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ICSE Class X Board Exam 2026 : Physics

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Nitin classes Std: 8th ICSE Sub: maths topic: Quadrilaterals Marks: 40 Time: 1.5 hr Q.1. Multiple Choice Questions: (5) 1. In the figure, ABCD is a rectangle whose diagonals intersect at O. If OD = 5x + 1 and OA = 4x + 19, then x equals (a) 12 (b) 15 (c) 16 (d) 18 2. A. What value of a would make the given quadrilateral a parallelogram? (a) 4 (b) 5 (c) 6 (d) 8 3. Which expression below represents the measure of B in rhombus ABCD? (a) x (b) (180 - x) (c) 2x (d) (180 - 2x) 4. In the adjoining figure, DEFG is a rhombus. Then, (q - p) is equal to (a) 20 (b) 30 (c) 40 (d) 50 5. In a parallelogram PQRS, and P + Q = a and P - R = b Then, a and b are respectively. (a) 90 , 90 (b) 120 , 60 (c) 180 , 0 (d) 180 , 90 Q.2 Assertion Reason type (3) 1. Assertion (A): Every kite is a trapezium. Reason (R): In a trapezium, a pair of opposite sides is equal. (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A). (b) Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A). (c) Assertion (A) is true but Reason (R) is false. (d) Assertion (A) is false but Reason (R) is true. 2. Assertion (A): Quadrilateral is a polygon sum of whose exterior angles is equal to the sum of its interior angles. Reason (R): The sum of exterior angles taken in order of a polygon is 360 . (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A). (b) Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A). (c) Assertion (A) is true but Reason (R) is false. (d) Assertion (A) is false but Reason (R) is true. 3. Assertion (A): If the diagonals of a quadrilateral bisect each other, it must be a parallelogram. Reason (R): The diagonals of a parallelogram are equal. (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A), (b) Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A). (c) Assertion (A) is true but Reason (R) is false. (d) Assertion (A) is false but Reason (R) is true. Q.3. Which of the following statements are true? (i) Every square is a rhombus. (2) (ii) Every rectangle is a parallelogram. (iii) Every rhombus is a square. (iv) The diagonals of a parallelogram bisect each other at right angles. Q.4 Solve the following: [10] 1. Three angles of a quadrilateral ABCD are A = 70 , B = 50 and C = 82 . Find D (2) 2. The angles of a quadrilateral are in the ratio 2:3:7: 6. Find the measure of each angle of the quadrilateral. (2) 3. The angles of a quadrilateral are (5x) , 5(x + 2), (6x - 20) and 6(x + 3) respectively. Find (3) (i) the value of x and (ii) each angle of the quadrilateral. 4. In the figure, OR and OS are the bisectors of QRS and PSR respectively. If SPQ = 100 . find the measure ROS and PQR. (3) Q.5 Solve the following: [10] 1. In a parallelogram ABCD, if A = 115 , find B, C and D. (2) 2. In the adjoining figure, ABCD is a rhombus. If angle A = 70 , find CDB. 3. In the adjoining figure, ABCD is a rectangle whose (3) diagonals AC and BD intersect at O. If OAB = 32 , find (i) ACB (ii) OB . 4. The lengths of the diagonals of a rhombus are 24 cm and 18 cm respectively. Find the length of each side of the rhombus. (3) Q.6 Solve the following: [10] 1. In Figure, ABCD is a trapezium in which AB || CD. Diagonal AC is joined. If AD = CD, BAD = 90 and CAB = 45 , find the angles of ADC. 2. In Figure, ABCD is a kite whose diagonals AC and BD intersect at O. If BCD = 120 and ADB = 25 , find the values x and y. 3. ABCD is an isosceles trapezium in which AB || CD, AB = 15 cm, BC = 10 cm and C = 60 , Find the length of CD. 4. In Figure, ABCD is a kite whose diagonals AC and BD intersect at O. If BAC = 50 and CDB = 35 , find a. ADC b. ABC and c. BCD. (2)

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