If *f* is a realvalued differentiable function satisfying *|f(x) - f(y)| <= (x-y) ^{2}, x, y*

**R**and

*f(0)*= 0, then

*f(1)*equals

An element crystallise in F.C.C whose crystal density 5.2 gm/cm^3 and limiting length is 300 pm.Calculate number of atoms present in 105.65 gm of an element.

Gold Au(197) crystallises in F.C.C whose crystal density is 19.3 gm/cm^3 .Calculate atomic radius of gold atom.

Li has a bcc structure. its is 530 kg and its atomic mass is 6.94 g/mol . Calculate length of a unit cell of lithium meta

A man throws balls with the same speed vertically upwards, one after the other at an interval of 2 seconds. What should be the speed of the throw so that more than two balls are in the sky at any time? (Given g = 9.8 m/s2)

A ball is projected upwards from a height h above the surface of the earth with velocity v. The time at which the ball strikes the ground is

A stone is dropped from a minar of height h and it reaches after t seconds on earth. From the same minar if two stones are thrown (one upwards and other downwards) with the same velocity u and they reach the earth surface after t1 and t2 seconds respectively, then

A car is moving with c/2 a stone is thrown from the car with speed c/root 2 at 45 degree with the direction of velocity of the car. What is the angle as seen from the ground?

If *f(x + y) = f(x) .f(y) x, y and f(5) = 2,*

*f'(0) = 3*, then

*f*is

**'**(5)

The maximum distance from origin of a point on the curve *x = a sint – b sin(at/b) *

*y = a cost – b cos(at/b)*, both *a, b > 0* is

If *f(1)* *= 1*, *f'(1) = 2*, then what is ?

*f(x)* and *g(x)* are two differentiable function on [0, 2] such that *f ^{n}(x) - g^{n}(x)* = 0,

*f'(1) = 2g' (1)*= 4,

*f*(2) = 3

*g*(2) = 9 then

*f(x) – g(x)*at

*x*= 3/2 is

*f* is defined in [–5, 5] as ,

([x] denotes greatest integer less than or equal to x)

The first two terms of a geometric progression add up to 12. The sum of the third and the fourth terms is 48. If the terms of the geometric progression are alternately positive and negative, then the first term is

In a geometric progression consisting of positive terms, each term equals the sum of the next two terms. Then what will be the common ratio of this progression?

The sum of the series upto infinity is

If *a _{1} , a_{2} , ..., a_{n}* are in H.P., then the expression

*a*is equal to

_{1}a_{2}+ a_{2}a_{3}+ ... + a_{n-1}a_{n}

Let *a _{1} , a_{2} , a_{3} ,* ... be terms of an A.P. If then equals

If the function *f(x) = 2x ^{3} – 9ax^{2} + 12a^{2}x + 1*, where

*a > 0*, attains its maximum and minumum at

*p*and

*q*respectively such that

*p*then

^{2}= q,*a*equals?

If *f(x) = x ^{n}*, then the value of is

If then what is the value of k?

If *2a+ 3b+ 6c= 0* *(a,b,c R)* then the quadratic equation *ax ^{2} + bx + c = 0* has

Let *f(2)* = 4 and *f '(2)* = 4 then equals

A car starts moving rectilinearly, first with acceleration 5 m/s^2 (the initial velocity is equal to zero), then uniformly , and finaly , decelerating at the same rate, comes to stop.Total time of motion equals to 25 sec . The avg velocity during that time is equal to 72 km/hr .How long does the car move uniformly?

Which is the smallest element in the periodic table and why ???

Find the angle of projection at when horizontal range and maximum height of a projectile are equal?

A swimmer wants to reach to a point just opposite on the other bank of the river. How should he swim and why?

A ball is dropped gently from the top of tower and another ball is thrown horizontally at same time.Which ball will hit the ground first?

A stone is projected horizontally with 20 m/s from top of a tall building. Calculate its position and velocity after 3 sec neglecting the air resistance?

A stone is projected horizontally with 20 m/s from top of a tall building. Calculate its position and velocity after 3 sec neglecting the air resistance?

If the displacement of a body is proportional of square of time, state whether the body is moving with uniform velocity or uniform acceleration?

Two stones P and Q of different masses m and 2m respectively are dropped simultaneously from top of a tower and reach the ground with different energies . Which one is faster?

Can an object with constant acceleration reverse its direction of travel ? Explain

If the constant of gravitation (G), Planck's constant (h) and the velocity of light (c) be chosen as fundamental units. The dimensions of the radius of gyration is

The magnitude of any physical quantity

What is the relationship between dyne and newton of force?

Wavelength of ray of light is 0.00006 m. It is equal to

X = 3YZ*Z find dimensions of Y in (MKSA) system, if X and Z are the dimensions of capacity and magnetic field respectively

Number of particles crossing unit area perpendicular to X-axis in unit time is given by

n =

are number of particles per unit volume in the position x1 and x2. Find dimensions of D called as diffusion constant

If L, C and R represent inductance, capacitance and resistance respectively, then which of the following does not represent dimensions of frequency?

A projectile is launched with an initial velocity of 30 m/s at angle of 60 degree above the horizontal. Calculate the magnitude and direction of its velocity 5s after launch?

An object is dropped from the top of the tower of height 156.8 m and the same time another object is thrown vertically upward with velocity of 78.1 mm/s from the foot of the tower, find when and where two object meet?

A cannon fires successively two shells from the same point with velocity v0 = 250m/s ; the first at the angle =60° and the second at the angle =45° to the horizontal, the azimuth being the same. Neglecting the air drag, find the approximate time interval between firings leading to the collision of the shells (g = 9.8 m/s2.)

A block of mass m is pulled on an incline surface having coefficient of friction = 1 & angle of inclination = 30°, with the horizontal, such that required external force is minimum. The angle made by this force with the incline is :

A particle is projected with speed 30m/s at angle 22.5° with horizontal from ground as shown. AB and CD are parallel to y-axis and B is highest point of trajectory of particle. CD/AB is

Each of the two block shown in the figure has mass m. The pulley is smooth and the coefficient of friction for all surfaces in contact is . A constant horizontal force P applied in two cases shown in such a way that block A start just sliding then the value of minimum force P in case-I and case-II is :

Let T_{r} be the *r ^{th}* term of an A.P. whose first term is

*a*and common difference is

*d*. If for some positive integers

*m, n, m n, Tm = 1/n*and

*Tn = 1/m,*then

*a – d*equals