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Light from a point source in air falls on a spherical glass surface whose radius of curvature and refractive index are 20
\( \mathrm{cm} \) and 1.5 respectively. If the distance of light source from the glass surface is \( 100 \mathrm{cm}, \) then at which position image will be formed?
\( A \cdot 25 \mathrm{cm} \)
B. 50 \( \mathrm{cm} \)
\( c .100 \mathrm{cm} \)
D. 200 cm
| 3 |
Physics
|
The binding energies per nucleon for
deuterium and helium are \( 1.1 \mathrm{MeV} \) and
\( 7.0 \mathrm{MeV} \) respectively. How much amount energy, in joules, will be
liberated when \( 10^{6} \) deuterons take part
in the reaction.
| 3 |
Physics
|
The construction of a triangle \( A B C \)
given that \( B C=6 \mathrm{cm}, B=45^{\circ} \) is not
possible when difference of \( A B \) and \( A C \) is equal to:
\( A .6 .9 \mathrm{cm} \)
B. \( 5.2 \mathrm{cm} \)
c. \( 5.0 \mathrm{cm} \)
D. \( 4.0 \mathrm{cm} \)
| 2 |
Maths
|
Induced current is produced in a coil,
only when its ends are
A. not closed
B. closed
\( c \cdot \operatorname{both} A \& B \)
D. None of the above
| 3 |
Physics
|
\( \frac{e^{1 / x}-e^{-1 / x}}{e^{1 / x}+e^{-1 / x}} \) check continuity at \( x= \)
\( \mathbf{0}^{-} \)
| 2 |
Maths
|
Insulin contains \( 3.4 \% \) sulphur. The
minimum molecular weight of insulin is :
A . 941.176
B. 944
c. 945.27
D. none
| 1 |
Chemistry
|
Under what condition will the direction
of sum and difference of two vectors be
same?
| 2 |
Maths
|
What is the SI prefix for \( 10^{-2} ? \)
A . Centi
B. Deci
c. мill
D. Kilo
| 1 |
Chemistry
|
What are the limitations of Rutherford's
nuclear model?
A. Electrons should undergoes spiral path and fall into nucleus
B. Could not explain hydrogen spectrumm
c. Electron lose energy while in motion
D. All of these
| 1 |
Chemistry
|
Tossing a coin is an example of
A. space
в. sample
c. experiment
D. event
| 2 |
Maths
|
A wire of length \( L \) and cross-sectional \( A \)
is made of a material of Young's
modulus. If the wire is stretched by an amount \( x, \) the work done is
| 3 |
Physics
|
Which is the human organ which
behaves like an optical instrument
having lens and a screen?
A. Ear
B. Eye
c. Nose
D. skin
| 3 |
Physics
|
Two coils, \( A \) and \( B \), are lined such that
emf \( \epsilon \) is induced in \( B \) when the current
in \( A \) is changing at the rate \( I \). If \( i \) current
is now made to flow in \( \mathrm{B} \), the flux linked
with \( A \) will be :
A. \( (\epsilon / I) i \)
i
B. \( \epsilon i I \)
c. \( (\epsilon I) \)
D. \( i I / \epsilon \)
| 3 |
Physics
|
Assertion
Positive catalysts increase the rate of
reaction.
Reason
Catalysts decrease the value of \( \Delta G^{o} \)
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
| 1 |
Chemistry
|
Force of attraction between two point charges \( Q \) and \( -Q \) separated by \( d \)
meter is \( F_{e} . \) When these charges are
placed two identical sphere of radius \( R=0.3 d \) whose centries are \( d \) meter
apart the force of attraction between
them is
A. Greater than \( F_{e} \)
B. Equal to \( F_{e} \)
c. Less than \( F_{e} \)
D. None of these
| 3 |
Physics
|
An electron in a Bohr orbit of a hydrogen
atom with the quantum number \( n_{2} \) has
an angular momentum \( 4.2176 \times \) \( 10^{-34} k g m^{2} s^{-1} . \) If electron drops from
this level to the next lower level, then the
wavelength of this line is:
A \( \cdot 18.75 \times 10^{-7} m \)
B. \( 1.87 \times 10^{-7} \mathrm{m} \)
c. \( 187.5 \times 10^{-7} \mathrm{m} \)
D. \( 0.187 \times 10^{-7} m \)
| 1 |
Chemistry
|
If \( A \) and \( B \) are two disjoint sets and \( N \) is
universal set, then \( \boldsymbol{A}^{\circ} \cup\left[(\boldsymbol{A} \cup \boldsymbol{B}) \cap \boldsymbol{B}^{\circ}\right] \)
is
\( A \cdot \phi \)
в. \( A \)
\( c . B \)
D. \( N \)
| 2 |
Maths
|
A flexible chain of length I and mass \( \mathrm{m} \) is slowly pulled at constant speed up over the edge of a table by a force \( F \) parallel to the surface of the table. Assuming that there is no friction between the table and chain, calculate
the work done by force \( F \) till the chain
reaches to the horizontal surface of the
table.
