Trigonometric Equations: JEE Questions & Solutions

Let ( +) = - 110 and ( -) = 38, where 0 < < 3 and 0 < < 4. If 2 = 3(1 - r 5) 11(s + 5), r, s N, then the value of r + s is.

Number of solutions of 3 2 + 8 + 3 3 = 0, [-3, 2 ] is:

The number of elements in the set x [0,180^ ]: (x+100^)= (x+50^) x (x-50^) is

The sum of all values of [0, 2 ] satisfying 2 ^2 = 2 and 2 ^2 = 3 is:

If [-2, 2 ], then the number of solutions of 2 2 ^2 + (2 - 6) - 3 = 0 is:

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 for [ - 3, 0 ], the points (x, y) = ( 3 ( + 3), 2 ( + 6)) lie on xy + x + y + = 0, then ^2 + ^2 + ^2 is equal to:

The number of solutions of the equation 2 ( 2) + ( 5 2) = 2 ^3 ( 5 2) in the interval - 2, 2 is:

Let A = [0, 2 ]: ( 2 + i - 3i) = 0. Then A ^2 is equal to:

If 2 ^2() - 5 () = 1 has exactly 7 solutions in the interval [0, n 2 ] for the least value of n N, then k=1^n k2^k is equal to:

If, with - /2 < < /2, is the solution of 4 () + 5 () = 1, then the value of () is:

If 2 ^3 x + ^2 x x + 4 ^n x - 4 = 0 has exactly 3 solutions in the interval (0, n /2), n N, then the roots of the equation x^2 + nx + (n-3)…

If A = 1 x(x^2 + x + 1), B = x x^2 + x + 1, and C = x^3 + x^2 + x^1/2, 0 < A, B, C < /2, then A + B is equal to:

If 2 ^2() - 5 () = 1 has exactly 7 solutions in the interval [0, n 2 ] for the least value of n N, then (k=1 to n) k2k is equal to:

If m and n respectively are the numbers of positive and negative values of in the interval [-, ] that satisfy the equation 2 2 = 3 9 2,…

Let f() = 3 ^4 ( 3 2 -) + ^4 (3 +) - 2 (1 - ^2(2)), and S = [0, ]: f'() = - 32. If 4 = S, then f() is equal to:

The set of all values of for which the equation ^2(2x) - 2 x - 2 (2x) = holds is:

96 ( 33) ( 2 33) ( 4 33) ( 8 33) ( 16 33) is equal to:

Let S = x ( - 2, 2): 9^1 - ^2 x + 9^ ^2 x = 10 b = x S ^2 ( x3), then ( - 14)^2 is equal to:

The number of elements in the set S = [0, 2 ]: 3 ^4 - 5 ^2 - 2 ^2 + 2 = 0 is:

For x (-1, 1), the number of solutions of the equation x = 2 x is equal to.