List of top Questions asked in KEAM

Let $B$ be a matrix of order $3 \times 2$ and $C$ be a matrix of order $3 \times 3$. If $A$ is a matrix such that $BA = C$, then the order of $A$ is

The constant term in $\left(\frac{\sqrt{x}}{2} + \frac{1}{3x^2}\right)^{10}$ is:

${}^{21}C_1 + {}^{21}C_2 + \dots + {}^{21}C_{10} =$

The coefficient of $x^{10}$ in $(1-x^2)(1-x^3)^9$ is:

$1 + {}^{100}C_1 + {}^{100}C_2 + \dots + {}^{100}C_{99} + 1 =$

25 distinct objects are divided into 5 groups and each group consists of exactly 5 objects. Then the number of ways of forming such groups, is

Let $G_1, G_2, G_3$ be geometric means between $l$ and $n$, where $l$ and $n$ are positive real numbers. Then the common ratio is

The sum of first $n$ terms of a G.P. is 1023. If the first term is 1 and the common ratio is 2, then the value of $n$ is

The first three terms in a G.P. are $a, b$ and $c$ where $a \neq b$. Then the fifth term is:

The 25th term of $9, 3, 1, \frac{1}{3}, \frac{1}{9}, \ldots$ is:

Real part of $\frac{1+\sin\frac{2\pi}{27}-i\cos\frac{2\pi}{27}}{1+\sin\frac{2\pi}{27}+i\cos\frac{2\pi}{27}}$ is equal to:

Let $z$ be a complex number such that $z^{3}+iz^{2}-iz+1=0$ where $i^{2}=-1$. Then $|z|=$

Let $z=x+iy$ be a complex number, where $i=\sqrt{-1}$ is the complex unit. Then $|z-1+i|=5$ is a circle with:

Let $s, t, r$ be non-zero distinct positive real numbers. If the complex number $z=x+iy$ satisfies $sz+t\overline{z}+r=0$, then $z$ lies on:

The range of the function $f(x)=\sqrt{x^{2}+4x+4}$ is:

The domain of the function $f(x)=\sqrt{x^{2}+x-2}$ is:

If two sets A and B are having 11 elements in common, then the number of elements common to $A\times B$ and $B\times A$ is:

The relation \( R = \{(1,3), (2,3), (2,4), (3,1), (4,4), (4,1)\} \) on the set \( X = \{1,2,3,4\} \) is:

The disease caused by the deficiency of riboflavin is

The order of basic strength of following amines is: (i) \( CH_3NH_2 \) (ii) \( (C_2H_5)_2NH \) (iii) \( C_6H_5NH_2 \) (iv) \( C_6H_5NHCH_3 \)

Fehling's reagent is a mixture of

Toluene on treatment with chromic oxide in presence of acetic anhydride at \( 273{-}283\,K \) gives compound (X). Compound (X) on hydrolysis with aqueous acid gives compound (Y). The compounds (X) and (Y) are respectively

Phenol on treatment with chloroform in the presence of NaOH, a -CHO group is introduced at ortho position of benzene ring. The reaction is known as

The IUPAC name of phenyl isopentyl ether is

The order of reactivity of the following compounds towards \( S_N2 \) displacement reaction is (i) 2-Bromo-2-methylbutane (ii) 1-Bromopentane (iii) 2-Bromopentane