Algebra - Progressions - Previous Year IPM/BBA Questions

The best way to prepare for Algebra - Progressions is by going through the previous year Algebra - Progressions questions for IPMAT - Indore. Here we bring you all previous year Algebra - Progressions IPMAT - Indore questions along with detailed solutions.

Click here for previous year questions of other topics.

It would be best if you clear your concepts before you practice previous year Algebra - Progressions questions for IPMAT - Indore.

ipm

1. IPMAT (I) 2023 QA MCQ | Algebra - Progressions IPMAT - Indore Question

Let a₁,a₂,a₃ be three distinct real numbers in geometric progression. If the equation a₁x² + 2a₂x + a₃ = 0 and b₁x² + 2b₂x + b₃ = 0 have a common root, then which of the following is necessarily true?

(a)
$\frac{a_{1}}{b_{1}}, \frac{a_{2}}{b_{2}}, \frac{a_{3}}{b_{3}}$ are in geometric progression
(b)
$\frac{b_{1}}{a_{1}}, \frac{b_{2}}{a_{2}}, \frac{b_{3}}{a_{3}}$ are in arithmetic progression
(c)
b₁, b₂, b₃ are in geometric progression
(d)
b₁, b₂, b₃ are in arithmetic progression

2. IPMAT (I) 2023 QA MCQ | Algebra - Progressions IPMAT - Indore Question

A rabbit is sitting at the base of a staircase which has 10 steps. It proceeds to the top of the staircase by climbing either one step at a time or two steps at a time. The number of ways it can reach the top is

(a)
34
(b)
89
(c)
144
(d)
55

3. IPMAT (I) 2022 QASA | Algebra - Progressions IPMAT - Indore Question

A new sequence is obtained from the sequence of positive integers (1,2,3,…) by deleting all the perfect squares. Then the 2022^nd term of the new sequence is ________.

Backspace

7 8 9 4 5 6 1 2 3 0 . -

Clear All Submit

4. IPMAT (I) 2022 QASA | Algebra - Progressions IPMAT - Indore Question

The 3^rd ,14^th and 69^th terms of an arithmetic progression form three distinct and consecutive terms of a geometric progression. If the next term of the geometric progression is the n^th term of the arithmetic progression, then n equals ________.

Backspace

7 8 9 4 5 6 1 2 3 0 . -

Clear All Submit

5. IPMAT (I) 2022 QASA | Algebra - Progressions IPMAT - Indore Question

The numbers −16, 2^x+3− 2^2x−1− 16, 2^2x−1+ 16 are in an arithmetic progression. Then x equals ________.

Backspace

7 8 9 4 5 6 1 2 3 0 . -

Clear All Submit

6. IPMAT (I) 2022 QA MCQ | Algebra - Progressions IPMAT - Indore Question

The sum of the first 15 terms in an arithmetic progression is 200 , while the sum of the next 15 terms is 350 . Then the common difference is

(a)
7/9
(b)
2/3
(c)
4/9
(d)
1/3

7. IPMAT (I) 2021 QASA | Algebra - Progressions IPMAT - Indore Question

The sum up to 10 terms of the series 1 × 3 + 5 × 7 + 9 × 11 + . . is

Backspace

7 8 9 4 5 6 1 2 3 0 . -

Clear All Submit

Answer: 5310

Text Explanation :

1 × 3 + 5 × 7 + 9 × 11 +

T₁ = 1 × 3
T₂ = 5 × 7 and so on

In each of these terms, the first number forms an AP whose first term is 1 and common difference is 4.
∴ first number of n^th term = 1 + (n - 1) × 4 = 4n - 3

In each of these terms, the second number forms an AP whose first term is 3 and common difference is 4.
∴ second number of n^th term = 3 + (n - 1) × 4 = 4n - 1

⇒ T_n = (4n - 3) × (4n - 1)
⇒ T_n = 16n² - 16n + 3

∴ ${\sum T_{n}}_{n = 1}^{10}$ = 16(1² + 2² + 3² + ... + 10²) + 16(1 + 2 + 3 + 3 + ... + 10) + (3 + 3 + 3 + ... + 3)

= $16 (\frac{10 \times 11 \times 21}{6})$ - $16 (\frac{10 \times 11}{2})$ + 30

= 6160 - 880 + 30 = 5310

Hence, 5310.

