Question

Find the value of J in the given below figure:

A. 30
B. 35
C. 40
D. 45

Answer 1

Hint: In this question, first of all identify that the given triangle is the Pascal triangle. In Pascal's triangle each entry of each subsequent row is constructed by adding the number above and to the left with the number above to the right. So, use this concept to reach the solution of the given problem.

Complete step-by-step answer:
The given triangle in the figure is Pascal's triangle. To build the triangle, start with “1” at the top, then each entry of each subsequent row is constructed by adding the number above and to the left with the number above to the right.
So, A is given by adding the two numbers above it i.e., 1 + 1 = 2. Therefore, A = 2
B is given by adding the two numbers above it i.e., 1 + 3 = 4. Therefore, B = 4
C is given by adding the two numbers above it i.e., 3 + 3 = 4. Therefore, C = 6
D is given by adding the two numbers above it i.e., C + 4 = 6 + 4 = 10. Therefore, D = 10
E is given by adding the two numbers above it i.e., 4 + 1 = 5. Therefore, E = 5
F is given by adding the two numbers above it i.e., 1 + 5 = 6. Therefore, F = 6
G is given by adding the two numbers above it i.e., 10 + D = 10 + 10 = 20. Therefore, G = 20
H is given by adding the two numbers above it i.e., E + 1 = 5 + 1 = 6. Therefore, H = 6
I is given by adding the two numbers above it i.e., 1 + F = 1 + 6 = 7. Therefore, I = 7
J is given by adding the two numbers above it i.e., G + 15 = 20 + 15 = 35. Therefore, J = 35
Hence, the value of J is 35
Thus, the correct option is B. 35.

Note:The pascal triangle is symmetric. The first diagonal shows the counting numbers. And each row represents the binomial coefficients of the expansion. For smaller powers of binomial expansions, we use Pascal's triangle. For greater powers of binomial expansions, we use binomial theorem.