List of top Mathematics Questions asked in JEE Main

The set of all values of \(\lambda\) for which the system of linear equations 
\(2x_1-2x_2+x_3=\lambda x_1\)
 \(2x_1-3x_2+2x_3=\lambda x_2\)
\(-x_1+2x_2=\lambda x_3\) has a non-trivial solution

The equation of the plane containing the lines $2x - 5y + z = 3, x + y + \, z = 5$ and parallel to the plane $x + 3 y+ 6 z = 1$ is

If $12$ identical balls are to be placed in $3$ different boxes, then the probability that one of the boxes contains excatly $3$ balls, is

If $f\left(x\right) = 2 \tan^{-1} x + \sin^{-1} \left(\frac{2x}{1+x^{2}}\right), x > 1$, then $f(t)$ is equal to :

If in a regular polygon the number of diagonals is $54$, then the number of sides of this polygon is :

If $\begin{vmatrix}x^{2}+x&x+1&x-2\\ 2x^{2}+3x-1&3x&3x-3\\ x^{2}+2x+3&2x-1&2x-1\end{vmatrix}=ax-12,$ then 'a' is equal to :

In a certain town, $25\%$ of the families own a phone and $15\%$ own a car $65\%$ families own neither a phone nor a car and $2,000$ families own both a car and a phone. Consider the following three statements : (a) $5\%$ families own both a car and a phone. (b) $35\%$ families own either a car or a phone. (c) $40,000$ families live in the town. Then,

The number of ways of selecting $15$ teams from $15$ men and $15$ women, such that each team consists of a man and a woman. is :

The value of $\int \limits \frac {dx}{x^2(x^4+1)^{3/4}}$ is

The value of $ \displaystyle \sum^{30}_{r = 16} (r + 2)(r - 3)$ is equal to :

The number of common tangents to the circles $x^2+y^2-4x-6y-12=0$ and $x^2+y^2+6x+18y+26=0$

The number of integers greater than $6,000$ that can be formed using the digits $3, 5, 6, 7$ and $ 8$ without repetition is

The term independent of $x$ in the binomial expansion of $\left(1-\frac{1}{x}+3x^{5}\right)\left(2x^{2}-\frac{1}{x}\right)^{8}$ is :

The solution of the differential equation $ydx - (x + 2y^2)dy = 0$ is $x = f(y)$. If $f(- 1) = 1$, then $f(1)$ is equal to :

A biased coin with probability p, \(0<\mathrm{p}<1\), of heads is tossed until a head appears for the first time. If the probability that the number of tosses required is even is \(\frac{2}{5}\), then p is equal to :

Let \(p\) and \(q\) be any two propositions.
Statement 1 : \((p \rightarrow q) \leftrightarrow q \vee \sim p\) is a tautology.
Statement 2 : \(\sim(\sim p \wedge q) \wedge(p \vee q) \leftrightarrow p\) is a fallacy.

If the mean and the standard deviation of 10 observations \(x_{1}, x_{2}, \ldots \ldots, x_{10}\) are 2 and 3 respectively, then the mean of \(\left(x_{1}+1\right)^{2}\), \(\left(x_{2}+1\right)^{2}, \ldots \ldots,\left(x_{10}+1\right)^{2}\) is equal to :

A vertical pole stands at a point A on the boundary of a circular park of radius \(a\) and subtends an angle \(\alpha\) at another point B on the boundary. If the chord AB subtends an angle \(\alpha\) at the centre of the park, the height of the pole is :

Let \(\frac{3 \pi}{4}<\theta<\pi\) and
\(\sqrt{2 \cot \theta+\frac{1}{\sin ^{2} \theta}}=\mathrm{K}-\cot \theta\),
then \(\mathrm{K}\) is equal to :

A variable plane is at a constant distance \(p\) from the origin \(\mathrm{O}\) and meets the set of rectangular axes \(\mathrm{OX}_{i}\) \((i=1,2,3)\) at points \(\mathrm{A}_{i}\) \((i=1,2,3)\), respectively. If planes are drawn through \(\mathrm{A}_{1}\), \(\mathrm{A}_{2}\), \(\mathrm{A}_{3}\), which are parallel to the coordinate planes, then the locus of their point of intersection is :

Unit vectors \(\vec{a}\), \(\vec{b}\), \(\vec{c}\) are coplanar. A unit vector \(\vec{d}\) is perpendicular to them. If \((\vec{a} \times \vec{b}) \times(\vec{c} \times \vec{d})=\frac{1}{6} \hat{i}-\frac{1}{3} \hat{j}+\frac{1}{3} \hat{k}\) and the angle between \(\vec{a}\) and \(\vec{b}\) is \(30^{\circ}\), then \(\vec{c}\) is/are :

If the lines \(\frac{x-4}{1}=\frac{y-2}{1}=\frac{z-\lambda}{3}\) and \(\frac{x}{1}=\frac{y+2}{2}=\frac{z}{4}\) intersect each other, then \(\lambda\) lies in the interval :

If a circle has two of its diameters along the lines \(x+y=5\) and \(x-y=1\) and has area \(9\pi\), then the equation of the circle is :

Let \(\mathrm{P}\) be a point in the first quadrant lying on the ellipse \(9x^{2}+16y^{2}=144\), such that the tangent at \(\mathrm{P}\) to the ellipse is inclined at an angle \(135^{\circ}\) to the positive direction of \(x\)-axis. Then the coordinates of \(\mathrm{P}\) are :

Consider the differential equation, \(y\,dx-\left(x+y^{2}\right)dy=0\). If for \(y=1\), \(x\) takes value 1, then value of \(x\) when \(y=4\) is :