In a step-up transformer the turn ratio is 1:10. A resistance of 200 ohm connected across the secondary is drawing a current of 0.5 amps. What is the primary voltage and current
The energy released in a typical nuclear fusion reaction is approximately
A particle is moving on a circular path with constant speed, then its acceleration will be
A ball A moving with a speed of 90 ms-1 collides directly with another identical ball B moving with a speed V in the opposite direction. A comes to rest after the collision. If the coefficient of restitution is 0.8, the speed of B before collision V =
Two electric bulbs A and B rated as 60 W and 100 W. If they are connected in parallel to the same source, then
In a discharge tube at 0.2 mm of Hg pressure, there is a formation of
How much force is required to produce an increase of 0.2% in the length of a brass wire of diameter 0.6 mm (Young's modulus for brass = 0.9 X 1011N/m2)
In a transformer, the number of turns of primary coil and secondary coil are 5 and 4 respectively. If 240 V is applied on the primary coil, then the ratio of current in primary and secondary coil is
The angular velocity of rotation of star at which the matter strat to escape from its equator will be
A crystal oscillator provides a very stable frequency because of
A pulling force making an angle θ to the horizontal is applied on a block of weight W placed on a horizontal table. If the angle of friction is φ, the magnitude of force required to move the body is equal to
The maximum wavelength of radiations emitted at 900 K is 4μm. What will be the maximum wavelength of radiations emitted at 1200 K
The velocity of the molecules of a gas at temperature 120 K is υ. At what temperature will the velocity be 2υ
Two equal charges q each are placed at a distance of 2a. If a third charge-2q is placed at the mid-point, then potential energy of the system is
P.E between q(left) and -2q =
P.E between q(right) and -2q =
P.E between q and q =
∴ Total P.E of the system =
A satellite in a force-free space sweeps stationary interplanetary dust at a rate (dM/dt)=αν. The acceleration of satellite is
Most of the substance show which of the following magnetic property?
A wire in the form of a circular loop, of one turn carrying a current, produces magnetic induction B at the centre. If the same wire is looped into a coil of two turns and carries the same current, the new value of magnetic induction at the centre is
Rain drops are spherical in shape, because of
A ball is thrown upwards and it returns to ground describing a parabolic path. Which of the following remains constant
A aprticle is dropped from a building . It takes 4 seconds for the particle to reach the ground. Then height of the building is (use g = 10 m/s2)
A body is executing simple harmonic motion with an angular frequency of 2 rad-s⁻1. The velocity of the body at 20 mm displacement,when amplitude of motion is 60 mm, is
A pulley fixed to the ceilling carries a string with blocks of mass m and 3 m attached to its ends. The masses of string and pulley are negligible. When the system is released. its centre of mass moves with what acceleration
The horizontal range is four times the maximum height attained by a projectile. The angle of projection is
A force 103 newton stretches the length of a hanging wire by 1 millimetre. The force required to stretch a wire of same material and length but having four times the diameter by 1 millimeter is
An automobile engine develops 100 kW when rotating at a speed of 1800 rev-min⁻1. What torque does it deliver?
A prism of refractive index ' μ ' and angle 'A' is placed in the minimum deviation position. If the angle of minimum deviation is 'A', then the value of 'A' in terms of ' μ ' is
Newton per square metre is the unit of
The surface tension of a liquid at its boiling point
The heat developed in an electric wire of resistance R by a current I for a time t is
The densities of a liquid at 0º C and 100º C are respectively 1.0127 and 1. A specific gravity bottle is filled with 300 gm of the liquid at 0º C upto the brim and it is heated 100º C . Then the mass of the liquid expelled in grams is [Coefficient of linear expansion of glass = 9 x 10 − 6 ∕ º C ]
If the heat of 110 J is added to a gaseous system, change in internal energy is 40 J. Then the amount of external work done is
In S = a + bt + ct2, S is measured in metres and t in seconds. The unit of c is
Soap bubble looks coloured due to
A man is standing between two parallel cliffs and fires a gun. If he hears first and second echoes after 1.5 s and 3.5 s respectively, the distance between the cliffs is (Velocity of sound in air = 340 ms⁻1)
The potential energy of a certain spring when stretched through a distance 'S' is 10 joule. The amount of work that must be done on this spring to stretch it throgh an additional distance 'S' will be
Telephone calls come into an exchange according to a Poisson Process with 5 calls per minute on an average. The probability that no call will come in during the two minute period 10 A.M. to 10 : 02 A.M. on a particular day is
How many isomeric acyclic alcohols and ethers are possible for C₄H₈O?
C₂H₅CHO and (CH₃)₂CO can be distinguished by testing with
In the following reaction X and Y are are respectively,
Action of caustic soda on Al(OH)₃ gives a compound having formula
Consider the ground state of Cr atom (Z=24), the number of electrons with the azimuthal quantum numbers l=1 and 2 respectively:
Benzene reacts with CH3Cl in the presence of anhydrous AlCl3 to form:
The reaction, CH₂ = CH-CH₃ + HBr → CH₃CHBr - CH₃ is
The hydrolysis of fats and oils in the body produces
How many σ and π bonds are there in the molecule of tetracyanoethylene ?
The acid showing salt like character in aqueous solutions is
The compound containing co-ordinate bond is
Which among the following is extensive property of the system ?
