Properties of Triangle

(a) Since AM≥G⋅M
∴‌‌‌

p+q

2

≥√pq
⇒P2+q2≥2qr
So (a) is correct.
(b) ‌+p‌cos‌Q
‌ [By projection formula ‌p=q‌cos‌R+r‌cos‌Q]
⇒‌q+p≥r
‌[‌ In triangle sum of two sides greater than third sides] ‌
‌‌ So (b) is correct. ‌
(c) Bysine rule, ‌‌[∵AM≥GM]
So (c) is incorrect.
(d) If p<q and q<r then p is smallest side, therefore one of Q or R be obtuse angle. So, one of cos‌Q or cos‌R can be negative. Therefore cos‌Q>‌

p

r

and cos‌R>‌

p

q

cannot hold always.
So (d) is incorrect.