English Medium कक्षा १० - CBSE Question Bank Solutions for Mathematics

If the distance between the points (4, P) and (1, 0) is 5, then the value of p is ______.

The distance between the point P(1, 4) and Q(4, 0) is ______.

The distance of the point (α, β) from the origin is ______.

If the distance between the points (x, -1) and (3, 2) is 5, then the value of x is ______.

The equation of the perpendicular bisector of line segment joining points A(4,5) and B(-2,3) is ______.

Case Study -2

A hockey field is the playing surface for the game of hockey. Historically, the game was played on natural turf (grass) but nowadays it is predominantly played on an artificial turf.

It is rectangular in shape - 100 yards by 60 yards. Goals consist of two upright posts placed equidistant from the centre of the backline, joined at the top by a horizontal crossbar. The inner edges of the posts must be 3.66 metres (4 yards) apart, and the lower edge of the crossbar must be 2.14 metres (7 feet) above the ground.

Each team plays with 11 players on the field during the game including the goalie. Positions you might play include -

• Forward: As shown by players A, B, C and D.
• Midfielders: As shown by players E, F and G.
• Fullbacks: As shown by players H, I and J.
• Goalie: As shown by player K.

Using the picture of a hockey field below, answer the questions that follow:

The coordinates of the centroid of ΔEHJ are ______.

Case Study -2

A hockey field is the playing surface for the game of hockey. Historically, the game was played on natural turf (grass) but nowadays it is predominantly played on an artificial turf.

It is rectangular in shape - 100 yards by 60 yards. Goals consist of two upright posts placed equidistant from the centre of the backline, joined at the top by a horizontal crossbar. The inner edges of the posts must be 3.66 metres (4 yards) apart, and the lower edge of the crossbar must be 2.14 metres (7 feet) above the ground.

Each team plays with 11 players on the field during the game including the goalie. Positions you might play include -

• Forward: As shown by players A, B, C and D.
• Midfielders: As shown by players E, F and G.
• Fullbacks: As shown by players H, I and J.
• Goalie: As shown by player K.

Using the picture of a hockey field below, answer the questions that follow:

If a player P needs to be at equal distances from A and G, such that A, P and G are in straight line, then position of P will be given by ______.

Case Study -2

A hockey field is the playing surface for the game of hockey. Historically, the game was played on natural turf (grass) but nowadays it is predominantly played on an artificial turf.

It is rectangular in shape - 100 yards by 60 yards. Goals consist of two upright posts placed equidistant from the centre of the backline, joined at the top by a horizontal crossbar. The inner edges of the posts must be 3.66 metres (4 yards) apart, and the lower edge of the crossbar must be 2.14 metres (7 feet) above the ground.

Each team plays with 11 players on the field during the game including the goalie. Positions you might play include -

• Forward: As shown by players A, B, C and D.
• Midfielders: As shown by players E, F and G.
• Fullbacks: As shown by players H, I and J.
• Goalie: As shown by player K.

Using the picture of a hockey field below, answer the questions that follow:

The point on x axis equidistant from I and E is ______.

Case Study -2

A hockey field is the playing surface for the game of hockey. Historically, the game was played on natural turf (grass) but nowadays it is predominantly played on an artificial turf.

It is rectangular in shape - 100 yards by 60 yards. Goals consist of two upright posts placed equidistant from the centre of the backline, joined at the top by a horizontal crossbar. The inner edges of the posts must be 3.66 metres (4 yards) apart, and the lower edge of the crossbar must be 2.14 metres (7 feet) above the ground.

Each team plays with 11 players on the field during the game including the goalie. Positions you might play include -

• Forward: As shown by players A, B, C and D.
• Midfielders: As shown by players E, F and G.
• Fullbacks: As shown by players H, I and J.
• Goalie: As shown by player K.

Using the picture of a hockey field below, answer the questions that follow:

What are the coordinates of the position of a player Q such that his distance from K is twice his distance from E and K, Q and E are collinear?

Case Study -2

A hockey field is the playing surface for the game of hockey. Historically, the game was played on natural turf (grass) but nowadays it is predominantly played on an artificial turf.

It is rectangular in shape - 100 yards by 60 yards. Goals consist of two upright posts placed equidistant from the centre of the backline, joined at the top by a horizontal crossbar. The inner edges of the posts must be 3.66 metres (4 yards) apart, and the lower edge of the crossbar must be 2.14 metres (7 feet) above the ground.

Each team plays with 11 players on the field during the game including the goalie. Positions you might play include -

• Forward: As shown by players A, B, C and D.
• Midfielders: As shown by players E, F and G.
• Fullbacks: As shown by players H, I and J.
• Goalie: As shown by player K.

Using the picture of a hockey field below, answer the questions that follow:

The point on y axis equidistant from B and C is ______.

If p - 1, p + 3, 3p - 1 are in AP, then p is equal to ______.

If the graph of a polynomial intersects the x-axis at only one point, it cannot be a quadratic polynomial.

If the graph of a polynomial intersects the x-axis at exactly two points, it need not be a quadratic polynomial.

The distance between the points A(0, 6) and B(0, –2) is ______.

The distance of the point P(–6, 8) from the origin is ______.

The points (– 4, 0), (4, 0), (0, 3) are the vertices of a ______.

∆ABC with vertices A(–2, 0), B(2, 0) and C(0, 2) is similar to ∆DEF with vertices D(–4, 0), E(4, 0) and F(0, 4).

Point P(0, 2) is the point of intersection of y-axis and perpendicular bisector of line segment joining the points A(–1, 1) and B(3, 3).

Points A(4, 3), B(6, 4), C(5, –6) and D(–3, 5) are the vertices of a parallelogram.

A circle has its centre at the origin and a point P(5, 0) lies on it. The point Q(6, 8) lies outside the circle.