List of top Mathematics Questions asked in VITEEE

If $(2, 7, 3)$ is one end of a diameter of the sphere $x^2 + y^2 + z^2 - 6\,x -12\,y -2\,z + 20 = 0$, then the coordinates of the other end of the diameter are

If $|z| \ge 3$, then the least value of $\left|z+\frac{1}{4}\right|$ is

The area bounded by the curves $y = cos\, x$ and $y = sin \,x$ between the ordinates $x = 0$ and $x = \frac{3\pi}{2}$ is

If line $y = 2\,x + c$ is a normal to the ellipse $\frac{x^2}{9} + \frac{y^2}{16} = 1 $, then

If there is an error of $k\%$ in measuring the edge of a cube, then the percent error in estimating its volume is

The minimum value of $\frac{x}{\log \, x}$ is

If the system of equations $x + ky - z = 0, 3x - ky - z = 0$ and $x - 3y + z = 0$, has non-zero solution, then $k$ is equal to

Two lines $ \frac{x-1}{2} = \frac{y+1}{3} = \frac{z -1}{4}$ and $ \frac{x-3}{1} = \frac{y-k}{2} = z $ intersect at a point, if $k$ is equal to

If $\Delta (x) \begin{vmatrix}1&\cos x&1 -\cos x\\ 1+ \sin x& \cos x &1+ \sin x - \cos x\\ \sin x &\sin x&1\end{vmatrix},$ then $ \int\limits^{\pi / 4}_{0} \Delta\left(x\right)dx $ is equal to

If the points $(1, 2, 3)$ and $(2, -1, 0)$ lie on the opposite sides of the plane $2x + 3y - 2z = k,$ then

Let $f ' (x),$ be differentiable $\forall \, x.$ If $f (1) = -2$ and $f '(x) \geq 2 \forall x \in [1, 6],$ then

If a plane meets the coordinate axes at $A,B$ and $C$ such that the centroid of the triangle is $(1, 2, 4)$, then the equation of the plane is

The value of $c$ from the Lagrange�s mean value theorem for which $f(x) = \sqrt{25 - x^2}$ in $[1,5]$, is

If $a, b, c$ are three non-coplanar vectors and $p, q, r$ are reciprocal vectors, then $(la + mb + nc). (lp + mq + nr)$ is equal to

The area in the first quadrant between $x^2 + y^2 = \pi^2$ and $y = \sin \, x$ is

The differential equation of the rectangular hyperbola hyperbola, where axes are the asymptotes of the hyperbola, is

The solution of $\frac{dy}{dx} = \frac{x^{2} + y^{2} + 1}{2xy}$, satisfying $ y\left(1\right) = 0$ is given by

The statement $(p \Rightarrow q ) \Leftrightarrow ( \sim p \Lambda q)$ is a

The triangle formed by the tangent to the curve $f (x) = x2 + bx - b$ at the point $(1,1)$ and the coordinate axes lies in the first quadrant. If its area is $2$, then the value of b is

If the integers $m$ and $n$ are chosen at random from $1$ to $100$ , then the probability that a number of the form $7^{n}+7^{m}$ is divisible by $5$ , equals to

If a tangent having slope of $-\frac{4}{3}$ to the ellipse $\frac{x^{2}}{18}+\frac{y^{2}}{34}=1$ intersects the major and minor axes in points $A$ and $B$ respectively, then the area of $\Delta OAB$ is equal to (O is the centre of the ellipse)

If $\alpha$ and $\beta$ are the roots of $x^{2}-ax+b=0$ and if $\alpha^{n}+\beta^{n}=V_{_n},$ then

The sum of the series $ \displaystyle\sum_{r = 0}^{n}\left(-1\right)^{r}\, ^{n}C_{r}\left(\frac{1}{2^{r}}+\frac{3^{r}}{2^{2r}}+\frac{7^{r}}{2^{3r}}+\frac{15^{r}}{2^{4r}}+...m \text{terms}\right)$ is

The line joining two points $A(2,0), B(3,1)$ is rotated about $A$ in anti-clockwise direction through an angle of $15^{\circ}$. The equation of the line in the now position,is

The value of the integral $\int\limits ^{1/2}_{-1/2}\left[\left(\frac{x+1}{x-1}\right)^{^2}+\left(\frac{x+1}{x-1}\right)^{^2}-2\right]^{^{1/2}}\:\:dx$ is