Numbers and Algebra

(a)a+b+c

(b)4b²

(c)abc

(d)a²+b²

(a)y(y+2)

(b)y-2

(c)2(y+2)

(d)(y+2)(y²-2y+4)

(a) (m²-4mn+2n²)/2n²

(b) ((m-2n)²-n²)/2n²

(c) (m²-4mn-n²)/2n²

(d) (m²-4mn-2n²)/2n²

(a) x≤2

(b) x≥2

(c) x≤6

(d) x≥6

(a) √2 +√5=√7

(b) √2+√5≤√7

(c) √2+√5+<√7

(d) √2+√5>√7

(a) y/x≥2, y/x≤2/3

(b) y/x≥-2/3,y/x≤2

(c) y/x≥-2/3,y/x≤1/4

(d) y/x≥-4,y/x≤4

(a) 2≤ 2ⁿ(n+1)ⁿ/nⁿ ≤3

(b) 2ⁿ⁺¹ ≤ 2ⁿ(n+1)ⁿ/nⁿ ≤ 3.2ⁿ

(c) 2ⁿ≤ 2ⁿ(n+1)ⁿ ≤ 3.2ⁿ

(d) None of these

(a) 10n <a! <n

(b) n <a! <10ⁿ

(c) 10n <a! <10ⁿ

(d) 10ⁿ <a

(a) Sum of four consecutive even numbers is always divisible by 8

(b) Sum of four consecutive odd numbers is always divisible by 8

(c) Product of any n consecutive natural numbers may not be divisible by n!.

(d) Product of 4 consecutive odd numbers is always divisible by 25.

(a) I and II only

(b) II and III only

(c) All of these.

(d) None of these.