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If a, b, c are in H.P., then straight line x/a + y/b + 1/c = 0 always passes thro' a fixed point and that point is
The correct option is C.
Since.a, band c are in HP. Then 1/a, 1/b and 1/c are in AP. 2/b = 1/a + 1/c ⇒ 1/a  2/b + 1/c = 0 Hence, straight line x/a + y/b + 1/c = 0 always passes through a fixed point (1, 2).
The angle between the line (x  2)/2 = (y + 1)/1 = (z  3)/2 and the plane 3x + 6y  2z + 5 = 0 is
D is the correct option.sin⁻1(4/21)
If a,b,c are any three vectors, the statement is true
D is the correct option.a.(bc)=a.ba.c is correct if a,b,c are any three vectors.
The equilibrium constant in a reversible chemical reaction at a given temperature
The correct option is C.
The equilibrium constant in a reversible reaction at a given temperature. Solution : Equilibrium constant is independent of original concentration of reactant.
C is the correct option.The structure of white phosphorus is tetrahedral.
White phosphorus, yellow phosphorus or simply tetraphosphorus (P4) exists as molecules made up of four atoms in a tetrahedral structure. The tetrahedral arrangement results in ring strain and instability. The molecule is described as consisting of six single P–P bonds.
The correct is C.
Isopropyl chloride undergoes hydrolysis via both SN1 and SN2 mechanisms. Both of them yield the same result/ products. Since, isopropyl chloride is a secondary alkyl halide.
An organic compound A reacts with methyl magnesium iodide to form an addition product which on hydrolysis forms the compound B. Compound B gives blue colour salt in Victor Meyer's test. The compounds A and B are respectively.
The correct option is C.
The area formed by triangular shaped region bounded by the curves y = sinx, y = cos x and x = 0 is
The coordinates of the pole of the line lx+my+n=0 with respect to the circle x^{2}+y^{2}=1 are
The complex numbers z₁,z₂,z₃ satisfying (z₁z₃)/(z₂z₃) = 1(i√3/2) then triangle is
(z_{1}z_{2})/(z_{2}z_{3})= cos(60)+sin(60)=ei60
taking mode on both sides
Absolute value of(z_{1}z_{2}/z_{2}z_{3})=1
Therefore z_{1}z_{2}=z_{2}z_{3}
Also angle between z_{1}z_{2} & z_{2}z_{3} is 60
So given triangle is equilateral triangle.
i^{2} + i^{4} + i^{6} + ... + upto (2n + 1) =
Integrating factor of dy/dx+y/x = x^{3}3 is
The foci of an ellipse are and minor axis is of unit length. Then the equation of the ellipse is
Given y = cot^{1 }(1+x)/(1x)
Put x = tan θ
θ = tan^{1 x}
Then y = cot^{1} (1 + tan θ)/(1 tan θ)
y = cot^{1} (tan π/4 + tan θ)/(1 tan π/4 tan θ)
= cot^{1} tan (π/4 +θ)
= cot^{1} cot (π/2 – (π/4 +θ))
= π/4 – θ
= π/4 – tan^{1} x
dy/dx = 1/(1+x^{2})
Which statement is logically equivalent to "If Yoda cannot use a lightsaber, then he cannot help Luke win the battle."
A statement is logically equivalent to its contrapositive.
To form the contrapositive, switch the "If" and "then" sections
of the statement AND insert "NOTs" into each section.
Notice in this situation, that inserting
"NOTs" turns the thoughts positive (you are negating negative thoughts).
In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer
Assertion(A): If
Reason(R) : When
In the following questions, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the statements carefully and mark the correct answer 
Assertion (A): The sum of the series
Reason (R): The numbers A_{1}, A_{2}, ....., A_{n} are said to be the n arithmetic means between two given numbers a and b if a, A_{1}, A_{2}, ...., A_{n}, b are in A.P.
In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer
Assertion(A):
Reason (R): If
The correct option is Option C.
When f(x) = g(x)
Then the range includes 1.
But it is already given that 1 is excluded.
Hence, the assertion is correct but the reason behind it is false.
