**Q1. **

(a) 8

(b) –8

(c) 4

(d) –4

**Q2. **

(a) 24

(b) 24.25

(c) 24.5

(d) 24.75

**Q3.**

(a) 9 : 4

(b) 3 : 4

(c) 9 : 8

(d) 8 : 3

**Q4. If the circumcenter of a triangle lies on one of the sides then the orthocenter of the triangle lies on. **

(a) One of the vertices

(b) On the same side of the triangle

(c) Outside of the triangle

(d) Strictly inside the triangle

**Q5. The circumcenter and the orthocenter of a triangle coincides. Then **

(a) The centroid also coincides with them

(b) The centroid will be different from them

(c) The triangle is isosceles

(d) The triangle is a right angle triangle

**Q6. **

**Q7. **

**Q8. If RS is the diameter of the circle and ∠ PQS = 32° and PQ = PS. If then find the value of the ∠QSR =?**

(a) 30°

(b) 60°

(c) 26°

(d) 40°

**Q9. AB is a vertical pole and C is its middle point. The end A is on the level ground and P is any point on the level ground other than A the portion CB subtends an angle β at P. If AP : AB = 2 : 1 then β = ?**

**Q10. In a regular heptagon PQRSTUV, Lines PS and RU meet at point X. What is the value of ∠UXS?**

(a) 102.86°

(b) 120.12°

(c) 128.57°

(d) 81.43°

**Solutions:**

**S4. Ans.(a)**

**Sol.** If the circumcentre of the triangle lies on one of the sides of triangle then the given triangle is a right angle triangle hence the orthocenter will lie on one of its vertices.

**S5. Ans.(a)**

**Sol.** If the circumcentre and the orthocenter of the triangle coincides then the given triangle is equilateral triangle hence option (a)

###### Important Questions on Simplification by Rohit Nama Sir | SSC CGL 2019 | Super Educator

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