VITEEE PCME Mock Test - 2

If n is any positive integer ,then the value of
[i⁽⁴ⁿ⁺¹⁾ - i^(4n-1)] /2 equals

 is a singular matrix, then x =

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

If x ≠ 0  , then x =

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

The differential equation for the family of curves x² + y² - 2ay = 0, where a is an arbitrary constant is

The slope of the tangent at (x,y) to a curve passing thro' a point (2,1) is x²+y²/2xy, then the eqution of the curve is

If x(dy/dx) = y(log y - log x + 1), then the solution of the equation is

The solution of differential equation (x+2y³) dy/dx = y is

The interval in which y=x²e^x is increasing with respect to x, is

Let f : R → R be defined by  

Then the value of f(-1.75) + f(0.5) + f(1.5) is

∫secx dx=

If cot^-1[(cos α)^1/2] - tan^-1[(cot α)^1/2] = x, then sin x =

"If Deb and Sam go to the mall, then it is snowing."
Which statement below is logically equivalent?

  and A²  = I then x =

Number of numbers greater than 1000 but less than 4000 that can be formed by using the digits 0, 1, 2, 3, 4 when repetition is allowed is

Two dice are thrown simultaneously. The probability of getting a pair of 1 is

In a Binomial distribution, the probability of getting a success is 1/4 and standard deviation is 3. Then its mean is

A and B are two independent events. P( A and B) = 1/6 and the probability that neither of them occur is 1/3 . Find the probability occurrence of A?

The angles of a triangle are in the ratio 3:5:10. Then the ratio of the smallest side to the greatest side is

11² + 12²+ 13² +....+20² is equal to

Given n = 10, ∑x = 4, ∑y = 3, ∑x² = 8, ∑y² = 9 and ∑xy = 3, then coefficient of correlation is

If each observation of a raw data, whose variance is σ², is multiplied by λ, then the variance of new set is

The roots of the equation |x²|+|x|-6=0 are

Distance between two parallel planes 2x + y + 2z = 8 and 4x + 2y + 4z + 5 = 0 is

The radius of the circle in which the sphere x² + y² + z² + 2x - 2y - 4z - 19 = 0 is cut by the plane x + 2y + 2z + 7 = 0, is

The general solution of tan²θ = 3 is

The normal to the curve x = a(1+cosθ), y = a sinθ at θ always passes through the fixed point

The lines 2x - 3y = 5 and 3x - 4y = 7 are diameters of a circle having area as 154 sq.units. Then the equation of the cirlce is

The angle between the vectors 2i+3j+k and 2i-j-k is

The value of c for which the angle between the vectors cxi-6j+3k, xi+2j+2cxk is obtuse is

In a pure inductive circuit or in an A.C. circuit containing inductance only, the current

Light rays of wavelengths 6000 Å and of photon intensity 39.6 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  ms^-1  ]

A capacitor of capacity C₁ is charged by connecting it across a battery of e.m.f. V₀. The battery is then removed and the capacitor is connected in parallel with an uncharged capacitor of capacity C₂. The potential difference across this combination is

In connection with chemical effect of current, Faraday constant is equal to

Intensity of X - rays in coolidge tube is controlled by

A laser beam is used for carrying out surgery because it

Resistance in the two gaps of a meter bridge are 10 ohm and 30 ohm respectively. If the resistances are interchanged the balance point shifts by

A resistance R is stretched to four times its length. Its new resistance will be

A wire of resistance 12 ohms per meter is bent to form a complete circle of radius 10 cm. The resistance between its two diametrically opposite points, A and B as shown in the Figure, is:

When a current flows through a conductor its temperature

A photon in motion has a mass

In a noiseless transformer, an alternating current of 2 ampere is flowing in the primary coil. The no. of turns in the primary and secondary coils are 100 and 20 respectively. The value of the current in secondary coil is

In an A.C. circuit, maximum value of voltage is 423 volt. Its effective voltage is

Which of the following electromagnetic waves have the smallest wavelength?

Choke coil works on the principle of

A sphere S₁ of radius r₁ encloses a total charge Q. If there is another concentric sphere S₁ of radius r ₂ > r 1 and there be no additional charges between S₁ and S₂, the ratio of electric flux through S₁ and S₂ is

Two charges -10 C and + 10 C are placed 10cm apart. Potential at the centre of the line joining two charges is

Two equal print charges are fixed at x = -a and x = +a on the X axis. Another point charge Q is placed at the origin. The change in electrical potential energy of Q, when it is displaced by a small distance x along the X-axis is approximately proportional to

A 5 μ F capacitor is fully charged across a 12V battery. It is then disconnected from the battery and connected to an uncharged capacitor. If the voltage across the capacitor becomes 3V, the capacitance of the uncharged capacitor is

The electric potential V is given as a function of distance x (metre) by V = (5x² + 10x - 9) volt. Value of electric field at x = 1m is

