  # 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 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. Question 3

# If p(x) is a polynomial, is x + 3 a factor of $$p(x^2 + 2)$$?I. p(-3) = 0II. p(11) = 0 Question 4

# If x is an integer, is $$9^x + 9^{-x} = b$$I. $$3^x + 3^{-x} = \sqrt{b + 2}$$II. $$x > 0$$ 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 = 20II. $$\angle BAD = 45^\circ$$ 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. Question 7

# Is n a prime?I. n leaves remainder 1 when divided by 6.II. n leaves remainder 7 when divided by 91. Question 8

# Can we construct the $$\triangle ABC$$ with sides a, b and c ?I. a = 3, b = 4II. The perimeter of $$\triangle ABC$$ is 18. Question 9

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