit 2 and circuit 3
D. circuit 2 only


The solubility of impurities in a metal in molten and solid states is different. This is principle involved in the refining of a metal by which of the following methods?
A. Poling
B. Liquation
c. zone refining
D. Electrolysis


If \( k(x)=4 x^{3} a \) and \( k(3)=27, \) what is
\( k(2) ? \)
\( A \cdot 9 \)
B. 8
c. 17
D. 12


Which of the following is not used as a food preservative?
A. Sodium salt of benzoic acid
B. Sodium salt of sorbic acid
c. Sodium salt of propanoic acid
D. Sodium salt of palmitic acid


The circum radius of the triangle formed by the points (0,0,0),(0,0,12) and (3,4,0) is
A. \( \sqrt{156} \)
B. 13
c. \( \frac{13}{2} \)
D.


The construction of a \( \Delta A B C \) in which
\( B C=6 \mathrm{cm} \) and \( \angle B=50^{\circ}, \) is not
possible when \( (A B-A C) \) is equal to:
A \( .5 .6 \mathrm{cm} \)
в. \( 5 \mathrm{cm} \)
\( c \cdot 6 c m \)
D. \( 4.8 \mathrm{cm} \)


The sum of series \( \frac{1^{2}}{1}+\frac{1^{2}+2^{2}}{1+2}+ \)
\( \frac{1^{2}+2^{2}+3^{2}}{1+2+3}+\ldots . \) upto \( n \) terms is
A \( \cdot \frac{1}{3}(2 n+1) \)
B. \( \frac{1}{3} n^{2} \)
c. \( \frac{1}{3}(n+2) \)
D. \( \frac{1}{3} n(n+2) \)


Assertion
Normal respiration of plant is also called dark respiration.
Reason
Only photorespiration occurs in light.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The opening of postcaval in mammalian heart is guarded by
A. Semilunar valves
B. Bicuspid valve
c. Tricuspid valve
D. Eustachiun valve


Which of the following scientists invented the mercury barometer?
A. Blaise Pascal
B. Evangelist Torricelli
c. James Joule
D. Robert Brown


\( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) reduces \( \boldsymbol{K}_{3}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{6}\right] \) in:
A. neutral medium
B. acidic medium.
c. alkaline medium.
D. non-polar solution


The IUPAC name of \( \boldsymbol{C}_{6} \boldsymbol{H}_{5}-\boldsymbol{C} \boldsymbol{H}= \)
\( \boldsymbol{C H}-\boldsymbol{C O O H} \) is:
A. cinnamic acid
B. 1-phenyl-2-carboxyethane
c. 3-phenyl prop-2-enoic acid
D. dihydroxy-3-phenyl propionic acid


The lattice energy of \( N a C l(s) \) is \( -790 k J . m o l^{-1} \) and enthalpy of hydration is \( -785 k J . m o l^{-1} . \) Calculate
the enthalpy of the solution of \( N a C l(s) \)


op
\( Q \) туре your question
generated across the coil during on
eycle is


Very short answer type.
Explain \( C O_{2} \) compensation point


The molar heat capacities at constant pressure (assume constant with
respect to temperature) of \( A, B \) and \( C \)
are in the ration of 1.5: 3.0: 2.0
If enthalpy change for the exothermic
reaction \( A+2 B \rightarrow 3 C \) at \( 300 K \) is
\( -10 k J / m o l \)
\( \& C_{p, m}(B) \) is \( 300 J / m o l \)
then enthalpy change at \( 310 K \) is:
A . \( -8.5 k J / m o l \)
B. \( 8.5 k J / \) mol
c. \( -11.5 k J / \) mol
D. none of these


Factorise: \( 5 x^{2}-x-4 \)


Transpiration and root pressure cause water to rise in plants by
A. Pushing it upward
B. Pushing and pulling it respectively
c. Pulling it upward
D. Pulling and pushing it respectively


Density of heavy water is maximum at:
\( \mathbf{A} \cdot 3.82^{\circ} C \)
B . \( 101.42^{\circ} \mathrm{C} \)
c. \( 11.6^{\circ} \mathrm{C} \)
D. \( 4^{\circ} \mathrm{C} \)


The difference in height of the mercury column in two arms of a U tube
manometer in arrangement-lis \( \boldsymbol{h}_{\mathbf{1}}= \)
\( 660 \mathrm{mm} . \) In another arrangement -II at the same temperature, 222 gm of
\( \mathrm{CaCl}_{2} \) is dissolved in \( 324 \mathrm{gm} \) of water and the difference in height of mercury
column in two arms is found to be \( h_{2}= \)
\( 680 \mathrm{mm} . \) If the value of degree of
dissociation for \( C a C l_{2} \) in arrangement
-II is \( \alpha, \) then the value of \( 64 \alpha \) is:
[Atmospheric pressure \( =1 \text { atm }] \)
\( : \mathbb{1} \)


A by product of soap industry is:
A. sodium hydroxide
B. sodium palmitate
c. glycerol
D. both \( B \) and \( C \)


The same quantity of electricity is passed through \( A l_{2}\left(S O_{4}\right)_{3} \) and \( A g N O_{3} \) solution with platinum electrodes. If \( n \) number of Al atoms are deposited on the cathode, the number of Ag atoms deposited on the cathode will be:
\( A \)
B. 2n
\( c \cdot 3 n \)
D. n/2


Give an equation for reaction of conc.
\( H N O_{3} \) with copper.
A \( \cdot 3 C u+4 H N O_{3}(\text { conc }) \rightarrow 3 C u\left(N O_{3}\right)_{2}+2 N O_{2}+H_{2} O \)
В \( \cdot \quad C u+2 H N O_{3}(\operatorname{conc}) \rightarrow C u\left(N O_{3}\right)_{2}+N O_{2}+2 H_{2} O \)
с. \( _{2 C u+4 H N O_{3}(\text {conc}) \rightarrow 2 C u\left(N O_{3}\right)_{2}+2 N O_{2}+2 H_{2} O} \)
D. \( C u+4 H N O_{3}(\text { conc }) \rightarrow C u\left(N O_{3}\right)_{2}+2 N O_{2}+2 H_{2} O \)


Synthesis gas is: [EAMCET - 94 - E]
A. Steam + CO
в. \( C O+N_{2} \)
c. \( C O+H_{2} \)
D. \( C H_{2}+H_{2} \)


\( \int\left(x^{2}-x+5\right) d x \)
A. \( \frac{x^{3}}{3}-\frac{x^{2}}{2}+5 x+c \)
B. \( \frac{x^{3}}{3}+\frac{x^{2}}{2}+5 x+c \)
c. \( \frac{x^{2}}{2}-\frac{x}{2}+5 x+c \)
D. \( \frac{x^{4}}{4}-\frac{x^{4}}{3}+5 \)


The \( C-O-C \) bond angle in diethyl
ether is:
\( \mathbf{A} \cdot 109^{\circ} 28 \)
B. \( 110^{\circ} \)
\( c \cdot 120^{\circ} \)
D. \( 180^{\circ} \)


State the function of the following
(a) pepsin
(b) HCI
(c) Bile
(d) Saiva


Which of the following flowers are pollinated by wind?
A. sunflower
B. corn and willow
c. buttercup and rose
D. orchid and wall flower


The resistance of a solution \( A \) is 50
ohms and that of solution B is 100
ohms, both solutions being taken in the same conductivity cell. If equal volumes
of solution \( A \) and \( B \) are mixed, the
resistance (in ohms) of the mixture
using the same cell will be \( 13 x+2 \)
Then \( x \) is:
Assume that there is no increase in the degree of dissociation of \( A \) and \( B \) on
mixing. (write the value to the nearest integer)


When no more of a solid can be
dissolved in a solvent ,it is called:
A. unsaturated solution
B. colloidal solution
c. saturated solution
D. none of the above


Which of the following oxidation state is common for all lanthanides?
\( A \cdot+2 \)
B. +3
\( c \cdot+4 \)
D. +5


A fuse in an electric circuit acts as a:
A. current multiplication
B. voltage multiplication
c. power multiplier
D. safety device


The differential equation of the family of hyperbolas having centres at the origin and whose axes are the co-ordinate
axes is
A \( \cdot x y y_{2}+x y_{1}^{2}+y y_{1}=0 \)
B. \( x y y_{2}-x y_{1}^{2}-y y_{1}=0 \)
c. \( x y y_{2}+x y_{1}^{2}-y y_{1}=0 \)
D. \( x y y_{2}+x y_{1}-y y_{1}=0 \)


Jute fibre is obtained from the
of jute plant.
A . leaves
B. seeds
c. roots
D. stem


Name the basic unit of biological classification.


Freon used as refrigent is:
A. \( C F_{2}=C F_{2} \)
в. \( C H_{2} F_{2} \)
c. \( C C l_{2} F_{2} \)
D. \( C F_{4} \)


(a) If \( x \) be real, then the expression \( \frac{2 a(x-1) \sin ^{2} \theta}{x^{2}-\sin ^{2} \theta} \) does not lie between
\( 2 a \sin ^{2}(\theta / 2) \) and \( 2 a \cos ^{2}(\theta / 2) \)
(b) A function \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R}, \) where \( \mathrm{R} \) is the
set of real numbers, is defined by \( f(x)=\frac{\alpha x^{2}+6 x-8}{\alpha+6 x-8 x^{2}} \) Find the interval of
values of \( \alpha \) for which \( f \) is onto.

Is the function one-to-one for \( \boldsymbol{\alpha}=\mathbf{3} ? \)
Justify yout answer.


Find the mean, variance and standard
deviation for the following frequency distribution.
Classes \( \begin{array}{lll}0- & 10- & 2 \\ 10 & 20 & 3\end{array} \) 30 40
Frequency
१५ 16


When an organic compound is present in an aqueous medium and is less soluble in any organic solvent then it is separated by?
A. Continuous extraction
B. Distillation
c. chromatography
D. Sublimation


If \( \boldsymbol{f}(\boldsymbol{x})=[\boldsymbol{x}]+\left[\boldsymbol{x}+\frac{1}{3}\right]+\left[\boldsymbol{x}+\frac{2}{3}\right], \) then
([.] denotes the greatest integer
function)
A. \( f(x) \) is discontinuous at \( x=1,10,15 \)
в. \( \lim _{x \rightarrow \frac{2}{3}} f(x)=2 \)
\( ^{\mathbf{c}} \cdot \int_{0}^{2 / 3} f(x) d x=\frac{1}{3} \)
D. \( f(x) \) is continuous at \( x=\frac{n}{3} \), where \( n \) is any intege


The straight line passing through the point of intersection of the straight lines
\( \boldsymbol{x}-\mathbf{3} \boldsymbol{y}+\mathbf{1}=\mathbf{0} \) and \( \mathbf{2} \boldsymbol{x}+\mathbf{5} \boldsymbol{y}-\mathbf{9}=\mathbf{0} \)
and having infinite slope and and at a distance 2 units from the origin has the
equation
\( \mathbf{A} \cdot x=2 \)
В. \( 3 x+y-1=0 \)
\( \mathbf{c} \cdot y=1 \)
D. None of these


Copper (II) sulfate solution is:
A . red
B. purple
c. orange
D. green
E. blue


Choose the correct answer from the
alternatives given :
In a DNA strand the nucleotides are
linked together by
A. Glycosidic bonds
B. Phosphodiester bonds
c. Peptide bonds
D. Hydrogen bonds


Which of the following is a characteristic of matter?
A. Particles are very small in size.
B. Particles have space among them
c. Particles posses kinetic energy
D. All of above


What is the phase difference
between acceleration and velocity of
a particle executing simple harmonic motion?


The binding energy per nucleon of \( ^{16} \mathrm{O} \) is
\( 7.97 M e V \) and that of \( 17 O \) is \( 7.75 M e V \)
The energy in MeV required to remove a
neutron from \( ^{17} \) O is:
A . 3.52
в. 3.64
c. 4.23
D. 7.86
E . 1.68


Critical mass is minimum mass
necessary for
A. chain reaction
B. fusion
c. hydrogen bomb
D. all of the above


Which one of the following reactions will
occur on heating \( \boldsymbol{A} \boldsymbol{g} \boldsymbol{N} \boldsymbol{O}_{3} ? \)
A \( \cdot 2 A g N O_{3} \rightarrow 2 A g+N_{2}+3 O_{2} \)
в. \( 2 A g N O_{3} \rightarrow A g_{2} O+N_{2} O_{3}+O_{2} \)
\( \mathrm{c} \cdot 2 \mathrm{AgNO}_{3} \rightarrow 2 \mathrm{AgNO}_{2}+\mathrm{O}_{2} \)
D. \( 2 A g N O_{3} \rightarrow 2 A g+2 N O_{2}+O_{2} \)


The instantaneous velocity of a point on the outer edge of a disk with a diameter of \( 4 \mathrm{m} \) that is rotating at 120 revolutions per minute is most nearly:
\( A \cdot 4 m / s \)
B. 6 \( \mathrm{m} / \mathrm{s} \)
\( c \cdot 12 m / s \)
D. 25 \( \mathrm{m} / \mathrm{s} \)
E. \( 50 \mathrm{m} / \mathrm{s} \)


In 1 L saturated solution of
\( A g C l\left[K_{s p}(A g C l)=1.6 \times 10^{10}\right], 0.1 \mathrm{mol} \)
of \( \boldsymbol{C u} \boldsymbol{C l}\left[\boldsymbol{K}_{s p}(\boldsymbol{C u} \boldsymbol{C l})=\mathbf{1 . 0} \times \mathbf{1 0}^{-\mathbf{6}}\right] \) is
added. The resultant concertraion of
\( A g^{+} \) in the solution is \( 1.6 \times 10^{-x} \). The
value of \( x \) is:


What percentage of ethyl alcohol does
wash or wort possess?
A . 95\%
B . 100\%
c. 66.9\%
D. 6 - 10\%


\( \mathbf{A B A}^{-1}=\mathbf{X} \) then \( \mathbf{B}^{\mathbf{2}}= \)
A \( \cdot x^{2} \)
B. AxA \( ^{-1} \)
c. \( A x^{2} A^{-1} \)
D. \( A^{-1} x^{2} A \)


Why is a photo-diode invariably reverse
biased, when it is used as a photo-
detector?
A. The power consumption is much reduced compared to reverse biased condition
B. Electron hole pairs can be produced by the incident photons only if the photo diode is reverse biased
C. Light variations can be converted into current variations only if the photo diode is reverse biased
D. When photons are incident on the diode, the fractional change in the reverse current is much greater than the fractional change in the forward current
E. The photo diode will be spoilt if it is operated under forward biased condition


Dalton's law of partial pressure is not applicable to which of the following mixture of gases? This question has multiple correct options
\( A \cdot H_{2}+F_{2} \)
в. \( N H_{3}+H C l \)
\( \mathbf{c} \cdot S O_{2}+C l_{2} \)
D. \( H_{2}+O_{2} \)


if force \( \overrightarrow{\boldsymbol{F}}=(\hat{\boldsymbol{i}}+\boldsymbol{3} \hat{\boldsymbol{j}}) \boldsymbol{N} \) acts on a body
at a point whose distance from the axis of rotation is given by \( \vec{r}=(3 \hat{i}+\hat{j}) N \) then torque acting on the body is:
\( \mathbf{A} \cdot 9 N m \)
B. \( 8 N m \)
\( \mathbf{c} .6 N m \)
D. \( 1 N m \)


The Venn diagram shows the
relationship between sets \( \xi, P, Q \) and \( R \)
The shaded region in the diagram
represents set:
\( A \cdot(P \cap R) \cap Q \)
B . \( \left(P \cap R^{\prime}\right) \cap Q^{\prime} \)
\( \mathrm{c} \cdot\left(P \cap R^{\prime}\right) \cap Q \)
\( \mathrm{D} \cdot Q^{\prime} \cap R^{\prime} \)


A particle executes simple harmonic
motion with a frequency \( v \). The
frequency with which the kinetic energy oscillates is
\( \mathbf{A} \cdot v / 2 \)
B. \( v \)
c. \( 2 v \)
D. Zero


Assign oxidation number to the underlined elements in each of the
following species.
\( \boldsymbol{C a} \underline{\boldsymbol{O}}_{2} \)


Test cross can not be performed in
A. Neurospora
B. Man
c. Pea
D. Dog


Find the equation of the ellipse whose
foci are (0,±7) and length of the minor
axis is 26


Let \( f(x)=x^{3}-12 x \) be function
such that the equation \( |\boldsymbol{f}(|\boldsymbol{x}|)|= \) \( \boldsymbol{n}(\boldsymbol{n} \in \boldsymbol{N}) \) has exactly \( \boldsymbol{6} \) distinct real
roots then number of possible values of
\( \boldsymbol{n} \) are :
A . 15
B . 16
c. 17
D. 14


Tne probability that Krishna will be alive
10 years is \( \frac{7}{15} \) and that Hari will be alive
is \( \frac{7}{10} . \) The probability that both Krishna
and Hari will be dead is -
A \( \cdot \frac{21}{150} \)
B. \( \frac{24}{150} \)
\( \mathbf{c} \cdot \frac{49}{150} \)
D. \( \frac{56}{150} \)


The product formed by the reaction
between 2,2,2 -trichloroethanal and
chlorobenzene in \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) is:
A. chloretone
B. DDT
C. chlorobenzaldichloride
D. benzene sulphonic acid


Differentiate the given function w.r.t. \( x \)
\( \log (\log x), x>1 \)


Which one of the following compound is both colored and paramagnetic?
A. \( S c C l_{3} \)
в. \( T i C l_{4} \)
\( \mathbf{c} \cdot C r C l_{3} \)
D. \( C u C l \)


A family has three children. Event \( A \) is
that family has at most one boy, Event
\( B^{\prime} \) is that family has at least one boy
and one girl, Event \( ^{\prime} C^{\prime} \) is that the family has at most one girl. Find whether
events \( ^{\prime} A^{\prime} \) and \( ^{\prime} B^{\prime} \) are independent. Also find whether \( A, B, C \) are independent or
not


Which is inert gas?
\( A \cdot 1 \)
B. 2
\( c \cdot 3 \)
D. 4


\( \left[\boldsymbol{F} \boldsymbol{e}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right]^{2+} \) and \( \left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{6}\right]^{4-} \) differ
in
A. Geometry, magnetic moment.
B. Geometry, hybridization
c. Magnetic moment, colour
D. Hybridization, number of d-electrons.


A vehicle is moving with a speed \( v \) on a
curved smooth road of width \( b \) and
radius \( R \) For counteracting the centrifugal force on the vehicle, the difference in elevation required in
between the outer and inner edges of
the road is
A \( \cdot \frac{v^{2} b}{R g} \)
в. \( \frac{v b}{R g} \)
\( c \)
\( D \)


The formal charge of the \( O \) atoms in the
ion is:
\[
[\because 0=N=0:]^{+}
\]
A . -2
B. -
\( c \)
D. +1


In the study of Geiger-Marsdon
experiment on scattering of \( \boldsymbol{\alpha} \) particles by a this foil of gold, draw the
trajectory of \( \boldsymbol{\alpha}- \) particles in the
coulomb field of target nucleus. Explain briefly how one gets the information on the size of the nucleus from this study:
From the relation \( \boldsymbol{R}=\boldsymbol{R}_{0} \boldsymbol{A}^{1 / 3}, \) where \( \boldsymbol{R}_{0} \)
is constant and \( A \) is the mass number
of the nucleus, show that nuclear matter density is independently of \( A \)


Let \( n_{p} \) and \( n_{e} \) the number of holes and
conduction electrons in an intrinsic
semiconductor. Then:
A \( \cdot n_{p}>n_{e} \)
в. \( n_{p}=n_{e} \)
c. \( n_{p}<n_{e} \)
D \( \cdot n_{p} \neq n_{e} \)


A cannon, shell is fired to hit a target at
a horizontal distance \( \boldsymbol{R} \). However, it
breaks into two equal parts at its highest point. One part (A) returns to the cannon. The other part:
This question has multiple correct options
A. will fall at a distance of \( R \) beyond the target
B. will fall at a distance of \( 3 R \) beyond the target
c. will hit the target
D. have nine times the kinetic energy of \( A \)


When a body is at a depth 'd' from the earth surface its distance from the
centre of the earth is
A \( \cdot(R-d) \)
В. \( 2(R-d) \)
c. \( (3 R-d) \)
D. \( (R-2 d) \)


Does photorespiration release energy?


The points \( P, Q, R, S, T, U, A \) and \( B \) on
the number line are such that, \( \boldsymbol{T} \boldsymbol{R}= \)
\( \boldsymbol{R S}=\boldsymbol{S U} \) and \( \boldsymbol{A P}=\boldsymbol{P Q}=\boldsymbol{Q B} . \) Name
the rational numbers represented by
\( P, Q, R \) and \( S \)
\( ^{\mathbf{A}} \cdot P=\frac{8}{3}, Q=\frac{7}{3}, R=\frac{-4}{3}, S=\frac{-5}{3} \)
B. \( P=\frac{7}{3}, Q=\frac{7}{3}, R=\frac{-5}{3}, S=\frac{-4}{3} \)
\( ^{\mathrm{C}} P=\frac{7}{3}, Q=\frac{8}{3}, R=\frac{-4}{3}, S=\frac{-5}{3} \)
D. \( \quad P=\frac{8}{3}, Q=\frac{7}{3}, R=\frac{-5}{3}, S=\frac{-4}{3} \)


Define the term and give one example
Coelom


Which is incorrect statement?
A. There are no mesodermal cells in pseudocoelomates
B. There is no body cavity in first triploblastic animals
C. There is no second opening in diploblastic animal gut
D. There is no co-ordination between cells of sponges.


Silkworm is a
A. Beetle
B. Butterfly
c. Fly
D. Larva


A current carrying loop is placed in a uniform magnetic field in four different
orientations I, II, III and IV as shown in
figure. Arrange them in decreasing order of potential energy.
\( A \cdot|>|||>||>\mid V \)
B. |> || > ||| > IV
c. ।>IV> || > ||


In sugarcane, length of internodes is variable due to
A. Intercalary meristem
B. Shoot apical meristem
c. Size of lamina of lower node
D. Position of axillary buds


Let \( \boldsymbol{A}=\{\mathbf{1}, \mathbf{2}\} \) and \( \boldsymbol{B}=\{\mathbf{2}, \mathbf{3}, \mathbf{4}\}, \) then
\( \boldsymbol{A} \times \boldsymbol{B}= \)
\{(1,2),(1,3),(1,4),(2,2),(2,3),(2,4)\}
If true enter 1 , or else enter 0 .


Consider the spectral line resulting from the transition \( n=2 \rightarrow n=1 \) in
the atoms and ions given below. The shortest wavelength is produced by
A. hydrogen atom
B. deuterium atom
c. singly ionized Helium
D. doubly ionised Lithium


The terminal velocity of a liquid drop of radius \( r \) falling through air is \( v \). If two such drops are combined to form a bigger drop, the terminal velocity with which the bigger drop falls through air is (lğnore any buoyant force due to air):
A \( \cdot \sqrt{2} v \)
B . \( 2 v \)
\( c \cdot \sqrt[3]{4 v} \)
D. \( \sqrt[3]{2} v \)


Solve the inequalities for real \( x \)
\( 3(2-x) \geq 2(1-x) \)


Which one is more basic,
\( \boldsymbol{C H}_{3} \boldsymbol{N} \boldsymbol{H}_{2} \boldsymbol{o r} \boldsymbol{C F}_{3} \boldsymbol{N H}_{2} \)
\( \mathbf{A} \cdot C H_{3} N H_{2} \)
В \( \cdot C F_{3} N H_{2} \)
c. Both have similar basicity
D. None of the above


An element with \( Z=46 \) belongs to :
A. 9 group
B. 10 group
c. 11 group
D. 12 group


State TRUE or FALSE
In a triangle \( A B C, \) right-angled at \( B, B D \) is drawn perpendicular to AC. hence,
\( \mathrm{CDB}=\angle \mathrm{A} \)
A. True
B. False


Which of the following pairs are
analogous?

This question has multiple correct options
A. Energy and power
B. Gravitational potential energy and electric potential energy
C. Electric field and gravitational field
D. None of the above


The beautiful natural phenomenon of
the rainbow is a combination of which
of the following different phenomena?
A. Refraction, reflection
B. Dispersion, refraction
c. Refraction, dispersion, reflection
D. Reflection, dispersion


The straight line \( A B \) is divided at \( C \) so that \( A C=3 C B . \) Circles are described
on \( A C \) and \( C B \) as diameters and a
common tangent meets AB produced at
D. Then \( B D \) equals.
A. the diameter of the smaller circle
B. the radius of the smaller circle
c. the radius of the larger circle
D. \( \overline{C B} \sqrt{3} \)
E. the difference of the two radi


Example of an aromatic ether islare:
\( A \)
Anisole
B.
\( c \)
D. All of these


A steel ball is dropped in a viscous
liquid. The distance of the steel ball
from the top of the liquid is shown
below. The terminal velocity of the ball
is closest to:
\( \mathbf{A} \cdot 0.26 m / s \)
B. \( 0.33 \mathrm{m} / \mathrm{s} \)
\( \mathrm{c} \cdot 0.45 \mathrm{m} / \mathrm{s} \)
D. \( 0.21 \mathrm{m} / \mathrm{s} \)


If \( A \) is a square matrix of order 3
then \( \left|\mathbf{A} \mathbf{d} \mathbf{j}\left(A d j A^{2}\right)\right|= \)
\( \mathbf{A} \cdot|A|^{2} \)
B . \( |A|^{4} \)
c. \( \left.|A|^{8}\right|^{8} \mid \)
D. \( |A|^{16} \)


Find the value(s) of the parameter'a' (a
9) for each of which the area of the
figure bounded by the straight line \( y= \) \( \frac{a^{2}-a x}{1+a^{4}} \& \) the parabola \( y= \)
\( \frac{x^{2}+2 a x+3 a^{2}}{1+a^{4}} \) is the greatest
A \( \cdot a=2^{1 / 4} \)
В . \( a=5^{1 / 4} \)
c. \( a=7^{1 / 4} \)


In what respect does a wire carrying a current differ from a wire, which carries
no current?


How is Teflon prepared? Give chemical
equation?


