A train \( 110 m \) long is travelling at \( 60 k m / h r, \) In what time it will cross a
cyclist moving at \( 6 k m / h r, \) in the
opposite direction?


Perianth occurs in family
A. Solanaceae
B. Fabaceae
c. Brassicaceae
D. Liliaceae


A graph is drawn between centigrade temperatures of body along x-axis and corresponding Fahrenheit temperatures along y-axis. Slope of the graph is
A \( .5 / 9 \)
B. 9/5
\( c \cdot 4 / 5 \)
D. \( 5 / 4 \)


Prove \( \sin ^{2} \frac{\pi}{8}+\sin ^{2} \frac{3 \pi}{8}+\sin ^{2} \frac{5 \pi}{8}+ \)
\( \sin ^{2} \frac{7 \pi}{8}=2 \)


If \( \boldsymbol{A}+\boldsymbol{B}=\left[\begin{array}{ll}\mathbf{2} & \mathbf{3} \\ \mathbf{4} & \mathbf{5}\end{array}\right] \) and \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{2} \\ \mathbf{0} & \mathbf{3}\end{array}\right] \)
then matrix \( B \) is
\( \mathbf{A} \cdot\left[\begin{array}{ll}1 & 1 \\ 4 & 2\end{array}\right] \)
в. \( \left[\begin{array}{ll}1 & 4 \\ 1 & 2\end{array}\right] \)
c. \( \left[\begin{array}{ll}2 & 4 \\ 1 & 1\end{array}\right] \)
D. \( \left[\begin{array}{ll}4 & 2 \\ 1 & 1\end{array}\right] \)


Equation of the line through the point of intersection of the lines \( 3 x+2 y+4= \)
0 and \( 2 x+5 y-1=0 \) whose distance
from (2,-1) is \( 2, \) is
A. \( 2 x-y+5=0 \)
B. \( 4 x+3 y+5=0 \)
c. \( x+2=0 \)
D. \( 3 x+y+5=0 \)


The mean and the standard devition
(s.d) of five observations are 9 and 0 respecively. If one of the observations is changed such that the mean of the new set of five obervatons becomes 10 , then
their s.d. is:
A.
B.
\( c \cdot 2 \)
\( D \cdot 4 \)


Name one aldehyde and ketone with high boiling point and one with low boiling point.


\( \int_{0}^{\infty} \boldsymbol{f}\left(\boldsymbol{x}+\frac{\mathbf{1}}{\boldsymbol{x}}\right) \cdot \frac{\ln \boldsymbol{x}}{\boldsymbol{x}} \boldsymbol{d} \boldsymbol{x} \)
A. Is equal to zero
B. Is equal to one
\( ^{\mathrm{c}} \). \( _{\text {Is equal to }} \frac{1}{2} \)
D. can not be evaluated


Factors of \( 16 x^{5}-144 x^{3} \) are
This question has multiple correct options
\( \mathbf{A} \cdot 16 x^{3} \)
B. 4
c. \( x+3 \)
D. \( x-3 \)


Root nodules are found in
A. Some leguminous plants only
B. In all plants
C. Some leguminous plants and some other plants also
D. All leguminous plants but never in other plants


A radioactive nucleus undergoes \( \alpha \)
emission to form a stable element.What
will be the recoil of the daughter
nucleus if \( v \) is the velocity of \( \alpha \) emission?
A \( \cdot \frac{4 v}{A-4} \)
в. \( \frac{2 v}{A-4} \)
c. \( \frac{4 v}{A+4} \)
D. \( \frac{2 v}{A+4} \)


Passage of ova through female reproductive tract is facilitated by
A. Ciliary movement
B. Amoeboid movement
c. Flagellar movement
D. Cyclosis


In the relation \( \Delta \boldsymbol{H}=\boldsymbol{\Delta} \boldsymbol{U}+\left(\boldsymbol{\Delta} \boldsymbol{n}_{\boldsymbol{g}}\right) \boldsymbol{R} \boldsymbol{T} \)
the units of \( \Delta n_{g} \) is mol.f true enter 1
else o
A.


To construct a triangle similar to given \( \Delta A B C \) with its sides \( \frac{3}{5} \) of that of \( \Delta A B C, \) a ray \( B X \) is drawn at acute
angle with \( B C . \) If we mark points
\( B_{1}, B_{2}, B_{3}, \dots . \) at equal distances from
\( B \) along \( B X, \) then point to be joined in
next step is?
A. \( B_{3} \)
в. \( B_{4} \)
\( c \cdot B_{5} \)
D. \( B_{6} \)


The value of \( \lim _{\alpha \rightarrow \beta}\left[\frac{\sin ^{2} \alpha-\sin ^{2} \beta}{\alpha^{2}-\beta^{2}}\right] \) is:
\( \mathbf{A} \cdot \mathbf{0} \)
B.
c. \( \frac{\sin \beta}{\beta} \)
D. \( \frac{\sin 2 \beta}{2 \beta} \)


Solve the differential equation:
\( \boldsymbol{y} \log \boldsymbol{y} \frac{\boldsymbol{d} \boldsymbol{x}}{\boldsymbol{d} \boldsymbol{y}}+\boldsymbol{x}-\log \boldsymbol{y}=\mathbf{0} \)


From below, which are the examples of conventional energy?
This question has multiple correct options
A. coal
B. Woodd
c. wind
D. Solar


Why does some liquid medicines kept in dark coloured bottles?


Which of the following is not a fat soluble vitamin?
A. Vitamin - B complex
B. Vitamin - D
c. vitamin - E
D. Vitamin - A


Following reaction is reversible
\( A g_{2} S+4 N a C N \rightleftharpoons 2 N a\left[A g(C N)_{2}\right]+ \)
\( N a_{2} S \)
When we pass air this reaction become spontaneous.
A. True
B. False


At \( 30^{\circ} C, \) the solubility of \( A g_{2} C O_{3} \)
\( \left(K_{s p}=8 \times 10^{-12}\right) \) would be greatest in
one litre of:
A. \( 0.05 M \) Na\( _{2} \) CO \( _{3} \)
B. \( 0.05 M A g N O_{3} \)
c. Pure water
D. \( 0.05 M N H_{3} \)


Reaction involved in
saponification process is \( \boldsymbol{C H}_{3} \boldsymbol{C O O C}_{2} \boldsymbol{H}_{5} \stackrel{N a O \boldsymbol{H}}{\longrightarrow} \)
\( \boldsymbol{C H}_{3} \boldsymbol{C O O N} \boldsymbol{a}+\boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{O H} \)
A. True
B. False


Solve \( \lim _{x \rightarrow 1}\left[\frac{x-1}{x^{2}-x}-\frac{1}{x^{3}-3 x^{2}+x}\right] \)


What is deforestation?
A. Clearing of forests
B. Planting of more trees
C. Grazing of animals in forest area
D. None of the above


When the angle between two plane
mirrors is \( 60^{\circ}, \) how many multiple images will be formed by the mirrors?
\( A \cdot 6 \)
B. 7
\( c \cdot 4 \)
D. 5


toppr
Q Type your question
\( 600 k g / m^{3} \) and \( \rho_{2}=1200 k g / m^{3} \) as
shown in the figure. A small hole having cross-sectional
area \( 5 c m^{2} \) is made in right side vertical
wall as shown. Take atmospheric
pressure as \( \boldsymbol{p}_{0}=\mathbf{1 0}^{5} \boldsymbol{N} / \boldsymbol{m}^{2}, \boldsymbol{g}= \)
\( 9.8 m / s^{2} . \) For this situation, mark out
the correct statements(s). (Take cross-
sectional area of the cylindrical vessel
as \( 1000 \mathrm{cm}^{2} \). Neglect the mass of the
vessel)
This question has multiple correct options
A. If the surface on which the vessel is placed is smooth, then a rightward force of magnitude 2N is to be applied on the vessel to maintain its static equilibrium.
B. If the surface on which the vessel is placed is smooth then no force is needed to maintain its static equilibrium
C. If the surface on which the vessel is placed is rough \( (\mu=0.04) \), then the minimum force (horizontal) needed to be applied on the vessel to maintains its static equilibrium is zero
D. If the surface on which the vessel is placed is rough \( \mu=0.04 \), then the maximum force (horizontal) needed to be applied on the vessel to maintain its static equilibrium is 19.8 N


Check whether \( \frac{1}{4} \) is a solution of the equation \( 3(x+1)-3(5-x)=2(5+x) \)


The brain capacity of Homo erectus was
A. 800 to 1300 cc
B. 1650 cc
\( c .650 \mathrm{cc} \)
D. 1400 cc


Write the formula of the functional
group present in caboxylic acids.


Check whether \( 2 x^{2}-3 x+5=0 \) has
real roots or no.
A. The equation has real roots.
B. The equation has no real roots.
c. Data insufficient
D. None of these


Match the following


In mitotic cell division
A. Amount of DNA in the daughter cells will be equal to the parent cell
B. Size will be half of the parent cell
C. DNA will be double of the parent cell
D. Both A and C


What is the temperature for which the
readings on Kelvin and Fahrenheit
Scales are same?


Aqua regia is a mixture of :
A. \( H C l \) and nitric acid
B. \( H_{2} S O_{4} \) and nitric acid
\( \mathbf{C} \cdot \mathrm{HCl} \) and \( \mathrm{H}_{2} \mathrm{SO}_{4} \)
D. vinyl chloride and HCI


Collision frequency depends upon concentration and temperature. If true enter 1 , if false enter 0 .


Convert \( \frac{14}{40} \) into percentage.
A . \( 0.35 \% \)
в. \( 3.5 \% \)
c. \( 35 \% \)
D. 350\%


A cross between two pink flowered Antirrhinum plants yielded a progency with red, pink and white flowered
individuals. Explain the pattern of inheritance and the phenomenon
involved in it. What will be phenotypic and genotypic ratios in the progency?


Number of interior angles formed in the
triangle are
A . 1
B. 2
\( c .3 \)
\( D \)


A \( 2 \mathrm{kg} \) object moving with the speed of 2 \( \mathrm{m} / \mathrm{s} \) collides with \( 4 \mathrm{kg} \) objects, which is at rest. if the final velcocities of the
odjects are same, then what would be
the final velocity?
A \( \cdot \frac{2}{3} \mathrm{m} / \mathrm{s} \)
в. \( \frac{1}{3} \mathrm{m} / \mathrm{s} \)
c. \( \frac{2}{5} \) m/s
D. \( \frac{3}{5} \mathrm{m} / \mathrm{s} \)


True or False.
All the elements having one electron in
their outermost shell are metals.


The life forms in aquatic biomes are dependent on
A. Sunlight
B. Salt
c. Pressure
D. All of the above


\( 50 \mathrm{mL} \) of sample of hard water gave good lather with \( 6 \mathrm{mL} \) of standard soap solution (1 mL soap solutions = 1 mg \( \mathrm{CaCO}_{3} \). If the hardness is only due to
\( M g\left(H C O_{3}\right)_{2}, \) the weight of milk of lime required to remove the hardness completely from \( 100 \mathrm{kg} \) of that sample of water is:
A. \( 17.8 \mathrm{g} \)
в. \( 8.9 \mathrm{g} \)
c. \( 178 g \)
D. 89 \( g \)


\( \mathbf{2} N \boldsymbol{O}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{2} \boldsymbol{N} \boldsymbol{O} \boldsymbol{C l}(\boldsymbol{g}) \)
The following data were collected. All the
measuremnets were taken at \( 263 \mathrm{K} \)
Initial rate
disappear:
\( \begin{array}{llll}\begin{array}{l}\text { Experiment } \\ \text { No. }\end{array} & \begin{array}{l}\text { Initial } \\ \text { [NO] } \\ \text { (M) }\end{array} & \begin{array}{l}\text { Initial } \\ {\left[C_{2}\right]} \\ \text { (M) }\end{array} & \begin{array}{l}\text { In } \\ \text { di }\end{array} \\ & & \text { of }\end{array} \) \( C l_{2} \) or \( C l_{2} \)
\( (M / m i n) \)
0.15 0.15 0.60
0.15 \( \quad 0.30 \) 1.20
3 \( \begin{array}{ll}\text { 0.30 } & \text { 0.15 }\end{array} \) 2.40
0.25 0.25
(a) Write the expression for rate law.
(b) Calculate the value of rate constant
and specify its units.
(c) What is the initial rate of
disappearance of \( C l_{2} \) in exp. \( 4 ? \)


The following reactions take place during the extraction of copper from copper ore:
(a) \( 2 C u_{2} S(l)+3 O_{2}(g) \rightarrow \)
\( 2 C u_{2} O(l) 2 C u_{2} O(l)+2 S O_{2}(g) \)
(b) \( 2 C u_{2} O(l)+C u_{2} S(l) \rightarrow 6 C u(l)+ \)
\( S O_{2}(g) \)
If \( C u_{2} O \) and \( C u_{2} S \) act as oxidising and
reducing agent respectively in reaction
(b) then enter 1 else 0.


How are the colloidal solutions
classified on the basis of physical states of the dispersed phase and dispersion medium?


