**Question 1 :**

The temperature at 12 noon was 10° C above zero.If it decreases at the rate of 2°C per hour until midnight, at what time would the temperature be 8°C below zero?

(A) 3 pm (B) 9 pm (C) 8 pm

**Solution :**

Temperature at 12 noon = 10° C

Decreasing rate = 2°C per hour

Total fall of temperature from 10° C to 0° C and 0° C to 8° C = -10 - 8 = -18

Time taken = -18/2 = 9 hours

At 9 pm the temperature will be 8°C below zero.

**Question 2 :**

An elevator decends into a mine shaft at the rate of 6 m/min.If the decline starts from 10 m above the ground level. Calculate how long will it take to reach -350 m ?

(A) 1 hour (B) 5 hours (C) 2 hours

**Solution :**

Starting position of mine shaft is 10 m above the ground but it moves in opposite direction.

So, it travels the distance (–350) m below the ground.

The total distance covered by mine shaft

= 10 m – (–350) m = 10 + 350 = 360 m

Now, time taken to cover a distance of 6 m by it

= (1/6) minute

Time taken to cover a distance of 360 m = (1/6) **⋅** 360

60 minutes = 1 hour

Thus, in one hour the mine shaft reaches –350 below the ground.

**Question 3 :**

How much less is 28 km than 46.2 km?

(A) 18.2 km (B) 14.6 km (C) 12.5 km

**Solution :**

In order to find 28 km is how much less than 46.2 km, we have to perform subtraction.

46.2 - 28 = 18.2 km

**Question 4 :**

Solve 5p + 2 = 17

(A) p = 2 (B) p = 5 (C) p = 3

**Solution :**

5p + 2 = 17

Subtract both sides by 2

5p = 17 - 2

5 p = 15

Divide both sides by 5

p = 15/5 = 3

So, the value of p is 3.

**Question 5 :**

When two lines l and m meet, we say they intersect, the meeting point is called the __________________

(A) Point of contact

(B) Point of intersection

(C) None of these

**Solution :**

The meeting point of two lines is called the point of intersection.

**Question 6 :**

Find the value of x in the following triangle

(A) 50° (B) 70° (C) 80°

**Solution :**

In a triangle, an exterior angle is equal to the sum of the interior opposite angles

x = <ABC + <ACB

x = 30 + 40

x = 70°

**Question 7 :**

The population of a city reduced from 25,000 to 24,500. Find the percentage decrease.

**(A) 5% (B) 2% (C) 1%**

**Solution :**

Original population = 25000

Reduced population = 24500

Difference between old and new population

= 25000 - 24500

= 500

Decrease percentage = (500 / 25000) ⋅ 100

= 2%

**Question 8 :**

A wire is in the shape of square of side 10 cm. If the wire is rebent in to a rectangle length 12 cm, calculate its width.

(A) 35% (B) 27% (C) 75%

**Solution :**

Perimeter of square = Perimeter of rectangle

Side length of square a = 10 cm

4a = 4 (10) = 40

Perimeter of rectangle = 40

2 (l + w) = 40

2(12 + w) = 40

12 + w = 20

Subtract both sides by 12

w = 20 - 12 = 8 cm

Hence the width of rectangle is 8 cm.

**Question 9 :**

Two sides of a parallelogram ABCD are 6cm and 4cm. The height corresponding to the base of CD is 3 cm. Find the area of the parallelogram

(A) 7 cm^{2} (B) 15 cm^{2} (C) 18 cm^{2}

**Solution :**

Area of parallelogram ABCD = Base ⋅ Height

Area of parallelogram ABCD = 6(3)

= 18 cm^{2}

**Question 10 :**

Diameter of a circular garden is 9.8 m. Calculate its area.

(A) 50 cm (B) 64 cm (C) 30 cm

**Solution :**

Diameter of circular garden = 9.8 m

r = 9.8/2 = 4.9

Area of circular garden = πr^{2}

= (22/7) (4.9)^{2}

= 75.46 m^{2}

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