Other Maths · JEE Main previous year questions

405 questions asked across 18 exam years, newest first

Year-wise papers Topic-wise questions

Practise this topic

2025 40 questions

Q132025 · 4 Apr 2025 · Shift 2
If $1^{2} \cdot (^{15} C_{1}) + 2^{2} \cdot (^{15} C_{2}) + 3^{2} \cdot (^{15} C_{3}) + \dots + 1 5^{2} \cdot (^{15} C_{15}) = 2^{m} \cdot 3^{n} \cdot 5^{k}$ , where $m, n, k \in N$ , then $m + n + k$ is equal to :
1. A.20
2. B.19
3. C.18
4. D.21
Show answer
Answer: B
Q242025 · 4 Apr 2025 · Shift 2· Numerical answer
If $α$ is a root of the equation $x^{2} + x + 1 = 0$ and $\sum_{k = 1}^{n} (α^{k} + \frac{1}{α ^{k}})^{2} = 20$ , then n is equal to ____ .
Show answer
Answer: 11
Q32025 · 3 Apr 2025 · Shift 1
The sum $1 + 3 + 11 + 25 + 45 + 71 + \dots$ upto 20 terms, is equal to
1. A.7240
2. B.8124
3. C.7130
4. D.6982
Show answer
Answer: A
Q102025 · 3 Apr 2025 · Shift 1
Let a line passing through the point $(4, 1, 0)$ intersect the line $L_{1} : \frac{x - 1}{2} = \frac{y - 2}{3} = \frac{z - 3}{4}$ at the point $A (α, β, γ)$ and the line $L_{2} : x - 6 = y = - z + 4$ at the point $B (a, b, c)$ . Then $1 α a 0 β b 1 γ c$ is equal to
1. A.16
2. B.6
3. C.8
4. D.12
Show answer
Answer: C
Q162025 · 3 Apr 2025 · Shift 1
If $\sum_{r = 1}^{9} (\frac{r + 3}{2 ^{r}}) \cdot^{9} C_{r} = α (\frac{3}{2})^{9} - β$ , $α, β \in N$ , then $(α + β)^{2}$ is equal to
1. A.27
2. B.81
3. C.18
4. D.9
Show answer
Answer: B
Q172025 · 3 Apr 2025 · Shift 1
Let $z \in C$ be such that $\frac{z ^{2} + 3 i}{z - 2 + i} = 2 + 3 i$ . Then the sum of all possible values of $z^{2}$ is :
1. A. $- 19 + 2 i$
2. B. $- 19 - 2 i$
3. C. $19 - 2 i$
4. D. $19 + 2 i$
Show answer
Answer: B
Q32025 · 3 Apr 2025 · Shift 2
Each of the angles $β$ and $γ$ that a given line makes with the positive $y$ - and $z$ -axes, respectively, is half of the angle that this line makes with the positive $x$ -axes. Then the sum of all possible values of the angle $β$ is
1. A. $\frac{π}{2}$
2. B. $π$
3. C. $\frac{3 π}{4}$
4. D. $\frac{3 π}{2}$
Show answer
Answer: C
Q72025 · 3 Apr 2025 · Shift 2
Consider the lines $x (3 λ + 1) + y (7 λ + 2) = 17 λ + 5$ , $λ$ being a parameter, all passing through a point $P$ . One of these lines (say $L$ ) is farthest from the origin. If the distance of $L$ from the point $(3, 6)$ is $d$ , then the value of $d^{2}$ is
1. A. $10$
2. B. $20$
3. C. $15$
4. D. $30$
Show answer
Answer: B
Q142025 · 3 Apr 2025 · Shift 2
The distance of the point $(7, 10, 11)$ from the line $\frac{x - 4}{1} = \frac{y - 4}{0} = \frac{z - 2}{3}$ along the line $\frac{x - 9}{2} = \frac{y - 13}{3} = \frac{z - 17}{6}$ is
1. A. $16$
2. B. $12$
3. C. $18$
4. D. $14$
Show answer
Answer: D
Q192025 · 3 Apr 2025 · Shift 2
The sum $1 + \frac{1 + 3}{2 !} + \frac{1 + 3 + 5}{3 !} + \frac{1 + 3 + 5 + 7}{4 !} + \dots$ upto $\infty$ terms, is equal to
1. A. $3 e$
2. B. $2 e$
3. C. $4 e$
4. D. $6 e$
Show answer
Answer: B
Q232025 · 3 Apr 2025 · Shift 2· Numerical answer
Let $(1 + x + x^{2})^{10} = a_{0} + a_{1} x + a_{2} x^{2} + \dots + a_{20} x^{20}$ . If $(a_{1} + a_{3} + a_{5} + \dots + a_{19}) - 11 a_{2} = 121 k$ , then $k$ is equal to_________.
Show answer
Answer: 239
Q22025 · 2 Apr 2025 · Shift 1
Let the vertices $Q$ and $R$ of the triangle $PQR$ lie on the line $\frac{x + 3}{5} = \frac{y - 1}{2} = \frac{z + 4}{3}$ , $QR = 5$ and the coordinates of the point $P$ be $(0, 2, 3)$ . If the area of the triangle $P QR$ is $\frac{m}{n}$ then :
1. A. $2 m - 521 n = 0$
