Hg
Name: Class 10 Date:
___________________________________________________________________________________________________________________________________
___________________________________________________________________________________________________________________________________
The Hg Classes (8
th
to 12
th
) By: Er Hershit Goyal (B.Tech. IIT BHU), 134-SF, Woodstock Floors, Nirvana Country, Sector 50, GURUGRAM +91 9599697178.
fb.me/thehgclasses linkedin.com/company/the-hg-classes instagram.com/the_hg_classes g.page/the-hg-classes-gurugram thehgclasses.co.in
Real Numbers, Polynomials
2 marks each
1. Show that 12
n
can’t end with digit 0 or 5 for any natural number n.
2. Show that n
2
– 1 is divisible by 8, if n is an odd positive number.
3. On a morning walk 3 persons step of together and their steps measure 40, 42 and 45 respectively. What is the
minimum distance each should walk so that each can cover the same distance and complete steps.
4. Prove that √5 + √3 is irrational.
5. If α and β are the zeroes of the quadratic polynomial kx
2
+ 4x + 4 such that α
2
+ β
2
= 24, find the values of k.
3 marks each
6. Show that one and only one out of n, n+2 or n+4 is divisible by 3, where n is any positive integer.
7. If p and q are the zeroes of the quadratic polynomial f(x) = 3x
2
– 4x + 1, find a quadratic polynomial whose zeroes
are p
2
/q and q
2
/p.
8. If the zeroes of the polynomial x
4
– 6x
3
– 26x
2
+ 138x – 35 are 2+√3 and 2-√3, find other zeroes.
1 mark each (Multiple Choice Questions) Show working where necessary:
9. If the HCF of 65 and 117 is expressible in the form 65m – 117, then the value of m is:
a. 1 b. 2 c. 4 d. 3
10. If n is any natural number, then 6
n
– 5
n
always ends with:
a. 1 b. 6 c. 5 d. 7
11. If two positive integers are written as x
3
y
2
& xy
3
where x an y are prime, then HCF of them is:
a. xy b. xy² c. x
3
y
3
d. x²y
2
12. If α and β are the zeroes of the polynomial x
2
– p(x+1) – c such that (α+1)(β +1) = 0, then c =
a. 1 b. 0 c. -1 d. 2
13. The no. of polynomials having zeroes -2 and 5 is
a. 1 b. 2 c. 3 d. more than 3
14. If one of the zeroes of a quadratic polynomial x
2
+ ax + b is the negative of the other, then it
a. Has no linear term, constant term is -ve d. Has no linear term, constant term is +ve
b. Can have linear term, constant term is -ve
c. Can have a linear term, constant term is +ve.
Hg
Name: Class 10 Date:
___________________________________________________________________________________________________________________________________
___________________________________________________________________________________________________________________________________
The Hg Classes (8
th
to 12
th
) By: Er Hershit Goyal (B.Tech. IIT BHU), 134-SF, Woodstock Floors, Nirvana Country, Sector 50, GURUGRAM +91 9599697178.
fb.me/thehgclasses linkedin.com/company/the-hg-classes instagram.com/the_hg_classes g.page/the-hg-classes-gurugram thehgclasses.co.in
Answers:
1) -
2) -
3) 2520
4) -
5)-a, -b
6) k =
2/3, k = -
1
8)
9) b
10) a
11) b
12) a
13) d
14) a