The co-efficient of \( x^{5} \) in the expansion of
\( (1+x)^{21}+(1+x)^{22}+\dots \dots+ \)
\( (1+x)^{30} \) is:
A . \( ^{51} C_{5} \)
в. \( ^{9} C_{5} \)
c. \( ^{31} C_{6}-^{21} C_{6} \)
D. \( ^{30} C_{5}+^{20} C_{5} \)


\( A \)
\( A \)
\( A \)
\( A \)


Solve: \( \frac{\boldsymbol{x}+\mathbf{2 0}}{\mathbf{9}}+\frac{\mathbf{3} \boldsymbol{x}}{\mathbf{7}}=\mathbf{6} \)


Carbylamine test is performed in the
presence of \( K O H \) by heating a mixture
of:
A. an alkyl halide and a primary amine
B. chloroform and silver powder
c. an alkyl cyanide and a primary amine
D. tri-halogenated methane and a primary amine


Identify the wrong statements for
asteroids:
A. Revolve around the Sun
B. Separate inner and outer planets
C. Can only be seen through any telescopes
D. Asteroids are rock-like structures


\( f_{2} \) are separated by a horizontal
distance \( \left.d \text { (where } d<f_{1} \text { and } d<f_{2}\right) \)
and their centers are displaced by a
vertical separation \( \Delta \) as shown in the
figure. Taking the origin of coordinates,
O at the center of left lens, the \( x \) and \( y \)
coordinates of the focal point of this
lens system for a parallel beam of rays coming from the left are given by
A \( x=\frac{f_{1} f_{2}}{f_{1}+f_{2}}, y=\Delta \)
B. \( x=\frac{f_{1}\left(f_{2}+d\right)}{f_{1}+f_{2}-d}, y=\frac{\Delta^{2}}{f_{1}+f_{2}} \)
c. \( x=\frac{f_{1} f_{2}+d\left(f_{1}-d\right)}{f_{1}+f_{2}-d}, y=\frac{\Delta\left(f_{1}-d\right)}{f_{1}+f_{2}-d} \)
D. \( x=\frac{f_{1} f_{2}+d\left(f_{1}-d\right)}{f_{1}+f_{2}-d}, y=0 \)


Meiosis I is reduction division. Meiosis
Il is equational division due to
A. Separation of chromatids
B. crossing over
c. Pairing of homologous chromosomes
D. Disjunction of homologous chromosomes


\( \left|\begin{array}{ccc}\mathbf{1} & \boldsymbol{a} & \boldsymbol{b} \boldsymbol{c} \\ \mathbf{1} & \boldsymbol{b} & \boldsymbol{c a} \\ \mathbf{1} & \boldsymbol{c} & \boldsymbol{a b}\end{array}\right|=\boldsymbol{\lambda}\left|\begin{array}{ccc}\boldsymbol{a}^{2} & \boldsymbol{b}^{2} & \boldsymbol{c}^{2} \\ \boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} \\ \boldsymbol{1} & \boldsymbol{1} & \boldsymbol{1}\end{array}\right| \) then
\( \lambda \) is equal to
\( A \)
B . -
\( c \)
\( D .- \)


\( _{6}^{14} C \) in upper atmosphere is generated by the nucleus reaction:
A \( \cdot \frac{14}{7} N+_{1}^{1} H \longrightarrow_{6}^{14} C+_{1}^{0} e+_{1}^{1} H \)
B . \( \frac{14}{7} N \longrightarrow_{6}^{14} C+_{1}^{0} e \)
C \( \cdot \frac{14}{7} N+_{0}^{1} n \longrightarrow_{6}^{14} C+_{1}^{1} H \)
D \( \cdot \frac{14}{7} N+\frac{1}{1} H \rightarrow \frac{11}{6} C+_{2}^{4} H e \)


Choose the correct statement from the
following:
This question has multiple correct options
A. Nitrogen is neutral to litmus
B. Nitrogen is a noncombustible and non-supporter of combustion
C. Nitrogen is a poisonous gas
D. At low temperature, nitrogen can be liquefied on compression


Differentiate the following function with
respect to \( x \)
\( \boldsymbol{x}^{5}\left(\boldsymbol{3}-\boldsymbol{6} \boldsymbol{x}^{-\boldsymbol{9}}\right) \)
A. \( 15 x^{-4}+24 x^{-5} \)
B \( \cdot 15 x^{5}+24 x^{-5} \)
\( \mathbf{c} \cdot 15 x^{4}+24 x^{-4} \)
D. \( 15 x^{4}+24 x^{-5} \)


The laws of multiple proportion was proposed by :
A. Lavoisier
B. Dalton
c. Proust
D. Gay Lussac


If plant is first exposed to light of 730 nm wavelength and then to of \( 600 \mathrm{nm} \) then plant will
A. Show inhibited growth
B. Resume normal growth
c. will not grow
D. Die immediately


State whether the given statement is True or False :

The force on a mass m due to gravity is
\( \mathrm{mg} \)
A. True
B. False


Write \( \tan ^{-1}\left(\frac{\sqrt{1+x^{2}}-1}{-x}\right), x \neq 0 \) in
the simplest form


The material used to slow the neutrons
in a reactor is called
A. Control rod
B. Moderator
c. Fuel
D. Heat exchanger


After a sperm has penetrated an ovum in the process of fertilisation, entry of further sperms is prevented by
A. Development of the pigment coat
B. Development of the vitelline membrane
c. condensation of yolk
D. Formation of fertilisation membrane


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


Using differentials, find the sum of digits approximate value of the following up to 3 places of decimal. \( (15)^{\frac{1}{4}} \)


toppr
Q Type your questic
instantaneous axis passing through the center of mass. These axes need not be
stationary. Consider, for example, a thin uniform disc welded (rigidly fixed) horizontally at its rim to a mass less stick, as shown in the figure. When the disc-stick system is rotated about the
origin on a horizontal friction less plane
with angular speed \( \omega \), the motion at any instant can be taken as a combination
of (i) a rotation of the center of mass of
the disc about the z-axis, and (ii) a
rotation of the disc through an
instantaneous vertical axis passing
through its center of mass (as is seen from the changed orientation of points
\( P \) and \( Q . \) Both these motions have the
same angular speed \( \omega \) in this case. Now consider two similar systems as
shown in the figure: Case
(a) the disc
with its face vertical and parallel to \{it
\( x-z\} \) plane; Case
(b) the disc with its
face making an angle of \( 45^{\circ} \) with \( \{\text { it } x-y\} \)
plane and its horizontal diameter parallel to x-axis. In both the cases, the
disc is welded at point \( P, \) and the
systems are rotated with constant
angular speed \( \omega \) about the z-axis.
Which of the following statements regarding the angular speed about the instantaneous axis (passing through the center of mass) is correct?
A. It is \( \sqrt{2} \omega \) for both the cases
B. It is \( \omega \) for case
(a); and \( \frac{\omega}{\sqrt{2}} \) for case (b)
\( c . \) It is \( \omega \) for case (a); and \( \sqrt{2} \omega \) for case (b)
D. It is \( \omega \) for both the ca


Assertion
Secondary succession takes place in
recently denuded area
Reason
It is caused due to baring of an area
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


For the given data, \( S D=10, A M=20 \)
the coefficient of variation is
A . 47
B. 24
c. 44
D. 50


Identify the compound that exhibits tautomerism.
A . 2-butene
B. Lactic acid
c. 2-Pentanone
D. Benzaldehyde


Find equivalent capacitance between
points \( A \) and \( B \) :
\( ^{A} \cdot \frac{5 C}{3} \)
в. \( \frac{4 C}{3} \)
\( c . C \)
0.20


If pressure of a gas contained in a closed vessel is increased by \( 0.4 \% \)
when heated by \( 1^{\circ} \mathrm{C} \) its initia
temperature must be:
\( \mathbf{A} \cdot 250 K \)
B . \( 250^{\circ} \mathrm{C} \)
c. \( 2500 K \)
D. \( 25^{\circ} \mathrm{C} \)


In meiosis I, the inter zonal fibers
appear in which stage?
A. Prophase I
B. Metaphase
c. Anaphase!
D. Telophase I


The half life period of a first order reaction is 10 minutes. The time
required for the concentration of the
reactant to change from \( 0.08 M \) to 0.02
\( M \) is:
A . 10 min
B. 20 min
c. 30 min
D. 40 min


Sexually reproducing organisms are
A. Monkey
B. Hydra
\( c . \) cat
D. Both A and C


By a bullet fire by a gun is more dangerous then bullet fire with medium
speed? Explain it properly


Kinetic energy of monoatomic gas at \( 300 \mathrm{K} \) in \( \mathrm{kJ} \) is:
A . 3.74
B. 348
c. 34.8
D. 3.48


What is Plasticity?


Let \( \boldsymbol{f}(\boldsymbol{x}) \) denotes the fractional part of \( \mathbf{a} \) real number \( x \). Then the value of
\( \int_{0}^{\sqrt{3}} f\left(x^{2}\right) d x \)
A \( \cdot 2 \sqrt{3}-\sqrt{2}-1 \)
1 1
в. \( 0(z e r o) \)
c. \( \sqrt{2}-\sqrt{3}+1 \)
D. \( \sqrt{3}-\sqrt{2}+1 \)


An organic compound \( \boldsymbol{X} \) give following laboratory tests.
(i) It gives white precipitate with tollen's reagent
(ii) it gives +ve iodoform test
(iii) It gives lucas test within 5 min
\( X \) can be:
A. \( H-C \equiv C-\left(C H_{2}\right)_{n}-_{O H}^{C H}-C H_{2}-C H_{3} \)
в. \( C H_{3}-C \equiv C-\left(C H_{2}\right) n-C H-C H_{3} \)
c. \( H-C \equiv C-\left(C H_{2}\right) n-C H-C H_{3} \)
D. none of the above


Obtain a differential equation by
eliminating \( c \) when it is given
\( \tan ^{-1} x+\tan ^{-1} y=\tan ^{-1} c \)


The number of lines of symmetry that
the given square has is
\( A \cdot 4 \)
B. 2
\( c \cdot 3 \)
D.


Find the principal value of \( \operatorname{cosec}^{-1}(-\sqrt{2}) \)


Q Type your question
parallel smooth conducting rails. A conducting rod lies on these fixed
horizontal rails and a uniform
constant magnetic field \( B \) exists
perpendicular to the plane of the rails as shown in the figure. If the rod is given
a velocity \( v \) and released as shown in
figure, it will stop after some time. The
total work done by magnetic field is negative

STATEMENT - 2 : If force acts opposite to direction of velocity its work done is negative.
A. Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement- -
B. Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-
c. Statement-1 is True, Statement-2 is False
D. Statement-1 is False, Statement-2 is True


Conditions for internal reflection is:
A. Light must travel from rare to denser medium
B. The angle of incidence should be greater than the critical angle for the given pair of media
c. Both
D. None


If the sequence of bases in one strand of DNA is ATGACTGTC then the sequence of bases in its complementary strands
is:
в. тบстяบссия
c. GUAGTUAUG
D. None of the above


Statement: In Dobernier classification
of elements, the atomic weight of the
middle element is equal to the average of the extreme elements of a triad.
State whether the given statement is true or false.
A. True
B. False


The atomic numbers of elements of
second inner transition elements lie in
the range of :
\( A \cdot 88 \) to 101
B. 89 to 102
\( c \cdot 90 \) to 103
D. 91 to 104


The percentage of copper and oxygen in samples of Cu0 obtained by different methods were found to be the same.
This illustrates the law of:
A. constant proportion
B. Conservation of mass
c. Multiple proportion
D. Reciprocal proportion


The frequency of radiation emitted when the electron falls from \( n=4 \) to
\( \boldsymbol{n}=\mathbf{1} \) in a hydrogen atom will be :
\( \left(\text { Given, } \boldsymbol{h}=\mathbf{6 . 6 2 5} \times \mathbf{1 0}^{-\mathbf{3 4}} \mathbf{J s}\right): \)
A \( \cdot 3.08 \times 10^{15} s^{-1} \)
В. \( 2.00 \times 10^{16} s^{-1} \)
c. \( 1.54 \times 10^{17} s^{-1} \)
D. \( 1.03 \times 10^{14} s^{-1} \)


One reason the Bohr model of the atom
ultimately failed was because it did not explain why?
A. moving electrons have a greater mass.
B. accelerating electrons do not emit electromagnetic radiation.
c. electrons in greater orbits of an atom have greater velocities
D. electrons in the orbits of an atom have negative energies.


(a) How would you account for the following:
(i) The chemistry of actinoids is more complicated as compared to lanthanoids
(ii) Transition metals form complex
compounds
(b) Complete the following equation:
\[
\mathbf{2} M n O_{4}^{-}+6 H^{+}+S O_{3}^{2-} \longrightarrow
\]


Chemical products, manufactured from nitric acid islare:
A. Nitroglycerine
B. TNT
c. xanthoproteic acid
D. all of the above


The number of valence electrons and
the valency with respect to hydrogen are equal for:
A. Sulphur
B. Silicon
c. Phosphorus
D. Chlorine


\( C u^{2+}+2 e^{-} \rightarrow C u \)
\( \boldsymbol{E}_{\text {red}} \boldsymbol{v s} \cdot \log \left[\boldsymbol{C u}^{2+}\right] \) graph is of the type
as shown in figure where \( O A=0.34 V \)
then electrode potential of the half cell of \( C u \mid C u^{2+}(0.1 M) \) will be :
A. \( _{-0.34}+\frac{0.0591}{2} \mathrm{V} \)
В. \( 0.34+0.0591 V \)
\( c .0 .34 V \)
D. none of thes


In Acacia species, the first few leaves are
pinnately compound. Then there are leaves with flattened petiole and fewer
pinnae. The leaves of adult plant has
parallel veined flattened petiole and no
pinnae. It shows that
A. Leaves of adult plant are reduced to phyllodes while those of the seedling are unreduced
B. The parallel-veined green structure of the adult plant are phylloclades
C. The plant shows developmental heterophylly, compound in seedling and simple in adult plant
D. The leaves of adult plant are unreduced while they are reduced in the seedling stage


The plot of \( \log _{e} R(R \) is radius of
nucleus) \( \boldsymbol{v} \boldsymbol{s} \log _{e} \boldsymbol{A}(\boldsymbol{A} \text { is mass no. }) \)
gives a straight line with slope equal to
A \( \cdot \frac{1}{2} \)
B. \( \frac{1}{3} \)
\( c \cdot \frac{1}{4} \)
D. 3


How many hydrogen atoms would you expect to find in a saturated
hydrocarbon with 7 carbon atoms?
A. 7
B. 16
\( c \cdot 18 \)
D. 14
E . 12


\( \boldsymbol{f}(\boldsymbol{x})=\mathbf{1} /\left(\mathbf{1}-\boldsymbol{e}^{-\mathbf{1} / \boldsymbol{x}}\right), \boldsymbol{x} \neq \mathbf{0}, \boldsymbol{f}(\mathbf{0})= \)
0 at \( x=0 \) Is function continuous at
\( x=0 ? \)


\( A M=8 x^{2}, M C=2 x^{2}, \) then find \( B M \)
and AB.


The freezing point of equimolal solution will be highest for:
A \( \cdot C_{6} H_{5} N H_{3} C l \)
в. \( A g N O_{3} \)
\( \mathbf{c} \cdot C a\left(N O_{3}\right)_{2} \)
\( \mathbf{D} \cdot L a\left(N O_{3}\right) \)
E. \( D- \) fructose


1 dioptre is equal to
\( \mathbf{A} \cdot 1 m \)
в. 1 ст
\( \mathbf{c} \cdot 1 m^{-1} \)
D. \( 1 \mathrm{cm}^{-1} \)


If \( x=2, \) then \( \left(x^{4}\right)^{\frac{1}{2}}= \)
\( A \cdot 2 \)
B.
\( c \cdot 4 \)
D.


Column II give acid and base from
which salt mention in column I are
formed. Match them correctly.


