Which of the following given statement(s) is / are TRUE? A: Number of diagonals in a polygon of side ‘n’ is given by n (n + 6) / 4. B: Number of diagonals in a polygon of side is 12 are 54. C: Any quadrilateral in which opposite angles are supplementary is called a cyclic quadrilateral.

March List I with List II : List I List II (A) Supplementary angles (I) Angles less than 90° (B) Complementary angles (II) Two angles whose sum is 180° (C) Acute angles (III) Angles greater than 90° but less than 180° (D) Obtuse angles (IV) Two angles whose sum is 90° Choose the correct answer from the options given below :

A

(A) - (III), (B) - (II), (C) - (I), (D) - (IV)

B

(A) - (IV), (B) - (II), (C) - (III), (D) - (I)

C

(A) - (II), (B) - (IV), (C) - (I), (D) - (III)

D

(A) - (II), (B) - (IV), (C) - (III), (D) - (I)

Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements. Statements: All polygons are angles. All angles are diagonals. All cones are cubes. All cubes are decagons. No diagonal is a cube. Conclusions: I. Some diagonals are polygons. II. All diagonals are decagons. III. No polygon is a cone. IV. Some cubes are angles.

A

Both conclusions I and III follow

B

Both conclusions I and II follow

C

Only conclusion I follows

D

Both conclusions II and IV follow

Consider the following statements: (1) If n ≥ 3 and m ≥ 3 are distinct positive integers, then the sum of exterior angles of a regular polygon of m sides is different from the sum of exterior angles of regular polygon of n sides (2) Let m, n be integers such that m > n ≥ 3. Then the sum of the interior angles of regular polygon of sides is greater than the sum of interior angles of a regular polygon of n sides, and their sum is (m + n)π/2 Which of the above statements is/are correct?

A

1 only

B

2 only

C

Both 1 and 2

D

Neither 1 nor 2

Which of the following propertie(s) of circle is/are correct? I. Opposite angles of a cyclic quadrilateral are supplementary. ABCD is cyclic quadrilateral as its vertices lie on the circle. II. The degree measure of an arc is equal to twice the measure of an angle inscribed in the opposite arc.

A

Only I

B

Both I and II

C

Neither I nor II

D

Only II

The number of sides of polygon A is 6 more than the number of sides of polygon B. Interior angle of polygon A is 10° more than the interior angle of polygon B. Find the interior angle of polygon whose side is equal to sum of number of sides of polygon A and B.

A

155°

B

150°

C

160°

D

168°

Given that the angles of a polygon are all equal and each angle is a right angle. Statement 1: The quadrilateral has exactly four sides Statement 2: The sum of the angles of a polygon having n sides is (3n - 8) right angles. Which one of the following is correct in respect of the above statements?

A

Both Statement 1 and Statement 2 are true and Statement 2 is the correct explanation of statement 1

B

Both Statement 1 and Statement 2 are true and Statement 2 is not the correct explanation of statement 1

C

Statement 1 is true but Statement 2 is false

D

Statement 1 is false but Statement 2 is true

Which of the following statements is/are true? A: In a cyclic quadrilateral ABCD, If two diagonals AC and BD intersect each other at O, then OA × OB = OC × OD. B: In a quadrilateral (kite), the smaller diagonal divides the kite into two equilateral triangles. C: Diagonals of a rectangle are diameter of its circumcircle.

A

Only B and C

B

Only A

C

Only C

D

Only A and C

Consider the following a) Opposite angles of a cyclic quadrilateral are complementary b) The angle at the centre of a circle is twice the angle at the circumference. c) A cyclic quadrilateral has all its vertices on the circumference of the circle Which of the above statement is/are correct?

A

a & b

B

b & c

C

a & c

D

a, b & c

Consider the following statements & choose the correct option: When two straight lines intersect then, 1. Adjacent angles are supplementary 2. Opposite angles are supplementary

A

Both 1 & 2 are incorrect.

B

Both 1 & 2 are correct

C

1 is incorrect and 2 is correct

D

1 is correct and 2 is incorrect

Consider the following statements & choose the correct options When two straight lines intersect then, 1. Adjacent angles are supplementary 2. Opposite angles are supplementary

A

Both 1 & 2 are incorrect

B

Both 1 & 2 are correct

C

1 is incorrect and 2 is correct

D

1 is correct and 2 is incorrect

Which of the following given statement(s) is / are TRUE? A: Number of diagonals in a polygon of side ‘n’ is given by n (n + 6) / 4. B: Number of diagonals in a polygon of side is 12 are 54. C: Any quadrilateral in which opposite angles are supplementary is called a cyclic quadrilateral.

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