Class 11 Mathematics Sequences and Series MCQs

Question. 5^1+x + 5^1–x, a/2 , 5^2x + 5^–2x are in A.P., then the value of a is:    
(a) a < 12
(b) a ≤ 12
(c) a ≥ 12
(d) none of these

Answer :  D
 

Question. The series ( √2 +1),1,( √2 -1) ... is in :    
(a) A.P.
(b) G.P.
(c) H.P.
(d) none of these

Answer :  B


Question. Which term of the G.P. 2, 2 2, 4,.....is 64 ?   
(a) 9th term
(b) 7th term
(c) 4th term
(d) 11th term

Answer :  D
 

Question. Three numbers form an increasing G.P. If the middle number is doubled, then the new numbers are in A.P. The common ratio of the G.P. is:    
(a) 2 – √3
(b) 2 +√3
(c) √3 – 2
(d) 3+ √2

Answer :  B

Question. The first and eight terms of a G.P. are x–4 and x⁵² respectively. If the second term is xt, then t is equal to:   
(a) –13
(b) 4
(c) 5/2
(d) 3

Answer :  B


Question. If the jth term and kth term of an A.P. are k and j respectively, the ( k + j) th term is:?    
(a) 0
(b) 1
(c) k + j + 1
(d) k + j –1

Answer :  A


Question. The product of n positive numbers is unity, then their sum is :    
(a) a positive integer
(b) divisible by n
(c) equal to n + 1/n
(d) never less than n

Answer :  D


Question. An infinite G.P has first term x and sum 5, then    
(a) x < – 10
(b) – 10 < x < 0
(c) 0 < x < 10
(d) x > 10

Answer :  C
 

Question. The arithmetic mean of three observations is x.     
If the values of two observations are y, z; then what is the value of the third observation ?
(a) x
(b) 2x – y – z
(c) 3x – y – z
(d) y + z – x

Answer :  C
 

Question. What is the sum of the series 1-1/2 + 1/4 - 1/8    
(a) 1/2
(b) 3/4
(c) 3/2
(d) 2/3

Answer :  D

Question. In a G.P. of even number of terms, the sum of all terms is 5 times the sum of the odd terms. The common ratio of the G.P. is   
(a) -4/5  
(b) 1/5
(c) 4
(d) None of these

Answer :  C


Question. If in A.P., S_n = qn2 and Sm = qm², where S_r denotes the sum of r terms of the A.P., then Sq equals    
(a) q³/2
(b) mnq
(c) q³
(d) (m + n)q²
Answer :  C
 

Question. If tn denotes the n th term of the series 2 + 3 + 6 + 11 + 18 + ... then t50 is    
(a) 492 – 1
(b) 492
(c) 502 + 1
(d) 492 + 2

Answer :  D


Question. The sum to 200 terms of the series 1 + 4 + 6 + 5 +11 + 6 + .......... is     
(a) 31,200
(b) 29,800
(c) 30,200
(d) None of these

Answer :  C


Question. If the sum of the series 54 + 51 + 48 + ........... is 513, then the number of terms are     
(a) 18
(b) 20
(c) 17
(d) None of these

Answer :  A
 

Question. The sum of 11 terms of an A.P. whose middle term is 30,     
(a) 320
(b) 330
(c) 340
(d) 350

Answer :  B


Question. If the sum of the first 2n terms of 2, 5, 8, ....... is equal to the sum of the first n terms of 57, 59,61......., then n is equal to    
(a) 10
(b) 12
(c) 11
(d) 13

Answer :  C


Question. There are four arithmetic means between 2 and –18. The means are    
(a) –4, –7, –10, –13
(b) 1, –4, –7, –10
(c) –2, –5, –9, –13
(d) –2, –6, –10, –14

Answer :  D


Question. 2, 3, 5 are the following terms of an A.P.:    
(a) 2nd, 3rd, and 5th
(b) 4th, 9th and 25th
(c) 4th, 6th, and 10th
(d) none of the above

Answer :  D
 

Question. The first term of an infinite G.P. is 1 and each term is twice the sum of the succeeding terms. then the sum of the series is    
(a) 2
(b) 3
(c) 3/2
(d) 5/2

Answer :  C
 

Question. The sum of the first nine terms of an arithmetic progression is 171. Which one of the following statements is not correct about this A.P.?   
(a) The sum of the first and the ninth terms cannot be determined
(b) No term of the A.P. can be determined
(c) The first term of the A.P. cannot be  determined
(d) The common difference cannot be determined

Answer :  A
 

Question. If the nth term of an arithmetic progression is 3n + 7, then what is the sum of its first 50 terms?    
(a) 3925
(b) 4100
(c) 4175
(d) 8200

Answer :  C


Question. What is the value of 91/3. 91/19. 91/27...... ∞ ?    
(a) 9
(b) 3
(c) 91/3
(d) 1

Answer :  B
 

Question. The minimum value of the expression    
3^x + 3^{1 – x}, x ∈ R, is
(a) 0
(b) 1/3
(c) 3
(d) 2√3

Answer :  D
 

Question. At the end of each year the value of a certain machine has depreciated by 20% of its value at the beginning of that year. If its initial value was `₹1250, the value at the end of 5 years is    
(a) 409.6
(b) 409
(c) 408
(d) 409.5

Answer :  A


Question. An even number of AM are inserted between two numbers whose sum is 13/6. If the sum of means exceeds their number by 1, what is the number of means?    
(a) 8
(b) 18
(c) 12
(d) 6

Answer :  C
 

Question. There are four numbers of which the first three are in G.P. and the last three are in A.P., whose common difference is 6. If the first and the last numbers are equal then two other numbers are
(a) –2, 4
(b) –4, 2
(c) 2, 6
(d) none

Answer :  B


Question. If in a series Sn = an2 + bn + c, Where Sn denotes the sum of n terms, then    
(a) The series is always arithmetic  
(b) The series is arithmetic from the second term onwards
(c) The series may or may not be arithmetic
(d) The series cannot be arithmetic

Answer :  B


Question. If the sum of the first ten terms of an arithmetic progression is four times the sum of the first five terms, then the ratio of the first term to the common difference is :   
(a) 1 : 2
(b) 2 : 1
(c) 1 : 4
(d) 4 : 1

Answer :  B


Question. If a, b and c are three positive numbers in an arithmetic progression, then:     
(a) ac > b²
(b) b² > a + c
(c) ab + bc ≤ 2ac
(d) ab + bc ≥ 2ac

Answer :  D