Myelin sheath is formed by
A. Ranvier cells
B. Muscle cells
c. Schwann cells
D. Axon


The name of genus begins with a and the name of species begins with
letter.
A. Capital letter, small letter
B. Small letter, capital Ietter
c. Capital letter, italics letter
D. Small letter, italics letter


A polynomial function \( f(x) \) satisfies the condition \( \boldsymbol{f}(\boldsymbol{x}+\mathbf{1})=\boldsymbol{f}(\boldsymbol{x})+\mathbf{2} \boldsymbol{x}+\mathbf{1} \)
Find \( \boldsymbol{f}(\boldsymbol{x}) \) if \( \boldsymbol{f}(\mathbf{0})=1 . \) Find also the
equations of the pair of tangents from
the origin on the curve \( y=f(x) \) and
compute the area enclosed by the curve
and the pair of tangents.
\( f(x)=x^{2}+1 ; y=\pm 2 x ;, A=\frac{2}{3} \) sq.units
B. \( f(x)=x^{2}-1 ; y=\pm 2 x ; A=\frac{2}{3} \) sq.units
c. \( f(x)=x^{2}+1 ; y=\pm 2 x ; \), \( A=\frac{3}{2} \) sq.units
D. \( f(x)=x^{2}-1 ; y=\pm 2 x ; A=\frac{3}{2} \) sq.units


A sample of a gas at STP contains \( 3.01 \times 10^{23} \) molecules and has a mass
of 20.0 grams. This gas would:
A. have a molar mass of 20.0 g/mol and occupy 11.2 liters
B. occupy 22.4 liters and have a molar mass of 30.0. g/mol
c. occupy 22.4 liters and have a molar mass of 20.0 g/mol
D. have a molar mass of \( 40.0 \mathrm{g} / \mathrm{mol} \) and occupy 33.6 liters
E. have a molar mass of 4 \( t \)


If \( y=3 \cos x, \) then \( \frac{d y}{d x} \) at \( x=\frac{\pi}{2} \) is
A. -3
B. 3
\( c .0 \)
D. -


What will be the effect of addition of
organic material on water?
A. coD remain unaffected
B. BOD remain unaffected
c. Increases BOD
D. Reduces BOD


What is \( \left[\boldsymbol{S O}_{4}^{2-}\right] \) when first solid gets precipitated?
A \( \cdot\left[S O_{4}^{2-}\right]=1.0 \times 10^{-8} M \)
B . \( \left[S O_{4}^{2-}\right]=1.1 \times 10^{-8} M \)
\( \mathbf{C} \cdot\left[S O_{4}^{2-}\right]=1.2 \times 10^{-8} M \)
D. None of these


The parabola \( (\boldsymbol{y}+\mathbf{1})^{2}=\boldsymbol{a}(\boldsymbol{x}-\boldsymbol{2}) \)
passes through the point (1,-2) then the equation of its directrix is
A \( .4 x+1=0 \)
B. \( 4 x-1=0 \)
\( \mathbf{c} \cdot 4 x+9=0 \)
D. \( 4 x-9=0 \)


Where is the Birbal Sahni Institute of
Palaeobotany located?
A. Aurangabad
B. Kanpur
c. New Delhi
D. Lucknow


Differentiate with respect to \( x \) :
\( e^{\sin ^{-1} 2 x} \)


Equivalent conductance and molar
conductance of \( \boldsymbol{F e}_{2}\left(\boldsymbol{S} \boldsymbol{O}_{4}\right)_{3} \) are related
by relation:
\( \mathbf{A} \cdot \wedge_{e}=\Lambda_{m} \)
B \( \cdot \wedge_{e q}=\frac{\Lambda_{m}}{3} \)
\( \mathbf{C} \cdot \wedge_{e q}=3 \wedge_{m} \)
D \( \cdot \wedge_{e q}=\frac{\Lambda_{m}}{6} \)


Figure shows two flasks connected to each other. The volume of the flask 1 is
twice that of flask 2. The system is filled with an ideal gas at temperature \( 100 \mathrm{K} \) and \( 200 \mathrm{K} \) respectively in the flasks. If the mass of the gas in \( 1 \mathrm{m} \), then what is the mass of the gas in flask 2 in equilibrium?
A . \( m \)
в. \( \frac{m}{2} \)
c. \( \frac{m}{4} \)
D. \( \frac{m}{8} \)


\( 510 m g \) of a liquid on vaporization in victor Mayer's apparatus displaces \( 67.2 m l \) of dry air (at NTP). The molecular weight of liquid is:
A. 130
B. 17
\( c .1700 \)
D. 170


Which one of the following does not have intermolecular H-bonding? This question has multiple correct options
A. \( C H_{4} \)
в. \( H_{2} S e \)
c. \( N_{2} H_{4} \)
D. \( H_{2} S \)


Which of the following are properties of non-metals?
A. Low melting point
B. Poor conductor of electricity
c. Low densities
D. All of these


In which phase of mitosis, the chromosomes are arranged around the equator of the spindle?
A. Prophase
B. Metaphase
c. Anaphase
D. Telophase


The gravitational force between two stones of mass \( 1 k g \) each, separated by
a distance of \( 1 \mathrm{m} \) in vacuum is
A . zero
B . \( 6.675 \times 10^{-5} N \)
c. \( 6.675 \times 10^{-8} N \)
D. \( 6.675 \times 10^{-11} N \)


Which of the following chemicals contains chlorine?
A. Fischer salt
B. Epsom salt
c. fremy's salt
D. Spirit of salt


An ideal gas at \( 27^{\circ} C \) is compressed adiabatically to \( \frac{8}{27} \) of its original volume. The rise in temperature is (Take
\( \gamma=5 / 3) \)
\( \mathbf{A} \cdot 475 K \)
в. \( 150 K \)
c. \( 275 K \)
D. 375K


A linear object of size \( 1.5 \mathrm{cm} \) placed at \( 10 \mathrm{cm} \) from a lens of focal length \( 20 \mathrm{cm} \)
The optic centre of lens and the object
are displaced a distance \( \Delta=0.5 \mathrm{cm} \) as
shown in the figure. The magnification
of the image formed is \( \mathrm{m} \) (Take optic centre as origin). The coordinates of
image of \( A \) and \( B \) are \( \left(x_{1}, y_{1}\right) \) and
\( \left(x_{2}, y_{2}\right) \) respectively. Then

This question has multiple correct options
A \( \cdot\left(x_{1}, y_{1}\right)=(-20 c m,-1 c m) \)
в. \( \left(x_{2}, y_{2}\right)=(-20 c m, 2 c m) \)
\( \mathrm{c} \cdot m=3 \)
D. \( m=2 \)


is not an adaptation for self
protection.
A. Migration
B. Change in colour
c. Moving in groups
D. Bearing eyelike patterns


Match the items in Column A with those
in Column B.


Find the probability of getting a head
when a coin is tossed once. Also find the
probability of getting a tail.


\( \operatorname{Let} P=\left(\begin{array}{cc}\cos \frac{\pi}{4} & -\sin \frac{\pi}{4} \\ \sin \frac{\pi}{4} & \cos \frac{\pi}{4}\end{array}\right) \) and \( x= \)
\( \left(\begin{array}{c}\frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}}\end{array}\right) \cdot \operatorname{Then} P^{3} X \) is equal to
A \( \cdot\left(\begin{array}{l}0 \\ 1\end{array}\right) \)
B. \( \left(\frac{-1}{\sqrt{2}}\right) \)
\( \left(\begin{array}{c}-1 \\ 0\end{array}\right) \)
D \( \left(\begin{array}{l}-\frac{1}{\sqrt{2}} \\ -\frac{1}{\sqrt{2}}\end{array}\right) \)


Assertion
Red phosphorus is used in match
industry.
Reason
Red phosphorus shows
phosphorescence.
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


If the \( x \) -axis divide the area of the region
bounded by the parabolas \( y=4 x-x^{2} \)
and \( y=x^{2}-x \) in the ratio of \( a: b \) then
\( a b \) is equal to


The length \( x \) of a rectangle is decreasing at a rate of \( 3 \mathrm{cm} / \mathrm{min} \) and
width \( y \) is increasing at a rate of \( 2 c m / m i n . \) When \( x=10 c m \) and \( y= \)
\( 6 c m, \) find the rates of change of (i) the
perimeter
(ii) the area of the rectangle.


Which of the following pair of sides can form triangle? This question has multiple correct options
\( \mathbf{A} \cdot 5 \mathrm{cm}, 6 \mathrm{cm}, 4 \mathrm{cm} \)
в. 13 ст, 12 ст, 24 ст
c. \( 2 \mathrm{cm}, 7 \mathrm{cm}, 9 \mathrm{cm} \)
D. \( 5.6 \mathrm{cm}, 6.5 \mathrm{cm}, 12 \mathrm{cm} \)


The concept that light energy is converted to chemical energy in photosynthesis was given by
A. Priestley
B. Meyer
c. stephen Hales
D. Helmont


What is \( \beta \) -decay? Give an example.


Use Euclid's division lemma to find the
HCF of the following 65 and 495
A . 5
B. 10
c. 15
D. 0


Which of the following organ system
takes in food, breaks it down into
smaller chemical units, and absorbs
the nutrient molecules?
A. Digestive system
c. circulatory system
D. Endocrine system
E. Nervous system


Which of the following alkanes can form only two monochloro derivatives?
A. hexane
B. 2-methyl pentane
c. 2,3-dimethyl butane
D. 3-methyl pentane


singly ionized helium(x), ionized deuteron(y), alpha(z) particles are projected into a uniform magnetic field \( \mathbf{3} \times \mathbf{1 0}^{-4} \) Tesla with velocities \( 10^{5} \boldsymbol{m} \boldsymbol{s}^{-1} \)
\( 0.4 \times 10^{4} m s^{-1} \) and \( 2 \times 10^{3} m s^{-1} \)
respectively. The correct relation between the ratio of the angular momentum to the magnetic moment of the particles is :
A. \( x>y=z \)
в. \( x<y<z \)
c. \( x<z<y \)
D. \( z>x>y \)


Among the following, which are not given a proper place in periodic table?
A. Alkali earth metalss
B. Lanthanides
c. Actinides
D. Both B and C


Liquid hydrogen is used as a fuel for rocket propulsion.
A. True
B. False


The resistance of a wire of length 100
\( \mathrm{cm} \) and \( 7 \times 10^{-3} \mathrm{cm} \) radius is 6 ohm. Its
specific resistance is
\( \mathbf{A} \cdot 924 \times 10^{-8} \Omega c m \)
В. \( 92.4 \times 10^{-8} \Omega c m \)
c. \( 900 \times 10^{-8} \Omega c m \)
D. \( 224 \times 10^{-8} \Omega c m \)


Assertion
Acetic acid is an unsaturated
compound.
Reason
it has two double bonds.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


If \( A \) and \( B \) are two non-zero square
matrices of the same order such that
the product \( A B=0, \) then
A. both A and B must be singular
B. exactly one of them must be singular
c. atleast one of them must be non-singular
D. none of these


When the temperature of medium is
\( 20^{\circ} \mathrm{C} \) a certain substance cools from
\( 100^{\circ} \mathrm{C} \) to \( 60^{\circ} \mathrm{C} \) in 10 minutes. Its
temperature after 40 minutes from the beginning is
A \( \cdot 15^{\circ} \mathrm{C} \)
B . \( 20^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 25^{\circ} C \)
D. \( 30^{\circ} \mathrm{C} \)


The wave fronts of light wave traveling in vacuum are given by \( \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}=\boldsymbol{c} \)
The angle made by the light ray with the X-axis is:
A \( \cdot 0^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 90^{\circ} \)
D. \( \cos ^{-1} \frac{1}{\sqrt{3}} \)


The remainder obtained when \( t^{6}+ \)
\( 3 t^{2}+10 \) is divided by \( t^{3}+1 \) is
A \( \cdot t^{2}-11 \)
B . \( 3 t^{2}+11 \)
\( \mathbf{c} \cdot t^{3}-1 \)
D. \( 1-t^{3} \)


If a simple pendulum of mass \( \boldsymbol{m} \) is
displaced by a distance of \( x \) from its
mean position, then find the potential energy stored in it.


Two particles of masses \( m \) and \( 2 m \)
having same charges \( q \) each, are placed
in a uniform electric field \( \boldsymbol{E} \) and allowed
to move for the same time. Find the
ratio of their kinetic energies:


Two parallel wires \( P \) and \( Q \) carry electric currents of \( 10 A \) and \( 2 A \) respectively in mutually opposite directions. The
distance between the wires is \( 10 \mathrm{cm} \). If
the wire \( P \) is of infinite length and wire \( \mathrm{Q} \) is \( 2 m \) long, then the force acting \( \mathrm{Q} \)
will be
\( \mathbf{A} \cdot 4 \times 10^{-5} N \)
B. \( 8 \times 10^{-5} N \)
c. \( 6 \times 10^{-5} N \)
D. \( 14 \times 10^{-5} N \)


n homogenous catalytic reactions,
there are three alternative paths \( A, B \) and \( C \) (shown in figure). Which one of the following indicates the relative ease with which the reaction can take place?
\( \mathbf{A} \cdot A>B>C \)
в. \( C>B>A \)
c. \( B>C>A \)
D. \( A=B=C \)


The energy required to transfer an electron from second Bohr orbit to third
Bohr orbit in a hydrogen like atom with
nuclear charge \( Z_{e} \) is \( 6.8 e V \) The wavelength of radiation required to shift the electron from first orbit to
infinite orbit will be :
A \( \cdot 2.527 A^{\circ} \)
B . 25.27 A \( ^{\circ} \)
c. \( 252.7 A^{\circ} \)
D . 2527 A \( ^{\circ} \)


A solid sphere of mass \( \mathrm{M} \& \) radius \( \mathrm{R} \) is divided in two parts of masses \( \frac{7 M}{8} \& \) \( \frac{M}{8}, \) and converted to a disc of radius \( 2 \mathrm{R} \)
\& solid sphere of radius 'r' resp. Find \( \frac{l_{1}}{l_{2}} \)
if \( l_{1} \& l_{2} \) are moment of inertia of disc
\& solid sphere respectively.
A . 200
в. 140
\( c \cdot 120 \)
D. 180


A cosmic body \( A \) moves to the Sun with
velocity \( v_{0} \) (when far from the Sun) and
aiming parameter \( l \) the arm of the
vector \( \vec{v}_{0} \) relative to the centre of the
Sun (figure shown above). Find the
minimum distance by which this body will get to the Sun.


Let \( \boldsymbol{f} \) be a function satisfying \( \boldsymbol{f}^{\prime \prime}(\boldsymbol{x})= \)
\( x^{-3 / 2}, f^{\prime}(4)=2 \) and \( f(0)=0 . \) Then
\( f(784) \) is equal to


Area of the region bounded by \( y^{2} \leq \) \( \mathbf{4} \boldsymbol{x}, \boldsymbol{x}+\boldsymbol{y} \leq \mathbf{1}, \boldsymbol{x} \geq \mathbf{0}, \boldsymbol{y} \geq \mathbf{0} \) is \( \boldsymbol{a} \sqrt{\mathbf{2}}+\boldsymbol{b} \)
then value of \( a-b \) is?
A .4
B. 6
\( c \cdot 8 \)
D. 12


Simplify \( (2 a+b)(c-2 d)+(a- \)
\( \boldsymbol{b})(\boldsymbol{2} \boldsymbol{c}+\boldsymbol{3} \boldsymbol{d})+\boldsymbol{4}(\boldsymbol{a} \boldsymbol{c}+\boldsymbol{b} \boldsymbol{d}) \)
A. \( 8 a d+a c b-c-b d \)
B. \( 8 a c-a d-b c-b d \)
c. \( 8 c-a d+b c-d \)
D. \( 8 a c+a d-b c d \)


Compound \( (A) C_{5} H_{10} O \) forms a
phenylhydrazone and gives negative Tollen's and iodoform test. Compound
(A) on reduction gives n-pentase. Compound \( (\boldsymbol{A}) \) is:
A . a primary alcohol
B. an aldehyde
c. a ketone
D. a secondary alcohol


Show that:
\( \left|\begin{array}{ccc}\boldsymbol{a}^{2} & \boldsymbol{b}^{2} & \boldsymbol{c}^{2} \\ \boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} \\ \mathbf{1} & \mathbf{1} & \mathbf{1}\end{array}\right|=-(\boldsymbol{a}-\boldsymbol{b})(\boldsymbol{b}-\boldsymbol{c})(\boldsymbol{c}- \)
\( \boldsymbol{a}) \)


How many endocrine glands are located in human brain?
\( A \cdot 3 \)
B. 4
\( c \cdot 2 \)
\( D \)


Find the domain of definition of the
following function. \( \boldsymbol{y}=\sqrt{\boldsymbol{x}-\boldsymbol{x}^{2}} \)


. If \( A, B, C \) are angles of angle and \( \mid \begin{array}{ccc}\mathbf{1} & \mathbf{1} \\ \mathbf{1}+\boldsymbol{s} \mathbf{i} \boldsymbol{n} \boldsymbol{A} & \mathbf{1}+\boldsymbol{\operatorname { s i n }} \boldsymbol{B} & \mathbf{1}+ \\ \boldsymbol{s i n} \boldsymbol{A}+\boldsymbol{s i n}^{2} \boldsymbol{A} & \boldsymbol{s i n} \boldsymbol{B}+\boldsymbol{s i n}^{2} \boldsymbol{B} & \boldsymbol{s i n} \boldsymbol{C}\end{array} \)
\( =0 \) then triangle is isosceles
II. If \( \boldsymbol{a}=\mathbf{1}+\mathbf{2}+\mathbf{4}+--- \) upto \( \mathbf{n} \)
terms \( \boldsymbol{b}=\mathbf{1}+\mathbf{3}+\mathbf{9}+--- \) up to \( \mathbf{n} \)
terms \( c=1+5+25+---- \) up to \( n \) terms then \( \Delta\left|\begin{array}{ccc}a & 2 b & 4 c \\ 2 & 2 & 2 \\ 2^{n} & 3^{n} & 5^{n}\end{array}\right|=0 \)
A. I, II both are true
B. only lis true
c. only I I is true
D. neither of them are true


A boy of height \( 1.5 \mathrm{m}, \) making move on a skateboard due east with velocity \( 4 \mathrm{m} \) s
\( -1, \) throws a coin vertically up with a
velocity of \( 3 \mathrm{m} \mathrm{s}^{-1} \) relative to himself.
a. Find the total displacement of the coin relative to ground till it comes to the hand of the boy.
b. What is the maximum height attained by the coin w.r.t to ground?


