List of top Questions asked in KEAM

Let $f(x) = |x - 2|$, where $x$ is a real number. Which one of the following is true?

If the operation $\oplus$ is defined by $a \oplus b = a^2 + b^2$ for all real numbers $a$ and $b$, then $(2 \oplus 3) \oplus 4 =$

If $A = \{1, 3, 5, 7\}$ and $B = \{1, 2, 3, 4, 5, 6, 7, 8\}$, then the number of one-to-one functions from $A$ into $B$ is:}

The number of students who take both the subjects mathematics and chemistry is 30. This represents 10% of the enrolment in mathematics and 12% of the enrolment in chemistry. How many students take at least one of these two subjects?

An integrating factor of the differential equation \( \sin x \frac{dy}{dx} + 2y \cos x = 1 \) is:

The solution of the differential equation \( \frac{dy}{dx} = e^x + 1 \) is:

The value of the integral \( \int_{2}^{4} \left( \frac{\log t}{t} \right) \, dt \) is equal to:

The solution of the differential equation \( (kx - y^2) dy = (x^2 - ky) dx \) is:

The order and degree of the differential equation \( \frac{d^2y}{dx^2} + \left( \frac{dy}{dx} \right)^{\frac{3{2}} = y \) are respectively:}

The value of the integral \( \int_{1}^{e} \frac{1 + \log x}{3x} \, dx \) is equal to:

The value of the integral \( \int_{0}^{1} \frac{x^3}{1 + x^8} \, dx \) is equal to:

\( \int e^x (\sin x + 2 \cos x) \sin x \, dx \) is equal to:

\( \int \sqrt{1 + \cos x} \, dx \) is equal to:

\( \int \frac{\sqrt{x^2 - 1}}{x} \, dx \) is equal to:

The value of \( \int_{0}^{1} \frac{dx}{e^x + e} \) is equal to:

\( \int \frac{\sqrt{5 + x^2}}{x^4} \, dx \) is equal to:

Area bounded by the curves \( y = e^x \), \( y = e^{-x} \) and the straight line \( x = 1 \) is (in sq. units):

\( \int \frac{1}{x^2 (x^4 + 1)^{3/4 dx \) is equal to:}

\( \int \frac{(1 + x) e^x{\sin^2(x e^x)} dx \) is equal to:}

\( \int \frac{xe^x}{(1+x)^2 \, dx \) is equal to:}

The slope of the normal to the curve \( y = x^2 - \frac{1}{x^2} \) at \( (-1, 0) \) is:

The minimum value of \( \sin x + \cos x \) is:

If \( y = \sin^{-1} \left( 2x \sqrt{1 - x^2} \right) \), \( -\frac{1}{\sqrt{2}} \le x \le \frac{1}{\sqrt{2}} \), then \( \frac{dy}{dx} \) is equal to:

A straight line parallel to the line \( 2x - y + 5 = 0 \) is also a tangent to the curve \( y^2 = 4x + 5 \). Then the point of contact is:

The slope of the tangent to the curve \( y^2 e^{xy} = 9e^{-3}x^2 \) at \( (-1, 3) \) is: