Exam Questions & Step-by-Step Markschemes (4 Problems)
Question 1 • 2023
4 Marks
A motor boat whose speed is 18\text{ km/h} in still water takes 1 hour more to go 24\text{ km} upstream than to return downstream to the same spot. Find the speed of the stream.
Answer: \text{Speed of stream} = 6\text{ km/h}
Question 2 • 2023
3 Marks
Find two consecutive positive integers, sum of whose squares is 365 .
Answer: 13 \text{ and } 14
Question 3 • 2024
3 Marks
દ્વિઘાત સમીકરણ 2x^2 - 6x + 3 = 0 માટે વિવેચક શોધો અને તે પરથી બીજના પ્રકાર નક્કી કરો. જો બીજ વાસ્તવિક હોય તો તે મેળવો.
Answer: D = 12 > 0, \quad x = \frac{3 \pm \sqrt{3}}{2}
Question 4 • 2024
4 Marks
An express train takes 1 hour less than a passenger train to travel 132\text{ km} between Mysore and Bangalore. If the average speed of the express train is 11\text{ km/h} more than that of the passenger train, find the average speed of the two trains.
Answer: \text{Passenger: } 33 \text{ km/h}, \quad \text{Express: } 44 \text{ km/h}