Class 9 Mathematics | CBSE (NCERT) Board | Mixed Level Practice Test - 40 Questions (2026)

If $x+y+z = 0$, show that $x^3+y^3+z^3 = 3xyz$.

Factories $27y^3 + 125z^3$.

Find the remainder when $x^3-ax^2+6x-a$ is divided by $x-a$.

Prove that the sum of the angles of a triangle is $180^ ext{o}$.

In a parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP = BQ (see Figure). Show that $\triangle APD \cong \triangle CQB$. (Note: Figure not provided, assume standard parallelogram with diagonal BD)

The angles of a quadrilateral are in the ratio $3:5:9:13$. Find all the angles of the quadrilateral.

A triangular park ABC has sides 120 m, 80 m and 50 m. A gardener has to put a fence all around it and also plant grass inside. How much area does he need to plant? Find the cost of fencing it with barbed wire at the rate of Rs 20 per metre, leaving a space 3 m wide for a gate on one side.

The length, breadth and height of a room are 5 m, 4 m and 3 m respectively. Find the cost of whitewashing the walls of the room and the ceiling at the rate of Rs 7.50 per m$^2$.

A conical tent is 10 m high and the radius of its base is 24 m. Find: \\(i) Slant height of the tent. \\(ii) Cost of the canvas required to make the tent, if the cost of 1 m$^2$ canvas is Rs 70.

A survey conducted by an organisation for the cause of illness and death among women between the ages of 15 and 44 (in years) worldwide, found the following figures (in %): \\\begin{tabular}{|l|c|} \hline Causes & Female fatality rate (in \%) \\ \hline Reproductive Health Conditions & 31.8 \\ Neuropsychiatric Conditions & 25.4 \\ Injuries & 12.4 \\ Cardiovascular Conditions & 4.3 \\ Respiratory Conditions & 4.1 \\ Other causes & 22.0 \\ \hline \end{tabular} \\(i) Represent the information given above graphically. \\(ii) Which condition is the major cause of women's illness and death worldwide?

If $x = 2 + \sqrt{3}$, find the value of $x + \frac{1}{x}$.

Factorize the polynomial $8x^3 + 27y^3 + 36x^2y + 54xy^2$ using a suitable identity.

In $\triangle ABC$, $D$ is the midpoint of $BC$. If $AD$ is produced to $E$ such that $AD = DE$, prove that $AB = EC$.

Find the coordinates of the point where the linear equation $2x + 3y = 6$ intersects the x-axis and the y-axis.

A survey conducted by an organization for causes of illness and death among the women between the ages 15-44 (in years) worldwide, found the following figures (in %): | S.No. | Causes | Female fatality rate (%) | |-------|---------------------------------|--------------------------| | 1 | Reproductive Health Conditions | 31.8 | | 2 | Neuropsychiatric Conditions | 25.7 | | 3 | Injuries | 12.4 | | 4 | Cardiovascular Conditions | 4.3 | | 5 | Respiratory Conditions | 4.1 | | 6 | Other Causes | 21.7 | Represent the information given above by a bar graph.

The angles of a quadrilateral are in the ratio $3:5:9:13$. Find all the angles of the quadrilateral.

Construct a triangle $ABC$ in which $BC = 7$ cm, $\angle B = 75^\circ$ and $AB + AC = 13$ cm. Write down the steps of construction.

The radii of two cylinders are in the ratio of $2:3$ and their heights are in the ratio of $5:3$. Calculate the ratio of their volumes.

Find the area of a triangle two sides of which are 18 cm and 10 cm and the perimeter is 42 cm.

If $(x-1)$ is a factor of $p(x) = x^3 - ax^2 + 11x - 6$, then find the value of $a$.

Simplify the expression: $(\sqrt{5} + \sqrt{2})^2$.

Factorize: $x^3 - 2x^2 - x + 2$.

If a point $(3, 4)$ lies on the graph of the equation $3y = ax + 7$, find the value of $a$.

In $\triangle ABC$, if $\angle A = 30^{\circ}$, $\angle B = 70^{\circ}$, find $\angle C$.

Prove that the sum of any two sides of a triangle is greater than the third side.

Find the area of a triangle whose sides are 13 cm, 14 cm and 15 cm.

Plot the points $A(2, 3)$, $B(-3, 1)$, $C(0, -2)$ on a Cartesian plane.

A coin is tossed 1000 times with the following frequencies: Head: 455, Tail: 545 Compute the probability for each event.

The angles of a quadrilateral are in the ratio $3:5:9:13$. Find all the angles of the quadrilateral.

Find the remainder when $x^3 + 3x^2 + 3x + 1$ is divided by $x+1$.