If reaction between A and B to give C shows first order kinetics in A and second order in B, the rate equation can be written as
The chemical equilibrium of a reversible reaction is not influenced by
Consider the following statements :
1. Entropy of the universe is continually increasing and tends to a maximum.
2. Total entropy change for a reversible isothermal cycle is zero.
3. In any irreversible cyclic process, there is a decrease in entropy.
Of these statements :
The chloramphenicol is an example of
Select the molecule which has only one π-bond
In a closed flask of 5 litres, 1.0 gm H₂ is heated from 300 to 600 K, which statement is not correct ?
Which of the following shows maximum no. of oxidation states?
The first ionisation potentials of four consecutive elements, present in the second period of the periodic table are 8.3, 11.3, 14.5 and 13.6 eV respectively. Which one of the following is the first ionisation potential (in eV) of nitrogen?
As N has extra stable half-filled electronic configuration (1s2 2s2 2p3) , therefore it is difficult to remove an electron from nitrogen and ionisation potential of N is higher.
When petroleum is heated gradually,the first batch of vapours evolved will be rich in
The solubility of AgCl will be minimum in
The alkane that yields two isomeric monobromo derivatives
The equipment used to carry out nuclear reaction in a controlled manner is called
Aniline in a set of reactions yielded a product D
The structure of D is
The compound which can form intramolecular hydrogen bond is
Most stable free radical is
Which of the following is an example of natural polymer?
The compound formed in the positive test for nitrogen with the Lassaigne's solution of an organic compound is
For the redox reaction MnO₄¯ + C₂O₄²⁻ + H⁺ → Mn²⁺ + CO₂ + H₂O correct stoichiometric coefficients of MnO₄¯ , C₂O₄²⁻ , H⁺ are
Due to Frenkel defect, the density of ionic solids
The process of osmosis was first discovered by
At the same temperature and pressure which of the following gas will have highest K.E. per mole
What volume of H2 gas at 273 K and 1 atm. Pressure will be consumed in obtaining 21.6 of elemental boron (atomic weight=10.8 g) from the reduction of BCl3 with H2 ?
2BCl3 + 3H2 → 2B + 6HCl
Mass of 2 moles of B = 10.8 x 2 = 21.6g
According to equation:
3 moles of H2 gas at STP reacts with BCl2 to give 21.6g of boron
Now, 1 mole of H2 at STP occupies a volume of 22.4L
Therefore, 3 moles will occupy 22.4 x 3 = 67.2L
In physical adsorption, the forces of association are
The curve y = ax3 + bx2 + cx is inclined at 45º to x-axis at (0, 0) but it touches x-axis at (1, 0), then the value of a, b, c are given by
The volume of the solid obtained by rotating the ellipse (x2/a2) + (y2/b2) = 1 about axis of x is
The locus of a point P which moves such that 2PA = 3PB, where A(0,0) and B(4,-3) are point, is
The approx value of (7.995)1∕3 correct to four decimal places is
If the line x+2by+7=0 is a diameter of the circle x²+y²-6x+2y=0, b =
The maximum distance from the origin to the point z satisfying z+(1/z) = 2, is
The difference of focal distances of any point on hyperbola 9x²-16y²=144 is
Let f(x) = Then the number of points of discontinuity of the function f(x)in the open interval (0, π) is
f ′ (x) = x sin 1/x . At all points in 0, π ,f ′ (x) has a definite finite value
∴ f (x) is differentiable finitely in 0, π . . As a finitely differentiable function is also continuous, we get f(x) is continuous in (0, π).
The particular integral of d²y/dx² + dy/dx=x²+2x+4 is :
If A ≠ A2 = I , then det I + A =
If cot⁻1α+cot⁻1β=cot⁻1x, then x=
The value of
If then An =
The C.V of a distribution is 80% and the mean of the distribution is 40, the S.D. of the distribution is
The point on the curve y = x2 which is nearest to (3, 0) is
A population consists of the numbers [2003, 1999, 2001, 1997, 2000, 2005, 1995]. The variance of the population is:
If equation λx2+2y2-5xy+5x-7y+3=0, represents two straight lines, the value of λ is
In how many different ways can the letters of the word 'AUCTION' be arranged so that the vowels always come together?
The probability that a person tossing three fair coins will get either all heads or all tails for the second time on the 5th toss is
Two sides of a triangle are given by the roots of the equation x2 - 5x + 6 =0 and the angle between the sides is π 3 . Then the perimeter of the triangle is
x2 - 5x + 6 = 0
or x2 - 3x - 2x + 6 = 0
or (x - 3) (x - 2) = 0
or x = 3, 2
So a = 3, b = 2, c = ?, ∠ A = π/3
∴ Perimeter of the triangle = a + b + c = 3 + 2 + √7 = 5 + √7
The number of values of k for which the equation x2 - 3x + k = 0 has two distinct roots lying between 0 and 1 is
If three positive real numbers a, b, c are in H.P., then log(a + c) + log (a - 2 b + c) is equal to
If f (x + y + z) = f (x) f(y) f(z) for all x, y, z and if f (2) = 4,f (0) = 5 and f (0) ≠ 0, then f (2) is equal to
The derivative of with respect to tan-1 x is :
The equation of one side of a right angled isosceles triangle whose diagonal and opposite vertex are 3x+4y=4 and (2,2) is
Let gradient of AB be m
y - 2 = 1/7 (x - 2)
⇒ x - 7y + 12 = 0
The number of roots of the equation 2 sin 2θ + 3sinθ + 1 = 0 in (0,2π) is
The angle between the curves xy = 2 and y2 = 4x is
If x=cos 10° cos 20° cos 40°, then x equlas
If P is the modulus of the resultant of two forces which is equal to one and perpendicular to the second, then the second force is
If a.b=b.c=c.a=0, then |abc|=