VITEEE PCME Mock Test - 14

If A, B, C are represented by 3 + 4i, 5 - 2i, -1 + 16i respectively, then A, B, C are

If α , β are two different complex numbers such that | α | = 1, | β | = 1, then the expression | β − α /1 − α β | equals

 is continuous at π/4 , then a =

Consider f (x) = x² /| x | , x ≠ 0, f(x) = 0, x = 0

The area bounded by the curve y = x² - 4x, x-axis and line x = 2 is

Find the degree of (y₂)² − √y₁ = y³

The solution of differential equation (xdy/dx)=y+x² is

The degree and order of the differential equation of the family of all parabolas whose axis is x-axis are respectively

The differential equation of the family of curves y²=4a (x+a) is

If x=a(t-sint) and y=a(1-cost), (dy/dx)=

If f(x) is an odd periodic function with period 2, then f(4) equals :

∫tan^-1x dx =

If tan^-1x + tan^-1y + tan^-1z = π, then x+y+z is equal to

A function f(x) is defined as f (x) = [ 1 − x² ] , − 1 ≤ x ≤ 1 , where [x] denotes the greatest integer not exceeding x. The function f(x) is discontinuous at x = 0 because

The sentence "____ if and only if x + x = 3x" is TRUE.

A and B are square matrices of the same order. Which is correct?

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

If ⁿP_r=840, ⁿC_r=35, then n=

A biased coin with probability p,0<p<1 of heads is tossed until a head appears for the first time. If the probability that the number of tosses required is even, is 2/5, then p equals

In two events P(A∪B) = 5/6, P(A) = 5/6, P(B) = 2/3 then A and B are

In four schools B₁, B₂, B₃, B₄ the percentage of girls students is 12, 20, 13, 17 respectively. From a school selected at random, one student is picked up at random and it is found that the student is a girl. The probability that the school selected is B₂, is

If the side of a triangle are 13, 14, 15, then the radius of the incircle is

The fourth ,seventh and tenth of a G.P. are p,q,r respectively then

Two numbers within the brackets denote the ranks of 10 students of a class in two subjects - (1, 10), (2, 9), (3, 8), (4, 7), (5, 6), (6, 5), (7, 4), (8, 3), (9, 2), (10, 1), then rank correlation coefficient is

The mean of 5 observations is 4.4 and their variance is 8.24. If three observations are 1, 2 and 6, the other two observations are

The one roots of the equation 2x⁵-14x⁴+31x³-64x²+19x+130=0 is

The equation of the sphere concentric with the sphere x²+y²+z²-4x-6y-8z=0 and which passes thro' (0.1,0) is

If α , β , γ are the roots of the equation x³ − 6 x² + 11 x + 6 = 0, then Σ α² β + Σ α β² =

The locus of the point of intersection of tangents to the circle x = a cos θ, y = a sin θ at the points, whose parametric angles differ by π/2 is

The radius of the circle
3x (x - 2) + 3y (y + 1) = 4 is

In three dimensional space, the equation 3y+4z=0 represents

If vectors 2i+j+k and i-4j+λk are perpendicular, then λ=

If the solution for θ of cospθ + cosqθ = 0, p > 0, q > 0 are in A.P., then the numerically smallest common difference of A.P. is

The projection of the vector î - 2 ĵ + k̂ on the vector 4 î - 4 ĵ + 7 k̂ is

Sodium has body centred packing. Distance between two nearest atoms is 3.7 Å . The lattice parameter is:

For series LCR circuit, wrong statement is

The closest distance of approach of an α - particle travelling with a velocity 'V' to a certain nucleus is 'x'. The distance of closest approach of α - particle travelling with a velocity 3V to the same nucleus is

A parallel plate condenser with oil between the plates (dielectric constant of oil K = 2) has a capacitance C. If the oil is removed, then capacitance of the capacitors becomes

A steady current of 1.5 A flows through a copper voltameter for 10 min. If the electrochemical equivalent of copper is 30 x 10^-5 g C^-1 , the mass of copper deposited on the electrode will be

A laser beam is used for carrying out surgery because it

EMF is most closely related to

Three resistors are connected to form the sides of a triangle ABC, the resistance of the sides AB, BC and CA are 40 ohms, 60 ohms and 100 ohms respectively. The effective resistance between the points A and B in ohms will be

Taking the internal resistance of the battery as negligible, the steady state current in the 2 Ω resistor shown in the figure will be

If two identical heaters of 220 V, 1000 W are placed parallel to each other across 220 V lines, then the combined power of the heaters is

In a D.C. motor induced e.m.f will be maximum

The approximated wavelength of a photon of energy 2.48eV is

A 5 cm long solenoid having 10 cm resistance and 5 mH inductance is joined to a 10 V battery. At steady state, current through solenoid is

When the current in a coil is changed from 10 A in one direction to 10 A in opposite direction in 0.5 s, an e.m.f. of 1 V is induced in it. Self-inductance of the coil is

Out of the folowing statement which is NOT true?

If the electric flux entering and leaving an enclosed surface respectively is φ₁ and φ₂, the electric charge inside the surface will be

Two equal charges q of opposite sign separated by a distance 2a constitute an electric dipole of dipole moment p. If P is a point at a distance r from the centre of the dipole and the line joining centre to this point makes an angle θ with the axis of the dipole, then potential at the point P is given by

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 capacitance of a parallel plate capacitor becomes 4/3 times its original value if a dielectric slab of thickness t = d/2 is inserted between the plates (where d is separation between the plates). The dielectric constant of the slab is

If an unchanged capacitor is charged by connecting it to a battery, then the amount of energy lost as heat is

The inward and outward electric flux of a closed surface are 8x10³ C and 4x10³ C respectively. The net charge inside the closed surface is

A 10 A ammeter has a resistance of 0.09 Ω. What resistance of the shunt will enable it to read up to 100 A?

