JEE MAIN Mathematics Previous Year Question Paper and Solution with PDF

JEE MAIN Previous Year Questions (PYQs)

JEE MAIN Mathematics PYQ

$T_r=\binom{n}{r-1}a^{,n-r+1}b^{,r-1}$ for $(a+b)^n$.

$15^{\text{th}}$ from the beginning: $T_{15}^{(beg)}=\binom{n}{14}a^{,n-14}b^{14}$.

$15^{\text{th}}$ from the end (swap $a,b$): $T_{15}^{(end)}=\binom{n}{14}b^{,n-14}a^{14}$.

Given $\dfrac{T_{15}^{(beg)}}{T_{15}^{(end)}}=\dfrac{1}{6}$,

coefficients cancel: $\left(\dfrac{a}{b}\right)^{n-28}=\dfrac{1}{6}$.

Here $a=2^{1/3},\ b=3^{-1/3}$

$\ \Rightarrow\ \dfrac{a}{b}=2^{1/3}\cdot 3^{1/3}=6^{1/3}$.

So $(6^{1/3})^{,n-28}=6^{-1}$

$\ \Rightarrow\ n-28=-3\ \Rightarrow\ n=25$.

Therefore, $\binom{n}{3}=\binom{25}{3}=\dfrac{25\cdot24\cdot23}{6}=2300$.

Qus : 17 JEE MAIN PYQ

The number of values of $\theta \in (0, \pi)$ for which the system of linear equations

$x + 3y + 7z = 0$

$-x + 4y + 7z = 0$

Let the 11 consecutive natural numbers be $1, 2, 3, \dots, 11.$ Total ways to choose any 3 numbers = $\displaystyle \binom{11}{3} = 165.$
Now, we need to count the number of 3-number selections that can form an arithmetic progression (A.P.) with positive common difference.
For an A.P., let the middle term be $a$ and common difference be $d>0$. Then the three terms are: $(a-d,\ a,\ a+d)$ These must all lie between $1$ and $11$.
That means $1 \le a-d$ and $a+d \le 11$ ⟹ $d \le \min(a-1,\ 11-a)$
Now we count possible values of $d$ for each $a$:

$a$	$\min(a-1,\ 11-a)$	Possible $d$ values
1	0	–
2	1	1
3	2	1,2
4	3	1,2,3
5	4	1,2,3,4
6	5	1,2,3,4,5
7	4	1,2,3,4
8	3	1,2,3
9	2	1,2
10	1	1
11	0	–

Total = $1 + 2 + 3 + 4 + 5 + 4 + 3 + 2 + 1 = 25.$
Hence, number of favorable triplets = $25.$
Therefore, $\displaystyle P = \frac{25}{165} = \frac{5}{33}.$
Final Answer: $\boxed{\dfrac{5}{33}}$

Let $m$ and $M$ be respectively the minimum and maximum values of \[ \left|\begin{matrix} \cos^2 x & 1+\sin^2 x & \sin 2x\\ 1+\cos^2 x & \sin^2 x & \sin 2x\\ \cos^2 x & \sin^2 x & 1+\sin 2x \end{matrix}\right|. \] Then the ordered pair $(m, M)$ is equal to : Solution: Apply $R_2 \to R_2 - R_1$ and $R_3 \to R_3 - R_1$ \[ \Delta = \left|\begin{matrix} \cos^2 x & 1+\sin^2 x & \sin 2x\\ 1 & -1 & 0\\ 0 & -1 & 1 \end{matrix}\right| \] Expanding along the first row, \[ \Delta = \cos^2 x(-1) - (1+\sin^2 x)(1) - \sin 2x(1) \] \[ \Delta = -(\cos^2 x + \sin^2 x + 1 + \sin 2x) \] \[ \Delta = -2 - \sin 2x \] Since $\sin 2x \in [-1,1]$, \[ \Delta \in [-3, -1] \] Hence, $m = -3$, $M = -1$ Therefore, the ordered pair is $\boxed{(-3, -1)}$.

