1. The decimal expansion of the rational number 6243
2
3 × 5
4 will terminate after how many
places?
2. If 241
4000
=
241
2 5
find the values of m & n where m & n are non-negative integers .Hence,
write its decimal expansion without actual division.
3. If HCF (a,b) =12 & axb =1800,then find LCM(a,b)
4. If α and β are the zeroes of the polynomial 21x2
– x – 2then find the value of α + β + αβ.
5. Find the zeroes of the polynomial x2 +
1
6
x – 2 and verify the relationship between the coefficients and the zeroes of the polynomial.
6. Is 7x6x5x4x3x2x1+7 a composite no. justify your answer.
7. If α andβ are the two zeroes of the polynomial 21x2
– x – 2. Find the quadratic
polynomial whose zeroes are 2α and 2β.
8. For what value of k, the pair of linear equations 2x + 7y = 5 , 6x + ky = 15 has no
solution.
9. Find the value of ‘k’ for which the pair of linear equations has infinitely many solutions.
(i) 2x + 3y – 7 = 0 and (k – 1)x + (k + 1)y = (3k – 1)
(ii)3 + 4 + 2 = 0 9 + 12 + = 0
10. HCF& LCM of two numbers is 9 & 459 respectively. If one of them is 27, find the other
number.
11. If the HCF of 408 and 1032 is expressed in the form 1032m – 408X5. Find m.
12. The HCF of 81 and 237 is express as a linear expression. i.e. HCF(81,237) = 81x –
237y.Find the value of x and y .
13. The length , breadth , height of room are 8m25cm, 6m75cm & 4m50cm respectively.
Find the length of the longest rod that can measure the three dimensions of the room
exactly.
14. Without drawing the graph ,find out whether the following system of linear equations
has a unique solution or are parallel or coincident :
(i) 2x – 3y = 6 and x + y = 1
(ii) 18 − 7 = 24 9
5
−
7
10
=
9
10
15. Determine by drawing graphs, whether the following pair of linear equations has infinite
number of solutions or unique solution or coincident lines :
(i) y = 5 ; y + 3 = 0 (ii) 3x + 4y = 12 ; 2x + 7y = 5 (iii) 3x – 2y = 12 ; x –
2
3
y – 4 = 0.
16. A merchant has 120 litres of oil of one kind,180litres of another kind & 240 litres of third
kind. He wants to sell the oil by filling the three kinds of oil in tins of equal capacity.
What should be the greatest capacity of such a tin.
16. Obtain the HCF of 420 & 272 by using Euclid’s division algorithm & verify the same by
using Fundamental Thm. of Arithmetic.
18. Prove that√3is an irrational no. Hence,show that 7-2√3is an irrational no.
19. Prove that 2√3 +√5 is an irrational number.
20. Use Euclid’s Division Lemma to show that the square of any positive integer is either of
the form 3m or 3m+1 for some integer of m.
21. Show that the cube of a positive integer of the form 6q+r,whereq is an integer &
r=0,1,2,3,4,5 is also of the form 6m+r.
22. For any positive integer n, prove that n3
-n is divisible by 6
23. Divide p(x) = x4
– 5x +6 by g(x) = 2 – x
2
and verify the result by division algorithm.
24. Obtain all the zeroes of the polynomial x4 + 4x3
– 2x3
– 20x – 15 if two of its zeroes are
√5 and -√5.
25. Obtain all the zeroes of the polynomial p(x) = x4
– 5x3 +3x2 +7x – 2 if two of its zeroes
are (2 + √3) and (2 -√3).
26. Find all the zeroes of the polynomial 2x4 + 7x3
– 19x2
– 14x + 30 if two of its zeroes are
√2 and -√2.
Answers
Answer:
ok wait so long ans
Step-by-step explanation:
2
3 × 5
4 will terminate after how many
places?
2. If 241
4000
=
241
2 5
find the values of m & n where m & n are non-negative integers .Hence,
write its decimal expansion without actual division.
3. If HCF (a,b) =12 & axb =1800,then find LCM(a,b)
4. If α and β are the zeroes of the polynomial 21x2
– x – 2then find the value of α + β + αβ.
5. Find the zeroes of the polynomial x2 +
1
6
x – 2 and verify the relationship between the coefficients and the zeroes of the polynomial.
6. Is 7x6x5x4x3x2x1+7 a composite no. justify your answer.
7. If α andβ are the two zeroes of the polynomial 21x2
– x – 2. Find the quadratic
polynomial whose zeroes are 2α and 2β.
8. For what value of k, the pair of linear equations 2x + 7y = 5 , 6x + ky = 15 has no
solution.
9. Find the value of ‘k’ for which the pair of linear equations has infinitely many solutions.
(i) 2x + 3y – 7 = 0 and (k – 1)x + (k + 1)y = (3k – 1)
(ii)3 + 4 + 2 = 0 9 + 12 + = 0
10. HCF& LCM of two numbers is 9 & 459 respectively. If one of them is 27, find the other
number.
11. If the HCF of 408 and 1032 is expressed in the form 1032m – 408X5. Find m.
12. The HCF of 81 and 237 is express as a linear expression. i.e. HCF(81,237) = 81x –
237y.Find the value of x and y .
13. The length , breadth , height of room are 8m25cm, 6m75cm & 4m50cm respectively.
Find the length of the longest rod that can measure the three dimensions of the room
exactly.
14. Without drawing the graph ,find out whether the following system of linear equations
has a unique solution or are parallel or coincident :
(i) 2x – 3y = 6 and x + y = 1
(ii) 18 − 7 = 24 9
5
−
7
10
=
9
10
15. Determine by drawing graphs, whether the following pair of linear equations has infinite
number of solutions or unique solution or coincident lines :
(i) y = 5 ; y + 3 = 0 (ii) 3x + 4y = 12 ; 2x + 7y = 5 (iii) 3x – 2y = 12 ; x –
2
3
y – 4 = 0.
16. A merchant has 120 litres of oil of one kind,180litres of another kind & 240 litres of third
kind. He wants to sell the oil by filling the three kinds of oil in tins of equal capacity.
What should be the greatest capacity of such a tin.
16. Obtain the HCF of 420 & 272 by using Euclid’s division algorithm & verify the same by
using Fundamental Thm. of Arithmetic.
18. Prove that√3is an irrational no. Hence,show that 7-2√3is an irrational no.
19. Prove that 2√3 +√5 is an irrational number.
20. Use Euclid’s Division Lemma to show that the square of any positive integer is either of
the form 3m or 3m+1 for some integer of m.
21. Show that the cube of a positive integer of the form 6q+r,whereq is an integer &
r=0,1,2,3,4,5 is also of the form 6m+r.
22. For any positive integer n, prove that n3
-n is divisible by 6
23. Divide p(x) = x4
– 5x +6 by g(x) = 2 – x
2
and verify the result by division algorithm.
24. Obtain all the zeroes of the polynomial x4 + 4x3
– 2x3
– 20x – 15 if two of its zeroes are
√5 and -√5.
25. Obtain all the zeroes of the polynomial p(x) = x4
– 5x3 +3x2 +7x – 2 if two of its zeroes
are (2 + √3) and (2 -√3).
26. Find all the zeroes of the polynomial 2x4 + 7x3
– 19x2
– 14x + 30 if two of its zeroes are
√2 and -√2.
Answer:
Step-by-step explanation:
for this long question what