List of top Mathematics Questions asked in JEE Main

The point $(2, 1)$ is translated parallel to the line $L : x-y = 4$ by $2\sqrt{3}$ units. If the new point $Q$ lies in the third quadrant, then the equation of the line passing through $Q$ and perpendicular to $L$ is :

The sum $\displaystyle\sum^{10}_{r=1}(r^2 + 1) \times (r!)$ is equal to :

Two sides of a rhombus are along the lines, $x - y + 1 = 0$ and $7x - y - 5 = 0$. If its diagonals intersect at $(-1, -2)$, then which one of the following is a vertex of this rhombus?

Consider the following statements :
P : Suman is brilliant.
Q : Suman is rich.
R : Suman is honest.
The negation of the statement, "Suman is brilliant and dishonest if and only if Suman is rich" can be equivalently expressed as :

Let 10 vertical poles standing at equal distances on a straight line, subtend the same angle of elevation \(\alpha\) at a point O on this line and all the poles are on the same side of O. If the height of the longest pole is 'h' and the distance of the foot of the smallest pole from O is 'a'; then the distance between two consecutive poles, is :

If \(\cos\alpha+\cos\beta=\frac{3}{2}\) and \(\sin\alpha+\sin\beta=\frac{1}{2}\) and \(\theta\) is the arithmetic mean of \(\alpha\) and \(\beta\), then \(\sin2\theta+\cos2\theta\) is equal to :

If the lengths of the sides of a triangle are decided by the three throws of a single fair die, then the probability that the triangle is of maximum area given that it is an isosceles triangle, is :

In a parallelogram ABCD, \(\left|\overrightarrow{AB}\right|=a\), \(\left|\overrightarrow{AD}\right|=b\) and \(\left|\overrightarrow{AC}\right|=c\), then \(\overrightarrow{DB}\cdot\overrightarrow{AB}\) has the value :

The shortest distance between the \(z\)-axis and the line \(x+y+2z-3=0=2x+3y+4z-4\), is :

If the distance between the foci of an ellipse is half the length of its latus rectum, then the eccentricity of the ellipse is :

A plane containing the point \((3,2,0)\) and the line \(\frac{x-1}{1}=\frac{y-2}{5}=\frac{z-3}{4}\) also contains the point :

If the incentre of an equilateral triangle is \((1,1)\) and the equation of its one side is \(3x+4y+3=0\), then the equation of the circumcircle of this triangle is :

If a circle passing through the point \((-1,0)\) touches \(y\)-axis at \((0,2)\), then the length of the chord of the circle along the \(x\)-axis is :

A straight line L through the point \((3,-2)\) is inclined at an angle of \(60^\circ\) to the line \(\sqrt{3}\,x+y=1\). If L also intersects the \(x\)-axis, then the equation of L is :

If \(\displaystyle\int\dfrac{\log\left(t+\sqrt{1+t^2}\right)}{\sqrt{1+t^2}}\,dt=\dfrac12\left(g(t)\right)^2+C\), where C is a constant, then \(g(2)\) is equal to :

Let \(f:(-1,1)\to\mathbf{R}\) be a continuous function. If \(\int_0^{\sin x} f(t)\,dt=\frac{\sqrt{3}}{2}x\), then \(f\left(\frac{\sqrt{3}}{2}\right)\) is equal to :

Let \(f:\mathbf{R}\to\mathbf{R}\) be a function such that \(f(2-x)=f(2+x)\) and \(f(4-x)=f(4+x)\), for all \(x\in\mathbf{R}\) and \(\int_0^2 f(x)\,dx=5\). Then the value of \(\int_{10}^{50} f(x)\,dx\) is :

From the top of a 64 metres high tower, a stone is thrown upwards vertically with the velocity of 48 m/s. The greatest height (in metres) attained by the stone, assuming the value of the gravitational acceleration \(g=32\) m/s\(^2\), is :

The equation of a normal to the curve, \(\sin y=x\sin\left(\dfrac{\pi}{3}+y\right)\) at \(x=0\), is :

Let k and K be the minimum and the maximum values of the function \(f(x)=\dfrac{(1+x)^{0.6}}{1+x^{0.6}}\) in \([0,1]\) respectively, then the ordered pair \((k, K)\) is equal to :

If A is a \(3\times3\) matrix such that \(|5\cdot \operatorname{adj}A|=5\), then \(|A|\) is equal to :

The sum of the \(3^{rd}\) and the \(4^{th}\) terms of a G.P. is 60 and the product of its first three terms is 1000. If the first term of this G.P. is positive, then its \(7^{th}\) term is :

If \(\displaystyle\sum_{n=1}^{5}\dfrac{1}{n(n+1)(n+2)(n+3)}=\dfrac{k}{3}\), then k is equal to :

If the two roots of the equation, \((a-1)(x^4+x^2+1)+(a+1)(x^2+x+1)^2=0\) are real and distinct, then the set of all values of 'a' is :

If \(z\) is a non-real complex number, then the minimum value of \(\dfrac{\operatorname{Im} z^5}{(\operatorname{Im} z)^5}\) is :