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n the following figure, \( \boldsymbol{O A}=\boldsymbol{O C} \) and
\( A B=B C . \) Prove that
\( \angle A O B=90^{\circ} \)
ii) \( \Delta A O D \cong \Delta C O D \)
iii) \( \boldsymbol{A} \boldsymbol{D}=\boldsymbol{C} \boldsymbol{D} \)
| 2 |
Maths
|
Primary alcohols can be prepared from alkenes by:
A. mercuration and demercuration of alkenes
B. direct hydration of alkenes
c. hydroboration of alkenes
D. all of the above
| 1 |
Chemistry
|
Magnesium hydroxide is the white milky substance in milk of magnesia.
What mass of \( M g(O H)_{2} \) is formed when \( 15 m l \) of \( 0.2 M-N a O H \) is
combined with \( 12 \mathrm{ml} \) of \( 0.15 M- \)
\( M g C l_{2} ? \)
A. \( 0.087 g \)
в. \( 0.079 g \)
c. \( 0.1044 g \)
D. \( 0.522 g \)
| 1 |
Chemistry
|
A diver under water, looks obliquely at a
fisherman standing on the bank of a
lake. Would the fisherman look taller or
shorter to the diver than what he
actually is?
| 3 |
Physics
|
For which change \( \Delta \boldsymbol{H} \neq \Delta \boldsymbol{U} \) ?
\( \mathbf{A} \cdot H_{2}(g)+I_{2}(g) \rightleftharpoons 2 H I(g) \)
B. \( H C l(l)+N a O H(l) \longrightarrow N a C l(l)+H_{2} 0(l) \)
\( \mathbf{c} \cdot C(s)+O_{2}(g) \rightleftharpoons C O_{2}(g) \)
D. \( N_{2}(g)+3 H_{2}(g) \longrightarrow 2 N H_{3}(g) \)
| 1 |
Chemistry
|
During adolescence, the body of a girl does not show which of the following changes?
A. Acne and pimple on face
B. Deep voice
c. Development of mammary gland
D. Growth of pubic hair
| 0 |
Biology
|
Based on the Maxwell-Boltzmann graph
below, which of the following
statements is TRUE?
\( A \cdot T_{1} \) is at a higher temperature than \( T_{2}, \) so more molecules will react to form products
B. The reaction is exothermic, so increasing kinetic energy decreases the rate of the reaction
\( \mathrm{c} \cdot T_{2} \) is at a higher temperature than \( T_{1}, \) so more molecules will react to form products
D. The reaction is endothermic, so increasing kinetic energy increases the rate of the reaction
| 1 |
Chemistry
|
The INCORRECT statement is:
A. The spin - only magnetic moments of \( \left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+} \) and \( \left[C r\left(H_{2} O\right)_{6}\right]^{2+} \) are nearly similar
B. The spin-only magnetic moment of \( \left[N i\left(N H_{3}\right)_{4}\left(H_{2} O\right)_{2}\right]^{2+} \) is \( 2.83 B M \)
C. The gemstone, ruby, has \( C r^{3+} \) ions occupying the octahedral sites of beryl
D. The color of \( \left[\mathrm{CoCl}\left(\mathrm{NH}_{3}\right)_{5}\right]^{2+} \) is violet as it absorbs the yellow light
| 1 |
Chemistry
|
Write the special characteristics/features of the human
digestive system
| 0 |
Biology
|
Calculate the HCF of \( 3^{3} \times 5 \) an \( 3^{2} \times 5^{2} \)
| 2 |
Maths
|
\( 6.022 \times 10^{20} \) atoms of silver (at mass
\( =108 u) \) weigh
A \( \cdot 108 \times 10^{3} g \)
B. \( 108 \mathrm{g} \)
c. 0.108 g
D. 10.8 g
| 1 |
Chemistry
|
A piece granulated zinc was dropped into copper sulphate solution. After sometime the colour of the solution
changed from blue to colourless. Why?
| 1 |
Chemistry
|
Reverse process of sublimation is:
A. fusion
B. condensation
c. deposition
D. freezing
| 3 |
Physics
|
The sum of integers from 1 to 100 which are divisible by 2 or 5 is-
A. 300
B. 3050
c. 3200
D. 3250
| 2 |
Maths
|
A basket contains 20 apples and 10 oranges out of which 5 apples and 3 oranges are defective. If a person takes out 2 at random, then the probability that either both are apples or both are \( \operatorname{good} \) is \( \frac{316}{435} \)
A. True
B. False
| 2 |
Maths
|
What causes the existence of very large
number of carbon compounds?
| 1 |
Chemistry
|
Define random experiment
| 2 |
Maths
|
The velocity of a ball of mass m density
d1d1 becomes constant after some
time.The viscous force acting on the
ball will be:
A. non of these
в. \( _{m g}\left(1-\frac{d_{2}}{d_{1}}\right) \)
c. \( m g\left(\frac{d_{1}+d_{2}}{d_{1}}\right) \)
D. \( _{m g}\left(\frac{d_{1}+d_{2}}{d_{2}}\right) \)
| 3 |
Physics
|
The diffraction effect can be observed in
A. only sound waves
B. only light waves
C. only ultrasonic waves
D. sound as well as light waves
| 3 |
Physics
|
What precautions should be taken
against nuclear radiations?
A. The radioactive elements should be kept in containers made up of thick lead walls.
B. The people working in the plants should wear special jackets and gloves made of lead linings.
C. The handling of the plants should be carried out from a distance.
D. All of the above.
| 3 |
Physics
|
In the redox reaction given below:
\( \boldsymbol{x} \boldsymbol{N} \boldsymbol{O}_{3}^{-}+\boldsymbol{y} \boldsymbol{A} \boldsymbol{s}_{2} \boldsymbol{S}_{3}+\boldsymbol{z} \boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \)
\( \boldsymbol{A} \boldsymbol{s} \boldsymbol{O}_{4}^{3-}+\boldsymbol{N} \boldsymbol{O}+\boldsymbol{S} \boldsymbol{O}_{4}^{2-}+\boldsymbol{H}^{+} \)
What is the value of \( \frac{x}{z} ? \)
| 1 |
Chemistry
|
Prove that the line joining a mid point of
a chord to the centre of circle is
perpendicular to it
| 2 |
Maths
|
An electron of charge 'e' and mass 'm' is
accelerated from rest by a potential difference 'V'. The de Broglie wavelength
is
A. Directly proportional to the square root of potential difference
B. Inversely proportional to the square root of potential difference
c. Directly proportional to the square root of electron mass
D. Inversely proportional to the cube root of electron mass
| 3 |
Physics
|
In the hystersis cycle, the value of \( \mathrm{H} \)
needed to make the intensity of magnetisation zero is called
A. retentivity
B. coercivity
c. Lorentz force
D. Pseudo force
| 3 |
Physics
|
The order decreasing reactivity towards an electrophilic reagent for the
following compound is:
(a) Benzene
(b) Toluene
(c) Chlorobenzene and
(d) Phenol
A. \( d>b>a>c \)
в. \( a>b>c>d \)
c. \( b>d>a>c \)
D. \( d>c>b>a \)
| 1 |
Chemistry
|
(i) If \( \sin (\theta+\alpha)=\cos (\theta+\alpha) \) then
express tan \( \theta \) in terms of \( \alpha \)
(ii) Find the value of \( \tan (\pi / 4+ \)
\( \theta) \cdot \tan (\pi / 4-\theta) \)
| 2 |
Maths
|
Find the value of \( \lim _{n \rightarrow \infty} \frac{1}{n} \sum_{r=1}^{n} \sin ^{2} \frac{r \pi}{n} \)
| 2 |
Maths
|
Corrosion of metals can be
prevented when contact between metal and \( \ldots \ldots \ldots . \) is cut off.
