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Sequences and Series

462 Questions Start JEE Mains Test
All Exams JEE Mains JEE Advanced TS-EAMCET AP-EAPCET BITSAT
1985 Q451 JEE Advanced MCQ
14 Mar 2026
If $a,\,b,\,c$ are in GP., then the equations $\,\,\alpha {x^2} + 2bx + c = 0$ and $d{x^2} + 2ex + f = 0$ have a common root if ${d \over a},\,{e \over b},{f \over c}$ are in ________.
A.
A.P.
B.
GP.
C.
H.P.
D.
none of these
1985 Q452 JEE Advanced Numerical
14 Mar 2026
Find the sum of the series : $$\sum\limits_{r = 0}^n {{{\left( { - 1} \right)}^r}\,{}^n{C_r}\left[ {{1 \over {{2^r}}} + {{{3^r}} \over {{2^{2r}}}} + {{{7^r}} \over {{2^{3r}}}} + {{{{15}^r}} \over {{2^{4r}}}}..........up\,\,to\,\,m\,\,terms} \right]} $$
1984 Q453 JEE Advanced Numerical
14 Mar 2026
If $n$ is a natural number such that
$n = {p_1}{}^{{\alpha _1}}{p_2}{}^{{\alpha _2}}.{p_3}{}^{{\alpha _3}}........{p_k}{}^{{\alpha _k}}$ and ${p_1},{p_2},\,\,......,\,{p_k}$ are distinct primes, then show that $In$ $n \ge k$ $in$ 2
1984 Q454 JEE Advanced Numerical
14 Mar 2026
If $a > 0,\,b > 0$ and $\,c > 0,$ prove that $\,c > 0,$ prove that $\left( {a + b + c} \right)\left( {{1 \over a} + {1 \over b} + {1 \over c}} \right) \ge 9$
1984 Q455 JEE Advanced Numerical
14 Mar 2026
The sum of integers from 1 to 100 that are divisible by 2 or 5 is ............
1983 Q456 JEE Advanced MCQ
14 Mar 2026
The rational number, which equals the number $2\overline {357} $ with recurring decimal is
A.
${{2355} \over {1001}}$
B.
${{2379} \over {997}}$
C.
${{2355} \over {999}}$
D.
none of these
1983 Q457 JEE Advanced Numerical
14 Mar 2026
Find three numbers $a,b,c$ between $2$ and $18$ such that
(i) their sum is $25$
(ii) the numbers $2,$ $a, b$ are consecutive terms of an A.P. and
(iii) the numbers $b,c,18$ are consecutive terms of a G.P.
1982 Q458 JEE Advanced MCQ
14 Mar 2026
The third term of a geometric progression is 4. The product of the first five terms is
A.
43
B.
45
C.
44
D.
none of these
1982 Q459 JEE Advanced MCQ
14 Mar 2026
If $x,\,y$ and $z$ are $pth$, $qth$ and $rth$ terms respectively of an A.P. and also of a G.P., then ${x^{y - z}}\,{y^{z - x}}\,{z^{x - y}}$ is equal to :
A.
$xyz$
B.
$0$
C.
$1$
D.
None of these
1982 Q460 JEE Advanced Numerical
14 Mar 2026
Does there exist a geometric progression containing $27, 8$ and $12$ as three of its terms? If it exits, how many such progressions are possible ?
1980 Q461 JEE Advanced Numerical
14 Mar 2026
The interior angles of a polygon are in arithmetic progression. The smallest angle is ${120^ \circ }$, and the common difference is ${5^ \circ }$, Find the number of sides of the polygon.
1979 Q462 JEE Advanced Numerical
14 Mar 2026
The harmonic mean of two numbers is 4.Their arithmetic mean $A$ and the geometric mean $G$ satisfy the relation. $2A + {G^2} = 27$