8. IPMAT (I) 2021 QASA | Algebra - Progressions IPMAT - Indore Question

It is given that the sequence {x_n} satisfies x₁ = 0, x_n+1 = x_n + 1 + $2 \sqrt{1 + x_{n}}$ for n = 1,2, . . . . . Then x₃₁ is

Backspace

7 8 9 4 5 6 1 2 3 0 . -

Clear All Submit

Answer: 960

Text Explanation :

x₁ = 0 = 1² - 1

x₂ = x₁ + 1 + $2 \sqrt{1 + x_{0}}$ = 0 + 1 + $2 \sqrt{1 + 0}$ = 3 = 2² - 1

x₃ = x₂ + 1 + $2 \sqrt{1 + x_{1}}$ = 3 + 1 + $2 \sqrt{1 + 3}$ = 8 = 3² - 1

∴ x_n = n² - 1

⇒ x₃₁ = 31² - 1 = 960

Hence, 960.

9. IPMAT (I) 2021 QA MCQ | Algebra - Progressions IPMAT - Indore Question

Let S_n be sum of the first n terms of an A.P. {a_n}. If S₅ = S₉ , what is the ratio of a₃ : a₅

(a)
9 : 5
(b)
5 : 9
(c)
3 : 5
(d)
5 : 3

10. IPMAT (I) 2020 QA MCQ | Algebra - Progressions IPMAT - Indore Question

If $\frac{1}{1^{2}}$ + $\frac{1}{2^{2}}$ + $\frac{1}{3^{2}}$ + ... upto ∞ = $\frac{π^{2}}{6}$ , then the value of $\frac{1}{1^{2}}$ + $\frac{1}{3^{2}}$ + $\frac{1}{5^{2}}$ + ... upto ∞ is

(a)
$\frac{π^{2}}{8}$
(b)
$\frac{π^{2}}{16}$
(c)
$\frac{π^{2}}{12}$
(d)
$\frac{π^{2}}{36}$

Answer: Option A

Text Explanation :

If $\frac{1}{1^{2}}$ + $\frac{1}{2^{2}}$ + $\frac{1}{3^{2}}$ + ... upto ∞ = $\frac{π^{2}}{6}$ , then the value of

Let X = $\frac{1}{1^{2}}$ + $\frac{1}{3^{2}}$ + $\frac{1}{5^{2}}$ + ... upto ∞

Adding and subtracting $\frac{1}{2^{2}}$ + $\frac{1}{4^{2}}$ + $\frac{1}{6^{2}}$ + ... upto ∞, we have

X = $\frac{1}{1^{2}}$ + $\frac{1}{2^{2}}$ + $\frac{1}{3^{2}}$ + ... upto ∞ - ( $\frac{1}{2^{2}}$ + $\frac{1}{4^{2}}$ + $\frac{1}{6^{2}}$ + ... upto ∞)

⇒ X = $\frac{π^{2}}{6}$ - $\frac{1}{2^{2}}$ ( $\frac{1}{1^{2}}$ + $\frac{1}{2^{2}}$ + $\frac{1}{3^{2}}$ + ... upto ∞)

⇒ X = $\frac{π^{2}}{6}$ - $\frac{1}{2^{2}}$ ( $\frac{π^{2}}{6}$ )

⇒ X = $\frac{π^{2}}{6}$ - $\frac{1}{4}$ ( $\frac{π^{2}}{6}$ )

⇒ X = $\frac{π^{2}}{8}$

Hence, option (a).

11. IPMAT (I) 2019 QASA | Algebra - Progressions IPMAT - Indore Question

If x, y, z are positive real numbers such that x¹² = y¹⁶ = z²⁴,and the three quantities 3log_yx, 4log_zy, nlog_xz are in arithmetic progression, then the value of n is

Backspace

7 8 9 4 5 6 1 2 3 0 . -

Clear All Submit

12. IPMAT (I) 2019 QASA | Algebra - Progressions IPMAT - Indore Question

Assume that all positive integers are written down consecutively from left to right as in 1234567891011...... The 6389^th digit in this sequence is

Backspace

7 8 9 4 5 6 1 2 3 0 . -

Clear All Submit

13. IPMAT (I) 2019 QA MCQ | Algebra - Progressions IPMAT - Indore Question

If (1 + x - 2x²)⁶ = A₀ + $\sum_{r = 1}^{12} A_{r} x^{r}$ , then value of A₂ + A₄ + A₆ + ... + A₁₂ is

(a)
31
(b)
32
(c)
30
(d)
29

14. IPMAT (I) 2019 QA MCQ | Algebra - Progressions IPMAT - Indore Question

The number of terms common to both the arithmetic progressions 2,5,8,11,...., 179 and 3,5,7,9,....., 101 is

(a)
17
(b)
16
(c)
19
(d)
15

Algebra - Progressions - Previous Year IPM/BBA Questions

Subscribe to our Newsletter