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In the ladder network shown, current
through the resistor \( 3 \Omega \) is \( 0.25 A . \) The
input voltage ' \( V^{\prime} \) is equal to
A . \( 10 V \)
B . \( 20 V \)
\( c .5 V \)
D. \( \frac{15}{2} v \) | 3 | Physics |
One card is drawn from a pack of 52 cards. What is the probability that the card drawn is either a red card or a
king?
A \( \cdot \frac{1}{2} \)
в. \( \frac{6}{13} \)
c. \( \frac{7}{13} \)
D. \( \frac{27}{52} \) | 2 | Maths |
Find the maximum value of \( f(x)=1 \)
\( x^{2} \) if \( -2 \leq x \leq 2 \)
A . 2
B.
c. 0
D. -
E . -2 | 2 | Maths |
Cube of all odd natural numbers are odd
A. True
B. False
c. Ambiguous
D. Data insufficient | 2 | Maths |
For constructing a triangle whose perimeter and both base angles are given, the first step is to:
A. Draw a base of any length
B. Draw the base of length = perimeter
c. Draw the base angles from a random line.
D. Draw a base of length \( =\frac{1}{3} \times \) perimeter. | 2 | Maths |
Which of the following represents the given sequence of hybridisation of carbon atoms from left to right :
\( \boldsymbol{s} \boldsymbol{p}^{2}, \boldsymbol{s} \boldsymbol{p}^{2}, \boldsymbol{s} \boldsymbol{p}, \boldsymbol{s} \boldsymbol{p} ? \)
A. \( H_{2} C=C H-C \equiv C H \)
В \( \cdot_{H C} \equiv C-C H=C H_{2} \)
c. \( H_{3} C-C H=C H-C H_{3} \)
D. \( H_{2} C=C H-C H=C H_{2} \) | 1 | Chemistry |
In a certain population \( 10 \% \) of the people are rich, \( 5 \% \) are famous and \( 3 \% \) are rich and famous. The probability that a person picked at random from the population is either famous or rich but not both, is equal to
A . 0.07
B. 0.08
c. 0.09
D. 0.12 | 2 | Maths |
Prove that square of any positive integer is always of the form \( 4 m, 4 m+ \) \( 1,4 m+4 \) or \( 4 m+9 \) | 2 | Maths |
On the voyage of the Beagle, Darwin \( (1809-1882) \) found that flora and fauna
of temperate South America are most
similar to that of
A. Tropical South America
B. Australia
c. Asia
D. Europe | 0 | Biology |
A large number of particles are placed around the origin, each at a distance \( \mathrm{R} \) from the origin. The distance of the center of mass of the system from the origin is.
\( \mathbf{A} \cdot+R \)
в. \( \leq R \)
\( c \cdot>R \)
\( D . \geq R \) | 3 | Physics |
Find the equation of the ellipse whose
vertices are \( (\pm \mathbf{9}, \mathbf{0}) \) and foci are
\( (\pm \mathbf{5}, \mathbf{0}) \) | 2 | Maths |
What is CFL?
A. Compact Fluorescent Lamp
B. Compact Fluorescent Lamina
C. Complete Fluorescent Light
D. Controlled Fluorescent Light | 3 | Physics |
A body, under the action of a force \( \overrightarrow{\boldsymbol{F}}= \) \( 6 \hat{i}-8 \hat{j}+10 \hat{k}, \) acquires an acceleration
of \( 1 m / s^{2} . \) The mass of this body must
be:
A \( \cdot 10 \sqrt{2} k g \)
в. \( 2 \sqrt{10} k g \)
c. \( 10 \mathrm{kg} \)
D. 20 kg | 3 | Physics |
Two identical balls each of mass in are
moving in opposite direction with a speed v. if they collide elastically maximum potentail energy stored in the ball is :
A. 0
в. \( \frac{1}{2} m v^{2} \)
\( \mathrm{c} \cdot m v^{2} \)
\( \mathbf{D} \cdot 2 m v^{2} \) | 3 | Physics |
Knowing that the Chemistry of lanthanoids (Ln) is dominated by its +3 oxidation state, which of the
following statements is incorrect?
A. Because of the large size of the \( \operatorname{Ln}( \) (II) ions the bonding in its compounds is predominantly ionic in character.
B. The ionic sizes of Ln
(III) decrease in general with increasing atomic number
c. \( \mathrm{Ln} \) (III) compounds are generally colourless
D. Ln (III) hydroxides are mainly basic in character | 1 | Chemistry |
The excitation energy of first excited
state of a hydrogen like atom is \( 40.8 e V \)
Find the energy needed to remove the electron to form the ion. | 1 | Chemistry |
The probability that \( A \) hits a target is \( \frac{1}{3} \) and the probability that \( B \) hits it, is \( \frac{2}{5} \) What is the probability that the target
will be hit, if each one of \( A \) and \( B \) shoots
at the target? | 2 | Maths |
\( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\frac{\boldsymbol{x}+\boldsymbol{y}+\mathbf{1}}{\mathbf{2} \boldsymbol{x}+\mathbf{2} \boldsymbol{y}+\mathbf{3}} \) | 2 | Maths |
Assertion
Suspended particulate matter (SPM) is an important pollutant released by diesel vehicles.
Reason
Catalytic converters greatly reduce pollution caused by automobiles.
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 | 0 | Biology |
The coeffecients of the middle term in
the binomial expansion in powers of \( x \) of \( (1+\alpha x)^{4} \) and \( (1+\alpha x)^{6} \) is the same
if \( \boldsymbol{\alpha} \) equals
A \( \cdot-\frac{5}{3} \)
в. \( \frac{10}{3} \)
\( c \cdot \frac{3}{10} \)
D. | 2 | Maths |
If \( a,(a-2) \) and \( 3 a \) are in \( A P, \) then the
value of \( a \) is
A . -3
B. -
\( c .3 \)
D. 2 | 2 | Maths |
Reaction \( \boldsymbol{A}+\boldsymbol{B} \longrightarrow \boldsymbol{C}+\boldsymbol{D} \) follows rate
\( \operatorname{law}, \boldsymbol{r}=\boldsymbol{k}[\boldsymbol{A}]^{1 / 2}[\boldsymbol{B}]^{1 / 2} \) starting with \( \mathbf{1} \boldsymbol{M} \)
of \( A \) and \( B \) each. What is the time taken
for concentration of \( \boldsymbol{A} \) become \( \mathbf{0 . 1} \boldsymbol{M} \) ?
\( \left[\text { Given } 2.303 \times 10^{-2} s e c^{-1}\right] \)
\( \mathbf{A} \cdot 10 \sec \)
B. 100sec
c. 1000 sec
D. 434 sec | 1 | Chemistry |
The values of current(l) flowing through a given resistor of resistance (R), for the corresponding values of potential difference (V) across the resistor are as
given
\( \begin{array}{lll}\mathbf{0 . 5} & \mathbf{1 . 0} & \mathbf{1 . 5}\end{array} \) V(volts) 2.0
0.1 0.3 I(amperes) 0.2
Plot a graph between current(l) and
potential difference (V) and determine the resistance (R) of the resistor. | 3 | Physics |
Action of paint-gun is based on:
A. Bernoulli's principle
B. Boyle's law
C. Faraday's law
D. Archimedes's principle | 3 | Physics |
Which of the following is considered Drosophila of a plant kingdom?
A. Neurospora
B. Synchytrium
c. Peziza
D. Amanita | 0 | Biology |
Select the correct statements about
SHE:
This question has multiple correct options
\( \mathbf{A} \cdot \) The \( E_{O P}^{o} / R_{R P}^{o} \) for SHE has been arbitrarily assigned to be zero at all temperatures.
