Sequences and Series

JEE Main · Mathematics · 14 past questions

These are the board's own papers. 246 more board questions reprinted in the books we use in class are for signed-in students: sign in.

Q1 2026 2 Apr Shift 1

Let A be the set of first 101 terms of an A.P., whose first term is 1 and the common difference is 5 and let…
Q2 2026 2 Apr Shift 1

If $\sum_{k=1}^{n} a_k = 6n^3$, then $\sum_{k=1}^{6}\left(\dfrac{a_{k+1}-a_k}{36}\right)^2$ is equal to…
Q3 2026 2 Apr Shift 2

Let $a_1, a_2, a_3, \ldots$ be an A.P. and $g_1 = a_1, g_2, g_3, \ldots$ be an increasing G.P. If…
Q4 2026 2 Apr Shift 2

The sum $\frac{1^3}{1}+\frac{1^3+2^3}{1+3}+\frac{1^3+2^3+3^3}{1+3+5}+\dots$ up to 8 terms, is…
Q5 2026 4 Apr Shift 1

The first term of an A.P. of 30 non-negative terms is $\frac{10}{3}$. If the sum of this A.P. is the cube of…
Q6 2026 5 Apr Shift 1

Let the sum of the first $n$ terms of an A.P. be $3n^2 + 5n$. Then the sum of squares of the first 10 terms…
Q7 2026 5 Apr Shift 1

$\sum_{n=1}^{10}\left(\dfrac{528}{n(n+1)(n+2)}\right)$ is equal to…
Q8 2026 5 Apr Shift 2

Let $\alpha, \beta$ be the roots of the equation $x^2 - x + p = 0$ and $\gamma, \delta$ be the roots the…
Q9 2026 5 Apr Shift 2

If the sum of the first 10 terms of the series…
Q10 2026 5 Apr Shift 2

Let $A_1, A_2, A_3, \dots, A_{39}$ be 39 arithmetic means between the numbers 59 and 159. Then the mean of…
Q11 2026 6 Apr Shift 1

The value of $1^3-2^3+3^3-\ldots+15^3$ is…
Q12 2026 6 Apr Shift 1

The sum of the first ten terms of an A.P. is 160 and the sum of the first two terms of a G.P. is 8. If the…
Q13 2026 6 Apr Shift 1

For the functions $f(\theta)=\alpha\tan^2\theta+\beta\cot^2\theta$, and…
Q14 2026 6 Apr Shift 2

The sum $1+\frac12(1^2+2^2)+\frac13(1^2+2^2+3^2)+\dots$ upto 10 terms is equal to…