List of practice Questions

The coordinates of the point on the x-axis and equidistant from the points (5, -2) and (-3, 2) will be:
A die is thrown once. Find the probability of getting: (i) A prime number. (ii) A number lying between 2 and 6.
If the sum of the first 8 terms of an A.P. is 64 and the sum of its first 17 terms is 289, then find the first term and the common difference of the progression.
A spherical glass vessel has a cylindrical neck 7 cm long and diameter 2 cm, while the diameter of the spherical part is 8.4 cm. Find how much water can be filled in the vessel.
A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of the same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.
The angles of depression of the top and bottom of a 10 m tall building from the top of a multi-storeyed building are 30° and 45° respectively. Find the height of the multi-storeyed building.
Find the coordinates of the point which divides the line segment joining the points (4, -3) and (8, 5) in the ratio 3 : 1 internally.
Find the values of \( y \) for which the distance between the points (5, -3) and (13, y) is 10 units.
Find the zeroes of the quadratic polynomial \( 3x^2 - x - 4 \) and verify the relationship between the zeroes and the coefficients.
Solve the following pair of linear equations:
\( 0.2x + 0.3y = 1.3 \) and \( 0.4x - 0.5y = -0.7 \).
Prove that the lengths of the tangents drawn from an external point to a circle are equal.
D is a point on the side BC of a triangle ABC such that \( \angle ADC = \angle BAC \). Prove that \( CA^2 = CB \times CD \).
If \( \sin\theta = \dfrac{3}{4} \), then the value of \( \tan\theta \) will be:
The value of \( (\csc A + \cot A)(1 - \cos A) \) will be:
The value of \( \dfrac{1 - \tan^2 A}{1 - \cot^2 A} \) will be:
Prove that \( \dfrac{1 + \sec A}{\sec A} = \dfrac{\sin^2 A}{1 - \cos A} \).
A chord of a circle of radius 21 cm subtends a right angle at the centre. Find the area of the corresponding minor segment.
If one root of the equation \( x^2 - kx - 8 = 0 \) is 2, then the value of \( k \) will be:
Find the 20th term of the Arithmetic Progression (A.P.) 10, 7, 4, …
A tangent PQ at a point P of a circle of radius 10 cm meets a line through the centre O at a point Q so that OQ = 12 cm. The length of PQ will be:
If two cubes each of volume 8 cm\(^3\) are joined end-to-end, then the surface area of the resulting cuboid will be:
If the area of a sector of a circle of radius 14 cm is 154 cm\(^2\), then the angle of the sector will be:
The value of \( 2\sin30^\circ \cos30^\circ \) is:
One card is drawn from a well-shuffled pack of 52 cards. The probability of getting a face card is:
The difference of a rational number and an irrational number is: