List of top Questions asked in KEAM

The constant term in the expansion of $(2x^{2}-\frac{1}{x^{2}})^{6}$ is ________.

Five digit number is formed using the digits 0, 1, 2, 3, 4 and 5 without repetitions. Number of five digit numbers which are divisible by 10 is ________.

The coefficient of $x^{9}$ in the expansion of $(4-\frac{x^{2}}{4})^{12}$ is ________.

The number of integers greater than 7000 using 2, 4, 6, 7, 8 without repetition is ________.

Let $\alpha$ and $\beta$ be the roots. If $A$ is the A.M. between $\alpha$ and $\beta$ and also $G$ is the G.M. between $\alpha$ and $\beta$, then $\alpha^{2}+\beta^{2}=$ ________.

Let $a_{1},a_{2},....,a_{n}$ be positive non-zero real numbers. If $a_{1},a_{2},....,a_{n}=k$, then the minimum value of $a_{1}+a_{2}+....+a_{n}$ is ________.

Let $a, \frac{3}{4}, ar^{2}, ar^{3}, \dots$ be in G.P. where $r>0$. If the product of the first four terms is $\frac{3^{6}}{4^{5}}$, then $a$ is equal to ________.

If $a, b, c$ are real numbers such that $(a-2)^{2}+(b-2)^{2}+(c-2)^{2}=0$, then ________.

Let $z=x+iy,$ where $x,y \in \mathbb{R}$ and $i^{2}=-1$. If $|z-i|=|z-1|$, then $y=$ ________.

If $x,y \in \mathbb{R}$ and $x+iy=-(6+i)^{3}, i^{2}=-1$, then $x-y$ is equal to ________.

$\sum_{n=1}^{2025}i^{n}(1+i), i^{2}=-1$ is equal to ________.

All the points in $A=\{\frac{\lambda+i}{\lambda-i}; \lambda \in \mathbb{R}\}$ lie on ________.

The domain of the function $f(x)=\sqrt{x^{2}+2x-15}$ is ________.

The range of the function $f(x)=\log_{e}(4x^{2}-4x+1)$ where $x \ne \frac{1}{2}$ is ________.

Let $A=\{1,2,3,4\}$ and $B=\{7,8,3,4\}$. Then the number of elements common to both $A \times B$ and $B \times A$ is ________.

The relation $R = \{(4,4), (4,5), (5, 7), (4, 8), (5, 5), (7, 8), (7, 7), (7, 5), (8, 8), (8, 7), (8, 5), (9, 9)\}$ on the set $A=\{4,5,7,8,9\}$ is ________.

If $f(x)=x|x|$, then $f^{\prime}(-10)=$ ________.

The solution set for $-12x > 38$, where $x$ is a natural number, is ________.

Four digit numbers are formed using \( 0, 3, 4, 5, 9, 8 \) without repetitions. Then the number of such 4 digit numbers is

Match the vitamins in Column I with their sources in Column II.

In the following reaction, the final product B is:
C\(_6\)H\(_5\)NH\(_2\) + (CH\(_3\)CO)\(_2\)O (Pyridine) \(\rightarrow\) A \(\xrightarrow{Br, CH_3COOH}\) B

Which of the following does not undergo Cannizzaro reaction?

Which one of the following compounds undergoes HVZ reaction?

Identify the correct sequence of reactions and products for the following scheme.

The correct decreasing order of acidic strength is