[{"id":158696,"question":"The solution of differential equation:","choices":[{"text":"dy/dx+y/x = x<sup>2 </sup>is :","value":"A"},{"text":"4xy = x<sup>4</sup>+ c","value":"B"},{"text":"4x = x<sup>4</sup>= c","value":"C"},{"text":"4 y = x<sup>4</sup>+ c","value":"D"},{"text":"4x=4x<sup>3</sup> + c","value":"E"}],"correctAnswer":1},{"id":158695,"question":"An equation in which at least one term contains dy/dx, d<sup>2</sup> y /dx<sup>2</sup>etc, is called.","choices":[{"text":"Differential equation","value":"A"},{"text":"Initial condition","value":"B"},{"text":"General solution","value":"C"},{"text":"Singular equation","value":"D"},{"value":"E"}],"correctAnswer":1},{"id":158694,"question":"The general solution of the differential equation x dy / dx = 1 + y is:","choices":[{"text":"2","value":"A"},{"text":"1","value":"B"},{"text":"3","value":"C"},{"text":"None","value":"D"},{"value":"E"}],"correctAnswer":2},{"id":158693,"question":"The area enclosed between the graph y = x<sup>2 </sup>-4x and the x- axis is:","choices":[{"text":"20/3","value":"A"},{"text":"41/3","value":"B"},{"text":"32/3","value":"C"},{"text":"25/3","value":"D"},{"value":"E"}],"correctAnswer":3},{"id":158692,"question":"The area under the curve y = 1/x<sup>2</sup> between x = 1 and x =4 is:","choices":[{"text":"-25","value":"A"},{"text":"0.75","value":"B"},{"text":"-0.35","value":"C"},{"text":"-10","value":"D"},{"value":"E"}],"correctAnswer":2},{"id":158691,"question":"The area between the x-axis the curve y =4x-x2 is :","choices":[{"text":"32/2","value":"A"},{"text":"15","value":"B"},{"text":"18","value":"C"},{"text":"21","value":"D"},{"value":"E"}],"correctAnswer":1},{"id":158690,"question":"The area between the x-axis and the curve y = x<sup>2</sup> + 1 from x = 1 to 2 is:","choices":[{"text":"15/6","value":"A"},{"text":"15/4","value":"B"},{"text":"10/4","value":"C"},{"text":"10/3","value":"D"},{"value":"E"}],"correctAnswer":4},{"id":158689,"question":"∫x/Sin<sup>2</sup> x dx is equal to:","choices":[{"text":"x cot x + ln|sin⁡x |","value":"A"},{"text":"-x cot x - ln|sin⁡x |","value":"B"},{"text":"x cot x - ln|sin⁡x |","value":"C"},{"text":"x. tan x- ln|sec⁡x |","value":"D"},{"value":"E"}],"correctAnswer":1},{"id":158688,"question":"∫x sin xdx is equal to:","choices":[{"text":"sin x/x + cos x","value":"A"},{"text":"sin x - cos x/x","value":"B"},{"text":"x cos x + sin x","value":"C"},{"text":"- x cos x + sin x","value":"D"},{"value":"E"}],"correctAnswer":4},{"id":158687,"question":" ∫ x cos dx is equal to :","choices":[{"text":"x cos x + sin x","value":"A"},{"text":"cos x + x sin x","value":"B"},{"text":"x cos x + x sin x","value":"C"},{"text":"x sin x + cos x","value":"D"},{"value":"E"}],"correctAnswer":4},{"id":158686,"question":"∫sin(ax+b) dx is equal to:","choices":[{"text":"1/2a cos (ax + b)","value":"A"},{"text":"-1/a cos (ax +b)","value":"B"},{"text":"1/a cos (ax +b)","value":"C"},{"text":"1/a ln (ax + b)","value":"D"},{"value":"E"}],"correctAnswer":2},{"id":158685,"question":"∫Sec<sup>2</sup> (ax + b) dx is equal to:","choices":[{"text":"tan<sup>2</sup> (ax + b)","value":"A"},{"text":"1/a tan<sup>2</sup> (ax + b)","value":"B"},{"text":"1/atan (ax +b)","value":"C"},{"text":"tan (ax + b)","value":"D"},{"value":"E"}],"correctAnswer":3},{"id":158684,"question":"The integral of 3x<sup>5</sup>dx is:","choices":[{"text":"15 x<sup>4</sup>","value":"A"},{"text":"x<sup>6 </sup>/2","value":"B"},{"text":"1/6x<sup>5</sup>","value":"C"},{"text":"x<sup>5 </sup>/ln3","value":"D"},{"value":"E"}],"correctAnswer":2},{"id":158683,"question":"∫<i>f</i>(x) is known as:","choices":[{"text":"Definite itegral","value":"A"},{"text":"Indefinite integral","value":"B"},{"text":"Fixed integral","value":"C"},{"text":"Multiple integral","value":"D"},{"value":"E"}],"correctAnswer":2},{"id":158682,"question":"An integral of 1/x dx is:","choices":[{"text":"1/x<sup>2</sup>","value":"A"},{"text":"1/-x<sup>2</sup>","value":"B"},{"text":"1/lnx","value":"C"},{"text":"lnx","value":"D"},{"value":"E"}],"correctAnswer":4},{"id":125092,"question":"Which of the following integrals can be