Join Our JEE Preparation Group
Prep with like-minded aspirants; Get access to free daily tests and study material.
Sign in
Please select an account to continue using cracku.in
↓ →
Join Our JEE Preparation Group
Prep with like-minded aspirants; Get access to free daily tests and study material.
This section has Four Questions. Each question is provided with 4 alternative answers. Exactly one of them is the correct answer. Indicate the correct answer by A, B, C, D.
If $$a$$, $$b$$, $$c$$ and $$d$$ are four real numbers such that $$a^2 + 2b^2 + 13c^2 + 5d^2 - 2ab + 4bc - 12cd - 6d + 9 = 0$$ then $$2a + b + 11c + 2d$$ is equal to
The left side can be written as $$(a - b)^2 + (b + 2c)^2 + (3c - 2d)^2 + (d - 3)^2 = 0$$. Each square must be 0, so $$d = 3$$, $$c = 2$$, $$b = -4$$ and $$a = -4$$. Then $$2a + b + 11c + 2d = -8 - 4 + 22 + 6 = 16$$.
Was this solution helpful?
Predict your JEE Main percentile, rank & performance in seconds
Educational materials for JEE preparation
Ask our AI anything
AI can make mistakes. Please verify important information.
AI can make mistakes. Please verify important information.