A. nitrogen
B. hydrogen
c. oxygen
D. carbon
| 1 |
Chemistry
|
Addition of phosphate and nitrate/fertilizers into water leads to:
A. increased growth of decomposers
B. reduced of algae growth
c. increased growth of algae
D. nutrient enrichment
| 1 |
Chemistry
|
Which of the following is not a noble
gas?
A. Helium
B. Neon
c. Argon
D. Hydrogen
| 1 |
Chemistry
|
If very small amount of phenolphthalein is added to 0.15 mol litre \( ^{-1} \) solution
of sodium benzoate, what fraction of the
indicator will exist in the coloured
form? State any assumption that you make.
\( K_{a}(\text { Benzoic acid })=6.2 \times \)
\( \mathbf{1 0}^{-\mathbf{5}}, \boldsymbol{K}_{\boldsymbol{w}}\left(\boldsymbol{H}_{\mathbf{2}} \boldsymbol{O}\right)=\mathbf{1} \times \mathbf{1 0}^{-\mathbf{1 4}} \)
\( \boldsymbol{K}_{l n} \) (Phenolphthalein) \( \mathbf{3} . \mathbf{1 6} \times \mathbf{1 0}^{-\mathbf{1 0}} \)
| 1 |
Chemistry
|
The unit vector which is orthogonal to the vector \( \vec{a}=3 \vec{i}+2 \vec{j}+6 \vec{k} \) and is coplanar with the vectors \( \overrightarrow{\boldsymbol{b}}=\mathbf{2} \overrightarrow{\mathbf{i}}+\overrightarrow{\boldsymbol{j}}+ \)
\( \vec{k} \) and \( \vec{c}=\vec{i}-\vec{j}+\vec{k} \) is
A \( \cdot \frac{1}{\sqrt{41}}(2 \vec{i}-6 \vec{j}+\vec{k}) \)
B. \( \frac{2 \vec{i}-3 \vec{j}}{\sqrt{13}} \)
c. \( \frac{3 \vec{j}-\vec{k}}{\sqrt{10}} \)
D. \( \frac{4 \vec{i}+3 \vec{j}-3 \vec{k}}{\sqrt{14}} \)
| 2 |
Maths
|
Find \( \int\left(1-\frac{1}{x^{2}}\right) e^{\left(x+\frac{1}{x}\right)} d x \) on I where \( I= \)
\( (0, \infty) \)
| 2 |
Maths
|
If air is blown through the space between a calendar suspended from a nail on wall and the wall, then:
A. The calendar moves close to the wall.
B. The calendar moves farther from the wall.
c. The position of the calendar does not change.
D. The position of the calendar may or maynot change
| 3 |
Physics
|
\( 1 \mathrm{mA}=_{-}-_{-}---^{\mathrm{A}} \)
\( \mathbf{A} \cdot 10^{3} A \)
B. \( 10^{-3} A \)
\( c \cdot 10^{6} A \)
D. \( 10^{-6} A \)
| 3 |
Physics
|
What is the nature of carbon atom
marked with asterisk \( (*) \) sign in the given compounds?
