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

2024 47 questions

Q142024 · 9 Apr 2024 · Shift 1
The shortest distance between the lines $\frac{x - 3}{4} = \frac{y + 7}{- 11} = \frac{z - 1}{5}$ and $\frac{x - 5}{3} = \frac{y - 9}{- 6} = \frac{z + 2}{1}$ is:
1. A. $\frac{185}{563}$
2. B. $\frac{187}{563}$
3. C. $\frac{178}{563}$
4. D. $\frac{179}{563}$
Show answer
Answer: B
Q182024 · 9 Apr 2024 · Shift 1
A ray of light coming from the point $P (1, 2)$ gets reflected from the point $Q$ on the $x$ -axis and then passes through the point $R (4, 3)$ . If the point $S (h, k)$ is such that $P QR S$ is a parallelogram, then $h k^{2}$ is equal to:
1. A.60
2. B.70
3. C.80
4. D.90
Show answer
Answer: B
Q192024 · 9 Apr 2024 · Shift 1
Let the line $L$ intersect the lines $x - 2 = - y = z - 1$ , $2 (x + 1) = 2 (y - 1) = z + 1$ and be parallel to the line $\frac{x - 2}{3} = \frac{y - 1}{1} = \frac{z - 2}{2}$ . Then which of the following points lies on $L$ ?
1. A. $(- \frac{1}{3}, 1, - 1)$
2. B. $(- \frac{1}{3}, - 1, 1)$
3. C. $(- \frac{1}{3}, - 1, - 1)$
4. D. $(- \frac{1}{3}, 1, 1)$
Show answer
Answer: A
Q242024 · 9 Apr 2024 · Shift 1· Numerical answer
The remainder when $42 8^{2024}$ is divided by 21 is ______.
Show answer
Answer: 1
Q162024 · 9 Apr 2024 · Shift 2
Consider the line $L$ passing through the points $(1, 2, 3)$ and $(2, 3, 5)$ . The distance of the point $(\frac{11}{3}, \frac{11}{3}, \frac{19}{3})$ from the line $L$ along the line $\frac{3 x - 11}{2} = \frac{3 y - 11}{1} = \frac{3 z - 19}{2}$ is equal to
1. A.6
2. B.3
3. C.5
4. D.4
Show answer
Answer: B
Q202024 · 9 Apr 2024 · Shift 2
Let $a = 2 \hat{i} + α \hat{j} + \hat{k}, b = - \hat{i} + \hat{k}, c = β \hat{j} - \hat{k}$ , where $α$ and $β$ are integers and $α β = - 6$ . Let the values of the ordered pair $(α, β)$ , for which the area of the parallelogram of diagonals $a + b$ and $b + c$ is $\frac{21}{2}$ , be $(α_{1}, β_{1})$ and $(α_{2}, β_{2})$ . Then $α_{1}^{2} + β_{1}^{2} - α_{2} β_{2}$ is equal to
1. A.21
2. B.24
3. C.19
4. D.17
Show answer
Answer: C
Q302024 · 9 Apr 2024 · Shift 2· Numerical answer
If $(\frac{1}{α + 1} + \frac{1}{α + 2} + \dots\dots + \frac{1}{α + 1012}) - (\frac{1}{2 \cdot 1} + \frac{1}{4 \cdot 3} + \frac{1}{6 \cdot 5} + \dots\dots + \frac{1}{2024 \cdot 2023}) = \frac{1}{2024}$ , then $α$ is equal to ____.
Show answer
Answer: 1011
Q142024 · 8 Apr 2024 · Shift 1
The sum of all the solutions of the equation $(8)^{2 x} - 16 \cdot (8)^{x} + 48 = 0$ is :
1. A. $1 + lo g_{8} (6)$
2. B. $1 + lo g_{6} (8)$
3. C. $lo g_{8} (6)$
4. D. $lo g_{8} (4)$
Show answer
Answer: A
Q242024 · 8 Apr 2024 · Shift 1· Numerical answer
Let the positive integers be written in the form : $47 \cdot \cdot 28159310 6 \cdot \cdot$ If the $k^{th}$ row contains exactly $k$ numbers for every natural number $k$ , then the row in which the number 5310 will be, is ________.
Show answer
Answer: 103
Q272024 · 8 Apr 2024 · Shift 1· Numerical answer
Let $α = \sum_{r = 0}^{n} (4 r^{2} + 2 r + 1)^{n} C_{r}$ and $β = (\sum_{r = 0}^{n} \frac{^{n} C _{r}}{r + 1}) + \frac{1}{n + 1}$ . If $140 < \frac{2 α}{β} < 281$ , then the value of $n$ is ________.
Show answer
Answer: 5
Q282024 · 8 Apr 2024 · Shift 1· Numerical answer
Let $A = [21 - 1 1]$ . If the sum of the diagonal elements of $A^{13}$ is $3^{n}$ , then $n$ is equal to ________.
