[{"id":156886,"question":"Another name of quadratic equation is","choices":[{"text":"Polynomial","value":"A"},{"text":"2nd degree polynomial","value":"B"},{"text":"Linear equation","value":"C"},{"text":"simaltaneous equations","value":"D"},{"value":"E"}],"correctAnswer":2},{"id":156884,"question":"A quadratic equation in x is an equation that can be witten in the form","choices":[{"text":"ax<sup>2 </sup>+ b = 0","value":"A"},{"text":"ax<sup>3</sup> +b<sup>2</sup>+c=0","value":"B"},{"text":"ax<sup>2</sup> +bx+c=0","value":"C"},{"text":"ax<sup>3</sup> +bx<sup>3</sup>+cx=0","value":"D"},{"value":"E"}],"correctAnswer":3},{"id":123741,"question":"If a (p + q)<sup>2</sup>+ bpq +c = 0 and a (p + r)<sup>2</sup>+ 2 bpr + c = 0, then qr equals","choices":[{"text":"p<sup>2</sup>+ c/a","value":"A"},{"text":"p<sup>2</sup>+ a/c","value":"B"},{"text":"p<sup>2</sup>+ c/a","value":"C"},{"text":"p<sup>2</sup>- c/a","value":"D"},{"value":"E"}],"correctAnswer":1},{"id":123735,"question":"If sin<span style=\"color: rgb(34, 34, 34); font-family: &quot;Times New Roman&quot;; font-size: 24px; text-align: center; background-color: rgb(255, 255, 224);\"><i>α</i></span>and cos<span style=\"color: rgb(34, 34, 34); font-family: &quot;Times New Roman&quot;; font-size: 24px; text-align: center; background-color: rgb(255, 255, 224);\"><i>α</i></span>are the roots of the equation px<sup>2</sup>+ qx + r =0, then","choices":[{"text":"p<sup>2</sup>- q<sup>2</sup>+ 2pr = 0","value":"A"},{"text":"(p + r)<sup>2</sup>= q<sup>2</sup>- r<sup>2</sup>","value":"B"},{"text":"p<sup>2</sup>+ q<sup>2</sup>- 2pr = 0","value":"C"},{"text":"(p - r)<sup>2</sup>= q<sup>2</sup>+ r<sup>2</sup>","value":"D"},{"value":"E"}],"correctAnswer":1},{"id":123734,"question":"Root of the equation 3<sup>x-1</sup>+ 3<sup>1-x</sup>= is","choices":[{"text":"2","value":"A"},{"text":"1","value":"B"},{"text":"0","value":"C"},{"text":"-1","value":"D"},{"value":"E"}],"correctAnswer":1},{"id":123733,"question":"For the equation |x<sup>2</sup>| + |x| -6 =0, the roots are","choices":[{"text":"One and only one real number","value":"A"},{"text":"Real with sum one","value":"B"},{"text":"Real with sum zero","value":"C"},{"text":"Real with product zero","value":"D"},{"value":"E"}],"correctAnswer":3},{"id":123731,"question":"","questionImage":"123731_636349529399482211-RQ.jpg","choices":[{"text":"Lies between 4 and 7","value":"A"},{"text":"Lies between 5 and 9","value":"B"},{"text":"Has no value between 4 and 7","value":"C"},{"text":"Has no value between 5 and 9","value":"D"},{"value":"E"}],"correctAnswer":4},{"id":123727,"question":"","questionImage":"123727_636349525561914691-RQ.jpg","choices":[{"text":"","img":"123727_636349525561914691-RA1.jpg","value":"A"},{"text":"","img":"123727_636349525561914691-RA2.jpg","value":"B"},{"text":"","img":"123727_636349525561914691-RA3.jpg","value":"C"},{"text":"","img":"123727_636349525561914691-RA4.jpg","value":"D"},{"value":"E"}],"correctAnswer":2},{"id":123724,"question":"","questionImage":"123724_636349522514913849-RQ.jpg","choices":[{"text":"15","value":"A"},{"text":"9","value":"B"},{"text":"7","value":"C"},{"text":"8","value":"D"},{"value":"E"}],"correctAnswer":3},{"id":123721,"question":"If the roots of ax<sup>2</sup>+ bx + c = 0 (a &gt; 0) be greater than unity, then","choices":[{"text":"a + b + c = 0","value":"A"},{"text":"a + b + c &gt; 0","value":"B"},{"text":"a + b + c &lt; 0","value":"C"},{"text":"None of these","value":"D"},{"value":"E"}],"correctAnswer":2},{"id":123718,"question":"If<span style=\"color: rgb(34, 34, 34); font-family: &quot;Times New Roman&quot;; font-size: 24px; text-align: center; background-color: rgb(255, 255, 248);\"><i>α</i></span>,<span style=\"color: rgb(34, 34, 34); font-family: &quot;Times New Roman&quot;; font-size: 