Solution

Qus : 207 JEE MAIN PYQ

Let $S = \left\{ {x \in R:0 < x < 1\,\mathrm{and}\,2{{\tan }^{ - 1}}\left( {{{1 - x} \over {1 + x}}} \right) = {{\cos }^{ - 1}}\left( {{{1 - {x^2}} \over {1 + {x^2}}}} \right)} \right\}$.

If $\mathrm{n(S)}$ denotes the number of elements in $\mathrm{S}$ then :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (1 February Evening Shift) PYQ

Solution

Qus : 208 JEE MAIN PYQ

Let $\vec a=\hat i+\hat j+\hat k,;\vec b=2\hat i+4\hat j-5\hat k$ and $\vec c=x\hat i+2\hat j+3\hat k,;x\in\mathbb R$. If $\vec d$ is the unit vector in the direction of $(\vec b+\vec c)$ such that $\vec a\cdot\vec d=1$, then $(\vec a\times\vec b)\cdot\vec c$ equals:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (4 April Evening Shift) PYQ

Solution

Qus : 209 JEE MAIN PYQ

A rod of length eight units moves such that its ends $A$ and $B$ always lie on the lines $x-y+2=0$ and $y+2=0$, respectively. If the locus of the point $P$, that divides the rod $A B$ internally in the ratio $2: 1$ is $9\left(x^2+\alpha y^2+\beta x y+\gamma x+28 y\right)-76=0$, then $\alpha-\beta-\gamma$ is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (23 January Evening Shift) PYQ

Qus : 230 JEE MAIN PYQ

Let $S$ be the set of all real values of $k$ for which the system of linear equations

$x + y + z = 2$

$2x + y - z = 3$

Qus : 274 JEE MAIN PYQ

For the system of linear equations: $x - 2y = 1,x - y + kz = - 2,ky + 4z = 6,k \in R$, consider the following statements :

(A) The system has unique solution if $k \ne 2,k \ne - 2$.
(B) The system has unique solution if k = $-$2
(C) The system has unique solution if k = 2
(D) The system has no solution if k = 2
(E) The system has infinite number of solutions if k $ \ne $ $-$2. Which of the following statements are correct?

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (24 February Evening Shift) PYQ

Solution

Qus : 291 JEE MAIN PYQ

Let a function $f: \mathbb{R} \rightarrow \mathbb{R}$ be defined as :

Qus : 311 JEE MAIN PYQ

Qus : 333 JEE MAIN PYQ

If the system of linear equations

$2x+2y+3z=a$

$3x-y+5z=b$

$x-3y+2z=c$

where $a,b,c$ are non-zero real numbers, has more than one solution, then :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (11 January Morning Shift) PYQ

Solution

Qus : 334 JEE MAIN PYQ

The value of the integral $\displaystyle \int_{-\pi/4}^{\pi/4} \sin^{4}x \left(1 + \log\left(\dfrac{2 + \sin 2x}{2 - \sin 2x}\right)\right),dx$ is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (15 April Morning Shift) PYQ

Solution

Qus : 335 JEE MAIN PYQ

The number of values of $k$, for which the system of equations : $\matrix{ {\left( {k + 1} \right)x + 8y = 4k} \cr {kx + \left( {k + 3} \right)y = 3k - 1} \cr } $

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2013 (Offline) PYQ

Solution

Qus : 336 JEE MAIN PYQ

The area of the region : $R = \{ (x,y):5{x^2} \le y \le 2{x^2} + 9\} $

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (24 February Evening Shift) PYQ

Solution

Qus : 337 JEE MAIN PYQ

Qus : 383 JEE MAIN PYQ

The number of values of $\alpha$ for which the system of equations :

x + y + z = $\alpha$

$\alpha$x + 2$\alpha$y + 3z = $-$1

Qus : 417 JEE MAIN PYQ

A six faced die is biased such that

Qus : 461 JEE MAIN PYQ

Let the sets A and B denote the domain and range respectively of the function $f(x)=\frac{1}{\sqrt{\lceil x\rceil-x}}$, where $\lceil x\rceil$ denotes the smallest integer greater than or equal to $x$. Then among the statements

