List of top Mathematics Questions asked in KEAM

If the second and fifth terms of a G.P. are 24 and 3 respectively, then the sum of first six terms is:

If the roots of the equation \( x^2 + 2bx + c = 0 \) are \( \alpha \) and \( \beta \), then \( b^2 - c = \)

The equation whose roots are the squares of the roots of the equation \( 2x^2 + 3x + 1 = 0 \) is:

If two positive numbers are in the ratio \( 3 + 2\sqrt{2} : 3 - 2\sqrt{2} \), then the ratio between their A.M. and G.M. is:

If \( \alpha \) and \( \beta \) are the roots of \( x^2 - ax + b^2 = 0 \), then \( \alpha^2 + \beta^2 \) is equal to:

The value of \( x \) such that \( 3^{2x} - 2(3^{x+2}) + 81 = 0 \) is:

If \( z_1 = 2\sqrt{2}(1 + i) \) and \( z_2 = 1 + i\sqrt{3} \), then \( z_1^2 z_2^3 \) is equal to:

If the complex numbers \( z_1, z_2 \) and \( z_3 \) denote the vertices of an isosceles triangle, right angled at \( z_1 \), then \( (z_1 - z_2)^2 + (z_1 - z_3)^2 \) is equal to:

If the roots of \( x^2 - ax + b = 0 \) are two consecutive odd integers, then \( a^2 - 4b \) is:

If \( \alpha \) and \( \beta \) are the roots of the equation \( x^2 + 3x - 4 = 0 \), then \( \frac{1}{\alpha} + \frac{1}{\beta} \) is equal to:

The range of the function \( f(x) = x^2 + 2x + 2 \) is:

If \( f(x) = \sqrt{x \) and \( g(x) = 2x - 3 \), then \( (f \circ g)(x) \) is:}

If \( z = \frac{(\sqrt{3} + i)^3 (3i + 4)^2{(8 + 6i)^2} \), then \( |z| \) is equal to:}

Let \( w \neq \pm 1 \) be a complex number. If \( |w| = 1 \) and \( z = \frac{w - 1}{w + 1} \), then \( \text{Re}(z) \) is equal to:

If \( z = e^{2\pi i / 3} \), then \( 1 + z + 3z^2 + 2z^3 + 2z^4 + 3z^5 \) is equal to:

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:}

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

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

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

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

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: