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Mark the correct alternative in each of the following:, Y The value of k for which the system of equations, kx - y = 2 and, 6x - 2y 3 has a unique solution, is, %3D, (a) = 3, (b) + 3, (c) # 0, (d) = 0, Y The value of k for which the system of equations 2x + 3y = 5 and, 4x + ky 10 has, infinite number of solutions, is, %3D, (a) 1, (b) 3, (c) 6, (d) 0, 3. The value of k for which thesystem of equations x+2y-3 = 0 and 5x + ky +7 = 0 has, no solution, is, (a) 10, .The value of k for which the system of equations 3x+5y 0 and kx + 10y = 0 has a, non-zero solution, is, (a) 0, (b) 6, (c) 3, (d) 1, (b) 2, (c) 6, (d) 8, If the system of equations 2x - 3y = 7 and, (a + b) x + (2a – b) y = 21 has infinitely, many solutions, then, (a) a = 1, b = 5, 6 If the system of equations 3x + y = 1 and, (2k – 1) x + (k – 1) y = 2k + 1 is inconsistent,, %3D, (b) a = 5, b = 1, (c) a = -1, b = 5, (d) a = 5, b = -1, %3D, then k =, (a) 1, (b) 0, (c) -1, (d) 2

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am bl, then the system of equations ax + by = c and, lx +my=", (a) has a unique solution, (c) has infinitely many solutions, %3D, (b) has no solution, (d) may or may not have a solution., Je the system of equations, 2x +3y = 7, 2ax + (a + b) y = 28, has infinitely many solutions, then, %3D, (b) b= 2a, (d) 2a + b = 0, (c) a + 2b = 0, The value of k for which the system of equations, (a) a = 2b, x+ 2y = 5, 3x + ky + 15 0, %D, has no solution is, (a) 6, (b) -6, (c) 3/2, (d) none of these, 19 If 2x-3y = 7 and (a +b) x- (a +b-3) y = 4a +b represent coincident lines, then a, and b satisfy the equation, %3D, (a) a + 5b = 0, (b) 5a + b 0, (c) a-5b 0, (d) 5a - b 0, If a pair of linear equations in two variables is consistent, then the lines represented by, two equations are, (a) intersecting, (b) parallel, (d) intersecting or coincident, (c) always coincident, The area of the triangle formed by the line+, = 1 with the coordinåte axes is, (a) ab, (b) 2ab, (c), (d) ab, 4, The area of the triangle formed by the lines y= x, x = 6 and y= 0 is, (a) 36 sq. units, (b) 18 sq. units, sun bs 6 (), (d) 72 sq. units, 4. If the system of equations 2x+ 3y = 5, 4x + ky = 10 has infinitely many solutions, then, %3D, %3D, k =, (a) 1, (b), 2, (c) 3, (d) 6, 15 If the system of equations kx-5y = 2, 6x + 2y =7 has no solution, then k=, %3D, (a) -10, (b) -5, (c)-6, (d) -15, The area of the triangle formed by the lines x 3, y = 4 and x =v is, Amsulz, (d) None of these, %3D, %3D, (c) 2 sq. unit, (a) 1/2 sq. unit, C. The area of the triangle formed by the lines 2x + 3y = 12, x-y-1 0 and x0, (as shown in Fig. 3.24), is, (a) 7sq. units, (b) 1 sq. unit, (b) 7.5 sq. units, (c) 6.5 sq. units, (d) 6 sq. units

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2r+3y-12=0, В (0,4), (3, 2)., A (6, 0), x', С (1, 0), D (0,-11, Ex-y-1-0, y, Fig. 3.24, s. The sum of the digits of a two digit number is 9. If 27 is added to it, the digits of the, number get reversed. The number is, (a) 25, U. If x = a, y = bis the solution of the systems of equations x-y= 2 and x+y = 4, then the, values of a andbare, respectively, (a) 3 and 1, (b) 72, (c) 63, (d) 36, (b) 3 and 5, (c) 5 and 3, (d) -1 and -3, For what value k, do the equations 3x-y+8=0 and 6x-ky+16=0 represent coincident, lines?, (b) -, (a), (c) 2, 2, Aruna has only 1 and2coins with her. If the total number of coins that she has is 50, and the amount of money with her is ? 75, then the number of 1 and 2 coins are,, (d) -2, respectively, (a) 35 and 15, (b) 35 and 20, (c) 15 and 35, (d) 25 and 25