Mathematics Tes...

It is given that n arithmetic means are inserted between two sets of numbers a, 2b and 2a, b where a, b ∈ R. If the m^th mean between these two sets of numbers is the same, then a : b equals

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

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

Let S₁, S₂, … be squares such that for each n ≥ 1, the length of a side of S_n equals the length of a diagonal of S_{n + 1}. If the length of a side of S₁ is 10 cm, then the smallest value of n for which Area (S_n) < 1 is

If A and B are two matrices such that AB = B and BA = A, then A² + B² 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 terms independent of x in the expansion of E are in

The coefficient of x^k in the expansion of E = 1 + (1 + x) + (1 + x)² + … + (1 + x)ⁿ is

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?

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