2. B. $m - 521 n = 0$
3. C. $5 m - 212 n = 0$
4. D. $5 m - 221 n = 0$
Show answer
Answer: A
Q112025 · 2 Apr 2025 · Shift 1
The largest $n \in N$ such that $3^{n}$ divides $50!$ is :
1. A.22
2. B.20
3. C.21
4. D.23
Show answer
Answer: A
Q172025 · 2 Apr 2025 · Shift 1
The number of sequences of ten terms, whose terms are either 0 or 1 or 2 , that contain exactly five 1 s and exactly three 2 s , is equal to :
1. A.360
2. B.2520
3. C.1820
4. D.45
Show answer
Answer: B
Q172025 · 2 Apr 2025 · Shift 2
If $\sum_{r = 0}^{10} (\frac{1 0 ^{r + 1} - 1}{1 0 ^{r}}) \cdot^{11} C_{r + 1} = \frac{α ^{11} - 1 1 ^{11}}{1 0 ^{10}}$ , then $α$ is equal to :
1. A.11
2. B.20
3. C.24
4. D.15
Show answer
Answer: B
Q102025 · 29 Jan 2025 · Shift 2
The remainder, when $7^{103}$ is divided by 23, is equal to:
1. A. $9$
2. B. $6$
3. C. $14$
4. D. $17$
Show answer
Answer: C
Q232025 · 29 Jan 2025 · Shift 2· Numerical answer
Let integers $a, b \in [- 3, 3]$ be such that $a + b \neq = 0$ . Then the number of all possible ordered pairs (a, b), for which $\frac{z - a}{z + b} = 1$ and $z + 1 ω ω^{2} ω z + ω^{2} 1 ω^{2} 1 z + ω = 1$ , $z \in C$ , where $ω$ and $ω^{2}$ are the roots of $x^{2} + x + 1 = 0$ , is equal to ____.
Show answer
Answer: 10
Q22025 · 28 Jan 2025 · Shift 1
If $f (x) = \frac{2 ^{x}}{2 ^{x} + 2}$ , $x \in R$ , then $\sum_{k = 1}^{81} f (\frac{k}{82})$ is equal to
1. A.82
2. B. $812$
3. C.41
4. D. $\frac{81}{2}$
Show answer
Answer: D
Q52025 · 28 Jan 2025 · Shift 1
Let $⟨ a_{n} ⟩$ be a sequence such that $a_{0} = 0, a_{1} = \frac{1}{2}$ and $2 a_{n + 2} = 5 a_{n + 1} - 3 a_{n}, n = 0, 1, 2, 3, \dots$ . Then $\sum_{k = 1}^{100} a_{k}$ is equal to
1. A. $3 a_{100} + 100$
2. B. $3 a_{100} - 100$
3. C. $3 a_{99} - 100$
4. D. $3 a_{99} + 100$
Show answer
Answer: B
Q72025 · 28 Jan 2025 · Shift 1
If $\int_{- \frac{π}{2}}^{\frac{π}{2}} \frac{96 x ^{2} c o s ^{2} x}{( 1 + e ^{x} )} d x = π (α π^{2} + β), α, β \in Z$ , then $(α + β)^{2}$ equals
1. A.196
2. B.100
3. C.64
4. D.144
Show answer
Answer: B
Q232025 · 28 Jan 2025 · Shift 1· Numerical answer
If $α = 1 + \sum_{r = 1}^{6} (- 3)^{r - 1}^{12} C_{2 r - 1}$ , then the distance of the point $(12, 3)$ from the line $α x - 3 y + 1 = 0$ is ____.
Show answer
Answer: 5
Q52025 · 24 Jan 2025 · Shift 1
Let $f (x) = \frac{2 ^{x + 2} + 16}{2 ^{2 x + 1} + 2 ^{x + 4} + 32}$ . Then the value of $8 (f (\frac{1}{15}) + f (\frac{2}{15}) + \dots + f (\frac{59}{15}))$ is equal to
1. A. $108$
2. B. $92$
3. C. $118$
4. D. $102$
Show answer
Answer: C
Q102025 · 24 Jan 2025 · Shift 1
Let in a $△ A B C$ , the length of the side $A C$ be $6$ , the vertex $B$ be $(1, 2, 3)$ and the vertices $A, C$ lie on the line $\frac{x - 6}{3} = \frac{y - 7}{2} = \frac{z - 7}{- 2}$ . Then the area (in sq. units) of $△ A B C$ is:
1. A. $42$
2. B. $17$
3. C. $56$
4. D. $21$
Show answer
Answer: D
Q112025 · 24 Jan 2025 · Shift 1
Let the line passing through the point $(- 1, 2, 1)$ and parallel to the line $\frac{x - 1}{2} = \frac{y + 1}{3} = \frac{z}{4}$ intersect the line $\frac{x + 2}{3} = \frac{y - 3}{2} = \frac{z - 4}{1}$ at the point $P$ . Then the distance of $P$ from the point $Q (4, - 5, 1)$ is
1. A. $56$
2. B. $5$
3. C. $55$
4. D. $10$
Show answer
Answer: C
Q112025 · 24 Jan 2025 · Shift 2
If $7 = 5 + \frac{1}{7} (5 + α) + \frac{1}{7 ^{2}} (5 + 2 α) + \frac{1}{7 ^{3}} (5 + 3 α) + \dots\dots\dots\dots \infty$ , then the value of $α$ is :
1. A. $\frac{1}{7}$
2. B.1
3. C. $\frac{6}{7}$
4. D.6
Show answer
Answer: D