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The instantaneous rate of change at t = 1 for the function f(t) = te-1 + 9 is
2x - y - 2z = 2, x - 2y + z = -4, x + y + λz = 4 then the value of λ such that system of equations has no solutions is
The complex numbers z₁, z₂ and z₃ satisfying (z₁-z₃)/(z₂-z₃) = (1 - i√3)/2 are the vertices of a triangle which is
Given that the function f defined by is continuous . Then the value of k is
If f(x) = sin π [ x ] then f ′(1 − 0) is equal to
The degree of the differential equation d2y/dx2+(dy/dx)3+6y=0 is
The differential equation representing the family of curves y2 = 2c(x + √c), where c>0, is a parameter, is of order and degree as follows
The solution of differential equation (dy/dx)=x2+sin3x is
The differential of sin-1[(1-x)/(1+x)] w.r.t. √x is equal to
When y = 3, which of the following is FALSE?
Remember what is TRUE: 3 is prime, odd and 2(3) is even.
Choice 1: T and T is TRUE
Choice 2: T or F is TRUE
Choice 3: F and T is FALSE
Choice 4: T and T is TRUE
If 3X+2Y=I and 2X-Y=0, where I and 0 are unit and null matrices of order 3, then
How many even numbers can be formed by using all the digits 2, 3, 4, 5, 6?
What is the chance that a leap year should have 53 sundays?
If P(B)=(3/4), P(A∩B∩C̅) = (1/3) and P(A̅∩B∩C̅) = 1/3, then P(B∩C) is
The probabilities of solving a problem by three student A,B,C are 1/2, 1/3, 1/4 respectively. The probability that problem will be solved is
We have, probability that A can solve the problem = P(A) = 1/2 ,
And in this way P(B) = 1/3 and P(C) = 1/4.
P(A cannot solve the problem) = 1 – P(A) = 1/2 ,
P(B cannot solve the problem) = 1 – P(B) = 1 – 1/3 = 2/3,
P(C cannot solve the problem) = 1 – P(C) = 1 – 1/4 = 3/4.
P(A, B, and C cannot solve the problem) = 1/2 x 2/3 x 3/4 = 1/4.
Therefore , P(Problem will be solve) = 1 – P(Problem is not solved by any of them)
= 1 – 1/4 = 3/4
If x is a positive real number different from 1, then the number 1/1 + √x, 1/1 - x , 1/1 - √x, .... are in
The value of covariance of two variables x and y is -(148/3) and the variance of x is (272/3) and the variance of y is (131/3). Then the coefficient of correlation is
The roots of the equation x3 + x2 + x + 1 = 0 are___
The given equation is
x3 + x2 + x + 1 = 0
or , (x2 + 1)( x + 1) = 0
or , x = i , x = − 1
In ∆ABC angle A is defined by 5 cos A + 3 = 0, the equation whose roots are sinA and tanA, is
The points (5,2,4),(6,-1,2) and (8,-7,k) are collinear if k is equal to
The equation of the sphere concentric with the sphere x2+y2+z2-4x-6y-8z=0 and which passes thro' (0.1,0) is
In any right angled triangle hypotenuse is equal to 2√2 times the perpendicular drawn from the opposite vertex on it, then other angles are
The line passing through (0, 1) and perpendicular to the line x - 2y + 11 = 0 is
If a is any vector then |a x i| 2 +|a x j|2 +|a x k|2 =
Two ions of the same charge and energy but different mass are passing through a uniform magnetic field. The radii of their paths are proportional to
The diagram shows the energy levels for an electron in a certain atom. Which transition shown represents the emission of a photon with the most energy?
The emission lines are II, III and IV. The line having maximum energy is III, because energy difference between successive levels decreases rapidly with increase of n
A capacitor is charged to store an energy U. The charging battery is disconnected. An identical capacitor is now connected to the first capacitor in parallel. The energy in each of the capacitor is
If a cell of constant electromotive force produces the same amount of heat during the same time in two independent resistances R₁ and R₂, when connected separately one after the other, across the cell, then the internal resistance of the cell is
A wire has a resistance of 6 Ω. If it is cut into two parts and connected in parallel, then the new resistance will be
In a circuit 5 percent of total current passes through a galvanometer. If resistance of the galvanometer is G then value of the shunt is
The temperature coefficient of resistance of a wire is 0.001250K-1 . Its resistance is 1 Ω at 300 K. Its resistance will be 2 Ω at
A dry cell has an e.m.f. of 1.5 V and an internal resistance of 0.05 Ω. The maximum current obtainable from this cell, for a very short interval is
When a proton is accelerated through 1 V, then its kinetic energy will be
Two inductors of inductance L each are connected in series with opposite magnetic fluxes. What is the resultant inductance ?
In an ideal transformer, the voltage and the current in the primary are 200 V, 2A and that in the secondary are 2000 V, 1A. The value of is (in A).
