MAINS MOCK TEST ---- 001 _________________________

3. The number of real roots of the equation z3 + iz - 1 = 0 is

1) 0 2) 1 3) 2 4) 3

4. | cos x cos x sin x -sinx| Let ∆ (x) = | cos x sin x sin x cosx | then (∆ (x) + ∆' (x)) dx | sin x -cos x 0 | equals to

1) π /3 2) π /2 3) 2 π 4) 3 π /2

10. If one G.M.G and two A.M's p and q be inserted between two given numbers then (2p -q) (2q -p) 1)4G 2) 2G 3) p + q 4) G

12. 1 1 |t - 1| 1 |2 + t| If the primitive of f (x) = _______________ =____ log |____| + ____ log ______ + c then 3 sin x + sin 3 x 6 |t +1| 12 |2 - t|

1) t = cos x 2) t = tan x/2 3) t = 2 cos x 4) t = sin x

21. If a,b,c are unit coplanar vectors then the scalar Triple product [2a-b,2b-c,2c-a] = 1) 3x 2) 8 3) 0 4) ± √3

26. The remainder when x = 1! + 2! + 3! + 4! +............+ 100! is divided by 240 is 1) 33 2) 153 3) 73 4) 187

29. If A = { 4 n − 3n − 1, n Є N } and B = {9n – 9, n Є N} then A U B is equal to 1) A 2) B 3) N 4) Ф

30. If ∑ (x1 − 8) = 9 and ∑ (x1 − 8) 2 = 45 then the standard deviation of x1,x 2,x3 ,.........x18 is 1) 4/9 2) 9/4 3) 3/2 4) 4