Scoring System Analysis
We need to determine the difference in incorrect answers between Candidate A and Candidate B, given they scored equally.
- Marks awarded: +4 for correct, -1 for incorrect.
- Candidate A: Attempted 18 questions.
- Candidate B: Attempted 13 questions.
Setting Up Equations
Let $C_A$ and $I_A$ be the number of correct and incorrect answers for Candidate A, respectively.
Let $C_B$ and $I_B$ be the number of correct and incorrect answers for Candidate B, respectively.
From the number of questions attempted:
- Equation 1: $C_A + I_A = 18 \implies C_A = 18 - I_A$
- Equation 2: $C_B + I_B = 13 \implies C_B = 13 - I_B$
From the equal marks scored:
Marks for A = Marks for B
$ 4 \times C_A - 1 \times I_A = 4 \times C_B - 1 \times I_B $
Calculating Incorrect Answers Difference
Substitute the expressions for $C_A$ and $C_B$ from the attempt equations into the marks equation:
$ 4(18 - I_A) - I_A = 4(13 - I_B) - I_B $
Simplify the equation:
$ 72 - 4I_A - I_A = 52 - 4I_B - I_B $
$ 72 - 5I_A = 52 - 5I_B $
Rearrange the terms to find the difference $I_A - I_B$:
$ 72 - 52 = 5I_A - 5I_B $
$ 20 = 5(I_A - I_B) $
$ I_A - I_B = \frac{20}{5} $
$ I_A - I_B = 4 $
Therefore, Candidate A has 4 more incorrect answers compared to Candidate B.
Important Questions from Algebra (Notes)
- What is the remainder when 2023²⁰²⁴ + 2025²⁰²⁴ is divided by 2024?
In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If she/he attempts all 60 questions and secures 130 marks, the number of questions she/he attempts wrongly, are?
Match List-I with List-II
List-1 List-II (A) If $\begin{bmatrix}\lambda-1 & 0 \\ 0 & \lambda-1 \end{bmatrix} $, then $\lambda$ is (I) 0 (B) If A=$ \begin{bmatrix}1 & 2 \\2 & 4 \end{bmatrix} $, then $\Delta$ is (II) 1 (C) If A = $ \begin{bmatrix}1 & 0 \\0 & \frac{1}{2} \end{bmatrix} $, then $|A^{-1}|$ is (III) -2 (D) If $ \begin{bmatrix}a+1 & 1 \\1 & 2 \end{bmatrix} = \begin{bmatrix}-1 & 1 \\1 & 2 \end{bmatrix} $, then a is (IV) 2 Choose the correct answer from the options given below:
- If (x - 1) is a factor of $2x^2 - 5x + k = 0$, then the value of k is:
- If $x = (2+\sqrt{3})^{\frac{1}{3}} + (2+\sqrt{3})^{-\frac{1}{3}}$ and $x^3-3x + k = 0$, then the value of k is:
