VITEEE PCME Mock Test - 11

If n is not a multiple of 3 then ωⁿ + ω²ⁿ =

If 1 , ω , ω²  , … ω^n-1 are the n, nth roots of unity and z₁ and z₂ are any two, complex numbers, then 

For solving dy/dx=4x+y+1 suitable substitution is

The solution of the equation cosx cosy (dy/dx)=-sinx siny is

The differential equation of family of lines which passes (1,-1) is

If f : R → R is defined by f x = 2 x + | x | then f (3x) − f (-x)   − 4 x =

If f(x)   = e ^-1/x² , x ≠ 0, and f(0) = 0 then f ′(0)    is

y = A e^x + B e^2x + C e^3x  satisfies the diferential equation

∫logx dx =

∫[(1)/(4x²+9)]dx =

If sin^-1x − cos^-1x = π/6 , then x =

if f : R→R be such that f(1) = 4 and f^'(1) = 12 then 

If A and B are two matrices such that AB = B and BA = A, then A²+ B² =

∼ [ p ∧ q → ∼ p ∨ q ] is

In how many ways can 4 boys and 3 girls be seated in a row of 7 chairs if the boys and girls alternate?

If A is a non-singular, then adj A is

When two dice are thrown, the probability of getting the sum 10 or 11 is

A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is a six. The probability that it is actually a six is

A bag contains 6 white and 4 black balls. Two balls are drawn at random. The probability that they are of the same colour is

If m is a root of the equation (1 - ab) x² - (a² + b²)x - (1 + ab) = 0, and m harmonic means are inserted between a and b, then the difference between the last and the first of the means equals

In a Δ A B C , 2s = perimeter and R = circumradius. Then s/R is equal to

The coefficient of correlation r satisfies

The harmonic mean of 4,8,16 is

The roots of the equation (q-r)x² + (r-p)x + (p-q)=0 are

If α , β , γ are the roots of x³ − 2 x² + 3x − 4 = 0, then the value of α ²β² + β²γ²+ γ²α ² is

The distance between the parallel planes x + 2y - 3z = 2 and 2x + 4y - 6z + 7 = 0 is

Lines OA, OB are drawn from 0 with directions cosines proportional to < 1, -2, -1 > ans < 3, -2, 3 > respectively. The direction ratios of the normal to the plane AOB are

If 5cos2θ+2cos²(θ/2)+1=0, -π<θ<π, then θ=

The equation of the parabola whose focus is (1,-1)and directrix is x + y + 7 = 0 is

If the straight lines x = 1 + s, y = -3 - λs, z = 1 + λs and x = t/2, y = 1 + t, z = 2 - t, with parameters s and t respectively, are co-planar, then λ equals

A force of magnitude 5 units along the vector 2 î − 2j^{^} + k^{^}  displaces the point of application from (1,2,3) to (5,3,7), then the work done is

If axb = cxb = 0, then

The time constant of an LR circuit represents the time in which the current in the circuit

The work function of Potassium is 2.0 eV. When it is illuminated by light of wavelength 3300 A⁰ photoelectrons are emitted. The stopping potential of photoelectrons is

X - rays are

Three capacitors each of capacitance C and of breakdown voltage V are joined in series. The capacitance and breakdown voltage of the combination will be:

The electrochemical equivalent of magnesium is 0.126 mg/C. A current of 5 A is passed in a suitable solution for one hour. The mass of the magnesium deposited will be

Optical fibres uses the phenomenon of

If the resistance of a conductor is 5 Ω at 50^oC and 7 Ω at 100^oC, then the mean temperature coefficient of resistance of the material is

The electric intensity E, current density j and specific resistance k are related to each other by the relation

In an experiment to measure the internal resistance of a cell, by a potentiometer, it is found that the balance point is at a length of 2 m, when the cell is shunted by a 5 Ω resistance and is at a length of 3m when the cell is shunted by a 10 Ω resistance. The internal resistance of the cell is

Two resistances R₁ and R₂ are made of different materials. The temperature coefficient of the material of R₁ is α and of the material of R₂ is −β. The resistance of the series combination of R₁ and R₂ will not change with temperature, if R₁/R₂ equals

Gases begin to conduct electricity at low pressure because

The primary and secondary coils of a transformer have 50 and 1500 turns respectively. If the magnetic flux φ linked with the primary coil is given by φ = φ ₀ + 4t, where φ is in weber, t is time in second and φ ₀ is a constant, the output voltage across the secondary coil is

At resonance, in a series LCR circuit, which relation does not hold

A solenoid of length 20 cm area of cross-section 4 cm² and having 4000 turns is placed inside another solenoid of 2000 turns having a cross-section area 8 cm² and length 10 cm. The mutual inductance of the system is

A charge is placed at the centre of a cube, the flux emitted through its one face is

A hollow metal sphere of radious 10 cm is charged such that the potential on its surface is 80V. The potential at the centre of the sphere is

Two equal charges, q each are placed at a distance of 2a, and a third charge -2q is placed at the mid point. The potential energy of the system is

The capacities of three capacitors are in ratio 1 : 2 : 3. Their equivalent capacity when connected in parallel is 60/11 μ F more than that when they are connected in series. The individual capacities of capacitors in μ F are

Two insulated matallic spheres of 3 μ F and 5 μ F are charged to 300V and 500V respectively. The energy loss when they are connected by a wires is...

