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The number of arbitrary constants in the solution of a differential equation of degree 2 and order 3 is
If y = y(x) is the solution of the differential equation ey such that y(0) = 0, then y(1) is equal to:
The solution of the equation (y log y) dx +(x - logy) dy = 0, is
The integrating factor of dy/dx - 3y/x = x3 sin x is
The distance of the point having position vector from the straight line passing through the point (2, 3, - 4) and parallel to the vector,
The value of k for which the points A (1, 0, 3), B (– 1, 3, 4), C (1, 2, 1) and D (k, 2, 5) are coplanar, is
Two systems of rectangular axes have the same origin. If a plane cuts them at distances a, b, c and a', b', c' from the origin, then
Equation of a plane bisecting the angle between the planes 2x - y + 2z + 3 = 0 and 3x - 2y + 6z + 8 = 0 is
Let a = i + j + k, b = I – j + 2k and c = xi + (x – 2)j – k. If the vector c lies in the plane of a and b, then x equals
A line passes through the points (6, –7, –1) and (2, –3, 1). If the angle which the line makes with the positive direction of the x-axis is acute, then the direction cosines of the line are
The equation of the line through the point (2, 1, 1) and the intersection of the lines 2x – y – 4 = 0 = y + 2z and x + 3z – 4 = 0 = 2x + 5z – 8 is
The equation of a plane containing the line of intersection of the planes 2x - y - 4 = 0 and y + 2z - 4 = 0 and passing through the point (1, 1, 0) is:
Four persons can hit a target correctly with probabilities 1/2, 1/3, 1/4 and 1/8. If all hit at the target independently, then the probability that the target would be hit is
If three of the six vertices of a regular hexagon are chosen at random, then the probability that the triangle formed with these chosen vertices is equilateral is
Out of 11 consecutive natural numbers, if three numbers are selected at random (without repetition), then the probability that they are in A.P. with positive common difference, is:
Let A and B be two non-null events such that A ⊂ B. Then, which of the following statements is always correct?
A random variable has the following probability distribution:
The value of k is
If (1 + 3p)/3, (1 – p)/4 and (1 – 2p)/2 are the probabilities of three mutually exclusive events, then the set of all values of p is
The mean and variance of a binomial distribution are 4 and 2, respectively. What is the probability of two successes?
The probability of a man hitting a target is 1/10. The least number of shots required, so that the probability of his hitting the target at least once is greater than 1/4, is ______ (in integer).
Directions: The answer to the following question is a single-digit integer, ranging from 0 to 9.
Three tangents are drawn at random to a given circle. If the odds against the circle being inscribed in the triangle formed by them are K : 1, find K.
A fair n (n > 1) faces die is rolled repeatedly until a number less than n appears. If the mean of the number of tosses required is n/9, then n is equal to ____________.
Let the probability of getting head for a biased coin be 1/4. It is tossed repeatedly until a head appears. Let N be the number of tosses required. If the probability that the equation 64x2 + 5Nx + 1 = 0 has no real root is p/q, where p and q are coprime, then q - p is equal to ________.
Let A be the event that the absolute difference between two randomly choosen real numbers in the sample space [0, 60] is less than or equal to a. If P(A) = 11/36, then a is equal to _______.
10-3 W of 5000 Å light is directed on a photoelectric cell. If the current in the cell is 0.16 mA, the percentage of incident photons which produce photoelectrons, is
Let nr and nb be respectively the number of photons emitted by a red bulb and a blue bulb of equal power in a given time.
The maximum kinetic energy of photoelectrons emitted from a surface when photons of energy 6 eV fall on it is 4eV. The stopping potential is Volts is
If the frequency of light in a photoelectric experiment is doubled, the stopping potential will
The stopping potential for the photo electrons emitted from a metal surface of work function 1.7eV is 10.4 V. Identify the energy levels corresponding to the transitions in hydrogen atom which will result in emission of wavelength equal to that of incident radiation for the above photoelectric effect
A point source of light is used in photoelectric effect. If the source is removed farther from the emitting metal, the stopping potential
Radiation of two photon energies twice and five times the work function of metal are incident sucessively on the metal surface. The ratio of the maximum velocity of photoelectrons emitted is the two cases will be
A point source causes photoelectric effect from a small metal plate. Which of the following curves may represent the saturation photocurrent as a function of the distance between the source and the metal?
When a photon of light collides with a metal surface, number of electrons, (if any) coming out is
Cut off potentials for a metal in photoelectric effect for light of wavelength l1, l2 and l3 is found to be V1, V2 and V3 volts if V1, V2 and V3 are in Arithmetic Progression and l1, l2 and l3 will be
The energy released by the fission of one uranium atom is 200 MeV. The number of fissions required per second to produce 3.2 W of power is
If in a nuclear fission, a piece of uranium of mass 0.5 g is lost, then the energy obtained in kWh is
What is the rest mass energy of an electron?
Which of the following are not emitted by a radioactive substance?
During a negative beta decay,
The half-life of Pa-218 is 3 minutes. What mass of a 16 g sample of Pa-218 will remain after 15 minutes?
Mp denotes the mass of a proton and Mn that of a neutron. A given nucleus of binding energy B contains Z protons and N neutrons. The mass M (N, Z) of the nucleus is given by
The circuit shown in the figure contains two diodes D1 and D2, each with a forward resistance of 50 ohms and infinite backward resistance. If the battery voltage is 6 V, the current (in amperes) through the 100 ohm resistance is
I is the current passing through a circular wire. If the radius of the wire is changed to twice, then what will be the current passing through the wire?
To obtain a p-type semiconductor germanium crystal, it must be doped with foreign atoms whose valency is
A monochromatic light is incident on a hydrogen sample in ground state. Hydrogen atoms absorb a fraction of light and subsequently emit radiation of six different wavelengths. The frequency of incident light is x × 1015 Hz. The value of x is ____________.
(Given h = 4.25 × 10-15 eVs)
The stopping potential for photoelectrons emitted from a surface illuminated by light of wavelength 6630 is 0.42 V. If the threshold frequency is x × 1013 /s, where x is _________ (nearest integer).
(Given, speed light = 3 × 108 m/s, Planck's constant = 6.63 × 10−34 Js)
When light of frequency twice the threshold frequency is incident on the metal plate, the maximum velocity of emitted electron is v1. When the frequency of incident radiation is increased to five times the threshold value, the maximum velocity of emitted electron becomes v2. If v2 = x v1, the value of x will be __________.
A nucleus disintegrates into two nuclear parts, in such a way that ratio of their nuclear sizes is 1: 21/3 Their respective speed have a ratio of n : 1. The value of n is __________.
A nucleus with mass number 242 and binding energy per nucleon as 7.6 Me V breaks into two fragment each with mass number 121. If each fragment nucleus has binding energy per nucleon as 8.1 MeV, the total gain in binding energy is _________MeV.
Choose the correct statement regarding the physical properties of carbonyl compound.
Ozonolysis of an organic compound gives formaldehyde as one of the products. This confirms the presence of:
The correct order of increasing acidic strength is:
Presence of unsaturation in organic compounds can be tested with:
Which of the following will not undergo aldol condensation?
Which of the following gives benzoic acid on oxidation?
Toluene reacts with halogen in presence of iron(III) chloride giving ortho and para halo compounds, the reaction is?
Which of the following carboxylic acid is highly insoluble in water?
What is the name of the above reaction?
Acetic acid is obtained when which of the given reaction takes place?
What is the name of the following compound?
CH3CH2COCI
Identify the product for the following reaction.
CH ≡ CH + HOCI →
Which of the following names is correct for
Propanal on treatment with dilute sodium hydroxide gives:
Which of the following organic compounds does not undergo diazotisation?
The coupling of diazonium salt of 4-amino benzene sulphonic acid with N, N-dimethyl benzamine produces
Which among the following statements is incorrect?
Which of the following compounds give carbylamine reaction?
Which of the following indicates open chain structure of glucose?
The numbers of stereo centres present in linear and cyclic structures of glucose are respectively:
A solution of phenol in chloroform when treated with aqueous NaOH gives compound P as a major product. The mass percentage of carbon in P is ______. (to the nearest integer) (Atomic mass: C = 12; H = 1; O = 16)
How many of the transformations given below would result in aromatic amines?
The number of sp3 hybridised carbons in an acyclic neutral compound with molecular formula C4H5N is ___________.
The mass of NH3 produced when 131.8 kg of cyclohexanecarbaldehyde undergoes Tollen's test is ________ kg. (Nearest Integer)
Molar Mass of C = 12g/mol N = 14g/mol O = 16g/mol
Number of isomeric compounds with molecular formula C9H10O which (i) do not dissolve in NaOH (ii) do not dissolve in HCI. (iii) do not give orange precipitate with 2,4-DNP (iv) on hydrogenation give identical compound with molecular formula C9H12O is __________.