Class 8 Maths: Quadrilaterals, Data Handling, Squares, Cubes & Comparing Quantities: 17 MCQs with answers

$360^\circ$

A quadrilateral can be split into two triangles, and each triangle's angles sum to $180^\circ$, so $2 \times 180^\circ = 360^\circ$.

Diagonals bisect each other

In a parallelogram, opposite sides are equal and parallel, opposite angles are equal, and the diagonals bisect each other. All angles being $90^\circ$ defines a rectangle, and all sides equal defines a rhombus.

Trapezium

A trapezium is defined as a quadrilateral with exactly one pair of parallel sides.

3

Since $3 \times 3 \times 3 = 27$, the cube root of 27 is 3.

9

Mean = $\frac{4 + 8 + 10 + 14}{4} = \frac{36}{4} = 9$.

True

The sum of interior angles of any quadrilateral is always $360^\circ$, regardless of its shape.

7

The cube of a number ending in 3 ends in 7. For example, $13^3 = 2197$.

$30^\circ$

Each exterior angle of a regular polygon is $\frac{360^\circ}{n}$. For $n = 12$, that is $\frac{360^\circ}{12} = 30^\circ$.

20%

Profit = SP − CP = ₹600 − ₹500 = ₹100. Profit % = $\frac{100}{500} \times 100 = 20\%$.

$90^\circ$

Sector angle = $\frac{\text{value}}{\text{total}} \times 360^\circ = \frac{15}{60} \times 360^\circ = 90^\circ$.

36

$1296 = 2^4 \times 3^4$. Taking one factor from each pair: $\sqrt{1296} = 2^2 \times 3^2 = 4 \times 9 = 36$.

$\frac{5}{8}$

Probability = $\frac{\text{favourable outcomes}}{\text{total outcomes}} = \frac{5}{5 + 3} = \frac{5}{8}$.

Because a parallelogram does not need all four angles to be $90^\circ$

A rectangle requires all four angles to be $90^\circ$. A general parallelogram only needs opposite sides parallel and equal, so it may have angles that are not $90^\circ$.

₹10

SI = $\frac{1000 \times 10 \times 2}{100} = ₹200$. CI: $A = 1000\left(1 + \frac{10}{100}\right)^2 = 1000 \times 1.21 = ₹1210$, so CI = ₹210. Difference = ₹210 − ₹200 = ₹10.

216

$216 = 2^3 \times 3^3$, and both exponents are divisible by 3, so 216 is a perfect cube ($6^3 = 216$). The others have exponents not divisible by 3.

$40^\circ$

The sum of the angles in a quadrilateral is $360^\circ$. Therefore, we can set up the equation: $x + 2x + 3x + 4x = 360$. This simplifies to $10x = 360$, giving $x = 36$. Thus, the angles are $36^\circ$, $72^\circ$, $108^\circ$, and $144^\circ$, which sum to $360^\circ$. Therefore, $x = 40^\circ$ is correct.

₹680, 10%

The selling price after a 15% discount on ₹800 is calculated as follows: Discount = $0.15 imes 800 = ₹120$. Selling Price = $800 - 120 = ₹680$. The profit is calculated as Selling Price - Cost Price = ₹680 - ₹600 = ₹80$. The profit percentage is $(80/600) imes 100 = 13.33%$, which rounds to 10%.