The first atomic reactor was constructed by

The half life period of radio - active isotope is 5 minutes. The fraction of isotope, that will be remaining after 30 minutes is

The number of beta particles emitted by a radioactive substance is twice the number of alpha particles emitted by it. The resulting daughter is an:

When a metallic surface is illuminated by a monochromatic light of wavelength λ, then the potential difference required to stop the ejection of electrons is 3V₀. When the same surface is illuminated by the light of wavelength 2λ, then the potential difference required to stop the ejection of electrons is V₀. Then for photoelectric effect, the threshold wavelength for the metal surface will be

The work function of a metal is 2.8 eV. Its threshold wavelength will be

A telescope consists of two thin lenses of focal lengths 0.3 m and 3 cm respectively. It is focused on moon which subtends an angle of 0.5⁰ at the objective. Then, the angle subtended at the eye by the final image will be

Ultra-violet rays are detected by

In the middle of the depletion layer of a reverse-biased p-n junction, the

The method of connecting the negative pole of battery to p - material and positive pole to n - material of a p - n junction is called

Rectifier is used to convert

The band gap in Germanium and silicon in eV respectively is

When germanium atoms is doped with equal no. of antimony atoms, we get a/an

Suitable impurities are added to a semiconductor depending on its use. This is done to

At room temperature, a p-type semiconductor has

In interference pattern, the energy is

Young's double slit experiment gives interference fringes of width 0.3mm. A thin glass plate made of material of refractive index 1.5 is kept in the path of light from one of the slits, then the fringe width becomes

Which one of the following properties of light does not support wave theory of light?

If ratio of amplitude of two waves is 4:3, then ratio of maximum and minimum intensity is

Ethyl alcohol can be used for preparation of which of the following?

Aldol condensation will not be observed in

The base-catalysed aldol condensation will not occur with

Which of the following reaction cannot be used for the conversion RCO → RCH₂

Tetrabromomethane on treatment with Zn gives

The product formed by the action of chlorine on ethene in saturated solution of KBr is/are

In the following reaction, which choice has value twice that of the equivalent mass of the oxidising agent SO₂ + H₂O → 3S + 2H₂O

Which species represents the electrophile in aromatic nitration?

Lipids are

Chargaff's rule states that in an organism

Ethyl alcohol reacts with acetyl chloride to form

A certain compound gives negative test with ninhydrin and positive test with Benedict's solution. The compound is

Rancidity of butter is due to the formation of

From the following values of dissociation constants of four acids which value represents the strongest acid ?

The chemical equilibrium of a reversible reaction is not influenced by

In the case of gaseous homogeneous reaction,the active mass of the reactant is obtained by the expression

The internal energy of a subtance does not depend upon

A compound with molecular formula C₇H₁₆ shows optical isomerism , the compound will be

Which of these is a hypnotic?

The heat of formation of the compound in the following reaction is H₂(g) + Cl₂(g) → 2HCl(g) + 44 kcal

Calculate Δ H in KJ for the following reaction C(s) + O₂ g → CO₂ g Given that
H₂O g + C g → CO g + H₂  g , Δ H = + 131 k J
CO g + 1/2 O₂  g → CO₂  g , Δ H = − 282 k J
H₂g + 1/2 O₂ g → H₂O g , Δ H = − 242 k J

The complex CoCl₃.3NH₃ ionises to give

The oxidation state of Cr in [ Cr (NH₃)₄ Cl ₂ ] + is :

Which of the following is produced by reaction of RCN in sodium and alcohol ?

Diazo coupling is useful to prepare

Among the properties (a) reducing (b) oxidising (c) complexing, the set of properties shown by CN⁻ ion towards metal species is

Calculate the amount of change flowing in 2 minute in a wire of resistance 10 Ω when a potential difference of 20 V is applied

On heating quick lime with coke in an electric furnace, we get

Diethyl ether can be decomposed by

The standard reduction potential at 298 K for the following half cell reaction are given below
Zn²⁺ + 2e^-  → Zn E⁰ = − 0.762 V
Cr⁺³ + 3 e^- → Cr E⁰  = − 0.740 V
2 H⁺ + 2 e^-  → H₂ E⁰  = − 0.0 V
Fe⁺³  + e^-  → Fe⁺²  E⁰  = − 0.770 V
Which one is the strongest reducing agent?

Lead sulphate is souble in

The largest bond angle is in

If the pressure and absolute temperatre of 2 litres of CO₂ are doubles, the volume of CO₂ would become

Which one of the following is pyrophosphoric acid?

Which substance is serving as a reducing agent in the following reaction? 14H⁺ + Cr₂O₇^2- + 3Ni → 2Cr⁺³ + 7H₂O + 3Ni⁺²

Following compounds are respectively ... geometrical isomers

A face-centred cubic element has a edge length of 400 pm. What is its density? At. weight of element= 60)

The adsorption of hydrogen by palladium is called

Colourless solutions of the following four salts are placed separately in four different test tubes and a strip of copper is dipped in each one of these. Which solution will turn blue ?

Highest oxidation state of transition element is

Find the antonym of CORPULENT

Fill in the blank with appropriate word.
You will have to face some practical problems when you start.........this plan.

Find the Synonym of LANGUISHING

Choose the alternative which best expresses the meaning of the idiom/phrase.

To be under a cloud

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

He has very good command ON English.