Find the remainder when the number (289n + 119) is divided

If a³ = 117 + b³ and a = 3 + b, then the value of a + b is:

The simple interest accrued on a sum at the rate of 10% p.a. for two years is Rs. 5,000.

If 8x² + y² − 12x − 4xy + 9 = 0, then the value of (14x − 5y) is :

If 2y cos θ  = x sin θ  and 2x sec θ -  y cosec θ  = 3, then the value of x²+ 4y² is

If P = 7 + 4√3 and PQ = 1, then what is the value of 1/P² + 1/Q²?

The total number of even factors of 2⁵ × 3³ × 5² is:

If x⁴ + 2x³ + ax² + bx + 9 is a perfect square, where a and b are positive real numbers, then the value of a and b are

Which is the largest six digit number, which when divided by 12, 15, 20, 24 and 30, leaves the remainders 8, 11, 16, 20 and 26 respectively.

If a³ + 3a² + 9a = 1, then what is the value of a³ + (3/a)?

If a + b² + c² = 16, x² + y² + z² = 25 and ax + by + cz = 20, then the value of (a+b+c)/(x+y+z)