JEE Questions for Maths Sequences And Series Quiz 16

The first four terms of an A.P are a, 9, 3a – b, 3a + b. the 2011^th term of the A.P is

0%
2015
0%
4025
0%
5030
0%
6035
0%
8045

A person is to count 4500 currency notes. Let a_n denotes the numbers of notes he counts in the n^th minute. If a₁ = a₂ = ..... = a₁₀ = 150 and a₁₀,a₁₁ , ... are in an A.P with common difference –2, then the time taken by him to count all notes is

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24 minutes
0%
34 minutes
0%
125 minutes
0%
135 minutes

The sum of all two digit natural numbers which leave a remainder 5 when they are divided by 7 is equal to

0%
715
0%
702
0%
615
0%
602
0%
589

An A.P. consists of 23 terms. If the sum of the three terms in the middle is 141 and the sum of the last three terms is 261, then the first term is

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6
0%
5
0%
4
0%
3
0%
2

If S₁ = a₂ + a₄ + a₆ + ... upto 100 terms and S₂ = a₁ + a₃ + a₅ + ... upto 100 terms of a certain A.P., then its common difference is

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S1 – S1
0%
S2 – S1
0%
0%
None of these

If 100 times the 100^th term of an A.P. with non-zero common difference equals the 50 times its 50^th term. then the 150^th term of this A.P. is

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–150
0%
150 times its 50th terms
0%
150
0%
Zero

Find a, b and c between 2 and 18 such that a + b + c = 25, 2,a,b are in A.P. and b,c, 18 are in G.P.

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5, 8, 12
0%
4, 8, 13
0%
3, 9, 13
0%
5, 9, 11

If two arithmetic means A₁, A₂, two geometric means G₁, G₂ and two harmonic means H₁, H₂ are inserted between two numbers p and q then _____

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0%
2)
0%
0%

0%
< 9
0%
≤ 9
0%
> 9
0%
≥ 9

In a G. P. the first term is a, second term is b and the last term is c, then the sum of the series is ________

0%
0%
2)
0%
0%

0%
0%
2)
0%
0%

If 2, b, c, 23 are in G. P. then (b – c)² + (c – 2)² + (23 – b)² =_____

0%
625
0%
525
0%
441
0%
442

If x,y,z are in G.P and a^x = b^y = c^z, then

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0%
2)
0%
0%
None of these

The first and last terms of a G.P. are a and l respectively; r being its common ratio; then the number of terms in this G.P is

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0%
2)
0%
0%

0%
0%
2)
0%
0%
None of these

The sum of infinite terms of a G.P. x and on squaring the each term of it, the will be y, then the common ratio of this series is

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0%
2)
0%
0%

If the ratio of A.M between two positive real numbers a and b to their H.M is m : n, then a : b is

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0%
2)
0%
0%
None of these

Given a + d > b + c where a, b, c, d are real numbers, then

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a, b, c, d are in A.P
0%
2)
0%
(a + b), (b + c), (c + d), (a + d) are in A.P
0%

If three real numbers a,b,c are in harmonic progression, then which of the following is true

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0%
2)
0%
ab, bc, ca are in H.P
0%

0%
0%
2)
0%
0%

If x,y,z are in A.P and tan^-1 x, tan^-1 y and tan^-1 z are also in A.P., then

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x = y = z
0%
x = y = -z
0%
x = 1; y = 2; z = 3
0%
x = 2; y = 4; z = 6
0%
x = 2y = 3z

The sixth term of an A.P is equal to 2, the value of the common difference of the A.P. which makes the product a₁a₄a₅ least is given by

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0%
2)
0%
0%
None of these

If the sum of first n terms of A.P in cn², then the sum of squares of these n terms is

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0%
2)
0%
0%

0%
0%
2)
0%
0%

If the first , second and last terms of an A.P be a,b,2a respectively, then its sum will be

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0%
2)
0%
0%

If a₁, a₂, a₃ ........... a_n are in A.P where a₁ > 0 for all i, then the value of
Maths-Sequences and Series-49254.png

0%
0%
2)
0%
0%

If a₁, a₂, .... , a_n are in A.P with common difference, d, then the sum of following series is
sin d(cosec a₁ • cosec a₂ + cosec a₂ • cosec a₃ + ..... + cosec a_{n – 1} cosec a_n )