Qus : 481 JEE MAIN PYQ

The values of $m, n$, for which the system of equations

4x + 3y - 3z = 7

Qus : 638 JEE MAIN PYQ

$(sin^{- 1} x)^{2} - (cos^{- 1} x)^{2} = a, 0 < x < 1, a; = 0$

then the value of

Qus : 648 JEE MAIN PYQ

Let f : N $\to$ R be a function such that $f(x + y) = 2f(x)f(y)$ for natural numbers x and y. If f(1) = 2, then the value of $\alpha$ for which

Qus : 672 JEE MAIN PYQ

If the system of linear equations

$x + ky + 3z = 0$

$3x + ky - 2z = 0$

Qus : 746 JEE MAIN PYQ

Let $(a_n)$ be a sequence such that $a_0=0$, $a_1=\dfrac{1}{2}$ and $2a_{n+2}=5a_{n+1}-3a_n,; n=0,1,2,\ldots$. Then $\displaystyle \sum_{k=1}^{100} a_k$ is equal to

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (28 January Morning Shift) PYQ

Qus : 788 JEE MAIN PYQ

Qus : 808 JEE MAIN PYQ

The system of equations

$ - kx + 3y - 14z = 25$

$ - 15x + 4y - kz = 3$

Qus : 838 JEE MAIN PYQ

The area of the region

$\left\{(x, y):|x-1| \leq y \leq \sqrt{5-x^{2}}\right\}$ is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (29 July Morning Shift) PYQ

Solution

Qus : 839 JEE MAIN PYQ

Let $N$ denote the sum of the numbers obtained when two dice are rolled. If the probability that $2^{N} < N!$ is $\dfrac{m}{n}$, where $m$ and $n$ are coprime, then $4m-3n$ is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (10 April Morning Shift) PYQ

Solution

Qus : 840 JEE MAIN PYQ

For $x\in\left(-\dfrac{\pi}{2},\dfrac{\pi}{2}\right)$, if $y(x)=\displaystyle\int \frac{\csc x+\sin x}{\csc x\sec x+\tan x\sin^2 x}\,dx$, and $\displaystyle\lim_{x\to \left(\frac{\pi}{2}\right)} y(x)=0$, then $y\!\left(\dfrac{\pi}{4}\right)$ is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (29 January Morning Shift) PYQ

Solution

Qus : 841 JEE MAIN PYQ

Let $f:(-\infty,\infty)\setminus{0}\to\mathbb{R}$ be differentiable such that $f'(1)=\lim_{a\to\infty} a^{2}f!\left(\tfrac{1}{a}\right)$. Then $\displaystyle \lim_{a\to\infty}\left(\frac{a(a+1)}{2}\tan^{-1}!\frac{1}{a}+a^{2}-2\log_{e}a\right)$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (6 April Morning Shift) PYQ

Solution

Qus : 842 JEE MAIN PYQ

Qus : 924 JEE MAIN PYQ

The ordered pair (a, b), for which the system of linear equations

3x $-$ 2y + z = b

5x $-$ 8y + 9z = 3

Qus : 985 JEE MAIN PYQ

Let $P(3,2,3)$, $Q(4,6,2)$ and $R(7,3,2)$ be the vertices of $\triangle PQR$. Then, the angle $\angle QPR$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (29 January Evening Shift) PYQ

Let the G.P. be $a,\ ar,\ ar^2$.
Given:
$$S = a(1 + r + r^2)$$ and $$a^3 r^3 = 27 \Rightarrow (ar)^3 = 27 \Rightarrow ar = 3.$$
Hence, $$a = \frac{3}{r}.$$
Substitute in $S$: $$ S = \frac{3}{r}(1 + r + r^2) = 3\left(r + \frac{1}{r} + 1\right) $$
For real $r \ne 0$:
If $r > 0,$ then $(r + \frac{1}{r} \ge 2 \Rightarrow S \ge 3(2 + 1) = 9)$
If $(r < 0)$ then $(r + \frac{1}{r} \le -2 \Rightarrow S \le 3(-2 + 1) = -3)$

Hence all possible values of $S$ lie in the intervals:
$$ \boxed{S \in (-\infty,\ -3]\ \cup\ [9,\ \infty)} $$

Let the cubic polynomial be $$p(x) = a x^3 + b x^2 + c x + d$$ where $a, b, c, d$ are real constants.

