List of top Mathematics Questions asked in JEE Main

A hyperbola passes through the foci of the ellipse $\frac{x^2}{25} + \frac{y^2}{16} = 1$ and its transverse and conjugate axes coincide with major and minor axes of the ellipse, respectively. If the product of their eccentricities is one, then the equation of the hyperbola is:
Three numbers are in an increasing geometric progression with common ratio \( r \). If the middle number is doubled, then the new numbers are in an arithmetic progression with common difference \( d \). If the fourth term of GP is \( 3 r^2 \), then \( r^2 - d \) is equal to :
The value of \(2 \sin(\frac{\pi}{8}) \sin(\frac{2\pi}{8}) \sin(\frac{3\pi}{8}) \sin(\frac{5\pi}{8}) \sin(\frac{6\pi}{8}) \sin(\frac{7\pi}{8})\) is :
The value of the integral \( \int_{0}^{1} \frac{\sqrt{x} dx}{(1+x)(1+3x)(3+x)} \) is :
The angle between the straight lines, whose direction cosines are given by the equations 2l + 2m - n = 0 and mn + nl + lm = 0, is :
Let the foot of perpendicular from a point $P(1, 2, -1)$ to the straight line $L: \frac{x}{1} = \frac{y}{0} = \frac{z}{-1}$ be $N$. Let a line be drawn from $P$ parallel to the plane $x + y + 2z = 0$ which meets $L$ at point $Q$. If $\alpha$ is the acute angle between the lines $PN$ and $PQ$, then $\cos \alpha$ is equal to ________.
The function \( f(x) = \dfrac{4x^3 - 3x^2}{6} - 2 \sin x + (2x - 1)\cos x \) :
The equation of one of the straight lines which passes through the point (1, 3) and makes an angle tan⁻¹(√2) with the straight line, y + 1 = 3√2 x is :
The domain of the function \(\text{cosec}^{-1}\left(\frac{1+x}{x}\right)\) is :
The local maximum value of the function \(f(x) = \left(\frac{2}{x}\right)^{x^2}, x>0\), is :
The value of \(\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{1+\sin^2x}{1+\pi^{\sin x}} dx\) is :
Let \(y(x)\) be the solution of the differential equation \(2x^2 dy + (e^y - 2x)dx = 0, x>0\). If \(y(e)=1\), then \(y(1)\) is equal to :
The point P\((-2\sqrt{6}, \sqrt{3})\) lies on the hyperbola \(\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\) having eccentricity \(\frac{\sqrt{5}}{2}\). If the tangent and normal at P to the hyperbola intersect its conjugate axis at the points Q and R respectively, then QR is equal to :
The locus of the mid points of the chords of the hyperbola \(x^2-y^2=4\), which touch the parabola \(y^2 = 8x\), is :
Consider the two statements :
(S1) : \((p \to q) \lor (\neg q \to p)\) is a tautology.
(S2) : \((p \land \neg q) \land (\neg p \lor q)\) is a fallacy.
Then :
Let \([t]\) denote the greatest integer less than or equal to t.
Let \(f(x)=x-[x]\), \(g(x)=1-x+[x]\), and \(h(x) = \min\{f(x), g(x)\}\), \(x \in [-2, 2]\).
Then h is :
A fair die is tossed until six is obtained on it. Let X be the number of required tosses, then the conditional probability P(\(X \ge 5 | X>2\)) is :
Let P be the plane passing through the point (1, 2, 3) and the line of intersection of the planes \(\vec{r} \cdot (\hat{i} + \hat{j} + 4\hat{k}) = 16\) and \(\vec{r} \cdot (-\hat{i} + \hat{j} + \hat{k}) = 6\). Then which of the following points does NOT lie on P ?
Let \(\lambda \neq 0\) be in R. If \(\alpha\) and \(\beta\) are the roots of the equation \(x^2 - x + 2\lambda = 0\), and \(\alpha\) and \(\gamma\) are the roots of the equation \(3x^2 - 10x + 27\lambda = 0\), then \(\frac{\beta\gamma}{\lambda}\) is equal to ___________.
Let A be a 3\(\times\)3 real matrix. If \(\det(2 \text{Adj}(2 \text{Adj}(\text{Adj} (2A)))) = 2^{41}\), then the value of \(\det (A^2)\) equals ___________.
Let \(\binom{n}{k}\) denote \(^nC_k\).
If \(A_k = \sum_{i=0}^{9} \binom{9}{i} \binom{12}{12-k+i} + \sum_{i=0}^{8} \binom{8}{i} \binom{13}{13-k+i}\) and \(A_4 - A_3 = 190 p\), then p is equal to ___________.
The sum of all 3-digit numbers less than or equal to 500, that are formed without using the digit "1" and they all are multiple of 11, is ___________.
Let a and b respectively be the points of local maximum and local minimum of the function \(f(x) = 2x^3 - 3x^2 - 12x\). If A is the total area of the region bounded by \(y=f(x)\), the x-axis and the lines \(x = a\) and \(x = b\), then 4A is equal to ___________.
Let the mean and variance of four numbers 3, 7, x and y (\(x>y\)) be 5 and 10 respectively. Then the mean of four numbers 3+2x, 7+2y, x+y and x-y is ___________.
If the projection of the vector \(\hat{i} + 2\hat{j} + \hat{k}\) on the sum of the two vectors \(2\hat{i} + 4\hat{j} - 5\hat{k}\) and \(-\lambda\hat{i} + 2\hat{j} + 3\hat{k}\) is 1, then \(\lambda\) is equal to ___________.