24px; text-align: center; background-color: rgb(255, 255, 248);\"><i>β</i></span>are the roots of ax<sup>2</sup>+ bx + c = 0 and<span style=\"color: rgb(34, 34, 34); font-family: &quot;Times New Roman&quot;; font-size: 24px; text-align: center; background-color: rgb(255, 255, 248);\"><i>α</i></span>+ h,<span style=\"color: rgb(34, 34, 34); font-family: &quot;Times New Roman&quot;; font-size: 24px; text-align: center; background-color: rgb(255, 255, 248);\"><i>β</i></span>+ h are the roots of px<sup>2</sup>+ qx + r=0, then h =","choices":[{"text":"","img":"123718_636349517839053518-RA1.jpg","value":"A"},{"text":"","img":"123718_636349517839053518-RA2.jpg","value":"B"},{"text":"","img":"123718_636349517839053518-RA3.jpg","value":"C"},{"text":"","img":"123718_636349517839053518-RA4.jpg","value":"D"},{"value":"E"}],"correctAnswer":2},{"id":123712,"question":"If the roots of ax<sup>2</sup>- bx - c = 0 change by the same quantity, then the expression in a, b, c that does not change is","choices":[{"text":"","img":"123712_636349510635711004-RA1.jpg","value":"A"},{"text":"","img":"123712_636349510635711004-RA2.jpg","value":"B"},{"text":"","img":"123712_636349510635711004-RA3.jpg","value":"C"},{"text":"","img":"123712_636349510635711004-RA4.jpg","value":"D"},{"value":"E"}],"correctAnswer":3},{"id":123710,"question":"Let the equation ax<sup>2</sup>- bx + c = 0 have distinct real roots both lying in the open interval (0, 1) where a, b, c are given to be positive integers. Then the value of the ordered triplet (a, b, c) can be","choices":[{"text":"(5, 3, 1)","value":"A"},{"text":"(4, 3, 2)","value":"B"},{"text":"(5, 5, 1)","value":"C"},{"text":"(6, 4, 1)","value":"D"},{"value":"E"}],"correctAnswer":3},{"id":123707,"question":"","questionImage":"123707_636349507282055448-RQ.jpg","choices":[{"text":"Two real roots","value":"A"},{"text":"Two positive roots","value":"B"},{"text":"Two negative roots","value":"C"},{"text":"One positive and one negative root","value":"D"},{"value":"E"}],"correctAnswer":1},{"id":123702,"question":"In a quadratic equation with leading co-efficient 1, a student reads the co-obtain the roots as - 15 and -4. The correct roots are","choices":[{"text":"6, 10","value":"A"},{"text":"-6, -10","value":"B"},{"text":"8, 8","value":"C"},{"text":"-8, -8","value":"D"},{"value":"E"}],"correctAnswer":2},{"id":123700,"question":"","questionImage":"123700_636349504479036564-RQ.jpg","choices":[{"text":"(-1, 2)","value":"A"},{"text":"(-1, 1)","value":"B"},{"text":"(1, 2)","value":"C"},{"text":"{-1}","value":"D"},{"value":"E"}],"correctAnswer":4},{"id":123697,"question":"","questionImage":"123697_636349503278160224-RQ.jpg","choices":[{"text":"1","value":"A"},{"text":"2","value":"B"},{"text":"0","value":"C"},{"text":"4","value":"D"},{"value":"E"}],"correctAnswer":3},{"id":123695,"question":"If the roots of x<sup>2</sup>+ ax + b = 0 are non-real, then for all real x, x<sup>2</sup>+ ax + b is","choices":[{"text":"Negative","value":"A"},{"text":"Positive","value":"B"},{"text":"Zero","value":"C"},{"text":"Nothing can be said","value":"D"},{"value":"E"}],"correctAnswer":2},{"id":123694,"question":"The equation (cos p - 1)x<sup>2</sup>+ x (cos p) + sin p = 0 in the variable x, has real roots, then p can take any value in the interval","choices":[{"text":"(0, 2<span style=\"color: rgb(34, 34, 34); font-family: &quot;Times New Roman&quot;; font-size: 24px; text-align: center; background-color: rgb(255, 255, 224);\"><i>π</i></span>)","value":"A"},{"text":"(-<span style=\"color: rgb(34, 34, 34); font-family: &quot;Times New Roman&quot;; font-size: 24px; text-align: center; background-color: rgb(255, 255, 224);\"><i>π</i></span>, -0)","value":"B"},{"text":"(0,<span style=\"color: rgb(34, 34, 34); font-family: &quot;Times New