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

2023 63 questions

Q102023 · 8 Apr 2023 · Shift 2
If $A = [1 λ 510], A^{- 1} = α A + β I$ and $α + β = - 2$ , then $4 α^{2} + β^{2} + λ^{2}$ is equal to :
1. A. $12$
2. B. $10$
3. C. $19$
4. D. $14$
Show answer
Answer: D
Q72023 · 6 Apr 2023 · Shift 1
Let $5 f (x) + 4 f (\frac{1}{x}) = \frac{1}{x} + 3, x > 0$ . Then $18 \int_{1}^{2} f (x) d x$ is equal to :
1. A. $10 lo g_{e} 2 + 6$
2. B. $5 lo g_{e} 2 - 3$
3. C. $10 lo g_{e} 2 - 6$
4. D. $5 lo g_{e} 2 + 3$
Show answer
Answer: C
Q132023 · 6 Apr 2023 · Shift 1
If $2 x^{y} + 3 y^{x} = 20$ , then $\frac{d y}{d x}$ at $(2, 2)$ is equal to :
1. A. $- (\frac{3 + l o g _{e} 16}{4 + l o g _{e} 8})$
2. B. $- (\frac{2 + l o g _{e} 8}{3 + l o g _{e} 4})$
3. C. $- (\frac{3 + l o g _{e} 8}{2 + l o g _{e} 4})$
4. D. $- (\frac{3 + l o g _{e} 4}{2 + l o g _{e} 8})$
Show answer
Answer: B
Q182023 · 6 Apr 2023 · Shift 1
From the top A of a vertical wall AB of height $30 m$ , the angles of depression of the top P and bottom Q of a vertical tower PQ are $1 5^{\circ}$ and $6 0^{\circ}$ respectively, B and Q are on the same horizontal level. If C is a point on AB such that $CB = PQ$ , then the area (in $m^{2}$ ) of the quadrilateral BCPQ is equal to :
1. A. $200 (3 - 3)$
2. B. $300 (3 - 1)$
3. C. $300 (3 + 1)$
4. D. $600 (3 - 1)$
Show answer
Answer: D
Q202023 · 6 Apr 2023 · Shift 1
If $^{2 n} C_{3} :^{n} C_{3} = 10 : 1$ , then the ratio $(n^{2} + 3 n) : (n^{2} - 3 n + 4)$ is :
1. A. $27 : 11$
2. B. $2 : 1$
3. C. $35 : 16$
4. D. $65 : 37$
Show answer
Answer: B
Q152023 · 6 Apr 2023 · Shift 2
If $g cd (m, n) = 1$ and $1^{2} - 2^{2} + 3^{2} - 4^{2} + \dots + (2021)^{2} - (2022)^{2} + (2023)^{2} = 1012 m^{2} n$ then $m^{2} - n^{2}$ is equal to :
1. A.220
2. B.200
3. C.240
4. D.180
Show answer
Answer: C
Q272023 · 6 Apr 2023 · Shift 2· Numerical answer
If $(20)^{19} + 2 (21) (20)^{18} + 3 (21)^{2} (20)^{17} + \dots + 20 (21)^{19} = k (20)^{19},$ then $k$ is equal to ________.
Show answer
Answer: 400
Q282023 · 6 Apr 2023 · Shift 2· Numerical answer
The number of points, where the curve $y = x^{5} - 20 x^{3} + 50 x + 2$ crosses the $x$ -axis, is ________.
Show answer
Answer: 5
Q12023 · 1 Feb 2023 · Shift 1
The value of $\frac{1}{1 ! 50 !} + \frac{1}{3 ! 48 !} + \frac{1}{5 ! 46 !} + \dots + \frac{1}{49 ! 2 !} + \frac{1}{51 ! 1 !}$ is :
1. A. $\frac{2 ^{51}}{50 !}$
2. B. $\frac{2 ^{51}}{51 !}$
3. C. $\frac{2 ^{50}}{50 !}$
4. D. $\frac{2 ^{50}}{51 !}$
Show answer
Answer: D
Q62023 · 1 Feb 2023 · Shift 1
Let $S = {x : x \in R and (3 + 2)^{x^{2} - 4} + (3 - 2)^{x^{2} - 4} = 10}$ . Then $n (S)$ is equal to
1. A. $6$
2. B. $4$
3. C. $0$
4. D. $2$
Show answer
Answer: B
Q142023 · 1 Feb 2023 · Shift 1
$n \to \infty lim [\frac{1}{1 + n} + \frac{1}{2 + n} + \frac{1}{3 + n} + \dots + \frac{1}{2 n}]$ is equal to
1. A. $0$
2. B. $lo g_{e} 2$
3. C. $lo g_{e} (\frac{2}{3})$
4. D. $lo g_{e} (\frac{3}{2})$
Show answer
Answer: B
Q212023 · 1 Feb 2023 · Shift 1· Numerical answer
If $\int_{0}^{1} (x^{21} + x^{14} + x^{7}) (2 x^{14} + 3 x^{7} + 6)^{1/7} d x = \frac{1}{l} (11)^{m / n}$ where $l, m, n \in N$ , $m$ and $n$ are coprime then $l + m + n$ is equal to ________.
