List of top Mathematics Questions asked in JEE Main

If the mean and variance of the data \( 65, 68, 58, 44, 48, 45, 60, \alpha, \beta, 60 \) where \( \alpha > \beta \) are \( 56 \) and \( 66.2 \) respectively, then \( \alpha^2 + \beta^2 \) is equal to

Let \( \alpha, \beta \) be the roots of the equation \( x^2 - x + 2 = 0 \) with \( \text{Im}(\alpha) > \text{Im}(\beta) \). Then \( \alpha^6 + \alpha^4 + \beta^4 - 5 \alpha^2 \) is equal to

A line with direction ratios \( 2, 1, 2 \) meets the lines \(x = y + 2 = z\) and \(x + 2 = 2y = 2z\) respectively at the points \( P \) and \( Q \). If the length of the perpendicular from the point \( (1, 2, 12) \) to the line \( PQ \) is \( l \), then \( l^2 \) is

In an A.P., the sixth term a_6​=2. If the product a₁​a₄​a₅ is the greatest, then the common difference of the A.P. is equal to:

Suppose\(f(x)=\frac{(2^x+2^{-x})tanx\sqrt{tan^{-1}(x^2-x+1)}}{(7x^2+3x+1)^{3}}\) then the value of \(f'(0)\) is equal to

If the solution curve \( y = y \, x \) of the differential equation \((1 + y^2) \left(1 + \log_e x\right) dx + x \, dy = 0, \quad x > 0\) passes through the point \( (1, 1) \) and\[y(e) = \frac{\alpha - \tan\left(\frac{3}{2}\right)}{\beta + \tan\left(\frac{3}{2}\right)},\]then \( \alpha + 2\beta \) is

Equation of two diameters of a circle are \(2x-3y=5\) and \(3x-4y=7\).The line joining the points \((-\frac{22}{7},-4)\) and \((-\frac{1}{7},3)\) intersects the circle at only one point \(P(\alpha,\beta)\).Then \(17\beta-\alpha\) is equal to.

Consider a circle \( (x - \alpha)^2 + (y - \beta)^2 = 50 \), where \( \alpha, \beta> 0 \). If the circle touches the line \( y + x = 0 \) at the point \( P \), whose distance from the origin is \( 4\sqrt{2} \), then \( (\alpha + \beta)^2 \) is equal to ....

A function \(y=f(x)\) satisfies\(f (x)sin2x+sinx-(1+cos^2x) f'(x)=0\) with condition\(f(0)=0\).Then\(f(\frac{\pi}{2})\) equals to

The lines \[ \frac{x - 2}{2} = \frac{y + 2}{-2} = \frac{z - 7}{16} \] and \[ \frac{x + 3}{4} = \frac{y + 2}{3} = \frac{z + 2}{1} \] intersect at the point \( P \). If the distance of \( P \) from the line \[ \frac{x + 1}{2} = \frac{y - 1}{3} = \frac{z - 1}{1} \] is \( l \), then \( 14l^2 \) is equal to \ldots

Let the complex numbers \( \alpha \) and \( \frac{1}{\alpha} \) lie on the circles \[ |z - z_0|^2 = 4 \] and \[ |z - z_0|^2 = 16 \] respectively, where \( z_0 = 1 + i \). Then, the value of \( 100 |\alpha|^2 \) is ....

Let\((5,\frac{a}{4})\),be the circumcenter of a triangle with vertices A (a, -2),B (a, 6)and C \((\frac{a}{4},-2)\).Let \(\alpha\) denote the circumradius, \(\beta\) denote the area and \(\gamma\) denote the perimeter of the triangle. Then \(\alpha+\beta+\gamma\) is

Let \( f(x) = 2^x - x^2, \, x \in \mathbb{R} \). If \( m \) and \( n \) are respectively the number of points at which the curves \( y = f(x) \) and \( y = f'(x) \) intersect the x-axis, then the value of \( m + n \) is

There are 20 lines numbered as 1,2,3,..., 20. And the odd numbered lines intersect at a point and all the even numbered lines are parallel. Find the maximum number of point of intersections

A coin is biased so that a head is twice as likely as a tail. If the coin is tossed 3 times, then the probability of getting two tails and one head is

\(\frac{dy}{dx}\) = \(\frac{(1-x-y^2)}{y}\) and \(x(1)=1\) , then \(5x(2)\) is equal to____.

The value of \(∫_{\frac \pi6}^{\frac \pi3}\sqrt {1-sin2x\ dx}\) is

If ln a, ln b, ln c are in AP and ln a – ln 2b, ln 2b – ln 3c, ln 3c – ln a are in AP then a : b : c is

If \(r = |z|,\ θ = arg(z)\) and \( z = 2 – 2\ tan (\frac {5\pi}{8})\) then find \((r, θ)\).

If \(\frac {3cos\ 2x+cos^32x}{cos^6x-sin^6x}=x^3-x^2+6\), then find sum of roots.

If first term of non-constant GP be \(\frac 18\) and every term is AM of next two, then \( \displaystyle\sum_{r=1}^{20} T_r- \displaystyle\sum_{r=1}^{18} T_r\) is

\(z_1^3+z_2^3=20+15i\) then \(|z_1^4+z_2^4|\) is equal to

For the following data table

\(x_i\)	\(f_i\)
0 - 4	2
4 - 8	4
8 - 12	7
12 - 16	8
16 - 20	6

Find the value of 20M (where M is median of the data)

If \(z = x + iy, \quad xy \neq 0\) satisfies the equation \(z^2 + iz = 0\), then \(|z^2|\); equal to