## Twentieth SSC CGL level Question Set, 2nd on topic Geometry

This is the twentieth question set of 10 practice problem exercise for SSC CGL exam and 2nd on topic Geometry. The questions generally are on basic concepts on quadrangles and circles.

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

**Before start,**go through the three relevant tutorials,**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 second tutorial. Don't do the exercise as you are preparing for a hard competitive test. For you, taking the test will involve a different and 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 12 minutes.**When the time limit of 12 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 12 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.

### Twentieth question set- 10 problems for SSC CGL exam: 2nd on Geometry - time 12 mins

#### Problem 1.

In a cyclic quadrilateral $ABCD$, side $AB$ is extended to $E$ so that $BE = BC$. If $\angle ADC=70^0$ and $\angle BAD=95^0$ then $\angle DCE$ is,

- $140^0$
- $165^0$
- $120^0$
- $110^0$

#### Problem 2.

The ratio between the number of sides of two regular polygons is $1 : 2$ and the ratio between their interior angles is $2 : 3$. The number of sides of the polygons are respectively,

- 5, 10
- 6, 12
- 7, 14
- 4, 8

#### Problem 3.

The length of the diagonal $BD$ of the parallelogram $ABCD$ is 18cm. If $P$ and $Q$ are the centroids $\triangle ABC$ and $\triangle ADC$ respectively, length of $PQ$ is,

- 4cm
- 12cm
- 6cm
- 9cm

#### Problem 4.

In rhombus $ABCD$, a straight line through $C$ cuts extended $AD$ at $P$ and extended $AB$ at $Q$. If $DP =\displaystyle\frac{1}{2}AB$ the ratio of the lengths of $BQ$ and $AB$ is,

- 1 : 2
- 2 : 1
- 3 : 1
- 1 : 1

#### Problem 5.

$A$, $B$ and $C$ are three points on the circumference of a circle. If $AB = AC = 5\sqrt{2}$cm and $\angle BAC=90^0$ the length of radius is,

- 15cm
- 5cm
- 10cm
- 20cm

#### Problem 6.

If $PN$ is the perpendicular from a point $P$ on the circumference of a circle of radius 7cm to its diameter $AB$ and the length of the chord $PB$ is 12cm, the length of $BN$ is,

- $6\displaystyle\frac{5}{7}$ cm
- $3\displaystyle\frac{5}{7}$ cm
- $12\displaystyle\frac{2}{7}$ cm
- $10\displaystyle\frac{2}{7}$ cm

#### Problem 7.

If the angle subtended by a chord at its center is $60^0$, the ratio between the lengths of the chord and the radius is,

- $1 : 1$
- $2 : 1$
- $\sqrt{2} : 1$
- $1 : 2$

#### Problem 8.

$AB$ and $CD$ are two parallel chords of respective lengths 8cm and 6cm on the same side of the center of a circle. The distance between them is 1cm. Then the radiius of the circle is,

- 4cm
- 5cm
- 3cm
- 2cm

#### Problem 9.

$ABCD$ is a trapezium whose side $AD$ is parallel to $BC$. Diagonals $AC$ and $BD$ intersect at $O$. If $AO = 3$, $CO = x - 3$, $BO = 3x - 19$ and $DO = x - 5$, the value(s) of $x$ will be,

- 7, 10
- 7, 6
- 12, 6
- 8, 9

#### Problem 10.

A quadrilateral $ABCD$ circumscribes a circle and $AB=6$cm, $CD=5$cm and $AD=7$cm. The length of side $BC$ is,

- 3cm
- 4cm
- 5cm
- 6cm

### Answers to the exercise problems

**Problem 1: **a: $140^0$.

**Problem 2: **d: 4, 8.

**Problem 3: **c: 6cm.

**Problem 4: **b: 2 : 1.

**Problem 5: **b: 5cm.

**Problem 6: **d: $10\displaystyle\frac{2}{7}$ cm.

**Problem 7: **a: 1 : 1.

**Problem 8: **b: 5cm.

**Problem 9: **d: 8, 9.

**Problem 10: **b: 4cm.

Detailed solutions to these questions are available in **SSC CGL level Solution Set 20, Geometry 2.**

**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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