| 1 |
Chemistry
|
Under low glomerular blood flow, juxta glomerular cells release
A. Angiotensin I
B. Angiotensin I
c. Aldosterone
D. Renin
| 0 |
Biology
|
Give Nernst equation:
Calculate the electrode potential of the
following single electrode. \( \boldsymbol{C u}_{(a q)}^{++}(\boldsymbol{C}=\mathbf{0 . 0 1 M}) / \boldsymbol{C u} ;\left(\boldsymbol{E}^{\circ}=\right. \)
\( +0.337 V) \)
| 1 |
Chemistry
|
Chlorine displaces the following from their salts:
This question has multiple correct options
A. fluorine
B. nitrogen
c. bromide
D. iodine
| 1 |
Chemistry
|
The glass bulb of electric bulbs becomes black due to the deposition of vapour from the:
A. glass of the bulb
B. metal filament
c. gas in the bulb
D. joint in the glass
| 1 |
Chemistry
|
The current flowing in the circuit is
\( \mathbf{A} \cdot 2.5 A \)
B. \( 5 A \)
\( c \cdot 1 A \)
\( \mathbf{D} \cdot 2 A \)
| 3 |
Physics
|
Compute \( \boldsymbol{P}(\boldsymbol{A} \mid \boldsymbol{B}), \) if \( \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 2 5} \) and
\( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})=\mathbf{0 . 1 8} \)
| 2 |
Maths
|
\( \operatorname{Let} z_{k}(k=0,1,2, \dots \dots \dots .6) \) be the roots
of the equation \( (z+1)^{7}+z^{7}=0, \) then
\( \sum_{k=0}^{6} R e\left(z_{k}\right) \) is equal to
\( A \cdot 0 \)
B. \( \frac{3}{2} \)
c. \( -\frac{7}{2} \)
D. \( \frac{7}{2} \)
| 2 |
Maths
|
The S.I. unit of universal gas constant is
A. \( W a t t K^{-1} m o l^{-1} \)
B. \( N K^{-1} \) mol \( ^{-1} \)
c. \( J K^{-1} m o l^{-1} \)
D. \( \operatorname{erg} K^{-1} \)mol\( ^{-1} \)
| 3 |
Physics
|
Distance between two parrallel lines, \( \overline{\boldsymbol{r}}=\overline{\boldsymbol{a}}_{1}+\boldsymbol{\lambda} \overline{\boldsymbol{b}} \) and \( \overline{\boldsymbol{r}}=\overline{\boldsymbol{a}}_{2}+\boldsymbol{\mu} \overline{\boldsymbol{b}}, \) is given
by
A \( \cdot d=\mid \frac{\left(\bar{a}_{2}-\bar{a}_{1}\right)}{\hat{b}} \)
B . \( d=\mid\left(\bar{a}_{2}-\bar{a}_{1}\right) \times \hat{b} \)
c. \( d=\mid\left(\bar{a}_{2}+\bar{a}_{1}\right) \times \hat{b} \)
D . \( d=\mid\left(\bar{a}_{2}-\bar{a}_{1}\right) \)
| 2 |
Maths
|
A truck weighing 1000 kgf changes its
speed from \( 36 k m h^{-1} \) to \( 72 k m h^{-1} \) in 2
minutes. \( \left(\boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} \boldsymbol{s}^{-2}\right) . \) Calculate the
work done by the engine
A \( \cdot 1.5 \times 10^{4} J \)
В. \( 1 \times 10^{5} J \)
c. \( 7.2 \times 10^{5} J \)
D. \( 0 . J \)
| 3 |
Physics
|
Explain tropospheric pollution in 100
words.
| 0 |
Biology
|
What occurs most often in nature:
oxidation or reduction?
A. Oxidation.
B. Reduction.
c. Both occur equally
D. Depends on the scenario
| 1 |
Chemistry
|
Which of the following are not nonluminous objects?
A. Moon
B. Planets
c. sun
D. Earth
| 3 |
Physics
|
Write the formula of the following compounds:
(i) Potassium trioxalatoaluminate (III)
(ii) Hexaaquairon(II) sulphate.
| 1 |
Chemistry
|
ff \( x y(y-x)=2 a^{3}, \) at what point does \( y \)
have a minimum value
A . a, 2a
B. a,-a
c. २а,२а
D. None of these
| 2 |
Maths
|
An object is placed at a distance of 30 \( \mathrm{cm} \) from a concave tens of focal length \( 30 \mathrm{cm} \)
(i) Use lens formula to determine the
distance of the image from the lens.
(ii) List four characteristics of the
image (nature position, size, erect/inverted) in this case.
