Download CLASS - X Mathematics (Real Number) 1. is a (a) Composite

CLASS - X Mathematics (Real Number)
1.
2.
7 ×11× 13 × 15 + 15 is a
(a) Composite number
(c) Prime number
(b) Whole number
(d) None of these
For what least value of ‘n’ a natural number, ( 24 ) is divisible by 8?
n
(a) 0
(c) 1
(b) -1
(d) No value of ‘n’ is possible
3.
The sum of a rational and an irrational is
(b) Irrational
(a) Rational
(c) Both (a) & (c)
(d) Either (a) or (b)
4.
HCF of two numbers is 113, their LCM is 56952. It one number is 904. The other
number is:
(a) 7719
(b) 7119
(c) 7791
(d) 7911
5.
Show that every positive even integer is of the from 2q and that every positive
odd integer is the four 2q+1 for some integer q.
6.
Show that any number of the form 4n , nEN can never end with the digit 0.
7.
Use Euclid’s division algorithm to find the HCF of 4052 and 12576
8.
Given that HCF of two numbers is 23 and their LCM is 1449. If one of the
numbers is 161, find the other.
9.
Find the greatest of 6 digits exactly divisible by 24, 15 and 36
10.
Prove that the square of any positive integer is of the form 4q or 4q+1 for some
integer.
11.
144 cartoons of coke can and 90 cartoons if Pepsi can are to be stacked in a
canteen It each stack is of the same height and is to contain cartoons of the same
Drink. What would be the greaten number of cartoons each stack would have
12.
Prove that Product of three consecutive positive integers is divisible by 6.
Class X- Mathematics (Real Number)
1.
2.
3.
4.
5.
A lemma is an axiom used for proving
[1]
(a) other statement
(b) no statement
(c) Contradictory statement
(d) none of these
If HCF of two numbers is 1, the Two number are called relatively ________ or________
(a) Prime, co-prime
(b) Composite, prime
(c) Both (a) and (b)
(d) None of these
[1]
[1]
2.35 is
(a) a terminating decimal number
(b) a rational number
(c) an irrational number
(d) Both (a) and (b)
2.13113111311113……is
[1]
(a) a rational number
(b) a non terminating decimal number
(c) an irrational number
(d) both (a) & (c)
Show that every positive odd integer is of the form (4q+1) or (4q+3) for same inter [2]
q.
6.
Show that any number of the form 6x, x ∈ N can never end with the digit 0
[2]
7.
Find HCF and LCM of 18 and 24 by the prime factorization method.
[2]
8.
The HCF of two numbers is 23 and their LCM is 1449. If one of the number is 161, [2]
find the other
9.
Prove that (3- 5 ) is irrational.
[3]
10.
Prove that if x and y are odd positive integers then x2+y2 is even but not divisible [3]
by 4
11.
Show that one and only one out of n, (n+2) or (n+4) is divisible by 3, where n ∈ N
12.
Use Euclid’s division lemma to show that the square of any positive integer of the [3]
from 3m or (3m+1) for some integer q
[3]
Class X - Mathematics (Real Numbers)
1.
The smallest composite number is:-
(a) 1
2.
3.
4.
[1]
(b) 2
(c) 3
(d) 4
[1]
1.2348 is
(a) an integer
(b) an irrational number
(c) a rational number
(d) None of there,
π is (a) rational
(b) irrational
[1]
(c) both (a) & (b)
(d) neither rational nor irrational
(2+ 5 ) is (a) rational
(b) irrational
(c) An integer
(d) Not real
[1]
5.
Prove that the square of any positive integer of the form 5g+1 is of the same form
[2]
6.
Use Euclid’s division algorithm to find the HCF of 4052 and 12576
[2]
7.
Find the largest number which divides 245 and 1029 leaving remainder 5 in each [2]
case
8.
A shop keeper has 120 litres of petrol, 180 litres of diesel and 240 litres of [2]
kerosene. He wants to sell oil by filling the three kinds of oils in tins of equal
capacity. What should be the greatest capacity of such a tin
9.
Prove that in n is not a rational number, if n is not perfect square
10.
Prove that the difference and quotient of 3 + 2 3 and 3 − 2 3 are irrational
[3]
11.
Show that (n2-1) is divisible by 8, if n is an odd positive integer
[3]
12.
Use Euclid division lemma to show that cube of any positive integer is either of the [3]
(
form 9m. (9m+1) or 9m+8
)
(
)
[3]
Class X - Mathematics (Polynomials)
1.
Which of the following is polynomial?
1
(a) x 2 − 6 x + 2
(b) x +
x
[1]
(c)
5
x − 3x + 1
2
(d) none of these
2.
Polynomial 2 x 4 + 3 x3 − 5 x 2 − 5 x 2 + 9 x + 1 is a
(a) Linear polynomial
(b) quadratic polynomial
(c) cubic polynomial
(d) Biquadratic polynomial
[1]
3.
If α and β are zero’s of x 2 + 5 x + 8 then the value of (α + β ) is
[1]
(a) 5
4.
5.
6.
8.