Given:
Local maximum at $x = 1 \Rightarrow p'(1) = 0,\ p(1) = 8$
Local minimum at $x = 2 \Rightarrow p'(2) = 0,\ p(2) = 4$

Derivative:
$$p'(x) = 3a x^2 + 2b x + c$$ Apply the stationary point conditions:
\[ \begin{cases} 3a(1)^2 + 2b(1) + c = 0 \\[4pt] 3a(2)^2 + 2b(2) + c = 0 \end{cases} \] Simplify: \[ \begin{cases} 3a + 2b + c = 0 \\[4pt] 12a + 4b + c = 0 \end{cases} \] Subtracting gives: \[ 9a + 2b = 0 \Rightarrow b = -\frac{9a}{2}. \] Substitute into $3a + 2b + c = 0$: \[ 3a + 2\left(-\frac{9a}{2}\right) + c = 0 \Rightarrow 3a - 9a + c = 0 \Rightarrow c = 6a. \]
Using the value conditions:
\[ \begin{cases} p(1) = a + b + c + d = 8 \\[4pt] p(2) = 8a + 4b + 2c + d = 4 \end{cases} \] Substitute $b = -\frac{9a}{2},\ c = 6a$:
\[ a - \frac{9a}{2} + 6a + d = 8 \Rightarrow \frac{5a}{2} + d = 8 \Rightarrow d = 8 - \frac{5a}{2}. \] and \[ 8a + 4\left(-\frac{9a}{2}\right) + 2(6a) + d = 4 \Rightarrow 2a + d = 4. \] Substitute $d = 8 - \frac{5a}{2}$: \[ 2a + 8 - \frac{5a}{2} = 4 \Rightarrow -\frac{a}{2} = -4 \Rightarrow a = 8. \]
Now, \[ b = -\frac{9a}{2} = -36, \quad c = 48, \quad d = 8 - \frac{5(8)}{2} = -12. \]
Therefore, $$p(0) = d = -12.$$
Final Answer: $$\boxed{p(0) = -12}$$

$x + y + z = 1$

$x + ay + z = 1$

and adding 2 to each element of

Let the quadratic polynomial be $ f(x) = a x^2 + b x + c $.

Given that $$ f(-1) + f(2) = 0 $$ and one of the roots of $ f(x) = 0 $ is $3$.

Let the other root be $\alpha$. Hence, $ f(x) = k(x - 3)(x - \alpha) $, where $k \ne 0$.

Substitute the condition $ f(-1) + f(2) = 0 $: $$ k(-1 - 3)(-1 - \alpha) + k(2 - 3)(2 - \alpha) = 0 $$ Simplify: $$ (-4)(-1 - \alpha) + (-1)(2 - \alpha) = 0 $$ $$ 4(1 + \alpha) - 2 + \alpha = 0 $$ $$ 2 + 5\alpha = 0 \Rightarrow \alpha = -\frac{2}{5}. $$
Therefore, the other root is $-\dfrac{2}{5}$, which lies in $$\boxed{(-1,\ 0)}.$$

Qus : 1164 JEE MAIN PYQ

Qus : 1228 JEE MAIN PYQ

The number of real values of $\lambda$ for which the system of linear equations

$2x+4y-\lambda z=0$

$4x+\lambda y+2z=0$

Qus : 1238 JEE MAIN PYQ

The greatest value of $c\in\mathbb{R}$ for which the system of linear equations

$x-cy-cz=0$

$cx-y+cz=0$

Qus : 1248 JEE MAIN PYQ

There are $n$ stations on a circle. Each pair is connected by a straight track.