(iii) Draw a labelled diagram to justify
your answer apart (ii)
| 3 |
Physics
|
The physical quantity can be expressed
as
| 3 |
Physics
|
\( 0.394 \mathrm{g} \) of an organic compound containing iodine on treatment by Carius method gave 0.705 g of silver iodide. Find the percentage of halogen in the compound.
A . \( 99 \% \)
B . \( 96.7 \% \)
c. \( 95 \% \)
D. \( 92 \% \),
| 1 |
Chemistry
|
Which of the following ions is encouraging for the formation of algae in water?
\( \mathbf{A} \cdot S O_{4}^{2-} \)
в. \( P O_{4}^{3} \)
c. \( A s O_{4}^{3} \)
D. \( C O_{3}^{2-} \)
| 1 |
Chemistry
|
Clean water would have Biochemical
oxygen demand (BOD) value of less
than:
A \( .17 \mathrm{ppm} \)
B. 5 ppm
c. 200,000 ppm
D. 10 ppm
| 1 |
Chemistry
|
If \( V_{A} \) and \( V_{B} \) denote the potentials of \( A \)
and \( \mathrm{B} \), then the equivalent resistance
between \( A \) and \( B \) in the adjoint electric
circuit is
\( A \cdot 10 \Omega \) if \( V_{A}>V_{B} \)
B. \( 5 \Omega \) if \( V_{A}<V_{B} \)
\( \mathrm{c} \cdot 5 \Omega \) if \( V_{A}>V_{B} \)
D. \( 20 \Omega \) if \( V_{A}>V_{B} \)
| 3 |
Physics
|
The p-V diagram of a gas system undergoing cyclic process is shown
here. The work done during isobaric
compression is
A . 100 J
в. 200
c. 600 J
D. 500
E. 400
| 3 |
Physics
|
Is \( x^{8}+a^{8} \) divisible by \( x+a ? \)
| 2 |
Maths
|
The value of \( \sin 75^{\circ}= \)
\( ^{A} \cdot \frac{2-\sqrt{3}}{\sqrt{2}} \)
в. \( \frac{\sqrt{3}+1}{2 \sqrt{2}} \)
c. \( \frac{\sqrt{3}-1}{2 \sqrt{2}} \)
D. \( \frac{\sqrt{3}+1}{\sqrt{2}} \)
| 2 |
Maths
|
Assertion: In a galvanic cell, the half-cel with higher reduction potential provides a reducing agent Reason: Easily reducible substances are good oxidants.
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false
| 1 |
Chemistry
|
Virat and Samrat together invested
5000 and 12000
rupees to start a business they
suffered a loss of \( 20 \% \)
How much lost did each of them incur.
| 2 |
Maths
|
If 'M' is the molecular weight of a gas, what volume in \( l \) at STP would be
occupied by M/4 g of that gas?
A . 11.2
B. 2.24
\( c .5 .6 \)
D. 22.4
| 1 |
Chemistry
|
We increase the charge on the plate of a capacitor, it means
A. increasing the capacitance
B. increasing P.D. between plates
c. decreasing P.D. between plates
D. no change in field between plates
| 3 |
Physics
|
Write down each pair of adjacent angles
shown in figure.
| 2 |
Maths
|
A wheel as the angular acceleration of
\( 3.0 \mathrm{rad} / \mathrm{sec}^{2} \) and initial angular speed of
2.00 rad/sec. In a time of 2 sec, it has
rotated through an angle (in radians) of
\( A \cdot 4 \)
B. 6
c. 10
D. 12
| 3 |
Physics
|
If the equation \( x^{2}+b x+c=0 \) and
\( \boldsymbol{x}^{2}+\boldsymbol{c} \boldsymbol{x}+\boldsymbol{b}=\mathbf{0},(\boldsymbol{b} \neq \boldsymbol{c}) \) have a
common root then
A. \( b+c=0 \)
B. \( b+c=1 \)
c. \( b+c+1=0 \)
D. None of these
| 2 |
Maths
|
Calculate the molar solubility of zinc tetrathiocyanato-N-mercurate (II) if its \( \boldsymbol{K}_{\boldsymbol{S P}}=\boldsymbol{2} \cdot \boldsymbol{2} \times 10^{-7} \)
A. 0.00380
B. 0.000469
c. 0.0095
D. 0.0183
| 1 |
Chemistry
|
An ideal gas as compared to a real gas at very high pressure occupies:
A. more volume
B. less volume
c. same volume
D. unpredictable behaviour
| 1 |
Chemistry
|
Amides are transported to the other parts of the plants via
A. phloem parenchyma
B. phloem companion cells
c. xylem vessels
D. phloem fibre
| 0 |
Biology
|
represents the variation of particle momentum with associated de Broglie
wavelength?
