List of practice Questions

If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then prove that the other two sides are divided in the same ratio.
Sides $AB$ and $BC$ and median $AD$ of a $△ABC$ are respectively proportional to sides $PQ$ and $PR$ and median $PM$ of $△PQR$. Show that $△ABC ∼ △PQR$.
How many terms of the $A.P.$ $27, 24, 21, . . .$ must be taken so that their sum is 105? Which term of the A.P. is zero?
The shadow of a tower standing on a level ground is found to be 40 m longer when the Sun’s altitude is 30° than when it was 60°. Find the height of the tower and the length of the original shadow. (use \(\sqrt{ 3}\) = 1.73)
The angles of depression of the top and the bottom of an 8 m tall building from the top of a multi-storeyed building are 30° and 45° respectively. Find the height of the multi-storeyed building and the distance between the two buildings. (use \(\sqrt{ 3}\) = 1.73)
A chord of a circle of radius 14 cm subtends an angle of 90° at the centre. Find the area of the corresponding minor and major segments of the circle.
Gurpreet is very fond of doing research on plants. She collected some leaves from different plants and measured their lengths in mm.
The length of the leaves from different plants are recorded in the following table.
Based on the above information, answer the following questions :
The picture given below shows a circular mirror hanging on the wall with a cord. The diagram represents the mirror as a circle with centre \(O\). \(AP\) and \(AQ\) are tangents to the circle at \(P\) and \(Q\) respectively such that \(AP = 30 \, \text{cm}\) and \(\angle PAQ = 60^\circ\).
Problem Figure
Based on the above information, answer the following questions:
The LCM of 24, 36 and 60 in terms of their prime factors is :
The graph of a polynomial intersects the y-axis at one point and the x-axis at two points. The number of zeroes of this polynomial are :
The solution of the pair of linear equations: \[ \frac{2x}{3} - \frac{y}{2} = -\frac{1}{6} \quad \text{and} \quad \frac{x}{2} + \frac{2y}{3} = 3 \] is:
The roots of the quadratic equation \(x^2 + x – p (p + 1) = 0 \)are :
The sum of the first three terms of an AP is 30 and the sum of the last three terms is 36. If the first term is 9, then the number of terms is :
The probability of getting a sum of 8, when two dice are thrown simultaneously, is :
The perpendicular bisector of the line segment joining the points A(–1, 3) and B(2, 4) cuts the y-axis at :
If in triangles $ABC$ and $PQR$, $\frac{AB}{QR} = \frac{BC}{PR}$, then they will be similar, when:
A line l intersects the sides PQ and PR of a \(\triangle\) PQR at L and M respectively such that LM || QR. If PL = 5·7 cm, PQ = 15·2 cm and MR = 5·5 cm, then the length of PM (in cm) is :
If two tangents inclined at an angle of 60º are drawn to a circle of radius 5 cm, then the length of each tangent is :
If tan A = 3 cot A, then the measure of the angle A is :
$(\sec \theta + \tan \theta)(1 - \sin \theta)$ is equal to:
A ladder 14 m long just reaches the top of a vertical wall. If the ladder makes an angle of $60^\circ$ with the wall, then the height of the wall is:
If the area of a sector is one-twelfth that of a complete circle, then the angle of the sector is :
The minute hand of a clock is 21 cm long. The area swept by it in 10 minutes is :
If the radius of Earth shrinks by 4% and mass of Earth unchanged, then the value of acceleration due to gravity will be changed by:
The median of 75, 21, 56, 36, 81, 05, and 42 is