JEE Maths - Progression

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Question - 1

If S1, S2, S3 are the sums of first n natural numbers, their squares, their cubes respectively. then find the value of \(\frac{\mathrm{S}_{3}\left(1+8 \mathrm{~S}_{1}\right)}{\mathrm{S}_{2}{ }^{2}}\)

  • A 9.00
  • B 12.00
  • C 4.00
  • D 1.00

Question - 2

Let \(S_{n}=\frac{1}{1^{3}}+\frac{1+2}{1^{3}+2^{3}}+\ldots+\frac{1+2+\ldots .+\mathrm{n}}{1^{3}+2^{3}+\ldots .+\mathrm{n}^{3}} ; n=1,2,3, \ldots \ldots \ldots\) Then find maximum value of Sn

  • A 3.00
  • B 2.00
  • C 7.00
  • D 5.00

Question - 3

A square is drawn by joining the mid-points of the sides of a given square. A third square is drawn inside the second square in the same way and this process continuous indefinitely. If a side of the first square is 4 cm and the sum of the area of all the squares is \(\alpha\) then find the value of \(\alpha\)/4.

  • A 2.00
  • B 6.00
  • C 3.00
  • D 8.00

Question - 4

Let 'p' and 'q' be the roots of the equation x2 - 2x + A = 0. and Let "r" and "s' be the roots of the equation x2 - 18x + B = 0. If p < q < r < s are in A.P. then find value of (A + B).

  • A 74.00
  • B 64.00
  • C 4.00
  • D 34.00

Question - 5

Find the number of terms common to the two sequences 17, 21, 25. ..... 417 and 16, 21, 26, ,..,, 466,

  • A 40.00
  • B 60.00
  • C 20.00
  • D 10.00

Question - 6

The repeating decimal 0.429642964296..... represents the fraction \(\frac{\mathrm{m}}{3333}\) then find value of m.

  • A 1432.00
  • B 1132.00
  • C 1232.00
  • D 1532.00

Question - 7

Between l and 31 are inserted m arithmetic means, so that the ratio of the 7th and (m - l)th means is 5 : 9. Then find the value of m.

  • A 4.00
  • B 14.00
  • C 5.00
  • D 7.00

Question - 8

If the ratio of sum of n terms of two different A.P's is \(\frac{3 n+5}{4 n+3}\) then find the ratio of their 7th terms.

  • A 1.80
  • B 2.80
  • C 0.80
  • D 1.80

Question - 9

Find the maximum value of the sum of the A.P. 30, 27, 24, 21, ..

  • A 160.00
  • B 165.00
  • C 155.00
  • D 145.00

Question - 10

If the sum of positive terms of the series \(10+9 \frac{4}{7}+9 \frac{1}{7}+\ldots \ldots \text { is } \frac{\mathrm{k}}{7}\) then find value of k

  • A 892.00
  • B 752.00
  • C 802.00
  • D 852.00
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