Previous Year Mathematics Questions of Class 10 Chapter {Pair of Linear Equations of two variables} for Examination 2023
One mark Questions
1. The value of K for which the system of linear equations x + 2y = 3, 5x + ky + 7 = 0 is inconsistent is … {CBSE 2020}
2. If x = a, y = b is the solution of the pair of linear equation x – y = 2 and x + y = , find the value of a and b.
3. The area of the triangle formed by line x/a + y/b = 1 with the co ordinate axis is…………. ?
4. The area of the triangle formed by the line x = 3, y = 4 and x = y is ………
5. If am ≠ bl then the system of equations ax + by = c and lx + my = n has a unique solution. ( T / F)
Two mark Questions
1. Find the value of k so that the pair of equation x = 2y = 5 and 3x + ky + 15 = 0 has a unique solutions. {CBSE 2019}
2. The larger of two supplementary angles includes the smaller by 180, Find the angles. {CBSE 2019}
3. Sumit is 3 times as old as his son. Five years later he shall be two and half times as old as his son. How old is Sumit at present. {CBSE 2019}
4. If the system of equations 6x + 2y = 3 and kx + y = 2 has a unique solution, find the value of K.
Three mark Questions
1. Solve graphically 2x – 3y + 13 = 0, 3x – 2y + 12 = 0 {CBSE 2020}
2. If 2x + y = 23 and 4x – y = 19, find the value of (5y – 2x) and y/x - 2. {CBSE 2020}
3. Solve using Cross Multiplication method : 2x + y = 5, 3x + 2y = 8
4. For what value of m and n the following system of linear equations has infinitely many solutions: 3x + 4y = 12, (m+n)x + 2(m – n)y = 5m – 1
5. Draw the graph for x – y = -1 and 3x + 2y – 12 = 0. Also shade the region bounded by these lines and x axis.
6. If 3 times the larger of the two numbers is divided by the smaller one, we get 4 as quotient and 3 as the remainder. Also if 7 times the smaller number is divided by the larger one, we get 5 as quotient and 1 as remainder. Find the numbers.
7. If x + 1 is a factor of 2x3 + ax2 + 2bx + 1, then find the value of a and b given that 2a – 3b = 4.
8. A lending library has a fixed charge for the first three days and the additional charge for each day there after Sunita paid Rs. 27 for a book kept for seven days, while Raveena paid Rs. 21 for the book she kept for five days. Find the fixed charge and the charge for add extra day.
Four mark Questions
1. It can take 12 hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for 4 hours and the pipe of smaller diameter for 9 hours, only half of the pool can be filled. How long would it take for each pipe to fill the pool separately? {CBSE 2020}
2. 2 men and 7 boys can do a piece of work in 4 days. It is done by 4 men and 4 boys in 3 days. How long would it take for one man or one boy to do it?
3. Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for ach wrong answer. Had 4 marks been awarded for each correct answer and 2 marks deducted for each wrong answer. Yash would have scored 50 marks. How many questions were there in test?
4. Ravi divided to distribute Some amount to poor Students for their books. If there are 8 students less, every one will get Rs. 10 more. If there are 16 students more, every one will get Rs. 10 less. What is the number of students and how much does each get? What is the total amount distributed?
5. Place A and B are 100 km apart on a highway. One car starts from A and another car starts From B at the same time. If the car 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?
6. The area of rectangle gets reduced by 9 square units if the length is reduced by 5 units and the breadth is increased by 3 units. If we increase the length by 3 units and breadth by 2 units the area is increased by 67 square units. Find the length and breadth of the rectangle.
7. A boat covers 32 km upstream and 36 km downstream in 7 hours. Also it covers 40 km upstream and 48 km downstream in 9 hours find the speed of the boat in still water and that of the stream.
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