The hysteresis cycle for the material of a transformer core is:
A. short and wide
B. tall and narrow.
c. tall and wide
D. short and narrow


Identify the compound \( \boldsymbol{A} \)
\( \mathbf{A} \cdot C_{6} H_{5} O H \)
B \( \cdot C_{6} H_{5} C O C H_{3} \)
\( \mathbf{c} \cdot C_{6} H_{5} C l \)
\( \mathbf{D} \cdot C_{6} H_{5} C H O \)


\( E^{o} \) values for the half cell reactions are
given:
\( \boldsymbol{C u}^{2+}+\boldsymbol{e}^{-} \rightarrow \boldsymbol{C u}^{+} ; \boldsymbol{E}^{o}=\mathbf{0 . 1 5 V} \)
\( \boldsymbol{C u}^{2+}+\mathbf{2} e^{-} \rightarrow \boldsymbol{C u} ; \boldsymbol{E}^{o}=\mathbf{0 . 3 4} \mathbf{v} \)
What will be the \( E^{o} \) of the half-cell:
\( \boldsymbol{C u}^{+}+\boldsymbol{e}^{-} \rightarrow \boldsymbol{C u} ? \)
A . \( +0.49 v \)
в. \( +0.19 v \)
\( c .+0.53 v \)
D. \( +0.30 v \)


A Force \( F \) is put on a test charge \( Q \) by an electric field. What is the strength of the electric field at that location?
A \( \cdot \frac{Q}{F} \)
в. \( \frac{F}{Q} \)
c. \( F Q \)
D. \( F Q^{2} \)


The magnetic moment of a transition metal ion is \( \sqrt{15} B M . \) Therefore, the number of unpaired electrons present in it is:
A . 4
B.
\( c \cdot 2 \)
D. 3


Calculate the means free path of
nitrogen molecule at \( 27^{\circ} \mathrm{C} \) when pressure is 1.0 atm. Given, diameter of nitrogen molecule \( =1.5 \stackrel{o}{A}, k_{B}= \)
\( 1.38 \times 10^{-23} J K^{-1} . \) If the average speed
of nitrogen molecule is \( 675 m s^{-1} \). The time taken by the molecule between two successive collisions is?
A. 0.6 ns
B. \( 0.4 \mathrm{ns} \)
c. \( 0.8 \mathrm{ns} \)
D. 0.3 ns


Find the value of \( \lim _{x \rightarrow 0} \frac{\sin 2 x}{2 x^{2}+x} \)


Find the degree of association when 1.0 gram benzoic acid, dissolved in 25
gram benzene is having depression in
freezing point \( 0.81 k . \) The mola
depression constant for solvent is \( 4.9 K \) kg mole \( ^{-1} \)


Find the fractional decrement of its
volume
A \( \cdot \frac{\Delta V}{V}=-\frac{3 p}{E}(1-2 \mu) \)
B. \( \frac{\Delta V}{V}=-\frac{3 p}{E}(1+2 \mu) \)
c. \( \frac{\Delta V}{V}=\frac{2 p}{E}(1+3 \mu) \)
D. None of these


The conductance of a solution of an
electrolyte is equal to that of its specific conductance. The cell constant of the
conductivity cell is equal to
A. Resistance
B. Faraday
c. zero
D. Unity


Two \( 2 \Omega \) resistances are connected in
parallel in circuit \( X \) and in series in
circuit Y. The batteries in the two
circuits are identical and have zero
internal resistance. Assume that the
energy transferred to resistor A in
circuit \( X \) within a certain time is \( W \). The
energy transferred to resistor \( \mathrm{B} \) in
circuit \( Y \) in the same time will be:
A \( \cdot \frac{1}{4} w \)
B. \( \frac{1}{2} w \)
c. \( 2 w \)
D. \( 4 \mathrm{w} \)


Distinguish between roles of flocs and anaerobic sludge digesters in sewage treatments.


Three waves are given below.
Sound waves
Il. Visible light waves
III. X-rays
Which of the above waves cannot be
polarised?
A. I only
B. III only
c. I and II only
D. I and III only
E. I, II and III


\( \sin 36^{\circ} \sin 72^{\circ} \sin 108^{\circ} \sin 144^{\circ}= \)
\( A \cdot 1 / 4 \)
B. 1/16
\( c \cdot 3 / 4 \)
D. 5/16


The area of a parallelogram is \( y c m^{2} \) and its height is \( h \) cm. The base of
another parallelogram is \( x \) cm more
than the base of the first parallelogram
and its area is twice the area of the first.
Find, in terms of \( y, h \) and \( x, \) the expression for the height of the
second parallelogram.
A \( \cdot \frac{2 h y}{y+x h} c m \)
B. \( \frac{2 h y}{x+x h} \) cm
c. \( \frac{2 y}{y+x h} c m \)
D. None of these


If 5 of a company's 10 delivery trucks do not meet emission standard and 3 of
them are chosen for inspection, then what is the probability that none of the trucks chosen will meet emission
standards ?
A \( \cdot \frac{1}{8} \)
в. \( \frac{3}{8} \)
c. \( \frac{1}{12} \)
D.


Actinides belong to which period?
A .4
B. 5
\( c .6 \)
D.


The angular momentum of electron can have the value(s):
This question has multiple correct options
A \( \cdot_{0.5} \frac{h}{\pi} \)
в. \( \frac{h}{\pi} \)
c. \( \frac{h}{0.5 \pi} \)
D. \( 2.5 \frac{h}{2 \pi} \)


Coefficients of variation of two
distributions are 50 and 60 and their
arithmetic mean are 30 and 25
respectively. Difference of their standard deviation is
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c .1 .5 \)
D. 2.5


A gaseous compound of nitrogen and
hydrogen contains \( 12.5 \% \) (by mass) of hydrogen. The density of the compound relative to hydrogen is 16. The molecular formula of the compound is:
A \( . N H_{3} \)
в. \( N_{2} H_{4} \)
c. \( N_{3} H \)
D. \( N H_{2} \)


Two bodies \( A \) and \( B \) have masses \( 20 k g \)
and \( 5 ~ k g \) respectively. Each one is acted
upon by a force of 4 kg wt. If they acquire the same kinetic energy in times \( t_{A} \) and \( t_{B}, \) then the ratio \( \frac{t_{A}}{t_{B}} \) is:
A \( \cdot \frac{1}{2} \)
B. 2
\( c \cdot \frac{2}{5} \)
D. \( \frac{5}{6} \)


An acidic buffer solution can be
prepared by mixing solution of
A. sodium acetate and acetic acid
B. ammonium chloride and ammonium hydroxide
C. sulphuric acid and sodium sulphate
D. sodium chloride and sodium hydroxide


Match the column


\( \left|\begin{array}{ccc}\boldsymbol{x}_{1} & \boldsymbol{y}_{1} & \mathbf{1} \\ \boldsymbol{x}_{2} & \boldsymbol{y}_{2} & \mathbf{1} \\ \boldsymbol{x}_{3} & \boldsymbol{y}_{3} & 1\end{array}\right|=\left|\begin{array}{ccc}\mathbf{1} & \mathbf{1} & \mathbf{1} \\ \boldsymbol{b}_{1} & \boldsymbol{b}_{2} & \boldsymbol{b}_{3} \\ \boldsymbol{a}_{1} & \boldsymbol{a}_{2} & \boldsymbol{a}_{3}\end{array}\right| \) then the
two triangles whose vertices are
\( \left(x_{1}, y_{1}\right),\left(x_{2}, y_{2}\right),\left(\left(x_{3}, y_{3}\right) \) and \right.
\( \left(a_{1}, b_{1}\right),\left(a_{2}, b_{2}\right),\left(a_{13}, b_{3}\right), \) are
A . congruent
B. similar
c. equal in area
D. none of these


Pure chloroform does not give a white
ppt with \( \boldsymbol{A} \boldsymbol{g} \boldsymbol{N} \boldsymbol{O}_{3} \) as:
A. It does not ionise to give chloride ion.
B. It forms a soluble complex.
c. It is immiscible with the solution.
D. \( A g N O_{3} \) solution is weak in conc.


Effervescence is seen when a bottle of
soda water is opened
A. True
B. False


The existence of intermolecular forces
is supported by the facts:
A. Non ideality of real gases
B. Liquefaction of gases
c. Both (a) and (b)
D. None of these


On commercial scale, phenol is
obtained from chlorobenzene. The
chlorobenzene needed for the purpose is prepared by:
\( A \)
\( \bigcirc]+\mathrm{cl}_{2} \frac{\mathrm{Anhy} \cdot \mathrm{AlCl}_{3}}{310-320 \mathrm{K}} \)
B.
\( c \)
\( \bigcirc]+\mathrm{H} \mathrm{c} \mathrm{t}+\mathrm{o}_{2(\mathrm{air})} \frac{\mathrm{cuc}_{2}}{500 \mathrm{K}}>\widehat{\bigcirc} \)


The specific latent heat of fusion of ice
is:
A \( \cdot 4.2 J g^{-1} 0 C^{-1} \)
B. 4200 Jkg \( ^{-10} C^{-1} \)
c. з36 \( J g^{-1} \)
D. 336,000 Jg \( ^{-1} \)


Which of the following pair of solutions
can we expect to be isotonic at the same temperature?
A . \( 0.1 \mathrm{M} \) NaCl and \( 0.1 \mathrm{M} \mathrm{Na}_{2} \mathrm{SO}_{4} \)
B. 0.1 M urea and 0.1 M Nacı
c. 0.1 M urea and 0.2 M \( M g C l_{2} \)
D. \( 0.1 \mathrm{M} \mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2} \) and \( 0.1 \mathrm{M} \mathrm{Na}_{2} \mathrm{SO}_{4} \)


Two charges each q nC. are placed at two vertices of an equilaterial triangle of side \( 1 \mathrm{m} \). The filed at the other vertex
is
A \( \cdot \sqrt{2} q \)
B. \( 9 \sqrt{3} q \)
c. \( \frac{\sqrt{3} q}{10} \)
D. \( \frac{9 q}{\sqrt{3}} \)


Which of the following reactions involves the combination of two
elements?
A. \( C a O+C O_{2} \rightarrow C a C O_{3} \)
в. \( 4 N a+O_{2} \rightarrow 2 N a_{2} O \)
\( \mathrm{c} \cdot \mathrm{SO}_{2}+\frac{1}{2} \mathrm{O}_{2} \rightarrow \mathrm{SO}_{3} \)
D. \( N H_{3}+H C l \rightarrow N H_{4} C l \)


To convert \( _{90} T h^{232} \) into \( _{90} T h^{228}, \) the least
number of \( \alpha \) and \( \beta \) particles that have
to be emitted are
respectively.
\( A \cdot 1,1 \)
B. 2,
\( c \cdot 1,2 \)
D. 2, 2


Six persons are situated at the corners
of a hexagon of side \( l \). They move at a
constant speed \( v . \) Each person
maintains a direction towards the
person at the next corner. When will the
persons meet?
A.
в. \( \frac{2 l}{3 v} \)
c. \( \frac{3 l}{2 v} \)
D. \( \frac{2 l}{v} \)


Concentration of urine is controlled by
A. Vasopressin
B. Aldosterone
c. Insulin
D. Adrenaline


A ball which is thrown vertically upwards reaches the roof of a house
100 \( m \) high. At the moment this ball is
thrown vertically upward, another ball is dropped from rest vertically downwards from the roof of the house. At which
height will the balls pass each other?
\( \left(g=9.8 m / s^{2}\right) \)


The mean of five observations is 4.4 and
the variance is \( 8.24 . \) Three of the five
observations are 1,2 and \( 6 . \) The remaining two are
\( \mathbf{A} \cdot 9,4 \)
в. 7,6
c. 6,5
D. 10,3


toppr
Q Type your question_
\( 4+3 \cup+1 \)
木
b. \( \left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{C}=\boldsymbol{C H}_{2}+\boldsymbol{H C l} \rightarrow \)
\( \left(\boldsymbol{C H}_{3}\right)_{2}(\boldsymbol{C l}) \boldsymbol{C}-\boldsymbol{C H}_{3} \)
c. \( \left(\boldsymbol{C H}_{3}\right)_{3} \boldsymbol{C}-\boldsymbol{C H}_{2} \boldsymbol{O H}+\boldsymbol{H} \boldsymbol{B r} \rightarrow \)
\( \left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{C}(\boldsymbol{B r}) \boldsymbol{C H}_{2} \boldsymbol{C H}_{3} \)
d. \( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{B r}+\boldsymbol{H O}^{\ominus} \rightarrow \boldsymbol{C H}_{2}= \)
\( \boldsymbol{C H}_{2} \)
A. a.Nucleophilic substitution and 1, 2-Methyl shift
b. Nucleophilic substitution reaction
c. Elimination reaction
d. Addition reaction
B. a.Addition reaction
b. Nucleophilic substitution reaction
c. Elimination reaction
d. Nucleophilic substitution and 1, 2-Methyl shift
c. a. Nucleophilic substitution reaction
b. Addition reaction
c. Nucleophilic substitution and 1, 2-Methyl shift
d. Elimination reaction
D. a.Addition reaction
b. Nucleophilic substitution reaction
c. Nucleophilic substitution and 1, 2-Methyl shift
d. Elimination reaction


Say true or false.
Zero can be the common ratio of a G.P.
A . True
B. False


A black hole is an object whose
gravitational field is so strong that even light cannot escape from it. To what approximate radius would earth
\( \left(m a s s=5.98 \times 10^{24} k g\right) \) have to be
compressed to be a black hole?
\( A \cdot 10^{-9} m \)
B. \( 10^{-6} \mathrm{m} \)
\( c \cdot 10^{-2} m \)
D. \( 100 m \)


In the figure, the value of \( x \)
\( A \cdot 40 \)
B. 70
\( c \cdot 110^{\circ} \)
D. 130


The ratio of velocities acquired by a freely falling body starting from rest at the end of 1 second and 2 seconds is?


thickness as shown in figure. One is made pf material \( \boldsymbol{A} \) of refractive index
1.5. The other is made of two materials
\( B \) and \( C \) with thickness in the ratio 1: 2
The refractive index of \( C \) is \( 1.6 . \) If a
monochromatic parallel beam passing
through the slabs has the same number of wavelengths inside both, the
refractive index of \( \boldsymbol{B} \) is
\( \mathbf{A} \cdot 1.1 \)
B. 1.2
c. 1.3
D . 1.4.


Differentiate the following function with
respect to \( x \)
\( x^{3} \sin x \)


Find the square roots of the given number by Prime factorization method: 441


A body of mass \( 3 \mathrm{kg} \) is under a force, which causes a displacement in it given by \( S=\frac{t^{3}}{3}(\text { in } \mathrm{m}) . \) Find the work
done by the force in first 2 seconds
A . 24
B. 3.83
c. 5.2 J
D . 2.6


Which of the following does not react with acids?
A. Sodium
B. Oxygen
c. Calcium
D. Aluminium


Light reflecting from surface of sea rocks is an example of
A. Regular reflection
B. Diffused reflection
c. Total internal reflection
D. None of these


The circuit has two oppositely
connected ideal diodes in parallel. The
current flowing in the circuit is
A . \( 1.71 A \)
B. \( 2.00 A \)
c. \( 2.31 A \)
D. \( 1.33 A \)


An aqueous solution contains \( 0.01 M \)
\( \boldsymbol{R} \boldsymbol{N} \boldsymbol{H}_{2}\left(\boldsymbol{K}_{\boldsymbol{b}}=\boldsymbol{2} \times \mathbf{1 0}^{-\boldsymbol{6}}\right) \) and
\( 10^{-4} M \) NaOH.The concentration of
\( \boldsymbol{O H}^{-} \) is nearly:
A. \( 2.414 \times 10^{-4} \)
В \( \cdot 10^{-4} M \)
c. \( 1.414 \times 10^{-4} \)
D. \( 2 \times 10^{-4} \)


Find the square root of \( \left(\boldsymbol{x}+\frac{1}{\boldsymbol{x}}\right)^{2} \)
\( 4\left(x-\frac{1}{x}\right) \)


Solve the differential equation:
\( \sec ^{2} y \frac{d y}{d x}+\tan y=x^{3} \)
A \( \cdot \tan y=x^{3}+3 x^{2}+6 x-6+c e^{-x} \)
B . \( \tan y=x^{3}-3 x^{2}-6 x-6+c e^{-x} \)
C. \( \tan y=x^{3}-3 x^{2}+6 x-6+c e^{-x} \)
D. None of these.


Magnetic field in a region is given by \( \vec{B}=B_{o} x \hat{k} . \) Two loops each of side a is
placed in this magnetic region in the \( x \) y plane with one of its sides on x-axis. If
\( F_{1} \) is the force on loop 1 and \( F_{2} \) be the
force on loop 2 then:
A \( . F_{1}=F_{2}=0 \)
B. \( F_{1}>\left\{F_{3},\{2\} \$ \$\right. \)
\( \mathbf{c} \cdot F_{2}>F_{1} \)
D. \( F_{1}=F_{2} \neq 0 \)


Phenol is used as a disinfectant
If this is true enter \( 1, \) if false enter 0 .


Match the Column-I with Column-II:
ColumnColumn-I (Process)
(a) \( \mathrm{Ni} \)
(p) Cracking of hydrocarbons
(b) \( A C l_{3} \)
(q) Fischer- - Tropsch process
(с) \( C o / A l_{2} O_{3} \)
(r) Hydrogenation of oil
(d) Zeolite
(s) Friedel-Crafts reaction


Find the exterior angle.
A . \( 31^{\circ} \)
B. \( 32^{\circ} \)
\( \mathbf{c} \cdot 33^{\circ} \)
D. 34


If \( \vec{a}=\hat{i}+2 \hat{j}+\hat{k}, \vec{b}=2 \hat{i}+\hat{j} \) and \( \vec{c}= \)
\( \mathbf{3} \hat{\mathbf{i}}-\mathbf{4} \hat{\mathbf{j}}-\mathbf{5} \hat{k}, \) then find a unit vector
perpendicular to both of the vectors \( (\vec{a}-\vec{b}) \) and \( (\vec{c}-\vec{b}) \)


Which of the following principles has been followed to propagate light waves through an optical fibre?
A. Difraction
B. Interference
c. Total internal reflection
D. Scattering


The mass of an electron is \( 9.1 \times 10^{-31} \mathrm{kg} \)
If its kinetic energy is \( 3.0 \times 10^{-25} \mathrm{J} \)
calculate its wave length.


A well is dug in a bed of rock containing
fluorspar \( \left(C a F_{2}\right) . \) If the well contains \( 20000 \mathrm{L} \) of water, what is the amount of
\( \boldsymbol{F}^{-} \) in it \( ?\left(\boldsymbol{K}_{s p}=\boldsymbol{4} \times \mathbf{1 0}^{-11}\right) \)
A . 4.2 mol
B . 13.6 mol
c. 8.6 mol
D. 10 mol


Find the coordinates of the point \( \boldsymbol{P} \) where the line through \( \boldsymbol{A}(\mathbf{3},-\mathbf{4},-\mathbf{5}) \)
and \( B(2,-3,1) \) crosses the plane
passing through three points \( \boldsymbol{L}(\mathbf{2}, \mathbf{2}, \mathbf{1}), \boldsymbol{M}(\mathbf{3}, \mathbf{0}, \mathbf{1}) \) and \( \boldsymbol{N}(\mathbf{4},-\mathbf{1}, \mathbf{0}) \)
Also, find the ratio in which \( P \) divides
the line segment \( \boldsymbol{A B} \)


Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \)
\( \boldsymbol{y}=-\boldsymbol{x}^{\mathbf{3}}+\boldsymbol{x} \)


The pair of species with similar shape
is :
A \( \cdot P C l_{3}, N H_{3} \)
B \( \cdot C F_{4}, S F_{4} \)
c. \( P b C l_{2}, C O_{2} \)
D \( \cdot P F_{5}, I F_{5} \)


Which of the following molecule does not have a linear arrangement of
atoms?
A \( . H_{2} S \)
в. \( C_{2} H_{2} \)
\( \mathbf{c} \cdot B e H_{2} \)
D. \( C O_{2} \)


Complete the following statements:
a) Two line segments are congruent if
b) Among two congruent angles, one
has measure of \( 70^{0} \), the measure of the
other angle is
c) When we write \( \angle A=\angle B \), we actually
mean..


If the shortest wavelength of the continuous X-ray spectrum coming out of a Coolidge tube is \( 0.01 n m \), then the de Broglie wavelength of the electron reaching the target metal in the Coolidge tube is approximately \( \left(h c=12400 e V A, h=6.63 \times 10^{-34} \) in \right.
MKS, mass of electron= \( 9.1 \times \)
\( \left.10^{-31} k g\right) \)
A . 0.35
в. 0.035
\( c .35 \)
D. 1350


Let \( A B C \) be a triangle with \( A B=A C \)
and \( D \) is mid-point of \( B C, E \) is the foot of perpendicular drawn from \( D \) to \( A C \) and \( F \) the mid point of \( D E . \) Angle
between the line \( A F \) and \( B E \) is \( \theta \). Then
the value of \( 4 \sin \theta \) is
A .4
B. 3
c. \( \frac{3}{2} \)
D. \( \frac{4}{3} \)


\( (A) \)
(i) Opening and closing of Scotoactive
stomata photoactive stomata
(B) Guttation
(ii) Transpiration
(C)Tensile
(iii) Water loss in liquid phase strength
(D) \( \mathrm{K}^{+} \) pump
(iv) Night transpiration theory
Match the above columns and choose the
correct combination.
\( A \cdot A-(i v), B-(i i i), C-(i i), D-(i) \)
B. \( A-(\text { iv }), B-(i), C-(i i), D-(i i i) \)
C \( . A- \) (iii), B- (iv), C- (i), D- (ii)
D. A- (iii), B- (i), C- (iv), D- (ii)


A student prepared solutions of (i) an acid and (ii) a base in two separate beakers. She forgot to label the solutions and litmus paper is not available in the laboratory. since both the solutions are colourless, how will
she distinguish between the two?
A. Use of china rose
B. Use of turmeric
c. use of phenolphthalein
D. All of the above


A student wishes to demonstrate
electromagnetic induction. He has a magnet and connecting wires.
Which other apparatus does he need? \( \boldsymbol{\gamma}=\boldsymbol{n e e d e d}, \quad \boldsymbol{X}=\boldsymbol{n o t n e e d e d} \)
A. Voltmeter - \( \gamma \), battery -
B. Voltmeter - , battery - \( X \)
c. voltmeter - \( X \), battery -
D. voltmeter - \( X \), battery \( -X \)


At a given temperature the rate constant for the decomposition of HI on
a metal surface is \( 0.06 M s^{-1}, \) i.e.
\( \mathbf{2} \boldsymbol{H} \boldsymbol{I} \rightarrow \boldsymbol{H}_{2(g)}+\boldsymbol{I}_{2(g)} . \) The time taken
for the concentration of HI to fall from
\( 1.50 \mathrm{M} 0.30 \mathrm{M} \) is :
A . 10 s
B. 5 s
c. 25 s
\( D \cdot 8 s \)


If \( P(n o t A)=0.7, P(B)=0.7 \) and
\( P(B / A)=0.5, \) find \( P(A \bigcup B) \)


The least positive value of \( x \) satisfying \( \frac{\sin ^{2} 2 x+4 \sin ^{4} x-4 \sin ^{2} x \cos ^{2} x}{4-\sin ^{2} 2 x-4 \sin ^{2} x}=\frac{1}{9} \)
is
A \( \cdot \frac{\pi}{3} \)
B. \( \frac{\pi}{6} \)
c. \( \frac{2 \pi}{3} \)
D. \( \frac{5 \pi}{6} \)


A charged ball of mass ' \( m \) ' and positive
charge ' \( q^{\prime} \) is projected from the ground with an initial velocity \( u \) and angle of
projection \( \theta . \) At the time of projection, a vertically upward electric field is present. It is then switched off at
maximum height and a horizontal electric field of same magnitude \( \boldsymbol{E} \) is switched on in the direction of velocity. (Assume \( m g>q E) \)
Then the maximum height \( h_{m a x} \)
reached by the projectile is :
\( ^{\text {A }} \cdot \frac{u^{2} \sin ^{2} \theta}{2 g} \)
\( ^{\mathrm{B}} \frac{u^{2} \sin ^{2} \theta}{2\left(g-\frac{q E}{M}\right)} \)
c. \( \frac{u^{2} \sin ^{2} \theta}{2\left(g+\frac{q E}{M}\right)} \)
D. \( \frac{u^{2} \sin ^{2} \theta}{2\left(\frac{q E}{M}-g\right)} \)


The slag obtained during the extraction of copper from copper pyrites is composed of
A. \( C u_{2} S \)
в. \( C u S i O_{3} \)
c. \( F e S i O_{3} \)
D. \( \operatorname{si} 0_{2} \)


is the removal of oxygen
for extraction of metal from ore.
A. Reduction
B. Electrolysis
c. oxidation
D. Distillation


Light is incident normally on a diffraction grating through which the
first order diffraction is seen at \( 32^{\circ} . \) The
second order diffraction will be seen at
\( A \cdot 48^{\circ} \)
B. 64
\( c \cdot 80 \)
D. there is no second order diffraction in this case


Fill in the blanks.
Plastic sulphur is of
\( \boldsymbol{S}_{8} \) molecule


A flywheel rotates at a constant speed
of 3000 rpm. The angle described by the
shaft in radian in one second is:
\( \mathbf{A} \cdot 3000 \pi \)
в. \( 100 \pi \)
\( c .50 \pi \)
D. \( 2 \pi \)


A plant that has both autotrophic and heterotrophic mode of nutrition.


Carbon and oxygen react to produce
carbon dioxide. What is the weight of
oxygen required to convert \( 1.5 g \) of
carbon to carbon dioxide?
A \( .2 g \)
B. \( 6 g \)
c. \( 1 g \)
D. \( 4 g \)


Write the following in decimal form and say what kind of decimal expansions
has:
\( \frac{2}{11} \)


The position of a particle at time \( t \) is given by the relation \( \boldsymbol{x}=\frac{\boldsymbol{v}_{0}}{\boldsymbol{\alpha}}\left(\mathbf{1}-\boldsymbol{e}^{-\boldsymbol{\alpha} t}\right) \)
The dimensional formula for \( \boldsymbol{\alpha}^{2} \boldsymbol{v}_{0}^{3} \) will
be :


Proteinaceous infectious particles
causing diseases are
A. Prions
B. Viroids
c. Viruses
D. chlamydia


\( \boldsymbol{y}=\sin \left(\boldsymbol{\pi} / \boldsymbol{6} e^{x y}\right) \) putting \( \boldsymbol{x}=\mathbf{0} \operatorname{than} \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \)


\( (2 x+3 y)^{5} \)


In an ellipse, the distance between its focii is 6 and minor axis is \( 8 . \) Then its'
eccentricity is
A \( \cdot \frac{3}{5} \)
B. \( \frac{1}{2} \)
\( c \cdot \frac{4}{5} \)
D. \( \frac{1}{\sqrt{5}} \)


Give the IUPAC name of the following compounds:
\[
\begin{array}{r}
\mathrm{CH}_{3}-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\mathrm{CH}_{3} \\
\mathrm{CH}_{3}-\mathrm{CH}_{2}-\mathrm{CH}-\mathrm{CH}-\mathrm{CH}_{3}
\end{array}
\]


In peritoneal dialysis, the blood is
A. Not removed from the body and and artificial filter is used
B. Removed from the body and an artificial filter is employed
C. Removed from the body and a natural filter is employed
D. Not removed from the body and a natural filter is used


Which of the following is not a typical property of an ionic compound?
A. High melting point.
B. Conducts electricity in the molten and in the aqueous solution state.
C. They are insoluble in water
D. They exist as oppositely charged ions even in the solid state


A line makes an angle \( \theta \) with each of the
\( x- \) and \( z^{-} \) axes. If the angle \( \beta, \) which it makes with the \( y \) -axis, is such that
\( \sin ^{2} \beta=3 \sin ^{2} \theta, \) then \( \cos ^{2} \theta \) equals-
A \( \cdot \frac{2}{3} \)
B. \( \frac{1}{5} \)
\( c \cdot \frac{3}{5} \)
D. \( \frac{2}{5} \)


Which of the following is not an example of a series?
A \( .1,2,3,4,5,6, \dots \)
в. \( -2,0,2,4,6,8, \ldots \)
c. \( 1,1,2,3,5,8, . . \)
D. None of the above


Which of the following scientists did the pioneering work to understand the splitting of white light in different components?
A. Thomas Edison
B. Albert Einstein
c. Issac Newton
D. Archimedes


\( A B C \) is a triangle. \( D \) is a point on \( A B \) such that \( A D=\frac{1}{4} A B \) and \( E \) is a point
on \( A C \) such that \( A E=\frac{1}{4} A C . \) Prove that \( D E=\frac{1}{4} B C \)


The direction of reversible reaction
spontaniety is always towards
equilibrium If true enter 1 , if false enter 0 .


If \( a=0.1039, \) then the value of \( \sqrt{4 a^{2}-4 a+1}+3 a \) is:
A . 0.1039
B. 0.2078
c. 1.1039
D. 2.1039


Matter consist of particles such as
A . ions
B. molecules
c. atoms
D. All of the above


Conversion of esters to aldehydes can be accomplished by:
A. Stephen reduction
B. Rosenmund reduction
c. Reduction with lithium aluminium hydride
D. Reduction with diisobutyl aluminium hydride


The depressions and elevations present on the surface of objects causes
friction.
A. True
B. False


State two differences between "Heat
Capacity" and "Specific Heat Capacity"


Find the gain or loss percent if S.P.\( =R s .500 \) and loss. \( =R s .100 \)


Fill in the blank.
The distance between any two given points of a rigid body in
time regardless of external forces
exerted on it.
A. increases
B. remains constant
c. decrease
D. depend of the external force


In the adjacent circuit, \( A \) and \( B \) represent two inputs and \( C \) represents the output. The circuit represents.
A. NOR gate
B. AND gate
\( a \quad \) " \( \quad \) " gate
\( D \)


Ozone in stratosphere extends
\( \mathbf{A} \cdot 10-20 \mathrm{km} \)
B. 20-25km
c. \( 15-30 k m \)
D. 25-40km


Assertion
Optical fibres make use of total internal reflection
Reason
Light undergoes successive total internal reflections as it moves through
an optical fibre.
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


\( S-S \) bond is present in the acid
\( \boldsymbol{H}_{2} \boldsymbol{S}_{2} \boldsymbol{O}_{3}(\text { thiosulphuric acid }) \)
If true enter 1 , else enter 0 .


In a standard ECG, which one of the following alphabets is the correct representation of the respective of the human heart?
A. R - repolarisation of ventricles
B. S - start of systole
c. \( T \) -end of diastole
D. P - depolarization of the atria


If \( \frac{x}{y}=\frac{\cos A}{\cos B} \operatorname{then} \frac{x \tan A+y \tan B}{x+y}= \)
A. \( \cot \frac{A+B}{2} \)
B. \( \cot \frac{A-B}{2} \)
c. \( \tan \frac{A-B}{2} \)
D. \( \tan \frac{A+B}{2} \)


Define stream line, streak line, path line and give their differences


Formation of polyethylene from calcium carbide takes place as given
below:
\( \boldsymbol{C a C}_{2}+\mathbf{2 H}_{2} \boldsymbol{O} \rightarrow \boldsymbol{C a}(\boldsymbol{O H})_{2}+\boldsymbol{C}_{2} \boldsymbol{H}_{2} \)
\( \boldsymbol{C}_{2} \boldsymbol{H}_{2}+\boldsymbol{H}_{2} \rightarrow \boldsymbol{C}_{2} \boldsymbol{H}_{4} \)
\( \boldsymbol{n} \boldsymbol{C}_{2} \boldsymbol{H}_{4} \rightarrow\left(-\boldsymbol{C} \boldsymbol{H}_{2}-\boldsymbol{C} \boldsymbol{H}_{2}-\right)_{n} \)
The amount (in kg) of polyethylene
obtained from 64.1 kg of \( C a C_{2} \) is
A. 7
B. 14
c. 21
D. 28


Divide a line segment of length \( 9 \mathrm{cm} \)
internally in the ratio 4: 3


Q Type your question
red. Similarly if you look through a price of blue-tinted glass. Everything will be
seen in shades of blue.
Consider the following statements
I. The tinting process makes the glass absorb the corresponding colour, i.e. red tinted glass strongly absorbs red light, making ever thing appear red.
II. The tinting process makes the glass absorb all colours except the corresponding colour, i.e., red -tinted glass will strongly absorb blue and green, but not red
III. If you stack the red and blue-tinted pieces of glass and look through them, everything will look quite dark.
Which of these statements is/are true?
A . I and ॥
B. I and III
c. ॥ and III
D. Only I


If the equation of the plane passing
through the points (4,5,1),(3,9,4)
(-4,4,4) is \( a x+b y+c z=d \) then
\( a^{4}+b^{3}+c^{2}+d \) is equal to


If \( \boldsymbol{A}=\left(\left[\begin{array}{llll}1 & 2 & 3 & 4\end{array}\right] \text { and } A B=\left[\begin{array}{lll}3 & 4 & -1\end{array}\right]\right. \)
then the order of
matrix B is
\( A \cdot 2 \times 3 \)
B. 3x3
\( c \cdot 4 \times 3 \)
D. \( 1 \times 3 \)


Which of the following quantity does not change due to damping of oscillations?
A. Angular frequency
B. Time period
c. Initial phase
D. Amplitude


Two charged capacitors, have their outer plates fixed and inner plates connected by a spring of force constant
\( k^{\prime} . \) The charge on each capacitor is \( q \) Find the extension in the spring at equilibrium.
\( ^{A} \cdot \frac{q^{2}}{2 A \epsilon_{0} k} \)
в. \( \frac{q^{2}}{4 A \epsilon_{6} k} \)
c. \( \frac{q^{2}}{A \epsilon_{6} k} \)
D. Zero


From the diagram, what is the angle
between the incident ray and the
reflected ray?
A \( \cdot 40 \)
B \( .50^{\circ} \)
\( c \cdot 60 \)
D. \( 70^{\circ} \)


Construct a \( 2 \times 2 \) matrix \( A=\left[a_{i j}\right] \)
whose elements \( a_{i j} \) are given by:
\( \boldsymbol{a}_{\boldsymbol{i} j}=\left|\frac{\boldsymbol{3} \boldsymbol{i}-\boldsymbol{j}}{\boldsymbol{2}}\right| \)


Which of the following matrix is inverse of itself
A. \( \left[\begin{array}{lll}1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1\end{array}\right] \)
В. \( \left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right] \)
C. \( \left[\begin{array}{lll}1 & 0 & 1 \\ 0 & 0 & 0 \\ 1 & 0 & 1\end{array}\right] \)
D. \( \left[\begin{array}{lll}0 & 1 & 0 \\ 1 & 1 & 1 \\ 0 & 1 & 0\end{array}\right] \)


Which one of the following is a transparent tissue?
A. Tendon
B. Ligament
c. Fibrous cartilage
D. Hyaline cartilage


Two rods of same length and same area
of cross section are joined. Temperature
of two ends are as shown in figure. As
we move along the rod, temperature are as shown in following.
\( \mathbf{A} \cdot K_{1}>K_{2} \)
B \( . K_{1}=K_{2} \)
\( \mathbf{c} \cdot K_{1}<K_{2} \)
D. None of these


A straight line passes through (1,-2,3) and perpendicular to the plane \( 2 x+ \) \( 3 y-z=7 . \) Find the direction ratios of
normal to plane
\( A \cdot<2,3,-1> \)
В. \( <2,3,1> \)
c. \( <-1,2,3> \)
D. None of the above


A copper ball of mass \( 100 g m \) is at a
temperature \( T . \) It is dropped in a copper
calorimeter of mass \( 100 g m \), filled with
\( 170 g m \) of water at room temperature. Subsequently the temperature of the system is found to \( 6475^{\circ} . T \) is given by
then (Given: room temperature \( =\mathbf{3 0}^{\circ} \boldsymbol{C} \)
specific heat of copper \( = \) \( \mathbf{0 . 1} c \mathbf{a l} / \mathbf{g m}^{o} \boldsymbol{C} \)
A. \( 825^{\circ} \mathrm{C} \)
в. \( 800^{\circ} \mathrm{C} \)
c. \( 885^{\circ} \mathrm{C} \)
D. \( 1250^{\circ} \mathrm{C} \)


Prove that if the areas of two similar
triangle are equal, then the triangles
are congruent


The differential equation corresponding
to \( x y=c^{2}, \) where \( c \) is an arbitrary
constant, is:
A. \( x y^{\prime \prime}+x=0 \)
B . \( y^{\prime \prime}=0 \)
c. \( x y^{\prime}+y=0 \)
D. \( x y^{\prime \prime}-x=0 \)


State : True or False
The thermal capacity of a substance is
fixed quantity, but its specific heat capacity is a variable quantity.


A machine takes 2 litres of petrol to
start and then 3 litres per hour while running. What will the no. of hours for
which machine run if total 20 litres of
petrol is used?
A .4
B. 5
\( c \cdot 6 \)
D. 8


If the current passing through an electric bell is doubled, the heat produced will become
A. four times
B. double
c. one-fourth
D. half


If an electric field is given by \( 10 \hat{i}+ \) \( \mathbf{3} \hat{\boldsymbol{j}}+\mathbf{4} \hat{\boldsymbol{k}}, \) calculate the electric flux
through a surface of area 10 units lying in \( \boldsymbol{y} \boldsymbol{z} \) plane


\( \boldsymbol{C}_{\mathbf{1}}+\mathbf{2} \boldsymbol{C}_{\mathbf{2}}+\mathbf{3} \boldsymbol{C}_{\mathbf{3}}+\ldots \ldots+\boldsymbol{n} \boldsymbol{C}_{\boldsymbol{n}} \) is equal
to
A \( \cdot 2^{n-1} \)
B . \( 2^{n+1} \)
c. \( n .2^{n-1} \)
D \( \cdot n \cdot 2^{n+1} \)


The species that do not contain peroxide ion (s) is/are:
A. \( P b O_{2} \)
в. \( \operatorname{Sr} \mathrm{O}_{2} \)
c. \( N a_{2} O_{2} \)
D. \( B a O_{2} \)


\[
\begin{array}{rlr}
\text { If } \boldsymbol{f}(\boldsymbol{x}) & =\frac{\boldsymbol{x}^{2}-\mathbf{9}}{\boldsymbol{x}-\mathbf{3}}+\boldsymbol{\alpha}, \text { for } \boldsymbol{x}>\mathbf{3} \\
& =\mathbf{5}, & \text { for } \boldsymbol{x}=\mathbf{3} \\
& =\mathbf{2} \boldsymbol{x}^{2}+\mathbf{3} \boldsymbol{x}+\boldsymbol{\beta}, & \text { for } \boldsymbol{x}<\mathbf{3}
\end{array}
\]
is continuous at \( x=3, \) find \( \alpha \) and \( \beta \)


While connecting 6 cells in a battery in series, in a tape recorder, by mistake one cell is connected with reverse
polarity. If the effective resistance of load is 24 ohm and internal resistance
of each cell is one ohm and emf \( 1.5 V \)
the current delivered by the battery is
\( \mathbf{A} \cdot 0.1 A \)
B. \( 0.2 A \)
\( \mathbf{c} \cdot 0.3 A \)
D. \( 0.4 A \)


Identify \( \mathbf{A}: \)
\( \mathbf{A} \cdot K N O_{2} \)
\( \mathbf{B} \cdot K N O_{3} \)
\( \mathbf{c} \cdot A g N O_{3} \)
D. \( N a N O_{2} \)


Explain how a square is a rectangle.
Answer: A square is a parallelogram with each angle a right angle; so it is a rectangle.
A. True
B. False


Write down the four quantum number
for \( 8 t h \) electron of oxygen atom?
A \( \cdot n=2, l=1, m=+2 \) or \( -2, s=+\frac{1}{2} \) or \( -\frac{1}{2} \)
B. \( n=2, l=1, m=+1 \) or \( -1, s=+\frac{1}{2} \) or \( -\frac{1}{2} \)
c. \( n=2, l=1, m=0, s=+\frac{1}{2} \) or \( -\frac{1}{2} \)
D. \( n=2, l=0, m=0, s=+\frac{1}{2} \) or \( -\frac{1}{2} \)


The wave theory in its original form was first postulated by
A. Issac Newton
B. Thomas Young
c. christian Huygens
D. Augustine Jean Fresnel


What indication do we get by
reappearance of dwarf plant in \( F_{2} \)
generation?


The crystals of ferrous sulphate on
heating gives:
A \( . F e O+S O_{2}+H_{2} O \)
в. \( F e_{2} O_{3}+H_{2} S O_{4}+H_{2} O \)
\( \mathrm{c} \cdot F e_{2} O_{3}+S O_{2}+S O_{3} \)


In passing through a boundary,
refraction will not take place if
This question has multiple correct options
A. light is incident normally on the boundary
B. the indices of refraction of the two media are same
C. the boundary is not visible
D. angle of incidence is lesser than angle of refraction but greater than \( \sin ^{-1}\left(\frac{\mu_{R}}{\mu_{D}}\right) \)


What would be the minimum
uncertainty in de-Broglie wavelength of a moving electron accelerated by potential difference of 6 volt and whose uncertainty in position is \( \frac{7}{22} n m ? \)
A \( .6 .25 \AA \)
в. 6 А
c. 0.625 ,
D. \( 0.3125 \dot{A} \)


The surface of a black body is at a
temperature \( 727^{\circ} C \) and its cross
section in \( 1 m^{2} . \) Heat radiated from this
surface in one minute in Joules is
(Stefan's constant \( =\mathbf{5 . 7} \times \)
\( \left.\mathbf{1 0}^{-8} \boldsymbol{W} / \boldsymbol{m}^{2} \boldsymbol{k}^{4}\right) \)
A \( \cdot 34.2 \times 10^{5} \)
B . \( 2.5 \times 10^{5} \)
c. \( 3.42 \times 10^{5} \)
D. \( 2.5 \times 10^{6} \)


Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}, \) if \( \boldsymbol{2} \boldsymbol{x}+\boldsymbol{3} \boldsymbol{y}=\sin \boldsymbol{y} \)


Incisor teeth in mammals are primarily
for
A. Weapons or for killing prey
B. Grinding and chewing food
c. cutting and slicing food
D. All of these


The medians of a triangle meet at
(0,-3) and its two vertices are at (-1,4) and \( (5,2) . \) Then the third vertex
is
A. (4,15)
B. (-4,-15)
c. (-4,15)
D. (4,-15)


The chemical formula of tear gas is :
A \( \cdot \mathrm{COCl}_{2} \)
в. \( \mathrm{CO}_{2} \)
\( c \cdot \mathrm{Cl}_{2} \)
D. None of the above


Find the incorrect match.
A. Fine duct of aluminium - Paints and Lacquers
B. Reducing agent in the manufacture of dye-stuffs, paints, etc. - copper dust
C. For cutting tools and crushing machines - Chrome steel
D. For making cables, automobiles and aeroplane parts Nickel steel


Factorize the following polynomial \( 4 x^{2}+12 x+9 \)


Number of possible alkynes with
molecular formula \( C_{5} H_{8} \) is:
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 5


The value of \( \frac{1}{2} \times\left(\frac{1}{3}+\frac{4}{9}\right) \) is
A \( \cdot \frac{7}{18} \)
B. \( \frac{1}{2} \)
c. \( \frac{7}{12} \)
D. \( \frac{7}{24} \)


Co-enzyme is
A. Always a protein
B. Often a vitamin
C. Always an inorganic compound
D. Often a metal


Find the common difference of \( 4, \frac{15}{2}, 11 \)
\( A \cdot \frac{7}{2} \)
B.
c. \( \frac{11}{41} \)
D. \( \frac{41}{11} \)


Predict the major product of acid catalysed dehydration:
(i) 1-methyl cyclohexanol
(ii) Butan-1-ol


Which of the following is wrong?
A. Sella turcica is a bony cavity where pituitary gland is located.
B. Parathyroid hormone decreases the \( \mathrm{Ca}^{2+} \) levels in blood.
C. Thymosins play a major role in T-cell differentiation.
D. Insulin stimulates glycogenesis.


A particle of charge \( q \) and mass \( m \) is moving through a region of space at right angles to an electric field and a
magnetic field, where the crossed magnetic and electric fields produce a zero net force on the charge. If the speed of the charge is doubled, which of the following changes will again produce a zero net force on the charge? This question has multiple correct options
A \( \cdot \) Reducing the Electric field to \( \frac{1}{2} E \)
B. Increasing the Electric field to \( 2 E \)
c. Reducing the Magnetic field to \( \frac{1}{2} B \)
D. Increasing the Magnetic field to \( 2 B \)
E. Doubling both the Magnetic and Electric Fields


Which is true for fungi?
A. They are heterotrophs.
B. They lack nuclear membrane.
C. They are phagotrophs.
D. They lack rigid cell wall.


The sum of three numbers which form a
geometric progression is 13 and the sum of their squares is \( 91 . \) Find the
numbers.


Calculate the followings.
An angle is equal to one third of its supplement. Find its measure.
2
If an angle is \( 30^{\circ} \) more than one half of its
complement, find the measure of the angle.


An astronaut is approaching the moon.
He sends a radio wave of frequency \( 5 \times \) \( 10^{9} H z \) towards the moon. The
frequency of the radio echo received by him has a frequency \( 9 \times 10^{4} H z \) more
than that of the real frequency. The velocity of the astronaut relative to the
moon is
A. \( 5.40 \mathrm{m} / \mathrm{s} \)
B. \( 4.05 k m / s \)
c. \( 2.70 k m / s \)
D. \( 1.35 k m / s \)


Find the equivalent set for \( \boldsymbol{A}-\boldsymbol{B} \)
A \( . A \cup(A \cap B) \)
B. B - A
c. \( A-(A \cap B) \)
D. \( A \cap B \)


Divide \( 5 x^{5}+4 x^{4}-3 x^{3}+2 x^{2}+2 \) by
\( x^{2}-x \)


If a magnet is suspended at angle \( 30^{\circ} \) to the magnet meridian, the dip of
needle makes angle of \( 45^{\circ} \) with the horizontal, the real dip is
\( ^{A} \cdot \tan ^{-1}\left(\frac{\sqrt{3}}{2}\right) \)
B \( \cdot \tan ^{-1}(\sqrt{3}) \)
\( ^{\mathrm{c}} \tan ^{-1}(\sqrt{\frac{3}{2}}) \)
D \( \cdot \tan ^{-1}\left(\frac{2}{\sqrt{3}}\right) \)


Among the following, the molecule of highest dipole moment is:
A. \( C C l_{4} \)
в. \( N H_{3} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{O} \)
D. \( C H C l_{3} \)
E. \( B F_{3} \)


One end of a nylon rope of length \( 4.5 m \)
and diameter \( 6 m m \) is fixed to a stem of
a tree. A monkey weighting \( 100 N \) jumps to catch the free end and stays there. what will be the change in the diameter of the rope. (Given Young's modulus of nylon \( =4.8 \times 10^{11} N m^{-2} \)
and Poisson's ratio of nylon \( =0.2 \) )
A. \( 8.8 \times 10^{-9} \mathrm{m} \)
в. \( 7.4 \times 10^{-9} \mathrm{m} \)
c. \( 6.4 \times 10^{-8} \mathrm{m} \)
D. \( 5.6 \times 10^{-9} \mathrm{m} \)


Which of the following molecule(s) gives only acid(s) on hydrolysis? This question has multiple correct options
A \( \cdot P C l_{3} \)
B. \( S F_{4} \)
c. \( N C l_{3} \)
D. \( P_{4} O_{6} \)


Identify the correct statement from the
given alternatives.
A. Intra molecular hydrogen bonding is not found to occur in \( 2- \) hydroxy benzaldehyde
B. The boiling point of hydrogen iodide \( (H I) \) is more that hydrogen fluoride \( (H F) \)
C. The dipole moment of \( C H_{3} C l \) is not equal to zero
D. \( C H_{3} F \) has a larger dipole moment that \( C H_{3} C l \)


Twinkling of stars is due to
A. variation of refractive index in the earth's atmosphere
B. the fact that light is not emitted by the stars continuously
C. the absorption oflight by earth's atmosphere
D. none of these


If \( 1, \log _{3}\left(3^{x}-2\right), 2 \log _{9}\left(3^{x}-8 / 3\right) \) are
in A.P., then the value of \( x \) can be-
\( \mathbf{A} \cdot \log \left(\frac{4}{3}\right) \)
B. \( \frac{\log 4}{\log 3} 4 \)
c.
\( \mathbf{D} \cdot \log _{3} 4 \)


Explain why fluorine forms only one oxoacid, HOF.


Why is common salt sometimes yellow instead of being pure white?


Assuming that the all volume is measured at the same temperature and pressure, state the volume ratios of the
reactants and products for the following gaseous reactions. Nitrogen reacting with oxygen to form nitrogen (III) oxide.
A \( \cdot 1: 3: 2 \)
B. 2:4:2
c. 2: 2:
D. 2: 3: 2


How is the reading of a barometer affected when it is taken to (i) a mine,
and (ii) a hill?
A . (i) increases
(ii) decreases.
B. (i) decreases
(ii) increases.
(ii) decreases
c. (i)remains same
D. (i) increases
(ii) remains same


If \( \boldsymbol{H}_{2}, \boldsymbol{H} e, \boldsymbol{O}_{2} \) and \( \boldsymbol{N}_{2} \) tarvel with same
velocity then the longest de-Brogile wavelength should be associated with:
A \( . H_{2} \)
в. \( H e \)
\( c \cdot O_{2} \)
D. \( N_{2} \)


A point object is placed at a distance of \( 12 \mathrm{cm} \) on the axis of a convex lens of
focal length \( 10 \mathrm{cm} . \) On the other side of the lens, a convex mirror is placed at a distance of \( 10 \mathrm{cm} \) from the lens such that the image formed by the combination coincides with the object
itself. The focal length of the convex
mirror is
\( A \cdot 20 \mathrm{cm} \)
B. 25 cm
\( c . \) 30 \( \mathrm{cm} \)
D. 22 cm


Prove that \( 3 n+1>3(n+1) \)


The velocities of two particles \( A \) and \( B \) are 0.05 and \( 0.02 m s^{-1} \) respectively.
The mass of \( B \) is five times the mass of
A. The ratio of their de-Broglie's wavelength is :
A .2: 1
B. 1: 4
\( c \cdot 1: 1 \)
D. 4: 1


The gravitational force of attraction between two bodies at a certain
distance is \( 10 \mathrm{N} \). If the distance
between them is doubled, the force of
attraction:
A. decreases by \( 50 \% \)
B. decreases by \( 75 \% \)
C. increases by \( 50 \% \)
D. increases by \( 75 \% \)


Two SHMs are given by \( \boldsymbol{Y}_{\mathbf{1}}= \)
\( A \sin \left(\frac{\pi}{2} t+\phi\right) \) and \( Y_{2}=B \sin \left(\frac{2 \pi t}{3} t+\right. \)
\( \phi \). The phase difference between these
two after '1' sec is
A . \( \pi \)
в. \( \frac{\pi}{2} \)
c. \( \frac{\pi}{4} \)
D.


Electric intensity is:
A . a scalar quantity
B. a vector quantity
C. neither scalar nor vector
D. sometimes scalar and sometimes vector


What is meant by Lanthanide contraction? Write the general
electronic configuration of inner transition elements.


The synonym for water gas when used in the production of methanol is:
A. natural gas
B. laughing gas
c. syn gas
D. fuel gas


A reflecting surface which is a part of a sphere is called:
A. concave mirror
B. convex mirror
c. spherical mirror
D. all of these


\( p: H e \) is hard working.
\( \boldsymbol{q}: \) He is intelligent.
Then \( \sim \boldsymbol{q} \Rightarrow \sim \boldsymbol{p}, \) represents
A. If he is hard working, then he is not intelligent.
B. If he is not hard working, then he is intelligent
c. If he is not intelligent, then he is not had working
D. If he is not intelligent, then he is hard working


A disc is rolling without slipping on a straight surface. The ratio of its translational kinetic energy to its total
kinetic energy is
A \( \cdot \frac{2}{3} \)
в. \( \frac{1}{3} \)
\( c \cdot \frac{2}{5} \)
D.


How many plants in the given list have marginal placentation? Mustard, Gram, Tulip, Asparagus, Arhar Sunn Hemp, Chilli, Colchicum, Onion,
Moong, Tobacco, Lupin.
A. Four
B. Five
\( c . \) six
D. Three


Vapour pressure of water at \( 293 K \) is
17.535 mm \( H g . \) Calculate the vapour
pressure of water at \( 293 K \) when \( 25 g \) of glucose is dissolved in \( 450 g \) of water.


Washing soda is :
A. \( N a_{2} C O_{3} \)
B. \( N a C l \)
c. \( N a_{a} C O_{3} \cdot 10 H_{2} O \)
D. \( N a_{2} S O_{4} \)


\( x \) and \( Y \) are two objects with masses
\( 100 k g \) and \( 75 k g \) respectively, then
A. Both will have the same inertia
B. Y will have more inertia
c. \( x \) will have more inertia
D. Both will have less inertia


Find the sum of
\( \left(^{100} C_{0}+^{100} C_{2}+^{100} C_{6}+\dots . .\right) \)
\( \mathbf{A} \cdot 2^{9} \)
в. -2
\( c \cdot 2^{5} \)
D. \( -2^{5} \)


f pressure increases then its effect on given equilibrium
\( \boldsymbol{C}(s)+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{C} \boldsymbol{O}(\boldsymbol{g})+\boldsymbol{H}_{2}(\boldsymbol{g}) \)
It is shifted in:
A. forward direction
B. backward direction
c. no effect
D. none of these


Given \( A=\{x: x \in N \text { and } 3<x \leq 6\} \)
and \( \mathrm{B}=\{x: x \in W \text { and } x<4\}, \) then
find \( : A-B \)


Let \( f(x)=x^{3}+3 x^{2}-9 x+2 . \) Then
A. \( f(x) \) has a maximum at \( x=1 \)
B. \( f(x) \) has neither a minimum nor a maximum at \( x= \) -3
c. \( f(x) \) has a minimum at \( x=1 \)
D. none of these


What is forward biasing and reverse biasing of a diode?


A step-down transformer is used to light
\( 12 V \) lamp from a \( 240 V \) mains
supply. The lamp lights at normal brightness. The primary coil
has 600 turns.

How many turns are in the secondary
coil?
A .12
B. 20
\( c .30 \)
D. 50


Four plates of same area of cross-
section are joined as shown in figure. The distance between each plate is d.
The equivalent capacity between \( A \) and
B will be
A \( \cdot \frac{2 \epsilon_{0} A}{d} \)
B. \( \frac{\epsilon_{0} A}{d} \)
с. \( \frac{3 \epsilon_{0} A}{d} \)
D. \( \frac{3 \epsilon_{0} A}{2 d} \)


The standard size of herabrium sheet is
\( \mathbf{A} \cdot 29 \times 41.5 \mathrm{cm} \)
B. \( 15 \times 30 c m \)
c. \( 21 \times 36 \mathrm{cm} \)
\( \mathbf{D} \cdot 25 \times 38 c m \)


Nitrolim is a:
A. mixture of calcium carbide and nitrogen
B. mixture of calcium cyanamide and carbon
C. mixture of calcium cyanide and carbon
D. mixture of \( N H_{4} C N \) and \( C a C N \)


Structures of \( ^{235} U \) and \( ^{238} U \) differ by
three :
A. isotopes
B. neutrons
c. electrons
D. protons


The numbers of iodine atoms present in
\( 1 \mathrm{ml} \) of its \( 0.1 \mathrm{M} \) solution is:
A. \( 6.02 \times 10^{23} \)
B . \( 6.02 \times 10^{22} \)
c. \( 6.02 \times 10^{19} \)
D. \( 1.204 \times 10^{20} \)


The ratio of number of electrons,
protons and neutrons in tritium is:
A. 1: 1: 1
B. 1: 1: 2
c. 2: 1: 1
D. 1: 2: 1


Glycogen is a/an
A. Polymer of amino acids.
B. Polymer of fatty acids.
c. Unsaturated fats.
D. Polymer of glucose.


A solid non conducting sphere charged
in such a way that in it as we move away from the centre, the electric field
decreases then which of the following statement is correct :
A. the sphere in uniformly charged
B. the potential at surface is less than that at its centre
c. the potential at surface is more than that at its centre
D. the potential at surface may be less than that at its centre


Name atleast five different deficiency symptoms in plants. Describe them and
correlate them with the concerned
mineral deficiency.