Blue lines connect nearest neighbours, so the number of blue lines is

Blue $ = n. $

Total lines is $ \binom{n}{2} = \frac{n(n-1)}{2}. $

Hence red lines are $ \text{Red} = \binom{n}{2} - n. $

Given Red =$ 99 \times \text{Blue} $

$ \binom{n}{2} - n = 99n $

$ \;\;\Longrightarrow\;\; \frac{n(n-1)}{2} - n = 99n$

$ \;\;\Longrightarrow\;\; \frac{n(n-1)}{2} = 100n$

$ \;\;\Longrightarrow\;\; n-1 = 200$

$ \;\;\Longrightarrow\;\; n = 201.$

Final Answer: $\boxed{201}$

Qus : 1276 JEE MAIN PYQ

If the set $R=\{(a, b): a+5 b=42, a, b \in \mathbb{N}\}$ has $m$ elements and $\sum_\limits{n=1}^m\left(1-i^{n !}\right)=x+i y$, where $i=\sqrt{-1}$, then the value of $m+x+y$ is

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (8 April Morning Shift) PYQ

Qus : 1337 JEE MAIN PYQ

Consider the function $f:\left[\frac{1}{2}, 1\right] \rightarrow \mathbb{R}$ defined by $f(x)=4 \sqrt{2} x^3-3 \sqrt{2} x-1$. Consider the statements

Qus : 1365 JEE MAIN PYQ

Let $R=\left(\begin{array}{ccc}x & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & z\end{array}\right)$ be a non-zero $3 \times 3$ matrix, where $x \sin \theta=y \sin \left(\theta+\frac{2 \pi}{3}\right)=z \sin \left(\theta+\frac{4 \pi}{3}\right) \neq 0, \theta \in(0,2 \pi)$. For a square matrix $M$, let trace $(M)$ denote the sum of all the diagonal entries of $M$. Then, among the statements:

Qus : 1405 JEE MAIN PYQ

In an increasing geometric progression of positive terms, the sum of the second and sixth terms is $\dfrac{70}{3}$ and the product of the third and fifth terms is $49$. Then the sum of the $4^{\text{th}},6^{\text{th}}$ and $8^{\text{th}}$ terms is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (8 April Evening Shift) PYQ

Qus : 1427 JEE MAIN PYQ

If the system of linear equations

$x-2y+kz=1$

$2x+y+z=2$

Qus : 1460 JEE MAIN PYQ

Qus : 1470 JEE MAIN PYQ

If the system of linear equations

$2x + 3y - z = - 2$

$x + y + z = 4$

$x - y + |\lambda |z = 4\lambda - 4$

where, $\lambda$ $\in$ R, has no solution, then

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (28 June Morning Shift) PYQ

Solution

Qus : 1471 JEE MAIN PYQ

Let $N$ be the sum of the numbers appeared when two fair dice are rolled and let the probability that $N-2,\ \sqrt{3N},\ N+2$ are in geometric progression be $\dfrac{k}{48}$. Then the value of $k$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (25 January Evening Shift) PYQ

Solution

Qus : 1472 JEE MAIN PYQ

Let $\vec{a}=\hat{i}+4\hat{j}+2\hat{k}$, $\vec{b}=3\hat{i}-2\hat{j}+7\hat{k}$ and $\vec{c}=2\hat{i}-\hat{j}+4\hat{k}$. If a vector $\vec{d}$ satisfies $\vec{d}\times\vec{b}=\vec{c}\times\vec{b}$ and $\vec{d}\cdot\vec{a}=24$, then $|\vec{d}|^{2}$ is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (13 April Morning Shift) PYQ

Solution

Qus : 1473 JEE MAIN PYQ

If the domain of the function $f(x)=\log_e\!\left(\frac{2x+3}{4x^{2}+x-3}\right)+\cos^{-1}\!\left(\frac{2x-1}{x+2}\right)$ is $(\alpha,\beta)$, then the value of $5\beta-4\alpha$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (30 January Evening Shift) PYQ

Solution

Qus : 1474 JEE MAIN PYQ

If the value of $\dfrac{5\cos36^{\circ}+5\sin18^{\circ}}{5\cos36^{\circ}-3\sin18^{\circ}}$ is $\dfrac{a\sqrt{5}-b}{c}$, where $a,b,c$ are natural numbers and $\gcd(a,c)=1$, then $a+b+c$ is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (8 April Evening Shift) PYQ

