English Medium कक्षा १० - CBSE Important Questions for Mathematics

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`

If `tan theta = 24/7`, find that sin θ + cos θ.

Prove the following trigonometric identities.

`(1 + sec theta)/sec theta = (sin^2 theta)/(1 - cos theta)`

Prove the following trigonometric identities.

`1/(sec A + tan A) - 1/cos A = 1/cos A - 1/(sec A - tan A)`

`1/((1+ sin θ)) + 1/((1 - sin θ)) = 2 sec^2 θ`

cos⁴ A − sin⁴ A is equal to ______.

(sec A + tan A) (1 − sin A) = ______.

Find the value of ( sin² 33° + sin² 57°).

Prove that :(sinθ+cosecθ)²+(cosθ+ secθ)² = 7 + tan² θ+cot² θ.

Prove that: (1+cot A - cosecA)(1 + tan A+ secA) =2.