B. SHE refers for \( P t, H_{2}(g) \mid H^{+}(a q) \)
C. SHE is very susceptible to electrode poisoning.
D. SHE is very susceptible to dissolved oxygen, \( \mathrm{H}_{2} \mathrm{S} \) and all other reducing species. | 1 | Chemistry |
Vant Hoff's equation is
A \( \cdot \log \frac{K_{2}}{K_{1}}=\frac{-\Delta H^{0}}{2.303 R}\left[\frac{T_{2}-T_{1}}{T_{2} T_{1}}\right] \)
B. \( \log \frac{K_{2}}{K_{1}}=\frac{\Delta H^{0}}{2.303 R}\left[\frac{T_{2}-T_{1}}{T_{2}+T_{1}}\right] \)
C. \( \log \frac{K_{2}}{K_{1}}=\frac{\Delta H^{0}}{2.303 R}\left[\frac{T_{2}-T_{1}}{T_{2} T_{1}}\right] \)
D. \( \log _{\frac{K_{1}}{L}=\frac{\Delta H^{0}}{2.203 R}}\left[\frac{T_{3}+T_{1}}{T_{1} 2_{1}}\right] \) | 1 | Chemistry |
\( \operatorname{Let} g(x)=2 f\left(\frac{x}{2}\right)+f(x-2) \) and
\( \boldsymbol{f}^{\prime \prime}(\boldsymbol{x})<\mathbf{0} \forall \boldsymbol{x} \in(\mathbf{0}, \mathbf{2}), \) then \( \boldsymbol{g}(\boldsymbol{x}) \)
increases in
A \( \cdot\left(\frac{1}{2}, 2\right) \)
в. \( \left(\frac{4}{3}, 2\right) \)
c. (0,2)
(年. \( 0,2,2) \)
D. \( \left(0, \frac{4}{3}\right) \) | 2 | Maths |
An object \( 10 \mathrm{cm} \) from lens, has a virtual image at \( 10 \mathrm{cm} \) from the object. The power of the lens is
A. 10 diopters
B. -10 diopters
c. 5 diopters
D. - diopters | 3 | Physics |
The water forecasting department uses as the unit of pressure
A. bar
в. \( N m^{-2} \)
\( c . P a \)
D. mm of \( H g \) | 3 | Physics |
Theoretical efficiency of fuel cell is:
A. nearly \( 60 \% \)
B. 50\%
c. \( 33 \% \)
D. nearly 100\% | 1 | Chemistry |
A can do a piece of work in 10 days, and
B can do the same work in 20 days. With the help of \( C \), they finished the work in 4 days. \( C \) can do the work in how many days, working alone? | 2 | Maths |
The \( p H \) of the solution 5 mL of \( \frac{M}{5} H C l+10 m L \) of \( \frac{M}{10} N a O H \) is:
A. 5
B. 3
\( c \cdot 7 \)
D. | 1 | Chemistry |
A coil has self inductance of 0.01 H. The
current through it is allowed to change
at the rate of \( 1 A \) in \( 10^{-2} \) s. The induced
emf is
A . \( 1 V \)
B. 2
\( c .3 V \)
D. \( 4 V \) | 3 | Physics |
The equilibrium concentration of \( [\boldsymbol{B}]_{e q} \) for the reversible reaction \( \boldsymbol{A} \rightleftharpoons \boldsymbol{B} \) can
be evaluated by the expression:
A \( \cdot K_{c}[A]_{e}^{-1} \)
B. \( \frac{K_{f}}{K_{b}}[A]_{e}^{-1} \)
\( \mathbf{c} \cdot K_{f} K_{b}^{-1}[A]_{e} \)
D. \( K_{f} K_{b}[A]^{-1} \) | 1 | Chemistry |
For two events, \( A \) and \( B \), it is given that \( \boldsymbol{P}(\boldsymbol{A})=\frac{\mathbf{3}}{\mathbf{5}}, \boldsymbol{P}(\boldsymbol{B})=\frac{\mathbf{3}}{\mathbf{1 0}} \) and \( \boldsymbol{P}(\boldsymbol{A} \mid \boldsymbol{B})= \)
\( \mathbf{2} \)
\( \frac{2}{3} . \) If \( \bar{A} \) and \( \bar{B} \) are the complementary
events of \( A \) and \( B \), then what is \( P(\bar{A} \mid \bar{B}) \)
equal to?
