List of top Mathematics Questions asked in KEAM

The roots of the equation \( \begin{vmatrix} x-1 & 1 & 1 \\ 1 & x-1 & 1 \\ 1 & 1 & x-1 \end{vmatrix} = 0 \) are:

Let \( f(x+y) = f(x)f(y) \) and \( f(x) = 1 + \sin(3x)g(x) \), where \( g \) is differentiable. Then \( f'(x) \) is equal to:

Let \( \vec{a} \) be a unit vector. If \( (\vec{x} - \vec{a}) \cdot (\vec{x} + \vec{a}) = 12 \), then the magnitude of \( \vec{x} \) is:

If \( nC_{r-1} = 36 \), \( nC_r = 84 \) and \( nC_{r+1} = 126 \), then the value of \( r \) is:

The area of the triangular region whose sides are \( y = 2x + 1 \), \( y = 3x + 1 \) and \( x = 4 \) is:

The value of \( \cos \left( \tan^{-1} \left( \frac{3}{4} \right) \right) \) is:

The equations \( \lambda x - y = 2 \), \( 2x - 3y = -\lambda \), and \( 3x - 2y = -1 \) are consistent for:

The set \( \{ (x, y) : |x| + |y| = 1 \ \) in the \( xy \) plane represents:}

Let \( A(6, -1) \), \( B(1, 3) \) and \( C(x, 8) \) be three points such that \( AB = BC \). The values of \( x \) are:

In an experiment with 15 observations on \( x \), the results \( \sum x^2 = 2830 \) and \( \sum x = 170 \) were available. One observation (20) was wrong and was replaced by 30. The corrected variance is:

The angle between the pair of lines \( \frac{x-2}{2} = \frac{y-1}{5} = \frac{z+3}{-3} \) and \( \frac{x+2}{-1} = \frac{y-4}{8} = \frac{z-5}{4} \) is:

The distance of the point \( (3, -5) \) from the line \( 3x - 4y - 26 = 0 \) is:

\( \sin 765^{\circ} \) is equal to:

If \( a \) and \( b \) are the non-zero distinct roots of \( x^2 + ax + b = 0 \), then the minimum value of \( x^2 + ax + b \) is:

If the straight line \( y = 4x + c \) touches the ellipse \( \frac{x^2}{4} + y^2 = 1 \), then \( c \) is equal to:

If \( x \in [0, \frac{\pi}{2}] \), \( y \in [0, \frac{\pi}{2}] \) and \( \sin x + \cos y = 2 \), then the value of \( x + y \) is equal to:

Let \( a, a + r \) and \( a + 2r \) be positive real numbers such that their product is 64. Then the minimum value of \( a + 2r \) is equal to:

\( \int_{-1}^{1} \max\{x, x^3\} \, dx \) is equal to:

The sum \( S = \frac{1}{9!} + \frac{1}{3!7!} + \frac{1}{5!5!} + \frac{1}{7!3!} + \frac{1}{9!} \) is equal to:

Let \( f(x) = 2x^3 - 9ax^2 + 12a^2x + 1 \), where \( a > 0 \). The minimum of \( f \) is attained at a point \( q \) and the maximum is attained at a point \( p \). If \( p^3 = q \), then \( a \) is equal to:

The equation of the plane that passes through the points \( (1, 0, 2), (-1, 1, 2) \) and \( (5, 0, 3) \) is:

If \( \vec{a}, \vec{b}, \vec{c} \) are vectors such that \( \vec{a} + \vec{b} + \vec{c} = 0 \) and \( |\vec{a}| = 7, |\vec{b}| = 5, |\vec{c}| = 3 \), then the angle between \( \vec{c} \) and \( \vec{b} \) is:

For all real numbers \( x \) and \( y \), it is known that the real valued function \( f \) satisfies \( f(x) + f(y) = f(x + y) \). If \( f(1) = 7 \), then \( \sum_{r=1}^{100} f(r) \) is equal to:

The vertex of the parabola \( y^2 - 4y - x + 3 = 0 \) is:

\( \int_{2016}^{2017} \frac{\sqrt{x}}{\sqrt{x} + \sqrt{4033 - x}} \, dx \) is equal to: