List of top Mathematics Questions asked in JEE Main

The slope of tangent at any point (x, y) on a curve y = y(x) is \(\frac{x^2+y^2}{2xy},x>0\) If y(2) = 0, then a value of y(8) is
 
Let f be a differentiable function such that x2 f(x) - x = \(4 \int^x_0tf(t)dt,f(1)=\frac{2}{3}. \;\text{Then 18f(3)is equal to}\)
 
If I(x) = \(\int e^{sin^2x}\)\((cos \;x \;sin \;2x - sin \;x)dx\) and I (0) = 1, then \(I(π/3)\) is equal to
From a square of side 30 cm the squares of side x cm is cut off to make a cuboid of maximum volume. The surface area of cuboid with open top is?
Let the first term a and the common ratio r of a geometric progression be positive integers. If the sum of its squares of first three terms is 33033, then the sum of these three terms is equal to
Let the complex number \( z = x + iy \) be such that \(\frac{2z - 3i}{2z + i}\) is purely imaginary. If \( x + y^2 = 0 \), then \( y^4 + y^2 - y \) is equal to

The total number of six digit numbers, formed using the digits 4,5,9 only and divisible by 6 , is __

Let the sixth term in the binomial expansion of \(({\sqrt{2}^{log_{2}}(10-3^{x})+\sqrt[5]{2^{(x-2)log_{2}{3}}}})^{m}\), in the increasing powers of \(2^{(x-2)log_{2}3}\), be 21 If the binomial coefficients of the second, third and fourth terms in the expansion are respectively the first, third and fifth terms of an AP, then the sum of the squares of all possible values of x is

If the term without \(x\) in the expansion of \(\left(x^{\frac{2}{3}}+\frac{\alpha}{x^3}\right)^{22}\)is 7315 , then \(|\alpha|\) is equal to ___

The sum of the common terms of the following three arithmetic progressions\(3,7,11,15, \ldots , 399\), \(2,5,8,11, \ldots , 359\)and \(2,7,12,17, \ldots , 197,\) is equal to _____

Number of integral solutions to the equation \(x+y+z=21\), where \(x \geq 1\), \(y \geq 3\), \(z \geq 4\), is equal to ___

The point of intersection \(C\) of the plane \(8 x+y+2 z=0\) and the line joining the points \(A (-3,-6,1)\) and \(B (2,4,-3)\)divides the line segment \(AB\) internally in the ratio\(k : 1 \  If a , b , c (| a |,| b |, | c |\)are coprime) are the direction ratios of the perpendicular from the point \(C\)on the line \(\frac{1-x}{1}=\frac{y+4}{2}=\frac{z+2}{3}\), then \(| a + b + c |\)is equal to ___

\(25 \%\) of the population are smokers A smoker has 27 times more chances to develop lung cancer than a non smoker A person is diagnosed with lung cancer and the probability that this person is a smoker is \(\frac{k}{10}\), Then the value of \(k\) is____
Points \(P(-3,2), Q(9,10)\) and \(R(\alpha, 4)\) lie on a circle \(C\) with \(P R\) as its diameter. The tangents to \(C\) at the points \(Q\) and \(R\) intersect at the point \(S\). If $S$ lies on the line \(2 x-k y-1\), then \(k\) is equal to_____
Suppose Anil's mother wants to give 5 whole fruits to Anil from a basket of 7 red apples, 5 white apples and 8 oranges If in the selected 5 fruits, at least 2 oranges, at least one red apple and at least one white apple must be given, then the number of ways, Anil's mother can ofter 5 fruits to Anil is______
If \(\int\limits_{\frac{1}{3}}^{3}\left|\log _e x\right| d x=\frac{m}{n} \log e\left(\frac{n^2}{v}\right)\), where \(m\) and \(n\) are coprime natural numbers, then \(m^2+n^2-5\) is equal to _____
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 \(\displaystyle\lim _{t \rightarrow \infty} y(t)\)
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