\( \mathbf{A} \)
B.
\( c \)
\( D \)
| 3 |
Physics
|
A steel wire of length \( 7 m \) and cross
section 1 mm\( ^{2} \) is hung from a rigid
support with a steel weight of volume 1000 \( c c \) hanging from the other end. Find the decreases in the length of wire, when steel weight is completely immersed in water
\( \left(\boldsymbol{Y}_{\text {steel}}=\mathbf{2} \times \mathbf{1 0}^{\mathbf{1 1}} \mathbf{N} / \boldsymbol{m}^{2}\right) \)
Density of water \( =\mathbf{1} \boldsymbol{g} / \boldsymbol{c} . \boldsymbol{c} \)
| 3 |
Physics
|
The difference between two positive numbers is 4 and difference of their
cubes is \( 316 . \) Find their product.
A .22
B . 20
\( c \cdot 21 \)
D. 19
| 2 |
Maths
|
\( C O \) can be used as a fuel but not \( C O_{2} \)
because
A. \( C O_{2} \) is not a good fuel.
B. \( C O \) is a good fuel
c. \( C O \) can be oxidized but \( C O_{2} \) can not can be oxidized
D. \( C O_{2} \) can be oxidized but not \( C O \)
| 1 |
Chemistry
|
The function of a fuse in independent of
| 3 |
Physics
|
A circuit has a section \( \mathrm{ABC} \) as shown in
figure. If the potentials at points \( A, B \)
and \( \mathrm{C} \) are \( V_{1}, V_{2} \) and \( V_{3} \) respectively.
The potential at point 0 is?
A \( \cdot V_{1}+V_{2}+V_{3} \)
\( ^{\mathbf{B}} \cdot\left[\frac{V_{1}}{R_{1}}+\frac{V_{2}}{R_{2}}+\frac{V_{3}}{R_{3}}\right]\left[\frac{1}{R_{1}}+\frac{1}{R_{2}}+\frac{1}{R_{3}}\right]^{-1} \)
c. zero
\( ^{\mathrm{D}} \cdot\left[\frac{V_{1}}{R_{1}}+\frac{V_{2}}{R_{2}}+\frac{V_{3}}{R_{3}}\right]\left(R_{1}+R_{2}+R_{3}\right) \)
| 3 |
Physics
|
What are complementary and supplementary angles?
| 2 |
Maths
|
If \( y=\frac{\sin ^{-1} x}{\sqrt{1-x^{2}}}, \) prove that
\( \left(1-x^{2}\right) \frac{d y}{d x}-x y=1 \)
| 2 |
Maths
|
The quantity of heat taken or given out by a unit mass of a substance when it
changes from solid to liquid state or liquid to solid state at constant temperature is known as
| 3 |
Physics
|
How would you rewrite Euclid's fifth postulate so that it would be easier to understand?
| 2 |
Maths
|
Solve \( \sin x+\sqrt{3} \cos x \geq 1 \)
| 2 |
Maths
|
Fill in the blank.
