[Download PDF] AP ICET 16th May 2016 Paper with Solutions

Instructions

For the following questions answer them individually

Question 111

If a set A has 7 elements, then the number of subsets of A with at most 5 elements is

Video Solution

Solution

We have to find subsets with atmost 5 elements. Hence from all the possible subsets, subtracts all those subsets having 6 and 7 elements.

$$2^7-^{^7C}6-^{^7C}7=128-8=120$$

Question 112

The statement $$p \rightarrow (q \rightarrow r)$$ is equivalent to

Video Solution

Question 113

The statement $$(p \wedge q) \vee ((\sim p) \wedge q)$$ is equivalent to

Video Solution

Question 114

If A is a set such that n(A) = 5, then the number of symmetric relations that can be defined on A is

Video Solution

Question 115

The function $$f : R \rightarrow R$$ defined by $$f(x) = 3x^2 + 5$$, for all $$x \epsilon R$$, is

Video Solution

Question 116

If A. B are two sets such that n(A) = 5, n(B) = 6, then the number of surjections that can be defined from A to B is

Video Solution

Question 117

The equation of the straight line passing through the point (7, -5) with slope $$\frac{-4}{5}$$ is

Video Solution

Solution

Equation of the straight line passing through the point (7, -5) with slope $$\frac{-4}{5}$$ is $$\left(y+5\right)=-\frac{4}{5}\left(x-7\right)$$

$$5y+25=-4x+28$$

$$5y+4x=3$$

$$4x+5y-3=0$$

Hence, the correct answer is Option B

Question 118

If a line makes intercepts 5, 12 on X, Y axes respectively, then the length of the perpendicular drawn from the origin to the line is

Video Solution

Solution

Equation of the line having 5 and 12 as intercepts is $$\frac{x}{5}+\frac{y}{12}=1\ or\ 12x+5y-60=0$$

Perpendicular distance from (0,0) is $$\frac{\left|12\left(0\right)+5\left(0\right)-60\right|}{\sqrt{\ 12^2+5^2}}=\frac{60}{13}$$

Question 119

$$\tan 20^\circ \tan 40^\circ \tan 60^\circ \tan 80^\circ =$$

Video Solution

Question 120

The value of $$\cot (1950^\circ)$$ is

Video Solution

Solution

$$\cot(1950^{\circ})=\cot\left(5\left(360^{\circ\ }\right)+150^{\circ\ }\right)$$

$$=\cot150^{\circ\ }$$

$$=\cot\left(180^{\circ}-30^{\circ\ }\right)$$

$$=-\cot30^{\circ\ }$$

$$=-\sqrt{3}$$

Hence, the correct answer is Option B

CAT Content

AP ICET 16th May 2016

If a set A has 7 elements, then the number of subsets of A with at most 5 elements is

The statement $$p \rightarrow (q \rightarrow r)$$ is equivalent to

The statement $$(p \wedge q) \vee ((\sim p) \wedge q)$$ is equivalent to

If A is a set such that n(A) = 5, then the number of symmetric relations that can be defined on A is

The function $$f : R \rightarrow R$$ defined by $$f(x) = 3x^2 + 5$$, for all $$x \epsilon R$$, is

If A. B are two sets such that n(A) = 5, n(B) = 6, then the number of surjections that can be defined from A to B is

The equation of the straight line passing through the point (7, -5) with slope $$\frac{-4}{5}$$ is

If a line makes intercepts 5, 12 on X, Y axes respectively, then the length of the perpendicular drawn from the origin to the line is

$$\tan 20^\circ \tan 40^\circ \tan 60^\circ \tan 80^\circ =$$

The value of $$\cot (1950^\circ)$$ is

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