List of top Mathematics Questions asked in VITEEE

If \( a_1, a_2, a_3 \) be any positive real numbers, then which of the following statement is true?

Which of the following is the correct expansion of the series \[ \sum_{n=0}^{\infty} \left( \binom{C}{n} \right) \left( \frac{3}{5} \right)^n \left( \frac{2}{5} \right)^{n+1} \]

A complex number \( z \) is such that \( \arg \left( \frac{-2}{3} + \frac{2i}{3} \right) = \frac{\pi}{3} \). The points representing this complex number will lie on

The centres of a set of circles, each of radius 3, lie on the circle \( x^2 + y^2 = 25 \). The locus of any point in the set is

The rate of change of the surface area of a sphere of radius \( r \), when the radius is increasing at the rate of \( 2 \, \text{cm/s} \), is proportional to

The value of \( 2 \tan^{-1} x - \left( \text{cosec} \, \tan^{-1} x - \tan \, \cot \, x \right) \)

If \( N \) denote the set of all natural numbers and \( R \) the relation on \( N \times N \) defined by \( (a, b) R (c, d) \), if \( a(b + c) = b(a + d) \), then \( R \) is

If two events A and B. If odds against A are 2:1 and those in favour of \( A \cup B \) are 3:1, then

The proposition \( \neg (p \iff q) \) is equivalent to

If truth values of \( p \) be F and \( q \) be T, then truth value of \( \neg(p \vee q) \) is

The relation \( R \) defined on set \( A = \{x : |x|<3, x \in \mathbb{R} \} \) by \( R = \{(x, y): y = |x|\} \) is

If \( a \), \( b \), and \( c \) are in AP, then determinant \[ \begin{vmatrix} x+2 & x+3 & x+4
x+4 & x+5 & x+6
x+7 & x+8 & x+9 \end{vmatrix} \]

The solution of the differential equation \[ \frac{dy}{dx} = \frac{y}{f(x)} - y^2 \] is

The solution of the differential equation $\frac{dy}{dx}=\frac{yf '\left(x\right)-y^{2}}{f \left(x\right)}$ is

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

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)

The number of integral values of $K$, for which the equation $7\, \cos \,x + 5\, \sin\, x = 2K + 1$ has a solution, is

The value of the determinant $\begin{vmatrix}1&cos \left(\alpha-\beta\right)&cos \alpha\\ cos \left(\alpha -\beta \right)&1&cos \beta\\ cos \alpha &cos \beta &1\end{vmatrix}$ is

The line $2x+\sqrt{6y}=2$ is a tangent to the curve $x^{2}-2y^{2}=4$. The point of contact is

The value of $2 \,tan^{-1} (cosec \,tan^{-1} x - tan \,cot^{-1} x))$ 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

The vector $b = 3j + 4k$ is to be written as the sum of a vector $b_1$ parallel to $a = i +j$ and a vector $b_2$ perpendicular to $a$. Then $b_1$ is equal to

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 angle of intersection of the circles $x^{2}+y^{2}-x+y-8=0$ and $x^{2}+y^{2}+2 x+2 y-11=0$ is