List of top Mathematics Questions asked in JEE Main

\(3 \times 7^{22} + 2 \times 10^{22} - 44\) when divided by 18 leaves the remainder _________.
An online exam is attempted by 50 candidates out of which 20 are boys. The average marks obtained by boys is 12 with a variance 2. The variance of marks obtained by 30 girls is also 2. The average marks of all 50 candidates is 15. If \(\mu\) is the average marks of girls and \(\sigma^2\) is the variance of marks of 50 candidates, then \(\mu + \sigma^2\) is equal to _________.
Two circles each of radius 5 units touch each other at the point (1, 2). If the equation of their common tangent is 4x + 3y = 10, and C\(_1\)(\(\alpha\), \(\beta\)) and C\(_2\)(\(\gamma\), \(\delta\)), C\(_1\) \(\neq\) C\(_2\) are their centres, then \(|(\alpha+\beta)(\gamma+\delta)|\) is equal to _________.
Let S be the sum of all solutions (in radians) of the equation \(\sin^4\theta + \cos^4\theta - \sin\theta \cos\theta = 0\) in [0, 4\(\pi\)]. Then \(\frac{8S}{\pi}\) is equal to _________.
Let A(sec\(\theta\), 2tan\(\theta\)) and B(sec\(\phi\), 2tan\(\phi\)), where \(\theta+\phi=\pi/2\), be two points on the hyperbola \(2x^2-y^2=2\). If (\(\alpha\), \(\beta\)) is the point of the intersection of the normals to the hyperbola at A and B, then \((2\beta)^2\) is equal to _________.
The angle between the straight lines, whose direction cosines are given by the equations 2l + 2m - n = 0 and mn + nl + lm = 0, is :
The equation of the plane passing through the line of intersection of the planes \( \vec{r} \cdot (\hat{i} + \hat{j} + \hat{k}) = 1 \) and \( \vec{r} \cdot (2\hat{i} + 3\hat{j} - \hat{k}) + 4 = 0 \) and parallel to the x-axis is :
The Boolean expression \((p \land q) \Rightarrow ((r \land q) \land p)\) is equivalent to :
Each of the persons A and B independently tosses three fair coins. The probability that both of them get the same number of heads is :
A differential equation representing the family of parabolas with axis parallel to y-axis and whose length of latus rectum is the distance of the point (2, -3) form the line 3x + 4y = 5, is given by :
The area of the region bounded by the parabola \((y-2)^2 = (x-1)\), the tangent to it at the point whose ordinate is 3 and the x-axis is :
If the solution curve of the differential equation \((2x - 10y^3)dy + y dx = 0\), passes through the points (0, 1) and (2, \(\beta\)), then \(\beta\) is a root of the equation :
Let A(a, 0), B(b, 2b + 1) and C(0, b), b \(\neq\) 0, |b| \(\neq\) 1, be points such that the area of triangle ABC is 1 sq. unit, then the sum of all possible values of a is :
If two tangents drawn from a point P to the parabola \(y^2 = 16(x-3)\) are at right angles, then the locus of point P is :
If \( \lim_{x \to \infty} (\sqrt{x^2 - x + 1} - ax) = b \), then the ordered pair (a, b) is :
If 0 \(<\) x \(<\) 1 and y = \(\frac{1}{2}x^2 + \frac{2}{3}x^3 + \frac{3}{4}x^4 + ...\), then the value of e\(^{1+y}\) at x = \(\frac{1}{2}\) is :
A box open from top is made from a rectangular sheet of dimension a \(\times\) b by cutting squares each of side x from each of the four corners and folding up the flaps. If the volume of the box is maximum, then x is equal to:
Let [\(\lambda\)] be the greatest integer less than or equal to \(\lambda\). The set of all values of \(\lambda\) for which the system of linear equations x+y+z=4, 3x+2y+5z=3, 9x + 4y + (28 + [\(\lambda\)])z = [\(\lambda\)] has a solution is :
The set of all values of k \(>\) -1, for which the equation
(3x\(^2\)+4x+3)\(^2\) - (k+1)(3x\(^2\)+4x+3)(3x\(^2\)+4x+2) + k(3x\(^2\)+4x+2)\(^2\) = 0 has real roots, is :
If $\int \frac{dx}{(x^2 + x + 1)^2} = a \tan^{-1} \left( \frac{2x + 1}{\sqrt{3}} \right) + b \left( \frac{2x + 1}{x^2 + x + 1} \right) + C, x>0$ where C is the constant of integration, then the value of $9(\sqrt{3}a + b)$ is equal to _________.
Let $\vec{a} = \hat{i} + 5\hat{j} + \alpha\hat{k}$, $\vec{b} = \hat{i} + 3\hat{j} + \beta\hat{k}$ and $\vec{c} = -\hat{i} + 2\hat{j} - 3\hat{k}$ be three vectors such that, $|\vec{b} \times \vec{c}| = 5\sqrt{3}$ and $\vec{a}$ is perpendicular to $\vec{b}$. Then the greatest amongst the values of $|\vec{a}|^2$ is _________.
If the minimum area of the triangle formed by a tangent to the ellipse $\frac{x^2}{b^2} + \frac{y^2}{4a^2} = 1$ and the co-ordinate axis is kab, then k is equal to _________.
Let the equation $x^2 + y^2 + px + (1 - p)y + 5 = 0$ represent circles of varying radius $r \in (0, 5]$. Then the number of elements in the set $S = \{q : q = p^2 \text{ and } q \text{ is an integer}\}$ is _________.
If $y^{1/4} + y^{-1/4} = 2x$, and $(x^2 - 1)\frac{d^2y}{dx^2} + \alpha x \frac{dy}{dx} + \beta y = 0$, then $|\alpha - \beta|$ is equal to _________.
If the system of linear equations
$2x + y - z = 3$
$x - y - z = \alpha$
$3x + 3y + \beta z = 3$
has infinitely many solutions, then $\alpha + \beta - \alpha\beta$ is equal to _________.