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Solve: \( x-3(2+x)>2(3 x-1) \)
| 2 |
Maths
|
Decrease in the pressure for the
following equilibrium: \( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{s}) \rightleftharpoons \)
\( \boldsymbol{H}_{2} \boldsymbol{O}(l) \) result in the:
A . formation of more \( H_{2} O(s) \)
B. formation of more \( H_{2} O(l) \)
C . increase in melting point of \( H_{2} O(s) \)
D. decrease in melting point of \( H_{2} O(s) \)
| 1 |
Chemistry
|
If \( t \) is a parameter,then \( \boldsymbol{x}=\boldsymbol{a}\left(\boldsymbol{t}+\frac{\mathbf{1}}{\boldsymbol{t}}\right) \)
and \( y=b\left(t-\frac{1}{t}\right) \) represent
A. An ellipse
B. A circle
c. A pair of straight lines
D. A hyperbola
| 2 |
Maths
|
In Lassigne's test for nitrogen in an organic compound, the blue colouration is due to the formation of:
A. ferro ferricyanide
B. ferric ferrocyanide
c. ferric cyanide
D. ferrocyanide
| 1 |
Chemistry
|
Nodal planes of \( \pi \) -bonds \( (\mathrm{s}) \) in \( \boldsymbol{C} \boldsymbol{H}_{2}= \)
\( C=C=C H_{2} \) are located in:
A. all are in molecular plane
B. perpendicular plane which contains \( C-C \sigma \) -bond
c. one in molecular plane and two in a plane perpendicular to molecular plane which contains \( C \) \( C \sigma \) -bonds
D. two in molecular plane and one in a plane perpendicular to molecular plane which bisects \( C-C \) \( \sigma \) -bonds at right angle
| 1 |
Chemistry
|
Assertion
Electron affinity value of \( C l^{-} \) has negative value.
Reason
Electron affinity values of all uninegative ions are negative.
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
|
A mixture of iodine and sand are
separated by method of
| 3 |
Physics
|
Fill in the blank:
If the system has infinite number of solutions, then the equations are said
to be
A. Consistent
B. Inconsistent
c. Dependent
D. Independent
| 2 |
Maths
|
Solve:
\( \boldsymbol{x}^{e}+\boldsymbol{e}^{\boldsymbol{x}}+\boldsymbol{e}^{\boldsymbol{e}} \)
| 2 |
Maths
|
Figure shows a meter bridge (which is nothing but a practical Wheatstone bridge), consisting of two resistors \( X \)
and Y together in parallel with a meter long constantan wire of uniform cross
section. Which the help of a movable
contact \( \mathrm{D} \), one can change the ratio of resistance of the two segments of the
wire until a sensitive galvanometer \( G \)
connected across B and D shows no
deflection. The null point is found to be a distance of \( 33.7 \mathrm{cm} . \) The resistor Y is
shunted by a resistance of \( 12 \omega, \) and the null point is found to shift by a distance of \( 18.2 \mathrm{cm} . \) Determine the approximate resistance of \( X \) and \( Y \) in ohm.
| 3 |
Physics
|
The paramagnetic lanthanoid ion among the following is:
A \( \cdot C e^{4} \)
в. \( Y b^{2} \)
c. \( L u^{3} \)
D. \( S m^{2+} \)
| 1 |
Chemistry
|
Which of the following is true regarding the function \( \boldsymbol{f}(\boldsymbol{x}, \boldsymbol{y})=\boldsymbol{x}^{4} \sin \frac{\boldsymbol{x}}{\boldsymbol{y}} ? \)
A. Not homogenous
B. Homogenous with degree 2
c. Homogenous with degree 3
D. None of the above
| 2 |
Maths
|
Probability cannot be expressed in
A. fraction form
B. ratio form
c. negative form
D. percentage form
| 2 |
Maths
|
Which is not characteristic of \( \pi \) -bond?
A. \( \pi \) - bond is formed when a sigma bond already formed
B. \( \pi \) - bond are formed from hybrid orbitals
C \( . \pi \) - bond may be formed by the overlapping of \( p \) orbitals
D. \( \pi \) - bond results from lateral overlap of atomic orbitals
| 1 |
Chemistry
|
Which transition in hydrogen spectrum
would have same wavelength as that in
\( H e^{+} \) ion for \( n=4 \) to \( n=2 \) transition?
| 1 |
Chemistry
|
David is observing his image in a plane mirror. The distance between the mirror
and his image is \( 4 \mathrm{m} \). If he moves \( 1 \mathrm{m} \) towards the mirror, then the distance between David and his image will be:
\( A \cdot 3 m \)
B. \( 5 \mathrm{m} \)
\( c \cdot 6 m \)
D. 8 m
| 3 |
Physics
|
If \( A=\left[\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right], \) then \( \operatorname{det}\left(A+A^{2}+\right. \)
\( \left.\boldsymbol{A}^{3}+\boldsymbol{A}^{4}+\boldsymbol{A}^{5}\right) \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B. 32
c. 25
D. 30
| 2 |
Maths
|
Statement-1: In the fermentation
process of molasses, along with yeast,
\( \left(N H_{4}\right)_{2} S O_{4} \) and \( \left(N H_{4}\right)_{3} P O_{4} \) are
added.
Statement-2: Both \( \left(N H_{4}\right)_{3} P O_{4} \) and
\( \left(N H_{4}\right)_{2} S O_{4} \) act as food and help in the
growth of yeast.
A. Statement-1 is True, statement-2 is True; statementis a correct explanation for statement-
B. Statement-1 is True, statement-2 is True; statementis NOT a correct explanation for statement-
c. Statement- - is True, statement-2 is False
D. Statement- 1 is False, statement- 2 is True
| 1 |
Chemistry
|
A drop of water detaches itself from the
exit of a tap when \( (\sigma= \) surface tension
of water. \( \rho= \) density of water, \( \boldsymbol{R}= \)
radius of the tap exit, \( r= \) radius of the
drop)
\( r>\left(\frac{2 R \sigma}{3 \rho g}\right)^{1 / 3} \)
В. \( \quad r>\frac{2}{3} \frac{\sigma}{\rho g} \)
\( ^{\mathrm{C}} \cdot \frac{2 \sigma}{r}> \) atmospheric pressure
\( r>\left(\frac{2 R \sigma}{3 \rho g}\right)^{2 / 3} \)
E. None of the above
| 3 |
Physics
|
The nucleus finally formed in fusion of
the proton in a proton cycle is that of:
A. Helium
B. Deuterium
c. carbon
D. Hydrogen
| 3 |
Physics
|
Compounds which contain oxides of carbon or carbonate hydrogencarbonate ions are called:
A. Hydrocarbons
B. Organic compounds
c. Inorganic compounds
D. Carbohydrogens
| 1 |
Chemistry
|
Consider the following reaction, Ethanol \( \stackrel{P B r_{3}}{\longrightarrow} X \stackrel{\text {alc. } K O H}{\longrightarrow} \)
\( \boldsymbol{Y} \frac{(i) \boldsymbol{H}_{2} \boldsymbol{S O}_{4} \text { room temperature }}{(i i) \boldsymbol{H}_{2} \boldsymbol{O}, \text { heat }} \boldsymbol{Z} \)
Product \( Z \) is:
\( \mathbf{A} \cdot C H_{2}=C H_{2} \)
в. \( C H_{3} C H_{2}-O-C H_{2}-C H_{3} \)
c. \( C H_{3} C H_{2}-O-S O_{3} H \)
D. \( C H_{3} C H_{2} \) О \( H \)
| 1 |
Chemistry
|
Which of the following statement(s) is/are true?
i. Adding a solute raises the
vapor pressure \& boiling point.
ii. The change in boiling \& freezing point depends on molality.
iii. The number of solute particles in
a solvent is an important factor
in determining the boiling point
elevation.
A. i only
B. ii only
c. i and ii
D. ii and iii
E. i, ii and iii
| 1 |
Chemistry
|
Calculate change in internal energy if \( \triangle H=-92.2 k J, P=40 a t m \) and
\( \triangle V=-1 L \)
A . -42 kJ
B. -88kJ
\( c \cdot+88 k J \)
D. +42 kJ
| 1 |
Chemistry
|
On the set of all integers defined as \( \boldsymbol{f} \)
\( Z \rightarrow Z \) such that \( f(x)=[x], \) then it is:
\( A \cdot \) not a function
B. a many-to-one function
c. an into function
D. an identity function
| 2 |
Maths
|
What is 'Rain Water Harvesting'? Write its main objectives.(Any two)
| 0 |
Biology
|
If a planet were suddenly stopped in its orbit supposed to be circular, show that it would fall into the sun in a time \( \boldsymbol{T} \times \) \( \left(\frac{\sqrt{2}}{8}\right), \) where \( T \) is the time period of revolution.
| 3 |
Physics
|
The oxidation state of Chlorine in
Bleaching Powder:
\( A \cdot-2 \)
B . - -
\( c \cdot+1 \)
D. -1 and +1
| 1 |
Chemistry
|
Explain : When \( M n(O H)_{2} \) is made by adding an alkali to a solution
containing \( M n^{2+} \) ions, the ppt quickly darkens, and eventually goes black
A. The black colour is due to the manganese (VI) oxide \( M n_{2} O_{3} \)
B. The black colour is due to the manganese (VI) oxide \( M n O_{2} \)
C. The black colour is due to the manganese (VI) oxide \( M n_{2} O_{5} \)
D. None of these
| 1 |
Chemistry
|
\( \boldsymbol{A}+\boldsymbol{B} \longrightarrow \boldsymbol{C} ; \boldsymbol{\Delta} \boldsymbol{H}=+\boldsymbol{6} \boldsymbol{0} \boldsymbol{K} \boldsymbol{J} / \boldsymbol{m o l} \)
\( \boldsymbol{E}_{\boldsymbol{a} t} \) is \( 150 \mathrm{kj} . \) What is the activation energy for the backward reation?
A . 210 k.
B. 105kJ
c. 90 k
D. 145kJ
| 1 |
Chemistry
|
A universal indicator is made by
dissolving methyl orange, bromothymol blue and phenolphthalein in alcohol. Which of the following processes could best be used to separate the methyl orange component from the universal
indicator solution?
A. Chromatography
B. Filtration
c. Distillation
D. Decantation
| 1 |
Chemistry
|
A solid disk is rolling without slipping on a level surface at a constant speed of
\( 2.00 m / s . \) How far can it roll up a \( 30^{\circ} \)
ramp before it stops? (Take \( \boldsymbol{g}= \)
\( \left.9.8 m / s^{2}\right) \)
| 3 |
Physics
|
The following table draws the income of finance of a grape season find the mean of their income.
ıncome \( \begin{array}{lll}\mathbf{2 0}- & \mathbf{3 0}- & \mathbf{4 0}- \\ \mathbf{3 0} & \mathbf{4 0} & \mathbf{5 0}\end{array} \) \( - \) (thousand
Rs)
Farmer 10
| 2 |
Maths
|
Aluminium foils are used for:
A. wrapping chocolates and food stuff
B. to prepare hydrogen
\( c \cdot \operatorname{both} A \) and \( B \)
D. none of these
| 1 |
Chemistry
|
When the free ends of a tester are
dipped into a solution, the magnetic needle shows deflection. Can you
explain the reason?
| 3 |
Physics
|
A horizontal uniform glass tube of \( 100 \mathrm{cm} \) length is sealed at both ends contains 10 \( \mathrm{cm} \) mercury column in the middle the
temperature and pressure of air on either side of mercury column are respectively \( 31^{0} \mathrm{C} \) and \( 76 \mathrm{cm} \) of mercury if the air
column at one end is kept at \( 0^{0} \mathrm{C} \) and the other end at \( 273^{0} \mathrm{C} \) the pressure of
air which is at \( 0^{0} \mathrm{C} \) is (in \( \mathrm{cm} \) of \( \mathrm{Hg} \) )
A. 76
B. 88.2
c. 102.4
D. 122
| 3 |
Physics
|
The rate of chemisorption:
A. decreases with increase of pressure
B. increases with increase of pressure
C. is independent of pressure
D. is independent of temperature
| 1 |
Chemistry
|
Find \( \frac{\boldsymbol{x}+\boldsymbol{u}+\boldsymbol{y}+\boldsymbol{z}}{\mathbf{5 0}} \)
| 2 |
Maths
|
\( A \) and \( B \) have 460 coins altogether. If \( \frac{3}{4} \) of \( A^{\prime} \) s number of coins is equal to \( \frac{2}{5} \) of
B's number of coins, find how many
coins must \( B \) give to \( A, \) so that they
both have equal number of coins.
A . 50
B. 70
c. 20
D. 90
| 2 |
Maths
|
If \( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}} \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{g}(\boldsymbol{x}) \) for \( \boldsymbol{a} \leq \boldsymbol{x} \leq \boldsymbol{b}, \) then
\( \int_{a}^{b} f(x) g(x) d x \) equals to:
A. \( f(2)-f(1) \)
В. \( g(2)-g(1) \)
c. \( \frac{[f(b)]^{2}-[f(a)]^{2}}{2} \)
D. \( \frac{[g(b)]^{2}-[g(a)]^{2}}{2} \)
| 2 |
Maths
|
Describe the digestive system of
cockroach.
| 0 |
Biology
|
The electron in a hydrogen atom makes
a transition \( n_{1} \rightarrow n_{2}, \) where \( n_{1} \) and \( n_{2} \)
are the principal quantum numbers of the two states. Assume the Bohr model
as valid in this case. The frequency of the orbital motion of the electron in the
initial state is \( 1 / 27 \) of that in the final
state. The possible values of \( n_{1} \) and \( n_{2} \)
are
A \( \cdot n_{1}=6, n_{2}=3 \)
в. \( n_{1}=4, n_{2}=2 \)
c. \( n_{1}=8, n_{2}=1 \)
D. \( n_{1}=3, n_{2}=1 \)
| 3 |
Physics
|
Solve :
\( \int_{1}^{2} \frac{x}{(x+1)(x+2)} d x \)
| 2 |
Maths
|
Hydrogen gas will reduce:
A. hot cupric oxide
B. hot ferric oxide
c. hot stanic oxide
D. hot aluminium oxide
| 1 |
Chemistry
|
Derive relation between Kinetic Energy and Momentum
| 3 |
Physics
|
The total number of compounds having at least one bridging oxo group among the molecules given below is:
\( N_{2} O_{3}, N_{2} O_{5}, P_{4} O_{6}, P_{4} O_{7}, H_{4} P_{2} O_{5}, H_{5} P \)
| 1 |
Chemistry
|
In an entrance test is graded on the basis of two examinations, the
probability of a randomly chosen
student passing the first examination
is 0.8 and the probability of passing the second examination is 0.7 . The
probability of passing at least of them is \( 0.95 . \) What is the probability of passing both?
