English Medium Class 10 - CBSE Question Bank Solutions for Mathematics

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 ratio of LCM and HCF of the least composite and the least prime numbers is ______.

If LCM(x, 18) = 36 and HCF(x, 18) = 2, then 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 ______.

For some integer m, every even integer is of the form ______.

For some integer q, every odd integer is of the form ______.

n² – 1 is divisible by 8, if n is ______.

If the HCF of 65 and 117 is expressible in the form 65m – 117, then the value of m is ______.

The largest number which divides 70 and 125, leaving remainders 5 and 8, respectively, is ______.

Explain why 3 × 5 × 7 + 7 is a composite number.

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.