The angular speed of a motor wheel is
increased from 1200 rpm to 3120 rpm in 16sec.? find.
(i) Angular acceleration
(ii) Assuming acceleration to be uniform how many rotations does the engine make this bike?
(iii) State law of conservation of linear
momentum?


A plant is transpiring rapidly. Will it
show root pressure also?


Which type of polymer based on
structure is obtained when phenol reacts with form aldehyde?


\( \boldsymbol{C H}_{3} \boldsymbol{C N}+\boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{M} \boldsymbol{g} \boldsymbol{B r} \rightarrow ? \stackrel{\boldsymbol{H}_{2} \boldsymbol{O}^{+}}{\longrightarrow} \)
Complete the reaction.


How do the atoms combine in \( C a C l_{2} \)
or Calcium Chloride?
A. By Forming metallic bond
B. By Forming co-ordinate covalent bond
c. By Forming ionic bond
D. By Forming covalent bond


The graph of \( 2 x+y=3 \) passes through
the origin. Is this statement true or
false?
A. True
B. False


Which of the following is characterized by the presence of an enormous float?
A. Physalia
B. Velella
c. Gorgonia
D. Alcyonium


If the distance between the points \( (k,-1) \) and (3,2) is \( 5, \) then the value of
k is
A . 2
B. -2
\( c \cdot-1 \)
D.


Calculate the wavelength of a wave if it travels with speed \( 2 \mathrm{cm} / \mathrm{s} \) and period is
2 s.
A. \( 0.25 \mathrm{cm} \)
B. \( 0.5 \mathrm{cm} \)
\( c \cdot 1 \mathrm{cm} \)
D. \( 2 \mathrm{cm} \)
E. \( 4 \mathrm{cm} \)


Calculate the e.m.f. (in \( V \) ) of the cell:
\( \boldsymbol{P t}\left|\boldsymbol{H}_{2}(\boldsymbol{g})\right| \boldsymbol{B O H}(\boldsymbol{a q}) \| \boldsymbol{H} \boldsymbol{A}(\boldsymbol{a q})\left|\boldsymbol{H}_{2}(\boldsymbol{g})\right| \boldsymbol{P} \)
Given: \( \boldsymbol{K}_{\boldsymbol{a}}(\boldsymbol{H} \boldsymbol{A})=\mathbf{1 0}^{-\mathbf{7}}, \boldsymbol{K}_{\boldsymbol{b}}(\boldsymbol{B O H})= \)
\( 10^{-5} \)
A . \( 0.43 \mathrm{V} \)
B . \( 0.36 V \)
c. \( 0.93 V \)
D. None of these


The photoelectric effect proves that light consists of:
A. Photons
B. Electrons
c. Electromagnetic waves
D. Mechanical waves


Derive the relationship between the
focal length and radius of curvature of
spherical mirror.


Vitamin A deficiency in food can cause:
A. blurred vision
B. eye defects
c. night blindness
D. all of these


S' waves are
A. Longitudinal
B. Electromagnetic
C. Ultrasonic
D. Transverse


If \( \sqrt{1-x^{2}}+\sqrt{1-y^{2}}=a(x-y) \) then
prove that \( \frac{d y}{d x}=\sqrt{\frac{1-y^{2}}{1-x^{2}}} \)


Mean of marks obtained by 10 students
is 30
Marks obtained are
\( \mathbf{2 5}, \mathbf{3 0}, \mathbf{2 1}, \mathbf{5 5}, \mathbf{4 7}, \mathbf{1 0}, \mathbf{1 5}, \boldsymbol{x}, \mathbf{4 5}, \mathbf{3 5} \)
Find the value of \( x \)
A . 25
B. 37
c. 69
D. 17


Range and standard deviation are
similar in that each looks
A. The difference between the high and the low scores
B. The numerical value that occurs the most often
c. How spread out the data is.
D. The central score


Draw and label the diagram of the T.S. of
stem


The shape of \( C l F_{3} \) molecule is:
A. trianglular planar
B. pyramidal
c. T-shape
D. trigonal bipyramidal


A couple has two children,
(i) Find the probability that both children are males, if it is known that at
least one of the children is male.
(ii) Find the probability that both children are females, if ti is known that the elder child is a female.
A. 0.55,0.38
В. 0.33,0.50
c. 0.67,0.78
D. 0.56,0.67


Prove that:
\( \mathbf{3} \boldsymbol{x}-\mathbf{5} \boldsymbol{y}=\mathbf{1 6} ; \boldsymbol{x}-\mathbf{3} \boldsymbol{y}=\mathbf{8} \)


The electric current passing through a metallic wire produces heating because
of:
A. collisions of conduction electrons with each other
B. collisions of the atoms of the metal with each other
c. the energy released in the ionisation of the atom of the metal
D. collisions of the conduction electrons with the atoms of the metallic wire


One day the contractor's workers appeared in the forest to cut the trees
but the men folk were absent. However,
the women from the village reached the forest quickly and elapsed the tree trunks preventing the workers from felling the trees. Thus, the forest trees
were saved.

The incident was originated in a remote village called "Reni" in Garhwal in the
early 1970 s. By which name is this andolan known as?
A. Amritadevi Andolan
B. Vankatai Andolan
c. Prakruti Samrakshan Andolan
D. Chipko Andolan


A unit is so chosen that the numerical
value of a measurement is as small as
possible. True=1; False=0


Balanced equation of the reaction of
formation of \( P b O_{2} \) at the anode is
\( P b^{2+}(a q)+x H_{2} O \rightleftharpoons P b O_{2} \downarrow \)
\( +\boldsymbol{y} \boldsymbol{H}^{+}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{z} \boldsymbol{e}^{-} \)
What will be value of y?


In the balmer series of atomic spectra
of hydrogen atom, a line corresponding to wavelength \( 656.4 n m \) was obtained.
Calculate the no. of higher orbit from which the electron drops to produce this line.


Find the range of the following function:
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}+\boldsymbol{2}, \boldsymbol{x} \in \boldsymbol{R} \)
\( A \cdot(-2, \infty) \)
B. \( (2, \infty) \)
c. \( (3, \infty) \)
D. None of these


One says, "Give me a hundred, friend! shall then become twice as rich as you."."
The other replies, "lf you give me ten, shall be six times as rich as you." Tell
me what is the amount of their (respective) capital? [From the Bijaganita of Bhaskara II]


The electrical energy in kilowatt hours consumed in operating ten \( 50 ~ W \)
bulbs for 10 hrs/day in a month of
30 days is
A. 1500
B. 15000
c. 15
D. 150


In the given figure \( \boldsymbol{P Q} \| \boldsymbol{R S}, \angle \boldsymbol{R} \boldsymbol{S F}= \)
\( 40^{\circ}, \angle P Q F=35^{\circ} \) and \( \angle Q F P=x^{o} \)
What is the value of \( x ? \)
A . \( 75^{\circ} \)
В. 105
с. 135
D. \( 140^{\circ} \)


Which of the following statement(s)
is/are correct?
This question has multiple correct options
A. Anti conformation of \( N H_{2}-C H_{2}-C H_{2}-N H_{2} \) is
always more stable than its Gauche conformation.
B. Gauche conformation of \( O H-C H_{2}-C H_{2}-F \) is
more stable than anti-conformation at room
temperature
C. On increasing temperature dipole moment of pure \( C I-C H_{2}-C H_{2}-C I \) increases
D. In case of 1,4 -dihydroxycyclohexane twist boat conformer is most stable.


The measures of angles of a triangle are in the ratio \( 1: 2: 3 . \) Determine the
measures of smallest angle of the
triangle.


Two parallel infinite wires separated by
distance ' \( d^{\prime} \) carry currents as shown in
figure. The distance from a third infinite wire
be kept parallel to wire carrying current
\( l_{1}, \) the wire such that it stays in equilibrium is
A \( \cdot \frac{I_{2}}{I_{2}+I_{1}} d \) or \( \frac{I_{1}}{I_{1}+I_{2}} d \)
в. \( \frac{I_{2}}{I_{2}-I_{1}} d \) or \( \frac{I_{1}}{I_{1}-I_{2}} d \)
c. \( \frac{I_{2}}{I_{1}-I_{2}} d \) or \( \frac{I_{1}}{I_{1}-I_{2}} d \)
D. \( \frac{2 I_{2}}{I_{2}+I_{1}} d \) or \( \frac{I_{1}}{I_{1}-I_{2}} d \)


\( A \) can hit target three times in six
shots, \( B \) can hit target 2 times in six
shots and \( C \) can hit target 4 times in a
6 shots. They fix a ball. But what is the probability that they hit ball in atleast two shots.


Three elephants \( A, B \) and \( C \) are moving along a straight line with constant speed in same direction as shown in figure. Speed of \( A \) is \( 5 \mathrm{m} / \mathrm{s} \) and speed of \( \mathrm{C} \) is \( 10 \mathrm{m} / \mathrm{s} \). Initially separation between
A and B is d and between B and C is also
d. When 'B catches 'C' separation between \( A \) and \( C \) becomes \( 3 d \). Then the
speed of B will be:
\( A \cdot 15 \mathrm{m} / \mathrm{s} \)
B. \( 7.5 \mathrm{m} / \mathrm{s} \)
\( c \cdot 20 m / s \)
D. \( 5 \mathrm{m} / \mathrm{s} \)


A particle of mass \( m \) and positive
charge \( \boldsymbol{q}, \) moving with a uniform
velocity \( v, \) enters a magnetic field \( B \) as
shown in figure.
(a) Find the radius of the circular arc it
describes in the magnetic field
(b) Find the angle subtended by the arc
at the centre
(c) How long does the particles stay inside the magnetic field?
(d) Solve the three parts of the above
problems if the charge \( q \) on the particle is negative then.


Solve the following inequation and represent the solution set on the
number line:
\( \mathbf{4} \boldsymbol{x}-\mathbf{1 9}<\frac{\mathbf{3} \boldsymbol{x}}{\mathbf{5}}-\mathbf{2} \leq-\frac{\mathbf{2}}{\mathbf{5}}+\boldsymbol{x}, \quad \boldsymbol{x} \in \boldsymbol{R} \)


The middle term in the expansion of
\( (1+x)^{2 n} \) is
A. \( \frac{1.3 .5 \ldots(2 n-1) 2^{n}}{n !} \)
в. \( \frac{1.2 .3 \ldots(2 n-1) 2^{n} x^{n}}{n !} \)
c. \( \frac{1.3 .5 \ldots(2 n-1) x^{n}}{n !} \)
D. \( \frac{1.3 .5 \ldots .(2 n-1) 2^{n} x^{n}}{n !} \)


\( \operatorname{Set} \boldsymbol{U}=\{1,2, \mathbf{3}, \mathbf{4}, \mathbf{5}, \mathbf{6}, \mathbf{7}, \mathbf{8}, \mathbf{9}\}, \boldsymbol{A}= \)
\( \left\{x: x \in N, 30 \leq x^{2} \leq 70\right\}, B=\{x: x \)
is a prime number \( <10\} . \) Which of the
following does NOT belong to the set
\( (A-B)^{\prime} ? \)
\( \mathbf{A} \cdot \mathbf{4} \)
B. 5
\( c \cdot 6 \)
D.


Assertion
In nature chlorine does not occur in free
state.
Reason
Chlorine is highly electronegative
element.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


The electric potential at a point \( \boldsymbol{P} \) inside a uniformly charged conducting sphere of radius \( R \) and charge \( Q \) at a
distance \( r \) from the centre is :
A . 0
B . \( \infty \)
c. \( \frac{Q}{4 \pi \epsilon_{0} r} \)
D. \( \frac{Q}{4 \pi \epsilon_{0} R} \)


Henry's law constant for molality of methane in benzene at \( 298 K \) is \( 4.27 \times \)
\( 10^{5} \) mm \( H g . \) The mole fraction of
methane in benzene at \( 298 K \) under
\( 760 m m H g \) is:
A. \( 1.78 \times 10^{-3} \)
B. 17.43
c. 0.114
D. 2.814


Select the correct order with respect to
acidic nature of the given compounds.
\( \mathbf{A} \cdot A l_{2} O_{3}<\operatorname{In}_{2} O_{3}<T l_{2} O<B_{2} O_{3} \)
B. \( T l_{2} O< \)In\( _{2} O_{3}<A l_{2} O_{3}<B_{2} O_{3} \)
\( \mathbf{c} \cdot A l_{2} O_{3}<B_{2} O_{3}<\operatorname{In}_{2} O_{3}<T l_{2} O \)
\( \mathbf{D} \cdot T l_{2} O<A l_{2} O_{3}<B r_{2} O_{3}<I n_{2} O_{3} \)


Construct the graphs of the following functions and carry out a complete investigation
\( y=\sin ^{4} x+\cos ^{4} x \)


What can you say about the motion of
an object whose distance time graph is a straight line parallel to the time axis?


Three very long straight current carrying conductors are placed parallel to each other as shown in the figure. The conductors \( 1 \& 3 \) are fixed where as
conductor 2 is free to move. If the
conductor 2 is pulled towards right through a very small distance \( x, \) find the net force acting on it and angular frequency of the resulting oscillation.


If a hexagon of perimeter \( 24 \mathrm{cm} \) has
equal side lengths, then the length of its
side is
\( A \cdot 2 \mathrm{cm} \)
B. \( 4 \mathrm{cm} \)
\( c \cdot 6 \mathrm{cm} \)
\( \mathbf{D} \cdot 8 \mathrm{cm} \)


Which of the following statements is true about hydrogen bonding?
A. \( C l \) and \( N \) have comparable electronegativities yet there is no \( H \) -bonding in \( H C I \) because size of \( C l \) is large
B. Intermolecular \( H \) - bonding results in decrease in \( \mathrm{m} \). and b.
C . lce has maximum density at \( 0^{\circ} \mathrm{C} \) due to \( H \) -bonding
D. \( K H C l_{2}\left(H C l_{2}^{-}\right) \) exists but \( K H F_{2}\left(H F_{2}^{-}\right) \) does not exist due to lack of \( H \) -bonding in \( H C l \)


Fill in the blanks.
Plasma: Fibrinogen; RBC: \( \ldots . . . . . . . . . . ; \mathrm{WBC} \)


What is a solenoid? Compare the
magnetic field produced by a solenoid with the magnetic field of a bar magnet.
Draw neat figures and name various
components.