Roman&quot;; font-size: 24px; text-align: center; background-color: rgb(255, 255, 224);\"><i>π</i></span>)","value":"C"},{"text":"None of these","value":"D"},{"value":"E"}],"correctAnswer":3},{"id":123691,"question":"If 2x<sup>1/3</sup>+ 2x<sup>-1/3</sup>= 5, then x is equal to","choices":[{"text":"1 or -1","value":"A"},{"text":"2 or 1/2","value":"B"},{"text":"8 or 1/8","value":"C"},{"text":"4 or 1/4","value":"D"},{"value":"E"}],"correctAnswer":3},{"id":123689,"question":"","questionImage":"123689_636349499599516099-RQ.jpg","choices":[{"text":"Rational","value":"A"},{"text":"Irrational","value":"B"},{"text":"Non-real","value":"C"},{"text":"Zero","value":"D"},{"value":"E"}],"correctAnswer":1},{"id":123686,"question":"","questionImage":"123686_636349497830714767-RQ.jpg","choices":[{"text":"Only one real solution","value":"A"},{"text":"Exactly three real solution","value":"B"},{"text":"Exactly one rational solution","value":"C"},{"text":"Non-real roots","value":"D"},{"value":"E"}],"correctAnswer":2},{"id":123683,"question":"The value of k (k &gt; 0) for which the equation x<sup>2</sup>+ kx + 64 = 0 and x<sup>2</sup>- 8x + k = 0 both will have real roots is","choices":[{"text":"8","value":"A"},{"text":"-16","value":"B"},{"text":"-64","value":"C"},{"text":"16","value":"D"},{"value":"E"}],"correctAnswer":4},{"id":123681,"question":"The set of real roots of the equation log<sub>(5x + 4)</sub>(2x +3)<sup>3</sup>- log<sub>(2x + 3)</sub>(10x<sup>2</sup>+ 23x + 12) = 1 is","choices":[{"text":"{-1}","value":"A"},{"text":"{-3/5}","value":"B"},{"text":"Empty set","value":"C"},{"text":"{-1/3}","value":"D"},{"value":"E"}],"correctAnswer":4},{"id":123679,"question":"","questionImage":"123679_636349493554392629-RQ.jpg","choices":[{"text":"(a - c)<sup>2</sup>= b<sup>2</sup>- c<sup>2</sup>","value":"A"},{"text":"(a - c)<sup>2</sup>= b<sup>2</sup>+ c<sup>2</sup>","value":"B"},{"text":"(a + c)<sup>2</sup>= b<sup>2</sup>- c<sup>2</sup>","value":"C"},{"text":"(a + c)<sup>2</sup>= b<sup>2</sup>+ c<sup>2</sup>","value":"D"},{"value":"E"}],"correctAnswer":4},{"id":123676,"question":"If x<sup>2</sup> + px + 1 is a factor of ax<sup>3</sup>+ bx +c, then","choices":[{"text":"a<sup>2</sup>+ c<sup>2</sup>= -ab","value":"A"},{"text":"a<sup>2</sup>- c<sup>2</sup>= -ab","value":"B"},{"text":"a<sup>2</sup>- c<sup>2</sup>= ab","value":"C"},{"text":"None of these","value":"D"},{"value":"E"}],"correctAnswer":3},{"id":123674,"question":"","questionImage":"123674_636349490972897507-RQ.jpg","choices":[{"text":"n if n is even","value":"A"},{"text":"0 for any natural number n","value":"B"},{"text":"1 if in odd","value":"C"},{"text":"None of these","value":"D"},{"value":"E"}],"correctAnswer":2},{"id":123671,"question":"The roots of the equation 2<sup>2x</sup>- 10.2<sup>x</sup>+ 16 = 0 are","choices":[{"text":"2, 8","value":"A"},{"text":"1, 3","value":"B"},{"text":"1, 8","value":"C"},{"text":"2, 3","value":"D"},{"value":"E"}],"correctAnswer":2},{"id":123669,"question":"","questionImage":"123669_636964569416062140-RQ.jpg","choices":[{"text":"","img":"123669_636349483769084239-RA1.jpg","value":"A"},{"text":"","img":"123669_636349483769084239-RA2.jpg","value":"B"},{"text":"","img":"123669_636349483769084239-RA3.jpg","value":"C"},{"text":"","img":"123669_636349483769084239-RA4.jpg","value":"D"},{"value":"E"}],"correctAnswer":2},{"id":123666,"question":"The value of p for which both the roots of the equation 4x2- 20x + (25p2+ 15 p - 66) = 0 are less than 2, lies in","choices":[{"text":"","img":"123666_636349481447342305-RA1.jpg","value":"A"},{"text":"","img":"123666_636349481447342305-RA2.jpg","value":"B"},{"text":"","img":"123666_636349481447342305-RA3.jpg","value":"C"},{"text":"","img":"123666_636349481447342305-RA4.jpg","value":"D"},{"value":"E"}],"correctAnswer":4}]