6th Standard Syllabus & Materials
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Published on: 25/11/2019
Download Tamil Nadu 6th Standard Maths question papers, model tests, one-mark questions, important questions, and public exam papers in PDF format. Free study materials and answer keys for TN State Board students.
Questions + Answers key
Take MCQ Maths Test1.
Which of the following statements is true? Why?
(a) Every equilateral triangle is an isosceles triangle.
(b) Every isosceles triangle is an equilateral triangle.
2.
Is a triangle possible with the angles 90°, 90° and 0°? Why?
3.
Draw a line segment AB of length 6 cm. At each end of this line segment AB, draw a line perpendicular to the line AB. Are these lines parallel?
4.
An electrician buys a used T.V. for Rs. 12,000 and a used Fridge for Rs. 11,000. After spending Rs. 1000 on repairing the T.V. and Rs. 1500 on painting the Fridge, he fixes up the M.P. of T.V. as Rs. 15,000 and that of Fridge as Rs. 15,500. If he gives Rs. 1000 discount on each find his profit or loss.
5.
A store purchased pens at Rs. 216 per dozen. He paid Rs. 58 for conveyance and sold the pens at the discount of Rs. 2 per pen and made a overall profit of Rs. 50. Find the M.P. of each pen.
6.
A man bought 75 Mangoes for Rs. 300 and sold 50 Mangoes for Rs. 300. If he sold all the mangoes at the same price, find his profit or loss.
7.
A squirrel wants to eat the grains quickly. Help the Squirrel to find the shortest way to reach the grains. (Use your scale to measure length of the line segments)
8.
The saplings are planted at a distance of 2 m 50 cm in the road of length 5 km by saravanan. If he has 2560 saplings, how many saplings will be planted by him? how many saplings are left?
9.
A flag pole is 5 m 35 cm long. What is the length of the flag pole in cm?
10.
The sum of three prime numbers is 80. The difference of two of them is 4. Find the numbers.
11.
The LCM of two numbers is 6 times their HCF. If the HCF is 12 and one of the numbers is 36, then find the other number.
12.
Find the prime factorisation of each number by factor tree method and division method.
a) 60
b) 128
c) 144
d) 198
e) 420
f) 999
13.
Which of the following is not possible?
An obtuse isosceles triangle
An acute isosceles triangle
An obtuse equilateral triangle
An acute equilateral triangle
14.
An equilateral triangle is
an obtuse angled triangle
a right angled triangle
an acute angled triangle
a scalene triangle
15.
Discount = M.P. - _____________
Profit
S.P.
Loss
C.P.
16.
There is no profit or loss when
C.P. = S.P.
C.P > S.P.
C.P < S.P.
M.P. = Discount
17.
3 weeks = ___________ days
21
7
14
28
18.
2 days = ____________ hours.
38
48
28
40
19.
Which is the greatest? 0.007 g, 70 mg, 0.07 cg
0.07 cg
0.007 g
70 mg
all are equal
20.
The HCF of two numbers is 2 and their LCM is 154. If the difference between the numbers is 8, then the sum is
26
36
46
56
21.
If the number 6354 * 97 is divisible by 9, then the value * is
2
4
6
7
22.
The factors of a number are 1, 2, 4, 5, 8, 10, 16, 20, 40 and 80. What is the number?
80
100
128
160
23.
The sum of three angles of a triangle is ___________.
24.
In an isosceles triangle ______________ angles are equal.
25.
20 l – 1 l 500 ml = _________l _________ml
26.
The least number that should be added to 57 so that the sum is exactly divisible by 2, 3, 4 and 5 is ______________
27.
If the LCM of 3 and 9 is 9, then their HCF is _______________
28.
A football team gains 3 and 4 points for successive 2 days and loses 5 points on the third day. Find the total points scored by the team and also represent this in tree diagram.
29.
Complete the following table.
| Sl. No | C.P. in Rs. | M.P. in Rs | S.P. in Rs. | Discount in Rs. | Profit in Rs. | Loss in Rs. |
|---|---|---|---|---|---|---|
| i | 110 | 130 | 5 | |||
| ii | 110 | 130 | 20 | |||
| iii | 130 | 15 | 30 | |||
| iv | 130 | Nil | 25 | |||
| v | 125 | Nil | Nil | Nil | ||
| vi | 350 | 50 | 100 | Nil |
30.
Find the LCM of 156 and 124.
31.
Convert '5a' into Tree diagram
32.
Can a triangle be formed with 7 cm, 10 cm and 5 cm as its sides?
