CLASS - XIth FULL SYLLABUS TEST Time : 120 Minutes Max. Marks : 60 GENERAL INSTRUCTIONS 1. All questions are compulsory. 2. The question paper consist of 24 questions divided into three sections A, B and C. Section A comprises of 10 questions of 1 mark each, section B comprises of 10 questions of 3 marks each, section C comprises of 5 questions of 4 marks each. 3. Use of calculators in not permitted. You may ask for logarithmic tables, if required. SECTION - A Question numbers 1 to 10 carry 1 marks each. Q.1 Find the value of cos (-1710º). Q.2 Find the vlaue of tan 75º. Q.3 Convert the complex number - 1 + i into polar form. Q.4 If Q.5 If nC9 = nC8, find nC17. Q.6 Find the coefficient of x6y3 in the expansion of (x + 2y)9. Q.7 The centroid of a triangle ABC is at the point (1, 1, 1). If the coordinates of A and B are (3, - 5, 7) 1 1 x + = , find x. 8! 9! 10! and (-1, 7, - 6), respectively, find the coordinates of the point C x15 − 1 . x10 − 1 Q.8 Evaluate : lim x →1 Q.9 Find the derivative of Q.10 A committee of two persons is selected from two men and two women. What is the probability that 2 x2 − . x + 1 3x − 1 the committee will have no man. SECTION - B Question numbers 11 to 20 carry 3 marks each. sin 2 x cos 9 x − cos 5x . =cos 10 x sin 17 x − sin 3x Q.11 Prove tht Q.12 Solve the equation sin 2x - sin 4x + sin 6x = 0. Q.13 Prove that (cos x - cos y)2 + (sin x - sin y)2 = 4 sin2 Q.14 If (a + ib) (c + id) (e + if ) (g + ih) = A + iB, then show that (a2 + b2) (c2 + d2) (e2 + f2) (g2 + h2) = A2 + B2. x−y . 2 S.C.O. 14 1 st & 2 nd Floor , Sector 23‐C, Chandigarh ‐ 160023. Ph: 9888228231, 9216338231 www.ssmconline.com, e‐mail : info@ssmconl ine.com 1 CLASS - XIth FULL SYLLABUS TEST Q.15 A solution of 8% boric acid is to be diluted by adding a 2% boric acid solution to it. The resulting mixture is to be more than 4% but less than 6% boric acid. If we have 640 litres of the 8% solution, how many litres of the 2% solution will have to be added? Q.16 How many numbers greater than 1000000 can be formed by using the digits 1, 2, 0, 2, 4, 2, 4? Q.17 Prove that the coefficient of xn in the expansion of (1 + x)2n is twice the coefficient of xn in the expansion of (1 + x)2n - 1. Q.18 In an A.P. if mth term is n and the nth term is m, where m ≠ n, find the pth term. Q.19 Find the coordinates of the centroid of the triangle whose vertices are (x1, y1, z1), (x2, y2, z2) and (x3, y3, z3). Q.20 Compute the derivative from 1st principle of tan x. SECTION - C Question numbers 21 to 25 carry 4 marks each. Q.21 In a relay race there are five teams A, B, C, D and E. (i) What is the probability that A, B and C finish first, second and third, respectively. (ii) What is the probability that A, B and C are first three to finish (in any order) (Assume that all finishing orders are equally likely) Q.22 The difference between any two consecutive interior angles of a polygon is 5º. If the smallest angle is 120º, find the number of the sides of the polygon. Q.23 Q.24 Find the number of arrangements of the letters of the word INDEPENDENCE. In how many of these arrangements, (i) do the words start with P (ii) do all the vowels always occur together (iii) do the vowels never occur together (iv) do the words begin with I and end in P? If α and β are different complex numbers with | β | = 1, then find β−α . 1 − αβ Q.25. Prove that : cos 6x = 32 cos6 x - 48 cos4 x + 18 cos2 x - 1. S.C.O. 14 1 st & 2 nd Floor , Sector 23‐C, Chandigarh ‐ 160023. Ph: 9888228231, 9216338231 www.ssmconline.com, e‐mail : info@ssmconl ine.com 2