Here are five multiple-choice questions (MCQs) on mathematics suitable for the Central Teacher Eligibility Test (CTET), along with their answers and explanations:

Question: What is the value of ( \frac{3}{4} \times \frac{5}{6} )?

A) ( \frac{5}{8} )

B) ( \frac{5}{9} )

C) ( \frac{5}{12} )

D) ( \frac{1}{2} )

Answer: C) ( \frac{5}{12} ) Explanation: To multiply fractions, multiply the numerators together and the denominators together. So, ( \frac{3}{4} \times \frac{5}{6} = \frac{3 \times 5}{4 \times 6} = \frac{15}{24} ). Simplifying further, ( \frac{15}{24} = \frac{5}{8} ).

Question: If a triangle has angles measuring 60°, 70°, and ( x )°, what is the value of ( x )?

A) 40°

B) 50°

C) 60°

D) 70°

Answer: A) 40° Explanation: The sum of angles in a triangle is always 180°. So, ( 60^\circ + 70^\circ + x^\circ = 180^\circ ). Solving for ( x ), we get ( x = 180^\circ – 60^\circ – 70^\circ = 50^\circ ).

Question: What is the perimeter of a rectangle with length 8 cm and width 5 cm?

A) 22 cm

B) 26 cm

C) 30 cm

D) 36 cm

Answer: B) 26 cm Explanation: The perimeter of a rectangle is given by ( 2 \times (\text{length} + \text{width}) ). Substituting the given values, ( 2 \times (8 \text{ cm} + 5 \text{ cm}) = 2 \times 13 \text{ cm} = 26 \text{ cm} ).

Question: If ( \frac{5}{x} = \frac{15}{20} ), what is the value of ( x )?

A) 3

B) 4

C) 5

D) 6

Answer: B) 4 Explanation: Cross-multiply to solve for ( x ): ( 5 \times 20 = 15 \times x ). So, ( 100 = 15x ). Dividing both sides by 15, we get ( x = \frac{100}{15} = 4 ).

Question: What is the square root of 121?

A) 11

B) 12

C) 13

D) 14

Answer: A) 11 Explanation: The square root of a number ( n ) is a value that, when multiplied by itself, gives ( n ). So, the square root of 121 is ( \sqrt{121} = 11 ).