TS ICET 2015

Instructions

For the following questions answer them individually

Question 111

$$\left(\frac{\sin 45^\circ + \cos 45^\circ + \tan 45^\circ}{\sin 45^\circ - \cos 45^\circ - \tan 45^\circ}\right)^2 =$$

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Question 112

$$\frac{1 - \cos \theta}{\sin \theta} + \frac{\sin \theta}{1 - \cos \theta} =$$

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Question 113

In $$\triangle ABC, \angle ABC = 45^\circ, \angle CAB = 30^\circ$$ and CD is perpendicular to AB. If CD = 100, then AB =

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Question 114

If $$7 + 10x - 5x^2$$ has maximum at $$x = \alpha \epsilon R$$, then $$\alpha =$$

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Question 115

The progression in which the roots of the equation $$6x^3 - 11x^2 + 6x - 1 = 0$$ lie is

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Question 116

The quadratic expression that leaves remainders 1, 2 and 4 respectively when divided by (x - 1), (x - 2) and (x - 3) is

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Question 117

If p(x) is a polynomial divisible by (x - 5), then a factor of $$p(x^3 - 3)$$ is

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Question 118

If $$\frac{xy}{x + y} = \frac{6}{5}$$ and $$\frac{xy}{x - y} = 6$$, then $$(x, y) =$$

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Question 119

The number of solutions of the system $$x - y + z = -6, x + y - z = 3, -x + y - z = 6$$ is

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Question 120

The sum of all the natural numbers between | and 100 which are divisible by 7 is

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