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The solution of differential equation (x2 y – 2x y 2) d x – (x3 – 3x2 y ) dy = 0, is
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If u = x log x y , where x3 + y 3 + 3x y = 1, then du /d x is
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The solution of differential equation
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If the imaginary part v = e x(x sin y + y cos y ) is part of analytic function f ( z ) = u + i v ,then f ( z ) is
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The first four terms of the Taylor series expansion of f ( z ) = z +1/( z-3)( z-4), when z = 2 is
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The mean deviation about mean µ of a normal distribution is nearly
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Consider the following regression equations obtained from a correlation table :
y = 0.516 x + 33.73
x = 0.512 y + 32.52
The value of the correlation coefficient will be
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If the probability of a bad reaction from a certain injection is 0.001, the chance that out of 2000 individuals, more than two will get a bad reaction will be
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As per de Broglie’s relationship, the wavelength λ related to its mass m and velocity v is
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Which of the following statements regarding an atom are correct?
1. If two atoms with similar ionization potential form a bond, then this bond will most probably be either covalent or metallic.
2. When atoms with different ionization potentials form a bond, the bond will be mainly ionic.
3. If the atom or molecule already has its outer shells completely full, then the bonding between the atoms or molecules will be a secondary bond when it solidifies
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A barium titanate crystal is inserted in a parallel plate condenser of area 10 mm × 10 mm. The plates having a separation of 2 mm, give a capacitance of 10–9 F. If the value of ε0 = 8.854 × 10–12 Fm–1, the relative dielectric constant of the crystal will be nearly
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A transformer core is wound with a coil carrying an alternating current at a frequency of 50 Hz. The hysteresis loop has an area of 60000 units when the axes are drawn in units of 10–4 Wb m–2 and 102 Am–1. If the magnetization is uniform throughout the core volume of 0.01 m3, the power loss due to hysteresis will be
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When ferromagnetic or ferrimagnetic materials are magnetized, the direction of magnetization in any domain will be rotated from its preferential direction. This will show an anisotropic behaviour. On removal of the magnetizing force, the total magnetization will in general have a non-zero value. This behaviour is due to