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Sequences and Series

JEE Main 2024 (Online) 5th April Evening ShiftNumericalHard📈 Topic in 17% papers+4
Ques. 1JEE Main 2024, 5 April (Evening Shift)

If 1 + 3 - 22 3 + 5 - 2 618 + 9 3 - 11 236 3 + 49 - 20 6180 + upto = 2 + ( ba + 1 ) e ( ab ), where a and b are integers with (a, b) = 1, then 11a + 18b is equal to .

Answer

76

Solution

Let t = 3 - 2 3 = 1 - 23: t2 = 5 - 2 63, t3 = 9 3 - 11 23 3, t4 = 49 - 20 69

S = 1 + t1 2 + t22 3 + t33 4 + t44 5 +

1n(n + 1) = 1n - 1n + 1, tnn = - e(1 - t), tnn + 1 = 1t [- e(1 - t) - t ]

S = 2 + ( 1t - 1 ) e(1 - t)

1 - t = 23, 1t - 1 = 2 3 - 2 = 6 + 2

S = 2 + 6 + 22 e 23 = 2 + ( 32 + 1 ) e ( 23 )

a = 2, b = 3 11a + 18b = 22 + 54 = 76

Answer: 76

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Ques. 2JEE Main 2024, 4 April (Morning Shift)

Let the first three terms 2, p and q, with q 2, of a G.P. be respectively the 7th, 8th and 13th terms of an A.P. If the 5th term of the G.P. is the nth term of the A.P., then n is equal to:

  1. 151
  2. 177
  3. 163
  4. 169
Ques. 3JEE Main 2024, 4 April (Morning Shift)

Let a=1+ 2C23!+ 3C24!+ 4C25!+ , b=1+ 1C0+1C11!+ 2C0+2C1+2C22! + 3C0+3C1+3C2+3C33!+ . Then 2ba2 is equal to .

Ques. 4JEE Main 2024, 4 April (Evening Shift)

The value of 1 22 + 2 32 + + 100 (101)212 2 + 22 3 + + 1002 101 is

  1. 305301
  2. 306305
  3. 3231
  4. 3130
Ques. 5JEE Main 2024, 4 April (Evening Shift)

Let three real numbers a, b, c be in arithmetic progression and a + 1, b, c + 3 be in geometric progression. If a > 10 and the arithmetic mean of a, b and c is 8, then the cube of the geometric mean of a, b and c is

  1. 120
  2. 316
  3. 312
  4. 128
Ques. 6JEE Main 2024, 1 February (Morning Shift)

Let 3, a, b, c be in A.P. and 3, a-1, b+1, c+9 be in G.P. Then, the arithmetic mean of a, b and c is :

  1. -4
  2. -1
  3. 13
  4. 11
Ques. 7JEE Main 2024, 1 February (Morning Shift)

Let 3, 7, 11, 15, , 403 and 2, 5, 8, 11, , 404 be two arithmetic progressions. Then the sum, of the common terms in them, is equal to .

Ques. 8JEE Main 2024, 1 February (Evening Shift)

Let Sn denote the sum of the first n terms of an arithmetic progression. If S10=390 and the ratio of the tenth and the fifth terms is 15:7, then S15-S5 is equal to :

  1. 800
  2. 890
  3. 790
  4. 690
Ques. 9JEE Main 2024, 1 February (Evening Shift)

If three successive terms of a G.P. with common ratio r(r>1) are the lengths of the sides of a triangle and [r] denotes the greatest integer less than or equal to r, then 3[r]+[-r] is equal to .

Ques. 10JEE Main 2024, 31 January (Morning Shift)

The sum of the series 11-3 12+14+ 21-3 22+24+ 31-3 32+34+ up to 10-terms is

  1. 45109
  2. - 55109
  3. 55109
  4. - 45109
Ques. 11JEE Main 2024, 31 January (Evening Shift)

Let 2nd, 8th and 44th terms of a non-constant A. P. be respectively the 1st, 2nd and 3rd terms of a G. P. If the first term of the A. P. is 1, then the sum of its first 20 terms is equal to -

  1. 990
  2. 980
  3. 960
  4. 970

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