-
What is the maximum possible value of a positive integer n,such that for any choice of seven distinct elements from {1,2,....n}, there will exist two numbers x and y satisfying 1<x/y≤2? ...
-
Consider 6 points located at A=(0,0),B=(0,4),C=(4,0),D=(-2,-2), E=(3,3) and F=(5,5).Let R be the region consisting of all points in the plane whose distance from A is smaller than that from any other of the given points (othe ...
-
Compute the maximum area of a rectangle which can be inscribed in a triangle of area M. ...
-
A real valued function f is defined on the interval (-1,2).A point x is said to be a fixed point of f if f(x)=x.Suppose that f is a differentiable function such that f(0)>0 and f(1)=1.Show that if f'(1)>1,then f has a f ...
-
FIND THE LOCUS OF THE COMPLEX NUMBER FOLLOWING THE RELATIONS arg(z-1)=pi/4 AND |z-2-3i|=2. ...
-
lim sin[x]/[x] as x→0 ...
-
SOLVE dy/dx=1/(x^2+y^2) ...
-
If a,b,c are integers and are the sides of a right angle triangle,where c is the largest,prove that the area of that triangle is divisible by 6. ...
-
let nCk denote the binomial coefficient and F[m] be the mth fibonaki number given by F[1]=F[2]=1 and F[m+2]=F[m]+F[m+1] for m≥1.Show that ∩(nCk)=F[m+1] for all m≥1. where n≥k≥0 and n+k=m ...
-
let a1,a2,........an be integers.Show that there exists integers k and r such that the sum ak,ak+1,ak+2+.........ak+r is divisible by n. ...
-
i,j positive integers f(i,i+1)=1/3(for all i) f(i,j)=f(i,k)+f(k,j)-2f(i,k)(k,j) Find the value of f(1,100) ...
-
show that ∫[sspi][/ss0]|(sin nx)/x|dx ≥ (2/pi)|1+(1/2)+(1/3)+.......(1/n)| ...
-
let f(x)=∫(0 to 1)|t-x|tdt for all real x. What is the minimum value of f(x). ...
-
*Image* ...
0·0·
-
A short linear object of length l lies along the axis of a concave mirror of focal length f at a distance u form the pole of the mirror. The size of the image is approximately equal to ...
-
Let a, b, c bc non-zero real numbers such that int_{,0}^{,3} {} (3,a{x^2} + 2,bx + c),,dx = int_{,1}^{,3} {} (3,a{x^2} + 2,bx + c),,dx, then ...
-
A rectangular loop with a sliding connector of length l = 1.0 m is situated in a uniform magnetic field B = 2T perpendicular to the plane of loop. Resistance of connector is r = 2W. Two resistance of 6W and 3W are connected a ...
-
A current carrying loop is placed in a uniform magnetic field in four different orientations, I, II, III and IV, arrange them in the decreasing order of potential energy *Image* ...
-
A non-planar loop of conducting wire carrying a current i is placed as shown in the figure. Each of the straight sections of the loop is of length 2a. The magnetic field due to this loop at the point P (a, 0, a) points in the ...
-
A long straight wire along the z-axis carries a current i in the negative z direction. The magnetic vector field vec{B} at a point having coordinates (x, y) in the z = 0 plane is ...
-
Two infinitely long insulated wires are kept perpendicular to each other. They carry currents i1 = 2 A. and i2 = 1.5 A. Find the direction and magnitude of magnetic field produced at P *Image* ...
-
In an oil experiment,oil droplets of mass m and charge q are droped from a height h at intervals ∂t> ( 2*h)/g . This drops are collected on a large hollow sphere of radius R,through a small hole on the surface of the sph ...
-
tan(cos-1x) = sin(cot-11/2), x is ...
-
A ROD OA OF LENGTH L IS STANDING ON A SMOOTH GROUND.A SLIGHT JERK SETS THE IN MOTION. THERE IS A POINT P ON THE ROD WHOES LOCUS IS A CIRCLE IN THE SUBSEQUENT MOTION.LOCATE P. ...
