यदि (a_1)/(a_2)=(b_1)/(b_2)=(c_1)/(c_2) तो समीकरण निकाय a_1x+b_1y+c_1=0 तथा a_2x+b_2y+c_2=0 का ह...

If (a_1)/(a_2) = (b_1)/(b_2) ne (c_1)/(c_2) , then the equations a_1x + b_1y + c_1 =0 and a_2x + b_2y + c_2=0 are _________. (consistent/inconsistent)

If the equations 4x + 6y = 15 and 8x +ky = 30 have infinite solutions, then find the value of k . The following are the steps involved in solving the above problem. Arrange them in sequential order. (A) (4)/(8) = (6)/(k) = (-15)/(-30) rArr (6)/(k) = (1)/(2) (B) We know that, if a_1x+ b_1y + c_1 =0 and a_2 x + b_2 y + c_2=0 have infinite solutions, then (a_1)/(a_2) = (b_1)/(b_2) = (c_1)/(c_2) . (C) Given that, 4x + 6y - 15 =0 and 8x + ky - 30 =0 have infinite solutions. (D) therefore k = 12 .

|(a_1,b_1,c_1),(a_2,b_2,c_2),(a_3,b_3,c_3)|=0 then the system of equations a_1x+b_1y+c_1z=0, a_2x+b_2y+c_2z=0, a_3x+b_3y+c_3z=0 has (A) no solution (B) one trivial and one non trivial solutions (C) only the trivial solution (0,0,0) (D) more than two solution

Statement-1: If the equations ax^2 + bx + c = 0 (a, b, c in R and a != 0) and 2x^2 + 7x+10=0 have a common root, then (2a+c)/b =2. Statement-2: If both roots of a_1 x^2 + b_1 x+c_1 = 0 and a_2 x^2 + b_2x + c_2 = 0 are same, then a_1/a_2=b_1/b_2=c_1/c_2. Given a_1,b_1,c_1,a_2,b_2,c_2 in R and a_1 a_2 != 0. (i) Statement I is true , Statement II is also true and Statement II is correct explanation of Statement I (ii)Statement I is true , Statement II is also true and Statement II is not correct explanation of Statement I (iii) Statement I is true , Statement II is False (iv) Statement I is False, Statement II is True

Three linear equations a_1x+b_1y+c_1z=0, a_2x+b_2y+c_2z=0,a_3x+b_3y+c_3z=0 are consistent if (A) |(a_1,b_1,c_1),(a_2,b_2,c_2),(a_3,b_3,c_3)|=0 (B) |(a_1,b_1,c_1),(a_2,b_2,c_2),(a_3,b_3,c_3)|=-1 (C) a_1b_1c_1+a_2b_2c_2+a_3b_3c_3=0 (D) none of these