Q: Number of solutions of equations 9 = in the interval [0,2 ] is

aligned & Given, 9 = \\ & 9 - =0 \\ & 2 ( 9 + 2 ) ( 9 - 2 )=0 \\ & [ C- D=2 ( C+D 2 ) ( C-D 2 ) ] \\ & 2 5 4 =0 \\ & Either 5 =0 or 4 =0 , also [0,2 ] \\ & 5 =(2 n+1) 2 \\ & or 4 =n \\ & =(2 n+1) 10 or = n 4 \\ & = 10 , 3 10 , 2 , 7 10 , 9 10 , 11 10 , 13 10 , 3 2 , 17 10 , 19 10 \\ & or 0, 4 , 2 , 3 4 , , 5 4 , 3 2 , 7 4 , 2 \\ & Total number of solutions =17 \\ & ( 2 and 3 2 are common ) aligned

Q: General solution of 5 = 2 is

We have 5 = 2 aligned & 5 = ( 2 -2 ) \\ & [ ( 2 - )= ] \\ & 5 =n + 2 -2 7 =n + 2 \\ & = n 7 + 14 . aligned

Q: The sum of all the solution of the equation ( 3 + ) ( 3 - )= 1 4 , [0,6 ]

aligned & 2 [ 120^ + 2 ]=1 \\ & 2 (- 1 2 +2 ^2 -1 )=1 \\ & 4 ^3 -3 -1=0 \\ & 3 =1= 0 \\ & 3 =2 n or = 2 n 3 , n z aligned Given the values so that 2 n does not exceed 18 . Hence, the sum = 2 3 _1^9 n= 2 3 9(9+1) 2 =30

Question 1

Number of solutions of equations 9 = in the interval [0,2 ] is

Accepted Answer

aligned & Given, 9 = \ & 9 - =0 \ & 2 ( 9 + 2 ) ( 9 - 2 )=0 \ & [ C- D=2 ( C+D 2 ) ( C-D 2 ) ] \ & 2 5 4 =0 \ & Either 5 =0 or 4 =0 , also [0,2 ] \ & 5 =(2 n+1) 2 \ & or 4 =n \ & =(2 n+1) 10 or = n 4 \ & = 10 , 3 10 , 2 , 7 10 , 9 10 , 11 10 , 13 10 , 3 2 , 17 10 , 19 10 \ & or 0, 4 , 2 , 3 4 , , 5 4 , 3 2 , 7 4 , 2 \ & Total number of solutions =17 \ & ( 2 and 3 2 are common ) aligned

Question 2

The range of (8 +6 )^2+2 is

Accepted Answer

-10 8 +6 10 0 (8 +6 )^2 100 2 (8 +6 )^2+2 102

Question 3

General solution of 5 = 2 is

Accepted Answer

We have 5 = 2 aligned & 5 = ( 2 -2 ) \ & [ ( 2 - )= ] \ & 5 =n + 2 -2 7 =n + 2 \ & = n 7 + 14 . aligned

Question 4

If ^2 = 4 3 , then the general value of is

Accepted Answer

We have ^2 = 4 3 ^2 = 3 4 ^2 = ^2 ( 6 ) =n 6

Question 5

The sum of all the solution of the equation ( 3 + ) ( 3 - )= 1 4 , [0,6 ]

Accepted Answer

aligned & 2 [ 120^ + 2 ]=1 \ & 2 (- 1 2 +2 ^2 -1 )=1 \ & 4 ^3 -3 -1=0 \ & 3 =1= 0 \ & 3 =2 n or = 2 n 3 , n z aligned Given the values so that 2 n does not exceed 18 . Hence, the sum = 2 3 _1^9 n= 2 3 9(9+1) 2 =30

Question 6

If y= 2 1+ + , then value of 1- + 1+ is

Accepted Answer

1- + 1+ = 1- + 1+ 1+ + 1+ + = (1+ )^ 2 - ^ 2 (1+ )(1+ + ) = (1+ ^ 2 +2 )- (1- ^ 2 ) (1+ )(1+ + ) = 2 1+ + =y

Trigonometric Equations — Previous Year Questions & Solutions