The area of the triangle formed by (-1, 2), (2, -1) and (0, 0) is
1
0
2
3
3
1
4
Official Solution
Correct Option: (4)
To find the area of a triangle formed by three points , we use the formula: Substituting the points :
The correct option is (D):
02
PYQ 2024
easy
mathematicsID: ap-polyc
The area of the shaded region in the given figure is
1
4π sq. units
2
16-16π sq. units
3
16-4π sq. units
4
None of these
Official Solution
Correct Option: (3)
The figure shows a circle inscribed in a square with radius .
Let the vertex of the square be . Since forms a square with , the side of the square is also 4.
The area of the square is .
The area of the quarter circle is .
The area of the shaded region is the area of the square minus the area of the quarter circle.
Area of shaded region = Area of square - Area of quarter circle sq. units.
03
PYQ 2025
medium
mathematicsID: ap-polyc
Area of a sector of a circle with radius 4 cm and angle 30° is (use ):
1
2
3
4
Official Solution
Correct Option: (1)
Step 1: Formula for the Area of a Sector. The area of a sector of a circle is given by the formula: where is the central angle, and is the radius of the circle. Step 2: Substituting the Given Values. Here, the radius and the angle . Substituting these values into the formula, we get: Step 3: Conclusion. Thus, the area of the sector is .
04
PYQ 2025
easy
mathematicsID: ap-polyc
Area of minor segment if a chord of a circle of radius 10 cm subtends a right angle at the centre is (use ):
1
28 cm
2
28.5 cm
3
27 cm
4
27.5 cm
Official Solution
Correct Option: (2)
Step 1: Understand the problem setup We are given a circle with a radius of 10 cm. A chord of the circle subtends a right angle at the center of the circle. Step 2: Find the area of the sector The formula for the area of a sector of a circle is given by: where (since the chord subtends a right angle), and . Substitute the values: Step 3: Find the area of the triangle The area of the triangle formed by the two radii and the chord can be found using the formula for the area of a right triangle: Here, the base and height are both the radius , since the triangle is isosceles and the angle at the center is . Step 4: Find the area of the minor segment The area of the minor segment is the area of the sector minus the area of the triangle: Thus, the area of the minor segment is .
