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 11

Can we find the orthocentre of $$\triangle ABC$$?
I. $$AB^2 = AC^2 - BC^2$$
II. AB + BC + CA = 100 cms

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Question 12

If p(x) is a polynomial is 2 a root of p(x) = 0?
I. p(1) = 0
II. $$p(p(1)) \neq 0$$

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Question 13

What is the value of $$\frac{x^2 + y^2 - z^2}{xy}$$?
I. x : y = 1 : 2
II. y : z = 2 : 3

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Question 14

What is the volume of the cylinder ?
I. The height of the cylinder is 3 units more than its radius.
II. Two identical spheres of radius 3 units fit into the cylinder.

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Question 15

For real numbers a and b, what is the value of 7a + 4b?
I. $$ab \neq 0$$
II. $$a^2 + b^2 = 0$$

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Question 16

What is the value of $$\sin 2 \theta$$?
I. $$\sec \theta + \cosec \theta = 4$$
II. $$\tan \theta + \cot \theta = 4$$

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Question 17

Fornon-zerointegersa, b, c, d andp,is theproduct $$(ap) \times (bp)^2 \times (cp)^3 \times (dp)^4$$ a positive integer?
I. a < c < p < 0
II. b < d < p < 0

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Question 18

For positive integers x and y with xy = 30, what is the value of x + y?
I. $$1 < \frac{x}{y} < 2$$
II. $$x > y$$

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Question 19

Is the matrix A singular?
I. A is a $$2 \times 2$$ matrix
II. The sum of the elements of the matrix A is zero.

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Question 20

What is the number of zero at the end of the number n?
I. $$2^8$$ divides n.
II. $$5^3$$ divides n but $$5^4$$ does not divide n.

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