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The line joining A(b cosα , b sinα) and B( a cosβ,a sinβ) is produced to point M(x,y) so that AM:MB = b:a, then what's the value of x cos α+β/2 + y sin α+β/2 ???? ...

$\textbf{In a $\mathbf{\triangle ABC},$ Prove that }$\\\\ \mathbf{\frac{1+Cos\;B\cdot Cos\;C}{1+cos \;A}+\frac{1+Cos\;C\cdot Cos\;A}{1+cos \;B}+\frac{1+Cos\;A\cdot Cos\;B}{1+cos \;C}\geq \frac{5}{2}}$ ...

1+ 2+ 3+ 4+.......∞ how to evaluate dis?? ...

Show that : sin5x+cos5x+sin4x≤2 for all values of x, ...

Q: Let f : [0,1] → R is a continuous function such that \int_{0}^{1}{f(x) dx=0} . Prove that there is some ' c ' ε (0,1) such that \int_{0}^{c}{f(x) dx} = f(c) ...

Q: (x4y2-y) dx + (x2y4-x) dy = 0 Q: \int \frac{x dx}{log x . sec x} ...

Q:1) *Image* Q:2) *Image* Q:3) *Image* Give A, X , and Product(s) if any. More will follow ...

Let f be twice differentiable in [0,2]. show that if f(0)=0,f(1)=2, f(2)=4, then there is an 'x' in (0,2) such that f''(x)=0 ...

Determine all pairs (a,b) of positive integer such : a2/2ab2-b3+1 positive integer ...

Here an Isosceles triangle is inscribed in a square. The angle A is given by 15 degree... prove that the triangle formed below is an equilateral triangle. *Image* ...

A plank of mass 'M' is placed on a smooth surface and a cylinder of mass 'm' and radius 'R' placed over the plank. now there is a horizontal force 'F' acting on the plank towards right. if the cylinder does not slip over the ...

1)Find all function from +ve reals to the same satisfying f(f(x)-x) = 2x for all x>0 2) f is a function from the set of natural numbers to the same. satisfying f(n+1)>f(f(n)) for all natural number n. Prove that f(n) = ...

Use the mean value theorem to prove that |sinx-siny| ≤|x-y| for all real numbers x,y ...

fin ...

The standard reduction potential of Li+/Li, Ba2+/Ba, Na+/Na & Mg2+/Mg are -3.03, -.73, -2.71 and -2.37 volt respectively. Which one is the strongest oxidizing agent? ...

A CHARGE q is istributed uniformly over a large plastic plate.The electric feidl at point P,which is near the centre is 10V/m.Now the plate is replaced bya copper one and all the conditions of the previous problem are exact. ...

Displacement of a particle in one dimension under action of a constant force is related to time t by eq. t= x +3 where x is in m and t in sec. a> Find the displacement of a particle when its velocity is 0. ...

a balloon of mass m is found to accelerate up at the rate of g/6. the quantity of water that should be put inside the balloon so that it may accelerate downwards at the rate of g/6 is: ...

What is the nth term of 1,2,3,6,24,108 ......? ...

can anyone tell me some info about the actuary course. who can apply, how to apply, etc etc. ...

A triangle has all its sides as integers marked l,m,n with l>m>n. Also given that \left\{\frac{3^l}{10^4} \right\}=\left\{\frac{3^m}{10^4} \right\}=\left\{\frac{3^n}{10^4} \right\} Find the minimum perimeter of the tria ...

\int \left(tan^{-1}x \right)^{2}dx ...

1) Ph=N=C=O ----(1. CH3MgBr)----> ----(2. H2O------> 2) Ph--Br ----(Mg)---> A --(1. C*H3COCH3)---(2.H+)---(3.heat)---> B B------(NBS)---->C-----(AgNO3/H2O)---->D D-----(O3/H2O, Zn)---------> E + F Identif ...

A lighthouse, facing north, sends out a fan-shaped beam of light extending fron north-east to north-west. An observer on a steamer, sailing due west, first sees the light when he is 5 km awayfrom the lighthouse, and continues ...

*Image* + HBr ------(in Non polarizing medium)------> Ph--S--CH2--CH2--CH2--Cl -----(NaOD/D2O)-----> *Image* ...

By using the concept of slope, prove that the diagonals of a rhombus are at right angles. ...

a uniform disc of radius R is first spinned to ang velocity 'w'. and the placed with its flat face on the horizontal surface. how long will the disc be rotating if the friction coeff = 'u'. ...

a ...

Let f(x) be a continuous function such that f(x) does not vanish for all real values of x if *Image* then f(x) (for all x ε R) is (a) an even function (b) an odd function (c) a periodic function (d) None of these Ans: (d) ...

sin^3x+sin^2x+sinx=1 ...