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Minimum value of bcx + cay + abz when xyz = abc is

1) abc 2) 2 abc 3) 3 abc 4) none of these Solution: (3) 3 abc AM ≥ GM [bcx +... View Article

1) 4 2) 6 3) 8 4) 10 Solution: (4) 10 AM > GM {(3x / 2) + (3x /... View Article

1) 4 2) 6 3) 8 4) 10 Solution: (3) 8 Using the relation AM ≥ GM, [xy + yz... View Article

1) (1 / 2) < (1 – x) (1 – y) (1 – z) < (1 / 3) 2) (1... View Article

1) < √(n + 1) / 2 2) > n √(n + 1) / 2 3) > √(n + 1)... View Article

1) < 3 / 2 2) ≥ 3 / 2 3) > 5 / 2 4) none of these Solution:... View Article

1) > nm 2) > nm+1 3) < nm 4) < nm+1 Solution: (2) > nm+1 [(1m + 3m +... View Article

1) > 22/3 2) < 22/3 3) > 42/3 4) < 42/3 Solution: (2) < 22/3 Since AM of (1... View Article

1) x + y ≥ 4 2) x + y ≤ 4 3) x + y = 1 4) none... View Article

1) > bn 2) > 2bn 3) < bn 4) < 2bn Solution: (2) > 2bn Consider two numbers an... View Article

1) > 2(a + b + c) 2) > a + b + c 3) > ab + bc +... View Article

1) ≤ 1 / √3 2) ≤ 1 / 2 √3 3) ≤ 1 / 3 √3 4) none of... View Article

1) > nn 2) nn (n)! 3) nn (n!)r for all r 4) none of these Solution: (3) nn (n!)r... View Article

1) ≥ 3 (a + b – c) (b + c – a) (c + a – b) 2) ≥ 9... View Article

1) ∈ (0, 1) 2) ∈ (0, 1 / 2] 3) ∈ (0, 1] 4) [0, 1] Solution: (2) ∈... View Article

1) > 1 2) < 1 3) > 6 4) < 6 Solution: (3) > 6 Since AM > GM... View Article

1) > a + b + c 2) > ab + bc + ca 3) < a + b +... View Article

1) > 1 2) < 1 3) > 0 4) < 0 Solution: (2) < 1 Since AM > GM... View Article

1) abc 2) 2abc 3) 4abc 4) 8abc Solution: (4) 8abc [b + c] / 2 > √bc [AM ≥... View Article

1) 1/2 2) 3/35 3) 34/31 4) 29/23 5) None of these Solution: (3) 34/31 Given that 2ax2 – 3bx... View Article