List of top Questions asked in KEAM

What is the working principle of a Bunsen Burner?
Matrix match: Match the items in the list with the appropriate compounds.

Matrix match
  • i) Non-reducing disaccharide → c) Sucrose
  • ii) Reducing disaccharide → e) Maltose
  • iii) Aldohexose → b) Glucose
  • iv) Ketohexose → a) Fructose
  • v) Polysaccharide → d) Lactose
What is the Reimer Tieman reaction?
What is Layer's test?

The point of intersection of the lines \(\frac{x-3}{2} = \frac{y-2}{2} = \frac{z-6}{1}\) and \(\frac{x-2}{3} = \frac{y-4}{2} = \frac{z-1}{3}\) is:

The area bounded by the curves \( y = x^2 \) and \( y = 2x \) in the first quadrant, is equal to:
Evaluate \( \int \frac{e^{6 \log x} - e^{5 \log x}}{e^{4 \log x} - e^{3 \log x}} \, dx \):
The value of \( \sin^2 \left( \frac{3\pi}{8} \right) + \sin^2 \left( \frac{7\pi}{8} \right) \) is:
If \( \alpha = \tan^2 x + \cot^2 x \), where \( x \in \left( 0, \frac{\pi}{2} \right) \), then \( \alpha \) lies in the interval:
The solution of \( \frac{e^y}{dx} = x + 2 \) is:

Let \( f(x) = \sqrt{4 - x^2} \), \( g(x) = \sqrt{x^2 - 1} \). Then the domain of the function \( h(x) = f(x) + g(x) \) is equal to:

If \( A = \begin{bmatrix} 4 & -1 \\ 12 & x \end{bmatrix} \) and \( A^2 = A \), then the value of \( x \) is:
The value of \( \lim_{x \to 0} \frac{\sin(5x)}{\sin(3x)} \) is:
The integral \( \int e^x \sec x (1 + \tan x) \, dx \) is equal to:
If \( f(x) = x + 8 \), and \( g(x) = 2x^2 \), then \( (g \circ f)(x) \) is equal to
The sum of the first 20 terms of the G.P. \( \sqrt{3} + \frac{-1}{\sqrt{3}} + \frac{1}{3\sqrt{3}} + \cdots \) is equal to
If \( a_1 = 3 \) and \( a_n = n \cdot a_{n-1} \), for \( n \geq 2 \), then \( a_6 \) is equal to
The period of the function \( \sin\left( \frac{\pi x}{4} \right) \) is
The solution of the inequality \( |3x - 4| \leq 5 \) is
The coefficient of \( x^3 \) in the expansion of \[ \frac{1}{(1 + 2x)^{-10}} \] is:
If

\[ R = \{(x, y) : x, y \in \mathbb{Z}, \, x^2 + 3y^2 \leq 7 \} \] is a relation on the set of integers \( \mathbb{Z} \), then the range of the relation \( R \) is:
The value of \( \tan \left( \cos^{-1} \left( \frac{-24}{25} \right) \right) \) is equal to

Let \( f(x) = x \sin(x^4) \). Then \( f'(x) \) at \( x = \sqrt[4]{\pi} \) is equal to:

If \( 2 \) is a solution of the inequality \( \frac{x-a}{a-2x}<-3 \), then \( a \) must lie in the interval:

If the function \[ f(x) = \begin{cases} x^2, & \text{for } x < 4 \\ 5x - k, & \text{for } x \geq 4 \end{cases} \] is continuous at \( x = 4 \), then the value of \( k \) is equal to