List of top Mathematics Questions asked in VITEEE

Domain of the function $f (x) = \log_x \; \cos \; x$, is

If $z$ satisfies the equation $|z|-z=1+2 i$, then $z$ is equal to

The numerically greatest term in the expansion of $(3-5x)^{11}$ when $x = \frac{1}{5},$ is

Let $S$ be a set containing $n$ elements. Then, number of binary operations on $S$ is

If $F$ is function such that $F (0) = 2, F (1) = 3, F (x+2) = 2F (x) - F (x+1)$ for $x \ge 0$, then $F (5)$ is equal to

If $z=\frac{1-i \sqrt{3}}{1+i \sqrt{3}}$, then $\arg (z)$ is

The number of solutions of the equation $\sin \; (e^{x}) = 5^x + 5^{-x}$, is

If $a^x = b^{y} = c^{z} = d^{u}$ and $a, b,\, c,\, d$ are in $GP$, then $x,\, y,\, z,\, u$ are in

The principal value of $\sin^{-1} \left\{\sin \frac{5\pi}{6}\right\} $ is

The value of $\frac{\cos\theta}{1+ \sin\theta}$ is equal to

If $f(x) = \sqrt{\log_{10} x^2} $ . The set of all values of $x$ for which $f(x)$ is real , is

$\displaystyle\lim_{n\to\infty} \left[\frac{1}{1.2} + \frac{1}{2.3} + \frac{1}{3.4} + .... + \frac{1}{n\left(n+1\right)}\right] $ is equal to

Range of the function $y =\sin^{-1} \left(\frac{x^{2}}{1+x^{2}}\right) $ is

For what values of m can the expression $2x^2 + mxy + 3y^2 - 5y - 2$ be expressed as the product of two linear factors

If $B$ is a non-singular matrix and $A$ is a square matrix, then det $(B^{-1} AB)$ is equal to

If $\int\limits^x_1 \frac{dt}{|t\, \sqrt{t^2 - 1}} = \frac{\pi}{6}$ , then $x$ can be equal to

\(\cos^{-1}\left(-\frac{1}{2}\right)-2\sin^{-1}\left(\frac{1}{2}\right)+3\cos^{-1}\left(-\frac{1}{\sqrt{2}}\right)-4\tan^{-1}(-1)\) equals

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

The solution of the differential equation
\[ \frac{dy}{dx}=\sin(x+y)\tan(x+y)-1 \] is

If \(p\Rightarrow(\sim p\vee q)\) is false, then the truth value of \(p\) and \(q\) are respectively

The line \(x=\frac{\pi}{4}\) divides the area of the region bounded by \(y=\sin x\), \(y=\cos x\) and x-axis \((0\leq x\leq \frac{\pi}{2})\) into two regions of areas \(A_1\) and \(A_2\). Then \(A_1:A_2\) equals

The function \(f(x)=x^3+ax^2+bx+c\), \(a^2\leq 3b\) has

If
\[ \int \left(\frac{2-\sin2x}{1-\cos2x}\right)e^x\,dx \] is equal to

If
\[ y=e^{a\sin^{-1}x}=(1-x^2)y_{n+2}-(2n+1)xy_{n+1} \] is equal to

If
\[ \frac{d}{dx}\left[a\tan^{-1}x+b\log\left(\frac{x-1}{x+1}\right)\right]=\frac{1}{x^4-1} \] then \(a-2b\) is equal to