List of top Mathematics Questions asked in VITEEE

The value of
\[ \lim_{n\to\infty}\left[\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\cdots+\frac{1}{n(n+1)}\right] \] is equal to

If \(3\sin\theta+5\cos\theta=5\), then the value of \(5\sin\theta-3\cos\theta\) is equal to

For what values of \(m\) can the expression
\[ 2x^2+mxy+3y^2-5y-2 \] be expressed as the product of two linear factors?

The chances of defective screws in three boxes \(A,B,C\) are \(\dfrac{1}{5},\dfrac{1}{6},\dfrac{1}{7}\) respectively. A box is selected at random and a screw drawn from it at random is found to be defective. The probability that it came from box \(A\), is

The value of \(\dfrac{\cos\theta}{1+\sin\theta}\) is equal to

If \(f(x), g(x)\) and \(h(x)\) are three polynomials of degree 2 and
\[ \Delta(x)= \begin{vmatrix} f(x) & g(x) & h(x)\\ f'(x) & g'(x) & h'(x)\\ f''(x) & g''(x) & h''(x) \end{vmatrix} \] then \(\Delta(x)\) is a polynomial of degree

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

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

If \(a^x=b^y=c^z=d^u\) and \(a,b,c,d\) are in GP, then \(x,y,z,u\) are in

Let \(S\) be a set containing \(n\) elements. Then, number of binary operation on \(S\) is

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

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

If \(F\) is function such that \(F(0)=2,\ F(1)=3\), and
\[ F(x+2)=2F(x)-F(x+1)\ \text{for}\ x\geq 0, \] then \(F(5)\) is equal to

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