[{"id":12236,"question":"The roots of (b-c)x2+(c-a) x+a-b=0 are equal if","choices":[{"text":"2b = a+c","value":"A"},{"text":"2a = b+c","value":"B"},{"text":"2c = a+b","value":"C"},{"text":"a + b + c =0","value":"D"},{"value":"E"}],"correctAnswer":1},{"id":12235,"question":"The roots of ax2+bx+c=0 are","choices":[{"text":"Rational ⇔ b2 -4 ac ≥ 0","value":"A"},{"text":"Irrational ⇔ b2-4 ac > 0","value":"B"},{"text":"Real ⇔ b2-4 ac ≠ 0","value":"C"},{"text":"Rational⇔ b2-4 ac = 0","value":"D"},{"value":"E"}],"correctAnswer":4},{"id":12234,"question":"If a,β are the roots of ax2+bx+c=0,the equation whose roots are doubled is","choices":[{"text":"ay2 +2by+c=0","value":"A"},{"text":"ay2+2by+4c=0","value":"B"},{"text":"ay2+2by+c=0","value":"C"},{"text":"ay2+by+4c=0","value":"D"},{"value":"E"}],"correctAnswer":2},{"id":12233,"question":"If w+w2 is a root of (x+1)(x+2)(x+3)(x+4) = k, then","choices":[{"text":"k=0","value":"A"},{"text":"k=1","value":"B"},{"text":"k=w","value":"C"},{"text":"k=w2","value":"D"},{"value":"E"}],"correctAnswer":1},{"id":12232,"question":"(x +a)(x +b)(x +c)(x +) = k, k≠0 is reducible to quadratic form only if","choices":[{"text":"a+b=c+d","value":"A"},{"text":"a+c=b+d","value":"B"},{"text":"a+d=b+c","value":"C"},{"text":"All are correct","value":"D"},{"value":"E"}],"correctAnswer":4},{"id":12231,"question":"The value of x for which the polynomials x2 - 1 and x2 -2x + 1 vanish simultaneously is","choices":[{"text":"2","value":"A"},{"text":"1","value":"B"},{"text":"-1","value":"C"},{"text":"-2","value":"D"},{"value":"E"}],"correctAnswer":2},{"id":12230,"question":"The expression x2 - x + 1 has","choices":[{"text":"One proper linear factor","value":"A"},{"text":"No proper linear factor","value":"B"},{"text":"Two proper linear factors","value":"C"},{"text":"None of these","value":"D"},{"value":"E"}],"correctAnswer":2},{"id":12229,"question":"The condition for ax2 + bx c to be expressed as the product of linear polynomials is","choices":[{"text":"b4 - 4ac =0","value":"A"},{"text":"b4- 4ac ≥0","value":"B"},{"text":"b4- 4ac <0","value":"C"},{"text":"b4= 4ac","value":"D"},{"value":"E"}],"correctAnswer":2},{"id":12228,"question":"If the equation x2+2x-3=0 and x2+3x-k=0 have a common root then the non - zero value of k is","choices":[{"text":"1","value":"A"},{"text":"3","value":"B"},{"text":"2","value":"C"},{"text":"4","value":"D"},{"value":"E"}],"correctAnswer":4},{"id":12227,"question":"Consider the equation px2 + qx + r = 0 where p,q,r are real The roots are equal in magnitude but opposite in sign when","choices":[{"text":"q = 0, r = 0,p ≠ 0","value":"A"},{"text":"p = 0,qr≠ 0","value":"B"},{"text":"r = 0,pq≠ 0","value":"C"},{"text":"q = 0, pq≠ 0","value":"D"},{"value":"E"}],"correctAnswer":4},{"id":12226,"question":"If a,β are the roots of the equation x2 + kx +12 = 0 such that a - β = 1, the value of k is","choices":[{"text":"0","value":"A"},{"text":"±1","value":"B"},{"text":"±5","value":"C"},{"text":"±7","value":"D"},{"value":"E"}],"correctAnswer":4},{"id":12225,"question":"The positive value