When we drink liquid with a straw,the
air pressure acting on the surface of liquid then becomes than
the pressure inside the straw
A. Greater
B. Smaller
c. Equal
D. None
| 3 |
Physics
|
The set of points where the function
\( \boldsymbol{f}(\boldsymbol{x})=[\boldsymbol{x}]+|\mathbf{1}-\boldsymbol{x}|,-\mathbf{1} \leq \boldsymbol{x} \leq \mathbf{3} \)
where [.] denotes the greatest integer
function, is not differentiable, is
A \( \cdot\{-1,0,1,2,3\} \)
B \( \cdot\{-1,0,2\} \)
c. \{0,1,2,3\}
D \( \cdot\{-1,0,1,2\} \)
| 2 |
Maths
|
The volume of a cube is \( 1000 \mathrm{cm}^{3} \). Find
its total surface area in \( \mathrm{cm}^{2} \)
| 2 |
Maths
|
\( K M n O_{4} \) is acidified for redox
titrations by:
A. \( H C l \)
в. \( H N O_{3} \)
c. \( H_{2} S O_{4} \)
D. any of these
| 1 |
Chemistry
|
Two point masses each equal to \( 1 k g \) attract one another with a force of
\( 10^{-9} k g w t . \) Find the distance between
the two point masses. Take: \( g= \)
\( 9.8 m / s^{2} \)
\( A \cdot 8 c m \)
B. \( 0.8 \mathrm{cm} \)
c. \( 80 \mathrm{cm} \)
D. \( 0.08 \mathrm{cm} \)
| 3 |
Physics
|
According to Faraday's law, the total charge induced in a conductor that is moved in a magnetic field depends up
on:
A. Initial magnetic flux
B. Final magnetic flux
c. Rate of change of magnetic flux
D. change in magnetic flux
| 3 |
Physics
|
A hydraulic press has a ram of \( 15 \mathrm{cm} \) diameter and plunger is \( 1.5 \mathrm{cm} . \) It is required to lift a weight of 1 tonne. The force required on plunger is
A. \( 10 \mathrm{kg} \)
B. \( 100 \mathrm{kg} \)
c. \( 1000 \mathrm{kg} \)
\( D \cdot 1 \mathrm{kg} \)
| 3 |
Physics
|
The statement "The change of enthalpy
of a chemical reaction is same whether
the reaction takes place in one or several steps" is:
A . Le Chatelier's law
B. van't Hoff's law
c. first law of thermodynamics
D. Hess's law.
| 1 |
Chemistry
|
An \( \alpha \) - particle of \( \mathrm{KE} \mathbf{5 . 4} M e V \) is projected towards \( C r \) - nucleus \( (Z= \)
24). What is its distance of closest
approach? \( \left(e=1.6 \times 10^{-19} C\right) \)
| 1 |
Chemistry
|
Suppose \( \boldsymbol{E}_{1}, \boldsymbol{E}_{2}, \boldsymbol{E}_{3} \) be three mutually
exclusive events such that \( \boldsymbol{P}\left(\boldsymbol{E}_{i}\right)=\boldsymbol{p}_{i} \)
for \( \boldsymbol{i}=\mathbf{1}, \mathbf{2}, \mathbf{3} \)
\( \operatorname{then} P\left(E_{1} \cap E_{2}^{\prime}\right)+P\left(E_{2} \cap E_{3}^{\prime}\right)+ \)
\( \boldsymbol{P}\left(\boldsymbol{E}_{3} \cap \boldsymbol{E}_{1}^{\prime}\right) \) equals
A \( \cdot p_{1}\left(1-p_{2}\right)+p_{2}\left(1-p_{3}\right)+p_{3}\left(1-p_{1}\right) \)
В. \( p_{1} p_{2}+p_{2} p_{3}+p_{3} p_{1} \)
c. \( p_{1}+p_{2}+p_{3} \)
D. None of these
| 2 |
Maths
|
Let \( \boldsymbol{f}: \mathbb{R} \rightarrow \mathbb{R} \) be a differentiable function such that \( \boldsymbol{f}(\mathbf{0})=\mathbf{0}, \boldsymbol{f}\left(\frac{\boldsymbol{\pi}}{\mathbf{2}}\right)=\mathbf{3} \)
and \( \boldsymbol{f}^{\prime}(\mathbf{0})=\mathbf{1 .} \) If \( \boldsymbol{g}(\boldsymbol{x})= \)
\( \int_{x}^{\frac{\pi}{2}}\left[f^{\prime}(t) \operatorname{cosec} t-\cot t \operatorname{cosec} t f(t)\right] d t \) for
\( \boldsymbol{x} \in\left(\mathbf{0}, \frac{\boldsymbol{\pi}}{\mathbf{2}}\right], \) then \( \lim _{\boldsymbol{x} \rightarrow 0} \boldsymbol{g}(\boldsymbol{x})= \)
| 2 |
Maths
|
Identify the correct statement from the
following in a chemical reaction.