If A and B are two matrices such that A + B and AB are both defined, then
Since A+B is defined, A and B are matrices of the same type,
say m×n; Also, AB is defined.
So, the number of columns in A must be equal to the number of rowsin B ie. n=m.
Hence, A and B are square matrices of the same order.
In the following question, a Statement1 is given followed by a corresponding Statement2 just below it. Read the statements carefully and mark the correct answer
Let the vectors represent the sides of a regular hexagon.
Statement1:
.
Statement2:
Let
Then the global minimum value of the function is
f ′ (x) = 4 So, for 0 ≤ x < 1, we get f ′ x < 0, i . e . , f x is m.d. and for 1 < x ≤ 2 we get f ′ (x) > 0, i . e . , f (x) is m.i .
∴ min f (x) =
The parabola y^{2}=4x passes thro' the point (2,6), then the length of its latus rectum is
It is given that the parabola passes through the point (2,6)
Length of its latus rectum is 4a
y^{2 }= 4ax
i.e.
(6)^{2 }= 4a(2)
⇒a = 9/2
∴ Length of the latus rectum is 4 x 9/2 = 18
We know that ,
1) ^{n}P_{r}. = n!/( n  r )!
2) ^{n}C_{r} = n!/ [ ( n  r )! r ! ]
3) r! = ( ^{n}P_{r} )/ ^{n}C_{r }
It is given that ,
nPr = 840 ( 1 )
nCr = 35 ( 2 )
r! = ( nPr )/ ( nCr )
= 840/35
= 24
r! = 4 × 3 × 2 × 1
r ! = 4!
Therefore,
r = 4
Substitute r value in equation ( 1 ),
We get
n!/ ( n  4 ) ! = 840
n( n  1 )( n  2 )( n  3 ) = 840
n( n  1 )( n  2 )( n  3 ) = 7× 6 × 5 × 4
Therefore ,
n = 7
In a Binomial distribution, the probability of getting a success is 1/4 and standard deviation is 3. Then its mean is
Let n be successive independent trials and p the probability of getting a success.
The the mean and variance of a binomial distribution is given by :
Mean = np
Variance = np(1  p)
In this case we have :
p = 1/4
Variance = (standard deviation) ²
Variance = 3² = 9
From this we can get the value of n as follows :
Variance = np(1  p)
Doing the substitution we have
9 = 1/4n( 1  1/4)
9 = 1/4n(3/4)
9 = 3/16n
n = 16/3 × 9
n = 48
Mean = np
Mean = 48 × 1/4 = 12
The mean of the binomial distribution is equal to 12.
If 4 sin⁻^{1}x + cos⁻^{1}x = π, then x is equal to
The probability distribution of a random variable X is given below. Then its mean is
X = x_{i } 1 2 3
If AB=π/4, then (1+tan A)(1tanB) is equal to
AB=π/4
Which implies A=B+π/4
Taking tan on both sides
tanA=tan(B+π/4)
tanA=(tanB + tan(π\4))/(1 tanB.tan(π/4))
tanA=(tanB+1)/(1tanB)
Substituting the value of tanA in
(1+tanA).(1tanB) we get
(1+(tanB+1)/(1tanB)).(1tanB)
= (1tanB+tanB+1)/(1tanB).(1tanB)
=2
Addition of a solution of oxalate to an aqueous solution of mixture of Ba^{2}⁺, Sr^{2}⁺ and Ca^{2}⁺ will precipitate
What is the lowest energy of the spectral line emitted by the hydrogen atom in the Lyman series ? (h = Planck constant; c = Velocity of light; R = Rydberg constant).
The nodal plane in the πbond of ethene is located in
Formation of a π  bond occurs by the sideways overlap of porbitals of two Catoms.The molecular plane does not have any π  electron density since the porbitals are perpendicular to the plane containing the ethene molecule.The nodal plane in the πbond of ethene is located in the molecular plane.
