Sequence And Series · Mathematics · NDA

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MCQ (Single Correct Answer)

1
The value of the infinite product $${6^{{1 \over 2}}} \times {6^{{1 \over 2}}} \times {6^{{3 \over 8}}} \times {6^{{1 \over 4}}} \times ...$$ is
NDA 2015 Paper 2
2
If the nth term of an AP is $${{3 + n} \over 4}$$, then the sum of first 105 terms is
NDA 2015 Paper 2
3
If p, q, r are in one geometric progression and a, b, c are in another geometric progression, then ap, bq, cr are in
NDA 2015 Paper 2
4
What is the sum of n terms of the series $$\sqrt 2 + \sqrt 8 + \sqrt {18} + \sqrt {32} + ...$$?
NDA 2015 Paper 2
5
What is the greatest value of the positive integer n satisfying the condition?

$$1 + {1 \over 2} + {1 \over 4} + {1 \over 8} + .... + {1 \over {{2^{n - 1}}}} < 2 - {1 \over {1000}}$$
NDA 2016 Paper 2
6
How many geometric progressions is/are possible containing 27, 8 and 12 as three of its/their terms?
NDA 2016 Paper 2
7
What is the value of ab?
NDA 2016 Paper 2
8
What is the value of xyz?
NDA 2016 Paper 2
9
What is the value of pqr?
NDA 2016 Paper 2
10
What is the common difference of the AP, so that the product of the first, fourth and fifth terms is greatest?
NDA 2016 Paper 2
11
What is the first term of the AP, so that the product of the first, fourth and fifth terms is greatest?
NDA 2016 Paper 2
12
How many possible values can n have?
NDA 2016 Paper 2
13
What is the largest interior angle of the polygon?
NDA 2016 Paper 2
14
If $${x^{\ln \left( {{y \over z}} \right)}}.{y^{\ln {{(xz)}^2}}}.{z^{\ln \left( {{x \over y}} \right)}} = {y^{4\,\ln \,y}}$$ for any x > 1, y > 1 and z > 1, then which one of the following is correct?
NDA 2016 Paper 2
15
Which one of the following is correct?

x, y and z are
NDA 2016 Paper 1
16
Which one of the following is correct?

xy, yz and zx are
NDA 2016 Paper 1
17
The value of the product $${6^{{1 \over 2}}} \times {6^{{1 \over 4}}} \times {6^{{1 \over 8}}} \times {6^{{1 \over {16}}}} \times ....$$ up to infinite terms is
NDA 2017 Paper 2
18
A person is to count 4500 notes. Let an denote the number of notes he counts in the nth minute.

If a1 = a2 = a3 = ...... = a10 = 150, and a10, a11, a12, ..... are in AP with the common difference $$-$$2, then the time taken by him to count all the notes is
NDA 2017 Paper 2
19
If $$y = x + {x^2} + {x^3} + ...$$ up to infinite terms where x < 1, then which one of the following is correct?
NDA 2017 Paper 2
20
The value of $${1 \over {{{\log }_3}e}} + {1 \over {{{\log }_3}{e^2}}} + {1 \over {{{\log }_3}{e^4}}} + ......$$ up to infinite terms is
NDA 2017 Paper 2
21
If $$1.3 + {2.3^2} + {3.3^3} + ... + n{.3^n} = {{(2n - 1){3^a} + b} \over 4}$$, then a and b are respectively.
NDA 2017 Paper 2
22
If $${S_n} = nP + {{n(n - 1)Q} \over 2}$$, where, Sn denotes the sum of the first n terms of an AP, then the common difference is
NDA 2017 Paper 2
23
What is the sum of the series 0.3 + 0.33 + 0.333 + ..... n terms?
NDA 2017 Paper 1
24
If the sum of m terms of an AP is n and the sum of n terms is m, then the sum of (m + n) terms is
NDA 2017 Paper 1
25
The fifth term of an AP of n terms, whose sum is n2 $$-$$ 2n, is
NDA 2017 Paper 1
26
The sum of all the two-digit odd numbers is
NDA 2017 Paper 1
27
The sum of the first n terms of the series $${1 \over 2} + {3 \over 4} + {7 \over 8} + {{15} \over {16}} + ....$$ is equal to
NDA 2017 Paper 1
28
If an infinite GP has the first term x and the sum 5, then which one of the following is correct?
NDA 2018 Paper 2
29
The sum of the series $$3 - 1 + {1 \over 3} - {1 \over 9} + .......$$ is equal to
NDA 2018 Paper 2
30
Let Tr be the rth term of an AP for r = 1, 2, 3, ...... If for some distinct positive integers m and n we have Tm = 1 / n and Tn = 1 / m, then what is Tmn equal to?
NDA 2018 Paper 2
31
If the second term of a GP is 2 and the sum of its infinite terms is 8, then the GP is
NDA 2018 Paper 2
32
If a, b, c are in AP or GP or HP, then $${{a - b} \over {b - c}}$$ is equal to
NDA 2018 Paper 2
33
If the ratio of AM and GM of two positive numbers a and b is 5 : 3, then a : b is equal to
NDA 2018 Paper 1
34
If $$x = 1 - y + {y^2} - {y^3}....$$ up to infinite terms, where $$\left| y \right| < 1$$, then which one of the following is correct?
NDA 2018 Paper 1
35
What is the sum of all two-digit numbers, which when divided by 3 leave 2 as the remainder?
NDA 2018 Paper 1
36
The third term of a GP is 3. What is the product of the first five terms?
NDA 2018 Paper 1
37
If $$x,{3 \over 2},z$$ are in AP, x, 3, z are in GP, then which one of the following will be in HP?
NDA 2018 Paper 1
38
If 3rd, 8th and 13th terms of a GP are p, q and r respectively, then which one of the following is correct?
NDA 2019 Paper 2
39
Let Sn be the sum of the first n terms of an AP. If S2n = 3n + 14n2, then what is the common difference?
NDA 2019 Paper 2
40
How many two-digit numbers are divisible by 4?
NDA 2019 Paper 2
41
If the sum of first n terms of a series is (n + 12), then what is its third term?
NDA 2019 Paper 2
42
Let a, b, c be in AP and k $$\ne$$ 0 be a real number. Which of the following are correct?

1. ka, kb, kc are in AP

2. k $$-$$ a, k $$-$$ b, k $$-$$ c are in AP

3. $${a \over k}$$, $${b \over k}$$, $${c \over k}$$ are in AP

Select the correct answer using the code given below.
NDA 2019 Paper 2
43
Let m and n(m < n) be the roots of the equation x2 $$-$$ 16x + 39 = 0. If four terms p, q, r and s are inserted between m and n to form an AP, then what is the value of p + q + r + s?
NDA 2019 Paper 2
44
A geometric progression (GP) consists of 200 terms. If the sum of odd terms of the GP is m, and the sum of even terms of the GP is n, then what is its common ratio?
NDA 2019 Paper 2
45
What is the value of 1 $$-$$ 2 + 3 $$-$$ 4 + 5 $$-$$ ......... + 101?
NDA 2019 Paper 2
46
What is the nth term of the sequence 25, $$-$$ 125, 625, $$-$$ 3125, ........ ?
NDA 2019 Paper 1
47
The numbers 1, 5 and 25 can be three terms (not necessarily consecutive) of
NDA 2019 Paper 1
48
The sum of (p + q) th and (p $$-$$ q)th terms of an AP is equal to
NDA 2019 Paper 1
49
What is the fourth term of an AP of n terms whos sum is n(n + 1)?
NDA 2019 Paper 1
50

What is the remainder when $2^{120}$ is divided by 7?

NDA Mathematics 21 April 2024
51

If $a, b, c$ are in AP; $b, c, d$ are in GP; $c, d, e$ are in HP, then which of the following is/are correct?

1. $a, c,$ and $e$ are in GP

2. $\frac{1}{a}, \frac{1}{c}, \frac{1}{e}$ are in GP

Select the correct answer using the code given below:

NDA Mathematics 21 April 2024
52

If $a, b, c$ are in HP, then what is $\frac{1}{b-a} + \frac{1}{b-c}$ equal to?

1. $\frac{2}{b}$

2. $\frac{1}{a} + \frac{1}{c}$

3. $\frac{1}{2} \left( \frac{1}{a} + \frac{1}{b} + \frac{1}{c} \right)$

Select the correct answer using the code given below:

NDA Mathematics 21 April 2024
53
If the nth term of a sequence is $\frac{2 n+5}{7}$, then what is the sum of its first 140 terms? 
NDA Mathematics 3 September 2023
54
If (a + b), 2b, (b + c) are in HP, then which one of the following is correct?
NDA Mathematics 3 September 2023
55
Let t1, t2, t3 ... be in GP. What is $\rm \left(t_1 t_3 \ldots t_{21}\right)^{\frac{1}{11}}$ equal to ?
NDA Mathematics 3 September 2023
56
What is a+ a- a10 - a15 - a20 - a25 + a30 + a34 equal to ?
NDA Mathematics 3 September 2023
57
What is $\displaystyle \sum_{n=1}^{34} a_n$ equal to ?
NDA Mathematics 3 September 2023
58
If logxa, ax and logbx are in GP, then what is x equal to ? 
NDA Mathematics 16 April 2023
59
If $2^{\frac{1}{c}}, 2^{\frac{b}{a c}}, 2^{\frac{1}{a}}$ are in GP, then which one of the following is correct ? 
NDA Mathematics 16 April 2023
60
The first and the second terms of an AP are $\frac{5}{2}$ and $\frac{23}{12}$ respectively. If nth term is the largest negative term, what is the value of n ? 
NDA Mathematics 16 April 2023
61
In an AP, the first term is x and the sum of the first n terms is zero. What is the sum of next m terms ?
NDA Mathematics 16 April 2023
62
p, q, r and s are in AP such that p + s = 8 and qr = 15. What is the difference between largest and smallest numbers ?  
NDA Mathematics 16 April 2023
63
If G is the geometric mean of numbers 1, 2, 22, 23,.....2n-1, then what is the value of 1 + 2log2G ?
NDA Mathematics 16 April 2023
64
If H is the harmonic mean of numbers 1, 2, 22, 23, ......2n-1 what is n/H equal to ? 
NDA Mathematics 16 April 2023
65

Consider the following statements :

1. 2 + 4 + 6 + ........ + 2n = n2 + n

2. The expression n2 + n + 41 always gives a prime number for every natural number n

Which of the above statements is/are correct ?

NDA Mathematics 4 September 2022
66
What is the ratio of the first term of A to that of B ?
NDA Mathematics 4 September 2022
67
What is the ratio of their 10th terms ?
NDA Mathematics 4 September 2022
68
If d is the common difference of A, and D is the common difference of B, then which one of the following is always correct ?
NDA Mathematics 4 September 2022
69

If $\displaystyle\sum_{x=2}^n$​f(x) = 2044, then what is the value of n ?

NDA Mathematics 4 September 2022
70
Let x be the mean of squares of first n natural numbers and y be the square of mean of first n natural numbers. If $\frac{\text{x}}{\text{y}} = \frac{55}{42}$, then what is the value of n ?
NDA Mathematics 4 September 2022
71

If a, b, c are in GP where a > 0, b > 0, c > 0, then which of the following are correct?

1. a2, b2, c2 are in GP

2. $\frac{1}{a}, \frac{1}{b}, \frac{1}{c}$ are in GP

3. $\sqrt {a}, \sqrt{b}, \sqrt{c} $ are in GP

Select the correct answer using the code given below :

NDA Mathematics 10 April 2022
72
If $\frac{a+b}{2}, b, \frac{b+c}{2}$ are in HP, then which one of the following is correct?
NDA Mathematics 10 April 2022
73
If the sum of the first 9 terms of an AP is equal to sum of the first 11 terms, then what is the sum of the first 20 terms ?
NDA Mathematics 10 April 2022
74
If the 5th term of an AP is $\frac{1}{10}$ and its 10th term is $\frac{1}{5},$ then what is the sum of first 50 terms ?
NDA Mathematics 10 April 2022
75
What is the arithmetic mean of 50 terms of an AP with first term 4 and common difference 4 ?
NDA Mathematics 10 April 2022
76
What is the mean of the marks ?
NDA Mathematics 10 April 2022
77
What is the median of the marks?
NDA Mathematics 10 April 2022
78
What is the sum of the deviations measured from the median?
NDA Mathematics 10 April 2022
79
If the first term of an AP is 2 and the sum of the first five terms is equal to one-fourth of the sum of the next five terms, then what is the sum of the first ten terms?
NDA Mathematics 18 April 2021
80

Consider the following statements:

1. If each term of a GP is multiplied by same non-zero number, then the resulting sequence is also a GP.

2. If each term of a GP is divided by same non-zero number, then the resulting sequence is also a GP.

Which of the above statements is/are correct?

NDA Mathematics 18 April 2021
81
If x2, x, -8 are in AP, then which one of the following is correct?
NDA Mathematics 18 April 2021
82
The third term of a GP is 3. What is the product of its first five terms?
NDA Mathematics 18 April 2021
83
Let x be the HM and y be the GM of two positive numbers m and n. If 5x = 4y, then which one of the following is correct?
NDA Mathematics 18 April 2021
84
The geometric mean of a set of observations is computed as 10. The geometric mean obtained when each observations xi is replaced by $\rm 3x_i^4$ is
NDA Mathematics 18 April 2021
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