\( A \cdot \frac{3}{7} \)
B. \( \frac{3}{4} \)
\( c \cdot \frac{1}{3} \)
D. | 2 | Maths |
Find the general solution of the
differential equation:
\( (1+x)\left(1+y^{2}\right) d x+ \)
\( (1+y)\left(1+x^{2}\right) d y=0 \) | 2 | Maths |
Let \( \boldsymbol{P}(\boldsymbol{x}) \) be a polynomial, which when divided by \( (x-3) \) and \( (x-5) \) leaves
remainders 10 and \( 6, \) respectively. If the polynomial is divided by \( (x-3)(x-5) \)
then the remainder is
A \( .-2 x+16 \)
B . 16
\( c \cdot 2 x-16 \)
D. 60 | 2 | Maths |
The radius of a sphere is measured to be \( (2.1 \pm 0.5) c m . \) Calculate its surface
area with error limits. | 3 | Physics |
Passage cells are found in
A. Epidermis
B. Endodermis
C. Pericycle
D. Lenticels | 0 | Biology |
What is the nature of the graph:
\( \boldsymbol{y}=\boldsymbol{6} e^{-4 \boldsymbol{x}} \)
A. monotonically increasing
B. monotonically decreasing
c. Increasing then decreasing
D. decreasing then increasing | 2 | Maths |
State whether the given reaction is true
or false:
Heavy water is used to control nuclear
reactions.
A. True
B. False | 1 | Chemistry |
Name the law or principle to which the following observations confirm:
(1) When water is added to a \( 1.0 M \)
aqueous solution of acetic acid, the
number of hydrogen ion \( \left(\boldsymbol{H}^{+}\right) \)
increases.
(2) When 9650 coulombs of electricity is passed through a solution of copper sulphate, \( 3.175 g \) of copper is deposited on the cathode (atomic weight of \( \boldsymbol{C u}= \)
63.5)
(3) When ammonium chloride is added
to a solution of ammonium hydroxide, the concentration of hydroxyl ions
decreases. | 1 | Chemistry |
The standard quantity used for comparison is called Unit.
A. True
B. False | 3 | Physics |
A fuse wire of radius \( 0.1 \mathrm{mm} \) melts when
a current(in A) of \( 10 \mathrm{A} \) is passed through
it. Find the current at which a fuse wire
of \( 0.12 \mathrm{mm} \) will melt. | 3 | Physics |
The equilibrium constant for a reaction is \( 1 \times 10^{20} \) at \( 300 K . \) The standard
Gibbs energy change for this reaction is
A . -115 kJ
B. +115 k
\( c .+166 k J \)
D. -166 k | 1 | Chemistry |
Consider the situation shown. The wire
AB is sliding on fixed rails with a constant velocity. If the wire \( A B \) is replaced by semi-circular wire, the magnitude of induced e.m.f will
A. increase
B. decrease
c. remain the same
D. increase or decrease depending on whether the semicircle buldges towards the resistance or away from it | 3 | Physics |
The velocity of an \( e^{-} \) in excited state of
H-atom is \( 1.093 \times 10^{6} \) m/s. What is the
circumference of this orbit?
A \( \cdot 3.32 \times 10^{-10} \mathrm{m} \)
В. \( 6.64 \times 10^{-10} \mathrm{m} \)
c. \( 13.30 \times 10^{-10} \mathrm{m} \)
D. \( 13.28 \times 10^{-8} \mathrm{m} \) | 1 | Chemistry |
If \( n(P \times Q)=0 \) then \( n(P) \) can possibly
be
A .
B. 10
c. 20
D. Any value | 2 | Maths |
Red phosphorus is less reactive than yellow phosphorus because
A. its colour is red
B. it is tetratomic
c. it is hard
D. it is highly polymerized | 1 | Chemistry |
Which of the following properties of halogens increases with the increasing atomic number?
(I) lonization energy,
(II) Ionic radius,
(III) The bond energy of the \( \boldsymbol{X}_{2} \)
molecule,
(IV) Enthalpy of vaporisation.
