List of top Mathematics Questions asked in JEE Main

Let $y=y(t)$ be a solution of the differential equation$\frac{d y}{d t}+\alpha y=\gamma e^{-\beta t}$ where, $\alpha > 0, \beta>0$ and $\gamma > 0$. Then $\displaystyle\lim _{t \rightarrow \infty} y(t)$

The number of functions $f:\{1,2,3,4\} \rightarrow\{ a \in: Z|a| \leq 8\}$ satisfying $f(n)+\frac{1}{n} f( n +1)=1, \forall n \in\{1,2,3\}$ is

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

Let the function $f(x)=2 x^3+(2 p-7) x^2+3(2 p-9) x-6$ have a maxima for some value of $x<0$ and a minima for some value of $x>0$ Then, the set of all values of $p$ is

Let $\Delta, \nabla \in\{\Lambda, V\}$ be such that $( p \rightarrow q ) \Delta( p \nabla q )$ is a tautology. Then

The shortest distance between the lines $x+1=2 y=-12 z$ and $x=y+2=6 z-6$ is

Let $ f(x) = 2x^n + \lambda $, where $ \lambda \in \mathbb{R} $ and $ n \in \mathbb{N} $ . Given that $ f(4) = 133 $ and $ f(5) = 255 $, What is the sum of all the positive integer divisors of $ f(3) - f(2) $?

Let $A=\left[\begin{array}{cc}\frac{1}{\sqrt{10}} & \frac{3}{\sqrt{10}} \\ \frac{-3}{\sqrt{10}} & \frac{1}{\sqrt{10}}\end{array}\right]$ and $B=\left[\begin{array}{cc}1 & -i \\ 0 & 1\end{array}\right]$, where $i=\sqrt{-1}$ If $M = A ^{ T } B A$, then the inverse of the matrix $AM ^{2023} A ^{ T }$ is

The number of numbers, strictly between 5000 and 10000 can be formed using the digits 1,3,5,7,9 without repetition, is

If 5f ( x+y ) = f(x).f(y) and f(3) = 320, then the value of f(1) is

Mean & Variance of 7 observations are 8 & 16 respectively, if number 14 is omitted then a & b are new mean & variance. The value of a + b is

The mean and variance of 7 observations are 8 and 16, respectively. If one observation 14 is omitted and a and b are respectively the mean and variance of the remaining 6 observations, then $a+3b−5$ is equal to

If $a_n=\frac{-2}{4n^2-16n+15}$ and a₁ + a₂ + …… + a₂₅ = m/n where m and n are coprime, then the value of m + n is

If $\mathbf{a}, \mathbf{b}, \mathbf{c}$ are three non-zero vectors and $\hat{\mathbf{n}}$ is a unit vector perpendicular to $\mathbf{c}$ such that: $\mathbf{a} = \alpha \mathbf{b} - \hat{\mathbf{n}}, \, (\alpha \neq 0)$ and $ \mathbf{b} \cdot \mathbf{c} = 12 $, then $ \mathbf{c} \times (\mathbf{a} \times \mathbf{b}) $ is equal to:

If [t] denotes the greatest integer $≤ 1$, then the value of $3\frac{(e - 1)^2}{e}$ is:

Let the solution curve y = y(x) of the differential equation$\frac{dy}{dx} - \frac{3x^5 \tan^{-1}(x^3)}{(1 + x^6)^{3/2}} y = 2x \exp\left(x^3 - \frac{\tan^{-1}(x^3)}{1 + x}\right)^6$pass through the origin. Then y(1) is equal to:

A straight line cuts off the intercepts OA = a and OB = b on the positive directions of the x-axis and y-axis, respectively. If the perpendicular from the origin O to this line makes an angle of $\frac{\pi}{6}$ with the positive direction of the y-axis and the area of △OAB is $\frac{98\sqrt{3}}{3},$ then a² − b² is equal to:

Let S = {1, 2, 3, 4, 5, 6}. Then the number of one-one functions $f : S → P(S)$, where $P(S)$ denotes the power set of S, such that $f(n) ⊂ f(m)$ where $n < m,$ is:

Let α be the area of the larger region bounded by the curve y² = 8x and the lines y = x and x = 2, which lies in the first quadrant. Then the value of 3α is equal to:

If $\lambda_1<\lambda_2$ are two values of $\lambda$ such that the angle between the planes $P_1: \vec{r}(3 \hat{i}-5 \hat{j}+\hat{k})=7$ and $P_2: \vec{r} \cdot(\lambda \hat{i}+\hat{j}-3 \hat{k})=9$ is $\sin ^{-1}\left(\frac{2 \sqrt{6}}{5}\right)$, then the square of the length of perpendicular from the point $\left(38 \lambda_1, 10 \lambda_2, 2\right)$ to the plane $P_1$ is _____

Let the lines l₁: $\frac{x+5}{3} =\frac{y+4}{1}=\frac{z−α}{−2}$ and l₂:3x+2y+z–2=0=x–3y+2z-13 be coplanar. If the point P(a, b, c) on l₁ is nearest to the point Q(-4,-3, 2), then |a| + |b|+|c| is equal to

The number of bijective functions $f :\{1,3,5$, $7, \ldots \ldots 99\} \rightarrow\{2,4,6,8, \ldots \ldots , 100\}$, such that $f (3) \geq f (9) \geq f (15) \geq f (21) \geq \ldots f (99), $ is _____

The sum of the maximum and minimum values of the function |5x-7|+[x²+2x] is the interval $\left[\frac{5}{4}, 2\right]$, where $[t]$ is the greatest integer $\leq t$ is ______

The value of $12 \int\limits_0^3\left|x^2-3 x+2\right| d x$ is

Let $f:(0,1) \rightarrow R$ be a function defined by $f(x)=\frac{1}{1-e^{-x}}$, and $g(x)=(f(-x)-f(x))$ Consider two statements (I) $g$ is an increasing function in $(0,1)$ (II) $g$ is one-one in $(0,1)$Then,