Question

(5 + √5) (5 - √5) on simplification gives ___________.

a) 20 b) 2√5 c) 10 d) 25

The coefficient of x

2

in the expansion of (x + 2)2

is _________.

a) 1 b) 6 c) 8 d) 12

The number of parts, the coordinates axes divide the plane are ________.

a) 2 parts b) 4 parts c) 6 parts d) 8 parts

The measure of each angle of an equilateral triangle is _________.

a) 30° b) 45° c) 60° d) 90°

Two equal sides of an isosceles triangle are 13 cm each and its perimeter is 36 cm, then the area of

the triangle is _____________.

a) 20 cm2

b) 30 cm2

c) 40 cm2

d) 60 cm2

The number of outcomes when a coin is tossed is _________.

a) 1 b) 2 c) 4 d) ​

Answer 1

1) (5 + √5) (5 - √5) on simplification gives:

➡ (5 + √5) (5 - √5) is the form (a + b) (a - b)

Applying the same identity here:

= (5 + √5) (5 - √5)

= 5² - (√5)²

= 25 - 5

= 20

The required correct option is Option A: 20.

2) The coefficient of x² in the expansion of (x + 2)² is:

➡ (x + 2)² is the form (a + b)²

Applying the same identity here:

= (x + 2)²

= x² + (2 × x × 2) + 2²

= x² + 4x + 4

Here, the coefficient of x² is 1.

The required correct option is Option A: 1.

3) The number of parts, the coordinate axes divide the plane are:

➡ The X and Y coordinate axes divide the plane into 4 quadrants namely first quadrant, second quadrant, third quadrant and fourth quadrant.

The required correct option is Option B: 4 parts.

4) The measure of each angle in a equilateral triangle is:

➡ The measure of each angle in an equilateral triangle is 60°. This can be confirmed by using the angle sum property as 60 x 3 is 180°.

The required correct option is Option C: 60°.

5) Two equal sides of an isosceles triangle are 13 cm each and its perimeter is 36 cm, then the area of  the triangle is:

➡ Perimeter of triangle = 36 cm

Sum of equal sides = 13 x 2 = 26 cm

Measure of non-equal side = 36 - 26 = 10 cm

Side 1 = 13 cm, Side 2 = 13 cm and Side 3 = 10 cm

To find the area, we need to apply the Heron's formula:

$\sf{\longrightarrow\:Semi\:perimeter=\dfrac{36}{2}=18\:cm}$

Applying the Heron's formula:

$\sf{\implies\:A=\sqrt{S(S-a)(S-b)(S-c)}}$

Applying the values:

$\sf{\longrightarrow\:A=\sqrt{18(18-13)(18-13)(18-10)}}$

$\sf{\longrightarrow\:A=\sqrt{18\times5\times5\times8}}$

$\sf{\longrightarrow\:A=5\sqrt{9\times2\times2\times4}}$

$\sf{\longrightarrow\:A=5\times3\times2\times2}$

$\bf{\longrightarrow\:A=60\:cm^2}$

The required correct option is Option D: 60 cm².

6) The number of outcomes when a coin is tossed is:

➡ When a coin is tossed, the outcome is either head or tail. So the total no. of outcomes is 2.

The required correct option is Option B: 2.

Identities used:

✳ (a + b) (a - b) = a² - b²

✳ (a + b)² = a² + 2ab + b²