# 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.

Lessons in Electric Engineering Orientation
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Lesson #2:
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Quiz Test 2:
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Mathematics Aptitude test2: Questionaire

1

 If a circle with centre Q is given by the following equation ${\displaystyle ax^{2}+y^{2}+8y-1=0}$ 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, ${\displaystyle r^{2}=x^{2}+y^{2}}$. (B) The product f gradients of a loci is -1. (C) ${\displaystyle (x-c)^{2}+(y-b)^{2}=r^{2}}$. (D) None of the above.

3

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

The gradient of PO then is ...

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

4

If ${\displaystyle \cot A=k}$ and A ${\displaystyle \in }$ [ 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 ${\displaystyle \tan 3x.\cot 33^{\circ }-1=0}$ ?

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

6

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

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

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

8

In the following diagram which statement is true?

 (A) ${\displaystyle NO=BO}$ thus ${\displaystyle {\hat {N}}_{1}={\hat {B}}_{1}}$ (B) ${\displaystyle CB\perp \ OB}$ (C) ${\displaystyle {\hat {N}}_{1}={\hat {N}}_{2}}$ (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 ${\displaystyle \triangle ABC}$ and ${\displaystyle \triangle DEF}$?

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

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