| 2 |
Maths
|
\( P, Q \) and \( R \) are three sets and \( \xi=P \cup \)
\( Q \cup R \) Given that \( n(\xi)=60, n(P \cap \)
\( Q)=5, n(Q \cap R)=10, n(P)=20 \) and
\( \boldsymbol{n}(\boldsymbol{Q})=23, \) find \( \boldsymbol{n}(\boldsymbol{P} \cup \boldsymbol{R}) \)
A . 37
B . 38
c. 45
D. 52
| 2 |
Maths
|
The middle term in the expansion of \( \left(1-3 x+3 x^{2}-x^{3}\right)^{2 n} \) is
\( \mathbf{A} \cdot 6 n_{C_{3 n}}(-x)^{3 n} \)
B . \( 6 n_{C_{2 \text { n }}}(-x)^{2 n+1} \)
\( \mathbf{c} \cdot 4 n_{C_{S n}}(-x)^{3 n} \)
D. \( 6 n_{C_{3 n}}(-x)^{3 n-1} \)
| 2 |
Maths
|
One gram of charcoal adsorbs \( 400 \mathrm{mL} \) of
\( 0.5 M \) acetic acid to form a monolayer,
and the molarity of acetic acid reduces
to \( 0.49 M . \) Calculate the surface area of
charcoal adsorbed by each molecule of acetic acid, where the surface area of
charcoal is \( 3.01 \times 10^{2} \mathrm{m}^{2} \mathrm{g}^{-1} \)
A. \( 1 \times 10^{-19} \mathrm{m}^{2} \)
В. \( 1.2 \times 10^{-19} \mathrm{m}^{2} \)
D. None of these
| 1 |
Chemistry
|
The volume of \( 1 m^{3} \) of gas is doubled at
atmospheric pressure. The work done at
constant pressure will be
\( A \cdot 0 \)
B . \( 10^{5} \) call
\( \mathbf{c} \cdot 10^{5} J \)
D. \( 10^{5} \) erg
| 3 |
Physics
|
What is the role of following chemicals in food?
¡) Saccharin
ii) Sodium benzoate
| 1 |
Chemistry
|
The differential equation of all conics
whose axes coincide with the co-
ordinate axes, is
A \( . x y y_{2}+x y_{1}^{2}-y y_{1}=0 \)
B . \( y y_{2}+y_{1}^{2}-y y_{1}=0 \)
c. \( x y y_{2}+(x-y) y_{1}=0 \)
D. \( \left(y y_{1}\right)^{2}-x y_{1}-y x=0 \)
| 2 |
Maths
|
The blocks are attached by an in extensible light string and pulled vertically upward by force \( 100 \mathrm{N} \) as shown. Find the common acceleration
and tension the string.
| 3 |
Physics
|
When there is a decrease in the
concentration of oxygen in the blood,
the rate of breathing
A. Does not change
B. Increases
c. Decreases
D. Increases or decreases depending on the density of blood
| 0 |
Biology
|
All floral leaves are placed on the
of flower.
A. Thalamus
B. Petal
c. Sepal
D. Ovule
| 0 |
Biology
|
If the EMF of a cell :
\( \boldsymbol{M}\left|\boldsymbol{M}^{2+}(\mathbf{0 . 0 2} \boldsymbol{M}) \| \boldsymbol{H}^{+}(\mathbf{0 . 1} \boldsymbol{M})\right| \boldsymbol{H}_{2} \)
\( a t m) \)
at \( 25^{\circ} \mathrm{C} \) is \( 0.81 \mathrm{V} \). Find the standard
reduction potential of \( M \)
(Write a value to the nearest integer. If an answer is negative then write its
magnitude)
| 1 |
Chemistry
|
Choose the correct option which describe the simple harmonic motion.
I. The acceleration is constant.
II. The restoring force is proportional to the displacement
III. The frequency is independent of the
amplitude.