| 3 |
Physics
|
A solid material is supplied with heat at
a constant rate. The temperature of the
material is changing with heat input as shown in the figure. What does slope
DE represent?
A. latent heat of liquid
B. latent heat of vapour
c. heat capacity of vapour
D. inverse of heat capacity of vapour
| 3 |
Physics
|
The angular velocity of a body changes
fro \( \omega_{1} \) to \( \omega_{2} \) without applying a torque
but by changing the moment of inertia. The ratio of corresponding radii of
gyration \( \boldsymbol{K}_{\mathbf{1}}: \boldsymbol{K}_{\mathbf{2}} \) is
\( A \cdot \omega_{1}: \omega_{2} \)
B . \( \sqrt{\omega_{1}}: \sqrt{\omega_{2}} \)
D. \( \omega_{2}: \omega_{1} \)
| 3 |
Physics
|
The number of ordered triplets of positive integral solutions of \( \left|\begin{array}{ccc}\boldsymbol{y}^{3}+\mathbf{1} & \boldsymbol{y}^{2} \boldsymbol{z} & \boldsymbol{y}^{2} \boldsymbol{x} \\ \boldsymbol{y} \boldsymbol{z}^{2} & \boldsymbol{z}^{3}+\mathbf{1} & \boldsymbol{z}^{2} \boldsymbol{x} \\ \boldsymbol{y} \boldsymbol{x}^{2} & \boldsymbol{x}^{2} \boldsymbol{z} & \boldsymbol{x}^{3}+\mathbf{1}\end{array}\right|=\mathbf{1 1} \)
| 2 |
Maths
|
If \( \tan \theta=\frac{1}{\sqrt{2}}, \) find the value of \( \frac{\operatorname{cosec}^{2} \theta-\sec ^{2} \theta}{\operatorname{cosec}^{2} \theta+\cot ^{2} \theta} \)
A \( \cdot \frac{1}{10} \)
в. \( \frac{2}{10} \)
\( c \cdot \frac{3}{10} \)
D. \( \frac{4}{10} \)
| 2 |
Maths
|
In a study of diabetic patients in a village, the following observations were noted:
\( \begin{array}{llll}\text { Age in } & \mathbf{1 0}- & \mathbf{2 0}- & \mathbf{3 0}- \\ \text { years } & \mathbf{2 0} & \mathbf{3 0} & \mathbf{4 0}\end{array} \)
No. of \( ^{f}_{n t s}^{2} \) patien
Calculate the mean and standard
deviation. Also interpret the results
| 2 |
Maths
|
A solid copper sphere (density \( \rho \) and specific capacity \( C \) ) of radius \( r \) at an initial temperature of \( 200 \mathrm{K} \) is supended inside a chamber whose walls are at almost 0 K. The time
required for the temperature of the sphere to drop to \( 100 \mathrm{K} \) is
A \( \cdot \frac{7 r \rho C}{72 \times 10^{6} \sigma} \)
в. \( \frac{r \rho C}{6 \sigma} \)
c. \( \frac{r \rho C}{\sigma} \)
D. none of the above
| 3 |
Physics
|
If \( \boldsymbol{y}=\boldsymbol{a}^{\boldsymbol{x}}+\log \boldsymbol{x}+\boldsymbol{3} \boldsymbol{x}^{2}, \) find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \)
| 2 |
Maths
|
Match the following
\( \begin{array}{llll} & \text { List I } & & \text { List II } \\ & & & \\ \begin{array}{l}\text { Streamlined body } \\ \text { structure }\end{array} & \text { a } & \begin{array}{l}\text { Less no. of } \\ \text { irregularities }\end{array} \\ \text { 2 } & \begin{array}{l}\text { objects harder } \\ \text { againsteach } \\ \text { other }\end{array} & \text { b } & \text { Lubricant } \\ \text { 3 } & \text { Grease } & \text { c } & \begin{array}{l}\text { Increase } \\ \text { friction }\end{array} \\ \text { 4 } & \text { Smooth surface } & \text { d } & \begin{array}{l}\text { Decrease } \\ \text { friction }\end{array}\end{array} \)
A . \( 1-d, 2-c, 3-b, 4-a \)
\( , 4-b \)
B. \( 1-d, 2-c, 3-a \)
c. \( 1- \) a, \( 2-d, 3-b, 4-c \)
D. 1-a, 2-b, 3-c, 4-d
| 3 |
Physics
|
Anbarasan purchased a house for 17,75,000 and spent 1,25,000 on its interior decoration. He sold the house to
make a profit of \( 20 \% \). Find the S.P. of the
house.
