The arithmeic mean of the scores of a group of students ia a test was 52. The brightest 20% of them secured a mean score of 80 and the dullest 25%, a mean score of 31. The mean score of remaining 55% is
54.6%
45%
50%
51.4%
If cosx + cos2x = 1, then the numerical value of (sin12x + 3 sin10x + 3 sin8x + sin6x - 1) is
0
1
-1
2
A.
0
cosx + cos2x = 1
⟹ cos x = 1 - cos2x
⟹ cos x = sin2x ...(i)
Again,
cosx + cos2x = 1
Cubing both sides, we get
(cos x + cos2x)3 = (1)3
cos3x + (cos2x)3 + 3 cosx x cos2x [cos x + cos2 x] = 1
cos3x + cos6x + 3 cos3x[cos x + cos2x] = 1
cos3x + cos6x + 3 cos4x + 3cos5x - 1 = 0
Now, put cosx = sin2x [From equ (i)]
(sin2x)3 + (sin2x)6 + 3(sin2x)4 + 3(sin2x)5 - 1 = 0
⟹ sin12x + 3 sin10x + 3 sin8x + sin6x - 1 = 0
Hence, numerical value of
sin12x + 3 sin10x + 3 sin8x + sin6x - 1 is 0.
ABCD is a rhombus. AB is produced to F and B produced to E such that AB = AE = BF. Then,
ED2 + CF2 = EF2
ED || CF
ED > CF
If x ≠ 0, y ≠ 0 and z ≠ 0 and
, then the relation among x, y and z is
x = y = z
x + y + z = 0
x + y = z
Two pipes P and Q can fill a cistern in 12 and 15 min, respectively. If both are opened together and at the end of 3 min, the first is closed. How much longer will the cistern take to fill?
5 min
If x2 + y2 + z2 = 2(x - y - z) - 3, then the value of 2x - 3y + 4z is (assume that x, y and z) are all real numbers).
3
0
9
1
In a ΔABC, ∠A : ∠B : ∠C = 2 : 3 : 4, A line CD is drawn || to AB, then ∠ACD is
80°
20°
40°
60°
A, B and C walk 1 km in 5 min, 8 min and 10 min, respectively. C starts walking from a point, at a certain time, B starts from the same point 1 min later and A starts from the same point 2 min later than C. Then, A meet B and C at times
2 min, 3 min
2 min,
1 min, 2 min