The given figure is drawn for a
A. Freely falling body
B. Body at rest with no external force
C. Body at rest with balanced external forces
D. Body in non-uniform circular motion


The resultant of: \( \frac{20 \times(0.3)^{2}}{0.018} \div 0.5 \) of
0.2 is
A . 10
в. 100
\( c \cdot 20 \)
D. 1000


Motion of an oscillating liquid in a
tube is
A. periodic but not simple harmonic
B. non-periodic
C. simple harmonic and time period is independent of the density of the liquid.
D. simple harmonic and time period is directly proportional to the density of the liquid


Mass of negative ion is slightly greater than its neutral atom.
A. True
B. False


The momentum of a massive object at
rest is
i) very large ii) very small iii) zero iv infinity


A slit of width \( a \) is illuminated by a
monochromatic light of wavelength \( \mathbf{6 5 0} \) nm. The value of \( a \) when the first
minima falls at an angle of diffraction
of \( 30^{0} \) is
A. \( 1.3 \times 10^{-6} m \)
B . \( 2.6 \times 10^{-6} m \)
c. \( 3.9 \times 10^{-6} \mathrm{m} \)
D. \( 5.2 \times 10^{-6} m \)


Which of the following types of reactions occur when a hydrocarbon has a double bond?
A. Substitution reaction
B. Addition reaction
c. Photolysis
D. None of these


The digits of a two digit number differ by \( 7 . \) If the digits are interchanged and the resulting numbers is added to original numbers, we get \( 121 . \) What is the original number?


When sodium benzoate is heated with
sodalime, it gives:
A. Benzene
B. benzoic acid
c. calcium benzoate
D. none of these


The functional group, present in
\( \boldsymbol{C H}_{3} \boldsymbol{C O O C}_{2} \boldsymbol{H}_{5} \) is :
A. ketonic
B. aldehydic
c. ester
D. carboxylic


A \( 20 \mathrm{kg} \) metal block is place on a horizontal surface. The block just begins to slide when horizontal force of \( 100 \mathrm{N} \) is applied to it. Calculate the coefficient of static friction.
A . 78.4
B. 100 N
\( c \cdot 84 \mathrm{N} \)
D. 9.5 N


The lower jaw of a mammal is made up
A. Dentary
B. Maxilla
c. Premaxilla
D. Post maxilla


Nylon-6 is prepared by linear condensation homopolymerization
reaction of:
A. caprolactum
B. hexamethylene diamine and adipic acid
c. 6 -aminohexanoic acid
D. acrylonitrile


The percentage by mole of \( N O_{2}(g) \) in a
mixture of \( N O_{2}(g) \) and \( N O(g) \) having average molecular mass 34 is :
A . 25\%
B. 20\%
c. \( 40 \% \)
D. 75\%


Hormone oxytocin at the time to birth acts on uterus by
A. Stimulating the smooth muscles to contract
B. Reducing the lumen of uterus
c. Increasing the movement of foetus
D. Producing rhythmic movements in uterus


The principal solution of the equation \( \cot x=-\sqrt{3} \) is
A \( \cdot \frac{\pi}{6} \)
в. \( \frac{\pi}{3} \)
c. \( \frac{5 \pi}{6} \)
D. \( -\frac{5 \pi}{6} \)


If \( a<\frac{1}{32}, \) then the number of solutions
of \( \left(\sin ^{-1} x\right)^{3}+\left(\cos ^{-1} x\right)^{3}=a \pi^{3}, \) is
\( A \cdot 0 \)
B.
\( c \cdot 2 \)
D. infinite


What is the Sl unit of self-inductance?
A. Henry
B. Tesla
c. weber
D. Gauss


Complete the following chemical reactions. Classify the below into (a) hydrolysis, (b) redox and (c) hydration reactions.
(i) \( P b S(s)+H_{2} O_{2}(a q) \rightarrow \)
(ii) \( M n O_{4}^{-}(a q)+H_{2} O_{2}(a q) \rightarrow \)
(iii) \( \boldsymbol{C a O}(\boldsymbol{s})+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \rightarrow \)
(iv) \( A l C l_{3}(g)+H_{2} O(l) \rightarrow \)
\( (v) C a_{3} N_{2}(s)+H_{2} O(l) \rightarrow \)


Which of the following is a Quadratic Equation?
A \( .5 x+8=0 \)
B \( \cdot 6 x^{2}+7 x=19 \)
\( \mathbf{c} \cdot x+1 \)
D. None of these


If the roots of the equation \( x^{2}-15- \)
\( \boldsymbol{m}(\mathbf{2} \boldsymbol{x}-\mathbf{8})=\mathbf{0} \) are equal, then \( \boldsymbol{m}= \)
A. 3,-5
в. 3,5
c. -3,5
D. -3,-5


Length of the latus rectum of the
hyperbola \( \boldsymbol{x} \boldsymbol{y}-\boldsymbol{3} \boldsymbol{x}-\boldsymbol{4} \boldsymbol{y}+\boldsymbol{8}=\mathbf{0} \)
A .4
B. \( 4 \sqrt{2} \)
c. 8
D. none of these


Draw a labelled diagram to show
\( (i) \)
white appearance of the sun at noon when it is overhead.


If a body is projected horizontally from the top of the tower then acceleretions
of the body along the vertical direction of path is
A. Decreases
B. Increases
c. Remains same
D. zero


If value of \( x \) which satisfy equation
\( \cos ^{-1} x<2 \) is \( x \epsilon(a, b] \)
Find the value of \( a+b \)
A. \( -1-\cos 2 \)
B. \( 1-\cos 2 \)
c. \( -1+\cos 2 \)
D. \( 1+\cos 2 \)


Which of the following represents
saponification reaction?
\( \mathbf{A} \cdot C H_{3} C O O N a+N a O H \stackrel{C a O}{\longrightarrow} C H_{4}+N a_{2} C O_{3} \)
B \( \cdot C H_{3} C O O H+C_{2} H_{5} O H \frac{H_{2} S O_{4}}{\longrightarrow} C H_{3} C O O C_{2} H_{5}+ \)
\( H_{2} O \)
c. \( 2 C H_{3} C O O H+2 N a \rightarrow 2 C H_{3} C O O N a+H_{2} \)
D. \( C H_{3} C O O C_{2} H_{5}+N a O H \rightarrow C H_{3} C O O N a+C_{2} H_{5} O H \)


A gun of mass \( m_{1} \) fires a bullet of mass
\( m_{2} \) with a horizontal speed \( v_{0} . \) The gun
is fitted with a concave mirror of focal
length \( f \) facing toward a receding
bullet. Find the speed of separations of
the bullet and the image just after the
gun was fired.


Figure gives the \( x \) -t plot of particle executing one-dimensional simple harmonic motion.Give the signs of
position, velocity and acceleration variables of the particle at \( t=0.3 s, 1.2 s \)
-1.2 s.


List 1 and List 2 contains four entries
each. Entries of List 1 are to be matched
with some entries of List 2. One or more
than one entries of List 1 may have the matching with the same entries of List
2


A 6 volt battery is connected to the terminals of the three metre long wire of uniform thickness and the resistance of
100\Omega. The difference of potential between two points on the wire
separated by a distance of \( 50 \mathrm{cm} \) will be
A . \( 1.5 v \)
B. 3V
\( c .3 .5 v \)
D. \( 1 \mathrm{v} \)


A certain sum of money at simple interest amounts to Rs. 1012 in \( 2 \frac{1}{2} \) years and toRs.1067.20 in 4 years.The rate of interest per annum is
A . 2.5\%
B. 3\%
c. \( 4 \% \)
D. 5\%


The reduction potential of hydrogen
electrode will be positive if:
\( \mathbf{A} \cdot p\left(H_{2}\right)=1 a t m,\left[H^{+}\right]=1 M \)
B \( \cdot p\left(H_{2}\right)=1 a t m,\left[H^{+}\right]=2 M \)
\( \mathbf{c} \cdot p\left(H_{2}\right)=2 a t m,\left[H^{+}\right]=2 M \)
D \( \cdot p\left(H_{2}\right)=2.5 a t m,\left[H^{+}\right]=1.5 M \)


Solve: \( \frac{1}{\sqrt{4+3 x-2 x^{2}}} \)


The monomer that undergo radical
polymerisation most easily is:
\( \mathbf{A} \cdot C H_{2}=C H_{2} \)
\( \mathbf{B} \cdot C_{6} H_{5} C H=C H_{2} \)
\( \mathbf{c} \cdot C_{6} H_{6} \)
D. \( C H_{3}-C H=C H_{2} \)


Find the square root of -625 \( (\sqrt{-1}=i) \)
\( \mathbf{A} \cdot \mathbf{5} \)
B. -5
\( c .25 i \)
D. -25


Which of the following is the radio isotope in this pair?
\( _{15}^{30} P_{, 15}^{32} P \)
B . \( _{15}^{30} P \)
c. Both of them
D. None of them


A particle is projected vertically upwards from the surface of teh earth
(radius \( R_{e} \) ) with a kinetic energy equal to half of the minimum value needed for
it to escape. The height to which it rises above the surface ot the earth is \( \frac{\boldsymbol{R}}{\boldsymbol{n}} \) where \( n \) is:


Prove that \( 7 \sqrt{5} \) is irrationals number.


\( \int \frac{1}{x \sqrt{1-x^{3}}} d x= \)
\( a \log \left|\frac{\sqrt{1-x^{3}}-1}{\sqrt{1-x^{3}}+1}\right|+b, \) then a is equal
to
A \( \cdot \frac{1}{3} \)
B. \( \frac{2}{3} \)
\( c \cdot \frac{-1}{3} \)
D. \( \frac{-2}{3} \)


In a Zener diode regulated power supply, unregulated DC input of \( 10 V \) is
applied. If the resistance \( \left(R_{s}\right) \) connected
in series with a Zener diode is \( 200 \Omega \)
and the Zener voltage \( V_{z}=5 V \), the
current across the resistance \( \boldsymbol{R}_{s} \) is:
\( \mathbf{A} \cdot 15 m A \)
B. \( 10 \mathrm{mA} \)
c. \( 20 m A \)
D. \( 5 m A \)
E . \( 25 m A \)


If \( \mathrm{I}, \mathrm{m}, \mathrm{n} \& \mathrm{I}^{\prime}, \mathrm{m}^{\prime}, \mathrm{n}^{\prime} \) be the direction cosines
of two lines which include an angle \( \boldsymbol{\theta} \)
then
\( \mathbf{A} \cdot \cos \theta=l l^{\prime}+m m^{\prime}+n n^{\prime} \)
B . \( \sin \theta=l l^{\prime}+m m^{\prime}+n n^{\prime} \)
\( \mathbf{c} \cdot \cos \theta=m n^{\prime}+m^{\prime} n+n l+n^{\prime} l+l m^{\prime}+l^{\prime} m \)
\( \mathbf{D} \cdot \sin \theta=m n^{\prime}+m^{\prime} n+n l+n^{\prime} l+l m^{\prime}+l^{\prime} m \)


Solve :
\( (x+y-4)^{2}+(x-y-2)^{2}=0 \)
A \( . x=1, y=1 \)
в. \( x=4, y=1 \)
c. \( x=3, y=1 \)
D. \( x=5, y=1 \)


Indirect tax is:
A. Sales Tax
B. House Tax
C. Water Tax
D. Surcharge


Define Bulk modulus.


What is the smallest number by which
3645 be multiplied so that the product becomes a perfect cube?
A . 5
B . 25
c. 15
D. 35 5


Show that point \( A(7,5), B(2,3) \) and \( \mathrm{C}(6,-7) \) are the vertices of a right triangle. Also find its area.


Which of the following instrument can
be used to determine the radius of
curvature of a spherical surface?
A. Spherometer
B. Vernier callipers
c. screw gauge
D. simple pendulum


ABCDEF is a regular hexagon with
centre \( 0 . \) If area of triangle \( \mathrm{OAB} \) is \( 9 \mathrm{cm}^{2} \) find the area of the circle in which the
hexagon is inscribed.


