मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता ११ वी

Select the correct answer from the given alternative. The common ratio for the G.P. 0.12, 0.24, 0.48, is –

Advertisements
Advertisements

प्रश्न

Select the correct answer from the given alternative.

The common ratio for the G.P. 0.12, 0.24, 0.48, is –

पर्याय

  • 0.12

  • 0.2

  • 0.02

  • 2

MCQ
Advertisements

उत्तर

The common ratio for the G.P. 0.12, 0.24, 0.48, is 2

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 2: Sequences and Series - Miscellaneous Exercise 2.1 [पृष्ठ ४०]

APPEARS IN

बालभारती Mathematics and Statistics (Arts and Science) Part 2 [English] Standard 11 Maharashtra State Board
पाठ 2 Sequences and Series
Miscellaneous Exercise 2.1 | Q I. (1) | पृष्ठ ४०

संबंधित प्रश्‍न

The 5th, 8th and 11th terms of a G.P. are p, q and s, respectively. Show that q2 = ps.


The 4th term of a G.P. is square of its second term, and the first term is –3. Determine its 7thterm.


Which term of the following sequence:

`sqrt3, 3, 3sqrt3`, .... is 729?


How many terms of G.P. 3, 32, 33, … are needed to give the sum 120?


Given a G.P. with a = 729 and 7th term 64, determine S7.


Show that the products of the corresponding terms of the sequences a, ar, ar2, …arn – 1 and A, AR, AR2, … `AR^(n-1)` form a G.P, and find the common ratio


if `(a+ bx)/(a - bx) = (b +cx)/(b - cx) = (c + dx)/(c- dx) (x != 0)` then show that a, b, c and d are in G.P.


If a, b, c, d and p are different real numbers such that:
(a2 + b2 + c2) p2 − 2 (ab + bc + cd) p + (b2 + c2 + d2) ≤ 0, then show that a, b, c and d are in G.P.


The sum of three numbers in G.P. is 21 and the sum of their squares is 189. Find the numbers.


Find the sum of the following geometric series:

1, −a, a2, −a3, ....to n terms (a ≠ 1)


Evaluate the following:

\[\sum^{10}_{n = 2} 4^n\]


Find the sum of the following series:

7 + 77 + 777 + ... to n terms;


The common ratio of a G.P. is 3 and the last term is 486. If the sum of these terms be 728, find the first term.


If S1, S2, ..., Sn are the sums of n terms of n G.P.'s whose first term is 1 in each and common ratios are 1, 2, 3, ..., n respectively, then prove that S1 + S2 + 2S3 + 3S4 + ... (n − 1) Sn = 1n + 2n + 3n + ... + nn.


Find the sum of the terms of an infinite decreasing G.P. in which all the terms are positive, the first term is 4, and the difference between the third and fifth term is equal to 32/81.


Find the rational numbers having the following decimal expansion: 

\[0 .\overline {231 }\]


If a, b, c are in G.P., prove that:

(a + 2b + 2c) (a − 2b + 2c) = a2 + 4c2.


If (a − b), (b − c), (c − a) are in G.P., then prove that (a + b + c)2 = 3 (ab + bc + ca)


If a, b, c are in A.P. and a, x, b and b, y, c are in G.P., show that x2, b2, y2 are in A.P.


If pth, qth and rth terms of an A.P. and G.P. are both a, b and c respectively, show that \[a^{b - c} b^{c - a} c^{a - b} = 1\]


If (p + q)th and (p − q)th terms of a G.P. are m and n respectively, then write is pth term.


If the sum of an infinite decreasing G.P. is 3 and the sum of the squares of its term is \[\frac{9}{2}\], then write its first term and common difference.


If A be one A.M. and p, q be two G.M.'s between two numbers, then 2 A is equal to 


If x is positive, the sum to infinity of the series \[\frac{1}{1 + x} - \frac{1 - x}{(1 + x )^2} + \frac{(1 - x )^2}{(1 + x )^3} - \frac{(1 - x )^3}{(1 + x )^4} + . . . . . . is\]


For the G.P. if a = `7/243`, r = 3 find t6.


For the G.P. if a = `2/3`, t6 = 162, find r.


For what values of x, the terms `4/3`, x, `4/27` are in G.P.?


For the following G.P.s, find Sn.

p, q, `"q"^2/"p", "q"^3/"p"^2,` ...


For the following G.P.s, find Sn

0.7, 0.07, 0.007, .....


For a G.P. if S5 = 1023 , r = 4, Find a


If Sn, S2n, S3n are the sum of n, 2n, 3n terms of a G.P. respectively, then verify that Sn (S3n – S2n) = (S2n – Sn)2.


Express the following recurring decimal as a rational number:

`51.0bar(2)`


Answer the following:

Find three numbers in G.P. such that their sum is 35 and their product is 1000


Answer the following:

Find five numbers in G.P. such that their product is 243 and sum of second and fourth number is 10.


Answer the following:

For a G.P. if t2 = 7, t4 = 1575 find a


Answer the following:

If for a G.P. t3 = `1/3`, t6 = `1/81` find r


Let S be the sum, P be the product and R be the sum of the reciprocals of 3 terms of a G.P. Then P2 R3 : S3 is equal to ______.


If `e^((cos^2x + cos^4x + cos^6x + ...∞)log_e2` satisfies the equation t2 – 9t + 8 = 0, then the value of `(2sinx)/(sinx + sqrt(3)cosx)(0 < x ,< π/2)` is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×