Class – XI Subject – MATHEMATICS

Time Duration: 3 hours M.M.100

Section - A

(Question No 1 Compulsory and Attempt five other questions)

Question 1 [10 X 3 = 30] (i) If .Show that (ii) Differentiate the function x3 + 4x2 + 7x + 2 with respect to x

(iii) How many words can be formed with or without meaning by the letters of the word ‘ALLAHABAD’. (iv) Prove that:

(v) If f : R R and g : R R are defined f(x) = 2x + 3 and g(x) =X2 + 7, then find the Values of x for which (fog) (x) = 25 (vi) Evaluate:- (vii) If the angle between two lines is and the slope of one of the lines is , find the slope of the other line. (viii) Using the principle of mathematical induction. Prove that:- (ix) Find the equation of circle whose centre is ( 4, -3 ) and radius is 10. (x) Prove that :

Question 2 (a) Find the sum of n terms of the series [4]

(b) If the coefficient of in the expansion of are in A.P.prove that [6]

Question 3 (a) Find the value of the constant K so that function is continuous at x=0 [5]

Show that is continuous at x=0

(b) If [5]

Question 4

(a) Find General solution of Ө for the equation [5]

(b) If ,prove that [5]

Question 5

(a) Find the equation(s) of tangent (s) to the curve y = x3 + 2x + 6 which is perpendicular to the line x + 14y + 4 = 0 [5]

(b) Evaluate: (i) [4] (ii) [1]

Question 6 (a) Find the equation of circle through the intersection of the circles x2 + y2 – 8x – 2y + 7 = 0 and x2 + y2 – 4x + 10y + 8 = 0 and that passes through the point ( -1, -2 ) [5] (b) A line passing through the points ( a, 2a ) and ( -2, 3 ) is parallel to the line

4x + 3y + 5 = 0 Find the value of a and equation of that line. [5]

Question 7 (a) Out of 6 boys and 4