1st CHAPTER (REAL NUMBERS)
2
Marks
1.
Express
3825 as a product of prime factors.
2.
Prove
is an irrational number.
3.
Explain
why the numbers
is composite.
4.
Prove
that
is an irrational number.
5.
Write
21975 as product of its prime factors.
6.
Explain
why
is a composite number.
7.
Find
the LCM an HCF of 12 , 15 , 21 by applying the prime factorization method.
8.
Is
as a composite number.
3 marks
9.
Prove that
is an irrational number.
OR
Prove
that
is an irrational number.
10. Prove
that
is an irrational number.
11. prove that the square of any positive
integer is of the form of 3m, or 3m+1 but not of the form of 3m + 2.
12. Show that any positive integers is of the
form 4q + 1 or 4q + 3, where q is a positive integer.
13. Show that
I an irrational number.
OR
Prove
that
is irrational number.
14. Prove
is an irrational number.
15. Show that
can end with the digit zero for any natural
number n.
16. Prove that
is an irrational number.
4
marks
17. Prove that
is divisible by 2 for every positive integer
n.
18. Use Euclid division lemma to show that
the square of any positive integer is either of the form 3m, 3m+1 for some
integer m.
19. Show that
can not end with 2 for any integer n.
20. Show that
can not end with the digit 0, 2, 4, 6 and 8 for
any natural number n.
21. Show that any positive odd integer is of
the form of 6q + 1 or 6q + 3 or 6q + 5, where q is a positive integer.
22. Show that any even integer is of the form of 6q or 6q + 2 or 6q + 4,
where q is positive integer.
23. Show that an even integer is of the form
of 4q or 4q + 2 where q is a positive integer.
24. For any positive integer n,
is divisible by 6.
25. Show that
is divisible by 8, if n is odd positive
integer.
2ND CHAPTER
(POLYNOMIALS)
1.
Find
the zeros of the quadratic polynomial
and verify the relationship between zeros and
coefficient the polynomial.
2.
Divide
by
and verify
the division algorithm.
3.
If
α and β are the zeros of the quadratic polynomial
,
then find the value of
4.
Find
the zeros of the quadratic polynomial
and verify relationship between zeros and
coefficient of the polynomial.
5.
α,
β are the roots of the quadratic polynomial
find the value of k, if
.
6.
If
the polynomial
is divided by another polynomial
,
remainder comes out to be
find the value of a and b.
7.
If
the product of zeros of the polynomial,
is 6, find the value of k.
8.
On
dividing the polynomial
by a polynomial
the q(x)and r(x) were
and 5 respectively find g(x).
9.
What
are the q(x) and r (x), when
is divided by
10. Find the zeros of the quadratic
polynomial
and verify relationship between zeros and
coefficient of the polynomial..
3
marks
11. If
α and β are the zeros of the quadratic polynomial
find a quadratic polynomial whose zeros are
.
12. If α and β are the zeros of the quadratic
polynomial
,
find the value of a, if
13. If α and β are the zeros of the quadratic polynomial
find a quadratic polynomial whose zeros are
14. If α and β are the zeros of the quadratic polynomial
such
that
find the value of k.
15. If α and β are the zeros of the quadratic
polynomial
,
such that
find
the value of k.
16. If α and
are the zeros of the quadratic polynomial
,
find the value of k.
17. If α and β are the zeros of the quadratic
polynomial
,
satisfying
then
find the value of k for this to be possible.
18. If α and β are the zeros of the quadratic
polynomial
find a quadratic polynomial whose zeros are
.
19. On dividing
by a polynomial g(x) the q(x) and r(x) were
respectively. Find g(x).
20. If
the zeros of the polynomial
are
21. If 2 is a zero of both the polynomial
find the value of
4
MARKS
22. If
are the zeros of polynomial
then find the value of
23. If two zeros of the polynomial
are
find all the zeros.
24. If two zeros of the polynomial
are
find all the zeros.
25. Find all the zeros of
if it is given that two of its zeros are
26. Obtain all the zeros
if two of its zeros are
27. Divide
by
and verify the division algorithm.
28. Obtain all the zeros
if two of its zeros are
29. If the zeros of the polynomial
,
are
the
value of a and b.