| 2 |
Maths
|
The molar concentrations of \( A, B \) and \( C \) at equilibrium for the reaction \( \boldsymbol{A}+ \) \( 2 B \Leftrightarrow 3 C \) are 2,3 and 4 moles/lit
respectively. Its \( \boldsymbol{K}_{c} \) is:
\( A \cdot 2 \)
в. 3.56
\( c \cdot 0.2 \)
D. 0.026
| 1 |
Chemistry
|
Column I shows different positions in
which one pole of a magnet is placed near that of the other.
Column II indicates the resulting action between them for each situation. Fill in
the blanks.
Column I ||
\( N-N \)
Attraction
\( s-1 \)
Repulsion
| 3 |
Physics
|
Which element has a mass number of
20 and contains 11 neutrons??
A. copper
B. Gallium
c. calcium
D. Sodium
E. Fluorine
| 1 |
Chemistry
|
Simple pendulum of length I has a
maximum angular displacement \( \theta \). The maximum kinetic energy of the bob is?
A . \( m g \mid(1-\cos \theta) \)
B. \( 0.5 \mathrm{mgl} \)
c. \( \mathrm{mg} \)
D. 2mgl
| 3 |
Physics
|
6-furfuryl amino purine, \( 2-4 \)
dichlorophenoxy acetic acid and indole-
3 acetic acid are examples respectively
for
A. Synthetic auxin, kinetin and natural auxin
B. Gibberellin, natural auxin and kinetin
C. Natural auxin, kinetin and synthetic auxin
D. Kinetin, synthetic auxin and natural
E. Natural auxin, gibberellin and kinetin
| 0 |
Biology
|
The relative density of substance is numerically equal to its density in the system of units.
| 3 |
Physics
|
n the figure, two identical regular
hexagons are placed side by side as shown, then find the value of z.
