List of top Questions asked in KEAM

The numbers $a_1,a_2,a_3,\ldots$ form an arithmetic sequence with $a_1\ne a_2$. The three numbers $a_1,a_2$ and $a_6$ form a geometric sequence in that order. Then the common difference of the arithmetic sequence is

$\frac{10i}{1+2i}$ is equal to

If $2+i$ is a root of $x^2-4x+c=0$, where $c$ is a real number, then the value of $c$ is

Let $z_1$ and $z_2$ be complex numbers satisfying $|z_1|=|z_2|=2$ and $|z_1+z_2|=3$. Then $\left|\frac{1}{z_1}+\frac{1}{z_2}\right|=$

The principal argument of the complex number $z=\frac{1+\sin\pi-i\cos\pi}{1+\sin\pi+i\cos\pi}$ is

If $z_1=2+3i$ and $z_2=3+2i$, then $|z_1+z_2|$ is equal to

If $z=x-iy$ and $z^{1/3}=p+iq$, then $\frac{1}{p^{2}+q^{2}}\left(\frac{x}{p}+\frac{y}{q}\right)$ is equal to

The real part of $e^{(3+4i)x}$ is

Let z = x + iy be a complex number such that $|z+i|=2$. Then the locus of z is a circle whose centre and radius are

Let $A=\{2,3,4,5\}$, $B=\{36,45,49,60,77,90\}$ and let $R$ be the relation 'is factor of' from $A$ to $B$. Then the range of $R$ is the set

If $A=\{1,2,3,4,5\}$ and $B=\{2,4,6\}$, then $A-B=$

If $*$ is a binary operation defined by $a*b=\frac{a}{b}+\frac{b}{a}+\frac{1}{ab}$ for positive integers $a$ and $b$, then $2*5$ is equal to

In a group of 100 persons, 80 people can speak Malayalam and 60 can speak English. Then the number of people who speak English only is

Let $A$ and $B$ be finite sets such that $n(A-B)=18$, $n(A \cap B)=25$ and $n(A \cup B)=70$. Then $n(B)$ is equal to

Let $f(x)=-2x^2+1$ and $g(x)=4x-3$, then $(g \circ f)(-1)$ is equal to

The domain of the function $f(x)=\sqrt{x-1}$ is

The electric potential \(V\) at any point \((x,y,z)\) in space is given by \(V=4xz^2\) volt, where \(x,y,z\) are all in metre. The electric field at that point \((1\text{ m},0,2\text{ m})\) in \(\text{V m}^{-1}\) is

Which one of the following statements is not correct?

Which one of the following is an antifertility drug?

The antimicrobial drug that contains arsenic is

Which one of the following sets forms the biodegradable polymer?

Which one of the following is a greenhouse gas?

Among the following which one is a non-reducing sugar?

Choose the correct statement of the following.

Which one of the following can be prepared by Gabriel phthalimide synthesis?