# Electrical Engineering Orientation/Geometry and Data Representation

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## Important Notes & Instructions on Answering the questions

• This Aptitude test is on Geometry and data representation .
• Select the most correct answer of the four possible answers to each question.
• Attempt all questions before submitting to view your results.
• Use of calculator allowed.

Mathematics Aptitude test2: Questionaire

1

 If a circle with centre Q is given by the following equation $ax^{2}+y^{2}+8y-1=0$ Then the co-ordinates of Q are ...

 (A) ( 1 ; -1 ) (B) ( 0 ; -4 ) (C) ( 3 ; 0 ) (D) ( 2 ; 2 )

2

 Which of the following is the Phythagorus theorem.

 (A) In a right-angled triangle, $r^{2}=x^{2}+y^{2}$ . (B) The product f gradients of a loci is -1. (C) $(x-c)^{2}+(y-b)^{2}=r^{2}$ . (D) None of the above.

3

 The following ${\mathcal {4}}ABC$ cuts the Y-axis at Q. the ${\mathcal {4}}ABC$ has the following points: n( 0 ; r) ; o( 4 ; 3 ) & P( -5 ; -2 ) as vertices. The gradient of PO then is ...

 (A) ${\frac {4+(-5)}{3+(-2)}}$ $={\frac {-1}{1}}.$ (B) ${\frac {4-(5)}{3-(2)}}$ $={\frac {-1}{1}}.$ (C) ${\frac {4-(-2)}{3-(-5)}}$ $={\frac {6}{8}}.$ (D) ${\frac {4-(-5)}{3-(-2)}}$ $={\frac {9}{5}}.$ 4

 If $\cot A=k$ and A $\in$ [ 0° ; 90° ] which of the following diagrams is true?

 (A) (B) (C) (D) None of the above.

5

 Which of the following is a possible general solution to $\tan 3x.\cot 33^{\circ }-1=0$ ?

 (A) ${\begin{matrix}\tan 3x.\cot 33^{\circ }&=&1\\\ \tan 3x&=&{\frac {1}{\cot 33^{\circ }}}\\\ \\\ \tan 3x&=&\cot(33^{\circ }+66^{\circ })\end{matrix}}$ . (B) ${\begin{matrix}\tan 3x.\cot 33^{\circ }&=&1\\\ \tan 3x&=&{\frac {1}{\cot 33^{\circ }}}\\\ \\\ 3x&=&33^{\circ }\end{matrix}}$ . (C) ${\begin{matrix}\tan 3x.\cot 33^{\circ }&=&1\\\ \tan 3x&=&{\frac {\sin 33^{\circ }}{\cos 33^{\circ }}}\end{matrix}}$ . (D) None of the above.

6

 Which of the following is the correct expression of $\cos(x-y)$ in terms of Cosines of X and Y?

 (A) $\cos x\cos y+\sin x\sin y$ (B) $\cos x\sin y+\cos y\sin x$ (C) $\sec ^{2}x$ $\sec ^{2}y$ (D) ${\frac {1}{2}}(\cos ^{2}x-\sin ^{2}y)$ 7

 In the diagram below, points H; I & J lie on the circle with centre K as shown. Which of the following statements is true?

 (A) $K{\hat {H}}I=H{\hat {K}}J$ (B) $H{\hat {K}}J=2H{\hat {I}}J$ (C) $HK\|JI$ (D) $HK\perp \ JI$ 8

 In the following diagram which statement is true?

 (A) $NO=BO$ thus ${\hat {N}}_{1}={\hat {B}}_{1}$ (B) $CB\perp \ OB$ (C) ${\hat {N}}_{1}={\hat {N}}_{2}$ (D) None of the above

9

 Which of the following statements must be true to prove a cyclicquadrilateral ?

 (A) Atleast one side of a quadrilateral must be equal to the radius of the circle. (B) Opposite angles of a quadrilateral must sum up to 180°. (C) Exterior angle of a quadrilateral must be equal to twice the interior angle. (D) Atleast one vertex of a quadrilateral must lie at the centre of a circle.

10

 Which of the following statements does not prove similarity of $\triangle ABC$ and $\triangle DEF$ ?

 (A) All angles of $\triangle ABC$ are same as all angles of $\triangle DEF$ . (B) All pairs of corresponding sides of $\triangle ABC$ and $\triangle DEF$ are of the same ratio. (C) An angle of $\triangle ABC$ is equal to an angles of $\triangle DEF$ and the containing sides are of the same ratio. (D) $\triangle ABC$ and $\triangle DEF$ are enclosed in the same circle.