CBSE Important Questions

Q. 1. Solve the equations graphically: x – y = 1, 2x + y = 8. Shade the area bounded by these lines and y-axis and find its area.

Q. 2. Solve the equations graphically:2x + 3y = 12, x – y = 1 and find the verticies of the triangle formed by the lines and y-axis.

Q. 3. Solve the following equations: 37x + 41y = 70, 41x + 37y = 86.

Q. 4. Solve the following equations by elimination of y: 11x + 15y + 23 = 0, 7x – 2y – 20 = 0.

Q. 5. Solve the following equations by equating coefficients: 3(2u + v) = 7uv and 3(u + 3v) = 11uv.

Q. 6. Find the value of m for which the equations 4x + my + 5 = 0 and 2x + 3y + 7 = 0 represent only one solution.

Q. 7. Find the value of k for which the equations: kx + 3y = k – 3 and 12x + ky = k represent infinitely many solutions.

Q. 8. Find the values of m and n if the equations: 2x + 3y = 7 and 2mx + (m + n) y = 28 represent infinite solutions.

Q. 9. Solve the following equations by cross-multiplication method: ax – by = 0 and x²/b – y²/a = b – a.

Q. 10. Solve the following equations by cross-multiplication method: 6x + 5y = 11 and 9x + 10y = 21.

Q. 11. Seven times a two-digit number is the same as four times the number obtained on interchanging the digits. If the difference between the two digits is 3, find the number.

Q. 12. The ratio of monthly incomes of two persons is 9:7 and their expenditures are in the ratio 4:3. If each of them saves Rs. 200 per month, find their monthly incomes.

Q. 13. The sum of the numerator and the denominator of a fraction is 3 less than twice the denominator. If the numerator and the denominator are decreased by 1, the numerator becomes half the denominator. Find the fraction.

Q. 14. A two digit number is 4 times the sum of its digits. On adding 18 to this number, the digits are reversed. Find the number.

Q. 15. A boat goes 12 km upstream and 40 km downstream in 8 hours. It can go 16 km upstream and 32 km downstream in the same time. Find the speed of the boat in still water and the speed of the stream.