Current Affairs 6th Class

Logical Venn Diagrams

WHAT IS VENN DIAGRAM? Venn diagram is a pictorial representation of classes representing items and their common properties. We usually use circles to draw a venn diagram. A venn diagram consists of two or more circles. Circles may or may not have some common regions according as the respective classes have or do not have common properties amongst them. Let us illustrate venn diagrams with the following example. EXAMPLE Which of the following diagrams represents the best relation amongst 'Villages', 'India? and 'Moon'? (a)

(b)

(c)

(d)

Explanation (a): Villages are the parts of India. But moon is separate from these two. So, the correct option is (a).

Catgeory: 6th Class

Alpha-Numeric Sequence Puzzle, Number, Ranking and Time Sequence Test, Logical Sequence of Words, Alphabet Test

ALPHA - NUMERIC SEQUENCE PUZZLE Such type of puzzle is a jumbled sequence of numbers and letters. A puzzle is given and a candidate is asked how many times a number/letter follows a certain rule or which number/letter follows a certain rule. EXAMPLE 1. How many 4's are there in the following arrangement each of which is immediately preceded by an even number but not immediately followed by 6? 2 4 2 E D Q 3 9 2 4 7 M 6 6 T 6 4 1 N 8 4 6 (a) One (b) Two (c) Three (d) Four Explanation (c): Let us take the given arrangement. \[\] E D Q 3 9 \[\] M 6 6 T\[\]N 8 4 6 NUMBER, RANKING AND TIME SEQUENCE TEST Number Test: In problems on number Test, a sequence of numbers is given and a question is asked in that way as asked in Alpha-Numeric Sequence Puzzle. Ranking Test: In ranking based problems, usually the ranks of one or two persons from the top and from the bottom are mentioned. A candidate is required to compute either total number of persons or rank of a particular person. 2. If Sahil finds that he is twelfth from the right end in a line of boys and fourth from the left end, then how many boys should be added to the line such that there are 28 boys in the line? (a) 11 (b) 13 (c) 15 (d) 18 Explanation (b): Number of boys from the right end to Sahil = 12 Number of boys from the left end to Sahil = 4 In the above two statements Sahil is counted twice. So, the actual number of all the boys \[=12+4-1=15\] Now, the required number of additional boys \[=\text{ }28-15=13\] Time Sequence Test:

To solve time based problems the following information?s are very useful.
In every 1 hour, the hour hand rotates \[30{}^\circ \]and the minute hand rotates\[360{}^\circ \].
The year which is divisible by 4 is called a leap year. E.g. 2012 is a leap year.
A century year which is more...

Catgeory: 6th Class

Mathematical Operations

There are four fundamental operations. These are addition\[\left( + \right)\], subtraction\[\left( - \right)\], multiplication \[\left( \times \right)\] and division \[\left( \div \right)\] Whenever two or more of these operations occur simultaneously, we overcome on such complex situation by applying the "BODMAS" rule. This chapter is on the basis of the "BODMAS" rule. Let us explain this rule briefly. B \[\to \] Bracket, O \[\to \] Of, D \[\to \] Division, M \[\to \]Multiplication, A \[\to \] Addition, S \[\to \] Subtraction We solve an expression first for 'bracket' (if available), then for 'of? (if available). This process goes upto subtraction. EXAMPLE If 'L stands for \['+',\]M' stands for \['-',\] 'N' stands for \['\times ',\] 'P' stands for' \['\div ',\] then 14 N 10 L 42 P 2 M 8 = ? (a) 141 (b) 153 (c) 166 (d) 183 Explanation (b): Given expression \[=14\times 10+42\div 2-8=153\] Hence, the answer is (b).

Catgeory: 6th Class

Analytical Reasoning

In this chapter, problems are based upon numbers of lines, triangles, squares and circles in a complex figure.

To count number of lines, add all the numbers of horizontal, vertical and slanting lines.
To count the number of triangles, add all the numbers of triangles formed by 1 component, 2 components, 3 components and so on.
To count the number of circles, count all the centres of circles.

EXAMPLE How many triangles are there in the following figure?

(a) 14 (b) 12 (c) 10 (d) 8 Explanation (b): The figure may be labelled as shown below:

The triangles formed of 1 component are ABE, AEF, EFC, CED and BED. The triangles formed of two components are ABF, ACE, BCE and ABD. The triangles formed of three components are BFC and ACD. There is only one triangle ABC formed of five components. Thus, there are 5+4+2+1 =12 triangles in the figure. Hence, the correct option is (b).

Catgeory: 6th Class

Mirror and Water Images

Mirror Image Suppose someone stands in front of a plane mirror. If he lifts his left hand, the image in the mirror shows his right hand and vice-versa. The left half of a body becomes right half of its mirror image and right half becomes left half. Note: If not mentioned, the mirror is assumed to be placed to vertically right of the object. EXAMPLE 1. Choose the correct mirror image of the figure (X).

(a)

(b)

(c)

(d)

Explanation (d): The right side of the given figure will become the left side of the image.

Water Image The water image of an object is the vertically inverted (upside or downside) image of the object. The position of the water layer is horizontally just below the object. 2. Which of the following has no change in its water image? (a) 6E (b) 2D (c) 3J (d) 0l Explanation (d):

Thus, 0l and its water image are identical.

Catgeory: 6th Class

Embedded Figures, Figure Formation, Construction of Squares, Grouping of Identical Figures

EMBEDDED FIGURES In such type of problems, a simple figure is given followed by four other figures. Only one figure out of the four figures embeds the given figure. A candidate is required to choose that figure which embeds the given figure. 1. Choose a figure from the four options in which the figure (X) is exactly embedded as one of its part?

(a)

(b)

(c)

(d)

Explanation (a): The figure (X) is exactly embedded in figure (a).

So, the correct option is (a). FIGURE FORMATION This section deals us with the following types of problems. Formation of a Figure from its Segments: In such type of problems, all the parts to form a figure are given. A candidate requires to identify the figure so formed out of the four options. Choosing a Pattern which has the same components as a given Pattern. In such type of problems, a pattern of several components is given. Only one pattern out of four option patterns contains the same components. A candidate requires to choose such pattern. 2. Find out which of the figures (a), (b), (c) and (d) can be formed from the pieces given in figure (X).

(a)

(b)

(c)

(d)

Explanation (a): The parts of figure in option (a) are in figure (X). 3. Select that option which has the same components as the given figure (X).

(a)

(b)

(c)

(d)

Explanation (b): Components of figure (X) and figure (b) are exactly same. CONSTRUCTION OF SQUARES Such type of problems are on the basis of the geometrical figures. A candidate is required to identify the figure which can fit into each other to form a square. 4. Select a figure from the given four options which fits exactly into figure (X) to form a complete square.

(a)

Embedded Figures, Figure Formation, Construction of Squares, Grouping of Identical Figures

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Catgeory: 6th Class

Figure Matrix

In such type of problems a \[~2\times 2\] or \[3\times 3\] grid is given. This grid has some designs or symbols to form a pattern. But a cell of the grid is left empty. A candidate requires to fill up the cell. Now, one needs to analyse the grid and identify a rule along row-wise or column-wise in the grid. EXAMPLE Complete the given pattern.

(a)

(b)

(c)

(d)

Explanation (a): Let us consider horizontally. The second figure is obtained from the first figure by moving the line segment to the opposite side of the square boundary and replacing it with two similar line segments. Also, the element in the lower-left corner gets replaced by two similar elements - one placed in the upper-left and the other placed in the lower-right corner.

Catgeory: 6th Class

Paper Folding and Paper Cutting

FOLDING A TRANSPARENT SHEET In such type of problems a transparent sheet carrying a design on it is given. There is a dotted line on this sheet. This sheet has to be folded along the dotted line. A candidate requires to identify a figure from given options that looks similar to the folded sheet. EXAMPLE 1. A square transparent sheet X, with a design and a dotted line on it is given. Choose the correct figure from the options which represents the sheet X after folding along the dotted line.

(a)

(b)

(c)

(d)

Explanation (c): Clearly, the right half of the sheet X is put on the left half. The combination of the design in left half and mirror image of the design in the right half will appear on the folded sheet. So, the sheet will then appear as shown in figure (c). Hence, figure (c) is the correct option. CUTTING/PUNCHING A FOLDED PAPER In such type of problems a paper is folded twice or more than twice. Then one or more pieces of it are cut. After this the paper is unfolded. In this situation the paper has as many cuts or holes on it as folded. So it contains a pattern. A candidate requires to identify a figure from given four options that shows the similar paper sheet as the pattern made. Usually, the paper sheet is folded along the dotted lines marked on it. And arrows show the directions of the folds. 2. Figures X and Y respectively shows the two consecutive folds of the paper. Figure Z shows the cut on the folded paper. Choose one figure from the four options that is the unfolded form of the sheet.

(a)

(b)

(c)

(d)

Explanation (d): In figure (X) and (Y) sheet is folded along the dotted line or in the shown direction. In figure (Z) it has been punched as shown. Clearly, the punched square will be created in each quarter of the paper. Thus, when the paper is unfolded, four square punches will appear symmetrically over it and the paper will then appear as shown in figure (d). Hence, the correct option is (d).

Catgeory: 6th Class

Cubes and Dice

Cuboid: Cuboid is a uniform solid which has 6 rectangular faces, 8 corners and 12 edges.

Cube: Cube is a cuboid which has 6 square faces, 8 corners and 12 edges.

Dice: A dice is a cube which contains 6 different numbers on its 6 faces.

EXAMPLE 1. Count the number of blocks in the given solid.

(a) 24 (b) 36 (c) 48 (d) 60 Explanation (b): Each layer (say top most) of the solid contains 12 blocks. There are 3 identical layers in all. So, the total number of blocks

2. Two positions of a dice are shown below. How many dots will appear on the face opposite to the face containing 5 dots?

(a) 3 (b) 1 (c) 2 (d) 4 Explanation (d): From two positions, we observe that 4 dots are on the common adjacent face of dots 2 & 1. Hence, 4 dots are opposite to 5 dots. 3. A sheet of paper shown in the figure (X), is folded to form a box. Choose a box from the options that is similar to the box given in fig. (X).

(a) 1 and 3 only (b) 2 and 4 only (c) 2 and 3 only (d) 1, 2, 3 and 4 Explanation (d): Considering the positions of faces on forming a box, we deduce that the pairs of opposite faces are:

These three pairs of opposite faces are possible in all the boxes 1, 2, 3 and 4.

Catgeory: 6th Class

Dot Situation

DOT SITUATION In such type of problems one or more dot(s) is (are) placed somewhere in the region enclosed in between geometrical figures such as triangle, square, rectangle, circle, etc. A candidate is required to identify one option figure which has the same region(s) as the region(s) marked by dot(s) in the given figure. EXAMPLE 1. Select a figure from the four options that has the same conditions of the placement of the dots as in figure (X).