## 36th SSC CGL level Question Set, 4th on topic Geometry

This is the 36th question set of 10 practice problem exercise for SSC CGL exam and 4th on topic Geometry. You need to take this test before referring to the corresponding solution set. Some of the problem pictorial representation may seem to be complex, but once you represent a geometric figure properly even in a quick sketch, rest should not take much time.

### Method for taking the test and get the best results from the test set:

**Before start,**go through the**tutorials on****Geometry basic concepts part 1,**and**Geometry basic concepts part 2,**or any other short but good material to refresh your concepts if you so require. This question set is in fact the set of exercise problems at the end of the first tutorial. Don't do the exercise as you are preparing for a hard competitive test. For you, taking the test will involve a different more stringent method.**Geometry basic and rich concepts part 3 on Circles****Answer the questions**in an undisturbed environment with no interruption, full concentration and alarm set at 15 minutes.**When the time limit of 15 minutes is over,**mark up to which you have answered,**but go on to complete the set.****At the end,**refer to the answers given at the end to mark your score at 15 minutes. For every correct answer add 1 and for every incorrect answer deduct 0.25 (or whatever is the scoring pattern in the coming test). Write your score on top of the answer sheet with date and time.**Identify and analyze**the problems that**you couldn't do**to learn how to solve those problems.**Identify and analyze**the problems that**you solved incorrectly**. Identify the reasons behind the errors. If it is because of**your shortcoming in topic knowledge**improve it by referring to**only that part of concept**from the best source you get hold of. You might google it. If it is because of**your method of answering,**analyze and improve those aspects specifically.**Identify and analyze**the**problems that posed difficulties for you and delayed you**. Analyze and learn how to solve the problems using basic concepts and relevant problem solving strategies and techniques.**Give a gap**before you take a 10 problem practice test again.

Important:bothandpractice testsmust be timed, analyzed, improving actions taken and then repeated. With intelligent method, it is possible to reach highest excellence level in performance.mock tests

Now set the stopwatch alarm and start taking this test. It is not difficult.

### 36th question set- 10 problems for SSC CGL exam: 4th on Geometry - answering time 15 mins

#### Problem 1.

The radius of the circumcircle of a right angled triangle is 15 cm and the radius of the inscribed circle is 6 cm. Then the length of the three sides (in cm) are,

- 30, 24, 25
- 24, 36, 20
- 18, 24, 30
- 30, 40, 41

#### Problem 2.

A chord $AB$ of a circle of radius $(\sqrt{3} + 1)$ cm touches a second concentric circle of radius $(\sqrt{3} - 1)$ cm. The length of $AB$ (in cm) is,

- $2\sqrt[4]{3}$
- $4\sqrt{3}$
- $8\sqrt{3}$
- $4\sqrt[4]{3}$

#### Problem 3.

If the inradius of an equilateral triangle be 5 cm, its circumradius (in cm) is,

- 10
- 15
- 25
- 30

#### Problem 4.

In isosceles $\triangle ABC$ right-angled at B, DP and DQ are two perpendiculars dropped from a point D inside the triangle on the two sides AB and AC such that P and Q lie on AB and AC respectively. If $AP = a$ cm, $AQ=b$ cm and $\angle BAD=15^0$, then $\sin 75^0$ is,

- $\displaystyle\frac{a}{2b}$
- $\displaystyle\frac{2b}{\sqrt{3}a}$
- $\displaystyle\frac{\sqrt{3}a}{2b}$
- $\displaystyle\frac{2a}{\sqrt{3}b}$

#### Problem 5.

Sides of a right-angled triangle are in the ratio 4 : 5 : 6. If the in-radius of the triangle is 3 cm, the altitude of the triangle with base as the largest side is,

- 7.5 cm
- 6 cm
- 8 cm
- 10 cm

#### Problem 6.

Inside a square $\square ABCD$, $\triangle BCE$ is an equilateral triangle. If CE and BD intersect at O, then $\angle BOC$ is equal to,

- $75^0$
- $60^0$
- $90^0$
- $120^0$

#### Problem 7.

$ABCD$ is a rectangle where the ratio of the lengths $AB$ and $BC$ is 3 : 2. If $P$ is the midpoint of $AB$ then the value of $\sin \angle CPB$ is,

- $\displaystyle\frac{3}{5}$
- $\displaystyle\frac{3}{4}$
- $\displaystyle\frac{4}{5}$
- $\displaystyle\frac{2}{5}$

#### Problem 8.

The distance between two parallel chords of length 8 cm each in a circle of diameter 10 cm is,

- 7 cm
- 6 cm
- 5.5 cm
- 8 cm

#### Problem 9.

A square $ABCD$ is inscribed in a circle of unit radius. Semicircles are described externally on each side with the side as the diameter. The area of the region bounded by the semicircles and the circle is,

- 1 sq unit
- 2.5 sq units
- 1.5 sq units
- 2 sq units

#### Problem 10.

A, B and C are three points on a circle such that angles subtended by the chords AB and AC at the centre are non-overlapping $90^0$ and $110^0$ respectively. $\angle BAC$ is then equal to,

- $80^0$
- $90^0$
- $100^0$
- $70^0$

### Answers to the problems

**Problem 1: **c: 18, 24, 30.

**Problem 2: **d: $4\sqrt[4]{3}$.

**Problem 3: **a: 10.

**Problem 4: **c: $\displaystyle\frac{\sqrt{3}a}{2b}$.

**Problem 5: **a: 7.5 cm.

**Problem 6: **a: $75^0$.

**Problem 7: **c: $\displaystyle\frac{4}{5}$.

**Problem 8: **b: 6 cm.

**Problem 9: **d: 2 sq units.

**Problem 10: **a: $80^0$.

For detailed explanation of the solutions clarifying the concepts used for elegant solutions, you should refer to the corresponding **SSC CGL level Solution Set 36, Geometry 4.**

**Related resources that should be useful for you**

**You may refer to:**

* 7 steps for sure success in SSC CGL tier 1 and tier 2 competitive tests* or

*to access all the valuable student resources that we have created specifically for SSC CGL, but*

**section on SSC CGL****generally for any hard MCQ test.**

**Concept tutorials for SSC CGL and other competitive exams on Geometry**

**Basic and rich Geometry concepts part 7, Laws of sines and cosines**

**Basic and rich Geometry concepts part 6, proof of triangle area from medians**

**Basic and rich Geometry concepts part 5, proof of median relations**

**Basic and rich Geometry concepts part 4, proof of arc angle subtending concept**

**Geometry, basic and rich concepts part 3, Circles**

**Geometry, basic concepts part 2, Quadrilaterals polygons and squares**

**Geometry, basic concepts part 1, points lines and triangles**

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