List of top Mathematics Questions asked in AIEEE

An equation of a common tangent to the parabola $y^{2} = 16\sqrt{3}x$ and the ellipse $2x^{2} + y^{2} = 4$ is $y = 2x + 2\sqrt{3}$ If the line $y = mx + \frac{4\sqrt{3}}{m}, \left(m\ne0\right)$ is a common tangent to the parabola $y^{2} = 16\sqrt{3}x$ and the ellipse $2x^{2} + y^{2} = 4$, then m satisfies $m^{4} + 2m^{2} = 24.$

Let $p, q, r \,\in\, R$ and $r > p > 0$. If the quadratic equation $px^2 + qx + r = 0$ has two complex roots $\alpha$ and $\beta$, then $\left|\alpha\right|+\left|\beta\right|$ is

If $[x]$ is the greatest integer $ \le x,$ then the value of the integral $\int\limits^{0.9}_{-0.9}\left(\left[x^{2}\right]+\left(\frac{2-x}{2+x}\right)\right)dx$ is

If the line $y = mx + 1$ meets the circle $x^2 + y^2 + 3x = 0 $ in two points equidistant from and on opposite sides of $x$-axis, then

If the integral $\int \frac{5\,tan\, x }{tan \,x - 2} dx = x + a \ell n |sin x - 2 cos x| + k$, then $a$ is equal to :

If $n= \,^mC_2$, then the value of $^nC_2$ is given by

If f(x) = sin (log x) and $y = f\left(\frac{2x+3}{3-2x}\right)$, then $\frac{dy}{dx}$ equals

If $100$ times the $100^{th}$ term of an $A.P.$ with non zero common difference equals the $50$ times its $50^{th}$ term, then the $150^{th}$ term of this $A.P.$ is :

Consider a quadratic equation $ax^2 + bx + c = 0,$ where $2a + 3b + 6c = 0$ and let $g\left(x\right)=a \frac{x^{3}}{3}+b \frac{x^{2}}{2}+cx.$ The quadratic equation has at least one root in the interval $(0,1).$ The Rolle?? theorem is applicable to function $g(x)$ on the interval $[0,1].$

A value of $tan^{-1}\left[sin\left(cos^{-1}\left(\sqrt{\frac{2}{3}}\right)\right)\right]$ is

A unit vector which is perpendicular to the vector $2\hat{i} - \hat{j} + 2\hat{k}$ and is coplanar with the vectors $\hat{i} + \hat{j} - \hat{k}$ and $2\hat{i} + \hat{j} - 2\hat{k}$ is

The value of the integral $\int\limits^{0.9}_{{0}}[x - 2 [x]] dx ,$ where $[.]$ denotes the greatest integer function is

Let p and q denote the following statements p : The sun is shining q: I shall play tennis in the afternoon The negation of the statement "If the sun is shining then I shall play tennis in the afternoon", is

$\displaystyle \lim_{x\to0} \frac{sin\left(\pi\,cos^{2} x\right)}{x^{2}}$ equals

The equation of the normal to the parabola $x^2=8y$ at $x=4$ is

The middle term in the expansion of $\left(1-\frac{1}{x}\right)^{n} \left(1-x^{n}\right)$ in powers of x is

If the lines $\frac{x-2}{1}=\frac{y-3}{1}=\frac{z-4}{-k}$ and $\frac{x-1}{k}=\frac{y-4}{2}=\frac{z-5}{1}$ are coplanar, then k can have

Let $\vec{a} \,and\, \vec{b}$ be two unit vectors. If the vectors $\vec{c} = \hat{a} + 2\hat{b}$ and $\vec{d} = 5\hat{a} -4\hat{b}$ are perpendicular to each other,then the angle between $\hat{a}$ and $\hat{b}$ is :

There are 10 points in a plane, out of these 6 are collinear. If N is the number of triangles formed by joining these points. then :

For each natural number $n, (n + 1)^7 - n^7 -1$ is divisible by 7. For each natural number $n, n^7 - n$ is divisible by 7.

Sachin and Rahul attempted to solve a quadratic equaiton. Sachin made a mistake in writing down the constant term and ended up in roots (4, 3). Rahul made a mistake in writing down coefficient of x to get roots (3, 2). The correct roots of equation are :

The number of values of k for which the linear equations $4x + ky + 2z = 0$ , $kx + 4y + z = 0$ and $2x + 2y + z = 0$ possess a non-zero solution is

The possible values of $\theta \in \left(0, \pi\right)$ such that sin($\theta $) + $sin(4\,\theta $) + $sin(7\,\theta ) = 0$ are :

Determinant of a skew-symmetric matrix of order 3 is zero. For any matrix A, det $(A)^T = det(A)$ and $det (-A) = - det(A)$. Where det(B) denotes the determinant of matrix B. Then :

Let $I$ be the purchase value of an equipment and $V(t)$ be the value after it has been used for $t$ years. The value $V(t)$ depreciates at a rate given by differential equation $\frac{d V(t)}{d t}=-k(T-t),$ where $k>0$ is a constant and $T$ is the total life in years of the equipment. Then the scrap value $V(T)$ of the equipment is