Arjuna JEE AIR (2024)
SEQUENCE AND SERIES
Q.1
Q.2
Q.3
Q.4
Q.5
Q.6
Three distinct A.P.'s have same first term,
common differences as d1, d2, d3 and nth terms
a
2b
as an, bn, cn respectively such that 1 = 1
d1
d2
a
3
b7
3c
= 1 . If 7 =
then
is equal to
7
c6
c6
d3
14
17
(1)
(2)
49
21
40
13
(3)
(4)
49
21
Let a1, a2, a3, ……, an are in A.P. such that
3
an = 100, a40 – a39 = then 15th term of A.P..
5
from end is
448
452
(1)
(2)
5
5
454
458
(3)
(4)
5
5
2
Let ,  be the roots of ax + bx + c = 0 (a  0)
and ,  be the roots of px2 + qx + r = 0 (p  0),
and D1, D2 be the respective discriminants of these
equations. If , , ,  are in A.P., then D1 : D2
equals
a2
a2
(1) 2
(2) 2
p
b
2
b
c2
(3) 2
(4) 2
q
r
In a convex polygon, the degree measures of the
interior angles form an arithmetic progression. If
the smallest angle is 159° and the largest angle is
177°, then the number of sides in the polygon, is
(1) 21
(2) 27
(3) 30
(4) 31
The first term of an A.P. is 5, the last is 45 and their
sum is 400. If the number of terms is n and d is
n
the common difference, then   is equal to
d
(1) 9
(2) 8
(3) 7
(4) 6
In an arithmetic progression, if Sn = n(5 + 3n) and
tn = 32, then the value of n is
[Note : Sn and tn denote the sum of first n terms
and nth term of arithmetic progression respectively.]
(1) 4
(2) 5
(3) 6
(4) 7
DPP - 01
Paragraph for questions nos. 7 to 9
Let the quantities 1, logy x, logz y and – 15 logx
z be the first four terms of an arithmetical
progression with common difference d. All terms
of the A.P. being real.
Q.7
The value of (xz–3 + xy + yz3) is equal to
(1) 0
(2) 1
(3) 2
(4) 3
Q.8
Common difference d of the A.P. satisfies the
equation
(1) 6d3 + 11d2 + 6d – 16 = 0
(2) 6d3 + 11d2 – 6d – 16 = 0
(3) 6d3 + 11d2 + 6d + 16 = 0
(4) 6d3 + 11d2 – 6d + 16 = 0
Q.9
Magnitude of the sum of the first 25 terms of the
A.P. is equal to
(1) 575
(2) 675
(3) 625
(4) 552
Q.10 Positive integers a1, a2, a3, ........ form an A.P. If
a1 = 10 and a a 2  100 , then
(1) common difference of A.P. is equal to 6.
(2) The value of a3 is equal to 20.
(3) The value of a22 is equal to 136.
(4) The value of a a 3 is equal to 820.
Q.11
Let a1, a2, a3 ....... and b1, b2, b3 ...... be arithmetic
progressions such that a1 = 25, b1 = 75 and
a100 + b100 = 100. Then
(1) the difference between successive terms in
progression 'a' is opposite of the difference in
progression 'b'.
(2) an + bn = 100 for any n.
(3) (a1 + b1), (a2 + b2), (a3 + b3), ....... are in A.P.
100
(4)
 (a r  br ) = 10000
r 1
Q.12 Let 'p' and 'q' be 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 arithmatic
progression. Find the value of (A + B).
ANSWER KEY
Q.1
2
Q.7
4
Q.2
4
Q.8
3
Q.3
1
Q.9
1
Q.4
3
Q.10 1, 3
Q.5
4
Q.11
Q.6
2
Q.12 74
1, 2, 3, 4
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