A car travels first \( 30 k m \) with a uniform
speed of \( 60 k m p h \) and then next \( 30 k m \)
with a uniform speed of \( 40 k m p h \). Find
the average speed of the car.
A. \( 24 \mathrm{kmph} \)
B. \( 48 \mathrm{kmph} \)
c. 72 kmph
D. \( 96 \mathrm{kmph} \)


The value of \( \lim _{x \rightarrow 0} \frac{\sqrt{x^{2}+1}-1}{\sqrt{x^{2}+9}-3} \) is?
\( A \cdot 3 \)
B. 4
\( c \cdot 1 \)
D. 2


\( \left|\begin{array}{ccc}\mathbf{1} & \mathbf{1} & \mathbf{1} \\ \boldsymbol{x} & \boldsymbol{y} & \boldsymbol{z} \\ \boldsymbol{y} \boldsymbol{z} & \boldsymbol{z} \boldsymbol{x} & \boldsymbol{x} \boldsymbol{y}\end{array}\right|=\boldsymbol{b}(\boldsymbol{x}-\boldsymbol{y})(\boldsymbol{y}- \)
\( z)(z-x) . \) Find


The vector \( \overline{O P}=\hat{i}+2 \hat{j}+2 \hat{k} \) turns
through a right angle passing through the positive \( x \) -axis on the way. Find the vector in its new position.
A \( \cdot \frac{4}{\sqrt{2}} \hat{i}-\frac{1}{\sqrt{2}} \hat{j}-\frac{1}{\sqrt{2}} \hat{k} \)
B. \( -\frac{4}{\sqrt{2}} \hat{i}+\frac{1}{\sqrt{2}} \hat{j}-\frac{1}{\sqrt{2}} \hat{k} \)
\( ^{\mathrm{C}} \cdot-\frac{4}{\sqrt{2}} \hat{i}-\frac{1}{\sqrt{2}} \hat{j}+\frac{1}{\sqrt{2}} \hat{k} \)
D. \( \frac{4}{\sqrt{2}} \hat{i}+\frac{1}{\sqrt{2}} \hat{j}-\frac{1}{\sqrt{2}} \hat{k} \)


\( \boldsymbol{I}_{\mathrm{n}}=\int_{1}^{\mathrm{e}}(\log \mathrm{x})^{\mathrm{n}} \mathrm{d} \mathbf{x} \) and \( \mathbf{I}_{\mathrm{n}}=\mathbf{A}+\mathbf{B I}_{\mathbf{n}-\mathbf{1}} \)
then \( \mathbf{A}=\dots \dots \dots \dots . . \quad B=\dots . . . . . . . . . . . . . . \)
\( \mathbf{A} \cdot e,-n \)
B. \( 1 / e, n \)
c. \( -e, n \)
D. \( -e \)


Parallel venation is observed mostly in
A. Monocot plants
B. Dicot plants
c. Thallophytes
D. Bryophytes


A point moves rectilinearly in one
direction. Above figure shows the
distance \( s \) traversed by the point as a
function of the time \( t . \) Using the plot,
find the maximum velocity.
A. \( 1.5 \mathrm{m} / \mathrm{s} \)
B. \( 2.5 \mathrm{m} / \mathrm{s} \)
\( \mathbf{c} \cdot 2 m / s \)
D. \( 5 \mathrm{m} / \mathrm{s} \)


Heavy water is used as a:
A. fuel in engines
B. semiconductor
c. moderator in nuclear reactors
D. insulator in steam engines


The Glycosidic linkage present in
sucrose is between:
A. \( C-1 \) of \( \alpha \) - glucose and \( C-2 \) of \( \beta \) -fructose
B. C-1 of \( \beta \) -galactose and C-4 of \( \alpha \) -glucose
C. \( C-1 \) of \( \alpha \) -glucose and \( C-4 \) of \( \beta \) - fructose
D. \( \mathrm{C}-1 \) of \( \alpha \) -glucose and \( \mathrm{C}-4 \) of \( \alpha \) -glucose


A spherical drop of water carrying a charge of 0.032 nC has a potential of 512 V at its surface. If two such drops with the same radius and charge were to combine to form a single drop, what would be the potential at the surface of the new drop?
A . 136.2 \( v \)
в. 113 v
c. \( 999.08 \mathrm{v} \)
D. 812.756 V


The cell constant of a given cell is 0.47 \( c m^{-1} . \) The resistance of a solution
placed in this cell is measured to be
31.6 ohm. The conductivity of the solution \( \left(\text { in } S c m^{-1} \text {where } S \) has usual \right.
meaning) is:
A . 0.15
в. 1.5
c. 0.015
D. 150


a. Which ground tissue are you eating,
when you eat mashed potatoes?
Which ground tissue makes the shell of a groundnut hard?


Cork cambium is also called
A. Phelloderm
B. Phellem
c. Periderm
D. Phellogen


toppr
5
Q Type your question
first one is done for you.
This question has multiple correct options
\( \mathbf{A} \)
(i)
(1)
B.
(ii)
\( (\mathrm{i}) \)
\( c \)
(iii)
\( (\text { in }) \)
D.
(iv)
\( (\mathrm{iv}) \)
E .
\( (v) \)


The carbon - carbon bond length in graphite is :
A . \( 1.34 A^{\circ} \)
B . 1.54 \( A^{\circ} \)
c. \( 1.42 A^{\circ} \)
D . 1.20A


A body executes simple harmonic motion. At a displacement \( x \), its
potential energy is \( U_{1} . \) At a displacement \( y, \) its potential energy is
\( U_{2} . \) What is the potential energy of the body at a displacement \( (x+y) ? \)
A. \( U_{1}+U_{2} \)
В \( \cdot(\sqrt{U_{1}}+\sqrt{U_{2}})^{2} \)
c. \( \sqrt{U_{1}^{2}+U_{2}^{2}} \)
D. \( \sqrt{U_{1} U_{2}} \)


In the electrochemical cell:
\( Z n\left|Z n S O_{4}(0.01 M)\right|\left|C u S O_{4}(1.0 M)\right| C \)
the emf of this Daniel cell is \( E_{1} . \) When
the concentration of \( Z n S O_{4} \) is changed
to \( 1.0 M \) and that of \( C u S O_{4} \) changed to
\( \mathbf{0 . 0 1} \boldsymbol{M}, \) the emf changes to \( \boldsymbol{E}_{2} . \) From the followings, which one is the
relationship between \( \boldsymbol{E}_{1} \) and \( \boldsymbol{E}_{2} ? \) (Given, \( \left.\frac{\boldsymbol{R T}}{\boldsymbol{F}}=\mathbf{0 . 0 5 9}\right) \)
A \( . E_{2}=0 \neq E_{1} \)
B \( . E_{1}=E_{2} \)
c. \( E_{1}<E_{2} \)
D. \( E_{1}>E_{2} \)


At \( 20^{\circ} C \) temperature and latmosphere
pressure if a gas has a volume of \( 293 \mathrm{ml} \)
Its volume at NTP is
A .546 cc
B. 273 сс
c. 293 сс
D. 124 сс


Let \( A B C D \) be a square of side \( 2 a . \) Find
the coordinates of the vertices of this
square when
(i) A coincides with the origin and \( A B \)
and \( A D \) are along \( O X \) and \( O Y \)
respectively.
(ii) The centre of the square is at the
origin and coordinate axes are parallel
to the sides \( A B \) and \( A D \) respectivey.


Hybridisation in of \( X e O_{3} \) molecule?
\( \mathbf{A} \cdot s p \)
в. \( s p^{3} \)
\( c \cdot s p^{2} \)
D. none


A spherical metal shell A of radius \( \boldsymbol{R}_{\boldsymbol{A}} \)
and a solid metal sphere \( B \) of radius
\( R_{B}\left(<R_{A}\right) \) are kept far apart and each
is given ' \( +Q \) '. Now they are connected by thin metal wire. Then:
This question has multiple correct options
A \( \cdot E_{A}^{\text {inside }}=0 \)
в. \( Q_{A}>Q_{B} \)
C \( \frac{\sigma_{A}}{\sigma_{B}}=\frac{R_{B}}{R_{A}} \)
D. \( E_{A}^{\text {onsurface }}<E_{B}^{\text {onsurface }} \)


The metal oxide which can react with
acid as well as alkali is:
A. silver oxide
B. copper [II] oxide
c. aluminium oxide
D. calcium oxide


If the input frequency of half-wave
rectifier is \( n H z \) ac, then its output is
A. a constant dc.
B. \( 0.5 n H z \) pulsating dc.
c. \( n H z \) pulsating do
D. \( 2 n H z \) pulsating dc.


Which of the following reaction is most exothermic?
A. Propane \( +C l_{2} / h v \rightarrow 2- \) chloropropane \( +H C l \)
B. Propane \( +B r_{2} / h v \rightarrow 2- \) bromopropane \( +H B r \)
C. Isobutane \( +C l_{2} / h v \rightarrow t- \) butyl chloride \( +H C l \)
D. Isobutane \( +B r_{2} / h v \rightarrow t- \) butyl chloride \( +H B r \)


Which one of the following substance has highest specific heat capacity at room temperature and atmospheric pressure?
A. water
B. Ice
c. Aluminium
D. Mercury


Draw the graph of each of the equations \( 2 x+3 y+5=0 \) and \( 5 x+4 y+1=0 \)
and find the coordinates of the point where the lines meet.


Which oxide is colourless and neutral?
A. \( N_{2} O_{3} \)
в. \( N_{2} \),
\( \mathrm{c} \cdot \mathrm{N}_{2} \mathrm{O}_{4} \)
D. \( N_{2} O_{5} \)


A vibrating body possesses:
A. electrical energy
B. nuclear energy
C . potential energy
D. sound energy


n-propyl alcohol and isopropyl alcohol are examples of :
A. position isomerism
B. chain isomerism
c. tautomerism
D. geometrical isomerism


\( \ln \left[\boldsymbol{F e}(\boldsymbol{C N})_{5}\left(\boldsymbol{N O}^{+}\right)\right]^{2-}, \) Fe has +3 state
It can be decided by:
A. magnetic measurement
B. colligative property
c. colour
D. hybridisation


The odds in favour of India winning any
cricket match is \( 2: 3 . \) What is the
probability that if India plays 5 matches, it wins exactly 3 of them?
\( ^{\mathbf{A}} \cdot_{^{5}} C_{3}\left(\frac{2}{5}\right)^{2}\left(\frac{3}{5}\right)^{3} \)
\( ^{\mathrm{B}} \cdot_{^{5}} C_{3}\left(\frac{2}{3}\right)^{2}\left(\frac{1}{3}\right)^{3} \)
\( ^{\mathbf{c}} \cdot_{^{5}} C_{3}\left(\frac{2}{5}\right)^{3}\left(\frac{3}{5}\right)^{2} \)
\( ^{\mathrm{D} \cdot}^{5} C_{3}\left(\frac{2}{3}\right)^{2}\left(\frac{1}{3}\right)^{2} \)


How many moles of \( \boldsymbol{P t} \) may be deposited on the cathode when \( 0.80 \mathrm{F} \) of
electricity is passed through a \( 1.0 \mathrm{M} \)
solution of \( \boldsymbol{P} \boldsymbol{t}^{4+} \) ?
A. 0.1 mol
B. 0.2 mol
\( c .0 .4 \mathrm{mol} \)
D. 0.6 mo


Find the missing terms such that the given polynomial become a perfect square trinomial:
\( 81 x^{2}+\dots-1 \)


Which of the following methods does not help to minimize the error due to contact resistance in Wheatstone's
meter bridge experiment:
A. The wire used must be uniform
B. The wire used must be non-uniform
c. Null point is obtained near the middle of the wire
D. Interchange the positions of unknown resistance (X) and known resistance(R)


In an experiment on the specific heat of a metal, a \( 0.20 \mathrm{kg} \) block of the metal at
\( 150^{\circ} \mathrm{C} \) is dropped in a copper calorimeter (of water equivalent \( 0.025 k g \) ) containing \( 150 c m^{3} \) of water
\( \operatorname{at} 27^{\circ} \mathrm{C} . \) The final temperature is \( 40^{\circ} \mathrm{C} \)
Compute the specific heat of the metal. If heat losses to the surroundings are not negligible, is your answer greater or smaller than the actual value for specific heat of the metal?


A regular hexagon of \( 10 \mathrm{cm} \) side has charges of 5 u \( C \) at each of its vertices. calculate the potential at its centre.


Which of the following ligand is called chelating ligand?
A. Ethane -1,2 diamine
B. Oxalate
c. Glycinate
D. All are chelating ligands


Intercrescence of endothelium and
endodermis occurs in
A. sinuses
B. Rete mirabile
c. Great blood vessels
D. Corpus luteum


Difference between bone and cartilage
is in having
A . Haversian canal
B. Blood vessel
c. Lymph vessel
D. All of the above


Calculate the number of protons, electrons, neutrons in Bromine with atomic number 35 and mass number
80


Find general solution for \( x \) \( \sin 8 x-\cos 6 x=\sqrt{3}(\sin 6 x+\cos 8 x) \)


Masses \( 8 \mathrm{kg}, 2 \mathrm{kg}, 4 \mathrm{kg} \& 2 \mathrm{kg} \) are placed
at the corners \( P, Q, R \& S \) respectively of a square PQRS of side 80cm. The
distance of \( x \) co-ordinate centre of mass
from P will be?
\( \mathbf{A} \cdot 20 \mathrm{cm} \)
B. 30cm
c. \( 40 \mathrm{cm} \)
D. \( 60 \mathrm{cm} \)


Valence bond theory of Pauling and Slater accounts for the following characteristic of covalent bond:
A. directional
B. ionic
c. strength
D. hybrid


ff \( (x)=7 x^{2}-15, \) then find the value
of \( \boldsymbol{f}(\boldsymbol{3})-\boldsymbol{f}(\boldsymbol{5}) \)
A . 102
B. 66
c. -112
D. -54


toppr LOGIN
Q Type your question_
What is \( y \)
support. A uniform magnetic field of
\( 0.4 T \) is directed perpendicular and into
the plane of the spring-rod system. At
\( t=0, \) the rod is released with the
springs extended by \( 20 c m . \) If the spring
constant of each spring is \( 2 N m^{-1} \)
then
This question has multiple correct options
A. the maximum value of emf induced across the rod is \( 64 m V \)
B. the induced emf across the rod is reduced to zero in \( \frac{\pi}{8} \) S after releasing the rod.
C. the induced emf across the rod reaches maximum first time in \( \frac{\pi}{8} \mathrm{S} \) after releasing the rod
D. the maximum value of induced emf is \( 32 m V \)


State whether the statement is true or
false:

At constant temperature and pressure
the rate of diffusion of the gases is
inversely proportional to the square root
of their densities.


If \( a, b, c \) are non-coplanar vectors and \( \lambda \) is a real number, then \( \left[\lambda(\vec{a}+\vec{b}) \lambda^{2} \vec{b} \lambda \vec{c}\right]=[\vec{a} \quad \vec{b}+\vec{c} \quad \vec{b}] \) for
A. exactly two values of \( \lambda \)
B. exactly three values of \( \lambda \)
c. no value of \( \lambda \)
D. exactly one value of \( \lambda \)


Water stands at a height H in a tall cylinder (see figure). Two holes \( A \) and \( B \)
are made on the sides of the cylinder. If
hole \( A \) is at a height \( h \) above the ground,
what is the height of hole \( B \) above the
ground so that the two streams of water emerging from holes \( A \) and \( B \) strikes the ground at the same point?


Differentiate between A-band and I-
band.


