If α + β = - 2 and α3 + β3 = - 56, thenthe quadratic equation whose roots are α and β
x2 + 2x - 16 = 0
x2 + 2x + 15 = 0
x2 + 2x - 12 = 0
x2 + 2x - 8 = 0
The cubic equation whose roots are thrice to each of the roots of x3 + 2x2 - 4x + 1 = 0 is
x3 + 6x2 - 36x + 27 = 0
x3 + 6x2 + 36x + 27 = 0
x3 - 6x2 - 36x + 27 = 0
x3 - 6x2 + 36x + 27 = 0
The sum of the fourth powers of the roots of the equation
x3 + x + 1 = 0 is
- 2
- 1
1
2
If α + β + γ = 2θ, then cosθ + cosθ - α + cosθ - β + cosθ - γ = ?
4sinα2 . cosβ2cosγ2
4sinα2 . sinβ2sinγ2
4cosα2 . cosβ2 . cosγ2
4sinα . cosβ . cosγ
x ∈ R : cos2x + 2cos2x = 2 = ?
2nπ + π3 : n ∈ Z
nπ ± π6 : n ∈ Z
nπ + π3 : n ∈ Z
2nπ - π3 : n ∈ Z
1 + tanhx21 - tanhx2 = ?
e - x
ex
2ex2
2e - x2
In ∆ABC, if 1b + c + 1c + a = 3a + b + c, then C is equal to
90°
60°
45°
30°
Observe the following statementsI In ∆ABC, bcos2C2 + ccos2B2 = sII In ∆ABC, cotA2 = b + c2 ⇒ B = 90°Which of the following is correct ?
Both I and II are true
I is true, II is false
I is false, II is true
Both I and II are false
In a triangle, if r1 = 2r2 = 3r3, then ab + bc + ca = ?
7560
15560
17660
19160
From the top of a hill h metres high the angles of depressions of the top and the bottom of a pillar are α and β respectively.The height (in metres) of the pillar is
htanβ - tanαtanβ
htanα - tanβtanα
htanβ + tanαtanβ
htanβ + tanαtanα
B.
Let AB be a hill whose height is h metres andCD be a pillar of height h' metres.In ∆EDB,tanα = h - h'ED . . . iand in ∆ACB,
tanβ = hAC = hED . . . iiEliminate ED from eqs i and ii, we gettanα = h - h'htanβ⇒ h tanαtanβ = h - h'⇒ h' = htanβ - tanαtanβ