(c) 8
(d) -8
The sum and product of the zeros of a quadratic polynomial are 2 and -15 [1]
respectively. The quadratic polynomial is
(a) x 2 − 2 x + 15
(b) x 2 − 2 x − 15
(c) x 2 + 2 x − 15
(d) x 2 + 2 x + 15
Find the quadratic polynomial where sum and product of the zeros one a and
1
.
a
[2]
If α and β are the zeroes of the quadratic polynomial f ( x ) = x 2 − x − 4, find the [2]
value of
7.
(b) -5
1
α
+
1
β
− αβ
If the square of the difference of the zeroes of the quadratic polynomial [2]
f ( x ) = x 2 + px + 45 is equal to 144, find the value of p.
Divide ( 6 x3 − 26 x − 21 + x 2 ) by ( −7 + 3x )
[2]
9.
Apply division algorithms to find the quotient q(x) and remainder r(x) an dividing [3]
f(x) by g(x) where f ( x ) = x3 − 6 x 2 + 11x − 6, g ( x ) = x 2 + x + 1
10.
If two zeroes of the polynomial x 4 − 6 x 3 − 26 x 2 + 138 x − 35 are 2 ± 3 , find the other [3]
zeroes.
11.
What must be subtracted from the polynomial f ( x ) = x 4 + 2 x 3 − 13x 2 − 12 x + 21 so [3]
that the resulting polynomial is exactly divisible by g ( x ) = x 2 − 4 x + 3
12.
What must be added to 6 x5 + 5 x 4 + 11x3 − 3 x 2 + x + 5 so that it may be exactly [3]
divisible by 3 x 2 − 2 x + 4
Class X - Mathematics (polynomials)
1.
If P(x)= 2x2-3x+5,3x+5,then P(-1) is equal to
(a) 7
(b) 8
(c) 9
(d) 10
[1]
2.
Zeroes of P(x) = x2-2x-3 are
(a) 3 and 1
(c) -3 and -1
[1]
3.
If α and β are the zeros of 2x2+5x-10, them the value of αβ is
(a) −
5
2
[1]
(b) 5
(c)-5
4.
(b) 3 and -1
(d) 1 and -3
(d)
2
5
A quadratic polynomial, the sum and product of whore zeros are 0 and [1]
5 respectively is
(a) x2+ 5
(c) x2-5
(b) x2- 5
(d) None of these
5.
Find the value of ‘k’ such that the quadratic polynomial x2-(k+6) x+2(2k+1) has [2]
sum of the zeros is half of their product
6.
If α and β are the zeroes of the quadratic polynomial f(x) = x2-p(x+1)-c, show that [2]
( α +1) ( β +1)=1-c
7.
If the sum of the zeroes of the quadratic polynomial f(t) = kt2+2t+3k is equal to [2]
their product, find the value if ‘k’
8.
Divide (x4-5x+6) by (2-x2)
9.
Find all the zeroes of the polynomial f(x) = 2x4-3x3-3x2+6x-2, if being given that [3]
two of its zeroes are
10.
11.
12.
[2]
2 and - 2
On dividing x3-3x2+x+2 by a polynomial g(x) the quotient and the remainder were [3]
(x-2) and -2x+4 respectively find g(x)
Find all zeroes of f(x) = 2x3-7x2+3x+6 if its two zero one -
3
and
2
3
2
[3]
Obtain all zeroes of the polynomial f(x)= 2x4+x3-14x2-19x-6, if two of its zeros are - [3]
2 and -1
Class X - Mathematics (Polynomials)
1.
Degree of polynomial y3-2y2- 3 y +
(a)
2.
3.
4.
1
2
(b) 2
Zeroes of P(x) = 2x2+9x-35 are
5
5
(a) 7 and
(b) -7 and
2
2
[1]
1
is
2
(c) 3
(d)
3
2
[1]
(c) 7 and 5
The quadratic polynomial whore zeros are 3 and -5 is
(a) x2+2x-15
(b) x2+3x-8
(c) x2-5x-15
(d) 7 and 2
[1]
(d) None of these
If α and β are the zeros of the quadratic polynomial P(x) = x2-px+q, then the value [1]
of α 2 + β 2 is equal to
(a) p2-2q
(b)
p
q
(c) q2-2p
(d) none of these
5.
Find the zeros of the polynomial p(x) = 4 3 x2+5x -2 3 and verify the [2]
relationship b/w the zeros and its coefficients
6.
Find the value of ‘k’ so that the zeroes of the quadratic polynomial 3x2-kx+14 are in [2]
the ratio 7:6
7.
If one zero of the quadratic polynomial f(x) = 4x2-8kx-9 is negative of the other, [2]
find the value of ‘k’.
8.
Cheek whether the polynomial (t2-3) is a factor of the polynomial 2t4+3t3-2t2-9t-12 [2]
by Division method
9.
Obtain all other zeroes of 3x4+6x3-2x2-10x-5. If two of its zeroes are
5
5
and −
3
3
[3]
10.
If the polynomial x4-6x3+16x2-25x+10 id divided by another polynomial x2-2x+k, [3]
the remainder comes out to be (x+a), find ‘k’ and ‘a’
11.
Find the value of ‘k’ for which the polynomial x4+10x3+25x2+15x+k is exactly [3]
divisible by (x+7)
12.
If α , and β are the zeros of the polynomial f(x) = x2+px+q form polynomial whore [3]
zeros are ( α + β )2 and ( α - β )2