Kerala Syllabus Class 9 Maths: Unit 02 New Numbers - Questions and Answers


Questions and Answers for Class 9th Mathematics (English Medium) പുതിയസംഖ്യകള്‍ | Text Books Solution Mathematics (English Medium) Chapter 02 New Numbers

ഒമ്പതാം ക്ലാസ്സ്‌ Maths ലെ New Numbers എന്ന പാഠം ആസ്പദമാക്കി തയ്യാറാക്കിയ ചോദ്യോത്തരങ്ങള്‍ താഴെ നൽകിയിരിക്കുന്നു. 

Maths: Unit 02 New Numbers
∎Samagra Mathematics Notes
1. Perimeter of a square is 40cm. What is its area ?
(a) 10cm²        
(b) 100cm²           
(c) 200cm²           
(d) 60cm²
Answer: 100cm²
 
2. What is the side of the square having area and perimeter are equal numerically?
(a) 5cm            
(b) 4cm          
(c) 6cm            
(d) 10cm    
Answer: 4 cm  

3. Side of an equilateral triangle is 2cm. What is the height of this triangle?
(a) 1cm            
(b) √2cm             
(c) √3cm               
(d) 3cm
Answer: (c) √3cm     

4. Side of an equilateral triangle is 2cm. What is the area of square drawn on its height?
(a) 1 cm²           
(b) √2 cm²             
(c) √3 cm²             
(d) 3 cm²
Answer: d) 3 cm²  

5. If √2 ≈ 7/5  and x stands for √2 then x − 1 is equal to

a) 35

b) 25

c) 45

d)

Answer: c) 45
  
6. Length of the diagonal of a square is √2cm. What is its area?
a) 2 cm²       
b)  4/5  cm²        
c) 1/5  cm²        
d) 1 cm²
Answer: 1 cm²

7. Sides of a rectangle are √3 + √2cm and √3 − √2 cm. What is its area?
(a) 2 cm²               
(b) 1 cm²                
(c) 3 cm²                     
(d) 5 cm²  
Answer: 1 cm²

8. Which of the following is correct?
(a) √5 + √12 > √13                
(b) √5 + √12 < √13                  
(c) √5 + √12 = √13                        
(d) None of these
Answer: Squaring on both sides

9. Which of the following is the number in between √3 and √5?
(a) 1.9         
(b) 3           
(c) 1          
(d) 1.2
Answer: (a) 1.9    

10. A spiral of right triangles is given in the figure.
What is the hypotenuse of n th right triangle?
(a) √n          
(b) √(n − 1)         
(c) √(n + 1)        
(d)  (n + 1)
Answer: c) √(n+1)

11. A steel wire of length 4 metre is bent in the shape of a square. What is the approximate length of its diagonal?
(a) 1.123metre       
(b) 1.414metre         
(c) 1.732metre          
(d) 2metre
Answer: 1.414 metre

12. A steel wire of length 6 metre is bent in the shape of an equilateral triangle. What is the approximate height of the triangle?
(a) 1.123metre        
(b) 1.414metre         
(c) 1.732metre           
(d) 2metre
Answer: 1.732

13. If x = √3 then what is x² + x + 1?
(a) 4 + √3metre        
(b) 3 + √3metre        
(c) √3 − 1metre          
(d) 2metre
Answer: (a) 4 + √3 metres     

14. Height of an equilateral triangle is √3 metre. What is its perimeter?
(a) 6metre        
(b) 4metre          
(c) 5metre           
(d) 2metre
Answer: 6 metres  

15. Area and perimeter of an equilateral triangle are equal. What is its height?
(a) 4         
(b) 6         
(c) 5             
(d) 2 
Answer: 6 
16. Perimeter of a square is 4 metre.
a) What is the length of its side?
b) What is the area of the square drawn on its diagonal?
Answer: 
a) 1 metre 
b) 2 m 2

17. Perimeter of an equilateral triangle is 6 meter
a) What is the length of its side?
b) What is the area of the square drawn on its height?
Answer: 
a) 2 meter 
b) 3 square meter

18. A wire of length 4metre is bent in the shape of a square.
a) What is the length of its side?
b) What is the length of its diagonal ?
Answer: 
a) 1 metre 
b) √ 2 metre

19. A wire of length 6 metre is bent in the shape of an equilateral triangle.
a) What is the length of its side?
b) What is the height of the triangle?
Answer: 
a) 2 metre 
b) √3 metre

20. Three squares of area 2 cm 2, 3 cm 2 and 5 cm 2 are joined to make triangle ABC as in the figure.
a) What are the length of its sides?
b) What is the approximate perimeter?
Answer: 
a) √2 cm, √3 cm, √5 cm 
b) 1.41 + 1.73 + 2.23 = 5.37 metre

21. The longest side of a right triangle is 2 metre. Its shortest side is 1metre. A square is drawn on the third side
a) What is the area of square drawn on third side?
b) What is the approximate perimeter?
Answer: 
a) 3 Square metre 
b) 1 + 2 + 1.73 = 3.73 m

22. OAB is a triangle right angled at O, the centre of the circle. Other two vertices A and B are on the circle of radius 1 metre.
a) What is the length of AB?
b) What is the area of the square drawn with AB as side?
Answer: 
a) √2 metre 
b) 2 square metre

23. ABC is an equilateral triangle of side 2 metre. Another equilateral triangle APQ is drawn with the height of first triangle as the side.
a) What is the height of triangle ABC?
b) What is the approximate perimeter of the equilateral triangle APQ?
Answer: 
a) √3 metre 
b) √3 + √3 + √3 = 1.73 + 1.73 + 1.73 = 3 × 1.73 = 5.19 metre

24. Sides of a rectangle are √3 + 1 and √3 − 1 metre
a) What is the perimeter of the rectangle?
b) Write the perimeter in millimetre
Answer: 
a) (√3 + 1) + (√3 - 1) + (√3 + 1) + (√3 - 1) = 4 × 3 
b) 4 × 1.732 = 6.928 metre = 6928millimetre.

