If 10 4 + 15 4 = 6, then the value of 27 cosec6 + 8 6 16 8 is
(1) 25
Let 2 = t, so 2 = 1 - t:
10t2 + 15(1 - t)2 = 6
⇒ 25t2 - 30t + 9 = 0
⇒ (5t - 3)2 = 0 ⇒ t = 35
∴ 2 = 35, 2 = 25
cosec6 = ( 53 )3 = 12527, 6 = ( 52 )3 = 1258, 8 = ( 52 )4 = 62516
Required value = 27 12527 + 8 125816 62516
= 250625 = 25
Answer: (1)
The number of solutions of the equation 2x + 3 x = , x [-2 , 2 ] - \ 2, 3 2 \ is:
The number of solutions of the equation (4 - 3) x - 2 3 2 x = - 41 + 3, x [-2 , 5 2 ] is
If [-2 , 2 ], then the number of solutions of 2 2 2 + (2 - 6) - 3 = 0, is equal to:
If [- 7 6, 4 3 ], then the number of solutions of 3 cosec2 - 2( 3 - 1) cosec - 4 = 0, is equal to :
If x + 2 x = 1, x (0, 2 ), then ( 12x + 12x) + 3( 10x + 10x + 8 x + 8 x) + ( 6 x + 6 x) is equal to:
If r=113 \ 1 ( 4 + (r - 1) 6 ) ( 4 + r 6 ) \ = a 3 + b, a, b Z, then a2 + b2 is equal to :
Let A= \x (0, )- \ 2 \: (2/ )| x|+ (2/ )| x|=2 \ and B= \x 0: x( x-4)-3| x-2|+6=0 \. Then n(A ) is equal to :
Let the range of the function f(x)=6+16 x ( 3-x ) ( 3+x ) 3x 6x, x be [ , ]. Then the distance of the point ( , ) from the line 3x+4y+12=0 is :
The sum of all values of [0,2 ] satisfying 2 2 = 2 and 2 2 =3 is