The compound with carbon uses only its sp^{3} hybrid orbitals for bond formation is
The hydrolysis of fats and oils in the body produces
Fats and oils
1. Fats and oils are a concentrated source of energy.
2. Fats and oils are essential for the transport and storage of fatsoluble vitamins in the body.
3. Fats and oils are tri esters formed from the condensation of glycerol (propane1,2,3triol) and three carboxylic acid molecules.
4. The hydrolysis products of a fat or oil can be identified from the structure of the fat or oil.
Identify the least stable among the following?
Outer electronic configuration of Li^1 (2s^{2} most stable)
Be ^{–} ( 2s^{2} 2p^{1} less stable) than Be (2s^{2} most stable)
B ^{–} (2s^{2} 2p^{2 }stable) ; C ^{–} (2s^{2} 2p^{3} most stable)
As Be ^{–} is formed from highly stable configuration it tries to loose electron and form Be.
The common features among the species CN⁻, CO and NO⁺ are
According to Molecular Orbital theory,
CN^{−},CO and NO^{+} are isoelectronic (14e^{−}) and bond order is 3.
Heat exchanged in a chemical reaction, at constant temperature and pressure, is called
Define all the terms to find the correct answer:
(a) Entropy : It is the measurement of randomness or disorder of system.
(b) Enthalpy : It is the total heat content of system or it is the heat which is exchanged in a chemical reaction at constant temperature andpressure.
(c) Free energy : It is the energy of system which can be converted into useful work.
(d) Internal energy : It is the energy stored within a substance.
For a reaction 2N₂O₅ → 4NO₂ + O₂ rate and rate constant are 1.02 x 10^{4} mol L⁻^{1} s⁻^{1} and 3.4 x 10^{5} sec⁻1. The conc. of N₂O₅ at that time will be
A Carnot engine, working between 500 K to 300 K has a work output of 800 Jcycle⁻^{1}. What is the amount of heat energy supplied to the engine from the source per cycle?
An ideal gas heat engine operates in Carnot cycle between 227ºC and 127ºC. It absorbs 6 x 10^{4} cals of heat at higher temp. Amount of heat converted into work is
The densities of graphite and diamond at 298 K are 2.25 and 3.31 gcm^{3} respectively. If the standard free energy difference (ΔGº)is equal to 1895 Jmol^{1}, then pressure at which graphite will be transformed into diamond at 298 K is
Increasing order of stability among the three main conformations(i.e.,Eclipse,Anti,Gauche) of 2fluorethanol is
The anticonformation is most stable in which F and OH groups are far apart as possible and minimum repulsion between two groups occurs.
In fully eclipsed conformation F and OH groups are so close that the steric strain is maximum .
Hence this conformation is most unstable.
The order of stability of these conformations is anti > gauche > partially eclipsed > fully eclipsed.
Hence a is the correct answer.
Gallium and Germanium were unknown at the time when Mendeleev's periodic table was formulated. But Mendeleev's predicted the properties of these elements and named them ekaaluminium and ekasilicon. Later when these elements were discovered, their properties were found to be similar to those of aluminium and silicon.
The first ionisation potential of Li will be
As we move from left to right in a period, the ionisation potential increases with increasing atomic number and the ionisation potential keeps on decreasing regularly as we move down a group. Thus the first ionisation potential of Li is less than Be and higher than Na.
The CFSE (Crystal Field Stabilisation Energy) for a high spin octahedral complex having d^{1} configuration is __
CFSE = [− 0.4p + 0.6q]Δ_{0}
= [− 4p + 6q]Dq
p = electrons in e_{g} orbitals
q = electrons in t_{2g} orbitals
For d_{1} (high spin) configuration
CFSE = [ 0.4 x + 0.6 x 0]Δ_{0}
=[−0.40 + 0]Δ_{0} = − 0.4 Δ
= 4Dq.
(Configuration of d^{1} in high spin or low spin is same).
An aqueous solution of CoCl₂ on addition of excess of concentrated HCl, turns blue due to the formation of
CoCl_{2} is a weak Lewis acid, reacting with chloride ion to produce salt containing the tetrahedral [CoCl_{4}]^{2} ion. CoCl_{2} is blue when anhydrous, and a deep magneta colour when hydrated, for this reason it is widely used as an indicator for water.
