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DELHI PUBLIC SCHOOL
BOKARO STEEL CITY
ASSIGNMENT FOR THE SESSION 2010-2011
Class: X
Subject : Mathematics
Assignment No. 1
REAL NUMBERS
1.
Show that any positive odd integer is of the form of 4p+1 or 4p+3, where p is some integer.
2.
Consider a number (14)n , where n is a natural number. Check whether there is any value of nєN
for which (14)n is divisible by 5.
3.
Prove that each of the following are irrational
a] 4√3
4.
b] 7-3√2
1
52
Use Euclid’s division algorithm, to find the HCF of
a] 455 & 42
5.
c]
b] 126 & 1078
c] 392 & 267540
Express each of the following as a non-terminating recurring decimal
a] 1/7
b] 13/44
c] 1/15
d] 1/370
6.
Find the HCF and LCM of 30, 72 and 432 by using the fundamental theorem of arithmetic.
7.
Show that one and only one out of p, p + 2 or p + 4 is divisible by 3, where p is any positive
integer.
8.
Check whether the following are composite or not
i) 3  4  7 11 7  7
ii) 5  3 11 23  5  23  11
9.
Prove that there is no rational number whose square is 8.
10.
Express the numbers
i) 0.3 178
ii) 2. 31 in the form
p
q
POLYNOMIALS
1.
Find a quadratic polynomial when the sum and product of zeros of the polynomial are given as
a] 3 & 5
b] -3 & 5/2
c] 5/7 & 0
d] 0 & -10/3
e] -√2 & √3
2.
Find the zeroes of the polynomial, also verify the relationship between the zeros and its
coefficients
a] 3x2 –x
b] 5x2 + 2x
c] t2 -2
d] x2 -7x + 10
3.
If one of the zeroes of the quadratic polynomial f(x) = 4x2 – 8kx – 9 is negative of the other , find
the value of k.
4.
Verify whether the given numbers are zeros of the cubic polynomial or not. Also verify the
relationship between the zeros and the coefficients in each case.
a] x3 – x ; 0,1 & -1
b] 2x3 – 5x2 + x + 2 + 1; 1, 2 & -1/2
5.
Find all the zeros of the polynomial 2x4 – 10x3 + 5x2 + 15x – 12, if two zeros are √(3/2) and √(3/2) .
6.
If the zeroes of the polynomial f(x) = x3 – 3x2 +x + 1 are a – b, a, a + b, find a and b.
7.
Divide p(x) = x4 – 5x + 6 by g(x) = 2 – x2 and verify division algorithm.
8.
On dividing 3x3 – 2x2 + 5x – 5 by a polynomial p(x), the quotient and the remainder are x2 – x + 2
and -7 respectively. Find p(x).
9.
Find the zeroes of the polynomial 2x3 + 5x2 – 28x – 15.
10.
Find the value of k for which the polynomial x4+10x3+25x2+15x+k is exactly divisible by x+7.
PAIR OF LINEAR EQUATIONS IN TWO VARIABLES
1.
Solve the following:a)
3
2
5 3

 5and   1
2x 3y
x y
b) 7x -2y = 5xy and 8x + 7y = 15xy
c) a(x+y) + b(x-y) = a2 – ab + b2 and a(x+y) - b(x-y) = a2 + ab + b2
d)
x y
x
y
  a  b and 2  2  2
a b
a
b
2.
Solve graphically 4x – 3y +4 =0 and 4x + 3y – 20 = 0. What is the area of the triangle enclosed
by the given lines and the x-axis?
3.
Find graphically, the vertices of the triangle whose sides have the equations 2y – x = 8 ; 5y – x =
14 and y – 2x =1
4.
For what value of k, the system of equations, kx + 3y = k-3 and 12x + ky = k, will have no
solution?
5.
Find the values of a & b for which the following system of linear equations has infinite solutions;
2x – 3y = 7 and ( a + b )x – ( a + b – 3 )y = 4a + b
6.
Find whether the given equations have a unique solution, no solution or infinite number of
solutions:
i) 6x + 5y = 4; 9x + 7.5y = 6
ii) x – 3y – 3 = 0 ; 3x – 9y – 2 = 0 iii) 2x + y = 5; 3x + 2y = 8
7.
Taxi fare consists of a constant charge together with the charge for the distance covered. A person
travelling 15 km pays Rs.115 for the journey and person travelling 27 km pays Rs.199 for it. Find
the charges one will have to pay for a journey of 50km.
8.
X takes 3 hours more than Y to walk 30km. But if X doubles his pace, he is ahead of Y by 1.5
hours. Find their speeds of walking.
9.
A boat can go 20 km upstream and 30 km down stream in 3 hours. It can go 20 km downstream
2
and 10 km upstream in 1 hours. Find the speed of the boat in still water and the speed of the
3
stream.
10.
Places A and B are 80 km apart from each other on a highway. A car starts from A and another
from B at the same time. If they move in the same direction, they meet in 8 hours and if they
move in opposite direction they meet in 1 hour 20 minutes. Find the speeds of the cars.
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