Vidaara.orgClass 10 · Mathematics
CodeVID-M10-05-WRD-01
Special Results & Word Problems on AP — 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.
Sum of first $n$ odd numbers $=$
- A.$n^2$
- B.$n(n+1)$
- C.$2n$
- D.$\tfrac{n(n+1)}{2}$
2.
Sum of first $n$ even numbers $=$
- A.$n^2$
- B.$n(n+1)$
- C.$2n$
- D.$\tfrac{n(n-1)}{2}$
3.
Numbers from $1$ to $100$ divisible by $5$:
- A.$10$
- B.$20$
- C.$25$
- D.$5$
4.
The middle angle of a triangle whose angles are in AP is:
- A.$45^\circ$
- B.$60^\circ$
- C.$90^\circ$
- D.$30^\circ$
5.
For an AP with an odd number of terms, the sum equals:
- A.first $\times n$
- B.middle term $\times n$
- C.last $\times n$
- D.$d\times n$
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Find the sum of the first $20$ odd numbers.
7.
Find the sum of the first $15$ even numbers.
8.
The angles of a triangle are in AP; find the middle angle.
9.
How many numbers between $1$ and $100$ are divisible by $7$?
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
A man saves $\textsf{Rs }100$ in the first month, increasing by $\textsf{Rs }50$ each month. Find his savings in the 12th month.
11.
Find the sum of all multiples of $4$ between $10$ and $100$.
12.
The angles of a quadrilateral are in AP with common difference $10^\circ$. Find them.
13.
How many two-digit numbers are divisible by $7$?
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
A sum of $\textsf{Rs }700$ is used for $7$ cash prizes, each $\textsf{Rs }20$ less than the preceding one. Find each prize.
15.
The sum of the 4th and 8th terms of an AP is $24$ and that of the 6th and 10th terms is $44$. Find the first term and common difference.
Answer Key
Section A — Multiple Choice Questions
- (A) $n^2$
- (B) $n(n+1)$
- (B) $20$
- (B) $60^\circ$
- (B) middle term $\times n$
Section B — Short Answer (2 marks)
- $400$.
- $240$.
- $60^\circ$.
- $14$.
Section C — Short Answer (3 marks)
- $\textsf{Rs }650$.
- $1188$.
- $75^\circ,85^\circ,95^\circ,105^\circ$.
- $13$.
Section D — Long Answer (5 marks)
- $\textsf{Rs }160,140,120,100,80,60,40$.
- $a=-13,\ d=5$.
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