A. Il only
B. I and II only
c. I and III only
D. Il and III only
E. I, II and III
| 3 |
Physics
|
The preparation of sodium benzenesulphonate during the preparation of benzene sulphonic acid
involves:
A. dehydration
B. hydrolysis
c. hydration
D. sulfonation
| 1 |
Chemistry
|
The angle of incidence is given by the
angle :
A. PON
B. QOB
c. NOQ
D. AOP
| 3 |
Physics
|
Water formed is tested by :
A. Copper nitrate test
B. Anhydrous copper sulphate test
c. Aqueous copper sulphate test
D. copper
| 1 |
Chemistry
|
Electric flux through a surface of area
\( 100 m^{2} \) lying in the xy plane is (in \( V \) -m) if \( \overrightarrow{\boldsymbol{E}}=\hat{\boldsymbol{i}}+\sqrt{\mathbf{2}} \hat{\boldsymbol{j}}+\sqrt{\mathbf{3} \hat{\boldsymbol{k}}} \)
A. 100
B. 141.4
c. 173.2
D. 200
| 3 |
Physics
|
Assertion
The conversion of fresh precipitate to colloidal state is called peptization.
Reason
It is caused by addition of common ions
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
|
In the diagram above which spot was
most soluble (i.e. dissolved best) in the
Solvent.
A. \( \operatorname{spot} A \)
B. Spot \( B \)
c. \( \operatorname{spot} C \)
D. All of the above
| 1 |
Chemistry
|
A man gives \( 40 \% \) of his money to his children and \( 20 \% \) of the remaining to a trust. If he is still left with \( \mathrm{Rs} .9,600 \) then what did he originally have?
A. Rs.14, 000
B . Rs.19, 845
c. Rs.20, 000
D. Rs.25, 409
| 2 |
Maths
|
The value of the determinant
\( \left|\begin{array}{ccc}\left(a^{x}+a^{-x}\right)^{2} & \left(a^{x}-a^{-x}\right)^{2} & 1 \\ \left(b^{x}+b^{-x}\right)^{2} & \left(b^{x}-b^{-x}\right)^{2} & 1 \\ \left(c^{x}+c^{-x}\right)^{2} & \left(c^{x}-c^{-x}\right)^{2} & 1\end{array}\right| \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B. 2abc
\( \mathbf{c} \cdot a^{2} b^{2} c^{2} \)
D. None of these
| 2 |
Maths
|
Select odd one(w.r.t. heterotrophic
bacteria)
A. Saprophytic bacteria
B. Chemosynthetic bacteria
c. Parasitic bacteria
D. symbiotic bacteria
| 0 |
Biology
|
Carbohydrates that, on attempted hydrolysis, are not cleaved to smaller
carbohydrates are called:
A. oligosaccharides
B. polysaccharides
c. disaccharides
D. monosaccharides
| 1 |
Chemistry
|
In an election between two candidates,
one got \( 55 \% \) of the total valid votes, \( 20 \% \) of the votes were invalid. If the total
number of votes was 7500 , the number
of valid votes that the other candidates
got, was?
A. 2700
B. 2900
\( c .3000 \)
D. 3100
| 2 |
Maths
|
To which of the following the oldest fossils belong?
A. Algae
B. Fungi
c. Blue green algae
D. Both A and C
| 3 |
Physics
|
The angular momentum of electron in hydrogen atom is proportional to
A \( \cdot \sqrt{r} \)
B. \( \frac{1}{r} \)
c. \( r^{2} \)
D. \( \frac{1}{\sqrt{r}} \)
| 3 |
Physics
|
Two identical metallic spheres \( A \) and \( B \) of exactly equal masses are taken. Sphere \( A \) is given positive charge \( Q \) columb and B is given an equal negative charge. So initially before the
charge is given. What will be the masses after the charging?
| 3 |
Physics
|
If a person sitting on a rotating stool with his hands outstretched, suddenly lowers his hands, then his :
A. Kinetic energy will decrease
B. Moment of inertia will decrease.
c. Angular momentum will increase.