of k for which the equation x2 + kx + 64 = 0 has one of the roots 0","choices":[{"text":"4","value":"A"},{"text":"64","value":"B"},{"text":"8","value":"C"},{"text":"All values of k","value":"D"},{"value":"E"}],"correctAnswer":4},{"id":12224,"question":"The sum of the roots of the equation x2 -6x +2 = 0 is","choices":[{"text":"-6","value":"A"},{"text":"2","value":"B"},{"text":"-2","value":"C"},{"text":"6","value":"D"},{"value":"E"}],"correctAnswer":4},{"id":12223,"question":"The roots of ax2 + bx + c = 0 are always unequal if","choices":[{"text":"b2 - 4ac = 0","value":"A"},{"text":"b2- 4ac ≠ 0","value":"B"},{"text":"b2- 4ac > 0","value":"C"},{"text":"b2- 4ac ≥ 0","value":"D"},{"value":"E"}],"correctAnswer":2},{"id":12222,"question":"A polynomial of arbitrary degree","choices":[{"text":"f(x) = o","value":"A"},{"text":"f(x) = x","value":"B"},{"text":"f(x) = a","value":"C"},{"text":"f(x) = ax + b,a ≠ 0","value":"D"},{"value":"E"}],"correctAnswer":1},{"id":12221,"question":"(1+w)(1+w2)(1+w4)(1+w8)....50 factors","choices":[{"text":"0","value":"A"},{"text":"-1","value":"B"},{"text":"1","value":"C"},{"text":"2","value":"D"},{"value":"E"}],"correctAnswer":3},{"id":12220,"question":"If x - 1 is a factor of x4 - 5x2 + 4 then other factor is","choices":[{"text":"(x + 2)2(x - 1)","value":"A"},{"text":"(x + 2)(x - 1)2","value":"B"},{"text":"(x+2)(x2- x- 2)","value":"C"},{"text":"(x + 2)2(x - 1)2","value":"D"},{"value":"E"}],"correctAnswer":3},{"id":12219,"question":"The two parts into which 57 should be divided so that their product is 782 are","choices":[{"text":"43,14","value":"A"},{"text":"34,23","value":"B"},{"text":"33,24","value":"C"},{"text":"44,13","value":"D"},{"value":"E"}],"correctAnswer":2},{"id":12218,"question":"The roots of the equation 4x - 3.2x+2 + 32 = 0 would include","choices":[{"text":"1 and 3","value":"A"},{"text":"1 and 4","value":"B"},{"text":"1 and 2","value":"C"},{"text":"2 and 3","value":"D"},{"value":"E"}],"correctAnswer":4},{"id":12217,"question":"If one root of 5x2 + 13x + k = 0 be the reciprocal of the other root the value of k is","choices":[{"text":"0","value":"A"},{"text":"2","value":"B"},{"text":"1","value":"C"},{"text":"5","value":"D"},{"value":"E"}],"correctAnswer":4},{"id":12216,"question":"If a,βare the roots of the equation x2 - 8x + p = 0 and a2 + β2= 40,then value of p is","choices":[{"text":"8","value":"A"},{"text":"12","value":"B"},{"text":"10","value":"C"},{"text":"14","value":"D"},{"value":"E"}],"correctAnswer":2},{"id":12085,"question":"The solution of equation x2 + 2 = 0 in the set of real number is","choices":[{"text":"Infinite set","value":"A"},{"text":"Singleton set","value":"B"},{"text":"Null set","value":"C"},{"text":"None of these","value":"D"},{"value":"E"}],"correctAnswer":4},{"id":12067,"question":"","questionImage":"12067_52-q.jpg","choices":[{"text":"","img":"12067_52-a.jpg","value":"A"},{"text":"","img":"12067_52-b.jpg","value":"B"},{"text":"","img":"12067_52-c.jpg","value":"C"},{"text":"","img":"12067_52-d.jpg","value":"D"},{"value":"E"}],"correctAnswer":1}]