A. The entropy always increases
B. The change in entropy along with suitable change in enthalpy decides the rate of reaction
C. The enthalpy always decreases
D. Both the enthalpy and the entropy remains constant
| 1 |
Chemistry
|
If the percentage error in measuring the
surface area of a sphere is \( \alpha \% \), then the error in its volume is
A \( \cdot \frac{3}{2} \alpha \% \)
в. \( \frac{2}{3} \alpha \% \)
\( c .3 \alpha \% \)
D. none of these
| 2 |
Maths
|
Oxidation number of iodine varies from:
A. -1 to +1
B. -1 to +7
\( \mathbf{c} .+3 \) to +5
D. -1 to +5
| 1 |
Chemistry
|
Two blocks of the same metal having
the same mass and at temperature \( T_{1} \)
and \( T_{2}, \) respectively. are brought in
contact with each other and allowed to
attain thermal equilibrium at constant
pressure. The change in entropy, \( \Delta S \), for this process is :
\( ^{\mathbf{A}} \cdot 2 C_{p} \ln \left(\frac{T_{1}+T_{2}}{4 T_{1} T_{2}}\right) \)
\( ^{\mathrm{B}} 2 C_{p} \ln \left[\frac{\left(T_{1}+T_{2}\right)^{\frac{1}{2}}}{T_{1} T_{2}}\right] \)
\( ^{\mathbf{c}} \cdot_{C_{p} l n}\left[\frac{\left(T_{1}+T_{2}\right)^{2}}{4 T_{1} T_{2}}\right] \)
D \( \cdot 2 C_{p} \ln \left[\frac{T_{1}+T_{2}}{2 T_{1} T_{2}}\right] \)
| 3 |
Physics
|
Assertion
Tetravalency of carbon leading to formation of single, double and triple bonds.
Reason
The electronic configuration of carbon is \( 1 s^{2} 2 s^{2} 2 p^{2} . \) Carbon has 4 valence electrons and by sharing 4 electrons. It will have a stable configuration. It has all the valence electrons unpaired in the excited state.
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 solubility curve of \( \boldsymbol{K} \boldsymbol{N} \boldsymbol{O}_{3} \) in water is shown below.
The amount of \( K N O_{3} \) that dissolves in
\( 50 g \) of water at 40 is closest to:
A . 100 g
B. 150 g
c. \( 200 g \)
D. \( 50 g \)
| 1 |
Chemistry
|
Sphere (1) moving with velocity \( 4 \mathrm{m} / \mathrm{s} \)
collides another sphere (2) at rest. Find
final velocity of sphere (1) after collision collision perfectly elastic
\( A \cdot 2 \hat{\imath}+\sqrt{3} \hat{\jmath} \)
B . \( 2 \hat{i}-\sqrt{3} \hat{j} \)
\( c \cdot \hat{i}+\sqrt{3} \hat{j} \)
D. \( \hat{i}-\sqrt{3} \hat{j} \)
| 3 |
Physics
|
Write the converse, inverse and
contrapositive of the following statements: "If a function is
differentiable then it is continuous".
| 2 |
Maths
|
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