## Eighteenth SSC CGL level Question Set, 1st on topic Geometry

This is the eighteenth question set of 10 practice problem exercise for SSC CGL exam and 1st on topic Geometry. The questions generally are on basic concepts on triangles and circles.

### 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,****Geometry basic concepts part 2,****Geometry basic and rich concepts part 3 on Circles,****Basic and rich Geometry concepts part 4 on proof of arc angle subtending concept,****Basic and Rich concepts Geometry Part 5 on Proof of Median relations,****Basic and rich Geometry concepts Part 6 on proof of triangle area from medians,**, 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.**Basic and Rich Geometry concepts part 7 on laws of sines and laws of cosines****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:** both * practice tests* and

*must 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.

### Eighteenth question set- 10 problems for SSC CGL exam: 1st on Geometry - time 12 mins

#### Problem 1.

$\triangle ABC$ is an isosceles triangle with $AB=AC$ and $AD$ as the median to base $BC$. If $\angle ABC = 35^0$, the $\angle BAD$ is

- $70^0$
- $35^0$
- $55^0$
- $110^0$

#### Problem 2.

In isosceles triangle $\triangle FGH$, $FG \lt 3$ cm and $GH = 8$cm. Then the correct relation is,

- $GH = FH$
- $GH \lt FH$
- $GF = GH$
- $FH \gt GH$

#### Problem 3.

The sum of three altitudes of a triangle is,

- equal to the sum of three sides
- twice the sum of sides
- greater than the sum of sides
- less than the sum of sides

#### Problem 4.

The length of 3 sides of a triangle are, 6cm, 8cm and 10cm. The length of the median to the greatest side is then,

- 5cm
- 8cm
- 4.8cm
- 6cm

#### Problem 5.

$O$ and $C$ are the Orthocenter and the Circumcenter of an acute angled triangle $\triangle PQR$ respectively. The points $P$ and $O$ are joined and produced to meet the side $QR$ at $S$. If $\angle QCR = 130^0$ and $\angle PQS = 60^0$ then $\angle RPS$ is,

- $100^0$
- $35^0$
- $30^0$
- $60^0$

#### Problem 6.

If $I$ is the incenter of $\triangle ABC$, $\angle ABC = 65^0$ and $\angle ACB = 55^0$, the $\angle BIC$ is,

- $110^0$
- $120^0$
- $130^0$
- $140^0$

#### Problem 7.

If the median drawn on the base of a triangle is half its base, the triangle will be,

- acute-angled
- obtuse-angled
- right-angled
- equilateral

#### Problem 8.

In a right angled triangle the product of its two sides equals half of the square of the third side which is the hypotenuse. One of the acute angles must then be,

- $15^0$
- $30^0$
- $45^0$
- $60^0$

#### Problem 9.

In $\triangle ABC$, two points $D$ and $E$ are taken on the lines $AB$ and $BC$ respectively in such a way that $AC$ is parallel to $DE$. The $\triangle ABC$ and $\triangle DBE$ are then,

- always similar
- always congruent
- similar only if $D$ lies outside the line segment $AB$
- congruent only if $D$ lies outside the line segment $AB$

#### Problem 10.

$AD$ is a median of $\triangle ABC$ and $O$ is the centroid such that $AO = 10cm$. Length of $OD$ (in cm) is,

- 7
- 5
- 4
- 2

### Answers to the problems

**Problem 1: **c: $55^0$.

**Problem 2: **a: $GH=FH$.

**Problem 3: **d: less than sum of sides.

**Problem 4: **a: 5cm.

**Problem 5: **b: $35^0$.

**Problem 6: **b: $120^0$.

**Problem 7: **c: right-angled.

**Problem 8: **c: $45^0$.

**Problem 9: **a: always similar.

**Problem 10: **b: 5.

For detailed explanation of the solutions clarifying the concepts used for elegant solutions, you should refer to the corresponding **SSC CGL level Solution Set 18, Geometry 1.**

### Guided help on Geometry in Suresolv

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