List of top Mathematics Questions asked in JEE Main

If \(n \ge 1\), \(P_n = \int_1^e (\log x)^n\,dx\), then \(P_{10} - 90P_8\) is equal to:

Let for \(i = 1,2,3\), \(p_i(x)\) be a polynomial of degree 2 in x, \(p_i'(x)\) and \(p_i''(x)\) be the first and second order derivatives of \(p_i(x)\) respectively. Let, \(A(x) = \begin{bmatrix}p_1(x)&p_1'(x)&p_1''(x)\\p_2(x)&p_2'(x)&p_2''(x)\\p_3(x)&p_3'(x)&p_3''(x)\end{bmatrix}\) and \(B(x) = [A(x)]^{T}A(x)\). Then determinant of B(x):

Let \(A(2,3,5)\), \(B(-1,3,2)\) and \(C(\lambda,5,\mu)\) be the vertices of a \(\triangle ABC\). If the median through A is equally inclined to the coordinate axes, then:

The angle of elevation of the top of a vertical tower from a point P on the horizontal ground was observed to be \(\alpha\). After moving a distance 2 metres from P towards the foot of the tower, the angle of elevation changes to \(\beta\). Then the height (in metres) of the tower is:

Let A be a \(3\times3\) matrix such that \(A\begin{bmatrix}1&2&3\\0&2&3\\0&1&1\end{bmatrix}=\begin{bmatrix}0&0&1\\1&0&0\\0&1&0\end{bmatrix}\). Then \(A^{-1}\) is:

Two ships A and B are sailing straight away from a fixed point O along routes such that \(\angle AOB\) is always \(120^\circ\). At a certain instance, \(OA = 8\) km, \(OB = 6\) km and the ship A is sailing at the rate of 20 km/hr while the ship B sailing at the rate of 30 km/hr. Then the distance between A and B is changing at the rate (in km/hr):

The proposition \(\sim(p \vee \sim q) \vee \sim(p \vee q)\) is logically equivalent to:

The set of all real values of \(\lambda\) for which exactly two common tangents can be drawn to the circles \(x^2 + y^2 - 4x - 4y + 6 = 0\) and \(x^2 + y^2 - 10x - 10y + \lambda = 0\) is the interval:

A stair-case of length \(l\) rests against a vertical wall and a floor of a room. Let P be a point on the stair-case, nearer to its end on the wall, that divides its length in the ratio \(1 : 2\). If the staircase begins to slide on the floor, then the locus of P is:

If \(\lim_{x \to 2} \frac{\tan\left((x-2)\left\{x^2 + (k-2)x - 2k\right\}\right)}{x^2 - 4x + 4} = 5\), then \(k\) is equal to:

The base of an equilateral triangle is along the line given by \(3x + 4y = 9\). If a vertex of the triangle is \((1, 2)\), then the length of a side of the triangle is:

The sum of the first 20 terms common between the series \(3 + 7 + 11 + 15 + \ldots\) and \(1 + 6 + 11 + 16 + \ldots\) is:

In a geometric progression, if the ratio of the sum of first 5 terms to the sum of their reciprocals is 49, and the sum of the first and the third term is 35. Then the first term of this geometric progression is:

If \(2\cos\theta + \sin\theta = 1\) \(\left(\theta \ne \frac{\pi}{2}\right)\), then \(7\cos\theta + 6\sin\theta\) is equal to:

If \(z_1, z_2\) and \(z_3, z_4\) are 2 pairs of complex conjugate numbers, then \(\arg\left(\frac{z_1}{z_4}\right) + \arg\left(\frac{z_2}{z_3}\right)\) equals:

If \(\alpha\) and \(\beta\) are roots of the equation, \(x^2 - 4\sqrt{2}kx + 2e^{4\ln k} - 1 = 0\) for some \(k\), and \(\alpha^2 + \beta^2 = 66\), then \(\alpha^3 + \beta^3\) is equal to:

If \(A\) and \(B\) are two events such that \(P(A \cup B) = P(A \cap B)\), then the incorrect statement amongst the following statements is :

Equation of the plane which passes through the point of intersection of lines \(\frac{x-1}{3} = \frac{y-2}{1} = \frac{z-3}{2}\) and \(\frac{x-3}{1} = \frac{y-1}{2} = \frac{z-2}{3}\) and has the largest distance from the origin is:

A line in the 3-dimensional space makes an angle \(\theta\left(0 \lt \theta \le \frac\pi2\right)\) with both the \(X\) and \(Y\)-axes. Then, the set of all values of \(\theta\) is in the interval :

\(\int \frac{\sin^8 x - \cos^8 x}{(1 - 2\sin^2 x\cos^2 x)}\,dx\) is equal to

If \(\left|\vec{a}\right| = 2\), \(\left|\vec{b}\right| = 3\) and \(\left|2\vec{a} - \vec{b}\right| = 5\), then \(\left|2\vec{a} + \vec{b}\right|\) equals :

Let \(A = \{(x, y) : y^2 \le 4x,\ y - 2x \ge -4\}\). The area of the region \(A\) in square units is

If the differential equation representing the family of all circles touching \(x\)-axis at the origin is \((x^2 - y^2)\frac{dy}{dx} = g(x)y\), then \(g(x)\) equals

If \(a, b, c\) are non - zero real numbers and if the system of equations
\((a-1)x = y + z\)
\((b-1)y = x + z\)
\((c-1)z = x + y\)
has a non - trivial solution, then \(ab + bc + ca\) equals :

If \(f(x) = \left(\frac35\right)^x + \left(\frac45\right)^x - 1,\ x \in R\), then the equation \(f(x) = 0\) has :