The sides of an equilateral triangle are increasing at the rate of 2 cm/sec. The rate at which the area increases, when the side is 10 cm is
The area bounded by the parabola x = 4 − y2 and the y-axis, in square units is
The argument and modulus of [(1+i)/(1-i)] are respectively
If a is real number such that | z − a i | = | z + a i | , then the locus of z is
for x ≠ 0, f 0 = 0, then f(x) at x = 0 is
If - 9 is the root of the equation , then other two roots are
Let f(x) = log |x - 1|, x ≠ 1. The value of f ′(1/2) is
The order and degree of the differential equation (1 + 3dy/dx)2/3 = 4d3y/dx3 are
The differential equation representing the family of curves y2 = 2c(x+√c), where c is a positive perimeter, is of
The general solution of the differential equation is given by
The differential equation of all circles which pass through (0,0) and having centre on y-axis, is
then f'(1) is ?
∫tan-1x dx =
∫ tan5θ dθ =
The domain of sin-1x is
If f'(2) = 4 and f ' (1) = 2 then
The value of
If A and B are 2 x 2 matrices then (A+B)2=
If A is singular matrix of order n, then a (adj A) equals,
Reena says "The number I am thinking is divisible by 2 or it is divisible by 3". This statement is false if the number Reena is thinking of is
This sentence contains the word "or" (disjunction).
A disjunction is only false if BOTH conditions are false.
The only number that is not divisble by 2 and is not divisible by 3 is 11.
Box A contains 2 black and 3 red balls, while box B contains 3 black and 4 red balls. Out of these two boxes one is selected at random, and the probability of choosing box A is double that of box B. If a red ball is drawn from the selected box then the probability that it has come from box B is
In an examination there are three objective questions and in each question there are 4 options. The number of ways in which any candidate may not give correct answers to all questions is
If A and B are two events such that P(A) = 1/4 , P(B) = 1/2 , P(A ∪ B) = 5/8 then P(A ∩ B) =
A card is taken out of a pack of 52 cards numbered 2 to 53. The probability that the number on the card is a prime number less than 20 is
In ∆ABC, if cotA,cotB,cotC are in A.P., then a2,b2,c2 are in
The most stable measure of central tendency is
The harmonic mean of 4,8,16 is
If the sum of first n terms of an A.P. is pn + qn2 where p and q are constants, then common difference of A.P. will be
For the A.P.
Sn = pn + qn2
Now S1 = p x 1 + q(1)2
S1 = p x q ⇒ T1 = p + q
Also S2 = p x 2 + q(2)2
= 2p + 4q
We have T1 + T2 = 2p + 4q
or T2 = 2p + 4q - T1
or T2 = 2p + 4q - (p + q)
or T2 = p + 3q
Hence common difference = T2 - T1
= p + 3q - (p + q)
= p + 3q - p - q = 2q
The solution of the equation x+(1/x)=2 is
If the roots of x2+x+a=0 are greater than a, then
The points (5,-4,2),(4,-3,1),(7,-6,4),(8,-7,5) are vertices of a
If the planes x+2y+Kz=0 and 2x+y-2z=0 are at right angles, then the value of K is
If α is a root of 25cos2θ + 5cosθ - 12 = 0, (π/2)<α<π, then sin2α is equal to
If the pair of lines ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 intersect on the y-axis then
The equation of the parabola whose focus is (5, 3) and directrix is 3x - 4y + 1 = 0 is
If the position vectors of C and B with respect to B and A are i+j, i-j respectively, the position vector of C with respect to A is
A force of magnitude 5 units acting along the vector 2 î - 2 ĵ + k̂ displaces the point of application from (1, 2, 3) to (5, 3, 7), then the work done is
The de-Broglie wavelength of a particle moving with a velocity 2 .25 x 108 m s-1 is equal to the wavelength of a photon. The ratio of kinetic energy of the particle to the energy of the photon is [ velocity of light = 3 x 108 m s-1 ]
From Compton effect
λ = h/p = c/v [From de-Broglie wavelength]
c p = h v
The internal resistance of a primary cell is 4 Ω. It generates a current of 0.2 A in an external resistance of 21 Ω. The rate at which chemical energy is consumed in providing the current is
A wire of length L is drawn such that its diameter is reduced to half of its original diameter. If the initial resistance of the wire were 10Ω, its new resistance would be
What will be the ratio of de Broglie wavelengths of proton and α-particle of same energy
We know , mα = 2 mp
A dielectric of thickness 5 cm and dielectric constant 10 is introduced in between the plates of a parallel plate capacitor having plate area 500 sq.cm and separation between plates 10 cm. The capacitance of the capacitor is ∈o = 8.8x10-12 SI unit
The photoelectric work function for a metal surface is 4.125 eV. The cut off wavelength for this surface is
Work function W0 = hc/λ
∴ λ = hc/Wo = 12400/4.125 = 3000 Å
A man runs towards a mirror with a speed of 15 m-s-1. What is the speed of his image?
