[Download PDF] AP ICET 2014 Paper with Solutions

Instructions

For the following questions answer them individually

Question 111

For two statements p, q, it is given that $$p \rightarrow ((\sim p) \vee q)$$ is false, then the truth values of p and q are respectively

Video Solution

Question 112

Let p, q be two statements. Then the statement $$(\sim p) \vee (p \wedge q)$$ is equivalent to

Video Solution

Question 113

If $$1 \leq a \leq 100$$ and $$A = \left\{a \mid gcd(a, 100) = 1\right\}$$, then the number of elements in A is

Video Solution

Question 114

Let $$f(x) = \begin{cases}x & if x \epsilon Q\\1-x & if x \epsilon R-Q\end{cases}$$
where Q is the set of all rational numbers. Then f is

Video Solution

Question 115

Suppose A and B are two sets. Then a set, among the following, which is not cqual to $$A \cup B$$, in general, is

Video Solution

Solution

$$A^C\ inter\sec tion\ B^C$$

Question 116

If the lines $$3x - ky + 4 = 0$$ and $$4x + y + 2 = 0$$ are perpendicular to each other, then $$k^2 - 12k + 4 =$$

Video Solution

Solution

Slope of the line $$ax+by+c=0$$ is $$\frac{-a}{b}$$

Slope of the line $$3x - ky + 4 = 0$$ is $$\frac{-3}{-k}=\frac{3}{k}$$

Slope of the line $$4x + y + 2 = 0$$ is $$\frac{-4}{1}=-4$$

The product of slope of two lines perpendicular to each other is -1.

$$\Rightarrow$$ $$\frac{3}{k}\times\left(-4\right)=-1$$

$$\Rightarrow$$ $$k=12$$

$$\therefore\ $$ $$k^2-12k+4=12^2-12\left(12\right)+4=4$$

Hence, the correct answer is Option B

Question 117

The length of the line segment intercepted between the axes by the line joining (6, -4) and (-3, 8) is

Video Solution

Question 118

$$\sin 120^\circ \cos 60^\circ \cot 30^\circ \cosec^2 30^\circ =$$

Video Solution

Solution

$$\sin120^{\circ\ }\cos60^{\circ\ }\cot30^{\circ\ }\operatorname{cosec}^230^{\circ\ }=\sin\left(90+30^{\circ\ }\right)\cos60^{\circ\ }\cot30^{\circ\ }\operatorname{cosec}^230^{\circ\ }$$

$$=\cos30^{\circ\ }\ \cos60^{\circ\ }\cot30^{\circ\ }\operatorname{cosec}^230^{\circ\ }$$

$$=\frac{\sqrt{\ 3}}{2}\times\ \frac{1}{2}\times\ \sqrt{\ 3}\times\ 4$$

$$=3$$

Hence, the correct answer is Option B

Question 119

$$\tan \theta = \frac{5}{12} \Rightarrow \frac{5 \sin \theta + 4\cos \theta}{4 \sin \theta + 5\cos \theta} =$$

Video Solution

Question 120

$$4 \cos \theta \sin^3 \theta - 4 \sin \theta \cos^3 \theta =$$

Video Solution

Solution

$$4\cos\theta\ \sin^3\theta\ -4\ \sin\theta\ \cos^3\theta\ =4\ \sin\theta\ \cos\theta\ \left(\sin^2\theta\ -\cos^2\theta\ \right)=-4\ \sin\theta\ \cos\theta\ \left(\cos^2\theta\ -\sin^2\theta\ \right)=-4\ \sin2\theta\ \cos2\theta\ =-\sin4\theta\ $$

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AP ICET 2014

For two statements p, q, it is given that $$p \rightarrow ((\sim p) \vee q)$$ is false, then the truth values of p and q are respectively

Let p, q be two statements. Then the statement $$(\sim p) \vee (p \wedge q)$$ is equivalent to

If $$1 \leq a \leq 100$$ and $$A = \left\{a \mid gcd(a, 100) = 1\right\}$$, then the number of elements in A is

Let $$f(x) = \begin{cases}x & if x \epsilon Q\\1-x & if x \epsilon R-Q\end{cases}$$where Q is the set of all rational numbers. Then f is

Suppose A and B are two sets. Then a set, among the following, which is not cqual to $$A \cup B$$, in general, is

If the lines $$3x - ky + 4 = 0$$ and $$4x + y + 2 = 0$$ are perpendicular to each other, then $$k^2 - 12k + 4 =$$

The length of the line segment intercepted between the axes by the line joining (6, -4) and (-3, 8) is

$$\sin 120^\circ \cos 60^\circ \cot 30^\circ \cosec^2 30^\circ =$$

$$\tan \theta = \frac{5}{12} \Rightarrow \frac{5 \sin \theta + 4\cos \theta}{4 \sin \theta + 5\cos \theta} =$$

$$4 \cos \theta \sin^3 \theta - 4 \sin \theta \cos^3 \theta =$$

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Let $$f(x) = \begin{cases}x & if x \epsilon Q\\1-x & if x \epsilon R-Q\end{cases}$$
where Q is the set of all rational numbers. Then f is