List of top Mathematics Questions asked in JEE Main

Let \(\vec{u}\) be a vector coplanar with the vectors \(\vec{a}=2\hat{i}+3\hat{j}-\hat{k}\) and \(\vec{b}=\hat{j}+\hat{k}\). If \(\vec{u}\) is perpendicular to \(\vec{a}\) and \(\vec{u}\cdot\vec{b}=24\), then \(|\vec{u}|^2\) is equal to

From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is :

Let \(a_1,a_2,a_3,\ldots,a_{49}\) be in A.P. such that \(\sum_{k=0}^{12}a_{4k+1}=416\) and \(a_9+a_{43}=66\). If \(a_1^2+a_2^2+\cdots+a_{17}^2=140m\), then \(m\) is equal to

Let \(y=y(x)\) be the solution of the differential equation \(\sin x\frac{dy}{dx}+y\cos x=4x\), \(x\in(0,\pi)\). If \(y\left(\frac{\pi}{2}\right)=0\), then \(y\left(\frac{\pi}{6}\right)\) is equal to :

Let \(g(x)=\cos x^2\), \(f(x)=\sqrt{x}\) and \(\alpha,\beta\ (\alpha\lt\beta)\) be the roots of the quadratic equation \(18x^2-9\pi x+\pi^2=0\). Then the area (in sq. units) bounded by the curve \(y=(g\circ f)(x)\) and the lines \(x=\alpha\), \(x=\beta\) and \(y=0\) is :

The integral \(\int\frac{\sin^2x\cos^2x}{\left(\sin^5x+\cos^3x\sin^2x+\sin^3x\cos^2x+\cos^5x\right)^2}dx\) is equal to

If \(\begin{vmatrix}x-4&2x&2x\\2x&x-4&2x\\2x&2x&x-4\end{vmatrix}=(A+Bx)(x-A)^2\), then the ordered pair \((A,B)\) is equal to :

If \(\alpha,\beta\in C\) are the distinct roots of the equation \(x^2-x+1=0\), then \(\alpha^{101}+\beta^{107}\) is equal to :

For each \(t\in R\), let \([t]\) be the greatest integer less than or equal to \(t\). Then \(\lim_{x\to0^+}x\left(\left[\frac{1}{x}\right]+\left[\frac{2}{x}\right]+\cdots+\left[\frac{15}{x}\right]\right)\)

Let \(S=\{t\in R: f(x)=|x-\pi|\cdot\left(e^{|x|}-1\right)\sin|x|\) is not differentiable at \(t\}\), then the set \(S\) is equal to

Let \(f(x)=x^2+\frac{1}{x^2}\) and \(g(x)=x-\frac{1}{x}\), \(x\in R-\{-1,0,1\}\). If \(h(x)=\frac{f(x)}{g(x)}\), then the local minimum value of \(h(x)\) is

For a positive integer $n$, if the mean of the binomial coefficients in the expansion of $(a + b)^{2n - 3}$ is 16, then $n$ is equal to :

If the length of the latus rectum of an ellipse is $4$ units and the distance between a focus and its nearest vertex on the major axis is $\frac{3}{2}$ units, then its eccentricity is :

If the tangent at $(1, 7)$ to the curve $x^2 = y - 6$ touches the circle $x^2 + y^2 + 16x + 12y + c = 0$ then the value of c is:

The solution of the differential equation $\frac{y dx + x dy}{y dx - x dy} = \frac{x^{2} e^{xy}}{y^{4}} $ satisfying $y(0) = 1$, is :

If the system of linear equations : $x + 3y + 7z = 0 $ $-x + 4y + 7z = 0$ $(\sin 3 \theta ) x + (\cos 2 \theta) y + 2z = 0 $ has a non-trivial solution, then the number of values of 6 lying in the interval $[0, \pi ]$, is :

The foci of a hyperbola coincide with the foci of the ellipse $\frac{x^{2}}{25} + \frac{y^{2}}{9} = 1 $ If the eccentricity of the hyperbola is 2, then the equation of the tangent to this hyperbola passing through the point (4, 6) is :

From a point A with position vector $p(\hat{i} + \hat{j} + \hat{k})$, AB and AC are drawn perpendicular to the lines $\vec{r} = \hat{k} + \lambda (\hat{i} + \hat{j})$ and $\vec{r} = - \hat{k} + \mu (\hat{i} - \hat{j})$, respectively. A value of p is equal to :

If for a matrix A, |A| = 6 and adj $A = \begin{bmatrix}1&-2&4\\ 4&1&1\\ -1&k&0\end{bmatrix}$ , then k is equal to :

A box contains 5 black and 4 white balls. A ball is drawn at random and its colour is noted. The ball is then put back in the box along with two additional balls of its opposite colour. If a ball is drawn again from the box, then the probability? that the ball drawn now is black, is :

A ball is dropped from a platform $19.6\,m$ high. Its position function is -

A hyperbola, having the transverse axis of length $2 \, \sin \, \theta$ is confocal with the ellipse $3x^2 + 4y^2 = 12$. Its equation is

The sum of the series $S = \frac{1}{19! } + \frac{1}{3!7!} + \frac{1}{5! 5!} + ... $ to 10 terms is equal to :

The negation of $A \to (A \vee \sim B)$ is :

A bag contains $4$ red and $6$ black balls. A ball is drawn at random from the bag, its colour is observed and this ball along with two additional balls of the same colour are returned to the bag. If now a ball is drawn at random from the bag, then the probability that this drawn ball is red, is :