SSC CGL level Question Set 27, Mensuration 2

27th SSC CGL level Question Set, 2nd on topic Mensuration

SSC CGL question set 27 mensuration2

This is the 27th question set of 10 practice problem exercise for SSC CGL exam and 2nd on topic Mensuration. Students should complete this question set in prescribed time first and then only refer to the corresponding solution set.

We will repeat here the method of taking a 10 problem test if you have not gone through it already.

Method for taking this 10 problem test and get the best results from the test set:

  1. Before start, go through the tutorials Basic concepts on Geometry 1, Basic concepts on Geometry 2, Basic concepts on Geometry 3 or any other short but good material to refresh your concepts if you so require.
  2. Answer the questions in an undisturbed environment with no interruption, full concentration and alarm set at 15 minutes.
  3. When the time limit of 15 minutes is over, mark up to which you have answered, but go on to complete the set.
  4. At the end, refer to the answers given in the companion 27th solution set on mensuration, 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.
  5. Identify and analyze the problems that you couldn't do to learn how to solve those problems.
  6. 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.
  7. 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.
  8. Give a gap before you take a 10 problem practice test again.

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

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 section on SSC CGL to access all the valuable student resources that we have created specifically for SSC CGL, but generally for any hard MCQ test.

Tutorials that you should refer to

Basic concepts on Geometry 1

Basic concepts on Geometry 2

Basic concepts on Geometry 3

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27th question set - 10 problems for SSC CGL exam: topic Mensuration - Answering time 15 mins

Problem 1.

The area of a rectangle is thrice that of a square. The length of the rectangle is 20 cm and the breadth $\frac{3}{2}$ times the length of a side of the square. The side length of the square (in cm) is,

  1. 10
  2. 20
  3. 60
  4. 30

Problem 2.

The perimeter of a rhombus is 40 cm and its height is 5 cm. Its area in (cm$^2$) is,

  1. 45
  2. 60
  3. 55
  4. 50

Problem 3.

The sum of the length, breadth and height of a rectangular parallelepiped is 24 cm and the length of the diagonal is 15 cm. Then its total surface area is,

  1. 351 cm$^2$
  2. 256 cm$^2$
  3. 265 cm$^2$
  4. 315 cm$^2$

Problem 4.

In the figure given below two shaded regions are formed in a circle of radius $a$.

SSC-CGL-question-set-27-mensuration-q4.jpg

The area of the shaded region is,

  1. $\frac{a^2}{2}(\frac{\pi}{2} - 1)$
  2. $a^2(\pi - 1)$
  3. $\frac{a^2}{2}(\pi - 1)$
  4. $a^2(\frac{\pi}{2} - 1)$

Problem 5.

Three circles of radii $a$, $b$ and $c$ touch each other externally. The area of the triangle formed by the three centres is,

  1. $ab + bc + ca$
  2. $(a + b +c)\sqrt{ab + bc + ca}$
  3. $\sqrt{(a + b + c)abc}$
  4. none of the above

Problem 6.

The circumference of a circle is 11 cm. The area of a sector of the circle subtending an angle of $60^0$ at the periphery (take $\pi = \frac{22}{7})$ is,

  1. $1\displaystyle\frac{29}{48}$ cm$^2$
  2. $2\displaystyle\frac{27}{48}$ cm$^2$
  3. $2\displaystyle\frac{29}{48}$ cm$^2$
  4. $1\displaystyle\frac{27}{48}$ cm$^2$

Problem 7.

If the difference between the areas of the circumcircle and incircle of an equilateral triangle is 44 cm$^2$, then the area of the triangle (in cm$^2$, take $\pi = \frac{22}{7}$), is,

  1. $28$ cm$^2$
  2. $21$ cm$^2$
  3. $7\sqrt{3}$ cm$^2$
  4. $14\sqrt{3}$ cm$^2$

Problem 8.

If area of an equilateral triangle is $A$ and its height is $b$, the value of $\displaystyle\frac{b^2}{A}$ is,

  1. $\displaystyle\frac{1}{3}$
  2. $3$
  3. $\sqrt{3}$
  4. $\displaystyle\frac{1}{\sqrt{3}}$

Problem 9.

ABCD is a parallelogram. P and Q are the mid-points of sides BC and CD respectively. If the area of the $\triangle ABC$ is 12 cm$^2$, the area of $\triangle APQ$ is,

  1. 9 cm$^2$
  2. 12 cm$^2$
  3. 10 cm$^2$
  4. 8 cm$^2$

Problem 10.

A wire when bent in the form of a square encloses an area of 484 sq cm. What will be the enclosed area when the same wire is bent into the form of a circle?

  1. 616 sq cm
  2. 693 sq cm
  3. 462 sq cm
  4. 539 sq cm

Other related guideline, question set and solution set on SSC CGL mensuration

7 steps for sure success in SSC CGL tier 1 and tier 2 competitive tests or section on SSC CGL to access all the valuable student resources that we have created specifically for SSC CGL, but generally for any hard MCQ test.

Tutorials that you should refer to

Basic concepts on Geometry 1 lines points and triangles

Basic concepts on Geometry 2 quadrilaterals polygons squares

Basic and rich concepts on Geometry 3 Circles

Basic and rich Geometry concepts part 4 Arc angle subtending concept proof

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