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HIMACHAL PRADESH MAR 2008 : Mathematics

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MATHEMATICS Time allowed : 3 Hours Maximum Marks :100 Marks allotted to each question are indicated against it. Special Instructions :1. You must write question paper series in the circle at top left side of title page of your 2. 3. 4. 5. 6. answer book. While answering your questions you must indicate on your answer book the same questions number as appears in your question paper. Do not leave blank page / pages in your answer book. Question Nos. 1 to 10 multiple choice questions are of 1 mark each. Questions 11 to 14 are of 3 marks each. Question Nos. 15 to 26 are of 4 marks each. Question Nos. 27 to 31 are of 6 marks each. All questions are compulsory. 8. Internal choices have been provided in some questions. You have to attempt only one of the choices in such questions. Use of calculator is not permitted, however, you ask for Logarithmic tables, if required from the Superintendent of examination. Try to answer the questions in serial order as far as possible. Q1. The set of A = { x : x R, x = 16 and 2x = 6 } equals 7. (a) Q2. (b) {14, 3, 4} (c) {3} (d) {4} The set of intelligent student in a class is : (a) a null set (b) a singleton set (iii) Q3. 1 a finite set (iv) not a well defined collection. let f = {(1, 5), (2, 6), (3, 4)} g = { (4, 7), (5, 8), (6, 9)} 1 1 the gof is (a) {(4, 7), (5, 8), (6, 9), (1, 5), (2, 6), (3, 4)} (b) { (c) {(1, 8), (2, 9), (3, 7)} (d) None of these Mathematics } 53 +1 Q4. and cos = 3 If sin = 1 2 , then lies in 2 (a) (b) IInd quadrant (iii) Q5. Ist quadrant IIIrd quadrant (iv) IVth quadrant The maximum value of sin cos is (a) 1 1 2 (b) 1 (d) 2 The value of 15c11 15c10 is equal to 3 2 (a) 15 11 (b) 15 10 5 11 (d) 5 10 (c) Q6. (c) Q7. Q9. 1 1 The eccentricity of Parabola y = 8x is : (a) Q8. 1 2 (b) Lt. xd 2 (a) [sinx] is : 1 Lt. 2 (c) 1 (d) 1 1 (b) 0 (c) 1 (d) None of these 1 sin is : (b) 0 (c) 1 (d) None of these 1 1 (c) 0 (d) 1 1 d0 (a) 1 Q10. Complex conjugate of i is : (a) i (b) Q11. Let A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6} Find (i) A (BAC) (ii) (A B) 4 (A C) 3 Q12. Convert 6 radians into degree measure. 3 Q13. Express the following in the form a+ib 5 + 2i 1 2i OR Convert the complex number in the polar form 3 + i Mathematics 3 54 +1 Q14. Write the contra positive of the statement : (i) If a number is divisible by 9, then it is divisible by 3. (ii) If you are born in India, then you are citizen of India. (iii) If a triangle is equilateral, it is isosceles. 3 Q15. Let U = { 1, 2, 3, 4, 5, 6}, A = {2, 3} and B = {3, 4, 5} Find A', B', A'3B' and A4B 4 Q16. Let f(x) = x and g(x) = 2x + 1 be two real functions. Find (f + g) (x), (f g)(x), (fg) (x), f ( g) (x) 4 Or x + 2x + 1 Find the domain of the function f(x) = x 8x + 12 Q17. If cosx = 3 x lies in the third quadrant, find the values of other five trignometric 5 functions. 4 Q18. Using Principle of mathematical induction for all n N prove that : n(2n 1) (2n+1) 1 + 3 + 5 + .................. + (2n 1) = 3 Q19. Solve : 3x 2x + 3 3 = 0 4 4 Q20. Solve : 2(2x +3) 10 < 6 (x 2) Or Solve the system of inequalities : 3x 7 < 5 + x 11 5x 1 4 Q21. Find the value of n, such that n n P5 = 42 P3 ; n>4 4 Q22. Insert 6 numbers between 3 and 24 such that the resulting sequence is an A.P. 4 Q23. Find the angle between the lines y 3x 5 =0 and 3y x + 6 = 0 4 Q24. Find the co-ordinates of the foci, the vertices, the lengths of major and minor axes and the eccentricity of the ellipse 9x + 4y = 36 Or Find the equation for the ellipse that satisfies the given conditions vertices ( 5, 0), foci ( 4, 0) Mathematics 4 55 +1 Q25. Show that the points A(1, 2, 3), B( 1, 2, 1), C(2, 3, 2) and D(4, 7, 6) are the vertices of a parallelogram ABCD, but it is not a rectangle. 4 Q26. Find the derivative of 'x sin x' by the first Principle. Q27. If tan x = 3 , 4 4 x x 3 x , find the value of sin , cos and tan 2 2 2 2 <x< Or Find the value of tan 13 12 6 Q28. Show that middle term in the expansion of (1 + 2x)2n is 1. 3. 5. . . . . . (2n 1) n n 2.x n! where n is a positive Integer. 6 Or Find the term in dependent of x in the expansion of (3 x3 7 ) 6 Q29. Find the sum to n-terms of the series 7 + 77 + 777 + . . . . . . . . 6 Q30. Calculate the mean, variance and standard deviation for the following distribution : Class 30-40 frequency 40-50 50-60 60-70 70-80 80-90 3 7 12 15 8 3 90-100 2 6 Q31. A die is thrown, find the probability of following events : (i) A Prime number will appear, (ii) A number greater than or equal to 3 will appear, (iii) A number less than or equal to one will appear, (iv) A number more than 6 will appear, (v) A number less than 6 will appear. 6 Or One card is drawn from a well shuffled deck of 52 cards. If each out come is equally likely, calculate the probability that the card will be (i) a diamond (ii) not an ace (iii) a blackcard (i.e. a clubor or a spade) (iv) Mathematics not a black card. 6 56 +1

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Additional Info : Model Question Papers Of Plus One Examination March 2008 Mathematics
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