Quant CAT 2024 Actual Questions

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Question 1 Roots and Expression Value The roots \( \alpha, \beta \) of the equation \( 3x^2 + \lambda x - 1 = 0 \) satisfy \[ \frac{1}{\alpha^2} + \frac{1}{\beta^2} = 15. \] The va…

Ques 1 When 3^333 is divided by 11, the remainder is Solution Modular Arithmetic - Cyclicity body { font-family: Arial, sans-serif; padding: 20px; background-color: #f2f2f2; } .con…

Inequality Question body { font-family: Arial, sans-serif; padding: 20px; } .question { font-weight: bold; } .options { margin-top: 15px; } All the values of \( x \) satisfying the…

Ages + Ratios When Rajesh’s age was same as the present age of Garima, the ratio of their ages was 3 : 2. When Garima’s age becomes the same as the present age of Rajesh, the ratio…

MathJax Inequality Region Area .options { margin-left: 20px; } In the XY-plane, the area, in sq. units, of the region defined by the inequalities \( y \geq x + 4 \) and \( -4 \leq …

MathJax Question .options { margin-left: 20px; } Let \( x, y, \) and \( z \) be real numbers satisfying: \( 4(x^2 + y^2 + z^2) = a \), \( 4(x - y - z) = 3 + a \). Then \( a \) equa…

MathJax Question For any natural number \( n \), let \( a_n \) be the largest integer not exceeding \( \sqrt{n} \). Then the value of \( a_1 + a_2 + \cdots + a_{50} \) is Solution …

Two places A and B are 45 kms apart and connected by a straight road. Anil goes from A to B while Sunil goes from B to A. Starting at the same time, they cross each other in exactl…

Ratios + Simple Equations A fruit seller has a total of 187 fruits consisting of apples, mangoes and oranges. The number of apples and mangoes are in the ratio 5 : 2. After she sel…

Interactive Quiz: Renu and Seema's Work body { font-family: Arial, sans-serif; margin: 20px; background-color: #f9f9f9; } .quiz { border: 2px solid #4CAF50; border-radius: 10px; ba…

Interactive Quiz: Radius of Incircle body { font-family: Arial, sans-serif; margin: 20px; background-color: #f9f9f9; } .quiz { border: 2px solid #4CAF50; border-radius: 10px; backg…

Interactive Quiz: Initial Grains Quantity body { font-family: Arial, sans-serif; margin: 20px; background-color: #f9f9f9; } .quiz { border: 2px solid #4CAF50; border-radius: 10px; …

Interactive Quiz: Milk and Water Ratio body { font-family: Arial, sans-serif; margin: 20px; background-color: #f9f9f9; } .quiz { border: 2px solid #4CAF50; border-radius: 10px; bac…

Interactive Quiz body { font-family: Arial, sans-serif; margin: 20px; background-color: #f9f9f9; } .quiz { border: 2px solid #4CAF50; border-radius: 10px; background-color: #fff; p…