Aryabhatta Finals- Mock Test 1

If a = 26, b = 27 and c = 29 then find a3 + b3 + c3 − 3abc.

• 536

• 574

• 438

• 648

If x = √6 + √5, then the value of (√x + ) / √x is:

• √6 + 1

• 2(√6 + 1)

• √6

• 2√6

If a + b + c = 4 and a2 + b2 + c2 = 10 and 1 / a + 1 / b + 1 / c = 1 then find abc.

• 28

• 1

• 25

• 36

If x = (0.04)2, y = 1 / (0.04)2, and z = (1 / 0.04)2, then what is the value of x3 − 3x2 + 3x + 3y + 3y2 + y3?

• 230

• -224

• 224

• -230

If a + b + c = 8, ab + bc + ca = 24, a3 + b3 = 67, b3 + c3 = 70 and c3 + a3 = 43 then what is the value of 3abc?

• 154

• 84

• 230

• 63

If x = −5, y = −3, then the value of x3 − 3x2 + 3x + 3y + 3y2 + y3 is:

• 525

• 293

• 124

• 0

If x = √18 × √20 = x√10, then the value of x is:

• 8

• 12

• 10

• 6

If √18 × √20 = x√10, then the value of x is:

• 12

• 8

• 10

• 6

If x = (√15 + √14)/ (√15 - √14) and y = (√15 - √14)/ (√15 + √14) then find the value of 3x2 - xy + 3y2

• 10

• 4

• 8

• 6

If a2 + b2 + c2 = 29 and ab + bc + ca = 10 then find the value of (1/2)(a + b + c)[(a - b)2 + (b - c)2 + (c - a)2]

• 132

• 135

• 133

• 130