List of top Mathematics Questions asked in JEE Main

The shortest distance between the curves $ y^2 = 8x $ and $ x^2 + y^2 + 12y + 35 = 0 $ is:

If the four distinct points $ (4, 6) $, $ (-1, 5) $, $ (0, 0) $ and $ (k, 3k) $ lie on a circle of radius $ r $, then $ 10k + r^2 $ is equal to

Consider the lines $ x(3\lambda + 1) + y(7\lambda + 2) = 17\lambda + 5 $. If P is the point through which all these lines pass and the distance of L from the point $ Q(3, 6) $ is $ d $, then the distance of L from the point $ (3, 6) $ is $ d $, then the value of $ d^2 $ is

Let ABCD be a trapezium whose vertices lie on the parabola $ y^2 = 4x $. Let the sides AD and BC of the trapezium be parallel to the y-axis. If the diagonal AC is of length $ \frac{25}{4} $ and it passes through the point $ (1, 0) $, then the area of ABCD is:

If $a = 1 + \sum_{r=1}^{6} (-3)^{r-1} \binom{12}{2r-1}$, then the distance of the point $(12, \sqrt{3})$ from the line $\alpha x - \sqrt{3}y + 1 = 0$ is:

Let the line $x + y = 1$ meet the axes of x and y at A and B, respectively. A right-angled triangle AMN is inscribed in the triangle OAB, where O is the origin and the points M and N lie on the lines OB and AB, respectively. If the area of the triangle AMN is $\frac{4}{9}$ of the area of the triangle OAB and $AN : NB = \lambda : 1$, then the sum of all possible values of $\lambda$ is:

A line passing through the point P$(\sqrt{5}, \sqrt{5})$ intersects the ellipse $ \frac{x^2}{36} + \frac{y^2}{25} = 1 $ at A and B such that (PA).(PB) is maximum. Then 5(PA$^2$ + PB$^2$) is equal to :

If the equation of the hyperbola with foci $ (4, 2) $ and $ (8, 2) $ is $ 3x^2 - y^2 - \alpha x + \beta y + \gamma = 0 $, then $ \alpha + \beta + \gamma $ is equal to _______

Let the parabola $y = x^2 + px - 3$ meet the coordinate axes at the points P, Q and R. If the circle C with centre at (-1, -1) passes through the points P, Q and R, then the area of $\triangle PQR$ is:

If the orthocentre of the triangle formed by the lines $ y = x + 1 $, $ y = 4x - 8 $, and $ y = mx + c $ is at $ (3, -1) $, then $ m - c $ is:

Let \[ I(x) = \int \frac{dx}{(x-11)^{\frac{11}{13}} (x+15)^{\frac{15}{13}}} \] If \[ I(37) - I(24) = \frac{1}{4} \left( b^{\frac{1}{13}} - c^{\frac{1}{13}} \right) \] where $ b, c \in \mathbb{N} $, then \[ 3(b + c) \] is equal to:

If the set of all $ a \in \mathbb{R} \setminus \{1\} $, for which the roots of the equation $ (1 - a)x^2 + 2(a - 3)x + 9 = 0 $ are positive is $ (-\infty, -\alpha] \cup [\beta, \gamma] $, then $ 2\alpha + \beta + \gamma $ is equal to ...........

If the set of all values of $ a $, for which the equation $ 5x^3 - 15x - a = 0 $ has three distinct real roots, is the interval $ (\alpha, \beta) $, then $ \beta - 2\alpha $ is equal to

The product of all solutions of the equation $e^{5(\log_e x)^2 + 3 = x^8, x > 0}$ , is :

Let the foci of a hyperbola be $ (1, 14) $ and $ (1, -12) $. If it passes through the point $ (1, 6) $, then the length of its latus-rectum is:

Find the length of the chord whose midpoint is $ \left( \frac{3}{2}, 0 \right) $ of the ellipse \[ \frac{x^2}{2} + \frac{y^2}{4} = 1. \]

A circle C of radius 2 lies in the second quadrant and touches both the coordinate axes. Let $ r $ be the radius of a circle that has centre at the point $ (2, 5) $ and intersects the circle C at exactly two points. If the set of all possible values of $ r $ is the interval $ (\alpha, \beta) $, then $ 3\beta - 2\alpha $ is equal to:

If the system of equations \[ 2x - y + z = 4, \] \[ 5x + \lambda y + 3z = 12, \] \[ 100x - 47y + \mu z = 212, \] has infinitely many solutions, then $ \mu - 2\lambda $ is equal to:

The sum of all values of $ \theta \in [0, 2\pi] $ satisfying $ 2\sin^2\theta = \cos 2\theta $ and $ 2\cos^2\theta = 3\sin\theta $ is:

Let $ \alpha_1 $ and $ \beta_1 $ be the distinct roots of $ 2x^2 + (\cos\theta)x - 1 = 0, \ \theta \in (0, 2\pi) $. If $ m $ and $ M $ are the minimum and the maximum values of $ \alpha_1 + \beta_1 $, then $ 16(M + m) $ equals:

If the system of equations \[ x + 2y - 3z = 2, \quad 2x + \lambda y + 5z = 5, \quad 14x + 3y + \mu z = 33 \]

has infinitely many solutions, then $ \lambda + \mu $ is equal to:

If $ \sin x + \sin^2 x = 1 $, $ x \in \left(0, \frac{\pi}{2} \right) $, then the expression \[ (\cos^2 x + \tan^2 x) + 3(\cos^4 x + \tan^4 x + \cos^4 x + \tan^4 x) + (\cos^6 x + \tan^6 x) \] is equal to:

Let $ y^2 = 12x $ be the parabola and $ S $ its focus. Let $ PQ $ be a focal chord of the parabola such that $ (SP)(SQ) = \frac{147}{4} $. Let $ C $ be the circle described by taking $ PQ $ as a diameter. If the equation of the circle $ C $ is: \[ 64x^2 + 64y^2 - \alpha x - 64\sqrt{3}y = \beta, \] then $ \beta - \alpha $ is equal to:

Let the function $f(x) = (x^2 - 1)|x^2 - ax + 2| + \cos|x| $ be not differentiable at the two points $ x = \alpha = 2 $ and $ x = \beta $. Then the distance of the point $(\alpha, \beta)$ from the line $12x + 5y + 10 = 0$ is equal to:

Let $ A $ be a matrix of order $ 3 \times 3 $ and $ |A| = 5 $. If $ |2 \, \text{adj}(3A \, \text{adj}(2A))| = 2^{\alpha} \cdot 3^{\beta} \cdot 5^{\gamma}, \quad \alpha, \beta, \gamma \in \mathbb{N} $ then $ \alpha + \beta + \gamma $ is equal to