The function which is neither decreasing nor increasing in (π/2, 3π/2) is
If complex numbers z₁, z₂ and origin form an equilateral triangle then z₁2 + z₂2 =
The area of the region bounded by the curve y = x - x2 between x = 0 and x = 1 is
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 xy=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
∫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?
Every whole number is either odd or even.
A whole number is even if it can be divided evenly by two; the numbers 2, 4, 6, 8, 10, 12, . . . are even.
In this question we are given the information that n is an odd number.
Because n is odd, it must be one of the numbers 1, 3, 5, 7, 9, 11, 13, 15, and so on.
Now we have to reason mathematically.
If n is a member of this “odd” list, then what can we say for sure about n +1?
If we add 1 to each number in the odd list, we get the “ n +1 ” list: 2, 4, 6, 8, 10, 12, 14, 16, and so on, which are even numbers.
The system of equations
2x + 2y - 3z - 1 = 0
4x + 4y + z -2 = 0
6x + 6y - z -3 = 0
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 0oC(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
No. of turns across primary Np = 50
Number of turns across secondary Ns = 1500
Magnetic flux linked with primary, Φ = Φ0 + 4t
∴ Voltage across the primary,
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 60o , 30o and 90o 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
It does not go against first law of thermodynamics .
However it violates the 2nd law of thermodynamics.
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
Enthalpy of reaction = ∑ bond energyreactant - ∑ bond energyproduct
= bond energy (n2) + 3 x (bond energy) (h2) - 2 x (bond energy) (NH3)
= 941.5 + (3 x 433) - 2 x 3 x 391
= 2240.5 - 2346 = 105.4 ≅ -105kJ
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
Thyroxine is a hormone secreted by thyroid gland.
This hormone controls various biochemical reactions involving burning of proteins carbohydrates, fats to release energy.
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