A \( \cdot 60^{\circ} \)
В. \( 90^{\circ} \)
\( c \cdot 120^{\circ} \)
D. \( 160^{\circ} \)
| 2 |
Maths
|
Solve: \( \cos ^{2} x \frac{d y}{d x}+y=\tan x \)
| 2 |
Maths
|
Tracheids differ from other tracheary elements in
A. Having Casparian strips
B. Being imperforate
c. Lacking nucleus
D. Being lignified
| 0 |
Biology
|
When the left arm of a mercury manometer is connected to a cylinder filled with a gas, the level of the mercury in the right arm rises by \( 2 \mathrm{cm} \). If the pressure of the gas in the container \( 110160 \mathrm{Pa}, \) the atmospheric pressure is
cm of Hg. ( take \( g= \)
\( \left.10 m s^{-2}\right) \)
A . 79
B. 85 5
c. 76
D. 81
| 3 |
Physics
|
\( \boldsymbol{p} \boldsymbol{K}_{\boldsymbol{b}} \) for \( \boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{O} \boldsymbol{H} \) at certain
temperature is 4.74 The pH of basic buffer containing equimolar
concentration of \( N H_{4} O H \) and \( N H_{C} I \)
will be:
| 1 |
Chemistry
|
Find out the most efficient engine in the following
A. An engine converts \( 80 \mathrm{K} \). of heat energy into \( 20 \mathrm{KJ} \) of work
B. An engine converts 50 KJ of heat energy into 15 KJ of work
C. An engine converts 30 KJ of heat energy into 6 KJ of work
D. An engine converts 60 KJ of heat energy into 24 KJ of work
| 3 |
Physics
|
Among fluorine and chlorine, the electron affinity of the latter is high. This is due to:
A. high electronegativity of fluorine
B. low dissociation energy of fluorine
c. fluorine repels with the added electron due to its small size
D. small size of chlorine atom
| 1 |
Chemistry
|
The height at which liquid will stand in
the open end of the pipe is
A. \( 4 m \)
B. \( 3.5 m \)
c. \( 4.5 m \)
D. \( 5.6 m \)
| 3 |
Physics
|
Photosynthesis in plants is a change
A. chemical
B. physical
c. both \( A \) and \( B \)
D. none of the above
| 1 |
Chemistry
|
\( F e(O H)_{3} \) sol can be more easily
coagulated by \( N a_{3} P O_{4} \) in comparison
to \( K C l \) because:
A. mass of \( N a_{3} P O_{4} \) is more than \( K C l \) hence it is more effective than \( K C l \)
B. phosphate ion \( \left(P O^{3-}\right) \) has higher negative charge than \( C l^{-} \) ion hence are more effective for coagulation
c. \( K C l \) is more soluble than \( N a_{3} P O_{4} \) hence less effective
for coagulation
D. \( N a^{+} \) ions are more effective than \( K^{+} \) ions for coagulation
| 1 |
Chemistry
|
Solve the given equation for \( y: \) \( \frac{1-9 y}{19-3 y}=\frac{5}{8} \)
A \( -\frac{66}{103} \)
в. \( \frac{38}{73} \)
\( c \cdot-\frac{87}{57} \)
D. None of these
| 2 |
Maths
|
The father of modern chemistry is:
A. Priestley
B. Lavoisier
c. Dalton
D. Mendeleev
| 1 |
Chemistry
|
Earthquake can cause
A. Tsunami
B. Floods
c. Landslide
D. All of the above
| 3 |
Physics
|
"Heat cannot by itself flow from a body at lower temperature to a body at higher temperature" is a statement of the
consequence of
A. second law of thermodynamics
B. conservation of momentum
c. conservation of mass
D. first law of thermodynamics
| 1 |
Chemistry
|
The population in India is characterised
by birth rate and
death rate.
A. high, high
B. high, low
c. low, high
D. low, low
| 0 |
Biology
|
The resistance of germanium with rise in temperature.
A. increases
B. decreases
c. remains the same
D. first increases then decreases
| 3 |
Physics
|
A tent is in the form of a cylinder of diameter \( 8 \mathrm{m} \) and height \( 2 \mathrm{m}, \) and mounted by a cone of equal base and height 3 m. The canvas used for making the tent is equal to
