The power factor of an A.C. circuit having resistance (R) and inductance (L) connected in series and an angular velocity is ω is
Which of the following radiation series is found in the visible region?
A mass of 12Kg at rest explodes into two pieces of masses 4Kg and 8Kg which move in opposite directions. If the velocity of 8Kg piece is 6 ms^{1}, then the kinetic energy of the other piece in joules is
(Hint : Apply law of conservation of momentum)
A copper wire of resistance R is cut into ten parts of equal length. Two pieces each are joined in series and then five such combinations are joined in parallel. The new combination will have a resistance
Two racing cars of masses m₁ and m₂ are moving in circles of radii r₁ and r₂ respectively. Their speeds are such that each makes a complete circle in the same duration of time t. The ratio of the angular speed of the first to the second car is
The effective value of a.c. in a circuit is 10 A. The peak value of current is
4 eV is the energy of the incident photon and the work function in 2 eV. What is the stopping potential
To keep constant time, watches are fitted with balance wheel made of
The binary number 110000111101 corresponds to a hexadecimal number:
The force of gravitation is
A body of mass 100 g is sliding from an inclined plane of inclination 30º. What is the frictional force experienced if μ=1.7
A charged particle of mass 5 x 10^{−6} Kg is held stationary in space by placing it in an electric field of strength 10^{6} NC^{−1} directed vertically downwards. The charge on the particle is (g = 10ms^{−2})
A black body of surface area 10 cm^{2} is heated to 127ºC and is suspended in a room at temperature 27ºC. The initial rate of loss of heat from the body to the room will be
Mean kinetic energy (or average energy) per gm molecule of a monoatomic gas is given by
A block of mass M is pulled along a horizontal frictionless surface by a rope of mass m. If a force P is applied at the free end of the rope, then force exerted by the rope on the block is
Susceptibility is positive and large for a
Water is flowing over a fixed horizontal surface. If the velocity gradient at a distance 10 cm above the surface is 2 s⁻^{1}, then velocity of layer will be
When a charged particle moves perpendicular to a magnetic field, then
A ball is dropped on to the floor a height of 10 m. It rebounds to a height of 2.5 m. If the ball is in contact with the floor for 0.01 seconds, what is the average acceleration during contact?
Consider the following statements
Assertion (A) : On a rainy day, it is difficult to drive a car or bus at high speed
Reason (R) : The value of coefficient of friction is lowered due to wetting of the surface
Of these statements
A man fires a bullet of mass 200 g at a speed of 5 m/s. The gun is of one kg mass. by what velocity the gun rebounds backwards
To make the frequency double of a spring oscillator, we have to
An aeroplane is flying at a constant horizontal velocity of 600 km/hr at an elevation of 6 km towards a point directly above the target on the earth's surface. At an appropriate time, the pilot releases a ball so that it strikes the target at the earth. The ball will appear to be falling
In a streamline flows if the gravitational head is h. The kinetic and pressure heads are
The surface tension of a liquid is 70 dynes/cm. It may be expressed in MKS system as
A beam of light incident on a plane mirror forms a real image on reflection. The incident beam is
A dancer on ice spins faster when she folds her arms. This is due to
If pressure at half the depth of a lake is equal to 2/3 pressure at the bottom of the lake then what is the depth of the lake
Pressure at bottom of the lake
= P_{0} + hρg
and pressure at half the depth of a lake
The pressure of a gas in a closed vessel is increased by 0.4%, if the temperature of the gas is increased by 1º C , the initial temperature of the gas is
A constant voltage is applied on a uniform wire, then the heat is produced. The heat so produced will be doubled, if
Critical temperature may be defined as the temperature
Dimensions of the following three quantities are the same
A train is approaching a platform with a velocity ν. The frequency heard by an observer standing at the station is
Equation of the progressive wave is given by : y = a sin π(40t  x) where a and x are in metre and t in second. The velocity of the wave is
n small balls each of mass m impinge elastically each second on a surface with velocity u. The force experienced by the surface will be
The compound which can form intramolecular hydrogen bond is
Which of the following reagents reacts differently with HCHO, CH_{3}CHO and CH_{3}COCH_{3}?
When CHCl₃ is boiled with aqueous NaOH, it gives
Ferric ion forms a prussian blue coloured ppt. due to
The reaction of benzene with methyl chloride in presence of aluminium chloride is known is
The reaction, CH₂ = CHCH₃ + HBr → CH₃CHBr  CH₃ is
The values of four quantum numbers of valence electron of an element X are n = 4, l = 0, m = 0, s = + 1/2 . The element is
A strangth chain hydrocarbon has the molecular formula C_{8}H_{10}. The hybridisation for the carbon atom from one end of the chain to the other are respectively sp^{3},sp^{2},sp^{2},sp^{3},sp^{2},sp^{2}, sp and sp. The structure of the hydrocarbon is.
Which one of the following statements about fats is incorrect ?
Which of the following salt can be produced by the reaction of CO and caustic soda ?
According to VSEPR theory, shape of AB _{3} molecule with one lone pair of electrons on A is
Free energy change for a reversible process is
Diazonium salt decomposes as C_{6}H_{5}N_{2}^{+}Cl^{−} → C_{6}H_{5}Cl + N_{2} . At 0ºC, the evolution of N_{2} becomes two times faster when the initial concentration of the salt is doubled. Therefore, it is
For a first order reaction
r = k[A]
Hence when conc. of (C_{6}H_{5}N_{2}^{+}Cl^{−})is doubled the conc. of nitrogen gets doubled.
