Mathematics Tes...

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

Suppose a, b, and c are distinct real numbers such that a, 2b, 3c are in AP and a, b, c are in GP. Then, which of the following can be the common ratio of the GP

If \(I_{n}=\int_{0}^{\pi / 4} \tan ^{n} \theta d \theta,\) then \(\lg +1_{6}\) is equal to

C₁ and C₂ are circles of unit radii with centres at (0, 0) and (1, 0), respectively. C₃ is a circle of unit radius, which passes through the centres of the circles C₁ and C₂ and has its centre above the x-axis. The equation of the common tangent to C₁ and C₃, which does not pass through C₂, is

If ⁿC₄, ⁿC₅ and ⁿC₆ are in AP, then the value of n can be

If \(\cos ^{-1}\left(\frac{x^{2}-y^{2}}{x^{2}+y^{2}}\right)=\log a,\) then \(\frac{d y}{d x}\) is equal to

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

Which of the following is a constant term in the expansion of S?

The equation of a circle touching the coordinate axes and the line x cosα + y sinα = 2 is x² + y² – 2gx + 2gy + g² = 0, where g is equal to

The circles x² + y² – 10x + 16 = 0 and x² + y² = r² intersect each other at two distinct points if