\( \mathbf{A} \cdot 36 \pi m^{2} \)
В. \( 28 \pi m^{2} \)
\( \mathbf{c} \cdot 24 \pi m^{2} \)
D. \( 38 \pi m^{2} \)
| 2 |
Maths
|
\( \operatorname{Let} \overrightarrow{\boldsymbol{a}}=\hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}}, \overrightarrow{\boldsymbol{b}}=\hat{\boldsymbol{i}}-\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \) and
\( \vec{c}=\hat{i}-\hat{j}-\hat{k} \) be three vectors. A vector \( \vec{v} \) in the plane of \( \vec{a} \) and \( \vec{b}, \) whose projection on \( \vec{c} \) is \( \frac{1}{\sqrt{3}}, \) is given by
A \( \cdot \hat{i}-3 \hat{j}+3 \hat{k} \)
B . \( -3 \hat{i}-3 \hat{j}-3 \hat{k} \)
\( \mathbf{c} \cdot_{3 \hat{i}-\hat{j}+3 \hat{k}} \)
D \( \cdot \hat{i}+3 \hat{j}-3 \hat{k} \)
| 2 |
Maths
|
The coordinates of a point which divides the line joining the points \( P(2,3,1) \) and \( Q(5,0,4) \) in the ratio 1: 2 are
\( ^{\mathbf{A}} \cdot\left(\frac{7}{3}, 1, \frac{5}{3}\right) \)
в. (4,1,3)
c. (3,2,2)
D. (1,-1,1)
| 2 |
Maths
|
An unknown metal of mass 192 g heated
to a temperature of \( 100^{\circ} \mathrm{cwas} \) immersed into a brass calorimeter of mass \( 128 g \) containing 240 g of water a temperature of \( 8.4^{\circ} \mathrm{C} \) calculate the specific heat of the unknown metal if
water temperature stabilizes at \( 21.5^{\circ} c \)
(specific heat of brass is \( 394 j K g^{-1} k^{-1} \)
A . 1232 J \( k g^{-1} K^{-1} \)
B . 458 J \( k g^{-1} K^{-1} \)
c. 654 J \( k g^{-1} K^{-1} \)
D. 916 J \( k g^{-1} K^{-1} \)
| 3 |
Physics
|
You measure two quantities as \( A= \)
\( \mathbf{1 . 0 m} \pm \mathbf{0 . 2 m}, \boldsymbol{B}=\mathbf{2 . 0 m} \pm \mathbf{0 . 2 m .} \mathrm{We} \)
should report correct value for \( \sqrt{A B} \) as
A. \( 1.4 m \pm 0.4 m \)
в. \( 1.41 m \pm 0.15 m \)
c. \( 1.4 m \pm 0.3 m \)
D. \( 1.4 m \pm 0.2 m \)
| 3 |
Physics
|
Radish is an example of
A. Fusiform root
B. Napiform root
c. conical root
D. Tuberous root
| 0 |
Biology
|
What is rectifier? Explain with neat circuit diagram the action of semiconductor diode as a full wave
rectifier.
| 3 |
Physics
|
Which of the following statements is wrong? Magnetic lines of force
A. Form closed circuits
B. Never intersect
c. Are densest near the poles
D. None of the above
| 3 |
Physics
|
The quantity of heat required to raise the temperature of unit mass of a substance through one degree Celsius
is known as
A. Heat Capacity of body
B. Specific heat capacity of a body
c. Latent heat of body
D. Specific latent heat of a body
| 3 |
Physics
|
If \( \triangle \mathrm{ABC} \) and \( \triangle \mathrm{AMP} \) are right triangles, right-angled at \( \mathrm{B} \) and \( \mathrm{M} \) respectively and \( \angle M A P=\angle B A C \)
Prove that
(i) \( \triangle A B C \sim \triangle A M P \)
(ii) \( \frac{\boldsymbol{C A}}{\boldsymbol{P A}}=\frac{\boldsymbol{B C}}{\boldsymbol{M P}} \)
| 2 |
Maths
|
Find the mobility of the conduction electrons in a copper conductor if in Hall effect measurements performed in the magnetic field of induction \( \boldsymbol{B}= \)
100 \( m T \) the transverse electric field
strength of the given conductor turned out to be \( \eta=3.1 \times 10^{3} \) less than that of
the longitudinal electric field.
| 3 |
Physics
|
(i) Metals can be recovered from their ores by chemical methods.
(ii) High purity metals can be obtained by zone refining method.
Which one is true /false.
