If `W=2^4 .3^2 .5` then number of factors of `W^2` which are less than W but are not factors of W is:

If three resistors having resistances 2 Omega, 3 Omega and 5 Omega are connected in parallel, then will the value of the total resistacne be less than 2 Omega , or greater than 2 Omega or lie between 2 Omega and 5 Omega ? Explain.

Prove the following (1- omega + omega^(2)) (1- omega^(2) + omega^(4)) (1- omega^(4) + omega^(8)) …. to 2n factors = 2^(2n) where , ω is the cube root of unity.

Demonstrate thatat low damping the quality factor Q of a circuit maintaining forced oscillations is approximately equal to omega_(0)//Delta omega , where omega_(0) is the natural oscillation frequency , Delta omega is the width of the resonance curve I(omega) at the " height " which is sqrt(2) times less than the resonance current amplitude.

In an R.C. circuit resistance = 4 Omega and XC = 3 Omega , then power factor is

Given that R_1 = 2 Omega, R_2 = 3 Omega and R_3 = 6 Omega , combinations which will give an effective resistance of 4 Omega is

Let I, omega and omega^(2) be the cube roots of unity. The least possible degree of a polynomial, with real coefficients having 2omega^(2), 3 + 4 omega, 3 + 4 omega^(2) and 5- omega - omega^(2) as roots is -

Let I, omega and omega^(2) be the cube roots of unity. The least possible degree of a polynomial, with real coefficients having 2omega^(2), 3 + 4 omega, 3 + 4 omega^(2) and 5- omega - omega^(2) as roots is -

Let I, omega and omega^(2) be the cube roots of unity. The least possible degree of a polynomial, with real coefficients having 2omega^(2), 3 + 4 omega, 3 + 4 omega^(2) and 5- omega - omega^(2) as roots is -

If w is an imaginary cube root of unity then prove that If w is a complex cube root of unity , find the value of (1+w)(1+w^2)(1+w^4)(1+w^8)..... to n factors.