Half life period of lead is

A long copper pipe carries a current. Then the magnetic field is

In the following reaction the energy released is 4 ₁H¹ → ₂He⁴  + 2 ₊₁e⁰ + energy

An infinite number of identical capacitors, each of capacitance 1 μ F, are connected as in the figure. The equivalent capacitance between 'A' and 'B' is

When P₁₅³⁰  decays to become Si₁₄³⁰ the particle released is

When the light source is kept 20 cm away from a photocell, stopping potential is 0.6 V is obtained. When the source is kept 40 cm away, the stopping potential will be

The slope of frequency of incident light and stopping potential for a given surface will be

Continuous emission spectrum is also called

Rainbow is due to

The potential in the depletion layer is due to

In an n-p-n transistor, p-acts as a/an

In a n-p-n transistor amplifier, the collector current is 9 mA. If 90% of the electron from the emitter reach the collector, then

The band gap in Germanium and silicon in eV respectively is

The cause of the potential barrier in a p-n diode is

In the forward bias arrangement of a p-n junction diode

A p-type semiconductor is

The penetration of light into the region of geometrical shadow is called

When a source is linear, the wavefront is

What is the effect on the interference fringes in a Young's double slit experiment, if the monochromatic source is replaced by another monochromatic source of shorter wavelength?

Which of the following property of light waves is not observed in sound waves?

2R ― OH + 2Na → 2RONa + H₂. In the above reaction the reactivity of different alcohols is

Formaldehyde +NH₃→Y. The product of Y is

The reagent SnCl₂/HCl is used in

A compound A has molecular formula C₂Cl₃OH. It reduce Fehling's solution and on oxidation gives a monocarboxylic acid B. A is obtained by the action of Cl₂ on ethyl alcohol. A is

A compound possesses 8% sulphur by mass. The least molecular mass is

1-Butene may be converted to butane by reaction with

To which of the following four types does this reaction belong? B^- + R - A → B - R + A^-

The reaction/method that does not give an alkane is

Enzymes belong to the class of compounds

Oxytocin is

An example of water soluble vitamin is

Self condensation of two moles of ethyl acetate in presence of sodium ethoxide yields

The acid showing salt like character in aqueous solutions is

Reaction of acids with alcohols is also known as

If a mixture containing 3 moles of hydrogen and 1 mole of nitrogen is converted completely into ammonia, the ratio of volumes of reactants and products at the same temperature and pressure would be

The equilibrium constant for the following reaction will be 3 A + 2 B → C

A system is said to be in thermodynamic equilibrium when it is in

The heats of dissociation (k.cals/mole) of methane and ethane are 360 and 620 respectively. From these, C - C bond energy (k.cals/mole) in ethane can be evaluated as

If the enthalpy of vaporisation of water is 186.5 J mol^-1, the entropy of its vaporisation will be

Amoxillin is semi-synthetic modification of

The outer orbital hybridisation is involved in

The IUPAC name of (CH₃)₂CHCH₃ is

An electrolyte

Which of the following reagent can be used to convert benzene diazonium chloride into benzene ?

Aromatic nitriles (ArCN) are not prepared by

Hybridization of Fe in K₃Fe(CN)₆ is

Conductivity (Unit:siemen's S) is directly proportionally to the area of the vessel and the concentration of the solution in it and is inversely proportional to the length of vessel,then the unit of constant of proportionally is

When the densities of the ore particles and gangue particles are different, then the ore is concentrated by

White lead is

A gas a diffuses 5 times faster than gas B. Density of A compared with B is

The pH of aqueous KCl solution is 7.0. This solution was electrolysed for a few seconds using Pt electrodes. Which of the following is correct?

Heating of methyl phenyl ether with HI gives

Which of the following reacts rapidly with oxygen in air at ordinary temperature

In crystal structure of sodium chloride, the arrangement of Cl^- ions is

Adsorption due to strong chemical forces is called

Which one of the following is used in the industrial preparation of nitric acid by Ostwald's process ?

Which of the following is not a redox reaction?

Which is the correct statement for major product?

Bell metal is an alloy of

Transition metals mostly are

Find the Antonym of FLEXIBLE

Find the Syonym of AMBITION

Fill in the blank with appropriate word.
The twins are so alike that I cannot.......one from the other.

Out of the given alternatives, choose the one which can be substituted for the given capitalised word. 

The old man CUT TO THE QUICK when his rich son refused to recognise him.

Improve the sentence by choosing best alternative for capitalised part of the sentence.

After a few minutes the unconscious boxer began to come OUT.