A . (i) is true and (ii) is false
B. (ii) is true and (i) is false
c. (i) and (ii) are true
D. (i) and (ii) are false
| 1 |
Chemistry
|
Solubility curves of two ionic salts \( X \& \)
W are given below:
In which case the value of \( \Delta \boldsymbol{H}_{\text {sol.}}<\mathbf{0}: \)
\( A \cdot x \)
B. W
\( c \cdot \operatorname{Both}(x) \&(w) \)
D. None of these
| 1 |
Chemistry
|
The mole percentage of oxygen in a
mixture of \( 7 g N_{2} \) and \( 8 g O_{2} \) is :
A . 25
B. 75
c. 50
D. 40
| 1 |
Chemistry
|
Paulings values of electronegativities are dependent upon:
A. ionisation potentials
B. bond energies
c. electron affinities
D. atomic radii
| 1 |
Chemistry
|
The pair whose both species are used in antacid medicinal preparation is:
A. \( \operatorname{NaH} \mathrm{CO}_{3} \) nad \( \mathrm{Mg}(\mathrm{OH})_{2} \)
в. \( N a_{2} C O_{3} \) and \( C a\left(H C O_{3}\right) \)
c. \( C a\left(H C O_{3}\right)_{2} \) and \( M g(O H)_{2} \)
D. \( C a(O H)_{2} \) and \( N a H C O_{3} \)
| 1 |
Chemistry
|
Thermal stability of \( B a C O_{3}, C a C O_{3} \)
and \( M g C O_{3} \) is:
А. \( B a C O_{3}>C a C O_{3}>M g C O_{3} \)
в. \( B a C O_{3}>M g C O_{3}>C a C O_{3} \)
с. \( C a C O_{3}>M g C O_{3}>B a C O_{3} \)
D. \( M g C O_{3}>C a C O_{3}>B a C O_{3} \)
| 1 |
Chemistry
|
Why is it difficult to hold a school bag having a strap made of a thin and strong string?
A. The pressure exerted on the shoulder is very large
B. The pressure exerted on the shoulder is less than usual
c. The pressure exerted on the shoulder is almost zero
D. The thin string always slips down
| 3 |
Physics
|
If \( \cos A=\frac{4}{5} \) find \( \tan A \)
| 2 |
Maths
|
Which one of the following precedes reformation of the nuclear envelope, during M phase of the cell cycle?
A. Decondensation from chromosomes and reassembly of the nuclear lamina
B. Transcription from chromosomes and reassembly of the nuclear lamina
c. Formation of the contractile ring and formation of the phragmoplast
D. Formation of the contractile ring and transcription from chromosomes
| 0 |
Biology
|
\( \int\left[\log (1+\cos x)-x \tan \left(\frac{x}{2}\right)\right] d x \)
A \( \cdot x \log (1+\tan x) \)
B \( \cdot x \log (1+\sin x) \)
\( \mathbf{C} \cdot \log (1+\sin x) \)
D. \( x \log (1+\cos x) \)
| 2 |
Maths
|
Choose the correct sequence of events
occur in human reproduction.
A. Gametogenesis \( \rightarrow \) gestation \( \rightarrow \) insemination \( \rightarrow \) fertilization \( \rightarrow \) implantation \( \rightarrow \) parturition
B. Gametogenesis \( \rightarrow \) insemination \( \rightarrow \) gestation \( \rightarrow \) implantation \( \rightarrow \) fertilization \( \rightarrow \) parturition
C. Gametogenesis \( \rightarrow \) insemination \( \rightarrow \) fertilization \( \rightarrow \rightarrow \) implantation \( \rightarrow \) gestation \( \rightarrow \) parturition
D. Gestation \( \rightarrow \) gametogenesis \( \rightarrow \) insemination \( \rightarrow \) implantation \( \rightarrow \) fertilization \( \rightarrow \) parturition
| 0 |
Biology
|
If \( \boldsymbol{A}=\left[\begin{array}{cc}\cos \boldsymbol{\alpha} & \sin \boldsymbol{\alpha} \\ -\sin \boldsymbol{\alpha} & \cos \boldsymbol{\alpha}\end{array}\right], \) then verify that
\( \boldsymbol{A}^{\boldsymbol{T}} \boldsymbol{A}=\boldsymbol{I}_{2} \)
| 2 |
Maths
|
If
\( f(x) \) be an increasing function defined
on
\( [a, b] \) then \( \max \{f(t) \text { such that } a \leq t \leq x, a \leq x \leq \)
\( b\}=f(x) \)
\( \& \min \{\mathrm{f}(\mathrm{t}), a \leq t \leq x, a \leq x \leq \)
\( b\}=f(a) \) and if \( f(x) \) be decreasing
function defined on \( [a, b] \) then \( \max \{f(t), a \leq t \leq x, a \leq x \leq b\}=f(a) \)
\( \min \{f(t), a \leq t \leq x, a \leq x \leq b\}=f(x) \)
On the basis of above information
answer the following questions. \( \int_{0}^{\pi / 2} \min \{\sin x, \cos x\} d x \) equals
\( \mathbf{A} \cdot 2(\sqrt{3}-1) \)
B . \( \sqrt{2}(\sqrt{2}-1) \)
\( \mathbf{c} \cdot(\sqrt{3}-1) \)
D \cdot \( \sqrt{2}(\sqrt{2}+1) \)
| 2 |
Maths
|
Write the IUPAC name of the above
compound.