A quatity X is given by ε₀ L ΔV/Δt , where ε₀ is the permittivity of free space, L is a length, ΔV is potential difference and Δt is the time interval. The dimensional formula for X is the same as that of

A charged particle moves through a magnetic field in a direction perpendicular to it. then the

The average binding energy of the nucleon is

A radio active nucleus with mass number 'A' splits into the nuclei whose mass numbers are in the ratio 3:2, the ratio of their radii is

The source of stellar energy is

Photons of energy of 6 eV are incident on a metal surface whose work function is 4 eV. The minimum kinetic energy of the emitted photoelectrons will be

Which of the following pairs have linear relationship between themselves when photoelectrons are emitted from a surface :

In the formation of a spectrum of white light by a prism, the deviation of violet colour is

The majority charge carriers in p - type semiconductor are

Application of a forward bias to a p-n junction

A p-n photodiode is fabricated from a semiconductor with band gap of 2.8 eV. Which of the following wavelengths it can detect?

The difference in the number of wavelengths, when yellow light propagates through air and vacuum columns of the same thickness, is one. The thickness of the air column is
(Refractive index of air μ a = 1.0003 ; Wavelength of yellow light in vacuum 6000 Å )

Which of the following statements is wrong?

A semi-conducting device is connected in a series circuit with a battery and a resistance. A current is found to pass through the circuit. If the polarity of the battery is reversed, the current drops to almost zero the device may be

In a P-N junction diode

Which of the following when added as an impurity into the silicon produces n-type semiconductor?

When two coherent monochromatic light beams of intensities I and 4I are superimposed, the ratio between maximum and minimum intensities in the resultant beam is

If Young's double slit experiment of light, interference is performed in water, which one of the following is correct?

The superposition principle applies to

If the ratio of intensities of two waves causing interference be 9:4, then the ratio of maximum and minimum intensities will be

3 moles of ethanol react with one mole of phosphorus tribromide to form 3 moles of bromoethane and one mole of X. Which of the following is X?

Benzaldehyde can be prepared by the hydrolysis of

Which of the following compounds does not react with NaHSO₃?

In nucleophilic substitution reactions, the reactivity of carbonyl compounds follows the order

The reaction/method that does not give an alkane is

The authenticity of an observation, made from an instrument depends upon its

Ozonolysis of C₇H₁₄ gave 2-methyl-3-pentanone toluene. The alkene is

Assuming full decomposition, the volume of CO₂ released at STP on heating 9.85 g of BaCO₃ (At. mass Ba = 137) will be

Leucine amino acids is

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

Which of the following compounds is responsible for the transmission of heredity characters?

Which of the following compounds is formed when benzamide is warmed with bromine and alkali?

Formic acid when treated with H₂SO₄ gives

Which of the following salt can be produced by the reaction of CO and caustic soda ?

A glass bulb is filled with NO₂ gas and immersed in an ice bath at 0⁰C which becomes colourless after some time . This colourless gas will be

The rate, at which a substance reacts at constant temperature, depends upon its

One mole of an ideal gas at 300 K is expanded isothermally from an initial volume of 1 litre to 10 litres. The ΔE for this process is (R = 2 cal.K^-1 mol^-1)

An endothermic reaction is one in which

In which one the following reactions does the heat change represents the heat of formation of water

A drug that is antipyretic as well as analgesic is

The arrangement of hydrogen atoms around carbon in the methane molecule is

Considering H₂O as a weak field ligand, the number of unpaired electrons in [Mn(H₂O)₆]²⁺ will be (At no.Mn=25)

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

The oxidation state of copper in the above complex is

Hinsberg reagent is

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

The specific conductance of a 0.1 N KCl solution at 23⁰C is 0.012 ohm⁻¹ cm⁻¹. The resistance of cell containing the solution at the same temperature was found to be 55 ohm. The cell constant will be

Standard electrode potentials are Fe²⁺∕Fe (E⁰ = -0.44) Fe³⁺∕Fe²⁺(E⁰ = 0.77) Fe²⁺, Fe³⁺ and Fe blocks are kept together, then

Ether is obtained from ethyl alcohol

The natural materials from which an element can be extracted economically are called

At constant temperature, in a given mass of an ideal gas

Which of the following has no tin in its composition?

In nitrogen family, the H-M-H bond angle in the hydrides gradually becomes closer to 90^o on going from N to Sb. This shows that gradually

White phosphorus is

SnCl₂ gives a precipitate with a solution of HgCl₂. In this process HgCl₂ is

Space lattice of CaF₂ is

Types of geometrical isomerism shown at the points x, y and z of the following compound are respectively:

The CMC is the concentration at which

Both acid and base may react with which of the following oxides?

Most common oxidation states shown by cerium are

Find the antonym of ANTIPATHY

Fill in the blank with appropriate word.
He is working under such........conditions that it is difficult to maintain his self-respect.

Find the Syonym of ABSOLUTE

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

It was SHE NOT ME who put forth the attractive proposition.

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

The rebels HELD OUT for about a month.