**Numbers **

**Given that the units digit of 14 × N is same as the tens digit of 20 × M. If the unit’s digit of 3 × N is 8, then what is the unit’s digit of 4 × M?**

**Given that the units digit of 14 × N is same as the tens digit of 20 × M. If the unit’s digit of 3 × N is 8, then what is the unit’s digit of 4 × M?**

**When the curves x ^{3} – 2x^{2} – 11x + 12 and x^{3} – 3x^{2} + 4 are plotted, which of the following statements is correct ?**

If x and y are real numbers, find the number of solutions of the equation x^{2} + 2y^{2} – 2xy – 2x + 2 = 0

**1. No solution **

**2. One solution **

**3. Two solutions **

**4. Four solutions**

There is an escalator going up from the ground floor to the first floor. Varsha is climbing up the escalator while Sumit is climbing down (from the first floor to the ground floor) on the same escalator. On a stationary escalator, the time taken by Sumit to climb 8 steps is same as the time taken by Varsha to climb 6 steps. On the moving escalator, if Varsha takes 18 steps to reach the first floor while Sumit takes 60 steps to reach the ground floor, how many steps are there on the escalator?

The individual earnings of A, B and C are in the ratio 3 : 5 : 8 and their individual spending are in the ratio 2 : 3 : 5. If the individual earnings of A is equal to the individual spending of C, then what is the ratio of the individual savings of B and C?

How many different positive integral values, less than 1000, y = x[x] can take where x is a positive real number.

**Note:- [x] is greatest integer less than or equal to x**

**For eg. [3.5] = 3, as 3 is the largest integer less than or equal to 3.5**

**Similarly [4] = 4, [3.99] = 3
1. 31
2. 496
3. 30
**

**Two of the sides of a scalene triangle are 14 and 16. How many different integral values third side can take?**

How many solution the following equation will have (4x² + 6x + 4)(4y² – 12y + 25) = 28 ?