| 1 |
Chemistry
|
A water tap leaks such that water drops
fall at regular intervals. Tap is fixed \( 5 m \)
above the ground. First drop reaches the
ground and at that very instant third drop leaves the tap. At this instant the second drop is at a height of
\( A, 3 m \)
в. 4.5 т
\( \mathbf{c} .3 .75 \mathrm{m} \)
D. 2.5 .
| 3 |
Physics
|
Which of the following human activities is used to meet the ever-increasing demand in factories and for shelter?
A. Soil erosin
B. Pollution
c. Deforestation
D. Data insufficient
| 0 |
Biology
|
If the radius of a sphere is measured as
\( 7 \mathrm{m} \) with an error of \( 0.02 \mathrm{m}, \) find the
approximate error in calculating its volume
| 2 |
Maths
|
Q Type your question
conducting rod of length I. Another point
particle of the same mass is attached to the other end of the rod. The two
particles carry charges \( +q \) and \( -q \) respectively. This arrangement is held
in a region of a uniform electric field \( \mathrm{E} \)
such that the rod makes a small angle \( \theta \)
(say of about 5 degrees) with the field direction. Find an expression for the minimum time needed for the rod to
become parallel to the field after it is set free.
A \( \cdot \frac{\pi}{2}, \sqrt{\frac{M L}{2 q E}} \)
В \( \cdot \frac{\pi}{2}, \sqrt{\frac{M L}{q E}} \)
c. \( \pi, \sqrt{\frac{M L}{q E}} \)
D. None of these
| 3 |
Physics
|
In a reaction, 4 moles of electrons are
transferred to 1 mole of \( H N O_{3} \) when acted as an oxidant. The possible reduction product is:
A \( \cdot 1 / 2 \) mole of \( N_{2} \)
B. \( 1 / 2 \) mole of \( N_{2} O \)
c. 1 mole of \( N O_{2} \)
D. 1 mole of \( N H_{3} \)
| 1 |
Chemistry
|
Find \( \mathbf{5 0}-[\mathbf{4 0}]-[-\mathbf{2}] \)
| 2 |
Maths
|
Explain brown ring test with the help of chemical equation.
| 1 |
Chemistry
|
Meiosis is significant in terms of
evolution because it results
in
A. Genetically similar daughters
B. Four daughter cells
c. Eggs and sperms
D. Recombinations
| 0 |
Biology
|
The products obtained at cathode and anode on electrolysis of aqueous sodium succinate are :
A. anode: ethene \( +C O_{2} \), cathode : \( H_{2} \)
B. anode: ethyne \( +C O_{2} \), cathode : \( H_{2} \)
c. anode : ethyne + \( H_{2} \), cathode : Na
D. anode: ethyne \( +C O_{2} \), cathode : Na
| 1 |
Chemistry
|
Solve \( \int_{0}^{2}\left(x^{2}+1\right) d x \)
A \( \cdot \frac{2}{3} \)
в. \( \frac{14}{3} \)
\( c \cdot \frac{8}{3} \)
D. \( \frac{11}{3} \)
| 2 |
Maths
|
Derive an expression for integrated rate law for a zero order reaction.
| 1 |
Chemistry
|
Compare the motion of a body dropped to that of a horizontal projectile, both
falling from the same height.
| 3 |
Physics
|
In the expression \( \left(\frac{x}{m}\right)=K P^{1 / n}, x \)
represents the mass of adsorbent
If true enter 1 , else enter 0
A.
| 1 |
Chemistry
|
If in two triangles \( P Q R \) and \( D E F \)
\( \boldsymbol{P R}=\boldsymbol{E F}, \boldsymbol{Q} \boldsymbol{R}=\boldsymbol{D} \boldsymbol{E} \) and \( \boldsymbol{P Q}=\boldsymbol{F D} \)
then \( \triangle \boldsymbol{P Q R} \cong \triangle_{---} \)
\( \mathbf{A} \cdot F D E \)
в. \( D E F \)
c. \( F E D \)
D. \( D F E \)
| 2 |
Maths
|
Assertion
f more and more solute is added to a
solvent, the freezing point of the solution keeps on becoming higher and
higher.