A and B are gaseous substances which react reversibly to give two gaseous substances C and D,accompanied by the liberation of heat.When the reaction reaches equilibrium,it is observed that K_{p} = K_{c}.The equilibrium cannot be disturbed by
Identify the correct statement regarding entropy
IUPAC name of CCl₃CH₂CHO is
Which of the following could act as a propellant for rockets?
Al^{3+} has a lower ionic radius than Mg^{2+} ion because
Al^{3+} has a higher nuclear charge (+ 13) and consequently the larger force of attraction by the nucleus for the valence shell electrons than that of Mg^{2+} (+ 12).
Corrosion is basically a
Dalton's law of partial pressure is not applicable to
Bond length Ethane (I), Ethene (II), Acetylene (III) and Benzene (IV) follows the order
In radioactive delay, which one of the following moves the fastest?
An organic compound will show optical isomerism if
Which buffer solution out of the following will have pH > 7?
Aniline reacts with KOH and phosgene to form
Maximum number of active hydrogens are present in
Select correct statements(s):
The fibre obtained by the condensation of hexamethylene diamine and adipic acid is
If 0.183 of an aromatic monobasic acid requires 15ml of N/10 sodium hydroxide for complete neutralisation, then molecular weight of the acid is
When iron or zinc is added to CuSO₄ solution, copper is precipitated. It is due to
A semiconductor of Ge can be made ptype by adding
Commerical HCl is said to be 12 N. If 8.3 c.c. of this acid is dissolved in water to make one litre solution, the normality of the resulting solution is
There is more deviation in the behaviour of a gas from the ideal gas equation PV = nRT
2 gram of sulphur is completely burnt in oxygen to form SO_{2}. In this reaction what is the volume of oxygen consumed at STP in litres
In chemisorption, adsorption decreases after increase due to
For all real x, the minimum value of 1  x + x^{2}/1 + x + x^{2} is
To expand (1+2x)⁻^{1}/^{2} as an infinite series, the range of x should be
The area bounded by the curve y^{2} = 9x and the lines x = 1, x = 4 and y = 0 in the first quadrant is
The incentre of triangle whose vertices are (0,0), (5,12) and (16,12) is
The equation of the circle whose centre is (0,0) and which passes thro' the point (4,5) is
The complex numbers 1,1,i√3 form a triangle which is
The tangent to the parabola y^{2}=4ax and perpendicular line from the focus on it meet
The volume of a solid which is obtained by revolving area bounded by an ellipse x^{2}+9y^{2}=9 and straight line x+3y=3 about yaxis is
Given that the function f defined by is continuous . Then the value of k is
The order of the differential equation x^{2}+y^{2}+2gx+2fy+c=0, is
If y=log logx, e^{y}(dy/dx)=
The matrix having the same matrix as its inverse is
sec^{2}(tan⁻^{1} 2) + cosec^{2}(cot⁻^{1} 3) =
If A is singular matrix of order n, then a (adj A) equals,
The maximum value of [(logx)/x] is
For the given data : 1, 1, 0, 2, 3, 5, 5, 6, 8, 10, 11
Mode = Median = 5
The first quartile derived from a set of observations is 27 and its quartile deviation is 17. What is its third quartile?
Equation 9x^{2}6xy+y^{2}+18x6y+8=0 represents a pair of parallel lines, then distance between them is
In how many ways can a book or more than one book be chosen from 6 books?
If two dice are thrown, find the probability of getting an odd number of on one and multiple of 3 on the other is
If in a ∆ABC cosA=sinB cosC, then
If A = {1,2,3,4,5}, then the number of proper subsets of A is
α,β are be the root of x^{2}3x+a = 0 and γ, δ are the root of x^{2}12x+b = 0 and numbers α,β,γ,δ (in order) form an increasing G.P., then
If A is the single A.M. between two numbers a and b and S is the sum of n A.M.'s between them, then S/A depends upon
If y = then is given by 
The triangle formed by the tangent to the curve f(x) = x^{2} + bx  b at the point (1, 1) and the coordinate axes,lies in the first quadrant. If its area is 2, then the value of b is
A straight line makes angle 135º with xaxis and cut yaxis at distance 5 form origin. The equation of line is
The mean of a binomial distribution is 5, then its variance has to be
The number of roots of the equation x + 2 tanx = ( π/2 ) in interval [(0), (3 π/2 )] is
we have 2 tan x = π/2  x
the equation in the right hand side is a straight line from (0, π/2 ) to ( π/2 , 0) and further to (2π,  3π/2 )
2 tan x (which is almost same as tan x), as x goes from 0 to π/2 , the value increases from 0 to ∞ and will intersect once in between.
from π/2 to π, 2 tanx comes from ∞ to 0 and will intersect again as the line will also be below x axis.
from π to 3π/2 , 2 tan x is above x axis and line is below x axis and hence, no point of intersection.
Hence, there are 2 roots of this equation
The unit vector perpendicular to each of the vectors 2îĵ+k̂ and 3î+4ĵ is
sin50°sin70°+sin10°=
If a = i + 2 j + 3k, b =  i + 2 j + k and c = 3 i + j and a + tb is perpendicular to c, the value of t is
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