## 4th SSC CGL Tier II level Question Set, 1st on Geometry

This is the 4th question set of 10 practice problem exercise for SSC CGL Tier II exam and the 1st on topic Geometry.

For maximum gains, the test should be taken first, that is obvious. But more importantly, to absorb the concepts, techniques and deductive reasoning elaborated through the solutions, one must solve many problems in a systematic manner using this conceptual analytical approach.

Learning by doing is the best learning. There is no other alternative towards achieving excellence.

### 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 on points lines and triangles ,****Geometry basic concepts part 2 on Quadilaterals Squares Rectangles,****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 geometry concepts part 5 on proof of median relations,**or any other short but good material to refresh your concepts if you so require.**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: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.

### 4th question set - 10 problems for SSC CGL exam: 1st on topic Geometry - answering time 12 mins

**Problem 1. **

If P and Q are two points on sides AB and AD of a parallelogram ABCD respectively, and areas of $\triangle CPD=A_1$ and that of $\triangle BQC=A_2$, then,

- $2A_1=A_2$
- $A_1=A_2$
- $A_1=A_2$
- $2A_1=3A_2$

**Problem 2.**

If three non-colllinear points A, B and C lie on the periphery of a circle so that $AB=AC=BC=3$ cm, then the radius of the circle (in cm) is,

- $\sqrt{3}$
- $\displaystyle\frac{1}{\sqrt{3}}$
- $\displaystyle\frac{\sqrt{3}}{2}$
- $\displaystyle\frac{2}{\sqrt{3}}$

**Problem 3.**

Two similar triangles have areas 96 cm$^2$ and 150 cm$^2$. If the largest side of the larger triangle is 20 cm, the largest side of the smaller triangle (in cm) is,

- 20
- 15
- 16
- 18

**Problem 4. **

The interior bisectors of $\angle B$ and $\angle C$ of $\triangle ABC$ meet at point P. If $\angle A=70^0$, then the value of $\angle BPC$ is,

- $55^0$
- $125^0$
- $150^0$
- $135^0$

**Problem 5. **

In $\triangle ABC$ the medians BE and CF intersect at point G. If GD=3 cm, then the length of AD is,

- 12 cm
- 4.5 cm
- 6 cm
- 9 cm

**Problem 6.**

D is the mid-point of side AB of a right angled $\triangle ABC$ with right angle at B. If AD subtends an angle $\alpha$ at C and BC is $n$ times of AB, then $\tan \alpha$ is,

- $\displaystyle\frac{n}{2n^2+1}$
- $\displaystyle\frac{n}{n^2+1}$
- $\displaystyle\frac{n}{n^2-1}$
- $\displaystyle\frac{n^2-1}{n^2+1}$

** Problem 7.**

If A, B and C are three points lying on the same plane and $AB=5$ cm and $BC=10$ cm, then the possible length of AC (in cm) is,

- 15
- 5
- 3
- 6

** Problem 8.**

In the following figure, a square ABCD is formed with its vertices as the mid-points of a larger square PQRS. A circle is inscribed in square ABCD and the $\triangle EFG$ is an equilateral triangle inscribed in the circle. If length of side of square PQRS is $a$, the area of the $\triangle EFG$ is,

- $\displaystyle\frac{\sqrt{3}a^2}{16}$
- $\displaystyle\frac{3\sqrt{3}a^2}{32}$
- $\displaystyle\frac{5\sqrt{3}a^2}{32}$
- $\displaystyle\frac{5\sqrt{3}a^2}{64}$

**Problem 9.**

The radii of two non-intersecting circles are $r_1$ and $r_2$ with $r_1$ being the larger one and the smaller circle inscribed within the larger circle. If the least distance between their circumference be $S$, the distance between their centres is,

- $r_1-r_2+S$
- $r_1-r_2$
- $r_1+r_2-S$
- $r_1-r_2-S$

** Problem 10.**

If $\triangle ABC$, $AD$, $BE$ and $CF$ are the altitudes and $AD$ and $BE$ intersect at $G$ with $BE+EG=BG$, then,

- $FC+CG=FG$
- $CF+FG=CG$
- $CG+GF=CF$
- $CF-FG=CG$

### Answers to the problems

**Problem 1.** **Answer:** b: $A_1=A_2$.

**Problem 2. ****Answer:** a: $\sqrt{3}$.

**Problem 3.** **Answer:** c: 16.

**Problem 4**. **Answer:** b: $125^0$.

**Problem 5.** **Answer:** d: 9 cm.

**Problem 6.** **Answer:** a: $\displaystyle\frac{n}{2n^2+1}$.

**Problem 7.** **Answer:** d: 6.

**Problem 8.** **Answer:** b: $\displaystyle\frac{3\sqrt{3}a^2}{32}$.

**Problem 9.** **Answer:** d: $r_1-r_2-S$.

**Problem 10.** **Answer:** a: $FC+CG=FG$.

**Detailed Solution to this question set**

**SSC CGL Tier II level Solution Set 4, Geometry 1**

**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**

**How to solve difficult Geometry problems quickly in a few steps**

**How to solve intriguing SSC CGL level Geometry problem in a few steps 4**

**How to solve difficult SSC CGL Geometry problems in a few steps 3**

**How to solve difficult SSC CGL Geometry problems in a few steps 2**

**How to solve difficult SSC CGL Geometry problems in a few steps 1**

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