IIT JEE MODEL QUESTIONS MATHS SEQUENCES AND SERIES

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Franklin Warren
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1 . If tan (A +B), tan B, tan (B + C) are in AP, then tan A, cot B,tan C are in (a) AP (b) GP (c) HP (d) None of these. Consider an acute-angled triangle ABC having P as its orthocentre. If the distance of P from the sides BC, CA and AB are in AP, then (a) Cos A, Cos B, cos C are in AP (b) sin A, sinb, sin C are in AP (c) Cos A, Cos B, Cos C are in GP (d) Cos A, Cos B, Cos C are in HP. Let a, b and c be positive real numbers such that a + b + c = 6. Then, the range of ab c is (a) (0, ) (b) (0, ) (c) (0,08] (d) (6, 08] 4. Let a, a, a, a 4 and a 5 be such that a, a and a are in AP; a, a and a 4 are in GP;a, a 4 and a 5 are in HP. Then a,a and a 5 are in (a) GP (b) AP (c) HP (d) none of these 5. If three positive real numbers a, b, c are in AP such that abc = 4, then the minimum value of b is (a) / (b) / (c) / (d) / 6. If the sides of a triangle are in GP, and its largest angle is twice the smallest, then the common ration r satisfies the inequality (a) 0 < r < (b) < r < (c) < r < (d) none of the above 7. If the sides of a triangle are in AP, and the greatest angle of the triangle is double the smallest angle, then ration of the sides of the triangle is (a) :4:5 (b) 4: 5: 6 (c) 5: 6:7 (d) 7: 8: 9 8. The number of common terms to the two sequences 7,, 5,47 and 6,, 6,.. 466, is (a) (b) 9 (c) 0 (d) 9 x x x 9. If b c, b x and b a are in HP, then a, b and c are in (a) AP (b) GP (c) HP (d) none of these 0. The sixth term of an AP is, and its common difference is greater than one. The value of the common difference of the progressions so that the product of the first, fourth and fifth terms is the greatest, is 8 (a) 5 (b) 5 (c) 8 (d). If ax +bx +cx +d is divisible by ax + c, then a, b, c, d are in (a) AP (b) GP (c) HP (d) None of these. The sum of the series a (a + b) + (a +d) (a + d) + upto (n + ) terms is (a) nd (b) a + nd (c) a + nd (d) nd. If the first two terms of a HP are and, respectively, then the largest term is 5 (a) 5 th term (b) 6 th term (c) 4 th term (d) 7 th term 4. If x >, y >, z > are in GP, then,, ln x ln y ln z are in THIRUMURUGAN.K PGT Maths IIT Trainer Page

2 (a) AP (b) HP (c) GP (d) none of these 5. If the sum of the first n terms of the AP, 5 8, is equal to the sum of the first n terms of the AP 57, 59,6 then n equals (a) 0 (b) (c) (d) 6. Suppose a, b, c are in AP and a, b, c are in GP, if a a< b and a + b + c =, then the value of a is (a) (b) 7. If ( + a) (+ a ) (+a 4 ).. (+ a 8 ) = a n r0 r (c), then n equal to (d) (a) 55 (b) 7 (c) 6 (d) None of these 8. The 0 th common term of between the series , and is (a) 9 (b) 9 (c) (d) None of these 9. The largest term common to the sequences,,,.. to 00 terms and,6,4,46 to 00 terms is (a) 8 (b) 47 (c) 8 (d) None of these 0. The 5 th term of the series is (a) 49 - (b) 49 (c) 50 + (d) c g. If log, log and log a 5c lengths of sides of (a) an isosceles triangle (c) a scalene triangle a b are in AP where a, b, c are in GP, then a, b, c are the (b) an equilateral triangle (d) None of above. In the sequence,,,4,4,4,4, 8,8,8, 8,8,8, 8,8, where n consecutive terms have the value n, 05 th term will be : (a) 9 (b) 0 (c) (d) 8 THIRUMURUGAN.K PGT Maths IIT Trainer Page

