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The equation √x + 3 – 4 (√x – 1) + √x + 15 – 8 √x – 1) = 2 has

1) No real root 2) At least one real root 3) Exactly one root 4) An infinite number of real... View Article

1) [- 1, (- 1 + √5) / 2] 2) [- 1, 1] 3) [- 1, (1 + √5) /... View Article

1) All the roots real 2) One real and eight imaginary roots 3) Real roots necessary x = 3, 32,... View Article

1) (- 2, 0) 2) (- 2, 2) 3) (- 5, 5) 4) (0, ∞) Solution: (4) (0, ∞) 5x+2... View Article

1) (4 / 5, 2) 2) (- 1, – 4 / 5) 3) (2, ∞) 4) (- ∞, – 1)... View Article

1) p (p + q + r) > 0 2) r (p + q + r) > 0 3) q... View Article

1) (3 / 4, ∞) 2) (- ∞, – 3 / 4) 3) (- 3 / 4, 3 / 4)... View Article

1) Three real roots 2) a root in (- ∞, a1) 3) no real root in (a1, a2) 4) no... View Article

1) (ɑ, β) 2) (β, 𝛾) 3) (ɑ, 𝛾) 4) None of these Solution: (4) None of these If sec... View Article

1) ± 2, ± √3 2) ± 4, ± √14 3) ± 4, ± √5 4) ± 5, ± √20... View Article

1) {2-√2, 2√2} 2) {1 / 3, 3} 3) {1 / 4, 4} 4) None of these Solution: (1) {2-√2,... View Article

1) 4K2 2) 2K2 3) 5K2 4) None of these Solution: (2) 2K2 Let t = (x + √x2 +... View Article

1) x ∈ (2, ∞) 2) x ∈ (0, 1 / 5) ⋃ (5, ∞) 3) x ∈ (1, ∞)... View Article

1) – d / a 2) c / a 3) b / a 4) None of these Solution: (1) –... View Article

1) 5 2) 2 3) 3 4) 4 Solution: (3) 3 Let x = √7 + √7 – √7 +... View Article

1) Infinite 2) 4 3) 3 4) 2 Solution: (2) 4 |[x] – 2x| = 4 [x] – 2x =... View Article

1) x ∈ R 2) x ∈ N 3) x ∈ I 4) x ∈ Q Solution: (3) x ∈... View Article

1) x = 1 2) x = 2 3) x = 0 4) None of these Solution: (2) x =... View Article

1) a + b 2) a – b 3) (√a ± √b)2 4) None of these Solution: (3) (√a ±... View Article

1) 0 2) 4 3) 2 4) None of these Solution: (3) 2 (6 – x)4 + (8 – x)4... View Article