Basic Definitions — JEE Main Mathematics MCQs with Solutions
Free JEE Main Mathematics Basic Definitions MCQs with step-by-step solutions (9 questions). Part of Sequences and Series. Practise online on Prepizo — no login needed.
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Questions with solutions
Q1 — Basic Definitions · easy · theory
A sequence is best described as a function whose domain is:
A. the empty set
B. the set of rational numbers
C. the set of real numbers
D. the set of natural numbers ✓ Correct
Solution: A sequence is a function $f:\mathbb{N} \to \mathbb{R}$; its values $f(1), f(2), \dots$ are the terms.
Q2 — Basic Definitions · easy · theory
A series is obtained from a sequence by:
A. multiplying its terms
B. reversing its terms
C. adding its terms ✓ Correct
D. taking reciprocals of its terms
Solution: If $a_1, a_2, \dots$ is a sequence, the expression $a_1 + a_2 + \dots$ is the corresponding series.
Q3 — Basic Definitions · easy · numerical
If the general term of a sequence is $T_n = 2n + 3$, then $T_5$ equals:
A. $11$
B. $10$
C. $15$
D. $13$ ✓ Correct
Solution: $T_5 = 2(5) + 3 = 13$.
Q4 — Basic Definitions · easy · numerical
For the sequence with $T_n = n^2 - n$, the value of $T_4$ is:
A. $8$
B. $16$
C. $12$ ✓ Correct
D. $20$
Solution: $T_4 = 4^2 - 4 = 16 - 4 = 12$.
Q5 — Basic Definitions · easy · numerical
The general term of the sequence $\tfrac12, \tfrac23, \tfrac34, \tfrac45, \dots$ is:
A. $\dfrac{n}{n-1}$
B. $\dfrac{n}{n+1}$ ✓ Correct
C. $\dfrac{n+1}{n}$
D. $\dfrac{1}{n+1}$
Solution: Each term is $\tfrac{n}{n+1}$ for $n = 1, 2, 3, \dots$
Q6 — Basic Definitions · medium · numerical
Which term of the sequence $T_n = 4n - 3$ is equal to $45$?
A. $13$-th
B. $10$-th
C. $11$-th
D. $12$-th ✓ Correct
Solution: $4n - 3 = 45 \Rightarrow 4n = 48 \Rightarrow n = 12$.
Q7 — Basic Definitions · medium · numerical
For the sequence $a_1 = 2$ and $a_n = 3a_{n-1}$, the value of $a_4$ is:
A. $18$
B. $162$
C. $48$
D. $54$ ✓ Correct
Solution: $a_2 = 6,\ a_3 = 18,\ a_4 = 54$ (equivalently $2\cdot 3^3 = 54$).
Q8 — Basic Definitions · medium · numerical
The $5$-th term of the sequence whose $n$-th term is $T_n = \dfrac{n(n+1)}{2}$ (triangular numbers) is:
A. $21$
B. $10$
C. $15$ ✓ Correct
D. $12$
Solution: $T_5 = \tfrac{5 \cdot 6}{2} = 15$.
Q9 — Basic Definitions · medium · theory
For a sequence, the statement "$S_n - S_{n-1} = T_n$" is valid for:
A. no value of $n$
B. all $n \ge 1$ automatically
C. only even $n$
D. $n \ge 2$, with $T_1 = S_1$ ✓ Correct
Solution: The difference formula gives $T_n$ for $n \ge 2$; the first term is found separately as $T_1 = S_1$.