Show answer
Answer: 7
Q62024 · 8 Apr 2024 · Shift 2
If the line segment joining the points $(5, 2)$ and $(2, a)$ subtends an angle $\frac{π}{4}$ at the origin, then the absolute value of the product of all possible values of $a$ is :
1. A.4
2. B.8
3. C.6
4. D.2
Show answer
Answer: A
Q72024 · 8 Apr 2024 · Shift 2
If $α \neq = a, β \neq = b, γ \neq = c$ and $α a a b β b c c γ = 0$ , then $\frac{a}{α - a} + \frac{b}{β - b} + \frac{γ}{γ - c}$ is equal to :
1. A.2
2. B.3
3. C.1
4. D.0
Show answer
Answer: D
Q232024 · 6 Apr 2024 · Shift 2· Numerical answer
Let $[t]$ denote the largest integer less than or equal to $t$ . If $\int_{0}^{3} ([x^{2}] + [\frac{x ^{2}}{2}]) d x = a + b 2 - 3 - 5 + c 6 - 7$ , where $a, b, c \in Z$ , then $a + b + c$ is equal to ____.
Show answer
Answer: 23
Q252024 · 6 Apr 2024 · Shift 2· Numerical answer
If the shortest distance between the lines $\frac{x - λ}{3} = \frac{y - 2}{- 1} = \frac{z - 1}{1}$ and $\frac{x + 2}{- 3} = \frac{y + 5}{2} = \frac{z - 4}{4}$ is $\frac{44}{30}$ , then the largest possible value of $∣ λ ∣$ is equal to ____.
Show answer
Answer: 43
Q252024 · 5 Apr 2024 · Shift 2· Numerical answer
If $1 + \frac{3 - 2}{2 3} + \frac{5 - 2 6}{18} + \frac{9 3 - 11 2}{36 3} + \frac{49 - 20 6}{180} + \dots upto \infty = 2 + (\frac{b}{a} + 1) lo g_{e} (\frac{a}{b})$ , where a and b are integers with $g cd (a, b) = 1$ , then $11 a + 18 b$ is equal to _________.
Show answer
Answer: 76
Q272024 · 5 Apr 2024 · Shift 2· Numerical answer
If $f (t) = 0 \int π \frac{2 x d x}{1 - c o s ^{2} t s i n ^{2} x}, 0 < t < π$ , then the value of $0 \int \frac{π}{2} \frac{π ^{2} d t}{f ( t )}$ equals _________.
Show answer
Answer: 1
Q282024 · 5 Apr 2024 · Shift 2· Numerical answer
The number of real solutions of the equation $x ∣ x + 5∣ + 2∣ x + 7∣ - 2 = 0$ is _________.
Show answer
Answer: 3
Q102024 · 4 Apr 2024 · Shift 1
Let the point, on the line passing through the points $P (1, - 2, 3)$ and $Q (5, - 4, 7)$ , farther from the origin and at a distance of 9 units from the point $P$ , be $(α, β, γ)$ . Then $α^{2} + β^{2} + γ^{2}$ is equal to :
1. A.150
2. B.155
3. C.160
4. D.165
Show answer
Answer: B
Q112024 · 4 Apr 2024 · Shift 1
The vertices of a triangle are $A (- 1, 3)$ , $B (- 2, 2)$ and $C (3, - 1)$ . A new triangle is formed by shifting the sides of the triangle by one unit inwards. Then the equation of the side of the new triangle nearest to origin is :
1. A. $- x + y - (2 - 2) = 0$
2. B. $x + y - (2 - 2) = 0$
3. C. $x + y + (2 - 2) = 0$
4. D. $x - y - (2 + 2) = 0$
Show answer
Answer: B
Q32024 · 1 Feb 2024 · Shift 1
If $A = [2 - 1 12], B = [1101], C = AB A^{T}$ and $X = A^{T} C^{2} A$ , then $det X$ is equal to :
1. A.243
2. B.729
3. C.27
4. D.891
Show answer
Answer: B
Q92024 · 1 Feb 2024 · Shift 1
Let $S = {x \in R : (3 + 2)^{x} + (3 - 2)^{x} = 10}$ . Then the number of elements in $S$ is :
1. A.4
2. B.0
3. C.2
4. D.1
Show answer
Answer: C
Q162024 · 1 Feb 2024 · Shift 2
The value of $\int_{0}^{1} (2 x^{3} - 3 x^{2} - x + 1)^{\frac{1}{3}} d x$ is equal to :
1. A.-1
2. B.2
3. C.0
4. D.1
Show answer
Answer: C
Q202024 · 1 Feb 2024 · Shift 2
Let $f (x) = {x - 1, 2 x, x is even, x is odd, x \in N$ . If for some $a \in N$ , $f (f (f (a))) = 21$ , then $lim_{x \to a^{-}} {\frac{∣ x ∣ ^{3}}{a} - [\frac{x}{a}]}$ , where $[t]$ denotes the greatest integer less than or equal to $t$ , is equal to :
1. A.169
2. B.121
3. C.225
4. D.144
Show answer
Answer: D
Q242024 · 1 Feb 2024 · Shift 2· Numerical answer
If $\frac{d x}{d y} = \frac{1 + x - y ^{2}}{y}, x (1) = 1$ , then $5 x (2)$ is equal to ________ .
Show answer
Answer: 5