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Match the following ( array l Column - I & Column - II array l (A) Let f(x) be a non negative continuous function x 0, f(0)=0 If f(x) f(x) x x 0, then the value of f ( 3 2 ) is array & (p) 4 array l (B) If a ( x ^2+1 )+12 x +6-3 x ^2< ⁻¹ (100)+ ⁻¹ (100) x R ; a I then a can not be equal to array & (q) 3 array l (C) If two events A and B are such that P (A^C )=0.35, P(B)=0.4 and P(A B)=0.15, then 20 P ( B A B^C ) is a

Options

  1. A( A ) ( s ) ;( B ) ( p ) ;( C ) ( r ) ;( D ) ( q )
  2. B( A ) ( r ) ;( B ) ( p,q,r,s ) ;( C ) ( p ) ;( D ) ( q )
  3. C( A ) ( p ) ;( B ) ( r ) ;( C ) ( s ) ;( D ) ( q )
  4. D( A ) ( q ) ;( B ) ( r ) ;( C ) ( p ) ;( D ) ( s )

Correct answer

B. ( A ) ( r ) ;( B ) ( p,q,r,s ) ;( C ) ( p ) ;( D ) ( q )

Step-by-step solution

(A) Let g(x)=f(x) e^ x g(x) is a decreasing function g(x) g(0)=0 i.e. f(x) e^ x 0 but f(x) 0, e^ x 0 f(x)=0 f ( 3 2 )=0 (B) aligned & (a-3) x^2+12 x+6+a- ( ⁻¹ 100+ ⁻¹ 100 ) 0 & a 3 . D 0 & 144-4(a+6)(a-3) 0 & a -9 or a 6 . aligned (C) P ( B A B ^C )= P ( A B ) P ( A B ^C ) = 1 5 . (D) ⁻¹ (4 x^3-3 x )- 2 0 -1 4 x^3-3 x 0 i.e. x [-4,- 3 2 ] [0, 3 2 ] also (2 x+3)! x+2 is defined x -2 and (2 x+3) Wx=-1,0, 1 2 .

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