Mathematical ReasoningHard
Question
Consider three statements :
Statement-1 :
nCr. 2n.
= 5n
Statement-2 : If sides of ᐃABC are in A.P., then one angle of ᐃABC must be 60o.
Statement-3 : Equation a + a3 + a5 +.......infinite terms = √ 2 holds for two real values of a.
Statement-1 :
nCr. 2n. = 5nStatement-2 : If sides of ᐃABC are in A.P., then one angle of ᐃABC must be 60o.
Statement-3 : Equation a + a3 + a5 +.......infinite terms = √ 2 holds for two real values of a.
Options
A.exactly one statement is false.
B.exactly one statement is true.
C.statement-3 is true & statement-1 is false.
D.statement-1 is true & statement-3 is false.
Solution
Statement-1 :
= 2
nCr . 
= 2n
= 5n
Statement-2 : ∵ sides are in A.P
⇒ sinA, sinB and sinC are in A.P
⇒ A,B,C Need not be in A.P.
⇒ B need not be 60o false
Statement-3:
= √2 ⇒ a = √2 - √2a2
⇒ √2a2 + a - √2 = 0
a =
= 2
nCr . = 2n = 5nStatement-2 : ∵ sides are in A.P
⇒ sinA, sinB and sinC are in A.P
⇒ A,B,C Need not be in A.P.
⇒ B need not be 60o false
Statement-3:
= √2 ⇒ a = √2 - √2a2⇒ √2a2 + a - √2 = 0
a =
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