A. IV
B. ।,॥
c. ॥।,V
D. I,II, III | 1 | Chemistry |
Consider the ten numbers
\( \boldsymbol{a r}, \boldsymbol{a r}^{2}, \boldsymbol{a r} \boldsymbol{3}, \ldots \ldots \ldots \boldsymbol{a} \boldsymbol{r}^{10} \)
If their sum is 18 and the sum of their
reciprocal is 6 then the product of these ten numbers, is
A \( \cdot 3^{5} \)
B . \( 3^{8} \)
\( c \cdot 3^{1} 0 \)
D. \( 3^{1} 5 \) | 2 | Maths |
If \( \frac{1}{\sqrt{2}}<x<1, \) then \( \cos ^{-1} x+ \)
\( \cos ^{-1}\left(\frac{x+\sqrt{1-x^{2}}}{\sqrt{2}}\right) \) is equal to
A \( \cdot 2 \cos x^{-1} \)
B. \( 2 \cos ^{-1} x \)
\( c \cdot \frac{\pi}{4} \)
\( D \) | 2 | Maths |
Calculate the image distance for an object of height 12 mm at a distance of
\( 0.20 m \) from a concave lens of focal
length \( 0.30 m, \) and state the nature and
size of the image. | 3 | Physics |
Insulators are materials having an electrical conductivity equal to:
A. Between \( 10^{-8} \mathrm{S} / \mathrm{cm} \) to \( 10^{3} \mathrm{S} / \mathrm{cm} \)
B. \( <10^{-8} \) S/cm
C. Equal to \( 10^{3} \mathrm{S} / \mathrm{cm} \)
\( \mathbf{D} \cdot>10^{3} \mathrm{S} / \mathrm{cm} \) | 3 | Physics |
Gypsum on heating gives:
This question has multiple correct options
\( ^{\mathbf{A}} \cdot \operatorname{CaSO}_{4} \cdot \frac{1}{2} H_{2} O \)
B \( \cdot C a S O_{4} \)
\( \mathbf{c} \cdot C a O \)
\( \mathbf{D} \cdot C a S+O_{2} \) | 1 | Chemistry |
Hydrogen atom in the basic medium is balanced by which of the following species?
A \( \cdot O H^{-} \)
в. \( H^{+} \)
c. \( H_{3} O^{+} \)
D. \( H_{2} \) | 1 | Chemistry |
The number of stomatal and epidermal
in 1 m area of leaves of \( A, B, C, D \)
plants are given below.
Is \begin{tabular}{lll}
Plant & Number of Stomatal & Number of epidermal cells \\
\hline \( \mathrm{A} \) & 40 & 730 \\
\( \mathrm{B} \) & 60 & 510 \\
\( \mathrm{C} \) & 70 & 450 \\
\( \mathrm{D} \) & 30 & 620
\end{tabular}
Identify the two plants having least stomatal index.
\( A \cdot A, D \)
B. A, C
\( c \cdot A, B \)
D. B, C | 0 | Biology |
In a sample of radioactive material, what percentage of the initial number of active nuclei will decay during one
mean life?
A . \( 37 \% \)
B. \( 50 \% \)
\( c \cdot 63 \% \)
D. \( 69 \% \) | 3 | Physics |
Which of the following polymers has the empirical formula identical with its
monomer?
A. Teflon
B. Nylon - 6, 6
c. Dacron
D. Bakelite | 1 | Chemistry |
All of the following are true about ion
EXCEPT:
A. lons can be formed by adding electrons to a neutral atom
B. lons can be formed by removing electrons from a neutral atom
c. lons can be formed by removing neutrons from a neutral atom.
D. lons can be positive and negative in charge | 1 | Chemistry |
The Fahrenheit and Kelvin scales of
temperature will give the same reading
at
A . -40
в. 313
c. 574.25
D. 732.75 | 3 | Physics |
If the vectors \( \vec{A}=a \hat{i}+\hat{j}-2 \hat{k} \) and \( \hat{B}= \)
\( \boldsymbol{a} \hat{\boldsymbol{i}}-\boldsymbol{a} \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \) are perpendicular to each
other then the positive value then the positive value of 'a' is
A. zero
в.
\( c \cdot-1 \)
D. 3 | 3 | Physics |
Cell is the basic unit of life'. Explain the
statement. | 0 | Biology |
Taxol is obtained from
A. Taxus
B. Acetabularia
c. cycas
D. Pinus | 0 | Biology |
Which of the following statement(s)
is/are correct for Halogens.
This question has multiple correct options
A. A halogen which is liquid at room temperature is bromine
B. The most electro-negative element is fluorine
C. The most reactive halogen is fluorine
D. The strongest oxidizing agent iodine | 1 | Chemistry |
A shelf contains 15 books, of which 4
are single volume and the others are 8
and 3 volumes respectively. In how
many ways can these books be arranged on the shelf so that order of
the volumes of same work is
maintained ?
