Show that if a and b are real, the principal value of arg a is 0 or π according as a is positive or negative and that of bi is `pi/2 or -pi/2` according as b is positive or negative.

The value of xyz is 55 or (343)/(55) according as the series a,x,y,z,b is an AP or HP. Find the values of a and b given that they are positive integers.

Find the interval in which f(x) is positive or negative : f(x) = (x-1)(x-2)(x-3)

a and b are positive integers such that a^3 - b^2 is a prime number. Then a^2 - b^2=

Prove that for any value of a, the inequatiion (a^(2)+3)x^(2)+(a+2)x-6lt0 is true for atleast one negative x .

If A + B+ C = 3 pi//2 , then the value of cos 2 A + cos 2 B + cos2 C is equal to

If a and b are position vector of two points A,B and C divides AB in ratio 2:1, then position vector of C is

If tan theta+sec theta=sqrt(3), 0 lt theta lt pi , then theta is equal to or least positive value of theta is

The principal value of cos^(-1) {1/sqrt2 ("cos"(9pi)/10 - "sin"(9pi)/10)} is :

A and B are two points. The position vector of A is 6b-2a. A point P divides the line AB in the ratio 1:2. if a-b is the position vector of P, then the position vector of B is given by