List of practice Questions

If LCM of 26, 156 is 156, then the value of HCF will be:
The largest number which divides 245 and 1037, leaving remainder 5 in each case, will be:
If one root of the equation $2x^2 + ax + 6 = 0$ is 2, then the value of $a$ will be:
If the sum and difference of two numbers are 8 and 2 respectively, the numbers will be:
The roots of equation \( 4x^2 - 12x + 9 = 0 \) will be:
Distance between two points \( (2, 3) \) and \( (4, 1) \) will be:
Find the mode of the following data:
Solve the following pair of equations: \[ \frac{3}{x} + \frac{2}{y} = 11, \quad \frac{4}{x} - \frac{5}{y} = 7. \]
A fraction becomes \( \frac{1}{3} \) when 1 is added to the numerator and it becomes \( \frac{1}{4} \) when 1 is subtracted from its denominator. Find the fraction.
The height of a temple is 15 metre. From the top of the temple, the angle of elevation of the top of a building on the opposite side of the road is \( 30^\circ \) and the angle of depression of the foot of the building is \( 45^\circ \). Prove that the height of the building is \( 5(3 + \sqrt{3}) \) metre.
From the top of a building, the angle of elevation of the top of a tower is \( 60^\circ \). From the top of the building, the angle of depression of foot of the tower is \( 45^\circ \). If the height of the tower is 40 metres, then prove that the height of the building is \( 20(\sqrt{3} - 1) \) metres.
A solid is in the shape of a cone which is surmounted on a hemisphere of same base radius. If the curved surfaces of hemisphere and cone are equal, find the ratio of radius and height of the cone.
A solid sphere is made by melting the three metallic solid spheres of diameters 12 cm, 16 cm and 20 cm. Find the diameter of this solid sphere.
The distance between the points $P(2, -3)$ and $Q(10, v)$ is 10 units. The value of $v$ will be:
Find the median from the following table:
Find the co-ordinates of the point divided by x-axis to the line segment joining the points \( (1, -5) \) and \( (-4, 5) \).
Find the coordinates of the point A, where AB is the diameter of a circle whose center is \( (2, -3) \) and the coordinates of B are \( (1, 4) \).
Find the value of \( k \) for which the equations \( 2x + ky = 1 \) and \( 3x - 5y = 7 \) have a unique solution.
Solve the following pair of equations using the cross-multiplication method: \[ 2x + 3y - 46 = 0 \] \[ 3x + 5y - 74 = 0 \]
Draw a line segment of length 76 cm and divide it in the ratio 3:4. Write the measures of both the two parts.
If \( \cos \theta = \frac{4}{5} \), find the value of \( \sin \theta \cos \theta + \tan^2 \theta \).
Find the value of \( f \) from the following frequency table if 25 is the mean of marks obtained by the students:
The dimensions of a metallic solid cuboid are \( 9 \, \text{m} \times 8 \, \text{m} \times 2 \, \text{m} \). It is melted and recast into cubes of dimension 2 m. Thus the number of cubes so formed will be:
The mean of the following table will be:
If the arithmetic mean and mode of the given data are 28 and 16 respectively, the median will be: