GOUTHAM SANKEERTHMaths
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AKSHAY ARORA
Experience:
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Maths
Scope
S. No Name Of Concept Number Of Questions
1 Problems on AP 8
2 Problems on GP 4
3 Problems on AP GP 4
4 Problem on Infinite GP 3
5 Problem on AM GM 5
6 Special Series 10
7 Miscellaneous Problems 4
Analysis of the Number of Questions asked in JEE
Mains from 2013-20
Solve
Let a1, a2, a3, ….. be a sequence of positive integers in arithmetic
progression with common difference 2. Also, let b1, b2, b3, ….. be
a sequence of positive integers in geometric progression with
common ratio 2. If a1 = b1 = c, then the number of all possible
values of c, for which the equality 2(a1 + a2 + ….+an ) = b1 + b2 +
….. + bn holds for some positive integer n, is ______ JEE
Advance 2020
Solve
If 100 times the 100th term of an AP with non-zero common
difference equal to the 50 times its 50th term, then the 150th term
of this AP is JEE M 2012
(a) -150 (b) 150 times its 50th term (c) 150 (d)
zero
Solve
Let the sum of the first three terms of an AP be 39 and the sum of
its last four terms be 178. If the first term of this AP is 10, then the
median of the AP is JEE M 2015
(A) 26.5 (B) 28 (C) 29.5 (D) 31
Solve
Let a1,a2,a3,....., an ...... be in A.P. If a3+ a7+ a11 +a15 = 72, then the
sum of its first 17 terms is equal to : JEE M 2016
(a) 306
(b) 153
(c)612
(d) 204
Solve
Let a1, a2, .....,a30 be an A.P., S = Σai i ∈[i = 1, 30] and T = Σ a(2i-1) i ∈ [i
= 1, 15] If a5 = 27 and S – 2T = 75, then a10 is equal to JEE M 2019- Jan
(1) 47 (2) 52 (3) 57 (4) 42
Solve
Let f : R → R be such that for all x ∈ R (21 + x + 21 - x), f(x) and (3x +
3-x) are in A.P. then the minimum value of f(x) is JEE M 2020- Jan
(1) 0 (2) 3 (3) 2 (4) 4
Solve
The number of terms common to the two A.P. 's 3, 7, 11, ....., 407
and 2, 9, 16, ....., 709 is ______. JEE M 2020- Jan
Solve
The sum of the 3rd and the 4th terms of a G.P. is 60 and the
product of its first three terms is 1000. If the first term of this G.P.
is positive, then its 7th term is : JEE M 2015
(1) 7290 (2) 640 (3) 2430 (4) 320
Solve
If a, b and c be three distinct real numbers in G.P. and a + b + c =
xb, then x cannot be JEE M 2019- Jan
(1) –3 (2) –2 (3) 2 (4) 4
Solve
If three distinct numbers a, b, c are in G.P. and the equations
ax2 + 2bx + c = 0 and dx2 + 2ex + f = 0 have a common root, then
which one of the following statements is correct ? JEE M 2019-
Apr
(1) d, e, f are in A.P. (2) d/a, e/b, f/c are n A.P
(3) d, e, f are in G.P (4) d/a, e/b , f/c are n G.P
Solve
Let a1, a2, a3,… be a G.P. such that a1 < 0, a1 + a2 = 4 and a3 + a4
= 16. If ∑ai = 4λ, i ∈ [i = 1, 9], then λ is equal to : JEE M 2020- Jan
(1) –171 (2) 171 (3) 511/3 (4) -513
Solve
Three positive numbers form an increasing GP. If the middle term in
this GP is doubled, then new numbers are in AP. Then, the common
ratio of the GP is JEE M 2014
(a) √2 + √3 (b) 3 + √2 (c) 2 - √3 (d) 2 + √3
Solve
Let a, b and c be in G.P. with common ratio r, where a ≠ 0 < r ≤
1/2. If 3a, 7b and 15c are the first three terms of an A.P., then the
4th term of this A.P. is : JEE M 2019- Apr
(1) a (2) 7/3 a (3) 2/3 a (4) 5a
Solve
If |x| < 1, |y| < 1 and x ≠ y, then the sum to infinity of the following series (x+y) + (x2+xy+y2) + (x3+x2y + xy2+y3)+..... JEE M 2020- Sept(a) (x + y + xy)/ (1+x)(1+y)(b) (x + y –xy)/ (1-x) (1-y)(c) (x + y –xy)/ (1+x) (1+y)(d) (x + y +xy)/ (1-x) (1-y)
Solve
Let x, y, z be positive real numbers such that x + y + z = 12 and
x3y4z5 = (0.1)(600)3. Then, x3 + y3 + z3 is equal to JEE M 2017 ‘(A) 342 (B) 216 (C) 258 (D) 270
Problems On AM- GM
Solve
The minimum value of 2sin x + 2cos x is :- JEE M 2020- Sept
(1) 21 - (1/√2) (2) 2-1 + √2 (3) 21 - √2 (4) 2-1 + (1/√2)
Solve
The sum of first 9 terms of the series 13/1 + (13 + 23)/(1 + 3) + (13 + 23 +
33)/(1 + 3 + 5) + ... is JEE M 2015
(a) 71 (b) 96 (c) 142 (d) 192
Solve
The greatest positive integer k, for which 49k + 1 is a factor of the
sum 49125 + 49124 + ... 492 + 49 + 1, is : JEE M 2020- Jan
(1) 32 (2) 60 (3) 63 (4) 65
Solve
Let a,b,c,d and p be any non zero distinct real numbers such that (a2 + b2
+ c2)p2 – 2(ab + bc + cd)p + (b2 + c2 + d2) = 0. Then : JEE M 2020- Sept
(1) a,c,p are in G.P. (2) a,c,p are in A.P.
(3) a,b,c,d are in G.P. (4) a,b,c,d are in A.P.