\( \mathbf{f} \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{2} & \mathbf{- 3} \\ \mathbf{5} & \mathbf{0} & \mathbf{2} \\ \mathbf{1} & \mathbf{- 1} & \mathbf{1}\end{array}\right], \boldsymbol{B}= \)
\( \left[\begin{array}{ccc}\mathbf{3} & \mathbf{- 1} & \mathbf{2} \\ \mathbf{4} & \mathbf{2} & \mathbf{5} \\ \mathbf{2} & \mathbf{0} & \mathbf{3}\end{array}\right], \boldsymbol{C}=\left[\begin{array}{ccc}\mathbf{4} & \mathbf{1} & \mathbf{2} \\ \mathbf{0} & \mathbf{3} & \mathbf{2} \\ \mathbf{1} & \mathbf{- 2} & \mathbf{3}\end{array}\right], \) Then
Compute \( (\boldsymbol{A}+\boldsymbol{B}) \) and \( (\boldsymbol{B}-\boldsymbol{C}) . \) Also
verify that \( \boldsymbol{A}+(\boldsymbol{B}-\boldsymbol{C})=(\boldsymbol{A}+\boldsymbol{B})- \)
\( C \)


Which type of polymer is natural rubber?
A. Condensation polymer
B. Addition polymer
c. coordination polymer
D. None of the above


\( a_{1}=-2, r=-1 . \) Find the \( 5^{t h} \) term in
GP.
\( \mathbf{A} \cdot \mathbf{1} \)
B. -
\( c \cdot 2 \)
D. - 2


A force \( \overrightarrow{\boldsymbol{F}}=\boldsymbol{x} \hat{\boldsymbol{i}}+\boldsymbol{2} \boldsymbol{y} \hat{\boldsymbol{j}} \) is applied on a
particle. Find out work done by \( \boldsymbol{F} \) to
move the particle from point \( \boldsymbol{A} \) to \( \boldsymbol{B} \)
A . \( -3.5 ~ J \)
в. \( -2.5 \mathrm{J} \)
c. \( -4.5 J \)
D. -45


In hydrogen atom, an electron makes transition from \( n=3 \) to \( n=2 \) state in
time interval of \( 1.2 \times 10^{-8} \) s. Calculate
the average torque (in \( \mathrm{Nm} \) ) acting on the electron during this transition.
A . \( 1.055 \times 10^{-26} \)
В. \( 4.40 \times 10^{-27} \)
c. \( 1.7 \times 10^{-26} \)
D. \( 8.79 \times 10^{-27} \)


The output current versus time curve for a rectifies is shown in the figure. The
average value of output current in this case is
\( A \)
в. \( \frac{I_{0}}{2} \)
c. \( \frac{2 I_{0}}{\pi} \)
\( D \cdot l_{0} \)


Current \( ^{\prime} i^{\prime} \) coming from the battery and ammeter reading are
A \( \cdot \frac{3}{8} A, \frac{1}{8} A \)
в. \( \frac{1}{8} A, \frac{1}{8} A \)
c. \( 2 A, \frac{2}{3} \)
' \( 2 A, \frac{1}{8} \)


Direction of current in the loop at \( t= \)
\( \frac{\pi}{3 \omega} \)
\( A \). clockwise
B. anticlockwise
c. no current will flow at that time
D. cannot be determined


In which part of nephron absorption of filtrate maximum
A. Distal convoluted tubule
B. Proximal convoluted tubule
c. Glomerulus
D. Henles loop


A tuning fork vibrating with a sonometer wire of length \( 20 \mathrm{cm} \) produces 5 beats per second. The beat frequency does not change if the length of the wire is changed to \( 21 \mathrm{cm} . \) The frequency of the tuning fork must be:
A \( .200 \mathrm{Hz} \)
в. 210 Нг
c. \( 205 ~ H z \)
D. 215 Н


Three one dimensional mechanical
waves in an elastic medium is given as
and
\( \boldsymbol{y}_{1}=\mathbf{3} \boldsymbol{A} \sin (\boldsymbol{\omega} \boldsymbol{t}-\boldsymbol{k} \boldsymbol{x}) \)
\( \boldsymbol{y}_{2}=\boldsymbol{A} \sin (\boldsymbol{\omega} \boldsymbol{t}-\boldsymbol{k} \boldsymbol{x}+\boldsymbol{\pi}) \)
\( \boldsymbol{y}_{3}=2 \boldsymbol{A} \sin (\boldsymbol{\omega} \boldsymbol{t}+\boldsymbol{k} \boldsymbol{x}) \)
are superimposed with each other. The
maximum displacement amplitude of the medium particle would be
\( A \cdot 4 A \)
B. 3A
c. \( 2 A \)
D. A


Animals which eat their own faeces are
called
A. Omnivorous
B. Herbivorous
c. coprophagus
D. Carnivorous


Larger number of oxidation states are
exhibited by the actinides than those by lanthanoids, the main reason
being
A. more energy difference between 5 f and 6d than between 4 f and 5 d orbital
B. more reactive nature of the actinoids than the lanthanoids
c. \( 4 f \) orbitals more diffused than the 5 orbital
D. lesser energy difference between 5 fand 6 than between \( 4 \mathrm{f} \) and \( 5 \mathrm{d} \) orbital


The sum \( 1+\frac{2}{x}+\frac{4}{x^{2}}+\frac{8}{x^{3}}+ \)
\( \ldots(u p t o \infty), x \neq 0, \) is finite if
A \( \cdot|x|<2 \)
В . \( |x|>2 \)
c \( \cdot|x|<1 \)
D . \( 2|x|<1 \)


If \( \boldsymbol{P}=\left[\begin{array}{ll}\sqrt{\mathbf{3}} / \mathbf{2} & \mathbf{1} / \mathbf{2} \\ -\mathbf{1} / \mathbf{2} & \sqrt{\mathbf{3}} / \mathbf{2}\end{array}\right], \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{1} \\ \mathbf{0} & \mathbf{1}\end{array}\right] \)
\( \boldsymbol{Q}=\boldsymbol{P} \boldsymbol{A} \boldsymbol{P}^{\prime}, \operatorname{then} \boldsymbol{P}^{\prime} \boldsymbol{Q}^{2005} \boldsymbol{P} \) is
A. \( \left[\begin{array}{cc}1 & 1 \\ 2005 & 1\end{array}\right] \)
B. \( \left[\begin{array}{cc}1 & 2005 \\ 0 & 1\end{array}\right] \)
c. \( \left[\begin{array}{cc}1 & 0 \\ 0 & 1\end{array}\right] \)
D. \( \left[\begin{array}{cc}1 & 2005 \\ 2005 & 1\end{array}\right] \)


Consider the functions defined
implicitly by the equation \( y^{3}-3 y+ \)
\( \mathbf{x}=\mathbf{0} \) on various intervals in the real
line. If \( x \in(-\infty,-2) \cup(2, \infty), \) the equation implicitly defines a unique real valued differentiable function \( \mathbf{y}= \) \( f(x) \). If \( x \in(-2,2) \), the equation implicitly defines a unique real valued differentiable function \( \mathbf{y}=\mathbf{g}(\mathbf{x}) \)
satisfying \( \mathbf{g}(\mathbf{0})=\mathbf{0} \)
f \( \mathrm{f}(-10 \sqrt{2})=2 \sqrt{2}, \) then \( \mathrm{f}^{\prime \prime}(-10 \sqrt{2})= \)
A \( \cdot \frac{4 \sqrt{2}}{7^{3} 3^{2}} \)
в. \( -\frac{4 \sqrt{2}}{7^{3} 3^{2}} \)
c. \( \frac{4 \sqrt{2}}{7^{3} 3} \)
D. \( -\frac{4 \sqrt{2}}{7^{3} 3} \)


Which of the following pairs of complexes whose aqueous solutions gives pale yellow and white precipitates
respectively with \( 0.1 M A g N O_{3} ? \)
\( ^{\mathbf{A}} \cdot\left[P t\left(N H_{3}\right)_{4} B r_{2}\right] C l_{2} \) and \( \left[P t\left(N H_{3}\right)_{4} C l_{2}\right] B r_{2} \)
B. \( \left[C o\left(N H_{3}\right)_{5} N O_{3}\right] B r \) and \( \left[C o\left(N H_{3}\right)_{5} B r\right] N O_{3} \)
\( \mathbf{c} \cdot\left[P t\left(N H_{3}\right)_{4} C l_{2}\right] B r_{2} \) and \( \left[P t\left(N H_{3}\right)_{4} B r_{2}\right] C l_{2} \)
D \( \cdot\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5} \mathrm{NO}_{3}\right] \mathrm{Cl} \) and \( \left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5} \mathrm{Cl}\right] \mathrm{NO}_{3} \)


Each question below consists of two statements. I in the left-hand column
and II in the right-hand For each
question. determine whether statement is true or false and whether statement
II is true or false.
I: Potassium permanganate is a colored compound.
Il: Both potassium and manganese are
metals.
A. Both statements are true
B. Statement I is true and Statement II is false
c. Statement II is true and Statement I is false
D. Both Statements are false


Fuses used in a household generally have a rating of
\( A \cdot 500 A \)
B. 5A
c. \( 30 A \)
D. 220A


Two spheres of same size are made of the same metal but one is hollow and
the other is solid. They are heated to same temperature, then
A. both spheres will expand equally
B. hollow sphere will expand more than the solid one
c. solid sphere will expand more than the hallow one
D. none of these


For the arrangement of the potentiometer shown in the figure, the
balance point is obtained at a distance \( 75 \mathrm{cm} \) from A when the key k is
open. The second balance point is obtained at \( 60 \mathrm{cm} \) from A when thekey is closed. Find the internal resistance
\( (\operatorname{in} \Omega) \) of the battery \( E_{1} \)


A real image:
A. cannot be captured on a screen
B. can be captured on a screen
C . can be captured only on a celluloid screen
D. none of the above


In the trapezium \( A B C D, \) side \( A B \| \) side
DC. Diagonals \( A C \) and DB intersect each other at \( 0 . \) If \( A B=15, D C=10 \) find \( \frac{O C}{O A} \)
A \( \cdot \frac{O C}{O A}=\frac{1}{3} \)
в. \( \frac{O C}{O A}=\frac{7}{3} \)
c. \( \frac{O C}{O A}=\frac{2}{3} \)
D. \( \frac{O C}{O A}=\frac{5}{3} \)


Calculate the power factor of this
circuit and compare this value with one
at its resonant frequency.


The function \( \boldsymbol{f}(\boldsymbol{x})=\frac{\mathbf{1}}{\mathbf{1}+\boldsymbol{x}^{2}} \) is
decreasing in the interval
\( \mathbf{A} \cdot(-\infty,-1] \)
в. \( (-\infty, 0] \)
c. \( [1, \infty) \)
(i)
D. \( (0, \infty) \)


The trivalent ion having largest size in Lanthanide series is:
\( \mathbf{A} \cdot T i \)
в. \( Z r \)
c. \( H f \)
D. La


A monoatomic ideal gas, initially at
temperature \( T_{1}, \) is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature \( T_{2} \) by releasing the piston suddenly. If \( L_{1} \) and
\( L_{2} \) are lengths of gas column before and after expansion respectively, then \( \frac{\boldsymbol{T}_{1}}{\boldsymbol{T}_{2}} \) is given by
\( ^{\mathrm{A}}\left(\frac{L_{1}}{L_{2}}\right)^{2 / 3} \)
в. \( \frac{L_{1}}{L_{2}} \)
c. \( \frac{L_{2}}{L_{1}} \)
\( \left(\frac{L_{2}}{L_{1}}\right)^{2 / 3} \)


The number of solution of the equation \( \boldsymbol{a}^{f(\boldsymbol{x})}+\boldsymbol{g}(\boldsymbol{x})=\mathbf{0}, \) where \( \boldsymbol{a}>\mathbf{0}, \boldsymbol{g}(\boldsymbol{x}) \neq \)
0 and \( g(x) \) has minimum value \( \frac{1}{4}, \) is
A. one
B. two
c. infinitely many
D. zero


The medians of a right triangle which are drawn from the vertices of the acute angles are 5 and \( \sqrt{4} 0 . \) The value of the
hypotenuse is:
A . 10
в. \( 2 \sqrt{40} \)
\( c \cdot \sqrt{13} \)
D. \( 2 \sqrt{13} \)
E. none of these


Which of the following pairs of elements show similar set of oxidation state?
A. \( O^{16}, O^{18} \)
в. \( N a, K \)
c. \( C, B e \)
D. \( Z n, R b \)


Mammals and terrestrial amphibians mainly excrete urea and are called


Arrange the following compounds in increasing order of dipole moment.
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}_{3}, \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{N} \boldsymbol{H}_{2}, \boldsymbol{C H}_{3} \boldsymbol{C I} \)


A charge \( ^{\prime} \boldsymbol{q}^{\prime} \) is placed at the centre of the line joining two equal charges. The system will be in equilibrium if \( q \) is
equal to
A. \( -Q / 2 \)
в. \( -Q / 4 \)
\( c .-4 Q \)
D. \( +Q / 2 \)


A beam of light composed of red and green rays is incident obliquely at a point on the face of a rectangular glass slab. When coming out on the opposite parallel face, the red and green
rays emerge from :-
A. Two points propagating in two different parallel directions
B. One point propagating in two different directions through slab
c. one point propagating in the same direction through slab
D. Two points propagating in two different non paralle directions


A \( 5 \% \) solution of glucose is isotonic
with \( 1.1 \% \) solution of \( \mathrm{KCl} \) at \( 30^{\circ} \mathrm{C} \)
Calculate the degree of ionisation of KCI.
A . \( 90 \% \)
в. \( 88 \% \)
c. \( 78 \% \)
D. \( 80 \% \)


Angle between leaf and upper or younger part of stem is called as
A. node
B. internode
c. stem
D. axil


The maximum value of the expression \( \frac{3}{9 \cos ^{2} \Theta+8 \sin \Theta \cos \theta+3 \sin ^{2} \Theta} \)


f 12 identical balls are to be placed in 3 different boxes, then the probability that one of the boxes contains excatly 3
balls, is:


Find the current I in the given circuit.
A . \( 1 / 25 \) A
B. \( 1 / 10 \) A
\( c \cdot 1 / 20 A \)
D. \( 1 / 5 \) A


In \( \Delta A B C, \angle A=120, B C+C A=20 \)
\( A B+B C=21, \) then
\( \mathbf{A} \cdot A B>A C \)
B. AB
c. \( \triangle A B C \) is isosceles
D. Area of \( \Delta A B C=14 \sqrt{3} \)


The domain of the function \( y= \)
\( \sqrt{\sin x+\cos x}+\sqrt{7 x-x^{2}-6} \) is
\( \left[p, \frac{q \pi}{4}\right] \cup\left[\frac{r \pi}{4}, s\right] \) then value of \( p+ \)
\( \boldsymbol{q}+\boldsymbol{r}+\boldsymbol{s} \) is


In Young's double slit eperiment two disturbances arriving at a point P have phase difference of \( \frac{\pi}{3} . \) The intensity of this point expressed as a fraction of
maximum intensity \( I_{0} \) is then
A \( \cdot \frac{3}{2} I_{0} \)
в. \( \frac{1}{2} I_{0} \)
c. \( \frac{4}{3} I_{0} \)
D. \( \frac{3}{4} I_{0} \)


If a line makes angles \( \boldsymbol{\alpha}, \boldsymbol{\beta}, \boldsymbol{\gamma} \) with
positive axes, then the range of \( \sin \alpha \sin \beta+\sin \beta \sin \gamma+\sin \gamma \sin \alpha \) is
\( ^{\mathrm{A}} \cdot\left(\frac{-1}{2}, 1\right) \)
в. \( \left(\frac{1}{2}, 2\right) \)
c. (-1,2)
D. (-1,2]


The complete balanced equation is:
\( \boldsymbol{C u}+\boldsymbol{N} \boldsymbol{O}_{3}^{-}+\ldots . \rightarrow \boldsymbol{C u}^{2+}+\boldsymbol{N} \boldsymbol{O}_{2}+ \)
A \( \cdot C u+4 H^{+}+2 N O_{3}^{-} \rightarrow C u^{2+}+2 N O_{2}+2 H_{2} O \)
B . \( C u+6 H^{+}+N O_{3}^{-} \rightarrow C u^{2+}+2 N O_{2}+2 H_{2} O \)
c. \( C u+4 H^{+}+2 N O_{3}^{-} \rightarrow 2 C u^{2+}+N O_{2}+2 H_{2} O \)
D. none of these