Show answer
Answer: 63
Q242023 · 1 Feb 2023 · Shift 1· Numerical answer
The remainder, when $1 9^{200} + 2 3^{200}$ is divided by 49 , is ________.
Show answer
Answer: 29
Q282023 · 1 Feb 2023 · Shift 1· Numerical answer
$A (2, 6, 2), B (- 4, 0, λ), C (2, 3, - 1)$ and $D (4, 5, 0), ∣ λ ∣ \leq 5$ are the vertices of a quadrilateral $A B C D$ . If its area is 18 square units, then $5 - 6 λ$ is equal to ________.
Show answer
Answer: 11
Q212023 · 31 Jan 2023 · Shift 1· Numerical answer
The remainder on dividing $5^{99}$ by 11 is ___________.
Show answer
Answer: 9
Q32023 · 31 Jan 2023 · Shift 2
The equation $e^{4 x} + 8 e^{3 x} + 13 e^{2 x} - 8 e^{x} + 1 = 0, x \in R$ has :
1. A.two solutions and both are negative
2. B.two solutions and only one of them is negative
3. C.four solutions two of which are negative
4. D.no solution
Show answer
Answer: A
Q242023 · 31 Jan 2023 · Shift 2· Numerical answer
If $^{2 n + 1} P_{n - 1} :^{2 n - 1} P_{n} = 11 : 21$ , then $n^{2} + n + 15$ is equal to :
Show answer
Answer: 45
Q302023 · 31 Jan 2023 · Shift 2· Numerical answer
The sum $1^{2} - 2 \cdot 3^{2} + 3 \cdot 5^{2} - 4 \cdot 7^{2} + 5 \cdot 9^{2} - \dots + 15 \cdot 2 9^{2}$ is ___________.
Show answer
Answer: 6952
Q42023 · 30 Jan 2023 · Shift 1
If $[t]$ denotes the greatest integer $\leq t$ , then the value of $\frac{3 ( e - 1 )}{e} \int_{1}^{2} x^{2} e^{[x] + [x^{3}]} d x$ is :
1. A. $e^{8} - e$
2. B. $e^{7} - 1$
3. C. $e^{9} - e$
4. D. $e^{8} - 1$
Show answer
Answer: A
Q122023 · 30 Jan 2023 · Shift 1
If $a_{n} = \frac{- 2}{4 n ^{2} - 16 n + 15}$ , then $a_{1} + a_{2} + \dots + a_{25}$ is equal to :
1. A. $\frac{51}{144}$
2. B. $\frac{49}{138}$
3. C. $\frac{50}{141}$
4. D. $\frac{52}{147}$
Show answer
Answer: C
Q262023 · 30 Jan 2023 · Shift 1· Numerical answer
Let $f^{1} (x) = \frac{3 x + 2}{2 x + 3}$ , $x \in R - {- \frac{3}{2}}$ For $n \geq 2$ , define $f^{n} (x) = f^{1} \circ f^{n - 1} (x)$ . If $f^{5} (x) = \frac{a x + b}{b x + a}$ , $g cd (a, b) = 1$ , then $a + b$ is equal to ____.
Show answer
Answer: 3125
Q162023 · 29 Jan 2023 · Shift 1
Let $A = {(x, y) \in R^{2} : y \geq 0, 2 x \leq y \leq 4 - (x - 1)^{2}}$ and $B = {(x, y) \in R \times R : 0 \leq y \leq min {2 x, 4 - (x - 1)^{2}}}$ . Then the ratio of the area of A to the area of B is
1. A. $\frac{π}{π + 1}$
2. B. $\frac{π - 1}{π + 1}$
3. C. $\frac{π}{π - 1}$
4. D. $\frac{π + 1}{π - 1}$
Show answer
Answer: B
Q242023 · 29 Jan 2023 · Shift 1· Numerical answer
If the co-efficient of $x^{9}$ in $(α x^{3} + \frac{1}{β x})^{11}$ and the co-efficient of $x^{- 9}$ in $(α x - \frac{1}{β x ^{3}})^{11}$ are equal, then $(α β)^{2}$ is equal to ____.
Show answer
Answer: 1
Q282023 · 29 Jan 2023 · Shift 1· Numerical answer
Let the co-ordinates of one vertex of $Δ A B C$ be $A (0, 2, α)$ and the other two vertices lie on the line $\frac{x + α}{5} = \frac{y - 1}{2} = \frac{z + 4}{3}$ . For $α \in Z$ , if the area of $Δ A B C$ is 21 sq. units and the line segment $B C$ has length $221$ units, then $α^{2}$ is equal to ____.
Show answer
Answer: 9
Q292023 · 29 Jan 2023 · Shift 2· Numerical answer
Let $a_{1} = b_{1} = 1$ and $a_{n} = a_{n - 1} + (n - 1), b_{n} = b_{n - 1} + a_{n - 1}, \forall n \geq 2$ . If $S = n = 1 \sum 10 \frac{b _{n}}{2 ^{n}}$ and $T = n = 1 \sum 8 \frac{n}{2 ^{n - 1}}$ , then $2^{7} (2 S - T)$ is equal to ____.
Show answer
Answer: 461