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Which of the following cannot be a perfect square? (a) 841 (b) 529 (c) 198 (d) All of the above

The correct answer is (c) 198 Explanation A number with 2, 3, 7 or 8 at the unit’s place should never be a perfect square. In... View Article

How many natural numbers lie between 5² and 6²? (a) 9 (b) 10 (c) 11 (d) 12

The correct answer is (b) 10 Explanation The natural numbers lie between 52 and 62 i.e. 25 and 36 are, 26, 27, 28, 29, 30, 31, 32,... View Article

Which of the following will have 4 at the units place? (a) 14² (b) 62² (c) 27² (d) 35²

The correct answer is (b) 622 Explanation The square of a number having 2 or 8 at the units place ends in 4. Example: 12 x 12=144... View Article

A number ending in 9 will have the units place of its square as (a) 3 (b) 9 (c) 1 (d) 6

The correct answer is (c) 1 Explanation If a number has 1 or 9 in its units place, then its square ends in 1. Example: – 21... View Article

Which of the following is a square of an even number? (a) 144 (b) 169 (c) 441 (d) 625

The correct answer is (a) 144 Explanation Squares of even numbers are even, i.e, (2n)2 = 4n2. Square of even number is 144, = 12... View Article

196 is the square of (a) 11 (b) 12 (c) 14 (d) 16

The correct answer is (c) 14 Explanation 14 × 14 = 196 196 is the square of 14... View Article

2. What shape is (a) Your instrument box? (b) A brick? (c) A match box? (d) A road-roller? (e) A sweet laddu?

Solution: (a) The shape of an instrument box is cuboid (b) The shape of a brick is cuboid (c) The shape of a match box is cuboid (d) The shape of... View Article

Match the following and give two new examples of each shape.

Solution: (a) Traffic cone and Waffle cone are examples of cone (b) Moonand Sun are examples of sphere (c) Gas cylinder and Candle... View Article

A diagonal is a line segment that joins any two vertices of the polygon and is not a side of the polygon. Draw a rough sketch of a pentagon and draw its diagonals.

Solution From the figure we may find AC, AD, BD, BE and CE are the diagonals... View Article

Draw a rough sketch of a regular octagon. (Use squared paper if you wish). Draw a rectangle by joining exactly four of the vertices of the octagon.

Solution The below figure is a regular octagon in which a rectangle is drawn by joining four of the vertices of the octagon.... View Article

Draw a rough sketch of a regular hexagon. Connecting any three of its vertices, draw a triangle. Identify the type of the triangle you have drawn.

Solution We can draw an isosceles triangle by joining three of vertices of a hexagon as shown in below figure... View Article

Name each polygon and make two more examples of each of these.

Solution (a) It is a closed figure and is made of four line segments. Hence, the given figure is a quadrilateral. Two more examples are (b) The... View Article

Examine whether the following are polygons. If any one among them is not, say why?

Solution: (i) The figure given above is not a closed figure. Hence, it is not a polygon. (ii) The figure given above is a polygon... View Article

A figure is said to be regular if its sides are equal in length and angles are equal in measure. Can you identify the regular quadrilateral?

Solution: Square is a regular quadrilateral because all the interior angles are of 900 and all sides are of same length.... View Article

Give reasons for the following: (a) A square can be thought of as a special rectangle.(b) A rectangle can be thought of as a special parallelogram.(c) A square can be thought of as a special rhombus. (d) Squares, rectangles, parallelograms are all quadrilaterals.(e) Square is also a parallelogram.

Solution: (a)A rectangle in which all the interior angles are of same measure i.e 900 and only opposite sides of the rectangle are of same... View Article

Say True or False: (a) Each angle of a rectangle is a right angle. (b) The opposite sides of a rectangle are equal in length. (c) The diagonals of a square are perpendicular to one another. (d) All the sides of a rhombus are of equal length. (e) All the sides of a parallelogram are of equal length. (f) The opposite sides of a trapezium are parallel.

Solution: (a) The given statement is True. Each angle of a rectangle is a right angle (b) The given statement is True. The... View Article

Try to construct triangles using match sticks. Some are shown here. Can you make a triangle with (a) 3 matchsticks? (b) 4 matchsticks? (c) 5 matchsticks? (d) 6 matchsticks? (Remember you have to use all the available matchsticks in each case) Name the type of triangle in each case. If you cannot make a triangle, think of reasons for it

Solution: (a)By using three match sticks we can construct a triangle as shown below The triangle shown above is an equilateral triangle (b) By... View Article

Name each of the following triangles in two different ways: (you may judge the nature of the angle by observation)

Solution: (i)The given figure represents Acute angled and isosceles triangle (ii)The given figure represents Right angled and scalene... View Article

Name the types of following triangles: (a) Triangle with lengths of sides 7 cm, 8 cm and 9 cm. (b) ∆ABC with AB = 8.7 cm, AC = 7 cm and BC = 6 cm. (c) ∆PQR such that PQ = QR = PR = 5 cm. (d) ∆DEF with ∠D = 90° (e) ∆XYZ with ∠Y = 90° and XY = YZ. (f) ∆LMN with ∠L = 30°, ∠M = 70° and ∠N = 80°

Solution (a) Scalene triangle (b) Scalene triangle (c) Equilateral triangle (d) Right angled triangle (e) Right angled isosceles triangle (f)... View Article

Study the diagram. The line l is perpendicular to line m (a) Is CE = EG? (b) Does PE bisect CG? (c) Identify any two line segments for which PE is the perpendicular bisector. (d) Are these true? (i) AC > FG (ii) CD = GH (iii) BC < EH.

Solution: (a) Yes, since, CE = 2 units and EG = 2 units respectively (b) Yes. Since, CE = EG as both are of 2 units. Hence PE bisect CG... View Article