Use Remainder theorem to factorize the
following polynomial. \( 2 x^{3}+3 x^{2}-9 x- \)
\( \mathbf{1 0} \)


Jiah is doing an experiment in her math class. She flips four coins In the air. What is most likely to happen?
A. Two of the coins will be heads and two will be tails
B. Three of the coins will be heads and one will be tail
c. Allfour coins willbe heads
D. None of the coins willbe heads


The fundamental building block of
protein is:
A. Nitrogen
B. \( N H_{2} \) group
c. cooH group
D. Amino acid


In the gastrointestinal tract, the Meissner's plexus and the Auerbach's
plexus occur respectively in the
A. Lamina propria and muscularis mucosa
B. Submucosa and muscularis externa
c. Submucosa and mucosa
D. Mucosa and muscularis extema


Which of the following is aromatic in
nature?
B.
\( c \)
\( D \)


Predict which of the following reaction will have appreciable concentration of reactants and products:
a) \( C l_{2}(g) \rightleftharpoons 2 C l(g) ; K_{c}=5 \times 10^{-39} \)
b) \( C l_{2}(g)+2 N O(g) \rightleftharpoons \)
\( \mathbf{2} \boldsymbol{N} \boldsymbol{O} \boldsymbol{C l}(\boldsymbol{g}) ; \boldsymbol{K}_{c}=\mathbf{3 . 7} \times \mathbf{1 0}^{\mathbf{8}} \)
c) \( C l_{2}(g)+2 N O_{2}(g) \rightleftharpoons \)
\( \mathbf{2} \boldsymbol{N} \boldsymbol{O}_{2} \boldsymbol{C l}(\boldsymbol{g}) ; \boldsymbol{K}_{c}=\mathbf{1 . 8} \)


If the natural numbers are divided into
groups of \{1\},\{2,3\},\{4,5,6\},\{7,8,9,10\}
... Then the /sum of 50th group is
A. 65225
B. 56225
c. 62525
D. 53625


Which element among the following normally exist as monoatomic molecules?
A . \( c l \)
B.
\( c \cdot 0 \)
D.
E. не


The value of the largest term common
to the sequences \( 1,11,21,31, . . \) upto
100 terms and \( 31,36,41,46, \dots \) upto
100 terms, is
A . 281
в. 381
c. 471
D. 52


Using following data, draw timedisplacement graph for a moving object.
Time (s)
Displacemen
\( (m) \)
Use the graph to find average velocity for first 4 s, for next 4 s and for last 6 s?


\( K_{a} \) for \( H C N \) is \( 5 \times 10^{-10} \) at \( 25^{\circ} C . \) For
maintaining a constant \( p H \) of 9 , the
volume of \( 5 M K C N \) solution required
to be added to \( 10 m L \) of \( 2 M H C N \)
solution is:
A . 10
B. 8
\( c \cdot 2 \)
D. 6


Two identical small equally charged conducting balls are suspended from long threads secured at one point. The charges and masses of the balls are such that they are in equilibrium when the distance between them is a (the
length of thread \( L>> \) a). Then one of the
balls is discharged. What will be the distance \( b(b<<L) \) between the balls when equilibrium is restored?


Which of the following is known as anhydride of nitric acid?
A. \( N_{2} O_{3} \)
a
B. \( N_{2} O_{4} \)
c. \( N_{2} O_{5} \)
D. \( N_{2} \),


The current population of a town is \( 10,000 . \) If the population increases by \( 10 \% \) every year, then the population of the town after three years will be
A . 13,310
B. 13,500
c. 14,000
D. 14,500


Metals are good conductors because
A. Outer electrons are strongly bound to the atom.
B. Outer electrons are loosely bound to the atom.
C. Inner electrons are loosely bound to the atoms.
D. Protons can detach from the nucleus and conduct
electricity.


The value of
\( \frac{(\sqrt{\mathbf{2}}+\mathbf{1}) \mathbf{1 9 8}}{\boldsymbol{\pi}} \int_{\boldsymbol{\pi} / 4}^{\boldsymbol{3} \boldsymbol{\pi} / \boldsymbol{4}} \frac{\boldsymbol{\phi}}{\mathbf{1}+\sin \phi} \boldsymbol{d} \boldsymbol{\phi} \) is


Which of the following is not a base?
A. \( N a O H \)
в. КОН
c. \( N H_{4} O H \)
D. \( C_{2} H_{5} O H \)


What are neurotransmitters?
A. Transmit signals across synapse.
B. Transmit signal in the cell body.
C. Take the signal to the axon.
D. None of the above.


(a) Write a test to distinguish between aldehydes and ketones.
(b) How will you prepare benzaldehyde by Etard's reaction?
(c) How will you bring about the following conversions? (Write the chemical equations)
(i) Ethanol \( \rightarrow \) Ethanoic acid
(ii) Benzamide \( \rightarrow \) Benzoic acid
(iii) Benzaldehyde \( \rightarrow \) Meta nitrobenzaldehyde.


The A.M. of 'n' observations is M. If the
sum of \( (\boldsymbol{n}-\mathbf{4}) \) observation is 'a', what
is the mean of remaining 4 observations?
A \( . n M+a \)
в. \( \frac{n M-a}{2} \)
c. \( \frac{n M+a}{2} \)
D. \( \frac{n M-a}{4} \)


Two bodies are in thermal equilibrium. Which of the following quantities must be same for them?
A. internal energy
B. potential energy
c. temperature
D. mass


Reaction, \( 5 C \longrightarrow 3 A+2 B . \) The rate of
formation of \( \boldsymbol{A} \) is \( \mathbf{0 . 0 2 7 m o l} \boldsymbol{L}^{-1} \boldsymbol{s e c}^{-1} \)
What will be the rate of disappearance
of \( C ? \)
A. \( 0.090 \mathrm{molL}^{-1} \mathrm{sec}^{-1} \)
B. \( 0.027 \mathrm{molL}^{-1} \mathrm{sec}^{-1} \)
c. \( 0.063 m o l L^{-1} s e c^{-1} \)
D. \( 0.045 \mathrm{molL}^{-1} \mathrm{sec}^{-1} \)


A copper ball of radius \( 1 \mathrm{cm} \) work
function \( 4.47 e V \) is irradiated with
ultraviolet radiation of wavelength \( 2500 A \). The effect of irradiation results
in the emission of electrons from the
ball. Further the ball will require charge and due to this there will be finite value
of the potential on the ball. The charge acquired by the ball is:
A \( .5 .5 \times 10^{-13} \mathrm{C} \)
В. \( 7.5 \times 10^{-13} C \)
c. \( 4.5 \times 10^{-12} \mathrm{C} \)
D. \( 2.5 \times 10^{-11} C \)


\( \boldsymbol{C a} \boldsymbol{C}_{2} \frac{\boldsymbol{H y d r o l y s i s}}{\boldsymbol{A}} \boldsymbol{A} \frac{\boldsymbol{R e d} h_{o t}}{\boldsymbol{C u} \boldsymbol{t u b e}} \)
\( \frac{\boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3}-\boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4}}{\boldsymbol{5} \boldsymbol{0}-\boldsymbol{6} \boldsymbol{0}^{0} \boldsymbol{C}} \boldsymbol{C} \stackrel{\boldsymbol{F} \boldsymbol{e}+\boldsymbol{H} \boldsymbol{C l}}{\longrightarrow} \)
\( \boldsymbol{D} \stackrel{\boldsymbol{N a N O}_{2}+\boldsymbol{H C l}, \mathbf{0}^{0} \boldsymbol{C}}{\longrightarrow} \boldsymbol{E} \)
In the reaction sequence given above, \( \boldsymbol{E} \)
is:
A. aniline
B. benzene diazonium chloride
c. phenyl osazone
D. benzoyl chloride


Choose the incorrect statement:
\( \mathbf{A} \cdot B e C O_{3} \) is kept in the atmosphere of \( C O_{2} \) since it is thermally unstable.
B. \( B e \) dissolves in alkali forming \( \left[\operatorname{Be}(O H)_{4}\right]^{2-} \)
C. \( B e F_{2} \) forms a complex ion with \( N a F \) in which \( B e \) goes with the cation.
D. \( B e F_{2} \) forms a complex ion with \( N a F \) in which \( B e \) goes with the anion.


A balloon is filled with hydrogen at room temperature. It will burst if pressure
exceeds 0.2 bar

If at 1 bar pressure the gas occupies \( 22.7 \mathrm{L} \) volume up to what volume can the balloon be expanded?
A . 11.35 L
B. 22.7 L
c. \( 44.8 \mathrm{L} \)
D. 67.3 L


Standard electrode potential data are
useful for understanding the suitability
of an oxidant in a redox titration. Some
half cell reaction and their standard
potential are given below:
A \( \cdot M n O_{4}^{-}(a q .)+8 H^{+}(a q)+5 e^{-} \rightarrow M n^{2}(a q .)+ \)
\( 4 H_{2} O(l) \)
\[
E^{0}=1.51 V
\]
B \( \cdot C r_{2} O_{7}^{2}(a q .)+14 H^{+}(a q .)+6 e \rightarrow 2 C r^{3}(a q .)+ \)
\( 7 H_{2} O(l) \)
\[
E^{0}=1.38 V
\]
C \( \cdot F e^{3+}(a q \cdot)+e^{-} \rightarrow \)
\( F e^{2+}(a q .) \)
\( 0.77 V \)
\( \left.\mathbf{D} \cdot C\right|_{2}(g)+2 e^{-} \rightarrow \)
\( \left.2 C\right|^{-}(a q .) \)
\( 1.40 V \)


Current \( i \) is flowing in each of the two similar coaxial circular coils in the
same direction. If the loops are moved towards each other, the following
phenomenon will happen:
A. current in each loop will remain same
B. current in each loop will increase
c. current in each loop will decrease
D. current in one loop will increase and that in another loop will decrease


Two halves of pelvic girdle are joined by
A. A mere fissure
B. Ischiatic symphysis
c. Ischiopubic symphysis
D. Pubic symphysis


With the help of an experiment, state how will you identify whether a given beam of light is polarised or unpolarised.


Which of the following complexes has the least molar conductivity in the
solution?
A \( \cdot C O C I_{3} \cdot 3 N H_{3} \)
в. \( C O C I_{3} .4 N H_{3} \)
c. \( \operatorname{COCI}_{3} .5 \mathrm{NH}_{3} \)
D. \( C O C I_{3} .6 N H_{3} \)


The magnetic moment of current \( (\boldsymbol{I}) \)
carrying circular coil of radius \( (r) \) and
number of turns \( (n) \) varies as
A \( \cdot 1 / r^{2} \)
в. \( 1 / r \)
\( c \)
D \( \cdot r^{2} \)


The electron affinity values for the halogens show the following trends
A. \( F<C l>B r>I \)
B. \( F<C l<B r<I \)
c. \( F>C l>B r>I \)
D. \( F<C l>B r<I \)


The base angles of a issoceles trapezium are
A. unequal
B. equal
c. circular
D. diagonals


The degree measure of 1 radian (taking \( \left.\boldsymbol{\pi}=\frac{\boldsymbol{2} \boldsymbol{2}}{\boldsymbol{7}}\right) \) is
A \( \cdot 55^{\circ} 61^{\prime} 22^{\prime \prime} \) (approx.)
В \( \cdot 57^{\circ} 16^{\prime} 22^{\prime \prime} \) (approx.)
c. \( 57^{\circ} 22^{\prime} 16^{\text {" }} \) (approx.)
D. \( 57^{\circ} 22^{\prime} 22^{\prime \prime} \) (approx.)


Equation of the base of an equilateral triangle is \( 3 x+4 y=9 \) and its Vertex is
at the point \( (1,2) . \) Find the length of
each side of the triangle.


Which of the following waves does not
travel in vacuum?
A. Seismic waves
B. X-rays
c. Light
D. Radio waves


The banking angle is independent of
A. the velocity of the vehicle
B. mass of the vehicle
c. the radius of curvature of the roadd
D. the height of inclination


A man of mass \( 30 \mathrm{kg} \) uses a rope to
climb which bears only 450 N.The
maximum acceleration with which he
can climb safely,.......
A \( \cdot 10 m / s e c^{2} \)
B \( \cdot 15 \mathrm{m} / \mathrm{sec}^{2} \)
\( \mathrm{c} \cdot 20 \mathrm{m} / \mathrm{sec}^{2} \)
D. \( 25 \mathrm{m} / \mathrm{sec}^{2} \)


If
\( \boldsymbol{A}(1,2,-1), B(4,0,-3), C(1,2,-1), D( \)
find the distance between \( A B \) and \( C D \)


If a function \( \boldsymbol{f}:(2, \infty) \rightarrow \boldsymbol{B} \) defined by
\( f(x)=x^{2}-4 x+5 \) is a bijection, then
\( \boldsymbol{B}= \)
A. \( R \)
B. \( [1, \infty) \)
c. (0,1]
D. [0,1]


Explain System and Boundary


Differentiate
\( \cos x \)
\( A \cdot \cos x \)
\( \mathbf{B} \cdot \cos ^{2} x \)
\( c \cdot \sin x \)
D. - \( \sin x \)


All free charges are integral multiple of
a basic unit charge \( e . \) Then quantization rule of electric charge implies
\( \mathbf{A} \cdot Q=e \)
в. \( Q=\frac{1}{e} \)
c. \( Q=n e \)
D. \( Q=e^{2} \)


The branch of study dealing with microscopic anatomy of tissue is
A. Histology
B. Cytology
c. Morphology
D. Palaeontology


In a galvanic cell electrical energy is generated at the expense of chemical
energy. If true enter 1 , else enter 0


Electric field and magnetic field in a region of space is given by \( \vec{E}=E_{o} \hat{j} \) and
\( \vec{B}=B_{o} \hat{j} \cdot A \) particle of specific charge \( \alpha \)
is released from origin with velocity \( \vec{v}=v_{o} \hat{i} \).Then path of particle.
Note- \( \boldsymbol{E}_{\boldsymbol{o}}, \boldsymbol{B}_{\boldsymbol{o}} \) and \( \boldsymbol{v}_{\boldsymbol{o}} \) are constant values
\( A \). is a circle
B. is a helix with uniform pitch
c. is a helix with non-uniform pitch
D. is cycloid


Nitric acid is a/an:
A. oxidising agent
B. reducing agent
c. weak acid
D. indicator


Match the statements of column \( I \) with
values of column \( \boldsymbol{I} \boldsymbol{I} \)


Assertion
Two sugar units joined by \( 1,2- \)
glycosidic bond in sucralose.
Reason
It contains \( C_{1} \) -glucose and \( C_{2} \) -fructose
glycosidic bond.
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 area of a circle is \( (14+6 \sqrt{5}) \pi \)
units, Find its radius.


