Sequences and Series is an important topic in the Mathematics section in VITEEE exam. Practising this topic will increase your score overall and make your conceptual grip on VITEEE exam stronger.
This article gives you a full set of VITEEE PYQs for Sequences and Series with explanations for effective preparation. Practice of VITEEE Mathematics PYQs including Sequences and Series questions regularly will improve accuracy, speed, and confidence in the VITEEE 2026 exam.
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VITEEE PYQs for Sequences and Series with Solutions
1.
The sum of the first n terms of the series $$ 1^2 + 2 \cdot 2^2 + 3^2 + 2 \cdot 4^2 + 5^2 + 2 \cdot 6^2 + \cdots $$ is $$ \frac{n(n + 1)^2}{2} \quad \text{when n is even. When n is odd the sum is} $$- \( \left[ \frac{n(n + 1)}{2} \right]^2 \)
- \( \frac{n^2(n + 1)}{2} \)
- \( \frac{n(n + 1)^2}{4} \)
- \( \frac{3n(n + 1)}{2} \)
2.
What is the total marks obtained by Meera in all the subjects?- 448
- 580
- 470
- 74.67
3.
The fourth, seventh, and tenth terms of a G.P. are \( p, q, r \) respectively, then:- \( p^2 = q^2 + r^2 \)
- \( q^2 = pr \)
- \( p^2 = qr \)
- \( pqr + pq + 1 = 0 \)
4.
For which toy category has there been a continuous increase in production over the years?- Ludo
- Chess
- Monopoly
- Carrom
5.
The middle term in the expansion of \[ (10x + x^{10})^{10} \] {is:}- \( 10C5 \)
- \( 10C6 \)
- \( 10C5 x^{10} \)
- \( 10C5 x^{10} \)
6.
If
and $(A + B)^2 = A^2 + B^2$ then $x + y$ is:
- 2
- 3
- 4
- 5
7.
Find the missing number in the sequence: \[ 285, 253, 221, 189, ? \]- \( 150 \)
- \( 182 \)
- \( 157 \)
- \( 156 \)
8.
What is the approximate percentage increase in the production of Monopoly from 1993 to 1995?- \( 10 \)
- \( 20 \)
- \( 30 \)
- \( 25 \)
9.
The radius of the base of a cone is increasing at the rate of 3 cm/minute and the altitude is decreasing at the rate of 4 cm/minute. The rate of change of lateral surface when the radius is 7 cm and altitude is 24 cm is:- \( 54 \pi \, \text{cm}^2/\text{min} \)
- \( 7 \pi \, \text{cm}^2/\text{min} \)
- \( 27 \pi \, \text{cm}^2/\text{min} \)
- None of these
10.
The area of the parallelogram whose diagonals are \[ \mathbf{d_1} = \frac{3}{2} \hat{i} + \frac{1}{2} \hat{j} - \hat{k}, \quad \mathbf{d_2} = 2 \hat{i} - 6 \hat{j} + 8 \hat{k} \] is:- \( 5\sqrt{3} \)
- \( 5\sqrt{2} \)
- \( 25\sqrt{3} \)
- \( 25\sqrt{2} \)
11.
A series is given, with one term missing. Choose the correct alternative from the given ones that will complete the series. \[ 5, 11, 24, 51, 106, \_ ? \]- 122
- 217
- 120
- 153
12.
If \( |\mathbf{a}| = 3 \), \( |\mathbf{b}| = 4 \), then the value of \( \lambda \) for which \( \mathbf{a} + \lambda \mathbf{b} \) is perpendicular to \( \mathbf{a} - \lambda \mathbf{b} \) is:- \( \frac{9}{16} \)
- \( \frac{3}{4} \)
- \( \frac{3}{2} \)
- \( \frac{4}{3} \)
13.
What is the average marks obtained by these seven students in History? (rounded off to two digits)- 72.86
- 27.32
- 24.86
- 29.14
14.
If \[ \frac{1}{q + r}, \quad \frac{1}{r + p}, \quad \frac{1}{p + q} \] {are in A.P., then:}- \( p, q, r \) are in A.P.
- \( p^2, q^2, r^2 \) are in A.P.
- \( \frac{1}{p}, \frac{1}{q}, \frac{1}{r} \) are in A.P.
- \( p + q + r \) are in A.P.
15.
The determinant of the matrix:
is:
- 0
- \( abc \)
- \( 4a^2b^2c^2 \)
- None of these
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