D. Angular velocity will remain constant
| 3 |
Physics
|
Why do aldehydes and ketones have
high dipole moments?
| 1 |
Chemistry
|
Why do caesium \( (C s) \) and potassium
\( K \) ) find applications in photoelectric
cells?
| 1 |
Chemistry
|
The image of the point \( P(1,2,3) \) in the
plane \( 2 x-y+z+3=0 \) is
A \( \cdot(-3,4,1) \)
в. (3,5,2)
c. (-3,5,2)
D. (3,-5,2)
| 2 |
Maths
|
In the figure shown, the friction force
between the bead and the light string is
\( m g / 4, \) find the time which the bead
loses contact with string after the
system is released:
A. \( \sqrt{\frac{2 l}{7 a}} \)
в. \( \sqrt{\frac{4 l}{7 q}} \)
c. \( \sqrt{\frac{8 l}{7 q}} \)
D. \( \sqrt{\frac{7 l}{7 g}} \)
| 3 |
Physics
|
Compare and contrast the chemistry of group 1 metals with that of group 2 metals with respect to the following:
Polarizing power of cations increases on
going from group 1 to group 2.
| 1 |
Chemistry
|
If figure \( C E \) and \( D E \) are equal chords
of a circle with centre \( O \). If \( \angle A O B= \)
\( 90^{\circ}, \) find ratio of the area of \( \triangle C E D \) and
\( \triangle A O B \)
| 2 |
Maths
|
All terms of an arithmetic progression are natural numbers. The sum of its
nine successive terms, beginning with the first, is larger than 200 and smaller
than \( 220 . \) Find the progression if its
second term is 12
| 2 |
Maths
|
If \( \frac{x}{\cos \theta}=\frac{y}{\cos \left(\theta-\frac{2 \pi}{3}\right)}= \)
\( \frac{z}{\cos \left(\theta+\frac{2 \pi}{3}\right)}, \) then \( x+y+z \) is equal to
\( A \)
B.
\( c \cdot-1 \)
D. none of these
| 2 |
Maths
|
The inertial force acts in a
A. Opposite direction to that of acceleration force
B. Same direction as that of accelerating force
C. Perpendicular direction to that accelerating force
D. None of the above
| 3 |
Physics
|
By imparting heat to a body, its
temperature rises by \( 15^{\circ} \mathrm{C} \). What is the corresponding rise in temperature on kelvin scale?
A. \( 15 ~ K \)
B . \( 288 K \)
c. \( -15 ~ K \)
D. None of the above
| 3 |
Physics
|
Let \( f \) and \( g \) be functions satisfying
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{e}^{\boldsymbol{x}} \boldsymbol{g}(\boldsymbol{x}), \boldsymbol{f}(\boldsymbol{x}+\boldsymbol{y})=\boldsymbol{f}(\boldsymbol{x})+ \)
\( \boldsymbol{f}(\boldsymbol{y}), \boldsymbol{g}(\mathbf{0})=\mathbf{0}, \boldsymbol{g}^{\prime}(\mathbf{0})=\mathbf{4}, \boldsymbol{g} \) and \( \boldsymbol{g}^{\prime} \) are
continuous at 0
Then
A. \( f(x)=0 \) for all \( x \)
B. \( f(x)=x \) for all \( x \)
c. \( f(x)=x+4 \) for all \( x \)
D. \( f(x)=4 x \) for all \( x \)
| 2 |
Maths
|
Lightning quickly heats the air causing it to expand, which produces the sound
of thunder.
Sound travels approximately 1 mile in 5 seconds. Knowing \( \boldsymbol{X}=\boldsymbol{r} \cdot \boldsymbol{t} \) (where \( \boldsymbol{D}= \)
distance, \( r=\text { rate and } t=\text { time }), \) how
far away is a thunderstrom when you
notice a 3 -second delay between the
flash of lightning and the sound of
thunder?