What is meant by Precision?


The figure shows a circuit containing a
coil wound over a long and hollow thin
tube. Mention two methods to increase
the strength of the magnetic field
inside the coil.


A mans walks along a straight path at a speed of \( 4 f t / \) sec.A scarch light is
located on the ground \( 20 f t \) from the path and is kept focused on man. At what rate is the scarch light rotating when the man is \( 15 f t \) from the point on
the path closest to the search light.
A . 0.128 rad/sec
B. 1.6rad/sec
c. \( 0.8 \mathrm{rad} / \mathrm{sec} \)
D. \( 0.24 \mathrm{rad} / \mathrm{sec} \)


Let \( \boldsymbol{A}=\{-2,-1,0,1,2\} \) and \( \boldsymbol{f}: \boldsymbol{A} \rightarrow \)
\( Z \) be given by \( f(x)=x^{2}-2 x-3 . \) Find
the pre-image of 6,-3 and 5


Convert the given fractional numbers to
per cents.
(a) \( \frac{1}{8} \)


A reaction system in equilibrium
according to the equation \( 2 S O_{2}+ \)
\( O_{2} \rightleftharpoons 2 S O_{3} \) in 1 litre reaction vessel at
a given temperature was found to
contain 0.11 mol of \( S O_{2}, 0.12 \) of \( S O_{3} \) and
0.05 mol of \( O_{2 .} \) Another 1 litre reaction
vessel contains 64 g of \( S O_{2} \) at the
same temperature. What mass of \( \boldsymbol{O}_{2} \)
must be added to this vessel in order
that at equilibrium half of \( S O_{2} \) is
oxidised to \( \boldsymbol{S O}_{3} \) ?
A. 9.34 g
в. 10.87
c. \( 21.3 \mathrm{g} \)
D. 32.4 g


Using properties of determinant, prove
\[
\text { that }\left|\begin{array}{lll}
\boldsymbol{b}+\boldsymbol{c} & \boldsymbol{a}-\boldsymbol{b} & \boldsymbol{a} \\
\boldsymbol{c}+\boldsymbol{a} & \boldsymbol{b}-\boldsymbol{c} & \boldsymbol{b} \\
\boldsymbol{a}+\boldsymbol{b} & \boldsymbol{c}-\boldsymbol{a} & \boldsymbol{c}
\end{array}\right|=\mathbf{3} \boldsymbol{a} \boldsymbol{b} \boldsymbol{c}-\boldsymbol{a}^{3}-
\]
\( b^{3}-c^{3} \)


Among \( N a, H g, S, P t, \) and graphite which can be used as electrodes
in electrolytic cell having aqueous solutions ?
A. \( N \) aand \( S \)
в. \( H g, P t \), and \( S \)
c. \( N a, H g \), and \( S \)
D. \( H g, P t \), and graphite


A particle moves in \( X Y \) plane according to the law \( x=a \sin (t) \) and \( y= \) \( \boldsymbol{a}(1-\cos (\boldsymbol{t})) \) where a is constant. The
particle traces:
A . a parabola
B. a straight line equallyinclined to x and y axes
c. a circle
D. a distance proportional to time


Which of the following statements is
incorrect?
A. The epithelial layer allows the regulation of materials between the body and the external environment.
B. The epithelial layer does not allow regulation of materials between the body and the external environment.
C. The epithelial layer provides a large surface area provided by microvilli
D. Both B and C.


In a Television game show, the prize money of Rs 1,00,000 is to be divided equally amongst the winners. Complete the following table and find whether the prize money given to an individual winner is directly or inversely proportional to the number of winners??
Number of
winners
Prize of each
1,00,000
50,000
winner (in Rs)


In Young's double slit experiment:
A. only interference occurs
B. only diffraction occurs
c. both interference and diffraction occurs
D. polarisation occurs


Which reagent does not give oxygen as one of the product during oxidation with ozone?
\( A \cdot S O_{2} \)
в. \( S n C l_{2} / H C l \)
\( \mathrm{c} \cdot H_{2} \)
D. \( P b S \)


The radioactive decay of uranium into
thorium is expressed by the equation \( 92 U^{238} \rightarrow 90 T h^{234}+X \) Where \( X \) is
A. an electron
B. a proton
c. a deuteron
D. an alpha particle


The degree of the polynomial
\( (x+1)\left(x^{2}-x-x^{4}+1\right) \) is
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D.


Number of permutations of the word PANCHKULA where \( A \& U \) are separated (Note that PAANCHKUL is one such
word) is equal to:
A \( \cdot 15 \mid 7 \)
B. 21]
c. 241
D. \( 36 \mid 7 \)


For a polynomial \( \boldsymbol{p}(\boldsymbol{x}), \) the value of \( \boldsymbol{p}(\boldsymbol{3}) \)
is \( -2 . \) Which of the following must be
true about \( p(x) ? \)
A \( \cdot x-5 \) is a factor of \( p(x) \)
B . \( x-2 \) is a factor of \( p(x) \)
c. \( x+2 \) is a factor of \( p(x) \)
D. The remainder when \( p(x) \) is divided by \( x-3 \) is -2


O is any point inside a triangle ABC. The bisector of \( \angle A O B, \angle B O C \) and \( \angle C O A \)
meet the sides, \( A B, B C \) and \( C A \) in point D, E and F respectively, therefore,
\( A D \times B E=D B \times F A \)
A. True
B. False


Write the set of values of \( k \) for which
\( f(x)=k x-\sin x \) is increasing on \( R \)


The square root of the product
of inductance and capacitance has dimensions of
A . length
B. mass
\( c . \) time
D. dimensionless


The resistance in the two arms of the
meter bridge are \( 5 \Omega \) and \( R \Omega \)
respectively. When the resistance R
is shunted with an equal resistance, the
new balance point is at \( 1.6 l_{1} . \) The
resistance 'R' is
A . \( 10 \Omega \)
В. \( 15 \Omega \)
\( c .20 \Omega \)
D. \( 25 \Omega \)


A strong acid is completely deprotonated in solution whereas a weak acid is incompletely deprotonated in solution. If true write 1 , else write 0 .


The value of \( \sin ^{2} 20^{\circ}+\sin ^{2} 70^{\circ} \) is :
\( \mathbf{A} \cdot \mathbf{1} \)
B. 0
\( c \cdot 2 \)
D. 3


Which of the following are not the characteristic property of non-metal?
A. Sonorous
B. Not malleable
c. Not ductile
D. Not lustrous


Reflection is the \( \ldots \). Of light off a surface.
A. Bouncing
B. hitting
c. firing
D. all


A convex lens of focal length \( 30 \mathrm{cm} \). is
made of a material of refractive index 3
When it is placed in a liquid its focal length is increased by \( 50 \mathrm{cm} . \) The refractive index of the liquid is
A \( \cdot \frac{5}{4} \)
B. \( \frac{4}{3} \)
\( c \cdot \frac{7}{4} \)
D. \( \frac{6}{5} \)


Account for the following:
\( T i^{3+} \) is coloured whereas \( S c^{3+} \) is
colourless in aqueous solution.


The question is based on the Venn
Diagram. The circle stands for rural Triangle stands for educated, square
stands for hard-working and Rectangle stands for intelligent persons. The
number given represents a serial
number of the area

Which area represents " Intelligent hard-working and educated but not
rural" persons?
\( A \cdot 12 \)
в. 10
\( c \)
\( D \)


Why do transition elements form alloys?


Following is square shape loop, whose one arm \( B C \) produces magnetic field \( B \)
at the center of coil. The resultant
magnetic field due to all the arms will
be:
\( A \cdot 4 B \)
в. \( B / 2 \)
\( c . B \)
D. \( 2 B \)


If a diamagnetic substance is brought
near the north or the south pole of a bar magnet, it is
A. attracted by both the poles
B. repelled by both the poles
c. repelled by the north pole and attracted by the south pole
D. attracted by the north pole and repelled by the south pole


The observed wavelength of light
coming from a distant galaxy is found
to be increased by \( 0.5 \% \) as compared
with that coming from a terrestrial
source. The galaxy is.
A. Stationary with respect t to the earth
B. Approching the earth with velocity of light
C. Receding from the earth with velocity of light
D. Receding from the earth with a velocity equal to \( 1.5 \times \) \( 10^{6} \mathrm{m} / \mathrm{s} \)


Two discs have same mass and
thickness. Their materials are of
densities \( \pi_{1} \) and \( \pi_{2} . \) The ratio of their
moment of inertia about central axis will be
\( \mathbf{A} \cdot \pi_{1}: \pi_{2} \)
в. \( \pi_{1} \pi_{2}: \) ।
\( \mathbf{D} \cdot \pi_{2}: \pi_{1} \)


Find the value of \( \tan 25^{\circ} 15^{\prime} \)


Find the multiplicative inverse of each of the following numbers:
\( 2, \frac{6}{11}, \frac{-8}{15}, \frac{19}{18}, \frac{1}{1000} \)


The treatment of \( \left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{C}=\boldsymbol{C H} \boldsymbol{C H}_{3} \)
with boiling \( K M n O_{4} \) produces :
A. \( C H_{3} C O C H_{3}+C H_{3} C O C H_{3} \)
в. \( C H_{3} C O C H_{3}+C H_{3} C H O \)
c. \( C H_{3} C H O+C O_{2} \)
D. \( C H_{3} C O C H_{3} \quad \) only


A negatively charged rod is brought close to two metal spheres which are in
contact with each other, and the
spheres are separated in the presence
of the rod. Then
A. The sphere close to the rod acquires a negative charge and the other sphere acquires a positive charge
B. The sphere close to the rod acquires a positive charge and the other sphere acquires a negative charge
c. Both the spheres will acquire positive charge
D. Both the spheres will acquire negative charge


Find the length of a diagonal of rhombus whose area is \( 100 m^{2} \) and
length of other diagonal is \( 10 m^{2} \)
A. \( 10 \mathrm{m} \)
в. 20
\( c \cdot 2 m \)
D. \( 1 \mathrm{m} \)


Select the correct option:
This question has multiple correct options
A. carbonic acid is weaker acid than acetic acid
B. the boiling points of acids are higher than corresponding alcohols
C. chloroacetic acid is stronger acid than acetic acid
D. phenol is more acidic than ethanol


Find the components of vector \( \overrightarrow{\boldsymbol{a}}=\mathbf{3} \hat{\mathbf{i}}+ \)
\( 4 \hat{j} \) along the direction of vectors \( \hat{i}+\hat{j} \& \) \( \hat{\mathbf{i}}-\hat{\boldsymbol{j}} \)
A \( \cdot \frac{7}{2}(\hat{i}+\hat{j}),-\frac{1}{2}(\hat{i}-\hat{j}) \)
B \( \cdot \frac{1}{2}(\hat{i}+\hat{j}),-\frac{7}{2}(\hat{i}-\hat{j}) \)
c. \( \frac{-7}{2}(\hat{i}+\hat{j}),-\frac{1}{2}(\hat{i}-\hat{j}) \)
D \( \cdot \frac{7}{2}(\hat{i}+\hat{j}), \frac{1}{2}(\hat{i}-\hat{j}) \)


Assertion
A stationary charged particle in a magnetic field does not experience a force.
Reason
The force acting on a charged particle does not depend on velocity of the
particle
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


Explain the working of a common base transistor amplifier with the help of a circuit diagram. The load resistance of output circuit is \( 600 k \Omega \) and resistance
of input circuit is \( 150 p \Omega \) in a common
base amplifier. If current amplification
is \( 0.90, \) then calculate the voltage amplification.


Construct quadrilaterals to the given measurements; the order of the letters
in each case is \( A, B, C, D \)
\( A B=4.8 \mathrm{cm}, B C=4.4 \mathrm{cm}, C D=7 \mathrm{cm}, D A= \)
\( 3.4 \mathrm{cm}, \mathrm{BD}=6.2 \mathrm{cm} \)


If in \( \triangle A B C \) and \( \triangle D E F, \frac{A B}{D E}=\frac{B C}{F D} \)
then they will be similar if
A. \( \angle B=\angle E \)
в. \( \angle A=\angle D \)
c. \( \angle B=\angle D \)
\( \mathbf{D} \cdot \angle A=\angle F \)


A helium nucleus makes a full rotation
in a circle of radius \( 0.8 m \) in two
seconds. The value of the magnetic field
B at the centre of the circle will be
\( \mathbf{A} \cdot 10^{-19} / \mu_{0} \)
B . \( 10^{-19} \) p \( _{0} \)
c. \( 2 \times 10^{-19} \mu_{0} \)
D. \( 2 \times 10^{-19} / \mu_{0} \)


Solve then inequality \( \frac{x-1}{x} \geq 2 \)
\( \mathbf{A} \cdot x \leq 1 \)
B. \( x \leq-1 \)
c. \( x \leq 0 \)
D. \( x \in R \)


Dividing \( f(z) \) by \( z-i, \) we obtain the
remainder \( i \) and dividing it by \( z+i, \) we
get the remainder \( 1+i, \) then remainder
upon the division of \( f(z) \) by \( z^{2}+1 \) is
A \( \cdot \frac{1}{2}(z+1)+i \)
B \( \cdot \frac{1}{2}(i z+1)+i \)
c. \( \frac{1}{2}(i z-1)+i \)
D \( \cdot \frac{1}{2}(z+i)+1 \)


IUPAC name of the given compound is :
A. 2,6 -Dimethylphenol
B. 2-Hydroxy-3-Methyltoluene
c. 2 -Hydroxy- 1,3 -Dimethylbenzene
D. None of these