How many 4 - letter words (with or without meaning) containing two vowels can be constructed using only the letters (without repetition) of the word 'LUCKNOW'?

Suppose 20 distinct points are placed randomly on a circle. Which of the following statements is/are correct?

1. The number of straight lines that can be drawn by joining any two of these points is 380.

2. The number of triangles that can be drawn by joining any three of these points is 1140.

Select the correct answer using the code given below.

How many terms are there in the expansion of $\rm \left(\frac{a^2}{b^2}+\frac{b^2}{a^2}+2\right)^{21}$ where a ≠ 0, b ≠ 0? 

For what values of k is the system of equations 2k²x + 3y - 1 = 0, 7x - 2y + 3 = 0, 6kx + y + 1 = 0 consistent?