VITEEE PCME Mock Test - 15

The curve represented by Im (z²) = K where K is a non-zero real number is

The area of the curve |x|+|y|=4 is

 for x ≠ 5 and f is continuous at x = 5 then f(5) =

The order of differential equation (d²y/dx²)² = (1+dy/dx)^1/2 is

If the function f is defined by f(x)   = x/1 + | x | then at what points is f differentiable

If x^y=e^(x-y), (dy/dx)=

Let f(x) = [x], where [x] denotes the greatest integer contained in x. Which one of the following is correct?

If c is parameter then the differential equation whose solution is y = c² + c/x is

Solution of (x+y-1) dx+(2x+2y-3) dy = 0 is

The equation of the curve passing through the origin and satisfying the differential equation dy/dx = (x − y)² is

∫cos√x dx=

∫tan^-1x dx =

If Tan^-1x + 1 + Tan^-1(x − 1)   =Tan^-1(18/31) , then x =

The value of 

If n is any odd number, which of the following is true about n +1?

The system of equations
2x + 2y - 3z - 1 = 0
4x + 4y + z -2 = 0
6x + 6y - z -3 = 0
has-

If A = [x y z] ,  

then [ a x² + b y² + c z² + 2 hxy + 2 gzx + 2 fyz ] is

The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of there parallel lines is :

The number of ways in which 7 men and 7 women can sit on a round table such that no two woman sit together is, are

The probability of an event A occuring is 0.5 and of B occuring is 0.3. If A and B are mutually exclusive events,then the probability of neither A nor B occuring is

A coin is tossed 10 times. The probability of getting exactly six heads, is

If the sum of first n terms of an A.P. be 3n² - n and its common difference is 6, then its first term is

If in a ∆ABC 2cosA=sinB cosecC, then

If the matrix  is singular, then θ =

The means of two samples of sizes 50 and 100 respectively are 54.1 and 50.3 and the standard deviations are 8 and 7. The mean and standard deviations of the combined sample is

Given n = 10, ∑x = 4, ∑y = 3, ∑x² = 8, ∑y² = 9 ∑xy = 3, then the co-eff. of correlation is

The number of roots of the equation |x|²  - 7|x|+12=0 is

If there is a multiple root of order 3 for the equation x⁴ − 2 x³ + 2 x − a = 0 , then the other roots is

The ratio in which the plane r̅.(i̅−2j̅+3k̅)=17 divides the line joining the points -2i̅+4j̅+7k̅ and 3i̅+5j̅+8k is̅

The angle between the two planes 3x-4y+5z=0 and 2x-y-2z=5 is

If sin2x+sin4x=2sin3x, then x=

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

The vertex of the parabola
y² = 4(a' - a) (x - a) is

If a,b,c are position vectors of vertices ABC, then the position vector of a centroid of ∆ABC is

If vectors ai-2j+3k and 3i+6j-5k are mutually perpendicular, then the value of a is

A transformer is used to light 140 watt, 24 volt lamp from 240 volts A.C. mains. If the current in the mains is 0.7 A, then the efficiency of transformer is

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

Light rays of wavelengths 6000 Å and of photon intensity 39 x 6 watts/m² is incident on a metal surface. If only one percent of photons incident on the surface emit photo electrons, then the number of electrons emitted per second per unit area from the surface will be [ Planck constant = 6.64 x 10^-34  J − s ; Velocity of light = 3 x 10⁸ m s^-1 ]

The charge deposited on 4 μ F capacitor in the circuit is

Optical fibres uses the phenomenon of

We have two wires A and B of same mass and same material. The diameter of the wire A is half of that B. If the resistance of wire A is 24 ohm then the resistance of wire B will be

A cell whose e.m.f. is 2V and internal resistance is 0.1Ω, is connected with a resistance of 3.9Ω. The voltage across the cell terminal will be

The power of an electric bulb marked as 40 W and 200 V used in a circuit of supply voltage 100 V will be

At what temperature will the resistance of a copper wire become three times its value at 0^​oC(Temperature coefficient of resistance for copper = 4x10^-3 per ^oC)

What is the stopping potential when the metal with work function 0.6 eV is illuminated with the light of 2 eV?

