### Straightline Shortest distance

Set S contains points whose abscissa and ordinate are both natural numbers. Point P, an element in set S has the property that the sum of the distances from point P to the point (3,0) and the point (0,5) is the lowest among all elements in set S. What is the sum of abscissa and ordinate of point P?

- 2
- 3
- 5
- 4

**Correct Answer**Choice (D).

4 Correct answer- Explanatory Answer
- Integer coordinates
- Hard

### Coordinate Geometry and Probability

Region R is defined as the region in the first quadrant satisfying the condition 3x + 4y < 12. Given that a point P with coordinates (r, s) lies within the region R, what is the probability that r > 2?

**Correct Answer**Choice (A).

Correct answer- Explanatory Answer
- Geometric Probability
- Hard

### Coordinate geometry and greatest integer function

Region Q is defined by the equation 2x + y < 40. How many points (r, s) exist such that r is a natural number and s is a multiple of r?

- 84
- 92
- 105
- 72

**Correct Answer**Choice (B).

92 Correct answer- Explanatory Answer
- Integer values
- Hard

### Angle bisector theorem

What is the equation of a set of points equidistant from the lines y = 5 and x = –4?

- x + y = –1
- x – y = –1
- x + y = 1
- –x + y = –1

**Correct Answer**Choice (C).

x + y = 1 Correct answer- Explanatory Answer
- Points equidistant from lines
- Hard

### Area under curve

What is the area enclosed in the region defined by y = |x – 1| + 2, line x = 1, X–axis and Y–axis?

- 5 sq units
- 2.5 sq units
- 10 sq units
- 7 sq units

**Correct Answer**Choice (B).

2.5 sq units Correct answer- Explanatory Answer
- Modulus graph
- Medium

### Area of segment

Find the area of the region that comprises all points that satisfy the two conditions x

^{2}+ y^{2}+ 6x + 8y ≤ 0 and 4x ≥ 3y.- 25π
- None of these

**Correct Answer**Choice (C).

Correct answer- Explanatory Answer
- Circle and chord
- Hard

- Percents Profits & Interests
- DI - Bar Graphs
- Geometry
- VA - Sentence Rearrangement
- Speed Time Races
- DI - Pie Charts
- Coordinate Geometry
- VA - Sentence Elimination
- Ratio Mixtures, Averages
- DI - Multiple Graphs
- Trigonometry
- VA - Sentence Correction
- Logarithms and Exponents
- DI - Word Problems
- Mensuration
- VA - Para Completion
- Pipes Cisterns
- DI - Line Graphs
- Permutation; Probability
- VA - Text Completion