[Download PDF] AP ICET 2nd May 2018 Shift-1 Paper with Solutions

Instructions

For the following questions answer them individually

Question 111

If p and q are statements then $$\sim(p \vee q)$$ is equivalent to

Video Solution

Question 112

A tautology, among the following is

Video Solution

Question 113

If $$E_n = \left]\{x \epsilon R: -\frac{1}{n} < x < 0\right\}$$ for $$n = 1, 2, 3, ............ $$ then $$\bigcap_{n=1}^{\infty}E_n =$$

Video Solution

Question 114

The number of functions from {a, b, c, d, e} into {1,2} is

Video Solution

Question 115

If $$f(x) = \frac{x - 1}{x + 2}$$; x ≠ -2, then $$f^{-1}(4) =$$

Video Solution

Solution

$$f^'\left(x\right)=\frac{\left(\left(x-2\right)1\ -\left(x-1\right)1\right)}{\left(x-2\right)^2}=$$

Question 116

The equation of the line passing through(-4, 3) and parallel to the line joining the points (1, -3) and (-5, 1) is

Video Solution

Question 117

The equation of a straight line passing through the intersection of the lines x + 2y - 19 = 0 and x - 2y - 3 = 0 and at 5 units distance from(-2, 4) is

Video Solution

Question 118

$$\sin 0^\circ + \cos 30^\circ - \tan 45^\circ + \cosec 60^\circ + \cot 90^\circ =$$

Video Solution

Solution

$$\sin 0^\circ + \cos 30^\circ - \tan 45^\circ + \cosec 60^\circ + \cot 90^\circ $$ =$$0+\frac{\sqrt{\ 3}}{2}-1+\frac{2}{\sqrt{\ 3}}+0\ =\ \frac{\left(7-2\sqrt{\ 3}\right)}{2\sqrt{\ 3}}=\frac{\left(7\sqrt{\ 3}-6\right)}{6}$$

Question 119

If $$\sin \theta = -\frac{1}{2}$$ and $$\cot \theta = -\sqrt{3}$$ then the minimum value that $$\theta$$ can take is

Video Solution

Question 120

$$\sin^2 \frac{\pi}{4} + \sin^2 \frac{3\pi}{4} + \sin^2 \frac{5\pi}{4} + \sin^2 \frac{7\pi}{4} =$$

Video Solution

CAT Content

AP ICET 2nd May 2018 Shift-1

If p and q are statements then $$\sim(p \vee q)$$ is equivalent to

A tautology, among the following is

If $$E_n = \left]\{x \epsilon R: -\frac{1}{n} < x < 0\right\}$$ for $$n = 1, 2, 3, ............ $$ then $$\bigcap_{n=1}^{\infty}E_n =$$

The number of functions from {a, b, c, d, e} into {1,2} is

If $$f(x) = \frac{x - 1}{x + 2}$$; x ≠ -2, then $$f^{-1}(4) =$$

The equation of the line passing through(-4, 3) and parallel to the line joining the points (1, -3) and (-5, 1) is

The equation of a straight line passing through the intersection of the lines x + 2y - 19 = 0 and x - 2y - 3 = 0 and at 5 units distance from(-2, 4) is

$$\sin 0^\circ + \cos 30^\circ - \tan 45^\circ + \cosec 60^\circ + \cot 90^\circ =$$

If $$\sin \theta = -\frac{1}{2}$$ and $$\cot \theta = -\sqrt{3}$$ then the minimum value that $$\theta$$ can take is

$$\sin^2 \frac{\pi}{4} + \sin^2 \frac{3\pi}{4} + \sin^2 \frac{5\pi}{4} + \sin^2 \frac{7\pi}{4} =$$

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