linear equations cbse x sem-1

Section-A ` 1x10 = 10 Does the point (1,-2) lie on the line whose equation is 3x – y-5 =0 Is the pair of linear equations x-2y+4=0; 2x-4y-8 =0 inconsistent? How many solutions of the equation 5x-4y+11 =0 are possible? Find the value of K for which the pair of equations Kx-2y=3 & 3x+y=5 has a unique solution Find the number of solutions of x+2y-8=0; 2x+4y=16 Find the co-ordinates of the point where the line 2x-3y=6 meet the x and y axis. Find the value of the K for which the pair of linear equations (3K+1) x + 3y -2 = 0 & (k2 +1) x + (K-2) y-5=0 has no solution. For what value of K the pair of linear equations has infinitely many solutions? 10x +5y –(K-5)=0; 20x + 10y –K = 0 Write the condition that the pair of linear equations a1x + b1y +c1 = 0; a2x + b2y +c2 = 0; has unique solution. Is x=3 and y=-2 a solution of the linear equation 4x+3y=6? Section – B 2x5=10 solve graphically x-2y=6 ; 3x-6y=0 solve (x+1)/2 + (y-1)/3 = 8; (x-1)/3 + (y+1)/2 = 9 solve by cross multiplication method 11x+15y+23=0; 7x-2y-20=0 solve 148x+231y=527; 231y+148y = 610 One third of the number of the two digits is greater than one fourth of its successor by one .find the number. Section – C 3x10=30 Solve (a-b)x +(a + b)y = a2-2ab-b2;(a + b) (x + y) = a2 + b2 Five years ago A was thrice as old as B and ten years hence A shall be twice as old as B. What are the present ages of A and B A man travels 600Km partly by train and partly by car. If he covers 400Km by train and the rest by car, it takes him 6hours and 30 minutes. But if he travels 200Km by train and the rest by car, he takes half an hour longer. Find the speed of train and car. The sum of numerator and the denominator is 8.IUf 3 is added to both the numerator and denominator, the fraction becomes ¾ .Find the fraction. A two digit number is 4 times the sum of its digits and twice the product of its digits. Find the number. Two numbers are in the ratio 3:4.If 8 is added to each number, they become in the ratio of 4:5. Fine the numbers. A motor boat takes 6 hours to cover 100Km downstream and 30 Km upstream. If the boat goes 75Km downstream and returns back to the staring point in 8 hours, find the speed of the boat in still water and the speed of stream. 2men and 5 boys can do the work in 4 days and 5 men and 2 boys can do the work in 3 days. How long would it take for man alone and one boy alone to do the work? It takes 12 hours to fill a swimming pool using 2 pipes. If the larger pipe is used for 4 hours and smaller pipe for 9 hours, only half of the pool is filled. How long would it take for each pipe alone to fill the pool? X takes 3 hours more than Y to walk 30 Km.But if X doubles his pace, he is ahead of Y by 1 ½ hours. Find their speeds of walking. Linear equations 10 cbse test -1 max marks: 50 Max time: 1.30 All the best