MATHIZZZZ

coordinate geometry

100

For a point ( 3 , − 5 ) , the value of (abscissa − ordinate) is :
 

8

200

The distance between the points ( 𝑎 cos ⁡ 𝜃 + 𝑏 sin ⁡ 𝜃 ,   0 ) and ( 0 ,   𝑎 sin ⁡ 𝜃 − 𝑏 cos ⁡ 𝜃 ) is

sq.rt 𝑎 2 + 𝑏 2
 

300

 Find the coordinates of a point on the line 𝑥 + 𝑦 = 5 which is equidistant from (6, 4) and (5, 2).
 

( − 3 /2 , 13/ 2 ) .
 

400

Find the coordinates of the points which divide the line segment joining points P(-1, 7) and Q(4, -3) into three equal parts.
 

( 7 /3 ,   1/ 3 )
 

500

If two adjacent vertices of a parallelogram are (3, 2) and (-1, 0) and the diagonals intersect at  (2, -5), then find the coordinates of the other two vertices
 

(1, -12) and (5, -10).
 

Area related to circles

100

What is the area of a semi-circle of diameter 'd' ?
 
 

1/8πd2

200

A chord of a circle of radius 14 cm subtends a right angle at the centre. Find the area of the corresponding major segment.    

560 cm²
 

300

Find the area of the corresponding major sector of a circle of radius 42 cm and of central angle of a minor sector is 30°.

5082  cm 2
 

400

Chord AB subtends an angle of 40° at the centre of the circle of radius 9 cm. The length of arc AB is
 

44/7 cm

500

n the figure, the boundary of the shaded region consists of four semicircular arcs, two smallest being equal. If the diameter of the largest is 14 cm and that of the smallest is 3.5 cm, calculate the area of the shaded region.
Pic- Desktop

86.625 cm²

Real Numbers

100

The HCF of 2 ³ and 3 ² is
 

2 ⁰ ⋅ 3 ⁰
 

200

Two numbers are in the ratio 4: 5 and their HCF is 11. Find the LCM of these numbers
 
 

220

300

Find the length of the plank that can be used to measure the lengths 4 m 20 cm and 5 m 4 cm exactly, in the least time.
 

84

400

Find the greatest number less than 10,000 which is exactly divisible by 48, 60 and 65.
 

9360

500

The HCF of two numbers a and b is 5 and their LCM is 200. Find the product of ab.
 
 

1000

Circles

100

In the adjoining figure, TP and TQ are tangents drawn to a circle with centre O. If ∠OPQ = 15° and ∠PTQ = θ, then find the value of sin 2θ.  
 Pic - Dsk

sin 60

200

In the given figure, if PT is tangent to a circle with centre O and ∠TPO = 35º, then the measure of ∠x is
 Pic - Dsk

125

300

In the given figure, a circle is inscribed in a quadrilateral ABCD in which ∠B = 90°. If AD = 17 cm, AB = 20 cm and DS = 3 cm, then find the radius of the circle
 Pic - dsk

6 cm

400

Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.
 

8 cm

500

In Fig, AB is the diameter of a circle centred at O. BC is tangent to the circle at B. If OP bisects the chord AD and ∠AOP= 60°, then find m∠C.
 

60

Introduction to Trigonometry

100

The value of ( tan ^{⁡ 2} 𝐴 − 1 cos ^{⁡ 2} 𝐴 ) is:
 

-1

200

The value of sin ⁡ 9 0 ^∘ cos ⁡ 9 0 ^∘ − sin ⁡ ² 6 0 ^∘
 

- 3/4

300

In the given figure, △ 𝑀 𝐸 𝑁 is a right triangle, right-angled at 𝐸 . If ∠ 𝐸 𝑀 𝑁 = 6 0 ^∘ and 𝑀 𝐸 = 5 cm, find the length of 𝑀 𝑁 . Also, find the value of sin ⁡ ² 𝑁 .
 

1/4

400

Solve  sin ⁡ 𝐴 − 2 sin ⁡³𝐴 /  2 cos ³𝐴 − cos 𝐴 to a ratio
 

tan A

500

If 3 sin ⁡ 𝐴 = 1 , find the value of sec ⁡ 𝐴 .
 

3√ 2 / 4