Please enter the following details
Free Daily Targets & Mocks
Study Material & Formulas PDFs
1 on 1 Mentorship
Question 27
Let a, b, x, y be real numbers such that $$a^2 + b^2 = 25, x^2 + y^2 = 169$$, and $$ax + by = 65$$. If $$k = ay - bx$$, then
Solution
$$\left(ax+by\right)^2=65^2$$
$$a^2x^2\ +\ b^2y^2+\ 2abxy\ =\ 65^2$$
$$k = ay - bx$$
$$k^2\ =\ a^2y^2+b^2x^2-2abxy$$
$$(a^2 + b^2)(x^2 + y^2 )= 25* 169$$
$$a^2x^2+a^2y^2+b^2x^2+b^2y^2=\ 25\times\ 169$$
$$k^2=\ 65^2\ -\ \left(25\times\ 169\right)$$
k = 0
D is the correct answer.
Video Solution
Create a FREE account and get:
- All Quant CAT complete Formulas and shortcuts PDF
- 35+ CAT previous year papers with video solutions PDF
- 5000+ Topic-wise Previous year CAT Solved Questions for Free
CAT Quant Questions | CAT Quantitative Ability
CAT Logarithms, Surds and Indices QuestionsCAT Remainders QuestionsCAT Arithmetic QuestionsCAT Inequalities QuestionsCAT Simple Interest Compound Interest Questions
CAT DILR Questions | LRDI Questions For CAT
CAT Special Charts QuestionsCAT DI with connected data sets QuestionsCAT Coins and Weights QuestionsCAT Charts QuestionsCAT Arrangement Questions
