List of top Questions asked in KEAM

In Dumas method of nitrogen estimation, 0.14 g of an organic compound gave 22.4 mL of nitrogen at STP. The percentage of nitrogen in the compound is:

Which of the following carboxylic acids has the highest pKa?

What is the total number of sigma bonds found in the following compound?
\[ \text{CH}_3\text{CH} = \text{C} = \text{CH} - \text{C} \equiv \text{C} - \text{H} \]

Cheilosis disease and digestive disorders are caused by the deficiency of:

Evaluate the integral \[ \int_{-500}^{500} \ln \left( \frac{1000 + x}{1000 - x} \right) dx \]

The length of the latus rectum of the parabola \( y^2 = x \) is:

The area enclosed by the curve \[ x = 3 \cos \theta, \quad y = 5 \sin \theta, \quad 0 \leq \theta \leq 2\pi, \] is equal to:

If a charged particle enters a uniform magnetic field \( B \), with a velocity \( v \) such that \( v \) has a component along \( B \), then the charged particle describes:

The ratio between the magnetic dipole moment of a revolving electron in a circular orbit to its angular momentum is (where \( e \) is the charge and \( m \) is the mass of the electron):

The value of \[ \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{\cos^2 x}{1 + 2^{-x}} \, dx \] is equal to:

The limit: \[ \lim_{x \to 0} \frac{\sin \left( \pi \sin^2 x \right)}{x^2} \] is equal to:

If \[ \theta \in \left( 0, \frac{\pi}{3} \right) \quad \text{and} \quad \begin{vmatrix} 0 & -\sin^2 \theta & -2 - 4 \cos 6\theta \\ 0 & \cos^2 \theta & -2 - 4 \cos 6\theta \\ 1 & \sin \theta & \cos 2\theta \end{vmatrix} = 0, \] then \( \theta \) is equal to:

The integral

\[ \int \frac{dx}{x^8 \left( 1 + x^7 \right)^{2/3}} \] is equal to:

If\( \dfrac{1+sinx}{1-sinx}=\dfrac{(1+siny)^3}{(1-siny)^3}\) for some real values \(x\) and \(y\) ,then \(\dfrac{sinx}{siny}\)=

Let \(S=\){\(n∈NIn^3+3n^2+5n+3\) is not divisible by \(3\)}.Then, which of the following statements is true about \(S\)

The minimum of \(f(x)=\sqrt{(10-x^2)}\) in the interval \([-3,2]\) is

A thin particle moves from \((0,1)\) and gets reflected upon hitting the x-axis at \((√3,0)\). Then the slope of the reflected line is ?

For any real number \(x\), the least value of \(4cosx-3sinx+5\) is ?

Suppose the point \(P(1,1)\) is translated to \(Q\) in the direction of y = 2x. If \(PQ = 1\),then Qis

Let \(a,b,c,d \) be an increasing sequence of real numbers,which are in geometric progression .If \(a+d=112\) and \(b+c=48\) ,then the value of \(\dfrac{a+c+8}{b}\) is

If the median of the observations \(4,6,7,x,x+2,12,12,13\) arranged in an increasing order is 9,then the variance of these observations is