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

When the current changes from +2A to -2A in 0.05s, an emf of 8V is induced in a coil. The coefficient of self induction of the coil is

The oscillating electric and magnetic field vectors of electromagnetic wave are oriented along

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

In bringing an electron towards another electron, the electrostatic potential energy of the system

If a point charge q be rotated in a circle of radius r around a charge Q, the work done will be

Two spherical conductors A and B having equal radii and carrying equal charges on them, repel each other with a force F, when kept apart at some distance. A third spherical conductor C having same radius as that of A, but uncharged, is brought in contact with A, then brought in contact with B and finally removed away from both. The new force of repulsion between the conductors A and B is

Two metal spheres have their surface in the ratio 9 : 16. They are put into contact with each other. A charge of 7 x10^-6 C is given to the system and now they are separated so that each exerts no influence on the other . The potential due to smaller sphere at a distance of 50m from it is

A straight wire of length l and electric dipole moment p is bent to from a semicircle. The new electric dipole moment would be

A voltmeter has a resistance of G ohm and range V volt. The value of resistance used in series to convert it into voltmeter of range nV volt is

A radio active sample has a half life of 5 days. To decay from 8 micro curies to 1 micro-curie, the number of days taken will be

The radio of the radii of the nuclei ₁₃Al²⁷ and ₅₂Te¹⁵²  is

Neutron was discovered by

As the intensity of incident light increases

In a Huygen's eye piece with an eyepiece of focal length F, the distance between the eye-piece and field lens should be

Einstein's work on the photoelectric effect provied support for the equation

ABC is a right angled glass prism of refractive index 1.5. ∠ A , ∠ B and ∠ C are 60^o , 30^o and 90^o  respectively. A thin layer of liquid is on the face AB. For a ray of light which is incident normally on AC to be totally reflected at AB, the refractive index of the liquid on AB should be

Zener diode is used for

A zener diode works on the principle of

For a transistor working as common-base amplifier, the emitter current is 7.2 mA. If the current gain is 0.96, then the collector current is

If the lattice parameter for a crystalline structure is 3.6 Å , then the atomic radius in fcc crystal is

In intrinsic semiconductor at room temperature, number of electrons and holes are

Silicon is a semiconductor. If a small amount of As is added to it, then its electrical conductivity

In forward bias, the width of potential barrier in a p-n junction diode

The golden view of sea shell is due to

The wave theory of light was given by

A wavefront is an imaginary surface where

For the constructive interference the path difference between the two interfering waves must be equal to

Phenomenon of electrolysis was first given by

Ethyl alcohol is industrially prepared from ethylene by

Acetaldehyde cannot exhibit

Formalin is an aqueous solution of

When ethylbromide and n-propyl bromide is allowed to react with sodium, in ether, they form

Tollen's reagent is

Which alkene gives the same product by the Markownikoff's and anti-Markownikoff's method

The most stable ion is

The most stable free radical among the following is

The number of molecules of ATP produced in the lipid metabolism of a molecule of palmitic acid is

Rearrangement of an oxime to an amide in the presence of strong acid is called

The sequence in the structure of nucleic acid is

In which of the following, the number of carbon atoms does not remain same when carboxylic acid is obtained by oxidation

Which of the following favours the backward reaction in a chemical equilibrium?

What is the main reason for the fact that carboxylic acids can undergo ionization?

In a reversible reaction, the catalyst

A heat engine absorbs heat Q₁ at temperature T₁ and heat Q₂ at temperature T₂. Work done by the engine is (Q₁ + Q₂). This data

For an ideal gas, the relation between the enthalpy change and internal energy change at constant temperature is given by

Given the bond energies of N ≡ N , H − H and N − H bonds as 941.5, 433 and 391 kJ mole^-1 respectively, the enthalpy of reaction N₂ g + 3 H₂ g → 2 NH₃ g is

A drug that is antipyretic as well as analgesic is

The prefixes sys and anti are used to denote

Which of the following has largest number of isomers? (R is alkyl group, en is ethylediamine)

One mole of complex compound Co(NH₃)₅ Cl₃ gives 3 mol of ions on dissolution in water. One mol of same complex reacts with two mol of AgNO₃ solution to form two mol of AgCl(s). The struture of complex is

In the presence of acid, the hydrolysis of methyl cyanide gives

The hormone which controls the process like burning of fats, proteins and carbohydrates to liberate energy in the body is

Diazo coupling is useful to prepare

Which of the following shows maximum no. of oxidation states?

Electrolytes when dissolved in water dissociate into ions because

On passing a current through KCl solution 19.5gm of potassium is deposited. If the same quantity of electricity is passed through a solution of aluminium chloride, the amount of Aluminium deposited is

The ether that undergoes electrophilic substitution reactions is

Which of the following reacts with water at a high rate?

Wt. of 22.4 litres of Cl₂ gas at STP is

Lead sulphate is souble in

Among the trihalides of nitrogen which one is most basic?

HNO₂ acts as an/a

The interionic distance for cesium chloride cystal will be

Oxidation state of Fe in Fe₃O₄ is

Alkane, C₅H₁₂, in which all H-atoms are equivalent is:

The first element in the 3d-transition series is

Elements which generally exhibit mutiple oxidation states and whose ions are usually coloured are

Collodial solution of silver is prepared by

Find the antonym of ALIENATE

Fill in the blank with appropriate word.
To nobody else did the story seem..........

Find the synonym of RUPTURE

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.

Despite his old age, his movements were as spirited as A YOUNG MAN