1. If (x/y) = 1/2, then the value of the expression, (4x + 3y)/ (6x + 5y) is?

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**Correct answer is option - 4**

**Explanation: **In the given expression, (4x + 3y)/ (6x + 5y), divide every term in the numerator and the denominator by ‘y’.

This gives: [4(x/y) + 3(y/y)]/ [6(x/y) + 5(y/y)]

This gives: [4(x/y) + 3]/ [6(x/y) + 5)]

Since x/y = 1/2, this implies: [4(1/2) + 3]/ [6(1/2) + 5]

This gives: (2 + 3)/ (3 + 5) = 5/8.

2. If (4x + 3) – 16 = (2x + 7), then the value of ‘x’ is?

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**Correct answer is option - 5**

**Explanation: **The given equation can also be written as: 4x + 3 – 16 = 2x + 7.

Simplifying the given equation we get: 4x – 13 = 2x + 7.

Combining the like terms, we get 4x – 2x = 7 + 13.

This gives: 2x = 20 ==> x = 20/2 ==> x = 10.

3. If the two lines kx – 2y + 5 = 0 and 4x – y + 6 = 0 are perpendicular to each other, then the value of ‘k’ is?

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**Correct answer is option - 2**

**Explanation: **The given first line can be rearranged as: 2y = kx + 5 ==> y = (k/2)x + 5/2.

Similarly the second line can be rearranged as: y = 4x + 6.

The above two lines are now in the form of y = mx + b, where ‘m’ is the slope and ‘b’ is the y-intercept.

If two lines are perpendicular, then the product of their slopes is -1.

This gives: (k/2) * 4 = -1 ==> 2k = -1 ==> k = -1/2.

4. For the sequence, 2, 5, 8, 11… what is the value of the 25^{th} term?

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**Correct answer is option - 4**

**Explanation:**

In the given sequence of numbers, 2, 5, 7, 9…the first term, a = 2.

The common difference between the terms, d = 3.

Hence this sequence is an arithmetic sequence.

The nth term of an arithmetic sequence is = a + (n – 1)d

Therefore the 25^{th} term implies, a = 2, d = 3, n = 25

This gives: 25^{th} term = 2 + (25 – 1)*3

25^{th} term = 2 + (24 * 3) = 2 + 72 = 74.

5. If x = a + 5 and y = 7 – 3a, then what is ‘y’ in terms of ‘x’?

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**Correct answer is option - 5**

**Explanation: **Since we want ‘y’ in terms of ‘x’, we need to eliminate ‘a’ in the ‘y’ equation.

x = a + 5 which gives: a = x – 5. Now substitute this ‘a’ value into the ‘y’ equation.

This gives: y = 7 – 3a ==> y = 7 – 3(x – 5) which implies y = 7 – 3x + 15.

This gives: y = - 3x + 22.

6. If A, B are the points lying on the circle and ‘O’ is the center of the circle, then what is the length of the line segment AB passing through ‘O’ if the radius of the circle is 6.5m?

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**Correct answer is option - 5**

**Explanation: **Any line joining two points on the circle if it passes through the center of the circle, then that line is the diameter of the circle! Since AB line segment passes through the center of the circle, ‘O’, hence AB is the diameter of the circle.

Diameter = 2 * radius ==> since radius = 6.5m, hence the diameter = 2 * 6.5m = 13m.

7. A car travelling in a circular path completed one circular rotation after covering a distance of 36m. What would the angle be if the car covered 26m?

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**Correct answer is option - 4**

**Explanation:**If the car covered 36m in 1 complete circular rotation, this means that the total angle made by the car in a distance of 36m is 360°.Now if the distance travelled by the car is 26m, then 26m * (360°/ 36m) = 260°.