List of top Mathematics Questions asked in JEE Main

If the curve \(y=y(x)\) is the solution of the differential equation

\(2(x^2+x^{5/4})\,dy-y(x+x^{1/4})\,dx=2x^{9/4}\,dx\), \(x\gt 0\) which

passes through the point \(\left(1,\,1-\frac{4}{3}\log_e 2\right)\), then the value of \(y(16)\) is equal to :

If the integral

\(\int_0^{10}\frac{[\sin 2\pi x]}{e^{x-[x]}}\,dx=\alpha e^{-1}+\beta e^{-\frac{1}{2}}+\gamma\)

, where \(\alpha,\beta,\gamma\) are integers and \([x]\) denotes the greatest integer less than or equal to \(x\), then the value of \(\alpha+\beta+\gamma\) is equal to :

The value of the limit

\(\lim_{\theta\to 0}\frac{\tan(\pi\cos^2\theta)}{\sin(2\pi\sin^2\theta)}\)

is equal to :

Let \(S_1, S_2\) and \(S_3\) be three sets defined as

\(S_1=\{z\in\mathbb{C} : |z-1|\le\sqrt{2}\}\)

\(S_2=\{z\in\mathbb{C} : \mathrm{Re}((1-i)z)\ge 1\}\)

\(S_3=\{z\in\mathbb{C} : \mathrm{Im}(z)\le 1\}\)

Then the set \(S_1\cap S_2\cap S_3\) :

The number of solutions of the equation

\(\sin^{-1}\left[x^2+\frac{1}{3}\right]+\cos^{-1}\left[x^2-\frac{2}{3}\right]=x^2\), for \(x\in[-1,1]\), and \([x]\) denotes the greatest integer less than or equal to \(x\), is :

Let a computer program generate only the digits 0 and 1 to form a string of binary numbers with probability of occurrence of 0 at even places be \(\frac{1}{2}\) and probability of occurrence of 0 at the odd place be \(\frac{1}{3}\). Then the probability that '10' is followed by '01' is equal to :

Let \(f : \mathbb{R}\to\mathbb{R}\) be defined as \(f(x)=e^{-x}\sin x\). If \(F:[0,1]\to\mathbb{R}\) is a differentiable function with that \(F(x)=\int_0^x f(t)\,dt\), then the value of \(\int_0^1 \left(F'(x)+f(x)\right)e^{x}\,dx\) lies in the interval

The minimum distance between any two points \(P_1\) and \(P_2\) while considering point \(P_1\) on one circle and point \(P_2\) on the other circle for the given circles' equations
\(x^2 + y^2 - 10x - 10y + 41 = 0\)
\(x^2 + y^2 - 24x - 10y + 160 = 0\) is ___________.

If the equation of the plane passing through the line of intersection of the planes \(2x - 7y + 4z - 3 = 0\), \(3x - 5y + 4z + 11 = 0\) and the point \((-2, 1, 3)\) is \(ax + by + cz - 7 = 0\), then the value of \(2a + b + c - 7\) is ____________.

If \(A = \begin{bmatrix} 2 & 3 \\ 0 & -1 \end{bmatrix}\), then the value of \(\det(A^4) + \det\left(A^{10} - (\mathrm{Adj}(2A))^{10}\right)\) is equal to _____________.

Let there be three independent events \(E_1\), \(E_2\) and \(E_3\). The probability that only \(E_1\) occurs is \(\alpha\), only \(E_2\) occurs is \(\beta\) and only \(E_3\) occurs is \(\gamma\). Let 'p' denote the probability of none of events occurs that satisfies the equations \((\alpha - 2\beta)p = \alpha\beta\) and \((\beta - 3\gamma)p = 2\beta\gamma\). All the given probabilities are assumed to lie in the interval \((0, 1)\).
Then, \(\dfrac{\text{Probability of occurrence of } E_1}{\text{Probability of occurrence of } E_3}\) is equal to _____________.

If \(\vec{a} = \alpha\hat{i} + \beta\hat{j} + 3\hat{k}\), \(\vec{b} = -\beta\hat{i} - \alpha\hat{j} - \hat{k}\) and \(\vec{c} = \hat{i} - 2\hat{j} - \hat{k}\) such that \(\vec{a}\cdot\vec{b} = 1\) and \(\vec{b}\cdot\vec{c} = -3\), then \(\dfrac{1}{3}\left((\vec{a}\times\vec{b})\cdot\vec{c}\right)\) is equal to _____________.

If the function \(f(x) = \dfrac{\cos(\sin x) - \cos x}{x^4}\) is continuous at each point in its domain and \(f(0) = \dfrac{1}{k}\), then k is ____________.

The maximum value of z in the following equation \(z = 6xy + y^2\), where \(3x + 4y \le 100\) and \(4x + 3y \le 75\) for \(x \ge 0\) and \(y \ge 0\) is __________.

If \(f(x) = \sin\left(\cos^{-1}\left(\dfrac{1 - 2^{2x}}{1 + 2^{2x}}\right)\right)\) and its first derivative with respect to x is \(-\dfrac{b}{a}\log_e 2\) when \(x = 1\), where a and b are integers, then the minimum value of \(|a^2 - b^2|\) is ____________ .

If \((2021)^{3762}\) is divided by 17, then the remainder is __________.

The equation of the plane which contains the y-axis and passes through the point \((1, 2, 3)\) is :

Choose the incorrect statement about the two circles whose equations are given below :
\(x^2 + y^2 - 10x - 10y + 41 = 0\) and
\(x^2 + y^2 - 16x - 10y + 80 = 0\)

Let \(\vec{a} = 2\hat{i} - 3\hat{j} + 4\hat{k}\) and \(\vec{b} = 7\hat{i} + \hat{j} - 6\hat{k}\).
If \(\vec{r}\times\vec{a} = \vec{r}\times\vec{b}\), \(\vec{r}\cdot(\hat{i} + 2\hat{j} + \hat{k}) = -3\), then \(\vec{r}\cdot(2\hat{i} - 3\hat{j} + \hat{k})\) is equal to :

If \(A = \begin{pmatrix} 0 & \sin\alpha \\ \sin\alpha & 0 \end{pmatrix}\) and \(\det\left(A^2 - \frac{1}{2}I\right) = 0\), then a possible value of \(\alpha\) is :

Team 'A' consists of 7 boys and \(n\) girls and Team 'B' has 4 boys and 6 girls. If a total of 52 single matches can be arranged between these two teams when a boy plays against a boy and a girl plays against a girl, then \(n\) is equal to :

If the Boolean expression \((p \Rightarrow q) \Leftrightarrow (q * (\sim p))\) is a tautology, then the boolean expression \((p * (\sim q))\) is equivalent to :

The line \(2x - y + 1 = 0\) is a tangent to the circle at the point \((2, 5)\) and the centre of the circle lies on \(x - 2y = 4\). Then, the radius of the circle is :

The area of the triangle with vertices \(A(z)\), \(B(iz)\) and \(C(z + iz)\) is :

The system of equations \(kx + y + z = 1\), \(x + ky + z = k\) and \(x + y + zk = k^2\) has no solution if \(k\) is equal to :