In the propagation of light waves, the angle between the direction of vibration and plane of polarisation is
Which of the following does not give red ppt. with Fehling solution?
Which of the following statements is correct regarding ease of dehydration?
An aldehyde on oxidation gives
The reaction/method that does not give an alkane is
Which of the following compounds does not react with NaHSO₃?
1-Butene may be converted to butane by reaction with
Scurvy is caused due to the deficiency of vitamin
The set of numerical coefficients that balances the chamical equation K₂CrO₄ + HCl → K₂Cr₂O₇ + KCl + H₂O
Irrespective of the source, pure sample of water always yields 88.89% mass of oxygen and 11.11% mass of hydrogen. This is explained by the law of
phospholipids are esters of glycerol with
Enzymes, in the living systems
Identify the reaction in which the heat liberated corresponds to the heat of formation ( Δ H )
Formic acid when treated with H₂SO₄ gives
When propanamide reacts with Br₂ and NaOH then which of the following compounds is formed ?
Vinegar made from cane sugar, now-a-days synthetically contains
The rate, at which a substance reacts at constant temperature, depends upon its
A liquid is in equilibrium with its vapour at its boiling point. The molecules in these two phases will have equal
Which of the following is not correct?
In which one the following reactions does the heat change represents the heat of formation of water
Which of the following Fischer's projection formula is identical to D-glyceraldehyde ?
The propellants in which fuel and oxidiser are allowed to combine at the time of combustion are
If the pressure on a NaCl structure is increased, then its co-ordination number will
The IUPAC name of [Cr(NH₃)₆]3+ is
Alkyl cyanides are
The colour of p-aminoazobenzene is
If hydrogen electrode dipped into solution of pH = 3 and pH = 6 and salt bridge is connected the e.m.f. of resulting cell is
The standard oxidation no. of the most electronegative element in the products of the reaction BaO2 and dil. H2SO4 is-
Reaction between BaO2 and H2SO4 is
BaO2 + H2SO4 → BaSO4 + H2O2
The most electron negative element in products is oxygen
Oxidation no. of O in BaSO4 and H2O2 is -2 and -1 respectively
tert-Butyl methyl ether on heating with HI of one molar concentration gives
Standard electrode potentials are
Fe2+/Fe (Eo = -0.44 V)
Fe3+/Fe2+ (Eo = - 0.77 V)
Fe2+,Fe3+ and Fe blocks are kept together,then
The rate of diffusion of methane at a given temperature is twice that of a gas X. The molecular weight of X is
Nickel is purified by thermal decomposition of its
Sodium hexametaphosphate is known as
In the chemical reaction Ag₂O + H₂O + 2e- → 2Ag + 2OH-
Silicon is an important constituent of
What is the catalyst used during the manufacture of nitric acid by Ostwald's method ?
The 8 : 8 type of packing is present in
Number of optically active isomers of tartaric acid
Bonding in ferric chloride is
Which of the following is a hydrophilic colloidal sol?
The metal which is not ferromagnetic is
Find the antonym of BASE
Fill in the blank with appropriate word.
The man is so ill that he can.........walk.
Find the synonym of AUDACIOUS
Out of the given alternatives, choose the one which can be substituted for the given capitalised word.
He cannot MAKE BOTH ENDS MEET.
Improve the sentence by choosing best alternative for capitalised part of the sentence.
When the solider returned home after the war was over, his wife received him WITH OPEN HANDS.