Multiple Choice Questions (MCQ)
1 Mark Question
1.) If p-1, p+1 and 2p+3 are in A.P., then the value of p is
a) -2
b) 4
c) 0
d) 2
2.) If a, b, c form a A.P. with common difference d, then the value of a-2b-c is equal to
a) 2a+4d
b) 0
c) -2a-4d
d) -2a-3d
3.) The next term of the A.P. : √6, √24, √54 is :
a) √60
b) √96
c) √72
d) √216
4.) The next term of the AP: √7, √28, √63 is :
a) √70
b) √80
c) √97
d) √112
5.) The common difference of the A.P. whose nth term is given by an=3n+7, is :
a) 7
b) 3
c) 3n
d) 1
6.) The 11th term from the end of the A.P.:10,7,4,. . .,-62 is :
a) 25
b) 16
c) -32
d) 0
7.) The 13th term from the end of the A.P.: 20, 13, 6, -1, . . .,-148 is:
a) 57
b) -57
c) 64
d) -64
8.) The common difference of the A.P. whose nth term is given by an=5n-7 is:
a) -7
b) 7
c) 5
d) -2
9.) If the sum of first n terms of an A.P. be 3n²+n and its common difference is 6, then its first term is
a) 2
b) 3
c) 1
d) 4
Ans :
1.) c) 0
2.) c) -2a-4d
3.) b) √96
4.) d) √112
5.) b) 3
6.) c) -32
7.) d) -64
8.) c) 5
9.) d) 4
Assertion & Reason Question
1 Mark Questions
1.) Assertion (A) : a, b, c are in A.P. if and only if 2b=a+c.
Reason (R) : The sum of first n odd natural numbers is n².
a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explaination of Assertion (A).
b) Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explaination of Assertion (A).
c) Assertion (A) is true but Reason (R) is false.
d) Assertion (A) is false but Reason (R) is true.
Ans
1.) b) Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
1.) b) Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
3 Marks Questions
1.) How many terms are there in an A.P. whose first and fifth terms are -14 and 2 respectively and the last term is 62.
2.) Which term of the A.P. : 65, 61, 57, 53, . . . is the first negative term?
3.) The sum of first 15th terms of an A.P. is 750 and its first term is 15. Find its 20th term.
4.) Rohan repays his total loan of ₹ 1,18,000 by paying every month starting with the first installment of ₹ 1,000. If he increases the instalment by ₹ 100 every month, what amount will be paid by him in the 30th instalment? What amount of loan has he paid after 30th instalment?
5.) If pth term of an A.P. is q and qth term is p, then prove that its nth term is (p+q-n).
6.) In an A.P., the sum of first n terms is given by sn=6n-n². Find its 30th term.
7.) Find the common difference of an A.P. whose first term is 8, the last term is 65 and the sum of all its terms is 730.
Ans :
1.) n=20
2.) 18th term is the first negative term.
3.) a20=110
4.) ₹ 3,900, ₹73,500
5.) —
6.) a30=-53
7.) d=3
5 Marks Questions
1.) The ratio of the 11th term to 17th term of an A.P. is 3:4. Find the ratio of 5th term to 21st term of the same AP. Also, find the ratio of the sum of first 5 terms to that of first 21 terms.
2.) 250 logs are stacked in the following manner : 22 logs in the bottom row, 21 in the next row, 20 in the row next to it and so on (as shown by an example). In how many rows, are the 250 logs placed and how many logs are there in the top row?
3.) How many terms of the arithmetic progression 45, 39, 33, . . . must be taken so that their sum is 180? Explain the double answer.
4.) Solve the equation for x :
1+4+7+10+...+x=287
5.) Prerna saves ₹32 during the first month, ₹36 in the second month, and ₹40 in the third month. If she continues to save in this manner, in how many months she will save ₹ 2,000?
6.) The ratio of the 11th term to 18th term of an A.P. is 2:3. Find the ratio of 5th term to 21st term. Also, find the ratio of the sum of first 5 terms to that of first 21 terms.
7.) If the sum of first 6 terms of an A.P. is 36 and that of the first 16 terms is 256, find the sum of first 10 terms.
8.) Find the sum of integers between 100 and 200 which are (i) divisible by 9 (ii) not divisible by 9.
9.) Solve the equation :
-4+(-1)+2+5+...+x=437.
10.) The sum of first seven terms of an A.P. is 182. If its 4th term and the 17th term are in the ratio 1:5, find the A.P.
11.) The sum of first q terms of an A.P. is 63q-3q². If its pth term is -60, find the value of p. Also find the 11th term of this A.P.
Ans :
1.) a5:a21=3:7, s5:s21=25:189
2.) n=20, 3
3.) 10 or 6, Double answers are possible because there are some terms which are positive and some are negative.
4.) x=40
5.) 25 Months
6.) a5:a21=1:3, s5:s21=5:49
7.) s10=100
8.) (i) 1683 (ii) 13167
9.) x=50
10.) 2, 10, 18, 26, . . .
11.) p=21, a11=0
Case Study Based Question
Ravindra took a loan of ₹ 3,45,000 from a bank to buy a car, and decided to pay back by ₹ 2,000 at the end of the first month and then increased the instalment amount by ₹ 200 each month.
Based on the above, answer the following questions :
a) Find the amount paid by him in 10th instalment.
b) Find the total amount paid by him in first 10 instalments.
c) In how many instalments would he clear his total loan?
OR
d) What amount will he be able to clear in his first 45 instalments?
Ans :
a) ₹ 3,800
b) ₹ 29,000
c) n=50
OR
d) ₹ 2,88,000