Qus : 1481 JEE MAIN PYQ

For the system of linear equations

$2 x+4 y+2 a z=b$

$x+2 y+3 z=4$

Qus : 1565 JEE MAIN PYQ

Solution

Qus : 1607 JEE MAIN PYQ

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (13 April Evening Shift) PYQ

Solution

Qus : 1686 JEE MAIN PYQ

If the system of linear equations

Solution

Qus : 1744 JEE MAIN PYQ

A coin is biased so that a head is twice as likely to occur as a tail. If the coin is tossed 3 times, then the probability of getting two tails and one head is

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (31 January Evening Shift) PYQ

Solution

Qus : 1745 JEE MAIN PYQ

Let $\alpha,\beta;\ \alpha>\beta,$ be the roots of the equation $x^{2}-\sqrt{2},x-\sqrt{3}=0$. Let $P_{n}=\alpha^{n}-\beta^{n},\ n\in\mathbb{N}$. Then $(11\sqrt{3}-10\sqrt{2}),P_{10}+(11\sqrt{2}+10),P_{11}-11,P_{12}$ is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (9 April Evening Shift) PYQ

Solution

Qus : 1746 JEE MAIN PYQ

Let $a_1, a_2, a_3, \ldots$ be in an A.P. such that $ \displaystyle \sum_{k=1}^{12} 2a_{2k-1} = -\dfrac{72}{5}a_1, \quad a_1 \ne 0.$ If $ \displaystyle \sum_{k=1}^{n} a_k = 0, $ then $n$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (2 April Morning Shift) PYQ

Solution

Qus : 1747 JEE MAIN PYQ

The area (in sq. units) of the region $A={(x,y):\dfrac{y^{2}}{2}\le x\le y+4}$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (9 April Evening Shift) PYQ

Solution

Qus : 1748 JEE MAIN PYQ

The system of linear equations

$ x + \lambda y - z = 0 $

$ \lambda x - y - z = 0 $

$ x + y - \lambda z = 0 $

has a non-trivial solution for:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (Offline) PYQ

Solution

Qus : 1749 JEE MAIN PYQ

If the value of the integral $\int\limits_0^{{1 \over 2}} {{{{x^2}} \over {{{\left( {1 - {x^2}} \right)}^{{3 \over 2}}}}}} dx$ is ${k \over 6}$, then k is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 3 September 2020 (Evening) PYQ

Solution

Qus : 1750 JEE MAIN PYQ

Let g(x) = $\int_0^x {f(t)dt} $, where f is continuous function in [ 0, 3 ] such that ${1 \over 3}$ $ \le $ f(t) $ \le $ 1 for all t$\in$ [0, 1] and 0 $ \le $ f(t) $ \le $ ${1 \over 2}$ for all t$\in$ (1, 3]. The largest possible interval in which g(3) lies is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (18 March Evening Shift) PYQ

Solution

Qus : 1751 JEE MAIN PYQ

If ${{dy} \over {dx}} = {{{2^{x + y}} - {2^x}} \over {{2^y}}}$, y(0) = 1, then y(1) is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (31 August Morning Shift) PYQ

Solution

Qus : 1752 JEE MAIN PYQ

has infinitely many solutions, then $\left(\lambda^2+\mu^2\right)$ is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (2 April Evening Shift) PYQ

Solution

Qus : 1790 JEE MAIN PYQ

If one of the diameters of the circle, given by the equation, $ x^{2} + y^{2} - 4x + 6y - 12 = 0 $, is a chord of a circle $S$, whose centre is at $(-3, 2)$, then the radius of $S$ is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (Offline) PYQ

Solution

Qus : 1791 JEE MAIN PYQ

Let the centroid of an equilateral triangle ABC be at the origin. Let one of the sides of the equilateral triangle be along the straight line x + y = 3. If R and r be the radius of circumcircle and incircle respectively of $\Delta$ABC, then (R + r) is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (18 March Evening Shift) PYQ

