Vidaara.orgClass 11 · Mathematics
CodeVID-M11-08-SS-01
Special Series — Assignment
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- All questions are compulsory.
- Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
- Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions
5 × 1 = 5 marks
1.
$\displaystyle\sum_{k=1}^{n} k=$
- A.$n^2$
- B.$\tfrac{n(n+1)}{2}$
- C.$\tfrac{n(n+1)(2n+1)}{6}$
- D.$n!$
2.
$\displaystyle\sum_{k=1}^{n} k^2=$
- A.$\tfrac{n(n+1)}{2}$
- B.$\tfrac{n(n+1)(2n+1)}{6}$
- C.$\left[\tfrac{n(n+1)}{2}\right]^2$
- D.$n^3$
3.
$\displaystyle\sum_{k=1}^{n} k^3=$
- A.$\tfrac{n(n+1)(2n+1)}{6}$
- B.$\left[\tfrac{n(n+1)}{2}\right]^2$
- C.$\tfrac{n(n+1)}{2}$
- D.$n^4$
4.
$1+2+\dots+100=$
- A.$5000$
- B.$5050$
- C.$10100$
- D.$2550$
5.
$\displaystyle\sum_{k=1}^{5} k^2=$
- A.$30$
- B.$55$
- C.$25$
- D.$15$
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Find $1+2+\dots+50$.
7.
Find $\displaystyle\sum_{k=1}^{10} k^2$.
8.
Find $\displaystyle\sum_{k=1}^{4} k^3$.
9.
Find the sum of the first $20$ even natural numbers.
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
Find $1^2+2^2+\dots+15^2$.
11.
Find $1^3+2^3+\dots+10^3$.
12.
Find $\displaystyle\sum_{k=1}^{n}(2k-1)$.
13.
Find $1\cdot2+2\cdot3+\dots+n(n+1)$.
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
Find the sum to $n$ terms of $1\cdot2\cdot3+2\cdot3\cdot4+3\cdot4\cdot5+\dots$
15.
Find the sum to $n$ terms of the series whose $n$th term is $n(n+1)$.
Answer Key
Section A — Multiple Choice Questions
- (B) $\tfrac{n(n+1)}{2}$
- (B) $\tfrac{n(n+1)(2n+1)}{6}$
- (B) $\left[\tfrac{n(n+1)}{2}\right]^2$
- (B) $5050$
- (B) $55$
Section B — Short Answer (2 marks)
- $1275$.
- $385$.
- $100$.
- $420$.
Section C — Short Answer (3 marks)
- $1240$.
- $3025$.
- $n^2$.
- $\dfrac{n(n+1)(n+2)}{3}$.
Section D — Long Answer (5 marks)
- $\dfrac{n(n+1)(n+2)(n+3)}{4}$.
- $\dfrac{n(n+1)(n+2)}{3}$.
Generated by Vidaara.org · Assignment VID-M11-08-SS-01 · vidaara.org