Page 1 : Second Teriminal Examination, 2021-22, Class : XI, Mathematics, Marks : 100, Time : 3 Hrs, 1., , Answer the following questions:, , (20x1=20), , (a) The value of 1  i   1  i  is equal to, 3, , (i) 1, , 3, , (ii) –2, , (iii) 0, , (iv) –4, , (iii) 1, , (iv), , (b) The modulus of  3i  1 is, 2, , (i) 10, , (ii) –10, , (i) 6!.5!, , (ii)  5!, , 7, (c) If 3  3t  18  18 , then which one of the following is, correct?, (i) t  7 or t  12, (ii) 8  t  12, (iii) 7  t  12, (iv) 8  t or t  12, (d) The number of ways in which 5 boys and 5 girls can be, seated for a photograph so that no two girls sit next to each, other, is, 2, , 10!, (iii), 5!, , 10!, , (iv) 5! 2,  , , (e) The number of ways of arranging letters of the word ‘HAVANA’, so that V and N do not appear together, is, (i) 60, (ii) 80, (iii) 100, (iv) 120, (f) Find nC21 , if nC10  nC11, (i) 1, (ii) 0, (iii) 11, (iv) 10, (g) In how many ways, can a student choose a program of 5, courses, if 9 courses are available and 2 specific courses are, compulsory for every student?, (i) 34, (ii) 36, (iii) 35, (iv) 37, (h) If –5, k and –1 are in AP, then the value of k is equal to, (i) –5, (ii) –3, (iii) 5, (iv) 3

Page 2 : (i) If the second and fifth terms of a GP are 24 and 3 respectively, then the sum of first six terms is, 181, 189, (iii) 189, (iv), 2, 2, (j) In a geometric progression the ratio of the sum of the first, three terms and first six terms is 125:152. The common, ratio is, , (i) 181, , (i), , 1, 5, , (ii), , (ii), , 2, 5, , (k) What is the value of, (i), , 1, 3, , (ii) , , (iii), , 4, 5, , (iv), , 3, 5, , cos100  sin 200, ?, cos 200  sin100, 1, 3, , (iii), , 3, , (iv)  3, , cos 2 330  cos 2 57 0, ?, (l) Solve, sin 210  cos 21, 1, 1, , (ii) 1 2, (iii), (iv), 2, 2, (m)A wheel makes 240 revolutions is one minute. The measure of the angle is describes at the centre in 15 seconds is, (i) 60, (ii) 120, (iii) 8, (iv) , , (i)  2, , (n) The value of, (i) 1200, , 7, in degree measure is 9, , (ii) 1300, , (iii) 1400, , (o) If cos ec  sec , then value of  is, (i) 00, (ii) 450, (iii) 900, (p) The Principal solutions of sin x , ,  3, is, 2, , (iv) 1500, (iv) 300

Page 3 : (i), , 2, 4, and, 3, 3, , (iii), , , 3, , and, , (ii), , 5, 3, , 4, 5, and, 3, 3, , (iv) none of these, , (q) If the angle between twolines in  4 and the slope of one, line is 1 2 , then th eslope of the other line is, 1, 1, 1, 1, 1, (ii) 3 or, (iii) 4 or, (iv) or , 2, 3, 4, 2, 3, (r) The distance of the point P(4, 1) from the line 3x-4y+12=0, is, (i) 4 units, (ii) 5 units, (iii) 3 units, (iv) 6 units, , (i) 2 or, , (s) In the parabola y 2  12 x , the focus and the equation of, directrix are respectively, (i) F(3, 0), x = -3, (ii) F(-3, 0, x = 3, (iii) F(-3, 0), x = -3, (iv) None of these, (t) If the parabola y 2  4ax passes through the point P(3, 2),, then the length of its latus rection is, (i) 1 3, , (ii) 2 3, , (iii) 4 3, , 1  i , 3  i , , (iv) 4, , 2, , 2., , Write down the conjugate of, , 3., , Solve:, , 4., 5., , (2), , x5,  0, x  R, (2), x2, Find the sum of all integers between 101 and 500, which, are divisible by 9., (2), Find the geometric series whose 5th and 8th terms are 80, and 640 respectively., (2)

Page 4 : 6.,  15, and  2  x   , find the value of sin x, 4, [2], , 7., , If cos x , , 8., , 0, 0, Show that sin105  cos105 , , 9., , 10., , 1, 2, , Reduce tha equation 2 x  3 y  5  0 to slopoe inercept, form and find fromit the slope and y-intercept., [2],  , Find the equation of the ellipse whose foci are at  1, 0 ,  , and e  1 2, , 11., 12., , 13., , 14., , [2], , [2], , Solve 3 x 2  2 x  3 3  0, (4), From a class of 10 boys and 6 girls, 10 students are to be, selected for a competition, at least including 4 boys and 4, girls. The 2 girls who won the prizes last year should be, included. In how many ways the selection can be done?(4), A mint prepares metallic calendars specifying months,, dates and days in the form of monthly sheets ( one plate for, each month). How many types of February calendars, should it prepare to serve for all the possibilities in the, future years?, (4), Two cars start togethr in the same direction at the same, place. The first car goes with the uniform speed of 10, km/hr. The second car goes at a speed of 8 km/hr in the, 1, km each succeed2, ing hours. After how many hours will the second car, , first hour and increases the speed by

Page 5 : overtake the first car if both cars go non-stop?, , (4), , 15. (a) The number of bacteria in a certain culture doubles every, hour. If there were 50 bacteria present in the culture originally, how many bacteria would be present at the end of (i), 2nd hour, (ii) 5th hour?, (4), [OR], (b) What will Rs 5000 amount to in 10 years, compounded annually at 10% per annum? [Given 1.1  2.594 ] (4), 10, , 16., 17., , Find the general solution of 3 cos x  sin x  1, [6], Find the ratio in which the line segment having the end, points A  1, 3, 4  and B  4, 2, 1 is divided by the xz-, , 18., , plane. Also, find the co-ordinates of the points of division., Find the mean diviation about the meanfor the following, data :, [6], xi, fi, , 19., 20., , 3, 6, , 5, 8, , 7, 15, , 9, 25, , 11, 8, , 13, 4, , Prove that tan 6 0 tan 420 tan 660 tan 780  1, [6], Find the equatuon of the line passing through th epiont, (2, -5) and parallel to the line 2x - 3y = 7, [6], 21., A furniture dealer deals in only two items: tables and chairs., He has Rs. 15000 to invest and a space to store at most 60, pieces. A table costs him Rs 750 and a chair Rs 150. Formu, late the data in the form of inequations and draw a graph, representing the solution of these inequations., (6), 22. (a) A man saves Rs 32 during first year, Rs 36 in the next year, and Rs 40 in the third year. If he continues his savings in this, sequence, in how many years will he save Rs 2000?, (b) The interior angles of a polygon are in AP. The smallest angle, is 120o and the common difference is 5o. Find the numbers of, sides of a polygon., (3+3=6)

Page 6 : 0, 0, 0, 0, 23. a) Prove that sin10 sin 30 sin 50 sin 70  116, b) If A  B  C   ,, [6], Prove that sin 2 A  sin 2 B  sin 2C  4cos A cos B sin C, , 24., , Find the equation of the concentric with the circle, x 2  y 2  6 x  12 y  15  0 and of double its area., , ***********, , [6]