Practice Test


Q1) D. E. of lines, passing through the origin, is Show Answer


Q2) D. E. of all circles, having centres at the origin, is Show Answer


Q3) The standard unit circle satisfies the D. E. Show Answer


Q4) Population of city increases at a rate proportional to the population. Within a period of 30 years the population grew from 20 lakhs to 40 lakhs. After a further period of 15 years, the population of the city (in lakhs) will be Show Answer


Q5) A population grows at the rate of 5% per year. Then the population will be doubled in Show Answer


Q6) An ice ball melts at a rate proportional to the amount of ice present at that instant. If half the quantity of ice melts in 20 minutes, then after an hour, the amount of ice left will be Show Answer


Q7) Rate of decay of radium varies as the amount present. If 60 mg are present now and the half-life of radium is 1690 years, then the amount of radium present 100 years from now is Show Answer


Q8) A person's assets start reducing in such a way that the rate of reduction of assets is proportional to the square-root of the assets existing at that time. If the assets at the beginning are Rs. 10 lakhs and they dwindle down to Rs. 10,000 after 2 years, then the person will be bankrupt in n years from the start, where : n = Show Answer


Q9) The number of arbitrary constants in the general solution of a differential equation of fourth order is Show Answer


Q10) The number of arbitrary constant in the particular solution of a differential equation of third order is Show Answer


Q11) The differential equation of the family of parabolas having vertex at origin and axis along positive y - axis is Show Answer


Q12) The differential equation of the family of hyperbolas having foci on x- axis and centre at origin is Show Answer


Q13) The differential equation of the family of circles in the first quadrant which touch the coordinate axes is Show Answer


Q14) The differential equation of all circles which pass through origin and whose centres lie on y-axis is Show Answer


Q15) The differential equation of system of concentric circles with centre (1,2) is Show Answer


Q16) The differential equation of the rectangular hyperbola whose axes are the asymptotes of the hyperbola, is Show Answer


Q17) The differential equation of the family of parabolas with focus at the origin and the x-axis, as axis, is Show Answer


Q18) The differential equation of all circles passing through the origin and having their centres on the x -axis is Show Answer


Q19) A curve passes through the point (0, 1) and the gradient at (x, y) on it is y (xy - 1). The equation of the curve is Show Answer


Q20) A tangent to the curve y = f(x) cuts the line y = x at a point which is at a distance of 1 unit from y-axis. The equation of the curve is Show Answer


Q21) The differential equation of the family of curves for which the length of the normal is equal to a constant k, is given by Show Answer


Q22) The equation of the curve in which the portion of y-axis cut off between the origin and the tangent varies as the cube of the abscissa of the point of contact is Show Answer


Q23) The equation of the curve for which the square of the ordinate is twice the rectangle contained by the abscissa and the intercept of the normal on x-axis and passing through (2,1) is Show Answer


Q24) The differential equation representing all lines at a distance p from the origin is Show Answer


Q25) A tangent and a normal curve at any point P meet the x and y axes at A, B and C, D, respectively. If the centre of circle through O, C, P and B lies on the line y = x (O is the origin), then the differential equation of all such curves is Show Answer


Q26) A curve is such that the x-axis cut off between the origin and tangent at a point is twice the abscissa and which passes through the point (1,2). The equation of the curve is Show Answer


Q27) The curve f (x) is given by Show Answer


Q28) The curve g (x) is given by Show Answer


Q29) The number of positive integral solutions for f (x) = g (x), are Show Answer


Q30) Let F denotes the family of ellipses whose centre is at the origin and major axis is the y-axis. Then, equation of the family F is Show Answer


Q31) The differential equation cot y dx = x dy has a solution of the form Show Answer


Q32) The differential equation of all circles of radius a is of order Show Answer


Q33) The equation of one of the curves whose slope at any point is equal to y + 2x is Show Answer


Q34) The degree of the differential equation of all curves having normal of constant length c, is Show Answer


Q35) The degree and order of the differential equation whose solution is a parabola whose axis is x-axis, are Show Answer


Q36) The differential equation of the family of ellipse having major and minor axes respectively along the x and y-axes and the minor axis is equal to half of the major axis, is Show Answer


Q37) The differential equation of system of concentric circles with center (1, 2) is Show Answer


Q38) The differential equation of all circles which passes through the origin and whose center lies on y-axis, is Show Answer


Q39) The differential equation of all parabolas whose axes are parallel to y-axis, is Show Answer


Q40) The differential equation of all non-vertical lines in a plane is Show Answer


Q41) The order of differential equation of all parabolas having directrix parallel to x-axis is Show Answer


Q42) The difference equation of the family of circles with fixed radius r and with centre on y-axis is Show Answer


Q43) The order of the differential equation of all circles of radius r, having centre on y-axis and passing through the origin, is Show Answer


Q44) The differential equation of the curve for which the initial ordinate of any tangent is equal to the corresponding subnormal, is Show Answer


Q45) The equation of family of curves for which the length of the normal is equal to the radius vector, is Show Answer


Q46) The differential equation of all parabolas having their axis of symmetry coinciding with the axis of X, is Show Answer


Q47) The differential equation of all circles in the first quadrant which touch the coordinate axes is of order Show Answer


Q48) A normal is drawn at a P(x,y) of a curve. It meets the x-axis at Q. if PQ is of constant length k, then the differential equation describing such a curve is Show Answer


Q49) The differential equation of all parabolas whose axes are parallel to axis of x, is Show Answer


Q50) The differential equation of family of circles with fixed radius 5 unit & center on the line y = 2, is Show Answer


Q51) The differential equation of all ellipses centered at the origin is Show Answer


Q52) The differential equation of the family of curves y = a cos‚Ā° (x + b) is Show Answer


Q53) A curve having the condition that the slope of tangent at some point is two times the slope of the straight line joining the same point to the origin of coordinates, is a/an Show Answer


Q54) The differential equation of the family of lines whose slope is equal to y-intercept, is Show Answer


Q55) The curve in which the slope of the tangent at any point equals the ratio of the abscissa to the ordinate of the point is Show Answer


Q56) The differential equation of all straight lines passing through origin is Show Answer


Q57) The differential equation of the family of circles passing through the fixed points (a, 0) and (-a, 0) is Show Answer


Q58) Order of the differential equation of the family of all concentric circles centered at (h, k) is Show Answer


Q59) The differential equation of all non-horizontal lines in a plane is Show Answer


Q60) The slope of a curve at any point is the reciprocal of twice the ordinate at the point and it passes through the point (4, 3). The equation of the curve is Show Answer


Q61) The second order differential equation is Show Answer


Q62) The equation of the curve whose subnormal is twice the abscissa, is Show Answer