33.
Muthu has a car worth Rs. 8,50,000 and he wants to sell it at a profit of Rs. 25,000. What should be the selling price of the car?
34.
Convert into lower units:
(i) 15 km (m, cm, mm)
(ii) 12 kg (g, mg)
35.
Find A as required:
(i) The greatest 2 digit number 9A is divisible by 2.
(ii) The least number 567A is divisible by 3.
(iii) The greatest 3 digit number 9A6 is divisible by 6.
(iv) The number A08 is divisible by 4 and 9.
(v) The number 225A85 is divisible by 11.
36.
Karkuzhali's bag 1kg 250g and Poongkodi's bag 2kg 750g. The total weight of their bags 4kg
37.
Meena bought 250 ml of buttermilk which is equal to 2.5 l.
38.
Pugazhenthi ate 100 g of nuts which is equal to 0.1 kg.
39.
The HCF of two numbers is always a factor of their LCM
40.
Every natural number is either prime or composite
41.
All sides are equal
42.
Two sides of equal length
43.
One obtuse angle
44.
4.15
45.
11.50
1.
'a' is true.
An isosceles triangle need not have three equal sides.
2.
No, It is not possible with angles 90°, 90°, 0°.
Because there cannot be two right angles in a triangle
3.
l and m are parallel lines.
Yes lines are parallel
4.
c.p T.V. = Rs. 12,000
He spent = Rs. 1,000
= Rs. 13,000
m.p = Rs. 15,000
Discount = Rs. 1,000
c.p Fridge = Rs. 11,000
Painting Charges = Rs. 1,500
= Rs. 12,500
m.p = 15,500
Discount = Rs. 1,000
c.p of tv and fridge
= 13,000 + 12,500
c.p = Rs. 25,500
m.p = Rs. 15,000 + 15,500 = Rs. 30,500
Discount = Rs. 1,000 + Rs. 1,000 =
= Rs. 2000
Therefore s.p = m.p - Discount
= 30,500 - 2,000 = Rs. 28,500
s.p = Rs. 28,500
Here, s.p > c.p
Therefore profit = s.p - c.p
= 28,500 - 25,500
Therefore Profit = Rs. 3,000
5.
Given
Profit = Rs. 50
1 dozen Pens Rs. 216
Therefore 12 pens = 216
He paid = 48
c.p = Rs. 274
s.p = c.p + profit
= Rs. 274 + Rs. 50
s.p = Rs. 324
Discount = Rs. 2
1 dozen = 2 \(\times\)12 = Rs. 24
m.p = s.p + discount
= Rs. 324 + Rs. 24
12 pens = Rs. 348
Therefore 1 pen = 348 / 12 = 29
Therefore the m.p of each pen = Rs. 29
6.
If the man bought 75 Mangoes for Rs. 300 then, Cost Price of 1 Mango = 300/75 = Rs. 4
If 50 Mangoes were sold for Rs. 300 then, Selling Price of 1 Mango is 300/50 = Rs. 6
\(\therefore\) Selling price of 75 Mangoes at the rate of Rs 6 is 75 \(\times\) 6 = Rs. 450
Selling Price > Cost Price
\(\therefore\) Profit = Selling Price - Cost Price = 450 - 300 = Rs. 150
7.
Length of the line segments are
AB = 2 cm, BC = 2.5 cm, CD = 2.5 cm DE = 2 cm.
1st way distance = AB + BC + CD + DE = [2 + 2.5 + 2.5 + 2]cm = 9 cm
2nd way distance = AG = 2.5 cm, GF = 1.7 cm, F to E = 1.7 + 2.8 = 4.5 cm
= (2.5 + 1.7 + 4.5) cm = 8.7 cm
3rd way distance = AH = 3 cm, HI = 2.3 cm, IJ = 1 cm, JE = 3.2cm
= [3 + 2.3 + 1 + 3.2] cm = 9.5cm
Therefore the shortest way to reach the grains = 2nd way (middle way 8.7 cm distance)
8.
The saplings are planted at a distance = 2 m 50 cm = 2 m 50 cm
The road of length = 5 km = 5000 m
= 5000 \(\times\) 100
= 500000 cm
No. of Saplings = 2560
= 2000 saplings will be planted by him.
Therefore 560 saplings are left.
9.
The length of a flag pole = 5 m 35 cm long
= (5 \(\times\) 100) cm + 35 cm 1m = 100 cm
= 500 cm + 35 cm
= 535 cm
The flag pole is 535 cm long.