evaluated","choices":[{"text":"","img":"125092_636353800491878995-RA1.jpg","value":"A"},{"text":"","img":"125092_636353800491878995-RA2.jpg","value":"B"},{"text":"","img":"125092_636353800491878995-RA3.jpg","value":"C"},{"text":"","img":"125092_636353800491878995-RA4.jpg","value":"D"},{"value":"E"}],"correctAnswer":2},{"id":125090,"question":"","questionImage":"125090_636353793465716249-RQ.jpg","choices":[{"text":"","img":"125090_636353793465716249-RA1.jpg","value":"A"},{"text":"","img":"125090_636353793465716249-RA2.jpg","value":"B"},{"text":"","img":"125090_636353793465716249-RA3.jpg","value":"C"},{"text":"","img":"125090_636353793465716249-RA4.jpg","value":"D"},{"value":"E"}],"correctAnswer":4},{"id":125089,"question":"","questionImage":"125089_636353791086990561-RQ.jpg","choices":[{"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>","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/6</i></span>","value":"B"},{"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/2</i></span>","value":"C"},{"text":"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":"D"},{"value":"E"}],"correctAnswer":2},{"id":125088,"question":"","questionImage":"125088_636353790136101812-RQ.jpg","choices":[{"text":"0","value":"A"},{"text":"1","value":"B"},{"text":"2","value":"C"},{"text":"4","value":"D"},{"value":"E"}],"correctAnswer":4},{"id":125087,"question":"","questionImage":"125087_636353789614517039-RQ.jpg","choices":[{"text":"Always negative","value":"A"},{"text":"Zero","value":"B"},{"text":"Always positive","value":"C"},{"text":"Infinity","value":"D"},{"value":"E"}],"correctAnswer":3},{"id":125086,"question":"If the graph of f is entirely below the x-axis, then the value of definite integral is","choices":[{"text":"= 0","value":"A"},{"text":"&lt; 0","value":"B"},{"text":"&gt; 0","value":"C"},{"text":"None","value":"D"},{"value":"E"}],"correctAnswer":2},{"id":125085,"question":"If the lower limit of an integral is a constant and the upper limit is a variable, then the integral is a","choices":[{"text":"Constant function","value":"A"},{"text":"Variable value","value":"B"},{"text":"Function of upper limit","value":"C"},{"text":"All","value":"D"},{"value":"E"}],"correctAnswer":3},{"id":125084,"question":"The arbitrary constants involving in the solution can be determined by the given conditions. Such conditions are called","choices":[{"text":"Boundaries","value":"A"},{"text":"Variable separable","value":"B"},{"text":"Initial values","value":"C"},{"text":"None","value":"D"},{"value":"E"}],"correctAnswer":3},{"id":125083,"question":"","questionImage":"125083_636353786325958376-RQ.jpg","choices":[{"text":"Y = -x log x -x + c","value":"A"},{"text":"Y = x log x + x","value":"B"},{"text":"Y = x log x - x + c","value":"C"},{"text":"None of these","value":"D"},{"value":"E"}],"correctAnswer":3},{"id":125082,"question":"","questionImage":"125082_636353751804846620-RQ.jpg","choices":[{"text":"","img":"125082_636353751804846620-RA1.jpg","value":"A"},{"text":"","img":"125082_636353751804846620-RA2.jpg","value":"B"},{"text":"","img":"125082_636353751804846620-RA3.jpg","value":"C"},{"text":"","img":"125082_636353751804846620-RA4.jpg","value":"D"},{"value":"E"}],"correctAnswer":1},{"id":125081,"question":"","questionImage":"125081_636353748433134549-RQ.jpg","choices":[{"text":"","img":"125081_636353748433134549-RA1.jpg","value":"A"},{"text":"","img":"125081_636353748433134549-RA2.jpg","value":"B"},{"text":"","img":"125081_636353748433134549-RA3.jpg","value":"C"},{"text":"","img":"125081_636353748433134549-RA4.jpg","value":"D"},{"value":"E"}],"correctAnswer":1},{"id":125074,"question":"","questionImage":"125074_636353742909192591-RQ.jpg","choices":[{"text":"X = 100 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, 248);\"><i>θ</i></span>","value":"A"},{"text":"X = 10 sin<span style=\"font-family: &quot;Times New Roman&quot;; font-size: 24px; color: rgb(34, 34, 34); text-align: center; background-color: rgb(255, 255, 248);\"><i>θ</i></span>","value":"B"},{"text":"X = 100 sec<span style=\"font-family: &quot;Times New Roman&quot;; font-size: 24px; color: rgb(34, 34, 34); text-align: center; background-color: rgb(255, 255, 248);\"><i>θ</i></span>","value":"C"},{"text":"None of these","value":"D"},{"value":"E"}],"correctAnswer":2},{"id":125070,"question":"","questionImage":"125070_636353741295006398-RQ.jpg","choices":[{"text":"A variable","value":"A"},{"text":"A constant","value":"B"},{"text":"0","value":"C"},{"text":"None of these","value":"D"},{"value":"E"}],"correctAnswer":2},{"id":125067,"question":"","questionImage":"125067_636353739437983327-RQ.jpg","choices":[{"text":"","img":"125067_636353739437983327-RA1.jpg","value":"A"},{"text":"","img":"125067_636353739437983327-RA2.jpg","value":"B"},{"text":"","img":"125067_636353739437983327-RA3.jpg","value":"C"},{"text":"","img":"125067_636353739437983327-RA4.jpg","value":"D"},{"value":"E"}],"correctAnswer":2},{"id":125063,"question":"","questionImage":"125063_636353737388702212-RQ.jpg","choices":[{"text":"","img":"125063_636353737388702212-RA1.jpg","value":"A"},{"text":"","img":"125063_636353737388702212-RA2.jpg","value":"B"},{"text":"","img":"125063_636353737388702212-RA3.jpg","value":"C"},{"text":"","img":"125063_636353737388702212-RA4.jpg","value":"D"},{"value":"E"}],"correctAnswer":1}]