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Re: ISC Class 12 Mathematics Exam Question Papers
Indian School Certificate Examinations follows standard for education. As per your request I am sending you ISC class 12 Mathematics Exam Question Papers. Q1.(i). If , Show that M(x) + M(y) = M(x+y). (ii). The lines x- 2y + 6 = 0 and 2x – y – 10 = 0 intersect at the point A. Find the equation of the line making an angle 45 degree with the positive direction of the x-axis and passing through the point A. (iii). Find the equations of the tangents to parabola from the point (3, 8). (iv). Find the derivative of sin with respect to . (v). Evaluate the following integral : . (vi). Evaluate the following limit : . (vii). Two horses are considered for a race. The probability of selection of the first horse is 1/4 and that of the second is 1/3. What is the probability that : (a) both of them will be selected (b) only one of them will be selected (c) none of them will be selected. (viii) The mean weight of 70 students in a class is 60 kg. The mean weight of the girls in the class is 53 kg and that of the boys is 70.5 kg. Find the number of girls in the class. (ix) If find the real numbers a and b. With these values of a and b, also find the modulus of a + ib. (x) Solve the following differential equation : . Q2. (a) By using properties of determinants, prove that: 5 (b) Solve the following linear equations using the matrix method : 5 x+y+z=9 2x+5y+7z=52 2x+y-z=0 Q3. (a) Prove that the following equation represents a pair of straight lines. Find their point of intersection and the angle between them : 5 (b) P, Q and R represent switches in ‘on’ positions and represent switches in ‘off’ positions. Construct a switching circuit representing the polynomial Use Boolean algebra to prove that the above circuit can be simplified to an expression in which, when P and R are ‘on’ or Q and R ‘on’, the light is on. Construct an equivalent circuit. 5 Q4. (a) If prove that : 5 (b) Using a suitable substitution find the derivative of with respect to x. 5 Q5. (a) It is given that Rolle’s theorem holds good for the function at the point x = 4/3. Find the values of a and b. 5 (b) A wire of length 20 m is available to fence off a flower bed in the form of a sector of a circle. What must be the radius of the circle, if we wish to have a flower bed with the greatest possible area ? 5 Q6. (a) (i) Evaluate: log(tan x)dx. (ii) Evaluate (x + 1/2)dx as a limit of a sum. (b) Draw a rough sketch of the curve + y = 9 and find the area enclosed by the curve, the x-axis and the the lines x + 1 = 0 and x – 2 = 0. Q7. (a) An examination of 8 applicants for a clerical post was taken by a firm. The marks obtained by the applicants in the Reasoning and Aptitude tests and given below: Applicant A B C D E F G H Reasoning Test 20 28 15 60 40 80 20 12 Aptitude Test 30 50 40 20 10 60 30 30 Calculate the Spearman’s coefficient of rank correlation from the data given above. 5 (b) If the two regression lines of a vicariate distribution are 4x – 5y + 33 = 0 and 20x – 9y-107 = 0. (i) calculate x and Y, the arithmetic means of x and y respectively (ii) estimate the value of x when y = 7 (iii) find the variance of y when ax = 3. 5 Q8. (a) Bag A contains 5 white and 4 black balls, and bag B contains 7 white and 6 black balls. One ball is drawn from the bag A and without noticing its colour, is put in the bag B. If a ball is then drawn from bag B, find the probability that it is black in colour. 5 (b) An article manufactured by a company consists of two parts A and B. In the process of manufacture of part A, 9 out of 104 parts may be defective. Similarly, 5 out of 100 are likely to be defective in the manufacture of part B. Calculate the probability that the article manufactured will not be defective. 5 Q9. (a) If z= (13-5i)/(4-9i), Prove by using De Moivre’s theorem that 5 (b) Solve the following differential equestion for a particular solution. dy = (5x – 4y)dx , when y=0 and x=0. 5 SECTION B Q10. (a) Find the equation of the plane which contains the line (x-1)/2 = (y+1)/(-1) = (z-3)/4 perpendicular to the plane x + 2y + z = 12. 5 (b) Find the equation of the sphere which passes through the circle x+2y+2z=0 and whose centre lies on the plane 2x-y+z=1. 5 ICS mathematics question paper
__________________ Answered By StudyChaCha Member Last edited by Aakashd; August 2nd, 2018 at 08:41 AM. |