10.
Given statement
The sum of 3 prime numbers is 80.
The difference of two of them is 4.
Let the 3 prime numbers be x, y and z
x + y + z = 80 and z - y = 4
Prime numbers are
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79
80 = 2 + 37 + 41
= z - y
= 41 - 37 = 4
Therefore x = 2, y = 37, z = 41
Ans : The 3 prime numbers are 2, 37 and 41.
11.
Given LCM = 6 \(\times\) HCF
HCF = 12
one of the numbers = 36
Product of 2 given numbers = LCM \(\times\) HCF
Therefore 36 x other number = 6HCF \(\times\) 12 = 6 \(\times\) 12 \(\times\) 12
Therefore other number =( 6 \(\times\) 12 \(\times\) 12) / 36 = 6 \(\times\) 4 = 24
Other number is 24.
12.
a) 60
i) Division method:
Therefore 60 = \(2 \times 2 \times 3 \times 5\)
(ii) Factor Tree method:
b) 128
i) Division method:
Therefore 128 = \(2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2\)
(ii) Factor Tree method:
Therefore 128 = \(2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2\)
c) 144
i) Division method:
Therefore 144 = \(2\times 2 \times 2 \times 2 \times 3 \times 3\)
ii) Factor Tree method:
Therefore 144 = \(2 \times 2 \times 2 \times 2 \times 3 \times 3 .\)
d) 198
i) Division method:
Therefore 144 = \(2 \times 3 \times 3 \times 11\)
ii) Factor Tree method:
Therefore 144 = \(2 \times 3 \times 3 \times 11\)
e) 420
i) Division method:
Therefore 420 = \(2 \times 2 \times 3 \times 5 \times 7\)
ii) Factor Tree method.
Therefore 420 = \(2 \times 2 \times 3 \times 5 \times 7\)
f) 999
i) Division method:
Therefore 999 = \(3 \times 3 \times 3 \times 37\)
ii) Factor Tree method:
Therefore 999 = \(3 \times 3 \times 3 \times 37\)
13.
(c)
An obtuse equilateral triangle
14.
(c)
an acute angled triangle
15.
(b)
S.P.
16.
(a)
C.P. = S.P.
17.
(a)
21
18.
(b)
48
19.
(c)
70 mg
20.
(b)
36
21.
(a)
2
22.
(a)
80
23.
( )
180°
24.
( )
two
25.
( )
18 l 500 ml
26.
3
27.
3
28.
A football team gains
1st day = 3 points
2nd day = 4 points = 3 + 4
A football team loses 5 points = (-5)
Therefore 3rd day = (-5) points (loses)
Total Points scored
((3+4) - 5) = 2
Tree Diagram
29.
(i) C.P. = Rs. 110
M.P. = Rs. 130
Discount = Rs. 5
S.P. = M.P. - Discount
= Rs. 130 - Rs. 5
=Rs. 125
Profit = S.P. - C.P.
=Rs. 125 - Rs. 110
=Rs. 15
(ii) C.P. = Rs. 110
M.P. = Rs. 130
Discount = Rs. 20
S.P. = M.P. - Discount
= Rs. 130 - Rs. 20
= Rs.110
C.P. = S.P. \(\Rightarrow\) No profit or No loss.
(iii) M.P. = Rs. 130
Discount = Rs. 15
S.P. = M.P. - Discount
= Rs. 130 - Rs15
=Rs. 115
Profit = Rs. 30
Profit = S.P. - C.P.
Rs. 30 = Rs. 115 - C.P.
C.P. = Rs. 115 - Rs. 30
= Rs. 85
(iv) M.P. = Rs.130
Loss = Rs. 25
S.P. = M.P. - Discount
= Rs. 130 - Rs. 0
= Rs. 130
Loss = C.P. - S.P.
Rs. 25 = C.P. - Rs. 130
C.P. = Rs. 25 + Rs. 130
= Rs. 155
(v) M.P. = Rs. 125
Discount = Rs. 0
S.P. = M.P. - Discount
= Rs.125 - Rs. 0
= Rs. 125
No profit / No loss
C.P. = S.P.
C.P. = Rs. 125
(vi) S.P. = Rs. 350
Discount = Rs. 50
Profit = Rs. 100
M.P. = S.P.+ Discount
= Rs. 350+ Rs. 50 = Rs. 400
Profit = S.P. - C.P.
Rs 100 = Rs. 350 - C.P.
