R

CLASSROOM CONTACT PROGRAMME

(Academic Session : 2020 - 2021)

JEE (Main+Advanced):NURTURE COURSE

TARGET : JEE (M+A) 2021
TOPIC :SEQUENCE & SERIES DPP -4
b4 1
1. The sequence b n  is a geometric progression with b  4 and b 2  b5  216 . If b n  In  N , then
6

the value of b1 is
(a) 8 (b) 10
(c) 12 (d) 14
n 
1 1 1
2. Given Sn   r ,
S   r . If S  Sn  then the least value of 'n'
r 0 2 r0 2 1000
(a) 8 (b) 9
(c) 10 (d) 11
3. If the roots of the equation, x 3  px 2  qx  1  0 form an increasing G.P. where p and q are real, then
(ONE OR MORE THAN ONE CORRECT)
(a) p+q = 0
(b) p   3,  
(c) one of the roots is unity
(d) one root is smallar than 1 and one root is greater than 1
4. The first term of an infinite geometric series is 21. The second term and the sum of the series are both
positive integers. The possible value(s) of the second term can be
(ONE OR MORE THAN ONE CORRECT)
(a) 12 (b) 14
(c) 18 (d) 20
5. Column - I Column - II
(A) Let Sn ,S2n ,S3n are the sums of n, 2n,3n (P) 3
terms of an arithmetic progressions,
S3n
then S  S is equal to (Q) 4
2n n

(B) For an increasing G.P. a1 ,a 2 ,a 3 ,........., a n ,......

n

a 6  4a 4 ; a 9  a 7  192 . If a
i4
i  1016 (R) 6
then 'n' equals
(C) Let g n be the n th term of the (S) 8
geometric progression of positive numbers.
100
10 100
5
If g
n 1
2n
3
and  g 2n 1  , then the

n 1 9
common ratio of geometric progression, is
(D) A geometric progression consists of an (T) 10
even number of terms. If the sum of all the
terms is 5 times the sum of terms occupy the
odd place then its common ratio is

ALLEN Digital Classroom support Classes and material will continue until lockdown is lifted after which classroom course will commence
 R

TARGET :JEE(M+A)/NURTURE-2021/DPP-4
6. Let , ,  be the roots of the cubic 2x  9x  27x  54  0 . If , ,  are in G.P., then find the value
3 2

2
of
3
     .
7. If f  x   4x 4  ax 3  bx 2  cx  5  a, b, c  R  has four positive real zeros r1 , r2 , r3 ,r4 such that
r1 r2 r3 r4
    1 , then a is equal to
2 4 5 8
(a) 19 (b) 20
(c) 21 (d) 22
1
If ,  are roots of equation x  px  2p 2  0  p  R and p  0  , then the minimum value of     
2 4 4
8.

is equal to
(a) 2 (b) 4  2
(c) 2  2 (d) 3  2
9. If two positive real numbers are such that their arithmetic mean is 2k times their geometric mean, then
the minimum value of k equals
1
(a) (b) 4
4
1
(c) (d) 2
2
10. Let A 6 be the sum of first six terms of an arithmetic sequence, and G 6 be the sixth term of a geomet
ric sequence. Both sequences have the same first term, and the common difference of the arithmetic
A6
sequence equals the common ratio of the geometrical sequence, which is equal to two. If G is equal
6

1
to then  G 6  A 6  equals
2
(a) 1 (b) 3
(c) 48 (d) 144
x 4  2x 2  101
11. The minimum value of for x  R , is equal to
x2  1
4
(a) (b) 10
5
8
(c) (d) 20
3
12. Let a, b, c  R be such that a>-1, b>-2, c>3 and a+b+c=24, then the maximum value of (a+1)(b+2)(c-3)
is equal to
(a) 256 (b) 512
(c) 1024 (d) 2048
13. If x and y are positive real numbers and 3x+4y=5, then the greatest value of 16x 2 y3 is
(a) 2 (b) 3
(c) 4 (d) 5

ALLEN Digital Classroom support Classes and material will continue until lockdown is lifted after which classroom course will commence
 R

TARGET :JEE(M+A)/NURTURE-2021/DPP-4

2x x 3 y 4y 2
14. For any x,y  R, xy>0 then the minimum value of   4 equals
y3 3 9x
1
(a) 2 3 (b) 2
1
(c) 33 (d) 3

15. If a, b, c are three positive roots of the equation x 3  px 2  qx  48  0 (p, q>0) then find the minimum

 1 2 3
value of 2    
a b c

If 10   2 11 108   3 11 10   .....  10 11  k 10  , then k is equal to:
9 1 2 7 9 9
16.

121 441
(a) (b)
10 100
(c) 100 (d) 110

17. Let a1 , a 2 , a 3 ,..... and b1 , b 2 , b3 ..... be arithmetic progressions such that a1  25, b1  75 and a100  b100  100.
Then
(ONE OR MORE THAN ONE CORRECT)
(a) the difference between successive terms in progression 'a' is opposite of the difference in progression
'b'.
(b) a n  b n  100 for any n.
(c)  a1  b1  ,  a 2  b 2  ,  a 3  b3  ,.... are in A.P..
100

(d)  a
r 1
r  b r   10000

18. Positive integers a1 , a 2 ,a 3 ,..... form an A.P. If a1  10 and a a  100, then 2

(ONE OR MORE THAN ONE CORRECT)

(a) common difference of A.P. is equal to 6 (b) The value of a 3 is equal to 20
(c) The value of a 22 is equal to 136 (d) The value of a a is equal to 820
3

 2
k m
19. The value of 4
k 0
k can be written as
n
, where m and n are relatively prime positive integers.

Then the value of  m  n  is

(a) 28 (b) 47
(c) 66 (d) 85
1 2 3 n
20. The limiting sum of the infinite series,  2  3  .... whose n th term is n is
10 10 10 10
1 10
(a) (b)
9 81
1 17
(c) (d)
8 72

ALLEN Digital Classroom support Classes and material will continue until lockdown is lifted after which classroom course will commence