Solution

Qus : 1792 JEE MAIN PYQ

The domain of the function $f(x) = {\sin ^{ - 1}}\left( {{{3{x^2} + x - 1} \over {{{(x - 1)}^2}}}} \right) + {\cos ^{ - 1}}\left( {{{x - 1} \over {x + 1}}} \right)$ is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (31 August Evening Shift) PYQ

Solution

Qus : 1793 JEE MAIN PYQ

If the system of linear equations

2x + y $-$ z = 7

Solution

Qus : 1867 JEE MAIN PYQ

The system of linear equations

$x + y + z = 2$

$2x + 3y + 2z = 5$

Solution

Qus : 1941 JEE MAIN PYQ

Let f be a real valued continuous function on [0, 1] and $f(x) = x + \int\limits_0^1 {(x - t)f(t)dt} $.

Then, which of the following points (x, y) lies on the curve y = f(x) ?

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (29 June Evening Shift) PYQ

Solution

Qus : 1942 JEE MAIN PYQ

The minimum number of elements that must be added to the relation $R=\{(a,b),(b,c)\}$ on the set $\{a,b,c\}$ so that it becomes symmetric and transitive is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (30 January Morning Shift) PYQ

Solution

Qus : 1943 JEE MAIN PYQ

Let the mean and the variance of $6$ observations $a, b, 68, 44, 48, 60$ be $55$ and $194$, respectively. If $a>b$, then $a+3b$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (31 January Evening Shift) PYQ

Solution

Qus : 1944 JEE MAIN PYQ

$ \text { Given three indentical bags each containing } 10 \text { balls, whose colours are as follows : } $

Qus : 1972 JEE MAIN PYQ

$ \text{Suppose } f:\mathbb{R}\to(0,\infty) \text{ be a differentiable function such that } 5f(x+y)=f(x)\cdot f(y),\ \forall x,y\in\mathbb{R}. $ $ \text{If } f(3)=320,\ \text{then } \displaystyle \sum_{n=0}^{5} f(n) \text{ is equal to:} $

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (30 January Morning Shift) PYQ

Qus : 2040 JEE MAIN PYQ

where $a, b \in \mathbf{R}$, has infinitely many solutions, then $7 a+3 b$ is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (22 January Evening Shift) PYQ

Solution

Qus : 2215 JEE MAIN PYQ

Consider the lines $x(3\lambda+1)+y(7\lambda+2)=17\lambda+5$, $\lambda$ 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:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (3 April Evening Shift) PYQ

Solution

Qus : 2216 JEE MAIN PYQ

If the system of linear equations

$x-4y+7z=g$,

$3y-5z=h$,

has infinitely many solutions, then $\beta - \alpha =$

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (10 January Morning Shift) PYQ

Solution

Qus : 2305 JEE MAIN PYQ

The smallest natural number $n$ such that the coefficient of $x$ in the expansion of $\left(x^{2}+\dfrac{1}{x^{3}}\right)^{n}$ is ${}^nC_{23}$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (10 April Evening Shift) PYQ

Solution

Qus : 2306 JEE MAIN PYQ

$\displaystyle \lim_{x\to 0} \frac{(1-\cos 2x)^{2}}{2x\tan x - x\tan 2x}$ is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (10 April Morning Shift) PYQ

Solution

Qus : 2307 JEE MAIN PYQ

Let $\lambda \in $ R . The system of linear equations
2x₁- 4x₂ + $\lambda $x₃ = 1
x₁ - 6x₂ + x₃ = 2
$\lambda $x₁ - 10x₂ + 4x₃ = 3
is inconsistent for:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 5 September 2020 (Morning) PYQ

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (25 July Morning Shift) PYQ

Solution

Qus : 2335 JEE MAIN PYQ

Let the point $P(\alpha, \beta)$ be at a unit distance from each of the two lines

Qus : 2363 JEE MAIN PYQ

The shortest distance between the lines

$\dfrac{x+7}{-6} = \dfrac{y-6}{7} = z$

and

Solution

Qus : 2502 JEE MAIN PYQ

The variance of first $50$ even natural numbers is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2014 (Offline) PYQ

Solution

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