25. A paper piece in the shape of an equilateral triangle of side 2 metre is folded along its height to get a right triangle.
a) What is the height of triangle?
b) What is the approximate perimeter of a right triangle?
Answer: 
a) √3 metre 
b) 3 × 1.732 = 5.19 metres
26. A rectangle has sides of length 3 cm and 1 cm
a) Write the length of diagonal
b) What are the integers in between them the length of diagonal belongs to?
Answer: 
a) √3 cm b) Between 3 and 4.

27. In the spiral of triangles in the figure
a) What is the area of square on the hypotenuse of 5th triangle?
b) What is the hypotenuse of fifth triangle?
Answer: 
a) 6 Sq.cm 
b) √6 cm

28. A square is drawn by joining the midpoints of the sides of another square.If the area of outer square is 6 cm2 then
a) What is the area of coloured square ?
b) What is the side of new square?
c) What is the approximate perimeter of the new square?
Answer: 
a) 3 Sq. cm 
b) √3 cm 
c) 4 × 1.732 = 6.928cm

29. Two squares are drawn inside a semicircle. Area of each square is 1
a) What is the side of a square?
b) What is the radius of the semicircle?
c) What is the approximate perimeter of triangle ABC
Answer: 
a) 1 
b) √ 2 
c) √2 + √2 + 2 = 4.428

30. The diagonals of a square divide it into four equal right triangles. One of them is removed from a square paper of diagonal 2 cm.
a) What is the perimeter of the removed part?
b) What is the perimeter of the paper so formed?
c) Calculate the perimeter in centimetre
Answer: 
a) 1 + 1 + √2 = 2 + √2 cm 
b) √2 + √2 + √2 + 2cm 
c) 6.242 cm

31. The perpendicular sides of a right triangle are √2 metre and √3 metre.
a) What is the area of square on third side?
b) What is the third side?
c) What is the difference between total length of perpendicular sides and third side?
d) Write the difference in millimetre
Answer: 
a) 5cm 
b) √5cm 
c) √2 + √3 − √5 
d) 1.414 + 732 − 1.236 = 1.91metre
32. In the spiral of right triangles shown below. A triangle has perimeter 3 + √3
a) Which triangle has perimeter 3 + √3?
b) What is the hypotenuse of this triangle?
c) What are its perpendicular sides?
d) What is the difference between the longer side and shorter side of this triangle?
Answer: 
a) 5 cm 
b) √5 cm 
c) √5 − √2 d) 0.822metre

33. A steel wire is bent in the shape of a right triangle. The length of wire which makes the perpendicular sides are 1metre and 2 metre.
a) What is the length of third side?
b) What is the length of wire?
c) Write the length of wire in millimetre
Answer: 
a) √5 metre 
b) 3 + √5 metre 
c) 3 + 2.236 = 5.236metre = 5236 millimetre

34. Hypotenuse of a right triangle is 1 .5 metre.The shortest side is 0.5 metre.
a) What is the length of third side?
b) What is the perimeter of the triangle ?
c) Write the perimeter in millimetre. [√2 ≈ 1.414, √3 ≈ 1.732, √5 ≈ 2.236]
Answer: 
a) √2 metre 
b) 2 + √2 metre 
c) 2 + 1.414 = 3.414 metre = 3414 millimetre

35. A steel wire has length  √3 metre. A piece of length √2 metre is cut off from one end.
a) What is the length of the rest?
b) Write the approximate length of the remaining part in centimetre?
c) Write the length of the remaining part in millimetre [√2 = 1.414, √3 = 1.732, √5 = 2.236]
Answer: 
a) √3 - √2 
b) 0.318 metre = 31.8 metre 
c) 318 millimetre

36. Two square papers of area 3 m 2 and 2 m 2 are placed as shown on a table. Two vertices are joined by dotted lines.

a) What is the area of square drawn on the dotted line as side?
b) What is the length of dotted line?
c) If x and y are the area of squares shown in the figure then what is the length of dotted line?
( √2= 1.414, √3 = 1.732, √5 = 2.236)
Answer: 
a) 5 Sq.m 
b) √5 m 
c) √ (x + y) m

37. Look at the decimal form of fractions
a)  Write 4/9 as decimal 
b)  If x = 0.444 · · · then what is √x in the fractional form ?
c)  If x = 0.444 · · · then what is √x in the decimal form ?
Answer: 
a) 0.444 · · · 
b) 0.444 · · · = 4/9 
c) √0.444 · · · = √(4/9 )= 2/3 =6/9 = 0.666...


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