A . \( 4 ! \)
в. \( 8 ! \)
\( c .3 ! \)
D. 4!:8:3!3! | 2 | Maths |
If \( \lambda_{v}, \lambda_{x}, \lambda_{m} \) represents the wavelengths of vision, X-ray and microwaves
respectively then
A \( \cdot \lambda_{m}>\lambda_{x}>\lambda_{v} \)
в. \( \lambda_{m}>\lambda_{v}>\lambda_{x} \)
c. \( \lambda_{v}>\lambda_{x}>\lambda_{m} \)
D \( \cdot \lambda_{v}>\lambda_{m}>\lambda_{x} \) | 3 | Physics |
If \( a, b, c \) are distinct and the roots of \( (b- \)
c) \( x^{2}+(c-a) x+(a-b)=0 \) are equal ,then
\( a, b, c \) are in
A. Arithmetic progression
B. Geometric progression
c. Harmonic progression
D. Arithmetico-Geometric progression | 2 | Maths |
Predict whether the following equation
will take place or not. \( \boldsymbol{C u}_{(s)}+\mathbf{2 H}_{(a q)}^{+} \rightarrow \boldsymbol{C u}_{a q}^{2+}+\boldsymbol{H}_{2(g)} \)
Given that \( \boldsymbol{E}_{\boldsymbol{C u}^{2+} \mid \boldsymbol{C u}}^{0}=\boldsymbol{0 . 4 4} \boldsymbol{V} ; \boldsymbol{E}_{\boldsymbol{H}^{+} \mid \boldsymbol{H}_{2}}^{0}= \)
0 | 1 | Chemistry |
The area bounded by \( y=\cos x, y= \)
\( \boldsymbol{x}+\mathbf{1}, \boldsymbol{y}=\mathbf{0} \) is
A \( \cdot \frac{3}{2} \)
B. \( \frac{2}{3} \)
\( c \cdot \frac{1}{2} \)
D. \( \frac{5}{2} \) | 2 | Maths |
Assertion
The order of the differential equation of
all conics whose centre lies at (0,0) is 3
Reason
The order of differential equation.is
same as the number of arbitrary unknowns (constants) in the given
curve.
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 diatomic molecule is made of two
masses \( m_{1} \) and \( m_{2} \) which are
separated by a distance \( r . \) If we
calculate its rotational energy by applying Bohr's rule of angular momentum,its energy will be given by
\( n \) is an integer)
A \( \cdot \frac{\left(m_{1}+m_{2}\right)^{2} n^{2} h^{2}}{2 m_{1}^{2} m_{2}^{2} r^{2}} \)
В \( \cdot \frac{n^{2} h^{2}}{2\left(m_{1}+m_{2}\right) r^{2}} \)
c. \( \frac{2 n^{2} h^{2}}{\left(m_{1}+m_{2}\right) r^{2}} \)
D. \( \frac{\left(m_{1}+m_{2}\right) n^{2} h^{2}}{2 m_{1} m_{2} r^{2}} \) | 3 | Physics |
The algae which decomposes human urine is
A. Spirullina
B. Chlorella
c. volvox
D. chlamydomonas | 0 | Biology |
\( S_{1}, S_{2} \) are foci of an ellipse of major axis
of length 10 units and \( P \) is any point on the ellipse such that perimeter of
triangle \( P S_{1} S_{2} \) is \( 15 . \) Then eccentricity
of the ellipse is:
A . 0.5
B. 0.25
c. 0.28
D. 0.75 | 2 | Maths |
If we divide the unknown two-digit number by the number consisting of the same digits written in the reverse order,
we get 4 as a quotient and 3 as a remainder. Now if we divide the
required number by the sum of its
digits, we get 8 as a quotient and 7 as a remainder. Find the number. | 2 | Maths |
\( \operatorname{any} \Delta A B C, \Pi\left(\frac{\sin ^{2} A+\sin A+1}{\sin A}\right) \)
is always greater than This question has multiple correct options
\( A \cdot 9 \)
B. 3
c. 27
D. 81 | 2 | Maths |
The line spectra of two elements are
different because:
A. the elements do not have the same number of
neutrons
B. they have different mass numbers
C. their outermost electrons are at different energy levels
D. all of the above | 1 | Chemistry |
Which of the following will form hydrogen bond between the molecules
of the substances?
A \( \cdot C H_{4} \)
в. \( H B r \)
c. \( H C l \)
D. \( H_{2} O \)
E. \( H_{2} \) | 1 | Chemistry |
ff \( (x)=x+\sin x ; g(x)=e^{-x} ; u= \)
\( \sqrt{\boldsymbol{c}+\mathbf{1}}-\sqrt{\boldsymbol{c}} ; \boldsymbol{v}=\sqrt{\boldsymbol{c}}-\sqrt{\boldsymbol{c}-\mathbf{1}} ;(\boldsymbol{c}>\mathbf{1}) \)
A \( . f o g(u) \geq f o g(v) \)
B. \( f o g(u) \leq f o g(v) \)
\( \mathbf{c} . f o g(u)>f o g(v) \)
D. \( f o g(u)<f o g(v) \) | 2 | Maths |
A heat engine takes in \( 700 J \) of heat
from high-temperaturere reservoir and rejects \( 500 J \) of heat to a lower
temperature reservoir. How much work does the engine do in each cycle?
\( \mathbf{A} \cdot 100 J \)
в. 20 \( J \)
c. \( 200 J \)
D. \( 10 J \) | 3 | Physics |
At resonance, the angle \( \phi \) is
A.
B. \( \frac{\pi}{2} \)
c. \( \frac{\pi}{6} \)
D. zero | 3 | Physics |
The vertical component of the earth's magnetic field is:
A. zero at the magnetic pole
B. Zero at the geographic pole
c. Same everywhere
D. zero at the magnetic equator | 3 | Physics |
Draw parallelogram ABCD with the following data:
\( A B=6 \mathrm{cm}, A D=5 \mathrm{cm} \) and \( \angle D A B= \)
\( 45^{\circ} \)
Let \( A C \) and \( D B \) meet in 0 and let \( E \) be the
mid-point of Bc. Join OE. then,
OE II AB. ( Enter 1 if true or 0 otherwise) | 2 | Maths |
Which of the following is useful in explaining the polarity of water?
I. The solution process.
II. The ionization process.
III. The high conductivity of distilled
water
A. I only
B. II only
c. I and II only
D. Il and III only
E. I, II and III | 1 | Chemistry |
Evaluate: \( \int \frac{x^{4}+1}{1+x^{6}} d x \)
A \( \cdot \tan ^{-1}(x)-\tan ^{-1}\left(x^{3}\right)+c \)
B \cdot \( \tan ^{-1}(x)-\frac{1}{3} \tan ^{-1}\left(x^{3}\right)+c \)
c. \( \tan ^{-1}(x)+\tan ^{-1}\left(x^{3}\right)+c \)
D. \( \tan ^{-1}(x)+\frac{1}{3} \tan ^{-1}\left(x^{3}\right)+c \) | 2 | Maths |
If the points \( \boldsymbol{A}(1,2), B(2,3) C(a, 2) \) and \( D(4,3) \) form a parallelogram, find the
value of \( a \) and height of the
parallelogram taking \( A B \) as base.
