List of top Mathematics Questions asked in VITEEE

The equations of the circle which pass through the origin and makes intercepts of lengths \(4\) and \(8\) on the \(x\)-axis and \(y\)-axis respectively are

The point \((3,-4)\) lies on both the circles
\[ x^2+y^2-2x+8y+13=0 \] \[ x^2+y^2-4x+6y+11=0 \] Then, the angle between the circles is

The equation of the circle which passes through the origin and cuts orthogonally each of the circles
\[ x^2+y^2-6x+8=0 \] and
\[ x^2+y^2-2x-2y=7 \] is

If \(X\) is a binomial variable with the range \(\{0,1,2,3,4,5,6\}\) and \(P(X=2)=4P(X=4)\), then the parameter \(p\) of \(X\) is

The angle between the lines whose direction cosines satisfy the equations
\[ l+m+n=0,\quad l^2+m^2-n^2=0 \] is

The period of \(\sin^4x+\cos^4x\) is

If \(3\cos x \neq 2\sin x\), then the general solution of
\[ \sin^2x-\cos2x=2-\sin2x \] is

In a \(\triangle ABC\)
\[ \frac{(a+b-c)(b+c-a)(c+a-b)(a+b-c)}{4b^2c^2} \] equals

If \(m_1,m_2,m_3,m_4\) are respectively the magnitudes of the vectors
\[ \vec{a_1}=2\hat{i}-\hat{j}+\hat{k},\quad \vec{a_2}=3\hat{i}-4\hat{j}-4\hat{k}, \] \[ \vec{a_3}=\hat{i}+\hat{j}-\hat{k},\quad \vec{a_4}=-\hat{i}+3\hat{j}+\hat{k} \] then

If \(f(x)=2x^4-13x^2+ax+b\) is divisible by \(x^2-3x+2\), then \((a,b)\) is equal to

The roots of
\[ (x-a)(x-a-1)+(x-a-1)(x-a-2)+(x-a)(x-a-2)=0 \] where \(a\in \mathbb{R}\) are always

Let \(f(x)=x^2+ax+b\), where \(a,b\in \mathbb{R}\). If \(f(x)=0\) has all its roots imaginary, then the roots of \(f(x)+f'(x)+f''(x)=0\) are

If \(p,q,r\) are all positive and are the \(p^{th}\), \(q^{th}\) and \(r^{th}\) terms of a geometric progression respectively, then the value of the determinant
\[ \left|\begin{matrix} \log x & p & 1 \\ \log y & q & 1 \\ \log z & r & 1 \end{matrix}\right| \] equals

If \(n\) is an integer which leaves remainder one when divided by three, then
\[ (1+\sqrt{3}i)^{n}+(1-\sqrt{3}i)^{n} \] equals

If \(x\) is numerically so small so that \(x^2\) and higher powers of \(x\) can be neglected, then
\[ \left(1+\frac{2x}{3}\right)^{3/2}\left(32+5x\right)^{-1/5} \] is approximately equal to

The number of subsets of \(\{1,2,3,\ldots,9\}\) containing at least one odd number is

If \(f:[2,3]\rightarrow \mathbb{R}\) is defined by \(f(x)=x^3+3x-2\), then the range \(f(x)\) is contained in the interval

A binary sequence is an array of 0's and 1's. The number of \(n\)-digit binary sequences which contain even number of 0's is

The number of subsets of $\{1, 2, 3, ..., 9\} $containing at least one odd number is

If $X$ is a binomial variate with the range $\{0,1,2,3,4,5,6\}$ and $ P(X=2)=4 P(X=4)$ then the parameter $p$ of $X$ is

The area (in square unit) of the triangle formed by $x+y+1=0$ and the pair of straight lines $x^{2}-3xy=2y^{2}=0$ is

The angle between the lines whose direction cosines satisfy the equations $l+m+n=0, l^{2}+m^{2}-n^{2}=0$ is

If $f: R \rightarrow R$ is defined by $f(x)=\begin{cases}\frac{2 \sin x-\sin 2 x}{2 x \cos x}, & \text { if } x \neq 0 \\ a, & \text { if } x=0\end{cases}$ then the value of a so that f is continuous at $0$ is

The pairs of straight lines $x^{2}-3xy+2y^{2}=0 $ and $x^{2}-3xy+2y^{2}+x-2=0$ form a