TS ICET 24th May 2019 Shift-1

Instructions

For the following questions answer them individually

Question 111

If p, q are any two statements, the negation of the statement $$((\sim p \vee q) \wedge (p \vee \sim q)) \vee (p \wedge q)$$ is

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Question 112

For any two statements p, q a tautology amongthe following is:

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Question 113

Let A, B be subsets of a set X and let n(A) denote the number of elements in A. If $$n(A) = 15, n(A \cap B) = 4, n(A \cup B) = 21$$ then n(B - A) =

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Question 114

If a set X has four elements. then the number of relations on X that are symmetric is:

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Question 115

Let $$R = \left\{(m, n) \epsilon N^2 : m + n$$ is even}. Then the relation R on N is:

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Question 116

A line l which makes equal intercepts with the coordinate axes, passes through the point $$(3, - 4)$$. Then it also passes through the point:

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Question 117

If A(2, -3), B(3, 4) and C(-1, 5) are vertices of a triangle, then the length of median through A is:

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Question 118

If $$\sin \theta = \frac{5}{13}$$ and $$\theta$$ is not in the first quadrant, then $$\sec \theta + \tan \theta =$$

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Question 119

$$\sec \theta - \tan \theta = x \Rightarrow \frac{1 + x^2}{1 - x^2} =$$

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Question 120

$$A + B = \frac{\pi}{4} \Rightarrow (1 + \tan B)(1 + \tan B) =$$

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