Mathematics questions with solutions

Table of Contents

## 1. A regular polygon has each of its angles as 160⁰. What is the number of sides of the polygon?

1. A regular polygon has each of its angles as 160⁰. What is the number of sides of the polygon?

b) 9

c) 18

d) 20

Solution

Number of sides of the polygon » n

»180(n-2)/n

160 »180(n-2)/n

Cross multiply

160n » 180n-360

Collect like terms

360 »180n-160n

360 » 20n

Divide both sides by 20

n » 18 (C)

## 2. A girl walks 30m from a point p on a bearing of 040⁰ to a point Q. She then walks 30m on a bearing of 140⁰ to a point R. The bearing of R from P is?

2. A girl walks 30m from a point p on a bearing of 040⁰ to a point Q. She then walks 30m on a bearing of 140⁰ to a point R. The bearing of R from P is?

a) 90⁰

b) 50⁰

c) 45⁰

d) 40⁰

Solution

From the figure above, the bearing of R from P » 40⁰ + ø

Triangle PQR In isosceles,

Therefore, angle P = angle R = ø

Ø » (180-80)/2 » 50⁰

The bearing of R from P

Ø » 40⁰ + 50⁰

» 90⁰ [A]

a) 24

b) 120

c) 60

d) 48

Solution

The number of three digit number from integer 1 to 6

6P3 » n!/(n-r)!

6!/(6-3)!

6!/3!

6×5×4×3!/3!

120 [b]

## 4. In how many different ways can the letters of the word GEOLOGY be arranged in order?

a) 720

b) 1260

c) 2620

d) 5040

Solution

The word GEOLOGY has 7 letters » 7!

‘0’ occurs twice (2!)

‘G’ occurs twice = (2!)

The rest appears only ‘once’

In how many different ways can the letters be arranged in order

7!/(2!2!)

7×6×5×4×3×2!/(2!2!)

» 7×6×5×2×3

1260 [b]

a) X<14

b) X<20

c) X<29

d) X<28

Solution

Distance covered in the first part » speed × timetaken

X × 30/60

½xkm

Distance covered in the second part » 2(x-5)km

When distance covered is less than 60km

Therefore, 2(x-5)2 + ½x < 60

4x-20 + ½x < 60

4x-20 + x < 120

5x<140

X<28 [d]

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