Refer to the figure. When does the the
galvanometer (G) deflect?
A. The magnet is pushed into the coil
B. The magnet is rotated into the coil
c. The magnet is stationary at the centre of the coil.
D. The number of turns in the coil is reduced


Which of the following property(ies) of all the alkali metals increase(s) with
increase in their atomic number?
This question has multiple correct options
A. Solubility of their hydroxides
B. Thermal stability of their carbonates
c. softness
D. Hydration energy


Ratio of time of electron in first and
second orbit of \( \boldsymbol{H} \) - atom be:
\( \mathbf{A} \cdot 1: 18 \)
B. 1: 8
c. 1: 2
D. 2: 1


Dhoni scored twice as many runs as
Sehwag. Together they scored two runs less than double century. How many
runs did each of them score?


If \( z_{1}, z_{2} \) are two complex numbers \( \left(z_{1} \neq\right. \)
\( z_{2} \) ) satisfying \( \left|z_{1}^{2}-z_{2}^{2}\right|=\mid \overline{z_{1}^{2}}+\overline{z_{2}^{2}}- \)
\( \mathbf{2} \bar{z}_{1} \bar{z}_{2} \mid, \) then
This question has multiple correct options
A \( \cdot \frac{z_{1}}{z_{2}} \) is purely imaginary
B . \( \frac{z_{1}}{z_{2}} \) is purely real
C \( \cdot\left|a r g z_{1}-a r g z_{2}\right|=\pi \)
D \( \cdot\left|\arg z_{1}-\arg z_{2}\right|=\frac{\pi}{2} \)


Find the cube root of the following number by prime factorization method:
\( \mathbf{2 7 0 0 0} \)
\( A .30 \)
B . 40
c. 50
D. 80


A circular coil A of radius r carries
current i. Another circular coil B of
radius \( 2 r \) carries current of i. The
magnetic fields at the centres of the circular coils are in the ratio of
\( A \cdot 3: \)
B. 4:
\( c \cdot 1: 1 \)
\( D \cdot 2: \)


A wire of cross section \( A \) is stretched
horizontally between two clamps located \( 2 l \) m apart. A weight \( W \) kg is suspended from the mid-point of the wire. If the mid-point sags vertically through a distance \( x<1 \) the strain produced is
A \( \cdot \frac{2 x^{2}}{l^{2}} \)
в. \( \frac{x^{2}}{l^{2}} \)
c. \( \frac{x^{2}}{2 l^{2}} \)
D. None of these


The cartesian equation of plane \( \bar{r} \cdot(2,-3,4)=5 \) is
A. \( 3 y-2 x-4 z+5=0 \)
B. \( 2 x-3 y+4 z=0 \)
c. \( 2 x-3 y+4 z+5=0 \)
D. \( \frac{x-1}{2}=\frac{y-1}{-3}=\frac{z-1}{4} \)


\( \operatorname{acts} \) as the anode.
\( \mathbf{A} \cdot Z n(s) \)
B. \( C u^{2+}(a q) \)
\( \mathbf{c} \cdot Z n^{2+}(a q) \)
\( \mathbf{D} \cdot C u(s) \)
E \( . H_{2} O \)


\( 2 H I(g) \longrightarrow H_{2}(g)+I_{2}(g) \)
For this reaction relate \( \Delta H \) and \( \Delta U \)
A. \( \Delta H=\Delta U \)
в. \( \Delta H>\Delta U \)
c. \( \Delta H<\Delta U \)
D. None of these


The number of electrons required for deposition of one mole of copper on the
cathode during the electrolysis of CuSO \( _{4} \)
is:
B . 1.2x10 \( ^{2} \)
c. \( 4.8 \times 10^{24} \)
D. 3x10 \( ^{23} \)


Less active metals also react with nitric
acid. Why?


Solidified \( C u \) obtained from the
reverberatory furnace has blistered
appearance. This is due to:
A. evolution of \( C O_{2} \) gas
B. evolution of \( S O_{2} \) gas
C . evaporation of volatile materials
D. evolution of \( N O_{2} \)


Uncertainty in position and momentum are equal. Uncertainty in velocity is :
A. \( \sqrt{\frac{h}{\pi}} \)
в. \( \frac{h}{\pi} \)
c. \( \frac{1}{2 m} \sqrt{\frac{h}{\pi}} \)
D. none of these


A car of mass \( 1800 \mathrm{kg} \) moving with a speed of \( 10 m / s \) is brought to rest after a Covering a distance of 50 m. Calculate
the force acting on the car.
в. \( 900 N \)
\( c .3600 N \)
D. \( 1600 N \)


What is geotropism? Draw a labelled diagram of a potted plant showing
positive geotropism and negative geotropism.


A bone fragment found in a cave contains 0.21 times as much \( _{6}^{14} \mathrm{C} \) as in equal amount of carbon in air when the organism containing bone died. Find the approximate age of fragment \( t_{1 / 2} \) of
\( \frac{14}{6} \mathbf{C}=5730 \) years
A \( \cdot 1.15 \times 10^{4} y \)
B. \( 1.3 \times 10^{4} y \)
c. \( 1.24 \times 10^{4} y \)
D. \( 1.4 \times 10^{4} y \)


If fertilization doesn't occur, the ovum is
released out of
A. Urine
B. Menstrual cycle
c. Sweat
D. None of the above


Polarisation of electrons in acrolein
may be written as:
A \( \cdot \stackrel{-\delta}{C} H_{2}=C H-C^{+\delta}=O \)
B. \( \stackrel{-\delta}{C H_{2}}=C H-C H=\stackrel{+}{O} \)
c. \( \frac{-\delta}{C H_{2}}=\stackrel{+\delta}{C H}-C H=O \)
D. \( _{C H_{2}}^{+\delta}=C H-C H=O^{-\delta} \)


Obtain the expression for the deflecting torque acting on the current carrying rectangular coil of a galvanometer in a uniform magnetic field. Why is a radial magnetic field employed in the moving coil galvanometer?


Mark the odd one in each of the
following series:
Mitral valve, tricuspid valve, semilunar valve, venous valve.


A clear transparent glass sphere \( (\mu= \)
1.5) of radius \( R \) is immersed in a liquid of refractive index \( 1.25 . \) A parallel beam of light incident on it will converge to a point. The distance of this point from the center will be
A. \( -3 R \)
в. \( +3 R \)
c. \( -R \)
\( \mathrm{D} \cdot+R \)


On what factors does the force
experienced by a current carrying conductor placed in a uniform magnetic field depend?
A. Magnetic field
B. current
c. Length of the conductor
D. All


Emulsifying agent is used for:
A. precipitation of am emulsion
B. denaturation of an emulsion
C. stabilization of an emulsion
D. oxidation of an emulsion


Which of the following is a form class of red algae?
A. Deuteromycetes
B. Basidiomycetes
c. Rhodophyceae
D. Euglenophyceae


The structure of silica is:
A. Layer lattice
B. Tetrahedral
C . Trigonal
D. Linear


The shape of sulphate ion is:
A . Hexagonal
B. Square planar
c. Trigonal bipyramidal
D. Tetrahedral


Assertion
Secondary growth in dicot roots occur with the help of vascular cambium/ phellogen
Reason
Vascular cambium is formed from
conjuctive parenchyma and part of Pericycle.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Two blocks \( A \) and \( s \) of masses \( 100 k g \)
and \( 20 k g \) respectively, separated by a
distance of 5 in are kept on a smooth
surface. A mass of 60kg is then added
to the block \( A . \) Now, in order to
experience same attractive force as before, the two blocks should be separated by a distance of :


A perfect gas at \( 27^{\circ} \mathrm{C} \) heated at constant
pressure so as to double its volume. The
final temperature of the gas will be
\( \mathbf{A} \cdot 327^{0} \mathrm{C} \)
в. \( 327 K \)
\( c \cdot 600^{0} c \)
D. None


\( \int_{0}^{\pi / 2} \frac{\sin x}{\sqrt{1+\cos x}} d x= \)
A \( \cdot \sqrt{2}-1 \)
B. \( 2 \sqrt{2} \)
c. \( 2(\sqrt{2}-1) \)
D. \( \frac{\sqrt{2}+1}{2} \)


A concave lens of focal length \( 20 \mathrm{cm} \) placed in contact with a plane mirror acts as a convex mirror of focal length
\( A \cdot 10 \mathrm{cm} \)
B. 40 \( \mathrm{cm} \)
\( c \cdot 60 \mathrm{cm} \)
D. 20 cm


The charge required to reduce 1 mole
\( \mathrm{Cr}_{2} \mathrm{O}_{7}^{2-} \) to \( \mathrm{Cr}^{3+} \) ions is:
\( \mathbf{A} \cdot 3 F \)
B. \( 3 C \)
\( \mathbf{c} \cdot 6 F \)
D . \( 2 \times 6.023 \times 10^{23} e^{-} \)


A train runs along an unbanked circular
track of radius \( 30 m \) at a speed of
\( \mathbf{5 4 k m / h .} \) The mass of the train is \( 10^{6} k g \) What provides the centripetal force
required for this purpose-the engine or the rails? What is the angle of banking required to prevent wearing out of the rail?


The radius and height of an ice cream cone are in the ratio 4: 3 and area of its
base is \( 154 \mathrm{cm}^{2} \). Find its curved surface
area.
A \( \cdot 192.5 \mathrm{cm}^{3} \)
В. \( 150 \mathrm{cm}^{3} \)
c. \( 176.3 \mathrm{cm}^{3} \)
D. \( 115.36 \mathrm{cm}^{3} \)
E . None of these


In the given figure \( A B \| C D . \) Find \( x+y \) if
all measurements are indicated in
centimeter.
A. \( 4.5 \mathrm{cm} \)
B. 7.5 \( \mathrm{cm} \)
\( c .6 .5 \mathrm{cm} \)
D. \( 2.75 \mathrm{cm} \)


Which of the following is
cyclohexanone?
\( A \)
B. I
\( c . \) ॥
\( D \)


The function \( * \) on \( \boldsymbol{N} \) as
\( \boldsymbol{a} * \boldsymbol{b}=(\boldsymbol{a}-\boldsymbol{b})^{2} \) is a binary operator
A. True
B. False


Which of the following Venn diagrams
correctly represents persons, trees and
environment?
\( A \)
B.
\( c \)
D.


Inspite of danger involved with hydrogen, it is used as fuel for some applications. What are these?
A. Rocket fuel
B. Oxyhydrogen flame
c. carfuel
D. All of the above


Transitions between three energy levels in a particular atom give rise to three spectral lines of wavelengths, in
increasing magnitudes as \( \lambda_{1}, \lambda_{2} \) and \( \lambda_{3} \) Which one of the following equations
correctly relates \( \lambda_{1}, \lambda_{2} \) and \( \lambda_{3} ? \)
A \( \cdot \lambda_{1}=\lambda_{2}-\lambda_{3} \)
B. \( \lambda_{1}=\lambda_{3}-\lambda_{2} \)
c. \( \frac{1}{\lambda_{1}}=\frac{1}{\lambda_{2}}+\frac{1}{\lambda_{3}} \)
D. \( \frac{1}{\lambda_{1}}=\frac{1}{\lambda_{3}}-\frac{1}{\lambda_{2}} \)


A rectangular loop carrying a current
is situated near a long straight wire such that the wire is parallel to the one
of the sides of the loop and is in the plane of the loop. If a steady current lis established in wire as shown in
the figure, the loop will
A. Rotate about an axis parallel to the wire
B. Move away from the wire or towards right
c. Move towards the wire
D. Remain stationary


A compound lens is made of two lenses
in contact having power \( +12.5 D \) and \( -2.5 D . \) An object is placed at \( 15 \mathrm{cm} \) from compound lens. Find the position of image formed
\( \mathbf{A} \cdot 60 \mathrm{cm} \)
B. \( 30 \mathrm{cm} \)
c. \( 15 \mathrm{cm} \)
D. \( 45 \mathrm{cm} \)


A stone thrown vertically upwards with
an initial velocity \( u \) from the top of a tower, reaches the ground with a
velocity of 3 \( u \). The height of the tower is :
A. \( 3 u^{2} / g \)
B. \( 4 u^{2} / g \)
c. \( 6 u^{2} / g \)
D. \( 9 u^{2} / g \)


Chlorine water reacts as strong oxidiser due to formation of:
A. nascent oxygen
B. nascent chlorine
c. both of them
D. none of them


A ball is moving in the direction as
shown. What will be the direction of
momentum?
\( A . W \)
в. \( N \)
\( c . s \)
D.


How many atoms of \( \boldsymbol{P C l}_{5} \) lie in the
same plane?


A bullet of mass 60 g moving with the velocity of \( 500 \mathrm{m} / \mathrm{s} \) is brought to rest in \( 0.01 \mathrm{s} . \) Its impulse will be?


Rocket propulsion works on the
principle of:
A. Newtons laws of motion
B. Faradays laws of electromagnetic induction
C. Laws of thermodynamics
D. Archimedes


The sum of terms upto 10 terms of
series \( 12,15,18,21,24,27, \dots \dots \)


A car and a lorry are moving with same momentum, if same braking force is applied, then :
A. Car comes to rest in shorter distance
B. Lorry comes to rest in shorter distance
c. Both travels same distance before coming to rest.
D. None


The rate constant for the reaction, \( \mathbf{2} N_{2} O_{5} \rightarrow 4 N O_{2}+O_{2} \) is \( 2 \times 10^{-5} s^{-1} . \)
rate of reaction is \( 1.4 \times \)
\( 10^{-5} \) mol \( L^{-1} s^{-1}, \) what will be the
concentration of \( N_{2} O_{5} \) in mol \( L^{-1} \) ?
A. 0.8
B. 0.7
c. 1.2
D.


If \( n_{p} \) and \( n_{e} \) are 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 \( \cdot n_{p} \neq n_{e} \)


Which of the following compound on hydrolysis form white turbidity?
A \( \cdot N C l_{3} \)
в. \( P C l_{3} \)
c. \( A s C l_{3} \)
D. \( S b C l_{3} \)


A hollow closed conductor of irregular shape is given some charge. Which of
the following statements are correct? This question has multiple correct options
A. The entire charge will appear on its outer surface
B. All points on the conductor will have the same potential
c. All points on its surface will have the same charge density
D. All points near its surface and outside it will have the same electric intensity


Use the mirror equation to show that an object placed between \( f \) and \( 2 f \) of \( a \)
concave mirror produces a real image beyond \( 2 f \)
OR
Find an expression for intensity of transmitted light when a polaroid sheet is rotated between two crossed
polaroids. In which position of the polaroid sheet will the transmitted intensity be maximum?


For one electron vacancy,
A. no holes are created
B. 1 hole is created
C. 2 holes are created
D. 4 holes are created


The layered lens shown below is made of
two different transparent materials
A point object is placed on its axis. The
object will form
A. One image
B. Infinite images
C. No image
D. Two images


Jacket less archegonia occur in
A . Riccia
B. Funaria
c. Sphagnum
D. Anthoceros


Relation between wavelength of photon and electron of same energy is
\( \mathbf{A} \cdot \lambda_{p h}>\lambda_{e} \)
\( \mathbf{B} \cdot \lambda_{p h}<\lambda_{e} \)
\( \mathbf{c} \cdot \lambda_{p h}=\lambda_{e} \)
D. \( \frac{\lambda_{c}}{\lambda_{p h}}= \) constant


Which type of tissue forms the inner lining of a blood vessel?
A. Nervous
B. Muscular
c. Epithelial
D. connective