Mathematics Tes...

The number of times the digit 3 will be written when listing the integers from 1 to 1000 is

If a circle passes through (a, b) and cuts the circle x² + y² = 4 orthogonally, then the locus of its centre is

If p^th, q^th and r^th terms of an AP, respectively are a, b and c, then a(q - r) + b(r - p) + c(p - q) is equal to

In an isosceles triangle ABC, AB = AC. If vertical angle A measures 20°, then what is the value of a³ + b³?

The locus of the point of intersection of the lines x sinθ + (1 – cos θ) y = a sinθ and x sin – (1 + cosθ ) y + a sinθ = 0 is

If gof is continuous, then

Let S = (x – 1)¹⁰ + (x – 1)⁹ (x + 1) + (x – 1)⁸ (x + 1)² + ……. + (x + 1)¹⁰

If O is the sum of coefficients of odd powers of x and E is the sum of the coefficients of even powers of x, which of the following statements is correct?