Reason
Presence of large amount of the solid
solute does not allow the solution to
freeze.
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
| 1 |
Chemistry
|
The mean deviation from the mean 10 of
the data \( 6,7,10,12,13, \alpha, 12,16 \) is
A . 3.5
B. 3.25 5
\( c .3 \)
D. 3.75 5
| 2 |
Maths
|
The value of \( \frac{1}{1 \cdot 2 \cdot 3}+\frac{1}{2 \cdot 3 \cdot 4}+ \)
\( \frac{1}{3 \cdot 4 \cdot 5}+\frac{1}{4 \cdot 5 \cdot 6} \) is equal to
\( A \cdot \frac{7}{30} \)
в. \( \frac{11}{30} \)
c. \( \frac{13}{30} \)
D. \( \frac{17}{30} \)
| 2 |
Maths
|
Plot the given points on a graph paper and join them with straight lines. Give a special name to the figure obtained:
(3,2),(3,-4),(-2,2) and (-2,-4)
| 2 |
Maths
|
Which of the following pairs are
correctly matched?
a. spirogyra Fragmentatio an -
Planaria
ponges
b. \( \quad \) Regeneration Hydra, Planari
and sponges
\( \mathrm{c} \)
Scion an \( - \) The part of the
plant that is
grafted to other
plant
Development of
d. Parthenogenesis organisms
from an
unfertilized degg
The correctly paired ones are given
\( A \cdot a, c \) and \( d \)
B. \( a, b, c \) and \( d \)
\( c . b, c \) and \( d \)
D. a, b and d
| 0 |
Biology
|
Four \( 1-1 \) litre flasks are separately filled
with the gases \( H_{2}, H e, O_{2} \) and ozone.
The ratio of total number of atoms of
these gases present in different flask would be:
A .1: 1: 1: 1
B. 1: 2: 2: 3
c. 2: 1: 2: 3
D. 3:2:2:1
| 1 |
Chemistry
|
If linear function \( f(x) \) and \( g(x) \) satisfy \( \int[(3 x-1) \cos x+(1-2 x) \sin x] d x= \)
\( \boldsymbol{f}(\boldsymbol{x}) \cos \boldsymbol{x}+\boldsymbol{g}(\boldsymbol{x}) \sin \boldsymbol{x}+\boldsymbol{C}, \) then
A. \( f(x)=3 x-3 \)
B. \( g(x)=3+x \)
C. \( f(x)=3(x-1) \)
D. \( g(x)=3(x-1) \)
| 2 |
Maths
|
The arrow in following diagram shows
the direction a sailing ship moves. What happens if a strong wind blows from the same direction?
A. The sailing ship moves faster
B. The sailing ship moves slower
C. The sailing ship come to rest
D. Nothing happens
| 3 |
Physics
|
obtained by carbon reduction is In
liquid state?
\( A \)
B
\( c \)
fthes
| 1 |
Chemistry
|
Solve \( : \int \frac{2 x^{3}-3 x^{2}-8 x-26}{2 x^{2}-5 x+2} d x \)
| 2 |
Maths
|
How is nuclear power derived?
A. It is derived from energy i.e. released when relatively large atoms of uranium, thorium are split by shooting neutrons on them.
B. It is derived from energy i.e. released when relatively small atoms of uranium, thorium are split by shooting neutrons on them.
C. It is derived from energy i.e. released when relatively large atoms of uranium, thorium are split by shooting electrons on them.
D. None
| 3 |
Physics
|
The triple points of neon and carbon
dioxide are \( 24.57 \mathrm{K} \) and \( 216.55 \mathrm{K} \)
respectively. Express these
temperatures on the Celsius and
Fahrenheit scales
| 3 |
Physics
|
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