\( \mathbf{A} \cdot 1 \) mile away
B. \( 3 / 5 \) mile away
c. \( 1 / 2 \) mile away
D. \( 1 / 5 \) mile away
| 2 |
Maths
|
In the raction \( S O_{2}+2 H_{2} S \rightarrow 3 S+ \)
\( 2 H_{2} O, \) the substance that is oxidized is
\( A \cdot S O_{2} \)
в. \( H_{2} \) О
\( c \cdot s \)
D. \( H_{2} S_{S} \)
| 1 |
Chemistry
|
Humus is an example of
A. Crystalloids
B. Organic colloids
C. Soil structure
D. None of the above
| 0 |
Biology
|
L.S.D causes hallucinations. The full
chemical name of this drug is:
A. dextro-lysine
B. Iysergic acid diethylamide
c. lithium sulphide
D. lanthanum sulphide
| 1 |
Chemistry
|
Peroxides of alkali metals are:
A. Paramagnetic
c. Acidic in nature
D. Amphoteric in nature
| 1 |
Chemistry
|
In an isosceles \( \triangle A B C, \) if \( A B=A C \)
and \( D \) is a point on \( B C, \) then prove that \( A B^{2}-A D^{2}=B D . C D \)
| 2 |
Maths
|
The force \( F \) acting on a particle of mass is indicated by force-time graph shown below.The change in momentum of the
particle over the time interval from zero
to 8 s is
| 3 |
Physics
|
Assertion
Let \( f \) and \( g \) be increasing and
decreasing functions respectively from \( [0, \infty] \) to \( [0, \infty] . \operatorname{Let} h(x)=f(g(x)) . \) If
\( h(0)=0, \) then \( h(x) \) is always zero
Reason
\( h(x) \) is an increasing function of \( x \)
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
| 2 |
Maths
|
A radioactive sample at any instant has its disintegration rate 5000 disintegration per minute. After 5 minutes, the rate is 1250 disintegrations per minute. Then, the decay constant, per minute, is
A . \( 0.4 \ln 2 \)
B. \( 0.2 \ln 2 \)
c. \( 0.1 \ln 2 \)
D. \( 0.8 \ln 2 \)
| 3 |
Physics
|
The proteins found in the filaments of muscle fibres are
A. Actin and myosin
B. Myosin and elastin
c. Actin only
D. Myelin and tubulin
| 0 |
Biology
|
\( \ln \) an A.P. the first term is 2 , the last
term \( 29, \) the sum \( 155 ; \) find the
difference.
| 2 |
Maths
|
Alkynes occur in nature in:
\( \mathbf{A} \cdot \) free state
B. partially free state
c. combined state
D. none of these
| 1 |
Chemistry
|
\( \cos ^{-1}\left\{\frac{1}{2} x^{2}+\sqrt{1-x^{2}} \cdot \sqrt{1-\frac{x^{2}}{4}}\right\}= \)
\( \cos ^{-1} \frac{x}{2}-\cos ^{-1} x \) holds for
A. \( |x| \leq 1 \)
В. \( x \in R \)
c. \( 0 \leq x \leq 1 \)
D. \( -1 \leq x \leq 0 \)
| 2 |
Maths
|
Four identical plates each of area a are separated by a distance d. The connection is shown below. What is the
capacitance between \( \mathrm{P} \) and \( \mathrm{Q} \) ?
A \( \cdot 2 a \in_{0} / d \)
B \( \cdot a \epsilon_{0} /(2 d) \)
\( \mathrm{c} \cdot a \epsilon_{0} / d \)
D. \( 4 a \in_{0} / d \)
| 3 |
Physics
|
The r.m.s. value of potential difference
shown in the figure is :
\( A \cdot V_{0} / \sqrt{3} \)
в. \( V_{0} \)
\( c \cdot V_{0} / \sqrt{2} \)
D. \( V_{0} / 2 \)
| 3 |
Physics
|
\( \int e^{e^{x}+x} d x= \)
A \( \cdot e^{e^{x}}+x+c \)
B . \( e^{e^{x}}+c \)
\( \mathbf{c} \cdot e^{x}+c \)
\( \mathbf{D} \cdot e^{x}+x+c \)
| 2 |
Maths
|
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