Exams › JEE Advanced › Maths

In trapezium ABCD, AB is parallel to CD. Given that angle ADC = 2 * angle ABC, with AD = a cm and CD = b cm, find the length of AB in cm.

1. a/2 + 2b
2. a + b
3. (2/3)*a + b
4. a + (2/3)*b

Correct answer: a + b

Solution

Because AB || CD, co-interior and alternate angle relations combine with angle ADC = 2*angle ABC to make a sub-triangle isosceles, so AB splits into a segment equal to CD (b) plus a segment equal to AD (a).

Related JEE Advanced Maths questions

• In a trapezium ABCD with AB parallel to DC, E and F are the midpoints of the two diagonals. Given DC = 60 and EF = 5, find the length of AB.
• In a chemistry class, there are 20 students, while a physics class has 30 students. If 10 students are enrolled in both classes, and the two classes are held at separate times, determine the value of k/8, where k represents the total number of students attending either class.
• Given that A represents the divisors of 15, B contains prime numbers less than 10, and C includes even numbers less than 9, how many elements are there in the intersection of (A ∪ C) and B?
• Identify the periodic function among the following:
• The function f(x) = √|x² - 5| x + 6 + √8 + 2|x| - |x|² is defined as a real number for values of x within which range?
• Let f(x) = 4x / (4x² + 2). If the sum of the integrals ∫(1/1997) + ∫(2/1997) +... + ∫(1196/1997) equals 499q, what is the value of q?

⚔️ Practice JEE Advanced Maths free + battle 1v1 →