A charged particle q is placed at the centre O of a cube of length L. Another same charge q is placed at a distance L from O. Then electric flux through the cube is
Two charges -10 C and + 10 C are placed 10cm apart. Potential at the centre of the line joining two charges is
n small drops of same size are charged to V volt each. They coalesce to form a bigger drop. The potential of the bigger drop is
When a dielectric material is kept in between the plates of a condenser, its capacity
The distance between the plates of a condenser is reduced to 1/4 th and the space between the plates is filled up by a medium of dielectric constant (K) 2.8. The capacity is increases by
Two infinitely long parallel conducting plates having surface charge densities +σ and -σ respectively, are separated by a small distance. The medium between the plates is vacuum. If ε₀ is the dielectric permittvity of vacuum, then electric field in the region between the plates is
An electron revolves in a circle of radius 0.4 Å with a speed of 106 m s-1 in a hydrogen atom. The magnetic field produced at the centre of the orbit due to the motion of the electron in tesla is [ μ0 = 4 π x 10-7 H m-1 ; change on the electron = 1.6 x 10-19 C ]
If in a nuclear reactor using U235 as fuel, the power output is 4.8 mega watts, the number of fissions per second is:
(energy released per fission of U235 = 200 MeV; 1eV = 1.6 x 10-19 J)
A nucleus with Z = 92 emits the following in sequence: α , α , β − , β − , α , α , α , α ; β − , β − , α , β + , β + , α . The Z of the resulting nucleus is
Which of the following is not dependent on the intensity of incident radiation in a photoelectric experiment ?
A convex lens made of glass has focal length 0.15m in air. If the refractive index of glass is 3/2 and that of water is 4/3, the focal length of lens when immersed in water is
The maximum energy of photo-electrons emitted in a photo cell is 2eV. For no photo-electrons to reach the anode, the stopping potential should be
The distance travelled by light in glass (refractive index =1.5) in a nanosecond will be
Speed of light in glass
Distance travelled in one nanosecond
= 2 x 108 x 10-9 = 0.2 m = 20 cm
An n - type and p - silicon can be obtained by doping pure silicon with:
For obtaining ‘n’ type semi conductor V group element is doped with silicon.
For obtaining ‘p’ type semiconductor III group element is doped with silicon.
The region with free electrons and holes in a p-n junction diode is
If a full wave rectifier circuit is operating from 50 Hz mains, then fundamental frequency in the ripple will be
In a common base amplifier circuit, calculate the change in base current if that in the emitter current is 2 mA and α = 0.98
A semi-conducting device is connected in a series circuit with a battery and a resistance. A current is found to pass through the circuit. If the polarity of the battery is reversed, the current drops to almost zero the device may be
Laser light is considered to be coherent as it consists of
Two identical light waves, propagating in the same direction, have a phase difference δ . After they superpose the intensity of the resulting wave will be proportional to
Inverse square law of intensity (illuminance) is valid for
Light was producing interference have their amplitudes in the ratio 3:2. The intensity ratio of maximum and minimum of interference fringes is
When 3,3-Dimethyl-2-butanol is heated with H₂SO₄, the major product obtained is
In which of the following reactions, aldehydes and ketones are distinguished?
Aldehydes and ketones do not give addition reaction with
The product formed by the action of chlorine on ethene in saturated solution of KBr is/are
Molarity of liquid HCl with density equal to 1.17 g/cc is
In which of the following, the number of carbon atoms does not remain same when carboxylic acid is obtained by oxidation
A vessel at equilibrium, contains SO₃, SO₂ and O₂. Now some helium gas is added, so that total pressure increases while temperature and volume remain constant. According to Le-Chatelier's principle, the dissociation of SO₃
A reaction reaches a state of chemical equilibrium only when
In monatomic gases, ratio of specific heat at constant pressure to that at constant volume is
Which of the following gas molecule has the maximum specific heat at constant pressure?
The IUPAC name of the following compound
CH₃-C(CH₃)₂-CH = C(CH₃)₂ is
Which of the following is true for an isochoric processes
In the brown ring 'test', the brown colour of the ring is due to
Which of the following is produced by reaction of RCN in sodium and alcohol ?
To protect iron against corrosion, the most durable metal plating on it is
In the diazotisation of aniline with sodium nitrite and hydrochloric acid, the excess of hydrochloric acid is used primarily to
Which of the following metal is not attacked by the environment?
What is the time (in sec) required for depositing all the silver present in 125ml of 1M AgNO3 solution by passing a current of 241.25 amperes? (1F = 96500 coulombs)
The ether that undergoes electrophilic substitution reactions is
A sample of gas occupise 100 ml at 270C and 740 mm pressure. When its volume is changed to 80 ml at 740 mm pressure, the temperature of the gas will be
An oxide of lead which is used in lead storage batteries, in safety matches and is a powerful oxidising agent is
The number of P - O bonds and the lone pairs of eletrons present in P4O6 molecule, respectively
When KMnO₄ acts as an oxidising agent and ultimately forms MnO₄2- , MnO₂, Mn₂O₃ and Mn2+, then the number of electrons transferred in each case is
Which one of the following elements shows maximum number of different oxidation states in its compounds ?
Fill in the blank with appropriate word.
The passengers and crew members of the aeroplane had a.......escape when it was taking off from the runway.
Out of the given alternatives, choose the one which can be substituted for the given capitalised word.
OVER AND ABOVE the household work, she works in a factory on a part-time basis.
Improve the sentence by choosing best alternative for capitalised part of the sentence.
When are you LOOKING UP in dark?