Question 1
If a pair of linear equations is inconsistent, then the lines representing them graphically will be:
(A) Intersecting
(B) Always coincident
(C) Parallel
(D) Intersecting or coincident
Question 2
For what value of k do the equations 3x – y + 8 = 0 and 6x – ky = -16 represent coincident lines?
(A) 1/2
(B) -1/2
(C) 2
(D) -2
Question 3
Find the values of a and b for which the following pair of linear equations has infinitely many
2x + 3y = 7
(a – b)x + (a + b)y = 3a + b – 2
Question 4
Solve the following system of linear equations using the Substitution Method:
s – t = 3
s/3 + t/2 = 6
Question 5
For what value of p will the following system of equations have no solution?
(2p – 1)x + (p – 1)y = 2p + 1
3x + y = 1
Question 6
The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and the breadth by 2 units, the area increases by 67 square units. Find the dimensions (length and breadth) of the rectangle.
Question 7
A motor boat whose speed is 15 km/h in still water goes 30 km downstream and comes back upstream to the same spot in a total time of 4 hours 30 minutes. Find the speed of the stream.
Question 8
A part of monthly hostel charges is fixed and the remaining depends on the number of days one has taken food in the mess. When a student A takes food for 20 days she has to pay Rs 1000 as hostel charges whereas a student B, who takes food for 26 days, pays Rs 1180 as hostel charges. Find the fixed charges and the cost of food per day.
Question 9
Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?
Question 10
The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is Rs 105 and for a journey of 15 km, the charge paid is Rs 155. What are the fixed charges and the charge per km? How much does a person have to pay for travelling a distance of 25 km?