List of top Mathematics Questions asked in JEE Main

If \(x = a,\ y = b,\ z = c\) is a solution of the system of linear equations
\(x + 8y + 7z = 0\)
\(9x + 2y + 3z = 0\)
\(x + y + z = 0\)
such that the point \((a, b, c)\) lies on the plane \(x + 2y + z = 6\), then \(2a + b + c\) equals :

If three positive numbers a, b and c are in A.P. such that \(abc = 8\), then the minimum possible value of b is :

The value of k for which the function \(f(x) = \begin{cases} \left(\frac{4}{5}\right)^{\frac{\tan 4x}{\tan 5x}}, & 0 \lt x \lt \frac{\pi}{2} \\ k + \frac{2}{5}, & x = \frac{\pi}{2} \end{cases}\) is continuous at \(x = \frac{\pi}{2}\), is :

If \(2x = y^{\frac15} + y^{-\frac15}\) and \((x^2 - 1)\frac{d^2y}{dx^2} + \lambda x\frac{dy}{dx} + ky = 0\), then \(\lambda + k\) is equal to :

For two \(3 \times 3\) matrices A and B, let \(A + B = 2B'\) and \(3A + 2B = I_3\), where \(B'\) is the transpose of B and \(I_3\) is \(3 \times 3\) identity matrix. Then :

The function \(f : \mathbf{N} \to \mathbf{N}\) defined by \(f(x) = x - 5\left[\frac{x}{5}\right]\), where \(\mathbf{N}\) is the set of natural numbers and \([x]\) denotes the greatest integer less than or equal to \(x\), is :

The sum of all the real values of \(x\) satisfying the equation \(2^{(x-1)(x^2+5x-50)} = 1\) is :

The equation \(\mathrm{Im}\left(\frac{iz - 2}{z - i}\right) + 1 = 0,\ z \in \mathbf{C},\ z \neq i\) represents a part of a circle having radius equal to :

Three persons P, Q and R independently try to hit a target. If the probabilities of their hitting the target are \(\frac{3}{4}\), \(\frac{1}{2}\) and \(\frac{5}{8}\) respectively, then the probability that the target is hit by P or Q but not by R is :

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

If
\(S = \left\{x \in [0, 2\pi] : \begin{vmatrix} 0 \& \cos x \& -\sin x \\ \sin x \& 0 \& \cos x \\ \cos x \& \sin x \& 0 \end{vmatrix} = 0\right\}\),
then \(\sum_{x \in S} \tan\left(\frac{\pi}{3} + x\right)\) is equal to :

The mean age of 25 teachers in a school is 40 years. A teacher retires at the age of 60 years and a new teacher is appointed in his place. If now the mean age of the teachers in this school is 39 years, then the age (in years) of the newly appointed teacher is :

The area (in sq. units) of the parallelogram whose diagonals are along the vectors \(8\hat{i} - 6\hat{j}\) and \(3\hat{i} + 4\hat{j} - 12\hat{k}\), is :

The line of intersection of the planes \(\vec{r} \cdot (3\hat{i} - \hat{j} + \hat{k}) = 1\) and \(\vec{r} \cdot (\hat{i} + 4\hat{j} - 2\hat{k}) = 2\), is :

Consider an ellipse, whose centre is at the origin and its major axis is along the x-axis. If its eccentricity is \(\frac{3}{5}\) and the distance between its foci is 6, then the area (in sq. units) of the quadrilateral inscribed in the ellipse, with the vertices as the vertices of the ellipse, is :

The coordinates of the foot of the perpendicular from the point \((1, -2, 1)\) on the plane containing the lines, \(\frac{x+1}{6} = \frac{y-1}{7} = \frac{z-3}{8}\) and \(\frac{x-1}{3} = \frac{y-2}{5} = \frac{z-3}{7}\), is :

The integral \(\displaystyle\int_{\pi/12}^{\pi/4} \frac{8\cos 2x}{(\tan x + \cot x)^3}\,dx\) equals :

The locus of the point of intersection of the straight lines,
\(tx - 2y - 3t = 0\)
\(x - 2ty + 3 = 0\) \((t \in \mathbf{R})\), is :

If two parallel chords of a circle, having diameter 4 units, lie on the opposite sides of the centre and subtend angles \(\cos^{-1}\left(\frac{1}{7}\right)\) and \(\sec^{-1}(7)\) at the centre respectively, then the distance between these chords, is :

The curve satisfying the differential equation, \(y\,dx - (x + 3y^2)\,dy = 0\) and passing through the point \((1, 1)\), also passes through the point :

If the common tangents to the parabola, \(x^2 = 4y\) and the circle, \(x^2 + y^2 = 4\) intersect at the point P, then the distance of P from the origin, is :

The area (in sq. units) of the smaller portion enclosed between the curves, \(x^2 + y^2 = 4\) and \(y^2 = 3x\), is :

If a point \(P\) has co-ordinates \((0, -2)\) and \(Q\) is any point on the circle, \(x^2 + y^2 - 5x - y + 5 = 0\), then the maximum value of \((PQ)^2\) is :

If the sum of the first \(n\) terms of the series \(\sqrt{3} + \sqrt{75} + \sqrt{243} + \sqrt{507} + \ldots\) is \(435\sqrt{3}\), then \(n\) equals :

If the arithmetic mean of two numbers \(a\) and \(b\), \(a \gt b \gt 0\), is five times their geometric mean, then \(\frac{a+b}{a-b}\) is equal to :