C.P. = Rs. 350 - Rs. 100
= Rs. 250
30.
Solution: By Division method
Step 1: Start with the smallest prime factor and go on dividing till all the numbers are divided as given below.
Step 2: LCM = product of all prime factors
= 2 \(\times\) 2 \(\times\) 3 \(\times\) 13 \(\times\) 31 = 4836
Thus, the LCM of 156 and 124 is 4836.
By Prime Factorisation method
Step 1: We write the prime factors of 156 and 124 as given below (use of divisibility test rules will also help).
156 = 2 \(\times\) 78 = 2 \(\times\) 2 \(\times\) 39 = 2 \(\times\) 2 \(\times\) 3 \(\times\) 13
124 = 2 \(\times\) 62 = 2 \(\times\) 2 \(\times\) 31
Step 2: The product of common factors is 2 \(\times\)2 and also the product of the factors that are not common is 3 \(\times\) 13 \(\times\) 31.
Step 3: Now, LCM = product of common factors x product of factors that are not common
= (2 \(\times\) 2) \(\times\) (3 \(\times\) 13 \(\times\) 31) = 4 \(\times\) 1209 = 4836
Thus, LCM of 156 and 124 is 4836.
(or)
156 = 2 \(\times\) 78 = 2 \(\times\) 2 \(\times\) 39 = 2 \(\times\) 2 \(\times\) 3 \(\times\) 13;
124 = 2 \(\times\) 62 = 2 \(\times\) 2 \(\times\) 31
The prime factor 2 appears a maximum of 2 times in the prime factorization of 156 and 124, the prime factor 3 appears only 1 time in the prime factorization of 156, the prime factor 13 appears only 1 time in the prime factorization of 156 and the prime factor 31 appears only 1 time in the prime factorization of 124.
Hence, the required LCM = (2 \(\times\) 2) \(\times\) 3 \(\times\) 13 \(\times\) 31 = 4836.
31.
32.
Instead of checking triangle inequality by all the sides in the triangle, check only with two smaller sides.
Sum of two smaller sides of the triangle = 5+7=12 cm > 10 cm, the third side. It is greater than the third side. So, a triangle can be formed with the given sides.
33.
Given
Muthu has a car worth = Rs. 8,50,000
Profit = Rs. 25,000
s.p = c.p + profit
= 8,50,000 + 25,000
Therefore = Rs. 8,75,000
34.
15 km (m, cm, mm)
1 km = 1000 m
1 m = 100 cm
1 cm= 10mm
* 1 km = 1000 m
15 km = 15 \(\times\) 1000 m
= 15000 m
* 1 m = 100 m
15000 m = 15000 \(\times\) 100
= 150000 cm
* 1 cm = 10 mm
Therefore 1500000 em = 10 \(\times\) 1500000
= 15000000 mm
Ans : 15 km = 15000 m, 1500000 cm, 15000000mm
(ii) 12kg (g, mg)
1000 g = 1 kg
1000mg = 1 g
* 1000g = 1 kg
12kg = 12 \(\times\) (1000) g
= 12000 g
* 1g = 1000mg
12000 g = 12000 \(\times\) 1000 mg
= 12000000 mg
35.
i) The greatest 2 digit number 9A is divisible by 2.
Greatest two digit number = 99.
But, given 9A is divisible by 2,
So, two digit number = 98
Therefore A = 8
ii) The least number 567A is divisible by 3.
The least number = 5670
Sum of the digits = 5 + 6 + 7 + 0 = 18 is divisible by 3.
Therefore A = 0
iii) The greatest 3 digit number 9A6 is divisible by 6
The greatest 3 digit number = 999.
But, given 9A6 is divisible by 6.
Therefore 9A6 = 996.
Therefore A = 9
iv) The number A08 is divisible by 4 & 9
Given number = A08
A08 is divisible by 4 means 108.
A08 is divisible by 9 means 108.
Therefore 108 is divisible by both 4 & 9.
Therefore A = 1
v) The number 225A85 is divisible by H.
Given number = 225A85
Also given 225A85 is divisible by 11.
Difference between the sum of alternative digits = (2 + 5 + 8) - (2 + A + 5) = 15 - (2 + 8 + 5) = 15 - 15 = 0
Therefore 225A85 = 225885
Therefore A = 8
36.
(a)
37.
(b)
38.
(a)
39.
(a)
40.
(b)
41.
Equilateral triangle
42.
Isosceles triangle
43.
Obtuse angled triangle
44.
quarter past 4
45.
10 minutes to 12
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