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JEE Mathematics Solved Question Paper 2008

Multiple Choice Questions

21.

$If α + β = - 2 and α^{3} + β^{3} = - 56, then the quadratic equation whose roots are α and β$

x² + 2x - 16 = 0
x² + 2x + 15 = 0
x² + 2x - 12 = 0
x² + 2x - 8 = 0

22.

The cubic equation whose roots are thrice to each of the roots of x³ + 2x² - 4x + 1 = 0 is

$x^{3} + 6 x^{2} - 36 x + 27 = 0$
$x^{3} + 6 x^{2} + 36 x + 27 = 0$
$x^{3} - 6 x^{2} - 36 x + 27 = 0$
$x^{3} - 6 x^{2} + 36 x + 27 = 0$

23.

The sum of the fourth powers of the roots of the equation

x³ + x + 1 = 0 is

24.
$If α + β + γ = 2 θ, then \cos (θ) + \cos (θ - α) + \cos (θ - β) + \cos (θ - γ) = ?$

$4 \sin (\frac{α}{2}) . \cos (\frac{β}{2}) \cos (\frac{γ}{2})$

$4 \sin (\frac{α}{2}) . \sin (\frac{β}{2}) \sin (\frac{γ}{2})$

$4 \cos (\frac{α}{2}) . \cos (\frac{β}{2}) . \cos (\frac{γ}{2})$

$4 \sin (α) . \cos (β) . \cos (γ)$

$4 \cos (\frac{α}{2}) . \cos (\frac{β}{2}) . \cos (\frac{γ}{2})$

$Now, α + β + γ = 2 θ, then \cos (θ) + \cos (θ - α) + \cos (θ - β) + \cos (θ - γ) = 2 \cos (θ - (\frac{α + β}{2})) \cos (\frac{β - α}{2}) + 2 \cos (\frac{γ}{2}) \cos (θ - \frac{γ}{2}) = 2 \cos (\frac{γ}{2}) \cos (\frac{β - α}{2}) + 2 \cos (\frac{γ}{2}) \cos (\frac{α + β}{2}) = 2 \cos (\frac{γ}{2}) [\cos (\frac{β - α}{2}) + \cos (\frac{α + β}{2})] = 2 \cos (\frac{γ}{2}) 2 \cos (\frac{α}{2}) \cos (\frac{β}{2}) = 4 \cos (\frac{α}{2}) \cos (\frac{β}{2}) \cos (\frac{γ}{2})$

25.

$\{x \in R : \cos (2 x) + 2 \cos^{2} (x) = 2\} = ?$

$\{2 nπ + \frac{π}{3} : n \in Z\}$
$\{nπ \pm \frac{π}{6} : n \in Z\}$
$\{nπ + \frac{π}{3} : n \in Z\}$
$\{2 nπ - \frac{π}{3} : n \in Z\}$

26.

$\frac{1 + \tanh (\frac{x}{2})}{1 - \tanh (\frac{x}{2})} = ?$

$e^{- x}$
$e^{x}$
$2 e^{\frac{x}{2}}$
$2 e^{- \frac{x}{2}}$

27.

$In ∆ ABC, if \frac{1}{b + c} + \frac{1}{c + a} = \frac{3}{a + b + c}, then C is equal to$

$90 °$
$60 °$
$45 °$
$30 °$

28.

$Observe the following statements (I) In ∆ ABC, {bcos}^{2} (\frac{C}{2}) + {ccos}^{2} (\frac{B}{2}) = s (II) In ∆ ABC, \cot (\frac{A}{2}) = \frac{b + c}{2} \Rightarrow B = 90 ° Which of the following is correct ?$

Both I and II are true
I is true, II is false
I is false, II is true
Both I and II are false

29.

$In a triangle, if r_{1} = 2 r_{2} = 3 r_{3}, then \frac{a}{b} + \frac{b}{c} + \frac{c}{a} = ?$

$\frac{75}{60}$
$\frac{155}{60}$
$\frac{176}{60}$
$\frac{191}{60}$

30.

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