3 . The value of is n i i j k j (a) n (b) n (c) n (d) None of these 4. Three non- zero real numbers form an A.P. and the square of the numbers taken in the same order constitute a G.P. Then the number of all possible common ratios of the G.P are (a) (b) (c) (d) 4 5. Let a, b, c be the p th, q th, and r th term respectively of a H.P, then ab ( p-q )+ bc (q r) +ca (r-p) is (a) - (b) 0 (c) (d) none of these 6. Four geometric means are inserted between the numbers - and +. The product of these geometric means is (a) (b) (c) - + (d) If the sum of n terms of an A.P is given by S n = A. n + B. n, where A and B are constants, then the common difference of the A.P is (a) A (b) B (c) A (d) B 8. The sum of the latter half of the first 000 terms of any A.P is equal to one-third of the sum of the first n terms of the A.P.Then, n is equal to (a) 000 (b) 500 (c) 000 (d) If the sum of the four numbers in A.P. be 96 and that the ratio of the product of the means to the product of the extremes is 5 to 7, then the numbers are (a) 6, 8, 0,4 (b),0,8,6 (c) 4,6,8, 40 (d),, 5,7 0. The term of the sequence 5,,0,8. Which is numerically smallest is 4 4 (a) eleventh (b) twelfth (c) thirteenth (d) fourteenth. The third term of a G.P is 4. The product of its first 5 terms is (a) 4 (b) 4 4 (c) 4 5 (d) none of these. The middle term of the progression, 5, 8,,.. 9 is (a) 46 (b) 47 (c) 48 (d) 49. The first term of a G.P is 79 and the seventh term is 64. The sum of the G.P to infinity is (a) 48 (b) 87 (c) 047 (d) 4095 THIRUMURUGAN.K PGT Maths IIT Trainer Page

4 4.The common ratio of a G.P is 4 80 and the sum to infinity is.its first term is 5 9 (a) 6 (b) 8 (c) (d) 8 5. A ball is dropped from a height of 48 ft and it rebounds of the height it falls. If it continues to fall and rebound, the total distance that the ball can travel before coming to rest is (a) 40ft (b) 9ft (c) 44ft (d) 88 ft 6. If x, y, z are in A.P as well as in G.P., then (a) x = y z (b) x y = z (c) x y z (d) x = y = z 7. If a, b, c are in A.P. and a,b, c are in H.P., then (a) a = b c = (b) b = ac (c) a = b = c (d) b = ac 8. If m, m+,m+ are in G.P., then the fourth term is (a) -7 (b) -.5 (c).5 (d) 7 9. The sum of three numbers in G.P is 4. If is added to the first and the second and is subtracted from the third, the new numbers are in A.P. The smallest of them is (a) (b) (c) 4 (d) The sum of first two terms of an infinite G.P is and every term is twice the sum of the successive terms. Its first term is (a) 4 (b) (c) (d) 4 4. If x, y, z are the p th, q th and r th terms respectively of an A.P and also of a G.P, then x y-z. y z-x. z x-y equals (a) 0 (b) (c) xyz (d) 4. The G.M between -9 and -5 is (a) -5 (b) 5 (c) ± 5 (d) none of these THIRUMURUGAN.K PGT Maths IIT Trainer Page 4

5 4. The second, third and the sixth terms of an A.P. are consecutive terms of a G.P. The common ratio of the G.P is (a) - (b) - (c) (d) 44. A.G.P consists of an even number of terms. If the sum of all the terms is 5 times the sum of the terms occupying odd places, the common ratio will be equal to (a) (b) (c) 4 (d) If a, b, c are in A.P. b a, c-b and a are in G.P., then a: b: c is (a) :: (b) : :4 (c) : : 5 (d) : :4 46. In a G.P of positive terms,any term is equal to the sum of the next two terms The common ratio of the G.P is (a) sin 8 (b) cos 8 (c) cos 8 (d) sin The third term of geometric progression is 4, the product of the first 5 terms is, (a) 4 (b) 4 5 (c) 4 4 (d) none 48. If x >, y>, z > are in G.P. then / + ln x, / + ln y, / + ln z are in (a) A.P (b) H.P (c) G.P (d) none of these 49. Let the positive numbers a, b,c, d, be in A.P, then abc, abd, acd, bcd are (a) Not in A.P /G.P /H.P (c)in G.P (b) in A.P (d) in H.P 50. The H.M of the roots of the equation 5 x 4 5x (a) (b) 4 (c) 6 (d) 8 is THIRUMURUGAN.K PGT Maths IIT Trainer Page 5

Objective Mathematics

Objective Mathematics Multiple choice questions with ONE correct answer : ( Questions No. 1-5 ) 1. If the equation x n = (x + ) is having exactly three distinct real solutions, then exhaustive set of values of 'n' is given