English Medium इयत्ता १० - CBSE Important Questions

1. Make a labelled figure on the basis of the given information and calculate the distance of the boat from the foot of the observation tower.
2. After 10 minutes, the guard observed that the boat was approaching the tower and its distance from tower is reduced by 240(`sqrt(3)` - 1) m. He immediately raised the alarm. What was the new angle of depression of the boat from the top of the observation tower?

In which ratio the y-axis divides the line segment joining the points (5, – 6) and (–1, – 4)?

Assertion (A): The ratio in which the line segment joining (2, -3) and (5, 6) internally divided by x-axis is 1:2.

Reason (R): as formula for the internal division is `((mx_2 + nx_1)/(m + n) , (my_2 + ny_1)/(m + n))`

Based on the above information answer the following questions using the coordinate geometry.

1. Find the distance between Lucknow (L) to Bhuj (B).
2. If Kota (K), internally divide the line segment joining Lucknow (L) to Bhuj (B) into 3 : 2 then find the coordinate of Kota (K).
3. Name the type of triangle formed by the places Lucknow (L), Nashik (N) and Puri (P)
   [OR]
   Find a place (point) on the longitude (y-axis) which is equidistant from the points Lucknow (L) and Puri (P).

If the vertices of a parallelogram PQRS taken in order are P(3, 4), Q(–2, 3) and R(–3, –2), then the coordinates of its fourth vertex S are ______.

Statement A (Assertion): If the coordinates of the mid-points of the sides AB and AC of ∆ABC are D(3, 5) and E(–3, –3) respectively, then BC = 20 units.

Statement R (Reason): The line joining the mid-points of two sides of a triangle is parallel to the third side and equal to half of it.

A tiling or tessellation of a flat surface is the covering of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps. Historically, tessellations were used in ancient Rome and in Islamic art. You may find tessellation patterns on floors, walls, paintings etc. Shown below is a tiled floor in the archaeological Museum of Seville, made using squares, triangles and hexagons.

A craftsman thought of making a floor pattern after being inspired by the above design. To ensure accuracy in his work, he made the pattern on the Cartesian plane. He used regular octagons, squares and triangles for his floor tessellation pattern

Use the above figure to answer the questions that follow:

1. What is the length of the line segment joining points B and F?
2. The centre ‘Z’ of the figure will be the point of intersection of the diagonals of quadrilateral WXOP. Then what are the coordinates of Z?
3. What are the coordinates of the point on y-axis equidistant from A and G?
   OR
   What is the area of Trapezium AFGH?

The distance of the point (–4, 3) from y-axis is ______.

The coordinates of the point where the line 2y = 4x + 5 crosses x-axis is ______.

The distance between the points (0, 5) and (–3, 1) is ______.

The distance of the point (3, 5) from x-axis (in units) is ______.

Read the following passage:

Based on the above information, answer the following questions.

1. How far is Alia's house from Shagun's house?
2. How far is the library from Shagun's house?
3. Show that for Shagun, school is farther compared to Alia's house and library.
   OR
   Show that Alia’s house, shagun’s house and library for an isosceles right triangle.

The distance of the point (5, 0) from the origin is ______.

Distance of the point (6, 5) from the y-axis is ______.

A point (x, y) is at a distance of 5 units from the origin. How many such points lie in the third quadrant?

1. At an instance, the midfielders and forward formed a parallelogram. Find the position of the central midfielder (D) if the position of other players who formed the parallelogram are :- A(1, 2), B(4, 3) and C(6, 6)
2. Check if the Goal keeper G(–3, 5), Sweeper H(3, 1) and Wing-back K(0, 3) fall on a same straight line.
   [or]
   Check if the Full-back J(5, –3) and centre-back I(–4, 6) are equidistant from forward C(0, 1) and if C is the mid-point of IJ.
3. If Defensive midfielder A(1, 4), Attacking midfielder B(2, –3) and Striker E(a, b) lie on the same straight line and B is equidistant from A and E, find the position of E.

Ryan, from a very young age, was fascinated by the twinkling of stars and the vastness of space. He always dreamt of becoming an astronaut one day. So, he started to sketch his own rocket designs on the graph sheet. One such design is given below :

Based on the above, answer the following questions:

i. Find the mid-point of the segment joining F and G.    (1) 

ii. a. What is the distance between the points A and C?   (2)

OR

b. Find the coordinates of the points which divides the line segment joining the points A and B in the ratio 1 : 3 internally.    (2)

iii. What are the coordinates of the point D?    (1)

Assertion (A): Mid-point of a line segment divides the line segment in the ratio 1 : 1

Reason (R): The ratio in which the point (−3, k) divides the line segment joining the points (− 5, 4) and (− 2, 3) is 1 : 2.

Prove the following identities, where the angles involved are acute angles for which the expressions are defined:

`(cosec  θ  – cot θ)^2 = (1-cos theta)/(1 + cos theta)`

Prove the following identities, where the angles involved are acute angles for which the expressions are defined:

`(sin theta-2sin^3theta)/(2cos^3theta -costheta) = tan theta`