Oxidation state of N in HNO3 is +5
OS of H= +1, & O = 2
H = +1
O x 3 = 2 x 3
= 6
net charge on molecule = 0
So +1 6 +N = 0
=> N = 0+61
= +5
At cathode ,the electrolysis of aqueous Na₂SO₄ gives
Density ratio of O₂ and H₂ molecules is 16:1.The ratio of their r.m.s. velocities will be
The property of hydrogen which distinguishes it from other alkali metals is
Hydrogen is a nonmetal while all other members of group 1 (alkali metals) are metals.
Low reactivity of vinyl chloride and chlorobenzene is due to :
A pyridine derivative (I) reacts with (II), (II) can be a free radical, cation or anion. The structure of the intermediate (III) formed in the reaction is given below, (I) and (II) can be respectively:
if bromine water is added to a solution of phenol in water.
the bromine water is decolourised and a white precipitate is formed which smells of antiseptic .
The precipitate is 2,4,6 tribromophenol
Notice the multiple substitution around the ring  into all the activated positions.
Conformations are different arrangements of atoms that can be converted into one another by rotation about ___________
Conformational isomerism is a form of stereoisomerism in which the isomers can be interconverted exclusively by rotations about formally single bonds. Such isomers are generally referred to as conformational isomers or conformers and, specifically, as rotamers.
When two deuterium nuclei fuse together in addition to tritium, we get a
If a H₂ nucleus is completely converted into energy, the energy produced will be around
Mass of H2 nucleus =mass of proton =1 amu energy equivalent to 1 amu is 931 MeV so correct option is (b).
A uniform resistance wire of length L and diameter d has a resistance R. Another wire of same material has length 4 L and diameter 2 d, the resistance will be
Nichrome or Manganin is widely used in wire bound standard resistors because of their
If particles are moving with same velocity, then maximum deBroglie's wavelength will be for
de Broglie wavelength for a particle is given by λ = h/p = h/mv, where m, v and p are the mass, velocity and momentum respectively. it is Planck's constant. Now, since all the particles are moving with same velocity, the particle with least mass will have maximum deBroglie wavelength. Out of the given four particles (proton, α particles, i.e. He nucleus and βparticles. i.e. electrons) βparticles has the lowest mass and therefore it has maximum wavelength.
When ultraviolet rays are incident on metal plate, then photoelectric effect does not occurs. It occurs by the incidence of
For photoemission to take place from metal the wavelength of incident ray will be less than threshold value. For photoelectric emission from given metal plate, the incident wavelength must be less than that of ultraviolet rays assuming the wavelength of ultraviolet rays as the threshold value. Out of the given radiations, Xrays have wavelength less than that of ultraviolet rays. Thus, Xrays can cause photoelectric emission.
Which rays are not the portion of electro magnetic spectrum?
Two point charges +q and q are held fixed at (d,0) and (d,0) respectively of a xy coordinate system. Then
When you draw the electric field lines for these 2 charges they will starts from the positive charge and end at the negative charge. And when they pass through the Y axis they will be perpendicular to the Y axis, since both the charges are at equal distance and equal in magnitude. The direction of electric field is found by the tangents to the electric field at that point, since the line is parallel to x axis it's slope will also be zero, So the direction of the electric field line will be along the x axis.
If 1000 droplets each of charge q and radius r are mixed to form a big drop, then the potential of big drop, as compared to small droplet will be
If the value of potential on each small drop be V and potential on each small drop be V ^{'}
A satellite with kinetic energy E is revolving around the earth in a circular orbit. The minimum additional kinetic energy required to escape it in the outer space is
As we go from the equator to the poles, the value of g
Since the Earth is flattened at the poles and bulges at the equator, an oblate spheroid the distance from Earth's center to sea level is roughly 21 kilometers (13 miles) greater at the equator than at the poles. Since the value of g varies inversely with the square of the earth's radius, the shorter radius at the pole will result in a greater value of g.
The second reason is that at latitudes nearer the Equator, the outward centrifugal force produced by Earth's rotation is larger than at polar latitudes. This counteracts the Earth's gravity to a small degree – up to a maximum of 0.3% at the Equator – and reduces the value of g at the equator.
So as we move from equator to pole value of g will increase. Hence option C is the correct.
On a cold morning, a metal surface will feel colder to touch than a wooden surface because
Due to higher thermal conductivity of metal than wood, heat begins to flow readily from our body to the metal surface and so we feel colder.
A black body at a temperature of 1640 K has the wavelength corresponding to maximum emission equal to 1.75μ. Assuming the moon to be a perfectly black body, the temperature of the moon, if the wavelength corresponding to maximum emission is 14.35 μ is
A man weighs 80 kg. He stands on a weighing scale in a lift, which is moving upwards with a uniform acceleration of 5 m−s⁻^{2}. What would be the reading on the scale?(Take g = 10 m−s⁻^{2})
The reading on scale would be
w= M (g+a)
w=80 ( 10+ 5)
w=1200
If a car covers 2/5th of the total distance with ν₁ speed and 3/5th distance with ν₂ then average speed is
A current passing through a circular coil of two produces a magnetic field of 8 T at its centre. The coil is then rewound, so as to have four turns and current is passed through it is doubled. Now magnetic field at the centre of the coil will be
A simple pendulum oscillates in a vertical plane. When it passes through the mean position, the tension in the string is 3 times the weight of the pendulum bob. what is the maximum angular displacement of the pendulum of the string with respect to the vertical ?
Tension at mean position,
mg+
(i) and if the body displaces by angle q with the vertical then v =
(ii) Comparing (i) and (ii),
cosθ = 0 Þ θ = 90º
In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer
Assertion(A):A falling ball is attracted by the earth, because of which velocity of the ball goes on increasing in the downward direction. The ball also attracts the earth with same force but velocity developed in earth is negligible.
Reason(R):Momentum of ball and earth system is conserved.
Since the mass of the earth is infinitely large compared to that of the ball, hence velocity developed in the earth is negligible
In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer
Assertion(A): A thin hollow cylindrical shell of radius 0.5 m has a mass of 2 kg. Its moment of inertia about its own axis is 0.5 kgm^{2}.
Reason(R) : Moment of inertia of a cylindrical shell about its axis I = MR^{2}.
In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer
Assertion(A):Air is thrown on a sail attached to a boat from an electric fan placed on the boat, because of which some movement is caused in the boat.
Reason(R):When the fan pushes the sail by the air, then air also pushes the fan in the opposite direction, causing motion.
A force 10^{3} newton stretches the length of a hanging wire by 1 millimetre. The force required to stretch a wire of same material and length but having four times the diameter by 1 millimeter is
(Y,l and L are constant) If diameter is made four times then force required will be 16 times. i.e. 16 x 10^{3} N
A cylindrical vessel is filled with water up to height H. A hole is bored in the wall at a depth h from the free surface of water. For maximum range, h is equal to
The eyepiece used in biological microscope is
A ball rolls without slipping. The radius of gyration of the ball about an axis passing through its centre of mass is K. If radius of the ball be R, then the fraction of total energy associated with its rotational energy will be
We consider a thermodynamic system. If ∆U represents the increase in its internal energy and W the work done by the system, which of the following statements is true
Explanation: In an adiabatic process,
∆Q=0
∆U=∆Q∆W=0W=W.
A body of mass 5 g is executing S.H.M. with amplitude 10 cm. Its maximum velocity is 100 cm/s. Its velocity will be 50 cm/s at a displacement from the mean position equal to
When a ray of light falls on sea shell, then its small amount first gets refracted (slightly polarised) and then almost gets reflected back (fully polarised). That is why, view of sea shell is golden due to polarisation.
The maximum speed of a body vibrating under simple harmonic motion with a time period of π/4 sec and amplitude of 7 cm is
Calcorimeters are made of which of the following
Calorimeters are made up of metal only because they are good conductor of heat and hence the heat exchange is quick which the basic requirement for the working of calorimeter.
The position of a particle at time 't' is given by the equation Where V_{0} is constant and A > 0. Dimensions of V_{0} and A respectively are
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