A. \( a=1, h=2 \)
В. \( a=1, h=1 \)
c. \( a=3, h=1 \)
D. \( a=2, h=3 \) | 2 | Maths |
The position vector of a particle at time \( t^{\prime} \) is given by \( \vec{r}=t^{2} \hat{t}+t^{3} \hat{j} \). The velocity
makes an angle \( \theta \) with positive \( x \) -axis. Find the of \( \frac{\boldsymbol{d} \boldsymbol{\theta}}{\boldsymbol{d} \boldsymbol{t}} \) at \( \boldsymbol{t}=\frac{\sqrt{\mathbf{2}}}{\mathbf{3}} \) | 2 | Maths |
The expression for the determination of Poisson's ratio for rubber is
A \( \cdot \sigma=\frac{1}{2}\left[1-\frac{d V}{A d L}\right] \)
в. \( \sigma=\frac{1}{2}\left[1+\frac{d V}{A d L}\right] \)
c. \( _{\sigma}=\frac{1}{2} \frac{d V}{A d L} \)
D. \( \sigma=\frac{d V}{A d L} \) | 3 | Physics |
Two simple Harmonic Motions of
angular frequency 100 and 1000 rad \( S^{-1} \)
have the same displacement amplitude. The ratio of their maximum accelerations is :
A \( \cdot 1: 10^{3} \)
B \( \cdot 1: 10^{4} \)
c. 1: 10
D. \( 1: 10^{2} \) | 3 | Physics |
\( \frac{a^{n}+b^{n}}{a^{n-1}+b^{n-1}} \) is the AM between \( a \) and \( b \)
if \( n \) is
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( \frac{1}{2} \)
\( c \cdot 1 \)
D. - | 2 | Maths |
Which of the following conditions cannot be corrected by using a correcting lens? This question has multiple correct options
A. astigmatism
B. night blindness
c. cataract
D. colourblindness | 3 | Physics |
Find the area of the segment AYB shown
in figure, if radius of the circle is \( 21 \mathrm{cm} \) and \( <A O B=120^{\circ} .\left(U s e \pi=\frac{22}{7}\right) \) | 2 | Maths |
Which of the following represents the
correct IUPAC name for the
compounds concerned?
a) But-3-yn-1-ol
b) But-4-ol-1-yne | 1 | Chemistry |
Find the complementary of the angle
\( \mathbf{3 0}^{\circ} \) | 2 | Maths |
Let \( k \) be a positive real number and let \( \boldsymbol{A}=\left[\begin{array}{ccc}2 \boldsymbol{k}-\mathbf{1} & \boldsymbol{2} \sqrt{\boldsymbol{k}} & \boldsymbol{2} \sqrt{\boldsymbol{k}} \\ \boldsymbol{2} \sqrt{\boldsymbol{k}} & \boldsymbol{1} & -\boldsymbol{2} \boldsymbol{k} \\ -\boldsymbol{2} \sqrt{\boldsymbol{k}} & \boldsymbol{2} \boldsymbol{k} & -\boldsymbol{1}\end{array}\right] \) and \( \boldsymbol{B}= \)
\( \left[\begin{array}{ccc}0 & 2 k-1 & \sqrt{k} \\ 1-2 k & 0 & 2 \sqrt{k} \\ -\sqrt{k} & -2 \sqrt{k} & 0\end{array}\right] \)
f \( \operatorname{det}(a d j A)+\operatorname{det}(a d j B)= \)
\( \mathbf{1 0}^{\mathbf{6}}, \) then \( [\boldsymbol{k}] \) is equal to
[Note: adj M denotes the adjoint of a square matrix M and [k] denotes the largest integer less than or equal to \( \mathrm{k} \) ].
\( A \)
в.
\( c . \)
\( D \) | 2 | Maths |
A force of \( 16 \mathrm{N} \) is applied on a block of
mass \( 4 \mathrm{kg} \) with \( \mu=0.6 \) Then the force
of friction acting on the block is \( 4 K \) newton Find the value of \( K \)
\[
\mu=.6-\sqrt{4 k g} \mid \rightarrow F=16 \mathrm{N}
\]
\( A \cdot 4 \)
B. 3
\( c \cdot 6 \)
\( D \) | 3 | Physics |
Which are good conductors?
This question has multiple correct options
A. silicon
B. Silver
c. copper
D. glass | 3 | Physics |
Relation \( R \) in the set \( A \) of human beings
in a town at a particular time given by
\[
\boldsymbol{R}=\{(\boldsymbol{x}, \boldsymbol{y}): \boldsymbol{x} \text { is } \boldsymbol{w} \boldsymbol{i} f e \boldsymbol{o} \boldsymbol{f} \boldsymbol{y}\}
\]
enter 1 -reflexive and transitive but not
symmetric 2-reflexive only 3-Transitive only 4-Equivalence 5-Neither reflexive, nor symmetric, nor transitive | 2 | Maths |
The order in which the following oxides are arranged to decreasing basic nature is \( A l_{2} O_{3}<M g O<C u O<N a_{2} O \)
A. True
B. False | 1 | Chemistry |
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