TS ICET 2017

Instructions

A question isfollowed bydataintheform of two statements labelled as I and II. You must decide whether the data given in the Statements are sufficient to answerthe questions.

Question 1

Is m a divisor of n?
I. m is the smallest prime such that 9 m > 8.
II. n is an odd integer

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Question 2

Do P, Q and R lie on a circle?
I. P, Q lie on the circle and PQ passes through its centre.
II. $$\triangle PQR$$ is right-angled.

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Question 3

If p(x) is a polynomial, is x + 3 a factor of $$p(x^2 + 2)$$?
I. p(-3) = 0
II. p(11) = 0

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Question 4

If x is an integer, is $$9^x + 9^{-x} = b$$
I. $$3^x + 3^{-x} = \sqrt{b + 2}$$
II. $$x > 0$$

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Question 5

In $$\triangle ABC$$, if D is the foot of the peropendicular drawn from B onto AC, then what is the area of $$\triangle ABC$$?
I. BD.AC = 20
II. $$\angle BAD = 45^\circ$$

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Question 6

What is the value of k with 56 < k < 66?
I. k leaves remainder 1 when divided by 2.
II. k + 1 is divisible by 8.

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Question 7

Is n a prime?
I. n leaves remainder 1 when divided by 6.
II. n leaves remainder 7 when divided by 91.

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Question 8

Can we construct the $$\triangle ABC$$ with sides a, b and c ?
I. a = 3, b = 4
II. The perimeter of $$\triangle ABC$$ is 18.

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Question 9

What is the average of the numbers $$a_1, a_2, ....... a_{10}$$?
I. $$a_1 + a_2 + ..... + a_9 = 810$$
II. $$a_2 + a_3 + ..... + a_{10} = 900$$

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Question 10

If $$a \neq b$$ and $$c \neq d$$, what is the value of $$\frac{a^2 + d^2}{b^2 + c^2}$$?
I. $$\frac{a + b}{c - d} = \frac{c + d}{a - b}$$
II. $$ad \neq bc$$

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