Question
Find the simplified value of the given expression:
1.82Â + 2.42Â + 1.52Â - 1.8 x 2.4 - 2.4 x 1.5 - 1.8 x 1.5Solution
1.82Â + 2.42Â + 1.52Â - 1.8 X 2.4 - 2.4 X 1.5 - 1.8 X 1.5 a2Â + b2Â + c2Â - ab - bc - ac = (1/2) X [(a - b)Â 2Â + (b - c)Â 2Â + (c - a)Â 2] So, 1.82Â + 2.42Â + 1.52Â - 1.8 X 2.4 - 2.4 X 1.5 - 1.8 X 1.5 = (1/2) X [(1.8 - 2.4)Â 2Â + (2.4 - 1.5)Â 2Â + (1.5 - 1.8)Â 2] = (1/2) X (0.36 + 0.81 + 0.09) = (1/2) X (1.26) = 0.63
17, 19, 41, 127, 513, ?Â
What will come in place of the question mark (?) in the following series?
68, 76, 61, 85, ?, 98
30, 43, 58, 75, 94, ?
12, 34, 64, ?, 140, 182
124, 107, 91, ? , 62, 49
1140, ?, 1130, 1160, 1120, 1170
10, 10, 15, 30, 75, ?
13 52 208 ? 3328 13312
What will come in place of the question mark (?) in the following number series?
124, 131, 117, ?, 110, 145
2807, 1400, 697, 346, 171, 84, 41, ?