AP ICET 2011

Instructions

For the following questions answer them individually

Question 131

$$\lim_{x \rightarrow 0} \frac{\tan x - x}{x} =$$

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Question 132

$$\lim_{x \rightarrow -1} \frac{1 + \sqrt[3]{x}}{1 + \sqrt[5]{x}} =$$

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Question 133

If $$y = 2^{\sec x}$$, then $$\left(\frac{dy}{dx}\right)_{x = 0} = $$

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Question 134

If $$f(x) = \frac{x^2 + 1}{x^2 - 1}$$, then $$f'(2) =$$

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Question 135

The coefficient of $$x^{15}$$ in the product (x - 1) (x - 2) ..... (x - 16) is

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Question 136

If the sum of all the coefficients in the expansion of $$(1 + 3x - 2x^2)$$ is 128; then the greatest coefficient in the expansion of $$(1 + x)^n$$ is

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Question 137

If A, B are $$3 \times 3$$ matrices such that det A = 2, det B = -1, then det (4 AB) =

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Question 138

If $$A = \begin{bmatrix}2x + 3 & -4 \\x + 7 & 2 \end{bmatrix}$$ and if det A = 0, then x =

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Question 139

If $$\alpha, \beta$$ are the roots of the equation $$7x^2 - 8x + 6 = 0$$ then $$(\alpha^2 + \beta^2)(\alpha + \beta) =$$

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Question 140

The distance (in metres) between two parallel tangents drawn to a circle of area 616 sq.m. is (Take $$\pi = \frac{22}{7}$$)

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